Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,7,Mod(2,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.2");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.f (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99070308706\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 11.5 | ||
Character | \(\chi\) | \(=\) | 13.11 |
Dual form | 13.7.f.a.6.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.99444 | − | 7.44337i | 0.249305 | − | 0.930421i | −0.721865 | − | 0.692034i | \(-0.756715\pi\) |
0.971170 | − | 0.238387i | \(-0.0766186\pi\) | |||||||
\(3\) | 25.6304 | + | 44.3931i | 0.949273 | + | 1.64419i | 0.746960 | + | 0.664869i | \(0.231513\pi\) |
0.202313 | + | 0.979321i | \(0.435154\pi\) | |||||||
\(4\) | 3.99974 | + | 2.30925i | 0.0624959 | + | 0.0360820i | ||||
\(5\) | −23.8066 | − | 23.8066i | −0.190453 | − | 0.190453i | 0.605439 | − | 0.795892i | \(-0.292998\pi\) |
−0.795892 | + | 0.605439i | \(0.792998\pi\) | |||||||
\(6\) | 381.553 | − | 102.237i | 1.76645 | − | 0.473318i | ||||
\(7\) | −75.6362 | − | 282.278i | −0.220514 | − | 0.822969i | −0.984152 | − | 0.177325i | \(-0.943256\pi\) |
0.763639 | − | 0.645644i | \(-0.223411\pi\) | |||||||
\(8\) | 373.897 | − | 373.897i | 0.730267 | − | 0.730267i | ||||
\(9\) | −949.333 | + | 1644.29i | −1.30224 | + | 2.25555i | ||||
\(10\) | −224.682 | + | 129.720i | −0.224682 | + | 0.129720i | ||||
\(11\) | −427.378 | − | 114.516i | −0.321095 | − | 0.0860373i | 0.0946712 | − | 0.995509i | \(-0.469820\pi\) |
−0.415767 | + | 0.909471i | \(0.636487\pi\) | |||||||
\(12\) | 236.748i | 0.137007i | ||||||||
\(13\) | 40.6056 | − | 2196.62i | 0.0184823 | − | 0.999829i | ||||
\(14\) | −2251.95 | −0.820683 | ||||||||
\(15\) | 446.677 | − | 1667.02i | 0.132349 | − | 0.493933i | ||||
\(16\) | −1889.54 | − | 3272.78i | −0.461314 | − | 0.799020i | ||||
\(17\) | 2798.48 | + | 1615.70i | 0.569607 | + | 0.328863i | 0.756992 | − | 0.653424i | \(-0.226668\pi\) |
−0.187385 | + | 0.982287i | \(0.560001\pi\) | |||||||
\(18\) | 10345.7 | + | 10345.7i | 1.77395 | + | 1.77395i | ||||
\(19\) | −10133.1 | + | 2715.15i | −1.47734 | + | 0.395853i | −0.905442 | − | 0.424470i | \(-0.860460\pi\) |
−0.571900 | + | 0.820323i | \(0.693794\pi\) | |||||||
\(20\) | −40.2448 | − | 150.196i | −0.00503060 | − | 0.0187745i | ||||
\(21\) | 10592.6 | − | 10592.6i | 1.14379 | − | 1.14379i | ||||
\(22\) | −1704.76 | + | 2952.74i | −0.160102 | + | 0.277304i | ||||
\(23\) | 2637.16 | − | 1522.57i | 0.216747 | − | 0.125139i | −0.387696 | − | 0.921787i | \(-0.626729\pi\) |
0.604443 | + | 0.796648i | \(0.293396\pi\) | |||||||
\(24\) | 26181.6 | + | 7015.33i | 1.89392 | + | 0.507475i | ||||
\(25\) | − | 14491.5i | − | 0.927455i | ||||||
\(26\) | −16269.3 | − | 4683.29i | −0.925654 | − | 0.266459i | ||||
\(27\) | −59957.9 | −3.04618 | ||||||||
\(28\) | 349.326 | − | 1303.70i | 0.0159132 | − | 0.0593888i | ||||
\(29\) | 17327.5 | + | 30012.0i | 0.710462 | + | 1.23056i | 0.964684 | + | 0.263411i | \(0.0848474\pi\) |
−0.254222 | + | 0.967146i | \(0.581819\pi\) | |||||||
\(30\) | −11517.4 | − | 6649.57i | −0.426570 | − | 0.246280i | ||||
\(31\) | 5703.31 | + | 5703.31i | 0.191444 | + | 0.191444i | 0.796320 | − | 0.604876i | \(-0.206777\pi\) |
−0.604876 | + | 0.796320i | \(0.706777\pi\) | |||||||
\(32\) | 4559.05 | − | 1221.59i | 0.139131 | − | 0.0372801i | ||||
\(33\) | −5870.16 | − | 21907.7i | −0.163346 | − | 0.609615i | ||||
\(34\) | 17607.7 | − | 17607.7i | 0.447987 | − | 0.447987i | ||||
\(35\) | −4919.45 | + | 8520.73i | −0.114739 | + | 0.198734i | ||||
\(36\) | −7594.16 | + | 4384.49i | −0.162769 | + | 0.0939749i | ||||
\(37\) | 3123.71 | + | 836.996i | 0.0616689 | + | 0.0165241i | 0.289522 | − | 0.957171i | \(-0.406504\pi\) |
−0.227853 | + | 0.973696i | \(0.573170\pi\) | |||||||
\(38\) | 80839.5i | 1.47324i | ||||||||
\(39\) | 98555.8 | − | 54497.7i | 1.66145 | − | 0.918723i | ||||
\(40\) | −17802.4 | −0.278163 | ||||||||
\(41\) | −14330.9 | + | 53483.8i | −0.207933 | + | 0.776016i | 0.780603 | + | 0.625028i | \(0.214912\pi\) |
−0.988536 | + | 0.150988i | \(0.951754\pi\) | |||||||
\(42\) | −57718.4 | − | 99971.2i | −0.779052 | − | 1.34936i | ||||
\(43\) | 58195.9 | + | 33599.4i | 0.731960 | + | 0.422597i | 0.819139 | − | 0.573596i | \(-0.194452\pi\) |
−0.0871790 | + | 0.996193i | \(0.527785\pi\) | |||||||
\(44\) | −1444.96 | − | 1444.96i | −0.0169628 | − | 0.0169628i | ||||
\(45\) | 61745.4 | − | 16544.6i | 0.677591 | − | 0.181560i | ||||
\(46\) | −6073.35 | − | 22666.1i | −0.0623957 | − | 0.232864i | ||||
\(47\) | −70573.1 | + | 70573.1i | −0.679744 | + | 0.679744i | −0.959942 | − | 0.280198i | \(-0.909600\pi\) |
0.280198 | + | 0.959942i | \(0.409600\pi\) | |||||||
\(48\) | 96859.4 | − | 167765.i | 0.875826 | − | 1.51698i | ||||
\(49\) | 27926.8 | − | 16123.6i | 0.237374 | − | 0.137048i | ||||
\(50\) | −107865. | − | 28902.5i | −0.862924 | − | 0.231220i | ||||
\(51\) | 165644.i | 1.24872i | ||||||||
\(52\) | 5234.97 | − | 8692.16i | 0.0372309 | − | 0.0618184i | ||||
\(53\) | −41268.8 | −0.277201 | −0.138600 | − | 0.990348i | \(-0.544260\pi\) | ||||
−0.138600 | + | 0.990348i | \(0.544260\pi\) | |||||||
\(54\) | −119583. | + | 446289.i | −0.759429 | + | 2.83423i | ||||
\(55\) | 7448.20 | + | 12900.7i | 0.0447675 | + | 0.0775396i | ||||
\(56\) | −133823. | − | 77262.8i | −0.762021 | − | 0.439953i | ||||
\(57\) | −380249. | − | 380249.i | −2.05326 | − | 2.05326i | ||||
\(58\) | 257949. | − | 69117.3i | 1.32206 | − | 0.354244i | ||||
\(59\) | 11741.0 | + | 43818.1i | 0.0571676 | + | 0.213352i | 0.988601 | − | 0.150560i | \(-0.0481075\pi\) |
−0.931433 | + | 0.363912i | \(0.881441\pi\) | |||||||
\(60\) | 5636.16 | − | 5636.16i | 0.0260934 | − | 0.0260934i | ||||
\(61\) | 41964.6 | − | 72684.9i | 0.184882 | − | 0.320224i | −0.758655 | − | 0.651493i | \(-0.774143\pi\) |
0.943537 | + | 0.331268i | \(0.107476\pi\) | |||||||
\(62\) | 53826.7 | − | 31076.9i | 0.225851 | − | 0.130395i | ||||
\(63\) | 535952. | + | 143608.i | 2.14341 | + | 0.574324i | ||||
\(64\) | − | 278233.i | − | 1.06137i | ||||||
\(65\) | −53260.9 | + | 51327.5i | −0.193940 | + | 0.186900i | ||||
\(66\) | −174775. | −0.607921 | ||||||||
\(67\) | 41330.1 | − | 154246.i | 0.137417 | − | 0.512849i | −0.862559 | − | 0.505957i | \(-0.831140\pi\) |
0.999976 | − | 0.00689201i | \(-0.00219381\pi\) | |||||||
\(68\) | 7462.13 | + | 12924.8i | 0.0237321 | + | 0.0411052i | ||||
\(69\) | 135183. | + | 78048.0i | 0.411505 | + | 0.237582i | ||||
\(70\) | 53611.4 | + | 53611.4i | 0.156301 | + | 0.156301i | ||||
\(71\) | −22847.0 | + | 6121.83i | −0.0638342 | + | 0.0171043i | −0.290595 | − | 0.956846i | \(-0.593853\pi\) |
0.226761 | + | 0.973951i | \(0.427187\pi\) | |||||||
\(72\) | 259843. | + | 969748.i | 0.696168 | + | 2.59813i | ||||
\(73\) | −385026. | + | 385026.i | −0.989741 | + | 0.989741i | −0.999948 | − | 0.0102065i | \(-0.996751\pi\) |
0.0102065 | + | 0.999948i | \(0.496751\pi\) | |||||||
\(74\) | 12460.1 | − | 21581.6i | 0.0307488 | − | 0.0532584i | ||||
\(75\) | 643322. | − | 371422.i | 1.52491 | − | 0.880409i | ||||
\(76\) | −46799.7 | − | 12539.9i | −0.106611 | − | 0.0285663i | ||||
\(77\) | 129301.i | 0.283224i | ||||||||
\(78\) | −209083. | − | 842279.i | −0.440589 | − | 1.77489i | ||||
\(79\) | −512323. | −1.03911 | −0.519557 | − | 0.854436i | \(-0.673903\pi\) | ||||
−0.519557 | + | 0.854436i | \(0.673903\pi\) | |||||||
\(80\) | −32930.3 | + | 122898.i | −0.0643170 | + | 0.240034i | ||||
\(81\) | −844681. | − | 1.46303e6i | −1.58942 | − | 2.75295i | ||||
\(82\) | 369517. | + | 213341.i | 0.670182 | + | 0.386930i | ||||
\(83\) | 303058. | + | 303058.i | 0.530019 | + | 0.530019i | 0.920578 | − | 0.390559i | \(-0.127718\pi\) |
−0.390559 | + | 0.920578i | \(0.627718\pi\) | |||||||
\(84\) | 66828.8 | − | 17906.7i | 0.112752 | − | 0.0302119i | ||||
\(85\) | −28157.9 | − | 105087.i | −0.0458505 | − | 0.171116i | ||||
\(86\) | 366161. | − | 366161.i | 0.575675 | − | 0.575675i | ||||
\(87\) | −888219. | + | 1.53844e6i | −1.34885 | + | 2.33627i | ||||
\(88\) | −202612. | + | 116978.i | −0.297316 | + | 0.171655i | ||||
\(89\) | −96164.8 | − | 25767.3i | −0.136410 | − | 0.0365509i | 0.189968 | − | 0.981790i | \(-0.439162\pi\) |
−0.326378 | + | 0.945239i | \(0.605828\pi\) | |||||||
\(90\) | − | 492591.i | − | 0.675708i | ||||||
\(91\) | −623131. | + | 154682.i | −0.826904 | + | 0.205266i | ||||
\(92\) | 14064.0 | 0.0180611 | ||||||||
\(93\) | −107010. | + | 399365.i | −0.133037 | + | 0.496503i | ||||
\(94\) | 384547. | + | 666055.i | 0.462984 | + | 0.801912i | ||||
\(95\) | 305873. | + | 176596.i | 0.356755 | + | 0.205973i | ||||
\(96\) | 171081. | + | 171081.i | 0.193369 | + | 0.193369i | ||||
\(97\) | 398316. | − | 106728.i | 0.436428 | − | 0.116941i | −0.0339140 | − | 0.999425i | \(-0.510797\pi\) |
0.470342 | + | 0.882484i | \(0.344131\pi\) | |||||||
\(98\) | −64315.1 | − | 240027.i | −0.0683336 | − | 0.255025i | ||||
\(99\) | 594021. | − | 594021.i | 0.612204 | − | 0.612204i | ||||
\(100\) | 33464.5 | − | 57962.2i | 0.0334645 | − | 0.0579622i | ||||
\(101\) | 1.60799e6 | − | 928373.i | 1.56070 | − | 0.901070i | 0.563512 | − | 0.826108i | \(-0.309450\pi\) |
0.997186 | − | 0.0749623i | \(-0.0238836\pi\) | |||||||
\(102\) | 1.23295e6 | + | 330368.i | 1.16184 | + | 0.311314i | ||||
\(103\) | − | 158837.i | − | 0.145358i | −0.997355 | − | 0.0726790i | \(-0.976845\pi\) | ||
0.997355 | − | 0.0726790i | \(-0.0231549\pi\) | |||||||
\(104\) | −806129. | − | 836493.i | −0.716646 | − | 0.743640i | ||||
\(105\) | −504349. | −0.435676 | ||||||||
\(106\) | −82308.3 | + | 307179.i | −0.0691076 | + | 0.257913i | ||||
\(107\) | 396539. | + | 686825.i | 0.323694 | + | 0.560654i | 0.981247 | − | 0.192754i | \(-0.0617419\pi\) |
−0.657553 | + | 0.753408i | \(0.728409\pi\) | |||||||
\(108\) | −239816. | − | 138458.i | −0.190374 | − | 0.109912i | ||||
\(109\) | −727600. | − | 727600.i | −0.561840 | − | 0.561840i | 0.367990 | − | 0.929830i | \(-0.380046\pi\) |
−0.929830 | + | 0.367990i | \(0.880046\pi\) | |||||||
\(110\) | 110879. | − | 29710.0i | 0.0833053 | − | 0.0223216i | ||||
\(111\) | 42905.1 | + | 160124.i | 0.0313718 | + | 0.117081i | ||||
\(112\) | −780918. | + | 780918.i | −0.555842 | + | 0.555842i | ||||
\(113\) | 907361. | − | 1.57160e6i | 0.628847 | − | 1.08919i | −0.358937 | − | 0.933362i | \(-0.616861\pi\) |
0.987784 | − | 0.155832i | \(-0.0498060\pi\) | |||||||
\(114\) | −3.58872e6 | + | 2.07195e6i | −2.42228 | + | 1.39851i | ||||
\(115\) | −99029.1 | − | 26534.8i | −0.0651133 | − | 0.0174470i | ||||
\(116\) | 160054.i | 0.102540i | ||||||||
\(117\) | 3.57335e6 | + | 2.15210e6i | 2.23109 | + | 1.34370i | ||||
\(118\) | 349571. | 0.212760 | ||||||||
\(119\) | 244412. | − | 912156.i | 0.145038 | − | 0.541288i | ||||
\(120\) | −456283. | − | 790306.i | −0.264053 | − | 0.457353i | ||||
\(121\) | −1.36468e6 | − | 787898.i | −0.770326 | − | 0.444748i | ||||
\(122\) | −457324. | − | 457324.i | −0.251851 | − | 0.251851i | ||||
\(123\) | −2.74162e6 | + | 734615.i | −1.47330 | + | 0.394770i | ||||
\(124\) | 9641.37 | + | 35982.1i | 0.00505678 | + | 0.0188721i | ||||
\(125\) | −716972. | + | 716972.i | −0.367090 | + | 0.367090i | ||||
\(126\) | 2.13785e6 | − | 3.70287e6i | 1.06873 | − | 1.85109i | ||||
\(127\) | 988835. | − | 570904.i | 0.482739 | − | 0.278710i | −0.238818 | − | 0.971064i | \(-0.576760\pi\) |
0.721557 | + | 0.692355i | \(0.243427\pi\) | |||||||
\(128\) | −1.77921e6 | − | 476737.i | −0.848392 | − | 0.227326i | ||||
\(129\) | 3.44466e6i | 1.60464i | ||||||||
\(130\) | 275824. | + | 498810.i | 0.125546 | + | 0.227041i | ||||
\(131\) | −521776. | −0.232097 | −0.116049 | − | 0.993244i | \(-0.537023\pi\) | ||||
−0.116049 | + | 0.993244i | \(0.537023\pi\) | |||||||
\(132\) | 27111.3 | − | 101181.i | 0.0117877 | − | 0.0439923i | ||||
\(133\) | 1.53286e6 | + | 2.65499e6i | 0.651549 | + | 1.12852i | ||||
\(134\) | −1.06568e6 | − | 615270.i | −0.442906 | − | 0.255712i | ||||
\(135\) | 1.42740e6 | + | 1.42740e6i | 0.580154 | + | 0.580154i | ||||
\(136\) | 1.65045e6 | − | 442237.i | 0.656123 | − | 0.175808i | ||||
\(137\) | −1.10185e6 | − | 4.11217e6i | −0.428511 | − | 1.59922i | −0.756135 | − | 0.654415i | \(-0.772915\pi\) |
0.327625 | − | 0.944808i | \(-0.393752\pi\) | |||||||
\(138\) | 850554. | − | 850554.i | 0.323642 | − | 0.323642i | ||||
\(139\) | −317622. | + | 550138.i | −0.118268 | + | 0.204846i | −0.919081 | − | 0.394068i | \(-0.871067\pi\) |
0.800814 | + | 0.598914i | \(0.204401\pi\) | |||||||
\(140\) | −39353.0 | + | 22720.5i | −0.0143415 | + | 0.00828006i | ||||
\(141\) | −4.94177e6 | − | 1.32414e6i | −1.76289 | − | 0.472365i | ||||
\(142\) | 182268.i | 0.0636569i | ||||||||
\(143\) | −268902. | + | 934139.i | −0.0919572 | + | 0.319450i | ||||
\(144\) | 7.17522e6 | 2.40297 | ||||||||
\(145\) | 301977. | − | 1.12699e6i | 0.0990535 | − | 0.369673i | ||||
\(146\) | 2.09798e6 | + | 3.63380e6i | 0.674128 | + | 1.16762i | ||||
\(147\) | 1.43155e6 | + | 826506.i | 0.450666 | + | 0.260192i | ||||
\(148\) | 10561.2 | + | 10561.2i | 0.00325783 | + | 0.00325783i | ||||
\(149\) | 5.78714e6 | − | 1.55066e6i | 1.74946 | − | 0.468768i | 0.764953 | − | 0.644087i | \(-0.222762\pi\) |
0.984512 | + | 0.175319i | \(0.0560957\pi\) | |||||||
\(150\) | −1.48156e6 | − | 5.52927e6i | −0.438981 | − | 1.63830i | ||||
\(151\) | 2.26172e6 | − | 2.26172e6i | 0.656912 | − | 0.656912i | −0.297736 | − | 0.954648i | \(-0.596231\pi\) |
0.954648 | + | 0.297736i | \(0.0962315\pi\) | |||||||
\(152\) | −2.77354e6 | + | 4.80392e6i | −0.789776 | + | 1.36793i | ||||
\(153\) | −5.31338e6 | + | 3.06768e6i | −1.48353 | + | 0.856517i | ||||
\(154\) | 962435. | + | 257884.i | 0.263517 | + | 0.0706093i | ||||
\(155\) | − | 271553.i | − | 0.0729221i | ||||||
\(156\) | 520046. | + | 9613.29i | 0.136983 | + | 0.00253220i | ||||
\(157\) | −1.55389e6 | −0.401533 | −0.200767 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200767 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(158\) | −1.02180e6 | + | 3.81341e6i | −0.259057 | + | 0.966813i | ||||
\(159\) | −1.05773e6 | − | 1.83205e6i | −0.263139 | − | 0.455770i | ||||
\(160\) | −137618. | − | 79453.6i | −0.0335980 | − | 0.0193978i | ||||
\(161\) | −629253. | − | 629253.i | −0.150781 | − | 0.150781i | ||||
\(162\) | −1.25745e7 | + | 3.36934e6i | −2.95765 | + | 0.792500i | ||||
\(163\) | 947255. | + | 3.53520e6i | 0.218728 | + | 0.816304i | 0.984821 | + | 0.173574i | \(0.0555315\pi\) |
−0.766093 | + | 0.642730i | \(0.777802\pi\) | |||||||
\(164\) | −180827. | + | 180827.i | −0.0409952 | + | 0.0409952i | ||||
\(165\) | −381800. | + | 661297.i | −0.0849932 | + | 0.147213i | ||||
\(166\) | 2.86020e6 | − | 1.65134e6i | 0.625277 | − | 0.361004i | ||||
\(167\) | 1.34763e6 | + | 361097.i | 0.289349 | + | 0.0775308i | 0.400574 | − | 0.916264i | \(-0.368811\pi\) |
−0.111225 | + | 0.993795i | \(0.535477\pi\) | |||||||
\(168\) | − | 7.92110e6i | − | 1.67054i | ||||||
\(169\) | −4.82351e6 | − | 178391.i | −0.999317 | − | 0.0369583i | ||||
\(170\) | −838359. | −0.170641 | ||||||||
\(171\) | 5.15517e6 | − | 1.92393e7i | 1.03099 | − | 3.84771i | ||||
\(172\) | 155179. | + | 268778.i | 0.0304963 | + | 0.0528212i | ||||
\(173\) | 910586. | + | 525727.i | 0.175866 | + | 0.101536i | 0.585349 | − | 0.810781i | \(-0.300957\pi\) |
−0.409483 | + | 0.912318i | \(0.634291\pi\) | |||||||
\(174\) | 9.67967e6 | + | 9.67967e6i | 1.83744 | + | 1.83744i | ||||
\(175\) | −4.09063e6 | + | 1.09608e6i | −0.763267 | + | 0.204517i | ||||
\(176\) | 432764. | + | 1.61510e6i | 0.0793804 | + | 0.296252i | ||||
\(177\) | −1.64430e6 | + | 1.64430e6i | −0.296524 | + | 0.296524i | ||||
\(178\) | −383591. | + | 664399.i | −0.0680155 | + | 0.117806i | ||||
\(179\) | −5.09109e6 | + | 2.93934e6i | −0.887670 | + | 0.512496i | −0.873180 | − | 0.487399i | \(-0.837946\pi\) |
−0.0144903 | + | 0.999895i | \(0.504613\pi\) | |||||||
\(180\) | 285171. | + | 76411.4i | 0.0488977 | + | 0.0131021i | ||||
\(181\) | − | 3.79294e6i | − | 0.639646i | −0.947477 | − | 0.319823i | \(-0.896377\pi\) | ||
0.947477 | − | 0.319823i | \(-0.103623\pi\) | |||||||
\(182\) | −91441.9 | + | 4.94670e6i | −0.0151681 | + | 0.820542i | ||||
\(183\) | 4.30228e6 | 0.702013 | ||||||||
\(184\) | 416744. | − | 1.55531e6i | 0.0668985 | − | 0.249668i | ||||
\(185\) | −54439.0 | − | 94291.1i | −0.00859795 | − | 0.0148921i | ||||
\(186\) | 2.75920e6 | + | 1.59302e6i | 0.428789 | + | 0.247562i | ||||
\(187\) | −1.01099e6 | − | 1.01099e6i | −0.154604 | − | 0.154604i | ||||
\(188\) | −445245. | + | 119303.i | −0.0670078 | + | 0.0179547i | ||||
\(189\) | 4.53499e6 | + | 1.69248e7i | 0.671724 | + | 2.50691i | ||||
\(190\) | 1.92452e6 | − | 1.92452e6i | 0.280583 | − | 0.280583i | ||||
\(191\) | −3.51626e6 | + | 6.09034e6i | −0.504639 | + | 0.874060i | 0.495347 | + | 0.868695i | \(0.335041\pi\) |
−0.999986 | + | 0.00536504i | \(0.998292\pi\) | |||||||
\(192\) | 1.23516e7 | − | 7.13121e6i | 1.74510 | − | 1.00753i | ||||
\(193\) | 6.59881e6 | + | 1.76814e6i | 0.917896 | + | 0.245949i | 0.686686 | − | 0.726954i | \(-0.259065\pi\) |
0.231210 | + | 0.972904i | \(0.425732\pi\) | |||||||
\(194\) | − | 3.17768e6i | − | 0.435216i | ||||||
\(195\) | −3.64369e6 | − | 1.04887e6i | −0.491402 | − | 0.141455i | ||||
\(196\) | 148933. | 0.0197799 | ||||||||
\(197\) | −1.33330e6 | + | 4.97594e6i | −0.174393 | + | 0.650843i | 0.822261 | + | 0.569110i | \(0.192712\pi\) |
−0.996654 | + | 0.0817330i | \(0.973955\pi\) | |||||||
\(198\) | −3.23677e6 | − | 5.60626e6i | −0.416982 | − | 0.722233i | ||||
\(199\) | −1.11636e7 | − | 6.44530e6i | −1.41659 | − | 0.817869i | −0.420594 | − | 0.907249i | \(-0.638178\pi\) |
−0.995998 | + | 0.0893798i | \(0.971512\pi\) | |||||||
\(200\) | −5.41832e6 | − | 5.41832e6i | −0.677290 | − | 0.677290i | ||||
\(201\) | 7.90676e6 | − | 2.11861e6i | 0.973667 | − | 0.260893i | ||||
\(202\) | −3.70318e6 | − | 1.38204e7i | −0.449283 | − | 1.67675i | ||||
\(203\) | 7.16117e6 | − | 7.16117e6i | 0.856043 | − | 0.856043i | ||||
\(204\) | −382514. | + | 662534.i | −0.0450565 | + | 0.0780401i | ||||
\(205\) | 1.61444e6 | − | 932097.i | 0.187396 | − | 0.108193i | ||||
\(206\) | −1.18228e6 | − | 316791.i | −0.135244 | − | 0.0362386i | ||||
\(207\) | 5.78169e6i | 0.651844i | ||||||||
\(208\) | −7.26580e6 | + | 4.01772e6i | −0.807409 | + | 0.446468i | ||||
\(209\) | 4.64159e6 | 0.508426 | ||||||||
\(210\) | −1.00590e6 | + | 3.75406e6i | −0.108616 | + | 0.405362i | ||||
\(211\) | 4.79427e6 | + | 8.30391e6i | 0.510358 | + | 0.883966i | 0.999928 | + | 0.0120019i | \(0.00382043\pi\) |
−0.489570 | + | 0.871964i | \(0.662846\pi\) | |||||||
\(212\) | −165064. | − | 95299.9i | −0.0173239 | − | 0.0100020i | ||||
\(213\) | −857344. | − | 857344.i | −0.0887189 | − | 0.0887189i | ||||
\(214\) | 5.90317e6 | − | 1.58175e6i | 0.602343 | − | 0.161397i | ||||
\(215\) | −585559. | − | 2.18534e6i | −0.0589190 | − | 0.219889i | ||||
\(216\) | −2.24181e7 | + | 2.24181e7i | −2.22452 | + | 2.22452i | ||||
\(217\) | 1.17854e6 | − | 2.04130e6i | 0.115336 | − | 0.199768i | ||||
\(218\) | −6.86695e6 | + | 3.96463e6i | −0.662818 | + | 0.382678i | ||||
\(219\) | −2.69609e7 | − | 7.22415e6i | −2.56686 | − | 0.687787i | ||||
\(220\) | 68799.0i | 0.00646121i | ||||||||
\(221\) | 3.66273e6 | − | 6.08161e6i | 0.339334 | − | 0.563432i | ||||
\(222\) | 1.27743e6 | 0.116756 | ||||||||
\(223\) | −3.71781e6 | + | 1.38750e7i | −0.335253 | + | 1.25118i | 0.568343 | + | 0.822792i | \(0.307585\pi\) |
−0.903595 | + | 0.428388i | \(0.859082\pi\) | |||||||
\(224\) | −689659. | − | 1.19452e6i | −0.0613607 | − | 0.106280i | ||||
\(225\) | 2.38282e7 | + | 1.37572e7i | 2.09192 | + | 1.20777i | ||||
\(226\) | −9.88828e6 | − | 9.88828e6i | −0.856634 | − | 0.856634i | ||||
\(227\) | 9.94780e6 | − | 2.66550e6i | 0.850451 | − | 0.227878i | 0.192835 | − | 0.981231i | \(-0.438232\pi\) |
0.657616 | + | 0.753353i | \(0.271565\pi\) | |||||||
\(228\) | −642807. | − | 2.39899e6i | −0.0542345 | − | 0.202406i | ||||
\(229\) | 9.59875e6 | − | 9.59875e6i | 0.799297 | − | 0.799297i | −0.183688 | − | 0.982985i | \(-0.558804\pi\) |
0.982985 | + | 0.183688i | \(0.0588035\pi\) | |||||||
\(230\) | −395016. | + | 684188.i | −0.0324662 | + | 0.0562331i | ||||
\(231\) | −5.74008e6 | + | 3.31404e6i | −0.465674 | + | 0.268857i | ||||
\(232\) | 1.77001e7 | + | 4.74273e6i | 1.41746 | + | 0.379808i | ||||
\(233\) | 7.44667e6i | 0.588700i | 0.955698 | + | 0.294350i | \(0.0951032\pi\) | ||||
−0.955698 | + | 0.294350i | \(0.904897\pi\) | |||||||
\(234\) | 2.31457e7 | − | 2.23055e7i | 1.80643 | − | 1.74086i | ||||
\(235\) | 3.36021e6 | 0.258918 | ||||||||
\(236\) | −54225.9 | + | 202374.i | −0.00412545 | + | 0.0153964i | ||||
\(237\) | −1.31310e7 | − | 2.27436e7i | −0.986402 | − | 1.70850i | ||||
\(238\) | −6.30205e6 | − | 3.63849e6i | −0.467467 | − | 0.269892i | ||||
\(239\) | −9.06179e6 | − | 9.06179e6i | −0.663774 | − | 0.663774i | 0.292493 | − | 0.956268i | \(-0.405515\pi\) |
−0.956268 | + | 0.292493i | \(0.905515\pi\) | |||||||
\(240\) | −6.29982e6 | + | 1.68803e6i | −0.455716 | + | 0.122109i | ||||
\(241\) | 5.08365e6 | + | 1.89724e7i | 0.363182 | + | 1.35541i | 0.869869 | + | 0.493283i | \(0.164203\pi\) |
−0.506687 | + | 0.862130i | \(0.669130\pi\) | |||||||
\(242\) | −8.58638e6 | + | 8.58638e6i | −0.605849 | + | 0.605849i | ||||
\(243\) | 2.14443e7 | − | 3.71427e7i | 1.49449 | − | 2.58854i | ||||
\(244\) | 335695. | − | 193814.i | 0.0231087 | − | 0.0133418i | ||||
\(245\) | −1.04869e6 | − | 280996.i | −0.0713098 | − | 0.0191074i | ||||
\(246\) | 2.18720e7i | 1.46921i | ||||||||
\(247\) | 5.55271e6 | + | 2.23688e7i | 0.368480 | + | 1.48441i | ||||
\(248\) | 4.26490e6 | 0.279610 | ||||||||
\(249\) | −5.68620e6 | + | 2.12212e7i | −0.368319 | + | 1.37458i | ||||
\(250\) | 3.90672e6 | + | 6.76664e6i | 0.250030 | + | 0.433065i | ||||
\(251\) | −9.56884e6 | − | 5.52457e6i | −0.605115 | − | 0.349364i | 0.165936 | − | 0.986137i | \(-0.446936\pi\) |
−0.771051 | + | 0.636773i | \(0.780269\pi\) | |||||||
\(252\) | 1.81204e6 | + | 1.81204e6i | 0.113231 | + | 0.113231i | ||||
\(253\) | −1.30142e6 | + | 348715.i | −0.0803632 | + | 0.0215333i | ||||
\(254\) | −2.27727e6 | − | 8.49890e6i | −0.138968 | − | 0.518635i | ||||
\(255\) | 3.94343e6 | − | 3.94343e6i | 0.237823 | − | 0.237823i | ||||
\(256\) | 1.80638e6 | − | 3.12875e6i | 0.107669 | − | 0.186488i | ||||
\(257\) | 1.47153e7 | − | 8.49590e6i | 0.866904 | − | 0.500507i | 0.000585642 | − | 1.00000i | \(-0.499814\pi\) |
0.866318 | + | 0.499493i | \(0.166480\pi\) | |||||||
\(258\) | 2.56399e7 | + | 6.87019e6i | 1.49299 | + | 0.400046i | ||||
\(259\) | − | 945064.i | − | 0.0543953i | ||||||
\(260\) | −331558. | + | 82304.0i | −0.0188642 | + | 0.00468275i | ||||
\(261\) | −6.57981e7 | −3.70077 | ||||||||
\(262\) | −1.04065e6 | + | 3.88377e6i | −0.0578631 | + | 0.215948i | ||||
\(263\) | 7.31632e6 | + | 1.26722e7i | 0.402185 | + | 0.696604i | 0.993989 | − | 0.109477i | \(-0.0349177\pi\) |
−0.591805 | + | 0.806081i | \(0.701584\pi\) | |||||||
\(264\) | −1.03861e7 | − | 5.99640e6i | −0.564468 | − | 0.325896i | ||||
\(265\) | 982470. | + | 982470.i | 0.0527937 | + | 0.0527937i | ||||
\(266\) | 2.28192e7 | − | 6.11440e6i | 1.21243 | − | 0.324869i | ||||
\(267\) | −1.32085e6 | − | 4.92948e6i | −0.0693937 | − | 0.258981i | ||||
\(268\) | 521502. | − | 521502.i | 0.0270927 | − | 0.0270927i | ||||
\(269\) | −3.95274e6 | + | 6.84635e6i | −0.203068 | + | 0.351724i | −0.949515 | − | 0.313720i | \(-0.898425\pi\) |
0.746447 | + | 0.665444i | \(0.231758\pi\) | |||||||
\(270\) | 1.34715e7 | − | 7.77777e6i | 0.684422 | − | 0.395152i | ||||
\(271\) | 9.72876e6 | + | 2.60681e6i | 0.488820 | + | 0.130979i | 0.494807 | − | 0.869003i | \(-0.335239\pi\) |
−0.00598628 | + | 0.999982i | \(0.501906\pi\) | |||||||
\(272\) | − | 1.22118e7i | − | 0.606837i | ||||||
\(273\) | −2.28379e7 | − | 2.36981e7i | −1.12245 | − | 1.16473i | ||||
\(274\) | −3.28060e7 | −1.59478 | ||||||||
\(275\) | −1.65950e6 | + | 6.19335e6i | −0.0797957 | + | 0.297802i | ||||
\(276\) | 360464. | + | 624343.i | 0.0171449 | + | 0.0296959i | ||||
\(277\) | −8.97616e6 | − | 5.18239e6i | −0.422329 | − | 0.243832i | 0.273744 | − | 0.961803i | \(-0.411738\pi\) |
−0.696073 | + | 0.717971i | \(0.745071\pi\) | |||||||
\(278\) | 3.46140e6 | + | 3.46140e6i | 0.161108 | + | 0.161108i | ||||
\(279\) | −1.47922e7 | + | 3.96357e6i | −0.681116 | + | 0.182505i | ||||
\(280\) | 1.34651e6 | + | 5.02524e6i | 0.0613388 | + | 0.228920i | ||||
\(281\) | 2.56461e7 | − | 2.56461e7i | 1.15585 | − | 1.15585i | 0.170495 | − | 0.985358i | \(-0.445463\pi\) |
0.985358 | − | 0.170495i | \(-0.0545368\pi\) | |||||||
\(282\) | −1.97122e7 | + | 3.41425e7i | −0.878997 | + | 1.52247i | ||||
\(283\) | −1.16354e7 | + | 6.71768e6i | −0.513358 | + | 0.296388i | −0.734213 | − | 0.678919i | \(-0.762449\pi\) |
0.220855 | + | 0.975307i | \(0.429115\pi\) | |||||||
\(284\) | −105519. | − | 28273.7i | −0.00460654 | − | 0.00123432i | ||||
\(285\) | 1.81049e7i | 0.782098i | ||||||||
\(286\) | 6.41683e6 | + | 3.86462e6i | 0.274298 | + | 0.165200i | ||||
\(287\) | 1.61813e7 | 0.684489 | ||||||||
\(288\) | −2.31940e6 | + | 8.65611e6i | −0.0970952 | + | 0.362364i | ||||
\(289\) | −6.84779e6 | − | 1.18607e7i | −0.283698 | − | 0.491380i | ||||
\(290\) | −7.78635e6 | − | 4.49545e6i | −0.319257 | − | 0.184323i | ||||
\(291\) | 1.49470e7 | + | 1.49470e7i | 0.606562 | + | 0.606562i | ||||
\(292\) | −2.42913e6 | + | 650882.i | −0.0975667 | + | 0.0261429i | ||||
\(293\) | −6.65595e6 | − | 2.48403e7i | −0.264610 | − | 0.987540i | −0.962488 | − | 0.271323i | \(-0.912539\pi\) |
0.697878 | − | 0.716217i | \(-0.254128\pi\) | |||||||
\(294\) | 9.00713e6 | − | 9.00713e6i | 0.354442 | − | 0.354442i | ||||
\(295\) | 763647. | − | 1.32267e6i | 0.0297459 | − | 0.0515213i | ||||
\(296\) | 1.48090e6 | − | 854996.i | 0.0571018 | − | 0.0329677i | ||||
\(297\) | 2.56247e7 | + | 6.86612e6i | 0.978114 | + | 0.262085i | ||||
\(298\) | − | 4.61685e7i | − | 1.74460i | ||||||
\(299\) | −3.23743e6 | − | 5.85468e6i | −0.121112 | − | 0.219023i | ||||
\(300\) | 3.43083e6 | 0.127068 | ||||||||
\(301\) | 5.08267e6 | − | 1.89688e7i | 0.186377 | − | 0.695568i | ||||
\(302\) | −1.23239e7 | − | 2.13457e7i | −0.447433 | − | 0.774977i | ||||
\(303\) | 8.24268e7 | + | 4.75891e7i | 2.96306 | + | 1.71072i | ||||
\(304\) | 2.80330e7 | + | 2.80330e7i | 0.997813 | + | 0.997813i | ||||
\(305\) | −2.72942e6 | + | 731345.i | −0.0961990 | + | 0.0257764i | ||||
\(306\) | 1.22366e7 | + | 4.56677e7i | 0.427069 | + | 1.59384i | ||||
\(307\) | −1.50829e7 | + | 1.50829e7i | −0.521277 | + | 0.521277i | −0.917957 | − | 0.396680i | \(-0.870162\pi\) |
0.396680 | + | 0.917957i | \(0.370162\pi\) | |||||||
\(308\) | −298589. | + | 517171.i | −0.0102193 | + | 0.0177003i | ||||
\(309\) | 7.05126e6 | − | 4.07104e6i | 0.238996 | − | 0.137985i | ||||
\(310\) | −2.02127e6 | − | 541597.i | −0.0678482 | − | 0.0181799i | ||||
\(311\) | 3.47663e7i | 1.15578i | 0.816113 | + | 0.577892i | \(0.196125\pi\) | ||||
−0.816113 | + | 0.577892i | \(0.803875\pi\) | |||||||
\(312\) | 1.64732e7 | − | 5.72262e7i | 0.542392 | − | 1.88422i | ||||
\(313\) | −3.64685e7 | −1.18928 | −0.594641 | − | 0.803991i | \(-0.702706\pi\) | ||||
−0.594641 | + | 0.803991i | \(0.702706\pi\) | |||||||
\(314\) | −3.09915e6 | + | 1.15662e7i | −0.100104 | + | 0.373595i | ||||
\(315\) | −9.34039e6 | − | 1.61780e7i | −0.298836 | − | 0.517599i | ||||
\(316\) | −2.04916e6 | − | 1.18308e6i | −0.0649403 | − | 0.0374933i | ||||
\(317\) | −1.85512e7 | − | 1.85512e7i | −0.582362 | − | 0.582362i | 0.353189 | − | 0.935552i | \(-0.385097\pi\) |
−0.935552 | + | 0.353189i | \(0.885097\pi\) | |||||||
\(318\) | −1.57462e7 | + | 4.21918e6i | −0.489660 | + | 0.131204i | ||||
\(319\) | −3.96853e6 | − | 1.48108e7i | −0.122252 | − | 0.456252i | ||||
\(320\) | −6.62378e6 | + | 6.62378e6i | −0.202142 | + | 0.202142i | ||||
\(321\) | −2.03269e7 | + | 3.52072e7i | −0.614548 | + | 1.06443i | ||||
\(322\) | −5.93877e6 | + | 3.42875e6i | −0.177881 | + | 0.102699i | ||||
\(323\) | −3.27441e7 | − | 8.77377e6i | −0.971686 | − | 0.260363i | ||||
\(324\) | − | 7.80232e6i | − | 0.229397i | ||||||
\(325\) | −3.18324e7 | − | 588436.i | −0.927297 | − | 0.0171415i | ||||
\(326\) | 2.82031e7 | 0.814036 | ||||||||
\(327\) | 1.36518e7 | − | 5.09491e7i | 0.390432 | − | 1.45711i | ||||
\(328\) | 1.46391e7 | + | 2.53557e7i | 0.414852 | + | 0.718546i | ||||
\(329\) | 2.52591e7 | + | 1.45834e7i | 0.709301 | + | 0.409515i | ||||
\(330\) | 4.16080e6 | + | 4.16080e6i | 0.115780 | + | 0.115780i | ||||
\(331\) | −1.20933e7 | + | 3.24040e6i | −0.333474 | + | 0.0893542i | −0.421671 | − | 0.906749i | \(-0.638556\pi\) |
0.0881966 | + | 0.996103i | \(0.471890\pi\) | |||||||
\(332\) | 512316. | + | 1.91199e6i | 0.0139999 | + | 0.0522482i | ||||
\(333\) | −4.34171e6 | + | 4.34171e6i | −0.117579 | + | 0.117579i | ||||
\(334\) | 5.37555e6 | − | 9.31073e6i | 0.144272 | − | 0.249887i | ||||
\(335\) | −4.65600e6 | + | 2.68814e6i | −0.123845 | + | 0.0715020i | ||||
\(336\) | −5.46826e7 | − | 1.46522e7i | −1.44156 | − | 0.386264i | ||||
\(337\) | − | 3.06455e7i | − | 0.800712i | −0.916360 | − | 0.400356i | \(-0.868886\pi\) | ||
0.916360 | − | 0.400356i | \(-0.131114\pi\) | |||||||
\(338\) | −1.09480e7 | + | 3.55474e7i | −0.283522 | + | 0.920571i | ||||
\(339\) | 9.30240e7 | 2.38779 | ||||||||
\(340\) | 130047. | − | 485343.i | 0.00330876 | − | 0.0123484i | ||||
\(341\) | −1.78435e6 | − | 3.09059e6i | −0.0450005 | − | 0.0779431i | ||||
\(342\) | −1.32924e8 | − | 7.67436e7i | −3.32295 | − | 1.91851i | ||||
\(343\) | −3.09748e7 | − | 3.09748e7i | −0.767585 | − | 0.767585i | ||||
\(344\) | 3.43220e7 | − | 9.19655e6i | 0.843135 | − | 0.225917i | ||||
\(345\) | −1.36019e6 | − | 5.07631e6i | −0.0331240 | − | 0.123621i | ||||
\(346\) | 5.72929e6 | − | 5.72929e6i | 0.138316 | − | 0.138316i | ||||
\(347\) | 1.01234e7 | − | 1.75343e7i | 0.242292 | − | 0.419663i | −0.719074 | − | 0.694933i | \(-0.755434\pi\) |
0.961367 | + | 0.275270i | \(0.0887673\pi\) | |||||||
\(348\) | −7.10529e6 | + | 4.10224e6i | −0.168595 | + | 0.0973382i | ||||
\(349\) | 6.57989e7 | + | 1.76308e7i | 1.54790 | + | 0.414758i | 0.928808 | − | 0.370562i | \(-0.120835\pi\) |
0.619090 | + | 0.785320i | \(0.287502\pi\) | |||||||
\(350\) | 3.26342e7i | 0.761146i | ||||||||
\(351\) | −2.43463e6 | + | 1.31705e8i | −0.0563004 | + | 3.04566i | ||||
\(352\) | −2.08833e6 | −0.0478819 | ||||||||
\(353\) | −1.68597e7 | + | 6.29214e7i | −0.383289 | + | 1.43045i | 0.457557 | + | 0.889180i | \(0.348725\pi\) |
−0.840846 | + | 0.541274i | \(0.817942\pi\) | |||||||
\(354\) | 8.95964e6 | + | 1.55185e7i | 0.201967 | + | 0.349817i | ||||
\(355\) | 689649. | + | 398169.i | 0.0154150 | + | 0.00889985i | ||||
\(356\) | −325131. | − | 325131.i | −0.00720623 | − | 0.00720623i | ||||
\(357\) | 4.67578e7 | − | 1.25287e7i | 1.02766 | − | 0.275361i | ||||
\(358\) | 1.17247e7 | + | 4.37572e7i | 0.255536 | + | 0.953675i | ||||
\(359\) | −4.73091e7 | + | 4.73091e7i | −1.02250 | + | 1.02250i | −0.0227548 | + | 0.999741i | \(0.507244\pi\) |
−0.999741 | + | 0.0227548i | \(0.992756\pi\) | |||||||
\(360\) | 1.69004e7 | − | 2.92724e7i | 0.362235 | − | 0.627409i | ||||
\(361\) | 5.45645e7 | − | 3.15028e7i | 1.15982 | − | 0.669620i | ||||
\(362\) | −2.82322e7 | − | 7.56480e6i | −0.595140 | − | 0.159467i | ||||
\(363\) | − | 8.07765e7i | − | 1.68875i | ||||||
\(364\) | −2.84956e6 | − | 820276.i | −0.0590845 | − | 0.0170081i | ||||
\(365\) | 1.83323e7 | 0.376998 | ||||||||
\(366\) | 8.58065e6 | − | 3.20234e7i | 0.175016 | − | 0.653167i | ||||
\(367\) | 3.31711e7 | + | 5.74541e7i | 0.671061 | + | 1.16231i | 0.977604 | + | 0.210455i | \(0.0674945\pi\) |
−0.306543 | + | 0.951857i | \(0.599172\pi\) | |||||||
\(368\) | −9.96607e6 | − | 5.75391e6i | −0.199977 | − | 0.115457i | ||||
\(369\) | −7.43382e7 | − | 7.43382e7i | −1.47956 | − | 1.47956i | ||||
\(370\) | −810419. | + | 217151.i | −0.0159994 | + | 0.00428703i | ||||
\(371\) | 3.12142e6 | + | 1.16493e7i | 0.0611266 | + | 0.228127i | ||||
\(372\) | −1.35025e6 | + | 1.35025e6i | −0.0262291 | + | 0.0262291i | ||||
\(373\) | 3.03260e7 | − | 5.25262e7i | 0.584371 | − | 1.01216i | −0.410582 | − | 0.911823i | \(-0.634675\pi\) |
0.994954 | − | 0.100337i | \(-0.0319921\pi\) | |||||||
\(374\) | −9.54149e6 | + | 5.50878e6i | −0.182390 | + | 0.105303i | ||||
\(375\) | −5.02049e7 | − | 1.34524e7i | −0.952033 | − | 0.255097i | ||||
\(376\) | 5.27741e7i | 0.992790i | ||||||||
\(377\) | 6.66288e7 | − | 3.68433e7i | 1.24348 | − | 0.687597i | ||||
\(378\) | 1.35022e8 | 2.49995 | ||||||||
\(379\) | 2.58795e7 | − | 9.65836e7i | 0.475377 | − | 1.77413i | −0.144578 | − | 0.989493i | \(-0.546183\pi\) |
0.619955 | − | 0.784637i | \(-0.287151\pi\) | |||||||
\(380\) | 815609. | + | 1.41268e6i | 0.0148638 | + | 0.0257449i | ||||
\(381\) | 5.06884e7 | + | 2.92650e7i | 0.916503 | + | 0.529143i | ||||
\(382\) | 3.83197e7 | + | 3.83197e7i | 0.687435 | + | 0.687435i | ||||
\(383\) | −9.36816e7 | + | 2.51019e7i | −1.66747 | + | 0.446797i | −0.964427 | − | 0.264351i | \(-0.914842\pi\) |
−0.703043 | + | 0.711148i | \(0.748176\pi\) | |||||||
\(384\) | −2.44379e7 | − | 9.12035e7i | −0.431589 | − | 1.61071i | ||||
\(385\) | 3.07822e6 | − | 3.07822e6i | 0.0539408 | − | 0.0539408i | ||||
\(386\) | 2.63219e7 | − | 4.55909e7i | 0.457673 | − | 0.792713i | ||||
\(387\) | −1.10495e8 | + | 6.37941e7i | −1.90637 | + | 1.10065i | ||||
\(388\) | 1.83962e6 | + | 492925.i | 0.0314944 | + | 0.00843890i | ||||
\(389\) | 5.68950e7i | 0.966551i | 0.875468 | + | 0.483276i | \(0.160553\pi\) | ||||
−0.875468 | + | 0.483276i | \(0.839447\pi\) | |||||||
\(390\) | −1.50743e7 | + | 2.50294e7i | −0.254122 | + | 0.421945i | ||||
\(391\) | 9.84007e6 | 0.164614 | ||||||||
\(392\) | 4.41320e6 | − | 1.64703e7i | 0.0732649 | − | 0.273428i | ||||
\(393\) | −1.33733e7 | − | 2.31633e7i | −0.220324 | − | 0.381612i | ||||
\(394\) | 3.43785e7 | + | 1.98485e7i | 0.562081 | + | 0.324517i | ||||
\(395\) | 1.21967e7 | + | 1.21967e7i | 0.197902 | + | 0.197902i | ||||
\(396\) | 3.74767e6 | − | 1.00419e6i | 0.0603498 | − | 0.0161707i | ||||
\(397\) | 1.17638e7 | + | 4.39032e7i | 0.188008 | + | 0.701657i | 0.993966 | + | 0.109684i | \(0.0349839\pi\) |
−0.805958 | + | 0.591972i | \(0.798349\pi\) | |||||||
\(398\) | −7.02399e7 | + | 7.02399e7i | −1.11413 | + | 1.11413i | ||||
\(399\) | −7.85754e7 | + | 1.36097e8i | −1.23700 | + | 2.14254i | ||||
\(400\) | −4.74275e7 | + | 2.73823e7i | −0.741055 | + | 0.427848i | ||||
\(401\) | −1.05105e8 | − | 2.81628e7i | −1.63001 | − | 0.436759i | −0.676088 | − | 0.736821i | \(-0.736326\pi\) |
−0.953920 | + | 0.300062i | \(0.902993\pi\) | |||||||
\(402\) | − | 6.30784e7i | − | 0.970962i | ||||||
\(403\) | 1.27596e7 | − | 1.22964e7i | 0.194950 | − | 0.187873i | ||||
\(404\) | 8.57538e6 | 0.130050 | ||||||||
\(405\) | −1.47208e7 | + | 5.49388e7i | −0.221598 | + | 0.827016i | ||||
\(406\) | −3.90206e7 | − | 6.75857e7i | −0.583064 | − | 1.00990i | ||||
\(407\) | −1.23916e6 | − | 715428.i | −0.0183799 | − | 0.0106116i | ||||
\(408\) | 6.19339e7 | + | 6.19339e7i | 0.911902 | + | 0.911902i | ||||
\(409\) | −1.02741e8 | + | 2.75294e7i | −1.50167 | + | 0.402371i | −0.913658 | − | 0.406483i | \(-0.866755\pi\) |
−0.588010 | + | 0.808854i | \(0.700088\pi\) | |||||||
\(410\) | −3.71803e6 | − | 1.38759e7i | −0.0539463 | − | 0.201330i | ||||
\(411\) | 1.54311e8 | − | 1.54311e8i | 2.22265 | − | 2.22265i | ||||
\(412\) | 366794. | − | 635305.i | 0.00524481 | − | 0.00908428i | ||||
\(413\) | 1.14809e7 | − | 6.62847e6i | 0.162976 | − | 0.0940943i | ||||
\(414\) | 4.30352e7 | + | 1.15313e7i | 0.606489 | + | 0.162508i | ||||
\(415\) | − | 1.44296e7i | − | 0.201887i | ||||||
\(416\) | −2.49826e6 | − | 1.00641e7i | −0.0347023 | − | 0.139796i | ||||
\(417\) | −3.25631e7 | −0.449074 | ||||||||
\(418\) | 9.25739e6 | − | 3.45490e7i | 0.126753 | − | 0.473050i | ||||
\(419\) | 2.29636e7 | + | 3.97742e7i | 0.312175 | + | 0.540703i | 0.978833 | − | 0.204661i | \(-0.0656091\pi\) |
−0.666658 | + | 0.745364i | \(0.732276\pi\) | |||||||
\(420\) | −2.01727e6 | − | 1.16467e6i | −0.0272280 | − | 0.0157201i | ||||
\(421\) | 7.31482e6 | + | 7.31482e6i | 0.0980296 | + | 0.0980296i | 0.754421 | − | 0.656391i | \(-0.227918\pi\) |
−0.656391 | + | 0.754421i | \(0.727918\pi\) | |||||||
\(422\) | 7.13710e7 | − | 1.91238e7i | 0.949695 | − | 0.254470i | ||||
\(423\) | −4.90454e7 | − | 1.83040e8i | −0.648004 | − | 2.41838i | ||||
\(424\) | −1.54303e7 | + | 1.54303e7i | −0.202430 | + | 0.202430i | ||||
\(425\) | 2.34140e7 | − | 4.05542e7i | 0.305006 | − | 0.528285i | ||||
\(426\) | −8.09145e6 | + | 4.67160e6i | −0.104664 | + | 0.0604278i | ||||
\(427\) | −2.36914e7 | − | 6.34809e6i | −0.304304 | − | 0.0815379i | ||||
\(428\) | 3.66283e6i | 0.0467181i | ||||||||
\(429\) | −4.83614e7 | + | 1.20050e7i | −0.612530 | + | 0.152051i | ||||
\(430\) | −1.74341e7 | −0.219278 | ||||||||
\(431\) | 2.76741e7 | − | 1.03281e8i | 0.345654 | − | 1.29000i | −0.546193 | − | 0.837660i | \(-0.683923\pi\) |
0.891847 | − | 0.452338i | \(-0.149410\pi\) | |||||||
\(432\) | 1.13293e8 | + | 1.96229e8i | 1.40525 | + | 2.43396i | ||||
\(433\) | −5.85283e7 | − | 3.37913e7i | −0.720945 | − | 0.416238i | 0.0941553 | − | 0.995558i | \(-0.469985\pi\) |
−0.815100 | + | 0.579320i | \(0.803318\pi\) | |||||||
\(434\) | −1.28436e7 | − | 1.28436e7i | −0.157115 | − | 0.157115i | ||||
\(435\) | 5.77705e7 | − | 1.54796e7i | 0.701841 | − | 0.188058i | ||||
\(436\) | −1.23000e6 | − | 4.59042e6i | −0.0148404 | − | 0.0553851i | ||||
\(437\) | −2.25886e7 | + | 2.25886e7i | −0.270673 | + | 0.270673i | ||||
\(438\) | −1.07544e8 | + | 1.86272e8i | −1.27986 | + | 2.21679i | ||||
\(439\) | 1.06122e8 | − | 6.12697e7i | 1.25433 | − | 0.724190i | 0.282367 | − | 0.959307i | \(-0.408881\pi\) |
0.971967 | + | 0.235117i | \(0.0755472\pi\) | |||||||
\(440\) | 7.60837e6 | + | 2.03866e6i | 0.0893169 | + | 0.0239324i | ||||
\(441\) | 6.12265e7i | 0.713877i | ||||||||
\(442\) | −3.79625e7 | − | 3.93924e7i | −0.439631 | − | 0.456190i | ||||
\(443\) | −5.77308e7 | −0.664043 | −0.332022 | − | 0.943272i | \(-0.607731\pi\) | ||||
−0.332022 | + | 0.943272i | \(0.607731\pi\) | |||||||
\(444\) | −198157. | + | 739532.i | −0.00226392 | + | 0.00844906i | ||||
\(445\) | 1.67593e6 | + | 2.90279e6i | 0.0190184 | + | 0.0329409i | ||||
\(446\) | 9.58620e7 | + | 5.53460e7i | 1.08054 | + | 0.623852i | ||||
\(447\) | 2.17165e8 | + | 2.17165e8i | 2.43146 | + | 2.43146i | ||||
\(448\) | −7.85390e7 | + | 2.10445e7i | −0.873477 | + | 0.234047i | ||||
\(449\) | 6.40068e6 | + | 2.38877e7i | 0.0707110 | + | 0.263897i | 0.992227 | − | 0.124444i | \(-0.0397148\pi\) |
−0.921516 | + | 0.388341i | \(0.873048\pi\) | |||||||
\(450\) | 1.49924e8 | − | 1.49924e8i | 1.64526 | − | 1.64526i | ||||
\(451\) | 1.22495e7 | − | 2.12167e7i | 0.133533 | − | 0.231285i | ||||
\(452\) | 7.25841e6 | − | 4.19065e6i | 0.0786007 | − | 0.0453801i | ||||
\(453\) | 1.58373e8 | + | 4.24360e7i | 1.70368 | + | 0.456499i | ||||
\(454\) | − | 7.93613e7i | − | 0.848088i | ||||||
\(455\) | 1.85171e7 | + | 1.11522e7i | 0.196580 | + | 0.118393i | ||||
\(456\) | −2.84348e8 | −2.99885 | ||||||||
\(457\) | −1.88715e7 | + | 7.04296e7i | −0.197724 | + | 0.737915i | 0.793821 | + | 0.608151i | \(0.208089\pi\) |
−0.991545 | + | 0.129764i | \(0.958578\pi\) | |||||||
\(458\) | −5.23028e7 | − | 9.05911e7i | −0.544413 | − | 0.942951i | ||||
\(459\) | −1.67791e8 | − | 9.68743e7i | −1.73513 | − | 1.00178i | ||||
\(460\) | −334815. | − | 334815.i | −0.00343979 | − | 0.00343979i | ||||
\(461\) | 7.48291e7 | − | 2.00504e7i | 0.763779 | − | 0.204654i | 0.144158 | − | 0.989555i | \(-0.453953\pi\) |
0.619622 | + | 0.784901i | \(0.287286\pi\) | |||||||
\(462\) | 1.32193e7 | + | 4.93352e7i | 0.134055 | + | 0.500300i | ||||
\(463\) | −3.84509e6 | + | 3.84509e6i | −0.0387404 | + | 0.0387404i | −0.726212 | − | 0.687471i | \(-0.758721\pi\) |
0.687471 | + | 0.726212i | \(0.258721\pi\) | |||||||
\(464\) | 6.54820e7 | − | 1.13418e8i | 0.655493 | − | 1.13535i | ||||
\(465\) | 1.20551e7 | − | 6.96000e6i | 0.119898 | − | 0.0692230i | ||||
\(466\) | 5.54283e7 | + | 1.48520e7i | 0.547739 | + | 0.146766i | ||||
\(467\) | − | 2.27164e7i | − | 0.223043i | −0.993762 | − | 0.111521i | \(-0.964428\pi\) | ||
0.993762 | − | 0.111521i | \(-0.0355724\pi\) | |||||||
\(468\) | 9.32272e6 | + | 1.68596e7i | 0.0909505 | + | 0.164478i | ||||
\(469\) | −4.66663e7 | −0.452361 | ||||||||
\(470\) | 6.70175e6 | − | 2.50113e7i | 0.0645498 | − | 0.240903i | ||||
\(471\) | −3.98268e7 | − | 6.89821e7i | −0.381165 | − | 0.660197i | ||||
\(472\) | 2.07734e7 | + | 1.19935e7i | 0.197552 | + | 0.114057i | ||||
\(473\) | −2.10240e7 | − | 2.10240e7i | −0.198670 | − | 0.198670i | ||||
\(474\) | −1.95478e8 | + | 5.23783e7i | −1.83554 | + | 0.491831i | ||||
\(475\) | 3.93466e7 | + | 1.46844e8i | 0.367136 | + | 1.37017i | ||||
\(476\) | 3.08398e6 | − | 3.08398e6i | 0.0285950 | − | 0.0285950i | ||||
\(477\) | 3.91778e7 | − | 6.78579e7i | 0.360982 | − | 0.625238i | ||||
\(478\) | −8.55235e7 | + | 4.93770e7i | −0.783072 | + | 0.452107i | ||||
\(479\) | 2.53370e7 | + | 6.78903e6i | 0.230541 | + | 0.0617733i | 0.372240 | − | 0.928136i | \(-0.378590\pi\) |
−0.141699 | + | 0.989910i | \(0.545256\pi\) | |||||||
\(480\) | − | 8.14570e6i | − | 0.0736554i | ||||||
\(481\) | 1.96541e6 | − | 6.82764e6i | 0.0176611 | − | 0.0613529i | ||||
\(482\) | 1.51358e8 | 1.35165 | ||||||||
\(483\) | 1.18065e7 | − | 4.40625e7i | 0.104780 | − | 0.391046i | ||||
\(484\) | −3.63890e6 | − | 6.30277e6i | −0.0320948 | − | 0.0555898i | ||||
\(485\) | −1.20234e7 | − | 6.94171e6i | −0.105391 | − | 0.0608473i | ||||
\(486\) | −2.33697e8 | − | 2.33697e8i | −2.03584 | − | 2.03584i | ||||
\(487\) | −1.36679e8 | + | 3.66230e7i | −1.18335 | + | 0.317079i | −0.796256 | − | 0.604960i | \(-0.793189\pi\) |
−0.387098 | + | 0.922039i | \(0.626522\pi\) | |||||||
\(488\) | −1.14862e7 | − | 4.28671e7i | −0.0988364 | − | 0.368863i | ||||
\(489\) | −1.32660e8 | + | 1.32660e8i | −1.13453 | + | 1.13453i | ||||
\(490\) | −4.18311e6 | + | 7.24536e6i | −0.0355558 | + | 0.0615845i | ||||
\(491\) | −1.88164e8 | + | 1.08636e8i | −1.58961 | + | 0.917763i | −0.596241 | + | 0.802805i | \(0.703340\pi\) |
−0.993370 | + | 0.114957i | \(0.963327\pi\) | |||||||
\(492\) | −1.26622e7 | − | 3.39282e6i | −0.106319 | − | 0.0284882i | ||||
\(493\) | 1.11984e8i | 0.934579i | ||||||||
\(494\) | 1.77574e8 | + | 3.28254e6i | 1.47299 | + | 0.0272288i | ||||
\(495\) | −2.82833e7 | −0.233192 | ||||||||
\(496\) | 7.88905e6 | − | 2.94423e7i | 0.0646516 | − | 0.241283i | ||||
\(497\) | 3.45612e6 | + | 5.98617e6i | 0.0281527 | + | 0.0487618i | ||||
\(498\) | 1.46616e8 | + | 8.46489e7i | 1.18712 | + | 0.685383i | ||||
\(499\) | 8.51779e7 | + | 8.51779e7i | 0.685528 | + | 0.685528i | 0.961240 | − | 0.275712i | \(-0.0889137\pi\) |
−0.275712 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(500\) | −4.52337e6 | + | 1.21203e6i | −0.0361869 | + | 0.00969626i | ||||
\(501\) | 1.85101e7 | + | 6.90806e7i | 0.147196 | + | 0.549342i | ||||
\(502\) | −6.02059e7 | + | 6.02059e7i | −0.475914 | + | 0.475914i | ||||
\(503\) | 5.49564e7 | − | 9.51872e7i | 0.431831 | − | 0.747954i | −0.565200 | − | 0.824954i | \(-0.691201\pi\) |
0.997031 | + | 0.0770003i | \(0.0245342\pi\) | |||||||
\(504\) | 2.54085e8 | − | 1.46696e8i | 1.98467 | − | 1.14585i | ||||
\(505\) | −6.03822e7 | − | 1.61794e7i | −0.468851 | − | 0.125628i | ||||
\(506\) | 1.03825e7i | 0.0801399i | ||||||||
\(507\) | −1.15709e8 | − | 2.18703e8i | −0.887858 | − | 1.67815i | ||||
\(508\) | 5.27344e6 | 0.0402256 | ||||||||
\(509\) | −5.70922e7 | + | 2.13071e8i | −0.432936 | + | 1.61574i | 0.313023 | + | 0.949746i | \(0.398658\pi\) |
−0.745958 | + | 0.665993i | \(0.768008\pi\) | |||||||
\(510\) | −2.14875e7 | − | 3.72174e7i | −0.161985 | − | 0.280566i | ||||
\(511\) | 1.37806e8 | + | 7.95626e7i | 1.03278 | + | 0.596275i | ||||
\(512\) | −1.03044e8 | − | 1.03044e8i | −0.767736 | − | 0.767736i | ||||
\(513\) | 6.07559e8 | − | 1.62795e8i | 4.50025 | − | 1.20584i | ||||
\(514\) | −3.38892e7 | − | 1.26476e8i | −0.249558 | − | 0.931364i | ||||
\(515\) | −3.78136e6 | + | 3.78136e6i | −0.0276839 | + | 0.0276839i | ||||
\(516\) | −7.95459e6 | + | 1.37778e7i | −0.0578987 | + | 0.100283i | ||||
\(517\) | 3.82431e7 | − | 2.20797e7i | 0.276746 | − | 0.159779i | ||||
\(518\) | −7.03445e6 | − | 1.88488e6i | −0.0506106 | − | 0.0135611i | ||||
\(519\) | 5.38983e7i | 0.385543i | ||||||||
\(520\) | −722879. | + | 3.91053e7i | −0.00514109 | + | 0.278116i | ||||
\(521\) | 1.33068e8 | 0.940934 | 0.470467 | − | 0.882417i | \(-0.344085\pi\) | ||||
0.470467 | + | 0.882417i | \(0.344085\pi\) | |||||||
\(522\) | −1.31231e8 | + | 4.89759e8i | −0.922622 | + | 3.44327i | ||||
\(523\) | −6.57792e7 | − | 1.13933e8i | −0.459815 | − | 0.796423i | 0.539136 | − | 0.842219i | \(-0.318751\pi\) |
−0.998951 | + | 0.0457956i | \(0.985418\pi\) | |||||||
\(524\) | −2.08697e6 | − | 1.20491e6i | −0.0145051 | − | 0.00837454i | ||||
\(525\) | −1.53503e8 | − | 1.53503e8i | −1.06081 | − | 1.06081i | ||||
\(526\) | 1.08916e8 | − | 2.91840e7i | 0.748402 | − | 0.200534i | ||||
\(527\) | 6.74574e6 | + | 2.51754e7i | 0.0460890 | + | 0.172007i | ||||
\(528\) | −6.06073e7 | + | 6.06073e7i | −0.411740 | + | 0.411740i | ||||
\(529\) | −6.93815e7 | + | 1.20172e8i | −0.468680 | + | 0.811778i | ||||
\(530\) | 9.27237e6 | − | 5.35340e6i | 0.0622821 | − | 0.0359586i | ||||
\(531\) | −8.31959e7 | − | 2.22923e7i | −0.555672 | − | 0.148892i | ||||
\(532\) | 1.41590e7i | 0.0940368i | ||||||||
\(533\) | 1.16902e8 | + | 3.36514e7i | 0.772040 | + | 0.222240i | ||||
\(534\) | −3.93263e7 | −0.258261 | ||||||||
\(535\) | 6.91074e6 | − | 2.57912e7i | 0.0451298 | − | 0.168427i | ||||
\(536\) | −4.22189e7 | − | 7.31253e7i | −0.274165 | − | 0.474868i | ||||
\(537\) | −2.60973e8 | − | 1.50673e8i | −1.68528 | − | 0.972998i | ||||
\(538\) | 4.30764e7 | + | 4.30764e7i | 0.276626 | + | 0.276626i | ||||
\(539\) | −1.37817e7 | + | 3.69280e6i | −0.0880110 | + | 0.0235825i | ||||
\(540\) | 2.41300e6 | + | 9.00542e6i | 0.0153241 | + | 0.0571904i | ||||
\(541\) | 1.16236e8 | − | 1.16236e8i | 0.734088 | − | 0.734088i | −0.237339 | − | 0.971427i | \(-0.576275\pi\) |
0.971427 | + | 0.237339i | \(0.0762752\pi\) | |||||||
\(542\) | 3.88069e7 | − | 6.72155e7i | 0.243731 | − | 0.422155i | ||||
\(543\) | 1.68380e8 | − | 9.72144e7i | 1.05170 | − | 0.607199i | ||||
\(544\) | 1.47321e7 | + | 3.94747e6i | 0.0915102 | + | 0.0245201i | ||||
\(545\) | 3.46434e7i | 0.214008i | ||||||||
\(546\) | −2.21943e8 | + | 1.22726e8i | −1.36353 | + | 0.753980i | ||||
\(547\) | 1.69958e8 | 1.03844 | 0.519219 | − | 0.854642i | \(-0.326223\pi\) | ||||
0.519219 | + | 0.854642i | \(0.326223\pi\) | |||||||
\(548\) | 5.08890e6 | − | 1.89920e7i | 0.0309231 | − | 0.115406i | ||||
\(549\) | 7.96768e7 | + | 1.38004e8i | 0.481521 | + | 0.834018i | ||||
\(550\) | 4.27896e7 | + | 2.47046e7i | 0.257187 | + | 0.148487i | ||||
\(551\) | −2.57068e8 | − | 2.57068e8i | −1.53671 | − | 1.53671i | ||||
\(552\) | 7.97264e7 | − | 2.13626e7i | 0.474007 | − | 0.127010i | ||||
\(553\) | 3.87502e7 | + | 1.44618e8i | 0.229139 | + | 0.855158i | ||||
\(554\) | −5.64769e7 | + | 5.64769e7i | −0.332155 | + | 0.332155i | ||||
\(555\) | 2.79058e6 | − | 4.83343e6i | 0.0163236 | − | 0.0282733i | ||||
\(556\) | −2.54081e6 | + | 1.46694e6i | −0.0147825 | + | 0.00853468i | ||||
\(557\) | −5.54535e7 | − | 1.48587e7i | −0.320895 | − | 0.0859836i | 0.0947758 | − | 0.995499i | \(-0.469787\pi\) |
−0.415671 | + | 0.909515i | \(0.636453\pi\) | |||||||
\(558\) | 1.18009e8i | 0.679224i | ||||||||
\(559\) | 7.61684e7 | − | 1.26470e8i | 0.436053 | − | 0.724024i | ||||
\(560\) | 3.71820e7 | 0.211723 | ||||||||
\(561\) | 1.89689e7 | − | 7.07928e7i | 0.107437 | − | 0.400959i | ||||
\(562\) | −1.39744e8 | − | 2.42043e8i | −0.787270 | − | 1.36359i | ||||
\(563\) | −1.88817e8 | − | 1.09014e8i | −1.05808 | − | 0.610880i | −0.133176 | − | 0.991092i | \(-0.542518\pi\) |
−0.924899 | + | 0.380212i | \(0.875851\pi\) | |||||||
\(564\) | −1.67080e7 | − | 1.67080e7i | −0.0931296 | − | 0.0931296i | ||||
\(565\) | −5.90156e7 | + | 1.58132e7i | −0.327206 | + | 0.0876746i | ||||
\(566\) | 2.67961e7 | + | 1.00004e8i | 0.147782 | + | 0.551530i | ||||
\(567\) | −3.49093e8 | + | 3.49093e8i | −1.91510 | + | 1.91510i | ||||
\(568\) | −6.25348e6 | + | 1.08313e7i | −0.0341253 | + | 0.0591068i | ||||
\(569\) | −1.21331e7 | + | 7.00506e6i | −0.0658622 | + | 0.0380255i | −0.532569 | − | 0.846386i | \(-0.678773\pi\) |
0.466707 | + | 0.884412i | \(0.345440\pi\) | |||||||
\(570\) | 1.34761e8 | + | 3.61092e7i | 0.727680 | + | 0.194981i | ||||
\(571\) | − | 1.98776e8i | − | 1.06772i | −0.845573 | − | 0.533859i | \(-0.820741\pi\) | ||
0.845573 | − | 0.533859i | \(-0.179259\pi\) | |||||||
\(572\) | −3.23270e6 | + | 3.11535e6i | −0.0172734 | + | 0.0166463i | ||||
\(573\) | −3.60492e8 | −1.91616 | ||||||||
\(574\) | 3.22726e7 | − | 1.20443e8i | 0.170647 | − | 0.636863i | ||||
\(575\) | −2.20643e7 | − | 3.82164e7i | −0.116061 | − | 0.201023i | ||||
\(576\) | 4.57496e8 | + | 2.64135e8i | 2.39397 | + | 1.38216i | ||||
\(577\) | 1.71873e8 | + | 1.71873e8i | 0.894705 | + | 0.894705i | 0.994962 | − | 0.100257i | \(-0.0319664\pi\) |
−0.100257 | + | 0.994962i | \(0.531966\pi\) | |||||||
\(578\) | −1.01941e8 | + | 2.73151e7i | −0.527918 | + | 0.141455i | ||||
\(579\) | 9.06364e7 | + | 3.38260e8i | 0.466946 | + | 1.74267i | ||||
\(580\) | 3.81034e6 | − | 3.81034e6i | 0.0195290 | − | 0.0195290i | ||||
\(581\) | 6.26245e7 | − | 1.08469e8i | 0.319313 | − | 0.553066i | ||||
\(582\) | 1.41067e8 | − | 8.14450e7i | 0.715577 | − | 0.413138i | ||||
\(583\) | 1.76374e7 | + | 4.72592e6i | 0.0890078 | + | 0.0238496i | ||||
\(584\) | 2.87920e8i | 1.44555i | ||||||||
\(585\) | −3.38352e7 | − | 1.36303e8i | −0.169005 | − | 0.680830i | ||||
\(586\) | −1.98171e8 | −0.984796 | ||||||||
\(587\) | −2.54224e7 | + | 9.48775e7i | −0.125690 | + | 0.469082i | −0.999863 | − | 0.0165321i | \(-0.994737\pi\) |
0.874173 | + | 0.485614i | \(0.161404\pi\) | |||||||
\(588\) | 3.81722e6 | + | 6.61161e6i | 0.0187765 | + | 0.0325219i | ||||
\(589\) | −7.32775e7 | − | 4.23068e7i | −0.358612 | − | 0.207045i | ||||
\(590\) | −8.32210e6 | − | 8.32210e6i | −0.0405207 | − | 0.0405207i | ||||
\(591\) | −2.55070e8 | + | 6.83459e7i | −1.23566 | + | 0.331093i | ||||
\(592\) | −3.16308e6 | − | 1.18048e7i | −0.0152456 | − | 0.0568974i | ||||
\(593\) | −4.52139e7 | + | 4.52139e7i | −0.216824 | + | 0.216824i | −0.807159 | − | 0.590334i | \(-0.798996\pi\) |
0.590334 | + | 0.807159i | \(0.298996\pi\) | |||||||
\(594\) | 1.02214e8 | − | 1.77040e8i | 0.487698 | − | 0.844719i | ||||
\(595\) | −2.75340e7 | + | 1.58967e7i | −0.130713 | + | 0.0754670i | ||||
\(596\) | 2.67279e7 | + | 7.16172e6i | 0.126248 | + | 0.0338282i | ||||
\(597\) | − | 6.60782e8i | − | 3.10553i | ||||||
\(598\) | −5.00354e7 | + | 1.24205e7i | −0.233977 | + | 0.0580812i | ||||
\(599\) | 1.41911e8 | 0.660292 | 0.330146 | − | 0.943930i | \(-0.392902\pi\) | ||||
0.330146 | + | 0.943930i | \(0.392902\pi\) | |||||||
\(600\) | 1.01663e8 | − | 3.79410e8i | 0.470660 | − | 1.75653i | ||||
\(601\) | −4.95083e7 | − | 8.57509e7i | −0.228063 | − | 0.395017i | 0.729171 | − | 0.684331i | \(-0.239906\pi\) |
−0.957234 | + | 0.289315i | \(0.906573\pi\) | |||||||
\(602\) | −1.31054e8 | − | 7.56643e7i | −0.600706 | − | 0.346818i | ||||
\(603\) | 2.14389e8 | + | 2.14389e8i | 0.977803 | + | 0.977803i | ||||
\(604\) | 1.42691e7 | − | 3.82341e6i | 0.0647571 | − | 0.0173516i | ||||
\(605\) | 1.37312e7 | + | 5.12456e7i | 0.0620073 | + | 0.231414i | ||||
\(606\) | 5.18619e8 | − | 5.18619e8i | 2.33040 | − | 2.33040i | ||||
\(607\) | −1.90406e8 | + | 3.29792e8i | −0.851361 | + | 1.47460i | 0.0286197 | + | 0.999590i | \(0.490889\pi\) |
−0.879981 | + | 0.475010i | \(0.842445\pi\) | |||||||
\(608\) | −4.28805e7 | + | 2.47570e7i | −0.190787 | + | 0.110151i | ||||
\(609\) | 5.01450e8 | + | 1.34363e8i | 2.22012 | + | 0.594878i | ||||
\(610\) | 2.17747e7i | 0.0959317i | ||||||||
\(611\) | 1.52157e8 | + | 1.57888e8i | 0.667065 | + | 0.692191i | ||||
\(612\) | −2.83362e7 | −0.123619 | ||||||||
\(613\) | 4.37989e6 | − | 1.63460e7i | 0.0190144 | − | 0.0709626i | −0.955767 | − | 0.294126i | \(-0.904972\pi\) |
0.974781 | + | 0.223163i | \(0.0716382\pi\) | |||||||
\(614\) | 8.21853e7 | + | 1.42349e8i | 0.355050 | + | 0.614964i | ||||
\(615\) | 8.27574e7 | + | 4.77800e7i | 0.355780 | + | 0.205410i | ||||
\(616\) | 4.83453e7 | + | 4.83453e7i | 0.206829 | + | 0.206829i | ||||
\(617\) | −1.16111e8 | + | 3.11118e7i | −0.494330 | + | 0.132455i | −0.497367 | − | 0.867540i | \(-0.665700\pi\) |
0.00303756 | + | 0.999995i | \(0.499033\pi\) | |||||||
\(618\) | −1.62389e7 | − | 6.06045e7i | −0.0688006 | − | 0.256767i | ||||
\(619\) | 1.92617e8 | − | 1.92617e8i | 0.812127 | − | 0.812127i | −0.172826 | − | 0.984952i | \(-0.555290\pi\) |
0.984952 | + | 0.172826i | \(0.0552898\pi\) | |||||||
\(620\) | 627083. | − | 1.08614e6i | 0.00263118 | − | 0.00455733i | ||||
\(621\) | −1.58119e8 | + | 9.12900e7i | −0.660251 | + | 0.381196i | ||||
\(622\) | 2.58778e8 | + | 6.93394e7i | 1.07537 | + | 0.288143i | ||||
\(623\) | 2.90942e7i | 0.120321i | ||||||||
\(624\) | −3.64585e8 | − | 2.19576e8i | −1.50053 | − | 0.903714i | ||||
\(625\) | −1.92292e8 | −0.787629 | ||||||||
\(626\) | −7.27344e7 | + | 2.71448e8i | −0.296495 | + | 1.10653i | ||||
\(627\) | 1.18966e8 | + | 2.06055e8i | 0.482635 | + | 0.835949i | ||||
\(628\) | −6.21516e6 | − | 3.58832e6i | −0.0250942 | − | 0.0144881i | ||||
\(629\) | 7.38931e6 | + | 7.38931e6i | 0.0296929 | + | 0.0296929i | ||||
\(630\) | −1.39048e8 | + | 3.72578e7i | −0.556087 | + | 0.149003i | ||||
\(631\) | −9.37893e7 | − | 3.50026e8i | −0.373306 | − | 1.39320i | −0.855804 | − | 0.517300i | \(-0.826937\pi\) |
0.482498 | − | 0.875897i | \(-0.339730\pi\) | |||||||
\(632\) | −1.91556e8 | + | 1.91556e8i | −0.758830 | + | 0.758830i | ||||
\(633\) | −2.45758e8 | + | 4.25665e8i | −0.968938 | + | 1.67825i | ||||
\(634\) | −1.75082e8 | + | 1.01084e8i | −0.687028 | + | 0.396656i | ||||
\(635\) | −3.71321e7 | − | 9.94952e6i | −0.145020 | − | 0.0388580i | ||||
\(636\) | − | 9.77029e6i | − | 0.0379784i | ||||||
\(637\) | −3.42834e7 | − | 6.19995e7i | −0.132637 | − | 0.239867i | ||||
\(638\) | −1.18157e8 | −0.454985 | ||||||||
\(639\) | 1.16233e7 | − | 4.33788e7i | 0.0445479 | − | 0.166255i | ||||
\(640\) | 3.10074e7 | + | 5.37064e7i | 0.118284 | + | 0.204874i | ||||
\(641\) | 1.77643e8 | + | 1.02562e8i | 0.674486 | + | 0.389415i | 0.797774 | − | 0.602956i | \(-0.206011\pi\) |
−0.123288 | + | 0.992371i | \(0.539344\pi\) | |||||||
\(642\) | 2.21519e8 | + | 2.21519e8i | 0.837156 | + | 0.837156i | ||||
\(643\) | 3.95822e8 | − | 1.06060e8i | 1.48891 | − | 0.398951i | 0.579538 | − | 0.814945i | \(-0.303233\pi\) |
0.909367 | + | 0.415994i | \(0.136566\pi\) | |||||||
\(644\) | −1.06374e6 | − | 3.96995e6i | −0.00398272 | − | 0.0148637i | ||||
\(645\) | 8.20058e7 | − | 8.20058e7i | 0.305609 | − | 0.305609i | ||||
\(646\) | −1.30613e8 | + | 2.26228e8i | −0.484493 | + | 0.839167i | ||||
\(647\) | 1.86010e8 | − | 1.07393e8i | 0.686789 | − | 0.396518i | −0.115619 | − | 0.993294i | \(-0.536885\pi\) |
0.802408 | + | 0.596776i | \(0.203552\pi\) | |||||||
\(648\) | −8.62846e8 | − | 2.31199e8i | −3.17109 | − | 0.849690i | ||||
\(649\) | − | 2.00714e7i | − | 0.0734250i | ||||||
\(650\) | −6.78678e7 | + | 2.35766e8i | −0.247129 | + | 0.858503i | ||||
\(651\) | 1.20826e8 | 0.437943 | ||||||||
\(652\) | −4.37490e6 | + | 1.63273e7i | −0.0157843 | + | 0.0589078i | ||||
\(653\) | 5.02440e7 | + | 8.70251e7i | 0.180445 | + | 0.312540i | 0.942032 | − | 0.335523i | \(-0.108913\pi\) |
−0.761587 | + | 0.648062i | \(0.775580\pi\) | |||||||
\(654\) | −3.52005e8 | − | 2.03230e8i | −1.25839 | − | 0.726532i | ||||
\(655\) | 1.24217e7 | + | 1.24217e7i | 0.0442036 | + | 0.0442036i | ||||
\(656\) | 2.02120e8 | − | 5.41578e7i | 0.715974 | − | 0.191845i | ||||
\(657\) | −2.67578e8 | − | 9.98614e8i | −0.943526 | − | 3.52129i | ||||
\(658\) | 1.58927e8 | − | 1.58927e8i | 0.557854 | − | 0.557854i | ||||
\(659\) | 1.74601e8 | − | 3.02417e8i | 0.610084 | − | 1.05670i | −0.381141 | − | 0.924517i | \(-0.624469\pi\) |
0.991226 | − | 0.132180i | \(-0.0421978\pi\) | |||||||
\(660\) | −3.05420e6 | + | 1.76334e6i | −0.0106235 | + | 0.00613346i | ||||
\(661\) | −4.12015e8 | − | 1.10399e8i | −1.42662 | − | 0.382262i | −0.538794 | − | 0.842438i | \(-0.681120\pi\) |
−0.887828 | + | 0.460176i | \(0.847786\pi\) | |||||||
\(662\) | 9.64780e7i | 0.332548i | ||||||||
\(663\) | 3.63859e8 | + | 6.72609e6i | 1.24851 | + | 0.0230793i | ||||
\(664\) | 2.26625e8 | 0.774111 | ||||||||
\(665\) | 2.67141e7 | − | 9.96984e7i | 0.0908397 | − | 0.339018i | ||||
\(666\) | 2.36576e7 | + | 4.09762e7i | 0.0800845 | + | 0.138710i | ||||
\(667\) | 9.13907e7 | + | 5.27645e7i | 0.307981 | + | 0.177813i | ||||
\(668\) | 4.55631e6 | + | 4.55631e6i | 0.0152856 | + | 0.0152856i | ||||
\(669\) | −7.11245e8 | + | 1.90578e8i | −2.37542 | + | 0.636493i | ||||
\(670\) | 1.07227e7 | + | 4.00177e7i | 0.0356517 | + | 0.133054i | ||||
\(671\) | −2.62583e7 | + | 2.62583e7i | −0.0869159 | + | 0.0869159i | ||||
\(672\) | 3.53524e7 | − | 6.12322e7i | 0.116496 | − | 0.201777i | ||||
\(673\) | −8.43084e7 | + | 4.86755e7i | −0.276583 | + | 0.159685i | −0.631875 | − | 0.775070i | \(-0.717715\pi\) |
0.355292 | + | 0.934755i | \(0.384381\pi\) | |||||||
\(674\) | −2.28105e8 | − | 6.11207e7i | −0.744999 | − | 0.199622i | ||||
\(675\) | 8.68880e8i | 2.82519i | ||||||||
\(676\) | −1.88808e7 | − | 1.18522e7i | −0.0611197 | − | 0.0383671i | ||||
\(677\) | 3.36143e8 | 1.08332 | 0.541662 | − | 0.840597i | \(-0.317795\pi\) | ||||
0.541662 | + | 0.840597i | \(0.317795\pi\) | |||||||
\(678\) | 1.85531e8 | − | 6.92412e8i | 0.595289 | − | 2.22165i | ||||
\(679\) | −6.02543e7 | − | 1.04363e8i | −0.192477 | − | 0.333380i | ||||
\(680\) | −4.98198e7 | − | 2.87635e7i | −0.158444 | − | 0.0914775i | ||||
\(681\) | 3.73296e8 | + | 3.73296e8i | 1.18198 | + | 1.18198i | ||||
\(682\) | −2.65631e7 | + | 7.11757e6i | −0.0837387 | + | 0.0224377i | ||||
\(683\) | 2.77282e7 | + | 1.03483e8i | 0.0870281 | + | 0.324793i | 0.995691 | − | 0.0927383i | \(-0.0295620\pi\) |
−0.908662 | + | 0.417532i | \(0.862895\pi\) | |||||||
\(684\) | 6.50478e7 | − | 6.50478e7i | 0.203266 | − | 0.203266i | ||||
\(685\) | −7.16654e7 | + | 1.24128e8i | −0.222966 | + | 0.386188i | ||||
\(686\) | −2.92335e8 | + | 1.68779e8i | −0.905541 | + | 0.522814i | ||||
\(687\) | 6.72138e8 | + | 1.80099e8i | 2.07295 | + | 0.555444i | ||||
\(688\) | − | 2.53950e8i | − | 0.779800i | ||||||
\(689\) | −1.67574e6 | + | 9.06520e7i | −0.00512330 | + | 0.277153i | ||||
\(690\) | −4.04976e7 | −0.123277 | ||||||||
\(691\) | −8.75509e7 | + | 3.26745e8i | −0.265355 | + | 0.990317i | 0.696678 | + | 0.717384i | \(0.254660\pi\) |
−0.962033 | + | 0.272933i | \(0.912006\pi\) | |||||||
\(692\) | 2.42807e6 | + | 4.20554e6i | 0.00732728 | + | 0.0126912i | ||||
\(693\) | −2.12609e8 | − | 1.22750e8i | −0.638824 | − | 0.368825i | ||||
\(694\) | −1.10324e8 | − | 1.10324e8i | −0.330058 | − | 0.330058i | ||||
\(695\) | 2.06584e7 | − | 5.53541e6i | 0.0615379 | − | 0.0164890i | ||||
\(696\) | 2.43116e8 | + | 9.07320e8i | 0.721083 | + | 2.69112i | ||||
\(697\) | −1.26519e8 | + | 1.26519e8i | −0.373643 | + | 0.373643i | ||||
\(698\) | 2.62464e8 | − | 4.54601e8i | 0.771799 | − | 1.33679i | ||||
\(699\) | −3.30581e8 | + | 1.90861e8i | −0.967935 | + | 0.558838i | ||||
\(700\) | −1.88926e7 | − | 5.06225e6i | −0.0550804 | − | 0.0147588i | ||||
\(701\) | − | 1.37195e7i | − | 0.0398276i | −0.999802 | − | 0.0199138i | \(-0.993661\pi\) | ||
0.999802 | − | 0.0199138i | \(-0.00633918\pi\) | |||||||
\(702\) | 9.75473e8 | + | 2.80800e8i | 2.81971 | + | 0.811682i | ||||
\(703\) | −3.39254e7 | −0.0976471 | ||||||||
\(704\) | −3.18620e7 | + | 1.18910e8i | −0.0913176 | + | 0.340802i | ||||
\(705\) | 8.61235e7 | + | 1.49170e8i | 0.245784 | + | 0.425711i | ||||
\(706\) | 4.34721e8 | + | 2.50986e8i | 1.23537 | + | 0.713240i | ||||
\(707\) | −3.83682e8 | − | 3.83682e8i | −1.08571 | − | 1.08571i | ||||
\(708\) | −1.03738e7 | + | 2.77966e6i | −0.0292307 | + | 0.00783235i | ||||
\(709\) | −1.10767e8 | − | 4.13389e8i | −0.310794 | − | 1.15990i | −0.927842 | − | 0.372974i | \(-0.878338\pi\) |
0.617047 | − | 0.786926i | \(-0.288329\pi\) | |||||||
\(710\) | 4.33919e6 | − | 4.33919e6i | 0.0121236 | − | 0.0121236i | ||||
\(711\) | 4.86365e8 | − | 8.42409e8i | 1.35317 | − | 2.34377i | ||||
\(712\) | −4.55900e7 | + | 2.63214e7i | −0.126308 | + | 0.0729238i | ||||
\(713\) | 2.37242e7 | + | 6.35689e6i | 0.0654521 | + | 0.0175378i | ||||
\(714\) | − | 3.73023e8i | − | 1.02481i | ||||||
\(715\) | 2.86403e7 | − | 1.58371e7i | 0.0783538 | − | 0.0433268i | ||||
\(716\) | −2.71507e7 | −0.0739677 | ||||||||
\(717\) | 1.70024e8 | − | 6.34539e8i | 0.461268 | − | 1.72147i | ||||
\(718\) | 2.57784e8 | + | 4.46495e8i | 0.696438 | + | 1.20627i | ||||
\(719\) | −3.99579e8 | − | 2.30697e8i | −1.07502 | − | 0.620663i | −0.145471 | − | 0.989363i | \(-0.546470\pi\) |
−0.929548 | + | 0.368700i | \(0.879803\pi\) | |||||||
\(720\) | −1.70818e8 | − | 1.70818e8i | −0.457652 | − | 0.457652i | ||||
\(721\) | −4.48361e7 | + | 1.20138e7i | −0.119625 | + | 0.0320535i | ||||
\(722\) | −1.25661e8 | − | 4.68974e8i | −0.333880 | − | 1.24606i | ||||
\(723\) | −7.11950e8 | + | 7.11950e8i | −1.88380 | + | 1.88380i | ||||
\(724\) | 8.75884e6 | − | 1.51708e7i | 0.0230797 | − | 0.0399753i | ||||
\(725\) | 4.34919e8 | − | 2.51101e8i | 1.14129 | − | 0.658922i | ||||
\(726\) | −6.01249e8 | − | 1.61104e8i | −1.57125 | − | 0.421014i | ||||
\(727\) | 1.11362e8i | 0.289823i | 0.989445 | + | 0.144911i | \(0.0462897\pi\) | ||||
−0.989445 | + | 0.144911i | \(0.953710\pi\) | |||||||
\(728\) | −1.75151e8 | + | 2.90822e8i | −0.453962 | + | 0.753760i | ||||
\(729\) | 9.66960e8 | 2.49589 | ||||||||
\(730\) | 3.65628e7 | − | 1.36454e8i | 0.0939878 | − | 0.350767i | ||||
\(731\) | 1.08573e8 | + | 1.88055e8i | 0.277953 | + | 0.481429i | ||||
\(732\) | 1.72080e7 | + | 9.93503e6i | 0.0438729 | + | 0.0253301i | ||||
\(733\) | 1.83409e7 | + | 1.83409e7i | 0.0465703 | + | 0.0465703i | 0.730008 | − | 0.683438i | \(-0.239516\pi\) |
−0.683438 | + | 0.730008i | \(0.739516\pi\) | |||||||
\(734\) | 4.93810e8 | − | 1.32316e8i | 1.24874 | − | 0.334598i | ||||
\(735\) | −1.44041e7 | − | 5.37567e7i | −0.0362763 | − | 0.135385i | ||||
\(736\) | 1.01630e7 | − | 1.01630e7i | 0.0254911 | − | 0.0254911i | ||||
\(737\) | −3.53271e7 | + | 6.11884e7i | −0.0882482 | + | 0.152850i | ||||
\(738\) | −7.01589e8 | + | 4.05063e8i | −1.74548 | + | 1.00775i | ||||
\(739\) | −4.18839e8 | − | 1.12227e8i | −1.03780 | − | 0.278078i | −0.300598 | − | 0.953751i | \(-0.597186\pi\) |
−0.737201 | + | 0.675673i | \(0.763853\pi\) | |||||||
\(740\) | − | 502853.i | − | 0.00124093i | ||||||
\(741\) | −8.50705e8 | + | 8.19824e8i | −2.09086 | + | 2.01496i | ||||
\(742\) | 9.29354e7 | 0.227494 | ||||||||
\(743\) | −1.22923e8 | + | 4.58755e8i | −0.299686 | + | 1.11844i | 0.637738 | + | 0.770253i | \(0.279870\pi\) |
−0.937424 | + | 0.348190i | \(0.886796\pi\) | |||||||
\(744\) | 1.09311e8 | + | 1.89332e8i | 0.265427 | + | 0.459733i | ||||
\(745\) | −1.74688e8 | − | 1.00856e8i | −0.422469 | − | 0.243912i | ||||
\(746\) | −3.30488e8 | − | 3.30488e8i | −0.796048 | − | 0.796048i | ||||
\(747\) | −7.86019e8 | + | 2.10613e8i | −1.88569 | + | 0.505270i | ||||
\(748\) | −1.70906e6 | − | 6.37830e6i | −0.00408369 | − | 0.0152405i | ||||
\(749\) | 1.63883e8 | − | 1.63883e8i | 0.390022 | − | 0.390022i | ||||
\(750\) | −2.00262e8 | + | 3.46863e8i | −0.474694 | + | 0.822194i | ||||
\(751\) | 4.43339e8 | − | 2.55962e8i | 1.04669 | − | 0.604304i | 0.124966 | − | 0.992161i | \(-0.460118\pi\) |
0.921720 | + | 0.387857i | \(0.126784\pi\) | |||||||
\(752\) | 3.64321e8 | + | 9.76196e7i | 0.856704 | + | 0.229553i | ||||
\(753\) | − | 5.66388e8i | − | 1.32657i | ||||||
\(754\) | −1.41351e8 | − | 5.69424e8i | −0.329749 | − | 1.32838i | ||||
\(755\) | −1.07688e8 | −0.250222 | ||||||||
\(756\) | −2.09449e7 | + | 7.81673e7i | −0.0484744 | + | 0.180909i | ||||
\(757\) | 2.40493e8 | + | 4.16547e8i | 0.554390 | + | 0.960232i | 0.997951 | + | 0.0639876i | \(0.0203818\pi\) |
−0.443560 | + | 0.896244i | \(0.646285\pi\) | |||||||
\(758\) | −6.67292e8 | − | 3.85261e8i | −1.53217 | − | 0.884601i | ||||
\(759\) | −4.88366e7 | − | 4.88366e7i | −0.111691 | − | 0.111691i | ||||
\(760\) | 1.80394e8 | − | 4.83363e7i | 0.410942 | − | 0.110112i | ||||
\(761\) | −8.23634e7 | − | 3.07385e8i | −0.186888 | − | 0.697474i | −0.994219 | − | 0.107375i | \(-0.965755\pi\) |
0.807331 | − | 0.590099i | \(-0.200911\pi\) | |||||||
\(762\) | 3.18925e8 | − | 3.18925e8i | 0.720815 | − | 0.720815i | ||||
\(763\) | −1.50353e8 | + | 2.60418e8i | −0.338484 | + | 0.586271i | ||||
\(764\) | −2.81282e7 | + | 1.62398e7i | −0.0630758 | + | 0.0364168i | ||||
\(765\) | 1.99525e8 | + | 5.34625e7i | 0.445669 | + | 0.119417i | ||||
\(766\) | 7.47371e8i | 1.66284i | ||||||||
\(767\) | 9.67287e7 | − | 2.40114e7i | 0.214373 | − | 0.0532146i | ||||
\(768\) | 1.85193e8 | 0.408829 | ||||||||
\(769\) | −6.88910e7 | + | 2.57105e8i | −0.151490 | + | 0.565367i | 0.847891 | + | 0.530171i | \(0.177872\pi\) |
−0.999380 | + | 0.0351963i | \(0.988794\pi\) | |||||||
\(770\) | −1.67730e7 | − | 2.90517e7i | −0.0367399 | − | 0.0636354i | ||||
\(771\) | 7.54319e8 | + | 4.35506e8i | 1.64586 | + | 0.950236i | ||||
\(772\) | 2.23104e7 | + | 2.23104e7i | 0.0484904 | + | 0.0484904i | ||||
\(773\) | 7.46431e8 | − | 2.00006e8i | 1.61604 | − | 0.433016i | 0.666203 | − | 0.745771i | \(-0.267919\pi\) |
0.949834 | + | 0.312755i | \(0.101252\pi\) | |||||||
\(774\) | 2.54467e8 | + | 9.49685e8i | 0.548794 | + | 2.04813i | ||||
\(775\) | 8.26494e7 | − | 8.26494e7i | 0.177556 | − | 0.177556i | ||||
\(776\) | 1.09024e8 | − | 1.88835e8i | 0.233311 | − | 0.404107i | ||||
\(777\) | 4.19543e7 | − | 2.42223e7i | 0.0894363 | − | 0.0516360i | ||||
\(778\) | 4.23490e8 | + | 1.13474e8i | 0.899299 | + | 0.240967i | ||||
\(779\) | − | 5.80867e8i | − | 1.22875i | ||||||
\(780\) | −1.21517e7 | − | 1.26094e7i | −0.0256066 | − | 0.0265712i | ||||
\(781\) | 1.04653e7 | 0.0219685 | ||||||||
\(782\) | 1.96255e7 | − | 7.32432e7i | 0.0410393 | − | 0.153161i | ||||
\(783\) | −1.03892e9 | − | 1.79946e9i | −2.16419 | − | 3.74850i | ||||
\(784\) | −1.05538e8 | − | 6.09323e7i | −0.219008 | − | 0.126444i | ||||
\(785\) | 3.69929e7 | + | 3.69929e7i | 0.0764732 | + | 0.0764732i | ||||
\(786\) | −1.99085e8 | + | 5.33446e7i | −0.409988 | + | 0.109856i | ||||
\(787\) | −6.84923e6 | − | 2.55617e7i | −0.0140513 | − | 0.0524403i | 0.958544 | − | 0.284944i | \(-0.0919749\pi\) |
−0.972596 | + | 0.232504i | \(0.925308\pi\) | |||||||
\(788\) | −1.68235e7 | + | 1.68235e7i | −0.0343826 | + | 0.0343826i | ||||
\(789\) | −3.75040e8 | + | 6.49589e8i | −0.763566 | + | 1.32254i | ||||
\(790\) | 1.15110e8 | − | 6.64588e7i | 0.233470 | − | 0.134794i | ||||
\(791\) | −5.12257e8 | − | 1.37259e8i | −1.03504 | − | 0.277339i | ||||
\(792\) | − | 4.44205e8i | − | 0.894145i | ||||||
\(793\) | −1.57957e8 | − | 9.51320e7i | −0.316753 | − | 0.190769i | ||||
\(794\) | 3.50250e8 | 0.699707 | ||||||||
\(795\) | −1.84338e7 | + | 6.87960e7i | −0.0366872 | + | 0.136918i | ||||
\(796\) | −2.97676e7 | − | 5.15590e7i | −0.0590208 | − | 0.102227i | ||||
\(797\) | 4.01787e8 | + | 2.31972e8i | 0.793634 | + | 0.458205i | 0.841240 | − | 0.540661i | \(-0.181826\pi\) |
−0.0476061 | + | 0.998866i | \(0.515159\pi\) | |||||||
\(798\) | 8.56303e8 | + | 8.56303e8i | 1.68507 | + | 1.68507i | ||||
\(799\) | −3.11522e8 | + | 8.34722e7i | −0.610730 | + | 0.163645i | ||||
\(800\) | −1.77027e7 | − | 6.60674e7i | −0.0345756 | − | 0.129038i | ||||
\(801\) | 1.33661e8 | − | 1.33661e8i | 0.260081 | − | 0.260081i | ||||
\(802\) | −4.19251e8 | + | 7.26165e8i | −0.812739 | + | 1.40771i | ||||
\(803\) | 2.08643e8 | − | 1.20460e8i | 0.402956 | − | 0.232647i | ||||
\(804\) | 3.65174e7 | + | 9.78480e6i | 0.0702638 | + | 0.0188271i | ||||
\(805\) | 2.99608e7i | 0.0574335i | ||||||||
\(806\) | −6.60785e7 | − | 1.19499e8i | −0.126199 | − | 0.228223i | ||||
\(807\) | −4.05241e8 | −0.771068 | ||||||||
\(808\) | 2.54106e8 | − | 9.48338e8i | 0.481705 | − | 1.79775i | ||||
\(809\) | 5.04306e8 | + | 8.73483e8i | 0.952463 | + | 1.64971i | 0.740069 | + | 0.672531i | \(0.234793\pi\) |
0.212394 | + | 0.977184i | \(0.431874\pi\) | |||||||
\(810\) | 3.79570e8 | + | 2.19145e8i | 0.714228 | + | 0.412359i | ||||
\(811\) | 4.04247e8 | + | 4.04247e8i | 0.757852 | + | 0.757852i | 0.975931 | − | 0.218079i | \(-0.0699789\pi\) |
−0.218079 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(812\) | 4.51797e7 | − | 1.21059e7i | 0.0843870 | − | 0.0226114i | ||||
\(813\) | 1.33627e8 | + | 4.98703e8i | 0.248670 | + | 0.928048i | ||||
\(814\) | −7.79662e6 | + | 7.79662e6i | −0.0144555 | + | 0.0144555i | ||||
\(815\) | 6.16103e7 | − | 1.06712e8i | 0.113810 | − | 0.197125i | ||||
\(816\) | 5.42118e8 | − | 3.12992e8i | 0.997754 | − | 0.576054i | ||||
\(817\) | −6.80932e8 | − | 1.82455e8i | −1.24864 | − | 0.334572i | ||||
\(818\) | 8.19645e8i | 1.49750i | ||||||||
\(819\) | 3.37215e8 | − | 1.17145e9i | 0.613841 | − | 2.13242i | ||||
\(820\) | 8.60978e6 | 0.0156153 | ||||||||
\(821\) | 8.78007e7 | − | 3.27677e8i | 0.158660 | − | 0.592129i | −0.840104 | − | 0.542426i | \(-0.817506\pi\) |
0.998764 | − | 0.0497027i | \(-0.0158274\pi\) | |||||||
\(822\) | −8.40829e8 | − | 1.45636e9i | −1.51388 | − | 2.62212i | ||||
\(823\) | 4.84527e8 | + | 2.79742e8i | 0.869198 | + | 0.501832i | 0.867082 | − | 0.498166i | \(-0.165993\pi\) |
0.00211624 | + | 0.999998i | \(0.499326\pi\) | |||||||
\(824\) | −5.93885e7 | − | 5.93885e7i | −0.106150 | − | 0.106150i | ||||
\(825\) | −3.17476e8 | + | 8.50673e7i | −0.565390 | + | 0.151496i | ||||
\(826\) | −2.64402e7 | − | 9.86763e7i | −0.0469165 | − | 0.175095i | ||||
\(827\) | −4.82913e8 | + | 4.82913e8i | −0.853793 | + | 0.853793i | −0.990598 | − | 0.136805i | \(-0.956317\pi\) |
0.136805 | + | 0.990598i | \(0.456317\pi\) | |||||||
\(828\) | −1.33514e7 | + | 2.31253e7i | −0.0235199 | + | 0.0407376i | ||||
\(829\) | 1.04019e8 | − | 6.00555e7i | 0.182579 | − | 0.105412i | −0.405925 | − | 0.913906i | \(-0.633051\pi\) |
0.588504 | + | 0.808495i | \(0.299717\pi\) | |||||||
\(830\) | −1.07405e8 | − | 2.87790e7i | −0.187840 | − | 0.0503316i | ||||
\(831\) | − | 5.31306e8i | − | 0.925853i | ||||||
\(832\) | −6.11173e8 | − | 1.12978e7i | −1.06119 | − | 0.0196166i | ||||
\(833\) | 1.04204e8 | 0.180280 | ||||||||
\(834\) | −6.49453e7 | + | 2.42379e8i | −0.111957 | + | 0.417828i | ||||
\(835\) | −2.34861e7 | − | 4.06790e7i | −0.0403414 | − | 0.0698733i | ||||
\(836\) | 1.85651e7 | + | 1.07186e7i | 0.0317745 | + | 0.0183450i | ||||
\(837\) | −3.41958e8 | − | 3.41958e8i | −0.583172 | − | 0.583172i | ||||
\(838\) | 3.41853e8 | − | 9.15993e7i | 0.580909 | − | 0.155654i | ||||
\(839\) | 2.52286e8 | + | 9.41546e8i | 0.427177 | + | 1.59425i | 0.759122 | + | 0.650948i | \(0.225628\pi\) |
−0.331945 | + | 0.943299i | \(0.607705\pi\) | |||||||
\(840\) | −1.88575e8 | + | 1.88575e8i | −0.318160 | + | 0.318160i | ||||
\(841\) | −3.03070e8 | + | 5.24933e8i | −0.509513 | + | 0.882503i | ||||
\(842\) | 6.90359e7 | − | 3.98579e7i | 0.115648 | − | 0.0667695i | ||||
\(843\) | 1.79583e9 | + | 4.81192e8i | 2.99766 | + | 0.803222i | ||||
\(844\) | 4.42846e7i | 0.0736590i | ||||||||
\(845\) | 1.10585e8 | + | 1.19078e8i | 0.183284 | + | 0.197362i | ||||
\(846\) | −1.46025e9 | −2.41166 | ||||||||
\(847\) | −1.19187e8 | + | 4.44813e8i | −0.196146 | + | 0.732027i | ||||
\(848\) | 7.79791e7 | + | 1.35064e8i | 0.127877 | + | 0.221489i | ||||
\(849\) | −5.96437e8 | − | 3.44353e8i | −0.974634 | − | 0.562705i | ||||
\(850\) | −2.55162e8 | − | 2.55162e8i | −0.415488 | − | 0.415488i | ||||
\(851\) | 9.51213e6 | − | 2.54877e6i | 0.0154344 | − | 0.00413563i | ||||
\(852\) | −1.44933e6 | − | 5.40897e6i | −0.00234341 | − | 0.00874573i | ||||
\(853\) | 5.19562e8 | − | 5.19562e8i | 0.837125 | − | 0.837125i | −0.151355 | − | 0.988479i | \(-0.548364\pi\) |
0.988479 | + | 0.151355i | \(0.0483636\pi\) | |||||||
\(854\) | −9.45024e7 | + | 1.63683e8i | −0.151729 | + | 0.262803i | ||||
\(855\) | −5.80751e8 | + | 3.35297e8i | −0.929162 | + | 0.536452i | ||||
\(856\) | 4.05066e8 | + | 1.08537e8i | 0.645810 | + | 0.173044i | ||||
\(857\) | − | 6.26378e8i | − | 0.995163i | −0.867417 | − | 0.497581i | \(-0.834222\pi\) | ||
0.867417 | − | 0.497581i | \(-0.165778\pi\) | |||||||
\(858\) | −7.09684e6 | + | 3.83915e8i | −0.0112358 | + | 0.607817i | ||||
\(859\) | −7.70196e8 | −1.21513 | −0.607563 | − | 0.794271i | \(-0.707853\pi\) | ||||
−0.607563 | + | 0.794271i | \(0.707853\pi\) | |||||||
\(860\) | 2.70440e6 | − | 1.00930e7i | 0.00425183 | − | 0.0158681i | ||||
\(861\) | 4.14732e8 | + | 7.18336e8i | 0.649767 | + | 1.12543i | ||||
\(862\) | −7.13564e8 | − | 4.11977e8i | −1.11407 | − | 0.643207i | ||||
\(863\) | −2.80801e8 | − | 2.80801e8i | −0.436884 | − | 0.436884i | 0.454078 | − | 0.890962i | \(-0.349969\pi\) |
−0.890962 | + | 0.454078i | \(0.849969\pi\) | |||||||
\(864\) | −2.73351e8 | + | 7.32442e7i | −0.423818 | + | 0.113562i | ||||
\(865\) | −9.16219e6 | − | 3.41937e7i | −0.0141563 | − | 0.0528322i | ||||
\(866\) | −3.68253e8 | + | 3.68253e8i | −0.567012 | + | 0.567012i | ||||
\(867\) | 3.51023e8 | − | 6.07989e8i | 0.538615 | − | 0.932908i | ||||
\(868\) | 9.42773e6 | − | 5.44310e6i | 0.0144161 | − | 0.00832314i | ||||
\(869\) | 2.18956e8 | + | 5.86690e7i | 0.333655 | + | 0.0894025i | ||||
\(870\) | − | 4.60880e8i | − | 0.699891i | ||||||
\(871\) | −3.37142e8 | − | 9.70499e7i | −0.510221 | − | 0.146873i | ||||
\(872\) | −5.44094e8 | −0.820587 | ||||||||
\(873\) | −2.02642e8 | + | 7.56269e8i | −0.304569 | + | 1.13667i | ||||
\(874\) | 1.23084e8 | + | 2.13187e8i | 0.184360 | + | 0.319320i | ||||
\(875\) | 2.56615e8 | + | 1.48157e8i | 0.383052 | + | 0.221155i | ||||
\(876\) | −9.11541e7 | − | 9.11541e7i | −0.135601 | − | 0.135601i | ||||
\(877\) | 5.34920e8 | − | 1.43331e8i | 0.793031 | − | 0.212492i | 0.160509 | − | 0.987034i | \(-0.448686\pi\) |
0.632522 | + | 0.774542i | \(0.282020\pi\) | |||||||
\(878\) | −2.44398e8 | − | 9.12106e8i | −0.361089 | − | 1.34760i | ||||
\(879\) | 9.32146e8 | − | 9.32146e8i | 1.37251 | − | 1.37251i | ||||
\(880\) | 2.81474e7 | − | 4.87527e7i | 0.0413038 | − | 0.0715403i | ||||
\(881\) | −6.51277e8 | + | 3.76015e8i | −0.952442 | + | 0.549892i | −0.893839 | − | 0.448389i | \(-0.851998\pi\) |
−0.0586030 | + | 0.998281i | \(0.518665\pi\) | |||||||
\(882\) | 4.55731e8 | + | 1.22113e8i | 0.664206 | + | 0.177974i | ||||
\(883\) | − | 3.77400e8i | − | 0.548176i | −0.961705 | − | 0.274088i | \(-0.911624\pi\) | ||
0.961705 | − | 0.274088i | \(-0.0883759\pi\) | |||||||
\(884\) | 2.86939e7 | − | 1.58667e7i | 0.0415368 | − | 0.0229683i | ||||
\(885\) | 7.82902e7 | 0.112948 | ||||||||
\(886\) | −1.15141e8 | + | 4.29712e8i | −0.165550 | + | 0.617840i | ||||
\(887\) | 1.33314e8 | + | 2.30907e8i | 0.191032 | + | 0.330876i | 0.945592 | − | 0.325354i | \(-0.105483\pi\) |
−0.754561 | + | 0.656230i | \(0.772150\pi\) | |||||||
\(888\) | 7.59119e7 | + | 4.38277e7i | 0.108410 | + | 0.0625908i | ||||
\(889\) | −2.35946e8 | − | 2.35946e8i | −0.335820 | − | 0.335820i | ||||
\(890\) | 2.49491e7 | − | 6.68509e6i | 0.0353903 | − | 0.00948281i | ||||
\(891\) | 1.93458e8 | + | 7.21996e8i | 0.273498 | + | 1.02071i | ||||
\(892\) | −4.69112e7 | + | 4.69112e7i | −0.0660970 | + | 0.0660970i | ||||
\(893\) | 5.23506e8 | − | 9.06740e8i | 0.735136 | − | 1.27329i | ||||
\(894\) | 2.04956e9 | − | 1.18332e9i | 2.86846 | − | 1.65611i | ||||
\(895\) | 1.91177e8 | + | 5.12258e7i | 0.266666 | + | 0.0714529i | ||||
\(896\) | 5.38290e8i | 0.748329i | ||||||||
\(897\) | 1.76931e8 | − | 2.93777e8i | 0.245147 | − | 0.407043i | ||||
\(898\) | 1.90570e8 | 0.263164 | ||||||||
\(899\) | −7.23441e7 | + | 2.69992e8i | −0.0995689 | + | 0.371596i | ||||
\(900\) | 6.35378e7 | + | 1.10051e8i | 0.0871575 | + | 0.150961i | ||||
\(901\) | −1.15490e8 | − | 6.66781e7i | −0.157895 | − | 0.0911610i | ||||
\(902\) | −1.33493e8 | − | 1.33493e8i | −0.181902 | − | 0.181902i | ||||
\(903\) | 9.72354e8 | − | 2.60541e8i | 1.32057 | − | 0.353845i | ||||
\(904\) | −2.48355e8 | − | 9.26874e8i | −0.336177 | − | 1.25463i | ||||
\(905\) | −9.02970e7 | + | 9.02970e7i | −0.121823 | + | 0.121823i | ||||
\(906\) | 6.31734e8 | − | 1.09419e9i | 0.849473 | − | 1.47133i | ||||
\(907\) | 4.17600e8 | − | 2.41101e8i | 0.559678 | − | 0.323130i | −0.193338 | − | 0.981132i | \(-0.561931\pi\) |
0.753016 | + | 0.658002i | \(0.228598\pi\) | |||||||
\(908\) | 4.59439e7 | + | 1.23106e7i | 0.0613720 | + | 0.0164446i | ||||
\(909\) | 3.52534e9i | 4.69364i | ||||||||
\(910\) | 1.19941e8 | − | 1.15587e8i | 0.159164 | − | 0.153386i | ||||
\(911\) | −8.16911e8 | −1.08049 | −0.540243 | − | 0.841509i | \(-0.681668\pi\) | ||||
−0.540243 | + | 0.841509i | \(0.681668\pi\) | |||||||
\(912\) | −5.25976e8 | + | 1.96297e9i | −0.693396 | + | 2.58779i | ||||
\(913\) | −9.48155e7 | − | 1.64225e8i | −0.124585 | − | 0.215788i | ||||
\(914\) | 4.86595e8 | + | 2.80936e8i | 0.637278 | + | 0.367933i | ||||
\(915\) | −1.02423e8 | − | 1.02423e8i | −0.133700 | − | 0.133700i | ||||
\(916\) | 6.05584e7 | − | 1.62266e7i | 0.0787930 | − | 0.0211125i | ||||
\(917\) | 3.94652e7 | + | 1.47286e8i | 0.0511807 | + | 0.191009i | ||||
\(918\) | −1.05572e9 | + | 1.05572e9i | −1.36465 | + | 1.36465i | ||||
\(919\) | 3.44631e8 | − | 5.96918e8i | 0.444025 | − | 0.769074i | −0.553959 | − | 0.832544i | \(-0.686883\pi\) |
0.997984 | + | 0.0634702i | \(0.0202168\pi\) | |||||||
\(920\) | −4.69479e7 | + | 2.71054e7i | −0.0602911 | + | 0.0348091i | ||||
\(921\) | −1.05615e9 | − | 2.82996e8i | −1.35191 | − | 0.362244i | ||||
\(922\) | − | 5.96970e8i | − | 0.761657i | ||||||
\(923\) | 1.25196e7 | + | 5.04348e7i | 0.0159216 | + | 0.0641395i | ||||
\(924\) | −3.06118e7 | −0.0388036 | ||||||||
\(925\) | 1.21293e7 | − | 4.52673e7i | 0.0153254 | − | 0.0571951i | ||||
\(926\) | 2.09516e7 | + | 3.62892e7i | 0.0263867 | + | 0.0457030i | ||||
\(927\) | 2.61174e8 | + | 1.50789e8i | 0.327862 | + | 0.189291i | ||||
\(928\) | 1.15659e8 | + | 1.15659e8i | 0.144723 | + | 0.144723i | ||||
\(929\) | 1.96583e7 | − | 5.26742e6i | 0.0245187 | − | 0.00656977i | −0.246539 | − | 0.969133i | \(-0.579293\pi\) |
0.271058 | + | 0.962563i | \(0.412627\pi\) | |||||||
\(930\) | −2.77627e7 | − | 1.03612e8i | −0.0345154 | − | 0.128813i | ||||
\(931\) | −2.39207e8 | + | 2.39207e8i | −0.296432 | + | 0.296432i | ||||
\(932\) | −1.71962e7 | + | 2.97847e7i | −0.0212415 | + | 0.0367914i | ||||
\(933\) | −1.54338e9 | + | 8.91073e8i | −1.90033 | + | 1.09716i | ||||
\(934\) | −1.69086e8 | − | 4.53065e7i | −0.207524 | − | 0.0556058i | ||||
\(935\) | 4.81363e7i | 0.0588895i | ||||||||
\(936\) | 2.14072e9 | − | 5.31401e8i | 2.61056 | − | 0.648029i | ||||
\(937\) | 7.44790e8 | 0.905347 | 0.452673 | − | 0.891676i | \(-0.350470\pi\) | ||||
0.452673 | + | 0.891676i | \(0.350470\pi\) | |||||||
\(938\) | −9.30734e7 | + | 3.47355e8i | −0.112776 | + | 0.420886i | ||||
\(939\) | −9.34702e8 | − | 1.61895e9i | −1.12895 | − | 1.95541i | ||||
\(940\) | 1.34400e7 | + | 7.75957e6i | 0.0161813 | + | 0.00934230i | ||||
\(941\) | −4.61386e8 | − | 4.61386e8i | −0.553727 | − | 0.553727i | 0.373787 | − | 0.927514i | \(-0.378059\pi\) |
−0.927514 | + | 0.373787i | \(0.878059\pi\) | |||||||
\(942\) | −5.92891e8 | + | 1.58865e8i | −0.709287 | + | 0.190053i | ||||
\(943\) | 4.36396e7 | + | 1.62865e8i | 0.0520411 | + | 0.194220i | ||||
\(944\) | 1.21222e8 | − | 1.21222e8i | 0.144101 | − | 0.144101i | ||||
\(945\) | 2.94960e8 | − | 5.10886e8i | 0.349516 | − | 0.605380i | ||||
\(946\) | −1.98421e8 | + | 1.14558e8i | −0.234376 | + | 0.135317i | ||||
\(947\) | −7.52388e8 | − | 2.01602e8i | −0.885914 | − | 0.237380i | −0.212957 | − | 0.977062i | \(-0.568309\pi\) |
−0.672957 | + | 0.739682i | \(0.734976\pi\) | |||||||
\(948\) | − | 1.21291e8i | − | 0.142366i | ||||||
\(949\) | 8.30124e8 | + | 8.61392e8i | 0.971280 | + | 1.00787i | ||||
\(950\) | 1.17149e9 | 1.36636 | ||||||||
\(951\) | 3.48071e8 | − | 1.29902e9i | 0.404693 | − | 1.51034i | ||||
\(952\) | −2.49668e8 | − | 4.32437e8i | −0.289369 | − | 0.501201i | ||||
\(953\) | −5.13057e8 | − | 2.96214e8i | −0.592771 | − | 0.342236i | 0.173421 | − | 0.984848i | \(-0.444518\pi\) |
−0.766192 | + | 0.642611i | \(0.777851\pi\) | |||||||
\(954\) | −4.26954e8 | − | 4.26954e8i | −0.491740 | − | 0.491740i | ||||
\(955\) | 2.28701e8 | − | 6.12802e7i | 0.262577 | − | 0.0703574i | ||||
\(956\) | −1.53189e7 | − | 5.71708e7i | −0.0175329 | − | 0.0654335i | ||||
\(957\) | 5.55781e8 | − | 5.55781e8i | 0.634114 | − | 0.634114i | ||||
\(958\) | 1.01066e8 | − | 1.75052e8i | 0.114950 | − | 0.199100i | ||||
\(959\) | −1.07744e9 | + | 6.22058e8i | −1.22162 | + | 0.705302i | ||||
\(960\) | −4.63820e8 | − | 1.24280e8i | −0.524247 | − | 0.140471i | ||||
\(961\) | − | 8.22448e8i | − | 0.926698i | ||||||
\(962\) | −4.69007e7 | − | 2.82466e7i | −0.0526810 | − | 0.0317279i | ||||
\(963\) | −1.50579e9 | −1.68611 | ||||||||
\(964\) | −2.34788e7 | + | 8.76242e7i | −0.0262087 | + | 0.0978121i | ||||
\(965\) | −1.15002e8 | − | 1.99189e8i | −0.127974 | − | 0.221658i | ||||
\(966\) | −3.04426e8 | − | 1.75760e8i | −0.337715 | − | 0.194980i | ||||
\(967\) | 8.37670e8 | + | 8.37670e8i | 0.926390 | + | 0.926390i | 0.997471 | − | 0.0710807i | \(-0.0226448\pi\) |
−0.0710807 | + | 0.997471i | \(0.522645\pi\) | |||||||
\(968\) | −8.04841e8 | + | 2.15657e8i | −0.887328 | + | 0.237759i | ||||
\(969\) | −4.49750e8 | − | 1.67849e9i | −0.494310 | − | 1.84479i | ||||
\(970\) | −7.56497e7 | + | 7.56497e7i | −0.0828881 | + | 0.0828881i | ||||
\(971\) | −7.28123e8 | + | 1.26115e9i | −0.795329 | + | 1.37755i | 0.127300 | + | 0.991864i | \(0.459369\pi\) |
−0.922630 | + | 0.385687i | \(0.873965\pi\) | |||||||
\(972\) | 1.71543e8 | − | 9.90406e7i | 0.186799 | − | 0.107849i | ||||
\(973\) | 1.79316e8 | + | 4.80475e7i | 0.194661 | + | 0.0521594i | ||||
\(974\) | 1.09039e9i | 1.18007i | ||||||||
\(975\) | −7.89753e8 | − | 1.42822e9i | −0.852074 | − | 1.54092i | ||||
\(976\) | −3.17176e8 | −0.341154 | ||||||||
\(977\) | −1.72242e8 | + | 6.42814e8i | −0.184695 | + | 0.689290i | 0.810001 | + | 0.586428i | \(0.199466\pi\) |
−0.994696 | + | 0.102861i | \(0.967200\pi\) | |||||||
\(978\) | 7.22855e8 | + | 1.25202e9i | 0.772743 | + | 1.33843i | ||||
\(979\) | 3.81480e7 | + | 2.20247e7i | 0.0406559 | + | 0.0234727i | ||||
\(980\) | −3.54560e6 | − | 3.54560e6i | −0.00376714 | − | 0.00376714i | ||||
\(981\) | 1.88712e9 | − | 5.05652e8i | 1.99891 | − | 0.535606i | ||||
\(982\) | 4.33338e8 | + | 1.61724e9i | 0.457607 | + | 1.70781i | ||||
\(983\) | −4.95914e7 | + | 4.95914e7i | −0.0522090 | + | 0.0522090i | −0.732729 | − | 0.680520i | \(-0.761754\pi\) |
0.680520 | + | 0.732729i | \(0.261754\pi\) | |||||||
\(984\) | −7.50413e8 | + | 1.29975e9i | −0.787617 | + | 1.36419i | ||||
\(985\) | 1.50202e8 | − | 8.67189e7i | 0.157169 | − | 0.0907413i | ||||
\(986\) | 8.33539e8 | + | 2.23346e8i | 0.869551 | + | 0.232996i | ||||
\(987\) | 1.49511e9i | 1.55497i | ||||||||
\(988\) | −2.94459e7 | + | 1.02292e8i | −0.0305319 | + | 0.106065i | ||||
\(989\) | 2.04630e8 | 0.211534 | ||||||||
\(990\) | −5.64094e7 | + | 2.10523e8i | −0.0581361 | + | 0.216967i | ||||
\(991\) | −9.37823e7 | − | 1.62436e8i | −0.0963607 | − | 0.166902i | 0.813815 | − | 0.581124i | \(-0.197387\pi\) |
−0.910176 | + | 0.414222i | \(0.864054\pi\) | |||||||
\(992\) | 3.29688e7 | + | 1.90345e7i | 0.0337729 | + | 0.0194988i | ||||
\(993\) | −4.53809e8 | − | 4.53809e8i | −0.463474 | − | 0.463474i | ||||
\(994\) | 5.14503e7 | − | 1.37861e7i | 0.0523876 | − | 0.0140372i | ||||
\(995\) | 1.12326e8 | + | 4.19208e8i | 0.114028 | + | 0.425560i | ||||
\(996\) | −7.17483e7 | + | 7.17483e7i | −0.0726162 | + | 0.0726162i | ||||
\(997\) | 4.15652e8 | − | 7.19930e8i | 0.419415 | − | 0.726449i | −0.576465 | − | 0.817122i | \(-0.695568\pi\) |
0.995881 | + | 0.0906728i | \(0.0289017\pi\) | |||||||
\(998\) | 8.03893e8 | − | 4.64128e8i | 0.808735 | − | 0.466924i | ||||
\(999\) | −1.87291e8 | − | 5.01846e7i | −0.187854 | − | 0.0503354i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 13.7.f.a.11.5 | yes | 24 | |
13.6 | odd | 12 | inner | 13.7.f.a.6.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.7.f.a.6.5 | ✓ | 24 | 13.6 | odd | 12 | inner | |
13.7.f.a.11.5 | yes | 24 | 1.1 | even | 1 | trivial |