Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(21,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\), degree \(2\), 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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.13 | ||
Character | \(\chi\) | \(=\) | 80.21 |
Dual form | 80.6.l.a.61.13 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.36114 | + | 4.55002i | −0.594172 | + | 0.804338i | ||||
\(3\) | −18.2668 | + | 18.2668i | −1.17182 | + | 1.17182i | −0.190040 | + | 0.981776i | \(0.560862\pi\) |
−0.981776 | + | 0.190040i | \(0.939138\pi\) | |||||||
\(4\) | −9.40545 | − | 30.5866i | −0.293920 | − | 0.955830i | ||||
\(5\) | −17.6777 | − | 17.6777i | −0.316228 | − | 0.316228i | ||||
\(6\) | −21.7171 | − | 144.512i | −0.246277 | − | 1.63880i | ||||
\(7\) | 13.9157i | 0.107339i | 0.998559 | + | 0.0536697i | \(0.0170918\pi\) | ||||
−0.998559 | + | 0.0536697i | \(0.982908\pi\) | |||||||
\(8\) | 170.783 | + | 60.0107i | 0.943450 | + | 0.331516i | ||||
\(9\) | − | 424.353i | − | 1.74631i | ||||||
\(10\) | 139.851 | − | 21.0167i | 0.442248 | − | 0.0664606i | ||||
\(11\) | −220.571 | − | 220.571i | −0.549624 | − | 0.549624i | 0.376708 | − | 0.926332i | \(-0.377056\pi\) |
−0.926332 | + | 0.376708i | \(0.877056\pi\) | |||||||
\(12\) | 730.527 | + | 386.911i | 1.46448 | + | 0.775637i | ||||
\(13\) | 433.351 | − | 433.351i | 0.711182 | − | 0.711182i | −0.255600 | − | 0.966783i | \(-0.582273\pi\) |
0.966783 | + | 0.255600i | \(0.0822731\pi\) | |||||||
\(14\) | −63.3167 | − | 46.7726i | −0.0863372 | − | 0.0637781i | ||||
\(15\) | 645.829 | 0.741122 | ||||||||
\(16\) | −847.075 | + | 575.361i | −0.827222 | + | 0.561876i | ||||
\(17\) | −25.9583 | −0.0217848 | −0.0108924 | − | 0.999941i | \(-0.503467\pi\) | ||||
−0.0108924 | + | 0.999941i | \(0.503467\pi\) | |||||||
\(18\) | 1930.82 | + | 1426.31i | 1.40462 | + | 1.03761i | ||||
\(19\) | −1566.86 | + | 1566.86i | −0.995744 | + | 0.995744i | −0.999991 | − | 0.00424742i | \(-0.998648\pi\) |
0.00424742 | + | 0.999991i | \(0.498648\pi\) | |||||||
\(20\) | −374.433 | + | 706.965i | −0.209314 | + | 0.395206i | ||||
\(21\) | −254.195 | − | 254.195i | −0.125782 | − | 0.125782i | ||||
\(22\) | 1744.97 | − | 262.232i | 0.768655 | − | 0.115513i | ||||
\(23\) | 1496.29i | 0.589787i | 0.955530 | + | 0.294894i | \(0.0952843\pi\) | ||||
−0.955530 | + | 0.294894i | \(0.904716\pi\) | |||||||
\(24\) | −4215.86 | + | 2023.45i | −1.49403 | + | 0.717075i | ||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | 515.203 | + | 3428.31i | 0.149467 | + | 0.994596i | ||||
\(27\) | 3312.74 | + | 3312.74i | 0.874537 | + | 0.874537i | ||||
\(28\) | 425.633 | − | 130.883i | 0.102598 | − | 0.0315492i | ||||
\(29\) | 324.914 | − | 324.914i | 0.0717419 | − | 0.0717419i | −0.670325 | − | 0.742067i | \(-0.733845\pi\) |
0.742067 | + | 0.670325i | \(0.233845\pi\) | |||||||
\(30\) | −2170.72 | + | 2938.54i | −0.440354 | + | 0.596113i | ||||
\(31\) | 7904.77 | 1.47736 | 0.738678 | − | 0.674059i | \(-0.235451\pi\) | ||||
0.738678 | + | 0.674059i | \(0.235451\pi\) | |||||||
\(32\) | 229.235 | − | 5788.08i | 0.0395736 | − | 0.999217i | ||||
\(33\) | 8058.24 | 1.28812 | ||||||||
\(34\) | 87.2494 | − | 118.111i | 0.0129439 | − | 0.0175223i | ||||
\(35\) | 245.997 | − | 245.997i | 0.0339437 | − | 0.0339437i | ||||
\(36\) | −12979.5 | + | 3991.23i | −1.66917 | + | 0.513275i | ||||
\(37\) | −3034.60 | − | 3034.60i | −0.364416 | − | 0.364416i | 0.501020 | − | 0.865436i | \(-0.332958\pi\) |
−0.865436 | + | 0.501020i | \(0.832958\pi\) | |||||||
\(38\) | −1862.82 | − | 12395.7i | −0.209272 | − | 1.39256i | ||||
\(39\) | 15831.9i | 1.66675i | ||||||||
\(40\) | −1958.19 | − | 4079.89i | −0.193511 | − | 0.403179i | ||||
\(41\) | − | 17561.5i | − | 1.63155i | −0.578367 | − | 0.815776i | \(-0.696310\pi\) | ||
0.578367 | − | 0.815776i | \(-0.303690\pi\) | |||||||
\(42\) | 2010.98 | − | 302.208i | 0.175908 | − | 0.0264352i | ||||
\(43\) | 11258.4 | + | 11258.4i | 0.928547 | + | 0.928547i | 0.997612 | − | 0.0690650i | \(-0.0220016\pi\) |
−0.0690650 | + | 0.997612i | \(0.522002\pi\) | |||||||
\(44\) | −4671.93 | + | 8821.06i | −0.363802 | + | 0.686893i | ||||
\(45\) | −7501.57 | + | 7501.57i | −0.552231 | + | 0.552231i | ||||
\(46\) | −6808.15 | − | 5029.24i | −0.474389 | − | 0.350435i | ||||
\(47\) | 16959.8 | 1.11989 | 0.559944 | − | 0.828530i | \(-0.310822\pi\) | ||||
0.559944 | + | 0.828530i | \(0.310822\pi\) | |||||||
\(48\) | 4963.36 | − | 25983.4i | 0.310937 | − | 1.62777i | ||||
\(49\) | 16613.4 | 0.988478 | ||||||||
\(50\) | −2843.77 | − | 2100.71i | −0.160868 | − | 0.118834i | ||||
\(51\) | 474.175 | − | 474.175i | 0.0255278 | − | 0.0255278i | ||||
\(52\) | −17330.6 | − | 9178.85i | −0.888800 | − | 0.470739i | ||||
\(53\) | 15349.1 | + | 15349.1i | 0.750576 | + | 0.750576i | 0.974587 | − | 0.224011i | \(-0.0719151\pi\) |
−0.224011 | + | 0.974587i | \(0.571915\pi\) | |||||||
\(54\) | −26207.7 | + | 3938.46i | −1.22305 | + | 0.183799i | ||||
\(55\) | 7798.35i | 0.347613i | ||||||||
\(56\) | −835.090 | + | 2376.56i | −0.0355847 | + | 0.101269i | ||||
\(57\) | − | 57243.3i | − | 2.33366i | ||||||
\(58\) | 386.284 | + | 2570.45i | 0.0150778 | + | 0.100332i | ||||
\(59\) | −24469.4 | − | 24469.4i | −0.915151 | − | 0.915151i | 0.0815203 | − | 0.996672i | \(-0.474022\pi\) |
−0.996672 | + | 0.0815203i | \(0.974022\pi\) | |||||||
\(60\) | −6074.31 | − | 19753.7i | −0.217831 | − | 0.708387i | ||||
\(61\) | −28968.0 | + | 28968.0i | −0.996768 | + | 0.996768i | −0.999995 | − | 0.00322639i | \(-0.998973\pi\) |
0.00322639 | + | 0.999995i | \(0.498973\pi\) | |||||||
\(62\) | −26569.1 | + | 35966.9i | −0.877803 | + | 1.18829i | ||||
\(63\) | 5905.16 | 0.187448 | ||||||||
\(64\) | 25565.4 | + | 20497.6i | 0.780195 | + | 0.625537i | ||||
\(65\) | −15321.3 | −0.449791 | ||||||||
\(66\) | −27084.9 | + | 36665.2i | −0.765363 | + | 1.03608i | ||||
\(67\) | 42714.5 | − | 42714.5i | 1.16249 | − | 1.16249i | 0.178560 | − | 0.983929i | \(-0.442856\pi\) |
0.983929 | − | 0.178560i | \(-0.0571438\pi\) | |||||||
\(68\) | 244.149 | + | 793.974i | 0.00640299 | + | 0.0208225i | ||||
\(69\) | −27332.4 | − | 27332.4i | −0.691123 | − | 0.691123i | ||||
\(70\) | 292.461 | + | 1946.12i | 0.00713384 | + | 0.0474706i | ||||
\(71\) | − | 40585.1i | − | 0.955478i | −0.878502 | − | 0.477739i | \(-0.841456\pi\) | ||
0.878502 | − | 0.477739i | \(-0.158544\pi\) | |||||||
\(72\) | 25465.7 | − | 72472.1i | 0.578929 | − | 1.64755i | ||||
\(73\) | − | 872.108i | − | 0.0191542i | −0.999954 | − | 0.00957708i | \(-0.996951\pi\) | ||
0.999954 | − | 0.00957708i | \(-0.00304853\pi\) | |||||||
\(74\) | 24007.3 | − | 3607.79i | 0.509640 | − | 0.0765881i | ||||
\(75\) | −11416.8 | − | 11416.8i | −0.234363 | − | 0.234363i | ||||
\(76\) | 62662.1 | + | 33187.9i | 1.24443 | + | 0.659092i | ||||
\(77\) | 3069.39 | − | 3069.39i | 0.0589964 | − | 0.0589964i | ||||
\(78\) | −72035.4 | − | 53213.2i | −1.34063 | − | 0.990336i | ||||
\(79\) | 87124.5 | 1.57063 | 0.785313 | − | 0.619100i | \(-0.212502\pi\) | ||||
0.785313 | + | 0.619100i | \(0.212502\pi\) | |||||||
\(80\) | 25145.3 | + | 4803.28i | 0.439271 | + | 0.0839098i | ||||
\(81\) | −17908.7 | −0.303285 | ||||||||
\(82\) | 79905.1 | + | 59026.6i | 1.31232 | + | 0.969422i | ||||
\(83\) | −63039.3 | + | 63039.3i | −1.00442 | + | 1.00442i | −0.00443164 | + | 0.999990i | \(0.501411\pi\) |
−0.999990 | + | 0.00443164i | \(0.998589\pi\) | |||||||
\(84\) | −5384.14 | + | 10165.8i | −0.0832564 | + | 0.157196i | ||||
\(85\) | 458.881 | + | 458.881i | 0.00688895 | + | 0.00688895i | ||||
\(86\) | −89066.8 | + | 13384.9i | −1.29858 | + | 0.195150i | ||||
\(87\) | 11870.3i | 0.168137i | ||||||||
\(88\) | −24433.0 | − | 50906.2i | −0.336334 | − | 0.700752i | ||||
\(89\) | 51305.5i | 0.686577i | 0.939230 | + | 0.343288i | \(0.111541\pi\) | ||||
−0.939230 | + | 0.343288i | \(0.888459\pi\) | |||||||
\(90\) | −8918.49 | − | 59346.2i | −0.116061 | − | 0.772301i | ||||
\(91\) | 6030.37 | + | 6030.37i | 0.0763379 | + | 0.0763379i | ||||
\(92\) | 45766.3 | − | 14073.3i | 0.563737 | − | 0.173350i | ||||
\(93\) | −144395. | + | 144395.i | −1.73119 | + | 1.73119i | ||||
\(94\) | −57004.1 | + | 77167.3i | −0.665406 | + | 0.900770i | ||||
\(95\) | 55397.0 | 0.629764 | ||||||||
\(96\) | 101542. | + | 109917.i | 1.12453 | + | 1.21727i | ||||
\(97\) | 117514. | 1.26812 | 0.634060 | − | 0.773284i | \(-0.281387\pi\) | ||||
0.634060 | + | 0.773284i | \(0.281387\pi\) | |||||||
\(98\) | −55839.8 | + | 75591.2i | −0.587326 | + | 0.795071i | ||||
\(99\) | −93599.8 | + | 93599.8i | −0.959813 | + | 0.959813i | ||||
\(100\) | 19116.6 | − | 5878.40i | 0.191166 | − | 0.0587840i | ||||
\(101\) | −43034.0 | − | 43034.0i | −0.419767 | − | 0.419767i | 0.465356 | − | 0.885123i | \(-0.345926\pi\) |
−0.885123 | + | 0.465356i | \(0.845926\pi\) | |||||||
\(102\) | 563.738 | + | 3751.27i | 0.00536509 | + | 0.0357008i | ||||
\(103\) | 86467.5i | 0.803082i | 0.915841 | + | 0.401541i | \(0.131525\pi\) | ||||
−0.915841 | + | 0.401541i | \(0.868475\pi\) | |||||||
\(104\) | 100014. | − | 48003.1i | 0.906733 | − | 0.435197i | ||||
\(105\) | 8987.16i | 0.0795516i | ||||||||
\(106\) | −121430. | + | 18248.3i | −1.04969 | + | 0.157746i | ||||
\(107\) | 6956.94 | + | 6956.94i | 0.0587434 | + | 0.0587434i | 0.735868 | − | 0.677125i | \(-0.236774\pi\) |
−0.677125 | + | 0.735868i | \(0.736774\pi\) | |||||||
\(108\) | 70167.6 | − | 132483.i | 0.578865 | − | 1.09295i | ||||
\(109\) | 117017. | − | 117017.i | 0.943375 | − | 0.943375i | −0.0551055 | − | 0.998481i | \(-0.517550\pi\) |
0.998481 | + | 0.0551055i | \(0.0175495\pi\) | |||||||
\(110\) | −35482.7 | − | 26211.4i | −0.279598 | − | 0.206542i | ||||
\(111\) | 110865. | 0.854058 | ||||||||
\(112\) | −8006.53 | − | 11787.6i | −0.0603114 | − | 0.0887935i | ||||
\(113\) | 32246.3 | 0.237566 | 0.118783 | − | 0.992920i | \(-0.462101\pi\) | ||||
0.118783 | + | 0.992920i | \(0.462101\pi\) | |||||||
\(114\) | 260458. | + | 192403.i | 1.87705 | + | 1.38659i | ||||
\(115\) | 26450.9 | − | 26450.9i | 0.186507 | − | 0.186507i | ||||
\(116\) | −12994.0 | − | 6882.03i | −0.0896595 | − | 0.0474867i | ||||
\(117\) | −183894. | − | 183894.i | −1.24194 | − | 1.24194i | ||||
\(118\) | 193581. | − | 29091.2i | 1.27985 | − | 0.192334i | ||||
\(119\) | − | 361.227i | − | 0.00233837i | ||||||
\(120\) | 110296. | + | 38756.7i | 0.699211 | + | 0.245694i | ||||
\(121\) | − | 63748.3i | − | 0.395827i | ||||||
\(122\) | −34439.6 | − | 229171.i | −0.209488 | − | 1.39399i | ||||
\(123\) | 320792. | + | 320792.i | 1.91188 | + | 1.91188i | ||||
\(124\) | −74347.9 | − | 241780.i | −0.434225 | − | 1.41210i | ||||
\(125\) | 11048.5 | − | 11048.5i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | −19848.1 | + | 26868.6i | −0.111376 | + | 0.150771i | ||||
\(127\) | −312532. | −1.71943 | −0.859717 | − | 0.510772i | \(-0.829360\pi\) | ||||
−0.859717 | + | 0.510772i | \(0.829360\pi\) | |||||||
\(128\) | −179194. | + | 47428.0i | −0.966713 | + | 0.255864i | ||||
\(129\) | −411309. | −2.17617 | ||||||||
\(130\) | 51496.9 | − | 69712.1i | 0.267253 | − | 0.361784i | ||||
\(131\) | 145389. | − | 145389.i | 0.740206 | − | 0.740206i | −0.232411 | − | 0.972618i | \(-0.574662\pi\) |
0.972618 | + | 0.232411i | \(0.0746615\pi\) | |||||||
\(132\) | −75791.4 | − | 246474.i | −0.378604 | − | 1.23122i | ||||
\(133\) | −21804.0 | − | 21804.0i | −0.106883 | − | 0.106883i | ||||
\(134\) | 50782.6 | + | 337922.i | 0.244316 | + | 1.62575i | ||||
\(135\) | − | 117123.i | − | 0.553106i | ||||||
\(136\) | −4433.22 | − | 1557.77i | −0.0205528 | − | 0.00722200i | ||||
\(137\) | − | 337137.i | − | 1.53464i | −0.641267 | − | 0.767318i | \(-0.721591\pi\) | ||
0.641267 | − | 0.767318i | \(-0.278409\pi\) | |||||||
\(138\) | 216231. | − | 32495.0i | 0.966542 | − | 0.145251i | ||||
\(139\) | 193906. | + | 193906.i | 0.851245 | + | 0.851245i | 0.990287 | − | 0.139041i | \(-0.0444020\pi\) |
−0.139041 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(140\) | −9837.91 | − | 5210.49i | −0.0424212 | − | 0.0224677i | ||||
\(141\) | −309801. | + | 309801.i | −1.31230 | + | 1.31230i | ||||
\(142\) | 184663. | + | 136412.i | 0.768527 | + | 0.567718i | ||||
\(143\) | −191169. | −0.781766 | ||||||||
\(144\) | 244156. | + | 359459.i | 0.981208 | + | 1.44458i | ||||
\(145\) | −11487.4 | −0.0453736 | ||||||||
\(146\) | 3968.11 | + | 2931.28i | 0.0154064 | + | 0.0113809i | ||||
\(147\) | −303473. | + | 303473.i | −1.15832 | + | 1.15832i | ||||
\(148\) | −64276.3 | + | 121360.i | −0.241211 | + | 0.455429i | ||||
\(149\) | −218920. | − | 218920.i | −0.807829 | − | 0.807829i | 0.176476 | − | 0.984305i | \(-0.443530\pi\) |
−0.984305 | + | 0.176476i | \(0.943530\pi\) | |||||||
\(150\) | 90319.9 | − | 13573.2i | 0.327759 | − | 0.0492554i | ||||
\(151\) | − | 400584.i | − | 1.42972i | −0.699267 | − | 0.714861i | \(-0.746490\pi\) | ||
0.699267 | − | 0.714861i | \(-0.253510\pi\) | |||||||
\(152\) | −361622. | + | 173565.i | −1.26954 | + | 0.609329i | ||||
\(153\) | 11015.5i | 0.0380430i | ||||||||
\(154\) | 3649.14 | + | 24282.5i | 0.0123991 | + | 0.0825070i | ||||
\(155\) | −139738. | − | 139738.i | −0.467181 | − | 0.467181i | ||||
\(156\) | 484242. | − | 148906.i | 1.59313 | − | 0.489892i | ||||
\(157\) | 244052. | − | 244052.i | 0.790192 | − | 0.790192i | −0.191333 | − | 0.981525i | \(-0.561281\pi\) |
0.981525 | + | 0.191333i | \(0.0612811\pi\) | |||||||
\(158\) | −292838. | + | 396419.i | −0.933221 | + | 1.26331i | ||||
\(159\) | −560760. | −1.75907 | ||||||||
\(160\) | −106372. | + | 98267.4i | −0.328494 | + | 0.303466i | ||||
\(161\) | −20821.9 | −0.0633075 | ||||||||
\(162\) | 60193.7 | − | 81485.0i | 0.180204 | − | 0.243944i | ||||
\(163\) | 129841. | − | 129841.i | 0.382774 | − | 0.382774i | −0.489327 | − | 0.872101i | \(-0.662757\pi\) |
0.872101 | + | 0.489327i | \(0.162757\pi\) | |||||||
\(164\) | −537145. | + | 165173.i | −1.55949 | + | 0.479546i | ||||
\(165\) | −142451. | − | 142451.i | −0.407339 | − | 0.407339i | ||||
\(166\) | −74946.3 | − | 498714.i | −0.211096 | − | 1.40469i | ||||
\(167\) | 297250.i | 0.824765i | 0.911011 | + | 0.412383i | \(0.135303\pi\) | ||||
−0.911011 | + | 0.412383i | \(0.864697\pi\) | |||||||
\(168\) | −28157.7 | − | 58666.6i | −0.0769704 | − | 0.160368i | ||||
\(169\) | − | 4292.44i | − | 0.0115608i | ||||||
\(170\) | −3630.29 | + | 545.556i | −0.00963427 | + | 0.00144783i | ||||
\(171\) | 664904. | + | 664904.i | 1.73888 | + | 1.73888i | ||||
\(172\) | 238465. | − | 450244.i | 0.614614 | − | 1.16045i | ||||
\(173\) | 187953. | − | 187953.i | 0.477457 | − | 0.477457i | −0.426861 | − | 0.904317i | \(-0.640380\pi\) |
0.904317 | + | 0.426861i | \(0.140380\pi\) | |||||||
\(174\) | −54010.1 | − | 39897.7i | −0.135239 | − | 0.0999021i | ||||
\(175\) | −8697.30 | −0.0214679 | ||||||||
\(176\) | 313747. | + | 59932.2i | 0.763481 | + | 0.145841i | ||||
\(177\) | 893955. | 2.14478 | ||||||||
\(178\) | −233441. | − | 172445.i | −0.552240 | − | 0.407944i | ||||
\(179\) | −368128. | + | 368128.i | −0.858748 | + | 0.858748i | −0.991191 | − | 0.132442i | \(-0.957718\pi\) |
0.132442 | + | 0.991191i | \(0.457718\pi\) | |||||||
\(180\) | 300003. | + | 158892.i | 0.690151 | + | 0.365527i | ||||
\(181\) | 78950.2 | + | 78950.2i | 0.179125 | + | 0.179125i | 0.790974 | − | 0.611849i | \(-0.209574\pi\) |
−0.611849 | + | 0.790974i | \(0.709574\pi\) | |||||||
\(182\) | −47707.3 | + | 7169.40i | −0.106759 | + | 0.0160437i | ||||
\(183\) | − | 1.05831e6i | − | 2.33606i | ||||||
\(184\) | −89793.4 | + | 255540.i | −0.195524 | + | 0.556435i | ||||
\(185\) | 107289.i | 0.230477i | ||||||||
\(186\) | −171669. | − | 1.14233e6i | −0.363839 | − | 2.42109i | ||||
\(187\) | 5725.63 | + | 5725.63i | 0.0119734 | + | 0.0119734i | ||||
\(188\) | −159514. | − | 518741.i | −0.329158 | − | 1.07042i | ||||
\(189\) | −46099.1 | + | 46099.1i | −0.0938723 | + | 0.0938723i | ||||
\(190\) | −186197. | + | 252058.i | −0.374188 | + | 0.506543i | ||||
\(191\) | 160856. | 0.319047 | 0.159524 | − | 0.987194i | \(-0.449004\pi\) | ||||
0.159524 | + | 0.987194i | \(0.449004\pi\) | |||||||
\(192\) | −841424. | + | 92573.2i | −1.64726 | + | 0.181231i | ||||
\(193\) | 543608. | 1.05049 | 0.525246 | − | 0.850950i | \(-0.323973\pi\) | ||||
0.525246 | + | 0.850950i | \(0.323973\pi\) | |||||||
\(194\) | −394981. | + | 534692.i | −0.753481 | + | 1.02000i | ||||
\(195\) | 279871. | − | 279871.i | 0.527073 | − | 0.527073i | ||||
\(196\) | −156256. | − | 508145.i | −0.290534 | − | 0.944817i | ||||
\(197\) | −60916.8 | − | 60916.8i | −0.111833 | − | 0.111833i | 0.648976 | − | 0.760809i | \(-0.275198\pi\) |
−0.760809 | + | 0.648976i | \(0.775198\pi\) | |||||||
\(198\) | −111279. | − | 740483.i | −0.201721 | − | 1.34231i | ||||
\(199\) | − | 943709.i | − | 1.68930i | −0.535323 | − | 0.844648i | \(-0.679810\pi\) | ||
0.535323 | − | 0.844648i | \(-0.320190\pi\) | |||||||
\(200\) | −37506.7 | + | 106739.i | −0.0663031 | + | 0.188690i | ||||
\(201\) | 1.56052e6i | 2.72445i | ||||||||
\(202\) | 340449. | − | 51162.4i | 0.587049 | − | 0.0882211i | ||||
\(203\) | 4521.40 | + | 4521.40i | 0.00770074 | + | 0.00770074i | ||||
\(204\) | −18963.2 | − | 10043.5i | −0.0319033 | − | 0.0168971i | ||||
\(205\) | −310446. | + | 310446.i | −0.515942 | + | 0.515942i | ||||
\(206\) | −393429. | − | 290630.i | −0.645950 | − | 0.477169i | ||||
\(207\) | 634954. | 1.02995 | ||||||||
\(208\) | −117748. | + | 616413.i | −0.188710 | + | 0.987902i | ||||
\(209\) | 691208. | 1.09457 | ||||||||
\(210\) | −40891.8 | − | 30207.1i | −0.0639864 | − | 0.0472673i | ||||
\(211\) | 60603.7 | − | 60603.7i | 0.0937115 | − | 0.0937115i | −0.658697 | − | 0.752408i | \(-0.728892\pi\) |
0.752408 | + | 0.658697i | \(0.228892\pi\) | |||||||
\(212\) | 325112. | − | 613843.i | 0.496813 | − | 0.938032i | ||||
\(213\) | 741360. | + | 741360.i | 1.11964 | + | 1.11964i | ||||
\(214\) | −55037.5 | + | 8270.99i | −0.0821532 | + | 0.0123459i | ||||
\(215\) | − | 398043.i | − | 0.587265i | ||||||
\(216\) | 366959. | + | 764559.i | 0.535159 | + | 1.11500i | ||||
\(217\) | 110000.i | 0.158579i | ||||||||
\(218\) | 139120. | + | 925745.i | 0.198266 | + | 1.31932i | ||||
\(219\) | 15930.6 | + | 15930.6i | 0.0224452 | + | 0.0224452i | ||||
\(220\) | 238525. | − | 73346.9i | 0.332259 | − | 0.102170i | ||||
\(221\) | −11249.0 | + | 11249.0i | −0.0154930 | + | 0.0154930i | ||||
\(222\) | −372633. | + | 504439.i | −0.507457 | + | 0.686951i | ||||
\(223\) | 286362. | 0.385614 | 0.192807 | − | 0.981237i | \(-0.438241\pi\) | ||||
0.192807 | + | 0.981237i | \(0.438241\pi\) | |||||||
\(224\) | 80545.1 | + | 3189.96i | 0.107255 | + | 0.00424781i | ||||
\(225\) | 265221. | 0.349262 | ||||||||
\(226\) | −108384. | + | 146721.i | −0.141155 | + | 0.191083i | ||||
\(227\) | 173972. | − | 173972.i | 0.224086 | − | 0.224086i | −0.586130 | − | 0.810217i | \(-0.699349\pi\) |
0.810217 | + | 0.586130i | \(0.199349\pi\) | |||||||
\(228\) | −1.75087e6 | + | 538398.i | −2.23058 | + | 0.685909i | ||||
\(229\) | 670007. | + | 670007.i | 0.844287 | + | 0.844287i | 0.989413 | − | 0.145126i | \(-0.0463587\pi\) |
−0.145126 | + | 0.989413i | \(0.546359\pi\) | |||||||
\(230\) | 31447.0 | + | 209257.i | 0.0391976 | + | 0.260832i | ||||
\(231\) | 112136.i | 0.138266i | ||||||||
\(232\) | 74987.9 | − | 35991.3i | 0.0914685 | − | 0.0439013i | ||||
\(233\) | 855139.i | 1.03192i | 0.856612 | + | 0.515961i | \(0.172565\pi\) | ||||
−0.856612 | + | 0.515961i | \(0.827435\pi\) | |||||||
\(234\) | 1.45481e6 | − | 218628.i | 1.73687 | − | 0.261015i | ||||
\(235\) | −299809. | − | 299809.i | −0.354140 | − | 0.354140i | ||||
\(236\) | −518289. | + | 978580.i | −0.605748 | + | 1.14371i | ||||
\(237\) | −1.59149e6 | + | 1.59149e6i | −1.84048 | + | 1.84048i | ||||
\(238\) | 1643.59 | + | 1214.13i | 0.00188084 | + | 0.00138939i | ||||
\(239\) | −1.24908e6 | −1.41448 | −0.707238 | − | 0.706975i | \(-0.750059\pi\) | ||||
−0.707238 | + | 0.706975i | \(0.750059\pi\) | |||||||
\(240\) | −547066. | + | 371585.i | −0.613072 | + | 0.416418i | ||||
\(241\) | 738534. | 0.819083 | 0.409542 | − | 0.912291i | \(-0.365689\pi\) | ||||
0.409542 | + | 0.912291i | \(0.365689\pi\) | |||||||
\(242\) | 290056. | + | 214267.i | 0.318378 | + | 0.235189i | ||||
\(243\) | −477861. | + | 477861.i | −0.519142 | + | 0.519142i | ||||
\(244\) | 1.15849e6 | + | 613575.i | 1.24571 | + | 0.659771i | ||||
\(245\) | −293685. | − | 293685.i | −0.312584 | − | 0.312584i | ||||
\(246\) | −2.53784e6 | + | 381384.i | −2.67378 | + | 0.401814i | ||||
\(247\) | 1.35800e6i | 1.41631i | ||||||||
\(248\) | 1.35000e6 | + | 474371.i | 1.39381 | + | 0.489767i | ||||
\(249\) | − | 2.30305e6i | − | 2.35400i | ||||||
\(250\) | 13135.4 | + | 87406.9i | 0.0132921 | + | 0.0884495i | ||||
\(251\) | −180182. | − | 180182.i | −0.180520 | − | 0.180520i | 0.611062 | − | 0.791583i | \(-0.290742\pi\) |
−0.791583 | + | 0.611062i | \(0.790742\pi\) | |||||||
\(252\) | −55540.7 | − | 180619.i | −0.0550947 | − | 0.179168i | ||||
\(253\) | 330037. | − | 330037.i | 0.324161 | − | 0.324161i | ||||
\(254\) | 1.05046e6 | − | 1.42203e6i | 1.02164 | − | 1.38301i | ||||
\(255\) | −16764.6 | −0.0161452 | ||||||||
\(256\) | 386496. | − | 974747.i | 0.368592 | − | 0.929591i | ||||
\(257\) | 1.33681e6 | 1.26251 | 0.631256 | − | 0.775575i | \(-0.282540\pi\) | ||||
0.631256 | + | 0.775575i | \(0.282540\pi\) | |||||||
\(258\) | 1.38247e6 | − | 1.87146e6i | 1.29302 | − | 1.75038i | ||||
\(259\) | 42228.6 | − | 42228.6i | 0.0391162 | − | 0.0391162i | ||||
\(260\) | 144103. | + | 468625.i | 0.132203 | + | 0.429924i | ||||
\(261\) | −137878. | − | 137878.i | −0.125284 | − | 0.125284i | ||||
\(262\) | 172850. | + | 1.15020e6i | 0.155567 | + | 1.03519i | ||||
\(263\) | − | 265597.i | − | 0.236774i | −0.992968 | − | 0.118387i | \(-0.962228\pi\) | ||
0.992968 | − | 0.118387i | \(-0.0377724\pi\) | |||||||
\(264\) | 1.37621e6 | + | 483581.i | 1.21527 | + | 0.427031i | ||||
\(265\) | − | 542674.i | − | 0.474706i | ||||||
\(266\) | 172495. | − | 25922.4i | 0.149476 | − | 0.0224632i | ||||
\(267\) | −937188. | − | 937188.i | −0.804542 | − | 0.804542i | ||||
\(268\) | −1.70824e6 | − | 904741.i | −1.45282 | − | 0.769463i | ||||
\(269\) | 525286. | − | 525286.i | 0.442603 | − | 0.442603i | −0.450283 | − | 0.892886i | \(-0.648677\pi\) |
0.892886 | + | 0.450283i | \(0.148677\pi\) | |||||||
\(270\) | 532913. | + | 393667.i | 0.444884 | + | 0.328640i | ||||
\(271\) | −404175. | −0.334308 | −0.167154 | − | 0.985931i | \(-0.553458\pi\) | ||||
−0.167154 | + | 0.985931i | \(0.553458\pi\) | |||||||
\(272\) | 21988.6 | − | 14935.4i | 0.0180208 | − | 0.0122403i | ||||
\(273\) | −220311. | −0.178908 | ||||||||
\(274\) | 1.53398e6 | + | 1.13317e6i | 1.23437 | + | 0.911837i | ||||
\(275\) | 137857. | − | 137857.i | 0.109925 | − | 0.109925i | ||||
\(276\) | −578931. | + | 1.09308e6i | −0.457461 | + | 0.863731i | ||||
\(277\) | −359520. | − | 359520.i | −0.281529 | − | 0.281529i | 0.552189 | − | 0.833719i | \(-0.313793\pi\) |
−0.833719 | + | 0.552189i | \(0.813793\pi\) | |||||||
\(278\) | −1.53402e6 | + | 230532.i | −1.19048 | + | 0.178903i | ||||
\(279\) | − | 3.35441e6i | − | 2.57992i | ||||||
\(280\) | 56774.4 | − | 27249.5i | 0.0432771 | − | 0.0207713i | ||||
\(281\) | − | 2.11992e6i | − | 1.60160i | −0.598932 | − | 0.800800i | \(-0.704408\pi\) | ||
0.598932 | − | 0.800800i | \(-0.295592\pi\) | |||||||
\(282\) | −368317. | − | 2.45089e6i | −0.275803 | − | 1.83527i | ||||
\(283\) | −644887. | − | 644887.i | −0.478650 | − | 0.478650i | 0.426050 | − | 0.904700i | \(-0.359905\pi\) |
−0.904700 | + | 0.426050i | \(0.859905\pi\) | |||||||
\(284\) | −1.24136e6 | + | 381721.i | −0.913274 | + | 0.280834i | ||||
\(285\) | −1.01193e6 | + | 1.01193e6i | −0.737967 | + | 0.737967i | ||||
\(286\) | 642545. | − | 869823.i | 0.464503 | − | 0.628804i | ||||
\(287\) | 244380. | 0.175130 | ||||||||
\(288\) | −2.45619e6 | − | 97276.6i | −1.74494 | − | 0.0691078i | ||||
\(289\) | −1.41918e6 | −0.999525 | ||||||||
\(290\) | 38610.9 | − | 52268.1i | 0.0269597 | − | 0.0364957i | ||||
\(291\) | −2.14661e6 | + | 2.14661e6i | −1.48600 | + | 1.48600i | ||||
\(292\) | −26674.8 | + | 8202.57i | −0.0183081 | + | 0.00562980i | ||||
\(293\) | 811411. | + | 811411.i | 0.552169 | + | 0.552169i | 0.927066 | − | 0.374898i | \(-0.122322\pi\) |
−0.374898 | + | 0.927066i | \(0.622322\pi\) | |||||||
\(294\) | −360794. | − | 2.40083e6i | −0.243439 | − | 1.61992i | ||||
\(295\) | 865123.i | 0.578793i | ||||||||
\(296\) | −336149. | − | 700366.i | −0.222999 | − | 0.464618i | ||||
\(297\) | − | 1.46139e6i | − | 0.961333i | ||||||
\(298\) | 1.73191e6 | − | 260270.i | 1.12976 | − | 0.169779i | ||||
\(299\) | 648417. | + | 648417.i | 0.419446 | + | 0.419446i | ||||
\(300\) | −241820. | + | 456579.i | −0.155127 | + | 0.292896i | ||||
\(301\) | −156668. | + | 156668.i | −0.0996697 | + | 0.0996697i | ||||
\(302\) | 1.82267e6 | + | 1.34642e6i | 1.14998 | + | 0.849500i | ||||
\(303\) | 1.57219e6 | 0.983780 | ||||||||
\(304\) | 425740. | − | 2.22876e6i | 0.264217 | − | 1.38318i | ||||
\(305\) | 1.02417e6 | 0.630412 | ||||||||
\(306\) | −50120.6 | − | 37024.5i | −0.0305994 | − | 0.0226040i | ||||
\(307\) | 231288. | − | 231288.i | 0.140058 | − | 0.140058i | −0.633602 | − | 0.773660i | \(-0.718424\pi\) |
0.773660 | + | 0.633602i | \(0.218424\pi\) | |||||||
\(308\) | −122751. | − | 65013.1i | −0.0737307 | − | 0.0390503i | ||||
\(309\) | −1.57949e6 | − | 1.57949e6i | −0.941065 | − | 0.941065i | ||||
\(310\) | 1.10549e6 | − | 166132.i | 0.653357 | − | 0.0981859i | ||||
\(311\) | 1.08331e6i | 0.635114i | 0.948239 | + | 0.317557i | \(0.102863\pi\) | ||||
−0.948239 | + | 0.317557i | \(0.897137\pi\) | |||||||
\(312\) | −950082. | + | 2.70381e6i | −0.552554 | + | 1.57250i | ||||
\(313\) | 2.42505e6i | 1.39914i | 0.714566 | + | 0.699568i | \(0.246624\pi\) | ||||
−0.714566 | + | 0.699568i | \(0.753376\pi\) | |||||||
\(314\) | 290149. | + | 1.93073e6i | 0.166072 | + | 1.10509i | ||||
\(315\) | −104389. | − | 104389.i | −0.0592762 | − | 0.0592762i | ||||
\(316\) | −819445. | − | 2.66484e6i | −0.461639 | − | 1.50125i | ||||
\(317\) | −601112. | + | 601112.i | −0.335975 | + | 0.335975i | −0.854850 | − | 0.518875i | \(-0.826351\pi\) |
0.518875 | + | 0.854850i | \(0.326351\pi\) | |||||||
\(318\) | 1.88479e6 | − | 2.55147e6i | 1.04519 | − | 1.41489i | ||||
\(319\) | −143333. | −0.0788622 | ||||||||
\(320\) | −89587.5 | − | 814287.i | −0.0489071 | − | 0.444531i | ||||
\(321\) | −254162. | −0.137673 | ||||||||
\(322\) | 69985.3 | − | 94740.0i | 0.0376155 | − | 0.0509206i | ||||
\(323\) | 40673.1 | − | 40673.1i | 0.0216921 | − | 0.0216921i | ||||
\(324\) | 168439. | + | 547765.i | 0.0891417 | + | 0.289889i | ||||
\(325\) | 270844. | + | 270844.i | 0.142236 | + | 0.142236i | ||||
\(326\) | 154366. | + | 1.02719e6i | 0.0804464 | + | 0.535313i | ||||
\(327\) | 4.27507e6i | 2.21093i | ||||||||
\(328\) | 1.05388e6 | − | 2.99919e6i | 0.540885 | − | 1.53929i | ||||
\(329\) | 236007.i | 0.120208i | ||||||||
\(330\) | 1.12695e6 | − | 169357.i | 0.569667 | − | 0.0856090i | ||||
\(331\) | −510922. | − | 510922.i | −0.256321 | − | 0.256321i | 0.567235 | − | 0.823556i | \(-0.308013\pi\) |
−0.823556 | + | 0.567235i | \(0.808013\pi\) | |||||||
\(332\) | 2.52107e6 | + | 1.33524e6i | 1.25528 | + | 0.664837i | ||||
\(333\) | −1.28774e6 | + | 1.28774e6i | −0.636383 | + | 0.636383i | ||||
\(334\) | −1.35249e6 | − | 999099.i | −0.663390 | − | 0.490052i | ||||
\(335\) | −1.51019e6 | −0.735222 | ||||||||
\(336\) | 361576. | + | 69068.5i | 0.174724 | + | 0.0333758i | ||||
\(337\) | 2.57019e6 | 1.23279 | 0.616397 | − | 0.787436i | \(-0.288592\pi\) | ||||
0.616397 | + | 0.787436i | \(0.288592\pi\) | |||||||
\(338\) | 19530.7 | + | 14427.5i | 0.00929878 | + | 0.00686909i | ||||
\(339\) | −589037. | + | 589037.i | −0.278383 | + | 0.278383i | ||||
\(340\) | 9719.62 | − | 18351.6i | 0.00455986 | − | 0.00860947i | ||||
\(341\) | −1.74356e6 | − | 1.74356e6i | −0.811990 | − | 0.811990i | ||||
\(342\) | −5.26016e6 | + | 790492.i | −2.43183 | + | 0.365454i | ||||
\(343\) | 465067.i | 0.213442i | ||||||||
\(344\) | 1.24711e6 | + | 2.59835e6i | 0.568210 | + | 1.18387i | ||||
\(345\) | 966347.i | 0.437104i | ||||||||
\(346\) | 223454. | + | 1.48693e6i | 0.100346 | + | 0.667728i | ||||
\(347\) | −1.28231e6 | − | 1.28231e6i | −0.571701 | − | 0.571701i | 0.360903 | − | 0.932603i | \(-0.382469\pi\) |
−0.932603 | + | 0.360903i | \(0.882469\pi\) | |||||||
\(348\) | 363071. | − | 111645.i | 0.160710 | − | 0.0494188i | ||||
\(349\) | 888285. | − | 888285.i | 0.390381 | − | 0.390381i | −0.484442 | − | 0.874823i | \(-0.660977\pi\) |
0.874823 | + | 0.484442i | \(0.160977\pi\) | |||||||
\(350\) | 29232.9 | − | 39572.9i | 0.0127556 | − | 0.0172674i | ||||
\(351\) | 2.87116e6 | 1.24391 | ||||||||
\(352\) | −1.32724e6 | + | 1.22612e6i | −0.570944 | + | 0.527443i | ||||
\(353\) | −806589. | −0.344521 | −0.172260 | − | 0.985051i | \(-0.555107\pi\) | ||||
−0.172260 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(354\) | −3.00471e6 | + | 4.06752e6i | −1.27437 | + | 1.72513i | ||||
\(355\) | −717450. | + | 717450.i | −0.302149 | + | 0.302149i | ||||
\(356\) | 1.56926e6 | − | 482551.i | 0.656250 | − | 0.201799i | ||||
\(357\) | 6598.46 | + | 6598.46i | 0.00274014 | + | 0.00274014i | ||||
\(358\) | −437661. | − | 2.91232e6i | −0.180480 | − | 1.20097i | ||||
\(359\) | − | 3.12013e6i | − | 1.27772i | −0.769322 | − | 0.638861i | \(-0.779406\pi\) | ||
0.769322 | − | 0.638861i | \(-0.220594\pi\) | |||||||
\(360\) | −1.73131e6 | + | 830963.i | −0.704076 | + | 0.337929i | ||||
\(361\) | − | 2.43403e6i | − | 0.983010i | ||||||
\(362\) | −624588. | + | 93862.5i | −0.250508 | + | 0.0376462i | ||||
\(363\) | 1.16448e6 | + | 1.16448e6i | 0.463836 | + | 0.463836i | ||||
\(364\) | 127730. | − | 241167.i | 0.0505288 | − | 0.0954033i | ||||
\(365\) | −15416.8 | + | 15416.8i | −0.00605708 | + | 0.00605708i | ||||
\(366\) | 4.81532e6 | + | 3.55712e6i | 1.87898 | + | 1.38802i | ||||
\(367\) | −2.36989e6 | −0.918466 | −0.459233 | − | 0.888316i | \(-0.651876\pi\) | ||||
−0.459233 | + | 0.888316i | \(0.651876\pi\) | |||||||
\(368\) | −860905. | − | 1.26747e6i | −0.331387 | − | 0.487885i | ||||
\(369\) | −7.45226e6 | −2.84920 | ||||||||
\(370\) | −488170. | − | 360615.i | −0.185381 | − | 0.136943i | ||||
\(371\) | −213594. | + | 213594.i | −0.0805664 | + | 0.0805664i | ||||
\(372\) | 5.77465e6 | + | 3.05845e6i | 2.16356 | + | 1.14589i | ||||
\(373\) | 592951. | + | 592951.i | 0.220672 | + | 0.220672i | 0.808781 | − | 0.588110i | \(-0.200128\pi\) |
−0.588110 | + | 0.808781i | \(0.700128\pi\) | |||||||
\(374\) | −45296.4 | + | 6807.10i | −0.0167450 | + | 0.00251642i | ||||
\(375\) | 403643.i | 0.148224i | ||||||||
\(376\) | 2.89643e6 | + | 1.01777e6i | 1.05656 | + | 0.371261i | ||||
\(377\) | − | 281603.i | − | 0.102043i | ||||||
\(378\) | −54806.4 | − | 364697.i | −0.0197288 | − | 0.131281i | ||||
\(379\) | 1.55802e6 | + | 1.55802e6i | 0.557152 | + | 0.557152i | 0.928496 | − | 0.371343i | \(-0.121103\pi\) |
−0.371343 | + | 0.928496i | \(0.621103\pi\) | |||||||
\(380\) | −521034. | − | 1.69440e6i | −0.185100 | − | 0.601947i | ||||
\(381\) | 5.70896e6 | − | 5.70896e6i | 2.01486 | − | 2.01486i | ||||
\(382\) | −540661. | + | 731901.i | −0.189569 | + | 0.256622i | ||||
\(383\) | −1.73646e6 | −0.604877 | −0.302439 | − | 0.953169i | \(-0.597801\pi\) | ||||
−0.302439 | + | 0.953169i | \(0.597801\pi\) | |||||||
\(384\) | 2.40694e6 | − | 4.13965e6i | 0.832984 | − | 1.43264i | ||||
\(385\) | −108519. | −0.0373126 | ||||||||
\(386\) | −1.82714e6 | + | 2.47343e6i | −0.624173 | + | 0.844951i | ||||
\(387\) | 4.77752e6 | − | 4.77752e6i | 1.62153 | − | 1.62153i | ||||
\(388\) | −1.10527e6 | − | 3.59435e6i | −0.372726 | − | 1.21211i | ||||
\(389\) | 1.66357e6 | + | 1.66357e6i | 0.557400 | + | 0.557400i | 0.928566 | − | 0.371166i | \(-0.121042\pi\) |
−0.371166 | + | 0.928566i | \(0.621042\pi\) | |||||||
\(390\) | 332733. | + | 2.21410e6i | 0.110773 | + | 0.737117i | ||||
\(391\) | − | 38841.0i | − | 0.0128484i | ||||||
\(392\) | 2.83727e6 | + | 996980.i | 0.932580 | + | 0.327696i | ||||
\(393\) | 5.31158e6i | 1.73477i | ||||||||
\(394\) | 481923. | − | 72422.9i | 0.156400 | − | 0.0235037i | ||||
\(395\) | −1.54016e6 | − | 1.54016e6i | −0.496675 | − | 0.496675i | ||||
\(396\) | 3.74324e6 | + | 1.98255e6i | 1.19953 | + | 0.635310i | ||||
\(397\) | −3.80404e6 | + | 3.80404e6i | −1.21135 | + | 1.21135i | −0.240763 | + | 0.970584i | \(0.577398\pi\) |
−0.970584 | + | 0.240763i | \(0.922602\pi\) | |||||||
\(398\) | 4.29390e6 | + | 3.17194e6i | 1.35876 | + | 1.00373i | ||||
\(399\) | 796579. | 0.250494 | ||||||||
\(400\) | −359600. | − | 529422.i | −0.112375 | − | 0.165444i | ||||
\(401\) | 2.69674e6 | 0.837487 | 0.418744 | − | 0.908105i | \(-0.362471\pi\) | ||||
0.418744 | + | 0.908105i | \(0.362471\pi\) | |||||||
\(402\) | −7.10039e6 | − | 5.24512e6i | −2.19138 | − | 1.61879i | ||||
\(403\) | 3.42554e6 | − | 3.42554e6i | 1.05067 | − | 1.05067i | ||||
\(404\) | −911508. | + | 1.72102e6i | −0.277848 | + | 0.524604i | ||||
\(405\) | 316584. | + | 316584.i | 0.0959073 | + | 0.0959073i | ||||
\(406\) | −35769.5 | + | 5375.41i | −0.0107696 | + | 0.00161844i | ||||
\(407\) | 1.33869e6i | 0.400584i | ||||||||
\(408\) | 109436. | − | 52525.2i | 0.0325470 | − | 0.0156213i | ||||
\(409\) | 4.46773e6i | 1.32062i | 0.750992 | + | 0.660311i | \(0.229576\pi\) | ||||
−0.750992 | + | 0.660311i | \(0.770424\pi\) | |||||||
\(410\) | −369084. | − | 2.45599e6i | −0.108434 | − | 0.721550i | ||||
\(411\) | 6.15842e6 | + | 6.15842e6i | 1.79831 | + | 1.79831i | ||||
\(412\) | 2.64474e6 | − | 813266.i | 0.767610 | − | 0.236042i | ||||
\(413\) | 340508. | − | 340508.i | 0.0982319 | − | 0.0982319i | ||||
\(414\) | −2.13417e6 | + | 2.88906e6i | −0.611968 | + | 0.828429i | ||||
\(415\) | 2.22878e6 | 0.635252 | ||||||||
\(416\) | −2.40893e6 | − | 2.60761e6i | −0.682481 | − | 0.738769i | ||||
\(417\) | −7.08410e6 | −1.99501 | ||||||||
\(418\) | −2.32325e6 | + | 3.14502e6i | −0.650362 | + | 0.880404i | ||||
\(419\) | 1.17941e6 | − | 1.17941e6i | 0.328193 | − | 0.328193i | −0.523706 | − | 0.851899i | \(-0.675451\pi\) |
0.851899 | + | 0.523706i | \(0.175451\pi\) | |||||||
\(420\) | 274886. | − | 84528.2i | 0.0760378 | − | 0.0233818i | ||||
\(421\) | −846196. | − | 846196.i | −0.232684 | − | 0.232684i | 0.581128 | − | 0.813812i | \(-0.302611\pi\) |
−0.813812 | + | 0.581128i | \(0.802611\pi\) | |||||||
\(422\) | 72050.6 | + | 479446.i | 0.0196950 | + | 0.131056i | ||||
\(423\) | − | 7.19692e6i | − | 1.95567i | ||||||
\(424\) | 1.70025e6 | + | 3.54248e6i | 0.459303 | + | 0.956958i | ||||
\(425\) | − | 16223.9i | − | 0.00435696i | ||||||
\(426\) | −5.86503e6 | + | 881390.i | −1.56583 | + | 0.235312i | ||||
\(427\) | −403110. | − | 403110.i | −0.106993 | − | 0.106993i | ||||
\(428\) | 147356. | − | 278222.i | 0.0388828 | − | 0.0734146i | ||||
\(429\) | 3.49204e6 | − | 3.49204e6i | 0.916086 | − | 0.916086i | ||||
\(430\) | 1.81111e6 | + | 1.33788e6i | 0.472360 | + | 0.348936i | ||||
\(431\) | −3.51459e6 | −0.911342 | −0.455671 | − | 0.890148i | \(-0.650601\pi\) | ||||
−0.455671 | + | 0.890148i | \(0.650601\pi\) | |||||||
\(432\) | −4.71216e6 | − | 900120.i | −1.21482 | − | 0.232055i | ||||
\(433\) | −2.50659e6 | −0.642485 | −0.321243 | − | 0.946997i | \(-0.604101\pi\) | ||||
−0.321243 | + | 0.946997i | \(0.604101\pi\) | |||||||
\(434\) | −500504. | − | 369727.i | −0.127551 | − | 0.0942229i | ||||
\(435\) | 209839. | − | 209839.i | 0.0531695 | − | 0.0531695i | ||||
\(436\) | −4.67976e6 | − | 2.47856e6i | −1.17898 | − | 0.624429i | ||||
\(437\) | −2.34448e6 | − | 2.34448e6i | −0.587277 | − | 0.587277i | ||||
\(438\) | −126030. | + | 18939.7i | −0.0313898 | + | 0.00471723i | ||||
\(439\) | 7.36523e6i | 1.82400i | 0.410189 | + | 0.912001i | \(0.365463\pi\) | ||||
−0.410189 | + | 0.912001i | \(0.634537\pi\) | |||||||
\(440\) | −467985. | + | 1.33182e6i | −0.115239 | + | 0.327955i | ||||
\(441\) | − | 7.04993e6i | − | 1.72619i | ||||||
\(442\) | −13373.8 | − | 88992.9i | −0.00325610 | − | 0.0216670i | ||||
\(443\) | 707148. | + | 707148.i | 0.171199 | + | 0.171199i | 0.787506 | − | 0.616307i | \(-0.211372\pi\) |
−0.616307 | + | 0.787506i | \(0.711372\pi\) | |||||||
\(444\) | −1.04274e6 | − | 3.39098e6i | −0.251025 | − | 0.816334i | ||||
\(445\) | 906962. | − | 906962.i | 0.217115 | − | 0.217115i | ||||
\(446\) | −962502. | + | 1.30295e6i | −0.229121 | + | 0.310164i | ||||
\(447\) | 7.99793e6 | 1.89325 | ||||||||
\(448\) | −285238. | + | 355760.i | −0.0671448 | + | 0.0837457i | ||||
\(449\) | −3.60308e6 | −0.843449 | −0.421724 | − | 0.906724i | \(-0.638575\pi\) | ||||
−0.421724 | + | 0.906724i | \(0.638575\pi\) | |||||||
\(450\) | −891444. | + | 1.20676e6i | −0.207521 | + | 0.280925i | ||||
\(451\) | −3.87354e6 | + | 3.87354e6i | −0.896741 | + | 0.896741i | ||||
\(452\) | −303291. | − | 986303.i | −0.0698253 | − | 0.227072i | ||||
\(453\) | 7.31740e6 | + | 7.31740e6i | 1.67537 | + | 1.67537i | ||||
\(454\) | 206833. | + | 1.37632e6i | 0.0470955 | + | 0.313387i | ||||
\(455\) | − | 213206.i | − | 0.0482803i | ||||||
\(456\) | 3.43521e6 | − | 9.77615e6i | 0.773644 | − | 2.20169i | ||||
\(457\) | 4.29166e6i | 0.961246i | 0.876927 | + | 0.480623i | \(0.159589\pi\) | ||||
−0.876927 | + | 0.480623i | \(0.840411\pi\) | |||||||
\(458\) | −5.30053e6 | + | 796559.i | −1.18074 | + | 0.177441i | ||||
\(459\) | −85993.0 | − | 85993.0i | −0.0190516 | − | 0.0190516i | ||||
\(460\) | −1.05782e6 | − | 560259.i | −0.233087 | − | 0.123451i | ||||
\(461\) | 3.12730e6 | − | 3.12730e6i | 0.685358 | − | 0.685358i | −0.275845 | − | 0.961202i | \(-0.588958\pi\) |
0.961202 | + | 0.275845i | \(0.0889575\pi\) | |||||||
\(462\) | −510221. | − | 376905.i | −0.111213 | − | 0.0821536i | ||||
\(463\) | −3.19121e6 | −0.691836 | −0.345918 | − | 0.938265i | \(-0.612433\pi\) | ||||
−0.345918 | + | 0.938265i | \(0.612433\pi\) | |||||||
\(464\) | −88283.8 | + | 462169.i | −0.0190365 | + | 0.0996565i | ||||
\(465\) | 5.10513e6 | 1.09490 | ||||||||
\(466\) | −3.89090e6 | − | 2.87424e6i | −0.830014 | − | 0.613138i | ||||
\(467\) | 1.85914e6 | − | 1.85914e6i | 0.394476 | − | 0.394476i | −0.481803 | − | 0.876279i | \(-0.660018\pi\) |
0.876279 | + | 0.481803i | \(0.160018\pi\) | |||||||
\(468\) | −3.89507e6 | + | 7.35427e6i | −0.822055 | + | 1.55212i | ||||
\(469\) | 594402. | + | 594402.i | 0.124781 | + | 0.124781i | ||||
\(470\) | 2.37184e6 | − | 356438.i | 0.495268 | − | 0.0744284i | ||||
\(471\) | 8.91609e6i | 1.85192i | ||||||||
\(472\) | −2.71052e6 | − | 5.64737e6i | −0.560012 | − | 1.16679i | ||||
\(473\) | − | 4.96652e6i | − | 1.02070i | ||||||
\(474\) | −1.89209e6 | − | 1.25905e7i | −0.386809 | − | 2.57394i | ||||
\(475\) | −979290. | − | 979290.i | −0.199149 | − | 0.199149i | ||||
\(476\) | −11048.7 | + | 3397.50i | −0.00223508 | + | 0.000687293i | ||||
\(477\) | 6.51346e6 | − | 6.51346e6i | 1.31074 | − | 1.31074i | ||||
\(478\) | 4.19834e6 | − | 5.68335e6i | 0.840442 | − | 1.13772i | ||||
\(479\) | 1.42822e6 | 0.284418 | 0.142209 | − | 0.989837i | \(-0.454579\pi\) | ||||
0.142209 | + | 0.989837i | \(0.454579\pi\) | |||||||
\(480\) | 148047. | − | 3.73811e6i | 0.0293289 | − | 0.740541i | ||||
\(481\) | −2.63009e6 | −0.518333 | ||||||||
\(482\) | −2.48232e6 | + | 3.36035e6i | −0.486676 | + | 0.658820i | ||||
\(483\) | 380349. | − | 380349.i | 0.0741848 | − | 0.0741848i | ||||
\(484\) | −1.94984e6 | + | 599581.i | −0.378343 | + | 0.116341i | ||||
\(485\) | −2.07737e6 | − | 2.07737e6i | −0.401015 | − | 0.401015i | ||||
\(486\) | −568121. | − | 3.78044e6i | −0.109106 | − | 0.726025i | ||||
\(487\) | 6.60517e6i | 1.26201i | 0.775780 | + | 0.631003i | \(0.217357\pi\) | ||||
−0.775780 | + | 0.631003i | \(0.782643\pi\) | |||||||
\(488\) | −6.68563e6 | + | 3.20884e6i | −1.27085 | + | 0.609957i | ||||
\(489\) | 4.74356e6i | 0.897082i | ||||||||
\(490\) | 2.32339e6 | − | 349157.i | 0.437152 | − | 0.0656948i | ||||
\(491\) | −65912.2 | − | 65912.2i | −0.0123385 | − | 0.0123385i | 0.700911 | − | 0.713249i | \(-0.252777\pi\) |
−0.713249 | + | 0.700911i | \(0.752777\pi\) | |||||||
\(492\) | 6.79473e6 | − | 1.28291e7i | 1.26549 | − | 2.38937i | ||||
\(493\) | −8434.19 | + | 8434.19i | −0.00156288 | + | 0.00156288i | ||||
\(494\) | −6.17895e6 | − | 4.56444e6i | −1.13919 | − | 0.841531i | ||||
\(495\) | 3.30925e6 | 0.607039 | ||||||||
\(496\) | −6.69593e6 | + | 4.54809e6i | −1.22210 | + | 0.830090i | ||||
\(497\) | 564769. | 0.102560 | ||||||||
\(498\) | 1.04790e7 | + | 7.74089e6i | 1.89341 | + | 1.39868i | ||||
\(499\) | 3.20050e6 | − | 3.20050e6i | 0.575396 | − | 0.575396i | −0.358235 | − | 0.933631i | \(-0.616621\pi\) |
0.933631 | + | 0.358235i | \(0.116621\pi\) | |||||||
\(500\) | −441853. | − | 234020.i | −0.0790411 | − | 0.0418628i | ||||
\(501\) | −5.42981e6 | − | 5.42981e6i | −0.966474 | − | 0.966474i | ||||
\(502\) | 1.42545e6 | − | 214215.i | 0.252459 | − | 0.0379394i | ||||
\(503\) | − | 2.12538e6i | − | 0.374555i | −0.982307 | − | 0.187278i | \(-0.940034\pi\) | ||
0.982307 | − | 0.187278i | \(-0.0599664\pi\) | |||||||
\(504\) | 1.00850e6 | + | 354373.i | 0.176848 | + | 0.0621419i | ||||
\(505\) | 1.52148e6i | 0.265484i | ||||||||
\(506\) | 392375. | + | 2.61098e6i | 0.0681280 | + | 0.453343i | ||||
\(507\) | 78409.2 | + | 78409.2i | 0.0135471 | + | 0.0135471i | ||||
\(508\) | 2.93950e6 | + | 9.55928e6i | 0.505376 | + | 1.64349i | ||||
\(509\) | 6.65339e6 | − | 6.65339e6i | 1.13828 | − | 1.13828i | 0.149519 | − | 0.988759i | \(-0.452227\pi\) |
0.988759 | − | 0.149519i | \(-0.0477726\pi\) | |||||||
\(510\) | 56348.2 | − | 76279.4i | 0.00959301 | − | 0.0129862i | ||||
\(511\) | 12136.0 | 0.00205600 | ||||||||
\(512\) | 3.13605e6 | + | 5.03483e6i | 0.528699 | + | 0.848809i | ||||
\(513\) | −1.03812e7 | −1.74163 | ||||||||
\(514\) | −4.49319e6 | + | 6.08250e6i | −0.750149 | + | 1.01549i | ||||
\(515\) | 1.52854e6 | − | 1.52854e6i | 0.253957 | − | 0.253957i | ||||
\(516\) | 3.86854e6 | + | 1.25805e7i | 0.639622 | + | 2.08005i | ||||
\(517\) | −3.74082e6 | − | 3.74082e6i | −0.615518 | − | 0.615518i | ||||
\(518\) | 50204.8 | + | 334077.i | 0.00822093 | + | 0.0547044i | ||||
\(519\) | 6.86661e6i | 1.11898i | ||||||||
\(520\) | −2.61660e6 | − | 919440.i | −0.424355 | − | 0.149113i | ||||
\(521\) | 6.43393e6i | 1.03844i | 0.854640 | + | 0.519220i | \(0.173778\pi\) | ||||
−0.854640 | + | 0.519220i | \(0.826222\pi\) | |||||||
\(522\) | 1.09078e6 | − | 163921.i | 0.175210 | − | 0.0263304i | ||||
\(523\) | −5.14301e6 | − | 5.14301e6i | −0.822172 | − | 0.822172i | 0.164247 | − | 0.986419i | \(-0.447481\pi\) |
−0.986419 | + | 0.164247i | \(0.947481\pi\) | |||||||
\(524\) | −5.81439e6 | − | 3.07950e6i | −0.925073 | − | 0.489950i | ||||
\(525\) | 158872. | − | 158872.i | 0.0251564 | − | 0.0251564i | ||||
\(526\) | 1.20847e6 | + | 892711.i | 0.190447 | + | 0.140685i | ||||
\(527\) | −205194. | −0.0321839 | ||||||||
\(528\) | −6.82594e6 | + | 4.63639e6i | −1.06556 | + | 0.723762i | ||||
\(529\) | 4.19747e6 | 0.652151 | ||||||||
\(530\) | 2.46918e6 | + | 1.82401e6i | 0.381824 | + | 0.282057i | ||||
\(531\) | −1.03837e7 | + | 1.03837e7i | −1.59814 | + | 1.59814i | ||||
\(532\) | −461833. | + | 871985.i | −0.0707466 | + | 0.133577i | ||||
\(533\) | −7.61027e6 | − | 7.61027e6i | −1.16033 | − | 1.16033i | ||||
\(534\) | 7.41425e6 | − | 1.11421e6i | 1.12516 | − | 0.169088i | ||||
\(535\) | − | 245965.i | − | 0.0371526i | ||||||
\(536\) | 9.85823e6 | − | 4.73157e6i | 1.48213 | − | 0.711366i | ||||
\(537\) | − | 1.34490e7i | − | 2.01259i | ||||||
\(538\) | 624503. | + | 4.15562e6i | 0.0930205 | + | 0.618985i | ||||
\(539\) | −3.66442e6 | − | 3.66442e6i | −0.543292 | − | 0.543292i | ||||
\(540\) | −3.58239e6 | + | 1.10160e6i | −0.528675 | + | 0.162569i | ||||
\(541\) | −6.17708e6 | + | 6.17708e6i | −0.907381 | + | 0.907381i | −0.996060 | − | 0.0886790i | \(-0.971735\pi\) |
0.0886790 | + | 0.996060i | \(0.471735\pi\) | |||||||
\(542\) | 1.35849e6 | − | 1.83901e6i | 0.198636 | − | 0.268896i | ||||
\(543\) | −2.88434e6 | −0.419804 | ||||||||
\(544\) | −5950.54 | + | 150248.i | −0.000862103 | + | 0.0217677i | ||||
\(545\) | −4.13719e6 | −0.596643 | ||||||||
\(546\) | 740497. | − | 1.00242e6i | 0.106302 | − | 0.143903i | ||||
\(547\) | 5.33988e6 | − | 5.33988e6i | 0.763068 | − | 0.763068i | −0.213808 | − | 0.976876i | \(-0.568587\pi\) |
0.976876 | + | 0.213808i | \(0.0685866\pi\) | |||||||
\(548\) | −1.03119e7 | + | 3.17093e6i | −1.46685 | + | 0.451060i | ||||
\(549\) | 1.22927e7 | + | 1.22927e7i | 1.74067 | + | 1.74067i | ||||
\(550\) | 163895. | + | 1.09061e6i | 0.0231025 | + | 0.153731i | ||||
\(551\) | 1.01819e6i | 0.142873i | ||||||||
\(552\) | −3.02766e6 | − | 6.30814e6i | −0.422922 | − | 0.881158i | ||||
\(553\) | 1.21240e6i | 0.168590i | ||||||||
\(554\) | 2.84422e6 | − | 427427.i | 0.393722 | − | 0.0591681i | ||||
\(555\) | −1.95984e6 | − | 1.95984e6i | −0.270077 | − | 0.270077i | ||||
\(556\) | 4.10715e6 | − | 7.75470e6i | 0.563448 | − | 1.06384i | ||||
\(557\) | −1.67989e6 | + | 1.67989e6i | −0.229426 | + | 0.229426i | −0.812453 | − | 0.583027i | \(-0.801868\pi\) |
0.583027 | + | 0.812453i | \(0.301868\pi\) | |||||||
\(558\) | 1.52627e7 | + | 1.12747e7i | 2.07513 | + | 1.53291i | ||||
\(559\) | 9.75763e6 | 1.32073 | ||||||||
\(560\) | −66840.9 | + | 349915.i | −0.00900684 | + | 0.0471511i | ||||
\(561\) | −209178. | −0.0280614 | ||||||||
\(562\) | 9.64570e6 | + | 7.12536e6i | 1.28823 | + | 0.951625i | ||||
\(563\) | 5.06107e6 | − | 5.06107e6i | 0.672933 | − | 0.672933i | −0.285458 | − | 0.958391i | \(-0.592146\pi\) |
0.958391 | + | 0.285458i | \(0.0921458\pi\) | |||||||
\(564\) | 1.23896e7 | + | 6.56192e6i | 1.64005 | + | 0.868627i | ||||
\(565\) | −570039. | − | 570039.i | −0.0751248 | − | 0.0751248i | ||||
\(566\) | 5.10181e6 | − | 766695.i | 0.669396 | − | 0.100596i | ||||
\(567\) | − | 249212.i | − | 0.0325545i | ||||||
\(568\) | 2.43554e6 | − | 6.93123e6i | 0.316756 | − | 0.901445i | ||||
\(569\) | − | 8.18380e6i | − | 1.05968i | −0.848098 | − | 0.529839i | \(-0.822252\pi\) | ||
0.848098 | − | 0.529839i | \(-0.177748\pi\) | |||||||
\(570\) | −1.20306e6 | − | 8.00553e6i | −0.155096 | − | 1.03205i | ||||
\(571\) | −3.05274e6 | − | 3.05274e6i | −0.391832 | − | 0.391832i | 0.483508 | − | 0.875340i | \(-0.339362\pi\) |
−0.875340 | + | 0.483508i | \(0.839362\pi\) | |||||||
\(572\) | 1.79803e6 | + | 5.84719e6i | 0.229777 | + | 0.747235i | ||||
\(573\) | −2.93833e6 | + | 2.93833e6i | −0.373865 | + | 0.373865i | ||||
\(574\) | −821395. | + | 1.11193e6i | −0.104057 | + | 0.140864i | ||||
\(575\) | −935180. | −0.117957 | ||||||||
\(576\) | 8.69821e6 | − | 1.08488e7i | 1.09238 | − | 1.36246i | ||||
\(577\) | −4.77219e6 | −0.596730 | −0.298365 | − | 0.954452i | \(-0.596441\pi\) | ||||
−0.298365 | + | 0.954452i | \(0.596441\pi\) | |||||||
\(578\) | 4.77008e6 | − | 6.45732e6i | 0.593890 | − | 0.803957i | ||||
\(579\) | −9.92999e6 | + | 9.92999e6i | −1.23098 | + | 1.23098i | ||||
\(580\) | 108044. | + | 351361.i | 0.0133362 | + | 0.0433694i | ||||
\(581\) | −877235. | − | 877235.i | −0.107814 | − | 0.107814i | ||||
\(582\) | −2.55206e6 | − | 1.69822e7i | −0.312309 | − | 2.07819i | ||||
\(583\) | − | 6.77114e6i | − | 0.825069i | ||||||
\(584\) | 52335.9 | − | 148941.i | 0.00634991 | − | 0.0180710i | ||||
\(585\) | 6.50162e6i | 0.785474i | ||||||||
\(586\) | −6.41921e6 | + | 964672.i | −0.772213 | + | 0.116047i | ||||
\(587\) | −7.77494e6 | − | 7.77494e6i | −0.931327 | − | 0.931327i | 0.0664624 | − | 0.997789i | \(-0.478829\pi\) |
−0.997789 | + | 0.0664624i | \(0.978829\pi\) | |||||||
\(588\) | 1.21365e7 | + | 6.42790e6i | 1.44760 | + | 0.766700i | ||||
\(589\) | −1.23857e7 | + | 1.23857e7i | −1.47107 | + | 1.47107i | ||||
\(590\) | −3.93633e6 | − | 2.90780e6i | −0.465545 | − | 0.343902i | ||||
\(591\) | 2.22551e6 | 0.262097 | ||||||||
\(592\) | 4.31653e6 | + | 824546.i | 0.506209 | + | 0.0966964i | ||||
\(593\) | 1.63675e7 | 1.91137 | 0.955687 | − | 0.294384i | \(-0.0951146\pi\) | ||||
0.955687 | + | 0.294384i | \(0.0951146\pi\) | |||||||
\(594\) | 6.64934e6 | + | 4.91193e6i | 0.773237 | + | 0.571197i | ||||
\(595\) | −6385.65 | + | 6385.65i | −0.000739456 | + | 0.000739456i | ||||
\(596\) | −4.63696e6 | + | 8.75504e6i | −0.534710 | + | 1.00958i | ||||
\(597\) | 1.72386e7 | + | 1.72386e7i | 1.97954 | + | 1.97954i | ||||
\(598\) | −5.12974e6 | + | 770892.i | −0.586600 | + | 0.0881537i | ||||
\(599\) | 9.42265e6i | 1.07302i | 0.843895 | + | 0.536508i | \(0.180257\pi\) | ||||
−0.843895 | + | 0.536508i | \(0.819743\pi\) | |||||||
\(600\) | −1.26466e6 | − | 2.63491e6i | −0.143415 | − | 0.298805i | ||||
\(601\) | 3.73432e6i | 0.421722i | 0.977516 | + | 0.210861i | \(0.0676267\pi\) | ||||
−0.977516 | + | 0.210861i | \(0.932373\pi\) | |||||||
\(602\) | −186260. | − | 1.23942e6i | −0.0209473 | − | 0.139389i | ||||
\(603\) | −1.81260e7 | − | 1.81260e7i | −2.03006 | − | 2.03006i | ||||
\(604\) | −1.22525e7 | + | 3.76767e6i | −1.36657 | + | 0.420224i | ||||
\(605\) | −1.12692e6 | + | 1.12692e6i | −0.125171 | + | 0.125171i | ||||
\(606\) | −5.28435e6 | + | 7.15350e6i | −0.584534 | + | 0.791292i | ||||
\(607\) | −6.00207e6 | −0.661195 | −0.330598 | − | 0.943772i | \(-0.607250\pi\) | ||||
−0.330598 | + | 0.943772i | \(0.607250\pi\) | |||||||
\(608\) | 8.70996e6 | + | 9.42832e6i | 0.955558 | + | 1.03437i | ||||
\(609\) | −165183. | −0.0180477 | ||||||||
\(610\) | −3.44240e6 | + | 4.66002e6i | −0.374573 | + | 0.507064i | ||||
\(611\) | 7.34952e6 | − | 7.34952e6i | 0.796445 | − | 0.796445i | ||||
\(612\) | 336925. | − | 103605.i | 0.0363626 | − | 0.0111816i | ||||
\(613\) | 7.64426e6 | + | 7.64426e6i | 0.821645 | + | 0.821645i | 0.986344 | − | 0.164699i | \(-0.0526652\pi\) |
−0.164699 | + | 0.986344i | \(0.552665\pi\) | |||||||
\(614\) | 274975. | + | 1.82976e6i | 0.0294355 | + | 0.195872i | ||||
\(615\) | − | 1.13417e7i | − | 1.20918i | ||||||
\(616\) | 708395. | − | 340002.i | 0.0752183 | − | 0.0361019i | ||||
\(617\) | − | 1.13245e7i | − | 1.19759i | −0.800903 | − | 0.598794i | \(-0.795647\pi\) | ||
0.800903 | − | 0.598794i | \(-0.204353\pi\) | |||||||
\(618\) | 1.24956e7 | − | 1.87782e6i | 1.31609 | − | 0.197781i | ||||
\(619\) | 9.72348e6 | + | 9.72348e6i | 1.01999 | + | 1.01999i | 0.999796 | + | 0.0201917i | \(0.00642766\pi\) |
0.0201917 | + | 0.999796i | \(0.493572\pi\) | |||||||
\(620\) | −2.95980e6 | + | 5.58840e6i | −0.309232 | + | 0.583859i | ||||
\(621\) | −4.95682e6 | + | 4.95682e6i | −0.515791 | + | 0.515791i | ||||
\(622\) | −4.92909e6 | − | 3.64116e6i | −0.510847 | − | 0.377367i | ||||
\(623\) | −713951. | −0.0736968 | ||||||||
\(624\) | −9.10903e6 | − | 1.34108e7i | −0.936507 | − | 1.37877i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | −1.10340e7 | − | 8.15094e6i | −1.12538 | − | 0.831327i | ||||
\(627\) | −1.26262e7 | + | 1.26262e7i | −1.28263 | + | 1.28263i | ||||
\(628\) | −9.76011e6 | − | 5.16928e6i | −0.987542 | − | 0.523036i | ||||
\(629\) | 78773.0 | + | 78773.0i | 0.00793873 | + | 0.00793873i | ||||
\(630\) | 825843. | − | 124107.i | 0.0828984 | − | 0.0124579i | ||||
\(631\) | − | 6.32498e6i | − | 0.632392i | −0.948694 | − | 0.316196i | \(-0.897594\pi\) | ||
0.948694 | − | 0.316196i | \(-0.102406\pi\) | |||||||
\(632\) | 1.48794e7 | + | 5.22841e6i | 1.48181 | + | 0.520687i | ||||
\(633\) | 2.21407e6i | 0.219625i | ||||||||
\(634\) | −714652. | − | 4.75550e6i | −0.0706108 | − | 0.469865i | ||||
\(635\) | 5.52484e6 | + | 5.52484e6i | 0.543732 | + | 0.543732i | ||||
\(636\) | 5.27420e6 | + | 1.71517e7i | 0.517028 | + | 1.68138i | ||||
\(637\) | 7.19941e6 | − | 7.19941e6i | 0.702988 | − | 0.702988i | ||||
\(638\) | 481762. | − | 652168.i | 0.0468577 | − | 0.0634319i | ||||
\(639\) | −1.72224e7 | −1.66856 | ||||||||
\(640\) | 4.00614e6 | + | 2.32931e6i | 0.386613 | + | 0.224790i | ||||
\(641\) | 1.14227e7 | 1.09805 | 0.549025 | − | 0.835806i | \(-0.314999\pi\) | ||||
0.549025 | + | 0.835806i | \(0.314999\pi\) | |||||||
\(642\) | 854276. | − | 1.15644e6i | 0.0818014 | − | 0.110736i | ||||
\(643\) | 6.23986e6 | − | 6.23986e6i | 0.595179 | − | 0.595179i | −0.343847 | − | 0.939026i | \(-0.611730\pi\) |
0.939026 | + | 0.343847i | \(0.111730\pi\) | |||||||
\(644\) | 195839. | + | 636869.i | 0.0186073 | + | 0.0605112i | ||||
\(645\) | 7.27098e6 | + | 7.27098e6i | 0.688167 | + | 0.688167i | ||||
\(646\) | 48355.5 | + | 321771.i | 0.00455895 | + | 0.0303366i | ||||
\(647\) | 1.32619e7i | 1.24550i | 0.782420 | + | 0.622751i | \(0.213985\pi\) | ||||
−0.782420 | + | 0.622751i | \(0.786015\pi\) | |||||||
\(648\) | −3.05849e6 | − | 1.07471e6i | −0.286135 | − | 0.100544i | ||||
\(649\) | 1.07944e7i | 1.00598i | ||||||||
\(650\) | −2.14269e6 | + | 322002.i | −0.198919 | + | 0.0298934i | ||||
\(651\) | −2.00935e6 | − | 2.00935e6i | −0.185825 | − | 0.185825i | ||||
\(652\) | −5.19260e6 | − | 2.75017e6i | −0.478372 | − | 0.253362i | ||||
\(653\) | −6.10202e6 | + | 6.10202e6i | −0.560003 | + | 0.560003i | −0.929308 | − | 0.369305i | \(-0.879596\pi\) |
0.369305 | + | 0.929308i | \(0.379596\pi\) | |||||||
\(654\) | −1.94517e7 | − | 1.43691e7i | −1.77833 | − | 1.31367i | ||||
\(655\) | −5.14027e6 | −0.468148 | ||||||||
\(656\) | 1.01042e7 | + | 1.48759e7i | 0.916730 | + | 1.34966i | ||||
\(657\) | −370082. | −0.0334491 | ||||||||
\(658\) | −1.07384e6 | − | 793252.i | −0.0966881 | − | 0.0714243i | ||||
\(659\) | 7.32830e6 | − | 7.32830e6i | 0.657339 | − | 0.657339i | −0.297411 | − | 0.954750i | \(-0.596123\pi\) |
0.954750 | + | 0.297411i | \(0.0961230\pi\) | |||||||
\(660\) | −3.01727e6 | + | 5.69690e6i | −0.269621 | + | 0.509071i | ||||
\(661\) | −1.04059e7 | − | 1.04059e7i | −0.926356 | − | 0.926356i | 0.0711126 | − | 0.997468i | \(-0.477345\pi\) |
−0.997468 | + | 0.0711126i | \(0.977345\pi\) | |||||||
\(662\) | 4.04199e6 | − | 607426.i | 0.358468 | − | 0.0538702i | ||||
\(663\) | − | 410968.i | − | 0.0363098i | ||||||
\(664\) | −1.45491e7 | + | 6.98298e6i | −1.28060 | + | 0.614640i | ||||
\(665\) | 770888.i | 0.0675985i | ||||||||
\(666\) | −1.53098e6 | − | 1.01875e7i | −0.133747 | − | 0.889988i | ||||
\(667\) | 486164. | + | 486164.i | 0.0423125 | + | 0.0423125i | ||||
\(668\) | 9.09185e6 | − | 2.79577e6i | 0.788335 | − | 0.242415i | ||||
\(669\) | −5.23091e6 | + | 5.23091e6i | −0.451869 | + | 0.451869i | ||||
\(670\) | 5.07595e6 | − | 6.87139e6i | 0.436848 | − | 0.591368i | ||||
\(671\) | 1.27790e7 | 1.09570 | ||||||||
\(672\) | −1.52957e6 | + | 1.41303e6i | −0.130661 | + | 0.120706i | ||||
\(673\) | −9.64151e6 | −0.820554 | −0.410277 | − | 0.911961i | \(-0.634568\pi\) | ||||
−0.410277 | + | 0.911961i | \(0.634568\pi\) | |||||||
\(674\) | −8.63877e6 | + | 1.16944e7i | −0.732491 | + | 0.991583i | ||||
\(675\) | −2.07046e6 | + | 2.07046e6i | −0.174907 | + | 0.174907i | ||||
\(676\) | −131291. | + | 40372.3i | −0.0110501 | + | 0.00339795i | ||||
\(677\) | 7.87407e6 | + | 7.87407e6i | 0.660279 | + | 0.660279i | 0.955446 | − | 0.295167i | \(-0.0953752\pi\) |
−0.295167 | + | 0.955446i | \(0.595375\pi\) | |||||||
\(678\) | −700296. | − | 4.65997e6i | −0.0585069 | − | 0.389322i | ||||
\(679\) | 1.63529e6i | 0.136119i | ||||||||
\(680\) | 50831.2 | + | 105907.i | 0.00421558 | + | 0.00878318i | ||||
\(681\) | 6.35584e6i | 0.525176i | ||||||||
\(682\) | 1.37936e7 | − | 2.07289e6i | 1.13558 | − | 0.170653i | ||||
\(683\) | −6.41872e6 | − | 6.41872e6i | −0.526498 | − | 0.526498i | 0.393028 | − | 0.919526i | \(-0.371427\pi\) |
−0.919526 | + | 0.393028i | \(0.871427\pi\) | |||||||
\(684\) | 1.40834e7 | − | 2.65908e7i | 1.15098 | − | 2.17316i | ||||
\(685\) | −5.95980e6 | + | 5.95980e6i | −0.485294 | + | 0.485294i | ||||
\(686\) | −2.11607e6 | − | 1.56316e6i | −0.171680 | − | 0.126821i | ||||
\(687\) | −2.44778e7 | −1.97870 | ||||||||
\(688\) | −1.60143e7 | − | 3.05906e6i | −1.28984 | − | 0.246386i | ||||
\(689\) | 1.33031e7 | 1.06759 | ||||||||
\(690\) | −4.39690e6 | − | 3.24803e6i | −0.351580 | − | 0.259715i | ||||
\(691\) | 5.22227e6 | − | 5.22227e6i | 0.416068 | − | 0.416068i | −0.467778 | − | 0.883846i | \(-0.654945\pi\) |
0.883846 | + | 0.467778i | \(0.154945\pi\) | |||||||
\(692\) | −7.51662e6 | − | 3.98105e6i | −0.596702 | − | 0.316033i | ||||
\(693\) | −1.30250e6 | − | 1.30250e6i | −0.103026 | − | 0.103026i | ||||
\(694\) | 1.01446e7 | − | 1.52451e6i | 0.799529 | − | 0.120152i | ||||
\(695\) | − | 6.85562e6i | − | 0.538375i | ||||||
\(696\) | −712344. | + | 2.02724e6i | −0.0557400 | + | 0.158629i | ||||
\(697\) | 455865.i | 0.0355430i | ||||||||
\(698\) | 1.05607e6 | + | 7.02737e6i | 0.0820451 | + | 0.545952i | ||||
\(699\) | −1.56207e7 | − | 1.56207e7i | −1.20922 | − | 1.20922i | ||||
\(700\) | 81802.0 | + | 266021.i | 0.00630985 | + | 0.0205197i | ||||
\(701\) | 6.26872e6 | − | 6.26872e6i | 0.481819 | − | 0.481819i | −0.423894 | − | 0.905712i | \(-0.639337\pi\) |
0.905712 | + | 0.423894i | \(0.139337\pi\) | |||||||
\(702\) | −9.65037e6 | + | 1.30638e7i | −0.739096 | + | 1.00052i | ||||
\(703\) | 9.50963e6 | 0.725730 | ||||||||
\(704\) | −1.11781e6 | − | 1.01601e7i | −0.0850038 | − | 0.772624i | ||||
\(705\) | 1.09531e7 | 0.829974 | ||||||||
\(706\) | 2.71106e6 | − | 3.67000e6i | 0.204705 | − | 0.277111i | ||||
\(707\) | 598848. | − | 598848.i | 0.0450576 | − | 0.0450576i | ||||
\(708\) | −8.40805e6 | − | 2.73430e7i | −0.630394 | − | 2.05004i | ||||
\(709\) | −9.04563e6 | − | 9.04563e6i | −0.675808 | − | 0.675808i | 0.283241 | − | 0.959049i | \(-0.408590\pi\) |
−0.959049 | + | 0.283241i | \(0.908590\pi\) | |||||||
\(710\) | −852964. | − | 5.67587e6i | −0.0635016 | − | 0.422558i | ||||
\(711\) | − | 3.69715e7i | − | 2.74280i | ||||||
\(712\) | −3.07888e6 | + | 8.76209e6i | −0.227611 | + | 0.647750i | ||||
\(713\) | 1.18278e7i | 0.871326i | ||||||||
\(714\) | −52201.5 | + | 7844.80i | −0.00383211 | + | 0.000575886i | ||||
\(715\) | 3.37942e6 | + | 3.37942e6i | 0.247216 | + | 0.247216i | ||||
\(716\) | 1.47222e7 | + | 7.79735e6i | 1.07322 | + | 0.568414i | ||||
\(717\) | 2.28167e7 | − | 2.28167e7i | 1.65751 | − | 1.65751i | ||||
\(718\) | 1.41967e7 | + | 1.04872e7i | 1.02772 | + | 0.759186i | ||||
\(719\) | 6.51627e6 | 0.470085 | 0.235043 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235043 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(720\) | 2.03829e6 | − | 1.06705e7i | 0.146532 | − | 0.767103i | ||||
\(721\) | −1.20325e6 | −0.0862024 | ||||||||
\(722\) | 1.10749e7 | + | 8.18112e6i | 0.790673 | + | 0.584077i | ||||
\(723\) | −1.34907e7 | + | 1.34907e7i | −0.959815 | + | 0.959815i | ||||
\(724\) | 1.67225e6 | − | 3.15738e6i | 0.118565 | − | 0.223862i | ||||
\(725\) | 203071. | + | 203071.i | 0.0143484 | + | 0.0143484i | ||||
\(726\) | −9.21238e6 | + | 1.38443e6i | −0.648680 | + | 0.0974829i | ||||
\(727\) | − | 2.20343e7i | − | 1.54619i | −0.634290 | − | 0.773095i | \(-0.718707\pi\) | ||
0.634290 | − | 0.773095i | \(-0.281293\pi\) | |||||||
\(728\) | 667995. | + | 1.39177e6i | 0.0467138 | + | 0.0973282i | ||||
\(729\) | − | 2.18098e7i | − | 1.51996i | ||||||
\(730\) | −18328.8 | − | 121965.i | −0.00127300 | − | 0.00847088i | ||||
\(731\) | −292247. | − | 292247.i | −0.0202282 | − | 0.0202282i | ||||
\(732\) | −3.23700e7 | + | 9.95385e6i | −2.23288 | + | 0.686615i | ||||
\(733\) | 3.96665e6 | − | 3.96665e6i | 0.272687 | − | 0.272687i | −0.557494 | − | 0.830181i | \(-0.688237\pi\) |
0.830181 | + | 0.557494i | \(0.188237\pi\) | |||||||
\(734\) | 7.96554e6 | − | 1.07831e7i | 0.545726 | − | 0.738757i | ||||
\(735\) | 1.07294e7 | 0.732583 | ||||||||
\(736\) | 8.66064e6 | + | 343002.i | 0.589325 | + | 0.0233400i | ||||
\(737\) | −1.88431e7 | −1.27786 | ||||||||
\(738\) | 2.50481e7 | − | 3.39080e7i | 1.69291 | − | 2.29172i | ||||
\(739\) | 1.60917e7 | − | 1.60917e7i | 1.08391 | − | 1.08391i | 0.0877647 | − | 0.996141i | \(-0.472028\pi\) |
0.996141 | − | 0.0877647i | \(-0.0279724\pi\) | |||||||
\(740\) | 3.28161e6 | − | 1.00911e6i | 0.220297 | − | 0.0677419i | ||||
\(741\) | −2.48064e7 | − | 2.48064e7i | −1.65966 | − | 1.65966i | ||||
\(742\) | −253938. | − | 1.68978e6i | −0.0169324 | − | 0.112673i | ||||
\(743\) | 9.94157e6i | 0.660667i | 0.943864 | + | 0.330334i | \(0.107161\pi\) | ||||
−0.943864 | + | 0.330334i | \(0.892839\pi\) | |||||||
\(744\) | −3.33254e7 | + | 1.59949e7i | −2.20721 | + | 1.05937i | ||||
\(745\) | 7.73998e6i | 0.510916i | ||||||||
\(746\) | −4.69093e6 | + | 704949.i | −0.308612 | + | 0.0463779i | ||||
\(747\) | 2.67509e7 | + | 2.67509e7i | 1.75403 | + | 1.75403i | ||||
\(748\) | 121275. | − | 228979.i | 0.00792534 | − | 0.0149638i | ||||
\(749\) | −96810.6 | + | 96810.6i | −0.00630548 | + | 0.00630548i | ||||
\(750\) | −1.83659e6 | − | 1.35670e6i | −0.119223 | − | 0.0880707i | ||||
\(751\) | 1.68342e7 | 1.08916 | 0.544582 | − | 0.838708i | \(-0.316688\pi\) | ||||
0.544582 | + | 0.838708i | \(0.316688\pi\) | |||||||
\(752\) | −1.43662e7 | + | 9.75797e6i | −0.926396 | + | 0.629238i | ||||
\(753\) | 6.58268e6 | 0.423073 | ||||||||
\(754\) | 1.28130e6 | + | 946508.i | 0.0820773 | + | 0.0606312i | ||||
\(755\) | −7.08140e6 | + | 7.08140e6i | −0.452118 | + | 0.452118i | ||||
\(756\) | 1.84359e6 | + | 976429.i | 0.117317 | + | 0.0621350i | ||||
\(757\) | −9.43078e6 | − | 9.43078e6i | −0.598147 | − | 0.598147i | 0.341672 | − | 0.939819i | \(-0.389007\pi\) |
−0.939819 | + | 0.341672i | \(0.889007\pi\) | |||||||
\(758\) | −1.23257e7 | + | 1.85230e6i | −0.779183 | + | 0.117095i | ||||
\(759\) | 1.20575e7i | 0.759716i | ||||||||
\(760\) | 9.46085e6 | + | 3.32442e6i | 0.594150 | + | 0.208776i | ||||
\(761\) | − | 7.83368e6i | − | 0.490348i | −0.969479 | − | 0.245174i | \(-0.921155\pi\) | ||
0.969479 | − | 0.245174i | \(-0.0788450\pi\) | |||||||
\(762\) | 6.78729e6 | + | 4.51646e7i | 0.423457 | + | 2.81780i | ||||
\(763\) | 1.62838e6 | + | 1.62838e6i | 0.101261 | + | 0.101261i | ||||
\(764\) | −1.51293e6 | − | 4.92005e6i | −0.0937745 | − | 0.304955i | ||||
\(765\) | 194728. | − | 194728.i | 0.0120302 | − | 0.0120302i | ||||
\(766\) | 5.83648e6 | − | 7.90092e6i | 0.359401 | − | 0.486526i | ||||
\(767\) | −2.12076e7 | −1.30168 | ||||||||
\(768\) | 1.07455e7 | + | 2.48656e7i | 0.657389 | + | 1.52123i | ||||
\(769\) | 3.02031e7 | 1.84177 | 0.920887 | − | 0.389830i | \(-0.127466\pi\) | ||||
0.920887 | + | 0.389830i | \(0.127466\pi\) | |||||||
\(770\) | 364749. | − | 493766.i | 0.0221701 | − | 0.0300119i | ||||
\(771\) | −2.44192e7 | + | 2.44192e7i | −1.47943 | + | 1.47943i | ||||
\(772\) | −5.11288e6 | − | 1.66271e7i | −0.308761 | − | 1.00409i | ||||
\(773\) | −1.06293e6 | − | 1.06293e6i | −0.0639818 | − | 0.0639818i | 0.674392 | − | 0.738374i | \(-0.264406\pi\) |
−0.738374 | + | 0.674392i | \(0.764406\pi\) | |||||||
\(774\) | 5.67991e6 | + | 3.77957e7i | 0.340792 | + | 2.26773i | ||||
\(775\) | 4.94048e6i | 0.295471i | ||||||||
\(776\) | 2.00694e7 | + | 7.05210e6i | 1.19641 | + | 0.420402i | ||||
\(777\) | 1.54276e6i | 0.0916741i | ||||||||
\(778\) | −1.31608e7 | + | 1.97779e6i | −0.779529 | + | 0.117147i | ||||
\(779\) | 2.75164e7 | + | 2.75164e7i | 1.62461 | + | 1.62461i | ||||
\(780\) | −1.11926e7 | − | 5.92797e6i | −0.658709 | − | 0.348875i | ||||
\(781\) | −8.95188e6 | + | 8.95188e6i | −0.525154 | + | 0.525154i | ||||
\(782\) | 176728. | + | 130550.i | 0.0103345 | + | 0.00763415i | ||||
\(783\) | 2.15271e6 | 0.125482 | ||||||||
\(784\) | −1.40728e7 | + | 9.55867e6i | −0.817691 | + | 0.555402i | ||||
\(785\) | −8.62853e6 | −0.499761 | ||||||||
\(786\) | −2.41678e7 | − | 1.78530e7i | −1.39534 | − | 1.03075i | ||||
\(787\) | −7.28531e6 | + | 7.28531e6i | −0.419287 | + | 0.419287i | −0.884958 | − | 0.465671i | \(-0.845813\pi\) |
0.465671 | + | 0.884958i | \(0.345813\pi\) | |||||||
\(788\) | −1.29029e6 | + | 2.43619e6i | −0.0740236 | + | 0.139764i | ||||
\(789\) | 4.85162e6 | + | 4.85162e6i | 0.277456 | + | 0.277456i | ||||
\(790\) | 1.21844e7 | − | 1.83107e6i | 0.694605 | − | 0.104385i | ||||
\(791\) | 448729.i | 0.0255002i | ||||||||
\(792\) | −2.16022e7 | + | 1.03682e7i | −1.22373 | + | 0.587343i | ||||
\(793\) | 2.51066e7i | 1.41777i | ||||||||
\(794\) | −4.52255e6 | − | 3.00944e7i | −0.254585 | − | 1.69408i | ||||
\(795\) | 9.91293e6 | + | 9.91293e6i | 0.556268 | + | 0.556268i | ||||
\(796\) | −2.88648e7 | + | 8.87601e6i | −1.61468 | + | 0.496518i | ||||
\(797\) | 6.89591e6 | − | 6.89591e6i | 0.384544 | − | 0.384544i | −0.488192 | − | 0.872736i | \(-0.662344\pi\) |
0.872736 | + | 0.488192i | \(0.162344\pi\) | |||||||
\(798\) | −2.67742e6 | + | 3.62445e6i | −0.148836 | + | 0.201482i | ||||
\(799\) | −440246. | −0.0243965 | ||||||||
\(800\) | 3.61755e6 | + | 143272.i | 0.199843 | + | 0.00791473i | ||||
\(801\) | 2.17716e7 | 1.19897 | ||||||||
\(802\) | −9.06413e6 | + | 1.22702e7i | −0.497611 | + | 0.673623i | ||||
\(803\) | −192361. | + | 192361.i | −0.0105276 | + | 0.0105276i | ||||
\(804\) | 4.77309e7 | − | 1.46774e7i | 2.60411 | − | 0.800770i | ||||
\(805\) | 368082. | + | 368082.i | 0.0200196 | + | 0.0200196i | ||||
\(806\) | 4.07256e6 | + | 2.71000e7i | 0.220816 | + | 1.46937i | ||||
\(807\) | 1.91906e7i | 1.03730i | ||||||||
\(808\) | −4.76696e6 | − | 9.93197e6i | −0.256870 | − | 0.535189i | ||||
\(809\) | − | 2.38523e7i | − | 1.28132i | −0.767824 | − | 0.640661i | \(-0.778660\pi\) | ||
0.767824 | − | 0.640661i | \(-0.221340\pi\) | |||||||
\(810\) | −2.50455e6 | + | 376381.i | −0.134127 | + | 0.0201565i | ||||
\(811\) | 1.58590e7 | + | 1.58590e7i | 0.846690 | + | 0.846690i | 0.989719 | − | 0.143028i | \(-0.0456841\pi\) |
−0.143028 | + | 0.989719i | \(0.545684\pi\) | |||||||
\(812\) | 95768.2 | − | 180820.i | 0.00509719 | − | 0.00962400i | ||||
\(813\) | 7.38299e6 | − | 7.38299e6i | 0.391747 | − | 0.391747i | ||||
\(814\) | −6.09106e6 | − | 4.49952e6i | −0.322205 | − | 0.238016i | ||||
\(815\) | −4.59057e6 | −0.242088 | ||||||||
\(816\) | −128840. | + | 674483.i | −0.00677370 | + | 0.0354606i | ||||
\(817\) | −3.52807e7 | −1.84919 | ||||||||
\(818\) | −2.03283e7 | − | 1.50167e7i | −1.06223 | − | 0.784676i | ||||
\(819\) | 2.55901e6 | − | 2.55901e6i | 0.133310 | − | 0.133310i | ||||
\(820\) | 1.24154e7 | + | 6.57559e6i | 0.644799 | + | 0.341507i | ||||
\(821\) | 6.21577e6 | + | 6.21577e6i | 0.321838 | + | 0.321838i | 0.849472 | − | 0.527634i | \(-0.176921\pi\) |
−0.527634 | + | 0.849472i | \(0.676921\pi\) | |||||||
\(822\) | −4.87203e7 | + | 7.32164e6i | −2.51496 | + | 0.377945i | ||||
\(823\) | 5.28235e6i | 0.271849i | 0.990719 | + | 0.135924i | \(0.0434004\pi\) | ||||
−0.990719 | + | 0.135924i | \(0.956600\pi\) | |||||||
\(824\) | −5.18898e6 | + | 1.47672e7i | −0.266234 | + | 0.757668i | ||||
\(825\) | 5.03640e6i | 0.257624i | ||||||||
\(826\) | 404824. | + | 2.69382e6i | 0.0206451 | + | 0.137378i | ||||
\(827\) | 2.61896e7 | + | 2.61896e7i | 1.33157 | + | 1.33157i | 0.903962 | + | 0.427613i | \(0.140645\pi\) |
0.427613 | + | 0.903962i | \(0.359355\pi\) | |||||||
\(828\) | −5.97203e6 | − | 1.94211e7i | −0.302723 | − | 0.984458i | ||||
\(829\) | 4.93710e6 | − | 4.93710e6i | 0.249509 | − | 0.249509i | −0.571260 | − | 0.820769i | \(-0.693545\pi\) |
0.820769 | + | 0.571260i | \(0.193545\pi\) | |||||||
\(830\) | −7.49123e6 | + | 1.01410e7i | −0.377449 | + | 0.510958i | ||||
\(831\) | 1.31346e7 | 0.659802 | ||||||||
\(832\) | 1.99614e7 | − | 2.19615e6i | 0.999731 | − | 0.109990i | ||||
\(833\) | −431254. | −0.0215338 | ||||||||
\(834\) | 2.38107e7 | − | 3.22328e7i | 1.18538 | − | 1.60466i | ||||
\(835\) | 5.25468e6 | − | 5.25468e6i | 0.260814 | − | 0.260814i | ||||
\(836\) | −6.50112e6 | − | 2.11417e7i | −0.321716 | − | 1.04622i | ||||
\(837\) | 2.61865e7 | + | 2.61865e7i | 1.29200 | + | 1.29200i | ||||
\(838\) | 1.40218e6 | + | 9.33050e6i | 0.0689752 | + | 0.458981i | ||||
\(839\) | − | 4.12702e6i | − | 0.202410i | −0.994866 | − | 0.101205i | \(-0.967730\pi\) | ||
0.994866 | − | 0.101205i | \(-0.0322698\pi\) | |||||||
\(840\) | −539326. | + | 1.53485e6i | −0.0263726 | + | 0.0750530i | ||||
\(841\) | 2.03000e7i | 0.989706i | ||||||||
\(842\) | 6.69440e6 | − | 1.00603e6i | 0.325410 | − | 0.0489024i | ||||
\(843\) | 3.87242e7 | + | 3.87242e7i | 1.87678 | + | 1.87678i | ||||
\(844\) | −2.42366e6 | − | 1.28365e6i | −0.117116 | − | 0.0620285i | ||||
\(845\) | −75880.3 | + | 75880.3i | −0.00365584 | + | 0.00365584i | ||||
\(846\) | 3.27462e7 | + | 2.41899e7i | 1.57302 | + | 1.16200i | ||||
\(847\) | 887101. | 0.0424878 | ||||||||
\(848\) | −2.18332e7 | − | 4.17059e6i | −1.04262 | − | 0.199162i | ||||
\(849\) | 2.35601e7 | 1.12178 | ||||||||
\(850\) | 73819.2 | + | 54530.9i | 0.00350447 | + | 0.00258878i | ||||
\(851\) | 4.54064e6 | − | 4.54064e6i | 0.214928 | − | 0.214928i | ||||
\(852\) | 1.57028e7 | − | 2.96485e7i | 0.741104 | − | 1.39928i | ||||
\(853\) | −1.19481e7 | − | 1.19481e7i | −0.562244 | − | 0.562244i | 0.367700 | − | 0.929944i | \(-0.380145\pi\) |
−0.929944 | + | 0.367700i | \(0.880145\pi\) | |||||||
\(854\) | 3.18907e6 | − | 479250.i | 0.149630 | − | 0.0224863i | ||||
\(855\) | − | 2.35079e7i | − | 1.09976i | ||||||
\(856\) | 770634. | + | 1.60562e6i | 0.0359471 | + | 0.0748958i | ||||
\(857\) | 1.09807e7i | 0.510712i | 0.966847 | + | 0.255356i | \(0.0821927\pi\) | ||||
−0.966847 | + | 0.255356i | \(0.917807\pi\) | |||||||
\(858\) | 4.15163e6 | + | 2.76261e7i | 0.192531 | + | 1.28116i | ||||
\(859\) | −2.41728e7 | − | 2.41728e7i | −1.11775 | − | 1.11775i | −0.992071 | − | 0.125676i | \(-0.959890\pi\) |
−0.125676 | − | 0.992071i | \(-0.540110\pi\) | |||||||
\(860\) | −1.21748e7 | + | 3.74377e6i | −0.561325 | + | 0.172609i | ||||
\(861\) | −4.46404e6 | + | 4.46404e6i | −0.205220 | + | 0.205220i | ||||
\(862\) | 1.18130e7 | − | 1.59915e7i | 0.541493 | − | 0.733027i | ||||
\(863\) | −4.01497e7 | −1.83508 | −0.917541 | − | 0.397642i | \(-0.869828\pi\) | ||||
−0.917541 | + | 0.397642i | \(0.869828\pi\) | |||||||
\(864\) | 1.99338e7 | − | 1.84150e7i | 0.908461 | − | 0.839243i | ||||
\(865\) | −6.64514e6 | −0.301970 | ||||||||
\(866\) | 8.42500e6 | − | 1.14050e7i | 0.381746 | − | 0.516776i | ||||
\(867\) | 2.59240e7 | − | 2.59240e7i | 1.17126 | − | 1.17126i | ||||
\(868\) | 3.36453e6 | − | 1.03460e6i | 0.151574 | − | 0.0466095i | ||||
\(869\) | −1.92171e7 | − | 1.92171e7i | −0.863253 | − | 0.863253i | ||||
\(870\) | 249474. | + | 1.66007e6i | 0.0111745 | + | 0.0743581i | ||||
\(871\) | − | 3.70207e7i | − | 1.65348i | ||||||
\(872\) | 2.70069e7 | − | 1.29622e7i | 1.20277 | − | 0.577283i | ||||
\(873\) | − | 4.98674e7i | − | 2.21453i | ||||||
\(874\) | 1.85476e7 | − | 2.78731e6i | 0.821313 | − | 0.123426i | ||||
\(875\) | 153748. | + | 153748.i | 0.00678874 | + | 0.00678874i | ||||
\(876\) | 337429. | − | 637098.i | 0.0148567 | − | 0.0280509i | ||||
\(877\) | −1.59056e7 | + | 1.59056e7i | −0.698313 | + | 0.698313i | −0.964047 | − | 0.265734i | \(-0.914386\pi\) |
0.265734 | + | 0.964047i | \(0.414386\pi\) | |||||||
\(878\) | −3.35120e7 | − | 2.47556e7i | −1.46711 | − | 1.08377i | ||||
\(879\) | −2.96438e7 | −1.29408 | ||||||||
\(880\) | −4.48686e6 | − | 6.60579e6i | −0.195315 | − | 0.287553i | ||||
\(881\) | 1.28495e7 | 0.557760 | 0.278880 | − | 0.960326i | \(-0.410037\pi\) | ||||
0.278880 | + | 0.960326i | \(0.410037\pi\) | |||||||
\(882\) | 3.20773e7 | + | 2.36958e7i | 1.38844 | + | 1.02565i | ||||
\(883\) | 1.73039e7 | − | 1.73039e7i | 0.746863 | − | 0.746863i | −0.227025 | − | 0.973889i | \(-0.572900\pi\) |
0.973889 | + | 0.227025i | \(0.0729001\pi\) | |||||||
\(884\) | 449871. | + | 238267.i | 0.0193623 | + | 0.0102549i | ||||
\(885\) | −1.58030e7 | − | 1.58030e7i | −0.678239 | − | 0.678239i | ||||
\(886\) | −5.59436e6 | + | 840716.i | −0.239423 | + | 0.0359803i | ||||
\(887\) | − | 5.87969e6i | − | 0.250926i | −0.992098 | − | 0.125463i | \(-0.959958\pi\) | ||
0.992098 | − | 0.125463i | \(-0.0400416\pi\) | |||||||
\(888\) | 1.89338e7 | + | 6.65310e6i | 0.805761 | + | 0.283134i | ||||
\(889\) | − | 4.34910e6i | − | 0.184563i | ||||||
\(890\) | 1.07827e6 | + | 7.17513e6i | 0.0456303 | + | 0.303637i | ||||
\(891\) | 3.95013e6 | + | 3.95013e6i | 0.166693 | + | 0.166693i | ||||
\(892\) | −2.69336e6 | − | 8.75882e6i | −0.113340 | − | 0.368581i | ||||
\(893\) | −2.65736e7 | + | 2.65736e7i | −1.11512 | + | 1.11512i | ||||
\(894\) | −2.68822e7 | + | 3.63908e7i | −1.12492 | + | 1.52282i | ||||
\(895\) | 1.30153e7 | 0.543120 | ||||||||
\(896\) | −659993. | − | 2.49360e6i | −0.0274643 | − | 0.103766i | ||||
\(897\) | −2.36890e7 | −0.983029 | ||||||||
\(898\) | 1.21105e7 | − | 1.63941e7i | 0.501153 | − | 0.678418i | ||||
\(899\) | 2.56837e6 | − | 2.56837e6i | 0.105988 | − | 0.105988i | ||||
\(900\) | −2.49452e6 | − | 8.11219e6i | −0.102655 | − | 0.333835i | ||||
\(901\) | −398437. | − | 398437.i | −0.0163511 | − | 0.0163511i | ||||
\(902\) | −4.60519e6 | − | 3.06442e7i | −0.188465 | − | 1.25410i | ||||
\(903\) | − | 5.72364e6i | − | 0.233589i | ||||||
\(904\) | 5.50710e6 | + | 1.93512e6i | 0.224131 | + | 0.0787567i | ||||
\(905\) | − | 2.79131e6i | − | 0.113289i | ||||||
\(906\) | −5.78892e7 | + | 8.69953e6i | −2.34302 | + | 0.352107i | ||||
\(907\) | −7.51633e6 | − | 7.51633e6i | −0.303380 | − | 0.303380i | 0.538954 | − | 0.842335i | \(-0.318819\pi\) |
−0.842335 | + | 0.538954i | \(0.818819\pi\) | |||||||
\(908\) | −6.95750e6 | − | 3.68493e6i | −0.280052 | − | 0.148325i | ||||
\(909\) | −1.82616e7 | + | 1.82616e7i | −0.733043 | + | 0.733043i | ||||
\(910\) | 970091. | + | 716615.i | 0.0388337 | + | 0.0286868i | ||||
\(911\) | −6.38354e6 | −0.254839 | −0.127419 | − | 0.991849i | \(-0.540669\pi\) | ||||
−0.127419 | + | 0.991849i | \(0.540669\pi\) | |||||||
\(912\) | 3.29355e7 | + | 4.84893e7i | 1.31123 | + | 1.93045i | ||||
\(913\) | 2.78092e7 | 1.10411 | ||||||||
\(914\) | −1.95271e7 | − | 1.44249e7i | −0.773167 | − | 0.571145i | ||||
\(915\) | −1.87084e7 | + | 1.87084e7i | −0.738727 | + | 0.738727i | ||||
\(916\) | 1.41915e7 | − | 2.67949e7i | 0.558842 | − | 1.05515i | ||||
\(917\) | 2.02318e6 | + | 2.02318e6i | 0.0794533 | + | 0.0794533i | ||||
\(918\) | 680305. | − | 102236.i | 0.0266438 | − | 0.00400401i | ||||
\(919\) | 3.04004e7i | 1.18738i | 0.804693 | + | 0.593692i | \(0.202330\pi\) | ||||
−0.804693 | + | 0.593692i | \(0.797670\pi\) | |||||||
\(920\) | 6.10469e6 | − | 2.93001e6i | 0.237790 | − | 0.114130i | ||||
\(921\) | 8.44980e6i | 0.328245i | ||||||||
\(922\) | 3.71799e6 | + | 2.47406e7i | 0.144039 | + | 0.958479i | ||||
\(923\) | −1.75876e7 | − | 1.75876e7i | −0.679519 | − | 0.679519i | ||||
\(924\) | 3.42985e6 | − | 1.05469e6i | 0.132159 | − | 0.0406391i | ||||
\(925\) | 1.89663e6 | − | 1.89663e6i | 0.0728832 | − | 0.0728832i | ||||
\(926\) | 1.07261e7 | − | 1.45201e7i | 0.411070 | − | 0.556471i | ||||
\(927\) | 3.66928e7 | 1.40243 | ||||||||
\(928\) | −1.80615e6 | − | 1.95511e6i | −0.0688466 | − | 0.0745248i | ||||
\(929\) | −4.62504e7 | −1.75823 | −0.879116 | − | 0.476609i | \(-0.841866\pi\) | ||||
−0.879116 | + | 0.476609i | \(0.841866\pi\) | |||||||
\(930\) | −1.71591e7 | + | 2.32285e7i | −0.650559 | + | 0.880671i | ||||
\(931\) | −2.60309e7 | + | 2.60309e7i | −0.984271 | + | 0.984271i | ||||
\(932\) | 2.61557e7 | − | 8.04296e6i | 0.986342 | − | 0.303303i | ||||
\(933\) | −1.97886e7 | − | 1.97886e7i | −0.744237 | − | 0.744237i | ||||
\(934\) | 2.21030e6 | + | 1.47080e7i | 0.0829058 | + | 0.551679i | ||||
\(935\) | − | 202431.i | − | 0.00757267i | ||||||
\(936\) | −2.03702e7 | − | 4.24414e7i | −0.759988 | − | 1.58344i | ||||
\(937\) | 3.17166e6i | 0.118015i | 0.998258 | + | 0.0590075i | \(0.0187936\pi\) | ||||
−0.998258 | + | 0.0590075i | \(0.981206\pi\) | |||||||
\(938\) | −4.70241e6 | + | 706674.i | −0.174507 | + | 0.0262248i | ||||
\(939\) | −4.42980e7 | − | 4.42980e7i | −1.63953 | − | 1.63953i | ||||
\(940\) | −6.35029e6 | + | 1.19900e7i | −0.234409 | + | 0.442586i | ||||
\(941\) | −2.61002e7 | + | 2.61002e7i | −0.960880 | + | 0.960880i | −0.999263 | − | 0.0383828i | \(-0.987779\pi\) |
0.0383828 | + | 0.999263i | \(0.487779\pi\) | |||||||
\(942\) | −4.05684e7 | − | 2.99682e7i | −1.48957 | − | 1.10036i | ||||
\(943\) | 2.62770e7 | 0.962269 | ||||||||
\(944\) | 3.48061e7 | + | 6.64869e6i | 1.27123 | + | 0.242832i | ||||
\(945\) | 1.62985e6 | 0.0593701 | ||||||||
\(946\) | 2.25978e7 | + | 1.66932e7i | 0.820991 | + | 0.606473i | ||||
\(947\) | −2.58430e7 | + | 2.58430e7i | −0.936412 | + | 0.936412i | −0.998096 | − | 0.0616833i | \(-0.980353\pi\) |
0.0616833 | + | 0.998096i | \(0.480353\pi\) | |||||||
\(948\) | 6.36468e7 | + | 3.37095e7i | 2.30015 | + | 1.21823i | ||||
\(949\) | −377929. | − | 377929.i | −0.0136221 | − | 0.0136221i | ||||
\(950\) | 7.74733e6 | − | 1.16426e6i | 0.278511 | − | 0.0418544i | ||||
\(951\) | − | 2.19608e7i | − | 0.787403i | ||||||
\(952\) | 21677.5 | − | 61691.3i | 0.000775205 | − | 0.00220613i | ||||
\(953\) | − | 3.68799e7i | − | 1.31540i | −0.753280 | − | 0.657700i | \(-0.771529\pi\) | ||
0.753280 | − | 0.657700i | \(-0.228471\pi\) | |||||||
\(954\) | 7.74373e6 | + | 5.15290e7i | 0.275473 | + | 1.83308i | ||||
\(955\) | −2.84357e6 | − | 2.84357e6i | −0.100892 | − | 0.100892i | ||||
\(956\) | 1.17482e7 | + | 3.82051e7i | 0.415743 | + | 1.35200i | ||||
\(957\) | 2.61823e6 | − | 2.61823e6i | 0.0924120 | − | 0.0924120i | ||||
\(958\) | −4.80046e6 | + | 6.49845e6i | −0.168993 | + | 0.228768i | ||||
\(959\) | 4.69149e6 | 0.164727 | ||||||||
\(960\) | 1.65109e7 | + | 1.32379e7i | 0.578219 | + | 0.463599i | ||||
\(961\) | 3.38563e7 | 1.18258 | ||||||||
\(962\) | 8.84012e6 | − | 1.19670e7i | 0.307979 | − | 0.416915i | ||||
\(963\) | 2.95220e6 | − | 2.95220e6i | 0.102584 | − | 0.102584i | ||||
\(964\) | −6.94625e6 | − | 2.25892e7i | −0.240745 | − | 0.782904i | ||||
\(965\) | −9.60973e6 | − | 9.60973e6i | −0.332195 | − | 0.332195i | ||||
\(966\) | 452190. | + | 3.00901e6i | 0.0155912 | + | 0.103748i | ||||
\(967\) | − | 5.08603e7i | − | 1.74909i | −0.484941 | − | 0.874547i | \(-0.661159\pi\) | ||
0.484941 | − | 0.874547i | \(-0.338841\pi\) | |||||||
\(968\) | 3.82558e6 | − | 1.08871e7i | 0.131223 | − | 0.373442i | ||||
\(969\) | 1.48594e6i | 0.0508382i | ||||||||
\(970\) | 1.64345e7 | − | 2.46975e6i | 0.560823 | − | 0.0842799i | ||||
\(971\) | 1.70236e7 | + | 1.70236e7i | 0.579434 | + | 0.579434i | 0.934747 | − | 0.355313i | \(-0.115626\pi\) |
−0.355313 | + | 0.934747i | \(0.615626\pi\) | |||||||
\(972\) | 1.91106e7 | + | 1.01216e7i | 0.648798 | + | 0.343625i | ||||
\(973\) | −2.69834e6 | + | 2.69834e6i | −0.0913722 | + | 0.0913722i | ||||
\(974\) | −3.00537e7 | − | 2.22009e7i | −1.01508 | − | 0.749848i | ||||
\(975\) | −9.89492e6 | −0.333350 | ||||||||
\(976\) | 7.87103e6 | − | 4.12051e7i | 0.264489 | − | 1.38461i | ||||
\(977\) | −7.72986e6 | −0.259081 | −0.129540 | − | 0.991574i | \(-0.541350\pi\) | ||||
−0.129540 | + | 0.991574i | \(0.541350\pi\) | |||||||
\(978\) | −2.15833e7 | − | 1.59438e7i | −0.721557 | − | 0.533021i | ||||
\(979\) | 1.13165e7 | − | 1.13165e7i | 0.377359 | − | 0.377359i | ||||
\(980\) | −6.22058e6 | + | 1.17451e7i | −0.206903 | + | 0.390652i | ||||
\(981\) | −4.96567e7 | − | 4.96567e7i | −1.64742 | − | 1.64742i | ||||
\(982\) | 521443. | − | 78361.9i | 0.0172555 | − | 0.00259314i | ||||
\(983\) | 2.68033e7i | 0.884717i | 0.896838 | + | 0.442358i | \(0.145858\pi\) | ||||
−0.896838 | + | 0.442358i | \(0.854142\pi\) | |||||||
\(984\) | 3.55347e7 | + | 7.40367e7i | 1.16995 | + | 2.43758i | ||||
\(985\) | 2.15373e6i | 0.0707297i | ||||||||
\(986\) | −10027.3 | − | 66724.3i | −0.000328466 | − | 0.00218571i | ||||
\(987\) | −4.31109e6 | − | 4.31109e6i | −0.140862 | − | 0.140862i | ||||
\(988\) | 4.15367e7 | − | 1.27726e7i | 1.35375 | − | 0.416282i | ||||
\(989\) | −1.68457e7 | + | 1.68457e7i | −0.547645 | + | 0.547645i | ||||
\(990\) | −1.11229e7 | + | 1.50572e7i | −0.360686 | + | 0.488265i | ||||
\(991\) | −1.13975e7 | −0.368661 | −0.184330 | − | 0.982864i | \(-0.559012\pi\) | ||||
−0.184330 | + | 0.982864i | \(0.559012\pi\) | |||||||
\(992\) | 1.81205e6 | − | 4.57535e7i | 0.0584643 | − | 1.47620i | ||||
\(993\) | 1.86658e7 | 0.600723 | ||||||||
\(994\) | −1.89827e6 | + | 2.56971e6i | −0.0609385 | + | 0.0824933i | ||||
\(995\) | −1.66826e7 | + | 1.66826e7i | −0.534202 | + | 0.534202i | ||||
\(996\) | −7.04425e7 | + | 2.16613e7i | −2.25002 | + | 0.691887i | ||||
\(997\) | 8.77758e6 | + | 8.77758e6i | 0.279664 | + | 0.279664i | 0.832975 | − | 0.553311i | \(-0.186636\pi\) |
−0.553311 | + | 0.832975i | \(0.686636\pi\) | |||||||
\(998\) | 3.80502e6 | + | 2.53197e7i | 0.120929 | + | 0.804697i | ||||
\(999\) | − | 2.01057e7i | − | 0.637391i |
(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 | 80.6.l.a.21.13 | ✓ | 80 | |
4.3 | odd | 2 | 320.6.l.a.241.36 | 80 | |||
16.3 | odd | 4 | 320.6.l.a.81.36 | 80 | |||
16.13 | even | 4 | inner | 80.6.l.a.61.13 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.13 | ✓ | 80 | 1.1 | even | 1 | trivial | |
80.6.l.a.61.13 | yes | 80 | 16.13 | even | 4 | inner | |
320.6.l.a.81.36 | 80 | 16.3 | odd | 4 | |||
320.6.l.a.241.36 | 80 | 4.3 | odd | 2 |