Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,7,Mod(7,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(4))
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("25.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.c (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: | \(5.75135209050\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.333061916000256.23 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 90x^{6} - 12x^{5} + 3011x^{4} + 528x^{3} + 41202x^{2} + 17580x + 243850 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(1.22474 + 5.44174i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.7 |
Dual form | 25.7.c.d.18.2 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71525 | − | 2.71525i | −0.339406 | − | 0.339406i | 0.516738 | − | 0.856144i | \(-0.327146\pi\) |
−0.856144 | + | 0.516738i | \(0.827146\pi\) | |||||||
\(3\) | −16.9847 | + | 16.9847i | −0.629064 | + | 0.629064i | −0.947832 | − | 0.318769i | \(-0.896731\pi\) |
0.318769 | + | 0.947832i | \(0.396731\pi\) | |||||||
\(4\) | − | 49.2549i | − | 0.769607i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 92.2354 | 0.427016 | ||||||||
\(7\) | 383.600 | + | 383.600i | 1.11837 | + | 1.11837i | 0.991981 | + | 0.126385i | \(0.0403375\pi\) |
0.126385 | + | 0.991981i | \(0.459663\pi\) | |||||||
\(8\) | −307.515 | + | 307.515i | −0.600615 | + | 0.600615i | ||||
\(9\) | 152.039i | 0.208558i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2402.10 | 1.80473 | 0.902366 | − | 0.430971i | \(-0.141829\pi\) | ||||
0.902366 | + | 0.430971i | \(0.141829\pi\) | |||||||
\(12\) | 836.580 | + | 836.580i | 0.484132 | + | 0.484132i | ||||
\(13\) | −332.065 | + | 332.065i | −0.151145 | + | 0.151145i | −0.778629 | − | 0.627484i | \(-0.784085\pi\) |
0.627484 | + | 0.778629i | \(0.284085\pi\) | |||||||
\(14\) | − | 2083.14i | − | 0.759160i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1482.35 | −0.361902 | ||||||||
\(17\) | −373.542 | − | 373.542i | −0.0760314 | − | 0.0760314i | 0.668068 | − | 0.744100i | \(-0.267121\pi\) |
−0.744100 | + | 0.668068i | \(0.767121\pi\) | |||||||
\(18\) | 412.823 | − | 412.823i | 0.0707859 | − | 0.0707859i | ||||
\(19\) | 7032.37i | 1.02528i | 0.858605 | + | 0.512638i | \(0.171332\pi\) | ||||
−0.858605 | + | 0.512638i | \(0.828668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13030.7 | −1.40705 | ||||||||
\(22\) | −6522.29 | − | 6522.29i | −0.612537 | − | 0.612537i | ||||
\(23\) | 2610.56 | − | 2610.56i | 0.214560 | − | 0.214560i | −0.591641 | − | 0.806201i | \(-0.701520\pi\) |
0.806201 | + | 0.591641i | \(0.201520\pi\) | |||||||
\(24\) | − | 10446.1i | − | 0.755650i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1803.28 | 0.102599 | ||||||||
\(27\) | −14964.2 | − | 14964.2i | −0.760260 | − | 0.760260i | ||||
\(28\) | 18894.1 | − | 18894.1i | 0.860703 | − | 0.860703i | ||||
\(29\) | 13628.5i | 0.558797i | 0.960175 | + | 0.279399i | \(0.0901351\pi\) | ||||
−0.960175 | + | 0.279399i | \(0.909865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10751.8 | 0.360908 | 0.180454 | − | 0.983583i | \(-0.442243\pi\) | ||||
0.180454 | + | 0.983583i | \(0.442243\pi\) | |||||||
\(32\) | 23705.9 | + | 23705.9i | 0.723447 | + | 0.723447i | ||||
\(33\) | −40798.9 | + | 40798.9i | −1.13529 | + | 1.13529i | ||||
\(34\) | 2028.52i | 0.0516110i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7488.65 | 0.160508 | ||||||||
\(37\) | 29901.9 | + | 29901.9i | 0.590327 | + | 0.590327i | 0.937720 | − | 0.347392i | \(-0.112933\pi\) |
−0.347392 | + | 0.937720i | \(0.612933\pi\) | |||||||
\(38\) | 19094.6 | − | 19094.6i | 0.347985 | − | 0.347985i | ||||
\(39\) | − | 11280.1i | − | 0.190159i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60337.8 | 0.875463 | 0.437731 | − | 0.899106i | \(-0.355782\pi\) | ||||
0.437731 | + | 0.899106i | \(0.355782\pi\) | |||||||
\(42\) | 35381.5 | + | 35381.5i | 0.477560 | + | 0.477560i | ||||
\(43\) | −63899.3 | + | 63899.3i | −0.803695 | + | 0.803695i | −0.983671 | − | 0.179976i | \(-0.942398\pi\) |
0.179976 | + | 0.983671i | \(0.442398\pi\) | |||||||
\(44\) | − | 118315.i | − | 1.38893i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14176.6 | −0.145646 | ||||||||
\(47\) | −74307.8 | − | 74307.8i | −0.715716 | − | 0.715716i | 0.252009 | − | 0.967725i | \(-0.418909\pi\) |
−0.967725 | + | 0.252009i | \(0.918909\pi\) | |||||||
\(48\) | 25177.3 | − | 25177.3i | 0.227660 | − | 0.227660i | ||||
\(49\) | 176648.i | 1.50149i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12689.0 | 0.0956572 | ||||||||
\(52\) | 16355.8 | + | 16355.8i | 0.116322 | + | 0.116322i | ||||
\(53\) | 125220. | − | 125220.i | 0.841095 | − | 0.841095i | −0.147906 | − | 0.989001i | \(-0.547253\pi\) |
0.989001 | + | 0.147906i | \(0.0472534\pi\) | |||||||
\(54\) | 81263.0i | 0.516073i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −235925. | −1.34342 | ||||||||
\(57\) | −119443. | − | 119443.i | −0.644964 | − | 0.644964i | ||||
\(58\) | 37004.8 | − | 37004.8i | 0.189659 | − | 0.189659i | ||||
\(59\) | − | 152944.i | − | 0.744693i | −0.928094 | − | 0.372346i | \(-0.878553\pi\) | ||
0.928094 | − | 0.372346i | \(-0.121447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −134851. | −0.594105 | −0.297053 | − | 0.954861i | \(-0.596004\pi\) | ||||
−0.297053 | + | 0.954861i | \(0.596004\pi\) | |||||||
\(62\) | −29193.8 | − | 29193.8i | −0.122494 | − | 0.122494i | ||||
\(63\) | −58322.1 | + | 58322.1i | −0.233244 | + | 0.233244i | ||||
\(64\) | − | 33864.3i | − | 0.129182i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 221558. | 0.770649 | ||||||||
\(67\) | −69010.1 | − | 69010.1i | −0.229450 | − | 0.229450i | 0.583013 | − | 0.812463i | \(-0.301874\pi\) |
−0.812463 | + | 0.583013i | \(0.801874\pi\) | |||||||
\(68\) | −18398.8 | + | 18398.8i | −0.0585143 | + | 0.0585143i | ||||
\(69\) | 88679.1i | 0.269944i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −96191.6 | −0.268758 | −0.134379 | − | 0.990930i | \(-0.542904\pi\) | ||||
−0.134379 | + | 0.990930i | \(0.542904\pi\) | |||||||
\(72\) | −46754.2 | − | 46754.2i | −0.125263 | − | 0.125263i | ||||
\(73\) | −231651. | + | 231651.i | −0.595479 | + | 0.595479i | −0.939106 | − | 0.343627i | \(-0.888344\pi\) |
0.343627 | + | 0.939106i | \(0.388344\pi\) | |||||||
\(74\) | − | 162382.i | − | 0.400721i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 346378. | 0.789060 | ||||||||
\(77\) | 921444. | + | 921444.i | 2.01835 | + | 2.01835i | ||||
\(78\) | −30628.2 | + | 30628.2i | −0.0645412 | + | 0.0645412i | ||||
\(79\) | 28114.8i | 0.0570235i | 0.999593 | + | 0.0285118i | \(0.00907681\pi\) | ||||
−0.999593 | + | 0.0285118i | \(0.990923\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 397489. | 0.747945 | ||||||||
\(82\) | −163832. | − | 163832.i | −0.297137 | − | 0.297137i | ||||
\(83\) | 549687. | − | 549687.i | 0.961349 | − | 0.961349i | −0.0379309 | − | 0.999280i | \(-0.512077\pi\) |
0.999280 | + | 0.0379309i | \(0.0120767\pi\) | |||||||
\(84\) | 641823.i | 1.08287i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 347005. | 0.545557 | ||||||||
\(87\) | −231476. | − | 231476.i | −0.351519 | − | 0.351519i | ||||
\(88\) | −738681. | + | 738681.i | −1.08395 | + | 1.08395i | ||||
\(89\) | − | 1.19284e6i | − | 1.69205i | −0.533143 | − | 0.846025i | \(-0.678989\pi\) | ||
0.533143 | − | 0.846025i | \(-0.321011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −254760. | −0.338070 | ||||||||
\(92\) | −128583. | − | 128583.i | −0.165127 | − | 0.165127i | ||||
\(93\) | −182616. | + | 182616.i | −0.227034 | + | 0.227034i | ||||
\(94\) | 403528.i | 0.485836i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −805276. | −0.910188 | ||||||||
\(97\) | −469094. | − | 469094.i | −0.513978 | − | 0.513978i | 0.401765 | − | 0.915743i | \(-0.368397\pi\) |
−0.915743 | + | 0.401765i | \(0.868397\pi\) | |||||||
\(98\) | 479644. | − | 479644.i | 0.509613 | − | 0.509613i | ||||
\(99\) | 365212.i | 0.376391i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −610039. | −0.592098 | −0.296049 | − | 0.955173i | \(-0.595669\pi\) | ||||
−0.296049 | + | 0.955173i | \(0.595669\pi\) | |||||||
\(102\) | −34453.8 | − | 34453.8i | −0.0324666 | − | 0.0324666i | ||||
\(103\) | 1.05731e6 | − | 1.05731e6i | 0.967584 | − | 0.967584i | −0.0319069 | − | 0.999491i | \(-0.510158\pi\) |
0.999491 | + | 0.0319069i | \(0.0101580\pi\) | |||||||
\(104\) | − | 204230.i | − | 0.181560i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −680005. | −0.570945 | ||||||||
\(107\) | −76525.5 | − | 76525.5i | −0.0624676 | − | 0.0624676i | 0.675183 | − | 0.737650i | \(-0.264065\pi\) |
−0.737650 | + | 0.675183i | \(0.764065\pi\) | |||||||
\(108\) | −737059. | + | 737059.i | −0.585101 | + | 0.585101i | ||||
\(109\) | 441339.i | 0.340795i | 0.985375 | + | 0.170397i | \(0.0545052\pi\) | ||||
−0.985375 | + | 0.170397i | \(0.945495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.01575e6 | −0.742707 | ||||||||
\(112\) | −568630. | − | 568630.i | −0.404739 | − | 0.404739i | ||||
\(113\) | 756591. | − | 756591.i | 0.524356 | − | 0.524356i | −0.394528 | − | 0.918884i | \(-0.629092\pi\) |
0.918884 | + | 0.394528i | \(0.129092\pi\) | |||||||
\(114\) | 648634.i | 0.437809i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 671270. | 0.430054 | ||||||||
\(117\) | −50486.8 | − | 50486.8i | −0.0315225 | − | 0.0315225i | ||||
\(118\) | −415282. | + | 415282.i | −0.252753 | + | 0.252753i | ||||
\(119\) | − | 286581.i | − | 0.170062i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.99851e6 | 2.25705 | ||||||||
\(122\) | 366153. | + | 366153.i | 0.201643 | + | 0.201643i | ||||
\(123\) | −1.02482e6 | + | 1.02482e6i | −0.550722 | + | 0.550722i | ||||
\(124\) | − | 529579.i | − | 0.277757i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 316718. | 0.158329 | ||||||||
\(127\) | 269108. | + | 269108.i | 0.131376 | + | 0.131376i | 0.769737 | − | 0.638361i | \(-0.220387\pi\) |
−0.638361 | + | 0.769737i | \(0.720387\pi\) | |||||||
\(128\) | 1.42523e6 | − | 1.42523e6i | 0.679602 | − | 0.679602i | ||||
\(129\) | − | 2.17062e6i | − | 1.01115i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.45724e6 | −1.09304 | −0.546518 | − | 0.837447i | \(-0.684047\pi\) | ||||
−0.546518 | + | 0.837447i | \(0.684047\pi\) | |||||||
\(132\) | 2.00955e6 | + | 2.00955e6i | 0.873728 | + | 0.873728i | ||||
\(133\) | −2.69761e6 | + | 2.69761e6i | −1.14663 | + | 1.14663i | ||||
\(134\) | 374759.i | 0.155753i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 229740. | 0.0913312 | ||||||||
\(137\) | 2.13907e6 | + | 2.13907e6i | 0.831885 | + | 0.831885i | 0.987775 | − | 0.155889i | \(-0.0498242\pi\) |
−0.155889 | + | 0.987775i | \(0.549824\pi\) | |||||||
\(138\) | 240786. | − | 240786.i | 0.0916207 | − | 0.0916207i | ||||
\(139\) | 2.12039e6i | 0.789534i | 0.918781 | + | 0.394767i | \(0.129175\pi\) | ||||
−0.918781 | + | 0.394767i | \(0.870825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.52419e6 | 0.900462 | ||||||||
\(142\) | 261184. | + | 261184.i | 0.0912182 | + | 0.0912182i | ||||
\(143\) | −797653. | + | 797653.i | −0.272776 | + | 0.272776i | ||||
\(144\) | − | 225375.i | − | 0.0754777i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.25798e6 | 0.404218 | ||||||||
\(147\) | −3.00032e6 | − | 3.00032e6i | −0.944530 | − | 0.944530i | ||||
\(148\) | 1.47281e6 | − | 1.47281e6i | 0.454320 | − | 0.454320i | ||||
\(149\) | 1.39457e6i | 0.421582i | 0.977531 | + | 0.210791i | \(0.0676039\pi\) | ||||
−0.977531 | + | 0.210791i | \(0.932396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.09334e6 | −1.47935 | −0.739677 | − | 0.672962i | \(-0.765022\pi\) | ||||
−0.739677 | + | 0.672962i | \(0.765022\pi\) | |||||||
\(152\) | −2.16256e6 | − | 2.16256e6i | −0.615797 | − | 0.615797i | ||||
\(153\) | 56792.9 | − | 56792.9i | 0.0158570 | − | 0.0158570i | ||||
\(154\) | − | 5.00390e6i | − | 1.37008i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −555598. | −0.146348 | ||||||||
\(157\) | 248449. | + | 248449.i | 0.0642006 | + | 0.0642006i | 0.738478 | − | 0.674277i | \(-0.235545\pi\) |
−0.674277 | + | 0.738478i | \(0.735545\pi\) | |||||||
\(158\) | 76338.7 | − | 76338.7i | 0.0193541 | − | 0.0193541i | ||||
\(159\) | 4.25364e6i | 1.05820i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00282e6 | 0.479914 | ||||||||
\(162\) | −1.07928e6 | − | 1.07928e6i | −0.253857 | − | 0.253857i | ||||
\(163\) | 4.62194e6 | − | 4.62194e6i | 1.06724 | − | 1.06724i | 0.0696687 | − | 0.997570i | \(-0.477806\pi\) |
0.997570 | − | 0.0696687i | \(-0.0221942\pi\) | |||||||
\(164\) | − | 2.97193e6i | − | 0.673763i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.98507e6 | −0.652575 | ||||||||
\(167\) | −4.91675e6 | − | 4.91675e6i | −1.05567 | − | 1.05567i | −0.998356 | − | 0.0573154i | \(-0.981746\pi\) |
−0.0573154 | − | 0.998356i | \(-0.518254\pi\) | |||||||
\(168\) | 4.00712e6 | − | 4.00712e6i | 0.845094 | − | 0.845094i | ||||
\(169\) | 4.60627e6i | 0.954310i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.06919e6 | −0.213830 | ||||||||
\(172\) | 3.14735e6 | + | 3.14735e6i | 0.618529 | + | 0.618529i | ||||
\(173\) | −6.18056e6 | + | 6.18056e6i | −1.19368 | + | 1.19368i | −0.217659 | + | 0.976025i | \(0.569842\pi\) |
−0.976025 | + | 0.217659i | \(0.930158\pi\) | |||||||
\(174\) | 1.25703e6i | 0.238615i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.56075e6 | −0.653136 | ||||||||
\(177\) | 2.59771e6 | + | 2.59771e6i | 0.468459 | + | 0.468459i | ||||
\(178\) | −3.23887e6 | + | 3.23887e6i | −0.574292 | + | 0.574292i | ||||
\(179\) | 68910.2i | 0.0120150i | 0.999982 | + | 0.00600751i | \(0.00191226\pi\) | ||||
−0.999982 | + | 0.00600751i | \(0.998088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.75676e6 | −0.296263 | −0.148132 | − | 0.988968i | \(-0.547326\pi\) | ||||
−0.148132 | + | 0.988968i | \(0.547326\pi\) | |||||||
\(182\) | 691737. | + | 691737.i | 0.114743 | + | 0.114743i | ||||
\(183\) | 2.29040e6 | − | 2.29040e6i | 0.373730 | − | 0.373730i | ||||
\(184\) | 1.60557e6i | 0.257737i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 991697. | 0.154113 | ||||||||
\(187\) | −897285. | − | 897285.i | −0.137216 | − | 0.137216i | ||||
\(188\) | −3.66002e6 | + | 3.66002e6i | −0.550820 | + | 0.550820i | ||||
\(189\) | − | 1.14805e7i | − | 1.70050i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.14917e7 | 1.64924 | 0.824621 | − | 0.565685i | \(-0.191388\pi\) | ||||
0.824621 | + | 0.565685i | \(0.191388\pi\) | |||||||
\(192\) | 575176. | + | 575176.i | 0.0812638 | + | 0.0812638i | ||||
\(193\) | 1.34415e6 | − | 1.34415e6i | 0.186972 | − | 0.186972i | −0.607414 | − | 0.794386i | \(-0.707793\pi\) |
0.794386 | + | 0.607414i | \(0.207793\pi\) | |||||||
\(194\) | 2.54741e6i | 0.348894i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.70079e6 | 1.15555 | ||||||||
\(197\) | 7.13909e6 | + | 7.13909e6i | 0.933780 | + | 0.933780i | 0.997940 | − | 0.0641600i | \(-0.0204368\pi\) |
−0.0641600 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(198\) | 991641. | − | 991641.i | 0.127749 | − | 0.127749i | ||||
\(199\) | − | 6.08275e6i | − | 0.771864i | −0.922527 | − | 0.385932i | \(-0.873880\pi\) | ||
0.922527 | − | 0.385932i | \(-0.126120\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.34423e6 | 0.288677 | ||||||||
\(202\) | 1.65641e6 | + | 1.65641e6i | 0.200962 | + | 0.200962i | ||||
\(203\) | −5.22789e6 | + | 5.22789e6i | −0.624940 | + | 0.624940i | ||||
\(204\) | − | 624996.i | − | 0.0736184i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.74169e6 | −0.656808 | ||||||||
\(207\) | 396906. | + | 396906.i | 0.0447483 | + | 0.0447483i | ||||
\(208\) | 492237. | − | 492237.i | 0.0546997 | − | 0.0546997i | ||||
\(209\) | 1.68924e7i | 1.85035i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.05692e6 | −0.644769 | −0.322385 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322385 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(212\) | −6.16768e6 | − | 6.16768e6i | −0.647313 | − | 0.647313i | ||||
\(213\) | 1.63379e6 | − | 1.63379e6i | 0.169066 | − | 0.169066i | ||||
\(214\) | 415571.i | 0.0424037i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.20343e6 | 0.913247 | ||||||||
\(217\) | 4.12439e6 | + | 4.12439e6i | 0.403627 | + | 0.403627i | ||||
\(218\) | 1.19835e6 | − | 1.19835e6i | 0.115668 | − | 0.115668i | ||||
\(219\) | − | 7.86907e6i | − | 0.749188i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 248081. | 0.0229835 | ||||||||
\(222\) | 2.75801e6 | + | 2.75801e6i | 0.252079 | + | 0.252079i | ||||
\(223\) | 8.33971e6 | − | 8.33971e6i | 0.752032 | − | 0.752032i | −0.222826 | − | 0.974858i | \(-0.571528\pi\) |
0.974858 | + | 0.222826i | \(0.0715281\pi\) | |||||||
\(224\) | 1.81872e7i | 1.61816i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.10867e6 | −0.355939 | ||||||||
\(227\) | −1.19794e7 | − | 1.19794e7i | −1.02414 | − | 1.02414i | −0.999701 | − | 0.0244373i | \(-0.992221\pi\) |
−0.0244373 | − | 0.999701i | \(-0.507779\pi\) | |||||||
\(228\) | −5.88314e6 | + | 5.88314e6i | −0.496369 | + | 0.496369i | ||||
\(229\) | − | 2.19074e7i | − | 1.82425i | −0.409913 | − | 0.912125i | \(-0.634441\pi\) | ||
0.409913 | − | 0.912125i | \(-0.365559\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.13009e7 | −2.53934 | ||||||||
\(232\) | −4.19097e6 | − | 4.19097e6i | −0.335622 | − | 0.335622i | ||||
\(233\) | 3.44419e6 | − | 3.44419e6i | 0.272282 | − | 0.272282i | −0.557736 | − | 0.830018i | \(-0.688330\pi\) |
0.830018 | + | 0.557736i | \(0.188330\pi\) | |||||||
\(234\) | 274168.i | 0.0213978i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.53325e6 | −0.573121 | ||||||||
\(237\) | −477522. | − | 477522.i | −0.0358714 | − | 0.0358714i | ||||
\(238\) | −778139. | + | 778139.i | −0.0577200 | + | 0.0577200i | ||||
\(239\) | − | 1.25160e7i | − | 0.916796i | −0.888747 | − | 0.458398i | \(-0.848423\pi\) | ||
0.888747 | − | 0.458398i | \(-0.151577\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.42402e7 | 1.01734 | 0.508670 | − | 0.860961i | \(-0.330137\pi\) | ||||
0.508670 | + | 0.860961i | \(0.330137\pi\) | |||||||
\(242\) | −1.08569e7 | − | 1.08569e7i | −0.766058 | − | 0.766058i | ||||
\(243\) | 4.15766e6 | − | 4.15766e6i | 0.289755 | − | 0.289755i | ||||
\(244\) | 6.64205e6i | 0.457228i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.56528e6 | 0.373837 | ||||||||
\(247\) | −2.33520e6 | − | 2.33520e6i | −0.154965 | − | 0.154965i | ||||
\(248\) | −3.30634e6 | + | 3.30634e6i | −0.216767 | + | 0.216767i | ||||
\(249\) | 1.86726e7i | 1.20950i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.08845e6 | 0.385022 | 0.192511 | − | 0.981295i | \(-0.438337\pi\) | ||||
0.192511 | + | 0.981295i | \(0.438337\pi\) | |||||||
\(252\) | 2.87264e6 | + | 2.87264e6i | 0.179507 | + | 0.179507i | ||||
\(253\) | 6.27081e6 | − | 6.27081e6i | 0.387224 | − | 0.387224i | ||||
\(254\) | − | 1.46139e6i | − | 0.0891795i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.90701e6 | −0.590504 | ||||||||
\(257\) | 1.13295e7 | + | 1.13295e7i | 0.667437 | + | 0.667437i | 0.957122 | − | 0.289685i | \(-0.0935506\pi\) |
−0.289685 | + | 0.957122i | \(0.593551\pi\) | |||||||
\(258\) | −5.89378e6 | + | 5.89378e6i | −0.343190 | + | 0.343190i | ||||
\(259\) | 2.29407e7i | 1.32040i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.07206e6 | −0.116542 | ||||||||
\(262\) | 6.67203e6 | + | 6.67203e6i | 0.370983 | + | 0.370983i | ||||
\(263\) | −3.55449e6 | + | 3.55449e6i | −0.195394 | + | 0.195394i | −0.798022 | − | 0.602628i | \(-0.794120\pi\) |
0.602628 | + | 0.798022i | \(0.294120\pi\) | |||||||
\(264\) | − | 2.50926e7i | − | 1.36375i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.46494e7 | 0.778349 | ||||||||
\(267\) | 2.02601e7 | + | 2.02601e7i | 1.06441 | + | 1.06441i | ||||
\(268\) | −3.39908e6 | + | 3.39908e6i | −0.176586 | + | 0.176586i | ||||
\(269\) | − | 3.59971e6i | − | 0.184931i | −0.995716 | − | 0.0924657i | \(-0.970525\pi\) | ||
0.995716 | − | 0.0924657i | \(-0.0294749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.66998e7 | 1.34153 | 0.670764 | − | 0.741671i | \(-0.265966\pi\) | ||||
0.670764 | + | 0.741671i | \(0.265966\pi\) | |||||||
\(272\) | 553721. | + | 553721.i | 0.0275159 | + | 0.0275159i | ||||
\(273\) | 4.32703e6 | − | 4.32703e6i | 0.212668 | − | 0.212668i | ||||
\(274\) | − | 1.16162e7i | − | 0.564694i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.36788e6 | 0.207751 | ||||||||
\(277\) | −1.30361e7 | − | 1.30361e7i | −0.613351 | − | 0.613351i | 0.330466 | − | 0.943818i | \(-0.392794\pi\) |
−0.943818 | + | 0.330466i | \(0.892794\pi\) | |||||||
\(278\) | 5.75738e6 | − | 5.75738e6i | 0.267973 | − | 0.267973i | ||||
\(279\) | 1.63469e6i | 0.0752703i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.39152e6 | −0.0627150 | −0.0313575 | − | 0.999508i | \(-0.509983\pi\) | ||||
−0.0313575 | + | 0.999508i | \(0.509983\pi\) | |||||||
\(282\) | −6.85381e6 | − | 6.85381e6i | −0.305622 | − | 0.305622i | ||||
\(283\) | −1.57473e7 | + | 1.57473e7i | −0.694778 | + | 0.694778i | −0.963279 | − | 0.268501i | \(-0.913472\pi\) |
0.268501 | + | 0.963279i | \(0.413472\pi\) | |||||||
\(284\) | 4.73790e6i | 0.206838i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.33165e6 | 0.185163 | ||||||||
\(287\) | 2.31455e7 | + | 2.31455e7i | 0.979088 | + | 0.979088i | ||||
\(288\) | −3.60422e6 | + | 3.60422e6i | −0.150881 | + | 0.150881i | ||||
\(289\) | − | 2.38585e7i | − | 0.988438i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.59349e7 | 0.646650 | ||||||||
\(292\) | 1.14100e7 | + | 1.14100e7i | 0.458285 | + | 0.458285i | ||||
\(293\) | −2.78009e7 | + | 2.78009e7i | −1.10524 | + | 1.10524i | −0.111472 | + | 0.993768i | \(0.535557\pi\) |
−0.993768 | + | 0.111472i | \(0.964443\pi\) | |||||||
\(294\) | 1.62932e7i | 0.641158i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.83905e7 | −0.709119 | ||||||||
\(297\) | −3.59454e7 | − | 3.59454e7i | −1.37206 | − | 1.37206i | ||||
\(298\) | 3.78661e6 | − | 3.78661e6i | 0.143087 | − | 0.143087i | ||||
\(299\) | 1.73375e6i | 0.0648594i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.90235e7 | −1.79765 | ||||||||
\(302\) | 1.38297e7 | + | 1.38297e7i | 0.502102 | + | 0.502102i | ||||
\(303\) | 1.03613e7 | − | 1.03613e7i | 0.372467 | − | 0.372467i | ||||
\(304\) | − | 1.04244e7i | − | 0.371050i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −308414. | −0.0107639 | ||||||||
\(307\) | −1.91801e7 | − | 1.91801e7i | −0.662883 | − | 0.662883i | 0.293176 | − | 0.956059i | \(-0.405288\pi\) |
−0.956059 | + | 0.293176i | \(0.905288\pi\) | |||||||
\(308\) | 4.53856e7 | − | 4.53856e7i | 1.55334 | − | 1.55334i | ||||
\(309\) | 3.59161e7i | 1.21734i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −672506. | −0.0223571 | −0.0111785 | − | 0.999938i | \(-0.503558\pi\) | ||||
−0.0111785 | + | 0.999938i | \(0.503558\pi\) | |||||||
\(312\) | 3.46879e6 | + | 3.46879e6i | 0.114213 | + | 0.114213i | ||||
\(313\) | 3.01532e6 | − | 3.01532e6i | 0.0983331 | − | 0.0983331i | −0.656229 | − | 0.754562i | \(-0.727849\pi\) |
0.754562 | + | 0.656229i | \(0.227849\pi\) | |||||||
\(314\) | − | 1.34920e6i | − | 0.0435801i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.38479e6 | 0.0438857 | ||||||||
\(317\) | −3.55428e6 | − | 3.55428e6i | −0.111577 | − | 0.111577i | 0.649114 | − | 0.760691i | \(-0.275140\pi\) |
−0.760691 | + | 0.649114i | \(0.775140\pi\) | |||||||
\(318\) | 1.15497e7 | − | 1.15497e7i | 0.359161 | − | 0.359161i | ||||
\(319\) | 3.27370e7i | 1.00848i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.59953e6 | 0.0785922 | ||||||||
\(322\) | −5.43814e6 | − | 5.43814e6i | −0.162886 | − | 0.162886i | ||||
\(323\) | 2.62689e6 | − | 2.62689e6i | 0.0779532 | − | 0.0779532i | ||||
\(324\) | − | 1.95783e7i | − | 0.575624i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.50994e7 | −0.724455 | ||||||||
\(327\) | −7.49602e6 | − | 7.49602e6i | −0.214382 | − | 0.214382i | ||||
\(328\) | −1.85548e7 | + | 1.85548e7i | −0.525816 | + | 0.525816i | ||||
\(329\) | − | 5.70089e7i | − | 1.60086i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.60494e7 | −0.442564 | −0.221282 | − | 0.975210i | \(-0.571024\pi\) | ||||
−0.221282 | + | 0.975210i | \(0.571024\pi\) | |||||||
\(332\) | −2.70748e7 | − | 2.70748e7i | −0.739861 | − | 0.739861i | ||||
\(333\) | −4.54624e6 | + | 4.54624e6i | −0.123118 | + | 0.123118i | ||||
\(334\) | 2.67004e7i | 0.716602i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.93160e7 | 0.509214 | ||||||||
\(337\) | −2.58165e7 | − | 2.58165e7i | −0.674541 | − | 0.674541i | 0.284219 | − | 0.958760i | \(-0.408266\pi\) |
−0.958760 | + | 0.284219i | \(0.908266\pi\) | |||||||
\(338\) | 1.25072e7 | − | 1.25072e7i | 0.323899 | − | 0.323899i | ||||
\(339\) | 2.57010e7i | 0.659706i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.58269e7 | 0.651342 | ||||||||
\(342\) | 2.90313e6 | + | 2.90313e6i | 0.0725751 | + | 0.0725751i | ||||
\(343\) | −2.26321e7 | + | 2.26321e7i | −0.560845 | + | 0.560845i | ||||
\(344\) | − | 3.93000e7i | − | 0.965422i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.35635e7 | 0.810287 | ||||||||
\(347\) | 3.37727e7 | + | 3.37727e7i | 0.808308 | + | 0.808308i | 0.984378 | − | 0.176069i | \(-0.0563383\pi\) |
−0.176069 | + | 0.984378i | \(0.556338\pi\) | |||||||
\(348\) | −1.14013e7 | + | 1.14013e7i | −0.270532 | + | 0.270532i | ||||
\(349\) | 5.15245e7i | 1.21210i | 0.795427 | + | 0.606049i | \(0.207246\pi\) | ||||
−0.795427 | + | 0.606049i | \(0.792754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.93817e6 | 0.229819 | ||||||||
\(352\) | 5.69439e7 | + | 5.69439e7i | 1.30563 | + | 1.30563i | ||||
\(353\) | 2.59077e7 | − | 2.59077e7i | 0.588986 | − | 0.588986i | −0.348371 | − | 0.937357i | \(-0.613265\pi\) |
0.937357 | + | 0.348371i | \(0.113265\pi\) | |||||||
\(354\) | − | 1.41069e7i | − | 0.317996i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.87533e7 | −1.30221 | ||||||||
\(357\) | 4.86750e6 | + | 4.86750e6i | 0.106980 | + | 0.106980i | ||||
\(358\) | 187108. | − | 187108.i | 0.00407797 | − | 0.00407797i | ||||
\(359\) | − | 6.45192e7i | − | 1.39446i | −0.716848 | − | 0.697229i | \(-0.754416\pi\) | ||
0.716848 | − | 0.697229i | \(-0.245584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.40834e6 | −0.0511912 | ||||||||
\(362\) | 4.77005e6 | + | 4.77005e6i | 0.100554 | + | 0.100554i | ||||
\(363\) | −6.79136e7 | + | 6.79136e7i | −1.41983 | + | 1.41983i | ||||
\(364\) | 1.25482e7i | 0.260181i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.24380e7 | −0.253692 | ||||||||
\(367\) | 4.17545e7 | + | 4.17545e7i | 0.844705 | + | 0.844705i | 0.989467 | − | 0.144761i | \(-0.0462415\pi\) |
−0.144761 | + | 0.989467i | \(0.546241\pi\) | |||||||
\(368\) | −3.86976e6 | + | 3.86976e6i | −0.0776499 | + | 0.0776499i | ||||
\(369\) | 9.17369e6i | 0.182585i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.60685e7 | 1.88130 | ||||||||
\(372\) | 8.99474e6 | + | 8.99474e6i | 0.174727 | + | 0.174727i | ||||
\(373\) | 3.12116e7 | − | 3.12116e7i | 0.601436 | − | 0.601436i | −0.339258 | − | 0.940693i | \(-0.610176\pi\) |
0.940693 | + | 0.339258i | \(0.110176\pi\) | |||||||
\(374\) | 4.87270e6i | 0.0931440i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.57015e7 | 0.859740 | ||||||||
\(377\) | −4.52555e6 | − | 4.52555e6i | −0.0844593 | − | 0.0844593i | ||||
\(378\) | −3.11725e7 | + | 3.11725e7i | −0.577159 | + | 0.577159i | ||||
\(379\) | − | 1.15046e7i | − | 0.211326i | −0.994402 | − | 0.105663i | \(-0.966304\pi\) | ||
0.994402 | − | 0.105663i | \(-0.0336965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.14145e6 | −0.165287 | ||||||||
\(382\) | −3.12028e7 | − | 3.12028e7i | −0.559763 | − | 0.559763i | ||||
\(383\) | 4.25312e7 | − | 4.25312e7i | 0.757026 | − | 0.757026i | −0.218754 | − | 0.975780i | \(-0.570199\pi\) |
0.975780 | + | 0.218754i | \(0.0701992\pi\) | |||||||
\(384\) | 4.84142e7i | 0.855026i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.29940e6 | −0.126919 | ||||||||
\(387\) | −9.71518e6 | − | 9.71518e6i | −0.167617 | − | 0.167617i | ||||
\(388\) | −2.31052e7 | + | 2.31052e7i | −0.395561 | + | 0.395561i | ||||
\(389\) | 3.45253e7i | 0.586528i | 0.956032 | + | 0.293264i | \(0.0947415\pi\) | ||||
−0.956032 | + | 0.293264i | \(0.905259\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.95031e6 | −0.0326267 | ||||||||
\(392\) | −5.43220e7 | − | 5.43220e7i | −0.901815 | − | 0.901815i | ||||
\(393\) | 4.17356e7 | − | 4.17356e7i | 0.687589 | − | 0.687589i | ||||
\(394\) | − | 3.87688e7i | − | 0.633861i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.79885e7 | 0.289673 | ||||||||
\(397\) | −1.36149e7 | − | 1.36149e7i | −0.217592 | − | 0.217592i | 0.589891 | − | 0.807483i | \(-0.299171\pi\) |
−0.807483 | + | 0.589891i | \(0.799171\pi\) | |||||||
\(398\) | −1.65162e7 | + | 1.65162e7i | −0.261975 | + | 0.261975i | ||||
\(399\) | − | 9.16364e7i | − | 1.44261i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.91943e7 | −1.38326 | −0.691630 | − | 0.722252i | \(-0.743107\pi\) | ||||
−0.691630 | + | 0.722252i | \(0.743107\pi\) | |||||||
\(402\) | −6.36517e6 | − | 6.36517e6i | −0.0979788 | − | 0.0979788i | ||||
\(403\) | −3.57030e6 | + | 3.57030e6i | −0.0545493 | + | 0.0545493i | ||||
\(404\) | 3.00474e7i | 0.455683i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.83900e7 | 0.424217 | ||||||||
\(407\) | 7.18272e7 | + | 7.18272e7i | 1.06538 | + | 1.06538i | ||||
\(408\) | −3.90206e6 | + | 3.90206e6i | −0.0574532 | + | 0.0574532i | ||||
\(409\) | 2.75539e7i | 0.402729i | 0.979516 | + | 0.201364i | \(0.0645375\pi\) | ||||
−0.979516 | + | 0.201364i | \(0.935462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.26630e7 | −1.04662 | ||||||||
\(412\) | −5.20774e7 | − | 5.20774e7i | −0.744660 | − | 0.744660i | ||||
\(413\) | 5.86694e7 | − | 5.86694e7i | 0.832839 | − | 0.832839i | ||||
\(414\) | − | 2.15540e6i | − | 0.0303757i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.57438e7 | −0.218691 | ||||||||
\(417\) | −3.60142e7 | − | 3.60142e7i | −0.496667 | − | 0.496667i | ||||
\(418\) | 4.58671e7 | − | 4.58671e7i | 0.628019 | − | 0.628019i | ||||
\(419\) | 6.47061e7i | 0.879636i | 0.898087 | + | 0.439818i | \(0.144957\pi\) | ||||
−0.898087 | + | 0.439818i | \(0.855043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.48259e8 | −1.98690 | −0.993450 | − | 0.114267i | \(-0.963548\pi\) | ||||
−0.993450 | + | 0.114267i | \(0.963548\pi\) | |||||||
\(422\) | 1.64460e7 | + | 1.64460e7i | 0.218839 | + | 0.218839i | ||||
\(423\) | 1.12977e7 | − | 1.12977e7i | 0.149268 | − | 0.149268i | ||||
\(424\) | 7.70139e7i | 1.01035i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.87227e6 | −0.114764 | ||||||||
\(427\) | −5.17287e7 | − | 5.17287e7i | −0.664427 | − | 0.664427i | ||||
\(428\) | −3.76925e6 | + | 3.76925e6i | −0.0480755 | + | 0.0480755i | ||||
\(429\) | − | 2.70958e7i | − | 0.343187i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.24831e7 | 1.15513 | 0.577565 | − | 0.816345i | \(-0.304003\pi\) | ||||
0.577565 | + | 0.816345i | \(0.304003\pi\) | |||||||
\(432\) | 2.21822e7 | + | 2.21822e7i | 0.275140 | + | 0.275140i | ||||
\(433\) | −9.15871e7 | + | 9.15871e7i | −1.12816 | + | 1.12816i | −0.137683 | + | 0.990476i | \(0.543966\pi\) |
−0.990476 | + | 0.137683i | \(0.956034\pi\) | |||||||
\(434\) | − | 2.23975e7i | − | 0.273987i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.17381e7 | 0.262278 | ||||||||
\(437\) | 1.83584e7 | + | 1.83584e7i | 0.219984 | + | 0.219984i | ||||
\(438\) | −2.13665e7 | + | 2.13665e7i | −0.254279 | + | 0.254279i | ||||
\(439\) | − | 1.31005e8i | − | 1.54844i | −0.632915 | − | 0.774221i | \(-0.718142\pi\) | ||
0.632915 | − | 0.774221i | \(-0.281858\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.68574e7 | −0.313147 | ||||||||
\(442\) | −673601. | − | 673601.i | −0.00780074 | − | 0.00780074i | ||||
\(443\) | −5.10135e7 | + | 5.10135e7i | −0.586778 | + | 0.586778i | −0.936757 | − | 0.349979i | \(-0.886189\pi\) |
0.349979 | + | 0.936757i | \(0.386189\pi\) | |||||||
\(444\) | 5.00306e7i | 0.571593i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.52888e7 | −0.510489 | ||||||||
\(447\) | −2.36864e7 | − | 2.36864e7i | −0.265202 | − | 0.265202i | ||||
\(448\) | 1.29903e7 | − | 1.29903e7i | 0.144473 | − | 0.144473i | ||||
\(449\) | − | 6.85143e7i | − | 0.756906i | −0.925620 | − | 0.378453i | \(-0.876456\pi\) | ||
0.925620 | − | 0.378453i | \(-0.123544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.44937e8 | 1.57998 | ||||||||
\(452\) | −3.72658e7 | − | 3.72658e7i | −0.403548 | − | 0.403548i | ||||
\(453\) | 8.65090e7 | − | 8.65090e7i | 0.930608 | − | 0.930608i | ||||
\(454\) | 6.50543e7i | 0.695198i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34609e7 | 0.774750 | ||||||||
\(457\) | 9.03199e7 | + | 9.03199e7i | 0.946313 | + | 0.946313i | 0.998631 | − | 0.0523174i | \(-0.0166608\pi\) |
−0.0523174 | + | 0.998631i | \(0.516661\pi\) | |||||||
\(458\) | −5.94840e7 | + | 5.94840e7i | −0.619161 | + | 0.619161i | ||||
\(459\) | 1.11795e7i | 0.115607i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.44157e8 | 1.47141 | 0.735705 | − | 0.677303i | \(-0.236851\pi\) | ||||
0.735705 | + | 0.677303i | \(0.236851\pi\) | |||||||
\(462\) | 8.49897e7 | + | 8.49897e7i | 0.861868 | + | 0.861868i | ||||
\(463\) | 1.29520e8 | − | 1.29520e8i | 1.30495 | − | 1.30495i | 0.379934 | − | 0.925013i | \(-0.375947\pi\) |
0.925013 | − | 0.379934i | \(-0.124053\pi\) | |||||||
\(464\) | − | 2.02022e7i | − | 0.202230i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.87037e7 | −0.184829 | ||||||||
\(467\) | 6.96344e6 | + | 6.96344e6i | 0.0683712 | + | 0.0683712i | 0.740466 | − | 0.672094i | \(-0.234605\pi\) |
−0.672094 | + | 0.740466i | \(0.734605\pi\) | |||||||
\(468\) | −2.48672e6 | + | 2.48672e6i | −0.0242599 | + | 0.0242599i | ||||
\(469\) | − | 5.29445e7i | − | 0.513218i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.43969e6 | −0.0807725 | ||||||||
\(472\) | 4.70327e7 | + | 4.70327e7i | 0.447274 | + | 0.447274i | ||||
\(473\) | −1.53492e8 | + | 1.53492e8i | −1.45045 | + | 1.45045i | ||||
\(474\) | 2.59318e6i | 0.0243500i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.41155e7 | −0.130881 | ||||||||
\(477\) | 1.90383e7 | + | 1.90383e7i | 0.175417 | + | 0.175417i | ||||
\(478\) | −3.39841e7 | + | 3.39841e7i | −0.311166 | + | 0.311166i | ||||
\(479\) | 1.79225e8i | 1.63077i | 0.578919 | + | 0.815385i | \(0.303475\pi\) | ||||
−0.578919 | + | 0.815385i | \(0.696525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.98587e7 | −0.178450 | ||||||||
\(482\) | −3.86658e7 | − | 3.86658e7i | −0.345291 | − | 0.345291i | ||||
\(483\) | −3.40173e7 | + | 3.40173e7i | −0.301897 | + | 0.301897i | ||||
\(484\) | − | 1.96946e8i | − | 1.73705i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.25782e7 | −0.196689 | ||||||||
\(487\) | 2.11900e7 | + | 2.11900e7i | 0.183461 | + | 0.183461i | 0.792862 | − | 0.609401i | \(-0.208590\pi\) |
−0.609401 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(488\) | 4.14686e7 | − | 4.14686e7i | 0.356829 | − | 0.356829i | ||||
\(489\) | 1.57005e8i | 1.34272i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.72686e7 | −0.568288 | −0.284144 | − | 0.958782i | \(-0.591709\pi\) | ||||
−0.284144 | + | 0.958782i | \(0.591709\pi\) | |||||||
\(492\) | 5.04774e7 | + | 5.04774e7i | 0.423839 | + | 0.423839i | ||||
\(493\) | 5.09082e6 | − | 5.09082e6i | 0.0424861 | − | 0.0424861i | ||||
\(494\) | 1.26813e7i | 0.105192i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.59380e7 | −0.130613 | ||||||||
\(497\) | −3.68991e7 | − | 3.68991e7i | −0.300570 | − | 0.300570i | ||||
\(498\) | 5.07006e7 | − | 5.07006e7i | 0.410511 | − | 0.410511i | ||||
\(499\) | − | 6.42641e6i | − | 0.0517210i | −0.999666 | − | 0.0258605i | \(-0.991767\pi\) | ||
0.999666 | − | 0.0258605i | \(-0.00823257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.67019e8 | 1.32817 | ||||||||
\(502\) | −1.65317e7 | − | 1.65317e7i | −0.130679 | − | 0.130679i | ||||
\(503\) | −7.98868e7 | + | 7.98868e7i | −0.627727 | + | 0.627727i | −0.947496 | − | 0.319768i | \(-0.896395\pi\) |
0.319768 | + | 0.947496i | \(0.396395\pi\) | |||||||
\(504\) | − | 3.58698e7i | − | 0.280180i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.40536e7 | −0.262852 | ||||||||
\(507\) | −7.82363e7 | − | 7.82363e7i | −0.600322 | − | 0.600322i | ||||
\(508\) | 1.32549e7 | − | 1.32549e7i | 0.101108 | − | 0.101108i | ||||
\(509\) | − | 6.08449e7i | − | 0.461393i | −0.973026 | − | 0.230696i | \(-0.925900\pi\) | ||
0.973026 | − | 0.230696i | \(-0.0741004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.77723e8 | −1.33193 | ||||||||
\(512\) | −6.43146e7 | − | 6.43146e7i | −0.479181 | − | 0.479181i | ||||
\(513\) | 1.05234e8 | − | 1.05234e8i | 0.779476 | − | 0.779476i | ||||
\(514\) | − | 6.15246e7i | − | 0.453064i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.06914e8 | −0.778188 | ||||||||
\(517\) | −1.78494e8 | − | 1.78494e8i | −1.29167 | − | 1.29167i | ||||
\(518\) | 6.22896e7 | − | 6.22896e7i | 0.448153 | − | 0.448153i | ||||
\(519\) | − | 2.09950e8i | − | 1.50181i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.51477e8 | −1.07111 | −0.535555 | − | 0.844500i | \(-0.679898\pi\) | ||||
−0.535555 | + | 0.844500i | \(0.679898\pi\) | |||||||
\(522\) | 5.62616e6 | + | 5.62616e6i | 0.0395549 | + | 0.0395549i | ||||
\(523\) | −3.86508e7 | + | 3.86508e7i | −0.270180 | + | 0.270180i | −0.829173 | − | 0.558993i | \(-0.811188\pi\) |
0.558993 | + | 0.829173i | \(0.311188\pi\) | |||||||
\(524\) | 1.21031e8i | 0.841208i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.93027e7 | 0.132635 | ||||||||
\(527\) | −4.01625e6 | − | 4.01625e6i | −0.0274403 | − | 0.0274403i | ||||
\(528\) | 6.04784e7 | − | 6.04784e7i | 0.410864 | − | 0.410864i | ||||
\(529\) | 1.34406e8i | 0.907928i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.32535e7 | 0.155312 | ||||||||
\(532\) | 1.32871e8 | + | 1.32871e8i | 0.882458 | + | 0.882458i | ||||
\(533\) | −2.00361e7 | + | 2.00361e7i | −0.132322 | + | 0.132322i | ||||
\(534\) | − | 1.10022e8i | − | 0.722533i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.24433e7 | 0.275622 | ||||||||
\(537\) | −1.17042e6 | − | 1.17042e6i | −0.00755821 | − | 0.00755821i | ||||
\(538\) | −9.77411e6 | + | 9.77411e6i | −0.0627668 | + | 0.0627668i | ||||
\(539\) | 4.24326e8i | 2.70978i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00964e8 | 0.637637 | 0.318819 | − | 0.947816i | \(-0.396714\pi\) | ||||
0.318819 | + | 0.947816i | \(0.396714\pi\) | |||||||
\(542\) | −7.24965e7 | − | 7.24965e7i | −0.455323 | − | 0.455323i | ||||
\(543\) | 2.98382e7 | − | 2.98382e7i | 0.186368 | − | 0.186368i | ||||
\(544\) | − | 1.77103e7i | − | 0.110009i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.34979e7 | −0.144361 | ||||||||
\(547\) | 8.80351e6 | + | 8.80351e6i | 0.0537891 | + | 0.0537891i | 0.733490 | − | 0.679701i | \(-0.237890\pi\) |
−0.679701 | + | 0.733490i | \(0.737890\pi\) | |||||||
\(548\) | 1.05360e8 | − | 1.05360e8i | 0.640225 | − | 0.640225i | ||||
\(549\) | − | 2.05025e7i | − | 0.123905i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.58407e7 | −0.572921 | ||||||||
\(552\) | −2.72702e7 | − | 2.72702e7i | −0.162133 | − | 0.162133i | ||||
\(553\) | −1.07848e7 | + | 1.07848e7i | −0.0637732 | + | 0.0637732i | ||||
\(554\) | 7.07926e7i | 0.416350i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.04439e8 | 0.607631 | ||||||||
\(557\) | −6.07102e6 | − | 6.07102e6i | −0.0351314 | − | 0.0351314i | 0.689323 | − | 0.724454i | \(-0.257908\pi\) |
−0.724454 | + | 0.689323i | \(0.757908\pi\) | |||||||
\(558\) | 4.43859e6 | − | 4.43859e6i | 0.0255472 | − | 0.0255472i | ||||
\(559\) | − | 4.24375e7i | − | 0.242949i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.04803e7 | 0.172635 | ||||||||
\(562\) | 3.77833e6 | + | 3.77833e6i | 0.0212858 | + | 0.0212858i | ||||
\(563\) | −1.90242e8 | + | 1.90242e8i | −1.06606 | + | 1.06606i | −0.0684018 | + | 0.997658i | \(0.521790\pi\) |
−0.997658 | + | 0.0684018i | \(0.978210\pi\) | |||||||
\(564\) | − | 1.24329e8i | − | 0.693002i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.55155e7 | 0.471624 | ||||||||
\(567\) | 1.52477e8 | + | 1.52477e8i | 0.836477 | + | 0.836477i | ||||
\(568\) | 2.95804e7 | − | 2.95804e7i | 0.161420 | − | 0.161420i | ||||
\(569\) | − | 2.39087e8i | − | 1.29783i | −0.760859 | − | 0.648917i | \(-0.775222\pi\) | ||
0.760859 | − | 0.648917i | \(-0.224778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.51162e8 | −0.811960 | −0.405980 | − | 0.913882i | \(-0.633070\pi\) | ||||
−0.405980 | + | 0.913882i | \(0.633070\pi\) | |||||||
\(572\) | 3.92883e7 | + | 3.92883e7i | 0.209930 | + | 0.209930i | ||||
\(573\) | −1.95183e8 | + | 1.95183e8i | −1.03748 | + | 1.03748i | ||||
\(574\) | − | 1.25692e8i | − | 0.664617i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.14869e6 | 0.0269420 | ||||||||
\(577\) | 2.65297e8 | + | 2.65297e8i | 1.38103 | + | 1.38103i | 0.842786 | + | 0.538249i | \(0.180914\pi\) |
0.538249 | + | 0.842786i | \(0.319086\pi\) | |||||||
\(578\) | −6.47817e7 | + | 6.47817e7i | −0.335482 | + | 0.335482i | ||||
\(579\) | 4.56600e7i | 0.235234i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.21720e8 | 2.15028 | ||||||||
\(582\) | −4.32671e7 | − | 4.32671e7i | −0.219477 | − | 0.219477i | ||||
\(583\) | 3.00790e8 | − | 3.00790e8i | 1.51795 | − | 1.51795i | ||||
\(584\) | − | 1.42473e8i | − | 0.715308i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.50973e8 | 0.750250 | ||||||||
\(587\) | −1.66774e8 | − | 1.66774e8i | −0.824544 | − | 0.824544i | 0.162212 | − | 0.986756i | \(-0.448137\pi\) |
−0.986756 | + | 0.162212i | \(0.948137\pi\) | |||||||
\(588\) | −1.47780e8 | + | 1.47780e8i | −0.726917 | + | 0.726917i | ||||
\(589\) | 7.56107e7i | 0.370030i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.42511e8 | −1.17481 | ||||||||
\(592\) | −4.43251e7 | − | 4.43251e7i | −0.213641 | − | 0.213641i | ||||
\(593\) | −9.38190e7 | + | 9.38190e7i | −0.449911 | + | 0.449911i | −0.895325 | − | 0.445414i | \(-0.853057\pi\) |
0.445414 | + | 0.895325i | \(0.353057\pi\) | |||||||
\(594\) | 1.95202e8i | 0.931374i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.86894e7 | 0.324452 | ||||||||
\(597\) | 1.03314e8 | + | 1.03314e8i | 0.485552 | + | 0.485552i | ||||
\(598\) | 4.70756e6 | − | 4.70756e6i | 0.0220137 | − | 0.0220137i | ||||
\(599\) | − | 2.10159e8i | − | 0.977841i | −0.872328 | − | 0.488921i | \(-0.837391\pi\) | ||
0.872328 | − | 0.488921i | \(-0.162609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.79076e8 | 0.824924 | 0.412462 | − | 0.910975i | \(-0.364669\pi\) | ||||
0.412462 | + | 0.910975i | \(0.364669\pi\) | |||||||
\(602\) | 1.33111e8 | + | 1.33111e8i | 0.610133 | + | 0.610133i | ||||
\(603\) | 1.04922e7 | − | 1.04922e7i | 0.0478537 | − | 0.0478537i | ||||
\(604\) | 2.50872e8i | 1.13852i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.62672e7 | −0.252835 | ||||||||
\(607\) | −7.09085e7 | − | 7.09085e7i | −0.317053 | − | 0.317053i | 0.530581 | − | 0.847634i | \(-0.321974\pi\) |
−0.847634 | + | 0.530581i | \(0.821974\pi\) | |||||||
\(608\) | −1.66709e8 | + | 1.66709e8i | −0.741733 | + | 0.741733i | ||||
\(609\) | − | 1.77588e8i | − | 0.786254i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.93500e7 | 0.216353 | ||||||||
\(612\) | −2.79733e6 | − | 2.79733e6i | −0.0122036 | − | 0.0122036i | ||||
\(613\) | −1.20399e8 | + | 1.20399e8i | −0.522685 | + | 0.522685i | −0.918381 | − | 0.395696i | \(-0.870503\pi\) |
0.395696 | + | 0.918381i | \(0.370503\pi\) | |||||||
\(614\) | 1.04158e8i | 0.449973i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.66715e8 | −2.42450 | ||||||||
\(617\) | 9.83715e7 | + | 9.83715e7i | 0.418807 | + | 0.418807i | 0.884792 | − | 0.465985i | \(-0.154300\pi\) |
−0.465985 | + | 0.884792i | \(0.654300\pi\) | |||||||
\(618\) | 9.75210e7 | − | 9.75210e7i | 0.413174 | − | 0.413174i | ||||
\(619\) | 3.07649e8i | 1.29713i | 0.761159 | + | 0.648565i | \(0.224631\pi\) | ||||
−0.761159 | + | 0.648565i | \(0.775369\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.81298e7 | −0.326243 | ||||||||
\(622\) | 1.82602e6 | + | 1.82602e6i | 0.00758812 | + | 0.00758812i | ||||
\(623\) | 4.57574e8 | − | 4.57574e8i | 1.89233 | − | 1.89233i | ||||
\(624\) | 1.67210e7i | 0.0688191i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.63747e7 | −0.0667497 | ||||||||
\(627\) | −2.86913e8 | − | 2.86913e8i | −1.16399 | − | 1.16399i | ||||
\(628\) | 1.22373e7 | − | 1.22373e7i | 0.0494092 | − | 0.0494092i | ||||
\(629\) | − | 2.23392e7i | − | 0.0897668i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.86256e8 | 1.13938 | 0.569688 | − | 0.821861i | \(-0.307064\pi\) | ||||
0.569688 | + | 0.821861i | \(0.307064\pi\) | |||||||
\(632\) | −8.64573e6 | − | 8.64573e6i | −0.0342492 | − | 0.0342492i | ||||
\(633\) | 1.02875e8 | − | 1.02875e8i | 0.405601 | − | 0.405601i | ||||
\(634\) | 1.93015e7i | 0.0757396i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.09513e8 | 0.814402 | ||||||||
\(637\) | −5.86587e7 | − | 5.86587e7i | −0.226942 | − | 0.226942i | ||||
\(638\) | 8.88891e7 | − | 8.88891e7i | 0.342284 | − | 0.342284i | ||||
\(639\) | − | 1.46249e7i | − | 0.0560518i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.23492e8 | −0.848572 | −0.424286 | − | 0.905528i | \(-0.639475\pi\) | ||||
−0.424286 | + | 0.905528i | \(0.639475\pi\) | |||||||
\(642\) | −7.05836e6 | − | 7.05836e6i | −0.0266746 | − | 0.0266746i | ||||
\(643\) | −9.04760e7 | + | 9.04760e7i | −0.340330 | + | 0.340330i | −0.856491 | − | 0.516161i | \(-0.827360\pi\) |
0.516161 | + | 0.856491i | \(0.327360\pi\) | |||||||
\(644\) | − | 9.86485e7i | − | 0.369345i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.42653e7 | −0.0529156 | ||||||||
\(647\) | −1.42334e8 | − | 1.42334e8i | −0.525527 | − | 0.525527i | 0.393708 | − | 0.919235i | \(-0.371192\pi\) |
−0.919235 | + | 0.393708i | \(0.871192\pi\) | |||||||
\(648\) | −1.22234e8 | + | 1.22234e8i | −0.449227 | + | 0.449227i | ||||
\(649\) | − | 3.67387e8i | − | 1.34397i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.40103e8 | −0.507814 | ||||||||
\(652\) | −2.27653e8 | − | 2.27653e8i | −0.821355 | − | 0.821355i | ||||
\(653\) | 2.75946e8 | − | 2.75946e8i | 0.991025 | − | 0.991025i | −0.00893507 | − | 0.999960i | \(-0.502844\pi\) |
0.999960 | + | 0.00893507i | \(0.00284416\pi\) | |||||||
\(654\) | 4.07071e7i | 0.145525i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.94418e7 | −0.316832 | ||||||||
\(657\) | −3.52200e7 | − | 3.52200e7i | −0.124192 | − | 0.124192i | ||||
\(658\) | −1.54793e8 | + | 1.54793e8i | −0.543343 | + | 0.543343i | ||||
\(659\) | − | 1.82565e8i | − | 0.637913i | −0.947769 | − | 0.318957i | \(-0.896668\pi\) | ||
0.947769 | − | 0.318957i | \(-0.103332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.05107e8 | −1.40270 | −0.701352 | − | 0.712816i | \(-0.747420\pi\) | ||||
−0.701352 | + | 0.712816i | \(0.747420\pi\) | |||||||
\(662\) | 4.35782e7 | + | 4.35782e7i | 0.150209 | + | 0.150209i | ||||
\(663\) | −4.21358e6 | + | 4.21358e6i | −0.0144581 | + | 0.0144581i | ||||
\(664\) | 3.38074e8i | 1.15480i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.46884e7 | 0.0835737 | ||||||||
\(667\) | 3.55780e7 | + | 3.55780e7i | 0.119896 | + | 0.119896i | ||||
\(668\) | −2.42174e8 | + | 2.42174e8i | −0.812452 | + | 0.812452i | ||||
\(669\) | 2.83295e8i | 0.946152i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.23924e8 | −1.07220 | ||||||||
\(672\) | −3.08904e8 | − | 3.08904e8i | −1.01792 | − | 1.01792i | ||||
\(673\) | −7.51896e7 | + | 7.51896e7i | −0.246668 | + | 0.246668i | −0.819602 | − | 0.572934i | \(-0.805805\pi\) |
0.572934 | + | 0.819602i | \(0.305805\pi\) | |||||||
\(674\) | 1.40197e8i | 0.457886i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.26881e8 | 0.734444 | ||||||||
\(677\) | 4.04485e8 | + | 4.04485e8i | 1.30358 | + | 1.30358i | 0.925963 | + | 0.377613i | \(0.123255\pi\) |
0.377613 | + | 0.925963i | \(0.376745\pi\) | |||||||
\(678\) | 6.97845e7 | − | 6.97845e7i | 0.223908 | − | 0.223908i | ||||
\(679\) | − | 3.59888e8i | − | 1.14963i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.06935e8 | 1.28850 | ||||||||
\(682\) | −7.01264e7 | − | 7.01264e7i | −0.221069 | − | 0.221069i | ||||
\(683\) | 1.60273e7 | − | 1.60273e7i | 0.0503034 | − | 0.0503034i | −0.681508 | − | 0.731811i | \(-0.738675\pi\) |
0.731811 | + | 0.681508i | \(0.238675\pi\) | |||||||
\(684\) | 5.26630e7i | 0.164565i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.22904e8 | 0.380708 | ||||||||
\(687\) | 3.72091e8 | + | 3.72091e8i | 1.14757 | + | 1.14757i | ||||
\(688\) | 9.47213e7 | − | 9.47213e7i | 0.290859 | − | 0.290859i | ||||
\(689\) | 8.31622e7i | 0.254254i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.78407e8 | 0.540728 | 0.270364 | − | 0.962758i | \(-0.412856\pi\) | ||||
0.270364 | + | 0.962758i | \(0.412856\pi\) | |||||||
\(692\) | 3.04422e8 | + | 3.04422e8i | 0.918668 | + | 0.918668i | ||||
\(693\) | −1.40095e8 | + | 1.40095e8i | −0.420943 | + | 0.420943i | ||||
\(694\) | − | 1.83402e8i | − | 0.548689i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.42365e8 | 0.422255 | ||||||||
\(697\) | −2.25387e7 | − | 2.25387e7i | −0.0665627 | − | 0.0665627i | ||||
\(698\) | 1.39902e8 | − | 1.39902e8i | 0.411393 | − | 0.411393i | ||||
\(699\) | 1.16997e8i | 0.342566i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.67499e8 | −0.486249 | −0.243125 | − | 0.969995i | \(-0.578172\pi\) | ||||
−0.243125 | + | 0.969995i | \(0.578172\pi\) | |||||||
\(702\) | −2.69846e7 | − | 2.69846e7i | −0.0780018 | − | 0.0780018i | ||||
\(703\) | −2.10281e8 | + | 2.10281e8i | −0.605249 | + | 0.605249i | ||||
\(704\) | − | 8.13454e7i | − | 0.233139i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.40692e8 | −0.399811 | ||||||||
\(707\) | −2.34011e8 | − | 2.34011e8i | −0.662182 | − | 0.662182i | ||||
\(708\) | 1.27950e8 | − | 1.27950e8i | 0.360529 | − | 0.360529i | ||||
\(709\) | 7.42966e7i | 0.208463i | 0.994553 | + | 0.104232i | \(0.0332384\pi\) | ||||
−0.994553 | + | 0.104232i | \(0.966762\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.27455e6 | −0.0118927 | ||||||||
\(712\) | 3.66817e8 | + | 3.66817e8i | 1.01627 | + | 1.01627i | ||||
\(713\) | 2.80682e7 | − | 2.80682e7i | 0.0774365 | − | 0.0774365i | ||||
\(714\) | − | 2.64330e7i | − | 0.0726191i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.39416e6 | 0.00924685 | ||||||||
\(717\) | 2.12581e8 | + | 2.12581e8i | 0.576723 | + | 0.576723i | ||||
\(718\) | −1.75186e8 | + | 1.75186e8i | −0.473288 | + | 0.473288i | ||||
\(719\) | − | 5.82976e8i | − | 1.56843i | −0.620492 | − | 0.784213i | \(-0.713067\pi\) | ||
0.620492 | − | 0.784213i | \(-0.286933\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.11164e8 | 2.16423 | ||||||||
\(722\) | 6.53923e6 | + | 6.53923e6i | 0.0173746 | + | 0.0173746i | ||||
\(723\) | −2.41867e8 | + | 2.41867e8i | −0.639972 | + | 0.639972i | ||||
\(724\) | 8.65292e7i | 0.228006i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.68804e8 | 0.963798 | ||||||||
\(727\) | −2.21220e8 | − | 2.21220e8i | −0.575734 | − | 0.575734i | 0.357991 | − | 0.933725i | \(-0.383462\pi\) |
−0.933725 | + | 0.357991i | \(0.883462\pi\) | |||||||
\(728\) | 7.83426e7 | − | 7.83426e7i | 0.203050 | − | 0.203050i | ||||
\(729\) | 4.31003e8i | 1.11249i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.77382e7 | 0.122212 | ||||||||
\(732\) | −1.12813e8 | − | 1.12813e8i | −0.287625 | − | 0.287625i | ||||
\(733\) | 1.51730e6 | − | 1.51730e6i | 0.00385265 | − | 0.00385265i | −0.705178 | − | 0.709030i | \(-0.749133\pi\) |
0.709030 | + | 0.705178i | \(0.249133\pi\) | |||||||
\(734\) | − | 2.26748e8i | − | 0.573396i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.23771e8 | 0.310446 | ||||||||
\(737\) | −1.65769e8 | − | 1.65769e8i | −0.414096 | − | 0.414096i | ||||
\(738\) | 2.49088e7 | − | 2.49088e7i | 0.0619704 | − | 0.0619704i | ||||
\(739\) | 3.44636e8i | 0.853939i | 0.904266 | + | 0.426969i | \(0.140419\pi\) | ||||
−0.904266 | + | 0.426969i | \(0.859581\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.93256e7 | 0.194966 | ||||||||
\(742\) | −2.60850e8 | − | 2.60850e8i | −0.638526 | − | 0.638526i | ||||
\(743\) | 2.75120e8 | − | 2.75120e8i | 0.670743 | − | 0.670743i | −0.287144 | − | 0.957887i | \(-0.592706\pi\) |
0.957887 | + | 0.287144i | \(0.0927059\pi\) | |||||||
\(744\) | − | 1.12315e8i | − | 0.272720i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.69494e8 | −0.408262 | ||||||||
\(747\) | 8.35738e7 | + | 8.35738e7i | 0.200497 | + | 0.200497i | ||||
\(748\) | −4.41956e7 | + | 4.41956e7i | −0.105603 | + | 0.105603i | ||||
\(749\) | − | 5.87103e7i | − | 0.139723i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.61018e8 | −1.08842 | −0.544212 | − | 0.838948i | \(-0.683171\pi\) | ||||
−0.544212 | + | 0.838948i | \(0.683171\pi\) | |||||||
\(752\) | 1.10150e8 | + | 1.10150e8i | 0.259019 | + | 0.259019i | ||||
\(753\) | −1.03411e8 | + | 1.03411e8i | −0.242203 | + | 0.242203i | ||||
\(754\) | 2.45760e7i | 0.0573320i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.65471e8 | −1.30872 | ||||||||
\(757\) | 2.27312e8 | + | 2.27312e8i | 0.524005 | + | 0.524005i | 0.918778 | − | 0.394774i | \(-0.129177\pi\) |
−0.394774 | + | 0.918778i | \(0.629177\pi\) | |||||||
\(758\) | −3.12378e7 | + | 3.12378e7i | −0.0717253 | + | 0.0717253i | ||||
\(759\) | 2.13016e8i | 0.487177i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.25130e8 | −1.19155 | −0.595776 | − | 0.803151i | \(-0.703155\pi\) | ||||
−0.595776 | + | 0.803151i | \(0.703155\pi\) | |||||||
\(762\) | 2.48213e7 | + | 2.48213e7i | 0.0560996 | + | 0.0560996i | ||||
\(763\) | −1.69298e8 | + | 1.69298e8i | −0.381133 | + | 0.381133i | ||||
\(764\) | − | 5.66022e8i | − | 1.26927i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.30965e8 | −0.513878 | ||||||||
\(767\) | 5.07875e7 | + | 5.07875e7i | 0.112556 | + | 0.112556i | ||||
\(768\) | 1.68268e8 | − | 1.68268e8i | 0.371465 | − | 0.371465i | ||||
\(769\) | 3.58307e8i | 0.787909i | 0.919130 | + | 0.393955i | \(0.128893\pi\) | ||||
−0.919130 | + | 0.393955i | \(0.871107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.84856e8 | −0.839721 | ||||||||
\(772\) | −6.62059e7 | − | 6.62059e7i | −0.143895 | − | 0.143895i | ||||
\(773\) | 2.63294e8 | − | 2.63294e8i | 0.570037 | − | 0.570037i | −0.362101 | − | 0.932139i | \(-0.617941\pi\) |
0.932139 | + | 0.362101i | \(0.117941\pi\) | |||||||
\(774\) | 5.27583e7i | 0.113780i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.88507e8 | 0.617406 | ||||||||
\(777\) | −3.89641e8 | − | 3.89641e8i | −0.830618 | − | 0.830618i | ||||
\(778\) | 9.37447e7 | − | 9.37447e7i | 0.199071 | − | 0.199071i | ||||
\(779\) | 4.24318e8i | 0.897591i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.31062e8 | −0.485037 | ||||||||
\(782\) | 5.29557e6 | + | 5.29557e6i | 0.0110737 | + | 0.0110737i | ||||
\(783\) | 2.03940e8 | − | 2.03940e8i | 0.424831 | − | 0.424831i | ||||
\(784\) | − | 2.61855e8i | − | 0.543391i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.26645e8 | −0.466744 | ||||||||
\(787\) | −5.46180e8 | − | 5.46180e8i | −1.12050 | − | 1.12050i | −0.991666 | − | 0.128832i | \(-0.958877\pi\) |
−0.128832 | − | 0.991666i | \(-0.541123\pi\) | |||||||
\(788\) | 3.51635e8 | − | 3.51635e8i | 0.718643 | − | 0.718643i | ||||
\(789\) | − | 1.20744e8i | − | 0.245830i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.80456e8 | 1.17284 | ||||||||
\(792\) | −1.12308e8 | − | 1.12308e8i | −0.226066 | − | 0.226066i | ||||
\(793\) | 4.47792e7 | − | 4.47792e7i | 0.0897959 | − | 0.0897959i | ||||
\(794\) | 7.39355e7i | 0.147704i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.99605e8 | −0.594032 | ||||||||
\(797\) | −1.48436e8 | − | 1.48436e8i | −0.293201 | − | 0.293201i | 0.545143 | − | 0.838343i | \(-0.316475\pi\) |
−0.838343 | + | 0.545143i | \(0.816475\pi\) | |||||||
\(798\) | −2.48816e8 | + | 2.48816e8i | −0.489631 | + | 0.489631i | ||||
\(799\) | 5.55142e7i | 0.108834i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.81359e8 | 0.352891 | ||||||||
\(802\) | 2.42185e8 | + | 2.42185e8i | 0.469487 | + | 0.469487i | ||||
\(803\) | −5.56449e8 | + | 5.56449e8i | −1.07468 | + | 1.07468i | ||||
\(804\) | − | 1.15465e8i | − | 0.222168i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.93885e7 | 0.0370287 | ||||||||
\(807\) | 6.11401e7 | + | 6.11401e7i | 0.116334 | + | 0.116334i | ||||
\(808\) | 1.87596e8 | − | 1.87596e8i | 0.355623 | − | 0.355623i | ||||
\(809\) | 2.49688e8i | 0.471576i | 0.971805 | + | 0.235788i | \(0.0757671\pi\) | ||||
−0.971805 | + | 0.235788i | \(0.924233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.41776e8 | 1.39063 | 0.695313 | − | 0.718707i | \(-0.255266\pi\) | ||||
0.695313 | + | 0.718707i | \(0.255266\pi\) | |||||||
\(812\) | 2.57499e8 | + | 2.57499e8i | 0.480958 | + | 0.480958i | ||||
\(813\) | −4.53488e8 | + | 4.53488e8i | −0.843906 | + | 0.843906i | ||||
\(814\) | − | 3.90057e8i | − | 0.723194i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.88096e7 | −0.0346186 | ||||||||
\(817\) | −4.49364e8 | − | 4.49364e8i | −0.824009 | − | 0.824009i | ||||
\(818\) | 7.48156e7 | − | 7.48156e7i | 0.136689 | − | 0.136689i | ||||
\(819\) | − | 3.87334e7i | − | 0.0705073i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.35687e8 | −0.787309 | −0.393655 | − | 0.919258i | \(-0.628789\pi\) | ||||
−0.393655 | + | 0.919258i | \(0.628789\pi\) | |||||||
\(822\) | 1.97298e8 | + | 1.97298e8i | 0.355228 | + | 0.355228i | ||||
\(823\) | 4.41351e8 | − | 4.41351e8i | 0.791743 | − | 0.791743i | −0.190035 | − | 0.981777i | \(-0.560860\pi\) |
0.981777 | + | 0.190035i | \(0.0608600\pi\) | |||||||
\(824\) | 6.50274e8i | 1.16229i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.18604e8 | −0.565341 | ||||||||
\(827\) | 9.56220e7 | + | 9.56220e7i | 0.169060 | + | 0.169060i | 0.786566 | − | 0.617506i | \(-0.211857\pi\) |
−0.617506 | + | 0.786566i | \(0.711857\pi\) | |||||||
\(828\) | 1.95496e7 | − | 1.95496e7i | 0.0344386 | − | 0.0344386i | ||||
\(829\) | − | 7.80825e8i | − | 1.37054i | −0.728291 | − | 0.685268i | \(-0.759685\pi\) | ||
0.728291 | − | 0.685268i | \(-0.240315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.42830e8 | 0.771674 | ||||||||
\(832\) | 1.12452e7 | + | 1.12452e7i | 0.0195252 | + | 0.0195252i | ||||
\(833\) | 6.59856e7 | − | 6.59856e7i | 0.114160 | − | 0.114160i | ||||
\(834\) | 1.95575e8i | 0.337144i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.32034e8 | 1.42404 | ||||||||
\(837\) | −1.60892e8 | − | 1.60892e8i | −0.274384 | − | 0.274384i | ||||
\(838\) | 1.75693e8 | − | 1.75693e8i | 0.298554 | − | 0.298554i | ||||
\(839\) | − | 1.44468e8i | − | 0.244616i | −0.992492 | − | 0.122308i | \(-0.960970\pi\) | ||
0.992492 | − | 0.122308i | \(-0.0390296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.09087e8 | 0.687746 | ||||||||
\(842\) | 4.02561e8 | + | 4.02561e8i | 0.674366 | + | 0.674366i | ||||
\(843\) | 2.36346e7 | − | 2.36346e7i | 0.0394517 | − | 0.0394517i | ||||
\(844\) | 2.98333e8i | 0.496219i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.13519e7 | −0.101325 | ||||||||
\(847\) | 1.53383e9 | + | 1.53383e9i | 2.52421 | + | 2.52421i | ||||
\(848\) | −1.85620e8 | + | 1.85620e8i | −0.304394 | + | 0.304394i | ||||
\(849\) | − | 5.34926e8i | − | 0.874119i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.56121e8 | 0.253322 | ||||||||
\(852\) | −8.04719e7 | − | 8.04719e7i | −0.130115 | − | 0.130115i | ||||
\(853\) | −4.12270e8 | + | 4.12270e8i | −0.664254 | + | 0.664254i | −0.956380 | − | 0.292126i | \(-0.905637\pi\) |
0.292126 | + | 0.956380i | \(0.405637\pi\) | |||||||
\(854\) | 2.80912e8i | 0.451021i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.70655e7 | 0.0750380 | ||||||||
\(857\) | 5.18365e6 | + | 5.18365e6i | 0.00823556 | + | 0.00823556i | 0.711213 | − | 0.702977i | \(-0.248146\pi\) |
−0.702977 | + | 0.711213i | \(0.748146\pi\) | |||||||
\(858\) | −7.35718e7 | + | 7.35718e7i | −0.116480 | + | 0.116480i | ||||
\(859\) | 9.84492e8i | 1.55322i | 0.629982 | + | 0.776609i | \(0.283062\pi\) | ||||
−0.629982 | + | 0.776609i | \(0.716938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.86241e8 | −1.23182 | ||||||||
\(862\) | −2.51115e8 | − | 2.51115e8i | −0.392058 | − | 0.392058i | ||||
\(863\) | −7.16892e8 | + | 7.16892e8i | −1.11538 | + | 1.11538i | −0.122966 | + | 0.992411i | \(0.539241\pi\) |
−0.992411 | + | 0.122966i | \(0.960759\pi\) | |||||||
\(864\) | − | 7.09480e8i | − | 1.10002i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.97363e8 | 0.765808 | ||||||||
\(867\) | 4.05230e8 | + | 4.05230e8i | 0.621791 | + | 0.621791i | ||||
\(868\) | 2.03146e8 | − | 2.03146e8i | 0.310634 | − | 0.310634i | ||||
\(869\) | 6.75346e7i | 0.102912i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.58317e7 | 0.0693604 | ||||||||
\(872\) | −1.35718e8 | − | 1.35718e8i | −0.204687 | − | 0.204687i | ||||
\(873\) | 7.13205e7 | − | 7.13205e7i | 0.107194 | − | 0.107194i | ||||
\(874\) | − | 9.96952e7i | − | 0.149328i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.87590e8 | −0.576581 | ||||||||
\(877\) | −3.84095e8 | − | 3.84095e8i | −0.569429 | − | 0.569429i | 0.362539 | − | 0.931969i | \(-0.381910\pi\) |
−0.931969 | + | 0.362539i | \(0.881910\pi\) | |||||||
\(878\) | −3.55712e8 | + | 3.55712e8i | −0.525551 | + | 0.525551i | ||||
\(879\) | − | 9.44382e8i | − | 1.39053i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.55741e8 | −1.39769 | −0.698847 | − | 0.715271i | \(-0.746303\pi\) | ||||
−0.698847 | + | 0.715271i | \(0.746303\pi\) | |||||||
\(882\) | 7.29245e7 | + | 7.29245e7i | 0.106284 | + | 0.106284i | ||||
\(883\) | −3.85519e8 | + | 3.85519e8i | −0.559969 | + | 0.559969i | −0.929299 | − | 0.369329i | \(-0.879587\pi\) |
0.369329 | + | 0.929299i | \(0.379587\pi\) | |||||||
\(884\) | − | 1.22192e7i | − | 0.0176883i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.77029e8 | 0.398312 | ||||||||
\(887\) | −6.73645e8 | − | 6.73645e8i | −0.965296 | − | 0.965296i | 0.0341220 | − | 0.999418i | \(-0.489137\pi\) |
−0.999418 | + | 0.0341220i | \(0.989137\pi\) | |||||||
\(888\) | 3.12358e8 | − | 3.12358e8i | 0.446081 | − | 0.446081i | ||||
\(889\) | 2.06459e8i | 0.293853i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.54807e8 | 1.34984 | ||||||||
\(892\) | −4.10771e8 | − | 4.10771e8i | −0.578770 | − | 0.578770i | ||||
\(893\) | 5.22560e8 | − | 5.22560e8i | 0.733806 | − | 0.733806i | ||||
\(894\) | 1.28629e8i | 0.180022i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.09343e9 | 1.52009 | ||||||||
\(897\) | −2.94472e7 | − | 2.94472e7i | −0.0408007 | − | 0.0408007i | ||||
\(898\) | −1.86033e8 | + | 1.86033e8i | −0.256898 | + | 0.256898i | ||||
\(899\) | 1.46531e8i | 0.201674i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.35497e7 | −0.127899 | ||||||||
\(902\) | −3.93540e8 | − | 3.93540e8i | −0.536253 | − | 0.536253i | ||||
\(903\) | 8.32651e8 | − | 8.32651e8i | 1.13084 | − | 1.13084i | ||||
\(904\) | 4.65326e8i | 0.629872i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.69787e8 | −0.631708 | ||||||||
\(907\) | 8.67904e8 | + | 8.67904e8i | 1.16319 | + | 1.16319i | 0.983774 | + | 0.179414i | \(0.0574200\pi\) |
0.179414 | + | 0.983774i | \(0.442580\pi\) | |||||||
\(908\) | −5.90045e8 | + | 5.90045e8i | −0.788184 | + | 0.788184i | ||||
\(909\) | − | 9.27497e7i | − | 0.123487i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.07789e9 | −1.42567 | −0.712837 | − | 0.701330i | \(-0.752590\pi\) | ||||
−0.712837 | + | 0.701330i | \(0.752590\pi\) | |||||||
\(912\) | 1.77056e8 | + | 1.77056e8i | 0.233414 | + | 0.233414i | ||||
\(913\) | 1.32040e9 | − | 1.32040e9i | 1.73498 | − | 1.73498i | ||||
\(914\) | − | 4.90482e8i | − | 0.642369i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.07905e9 | −1.40396 | ||||||||
\(917\) | −9.42598e8 | − | 9.42598e8i | −1.22241 | − | 1.22241i | ||||
\(918\) | 3.03552e7 | − | 3.03552e7i | 0.0392378 | − | 0.0392378i | ||||
\(919\) | − | 6.68544e8i | − | 0.861357i | −0.902505 | − | 0.430679i | \(-0.858274\pi\) | ||
0.902505 | − | 0.430679i | \(-0.141726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.51538e8 | 0.833991 | ||||||||
\(922\) | −3.91422e8 | − | 3.91422e8i | −0.499405 | − | 0.499405i | ||||
\(923\) | 3.19419e7 | − | 3.19419e7i | 0.0406214 | − | 0.0406214i | ||||
\(924\) | 1.54172e9i | 1.95430i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.03357e8 | −0.885814 | ||||||||
\(927\) | 1.60751e8 | + | 1.60751e8i | 0.201797 | + | 0.201797i | ||||
\(928\) | −3.23076e8 | + | 3.23076e8i | −0.404260 | + | 0.404260i | ||||
\(929\) | 1.71956e8i | 0.214472i | 0.994234 | + | 0.107236i | \(0.0342001\pi\) | ||||
−0.994234 | + | 0.107236i | \(0.965800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.24226e9 | −1.53944 | ||||||||
\(932\) | −1.69643e8 | − | 1.69643e8i | −0.209551 | − | 0.209551i | ||||
\(933\) | 1.14223e7 | − | 1.14223e7i | 0.0140640 | − | 0.0140640i | ||||
\(934\) | − | 3.78149e7i | − | 0.0464112i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.10509e7 | 0.0378658 | ||||||||
\(937\) | 7.39804e8 | + | 7.39804e8i | 0.899286 | + | 0.899286i | 0.995373 | − | 0.0960869i | \(-0.0306327\pi\) |
−0.0960869 | + | 0.995373i | \(0.530633\pi\) | |||||||
\(938\) | −1.43757e8 | + | 1.43757e8i | −0.174189 | + | 0.174189i | ||||
\(939\) | 1.02429e8i | 0.123716i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.44325e8 | 1.13332 | 0.566660 | − | 0.823952i | \(-0.308235\pi\) | ||||
0.566660 | + | 0.823952i | \(0.308235\pi\) | |||||||
\(942\) | 2.29158e7 | + | 2.29158e7i | 0.0274147 | + | 0.0274147i | ||||
\(943\) | 1.57515e8 | − | 1.57515e8i | 0.187840 | − | 0.187840i | ||||
\(944\) | 2.26717e8i | 0.269506i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.33540e8 | 0.984585 | ||||||||
\(947\) | −8.16654e8 | − | 8.16654e8i | −0.961586 | − | 0.961586i | 0.0377034 | − | 0.999289i | \(-0.487996\pi\) |
−0.999289 | + | 0.0377034i | \(0.987996\pi\) | |||||||
\(948\) | −2.35203e7 | + | 2.35203e7i | −0.0276069 | + | 0.0276069i | ||||
\(949\) | − | 1.53847e8i | − | 0.180007i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.20737e8 | 0.140378 | ||||||||
\(952\) | 8.81281e7 | + | 8.81281e7i | 0.102142 | + | 0.102142i | ||||
\(953\) | 4.40051e8 | − | 4.40051e8i | 0.508422 | − | 0.508422i | −0.405620 | − | 0.914042i | \(-0.632944\pi\) |
0.914042 | + | 0.405620i | \(0.132944\pi\) | |||||||
\(954\) | − | 1.03387e8i | − | 0.119075i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.16475e8 | −0.705573 | ||||||||
\(957\) | −5.56029e8 | − | 5.56029e8i | −0.634397 | − | 0.634397i | ||||
\(958\) | 4.86641e8 | − | 4.86641e8i | 0.553493 | − | 0.553493i | ||||
\(959\) | 1.64109e9i | 1.86071i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.71902e8 | −0.869746 | ||||||||
\(962\) | 5.39214e7 | + | 5.39214e7i | 0.0605669 | + | 0.0605669i | ||||
\(963\) | 1.16348e7 | − | 1.16348e7i | 0.0130281 | − | 0.0130281i | ||||
\(964\) | − | 7.01401e8i | − | 0.782953i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.84731e8 | 0.204931 | ||||||||
\(967\) | 1.38431e8 | + | 1.38431e8i | 0.153092 | + | 0.153092i | 0.779497 | − | 0.626405i | \(-0.215475\pi\) |
−0.626405 | + | 0.779497i | \(0.715475\pi\) | |||||||
\(968\) | −1.22960e9 | + | 1.22960e9i | −1.35562 | + | 1.35562i | ||||
\(969\) | 8.92339e7i | 0.0980750i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.70863e8 | 0.514324 | 0.257162 | − | 0.966368i | \(-0.417213\pi\) | ||||
0.257162 | + | 0.966368i | \(0.417213\pi\) | |||||||
\(972\) | −2.04785e8 | − | 2.04785e8i | −0.222997 | − | 0.222997i | ||||
\(973\) | −8.13380e8 | + | 8.13380e8i | −0.882989 | + | 0.882989i | ||||
\(974\) | − | 1.15072e8i | − | 0.124536i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.99896e8 | 0.215008 | ||||||||
\(977\) | 9.36496e8 | + | 9.36496e8i | 1.00420 | + | 1.00420i | 0.999991 | + | 0.00421351i | \(0.00134121\pi\) |
0.00421351 | + | 0.999991i | \(0.498659\pi\) | |||||||
\(978\) | 4.26307e8 | − | 4.26307e8i | 0.455728 | − | 0.455728i | ||||
\(979\) | − | 2.86533e9i | − | 3.05370i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.71007e7 | −0.0710755 | ||||||||
\(982\) | 1.82651e8 | + | 1.82651e8i | 0.192880 | + | 0.192880i | ||||
\(983\) | −7.76947e8 | + | 7.76947e8i | −0.817957 | + | 0.817957i | −0.985812 | − | 0.167854i | \(-0.946316\pi\) |
0.167854 | + | 0.985812i | \(0.446316\pi\) | |||||||
\(984\) | − | 6.30295e8i | − | 0.661544i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.76457e7 | −0.0288401 | ||||||||
\(987\) | 9.68279e8 | + | 9.68279e8i | 1.00705 | + | 1.00705i | ||||
\(988\) | −1.15020e8 | + | 1.15020e8i | −0.119262 | + | 0.119262i | ||||
\(989\) | 3.33626e8i | 0.344882i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.22547e9 | 1.25916 | 0.629579 | − | 0.776937i | \(-0.283228\pi\) | ||||
0.629579 | + | 0.776937i | \(0.283228\pi\) | |||||||
\(992\) | 2.54881e8 | + | 2.54881e8i | 0.261098 | + | 0.261098i | ||||
\(993\) | 2.72595e8 | − | 2.72595e8i | 0.278401 | − | 0.278401i | ||||
\(994\) | 2.00380e8i | 0.204031i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.19714e8 | 0.930840 | ||||||||
\(997\) | −3.22586e8 | − | 3.22586e8i | −0.325507 | − | 0.325507i | 0.525368 | − | 0.850875i | \(-0.323928\pi\) |
−0.850875 | + | 0.525368i | \(0.823928\pi\) | |||||||
\(998\) | −1.74493e7 | + | 1.74493e7i | −0.0175544 | + | 0.0175544i | ||||
\(999\) | − | 8.94914e8i | − | 0.897604i |
(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 | 25.7.c.d.7.2 | ✓ | 8 | |
3.2 | odd | 2 | 225.7.g.f.82.3 | 8 | |||
5.2 | odd | 4 | inner | 25.7.c.d.18.3 | yes | 8 | |
5.3 | odd | 4 | inner | 25.7.c.d.18.2 | yes | 8 | |
5.4 | even | 2 | inner | 25.7.c.d.7.3 | yes | 8 | |
15.2 | even | 4 | 225.7.g.f.118.2 | 8 | |||
15.8 | even | 4 | 225.7.g.f.118.3 | 8 | |||
15.14 | odd | 2 | 225.7.g.f.82.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.7.c.d.7.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
25.7.c.d.7.3 | yes | 8 | 5.4 | even | 2 | inner | |
25.7.c.d.18.2 | yes | 8 | 5.3 | odd | 4 | inner | |
25.7.c.d.18.3 | yes | 8 | 5.2 | odd | 4 | inner | |
225.7.g.f.82.2 | 8 | 15.14 | odd | 2 | |||
225.7.g.f.82.3 | 8 | 3.2 | odd | 2 | |||
225.7.g.f.118.2 | 8 | 15.2 | even | 4 | |||
225.7.g.f.118.3 | 8 | 15.8 | even | 4 |