Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,6,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.a (trivial) |
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: | yes |
Analytic conductor: | \(77.4653849697\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 268 x^{10} + 83 x^{9} + 25315 x^{8} + 5134 x^{7} - 993368 x^{6} - 511968 x^{5} + 14212480 x^{4} + 10085312 x^{3} - 18833856 x^{2} + \cdots + 102912 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(9.45158\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.45158 | −1.67082 | −0.835410 | − | 0.549628i | \(-0.814770\pi\) | ||||
−0.835410 | + | 0.549628i | \(0.814770\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 57.3324 | 1.79164 | ||||||||
\(5\) | 43.5642 | 0.779301 | 0.389650 | − | 0.920963i | \(-0.372596\pi\) | ||||
0.389650 | + | 0.920963i | \(0.372596\pi\) | |||||||
\(6\) | −85.0642 | −0.964648 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −239.431 | −1.32268 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −411.751 | −1.30207 | ||||||||
\(11\) | −280.372 | −0.698638 | −0.349319 | − | 0.937004i | \(-0.613587\pi\) | ||||
−0.349319 | + | 0.937004i | \(0.613587\pi\) | |||||||
\(12\) | 515.992 | 1.03440 | ||||||||
\(13\) | −66.9269 | −0.109835 | −0.0549177 | − | 0.998491i | \(-0.517490\pi\) | ||||
−0.0549177 | + | 0.998491i | \(0.517490\pi\) | |||||||
\(14\) | 463.127 | 0.631510 | ||||||||
\(15\) | 392.078 | 0.449929 | ||||||||
\(16\) | 428.367 | 0.418327 | ||||||||
\(17\) | 1147.68 | 0.963157 | 0.481579 | − | 0.876403i | \(-0.340064\pi\) | ||||
0.481579 | + | 0.876403i | \(0.340064\pi\) | |||||||
\(18\) | −765.578 | −0.556940 | ||||||||
\(19\) | 832.663 | 0.529158 | 0.264579 | − | 0.964364i | \(-0.414767\pi\) | ||||
0.264579 | + | 0.964364i | \(0.414767\pi\) | |||||||
\(20\) | 2497.64 | 1.39622 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 2649.96 | 1.16730 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | −2154.88 | −0.763651 | ||||||||
\(25\) | −1227.16 | −0.392690 | ||||||||
\(26\) | 632.565 | 0.183515 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −2809.29 | −0.677175 | ||||||||
\(29\) | −7403.94 | −1.63481 | −0.817406 | − | 0.576062i | \(-0.804589\pi\) | ||||
−0.817406 | + | 0.576062i | \(0.804589\pi\) | |||||||
\(30\) | −3705.76 | −0.751751 | ||||||||
\(31\) | 3551.90 | 0.663829 | 0.331915 | − | 0.943309i | \(-0.392305\pi\) | ||||
0.331915 | + | 0.943309i | \(0.392305\pi\) | |||||||
\(32\) | 3613.05 | 0.623734 | ||||||||
\(33\) | −2523.35 | −0.403359 | ||||||||
\(34\) | −10847.4 | −1.60926 | ||||||||
\(35\) | −2134.65 | −0.294548 | ||||||||
\(36\) | 4643.92 | 0.597212 | ||||||||
\(37\) | −997.957 | −0.119842 | −0.0599208 | − | 0.998203i | \(-0.519085\pi\) | ||||
−0.0599208 | + | 0.998203i | \(0.519085\pi\) | |||||||
\(38\) | −7869.98 | −0.884127 | ||||||||
\(39\) | −602.342 | −0.0634135 | ||||||||
\(40\) | −10430.6 | −1.03077 | ||||||||
\(41\) | −11509.2 | −1.06926 | −0.534631 | − | 0.845086i | \(-0.679549\pi\) | ||||
−0.534631 | + | 0.845086i | \(0.679549\pi\) | |||||||
\(42\) | 4168.15 | 0.364603 | ||||||||
\(43\) | −9987.91 | −0.823765 | −0.411882 | − | 0.911237i | \(-0.635129\pi\) | ||||
−0.411882 | + | 0.911237i | \(0.635129\pi\) | |||||||
\(44\) | −16074.4 | −1.25171 | ||||||||
\(45\) | 3528.70 | 0.259767 | ||||||||
\(46\) | −4999.89 | −0.348390 | ||||||||
\(47\) | −3589.49 | −0.237022 | −0.118511 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118511 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(48\) | 3855.30 | 0.241521 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 11598.6 | 0.656115 | ||||||||
\(51\) | 10329.1 | 0.556079 | ||||||||
\(52\) | −3837.08 | −0.196785 | ||||||||
\(53\) | −1360.92 | −0.0665491 | −0.0332745 | − | 0.999446i | \(-0.510594\pi\) | ||||
−0.0332745 | + | 0.999446i | \(0.510594\pi\) | |||||||
\(54\) | −6890.20 | −0.321549 | ||||||||
\(55\) | −12214.2 | −0.544449 | ||||||||
\(56\) | 11732.1 | 0.499927 | ||||||||
\(57\) | 7493.96 | 0.305509 | ||||||||
\(58\) | 69979.0 | 2.73148 | ||||||||
\(59\) | −41158.9 | −1.53934 | −0.769668 | − | 0.638445i | \(-0.779578\pi\) | ||||
−0.769668 | + | 0.638445i | \(0.779578\pi\) | |||||||
\(60\) | 22478.8 | 0.806110 | ||||||||
\(61\) | 17699.0 | 0.609009 | 0.304505 | − | 0.952511i | \(-0.401509\pi\) | ||||
0.304505 | + | 0.952511i | \(0.401509\pi\) | |||||||
\(62\) | −33571.1 | −1.10914 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | −47856.8 | −1.46047 | ||||||||
\(65\) | −2915.62 | −0.0855948 | ||||||||
\(66\) | 23849.6 | 0.673940 | ||||||||
\(67\) | −24228.6 | −0.659387 | −0.329694 | − | 0.944088i | \(-0.606945\pi\) | ||||
−0.329694 | + | 0.944088i | \(0.606945\pi\) | |||||||
\(68\) | 65799.0 | 1.72563 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | 20175.8 | 0.492136 | ||||||||
\(71\) | 10714.2 | 0.252239 | 0.126120 | − | 0.992015i | \(-0.459748\pi\) | ||||
0.126120 | + | 0.992015i | \(0.459748\pi\) | |||||||
\(72\) | −19393.9 | −0.440894 | ||||||||
\(73\) | 52743.5 | 1.15841 | 0.579205 | − | 0.815182i | \(-0.303363\pi\) | ||||
0.579205 | + | 0.815182i | \(0.303363\pi\) | |||||||
\(74\) | 9432.27 | 0.200234 | ||||||||
\(75\) | −11044.4 | −0.226720 | ||||||||
\(76\) | 47738.5 | 0.948058 | ||||||||
\(77\) | 13738.2 | 0.264060 | ||||||||
\(78\) | 5693.08 | 0.105952 | ||||||||
\(79\) | 94926.3 | 1.71127 | 0.855635 | − | 0.517579i | \(-0.173167\pi\) | ||||
0.855635 | + | 0.517579i | \(0.173167\pi\) | |||||||
\(80\) | 18661.5 | 0.326002 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 108780. | 1.78654 | ||||||||
\(83\) | −38010.8 | −0.605636 | −0.302818 | − | 0.953048i | \(-0.597927\pi\) | ||||
−0.302818 | + | 0.953048i | \(0.597927\pi\) | |||||||
\(84\) | −25283.6 | −0.390967 | ||||||||
\(85\) | 49997.7 | 0.750589 | ||||||||
\(86\) | 94401.5 | 1.37636 | ||||||||
\(87\) | −66635.5 | −0.943860 | ||||||||
\(88\) | 67129.7 | 0.924077 | ||||||||
\(89\) | −48776.9 | −0.652738 | −0.326369 | − | 0.945242i | \(-0.605825\pi\) | ||||
−0.326369 | + | 0.945242i | \(0.605825\pi\) | |||||||
\(90\) | −33351.8 | −0.434024 | ||||||||
\(91\) | 3279.42 | 0.0415139 | ||||||||
\(92\) | 30328.8 | 0.373582 | ||||||||
\(93\) | 31967.1 | 0.383262 | ||||||||
\(94\) | 33926.4 | 0.396020 | ||||||||
\(95\) | 36274.3 | 0.412373 | ||||||||
\(96\) | 32517.5 | 0.360113 | ||||||||
\(97\) | 46593.3 | 0.502799 | 0.251399 | − | 0.967883i | \(-0.419109\pi\) | ||||
0.251399 | + | 0.967883i | \(0.419109\pi\) | |||||||
\(98\) | −22693.2 | −0.238688 | ||||||||
\(99\) | −22710.1 | −0.232879 | ||||||||
\(100\) | −70355.9 | −0.703559 | ||||||||
\(101\) | 66377.4 | 0.647466 | 0.323733 | − | 0.946148i | \(-0.395062\pi\) | ||||
0.323733 | + | 0.946148i | \(0.395062\pi\) | |||||||
\(102\) | −97626.2 | −0.929108 | ||||||||
\(103\) | −27114.2 | −0.251828 | −0.125914 | − | 0.992041i | \(-0.540186\pi\) | ||||
−0.125914 | + | 0.992041i | \(0.540186\pi\) | |||||||
\(104\) | 16024.4 | 0.145277 | ||||||||
\(105\) | −19211.8 | −0.170057 | ||||||||
\(106\) | 12862.8 | 0.111191 | ||||||||
\(107\) | −67083.0 | −0.566439 | −0.283220 | − | 0.959055i | \(-0.591403\pi\) | ||||
−0.283220 | + | 0.959055i | \(0.591403\pi\) | |||||||
\(108\) | 41795.3 | 0.344801 | ||||||||
\(109\) | −62940.7 | −0.507417 | −0.253709 | − | 0.967281i | \(-0.581650\pi\) | ||||
−0.253709 | + | 0.967281i | \(0.581650\pi\) | |||||||
\(110\) | 115443. | 0.909677 | ||||||||
\(111\) | −8981.61 | −0.0691905 | ||||||||
\(112\) | −20990.0 | −0.158113 | ||||||||
\(113\) | 171135. | 1.26079 | 0.630394 | − | 0.776275i | \(-0.282893\pi\) | ||||
0.630394 | + | 0.776275i | \(0.282893\pi\) | |||||||
\(114\) | −70829.8 | −0.510451 | ||||||||
\(115\) | 23045.5 | 0.162495 | ||||||||
\(116\) | −424486. | −2.92899 | ||||||||
\(117\) | −5421.08 | −0.0366118 | ||||||||
\(118\) | 389016. | 2.57195 | ||||||||
\(119\) | −56236.2 | −0.364039 | ||||||||
\(120\) | −93875.7 | −0.595114 | ||||||||
\(121\) | −82442.7 | −0.511904 | ||||||||
\(122\) | −167283. | −1.01754 | ||||||||
\(123\) | −103582. | −0.617339 | ||||||||
\(124\) | 203639. | 1.18934 | ||||||||
\(125\) | −189598. | −1.08532 | ||||||||
\(126\) | 37513.3 | 0.210503 | ||||||||
\(127\) | 142616. | 0.784617 | 0.392309 | − | 0.919834i | \(-0.371677\pi\) | ||||
0.392309 | + | 0.919834i | \(0.371677\pi\) | |||||||
\(128\) | 336705. | 1.81645 | ||||||||
\(129\) | −89891.2 | −0.475601 | ||||||||
\(130\) | 27557.2 | 0.143013 | ||||||||
\(131\) | −306953. | −1.56276 | −0.781381 | − | 0.624054i | \(-0.785485\pi\) | ||||
−0.781381 | + | 0.624054i | \(0.785485\pi\) | |||||||
\(132\) | −144669. | −0.722673 | ||||||||
\(133\) | −40800.5 | −0.200003 | ||||||||
\(134\) | 228998. | 1.10172 | ||||||||
\(135\) | 31758.3 | 0.149976 | ||||||||
\(136\) | −274790. | −1.27395 | ||||||||
\(137\) | −258887. | −1.17844 | −0.589221 | − | 0.807972i | \(-0.700565\pi\) | ||||
−0.589221 | + | 0.807972i | \(0.700565\pi\) | |||||||
\(138\) | −44999.0 | −0.201143 | ||||||||
\(139\) | 6303.56 | 0.0276726 | 0.0138363 | − | 0.999904i | \(-0.495596\pi\) | ||||
0.0138363 | + | 0.999904i | \(0.495596\pi\) | |||||||
\(140\) | −122384. | −0.527723 | ||||||||
\(141\) | −32305.4 | −0.136845 | ||||||||
\(142\) | −101266. | −0.421446 | ||||||||
\(143\) | 18764.4 | 0.0767352 | ||||||||
\(144\) | 34697.7 | 0.139442 | ||||||||
\(145\) | −322547. | −1.27401 | ||||||||
\(146\) | −498510. | −1.93549 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | −57215.2 | −0.214713 | ||||||||
\(149\) | 61201.8 | 0.225839 | 0.112919 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112919 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(150\) | 104387. | 0.378808 | ||||||||
\(151\) | −270243. | −0.964523 | −0.482262 | − | 0.876027i | \(-0.660185\pi\) | ||||
−0.482262 | + | 0.876027i | \(0.660185\pi\) | |||||||
\(152\) | −199365. | −0.699908 | ||||||||
\(153\) | 92961.8 | 0.321052 | ||||||||
\(154\) | −129848. | −0.441197 | ||||||||
\(155\) | 154736. | 0.517323 | ||||||||
\(156\) | −34533.7 | −0.113614 | ||||||||
\(157\) | −97760.9 | −0.316531 | −0.158265 | − | 0.987397i | \(-0.550590\pi\) | ||||
−0.158265 | + | 0.987397i | \(0.550590\pi\) | |||||||
\(158\) | −897203. | −2.85922 | ||||||||
\(159\) | −12248.3 | −0.0384221 | ||||||||
\(160\) | 157400. | 0.486077 | ||||||||
\(161\) | −25921.0 | −0.0788110 | ||||||||
\(162\) | −62011.8 | −0.185647 | ||||||||
\(163\) | 40884.2 | 0.120527 | 0.0602637 | − | 0.998182i | \(-0.480806\pi\) | ||||
0.0602637 | + | 0.998182i | \(0.480806\pi\) | |||||||
\(164\) | −659848. | −1.91573 | ||||||||
\(165\) | −109928. | −0.314338 | ||||||||
\(166\) | 359262. | 1.01191 | ||||||||
\(167\) | −132106. | −0.366547 | −0.183274 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183274 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(168\) | 105589. | 0.288633 | ||||||||
\(169\) | −366814. | −0.987936 | ||||||||
\(170\) | −472557. | −1.25410 | ||||||||
\(171\) | 67445.7 | 0.176386 | ||||||||
\(172\) | −572631. | −1.47589 | ||||||||
\(173\) | −686455. | −1.74380 | −0.871900 | − | 0.489683i | \(-0.837112\pi\) | ||||
−0.871900 | + | 0.489683i | \(0.837112\pi\) | |||||||
\(174\) | 629811. | 1.57702 | ||||||||
\(175\) | 60130.7 | 0.148423 | ||||||||
\(176\) | −120102. | −0.292259 | ||||||||
\(177\) | −370430. | −0.888736 | ||||||||
\(178\) | 461019. | 1.09061 | ||||||||
\(179\) | −625254. | −1.45856 | −0.729279 | − | 0.684217i | \(-0.760144\pi\) | ||||
−0.729279 | + | 0.684217i | \(0.760144\pi\) | |||||||
\(180\) | 202309. | 0.465408 | ||||||||
\(181\) | −26029.4 | −0.0590564 | −0.0295282 | − | 0.999564i | \(-0.509400\pi\) | ||||
−0.0295282 | + | 0.999564i | \(0.509400\pi\) | |||||||
\(182\) | −30995.7 | −0.0693622 | ||||||||
\(183\) | 159291. | 0.351612 | ||||||||
\(184\) | −126659. | −0.275798 | ||||||||
\(185\) | −43475.2 | −0.0933926 | ||||||||
\(186\) | −302140. | −0.640362 | ||||||||
\(187\) | −321776. | −0.672899 | ||||||||
\(188\) | −205794. | −0.424657 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | −342850. | −0.689001 | ||||||||
\(191\) | 131095. | 0.260018 | 0.130009 | − | 0.991513i | \(-0.458499\pi\) | ||||
0.130009 | + | 0.991513i | \(0.458499\pi\) | |||||||
\(192\) | −430711. | −0.843205 | ||||||||
\(193\) | 410139. | 0.792571 | 0.396285 | − | 0.918127i | \(-0.370299\pi\) | ||||
0.396285 | + | 0.918127i | \(0.370299\pi\) | |||||||
\(194\) | −440381. | −0.840086 | ||||||||
\(195\) | −26240.6 | −0.0494182 | ||||||||
\(196\) | 137655. | 0.255948 | ||||||||
\(197\) | −621690. | −1.14132 | −0.570661 | − | 0.821186i | \(-0.693313\pi\) | ||||
−0.570661 | + | 0.821186i | \(0.693313\pi\) | |||||||
\(198\) | 214646. | 0.389100 | ||||||||
\(199\) | 921494. | 1.64953 | 0.824764 | − | 0.565477i | \(-0.191308\pi\) | ||||
0.824764 | + | 0.565477i | \(0.191308\pi\) | |||||||
\(200\) | 293820. | 0.519405 | ||||||||
\(201\) | −218057. | −0.380697 | ||||||||
\(202\) | −627372. | −1.08180 | ||||||||
\(203\) | 362793. | 0.617901 | ||||||||
\(204\) | 592191. | 0.996292 | ||||||||
\(205\) | −501388. | −0.833277 | ||||||||
\(206\) | 256272. | 0.420759 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | −28669.2 | −0.0459471 | ||||||||
\(209\) | −233455. | −0.369690 | ||||||||
\(210\) | 181582. | 0.284135 | ||||||||
\(211\) | 863819. | 1.33572 | 0.667862 | − | 0.744285i | \(-0.267210\pi\) | ||||
0.667862 | + | 0.744285i | \(0.267210\pi\) | |||||||
\(212\) | −78024.6 | −0.119232 | ||||||||
\(213\) | 96427.6 | 0.145630 | ||||||||
\(214\) | 634041. | 0.946418 | ||||||||
\(215\) | −435115. | −0.641961 | ||||||||
\(216\) | −174545. | −0.254550 | ||||||||
\(217\) | −174043. | −0.250904 | ||||||||
\(218\) | 594889. | 0.847803 | ||||||||
\(219\) | 474692. | 0.668808 | ||||||||
\(220\) | −700268. | −0.975456 | ||||||||
\(221\) | −76810.4 | −0.105789 | ||||||||
\(222\) | 84890.4 | 0.115605 | ||||||||
\(223\) | −345030. | −0.464616 | −0.232308 | − | 0.972642i | \(-0.574628\pi\) | ||||
−0.232308 | + | 0.972642i | \(0.574628\pi\) | |||||||
\(224\) | −177040. | −0.235749 | ||||||||
\(225\) | −99399.8 | −0.130897 | ||||||||
\(226\) | −1.61749e6 | −2.10655 | ||||||||
\(227\) | −542412. | −0.698658 | −0.349329 | − | 0.937000i | \(-0.613590\pi\) | ||||
−0.349329 | + | 0.937000i | \(0.613590\pi\) | |||||||
\(228\) | 429647. | 0.547362 | ||||||||
\(229\) | 94472.2 | 0.119046 | 0.0595231 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595231 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(230\) | −217816. | −0.271501 | ||||||||
\(231\) | 123644. | 0.152455 | ||||||||
\(232\) | 1.77273e6 | 2.16234 | ||||||||
\(233\) | −727236. | −0.877578 | −0.438789 | − | 0.898590i | \(-0.644592\pi\) | ||||
−0.438789 | + | 0.898590i | \(0.644592\pi\) | |||||||
\(234\) | 51237.7 | 0.0611717 | ||||||||
\(235\) | −156373. | −0.184711 | ||||||||
\(236\) | −2.35974e6 | −2.75793 | ||||||||
\(237\) | 854336. | 0.988003 | ||||||||
\(238\) | 531521. | 0.608244 | ||||||||
\(239\) | 1.26515e6 | 1.43268 | 0.716340 | − | 0.697752i | \(-0.245816\pi\) | ||||
0.716340 | + | 0.697752i | \(0.245816\pi\) | |||||||
\(240\) | 167953. | 0.188218 | ||||||||
\(241\) | 655951. | 0.727493 | 0.363746 | − | 0.931498i | \(-0.381498\pi\) | ||||
0.363746 | + | 0.931498i | \(0.381498\pi\) | |||||||
\(242\) | 779214. | 0.855300 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 1.01473e6 | 1.09112 | ||||||||
\(245\) | 104598. | 0.111329 | ||||||||
\(246\) | 979018. | 1.03146 | ||||||||
\(247\) | −55727.5 | −0.0581202 | ||||||||
\(248\) | −850435. | −0.878036 | ||||||||
\(249\) | −342097. | −0.349664 | ||||||||
\(250\) | 1.79200e6 | 1.81338 | ||||||||
\(251\) | 341516. | 0.342158 | 0.171079 | − | 0.985257i | \(-0.445275\pi\) | ||||
0.171079 | + | 0.985257i | \(0.445275\pi\) | |||||||
\(252\) | −227552. | −0.225725 | ||||||||
\(253\) | −148317. | −0.145676 | ||||||||
\(254\) | −1.34794e6 | −1.31095 | ||||||||
\(255\) | 449979. | 0.433353 | ||||||||
\(256\) | −1.65098e6 | −1.57449 | ||||||||
\(257\) | 248822. | 0.234993 | 0.117497 | − | 0.993073i | \(-0.462513\pi\) | ||||
0.117497 | + | 0.993073i | \(0.462513\pi\) | |||||||
\(258\) | 849614. | 0.794643 | ||||||||
\(259\) | 48899.9 | 0.0452958 | ||||||||
\(260\) | −167159. | −0.153355 | ||||||||
\(261\) | −599719. | −0.544938 | ||||||||
\(262\) | 2.90119e6 | 2.61109 | ||||||||
\(263\) | −1.66537e6 | −1.48464 | −0.742321 | − | 0.670044i | \(-0.766275\pi\) | ||||
−0.742321 | + | 0.670044i | \(0.766275\pi\) | |||||||
\(264\) | 604167. | 0.533516 | ||||||||
\(265\) | −59287.3 | −0.0518617 | ||||||||
\(266\) | 385629. | 0.334169 | ||||||||
\(267\) | −438992. | −0.376858 | ||||||||
\(268\) | −1.38908e6 | −1.18138 | ||||||||
\(269\) | −1.52750e6 | −1.28707 | −0.643534 | − | 0.765417i | \(-0.722533\pi\) | ||||
−0.643534 | + | 0.765417i | \(0.722533\pi\) | |||||||
\(270\) | −300166. | −0.250584 | ||||||||
\(271\) | −887513. | −0.734094 | −0.367047 | − | 0.930202i | \(-0.619631\pi\) | ||||
−0.367047 | + | 0.930202i | \(0.619631\pi\) | |||||||
\(272\) | 491626. | 0.402915 | ||||||||
\(273\) | 29514.7 | 0.0239680 | ||||||||
\(274\) | 2.44689e6 | 1.96896 | ||||||||
\(275\) | 344060. | 0.274349 | ||||||||
\(276\) | 272960. | 0.215688 | ||||||||
\(277\) | −568262. | −0.444989 | −0.222495 | − | 0.974934i | \(-0.571420\pi\) | ||||
−0.222495 | + | 0.974934i | \(0.571420\pi\) | |||||||
\(278\) | −59578.7 | −0.0462358 | ||||||||
\(279\) | 287704. | 0.221276 | ||||||||
\(280\) | 511101. | 0.389594 | ||||||||
\(281\) | 85997.1 | 0.0649708 | 0.0324854 | − | 0.999472i | \(-0.489658\pi\) | ||||
0.0324854 | + | 0.999472i | \(0.489658\pi\) | |||||||
\(282\) | 305337. | 0.228643 | ||||||||
\(283\) | −1.71331e6 | −1.27165 | −0.635827 | − | 0.771832i | \(-0.719341\pi\) | ||||
−0.635827 | + | 0.771832i | \(0.719341\pi\) | |||||||
\(284\) | 614269. | 0.451921 | ||||||||
\(285\) | 326469. | 0.238084 | ||||||||
\(286\) | −177353. | −0.128211 | ||||||||
\(287\) | 563949. | 0.404143 | ||||||||
\(288\) | 292657. | 0.207911 | ||||||||
\(289\) | −102695. | −0.0723280 | ||||||||
\(290\) | 3.04858e6 | 2.12864 | ||||||||
\(291\) | 419340. | 0.290291 | ||||||||
\(292\) | 3.02391e6 | 2.07545 | ||||||||
\(293\) | 775969. | 0.528050 | 0.264025 | − | 0.964516i | \(-0.414950\pi\) | ||||
0.264025 | + | 0.964516i | \(0.414950\pi\) | |||||||
\(294\) | −204239. | −0.137807 | ||||||||
\(295\) | −1.79305e6 | −1.19961 | ||||||||
\(296\) | 238942. | 0.158512 | ||||||||
\(297\) | −204391. | −0.134453 | ||||||||
\(298\) | −578454. | −0.377336 | ||||||||
\(299\) | −35404.3 | −0.0229023 | ||||||||
\(300\) | −633203. | −0.406200 | ||||||||
\(301\) | 489407. | 0.311354 | ||||||||
\(302\) | 2.55423e6 | 1.61154 | ||||||||
\(303\) | 597397. | 0.373815 | ||||||||
\(304\) | 356685. | 0.221361 | ||||||||
\(305\) | 771043. | 0.474601 | ||||||||
\(306\) | −878636. | −0.536421 | ||||||||
\(307\) | −125127. | −0.0757714 | −0.0378857 | − | 0.999282i | \(-0.512062\pi\) | ||||
−0.0378857 | + | 0.999282i | \(0.512062\pi\) | |||||||
\(308\) | 787645. | 0.473101 | ||||||||
\(309\) | −244028. | −0.145393 | ||||||||
\(310\) | −1.46250e6 | −0.864353 | ||||||||
\(311\) | −1.06602e6 | −0.624977 | −0.312489 | − | 0.949921i | \(-0.601163\pi\) | ||||
−0.312489 | + | 0.949921i | \(0.601163\pi\) | |||||||
\(312\) | 144219. | 0.0838759 | ||||||||
\(313\) | −2.00246e6 | −1.15532 | −0.577660 | − | 0.816278i | \(-0.696034\pi\) | ||||
−0.577660 | + | 0.816278i | \(0.696034\pi\) | |||||||
\(314\) | 923996. | 0.528866 | ||||||||
\(315\) | −172906. | −0.0981827 | ||||||||
\(316\) | 5.44235e6 | 3.06598 | ||||||||
\(317\) | −3.07793e6 | −1.72032 | −0.860162 | − | 0.510021i | \(-0.829638\pi\) | ||||
−0.860162 | + | 0.510021i | \(0.829638\pi\) | |||||||
\(318\) | 115765. | 0.0641964 | ||||||||
\(319\) | 2.07586e6 | 1.14214 | ||||||||
\(320\) | −2.08485e6 | −1.13815 | ||||||||
\(321\) | −603747. | −0.327034 | ||||||||
\(322\) | 244994. | 0.131679 | ||||||||
\(323\) | 955627. | 0.509662 | ||||||||
\(324\) | 376158. | 0.199071 | ||||||||
\(325\) | 82129.8 | 0.0431313 | ||||||||
\(326\) | −386420. | −0.201380 | ||||||||
\(327\) | −566466. | −0.292957 | ||||||||
\(328\) | 2.75565e6 | 1.41429 | ||||||||
\(329\) | 175885. | 0.0895858 | ||||||||
\(330\) | 1.03899e6 | 0.525202 | ||||||||
\(331\) | −2.80698e6 | −1.40822 | −0.704108 | − | 0.710093i | \(-0.748653\pi\) | ||||
−0.704108 | + | 0.710093i | \(0.748653\pi\) | |||||||
\(332\) | −2.17925e6 | −1.08508 | ||||||||
\(333\) | −80834.5 | −0.0399472 | ||||||||
\(334\) | 1.24861e6 | 0.612434 | ||||||||
\(335\) | −1.05550e6 | −0.513861 | ||||||||
\(336\) | −188910. | −0.0912864 | ||||||||
\(337\) | 1.07786e6 | 0.516995 | 0.258497 | − | 0.966012i | \(-0.416773\pi\) | ||||
0.258497 | + | 0.966012i | \(0.416773\pi\) | |||||||
\(338\) | 3.46697e6 | 1.65066 | ||||||||
\(339\) | 1.54021e6 | 0.727916 | ||||||||
\(340\) | 2.86649e6 | 1.34478 | ||||||||
\(341\) | −995852. | −0.463777 | ||||||||
\(342\) | −637468. | −0.294709 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 2.39142e6 | 1.08958 | ||||||||
\(345\) | 207409. | 0.0938168 | ||||||||
\(346\) | 6.48809e6 | 2.91358 | ||||||||
\(347\) | 1.11455e6 | 0.496909 | 0.248454 | − | 0.968644i | \(-0.420077\pi\) | ||||
0.248454 | + | 0.968644i | \(0.420077\pi\) | |||||||
\(348\) | −3.82037e6 | −1.69105 | ||||||||
\(349\) | −1.51049e6 | −0.663825 | −0.331912 | − | 0.943310i | \(-0.607694\pi\) | ||||
−0.331912 | + | 0.943310i | \(0.607694\pi\) | |||||||
\(350\) | −568330. | −0.247988 | ||||||||
\(351\) | −48789.7 | −0.0211378 | ||||||||
\(352\) | −1.01300e6 | −0.435765 | ||||||||
\(353\) | 2.25980e6 | 0.965235 | 0.482618 | − | 0.875831i | \(-0.339686\pi\) | ||||
0.482618 | + | 0.875831i | \(0.339686\pi\) | |||||||
\(354\) | 3.50115e6 | 1.48492 | ||||||||
\(355\) | 466755. | 0.196570 | ||||||||
\(356\) | −2.79649e6 | −1.16947 | ||||||||
\(357\) | −506125. | −0.210178 | ||||||||
\(358\) | 5.90963e6 | 2.43699 | ||||||||
\(359\) | 3.83389e6 | 1.57001 | 0.785007 | − | 0.619487i | \(-0.212659\pi\) | ||||
0.785007 | + | 0.619487i | \(0.212659\pi\) | |||||||
\(360\) | −844881. | −0.343589 | ||||||||
\(361\) | −1.78277e6 | −0.719992 | ||||||||
\(362\) | 246019. | 0.0986726 | ||||||||
\(363\) | −741984. | −0.295548 | ||||||||
\(364\) | 188017. | 0.0743778 | ||||||||
\(365\) | 2.29773e6 | 0.902750 | ||||||||
\(366\) | −1.50555e6 | −0.587479 | ||||||||
\(367\) | −3.92836e6 | −1.52246 | −0.761231 | − | 0.648480i | \(-0.775405\pi\) | ||||
−0.761231 | + | 0.648480i | \(0.775405\pi\) | |||||||
\(368\) | 226606. | 0.0872272 | ||||||||
\(369\) | −932242. | −0.356421 | ||||||||
\(370\) | 410910. | 0.156042 | ||||||||
\(371\) | 66684.9 | 0.0251532 | ||||||||
\(372\) | 1.83275e6 | 0.686666 | ||||||||
\(373\) | −1.95136e6 | −0.726215 | −0.363107 | − | 0.931747i | \(-0.618284\pi\) | ||||
−0.363107 | + | 0.931747i | \(0.618284\pi\) | |||||||
\(374\) | 3.04129e6 | 1.12429 | ||||||||
\(375\) | −1.70639e6 | −0.626612 | ||||||||
\(376\) | 859436. | 0.313505 | ||||||||
\(377\) | 495523. | 0.179560 | ||||||||
\(378\) | 337620. | 0.121534 | ||||||||
\(379\) | −1.20683e6 | −0.431567 | −0.215784 | − | 0.976441i | \(-0.569231\pi\) | ||||
−0.215784 | + | 0.976441i | \(0.569231\pi\) | |||||||
\(380\) | 2.07969e6 | 0.738823 | ||||||||
\(381\) | 1.28354e6 | 0.452999 | ||||||||
\(382\) | −1.23906e6 | −0.434443 | ||||||||
\(383\) | 2.15608e6 | 0.751049 | 0.375525 | − | 0.926812i | \(-0.377463\pi\) | ||||
0.375525 | + | 0.926812i | \(0.377463\pi\) | |||||||
\(384\) | 3.03034e6 | 1.04873 | ||||||||
\(385\) | 598495. | 0.205783 | ||||||||
\(386\) | −3.87646e6 | −1.32424 | ||||||||
\(387\) | −809020. | −0.274588 | ||||||||
\(388\) | 2.67131e6 | 0.900833 | ||||||||
\(389\) | 79987.4 | 0.0268008 | 0.0134004 | − | 0.999910i | \(-0.495734\pi\) | ||||
0.0134004 | + | 0.999910i | \(0.495734\pi\) | |||||||
\(390\) | 248015. | 0.0825688 | ||||||||
\(391\) | 607121. | 0.200832 | ||||||||
\(392\) | −574874. | −0.188955 | ||||||||
\(393\) | −2.76257e6 | −0.902261 | ||||||||
\(394\) | 5.87595e6 | 1.90694 | ||||||||
\(395\) | 4.13539e6 | 1.33359 | ||||||||
\(396\) | −1.30202e6 | −0.417236 | ||||||||
\(397\) | −3.48448e6 | −1.10959 | −0.554795 | − | 0.831987i | \(-0.687203\pi\) | ||||
−0.554795 | + | 0.831987i | \(0.687203\pi\) | |||||||
\(398\) | −8.70957e6 | −2.75606 | ||||||||
\(399\) | −367204. | −0.115472 | ||||||||
\(400\) | −525673. | −0.164273 | ||||||||
\(401\) | −798809. | −0.248074 | −0.124037 | − | 0.992278i | \(-0.539584\pi\) | ||||
−0.124037 | + | 0.992278i | \(0.539584\pi\) | |||||||
\(402\) | 2.06098e6 | 0.636076 | ||||||||
\(403\) | −237717. | −0.0729119 | ||||||||
\(404\) | 3.80558e6 | 1.16002 | ||||||||
\(405\) | 285825. | 0.0865890 | ||||||||
\(406\) | −3.42897e6 | −1.03240 | ||||||||
\(407\) | 279799. | 0.0837259 | ||||||||
\(408\) | −2.47311e6 | −0.735516 | ||||||||
\(409\) | 3.44063e6 | 1.01702 | 0.508510 | − | 0.861056i | \(-0.330196\pi\) | ||||
0.508510 | + | 0.861056i | \(0.330196\pi\) | |||||||
\(410\) | 4.73891e6 | 1.39225 | ||||||||
\(411\) | −2.32998e6 | −0.680374 | ||||||||
\(412\) | −1.55452e6 | −0.451185 | ||||||||
\(413\) | 2.01678e6 | 0.581814 | ||||||||
\(414\) | −404991. | −0.116130 | ||||||||
\(415\) | −1.65591e6 | −0.471973 | ||||||||
\(416\) | −241810. | −0.0685081 | ||||||||
\(417\) | 56732.1 | 0.0159768 | ||||||||
\(418\) | 2.20652e6 | 0.617685 | ||||||||
\(419\) | −3.88408e6 | −1.08082 | −0.540409 | − | 0.841402i | \(-0.681731\pi\) | ||||
−0.540409 | + | 0.841402i | \(0.681731\pi\) | |||||||
\(420\) | −1.10146e6 | −0.304681 | ||||||||
\(421\) | 1.03769e6 | 0.285340 | 0.142670 | − | 0.989770i | \(-0.454431\pi\) | ||||
0.142670 | + | 0.989770i | \(0.454431\pi\) | |||||||
\(422\) | −8.16446e6 | −2.23175 | ||||||||
\(423\) | −290749. | −0.0790072 | ||||||||
\(424\) | 325846. | 0.0880233 | ||||||||
\(425\) | −1.40838e6 | −0.378223 | ||||||||
\(426\) | −911393. | −0.243322 | ||||||||
\(427\) | −867250. | −0.230184 | ||||||||
\(428\) | −3.84603e6 | −1.01485 | ||||||||
\(429\) | 168880. | 0.0443031 | ||||||||
\(430\) | 4.11253e6 | 1.07260 | ||||||||
\(431\) | −1.16941e6 | −0.303232 | −0.151616 | − | 0.988439i | \(-0.548448\pi\) | ||||
−0.151616 | + | 0.988439i | \(0.548448\pi\) | |||||||
\(432\) | 312279. | 0.0805070 | ||||||||
\(433\) | −787842. | −0.201939 | −0.100969 | − | 0.994890i | \(-0.532194\pi\) | ||||
−0.100969 | + | 0.994890i | \(0.532194\pi\) | |||||||
\(434\) | 1.64498e6 | 0.419215 | ||||||||
\(435\) | −2.90292e6 | −0.735550 | ||||||||
\(436\) | −3.60854e6 | −0.909108 | ||||||||
\(437\) | 440479. | 0.110337 | ||||||||
\(438\) | −4.48659e6 | −1.11746 | ||||||||
\(439\) | 1.47818e6 | 0.366072 | 0.183036 | − | 0.983106i | \(-0.441407\pi\) | ||||
0.183036 | + | 0.983106i | \(0.441407\pi\) | |||||||
\(440\) | 2.92445e6 | 0.720134 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 725980. | 0.176754 | ||||||||
\(443\) | 3.46335e6 | 0.838470 | 0.419235 | − | 0.907878i | \(-0.362298\pi\) | ||||
0.419235 | + | 0.907878i | \(0.362298\pi\) | |||||||
\(444\) | −514937. | −0.123964 | ||||||||
\(445\) | −2.12493e6 | −0.508679 | ||||||||
\(446\) | 3.26108e6 | 0.776290 | ||||||||
\(447\) | 550816. | 0.130388 | ||||||||
\(448\) | 2.34498e6 | 0.552007 | ||||||||
\(449\) | 502703. | 0.117678 | 0.0588391 | − | 0.998267i | \(-0.481260\pi\) | ||||
0.0588391 | + | 0.998267i | \(0.481260\pi\) | |||||||
\(450\) | 939485. | 0.218705 | ||||||||
\(451\) | 3.22684e6 | 0.747027 | ||||||||
\(452\) | 9.81157e6 | 2.25888 | ||||||||
\(453\) | −2.43219e6 | −0.556868 | ||||||||
\(454\) | 5.12665e6 | 1.16733 | ||||||||
\(455\) | 142865. | 0.0323518 | ||||||||
\(456\) | −1.79429e6 | −0.404092 | ||||||||
\(457\) | 6.33402e6 | 1.41870 | 0.709348 | − | 0.704859i | \(-0.248990\pi\) | ||||
0.709348 | + | 0.704859i | \(0.248990\pi\) | |||||||
\(458\) | −892912. | −0.198905 | ||||||||
\(459\) | 836656. | 0.185360 | ||||||||
\(460\) | 1.32125e6 | 0.291133 | ||||||||
\(461\) | −6.42752e6 | −1.40861 | −0.704306 | − | 0.709897i | \(-0.748742\pi\) | ||||
−0.704306 | + | 0.709897i | \(0.748742\pi\) | |||||||
\(462\) | −1.16863e6 | −0.254725 | ||||||||
\(463\) | 1.01387e6 | 0.219800 | 0.109900 | − | 0.993943i | \(-0.464947\pi\) | ||||
0.109900 | + | 0.993943i | \(0.464947\pi\) | |||||||
\(464\) | −3.17160e6 | −0.683886 | ||||||||
\(465\) | 1.39262e6 | 0.298676 | ||||||||
\(466\) | 6.87353e6 | 1.46627 | ||||||||
\(467\) | −4.23941e6 | −0.899524 | −0.449762 | − | 0.893148i | \(-0.648491\pi\) | ||||
−0.449762 | + | 0.893148i | \(0.648491\pi\) | |||||||
\(468\) | −310803. | −0.0655950 | ||||||||
\(469\) | 1.18720e6 | 0.249225 | ||||||||
\(470\) | 1.47798e6 | 0.308619 | ||||||||
\(471\) | −879848. | −0.182749 | ||||||||
\(472\) | 9.85471e6 | 2.03605 | ||||||||
\(473\) | 2.80033e6 | 0.575514 | ||||||||
\(474\) | −8.07483e6 | −1.65077 | ||||||||
\(475\) | −1.02181e6 | −0.207795 | ||||||||
\(476\) | −3.22415e6 | −0.652226 | ||||||||
\(477\) | −110234. | −0.0221830 | ||||||||
\(478\) | −1.19577e7 | −2.39375 | ||||||||
\(479\) | 4.42492e6 | 0.881185 | 0.440592 | − | 0.897707i | \(-0.354768\pi\) | ||||
0.440592 | + | 0.897707i | \(0.354768\pi\) | |||||||
\(480\) | 1.41660e6 | 0.280636 | ||||||||
\(481\) | 66790.1 | 0.0131628 | ||||||||
\(482\) | −6.19977e6 | −1.21551 | ||||||||
\(483\) | −233289. | −0.0455016 | ||||||||
\(484\) | −4.72664e6 | −0.917147 | ||||||||
\(485\) | 2.02980e6 | 0.391832 | ||||||||
\(486\) | −558106. | −0.107183 | ||||||||
\(487\) | 783310. | 0.149662 | 0.0748309 | − | 0.997196i | \(-0.476158\pi\) | ||||
0.0748309 | + | 0.997196i | \(0.476158\pi\) | |||||||
\(488\) | −4.23769e6 | −0.805526 | ||||||||
\(489\) | 367957. | 0.0695866 | ||||||||
\(490\) | −988614. | −0.186010 | ||||||||
\(491\) | 5.03694e6 | 0.942894 | 0.471447 | − | 0.881895i | \(-0.343732\pi\) | ||||
0.471447 | + | 0.881895i | \(0.343732\pi\) | |||||||
\(492\) | −5.93863e6 | −1.10605 | ||||||||
\(493\) | −8.49733e6 | −1.57458 | ||||||||
\(494\) | 526713. | 0.0971084 | ||||||||
\(495\) | −989348. | −0.181483 | ||||||||
\(496\) | 1.52152e6 | 0.277698 | ||||||||
\(497\) | −524995. | −0.0953375 | ||||||||
\(498\) | 3.23336e6 | 0.584226 | ||||||||
\(499\) | −2.06678e6 | −0.371573 | −0.185786 | − | 0.982590i | \(-0.559483\pi\) | ||||
−0.185786 | + | 0.982590i | \(0.559483\pi\) | |||||||
\(500\) | −1.08701e7 | −1.94451 | ||||||||
\(501\) | −1.18895e6 | −0.211626 | ||||||||
\(502\) | −3.22786e6 | −0.571684 | ||||||||
\(503\) | −1.31778e6 | −0.232232 | −0.116116 | − | 0.993236i | \(-0.537044\pi\) | ||||
−0.116116 | + | 0.993236i | \(0.537044\pi\) | |||||||
\(504\) | 950302. | 0.166642 | ||||||||
\(505\) | 2.89168e6 | 0.504571 | ||||||||
\(506\) | 1.40183e6 | 0.243399 | ||||||||
\(507\) | −3.30132e6 | −0.570385 | ||||||||
\(508\) | 8.17649e6 | 1.40575 | ||||||||
\(509\) | −1.06692e7 | −1.82532 | −0.912660 | − | 0.408720i | \(-0.865975\pi\) | ||||
−0.912660 | + | 0.408720i | \(0.865975\pi\) | |||||||
\(510\) | −4.25301e6 | −0.724054 | ||||||||
\(511\) | −2.58443e6 | −0.437838 | ||||||||
\(512\) | 4.82977e6 | 0.814239 | ||||||||
\(513\) | 607011. | 0.101836 | ||||||||
\(514\) | −2.35176e6 | −0.392631 | ||||||||
\(515\) | −1.18121e6 | −0.196250 | ||||||||
\(516\) | −5.15368e6 | −0.852104 | ||||||||
\(517\) | 1.00639e6 | 0.165592 | ||||||||
\(518\) | −462181. | −0.0756812 | ||||||||
\(519\) | −6.17810e6 | −1.00678 | ||||||||
\(520\) | 698090. | 0.113215 | ||||||||
\(521\) | −9.37667e6 | −1.51340 | −0.756701 | − | 0.653761i | \(-0.773190\pi\) | ||||
−0.756701 | + | 0.653761i | \(0.773190\pi\) | |||||||
\(522\) | 5.66830e6 | 0.910492 | ||||||||
\(523\) | −8.94470e6 | −1.42992 | −0.714960 | − | 0.699165i | \(-0.753555\pi\) | ||||
−0.714960 | + | 0.699165i | \(0.753555\pi\) | |||||||
\(524\) | −1.75983e7 | −2.79990 | ||||||||
\(525\) | 541176. | 0.0856921 | ||||||||
\(526\) | 1.57404e7 | 2.48057 | ||||||||
\(527\) | 4.07643e6 | 0.639372 | ||||||||
\(528\) | −1.08092e6 | −0.168736 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 560359. | 0.0866516 | ||||||||
\(531\) | −3.33387e6 | −0.513112 | ||||||||
\(532\) | −2.33919e6 | −0.358332 | ||||||||
\(533\) | 770272. | 0.117443 | ||||||||
\(534\) | 4.14917e6 | 0.629662 | ||||||||
\(535\) | −2.92242e6 | −0.441426 | ||||||||
\(536\) | 5.80107e6 | 0.872160 | ||||||||
\(537\) | −5.62728e6 | −0.842099 | ||||||||
\(538\) | 1.44373e7 | 2.15046 | ||||||||
\(539\) | −673172. | −0.0998055 | ||||||||
\(540\) | 1.82078e6 | 0.268703 | ||||||||
\(541\) | −1.48099e6 | −0.217550 | −0.108775 | − | 0.994066i | \(-0.534693\pi\) | ||||
−0.108775 | + | 0.994066i | \(0.534693\pi\) | |||||||
\(542\) | 8.38840e6 | 1.22654 | ||||||||
\(543\) | −234264. | −0.0340963 | ||||||||
\(544\) | 4.14662e6 | 0.600754 | ||||||||
\(545\) | −2.74196e6 | −0.395431 | ||||||||
\(546\) | −278961. | −0.0400463 | ||||||||
\(547\) | −3.38141e6 | −0.483203 | −0.241602 | − | 0.970376i | \(-0.577673\pi\) | ||||
−0.241602 | + | 0.970376i | \(0.577673\pi\) | |||||||
\(548\) | −1.48426e7 | −2.11134 | ||||||||
\(549\) | 1.43362e6 | 0.203003 | ||||||||
\(550\) | −3.25191e6 | −0.458387 | ||||||||
\(551\) | −6.16499e6 | −0.865074 | ||||||||
\(552\) | −1.13993e6 | −0.159232 | ||||||||
\(553\) | −4.65139e6 | −0.646800 | ||||||||
\(554\) | 5.37098e6 | 0.743496 | ||||||||
\(555\) | −391277. | −0.0539202 | ||||||||
\(556\) | 361398. | 0.0495792 | ||||||||
\(557\) | −1.17512e7 | −1.60488 | −0.802442 | − | 0.596730i | \(-0.796466\pi\) | ||||
−0.802442 | + | 0.596730i | \(0.796466\pi\) | |||||||
\(558\) | −2.71926e6 | −0.369713 | ||||||||
\(559\) | 668459. | 0.0904785 | ||||||||
\(560\) | −914412. | −0.123217 | ||||||||
\(561\) | −2.89598e6 | −0.388498 | ||||||||
\(562\) | −812809. | −0.108554 | ||||||||
\(563\) | 3.08008e6 | 0.409535 | 0.204767 | − | 0.978811i | \(-0.434356\pi\) | ||||
0.204767 | + | 0.978811i | \(0.434356\pi\) | |||||||
\(564\) | −1.85215e6 | −0.245176 | ||||||||
\(565\) | 7.45536e6 | 0.982533 | ||||||||
\(566\) | 1.61935e7 | 2.12470 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | −2.56531e6 | −0.333633 | ||||||||
\(569\) | 2.42613e6 | 0.314148 | 0.157074 | − | 0.987587i | \(-0.449794\pi\) | ||||
0.157074 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(570\) | −3.08565e6 | −0.397795 | ||||||||
\(571\) | 6.72920e6 | 0.863721 | 0.431860 | − | 0.901940i | \(-0.357857\pi\) | ||||
0.431860 | + | 0.901940i | \(0.357857\pi\) | |||||||
\(572\) | 1.07581e6 | 0.137482 | ||||||||
\(573\) | 1.17986e6 | 0.150121 | ||||||||
\(574\) | −5.33021e6 | −0.675250 | ||||||||
\(575\) | −649166. | −0.0818816 | ||||||||
\(576\) | −3.87640e6 | −0.486825 | ||||||||
\(577\) | −1.07527e7 | −1.34456 | −0.672280 | − | 0.740297i | \(-0.734685\pi\) | ||||
−0.672280 | + | 0.740297i | \(0.734685\pi\) | |||||||
\(578\) | 970633. | 0.120847 | ||||||||
\(579\) | 3.69125e6 | 0.457591 | ||||||||
\(580\) | −1.84924e7 | −2.28256 | ||||||||
\(581\) | 1.86253e6 | 0.228909 | ||||||||
\(582\) | −3.96343e6 | −0.485024 | ||||||||
\(583\) | 381563. | 0.0464937 | ||||||||
\(584\) | −1.26284e7 | −1.53221 | ||||||||
\(585\) | −236165. | −0.0285316 | ||||||||
\(586\) | −7.33413e6 | −0.882276 | ||||||||
\(587\) | 3.00125e6 | 0.359507 | 0.179754 | − | 0.983712i | \(-0.442470\pi\) | ||||
0.179754 | + | 0.983712i | \(0.442470\pi\) | |||||||
\(588\) | 1.23890e6 | 0.147772 | ||||||||
\(589\) | 2.95753e6 | 0.351270 | ||||||||
\(590\) | 1.69472e7 | 2.00432 | ||||||||
\(591\) | −5.59521e6 | −0.658942 | ||||||||
\(592\) | −427491. | −0.0501329 | ||||||||
\(593\) | −8.19366e6 | −0.956844 | −0.478422 | − | 0.878130i | \(-0.658791\pi\) | ||||
−0.478422 | + | 0.878130i | \(0.658791\pi\) | |||||||
\(594\) | 1.93182e6 | 0.224647 | ||||||||
\(595\) | −2.44988e6 | −0.283696 | ||||||||
\(596\) | 3.50884e6 | 0.404621 | ||||||||
\(597\) | 8.29344e6 | 0.952355 | ||||||||
\(598\) | 334627. | 0.0382655 | ||||||||
\(599\) | 1.11379e7 | 1.26835 | 0.634173 | − | 0.773191i | \(-0.281341\pi\) | ||||
0.634173 | + | 0.773191i | \(0.281341\pi\) | |||||||
\(600\) | 2.64438e6 | 0.299879 | ||||||||
\(601\) | 813772. | 0.0919002 | 0.0459501 | − | 0.998944i | \(-0.485368\pi\) | ||||
0.0459501 | + | 0.998944i | \(0.485368\pi\) | |||||||
\(602\) | −4.62567e6 | −0.520216 | ||||||||
\(603\) | −1.96251e6 | −0.219796 | ||||||||
\(604\) | −1.54937e7 | −1.72808 | ||||||||
\(605\) | −3.59155e6 | −0.398927 | ||||||||
\(606\) | −5.64635e6 | −0.624577 | ||||||||
\(607\) | 1.11311e7 | 1.22621 | 0.613107 | − | 0.790000i | \(-0.289919\pi\) | ||||
0.613107 | + | 0.790000i | \(0.289919\pi\) | |||||||
\(608\) | 3.00846e6 | 0.330054 | ||||||||
\(609\) | 3.26514e6 | 0.356745 | ||||||||
\(610\) | −7.28757e6 | −0.792973 | ||||||||
\(611\) | 240233. | 0.0260334 | ||||||||
\(612\) | 5.32972e6 | 0.575210 | ||||||||
\(613\) | 497094. | 0.0534302 | 0.0267151 | − | 0.999643i | \(-0.491495\pi\) | ||||
0.0267151 | + | 0.999643i | \(0.491495\pi\) | |||||||
\(614\) | 1.18265e6 | 0.126600 | ||||||||
\(615\) | −4.51249e6 | −0.481092 | ||||||||
\(616\) | −3.28936e6 | −0.349268 | ||||||||
\(617\) | 1.33391e7 | 1.41064 | 0.705318 | − | 0.708891i | \(-0.250804\pi\) | ||||
0.705318 | + | 0.708891i | \(0.250804\pi\) | |||||||
\(618\) | 2.30645e6 | 0.242925 | ||||||||
\(619\) | 1.40742e6 | 0.147638 | 0.0738188 | − | 0.997272i | \(-0.476481\pi\) | ||||
0.0738188 | + | 0.997272i | \(0.476481\pi\) | |||||||
\(620\) | 8.87137e6 | 0.926854 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | 1.00756e7 | 1.04422 | ||||||||
\(623\) | 2.39007e6 | 0.246712 | ||||||||
\(624\) | −258023. | −0.0265276 | ||||||||
\(625\) | −4.42484e6 | −0.453104 | ||||||||
\(626\) | 1.89264e7 | 1.93033 | ||||||||
\(627\) | −2.10110e6 | −0.213441 | ||||||||
\(628\) | −5.60487e6 | −0.567109 | ||||||||
\(629\) | −1.14533e6 | −0.115426 | ||||||||
\(630\) | 1.63424e6 | 0.164045 | ||||||||
\(631\) | 1.52181e7 | 1.52155 | 0.760777 | − | 0.649014i | \(-0.224818\pi\) | ||||
0.760777 | + | 0.649014i | \(0.224818\pi\) | |||||||
\(632\) | −2.27283e7 | −2.26347 | ||||||||
\(633\) | 7.77438e6 | 0.771181 | ||||||||
\(634\) | 2.90913e7 | 2.87435 | ||||||||
\(635\) | 6.21294e6 | 0.611453 | ||||||||
\(636\) | −702222. | −0.0688385 | ||||||||
\(637\) | −160691. | −0.0156908 | ||||||||
\(638\) | −1.96201e7 | −1.90831 | ||||||||
\(639\) | 867848. | 0.0840798 | ||||||||
\(640\) | 1.46683e7 | 1.41556 | ||||||||
\(641\) | 1.94866e7 | 1.87323 | 0.936613 | − | 0.350366i | \(-0.113943\pi\) | ||||
0.936613 | + | 0.350366i | \(0.113943\pi\) | |||||||
\(642\) | 5.70637e6 | 0.546414 | ||||||||
\(643\) | −6.13077e6 | −0.584774 | −0.292387 | − | 0.956300i | \(-0.594450\pi\) | ||||
−0.292387 | + | 0.956300i | \(0.594450\pi\) | |||||||
\(644\) | −1.48611e6 | −0.141201 | ||||||||
\(645\) | −3.91604e6 | −0.370636 | ||||||||
\(646\) | −9.03219e6 | −0.851553 | ||||||||
\(647\) | 267659. | 0.0251374 | 0.0125687 | − | 0.999921i | \(-0.495999\pi\) | ||||
0.0125687 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(648\) | −1.57091e6 | −0.146965 | ||||||||
\(649\) | 1.15398e7 | 1.07544 | ||||||||
\(650\) | −776257. | −0.0720646 | ||||||||
\(651\) | −1.56639e6 | −0.144859 | ||||||||
\(652\) | 2.34399e6 | 0.215942 | ||||||||
\(653\) | 4.89649e6 | 0.449367 | 0.224684 | − | 0.974432i | \(-0.427865\pi\) | ||||
0.224684 | + | 0.974432i | \(0.427865\pi\) | |||||||
\(654\) | 5.35400e6 | 0.489479 | ||||||||
\(655\) | −1.33722e7 | −1.21786 | ||||||||
\(656\) | −4.93014e6 | −0.447301 | ||||||||
\(657\) | 4.27223e6 | 0.386137 | ||||||||
\(658\) | −1.66239e6 | −0.149682 | ||||||||
\(659\) | 1.29049e7 | 1.15755 | 0.578775 | − | 0.815487i | \(-0.303531\pi\) | ||||
0.578775 | + | 0.815487i | \(0.303531\pi\) | |||||||
\(660\) | −6.30241e6 | −0.563180 | ||||||||
\(661\) | −5.68181e6 | −0.505805 | −0.252902 | − | 0.967492i | \(-0.581385\pi\) | ||||
−0.252902 | + | 0.967492i | \(0.581385\pi\) | |||||||
\(662\) | 2.65304e7 | 2.35287 | ||||||||
\(663\) | −691294. | −0.0610771 | ||||||||
\(664\) | 9.10097e6 | 0.801065 | ||||||||
\(665\) | −1.77744e6 | −0.155862 | ||||||||
\(666\) | 764014. | 0.0667445 | ||||||||
\(667\) | −3.91669e6 | −0.340882 | ||||||||
\(668\) | −7.57393e6 | −0.656719 | ||||||||
\(669\) | −3.10527e6 | −0.268246 | ||||||||
\(670\) | 9.97613e6 | 0.858569 | ||||||||
\(671\) | −4.96229e6 | −0.425477 | ||||||||
\(672\) | −1.59336e6 | −0.136110 | ||||||||
\(673\) | 2.09836e7 | 1.78584 | 0.892918 | − | 0.450219i | \(-0.148654\pi\) | ||||
0.892918 | + | 0.450219i | \(0.148654\pi\) | |||||||
\(674\) | −1.01874e7 | −0.863805 | ||||||||
\(675\) | −894598. | −0.0755733 | ||||||||
\(676\) | −2.10303e7 | −1.77002 | ||||||||
\(677\) | 1.55182e7 | 1.30128 | 0.650640 | − | 0.759386i | \(-0.274501\pi\) | ||||
0.650640 | + | 0.759386i | \(0.274501\pi\) | |||||||
\(678\) | −1.45574e7 | −1.21622 | ||||||||
\(679\) | −2.28307e6 | −0.190040 | ||||||||
\(680\) | −1.19710e7 | −0.992791 | ||||||||
\(681\) | −4.88171e6 | −0.403370 | ||||||||
\(682\) | 9.41238e6 | 0.774887 | ||||||||
\(683\) | 6.40256e6 | 0.525172 | 0.262586 | − | 0.964909i | \(-0.415425\pi\) | ||||
0.262586 | + | 0.964909i | \(0.415425\pi\) | |||||||
\(684\) | 3.86682e6 | 0.316019 | ||||||||
\(685\) | −1.12782e7 | −0.918361 | ||||||||
\(686\) | 1.11197e6 | 0.0902158 | ||||||||
\(687\) | 850250. | 0.0687314 | ||||||||
\(688\) | −4.27849e6 | −0.344603 | ||||||||
\(689\) | 91081.9 | 0.00730944 | ||||||||
\(690\) | −1.96035e6 | −0.156751 | ||||||||
\(691\) | 448684. | 0.0357475 | 0.0178738 | − | 0.999840i | \(-0.494310\pi\) | ||||
0.0178738 | + | 0.999840i | \(0.494310\pi\) | |||||||
\(692\) | −3.93561e7 | −3.12426 | ||||||||
\(693\) | 1.11280e6 | 0.0880202 | ||||||||
\(694\) | −1.05343e7 | −0.830244 | ||||||||
\(695\) | 274610. | 0.0215652 | ||||||||
\(696\) | 1.59546e7 | 1.24843 | ||||||||
\(697\) | −1.32088e7 | −1.02987 | ||||||||
\(698\) | 1.42765e7 | 1.10913 | ||||||||
\(699\) | −6.54513e6 | −0.506670 | ||||||||
\(700\) | 3.44744e6 | 0.265920 | ||||||||
\(701\) | 2.63513e6 | 0.202538 | 0.101269 | − | 0.994859i | \(-0.467710\pi\) | ||||
0.101269 | + | 0.994859i | \(0.467710\pi\) | |||||||
\(702\) | 461140. | 0.0353175 | ||||||||
\(703\) | −830961. | −0.0634151 | ||||||||
\(704\) | 1.34177e7 | 1.02034 | ||||||||
\(705\) | −1.40736e6 | −0.106643 | ||||||||
\(706\) | −2.13587e7 | −1.61273 | ||||||||
\(707\) | −3.25249e6 | −0.244719 | ||||||||
\(708\) | −2.12376e7 | −1.59229 | ||||||||
\(709\) | −5.40731e6 | −0.403985 | −0.201993 | − | 0.979387i | \(-0.564742\pi\) | ||||
−0.201993 | + | 0.979387i | \(0.564742\pi\) | |||||||
\(710\) | −4.41157e6 | −0.328433 | ||||||||
\(711\) | 7.68903e6 | 0.570424 | ||||||||
\(712\) | 1.16787e7 | 0.863365 | ||||||||
\(713\) | 1.87895e6 | 0.138418 | ||||||||
\(714\) | 4.78369e6 | 0.351170 | ||||||||
\(715\) | 817457. | 0.0597998 | ||||||||
\(716\) | −3.58473e7 | −2.61321 | ||||||||
\(717\) | 1.13864e7 | 0.827158 | ||||||||
\(718\) | −3.62363e7 | −2.62321 | ||||||||
\(719\) | 2.14255e7 | 1.54564 | 0.772820 | − | 0.634626i | \(-0.218846\pi\) | ||||
0.772820 | + | 0.634626i | \(0.218846\pi\) | |||||||
\(720\) | 1.51158e6 | 0.108667 | ||||||||
\(721\) | 1.32860e6 | 0.0951821 | ||||||||
\(722\) | 1.68500e7 | 1.20298 | ||||||||
\(723\) | 5.90356e6 | 0.420018 | ||||||||
\(724\) | −1.49233e6 | −0.105808 | ||||||||
\(725\) | 9.08580e6 | 0.641975 | ||||||||
\(726\) | 7.01293e6 | 0.493808 | ||||||||
\(727\) | −8.23407e6 | −0.577801 | −0.288901 | − | 0.957359i | \(-0.593290\pi\) | ||||
−0.288901 | + | 0.957359i | \(0.593290\pi\) | |||||||
\(728\) | −785194. | −0.0549097 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.17172e7 | −1.50833 | ||||||||
\(731\) | −1.14629e7 | −0.793415 | ||||||||
\(732\) | 9.13253e6 | 0.629960 | ||||||||
\(733\) | 640189. | 0.0440097 | 0.0220048 | − | 0.999758i | \(-0.492995\pi\) | ||||
0.0220048 | + | 0.999758i | \(0.492995\pi\) | |||||||
\(734\) | 3.71293e7 | 2.54376 | ||||||||
\(735\) | 941380. | 0.0642756 | ||||||||
\(736\) | 1.91131e6 | 0.130058 | ||||||||
\(737\) | 6.79300e6 | 0.460673 | ||||||||
\(738\) | 8.81116e6 | 0.595515 | ||||||||
\(739\) | 1.46203e7 | 0.984794 | 0.492397 | − | 0.870371i | \(-0.336121\pi\) | ||||
0.492397 | + | 0.870371i | \(0.336121\pi\) | |||||||
\(740\) | −2.49254e6 | −0.167326 | ||||||||
\(741\) | −501547. | −0.0335557 | ||||||||
\(742\) | −630278. | −0.0420264 | ||||||||
\(743\) | 1.97843e7 | 1.31477 | 0.657383 | − | 0.753557i | \(-0.271664\pi\) | ||||
0.657383 | + | 0.753557i | \(0.271664\pi\) | |||||||
\(744\) | −7.65392e6 | −0.506934 | ||||||||
\(745\) | 2.66621e6 | 0.175996 | ||||||||
\(746\) | 1.84434e7 | 1.21337 | ||||||||
\(747\) | −3.07887e6 | −0.201879 | ||||||||
\(748\) | −1.84482e7 | −1.20559 | ||||||||
\(749\) | 3.28707e6 | 0.214094 | ||||||||
\(750\) | 1.61280e7 | 1.04696 | ||||||||
\(751\) | −1.13853e7 | −0.736619 | −0.368310 | − | 0.929703i | \(-0.620063\pi\) | ||||
−0.368310 | + | 0.929703i | \(0.620063\pi\) | |||||||
\(752\) | −1.53762e6 | −0.0991525 | ||||||||
\(753\) | 3.07364e6 | 0.197545 | ||||||||
\(754\) | −4.68347e6 | −0.300013 | ||||||||
\(755\) | −1.17729e7 | −0.751654 | ||||||||
\(756\) | −2.04797e6 | −0.130322 | ||||||||
\(757\) | 4.36996e6 | 0.277165 | 0.138582 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138582 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(758\) | 1.14065e7 | 0.721071 | ||||||||
\(759\) | −1.33485e6 | −0.0841062 | ||||||||
\(760\) | −8.68520e6 | −0.545439 | ||||||||
\(761\) | −3.29286e6 | −0.206116 | −0.103058 | − | 0.994675i | \(-0.532863\pi\) | ||||
−0.103058 | + | 0.994675i | \(0.532863\pi\) | |||||||
\(762\) | −1.21315e7 | −0.756879 | ||||||||
\(763\) | 3.08409e6 | 0.191786 | ||||||||
\(764\) | 7.51600e6 | 0.465858 | ||||||||
\(765\) | 4.04981e6 | 0.250196 | ||||||||
\(766\) | −2.03784e7 | −1.25487 | ||||||||
\(767\) | 2.75463e6 | 0.169073 | ||||||||
\(768\) | −1.48588e7 | −0.909034 | ||||||||
\(769\) | 1.15568e7 | 0.704726 | 0.352363 | − | 0.935863i | \(-0.385378\pi\) | ||||
0.352363 | + | 0.935863i | \(0.385378\pi\) | |||||||
\(770\) | −5.65672e6 | −0.343825 | ||||||||
\(771\) | 2.23940e6 | 0.135673 | ||||||||
\(772\) | 2.35143e7 | 1.42000 | ||||||||
\(773\) | 2.15820e7 | 1.29910 | 0.649550 | − | 0.760319i | \(-0.274957\pi\) | ||||
0.649550 | + | 0.760319i | \(0.274957\pi\) | |||||||
\(774\) | 7.64652e6 | 0.458787 | ||||||||
\(775\) | −4.35874e6 | −0.260679 | ||||||||
\(776\) | −1.11559e7 | −0.665043 | ||||||||
\(777\) | 440099. | 0.0261516 | ||||||||
\(778\) | −756008. | −0.0447793 | ||||||||
\(779\) | −9.58325e6 | −0.565808 | ||||||||
\(780\) | −1.50443e6 | −0.0885394 | ||||||||
\(781\) | −3.00395e6 | −0.176224 | ||||||||
\(782\) | −5.73825e6 | −0.335554 | ||||||||
\(783\) | −5.39747e6 | −0.314620 | ||||||||
\(784\) | 1.02851e6 | 0.0597610 | ||||||||
\(785\) | −4.25888e6 | −0.246673 | ||||||||
\(786\) | 2.61107e7 | 1.50752 | ||||||||
\(787\) | 3.76994e6 | 0.216969 | 0.108484 | − | 0.994098i | \(-0.465400\pi\) | ||||
0.108484 | + | 0.994098i | \(0.465400\pi\) | |||||||
\(788\) | −3.56430e7 | −2.04483 | ||||||||
\(789\) | −1.49883e7 | −0.857159 | ||||||||
\(790\) | −3.90860e7 | −2.22820 | ||||||||
\(791\) | −8.38560e6 | −0.476533 | ||||||||
\(792\) | 5.43751e6 | 0.308026 | ||||||||
\(793\) | −1.18454e6 | −0.0668907 | ||||||||
\(794\) | 3.29339e7 | 1.85392 | ||||||||
\(795\) | −533586. | −0.0299424 | ||||||||
\(796\) | 5.28314e7 | 2.95536 | ||||||||
\(797\) | 4.11076e6 | 0.229232 | 0.114616 | − | 0.993410i | \(-0.463436\pi\) | ||||
0.114616 | + | 0.993410i | \(0.463436\pi\) | |||||||
\(798\) | 3.47066e6 | 0.192932 | ||||||||
\(799\) | −4.11957e6 | −0.228289 | ||||||||
\(800\) | −4.43379e6 | −0.244934 | ||||||||
\(801\) | −3.95093e6 | −0.217579 | ||||||||
\(802\) | 7.55001e6 | 0.414487 | ||||||||
\(803\) | −1.47878e7 | −0.809309 | ||||||||
\(804\) | −1.25017e7 | −0.682072 | ||||||||
\(805\) | −1.12923e6 | −0.0614175 | ||||||||
\(806\) | 2.24681e6 | 0.121823 | ||||||||
\(807\) | −1.37475e7 | −0.743089 | ||||||||
\(808\) | −1.58928e7 | −0.856392 | ||||||||
\(809\) | 2.33800e7 | 1.25595 | 0.627977 | − | 0.778232i | \(-0.283883\pi\) | ||||
0.627977 | + | 0.778232i | \(0.283883\pi\) | |||||||
\(810\) | −2.70150e6 | −0.144675 | ||||||||
\(811\) | 1.89532e7 | 1.01188 | 0.505942 | − | 0.862567i | \(-0.331145\pi\) | ||||
0.505942 | + | 0.862567i | \(0.331145\pi\) | |||||||
\(812\) | 2.07998e7 | 1.10705 | ||||||||
\(813\) | −7.98762e6 | −0.423829 | ||||||||
\(814\) | −2.64454e6 | −0.139891 | ||||||||
\(815\) | 1.78109e6 | 0.0939272 | ||||||||
\(816\) | 4.42464e6 | 0.232623 | ||||||||
\(817\) | −8.31656e6 | −0.435902 | ||||||||
\(818\) | −3.25194e7 | −1.69926 | ||||||||
\(819\) | 265633. | 0.0138380 | ||||||||
\(820\) | −2.87458e7 | −1.49293 | ||||||||
\(821\) | −2.37660e7 | −1.23055 | −0.615273 | − | 0.788314i | \(-0.710954\pi\) | ||||
−0.615273 | + | 0.788314i | \(0.710954\pi\) | |||||||
\(822\) | 2.20220e7 | 1.13678 | ||||||||
\(823\) | −2.72873e7 | −1.40430 | −0.702151 | − | 0.712028i | \(-0.747777\pi\) | ||||
−0.702151 | + | 0.712028i | \(0.747777\pi\) | |||||||
\(824\) | 6.49199e6 | 0.333089 | ||||||||
\(825\) | 3.09654e6 | 0.158395 | ||||||||
\(826\) | −1.90618e7 | −0.972106 | ||||||||
\(827\) | −1.87246e7 | −0.952023 | −0.476012 | − | 0.879439i | \(-0.657918\pi\) | ||||
−0.476012 | + | 0.879439i | \(0.657918\pi\) | |||||||
\(828\) | 2.45664e6 | 0.124527 | ||||||||
\(829\) | 2.88037e7 | 1.45567 | 0.727833 | − | 0.685754i | \(-0.240527\pi\) | ||||
0.727833 | + | 0.685754i | \(0.240527\pi\) | |||||||
\(830\) | 1.56510e7 | 0.788581 | ||||||||
\(831\) | −5.11436e6 | −0.256915 | ||||||||
\(832\) | 3.20291e6 | 0.160412 | ||||||||
\(833\) | 2.75557e6 | 0.137594 | ||||||||
\(834\) | −536208. | −0.0266943 | ||||||||
\(835\) | −5.75508e6 | −0.285650 | ||||||||
\(836\) | −1.33845e7 | −0.662350 | ||||||||
\(837\) | 2.58933e6 | 0.127754 | ||||||||
\(838\) | 3.67107e7 | 1.80585 | ||||||||
\(839\) | 1.80901e7 | 0.887228 | 0.443614 | − | 0.896218i | \(-0.353696\pi\) | ||||
0.443614 | + | 0.896218i | \(0.353696\pi\) | |||||||
\(840\) | 4.59991e6 | 0.224932 | ||||||||
\(841\) | 3.43072e7 | 1.67261 | ||||||||
\(842\) | −9.80780e6 | −0.476751 | ||||||||
\(843\) | 773974. | 0.0375109 | ||||||||
\(844\) | 4.95248e7 | 2.39313 | ||||||||
\(845\) | −1.59800e7 | −0.769899 | ||||||||
\(846\) | 2.74804e6 | 0.132007 | ||||||||
\(847\) | 4.03969e6 | 0.193482 | ||||||||
\(848\) | −582972. | −0.0278393 | ||||||||
\(849\) | −1.54198e7 | −0.734190 | ||||||||
\(850\) | 1.33114e7 | 0.631942 | ||||||||
\(851\) | −527919. | −0.0249887 | ||||||||
\(852\) | 5.52842e6 | 0.260917 | ||||||||
\(853\) | 2.27481e6 | 0.107047 | 0.0535233 | − | 0.998567i | \(-0.482955\pi\) | ||||
0.0535233 | + | 0.998567i | \(0.482955\pi\) | |||||||
\(854\) | 8.19689e6 | 0.384596 | ||||||||
\(855\) | 2.93822e6 | 0.137458 | ||||||||
\(856\) | 1.60618e7 | 0.749219 | ||||||||
\(857\) | 8.68568e6 | 0.403972 | 0.201986 | − | 0.979388i | \(-0.435260\pi\) | ||||
0.201986 | + | 0.979388i | \(0.435260\pi\) | |||||||
\(858\) | −1.59618e6 | −0.0740224 | ||||||||
\(859\) | 2.67321e7 | 1.23609 | 0.618045 | − | 0.786142i | \(-0.287925\pi\) | ||||
0.618045 | + | 0.786142i | \(0.287925\pi\) | |||||||
\(860\) | −2.49462e7 | −1.15016 | ||||||||
\(861\) | 5.07554e6 | 0.233332 | ||||||||
\(862\) | 1.10528e7 | 0.506646 | ||||||||
\(863\) | −1.82060e7 | −0.832122 | −0.416061 | − | 0.909337i | \(-0.636590\pi\) | ||||
−0.416061 | + | 0.909337i | \(0.636590\pi\) | |||||||
\(864\) | 2.63392e6 | 0.120038 | ||||||||
\(865\) | −2.99049e7 | −1.35895 | ||||||||
\(866\) | 7.44636e6 | 0.337403 | ||||||||
\(867\) | −924258. | −0.0417586 | ||||||||
\(868\) | −9.97831e6 | −0.449529 | ||||||||
\(869\) | −2.66146e7 | −1.19556 | ||||||||
\(870\) | 2.74372e7 | 1.22897 | ||||||||
\(871\) | 1.62154e6 | 0.0724240 | ||||||||
\(872\) | 1.50700e7 | 0.671152 | ||||||||
\(873\) | 3.77406e6 | 0.167600 | ||||||||
\(874\) | −4.16322e6 | −0.184353 | ||||||||
\(875\) | 9.29032e6 | 0.410214 | ||||||||
\(876\) | 2.72152e7 | 1.19826 | ||||||||
\(877\) | 5.85269e6 | 0.256955 | 0.128477 | − | 0.991712i | \(-0.458991\pi\) | ||||
0.128477 | + | 0.991712i | \(0.458991\pi\) | |||||||
\(878\) | −1.39712e7 | −0.611641 | ||||||||
\(879\) | 6.98372e6 | 0.304870 | ||||||||
\(880\) | −5.23215e6 | −0.227758 | ||||||||
\(881\) | −2.29356e7 | −0.995567 | −0.497783 | − | 0.867301i | \(-0.665853\pi\) | ||||
−0.497783 | + | 0.867301i | \(0.665853\pi\) | |||||||
\(882\) | −1.83815e6 | −0.0795628 | ||||||||
\(883\) | −1.27042e6 | −0.0548335 | −0.0274167 | − | 0.999624i | \(-0.508728\pi\) | ||||
−0.0274167 | + | 0.999624i | \(0.508728\pi\) | |||||||
\(884\) | −4.40372e6 | −0.189535 | ||||||||
\(885\) | −1.61375e7 | −0.692592 | ||||||||
\(886\) | −3.27342e7 | −1.40093 | ||||||||
\(887\) | −3.72691e6 | −0.159052 | −0.0795261 | − | 0.996833i | \(-0.525341\pi\) | ||||
−0.0795261 | + | 0.996833i | \(0.525341\pi\) | |||||||
\(888\) | 2.15048e6 | 0.0915171 | ||||||||
\(889\) | −6.98817e6 | −0.296557 | ||||||||
\(890\) | 2.00839e7 | 0.849911 | ||||||||
\(891\) | −1.83952e6 | −0.0776265 | ||||||||
\(892\) | −1.97814e7 | −0.832424 | ||||||||
\(893\) | −2.98883e6 | −0.125422 | ||||||||
\(894\) | −5.20608e6 | −0.217855 | ||||||||
\(895\) | −2.72387e7 | −1.13665 | ||||||||
\(896\) | −1.64985e7 | −0.686555 | ||||||||
\(897\) | −318639. | −0.0132226 | ||||||||
\(898\) | −4.75134e6 | −0.196619 | ||||||||
\(899\) | −2.62981e7 | −1.08524 | ||||||||
\(900\) | −5.69883e6 | −0.234520 | ||||||||
\(901\) | −1.56189e6 | −0.0640972 | ||||||||
\(902\) | −3.04988e7 | −1.24815 | ||||||||
\(903\) | 4.40467e6 | 0.179760 | ||||||||
\(904\) | −4.09750e7 | −1.66762 | ||||||||
\(905\) | −1.13395e6 | −0.0460227 | ||||||||
\(906\) | 2.29881e7 | 0.930426 | ||||||||
\(907\) | 1.38899e7 | 0.560636 | 0.280318 | − | 0.959907i | \(-0.409560\pi\) | ||||
0.280318 | + | 0.959907i | \(0.409560\pi\) | |||||||
\(908\) | −3.10978e7 | −1.25174 | ||||||||
\(909\) | 5.37657e6 | 0.215822 | ||||||||
\(910\) | −1.35030e6 | −0.0540540 | ||||||||
\(911\) | −5.94594e6 | −0.237369 | −0.118685 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118685 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(912\) | 3.21016e6 | 0.127803 | ||||||||
\(913\) | 1.06572e7 | 0.423121 | ||||||||
\(914\) | −5.98665e7 | −2.37038 | ||||||||
\(915\) | 6.93938e6 | 0.274011 | ||||||||
\(916\) | 5.41632e6 | 0.213288 | ||||||||
\(917\) | 1.50407e7 | 0.590669 | ||||||||
\(918\) | −7.90772e6 | −0.309703 | ||||||||
\(919\) | 4.55301e7 | 1.77832 | 0.889161 | − | 0.457595i | \(-0.151289\pi\) | ||||
0.889161 | + | 0.457595i | \(0.151289\pi\) | |||||||
\(920\) | −5.51781e6 | −0.214930 | ||||||||
\(921\) | −1.12614e6 | −0.0437466 | ||||||||
\(922\) | 6.07502e7 | 2.35353 | ||||||||
\(923\) | −717066. | −0.0277048 | ||||||||
\(924\) | 7.08880e6 | 0.273145 | ||||||||
\(925\) | 1.22465e6 | 0.0470606 | ||||||||
\(926\) | −9.58263e6 | −0.367246 | ||||||||
\(927\) | −2.19625e6 | −0.0839427 | ||||||||
\(928\) | −2.67508e7 | −1.01969 | ||||||||
\(929\) | −5.10171e7 | −1.93944 | −0.969720 | − | 0.244219i | \(-0.921468\pi\) | ||||
−0.969720 | + | 0.244219i | \(0.921468\pi\) | |||||||
\(930\) | −1.31625e7 | −0.499034 | ||||||||
\(931\) | 1.99922e6 | 0.0755939 | ||||||||
\(932\) | −4.16942e7 | −1.57230 | ||||||||
\(933\) | −9.59418e6 | −0.360831 | ||||||||
\(934\) | 4.00691e7 | 1.50294 | ||||||||
\(935\) | −1.40179e7 | −0.524390 | ||||||||
\(936\) | 1.29797e6 | 0.0484258 | ||||||||
\(937\) | −1.78745e7 | −0.665097 | −0.332549 | − | 0.943086i | \(-0.607909\pi\) | ||||
−0.332549 | + | 0.943086i | \(0.607909\pi\) | |||||||
\(938\) | −1.12209e7 | −0.416410 | ||||||||
\(939\) | −1.80221e7 | −0.667024 | ||||||||
\(940\) | −8.96526e6 | −0.330935 | ||||||||
\(941\) | −9.76160e6 | −0.359374 | −0.179687 | − | 0.983724i | \(-0.557509\pi\) | ||||
−0.179687 | + | 0.983724i | \(0.557509\pi\) | |||||||
\(942\) | 8.31596e6 | 0.305341 | ||||||||
\(943\) | −6.08835e6 | −0.222957 | ||||||||
\(944\) | −1.76311e7 | −0.643945 | ||||||||
\(945\) | −1.55616e6 | −0.0566858 | ||||||||
\(946\) | −2.64675e7 | −0.961580 | ||||||||
\(947\) | −1.90931e7 | −0.691835 | −0.345918 | − | 0.938265i | \(-0.612432\pi\) | ||||
−0.345918 | + | 0.938265i | \(0.612432\pi\) | |||||||
\(948\) | 4.89812e7 | 1.77014 | ||||||||
\(949\) | −3.52996e6 | −0.127234 | ||||||||
\(950\) | 9.65770e6 | 0.347188 | ||||||||
\(951\) | −2.77014e7 | −0.993230 | ||||||||
\(952\) | 1.34647e7 | 0.481508 | ||||||||
\(953\) | −4.18953e7 | −1.49428 | −0.747142 | − | 0.664665i | \(-0.768574\pi\) | ||||
−0.747142 | + | 0.664665i | \(0.768574\pi\) | |||||||
\(954\) | 1.04189e6 | 0.0370638 | ||||||||
\(955\) | 5.71106e6 | 0.202632 | ||||||||
\(956\) | 7.25344e7 | 2.56684 | ||||||||
\(957\) | 1.86827e7 | 0.659416 | ||||||||
\(958\) | −4.18225e7 | −1.47230 | ||||||||
\(959\) | 1.26854e7 | 0.445409 | ||||||||
\(960\) | −1.87636e7 | −0.657110 | ||||||||
\(961\) | −1.60132e7 | −0.559331 | ||||||||
\(962\) | −631272. | −0.0219927 | ||||||||
\(963\) | −5.43373e6 | −0.188813 | ||||||||
\(964\) | 3.76072e7 | 1.30340 | ||||||||
\(965\) | 1.78674e7 | 0.617651 | ||||||||
\(966\) | 2.20495e6 | 0.0760249 | ||||||||
\(967\) | −7.15505e6 | −0.246063 | −0.123032 | − | 0.992403i | \(-0.539262\pi\) | ||||
−0.123032 | + | 0.992403i | \(0.539262\pi\) | |||||||
\(968\) | 1.97394e7 | 0.677087 | ||||||||
\(969\) | 8.60065e6 | 0.294254 | ||||||||
\(970\) | −1.91848e7 | −0.654680 | ||||||||
\(971\) | 3.97454e7 | 1.35282 | 0.676408 | − | 0.736527i | \(-0.263536\pi\) | ||||
0.676408 | + | 0.736527i | \(0.263536\pi\) | |||||||
\(972\) | 3.38542e6 | 0.114934 | ||||||||
\(973\) | −308875. | −0.0104592 | ||||||||
\(974\) | −7.40352e6 | −0.250058 | ||||||||
\(975\) | 739168. | 0.0249019 | ||||||||
\(976\) | 7.58166e6 | 0.254765 | ||||||||
\(977\) | −3.04507e6 | −0.102061 | −0.0510306 | − | 0.998697i | \(-0.516251\pi\) | ||||
−0.0510306 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(978\) | −3.47778e6 | −0.116267 | ||||||||
\(979\) | 1.36757e7 | 0.456028 | ||||||||
\(980\) | 5.99684e6 | 0.199461 | ||||||||
\(981\) | −5.09820e6 | −0.169139 | ||||||||
\(982\) | −4.76070e7 | −1.57540 | ||||||||
\(983\) | −5.24955e7 | −1.73276 | −0.866380 | − | 0.499385i | \(-0.833559\pi\) | ||||
−0.866380 | + | 0.499385i | \(0.833559\pi\) | |||||||
\(984\) | 2.48009e7 | 0.816543 | ||||||||
\(985\) | −2.70834e7 | −0.889433 | ||||||||
\(986\) | 8.03132e7 | 2.63084 | ||||||||
\(987\) | 1.58297e6 | 0.0517224 | ||||||||
\(988\) | −3.19499e6 | −0.104130 | ||||||||
\(989\) | −5.28360e6 | −0.171767 | ||||||||
\(990\) | 9.35091e6 | 0.303226 | ||||||||
\(991\) | −6.26275e6 | −0.202573 | −0.101286 | − | 0.994857i | \(-0.532296\pi\) | ||||
−0.101286 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(992\) | 1.28332e7 | 0.414053 | ||||||||
\(993\) | −2.52628e7 | −0.813034 | ||||||||
\(994\) | 4.96203e6 | 0.159292 | ||||||||
\(995\) | 4.01442e7 | 1.28548 | ||||||||
\(996\) | −1.96133e7 | −0.626471 | ||||||||
\(997\) | 1.28695e7 | 0.410036 | 0.205018 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205018 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(998\) | 1.95344e7 | 0.620831 | ||||||||
\(999\) | −727510. | −0.0230635 |
(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 | 483.6.a.b.1.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.6.a.b.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial |