Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.17253\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.17253 | −1.62149 | −0.810745 | − | 0.585400i | \(-0.800937\pi\) | ||||
−0.810745 | + | 0.585400i | \(0.800937\pi\) | |||||||
\(3\) | 14.3258 | 0.918999 | 0.459499 | − | 0.888178i | \(-0.348029\pi\) | ||||
0.459499 | + | 0.888178i | \(0.348029\pi\) | |||||||
\(4\) | 52.1353 | 1.62923 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −131.404 | −1.49015 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −184.691 | −1.02028 | ||||||||
\(9\) | −37.7723 | −0.155441 | ||||||||
\(10\) | 229.313 | 0.725152 | ||||||||
\(11\) | 215.386 | 0.536704 | 0.268352 | − | 0.963321i | \(-0.413521\pi\) | ||||
0.268352 | + | 0.963321i | \(0.413521\pi\) | |||||||
\(12\) | 746.878 | 1.49726 | ||||||||
\(13\) | 132.696 | 0.217771 | 0.108886 | − | 0.994054i | \(-0.465272\pi\) | ||||
0.108886 | + | 0.994054i | \(0.465272\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −358.144 | −0.410989 | ||||||||
\(16\) | 25.7572 | 0.0251535 | ||||||||
\(17\) | 441.638 | 0.370633 | 0.185317 | − | 0.982679i | \(-0.440669\pi\) | ||||
0.185317 | + | 0.982679i | \(0.440669\pi\) | |||||||
\(18\) | 346.467 | 0.252047 | ||||||||
\(19\) | 519.002 | 0.329826 | 0.164913 | − | 0.986308i | \(-0.447266\pi\) | ||||
0.164913 | + | 0.986308i | \(0.447266\pi\) | |||||||
\(20\) | −1303.38 | −0.728612 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1975.63 | −0.870260 | ||||||||
\(23\) | −4389.66 | −1.73026 | −0.865129 | − | 0.501549i | \(-0.832764\pi\) | ||||
−0.865129 | + | 0.501549i | \(0.832764\pi\) | |||||||
\(24\) | −2645.84 | −0.937640 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −1217.16 | −0.353114 | ||||||||
\(27\) | −4022.28 | −1.06185 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7114.31 | 1.57086 | 0.785430 | − | 0.618950i | \(-0.212442\pi\) | ||||
0.785430 | + | 0.618950i | \(0.212442\pi\) | |||||||
\(30\) | 3285.09 | 0.666414 | ||||||||
\(31\) | −10304.7 | −1.92589 | −0.962946 | − | 0.269693i | \(-0.913078\pi\) | ||||
−0.962946 | + | 0.269693i | \(0.913078\pi\) | |||||||
\(32\) | 5673.86 | 0.979499 | ||||||||
\(33\) | 3085.56 | 0.493230 | ||||||||
\(34\) | −4050.94 | −0.600978 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1969.27 | −0.253249 | ||||||||
\(37\) | 5568.08 | 0.668654 | 0.334327 | − | 0.942457i | \(-0.391491\pi\) | ||||
0.334327 | + | 0.942457i | \(0.391491\pi\) | |||||||
\(38\) | −4760.56 | −0.534810 | ||||||||
\(39\) | 1900.98 | 0.200132 | ||||||||
\(40\) | 4617.28 | 0.456285 | ||||||||
\(41\) | 7246.54 | 0.673242 | 0.336621 | − | 0.941640i | \(-0.390716\pi\) | ||||
0.336621 | + | 0.941640i | \(0.390716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −184.308 | −0.0152010 | −0.00760050 | − | 0.999971i | \(-0.502419\pi\) | ||||
−0.00760050 | + | 0.999971i | \(0.502419\pi\) | |||||||
\(44\) | 11229.2 | 0.874413 | ||||||||
\(45\) | 944.307 | 0.0695155 | ||||||||
\(46\) | 40264.3 | 2.80560 | ||||||||
\(47\) | 16174.2 | 1.06802 | 0.534008 | − | 0.845480i | \(-0.320685\pi\) | ||||
0.534008 | + | 0.845480i | \(0.320685\pi\) | |||||||
\(48\) | 368.991 | 0.0231160 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5732.83 | −0.324298 | ||||||||
\(51\) | 6326.81 | 0.340611 | ||||||||
\(52\) | 6918.16 | 0.354799 | ||||||||
\(53\) | 7275.69 | 0.355782 | 0.177891 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177891 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(54\) | 36894.5 | 1.72178 | ||||||||
\(55\) | −5384.64 | −0.240021 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7435.11 | 0.303110 | ||||||||
\(58\) | −65256.2 | −2.54713 | ||||||||
\(59\) | −45301.7 | −1.69428 | −0.847138 | − | 0.531373i | \(-0.821676\pi\) | ||||
−0.847138 | + | 0.531373i | \(0.821676\pi\) | |||||||
\(60\) | −18671.9 | −0.669594 | ||||||||
\(61\) | −7369.70 | −0.253586 | −0.126793 | − | 0.991929i | \(-0.540468\pi\) | ||||
−0.126793 | + | 0.991929i | \(0.540468\pi\) | |||||||
\(62\) | 94520.4 | 3.12281 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −52867.9 | −1.61340 | ||||||||
\(65\) | −3317.41 | −0.0973903 | ||||||||
\(66\) | −28302.4 | −0.799767 | ||||||||
\(67\) | −64443.0 | −1.75383 | −0.876917 | − | 0.480641i | \(-0.840404\pi\) | ||||
−0.876917 | + | 0.480641i | \(0.840404\pi\) | |||||||
\(68\) | 23024.9 | 0.603846 | ||||||||
\(69\) | −62885.2 | −1.59011 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −343.451 | −0.00808573 | −0.00404286 | − | 0.999992i | \(-0.501287\pi\) | ||||
−0.00404286 | + | 0.999992i | \(0.501287\pi\) | |||||||
\(72\) | 6976.21 | 0.158595 | ||||||||
\(73\) | 45357.4 | 0.996187 | 0.498094 | − | 0.867123i | \(-0.334034\pi\) | ||||
0.498094 | + | 0.867123i | \(0.334034\pi\) | |||||||
\(74\) | −51073.4 | −1.08421 | ||||||||
\(75\) | 8953.61 | 0.183800 | ||||||||
\(76\) | 27058.3 | 0.537362 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −17436.8 | −0.324511 | ||||||||
\(79\) | −74587.6 | −1.34462 | −0.672309 | − | 0.740271i | \(-0.734697\pi\) | ||||
−0.672309 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(80\) | −643.929 | −0.0112490 | ||||||||
\(81\) | −48443.6 | −0.820396 | ||||||||
\(82\) | −66469.1 | −1.09165 | ||||||||
\(83\) | −54772.9 | −0.872711 | −0.436356 | − | 0.899774i | \(-0.643731\pi\) | ||||
−0.436356 | + | 0.899774i | \(0.643731\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11041.0 | −0.165752 | ||||||||
\(86\) | 1690.57 | 0.0246483 | ||||||||
\(87\) | 101918. | 1.44362 | ||||||||
\(88\) | −39779.8 | −0.547591 | ||||||||
\(89\) | −106839. | −1.42974 | −0.714868 | − | 0.699260i | \(-0.753513\pi\) | ||||
−0.714868 | + | 0.699260i | \(0.753513\pi\) | |||||||
\(90\) | −8661.68 | −0.112719 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −228856. | −2.81898 | ||||||||
\(93\) | −147623. | −1.76989 | ||||||||
\(94\) | −148358. | −1.73178 | ||||||||
\(95\) | −12975.1 | −0.147503 | ||||||||
\(96\) | 81282.4 | 0.900158 | ||||||||
\(97\) | 19313.9 | 0.208421 | 0.104210 | − | 0.994555i | \(-0.466769\pi\) | ||||
0.104210 | + | 0.994555i | \(0.466769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8135.60 | −0.0834261 | ||||||||
\(100\) | 32584.5 | 0.325845 | ||||||||
\(101\) | −24524.6 | −0.239221 | −0.119610 | − | 0.992821i | \(-0.538165\pi\) | ||||
−0.119610 | + | 0.992821i | \(0.538165\pi\) | |||||||
\(102\) | −58032.8 | −0.552298 | ||||||||
\(103\) | −46312.7 | −0.430137 | −0.215069 | − | 0.976599i | \(-0.568997\pi\) | ||||
−0.215069 | + | 0.976599i | \(0.568997\pi\) | |||||||
\(104\) | −24507.9 | −0.222189 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −66736.4 | −0.576897 | ||||||||
\(107\) | 157154. | 1.32699 | 0.663495 | − | 0.748181i | \(-0.269073\pi\) | ||||
0.663495 | + | 0.748181i | \(0.269073\pi\) | |||||||
\(108\) | −209703. | −1.72999 | ||||||||
\(109\) | −141538. | −1.14106 | −0.570530 | − | 0.821277i | \(-0.693262\pi\) | ||||
−0.570530 | + | 0.821277i | \(0.693262\pi\) | |||||||
\(110\) | 49390.7 | 0.389192 | ||||||||
\(111\) | 79767.0 | 0.614492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −157706. | −1.16186 | −0.580928 | − | 0.813955i | \(-0.697310\pi\) | ||||
−0.580928 | + | 0.813955i | \(0.697310\pi\) | |||||||
\(114\) | −68198.7 | −0.491489 | ||||||||
\(115\) | 109741. | 0.773795 | ||||||||
\(116\) | 370906. | 2.55929 | ||||||||
\(117\) | −5012.25 | −0.0338507 | ||||||||
\(118\) | 415531. | 2.74725 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 66146.1 | 0.419325 | ||||||||
\(121\) | −114660. | −0.711949 | ||||||||
\(122\) | 67598.8 | 0.411187 | ||||||||
\(123\) | 103812. | 0.618709 | ||||||||
\(124\) | −537239. | −3.13772 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −249665. | −1.37356 | −0.686782 | − | 0.726864i | \(-0.740977\pi\) | ||||
−0.686782 | + | 0.726864i | \(0.740977\pi\) | |||||||
\(128\) | 303369. | 1.63661 | ||||||||
\(129\) | −2640.35 | −0.0139697 | ||||||||
\(130\) | 30429.0 | 0.157917 | ||||||||
\(131\) | 216534. | 1.10242 | 0.551210 | − | 0.834366i | \(-0.314166\pi\) | ||||
0.551210 | + | 0.834366i | \(0.314166\pi\) | |||||||
\(132\) | 160867. | 0.803584 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 591105. | 2.84382 | ||||||||
\(135\) | 100557. | 0.474873 | ||||||||
\(136\) | −81566.7 | −0.378151 | ||||||||
\(137\) | −58644.1 | −0.266946 | −0.133473 | − | 0.991052i | \(-0.542613\pi\) | ||||
−0.133473 | + | 0.991052i | \(0.542613\pi\) | |||||||
\(138\) | 576816. | 2.57834 | ||||||||
\(139\) | −353961. | −1.55388 | −0.776941 | − | 0.629573i | \(-0.783230\pi\) | ||||
−0.776941 | + | 0.629573i | \(0.783230\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 231708. | 0.981505 | ||||||||
\(142\) | 3150.32 | 0.0131109 | ||||||||
\(143\) | 28580.9 | 0.116879 | ||||||||
\(144\) | −972.907 | −0.00390989 | ||||||||
\(145\) | −177858. | −0.702510 | ||||||||
\(146\) | −416042. | −1.61531 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 290293. | 1.08939 | ||||||||
\(149\) | 73724.4 | 0.272048 | 0.136024 | − | 0.990706i | \(-0.456568\pi\) | ||||
0.136024 | + | 0.990706i | \(0.456568\pi\) | |||||||
\(150\) | −82127.2 | −0.298029 | ||||||||
\(151\) | −322597. | −1.15138 | −0.575689 | − | 0.817669i | \(-0.695266\pi\) | ||||
−0.575689 | + | 0.817669i | \(0.695266\pi\) | |||||||
\(152\) | −95855.2 | −0.336517 | ||||||||
\(153\) | −16681.7 | −0.0576118 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 257618. | 0.861285 | ||||||||
\(156\) | 99108.0 | 0.326060 | ||||||||
\(157\) | 224924. | 0.728261 | 0.364131 | − | 0.931348i | \(-0.381366\pi\) | ||||
0.364131 | + | 0.931348i | \(0.381366\pi\) | |||||||
\(158\) | 684156. | 2.18028 | ||||||||
\(159\) | 104230. | 0.326963 | ||||||||
\(160\) | −141847. | −0.438045 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 444350. | 1.33026 | ||||||||
\(163\) | −158217. | −0.466427 | −0.233214 | − | 0.972426i | \(-0.574924\pi\) | ||||
−0.233214 | + | 0.972426i | \(0.574924\pi\) | |||||||
\(164\) | 377800. | 1.09686 | ||||||||
\(165\) | −77139.1 | −0.220579 | ||||||||
\(166\) | 502406. | 1.41509 | ||||||||
\(167\) | −316938. | −0.879392 | −0.439696 | − | 0.898147i | \(-0.644914\pi\) | ||||
−0.439696 | + | 0.898147i | \(0.644914\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −353685. | −0.952576 | ||||||||
\(170\) | 101273. | 0.268765 | ||||||||
\(171\) | −19603.9 | −0.0512687 | ||||||||
\(172\) | −9608.93 | −0.0247659 | ||||||||
\(173\) | 360124. | 0.914824 | 0.457412 | − | 0.889255i | \(-0.348777\pi\) | ||||
0.457412 | + | 0.889255i | \(0.348777\pi\) | |||||||
\(174\) | −934845. | −2.34081 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5547.72 | 0.0135000 | ||||||||
\(177\) | −648981. | −1.55704 | ||||||||
\(178\) | 979986. | 2.31830 | ||||||||
\(179\) | −440948. | −1.02862 | −0.514310 | − | 0.857604i | \(-0.671952\pi\) | ||||
−0.514310 | + | 0.857604i | \(0.671952\pi\) | |||||||
\(180\) | 49231.7 | 0.113257 | ||||||||
\(181\) | 19489.0 | 0.0442175 | 0.0221087 | − | 0.999756i | \(-0.492962\pi\) | ||||
0.0221087 | + | 0.999756i | \(0.492962\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −105577. | −0.233045 | ||||||||
\(184\) | 810731. | 1.76536 | ||||||||
\(185\) | −139202. | −0.299031 | ||||||||
\(186\) | 1.35408e6 | 2.86986 | ||||||||
\(187\) | 95122.5 | 0.198920 | ||||||||
\(188\) | 843245. | 1.74004 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 119014. | 0.239174 | ||||||||
\(191\) | −418719. | −0.830499 | −0.415250 | − | 0.909708i | \(-0.636306\pi\) | ||||
−0.415250 | + | 0.909708i | \(0.636306\pi\) | |||||||
\(192\) | −757373. | −1.48271 | ||||||||
\(193\) | 4008.29 | 0.00774578 | 0.00387289 | − | 0.999993i | \(-0.498767\pi\) | ||||
0.00387289 | + | 0.999993i | \(0.498767\pi\) | |||||||
\(194\) | −177157. | −0.337952 | ||||||||
\(195\) | −47524.5 | −0.0895016 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.02060e6 | 1.87366 | 0.936830 | − | 0.349786i | \(-0.113746\pi\) | ||||
0.936830 | + | 0.349786i | \(0.113746\pi\) | |||||||
\(198\) | 74624.0 | 0.135274 | ||||||||
\(199\) | −157196. | −0.281391 | −0.140695 | − | 0.990053i | \(-0.544934\pi\) | ||||
−0.140695 | + | 0.990053i | \(0.544934\pi\) | |||||||
\(200\) | −115432. | −0.204057 | ||||||||
\(201\) | −923195. | −1.61177 | ||||||||
\(202\) | 224953. | 0.387894 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 329850. | 0.554933 | ||||||||
\(205\) | −181164. | −0.301083 | ||||||||
\(206\) | 424804. | 0.697463 | ||||||||
\(207\) | 165807. | 0.268954 | ||||||||
\(208\) | 3417.88 | 0.00547771 | ||||||||
\(209\) | 111786. | 0.177019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −797769. | −1.23359 | −0.616795 | − | 0.787124i | \(-0.711569\pi\) | ||||
−0.616795 | + | 0.787124i | \(0.711569\pi\) | |||||||
\(212\) | 379320. | 0.579650 | ||||||||
\(213\) | −4920.20 | −0.00743077 | ||||||||
\(214\) | −1.44150e6 | −2.15170 | ||||||||
\(215\) | 4607.69 | 0.00679810 | ||||||||
\(216\) | 742880. | 1.08339 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.29827e6 | 1.85022 | ||||||||
\(219\) | 649780. | 0.915495 | ||||||||
\(220\) | −280730. | −0.391049 | ||||||||
\(221\) | 58603.8 | 0.0807133 | ||||||||
\(222\) | −731665. | −0.996392 | ||||||||
\(223\) | 1.17028e6 | 1.57590 | 0.787951 | − | 0.615739i | \(-0.211142\pi\) | ||||
0.787951 | + | 0.615739i | \(0.211142\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23607.7 | −0.0310883 | ||||||||
\(226\) | 1.44656e6 | 1.88394 | ||||||||
\(227\) | 419223. | 0.539983 | 0.269991 | − | 0.962863i | \(-0.412979\pi\) | ||||
0.269991 | + | 0.962863i | \(0.412979\pi\) | |||||||
\(228\) | 387631. | 0.493835 | ||||||||
\(229\) | −457265. | −0.576208 | −0.288104 | − | 0.957599i | \(-0.593025\pi\) | ||||
−0.288104 | + | 0.957599i | \(0.593025\pi\) | |||||||
\(230\) | −1.00661e6 | −1.25470 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.31395e6 | −1.60273 | ||||||||
\(233\) | −669972. | −0.808475 | −0.404237 | − | 0.914654i | \(-0.632463\pi\) | ||||
−0.404237 | + | 0.914654i | \(0.632463\pi\) | |||||||
\(234\) | 45975.0 | 0.0548886 | ||||||||
\(235\) | −404354. | −0.477631 | ||||||||
\(236\) | −2.36181e6 | −2.76036 | ||||||||
\(237\) | −1.06852e6 | −1.23570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −550244. | −0.623104 | −0.311552 | − | 0.950229i | \(-0.600849\pi\) | ||||
−0.311552 | + | 0.950229i | \(0.600849\pi\) | |||||||
\(240\) | −9224.78 | −0.0103378 | ||||||||
\(241\) | 163023. | 0.180804 | 0.0904018 | − | 0.995905i | \(-0.471185\pi\) | ||||
0.0904018 | + | 0.995905i | \(0.471185\pi\) | |||||||
\(242\) | 1.05172e6 | 1.15442 | ||||||||
\(243\) | 283422. | 0.307906 | ||||||||
\(244\) | −384221. | −0.413149 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −952221. | −1.00323 | ||||||||
\(247\) | 68869.8 | 0.0718267 | ||||||||
\(248\) | 1.90319e6 | 1.96496 | ||||||||
\(249\) | −784664. | −0.802020 | ||||||||
\(250\) | 143321. | 0.145030 | ||||||||
\(251\) | 1.31883e6 | 1.32131 | 0.660654 | − | 0.750690i | \(-0.270279\pi\) | ||||
0.660654 | + | 0.750690i | \(0.270279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −945469. | −0.928637 | ||||||||
\(254\) | 2.29006e6 | 2.22722 | ||||||||
\(255\) | −158170. | −0.152326 | ||||||||
\(256\) | −1.09088e6 | −1.04035 | ||||||||
\(257\) | −832987. | −0.786693 | −0.393347 | − | 0.919390i | \(-0.628683\pi\) | ||||
−0.393347 | + | 0.919390i | \(0.628683\pi\) | |||||||
\(258\) | 24218.7 | 0.0226517 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −172954. | −0.158671 | ||||||||
\(261\) | −268724. | −0.244177 | ||||||||
\(262\) | −1.98616e6 | −1.78756 | ||||||||
\(263\) | −1.64512e6 | −1.46659 | −0.733296 | − | 0.679910i | \(-0.762019\pi\) | ||||
−0.733296 | + | 0.679910i | \(0.762019\pi\) | |||||||
\(264\) | −569877. | −0.503235 | ||||||||
\(265\) | −181892. | −0.159111 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.53055e6 | −1.31392 | ||||||||
\(268\) | −3.35975e6 | −2.85739 | ||||||||
\(269\) | 454521. | 0.382978 | 0.191489 | − | 0.981495i | \(-0.438668\pi\) | ||||
0.191489 | + | 0.981495i | \(0.438668\pi\) | |||||||
\(270\) | −922362. | −0.770002 | ||||||||
\(271\) | 831066. | 0.687405 | 0.343702 | − | 0.939079i | \(-0.388319\pi\) | ||||
0.343702 | + | 0.939079i | \(0.388319\pi\) | |||||||
\(272\) | 11375.3 | 0.00932272 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 537915. | 0.432850 | ||||||||
\(275\) | 134616. | 0.107341 | ||||||||
\(276\) | −3.27854e6 | −2.59064 | ||||||||
\(277\) | 1.30960e6 | 1.02551 | 0.512756 | − | 0.858534i | \(-0.328625\pi\) | ||||
0.512756 | + | 0.858534i | \(0.328625\pi\) | |||||||
\(278\) | 3.24671e6 | 2.51960 | ||||||||
\(279\) | 389233. | 0.299364 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 175721. | 0.132757 | 0.0663784 | − | 0.997795i | \(-0.478856\pi\) | ||||
0.0663784 | + | 0.997795i | \(0.478856\pi\) | |||||||
\(282\) | −2.12534e6 | −1.59150 | ||||||||
\(283\) | 953011. | 0.707346 | 0.353673 | − | 0.935369i | \(-0.384933\pi\) | ||||
0.353673 | + | 0.935369i | \(0.384933\pi\) | |||||||
\(284\) | −17905.9 | −0.0131735 | ||||||||
\(285\) | −185878. | −0.135555 | ||||||||
\(286\) | −262159. | −0.189518 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −214315. | −0.152255 | ||||||||
\(289\) | −1.22481e6 | −0.862631 | ||||||||
\(290\) | 1.63140e6 | 1.13911 | ||||||||
\(291\) | 276686. | 0.191538 | ||||||||
\(292\) | 2.36472e6 | 1.62302 | ||||||||
\(293\) | 275025. | 0.187156 | 0.0935778 | − | 0.995612i | \(-0.470170\pi\) | ||||
0.0935778 | + | 0.995612i | \(0.470170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.13254e6 | 0.757703 | ||||||||
\(296\) | −1.02838e6 | −0.682217 | ||||||||
\(297\) | −866341. | −0.569899 | ||||||||
\(298\) | −676239. | −0.441123 | ||||||||
\(299\) | −582492. | −0.376801 | ||||||||
\(300\) | 466799. | 0.299451 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.95903e6 | 1.86695 | ||||||||
\(303\) | −351334. | −0.219843 | ||||||||
\(304\) | 13368.0 | 0.00829628 | ||||||||
\(305\) | 184242. | 0.113407 | ||||||||
\(306\) | 153013. | 0.0934169 | ||||||||
\(307\) | 473977. | 0.287019 | 0.143510 | − | 0.989649i | \(-0.454161\pi\) | ||||
0.143510 | + | 0.989649i | \(0.454161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −663465. | −0.395295 | ||||||||
\(310\) | −2.36301e6 | −1.39656 | ||||||||
\(311\) | 3.10860e6 | 1.82248 | 0.911241 | − | 0.411873i | \(-0.135125\pi\) | ||||
0.911241 | + | 0.411873i | \(0.135125\pi\) | |||||||
\(312\) | −351094. | −0.204191 | ||||||||
\(313\) | 1.51927e6 | 0.876544 | 0.438272 | − | 0.898842i | \(-0.355591\pi\) | ||||
0.438272 | + | 0.898842i | \(0.355591\pi\) | |||||||
\(314\) | −2.06312e6 | −1.18087 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.88864e6 | −2.19069 | ||||||||
\(317\) | 2.53235e6 | 1.41539 | 0.707695 | − | 0.706518i | \(-0.249735\pi\) | ||||
0.707695 | + | 0.706518i | \(0.249735\pi\) | |||||||
\(318\) | −956051. | −0.530168 | ||||||||
\(319\) | 1.53232e6 | 0.843087 | ||||||||
\(320\) | 1.32170e6 | 0.721534 | ||||||||
\(321\) | 2.25136e6 | 1.21950 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 229211. | 0.122245 | ||||||||
\(324\) | −2.52562e6 | −1.33661 | ||||||||
\(325\) | 82935.3 | 0.0435543 | ||||||||
\(326\) | 1.45125e6 | 0.756307 | ||||||||
\(327\) | −2.02765e6 | −1.04863 | ||||||||
\(328\) | −1.33837e6 | −0.686899 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 707560. | 0.357667 | ||||||||
\(331\) | 557600. | 0.279739 | 0.139869 | − | 0.990170i | \(-0.455332\pi\) | ||||
0.139869 | + | 0.990170i | \(0.455332\pi\) | |||||||
\(332\) | −2.85560e6 | −1.42184 | ||||||||
\(333\) | −210319. | −0.103937 | ||||||||
\(334\) | 2.90712e6 | 1.42592 | ||||||||
\(335\) | 1.61107e6 | 0.784339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 501783. | 0.240681 | 0.120340 | − | 0.992733i | \(-0.461601\pi\) | ||||
0.120340 | + | 0.992733i | \(0.461601\pi\) | |||||||
\(338\) | 3.24418e6 | 1.54459 | ||||||||
\(339\) | −2.25926e6 | −1.06774 | ||||||||
\(340\) | −575623. | −0.270048 | ||||||||
\(341\) | −2.21949e6 | −1.03363 | ||||||||
\(342\) | 179817. | 0.0831316 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 34040.0 | 0.0155094 | ||||||||
\(345\) | 1.57213e6 | 0.711117 | ||||||||
\(346\) | −3.30325e6 | −1.48338 | ||||||||
\(347\) | 283359. | 0.126332 | 0.0631661 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631661 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(348\) | 5.31352e6 | 2.35198 | ||||||||
\(349\) | 569924. | 0.250469 | 0.125234 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125234 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −533742. | −0.231240 | ||||||||
\(352\) | 1.22207e6 | 0.525701 | ||||||||
\(353\) | −1.74073e6 | −0.743522 | −0.371761 | − | 0.928328i | \(-0.621246\pi\) | ||||
−0.371761 | + | 0.928328i | \(0.621246\pi\) | |||||||
\(354\) | 5.95280e6 | 2.52472 | ||||||||
\(355\) | 8586.28 | 0.00361605 | ||||||||
\(356\) | −5.57009e6 | −2.32936 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.04461e6 | 1.66790 | ||||||||
\(359\) | 933824. | 0.382410 | 0.191205 | − | 0.981550i | \(-0.438761\pi\) | ||||
0.191205 | + | 0.981550i | \(0.438761\pi\) | |||||||
\(360\) | −174405. | −0.0709256 | ||||||||
\(361\) | −2.20674e6 | −0.891215 | ||||||||
\(362\) | −178764. | −0.0716982 | ||||||||
\(363\) | −1.64259e6 | −0.654280 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.13394e6 | −0.445509 | ||||||||
\(366\) | 968404. | 0.377880 | ||||||||
\(367\) | 1.52484e6 | 0.590962 | 0.295481 | − | 0.955349i | \(-0.404520\pi\) | ||||
0.295481 | + | 0.955349i | \(0.404520\pi\) | |||||||
\(368\) | −113065. | −0.0435220 | ||||||||
\(369\) | −273719. | −0.104650 | ||||||||
\(370\) | 1.27683e6 | 0.484875 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.69637e6 | −2.88356 | ||||||||
\(373\) | 2.28822e6 | 0.851579 | 0.425789 | − | 0.904822i | \(-0.359996\pi\) | ||||
0.425789 | + | 0.904822i | \(0.359996\pi\) | |||||||
\(374\) | −872514. | −0.322547 | ||||||||
\(375\) | −223840. | −0.0821977 | ||||||||
\(376\) | −2.98723e6 | −1.08968 | ||||||||
\(377\) | 944044. | 0.342089 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −210030. | −0.0751074 | −0.0375537 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375537 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(380\) | −676458. | −0.240316 | ||||||||
\(381\) | −3.57665e6 | −1.26230 | ||||||||
\(382\) | 3.84071e6 | 1.34665 | ||||||||
\(383\) | −3.37503e6 | −1.17566 | −0.587828 | − | 0.808986i | \(-0.700017\pi\) | ||||
−0.587828 | + | 0.808986i | \(0.700017\pi\) | |||||||
\(384\) | 4.34599e6 | 1.50404 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −36766.1 | −0.0125597 | ||||||||
\(387\) | 6961.72 | 0.00236287 | ||||||||
\(388\) | 1.00693e6 | 0.339564 | ||||||||
\(389\) | 1.98548e6 | 0.665259 | 0.332630 | − | 0.943058i | \(-0.392064\pi\) | ||||
0.332630 | + | 0.943058i | \(0.392064\pi\) | |||||||
\(390\) | 435920. | 0.145126 | ||||||||
\(391\) | −1.93864e6 | −0.641291 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.10201e6 | 1.01312 | ||||||||
\(394\) | −9.36150e6 | −3.03812 | ||||||||
\(395\) | 1.86469e6 | 0.601331 | ||||||||
\(396\) | −424152. | −0.135920 | ||||||||
\(397\) | 2.53409e6 | 0.806948 | 0.403474 | − | 0.914991i | \(-0.367803\pi\) | ||||
0.403474 | + | 0.914991i | \(0.367803\pi\) | |||||||
\(398\) | 1.44189e6 | 0.456272 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16098.2 | 0.00503070 | ||||||||
\(401\) | 3.79055e6 | 1.17717 | 0.588587 | − | 0.808434i | \(-0.299684\pi\) | ||||
0.588587 | + | 0.808434i | \(0.299684\pi\) | |||||||
\(402\) | 8.46804e6 | 2.61347 | ||||||||
\(403\) | −1.36740e6 | −0.419404 | ||||||||
\(404\) | −1.27860e6 | −0.389745 | ||||||||
\(405\) | 1.21109e6 | 0.366892 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.19928e6 | 0.358869 | ||||||||
\(408\) | −1.16851e6 | −0.347521 | ||||||||
\(409\) | −5.10159e6 | −1.50798 | −0.753992 | − | 0.656883i | \(-0.771874\pi\) | ||||
−0.753992 | + | 0.656883i | \(0.771874\pi\) | |||||||
\(410\) | 1.66173e6 | 0.488203 | ||||||||
\(411\) | −840122. | −0.245323 | ||||||||
\(412\) | −2.41452e6 | −0.700791 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.52087e6 | −0.436106 | ||||||||
\(415\) | 1.36932e6 | 0.390288 | ||||||||
\(416\) | 752901. | 0.213307 | ||||||||
\(417\) | −5.07076e6 | −1.42802 | ||||||||
\(418\) | −1.02536e6 | −0.287035 | ||||||||
\(419\) | 6.31053e6 | 1.75603 | 0.878013 | − | 0.478637i | \(-0.158869\pi\) | ||||
0.878013 | + | 0.478637i | \(0.158869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.26642e6 | −0.898186 | −0.449093 | − | 0.893485i | \(-0.648253\pi\) | ||||
−0.449093 | + | 0.893485i | \(0.648253\pi\) | |||||||
\(422\) | 7.31756e6 | 2.00025 | ||||||||
\(423\) | −610935. | −0.166014 | ||||||||
\(424\) | −1.34376e6 | −0.362999 | ||||||||
\(425\) | 276024. | 0.0741267 | ||||||||
\(426\) | 45130.7 | 0.0120489 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.19329e6 | 2.16197 | ||||||||
\(429\) | 409443. | 0.107411 | ||||||||
\(430\) | −42264.2 | −0.0110230 | ||||||||
\(431\) | −2.31016e6 | −0.599031 | −0.299516 | − | 0.954091i | \(-0.596825\pi\) | ||||
−0.299516 | + | 0.954091i | \(0.596825\pi\) | |||||||
\(432\) | −103603. | −0.0267092 | ||||||||
\(433\) | −3.81574e6 | −0.978044 | −0.489022 | − | 0.872271i | \(-0.662646\pi\) | ||||
−0.489022 | + | 0.872271i | \(0.662646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.54795e6 | −0.645606 | ||||||||
\(436\) | −7.37915e6 | −1.85905 | ||||||||
\(437\) | −2.27824e6 | −0.570685 | ||||||||
\(438\) | −5.96012e6 | −1.48446 | ||||||||
\(439\) | −673888. | −0.166889 | −0.0834443 | − | 0.996512i | \(-0.526592\pi\) | ||||
−0.0834443 | + | 0.996512i | \(0.526592\pi\) | |||||||
\(440\) | 994496. | 0.244890 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −537545. | −0.130876 | ||||||||
\(443\) | −4.84599e6 | −1.17320 | −0.586602 | − | 0.809875i | \(-0.699535\pi\) | ||||
−0.586602 | + | 0.809875i | \(0.699535\pi\) | |||||||
\(444\) | 4.15868e6 | 1.00115 | ||||||||
\(445\) | 2.67098e6 | 0.639397 | ||||||||
\(446\) | −1.07345e7 | −2.55531 | ||||||||
\(447\) | 1.05616e6 | 0.250012 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.09732e6 | 0.725055 | 0.362527 | − | 0.931973i | \(-0.381914\pi\) | ||||
0.362527 | + | 0.931973i | \(0.381914\pi\) | |||||||
\(450\) | 216542. | 0.0504093 | ||||||||
\(451\) | 1.56080e6 | 0.361332 | ||||||||
\(452\) | −8.22204e6 | −1.89293 | ||||||||
\(453\) | −4.62145e6 | −1.05812 | ||||||||
\(454\) | −3.84533e6 | −0.875577 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.37320e6 | −0.309258 | ||||||||
\(457\) | −6.58726e6 | −1.47542 | −0.737708 | − | 0.675120i | \(-0.764092\pi\) | ||||
−0.737708 | + | 0.675120i | \(0.764092\pi\) | |||||||
\(458\) | 4.19428e6 | 0.934315 | ||||||||
\(459\) | −1.77639e6 | −0.393557 | ||||||||
\(460\) | 5.72140e6 | 1.26069 | ||||||||
\(461\) | −5.26481e6 | −1.15380 | −0.576900 | − | 0.816815i | \(-0.695738\pi\) | ||||
−0.576900 | + | 0.816815i | \(0.695738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.79127e6 | −0.605131 | −0.302565 | − | 0.953129i | \(-0.597843\pi\) | ||||
−0.302565 | + | 0.953129i | \(0.597843\pi\) | |||||||
\(464\) | 183244. | 0.0395126 | ||||||||
\(465\) | 3.69058e6 | 0.791520 | ||||||||
\(466\) | 6.14533e6 | 1.31093 | ||||||||
\(467\) | −3.23304e6 | −0.685992 | −0.342996 | − | 0.939337i | \(-0.611442\pi\) | ||||
−0.342996 | + | 0.939337i | \(0.611442\pi\) | |||||||
\(468\) | −261315. | −0.0551505 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.70895e6 | 0.774473 | ||||||||
\(471\) | 3.22221e6 | 0.669271 | ||||||||
\(472\) | 8.36682e6 | 1.72864 | ||||||||
\(473\) | −39697.2 | −0.00815844 | ||||||||
\(474\) | 9.80107e6 | 2.00368 | ||||||||
\(475\) | 324376. | 0.0659653 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −274819. | −0.0553033 | ||||||||
\(478\) | 5.04713e6 | 1.01036 | ||||||||
\(479\) | 3.97758e6 | 0.792100 | 0.396050 | − | 0.918229i | \(-0.370381\pi\) | ||||
0.396050 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(480\) | −2.03206e6 | −0.402563 | ||||||||
\(481\) | 738864. | 0.145614 | ||||||||
\(482\) | −1.49534e6 | −0.293171 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.97783e6 | −1.15993 | ||||||||
\(485\) | −482847. | −0.0932085 | ||||||||
\(486\) | −2.59970e6 | −0.499266 | ||||||||
\(487\) | 517375. | 0.0988515 | 0.0494257 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494257 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(488\) | 1.36112e6 | 0.258730 | ||||||||
\(489\) | −2.26658e6 | −0.428646 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −992388. | −0.185771 | −0.0928854 | − | 0.995677i | \(-0.529609\pi\) | ||||
−0.0928854 | + | 0.995677i | \(0.529609\pi\) | |||||||
\(492\) | 5.41228e6 | 1.00802 | ||||||||
\(493\) | 3.14195e6 | 0.582213 | ||||||||
\(494\) | −631710. | −0.116466 | ||||||||
\(495\) | 203390. | 0.0373093 | ||||||||
\(496\) | −265420. | −0.0484429 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.19735e6 | 1.30047 | ||||||||
\(499\) | 2.95997e6 | 0.532153 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(500\) | −814613. | −0.145722 | ||||||||
\(501\) | −4.54038e6 | −0.808160 | ||||||||
\(502\) | −1.20970e7 | −2.14249 | ||||||||
\(503\) | −2.55586e6 | −0.450419 | −0.225210 | − | 0.974310i | \(-0.572307\pi\) | ||||
−0.225210 | + | 0.974310i | \(0.572307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 613115. | 0.106983 | ||||||||
\(506\) | 8.67234e6 | 1.50577 | ||||||||
\(507\) | −5.06681e6 | −0.875416 | ||||||||
\(508\) | −1.30164e7 | −2.23785 | ||||||||
\(509\) | −571600. | −0.0977907 | −0.0488953 | − | 0.998804i | \(-0.515570\pi\) | ||||
−0.0488953 | + | 0.998804i | \(0.515570\pi\) | |||||||
\(510\) | 1.45082e6 | 0.246995 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 298370. | 0.0503015 | ||||||||
\(513\) | −2.08757e6 | −0.350226 | ||||||||
\(514\) | 7.64060e6 | 1.27561 | ||||||||
\(515\) | 1.15782e6 | 0.192363 | ||||||||
\(516\) | −137655. | −0.0227598 | ||||||||
\(517\) | 3.48368e6 | 0.573208 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.15906e6 | 0.840722 | ||||||||
\(520\) | 612697. | 0.0993659 | ||||||||
\(521\) | 3.84947e6 | 0.621307 | 0.310653 | − | 0.950523i | \(-0.399452\pi\) | ||||
0.310653 | + | 0.950523i | \(0.399452\pi\) | |||||||
\(522\) | 2.46488e6 | 0.395930 | ||||||||
\(523\) | 3.34856e6 | 0.535308 | 0.267654 | − | 0.963515i | \(-0.413752\pi\) | ||||
0.267654 | + | 0.963515i | \(0.413752\pi\) | |||||||
\(524\) | 1.12890e7 | 1.79609 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.50899e7 | 2.37806 | ||||||||
\(527\) | −4.55096e6 | −0.713800 | ||||||||
\(528\) | 79475.4 | 0.0124065 | ||||||||
\(529\) | 1.28327e7 | 1.99379 | ||||||||
\(530\) | 1.66841e6 | 0.257996 | ||||||||
\(531\) | 1.71115e6 | 0.263361 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 961591. | 0.146613 | ||||||||
\(534\) | 1.40391e7 | 2.13052 | ||||||||
\(535\) | −3.92886e6 | −0.593448 | ||||||||
\(536\) | 1.19021e7 | 1.78941 | ||||||||
\(537\) | −6.31692e6 | −0.945301 | ||||||||
\(538\) | −4.16911e6 | −0.620994 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.24256e6 | 0.773677 | ||||||||
\(541\) | 3.28206e6 | 0.482117 | 0.241059 | − | 0.970511i | \(-0.422505\pi\) | ||||
0.241059 | + | 0.970511i | \(0.422505\pi\) | |||||||
\(542\) | −7.62298e6 | −1.11462 | ||||||||
\(543\) | 279196. | 0.0406358 | ||||||||
\(544\) | 2.50579e6 | 0.363035 | ||||||||
\(545\) | 3.53846e6 | 0.510297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.92785e6 | 1.13289 | 0.566444 | − | 0.824100i | \(-0.308319\pi\) | ||||
0.566444 | + | 0.824100i | \(0.308319\pi\) | |||||||
\(548\) | −3.05743e6 | −0.434915 | ||||||||
\(549\) | 278370. | 0.0394178 | ||||||||
\(550\) | −1.23477e6 | −0.174052 | ||||||||
\(551\) | 3.69234e6 | 0.518111 | ||||||||
\(552\) | 1.16144e7 | 1.62236 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.20124e7 | −1.66286 | ||||||||
\(555\) | −1.99418e6 | −0.274809 | ||||||||
\(556\) | −1.84538e7 | −2.53163 | ||||||||
\(557\) | 9.22341e6 | 1.25966 | 0.629830 | − | 0.776733i | \(-0.283124\pi\) | ||||
0.629830 | + | 0.776733i | \(0.283124\pi\) | |||||||
\(558\) | −3.57025e6 | −0.485415 | ||||||||
\(559\) | −24457.0 | −0.00331035 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.36270e6 | 0.182808 | ||||||||
\(562\) | −1.61180e6 | −0.215264 | ||||||||
\(563\) | 1.16920e7 | 1.55460 | 0.777298 | − | 0.629132i | \(-0.216590\pi\) | ||||
0.777298 | + | 0.629132i | \(0.216590\pi\) | |||||||
\(564\) | 1.20801e7 | 1.59909 | ||||||||
\(565\) | 3.94265e6 | 0.519598 | ||||||||
\(566\) | −8.74152e6 | −1.14695 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 63432.4 | 0.00824974 | ||||||||
\(569\) | 252494. | 0.0326941 | 0.0163471 | − | 0.999866i | \(-0.494796\pi\) | ||||
0.0163471 | + | 0.999866i | \(0.494796\pi\) | |||||||
\(570\) | 1.70497e6 | 0.219801 | ||||||||
\(571\) | 4.62266e6 | 0.593337 | 0.296669 | − | 0.954981i | \(-0.404124\pi\) | ||||
0.296669 | + | 0.954981i | \(0.404124\pi\) | |||||||
\(572\) | 1.49007e6 | 0.190422 | ||||||||
\(573\) | −5.99847e6 | −0.763228 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.74354e6 | −0.346052 | ||||||||
\(576\) | 1.99694e6 | 0.250789 | ||||||||
\(577\) | −1.36752e7 | −1.71000 | −0.854999 | − | 0.518630i | \(-0.826442\pi\) | ||||
−0.854999 | + | 0.518630i | \(0.826442\pi\) | |||||||
\(578\) | 1.12346e7 | 1.39875 | ||||||||
\(579\) | 57421.8 | 0.00711836 | ||||||||
\(580\) | −9.27266e6 | −1.14455 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.53791e6 | −0.310577 | ||||||||
\(583\) | 1.56708e6 | 0.190950 | ||||||||
\(584\) | −8.37712e6 | −1.01639 | ||||||||
\(585\) | 125306. | 0.0151385 | ||||||||
\(586\) | −2.52267e6 | −0.303471 | ||||||||
\(587\) | −1.08136e7 | −1.29532 | −0.647659 | − | 0.761930i | \(-0.724252\pi\) | ||||
−0.647659 | + | 0.761930i | \(0.724252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.34817e6 | −0.635210 | ||||||||
\(590\) | −1.03883e7 | −1.22861 | ||||||||
\(591\) | 1.46209e7 | 1.72189 | ||||||||
\(592\) | 143418. | 0.0168190 | ||||||||
\(593\) | 5.20786e6 | 0.608166 | 0.304083 | − | 0.952645i | \(-0.401650\pi\) | ||||
0.304083 | + | 0.952645i | \(0.401650\pi\) | |||||||
\(594\) | 7.94654e6 | 0.924085 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.84364e6 | 0.443228 | ||||||||
\(597\) | −2.25196e6 | −0.258598 | ||||||||
\(598\) | 5.34292e6 | 0.610979 | ||||||||
\(599\) | −1.43236e7 | −1.63112 | −0.815561 | − | 0.578671i | \(-0.803572\pi\) | ||||
−0.815561 | + | 0.578671i | \(0.803572\pi\) | |||||||
\(600\) | −1.65365e6 | −0.187528 | ||||||||
\(601\) | 5.68832e6 | 0.642389 | 0.321194 | − | 0.947013i | \(-0.395916\pi\) | ||||
0.321194 | + | 0.947013i | \(0.395916\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.43416e6 | 0.272619 | ||||||||
\(604\) | −1.68187e7 | −1.87586 | ||||||||
\(605\) | 2.86650e6 | 0.318393 | ||||||||
\(606\) | 3.22262e6 | 0.356474 | ||||||||
\(607\) | 1.54940e7 | 1.70683 | 0.853417 | − | 0.521228i | \(-0.174526\pi\) | ||||
0.853417 | + | 0.521228i | \(0.174526\pi\) | |||||||
\(608\) | 2.94475e6 | 0.323064 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.68997e6 | −0.183888 | ||||||||
\(611\) | 2.14626e6 | 0.232583 | ||||||||
\(612\) | −869704. | −0.0938627 | ||||||||
\(613\) | −1.68053e7 | −1.80632 | −0.903161 | − | 0.429303i | \(-0.858759\pi\) | ||||
−0.903161 | + | 0.429303i | \(0.858759\pi\) | |||||||
\(614\) | −4.34756e6 | −0.465399 | ||||||||
\(615\) | −2.59531e6 | −0.276695 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.82924e6 | −0.510700 | −0.255350 | − | 0.966849i | \(-0.582191\pi\) | ||||
−0.255350 | + | 0.966849i | \(0.582191\pi\) | |||||||
\(618\) | 6.08565e6 | 0.640967 | ||||||||
\(619\) | −2.06396e6 | −0.216508 | −0.108254 | − | 0.994123i | \(-0.534526\pi\) | ||||
−0.108254 | + | 0.994123i | \(0.534526\pi\) | |||||||
\(620\) | 1.34310e7 | 1.40323 | ||||||||
\(621\) | 1.76564e7 | 1.83727 | ||||||||
\(622\) | −2.85137e7 | −2.95514 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 48963.8 | 0.00503401 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.39355e7 | −1.42131 | ||||||||
\(627\) | 1.60141e6 | 0.162680 | ||||||||
\(628\) | 1.17265e7 | 1.18650 | ||||||||
\(629\) | 2.45908e6 | 0.247825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.37020e7 | −1.36997 | −0.684986 | − | 0.728556i | \(-0.740192\pi\) | ||||
−0.684986 | + | 0.728556i | \(0.740192\pi\) | |||||||
\(632\) | 1.37757e7 | 1.37189 | ||||||||
\(633\) | −1.14287e7 | −1.13367 | ||||||||
\(634\) | −2.32281e7 | −2.29504 | ||||||||
\(635\) | 6.24163e6 | 0.614276 | ||||||||
\(636\) | 5.43405e6 | 0.532698 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.40552e7 | −1.36706 | ||||||||
\(639\) | 12972.9 | 0.00125686 | ||||||||
\(640\) | −7.58421e6 | −0.731915 | ||||||||
\(641\) | 1.70359e6 | 0.163764 | 0.0818821 | − | 0.996642i | \(-0.473907\pi\) | ||||
0.0818821 | + | 0.996642i | \(0.473907\pi\) | |||||||
\(642\) | −2.06507e7 | −1.97741 | ||||||||
\(643\) | −1.74387e7 | −1.66336 | −0.831682 | − | 0.555252i | \(-0.812622\pi\) | ||||
−0.831682 | + | 0.555252i | \(0.812622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 66008.8 | 0.00624744 | ||||||||
\(646\) | −2.10245e6 | −0.198218 | ||||||||
\(647\) | −1.08759e7 | −1.02142 | −0.510712 | − | 0.859752i | \(-0.670618\pi\) | ||||
−0.510712 | + | 0.859752i | \(0.670618\pi\) | |||||||
\(648\) | 8.94711e6 | 0.837038 | ||||||||
\(649\) | −9.75732e6 | −0.909325 | ||||||||
\(650\) | −760726. | −0.0706228 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.24868e6 | −0.759916 | ||||||||
\(653\) | −4.27466e6 | −0.392300 | −0.196150 | − | 0.980574i | \(-0.562844\pi\) | ||||
−0.196150 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(654\) | 1.85987e7 | 1.70035 | ||||||||
\(655\) | −5.41334e6 | −0.493018 | ||||||||
\(656\) | 186650. | 0.0169344 | ||||||||
\(657\) | −1.71325e6 | −0.154849 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.15036e7 | 1.03186 | 0.515931 | − | 0.856630i | \(-0.327446\pi\) | ||||
0.515931 | + | 0.856630i | \(0.327446\pi\) | |||||||
\(660\) | −4.02167e6 | −0.359374 | ||||||||
\(661\) | 2.11275e7 | 1.88081 | 0.940403 | − | 0.340062i | \(-0.110448\pi\) | ||||
0.940403 | + | 0.340062i | \(0.110448\pi\) | |||||||
\(662\) | −5.11460e6 | −0.453593 | ||||||||
\(663\) | 839545. | 0.0741755 | ||||||||
\(664\) | 1.01161e7 | 0.890414 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.92916e6 | 0.168532 | ||||||||
\(667\) | −3.12294e7 | −2.71800 | ||||||||
\(668\) | −1.65236e7 | −1.43273 | ||||||||
\(669\) | 1.67652e7 | 1.44825 | ||||||||
\(670\) | −1.47776e7 | −1.27180 | ||||||||
\(671\) | −1.58733e6 | −0.136101 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.51341e6 | 0.724546 | 0.362273 | − | 0.932072i | \(-0.382001\pi\) | ||||
0.362273 | + | 0.932072i | \(0.382001\pi\) | |||||||
\(674\) | −4.60262e6 | −0.390261 | ||||||||
\(675\) | −2.51392e6 | −0.212370 | ||||||||
\(676\) | −1.84394e7 | −1.55196 | ||||||||
\(677\) | 9.53112e6 | 0.799231 | 0.399616 | − | 0.916683i | \(-0.369144\pi\) | ||||
0.399616 | + | 0.916683i | \(0.369144\pi\) | |||||||
\(678\) | 2.07231e7 | 1.73133 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.03917e6 | 0.169114 | ||||||||
\(681\) | 6.00569e6 | 0.496244 | ||||||||
\(682\) | 2.03583e7 | 1.67603 | ||||||||
\(683\) | 2.84219e6 | 0.233132 | 0.116566 | − | 0.993183i | \(-0.462811\pi\) | ||||
0.116566 | + | 0.993183i | \(0.462811\pi\) | |||||||
\(684\) | −1.02205e6 | −0.0835283 | ||||||||
\(685\) | 1.46610e6 | 0.119382 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.55067e6 | −0.529534 | ||||||||
\(688\) | −4747.24 | −0.000382358 0 | ||||||||
\(689\) | 965458. | 0.0774792 | ||||||||
\(690\) | −1.44204e7 | −1.15307 | ||||||||
\(691\) | −7.23494e6 | −0.576421 | −0.288210 | − | 0.957567i | \(-0.593060\pi\) | ||||
−0.288210 | + | 0.957567i | \(0.593060\pi\) | |||||||
\(692\) | 1.87752e7 | 1.49046 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.59912e6 | −0.204846 | ||||||||
\(695\) | 8.84902e6 | 0.694917 | ||||||||
\(696\) | −1.88234e7 | −1.47290 | ||||||||
\(697\) | 3.20035e6 | 0.249526 | ||||||||
\(698\) | −5.22764e6 | −0.406132 | ||||||||
\(699\) | −9.59786e6 | −0.742987 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.46129e6 | −0.266038 | −0.133019 | − | 0.991114i | \(-0.542467\pi\) | ||||
−0.133019 | + | 0.991114i | \(0.542467\pi\) | |||||||
\(702\) | 4.89576e6 | 0.374954 | ||||||||
\(703\) | 2.88985e6 | 0.220540 | ||||||||
\(704\) | −1.13870e7 | −0.865918 | ||||||||
\(705\) | −5.79269e6 | −0.438942 | ||||||||
\(706\) | 1.59669e7 | 1.20561 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.38348e7 | −2.53677 | ||||||||
\(709\) | 1.40088e6 | 0.104661 | 0.0523306 | − | 0.998630i | \(-0.483335\pi\) | ||||
0.0523306 | + | 0.998630i | \(0.483335\pi\) | |||||||
\(710\) | −78757.9 | −0.00586338 | ||||||||
\(711\) | 2.81734e6 | 0.209009 | ||||||||
\(712\) | 1.97323e7 | 1.45874 | ||||||||
\(713\) | 4.52342e7 | 3.33229 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −714522. | −0.0522698 | ||||||||
\(716\) | −2.29890e7 | −1.67586 | ||||||||
\(717\) | −7.88267e6 | −0.572631 | ||||||||
\(718\) | −8.56553e6 | −0.620073 | ||||||||
\(719\) | 5.86524e6 | 0.423120 | 0.211560 | − | 0.977365i | \(-0.432146\pi\) | ||||
0.211560 | + | 0.977365i | \(0.432146\pi\) | |||||||
\(720\) | 24322.7 | 0.00174856 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.02413e7 | 1.44509 | ||||||||
\(723\) | 2.33543e6 | 0.166158 | ||||||||
\(724\) | 1.01607e6 | 0.0720403 | ||||||||
\(725\) | 4.44644e6 | 0.314172 | ||||||||
\(726\) | 1.50667e7 | 1.06091 | ||||||||
\(727\) | 1.11670e7 | 0.783609 | 0.391804 | − | 0.920049i | \(-0.371851\pi\) | ||||
0.391804 | + | 0.920049i | \(0.371851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.58320e7 | 1.10336 | ||||||||
\(730\) | 1.04011e7 | 0.722387 | ||||||||
\(731\) | −81397.3 | −0.00563400 | ||||||||
\(732\) | −5.50426e6 | −0.379683 | ||||||||
\(733\) | 6.21665e6 | 0.427362 | 0.213681 | − | 0.976903i | \(-0.431455\pi\) | ||||
0.213681 | + | 0.976903i | \(0.431455\pi\) | |||||||
\(734\) | −1.39866e7 | −0.958238 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.49063e7 | −1.69479 | ||||||||
\(737\) | −1.38801e7 | −0.941290 | ||||||||
\(738\) | 2.51069e6 | 0.169688 | ||||||||
\(739\) | −1.07075e7 | −0.721236 | −0.360618 | − | 0.932714i | \(-0.617434\pi\) | ||||
−0.360618 | + | 0.932714i | \(0.617434\pi\) | |||||||
\(740\) | −7.25733e6 | −0.487189 | ||||||||
\(741\) | 986612. | 0.0660087 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.87985e6 | −0.523656 | −0.261828 | − | 0.965115i | \(-0.584325\pi\) | ||||
−0.261828 | + | 0.965115i | \(0.584325\pi\) | |||||||
\(744\) | 2.72647e7 | 1.80579 | ||||||||
\(745\) | −1.84311e6 | −0.121664 | ||||||||
\(746\) | −2.09887e7 | −1.38083 | ||||||||
\(747\) | 2.06890e6 | 0.135656 | ||||||||
\(748\) | 4.95924e6 | 0.324086 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.05318e6 | 0.133283 | ||||||||
\(751\) | −9.79080e6 | −0.633459 | −0.316729 | − | 0.948516i | \(-0.602585\pi\) | ||||
−0.316729 | + | 0.948516i | \(0.602585\pi\) | |||||||
\(752\) | 416601. | 0.0268643 | ||||||||
\(753\) | 1.88932e7 | 1.21428 | ||||||||
\(754\) | −8.65927e6 | −0.554693 | ||||||||
\(755\) | 8.06493e6 | 0.514912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.46073e6 | 0.600047 | 0.300023 | − | 0.953932i | \(-0.403006\pi\) | ||||
0.300023 | + | 0.953932i | \(0.403006\pi\) | |||||||
\(758\) | 1.92650e6 | 0.121786 | ||||||||
\(759\) | −1.35446e7 | −0.853416 | ||||||||
\(760\) | 2.39638e6 | 0.150495 | ||||||||
\(761\) | −1.23890e7 | −0.775488 | −0.387744 | − | 0.921767i | \(-0.626745\pi\) | ||||
−0.387744 | + | 0.921767i | \(0.626745\pi\) | |||||||
\(762\) | 3.28069e7 | 2.04681 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.18300e7 | −1.35307 | ||||||||
\(765\) | 417042. | 0.0257648 | ||||||||
\(766\) | 3.09575e7 | 1.90631 | ||||||||
\(767\) | −6.01137e6 | −0.368965 | ||||||||
\(768\) | −1.56278e7 | −0.956078 | ||||||||
\(769\) | −2.81052e7 | −1.71384 | −0.856921 | − | 0.515447i | \(-0.827626\pi\) | ||||
−0.856921 | + | 0.515447i | \(0.827626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.19332e7 | −0.722970 | ||||||||
\(772\) | 208973. | 0.0126196 | ||||||||
\(773\) | −2.36299e7 | −1.42237 | −0.711187 | − | 0.703003i | \(-0.751842\pi\) | ||||
−0.711187 | + | 0.703003i | \(0.751842\pi\) | |||||||
\(774\) | −63856.6 | −0.00383136 | ||||||||
\(775\) | −6.44045e6 | −0.385179 | ||||||||
\(776\) | −3.56711e6 | −0.212648 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.82119e7 | −1.07871 | ||||||||
\(779\) | 3.76097e6 | 0.222053 | ||||||||
\(780\) | −2.47770e6 | −0.145818 | ||||||||
\(781\) | −73974.4 | −0.00433964 | ||||||||
\(782\) | 1.77822e7 | 1.03985 | ||||||||
\(783\) | −2.86157e7 | −1.66802 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.62311e6 | −0.325688 | ||||||||
\(786\) | −2.84533e7 | −1.64277 | ||||||||
\(787\) | 1.10151e7 | 0.633946 | 0.316973 | − | 0.948435i | \(-0.397333\pi\) | ||||
0.316973 | + | 0.948435i | \(0.397333\pi\) | |||||||
\(788\) | 5.32093e7 | 3.05262 | ||||||||
\(789\) | −2.35677e7 | −1.34780 | ||||||||
\(790\) | −1.71039e7 | −0.975052 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.50257e6 | 0.0851183 | ||||||||
\(793\) | −977933. | −0.0552238 | ||||||||
\(794\) | −2.32440e7 | −1.30846 | ||||||||
\(795\) | −2.60575e6 | −0.146223 | ||||||||
\(796\) | −8.19547e6 | −0.458449 | ||||||||
\(797\) | −1.94131e7 | −1.08256 | −0.541278 | − | 0.840844i | \(-0.682059\pi\) | ||||
−0.541278 | + | 0.840844i | \(0.682059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.14313e6 | 0.395842 | ||||||||
\(800\) | 3.54616e6 | 0.195900 | ||||||||
\(801\) | 4.03556e6 | 0.222240 | ||||||||
\(802\) | −3.47689e7 | −1.90878 | ||||||||
\(803\) | 9.76933e6 | 0.534658 | ||||||||
\(804\) | −4.81310e7 | −2.62594 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.25425e7 | 0.680060 | ||||||||
\(807\) | 6.51137e6 | 0.351956 | ||||||||
\(808\) | 4.52948e6 | 0.244073 | ||||||||
\(809\) | −1.03581e7 | −0.556427 | −0.278213 | − | 0.960519i | \(-0.589742\pi\) | ||||
−0.278213 | + | 0.960519i | \(0.589742\pi\) | |||||||
\(810\) | −1.11088e7 | −0.594912 | ||||||||
\(811\) | 1.22637e6 | 0.0654740 | 0.0327370 | − | 0.999464i | \(-0.489578\pi\) | ||||
0.0327370 | + | 0.999464i | \(0.489578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.19057e7 | 0.631724 | ||||||||
\(814\) | −1.10005e7 | −0.581902 | ||||||||
\(815\) | 3.95542e6 | 0.208593 | ||||||||
\(816\) | 162961. | 0.00856756 | ||||||||
\(817\) | −95656.1 | −0.00501369 | ||||||||
\(818\) | 4.67944e7 | 2.44518 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.44501e6 | −0.490533 | ||||||||
\(821\) | 1.50056e7 | 0.776955 | 0.388478 | − | 0.921458i | \(-0.373001\pi\) | ||||
0.388478 | + | 0.921458i | \(0.373001\pi\) | |||||||
\(822\) | 7.70604e6 | 0.397788 | ||||||||
\(823\) | 2.08511e7 | 1.07307 | 0.536537 | − | 0.843877i | \(-0.319732\pi\) | ||||
0.536537 | + | 0.843877i | \(0.319732\pi\) | |||||||
\(824\) | 8.55355e6 | 0.438862 | ||||||||
\(825\) | 1.92848e6 | 0.0986460 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.11289e7 | −0.565833 | −0.282917 | − | 0.959145i | \(-0.591302\pi\) | ||||
−0.282917 | + | 0.959145i | \(0.591302\pi\) | |||||||
\(828\) | 8.64441e6 | 0.438187 | ||||||||
\(829\) | 1.49680e7 | 0.756446 | 0.378223 | − | 0.925714i | \(-0.376535\pi\) | ||||
0.378223 | + | 0.925714i | \(0.376535\pi\) | |||||||
\(830\) | −1.25601e7 | −0.632848 | ||||||||
\(831\) | 1.87611e7 | 0.942444 | ||||||||
\(832\) | −7.01538e6 | −0.351352 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.65117e7 | 2.31551 | ||||||||
\(835\) | 7.92344e6 | 0.393276 | ||||||||
\(836\) | 5.82797e6 | 0.288404 | ||||||||
\(837\) | 4.14485e7 | 2.04501 | ||||||||
\(838\) | −5.78835e7 | −2.84738 | ||||||||
\(839\) | −3.53209e7 | −1.73232 | −0.866159 | − | 0.499769i | \(-0.833418\pi\) | ||||
−0.866159 | + | 0.499769i | \(0.833418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.01022e7 | 1.46760 | ||||||||
\(842\) | 2.99613e7 | 1.45640 | ||||||||
\(843\) | 2.51733e6 | 0.122003 | ||||||||
\(844\) | −4.15919e7 | −2.00980 | ||||||||
\(845\) | 8.84212e6 | 0.426005 | ||||||||
\(846\) | 5.60382e6 | 0.269190 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 187401. | 0.00894916 | ||||||||
\(849\) | 1.36526e7 | 0.650050 | ||||||||
\(850\) | −2.53184e6 | −0.120196 | ||||||||
\(851\) | −2.44420e7 | −1.15694 | ||||||||
\(852\) | −256516. | −0.0121064 | ||||||||
\(853\) | −9.41887e6 | −0.443227 | −0.221613 | − | 0.975135i | \(-0.571132\pi\) | ||||
−0.221613 | + | 0.975135i | \(0.571132\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 490098. | 0.0229281 | ||||||||
\(856\) | −2.90251e7 | −1.35391 | ||||||||
\(857\) | 1.05121e7 | 0.488918 | 0.244459 | − | 0.969660i | \(-0.421390\pi\) | ||||
0.244459 | + | 0.969660i | \(0.421390\pi\) | |||||||
\(858\) | −3.75563e6 | −0.174167 | ||||||||
\(859\) | 3.10282e7 | 1.43474 | 0.717371 | − | 0.696692i | \(-0.245345\pi\) | ||||
0.717371 | + | 0.696692i | \(0.245345\pi\) | |||||||
\(860\) | 240223. | 0.0110756 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.11900e7 | 0.971323 | ||||||||
\(863\) | −2.79996e7 | −1.27975 | −0.639876 | − | 0.768479i | \(-0.721014\pi\) | ||||
−0.639876 | + | 0.768479i | \(0.721014\pi\) | |||||||
\(864\) | −2.28219e7 | −1.04008 | ||||||||
\(865\) | −9.00311e6 | −0.409122 | ||||||||
\(866\) | 3.49999e7 | 1.58589 | ||||||||
\(867\) | −1.75464e7 | −0.792757 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.60651e7 | −0.721661 | ||||||||
\(870\) | 2.33711e7 | 1.04684 | ||||||||
\(871\) | −8.55136e6 | −0.381935 | ||||||||
\(872\) | 2.61409e7 | 1.16421 | ||||||||
\(873\) | −729530. | −0.0323972 | ||||||||
\(874\) | 2.08972e7 | 0.925359 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.38764e7 | 1.49155 | ||||||||
\(877\) | 2.14218e7 | 0.940497 | 0.470248 | − | 0.882534i | \(-0.344164\pi\) | ||||
0.470248 | + | 0.882534i | \(0.344164\pi\) | |||||||
\(878\) | 6.18126e6 | 0.270608 | ||||||||
\(879\) | 3.93994e6 | 0.171996 | ||||||||
\(880\) | −138693. | −0.00603737 | ||||||||
\(881\) | 3.42843e7 | 1.48818 | 0.744090 | − | 0.668079i | \(-0.232883\pi\) | ||||
0.744090 | + | 0.668079i | \(0.232883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.15229e7 | 0.497346 | 0.248673 | − | 0.968587i | \(-0.420006\pi\) | ||||
0.248673 | + | 0.968587i | \(0.420006\pi\) | |||||||
\(884\) | 3.05533e6 | 0.131500 | ||||||||
\(885\) | 1.62245e7 | 0.696328 | ||||||||
\(886\) | 4.44500e7 | 1.90234 | ||||||||
\(887\) | −4.07371e6 | −0.173853 | −0.0869263 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869263 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(888\) | −1.47323e7 | −0.626956 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.44996e7 | −1.03678 | ||||||||
\(891\) | −1.04340e7 | −0.440310 | ||||||||
\(892\) | 6.10130e7 | 2.56750 | ||||||||
\(893\) | 8.39443e6 | 0.352259 | ||||||||
\(894\) | −9.68764e6 | −0.405391 | ||||||||
\(895\) | 1.10237e7 | 0.460013 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.34465e6 | −0.346280 | ||||||||
\(898\) | −2.84103e7 | −1.17567 | ||||||||
\(899\) | −7.33110e7 | −3.02531 | ||||||||
\(900\) | −1.23079e6 | −0.0506499 | ||||||||
\(901\) | 3.21322e6 | 0.131865 | ||||||||
\(902\) | −1.43165e7 | −0.585895 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.91269e7 | 1.18542 | ||||||||
\(905\) | −487226. | −0.0197747 | ||||||||
\(906\) | 4.23904e7 | 1.71572 | ||||||||
\(907\) | 4.25486e7 | 1.71738 | 0.858690 | − | 0.512495i | \(-0.171279\pi\) | ||||
0.858690 | + | 0.512495i | \(0.171279\pi\) | |||||||
\(908\) | 2.18563e7 | 0.879755 | ||||||||
\(909\) | 926350. | 0.0371848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.33369e7 | 0.931638 | 0.465819 | − | 0.884880i | \(-0.345760\pi\) | ||||
0.465819 | + | 0.884880i | \(0.345760\pi\) | |||||||
\(912\) | 191507. | 0.00762427 | ||||||||
\(913\) | −1.17973e7 | −0.468388 | ||||||||
\(914\) | 6.04218e7 | 2.39237 | ||||||||
\(915\) | 2.63941e6 | 0.104221 | ||||||||
\(916\) | −2.38396e7 | −0.938773 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.62940e7 | 0.638148 | ||||||||
\(919\) | −1.46257e7 | −0.571251 | −0.285626 | − | 0.958341i | \(-0.592201\pi\) | ||||
−0.285626 | + | 0.958341i | \(0.592201\pi\) | |||||||
\(920\) | −2.02683e7 | −0.789491 | ||||||||
\(921\) | 6.79008e6 | 0.263770 | ||||||||
\(922\) | 4.82916e7 | 1.87087 | ||||||||
\(923\) | −45574.7 | −0.00176084 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.48005e6 | 0.133731 | ||||||||
\(926\) | 2.56030e7 | 0.981213 | ||||||||
\(927\) | 1.74934e6 | 0.0668612 | ||||||||
\(928\) | 4.03656e7 | 1.53866 | ||||||||
\(929\) | −3.12828e7 | −1.18923 | −0.594616 | − | 0.804010i | \(-0.702696\pi\) | ||||
−0.594616 | + | 0.804010i | \(0.702696\pi\) | |||||||
\(930\) | −3.38519e7 | −1.28344 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.49291e7 | −1.31719 | ||||||||
\(933\) | 4.45330e7 | 1.67486 | ||||||||
\(934\) | 2.96552e7 | 1.11233 | ||||||||
\(935\) | −2.37806e6 | −0.0889599 | ||||||||
\(936\) | 925718. | 0.0345374 | ||||||||
\(937\) | 4.86044e7 | 1.80853 | 0.904266 | − | 0.426969i | \(-0.140419\pi\) | ||||
0.904266 | + | 0.426969i | \(0.140419\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.17647e7 | 0.805543 | ||||||||
\(940\) | −2.10811e7 | −0.778169 | ||||||||
\(941\) | 2.53759e7 | 0.934217 | 0.467109 | − | 0.884200i | \(-0.345296\pi\) | ||||
0.467109 | + | 0.884200i | \(0.345296\pi\) | |||||||
\(942\) | −2.95558e7 | −1.08522 | ||||||||
\(943\) | −3.18098e7 | −1.16488 | ||||||||
\(944\) | −1.16684e6 | −0.0426169 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 364124. | 0.0132288 | ||||||||
\(947\) | 2.04500e7 | 0.740999 | 0.370500 | − | 0.928833i | \(-0.379186\pi\) | ||||
0.370500 | + | 0.928833i | \(0.379186\pi\) | |||||||
\(948\) | −5.57078e7 | −2.01324 | ||||||||
\(949\) | 6.01877e6 | 0.216941 | ||||||||
\(950\) | −2.97535e6 | −0.106962 | ||||||||
\(951\) | 3.62779e7 | 1.30074 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.96732e7 | −1.05836 | −0.529178 | − | 0.848511i | \(-0.677500\pi\) | ||||
−0.529178 | + | 0.848511i | \(0.677500\pi\) | |||||||
\(954\) | 2.52079e6 | 0.0896738 | ||||||||
\(955\) | 1.04680e7 | 0.371411 | ||||||||
\(956\) | −2.86871e7 | −1.01518 | ||||||||
\(957\) | 2.19517e7 | 0.774796 | ||||||||
\(958\) | −3.64844e7 | −1.28438 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.89343e7 | 0.663089 | ||||||||
\(961\) | 7.75582e7 | 2.70906 | ||||||||
\(962\) | −6.77725e6 | −0.236111 | ||||||||
\(963\) | −5.93608e6 | −0.206269 | ||||||||
\(964\) | 8.49926e6 | 0.294570 | ||||||||
\(965\) | −100207. | −0.00346402 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.86315e7 | 1.67245 | 0.836223 | − | 0.548390i | \(-0.184759\pi\) | ||||
0.836223 | + | 0.548390i | \(0.184759\pi\) | |||||||
\(968\) | 2.11767e7 | 0.726390 | ||||||||
\(969\) | 3.28363e6 | 0.112343 | ||||||||
\(970\) | 4.42893e6 | 0.151137 | ||||||||
\(971\) | 8.43394e6 | 0.287067 | 0.143533 | − | 0.989645i | \(-0.454154\pi\) | ||||
0.143533 | + | 0.989645i | \(0.454154\pi\) | |||||||
\(972\) | 1.47763e7 | 0.501649 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.74564e6 | −0.160287 | ||||||||
\(975\) | 1.18811e6 | 0.0400263 | ||||||||
\(976\) | −189822. | −0.00637857 | ||||||||
\(977\) | −2.01326e7 | −0.674781 | −0.337391 | − | 0.941365i | \(-0.609544\pi\) | ||||
−0.337391 | + | 0.941365i | \(0.609544\pi\) | |||||||
\(978\) | 2.07903e7 | 0.695045 | ||||||||
\(979\) | −2.30116e7 | −0.767345 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.34623e6 | 0.177368 | ||||||||
\(982\) | 9.10270e6 | 0.301225 | ||||||||
\(983\) | 4.21959e7 | 1.39279 | 0.696396 | − | 0.717658i | \(-0.254786\pi\) | ||||
0.696396 | + | 0.717658i | \(0.254786\pi\) | |||||||
\(984\) | −1.91732e7 | −0.631259 | ||||||||
\(985\) | −2.55150e7 | −0.837926 | ||||||||
\(986\) | −2.88196e7 | −0.944053 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.59054e6 | 0.117022 | ||||||||
\(989\) | 809048. | 0.0263017 | ||||||||
\(990\) | −1.86560e6 | −0.0604966 | ||||||||
\(991\) | 1.35590e6 | 0.0438574 | 0.0219287 | − | 0.999760i | \(-0.493019\pi\) | ||||
0.0219287 | + | 0.999760i | \(0.493019\pi\) | |||||||
\(992\) | −5.84676e7 | −1.88641 | ||||||||
\(993\) | 7.98805e6 | 0.257080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.92991e6 | 0.125842 | ||||||||
\(996\) | −4.09087e7 | −1.30667 | ||||||||
\(997\) | −4.39971e7 | −1.40180 | −0.700900 | − | 0.713259i | \(-0.747218\pi\) | ||||
−0.700900 | + | 0.713259i | \(0.747218\pi\) | |||||||
\(998\) | −2.71504e7 | −0.862880 | ||||||||
\(999\) | −2.23964e7 | −0.710009 |
(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 | 245.6.a.i.1.1 | 6 | ||
7.2 | even | 3 | 35.6.e.a.11.6 | ✓ | 12 | ||
7.4 | even | 3 | 35.6.e.a.16.6 | yes | 12 | ||
7.6 | odd | 2 | 245.6.a.h.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.e.a.11.6 | ✓ | 12 | 7.2 | even | 3 | ||
35.6.e.a.16.6 | yes | 12 | 7.4 | even | 3 | ||
245.6.a.h.1.1 | 6 | 7.6 | odd | 2 | |||
245.6.a.i.1.1 | 6 | 1.1 | even | 1 | trivial |