Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + 81977088 x^{5} - 3773728 x^{4} - 1245415104 x^{3} + \cdots - 6400833792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.96558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.96558 | −0.701023 | −0.350511 | − | 0.936558i | \(-0.613992\pi\) | ||||
−0.350511 | + | 0.936558i | \(0.613992\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −16.2741 | −0.508567 | ||||||||
\(5\) | 45.8225 | 0.819698 | 0.409849 | − | 0.912153i | \(-0.365581\pi\) | ||||
0.409849 | + | 0.912153i | \(0.365581\pi\) | |||||||
\(6\) | 35.6903 | 0.404736 | ||||||||
\(7\) | 214.983 | 1.65829 | 0.829143 | − | 0.559036i | \(-0.188829\pi\) | ||||
0.829143 | + | 0.559036i | \(0.188829\pi\) | |||||||
\(8\) | 191.435 | 1.05754 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −181.713 | −0.574627 | ||||||||
\(11\) | −156.057 | −0.388869 | −0.194434 | − | 0.980916i | \(-0.562287\pi\) | ||||
−0.194434 | + | 0.980916i | \(0.562287\pi\) | |||||||
\(12\) | 146.467 | 0.293621 | ||||||||
\(13\) | 176.241 | 0.289233 | 0.144616 | − | 0.989488i | \(-0.453805\pi\) | ||||
0.144616 | + | 0.989488i | \(0.453805\pi\) | |||||||
\(14\) | −852.534 | −1.16250 | ||||||||
\(15\) | −412.403 | −0.473253 | ||||||||
\(16\) | −238.380 | −0.232793 | ||||||||
\(17\) | −992.973 | −0.833327 | −0.416663 | − | 0.909061i | \(-0.636801\pi\) | ||||
−0.416663 | + | 0.909061i | \(0.636801\pi\) | |||||||
\(18\) | −321.212 | −0.233674 | ||||||||
\(19\) | −1346.21 | −0.855517 | −0.427758 | − | 0.903893i | \(-0.640697\pi\) | ||||
−0.427758 | + | 0.903893i | \(0.640697\pi\) | |||||||
\(20\) | −745.722 | −0.416871 | ||||||||
\(21\) | −1934.85 | −0.957412 | ||||||||
\(22\) | 618.859 | 0.272606 | ||||||||
\(23\) | 3041.14 | 1.19872 | 0.599359 | − | 0.800480i | \(-0.295422\pi\) | ||||
0.599359 | + | 0.800480i | \(0.295422\pi\) | |||||||
\(24\) | −1722.92 | −0.610571 | ||||||||
\(25\) | −1025.30 | −0.328095 | ||||||||
\(26\) | −698.897 | −0.202759 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3498.67 | −0.843349 | ||||||||
\(29\) | 7850.14 | 1.73334 | 0.866668 | − | 0.498886i | \(-0.166257\pi\) | ||||
0.866668 | + | 0.498886i | \(0.166257\pi\) | |||||||
\(30\) | 1635.42 | 0.331761 | ||||||||
\(31\) | 2343.28 | 0.437945 | 0.218973 | − | 0.975731i | \(-0.429729\pi\) | ||||
0.218973 | + | 0.975731i | \(0.429729\pi\) | |||||||
\(32\) | −5180.61 | −0.894347 | ||||||||
\(33\) | 1404.52 | 0.224513 | ||||||||
\(34\) | 3937.72 | 0.584181 | ||||||||
\(35\) | 9851.07 | 1.35929 | ||||||||
\(36\) | −1318.21 | −0.169522 | ||||||||
\(37\) | 10906.3 | 1.30971 | 0.654854 | − | 0.755755i | \(-0.272730\pi\) | ||||
0.654854 | + | 0.755755i | \(0.272730\pi\) | |||||||
\(38\) | 5338.51 | 0.599737 | ||||||||
\(39\) | −1586.17 | −0.166989 | ||||||||
\(40\) | 8772.04 | 0.866864 | ||||||||
\(41\) | −8949.04 | −0.831413 | −0.415707 | − | 0.909499i | \(-0.636466\pi\) | ||||
−0.415707 | + | 0.909499i | \(0.636466\pi\) | |||||||
\(42\) | 7672.81 | 0.671168 | ||||||||
\(43\) | −6627.71 | −0.546629 | −0.273314 | − | 0.961925i | \(-0.588120\pi\) | ||||
−0.273314 | + | 0.961925i | \(0.588120\pi\) | |||||||
\(44\) | 2539.70 | 0.197766 | ||||||||
\(45\) | 3711.62 | 0.273233 | ||||||||
\(46\) | −12059.9 | −0.840329 | ||||||||
\(47\) | −3598.67 | −0.237628 | −0.118814 | − | 0.992917i | \(-0.537909\pi\) | ||||
−0.118814 | + | 0.992917i | \(0.537909\pi\) | |||||||
\(48\) | 2145.42 | 0.134403 | ||||||||
\(49\) | 29410.8 | 1.74991 | ||||||||
\(50\) | 4065.90 | 0.230002 | ||||||||
\(51\) | 8936.76 | 0.481121 | ||||||||
\(52\) | −2868.17 | −0.147094 | ||||||||
\(53\) | −29978.1 | −1.46593 | −0.732966 | − | 0.680265i | \(-0.761865\pi\) | ||||
−0.732966 | + | 0.680265i | \(0.761865\pi\) | |||||||
\(54\) | 2890.91 | 0.134912 | ||||||||
\(55\) | −7150.95 | −0.318755 | ||||||||
\(56\) | 41155.4 | 1.75370 | ||||||||
\(57\) | 12115.9 | 0.493933 | ||||||||
\(58\) | −31130.4 | −1.21511 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 6711.50 | 0.240681 | ||||||||
\(61\) | 50916.8 | 1.75201 | 0.876005 | − | 0.482301i | \(-0.160199\pi\) | ||||
0.876005 | + | 0.482301i | \(0.160199\pi\) | |||||||
\(62\) | −9292.47 | −0.307010 | ||||||||
\(63\) | 17413.6 | 0.552762 | ||||||||
\(64\) | 28172.3 | 0.859751 | ||||||||
\(65\) | 8075.79 | 0.237084 | ||||||||
\(66\) | −5569.73 | −0.157389 | ||||||||
\(67\) | 20194.9 | 0.549609 | 0.274805 | − | 0.961500i | \(-0.411387\pi\) | ||||
0.274805 | + | 0.961500i | \(0.411387\pi\) | |||||||
\(68\) | 16159.8 | 0.423802 | ||||||||
\(69\) | −27370.3 | −0.692080 | ||||||||
\(70\) | −39065.3 | −0.952897 | ||||||||
\(71\) | 37228.5 | 0.876455 | 0.438227 | − | 0.898864i | \(-0.355606\pi\) | ||||
0.438227 | + | 0.898864i | \(0.355606\pi\) | |||||||
\(72\) | 15506.3 | 0.352513 | ||||||||
\(73\) | 32443.0 | 0.712547 | 0.356274 | − | 0.934382i | \(-0.384047\pi\) | ||||
0.356274 | + | 0.934382i | \(0.384047\pi\) | |||||||
\(74\) | −43250.0 | −0.918136 | ||||||||
\(75\) | 9227.67 | 0.189426 | ||||||||
\(76\) | 21908.4 | 0.435087 | ||||||||
\(77\) | −33549.7 | −0.644856 | ||||||||
\(78\) | 6290.08 | 0.117063 | ||||||||
\(79\) | 47234.2 | 0.851507 | 0.425754 | − | 0.904839i | \(-0.360009\pi\) | ||||
0.425754 | + | 0.904839i | \(0.360009\pi\) | |||||||
\(80\) | −10923.2 | −0.190820 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 35488.2 | 0.582840 | ||||||||
\(83\) | −5522.34 | −0.0879889 | −0.0439944 | − | 0.999032i | \(-0.514008\pi\) | ||||
−0.0439944 | + | 0.999032i | \(0.514008\pi\) | |||||||
\(84\) | 31488.0 | 0.486908 | ||||||||
\(85\) | −45500.5 | −0.683076 | ||||||||
\(86\) | 26282.8 | 0.383199 | ||||||||
\(87\) | −70651.3 | −1.00074 | ||||||||
\(88\) | −29874.9 | −0.411244 | ||||||||
\(89\) | −76315.0 | −1.02126 | −0.510628 | − | 0.859802i | \(-0.670587\pi\) | ||||
−0.510628 | + | 0.859802i | \(0.670587\pi\) | |||||||
\(90\) | −14718.8 | −0.191542 | ||||||||
\(91\) | 37888.8 | 0.479631 | ||||||||
\(92\) | −49491.9 | −0.609628 | ||||||||
\(93\) | −21089.5 | −0.252848 | ||||||||
\(94\) | 14270.8 | 0.166583 | ||||||||
\(95\) | −61686.7 | −0.701265 | ||||||||
\(96\) | 46625.5 | 0.516351 | ||||||||
\(97\) | 80922.3 | 0.873251 | 0.436625 | − | 0.899643i | \(-0.356174\pi\) | ||||
0.436625 | + | 0.899643i | \(0.356174\pi\) | |||||||
\(98\) | −116631. | −1.22673 | ||||||||
\(99\) | −12640.7 | −0.129623 | ||||||||
\(100\) | 16685.8 | 0.166858 | ||||||||
\(101\) | 82048.8 | 0.800329 | 0.400165 | − | 0.916443i | \(-0.368953\pi\) | ||||
0.400165 | + | 0.916443i | \(0.368953\pi\) | |||||||
\(102\) | −35439.5 | −0.337277 | ||||||||
\(103\) | 133604. | 1.24087 | 0.620434 | − | 0.784259i | \(-0.286957\pi\) | ||||
0.620434 | + | 0.784259i | \(0.286957\pi\) | |||||||
\(104\) | 33738.7 | 0.305875 | ||||||||
\(105\) | −88659.7 | −0.784789 | ||||||||
\(106\) | 118881. | 1.02765 | ||||||||
\(107\) | −73779.6 | −0.622984 | −0.311492 | − | 0.950249i | \(-0.600829\pi\) | ||||
−0.311492 | + | 0.950249i | \(0.600829\pi\) | |||||||
\(108\) | 11863.8 | 0.0978737 | ||||||||
\(109\) | 156032. | 1.25790 | 0.628952 | − | 0.777444i | \(-0.283484\pi\) | ||||
0.628952 | + | 0.777444i | \(0.283484\pi\) | |||||||
\(110\) | 28357.7 | 0.223454 | ||||||||
\(111\) | −98157.0 | −0.756160 | ||||||||
\(112\) | −51247.7 | −0.386038 | ||||||||
\(113\) | −34300.6 | −0.252700 | −0.126350 | − | 0.991986i | \(-0.540326\pi\) | ||||
−0.126350 | + | 0.991986i | \(0.540326\pi\) | |||||||
\(114\) | −48046.6 | −0.346258 | ||||||||
\(115\) | 139353. | 0.982587 | ||||||||
\(116\) | −127754. | −0.881517 | ||||||||
\(117\) | 14275.5 | 0.0964110 | ||||||||
\(118\) | −13804.2 | −0.0912654 | ||||||||
\(119\) | −213473. | −1.38189 | ||||||||
\(120\) | −78948.4 | −0.500484 | ||||||||
\(121\) | −136697. | −0.848781 | ||||||||
\(122\) | −201915. | −1.22820 | ||||||||
\(123\) | 80541.4 | 0.480017 | ||||||||
\(124\) | −38134.8 | −0.222724 | ||||||||
\(125\) | −190177. | −1.08864 | ||||||||
\(126\) | −69055.3 | −0.387499 | ||||||||
\(127\) | −156876. | −0.863073 | −0.431536 | − | 0.902096i | \(-0.642028\pi\) | ||||
−0.431536 | + | 0.902096i | \(0.642028\pi\) | |||||||
\(128\) | 54059.8 | 0.291642 | ||||||||
\(129\) | 59649.4 | 0.315596 | ||||||||
\(130\) | −32025.2 | −0.166201 | ||||||||
\(131\) | 248564. | 1.26549 | 0.632746 | − | 0.774360i | \(-0.281928\pi\) | ||||
0.632746 | + | 0.774360i | \(0.281928\pi\) | |||||||
\(132\) | −22857.3 | −0.114180 | ||||||||
\(133\) | −289412. | −1.41869 | ||||||||
\(134\) | −80084.5 | −0.385289 | ||||||||
\(135\) | −33404.6 | −0.157751 | ||||||||
\(136\) | −190090. | −0.881276 | ||||||||
\(137\) | 130816. | 0.595469 | 0.297735 | − | 0.954649i | \(-0.403769\pi\) | ||||
0.297735 | + | 0.954649i | \(0.403769\pi\) | |||||||
\(138\) | 108539. | 0.485164 | ||||||||
\(139\) | 283883. | 1.24624 | 0.623121 | − | 0.782125i | \(-0.285864\pi\) | ||||
0.623121 | + | 0.782125i | \(0.285864\pi\) | |||||||
\(140\) | −160318. | −0.691292 | ||||||||
\(141\) | 32388.0 | 0.137194 | ||||||||
\(142\) | −147633. | −0.614415 | ||||||||
\(143\) | −27503.7 | −0.112474 | ||||||||
\(144\) | −19308.8 | −0.0775977 | ||||||||
\(145\) | 359713. | 1.42081 | ||||||||
\(146\) | −128655. | −0.499512 | ||||||||
\(147\) | −264697. | −1.01031 | ||||||||
\(148\) | −177491. | −0.666074 | ||||||||
\(149\) | 102655. | 0.378805 | 0.189403 | − | 0.981900i | \(-0.439345\pi\) | ||||
0.189403 | + | 0.981900i | \(0.439345\pi\) | |||||||
\(150\) | −36593.1 | −0.132792 | ||||||||
\(151\) | −321646. | −1.14798 | −0.573992 | − | 0.818861i | \(-0.694606\pi\) | ||||
−0.573992 | + | 0.818861i | \(0.694606\pi\) | |||||||
\(152\) | −257712. | −0.904743 | ||||||||
\(153\) | −80430.8 | −0.277776 | ||||||||
\(154\) | 133044. | 0.452059 | ||||||||
\(155\) | 107375. | 0.358983 | ||||||||
\(156\) | 25813.5 | 0.0849249 | ||||||||
\(157\) | 20173.1 | 0.0653167 | 0.0326583 | − | 0.999467i | \(-0.489603\pi\) | ||||
0.0326583 | + | 0.999467i | \(0.489603\pi\) | |||||||
\(158\) | −187311. | −0.596926 | ||||||||
\(159\) | 269803. | 0.846357 | ||||||||
\(160\) | −237389. | −0.733094 | ||||||||
\(161\) | 653794. | 1.98782 | ||||||||
\(162\) | −26018.2 | −0.0778914 | ||||||||
\(163\) | 304847. | 0.898697 | 0.449348 | − | 0.893357i | \(-0.351656\pi\) | ||||
0.449348 | + | 0.893357i | \(0.351656\pi\) | |||||||
\(164\) | 145638. | 0.422829 | ||||||||
\(165\) | 64358.5 | 0.184033 | ||||||||
\(166\) | 21899.3 | 0.0616822 | ||||||||
\(167\) | 399173. | 1.10757 | 0.553784 | − | 0.832660i | \(-0.313183\pi\) | ||||
0.553784 | + | 0.832660i | \(0.313183\pi\) | |||||||
\(168\) | −370398. | −1.01250 | ||||||||
\(169\) | −340232. | −0.916344 | ||||||||
\(170\) | 180436. | 0.478852 | ||||||||
\(171\) | −109043. | −0.285172 | ||||||||
\(172\) | 107860. | 0.277997 | ||||||||
\(173\) | −269280. | −0.684052 | −0.342026 | − | 0.939691i | \(-0.611113\pi\) | ||||
−0.342026 | + | 0.939691i | \(0.611113\pi\) | |||||||
\(174\) | 280174. | 0.701543 | ||||||||
\(175\) | −220422. | −0.544075 | ||||||||
\(176\) | 37201.0 | 0.0905259 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | 302634. | 0.715924 | ||||||||
\(179\) | −587301. | −1.37002 | −0.685012 | − | 0.728532i | \(-0.740203\pi\) | ||||
−0.685012 | + | 0.728532i | \(0.740203\pi\) | |||||||
\(180\) | −60403.5 | −0.138957 | ||||||||
\(181\) | 440471. | 0.999357 | 0.499678 | − | 0.866211i | \(-0.333452\pi\) | ||||
0.499678 | + | 0.866211i | \(0.333452\pi\) | |||||||
\(182\) | −150251. | −0.336232 | ||||||||
\(183\) | −458251. | −1.01152 | ||||||||
\(184\) | 582181. | 1.26769 | ||||||||
\(185\) | 499756. | 1.07357 | ||||||||
\(186\) | 83632.2 | 0.177252 | ||||||||
\(187\) | 154961. | 0.324055 | ||||||||
\(188\) | 58565.2 | 0.120850 | ||||||||
\(189\) | −156723. | −0.319137 | ||||||||
\(190\) | 244624. | 0.491603 | ||||||||
\(191\) | 372603. | 0.739031 | 0.369515 | − | 0.929225i | \(-0.379524\pi\) | ||||
0.369515 | + | 0.929225i | \(0.379524\pi\) | |||||||
\(192\) | −253551. | −0.496377 | ||||||||
\(193\) | 958360. | 1.85198 | 0.925988 | − | 0.377552i | \(-0.123234\pi\) | ||||
0.925988 | + | 0.377552i | \(0.123234\pi\) | |||||||
\(194\) | −320904. | −0.612169 | ||||||||
\(195\) | −72682.1 | −0.136880 | ||||||||
\(196\) | −478635. | −0.889948 | ||||||||
\(197\) | −366511. | −0.672855 | −0.336428 | − | 0.941709i | \(-0.609219\pi\) | ||||
−0.336428 | + | 0.941709i | \(0.609219\pi\) | |||||||
\(198\) | 50127.6 | 0.0908686 | ||||||||
\(199\) | 456957. | 0.817980 | 0.408990 | − | 0.912539i | \(-0.365881\pi\) | ||||
0.408990 | + | 0.912539i | \(0.365881\pi\) | |||||||
\(200\) | −196278. | −0.346974 | ||||||||
\(201\) | −181754. | −0.317317 | ||||||||
\(202\) | −325371. | −0.561049 | ||||||||
\(203\) | 1.68765e6 | 2.87437 | ||||||||
\(204\) | −145438. | −0.244682 | ||||||||
\(205\) | −410068. | −0.681508 | ||||||||
\(206\) | −529817. | −0.869877 | ||||||||
\(207\) | 246332. | 0.399573 | ||||||||
\(208\) | −42012.3 | −0.0673314 | ||||||||
\(209\) | 210086. | 0.332684 | ||||||||
\(210\) | 351587. | 0.550155 | ||||||||
\(211\) | −127342. | −0.196909 | −0.0984546 | − | 0.995142i | \(-0.531390\pi\) | ||||
−0.0984546 | + | 0.995142i | \(0.531390\pi\) | |||||||
\(212\) | 487867. | 0.745525 | ||||||||
\(213\) | −335056. | −0.506021 | ||||||||
\(214\) | 292579. | 0.436726 | ||||||||
\(215\) | −303698. | −0.448071 | ||||||||
\(216\) | −139556. | −0.203524 | ||||||||
\(217\) | 503766. | 0.726239 | ||||||||
\(218\) | −618758. | −0.881819 | ||||||||
\(219\) | −291987. | −0.411389 | ||||||||
\(220\) | 116375. | 0.162108 | ||||||||
\(221\) | −175002. | −0.241026 | ||||||||
\(222\) | 389250. | 0.530086 | ||||||||
\(223\) | 998142. | 1.34410 | 0.672048 | − | 0.740508i | \(-0.265415\pi\) | ||||
0.672048 | + | 0.740508i | \(0.265415\pi\) | |||||||
\(224\) | −1.11374e6 | −1.48308 | ||||||||
\(225\) | −83049.0 | −0.109365 | ||||||||
\(226\) | 136022. | 0.177149 | ||||||||
\(227\) | −1.00518e6 | −1.29474 | −0.647368 | − | 0.762178i | \(-0.724130\pi\) | ||||
−0.647368 | + | 0.762178i | \(0.724130\pi\) | |||||||
\(228\) | −197175. | −0.251198 | ||||||||
\(229\) | −363463. | −0.458006 | −0.229003 | − | 0.973426i | \(-0.573547\pi\) | ||||
−0.229003 | + | 0.973426i | \(0.573547\pi\) | |||||||
\(230\) | −552615. | −0.688816 | ||||||||
\(231\) | 301948. | 0.372307 | ||||||||
\(232\) | 1.50279e6 | 1.83307 | ||||||||
\(233\) | 74441.9 | 0.0898312 | 0.0449156 | − | 0.998991i | \(-0.485698\pi\) | ||||
0.0449156 | + | 0.998991i | \(0.485698\pi\) | |||||||
\(234\) | −56610.7 | −0.0675863 | ||||||||
\(235\) | −164900. | −0.194783 | ||||||||
\(236\) | −56650.3 | −0.0662098 | ||||||||
\(237\) | −425107. | −0.491618 | ||||||||
\(238\) | 846544. | 0.968740 | ||||||||
\(239\) | 1.09860e6 | 1.24407 | 0.622036 | − | 0.782988i | \(-0.286306\pi\) | ||||
0.622036 | + | 0.782988i | \(0.286306\pi\) | |||||||
\(240\) | 98308.6 | 0.110170 | ||||||||
\(241\) | 120611. | 0.133765 | 0.0668826 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668826 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(242\) | 542084. | 0.595015 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −828627. | −0.891014 | ||||||||
\(245\) | 1.34768e6 | 1.43440 | ||||||||
\(246\) | −319394. | −0.336503 | ||||||||
\(247\) | −237257. | −0.247444 | ||||||||
\(248\) | 448586. | 0.463145 | ||||||||
\(249\) | 49701.1 | 0.0508004 | ||||||||
\(250\) | 754163. | 0.763160 | ||||||||
\(251\) | −133146. | −0.133396 | −0.0666979 | − | 0.997773i | \(-0.521246\pi\) | ||||
−0.0666979 | + | 0.997773i | \(0.521246\pi\) | |||||||
\(252\) | −283392. | −0.281116 | ||||||||
\(253\) | −474593. | −0.466144 | ||||||||
\(254\) | 622105. | 0.605034 | ||||||||
\(255\) | 409505. | 0.394374 | ||||||||
\(256\) | −1.11589e6 | −1.06420 | ||||||||
\(257\) | −932083. | −0.880282 | −0.440141 | − | 0.897929i | \(-0.645072\pi\) | ||||
−0.440141 | + | 0.897929i | \(0.645072\pi\) | |||||||
\(258\) | −236545. | −0.221240 | ||||||||
\(259\) | 2.34468e6 | 2.17187 | ||||||||
\(260\) | −131427. | −0.120573 | ||||||||
\(261\) | 635862. | 0.577778 | ||||||||
\(262\) | −985700. | −0.887139 | ||||||||
\(263\) | 1.66088e6 | 1.48064 | 0.740320 | − | 0.672254i | \(-0.234674\pi\) | ||||
0.740320 | + | 0.672254i | \(0.234674\pi\) | |||||||
\(264\) | 268874. | 0.237432 | ||||||||
\(265\) | −1.37367e6 | −1.20162 | ||||||||
\(266\) | 1.14769e6 | 0.994535 | ||||||||
\(267\) | 686835. | 0.589623 | ||||||||
\(268\) | −328654. | −0.279513 | ||||||||
\(269\) | −746269. | −0.628803 | −0.314401 | − | 0.949290i | \(-0.601804\pi\) | ||||
−0.314401 | + | 0.949290i | \(0.601804\pi\) | |||||||
\(270\) | 132469. | 0.110587 | ||||||||
\(271\) | 1.84347e6 | 1.52480 | 0.762398 | − | 0.647108i | \(-0.224022\pi\) | ||||
0.762398 | + | 0.647108i | \(0.224022\pi\) | |||||||
\(272\) | 236705. | 0.193993 | ||||||||
\(273\) | −340999. | −0.276915 | ||||||||
\(274\) | −518762. | −0.417438 | ||||||||
\(275\) | 160005. | 0.127586 | ||||||||
\(276\) | 445427. | 0.351969 | ||||||||
\(277\) | −1.57925e6 | −1.23666 | −0.618331 | − | 0.785918i | \(-0.712191\pi\) | ||||
−0.618331 | + | 0.785918i | \(0.712191\pi\) | |||||||
\(278\) | −1.12576e6 | −0.873645 | ||||||||
\(279\) | 189806. | 0.145982 | ||||||||
\(280\) | 1.88584e6 | 1.43751 | ||||||||
\(281\) | −1.09989e6 | −0.830967 | −0.415483 | − | 0.909601i | \(-0.636388\pi\) | ||||
−0.415483 | + | 0.909601i | \(0.636388\pi\) | |||||||
\(282\) | −128437. | −0.0961765 | ||||||||
\(283\) | −2.43606e6 | −1.80810 | −0.904050 | − | 0.427426i | \(-0.859420\pi\) | ||||
−0.904050 | + | 0.427426i | \(0.859420\pi\) | |||||||
\(284\) | −605862. | −0.445736 | ||||||||
\(285\) | 555180. | 0.404876 | ||||||||
\(286\) | 109068. | 0.0788466 | ||||||||
\(287\) | −1.92389e6 | −1.37872 | ||||||||
\(288\) | −419629. | −0.298116 | ||||||||
\(289\) | −433861. | −0.305567 | ||||||||
\(290\) | −1.42647e6 | −0.996022 | ||||||||
\(291\) | −728301. | −0.504171 | ||||||||
\(292\) | −527982. | −0.362378 | ||||||||
\(293\) | −696507. | −0.473976 | −0.236988 | − | 0.971513i | \(-0.576160\pi\) | ||||
−0.236988 | + | 0.971513i | \(0.576160\pi\) | |||||||
\(294\) | 1.04968e6 | 0.708253 | ||||||||
\(295\) | 159508. | 0.106716 | ||||||||
\(296\) | 2.08786e6 | 1.38507 | ||||||||
\(297\) | 113766. | 0.0748378 | ||||||||
\(298\) | −407088. | −0.265551 | ||||||||
\(299\) | 535973. | 0.346709 | ||||||||
\(300\) | −150172. | −0.0963356 | ||||||||
\(301\) | −1.42485e6 | −0.906467 | ||||||||
\(302\) | 1.27552e6 | 0.804764 | ||||||||
\(303\) | −738439. | −0.462070 | ||||||||
\(304\) | 320909. | 0.199158 | ||||||||
\(305\) | 2.33314e6 | 1.43612 | ||||||||
\(306\) | 318955. | 0.194727 | ||||||||
\(307\) | 2.06876e6 | 1.25275 | 0.626375 | − | 0.779522i | \(-0.284538\pi\) | ||||
0.626375 | + | 0.779522i | \(0.284538\pi\) | |||||||
\(308\) | 545993. | 0.327952 | ||||||||
\(309\) | −1.20243e6 | −0.716415 | ||||||||
\(310\) | −425804. | −0.251655 | ||||||||
\(311\) | −245921. | −0.144177 | −0.0720883 | − | 0.997398i | \(-0.522966\pi\) | ||||
−0.0720883 | + | 0.997398i | \(0.522966\pi\) | |||||||
\(312\) | −303648. | −0.176597 | ||||||||
\(313\) | −909246. | −0.524591 | −0.262295 | − | 0.964988i | \(-0.584479\pi\) | ||||
−0.262295 | + | 0.964988i | \(0.584479\pi\) | |||||||
\(314\) | −79998.3 | −0.0457885 | ||||||||
\(315\) | 797937. | 0.453098 | ||||||||
\(316\) | −768695. | −0.433048 | ||||||||
\(317\) | −1.71664e6 | −0.959467 | −0.479733 | − | 0.877414i | \(-0.659267\pi\) | ||||
−0.479733 | + | 0.877414i | \(0.659267\pi\) | |||||||
\(318\) | −1.06993e6 | −0.593316 | ||||||||
\(319\) | −1.22507e6 | −0.674040 | ||||||||
\(320\) | 1.29093e6 | 0.704736 | ||||||||
\(321\) | 664017. | 0.359680 | ||||||||
\(322\) | −2.59268e6 | −1.39351 | ||||||||
\(323\) | 1.33675e6 | 0.712925 | ||||||||
\(324\) | −106775. | −0.0565074 | ||||||||
\(325\) | −180699. | −0.0948959 | ||||||||
\(326\) | −1.20890e6 | −0.630007 | ||||||||
\(327\) | −1.40429e6 | −0.726251 | ||||||||
\(328\) | −1.71316e6 | −0.879253 | ||||||||
\(329\) | −773654. | −0.394055 | ||||||||
\(330\) | −255219. | −0.129012 | ||||||||
\(331\) | 3.18458e6 | 1.59765 | 0.798827 | − | 0.601561i | \(-0.205454\pi\) | ||||
0.798827 | + | 0.601561i | \(0.205454\pi\) | |||||||
\(332\) | 89871.3 | 0.0447482 | ||||||||
\(333\) | 883413. | 0.436569 | ||||||||
\(334\) | −1.58296e6 | −0.776431 | ||||||||
\(335\) | 925380. | 0.450514 | ||||||||
\(336\) | 461230. | 0.222879 | ||||||||
\(337\) | −604758. | −0.290073 | −0.145036 | − | 0.989426i | \(-0.546330\pi\) | ||||
−0.145036 | + | 0.989426i | \(0.546330\pi\) | |||||||
\(338\) | 1.34922e6 | 0.642378 | ||||||||
\(339\) | 308705. | 0.145896 | ||||||||
\(340\) | 740482. | 0.347390 | ||||||||
\(341\) | −365686. | −0.170303 | ||||||||
\(342\) | 432419. | 0.199912 | ||||||||
\(343\) | 2.70961e6 | 1.24357 | ||||||||
\(344\) | −1.26878e6 | −0.578082 | ||||||||
\(345\) | −1.25417e6 | −0.567297 | ||||||||
\(346\) | 1.06785e6 | 0.479536 | ||||||||
\(347\) | −3.66370e6 | −1.63341 | −0.816706 | − | 0.577053i | \(-0.804202\pi\) | ||||
−0.816706 | + | 0.577053i | \(0.804202\pi\) | |||||||
\(348\) | 1.14979e6 | 0.508944 | ||||||||
\(349\) | −4.26413e6 | −1.87399 | −0.936995 | − | 0.349343i | \(-0.886405\pi\) | ||||
−0.936995 | + | 0.349343i | \(0.886405\pi\) | |||||||
\(350\) | 874101. | 0.381409 | ||||||||
\(351\) | −128479. | −0.0556629 | ||||||||
\(352\) | 808473. | 0.347783 | ||||||||
\(353\) | 2.74711e6 | 1.17338 | 0.586692 | − | 0.809810i | \(-0.300430\pi\) | ||||
0.586692 | + | 0.809810i | \(0.300430\pi\) | |||||||
\(354\) | 124238. | 0.0526921 | ||||||||
\(355\) | 1.70590e6 | 0.718428 | ||||||||
\(356\) | 1.24196e6 | 0.519377 | ||||||||
\(357\) | 1.92125e6 | 0.797837 | ||||||||
\(358\) | 2.32899e6 | 0.960418 | ||||||||
\(359\) | −1.97611e6 | −0.809236 | −0.404618 | − | 0.914486i | \(-0.632595\pi\) | ||||
−0.404618 | + | 0.914486i | \(0.632595\pi\) | |||||||
\(360\) | 710535. | 0.288955 | ||||||||
\(361\) | −663821. | −0.268091 | ||||||||
\(362\) | −1.74672e6 | −0.700572 | ||||||||
\(363\) | 1.23027e6 | 0.490044 | ||||||||
\(364\) | −616607. | −0.243924 | ||||||||
\(365\) | 1.48662e6 | 0.584074 | ||||||||
\(366\) | 1.81724e6 | 0.709101 | ||||||||
\(367\) | 2.43373e6 | 0.943206 | 0.471603 | − | 0.881811i | \(-0.343676\pi\) | ||||
0.471603 | + | 0.881811i | \(0.343676\pi\) | |||||||
\(368\) | −724948. | −0.279053 | ||||||||
\(369\) | −724872. | −0.277138 | ||||||||
\(370\) | −1.98182e6 | −0.752594 | ||||||||
\(371\) | −6.44478e6 | −2.43094 | ||||||||
\(372\) | 343214. | 0.128590 | ||||||||
\(373\) | 2.63259e6 | 0.979740 | 0.489870 | − | 0.871796i | \(-0.337044\pi\) | ||||
0.489870 | + | 0.871796i | \(0.337044\pi\) | |||||||
\(374\) | −614511. | −0.227170 | ||||||||
\(375\) | 1.71159e6 | 0.628525 | ||||||||
\(376\) | −688912. | −0.251301 | ||||||||
\(377\) | 1.38351e6 | 0.501338 | ||||||||
\(378\) | 621498. | 0.223723 | ||||||||
\(379\) | −2.43570e6 | −0.871016 | −0.435508 | − | 0.900185i | \(-0.643431\pi\) | ||||
−0.435508 | + | 0.900185i | \(0.643431\pi\) | |||||||
\(380\) | 1.00390e6 | 0.356640 | ||||||||
\(381\) | 1.41188e6 | 0.498295 | ||||||||
\(382\) | −1.47759e6 | −0.518078 | ||||||||
\(383\) | −2.55420e6 | −0.889728 | −0.444864 | − | 0.895598i | \(-0.646748\pi\) | ||||
−0.444864 | + | 0.895598i | \(0.646748\pi\) | |||||||
\(384\) | −486538. | −0.168379 | ||||||||
\(385\) | −1.53733e6 | −0.528587 | ||||||||
\(386\) | −3.80046e6 | −1.29828 | ||||||||
\(387\) | −536845. | −0.182210 | ||||||||
\(388\) | −1.31694e6 | −0.444106 | ||||||||
\(389\) | −4.16114e6 | −1.39424 | −0.697121 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697121 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(390\) | 288227. | 0.0959563 | ||||||||
\(391\) | −3.01977e6 | −0.998924 | ||||||||
\(392\) | 5.63026e6 | 1.85060 | ||||||||
\(393\) | −2.23707e6 | −0.730632 | ||||||||
\(394\) | 1.45343e6 | 0.471687 | ||||||||
\(395\) | 2.16439e6 | 0.697979 | ||||||||
\(396\) | 205716. | 0.0659219 | ||||||||
\(397\) | 3.12738e6 | 0.995873 | 0.497937 | − | 0.867213i | \(-0.334091\pi\) | ||||
0.497937 | + | 0.867213i | \(0.334091\pi\) | |||||||
\(398\) | −1.81210e6 | −0.573423 | ||||||||
\(399\) | 2.60471e6 | 0.819082 | ||||||||
\(400\) | 244410. | 0.0763782 | ||||||||
\(401\) | 4.53732e6 | 1.40909 | 0.704544 | − | 0.709660i | \(-0.251151\pi\) | ||||
0.704544 | + | 0.709660i | \(0.251151\pi\) | |||||||
\(402\) | 720760. | 0.222447 | ||||||||
\(403\) | 412981. | 0.126668 | ||||||||
\(404\) | −1.33527e6 | −0.407021 | ||||||||
\(405\) | 300642. | 0.0910776 | ||||||||
\(406\) | −6.69252e6 | −2.01500 | ||||||||
\(407\) | −1.70202e6 | −0.509304 | ||||||||
\(408\) | 1.71081e6 | 0.508805 | ||||||||
\(409\) | −3.30951e6 | −0.978263 | −0.489132 | − | 0.872210i | \(-0.662686\pi\) | ||||
−0.489132 | + | 0.872210i | \(0.662686\pi\) | |||||||
\(410\) | 1.62616e6 | 0.477753 | ||||||||
\(411\) | −1.17734e6 | −0.343794 | ||||||||
\(412\) | −2.17428e6 | −0.631064 | ||||||||
\(413\) | 748357. | 0.215890 | ||||||||
\(414\) | −976852. | −0.280110 | ||||||||
\(415\) | −253047. | −0.0721243 | ||||||||
\(416\) | −913034. | −0.258675 | ||||||||
\(417\) | −2.55495e6 | −0.719518 | ||||||||
\(418\) | −833114. | −0.233219 | ||||||||
\(419\) | −4.28215e6 | −1.19159 | −0.595795 | − | 0.803136i | \(-0.703163\pi\) | ||||
−0.595795 | + | 0.803136i | \(0.703163\pi\) | |||||||
\(420\) | 1.44286e6 | 0.399118 | ||||||||
\(421\) | −5.73100e6 | −1.57589 | −0.787944 | − | 0.615747i | \(-0.788855\pi\) | ||||
−0.787944 | + | 0.615747i | \(0.788855\pi\) | |||||||
\(422\) | 504986. | 0.138038 | ||||||||
\(423\) | −291492. | −0.0792093 | ||||||||
\(424\) | −5.73886e6 | −1.55028 | ||||||||
\(425\) | 1.01809e6 | 0.273410 | ||||||||
\(426\) | 1.32869e6 | 0.354733 | ||||||||
\(427\) | 1.09463e7 | 2.90534 | ||||||||
\(428\) | 1.20070e6 | 0.316829 | ||||||||
\(429\) | 247533. | 0.0649367 | ||||||||
\(430\) | 1.20434e6 | 0.314108 | ||||||||
\(431\) | 1.51057e6 | 0.391694 | 0.195847 | − | 0.980634i | \(-0.437254\pi\) | ||||
0.195847 | + | 0.980634i | \(0.437254\pi\) | |||||||
\(432\) | 173779. | 0.0448011 | ||||||||
\(433\) | −1.90848e6 | −0.489179 | −0.244589 | − | 0.969627i | \(-0.578653\pi\) | ||||
−0.244589 | + | 0.969627i | \(0.578653\pi\) | |||||||
\(434\) | −1.99773e6 | −0.509110 | ||||||||
\(435\) | −3.23742e6 | −0.820306 | ||||||||
\(436\) | −2.53929e6 | −0.639728 | ||||||||
\(437\) | −4.09401e6 | −1.02552 | ||||||||
\(438\) | 1.15790e6 | 0.288393 | ||||||||
\(439\) | −2.71946e6 | −0.673475 | −0.336737 | − | 0.941599i | \(-0.609323\pi\) | ||||
−0.336737 | + | 0.941599i | \(0.609323\pi\) | |||||||
\(440\) | −1.36894e6 | −0.337096 | ||||||||
\(441\) | 2.38227e6 | 0.583305 | ||||||||
\(442\) | 693987. | 0.168964 | ||||||||
\(443\) | 5.21524e6 | 1.26260 | 0.631298 | − | 0.775540i | \(-0.282522\pi\) | ||||
0.631298 | + | 0.775540i | \(0.282522\pi\) | |||||||
\(444\) | 1.59742e6 | 0.384558 | ||||||||
\(445\) | −3.49695e6 | −0.837122 | ||||||||
\(446\) | −3.95822e6 | −0.942242 | ||||||||
\(447\) | −923898. | −0.218703 | ||||||||
\(448\) | 6.05657e6 | 1.42571 | ||||||||
\(449\) | 4.09107e6 | 0.957680 | 0.478840 | − | 0.877902i | \(-0.341057\pi\) | ||||
0.478840 | + | 0.877902i | \(0.341057\pi\) | |||||||
\(450\) | 329338. | 0.0766674 | ||||||||
\(451\) | 1.39656e6 | 0.323310 | ||||||||
\(452\) | 558212. | 0.128515 | ||||||||
\(453\) | 2.89482e6 | 0.662789 | ||||||||
\(454\) | 3.98615e6 | 0.907640 | ||||||||
\(455\) | 1.73616e6 | 0.393153 | ||||||||
\(456\) | 2.31941e6 | 0.522354 | ||||||||
\(457\) | −1.16165e6 | −0.260188 | −0.130094 | − | 0.991502i | \(-0.541528\pi\) | ||||
−0.130094 | + | 0.991502i | \(0.541528\pi\) | |||||||
\(458\) | 1.44134e6 | 0.321073 | ||||||||
\(459\) | 723878. | 0.160374 | ||||||||
\(460\) | −2.26785e6 | −0.499711 | ||||||||
\(461\) | 2.86009e6 | 0.626799 | 0.313399 | − | 0.949621i | \(-0.398532\pi\) | ||||
0.313399 | + | 0.949621i | \(0.398532\pi\) | |||||||
\(462\) | −1.19740e6 | −0.260996 | ||||||||
\(463\) | −6.88483e6 | −1.49259 | −0.746296 | − | 0.665614i | \(-0.768170\pi\) | ||||
−0.746296 | + | 0.665614i | \(0.768170\pi\) | |||||||
\(464\) | −1.87132e6 | −0.403509 | ||||||||
\(465\) | −966374. | −0.207259 | ||||||||
\(466\) | −295206. | −0.0629738 | ||||||||
\(467\) | 7.95572e6 | 1.68806 | 0.844028 | − | 0.536298i | \(-0.180178\pi\) | ||||
0.844028 | + | 0.536298i | \(0.180178\pi\) | |||||||
\(468\) | −232321. | −0.0490314 | ||||||||
\(469\) | 4.34156e6 | 0.911410 | ||||||||
\(470\) | 653925. | 0.136547 | ||||||||
\(471\) | −181558. | −0.0377106 | ||||||||
\(472\) | 666386. | 0.137680 | ||||||||
\(473\) | 1.03430e6 | 0.212567 | ||||||||
\(474\) | 1.68580e6 | 0.344636 | ||||||||
\(475\) | 1.38026e6 | 0.280691 | ||||||||
\(476\) | 3.47408e6 | 0.702786 | ||||||||
\(477\) | −2.42822e6 | −0.488644 | ||||||||
\(478\) | −4.35660e6 | −0.872123 | ||||||||
\(479\) | −2.55762e6 | −0.509328 | −0.254664 | − | 0.967030i | \(-0.581965\pi\) | ||||
−0.254664 | + | 0.967030i | \(0.581965\pi\) | |||||||
\(480\) | 2.13650e6 | 0.423252 | ||||||||
\(481\) | 1.92214e6 | 0.378811 | ||||||||
\(482\) | −478292. | −0.0937725 | ||||||||
\(483\) | −5.88415e6 | −1.14767 | ||||||||
\(484\) | 2.22463e6 | 0.431662 | ||||||||
\(485\) | 3.70806e6 | 0.715802 | ||||||||
\(486\) | 234164. | 0.0449706 | ||||||||
\(487\) | −1.26363e6 | −0.241434 | −0.120717 | − | 0.992687i | \(-0.538519\pi\) | ||||
−0.120717 | + | 0.992687i | \(0.538519\pi\) | |||||||
\(488\) | 9.74727e6 | 1.85282 | ||||||||
\(489\) | −2.74362e6 | −0.518863 | ||||||||
\(490\) | −5.34433e6 | −1.00555 | ||||||||
\(491\) | 2.84633e6 | 0.532820 | 0.266410 | − | 0.963860i | \(-0.414162\pi\) | ||||
0.266410 | + | 0.963860i | \(0.414162\pi\) | |||||||
\(492\) | −1.31074e6 | −0.244121 | ||||||||
\(493\) | −7.79498e6 | −1.44443 | ||||||||
\(494\) | 940862. | 0.173464 | ||||||||
\(495\) | −579227. | −0.106252 | ||||||||
\(496\) | −558591. | −0.101951 | ||||||||
\(497\) | 8.00350e6 | 1.45341 | ||||||||
\(498\) | −197094. | −0.0356123 | ||||||||
\(499\) | 3.80322e6 | 0.683754 | 0.341877 | − | 0.939745i | \(-0.388937\pi\) | ||||
0.341877 | + | 0.939745i | \(0.388937\pi\) | |||||||
\(500\) | 3.09497e6 | 0.553645 | ||||||||
\(501\) | −3.59256e6 | −0.639455 | ||||||||
\(502\) | 528000. | 0.0935136 | ||||||||
\(503\) | 4.91618e6 | 0.866378 | 0.433189 | − | 0.901303i | \(-0.357388\pi\) | ||||
0.433189 | + | 0.901303i | \(0.357388\pi\) | |||||||
\(504\) | 3.33358e6 | 0.584568 | ||||||||
\(505\) | 3.75968e6 | 0.656029 | ||||||||
\(506\) | 1.88204e6 | 0.326777 | ||||||||
\(507\) | 3.06209e6 | 0.529052 | ||||||||
\(508\) | 2.55302e6 | 0.438930 | ||||||||
\(509\) | −5.90046e6 | −1.00947 | −0.504733 | − | 0.863276i | \(-0.668409\pi\) | ||||
−0.504733 | + | 0.863276i | \(0.668409\pi\) | |||||||
\(510\) | −1.62393e6 | −0.276465 | ||||||||
\(511\) | 6.97470e6 | 1.18161 | ||||||||
\(512\) | 2.69525e6 | 0.454386 | ||||||||
\(513\) | 981386. | 0.164644 | ||||||||
\(514\) | 3.69626e6 | 0.617098 | ||||||||
\(515\) | 6.12206e6 | 1.01714 | ||||||||
\(516\) | −970743. | −0.160502 | ||||||||
\(517\) | 561599. | 0.0924060 | ||||||||
\(518\) | −9.29803e6 | −1.52253 | ||||||||
\(519\) | 2.42352e6 | 0.394937 | ||||||||
\(520\) | 1.54599e6 | 0.250726 | ||||||||
\(521\) | 1.04083e7 | 1.67992 | 0.839958 | − | 0.542651i | \(-0.182580\pi\) | ||||
0.839958 | + | 0.542651i | \(0.182580\pi\) | |||||||
\(522\) | −2.52156e6 | −0.405036 | ||||||||
\(523\) | 7.39494e6 | 1.18217 | 0.591086 | − | 0.806609i | \(-0.298699\pi\) | ||||
0.591086 | + | 0.806609i | \(0.298699\pi\) | |||||||
\(524\) | −4.04516e6 | −0.643587 | ||||||||
\(525\) | 1.98379e6 | 0.314122 | ||||||||
\(526\) | −6.58637e6 | −1.03796 | ||||||||
\(527\) | −2.32681e6 | −0.364951 | ||||||||
\(528\) | −334809. | −0.0522652 | ||||||||
\(529\) | 2.81220e6 | 0.436924 | ||||||||
\(530\) | 5.44741e6 | 0.842365 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | 4.70994e6 | 0.721499 | ||||||||
\(533\) | −1.57719e6 | −0.240472 | ||||||||
\(534\) | −2.72370e6 | −0.413339 | ||||||||
\(535\) | −3.38077e6 | −0.510659 | ||||||||
\(536\) | 3.86601e6 | 0.581234 | ||||||||
\(537\) | 5.28571e6 | 0.790983 | ||||||||
\(538\) | 2.95939e6 | 0.440805 | ||||||||
\(539\) | −4.58978e6 | −0.680486 | ||||||||
\(540\) | 543631. | 0.0802269 | ||||||||
\(541\) | 5.70318e6 | 0.837768 | 0.418884 | − | 0.908040i | \(-0.362421\pi\) | ||||
0.418884 | + | 0.908040i | \(0.362421\pi\) | |||||||
\(542\) | −7.31042e6 | −1.06892 | ||||||||
\(543\) | −3.96424e6 | −0.576979 | ||||||||
\(544\) | 5.14421e6 | 0.745283 | ||||||||
\(545\) | 7.14978e6 | 1.03110 | ||||||||
\(546\) | 1.35226e6 | 0.194124 | ||||||||
\(547\) | −602941. | −0.0861602 | −0.0430801 | − | 0.999072i | \(-0.513717\pi\) | ||||
−0.0430801 | + | 0.999072i | \(0.513717\pi\) | |||||||
\(548\) | −2.12892e6 | −0.302836 | ||||||||
\(549\) | 4.12426e6 | 0.584004 | ||||||||
\(550\) | −634514. | −0.0894406 | ||||||||
\(551\) | −1.05679e7 | −1.48290 | ||||||||
\(552\) | −5.23963e6 | −0.731902 | ||||||||
\(553\) | 1.01546e7 | 1.41204 | ||||||||
\(554\) | 6.26264e6 | 0.866929 | ||||||||
\(555\) | −4.49780e6 | −0.619823 | ||||||||
\(556\) | −4.61995e6 | −0.633797 | ||||||||
\(557\) | −5.42243e6 | −0.740552 | −0.370276 | − | 0.928922i | \(-0.620737\pi\) | ||||
−0.370276 | + | 0.928922i | \(0.620737\pi\) | |||||||
\(558\) | −752690. | −0.102337 | ||||||||
\(559\) | −1.16807e6 | −0.158103 | ||||||||
\(560\) | −2.34830e6 | −0.316434 | ||||||||
\(561\) | −1.39465e6 | −0.187093 | ||||||||
\(562\) | 4.36171e6 | 0.582527 | ||||||||
\(563\) | −6.66231e6 | −0.885837 | −0.442918 | − | 0.896562i | \(-0.646057\pi\) | ||||
−0.442918 | + | 0.896562i | \(0.646057\pi\) | |||||||
\(564\) | −527087. | −0.0697726 | ||||||||
\(565\) | −1.57174e6 | −0.207138 | ||||||||
\(566\) | 9.66042e6 | 1.26752 | ||||||||
\(567\) | 1.41051e6 | 0.184254 | ||||||||
\(568\) | 7.12684e6 | 0.926886 | ||||||||
\(569\) | −1.31747e7 | −1.70593 | −0.852964 | − | 0.521970i | \(-0.825197\pi\) | ||||
−0.852964 | + | 0.521970i | \(0.825197\pi\) | |||||||
\(570\) | −2.20161e6 | −0.283827 | ||||||||
\(571\) | −1.36489e7 | −1.75189 | −0.875946 | − | 0.482410i | \(-0.839762\pi\) | ||||
−0.875946 | + | 0.482410i | \(0.839762\pi\) | |||||||
\(572\) | 447599. | 0.0572004 | ||||||||
\(573\) | −3.35342e6 | −0.426680 | ||||||||
\(574\) | 7.62937e6 | 0.966515 | ||||||||
\(575\) | −3.11807e6 | −0.393293 | ||||||||
\(576\) | 2.28196e6 | 0.286584 | ||||||||
\(577\) | 4.83210e6 | 0.604222 | 0.302111 | − | 0.953273i | \(-0.402309\pi\) | ||||
0.302111 | + | 0.953273i | \(0.402309\pi\) | |||||||
\(578\) | 1.72051e6 | 0.214209 | ||||||||
\(579\) | −8.62524e6 | −1.06924 | ||||||||
\(580\) | −5.85402e6 | −0.722578 | ||||||||
\(581\) | −1.18721e6 | −0.145911 | ||||||||
\(582\) | 2.88814e6 | 0.353436 | ||||||||
\(583\) | 4.67830e6 | 0.570055 | ||||||||
\(584\) | 6.21073e6 | 0.753547 | ||||||||
\(585\) | 654139. | 0.0790279 | ||||||||
\(586\) | 2.76206e6 | 0.332268 | ||||||||
\(587\) | 4.56230e6 | 0.546498 | 0.273249 | − | 0.961943i | \(-0.411902\pi\) | ||||
0.273249 | + | 0.961943i | \(0.411902\pi\) | |||||||
\(588\) | 4.30772e6 | 0.513812 | ||||||||
\(589\) | −3.15454e6 | −0.374669 | ||||||||
\(590\) | −632543. | −0.0748101 | ||||||||
\(591\) | 3.29860e6 | 0.388473 | ||||||||
\(592\) | −2.59985e6 | −0.304891 | ||||||||
\(593\) | −1.33301e7 | −1.55667 | −0.778333 | − | 0.627852i | \(-0.783934\pi\) | ||||
−0.778333 | + | 0.627852i | \(0.783934\pi\) | |||||||
\(594\) | −451148. | −0.0524630 | ||||||||
\(595\) | −9.78185e6 | −1.13274 | ||||||||
\(596\) | −1.67063e6 | −0.192648 | ||||||||
\(597\) | −4.11261e6 | −0.472261 | ||||||||
\(598\) | −2.12545e6 | −0.243051 | ||||||||
\(599\) | 6.73748e6 | 0.767238 | 0.383619 | − | 0.923491i | \(-0.374678\pi\) | ||||
0.383619 | + | 0.923491i | \(0.374678\pi\) | |||||||
\(600\) | 1.76650e6 | 0.200325 | ||||||||
\(601\) | 2.33351e6 | 0.263526 | 0.131763 | − | 0.991281i | \(-0.457936\pi\) | ||||
0.131763 | + | 0.991281i | \(0.457936\pi\) | |||||||
\(602\) | 5.65035e6 | 0.635454 | ||||||||
\(603\) | 1.63578e6 | 0.183203 | ||||||||
\(604\) | 5.23451e6 | 0.583827 | ||||||||
\(605\) | −6.26380e6 | −0.695744 | ||||||||
\(606\) | 2.92834e6 | 0.323922 | ||||||||
\(607\) | −3.92089e6 | −0.431930 | −0.215965 | − | 0.976401i | \(-0.569290\pi\) | ||||
−0.215965 | + | 0.976401i | \(0.569290\pi\) | |||||||
\(608\) | 6.97418e6 | 0.765128 | ||||||||
\(609\) | −1.51888e7 | −1.65952 | ||||||||
\(610\) | −9.25225e6 | −1.00675 | ||||||||
\(611\) | −634232. | −0.0687298 | ||||||||
\(612\) | 1.30894e6 | 0.141267 | ||||||||
\(613\) | −4.90899e6 | −0.527644 | −0.263822 | − | 0.964571i | \(-0.584983\pi\) | ||||
−0.263822 | + | 0.964571i | \(0.584983\pi\) | |||||||
\(614\) | −8.20385e6 | −0.878207 | ||||||||
\(615\) | 3.69061e6 | 0.393469 | ||||||||
\(616\) | −6.42260e6 | −0.681960 | ||||||||
\(617\) | −760974. | −0.0804742 | −0.0402371 | − | 0.999190i | \(-0.512811\pi\) | ||||
−0.0402371 | + | 0.999190i | \(0.512811\pi\) | |||||||
\(618\) | 4.76835e6 | 0.502224 | ||||||||
\(619\) | −1.88832e7 | −1.98083 | −0.990417 | − | 0.138109i | \(-0.955898\pi\) | ||||
−0.990417 | + | 0.138109i | \(0.955898\pi\) | |||||||
\(620\) | −1.74743e6 | −0.182567 | ||||||||
\(621\) | −2.21699e6 | −0.230693 | ||||||||
\(622\) | 975221. | 0.101071 | ||||||||
\(623\) | −1.64064e7 | −1.69354 | ||||||||
\(624\) | 378111. | 0.0388738 | ||||||||
\(625\) | −5.51034e6 | −0.564259 | ||||||||
\(626\) | 3.60569e6 | 0.367750 | ||||||||
\(627\) | −1.89077e6 | −0.192075 | ||||||||
\(628\) | −328300. | −0.0332179 | ||||||||
\(629\) | −1.08297e7 | −1.09141 | ||||||||
\(630\) | −3.16429e6 | −0.317632 | ||||||||
\(631\) | −153973. | −0.0153947 | −0.00769735 | − | 0.999970i | \(-0.502450\pi\) | ||||
−0.00769735 | + | 0.999970i | \(0.502450\pi\) | |||||||
\(632\) | 9.04228e6 | 0.900503 | ||||||||
\(633\) | 1.14608e6 | 0.113686 | ||||||||
\(634\) | 6.80746e6 | 0.672608 | ||||||||
\(635\) | −7.18846e6 | −0.707459 | ||||||||
\(636\) | −4.39081e6 | −0.430429 | ||||||||
\(637\) | 5.18338e6 | 0.506133 | ||||||||
\(638\) | 4.85813e6 | 0.472517 | ||||||||
\(639\) | 3.01551e6 | 0.292152 | ||||||||
\(640\) | 2.47716e6 | 0.239058 | ||||||||
\(641\) | 8.57968e6 | 0.824757 | 0.412378 | − | 0.911013i | \(-0.364698\pi\) | ||||
0.412378 | + | 0.911013i | \(0.364698\pi\) | |||||||
\(642\) | −2.63321e6 | −0.252144 | ||||||||
\(643\) | 1.98269e6 | 0.189116 | 0.0945578 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945578 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(644\) | −1.06399e7 | −1.01094 | ||||||||
\(645\) | 2.73329e6 | 0.258694 | ||||||||
\(646\) | −5.30099e6 | −0.499777 | ||||||||
\(647\) | 4.49937e6 | 0.422563 | 0.211281 | − | 0.977425i | \(-0.432236\pi\) | ||||
0.211281 | + | 0.977425i | \(0.432236\pi\) | |||||||
\(648\) | 1.25601e6 | 0.117504 | ||||||||
\(649\) | −543236. | −0.0506264 | ||||||||
\(650\) | 716577. | 0.0665242 | ||||||||
\(651\) | −4.53389e6 | −0.419294 | ||||||||
\(652\) | −4.96112e6 | −0.457047 | ||||||||
\(653\) | −1.51102e7 | −1.38672 | −0.693359 | − | 0.720593i | \(-0.743870\pi\) | ||||
−0.693359 | + | 0.720593i | \(0.743870\pi\) | |||||||
\(654\) | 5.56882e6 | 0.509119 | ||||||||
\(655\) | 1.13898e7 | 1.03732 | ||||||||
\(656\) | 2.13327e6 | 0.193547 | ||||||||
\(657\) | 2.62788e6 | 0.237516 | ||||||||
\(658\) | 3.06799e6 | 0.276242 | ||||||||
\(659\) | 43879.4 | 0.00393593 | 0.00196796 | − | 0.999998i | \(-0.499374\pi\) | ||||
0.00196796 | + | 0.999998i | \(0.499374\pi\) | |||||||
\(660\) | −1.04738e6 | −0.0935932 | ||||||||
\(661\) | −1.40264e7 | −1.24866 | −0.624328 | − | 0.781162i | \(-0.714627\pi\) | ||||
−0.624328 | + | 0.781162i | \(0.714627\pi\) | |||||||
\(662\) | −1.26287e7 | −1.11999 | ||||||||
\(663\) | 1.57502e6 | 0.139156 | ||||||||
\(664\) | −1.05717e6 | −0.0930518 | ||||||||
\(665\) | −1.32616e7 | −1.16290 | ||||||||
\(666\) | −3.50325e6 | −0.306045 | ||||||||
\(667\) | 2.38734e7 | 2.07778 | ||||||||
\(668\) | −6.49620e6 | −0.563272 | ||||||||
\(669\) | −8.98328e6 | −0.776014 | ||||||||
\(670\) | −3.66967e6 | −0.315820 | ||||||||
\(671\) | −7.94595e6 | −0.681302 | ||||||||
\(672\) | 1.00237e7 | 0.856258 | ||||||||
\(673\) | −5.91918e6 | −0.503760 | −0.251880 | − | 0.967758i | \(-0.581049\pi\) | ||||
−0.251880 | + | 0.967758i | \(0.581049\pi\) | |||||||
\(674\) | 2.39822e6 | 0.203348 | ||||||||
\(675\) | 747441. | 0.0631419 | ||||||||
\(676\) | 5.53699e6 | 0.466022 | ||||||||
\(677\) | 164350. | 0.0137815 | 0.00689077 | − | 0.999976i | \(-0.497807\pi\) | ||||
0.00689077 | + | 0.999976i | \(0.497807\pi\) | |||||||
\(678\) | −1.22420e6 | −0.102277 | ||||||||
\(679\) | 1.73969e7 | 1.44810 | ||||||||
\(680\) | −8.71040e6 | −0.722381 | ||||||||
\(681\) | 9.04666e6 | 0.747516 | ||||||||
\(682\) | 1.45016e6 | 0.119386 | ||||||||
\(683\) | 1.51914e6 | 0.124608 | 0.0623042 | − | 0.998057i | \(-0.480155\pi\) | ||||
0.0623042 | + | 0.998057i | \(0.480155\pi\) | |||||||
\(684\) | 1.77458e6 | 0.145029 | ||||||||
\(685\) | 5.99432e6 | 0.488105 | ||||||||
\(686\) | −1.07452e7 | −0.871772 | ||||||||
\(687\) | 3.27116e6 | 0.264430 | ||||||||
\(688\) | 1.57991e6 | 0.127251 | ||||||||
\(689\) | −5.28336e6 | −0.423996 | ||||||||
\(690\) | 4.97354e6 | 0.397688 | ||||||||
\(691\) | −1.86505e7 | −1.48592 | −0.742962 | − | 0.669334i | \(-0.766580\pi\) | ||||
−0.742962 | + | 0.669334i | \(0.766580\pi\) | |||||||
\(692\) | 4.38230e6 | 0.347886 | ||||||||
\(693\) | −2.71753e6 | −0.214952 | ||||||||
\(694\) | 1.45287e7 | 1.14506 | ||||||||
\(695\) | 1.30082e7 | 1.02154 | ||||||||
\(696\) | −1.35251e7 | −1.05832 | ||||||||
\(697\) | 8.88616e6 | 0.692839 | ||||||||
\(698\) | 1.69098e7 | 1.31371 | ||||||||
\(699\) | −669977. | −0.0518641 | ||||||||
\(700\) | 3.58717e6 | 0.276699 | ||||||||
\(701\) | −9.85850e6 | −0.757733 | −0.378866 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378866 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(702\) | 509496. | 0.0390210 | ||||||||
\(703\) | −1.46822e7 | −1.12048 | ||||||||
\(704\) | −4.39650e6 | −0.334330 | ||||||||
\(705\) | 1.48410e6 | 0.112458 | ||||||||
\(706\) | −1.08939e7 | −0.822569 | ||||||||
\(707\) | 1.76391e7 | 1.32718 | ||||||||
\(708\) | 509852. | 0.0382262 | ||||||||
\(709\) | −1.64862e7 | −1.23170 | −0.615852 | − | 0.787862i | \(-0.711188\pi\) | ||||
−0.615852 | + | 0.787862i | \(0.711188\pi\) | |||||||
\(710\) | −6.76490e6 | −0.503635 | ||||||||
\(711\) | 3.82597e6 | 0.283836 | ||||||||
\(712\) | −1.46094e7 | −1.08002 | ||||||||
\(713\) | 7.12624e6 | 0.524973 | ||||||||
\(714\) | −7.61890e6 | −0.559302 | ||||||||
\(715\) | −1.26029e6 | −0.0921944 | ||||||||
\(716\) | 9.55781e6 | 0.696748 | ||||||||
\(717\) | −9.88742e6 | −0.718266 | ||||||||
\(718\) | 7.83643e6 | 0.567293 | ||||||||
\(719\) | 8.27077e6 | 0.596656 | 0.298328 | − | 0.954463i | \(-0.403571\pi\) | ||||
0.298328 | + | 0.954463i | \(0.403571\pi\) | |||||||
\(720\) | −884777. | −0.0636067 | ||||||||
\(721\) | 2.87226e7 | 2.05771 | ||||||||
\(722\) | 2.63244e6 | 0.187938 | ||||||||
\(723\) | −1.08550e6 | −0.0772294 | ||||||||
\(724\) | −7.16828e6 | −0.508240 | ||||||||
\(725\) | −8.04873e6 | −0.568699 | ||||||||
\(726\) | −4.87875e6 | −0.343532 | ||||||||
\(727\) | 2.13214e7 | 1.49617 | 0.748083 | − | 0.663605i | \(-0.230974\pi\) | ||||
0.748083 | + | 0.663605i | \(0.230974\pi\) | |||||||
\(728\) | 7.25325e6 | 0.507229 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −5.89532e6 | −0.409449 | ||||||||
\(731\) | 6.58114e6 | 0.455520 | ||||||||
\(732\) | 7.45765e6 | 0.514427 | ||||||||
\(733\) | −193507. | −0.0133026 | −0.00665131 | − | 0.999978i | \(-0.502117\pi\) | ||||
−0.00665131 | + | 0.999978i | \(0.502117\pi\) | |||||||
\(734\) | −9.65115e6 | −0.661209 | ||||||||
\(735\) | −1.21291e7 | −0.828152 | ||||||||
\(736\) | −1.57550e7 | −1.07207 | ||||||||
\(737\) | −3.15156e6 | −0.213726 | ||||||||
\(738\) | 2.87454e6 | 0.194280 | ||||||||
\(739\) | 2.19214e7 | 1.47658 | 0.738289 | − | 0.674484i | \(-0.235634\pi\) | ||||
0.738289 | + | 0.674484i | \(0.235634\pi\) | |||||||
\(740\) | −8.13309e6 | −0.545980 | ||||||||
\(741\) | 2.13531e6 | 0.142862 | ||||||||
\(742\) | 2.55573e7 | 1.70414 | ||||||||
\(743\) | −6.22559e6 | −0.413722 | −0.206861 | − | 0.978370i | \(-0.566325\pi\) | ||||
−0.206861 | + | 0.978370i | \(0.566325\pi\) | |||||||
\(744\) | −4.03727e6 | −0.267397 | ||||||||
\(745\) | 4.70393e6 | 0.310506 | ||||||||
\(746\) | −1.04397e7 | −0.686820 | ||||||||
\(747\) | −447309. | −0.0293296 | ||||||||
\(748\) | −2.52186e6 | −0.164803 | ||||||||
\(749\) | −1.58614e7 | −1.03309 | ||||||||
\(750\) | −6.78747e6 | −0.440610 | ||||||||
\(751\) | 3.89671e6 | 0.252114 | 0.126057 | − | 0.992023i | \(-0.459768\pi\) | ||||
0.126057 | + | 0.992023i | \(0.459768\pi\) | |||||||
\(752\) | 857851. | 0.0553181 | ||||||||
\(753\) | 1.19831e6 | 0.0770161 | ||||||||
\(754\) | −5.48645e6 | −0.351449 | ||||||||
\(755\) | −1.47386e7 | −0.941001 | ||||||||
\(756\) | 2.55053e6 | 0.162303 | ||||||||
\(757\) | 1.24098e7 | 0.787094 | 0.393547 | − | 0.919304i | \(-0.371248\pi\) | ||||
0.393547 | + | 0.919304i | \(0.371248\pi\) | |||||||
\(758\) | 9.65898e6 | 0.610602 | ||||||||
\(759\) | 4.27134e6 | 0.269128 | ||||||||
\(760\) | −1.18090e7 | −0.741616 | ||||||||
\(761\) | −7.36214e6 | −0.460832 | −0.230416 | − | 0.973092i | \(-0.574009\pi\) | ||||
−0.230416 | + | 0.973092i | \(0.574009\pi\) | |||||||
\(762\) | −5.59895e6 | −0.349316 | ||||||||
\(763\) | 3.35443e7 | 2.08596 | ||||||||
\(764\) | −6.06379e6 | −0.375847 | ||||||||
\(765\) | −3.68554e6 | −0.227692 | ||||||||
\(766\) | 1.01289e7 | 0.623720 | ||||||||
\(767\) | 613494. | 0.0376549 | ||||||||
\(768\) | 1.00430e7 | 0.614415 | ||||||||
\(769\) | −1.51054e7 | −0.921121 | −0.460561 | − | 0.887628i | \(-0.652352\pi\) | ||||
−0.460561 | + | 0.887628i | \(0.652352\pi\) | |||||||
\(770\) | 6.09643e6 | 0.370552 | ||||||||
\(771\) | 8.38875e6 | 0.508231 | ||||||||
\(772\) | −1.55965e7 | −0.941854 | ||||||||
\(773\) | 3.12428e6 | 0.188062 | 0.0940309 | − | 0.995569i | \(-0.470025\pi\) | ||||
0.0940309 | + | 0.995569i | \(0.470025\pi\) | |||||||
\(774\) | 2.12890e6 | 0.127733 | ||||||||
\(775\) | −2.40256e6 | −0.143688 | ||||||||
\(776\) | 1.54914e7 | 0.923497 | ||||||||
\(777\) | −2.11021e7 | −1.25393 | ||||||||
\(778\) | 1.65014e7 | 0.977396 | ||||||||
\(779\) | 1.20473e7 | 0.711288 | ||||||||
\(780\) | 1.18284e6 | 0.0696128 | ||||||||
\(781\) | −5.80978e6 | −0.340826 | ||||||||
\(782\) | 1.19752e7 | 0.700268 | ||||||||
\(783\) | −5.72275e6 | −0.333581 | ||||||||
\(784\) | −7.01095e6 | −0.407368 | ||||||||
\(785\) | 924384. | 0.0535400 | ||||||||
\(786\) | 8.87130e6 | 0.512190 | ||||||||
\(787\) | 2.95424e7 | 1.70023 | 0.850117 | − | 0.526593i | \(-0.176531\pi\) | ||||
0.850117 | + | 0.526593i | \(0.176531\pi\) | |||||||
\(788\) | 5.96465e6 | 0.342192 | ||||||||
\(789\) | −1.49479e7 | −0.854848 | ||||||||
\(790\) | −8.58306e6 | −0.489299 | ||||||||
\(791\) | −7.37405e6 | −0.419049 | ||||||||
\(792\) | −2.41987e6 | −0.137081 | ||||||||
\(793\) | 8.97362e6 | 0.506739 | ||||||||
\(794\) | −1.24019e7 | −0.698130 | ||||||||
\(795\) | 1.23630e7 | 0.693757 | ||||||||
\(796\) | −7.43658e6 | −0.415997 | ||||||||
\(797\) | −1.70039e7 | −0.948207 | −0.474104 | − | 0.880469i | \(-0.657228\pi\) | ||||
−0.474104 | + | 0.880469i | \(0.657228\pi\) | |||||||
\(798\) | −1.03292e7 | −0.574195 | ||||||||
\(799\) | 3.57338e6 | 0.198022 | ||||||||
\(800\) | 5.31166e6 | 0.293431 | ||||||||
\(801\) | −6.18152e6 | −0.340419 | ||||||||
\(802\) | −1.79931e7 | −0.987804 | ||||||||
\(803\) | −5.06297e6 | −0.277087 | ||||||||
\(804\) | 2.95789e6 | 0.161377 | ||||||||
\(805\) | 2.99585e7 | 1.62941 | ||||||||
\(806\) | −1.63771e6 | −0.0887973 | ||||||||
\(807\) | 6.71642e6 | 0.363039 | ||||||||
\(808\) | 1.57070e7 | 0.846380 | ||||||||
\(809\) | −3.02312e6 | −0.162399 | −0.0811997 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811997 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(810\) | −1.19222e6 | −0.0638475 | ||||||||
\(811\) | 9.96223e6 | 0.531869 | 0.265934 | − | 0.963991i | \(-0.414320\pi\) | ||||
0.265934 | + | 0.963991i | \(0.414320\pi\) | |||||||
\(812\) | −2.74650e7 | −1.46181 | ||||||||
\(813\) | −1.65912e7 | −0.880341 | ||||||||
\(814\) | 6.74949e6 | 0.357034 | ||||||||
\(815\) | 1.39689e7 | 0.736660 | ||||||||
\(816\) | −2.13035e6 | −0.112002 | ||||||||
\(817\) | 8.92229e6 | 0.467650 | ||||||||
\(818\) | 1.31242e7 | 0.685785 | ||||||||
\(819\) | 3.06899e6 | 0.159877 | ||||||||
\(820\) | 6.67350e6 | 0.346592 | ||||||||
\(821\) | 3.74560e7 | 1.93938 | 0.969690 | − | 0.244337i | \(-0.0785704\pi\) | ||||
0.969690 | + | 0.244337i | \(0.0785704\pi\) | |||||||
\(822\) | 4.66886e6 | 0.241008 | ||||||||
\(823\) | 2.70732e7 | 1.39329 | 0.696643 | − | 0.717418i | \(-0.254676\pi\) | ||||
0.696643 | + | 0.717418i | \(0.254676\pi\) | |||||||
\(824\) | 2.55765e7 | 1.31227 | ||||||||
\(825\) | −1.44005e6 | −0.0736617 | ||||||||
\(826\) | −2.96767e6 | −0.151344 | ||||||||
\(827\) | −2.45396e7 | −1.24768 | −0.623841 | − | 0.781551i | \(-0.714429\pi\) | ||||
−0.623841 | + | 0.781551i | \(0.714429\pi\) | |||||||
\(828\) | −4.00885e6 | −0.203209 | ||||||||
\(829\) | −3.73139e6 | −0.188575 | −0.0942876 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942876 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(830\) | 1.00348e6 | 0.0505608 | ||||||||
\(831\) | 1.42132e7 | 0.713987 | ||||||||
\(832\) | 4.96511e6 | 0.248668 | ||||||||
\(833\) | −2.92041e7 | −1.45825 | ||||||||
\(834\) | 1.01319e7 | 0.504399 | ||||||||
\(835\) | 1.82911e7 | 0.907872 | ||||||||
\(836\) | −3.41897e6 | −0.169192 | ||||||||
\(837\) | −1.70825e6 | −0.0842826 | ||||||||
\(838\) | 1.69812e7 | 0.835333 | ||||||||
\(839\) | −7.37449e6 | −0.361682 | −0.180841 | − | 0.983512i | \(-0.557882\pi\) | ||||
−0.180841 | + | 0.983512i | \(0.557882\pi\) | |||||||
\(840\) | −1.69726e7 | −0.829946 | ||||||||
\(841\) | 4.11136e7 | 2.00445 | ||||||||
\(842\) | 2.27268e7 | 1.10473 | ||||||||
\(843\) | 9.89901e6 | 0.479759 | ||||||||
\(844\) | 2.07238e6 | 0.100142 | ||||||||
\(845\) | −1.55903e7 | −0.751126 | ||||||||
\(846\) | 1.15594e6 | 0.0555275 | ||||||||
\(847\) | −2.93876e7 | −1.40752 | ||||||||
\(848\) | 7.14618e6 | 0.341259 | ||||||||
\(849\) | 2.19246e7 | 1.04391 | ||||||||
\(850\) | −4.03733e6 | −0.191667 | ||||||||
\(851\) | 3.31677e7 | 1.56997 | ||||||||
\(852\) | 5.45275e6 | 0.257346 | ||||||||
\(853\) | −3.00729e7 | −1.41515 | −0.707576 | − | 0.706637i | \(-0.750211\pi\) | ||||
−0.707576 | + | 0.706637i | \(0.750211\pi\) | |||||||
\(854\) | −4.34083e7 | −2.03671 | ||||||||
\(855\) | −4.99662e6 | −0.233755 | ||||||||
\(856\) | −1.41240e7 | −0.658831 | ||||||||
\(857\) | −2.61992e7 | −1.21853 | −0.609265 | − | 0.792966i | \(-0.708536\pi\) | ||||
−0.609265 | + | 0.792966i | \(0.708536\pi\) | |||||||
\(858\) | −981614. | −0.0455221 | ||||||||
\(859\) | 4.01687e6 | 0.185740 | 0.0928700 | − | 0.995678i | \(-0.470396\pi\) | ||||
0.0928700 | + | 0.995678i | \(0.470396\pi\) | |||||||
\(860\) | 4.94243e6 | 0.227874 | ||||||||
\(861\) | 1.73150e7 | 0.796005 | ||||||||
\(862\) | −5.99029e6 | −0.274587 | ||||||||
\(863\) | 5.54567e6 | 0.253470 | 0.126735 | − | 0.991937i | \(-0.459550\pi\) | ||||
0.126735 | + | 0.991937i | \(0.459550\pi\) | |||||||
\(864\) | 3.77666e6 | 0.172117 | ||||||||
\(865\) | −1.23391e7 | −0.560716 | ||||||||
\(866\) | 7.56824e6 | 0.342926 | ||||||||
\(867\) | 3.90475e6 | 0.176419 | ||||||||
\(868\) | −8.19835e6 | −0.369341 | ||||||||
\(869\) | −7.37124e6 | −0.331125 | ||||||||
\(870\) | 1.28383e7 | 0.575053 | ||||||||
\(871\) | 3.55916e6 | 0.158965 | ||||||||
\(872\) | 2.98700e7 | 1.33028 | ||||||||
\(873\) | 6.55471e6 | 0.291084 | ||||||||
\(874\) | 1.62351e7 | 0.718915 | ||||||||
\(875\) | −4.08849e7 | −1.80527 | ||||||||
\(876\) | 4.75184e6 | 0.209219 | ||||||||
\(877\) | −1.76530e7 | −0.775034 | −0.387517 | − | 0.921863i | \(-0.626667\pi\) | ||||
−0.387517 | + | 0.921863i | \(0.626667\pi\) | |||||||
\(878\) | 1.07842e7 | 0.472121 | ||||||||
\(879\) | 6.26856e6 | 0.273650 | ||||||||
\(880\) | 1.70464e6 | 0.0742039 | ||||||||
\(881\) | 1.92089e7 | 0.833802 | 0.416901 | − | 0.908952i | \(-0.363116\pi\) | ||||
0.416901 | + | 0.908952i | \(0.363116\pi\) | |||||||
\(882\) | −9.44711e6 | −0.408910 | ||||||||
\(883\) | 2.29461e6 | 0.0990391 | 0.0495195 | − | 0.998773i | \(-0.484231\pi\) | ||||
0.0495195 | + | 0.998773i | \(0.484231\pi\) | |||||||
\(884\) | 2.84801e6 | 0.122578 | ||||||||
\(885\) | −1.43557e6 | −0.0616123 | ||||||||
\(886\) | −2.06815e7 | −0.885109 | ||||||||
\(887\) | −2.42072e7 | −1.03308 | −0.516542 | − | 0.856262i | \(-0.672781\pi\) | ||||
−0.516542 | + | 0.856262i | \(0.672781\pi\) | |||||||
\(888\) | −1.87907e7 | −0.799670 | ||||||||
\(889\) | −3.37257e7 | −1.43122 | ||||||||
\(890\) | 1.38674e7 | 0.586842 | ||||||||
\(891\) | −1.02389e6 | −0.0432076 | ||||||||
\(892\) | −1.62439e7 | −0.683562 | ||||||||
\(893\) | 4.84456e6 | 0.203295 | ||||||||
\(894\) | 3.66380e6 | 0.153316 | ||||||||
\(895\) | −2.69116e7 | −1.12301 | ||||||||
\(896\) | 1.16220e7 | 0.483625 | ||||||||
\(897\) | −4.82376e6 | −0.200172 | ||||||||
\(898\) | −1.62235e7 | −0.671356 | ||||||||
\(899\) | 1.83951e7 | 0.759106 | ||||||||
\(900\) | 1.35155e6 | 0.0556194 | ||||||||
\(901\) | 2.97674e7 | 1.22160 | ||||||||
\(902\) | −5.53820e6 | −0.226648 | ||||||||
\(903\) | 1.28236e7 | 0.523349 | ||||||||
\(904\) | −6.56634e6 | −0.267240 | ||||||||
\(905\) | 2.01835e7 | 0.819171 | ||||||||
\(906\) | −1.14796e7 | −0.464631 | ||||||||
\(907\) | 4.34909e7 | 1.75542 | 0.877708 | − | 0.479195i | \(-0.159071\pi\) | ||||
0.877708 | + | 0.479195i | \(0.159071\pi\) | |||||||
\(908\) | 1.63585e7 | 0.658460 | ||||||||
\(909\) | 6.64595e6 | 0.266776 | ||||||||
\(910\) | −6.88489e6 | −0.275609 | ||||||||
\(911\) | −1.85525e7 | −0.740637 | −0.370319 | − | 0.928905i | \(-0.620752\pi\) | ||||
−0.370319 | + | 0.928905i | \(0.620752\pi\) | |||||||
\(912\) | −2.88819e6 | −0.114984 | ||||||||
\(913\) | 861802. | 0.0342161 | ||||||||
\(914\) | 4.60664e6 | 0.182397 | ||||||||
\(915\) | −2.09982e7 | −0.829144 | ||||||||
\(916\) | 5.91504e6 | 0.232927 | ||||||||
\(917\) | 5.34370e7 | 2.09855 | ||||||||
\(918\) | −2.87060e6 | −0.112426 | ||||||||
\(919\) | −1.49752e7 | −0.584904 | −0.292452 | − | 0.956280i | \(-0.594471\pi\) | ||||
−0.292452 | + | 0.956280i | \(0.594471\pi\) | |||||||
\(920\) | 2.66770e7 | 1.03912 | ||||||||
\(921\) | −1.86189e7 | −0.723276 | ||||||||
\(922\) | −1.13419e7 | −0.439400 | ||||||||
\(923\) | 6.56118e6 | 0.253500 | ||||||||
\(924\) | −4.91394e6 | −0.189343 | ||||||||
\(925\) | −1.11822e7 | −0.429709 | ||||||||
\(926\) | 2.73024e7 | 1.04634 | ||||||||
\(927\) | 1.08219e7 | 0.413623 | ||||||||
\(928\) | −4.06685e7 | −1.55020 | ||||||||
\(929\) | −3.39663e7 | −1.29124 | −0.645622 | − | 0.763657i | \(-0.723402\pi\) | ||||
−0.645622 | + | 0.763657i | \(0.723402\pi\) | |||||||
\(930\) | 3.83224e6 | 0.145293 | ||||||||
\(931\) | −3.95931e7 | −1.49708 | ||||||||
\(932\) | −1.21148e6 | −0.0456852 | ||||||||
\(933\) | 2.21329e6 | 0.0832404 | ||||||||
\(934\) | −3.15491e7 | −1.18337 | ||||||||
\(935\) | 7.10070e6 | 0.265627 | ||||||||
\(936\) | 2.73283e6 | 0.101958 | ||||||||
\(937\) | 1.94117e7 | 0.722296 | 0.361148 | − | 0.932508i | \(-0.382385\pi\) | ||||
0.361148 | + | 0.932508i | \(0.382385\pi\) | |||||||
\(938\) | −1.72168e7 | −0.638919 | ||||||||
\(939\) | 8.18322e6 | 0.302873 | ||||||||
\(940\) | 2.68361e6 | 0.0990602 | ||||||||
\(941\) | −3.93557e6 | −0.144888 | −0.0724442 | − | 0.997372i | \(-0.523080\pi\) | ||||
−0.0724442 | + | 0.997372i | \(0.523080\pi\) | |||||||
\(942\) | 719984. | 0.0264360 | ||||||||
\(943\) | −2.72153e7 | −0.996630 | ||||||||
\(944\) | −829801. | −0.0303071 | ||||||||
\(945\) | −7.18143e6 | −0.261596 | ||||||||
\(946\) | −4.10162e6 | −0.149014 | ||||||||
\(947\) | 2.75055e7 | 0.996654 | 0.498327 | − | 0.866989i | \(-0.333948\pi\) | ||||
0.498327 | + | 0.866989i | \(0.333948\pi\) | |||||||
\(948\) | 6.91826e6 | 0.250021 | ||||||||
\(949\) | 5.71778e6 | 0.206092 | ||||||||
\(950\) | −5.47355e6 | −0.196771 | ||||||||
\(951\) | 1.54497e7 | 0.553948 | ||||||||
\(952\) | −4.08662e7 | −1.46141 | ||||||||
\(953\) | 1.01583e7 | 0.362317 | 0.181159 | − | 0.983454i | \(-0.442015\pi\) | ||||
0.181159 | + | 0.983454i | \(0.442015\pi\) | |||||||
\(954\) | 9.62933e6 | 0.342551 | ||||||||
\(955\) | 1.70736e7 | 0.605782 | ||||||||
\(956\) | −1.78788e7 | −0.632694 | ||||||||
\(957\) | 1.10257e7 | 0.389157 | ||||||||
\(958\) | 1.01425e7 | 0.357050 | ||||||||
\(959\) | 2.81232e7 | 0.987459 | ||||||||
\(960\) | −1.16183e7 | −0.406880 | ||||||||
\(961\) | −2.31382e7 | −0.808204 | ||||||||
\(962\) | −7.62241e6 | −0.265555 | ||||||||
\(963\) | −5.97615e6 | −0.207661 | ||||||||
\(964\) | −1.96283e6 | −0.0680285 | ||||||||
\(965\) | 4.39145e7 | 1.51806 | ||||||||
\(966\) | 2.33341e7 | 0.804541 | ||||||||
\(967\) | −6.62411e6 | −0.227804 | −0.113902 | − | 0.993492i | \(-0.536335\pi\) | ||||
−0.113902 | + | 0.993492i | \(0.536335\pi\) | |||||||
\(968\) | −2.61686e7 | −0.897620 | ||||||||
\(969\) | −1.20307e7 | −0.411607 | ||||||||
\(970\) | −1.47046e7 | −0.501794 | ||||||||
\(971\) | 5.52548e7 | 1.88071 | 0.940355 | − | 0.340196i | \(-0.110493\pi\) | ||||
0.940355 | + | 0.340196i | \(0.110493\pi\) | |||||||
\(972\) | 960971. | 0.0326246 | ||||||||
\(973\) | 6.10301e7 | 2.06663 | ||||||||
\(974\) | 5.01105e6 | 0.169251 | ||||||||
\(975\) | 1.62629e6 | 0.0547882 | ||||||||
\(976\) | −1.21376e7 | −0.407856 | ||||||||
\(977\) | −3.42955e7 | −1.14948 | −0.574739 | − | 0.818337i | \(-0.694896\pi\) | ||||
−0.574739 | + | 0.818337i | \(0.694896\pi\) | |||||||
\(978\) | 1.08801e7 | 0.363735 | ||||||||
\(979\) | 1.19095e7 | 0.397135 | ||||||||
\(980\) | −2.19323e7 | −0.729489 | ||||||||
\(981\) | 1.26386e7 | 0.419301 | ||||||||
\(982\) | −1.12873e7 | −0.373519 | ||||||||
\(983\) | −1.09463e7 | −0.361314 | −0.180657 | − | 0.983546i | \(-0.557822\pi\) | ||||
−0.180657 | + | 0.983546i | \(0.557822\pi\) | |||||||
\(984\) | 1.54185e7 | 0.507637 | ||||||||
\(985\) | −1.67945e7 | −0.551538 | ||||||||
\(986\) | 3.09117e7 | 1.01258 | ||||||||
\(987\) | 6.96288e6 | 0.227508 | ||||||||
\(988\) | 3.86115e6 | 0.125842 | ||||||||
\(989\) | −2.01558e7 | −0.655254 | ||||||||
\(990\) | 2.29697e6 | 0.0744848 | ||||||||
\(991\) | 1.32919e7 | 0.429936 | 0.214968 | − | 0.976621i | \(-0.431035\pi\) | ||||
0.214968 | + | 0.976621i | \(0.431035\pi\) | |||||||
\(992\) | −1.21396e7 | −0.391675 | ||||||||
\(993\) | −2.86612e7 | −0.922406 | ||||||||
\(994\) | −3.17386e7 | −1.01888 | ||||||||
\(995\) | 2.09389e7 | 0.670497 | ||||||||
\(996\) | −808842. | −0.0258354 | ||||||||
\(997\) | 5.22001e7 | 1.66316 | 0.831579 | − | 0.555407i | \(-0.187437\pi\) | ||||
0.831579 | + | 0.555407i | \(0.187437\pi\) | |||||||
\(998\) | −1.50820e7 | −0.479328 | ||||||||
\(999\) | −7.95072e6 | −0.252053 |
(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 | 177.6.a.d.1.6 | ✓ | 13 | |
3.2 | odd | 2 | 531.6.a.e.1.8 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.d.1.6 | ✓ | 13 | 1.1 | even | 1 | trivial | |
531.6.a.e.1.8 | 13 | 3.2 | odd | 2 |