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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-8.49197\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.4920 | 1.85474 | 0.927368 | − | 0.374150i | \(-0.122065\pi\) | ||||
0.927368 | + | 0.374150i | \(0.122065\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 78.0815 | 2.44005 | ||||||||
\(5\) | 46.0665 | 0.824062 | 0.412031 | − | 0.911170i | \(-0.364819\pi\) | ||||
0.412031 | + | 0.911170i | \(0.364819\pi\) | |||||||
\(6\) | 94.4278 | 1.07083 | ||||||||
\(7\) | 183.145 | 1.41270 | 0.706351 | − | 0.707862i | \(-0.250340\pi\) | ||||
0.706351 | + | 0.707862i | \(0.250340\pi\) | |||||||
\(8\) | 483.486 | 2.67091 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 483.328 | 1.52842 | ||||||||
\(11\) | −536.597 | −1.33711 | −0.668554 | − | 0.743664i | \(-0.733086\pi\) | ||||
−0.668554 | + | 0.743664i | \(0.733086\pi\) | |||||||
\(12\) | 702.734 | 1.40876 | ||||||||
\(13\) | −601.772 | −0.987583 | −0.493792 | − | 0.869580i | \(-0.664389\pi\) | ||||
−0.493792 | + | 0.869580i | \(0.664389\pi\) | |||||||
\(14\) | 1921.55 | 2.62019 | ||||||||
\(15\) | 414.598 | 0.475773 | ||||||||
\(16\) | 2574.11 | 2.51378 | ||||||||
\(17\) | −1948.89 | −1.63555 | −0.817776 | − | 0.575536i | \(-0.804793\pi\) | ||||
−0.817776 | + | 0.575536i | \(0.804793\pi\) | |||||||
\(18\) | 849.850 | 0.618245 | ||||||||
\(19\) | −1829.58 | −1.16270 | −0.581349 | − | 0.813654i | \(-0.697475\pi\) | ||||
−0.581349 | + | 0.813654i | \(0.697475\pi\) | |||||||
\(20\) | 3596.94 | 2.01075 | ||||||||
\(21\) | 1648.31 | 0.815624 | ||||||||
\(22\) | −5629.96 | −2.47998 | ||||||||
\(23\) | −143.630 | −0.0566143 | −0.0283071 | − | 0.999599i | \(-0.509012\pi\) | ||||
−0.0283071 | + | 0.999599i | \(0.509012\pi\) | |||||||
\(24\) | 4351.37 | 1.54205 | ||||||||
\(25\) | −1002.88 | −0.320921 | ||||||||
\(26\) | −6313.78 | −1.83171 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 14300.3 | 3.44706 | ||||||||
\(29\) | 4181.48 | 0.923284 | 0.461642 | − | 0.887066i | \(-0.347261\pi\) | ||||
0.461642 | + | 0.887066i | \(0.347261\pi\) | |||||||
\(30\) | 4349.96 | 0.882433 | ||||||||
\(31\) | 6331.93 | 1.18340 | 0.591701 | − | 0.806158i | \(-0.298457\pi\) | ||||
0.591701 | + | 0.806158i | \(0.298457\pi\) | |||||||
\(32\) | 11536.0 | 1.99150 | ||||||||
\(33\) | −4829.37 | −0.771980 | ||||||||
\(34\) | −20447.7 | −3.03352 | ||||||||
\(35\) | 8436.86 | 1.16415 | ||||||||
\(36\) | 6324.60 | 0.813349 | ||||||||
\(37\) | −1983.22 | −0.238159 | −0.119079 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119079 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(38\) | −19195.9 | −2.15650 | ||||||||
\(39\) | −5415.95 | −0.570181 | ||||||||
\(40\) | 22272.5 | 2.20099 | ||||||||
\(41\) | 18079.8 | 1.67970 | 0.839852 | − | 0.542815i | \(-0.182641\pi\) | ||||
0.839852 | + | 0.542815i | \(0.182641\pi\) | |||||||
\(42\) | 17294.0 | 1.51277 | ||||||||
\(43\) | −16207.9 | −1.33677 | −0.668383 | − | 0.743817i | \(-0.733013\pi\) | ||||
−0.668383 | + | 0.743817i | \(0.733013\pi\) | |||||||
\(44\) | −41898.3 | −3.26261 | ||||||||
\(45\) | 3731.39 | 0.274687 | ||||||||
\(46\) | −1506.96 | −0.105005 | ||||||||
\(47\) | 10082.4 | 0.665763 | 0.332881 | − | 0.942969i | \(-0.391979\pi\) | ||||
0.332881 | + | 0.942969i | \(0.391979\pi\) | |||||||
\(48\) | 23167.0 | 1.45133 | ||||||||
\(49\) | 16735.2 | 0.995726 | ||||||||
\(50\) | −10522.2 | −0.595224 | ||||||||
\(51\) | −17540.0 | −0.944287 | ||||||||
\(52\) | −46987.3 | −2.40975 | ||||||||
\(53\) | 17087.2 | 0.835565 | 0.417783 | − | 0.908547i | \(-0.362807\pi\) | ||||
0.417783 | + | 0.908547i | \(0.362807\pi\) | |||||||
\(54\) | 7648.65 | 0.356944 | ||||||||
\(55\) | −24719.1 | −1.10186 | ||||||||
\(56\) | 88548.1 | 3.77320 | ||||||||
\(57\) | −16466.2 | −0.671284 | ||||||||
\(58\) | 43872.0 | 1.71245 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 32372.5 | 1.16091 | ||||||||
\(61\) | −10827.9 | −0.372582 | −0.186291 | − | 0.982495i | \(-0.559647\pi\) | ||||
−0.186291 | + | 0.982495i | \(0.559647\pi\) | |||||||
\(62\) | 66434.5 | 2.19490 | ||||||||
\(63\) | 14834.8 | 0.470901 | ||||||||
\(64\) | 38663.6 | 1.17992 | ||||||||
\(65\) | −27721.5 | −0.813830 | ||||||||
\(66\) | −50669.6 | −1.43182 | ||||||||
\(67\) | 53212.3 | 1.44819 | 0.724094 | − | 0.689701i | \(-0.242258\pi\) | ||||
0.724094 | + | 0.689701i | \(0.242258\pi\) | |||||||
\(68\) | −152172. | −3.99082 | ||||||||
\(69\) | −1292.67 | −0.0326863 | ||||||||
\(70\) | 88519.3 | 2.15920 | ||||||||
\(71\) | −82455.8 | −1.94122 | −0.970611 | − | 0.240653i | \(-0.922638\pi\) | ||||
−0.970611 | + | 0.240653i | \(0.922638\pi\) | |||||||
\(72\) | 39162.4 | 0.890303 | ||||||||
\(73\) | −25989.7 | −0.570813 | −0.285406 | − | 0.958407i | \(-0.592129\pi\) | ||||
−0.285406 | + | 0.958407i | \(0.592129\pi\) | |||||||
\(74\) | −20807.9 | −0.441722 | ||||||||
\(75\) | −9025.91 | −0.185284 | ||||||||
\(76\) | −142856. | −2.83704 | ||||||||
\(77\) | −98275.1 | −1.88893 | ||||||||
\(78\) | −56824.0 | −1.05754 | ||||||||
\(79\) | 18631.5 | 0.335877 | 0.167938 | − | 0.985798i | \(-0.446289\pi\) | ||||
0.167938 | + | 0.985798i | \(0.446289\pi\) | |||||||
\(80\) | 118580. | 2.07151 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 189692. | 3.11541 | ||||||||
\(83\) | 105042. | 1.67367 | 0.836833 | − | 0.547458i | \(-0.184404\pi\) | ||||
0.836833 | + | 0.547458i | \(0.184404\pi\) | |||||||
\(84\) | 128702. | 1.99016 | ||||||||
\(85\) | −89778.4 | −1.34780 | ||||||||
\(86\) | −170053. | −2.47935 | ||||||||
\(87\) | 37633.3 | 0.533058 | ||||||||
\(88\) | −259437. | −3.57129 | ||||||||
\(89\) | −61443.6 | −0.822246 | −0.411123 | − | 0.911580i | \(-0.634863\pi\) | ||||
−0.411123 | + | 0.911580i | \(0.634863\pi\) | |||||||
\(90\) | 39149.6 | 0.509473 | ||||||||
\(91\) | −110212. | −1.39516 | ||||||||
\(92\) | −11214.9 | −0.138142 | ||||||||
\(93\) | 56987.4 | 0.683237 | ||||||||
\(94\) | 105784. | 1.23481 | ||||||||
\(95\) | −84282.2 | −0.958136 | ||||||||
\(96\) | 103824. | 1.14979 | ||||||||
\(97\) | 170505. | 1.83996 | 0.919980 | − | 0.391966i | \(-0.128205\pi\) | ||||
0.919980 | + | 0.391966i | \(0.128205\pi\) | |||||||
\(98\) | 175585. | 1.84681 | ||||||||
\(99\) | −43464.3 | −0.445703 | ||||||||
\(100\) | −78306.3 | −0.783063 | ||||||||
\(101\) | 38589.6 | 0.376415 | 0.188208 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188208 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(102\) | −184029. | −1.75140 | ||||||||
\(103\) | −8597.79 | −0.0798534 | −0.0399267 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399267 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(104\) | −290948. | −2.63774 | ||||||||
\(105\) | 75931.7 | 0.672125 | ||||||||
\(106\) | 179278. | 1.54975 | ||||||||
\(107\) | −45162.4 | −0.381345 | −0.190672 | − | 0.981654i | \(-0.561067\pi\) | ||||
−0.190672 | + | 0.981654i | \(0.561067\pi\) | |||||||
\(108\) | 56921.4 | 0.469587 | ||||||||
\(109\) | 74420.5 | 0.599966 | 0.299983 | − | 0.953945i | \(-0.403019\pi\) | ||||
0.299983 | + | 0.953945i | \(0.403019\pi\) | |||||||
\(110\) | −259352. | −2.04366 | ||||||||
\(111\) | −17849.0 | −0.137501 | ||||||||
\(112\) | 471437. | 3.55123 | ||||||||
\(113\) | 119180. | 0.878026 | 0.439013 | − | 0.898481i | \(-0.355328\pi\) | ||||
0.439013 | + | 0.898481i | \(0.355328\pi\) | |||||||
\(114\) | −172763. | −1.24506 | ||||||||
\(115\) | −6616.54 | −0.0466537 | ||||||||
\(116\) | 326496. | 2.25286 | ||||||||
\(117\) | −48743.5 | −0.329194 | ||||||||
\(118\) | −36522.6 | −0.241466 | ||||||||
\(119\) | −356929. | −2.31055 | ||||||||
\(120\) | 200453. | 1.27074 | ||||||||
\(121\) | 126885. | 0.787857 | ||||||||
\(122\) | −113607. | −0.691041 | ||||||||
\(123\) | 162718. | 0.969778 | ||||||||
\(124\) | 494407. | 2.88756 | ||||||||
\(125\) | −190157. | −1.08852 | ||||||||
\(126\) | 155646. | 0.873396 | ||||||||
\(127\) | 187431. | 1.03118 | 0.515588 | − | 0.856837i | \(-0.327574\pi\) | ||||
0.515588 | + | 0.856837i | \(0.327574\pi\) | |||||||
\(128\) | 36506.0 | 0.196942 | ||||||||
\(129\) | −145871. | −0.771783 | ||||||||
\(130\) | −290854. | −1.50944 | ||||||||
\(131\) | 200431. | 1.02044 | 0.510220 | − | 0.860044i | \(-0.329564\pi\) | ||||
0.510220 | + | 0.860044i | \(0.329564\pi\) | |||||||
\(132\) | −377085. | −1.88367 | ||||||||
\(133\) | −335078. | −1.64255 | ||||||||
\(134\) | 558302. | 2.68601 | ||||||||
\(135\) | 33582.5 | 0.158591 | ||||||||
\(136\) | −942260. | −4.36841 | ||||||||
\(137\) | 65393.6 | 0.297669 | 0.148834 | − | 0.988862i | \(-0.452448\pi\) | ||||
0.148834 | + | 0.988862i | \(0.452448\pi\) | |||||||
\(138\) | −13562.7 | −0.0606244 | ||||||||
\(139\) | −102562. | −0.450245 | −0.225123 | − | 0.974330i | \(-0.572278\pi\) | ||||
−0.225123 | + | 0.974330i | \(0.572278\pi\) | |||||||
\(140\) | 658762. | 2.84059 | ||||||||
\(141\) | 90741.7 | 0.384378 | ||||||||
\(142\) | −865124. | −3.60046 | ||||||||
\(143\) | 322909. | 1.32051 | ||||||||
\(144\) | 208503. | 0.837928 | ||||||||
\(145\) | 192626. | 0.760843 | ||||||||
\(146\) | −272683. | −1.05871 | ||||||||
\(147\) | 150617. | 0.574883 | ||||||||
\(148\) | −154853. | −0.581119 | ||||||||
\(149\) | 412586. | 1.52247 | 0.761235 | − | 0.648476i | \(-0.224593\pi\) | ||||
0.761235 | + | 0.648476i | \(0.224593\pi\) | |||||||
\(150\) | −94699.6 | −0.343653 | ||||||||
\(151\) | −344222. | −1.22856 | −0.614280 | − | 0.789088i | \(-0.710553\pi\) | ||||
−0.614280 | + | 0.789088i | \(0.710553\pi\) | |||||||
\(152\) | −884575. | −3.10546 | ||||||||
\(153\) | −157860. | −0.545184 | ||||||||
\(154\) | −1.03110e6 | −3.50348 | ||||||||
\(155\) | 291690. | 0.975197 | ||||||||
\(156\) | −422885. | −1.39127 | ||||||||
\(157\) | −69151.6 | −0.223900 | −0.111950 | − | 0.993714i | \(-0.535710\pi\) | ||||
−0.111950 | + | 0.993714i | \(0.535710\pi\) | |||||||
\(158\) | 195481. | 0.622963 | ||||||||
\(159\) | 153784. | 0.482414 | ||||||||
\(160\) | 531422. | 1.64112 | ||||||||
\(161\) | −26305.2 | −0.0799791 | ||||||||
\(162\) | 68837.8 | 0.206082 | ||||||||
\(163\) | −435248. | −1.28312 | −0.641561 | − | 0.767072i | \(-0.721713\pi\) | ||||
−0.641561 | + | 0.767072i | \(0.721713\pi\) | |||||||
\(164\) | 1.41169e6 | 4.09856 | ||||||||
\(165\) | −222472. | −0.636159 | ||||||||
\(166\) | 1.10210e6 | 3.10421 | ||||||||
\(167\) | −282385. | −0.783521 | −0.391761 | − | 0.920067i | \(-0.628134\pi\) | ||||
−0.391761 | + | 0.920067i | \(0.628134\pi\) | |||||||
\(168\) | 796933. | 2.17846 | ||||||||
\(169\) | −9163.31 | −0.0246795 | ||||||||
\(170\) | −941952. | −2.49981 | ||||||||
\(171\) | −148196. | −0.387566 | ||||||||
\(172\) | −1.26554e6 | −3.26177 | ||||||||
\(173\) | −542664. | −1.37853 | −0.689265 | − | 0.724510i | \(-0.742066\pi\) | ||||
−0.689265 | + | 0.724510i | \(0.742066\pi\) | |||||||
\(174\) | 394848. | 0.988682 | ||||||||
\(175\) | −183672. | −0.453366 | ||||||||
\(176\) | −1.38126e6 | −3.36120 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | −644665. | −1.52505 | ||||||||
\(179\) | −36141.3 | −0.0843084 | −0.0421542 | − | 0.999111i | \(-0.513422\pi\) | ||||
−0.0421542 | + | 0.999111i | \(0.513422\pi\) | |||||||
\(180\) | 291352. | 0.670250 | ||||||||
\(181\) | −597328. | −1.35524 | −0.677620 | − | 0.735412i | \(-0.736989\pi\) | ||||
−0.677620 | + | 0.735412i | \(0.736989\pi\) | |||||||
\(182\) | −1.15634e6 | −2.58765 | ||||||||
\(183\) | −97451.5 | −0.215110 | ||||||||
\(184\) | −69443.2 | −0.151212 | ||||||||
\(185\) | −91360.0 | −0.196258 | ||||||||
\(186\) | 597910. | 1.26723 | ||||||||
\(187\) | 1.04577e6 | 2.18691 | ||||||||
\(188\) | 787250. | 1.62449 | ||||||||
\(189\) | 133513. | 0.271875 | ||||||||
\(190\) | −884287. | −1.77709 | ||||||||
\(191\) | 653350. | 1.29587 | 0.647936 | − | 0.761695i | \(-0.275632\pi\) | ||||
0.647936 | + | 0.761695i | \(0.275632\pi\) | |||||||
\(192\) | 347972. | 0.681227 | ||||||||
\(193\) | −339340. | −0.655755 | −0.327878 | − | 0.944720i | \(-0.606333\pi\) | ||||
−0.327878 | + | 0.944720i | \(0.606333\pi\) | |||||||
\(194\) | 1.78894e6 | 3.41264 | ||||||||
\(195\) | −249494. | −0.469865 | ||||||||
\(196\) | 1.30671e6 | 2.42962 | ||||||||
\(197\) | −375530. | −0.689411 | −0.344706 | − | 0.938711i | \(-0.612021\pi\) | ||||
−0.344706 | + | 0.938711i | \(0.612021\pi\) | |||||||
\(198\) | −456027. | −0.826661 | ||||||||
\(199\) | −314088. | −0.562235 | −0.281118 | − | 0.959673i | \(-0.590705\pi\) | ||||
−0.281118 | + | 0.959673i | \(0.590705\pi\) | |||||||
\(200\) | −484878. | −0.857151 | ||||||||
\(201\) | 478911. | 0.836112 | ||||||||
\(202\) | 404882. | 0.698151 | ||||||||
\(203\) | 765818. | 1.30432 | ||||||||
\(204\) | −1.36955e6 | −2.30410 | ||||||||
\(205\) | 832871. | 1.38418 | ||||||||
\(206\) | −90207.8 | −0.148107 | ||||||||
\(207\) | −11634.0 | −0.0188714 | ||||||||
\(208\) | −1.54903e6 | −2.48257 | ||||||||
\(209\) | 981746. | 1.55465 | ||||||||
\(210\) | 796673. | 1.24661 | ||||||||
\(211\) | −383881. | −0.593595 | −0.296797 | − | 0.954941i | \(-0.595919\pi\) | ||||
−0.296797 | + | 0.954941i | \(0.595919\pi\) | |||||||
\(212\) | 1.33419e6 | 2.03882 | ||||||||
\(213\) | −742102. | −1.12077 | ||||||||
\(214\) | −473843. | −0.707294 | ||||||||
\(215\) | −746641. | −1.10158 | ||||||||
\(216\) | 352461. | 0.514017 | ||||||||
\(217\) | 1.15966e6 | 1.67179 | ||||||||
\(218\) | 780818. | 1.11278 | ||||||||
\(219\) | −233907. | −0.329559 | ||||||||
\(220\) | −1.93011e6 | −2.68859 | ||||||||
\(221\) | 1.17279e6 | 1.61524 | ||||||||
\(222\) | −187271. | −0.255028 | ||||||||
\(223\) | −507820. | −0.683829 | −0.341915 | − | 0.939731i | \(-0.611075\pi\) | ||||
−0.341915 | + | 0.939731i | \(0.611075\pi\) | |||||||
\(224\) | 2.11276e6 | 2.81339 | ||||||||
\(225\) | −81233.2 | −0.106974 | ||||||||
\(226\) | 1.25043e6 | 1.62851 | ||||||||
\(227\) | 1.23528e6 | 1.59111 | 0.795554 | − | 0.605882i | \(-0.207180\pi\) | ||||
0.795554 | + | 0.605882i | \(0.207180\pi\) | |||||||
\(228\) | −1.28571e6 | −1.63796 | ||||||||
\(229\) | 941944. | 1.18696 | 0.593481 | − | 0.804848i | \(-0.297753\pi\) | ||||
0.593481 | + | 0.804848i | \(0.297753\pi\) | |||||||
\(230\) | −69420.5 | −0.0865303 | ||||||||
\(231\) | −884476. | −1.09058 | ||||||||
\(232\) | 2.02169e6 | 2.46601 | ||||||||
\(233\) | 249966. | 0.301641 | 0.150821 | − | 0.988561i | \(-0.451808\pi\) | ||||
0.150821 | + | 0.988561i | \(0.451808\pi\) | |||||||
\(234\) | −511416. | −0.610569 | ||||||||
\(235\) | 464461. | 0.548630 | ||||||||
\(236\) | −271802. | −0.317667 | ||||||||
\(237\) | 167683. | 0.193918 | ||||||||
\(238\) | −3.74489e6 | −4.28546 | ||||||||
\(239\) | 1.41078e6 | 1.59759 | 0.798794 | − | 0.601604i | \(-0.205472\pi\) | ||||
0.798794 | + | 0.601604i | \(0.205472\pi\) | |||||||
\(240\) | 1.06722e6 | 1.19599 | ||||||||
\(241\) | 25730.6 | 0.0285369 | 0.0142685 | − | 0.999898i | \(-0.495458\pi\) | ||||
0.0142685 | + | 0.999898i | \(0.495458\pi\) | |||||||
\(242\) | 1.33128e6 | 1.46127 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −845462. | −0.909117 | ||||||||
\(245\) | 770930. | 0.820540 | ||||||||
\(246\) | 1.70723e6 | 1.79868 | ||||||||
\(247\) | 1.10099e6 | 1.14826 | ||||||||
\(248\) | 3.06140e6 | 3.16076 | ||||||||
\(249\) | 945381. | 0.966292 | ||||||||
\(250\) | −1.99512e6 | −2.01892 | ||||||||
\(251\) | −1.03590e6 | −1.03785 | −0.518925 | − | 0.854820i | \(-0.673668\pi\) | ||||
−0.518925 | + | 0.854820i | \(0.673668\pi\) | |||||||
\(252\) | 1.15832e6 | 1.14902 | ||||||||
\(253\) | 77071.5 | 0.0756994 | ||||||||
\(254\) | 1.96652e6 | 1.91256 | ||||||||
\(255\) | −808005. | −0.778151 | ||||||||
\(256\) | −854215. | −0.814643 | ||||||||
\(257\) | 1.04974e6 | 0.991403 | 0.495702 | − | 0.868493i | \(-0.334911\pi\) | ||||
0.495702 | + | 0.868493i | \(0.334911\pi\) | |||||||
\(258\) | −1.53048e6 | −1.43145 | ||||||||
\(259\) | −363217. | −0.336447 | ||||||||
\(260\) | −2.16454e6 | −1.98578 | ||||||||
\(261\) | 338700. | 0.307761 | ||||||||
\(262\) | 2.10292e6 | 1.89265 | ||||||||
\(263\) | −1.38970e6 | −1.23889 | −0.619445 | − | 0.785040i | \(-0.712642\pi\) | ||||
−0.619445 | + | 0.785040i | \(0.712642\pi\) | |||||||
\(264\) | −2.33493e6 | −2.06189 | ||||||||
\(265\) | 787146. | 0.688558 | ||||||||
\(266\) | −3.51563e6 | −3.04649 | ||||||||
\(267\) | −552993. | −0.474724 | ||||||||
\(268\) | 4.15490e6 | 3.53365 | ||||||||
\(269\) | −1.65552e6 | −1.39494 | −0.697469 | − | 0.716615i | \(-0.745690\pi\) | ||||
−0.697469 | + | 0.716615i | \(0.745690\pi\) | |||||||
\(270\) | 352346. | 0.294144 | ||||||||
\(271\) | 890523. | 0.736583 | 0.368292 | − | 0.929710i | \(-0.379943\pi\) | ||||
0.368292 | + | 0.929710i | \(0.379943\pi\) | |||||||
\(272\) | −5.01666e6 | −4.11142 | ||||||||
\(273\) | −991905. | −0.805496 | ||||||||
\(274\) | 686107. | 0.552097 | ||||||||
\(275\) | 538142. | 0.429106 | ||||||||
\(276\) | −100934. | −0.0797561 | ||||||||
\(277\) | −748295. | −0.585967 | −0.292984 | − | 0.956117i | \(-0.594648\pi\) | ||||
−0.292984 | + | 0.956117i | \(0.594648\pi\) | |||||||
\(278\) | −1.07608e6 | −0.835087 | ||||||||
\(279\) | 512887. | 0.394467 | ||||||||
\(280\) | 4.07910e6 | 3.10935 | ||||||||
\(281\) | 110769. | 0.0836861 | 0.0418430 | − | 0.999124i | \(-0.486677\pi\) | ||||
0.0418430 | + | 0.999124i | \(0.486677\pi\) | |||||||
\(282\) | 952059. | 0.712921 | ||||||||
\(283\) | −220603. | −0.163736 | −0.0818682 | − | 0.996643i | \(-0.526089\pi\) | ||||
−0.0818682 | + | 0.996643i | \(0.526089\pi\) | |||||||
\(284\) | −6.43827e6 | −4.73667 | ||||||||
\(285\) | −758540. | −0.553180 | ||||||||
\(286\) | 3.38795e6 | 2.44919 | ||||||||
\(287\) | 3.31122e6 | 2.37292 | ||||||||
\(288\) | 934415. | 0.663833 | ||||||||
\(289\) | 2.37830e6 | 1.67503 | ||||||||
\(290\) | 2.02103e6 | 1.41116 | ||||||||
\(291\) | 1.53455e6 | 1.06230 | ||||||||
\(292\) | −2.02931e6 | −1.39281 | ||||||||
\(293\) | 1.55524e6 | 1.05835 | 0.529173 | − | 0.848514i | \(-0.322502\pi\) | ||||
0.529173 | + | 0.848514i | \(0.322502\pi\) | |||||||
\(294\) | 1.58026e6 | 1.06626 | ||||||||
\(295\) | −160357. | −0.107284 | ||||||||
\(296\) | −958859. | −0.636100 | ||||||||
\(297\) | −391179. | −0.257327 | ||||||||
\(298\) | 4.32884e6 | 2.82378 | ||||||||
\(299\) | 86432.6 | 0.0559113 | ||||||||
\(300\) | −704757. | −0.452102 | ||||||||
\(301\) | −2.96840e6 | −1.88845 | ||||||||
\(302\) | −3.61157e6 | −2.27865 | ||||||||
\(303\) | 347307. | 0.217324 | ||||||||
\(304\) | −4.70954e6 | −2.92277 | ||||||||
\(305\) | −498805. | −0.307031 | ||||||||
\(306\) | −1.65626e6 | −1.01117 | ||||||||
\(307\) | −1.00187e6 | −0.606686 | −0.303343 | − | 0.952881i | \(-0.598103\pi\) | ||||
−0.303343 | + | 0.952881i | \(0.598103\pi\) | |||||||
\(308\) | −7.67347e6 | −4.60909 | ||||||||
\(309\) | −77380.1 | −0.0461034 | ||||||||
\(310\) | 3.06040e6 | 1.80873 | ||||||||
\(311\) | 2.66702e6 | 1.56360 | 0.781800 | − | 0.623529i | \(-0.214302\pi\) | ||||
0.781800 | + | 0.623529i | \(0.214302\pi\) | |||||||
\(312\) | −2.61854e6 | −1.52290 | ||||||||
\(313\) | 1.88511e6 | 1.08762 | 0.543808 | − | 0.839210i | \(-0.316982\pi\) | ||||
0.543808 | + | 0.839210i | \(0.316982\pi\) | |||||||
\(314\) | −725537. | −0.415275 | ||||||||
\(315\) | 683385. | 0.388051 | ||||||||
\(316\) | 1.45477e6 | 0.819555 | ||||||||
\(317\) | −2.77185e6 | −1.54925 | −0.774624 | − | 0.632422i | \(-0.782061\pi\) | ||||
−0.774624 | + | 0.632422i | \(0.782061\pi\) | |||||||
\(318\) | 1.61350e6 | 0.894750 | ||||||||
\(319\) | −2.24377e6 | −1.23453 | ||||||||
\(320\) | 1.78110e6 | 0.972327 | ||||||||
\(321\) | −406462. | −0.220169 | ||||||||
\(322\) | −275993. | −0.148340 | ||||||||
\(323\) | 3.56564e6 | 1.90165 | ||||||||
\(324\) | 512293. | 0.271116 | ||||||||
\(325\) | 603505. | 0.316936 | ||||||||
\(326\) | −4.56661e6 | −2.37985 | ||||||||
\(327\) | 669785. | 0.346390 | ||||||||
\(328\) | 8.74131e6 | 4.48634 | ||||||||
\(329\) | 1.84654e6 | 0.940524 | ||||||||
\(330\) | −2.33417e6 | −1.17991 | ||||||||
\(331\) | −3.55141e6 | −1.78168 | −0.890842 | − | 0.454312i | \(-0.849885\pi\) | ||||
−0.890842 | + | 0.454312i | \(0.849885\pi\) | |||||||
\(332\) | 8.20186e6 | 4.08383 | ||||||||
\(333\) | −160641. | −0.0793863 | ||||||||
\(334\) | −2.96278e6 | −1.45323 | ||||||||
\(335\) | 2.45130e6 | 1.19340 | ||||||||
\(336\) | 4.24293e6 | 2.05030 | ||||||||
\(337\) | 3.41206e6 | 1.63660 | 0.818298 | − | 0.574794i | \(-0.194918\pi\) | ||||
0.818298 | + | 0.574794i | \(0.194918\pi\) | |||||||
\(338\) | −96141.2 | −0.0457739 | ||||||||
\(339\) | 1.07262e6 | 0.506928 | ||||||||
\(340\) | −7.01003e6 | −3.28869 | ||||||||
\(341\) | −3.39770e6 | −1.58234 | ||||||||
\(342\) | −1.55487e6 | −0.718833 | ||||||||
\(343\) | −13155.6 | −0.00603774 | ||||||||
\(344\) | −7.83629e6 | −3.57038 | ||||||||
\(345\) | −59548.8 | −0.0269355 | ||||||||
\(346\) | −5.69362e6 | −2.55681 | ||||||||
\(347\) | −111495. | −0.0497088 | −0.0248544 | − | 0.999691i | \(-0.507912\pi\) | ||||
−0.0248544 | + | 0.999691i | \(0.507912\pi\) | |||||||
\(348\) | 2.93847e6 | 1.30069 | ||||||||
\(349\) | −691993. | −0.304115 | −0.152058 | − | 0.988372i | \(-0.548590\pi\) | ||||
−0.152058 | + | 0.988372i | \(0.548590\pi\) | |||||||
\(350\) | −1.92709e6 | −0.840875 | ||||||||
\(351\) | −438692. | −0.190060 | ||||||||
\(352\) | −6.19017e6 | −2.66285 | ||||||||
\(353\) | −2.81613e6 | −1.20286 | −0.601432 | − | 0.798924i | \(-0.705403\pi\) | ||||
−0.601432 | + | 0.798924i | \(0.705403\pi\) | |||||||
\(354\) | −328703. | −0.139411 | ||||||||
\(355\) | −3.79845e6 | −1.59969 | ||||||||
\(356\) | −4.79761e6 | −2.00632 | ||||||||
\(357\) | −3.21236e6 | −1.33400 | ||||||||
\(358\) | −379193. | −0.156370 | ||||||||
\(359\) | 2.09260e6 | 0.856940 | 0.428470 | − | 0.903556i | \(-0.359053\pi\) | ||||
0.428470 | + | 0.903556i | \(0.359053\pi\) | |||||||
\(360\) | 1.80407e6 | 0.733665 | ||||||||
\(361\) | 871258. | 0.351867 | ||||||||
\(362\) | −6.26715e6 | −2.51361 | ||||||||
\(363\) | 1.14197e6 | 0.454870 | ||||||||
\(364\) | −8.60549e6 | −3.40426 | ||||||||
\(365\) | −1.19725e6 | −0.470385 | ||||||||
\(366\) | −1.02246e6 | −0.398973 | ||||||||
\(367\) | 3.12044e6 | 1.20935 | 0.604674 | − | 0.796473i | \(-0.293304\pi\) | ||||
0.604674 | + | 0.796473i | \(0.293304\pi\) | |||||||
\(368\) | −369720. | −0.142316 | ||||||||
\(369\) | 1.46446e6 | 0.559902 | ||||||||
\(370\) | −958547. | −0.364006 | ||||||||
\(371\) | 3.12943e6 | 1.18040 | ||||||||
\(372\) | 4.44966e6 | 1.66713 | ||||||||
\(373\) | −696892. | −0.259354 | −0.129677 | − | 0.991556i | \(-0.541394\pi\) | ||||
−0.129677 | + | 0.991556i | \(0.541394\pi\) | |||||||
\(374\) | 1.09722e7 | 4.05614 | ||||||||
\(375\) | −1.71141e6 | −0.628458 | ||||||||
\(376\) | 4.87470e6 | 1.77819 | ||||||||
\(377\) | −2.51630e6 | −0.911820 | ||||||||
\(378\) | 1.40081e6 | 0.504256 | ||||||||
\(379\) | −5.00770e6 | −1.79077 | −0.895386 | − | 0.445291i | \(-0.853100\pi\) | ||||
−0.895386 | + | 0.445291i | \(0.853100\pi\) | |||||||
\(380\) | −6.58088e6 | −2.33790 | ||||||||
\(381\) | 1.68688e6 | 0.595349 | ||||||||
\(382\) | 6.85493e6 | 2.40350 | ||||||||
\(383\) | 359356. | 0.125178 | 0.0625890 | − | 0.998039i | \(-0.480064\pi\) | ||||
0.0625890 | + | 0.998039i | \(0.480064\pi\) | |||||||
\(384\) | 328554. | 0.113705 | ||||||||
\(385\) | −4.52719e6 | −1.55660 | ||||||||
\(386\) | −3.56035e6 | −1.21625 | ||||||||
\(387\) | −1.31284e6 | −0.445589 | ||||||||
\(388\) | 1.33133e7 | 4.48959 | ||||||||
\(389\) | 2.58030e6 | 0.864561 | 0.432280 | − | 0.901739i | \(-0.357709\pi\) | ||||
0.432280 | + | 0.901739i | \(0.357709\pi\) | |||||||
\(390\) | −2.61768e6 | −0.871476 | ||||||||
\(391\) | 279919. | 0.0925956 | ||||||||
\(392\) | 8.09122e6 | 2.65949 | ||||||||
\(393\) | 1.80388e6 | 0.589152 | ||||||||
\(394\) | −3.94005e6 | −1.27868 | ||||||||
\(395\) | 858287. | 0.276783 | ||||||||
\(396\) | −3.39376e6 | −1.08754 | ||||||||
\(397\) | −2.84643e6 | −0.906409 | −0.453204 | − | 0.891407i | \(-0.649719\pi\) | ||||
−0.453204 | + | 0.891407i | \(0.649719\pi\) | |||||||
\(398\) | −3.29540e6 | −1.04280 | ||||||||
\(399\) | −3.01571e6 | −0.948324 | ||||||||
\(400\) | −2.58153e6 | −0.806727 | ||||||||
\(401\) | −2.13470e6 | −0.662944 | −0.331472 | − | 0.943465i | \(-0.607545\pi\) | ||||
−0.331472 | + | 0.943465i | \(0.607545\pi\) | |||||||
\(402\) | 5.02472e6 | 1.55077 | ||||||||
\(403\) | −3.81038e6 | −1.16871 | ||||||||
\(404\) | 3.01314e6 | 0.918471 | ||||||||
\(405\) | 302242. | 0.0915625 | ||||||||
\(406\) | 8.03495e6 | 2.41918 | ||||||||
\(407\) | 1.06419e6 | 0.318444 | ||||||||
\(408\) | −8.48034e6 | −2.52210 | ||||||||
\(409\) | 1.68398e6 | 0.497771 | 0.248885 | − | 0.968533i | \(-0.419936\pi\) | ||||
0.248885 | + | 0.968533i | \(0.419936\pi\) | |||||||
\(410\) | 8.73846e6 | 2.56729 | ||||||||
\(411\) | 588542. | 0.171859 | ||||||||
\(412\) | −671328. | −0.194846 | ||||||||
\(413\) | −637528. | −0.183918 | ||||||||
\(414\) | −122064. | −0.0350015 | ||||||||
\(415\) | 4.83893e6 | 1.37921 | ||||||||
\(416\) | −6.94203e6 | −1.96677 | ||||||||
\(417\) | −923058. | −0.259949 | ||||||||
\(418\) | 1.03005e7 | 2.88347 | ||||||||
\(419\) | 6.14268e6 | 1.70932 | 0.854659 | − | 0.519190i | \(-0.173766\pi\) | ||||
0.854659 | + | 0.519190i | \(0.173766\pi\) | |||||||
\(420\) | 5.92886e6 | 1.64002 | ||||||||
\(421\) | −1.00451e6 | −0.276217 | −0.138108 | − | 0.990417i | \(-0.544102\pi\) | ||||
−0.138108 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(422\) | −4.02766e6 | −1.10096 | ||||||||
\(423\) | 816675. | 0.221921 | ||||||||
\(424\) | 8.26141e6 | 2.23172 | ||||||||
\(425\) | 1.95450e6 | 0.524884 | ||||||||
\(426\) | −7.78612e6 | −2.07872 | ||||||||
\(427\) | −1.98309e6 | −0.526347 | ||||||||
\(428\) | −3.52635e6 | −0.930499 | ||||||||
\(429\) | 2.90618e6 | 0.762394 | ||||||||
\(430\) | −7.83374e6 | −2.04314 | ||||||||
\(431\) | 2.54886e6 | 0.660927 | 0.330464 | − | 0.943819i | \(-0.392795\pi\) | ||||
0.330464 | + | 0.943819i | \(0.392795\pi\) | |||||||
\(432\) | 1.87653e6 | 0.483778 | ||||||||
\(433\) | −4.98914e6 | −1.27881 | −0.639404 | − | 0.768871i | \(-0.720819\pi\) | ||||
−0.639404 | + | 0.768871i | \(0.720819\pi\) | |||||||
\(434\) | 1.21672e7 | 3.10074 | ||||||||
\(435\) | 1.73364e6 | 0.439273 | ||||||||
\(436\) | 5.81087e6 | 1.46395 | ||||||||
\(437\) | 262783. | 0.0658253 | ||||||||
\(438\) | −2.45415e6 | −0.611245 | ||||||||
\(439\) | −996560. | −0.246798 | −0.123399 | − | 0.992357i | \(-0.539380\pi\) | ||||
−0.123399 | + | 0.992357i | \(0.539380\pi\) | |||||||
\(440\) | −1.19514e7 | −2.94297 | ||||||||
\(441\) | 1.35555e6 | 0.331909 | ||||||||
\(442\) | 1.23048e7 | 2.99585 | ||||||||
\(443\) | −6.09227e6 | −1.47493 | −0.737463 | − | 0.675388i | \(-0.763976\pi\) | ||||
−0.737463 | + | 0.675388i | \(0.763976\pi\) | |||||||
\(444\) | −1.39368e6 | −0.335509 | ||||||||
\(445\) | −2.83049e6 | −0.677582 | ||||||||
\(446\) | −5.32804e6 | −1.26832 | ||||||||
\(447\) | 3.71327e6 | 0.878999 | ||||||||
\(448\) | 7.08105e6 | 1.66687 | ||||||||
\(449\) | 1.80157e6 | 0.421732 | 0.210866 | − | 0.977515i | \(-0.432372\pi\) | ||||
0.210866 | + | 0.977515i | \(0.432372\pi\) | |||||||
\(450\) | −852297. | −0.198408 | ||||||||
\(451\) | −9.70154e6 | −2.24595 | ||||||||
\(452\) | 9.30576e6 | 2.14242 | ||||||||
\(453\) | −3.09800e6 | −0.709309 | ||||||||
\(454\) | 1.29605e7 | 2.95109 | ||||||||
\(455\) | −5.07706e6 | −1.14970 | ||||||||
\(456\) | −7.96118e6 | −1.79294 | ||||||||
\(457\) | −3.51589e6 | −0.787489 | −0.393744 | − | 0.919220i | \(-0.628820\pi\) | ||||
−0.393744 | + | 0.919220i | \(0.628820\pi\) | |||||||
\(458\) | 9.88286e6 | 2.20150 | ||||||||
\(459\) | −1.42074e6 | −0.314762 | ||||||||
\(460\) | −516629. | −0.113837 | ||||||||
\(461\) | 6.94554e6 | 1.52214 | 0.761068 | − | 0.648672i | \(-0.224675\pi\) | ||||
0.761068 | + | 0.648672i | \(0.224675\pi\) | |||||||
\(462\) | −9.27990e6 | −2.02273 | ||||||||
\(463\) | −4.78918e6 | −1.03827 | −0.519133 | − | 0.854693i | \(-0.673745\pi\) | ||||
−0.519133 | + | 0.854693i | \(0.673745\pi\) | |||||||
\(464\) | 1.07636e7 | 2.32094 | ||||||||
\(465\) | 2.62521e6 | 0.563030 | ||||||||
\(466\) | 2.62264e6 | 0.559465 | ||||||||
\(467\) | 2.62555e6 | 0.557094 | 0.278547 | − | 0.960423i | \(-0.410147\pi\) | ||||
0.278547 | + | 0.960423i | \(0.410147\pi\) | |||||||
\(468\) | −3.80597e6 | −0.803250 | ||||||||
\(469\) | 9.74557e6 | 2.04586 | ||||||||
\(470\) | 4.87311e6 | 1.01756 | ||||||||
\(471\) | −622365. | −0.129269 | ||||||||
\(472\) | −1.68301e6 | −0.347723 | ||||||||
\(473\) | 8.69711e6 | 1.78740 | ||||||||
\(474\) | 1.75933e6 | 0.359668 | ||||||||
\(475\) | 1.83485e6 | 0.373135 | ||||||||
\(476\) | −2.78696e7 | −5.63784 | ||||||||
\(477\) | 1.38406e6 | 0.278522 | ||||||||
\(478\) | 1.48019e7 | 2.96311 | ||||||||
\(479\) | −2.10029e6 | −0.418255 | −0.209128 | − | 0.977888i | \(-0.567062\pi\) | ||||
−0.209128 | + | 0.977888i | \(0.567062\pi\) | |||||||
\(480\) | 4.78280e6 | 0.947500 | ||||||||
\(481\) | 1.19345e6 | 0.235202 | ||||||||
\(482\) | 269965. | 0.0529285 | ||||||||
\(483\) | −236747. | −0.0461760 | ||||||||
\(484\) | 9.90739e6 | 1.92241 | ||||||||
\(485\) | 7.85458e6 | 1.51624 | ||||||||
\(486\) | 619541. | 0.118981 | ||||||||
\(487\) | −3.94358e6 | −0.753474 | −0.376737 | − | 0.926320i | \(-0.622954\pi\) | ||||
−0.376737 | + | 0.926320i | \(0.622954\pi\) | |||||||
\(488\) | −5.23516e6 | −0.995131 | ||||||||
\(489\) | −3.91723e6 | −0.740811 | ||||||||
\(490\) | 8.08858e6 | 1.52189 | ||||||||
\(491\) | 377373. | 0.0706427 | 0.0353213 | − | 0.999376i | \(-0.488755\pi\) | ||||
0.0353213 | + | 0.999376i | \(0.488755\pi\) | |||||||
\(492\) | 1.27053e7 | 2.36630 | ||||||||
\(493\) | −8.14924e6 | −1.51008 | ||||||||
\(494\) | 1.15515e7 | 2.12972 | ||||||||
\(495\) | −2.00225e6 | −0.367287 | ||||||||
\(496\) | 1.62991e7 | 2.97482 | ||||||||
\(497\) | −1.51014e7 | −2.74237 | ||||||||
\(498\) | 9.91891e6 | 1.79222 | ||||||||
\(499\) | −2.96483e6 | −0.533026 | −0.266513 | − | 0.963831i | \(-0.585872\pi\) | ||||
−0.266513 | + | 0.963831i | \(0.585872\pi\) | |||||||
\(500\) | −1.48477e7 | −2.65604 | ||||||||
\(501\) | −2.54147e6 | −0.452366 | ||||||||
\(502\) | −1.08687e7 | −1.92494 | ||||||||
\(503\) | −3.33200e6 | −0.587198 | −0.293599 | − | 0.955929i | \(-0.594853\pi\) | ||||
−0.293599 | + | 0.955929i | \(0.594853\pi\) | |||||||
\(504\) | 7.17240e6 | 1.25773 | ||||||||
\(505\) | 1.77769e6 | 0.310190 | ||||||||
\(506\) | 808632. | 0.140402 | ||||||||
\(507\) | −82469.8 | −0.0142487 | ||||||||
\(508\) | 1.46349e7 | 2.51612 | ||||||||
\(509\) | −3.15713e6 | −0.540129 | −0.270065 | − | 0.962842i | \(-0.587045\pi\) | ||||
−0.270065 | + | 0.962842i | \(0.587045\pi\) | |||||||
\(510\) | −8.47757e6 | −1.44326 | ||||||||
\(511\) | −4.75988e6 | −0.806388 | ||||||||
\(512\) | −1.01306e7 | −1.70789 | ||||||||
\(513\) | −1.33376e6 | −0.223761 | ||||||||
\(514\) | 1.10139e7 | 1.83879 | ||||||||
\(515\) | −396070. | −0.0658042 | ||||||||
\(516\) | −1.13898e7 | −1.88319 | ||||||||
\(517\) | −5.41019e6 | −0.890197 | ||||||||
\(518\) | −3.81087e6 | −0.624021 | ||||||||
\(519\) | −4.88398e6 | −0.795894 | ||||||||
\(520\) | −1.34030e7 | −2.17367 | ||||||||
\(521\) | −9.78221e6 | −1.57886 | −0.789429 | − | 0.613842i | \(-0.789623\pi\) | ||||
−0.789429 | + | 0.613842i | \(0.789623\pi\) | |||||||
\(522\) | 3.55363e6 | 0.570816 | ||||||||
\(523\) | 1.09469e7 | 1.75000 | 0.874999 | − | 0.484124i | \(-0.160862\pi\) | ||||
0.874999 | + | 0.484124i | \(0.160862\pi\) | |||||||
\(524\) | 1.56500e7 | 2.48992 | ||||||||
\(525\) | −1.65305e6 | −0.261751 | ||||||||
\(526\) | −1.45807e7 | −2.29781 | ||||||||
\(527\) | −1.23402e7 | −1.93552 | ||||||||
\(528\) | −1.24314e7 | −1.94059 | ||||||||
\(529\) | −6.41571e6 | −0.996795 | ||||||||
\(530\) | 8.25871e6 | 1.27709 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | −2.61634e7 | −4.00789 | ||||||||
\(533\) | −1.08799e7 | −1.65885 | ||||||||
\(534\) | −5.80198e6 | −0.880488 | ||||||||
\(535\) | −2.08047e6 | −0.314252 | ||||||||
\(536\) | 2.57274e7 | 3.86798 | ||||||||
\(537\) | −325271. | −0.0486755 | ||||||||
\(538\) | −1.73697e7 | −2.58724 | ||||||||
\(539\) | −8.98004e6 | −1.33139 | ||||||||
\(540\) | 2.62217e6 | 0.386969 | ||||||||
\(541\) | −9.12573e6 | −1.34052 | −0.670262 | − | 0.742125i | \(-0.733818\pi\) | ||||
−0.670262 | + | 0.742125i | \(0.733818\pi\) | |||||||
\(542\) | 9.34334e6 | 1.36617 | ||||||||
\(543\) | −5.37595e6 | −0.782449 | ||||||||
\(544\) | −2.24823e7 | −3.25720 | ||||||||
\(545\) | 3.42829e6 | 0.494409 | ||||||||
\(546\) | −1.04070e7 | −1.49398 | ||||||||
\(547\) | 6.24984e6 | 0.893100 | 0.446550 | − | 0.894759i | \(-0.352652\pi\) | ||||
0.446550 | + | 0.894759i | \(0.352652\pi\) | |||||||
\(548\) | 5.10603e6 | 0.726326 | ||||||||
\(549\) | −877064. | −0.124194 | ||||||||
\(550\) | 5.64617e6 | 0.795879 | ||||||||
\(551\) | −7.65035e6 | −1.07350 | ||||||||
\(552\) | −624989. | −0.0873020 | ||||||||
\(553\) | 3.41227e6 | 0.474493 | ||||||||
\(554\) | −7.85109e6 | −1.08681 | ||||||||
\(555\) | −822240. | −0.113309 | ||||||||
\(556\) | −8.00819e6 | −1.09862 | ||||||||
\(557\) | −8.18033e6 | −1.11721 | −0.558603 | − | 0.829435i | \(-0.688662\pi\) | ||||
−0.558603 | + | 0.829435i | \(0.688662\pi\) | |||||||
\(558\) | 5.38119e6 | 0.731633 | ||||||||
\(559\) | 9.75346e6 | 1.32017 | ||||||||
\(560\) | 2.17174e7 | 2.92643 | ||||||||
\(561\) | 9.41190e6 | 1.26261 | ||||||||
\(562\) | 1.16219e6 | 0.155216 | ||||||||
\(563\) | 6.48080e6 | 0.861704 | 0.430852 | − | 0.902423i | \(-0.358213\pi\) | ||||
0.430852 | + | 0.902423i | \(0.358213\pi\) | |||||||
\(564\) | 7.08525e6 | 0.937901 | ||||||||
\(565\) | 5.49020e6 | 0.723548 | ||||||||
\(566\) | −2.31456e6 | −0.303688 | ||||||||
\(567\) | 1.20162e6 | 0.156967 | ||||||||
\(568\) | −3.98662e7 | −5.18483 | ||||||||
\(569\) | −708193. | −0.0917004 | −0.0458502 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458502 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(570\) | −7.95858e6 | −1.02600 | ||||||||
\(571\) | 4.84800e6 | 0.622260 | 0.311130 | − | 0.950367i | \(-0.399292\pi\) | ||||
0.311130 | + | 0.950367i | \(0.399292\pi\) | |||||||
\(572\) | 2.52132e7 | 3.22209 | ||||||||
\(573\) | 5.88015e6 | 0.748172 | ||||||||
\(574\) | 3.47412e7 | 4.40114 | ||||||||
\(575\) | 144044. | 0.0181687 | ||||||||
\(576\) | 3.13175e6 | 0.393307 | ||||||||
\(577\) | 5.03751e6 | 0.629907 | 0.314954 | − | 0.949107i | \(-0.398011\pi\) | ||||
0.314954 | + | 0.949107i | \(0.398011\pi\) | |||||||
\(578\) | 2.49531e7 | 3.10674 | ||||||||
\(579\) | −3.05406e6 | −0.378600 | ||||||||
\(580\) | 1.50405e7 | 1.85649 | ||||||||
\(581\) | 1.92380e7 | 2.36439 | ||||||||
\(582\) | 1.61004e7 | 1.97029 | ||||||||
\(583\) | −9.16892e6 | −1.11724 | ||||||||
\(584\) | −1.25656e7 | −1.52459 | ||||||||
\(585\) | −2.24544e6 | −0.271277 | ||||||||
\(586\) | 1.63175e7 | 1.96295 | ||||||||
\(587\) | −714405. | −0.0855755 | −0.0427878 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427878 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(588\) | 1.17604e7 | 1.40274 | ||||||||
\(589\) | −1.15848e7 | −1.37594 | ||||||||
\(590\) | −1.68247e6 | −0.198983 | ||||||||
\(591\) | −3.37977e6 | −0.398032 | ||||||||
\(592\) | −5.10504e6 | −0.598680 | ||||||||
\(593\) | 1.42859e7 | 1.66829 | 0.834145 | − | 0.551545i | \(-0.185962\pi\) | ||||
0.834145 | + | 0.551545i | \(0.185962\pi\) | |||||||
\(594\) | −4.10424e6 | −0.477273 | ||||||||
\(595\) | −1.64425e7 | −1.90404 | ||||||||
\(596\) | 3.22153e7 | 3.71490 | ||||||||
\(597\) | −2.82679e6 | −0.324607 | ||||||||
\(598\) | 906849. | 0.103701 | ||||||||
\(599\) | 1.22307e7 | 1.39279 | 0.696395 | − | 0.717659i | \(-0.254786\pi\) | ||||
0.696395 | + | 0.717659i | \(0.254786\pi\) | |||||||
\(600\) | −4.36390e6 | −0.494877 | ||||||||
\(601\) | 1.62678e7 | 1.83714 | 0.918571 | − | 0.395257i | \(-0.129344\pi\) | ||||
0.918571 | + | 0.395257i | \(0.129344\pi\) | |||||||
\(602\) | −3.11444e7 | −3.50258 | ||||||||
\(603\) | 4.31019e6 | 0.482729 | ||||||||
\(604\) | −2.68774e7 | −2.99774 | ||||||||
\(605\) | 5.84515e6 | 0.649243 | ||||||||
\(606\) | 3.64393e6 | 0.403078 | ||||||||
\(607\) | −4.79971e6 | −0.528741 | −0.264371 | − | 0.964421i | \(-0.585164\pi\) | ||||
−0.264371 | + | 0.964421i | \(0.585164\pi\) | |||||||
\(608\) | −2.11060e7 | −2.31551 | ||||||||
\(609\) | 6.89237e6 | 0.753052 | ||||||||
\(610\) | −5.23345e6 | −0.569461 | ||||||||
\(611\) | −6.06731e6 | −0.657496 | ||||||||
\(612\) | −1.23259e7 | −1.33027 | ||||||||
\(613\) | 7.16201e6 | 0.769810 | 0.384905 | − | 0.922956i | \(-0.374234\pi\) | ||||
0.384905 | + | 0.922956i | \(0.374234\pi\) | |||||||
\(614\) | −1.05116e7 | −1.12524 | ||||||||
\(615\) | 7.49584e6 | 0.799157 | ||||||||
\(616\) | −4.75147e7 | −5.04517 | ||||||||
\(617\) | −1.31807e6 | −0.139388 | −0.0696942 | − | 0.997568i | \(-0.522202\pi\) | ||||
−0.0696942 | + | 0.997568i | \(0.522202\pi\) | |||||||
\(618\) | −811870. | −0.0855097 | ||||||||
\(619\) | 8.49355e6 | 0.890969 | 0.445485 | − | 0.895290i | \(-0.353031\pi\) | ||||
0.445485 | + | 0.895290i | \(0.353031\pi\) | |||||||
\(620\) | 2.27756e7 | 2.37953 | ||||||||
\(621\) | −104706. | −0.0108954 | ||||||||
\(622\) | 2.79823e7 | 2.90007 | ||||||||
\(623\) | −1.12531e7 | −1.16159 | ||||||||
\(624\) | −1.39413e7 | −1.43331 | ||||||||
\(625\) | −5.62586e6 | −0.576088 | ||||||||
\(626\) | 1.97785e7 | 2.01724 | ||||||||
\(627\) | 8.83571e6 | 0.897579 | ||||||||
\(628\) | −5.39947e6 | −0.546326 | ||||||||
\(629\) | 3.86507e6 | 0.389521 | ||||||||
\(630\) | 7.17006e6 | 0.719733 | ||||||||
\(631\) | 2.71872e6 | 0.271826 | 0.135913 | − | 0.990721i | \(-0.456603\pi\) | ||||
0.135913 | + | 0.990721i | \(0.456603\pi\) | |||||||
\(632\) | 9.00806e6 | 0.897096 | ||||||||
\(633\) | −3.45492e6 | −0.342712 | ||||||||
\(634\) | −2.90821e7 | −2.87345 | ||||||||
\(635\) | 8.63430e6 | 0.849753 | ||||||||
\(636\) | 1.20077e7 | 1.17711 | ||||||||
\(637\) | −1.00708e7 | −0.983362 | ||||||||
\(638\) | −2.35416e7 | −2.28973 | ||||||||
\(639\) | −6.67892e6 | −0.647074 | ||||||||
\(640\) | 1.68170e6 | 0.162293 | ||||||||
\(641\) | −9.82087e6 | −0.944071 | −0.472036 | − | 0.881579i | \(-0.656481\pi\) | ||||
−0.472036 | + | 0.881579i | \(0.656481\pi\) | |||||||
\(642\) | −4.26458e6 | −0.408356 | ||||||||
\(643\) | 1.88105e7 | 1.79421 | 0.897103 | − | 0.441822i | \(-0.145668\pi\) | ||||
0.897103 | + | 0.441822i | \(0.145668\pi\) | |||||||
\(644\) | −2.05395e6 | −0.195153 | ||||||||
\(645\) | −6.71977e6 | −0.635997 | ||||||||
\(646\) | 3.74106e7 | 3.52707 | ||||||||
\(647\) | 1.01896e7 | 0.956964 | 0.478482 | − | 0.878097i | \(-0.341187\pi\) | ||||
0.478482 | + | 0.878097i | \(0.341187\pi\) | |||||||
\(648\) | 3.17215e6 | 0.296768 | ||||||||
\(649\) | 1.86789e6 | 0.174077 | ||||||||
\(650\) | 6.33195e6 | 0.587834 | ||||||||
\(651\) | 1.04370e7 | 0.965210 | ||||||||
\(652\) | −3.39848e7 | −3.13088 | ||||||||
\(653\) | −7.39824e6 | −0.678962 | −0.339481 | − | 0.940613i | \(-0.610251\pi\) | ||||
−0.339481 | + | 0.940613i | \(0.610251\pi\) | |||||||
\(654\) | 7.02737e6 | 0.642463 | ||||||||
\(655\) | 9.23317e6 | 0.840907 | ||||||||
\(656\) | 4.65394e7 | 4.22241 | ||||||||
\(657\) | −2.10516e6 | −0.190271 | ||||||||
\(658\) | 1.93739e7 | 1.74442 | ||||||||
\(659\) | 2.69270e6 | 0.241532 | 0.120766 | − | 0.992681i | \(-0.461465\pi\) | ||||
0.120766 | + | 0.992681i | \(0.461465\pi\) | |||||||
\(660\) | −1.73710e7 | −1.55226 | ||||||||
\(661\) | −1.86231e7 | −1.65786 | −0.828930 | − | 0.559352i | \(-0.811050\pi\) | ||||
−0.828930 | + | 0.559352i | \(0.811050\pi\) | |||||||
\(662\) | −3.72613e7 | −3.30456 | ||||||||
\(663\) | 1.05551e7 | 0.932561 | ||||||||
\(664\) | 5.07865e7 | 4.47021 | ||||||||
\(665\) | −1.54359e7 | −1.35356 | ||||||||
\(666\) | −1.68544e6 | −0.147241 | ||||||||
\(667\) | −600587. | −0.0522711 | ||||||||
\(668\) | −2.20491e7 | −1.91183 | ||||||||
\(669\) | −4.57038e6 | −0.394809 | ||||||||
\(670\) | 2.57190e7 | 2.21344 | ||||||||
\(671\) | 5.81024e6 | 0.498182 | ||||||||
\(672\) | 1.90148e7 | 1.62431 | ||||||||
\(673\) | −4.21307e6 | −0.358559 | −0.179280 | − | 0.983798i | \(-0.557377\pi\) | ||||
−0.179280 | + | 0.983798i | \(0.557377\pi\) | |||||||
\(674\) | 3.57992e7 | 3.03546 | ||||||||
\(675\) | −731099. | −0.0617613 | ||||||||
\(676\) | −715485. | −0.0602191 | ||||||||
\(677\) | −208397. | −0.0174751 | −0.00873756 | − | 0.999962i | \(-0.502781\pi\) | ||||
−0.00873756 | + | 0.999962i | \(0.502781\pi\) | |||||||
\(678\) | 1.12539e7 | 0.940219 | ||||||||
\(679\) | 3.12272e7 | 2.59931 | ||||||||
\(680\) | −4.34066e7 | −3.59984 | ||||||||
\(681\) | 1.11175e7 | 0.918627 | ||||||||
\(682\) | −3.56485e7 | −2.93482 | ||||||||
\(683\) | −4.15227e6 | −0.340591 | −0.170296 | − | 0.985393i | \(-0.554472\pi\) | ||||
−0.170296 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(684\) | −1.15714e7 | −0.945679 | ||||||||
\(685\) | 3.01245e6 | 0.245298 | ||||||||
\(686\) | −138028. | −0.0111984 | ||||||||
\(687\) | 8.47750e6 | 0.685292 | ||||||||
\(688\) | −4.17210e7 | −3.36034 | ||||||||
\(689\) | −1.02826e7 | −0.825190 | ||||||||
\(690\) | −624785. | −0.0499583 | ||||||||
\(691\) | 8.97043e6 | 0.714691 | 0.357345 | − | 0.933972i | \(-0.383682\pi\) | ||||
0.357345 | + | 0.933972i | \(0.383682\pi\) | |||||||
\(692\) | −4.23720e7 | −3.36368 | ||||||||
\(693\) | −7.96029e6 | −0.629645 | ||||||||
\(694\) | −1.16981e6 | −0.0921967 | ||||||||
\(695\) | −4.72467e6 | −0.371030 | ||||||||
\(696\) | 1.81952e7 | 1.42375 | ||||||||
\(697\) | −3.52354e7 | −2.74724 | ||||||||
\(698\) | −7.26037e6 | −0.564053 | ||||||||
\(699\) | 2.24969e6 | 0.174153 | ||||||||
\(700\) | −1.43414e7 | −1.10623 | ||||||||
\(701\) | 1.23886e7 | 0.952195 | 0.476097 | − | 0.879393i | \(-0.342051\pi\) | ||||
0.476097 | + | 0.879393i | \(0.342051\pi\) | |||||||
\(702\) | −4.60274e6 | −0.352512 | ||||||||
\(703\) | 3.62846e6 | 0.276907 | ||||||||
\(704\) | −2.07468e7 | −1.57768 | ||||||||
\(705\) | 4.18015e6 | 0.316752 | ||||||||
\(706\) | −2.95468e7 | −2.23100 | ||||||||
\(707\) | 7.06751e6 | 0.531763 | ||||||||
\(708\) | −2.44622e6 | −0.183405 | ||||||||
\(709\) | −7.98264e6 | −0.596391 | −0.298195 | − | 0.954505i | \(-0.596385\pi\) | ||||
−0.298195 | + | 0.954505i | \(0.596385\pi\) | |||||||
\(710\) | −3.98532e7 | −2.96700 | ||||||||
\(711\) | 1.50915e6 | 0.111959 | ||||||||
\(712\) | −2.97071e7 | −2.19614 | ||||||||
\(713\) | −909457. | −0.0669974 | ||||||||
\(714\) | −3.37040e7 | −2.47421 | ||||||||
\(715\) | 1.48753e7 | 1.08818 | ||||||||
\(716\) | −2.82197e6 | −0.205717 | ||||||||
\(717\) | 1.26970e7 | 0.922368 | ||||||||
\(718\) | 2.19555e7 | 1.58940 | ||||||||
\(719\) | 1.40569e7 | 1.01407 | 0.507035 | − | 0.861926i | \(-0.330742\pi\) | ||||
0.507035 | + | 0.861926i | \(0.330742\pi\) | |||||||
\(720\) | 9.60501e6 | 0.690505 | ||||||||
\(721\) | −1.57464e6 | −0.112809 | ||||||||
\(722\) | 9.14121e6 | 0.652621 | ||||||||
\(723\) | 231575. | 0.0164758 | ||||||||
\(724\) | −4.66403e7 | −3.30685 | ||||||||
\(725\) | −4.19352e6 | −0.296301 | ||||||||
\(726\) | 1.19815e7 | 0.843663 | ||||||||
\(727\) | −1.08044e7 | −0.758166 | −0.379083 | − | 0.925363i | \(-0.623760\pi\) | ||||
−0.379083 | + | 0.925363i | \(0.623760\pi\) | |||||||
\(728\) | −5.32858e7 | −3.72635 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.25615e7 | −0.872440 | ||||||||
\(731\) | 3.15874e7 | 2.18635 | ||||||||
\(732\) | −7.60916e6 | −0.524879 | ||||||||
\(733\) | −1.13233e7 | −0.778419 | −0.389210 | − | 0.921149i | \(-0.627252\pi\) | ||||
−0.389210 | + | 0.921149i | \(0.627252\pi\) | |||||||
\(734\) | 3.27396e7 | 2.24302 | ||||||||
\(735\) | 6.93837e6 | 0.473739 | ||||||||
\(736\) | −1.65692e6 | −0.112747 | ||||||||
\(737\) | −2.85535e7 | −1.93638 | ||||||||
\(738\) | 1.53651e7 | 1.03847 | ||||||||
\(739\) | 7.10841e6 | 0.478808 | 0.239404 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239404 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(740\) | −7.13353e6 | −0.478878 | ||||||||
\(741\) | 9.90890e6 | 0.662949 | ||||||||
\(742\) | 3.28339e7 | 2.18934 | ||||||||
\(743\) | 2.17570e7 | 1.44586 | 0.722932 | − | 0.690919i | \(-0.242794\pi\) | ||||
0.722932 | + | 0.690919i | \(0.242794\pi\) | |||||||
\(744\) | 2.75526e7 | 1.82486 | ||||||||
\(745\) | 1.90064e7 | 1.25461 | ||||||||
\(746\) | −7.31178e6 | −0.481034 | ||||||||
\(747\) | 8.50843e6 | 0.557889 | ||||||||
\(748\) | 8.16551e7 | 5.33616 | ||||||||
\(749\) | −8.27128e6 | −0.538726 | ||||||||
\(750\) | −1.79561e7 | −1.16562 | ||||||||
\(751\) | 1.14558e7 | 0.741180 | 0.370590 | − | 0.928797i | \(-0.379155\pi\) | ||||
0.370590 | + | 0.928797i | \(0.379155\pi\) | |||||||
\(752\) | 2.59533e7 | 1.67358 | ||||||||
\(753\) | −9.32313e6 | −0.599203 | ||||||||
\(754\) | −2.64009e7 | −1.69118 | ||||||||
\(755\) | −1.58571e7 | −1.01241 | ||||||||
\(756\) | 1.04249e7 | 0.663387 | ||||||||
\(757\) | −2.26799e7 | −1.43847 | −0.719236 | − | 0.694766i | \(-0.755508\pi\) | ||||
−0.719236 | + | 0.694766i | \(0.755508\pi\) | |||||||
\(758\) | −5.25407e7 | −3.32141 | ||||||||
\(759\) | 693643. | 0.0437051 | ||||||||
\(760\) | −4.07493e7 | −2.55909 | ||||||||
\(761\) | 1.63222e7 | 1.02169 | 0.510844 | − | 0.859673i | \(-0.329333\pi\) | ||||
0.510844 | + | 0.859673i | \(0.329333\pi\) | |||||||
\(762\) | 1.76987e7 | 1.10422 | ||||||||
\(763\) | 1.36298e7 | 0.847573 | ||||||||
\(764\) | 5.10145e7 | 3.16199 | ||||||||
\(765\) | −7.27205e6 | −0.449266 | ||||||||
\(766\) | 3.77035e6 | 0.232172 | ||||||||
\(767\) | 2.09477e6 | 0.128572 | ||||||||
\(768\) | −7.68794e6 | −0.470335 | ||||||||
\(769\) | −2.90386e7 | −1.77076 | −0.885379 | − | 0.464870i | \(-0.846101\pi\) | ||||
−0.885379 | + | 0.464870i | \(0.846101\pi\) | |||||||
\(770\) | −4.74992e7 | −2.88708 | ||||||||
\(771\) | 9.44769e6 | 0.572387 | ||||||||
\(772\) | −2.64962e7 | −1.60007 | ||||||||
\(773\) | 7.51073e6 | 0.452099 | 0.226050 | − | 0.974116i | \(-0.427419\pi\) | ||||
0.226050 | + | 0.974116i | \(0.427419\pi\) | |||||||
\(774\) | −1.37743e7 | −0.826450 | ||||||||
\(775\) | −6.35016e6 | −0.379779 | ||||||||
\(776\) | 8.24369e7 | 4.91436 | ||||||||
\(777\) | −3.26896e6 | −0.194248 | ||||||||
\(778\) | 2.70724e7 | 1.60353 | ||||||||
\(779\) | −3.30783e7 | −1.95299 | ||||||||
\(780\) | −1.94808e7 | −1.14649 | ||||||||
\(781\) | 4.42455e7 | 2.59562 | ||||||||
\(782\) | 2.93690e6 | 0.171740 | ||||||||
\(783\) | 3.04830e6 | 0.177686 | ||||||||
\(784\) | 4.30782e7 | 2.50304 | ||||||||
\(785\) | −3.18557e6 | −0.184507 | ||||||||
\(786\) | 1.89263e7 | 1.09272 | ||||||||
\(787\) | 2.97607e7 | 1.71280 | 0.856399 | − | 0.516315i | \(-0.172697\pi\) | ||||
0.856399 | + | 0.516315i | \(0.172697\pi\) | |||||||
\(788\) | −2.93219e7 | −1.68220 | ||||||||
\(789\) | −1.25073e7 | −0.715273 | ||||||||
\(790\) | 9.00513e6 | 0.513360 | ||||||||
\(791\) | 2.18272e7 | 1.24039 | ||||||||
\(792\) | −2.10144e7 | −1.19043 | ||||||||
\(793\) | 6.51596e6 | 0.367955 | ||||||||
\(794\) | −2.98647e7 | −1.68115 | ||||||||
\(795\) | 7.08431e6 | 0.397539 | ||||||||
\(796\) | −2.45244e7 | −1.37188 | ||||||||
\(797\) | 1.18682e7 | 0.661817 | 0.330909 | − | 0.943663i | \(-0.392645\pi\) | ||||
0.330909 | + | 0.943663i | \(0.392645\pi\) | |||||||
\(798\) | −3.16407e7 | −1.75889 | ||||||||
\(799\) | −1.96495e7 | −1.08889 | ||||||||
\(800\) | −1.15692e7 | −0.639114 | ||||||||
\(801\) | −4.97693e6 | −0.274082 | ||||||||
\(802\) | −2.23973e7 | −1.22959 | ||||||||
\(803\) | 1.39460e7 | 0.763238 | ||||||||
\(804\) | 3.73941e7 | 2.04015 | ||||||||
\(805\) | −1.21179e6 | −0.0659078 | ||||||||
\(806\) | −3.99784e7 | −2.16764 | ||||||||
\(807\) | −1.48997e7 | −0.805368 | ||||||||
\(808\) | 1.86576e7 | 1.00537 | ||||||||
\(809\) | −1.20080e7 | −0.645057 | −0.322528 | − | 0.946560i | \(-0.604533\pi\) | ||||
−0.322528 | + | 0.946560i | \(0.604533\pi\) | |||||||
\(810\) | 3.17112e6 | 0.169824 | ||||||||
\(811\) | 3.34804e7 | 1.78747 | 0.893734 | − | 0.448597i | \(-0.148076\pi\) | ||||
0.893734 | + | 0.448597i | \(0.148076\pi\) | |||||||
\(812\) | 5.97963e7 | 3.18261 | ||||||||
\(813\) | 8.01470e6 | 0.425266 | ||||||||
\(814\) | 1.11655e7 | 0.590630 | ||||||||
\(815\) | −2.00503e7 | −1.05737 | ||||||||
\(816\) | −4.51499e7 | −2.37373 | ||||||||
\(817\) | 2.96536e7 | 1.55426 | ||||||||
\(818\) | 1.76683e7 | 0.923233 | ||||||||
\(819\) | −8.92715e6 | −0.465053 | ||||||||
\(820\) | 6.50318e7 | 3.37747 | ||||||||
\(821\) | −2.19093e7 | −1.13441 | −0.567207 | − | 0.823575i | \(-0.691976\pi\) | ||||
−0.567207 | + | 0.823575i | \(0.691976\pi\) | |||||||
\(822\) | 6.17497e6 | 0.318754 | ||||||||
\(823\) | −1.77211e7 | −0.911994 | −0.455997 | − | 0.889981i | \(-0.650717\pi\) | ||||
−0.455997 | + | 0.889981i | \(0.650717\pi\) | |||||||
\(824\) | −4.15691e6 | −0.213281 | ||||||||
\(825\) | 4.84328e6 | 0.247745 | ||||||||
\(826\) | −6.68893e6 | −0.341120 | ||||||||
\(827\) | 1.64575e7 | 0.836759 | 0.418380 | − | 0.908272i | \(-0.362598\pi\) | ||||
0.418380 | + | 0.908272i | \(0.362598\pi\) | |||||||
\(828\) | −908404. | −0.0460472 | ||||||||
\(829\) | −7.42705e6 | −0.375345 | −0.187672 | − | 0.982232i | \(-0.560094\pi\) | ||||
−0.187672 | + | 0.982232i | \(0.560094\pi\) | |||||||
\(830\) | 5.07699e7 | 2.55806 | ||||||||
\(831\) | −6.73465e6 | −0.338308 | ||||||||
\(832\) | −2.32667e7 | −1.16527 | ||||||||
\(833\) | −3.26150e7 | −1.62856 | ||||||||
\(834\) | −9.68470e6 | −0.482138 | ||||||||
\(835\) | −1.30085e7 | −0.645670 | ||||||||
\(836\) | 7.66562e7 | 3.79343 | ||||||||
\(837\) | 4.61598e6 | 0.227746 | ||||||||
\(838\) | 6.44488e7 | 3.17033 | ||||||||
\(839\) | 728562. | 0.0357324 | 0.0178662 | − | 0.999840i | \(-0.494313\pi\) | ||||
0.0178662 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(840\) | 3.67119e7 | 1.79518 | ||||||||
\(841\) | −3.02636e6 | −0.147547 | ||||||||
\(842\) | −1.05393e7 | −0.512309 | ||||||||
\(843\) | 996923. | 0.0483162 | ||||||||
\(844\) | −2.99740e7 | −1.44840 | ||||||||
\(845\) | −422122. | −0.0203374 | ||||||||
\(846\) | 8.56853e6 | 0.411605 | ||||||||
\(847\) | 2.32384e7 | 1.11301 | ||||||||
\(848\) | 4.39843e7 | 2.10043 | ||||||||
\(849\) | −1.98543e6 | −0.0945332 | ||||||||
\(850\) | 2.05065e7 | 0.973521 | ||||||||
\(851\) | 284850. | 0.0134832 | ||||||||
\(852\) | −5.79445e7 | −2.73472 | ||||||||
\(853\) | 325772. | 0.0153300 | 0.00766499 | − | 0.999971i | \(-0.497560\pi\) | ||||
0.00766499 | + | 0.999971i | \(0.497560\pi\) | |||||||
\(854\) | −2.08065e7 | −0.976235 | ||||||||
\(855\) | −6.82686e6 | −0.319379 | ||||||||
\(856\) | −2.18354e7 | −1.01854 | ||||||||
\(857\) | 6.77652e6 | 0.315177 | 0.157589 | − | 0.987505i | \(-0.449628\pi\) | ||||
0.157589 | + | 0.987505i | \(0.449628\pi\) | |||||||
\(858\) | 3.04916e7 | 1.41404 | ||||||||
\(859\) | −1.74661e7 | −0.807631 | −0.403815 | − | 0.914840i | \(-0.632316\pi\) | ||||
−0.403815 | + | 0.914840i | \(0.632316\pi\) | |||||||
\(860\) | −5.82989e7 | −2.68790 | ||||||||
\(861\) | 2.98010e7 | 1.37001 | ||||||||
\(862\) | 2.67426e7 | 1.22585 | ||||||||
\(863\) | −1.22281e7 | −0.558897 | −0.279449 | − | 0.960161i | \(-0.590152\pi\) | ||||
−0.279449 | + | 0.960161i | \(0.590152\pi\) | |||||||
\(864\) | 8.40973e6 | 0.383264 | ||||||||
\(865\) | −2.49986e7 | −1.13599 | ||||||||
\(866\) | −5.23459e7 | −2.37185 | ||||||||
\(867\) | 2.14047e7 | 0.967080 | ||||||||
\(868\) | 9.05483e7 | 4.07926 | ||||||||
\(869\) | −9.99760e6 | −0.449103 | ||||||||
\(870\) | 1.81893e7 | 0.814736 | ||||||||
\(871\) | −3.20217e7 | −1.43021 | ||||||||
\(872\) | 3.59813e7 | 1.60245 | ||||||||
\(873\) | 1.38109e7 | 0.613320 | ||||||||
\(874\) | 2.75711e6 | 0.122089 | ||||||||
\(875\) | −3.48263e7 | −1.53776 | ||||||||
\(876\) | −1.82638e7 | −0.804139 | ||||||||
\(877\) | −2.26822e7 | −0.995834 | −0.497917 | − | 0.867225i | \(-0.665902\pi\) | ||||
−0.497917 | + | 0.867225i | \(0.665902\pi\) | |||||||
\(878\) | −1.04559e7 | −0.457746 | ||||||||
\(879\) | 1.39971e7 | 0.611037 | ||||||||
\(880\) | −6.36299e7 | −2.76984 | ||||||||
\(881\) | −1.07389e7 | −0.466145 | −0.233073 | − | 0.972459i | \(-0.574878\pi\) | ||||
−0.233073 | + | 0.972459i | \(0.574878\pi\) | |||||||
\(882\) | 1.42224e7 | 0.615603 | ||||||||
\(883\) | 1.63107e7 | 0.703997 | 0.351999 | − | 0.936001i | \(-0.385502\pi\) | ||||
0.351999 | + | 0.936001i | \(0.385502\pi\) | |||||||
\(884\) | 9.15729e7 | 3.94127 | ||||||||
\(885\) | −1.44322e6 | −0.0619403 | ||||||||
\(886\) | −6.39200e7 | −2.73560 | ||||||||
\(887\) | 1.28289e6 | 0.0547493 | 0.0273747 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273747 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(888\) | −8.62973e6 | −0.367253 | ||||||||
\(889\) | 3.43271e7 | 1.45674 | ||||||||
\(890\) | −2.96974e7 | −1.25674 | ||||||||
\(891\) | −3.52061e6 | −0.148568 | ||||||||
\(892\) | −3.96514e7 | −1.66858 | ||||||||
\(893\) | −1.84466e7 | −0.774081 | ||||||||
\(894\) | 3.89596e7 | 1.63031 | ||||||||
\(895\) | −1.66490e6 | −0.0694754 | ||||||||
\(896\) | 6.68590e6 | 0.278221 | ||||||||
\(897\) | 777894. | 0.0322804 | ||||||||
\(898\) | 1.89021e7 | 0.782201 | ||||||||
\(899\) | 2.64769e7 | 1.09262 | ||||||||
\(900\) | −6.34281e6 | −0.261021 | ||||||||
\(901\) | −3.33010e7 | −1.36661 | ||||||||
\(902\) | −1.01788e8 | −4.16564 | ||||||||
\(903\) | −2.67156e7 | −1.09030 | ||||||||
\(904\) | 5.76219e7 | 2.34513 | ||||||||
\(905\) | −2.75168e7 | −1.11680 | ||||||||
\(906\) | −3.25041e7 | −1.31558 | ||||||||
\(907\) | −2.80898e7 | −1.13379 | −0.566893 | − | 0.823791i | \(-0.691855\pi\) | ||||
−0.566893 | + | 0.823791i | \(0.691855\pi\) | |||||||
\(908\) | 9.64523e7 | 3.88238 | ||||||||
\(909\) | 3.12576e6 | 0.125472 | ||||||||
\(910\) | −5.32684e7 | −2.13239 | ||||||||
\(911\) | 3.24554e7 | 1.29566 | 0.647829 | − | 0.761785i | \(-0.275677\pi\) | ||||
0.647829 | + | 0.761785i | \(0.275677\pi\) | |||||||
\(912\) | −4.23859e7 | −1.68746 | ||||||||
\(913\) | −5.63654e7 | −2.23787 | ||||||||
\(914\) | −3.68886e7 | −1.46058 | ||||||||
\(915\) | −4.48925e6 | −0.177264 | ||||||||
\(916\) | 7.35484e7 | 2.89624 | ||||||||
\(917\) | 3.67081e7 | 1.44158 | ||||||||
\(918\) | −1.49064e7 | −0.583801 | ||||||||
\(919\) | −2.73570e7 | −1.06851 | −0.534256 | − | 0.845323i | \(-0.679408\pi\) | ||||
−0.534256 | + | 0.845323i | \(0.679408\pi\) | |||||||
\(920\) | −3.19900e6 | −0.124608 | ||||||||
\(921\) | −9.01680e6 | −0.350270 | ||||||||
\(922\) | 7.28724e7 | 2.82316 | ||||||||
\(923\) | 4.96196e7 | 1.91712 | ||||||||
\(924\) | −6.90612e7 | −2.66106 | ||||||||
\(925\) | 1.98893e6 | 0.0764302 | ||||||||
\(926\) | −5.02480e7 | −1.92571 | ||||||||
\(927\) | −696421. | −0.0266178 | ||||||||
\(928\) | 4.82375e7 | 1.83872 | ||||||||
\(929\) | −2.68916e7 | −1.02230 | −0.511148 | − | 0.859493i | \(-0.670780\pi\) | ||||
−0.511148 | + | 0.859493i | \(0.670780\pi\) | |||||||
\(930\) | 2.75436e7 | 1.04427 | ||||||||
\(931\) | −3.06183e7 | −1.15773 | ||||||||
\(932\) | 1.95177e7 | 0.736019 | ||||||||
\(933\) | 2.40032e7 | 0.902745 | ||||||||
\(934\) | 2.75472e7 | 1.03326 | ||||||||
\(935\) | 4.81748e7 | 1.80215 | ||||||||
\(936\) | −2.35668e7 | −0.879248 | ||||||||
\(937\) | −3.27080e7 | −1.21704 | −0.608520 | − | 0.793538i | \(-0.708237\pi\) | ||||
−0.608520 | + | 0.793538i | \(0.708237\pi\) | |||||||
\(938\) | 1.02250e8 | 3.79453 | ||||||||
\(939\) | 1.69660e7 | 0.627935 | ||||||||
\(940\) | 3.62658e7 | 1.33868 | ||||||||
\(941\) | 2.24893e7 | 0.827947 | 0.413973 | − | 0.910289i | \(-0.364141\pi\) | ||||
0.413973 | + | 0.910289i | \(0.364141\pi\) | |||||||
\(942\) | −6.52984e6 | −0.239759 | ||||||||
\(943\) | −2.59680e6 | −0.0950953 | ||||||||
\(944\) | −8.96049e6 | −0.327267 | ||||||||
\(945\) | 6.15047e6 | 0.224042 | ||||||||
\(946\) | 9.12498e7 | 3.31516 | ||||||||
\(947\) | −2.60237e7 | −0.942963 | −0.471482 | − | 0.881876i | \(-0.656281\pi\) | ||||
−0.471482 | + | 0.881876i | \(0.656281\pi\) | |||||||
\(948\) | 1.30930e7 | 0.473170 | ||||||||
\(949\) | 1.56399e7 | 0.563725 | ||||||||
\(950\) | 1.92512e7 | 0.692066 | ||||||||
\(951\) | −2.49466e7 | −0.894459 | ||||||||
\(952\) | −1.72570e8 | −6.17126 | ||||||||
\(953\) | −4.54892e7 | −1.62247 | −0.811233 | − | 0.584722i | \(-0.801203\pi\) | ||||
−0.811233 | + | 0.584722i | \(0.801203\pi\) | |||||||
\(954\) | 1.45215e7 | 0.516584 | ||||||||
\(955\) | 3.00975e7 | 1.06788 | ||||||||
\(956\) | 1.10156e8 | 3.89819 | ||||||||
\(957\) | −2.01939e7 | −0.712756 | ||||||||
\(958\) | −2.20362e7 | −0.775753 | ||||||||
\(959\) | 1.19765e7 | 0.420517 | ||||||||
\(960\) | 1.60299e7 | 0.561373 | ||||||||
\(961\) | 1.14642e7 | 0.400439 | ||||||||
\(962\) | 1.25216e7 | 0.436237 | ||||||||
\(963\) | −3.65815e6 | −0.127115 | ||||||||
\(964\) | 2.00908e6 | 0.0696315 | ||||||||
\(965\) | −1.56322e7 | −0.540383 | ||||||||
\(966\) | −2.48394e6 | −0.0856442 | ||||||||
\(967\) | 3.16445e7 | 1.08826 | 0.544129 | − | 0.839002i | \(-0.316860\pi\) | ||||
0.544129 | + | 0.839002i | \(0.316860\pi\) | |||||||
\(968\) | 6.13472e7 | 2.10429 | ||||||||
\(969\) | 3.20908e7 | 1.09792 | ||||||||
\(970\) | 8.24100e7 | 2.81223 | ||||||||
\(971\) | −2.31685e7 | −0.788587 | −0.394293 | − | 0.918985i | \(-0.629011\pi\) | ||||
−0.394293 | + | 0.918985i | \(0.629011\pi\) | |||||||
\(972\) | 4.61064e6 | 0.156529 | ||||||||
\(973\) | −1.87837e7 | −0.636063 | ||||||||
\(974\) | −4.13760e7 | −1.39750 | ||||||||
\(975\) | 5.43154e6 | 0.182983 | ||||||||
\(976\) | −2.78724e7 | −0.936590 | ||||||||
\(977\) | −1.39480e7 | −0.467492 | −0.233746 | − | 0.972298i | \(-0.575098\pi\) | ||||
−0.233746 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(978\) | −4.10995e7 | −1.37401 | ||||||||
\(979\) | 3.29704e7 | 1.09943 | ||||||||
\(980\) | 6.01954e7 | 2.00216 | ||||||||
\(981\) | 6.02806e6 | 0.199989 | ||||||||
\(982\) | 3.95939e6 | 0.131024 | ||||||||
\(983\) | −9.57136e6 | −0.315929 | −0.157965 | − | 0.987445i | \(-0.550493\pi\) | ||||
−0.157965 | + | 0.987445i | \(0.550493\pi\) | |||||||
\(984\) | 7.86718e7 | 2.59019 | ||||||||
\(985\) | −1.72993e7 | −0.568118 | ||||||||
\(986\) | −8.55016e7 | −2.80080 | ||||||||
\(987\) | 1.66189e7 | 0.543012 | ||||||||
\(988\) | 8.59669e7 | 2.80181 | ||||||||
\(989\) | 2.32794e6 | 0.0756801 | ||||||||
\(990\) | −2.10075e7 | −0.681220 | ||||||||
\(991\) | −3.03725e7 | −0.982417 | −0.491209 | − | 0.871042i | \(-0.663445\pi\) | ||||
−0.491209 | + | 0.871042i | \(0.663445\pi\) | |||||||
\(992\) | 7.30451e7 | 2.35674 | ||||||||
\(993\) | −3.19627e7 | −1.02866 | ||||||||
\(994\) | −1.58443e8 | −5.08637 | ||||||||
\(995\) | −1.44689e7 | −0.463317 | ||||||||
\(996\) | 7.38167e7 | 2.35780 | ||||||||
\(997\) | −2.69504e7 | −0.858671 | −0.429336 | − | 0.903145i | \(-0.641252\pi\) | ||||
−0.429336 | + | 0.903145i | \(0.641252\pi\) | |||||||
\(998\) | −3.11069e7 | −0.988623 | ||||||||
\(999\) | −1.44577e6 | −0.0458337 |
(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.c.1.11 | ✓ | 12 | |
3.2 | odd | 2 | 531.6.a.c.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.c.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial | |
531.6.a.c.1.2 | 12 | 3.2 | odd | 2 |