Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
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, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.6 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.35 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.10324i | − | 1.52581i | −0.646511 | − | 0.762905i | \(-0.723773\pi\) | ||
0.646511 | − | 0.762905i | \(-0.276227\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −21.2495 | −1.32809 | ||||||||
\(5\) | −12.8499 | −0.513997 | −0.256999 | − | 0.966412i | \(-0.582734\pi\) | ||||
−0.256999 | + | 0.966412i | \(0.582734\pi\) | |||||||
\(6\) | 31.7133i | 0.880926i | ||||||||
\(7\) | 4.61608 | 0.0942058 | 0.0471029 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471029 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(8\) | 32.0389i | 0.500608i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 78.4262i | 0.784262i | ||||||||
\(11\) | 159.523i | 1.31837i | 0.751980 | + | 0.659186i | \(0.229099\pi\) | ||||
−0.751980 | + | 0.659186i | \(0.770901\pi\) | |||||||
\(12\) | 110.416 | 0.766775 | ||||||||
\(13\) | 148.997i | 0.881638i | 0.897596 | + | 0.440819i | \(0.145312\pi\) | ||||
−0.897596 | + | 0.440819i | \(0.854688\pi\) | |||||||
\(14\) | − | 28.1731i | − | 0.143740i | ||||||
\(15\) | 66.7702 | 0.296756 | ||||||||
\(16\) | −144.451 | −0.564261 | ||||||||
\(17\) | 154.411 | 0.534293 | 0.267147 | − | 0.963656i | \(-0.413919\pi\) | ||||
0.267147 | + | 0.963656i | \(0.413919\pi\) | |||||||
\(18\) | − | 164.787i | − | 0.508603i | ||||||
\(19\) | 313.342 | 0.867982 | 0.433991 | − | 0.900917i | \(-0.357105\pi\) | ||||
0.433991 | + | 0.900917i | \(0.357105\pi\) | |||||||
\(20\) | 273.055 | 0.682636 | ||||||||
\(21\) | −23.9859 | −0.0543897 | ||||||||
\(22\) | 973.607 | 2.01158 | ||||||||
\(23\) | − | 420.147i | − | 0.794228i | −0.917769 | − | 0.397114i | \(-0.870012\pi\) | ||
0.917769 | − | 0.397114i | \(-0.129988\pi\) | |||||||
\(24\) | − | 166.479i | − | 0.289026i | ||||||
\(25\) | −459.879 | −0.735807 | ||||||||
\(26\) | 909.363 | 1.34521 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −98.0895 | −0.125114 | ||||||||
\(29\) | 1422.43 | 1.69136 | 0.845680 | − | 0.533690i | \(-0.179195\pi\) | ||||
0.845680 | + | 0.533690i | \(0.179195\pi\) | |||||||
\(30\) | − | 407.514i | − | 0.452794i | ||||||
\(31\) | − | 1100.16i | − | 1.14481i | −0.819972 | − | 0.572403i | \(-0.806011\pi\) | ||
0.819972 | − | 0.572403i | \(-0.193989\pi\) | |||||||
\(32\) | 1394.24i | 1.36156i | ||||||||
\(33\) | − | 828.906i | − | 0.761163i | ||||||
\(34\) | − | 942.405i | − | 0.815230i | ||||||
\(35\) | −59.3164 | −0.0484215 | ||||||||
\(36\) | −573.736 | −0.442698 | ||||||||
\(37\) | − | 186.690i | − | 0.136370i | −0.997673 | − | 0.0681848i | \(-0.978279\pi\) | ||
0.997673 | − | 0.0681848i | \(-0.0217207\pi\) | |||||||
\(38\) | − | 1912.40i | − | 1.32437i | ||||||
\(39\) | − | 774.211i | − | 0.509014i | ||||||
\(40\) | − | 411.698i | − | 0.257311i | ||||||
\(41\) | 435.578 | 0.259118 | 0.129559 | − | 0.991572i | \(-0.458644\pi\) | ||||
0.129559 | + | 0.991572i | \(0.458644\pi\) | |||||||
\(42\) | 146.391i | 0.0829884i | ||||||||
\(43\) | 2365.57i | 1.27938i | 0.768634 | + | 0.639689i | \(0.220937\pi\) | ||||
−0.768634 | + | 0.639689i | \(0.779063\pi\) | |||||||
\(44\) | − | 3389.78i | − | 1.75092i | ||||||
\(45\) | −346.948 | −0.171332 | ||||||||
\(46\) | −2564.25 | −1.21184 | ||||||||
\(47\) | 2367.77i | 1.07187i | 0.844258 | + | 0.535937i | \(0.180042\pi\) | ||||
−0.844258 | + | 0.535937i | \(0.819958\pi\) | |||||||
\(48\) | 750.588 | 0.325776 | ||||||||
\(49\) | −2379.69 | −0.991125 | ||||||||
\(50\) | 2806.75i | 1.12270i | ||||||||
\(51\) | −802.342 | −0.308474 | ||||||||
\(52\) | − | 3166.11i | − | 1.17090i | ||||||
\(53\) | 3945.26 | 1.40451 | 0.702254 | − | 0.711927i | \(-0.252177\pi\) | ||||
0.702254 | + | 0.711927i | \(0.252177\pi\) | |||||||
\(54\) | 856.260i | 0.293642i | ||||||||
\(55\) | − | 2049.86i | − | 0.677640i | ||||||
\(56\) | 147.894i | 0.0471602i | ||||||||
\(57\) | −1628.17 | −0.501130 | ||||||||
\(58\) | − | 8681.45i | − | 2.58069i | ||||||
\(59\) | 2040.07 | + | 2820.55i | 0.586057 | + | 0.810270i | ||||
\(60\) | −1418.83 | −0.394120 | ||||||||
\(61\) | 1734.71i | 0.466194i | 0.972453 | + | 0.233097i | \(0.0748860\pi\) | ||||
−0.972453 | + | 0.233097i | \(0.925114\pi\) | |||||||
\(62\) | −6714.53 | −1.74676 | ||||||||
\(63\) | 124.634 | 0.0314019 | ||||||||
\(64\) | 6198.17 | 1.51322 | ||||||||
\(65\) | − | 1914.60i | − | 0.453160i | ||||||
\(66\) | −5059.01 | −1.16139 | ||||||||
\(67\) | − | 2714.23i | − | 0.604640i | −0.953206 | − | 0.302320i | \(-0.902239\pi\) | ||
0.953206 | − | 0.302320i | \(-0.0977611\pi\) | |||||||
\(68\) | −3281.15 | −0.709592 | ||||||||
\(69\) | 2183.15i | 0.458548i | ||||||||
\(70\) | 362.022i | 0.0738820i | ||||||||
\(71\) | 5431.15 | 1.07740 | 0.538698 | − | 0.842499i | \(-0.318916\pi\) | ||||
0.538698 | + | 0.842499i | \(0.318916\pi\) | |||||||
\(72\) | 865.051i | 0.166869i | ||||||||
\(73\) | − | 2072.73i | − | 0.388953i | −0.980907 | − | 0.194476i | \(-0.937699\pi\) | ||
0.980907 | − | 0.194476i | \(-0.0623008\pi\) | |||||||
\(74\) | −1139.41 | −0.208074 | ||||||||
\(75\) | 2389.60 | 0.424818 | ||||||||
\(76\) | −6658.35 | −1.15276 | ||||||||
\(77\) | 736.372i | 0.124198i | ||||||||
\(78\) | −4725.19 | −0.776659 | ||||||||
\(79\) | 10773.3 | 1.72622 | 0.863108 | − | 0.505019i | \(-0.168515\pi\) | ||||
0.863108 | + | 0.505019i | \(0.168515\pi\) | |||||||
\(80\) | 1856.18 | 0.290029 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 2658.44i | − | 0.395365i | ||||||
\(83\) | 10956.5i | 1.59044i | 0.606321 | + | 0.795220i | \(0.292645\pi\) | ||||
−0.606321 | + | 0.795220i | \(0.707355\pi\) | |||||||
\(84\) | 509.688 | 0.0722347 | ||||||||
\(85\) | −1984.17 | −0.274625 | ||||||||
\(86\) | 14437.6 | 1.95209 | ||||||||
\(87\) | −7391.19 | −0.976508 | ||||||||
\(88\) | −5110.95 | −0.659988 | ||||||||
\(89\) | 1731.25i | 0.218565i | 0.994011 | + | 0.109283i | \(0.0348553\pi\) | ||||
−0.994011 | + | 0.109283i | \(0.965145\pi\) | |||||||
\(90\) | 2117.51i | 0.261421i | ||||||||
\(91\) | 687.782i | 0.0830555i | ||||||||
\(92\) | 8927.90i | 1.05481i | ||||||||
\(93\) | 5716.59i | 0.660954i | ||||||||
\(94\) | 14451.1 | 1.63547 | ||||||||
\(95\) | −4026.42 | −0.446140 | ||||||||
\(96\) | − | 7244.69i | − | 0.786099i | ||||||
\(97\) | 3594.71i | 0.382050i | 0.981585 | + | 0.191025i | \(0.0611812\pi\) | ||||
−0.981585 | + | 0.191025i | \(0.938819\pi\) | |||||||
\(98\) | 14523.8i | 1.51227i | ||||||||
\(99\) | 4307.12i | 0.439457i | ||||||||
\(100\) | 9772.20 | 0.977220 | ||||||||
\(101\) | 9157.70i | 0.897726i | 0.893601 | + | 0.448863i | \(0.148171\pi\) | ||||
−0.893601 | + | 0.448863i | \(0.851829\pi\) | |||||||
\(102\) | 4896.88i | 0.470673i | ||||||||
\(103\) | 2682.66i | 0.252866i | 0.991975 | + | 0.126433i | \(0.0403529\pi\) | ||||
−0.991975 | + | 0.126433i | \(0.959647\pi\) | |||||||
\(104\) | −4773.70 | −0.441355 | ||||||||
\(105\) | 308.217 | 0.0279562 | ||||||||
\(106\) | − | 24078.9i | − | 2.14301i | ||||||
\(107\) | −3938.64 | −0.344016 | −0.172008 | − | 0.985096i | \(-0.555026\pi\) | ||||
−0.172008 | + | 0.985096i | \(0.555026\pi\) | |||||||
\(108\) | 2981.22 | 0.255592 | ||||||||
\(109\) | 11260.3i | 0.947754i | 0.880591 | + | 0.473877i | \(0.157146\pi\) | ||||
−0.880591 | + | 0.473877i | \(0.842854\pi\) | |||||||
\(110\) | −12510.8 | −1.03395 | ||||||||
\(111\) | 970.069i | 0.0787330i | ||||||||
\(112\) | −666.797 | −0.0531567 | ||||||||
\(113\) | 9397.40i | 0.735954i | 0.929835 | + | 0.367977i | \(0.119950\pi\) | ||||
−0.929835 | + | 0.367977i | \(0.880050\pi\) | |||||||
\(114\) | 9937.11i | 0.764628i | ||||||||
\(115\) | 5398.85i | 0.408231i | ||||||||
\(116\) | −30226.0 | −2.24629 | ||||||||
\(117\) | 4022.92i | 0.293879i | ||||||||
\(118\) | 17214.5 | − | 12451.0i | 1.23632 | − | 0.894212i | ||||
\(119\) | 712.773 | 0.0503335 | ||||||||
\(120\) | 2139.25i | 0.148559i | ||||||||
\(121\) | −10806.6 | −0.738105 | ||||||||
\(122\) | 10587.3 | 0.711323 | ||||||||
\(123\) | −2263.33 | −0.149602 | ||||||||
\(124\) | 23377.8i | 1.52041i | ||||||||
\(125\) | 13940.6 | 0.892200 | ||||||||
\(126\) | − | 760.673i | − | 0.0479134i | ||||||
\(127\) | −9401.70 | −0.582906 | −0.291453 | − | 0.956585i | \(-0.594139\pi\) | ||||
−0.291453 | + | 0.956585i | \(0.594139\pi\) | |||||||
\(128\) | − | 15521.0i | − | 0.947328i | ||||||
\(129\) | − | 12291.9i | − | 0.738649i | ||||||
\(130\) | −11685.3 | −0.691435 | ||||||||
\(131\) | − | 28050.5i | − | 1.63455i | −0.576249 | − | 0.817274i | \(-0.695484\pi\) | ||
0.576249 | − | 0.817274i | \(-0.304516\pi\) | |||||||
\(132\) | 17613.8i | 1.01090i | ||||||||
\(133\) | 1446.41 | 0.0817690 | ||||||||
\(134\) | −16565.6 | −0.922566 | ||||||||
\(135\) | 1802.80 | 0.0989188 | ||||||||
\(136\) | 4947.16i | 0.267472i | ||||||||
\(137\) | −10546.1 | −0.561888 | −0.280944 | − | 0.959724i | \(-0.590648\pi\) | ||||
−0.280944 | + | 0.959724i | \(0.590648\pi\) | |||||||
\(138\) | 13324.3 | 0.699656 | ||||||||
\(139\) | 13525.1 | 0.700020 | 0.350010 | − | 0.936746i | \(-0.386178\pi\) | ||||
0.350010 | + | 0.936746i | \(0.386178\pi\) | |||||||
\(140\) | 1260.44 | 0.0643083 | ||||||||
\(141\) | − | 12303.3i | − | 0.618847i | ||||||
\(142\) | − | 33147.6i | − | 1.64390i | ||||||
\(143\) | −23768.4 | −1.16233 | ||||||||
\(144\) | −3900.17 | −0.188087 | ||||||||
\(145\) | −18278.2 | −0.869355 | ||||||||
\(146\) | −12650.4 | −0.593468 | ||||||||
\(147\) | 12365.2 | 0.572226 | ||||||||
\(148\) | 3967.07i | 0.181112i | ||||||||
\(149\) | − | 4534.58i | − | 0.204251i | −0.994772 | − | 0.102126i | \(-0.967436\pi\) | ||
0.994772 | − | 0.102126i | \(-0.0325644\pi\) | |||||||
\(150\) | − | 14584.3i | − | 0.648192i | ||||||
\(151\) | 28293.6i | 1.24089i | 0.784249 | + | 0.620446i | \(0.213048\pi\) | ||||
−0.784249 | + | 0.620446i | \(0.786952\pi\) | |||||||
\(152\) | 10039.1i | 0.434519i | ||||||||
\(153\) | 4169.09 | 0.178098 | ||||||||
\(154\) | 4494.25 | 0.189503 | ||||||||
\(155\) | 14137.0i | 0.588427i | ||||||||
\(156\) | 16451.6i | 0.676019i | ||||||||
\(157\) | − | 8264.64i | − | 0.335293i | −0.985847 | − | 0.167647i | \(-0.946383\pi\) | ||
0.985847 | − | 0.167647i | \(-0.0536167\pi\) | |||||||
\(158\) | − | 65752.1i | − | 2.63388i | ||||||
\(159\) | −20500.2 | −0.810893 | ||||||||
\(160\) | − | 17915.9i | − | 0.699839i | ||||||
\(161\) | − | 1939.43i | − | 0.0748209i | ||||||
\(162\) | − | 4449.26i | − | 0.169534i | ||||||
\(163\) | −22072.4 | −0.830759 | −0.415379 | − | 0.909648i | \(-0.636351\pi\) | ||||
−0.415379 | + | 0.909648i | \(0.636351\pi\) | |||||||
\(164\) | −9255.81 | −0.344133 | ||||||||
\(165\) | 10651.4i | 0.391235i | ||||||||
\(166\) | 66870.4 | 2.42671 | ||||||||
\(167\) | −13873.2 | −0.497445 | −0.248723 | − | 0.968575i | \(-0.580011\pi\) | ||||
−0.248723 | + | 0.968575i | \(0.580011\pi\) | |||||||
\(168\) | − | 768.482i | − | 0.0272280i | ||||||
\(169\) | 6360.93 | 0.222714 | ||||||||
\(170\) | 12109.8i | 0.419026i | ||||||||
\(171\) | 8460.22 | 0.289327 | ||||||||
\(172\) | − | 50267.2i | − | 1.69913i | ||||||
\(173\) | 26589.0i | 0.888402i | 0.895927 | + | 0.444201i | \(0.146512\pi\) | ||||
−0.895927 | + | 0.444201i | \(0.853488\pi\) | |||||||
\(174\) | 45110.2i | 1.48996i | ||||||||
\(175\) | −2122.84 | −0.0693173 | ||||||||
\(176\) | − | 23043.2i | − | 0.743906i | ||||||
\(177\) | −10600.5 | − | 14656.0i | −0.338360 | − | 0.467809i | ||||
\(178\) | 10566.3 | 0.333489 | ||||||||
\(179\) | − | 23765.9i | − | 0.741735i | −0.928686 | − | 0.370867i | \(-0.879060\pi\) | ||
0.928686 | − | 0.370867i | \(-0.120940\pi\) | |||||||
\(180\) | 7372.47 | 0.227545 | ||||||||
\(181\) | −25062.8 | −0.765019 | −0.382510 | − | 0.923951i | \(-0.624940\pi\) | ||||
−0.382510 | + | 0.923951i | \(0.624940\pi\) | |||||||
\(182\) | 4197.70 | 0.126727 | ||||||||
\(183\) | − | 9013.81i | − | 0.269157i | ||||||
\(184\) | 13461.0 | 0.397597 | ||||||||
\(185\) | 2398.95i | 0.0700936i | ||||||||
\(186\) | 34889.7 | 1.00849 | ||||||||
\(187\) | 24632.1i | 0.704397i | ||||||||
\(188\) | − | 50313.9i | − | 1.42355i | ||||||
\(189\) | −647.619 | −0.0181299 | ||||||||
\(190\) | 24574.2i | 0.680725i | ||||||||
\(191\) | − | 8426.68i | − | 0.230988i | −0.993308 | − | 0.115494i | \(-0.963155\pi\) | ||
0.993308 | − | 0.115494i | \(-0.0368451\pi\) | |||||||
\(192\) | −32206.6 | −0.873660 | ||||||||
\(193\) | 5162.04 | 0.138582 | 0.0692910 | − | 0.997596i | \(-0.477926\pi\) | ||||
0.0692910 | + | 0.997596i | \(0.477926\pi\) | |||||||
\(194\) | 21939.4 | 0.582936 | ||||||||
\(195\) | 9948.55i | 0.261632i | ||||||||
\(196\) | 50567.3 | 1.31631 | ||||||||
\(197\) | 13261.3 | 0.341707 | 0.170853 | − | 0.985296i | \(-0.445348\pi\) | ||||
0.170853 | + | 0.985296i | \(0.445348\pi\) | |||||||
\(198\) | 26287.4 | 0.670528 | ||||||||
\(199\) | −19128.2 | −0.483022 | −0.241511 | − | 0.970398i | \(-0.577643\pi\) | ||||
−0.241511 | + | 0.970398i | \(0.577643\pi\) | |||||||
\(200\) | − | 14734.0i | − | 0.368351i | ||||||
\(201\) | 14103.6i | 0.349089i | ||||||||
\(202\) | 55891.6 | 1.36976 | ||||||||
\(203\) | 6566.08 | 0.159336 | ||||||||
\(204\) | 17049.4 | 0.409683 | ||||||||
\(205\) | −5597.15 | −0.133186 | ||||||||
\(206\) | 16372.9 | 0.385825 | ||||||||
\(207\) | − | 11344.0i | − | 0.264743i | ||||||
\(208\) | − | 21522.7i | − | 0.497474i | ||||||
\(209\) | 49985.2i | 1.14432i | ||||||||
\(210\) | − | 1881.12i | − | 0.0426558i | ||||||
\(211\) | − | 88561.9i | − | 1.98922i | −0.103705 | − | 0.994608i | \(-0.533070\pi\) | ||
0.103705 | − | 0.994608i | \(-0.466930\pi\) | |||||||
\(212\) | −83834.9 | −1.86532 | ||||||||
\(213\) | −28221.1 | −0.622035 | ||||||||
\(214\) | 24038.5i | 0.524903i | ||||||||
\(215\) | − | 30397.4i | − | 0.657597i | ||||||
\(216\) | − | 4494.94i | − | 0.0963421i | ||||||
\(217\) | − | 5078.43i | − | 0.107847i | ||||||
\(218\) | 68724.1 | 1.44609 | ||||||||
\(219\) | 10770.2i | 0.224562i | ||||||||
\(220\) | 43558.5i | 0.899969i | ||||||||
\(221\) | 23006.7i | 0.471053i | ||||||||
\(222\) | 5920.56 | 0.120132 | ||||||||
\(223\) | 19289.2 | 0.387885 | 0.193943 | − | 0.981013i | \(-0.437872\pi\) | ||||
0.193943 | + | 0.981013i | \(0.437872\pi\) | |||||||
\(224\) | 6435.93i | 0.128267i | ||||||||
\(225\) | −12416.7 | −0.245269 | ||||||||
\(226\) | 57354.6 | 1.12293 | ||||||||
\(227\) | 27309.5i | 0.529983i | 0.964251 | + | 0.264991i | \(0.0853691\pi\) | ||||
−0.964251 | + | 0.264991i | \(0.914631\pi\) | |||||||
\(228\) | 34597.8 | 0.665547 | ||||||||
\(229\) | − | 7085.68i | − | 0.135117i | −0.997715 | − | 0.0675586i | \(-0.978479\pi\) | ||
0.997715 | − | 0.0675586i | \(-0.0215210\pi\) | |||||||
\(230\) | 32950.5 | 0.622882 | ||||||||
\(231\) | − | 3826.30i | − | 0.0717059i | ||||||
\(232\) | 45573.3i | 0.846709i | ||||||||
\(233\) | 59816.5i | 1.10182i | 0.834566 | + | 0.550908i | \(0.185719\pi\) | ||||
−0.834566 | + | 0.550908i | \(0.814281\pi\) | |||||||
\(234\) | 24552.8 | 0.448404 | ||||||||
\(235\) | − | 30425.7i | − | 0.550940i | ||||||
\(236\) | −43350.4 | − | 59935.2i | −0.778339 | − | 1.07611i | ||||
\(237\) | −55979.8 | −0.996631 | ||||||||
\(238\) | − | 4350.22i | − | 0.0767994i | ||||||
\(239\) | 78985.4 | 1.38277 | 0.691387 | − | 0.722485i | \(-0.257000\pi\) | ||||
0.691387 | + | 0.722485i | \(0.257000\pi\) | |||||||
\(240\) | −9645.01 | −0.167448 | ||||||||
\(241\) | −50419.4 | −0.868088 | −0.434044 | − | 0.900892i | \(-0.642914\pi\) | ||||
−0.434044 | + | 0.900892i | \(0.642914\pi\) | |||||||
\(242\) | 65955.2i | 1.12621i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | − | 36861.7i | − | 0.619149i | ||||||
\(245\) | 30578.9 | 0.509436 | ||||||||
\(246\) | 13813.6i | 0.228264i | ||||||||
\(247\) | 46686.9i | 0.765246i | ||||||||
\(248\) | 35247.9 | 0.573099 | ||||||||
\(249\) | − | 56931.9i | − | 0.918241i | ||||||
\(250\) | − | 85082.9i | − | 1.36133i | ||||||
\(251\) | 107267. | 1.70262 | 0.851312 | − | 0.524660i | \(-0.175807\pi\) | ||||
0.851312 | + | 0.524660i | \(0.175807\pi\) | |||||||
\(252\) | −2648.42 | −0.0417047 | ||||||||
\(253\) | 67023.0 | 1.04709 | ||||||||
\(254\) | 57380.8i | 0.889404i | ||||||||
\(255\) | 10310.0 | 0.158555 | ||||||||
\(256\) | 4442.15 | 0.0677818 | ||||||||
\(257\) | 52186.5 | 0.790118 | 0.395059 | − | 0.918656i | \(-0.370724\pi\) | ||||
0.395059 | + | 0.918656i | \(0.370724\pi\) | |||||||
\(258\) | −75020.2 | −1.12704 | ||||||||
\(259\) | − | 861.776i | − | 0.0128468i | ||||||
\(260\) | 40684.3i | 0.601838i | ||||||||
\(261\) | 38405.7 | 0.563787 | ||||||||
\(262\) | −171199. | −2.49401 | ||||||||
\(263\) | −109997. | −1.59026 | −0.795132 | − | 0.606436i | \(-0.792599\pi\) | ||||
−0.795132 | + | 0.606436i | \(0.792599\pi\) | |||||||
\(264\) | 26557.3 | 0.381044 | ||||||||
\(265\) | −50696.3 | −0.721913 | ||||||||
\(266\) | − | 8827.79i | − | 0.124764i | ||||||
\(267\) | − | 8995.86i | − | 0.126189i | ||||||
\(268\) | 57676.0i | 0.803019i | ||||||||
\(269\) | 60277.7i | 0.833014i | 0.909133 | + | 0.416507i | \(0.136746\pi\) | ||||
−0.909133 | + | 0.416507i | \(0.863254\pi\) | |||||||
\(270\) | − | 11002.9i | − | 0.150931i | ||||||
\(271\) | −68787.2 | −0.936633 | −0.468316 | − | 0.883561i | \(-0.655139\pi\) | ||||
−0.468316 | + | 0.883561i | \(0.655139\pi\) | |||||||
\(272\) | −22304.8 | −0.301481 | ||||||||
\(273\) | − | 3573.82i | − | 0.0479521i | ||||||
\(274\) | 64365.2i | 0.857334i | ||||||||
\(275\) | − | 73361.3i | − | 0.970067i | ||||||
\(276\) | − | 46390.7i | − | 0.608994i | ||||||
\(277\) | −136750. | −1.78225 | −0.891126 | − | 0.453755i | \(-0.850084\pi\) | ||||
−0.891126 | + | 0.453755i | \(0.850084\pi\) | |||||||
\(278\) | − | 82546.8i | − | 1.06810i | ||||||
\(279\) | − | 29704.3i | − | 0.381602i | ||||||
\(280\) | − | 1900.43i | − | 0.0242402i | ||||||
\(281\) | −128919. | −1.63270 | −0.816349 | − | 0.577559i | \(-0.804005\pi\) | ||||
−0.816349 | + | 0.577559i | \(0.804005\pi\) | |||||||
\(282\) | −75089.9 | −0.944242 | ||||||||
\(283\) | − | 35381.9i | − | 0.441782i | −0.975298 | − | 0.220891i | \(-0.929103\pi\) | ||
0.975298 | − | 0.220891i | \(-0.0708965\pi\) | |||||||
\(284\) | −115409. | −1.43088 | ||||||||
\(285\) | 20921.9 | 0.257579 | ||||||||
\(286\) | 145064.i | 1.77349i | ||||||||
\(287\) | 2010.66 | 0.0244105 | ||||||||
\(288\) | 37644.5i | 0.453854i | ||||||||
\(289\) | −59678.3 | −0.714531 | ||||||||
\(290\) | 111556.i | 1.32647i | ||||||||
\(291\) | − | 18678.7i | − | 0.220577i | ||||||
\(292\) | 44044.5i | 0.516566i | ||||||||
\(293\) | −27782.7 | −0.323622 | −0.161811 | − | 0.986822i | \(-0.551734\pi\) | ||||
−0.161811 | + | 0.986822i | \(0.551734\pi\) | |||||||
\(294\) | − | 75468.0i | − | 0.873108i | ||||||
\(295\) | −26214.7 | − | 36243.8i | −0.301232 | − | 0.416476i | ||||
\(296\) | 5981.34 | 0.0682677 | ||||||||
\(297\) | − | 22380.5i | − | 0.253721i | ||||||
\(298\) | −27675.6 | −0.311648 | ||||||||
\(299\) | 62600.5 | 0.700222 | ||||||||
\(300\) | −50777.9 | −0.564199 | ||||||||
\(301\) | 10919.7i | 0.120525i | ||||||||
\(302\) | 172682. | 1.89336 | ||||||||
\(303\) | − | 47584.8i | − | 0.518302i | ||||||
\(304\) | −45262.4 | −0.489768 | ||||||||
\(305\) | − | 22290.9i | − | 0.239622i | ||||||
\(306\) | − | 25444.9i | − | 0.271743i | ||||||
\(307\) | −87467.0 | −0.928042 | −0.464021 | − | 0.885824i | \(-0.653594\pi\) | ||||
−0.464021 | + | 0.885824i | \(0.653594\pi\) | |||||||
\(308\) | − | 15647.5i | − | 0.164947i | ||||||
\(309\) | − | 13939.5i | − | 0.145992i | ||||||
\(310\) | 86281.2 | 0.897827 | ||||||||
\(311\) | 122891. | 1.27057 | 0.635284 | − | 0.772279i | \(-0.280883\pi\) | ||||
0.635284 | + | 0.772279i | \(0.280883\pi\) | |||||||
\(312\) | 24804.9 | 0.254817 | ||||||||
\(313\) | 13347.4i | 0.136242i | 0.997677 | + | 0.0681208i | \(0.0217003\pi\) | ||||
−0.997677 | + | 0.0681208i | \(0.978300\pi\) | |||||||
\(314\) | −50441.0 | −0.511593 | ||||||||
\(315\) | −1601.54 | −0.0161405 | ||||||||
\(316\) | −228928. | −2.29258 | ||||||||
\(317\) | −1111.83 | −0.0110642 | −0.00553210 | − | 0.999985i | \(-0.501761\pi\) | ||||
−0.00553210 | + | 0.999985i | \(0.501761\pi\) | |||||||
\(318\) | 125117.i | 1.23727i | ||||||||
\(319\) | 226911.i | 2.22984i | ||||||||
\(320\) | −79646.0 | −0.777793 | ||||||||
\(321\) | 20465.8 | 0.198618 | ||||||||
\(322\) | −11836.8 | −0.114162 | ||||||||
\(323\) | 48383.3 | 0.463757 | ||||||||
\(324\) | −15490.9 | −0.147566 | ||||||||
\(325\) | − | 68520.6i | − | 0.648716i | ||||||
\(326\) | 134713.i | 1.26758i | ||||||||
\(327\) | − | 58510.1i | − | 0.547186i | ||||||
\(328\) | 13955.5i | 0.129717i | ||||||||
\(329\) | 10929.8i | 0.100977i | ||||||||
\(330\) | 65007.9 | 0.596951 | ||||||||
\(331\) | 141657. | 1.29295 | 0.646476 | − | 0.762935i | \(-0.276242\pi\) | ||||
0.646476 | + | 0.762935i | \(0.276242\pi\) | |||||||
\(332\) | − | 232821.i | − | 2.11225i | ||||||
\(333\) | − | 5040.63i | − | 0.0454565i | ||||||
\(334\) | 84671.7i | 0.759006i | ||||||||
\(335\) | 34877.7i | 0.310783i | ||||||||
\(336\) | 3464.78 | 0.0306900 | ||||||||
\(337\) | 163985.i | 1.44392i | 0.691935 | + | 0.721960i | \(0.256758\pi\) | ||||
−0.691935 | + | 0.721960i | \(0.743242\pi\) | |||||||
\(338\) | − | 38822.2i | − | 0.339819i | ||||||
\(339\) | − | 48830.3i | − | 0.424904i | ||||||
\(340\) | 42162.6 | 0.364728 | ||||||||
\(341\) | 175501. | 1.50928 | ||||||||
\(342\) | − | 51634.7i | − | 0.441458i | ||||||
\(343\) | −22068.1 | −0.187576 | ||||||||
\(344\) | −75790.3 | −0.640467 | ||||||||
\(345\) | − | 28053.3i | − | 0.235692i | ||||||
\(346\) | 162279. | 1.35553 | ||||||||
\(347\) | − | 163886.i | − | 1.36108i | −0.732710 | − | 0.680541i | \(-0.761745\pi\) | ||
0.732710 | − | 0.680541i | \(-0.238255\pi\) | |||||||
\(348\) | 157059. | 1.29689 | ||||||||
\(349\) | 63926.5i | 0.524844i | 0.964953 | + | 0.262422i | \(0.0845212\pi\) | ||||
−0.964953 | + | 0.262422i | \(0.915479\pi\) | |||||||
\(350\) | 12956.2i | 0.105765i | ||||||||
\(351\) | − | 20903.7i | − | 0.169671i | ||||||
\(352\) | −222413. | −1.79505 | ||||||||
\(353\) | − | 87690.5i | − | 0.703725i | −0.936052 | − | 0.351863i | \(-0.885548\pi\) | ||
0.936052 | − | 0.351863i | \(-0.114452\pi\) | |||||||
\(354\) | −89449.0 | + | 64697.3i | −0.713788 | + | 0.516273i | ||||
\(355\) | −69789.9 | −0.553779 | ||||||||
\(356\) | − | 36788.3i | − | 0.290275i | ||||||
\(357\) | −3703.68 | −0.0290601 | ||||||||
\(358\) | −145049. | −1.13175 | ||||||||
\(359\) | 119280. | 0.925504 | 0.462752 | − | 0.886488i | \(-0.346862\pi\) | ||||
0.462752 | + | 0.886488i | \(0.346862\pi\) | |||||||
\(360\) | − | 11115.8i | − | 0.0857704i | ||||||
\(361\) | −32138.1 | −0.246607 | ||||||||
\(362\) | 152964.i | 1.16727i | ||||||||
\(363\) | 56152.7 | 0.426145 | ||||||||
\(364\) | − | 14615.0i | − | 0.110305i | ||||||
\(365\) | 26634.4i | 0.199921i | ||||||||
\(366\) | −55013.4 | −0.410683 | ||||||||
\(367\) | − | 56563.1i | − | 0.419953i | −0.977706 | − | 0.209977i | \(-0.932661\pi\) | ||
0.977706 | − | 0.209977i | \(-0.0673388\pi\) | |||||||
\(368\) | 60690.5i | 0.448152i | ||||||||
\(369\) | 11760.6 | 0.0863728 | ||||||||
\(370\) | 14641.4 | 0.106949 | ||||||||
\(371\) | 18211.7 | 0.132313 | ||||||||
\(372\) | − | 121475.i | − | 0.877809i | ||||||
\(373\) | 123782. | 0.889691 | 0.444846 | − | 0.895607i | \(-0.353259\pi\) | ||||
0.444846 | + | 0.895607i | \(0.353259\pi\) | |||||||
\(374\) | 150335. | 1.07478 | ||||||||
\(375\) | −72437.6 | −0.515112 | ||||||||
\(376\) | −75860.8 | −0.536589 | ||||||||
\(377\) | 211938.i | 1.49117i | ||||||||
\(378\) | 3952.57i | 0.0276628i | ||||||||
\(379\) | 237594. | 1.65408 | 0.827042 | − | 0.562140i | \(-0.190022\pi\) | ||||
0.827042 | + | 0.562140i | \(0.190022\pi\) | |||||||
\(380\) | 85559.3 | 0.592516 | ||||||||
\(381\) | 48852.6 | 0.336541 | ||||||||
\(382\) | −51430.0 | −0.352444 | ||||||||
\(383\) | 271890. | 1.85351 | 0.926757 | − | 0.375661i | \(-0.122584\pi\) | ||||
0.926757 | + | 0.375661i | \(0.122584\pi\) | |||||||
\(384\) | 80649.6i | 0.546940i | ||||||||
\(385\) | − | 9462.33i | − | 0.0638376i | ||||||
\(386\) | − | 31505.2i | − | 0.211450i | ||||||
\(387\) | 63870.4i | 0.426459i | ||||||||
\(388\) | − | 76385.8i | − | 0.507398i | ||||||
\(389\) | −76616.7 | −0.506319 | −0.253160 | − | 0.967425i | \(-0.581470\pi\) | ||||
−0.253160 | + | 0.967425i | \(0.581470\pi\) | |||||||
\(390\) | 60718.4 | 0.399200 | ||||||||
\(391\) | − | 64875.1i | − | 0.424351i | ||||||
\(392\) | − | 76242.8i | − | 0.496166i | ||||||
\(393\) | 145755.i | 0.943707i | ||||||||
\(394\) | − | 80936.8i | − | 0.521379i | ||||||
\(395\) | −138436. | −0.887270 | ||||||||
\(396\) | − | 91524.2i | − | 0.583641i | ||||||
\(397\) | − | 2682.43i | − | 0.0170195i | −0.999964 | − | 0.00850977i | \(-0.997291\pi\) | ||
0.999964 | − | 0.00850977i | \(-0.00270878\pi\) | |||||||
\(398\) | 116744.i | 0.737000i | ||||||||
\(399\) | −7515.77 | −0.0472093 | ||||||||
\(400\) | 66429.9 | 0.415187 | ||||||||
\(401\) | − | 208279.i | − | 1.29526i | −0.761955 | − | 0.647630i | \(-0.775760\pi\) | ||
0.761955 | − | 0.647630i | \(-0.224240\pi\) | |||||||
\(402\) | 86077.3 | 0.532643 | ||||||||
\(403\) | 163920. | 1.00931 | ||||||||
\(404\) | − | 194597.i | − | 1.19226i | ||||||
\(405\) | −9367.60 | −0.0571108 | ||||||||
\(406\) | − | 40074.3i | − | 0.243116i | ||||||
\(407\) | 29781.3 | 0.179786 | ||||||||
\(408\) | − | 25706.2i | − | 0.154425i | ||||||
\(409\) | 306294.i | 1.83102i | 0.402299 | + | 0.915508i | \(0.368211\pi\) | ||||
−0.402299 | + | 0.915508i | \(0.631789\pi\) | |||||||
\(410\) | 34160.7i | 0.203217i | ||||||||
\(411\) | 54799.0 | 0.324406 | ||||||||
\(412\) | − | 57005.1i | − | 0.335830i | ||||||
\(413\) | 9417.11 | + | 13019.9i | 0.0552100 | + | 0.0763321i | ||||
\(414\) | −69234.8 | −0.403947 | ||||||||
\(415\) | − | 140791.i | − | 0.817482i | ||||||
\(416\) | −207737. | −1.20041 | ||||||||
\(417\) | −70278.4 | −0.404157 | ||||||||
\(418\) | 305071. | 1.74602 | ||||||||
\(419\) | 214239.i | 1.22031i | 0.792282 | + | 0.610155i | \(0.208893\pi\) | ||||
−0.792282 | + | 0.610155i | \(0.791107\pi\) | |||||||
\(420\) | −6549.45 | −0.0371284 | ||||||||
\(421\) | 211231.i | 1.19177i | 0.803069 | + | 0.595886i | \(0.203199\pi\) | ||||
−0.803069 | + | 0.595886i | \(0.796801\pi\) | |||||||
\(422\) | −540514. | −3.03516 | ||||||||
\(423\) | 63929.8i | 0.357291i | ||||||||
\(424\) | 126402.i | 0.703108i | ||||||||
\(425\) | −71010.3 | −0.393137 | ||||||||
\(426\) | 172240.i | 0.949107i | ||||||||
\(427\) | 8007.56i | 0.0439182i | ||||||||
\(428\) | 83694.2 | 0.456886 | ||||||||
\(429\) | 123504. | 0.671070 | ||||||||
\(430\) | −185523. | −1.00337 | ||||||||
\(431\) | − | 77388.2i | − | 0.416601i | −0.978065 | − | 0.208300i | \(-0.933207\pi\) | ||
0.978065 | − | 0.208300i | \(-0.0667932\pi\) | |||||||
\(432\) | 20265.9 | 0.108592 | ||||||||
\(433\) | 246940. | 1.31709 | 0.658546 | − | 0.752541i | \(-0.271172\pi\) | ||||
0.658546 | + | 0.752541i | \(0.271172\pi\) | |||||||
\(434\) | −30994.8 | −0.164555 | ||||||||
\(435\) | 94976.2 | 0.501922 | ||||||||
\(436\) | − | 239275.i | − | 1.25871i | ||||||
\(437\) | − | 131649.i | − | 0.689375i | ||||||
\(438\) | 65733.2 | 0.342639 | ||||||||
\(439\) | −43951.4 | −0.228057 | −0.114028 | − | 0.993477i | \(-0.536376\pi\) | ||||
−0.114028 | + | 0.993477i | \(0.536376\pi\) | |||||||
\(440\) | 65675.3 | 0.339232 | ||||||||
\(441\) | −64251.7 | −0.330375 | ||||||||
\(442\) | 140415. | 0.718738 | ||||||||
\(443\) | − | 204422.i | − | 1.04165i | −0.853665 | − | 0.520823i | \(-0.825625\pi\) | ||
0.853665 | − | 0.520823i | \(-0.174375\pi\) | |||||||
\(444\) | − | 20613.5i | − | 0.104565i | ||||||
\(445\) | − | 22246.5i | − | 0.112342i | ||||||
\(446\) | − | 117726.i | − | 0.591839i | ||||||
\(447\) | 23562.4i | 0.117925i | ||||||||
\(448\) | 28611.3 | 0.142554 | ||||||||
\(449\) | 37083.0 | 0.183943 | 0.0919713 | − | 0.995762i | \(-0.470683\pi\) | ||||
0.0919713 | + | 0.995762i | \(0.470683\pi\) | |||||||
\(450\) | 75782.3i | 0.374234i | ||||||||
\(451\) | 69484.7i | 0.341614i | ||||||||
\(452\) | − | 199690.i | − | 0.977416i | ||||||
\(453\) | − | 147018.i | − | 0.716429i | ||||||
\(454\) | 166676. | 0.808653 | ||||||||
\(455\) | − | 8837.95i | − | 0.0426903i | ||||||
\(456\) | − | 52164.8i | − | 0.250870i | ||||||
\(457\) | 29076.9i | 0.139225i | 0.997574 | + | 0.0696123i | \(0.0221762\pi\) | ||||
−0.997574 | + | 0.0696123i | \(0.977824\pi\) | |||||||
\(458\) | −43245.6 | −0.206163 | ||||||||
\(459\) | −21663.2 | −0.102825 | ||||||||
\(460\) | − | 114723.i | − | 0.542169i | ||||||
\(461\) | −254103. | −1.19566 | −0.597831 | − | 0.801622i | \(-0.703971\pi\) | ||||
−0.597831 | + | 0.801622i | \(0.703971\pi\) | |||||||
\(462\) | −23352.8 | −0.109410 | ||||||||
\(463\) | − | 386615.i | − | 1.80350i | −0.432256 | − | 0.901751i | \(-0.642282\pi\) | ||
0.432256 | − | 0.901751i | \(-0.357718\pi\) | |||||||
\(464\) | −205472. | −0.954369 | ||||||||
\(465\) | − | 73457.8i | − | 0.339729i | ||||||
\(466\) | 365074. | 1.68116 | ||||||||
\(467\) | − | 344576.i | − | 1.57998i | −0.613122 | − | 0.789988i | \(-0.710087\pi\) | ||
0.613122 | − | 0.789988i | \(-0.289913\pi\) | |||||||
\(468\) | − | 85484.9i | − | 0.390299i | ||||||
\(469\) | − | 12529.1i | − | 0.0569606i | ||||||
\(470\) | −185695. | −0.840629 | ||||||||
\(471\) | 42944.3i | 0.193582i | ||||||||
\(472\) | −90367.4 | + | 65361.5i | −0.405628 | + | 0.293385i | ||||
\(473\) | −377363. | −1.68670 | ||||||||
\(474\) | 341658.i | 1.52067i | ||||||||
\(475\) | −144099. | −0.638667 | ||||||||
\(476\) | −15146.1 | −0.0668476 | ||||||||
\(477\) | 106522. | 0.468169 | ||||||||
\(478\) | − | 482067.i | − | 2.10985i | ||||||
\(479\) | 304897. | 1.32887 | 0.664435 | − | 0.747346i | \(-0.268672\pi\) | ||||
0.664435 | + | 0.747346i | \(0.268672\pi\) | |||||||
\(480\) | 93093.7i | 0.404052i | ||||||||
\(481\) | 27816.2 | 0.120229 | ||||||||
\(482\) | 307722.i | 1.32454i | ||||||||
\(483\) | 10077.6i | 0.0431979i | ||||||||
\(484\) | 229635. | 0.980273 | ||||||||
\(485\) | − | 46191.8i | − | 0.196373i | ||||||
\(486\) | 23119.0i | 0.0978807i | ||||||||
\(487\) | −327375. | −1.38034 | −0.690171 | − | 0.723646i | \(-0.742465\pi\) | ||||
−0.690171 | + | 0.723646i | \(0.742465\pi\) | |||||||
\(488\) | −55578.2 | −0.233381 | ||||||||
\(489\) | 114692. | 0.479639 | ||||||||
\(490\) | − | 186630.i | − | 0.777301i | ||||||
\(491\) | −330527. | −1.37102 | −0.685511 | − | 0.728063i | \(-0.740421\pi\) | ||||
−0.685511 | + | 0.728063i | \(0.740421\pi\) | |||||||
\(492\) | 48094.6 | 0.198686 | ||||||||
\(493\) | 219639. | 0.903683 | ||||||||
\(494\) | 284941. | 1.16762 | ||||||||
\(495\) | − | 55346.2i | − | 0.225880i | ||||||
\(496\) | 158919.i | 0.645969i | ||||||||
\(497\) | 25070.7 | 0.101497 | ||||||||
\(498\) | −347469. | −1.40106 | ||||||||
\(499\) | −207100. | −0.831724 | −0.415862 | − | 0.909428i | \(-0.636520\pi\) | ||||
−0.415862 | + | 0.909428i | \(0.636520\pi\) | |||||||
\(500\) | −296231. | −1.18492 | ||||||||
\(501\) | 72087.5 | 0.287200 | ||||||||
\(502\) | − | 654676.i | − | 2.59788i | ||||||
\(503\) | 187431.i | 0.740807i | 0.928871 | + | 0.370403i | \(0.120781\pi\) | ||||
−0.928871 | + | 0.370403i | \(0.879219\pi\) | |||||||
\(504\) | 3993.15i | 0.0157201i | ||||||||
\(505\) | − | 117676.i | − | 0.461429i | ||||||
\(506\) | − | 409058.i | − | 1.59766i | ||||||
\(507\) | −33052.3 | −0.128584 | ||||||||
\(508\) | 199781. | 0.774154 | ||||||||
\(509\) | 27177.2i | 0.104899i | 0.998624 | + | 0.0524493i | \(0.0167028\pi\) | ||||
−0.998624 | + | 0.0524493i | \(0.983297\pi\) | |||||||
\(510\) | − | 62924.6i | − | 0.241925i | ||||||
\(511\) | − | 9567.90i | − | 0.0366416i | ||||||
\(512\) | − | 275448.i | − | 1.05075i | ||||||
\(513\) | −43960.6 | −0.167043 | ||||||||
\(514\) | − | 318507.i | − | 1.20557i | ||||||
\(515\) | − | 34471.9i | − | 0.129972i | ||||||
\(516\) | 261196.i | 0.980995i | ||||||||
\(517\) | −377714. | −1.41313 | ||||||||
\(518\) | −5259.63 | −0.0196018 | ||||||||
\(519\) | − | 138160.i | − | 0.512919i | ||||||
\(520\) | 61341.7 | 0.226855 | ||||||||
\(521\) | 492814. | 1.81555 | 0.907774 | − | 0.419460i | \(-0.137781\pi\) | ||||
0.907774 | + | 0.419460i | \(0.137781\pi\) | |||||||
\(522\) | − | 234399.i | − | 0.860231i | ||||||
\(523\) | −154182. | −0.563678 | −0.281839 | − | 0.959462i | \(-0.590944\pi\) | ||||
−0.281839 | + | 0.959462i | \(0.590944\pi\) | |||||||
\(524\) | 596059.i | 2.17083i | ||||||||
\(525\) | 11030.6 | 0.0400204 | ||||||||
\(526\) | 671338.i | 2.42644i | ||||||||
\(527\) | − | 169876.i | − | 0.611662i | ||||||
\(528\) | 119736.i | 0.429494i | ||||||||
\(529\) | 103318. | 0.369202 | ||||||||
\(530\) | 309412.i | 1.10150i | ||||||||
\(531\) | 55081.8 | + | 76154.8i | 0.195352 | + | 0.270090i | ||||
\(532\) | −30735.5 | −0.108597 | ||||||||
\(533\) | 64899.8i | 0.228449i | ||||||||
\(534\) | −54903.9 | −0.192540 | ||||||||
\(535\) | 50611.3 | 0.176823 | ||||||||
\(536\) | 86961.0 | 0.302688 | ||||||||
\(537\) | 123491.i | 0.428241i | ||||||||
\(538\) | 367889. | 1.27102 | ||||||||
\(539\) | − | 379616.i | − | 1.30667i | ||||||
\(540\) | −38308.5 | −0.131373 | ||||||||
\(541\) | 175670.i | 0.600210i | 0.953906 | + | 0.300105i | \(0.0970217\pi\) | ||||
−0.953906 | + | 0.300105i | \(0.902978\pi\) | |||||||
\(542\) | 419825.i | 1.42912i | ||||||||
\(543\) | 130230. | 0.441684 | ||||||||
\(544\) | 215286.i | 0.727474i | ||||||||
\(545\) | − | 144694.i | − | 0.487143i | ||||||
\(546\) | −21811.9 | −0.0731657 | ||||||||
\(547\) | 22187.9 | 0.0741552 | 0.0370776 | − | 0.999312i | \(-0.488195\pi\) | ||||
0.0370776 | + | 0.999312i | \(0.488195\pi\) | |||||||
\(548\) | 224099. | 0.746240 | ||||||||
\(549\) | 46837.1i | 0.155398i | ||||||||
\(550\) | −447742. | −1.48014 | ||||||||
\(551\) | 445708. | 1.46807 | ||||||||
\(552\) | −69945.6 | −0.229553 | ||||||||
\(553\) | 49730.5 | 0.162620 | ||||||||
\(554\) | 834620.i | 2.71938i | ||||||||
\(555\) | − | 12465.3i | − | 0.0404685i | ||||||
\(556\) | −287401. | −0.929692 | ||||||||
\(557\) | −475276. | −1.53192 | −0.765959 | − | 0.642890i | \(-0.777735\pi\) | ||||
−0.765959 | + | 0.642890i | \(0.777735\pi\) | |||||||
\(558\) | −181292. | −0.582252 | ||||||||
\(559\) | −352463. | −1.12795 | ||||||||
\(560\) | 8568.30 | 0.0273224 | ||||||||
\(561\) | − | 127992.i | − | 0.406684i | ||||||
\(562\) | 786826.i | 2.49118i | ||||||||
\(563\) | − | 28507.6i | − | 0.0899382i | −0.998988 | − | 0.0449691i | \(-0.985681\pi\) | ||
0.998988 | − | 0.0449691i | \(-0.0143189\pi\) | |||||||
\(564\) | 261439.i | 0.821886i | ||||||||
\(565\) | − | 120756.i | − | 0.378278i | ||||||
\(566\) | −215944. | −0.674075 | ||||||||
\(567\) | 3365.13 | 0.0104673 | ||||||||
\(568\) | 174008.i | 0.539353i | ||||||||
\(569\) | − | 112438.i | − | 0.347287i | −0.984809 | − | 0.173644i | \(-0.944446\pi\) | ||
0.984809 | − | 0.173644i | \(-0.0555541\pi\) | |||||||
\(570\) | − | 127691.i | − | 0.393017i | ||||||
\(571\) | 428720.i | 1.31493i | 0.753486 | + | 0.657464i | \(0.228371\pi\) | ||||
−0.753486 | + | 0.657464i | \(0.771629\pi\) | |||||||
\(572\) | 505067. | 1.54368 | ||||||||
\(573\) | 43786.3i | 0.133361i | ||||||||
\(574\) | − | 12271.6i | − | 0.0372457i | ||||||
\(575\) | 193217.i | 0.584398i | ||||||||
\(576\) | 167350. | 0.504408 | ||||||||
\(577\) | −75213.5 | −0.225915 | −0.112957 | − | 0.993600i | \(-0.536032\pi\) | ||||
−0.112957 | + | 0.993600i | \(0.536032\pi\) | |||||||
\(578\) | 364231.i | 1.09024i | ||||||||
\(579\) | −26822.8 | −0.0800104 | ||||||||
\(580\) | 388402. | 1.15458 | ||||||||
\(581\) | 50576.3i | 0.149829i | ||||||||
\(582\) | −114000. | −0.336558 | ||||||||
\(583\) | 629360.i | 1.85166i | ||||||||
\(584\) | 66408.0 | 0.194713 | ||||||||
\(585\) | − | 51694.2i | − | 0.151053i | ||||||
\(586\) | 169564.i | 0.493786i | ||||||||
\(587\) | − | 134395.i | − | 0.390039i | −0.980799 | − | 0.195019i | \(-0.937523\pi\) | ||
0.980799 | − | 0.195019i | \(-0.0624770\pi\) | |||||||
\(588\) | −262755. | −0.759970 | ||||||||
\(589\) | − | 344725.i | − | 0.993671i | ||||||
\(590\) | −221205. | + | 159994.i | −0.635463 | + | 0.459622i | ||||
\(591\) | −68907.7 | −0.197284 | ||||||||
\(592\) | 26967.5i | 0.0769480i | ||||||||
\(593\) | −351119. | −0.998493 | −0.499247 | − | 0.866460i | \(-0.666390\pi\) | ||||
−0.499247 | + | 0.866460i | \(0.666390\pi\) | |||||||
\(594\) | −136593. | −0.387130 | ||||||||
\(595\) | −9159.08 | −0.0258713 | ||||||||
\(596\) | 96357.6i | 0.271265i | ||||||||
\(597\) | 99392.9 | 0.278873 | ||||||||
\(598\) | − | 382066.i | − | 1.06840i | ||||||
\(599\) | 31310.5 | 0.0872641 | 0.0436321 | − | 0.999048i | \(-0.486107\pi\) | ||||
0.0436321 | + | 0.999048i | \(0.486107\pi\) | |||||||
\(600\) | 76560.3i | 0.212668i | ||||||||
\(601\) | 583406.i | 1.61518i | 0.589742 | + | 0.807592i | \(0.299229\pi\) | ||||
−0.589742 | + | 0.807592i | \(0.700771\pi\) | |||||||
\(602\) | 66645.3 | 0.183898 | ||||||||
\(603\) | − | 73284.2i | − | 0.201547i | ||||||
\(604\) | − | 601224.i | − | 1.64802i | ||||||
\(605\) | 138864. | 0.379384 | ||||||||
\(606\) | −290421. | −0.790830 | ||||||||
\(607\) | 470041. | 1.27573 | 0.637864 | − | 0.770149i | \(-0.279818\pi\) | ||||
0.637864 | + | 0.770149i | \(0.279818\pi\) | |||||||
\(608\) | 436873.i | 1.18181i | ||||||||
\(609\) | −34118.3 | −0.0919927 | ||||||||
\(610\) | −136046. | −0.365618 | ||||||||
\(611\) | −352790. | −0.945005 | ||||||||
\(612\) | −88591.1 | −0.236531 | ||||||||
\(613\) | − | 463701.i | − | 1.23400i | −0.786961 | − | 0.617002i | \(-0.788347\pi\) | ||
0.786961 | − | 0.617002i | \(-0.211653\pi\) | |||||||
\(614\) | 533832.i | 1.41602i | ||||||||
\(615\) | 29083.6 | 0.0768950 | ||||||||
\(616\) | −23592.6 | −0.0621747 | ||||||||
\(617\) | 23997.3 | 0.0630365 | 0.0315183 | − | 0.999503i | \(-0.489966\pi\) | ||||
0.0315183 | + | 0.999503i | \(0.489966\pi\) | |||||||
\(618\) | −85076.0 | −0.222756 | ||||||||
\(619\) | 479797. | 1.25221 | 0.626104 | − | 0.779739i | \(-0.284648\pi\) | ||||
0.626104 | + | 0.779739i | \(0.284648\pi\) | |||||||
\(620\) | − | 300403.i | − | 0.781486i | ||||||
\(621\) | 58944.9i | 0.152849i | ||||||||
\(622\) | − | 750031.i | − | 1.93864i | ||||||
\(623\) | 7991.61i | 0.0205901i | ||||||||
\(624\) | 111835.i | 0.287217i | ||||||||
\(625\) | 108289. | 0.277219 | ||||||||
\(626\) | 81462.6 | 0.207879 | ||||||||
\(627\) | − | 259731.i | − | 0.660675i | ||||||
\(628\) | 175619.i | 0.445301i | ||||||||
\(629\) | − | 28826.9i | − | 0.0728613i | ||||||
\(630\) | 9774.59i | 0.0246273i | ||||||||
\(631\) | −359273. | −0.902331 | −0.451166 | − | 0.892440i | \(-0.648992\pi\) | ||||
−0.451166 | + | 0.892440i | \(0.648992\pi\) | |||||||
\(632\) | 345166.i | 0.864158i | ||||||||
\(633\) | 460181.i | 1.14847i | ||||||||
\(634\) | 6785.76i | 0.0168818i | ||||||||
\(635\) | 120811. | 0.299612 | ||||||||
\(636\) | 435619. | 1.07694 | ||||||||
\(637\) | − | 354567.i | − | 0.873814i | ||||||
\(638\) | 1.38489e6 | 3.40232 | ||||||||
\(639\) | 146641. | 0.359132 | ||||||||
\(640\) | 199444.i | 0.486924i | ||||||||
\(641\) | −107842. | −0.262465 | −0.131232 | − | 0.991352i | \(-0.541893\pi\) | ||||
−0.131232 | + | 0.991352i | \(0.541893\pi\) | |||||||
\(642\) | − | 124908.i | − | 0.303053i | ||||||
\(643\) | 727011. | 1.75840 | 0.879202 | − | 0.476448i | \(-0.158076\pi\) | ||||
0.879202 | + | 0.476448i | \(0.158076\pi\) | |||||||
\(644\) | 41212.0i | 0.0993691i | ||||||||
\(645\) | 157950.i | 0.379664i | ||||||||
\(646\) | − | 295295.i | − | 0.707605i | ||||||
\(647\) | −413352. | −0.987443 | −0.493721 | − | 0.869620i | \(-0.664364\pi\) | ||||
−0.493721 | + | 0.869620i | \(0.664364\pi\) | |||||||
\(648\) | 23356.4i | 0.0556231i | ||||||||
\(649\) | −449942. | + | 325437.i | −1.06824 | + | 0.772642i | ||||
\(650\) | −418197. | −0.989816 | ||||||||
\(651\) | 26388.3i | 0.0622657i | ||||||||
\(652\) | 469028. | 1.10333 | ||||||||
\(653\) | −189327. | −0.444002 | −0.222001 | − | 0.975046i | \(-0.571259\pi\) | ||||
−0.222001 | + | 0.975046i | \(0.571259\pi\) | |||||||
\(654\) | −357101. | −0.834901 | ||||||||
\(655\) | 360447.i | 0.840153i | ||||||||
\(656\) | −62919.6 | −0.146210 | ||||||||
\(657\) | − | 55963.7i | − | 0.129651i | ||||||
\(658\) | 66707.3 | 0.154071 | ||||||||
\(659\) | − | 496507.i | − | 1.14328i | −0.820503 | − | 0.571642i | \(-0.806307\pi\) | ||
0.820503 | − | 0.571642i | \(-0.193693\pi\) | |||||||
\(660\) | − | 226337.i | − | 0.519597i | ||||||
\(661\) | −542654. | −1.24199 | −0.620997 | − | 0.783813i | \(-0.713272\pi\) | ||||
−0.620997 | + | 0.783813i | \(0.713272\pi\) | |||||||
\(662\) | − | 864566.i | − | 1.97280i | ||||||
\(663\) | − | 119546.i | − | 0.271963i | ||||||
\(664\) | −351036. | −0.796188 | ||||||||
\(665\) | −18586.3 | −0.0420290 | ||||||||
\(666\) | −30764.1 | −0.0693580 | ||||||||
\(667\) | − | 597631.i | − | 1.34333i | ||||||
\(668\) | 294799. | 0.660654 | ||||||||
\(669\) | −100229. | −0.223946 | ||||||||
\(670\) | 212867. | 0.474196 | ||||||||
\(671\) | −276726. | −0.614617 | ||||||||
\(672\) | − | 33442.1i | − | 0.0740551i | ||||||
\(673\) | − | 243660.i | − | 0.537964i | −0.963145 | − | 0.268982i | \(-0.913313\pi\) | ||
0.963145 | − | 0.268982i | \(-0.0866873\pi\) | |||||||
\(674\) | 1.00084e6 | 2.20315 | ||||||||
\(675\) | 64519.3 | 0.141606 | ||||||||
\(676\) | −135166. | −0.295785 | ||||||||
\(677\) | 430256. | 0.938750 | 0.469375 | − | 0.882999i | \(-0.344479\pi\) | ||||
0.469375 | + | 0.882999i | \(0.344479\pi\) | |||||||
\(678\) | −298023. | −0.648322 | ||||||||
\(679\) | 16593.5i | 0.0359913i | ||||||||
\(680\) | − | 63570.6i | − | 0.137480i | ||||||
\(681\) | − | 141904.i | − | 0.305986i | ||||||
\(682\) | − | 1.07112e6i | − | 2.30287i | ||||||
\(683\) | − | 163345.i | − | 0.350158i | −0.984554 | − | 0.175079i | \(-0.943982\pi\) | ||
0.984554 | − | 0.175079i | \(-0.0560181\pi\) | |||||||
\(684\) | −179775. | −0.384254 | ||||||||
\(685\) | 135516. | 0.288809 | ||||||||
\(686\) | 134687.i | 0.286205i | ||||||||
\(687\) | 36818.3i | 0.0780100i | ||||||||
\(688\) | − | 341709.i | − | 0.721903i | ||||||
\(689\) | 587832.i | 1.23827i | ||||||||
\(690\) | −171216. | −0.359621 | ||||||||
\(691\) | − | 529874.i | − | 1.10973i | −0.831941 | − | 0.554864i | \(-0.812770\pi\) | ||
0.831941 | − | 0.554864i | \(-0.187230\pi\) | |||||||
\(692\) | − | 565002.i | − | 1.17988i | ||||||
\(693\) | 19882.0i | 0.0413994i | ||||||||
\(694\) | −1.00024e6 | −2.07675 | ||||||||
\(695\) | −173796. | −0.359808 | ||||||||
\(696\) | − | 236806.i | − | 0.488848i | ||||||
\(697\) | 67257.9 | 0.138445 | ||||||||
\(698\) | 390159. | 0.800812 | ||||||||
\(699\) | − | 310816.i | − | 0.636134i | ||||||
\(700\) | 45109.3 | 0.0920598 | ||||||||
\(701\) | 182341.i | 0.371064i | 0.982638 | + | 0.185532i | \(0.0594008\pi\) | ||||
−0.982638 | + | 0.185532i | \(0.940599\pi\) | |||||||
\(702\) | −127580. | −0.258886 | ||||||||
\(703\) | − | 58497.7i | − | 0.118366i | ||||||
\(704\) | 988750.i | 1.99499i | ||||||||
\(705\) | 158096.i | 0.318085i | ||||||||
\(706\) | −535196. | −1.07375 | ||||||||
\(707\) | 42272.7i | 0.0845710i | ||||||||
\(708\) | 225255. | + | 311433.i | 0.449374 | + | 0.621295i | ||||
\(709\) | −860411. | −1.71164 | −0.855822 | − | 0.517271i | \(-0.826948\pi\) | ||||
−0.855822 | + | 0.517271i | \(0.826948\pi\) | |||||||
\(710\) | 425945.i | 0.844960i | ||||||||
\(711\) | 290880. | 0.575405 | ||||||||
\(712\) | −55467.5 | −0.109415 | ||||||||
\(713\) | −462228. | −0.909237 | ||||||||
\(714\) | 22604.4i | 0.0443401i | ||||||||
\(715\) | 305423. | 0.597433 | ||||||||
\(716\) | 505014.i | 0.985093i | ||||||||
\(717\) | −410420. | −0.798345 | ||||||||
\(718\) | − | 727993.i | − | 1.41214i | ||||||
\(719\) | 198523.i | 0.384019i | 0.981393 | + | 0.192010i | \(0.0615005\pi\) | ||||
−0.981393 | + | 0.192010i | \(0.938499\pi\) | |||||||
\(720\) | 50116.9 | 0.0966762 | ||||||||
\(721\) | 12383.4i | 0.0238215i | ||||||||
\(722\) | 196146.i | 0.376275i | ||||||||
\(723\) | 261987. | 0.501191 | ||||||||
\(724\) | 532572. | 1.01602 | ||||||||
\(725\) | −654148. | −1.24452 | ||||||||
\(726\) | − | 342713.i | − | 0.650216i | ||||||
\(727\) | −649.946 | −0.00122973 | −0.000614863 | − | 1.00000i | \(-0.500196\pi\) | ||||
−0.000614863 | 1.00000i | \(0.500196\pi\) | ||||||||
\(728\) | −22035.8 | −0.0415783 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 162556. | 0.305041 | ||||||||
\(731\) | 365269.i | 0.683563i | ||||||||
\(732\) | 191539.i | 0.357466i | ||||||||
\(733\) | 27948.5 | 0.0520176 | 0.0260088 | − | 0.999662i | \(-0.491720\pi\) | ||||
0.0260088 | + | 0.999662i | \(0.491720\pi\) | |||||||
\(734\) | −345218. | −0.640769 | ||||||||
\(735\) | −158892. | −0.294123 | ||||||||
\(736\) | 585785. | 1.08139 | ||||||||
\(737\) | 432982. | 0.797141 | ||||||||
\(738\) | − | 71777.8i | − | 0.131788i | ||||||
\(739\) | 406137.i | 0.743675i | 0.928298 | + | 0.371838i | \(0.121272\pi\) | ||||
−0.928298 | + | 0.371838i | \(0.878728\pi\) | |||||||
\(740\) | − | 50976.5i | − | 0.0930908i | ||||||
\(741\) | − | 242592.i | − | 0.441815i | ||||||
\(742\) | − | 111150.i | − | 0.201884i | ||||||
\(743\) | −426473. | −0.772528 | −0.386264 | − | 0.922388i | \(-0.626235\pi\) | ||||
−0.386264 | + | 0.922388i | \(0.626235\pi\) | |||||||
\(744\) | −183153. | −0.330879 | ||||||||
\(745\) | 58269.1i | 0.104985i | ||||||||
\(746\) | − | 755470.i | − | 1.35750i | ||||||
\(747\) | 295827.i | 0.530147i | ||||||||
\(748\) | − | 523419.i | − | 0.935506i | ||||||
\(749\) | −18181.1 | −0.0324083 | ||||||||
\(750\) | 442104.i | 0.785962i | ||||||||
\(751\) | 625542.i | 1.10911i | 0.832146 | + | 0.554557i | \(0.187112\pi\) | ||||
−0.832146 | + | 0.554557i | \(0.812888\pi\) | |||||||
\(752\) | − | 342026.i | − | 0.604816i | ||||||
\(753\) | −557376. | −0.983010 | ||||||||
\(754\) | 1.29351e6 | 2.27524 | ||||||||
\(755\) | − | 363570.i | − | 0.637815i | ||||||
\(756\) | 13761.6 | 0.0240782 | ||||||||
\(757\) | −42832.4 | −0.0747448 | −0.0373724 | − | 0.999301i | \(-0.511899\pi\) | ||||
−0.0373724 | + | 0.999301i | \(0.511899\pi\) | |||||||
\(758\) | − | 1.45009e6i | − | 2.52382i | ||||||
\(759\) | −348262. | −0.604536 | ||||||||
\(760\) | − | 129002.i | − | 0.223342i | ||||||
\(761\) | 297397. | 0.513532 | 0.256766 | − | 0.966474i | \(-0.417343\pi\) | ||||
0.256766 | + | 0.966474i | \(0.417343\pi\) | |||||||
\(762\) | − | 298159.i | − | 0.513497i | ||||||
\(763\) | 51978.3i | 0.0892839i | ||||||||
\(764\) | 179063.i | 0.306774i | ||||||||
\(765\) | −53572.5 | −0.0915417 | ||||||||
\(766\) | − | 1.65941e6i | − | 2.82811i | ||||||
\(767\) | −420253. | + | 303963.i | −0.714365 | + | 0.516691i | ||||
\(768\) | −23082.1 | −0.0391338 | ||||||||
\(769\) | 211683.i | 0.357960i | 0.983853 | + | 0.178980i | \(0.0572797\pi\) | ||||
−0.983853 | + | 0.178980i | \(0.942720\pi\) | |||||||
\(770\) | −57750.8 | −0.0974040 | ||||||||
\(771\) | −271169. | −0.456175 | ||||||||
\(772\) | −109691. | −0.184050 | ||||||||
\(773\) | 869866.i | 1.45577i | 0.685698 | + | 0.727886i | \(0.259497\pi\) | ||||
−0.685698 | + | 0.727886i | \(0.740503\pi\) | |||||||
\(774\) | 389816. | 0.650696 | ||||||||
\(775\) | 505940.i | 0.842356i | ||||||||
\(776\) | −115171. | −0.191257 | ||||||||
\(777\) | 4477.92i | 0.00741711i | ||||||||
\(778\) | 467610.i | 0.772546i | ||||||||
\(779\) | 136485. | 0.224910 | ||||||||
\(780\) | − | 211402.i | − | 0.347472i | ||||||
\(781\) | 866394.i | 1.42041i | ||||||||
\(782\) | −395948. | −0.647478 | ||||||||
\(783\) | −199562. | −0.325503 | ||||||||
\(784\) | 343748. | 0.559253 | ||||||||
\(785\) | 106200.i | 0.172340i | ||||||||
\(786\) | 889575. | 1.43992 | ||||||||
\(787\) | −281012. | −0.453707 | −0.226853 | − | 0.973929i | \(-0.572844\pi\) | ||||
−0.226853 | + | 0.973929i | \(0.572844\pi\) | |||||||
\(788\) | −281796. | −0.453818 | ||||||||
\(789\) | 571561. | 0.918140 | ||||||||
\(790\) | 844910.i | 1.35381i | ||||||||
\(791\) | 43379.2i | 0.0693312i | ||||||||
\(792\) | −137996. | −0.219996 | ||||||||
\(793\) | −258466. | −0.411015 | ||||||||
\(794\) | −16371.5 | −0.0259686 | ||||||||
\(795\) | 263426. | 0.416797 | ||||||||
\(796\) | 406464. | 0.641499 | ||||||||
\(797\) | − | 515861.i | − | 0.812112i | −0.913848 | − | 0.406056i | \(-0.866904\pi\) | ||
0.913848 | − | 0.406056i | \(-0.133096\pi\) | |||||||
\(798\) | 45870.5i | 0.0720324i | ||||||||
\(799\) | 365609.i | 0.572695i | ||||||||
\(800\) | − | 641182.i | − | 1.00185i | ||||||
\(801\) | 46743.9i | 0.0728550i | ||||||||
\(802\) | −1.27118e6 | −1.97632 | ||||||||
\(803\) | 330648. | 0.512785 | ||||||||
\(804\) | − | 299693.i | − | 0.463623i | ||||||
\(805\) | 24921.6i | 0.0384577i | ||||||||
\(806\) | − | 1.00044e6i | − | 1.54001i | ||||||
\(807\) | − | 313212.i | − | 0.480941i | ||||||
\(808\) | −293403. | −0.449409 | ||||||||
\(809\) | − | 568738.i | − | 0.868991i | −0.900674 | − | 0.434496i | \(-0.856927\pi\) | ||
0.900674 | − | 0.434496i | \(-0.143073\pi\) | |||||||
\(810\) | 57172.7i | 0.0871402i | ||||||||
\(811\) | 2103.38i | 0.00319798i | 0.999999 | + | 0.00159899i | \(0.000508974\pi\) | ||||
−0.999999 | + | 0.00159899i | \(0.999491\pi\) | |||||||
\(812\) | −139526. | −0.211613 | ||||||||
\(813\) | 357429. | 0.540765 | ||||||||
\(814\) | − | 181763.i | − | 0.274319i | ||||||
\(815\) | 283629. | 0.427008 | ||||||||
\(816\) | 115899. | 0.174060 | ||||||||
\(817\) | 741231.i | 1.11048i | ||||||||
\(818\) | 1.86939e6 | 2.79378 | ||||||||
\(819\) | 18570.1i | 0.0276852i | ||||||||
\(820\) | 118937. | 0.176884 | ||||||||
\(821\) | − | 442834.i | − | 0.656984i | −0.944507 | − | 0.328492i | \(-0.893460\pi\) | ||
0.944507 | − | 0.328492i | \(-0.106540\pi\) | |||||||
\(822\) | − | 334451.i | − | 0.494982i | ||||||
\(823\) | − | 814438.i | − | 1.20243i | −0.799089 | − | 0.601213i | \(-0.794684\pi\) | ||
0.799089 | − | 0.601213i | \(-0.205316\pi\) | |||||||
\(824\) | −85949.4 | −0.126587 | ||||||||
\(825\) | 381197.i | 0.560069i | ||||||||
\(826\) | 79463.5 | − | 57474.9i | 0.116468 | − | 0.0842399i | ||||
\(827\) | 842514. | 1.23187 | 0.615936 | − | 0.787796i | \(-0.288778\pi\) | ||||
0.615936 | + | 0.787796i | \(0.288778\pi\) | |||||||
\(828\) | 241053.i | 0.351603i | ||||||||
\(829\) | 589973. | 0.858467 | 0.429233 | − | 0.903194i | \(-0.358784\pi\) | ||||
0.429233 | + | 0.903194i | \(0.358784\pi\) | |||||||
\(830\) | −859280. | −1.24732 | ||||||||
\(831\) | 710576. | 1.02898 | ||||||||
\(832\) | 923507.i | 1.33412i | ||||||||
\(833\) | −367450. | −0.529552 | ||||||||
\(834\) | 428926.i | 0.616666i | ||||||||
\(835\) | 178270. | 0.255685 | ||||||||
\(836\) | − | 1.06216e6i | − | 1.51977i | ||||||
\(837\) | 154348.i | 0.220318i | ||||||||
\(838\) | 1.30755e6 | 1.86196 | ||||||||
\(839\) | − | 999621.i | − | 1.42008i | −0.704164 | − | 0.710038i | \(-0.748678\pi\) | ||
0.704164 | − | 0.710038i | \(-0.251322\pi\) | |||||||
\(840\) | 9874.94i | 0.0139951i | ||||||||
\(841\) | 1.31604e6 | 1.86070 | ||||||||
\(842\) | 1.28919e6 | 1.81842 | ||||||||
\(843\) | 669885. | 0.942638 | ||||||||
\(844\) | 1.88190e6i | 2.64187i | ||||||||
\(845\) | −81737.4 | −0.114474 | ||||||||
\(846\) | 390179. | 0.545158 | ||||||||
\(847\) | −49884.2 | −0.0695338 | ||||||||
\(848\) | −569896. | −0.792509 | ||||||||
\(849\) | 183850.i | 0.255063i | ||||||||
\(850\) | 433393.i | 0.599852i | ||||||||
\(851\) | −78437.1 | −0.108308 | ||||||||
\(852\) | 599684. | 0.826121 | ||||||||
\(853\) | 11376.6 | 0.0156356 | 0.00781781 | − | 0.999969i | \(-0.497511\pi\) | ||||
0.00781781 | + | 0.999969i | \(0.497511\pi\) | |||||||
\(854\) | 48872.0 | 0.0670108 | ||||||||
\(855\) | −108713. | −0.148713 | ||||||||
\(856\) | − | 126190.i | − | 0.172217i | ||||||
\(857\) | 404528.i | 0.550791i | 0.961331 | + | 0.275396i | \(0.0888089\pi\) | ||||
−0.961331 | + | 0.275396i | \(0.911191\pi\) | |||||||
\(858\) | − | 753777.i | − | 1.02392i | ||||||
\(859\) | 633417.i | 0.858427i | 0.903203 | + | 0.429213i | \(0.141209\pi\) | ||||
−0.903203 | + | 0.429213i | \(0.858791\pi\) | |||||||
\(860\) | 645930.i | 0.873350i | ||||||||
\(861\) | −10447.7 | −0.0140934 | ||||||||
\(862\) | −472318. | −0.635653 | ||||||||
\(863\) | − | 1.26751e6i | − | 1.70188i | −0.525262 | − | 0.850941i | \(-0.676033\pi\) | ||
0.525262 | − | 0.850941i | \(-0.323967\pi\) | |||||||
\(864\) | − | 195606.i | − | 0.262033i | ||||||
\(865\) | − | 341666.i | − | 0.456636i | ||||||
\(866\) | − | 1.50713e6i | − | 2.00963i | ||||||
\(867\) | 310098. | 0.412534 | ||||||||
\(868\) | 107914.i | 0.143231i | ||||||||
\(869\) | 1.71859e6i | 2.27580i | ||||||||
\(870\) | − | 579662.i | − | 0.765837i | ||||||
\(871\) | 404412. | 0.533074 | ||||||||
\(872\) | −360767. | −0.474453 | ||||||||
\(873\) | 97057.2i | 0.127350i | ||||||||
\(874\) | −803487. | −1.05186 | ||||||||
\(875\) | 64351.1 | 0.0840504 | ||||||||
\(876\) | − | 228862.i | − | 0.298239i | ||||||
\(877\) | 496024. | 0.644917 | 0.322458 | − | 0.946584i | \(-0.395491\pi\) | ||||
0.322458 | + | 0.946584i | \(0.395491\pi\) | |||||||
\(878\) | 268246.i | 0.347971i | ||||||||
\(879\) | 144363. | 0.186844 | ||||||||
\(880\) | 296104.i | 0.382366i | ||||||||
\(881\) | 1.10943e6i | 1.42938i | 0.699442 | + | 0.714690i | \(0.253432\pi\) | ||||
−0.699442 | + | 0.714690i | \(0.746568\pi\) | |||||||
\(882\) | 392143.i | 0.504089i | ||||||||
\(883\) | −1.09641e6 | −1.40622 | −0.703109 | − | 0.711082i | \(-0.748205\pi\) | ||||
−0.703109 | + | 0.711082i | \(0.748205\pi\) | |||||||
\(884\) | − | 488881.i | − | 0.625603i | ||||||
\(885\) | 136216. | + | 188329.i | 0.173916 | + | 0.240453i | ||||
\(886\) | −1.24764e6 | −1.58935 | ||||||||
\(887\) | 1.14912e6i | 1.46055i | 0.683153 | + | 0.730275i | \(0.260608\pi\) | ||||
−0.683153 | + | 0.730275i | \(0.739392\pi\) | |||||||
\(888\) | −31080.0 | −0.0394144 | ||||||||
\(889\) | −43399.0 | −0.0549132 | ||||||||
\(890\) | −135776. | −0.171412 | ||||||||
\(891\) | 116292.i | 0.146486i | ||||||||
\(892\) | −409885. | −0.515148 | ||||||||
\(893\) | 741920.i | 0.930367i | ||||||||
\(894\) | 143807. | 0.179930 | ||||||||
\(895\) | 305390.i | 0.381250i | ||||||||
\(896\) | − | 71646.4i | − | 0.0892438i | ||||||
\(897\) | −325282. | −0.404273 | ||||||||
\(898\) | − | 226326.i | − | 0.280661i | ||||||
\(899\) | − | 1.56490e6i | − | 1.93628i | ||||||
\(900\) | 263850. | 0.325740 | ||||||||
\(901\) | 609191. | 0.750419 | ||||||||
\(902\) | 424082. | 0.521238 | ||||||||
\(903\) | − | 56740.3i | − | 0.0695851i | ||||||
\(904\) | −301083. | −0.368425 | ||||||||
\(905\) | 322055. | 0.393218 | ||||||||
\(906\) | −897284. | −1.09313 | ||||||||
\(907\) | 152142. | 0.184941 | 0.0924706 | − | 0.995715i | \(-0.470524\pi\) | ||||
0.0924706 | + | 0.995715i | \(0.470524\pi\) | |||||||
\(908\) | − | 580313.i | − | 0.703867i | ||||||
\(909\) | 247258.i | 0.299242i | ||||||||
\(910\) | −53940.1 | −0.0651372 | ||||||||
\(911\) | 38792.0 | 0.0467418 | 0.0233709 | − | 0.999727i | \(-0.492560\pi\) | ||||
0.0233709 | + | 0.999727i | \(0.492560\pi\) | |||||||
\(912\) | 235190. | 0.282768 | ||||||||
\(913\) | −1.74782e6 | −2.09679 | ||||||||
\(914\) | 177463. | 0.212430 | ||||||||
\(915\) | 115827.i | 0.138346i | ||||||||
\(916\) | 150567.i | 0.179448i | ||||||||
\(917\) | − | 129483.i | − | 0.153984i | ||||||
\(918\) | 132216.i | 0.156891i | ||||||||
\(919\) | − | 1.11869e6i | − | 1.32459i | −0.749245 | − | 0.662293i | \(-0.769584\pi\) | ||
0.749245 | − | 0.662293i | \(-0.230416\pi\) | |||||||
\(920\) | −172973. | −0.204364 | ||||||||
\(921\) | 454492. | 0.535805 | ||||||||
\(922\) | 1.55085e6i | 1.82435i | ||||||||
\(923\) | 809225.i | 0.949874i | ||||||||
\(924\) | 81307.0i | 0.0952322i | ||||||||
\(925\) | 85854.8i | 0.100342i | ||||||||
\(926\) | −2.35960e6 | −2.75180 | ||||||||
\(927\) | 72431.7i | 0.0842887i | ||||||||
\(928\) | 1.98322e6i | 2.30289i | ||||||||
\(929\) | 872704.i | 1.01120i | 0.862769 | + | 0.505598i | \(0.168728\pi\) | ||||
−0.862769 | + | 0.505598i | \(0.831272\pi\) | |||||||
\(930\) | −448330. | −0.518361 | ||||||||
\(931\) | −745656. | −0.860279 | ||||||||
\(932\) | − | 1.27107e6i | − | 1.46332i | ||||||
\(933\) | −638558. | −0.733563 | ||||||||
\(934\) | −2.10303e6 | −2.41074 | ||||||||
\(935\) | − | 316520.i | − | 0.362058i | ||||||
\(936\) | −128890. | −0.147118 | ||||||||
\(937\) | 1.09424e6i | 1.24633i | 0.782089 | + | 0.623167i | \(0.214154\pi\) | ||||
−0.782089 | + | 0.623167i | \(0.785846\pi\) | |||||||
\(938\) | −76468.1 | −0.0869110 | ||||||||
\(939\) | − | 69355.4i | − | 0.0786591i | ||||||
\(940\) | 646530.i | 0.731700i | ||||||||
\(941\) | − | 145369.i | − | 0.164169i | −0.996625 | − | 0.0820845i | \(-0.973842\pi\) | ||
0.996625 | − | 0.0820845i | \(-0.0261578\pi\) | |||||||
\(942\) | 262099. | 0.295368 | ||||||||
\(943\) | − | 183007.i | − | 0.205799i | ||||||
\(944\) | −294689. | − | 407431.i | −0.330689 | − | 0.457204i | ||||
\(945\) | 8321.85 | 0.00931873 | ||||||||
\(946\) | 2.30314e6i | 2.57358i | ||||||||
\(947\) | −1.33630e6 | −1.49006 | −0.745032 | − | 0.667028i | \(-0.767566\pi\) | ||||
−0.745032 | + | 0.667028i | \(0.767566\pi\) | |||||||
\(948\) | 1.18954e6 | 1.32362 | ||||||||
\(949\) | 308830. | 0.342916 | ||||||||
\(950\) | 879472.i | 0.974484i | ||||||||
\(951\) | 5777.24 | 0.00638792 | ||||||||
\(952\) | 22836.5i | 0.0251974i | ||||||||
\(953\) | −699411. | −0.770099 | −0.385050 | − | 0.922896i | \(-0.625816\pi\) | ||||
−0.385050 | + | 0.922896i | \(0.625816\pi\) | |||||||
\(954\) | − | 650130.i | − | 0.714337i | ||||||
\(955\) | 108282.i | 0.118727i | ||||||||
\(956\) | −1.67840e6 | −1.83645 | ||||||||
\(957\) | − | 1.17906e6i | − | 1.28740i | ||||||
\(958\) | − | 1.86086e6i | − | 2.02760i | ||||||
\(959\) | −48681.6 | −0.0529331 | ||||||||
\(960\) | 413853. | 0.449059 | ||||||||
\(961\) | −286828. | −0.310581 | ||||||||
\(962\) | − | 169769.i | − | 0.183446i | ||||||
\(963\) | −106343. | −0.114672 | ||||||||
\(964\) | 1.07139e6 | 1.15290 | ||||||||
\(965\) | −66331.9 | −0.0712308 | ||||||||
\(966\) | 61505.9 | 0.0659117 | ||||||||
\(967\) | − | 776605.i | − | 0.830514i | −0.909704 | − | 0.415257i | \(-0.863692\pi\) | ||
0.909704 | − | 0.415257i | \(-0.136308\pi\) | |||||||
\(968\) | − | 346232.i | − | 0.369502i | ||||||
\(969\) | −251407. | −0.267750 | ||||||||
\(970\) | −281919. | −0.299627 | ||||||||
\(971\) | 1.06596e6 | 1.13058 | 0.565292 | − | 0.824891i | \(-0.308764\pi\) | ||||
0.565292 | + | 0.824891i | \(0.308764\pi\) | |||||||
\(972\) | 80493.0 | 0.0851972 | ||||||||
\(973\) | 62433.0 | 0.0659460 | ||||||||
\(974\) | 1.99804e6i | 2.10614i | ||||||||
\(975\) | 356043.i | 0.374536i | ||||||||
\(976\) | − | 250580.i | − | 0.263055i | ||||||
\(977\) | − | 637748.i | − | 0.668129i | −0.942550 | − | 0.334064i | \(-0.891580\pi\) | ||
0.942550 | − | 0.334064i | \(-0.108420\pi\) | |||||||
\(978\) | − | 699990.i | − | 0.731837i | ||||||
\(979\) | −276175. | −0.288150 | ||||||||
\(980\) | −649786. | −0.676578 | ||||||||
\(981\) | 304027.i | 0.315918i | ||||||||
\(982\) | 2.01729e6i | 2.09192i | ||||||||
\(983\) | − | 317307.i | − | 0.328377i | −0.986429 | − | 0.164189i | \(-0.947499\pi\) | ||
0.986429 | − | 0.164189i | \(-0.0525006\pi\) | |||||||
\(984\) | − | 72514.7i | − | 0.0748920i | ||||||
\(985\) | −170407. | −0.175636 | ||||||||
\(986\) | − | 1.34051e6i | − | 1.37885i | ||||||
\(987\) | − | 56793.0i | − | 0.0582989i | ||||||
\(988\) | − | 992073.i | − | 1.01632i | ||||||
\(989\) | 993886. | 1.01612 | ||||||||
\(990\) | −337791. | −0.344650 | ||||||||
\(991\) | − | 784221.i | − | 0.798530i | −0.916836 | − | 0.399265i | \(-0.869265\pi\) | ||
0.916836 | − | 0.399265i | \(-0.130735\pi\) | |||||||
\(992\) | 1.53389e6 | 1.55873 | ||||||||
\(993\) | −736071. | −0.746486 | ||||||||
\(994\) | − | 153012.i | − | 0.154865i | ||||||
\(995\) | 245796. | 0.248272 | ||||||||
\(996\) | 1.20977e6i | 1.21951i | ||||||||
\(997\) | 353252. | 0.355381 | 0.177691 | − | 0.984086i | \(-0.443137\pi\) | ||||
0.177691 | + | 0.984086i | \(0.443137\pi\) | |||||||
\(998\) | 1.26398e6i | 1.26905i | ||||||||
\(999\) | 26191.9i | 0.0262443i |
(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 | 177.5.c.a.58.6 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.35 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.35 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.6 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.6 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.35 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.6 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.35 | 40 | 3.2 | odd | 2 |