Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.504544\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.504544 | 0.225639 | 0.112820 | − | 0.993615i | \(-0.464012\pi\) | ||||
0.112820 | + | 0.993615i | \(0.464012\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.39214 | 0.904144 | 0.452072 | − | 0.891981i | \(-0.350685\pi\) | ||||
0.452072 | + | 0.891981i | \(0.350685\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.504544 | 0.159551 | ||||||||
\(11\) | 1.10857 | 0.334246 | 0.167123 | − | 0.985936i | \(-0.446552\pi\) | ||||
0.167123 | + | 0.985936i | \(0.446552\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.49075 | 0.690811 | 0.345405 | − | 0.938454i | \(-0.387741\pi\) | ||||
0.345405 | + | 0.938454i | \(0.387741\pi\) | |||||||
\(14\) | 2.39214 | 0.639327 | ||||||||
\(15\) | −0.504544 | −0.130273 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 8.61570 | 1.97658 | 0.988288 | − | 0.152599i | \(-0.0487641\pi\) | ||||
0.988288 | + | 0.152599i | \(0.0487641\pi\) | |||||||
\(20\) | 0.504544 | 0.112820 | ||||||||
\(21\) | −2.39214 | −0.522008 | ||||||||
\(22\) | 1.10857 | 0.236348 | ||||||||
\(23\) | −0.297149 | −0.0619599 | −0.0309800 | − | 0.999520i | \(-0.509863\pi\) | ||||
−0.0309800 | + | 0.999520i | \(0.509863\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.74544 | −0.949087 | ||||||||
\(26\) | 2.49075 | 0.488477 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.39214 | 0.452072 | ||||||||
\(29\) | 7.46215 | 1.38569 | 0.692844 | − | 0.721088i | \(-0.256358\pi\) | ||||
0.692844 | + | 0.721088i | \(0.256358\pi\) | |||||||
\(30\) | −0.504544 | −0.0921168 | ||||||||
\(31\) | 5.69421 | 1.02271 | 0.511355 | − | 0.859369i | \(-0.329144\pi\) | ||||
0.511355 | + | 0.859369i | \(0.329144\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.10857 | −0.192977 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 1.20694 | 0.204010 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.5598 | −1.90042 | −0.950212 | − | 0.311603i | \(-0.899134\pi\) | ||||
−0.950212 | + | 0.311603i | \(0.899134\pi\) | |||||||
\(38\) | 8.61570 | 1.39765 | ||||||||
\(39\) | −2.49075 | −0.398840 | ||||||||
\(40\) | 0.504544 | 0.0797755 | ||||||||
\(41\) | −4.27848 | −0.668187 | −0.334093 | − | 0.942540i | \(-0.608430\pi\) | ||||
−0.334093 | + | 0.942540i | \(0.608430\pi\) | |||||||
\(42\) | −2.39214 | −0.369115 | ||||||||
\(43\) | 0.580112 | 0.0884662 | 0.0442331 | − | 0.999021i | \(-0.485916\pi\) | ||||
0.0442331 | + | 0.999021i | \(0.485916\pi\) | |||||||
\(44\) | 1.10857 | 0.167123 | ||||||||
\(45\) | 0.504544 | 0.0752130 | ||||||||
\(46\) | −0.297149 | −0.0438123 | ||||||||
\(47\) | 10.6814 | 1.55805 | 0.779023 | − | 0.626996i | \(-0.215716\pi\) | ||||
0.779023 | + | 0.626996i | \(0.215716\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.27766 | −0.182523 | ||||||||
\(50\) | −4.74544 | −0.671106 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 2.49075 | 0.345405 | ||||||||
\(53\) | 1.44391 | 0.198336 | 0.0991680 | − | 0.995071i | \(-0.468382\pi\) | ||||
0.0991680 | + | 0.995071i | \(0.468382\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.559322 | 0.0754190 | ||||||||
\(56\) | 2.39214 | 0.319663 | ||||||||
\(57\) | −8.61570 | −1.14118 | ||||||||
\(58\) | 7.46215 | 0.979829 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −0.504544 | −0.0651364 | ||||||||
\(61\) | 2.02440 | 0.259198 | 0.129599 | − | 0.991567i | \(-0.458631\pi\) | ||||
0.129599 | + | 0.991567i | \(0.458631\pi\) | |||||||
\(62\) | 5.69421 | 0.723166 | ||||||||
\(63\) | 2.39214 | 0.301381 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.25670 | 0.155874 | ||||||||
\(66\) | −1.10857 | −0.136455 | ||||||||
\(67\) | −6.76235 | −0.826153 | −0.413076 | − | 0.910696i | \(-0.635546\pi\) | ||||
−0.413076 | + | 0.910696i | \(0.635546\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 0.297149 | 0.0357726 | ||||||||
\(70\) | 1.20694 | 0.144257 | ||||||||
\(71\) | −3.30733 | −0.392507 | −0.196254 | − | 0.980553i | \(-0.562878\pi\) | ||||
−0.196254 | + | 0.980553i | \(0.562878\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 16.7045 | 1.95511 | 0.977557 | − | 0.210672i | \(-0.0675651\pi\) | ||||
0.977557 | + | 0.210672i | \(0.0675651\pi\) | |||||||
\(74\) | −11.5598 | −1.34380 | ||||||||
\(75\) | 4.74544 | 0.547956 | ||||||||
\(76\) | 8.61570 | 0.988288 | ||||||||
\(77\) | 2.65185 | 0.302207 | ||||||||
\(78\) | −2.49075 | −0.282022 | ||||||||
\(79\) | 5.03441 | 0.566415 | 0.283208 | − | 0.959059i | \(-0.408601\pi\) | ||||
0.283208 | + | 0.959059i | \(0.408601\pi\) | |||||||
\(80\) | 0.504544 | 0.0564098 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.27848 | −0.472479 | ||||||||
\(83\) | −11.1379 | −1.22254 | −0.611271 | − | 0.791421i | \(-0.709342\pi\) | ||||
−0.611271 | + | 0.791421i | \(0.709342\pi\) | |||||||
\(84\) | −2.39214 | −0.261004 | ||||||||
\(85\) | −0.504544 | −0.0547255 | ||||||||
\(86\) | 0.580112 | 0.0625551 | ||||||||
\(87\) | −7.46215 | −0.800027 | ||||||||
\(88\) | 1.10857 | 0.118174 | ||||||||
\(89\) | −10.9550 | −1.16123 | −0.580615 | − | 0.814178i | \(-0.697188\pi\) | ||||
−0.580615 | + | 0.814178i | \(0.697188\pi\) | |||||||
\(90\) | 0.504544 | 0.0531836 | ||||||||
\(91\) | 5.95823 | 0.624592 | ||||||||
\(92\) | −0.297149 | −0.0309800 | ||||||||
\(93\) | −5.69421 | −0.590462 | ||||||||
\(94\) | 10.6814 | 1.10170 | ||||||||
\(95\) | 4.34700 | 0.445993 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.46768 | −0.758228 | −0.379114 | − | 0.925350i | \(-0.623771\pi\) | ||||
−0.379114 | + | 0.925350i | \(0.623771\pi\) | |||||||
\(98\) | −1.27766 | −0.129063 | ||||||||
\(99\) | 1.10857 | 0.111415 | ||||||||
\(100\) | −4.74544 | −0.474544 | ||||||||
\(101\) | −11.0160 | −1.09613 | −0.548066 | − | 0.836435i | \(-0.684636\pi\) | ||||
−0.548066 | + | 0.836435i | \(0.684636\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 0.756325 | 0.0745229 | 0.0372615 | − | 0.999306i | \(-0.488137\pi\) | ||||
0.0372615 | + | 0.999306i | \(0.488137\pi\) | |||||||
\(104\) | 2.49075 | 0.244238 | ||||||||
\(105\) | −1.20694 | −0.117785 | ||||||||
\(106\) | 1.44391 | 0.140245 | ||||||||
\(107\) | −11.2590 | −1.08845 | −0.544225 | − | 0.838939i | \(-0.683176\pi\) | ||||
−0.544225 | + | 0.838939i | \(0.683176\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.4184 | 1.57259 | 0.786297 | − | 0.617848i | \(-0.211995\pi\) | ||||
0.786297 | + | 0.617848i | \(0.211995\pi\) | |||||||
\(110\) | 0.559322 | 0.0533293 | ||||||||
\(111\) | 11.5598 | 1.09721 | ||||||||
\(112\) | 2.39214 | 0.226036 | ||||||||
\(113\) | 3.44593 | 0.324166 | 0.162083 | − | 0.986777i | \(-0.448179\pi\) | ||||
0.162083 | + | 0.986777i | \(0.448179\pi\) | |||||||
\(114\) | −8.61570 | −0.806934 | ||||||||
\(115\) | −0.149925 | −0.0139806 | ||||||||
\(116\) | 7.46215 | 0.692844 | ||||||||
\(117\) | 2.49075 | 0.230270 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −2.39214 | −0.219287 | ||||||||
\(120\) | −0.504544 | −0.0460584 | ||||||||
\(121\) | −9.77107 | −0.888279 | ||||||||
\(122\) | 2.02440 | 0.183280 | ||||||||
\(123\) | 4.27848 | 0.385778 | ||||||||
\(124\) | 5.69421 | 0.511355 | ||||||||
\(125\) | −4.91700 | −0.439790 | ||||||||
\(126\) | 2.39214 | 0.213109 | ||||||||
\(127\) | 12.7425 | 1.13071 | 0.565357 | − | 0.824847i | \(-0.308739\pi\) | ||||
0.565357 | + | 0.824847i | \(0.308739\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.580112 | −0.0510760 | ||||||||
\(130\) | 1.25670 | 0.110219 | ||||||||
\(131\) | −6.32230 | −0.552382 | −0.276191 | − | 0.961103i | \(-0.589072\pi\) | ||||
−0.276191 | + | 0.961103i | \(0.589072\pi\) | |||||||
\(132\) | −1.10857 | −0.0964886 | ||||||||
\(133\) | 20.6100 | 1.78711 | ||||||||
\(134\) | −6.76235 | −0.584178 | ||||||||
\(135\) | −0.504544 | −0.0434243 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 2.01041 | 0.171761 | 0.0858805 | − | 0.996305i | \(-0.472630\pi\) | ||||
0.0858805 | + | 0.996305i | \(0.472630\pi\) | |||||||
\(138\) | 0.297149 | 0.0252950 | ||||||||
\(139\) | 16.0190 | 1.35872 | 0.679358 | − | 0.733807i | \(-0.262259\pi\) | ||||
0.679358 | + | 0.733807i | \(0.262259\pi\) | |||||||
\(140\) | 1.20694 | 0.102005 | ||||||||
\(141\) | −10.6814 | −0.899538 | ||||||||
\(142\) | −3.30733 | −0.277545 | ||||||||
\(143\) | 2.76117 | 0.230901 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.76499 | 0.312665 | ||||||||
\(146\) | 16.7045 | 1.38247 | ||||||||
\(147\) | 1.27766 | 0.105380 | ||||||||
\(148\) | −11.5598 | −0.950212 | ||||||||
\(149\) | 4.02796 | 0.329983 | 0.164992 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164992 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(150\) | 4.74544 | 0.387463 | ||||||||
\(151\) | −3.76173 | −0.306125 | −0.153063 | − | 0.988216i | \(-0.548914\pi\) | ||||
−0.153063 | + | 0.988216i | \(0.548914\pi\) | |||||||
\(152\) | 8.61570 | 0.698825 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 2.65185 | 0.213693 | ||||||||
\(155\) | 2.87298 | 0.230763 | ||||||||
\(156\) | −2.49075 | −0.199420 | ||||||||
\(157\) | 0.703406 | 0.0561379 | 0.0280690 | − | 0.999606i | \(-0.491064\pi\) | ||||
0.0280690 | + | 0.999606i | \(0.491064\pi\) | |||||||
\(158\) | 5.03441 | 0.400516 | ||||||||
\(159\) | −1.44391 | −0.114509 | ||||||||
\(160\) | 0.504544 | 0.0398877 | ||||||||
\(161\) | −0.710823 | −0.0560207 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 7.07001 | 0.553766 | 0.276883 | − | 0.960904i | \(-0.410699\pi\) | ||||
0.276883 | + | 0.960904i | \(0.410699\pi\) | |||||||
\(164\) | −4.27848 | −0.334093 | ||||||||
\(165\) | −0.559322 | −0.0435432 | ||||||||
\(166\) | −11.1379 | −0.864468 | ||||||||
\(167\) | 14.6374 | 1.13268 | 0.566339 | − | 0.824172i | \(-0.308359\pi\) | ||||
0.566339 | + | 0.824172i | \(0.308359\pi\) | |||||||
\(168\) | −2.39214 | −0.184558 | ||||||||
\(169\) | −6.79615 | −0.522781 | ||||||||
\(170\) | −0.504544 | −0.0386968 | ||||||||
\(171\) | 8.61570 | 0.658859 | ||||||||
\(172\) | 0.580112 | 0.0442331 | ||||||||
\(173\) | 14.1671 | 1.07711 | 0.538554 | − | 0.842591i | \(-0.318971\pi\) | ||||
0.538554 | + | 0.842591i | \(0.318971\pi\) | |||||||
\(174\) | −7.46215 | −0.565704 | ||||||||
\(175\) | −11.3518 | −0.858112 | ||||||||
\(176\) | 1.10857 | 0.0835616 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | −10.9550 | −0.821113 | ||||||||
\(179\) | −13.8282 | −1.03357 | −0.516786 | − | 0.856115i | \(-0.672872\pi\) | ||||
−0.516786 | + | 0.856115i | \(0.672872\pi\) | |||||||
\(180\) | 0.504544 | 0.0376065 | ||||||||
\(181\) | −17.2329 | −1.28091 | −0.640456 | − | 0.767995i | \(-0.721254\pi\) | ||||
−0.640456 | + | 0.767995i | \(0.721254\pi\) | |||||||
\(182\) | 5.95823 | 0.441654 | ||||||||
\(183\) | −2.02440 | −0.149648 | ||||||||
\(184\) | −0.297149 | −0.0219061 | ||||||||
\(185\) | −5.83245 | −0.428810 | ||||||||
\(186\) | −5.69421 | −0.417520 | ||||||||
\(187\) | −1.10857 | −0.0810666 | ||||||||
\(188\) | 10.6814 | 0.779023 | ||||||||
\(189\) | −2.39214 | −0.174003 | ||||||||
\(190\) | 4.34700 | 0.315365 | ||||||||
\(191\) | −15.1512 | −1.09630 | −0.548151 | − | 0.836379i | \(-0.684668\pi\) | ||||
−0.548151 | + | 0.836379i | \(0.684668\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 19.2590 | 1.38630 | 0.693148 | − | 0.720795i | \(-0.256223\pi\) | ||||
0.693148 | + | 0.720795i | \(0.256223\pi\) | |||||||
\(194\) | −7.46768 | −0.536148 | ||||||||
\(195\) | −1.25670 | −0.0899938 | ||||||||
\(196\) | −1.27766 | −0.0912615 | ||||||||
\(197\) | 20.0314 | 1.42718 | 0.713589 | − | 0.700565i | \(-0.247069\pi\) | ||||
0.713589 | + | 0.700565i | \(0.247069\pi\) | |||||||
\(198\) | 1.10857 | 0.0787826 | ||||||||
\(199\) | 16.4279 | 1.16454 | 0.582270 | − | 0.812996i | \(-0.302165\pi\) | ||||
0.582270 | + | 0.812996i | \(0.302165\pi\) | |||||||
\(200\) | −4.74544 | −0.335553 | ||||||||
\(201\) | 6.76235 | 0.476980 | ||||||||
\(202\) | −11.0160 | −0.775082 | ||||||||
\(203\) | 17.8505 | 1.25286 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −2.15868 | −0.150769 | ||||||||
\(206\) | 0.756325 | 0.0526957 | ||||||||
\(207\) | −0.297149 | −0.0206533 | ||||||||
\(208\) | 2.49075 | 0.172703 | ||||||||
\(209\) | 9.55110 | 0.660663 | ||||||||
\(210\) | −1.20694 | −0.0832869 | ||||||||
\(211\) | −18.4141 | −1.26768 | −0.633839 | − | 0.773465i | \(-0.718522\pi\) | ||||
−0.633839 | + | 0.773465i | \(0.718522\pi\) | |||||||
\(212\) | 1.44391 | 0.0991680 | ||||||||
\(213\) | 3.30733 | 0.226614 | ||||||||
\(214\) | −11.2590 | −0.769651 | ||||||||
\(215\) | 0.292692 | 0.0199614 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 13.6214 | 0.924678 | ||||||||
\(218\) | 16.4184 | 1.11199 | ||||||||
\(219\) | −16.7045 | −1.12879 | ||||||||
\(220\) | 0.559322 | 0.0377095 | ||||||||
\(221\) | −2.49075 | −0.167546 | ||||||||
\(222\) | 11.5598 | 0.775845 | ||||||||
\(223\) | 18.3528 | 1.22899 | 0.614497 | − | 0.788919i | \(-0.289359\pi\) | ||||
0.614497 | + | 0.788919i | \(0.289359\pi\) | |||||||
\(224\) | 2.39214 | 0.159832 | ||||||||
\(225\) | −4.74544 | −0.316362 | ||||||||
\(226\) | 3.44593 | 0.229220 | ||||||||
\(227\) | −10.3618 | −0.687735 | −0.343867 | − | 0.939018i | \(-0.611737\pi\) | ||||
−0.343867 | + | 0.939018i | \(0.611737\pi\) | |||||||
\(228\) | −8.61570 | −0.570588 | ||||||||
\(229\) | 14.7633 | 0.975586 | 0.487793 | − | 0.872959i | \(-0.337802\pi\) | ||||
0.487793 | + | 0.872959i | \(0.337802\pi\) | |||||||
\(230\) | −0.149925 | −0.00988576 | ||||||||
\(231\) | −2.65185 | −0.174479 | ||||||||
\(232\) | 7.46215 | 0.489914 | ||||||||
\(233\) | 9.14378 | 0.599029 | 0.299514 | − | 0.954092i | \(-0.403175\pi\) | ||||
0.299514 | + | 0.954092i | \(0.403175\pi\) | |||||||
\(234\) | 2.49075 | 0.162826 | ||||||||
\(235\) | 5.38925 | 0.351556 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −5.03441 | −0.327020 | ||||||||
\(238\) | −2.39214 | −0.155059 | ||||||||
\(239\) | −18.7515 | −1.21293 | −0.606466 | − | 0.795109i | \(-0.707413\pi\) | ||||
−0.606466 | + | 0.795109i | \(0.707413\pi\) | |||||||
\(240\) | −0.504544 | −0.0325682 | ||||||||
\(241\) | −26.0481 | −1.67791 | −0.838954 | − | 0.544203i | \(-0.816832\pi\) | ||||
−0.838954 | + | 0.544203i | \(0.816832\pi\) | |||||||
\(242\) | −9.77107 | −0.628108 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.02440 | 0.129599 | ||||||||
\(245\) | −0.644637 | −0.0411843 | ||||||||
\(246\) | 4.27848 | 0.272786 | ||||||||
\(247\) | 21.4596 | 1.36544 | ||||||||
\(248\) | 5.69421 | 0.361583 | ||||||||
\(249\) | 11.1379 | 0.705835 | ||||||||
\(250\) | −4.91700 | −0.310979 | ||||||||
\(251\) | 13.1829 | 0.832098 | 0.416049 | − | 0.909342i | \(-0.363415\pi\) | ||||
0.416049 | + | 0.909342i | \(0.363415\pi\) | |||||||
\(252\) | 2.39214 | 0.150691 | ||||||||
\(253\) | −0.329411 | −0.0207099 | ||||||||
\(254\) | 12.7425 | 0.799535 | ||||||||
\(255\) | 0.504544 | 0.0315958 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.11818 | 0.444020 | 0.222010 | − | 0.975044i | \(-0.428738\pi\) | ||||
0.222010 | + | 0.975044i | \(0.428738\pi\) | |||||||
\(258\) | −0.580112 | −0.0361162 | ||||||||
\(259\) | −27.6527 | −1.71826 | ||||||||
\(260\) | 1.25670 | 0.0779369 | ||||||||
\(261\) | 7.46215 | 0.461896 | ||||||||
\(262\) | −6.32230 | −0.390593 | ||||||||
\(263\) | −1.95363 | −0.120466 | −0.0602329 | − | 0.998184i | \(-0.519184\pi\) | ||||
−0.0602329 | + | 0.998184i | \(0.519184\pi\) | |||||||
\(264\) | −1.10857 | −0.0682277 | ||||||||
\(265\) | 0.728516 | 0.0447524 | ||||||||
\(266\) | 20.6100 | 1.26368 | ||||||||
\(267\) | 10.9550 | 0.670436 | ||||||||
\(268\) | −6.76235 | −0.413076 | ||||||||
\(269\) | −16.9311 | −1.03231 | −0.516155 | − | 0.856495i | \(-0.672637\pi\) | ||||
−0.516155 | + | 0.856495i | \(0.672637\pi\) | |||||||
\(270\) | −0.504544 | −0.0307056 | ||||||||
\(271\) | 3.34033 | 0.202911 | 0.101455 | − | 0.994840i | \(-0.467650\pi\) | ||||
0.101455 | + | 0.994840i | \(0.467650\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −5.95823 | −0.360609 | ||||||||
\(274\) | 2.01041 | 0.121453 | ||||||||
\(275\) | −5.26064 | −0.317229 | ||||||||
\(276\) | 0.297149 | 0.0178863 | ||||||||
\(277\) | 5.13891 | 0.308767 | 0.154384 | − | 0.988011i | \(-0.450661\pi\) | ||||
0.154384 | + | 0.988011i | \(0.450661\pi\) | |||||||
\(278\) | 16.0190 | 0.960757 | ||||||||
\(279\) | 5.69421 | 0.340904 | ||||||||
\(280\) | 1.20694 | 0.0721285 | ||||||||
\(281\) | 22.1434 | 1.32096 | 0.660481 | − | 0.750843i | \(-0.270352\pi\) | ||||
0.660481 | + | 0.750843i | \(0.270352\pi\) | |||||||
\(282\) | −10.6814 | −0.636069 | ||||||||
\(283\) | −0.0742288 | −0.00441245 | −0.00220622 | − | 0.999998i | \(-0.500702\pi\) | ||||
−0.00220622 | + | 0.999998i | \(0.500702\pi\) | |||||||
\(284\) | −3.30733 | −0.196254 | ||||||||
\(285\) | −4.34700 | −0.257494 | ||||||||
\(286\) | 2.76117 | 0.163272 | ||||||||
\(287\) | −10.2347 | −0.604137 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.76499 | 0.221088 | ||||||||
\(291\) | 7.46768 | 0.437763 | ||||||||
\(292\) | 16.7045 | 0.977557 | ||||||||
\(293\) | 20.8035 | 1.21535 | 0.607676 | − | 0.794185i | \(-0.292102\pi\) | ||||
0.607676 | + | 0.794185i | \(0.292102\pi\) | |||||||
\(294\) | 1.27766 | 0.0745147 | ||||||||
\(295\) | −0.504544 | −0.0293757 | ||||||||
\(296\) | −11.5598 | −0.671902 | ||||||||
\(297\) | −1.10857 | −0.0643257 | ||||||||
\(298\) | 4.02796 | 0.233333 | ||||||||
\(299\) | −0.740126 | −0.0428026 | ||||||||
\(300\) | 4.74544 | 0.273978 | ||||||||
\(301\) | 1.38771 | 0.0799862 | ||||||||
\(302\) | −3.76173 | −0.216463 | ||||||||
\(303\) | 11.0160 | 0.632852 | ||||||||
\(304\) | 8.61570 | 0.494144 | ||||||||
\(305\) | 1.02140 | 0.0584851 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −1.86618 | −0.106509 | −0.0532543 | − | 0.998581i | \(-0.516959\pi\) | ||||
−0.0532543 | + | 0.998581i | \(0.516959\pi\) | |||||||
\(308\) | 2.65185 | 0.151103 | ||||||||
\(309\) | −0.756325 | −0.0430258 | ||||||||
\(310\) | 2.87298 | 0.163174 | ||||||||
\(311\) | 7.60542 | 0.431264 | 0.215632 | − | 0.976475i | \(-0.430819\pi\) | ||||
0.215632 | + | 0.976475i | \(0.430819\pi\) | |||||||
\(312\) | −2.49075 | −0.141011 | ||||||||
\(313\) | −13.4270 | −0.758938 | −0.379469 | − | 0.925204i | \(-0.623893\pi\) | ||||
−0.379469 | + | 0.925204i | \(0.623893\pi\) | |||||||
\(314\) | 0.703406 | 0.0396955 | ||||||||
\(315\) | 1.20694 | 0.0680034 | ||||||||
\(316\) | 5.03441 | 0.283208 | ||||||||
\(317\) | −5.58422 | −0.313641 | −0.156821 | − | 0.987627i | \(-0.550124\pi\) | ||||
−0.156821 | + | 0.987627i | \(0.550124\pi\) | |||||||
\(318\) | −1.44391 | −0.0809703 | ||||||||
\(319\) | 8.27232 | 0.463161 | ||||||||
\(320\) | 0.504544 | 0.0282049 | ||||||||
\(321\) | 11.2590 | 0.628417 | ||||||||
\(322\) | −0.710823 | −0.0396126 | ||||||||
\(323\) | −8.61570 | −0.479390 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −11.8197 | −0.655639 | ||||||||
\(326\) | 7.07001 | 0.391572 | ||||||||
\(327\) | −16.4184 | −0.907938 | ||||||||
\(328\) | −4.27848 | −0.236240 | ||||||||
\(329\) | 25.5515 | 1.40870 | ||||||||
\(330\) | −0.559322 | −0.0307897 | ||||||||
\(331\) | −8.47838 | −0.466014 | −0.233007 | − | 0.972475i | \(-0.574856\pi\) | ||||
−0.233007 | + | 0.972475i | \(0.574856\pi\) | |||||||
\(332\) | −11.1379 | −0.611271 | ||||||||
\(333\) | −11.5598 | −0.633475 | ||||||||
\(334\) | 14.6374 | 0.800924 | ||||||||
\(335\) | −3.41191 | −0.186412 | ||||||||
\(336\) | −2.39214 | −0.130502 | ||||||||
\(337\) | −14.0945 | −0.767779 | −0.383889 | − | 0.923379i | \(-0.625416\pi\) | ||||
−0.383889 | + | 0.923379i | \(0.625416\pi\) | |||||||
\(338\) | −6.79615 | −0.369662 | ||||||||
\(339\) | −3.44593 | −0.187157 | ||||||||
\(340\) | −0.504544 | −0.0273628 | ||||||||
\(341\) | 6.31243 | 0.341837 | ||||||||
\(342\) | 8.61570 | 0.465884 | ||||||||
\(343\) | −19.8013 | −1.06917 | ||||||||
\(344\) | 0.580112 | 0.0312775 | ||||||||
\(345\) | 0.149925 | 0.00807169 | ||||||||
\(346\) | 14.1671 | 0.761630 | ||||||||
\(347\) | 1.41517 | 0.0759702 | 0.0379851 | − | 0.999278i | \(-0.487906\pi\) | ||||
0.0379851 | + | 0.999278i | \(0.487906\pi\) | |||||||
\(348\) | −7.46215 | −0.400013 | ||||||||
\(349\) | 28.2991 | 1.51482 | 0.757408 | − | 0.652942i | \(-0.226466\pi\) | ||||
0.757408 | + | 0.652942i | \(0.226466\pi\) | |||||||
\(350\) | −11.3518 | −0.606777 | ||||||||
\(351\) | −2.49075 | −0.132947 | ||||||||
\(352\) | 1.10857 | 0.0590870 | ||||||||
\(353\) | 25.1682 | 1.33957 | 0.669783 | − | 0.742557i | \(-0.266387\pi\) | ||||
0.669783 | + | 0.742557i | \(0.266387\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −1.66869 | −0.0885650 | ||||||||
\(356\) | −10.9550 | −0.580615 | ||||||||
\(357\) | 2.39214 | 0.126606 | ||||||||
\(358\) | −13.8282 | −0.730845 | ||||||||
\(359\) | −25.8153 | −1.36248 | −0.681239 | − | 0.732061i | \(-0.738559\pi\) | ||||
−0.681239 | + | 0.732061i | \(0.738559\pi\) | |||||||
\(360\) | 0.504544 | 0.0265918 | ||||||||
\(361\) | 55.2302 | 2.90685 | ||||||||
\(362\) | −17.2329 | −0.905741 | ||||||||
\(363\) | 9.77107 | 0.512848 | ||||||||
\(364\) | 5.95823 | 0.312296 | ||||||||
\(365\) | 8.42816 | 0.441150 | ||||||||
\(366\) | −2.02440 | −0.105817 | ||||||||
\(367\) | −19.5427 | −1.02012 | −0.510060 | − | 0.860139i | \(-0.670377\pi\) | ||||
−0.510060 | + | 0.860139i | \(0.670377\pi\) | |||||||
\(368\) | −0.297149 | −0.0154900 | ||||||||
\(369\) | −4.27848 | −0.222729 | ||||||||
\(370\) | −5.83245 | −0.303214 | ||||||||
\(371\) | 3.45403 | 0.179324 | ||||||||
\(372\) | −5.69421 | −0.295231 | ||||||||
\(373\) | −15.6479 | −0.810218 | −0.405109 | − | 0.914268i | \(-0.632767\pi\) | ||||
−0.405109 | + | 0.914268i | \(0.632767\pi\) | |||||||
\(374\) | −1.10857 | −0.0573228 | ||||||||
\(375\) | 4.91700 | 0.253913 | ||||||||
\(376\) | 10.6814 | 0.550852 | ||||||||
\(377\) | 18.5864 | 0.957247 | ||||||||
\(378\) | −2.39214 | −0.123038 | ||||||||
\(379\) | 19.6388 | 1.00878 | 0.504389 | − | 0.863477i | \(-0.331718\pi\) | ||||
0.504389 | + | 0.863477i | \(0.331718\pi\) | |||||||
\(380\) | 4.34700 | 0.222996 | ||||||||
\(381\) | −12.7425 | −0.652817 | ||||||||
\(382\) | −15.1512 | −0.775203 | ||||||||
\(383\) | −27.4639 | −1.40334 | −0.701669 | − | 0.712503i | \(-0.747562\pi\) | ||||
−0.701669 | + | 0.712503i | \(0.747562\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 1.33798 | 0.0681897 | ||||||||
\(386\) | 19.2590 | 0.980259 | ||||||||
\(387\) | 0.580112 | 0.0294887 | ||||||||
\(388\) | −7.46768 | −0.379114 | ||||||||
\(389\) | 0.794891 | 0.0403026 | 0.0201513 | − | 0.999797i | \(-0.493585\pi\) | ||||
0.0201513 | + | 0.999797i | \(0.493585\pi\) | |||||||
\(390\) | −1.25670 | −0.0636352 | ||||||||
\(391\) | 0.297149 | 0.0150275 | ||||||||
\(392\) | −1.27766 | −0.0645316 | ||||||||
\(393\) | 6.32230 | 0.318918 | ||||||||
\(394\) | 20.0314 | 1.00917 | ||||||||
\(395\) | 2.54008 | 0.127805 | ||||||||
\(396\) | 1.10857 | 0.0557077 | ||||||||
\(397\) | 34.5396 | 1.73349 | 0.866746 | − | 0.498749i | \(-0.166207\pi\) | ||||
0.866746 | + | 0.498749i | \(0.166207\pi\) | |||||||
\(398\) | 16.4279 | 0.823454 | ||||||||
\(399\) | −20.6100 | −1.03179 | ||||||||
\(400\) | −4.74544 | −0.237272 | ||||||||
\(401\) | 14.5890 | 0.728540 | 0.364270 | − | 0.931293i | \(-0.381319\pi\) | ||||
0.364270 | + | 0.931293i | \(0.381319\pi\) | |||||||
\(402\) | 6.76235 | 0.337276 | ||||||||
\(403\) | 14.1829 | 0.706499 | ||||||||
\(404\) | −11.0160 | −0.548066 | ||||||||
\(405\) | 0.504544 | 0.0250710 | ||||||||
\(406\) | 17.8505 | 0.885907 | ||||||||
\(407\) | −12.8149 | −0.635210 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −15.2900 | −0.756041 | −0.378020 | − | 0.925797i | \(-0.623395\pi\) | ||||
−0.378020 | + | 0.925797i | \(0.623395\pi\) | |||||||
\(410\) | −2.15868 | −0.106610 | ||||||||
\(411\) | −2.01041 | −0.0991663 | ||||||||
\(412\) | 0.756325 | 0.0372615 | ||||||||
\(413\) | −2.39214 | −0.117710 | ||||||||
\(414\) | −0.297149 | −0.0146041 | ||||||||
\(415\) | −5.61956 | −0.275853 | ||||||||
\(416\) | 2.49075 | 0.122119 | ||||||||
\(417\) | −16.0190 | −0.784455 | ||||||||
\(418\) | 9.55110 | 0.467160 | ||||||||
\(419\) | −17.9073 | −0.874830 | −0.437415 | − | 0.899260i | \(-0.644106\pi\) | ||||
−0.437415 | + | 0.899260i | \(0.644106\pi\) | |||||||
\(420\) | −1.20694 | −0.0588927 | ||||||||
\(421\) | 32.9581 | 1.60628 | 0.803139 | − | 0.595791i | \(-0.203161\pi\) | ||||
0.803139 | + | 0.595791i | \(0.203161\pi\) | |||||||
\(422\) | −18.4141 | −0.896384 | ||||||||
\(423\) | 10.6814 | 0.519349 | ||||||||
\(424\) | 1.44391 | 0.0701224 | ||||||||
\(425\) | 4.74544 | 0.230187 | ||||||||
\(426\) | 3.30733 | 0.160240 | ||||||||
\(427\) | 4.84265 | 0.234352 | ||||||||
\(428\) | −11.2590 | −0.544225 | ||||||||
\(429\) | −2.76117 | −0.133311 | ||||||||
\(430\) | 0.292692 | 0.0141149 | ||||||||
\(431\) | −23.3410 | −1.12430 | −0.562148 | − | 0.827037i | \(-0.690025\pi\) | ||||
−0.562148 | + | 0.827037i | \(0.690025\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 0.989051 | 0.0475308 | 0.0237654 | − | 0.999718i | \(-0.492435\pi\) | ||||
0.0237654 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(434\) | 13.6214 | 0.653846 | ||||||||
\(435\) | −3.76499 | −0.180517 | ||||||||
\(436\) | 16.4184 | 0.786297 | ||||||||
\(437\) | −2.56015 | −0.122469 | ||||||||
\(438\) | −16.7045 | −0.798172 | ||||||||
\(439\) | 12.8751 | 0.614493 | 0.307247 | − | 0.951630i | \(-0.400592\pi\) | ||||
0.307247 | + | 0.951630i | \(0.400592\pi\) | |||||||
\(440\) | 0.559322 | 0.0266647 | ||||||||
\(441\) | −1.27766 | −0.0608410 | ||||||||
\(442\) | −2.49075 | −0.118473 | ||||||||
\(443\) | 5.89332 | 0.280000 | 0.140000 | − | 0.990151i | \(-0.455290\pi\) | ||||
0.140000 | + | 0.990151i | \(0.455290\pi\) | |||||||
\(444\) | 11.5598 | 0.548605 | ||||||||
\(445\) | −5.52729 | −0.262019 | ||||||||
\(446\) | 18.3528 | 0.869031 | ||||||||
\(447\) | −4.02796 | −0.190516 | ||||||||
\(448\) | 2.39214 | 0.113018 | ||||||||
\(449\) | −38.4053 | −1.81246 | −0.906229 | − | 0.422786i | \(-0.861052\pi\) | ||||
−0.906229 | + | 0.422786i | \(0.861052\pi\) | |||||||
\(450\) | −4.74544 | −0.223702 | ||||||||
\(451\) | −4.74300 | −0.223339 | ||||||||
\(452\) | 3.44593 | 0.162083 | ||||||||
\(453\) | 3.76173 | 0.176742 | ||||||||
\(454\) | −10.3618 | −0.486302 | ||||||||
\(455\) | 3.00619 | 0.140932 | ||||||||
\(456\) | −8.61570 | −0.403467 | ||||||||
\(457\) | 17.1916 | 0.804188 | 0.402094 | − | 0.915598i | \(-0.368282\pi\) | ||||
0.402094 | + | 0.915598i | \(0.368282\pi\) | |||||||
\(458\) | 14.7633 | 0.689843 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −0.149925 | −0.00699029 | ||||||||
\(461\) | −6.69144 | −0.311651 | −0.155826 | − | 0.987785i | \(-0.549804\pi\) | ||||
−0.155826 | + | 0.987785i | \(0.549804\pi\) | |||||||
\(462\) | −2.65185 | −0.123375 | ||||||||
\(463\) | 15.1088 | 0.702167 | 0.351083 | − | 0.936344i | \(-0.385813\pi\) | ||||
0.351083 | + | 0.936344i | \(0.385813\pi\) | |||||||
\(464\) | 7.46215 | 0.346422 | ||||||||
\(465\) | −2.87298 | −0.133231 | ||||||||
\(466\) | 9.14378 | 0.423577 | ||||||||
\(467\) | 12.6074 | 0.583400 | 0.291700 | − | 0.956510i | \(-0.405779\pi\) | ||||
0.291700 | + | 0.956510i | \(0.405779\pi\) | |||||||
\(468\) | 2.49075 | 0.115135 | ||||||||
\(469\) | −16.1765 | −0.746962 | ||||||||
\(470\) | 5.38925 | 0.248588 | ||||||||
\(471\) | −0.703406 | −0.0324113 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | 0.643094 | 0.0295695 | ||||||||
\(474\) | −5.03441 | −0.231238 | ||||||||
\(475\) | −40.8852 | −1.87594 | ||||||||
\(476\) | −2.39214 | −0.109644 | ||||||||
\(477\) | 1.44391 | 0.0661120 | ||||||||
\(478\) | −18.7515 | −0.857672 | ||||||||
\(479\) | −25.2284 | −1.15272 | −0.576358 | − | 0.817198i | \(-0.695526\pi\) | ||||
−0.576358 | + | 0.817198i | \(0.695526\pi\) | |||||||
\(480\) | −0.504544 | −0.0230292 | ||||||||
\(481\) | −28.7927 | −1.31283 | ||||||||
\(482\) | −26.0481 | −1.18646 | ||||||||
\(483\) | 0.710823 | 0.0323436 | ||||||||
\(484\) | −9.77107 | −0.444140 | ||||||||
\(485\) | −3.76778 | −0.171086 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 28.3456 | 1.28446 | 0.642231 | − | 0.766511i | \(-0.278009\pi\) | ||||
0.642231 | + | 0.766511i | \(0.278009\pi\) | |||||||
\(488\) | 2.02440 | 0.0916402 | ||||||||
\(489\) | −7.07001 | −0.319717 | ||||||||
\(490\) | −0.644637 | −0.0291217 | ||||||||
\(491\) | 11.1301 | 0.502293 | 0.251147 | − | 0.967949i | \(-0.419192\pi\) | ||||
0.251147 | + | 0.967949i | \(0.419192\pi\) | |||||||
\(492\) | 4.27848 | 0.192889 | ||||||||
\(493\) | −7.46215 | −0.336078 | ||||||||
\(494\) | 21.4596 | 0.965512 | ||||||||
\(495\) | 0.559322 | 0.0251397 | ||||||||
\(496\) | 5.69421 | 0.255678 | ||||||||
\(497\) | −7.91159 | −0.354883 | ||||||||
\(498\) | 11.1379 | 0.499101 | ||||||||
\(499\) | 2.70729 | 0.121195 | 0.0605975 | − | 0.998162i | \(-0.480699\pi\) | ||||
0.0605975 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(500\) | −4.91700 | −0.219895 | ||||||||
\(501\) | −14.6374 | −0.653952 | ||||||||
\(502\) | 13.1829 | 0.588382 | ||||||||
\(503\) | 30.5328 | 1.36139 | 0.680695 | − | 0.732567i | \(-0.261678\pi\) | ||||
0.680695 | + | 0.732567i | \(0.261678\pi\) | |||||||
\(504\) | 2.39214 | 0.106554 | ||||||||
\(505\) | −5.55806 | −0.247330 | ||||||||
\(506\) | −0.329411 | −0.0146441 | ||||||||
\(507\) | 6.79615 | 0.301828 | ||||||||
\(508\) | 12.7425 | 0.565357 | ||||||||
\(509\) | 5.62596 | 0.249366 | 0.124683 | − | 0.992197i | \(-0.460209\pi\) | ||||
0.124683 | + | 0.992197i | \(0.460209\pi\) | |||||||
\(510\) | 0.504544 | 0.0223416 | ||||||||
\(511\) | 39.9595 | 1.76771 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −8.61570 | −0.380392 | ||||||||
\(514\) | 7.11818 | 0.313969 | ||||||||
\(515\) | 0.381600 | 0.0168153 | ||||||||
\(516\) | −0.580112 | −0.0255380 | ||||||||
\(517\) | 11.8411 | 0.520771 | ||||||||
\(518\) | −27.6527 | −1.21499 | ||||||||
\(519\) | −14.1671 | −0.621869 | ||||||||
\(520\) | 1.25670 | 0.0551097 | ||||||||
\(521\) | 1.66052 | 0.0727486 | 0.0363743 | − | 0.999338i | \(-0.488419\pi\) | ||||
0.0363743 | + | 0.999338i | \(0.488419\pi\) | |||||||
\(522\) | 7.46215 | 0.326610 | ||||||||
\(523\) | −20.2227 | −0.884279 | −0.442139 | − | 0.896946i | \(-0.645780\pi\) | ||||
−0.442139 | + | 0.896946i | \(0.645780\pi\) | |||||||
\(524\) | −6.32230 | −0.276191 | ||||||||
\(525\) | 11.3518 | 0.495431 | ||||||||
\(526\) | −1.95363 | −0.0851822 | ||||||||
\(527\) | −5.69421 | −0.248044 | ||||||||
\(528\) | −1.10857 | −0.0482443 | ||||||||
\(529\) | −22.9117 | −0.996161 | ||||||||
\(530\) | 0.728516 | 0.0316447 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 20.6100 | 0.893555 | ||||||||
\(533\) | −10.6566 | −0.461591 | ||||||||
\(534\) | 10.9550 | 0.474070 | ||||||||
\(535\) | −5.68068 | −0.245597 | ||||||||
\(536\) | −6.76235 | −0.292089 | ||||||||
\(537\) | 13.8282 | 0.596733 | ||||||||
\(538\) | −16.9311 | −0.729953 | ||||||||
\(539\) | −1.41638 | −0.0610076 | ||||||||
\(540\) | −0.504544 | −0.0217121 | ||||||||
\(541\) | −8.72783 | −0.375239 | −0.187619 | − | 0.982242i | \(-0.560077\pi\) | ||||
−0.187619 | + | 0.982242i | \(0.560077\pi\) | |||||||
\(542\) | 3.34033 | 0.143479 | ||||||||
\(543\) | 17.2329 | 0.739534 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 8.28380 | 0.354839 | ||||||||
\(546\) | −5.95823 | −0.254989 | ||||||||
\(547\) | −25.2236 | −1.07848 | −0.539241 | − | 0.842152i | \(-0.681289\pi\) | ||||
−0.539241 | + | 0.842152i | \(0.681289\pi\) | |||||||
\(548\) | 2.01041 | 0.0858805 | ||||||||
\(549\) | 2.02440 | 0.0863992 | ||||||||
\(550\) | −5.26064 | −0.224315 | ||||||||
\(551\) | 64.2917 | 2.73892 | ||||||||
\(552\) | 0.297149 | 0.0126475 | ||||||||
\(553\) | 12.0430 | 0.512121 | ||||||||
\(554\) | 5.13891 | 0.218331 | ||||||||
\(555\) | 5.83245 | 0.247574 | ||||||||
\(556\) | 16.0190 | 0.679358 | ||||||||
\(557\) | 33.2320 | 1.40809 | 0.704043 | − | 0.710158i | \(-0.251376\pi\) | ||||
0.704043 | + | 0.710158i | \(0.251376\pi\) | |||||||
\(558\) | 5.69421 | 0.241055 | ||||||||
\(559\) | 1.44492 | 0.0611134 | ||||||||
\(560\) | 1.20694 | 0.0510026 | ||||||||
\(561\) | 1.10857 | 0.0468038 | ||||||||
\(562\) | 22.1434 | 0.934062 | ||||||||
\(563\) | −23.5533 | −0.992652 | −0.496326 | − | 0.868136i | \(-0.665318\pi\) | ||||
−0.496326 | + | 0.868136i | \(0.665318\pi\) | |||||||
\(564\) | −10.6814 | −0.449769 | ||||||||
\(565\) | 1.73862 | 0.0731445 | ||||||||
\(566\) | −0.0742288 | −0.00312007 | ||||||||
\(567\) | 2.39214 | 0.100460 | ||||||||
\(568\) | −3.30733 | −0.138772 | ||||||||
\(569\) | 10.5300 | 0.441440 | 0.220720 | − | 0.975337i | \(-0.429159\pi\) | ||||
0.220720 | + | 0.975337i | \(0.429159\pi\) | |||||||
\(570\) | −4.34700 | −0.182076 | ||||||||
\(571\) | 2.09884 | 0.0878339 | 0.0439169 | − | 0.999035i | \(-0.486016\pi\) | ||||
0.0439169 | + | 0.999035i | \(0.486016\pi\) | |||||||
\(572\) | 2.76117 | 0.115450 | ||||||||
\(573\) | 15.1512 | 0.632950 | ||||||||
\(574\) | −10.2347 | −0.427190 | ||||||||
\(575\) | 1.41010 | 0.0588054 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −10.9289 | −0.454974 | −0.227487 | − | 0.973781i | \(-0.573051\pi\) | ||||
−0.227487 | + | 0.973781i | \(0.573051\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −19.2590 | −0.800378 | ||||||||
\(580\) | 3.76499 | 0.156333 | ||||||||
\(581\) | −26.6434 | −1.10535 | ||||||||
\(582\) | 7.46768 | 0.309545 | ||||||||
\(583\) | 1.60067 | 0.0662931 | ||||||||
\(584\) | 16.7045 | 0.691237 | ||||||||
\(585\) | 1.25670 | 0.0519579 | ||||||||
\(586\) | 20.8035 | 0.859384 | ||||||||
\(587\) | −39.4414 | −1.62792 | −0.813961 | − | 0.580920i | \(-0.802693\pi\) | ||||
−0.813961 | + | 0.580920i | \(0.802693\pi\) | |||||||
\(588\) | 1.27766 | 0.0526899 | ||||||||
\(589\) | 49.0596 | 2.02147 | ||||||||
\(590\) | −0.504544 | −0.0207718 | ||||||||
\(591\) | −20.0314 | −0.823981 | ||||||||
\(592\) | −11.5598 | −0.475106 | ||||||||
\(593\) | −12.9734 | −0.532753 | −0.266376 | − | 0.963869i | \(-0.585826\pi\) | ||||
−0.266376 | + | 0.963869i | \(0.585826\pi\) | |||||||
\(594\) | −1.10857 | −0.0454852 | ||||||||
\(595\) | −1.20694 | −0.0494798 | ||||||||
\(596\) | 4.02796 | 0.164992 | ||||||||
\(597\) | −16.4279 | −0.672347 | ||||||||
\(598\) | −0.740126 | −0.0302660 | ||||||||
\(599\) | −20.4463 | −0.835412 | −0.417706 | − | 0.908582i | \(-0.637166\pi\) | ||||
−0.417706 | + | 0.908582i | \(0.637166\pi\) | |||||||
\(600\) | 4.74544 | 0.193732 | ||||||||
\(601\) | −23.0064 | −0.938451 | −0.469225 | − | 0.883078i | \(-0.655467\pi\) | ||||
−0.469225 | + | 0.883078i | \(0.655467\pi\) | |||||||
\(602\) | 1.38771 | 0.0565588 | ||||||||
\(603\) | −6.76235 | −0.275384 | ||||||||
\(604\) | −3.76173 | −0.153063 | ||||||||
\(605\) | −4.92994 | −0.200431 | ||||||||
\(606\) | 11.0160 | 0.447494 | ||||||||
\(607\) | 30.4276 | 1.23502 | 0.617508 | − | 0.786564i | \(-0.288142\pi\) | ||||
0.617508 | + | 0.786564i | \(0.288142\pi\) | |||||||
\(608\) | 8.61570 | 0.349413 | ||||||||
\(609\) | −17.8505 | −0.723340 | ||||||||
\(610\) | 1.02140 | 0.0413552 | ||||||||
\(611\) | 26.6048 | 1.07631 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 1.10836 | 0.0447663 | 0.0223831 | − | 0.999749i | \(-0.492875\pi\) | ||||
0.0223831 | + | 0.999749i | \(0.492875\pi\) | |||||||
\(614\) | −1.86618 | −0.0753129 | ||||||||
\(615\) | 2.15868 | 0.0870466 | ||||||||
\(616\) | 2.65185 | 0.106846 | ||||||||
\(617\) | 9.67515 | 0.389507 | 0.194753 | − | 0.980852i | \(-0.437609\pi\) | ||||
0.194753 | + | 0.980852i | \(0.437609\pi\) | |||||||
\(618\) | −0.756325 | −0.0304239 | ||||||||
\(619\) | −3.57748 | −0.143791 | −0.0718956 | − | 0.997412i | \(-0.522905\pi\) | ||||
−0.0718956 | + | 0.997412i | \(0.522905\pi\) | |||||||
\(620\) | 2.87298 | 0.115382 | ||||||||
\(621\) | 0.297149 | 0.0119242 | ||||||||
\(622\) | 7.60542 | 0.304950 | ||||||||
\(623\) | −26.2060 | −1.04992 | ||||||||
\(624\) | −2.49075 | −0.0997099 | ||||||||
\(625\) | 21.2463 | 0.849853 | ||||||||
\(626\) | −13.4270 | −0.536650 | ||||||||
\(627\) | −9.55110 | −0.381434 | ||||||||
\(628\) | 0.703406 | 0.0280690 | ||||||||
\(629\) | 11.5598 | 0.460921 | ||||||||
\(630\) | 1.20694 | 0.0480857 | ||||||||
\(631\) | −5.60227 | −0.223023 | −0.111511 | − | 0.993763i | \(-0.535569\pi\) | ||||
−0.111511 | + | 0.993763i | \(0.535569\pi\) | |||||||
\(632\) | 5.03441 | 0.200258 | ||||||||
\(633\) | 18.4141 | 0.731894 | ||||||||
\(634\) | −5.58422 | −0.221778 | ||||||||
\(635\) | 6.42915 | 0.255133 | ||||||||
\(636\) | −1.44391 | −0.0572547 | ||||||||
\(637\) | −3.18234 | −0.126089 | ||||||||
\(638\) | 8.27232 | 0.327504 | ||||||||
\(639\) | −3.30733 | −0.130836 | ||||||||
\(640\) | 0.504544 | 0.0199439 | ||||||||
\(641\) | −21.3042 | −0.841464 | −0.420732 | − | 0.907185i | \(-0.638227\pi\) | ||||
−0.420732 | + | 0.907185i | \(0.638227\pi\) | |||||||
\(642\) | 11.2590 | 0.444358 | ||||||||
\(643\) | 31.4256 | 1.23930 | 0.619652 | − | 0.784877i | \(-0.287274\pi\) | ||||
0.619652 | + | 0.784877i | \(0.287274\pi\) | |||||||
\(644\) | −0.710823 | −0.0280104 | ||||||||
\(645\) | −0.292692 | −0.0115247 | ||||||||
\(646\) | −8.61570 | −0.338980 | ||||||||
\(647\) | 13.6932 | 0.538336 | 0.269168 | − | 0.963093i | \(-0.413251\pi\) | ||||
0.269168 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −1.10857 | −0.0435152 | ||||||||
\(650\) | −11.8197 | −0.463607 | ||||||||
\(651\) | −13.6214 | −0.533863 | ||||||||
\(652\) | 7.07001 | 0.276883 | ||||||||
\(653\) | 3.21180 | 0.125687 | 0.0628437 | − | 0.998023i | \(-0.479983\pi\) | ||||
0.0628437 | + | 0.998023i | \(0.479983\pi\) | |||||||
\(654\) | −16.4184 | −0.642009 | ||||||||
\(655\) | −3.18988 | −0.124639 | ||||||||
\(656\) | −4.27848 | −0.167047 | ||||||||
\(657\) | 16.7045 | 0.651705 | ||||||||
\(658\) | 25.5515 | 0.996100 | ||||||||
\(659\) | −30.5900 | −1.19162 | −0.595809 | − | 0.803126i | \(-0.703168\pi\) | ||||
−0.595809 | + | 0.803126i | \(0.703168\pi\) | |||||||
\(660\) | −0.559322 | −0.0217716 | ||||||||
\(661\) | −35.0348 | −1.36270 | −0.681348 | − | 0.731959i | \(-0.738606\pi\) | ||||
−0.681348 | + | 0.731959i | \(0.738606\pi\) | |||||||
\(662\) | −8.47838 | −0.329522 | ||||||||
\(663\) | 2.49075 | 0.0967328 | ||||||||
\(664\) | −11.1379 | −0.432234 | ||||||||
\(665\) | 10.3986 | 0.403242 | ||||||||
\(666\) | −11.5598 | −0.447934 | ||||||||
\(667\) | −2.21737 | −0.0858571 | ||||||||
\(668\) | 14.6374 | 0.566339 | ||||||||
\(669\) | −18.3528 | −0.709561 | ||||||||
\(670\) | −3.41191 | −0.131813 | ||||||||
\(671\) | 2.24419 | 0.0866358 | ||||||||
\(672\) | −2.39214 | −0.0922788 | ||||||||
\(673\) | 38.1022 | 1.46873 | 0.734365 | − | 0.678755i | \(-0.237480\pi\) | ||||
0.734365 | + | 0.678755i | \(0.237480\pi\) | |||||||
\(674\) | −14.0945 | −0.542902 | ||||||||
\(675\) | 4.74544 | 0.182652 | ||||||||
\(676\) | −6.79615 | −0.261390 | ||||||||
\(677\) | −12.6958 | −0.487938 | −0.243969 | − | 0.969783i | \(-0.578449\pi\) | ||||
−0.243969 | + | 0.969783i | \(0.578449\pi\) | |||||||
\(678\) | −3.44593 | −0.132340 | ||||||||
\(679\) | −17.8638 | −0.685548 | ||||||||
\(680\) | −0.504544 | −0.0193484 | ||||||||
\(681\) | 10.3618 | 0.397064 | ||||||||
\(682\) | 6.31243 | 0.241715 | ||||||||
\(683\) | 10.2184 | 0.390994 | 0.195497 | − | 0.980704i | \(-0.437368\pi\) | ||||
0.195497 | + | 0.980704i | \(0.437368\pi\) | |||||||
\(684\) | 8.61570 | 0.329429 | ||||||||
\(685\) | 1.01434 | 0.0387560 | ||||||||
\(686\) | −19.8013 | −0.756018 | ||||||||
\(687\) | −14.7633 | −0.563255 | ||||||||
\(688\) | 0.580112 | 0.0221166 | ||||||||
\(689\) | 3.59642 | 0.137013 | ||||||||
\(690\) | 0.149925 | 0.00570755 | ||||||||
\(691\) | 25.0757 | 0.953923 | 0.476962 | − | 0.878924i | \(-0.341738\pi\) | ||||
0.476962 | + | 0.878924i | \(0.341738\pi\) | |||||||
\(692\) | 14.1671 | 0.538554 | ||||||||
\(693\) | 2.65185 | 0.100736 | ||||||||
\(694\) | 1.41517 | 0.0537190 | ||||||||
\(695\) | 8.08230 | 0.306579 | ||||||||
\(696\) | −7.46215 | −0.282852 | ||||||||
\(697\) | 4.27848 | 0.162059 | ||||||||
\(698\) | 28.2991 | 1.07114 | ||||||||
\(699\) | −9.14378 | −0.345849 | ||||||||
\(700\) | −11.3518 | −0.429056 | ||||||||
\(701\) | −38.8909 | −1.46889 | −0.734445 | − | 0.678668i | \(-0.762557\pi\) | ||||
−0.734445 | + | 0.678668i | \(0.762557\pi\) | |||||||
\(702\) | −2.49075 | −0.0940074 | ||||||||
\(703\) | −99.5960 | −3.75633 | ||||||||
\(704\) | 1.10857 | 0.0417808 | ||||||||
\(705\) | −5.38925 | −0.202971 | ||||||||
\(706\) | 25.1682 | 0.947216 | ||||||||
\(707\) | −26.3518 | −0.991062 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −10.1284 | −0.380381 | −0.190190 | − | 0.981747i | \(-0.560911\pi\) | ||||
−0.190190 | + | 0.981747i | \(0.560911\pi\) | |||||||
\(710\) | −1.66869 | −0.0626249 | ||||||||
\(711\) | 5.03441 | 0.188805 | ||||||||
\(712\) | −10.9550 | −0.410557 | ||||||||
\(713\) | −1.69203 | −0.0633671 | ||||||||
\(714\) | 2.39214 | 0.0895236 | ||||||||
\(715\) | 1.39313 | 0.0521003 | ||||||||
\(716\) | −13.8282 | −0.516786 | ||||||||
\(717\) | 18.7515 | 0.700287 | ||||||||
\(718\) | −25.8153 | −0.963418 | ||||||||
\(719\) | −11.7671 | −0.438839 | −0.219420 | − | 0.975631i | \(-0.570416\pi\) | ||||
−0.219420 | + | 0.975631i | \(0.570416\pi\) | |||||||
\(720\) | 0.504544 | 0.0188033 | ||||||||
\(721\) | 1.80924 | 0.0673795 | ||||||||
\(722\) | 55.2302 | 2.05546 | ||||||||
\(723\) | 26.0481 | 0.968740 | ||||||||
\(724\) | −17.2329 | −0.640456 | ||||||||
\(725\) | −35.4112 | −1.31514 | ||||||||
\(726\) | 9.77107 | 0.362639 | ||||||||
\(727\) | 13.9324 | 0.516723 | 0.258362 | − | 0.966048i | \(-0.416817\pi\) | ||||
0.258362 | + | 0.966048i | \(0.416817\pi\) | |||||||
\(728\) | 5.95823 | 0.220827 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.42816 | 0.311940 | ||||||||
\(731\) | −0.580112 | −0.0214562 | ||||||||
\(732\) | −2.02440 | −0.0748239 | ||||||||
\(733\) | −16.1110 | −0.595072 | −0.297536 | − | 0.954711i | \(-0.596165\pi\) | ||||
−0.297536 | + | 0.954711i | \(0.596165\pi\) | |||||||
\(734\) | −19.5427 | −0.721333 | ||||||||
\(735\) | 0.644637 | 0.0237778 | ||||||||
\(736\) | −0.297149 | −0.0109531 | ||||||||
\(737\) | −7.49654 | −0.276139 | ||||||||
\(738\) | −4.27848 | −0.157493 | ||||||||
\(739\) | −42.0875 | −1.54822 | −0.774108 | − | 0.633054i | \(-0.781801\pi\) | ||||
−0.774108 | + | 0.633054i | \(0.781801\pi\) | |||||||
\(740\) | −5.83245 | −0.214405 | ||||||||
\(741\) | −21.4596 | −0.788337 | ||||||||
\(742\) | 3.45403 | 0.126801 | ||||||||
\(743\) | −24.5756 | −0.901592 | −0.450796 | − | 0.892627i | \(-0.648860\pi\) | ||||
−0.450796 | + | 0.892627i | \(0.648860\pi\) | |||||||
\(744\) | −5.69421 | −0.208760 | ||||||||
\(745\) | 2.03228 | 0.0744571 | ||||||||
\(746\) | −15.6479 | −0.572911 | ||||||||
\(747\) | −11.1379 | −0.407514 | ||||||||
\(748\) | −1.10857 | −0.0405333 | ||||||||
\(749\) | −26.9332 | −0.984117 | ||||||||
\(750\) | 4.91700 | 0.179544 | ||||||||
\(751\) | 0.617599 | 0.0225365 | 0.0112683 | − | 0.999937i | \(-0.496413\pi\) | ||||
0.0112683 | + | 0.999937i | \(0.496413\pi\) | |||||||
\(752\) | 10.6814 | 0.389511 | ||||||||
\(753\) | −13.1829 | −0.480412 | ||||||||
\(754\) | 18.5864 | 0.676876 | ||||||||
\(755\) | −1.89796 | −0.0690738 | ||||||||
\(756\) | −2.39214 | −0.0870013 | ||||||||
\(757\) | −14.9892 | −0.544791 | −0.272396 | − | 0.962185i | \(-0.587816\pi\) | ||||
−0.272396 | + | 0.962185i | \(0.587816\pi\) | |||||||
\(758\) | 19.6388 | 0.713314 | ||||||||
\(759\) | 0.329411 | 0.0119569 | ||||||||
\(760\) | 4.34700 | 0.157682 | ||||||||
\(761\) | 1.22757 | 0.0444993 | 0.0222496 | − | 0.999752i | \(-0.492917\pi\) | ||||
0.0222496 | + | 0.999752i | \(0.492917\pi\) | |||||||
\(762\) | −12.7425 | −0.461612 | ||||||||
\(763\) | 39.2751 | 1.42185 | ||||||||
\(764\) | −15.1512 | −0.548151 | ||||||||
\(765\) | −0.504544 | −0.0182418 | ||||||||
\(766\) | −27.4639 | −0.992310 | ||||||||
\(767\) | −2.49075 | −0.0899359 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −33.5426 | −1.20958 | −0.604789 | − | 0.796386i | \(-0.706743\pi\) | ||||
−0.604789 | + | 0.796386i | \(0.706743\pi\) | |||||||
\(770\) | 1.33798 | 0.0482174 | ||||||||
\(771\) | −7.11818 | −0.256355 | ||||||||
\(772\) | 19.2590 | 0.693148 | ||||||||
\(773\) | −14.5190 | −0.522211 | −0.261105 | − | 0.965310i | \(-0.584087\pi\) | ||||
−0.261105 | + | 0.965310i | \(0.584087\pi\) | |||||||
\(774\) | 0.580112 | 0.0208517 | ||||||||
\(775\) | −27.0215 | −0.970641 | ||||||||
\(776\) | −7.46768 | −0.268074 | ||||||||
\(777\) | 27.6527 | 0.992037 | ||||||||
\(778\) | 0.794891 | 0.0284982 | ||||||||
\(779\) | −36.8621 | −1.32072 | ||||||||
\(780\) | −1.25670 | −0.0449969 | ||||||||
\(781\) | −3.66640 | −0.131194 | ||||||||
\(782\) | 0.297149 | 0.0106260 | ||||||||
\(783\) | −7.46215 | −0.266676 | ||||||||
\(784\) | −1.27766 | −0.0456308 | ||||||||
\(785\) | 0.354900 | 0.0126669 | ||||||||
\(786\) | 6.32230 | 0.225509 | ||||||||
\(787\) | −35.0506 | −1.24942 | −0.624709 | − | 0.780857i | \(-0.714783\pi\) | ||||
−0.624709 | + | 0.780857i | \(0.714783\pi\) | |||||||
\(788\) | 20.0314 | 0.713589 | ||||||||
\(789\) | 1.95363 | 0.0695510 | ||||||||
\(790\) | 2.54008 | 0.0903720 | ||||||||
\(791\) | 8.24315 | 0.293093 | ||||||||
\(792\) | 1.10857 | 0.0393913 | ||||||||
\(793\) | 5.04227 | 0.179056 | ||||||||
\(794\) | 34.5396 | 1.22576 | ||||||||
\(795\) | −0.728516 | −0.0258378 | ||||||||
\(796\) | 16.4279 | 0.582270 | ||||||||
\(797\) | −12.7732 | −0.452449 | −0.226224 | − | 0.974075i | \(-0.572638\pi\) | ||||
−0.226224 | + | 0.974075i | \(0.572638\pi\) | |||||||
\(798\) | −20.6100 | −0.729585 | ||||||||
\(799\) | −10.6814 | −0.377882 | ||||||||
\(800\) | −4.74544 | −0.167776 | ||||||||
\(801\) | −10.9550 | −0.387077 | ||||||||
\(802\) | 14.5890 | 0.515155 | ||||||||
\(803\) | 18.5181 | 0.653490 | ||||||||
\(804\) | 6.76235 | 0.238490 | ||||||||
\(805\) | −0.358642 | −0.0126405 | ||||||||
\(806\) | 14.1829 | 0.499570 | ||||||||
\(807\) | 16.9311 | 0.596004 | ||||||||
\(808\) | −11.0160 | −0.387541 | ||||||||
\(809\) | 28.0387 | 0.985789 | 0.492894 | − | 0.870089i | \(-0.335939\pi\) | ||||
0.492894 | + | 0.870089i | \(0.335939\pi\) | |||||||
\(810\) | 0.504544 | 0.0177279 | ||||||||
\(811\) | 20.2701 | 0.711780 | 0.355890 | − | 0.934528i | \(-0.384178\pi\) | ||||
0.355890 | + | 0.934528i | \(0.384178\pi\) | |||||||
\(812\) | 17.8505 | 0.626431 | ||||||||
\(813\) | −3.34033 | −0.117150 | ||||||||
\(814\) | −12.8149 | −0.449161 | ||||||||
\(815\) | 3.56713 | 0.124951 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 4.99807 | 0.174860 | ||||||||
\(818\) | −15.2900 | −0.534602 | ||||||||
\(819\) | 5.95823 | 0.208197 | ||||||||
\(820\) | −2.15868 | −0.0753845 | ||||||||
\(821\) | −41.4149 | −1.44539 | −0.722694 | − | 0.691168i | \(-0.757097\pi\) | ||||
−0.722694 | + | 0.691168i | \(0.757097\pi\) | |||||||
\(822\) | −2.01041 | −0.0701212 | ||||||||
\(823\) | 3.06872 | 0.106969 | 0.0534844 | − | 0.998569i | \(-0.482967\pi\) | ||||
0.0534844 | + | 0.998569i | \(0.482967\pi\) | |||||||
\(824\) | 0.756325 | 0.0263478 | ||||||||
\(825\) | 5.26064 | 0.183152 | ||||||||
\(826\) | −2.39214 | −0.0832332 | ||||||||
\(827\) | −23.2288 | −0.807746 | −0.403873 | − | 0.914815i | \(-0.632336\pi\) | ||||
−0.403873 | + | 0.914815i | \(0.632336\pi\) | |||||||
\(828\) | −0.297149 | −0.0103267 | ||||||||
\(829\) | −34.8779 | −1.21136 | −0.605680 | − | 0.795709i | \(-0.707099\pi\) | ||||
−0.605680 | + | 0.795709i | \(0.707099\pi\) | |||||||
\(830\) | −5.61956 | −0.195058 | ||||||||
\(831\) | −5.13891 | −0.178267 | ||||||||
\(832\) | 2.49075 | 0.0863513 | ||||||||
\(833\) | 1.27766 | 0.0442683 | ||||||||
\(834\) | −16.0190 | −0.554693 | ||||||||
\(835\) | 7.38523 | 0.255576 | ||||||||
\(836\) | 9.55110 | 0.330332 | ||||||||
\(837\) | −5.69421 | −0.196821 | ||||||||
\(838\) | −17.9073 | −0.618598 | ||||||||
\(839\) | 10.4365 | 0.360309 | 0.180155 | − | 0.983638i | \(-0.442340\pi\) | ||||
0.180155 | + | 0.983638i | \(0.442340\pi\) | |||||||
\(840\) | −1.20694 | −0.0416434 | ||||||||
\(841\) | 26.6837 | 0.920129 | ||||||||
\(842\) | 32.9581 | 1.13581 | ||||||||
\(843\) | −22.1434 | −0.762658 | ||||||||
\(844\) | −18.4141 | −0.633839 | ||||||||
\(845\) | −3.42896 | −0.117960 | ||||||||
\(846\) | 10.6814 | 0.367235 | ||||||||
\(847\) | −23.3738 | −0.803133 | ||||||||
\(848\) | 1.44391 | 0.0495840 | ||||||||
\(849\) | 0.0742288 | 0.00254753 | ||||||||
\(850\) | 4.74544 | 0.162767 | ||||||||
\(851\) | 3.43500 | 0.117750 | ||||||||
\(852\) | 3.30733 | 0.113307 | ||||||||
\(853\) | −21.1065 | −0.722673 | −0.361337 | − | 0.932435i | \(-0.617679\pi\) | ||||
−0.361337 | + | 0.932435i | \(0.617679\pi\) | |||||||
\(854\) | 4.84265 | 0.165712 | ||||||||
\(855\) | 4.34700 | 0.148664 | ||||||||
\(856\) | −11.2590 | −0.384825 | ||||||||
\(857\) | −5.23109 | −0.178690 | −0.0893452 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893452 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(858\) | −2.76117 | −0.0942649 | ||||||||
\(859\) | 15.2586 | 0.520617 | 0.260309 | − | 0.965525i | \(-0.416176\pi\) | ||||
0.260309 | + | 0.965525i | \(0.416176\pi\) | |||||||
\(860\) | 0.292692 | 0.00998072 | ||||||||
\(861\) | 10.2347 | 0.348799 | ||||||||
\(862\) | −23.3410 | −0.794997 | ||||||||
\(863\) | −49.1199 | −1.67206 | −0.836030 | − | 0.548684i | \(-0.815129\pi\) | ||||
−0.836030 | + | 0.548684i | \(0.815129\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 7.14795 | 0.243038 | ||||||||
\(866\) | 0.989051 | 0.0336093 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 13.6214 | 0.462339 | ||||||||
\(869\) | 5.58099 | 0.189322 | ||||||||
\(870\) | −3.76499 | −0.127645 | ||||||||
\(871\) | −16.8434 | −0.570715 | ||||||||
\(872\) | 16.4184 | 0.555996 | ||||||||
\(873\) | −7.46768 | −0.252743 | ||||||||
\(874\) | −2.56015 | −0.0865983 | ||||||||
\(875\) | −11.7622 | −0.397634 | ||||||||
\(876\) | −16.7045 | −0.564393 | ||||||||
\(877\) | 30.5044 | 1.03006 | 0.515030 | − | 0.857172i | \(-0.327781\pi\) | ||||
0.515030 | + | 0.857172i | \(0.327781\pi\) | |||||||
\(878\) | 12.8751 | 0.434512 | ||||||||
\(879\) | −20.8035 | −0.701684 | ||||||||
\(880\) | 0.559322 | 0.0188548 | ||||||||
\(881\) | −56.2584 | −1.89539 | −0.947697 | − | 0.319170i | \(-0.896596\pi\) | ||||
−0.947697 | + | 0.319170i | \(0.896596\pi\) | |||||||
\(882\) | −1.27766 | −0.0430211 | ||||||||
\(883\) | −33.7703 | −1.13646 | −0.568230 | − | 0.822870i | \(-0.692372\pi\) | ||||
−0.568230 | + | 0.822870i | \(0.692372\pi\) | |||||||
\(884\) | −2.49075 | −0.0837731 | ||||||||
\(885\) | 0.504544 | 0.0169601 | ||||||||
\(886\) | 5.89332 | 0.197990 | ||||||||
\(887\) | 37.2395 | 1.25038 | 0.625191 | − | 0.780472i | \(-0.285021\pi\) | ||||
0.625191 | + | 0.780472i | \(0.285021\pi\) | |||||||
\(888\) | 11.5598 | 0.387923 | ||||||||
\(889\) | 30.4818 | 1.02233 | ||||||||
\(890\) | −5.52729 | −0.185275 | ||||||||
\(891\) | 1.10857 | 0.0371385 | ||||||||
\(892\) | 18.3528 | 0.614497 | ||||||||
\(893\) | 92.0279 | 3.07960 | ||||||||
\(894\) | −4.02796 | −0.134715 | ||||||||
\(895\) | −6.97696 | −0.233214 | ||||||||
\(896\) | 2.39214 | 0.0799158 | ||||||||
\(897\) | 0.740126 | 0.0247121 | ||||||||
\(898\) | −38.4053 | −1.28160 | ||||||||
\(899\) | 42.4911 | 1.41716 | ||||||||
\(900\) | −4.74544 | −0.158181 | ||||||||
\(901\) | −1.44391 | −0.0481036 | ||||||||
\(902\) | −4.74300 | −0.157925 | ||||||||
\(903\) | −1.38771 | −0.0461801 | ||||||||
\(904\) | 3.44593 | 0.114610 | ||||||||
\(905\) | −8.69476 | −0.289024 | ||||||||
\(906\) | 3.76173 | 0.124975 | ||||||||
\(907\) | 16.4577 | 0.546470 | 0.273235 | − | 0.961947i | \(-0.411906\pi\) | ||||
0.273235 | + | 0.961947i | \(0.411906\pi\) | |||||||
\(908\) | −10.3618 | −0.343867 | ||||||||
\(909\) | −11.0160 | −0.365377 | ||||||||
\(910\) | 3.00619 | 0.0996543 | ||||||||
\(911\) | 13.8845 | 0.460014 | 0.230007 | − | 0.973189i | \(-0.426125\pi\) | ||||
0.230007 | + | 0.973189i | \(0.426125\pi\) | |||||||
\(912\) | −8.61570 | −0.285294 | ||||||||
\(913\) | −12.3471 | −0.408630 | ||||||||
\(914\) | 17.1916 | 0.568647 | ||||||||
\(915\) | −1.02140 | −0.0337664 | ||||||||
\(916\) | 14.7633 | 0.487793 | ||||||||
\(917\) | −15.1238 | −0.499433 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −35.6337 | −1.17545 | −0.587724 | − | 0.809062i | \(-0.699976\pi\) | ||||
−0.587724 | + | 0.809062i | \(0.699976\pi\) | |||||||
\(920\) | −0.149925 | −0.00494288 | ||||||||
\(921\) | 1.86618 | 0.0614928 | ||||||||
\(922\) | −6.69144 | −0.220371 | ||||||||
\(923\) | −8.23773 | −0.271148 | ||||||||
\(924\) | −2.65185 | −0.0872396 | ||||||||
\(925\) | 54.8564 | 1.80367 | ||||||||
\(926\) | 15.1088 | 0.496507 | ||||||||
\(927\) | 0.756325 | 0.0248410 | ||||||||
\(928\) | 7.46215 | 0.244957 | ||||||||
\(929\) | 35.2337 | 1.15598 | 0.577990 | − | 0.816044i | \(-0.303837\pi\) | ||||
0.577990 | + | 0.816044i | \(0.303837\pi\) | |||||||
\(930\) | −2.87298 | −0.0942088 | ||||||||
\(931\) | −11.0079 | −0.360771 | ||||||||
\(932\) | 9.14378 | 0.299514 | ||||||||
\(933\) | −7.60542 | −0.248990 | ||||||||
\(934\) | 12.6074 | 0.412526 | ||||||||
\(935\) | −0.559322 | −0.0182918 | ||||||||
\(936\) | 2.49075 | 0.0814128 | ||||||||
\(937\) | −44.2551 | −1.44575 | −0.722875 | − | 0.690979i | \(-0.757180\pi\) | ||||
−0.722875 | + | 0.690979i | \(0.757180\pi\) | |||||||
\(938\) | −16.1765 | −0.528182 | ||||||||
\(939\) | 13.4270 | 0.438173 | ||||||||
\(940\) | 5.38925 | 0.175778 | ||||||||
\(941\) | 1.66900 | 0.0544078 | 0.0272039 | − | 0.999630i | \(-0.491340\pi\) | ||||
0.0272039 | + | 0.999630i | \(0.491340\pi\) | |||||||
\(942\) | −0.703406 | −0.0229182 | ||||||||
\(943\) | 1.27135 | 0.0414008 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −1.20694 | −0.0392618 | ||||||||
\(946\) | 0.643094 | 0.0209088 | ||||||||
\(947\) | 8.85192 | 0.287649 | 0.143824 | − | 0.989603i | \(-0.454060\pi\) | ||||
0.143824 | + | 0.989603i | \(0.454060\pi\) | |||||||
\(948\) | −5.03441 | −0.163510 | ||||||||
\(949\) | 41.6068 | 1.35061 | ||||||||
\(950\) | −40.8852 | −1.32649 | ||||||||
\(951\) | 5.58422 | 0.181081 | ||||||||
\(952\) | −2.39214 | −0.0775297 | ||||||||
\(953\) | 8.56063 | 0.277306 | 0.138653 | − | 0.990341i | \(-0.455723\pi\) | ||||
0.138653 | + | 0.990341i | \(0.455723\pi\) | |||||||
\(954\) | 1.44391 | 0.0467483 | ||||||||
\(955\) | −7.64445 | −0.247369 | ||||||||
\(956\) | −18.7515 | −0.606466 | ||||||||
\(957\) | −8.27232 | −0.267406 | ||||||||
\(958\) | −25.2284 | −0.815093 | ||||||||
\(959\) | 4.80919 | 0.155297 | ||||||||
\(960\) | −0.504544 | −0.0162841 | ||||||||
\(961\) | 1.42405 | 0.0459372 | ||||||||
\(962\) | −28.7927 | −0.928313 | ||||||||
\(963\) | −11.2590 | −0.362817 | ||||||||
\(964\) | −26.0481 | −0.838954 | ||||||||
\(965\) | 9.71704 | 0.312802 | ||||||||
\(966\) | 0.710823 | 0.0228704 | ||||||||
\(967\) | −3.10825 | −0.0999544 | −0.0499772 | − | 0.998750i | \(-0.515915\pi\) | ||||
−0.0499772 | + | 0.998750i | \(0.515915\pi\) | |||||||
\(968\) | −9.77107 | −0.314054 | ||||||||
\(969\) | 8.61570 | 0.276776 | ||||||||
\(970\) | −3.76778 | −0.120976 | ||||||||
\(971\) | −15.1937 | −0.487589 | −0.243794 | − | 0.969827i | \(-0.578392\pi\) | ||||
−0.243794 | + | 0.969827i | \(0.578392\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 38.3197 | 1.22847 | ||||||||
\(974\) | 28.3456 | 0.908252 | ||||||||
\(975\) | 11.8197 | 0.378534 | ||||||||
\(976\) | 2.02440 | 0.0647994 | ||||||||
\(977\) | −51.2713 | −1.64031 | −0.820157 | − | 0.572138i | \(-0.806114\pi\) | ||||
−0.820157 | + | 0.572138i | \(0.806114\pi\) | |||||||
\(978\) | −7.07001 | −0.226074 | ||||||||
\(979\) | −12.1444 | −0.388137 | ||||||||
\(980\) | −0.644637 | −0.0205922 | ||||||||
\(981\) | 16.4184 | 0.524198 | ||||||||
\(982\) | 11.1301 | 0.355175 | ||||||||
\(983\) | −51.6796 | −1.64832 | −0.824161 | − | 0.566356i | \(-0.808353\pi\) | ||||
−0.824161 | + | 0.566356i | \(0.808353\pi\) | |||||||
\(984\) | 4.27848 | 0.136393 | ||||||||
\(985\) | 10.1067 | 0.322027 | ||||||||
\(986\) | −7.46215 | −0.237643 | ||||||||
\(987\) | −25.5515 | −0.813312 | ||||||||
\(988\) | 21.4596 | 0.682720 | ||||||||
\(989\) | −0.172380 | −0.00548136 | ||||||||
\(990\) | 0.559322 | 0.0177764 | ||||||||
\(991\) | 31.3000 | 0.994278 | 0.497139 | − | 0.867671i | \(-0.334384\pi\) | ||||
0.497139 | + | 0.867671i | \(0.334384\pi\) | |||||||
\(992\) | 5.69421 | 0.180791 | ||||||||
\(993\) | 8.47838 | 0.269053 | ||||||||
\(994\) | −7.91159 | −0.250940 | ||||||||
\(995\) | 8.28858 | 0.262766 | ||||||||
\(996\) | 11.1379 | 0.352918 | ||||||||
\(997\) | 35.0239 | 1.10922 | 0.554609 | − | 0.832111i | \(-0.312868\pi\) | ||||
0.554609 | + | 0.832111i | \(0.312868\pi\) | |||||||
\(998\) | 2.70729 | 0.0856978 | ||||||||
\(999\) | 11.5598 | 0.365737 |
(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 | 6018.2.a.z.1.6 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.z.1.6 | ✓ | 11 | 1.1 | even | 1 | trivial |