Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.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: | \(64.1597980241\) |
Analytic rank: | \(0\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41769 | −1.70956 | −0.854781 | − | 0.518989i | \(-0.826309\pi\) | ||||
−0.854781 | + | 0.518989i | \(0.826309\pi\) | |||||||
\(3\) | −0.844619 | −0.487641 | −0.243821 | − | 0.969820i | \(-0.578401\pi\) | ||||
−0.243821 | + | 0.969820i | \(0.578401\pi\) | |||||||
\(4\) | 3.84521 | 1.92260 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.04202 | 0.833653 | ||||||||
\(7\) | 0.104455 | 0.0394802 | 0.0197401 | − | 0.999805i | \(-0.493716\pi\) | ||||
0.0197401 | + | 0.999805i | \(0.493716\pi\) | |||||||
\(8\) | −4.46113 | −1.57725 | ||||||||
\(9\) | −2.28662 | −0.762206 | ||||||||
\(10\) | −2.41769 | −0.764539 | ||||||||
\(11\) | −4.33837 | −1.30807 | −0.654034 | − | 0.756465i | \(-0.726925\pi\) | ||||
−0.654034 | + | 0.756465i | \(0.726925\pi\) | |||||||
\(12\) | −3.24773 | −0.937540 | ||||||||
\(13\) | 1.66281 | 0.461182 | 0.230591 | − | 0.973051i | \(-0.425934\pi\) | ||||
0.230591 | + | 0.973051i | \(0.425934\pi\) | |||||||
\(14\) | −0.252539 | −0.0674938 | ||||||||
\(15\) | −0.844619 | −0.218080 | ||||||||
\(16\) | 3.09520 | 0.773799 | ||||||||
\(17\) | −2.04843 | −0.496817 | −0.248409 | − | 0.968655i | \(-0.579908\pi\) | ||||
−0.248409 | + | 0.968655i | \(0.579908\pi\) | |||||||
\(18\) | 5.52833 | 1.30304 | ||||||||
\(19\) | −3.17857 | −0.729214 | −0.364607 | − | 0.931162i | \(-0.618797\pi\) | ||||
−0.364607 | + | 0.931162i | \(0.618797\pi\) | |||||||
\(20\) | 3.84521 | 0.859814 | ||||||||
\(21\) | −0.0882245 | −0.0192522 | ||||||||
\(22\) | 10.4888 | 2.23622 | ||||||||
\(23\) | −3.39580 | −0.708073 | −0.354037 | − | 0.935232i | \(-0.615191\pi\) | ||||
−0.354037 | + | 0.935232i | \(0.615191\pi\) | |||||||
\(24\) | 3.76795 | 0.769130 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.02016 | −0.788419 | ||||||||
\(27\) | 4.46518 | 0.859324 | ||||||||
\(28\) | 0.401650 | 0.0759047 | ||||||||
\(29\) | 3.48617 | 0.647365 | 0.323682 | − | 0.946166i | \(-0.395079\pi\) | ||||
0.323682 | + | 0.946166i | \(0.395079\pi\) | |||||||
\(30\) | 2.04202 | 0.372821 | ||||||||
\(31\) | 1.88643 | 0.338812 | 0.169406 | − | 0.985546i | \(-0.445815\pi\) | ||||
0.169406 | + | 0.985546i | \(0.445815\pi\) | |||||||
\(32\) | 1.43905 | 0.254390 | ||||||||
\(33\) | 3.66427 | 0.637868 | ||||||||
\(34\) | 4.95246 | 0.849340 | ||||||||
\(35\) | 0.104455 | 0.0176561 | ||||||||
\(36\) | −8.79252 | −1.46542 | ||||||||
\(37\) | −2.54978 | −0.419182 | −0.209591 | − | 0.977789i | \(-0.567213\pi\) | ||||
−0.209591 | + | 0.977789i | \(0.567213\pi\) | |||||||
\(38\) | 7.68478 | 1.24664 | ||||||||
\(39\) | −1.40444 | −0.224891 | ||||||||
\(40\) | −4.46113 | −0.705366 | ||||||||
\(41\) | 1.81376 | 0.283262 | 0.141631 | − | 0.989920i | \(-0.454765\pi\) | ||||
0.141631 | + | 0.989920i | \(0.454765\pi\) | |||||||
\(42\) | 0.213299 | 0.0329128 | ||||||||
\(43\) | −6.32258 | −0.964184 | −0.482092 | − | 0.876121i | \(-0.660123\pi\) | ||||
−0.482092 | + | 0.876121i | \(0.660123\pi\) | |||||||
\(44\) | −16.6819 | −2.51490 | ||||||||
\(45\) | −2.28662 | −0.340869 | ||||||||
\(46\) | 8.20998 | 1.21050 | ||||||||
\(47\) | 10.7097 | 1.56217 | 0.781085 | − | 0.624425i | \(-0.214666\pi\) | ||||
0.781085 | + | 0.624425i | \(0.214666\pi\) | |||||||
\(48\) | −2.61426 | −0.377336 | ||||||||
\(49\) | −6.98909 | −0.998441 | ||||||||
\(50\) | −2.41769 | −0.341912 | ||||||||
\(51\) | 1.73014 | 0.242268 | ||||||||
\(52\) | 6.39386 | 0.886669 | ||||||||
\(53\) | −11.1272 | −1.52844 | −0.764220 | − | 0.644956i | \(-0.776876\pi\) | ||||
−0.764220 | + | 0.644956i | \(0.776876\pi\) | |||||||
\(54\) | −10.7954 | −1.46907 | ||||||||
\(55\) | −4.33837 | −0.584986 | ||||||||
\(56\) | −0.465986 | −0.0622700 | ||||||||
\(57\) | 2.68468 | 0.355595 | ||||||||
\(58\) | −8.42845 | −1.10671 | ||||||||
\(59\) | 13.0910 | 1.70430 | 0.852149 | − | 0.523299i | \(-0.175299\pi\) | ||||
0.852149 | + | 0.523299i | \(0.175299\pi\) | |||||||
\(60\) | −3.24773 | −0.419281 | ||||||||
\(61\) | −8.38124 | −1.07311 | −0.536554 | − | 0.843866i | \(-0.680274\pi\) | ||||
−0.536554 | + | 0.843866i | \(0.680274\pi\) | |||||||
\(62\) | −4.56079 | −0.579220 | ||||||||
\(63\) | −0.238848 | −0.0300920 | ||||||||
\(64\) | −9.66955 | −1.20869 | ||||||||
\(65\) | 1.66281 | 0.206247 | ||||||||
\(66\) | −8.85906 | −1.09047 | ||||||||
\(67\) | −13.6304 | −1.66522 | −0.832609 | − | 0.553861i | \(-0.813154\pi\) | ||||
−0.832609 | + | 0.553861i | \(0.813154\pi\) | |||||||
\(68\) | −7.87663 | −0.955182 | ||||||||
\(69\) | 2.86816 | 0.345286 | ||||||||
\(70\) | −0.252539 | −0.0301842 | ||||||||
\(71\) | −0.521308 | −0.0618678 | −0.0309339 | − | 0.999521i | \(-0.509848\pi\) | ||||
−0.0309339 | + | 0.999521i | \(0.509848\pi\) | |||||||
\(72\) | 10.2009 | 1.20219 | ||||||||
\(73\) | −4.01401 | −0.469805 | −0.234902 | − | 0.972019i | \(-0.575477\pi\) | ||||
−0.234902 | + | 0.972019i | \(0.575477\pi\) | |||||||
\(74\) | 6.16457 | 0.716617 | ||||||||
\(75\) | −0.844619 | −0.0975282 | ||||||||
\(76\) | −12.2223 | −1.40199 | ||||||||
\(77\) | −0.453164 | −0.0516428 | ||||||||
\(78\) | 3.39551 | 0.384465 | ||||||||
\(79\) | 12.4879 | 1.40499 | 0.702497 | − | 0.711687i | \(-0.252068\pi\) | ||||
0.702497 | + | 0.711687i | \(0.252068\pi\) | |||||||
\(80\) | 3.09520 | 0.346053 | ||||||||
\(81\) | 3.08848 | 0.343164 | ||||||||
\(82\) | −4.38511 | −0.484254 | ||||||||
\(83\) | −2.23895 | −0.245756 | −0.122878 | − | 0.992422i | \(-0.539212\pi\) | ||||
−0.122878 | + | 0.992422i | \(0.539212\pi\) | |||||||
\(84\) | −0.339241 | −0.0370143 | ||||||||
\(85\) | −2.04843 | −0.222183 | ||||||||
\(86\) | 15.2860 | 1.64833 | ||||||||
\(87\) | −2.94448 | −0.315682 | ||||||||
\(88\) | 19.3540 | 2.06315 | ||||||||
\(89\) | −15.5780 | −1.65127 | −0.825634 | − | 0.564206i | \(-0.809182\pi\) | ||||
−0.825634 | + | 0.564206i | \(0.809182\pi\) | |||||||
\(90\) | 5.52833 | 0.582737 | ||||||||
\(91\) | 0.173689 | 0.0182075 | ||||||||
\(92\) | −13.0575 | −1.36134 | ||||||||
\(93\) | −1.59331 | −0.165219 | ||||||||
\(94\) | −25.8927 | −2.67063 | ||||||||
\(95\) | −3.17857 | −0.326114 | ||||||||
\(96\) | −1.21545 | −0.124051 | ||||||||
\(97\) | −16.2681 | −1.65178 | −0.825889 | − | 0.563832i | \(-0.809326\pi\) | ||||
−0.825889 | + | 0.563832i | \(0.809326\pi\) | |||||||
\(98\) | 16.8974 | 1.70690 | ||||||||
\(99\) | 9.92020 | 0.997018 | ||||||||
\(100\) | 3.84521 | 0.384521 | ||||||||
\(101\) | −7.87060 | −0.783154 | −0.391577 | − | 0.920145i | \(-0.628070\pi\) | ||||
−0.391577 | + | 0.920145i | \(0.628070\pi\) | |||||||
\(102\) | −4.18294 | −0.414173 | ||||||||
\(103\) | −10.2337 | −1.00836 | −0.504180 | − | 0.863599i | \(-0.668205\pi\) | ||||
−0.504180 | + | 0.863599i | \(0.668205\pi\) | |||||||
\(104\) | −7.41803 | −0.727397 | ||||||||
\(105\) | −0.0882245 | −0.00860983 | ||||||||
\(106\) | 26.9021 | 2.61296 | ||||||||
\(107\) | 1.53276 | 0.148178 | 0.0740889 | − | 0.997252i | \(-0.476395\pi\) | ||||
0.0740889 | + | 0.997252i | \(0.476395\pi\) | |||||||
\(108\) | 17.1695 | 1.65214 | ||||||||
\(109\) | 13.3391 | 1.27765 | 0.638825 | − | 0.769352i | \(-0.279421\pi\) | ||||
0.638825 | + | 0.769352i | \(0.279421\pi\) | |||||||
\(110\) | 10.4888 | 1.00007 | ||||||||
\(111\) | 2.15359 | 0.204410 | ||||||||
\(112\) | 0.323308 | 0.0305497 | ||||||||
\(113\) | 13.0921 | 1.23160 | 0.615800 | − | 0.787902i | \(-0.288833\pi\) | ||||
0.615800 | + | 0.787902i | \(0.288833\pi\) | |||||||
\(114\) | −6.49071 | −0.607911 | ||||||||
\(115\) | −3.39580 | −0.316660 | ||||||||
\(116\) | 13.4050 | 1.24463 | ||||||||
\(117\) | −3.80222 | −0.351515 | ||||||||
\(118\) | −31.6498 | −2.91360 | ||||||||
\(119\) | −0.213968 | −0.0196144 | ||||||||
\(120\) | 3.76795 | 0.343966 | ||||||||
\(121\) | 7.82147 | 0.711043 | ||||||||
\(122\) | 20.2632 | 1.83455 | ||||||||
\(123\) | −1.53194 | −0.138130 | ||||||||
\(124\) | 7.25370 | 0.651401 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.577460 | 0.0514442 | ||||||||
\(127\) | −19.9805 | −1.77298 | −0.886491 | − | 0.462746i | \(-0.846864\pi\) | ||||
−0.886491 | + | 0.462746i | \(0.846864\pi\) | |||||||
\(128\) | 20.4998 | 1.81195 | ||||||||
\(129\) | 5.34017 | 0.470176 | ||||||||
\(130\) | −4.02016 | −0.352592 | ||||||||
\(131\) | 16.4794 | 1.43981 | 0.719905 | − | 0.694072i | \(-0.244185\pi\) | ||||
0.719905 | + | 0.694072i | \(0.244185\pi\) | |||||||
\(132\) | 14.0899 | 1.22637 | ||||||||
\(133\) | −0.332017 | −0.0287895 | ||||||||
\(134\) | 32.9540 | 2.84679 | ||||||||
\(135\) | 4.46518 | 0.384301 | ||||||||
\(136\) | 9.13831 | 0.783603 | ||||||||
\(137\) | 12.5847 | 1.07518 | 0.537590 | − | 0.843206i | \(-0.319335\pi\) | ||||
0.537590 | + | 0.843206i | \(0.319335\pi\) | |||||||
\(138\) | −6.93430 | −0.590287 | ||||||||
\(139\) | −14.8147 | −1.25657 | −0.628283 | − | 0.777985i | \(-0.716242\pi\) | ||||
−0.628283 | + | 0.777985i | \(0.716242\pi\) | |||||||
\(140\) | 0.401650 | 0.0339456 | ||||||||
\(141\) | −9.04562 | −0.761778 | ||||||||
\(142\) | 1.26036 | 0.105767 | ||||||||
\(143\) | −7.21391 | −0.603257 | ||||||||
\(144\) | −7.07753 | −0.589794 | ||||||||
\(145\) | 3.48617 | 0.289510 | ||||||||
\(146\) | 9.70462 | 0.803160 | ||||||||
\(147\) | 5.90312 | 0.486881 | ||||||||
\(148\) | −9.80444 | −0.805920 | ||||||||
\(149\) | 11.6967 | 0.958230 | 0.479115 | − | 0.877752i | \(-0.340958\pi\) | ||||
0.479115 | + | 0.877752i | \(0.340958\pi\) | |||||||
\(150\) | 2.04202 | 0.166731 | ||||||||
\(151\) | −3.33737 | −0.271591 | −0.135796 | − | 0.990737i | \(-0.543359\pi\) | ||||
−0.135796 | + | 0.990737i | \(0.543359\pi\) | |||||||
\(152\) | 14.1800 | 1.15015 | ||||||||
\(153\) | 4.68398 | 0.378677 | ||||||||
\(154\) | 1.09561 | 0.0882866 | ||||||||
\(155\) | 1.88643 | 0.151521 | ||||||||
\(156\) | −5.40038 | −0.432376 | ||||||||
\(157\) | −3.39499 | −0.270950 | −0.135475 | − | 0.990781i | \(-0.543256\pi\) | ||||
−0.135475 | + | 0.990781i | \(0.543256\pi\) | |||||||
\(158\) | −30.1917 | −2.40193 | ||||||||
\(159\) | 9.39825 | 0.745330 | ||||||||
\(160\) | 1.43905 | 0.113767 | ||||||||
\(161\) | −0.354707 | −0.0279549 | ||||||||
\(162\) | −7.46697 | −0.586661 | ||||||||
\(163\) | 4.41601 | 0.345889 | 0.172944 | − | 0.984932i | \(-0.444672\pi\) | ||||
0.172944 | + | 0.984932i | \(0.444672\pi\) | |||||||
\(164\) | 6.97429 | 0.544600 | ||||||||
\(165\) | 3.66427 | 0.285263 | ||||||||
\(166\) | 5.41307 | 0.420136 | ||||||||
\(167\) | −11.7157 | −0.906589 | −0.453295 | − | 0.891361i | \(-0.649751\pi\) | ||||
−0.453295 | + | 0.891361i | \(0.649751\pi\) | |||||||
\(168\) | 0.393581 | 0.0303654 | ||||||||
\(169\) | −10.2350 | −0.787312 | ||||||||
\(170\) | 4.95246 | 0.379836 | ||||||||
\(171\) | 7.26817 | 0.555811 | ||||||||
\(172\) | −24.3116 | −1.85374 | ||||||||
\(173\) | −10.4578 | −0.795095 | −0.397548 | − | 0.917582i | \(-0.630139\pi\) | ||||
−0.397548 | + | 0.917582i | \(0.630139\pi\) | |||||||
\(174\) | 7.11883 | 0.539677 | ||||||||
\(175\) | 0.104455 | 0.00789604 | ||||||||
\(176\) | −13.4281 | −1.01218 | ||||||||
\(177\) | −11.0569 | −0.831086 | ||||||||
\(178\) | 37.6628 | 2.82295 | ||||||||
\(179\) | 5.05332 | 0.377703 | 0.188851 | − | 0.982006i | \(-0.439524\pi\) | ||||
0.188851 | + | 0.982006i | \(0.439524\pi\) | |||||||
\(180\) | −8.79252 | −0.655356 | ||||||||
\(181\) | 12.0260 | 0.893885 | 0.446942 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446942 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(182\) | −0.419925 | −0.0311269 | ||||||||
\(183\) | 7.07896 | 0.523292 | ||||||||
\(184\) | 15.1491 | 1.11681 | ||||||||
\(185\) | −2.54978 | −0.187464 | ||||||||
\(186\) | 3.85213 | 0.282452 | ||||||||
\(187\) | 8.88685 | 0.649871 | ||||||||
\(188\) | 41.1810 | 3.00343 | ||||||||
\(189\) | 0.466409 | 0.0339263 | ||||||||
\(190\) | 7.68478 | 0.557513 | ||||||||
\(191\) | 10.2222 | 0.739653 | 0.369826 | − | 0.929101i | \(-0.379417\pi\) | ||||
0.369826 | + | 0.929101i | \(0.379417\pi\) | |||||||
\(192\) | 8.16709 | 0.589409 | ||||||||
\(193\) | 3.92688 | 0.282663 | 0.141332 | − | 0.989962i | \(-0.454862\pi\) | ||||
0.141332 | + | 0.989962i | \(0.454862\pi\) | |||||||
\(194\) | 39.3312 | 2.82382 | ||||||||
\(195\) | −1.40444 | −0.100574 | ||||||||
\(196\) | −26.8745 | −1.91961 | ||||||||
\(197\) | −0.838466 | −0.0597382 | −0.0298691 | − | 0.999554i | \(-0.509509\pi\) | ||||
−0.0298691 | + | 0.999554i | \(0.509509\pi\) | |||||||
\(198\) | −23.9839 | −1.70446 | ||||||||
\(199\) | 22.2877 | 1.57993 | 0.789966 | − | 0.613151i | \(-0.210098\pi\) | ||||
0.789966 | + | 0.613151i | \(0.210098\pi\) | |||||||
\(200\) | −4.46113 | −0.315449 | ||||||||
\(201\) | 11.5125 | 0.812029 | ||||||||
\(202\) | 19.0286 | 1.33885 | ||||||||
\(203\) | 0.364147 | 0.0255581 | ||||||||
\(204\) | 6.65276 | 0.465786 | ||||||||
\(205\) | 1.81376 | 0.126679 | ||||||||
\(206\) | 24.7420 | 1.72385 | ||||||||
\(207\) | 7.76490 | 0.539698 | ||||||||
\(208\) | 5.14673 | 0.356862 | ||||||||
\(209\) | 13.7898 | 0.953861 | ||||||||
\(210\) | 0.213299 | 0.0147190 | ||||||||
\(211\) | −15.3686 | −1.05802 | −0.529009 | − | 0.848616i | \(-0.677436\pi\) | ||||
−0.529009 | + | 0.848616i | \(0.677436\pi\) | |||||||
\(212\) | −42.7864 | −2.93858 | ||||||||
\(213\) | 0.440306 | 0.0301693 | ||||||||
\(214\) | −3.70574 | −0.253319 | ||||||||
\(215\) | −6.32258 | −0.431196 | ||||||||
\(216\) | −19.9197 | −1.35537 | ||||||||
\(217\) | 0.197046 | 0.0133764 | ||||||||
\(218\) | −32.2497 | −2.18422 | ||||||||
\(219\) | 3.39031 | 0.229096 | ||||||||
\(220\) | −16.6819 | −1.12470 | ||||||||
\(221\) | −3.40616 | −0.229123 | ||||||||
\(222\) | −5.20672 | −0.349452 | ||||||||
\(223\) | −0.113837 | −0.00762312 | −0.00381156 | − | 0.999993i | \(-0.501213\pi\) | ||||
−0.00381156 | + | 0.999993i | \(0.501213\pi\) | |||||||
\(224\) | 0.150315 | 0.0100434 | ||||||||
\(225\) | −2.28662 | −0.152441 | ||||||||
\(226\) | −31.6526 | −2.10550 | ||||||||
\(227\) | −13.7564 | −0.913042 | −0.456521 | − | 0.889713i | \(-0.650905\pi\) | ||||
−0.456521 | + | 0.889713i | \(0.650905\pi\) | |||||||
\(228\) | 10.3231 | 0.683667 | ||||||||
\(229\) | 26.0780 | 1.72328 | 0.861640 | − | 0.507520i | \(-0.169438\pi\) | ||||
0.861640 | + | 0.507520i | \(0.169438\pi\) | |||||||
\(230\) | 8.20998 | 0.541350 | ||||||||
\(231\) | 0.382751 | 0.0251831 | ||||||||
\(232\) | −15.5522 | −1.02105 | ||||||||
\(233\) | 22.1695 | 1.45237 | 0.726186 | − | 0.687499i | \(-0.241291\pi\) | ||||
0.726186 | + | 0.687499i | \(0.241291\pi\) | |||||||
\(234\) | 9.19258 | 0.600938 | ||||||||
\(235\) | 10.7097 | 0.698624 | ||||||||
\(236\) | 50.3375 | 3.27669 | ||||||||
\(237\) | −10.5475 | −0.685133 | ||||||||
\(238\) | 0.517308 | 0.0335321 | ||||||||
\(239\) | −19.3646 | −1.25259 | −0.626296 | − | 0.779586i | \(-0.715430\pi\) | ||||
−0.626296 | + | 0.779586i | \(0.715430\pi\) | |||||||
\(240\) | −2.61426 | −0.168750 | ||||||||
\(241\) | −4.97732 | −0.320617 | −0.160309 | − | 0.987067i | \(-0.551249\pi\) | ||||
−0.160309 | + | 0.987067i | \(0.551249\pi\) | |||||||
\(242\) | −18.9099 | −1.21557 | ||||||||
\(243\) | −16.0041 | −1.02667 | ||||||||
\(244\) | −32.2276 | −2.06316 | ||||||||
\(245\) | −6.98909 | −0.446517 | ||||||||
\(246\) | 3.70375 | 0.236142 | ||||||||
\(247\) | −5.28537 | −0.336300 | ||||||||
\(248\) | −8.41559 | −0.534390 | ||||||||
\(249\) | 1.89106 | 0.119841 | ||||||||
\(250\) | −2.41769 | −0.152908 | ||||||||
\(251\) | −9.57536 | −0.604391 | −0.302196 | − | 0.953246i | \(-0.597720\pi\) | ||||
−0.302196 | + | 0.953246i | \(0.597720\pi\) | |||||||
\(252\) | −0.918421 | −0.0578551 | ||||||||
\(253\) | 14.7322 | 0.926208 | ||||||||
\(254\) | 48.3065 | 3.03102 | ||||||||
\(255\) | 1.73014 | 0.108346 | ||||||||
\(256\) | −30.2231 | −1.88894 | ||||||||
\(257\) | −0.881268 | −0.0549720 | −0.0274860 | − | 0.999622i | \(-0.508750\pi\) | ||||
−0.0274860 | + | 0.999622i | \(0.508750\pi\) | |||||||
\(258\) | −12.9109 | −0.803795 | ||||||||
\(259\) | −0.266337 | −0.0165494 | ||||||||
\(260\) | 6.39386 | 0.396530 | ||||||||
\(261\) | −7.97153 | −0.493425 | ||||||||
\(262\) | −39.8420 | −2.46145 | ||||||||
\(263\) | −6.00564 | −0.370324 | −0.185162 | − | 0.982708i | \(-0.559281\pi\) | ||||
−0.185162 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(264\) | −16.3468 | −1.00608 | ||||||||
\(265\) | −11.1272 | −0.683539 | ||||||||
\(266\) | 0.802712 | 0.0492174 | ||||||||
\(267\) | 13.1575 | 0.805226 | ||||||||
\(268\) | −52.4117 | −3.20155 | ||||||||
\(269\) | 15.3180 | 0.933956 | 0.466978 | − | 0.884269i | \(-0.345343\pi\) | ||||
0.466978 | + | 0.884269i | \(0.345343\pi\) | |||||||
\(270\) | −10.7954 | −0.656987 | ||||||||
\(271\) | 28.8293 | 1.75125 | 0.875627 | − | 0.482987i | \(-0.160448\pi\) | ||||
0.875627 | + | 0.482987i | \(0.160448\pi\) | |||||||
\(272\) | −6.34029 | −0.384437 | ||||||||
\(273\) | −0.146701 | −0.00887874 | ||||||||
\(274\) | −30.4258 | −1.83809 | ||||||||
\(275\) | −4.33837 | −0.261614 | ||||||||
\(276\) | 11.0287 | 0.663847 | ||||||||
\(277\) | 15.1871 | 0.912507 | 0.456253 | − | 0.889850i | \(-0.349191\pi\) | ||||
0.456253 | + | 0.889850i | \(0.349191\pi\) | |||||||
\(278\) | 35.8173 | 2.14818 | ||||||||
\(279\) | −4.31354 | −0.258245 | ||||||||
\(280\) | −0.465986 | −0.0278480 | ||||||||
\(281\) | 21.8786 | 1.30517 | 0.652584 | − | 0.757716i | \(-0.273685\pi\) | ||||
0.652584 | + | 0.757716i | \(0.273685\pi\) | |||||||
\(282\) | 21.8695 | 1.30231 | ||||||||
\(283\) | −16.0809 | −0.955908 | −0.477954 | − | 0.878385i | \(-0.658621\pi\) | ||||
−0.477954 | + | 0.878385i | \(0.658621\pi\) | |||||||
\(284\) | −2.00454 | −0.118947 | ||||||||
\(285\) | 2.68468 | 0.159027 | ||||||||
\(286\) | 17.4410 | 1.03131 | ||||||||
\(287\) | 0.189456 | 0.0111832 | ||||||||
\(288\) | −3.29055 | −0.193897 | ||||||||
\(289\) | −12.8039 | −0.753173 | ||||||||
\(290\) | −8.42845 | −0.494936 | ||||||||
\(291\) | 13.7404 | 0.805475 | ||||||||
\(292\) | −15.4347 | −0.903248 | ||||||||
\(293\) | 14.0914 | 0.823227 | 0.411613 | − | 0.911359i | \(-0.364965\pi\) | ||||
0.411613 | + | 0.911359i | \(0.364965\pi\) | |||||||
\(294\) | −14.2719 | −0.832353 | ||||||||
\(295\) | 13.0910 | 0.762186 | ||||||||
\(296\) | 11.3749 | 0.661153 | ||||||||
\(297\) | −19.3716 | −1.12405 | ||||||||
\(298\) | −28.2789 | −1.63815 | ||||||||
\(299\) | −5.64658 | −0.326550 | ||||||||
\(300\) | −3.24773 | −0.187508 | ||||||||
\(301\) | −0.660423 | −0.0380662 | ||||||||
\(302\) | 8.06871 | 0.464302 | ||||||||
\(303\) | 6.64766 | 0.381898 | ||||||||
\(304\) | −9.83829 | −0.564265 | ||||||||
\(305\) | −8.38124 | −0.479909 | ||||||||
\(306\) | −11.3244 | −0.647372 | ||||||||
\(307\) | −17.2957 | −0.987117 | −0.493559 | − | 0.869713i | \(-0.664304\pi\) | ||||
−0.493559 | + | 0.869713i | \(0.664304\pi\) | |||||||
\(308\) | −1.74251 | −0.0992886 | ||||||||
\(309\) | 8.64361 | 0.491718 | ||||||||
\(310\) | −4.56079 | −0.259035 | ||||||||
\(311\) | 4.52172 | 0.256403 | 0.128202 | − | 0.991748i | \(-0.459080\pi\) | ||||
0.128202 | + | 0.991748i | \(0.459080\pi\) | |||||||
\(312\) | 6.26541 | 0.354709 | ||||||||
\(313\) | 29.9128 | 1.69077 | 0.845386 | − | 0.534155i | \(-0.179370\pi\) | ||||
0.845386 | + | 0.534155i | \(0.179370\pi\) | |||||||
\(314\) | 8.20803 | 0.463206 | ||||||||
\(315\) | −0.238848 | −0.0134576 | ||||||||
\(316\) | 48.0184 | 2.70125 | ||||||||
\(317\) | 10.6496 | 0.598139 | 0.299069 | − | 0.954231i | \(-0.403324\pi\) | ||||
0.299069 | + | 0.954231i | \(0.403324\pi\) | |||||||
\(318\) | −22.7220 | −1.27419 | ||||||||
\(319\) | −15.1243 | −0.846797 | ||||||||
\(320\) | −9.66955 | −0.540544 | ||||||||
\(321\) | −1.29460 | −0.0722575 | ||||||||
\(322\) | 0.857571 | 0.0477906 | ||||||||
\(323\) | 6.51108 | 0.362286 | ||||||||
\(324\) | 11.8758 | 0.659769 | ||||||||
\(325\) | 1.66281 | 0.0922363 | ||||||||
\(326\) | −10.6765 | −0.591319 | ||||||||
\(327\) | −11.2664 | −0.623035 | ||||||||
\(328\) | −8.09142 | −0.446774 | ||||||||
\(329\) | 1.11868 | 0.0616748 | ||||||||
\(330\) | −8.85906 | −0.487675 | ||||||||
\(331\) | 14.3950 | 0.791219 | 0.395610 | − | 0.918419i | \(-0.370533\pi\) | ||||
0.395610 | + | 0.918419i | \(0.370533\pi\) | |||||||
\(332\) | −8.60921 | −0.472492 | ||||||||
\(333\) | 5.83038 | 0.319503 | ||||||||
\(334\) | 28.3249 | 1.54987 | ||||||||
\(335\) | −13.6304 | −0.744708 | ||||||||
\(336\) | −0.273072 | −0.0148973 | ||||||||
\(337\) | −30.9679 | −1.68693 | −0.843464 | − | 0.537186i | \(-0.819487\pi\) | ||||
−0.843464 | + | 0.537186i | \(0.819487\pi\) | |||||||
\(338\) | 24.7451 | 1.34596 | ||||||||
\(339\) | −11.0578 | −0.600579 | ||||||||
\(340\) | −7.87663 | −0.427170 | ||||||||
\(341\) | −8.18402 | −0.443189 | ||||||||
\(342\) | −17.5722 | −0.950194 | ||||||||
\(343\) | −1.46123 | −0.0788989 | ||||||||
\(344\) | 28.2058 | 1.52076 | ||||||||
\(345\) | 2.86816 | 0.154416 | ||||||||
\(346\) | 25.2838 | 1.35926 | ||||||||
\(347\) | −12.7815 | −0.686146 | −0.343073 | − | 0.939309i | \(-0.611468\pi\) | ||||
−0.343073 | + | 0.939309i | \(0.611468\pi\) | |||||||
\(348\) | −11.3221 | −0.606930 | ||||||||
\(349\) | 4.64674 | 0.248734 | 0.124367 | − | 0.992236i | \(-0.460310\pi\) | ||||
0.124367 | + | 0.992236i | \(0.460310\pi\) | |||||||
\(350\) | −0.252539 | −0.0134988 | ||||||||
\(351\) | 7.42476 | 0.396304 | ||||||||
\(352\) | −6.24311 | −0.332759 | ||||||||
\(353\) | −4.85486 | −0.258398 | −0.129199 | − | 0.991619i | \(-0.541241\pi\) | ||||
−0.129199 | + | 0.991619i | \(0.541241\pi\) | |||||||
\(354\) | 26.7321 | 1.42079 | ||||||||
\(355\) | −0.521308 | −0.0276681 | ||||||||
\(356\) | −59.9008 | −3.17473 | ||||||||
\(357\) | 0.180722 | 0.00956481 | ||||||||
\(358\) | −12.2173 | −0.645706 | ||||||||
\(359\) | −29.4161 | −1.55252 | −0.776262 | − | 0.630410i | \(-0.782887\pi\) | ||||
−0.776262 | + | 0.630410i | \(0.782887\pi\) | |||||||
\(360\) | 10.2009 | 0.537635 | ||||||||
\(361\) | −8.89670 | −0.468247 | ||||||||
\(362\) | −29.0751 | −1.52815 | ||||||||
\(363\) | −6.60617 | −0.346734 | ||||||||
\(364\) | 0.667869 | 0.0350059 | ||||||||
\(365\) | −4.01401 | −0.210103 | ||||||||
\(366\) | −17.1147 | −0.894600 | ||||||||
\(367\) | −4.40442 | −0.229909 | −0.114954 | − | 0.993371i | \(-0.536672\pi\) | ||||
−0.114954 | + | 0.993371i | \(0.536672\pi\) | |||||||
\(368\) | −10.5107 | −0.547906 | ||||||||
\(369\) | −4.14738 | −0.215904 | ||||||||
\(370\) | 6.16457 | 0.320481 | ||||||||
\(371\) | −1.16229 | −0.0603431 | ||||||||
\(372\) | −6.12661 | −0.317650 | ||||||||
\(373\) | 14.9927 | 0.776294 | 0.388147 | − | 0.921597i | \(-0.373115\pi\) | ||||
0.388147 | + | 0.921597i | \(0.373115\pi\) | |||||||
\(374\) | −21.4856 | −1.11099 | ||||||||
\(375\) | −0.844619 | −0.0436159 | ||||||||
\(376\) | −47.7773 | −2.46393 | ||||||||
\(377\) | 5.79684 | 0.298553 | ||||||||
\(378\) | −1.12763 | −0.0579991 | ||||||||
\(379\) | 6.69151 | 0.343720 | 0.171860 | − | 0.985121i | \(-0.445022\pi\) | ||||
0.171860 | + | 0.985121i | \(0.445022\pi\) | |||||||
\(380\) | −12.2223 | −0.626988 | ||||||||
\(381\) | 16.8759 | 0.864579 | ||||||||
\(382\) | −24.7141 | −1.26448 | ||||||||
\(383\) | −9.14533 | −0.467305 | −0.233652 | − | 0.972320i | \(-0.575068\pi\) | ||||
−0.233652 | + | 0.972320i | \(0.575068\pi\) | |||||||
\(384\) | −17.3146 | −0.883580 | ||||||||
\(385\) | −0.453164 | −0.0230954 | ||||||||
\(386\) | −9.49396 | −0.483230 | ||||||||
\(387\) | 14.4573 | 0.734907 | ||||||||
\(388\) | −62.5543 | −3.17571 | ||||||||
\(389\) | −0.947406 | −0.0480354 | −0.0240177 | − | 0.999712i | \(-0.507646\pi\) | ||||
−0.0240177 | + | 0.999712i | \(0.507646\pi\) | |||||||
\(390\) | 3.39551 | 0.171938 | ||||||||
\(391\) | 6.95606 | 0.351783 | ||||||||
\(392\) | 31.1792 | 1.57479 | ||||||||
\(393\) | −13.9188 | −0.702111 | ||||||||
\(394\) | 2.02715 | 0.102126 | ||||||||
\(395\) | 12.4879 | 0.628333 | ||||||||
\(396\) | 38.1452 | 1.91687 | ||||||||
\(397\) | 19.6565 | 0.986530 | 0.493265 | − | 0.869879i | \(-0.335803\pi\) | ||||
0.493265 | + | 0.869879i | \(0.335803\pi\) | |||||||
\(398\) | −53.8846 | −2.70099 | ||||||||
\(399\) | 0.280428 | 0.0140389 | ||||||||
\(400\) | 3.09520 | 0.154760 | ||||||||
\(401\) | −5.35715 | −0.267523 | −0.133762 | − | 0.991014i | \(-0.542706\pi\) | ||||
−0.133762 | + | 0.991014i | \(0.542706\pi\) | |||||||
\(402\) | −27.8336 | −1.38821 | ||||||||
\(403\) | 3.13678 | 0.156254 | ||||||||
\(404\) | −30.2641 | −1.50569 | ||||||||
\(405\) | 3.08848 | 0.153468 | ||||||||
\(406\) | −0.880392 | −0.0436931 | ||||||||
\(407\) | 11.0619 | 0.548318 | ||||||||
\(408\) | −7.71839 | −0.382117 | ||||||||
\(409\) | 1.96328 | 0.0970781 | 0.0485390 | − | 0.998821i | \(-0.484543\pi\) | ||||
0.0485390 | + | 0.998821i | \(0.484543\pi\) | |||||||
\(410\) | −4.38511 | −0.216565 | ||||||||
\(411\) | −10.6292 | −0.524302 | ||||||||
\(412\) | −39.3508 | −1.93868 | ||||||||
\(413\) | 1.36741 | 0.0672860 | ||||||||
\(414\) | −18.7731 | −0.922647 | ||||||||
\(415\) | −2.23895 | −0.109906 | ||||||||
\(416\) | 2.39286 | 0.117320 | ||||||||
\(417\) | 12.5128 | 0.612753 | ||||||||
\(418\) | −33.3394 | −1.63069 | ||||||||
\(419\) | −19.4882 | −0.952062 | −0.476031 | − | 0.879428i | \(-0.657925\pi\) | ||||
−0.476031 | + | 0.879428i | \(0.657925\pi\) | |||||||
\(420\) | −0.339241 | −0.0165533 | ||||||||
\(421\) | 29.4640 | 1.43599 | 0.717993 | − | 0.696050i | \(-0.245061\pi\) | ||||
0.717993 | + | 0.696050i | \(0.245061\pi\) | |||||||
\(422\) | 37.1565 | 1.80875 | ||||||||
\(423\) | −24.4890 | −1.19070 | ||||||||
\(424\) | 49.6399 | 2.41073 | ||||||||
\(425\) | −2.04843 | −0.0993634 | ||||||||
\(426\) | −1.06452 | −0.0515763 | ||||||||
\(427\) | −0.875461 | −0.0423665 | ||||||||
\(428\) | 5.89379 | 0.284887 | ||||||||
\(429\) | 6.09300 | 0.294173 | ||||||||
\(430\) | 15.2860 | 0.737157 | ||||||||
\(431\) | 29.9583 | 1.44304 | 0.721521 | − | 0.692393i | \(-0.243443\pi\) | ||||
0.721521 | + | 0.692393i | \(0.243443\pi\) | |||||||
\(432\) | 13.8206 | 0.664944 | ||||||||
\(433\) | −33.0683 | −1.58916 | −0.794581 | − | 0.607158i | \(-0.792309\pi\) | ||||
−0.794581 | + | 0.607158i | \(0.792309\pi\) | |||||||
\(434\) | −0.476396 | −0.0228677 | ||||||||
\(435\) | −2.94448 | −0.141177 | ||||||||
\(436\) | 51.2914 | 2.45641 | ||||||||
\(437\) | 10.7938 | 0.516337 | ||||||||
\(438\) | −8.19671 | −0.391654 | ||||||||
\(439\) | 7.52782 | 0.359283 | 0.179642 | − | 0.983732i | \(-0.442506\pi\) | ||||
0.179642 | + | 0.983732i | \(0.442506\pi\) | |||||||
\(440\) | 19.3540 | 0.922667 | ||||||||
\(441\) | 15.9814 | 0.761018 | ||||||||
\(442\) | 8.23502 | 0.391700 | ||||||||
\(443\) | 8.00794 | 0.380469 | 0.190234 | − | 0.981739i | \(-0.439075\pi\) | ||||
0.190234 | + | 0.981739i | \(0.439075\pi\) | |||||||
\(444\) | 8.28101 | 0.393000 | ||||||||
\(445\) | −15.5780 | −0.738470 | ||||||||
\(446\) | 0.275223 | 0.0130322 | ||||||||
\(447\) | −9.87924 | −0.467272 | ||||||||
\(448\) | −1.01003 | −0.0477195 | ||||||||
\(449\) | −2.17867 | −0.102818 | −0.0514088 | − | 0.998678i | \(-0.516371\pi\) | ||||
−0.0514088 | + | 0.998678i | \(0.516371\pi\) | |||||||
\(450\) | 5.52833 | 0.260608 | ||||||||
\(451\) | −7.86877 | −0.370526 | ||||||||
\(452\) | 50.3418 | 2.36788 | ||||||||
\(453\) | 2.81880 | 0.132439 | ||||||||
\(454\) | 33.2586 | 1.56090 | ||||||||
\(455\) | 0.173689 | 0.00814266 | ||||||||
\(456\) | −11.9767 | −0.560860 | ||||||||
\(457\) | 32.2904 | 1.51048 | 0.755241 | − | 0.655447i | \(-0.227520\pi\) | ||||
0.755241 | + | 0.655447i | \(0.227520\pi\) | |||||||
\(458\) | −63.0483 | −2.94605 | ||||||||
\(459\) | −9.14661 | −0.426927 | ||||||||
\(460\) | −13.0575 | −0.608811 | ||||||||
\(461\) | −23.4545 | −1.09239 | −0.546193 | − | 0.837659i | \(-0.683924\pi\) | ||||
−0.546193 | + | 0.837659i | \(0.683924\pi\) | |||||||
\(462\) | −0.925371 | −0.0430522 | ||||||||
\(463\) | −28.8247 | −1.33960 | −0.669798 | − | 0.742543i | \(-0.733619\pi\) | ||||
−0.669798 | + | 0.742543i | \(0.733619\pi\) | |||||||
\(464\) | 10.7904 | 0.500930 | ||||||||
\(465\) | −1.59331 | −0.0738880 | ||||||||
\(466\) | −53.5989 | −2.48292 | ||||||||
\(467\) | −1.68316 | −0.0778872 | −0.0389436 | − | 0.999241i | \(-0.512399\pi\) | ||||
−0.0389436 | + | 0.999241i | \(0.512399\pi\) | |||||||
\(468\) | −14.6203 | −0.675825 | ||||||||
\(469\) | −1.42376 | −0.0657431 | ||||||||
\(470\) | −25.8927 | −1.19434 | ||||||||
\(471\) | 2.86748 | 0.132126 | ||||||||
\(472\) | −58.4005 | −2.68810 | ||||||||
\(473\) | 27.4297 | 1.26122 | ||||||||
\(474\) | 25.5005 | 1.17128 | ||||||||
\(475\) | −3.17857 | −0.145843 | ||||||||
\(476\) | −0.822752 | −0.0377108 | ||||||||
\(477\) | 25.4437 | 1.16499 | ||||||||
\(478\) | 46.8175 | 2.14138 | ||||||||
\(479\) | −31.2436 | −1.42756 | −0.713779 | − | 0.700371i | \(-0.753018\pi\) | ||||
−0.713779 | + | 0.700371i | \(0.753018\pi\) | |||||||
\(480\) | −1.21545 | −0.0554772 | ||||||||
\(481\) | −4.23981 | −0.193319 | ||||||||
\(482\) | 12.0336 | 0.548115 | ||||||||
\(483\) | 0.299593 | 0.0136319 | ||||||||
\(484\) | 30.0752 | 1.36705 | ||||||||
\(485\) | −16.2681 | −0.738698 | ||||||||
\(486\) | 38.6930 | 1.75515 | ||||||||
\(487\) | −40.2455 | −1.82370 | −0.911850 | − | 0.410524i | \(-0.865346\pi\) | ||||
−0.911850 | + | 0.410524i | \(0.865346\pi\) | |||||||
\(488\) | 37.3898 | 1.69256 | ||||||||
\(489\) | −3.72985 | −0.168670 | ||||||||
\(490\) | 16.8974 | 0.763348 | ||||||||
\(491\) | −29.1839 | −1.31705 | −0.658526 | − | 0.752558i | \(-0.728820\pi\) | ||||
−0.658526 | + | 0.752558i | \(0.728820\pi\) | |||||||
\(492\) | −5.89062 | −0.265570 | ||||||||
\(493\) | −7.14116 | −0.321622 | ||||||||
\(494\) | 12.7784 | 0.574926 | ||||||||
\(495\) | 9.92020 | 0.445880 | ||||||||
\(496\) | 5.83886 | 0.262172 | ||||||||
\(497\) | −0.0544531 | −0.00244255 | ||||||||
\(498\) | −4.57198 | −0.204875 | ||||||||
\(499\) | −8.91261 | −0.398983 | −0.199492 | − | 0.979900i | \(-0.563929\pi\) | ||||
−0.199492 | + | 0.979900i | \(0.563929\pi\) | |||||||
\(500\) | 3.84521 | 0.171963 | ||||||||
\(501\) | 9.89532 | 0.442090 | ||||||||
\(502\) | 23.1502 | 1.03324 | ||||||||
\(503\) | 13.6653 | 0.609304 | 0.304652 | − | 0.952464i | \(-0.401460\pi\) | ||||
0.304652 | + | 0.952464i | \(0.401460\pi\) | |||||||
\(504\) | 1.06553 | 0.0474626 | ||||||||
\(505\) | −7.87060 | −0.350237 | ||||||||
\(506\) | −35.6179 | −1.58341 | ||||||||
\(507\) | 8.64472 | 0.383925 | ||||||||
\(508\) | −76.8291 | −3.40874 | ||||||||
\(509\) | 40.6650 | 1.80244 | 0.901222 | − | 0.433358i | \(-0.142671\pi\) | ||||
0.901222 | + | 0.433358i | \(0.142671\pi\) | |||||||
\(510\) | −4.18294 | −0.185224 | ||||||||
\(511\) | −0.419283 | −0.0185480 | ||||||||
\(512\) | 32.0703 | 1.41732 | ||||||||
\(513\) | −14.1929 | −0.626631 | ||||||||
\(514\) | 2.13063 | 0.0939780 | ||||||||
\(515\) | −10.2337 | −0.450952 | ||||||||
\(516\) | 20.5340 | 0.903961 | ||||||||
\(517\) | −46.4627 | −2.04343 | ||||||||
\(518\) | 0.643919 | 0.0282922 | ||||||||
\(519\) | 8.83290 | 0.387721 | ||||||||
\(520\) | −7.41803 | −0.325302 | ||||||||
\(521\) | 13.0700 | 0.572607 | 0.286304 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286304 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(522\) | 19.2727 | 0.843541 | ||||||||
\(523\) | 29.4948 | 1.28972 | 0.644859 | − | 0.764302i | \(-0.276916\pi\) | ||||
0.644859 | + | 0.764302i | \(0.276916\pi\) | |||||||
\(524\) | 63.3666 | 2.76818 | ||||||||
\(525\) | −0.0882245 | −0.00385043 | ||||||||
\(526\) | 14.5198 | 0.633091 | ||||||||
\(527\) | −3.86421 | −0.168328 | ||||||||
\(528\) | 11.3416 | 0.493581 | ||||||||
\(529\) | −11.4685 | −0.498632 | ||||||||
\(530\) | 26.9021 | 1.16855 | ||||||||
\(531\) | −29.9340 | −1.29903 | ||||||||
\(532\) | −1.27667 | −0.0553508 | ||||||||
\(533\) | 3.01595 | 0.130635 | ||||||||
\(534\) | −31.8107 | −1.37658 | ||||||||
\(535\) | 1.53276 | 0.0662671 | ||||||||
\(536\) | 60.8070 | 2.62646 | ||||||||
\(537\) | −4.26813 | −0.184183 | ||||||||
\(538\) | −37.0341 | −1.59666 | ||||||||
\(539\) | 30.3213 | 1.30603 | ||||||||
\(540\) | 17.1695 | 0.738859 | ||||||||
\(541\) | −5.31616 | −0.228560 | −0.114280 | − | 0.993449i | \(-0.536456\pi\) | ||||
−0.114280 | + | 0.993449i | \(0.536456\pi\) | |||||||
\(542\) | −69.7002 | −2.99388 | ||||||||
\(543\) | −10.1574 | −0.435895 | ||||||||
\(544\) | −2.94778 | −0.126385 | ||||||||
\(545\) | 13.3391 | 0.571383 | ||||||||
\(546\) | 0.354677 | 0.0151788 | ||||||||
\(547\) | −16.8087 | −0.718689 | −0.359345 | − | 0.933205i | \(-0.617000\pi\) | ||||
−0.359345 | + | 0.933205i | \(0.617000\pi\) | |||||||
\(548\) | 48.3906 | 2.06714 | ||||||||
\(549\) | 19.1647 | 0.817930 | ||||||||
\(550\) | 10.4888 | 0.447245 | ||||||||
\(551\) | −11.0810 | −0.472067 | ||||||||
\(552\) | −12.7952 | −0.544601 | ||||||||
\(553\) | 1.30442 | 0.0554695 | ||||||||
\(554\) | −36.7177 | −1.55999 | ||||||||
\(555\) | 2.15359 | 0.0914150 | ||||||||
\(556\) | −56.9655 | −2.41588 | ||||||||
\(557\) | 24.1887 | 1.02491 | 0.512455 | − | 0.858714i | \(-0.328736\pi\) | ||||
0.512455 | + | 0.858714i | \(0.328736\pi\) | |||||||
\(558\) | 10.4288 | 0.441485 | ||||||||
\(559\) | −10.5133 | −0.444664 | ||||||||
\(560\) | 0.323308 | 0.0136623 | ||||||||
\(561\) | −7.50600 | −0.316904 | ||||||||
\(562\) | −52.8956 | −2.23127 | ||||||||
\(563\) | −9.81018 | −0.413450 | −0.206725 | − | 0.978399i | \(-0.566280\pi\) | ||||
−0.206725 | + | 0.978399i | \(0.566280\pi\) | |||||||
\(564\) | −34.7823 | −1.46460 | ||||||||
\(565\) | 13.0921 | 0.550788 | ||||||||
\(566\) | 38.8785 | 1.63418 | ||||||||
\(567\) | 0.322606 | 0.0135482 | ||||||||
\(568\) | 2.32562 | 0.0975809 | ||||||||
\(569\) | 28.1377 | 1.17959 | 0.589797 | − | 0.807552i | \(-0.299208\pi\) | ||||
0.589797 | + | 0.807552i | \(0.299208\pi\) | |||||||
\(570\) | −6.49071 | −0.271866 | ||||||||
\(571\) | 31.0041 | 1.29748 | 0.648741 | − | 0.761009i | \(-0.275296\pi\) | ||||
0.648741 | + | 0.761009i | \(0.275296\pi\) | |||||||
\(572\) | −27.7390 | −1.15982 | ||||||||
\(573\) | −8.63387 | −0.360685 | ||||||||
\(574\) | −0.458045 | −0.0191184 | ||||||||
\(575\) | −3.39580 | −0.141615 | ||||||||
\(576\) | 22.1106 | 0.921274 | ||||||||
\(577\) | 26.0634 | 1.08503 | 0.542516 | − | 0.840045i | \(-0.317472\pi\) | ||||
0.542516 | + | 0.840045i | \(0.317472\pi\) | |||||||
\(578\) | 30.9559 | 1.28760 | ||||||||
\(579\) | −3.31672 | −0.137838 | ||||||||
\(580\) | 13.4050 | 0.556613 | ||||||||
\(581\) | −0.233869 | −0.00970250 | ||||||||
\(582\) | −33.2199 | −1.37701 | ||||||||
\(583\) | 48.2740 | 1.99930 | ||||||||
\(584\) | 17.9070 | 0.740998 | ||||||||
\(585\) | −3.80222 | −0.157202 | ||||||||
\(586\) | −34.0685 | −1.40736 | ||||||||
\(587\) | 17.6837 | 0.729886 | 0.364943 | − | 0.931030i | \(-0.381088\pi\) | ||||
0.364943 | + | 0.931030i | \(0.381088\pi\) | |||||||
\(588\) | 22.6987 | 0.936079 | ||||||||
\(589\) | −5.99613 | −0.247066 | ||||||||
\(590\) | −31.6498 | −1.30300 | ||||||||
\(591\) | 0.708185 | 0.0291308 | ||||||||
\(592\) | −7.89207 | −0.324362 | ||||||||
\(593\) | 24.9555 | 1.02480 | 0.512400 | − | 0.858747i | \(-0.328756\pi\) | ||||
0.512400 | + | 0.858747i | \(0.328756\pi\) | |||||||
\(594\) | 46.8345 | 1.92164 | ||||||||
\(595\) | −0.213968 | −0.00877184 | ||||||||
\(596\) | 44.9762 | 1.84230 | ||||||||
\(597\) | −18.8246 | −0.770440 | ||||||||
\(598\) | 13.6517 | 0.558258 | ||||||||
\(599\) | 3.49052 | 0.142619 | 0.0713093 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713093 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(600\) | 3.76795 | 0.153826 | ||||||||
\(601\) | 28.5329 | 1.16388 | 0.581941 | − | 0.813231i | \(-0.302294\pi\) | ||||
0.581941 | + | 0.813231i | \(0.302294\pi\) | |||||||
\(602\) | 1.59670 | 0.0650765 | ||||||||
\(603\) | 31.1675 | 1.26924 | ||||||||
\(604\) | −12.8329 | −0.522162 | ||||||||
\(605\) | 7.82147 | 0.317988 | ||||||||
\(606\) | −16.0720 | −0.652879 | ||||||||
\(607\) | −29.7118 | −1.20597 | −0.602983 | − | 0.797754i | \(-0.706021\pi\) | ||||
−0.602983 | + | 0.797754i | \(0.706021\pi\) | |||||||
\(608\) | −4.57411 | −0.185504 | ||||||||
\(609\) | −0.307565 | −0.0124632 | ||||||||
\(610\) | 20.2632 | 0.820433 | ||||||||
\(611\) | 17.8082 | 0.720444 | ||||||||
\(612\) | 18.0109 | 0.728046 | ||||||||
\(613\) | 30.9697 | 1.25085 | 0.625426 | − | 0.780283i | \(-0.284925\pi\) | ||||
0.625426 | + | 0.780283i | \(0.284925\pi\) | |||||||
\(614\) | 41.8155 | 1.68754 | ||||||||
\(615\) | −1.53194 | −0.0617737 | ||||||||
\(616\) | 2.02162 | 0.0814534 | ||||||||
\(617\) | 39.1508 | 1.57615 | 0.788077 | − | 0.615577i | \(-0.211077\pi\) | ||||
0.788077 | + | 0.615577i | \(0.211077\pi\) | |||||||
\(618\) | −20.8975 | −0.840622 | ||||||||
\(619\) | 1.32237 | 0.0531507 | 0.0265754 | − | 0.999647i | \(-0.491540\pi\) | ||||
0.0265754 | + | 0.999647i | \(0.491540\pi\) | |||||||
\(620\) | 7.25370 | 0.291315 | ||||||||
\(621\) | −15.1629 | −0.608464 | ||||||||
\(622\) | −10.9321 | −0.438338 | ||||||||
\(623\) | −1.62720 | −0.0651924 | ||||||||
\(624\) | −4.34703 | −0.174020 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −72.3198 | −2.89048 | ||||||||
\(627\) | −11.6471 | −0.465142 | ||||||||
\(628\) | −13.0544 | −0.520929 | ||||||||
\(629\) | 5.22305 | 0.208257 | ||||||||
\(630\) | 0.577460 | 0.0230066 | ||||||||
\(631\) | −15.0516 | −0.599193 | −0.299596 | − | 0.954066i | \(-0.596852\pi\) | ||||
−0.299596 | + | 0.954066i | \(0.596852\pi\) | |||||||
\(632\) | −55.7100 | −2.21602 | ||||||||
\(633\) | 12.9806 | 0.515934 | ||||||||
\(634\) | −25.7473 | −1.02256 | ||||||||
\(635\) | −19.9805 | −0.792901 | ||||||||
\(636\) | 36.1382 | 1.43297 | ||||||||
\(637\) | −11.6216 | −0.460463 | ||||||||
\(638\) | 36.5658 | 1.44765 | ||||||||
\(639\) | 1.19203 | 0.0471561 | ||||||||
\(640\) | 20.4998 | 0.810328 | ||||||||
\(641\) | 32.6162 | 1.28826 | 0.644131 | − | 0.764915i | \(-0.277219\pi\) | ||||
0.644131 | + | 0.764915i | \(0.277219\pi\) | |||||||
\(642\) | 3.12994 | 0.123529 | ||||||||
\(643\) | 24.9480 | 0.983851 | 0.491926 | − | 0.870637i | \(-0.336293\pi\) | ||||
0.491926 | + | 0.870637i | \(0.336293\pi\) | |||||||
\(644\) | −1.36392 | −0.0537461 | ||||||||
\(645\) | 5.34017 | 0.210269 | ||||||||
\(646\) | −15.7417 | −0.619350 | ||||||||
\(647\) | 1.93744 | 0.0761688 | 0.0380844 | − | 0.999275i | \(-0.487874\pi\) | ||||
0.0380844 | + | 0.999275i | \(0.487874\pi\) | |||||||
\(648\) | −13.7781 | −0.541255 | ||||||||
\(649\) | −56.7935 | −2.22934 | ||||||||
\(650\) | −4.02016 | −0.157684 | ||||||||
\(651\) | −0.166429 | −0.00652287 | ||||||||
\(652\) | 16.9805 | 0.665007 | ||||||||
\(653\) | −22.3056 | −0.872886 | −0.436443 | − | 0.899732i | \(-0.643762\pi\) | ||||
−0.436443 | + | 0.899732i | \(0.643762\pi\) | |||||||
\(654\) | 27.2387 | 1.06512 | ||||||||
\(655\) | 16.4794 | 0.643903 | ||||||||
\(656\) | 5.61395 | 0.219188 | ||||||||
\(657\) | 9.17851 | 0.358088 | ||||||||
\(658\) | −2.70462 | −0.105437 | ||||||||
\(659\) | −9.73679 | −0.379291 | −0.189646 | − | 0.981853i | \(-0.560734\pi\) | ||||
−0.189646 | + | 0.981853i | \(0.560734\pi\) | |||||||
\(660\) | 14.0899 | 0.548448 | ||||||||
\(661\) | −45.3185 | −1.76268 | −0.881342 | − | 0.472479i | \(-0.843359\pi\) | ||||
−0.881342 | + | 0.472479i | \(0.843359\pi\) | |||||||
\(662\) | −34.8025 | −1.35264 | ||||||||
\(663\) | 2.87691 | 0.111730 | ||||||||
\(664\) | 9.98822 | 0.387618 | ||||||||
\(665\) | −0.332017 | −0.0128751 | ||||||||
\(666\) | −14.0960 | −0.546210 | ||||||||
\(667\) | −11.8383 | −0.458382 | ||||||||
\(668\) | −45.0493 | −1.74301 | ||||||||
\(669\) | 0.0961493 | 0.00371735 | ||||||||
\(670\) | 32.9540 | 1.27313 | ||||||||
\(671\) | 36.3609 | 1.40370 | ||||||||
\(672\) | −0.126959 | −0.00489755 | ||||||||
\(673\) | 24.7710 | 0.954851 | 0.477425 | − | 0.878672i | \(-0.341570\pi\) | ||||
0.477425 | + | 0.878672i | \(0.341570\pi\) | |||||||
\(674\) | 74.8706 | 2.88391 | ||||||||
\(675\) | 4.46518 | 0.171865 | ||||||||
\(676\) | −39.3559 | −1.51369 | ||||||||
\(677\) | −20.6154 | −0.792314 | −0.396157 | − | 0.918183i | \(-0.629656\pi\) | ||||
−0.396157 | + | 0.918183i | \(0.629656\pi\) | |||||||
\(678\) | 26.7344 | 1.02673 | ||||||||
\(679\) | −1.69928 | −0.0652125 | ||||||||
\(680\) | 9.13831 | 0.350438 | ||||||||
\(681\) | 11.6189 | 0.445237 | ||||||||
\(682\) | 19.7864 | 0.757660 | ||||||||
\(683\) | 0.616035 | 0.0235719 | 0.0117860 | − | 0.999931i | \(-0.496248\pi\) | ||||
0.0117860 | + | 0.999931i | \(0.496248\pi\) | |||||||
\(684\) | 27.9476 | 1.06860 | ||||||||
\(685\) | 12.5847 | 0.480835 | ||||||||
\(686\) | 3.53279 | 0.134882 | ||||||||
\(687\) | −22.0259 | −0.840342 | ||||||||
\(688\) | −19.5696 | −0.746084 | ||||||||
\(689\) | −18.5025 | −0.704888 | ||||||||
\(690\) | −6.93430 | −0.263984 | ||||||||
\(691\) | 17.8270 | 0.678173 | 0.339086 | − | 0.940755i | \(-0.389882\pi\) | ||||
0.339086 | + | 0.940755i | \(0.389882\pi\) | |||||||
\(692\) | −40.2126 | −1.52865 | ||||||||
\(693\) | 1.03621 | 0.0393625 | ||||||||
\(694\) | 30.9016 | 1.17301 | ||||||||
\(695\) | −14.8147 | −0.561953 | ||||||||
\(696\) | 13.1357 | 0.497908 | ||||||||
\(697\) | −3.71536 | −0.140729 | ||||||||
\(698\) | −11.2343 | −0.425226 | ||||||||
\(699\) | −18.7248 | −0.708236 | ||||||||
\(700\) | 0.401650 | 0.0151809 | ||||||||
\(701\) | 18.7168 | 0.706922 | 0.353461 | − | 0.935449i | \(-0.385005\pi\) | ||||
0.353461 | + | 0.935449i | \(0.385005\pi\) | |||||||
\(702\) | −17.9507 | −0.677507 | ||||||||
\(703\) | 8.10466 | 0.305673 | ||||||||
\(704\) | 41.9501 | 1.58105 | ||||||||
\(705\) | −9.04562 | −0.340678 | ||||||||
\(706\) | 11.7375 | 0.441748 | ||||||||
\(707\) | −0.822122 | −0.0309191 | ||||||||
\(708\) | −42.5160 | −1.59785 | ||||||||
\(709\) | 22.1260 | 0.830961 | 0.415481 | − | 0.909602i | \(-0.363613\pi\) | ||||
0.415481 | + | 0.909602i | \(0.363613\pi\) | |||||||
\(710\) | 1.26036 | 0.0473004 | ||||||||
\(711\) | −28.5550 | −1.07090 | ||||||||
\(712\) | 69.4956 | 2.60446 | ||||||||
\(713\) | −6.40592 | −0.239904 | ||||||||
\(714\) | −0.436928 | −0.0163516 | ||||||||
\(715\) | −7.21391 | −0.269785 | ||||||||
\(716\) | 19.4310 | 0.726172 | ||||||||
\(717\) | 16.3557 | 0.610815 | ||||||||
\(718\) | 71.1190 | 2.65414 | ||||||||
\(719\) | 23.8375 | 0.888987 | 0.444493 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444493 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(720\) | −7.07753 | −0.263764 | ||||||||
\(721\) | −1.06896 | −0.0398102 | ||||||||
\(722\) | 21.5094 | 0.800498 | ||||||||
\(723\) | 4.20394 | 0.156346 | ||||||||
\(724\) | 46.2424 | 1.71859 | ||||||||
\(725\) | 3.48617 | 0.129473 | ||||||||
\(726\) | 15.9716 | 0.592763 | ||||||||
\(727\) | 35.9199 | 1.33220 | 0.666098 | − | 0.745864i | \(-0.267963\pi\) | ||||
0.666098 | + | 0.745864i | \(0.267963\pi\) | |||||||
\(728\) | −0.774848 | −0.0287178 | ||||||||
\(729\) | 4.25195 | 0.157480 | ||||||||
\(730\) | 9.70462 | 0.359184 | ||||||||
\(731\) | 12.9514 | 0.479023 | ||||||||
\(732\) | 27.2200 | 1.00608 | ||||||||
\(733\) | 49.6436 | 1.83363 | 0.916813 | − | 0.399316i | \(-0.130752\pi\) | ||||
0.916813 | + | 0.399316i | \(0.130752\pi\) | |||||||
\(734\) | 10.6485 | 0.393043 | ||||||||
\(735\) | 5.90312 | 0.217740 | ||||||||
\(736\) | −4.88671 | −0.180127 | ||||||||
\(737\) | 59.1337 | 2.17822 | ||||||||
\(738\) | 10.0271 | 0.369101 | ||||||||
\(739\) | −5.97744 | −0.219884 | −0.109942 | − | 0.993938i | \(-0.535066\pi\) | ||||
−0.109942 | + | 0.993938i | \(0.535066\pi\) | |||||||
\(740\) | −9.80444 | −0.360418 | ||||||||
\(741\) | 4.46412 | 0.163994 | ||||||||
\(742\) | 2.81005 | 0.103160 | ||||||||
\(743\) | −17.2264 | −0.631977 | −0.315988 | − | 0.948763i | \(-0.602336\pi\) | ||||
−0.315988 | + | 0.948763i | \(0.602336\pi\) | |||||||
\(744\) | 7.10797 | 0.260591 | ||||||||
\(745\) | 11.6967 | 0.428533 | ||||||||
\(746\) | −36.2477 | −1.32712 | ||||||||
\(747\) | 5.11962 | 0.187317 | ||||||||
\(748\) | 34.1718 | 1.24944 | ||||||||
\(749\) | 0.160104 | 0.00585008 | ||||||||
\(750\) | 2.04202 | 0.0745642 | ||||||||
\(751\) | 46.3306 | 1.69063 | 0.845313 | − | 0.534272i | \(-0.179414\pi\) | ||||
0.845313 | + | 0.534272i | \(0.179414\pi\) | |||||||
\(752\) | 33.1486 | 1.20881 | ||||||||
\(753\) | 8.08753 | 0.294726 | ||||||||
\(754\) | −14.0149 | −0.510394 | ||||||||
\(755\) | −3.33737 | −0.121459 | ||||||||
\(756\) | 1.79344 | 0.0652268 | ||||||||
\(757\) | −35.9850 | −1.30790 | −0.653949 | − | 0.756538i | \(-0.726889\pi\) | ||||
−0.653949 | + | 0.756538i | \(0.726889\pi\) | |||||||
\(758\) | −16.1780 | −0.587611 | ||||||||
\(759\) | −12.4431 | −0.451657 | ||||||||
\(760\) | 14.1800 | 0.514363 | ||||||||
\(761\) | 50.2019 | 1.81982 | 0.909908 | − | 0.414810i | \(-0.136152\pi\) | ||||
0.909908 | + | 0.414810i | \(0.136152\pi\) | |||||||
\(762\) | −40.8006 | −1.47805 | ||||||||
\(763\) | 1.39333 | 0.0504419 | ||||||||
\(764\) | 39.3065 | 1.42206 | ||||||||
\(765\) | 4.68398 | 0.169350 | ||||||||
\(766\) | 22.1105 | 0.798886 | ||||||||
\(767\) | 21.7678 | 0.785991 | ||||||||
\(768\) | 25.5270 | 0.921126 | ||||||||
\(769\) | 34.4616 | 1.24272 | 0.621358 | − | 0.783527i | \(-0.286581\pi\) | ||||
0.621358 | + | 0.783527i | \(0.286581\pi\) | |||||||
\(770\) | 1.09561 | 0.0394830 | ||||||||
\(771\) | 0.744336 | 0.0268066 | ||||||||
\(772\) | 15.0997 | 0.543449 | ||||||||
\(773\) | 34.1443 | 1.22808 | 0.614042 | − | 0.789274i | \(-0.289543\pi\) | ||||
0.614042 | + | 0.789274i | \(0.289543\pi\) | |||||||
\(774\) | −34.9533 | −1.25637 | ||||||||
\(775\) | 1.88643 | 0.0677624 | ||||||||
\(776\) | 72.5742 | 2.60526 | ||||||||
\(777\) | 0.224953 | 0.00807015 | ||||||||
\(778\) | 2.29053 | 0.0821195 | ||||||||
\(779\) | −5.76517 | −0.206559 | ||||||||
\(780\) | −5.40038 | −0.193365 | ||||||||
\(781\) | 2.26163 | 0.0809274 | ||||||||
\(782\) | −16.8176 | −0.601395 | ||||||||
\(783\) | 15.5664 | 0.556296 | ||||||||
\(784\) | −21.6326 | −0.772593 | ||||||||
\(785\) | −3.39499 | −0.121173 | ||||||||
\(786\) | 33.6513 | 1.20030 | ||||||||
\(787\) | 49.1699 | 1.75272 | 0.876359 | − | 0.481659i | \(-0.159965\pi\) | ||||
0.876359 | + | 0.481659i | \(0.159965\pi\) | |||||||
\(788\) | −3.22407 | −0.114853 | ||||||||
\(789\) | 5.07248 | 0.180585 | ||||||||
\(790\) | −30.1917 | −1.07417 | ||||||||
\(791\) | 1.36753 | 0.0486238 | ||||||||
\(792\) | −44.2553 | −1.57254 | ||||||||
\(793\) | −13.9364 | −0.494898 | ||||||||
\(794\) | −47.5232 | −1.68654 | ||||||||
\(795\) | 9.39825 | 0.333322 | ||||||||
\(796\) | 85.7007 | 3.03758 | ||||||||
\(797\) | −1.19443 | −0.0423089 | −0.0211544 | − | 0.999776i | \(-0.506734\pi\) | ||||
−0.0211544 | + | 0.999776i | \(0.506734\pi\) | |||||||
\(798\) | −0.677986 | −0.0240004 | ||||||||
\(799\) | −21.9381 | −0.776113 | ||||||||
\(800\) | 1.43905 | 0.0508779 | ||||||||
\(801\) | 35.6210 | 1.25861 | ||||||||
\(802\) | 12.9519 | 0.457348 | ||||||||
\(803\) | 17.4143 | 0.614537 | ||||||||
\(804\) | 44.2679 | 1.56121 | ||||||||
\(805\) | −0.354707 | −0.0125018 | ||||||||
\(806\) | −7.58374 | −0.267126 | ||||||||
\(807\) | −12.9379 | −0.455435 | ||||||||
\(808\) | 35.1118 | 1.23523 | ||||||||
\(809\) | 26.1186 | 0.918281 | 0.459141 | − | 0.888364i | \(-0.348157\pi\) | ||||
0.459141 | + | 0.888364i | \(0.348157\pi\) | |||||||
\(810\) | −7.46697 | −0.262363 | ||||||||
\(811\) | 21.4096 | 0.751794 | 0.375897 | − | 0.926661i | \(-0.377335\pi\) | ||||
0.375897 | + | 0.926661i | \(0.377335\pi\) | |||||||
\(812\) | 1.40022 | 0.0491380 | ||||||||
\(813\) | −24.3498 | −0.853984 | ||||||||
\(814\) | −26.7442 | −0.937384 | ||||||||
\(815\) | 4.41601 | 0.154686 | ||||||||
\(816\) | 5.35513 | 0.187467 | ||||||||
\(817\) | 20.0967 | 0.703096 | ||||||||
\(818\) | −4.74660 | −0.165961 | ||||||||
\(819\) | −0.397160 | −0.0138779 | ||||||||
\(820\) | 6.97429 | 0.243553 | ||||||||
\(821\) | −40.4726 | −1.41250 | −0.706252 | − | 0.707960i | \(-0.749616\pi\) | ||||
−0.706252 | + | 0.707960i | \(0.749616\pi\) | |||||||
\(822\) | 25.6982 | 0.896327 | ||||||||
\(823\) | −26.8616 | −0.936335 | −0.468168 | − | 0.883640i | \(-0.655086\pi\) | ||||
−0.468168 | + | 0.883640i | \(0.655086\pi\) | |||||||
\(824\) | 45.6540 | 1.59043 | ||||||||
\(825\) | 3.66427 | 0.127574 | ||||||||
\(826\) | −3.30598 | −0.115030 | ||||||||
\(827\) | −9.44610 | −0.328473 | −0.164237 | − | 0.986421i | \(-0.552516\pi\) | ||||
−0.164237 | + | 0.986421i | \(0.552516\pi\) | |||||||
\(828\) | 29.8576 | 1.03762 | ||||||||
\(829\) | 53.9909 | 1.87518 | 0.937590 | − | 0.347743i | \(-0.113052\pi\) | ||||
0.937590 | + | 0.347743i | \(0.113052\pi\) | |||||||
\(830\) | 5.41307 | 0.187890 | ||||||||
\(831\) | −12.8274 | −0.444976 | ||||||||
\(832\) | −16.0787 | −0.557427 | ||||||||
\(833\) | 14.3167 | 0.496043 | ||||||||
\(834\) | −30.2520 | −1.04754 | ||||||||
\(835\) | −11.7157 | −0.405439 | ||||||||
\(836\) | 53.0247 | 1.83390 | ||||||||
\(837\) | 8.42323 | 0.291149 | ||||||||
\(838\) | 47.1164 | 1.62761 | ||||||||
\(839\) | 0.817512 | 0.0282237 | 0.0141118 | − | 0.999900i | \(-0.495508\pi\) | ||||
0.0141118 | + | 0.999900i | \(0.495508\pi\) | |||||||
\(840\) | 0.393581 | 0.0135798 | ||||||||
\(841\) | −16.8467 | −0.580919 | ||||||||
\(842\) | −71.2347 | −2.45491 | ||||||||
\(843\) | −18.4791 | −0.636454 | ||||||||
\(844\) | −59.0955 | −2.03415 | ||||||||
\(845\) | −10.2350 | −0.352096 | ||||||||
\(846\) | 59.2067 | 2.03557 | ||||||||
\(847\) | 0.816990 | 0.0280721 | ||||||||
\(848\) | −34.4409 | −1.18270 | ||||||||
\(849\) | 13.5822 | 0.466140 | ||||||||
\(850\) | 4.95246 | 0.169868 | ||||||||
\(851\) | 8.65855 | 0.296811 | ||||||||
\(852\) | 1.69307 | 0.0580036 | ||||||||
\(853\) | −3.25549 | −0.111466 | −0.0557330 | − | 0.998446i | \(-0.517750\pi\) | ||||
−0.0557330 | + | 0.998446i | \(0.517750\pi\) | |||||||
\(854\) | 2.11659 | 0.0724282 | ||||||||
\(855\) | 7.26817 | 0.248566 | ||||||||
\(856\) | −6.83785 | −0.233713 | ||||||||
\(857\) | −6.87376 | −0.234803 | −0.117402 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117402 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(858\) | −14.7310 | −0.502907 | ||||||||
\(859\) | 0.0404079 | 0.00137870 | 0.000689349 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000689349 | 1.00000i | \(0.499781\pi\) | ||||||||
\(860\) | −24.3116 | −0.829019 | ||||||||
\(861\) | −0.160018 | −0.00545341 | ||||||||
\(862\) | −72.4298 | −2.46697 | ||||||||
\(863\) | −6.31529 | −0.214975 | −0.107487 | − | 0.994206i | \(-0.534281\pi\) | ||||
−0.107487 | + | 0.994206i | \(0.534281\pi\) | |||||||
\(864\) | 6.42560 | 0.218603 | ||||||||
\(865\) | −10.4578 | −0.355577 | ||||||||
\(866\) | 79.9488 | 2.71677 | ||||||||
\(867\) | 10.8144 | 0.367278 | ||||||||
\(868\) | 0.757683 | 0.0257174 | ||||||||
\(869\) | −54.1770 | −1.83783 | ||||||||
\(870\) | 7.11883 | 0.241351 | ||||||||
\(871\) | −22.6648 | −0.767968 | ||||||||
\(872\) | −59.5073 | −2.01517 | ||||||||
\(873\) | 37.1990 | 1.25900 | ||||||||
\(874\) | −26.0960 | −0.882710 | ||||||||
\(875\) | 0.104455 | 0.00353122 | ||||||||
\(876\) | 13.0364 | 0.440461 | ||||||||
\(877\) | −48.9066 | −1.65146 | −0.825730 | − | 0.564066i | \(-0.809236\pi\) | ||||
−0.825730 | + | 0.564066i | \(0.809236\pi\) | |||||||
\(878\) | −18.1999 | −0.614217 | ||||||||
\(879\) | −11.9018 | −0.401439 | ||||||||
\(880\) | −13.4281 | −0.452661 | ||||||||
\(881\) | −19.0695 | −0.642469 | −0.321235 | − | 0.947000i | \(-0.604098\pi\) | ||||
−0.321235 | + | 0.947000i | \(0.604098\pi\) | |||||||
\(882\) | −38.6380 | −1.30101 | ||||||||
\(883\) | 35.3490 | 1.18959 | 0.594794 | − | 0.803878i | \(-0.297234\pi\) | ||||
0.594794 | + | 0.803878i | \(0.297234\pi\) | |||||||
\(884\) | −13.0974 | −0.440512 | ||||||||
\(885\) | −11.0569 | −0.371673 | ||||||||
\(886\) | −19.3607 | −0.650435 | ||||||||
\(887\) | 34.5067 | 1.15862 | 0.579311 | − | 0.815107i | \(-0.303322\pi\) | ||||
0.579311 | + | 0.815107i | \(0.303322\pi\) | |||||||
\(888\) | −9.60746 | −0.322405 | ||||||||
\(889\) | −2.08706 | −0.0699976 | ||||||||
\(890\) | 37.6628 | 1.26246 | ||||||||
\(891\) | −13.3990 | −0.448883 | ||||||||
\(892\) | −0.437729 | −0.0146562 | ||||||||
\(893\) | −34.0415 | −1.13916 | ||||||||
\(894\) | 23.8849 | 0.798831 | ||||||||
\(895\) | 5.05332 | 0.168914 | ||||||||
\(896\) | 2.14131 | 0.0715360 | ||||||||
\(897\) | 4.76921 | 0.159239 | ||||||||
\(898\) | 5.26733 | 0.175773 | ||||||||
\(899\) | 6.57639 | 0.219335 | ||||||||
\(900\) | −8.79252 | −0.293084 | ||||||||
\(901\) | 22.7933 | 0.759355 | ||||||||
\(902\) | 19.0242 | 0.633437 | ||||||||
\(903\) | 0.557806 | 0.0185626 | ||||||||
\(904\) | −58.4055 | −1.94254 | ||||||||
\(905\) | 12.0260 | 0.399757 | ||||||||
\(906\) | −6.81498 | −0.226413 | ||||||||
\(907\) | 12.5195 | 0.415703 | 0.207851 | − | 0.978160i | \(-0.433353\pi\) | ||||
0.207851 | + | 0.978160i | \(0.433353\pi\) | |||||||
\(908\) | −52.8961 | −1.75542 | ||||||||
\(909\) | 17.9971 | 0.596925 | ||||||||
\(910\) | −0.419925 | −0.0139204 | ||||||||
\(911\) | −14.5086 | −0.480692 | −0.240346 | − | 0.970687i | \(-0.577261\pi\) | ||||
−0.240346 | + | 0.970687i | \(0.577261\pi\) | |||||||
\(912\) | 8.30961 | 0.275159 | ||||||||
\(913\) | 9.71338 | 0.321466 | ||||||||
\(914\) | −78.0681 | −2.58226 | ||||||||
\(915\) | 7.07896 | 0.234023 | ||||||||
\(916\) | 100.275 | 3.31318 | ||||||||
\(917\) | 1.72135 | 0.0568440 | ||||||||
\(918\) | 22.1136 | 0.729858 | ||||||||
\(919\) | 43.6588 | 1.44017 | 0.720085 | − | 0.693885i | \(-0.244103\pi\) | ||||
0.720085 | + | 0.693885i | \(0.244103\pi\) | |||||||
\(920\) | 15.1491 | 0.499451 | ||||||||
\(921\) | 14.6083 | 0.481359 | ||||||||
\(922\) | 56.7057 | 1.86750 | ||||||||
\(923\) | −0.866838 | −0.0285323 | ||||||||
\(924\) | 1.47176 | 0.0484172 | ||||||||
\(925\) | −2.54978 | −0.0838363 | ||||||||
\(926\) | 69.6890 | 2.29012 | ||||||||
\(927\) | 23.4007 | 0.768578 | ||||||||
\(928\) | 5.01675 | 0.164683 | ||||||||
\(929\) | 37.3685 | 1.22602 | 0.613010 | − | 0.790075i | \(-0.289958\pi\) | ||||
0.613010 | + | 0.790075i | \(0.289958\pi\) | |||||||
\(930\) | 3.85213 | 0.126316 | ||||||||
\(931\) | 22.2153 | 0.728077 | ||||||||
\(932\) | 85.2462 | 2.79233 | ||||||||
\(933\) | −3.81913 | −0.125033 | ||||||||
\(934\) | 4.06935 | 0.133153 | ||||||||
\(935\) | 8.88685 | 0.290631 | ||||||||
\(936\) | 16.9622 | 0.554427 | ||||||||
\(937\) | −6.91459 | −0.225890 | −0.112945 | − | 0.993601i | \(-0.536028\pi\) | ||||
−0.112945 | + | 0.993601i | \(0.536028\pi\) | |||||||
\(938\) | 3.44221 | 0.112392 | ||||||||
\(939\) | −25.2649 | −0.824490 | ||||||||
\(940\) | 41.1810 | 1.34318 | ||||||||
\(941\) | −11.8124 | −0.385074 | −0.192537 | − | 0.981290i | \(-0.561672\pi\) | ||||
−0.192537 | + | 0.981290i | \(0.561672\pi\) | |||||||
\(942\) | −6.93266 | −0.225878 | ||||||||
\(943\) | −6.15917 | −0.200570 | ||||||||
\(944\) | 40.5191 | 1.31878 | ||||||||
\(945\) | 0.466409 | 0.0151723 | ||||||||
\(946\) | −66.3164 | −2.15613 | ||||||||
\(947\) | −58.2529 | −1.89297 | −0.946483 | − | 0.322754i | \(-0.895391\pi\) | ||||
−0.946483 | + | 0.322754i | \(0.895391\pi\) | |||||||
\(948\) | −40.5573 | −1.31724 | ||||||||
\(949\) | −6.67456 | −0.216665 | ||||||||
\(950\) | 7.68478 | 0.249327 | ||||||||
\(951\) | −8.99482 | −0.291677 | ||||||||
\(952\) | 0.954540 | 0.0309368 | ||||||||
\(953\) | −4.74730 | −0.153780 | −0.0768900 | − | 0.997040i | \(-0.524499\pi\) | ||||
−0.0768900 | + | 0.997040i | \(0.524499\pi\) | |||||||
\(954\) | −61.5148 | −1.99162 | ||||||||
\(955\) | 10.2222 | 0.330783 | ||||||||
\(956\) | −74.4608 | −2.40824 | ||||||||
\(957\) | 12.7743 | 0.412933 | ||||||||
\(958\) | 75.5373 | 2.44050 | ||||||||
\(959\) | 1.31453 | 0.0424483 | ||||||||
\(960\) | 8.16709 | 0.263592 | ||||||||
\(961\) | −27.4414 | −0.885206 | ||||||||
\(962\) | 10.2505 | 0.330491 | ||||||||
\(963\) | −3.50484 | −0.112942 | ||||||||
\(964\) | −19.1388 | −0.616420 | ||||||||
\(965\) | 3.92688 | 0.126411 | ||||||||
\(966\) | −0.724321 | −0.0233047 | ||||||||
\(967\) | 6.34545 | 0.204056 | 0.102028 | − | 0.994782i | \(-0.467467\pi\) | ||||
0.102028 | + | 0.994782i | \(0.467467\pi\) | |||||||
\(968\) | −34.8926 | −1.12149 | ||||||||
\(969\) | −5.49938 | −0.176666 | ||||||||
\(970\) | 39.3312 | 1.26285 | ||||||||
\(971\) | 49.5490 | 1.59010 | 0.795051 | − | 0.606542i | \(-0.207444\pi\) | ||||
0.795051 | + | 0.606542i | \(0.207444\pi\) | |||||||
\(972\) | −61.5392 | −1.97387 | ||||||||
\(973\) | −1.54747 | −0.0496095 | ||||||||
\(974\) | 97.3011 | 3.11773 | ||||||||
\(975\) | −1.40444 | −0.0449782 | ||||||||
\(976\) | −25.9416 | −0.830370 | ||||||||
\(977\) | −33.9307 | −1.08554 | −0.542770 | − | 0.839881i | \(-0.682625\pi\) | ||||
−0.542770 | + | 0.839881i | \(0.682625\pi\) | |||||||
\(978\) | 9.01761 | 0.288351 | ||||||||
\(979\) | 67.5833 | 2.15997 | ||||||||
\(980\) | −26.8745 | −0.858474 | ||||||||
\(981\) | −30.5013 | −0.973833 | ||||||||
\(982\) | 70.5576 | 2.25158 | ||||||||
\(983\) | −52.2834 | −1.66758 | −0.833791 | − | 0.552080i | \(-0.813834\pi\) | ||||
−0.833791 | + | 0.552080i | \(0.813834\pi\) | |||||||
\(984\) | 6.83417 | 0.217865 | ||||||||
\(985\) | −0.838466 | −0.0267158 | ||||||||
\(986\) | 17.2651 | 0.549833 | ||||||||
\(987\) | −0.944858 | −0.0300752 | ||||||||
\(988\) | −20.3233 | −0.646571 | ||||||||
\(989\) | 21.4702 | 0.682713 | ||||||||
\(990\) | −23.9839 | −0.762259 | ||||||||
\(991\) | −48.3161 | −1.53481 | −0.767406 | − | 0.641162i | \(-0.778453\pi\) | ||||
−0.767406 | + | 0.641162i | \(0.778453\pi\) | |||||||
\(992\) | 2.71465 | 0.0861903 | ||||||||
\(993\) | −12.1583 | −0.385831 | ||||||||
\(994\) | 0.131650 | 0.00417570 | ||||||||
\(995\) | 22.2877 | 0.706567 | ||||||||
\(996\) | 7.27150 | 0.230406 | ||||||||
\(997\) | −39.3971 | −1.24772 | −0.623860 | − | 0.781536i | \(-0.714436\pi\) | ||||
−0.623860 | + | 0.781536i | \(0.714436\pi\) | |||||||
\(998\) | 21.5479 | 0.682087 | ||||||||
\(999\) | −11.3852 | −0.360213 |
(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 | 8035.2.a.e.1.14 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.e.1.14 | ✓ | 153 | 1.1 | even | 1 | trivial |