Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62362 | −1.85518 | −0.927591 | − | 0.373598i | \(-0.878124\pi\) | ||||
−0.927591 | + | 0.373598i | \(0.878124\pi\) | |||||||
\(3\) | −1.27143 | −0.734062 | −0.367031 | − | 0.930209i | \(-0.619626\pi\) | ||||
−0.367031 | + | 0.930209i | \(0.619626\pi\) | |||||||
\(4\) | 4.88340 | 2.44170 | ||||||||
\(5\) | 1.41870 | 0.634461 | 0.317230 | − | 0.948348i | \(-0.397247\pi\) | ||||
0.317230 | + | 0.948348i | \(0.397247\pi\) | |||||||
\(6\) | 3.33576 | 1.36182 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.56495 | −2.67461 | ||||||||
\(9\) | −1.38346 | −0.461154 | ||||||||
\(10\) | −3.72213 | −1.17704 | ||||||||
\(11\) | 1.00335 | 0.302521 | 0.151261 | − | 0.988494i | \(-0.451667\pi\) | ||||
0.151261 | + | 0.988494i | \(0.451667\pi\) | |||||||
\(12\) | −6.20891 | −1.79236 | ||||||||
\(13\) | 2.84063 | 0.787850 | 0.393925 | − | 0.919143i | \(-0.371117\pi\) | ||||
0.393925 | + | 0.919143i | \(0.371117\pi\) | |||||||
\(14\) | −2.62362 | −0.701193 | ||||||||
\(15\) | −1.80378 | −0.465733 | ||||||||
\(16\) | 10.0808 | 2.52019 | ||||||||
\(17\) | −0.358679 | −0.0869925 | −0.0434962 | − | 0.999054i | \(-0.513850\pi\) | ||||
−0.0434962 | + | 0.999054i | \(0.513850\pi\) | |||||||
\(18\) | 3.62968 | 0.855524 | ||||||||
\(19\) | 5.52965 | 1.26859 | 0.634294 | − | 0.773092i | \(-0.281291\pi\) | ||||
0.634294 | + | 0.773092i | \(0.281291\pi\) | |||||||
\(20\) | 6.92806 | 1.54916 | ||||||||
\(21\) | −1.27143 | −0.277449 | ||||||||
\(22\) | −2.63241 | −0.561232 | ||||||||
\(23\) | −1.69823 | −0.354105 | −0.177052 | − | 0.984201i | \(-0.556656\pi\) | ||||
−0.177052 | + | 0.984201i | \(0.556656\pi\) | |||||||
\(24\) | 9.61832 | 1.96333 | ||||||||
\(25\) | −2.98730 | −0.597459 | ||||||||
\(26\) | −7.45275 | −1.46160 | ||||||||
\(27\) | 5.57327 | 1.07258 | ||||||||
\(28\) | 4.88340 | 0.922875 | ||||||||
\(29\) | 5.52479 | 1.02593 | 0.512964 | − | 0.858410i | \(-0.328548\pi\) | ||||
0.512964 | + | 0.858410i | \(0.328548\pi\) | |||||||
\(30\) | 4.73243 | 0.864020 | ||||||||
\(31\) | 5.40586 | 0.970921 | 0.485460 | − | 0.874259i | \(-0.338652\pi\) | ||||
0.485460 | + | 0.874259i | \(0.338652\pi\) | |||||||
\(32\) | −11.3183 | −2.00081 | ||||||||
\(33\) | −1.27569 | −0.222069 | ||||||||
\(34\) | 0.941039 | 0.161387 | ||||||||
\(35\) | 1.41870 | 0.239804 | ||||||||
\(36\) | −6.75599 | −1.12600 | ||||||||
\(37\) | 7.60429 | 1.25014 | 0.625068 | − | 0.780570i | \(-0.285071\pi\) | ||||
0.625068 | + | 0.780570i | \(0.285071\pi\) | |||||||
\(38\) | −14.5077 | −2.35346 | ||||||||
\(39\) | −3.61167 | −0.578330 | ||||||||
\(40\) | −10.7324 | −1.69694 | ||||||||
\(41\) | 7.89719 | 1.23333 | 0.616667 | − | 0.787224i | \(-0.288482\pi\) | ||||
0.616667 | + | 0.787224i | \(0.288482\pi\) | |||||||
\(42\) | 3.33576 | 0.514719 | ||||||||
\(43\) | −1.43388 | −0.218664 | −0.109332 | − | 0.994005i | \(-0.534871\pi\) | ||||
−0.109332 | + | 0.994005i | \(0.534871\pi\) | |||||||
\(44\) | 4.89975 | 0.738665 | ||||||||
\(45\) | −1.96271 | −0.292584 | ||||||||
\(46\) | 4.45551 | 0.656929 | ||||||||
\(47\) | −3.18421 | −0.464465 | −0.232233 | − | 0.972660i | \(-0.574603\pi\) | ||||
−0.232233 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(48\) | −12.8170 | −1.84998 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.83754 | 1.10840 | ||||||||
\(51\) | 0.456036 | 0.0638578 | ||||||||
\(52\) | 13.8719 | 1.92369 | ||||||||
\(53\) | −12.9323 | −1.77639 | −0.888197 | − | 0.459462i | \(-0.848042\pi\) | ||||
−0.888197 | + | 0.459462i | \(0.848042\pi\) | |||||||
\(54\) | −14.6222 | −1.98982 | ||||||||
\(55\) | 1.42345 | 0.191938 | ||||||||
\(56\) | −7.56495 | −1.01091 | ||||||||
\(57\) | −7.03057 | −0.931222 | ||||||||
\(58\) | −14.4950 | −1.90328 | ||||||||
\(59\) | 0.388087 | 0.0505246 | 0.0252623 | − | 0.999681i | \(-0.491958\pi\) | ||||
0.0252623 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(60\) | −8.80856 | −1.13718 | ||||||||
\(61\) | 4.85277 | 0.621334 | 0.310667 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310667 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(62\) | −14.1829 | −1.80123 | ||||||||
\(63\) | −1.38346 | −0.174300 | ||||||||
\(64\) | 9.53330 | 1.19166 | ||||||||
\(65\) | 4.03000 | 0.499860 | ||||||||
\(66\) | 3.34693 | 0.411978 | ||||||||
\(67\) | −8.67990 | −1.06042 | −0.530209 | − | 0.847867i | \(-0.677887\pi\) | ||||
−0.530209 | + | 0.847867i | \(0.677887\pi\) | |||||||
\(68\) | −1.75157 | −0.212409 | ||||||||
\(69\) | 2.15918 | 0.259935 | ||||||||
\(70\) | −3.72213 | −0.444879 | ||||||||
\(71\) | −11.8443 | −1.40566 | −0.702831 | − | 0.711357i | \(-0.748081\pi\) | ||||
−0.702831 | + | 0.711357i | \(0.748081\pi\) | |||||||
\(72\) | 10.4658 | 1.23341 | ||||||||
\(73\) | 13.4684 | 1.57635 | 0.788177 | − | 0.615449i | \(-0.211025\pi\) | ||||
0.788177 | + | 0.615449i | \(0.211025\pi\) | |||||||
\(74\) | −19.9508 | −2.31923 | ||||||||
\(75\) | 3.79815 | 0.438572 | ||||||||
\(76\) | 27.0035 | 3.09751 | ||||||||
\(77\) | 1.00335 | 0.114342 | ||||||||
\(78\) | 9.47567 | 1.07291 | ||||||||
\(79\) | 2.15817 | 0.242813 | 0.121406 | − | 0.992603i | \(-0.461260\pi\) | ||||
0.121406 | + | 0.992603i | \(0.461260\pi\) | |||||||
\(80\) | 14.3016 | 1.59896 | ||||||||
\(81\) | −2.93565 | −0.326184 | ||||||||
\(82\) | −20.7193 | −2.28806 | ||||||||
\(83\) | 8.98617 | 0.986361 | 0.493180 | − | 0.869927i | \(-0.335834\pi\) | ||||
0.493180 | + | 0.869927i | \(0.335834\pi\) | |||||||
\(84\) | −6.20891 | −0.677447 | ||||||||
\(85\) | −0.508857 | −0.0551933 | ||||||||
\(86\) | 3.76195 | 0.405662 | ||||||||
\(87\) | −7.02439 | −0.753094 | ||||||||
\(88\) | −7.59028 | −0.809127 | ||||||||
\(89\) | 11.1380 | 1.18063 | 0.590314 | − | 0.807173i | \(-0.299004\pi\) | ||||
0.590314 | + | 0.807173i | \(0.299004\pi\) | |||||||
\(90\) | 5.14942 | 0.542796 | ||||||||
\(91\) | 2.84063 | 0.297779 | ||||||||
\(92\) | −8.29312 | −0.864617 | ||||||||
\(93\) | −6.87318 | −0.712716 | ||||||||
\(94\) | 8.35418 | 0.861668 | ||||||||
\(95\) | 7.84490 | 0.804869 | ||||||||
\(96\) | 14.3904 | 1.46871 | ||||||||
\(97\) | −10.7738 | −1.09391 | −0.546957 | − | 0.837161i | \(-0.684214\pi\) | ||||
−0.546957 | + | 0.837161i | \(0.684214\pi\) | |||||||
\(98\) | −2.62362 | −0.265026 | ||||||||
\(99\) | −1.38809 | −0.139509 | ||||||||
\(100\) | −14.5882 | −1.45882 | ||||||||
\(101\) | 4.40333 | 0.438147 | 0.219074 | − | 0.975708i | \(-0.429697\pi\) | ||||
0.219074 | + | 0.975708i | \(0.429697\pi\) | |||||||
\(102\) | −1.19647 | −0.118468 | ||||||||
\(103\) | 8.24817 | 0.812717 | 0.406358 | − | 0.913714i | \(-0.366798\pi\) | ||||
0.406358 | + | 0.913714i | \(0.366798\pi\) | |||||||
\(104\) | −21.4892 | −2.10719 | ||||||||
\(105\) | −1.80378 | −0.176031 | ||||||||
\(106\) | 33.9296 | 3.29554 | ||||||||
\(107\) | 20.5661 | 1.98820 | 0.994098 | − | 0.108489i | \(-0.0346013\pi\) | ||||
0.994098 | + | 0.108489i | \(0.0346013\pi\) | |||||||
\(108\) | 27.2165 | 2.61891 | ||||||||
\(109\) | 5.76817 | 0.552490 | 0.276245 | − | 0.961087i | \(-0.410910\pi\) | ||||
0.276245 | + | 0.961087i | \(0.410910\pi\) | |||||||
\(110\) | −3.73459 | −0.356079 | ||||||||
\(111\) | −9.66833 | −0.917677 | ||||||||
\(112\) | 10.0808 | 0.952544 | ||||||||
\(113\) | −10.4969 | −0.987468 | −0.493734 | − | 0.869613i | \(-0.664368\pi\) | ||||
−0.493734 | + | 0.869613i | \(0.664368\pi\) | |||||||
\(114\) | 18.4456 | 1.72759 | ||||||||
\(115\) | −2.40927 | −0.224666 | ||||||||
\(116\) | 26.9797 | 2.50501 | ||||||||
\(117\) | −3.92991 | −0.363320 | ||||||||
\(118\) | −1.01819 | −0.0937322 | ||||||||
\(119\) | −0.358679 | −0.0328801 | ||||||||
\(120\) | 13.6455 | 1.24566 | ||||||||
\(121\) | −9.99329 | −0.908481 | ||||||||
\(122\) | −12.7318 | −1.15269 | ||||||||
\(123\) | −10.0407 | −0.905343 | ||||||||
\(124\) | 26.3990 | 2.37070 | ||||||||
\(125\) | −11.3316 | −1.01353 | ||||||||
\(126\) | 3.62968 | 0.323358 | ||||||||
\(127\) | −7.74654 | −0.687394 | −0.343697 | − | 0.939081i | \(-0.611679\pi\) | ||||
−0.343697 | + | 0.939081i | \(0.611679\pi\) | |||||||
\(128\) | −2.37526 | −0.209945 | ||||||||
\(129\) | 1.82308 | 0.160513 | ||||||||
\(130\) | −10.5732 | −0.927331 | ||||||||
\(131\) | −10.6972 | −0.934616 | −0.467308 | − | 0.884095i | \(-0.654776\pi\) | ||||
−0.467308 | + | 0.884095i | \(0.654776\pi\) | |||||||
\(132\) | −6.22970 | −0.542226 | ||||||||
\(133\) | 5.52965 | 0.479481 | ||||||||
\(134\) | 22.7728 | 1.96727 | ||||||||
\(135\) | 7.90679 | 0.680508 | ||||||||
\(136\) | 2.71339 | 0.232671 | ||||||||
\(137\) | −15.1157 | −1.29142 | −0.645711 | − | 0.763582i | \(-0.723439\pi\) | ||||
−0.645711 | + | 0.763582i | \(0.723439\pi\) | |||||||
\(138\) | −5.66487 | −0.482226 | ||||||||
\(139\) | 10.2572 | 0.870008 | 0.435004 | − | 0.900429i | \(-0.356747\pi\) | ||||
0.435004 | + | 0.900429i | \(0.356747\pi\) | |||||||
\(140\) | 6.92806 | 0.585528 | ||||||||
\(141\) | 4.04851 | 0.340946 | ||||||||
\(142\) | 31.0750 | 2.60776 | ||||||||
\(143\) | 2.85015 | 0.238341 | ||||||||
\(144\) | −13.9464 | −1.16220 | ||||||||
\(145\) | 7.83800 | 0.650911 | ||||||||
\(146\) | −35.3359 | −2.92442 | ||||||||
\(147\) | −1.27143 | −0.104866 | ||||||||
\(148\) | 37.1347 | 3.05246 | ||||||||
\(149\) | −7.02431 | −0.575454 | −0.287727 | − | 0.957713i | \(-0.592900\pi\) | ||||
−0.287727 | + | 0.957713i | \(0.592900\pi\) | |||||||
\(150\) | −9.96490 | −0.813631 | ||||||||
\(151\) | 14.6847 | 1.19502 | 0.597512 | − | 0.801860i | \(-0.296156\pi\) | ||||
0.597512 | + | 0.801860i | \(0.296156\pi\) | |||||||
\(152\) | −41.8315 | −3.39298 | ||||||||
\(153\) | 0.496219 | 0.0401169 | ||||||||
\(154\) | −2.63241 | −0.212126 | ||||||||
\(155\) | 7.66928 | 0.616011 | ||||||||
\(156\) | −17.6372 | −1.41211 | ||||||||
\(157\) | 16.7482 | 1.33665 | 0.668324 | − | 0.743870i | \(-0.267012\pi\) | ||||
0.668324 | + | 0.743870i | \(0.267012\pi\) | |||||||
\(158\) | −5.66222 | −0.450462 | ||||||||
\(159\) | 16.4426 | 1.30398 | ||||||||
\(160\) | −16.0572 | −1.26943 | ||||||||
\(161\) | −1.69823 | −0.133839 | ||||||||
\(162\) | 7.70205 | 0.605130 | ||||||||
\(163\) | 21.2624 | 1.66540 | 0.832698 | − | 0.553727i | \(-0.186795\pi\) | ||||
0.832698 | + | 0.553727i | \(0.186795\pi\) | |||||||
\(164\) | 38.5651 | 3.01143 | ||||||||
\(165\) | −1.80982 | −0.140894 | ||||||||
\(166\) | −23.5763 | −1.82988 | ||||||||
\(167\) | 14.3356 | 1.10932 | 0.554661 | − | 0.832077i | \(-0.312848\pi\) | ||||
0.554661 | + | 0.832077i | \(0.312848\pi\) | |||||||
\(168\) | 9.61832 | 0.742069 | ||||||||
\(169\) | −4.93080 | −0.379292 | ||||||||
\(170\) | 1.33505 | 0.102394 | ||||||||
\(171\) | −7.65005 | −0.585014 | ||||||||
\(172\) | −7.00219 | −0.533912 | ||||||||
\(173\) | 13.5304 | 1.02870 | 0.514350 | − | 0.857580i | \(-0.328033\pi\) | ||||
0.514350 | + | 0.857580i | \(0.328033\pi\) | |||||||
\(174\) | 18.4294 | 1.39713 | ||||||||
\(175\) | −2.98730 | −0.225818 | ||||||||
\(176\) | 10.1145 | 0.762412 | ||||||||
\(177\) | −0.493426 | −0.0370881 | ||||||||
\(178\) | −29.2220 | −2.19028 | ||||||||
\(179\) | −12.8676 | −0.961771 | −0.480886 | − | 0.876783i | \(-0.659685\pi\) | ||||
−0.480886 | + | 0.876783i | \(0.659685\pi\) | |||||||
\(180\) | −9.58471 | −0.714402 | ||||||||
\(181\) | −12.1559 | −0.903540 | −0.451770 | − | 0.892134i | \(-0.649207\pi\) | ||||
−0.451770 | + | 0.892134i | \(0.649207\pi\) | |||||||
\(182\) | −7.45275 | −0.552435 | ||||||||
\(183\) | −6.16997 | −0.456097 | ||||||||
\(184\) | 12.8470 | 0.947093 | ||||||||
\(185\) | 10.7882 | 0.793163 | ||||||||
\(186\) | 18.0326 | 1.32222 | ||||||||
\(187\) | −0.359880 | −0.0263171 | ||||||||
\(188\) | −15.5498 | −1.13408 | ||||||||
\(189\) | 5.57327 | 0.405396 | ||||||||
\(190\) | −20.5821 | −1.49318 | ||||||||
\(191\) | 4.58823 | 0.331993 | 0.165996 | − | 0.986126i | \(-0.446916\pi\) | ||||
0.165996 | + | 0.986126i | \(0.446916\pi\) | |||||||
\(192\) | −12.1209 | −0.874754 | ||||||||
\(193\) | −12.2706 | −0.883254 | −0.441627 | − | 0.897199i | \(-0.645599\pi\) | ||||
−0.441627 | + | 0.897199i | \(0.645599\pi\) | |||||||
\(194\) | 28.2664 | 2.02941 | ||||||||
\(195\) | −5.12387 | −0.366928 | ||||||||
\(196\) | 4.88340 | 0.348814 | ||||||||
\(197\) | 1.99005 | 0.141785 | 0.0708926 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708926 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(198\) | 3.64184 | 0.258814 | ||||||||
\(199\) | −7.22899 | −0.512449 | −0.256225 | − | 0.966617i | \(-0.582479\pi\) | ||||
−0.256225 | + | 0.966617i | \(0.582479\pi\) | |||||||
\(200\) | 22.5988 | 1.59797 | ||||||||
\(201\) | 11.0359 | 0.778412 | ||||||||
\(202\) | −11.5527 | −0.812843 | ||||||||
\(203\) | 5.52479 | 0.387764 | ||||||||
\(204\) | 2.22701 | 0.155922 | ||||||||
\(205\) | 11.2037 | 0.782502 | ||||||||
\(206\) | −21.6401 | −1.50774 | ||||||||
\(207\) | 2.34943 | 0.163297 | ||||||||
\(208\) | 28.6358 | 1.98554 | ||||||||
\(209\) | 5.54817 | 0.383775 | ||||||||
\(210\) | 4.73243 | 0.326569 | ||||||||
\(211\) | 12.7426 | 0.877234 | 0.438617 | − | 0.898674i | \(-0.355469\pi\) | ||||
0.438617 | + | 0.898674i | \(0.355469\pi\) | |||||||
\(212\) | −63.1538 | −4.33742 | ||||||||
\(213\) | 15.0592 | 1.03184 | ||||||||
\(214\) | −53.9576 | −3.68846 | ||||||||
\(215\) | −2.03424 | −0.138734 | ||||||||
\(216\) | −42.1615 | −2.86873 | ||||||||
\(217\) | 5.40586 | 0.366974 | ||||||||
\(218\) | −15.1335 | −1.02497 | ||||||||
\(219\) | −17.1241 | −1.15714 | ||||||||
\(220\) | 6.95127 | 0.468654 | ||||||||
\(221\) | −1.01888 | −0.0685370 | ||||||||
\(222\) | 25.3661 | 1.70246 | ||||||||
\(223\) | −25.5811 | −1.71303 | −0.856517 | − | 0.516119i | \(-0.827376\pi\) | ||||
−0.856517 | + | 0.516119i | \(0.827376\pi\) | |||||||
\(224\) | −11.3183 | −0.756233 | ||||||||
\(225\) | 4.13281 | 0.275521 | ||||||||
\(226\) | 27.5400 | 1.83193 | ||||||||
\(227\) | −0.774330 | −0.0513941 | −0.0256970 | − | 0.999670i | \(-0.508181\pi\) | ||||
−0.0256970 | + | 0.999670i | \(0.508181\pi\) | |||||||
\(228\) | −34.3331 | −2.27376 | ||||||||
\(229\) | 20.2797 | 1.34012 | 0.670061 | − | 0.742306i | \(-0.266268\pi\) | ||||
0.670061 | + | 0.742306i | \(0.266268\pi\) | |||||||
\(230\) | 6.32102 | 0.416796 | ||||||||
\(231\) | −1.27569 | −0.0839342 | ||||||||
\(232\) | −41.7947 | −2.74396 | ||||||||
\(233\) | −3.89638 | −0.255260 | −0.127630 | − | 0.991822i | \(-0.540737\pi\) | ||||
−0.127630 | + | 0.991822i | \(0.540737\pi\) | |||||||
\(234\) | 10.3106 | 0.674024 | ||||||||
\(235\) | −4.51744 | −0.294685 | ||||||||
\(236\) | 1.89518 | 0.123366 | ||||||||
\(237\) | −2.74396 | −0.178240 | ||||||||
\(238\) | 0.941039 | 0.0609985 | ||||||||
\(239\) | 11.2504 | 0.727727 | 0.363864 | − | 0.931452i | \(-0.381457\pi\) | ||||
0.363864 | + | 0.931452i | \(0.381457\pi\) | |||||||
\(240\) | −18.1835 | −1.17374 | ||||||||
\(241\) | 13.1433 | 0.846637 | 0.423318 | − | 0.905981i | \(-0.360865\pi\) | ||||
0.423318 | + | 0.905981i | \(0.360865\pi\) | |||||||
\(242\) | 26.2186 | 1.68540 | ||||||||
\(243\) | −12.9873 | −0.833138 | ||||||||
\(244\) | 23.6980 | 1.51711 | ||||||||
\(245\) | 1.41870 | 0.0906373 | ||||||||
\(246\) | 26.3431 | 1.67958 | ||||||||
\(247\) | 15.7077 | 0.999457 | ||||||||
\(248\) | −40.8950 | −2.59684 | ||||||||
\(249\) | −11.4253 | −0.724049 | ||||||||
\(250\) | 29.7297 | 1.88027 | ||||||||
\(251\) | 20.4839 | 1.29293 | 0.646465 | − | 0.762944i | \(-0.276247\pi\) | ||||
0.646465 | + | 0.762944i | \(0.276247\pi\) | |||||||
\(252\) | −6.75599 | −0.425587 | ||||||||
\(253\) | −1.70391 | −0.107124 | ||||||||
\(254\) | 20.3240 | 1.27524 | ||||||||
\(255\) | 0.646977 | 0.0405153 | ||||||||
\(256\) | −12.8348 | −0.802176 | ||||||||
\(257\) | −29.4392 | −1.83637 | −0.918185 | − | 0.396152i | \(-0.870345\pi\) | ||||
−0.918185 | + | 0.396152i | \(0.870345\pi\) | |||||||
\(258\) | −4.78306 | −0.297781 | ||||||||
\(259\) | 7.60429 | 0.472507 | ||||||||
\(260\) | 19.6801 | 1.22051 | ||||||||
\(261\) | −7.64333 | −0.473110 | ||||||||
\(262\) | 28.0653 | 1.73388 | ||||||||
\(263\) | −30.4121 | −1.87529 | −0.937644 | − | 0.347597i | \(-0.886998\pi\) | ||||
−0.937644 | + | 0.347597i | \(0.886998\pi\) | |||||||
\(264\) | 9.65053 | 0.593949 | ||||||||
\(265\) | −18.3471 | −1.12705 | ||||||||
\(266\) | −14.5077 | −0.889525 | ||||||||
\(267\) | −14.1612 | −0.866654 | ||||||||
\(268\) | −42.3874 | −2.58922 | ||||||||
\(269\) | 1.92312 | 0.117254 | 0.0586272 | − | 0.998280i | \(-0.481328\pi\) | ||||
0.0586272 | + | 0.998280i | \(0.481328\pi\) | |||||||
\(270\) | −20.7444 | −1.26247 | ||||||||
\(271\) | −8.56791 | −0.520463 | −0.260232 | − | 0.965546i | \(-0.583799\pi\) | ||||
−0.260232 | + | 0.965546i | \(0.583799\pi\) | |||||||
\(272\) | −3.61576 | −0.219238 | ||||||||
\(273\) | −3.61167 | −0.218588 | ||||||||
\(274\) | 39.6579 | 2.39582 | ||||||||
\(275\) | −2.99730 | −0.180744 | ||||||||
\(276\) | 10.5441 | 0.634682 | ||||||||
\(277\) | −12.0706 | −0.725249 | −0.362625 | − | 0.931935i | \(-0.618119\pi\) | ||||
−0.362625 | + | 0.931935i | \(0.618119\pi\) | |||||||
\(278\) | −26.9111 | −1.61402 | ||||||||
\(279\) | −7.47880 | −0.447744 | ||||||||
\(280\) | −10.7324 | −0.641382 | ||||||||
\(281\) | −24.4139 | −1.45641 | −0.728206 | − | 0.685359i | \(-0.759645\pi\) | ||||
−0.728206 | + | 0.685359i | \(0.759645\pi\) | |||||||
\(282\) | −10.6218 | −0.632517 | ||||||||
\(283\) | 1.38787 | 0.0825001 | 0.0412501 | − | 0.999149i | \(-0.486866\pi\) | ||||
0.0412501 | + | 0.999149i | \(0.486866\pi\) | |||||||
\(284\) | −57.8405 | −3.43220 | ||||||||
\(285\) | −9.97425 | −0.590824 | ||||||||
\(286\) | −7.47771 | −0.442166 | ||||||||
\(287\) | 7.89719 | 0.466157 | ||||||||
\(288\) | 15.6584 | 0.922679 | ||||||||
\(289\) | −16.8713 | −0.992432 | ||||||||
\(290\) | −20.5640 | −1.20756 | ||||||||
\(291\) | 13.6982 | 0.803000 | ||||||||
\(292\) | 65.7714 | 3.84898 | ||||||||
\(293\) | −14.5443 | −0.849688 | −0.424844 | − | 0.905267i | \(-0.639671\pi\) | ||||
−0.424844 | + | 0.905267i | \(0.639671\pi\) | |||||||
\(294\) | 3.33576 | 0.194545 | ||||||||
\(295\) | 0.550577 | 0.0320559 | ||||||||
\(296\) | −57.5260 | −3.34363 | ||||||||
\(297\) | 5.59194 | 0.324477 | ||||||||
\(298\) | 18.4291 | 1.06757 | ||||||||
\(299\) | −4.82404 | −0.278982 | ||||||||
\(300\) | 18.5479 | 1.07086 | ||||||||
\(301\) | −1.43388 | −0.0826473 | ||||||||
\(302\) | −38.5271 | −2.21699 | ||||||||
\(303\) | −5.59853 | −0.321627 | ||||||||
\(304\) | 55.7431 | 3.19709 | ||||||||
\(305\) | 6.88461 | 0.394212 | ||||||||
\(306\) | −1.30189 | −0.0744241 | ||||||||
\(307\) | −9.31668 | −0.531731 | −0.265866 | − | 0.964010i | \(-0.585658\pi\) | ||||
−0.265866 | + | 0.964010i | \(0.585658\pi\) | |||||||
\(308\) | 4.89975 | 0.279189 | ||||||||
\(309\) | −10.4870 | −0.596584 | ||||||||
\(310\) | −20.1213 | −1.14281 | ||||||||
\(311\) | −19.4038 | −1.10029 | −0.550145 | − | 0.835069i | \(-0.685428\pi\) | ||||
−0.550145 | + | 0.835069i | \(0.685428\pi\) | |||||||
\(312\) | 27.3221 | 1.54681 | ||||||||
\(313\) | 7.37349 | 0.416774 | 0.208387 | − | 0.978046i | \(-0.433179\pi\) | ||||
0.208387 | + | 0.978046i | \(0.433179\pi\) | |||||||
\(314\) | −43.9409 | −2.47973 | ||||||||
\(315\) | −1.96271 | −0.110586 | ||||||||
\(316\) | 10.5392 | 0.592876 | ||||||||
\(317\) | 13.4956 | 0.757990 | 0.378995 | − | 0.925399i | \(-0.376270\pi\) | ||||
0.378995 | + | 0.925399i | \(0.376270\pi\) | |||||||
\(318\) | −43.1392 | −2.41913 | ||||||||
\(319\) | 5.54329 | 0.310365 | ||||||||
\(320\) | 13.5249 | 0.756063 | ||||||||
\(321\) | −26.1483 | −1.45946 | ||||||||
\(322\) | 4.45551 | 0.248296 | ||||||||
\(323\) | −1.98337 | −0.110358 | ||||||||
\(324\) | −14.3360 | −0.796442 | ||||||||
\(325\) | −8.48582 | −0.470708 | ||||||||
\(326\) | −55.7844 | −3.08961 | ||||||||
\(327\) | −7.33383 | −0.405562 | ||||||||
\(328\) | −59.7419 | −3.29869 | ||||||||
\(329\) | −3.18421 | −0.175551 | ||||||||
\(330\) | 4.74828 | 0.261384 | ||||||||
\(331\) | 28.7446 | 1.57994 | 0.789972 | − | 0.613143i | \(-0.210095\pi\) | ||||
0.789972 | + | 0.613143i | \(0.210095\pi\) | |||||||
\(332\) | 43.8831 | 2.40840 | ||||||||
\(333\) | −10.5202 | −0.576505 | ||||||||
\(334\) | −37.6112 | −2.05799 | ||||||||
\(335\) | −12.3142 | −0.672794 | ||||||||
\(336\) | −12.8170 | −0.699226 | ||||||||
\(337\) | −10.8952 | −0.593502 | −0.296751 | − | 0.954955i | \(-0.595903\pi\) | ||||
−0.296751 | + | 0.954955i | \(0.595903\pi\) | |||||||
\(338\) | 12.9366 | 0.703656 | ||||||||
\(339\) | 13.3461 | 0.724863 | ||||||||
\(340\) | −2.48495 | −0.134765 | ||||||||
\(341\) | 5.42396 | 0.293724 | ||||||||
\(342\) | 20.0709 | 1.08531 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 10.8472 | 0.584842 | ||||||||
\(345\) | 3.06322 | 0.164918 | ||||||||
\(346\) | −35.4988 | −1.90843 | ||||||||
\(347\) | −36.3110 | −1.94927 | −0.974637 | − | 0.223790i | \(-0.928157\pi\) | ||||
−0.974637 | + | 0.223790i | \(0.928157\pi\) | |||||||
\(348\) | −34.3029 | −1.83883 | ||||||||
\(349\) | 4.74346 | 0.253912 | 0.126956 | − | 0.991908i | \(-0.459479\pi\) | ||||
0.126956 | + | 0.991908i | \(0.459479\pi\) | |||||||
\(350\) | 7.83754 | 0.418934 | ||||||||
\(351\) | 15.8316 | 0.845030 | ||||||||
\(352\) | −11.3562 | −0.605286 | ||||||||
\(353\) | 24.8401 | 1.32210 | 0.661052 | − | 0.750340i | \(-0.270110\pi\) | ||||
0.661052 | + | 0.750340i | \(0.270110\pi\) | |||||||
\(354\) | 1.29456 | 0.0688052 | ||||||||
\(355\) | −16.8035 | −0.891837 | ||||||||
\(356\) | 54.3914 | 2.88274 | ||||||||
\(357\) | 0.456036 | 0.0241360 | ||||||||
\(358\) | 33.7598 | 1.78426 | ||||||||
\(359\) | −0.364763 | −0.0192514 | −0.00962572 | − | 0.999954i | \(-0.503064\pi\) | ||||
−0.00962572 | + | 0.999954i | \(0.503064\pi\) | |||||||
\(360\) | 14.8478 | 0.782549 | ||||||||
\(361\) | 11.5770 | 0.609316 | ||||||||
\(362\) | 31.8925 | 1.67623 | ||||||||
\(363\) | 12.7058 | 0.666881 | ||||||||
\(364\) | 13.8719 | 0.727087 | ||||||||
\(365\) | 19.1075 | 1.00013 | ||||||||
\(366\) | 16.1877 | 0.846143 | ||||||||
\(367\) | −16.7597 | −0.874848 | −0.437424 | − | 0.899255i | \(-0.644109\pi\) | ||||
−0.437424 | + | 0.899255i | \(0.644109\pi\) | |||||||
\(368\) | −17.1195 | −0.892413 | ||||||||
\(369\) | −10.9255 | −0.568757 | ||||||||
\(370\) | −28.3041 | −1.47146 | ||||||||
\(371\) | −12.9323 | −0.671414 | ||||||||
\(372\) | −33.5645 | −1.74024 | ||||||||
\(373\) | 4.97701 | 0.257700 | 0.128850 | − | 0.991664i | \(-0.458871\pi\) | ||||
0.128850 | + | 0.991664i | \(0.458871\pi\) | |||||||
\(374\) | 0.944190 | 0.0488229 | ||||||||
\(375\) | 14.4073 | 0.743990 | ||||||||
\(376\) | 24.0884 | 1.24227 | ||||||||
\(377\) | 15.6939 | 0.808277 | ||||||||
\(378\) | −14.6222 | −0.752083 | ||||||||
\(379\) | −4.43273 | −0.227694 | −0.113847 | − | 0.993498i | \(-0.536317\pi\) | ||||
−0.113847 | + | 0.993498i | \(0.536317\pi\) | |||||||
\(380\) | 38.3097 | 1.96525 | ||||||||
\(381\) | 9.84920 | 0.504590 | ||||||||
\(382\) | −12.0378 | −0.615907 | ||||||||
\(383\) | 0.741365 | 0.0378820 | 0.0189410 | − | 0.999821i | \(-0.493971\pi\) | ||||
0.0189410 | + | 0.999821i | \(0.493971\pi\) | |||||||
\(384\) | 3.01998 | 0.154113 | ||||||||
\(385\) | 1.42345 | 0.0725457 | ||||||||
\(386\) | 32.1933 | 1.63860 | ||||||||
\(387\) | 1.98371 | 0.100838 | ||||||||
\(388\) | −52.6128 | −2.67101 | ||||||||
\(389\) | 19.8357 | 1.00571 | 0.502854 | − | 0.864371i | \(-0.332283\pi\) | ||||
0.502854 | + | 0.864371i | \(0.332283\pi\) | |||||||
\(390\) | 13.4431 | 0.680718 | ||||||||
\(391\) | 0.609119 | 0.0308045 | ||||||||
\(392\) | −7.56495 | −0.382088 | ||||||||
\(393\) | 13.6007 | 0.686066 | ||||||||
\(394\) | −5.22114 | −0.263037 | ||||||||
\(395\) | 3.06179 | 0.154055 | ||||||||
\(396\) | −6.77862 | −0.340638 | ||||||||
\(397\) | −0.940959 | −0.0472254 | −0.0236127 | − | 0.999721i | \(-0.507517\pi\) | ||||
−0.0236127 | + | 0.999721i | \(0.507517\pi\) | |||||||
\(398\) | 18.9661 | 0.950686 | ||||||||
\(399\) | −7.03057 | −0.351969 | ||||||||
\(400\) | −30.1143 | −1.50571 | ||||||||
\(401\) | 27.1068 | 1.35365 | 0.676825 | − | 0.736144i | \(-0.263355\pi\) | ||||
0.676825 | + | 0.736144i | \(0.263355\pi\) | |||||||
\(402\) | −28.9540 | −1.44410 | ||||||||
\(403\) | 15.3561 | 0.764940 | ||||||||
\(404\) | 21.5032 | 1.06982 | ||||||||
\(405\) | −4.16480 | −0.206951 | ||||||||
\(406\) | −14.4950 | −0.719373 | ||||||||
\(407\) | 7.62975 | 0.378193 | ||||||||
\(408\) | −3.44989 | −0.170795 | ||||||||
\(409\) | 6.45681 | 0.319268 | 0.159634 | − | 0.987176i | \(-0.448969\pi\) | ||||
0.159634 | + | 0.987176i | \(0.448969\pi\) | |||||||
\(410\) | −29.3944 | −1.45168 | ||||||||
\(411\) | 19.2186 | 0.947984 | ||||||||
\(412\) | 40.2791 | 1.98441 | ||||||||
\(413\) | 0.388087 | 0.0190965 | ||||||||
\(414\) | −6.16402 | −0.302945 | ||||||||
\(415\) | 12.7487 | 0.625807 | ||||||||
\(416\) | −32.1510 | −1.57633 | ||||||||
\(417\) | −13.0414 | −0.638639 | ||||||||
\(418\) | −14.5563 | −0.711972 | ||||||||
\(419\) | 0.669887 | 0.0327261 | 0.0163631 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163631 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(420\) | −8.80856 | −0.429814 | ||||||||
\(421\) | 7.71126 | 0.375824 | 0.187912 | − | 0.982186i | \(-0.439828\pi\) | ||||
0.187912 | + | 0.982186i | \(0.439828\pi\) | |||||||
\(422\) | −33.4317 | −1.62743 | ||||||||
\(423\) | 4.40524 | 0.214190 | ||||||||
\(424\) | 97.8326 | 4.75117 | ||||||||
\(425\) | 1.07148 | 0.0519745 | ||||||||
\(426\) | −39.5098 | −1.91426 | ||||||||
\(427\) | 4.85277 | 0.234842 | ||||||||
\(428\) | 100.432 | 4.85457 | ||||||||
\(429\) | −3.62377 | −0.174957 | ||||||||
\(430\) | 5.33707 | 0.257376 | ||||||||
\(431\) | −6.20495 | −0.298882 | −0.149441 | − | 0.988771i | \(-0.547747\pi\) | ||||
−0.149441 | + | 0.988771i | \(0.547747\pi\) | |||||||
\(432\) | 56.1829 | 2.70310 | ||||||||
\(433\) | 27.0266 | 1.29882 | 0.649409 | − | 0.760440i | \(-0.275017\pi\) | ||||
0.649409 | + | 0.760440i | \(0.275017\pi\) | |||||||
\(434\) | −14.1829 | −0.680803 | ||||||||
\(435\) | −9.96549 | −0.477809 | ||||||||
\(436\) | 28.1683 | 1.34901 | ||||||||
\(437\) | −9.39060 | −0.449213 | ||||||||
\(438\) | 44.9272 | 2.14671 | ||||||||
\(439\) | 7.68565 | 0.366816 | 0.183408 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183408 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(440\) | −10.7683 | −0.513359 | ||||||||
\(441\) | −1.38346 | −0.0658791 | ||||||||
\(442\) | 2.67315 | 0.127149 | ||||||||
\(443\) | −3.68603 | −0.175128 | −0.0875642 | − | 0.996159i | \(-0.527908\pi\) | ||||
−0.0875642 | + | 0.996159i | \(0.527908\pi\) | |||||||
\(444\) | −47.2143 | −2.24069 | ||||||||
\(445\) | 15.8015 | 0.749063 | ||||||||
\(446\) | 67.1150 | 3.17799 | ||||||||
\(447\) | 8.93093 | 0.422418 | ||||||||
\(448\) | 9.53330 | 0.450406 | ||||||||
\(449\) | 8.92995 | 0.421431 | 0.210715 | − | 0.977547i | \(-0.432421\pi\) | ||||
0.210715 | + | 0.977547i | \(0.432421\pi\) | |||||||
\(450\) | −10.8429 | −0.511141 | ||||||||
\(451\) | 7.92364 | 0.373110 | ||||||||
\(452\) | −51.2607 | −2.41110 | ||||||||
\(453\) | −18.6706 | −0.877221 | ||||||||
\(454\) | 2.03155 | 0.0953453 | ||||||||
\(455\) | 4.03000 | 0.188929 | ||||||||
\(456\) | 53.1859 | 2.49066 | ||||||||
\(457\) | 16.5931 | 0.776190 | 0.388095 | − | 0.921619i | \(-0.373133\pi\) | ||||
0.388095 | + | 0.921619i | \(0.373133\pi\) | |||||||
\(458\) | −53.2064 | −2.48617 | ||||||||
\(459\) | −1.99902 | −0.0933061 | ||||||||
\(460\) | −11.7654 | −0.548566 | ||||||||
\(461\) | 31.7615 | 1.47928 | 0.739640 | − | 0.673003i | \(-0.234996\pi\) | ||||
0.739640 | + | 0.673003i | \(0.234996\pi\) | |||||||
\(462\) | 3.34693 | 0.155713 | ||||||||
\(463\) | −9.40780 | −0.437218 | −0.218609 | − | 0.975813i | \(-0.570152\pi\) | ||||
−0.218609 | + | 0.975813i | \(0.570152\pi\) | |||||||
\(464\) | 55.6942 | 2.58554 | ||||||||
\(465\) | −9.75096 | −0.452190 | ||||||||
\(466\) | 10.2226 | 0.473554 | ||||||||
\(467\) | −34.8129 | −1.61095 | −0.805475 | − | 0.592629i | \(-0.798090\pi\) | ||||
−0.805475 | + | 0.592629i | \(0.798090\pi\) | |||||||
\(468\) | −19.1913 | −0.887118 | ||||||||
\(469\) | −8.67990 | −0.400801 | ||||||||
\(470\) | 11.8521 | 0.546694 | ||||||||
\(471\) | −21.2941 | −0.981182 | ||||||||
\(472\) | −2.93585 | −0.135134 | ||||||||
\(473\) | −1.43868 | −0.0661505 | ||||||||
\(474\) | 7.19913 | 0.330667 | ||||||||
\(475\) | −16.5187 | −0.757930 | ||||||||
\(476\) | −1.75157 | −0.0802832 | ||||||||
\(477\) | 17.8914 | 0.819191 | ||||||||
\(478\) | −29.5168 | −1.35007 | ||||||||
\(479\) | 21.8378 | 0.997796 | 0.498898 | − | 0.866661i | \(-0.333738\pi\) | ||||
0.498898 | + | 0.866661i | \(0.333738\pi\) | |||||||
\(480\) | 20.4156 | 0.931841 | ||||||||
\(481\) | 21.6010 | 0.984920 | ||||||||
\(482\) | −34.4832 | −1.57066 | ||||||||
\(483\) | 2.15918 | 0.0982461 | ||||||||
\(484\) | −48.8012 | −2.21824 | ||||||||
\(485\) | −15.2848 | −0.694046 | ||||||||
\(486\) | 34.0739 | 1.54562 | ||||||||
\(487\) | 37.6515 | 1.70615 | 0.853077 | − | 0.521785i | \(-0.174734\pi\) | ||||
0.853077 | + | 0.521785i | \(0.174734\pi\) | |||||||
\(488\) | −36.7110 | −1.66183 | ||||||||
\(489\) | −27.0336 | −1.22250 | ||||||||
\(490\) | −3.72213 | −0.168149 | ||||||||
\(491\) | −10.1391 | −0.457571 | −0.228785 | − | 0.973477i | \(-0.573475\pi\) | ||||
−0.228785 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(492\) | −49.0329 | −2.21058 | ||||||||
\(493\) | −1.98163 | −0.0892480 | ||||||||
\(494\) | −41.2111 | −1.85417 | ||||||||
\(495\) | −1.96929 | −0.0885128 | ||||||||
\(496\) | 54.4953 | 2.44691 | ||||||||
\(497\) | −11.8443 | −0.531290 | ||||||||
\(498\) | 29.9757 | 1.34324 | ||||||||
\(499\) | −5.93453 | −0.265666 | −0.132833 | − | 0.991138i | \(-0.542407\pi\) | ||||
−0.132833 | + | 0.991138i | \(0.542407\pi\) | |||||||
\(500\) | −55.3365 | −2.47472 | ||||||||
\(501\) | −18.2267 | −0.814310 | ||||||||
\(502\) | −53.7419 | −2.39862 | ||||||||
\(503\) | −4.78204 | −0.213221 | −0.106610 | − | 0.994301i | \(-0.534000\pi\) | ||||
−0.106610 | + | 0.994301i | \(0.534000\pi\) | |||||||
\(504\) | 10.4658 | 0.466184 | ||||||||
\(505\) | 6.24699 | 0.277987 | ||||||||
\(506\) | 4.47043 | 0.198735 | ||||||||
\(507\) | 6.26918 | 0.278424 | ||||||||
\(508\) | −37.8294 | −1.67841 | ||||||||
\(509\) | 41.8774 | 1.85618 | 0.928092 | − | 0.372350i | \(-0.121448\pi\) | ||||
0.928092 | + | 0.372350i | \(0.121448\pi\) | |||||||
\(510\) | −1.69742 | −0.0751632 | ||||||||
\(511\) | 13.4684 | 0.595806 | ||||||||
\(512\) | 38.4242 | 1.69813 | ||||||||
\(513\) | 30.8182 | 1.36066 | ||||||||
\(514\) | 77.2375 | 3.40680 | ||||||||
\(515\) | 11.7017 | 0.515637 | ||||||||
\(516\) | 8.90280 | 0.391924 | ||||||||
\(517\) | −3.19488 | −0.140511 | ||||||||
\(518\) | −19.9508 | −0.876587 | ||||||||
\(519\) | −17.2030 | −0.755129 | ||||||||
\(520\) | −30.4867 | −1.33693 | ||||||||
\(521\) | −16.9223 | −0.741381 | −0.370691 | − | 0.928756i | \(-0.620879\pi\) | ||||
−0.370691 | + | 0.928756i | \(0.620879\pi\) | |||||||
\(522\) | 20.0532 | 0.877705 | ||||||||
\(523\) | 1.70053 | 0.0743589 | 0.0371794 | − | 0.999309i | \(-0.488163\pi\) | ||||
0.0371794 | + | 0.999309i | \(0.488163\pi\) | |||||||
\(524\) | −52.2385 | −2.28205 | ||||||||
\(525\) | 3.79815 | 0.165765 | ||||||||
\(526\) | 79.7898 | 3.47900 | ||||||||
\(527\) | −1.93897 | −0.0844628 | ||||||||
\(528\) | −12.8599 | −0.559657 | ||||||||
\(529\) | −20.1160 | −0.874610 | ||||||||
\(530\) | 48.1359 | 2.09089 | ||||||||
\(531\) | −0.536903 | −0.0232996 | ||||||||
\(532\) | 27.0035 | 1.17075 | ||||||||
\(533\) | 22.4330 | 0.971683 | ||||||||
\(534\) | 37.1538 | 1.60780 | ||||||||
\(535\) | 29.1770 | 1.26143 | ||||||||
\(536\) | 65.6630 | 2.83621 | ||||||||
\(537\) | 16.3603 | 0.705999 | ||||||||
\(538\) | −5.04553 | −0.217528 | ||||||||
\(539\) | 1.00335 | 0.0432173 | ||||||||
\(540\) | 38.6120 | 1.66160 | ||||||||
\(541\) | 24.6674 | 1.06053 | 0.530267 | − | 0.847831i | \(-0.322092\pi\) | ||||
0.530267 | + | 0.847831i | \(0.322092\pi\) | |||||||
\(542\) | 22.4790 | 0.965554 | ||||||||
\(543\) | 15.4554 | 0.663254 | ||||||||
\(544\) | 4.05962 | 0.174055 | ||||||||
\(545\) | 8.18328 | 0.350533 | ||||||||
\(546\) | 9.47567 | 0.405521 | ||||||||
\(547\) | −36.5380 | −1.56225 | −0.781125 | − | 0.624374i | \(-0.785354\pi\) | ||||
−0.781125 | + | 0.624374i | \(0.785354\pi\) | |||||||
\(548\) | −73.8160 | −3.15326 | ||||||||
\(549\) | −6.71362 | −0.286530 | ||||||||
\(550\) | 7.86379 | 0.335313 | ||||||||
\(551\) | 30.5501 | 1.30148 | ||||||||
\(552\) | −16.3341 | −0.695225 | ||||||||
\(553\) | 2.15817 | 0.0917747 | ||||||||
\(554\) | 31.6686 | 1.34547 | ||||||||
\(555\) | −13.7164 | −0.582230 | ||||||||
\(556\) | 50.0902 | 2.12430 | ||||||||
\(557\) | −12.5265 | −0.530763 | −0.265381 | − | 0.964144i | \(-0.585498\pi\) | ||||
−0.265381 | + | 0.964144i | \(0.585498\pi\) | |||||||
\(558\) | 19.6215 | 0.830646 | ||||||||
\(559\) | −4.07312 | −0.172274 | ||||||||
\(560\) | 14.3016 | 0.604352 | ||||||||
\(561\) | 0.457563 | 0.0193183 | ||||||||
\(562\) | 64.0529 | 2.70191 | ||||||||
\(563\) | 41.0593 | 1.73044 | 0.865221 | − | 0.501391i | \(-0.167178\pi\) | ||||
0.865221 | + | 0.501391i | \(0.167178\pi\) | |||||||
\(564\) | 19.7705 | 0.832488 | ||||||||
\(565\) | −14.8920 | −0.626510 | ||||||||
\(566\) | −3.64124 | −0.153053 | ||||||||
\(567\) | −2.93565 | −0.123286 | ||||||||
\(568\) | 89.6017 | 3.75960 | ||||||||
\(569\) | 10.7698 | 0.451495 | 0.225747 | − | 0.974186i | \(-0.427518\pi\) | ||||
0.225747 | + | 0.974186i | \(0.427518\pi\) | |||||||
\(570\) | 26.1687 | 1.09609 | ||||||||
\(571\) | 12.5226 | 0.524055 | 0.262028 | − | 0.965060i | \(-0.415609\pi\) | ||||
0.262028 | + | 0.965060i | \(0.415609\pi\) | |||||||
\(572\) | 13.9184 | 0.581958 | ||||||||
\(573\) | −5.83362 | −0.243703 | ||||||||
\(574\) | −20.7193 | −0.864805 | ||||||||
\(575\) | 5.07311 | 0.211563 | ||||||||
\(576\) | −13.1889 | −0.549540 | ||||||||
\(577\) | −6.88690 | −0.286705 | −0.143353 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143353 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(578\) | 44.2641 | 1.84114 | ||||||||
\(579\) | 15.6012 | 0.648363 | ||||||||
\(580\) | 38.2761 | 1.58933 | ||||||||
\(581\) | 8.98617 | 0.372809 | ||||||||
\(582\) | −35.9388 | −1.48971 | ||||||||
\(583\) | −12.9757 | −0.537397 | ||||||||
\(584\) | −101.888 | −4.21614 | ||||||||
\(585\) | −5.57535 | −0.230512 | ||||||||
\(586\) | 38.1588 | 1.57633 | ||||||||
\(587\) | 39.2707 | 1.62087 | 0.810437 | − | 0.585826i | \(-0.199230\pi\) | ||||
0.810437 | + | 0.585826i | \(0.199230\pi\) | |||||||
\(588\) | −6.20891 | −0.256051 | ||||||||
\(589\) | 29.8925 | 1.23170 | ||||||||
\(590\) | −1.44451 | −0.0594694 | ||||||||
\(591\) | −2.53021 | −0.104079 | ||||||||
\(592\) | 76.6571 | 3.15059 | ||||||||
\(593\) | −15.6776 | −0.643803 | −0.321901 | − | 0.946773i | \(-0.604322\pi\) | ||||
−0.321901 | + | 0.946773i | \(0.604322\pi\) | |||||||
\(594\) | −14.6711 | −0.601964 | ||||||||
\(595\) | −0.508857 | −0.0208611 | ||||||||
\(596\) | −34.3025 | −1.40508 | ||||||||
\(597\) | 9.19116 | 0.376169 | ||||||||
\(598\) | 12.6565 | 0.517561 | ||||||||
\(599\) | −45.7991 | −1.87130 | −0.935650 | − | 0.352929i | \(-0.885186\pi\) | ||||
−0.935650 | + | 0.352929i | \(0.885186\pi\) | |||||||
\(600\) | −28.7328 | −1.17301 | ||||||||
\(601\) | −6.99513 | −0.285337 | −0.142669 | − | 0.989771i | \(-0.545568\pi\) | ||||
−0.142669 | + | 0.989771i | \(0.545568\pi\) | |||||||
\(602\) | 3.76195 | 0.153326 | ||||||||
\(603\) | 12.0083 | 0.489016 | ||||||||
\(604\) | 71.7112 | 2.91789 | ||||||||
\(605\) | −14.1775 | −0.576396 | ||||||||
\(606\) | 14.6884 | 0.596677 | ||||||||
\(607\) | 26.5766 | 1.07871 | 0.539356 | − | 0.842078i | \(-0.318668\pi\) | ||||
0.539356 | + | 0.842078i | \(0.318668\pi\) | |||||||
\(608\) | −62.5860 | −2.53820 | ||||||||
\(609\) | −7.02439 | −0.284643 | ||||||||
\(610\) | −18.0626 | −0.731335 | ||||||||
\(611\) | −9.04519 | −0.365929 | ||||||||
\(612\) | 2.42323 | 0.0979534 | ||||||||
\(613\) | 38.4416 | 1.55264 | 0.776322 | − | 0.630337i | \(-0.217083\pi\) | ||||
0.776322 | + | 0.630337i | \(0.217083\pi\) | |||||||
\(614\) | 24.4435 | 0.986458 | ||||||||
\(615\) | −14.2448 | −0.574405 | ||||||||
\(616\) | −7.59028 | −0.305821 | ||||||||
\(617\) | −31.4730 | −1.26705 | −0.633527 | − | 0.773721i | \(-0.718393\pi\) | ||||
−0.633527 | + | 0.773721i | \(0.718393\pi\) | |||||||
\(618\) | 27.5139 | 1.10677 | ||||||||
\(619\) | 39.5958 | 1.59149 | 0.795745 | − | 0.605631i | \(-0.207079\pi\) | ||||
0.795745 | + | 0.605631i | \(0.207079\pi\) | |||||||
\(620\) | 37.4521 | 1.50411 | ||||||||
\(621\) | −9.46468 | −0.379805 | ||||||||
\(622\) | 50.9083 | 2.04124 | ||||||||
\(623\) | 11.1380 | 0.446236 | ||||||||
\(624\) | −36.4085 | −1.45751 | ||||||||
\(625\) | −1.13957 | −0.0455827 | ||||||||
\(626\) | −19.3452 | −0.773192 | ||||||||
\(627\) | −7.05411 | −0.281714 | ||||||||
\(628\) | 81.7879 | 3.26369 | ||||||||
\(629\) | −2.72750 | −0.108752 | ||||||||
\(630\) | 5.14942 | 0.205158 | ||||||||
\(631\) | 43.3957 | 1.72755 | 0.863777 | − | 0.503875i | \(-0.168093\pi\) | ||||
0.863777 | + | 0.503875i | \(0.168093\pi\) | |||||||
\(632\) | −16.3264 | −0.649431 | ||||||||
\(633\) | −16.2013 | −0.643944 | ||||||||
\(634\) | −35.4075 | −1.40621 | ||||||||
\(635\) | −10.9900 | −0.436125 | ||||||||
\(636\) | 80.2958 | 3.18393 | ||||||||
\(637\) | 2.84063 | 0.112550 | ||||||||
\(638\) | −14.5435 | −0.575783 | ||||||||
\(639\) | 16.3862 | 0.648226 | ||||||||
\(640\) | −3.36977 | −0.133202 | ||||||||
\(641\) | −33.7650 | −1.33364 | −0.666818 | − | 0.745220i | \(-0.732344\pi\) | ||||
−0.666818 | + | 0.745220i | \(0.732344\pi\) | |||||||
\(642\) | 68.6034 | 2.70756 | ||||||||
\(643\) | 37.5203 | 1.47966 | 0.739829 | − | 0.672795i | \(-0.234906\pi\) | ||||
0.739829 | + | 0.672795i | \(0.234906\pi\) | |||||||
\(644\) | −8.29312 | −0.326795 | ||||||||
\(645\) | 2.58639 | 0.101839 | ||||||||
\(646\) | 5.20361 | 0.204733 | ||||||||
\(647\) | −0.762837 | −0.0299902 | −0.0149951 | − | 0.999888i | \(-0.504773\pi\) | ||||
−0.0149951 | + | 0.999888i | \(0.504773\pi\) | |||||||
\(648\) | 22.2081 | 0.872415 | ||||||||
\(649\) | 0.389386 | 0.0152847 | ||||||||
\(650\) | 22.2636 | 0.873250 | ||||||||
\(651\) | −6.87318 | −0.269381 | ||||||||
\(652\) | 103.833 | 4.06640 | ||||||||
\(653\) | −24.0453 | −0.940963 | −0.470482 | − | 0.882410i | \(-0.655920\pi\) | ||||
−0.470482 | + | 0.882410i | \(0.655920\pi\) | |||||||
\(654\) | 19.2412 | 0.752391 | ||||||||
\(655\) | −15.1760 | −0.592977 | ||||||||
\(656\) | 79.6099 | 3.10824 | ||||||||
\(657\) | −18.6330 | −0.726941 | ||||||||
\(658\) | 8.35418 | 0.325680 | ||||||||
\(659\) | 10.7830 | 0.420046 | 0.210023 | − | 0.977696i | \(-0.432646\pi\) | ||||
0.210023 | + | 0.977696i | \(0.432646\pi\) | |||||||
\(660\) | −8.83806 | −0.344021 | ||||||||
\(661\) | −27.0293 | −1.05132 | −0.525660 | − | 0.850695i | \(-0.676181\pi\) | ||||
−0.525660 | + | 0.850695i | \(0.676181\pi\) | |||||||
\(662\) | −75.4149 | −2.93108 | ||||||||
\(663\) | 1.29543 | 0.0503104 | ||||||||
\(664\) | −67.9799 | −2.63813 | ||||||||
\(665\) | 7.84490 | 0.304212 | ||||||||
\(666\) | 27.6011 | 1.06952 | ||||||||
\(667\) | −9.38235 | −0.363286 | ||||||||
\(668\) | 70.0064 | 2.70863 | ||||||||
\(669\) | 32.5246 | 1.25747 | ||||||||
\(670\) | 32.3077 | 1.24815 | ||||||||
\(671\) | 4.86902 | 0.187967 | ||||||||
\(672\) | 14.3904 | 0.555122 | ||||||||
\(673\) | −23.2270 | −0.895336 | −0.447668 | − | 0.894200i | \(-0.647745\pi\) | ||||
−0.447668 | + | 0.894200i | \(0.647745\pi\) | |||||||
\(674\) | 28.5850 | 1.10105 | ||||||||
\(675\) | −16.6490 | −0.640821 | ||||||||
\(676\) | −24.0791 | −0.926118 | ||||||||
\(677\) | 21.5465 | 0.828098 | 0.414049 | − | 0.910255i | \(-0.364114\pi\) | ||||
0.414049 | + | 0.910255i | \(0.364114\pi\) | |||||||
\(678\) | −35.0152 | −1.34475 | ||||||||
\(679\) | −10.7738 | −0.413461 | ||||||||
\(680\) | 3.84948 | 0.147621 | ||||||||
\(681\) | 0.984507 | 0.0377264 | ||||||||
\(682\) | −14.2304 | −0.544911 | ||||||||
\(683\) | 36.8466 | 1.40990 | 0.704948 | − | 0.709259i | \(-0.250970\pi\) | ||||
0.704948 | + | 0.709259i | \(0.250970\pi\) | |||||||
\(684\) | −37.3582 | −1.42843 | ||||||||
\(685\) | −21.4446 | −0.819357 | ||||||||
\(686\) | −2.62362 | −0.100170 | ||||||||
\(687\) | −25.7843 | −0.983732 | ||||||||
\(688\) | −14.4546 | −0.551076 | ||||||||
\(689\) | −36.7361 | −1.39953 | ||||||||
\(690\) | −8.03674 | −0.305954 | ||||||||
\(691\) | 32.3596 | 1.23102 | 0.615508 | − | 0.788131i | \(-0.288951\pi\) | ||||
0.615508 | + | 0.788131i | \(0.288951\pi\) | |||||||
\(692\) | 66.0745 | 2.51178 | ||||||||
\(693\) | −1.38809 | −0.0527293 | ||||||||
\(694\) | 95.2663 | 3.61626 | ||||||||
\(695\) | 14.5519 | 0.551986 | ||||||||
\(696\) | 53.1392 | 2.01423 | ||||||||
\(697\) | −2.83256 | −0.107291 | ||||||||
\(698\) | −12.4451 | −0.471052 | ||||||||
\(699\) | 4.95398 | 0.187377 | ||||||||
\(700\) | −14.5882 | −0.551381 | ||||||||
\(701\) | −10.2804 | −0.388286 | −0.194143 | − | 0.980973i | \(-0.562193\pi\) | ||||
−0.194143 | + | 0.980973i | \(0.562193\pi\) | |||||||
\(702\) | −41.5362 | −1.56768 | ||||||||
\(703\) | 42.0490 | 1.58591 | ||||||||
\(704\) | 9.56523 | 0.360503 | ||||||||
\(705\) | 5.74361 | 0.216317 | ||||||||
\(706\) | −65.1710 | −2.45274 | ||||||||
\(707\) | 4.40333 | 0.165604 | ||||||||
\(708\) | −2.40959 | −0.0905581 | ||||||||
\(709\) | −2.01430 | −0.0756488 | −0.0378244 | − | 0.999284i | \(-0.512043\pi\) | ||||
−0.0378244 | + | 0.999284i | \(0.512043\pi\) | |||||||
\(710\) | 44.0861 | 1.65452 | ||||||||
\(711\) | −2.98574 | −0.111974 | ||||||||
\(712\) | −84.2586 | −3.15773 | ||||||||
\(713\) | −9.18038 | −0.343808 | ||||||||
\(714\) | −1.19647 | −0.0447766 | ||||||||
\(715\) | 4.04350 | 0.151218 | ||||||||
\(716\) | −62.8377 | −2.34836 | ||||||||
\(717\) | −14.3041 | −0.534197 | ||||||||
\(718\) | 0.957000 | 0.0357149 | ||||||||
\(719\) | 6.09844 | 0.227433 | 0.113717 | − | 0.993513i | \(-0.463724\pi\) | ||||
0.113717 | + | 0.993513i | \(0.463724\pi\) | |||||||
\(720\) | −19.7857 | −0.737368 | ||||||||
\(721\) | 8.24817 | 0.307178 | ||||||||
\(722\) | −30.3737 | −1.13039 | ||||||||
\(723\) | −16.7109 | −0.621483 | ||||||||
\(724\) | −59.3620 | −2.20617 | ||||||||
\(725\) | −16.5042 | −0.612950 | ||||||||
\(726\) | −33.3352 | −1.23719 | ||||||||
\(727\) | 16.2330 | 0.602049 | 0.301024 | − | 0.953616i | \(-0.402671\pi\) | ||||
0.301024 | + | 0.953616i | \(0.402671\pi\) | |||||||
\(728\) | −21.4892 | −0.796445 | ||||||||
\(729\) | 25.3195 | 0.937758 | ||||||||
\(730\) | −50.1310 | −1.85543 | ||||||||
\(731\) | 0.514301 | 0.0190221 | ||||||||
\(732\) | −30.1304 | −1.11365 | ||||||||
\(733\) | −29.7793 | −1.09992 | −0.549961 | − | 0.835190i | \(-0.685357\pi\) | ||||
−0.549961 | + | 0.835190i | \(0.685357\pi\) | |||||||
\(734\) | 43.9711 | 1.62300 | ||||||||
\(735\) | −1.80378 | −0.0665333 | ||||||||
\(736\) | 19.2210 | 0.708495 | ||||||||
\(737\) | −8.70897 | −0.320799 | ||||||||
\(738\) | 28.6643 | 1.05515 | ||||||||
\(739\) | 24.2669 | 0.892671 | 0.446335 | − | 0.894866i | \(-0.352729\pi\) | ||||
0.446335 | + | 0.894866i | \(0.352729\pi\) | |||||||
\(740\) | 52.6830 | 1.93666 | ||||||||
\(741\) | −19.9713 | −0.733663 | ||||||||
\(742\) | 33.9296 | 1.24560 | ||||||||
\(743\) | −12.6911 | −0.465593 | −0.232797 | − | 0.972525i | \(-0.574788\pi\) | ||||
−0.232797 | + | 0.972525i | \(0.574788\pi\) | |||||||
\(744\) | 51.9953 | 1.90624 | ||||||||
\(745\) | −9.96537 | −0.365103 | ||||||||
\(746\) | −13.0578 | −0.478080 | ||||||||
\(747\) | −12.4320 | −0.454864 | ||||||||
\(748\) | −1.75744 | −0.0642583 | ||||||||
\(749\) | 20.5661 | 0.751467 | ||||||||
\(750\) | −37.7993 | −1.38024 | ||||||||
\(751\) | 0.551230 | 0.0201147 | 0.0100573 | − | 0.999949i | \(-0.496799\pi\) | ||||
0.0100573 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(752\) | −32.0994 | −1.17054 | ||||||||
\(753\) | −26.0438 | −0.949090 | ||||||||
\(754\) | −41.1749 | −1.49950 | ||||||||
\(755\) | 20.8331 | 0.758196 | ||||||||
\(756\) | 27.2165 | 0.989855 | ||||||||
\(757\) | 14.1085 | 0.512784 | 0.256392 | − | 0.966573i | \(-0.417466\pi\) | ||||
0.256392 | + | 0.966573i | \(0.417466\pi\) | |||||||
\(758\) | 11.6298 | 0.422414 | ||||||||
\(759\) | 2.16641 | 0.0786357 | ||||||||
\(760\) | −59.3462 | −2.15271 | ||||||||
\(761\) | 7.29511 | 0.264448 | 0.132224 | − | 0.991220i | \(-0.457788\pi\) | ||||
0.132224 | + | 0.991220i | \(0.457788\pi\) | |||||||
\(762\) | −25.8406 | −0.936106 | ||||||||
\(763\) | 5.76817 | 0.208822 | ||||||||
\(764\) | 22.4062 | 0.810626 | ||||||||
\(765\) | 0.703984 | 0.0254526 | ||||||||
\(766\) | −1.94506 | −0.0702779 | ||||||||
\(767\) | 1.10241 | 0.0398058 | ||||||||
\(768\) | 16.3186 | 0.588846 | ||||||||
\(769\) | 38.3516 | 1.38300 | 0.691498 | − | 0.722379i | \(-0.256951\pi\) | ||||
0.691498 | + | 0.722379i | \(0.256951\pi\) | |||||||
\(770\) | −3.73459 | −0.134585 | ||||||||
\(771\) | 37.4300 | 1.34801 | ||||||||
\(772\) | −59.9220 | −2.15664 | ||||||||
\(773\) | −7.46079 | −0.268346 | −0.134173 | − | 0.990958i | \(-0.542838\pi\) | ||||
−0.134173 | + | 0.990958i | \(0.542838\pi\) | |||||||
\(774\) | −5.20451 | −0.187072 | ||||||||
\(775\) | −16.1489 | −0.580086 | ||||||||
\(776\) | 81.5033 | 2.92580 | ||||||||
\(777\) | −9.66833 | −0.346849 | ||||||||
\(778\) | −52.0413 | −1.86577 | ||||||||
\(779\) | 43.6687 | 1.56459 | ||||||||
\(780\) | −25.0219 | −0.895928 | ||||||||
\(781\) | −11.8840 | −0.425242 | ||||||||
\(782\) | −1.59810 | −0.0571479 | ||||||||
\(783\) | 30.7911 | 1.10039 | ||||||||
\(784\) | 10.0808 | 0.360028 | ||||||||
\(785\) | 23.7606 | 0.848051 | ||||||||
\(786\) | −35.6832 | −1.27278 | ||||||||
\(787\) | −42.7412 | −1.52356 | −0.761779 | − | 0.647837i | \(-0.775674\pi\) | ||||
−0.761779 | + | 0.647837i | \(0.775674\pi\) | |||||||
\(788\) | 9.71821 | 0.346197 | ||||||||
\(789\) | 38.6669 | 1.37658 | ||||||||
\(790\) | −8.03298 | −0.285801 | ||||||||
\(791\) | −10.4969 | −0.373228 | ||||||||
\(792\) | 10.5009 | 0.373132 | ||||||||
\(793\) | 13.7849 | 0.489518 | ||||||||
\(794\) | 2.46872 | 0.0876117 | ||||||||
\(795\) | 23.3271 | 0.827326 | ||||||||
\(796\) | −35.3020 | −1.25125 | ||||||||
\(797\) | 24.8675 | 0.880852 | 0.440426 | − | 0.897789i | \(-0.354827\pi\) | ||||
0.440426 | + | 0.897789i | \(0.354827\pi\) | |||||||
\(798\) | 18.4456 | 0.652966 | ||||||||
\(799\) | 1.14211 | 0.0404050 | ||||||||
\(800\) | 33.8110 | 1.19540 | ||||||||
\(801\) | −15.4090 | −0.544451 | ||||||||
\(802\) | −71.1181 | −2.51127 | ||||||||
\(803\) | 13.5135 | 0.476880 | ||||||||
\(804\) | 53.8927 | 1.90065 | ||||||||
\(805\) | −2.40927 | −0.0849156 | ||||||||
\(806\) | −40.2885 | −1.41910 | ||||||||
\(807\) | −2.44511 | −0.0860720 | ||||||||
\(808\) | −33.3109 | −1.17187 | ||||||||
\(809\) | −35.2861 | −1.24059 | −0.620296 | − | 0.784368i | \(-0.712988\pi\) | ||||
−0.620296 | + | 0.784368i | \(0.712988\pi\) | |||||||
\(810\) | 10.9269 | 0.383931 | ||||||||
\(811\) | 52.0766 | 1.82866 | 0.914329 | − | 0.404972i | \(-0.132719\pi\) | ||||
0.914329 | + | 0.404972i | \(0.132719\pi\) | |||||||
\(812\) | 26.9797 | 0.946803 | ||||||||
\(813\) | 10.8935 | 0.382052 | ||||||||
\(814\) | −20.0176 | −0.701616 | ||||||||
\(815\) | 30.1649 | 1.05663 | ||||||||
\(816\) | 4.59720 | 0.160934 | ||||||||
\(817\) | −7.92883 | −0.277395 | ||||||||
\(818\) | −16.9402 | −0.592301 | ||||||||
\(819\) | −3.92991 | −0.137322 | ||||||||
\(820\) | 54.7123 | 1.91064 | ||||||||
\(821\) | 27.5507 | 0.961526 | 0.480763 | − | 0.876851i | \(-0.340360\pi\) | ||||
0.480763 | + | 0.876851i | \(0.340360\pi\) | |||||||
\(822\) | −50.4224 | −1.75868 | ||||||||
\(823\) | −18.6228 | −0.649149 | −0.324574 | − | 0.945860i | \(-0.605221\pi\) | ||||
−0.324574 | + | 0.945860i | \(0.605221\pi\) | |||||||
\(824\) | −62.3970 | −2.17370 | ||||||||
\(825\) | 3.81086 | 0.132677 | ||||||||
\(826\) | −1.01819 | −0.0354275 | ||||||||
\(827\) | −41.2752 | −1.43528 | −0.717639 | − | 0.696415i | \(-0.754777\pi\) | ||||
−0.717639 | + | 0.696415i | \(0.754777\pi\) | |||||||
\(828\) | 11.4732 | 0.398721 | ||||||||
\(829\) | −41.5670 | −1.44368 | −0.721841 | − | 0.692059i | \(-0.756704\pi\) | ||||
−0.721841 | + | 0.692059i | \(0.756704\pi\) | |||||||
\(830\) | −33.4477 | −1.16099 | ||||||||
\(831\) | 15.3469 | 0.532378 | ||||||||
\(832\) | 27.0806 | 0.938851 | ||||||||
\(833\) | −0.358679 | −0.0124275 | ||||||||
\(834\) | 34.2157 | 1.18479 | ||||||||
\(835\) | 20.3379 | 0.703821 | ||||||||
\(836\) | 27.0939 | 0.937062 | ||||||||
\(837\) | 30.1283 | 1.04139 | ||||||||
\(838\) | −1.75753 | −0.0607129 | ||||||||
\(839\) | 25.6470 | 0.885434 | 0.442717 | − | 0.896661i | \(-0.354015\pi\) | ||||
0.442717 | + | 0.896661i | \(0.354015\pi\) | |||||||
\(840\) | 13.6455 | 0.470814 | ||||||||
\(841\) | 1.52329 | 0.0525272 | ||||||||
\(842\) | −20.2314 | −0.697221 | ||||||||
\(843\) | 31.0406 | 1.06910 | ||||||||
\(844\) | 62.2270 | 2.14194 | ||||||||
\(845\) | −6.99531 | −0.240646 | ||||||||
\(846\) | −11.5577 | −0.397361 | ||||||||
\(847\) | −9.99329 | −0.343374 | ||||||||
\(848\) | −130.368 | −4.47686 | ||||||||
\(849\) | −1.76458 | −0.0605602 | ||||||||
\(850\) | −2.81116 | −0.0964221 | ||||||||
\(851\) | −12.9138 | −0.442679 | ||||||||
\(852\) | 73.5403 | 2.51945 | ||||||||
\(853\) | 26.0641 | 0.892416 | 0.446208 | − | 0.894929i | \(-0.352774\pi\) | ||||
0.446208 | + | 0.894929i | \(0.352774\pi\) | |||||||
\(854\) | −12.7318 | −0.435675 | ||||||||
\(855\) | −10.8531 | −0.371168 | ||||||||
\(856\) | −155.581 | −5.31765 | ||||||||
\(857\) | −36.3613 | −1.24208 | −0.621039 | − | 0.783780i | \(-0.713289\pi\) | ||||
−0.621039 | + | 0.783780i | \(0.713289\pi\) | |||||||
\(858\) | 9.50740 | 0.324577 | ||||||||
\(859\) | −30.8138 | −1.05135 | −0.525677 | − | 0.850684i | \(-0.676188\pi\) | ||||
−0.525677 | + | 0.850684i | \(0.676188\pi\) | |||||||
\(860\) | −9.93399 | −0.338746 | ||||||||
\(861\) | −10.0407 | −0.342188 | ||||||||
\(862\) | 16.2794 | 0.554480 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −63.0798 | −2.14602 | ||||||||
\(865\) | 19.1956 | 0.652670 | ||||||||
\(866\) | −70.9077 | −2.40954 | ||||||||
\(867\) | 21.4508 | 0.728506 | ||||||||
\(868\) | 26.3990 | 0.896039 | ||||||||
\(869\) | 2.16540 | 0.0734560 | ||||||||
\(870\) | 26.1457 | 0.886422 | ||||||||
\(871\) | −24.6564 | −0.835451 | ||||||||
\(872\) | −43.6359 | −1.47770 | ||||||||
\(873\) | 14.9051 | 0.504463 | ||||||||
\(874\) | 24.6374 | 0.833372 | ||||||||
\(875\) | −11.3316 | −0.383077 | ||||||||
\(876\) | −83.6239 | −2.82539 | ||||||||
\(877\) | −23.5148 | −0.794037 | −0.397019 | − | 0.917811i | \(-0.629955\pi\) | ||||
−0.397019 | + | 0.917811i | \(0.629955\pi\) | |||||||
\(878\) | −20.1642 | −0.680510 | ||||||||
\(879\) | 18.4921 | 0.623723 | ||||||||
\(880\) | 14.3495 | 0.483720 | ||||||||
\(881\) | 43.2880 | 1.45841 | 0.729206 | − | 0.684295i | \(-0.239890\pi\) | ||||
0.729206 | + | 0.684295i | \(0.239890\pi\) | |||||||
\(882\) | 3.62968 | 0.122218 | ||||||||
\(883\) | 53.1004 | 1.78697 | 0.893485 | − | 0.449092i | \(-0.148253\pi\) | ||||
0.893485 | + | 0.449092i | \(0.148253\pi\) | |||||||
\(884\) | −4.97558 | −0.167347 | ||||||||
\(885\) | −0.700022 | −0.0235310 | ||||||||
\(886\) | 9.67074 | 0.324895 | ||||||||
\(887\) | 15.4190 | 0.517719 | 0.258859 | − | 0.965915i | \(-0.416653\pi\) | ||||
0.258859 | + | 0.965915i | \(0.416653\pi\) | |||||||
\(888\) | 73.1404 | 2.45443 | ||||||||
\(889\) | −7.74654 | −0.259811 | ||||||||
\(890\) | −41.4572 | −1.38965 | ||||||||
\(891\) | −2.94548 | −0.0986774 | ||||||||
\(892\) | −124.922 | −4.18271 | ||||||||
\(893\) | −17.6076 | −0.589215 | ||||||||
\(894\) | −23.4314 | −0.783663 | ||||||||
\(895\) | −18.2553 | −0.610206 | ||||||||
\(896\) | −2.37526 | −0.0793518 | ||||||||
\(897\) | 6.13344 | 0.204790 | ||||||||
\(898\) | −23.4288 | −0.781830 | ||||||||
\(899\) | 29.8662 | 0.996094 | ||||||||
\(900\) | 20.1822 | 0.672738 | ||||||||
\(901\) | 4.63856 | 0.154533 | ||||||||
\(902\) | −20.7886 | −0.692186 | ||||||||
\(903\) | 1.82308 | 0.0606682 | ||||||||
\(904\) | 79.4088 | 2.64110 | ||||||||
\(905\) | −17.2455 | −0.573261 | ||||||||
\(906\) | 48.9846 | 1.62740 | ||||||||
\(907\) | 33.3959 | 1.10889 | 0.554447 | − | 0.832219i | \(-0.312930\pi\) | ||||
0.554447 | + | 0.832219i | \(0.312930\pi\) | |||||||
\(908\) | −3.78136 | −0.125489 | ||||||||
\(909\) | −6.09183 | −0.202053 | ||||||||
\(910\) | −10.5732 | −0.350498 | ||||||||
\(911\) | 46.6324 | 1.54500 | 0.772501 | − | 0.635014i | \(-0.219006\pi\) | ||||
0.772501 | + | 0.635014i | \(0.219006\pi\) | |||||||
\(912\) | −70.8736 | −2.34686 | ||||||||
\(913\) | 9.01627 | 0.298395 | ||||||||
\(914\) | −43.5339 | −1.43997 | ||||||||
\(915\) | −8.75332 | −0.289376 | ||||||||
\(916\) | 99.0340 | 3.27218 | ||||||||
\(917\) | −10.6972 | −0.353252 | ||||||||
\(918\) | 5.24466 | 0.173100 | ||||||||
\(919\) | −1.44613 | −0.0477035 | −0.0238518 | − | 0.999716i | \(-0.507593\pi\) | ||||
−0.0238518 | + | 0.999716i | \(0.507593\pi\) | |||||||
\(920\) | 18.2260 | 0.600894 | ||||||||
\(921\) | 11.8455 | 0.390323 | ||||||||
\(922\) | −83.3302 | −2.74433 | ||||||||
\(923\) | −33.6454 | −1.10745 | ||||||||
\(924\) | −6.22970 | −0.204942 | ||||||||
\(925\) | −22.7163 | −0.746906 | ||||||||
\(926\) | 24.6825 | 0.811118 | ||||||||
\(927\) | −11.4110 | −0.374787 | ||||||||
\(928\) | −62.5310 | −2.05268 | ||||||||
\(929\) | −2.65734 | −0.0871846 | −0.0435923 | − | 0.999049i | \(-0.513880\pi\) | ||||
−0.0435923 | + | 0.999049i | \(0.513880\pi\) | |||||||
\(930\) | 25.5829 | 0.838895 | ||||||||
\(931\) | 5.52965 | 0.181227 | ||||||||
\(932\) | −19.0276 | −0.623269 | ||||||||
\(933\) | 24.6707 | 0.807681 | ||||||||
\(934\) | 91.3360 | 2.98861 | ||||||||
\(935\) | −0.510561 | −0.0166971 | ||||||||
\(936\) | 29.7295 | 0.971740 | ||||||||
\(937\) | 0.769474 | 0.0251376 | 0.0125688 | − | 0.999921i | \(-0.495999\pi\) | ||||
0.0125688 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(938\) | 22.7728 | 0.743558 | ||||||||
\(939\) | −9.37489 | −0.305938 | ||||||||
\(940\) | −22.0604 | −0.719532 | ||||||||
\(941\) | −37.8046 | −1.23239 | −0.616197 | − | 0.787592i | \(-0.711328\pi\) | ||||
−0.616197 | + | 0.787592i | \(0.711328\pi\) | |||||||
\(942\) | 55.8678 | 1.82027 | ||||||||
\(943\) | −13.4112 | −0.436730 | ||||||||
\(944\) | 3.91221 | 0.127332 | ||||||||
\(945\) | 7.90679 | 0.257208 | ||||||||
\(946\) | 3.77455 | 0.122721 | ||||||||
\(947\) | 0.244560 | 0.00794712 | 0.00397356 | − | 0.999992i | \(-0.498735\pi\) | ||||
0.00397356 | + | 0.999992i | \(0.498735\pi\) | |||||||
\(948\) | −13.3999 | −0.435208 | ||||||||
\(949\) | 38.2587 | 1.24193 | ||||||||
\(950\) | 43.3388 | 1.40610 | ||||||||
\(951\) | −17.1588 | −0.556412 | ||||||||
\(952\) | 2.71339 | 0.0879414 | ||||||||
\(953\) | −37.9064 | −1.22791 | −0.613955 | − | 0.789341i | \(-0.710422\pi\) | ||||
−0.613955 | + | 0.789341i | \(0.710422\pi\) | |||||||
\(954\) | −46.9403 | −1.51975 | ||||||||
\(955\) | 6.50931 | 0.210636 | ||||||||
\(956\) | 54.9401 | 1.77689 | ||||||||
\(957\) | −7.04792 | −0.227827 | ||||||||
\(958\) | −57.2943 | −1.85109 | ||||||||
\(959\) | −15.1157 | −0.488112 | ||||||||
\(960\) | −17.1959 | −0.554997 | ||||||||
\(961\) | −1.77669 | −0.0573126 | ||||||||
\(962\) | −56.6729 | −1.82721 | ||||||||
\(963\) | −28.4523 | −0.916864 | ||||||||
\(964\) | 64.1841 | 2.06723 | ||||||||
\(965\) | −17.4082 | −0.560390 | ||||||||
\(966\) | −5.66487 | −0.182264 | ||||||||
\(967\) | −4.93632 | −0.158741 | −0.0793707 | − | 0.996845i | \(-0.525291\pi\) | ||||
−0.0793707 | + | 0.996845i | \(0.525291\pi\) | |||||||
\(968\) | 75.5987 | 2.42984 | ||||||||
\(969\) | 2.52172 | 0.0810093 | ||||||||
\(970\) | 40.1015 | 1.28758 | ||||||||
\(971\) | 46.5158 | 1.49276 | 0.746381 | − | 0.665519i | \(-0.231790\pi\) | ||||
0.746381 | + | 0.665519i | \(0.231790\pi\) | |||||||
\(972\) | −63.4223 | −2.03427 | ||||||||
\(973\) | 10.2572 | 0.328832 | ||||||||
\(974\) | −98.7835 | −3.16523 | ||||||||
\(975\) | 10.7891 | 0.345529 | ||||||||
\(976\) | 48.9197 | 1.56588 | ||||||||
\(977\) | 23.0833 | 0.738499 | 0.369250 | − | 0.929330i | \(-0.379615\pi\) | ||||
0.369250 | + | 0.929330i | \(0.379615\pi\) | |||||||
\(978\) | 70.9261 | 2.26797 | ||||||||
\(979\) | 11.1753 | 0.357165 | ||||||||
\(980\) | 6.92806 | 0.221309 | ||||||||
\(981\) | −7.98003 | −0.254783 | ||||||||
\(982\) | 26.6011 | 0.848877 | ||||||||
\(983\) | 4.63684 | 0.147892 | 0.0739461 | − | 0.997262i | \(-0.476441\pi\) | ||||
0.0739461 | + | 0.997262i | \(0.476441\pi\) | |||||||
\(984\) | 75.9577 | 2.42144 | ||||||||
\(985\) | 2.82328 | 0.0899572 | ||||||||
\(986\) | 5.19904 | 0.165571 | ||||||||
\(987\) | 4.04851 | 0.128866 | ||||||||
\(988\) | 76.7070 | 2.44037 | ||||||||
\(989\) | 2.43505 | 0.0774300 | ||||||||
\(990\) | 5.16666 | 0.164207 | ||||||||
\(991\) | −49.5792 | −1.57494 | −0.787468 | − | 0.616356i | \(-0.788608\pi\) | ||||
−0.787468 | + | 0.616356i | \(0.788608\pi\) | |||||||
\(992\) | −61.1849 | −1.94262 | ||||||||
\(993\) | −36.5468 | −1.15978 | ||||||||
\(994\) | 31.0750 | 0.985640 | ||||||||
\(995\) | −10.2557 | −0.325129 | ||||||||
\(996\) | −55.7943 | −1.76791 | ||||||||
\(997\) | −38.6510 | −1.22409 | −0.612045 | − | 0.790823i | \(-0.709653\pi\) | ||||
−0.612045 | + | 0.790823i | \(0.709653\pi\) | |||||||
\(998\) | 15.5700 | 0.492859 | ||||||||
\(999\) | 42.3808 | 1.34087 |
(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 | 6041.2.a.f.1.7 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.7 | ✓ | 132 | 1.1 | even | 1 | trivial |