Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,7,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.7195728007\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.4 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.7.c.a.58.57 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 14.6202i | − | 1.82752i | −0.406254 | − | 0.913760i | \(-0.633165\pi\) | ||
0.406254 | − | 0.913760i | \(-0.366835\pi\) | |||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −149.749 | −2.33983 | ||||||||
\(5\) | −98.4329 | −0.787463 | −0.393732 | − | 0.919225i | \(-0.628816\pi\) | ||||
−0.393732 | + | 0.919225i | \(0.628816\pi\) | |||||||
\(6\) | 227.906i | 1.05512i | ||||||||
\(7\) | −154.279 | −0.449793 | −0.224897 | − | 0.974383i | \(-0.572204\pi\) | ||||
−0.224897 | + | 0.974383i | \(0.572204\pi\) | |||||||
\(8\) | 1253.67i | 2.44857i | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 1439.11i | 1.43911i | ||||||||
\(11\) | 1555.09i | 1.16836i | 0.811625 | + | 0.584179i | \(0.198583\pi\) | ||||
−0.811625 | + | 0.584179i | \(0.801417\pi\) | |||||||
\(12\) | 2334.36 | 1.35090 | ||||||||
\(13\) | − | 1347.92i | − | 0.613528i | −0.951786 | − | 0.306764i | \(-0.900754\pi\) | ||
0.951786 | − | 0.306764i | \(-0.0992462\pi\) | |||||||
\(14\) | 2255.59i | 0.822006i | ||||||||
\(15\) | 1534.42 | 0.454642 | ||||||||
\(16\) | 8744.86 | 2.13498 | ||||||||
\(17\) | 345.025 | 0.0702269 | 0.0351134 | − | 0.999383i | \(-0.488821\pi\) | ||||
0.0351134 | + | 0.999383i | \(0.488821\pi\) | |||||||
\(18\) | − | 3552.70i | − | 0.609173i | ||||||
\(19\) | 647.386 | 0.0943848 | 0.0471924 | − | 0.998886i | \(-0.484973\pi\) | ||||
0.0471924 | + | 0.998886i | \(0.484973\pi\) | |||||||
\(20\) | 14740.2 | 1.84253 | ||||||||
\(21\) | 2404.97 | 0.259688 | ||||||||
\(22\) | 22735.6 | 2.13520 | ||||||||
\(23\) | 8417.87i | 0.691861i | 0.938260 | + | 0.345931i | \(0.112437\pi\) | ||||
−0.938260 | + | 0.345931i | \(0.887563\pi\) | |||||||
\(24\) | − | 19542.7i | − | 1.41368i | ||||||
\(25\) | −5935.96 | −0.379901 | ||||||||
\(26\) | −19706.8 | −1.12123 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | 23103.2 | 1.05244 | ||||||||
\(29\) | 194.502 | 0.00797498 | 0.00398749 | − | 0.999992i | \(-0.498731\pi\) | ||||
0.00398749 | + | 0.999992i | \(0.498731\pi\) | |||||||
\(30\) | − | 22433.4i | − | 0.830868i | ||||||
\(31\) | 2402.92i | 0.0806592i | 0.999186 | + | 0.0403296i | \(0.0128408\pi\) | ||||
−0.999186 | + | 0.0403296i | \(0.987159\pi\) | |||||||
\(32\) | − | 47616.7i | − | 1.45315i | ||||||
\(33\) | − | 24241.4i | − | 0.674552i | ||||||
\(34\) | − | 5044.31i | − | 0.128341i | ||||||
\(35\) | 15186.1 | 0.354196 | ||||||||
\(36\) | −36389.0 | −0.779944 | ||||||||
\(37\) | 25370.8i | 0.500875i | 0.968133 | + | 0.250437i | \(0.0805744\pi\) | ||||
−0.968133 | + | 0.250437i | \(0.919426\pi\) | |||||||
\(38\) | − | 9464.88i | − | 0.172490i | ||||||
\(39\) | 21012.0i | 0.354220i | ||||||||
\(40\) | − | 123402.i | − | 1.92816i | ||||||
\(41\) | −79708.2 | −1.15652 | −0.578258 | − | 0.815854i | \(-0.696267\pi\) | ||||
−0.578258 | + | 0.815854i | \(0.696267\pi\) | |||||||
\(42\) | − | 35161.1i | − | 0.474586i | ||||||
\(43\) | − | 29935.6i | − | 0.376515i | −0.982120 | − | 0.188258i | \(-0.939716\pi\) | ||
0.982120 | − | 0.188258i | \(-0.0602840\pi\) | |||||||
\(44\) | − | 232873.i | − | 2.73376i | ||||||
\(45\) | −23919.2 | −0.262488 | ||||||||
\(46\) | 123071. | 1.26439 | ||||||||
\(47\) | − | 160549.i | − | 1.54637i | −0.634179 | − | 0.773186i | \(-0.718662\pi\) | ||
0.634179 | − | 0.773186i | \(-0.281338\pi\) | |||||||
\(48\) | −136319. | −1.23263 | ||||||||
\(49\) | −93847.0 | −0.797686 | ||||||||
\(50\) | 86784.7i | 0.694277i | ||||||||
\(51\) | −5378.40 | −0.0405455 | ||||||||
\(52\) | 201850.i | 1.43555i | ||||||||
\(53\) | 96330.9 | 0.647050 | 0.323525 | − | 0.946220i | \(-0.395132\pi\) | ||||
0.323525 | + | 0.946220i | \(0.395132\pi\) | |||||||
\(54\) | 55381.1i | 0.351706i | ||||||||
\(55\) | − | 153072.i | − | 0.920040i | ||||||
\(56\) | − | 193415.i | − | 1.10135i | ||||||
\(57\) | −10091.7 | −0.0544931 | ||||||||
\(58\) | − | 2843.65i | − | 0.0145744i | ||||||
\(59\) | 155306. | − | 134390.i | 0.756191 | − | 0.654351i | ||||
\(60\) | −229778. | −1.06379 | ||||||||
\(61\) | 127221.i | 0.560494i | 0.959928 | + | 0.280247i | \(0.0904164\pi\) | ||||
−0.959928 | + | 0.280247i | \(0.909584\pi\) | |||||||
\(62\) | 35131.1 | 0.147406 | ||||||||
\(63\) | −37489.8 | −0.149931 | ||||||||
\(64\) | −136492. | −0.520676 | ||||||||
\(65\) | 132680.i | 0.483131i | ||||||||
\(66\) | −354413. | −1.23276 | ||||||||
\(67\) | 401421.i | 1.33467i | 0.744755 | + | 0.667337i | \(0.232566\pi\) | ||||
−0.744755 | + | 0.667337i | \(0.767434\pi\) | |||||||
\(68\) | −51667.1 | −0.164319 | ||||||||
\(69\) | − | 131222.i | − | 0.399446i | ||||||
\(70\) | − | 222024.i | − | 0.647300i | ||||||
\(71\) | −108092. | −0.302008 | −0.151004 | − | 0.988533i | \(-0.548251\pi\) | ||||
−0.151004 | + | 0.988533i | \(0.548251\pi\) | |||||||
\(72\) | 304641.i | 0.816189i | ||||||||
\(73\) | 420503.i | 1.08094i | 0.841364 | + | 0.540469i | \(0.181753\pi\) | ||||
−0.841364 | + | 0.540469i | \(0.818247\pi\) | |||||||
\(74\) | 370925. | 0.915359 | ||||||||
\(75\) | 92532.4 | 0.219336 | ||||||||
\(76\) | −96945.4 | −0.220845 | ||||||||
\(77\) | − | 239917.i | − | 0.525520i | ||||||
\(78\) | 307199. | 0.647345 | ||||||||
\(79\) | 163438. | 0.331492 | 0.165746 | − | 0.986168i | \(-0.446997\pi\) | ||||
0.165746 | + | 0.986168i | \(0.446997\pi\) | |||||||
\(80\) | −860783. | −1.68122 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 1.16535e6i | 2.11356i | ||||||||
\(83\) | − | 710122.i | − | 1.24194i | −0.783836 | − | 0.620968i | \(-0.786740\pi\) | ||
0.783836 | − | 0.620968i | \(-0.213260\pi\) | |||||||
\(84\) | −360143. | −0.607626 | ||||||||
\(85\) | −33961.8 | −0.0553011 | ||||||||
\(86\) | −437663. | −0.688089 | ||||||||
\(87\) | −3031.98 | −0.00460436 | ||||||||
\(88\) | −1.94956e6 | −2.86080 | ||||||||
\(89\) | − | 405485.i | − | 0.575181i | −0.957753 | − | 0.287591i | \(-0.907146\pi\) | ||
0.957753 | − | 0.287591i | \(-0.0928543\pi\) | |||||||
\(90\) | 349703.i | 0.479702i | ||||||||
\(91\) | 207956.i | 0.275961i | ||||||||
\(92\) | − | 1.26057e6i | − | 1.61884i | ||||||
\(93\) | − | 37457.8i | − | 0.0465686i | ||||||
\(94\) | −2.34725e6 | −2.82603 | ||||||||
\(95\) | −63724.1 | −0.0743246 | ||||||||
\(96\) | 742270.i | 0.838974i | ||||||||
\(97\) | − | 366961.i | − | 0.402072i | −0.979584 | − | 0.201036i | \(-0.935569\pi\) | ||
0.979584 | − | 0.201036i | \(-0.0644309\pi\) | |||||||
\(98\) | 1.37206e6i | 1.45779i | ||||||||
\(99\) | 377886.i | 0.389453i | ||||||||
\(100\) | 888905. | 0.888905 | ||||||||
\(101\) | − | 185867.i | − | 0.180401i | −0.995924 | − | 0.0902006i | \(-0.971249\pi\) | ||
0.995924 | − | 0.0902006i | \(-0.0287508\pi\) | |||||||
\(102\) | 78633.1i | 0.0740977i | ||||||||
\(103\) | − | 1.31011e6i | − | 1.19893i | −0.800399 | − | 0.599467i | \(-0.795379\pi\) | ||
0.800399 | − | 0.599467i | \(-0.204621\pi\) | |||||||
\(104\) | 1.68984e6 | 1.50226 | ||||||||
\(105\) | −236729. | −0.204495 | ||||||||
\(106\) | − | 1.40837e6i | − | 1.18250i | ||||||
\(107\) | 1.51953e6 | 1.24039 | 0.620195 | − | 0.784448i | \(-0.287054\pi\) | ||||
0.620195 | + | 0.784448i | \(0.287054\pi\) | |||||||
\(108\) | 567249. | 0.450301 | ||||||||
\(109\) | 228264.i | 0.176262i | 0.996109 | + | 0.0881309i | \(0.0280894\pi\) | ||||
−0.996109 | + | 0.0881309i | \(0.971911\pi\) | |||||||
\(110\) | −2.23793e6 | −1.68139 | ||||||||
\(111\) | − | 395492.i | − | 0.289180i | ||||||
\(112\) | −1.34915e6 | −0.960298 | ||||||||
\(113\) | − | 287034.i | − | 0.198929i | −0.995041 | − | 0.0994643i | \(-0.968287\pi\) | ||
0.995041 | − | 0.0994643i | \(-0.0317129\pi\) | |||||||
\(114\) | 147543.i | 0.0995873i | ||||||||
\(115\) | − | 828596.i | − | 0.544815i | ||||||
\(116\) | −29126.5 | −0.0186601 | ||||||||
\(117\) | − | 327545.i | − | 0.204509i | ||||||
\(118\) | −1.96480e6 | − | 2.27060e6i | −1.19584 | − | 1.38195i | ||||
\(119\) | −53230.1 | −0.0315876 | ||||||||
\(120\) | 1.92365e6i | 1.11322i | ||||||||
\(121\) | −646729. | −0.365062 | ||||||||
\(122\) | 1.86000e6 | 1.02431 | ||||||||
\(123\) | 1.24253e6 | 0.667714 | ||||||||
\(124\) | − | 359835.i | − | 0.188729i | ||||||
\(125\) | 2.12231e6 | 1.08662 | ||||||||
\(126\) | 548107.i | 0.274002i | ||||||||
\(127\) | −447324. | −0.218379 | −0.109190 | − | 0.994021i | \(-0.534826\pi\) | ||||
−0.109190 | + | 0.994021i | \(0.534826\pi\) | |||||||
\(128\) | − | 1.05193e6i | − | 0.501599i | ||||||
\(129\) | 466650.i | 0.217381i | ||||||||
\(130\) | 1.93980e6 | 0.882931 | ||||||||
\(131\) | − | 2.31531e6i | − | 1.02990i | −0.857220 | − | 0.514950i | \(-0.827811\pi\) | ||
0.857220 | − | 0.514950i | \(-0.172189\pi\) | |||||||
\(132\) | 3.63013e6i | 1.57834i | ||||||||
\(133\) | −99878.0 | −0.0424537 | ||||||||
\(134\) | 5.86884e6 | 2.43915 | ||||||||
\(135\) | 372863. | 0.151547 | ||||||||
\(136\) | 432546.i | 0.171955i | ||||||||
\(137\) | 3.74495e6 | 1.45641 | 0.728207 | − | 0.685358i | \(-0.240354\pi\) | ||||
0.728207 | + | 0.685358i | \(0.240354\pi\) | |||||||
\(138\) | −1.91848e6 | −0.729996 | ||||||||
\(139\) | 4.17555e6 | 1.55478 | 0.777391 | − | 0.629018i | \(-0.216543\pi\) | ||||
0.777391 | + | 0.629018i | \(0.216543\pi\) | |||||||
\(140\) | −2.27411e6 | −0.828758 | ||||||||
\(141\) | 2.50271e6i | 0.892798i | ||||||||
\(142\) | 1.58032e6i | 0.551926i | ||||||||
\(143\) | 2.09613e6 | 0.716820 | ||||||||
\(144\) | 2.12500e6 | 0.711659 | ||||||||
\(145\) | −19145.4 | −0.00628001 | ||||||||
\(146\) | 6.14782e6 | 1.97543 | ||||||||
\(147\) | 1.46293e6 | 0.460544 | ||||||||
\(148\) | − | 3.79926e6i | − | 1.17196i | ||||||
\(149\) | − | 1.07748e6i | − | 0.325725i | −0.986649 | − | 0.162862i | \(-0.947927\pi\) | ||
0.986649 | − | 0.162862i | \(-0.0520726\pi\) | |||||||
\(150\) | − | 1.35284e6i | − | 0.400841i | ||||||
\(151\) | − | 1.49993e6i | − | 0.435653i | −0.975987 | − | 0.217827i | \(-0.930103\pi\) | ||
0.975987 | − | 0.217827i | \(-0.0698967\pi\) | |||||||
\(152\) | 811606.i | 0.231108i | ||||||||
\(153\) | 83841.0 | 0.0234090 | ||||||||
\(154\) | −3.50763e6 | −0.960398 | ||||||||
\(155\) | − | 236526.i | − | 0.0635162i | ||||||
\(156\) | − | 3.14653e6i | − | 0.828816i | ||||||
\(157\) | − | 974234.i | − | 0.251747i | −0.992046 | − | 0.125874i | \(-0.959827\pi\) | ||
0.992046 | − | 0.125874i | \(-0.0401734\pi\) | |||||||
\(158\) | − | 2.38950e6i | − | 0.605808i | ||||||
\(159\) | −1.50165e6 | −0.373575 | ||||||||
\(160\) | 4.68705e6i | 1.14430i | ||||||||
\(161\) | − | 1.29870e6i | − | 0.311194i | ||||||
\(162\) | − | 863306.i | − | 0.203058i | ||||||
\(163\) | −4.02568e6 | −0.929557 | −0.464779 | − | 0.885427i | \(-0.653866\pi\) | ||||
−0.464779 | + | 0.885427i | \(0.653866\pi\) | |||||||
\(164\) | 1.19362e7 | 2.70605 | ||||||||
\(165\) | 2.38615e6i | 0.531185i | ||||||||
\(166\) | −1.03821e7 | −2.26966 | ||||||||
\(167\) | −4.64702e6 | −0.997758 | −0.498879 | − | 0.866672i | \(-0.666255\pi\) | ||||
−0.498879 | + | 0.866672i | \(0.666255\pi\) | |||||||
\(168\) | 3.01503e6i | 0.635864i | ||||||||
\(169\) | 3.00992e6 | 0.623584 | ||||||||
\(170\) | 496527.i | 0.101064i | ||||||||
\(171\) | 157315. | 0.0314616 | ||||||||
\(172\) | 4.48283e6i | 0.880982i | ||||||||
\(173\) | − | 3.95135e6i | − | 0.763146i | −0.924339 | − | 0.381573i | \(-0.875383\pi\) | ||
0.924339 | − | 0.381573i | \(-0.124617\pi\) | |||||||
\(174\) | 44328.1i | 0.00841456i | ||||||||
\(175\) | 915794. | 0.170877 | ||||||||
\(176\) | 1.35990e7i | 2.49442i | ||||||||
\(177\) | −2.42098e6 | + | 2.09493e6i | −0.436587 | + | 0.377790i | ||||
\(178\) | −5.92826e6 | −1.05116 | ||||||||
\(179\) | − | 1.26718e6i | − | 0.220943i | −0.993879 | − | 0.110472i | \(-0.964764\pi\) | ||
0.993879 | − | 0.110472i | \(-0.0352361\pi\) | |||||||
\(180\) | 3.58188e6 | 0.614177 | ||||||||
\(181\) | 295579. | 0.0498469 | 0.0249235 | − | 0.999689i | \(-0.492066\pi\) | ||||
0.0249235 | + | 0.999689i | \(0.492066\pi\) | |||||||
\(182\) | 3.04035e6 | 0.504324 | ||||||||
\(183\) | − | 1.98319e6i | − | 0.323601i | ||||||
\(184\) | −1.05532e7 | −1.69407 | ||||||||
\(185\) | − | 2.49732e6i | − | 0.394421i | ||||||
\(186\) | −547639. | −0.0851051 | ||||||||
\(187\) | 536543.i | 0.0820501i | ||||||||
\(188\) | 2.40421e7i | 3.61825i | ||||||||
\(189\) | 584408. | 0.0865627 | ||||||||
\(190\) | 931656.i | 0.135830i | ||||||||
\(191\) | 5.51720e6i | 0.791806i | 0.918292 | + | 0.395903i | \(0.129568\pi\) | ||||
−0.918292 | + | 0.395903i | \(0.870432\pi\) | |||||||
\(192\) | 2.12770e6 | 0.300612 | ||||||||
\(193\) | 1.00178e7 | 1.39347 | 0.696737 | − | 0.717326i | \(-0.254634\pi\) | ||||
0.696737 | + | 0.717326i | \(0.254634\pi\) | |||||||
\(194\) | −5.36502e6 | −0.734796 | ||||||||
\(195\) | − | 2.06827e6i | − | 0.278936i | ||||||
\(196\) | 1.40535e7 | 1.86645 | ||||||||
\(197\) | −7.50245e6 | −0.981306 | −0.490653 | − | 0.871355i | \(-0.663242\pi\) | ||||
−0.490653 | + | 0.871355i | \(0.663242\pi\) | |||||||
\(198\) | 5.52475e6 | 0.711733 | ||||||||
\(199\) | 2.22620e6 | 0.282492 | 0.141246 | − | 0.989975i | \(-0.454889\pi\) | ||||
0.141246 | + | 0.989975i | \(0.454889\pi\) | |||||||
\(200\) | − | 7.44171e6i | − | 0.930214i | ||||||
\(201\) | − | 6.25753e6i | − | 0.770575i | ||||||
\(202\) | −2.71741e6 | −0.329687 | ||||||||
\(203\) | −30007.6 | −0.00358709 | ||||||||
\(204\) | 805411. | 0.0948696 | ||||||||
\(205\) | 7.84591e6 | 0.910714 | ||||||||
\(206\) | −1.91540e7 | −2.19108 | ||||||||
\(207\) | 2.04554e6i | 0.230620i | ||||||||
\(208\) | − | 1.17874e7i | − | 1.30987i | ||||||
\(209\) | 1.00674e6i | 0.110275i | ||||||||
\(210\) | 3.46101e6i | 0.373719i | ||||||||
\(211\) | 5.41139e6i | 0.576052i | 0.957623 | + | 0.288026i | \(0.0929989\pi\) | ||||
−0.957623 | + | 0.288026i | \(0.907001\pi\) | |||||||
\(212\) | −1.44255e7 | −1.51399 | ||||||||
\(213\) | 1.68499e6 | 0.174364 | ||||||||
\(214\) | − | 2.22158e7i | − | 2.26684i | ||||||
\(215\) | 2.94665e6i | 0.296492i | ||||||||
\(216\) | − | 4.74888e6i | − | 0.471227i | ||||||
\(217\) | − | 370720.i | − | 0.0362800i | ||||||
\(218\) | 3.33726e6 | 0.322122 | ||||||||
\(219\) | − | 6.55499e6i | − | 0.624079i | ||||||
\(220\) | 2.29223e7i | 2.15274i | ||||||||
\(221\) | − | 465066.i | − | 0.0430861i | ||||||
\(222\) | −5.78216e6 | −0.528483 | ||||||||
\(223\) | 1.88110e7 | 1.69628 | 0.848140 | − | 0.529772i | \(-0.177723\pi\) | ||||
0.848140 | + | 0.529772i | \(0.177723\pi\) | |||||||
\(224\) | 7.34626e6i | 0.653615i | ||||||||
\(225\) | −1.44244e6 | −0.126634 | ||||||||
\(226\) | −4.19648e6 | −0.363546 | ||||||||
\(227\) | 9.53659e6i | 0.815297i | 0.913139 | + | 0.407648i | \(0.133651\pi\) | ||||
−0.913139 | + | 0.407648i | \(0.866349\pi\) | |||||||
\(228\) | 1.51123e6 | 0.127505 | ||||||||
\(229\) | 8.14845e6i | 0.678529i | 0.940691 | + | 0.339264i | \(0.110178\pi\) | ||||
−0.940691 | + | 0.339264i | \(0.889822\pi\) | |||||||
\(230\) | −1.21142e7 | −0.995661 | ||||||||
\(231\) | 3.73994e6i | 0.303409i | ||||||||
\(232\) | 243841.i | 0.0195273i | ||||||||
\(233\) | 7.11460e6i | 0.562449i | 0.959642 | + | 0.281224i | \(0.0907405\pi\) | ||||
−0.959642 | + | 0.281224i | \(0.909260\pi\) | |||||||
\(234\) | −4.78876e6 | −0.373745 | ||||||||
\(235\) | 1.58033e7i | 1.21771i | ||||||||
\(236\) | −2.32569e7 | + | 2.01248e7i | −1.76936 | + | 1.53107i | ||||
\(237\) | −2.54775e6 | −0.191387 | ||||||||
\(238\) | 778232.i | 0.0577269i | ||||||||
\(239\) | −2.18707e6 | −0.160202 | −0.0801010 | − | 0.996787i | \(-0.525524\pi\) | ||||
−0.0801010 | + | 0.996787i | \(0.525524\pi\) | |||||||
\(240\) | 1.34183e7 | 0.970650 | ||||||||
\(241\) | 1.04964e7 | 0.749872 | 0.374936 | − | 0.927051i | \(-0.377665\pi\) | ||||
0.374936 | + | 0.927051i | \(0.377665\pi\) | |||||||
\(242\) | 9.45528e6i | 0.667158i | ||||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | − | 1.90513e7i | − | 1.31146i | ||||||
\(245\) | 9.23763e6 | 0.628149 | ||||||||
\(246\) | − | 1.81660e7i | − | 1.22026i | ||||||
\(247\) | − | 872624.i | − | 0.0579077i | ||||||
\(248\) | −3.01246e6 | −0.197500 | ||||||||
\(249\) | 1.10697e7i | 0.717032i | ||||||||
\(250\) | − | 3.10285e7i | − | 1.98582i | ||||||
\(251\) | −2.38289e7 | −1.50689 | −0.753447 | − | 0.657509i | \(-0.771610\pi\) | ||||
−0.753447 | + | 0.657509i | \(0.771610\pi\) | |||||||
\(252\) | 5.61407e6 | 0.350813 | ||||||||
\(253\) | −1.30905e7 | −0.808342 | ||||||||
\(254\) | 6.53995e6i | 0.399092i | ||||||||
\(255\) | 529412. | 0.0319281 | ||||||||
\(256\) | −2.41149e7 | −1.43736 | ||||||||
\(257\) | 1.58733e7 | 0.935122 | 0.467561 | − | 0.883961i | \(-0.345133\pi\) | ||||
0.467561 | + | 0.883961i | \(0.345133\pi\) | |||||||
\(258\) | 6.82249e6 | 0.397268 | ||||||||
\(259\) | − | 3.91419e6i | − | 0.225290i | ||||||
\(260\) | − | 1.98687e7i | − | 1.13044i | ||||||
\(261\) | 47264.0 | 0.00265833 | ||||||||
\(262\) | −3.38502e7 | −1.88216 | ||||||||
\(263\) | 3.26353e7 | 1.79399 | 0.896995 | − | 0.442041i | \(-0.145745\pi\) | ||||
0.896995 | + | 0.442041i | \(0.145745\pi\) | |||||||
\(264\) | 3.03906e7 | 1.65169 | ||||||||
\(265\) | −9.48213e6 | −0.509528 | ||||||||
\(266\) | 1.46023e6i | 0.0775849i | ||||||||
\(267\) | 6.32089e6i | 0.332081i | ||||||||
\(268\) | − | 6.01124e7i | − | 3.12291i | ||||||
\(269\) | − | 1.73683e7i | − | 0.892277i | −0.894964 | − | 0.446138i | \(-0.852799\pi\) | ||
0.894964 | − | 0.446138i | \(-0.147201\pi\) | |||||||
\(270\) | − | 5.45132e6i | − | 0.276956i | ||||||
\(271\) | −1.53995e7 | −0.773746 | −0.386873 | − | 0.922133i | \(-0.626445\pi\) | ||||
−0.386873 | + | 0.922133i | \(0.626445\pi\) | |||||||
\(272\) | 3.01719e6 | 0.149933 | ||||||||
\(273\) | − | 3.24171e6i | − | 0.159326i | ||||||
\(274\) | − | 5.47518e7i | − | 2.66163i | ||||||
\(275\) | − | 9.23092e6i | − | 0.443861i | ||||||
\(276\) | 1.96503e7i | 0.934636i | ||||||||
\(277\) | 1.44727e7 | 0.680941 | 0.340470 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340470 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(278\) | − | 6.10472e7i | − | 2.84140i | ||||||
\(279\) | 583909.i | 0.0268864i | ||||||||
\(280\) | 1.90384e7i | 0.867272i | ||||||||
\(281\) | 2.79711e6 | 0.126064 | 0.0630319 | − | 0.998012i | \(-0.479923\pi\) | ||||
0.0630319 | + | 0.998012i | \(0.479923\pi\) | |||||||
\(282\) | 3.65900e7 | 1.63161 | ||||||||
\(283\) | 2.68560e7i | 1.18490i | 0.805607 | + | 0.592451i | \(0.201840\pi\) | ||||
−0.805607 | + | 0.592451i | \(0.798160\pi\) | |||||||
\(284\) | 1.61867e7 | 0.706648 | ||||||||
\(285\) | 993360. | 0.0429113 | ||||||||
\(286\) | − | 3.06458e7i | − | 1.31000i | ||||||
\(287\) | 1.22973e7 | 0.520193 | ||||||||
\(288\) | − | 1.15708e7i | − | 0.484382i | ||||||
\(289\) | −2.40185e7 | −0.995068 | ||||||||
\(290\) | 279909.i | 0.0114768i | ||||||||
\(291\) | 5.72035e6i | 0.232137i | ||||||||
\(292\) | − | 6.29700e7i | − | 2.52921i | ||||||
\(293\) | 2.53416e7 | 1.00747 | 0.503735 | − | 0.863858i | \(-0.331959\pi\) | ||||
0.503735 | + | 0.863858i | \(0.331959\pi\) | |||||||
\(294\) | − | 2.13883e7i | − | 0.841654i | ||||||
\(295\) | −1.52872e7 | + | 1.32284e7i | −0.595473 | + | 0.515277i | ||||
\(296\) | −3.18065e7 | −1.22643 | ||||||||
\(297\) | − | 5.89066e6i | − | 0.224851i | ||||||
\(298\) | −1.57529e7 | −0.595268 | ||||||||
\(299\) | 1.13466e7 | 0.424476 | ||||||||
\(300\) | −1.38567e7 | −0.513209 | ||||||||
\(301\) | 4.61843e6i | 0.169354i | ||||||||
\(302\) | −2.19293e7 | −0.796165 | ||||||||
\(303\) | 2.89739e6i | 0.104155i | ||||||||
\(304\) | 5.66130e6 | 0.201509 | ||||||||
\(305\) | − | 1.25228e7i | − | 0.441368i | ||||||
\(306\) | − | 1.22577e6i | − | 0.0427803i | ||||||
\(307\) | 2.71219e7 | 0.937359 | 0.468679 | − | 0.883368i | \(-0.344730\pi\) | ||||
0.468679 | + | 0.883368i | \(0.344730\pi\) | |||||||
\(308\) | 3.59274e7i | 1.22963i | ||||||||
\(309\) | 2.04226e7i | 0.692205i | ||||||||
\(310\) | −3.45805e6 | −0.116077 | ||||||||
\(311\) | −1.23118e7 | −0.409300 | −0.204650 | − | 0.978835i | \(-0.565606\pi\) | ||||
−0.204650 | + | 0.978835i | \(0.565606\pi\) | |||||||
\(312\) | −2.63420e7 | −0.867332 | ||||||||
\(313\) | 1.98794e7i | 0.648290i | 0.946007 | + | 0.324145i | \(0.105077\pi\) | ||||
−0.946007 | + | 0.324145i | \(0.894923\pi\) | |||||||
\(314\) | −1.42435e7 | −0.460073 | ||||||||
\(315\) | 3.69023e6 | 0.118065 | ||||||||
\(316\) | −2.44748e7 | −0.775635 | ||||||||
\(317\) | 6.74191e6 | 0.211644 | 0.105822 | − | 0.994385i | \(-0.466253\pi\) | ||||
0.105822 | + | 0.994385i | \(0.466253\pi\) | |||||||
\(318\) | 2.19544e7i | 0.682715i | ||||||||
\(319\) | 302467.i | 0.00931764i | ||||||||
\(320\) | 1.34353e7 | 0.410013 | ||||||||
\(321\) | −2.36871e7 | −0.716139 | ||||||||
\(322\) | −1.89872e7 | −0.568714 | ||||||||
\(323\) | 223364. | 0.00662835 | ||||||||
\(324\) | −8.84254e6 | −0.259981 | ||||||||
\(325\) | 8.00120e6i | 0.233080i | ||||||||
\(326\) | 5.88561e7i | 1.69879i | ||||||||
\(327\) | − | 3.55829e6i | − | 0.101765i | ||||||
\(328\) | − | 9.99275e7i | − | 2.83181i | ||||||
\(329\) | 2.47694e7i | 0.695548i | ||||||||
\(330\) | 3.48859e7 | 0.970752 | ||||||||
\(331\) | −5.11403e7 | −1.41019 | −0.705097 | − | 0.709110i | \(-0.749097\pi\) | ||||
−0.705097 | + | 0.709110i | \(0.749097\pi\) | |||||||
\(332\) | 1.06340e8i | 2.90592i | ||||||||
\(333\) | 6.16511e6i | 0.166958i | ||||||||
\(334\) | 6.79402e7i | 1.82342i | ||||||||
\(335\) | − | 3.95130e7i | − | 1.05101i | ||||||
\(336\) | 2.10312e7 | 0.554428 | ||||||||
\(337\) | 3.66422e7i | 0.957397i | 0.877979 | + | 0.478698i | \(0.158891\pi\) | ||||
−0.877979 | + | 0.478698i | \(0.841109\pi\) | |||||||
\(338\) | − | 4.40055e7i | − | 1.13961i | ||||||
\(339\) | 4.47441e6i | 0.114852i | ||||||||
\(340\) | 5.08575e6 | 0.129395 | ||||||||
\(341\) | −3.73674e6 | −0.0942389 | ||||||||
\(342\) | − | 2.29997e6i | − | 0.0574967i | ||||||
\(343\) | 3.26294e7 | 0.808587 | ||||||||
\(344\) | 3.75292e7 | 0.921923 | ||||||||
\(345\) | 1.29165e7i | 0.314549i | ||||||||
\(346\) | −5.77694e7 | −1.39466 | ||||||||
\(347\) | 3.17394e7i | 0.759645i | 0.925059 | + | 0.379822i | \(0.124015\pi\) | ||||
−0.925059 | + | 0.379822i | \(0.875985\pi\) | |||||||
\(348\) | 454037. | 0.0107734 | ||||||||
\(349\) | − | 4.67911e7i | − | 1.10075i | −0.834919 | − | 0.550373i | \(-0.814486\pi\) | ||
0.834919 | − | 0.550373i | \(-0.185514\pi\) | |||||||
\(350\) | − | 1.33891e7i | − | 0.312281i | ||||||
\(351\) | 5.10591e6i | 0.118073i | ||||||||
\(352\) | 7.40480e7 | 1.69779 | ||||||||
\(353\) | 6.73316e7i | 1.53072i | 0.643605 | + | 0.765358i | \(0.277438\pi\) | ||||
−0.643605 | + | 0.765358i | \(0.722562\pi\) | |||||||
\(354\) | 3.06282e7 | + | 3.53951e7i | 0.690418 | + | 0.797872i | ||||
\(355\) | 1.06398e7 | 0.237820 | ||||||||
\(356\) | 6.07211e7i | 1.34583i | ||||||||
\(357\) | 829775. | 0.0182371 | ||||||||
\(358\) | −1.85264e7 | −0.403778 | ||||||||
\(359\) | 5.75944e7 | 1.24479 | 0.622397 | − | 0.782702i | \(-0.286159\pi\) | ||||
0.622397 | + | 0.782702i | \(0.286159\pi\) | |||||||
\(360\) | − | 2.99867e7i | − | 0.642719i | ||||||
\(361\) | −4.66268e7 | −0.991092 | ||||||||
\(362\) | − | 4.32142e6i | − | 0.0910963i | ||||||
\(363\) | 1.00815e7 | 0.210768 | ||||||||
\(364\) | − | 3.11412e7i | − | 0.645701i | ||||||
\(365\) | − | 4.13913e7i | − | 0.851199i | ||||||
\(366\) | −2.89945e7 | −0.591388 | ||||||||
\(367\) | 7.41560e7i | 1.50020i | 0.661326 | + | 0.750098i | \(0.269994\pi\) | ||||
−0.661326 | + | 0.750098i | \(0.730006\pi\) | |||||||
\(368\) | 7.36132e7i | 1.47711i | ||||||||
\(369\) | −1.93691e7 | −0.385505 | ||||||||
\(370\) | −3.65113e7 | −0.720812 | ||||||||
\(371\) | −1.48618e7 | −0.291039 | ||||||||
\(372\) | 5.60927e6i | 0.108963i | ||||||||
\(373\) | −4.34155e7 | −0.836600 | −0.418300 | − | 0.908309i | \(-0.637374\pi\) | ||||
−0.418300 | + | 0.908309i | \(0.637374\pi\) | |||||||
\(374\) | 7.84434e6 | 0.149948 | ||||||||
\(375\) | −3.30835e7 | −0.627361 | ||||||||
\(376\) | 2.01275e8 | 3.78640 | ||||||||
\(377\) | − | 262173.i | − | 0.00489287i | ||||||
\(378\) | − | 8.54415e6i | − | 0.158195i | ||||||
\(379\) | 3.61061e6 | 0.0663229 | 0.0331614 | − | 0.999450i | \(-0.489442\pi\) | ||||
0.0331614 | + | 0.999450i | \(0.489442\pi\) | |||||||
\(380\) | 9.54262e6 | 0.173907 | ||||||||
\(381\) | 6.97309e6 | 0.126081 | ||||||||
\(382\) | 8.06624e7 | 1.44704 | ||||||||
\(383\) | −6.55881e7 | −1.16742 | −0.583712 | − | 0.811961i | \(-0.698400\pi\) | ||||
−0.583712 | + | 0.811961i | \(0.698400\pi\) | |||||||
\(384\) | 1.63980e7i | 0.289598i | ||||||||
\(385\) | 2.36157e7i | 0.413828i | ||||||||
\(386\) | − | 1.46461e8i | − | 2.54660i | ||||||
\(387\) | − | 7.27435e6i | − | 0.125505i | ||||||
\(388\) | 5.49520e7i | 0.940781i | ||||||||
\(389\) | 8.08472e7 | 1.37346 | 0.686730 | − | 0.726912i | \(-0.259045\pi\) | ||||
0.686730 | + | 0.726912i | \(0.259045\pi\) | |||||||
\(390\) | −3.02385e7 | −0.509760 | ||||||||
\(391\) | 2.90437e6i | 0.0485872i | ||||||||
\(392\) | − | 1.17653e8i | − | 1.95319i | ||||||
\(393\) | 3.60921e7i | 0.594613i | ||||||||
\(394\) | 1.09687e8i | 1.79336i | ||||||||
\(395\) | −1.60877e7 | −0.261038 | ||||||||
\(396\) | − | 5.65881e7i | − | 0.911254i | ||||||
\(397\) | 1.19035e8i | 1.90241i | 0.308562 | + | 0.951204i | \(0.400152\pi\) | ||||
−0.308562 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(398\) | − | 3.25475e7i | − | 0.516259i | ||||||
\(399\) | 1.55694e6 | 0.0245106 | ||||||||
\(400\) | −5.19091e7 | −0.811080 | ||||||||
\(401\) | − | 2.51016e7i | − | 0.389286i | −0.980874 | − | 0.194643i | \(-0.937645\pi\) | ||
0.980874 | − | 0.194643i | \(-0.0623548\pi\) | |||||||
\(402\) | −9.14861e7 | −1.40824 | ||||||||
\(403\) | 3.23894e6 | 0.0494867 | ||||||||
\(404\) | 2.78335e7i | 0.422108i | ||||||||
\(405\) | −5.81237e6 | −0.0874959 | ||||||||
\(406\) | 438716.i | 0.00655549i | ||||||||
\(407\) | −3.94538e7 | −0.585201 | ||||||||
\(408\) | − | 6.74272e6i | − | 0.0992784i | ||||||
\(409\) | 9.64133e7i | 1.40918i | 0.709614 | + | 0.704591i | \(0.248870\pi\) | ||||
−0.709614 | + | 0.704591i | \(0.751130\pi\) | |||||||
\(410\) | − | 1.14708e8i | − | 1.66435i | ||||||
\(411\) | −5.83780e7 | −0.840861 | ||||||||
\(412\) | 1.96188e8i | 2.80530i | ||||||||
\(413\) | −2.39604e7 | + | 2.07336e7i | −0.340130 | + | 0.294323i | ||||
\(414\) | 2.99062e7 | 0.421463 | ||||||||
\(415\) | 6.98994e7i | 0.977979i | ||||||||
\(416\) | −6.41835e7 | −0.891545 | ||||||||
\(417\) | −6.50904e7 | −0.897654 | ||||||||
\(418\) | 1.47187e7 | 0.201530 | ||||||||
\(419\) | − | 5.91334e7i | − | 0.803879i | −0.915666 | − | 0.401939i | \(-0.868336\pi\) | ||
0.915666 | − | 0.401939i | \(-0.131664\pi\) | |||||||
\(420\) | 3.54499e7 | 0.478484 | ||||||||
\(421\) | − | 5.51580e7i | − | 0.739201i | −0.929191 | − | 0.369600i | \(-0.879495\pi\) | ||
0.929191 | − | 0.369600i | \(-0.120505\pi\) | |||||||
\(422\) | 7.91154e7 | 1.05275 | ||||||||
\(423\) | − | 3.90134e7i | − | 0.515457i | ||||||
\(424\) | 1.20767e8i | 1.58435i | ||||||||
\(425\) | −2.04805e6 | −0.0266793 | ||||||||
\(426\) | − | 2.46348e7i | − | 0.318655i | ||||||
\(427\) | − | 1.96276e7i | − | 0.252106i | ||||||
\(428\) | −2.27548e8 | −2.90230 | ||||||||
\(429\) | −3.26754e7 | −0.413856 | ||||||||
\(430\) | 4.30805e7 | 0.541845 | ||||||||
\(431\) | − | 1.45357e8i | − | 1.81554i | −0.419470 | − | 0.907769i | \(-0.637784\pi\) | ||
0.419470 | − | 0.907769i | \(-0.362216\pi\) | |||||||
\(432\) | −3.31255e7 | −0.410876 | ||||||||
\(433\) | 3.15671e7 | 0.388840 | 0.194420 | − | 0.980918i | \(-0.437718\pi\) | ||||
0.194420 | + | 0.980918i | \(0.437718\pi\) | |||||||
\(434\) | −5.41999e6 | −0.0663024 | ||||||||
\(435\) | 298447. | 0.00362576 | ||||||||
\(436\) | − | 3.41824e7i | − | 0.412423i | ||||||
\(437\) | 5.44961e6i | 0.0653012i | ||||||||
\(438\) | −9.58351e7 | −1.14052 | ||||||||
\(439\) | 3.52974e7 | 0.417205 | 0.208602 | − | 0.978001i | \(-0.433109\pi\) | ||||
0.208602 | + | 0.978001i | \(0.433109\pi\) | |||||||
\(440\) | 1.91901e8 | 2.25278 | ||||||||
\(441\) | −2.28048e7 | −0.265895 | ||||||||
\(442\) | −6.79933e6 | −0.0787407 | ||||||||
\(443\) | 1.02025e7i | 0.117353i | 0.998277 | + | 0.0586766i | \(0.0186881\pi\) | ||||
−0.998277 | + | 0.0586766i | \(0.981312\pi\) | |||||||
\(444\) | 5.92246e7i | 0.676633i | ||||||||
\(445\) | 3.99131e7i | 0.452934i | ||||||||
\(446\) | − | 2.75020e8i | − | 3.09999i | ||||||
\(447\) | 1.67963e7i | 0.188057i | ||||||||
\(448\) | 2.10579e7 | 0.234197 | ||||||||
\(449\) | 1.64804e8 | 1.82066 | 0.910330 | − | 0.413884i | \(-0.135828\pi\) | ||||
0.910330 | + | 0.413884i | \(0.135828\pi\) | |||||||
\(450\) | 2.10887e7i | 0.231426i | ||||||||
\(451\) | − | 1.23953e8i | − | 1.35122i | ||||||
\(452\) | 4.29830e7i | 0.465459i | ||||||||
\(453\) | 2.33816e7i | 0.251525i | ||||||||
\(454\) | 1.39427e8 | 1.48997 | ||||||||
\(455\) | − | 2.04697e7i | − | 0.217309i | ||||||
\(456\) | − | 1.26517e7i | − | 0.133430i | ||||||
\(457\) | − | 1.21465e8i | − | 1.27263i | −0.771428 | − | 0.636317i | \(-0.780457\pi\) | ||
0.771428 | − | 0.636317i | \(-0.219543\pi\) | |||||||
\(458\) | 1.19132e8 | 1.24003 | ||||||||
\(459\) | −1.30695e6 | −0.0135152 | ||||||||
\(460\) | 1.24082e8i | 1.27478i | ||||||||
\(461\) | 1.25615e8 | 1.28215 | 0.641073 | − | 0.767480i | \(-0.278490\pi\) | ||||
0.641073 | + | 0.767480i | \(0.278490\pi\) | |||||||
\(462\) | 5.46785e7 | 0.554486 | ||||||||
\(463\) | − | 9.50535e7i | − | 0.957690i | −0.877899 | − | 0.478845i | \(-0.841056\pi\) | ||
0.877899 | − | 0.478845i | \(-0.158944\pi\) | |||||||
\(464\) | 1.70089e6 | 0.0170264 | ||||||||
\(465\) | 3.68708e6i | 0.0366711i | ||||||||
\(466\) | 1.04017e8 | 1.02789 | ||||||||
\(467\) | − | 1.11809e8i | − | 1.09781i | −0.835884 | − | 0.548906i | \(-0.815045\pi\) | ||
0.835884 | − | 0.548906i | \(-0.184955\pi\) | |||||||
\(468\) | 4.90495e7i | 0.478517i | ||||||||
\(469\) | − | 6.19308e7i | − | 0.600328i | ||||||
\(470\) | 2.31047e8 | 2.22539 | ||||||||
\(471\) | 1.51868e7i | 0.145346i | ||||||||
\(472\) | 1.68480e8 | + | 1.94702e8i | 1.60222 | + | 1.85159i | ||||
\(473\) | 4.65524e7 | 0.439905 | ||||||||
\(474\) | 3.72486e7i | 0.349763i | ||||||||
\(475\) | −3.84285e6 | −0.0358569 | ||||||||
\(476\) | 7.97116e6 | 0.0739095 | ||||||||
\(477\) | 2.34084e7 | 0.215683 | ||||||||
\(478\) | 3.19753e7i | 0.292773i | ||||||||
\(479\) | 1.79395e8 | 1.63231 | 0.816157 | − | 0.577831i | \(-0.196101\pi\) | ||||
0.816157 | + | 0.577831i | \(0.196101\pi\) | |||||||
\(480\) | − | 7.30638e7i | − | 0.660661i | ||||||
\(481\) | 3.41978e7 | 0.307301 | ||||||||
\(482\) | − | 1.53458e8i | − | 1.37041i | ||||||
\(483\) | 2.02448e7i | 0.179668i | ||||||||
\(484\) | 9.68471e7 | 0.854182 | ||||||||
\(485\) | 3.61210e7i | 0.316617i | ||||||||
\(486\) | 1.34576e7i | 0.117235i | ||||||||
\(487\) | 5.56871e6 | 0.0482134 | 0.0241067 | − | 0.999709i | \(-0.492326\pi\) | ||||
0.0241067 | + | 0.999709i | \(0.492326\pi\) | |||||||
\(488\) | −1.59493e8 | −1.37241 | ||||||||
\(489\) | 6.27541e7 | 0.536680 | ||||||||
\(490\) | − | 1.35056e8i | − | 1.14795i | ||||||
\(491\) | −1.62969e8 | −1.37677 | −0.688384 | − | 0.725347i | \(-0.741679\pi\) | ||||
−0.688384 | + | 0.725347i | \(0.741679\pi\) | |||||||
\(492\) | −1.86067e8 | −1.56234 | ||||||||
\(493\) | 67107.9 | 0.000560058 | ||||||||
\(494\) | −1.27579e7 | −0.105827 | ||||||||
\(495\) | − | 3.71964e7i | − | 0.306680i | ||||||
\(496\) | 2.10132e7i | 0.172206i | ||||||||
\(497\) | 1.66763e7 | 0.135841 | ||||||||
\(498\) | 1.61841e8 | 1.31039 | ||||||||
\(499\) | −1.15293e8 | −0.927897 | −0.463949 | − | 0.885862i | \(-0.653568\pi\) | ||||
−0.463949 | + | 0.885862i | \(0.653568\pi\) | |||||||
\(500\) | −3.17814e8 | −2.54251 | ||||||||
\(501\) | 7.24399e7 | 0.576056 | ||||||||
\(502\) | 3.48382e8i | 2.75388i | ||||||||
\(503\) | 5.21389e7i | 0.409693i | 0.978794 | + | 0.204846i | \(0.0656694\pi\) | ||||
−0.978794 | + | 0.204846i | \(0.934331\pi\) | |||||||
\(504\) | − | 4.69997e7i | − | 0.367116i | ||||||
\(505\) | 1.82955e7i | 0.142059i | ||||||||
\(506\) | 1.91385e8i | 1.47726i | ||||||||
\(507\) | −4.69200e7 | −0.360026 | ||||||||
\(508\) | 6.69864e7 | 0.510970 | ||||||||
\(509\) | − | 2.31503e8i | − | 1.75551i | −0.479107 | − | 0.877757i | \(-0.659039\pi\) | ||
0.479107 | − | 0.877757i | \(-0.340961\pi\) | |||||||
\(510\) | − | 7.74008e6i | − | 0.0583492i | ||||||
\(511\) | − | 6.48748e7i | − | 0.486198i | ||||||
\(512\) | 2.85240e8i | 2.12520i | ||||||||
\(513\) | −2.45229e6 | −0.0181644 | ||||||||
\(514\) | − | 2.32070e8i | − | 1.70895i | ||||||
\(515\) | 1.28958e8i | 0.944117i | ||||||||
\(516\) | − | 6.98804e7i | − | 0.508635i | ||||||
\(517\) | 2.49667e8 | 1.80672 | ||||||||
\(518\) | −5.72260e7 | −0.411722 | ||||||||
\(519\) | 6.15955e7i | 0.440602i | ||||||||
\(520\) | −1.66336e8 | −1.18298 | ||||||||
\(521\) | −1.05626e8 | −0.746891 | −0.373445 | − | 0.927652i | \(-0.621824\pi\) | ||||
−0.373445 | + | 0.927652i | \(0.621824\pi\) | |||||||
\(522\) | − | 691007.i | − | 0.00485815i | ||||||
\(523\) | 2.56497e7 | 0.179299 | 0.0896494 | − | 0.995973i | \(-0.471425\pi\) | ||||
0.0896494 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(524\) | 3.46715e8i | 2.40979i | ||||||||
\(525\) | −1.42758e7 | −0.0986559 | ||||||||
\(526\) | − | 4.77133e8i | − | 3.27855i | ||||||
\(527\) | 829066.i | 0.00566444i | ||||||||
\(528\) | − | 2.11988e8i | − | 1.44015i | ||||||
\(529\) | 7.71753e7 | 0.521328 | ||||||||
\(530\) | 1.38630e8i | 0.931173i | ||||||||
\(531\) | 3.77393e7 | − | 3.26567e7i | 0.252064 | − | 0.218117i | ||||
\(532\) | 1.49567e7 | 0.0993344 | ||||||||
\(533\) | 1.07440e8i | 0.709554i | ||||||||
\(534\) | 9.24124e7 | 0.606885 | ||||||||
\(535\) | −1.49572e8 | −0.976761 | ||||||||
\(536\) | −5.03248e8 | −3.26804 | ||||||||
\(537\) | 1.97535e7i | 0.127562i | ||||||||
\(538\) | −2.53927e8 | −1.63065 | ||||||||
\(539\) | − | 1.45940e8i | − | 0.931983i | ||||||
\(540\) | −5.58360e7 | −0.354595 | ||||||||
\(541\) | − | 3.67500e7i | − | 0.232095i | −0.993244 | − | 0.116047i | \(-0.962978\pi\) | ||
0.993244 | − | 0.116047i | \(-0.0370224\pi\) | |||||||
\(542\) | 2.25143e8i | 1.41404i | ||||||||
\(543\) | −4.60763e6 | −0.0287791 | ||||||||
\(544\) | − | 1.64289e7i | − | 0.102050i | ||||||
\(545\) | − | 2.24687e7i | − | 0.138800i | ||||||
\(546\) | −4.73943e7 | −0.291171 | ||||||||
\(547\) | 4.91319e7 | 0.300194 | 0.150097 | − | 0.988671i | \(-0.452041\pi\) | ||||
0.150097 | + | 0.988671i | \(0.452041\pi\) | |||||||
\(548\) | −5.60804e8 | −3.40776 | ||||||||
\(549\) | 3.09148e7i | 0.186831i | ||||||||
\(550\) | −1.34958e8 | −0.811165 | ||||||||
\(551\) | 125918. | 0.000752718 | ||||||||
\(552\) | 1.64508e8 | 0.978071 | ||||||||
\(553\) | −2.52151e7 | −0.149103 | ||||||||
\(554\) | − | 2.11593e8i | − | 1.24443i | ||||||
\(555\) | 3.89294e7i | 0.227719i | ||||||||
\(556\) | −6.25285e8 | −3.63793 | ||||||||
\(557\) | 2.64230e8 | 1.52903 | 0.764516 | − | 0.644605i | \(-0.222978\pi\) | ||||
0.764516 | + | 0.644605i | \(0.222978\pi\) | |||||||
\(558\) | 8.53685e6 | 0.0491355 | ||||||||
\(559\) | −4.03508e7 | −0.231002 | ||||||||
\(560\) | 1.32801e8 | 0.756200 | ||||||||
\(561\) | − | 8.36387e6i | − | 0.0473717i | ||||||
\(562\) | − | 4.08942e7i | − | 0.230384i | ||||||
\(563\) | − | 7.91202e7i | − | 0.443366i | −0.975119 | − | 0.221683i | \(-0.928845\pi\) | ||
0.975119 | − | 0.221683i | \(-0.0711550\pi\) | |||||||
\(564\) | − | 3.74779e8i | − | 2.08900i | ||||||
\(565\) | 2.82536e7i | 0.156649i | ||||||||
\(566\) | 3.92639e8 | 2.16543 | ||||||||
\(567\) | −9.11003e6 | −0.0499770 | ||||||||
\(568\) | − | 1.35511e8i | − | 0.739487i | ||||||
\(569\) | − | 1.27333e8i | − | 0.691199i | −0.938382 | − | 0.345600i | \(-0.887676\pi\) | ||
0.938382 | − | 0.345600i | \(-0.112324\pi\) | |||||||
\(570\) | − | 1.45231e7i | − | 0.0784213i | ||||||
\(571\) | − | 2.14936e7i | − | 0.115452i | −0.998332 | − | 0.0577258i | \(-0.981615\pi\) | ||
0.998332 | − | 0.0577258i | \(-0.0183849\pi\) | |||||||
\(572\) | −3.13894e8 | −1.67724 | ||||||||
\(573\) | − | 8.60047e7i | − | 0.457150i | ||||||
\(574\) | − | 1.79789e8i | − | 0.950663i | ||||||
\(575\) | − | 4.99681e7i | − | 0.262839i | ||||||
\(576\) | −3.31676e7 | −0.173559 | ||||||||
\(577\) | −1.75877e8 | −0.915549 | −0.457774 | − | 0.889068i | \(-0.651353\pi\) | ||||
−0.457774 | + | 0.889068i | \(0.651353\pi\) | |||||||
\(578\) | 3.51155e8i | 1.81851i | ||||||||
\(579\) | −1.56162e8 | −0.804523 | ||||||||
\(580\) | 2.86701e6 | 0.0146942 | ||||||||
\(581\) | 1.09557e8i | 0.558614i | ||||||||
\(582\) | 8.36325e7 | 0.424234 | ||||||||
\(583\) | 1.49803e8i | 0.755986i | ||||||||
\(584\) | −5.27171e8 | −2.64675 | ||||||||
\(585\) | 3.22412e7i | 0.161044i | ||||||||
\(586\) | − | 3.70499e8i | − | 1.84117i | ||||||
\(587\) | − | 3.63690e8i | − | 1.79811i | −0.437834 | − | 0.899056i | \(-0.644254\pi\) | ||
0.437834 | − | 0.899056i | \(-0.355746\pi\) | |||||||
\(588\) | −2.19072e8 | −1.07760 | ||||||||
\(589\) | 1.55562e6i | 0.00761301i | ||||||||
\(590\) | 1.93401e8 | + | 2.23501e8i | 0.941680 | + | 1.08824i | ||||
\(591\) | 1.16952e8 | 0.566557 | ||||||||
\(592\) | 2.21864e8i | 1.06936i | ||||||||
\(593\) | −3.10986e7 | −0.149134 | −0.0745670 | − | 0.997216i | \(-0.523757\pi\) | ||||
−0.0745670 | + | 0.997216i | \(0.523757\pi\) | |||||||
\(594\) | −8.61223e7 | −0.410919 | ||||||||
\(595\) | 5.23959e6 | 0.0248741 | ||||||||
\(596\) | 1.61352e8i | 0.762140i | ||||||||
\(597\) | −3.47031e7 | −0.163097 | ||||||||
\(598\) | − | 1.65889e8i | − | 0.775738i | ||||||
\(599\) | −3.39747e8 | −1.58079 | −0.790397 | − | 0.612595i | \(-0.790126\pi\) | ||||
−0.790397 | + | 0.612595i | \(0.790126\pi\) | |||||||
\(600\) | 1.16005e8i | 0.537059i | ||||||||
\(601\) | 3.43788e8i | 1.58368i | 0.610728 | + | 0.791840i | \(0.290877\pi\) | ||||
−0.610728 | + | 0.791840i | \(0.709123\pi\) | |||||||
\(602\) | 6.75223e7 | 0.309498 | ||||||||
\(603\) | 9.75453e7i | 0.444892i | ||||||||
\(604\) | 2.24614e8i | 1.01935i | ||||||||
\(605\) | 6.36594e7 | 0.287473 | ||||||||
\(606\) | 4.23603e7 | 0.190345 | ||||||||
\(607\) | 2.24070e7 | 0.100188 | 0.0500942 | − | 0.998744i | \(-0.484048\pi\) | ||||
0.0500942 | + | 0.998744i | \(0.484048\pi\) | |||||||
\(608\) | − | 3.08263e7i | − | 0.137155i | ||||||
\(609\) | 467772. | 0.00207101 | ||||||||
\(610\) | −1.83085e8 | −0.806610 | ||||||||
\(611\) | −2.16407e8 | −0.948742 | ||||||||
\(612\) | −1.25551e7 | −0.0547730 | ||||||||
\(613\) | − | 9.41425e7i | − | 0.408700i | −0.978898 | − | 0.204350i | \(-0.934492\pi\) | ||
0.978898 | − | 0.204350i | \(-0.0655080\pi\) | |||||||
\(614\) | − | 3.96527e8i | − | 1.71304i | ||||||
\(615\) | −1.22306e8 | −0.525801 | ||||||||
\(616\) | 3.00776e8 | 1.28677 | ||||||||
\(617\) | 6.71253e7 | 0.285779 | 0.142890 | − | 0.989739i | \(-0.454361\pi\) | ||||
0.142890 | + | 0.989739i | \(0.454361\pi\) | |||||||
\(618\) | 2.98581e8 | 1.26502 | ||||||||
\(619\) | −2.50796e8 | −1.05742 | −0.528712 | − | 0.848801i | \(-0.677325\pi\) | ||||
−0.528712 | + | 0.848801i | \(0.677325\pi\) | |||||||
\(620\) | 3.54196e7i | 0.148617i | ||||||||
\(621\) | − | 3.18869e7i | − | 0.133149i | ||||||
\(622\) | 1.80001e8i | 0.748004i | ||||||||
\(623\) | 6.25579e7i | 0.258713i | ||||||||
\(624\) | 1.83747e8i | 0.756252i | ||||||||
\(625\) | −1.16156e8 | −0.475774 | ||||||||
\(626\) | 2.90639e8 | 1.18476 | ||||||||
\(627\) | − | 1.56935e7i | − | 0.0636675i | ||||||
\(628\) | 1.45891e8i | 0.589046i | ||||||||
\(629\) | 8.75355e6i | 0.0351749i | ||||||||
\(630\) | − | 5.39518e7i | − | 0.215767i | ||||||
\(631\) | 3.43892e8 | 1.36878 | 0.684391 | − | 0.729115i | \(-0.260068\pi\) | ||||
0.684391 | + | 0.729115i | \(0.260068\pi\) | |||||||
\(632\) | 2.04897e8i | 0.811680i | ||||||||
\(633\) | − | 8.43552e7i | − | 0.332584i | ||||||
\(634\) | − | 9.85679e7i | − | 0.386783i | ||||||
\(635\) | 4.40314e7 | 0.171966 | ||||||||
\(636\) | 2.24871e8 | 0.874101 | ||||||||
\(637\) | 1.26498e8i | 0.489402i | ||||||||
\(638\) | 4.42212e6 | 0.0170282 | ||||||||
\(639\) | −2.62664e7 | −0.100669 | ||||||||
\(640\) | 1.03545e8i | 0.394991i | ||||||||
\(641\) | 1.75124e8 | 0.664922 | 0.332461 | − | 0.943117i | \(-0.392121\pi\) | ||||
0.332461 | + | 0.943117i | \(0.392121\pi\) | |||||||
\(642\) | 3.46310e8i | 1.30876i | ||||||||
\(643\) | 2.40631e8 | 0.905144 | 0.452572 | − | 0.891728i | \(-0.350507\pi\) | ||||
0.452572 | + | 0.891728i | \(0.350507\pi\) | |||||||
\(644\) | 1.94479e8i | 0.728142i | ||||||||
\(645\) | − | 4.59337e7i | − | 0.171180i | ||||||
\(646\) | − | 3.26562e6i | − | 0.0121134i | ||||||
\(647\) | 2.99942e8 | 1.10745 | 0.553726 | − | 0.832699i | \(-0.313206\pi\) | ||||
0.553726 | + | 0.832699i | \(0.313206\pi\) | |||||||
\(648\) | 7.40278e7i | 0.272063i | ||||||||
\(649\) | 2.08988e8 | + | 2.41514e8i | 0.764516 | + | 0.883502i | ||||
\(650\) | 1.16979e8 | 0.425958 | ||||||||
\(651\) | 5.77896e6i | 0.0209463i | ||||||||
\(652\) | 6.02842e8 | 2.17501 | ||||||||
\(653\) | 1.69558e8 | 0.608947 | 0.304473 | − | 0.952521i | \(-0.401520\pi\) | ||||
0.304473 | + | 0.952521i | \(0.401520\pi\) | |||||||
\(654\) | −5.20227e7 | −0.185977 | ||||||||
\(655\) | 2.27903e8i | 0.811008i | ||||||||
\(656\) | −6.97037e8 | −2.46913 | ||||||||
\(657\) | 1.02182e8i | 0.360312i | ||||||||
\(658\) | 3.62132e8 | 1.27113 | ||||||||
\(659\) | − | 4.22378e8i | − | 1.47586i | −0.674878 | − | 0.737929i | \(-0.735804\pi\) | ||
0.674878 | − | 0.737929i | \(-0.264196\pi\) | |||||||
\(660\) | − | 3.57324e8i | − | 1.24288i | ||||||
\(661\) | 3.36981e8 | 1.16681 | 0.583407 | − | 0.812180i | \(-0.301719\pi\) | ||||
0.583407 | + | 0.812180i | \(0.301719\pi\) | |||||||
\(662\) | 7.47679e8i | 2.57716i | ||||||||
\(663\) | 7.24965e6i | 0.0248758i | ||||||||
\(664\) | 8.90257e8 | 3.04096 | ||||||||
\(665\) | 9.83129e6 | 0.0334307 | ||||||||
\(666\) | 9.01349e7 | 0.305120 | ||||||||
\(667\) | 1.63729e6i | 0.00551758i | ||||||||
\(668\) | 6.95887e8 | 2.33458 | ||||||||
\(669\) | −2.93235e8 | −0.979348 | ||||||||
\(670\) | −5.77687e8 | −1.92074 | ||||||||
\(671\) | −1.97840e8 | −0.654858 | ||||||||
\(672\) | − | 1.14517e8i | − | 0.377365i | ||||||
\(673\) | − | 5.80418e8i | − | 1.90413i | −0.305900 | − | 0.952064i | \(-0.598957\pi\) | ||
0.305900 | − | 0.952064i | \(-0.401043\pi\) | |||||||
\(674\) | 5.35715e8 | 1.74966 | ||||||||
\(675\) | 2.24854e7 | 0.0731120 | ||||||||
\(676\) | −4.50733e8 | −1.45908 | ||||||||
\(677\) | −2.93634e8 | −0.946326 | −0.473163 | − | 0.880975i | \(-0.656888\pi\) | ||||
−0.473163 | + | 0.880975i | \(0.656888\pi\) | |||||||
\(678\) | 6.54166e7 | 0.209893 | ||||||||
\(679\) | 5.66144e7i | 0.180849i | ||||||||
\(680\) | − | 4.25767e7i | − | 0.135408i | ||||||
\(681\) | − | 1.48661e8i | − | 0.470712i | ||||||
\(682\) | 5.46318e7i | 0.172224i | ||||||||
\(683\) | − | 1.75942e8i | − | 0.552214i | −0.961127 | − | 0.276107i | \(-0.910956\pi\) | ||
0.961127 | − | 0.276107i | \(-0.0890444\pi\) | |||||||
\(684\) | −2.35577e7 | −0.0736148 | ||||||||
\(685\) | −3.68627e8 | −1.14687 | ||||||||
\(686\) | − | 4.77047e8i | − | 1.47771i | ||||||
\(687\) | − | 1.27022e8i | − | 0.391749i | ||||||
\(688\) | − | 2.61783e8i | − | 0.803851i | ||||||
\(689\) | − | 1.29846e8i | − | 0.396983i | ||||||
\(690\) | 1.88842e8 | 0.574845 | ||||||||
\(691\) | − | 2.69736e8i | − | 0.817531i | −0.912639 | − | 0.408766i | \(-0.865959\pi\) | ||
0.912639 | − | 0.408766i | \(-0.134041\pi\) | |||||||
\(692\) | 5.91712e8i | 1.78563i | ||||||||
\(693\) | − | 5.82999e7i | − | 0.175173i | ||||||
\(694\) | 4.64035e8 | 1.38827 | ||||||||
\(695\) | −4.11012e8 | −1.22433 | ||||||||
\(696\) | − | 3.80110e6i | − | 0.0112741i | ||||||
\(697\) | −2.75013e7 | −0.0812184 | ||||||||
\(698\) | −6.84094e8 | −2.01164 | ||||||||
\(699\) | − | 1.10906e8i | − | 0.324730i | ||||||
\(700\) | −1.37139e8 | −0.399823 | ||||||||
\(701\) | 3.13562e8i | 0.910267i | 0.890423 | + | 0.455133i | \(0.150408\pi\) | ||||
−0.890423 | + | 0.455133i | \(0.849592\pi\) | |||||||
\(702\) | 7.46493e7 | 0.215782 | ||||||||
\(703\) | 1.64247e7i | 0.0472750i | ||||||||
\(704\) | − | 2.12257e8i | − | 0.608336i | ||||||
\(705\) | − | 2.46349e8i | − | 0.703046i | ||||||
\(706\) | 9.84399e8 | 2.79742 | ||||||||
\(707\) | 2.86755e7i | 0.0811432i | ||||||||
\(708\) | 3.62539e8 | − | 3.13714e8i | 1.02154 | − | 0.883964i | ||||
\(709\) | 5.67397e8 | 1.59202 | 0.796010 | − | 0.605284i | \(-0.206940\pi\) | ||||
0.796010 | + | 0.605284i | \(0.206940\pi\) | |||||||
\(710\) | − | 1.55556e8i | − | 0.434621i | ||||||
\(711\) | 3.97155e7 | 0.110497 | ||||||||
\(712\) | 5.08343e8 | 1.40837 | ||||||||
\(713\) | −2.02275e7 | −0.0558050 | ||||||||
\(714\) | − | 1.21314e7i | − | 0.0333287i | ||||||
\(715\) | −2.06328e8 | −0.564470 | ||||||||
\(716\) | 1.89760e8i | 0.516970i | ||||||||
\(717\) | 3.40930e7 | 0.0924927 | ||||||||
\(718\) | − | 8.42040e8i | − | 2.27489i | ||||||
\(719\) | − | 6.89644e8i | − | 1.85540i | −0.373324 | − | 0.927701i | \(-0.621782\pi\) | ||
0.373324 | − | 0.927701i | \(-0.378218\pi\) | |||||||
\(720\) | −2.09170e8 | −0.560405 | ||||||||
\(721\) | 2.02122e8i | 0.539273i | ||||||||
\(722\) | 6.81691e8i | 1.81124i | ||||||||
\(723\) | −1.63622e8 | −0.432939 | ||||||||
\(724\) | −4.42628e7 | −0.116633 | ||||||||
\(725\) | −1.15456e6 | −0.00302971 | ||||||||
\(726\) | − | 1.47393e8i | − | 0.385184i | ||||||
\(727\) | 3.00693e8 | 0.782564 | 0.391282 | − | 0.920271i | \(-0.372032\pi\) | ||||
0.391282 | + | 0.920271i | \(0.372032\pi\) | |||||||
\(728\) | −2.60707e8 | −0.675708 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −6.05148e8 | −1.55558 | ||||||||
\(731\) | − | 1.03285e7i | − | 0.0264415i | ||||||
\(732\) | 2.96981e8i | 0.757172i | ||||||||
\(733\) | −3.35833e8 | −0.852729 | −0.426364 | − | 0.904551i | \(-0.640206\pi\) | ||||
−0.426364 | + | 0.904551i | \(0.640206\pi\) | |||||||
\(734\) | 1.08417e9 | 2.74164 | ||||||||
\(735\) | −1.44000e8 | −0.362662 | ||||||||
\(736\) | 4.00831e8 | 1.00537 | ||||||||
\(737\) | −6.24244e8 | −1.55938 | ||||||||
\(738\) | 2.83179e8i | 0.704518i | ||||||||
\(739\) | 6.36157e8i | 1.57627i | 0.615501 | + | 0.788136i | \(0.288954\pi\) | ||||
−0.615501 | + | 0.788136i | \(0.711046\pi\) | |||||||
\(740\) | 3.73972e8i | 0.922878i | ||||||||
\(741\) | 1.36029e7i | 0.0334330i | ||||||||
\(742\) | 2.17283e8i | 0.531879i | ||||||||
\(743\) | −5.72867e8 | −1.39665 | −0.698325 | − | 0.715781i | \(-0.746071\pi\) | ||||
−0.698325 | + | 0.715781i | \(0.746071\pi\) | |||||||
\(744\) | 4.69596e7 | 0.114026 | ||||||||
\(745\) | 1.06060e8i | 0.256496i | ||||||||
\(746\) | 6.34741e8i | 1.52890i | ||||||||
\(747\) | − | 1.72560e8i | − | 0.413978i | ||||||
\(748\) | − | 8.03468e7i | − | 0.191983i | ||||||
\(749\) | −2.34432e8 | −0.557919 | ||||||||
\(750\) | 4.83686e8i | 1.14652i | ||||||||
\(751\) | − | 3.15394e8i | − | 0.744619i | −0.928109 | − | 0.372310i | \(-0.878566\pi\) | ||
0.928109 | − | 0.372310i | \(-0.121434\pi\) | |||||||
\(752\) | − | 1.40398e9i | − | 3.30147i | ||||||
\(753\) | 3.71456e8 | 0.870006 | ||||||||
\(754\) | −3.83301e6 | −0.00894182 | ||||||||
\(755\) | 1.47643e8i | 0.343061i | ||||||||
\(756\) | −8.75147e7 | −0.202542 | ||||||||
\(757\) | −6.71386e8 | −1.54769 | −0.773847 | − | 0.633373i | \(-0.781670\pi\) | ||||
−0.773847 | + | 0.633373i | \(0.781670\pi\) | |||||||
\(758\) | − | 5.27878e7i | − | 0.121206i | ||||||
\(759\) | 2.04061e8 | 0.466696 | ||||||||
\(760\) | − | 7.98887e7i | − | 0.181989i | ||||||
\(761\) | −1.89435e8 | −0.429840 | −0.214920 | − | 0.976632i | \(-0.568949\pi\) | ||||
−0.214920 | + | 0.976632i | \(0.568949\pi\) | |||||||
\(762\) | − | 1.01948e8i | − | 0.230416i | ||||||
\(763\) | − | 3.52164e7i | − | 0.0792814i | ||||||
\(764\) | − | 8.26197e8i | − | 1.85269i | ||||||
\(765\) | −8.25271e6 | −0.0184337 | ||||||||
\(766\) | 9.58909e8i | 2.13349i | ||||||||
\(767\) | −1.81147e8 | − | 2.09340e8i | −0.401462 | − | 0.463944i | ||||
\(768\) | 3.75914e8 | 0.829859 | ||||||||
\(769\) | 1.56205e8i | 0.343492i | 0.985141 | + | 0.171746i | \(0.0549408\pi\) | ||||
−0.985141 | + | 0.171746i | \(0.945059\pi\) | |||||||
\(770\) | 3.45266e8 | 0.756278 | ||||||||
\(771\) | −2.47440e8 | −0.539893 | ||||||||
\(772\) | −1.50015e9 | −3.26049 | ||||||||
\(773\) | − | 3.30339e8i | − | 0.715190i | −0.933877 | − | 0.357595i | \(-0.883597\pi\) | ||
0.933877 | − | 0.357595i | \(-0.116403\pi\) | |||||||
\(774\) | −1.06352e8 | −0.229363 | ||||||||
\(775\) | − | 1.42636e7i | − | 0.0306426i | ||||||
\(776\) | 4.60046e8 | 0.984501 | ||||||||
\(777\) | 6.10161e7i | 0.130071i | ||||||||
\(778\) | − | 1.18200e9i | − | 2.51003i | ||||||
\(779\) | −5.16019e7 | −0.109158 | ||||||||
\(780\) | 3.09722e8i | 0.652662i | ||||||||
\(781\) | − | 1.68092e8i | − | 0.352854i | ||||||
\(782\) | 4.24624e7 | 0.0887941 | ||||||||
\(783\) | −736772. | −0.00153479 | ||||||||
\(784\) | −8.20679e8 | −1.70304 | ||||||||
\(785\) | 9.58967e7i | 0.198242i | ||||||||
\(786\) | 5.27672e8 | 1.08667 | ||||||||
\(787\) | −2.82997e8 | −0.580573 | −0.290287 | − | 0.956940i | \(-0.593751\pi\) | ||||
−0.290287 | + | 0.956940i | \(0.593751\pi\) | |||||||
\(788\) | 1.12349e9 | 2.29609 | ||||||||
\(789\) | −5.08734e8 | −1.03576 | ||||||||
\(790\) | 2.35205e8i | 0.477052i | ||||||||
\(791\) | 4.42833e7i | 0.0894768i | ||||||||
\(792\) | −4.73743e8 | −0.953602 | ||||||||
\(793\) | 1.71484e8 | 0.343878 | ||||||||
\(794\) | 1.74031e9 | 3.47669 | ||||||||
\(795\) | 1.47812e8 | 0.294176 | ||||||||
\(796\) | −3.33372e8 | −0.660983 | ||||||||
\(797\) | 6.47124e8i | 1.27824i | 0.769107 | + | 0.639120i | \(0.220701\pi\) | ||||
−0.769107 | + | 0.639120i | \(0.779299\pi\) | |||||||
\(798\) | − | 2.27628e7i | − | 0.0447937i | ||||||
\(799\) | − | 5.53933e7i | − | 0.108597i | ||||||
\(800\) | 2.82651e8i | 0.552052i | ||||||||
\(801\) | − | 9.85329e7i | − | 0.191727i | ||||||
\(802\) | −3.66990e8 | −0.711428 | ||||||||
\(803\) | −6.53918e8 | −1.26292 | ||||||||
\(804\) | 9.37060e8i | 1.80301i | ||||||||
\(805\) | 1.27835e8i | 0.245054i | ||||||||
\(806\) | − | 4.73539e7i | − | 0.0904379i | ||||||
\(807\) | 2.70744e8i | 0.515156i | ||||||||
\(808\) | 2.33016e8 | 0.441724 | ||||||||
\(809\) | 6.14882e8i | 1.16131i | 0.814151 | + | 0.580653i | \(0.197203\pi\) | ||||
−0.814151 | + | 0.580653i | \(0.802797\pi\) | |||||||
\(810\) | 8.49777e7i | 0.159901i | ||||||||
\(811\) | − | 4.14124e6i | − | 0.00776369i | −0.999992 | − | 0.00388185i | \(-0.998764\pi\) | ||
0.999992 | − | 0.00388185i | \(-0.00123563\pi\) | |||||||
\(812\) | 4.49361e6 | 0.00839319 | ||||||||
\(813\) | 2.40054e8 | 0.446722 | ||||||||
\(814\) | 5.76821e8i | 1.06947i | ||||||||
\(815\) | 3.96259e8 | 0.731993 | ||||||||
\(816\) | −4.70334e7 | −0.0865637 | ||||||||
\(817\) | − | 1.93799e7i | − | 0.0355373i | ||||||
\(818\) | 1.40958e9 | 2.57531 | ||||||||
\(819\) | 5.05333e7i | 0.0919869i | ||||||||
\(820\) | −1.17492e9 | −2.13092 | ||||||||
\(821\) | 5.97061e8i | 1.07892i | 0.842011 | + | 0.539460i | \(0.181372\pi\) | ||||
−0.842011 | + | 0.539460i | \(0.818628\pi\) | |||||||
\(822\) | 8.53496e8i | 1.53669i | ||||||||
\(823\) | 4.03704e8i | 0.724209i | 0.932138 | + | 0.362104i | \(0.117942\pi\) | ||||
−0.932138 | + | 0.362104i | \(0.882058\pi\) | |||||||
\(824\) | 1.64244e9 | 2.93567 | ||||||||
\(825\) | 1.43896e8i | 0.256263i | ||||||||
\(826\) | 3.03128e8 | + | 3.50305e8i | 0.537880 | + | 0.621594i | ||||
\(827\) | 8.05109e7 | 0.142344 | 0.0711718 | − | 0.997464i | \(-0.477326\pi\) | ||||
0.0711718 | + | 0.997464i | \(0.477326\pi\) | |||||||
\(828\) | − | 3.06318e8i | − | 0.539613i | ||||||
\(829\) | 4.07181e8 | 0.714700 | 0.357350 | − | 0.933971i | \(-0.383680\pi\) | ||||
0.357350 | + | 0.933971i | \(0.383680\pi\) | |||||||
\(830\) | 1.02194e9 | 1.78728 | ||||||||
\(831\) | −2.25607e8 | −0.393141 | ||||||||
\(832\) | 1.83980e8i | 0.319449i | ||||||||
\(833\) | −3.23795e7 | −0.0560190 | ||||||||
\(834\) | 9.51632e8i | 1.64048i | ||||||||
\(835\) | 4.57420e8 | 0.785698 | ||||||||
\(836\) | − | 1.50758e8i | − | 0.258026i | ||||||
\(837\) | − | 9.10225e6i | − | 0.0155229i | ||||||
\(838\) | −8.64539e8 | −1.46910 | ||||||||
\(839\) | 2.34397e8i | 0.396886i | 0.980112 | + | 0.198443i | \(0.0635884\pi\) | ||||
−0.980112 | + | 0.198443i | \(0.936412\pi\) | |||||||
\(840\) | − | 2.96779e8i | − | 0.500720i | ||||||
\(841\) | −5.94785e8 | −0.999936 | ||||||||
\(842\) | −8.06419e8 | −1.35090 | ||||||||
\(843\) | −4.36026e7 | −0.0727830 | ||||||||
\(844\) | − | 8.10351e8i | − | 1.34786i | ||||||
\(845\) | −2.96275e8 | −0.491050 | ||||||||
\(846\) | −5.70382e8 | −0.942009 | ||||||||
\(847\) | 9.97767e7 | 0.164202 | ||||||||
\(848\) | 8.42400e8 | 1.38144 | ||||||||
\(849\) | − | 4.18644e8i | − | 0.684103i | ||||||
\(850\) | 2.99428e7i | 0.0487569i | ||||||||
\(851\) | −2.13568e8 | −0.346536 | ||||||||
\(852\) | −2.52325e8 | −0.407983 | ||||||||
\(853\) | 2.85238e8 | 0.459579 | 0.229789 | − | 0.973240i | \(-0.426196\pi\) | ||||
0.229789 | + | 0.973240i | \(0.426196\pi\) | |||||||
\(854\) | −2.86959e8 | −0.460730 | ||||||||
\(855\) | −1.54849e7 | −0.0247749 | ||||||||
\(856\) | 1.90498e9i | 3.03718i | ||||||||
\(857\) | − | 5.05709e8i | − | 0.803449i | −0.915761 | − | 0.401724i | \(-0.868411\pi\) | ||
0.915761 | − | 0.401724i | \(-0.131589\pi\) | |||||||
\(858\) | 4.77720e8i | 0.756331i | ||||||||
\(859\) | − | 6.99413e7i | − | 0.110345i | −0.998477 | − | 0.0551727i | \(-0.982429\pi\) | ||
0.998477 | − | 0.0551727i | \(-0.0175709\pi\) | |||||||
\(860\) | − | 4.41258e8i | − | 0.693741i | ||||||
\(861\) | −1.91696e8 | −0.300333 | ||||||||
\(862\) | −2.12515e9 | −3.31793 | ||||||||
\(863\) | 9.58366e8i | 1.49107i | 0.666464 | + | 0.745537i | \(0.267807\pi\) | ||||
−0.666464 | + | 0.745537i | \(0.732193\pi\) | |||||||
\(864\) | 1.80372e8i | 0.279658i | ||||||||
\(865\) | 3.88943e8i | 0.600949i | ||||||||
\(866\) | − | 4.61516e8i | − | 0.710612i | ||||||
\(867\) | 3.74412e8 | 0.574503 | ||||||||
\(868\) | 5.55150e7i | 0.0848890i | ||||||||
\(869\) | 2.54161e8i | 0.387301i | ||||||||
\(870\) | − | 4.36335e6i | − | 0.00662616i | ||||||
\(871\) | 5.41083e8 | 0.818860 | ||||||||
\(872\) | −2.86167e8 | −0.431589 | ||||||||
\(873\) | − | 8.91714e7i | − | 0.134024i | ||||||
\(874\) | 7.96742e7 | 0.119339 | ||||||||
\(875\) | −3.27428e8 | −0.488755 | ||||||||
\(876\) | 9.81605e8i | 1.46024i | ||||||||
\(877\) | −8.42121e6 | −0.0124846 | −0.00624232 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624232 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(878\) | − | 5.16054e8i | − | 0.762450i | ||||||
\(879\) | −3.95037e8 | −0.581663 | ||||||||
\(880\) | − | 1.33859e9i | − | 1.96426i | ||||||
\(881\) | − | 1.42667e8i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332665\pi\) | |||||||
\(882\) | 3.33410e8i | 0.485929i | ||||||||
\(883\) | −7.80858e8 | −1.13420 | −0.567101 | − | 0.823649i | \(-0.691935\pi\) | ||||
−0.567101 | + | 0.823649i | \(0.691935\pi\) | |||||||
\(884\) | 6.96432e7i | 0.100814i | ||||||||
\(885\) | 2.38304e8 | − | 2.06210e8i | 0.343796 | − | 0.297495i | ||||
\(886\) | 1.49162e8 | 0.214465 | ||||||||
\(887\) | 1.26001e8i | 0.180553i | 0.995917 | + | 0.0902765i | \(0.0287751\pi\) | ||||
−0.995917 | + | 0.0902765i | \(0.971225\pi\) | |||||||
\(888\) | 4.95815e8 | 0.708077 | ||||||||
\(889\) | 6.90127e7 | 0.0982254 | ||||||||
\(890\) | 5.83536e8 | 0.827747 | ||||||||
\(891\) | 9.18262e7i | 0.129818i | ||||||||
\(892\) | −2.81693e9 | −3.96901 | ||||||||
\(893\) | − | 1.03937e8i | − | 0.145954i | ||||||
\(894\) | 2.45564e8 | 0.343678 | ||||||||
\(895\) | 1.24733e8i | 0.173985i | ||||||||
\(896\) | 1.62291e8i | 0.225616i | ||||||||
\(897\) | −1.76876e8 | −0.245071 | ||||||||
\(898\) | − | 2.40946e9i | − | 3.32729i | ||||||
\(899\) | 467372.i | 0.000643256i | ||||||||
\(900\) | 2.16004e8 | 0.296302 | ||||||||
\(901\) | 3.32365e7 | 0.0454403 | ||||||||
\(902\) | −1.81221e9 | −2.46939 | ||||||||
\(903\) | − | 7.19943e7i | − | 0.0977765i | ||||||
\(904\) | 3.59844e8 | 0.487090 | ||||||||
\(905\) | −2.90947e7 | −0.0392526 | ||||||||
\(906\) | 3.41843e8 | 0.459666 | ||||||||
\(907\) | 2.02236e8 | 0.271042 | 0.135521 | − | 0.990775i | \(-0.456729\pi\) | ||||
0.135521 | + | 0.990775i | \(0.456729\pi\) | |||||||
\(908\) | − | 1.42810e9i | − | 1.90766i | ||||||
\(909\) | − | 4.51658e7i | − | 0.0601337i | ||||||
\(910\) | −2.99270e8 | −0.397136 | ||||||||
\(911\) | 1.03541e9 | 1.36949 | 0.684746 | − | 0.728782i | \(-0.259913\pi\) | ||||
0.684746 | + | 0.728782i | \(0.259913\pi\) | |||||||
\(912\) | −8.82509e7 | −0.116341 | ||||||||
\(913\) | 1.10430e9 | 1.45103 | ||||||||
\(914\) | −1.77584e9 | −2.32576 | ||||||||
\(915\) | 1.95211e8i | 0.254824i | ||||||||
\(916\) | − | 1.22022e9i | − | 1.58764i | ||||||
\(917\) | 3.57204e8i | 0.463242i | ||||||||
\(918\) | 1.91078e7i | 0.0246992i | ||||||||
\(919\) | 6.73309e8i | 0.867497i | 0.901034 | + | 0.433749i | \(0.142809\pi\) | ||||
−0.901034 | + | 0.433749i | \(0.857191\pi\) | |||||||
\(920\) | 1.03878e9 | 1.33402 | ||||||||
\(921\) | −4.22789e8 | −0.541184 | ||||||||
\(922\) | − | 1.83651e9i | − | 2.34315i | ||||||
\(923\) | 1.45699e8i | 0.185290i | ||||||||
\(924\) | − | 5.60053e8i | − | 0.709926i | ||||||
\(925\) | − | 1.50600e8i | − | 0.190283i | ||||||
\(926\) | −1.38970e9 | −1.75020 | ||||||||
\(927\) | − | 3.18356e8i | − | 0.399645i | ||||||
\(928\) | − | 9.26153e6i | − | 0.0115888i | ||||||
\(929\) | − | 2.01494e8i | − | 0.251313i | −0.992074 | − | 0.125656i | \(-0.959896\pi\) | ||
0.992074 | − | 0.125656i | \(-0.0401037\pi\) | |||||||
\(930\) | 5.39057e7 | 0.0670172 | ||||||||
\(931\) | −6.07552e7 | −0.0752895 | ||||||||
\(932\) | − | 1.06541e9i | − | 1.31603i | ||||||
\(933\) | 1.91922e8 | 0.236309 | ||||||||
\(934\) | −1.63467e9 | −2.00627 | ||||||||
\(935\) | − | 5.28135e7i | − | 0.0646115i | ||||||
\(936\) | 4.10632e8 | 0.500755 | ||||||||
\(937\) | − | 1.95879e8i | − | 0.238106i | −0.992888 | − | 0.119053i | \(-0.962014\pi\) | ||
0.992888 | − | 0.119053i | \(-0.0379858\pi\) | |||||||
\(938\) | −9.05439e8 | −1.09711 | ||||||||
\(939\) | − | 3.09888e8i | − | 0.374290i | ||||||
\(940\) | − | 2.36653e9i | − | 2.84924i | ||||||
\(941\) | 4.76986e7i | 0.0572449i | 0.999590 | + | 0.0286225i | \(0.00911206\pi\) | ||||
−0.999590 | + | 0.0286225i | \(0.990888\pi\) | |||||||
\(942\) | 2.22034e8 | 0.265623 | ||||||||
\(943\) | − | 6.70974e8i | − | 0.800148i | ||||||
\(944\) | 1.35813e9 | − | 1.17522e9i | 1.61445 | − | 1.39702i | ||||
\(945\) | −5.75250e7 | −0.0681650 | ||||||||
\(946\) | − | 6.80603e8i | − | 0.803935i | ||||||
\(947\) | 8.14010e7 | 0.0958472 | 0.0479236 | − | 0.998851i | \(-0.484740\pi\) | ||||
0.0479236 | + | 0.998851i | \(0.484740\pi\) | |||||||
\(948\) | 3.81524e8 | 0.447813 | ||||||||
\(949\) | 5.66804e8 | 0.663185 | ||||||||
\(950\) | 5.61831e7i | 0.0655293i | ||||||||
\(951\) | −1.05096e8 | −0.122193 | ||||||||
\(952\) | − | 6.67328e7i | − | 0.0773443i | ||||||
\(953\) | 1.87967e8 | 0.217171 | 0.108586 | − | 0.994087i | \(-0.465368\pi\) | ||||
0.108586 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(954\) | − | 3.42235e8i | − | 0.394166i | ||||||
\(955\) | − | 5.43075e8i | − | 0.623519i | ||||||
\(956\) | 3.27511e8 | 0.374846 | ||||||||
\(957\) | − | 4.71499e6i | − | 0.00537954i | ||||||
\(958\) | − | 2.62278e9i | − | 2.98309i | ||||||
\(959\) | −5.77768e8 | −0.655085 | ||||||||
\(960\) | −2.09436e8 | −0.236721 | ||||||||
\(961\) | 8.81730e8 | 0.993494 | ||||||||
\(962\) | − | 4.99978e8i | − | 0.561598i | ||||||
\(963\) | 3.69246e8 | 0.413463 | ||||||||
\(964\) | −1.57182e9 | −1.75457 | ||||||||
\(965\) | −9.86078e8 | −1.09731 | ||||||||
\(966\) | 2.95982e8 | 0.328347 | ||||||||
\(967\) | 3.28096e8i | 0.362845i | 0.983405 | + | 0.181422i | \(0.0580701\pi\) | ||||
−0.983405 | + | 0.181422i | \(0.941930\pi\) | |||||||
\(968\) | − | 8.10782e8i | − | 0.893878i | ||||||
\(969\) | −3.48190e6 | −0.00382688 | ||||||||
\(970\) | 5.28095e8 | 0.578625 | ||||||||
\(971\) | 1.28334e9 | 1.40180 | 0.700899 | − | 0.713260i | \(-0.252782\pi\) | ||||
0.700899 | + | 0.713260i | \(0.252782\pi\) | |||||||
\(972\) | 1.37842e8 | 0.150100 | ||||||||
\(973\) | −6.44200e8 | −0.699330 | ||||||||
\(974\) | − | 8.14155e7i | − | 0.0881110i | ||||||
\(975\) | − | 1.24726e8i | − | 0.134569i | ||||||
\(976\) | 1.11253e9i | 1.19664i | ||||||||
\(977\) | 1.08598e9i | 1.16450i | 0.813011 | + | 0.582248i | \(0.197827\pi\) | ||||
−0.813011 | + | 0.582248i | \(0.802173\pi\) | |||||||
\(978\) | − | 9.17475e8i | − | 0.980794i | ||||||
\(979\) | 6.30564e8 | 0.672018 | ||||||||
\(980\) | −1.38333e9 | −1.46976 | ||||||||
\(981\) | 5.54682e7i | 0.0587539i | ||||||||
\(982\) | 2.38263e9i | 2.51607i | ||||||||
\(983\) | − | 1.27972e8i | − | 0.134727i | −0.997729 | − | 0.0673633i | \(-0.978541\pi\) | ||
0.997729 | − | 0.0673633i | \(-0.0214587\pi\) | |||||||
\(984\) | 1.55772e9i | 1.63494i | ||||||||
\(985\) | 7.38488e8 | 0.772743 | ||||||||
\(986\) | − | 981129.i | − | 0.00102352i | ||||||
\(987\) | − | 3.86116e8i | − | 0.401575i | ||||||
\(988\) | 1.30675e8i | 0.135494i | ||||||||
\(989\) | 2.51994e8 | 0.260496 | ||||||||
\(990\) | −5.43817e8 | −0.560464 | ||||||||
\(991\) | 1.66139e9i | 1.70707i | 0.521036 | + | 0.853534i | \(0.325546\pi\) | ||||
−0.521036 | + | 0.853534i | \(0.674454\pi\) | |||||||
\(992\) | 1.14419e8 | 0.117210 | ||||||||
\(993\) | 7.97198e8 | 0.814176 | ||||||||
\(994\) | − | 2.43811e8i | − | 0.248253i | ||||||
\(995\) | −2.19132e8 | −0.222452 | ||||||||
\(996\) | − | 1.65768e9i | − | 1.67773i | ||||||
\(997\) | 5.98877e8 | 0.604299 | 0.302150 | − | 0.953261i | \(-0.402296\pi\) | ||||
0.302150 | + | 0.953261i | \(0.402296\pi\) | |||||||
\(998\) | 1.68560e9i | 1.69575i | ||||||||
\(999\) | − | 9.61045e7i | − | 0.0963934i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.7.c.a.58.4 | ✓ | 60 | |
59.58 | odd | 2 | inner | 177.7.c.a.58.57 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.7.c.a.58.4 | ✓ | 60 | 1.1 | even | 1 | trivial | |
177.7.c.a.58.57 | yes | 60 | 59.58 | odd | 2 | inner |