Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,7,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, 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("69.22");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.d (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: | \(15.8737317698\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.2 | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.7.d.a.22.1 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −15.4071 | −1.92588 | −0.962942 | − | 0.269709i | \(-0.913072\pi\) | ||||
−0.962942 | + | 0.269709i | \(0.913072\pi\) | |||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 173.378 | 2.70903 | ||||||||
\(5\) | 161.383i | 1.29106i | 0.763734 | + | 0.645531i | \(0.223364\pi\) | ||||
−0.763734 | + | 0.645531i | \(0.776636\pi\) | |||||||
\(6\) | −240.172 | −1.11191 | ||||||||
\(7\) | 585.691i | 1.70756i | 0.520638 | + | 0.853778i | \(0.325694\pi\) | ||||
−0.520638 | + | 0.853778i | \(0.674306\pi\) | |||||||
\(8\) | −1685.19 | −3.29139 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 2486.44i | − | 2.48644i | ||||||
\(11\) | 2121.45i | 1.59387i | 0.604062 | + | 0.796937i | \(0.293548\pi\) | ||||
−0.604062 | + | 0.796937i | \(0.706452\pi\) | |||||||
\(12\) | 2702.69 | 1.56406 | ||||||||
\(13\) | 1927.08 | 0.877139 | 0.438570 | − | 0.898697i | \(-0.355485\pi\) | ||||
0.438570 | + | 0.898697i | \(0.355485\pi\) | |||||||
\(14\) | − | 9023.79i | − | 3.28855i | ||||||
\(15\) | 2515.71i | 0.745395i | ||||||||
\(16\) | 14867.7 | 3.62980 | ||||||||
\(17\) | − | 1375.26i | − | 0.279923i | −0.990157 | − | 0.139961i | \(-0.955302\pi\) | ||
0.990157 | − | 0.139961i | \(-0.0446978\pi\) | |||||||
\(18\) | −3743.92 | −0.641961 | ||||||||
\(19\) | − | 3652.93i | − | 0.532574i | −0.963894 | − | 0.266287i | \(-0.914203\pi\) | ||
0.963894 | − | 0.266287i | \(-0.0857969\pi\) | |||||||
\(20\) | 27980.2i | 3.49752i | ||||||||
\(21\) | 9130.03i | 0.985857i | ||||||||
\(22\) | − | 32685.3i | − | 3.06962i | ||||||
\(23\) | −10900.5 | − | 5405.04i | −0.895909 | − | 0.444238i | ||||
\(24\) | −26269.5 | −1.90028 | ||||||||
\(25\) | −10419.4 | −0.666842 | ||||||||
\(26\) | −29690.6 | −1.68927 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 101546.i | 4.62581i | ||||||||
\(29\) | 6030.06 | 0.247245 | 0.123623 | − | 0.992329i | \(-0.460549\pi\) | ||||
0.123623 | + | 0.992329i | \(0.460549\pi\) | |||||||
\(30\) | − | 38759.7i | − | 1.43554i | ||||||
\(31\) | 3253.53 | 0.109212 | 0.0546060 | − | 0.998508i | \(-0.482610\pi\) | ||||
0.0546060 | + | 0.998508i | \(0.482610\pi\) | |||||||
\(32\) | −121215. | −3.69919 | ||||||||
\(33\) | 33070.1i | 0.920224i | ||||||||
\(34\) | 21188.7i | 0.539098i | ||||||||
\(35\) | −94520.5 | −2.20456 | ||||||||
\(36\) | 42130.8 | 0.903009 | ||||||||
\(37\) | 25548.1i | 0.504375i | 0.967678 | + | 0.252187i | \(0.0811499\pi\) | ||||
−0.967678 | + | 0.252187i | \(0.918850\pi\) | |||||||
\(38\) | 56280.9i | 1.02568i | ||||||||
\(39\) | 30040.1 | 0.506417 | ||||||||
\(40\) | − | 271961.i | − | 4.24939i | ||||||
\(41\) | 101808. | 1.47717 | 0.738587 | − | 0.674158i | \(-0.235493\pi\) | ||||
0.738587 | + | 0.674158i | \(0.235493\pi\) | |||||||
\(42\) | − | 140667.i | − | 1.89865i | ||||||
\(43\) | − | 83443.8i | − | 1.04952i | −0.851252 | − | 0.524758i | \(-0.824156\pi\) | ||
0.851252 | − | 0.524758i | \(-0.175844\pi\) | |||||||
\(44\) | 367812.i | 4.31785i | ||||||||
\(45\) | 39216.0i | 0.430354i | ||||||||
\(46\) | 167945. | + | 83275.8i | 1.72542 | + | 0.855550i | ||||
\(47\) | −119152. | −1.14765 | −0.573824 | − | 0.818979i | \(-0.694541\pi\) | ||||
−0.573824 | + | 0.818979i | \(0.694541\pi\) | |||||||
\(48\) | 231764. | 2.09567 | ||||||||
\(49\) | −225385. | −1.91574 | ||||||||
\(50\) | 160532. | 1.28426 | ||||||||
\(51\) | − | 21438.2i | − | 0.161613i | ||||||
\(52\) | 334112. | 2.37619 | ||||||||
\(53\) | 87012.7i | 0.584461i | 0.956348 | + | 0.292230i | \(0.0943974\pi\) | ||||
−0.956348 | + | 0.292230i | \(0.905603\pi\) | |||||||
\(54\) | −58361.9 | −0.370636 | ||||||||
\(55\) | −342365. | −2.05779 | ||||||||
\(56\) | − | 987001.i | − | 5.62023i | ||||||
\(57\) | − | 56943.5i | − | 0.307482i | ||||||
\(58\) | −92905.5 | −0.476165 | ||||||||
\(59\) | 42117.7 | 0.205073 | 0.102537 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102537 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(60\) | 436168.i | 2.01930i | ||||||||
\(61\) | 112804.i | 0.496974i | 0.968635 | + | 0.248487i | \(0.0799333\pi\) | ||||
−0.968635 | + | 0.248487i | \(0.920067\pi\) | |||||||
\(62\) | −50127.4 | −0.210329 | ||||||||
\(63\) | 142323.i | 0.569185i | ||||||||
\(64\) | 916036. | 3.49440 | ||||||||
\(65\) | 310997.i | 1.13244i | ||||||||
\(66\) | − | 509513.i | − | 1.77224i | ||||||
\(67\) | 49872.3i | 0.165819i | 0.996557 | + | 0.0829096i | \(0.0264213\pi\) | ||||
−0.996557 | + | 0.0829096i | \(0.973579\pi\) | |||||||
\(68\) | − | 238439.i | − | 0.758318i | ||||||
\(69\) | −169922. | − | 84256.3i | −0.517253 | − | 0.256481i | ||||
\(70\) | 1.45628e6 | 4.24573 | ||||||||
\(71\) | 234036. | 0.653896 | 0.326948 | − | 0.945042i | \(-0.393980\pi\) | ||||
0.326948 | + | 0.945042i | \(0.393980\pi\) | |||||||
\(72\) | −409501. | −1.09713 | ||||||||
\(73\) | −75271.3 | −0.193491 | −0.0967455 | − | 0.995309i | \(-0.530843\pi\) | ||||
−0.0967455 | + | 0.995309i | \(0.530843\pi\) | |||||||
\(74\) | − | 393621.i | − | 0.971367i | ||||||
\(75\) | −162422. | −0.385001 | ||||||||
\(76\) | − | 633336.i | − | 1.44276i | ||||||
\(77\) | −1.24251e6 | −2.72163 | ||||||||
\(78\) | −462830. | −0.975300 | ||||||||
\(79\) | 539646.i | 1.09453i | 0.836960 | + | 0.547265i | \(0.184331\pi\) | ||||
−0.836960 | + | 0.547265i | \(0.815669\pi\) | |||||||
\(80\) | 2.39938e6i | 4.68630i | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −1.56857e6 | −2.84487 | ||||||||
\(83\) | − | 221270.i | − | 0.386981i | −0.981102 | − | 0.193490i | \(-0.938019\pi\) | ||
0.981102 | − | 0.193490i | \(-0.0619808\pi\) | |||||||
\(84\) | 1.58294e6i | 2.67071i | ||||||||
\(85\) | 221943. | 0.361398 | ||||||||
\(86\) | 1.28562e6i | 2.02124i | ||||||||
\(87\) | 93999.3 | 0.142747 | ||||||||
\(88\) | − | 3.57504e6i | − | 5.24606i | ||||||
\(89\) | − | 1.34727e6i | − | 1.91110i | −0.294825 | − | 0.955551i | \(-0.595261\pi\) | ||
0.294825 | − | 0.955551i | \(-0.404739\pi\) | |||||||
\(90\) | − | 604204.i | − | 0.828812i | ||||||
\(91\) | 1.12867e6i | 1.49776i | ||||||||
\(92\) | −1.88991e6 | − | 937114.i | −2.42704 | − | 1.20345i | ||||
\(93\) | 50717.6 | 0.0630535 | ||||||||
\(94\) | 1.83579e6 | 2.21024 | ||||||||
\(95\) | 589519. | 0.687586 | ||||||||
\(96\) | −1.88955e6 | −2.13573 | ||||||||
\(97\) | 1.22527e6i | 1.34251i | 0.741229 | + | 0.671253i | \(0.234243\pi\) | ||||
−0.741229 | + | 0.671253i | \(0.765757\pi\) | |||||||
\(98\) | 3.47253e6 | 3.68950 | ||||||||
\(99\) | 515512.i | 0.531292i | ||||||||
\(100\) | −1.80649e6 | −1.80649 | ||||||||
\(101\) | 1.49877e6 | 1.45469 | 0.727346 | − | 0.686271i | \(-0.240754\pi\) | ||||
0.727346 | + | 0.686271i | \(0.240754\pi\) | |||||||
\(102\) | 330300.i | 0.311249i | ||||||||
\(103\) | 505604.i | 0.462700i | 0.972871 | + | 0.231350i | \(0.0743142\pi\) | ||||
−0.972871 | + | 0.231350i | \(0.925686\pi\) | |||||||
\(104\) | −3.24749e6 | −2.88701 | ||||||||
\(105\) | −1.47343e6 | −1.27280 | ||||||||
\(106\) | − | 1.34061e6i | − | 1.12560i | ||||||
\(107\) | − | 1.43394e6i | − | 1.17052i | −0.810846 | − | 0.585260i | \(-0.800993\pi\) | ||
0.810846 | − | 0.585260i | \(-0.199007\pi\) | |||||||
\(108\) | 656754. | 0.521353 | ||||||||
\(109\) | − | 2.08905e6i | − | 1.61313i | −0.591146 | − | 0.806565i | \(-0.701324\pi\) | ||
0.591146 | − | 0.806565i | \(-0.298676\pi\) | |||||||
\(110\) | 5.27484e6 | 3.96307 | ||||||||
\(111\) | 398255.i | 0.291201i | ||||||||
\(112\) | 8.70786e6i | 6.19809i | ||||||||
\(113\) | − | 320916.i | − | 0.222411i | −0.993797 | − | 0.111205i | \(-0.964529\pi\) | ||
0.993797 | − | 0.111205i | \(-0.0354711\pi\) | |||||||
\(114\) | 877332.i | 0.592174i | ||||||||
\(115\) | 872281. | − | 1.75916e6i | 0.573539 | − | 1.15667i | ||||
\(116\) | 1.04548e6 | 0.669794 | ||||||||
\(117\) | 468279. | 0.292380 | ||||||||
\(118\) | −648911. | −0.394947 | ||||||||
\(119\) | 805478. | 0.477983 | ||||||||
\(120\) | − | 4.23945e6i | − | 2.45338i | ||||||
\(121\) | −2.72898e6 | −1.54044 | ||||||||
\(122\) | − | 1.73797e6i | − | 0.957113i | ||||||
\(123\) | 1.58703e6 | 0.852847 | ||||||||
\(124\) | 564090. | 0.295858 | ||||||||
\(125\) | 840094.i | 0.430128i | ||||||||
\(126\) | − | 2.19278e6i | − | 1.09618i | ||||||
\(127\) | −2.62996e6 | −1.28392 | −0.641960 | − | 0.766738i | \(-0.721878\pi\) | ||||
−0.641960 | + | 0.766738i | \(0.721878\pi\) | |||||||
\(128\) | −6.35568e6 | −3.03062 | ||||||||
\(129\) | − | 1.30076e6i | − | 0.605938i | ||||||
\(130\) | − | 4.79155e6i | − | 2.18095i | ||||||
\(131\) | 1.69152e6 | 0.752423 | 0.376212 | − | 0.926534i | \(-0.377227\pi\) | ||||
0.376212 | + | 0.926534i | \(0.377227\pi\) | |||||||
\(132\) | 5.73362e6i | 2.49291i | ||||||||
\(133\) | 2.13949e6 | 0.909400 | ||||||||
\(134\) | − | 768386.i | − | 0.319349i | ||||||
\(135\) | 611317.i | 0.248465i | ||||||||
\(136\) | 2.31757e6i | 0.921334i | ||||||||
\(137\) | 2.53094e6i | 0.984283i | 0.870515 | + | 0.492141i | \(0.163786\pi\) | ||||
−0.870515 | + | 0.492141i | \(0.836214\pi\) | |||||||
\(138\) | 2.61801e6 | + | 1.29814e6i | 0.996169 | + | 0.493952i | ||||
\(139\) | 704489. | 0.262319 | 0.131160 | − | 0.991361i | \(-0.458130\pi\) | ||||
0.131160 | + | 0.991361i | \(0.458130\pi\) | |||||||
\(140\) | −1.63878e7 | −5.97221 | ||||||||
\(141\) | −1.85740e6 | −0.662595 | ||||||||
\(142\) | −3.60582e6 | −1.25933 | ||||||||
\(143\) | 4.08819e6i | 1.39805i | ||||||||
\(144\) | 3.61284e6 | 1.20993 | ||||||||
\(145\) | 973148.i | 0.319209i | ||||||||
\(146\) | 1.15971e6 | 0.372641 | ||||||||
\(147\) | −3.51341e6 | −1.10606 | ||||||||
\(148\) | 4.42947e6i | 1.36636i | ||||||||
\(149\) | − | 541350.i | − | 0.163651i | −0.996647 | − | 0.0818256i | \(-0.973925\pi\) | ||
0.996647 | − | 0.0818256i | \(-0.0260751\pi\) | |||||||
\(150\) | 2.50245e6 | 0.741467 | ||||||||
\(151\) | 56757.2 | 0.0164850 | 0.00824252 | − | 0.999966i | \(-0.497376\pi\) | ||||
0.00824252 | + | 0.999966i | \(0.497376\pi\) | |||||||
\(152\) | 6.15587e6i | 1.75291i | ||||||||
\(153\) | − | 334188.i | − | 0.0933076i | ||||||
\(154\) | 1.91435e7 | 5.24154 | ||||||||
\(155\) | 525064.i | 0.140999i | ||||||||
\(156\) | 5.20829e6 | 1.37190 | ||||||||
\(157\) | 1.67461e6i | 0.432727i | 0.976313 | + | 0.216363i | \(0.0694195\pi\) | ||||
−0.976313 | + | 0.216363i | \(0.930580\pi\) | |||||||
\(158\) | − | 8.31436e6i | − | 2.10794i | ||||||
\(159\) | 1.35639e6i | 0.337439i | ||||||||
\(160\) | − | 1.95620e7i | − | 4.77588i | ||||||
\(161\) | 3.16569e6 | − | 6.38434e6i | 0.758561 | − | 1.52981i | ||||
\(162\) | −909772. | −0.213987 | ||||||||
\(163\) | −5.46518e6 | −1.26195 | −0.630974 | − | 0.775804i | \(-0.717345\pi\) | ||||
−0.630974 | + | 0.775804i | \(0.717345\pi\) | |||||||
\(164\) | 1.76513e7 | 4.00171 | ||||||||
\(165\) | −5.33694e6 | −1.18807 | ||||||||
\(166\) | 3.40913e6i | 0.745279i | ||||||||
\(167\) | 5.53280e6 | 1.18794 | 0.593971 | − | 0.804486i | \(-0.297559\pi\) | ||||
0.593971 | + | 0.804486i | \(0.297559\pi\) | |||||||
\(168\) | − | 1.53858e7i | − | 3.24484i | ||||||
\(169\) | −1.11319e6 | −0.230626 | ||||||||
\(170\) | −3.41950e6 | −0.696010 | ||||||||
\(171\) | − | 887661.i | − | 0.177525i | ||||||
\(172\) | − | 1.44673e7i | − | 2.84317i | ||||||
\(173\) | −254750. | −0.0492012 | −0.0246006 | − | 0.999697i | \(-0.507831\pi\) | ||||
−0.0246006 | + | 0.999697i | \(0.507831\pi\) | |||||||
\(174\) | −1.44825e6 | −0.274914 | ||||||||
\(175\) | − | 6.10255e6i | − | 1.13867i | ||||||
\(176\) | 3.15410e7i | 5.78545i | ||||||||
\(177\) | 656550. | 0.118399 | ||||||||
\(178\) | 2.07574e7i | 3.68056i | ||||||||
\(179\) | −2.38809e6 | −0.416381 | −0.208190 | − | 0.978088i | \(-0.566757\pi\) | ||||
−0.208190 | + | 0.978088i | \(0.566757\pi\) | |||||||
\(180\) | 6.79918e6i | 1.16584i | ||||||||
\(181\) | 1.11133e6i | 0.187416i | 0.995600 | + | 0.0937082i | \(0.0298721\pi\) | ||||
−0.995600 | + | 0.0937082i | \(0.970128\pi\) | |||||||
\(182\) | − | 1.73895e7i | − | 2.88452i | ||||||
\(183\) | 1.75843e6i | 0.286928i | ||||||||
\(184\) | 1.83695e7 | + | 9.10852e6i | 2.94878 | + | 1.46216i | ||||
\(185\) | −4.12302e6 | −0.651179 | ||||||||
\(186\) | −781409. | −0.121434 | ||||||||
\(187\) | 2.91754e6 | 0.446162 | ||||||||
\(188\) | −2.06583e7 | −3.10901 | ||||||||
\(189\) | 2.21860e6i | 0.328619i | ||||||||
\(190\) | −9.08276e6 | −1.32421 | ||||||||
\(191\) | 1.57559e6i | 0.226122i | 0.993588 | + | 0.113061i | \(0.0360655\pi\) | ||||
−0.993588 | + | 0.113061i | \(0.963934\pi\) | |||||||
\(192\) | 1.42796e7 | 2.01749 | ||||||||
\(193\) | 1.05732e7 | 1.47074 | 0.735370 | − | 0.677665i | \(-0.237008\pi\) | ||||
0.735370 | + | 0.677665i | \(0.237008\pi\) | |||||||
\(194\) | − | 1.88778e7i | − | 2.58551i | ||||||
\(195\) | 4.84796e6i | 0.653815i | ||||||||
\(196\) | −3.90768e7 | −5.18980 | ||||||||
\(197\) | −5.56206e6 | −0.727507 | −0.363753 | − | 0.931495i | \(-0.618505\pi\) | ||||
−0.363753 | + | 0.931495i | \(0.618505\pi\) | |||||||
\(198\) | − | 7.94252e6i | − | 1.02321i | ||||||
\(199\) | − | 1.20492e7i | − | 1.52897i | −0.644639 | − | 0.764487i | \(-0.722992\pi\) | ||
0.644639 | − | 0.764487i | \(-0.277008\pi\) | |||||||
\(200\) | 1.75587e7 | 2.19483 | ||||||||
\(201\) | 777432.i | 0.0957358i | ||||||||
\(202\) | −2.30916e7 | −2.80157 | ||||||||
\(203\) | 3.53175e6i | 0.422185i | ||||||||
\(204\) | − | 3.71690e6i | − | 0.437815i | ||||||
\(205\) | 1.64301e7i | 1.90712i | ||||||||
\(206\) | − | 7.78988e6i | − | 0.891105i | ||||||
\(207\) | −2.64883e6 | − | 1.31343e6i | −0.298636 | − | 0.148079i | ||||
\(208\) | 2.86511e7 | 3.18384 | ||||||||
\(209\) | 7.74949e6 | 0.848856 | ||||||||
\(210\) | 2.27012e7 | 2.45127 | ||||||||
\(211\) | −2.56616e6 | −0.273172 | −0.136586 | − | 0.990628i | \(-0.543613\pi\) | ||||
−0.136586 | + | 0.990628i | \(0.543613\pi\) | |||||||
\(212\) | 1.50861e7i | 1.58332i | ||||||||
\(213\) | 3.64827e6 | 0.377527 | ||||||||
\(214\) | 2.20928e7i | 2.25428i | ||||||||
\(215\) | 1.34664e7 | 1.35499 | ||||||||
\(216\) | −6.38349e6 | −0.633428 | ||||||||
\(217\) | 1.90557e6i | 0.186485i | ||||||||
\(218\) | 3.21861e7i | 3.10670i | ||||||||
\(219\) | −1.17336e6 | −0.111712 | ||||||||
\(220\) | −5.93585e7 | −5.57461 | ||||||||
\(221\) | − | 2.65023e6i | − | 0.245531i | ||||||
\(222\) | − | 6.13595e6i | − | 0.560819i | ||||||
\(223\) | −3.21603e6 | −0.290005 | −0.145002 | − | 0.989431i | \(-0.546319\pi\) | ||||
−0.145002 | + | 0.989431i | \(0.546319\pi\) | |||||||
\(224\) | − | 7.09946e7i | − | 6.31656i | ||||||
\(225\) | −2.53191e6 | −0.222281 | ||||||||
\(226\) | 4.94437e6i | 0.428337i | ||||||||
\(227\) | − | 4.49495e6i | − | 0.384280i | −0.981368 | − | 0.192140i | \(-0.938457\pi\) | ||
0.981368 | − | 0.192140i | \(-0.0615427\pi\) | |||||||
\(228\) | − | 9.87273e6i | − | 0.832976i | ||||||
\(229\) | 1.69502e7i | 1.41146i | 0.708483 | + | 0.705728i | \(0.249380\pi\) | ||||
−0.708483 | + | 0.705728i | \(0.750620\pi\) | |||||||
\(230\) | −1.34393e7 | + | 2.71034e7i | −1.10457 | + | 2.22762i | ||||
\(231\) | −1.93689e7 | −1.57133 | ||||||||
\(232\) | −1.01618e7 | −0.813779 | ||||||||
\(233\) | 8.99993e6 | 0.711494 | 0.355747 | − | 0.934582i | \(-0.384226\pi\) | ||||
0.355747 | + | 0.934582i | \(0.384226\pi\) | |||||||
\(234\) | −7.21481e6 | −0.563089 | ||||||||
\(235\) | − | 1.92291e7i | − | 1.48168i | ||||||
\(236\) | 7.30228e6 | 0.555549 | ||||||||
\(237\) | 8.41224e6i | 0.631927i | ||||||||
\(238\) | −1.24101e7 | −0.920540 | ||||||||
\(239\) | −2.11370e7 | −1.54828 | −0.774141 | − | 0.633013i | \(-0.781818\pi\) | ||||
−0.774141 | + | 0.633013i | \(0.781818\pi\) | |||||||
\(240\) | 3.74027e7i | 2.70564i | ||||||||
\(241\) | 9.50399e6i | 0.678977i | 0.940610 | + | 0.339488i | \(0.110254\pi\) | ||||
−0.940610 | + | 0.339488i | \(0.889746\pi\) | |||||||
\(242\) | 4.20455e7 | 2.96670 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 1.95576e7i | 1.34632i | ||||||||
\(245\) | − | 3.63733e7i | − | 2.47335i | ||||||
\(246\) | −2.44516e7 | −1.64248 | ||||||||
\(247\) | − | 7.03946e6i | − | 0.467142i | ||||||
\(248\) | −5.48282e6 | −0.359459 | ||||||||
\(249\) | − | 3.44926e6i | − | 0.223423i | ||||||
\(250\) | − | 1.29434e7i | − | 0.828377i | ||||||
\(251\) | 6.04218e6i | 0.382096i | 0.981581 | + | 0.191048i | \(0.0611886\pi\) | ||||
−0.981581 | + | 0.191048i | \(0.938811\pi\) | |||||||
\(252\) | 2.46756e7i | 1.54194i | ||||||||
\(253\) | 1.14665e7 | − | 2.31249e7i | 0.708059 | − | 1.42797i | ||||
\(254\) | 4.05200e7 | 2.47268 | ||||||||
\(255\) | 3.45975e6 | 0.208653 | ||||||||
\(256\) | 3.92960e7 | 2.34223 | ||||||||
\(257\) | −2.02760e7 | −1.19449 | −0.597246 | − | 0.802058i | \(-0.703738\pi\) | ||||
−0.597246 | + | 0.802058i | \(0.703738\pi\) | |||||||
\(258\) | 2.00409e7i | 1.16697i | ||||||||
\(259\) | −1.49633e7 | −0.861247 | ||||||||
\(260\) | 5.39199e7i | 3.06781i | ||||||||
\(261\) | 1.46530e6 | 0.0824150 | ||||||||
\(262\) | −2.60613e7 | −1.44908 | ||||||||
\(263\) | 2.16567e7i | 1.19049i | 0.803544 | + | 0.595245i | \(0.202945\pi\) | ||||
−0.803544 | + | 0.595245i | \(0.797055\pi\) | |||||||
\(264\) | − | 5.57294e7i | − | 3.02881i | ||||||
\(265\) | −1.40424e7 | −0.754575 | ||||||||
\(266\) | −3.29632e7 | −1.75140 | ||||||||
\(267\) | − | 2.10018e7i | − | 1.10338i | ||||||
\(268\) | 8.64675e6i | 0.449209i | ||||||||
\(269\) | 3.45160e7 | 1.77323 | 0.886613 | − | 0.462512i | \(-0.153052\pi\) | ||||
0.886613 | + | 0.462512i | \(0.153052\pi\) | |||||||
\(270\) | − | 9.41861e6i | − | 0.478515i | ||||||
\(271\) | 1.67829e7 | 0.843255 | 0.421627 | − | 0.906769i | \(-0.361459\pi\) | ||||
0.421627 | + | 0.906769i | \(0.361459\pi\) | |||||||
\(272\) | − | 2.04469e7i | − | 1.01606i | ||||||
\(273\) | 1.75942e7i | 0.864734i | ||||||||
\(274\) | − | 3.89943e7i | − | 1.89561i | ||||||
\(275\) | − | 2.21042e7i | − | 1.06286i | ||||||
\(276\) | −2.94608e7 | − | 1.46082e7i | −1.40125 | − | 0.694814i | ||||
\(277\) | 3.71225e7 | 1.74662 | 0.873308 | − | 0.487168i | \(-0.161970\pi\) | ||||
0.873308 | + | 0.487168i | \(0.161970\pi\) | |||||||
\(278\) | −1.08541e7 | −0.505196 | ||||||||
\(279\) | 790609. | 0.0364040 | ||||||||
\(280\) | 1.59285e8 | 7.25606 | ||||||||
\(281\) | − | 3.49045e7i | − | 1.57312i | −0.617511 | − | 0.786562i | \(-0.711859\pi\) | ||
0.617511 | − | 0.786562i | \(-0.288141\pi\) | |||||||
\(282\) | 2.86171e7 | 1.27608 | ||||||||
\(283\) | 6.06094e6i | 0.267412i | 0.991021 | + | 0.133706i | \(0.0426878\pi\) | ||||
−0.991021 | + | 0.133706i | \(0.957312\pi\) | |||||||
\(284\) | 4.05767e7 | 1.77142 | ||||||||
\(285\) | 9.18970e6 | 0.396978 | ||||||||
\(286\) | − | 6.29870e7i | − | 2.69248i | ||||||
\(287\) | 5.96283e7i | 2.52236i | ||||||||
\(288\) | −2.94552e7 | −1.23306 | ||||||||
\(289\) | 2.22462e7 | 0.921643 | ||||||||
\(290\) | − | 1.49934e7i | − | 0.614759i | ||||||
\(291\) | 1.91000e7i | 0.775096i | ||||||||
\(292\) | −1.30504e7 | −0.524173 | ||||||||
\(293\) | 3.32779e7i | 1.32298i | 0.749954 | + | 0.661490i | \(0.230076\pi\) | ||||
−0.749954 | + | 0.661490i | \(0.769924\pi\) | |||||||
\(294\) | 5.41314e7 | 2.13013 | ||||||||
\(295\) | 6.79708e6i | 0.264762i | ||||||||
\(296\) | − | 4.30534e7i | − | 1.66009i | ||||||
\(297\) | 8.03603e6i | 0.306741i | ||||||||
\(298\) | 8.34061e6i | 0.315173i | ||||||||
\(299\) | −2.10061e7 | − | 1.04159e7i | −0.785837 | − | 0.389659i | ||||
\(300\) | −2.81604e7 | −1.04298 | ||||||||
\(301\) | 4.88723e7 | 1.79211 | ||||||||
\(302\) | −874462. | −0.0317483 | ||||||||
\(303\) | 2.33635e7 | 0.839866 | ||||||||
\(304\) | − | 5.43105e7i | − | 1.93314i | ||||||
\(305\) | −1.82046e7 | −0.641624 | ||||||||
\(306\) | 5.14886e6i | 0.179699i | ||||||||
\(307\) | 8.91735e6 | 0.308192 | 0.154096 | − | 0.988056i | \(-0.450754\pi\) | ||||
0.154096 | + | 0.988056i | \(0.450754\pi\) | |||||||
\(308\) | −2.15424e8 | −7.37297 | ||||||||
\(309\) | 7.88159e6i | 0.267140i | ||||||||
\(310\) | − | 8.08970e6i | − | 0.271548i | ||||||
\(311\) | 3.92020e7 | 1.30325 | 0.651625 | − | 0.758542i | \(-0.274088\pi\) | ||||
0.651625 | + | 0.758542i | \(0.274088\pi\) | |||||||
\(312\) | −5.06233e7 | −1.66681 | ||||||||
\(313\) | − | 2.03457e7i | − | 0.663497i | −0.943368 | − | 0.331749i | \(-0.892361\pi\) | ||
0.943368 | − | 0.331749i | \(-0.107639\pi\) | |||||||
\(314\) | − | 2.58008e7i | − | 0.833381i | ||||||
\(315\) | −2.29685e7 | −0.734853 | ||||||||
\(316\) | 9.35625e7i | 2.96511i | ||||||||
\(317\) | −1.36669e7 | −0.429033 | −0.214517 | − | 0.976720i | \(-0.568818\pi\) | ||||
−0.214517 | + | 0.976720i | \(0.568818\pi\) | |||||||
\(318\) | − | 2.08981e7i | − | 0.649867i | ||||||
\(319\) | 1.27925e7i | 0.394078i | ||||||||
\(320\) | 1.47832e8i | 4.51149i | ||||||||
\(321\) | − | 2.23529e7i | − | 0.675800i | ||||||
\(322\) | −4.87739e7 | + | 9.83640e7i | −1.46090 | + | 2.94624i | ||||
\(323\) | −5.02372e6 | −0.149080 | ||||||||
\(324\) | 1.02378e7 | 0.301003 | ||||||||
\(325\) | −2.00790e7 | −0.584913 | ||||||||
\(326\) | 8.42024e7 | 2.43037 | ||||||||
\(327\) | − | 3.25651e7i | − | 0.931341i | ||||||
\(328\) | −1.71566e8 | −4.86195 | ||||||||
\(329\) | − | 6.97864e7i | − | 1.95967i | ||||||
\(330\) | 8.22266e7 | 2.28808 | ||||||||
\(331\) | −9.55678e6 | −0.263528 | −0.131764 | − | 0.991281i | \(-0.542064\pi\) | ||||
−0.131764 | + | 0.991281i | \(0.542064\pi\) | |||||||
\(332\) | − | 3.83634e7i | − | 1.04834i | ||||||
\(333\) | 6.20818e6i | 0.168125i | ||||||||
\(334\) | −8.52442e7 | −2.28784 | ||||||||
\(335\) | −8.04853e6 | −0.214083 | ||||||||
\(336\) | 1.35742e8i | 3.57847i | ||||||||
\(337\) | − | 3.96943e6i | − | 0.103714i | −0.998655 | − | 0.0518572i | \(-0.983486\pi\) | ||
0.998655 | − | 0.0518572i | \(-0.0165141\pi\) | |||||||
\(338\) | 1.71510e7 | 0.444160 | ||||||||
\(339\) | − | 5.00258e6i | − | 0.128409i | ||||||
\(340\) | 3.84800e7 | 0.979036 | ||||||||
\(341\) | 6.90220e6i | 0.174070i | ||||||||
\(342\) | 1.36763e7i | 0.341892i | ||||||||
\(343\) | − | 6.31003e7i | − | 1.56368i | ||||||
\(344\) | 1.40619e8i | 3.45436i | ||||||||
\(345\) | 1.35975e7 | − | 2.74225e7i | 0.331133 | − | 0.667806i | ||||
\(346\) | 3.92495e6 | 0.0947558 | ||||||||
\(347\) | 4.00398e6 | 0.0958304 | 0.0479152 | − | 0.998851i | \(-0.484742\pi\) | ||||
0.0479152 | + | 0.998851i | \(0.484742\pi\) | |||||||
\(348\) | 1.62974e7 | 0.386705 | ||||||||
\(349\) | 6.77965e7 | 1.59489 | 0.797446 | − | 0.603391i | \(-0.206184\pi\) | ||||
0.797446 | + | 0.603391i | \(0.206184\pi\) | |||||||
\(350\) | 9.40225e7i | 2.19294i | ||||||||
\(351\) | 7.29975e6 | 0.168806 | ||||||||
\(352\) | − | 2.57151e8i | − | 5.89604i | ||||||
\(353\) | −3.84370e7 | −0.873826 | −0.436913 | − | 0.899504i | \(-0.643928\pi\) | ||||
−0.436913 | + | 0.899504i | \(0.643928\pi\) | |||||||
\(354\) | −1.01155e7 | −0.228023 | ||||||||
\(355\) | 3.77695e7i | 0.844220i | ||||||||
\(356\) | − | 2.33586e8i | − | 5.17723i | ||||||
\(357\) | 1.25562e7 | 0.275964 | ||||||||
\(358\) | 3.67934e7 | 0.801901 | ||||||||
\(359\) | 7.06002e7i | 1.52589i | 0.646465 | + | 0.762944i | \(0.276247\pi\) | ||||
−0.646465 | + | 0.762944i | \(0.723753\pi\) | |||||||
\(360\) | − | 6.60864e7i | − | 1.41646i | ||||||
\(361\) | 3.37020e7 | 0.716365 | ||||||||
\(362\) | − | 1.71223e7i | − | 0.360942i | ||||||
\(363\) | −4.25406e7 | −0.889372 | ||||||||
\(364\) | 1.95687e8i | 4.05748i | ||||||||
\(365\) | − | 1.21475e7i | − | 0.249809i | ||||||
\(366\) | − | 2.70923e7i | − | 0.552590i | ||||||
\(367\) | 7.35519e7i | 1.48797i | 0.668194 | + | 0.743987i | \(0.267068\pi\) | ||||
−0.668194 | + | 0.743987i | \(0.732932\pi\) | |||||||
\(368\) | −1.62065e8 | − | 8.03603e7i | −3.25197 | − | 1.61249i | ||||
\(369\) | 2.47394e7 | 0.492391 | ||||||||
\(370\) | 6.35237e7 | 1.25409 | ||||||||
\(371\) | −5.09626e7 | −0.997999 | ||||||||
\(372\) | 8.79330e6 | 0.170814 | ||||||||
\(373\) | − | 4.00245e7i | − | 0.771257i | −0.922654 | − | 0.385629i | \(-0.873985\pi\) | ||
0.922654 | − | 0.385629i | \(-0.126015\pi\) | |||||||
\(374\) | −4.49508e7 | −0.859255 | ||||||||
\(375\) | 1.30958e7i | 0.248335i | ||||||||
\(376\) | 2.00794e8 | 3.77735 | ||||||||
\(377\) | 1.16204e7 | 0.216868 | ||||||||
\(378\) | − | 3.41821e7i | − | 0.632882i | ||||||
\(379\) | − | 1.08610e7i | − | 0.199504i | −0.995012 | − | 0.0997522i | \(-0.968195\pi\) | ||
0.995012 | − | 0.0997522i | \(-0.0318050\pi\) | |||||||
\(380\) | 1.02210e8 | 1.86269 | ||||||||
\(381\) | −4.09970e7 | −0.741272 | ||||||||
\(382\) | − | 2.42752e7i | − | 0.435484i | ||||||
\(383\) | 9.30194e7i | 1.65568i | 0.560962 | + | 0.827842i | \(0.310431\pi\) | ||||
−0.560962 | + | 0.827842i | \(0.689569\pi\) | |||||||
\(384\) | −9.90752e7 | −1.74973 | ||||||||
\(385\) | − | 2.00520e8i | − | 3.51379i | ||||||
\(386\) | −1.62903e8 | −2.83248 | ||||||||
\(387\) | − | 2.02768e7i | − | 0.349838i | ||||||
\(388\) | 2.12434e8i | 3.63688i | ||||||||
\(389\) | − | 1.08899e7i | − | 0.185001i | −0.995713 | − | 0.0925004i | \(-0.970514\pi\) | ||
0.995713 | − | 0.0925004i | \(-0.0294859\pi\) | |||||||
\(390\) | − | 7.46928e7i | − | 1.25917i | ||||||
\(391\) | −7.43334e6 | + | 1.49911e7i | −0.124352 | + | 0.250785i | ||||
\(392\) | 3.79817e8 | 6.30546 | ||||||||
\(393\) | 2.63681e7 | 0.434412 | ||||||||
\(394\) | 8.56950e7 | 1.40109 | ||||||||
\(395\) | −8.70895e7 | −1.41311 | ||||||||
\(396\) | 8.93783e7i | 1.43928i | ||||||||
\(397\) | −2.63976e7 | −0.421883 | −0.210942 | − | 0.977499i | \(-0.567653\pi\) | ||||
−0.210942 | + | 0.977499i | \(0.567653\pi\) | |||||||
\(398\) | 1.85643e8i | 2.94463i | ||||||||
\(399\) | 3.33513e7 | 0.525042 | ||||||||
\(400\) | −1.54912e8 | −2.42050 | ||||||||
\(401\) | 9.57063e7i | 1.48425i | 0.670261 | + | 0.742125i | \(0.266182\pi\) | ||||
−0.670261 | + | 0.742125i | \(0.733818\pi\) | |||||||
\(402\) | − | 1.19780e7i | − | 0.184376i | ||||||
\(403\) | 6.26980e6 | 0.0957941 | ||||||||
\(404\) | 2.59853e8 | 3.94080 | ||||||||
\(405\) | 9.52949e6i | 0.143451i | ||||||||
\(406\) | − | 5.44140e7i | − | 0.813078i | ||||||
\(407\) | −5.41989e7 | −0.803910 | ||||||||
\(408\) | 3.61274e7i | 0.531932i | ||||||||
\(409\) | −7.91380e7 | −1.15669 | −0.578343 | − | 0.815794i | \(-0.696300\pi\) | ||||
−0.578343 | + | 0.815794i | \(0.696300\pi\) | |||||||
\(410\) | − | 2.53140e8i | − | 3.67290i | ||||||
\(411\) | 3.94534e7i | 0.568276i | ||||||||
\(412\) | 8.76605e7i | 1.25347i | ||||||||
\(413\) | 2.46680e7i | 0.350174i | ||||||||
\(414\) | 4.08107e7 | + | 2.02360e7i | 0.575139 | + | 0.285183i | ||||
\(415\) | 3.57092e7 | 0.499616 | ||||||||
\(416\) | −2.33590e8 | −3.24470 | ||||||||
\(417\) | 1.09819e7 | 0.151450 | ||||||||
\(418\) | −1.19397e8 | −1.63480 | ||||||||
\(419\) | − | 2.39477e7i | − | 0.325553i | −0.986663 | − | 0.162777i | \(-0.947955\pi\) | ||
0.986663 | − | 0.162777i | \(-0.0520450\pi\) | |||||||
\(420\) | −2.55460e8 | −3.44806 | ||||||||
\(421\) | 1.75288e7i | 0.234912i | 0.993078 | + | 0.117456i | \(0.0374740\pi\) | ||||
−0.993078 | + | 0.117456i | \(0.962526\pi\) | |||||||
\(422\) | 3.95371e7 | 0.526098 | ||||||||
\(423\) | −2.89540e7 | −0.382549 | ||||||||
\(424\) | − | 1.46633e8i | − | 1.92369i | ||||||
\(425\) | 1.43294e7i | 0.186664i | ||||||||
\(426\) | −5.62091e7 | −0.727073 | ||||||||
\(427\) | −6.60681e7 | −0.848610 | ||||||||
\(428\) | − | 2.48613e8i | − | 3.17097i | ||||||
\(429\) | 6.37286e7i | 0.807165i | ||||||||
\(430\) | −2.07478e8 | −2.60955 | ||||||||
\(431\) | 1.35583e8i | 1.69345i | 0.532030 | + | 0.846725i | \(0.321429\pi\) | ||||
−0.532030 | + | 0.846725i | \(0.678571\pi\) | |||||||
\(432\) | 5.63186e7 | 0.698556 | ||||||||
\(433\) | − | 3.97273e7i | − | 0.489356i | −0.969604 | − | 0.244678i | \(-0.921318\pi\) | ||
0.969604 | − | 0.244678i | \(-0.0786822\pi\) | |||||||
\(434\) | − | 2.93592e7i | − | 0.359149i | ||||||
\(435\) | 1.51699e7i | 0.184295i | ||||||||
\(436\) | − | 3.62195e8i | − | 4.37001i | ||||||
\(437\) | −1.97442e7 | + | 3.98188e7i | −0.236590 | + | 0.477138i | ||||
\(438\) | 1.80781e7 | 0.215145 | ||||||||
\(439\) | −1.21074e7 | −0.143106 | −0.0715528 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715528 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(440\) | 5.76950e8 | 6.77299 | ||||||||
\(441\) | −5.47687e7 | −0.638582 | ||||||||
\(442\) | 4.08323e7i | 0.472865i | ||||||||
\(443\) | −3.79840e7 | −0.436908 | −0.218454 | − | 0.975847i | \(-0.570101\pi\) | ||||
−0.218454 | + | 0.975847i | \(0.570101\pi\) | |||||||
\(444\) | 6.90486e7i | 0.788871i | ||||||||
\(445\) | 2.17426e8 | 2.46735 | ||||||||
\(446\) | 4.95495e7 | 0.558515 | ||||||||
\(447\) | − | 8.43881e6i | − | 0.0944841i | ||||||
\(448\) | 5.36515e8i | 5.96688i | ||||||||
\(449\) | −6.88185e7 | −0.760267 | −0.380133 | − | 0.924932i | \(-0.624122\pi\) | ||||
−0.380133 | + | 0.924932i | \(0.624122\pi\) | |||||||
\(450\) | 3.90094e7 | 0.428086 | ||||||||
\(451\) | 2.15981e8i | 2.35443i | ||||||||
\(452\) | − | 5.56396e7i | − | 0.602516i | ||||||
\(453\) | 884757. | 0.00951764 | ||||||||
\(454\) | 6.92540e7i | 0.740078i | ||||||||
\(455\) | −1.82148e8 | −1.93371 | ||||||||
\(456\) | 9.59606e7i | 1.01204i | ||||||||
\(457\) | − | 3.14473e7i | − | 0.329485i | −0.986337 | − | 0.164742i | \(-0.947321\pi\) | ||
0.986337 | − | 0.164742i | \(-0.0526792\pi\) | |||||||
\(458\) | − | 2.61152e8i | − | 2.71830i | ||||||
\(459\) | − | 5.20948e6i | − | 0.0538711i | ||||||
\(460\) | 1.51234e8 | − | 3.04999e8i | 1.55373 | − | 3.13346i | ||||
\(461\) | 3.45124e7 | 0.352267 | 0.176134 | − | 0.984366i | \(-0.443641\pi\) | ||||
0.176134 | + | 0.984366i | \(0.443641\pi\) | |||||||
\(462\) | 2.98417e8 | 3.02620 | ||||||||
\(463\) | −1.45561e8 | −1.46656 | −0.733281 | − | 0.679925i | \(-0.762012\pi\) | ||||
−0.733281 | + | 0.679925i | \(0.762012\pi\) | |||||||
\(464\) | 8.96529e7 | 0.897450 | ||||||||
\(465\) | 8.18494e6i | 0.0814060i | ||||||||
\(466\) | −1.38663e8 | −1.37025 | ||||||||
\(467\) | − | 1.85068e8i | − | 1.81711i | −0.417768 | − | 0.908554i | \(-0.637188\pi\) | ||
0.417768 | − | 0.908554i | \(-0.362812\pi\) | |||||||
\(468\) | 8.11892e7 | 0.792065 | ||||||||
\(469\) | −2.92098e7 | −0.283146 | ||||||||
\(470\) | 2.96264e8i | 2.85355i | ||||||||
\(471\) | 2.61045e7i | 0.249835i | ||||||||
\(472\) | −7.09764e7 | −0.674975 | ||||||||
\(473\) | 1.77022e8 | 1.67280 | ||||||||
\(474\) | − | 1.29608e8i | − | 1.21702i | ||||||
\(475\) | 3.80613e7i | 0.355143i | ||||||||
\(476\) | 1.39652e8 | 1.29487 | ||||||||
\(477\) | 2.11441e7i | 0.194820i | ||||||||
\(478\) | 3.25660e8 | 2.98181 | ||||||||
\(479\) | − | 8.37663e7i | − | 0.762189i | −0.924536 | − | 0.381095i | \(-0.875547\pi\) | ||
0.924536 | − | 0.381095i | \(-0.124453\pi\) | |||||||
\(480\) | − | 3.04941e8i | − | 2.75736i | ||||||
\(481\) | 4.92331e7i | 0.442407i | ||||||||
\(482\) | − | 1.46429e8i | − | 1.30763i | ||||||
\(483\) | 4.93482e7 | − | 9.95221e7i | 0.437955 | − | 0.883238i | ||||
\(484\) | −4.73144e8 | −4.17308 | ||||||||
\(485\) | −1.97737e8 | −1.73326 | ||||||||
\(486\) | −1.41819e7 | −0.123545 | ||||||||
\(487\) | −1.52782e8 | −1.32277 | −0.661387 | − | 0.750045i | \(-0.730032\pi\) | ||||
−0.661387 | + | 0.750045i | \(0.730032\pi\) | |||||||
\(488\) | − | 1.90096e8i | − | 1.63573i | ||||||
\(489\) | −8.51937e7 | −0.728587 | ||||||||
\(490\) | 5.60406e8i | 4.76338i | ||||||||
\(491\) | −1.77832e8 | −1.50233 | −0.751165 | − | 0.660115i | \(-0.770508\pi\) | ||||
−0.751165 | + | 0.660115i | \(0.770508\pi\) | |||||||
\(492\) | 2.75157e8 | 2.31039 | ||||||||
\(493\) | − | 8.29290e6i | − | 0.0692095i | ||||||
\(494\) | 1.08457e8i | 0.899660i | ||||||||
\(495\) | −8.31947e7 | −0.685930 | ||||||||
\(496\) | 4.83724e7 | 0.396418 | ||||||||
\(497\) | 1.37073e8i | 1.11656i | ||||||||
\(498\) | 5.31431e7i | 0.430287i | ||||||||
\(499\) | 1.78735e8 | 1.43850 | 0.719248 | − | 0.694753i | \(-0.244486\pi\) | ||||
0.719248 | + | 0.694753i | \(0.244486\pi\) | |||||||
\(500\) | 1.45654e8i | 1.16523i | ||||||||
\(501\) | 8.62478e7 | 0.685859 | ||||||||
\(502\) | − | 9.30922e7i | − | 0.735872i | ||||||
\(503\) | − | 1.25380e8i | − | 0.985204i | −0.870255 | − | 0.492602i | \(-0.836046\pi\) | ||
0.870255 | − | 0.492602i | \(-0.163954\pi\) | |||||||
\(504\) | − | 2.39841e8i | − | 1.87341i | ||||||
\(505\) | 2.41876e8i | 1.87810i | ||||||||
\(506\) | −1.76665e8 | + | 3.56287e8i | −1.36364 | + | 2.75010i | ||||
\(507\) | −1.73529e7 | −0.133152 | ||||||||
\(508\) | −4.55976e8 | −3.47817 | ||||||||
\(509\) | 3.45688e7 | 0.262139 | 0.131069 | − | 0.991373i | \(-0.458159\pi\) | ||||
0.131069 | + | 0.991373i | \(0.458159\pi\) | |||||||
\(510\) | −5.33047e7 | −0.401841 | ||||||||
\(511\) | − | 4.40858e7i | − | 0.330397i | ||||||
\(512\) | −1.98673e8 | −1.48023 | ||||||||
\(513\) | − | 1.38373e7i | − | 0.102494i | ||||||
\(514\) | 3.12394e8 | 2.30045 | ||||||||
\(515\) | −8.15958e7 | −0.597374 | ||||||||
\(516\) | − | 2.25523e8i | − | 1.64150i | ||||||
\(517\) | − | 2.52775e8i | − | 1.82921i | ||||||
\(518\) | 2.30540e8 | 1.65866 | ||||||||
\(519\) | −3.97116e6 | −0.0284063 | ||||||||
\(520\) | − | 5.24089e8i | − | 3.72730i | ||||||
\(521\) | 1.84179e8i | 1.30235i | 0.758928 | + | 0.651175i | \(0.225724\pi\) | ||||
−0.758928 | + | 0.651175i | \(0.774276\pi\) | |||||||
\(522\) | −2.25760e7 | −0.158722 | ||||||||
\(523\) | − | 1.67317e8i | − | 1.16959i | −0.811180 | − | 0.584797i | \(-0.801174\pi\) | ||
0.811180 | − | 0.584797i | \(-0.198826\pi\) | |||||||
\(524\) | 2.93271e8 | 2.03834 | ||||||||
\(525\) | − | 9.51294e7i | − | 0.657411i | ||||||
\(526\) | − | 3.33667e8i | − | 2.29274i | ||||||
\(527\) | − | 4.47445e6i | − | 0.0305709i | ||||||
\(528\) | 4.91675e8i | 3.34023i | ||||||||
\(529\) | 8.96069e7 | + | 1.17836e8i | 0.605306 | + | 0.795993i | ||||
\(530\) | 2.16352e8 | 1.45322 | ||||||||
\(531\) | 1.02346e7 | 0.0683577 | ||||||||
\(532\) | 3.70939e8 | 2.46359 | ||||||||
\(533\) | 1.96192e8 | 1.29569 | ||||||||
\(534\) | 3.23577e8i | 2.12497i | ||||||||
\(535\) | 2.31413e8 | 1.51121 | ||||||||
\(536\) | − | 8.40443e7i | − | 0.545775i | ||||||
\(537\) | −3.72266e7 | −0.240398 | ||||||||
\(538\) | −5.31791e8 | −3.41503 | ||||||||
\(539\) | − | 4.78143e8i | − | 3.05346i | ||||||
\(540\) | 1.05989e8i | 0.673099i | ||||||||
\(541\) | 1.47750e8 | 0.933115 | 0.466557 | − | 0.884491i | \(-0.345494\pi\) | ||||
0.466557 | + | 0.884491i | \(0.345494\pi\) | |||||||
\(542\) | −2.58575e8 | −1.62401 | ||||||||
\(543\) | 1.73239e7i | 0.108205i | ||||||||
\(544\) | 1.66702e8i | 1.03549i | ||||||||
\(545\) | 3.37137e8 | 2.08265 | ||||||||
\(546\) | − | 2.71076e8i | − | 1.66538i | ||||||
\(547\) | 5.42473e7 | 0.331449 | 0.165724 | − | 0.986172i | \(-0.447004\pi\) | ||||
0.165724 | + | 0.986172i | \(0.447004\pi\) | |||||||
\(548\) | 4.38808e8i | 2.66645i | ||||||||
\(549\) | 2.74113e7i | 0.165658i | ||||||||
\(550\) | 3.40561e8i | 2.04695i | ||||||||
\(551\) | − | 2.20274e7i | − | 0.131676i | ||||||
\(552\) | 2.86351e8 | + | 1.41988e8i | 1.70248 | + | 0.844178i | ||||
\(553\) | −3.16066e8 | −1.86897 | ||||||||
\(554\) | −5.71948e8 | −3.36378 | ||||||||
\(555\) | −6.42715e7 | −0.375958 | ||||||||
\(556\) | 1.22143e8 | 0.710630 | ||||||||
\(557\) | 1.34098e7i | 0.0775991i | 0.999247 | + | 0.0387995i | \(0.0123534\pi\) | ||||
−0.999247 | + | 0.0387995i | \(0.987647\pi\) | |||||||
\(558\) | −1.21810e7 | −0.0701098 | ||||||||
\(559\) | − | 1.60802e8i | − | 0.920571i | ||||||
\(560\) | −1.40530e9 | −8.00211 | ||||||||
\(561\) | 4.54800e7 | 0.257592 | ||||||||
\(562\) | 5.37777e8i | 3.02965i | ||||||||
\(563\) | 1.61409e8i | 0.904490i | 0.891894 | + | 0.452245i | \(0.149377\pi\) | ||||
−0.891894 | + | 0.452245i | \(0.850623\pi\) | |||||||
\(564\) | −3.22032e8 | −1.79499 | ||||||||
\(565\) | 5.17902e7 | 0.287146 | ||||||||
\(566\) | − | 9.33813e7i | − | 0.515004i | ||||||
\(567\) | 3.45845e7i | 0.189728i | ||||||||
\(568\) | −3.94396e8 | −2.15222 | ||||||||
\(569\) | 1.91072e6i | 0.0103720i | 0.999987 | + | 0.00518598i | \(0.00165076\pi\) | ||||
−0.999987 | + | 0.00518598i | \(0.998349\pi\) | |||||||
\(570\) | −1.41586e8 | −0.764534 | ||||||||
\(571\) | 2.08656e8i | 1.12078i | 0.828228 | + | 0.560392i | \(0.189350\pi\) | ||||
−0.828228 | + | 0.560392i | \(0.810650\pi\) | |||||||
\(572\) | 7.08801e8i | 3.78736i | ||||||||
\(573\) | 2.45610e7i | 0.130551i | ||||||||
\(574\) | − | 9.18697e8i | − | 4.85776i | ||||||
\(575\) | 1.13577e8 | + | 5.63173e7i | 0.597429 | + | 0.296236i | ||||
\(576\) | 2.22597e8 | 1.16480 | ||||||||
\(577\) | 3.82528e8 | 1.99129 | 0.995647 | − | 0.0932020i | \(-0.0297102\pi\) | ||||
0.995647 | + | 0.0932020i | \(0.0297102\pi\) | |||||||
\(578\) | −3.42749e8 | −1.77498 | ||||||||
\(579\) | 1.64820e8 | 0.849133 | ||||||||
\(580\) | 1.68722e8i | 0.864745i | ||||||||
\(581\) | 1.29596e8 | 0.660791 | ||||||||
\(582\) | − | 2.94276e8i | − | 1.49274i | ||||||
\(583\) | −1.84593e8 | −0.931557 | ||||||||
\(584\) | 1.26846e8 | 0.636854 | ||||||||
\(585\) | 7.55722e7i | 0.377481i | ||||||||
\(586\) | − | 5.12715e8i | − | 2.54791i | ||||||
\(587\) | 7.94636e7 | 0.392874 | 0.196437 | − | 0.980516i | \(-0.437063\pi\) | ||||
0.196437 | + | 0.980516i | \(0.437063\pi\) | |||||||
\(588\) | −6.09147e8 | −2.99633 | ||||||||
\(589\) | − | 1.18849e7i | − | 0.0581634i | ||||||
\(590\) | − | 1.04723e8i | − | 0.509901i | ||||||
\(591\) | −8.67039e7 | −0.420026 | ||||||||
\(592\) | 3.79840e8i | 1.83078i | ||||||||
\(593\) | 3.55660e7 | 0.170557 | 0.0852787 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852787 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(594\) | − | 1.23812e8i | − | 0.590748i | ||||||
\(595\) | 1.29990e8i | 0.617106i | ||||||||
\(596\) | − | 9.38580e7i | − | 0.443336i | ||||||
\(597\) | − | 1.87829e8i | − | 0.882754i | ||||||
\(598\) | 3.23643e8 | + | 1.60479e8i | 1.51343 | + | 0.750437i | ||||
\(599\) | 3.23906e8 | 1.50709 | 0.753543 | − | 0.657398i | \(-0.228343\pi\) | ||||
0.753543 | + | 0.657398i | \(0.228343\pi\) | |||||||
\(600\) | 2.73713e8 | 1.26719 | ||||||||
\(601\) | 1.25196e8 | 0.576721 | 0.288360 | − | 0.957522i | \(-0.406890\pi\) | ||||
0.288360 | + | 0.957522i | \(0.406890\pi\) | |||||||
\(602\) | −7.52979e8 | −3.45139 | ||||||||
\(603\) | 1.21190e7i | 0.0552731i | ||||||||
\(604\) | 9.84043e6 | 0.0446584 | ||||||||
\(605\) | − | 4.40410e8i | − | 1.98880i | ||||||
\(606\) | −3.59963e8 | −1.61748 | ||||||||
\(607\) | −1.10872e8 | −0.495743 | −0.247871 | − | 0.968793i | \(-0.579731\pi\) | ||||
−0.247871 | + | 0.968793i | \(0.579731\pi\) | |||||||
\(608\) | 4.42789e8i | 1.97009i | ||||||||
\(609\) | 5.50546e7i | 0.243748i | ||||||||
\(610\) | 2.80479e8 | 1.23569 | ||||||||
\(611\) | −2.29615e8 | −1.00665 | ||||||||
\(612\) | − | 5.79408e7i | − | 0.252773i | ||||||
\(613\) | − | 4.30728e8i | − | 1.86992i | −0.354758 | − | 0.934958i | \(-0.615437\pi\) | ||
0.354758 | − | 0.934958i | \(-0.384563\pi\) | |||||||
\(614\) | −1.37390e8 | −0.593541 | ||||||||
\(615\) | 2.56120e8i | 1.10108i | ||||||||
\(616\) | 2.09387e9 | 8.95793 | ||||||||
\(617\) | 4.44968e7i | 0.189441i | 0.995504 | + | 0.0947203i | \(0.0301957\pi\) | ||||
−0.995504 | + | 0.0947203i | \(0.969804\pi\) | |||||||
\(618\) | − | 1.21432e8i | − | 0.514480i | ||||||
\(619\) | 3.26072e8i | 1.37480i | 0.726277 | + | 0.687402i | \(0.241249\pi\) | ||||
−0.726277 | + | 0.687402i | \(0.758751\pi\) | |||||||
\(620\) | 9.10344e7i | 0.381971i | ||||||||
\(621\) | −4.12911e7 | − | 2.04743e7i | −0.172418 | − | 0.0854936i | ||||
\(622\) | −6.03988e8 | −2.50991 | ||||||||
\(623\) | 7.89083e8 | 3.26331 | ||||||||
\(624\) | 4.46627e8 | 1.83819 | ||||||||
\(625\) | −2.98380e8 | −1.22216 | ||||||||
\(626\) | 3.13467e8i | 1.27782i | ||||||||
\(627\) | 1.20803e8 | 0.490087 | ||||||||
\(628\) | 2.90339e8i | 1.17227i | ||||||||
\(629\) | 3.51353e7 | 0.141186 | ||||||||
\(630\) | 3.53877e8 | 1.41524 | ||||||||
\(631\) | − | 2.03802e8i | − | 0.811187i | −0.914054 | − | 0.405594i | \(-0.867065\pi\) | ||
0.914054 | − | 0.405594i | \(-0.132935\pi\) | |||||||
\(632\) | − | 9.09405e8i | − | 3.60252i | ||||||
\(633\) | −4.00025e7 | −0.157716 | ||||||||
\(634\) | 2.10566e8 | 0.826268 | ||||||||
\(635\) | − | 4.24430e8i | − | 1.65762i | ||||||
\(636\) | 2.35169e8i | 0.914130i | ||||||||
\(637\) | −4.34335e8 | −1.68038 | ||||||||
\(638\) | − | 1.97094e8i | − | 0.758948i | ||||||
\(639\) | 5.68709e7 | 0.217965 | ||||||||
\(640\) | − | 1.02570e9i | − | 3.91272i | ||||||
\(641\) | − | 7.89353e7i | − | 0.299707i | −0.988708 | − | 0.149854i | \(-0.952120\pi\) | ||
0.988708 | − | 0.149854i | \(-0.0478802\pi\) | |||||||
\(642\) | 3.44392e8i | 1.30151i | ||||||||
\(643\) | 6.79395e7i | 0.255558i | 0.991803 | + | 0.127779i | \(0.0407848\pi\) | ||||
−0.991803 | + | 0.127779i | \(0.959215\pi\) | |||||||
\(644\) | 5.48860e8 | − | 1.10690e9i | 2.05496 | − | 4.14431i | ||||
\(645\) | 2.09920e8 | 0.782303 | ||||||||
\(646\) | 7.74008e7 | 0.287110 | ||||||||
\(647\) | 9.78812e7 | 0.361399 | 0.180699 | − | 0.983538i | \(-0.442164\pi\) | ||||
0.180699 | + | 0.983538i | \(0.442164\pi\) | |||||||
\(648\) | −9.95088e7 | −0.365710 | ||||||||
\(649\) | 8.93505e7i | 0.326861i | ||||||||
\(650\) | 3.09358e8 | 1.12647 | ||||||||
\(651\) | 2.97048e7i | 0.107667i | ||||||||
\(652\) | −9.47541e8 | −3.41865 | ||||||||
\(653\) | −3.62932e7 | −0.130342 | −0.0651712 | − | 0.997874i | \(-0.520759\pi\) | ||||
−0.0651712 | + | 0.997874i | \(0.520759\pi\) | |||||||
\(654\) | 5.01732e8i | 1.79365i | ||||||||
\(655\) | 2.72982e8i | 0.971425i | ||||||||
\(656\) | 1.51365e9 | 5.36185 | ||||||||
\(657\) | −1.82909e7 | −0.0644970 | ||||||||
\(658\) | 1.07520e9i | 3.77410i | ||||||||
\(659\) | 4.37953e8i | 1.53028i | 0.643863 | + | 0.765141i | \(0.277331\pi\) | ||||
−0.643863 | + | 0.765141i | \(0.722669\pi\) | |||||||
\(660\) | −9.25307e8 | −3.21850 | ||||||||
\(661\) | − | 3.87843e8i | − | 1.34292i | −0.741039 | − | 0.671462i | \(-0.765667\pi\) | ||
0.741039 | − | 0.671462i | \(-0.234333\pi\) | |||||||
\(662\) | 1.47242e8 | 0.507525 | ||||||||
\(663\) | − | 4.13130e7i | − | 0.141758i | ||||||
\(664\) | 3.72883e8i | 1.27370i | ||||||||
\(665\) | 3.45276e8i | 1.17409i | ||||||||
\(666\) | − | 9.56499e7i | − | 0.323789i | ||||||
\(667\) | −6.57308e7 | − | 3.25927e7i | −0.221509 | − | 0.109836i | ||||
\(668\) | 9.59264e8 | 3.21817 | ||||||||
\(669\) | −5.01329e7 | −0.167434 | ||||||||
\(670\) | 1.24004e8 | 0.412299 | ||||||||
\(671\) | −2.39307e8 | −0.792114 | ||||||||
\(672\) | − | 1.10670e9i | − | 3.64687i | ||||||
\(673\) | 5.10336e8 | 1.67422 | 0.837108 | − | 0.547038i | \(-0.184245\pi\) | ||||
0.837108 | + | 0.547038i | \(0.184245\pi\) | |||||||
\(674\) | 6.11573e7i | 0.199742i | ||||||||
\(675\) | −3.94686e7 | −0.128334 | ||||||||
\(676\) | −1.93002e8 | −0.624773 | ||||||||
\(677\) | − | 5.73800e8i | − | 1.84924i | −0.380886 | − | 0.924622i | \(-0.624381\pi\) | ||
0.380886 | − | 0.924622i | \(-0.375619\pi\) | |||||||
\(678\) | 7.70751e7i | 0.247300i | ||||||||
\(679\) | −7.17629e8 | −2.29240 | ||||||||
\(680\) | −3.74017e8 | −1.18950 | ||||||||
\(681\) | − | 7.00694e7i | − | 0.221864i | ||||||
\(682\) | − | 1.06343e8i | − | 0.335239i | ||||||
\(683\) | 4.32001e8 | 1.35588 | 0.677942 | − | 0.735115i | \(-0.262872\pi\) | ||||
0.677942 | + | 0.735115i | \(0.262872\pi\) | |||||||
\(684\) | − | 1.53901e8i | − | 0.480919i | ||||||
\(685\) | −4.08450e8 | −1.27077 | ||||||||
\(686\) | 9.72191e8i | 3.01147i | ||||||||
\(687\) | 2.64227e8i | 0.814905i | ||||||||
\(688\) | − | 1.24061e9i | − | 3.80953i | ||||||
\(689\) | 1.67680e8i | 0.512653i | ||||||||
\(690\) | −2.09498e8 | + | 4.22501e8i | −0.637723 | + | 1.28612i | ||||
\(691\) | −5.16043e7 | −0.156405 | −0.0782027 | − | 0.996937i | \(-0.524918\pi\) | ||||
−0.0782027 | + | 0.996937i | \(0.524918\pi\) | |||||||
\(692\) | −4.41680e7 | −0.133287 | ||||||||
\(693\) | −3.01931e8 | −0.907210 | ||||||||
\(694\) | −6.16896e7 | −0.184558 | ||||||||
\(695\) | 1.13692e8i | 0.338670i | ||||||||
\(696\) | −1.58407e8 | −0.469836 | ||||||||
\(697\) | − | 1.40013e8i | − | 0.413495i | ||||||
\(698\) | −1.04455e9 | −3.07158 | ||||||||
\(699\) | 1.40295e8 | 0.410781 | ||||||||
\(700\) | − | 1.05805e9i | − | 3.08468i | ||||||
\(701\) | − | 6.70008e8i | − | 1.94503i | −0.232847 | − | 0.972513i | \(-0.574804\pi\) | ||
0.232847 | − | 0.972513i | \(-0.425196\pi\) | |||||||
\(702\) | −1.12468e8 | −0.325100 | ||||||||
\(703\) | 9.33253e7 | 0.268617 | ||||||||
\(704\) | 1.94332e9i | 5.56964i | ||||||||
\(705\) | − | 2.99752e8i | − | 0.855451i | ||||||
\(706\) | 5.92201e8 | 1.68289 | ||||||||
\(707\) | 8.77817e8i | 2.48397i | ||||||||
\(708\) | 1.13831e8 | 0.320746 | ||||||||
\(709\) | 3.62760e8i | 1.01784i | 0.860813 | + | 0.508921i | \(0.169955\pi\) | ||||
−0.860813 | + | 0.508921i | \(0.830045\pi\) | |||||||
\(710\) | − | 5.81916e8i | − | 1.62587i | ||||||
\(711\) | 1.31134e8i | 0.364843i | ||||||||
\(712\) | 2.27040e9i | 6.29018i | ||||||||
\(713\) | −3.54652e7 | − | 1.75855e7i | −0.0978440 | − | 0.0485161i | ||||
\(714\) | −1.93454e8 | −0.531474 | ||||||||
\(715\) | −6.59763e8 | −1.80497 | ||||||||
\(716\) | −4.14041e8 | −1.12799 | ||||||||
\(717\) | −3.29494e8 | −0.893901 | ||||||||
\(718\) | − | 1.08774e9i | − | 2.93868i | ||||||
\(719\) | −1.42205e8 | −0.382586 | −0.191293 | − | 0.981533i | \(-0.561268\pi\) | ||||
−0.191293 | + | 0.981533i | \(0.561268\pi\) | |||||||
\(720\) | 5.83051e8i | 1.56210i | ||||||||
\(721\) | −2.96128e8 | −0.790085 | ||||||||
\(722\) | −5.19249e8 | −1.37964 | ||||||||
\(723\) | 1.48153e8i | 0.392007i | ||||||||
\(724\) | 1.92680e8i | 0.507716i | ||||||||
\(725\) | −6.28296e7 | −0.164873 | ||||||||
\(726\) | 6.55425e8 | 1.71283 | ||||||||
\(727\) | − | 1.81413e8i | − | 0.472134i | −0.971737 | − | 0.236067i | \(-0.924142\pi\) | ||
0.971737 | − | 0.236067i | \(-0.0758584\pi\) | |||||||
\(728\) | − | 1.90203e9i | − | 4.92972i | ||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 1.87157e8i | 0.481103i | ||||||||
\(731\) | −1.14757e8 | −0.293783 | ||||||||
\(732\) | 3.04873e8i | 0.777296i | ||||||||
\(733\) | 2.56165e8i | 0.650441i | 0.945638 | + | 0.325221i | \(0.105439\pi\) | ||||
−0.945638 | + | 0.325221i | \(0.894561\pi\) | |||||||
\(734\) | − | 1.13322e9i | − | 2.86567i | ||||||
\(735\) | − | 5.67004e8i | − | 1.42799i | ||||||
\(736\) | 1.32131e9 | + | 6.55172e8i | 3.31413 | + | 1.64332i | ||||
\(737\) | −1.05801e8 | −0.264295 | ||||||||
\(738\) | −3.81162e8 | −0.948289 | ||||||||
\(739\) | −4.29689e8 | −1.06468 | −0.532342 | − | 0.846529i | \(-0.678688\pi\) | ||||
−0.532342 | + | 0.846529i | \(0.678688\pi\) | |||||||
\(740\) | −7.14840e8 | −1.76406 | ||||||||
\(741\) | − | 1.09734e8i | − | 0.269704i | ||||||
\(742\) | 7.85185e8 | 1.92203 | ||||||||
\(743\) | 3.88763e8i | 0.947804i | 0.880578 | + | 0.473902i | \(0.157155\pi\) | ||||
−0.880578 | + | 0.473902i | \(0.842845\pi\) | |||||||
\(744\) | −8.54687e7 | −0.207534 | ||||||||
\(745\) | 8.73645e7 | 0.211284 | ||||||||
\(746\) | 6.16660e8i | 1.48535i | ||||||||
\(747\) | − | 5.37687e7i | − | 0.128994i | ||||||
\(748\) | 5.05837e8 | 1.20866 | ||||||||
\(749\) | 8.39845e8 | 1.99873 | ||||||||
\(750\) | − | 2.01767e8i | − | 0.478264i | ||||||
\(751\) | − | 5.69395e8i | − | 1.34429i | −0.740418 | − | 0.672146i | \(-0.765373\pi\) | ||
0.740418 | − | 0.672146i | \(-0.234627\pi\) | |||||||
\(752\) | −1.77151e9 | −4.16573 | ||||||||
\(753\) | 9.41882e7i | 0.220603i | ||||||||
\(754\) | −1.79036e8 | −0.417663 | ||||||||
\(755\) | 9.15963e6i | 0.0212832i | ||||||||
\(756\) | 3.84655e8i | 0.890238i | ||||||||
\(757\) | 4.17955e8i | 0.963479i | 0.876315 | + | 0.481739i | \(0.159995\pi\) | ||||
−0.876315 | + | 0.481739i | \(0.840005\pi\) | |||||||
\(758\) | 1.67336e8i | 0.384222i | ||||||||
\(759\) | 1.78745e8 | − | 3.60481e8i | 0.408798 | − | 0.824437i | ||||
\(760\) | −9.93452e8 | −2.26311 | ||||||||
\(761\) | −5.53264e7 | −0.125539 | −0.0627695 | − | 0.998028i | \(-0.519993\pi\) | ||||
−0.0627695 | + | 0.998028i | \(0.519993\pi\) | |||||||
\(762\) | 6.31644e8 | 1.42760 | ||||||||
\(763\) | 1.22354e9 | 2.75451 | ||||||||
\(764\) | 2.73172e8i | 0.612570i | ||||||||
\(765\) | 5.39322e7 | 0.120466 | ||||||||
\(766\) | − | 1.43316e9i | − | 3.18865i | ||||||
\(767\) | 8.11640e7 | 0.179878 | ||||||||
\(768\) | 6.12564e8 | 1.35228 | ||||||||
\(769\) | 3.30904e8i | 0.727652i | 0.931467 | + | 0.363826i | \(0.118530\pi\) | ||||
−0.931467 | + | 0.363826i | \(0.881470\pi\) | |||||||
\(770\) | 3.08943e9i | 6.76715i | ||||||||
\(771\) | −3.16072e8 | −0.689640 | ||||||||
\(772\) | 1.83316e9 | 3.98428 | ||||||||
\(773\) | 7.66293e7i | 0.165904i | 0.996554 | + | 0.0829519i | \(0.0264348\pi\) | ||||
−0.996554 | + | 0.0829519i | \(0.973565\pi\) | |||||||
\(774\) | 3.12407e8i | 0.673748i | ||||||||
\(775\) | −3.38999e7 | −0.0728271 | ||||||||
\(776\) | − | 2.06481e9i | − | 4.41870i | ||||||
\(777\) | −2.33255e8 | −0.497241 | ||||||||
\(778\) | 1.67781e8i | 0.356290i | ||||||||
\(779\) | − | 3.71898e8i | − | 0.786705i | ||||||
\(780\) | 8.40528e8i | 1.77120i | ||||||||
\(781\) | 4.96496e8i | 1.04223i | ||||||||
\(782\) | 1.14526e8 | − | 2.30968e8i | 0.239488 | − | 0.482983i | ||||
\(783\) | 2.28418e7 | 0.0475823 | ||||||||
\(784\) | −3.35096e9 | −6.95377 | ||||||||
\(785\) | −2.70252e8 | −0.558677 | ||||||||
\(786\) | −4.06256e8 | −0.836627 | ||||||||
\(787\) | 6.20091e8i | 1.27213i | 0.771636 | + | 0.636065i | \(0.219439\pi\) | ||||
−0.771636 | + | 0.636065i | \(0.780561\pi\) | |||||||
\(788\) | −9.64337e8 | −1.97083 | ||||||||
\(789\) | 3.37595e8i | 0.687329i | ||||||||
\(790\) | 1.34179e9 | 2.72148 | ||||||||
\(791\) | 1.87957e8 | 0.379778 | ||||||||
\(792\) | − | 8.68735e8i | − | 1.74869i | ||||||
\(793\) | 2.17381e8i | 0.435915i | ||||||||
\(794\) | 4.06709e8 | 0.812498 | ||||||||
\(795\) | −2.18899e8 | −0.435654 | ||||||||
\(796\) | − | 2.08907e9i | − | 4.14203i | ||||||
\(797\) | 5.15952e8i | 1.01914i | 0.860429 | + | 0.509571i | \(0.170196\pi\) | ||||
−0.860429 | + | 0.509571i | \(0.829804\pi\) | |||||||
\(798\) | −5.13846e8 | −1.01117 | ||||||||
\(799\) | 1.63865e8i | 0.321253i | ||||||||
\(800\) | 1.26299e9 | 2.46677 | ||||||||
\(801\) | − | 3.27386e8i | − | 0.637034i | ||||||
\(802\) | − | 1.47455e9i | − | 2.85849i | ||||||
\(803\) | − | 1.59684e8i | − | 0.308401i | ||||||
\(804\) | 1.34789e8i | 0.259351i | ||||||||
\(805\) | 1.03032e9 | + | 5.10887e8i | 1.97508 | + | 0.979349i | ||||
\(806\) | −9.65993e7 | −0.184488 | ||||||||
\(807\) | 5.38052e8 | 1.02377 | ||||||||
\(808\) | −2.52571e9 | −4.78795 | ||||||||
\(809\) | −5.79553e8 | −1.09458 | −0.547290 | − | 0.836943i | \(-0.684340\pi\) | ||||
−0.547290 | + | 0.836943i | \(0.684340\pi\) | |||||||
\(810\) | − | 1.46822e8i | − | 0.276271i | ||||||
\(811\) | −8.98110e8 | −1.68371 | −0.841855 | − | 0.539705i | \(-0.818536\pi\) | ||||
−0.841855 | + | 0.539705i | \(0.818536\pi\) | |||||||
\(812\) | 6.12328e8i | 1.14371i | ||||||||
\(813\) | 2.61619e8 | 0.486853 | ||||||||
\(814\) | 8.35046e8 | 1.54824 | ||||||||
\(815\) | − | 8.81986e8i | − | 1.62925i | ||||||
\(816\) | − | 3.18736e8i | − | 0.586625i | ||||||
\(817\) | −3.04814e8 | −0.558945 | ||||||||
\(818\) | 1.21928e9 | 2.22764 | ||||||||
\(819\) | 2.74267e8i | 0.499255i | ||||||||
\(820\) | 2.84862e9i | 5.16645i | ||||||||
\(821\) | −9.78455e8 | −1.76812 | −0.884059 | − | 0.467375i | \(-0.845200\pi\) | ||||
−0.884059 | + | 0.467375i | \(0.845200\pi\) | |||||||
\(822\) | − | 6.07862e8i | − | 1.09443i | ||||||
\(823\) | −3.80620e8 | −0.682797 | −0.341399 | − | 0.939919i | \(-0.610901\pi\) | ||||
−0.341399 | + | 0.939919i | \(0.610901\pi\) | |||||||
\(824\) | − | 8.52039e8i | − | 1.52292i | ||||||
\(825\) | − | 3.44571e8i | − | 0.613644i | ||||||
\(826\) | − | 3.80061e8i | − | 0.674394i | ||||||
\(827\) | − | 4.38363e8i | − | 0.775029i | −0.921864 | − | 0.387514i | \(-0.873334\pi\) | ||
0.921864 | − | 0.387514i | \(-0.126666\pi\) | |||||||
\(828\) | −4.59248e8 | − | 2.27719e8i | −0.809014 | − | 0.401151i | ||||
\(829\) | 2.92030e8 | 0.512583 | 0.256291 | − | 0.966600i | \(-0.417499\pi\) | ||||
0.256291 | + | 0.966600i | \(0.417499\pi\) | |||||||
\(830\) | −5.50175e8 | −0.962202 | ||||||||
\(831\) | 5.78682e8 | 1.00841 | ||||||||
\(832\) | 1.76527e9 | 3.06508 | ||||||||
\(833\) | 3.09964e8i | 0.536260i | ||||||||
\(834\) | −1.69199e8 | −0.291675 | ||||||||
\(835\) | 8.92898e8i | 1.53371i | ||||||||
\(836\) | 1.34359e9 | 2.29957 | ||||||||
\(837\) | 1.23244e7 | 0.0210178 | ||||||||
\(838\) | 3.68964e8i | 0.626977i | ||||||||
\(839\) | − | 6.83425e8i | − | 1.15719i | −0.815615 | − | 0.578595i | \(-0.803601\pi\) | ||
0.815615 | − | 0.578595i | \(-0.196399\pi\) | |||||||
\(840\) | 2.48301e9 | 4.18929 | ||||||||
\(841\) | −5.58462e8 | −0.938870 | ||||||||
\(842\) | − | 2.70067e8i | − | 0.452414i | ||||||
\(843\) | − | 5.44108e8i | − | 0.908244i | ||||||
\(844\) | −4.44916e8 | −0.740032 | ||||||||
\(845\) | − | 1.79650e8i | − | 0.297753i | ||||||
\(846\) | 4.46096e8 | 0.736745 | ||||||||
\(847\) | − | 1.59834e9i | − | 2.63038i | ||||||
\(848\) | 1.29368e9i | 2.12148i | ||||||||
\(849\) | 9.44807e7i | 0.154390i | ||||||||
\(850\) | − | 2.20774e8i | − | 0.359493i | ||||||
\(851\) | 1.38088e8 | − | 2.78488e8i | 0.224062 | − | 0.451874i | ||||
\(852\) | 6.32528e8 | 1.02273 | ||||||||
\(853\) | 6.12987e8 | 0.987652 | 0.493826 | − | 0.869561i | \(-0.335598\pi\) | ||||
0.493826 | + | 0.869561i | \(0.335598\pi\) | |||||||
\(854\) | 1.01792e9 | 1.63432 | ||||||||
\(855\) | 1.43253e8 | 0.229195 | ||||||||
\(856\) | 2.41646e9i | 3.85263i | ||||||||
\(857\) | 3.56047e8 | 0.565673 | 0.282836 | − | 0.959168i | \(-0.408725\pi\) | ||||
0.282836 | + | 0.959168i | \(0.408725\pi\) | |||||||
\(858\) | − | 9.81870e8i | − | 1.55451i | ||||||
\(859\) | −4.90978e8 | −0.774609 | −0.387304 | − | 0.921952i | \(-0.626594\pi\) | ||||
−0.387304 | + | 0.921952i | \(0.626594\pi\) | |||||||
\(860\) | 2.33477e9 | 3.67070 | ||||||||
\(861\) | 9.29513e8i | 1.45628i | ||||||||
\(862\) | − | 2.08893e9i | − | 3.26139i | ||||||
\(863\) | −6.95860e8 | −1.08265 | −0.541327 | − | 0.840812i | \(-0.682078\pi\) | ||||
−0.541327 | + | 0.840812i | \(0.682078\pi\) | |||||||
\(864\) | −4.59162e8 | −0.711909 | ||||||||
\(865\) | − | 4.11123e7i | − | 0.0635218i | ||||||
\(866\) | 6.12081e8i | 0.942443i | ||||||||
\(867\) | 3.46784e8 | 0.532111 | ||||||||
\(868\) | 3.30383e8i | 0.505194i | ||||||||
\(869\) | −1.14483e9 | −1.74454 | ||||||||
\(870\) | − | 2.33723e8i | − | 0.354931i | ||||||
\(871\) | 9.61077e7i | 0.145447i | ||||||||
\(872\) | 3.52044e9i | 5.30943i | ||||||||
\(873\) | 2.97740e8i | 0.447502i | ||||||||
\(874\) | 3.04200e8 | − | 6.13491e8i | 0.455644 | − | 0.918912i | ||||
\(875\) | −4.92036e8 | −0.734468 | ||||||||
\(876\) | −2.03435e8 | −0.302631 | ||||||||
\(877\) | 8.71349e8 | 1.29179 | 0.645897 | − | 0.763425i | \(-0.276484\pi\) | ||||
0.645897 | + | 0.763425i | \(0.276484\pi\) | |||||||
\(878\) | 1.86539e8 | 0.275605 | ||||||||
\(879\) | 5.18752e8i | 0.763823i | ||||||||
\(880\) | −5.09017e9 | −7.46937 | ||||||||
\(881\) | 3.09398e8i | 0.452470i | 0.974073 | + | 0.226235i | \(0.0726418\pi\) | ||||
−0.974073 | + | 0.226235i | \(0.927358\pi\) | |||||||
\(882\) | 8.43824e8 | 1.22983 | ||||||||
\(883\) | −7.52724e8 | −1.09334 | −0.546668 | − | 0.837350i | \(-0.684104\pi\) | ||||
−0.546668 | + | 0.837350i | \(0.684104\pi\) | |||||||
\(884\) | − | 4.59491e8i | − | 0.665151i | ||||||
\(885\) | 1.05956e8i | 0.152861i | ||||||||
\(886\) | 5.85222e8 | 0.841433 | ||||||||
\(887\) | 8.11020e8 | 1.16215 | 0.581073 | − | 0.813852i | \(-0.302633\pi\) | ||||
0.581073 | + | 0.813852i | \(0.302633\pi\) | |||||||
\(888\) | − | 6.71136e8i | − | 0.958455i | ||||||
\(889\) | − | 1.54034e9i | − | 2.19236i | ||||||
\(890\) | −3.34989e9 | −4.75183 | ||||||||
\(891\) | 1.25269e8i | 0.177097i | ||||||||
\(892\) | −5.57587e8 | −0.785631 | ||||||||
\(893\) | 4.35254e8i | 0.611207i | ||||||||
\(894\) | 1.30017e8i | 0.181965i | ||||||||
\(895\) | − | 3.85396e8i | − | 0.537574i | ||||||
\(896\) | − | 3.72247e9i | − | 5.17496i | ||||||
\(897\) | −3.27453e8 | − | 1.62368e8i | −0.453703 | − | 0.224969i | ||||
\(898\) | 1.06029e9 | 1.46419 | ||||||||
\(899\) | 1.96190e7 | 0.0270021 | ||||||||
\(900\) | −4.38978e8 | −0.602164 | ||||||||
\(901\) | 1.19665e8 | 0.163604 | ||||||||
\(902\) | − | 3.32763e9i | − | 4.53436i | ||||||
\(903\) | 7.61844e8 | 1.03467 | ||||||||
\(904\) | 5.40804e8i | 0.732039i | ||||||||
\(905\) | −1.79350e8 | −0.241966 | ||||||||
\(906\) | −1.36315e7 | −0.0183299 | ||||||||
\(907\) | 6.91993e8i | 0.927427i | 0.885985 | + | 0.463714i | \(0.153483\pi\) | ||||
−0.885985 | + | 0.463714i | \(0.846517\pi\) | |||||||
\(908\) | − | 7.79325e8i | − | 1.04102i | ||||||
\(909\) | 3.64201e8 | 0.484897 | ||||||||
\(910\) | 2.80637e9 | 3.72409 | ||||||||
\(911\) | 8.23121e8i | 1.08870i | 0.838858 | + | 0.544351i | \(0.183224\pi\) | ||||
−0.838858 | + | 0.544351i | \(0.816776\pi\) | |||||||
\(912\) | − | 8.46616e8i | − | 1.11610i | ||||||
\(913\) | 4.69414e8 | 0.616798 | ||||||||
\(914\) | 4.84511e8i | 0.634549i | ||||||||
\(915\) | −2.83781e8 | −0.370442 | ||||||||
\(916\) | 2.93878e9i | 3.82367i | ||||||||
\(917\) | 9.90706e8i | 1.28480i | ||||||||
\(918\) | 8.02628e7i | 0.103750i | ||||||||
\(919\) | − | 5.85375e8i | − | 0.754201i | −0.926172 | − | 0.377101i | \(-0.876921\pi\) | ||
0.926172 | − | 0.377101i | \(-0.123079\pi\) | |||||||
\(920\) | −1.46996e9 | + | 2.96451e9i | −1.88774 | + | 3.80706i | ||||
\(921\) | 1.39008e8 | 0.177934 | ||||||||
\(922\) | −5.31735e8 | −0.678426 | ||||||||
\(923\) | 4.51006e8 | 0.573558 | ||||||||
\(924\) | −3.35813e9 | −4.25678 | ||||||||
\(925\) | − | 2.66196e8i | − | 0.336338i | ||||||
\(926\) | 2.24266e9 | 2.82443 | ||||||||
\(927\) | 1.22862e8i | 0.154233i | ||||||||
\(928\) | −7.30933e8 | −0.914605 | ||||||||
\(929\) | 1.03227e9 | 1.28750 | 0.643748 | − | 0.765237i | \(-0.277378\pi\) | ||||
0.643748 | + | 0.765237i | \(0.277378\pi\) | |||||||
\(930\) | − | 1.26106e8i | − | 0.156779i | ||||||
\(931\) | 8.23316e8i | 1.02028i | ||||||||
\(932\) | 1.56039e9 | 1.92746 | ||||||||
\(933\) | 6.11099e8 | 0.752431 | ||||||||
\(934\) | 2.85135e9i | 3.49954i | ||||||||
\(935\) | 4.70841e8i | 0.576023i | ||||||||
\(936\) | −7.89140e8 | −0.962335 | ||||||||
\(937\) | − | 8.43729e8i | − | 1.02561i | −0.858504 | − | 0.512807i | \(-0.828606\pi\) | ||
0.858504 | − | 0.512807i | \(-0.171394\pi\) | |||||||
\(938\) | 4.50037e8 | 0.545305 | ||||||||
\(939\) | − | 3.17158e8i | − | 0.383070i | ||||||
\(940\) | − | 3.33390e9i | − | 4.01392i | ||||||
\(941\) | − | 1.50332e9i | − | 1.80420i | −0.431530 | − | 0.902098i | \(-0.642026\pi\) | ||
0.431530 | − | 0.902098i | \(-0.357974\pi\) | |||||||
\(942\) | − | 4.02194e8i | − | 0.481153i | ||||||
\(943\) | −1.10976e9 | − | 5.50278e8i | −1.32341 | − | 0.656217i | ||||
\(944\) | 6.26192e8 | 0.744375 | ||||||||
\(945\) | −3.58043e8 | −0.424268 | ||||||||
\(946\) | −2.72738e9 | −3.22161 | ||||||||
\(947\) | 6.65696e8 | 0.783837 | 0.391919 | − | 0.920000i | \(-0.371811\pi\) | ||||
0.391919 | + | 0.920000i | \(0.371811\pi\) | |||||||
\(948\) | 1.45850e9i | 1.71191i | ||||||||
\(949\) | −1.45053e8 | −0.169719 | ||||||||
\(950\) | − | 5.86413e8i | − | 0.683963i | ||||||
\(951\) | −2.13045e8 | −0.247703 | ||||||||
\(952\) | −1.35738e9 | −1.57323 | ||||||||
\(953\) | − | 8.53637e7i | − | 0.0986267i | −0.998783 | − | 0.0493133i | \(-0.984297\pi\) | ||
0.998783 | − | 0.0493133i | \(-0.0157033\pi\) | |||||||
\(954\) | − | 3.25769e8i | − | 0.375201i | ||||||
\(955\) | −2.54273e8 | −0.291937 | ||||||||
\(956\) | −3.66469e9 | −4.19434 | ||||||||
\(957\) | 1.99415e8i | 0.227521i | ||||||||
\(958\) | 1.29059e9i | 1.46789i | ||||||||
\(959\) | −1.48235e9 | −1.68072 | ||||||||
\(960\) | 2.30448e9i | 2.60471i | ||||||||
\(961\) | −8.76918e8 | −0.988073 | ||||||||
\(962\) | − | 7.58537e8i | − | 0.852024i | ||||||
\(963\) | − | 3.48447e8i | − | 0.390173i | ||||||
\(964\) | 1.64778e9i | 1.83937i | ||||||||
\(965\) | 1.70634e9i | 1.89882i | ||||||||
\(966\) | −7.60311e8 | + | 1.53334e9i | −0.843451 | + | 1.70101i | ||||
\(967\) | 1.10914e9 | 1.22661 | 0.613307 | − | 0.789845i | \(-0.289839\pi\) | ||||
0.613307 | + | 0.789845i | \(0.289839\pi\) | |||||||
\(968\) | 4.59885e9 | 5.07017 | ||||||||
\(969\) | −7.83121e7 | −0.0860711 | ||||||||
\(970\) | 3.04655e9 | 3.33805 | ||||||||
\(971\) | 6.69724e7i | 0.0731540i | 0.999331 | + | 0.0365770i | \(0.0116454\pi\) | ||||
−0.999331 | + | 0.0365770i | \(0.988355\pi\) | |||||||
\(972\) | 1.59591e8 | 0.173784 | ||||||||
\(973\) | 4.12613e8i | 0.447924i | ||||||||
\(974\) | 2.35392e9 | 2.54751 | ||||||||
\(975\) | −3.13000e8 | −0.337700 | ||||||||
\(976\) | 1.67713e9i | 1.80392i | ||||||||
\(977\) | − | 3.19020e8i | − | 0.342086i | −0.985264 | − | 0.171043i | \(-0.945286\pi\) | ||
0.985264 | − | 0.171043i | \(-0.0547136\pi\) | |||||||
\(978\) | 1.31259e9 | 1.40317 | ||||||||
\(979\) | 2.85816e9 | 3.04606 | ||||||||
\(980\) | − | 6.30633e9i | − | 6.70036i | ||||||
\(981\) | − | 5.07639e8i | − | 0.537710i | ||||||
\(982\) | 2.73987e9 | 2.89331 | ||||||||
\(983\) | 4.41798e7i | 0.0465118i | 0.999730 | + | 0.0232559i | \(0.00740325\pi\) | ||||
−0.999730 | + | 0.0232559i | \(0.992597\pi\) | |||||||
\(984\) | −2.67446e9 | −2.80705 | ||||||||
\(985\) | − | 8.97621e8i | − | 0.939256i | ||||||
\(986\) | 1.27769e8i | 0.133289i | ||||||||
\(987\) | − | 1.08786e9i | − | 1.13142i | ||||||
\(988\) | − | 1.22049e9i | − | 1.26550i | ||||||
\(989\) | −4.51017e8 | + | 9.09581e8i | −0.466234 | + | 0.940270i | ||||
\(990\) | 1.28179e9 | 1.32102 | ||||||||
\(991\) | 1.67599e9 | 1.72207 | 0.861035 | − | 0.508546i | \(-0.169817\pi\) | ||||
0.861035 | + | 0.508546i | \(0.169817\pi\) | |||||||
\(992\) | −3.94377e8 | −0.403995 | ||||||||
\(993\) | −1.48975e8 | −0.152148 | ||||||||
\(994\) | − | 2.11190e9i | − | 2.15037i | ||||||
\(995\) | 1.94454e9 | 1.97400 | ||||||||
\(996\) | − | 5.98026e8i | − | 0.605260i | ||||||
\(997\) | −5.36246e8 | −0.541102 | −0.270551 | − | 0.962706i | \(-0.587206\pi\) | ||||
−0.270551 | + | 0.962706i | \(0.587206\pi\) | |||||||
\(998\) | −2.75379e9 | −2.77038 | ||||||||
\(999\) | 9.67760e7i | 0.0970669i |
(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 | 69.7.d.a.22.2 | yes | 24 | |
3.2 | odd | 2 | 207.7.d.e.91.23 | 24 | |||
23.22 | odd | 2 | inner | 69.7.d.a.22.1 | ✓ | 24 | |
69.68 | even | 2 | 207.7.d.e.91.24 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.7.d.a.22.1 | ✓ | 24 | 23.22 | odd | 2 | inner | |
69.7.d.a.22.2 | yes | 24 | 1.1 | even | 1 | trivial | |
207.7.d.e.91.23 | 24 | 3.2 | odd | 2 | |||
207.7.d.e.91.24 | 24 | 69.68 | even | 2 |