Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,6,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.b (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: | \(2.72652493682\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 167x^{4} + 9076x^{2} + 159156 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(6.22955i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.6.b.a.16.2 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.50095 | −1.50277 | −0.751385 | − | 0.659864i | \(-0.770614\pi\) | ||||
−0.751385 | + | 0.659864i | \(0.770614\pi\) | |||||||
\(3\) | − | 12.4591i | − | 0.799252i | −0.916678 | − | 0.399626i | \(-0.869140\pi\) | ||
0.916678 | − | 0.399626i | \(-0.130860\pi\) | |||||||
\(4\) | 40.2661 | 1.25832 | ||||||||
\(5\) | 92.1671i | 1.64873i | 0.566055 | + | 0.824367i | \(0.308469\pi\) | ||||
−0.566055 | + | 0.824367i | \(0.691531\pi\) | |||||||
\(6\) | 105.914i | 1.20109i | ||||||||
\(7\) | 52.2138i | 0.402755i | 0.979514 | + | 0.201377i | \(0.0645417\pi\) | ||||
−0.979514 | + | 0.201377i | \(0.935458\pi\) | |||||||
\(8\) | −70.2699 | −0.388190 | ||||||||
\(9\) | 87.7709 | 0.361197 | ||||||||
\(10\) | − | 783.508i | − | 2.47767i | ||||||
\(11\) | 426.209i | 1.06204i | 0.847359 | + | 0.531020i | \(0.178191\pi\) | ||||
−0.847359 | + | 0.531020i | \(0.821809\pi\) | |||||||
\(12\) | − | 501.680i | − | 1.00571i | ||||||
\(13\) | −682.449 | −1.11998 | −0.559992 | − | 0.828498i | \(-0.689196\pi\) | ||||
−0.559992 | + | 0.828498i | \(0.689196\pi\) | |||||||
\(14\) | − | 443.867i | − | 0.605247i | ||||||
\(15\) | 1148.32 | 1.31775 | ||||||||
\(16\) | −691.155 | −0.674956 | ||||||||
\(17\) | −335.976 | + | 1143.23i | −0.281959 | + | 0.959427i | ||||
\(18\) | −746.136 | −0.542796 | ||||||||
\(19\) | 1924.19 | 1.22283 | 0.611413 | − | 0.791311i | \(-0.290601\pi\) | ||||
0.611413 | + | 0.791311i | \(0.290601\pi\) | |||||||
\(20\) | 3711.21i | 2.07463i | ||||||||
\(21\) | 650.537 | 0.321902 | ||||||||
\(22\) | − | 3623.18i | − | 1.59600i | ||||||
\(23\) | − | 187.713i | − | 0.0739905i | −0.999315 | − | 0.0369952i | \(-0.988221\pi\) | ||
0.999315 | − | 0.0369952i | \(-0.0117786\pi\) | |||||||
\(24\) | 875.500i | 0.310262i | ||||||||
\(25\) | −5369.77 | −1.71833 | ||||||||
\(26\) | 5801.47 | 1.68308 | ||||||||
\(27\) | − | 4121.11i | − | 1.08794i | ||||||
\(28\) | 2102.45i | 0.506793i | ||||||||
\(29\) | 2531.86i | 0.559043i | 0.960139 | + | 0.279521i | \(0.0901758\pi\) | ||||
−0.960139 | + | 0.279521i | \(0.909824\pi\) | |||||||
\(30\) | −9761.80 | −1.98028 | ||||||||
\(31\) | 6165.74i | 1.15234i | 0.817330 | + | 0.576170i | \(0.195453\pi\) | ||||
−0.817330 | + | 0.576170i | \(0.804547\pi\) | |||||||
\(32\) | 8124.11 | 1.40249 | ||||||||
\(33\) | 5310.18 | 0.848837 | ||||||||
\(34\) | 2856.11 | − | 9718.55i | 0.423719 | − | 1.44180i | ||||
\(35\) | −4812.40 | −0.664036 | ||||||||
\(36\) | 3534.19 | 0.454500 | ||||||||
\(37\) | − | 15440.4i | − | 1.85419i | −0.374827 | − | 0.927095i | \(-0.622298\pi\) | ||
0.374827 | − | 0.927095i | \(-0.377702\pi\) | |||||||
\(38\) | −16357.5 | −1.83763 | ||||||||
\(39\) | 8502.70i | 0.895149i | ||||||||
\(40\) | − | 6476.57i | − | 0.640023i | ||||||
\(41\) | − | 2173.03i | − | 0.201886i | −0.994892 | − | 0.100943i | \(-0.967814\pi\) | ||
0.994892 | − | 0.100943i | \(-0.0321859\pi\) | |||||||
\(42\) | −5530.18 | −0.483745 | ||||||||
\(43\) | 13046.4 | 1.07602 | 0.538010 | − | 0.842938i | \(-0.319176\pi\) | ||||
0.538010 | + | 0.842938i | \(0.319176\pi\) | |||||||
\(44\) | 17161.8i | 1.33638i | ||||||||
\(45\) | 8089.59i | 0.595518i | ||||||||
\(46\) | 1595.74i | 0.111191i | ||||||||
\(47\) | −10748.6 | −0.709754 | −0.354877 | − | 0.934913i | \(-0.615477\pi\) | ||||
−0.354877 | + | 0.934913i | \(0.615477\pi\) | |||||||
\(48\) | 8611.17i | 0.539460i | ||||||||
\(49\) | 14080.7 | 0.837789 | ||||||||
\(50\) | 45648.1 | 2.58225 | ||||||||
\(51\) | 14243.6 | + | 4185.96i | 0.766823 | + | 0.225356i | ||||
\(52\) | −27479.6 | −1.40929 | ||||||||
\(53\) | −18910.1 | −0.924708 | −0.462354 | − | 0.886695i | \(-0.652995\pi\) | ||||
−0.462354 | + | 0.886695i | \(0.652995\pi\) | |||||||
\(54\) | 35033.3i | 1.63492i | ||||||||
\(55\) | −39282.4 | −1.75102 | ||||||||
\(56\) | − | 3669.06i | − | 0.156345i | ||||||
\(57\) | − | 23973.7i | − | 0.977346i | ||||||
\(58\) | − | 21523.2i | − | 0.840113i | ||||||
\(59\) | 2512.88 | 0.0939815 | 0.0469907 | − | 0.998895i | \(-0.485037\pi\) | ||||
0.0469907 | + | 0.998895i | \(0.485037\pi\) | |||||||
\(60\) | 46238.3 | 1.65815 | ||||||||
\(61\) | − | 5101.84i | − | 0.175551i | −0.996140 | − | 0.0877753i | \(-0.972024\pi\) | ||
0.996140 | − | 0.0877753i | \(-0.0279758\pi\) | |||||||
\(62\) | − | 52414.6i | − | 1.73170i | ||||||
\(63\) | 4582.85i | 0.145474i | ||||||||
\(64\) | −46945.7 | −1.43267 | ||||||||
\(65\) | − | 62899.4i | − | 1.84656i | ||||||
\(66\) | −45141.6 | −1.27561 | ||||||||
\(67\) | 39943.1 | 1.08706 | 0.543532 | − | 0.839388i | \(-0.317087\pi\) | ||||
0.543532 | + | 0.839388i | \(0.317087\pi\) | |||||||
\(68\) | −13528.4 | + | 46033.5i | −0.354793 | + | 1.20726i | ||||
\(69\) | −2338.74 | −0.0591370 | ||||||||
\(70\) | 40909.9 | 0.997893 | ||||||||
\(71\) | − | 38560.9i | − | 0.907823i | −0.891047 | − | 0.453911i | \(-0.850028\pi\) | ||
0.891047 | − | 0.453911i | \(-0.149972\pi\) | |||||||
\(72\) | −6167.65 | −0.140213 | ||||||||
\(73\) | 21745.2i | 0.477590i | 0.971070 | + | 0.238795i | \(0.0767524\pi\) | ||||
−0.971070 | + | 0.238795i | \(0.923248\pi\) | |||||||
\(74\) | 131258.i | 2.78642i | ||||||||
\(75\) | 66902.5i | 1.37338i | ||||||||
\(76\) | 77479.9 | 1.53870 | ||||||||
\(77\) | −22254.0 | −0.427741 | ||||||||
\(78\) | − | 72281.0i | − | 1.34520i | ||||||
\(79\) | 83096.5i | 1.49801i | 0.662564 | + | 0.749006i | \(0.269468\pi\) | ||||
−0.662564 | + | 0.749006i | \(0.730532\pi\) | |||||||
\(80\) | − | 63701.7i | − | 1.11282i | ||||||
\(81\) | −30017.0 | −0.508340 | ||||||||
\(82\) | 18472.8i | 0.303387i | ||||||||
\(83\) | 23872.9 | 0.380374 | 0.190187 | − | 0.981748i | \(-0.439091\pi\) | ||||
0.190187 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(84\) | 26194.6 | 0.405055 | ||||||||
\(85\) | −105368. | − | 30965.9i | −1.58184 | − | 0.464875i | ||||
\(86\) | −110907. | −1.61701 | ||||||||
\(87\) | 31544.7 | 0.446816 | ||||||||
\(88\) | − | 29949.7i | − | 0.412273i | ||||||
\(89\) | 132869. | 1.77807 | 0.889035 | − | 0.457839i | \(-0.151376\pi\) | ||||
0.889035 | + | 0.457839i | \(0.151376\pi\) | |||||||
\(90\) | − | 68769.1i | − | 0.894926i | ||||||
\(91\) | − | 35633.3i | − | 0.451079i | ||||||
\(92\) | − | 7558.50i | − | 0.0931035i | ||||||
\(93\) | 76819.5 | 0.921010 | ||||||||
\(94\) | 91373.5 | 1.06660 | ||||||||
\(95\) | 177347.i | 2.01612i | ||||||||
\(96\) | − | 101219.i | − | 1.12095i | ||||||
\(97\) | 8645.71i | 0.0932978i | 0.998911 | + | 0.0466489i | \(0.0148542\pi\) | ||||
−0.998911 | + | 0.0466489i | \(0.985146\pi\) | |||||||
\(98\) | −119699. | −1.25900 | ||||||||
\(99\) | 37408.7i | 0.383606i | ||||||||
\(100\) | −216220. | −2.16220 | ||||||||
\(101\) | −34784.3 | −0.339297 | −0.169648 | − | 0.985505i | \(-0.554263\pi\) | ||||
−0.169648 | + | 0.985505i | \(0.554263\pi\) | |||||||
\(102\) | −121084. | − | 35584.6i | −1.15236 | − | 0.338658i | ||||
\(103\) | 54298.8 | 0.504309 | 0.252155 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252155 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(104\) | 47955.7 | 0.434767 | ||||||||
\(105\) | 59958.1i | 0.530731i | ||||||||
\(106\) | 160754. | 1.38962 | ||||||||
\(107\) | − | 33711.5i | − | 0.284655i | −0.989820 | − | 0.142327i | \(-0.954541\pi\) | ||
0.989820 | − | 0.142327i | \(-0.0454586\pi\) | |||||||
\(108\) | − | 165941.i | − | 1.36897i | ||||||
\(109\) | − | 64485.4i | − | 0.519870i | −0.965626 | − | 0.259935i | \(-0.916299\pi\) | ||
0.965626 | − | 0.259935i | \(-0.0837012\pi\) | |||||||
\(110\) | 333938. | 2.63138 | ||||||||
\(111\) | −192373. | −1.48196 | ||||||||
\(112\) | − | 36087.9i | − | 0.271842i | ||||||
\(113\) | − | 101591.i | − | 0.748445i | −0.927339 | − | 0.374222i | \(-0.877910\pi\) | ||
0.927339 | − | 0.374222i | \(-0.122090\pi\) | |||||||
\(114\) | 203799.i | 1.46873i | ||||||||
\(115\) | 17301.0 | 0.121991 | ||||||||
\(116\) | 101948.i | 0.703453i | ||||||||
\(117\) | −59899.2 | −0.404535 | ||||||||
\(118\) | −21361.9 | −0.141232 | ||||||||
\(119\) | −59692.5 | − | 17542.6i | −0.386413 | − | 0.113560i | ||||
\(120\) | −80692.3 | −0.511539 | ||||||||
\(121\) | −20603.0 | −0.127929 | ||||||||
\(122\) | 43370.5i | 0.263812i | ||||||||
\(123\) | −27073.9 | −0.161357 | ||||||||
\(124\) | 248270.i | 1.45001i | ||||||||
\(125\) | − | 206894.i | − | 1.18433i | ||||||
\(126\) | − | 38958.6i | − | 0.218614i | ||||||
\(127\) | 64216.1 | 0.353293 | 0.176646 | − | 0.984274i | \(-0.443475\pi\) | ||||
0.176646 | + | 0.984274i | \(0.443475\pi\) | |||||||
\(128\) | 139111. | 0.750477 | ||||||||
\(129\) | − | 162547.i | − | 0.860011i | ||||||
\(130\) | 534704.i | 2.77495i | ||||||||
\(131\) | 44738.8i | 0.227775i | 0.993494 | + | 0.113887i | \(0.0363303\pi\) | ||||
−0.993494 | + | 0.113887i | \(0.963670\pi\) | |||||||
\(132\) | 213820. | 1.06811 | ||||||||
\(133\) | 100470.i | 0.492499i | ||||||||
\(134\) | −339555. | −1.63361 | ||||||||
\(135\) | 379830. | 1.79372 | ||||||||
\(136\) | 23609.0 | − | 80334.8i | 0.109454 | − | 0.372440i | ||||
\(137\) | −56704.2 | −0.258115 | −0.129058 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129058 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(138\) | 19881.5 | 0.0888693 | ||||||||
\(139\) | − | 179460.i | − | 0.787828i | −0.919147 | − | 0.393914i | \(-0.871121\pi\) | ||
0.919147 | − | 0.393914i | \(-0.128879\pi\) | |||||||
\(140\) | −193777. | −0.835567 | ||||||||
\(141\) | 133918.i | 0.567272i | ||||||||
\(142\) | 327804.i | 1.36425i | ||||||||
\(143\) | − | 290866.i | − | 1.18947i | ||||||
\(144\) | −60663.3 | −0.243792 | ||||||||
\(145\) | −233354. | −0.921714 | ||||||||
\(146\) | − | 184854.i | − | 0.717708i | ||||||
\(147\) | − | 175433.i | − | 0.669604i | ||||||
\(148\) | − | 621725.i | − | 2.33316i | ||||||
\(149\) | 22888.7 | 0.0844607 | 0.0422304 | − | 0.999108i | \(-0.486554\pi\) | ||||
0.0422304 | + | 0.999108i | \(0.486554\pi\) | |||||||
\(150\) | − | 568735.i | − | 2.06387i | ||||||
\(151\) | 369543. | 1.31893 | 0.659466 | − | 0.751735i | \(-0.270783\pi\) | ||||
0.659466 | + | 0.751735i | \(0.270783\pi\) | |||||||
\(152\) | −135213. | −0.474689 | ||||||||
\(153\) | −29488.9 | + | 100342.i | −0.101843 | + | 0.346542i | ||||
\(154\) | 189180. | 0.642797 | ||||||||
\(155\) | −568278. | −1.89990 | ||||||||
\(156\) | 342371.i | 1.12638i | ||||||||
\(157\) | −129581. | −0.419557 | −0.209779 | − | 0.977749i | \(-0.567274\pi\) | ||||
−0.209779 | + | 0.977749i | \(0.567274\pi\) | |||||||
\(158\) | − | 706399.i | − | 2.25117i | ||||||
\(159\) | 235603.i | 0.739075i | ||||||||
\(160\) | 748776.i | 2.31234i | ||||||||
\(161\) | 9801.24 | 0.0298000 | ||||||||
\(162\) | 255173. | 0.763917 | ||||||||
\(163\) | 24333.5i | 0.0717358i | 0.999357 | + | 0.0358679i | \(0.0114196\pi\) | ||||
−0.999357 | + | 0.0358679i | \(0.988580\pi\) | |||||||
\(164\) | − | 87499.3i | − | 0.254036i | ||||||
\(165\) | 489424.i | 1.39951i | ||||||||
\(166\) | −202943. | −0.571615 | ||||||||
\(167\) | 497838.i | 1.38133i | 0.723175 | + | 0.690664i | \(0.242682\pi\) | ||||
−0.723175 | + | 0.690664i | \(0.757318\pi\) | |||||||
\(168\) | −45713.2 | −0.124959 | ||||||||
\(169\) | 94443.9 | 0.254365 | ||||||||
\(170\) | 895730. | + | 263240.i | 2.37714 | + | 0.698601i | ||||
\(171\) | 168888. | 0.441681 | ||||||||
\(172\) | 525329. | 1.35397 | ||||||||
\(173\) | 477076.i | 1.21192i | 0.795496 | + | 0.605958i | \(0.207210\pi\) | ||||
−0.795496 | + | 0.605958i | \(0.792790\pi\) | |||||||
\(174\) | −268160. | −0.671461 | ||||||||
\(175\) | − | 280376.i | − | 0.692064i | ||||||
\(176\) | − | 294576.i | − | 0.716830i | ||||||
\(177\) | − | 31308.3i | − | 0.0751148i | ||||||
\(178\) | −1.12951e6 | −2.67203 | ||||||||
\(179\) | 21656.5 | 0.0505192 | 0.0252596 | − | 0.999681i | \(-0.491959\pi\) | ||||
0.0252596 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(180\) | 325736.i | 0.749350i | ||||||||
\(181\) | − | 609467.i | − | 1.38278i | −0.722481 | − | 0.691391i | \(-0.756998\pi\) | ||
0.722481 | − | 0.691391i | \(-0.243002\pi\) | |||||||
\(182\) | 302917.i | 0.677868i | ||||||||
\(183\) | −63564.3 | −0.140309 | ||||||||
\(184\) | 13190.6i | 0.0287224i | ||||||||
\(185\) | 1.42310e6 | 3.05707 | ||||||||
\(186\) | −653039. | −1.38407 | ||||||||
\(187\) | −487255. | − | 143196.i | −1.01895 | − | 0.299452i | ||||
\(188\) | −432805. | −0.893096 | ||||||||
\(189\) | 215179. | 0.438172 | ||||||||
\(190\) | − | 1.50762e6i | − | 3.02976i | ||||||
\(191\) | −168091. | −0.333396 | −0.166698 | − | 0.986008i | \(-0.553310\pi\) | ||||
−0.166698 | + | 0.986008i | \(0.553310\pi\) | |||||||
\(192\) | 584901.i | 1.14506i | ||||||||
\(193\) | 683389.i | 1.32061i | 0.750998 | + | 0.660305i | \(0.229573\pi\) | ||||
−0.750998 | + | 0.660305i | \(0.770427\pi\) | |||||||
\(194\) | − | 73496.7i | − | 0.140205i | ||||||
\(195\) | −783669. | −1.47586 | ||||||||
\(196\) | 566976. | 1.05420 | ||||||||
\(197\) | 269740.i | 0.495199i | 0.968862 | + | 0.247600i | \(0.0796418\pi\) | ||||
−0.968862 | + | 0.247600i | \(0.920358\pi\) | |||||||
\(198\) | − | 318010.i | − | 0.576471i | ||||||
\(199\) | − | 972158.i | − | 1.74022i | −0.492857 | − | 0.870110i | \(-0.664047\pi\) | ||
0.492857 | − | 0.870110i | \(-0.335953\pi\) | |||||||
\(200\) | 377333. | 0.667038 | ||||||||
\(201\) | − | 497656.i | − | 0.868838i | ||||||
\(202\) | 295699. | 0.509885 | ||||||||
\(203\) | −132198. | −0.225157 | ||||||||
\(204\) | 573536. | + | 168552.i | 0.964906 | + | 0.283569i | ||||
\(205\) | 200281. | 0.332856 | ||||||||
\(206\) | −461591. | −0.757861 | ||||||||
\(207\) | − | 16475.8i | − | 0.0267251i | ||||||
\(208\) | 471678. | 0.755940 | ||||||||
\(209\) | 820109.i | 1.29869i | ||||||||
\(210\) | − | 509701.i | − | 0.797567i | ||||||
\(211\) | − | 535453.i | − | 0.827971i | −0.910283 | − | 0.413986i | \(-0.864136\pi\) | ||
0.910283 | − | 0.413986i | \(-0.135864\pi\) | |||||||
\(212\) | −761438. | −1.16358 | ||||||||
\(213\) | −480434. | −0.725579 | ||||||||
\(214\) | 286579.i | 0.427770i | ||||||||
\(215\) | 1.20245e6i | 1.77407i | ||||||||
\(216\) | 289590.i | 0.422327i | ||||||||
\(217\) | −321937. | −0.464110 | ||||||||
\(218\) | 548187.i | 0.781245i | ||||||||
\(219\) | 270925. | 0.381715 | ||||||||
\(220\) | −1.58175e6 | −2.20334 | ||||||||
\(221\) | 229286. | − | 780197.i | 0.315789 | − | 1.07454i | ||||
\(222\) | 1.63536e6 | 2.22705 | ||||||||
\(223\) | 939911. | 1.26568 | 0.632841 | − | 0.774282i | \(-0.281889\pi\) | ||||
0.632841 | + | 0.774282i | \(0.281889\pi\) | |||||||
\(224\) | 424191.i | 0.564861i | ||||||||
\(225\) | −471309. | −0.620654 | ||||||||
\(226\) | 863621.i | 1.12474i | ||||||||
\(227\) | − | 722316.i | − | 0.930385i | −0.885210 | − | 0.465192i | \(-0.845985\pi\) | ||
0.885210 | − | 0.465192i | \(-0.154015\pi\) | |||||||
\(228\) | − | 965329.i | − | 1.22981i | ||||||
\(229\) | −587808. | −0.740708 | −0.370354 | − | 0.928891i | \(-0.620764\pi\) | ||||
−0.370354 | + | 0.928891i | \(0.620764\pi\) | |||||||
\(230\) | −147075. | −0.183324 | ||||||||
\(231\) | 277265.i | 0.341873i | ||||||||
\(232\) | − | 177914.i | − | 0.217015i | ||||||
\(233\) | 377987.i | 0.456129i | 0.973646 | + | 0.228064i | \(0.0732396\pi\) | ||||
−0.973646 | + | 0.228064i | \(0.926760\pi\) | |||||||
\(234\) | 509200. | 0.607923 | ||||||||
\(235\) | − | 990669.i | − | 1.17020i | ||||||
\(236\) | 101184. | 0.118258 | ||||||||
\(237\) | 1.03531e6 | 1.19729 | ||||||||
\(238\) | 507443. | + | 149129.i | 0.580690 | + | 0.170655i | ||||
\(239\) | −435638. | −0.493323 | −0.246662 | − | 0.969102i | \(-0.579334\pi\) | ||||
−0.246662 | + | 0.969102i | \(0.579334\pi\) | |||||||
\(240\) | −793666. | −0.889426 | ||||||||
\(241\) | 826581.i | 0.916733i | 0.888763 | + | 0.458366i | \(0.151565\pi\) | ||||
−0.888763 | + | 0.458366i | \(0.848435\pi\) | |||||||
\(242\) | 175145. | 0.192247 | ||||||||
\(243\) | − | 627445.i | − | 0.681647i | ||||||
\(244\) | − | 205431.i | − | 0.220898i | ||||||
\(245\) | 1.29778e6i | 1.38129i | ||||||||
\(246\) | 230154. | 0.242483 | ||||||||
\(247\) | −1.31316e6 | −1.36955 | ||||||||
\(248\) | − | 433266.i | − | 0.447327i | ||||||
\(249\) | − | 297435.i | − | 0.304015i | ||||||
\(250\) | 1.75880e6i | 1.77978i | ||||||||
\(251\) | 1.48284e6 | 1.48562 | 0.742812 | − | 0.669500i | \(-0.233492\pi\) | ||||
0.742812 | + | 0.669500i | \(0.233492\pi\) | |||||||
\(252\) | 184534.i | 0.183052i | ||||||||
\(253\) | 80005.2 | 0.0785809 | ||||||||
\(254\) | −545898. | −0.530918 | ||||||||
\(255\) | −385807. | + | 1.31279e6i | −0.371552 | + | 1.26429i | ||||
\(256\) | 319684. | 0.304874 | ||||||||
\(257\) | −1.83706e6 | −1.73497 | −0.867483 | − | 0.497466i | \(-0.834264\pi\) | ||||
−0.867483 | + | 0.497466i | \(0.834264\pi\) | |||||||
\(258\) | 1.38180e6i | 1.29240i | ||||||||
\(259\) | 806202. | 0.746783 | ||||||||
\(260\) | − | 2.53271e6i | − | 2.32355i | ||||||
\(261\) | 222224.i | 0.201925i | ||||||||
\(262\) | − | 380322.i | − | 0.342293i | ||||||
\(263\) | 2.05639e6 | 1.83323 | 0.916613 | − | 0.399777i | \(-0.130912\pi\) | ||||
0.916613 | + | 0.399777i | \(0.130912\pi\) | |||||||
\(264\) | −373146. | −0.329510 | ||||||||
\(265\) | − | 1.74289e6i | − | 1.52460i | ||||||
\(266\) | − | 854087.i | − | 0.740113i | ||||||
\(267\) | − | 1.65543e6i | − | 1.42113i | ||||||
\(268\) | 1.60836e6 | 1.36787 | ||||||||
\(269\) | 521583.i | 0.439484i | 0.975558 | + | 0.219742i | \(0.0705215\pi\) | ||||
−0.975558 | + | 0.219742i | \(0.929478\pi\) | |||||||
\(270\) | −3.22892e6 | −2.69555 | ||||||||
\(271\) | −1.22269e6 | −1.01133 | −0.505665 | − | 0.862730i | \(-0.668753\pi\) | ||||
−0.505665 | + | 0.862730i | \(0.668753\pi\) | |||||||
\(272\) | 232211. | − | 790150.i | 0.190310 | − | 0.647571i | ||||
\(273\) | −443959. | −0.360525 | ||||||||
\(274\) | 482039. | 0.387888 | ||||||||
\(275\) | − | 2.28864e6i | − | 1.82493i | ||||||
\(276\) | −94172.0 | −0.0744131 | ||||||||
\(277\) | − | 812339.i | − | 0.636119i | −0.948071 | − | 0.318059i | \(-0.896969\pi\) | ||
0.948071 | − | 0.318059i | \(-0.103031\pi\) | |||||||
\(278\) | 1.52558e6i | 1.18392i | ||||||||
\(279\) | 541172.i | 0.416222i | ||||||||
\(280\) | 338167. | 0.257772 | ||||||||
\(281\) | −1.24006e6 | −0.936863 | −0.468431 | − | 0.883500i | \(-0.655181\pi\) | ||||
−0.468431 | + | 0.883500i | \(0.655181\pi\) | |||||||
\(282\) | − | 1.13843e6i | − | 0.852480i | ||||||
\(283\) | 1.97855e6i | 1.46852i | 0.678868 | + | 0.734260i | \(0.262471\pi\) | ||||
−0.678868 | + | 0.734260i | \(0.737529\pi\) | |||||||
\(284\) | − | 1.55270e6i | − | 1.14233i | ||||||
\(285\) | 2.20959e6 | 1.61138 | ||||||||
\(286\) | 2.47264e6i | 1.78750i | ||||||||
\(287\) | 113462. | 0.0813103 | ||||||||
\(288\) | 713060. | 0.506577 | ||||||||
\(289\) | −1.19410e6 | − | 768196.i | −0.840998 | − | 0.541038i | ||||
\(290\) | 1.98373e6 | 1.38512 | ||||||||
\(291\) | 107718. | 0.0745684 | ||||||||
\(292\) | 875593.i | 0.600959i | ||||||||
\(293\) | −1.08246e6 | −0.736619 | −0.368309 | − | 0.929703i | \(-0.620063\pi\) | ||||
−0.368309 | + | 0.929703i | \(0.620063\pi\) | |||||||
\(294\) | 1.49135e6i | 1.00626i | ||||||||
\(295\) | 231605.i | 0.154951i | ||||||||
\(296\) | 1.08500e6i | 0.719778i | ||||||||
\(297\) | 1.75645e6 | 1.15543 | ||||||||
\(298\) | −194575. | −0.126925 | ||||||||
\(299\) | 128105.i | 0.0828682i | ||||||||
\(300\) | 2.69390e6i | 1.72814i | ||||||||
\(301\) | 681204.i | 0.433372i | ||||||||
\(302\) | −3.14146e6 | −1.98205 | ||||||||
\(303\) | 433381.i | 0.271183i | ||||||||
\(304\) | −1.32992e6 | −0.825354 | ||||||||
\(305\) | 470222. | 0.289436 | ||||||||
\(306\) | 250684. | − | 853005.i | 0.153046 | − | 0.520773i | ||||
\(307\) | −266625. | −0.161456 | −0.0807282 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807282 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(308\) | −896083. | −0.538234 | ||||||||
\(309\) | − | 676514.i | − | 0.403070i | ||||||
\(310\) | 4.83090e6 | 2.85512 | ||||||||
\(311\) | 858418.i | 0.503266i | 0.967823 | + | 0.251633i | \(0.0809676\pi\) | ||||
−0.967823 | + | 0.251633i | \(0.919032\pi\) | |||||||
\(312\) | − | 597484.i | − | 0.347488i | ||||||
\(313\) | 2.21844e6i | 1.27993i | 0.768404 | + | 0.639965i | \(0.221051\pi\) | ||||
−0.768404 | + | 0.639965i | \(0.778949\pi\) | |||||||
\(314\) | 1.10156e6 | 0.630498 | ||||||||
\(315\) | −422388. | −0.239848 | ||||||||
\(316\) | 3.34597e6i | 1.88497i | ||||||||
\(317\) | − | 3.11459e6i | − | 1.74082i | −0.492330 | − | 0.870409i | \(-0.663855\pi\) | ||
0.492330 | − | 0.870409i | \(-0.336145\pi\) | |||||||
\(318\) | − | 2.00285e6i | − | 1.11066i | ||||||
\(319\) | −1.07910e6 | −0.593726 | ||||||||
\(320\) | − | 4.32685e6i | − | 2.36209i | ||||||
\(321\) | −420015. | −0.227511 | ||||||||
\(322\) | −83319.9 | −0.0447826 | ||||||||
\(323\) | −646483. | + | 2.19980e6i | −0.344787 | + | 1.17321i | ||||
\(324\) | −1.20867e6 | −0.639652 | ||||||||
\(325\) | 3.66460e6 | 1.92450 | ||||||||
\(326\) | − | 206858.i | − | 0.107802i | ||||||
\(327\) | −803430. | −0.415507 | ||||||||
\(328\) | 152698.i | 0.0783700i | ||||||||
\(329\) | − | 561227.i | − | 0.285857i | ||||||
\(330\) | − | 4.16057e6i | − | 2.10314i | ||||||
\(331\) | −662879. | −0.332556 | −0.166278 | − | 0.986079i | \(-0.553175\pi\) | ||||
−0.166278 | + | 0.986079i | \(0.553175\pi\) | |||||||
\(332\) | 961271. | 0.478631 | ||||||||
\(333\) | − | 1.35522e6i | − | 0.669728i | ||||||
\(334\) | − | 4.23210e6i | − | 2.07582i | ||||||
\(335\) | 3.68144e6i | 1.79228i | ||||||||
\(336\) | −449622. | −0.217270 | ||||||||
\(337\) | 541004.i | 0.259493i | 0.991547 | + | 0.129746i | \(0.0414164\pi\) | ||||
−0.991547 | + | 0.129746i | \(0.958584\pi\) | |||||||
\(338\) | −802863. | −0.382252 | ||||||||
\(339\) | −1.26573e6 | −0.598195 | ||||||||
\(340\) | −4.24277e6 | − | 1.24688e6i | −1.99046 | − | 0.584960i | ||||
\(341\) | −2.62789e6 | −1.22383 | ||||||||
\(342\) | −1.43571e6 | −0.663745 | ||||||||
\(343\) | 1.61277e6i | 0.740178i | ||||||||
\(344\) | −916772. | −0.417701 | ||||||||
\(345\) | − | 215555.i | − | 0.0975013i | ||||||
\(346\) | − | 4.05560e6i | − | 1.82123i | ||||||
\(347\) | − | 2.28483e6i | − | 1.01866i | −0.860571 | − | 0.509331i | \(-0.829893\pi\) | ||
0.860571 | − | 0.509331i | \(-0.170107\pi\) | |||||||
\(348\) | 1.27018e6 | 0.562236 | ||||||||
\(349\) | 3.20796e6 | 1.40982 | 0.704912 | − | 0.709295i | \(-0.250987\pi\) | ||||
0.704912 | + | 0.709295i | \(0.250987\pi\) | |||||||
\(350\) | 2.38347e6i | 1.04001i | ||||||||
\(351\) | 2.81245e6i | 1.21847i | ||||||||
\(352\) | 3.46257e6i | 1.48950i | ||||||||
\(353\) | 1.52041e6 | 0.649416 | 0.324708 | − | 0.945814i | \(-0.394734\pi\) | ||||
0.324708 | + | 0.945814i | \(0.394734\pi\) | |||||||
\(354\) | 266150.i | 0.112880i | ||||||||
\(355\) | 3.55404e6 | 1.49676 | ||||||||
\(356\) | 5.35012e6 | 2.23738 | ||||||||
\(357\) | −218565. | + | 743715.i | −0.0907632 | + | 0.308842i | ||||
\(358\) | −184101. | −0.0759187 | ||||||||
\(359\) | 2.32904e6 | 0.953765 | 0.476883 | − | 0.878967i | \(-0.341767\pi\) | ||||
0.476883 | + | 0.878967i | \(0.341767\pi\) | |||||||
\(360\) | − | 568455.i | − | 0.231174i | ||||||
\(361\) | 1.22643e6 | 0.495305 | ||||||||
\(362\) | 5.18105e6i | 2.07800i | ||||||||
\(363\) | 256695.i | 0.102247i | ||||||||
\(364\) | − | 1.43481e6i | − | 0.567600i | ||||||
\(365\) | −2.00419e6 | −0.787419 | ||||||||
\(366\) | 540357. | 0.210852 | ||||||||
\(367\) | 2.24848e6i | 0.871413i | 0.900089 | + | 0.435707i | \(0.143501\pi\) | ||||
−0.900089 | + | 0.435707i | \(0.856499\pi\) | |||||||
\(368\) | 129739.i | 0.0499403i | ||||||||
\(369\) | − | 190728.i | − | 0.0729205i | ||||||
\(370\) | −1.20977e7 | −4.59407 | ||||||||
\(371\) | − | 987371.i | − | 0.372431i | ||||||
\(372\) | 3.09322e6 | 1.15892 | ||||||||
\(373\) | −3.85968e6 | −1.43641 | −0.718207 | − | 0.695830i | \(-0.755037\pi\) | ||||
−0.718207 | + | 0.695830i | \(0.755037\pi\) | |||||||
\(374\) | 4.14213e6 | + | 1.21730e6i | 1.53125 | + | 0.450007i | ||||
\(375\) | −2.57771e6 | −0.946578 | ||||||||
\(376\) | 755305. | 0.275520 | ||||||||
\(377\) | − | 1.72787e6i | − | 0.626119i | ||||||
\(378\) | −1.82922e6 | −0.658472 | ||||||||
\(379\) | − | 3.79587e6i | − | 1.35742i | −0.734408 | − | 0.678709i | \(-0.762540\pi\) | ||
0.734408 | − | 0.678709i | \(-0.237460\pi\) | |||||||
\(380\) | 7.14109e6i | 2.53691i | ||||||||
\(381\) | − | 800075.i | − | 0.282370i | ||||||
\(382\) | 1.42893e6 | 0.501017 | ||||||||
\(383\) | 4.39219e6 | 1.52997 | 0.764987 | − | 0.644046i | \(-0.222746\pi\) | ||||
0.764987 | + | 0.644046i | \(0.222746\pi\) | |||||||
\(384\) | − | 1.73320e6i | − | 0.599820i | ||||||
\(385\) | − | 2.05109e6i | − | 0.705232i | ||||||
\(386\) | − | 5.80945e6i | − | 1.98457i | ||||||
\(387\) | 1.14510e6 | 0.388655 | ||||||||
\(388\) | 348129.i | 0.117398i | ||||||||
\(389\) | −3.77518e6 | −1.26492 | −0.632461 | − | 0.774592i | \(-0.717955\pi\) | ||||
−0.632461 | + | 0.774592i | \(0.717955\pi\) | |||||||
\(390\) | 6.66193e6 | 2.21788 | ||||||||
\(391\) | 214600. | + | 63067.2i | 0.0709884 | + | 0.0208623i | ||||
\(392\) | −989451. | −0.325221 | ||||||||
\(393\) | 557405. | 0.182049 | ||||||||
\(394\) | − | 2.29305e6i | − | 0.744171i | ||||||
\(395\) | −7.65876e6 | −2.46982 | ||||||||
\(396\) | 1.50630e6i | 0.482697i | ||||||||
\(397\) | 892552.i | 0.284222i | 0.989851 | + | 0.142111i | \(0.0453890\pi\) | ||||
−0.989851 | + | 0.142111i | \(0.954611\pi\) | |||||||
\(398\) | 8.26427e6i | 2.61515i | ||||||||
\(399\) | 1.25176e6 | 0.393631 | ||||||||
\(400\) | 3.71134e6 | 1.15980 | ||||||||
\(401\) | − | 25330.1i | − | 0.00786639i | −0.999992 | − | 0.00393319i | \(-0.998748\pi\) | ||
0.999992 | − | 0.00393319i | \(-0.00125198\pi\) | |||||||
\(402\) | 4.23054e6i | 1.30566i | ||||||||
\(403\) | − | 4.20780e6i | − | 1.29060i | ||||||
\(404\) | −1.40063e6 | −0.426942 | ||||||||
\(405\) | − | 2.76657e6i | − | 0.838117i | ||||||
\(406\) | 1.12381e6 | 0.338359 | ||||||||
\(407\) | 6.58083e6 | 1.96922 | ||||||||
\(408\) | −1.00090e6 | − | 294147.i | −0.297673 | − | 0.0874810i | ||||
\(409\) | −4.23404e6 | −1.25154 | −0.625772 | − | 0.780006i | \(-0.715216\pi\) | ||||
−0.625772 | + | 0.780006i | \(0.715216\pi\) | |||||||
\(410\) | −1.70258e6 | −0.500206 | ||||||||
\(411\) | 706483.i | 0.206299i | ||||||||
\(412\) | 2.18640e6 | 0.634581 | ||||||||
\(413\) | 131207.i | 0.0378515i | ||||||||
\(414\) | 140060.i | 0.0401617i | ||||||||
\(415\) | 2.20030e6i | 0.627136i | ||||||||
\(416\) | −5.54429e6 | −1.57077 | ||||||||
\(417\) | −2.23591e6 | −0.629673 | ||||||||
\(418\) | − | 6.97170e6i | − | 1.95163i | ||||||
\(419\) | − | 246703.i | − | 0.0686499i | −0.999411 | − | 0.0343249i | \(-0.989072\pi\) | ||
0.999411 | − | 0.0343249i | \(-0.0109281\pi\) | |||||||
\(420\) | 2.41428e6i | 0.667828i | ||||||||
\(421\) | 1.35295e6 | 0.372029 | 0.186014 | − | 0.982547i | \(-0.440443\pi\) | ||||
0.186014 | + | 0.982547i | \(0.440443\pi\) | |||||||
\(422\) | 4.55186e6i | 1.24425i | ||||||||
\(423\) | −943416. | −0.256361 | ||||||||
\(424\) | 1.32881e6 | 0.358963 | ||||||||
\(425\) | 1.80411e6 | − | 6.13889e6i | 0.484497 | − | 1.64861i | ||||
\(426\) | 4.08414e6 | 1.09038 | ||||||||
\(427\) | 266387. | 0.0707038 | ||||||||
\(428\) | − | 1.35743e6i | − | 0.358186i | ||||||
\(429\) | −3.62393e6 | −0.950684 | ||||||||
\(430\) | − | 1.02220e7i | − | 2.66602i | ||||||
\(431\) | − | 4.17269e6i | − | 1.08199i | −0.841026 | − | 0.540995i | \(-0.818048\pi\) | ||
0.841026 | − | 0.540995i | \(-0.181952\pi\) | |||||||
\(432\) | 2.84832e6i | 0.734311i | ||||||||
\(433\) | 501987. | 0.128669 | 0.0643343 | − | 0.997928i | \(-0.479508\pi\) | ||||
0.0643343 | + | 0.997928i | \(0.479508\pi\) | |||||||
\(434\) | 2.73677e6 | 0.697451 | ||||||||
\(435\) | 2.90739e6i | 0.736681i | ||||||||
\(436\) | − | 2.59658e6i | − | 0.654162i | ||||||
\(437\) | − | 361197.i | − | 0.0904776i | ||||||
\(438\) | −2.30312e6 | −0.573629 | ||||||||
\(439\) | 1.51628e6i | 0.375508i | 0.982216 | + | 0.187754i | \(0.0601208\pi\) | ||||
−0.982216 | + | 0.187754i | \(0.939879\pi\) | |||||||
\(440\) | 2.76037e6 | 0.679730 | ||||||||
\(441\) | 1.23588e6 | 0.302607 | ||||||||
\(442\) | −1.94915e6 | + | 6.63242e6i | −0.474559 | + | 1.61479i | ||||
\(443\) | −3.64921e6 | −0.883466 | −0.441733 | − | 0.897147i | \(-0.645636\pi\) | ||||
−0.441733 | + | 0.897147i | \(0.645636\pi\) | |||||||
\(444\) | −7.74613e6 | −1.86478 | ||||||||
\(445\) | 1.22462e7i | 2.93157i | ||||||||
\(446\) | −7.99014e6 | −1.90203 | ||||||||
\(447\) | − | 285172.i | − | 0.0675054i | ||||||
\(448\) | − | 2.45121e6i | − | 0.577014i | ||||||
\(449\) | − | 5.94186e6i | − | 1.39093i | −0.718558 | − | 0.695467i | \(-0.755197\pi\) | ||
0.718558 | − | 0.695467i | \(-0.244803\pi\) | |||||||
\(450\) | 4.00658e6 | 0.932701 | ||||||||
\(451\) | 926163. | 0.214411 | ||||||||
\(452\) | − | 4.09068e6i | − | 0.941780i | ||||||
\(453\) | − | 4.60417e6i | − | 1.05416i | ||||||
\(454\) | 6.14037e6i | 1.39815i | ||||||||
\(455\) | 3.28422e6 | 0.743710 | ||||||||
\(456\) | 1.68463e6i | 0.379396i | ||||||||
\(457\) | 5.20530e6 | 1.16588 | 0.582942 | − | 0.812513i | \(-0.301901\pi\) | ||||
0.582942 | + | 0.812513i | \(0.301901\pi\) | |||||||
\(458\) | 4.99693e6 | 1.11311 | ||||||||
\(459\) | 4.71138e6 | + | 1.38459e6i | 1.04380 | + | 0.306754i | ||||
\(460\) | 696644. | 0.153503 | ||||||||
\(461\) | 7.05940e6 | 1.54709 | 0.773545 | − | 0.633742i | \(-0.218482\pi\) | ||||
0.773545 | + | 0.633742i | \(0.218482\pi\) | |||||||
\(462\) | − | 2.35701e6i | − | 0.513756i | ||||||
\(463\) | 1.43048e6 | 0.310119 | 0.155059 | − | 0.987905i | \(-0.450443\pi\) | ||||
0.155059 | + | 0.987905i | \(0.450443\pi\) | |||||||
\(464\) | − | 1.74991e6i | − | 0.377329i | ||||||
\(465\) | 7.08023e6i | 1.51850i | ||||||||
\(466\) | − | 3.21325e6i | − | 0.685456i | ||||||
\(467\) | −734225. | −0.155789 | −0.0778945 | − | 0.996962i | \(-0.524820\pi\) | ||||
−0.0778945 | + | 0.996962i | \(0.524820\pi\) | |||||||
\(468\) | −2.41191e6 | −0.509033 | ||||||||
\(469\) | 2.08559e6i | 0.437820i | ||||||||
\(470\) | 8.42163e6i | 1.75854i | ||||||||
\(471\) | 1.61446e6i | 0.335332i | ||||||||
\(472\) | −176580. | −0.0364827 | ||||||||
\(473\) | 5.56051e6i | 1.14278i | ||||||||
\(474\) | −8.80110e6 | −1.79925 | ||||||||
\(475\) | −1.03325e7 | −2.10122 | ||||||||
\(476\) | −2.40359e6 | − | 706372.i | −0.486230 | − | 0.142895i | ||||
\(477\) | −1.65976e6 | −0.334002 | ||||||||
\(478\) | 3.70334e6 | 0.741351 | ||||||||
\(479\) | − | 1.72368e6i | − | 0.343256i | −0.985162 | − | 0.171628i | \(-0.945097\pi\) | ||
0.985162 | − | 0.171628i | \(-0.0549027\pi\) | |||||||
\(480\) | 9.32907e6 | 1.84814 | ||||||||
\(481\) | 1.05373e7i | 2.07666i | ||||||||
\(482\) | − | 7.02672e6i | − | 1.37764i | ||||||
\(483\) | − | 122115.i | − | 0.0238177i | ||||||
\(484\) | −829605. | −0.160975 | ||||||||
\(485\) | −796850. | −0.153823 | ||||||||
\(486\) | 5.33388e6i | 1.02436i | ||||||||
\(487\) | 3.22348e6i | 0.615890i | 0.951404 | + | 0.307945i | \(0.0996412\pi\) | ||||
−0.951404 | + | 0.307945i | \(0.900359\pi\) | |||||||
\(488\) | 358506.i | 0.0681470i | ||||||||
\(489\) | 303174. | 0.0573349 | ||||||||
\(490\) | − | 1.10323e7i | − | 2.07576i | ||||||
\(491\) | −3.53364e6 | −0.661482 | −0.330741 | − | 0.943722i | \(-0.607299\pi\) | ||||
−0.330741 | + | 0.943722i | \(0.607299\pi\) | |||||||
\(492\) | −1.09016e6 | −0.203039 | ||||||||
\(493\) | −2.89450e6 | − | 850645.i | −0.536361 | − | 0.157627i | ||||
\(494\) | 1.11631e7 | 2.05811 | ||||||||
\(495\) | −3.44785e6 | −0.632464 | ||||||||
\(496\) | − | 4.26148e6i | − | 0.777779i | ||||||
\(497\) | 2.01341e6 | 0.365630 | ||||||||
\(498\) | 2.52848e6i | 0.456864i | ||||||||
\(499\) | − | 4.37349e6i | − | 0.786279i | −0.919479 | − | 0.393139i | \(-0.871389\pi\) | ||
0.919479 | − | 0.393139i | \(-0.128611\pi\) | |||||||
\(500\) | − | 8.33082e6i | − | 1.49026i | ||||||
\(501\) | 6.20262e6 | 1.10403 | ||||||||
\(502\) | −1.26055e7 | −2.23255 | ||||||||
\(503\) | − | 6.22586e6i | − | 1.09718i | −0.836090 | − | 0.548592i | \(-0.815164\pi\) | ||
0.836090 | − | 0.548592i | \(-0.184836\pi\) | |||||||
\(504\) | − | 322037.i | − | 0.0564715i | ||||||
\(505\) | − | 3.20596e6i | − | 0.559410i | ||||||
\(506\) | −680120. | −0.118089 | ||||||||
\(507\) | − | 1.17669e6i | − | 0.203302i | ||||||
\(508\) | 2.58573e6 | 0.444554 | ||||||||
\(509\) | −5.11234e6 | −0.874631 | −0.437316 | − | 0.899308i | \(-0.644071\pi\) | ||||
−0.437316 | + | 0.899308i | \(0.644071\pi\) | |||||||
\(510\) | 3.27973e6 | − | 1.11600e7i | 0.558358 | − | 1.89993i | ||||
\(511\) | −1.13540e6 | −0.192352 | ||||||||
\(512\) | −7.16918e6 | −1.20863 | ||||||||
\(513\) | − | 7.92981e6i | − | 1.33036i | ||||||
\(514\) | 1.56168e7 | 2.60725 | ||||||||
\(515\) | 5.00456e6i | 0.831472i | ||||||||
\(516\) | − | 6.54513e6i | − | 1.08217i | ||||||
\(517\) | − | 4.58116e6i | − | 0.753787i | ||||||
\(518\) | −6.85349e6 | −1.12224 | ||||||||
\(519\) | 5.94394e6 | 0.968626 | ||||||||
\(520\) | 4.41993e6i | 0.716815i | ||||||||
\(521\) | 7.91571e6i | 1.27760i | 0.769372 | + | 0.638801i | \(0.220569\pi\) | ||||
−0.769372 | + | 0.638801i | \(0.779431\pi\) | |||||||
\(522\) | − | 1.88911e6i | − | 0.303446i | ||||||
\(523\) | 7.72670e6 | 1.23521 | 0.617604 | − | 0.786489i | \(-0.288104\pi\) | ||||
0.617604 | + | 0.786489i | \(0.288104\pi\) | |||||||
\(524\) | 1.80146e6i | 0.286613i | ||||||||
\(525\) | −3.49324e6 | −0.553133 | ||||||||
\(526\) | −1.74813e7 | −2.75492 | ||||||||
\(527\) | −7.04886e6 | − | 2.07154e6i | −1.10559 | − | 0.324912i | ||||
\(528\) | −3.67016e6 | −0.572928 | ||||||||
\(529\) | 6.40111e6 | 0.994525 | ||||||||
\(530\) | 1.48162e7i | 2.29112i | ||||||||
\(531\) | 220558. | 0.0339458 | ||||||||
\(532\) | 4.04552e6i | 0.619720i | ||||||||
\(533\) | 1.48298e6i | 0.226109i | ||||||||
\(534\) | 1.40727e7i | 2.13562i | ||||||||
\(535\) | 3.10709e6 | 0.469320 | ||||||||
\(536\) | −2.80680e6 | −0.421988 | ||||||||
\(537\) | − | 269821.i | − | 0.0403776i | ||||||
\(538\) | − | 4.43395e6i | − | 0.660443i | ||||||
\(539\) | 6.00133e6i | 0.889765i | ||||||||
\(540\) | 1.52943e7 | 2.25707 | ||||||||
\(541\) | 2.33668e6i | 0.343246i | 0.985163 | + | 0.171623i | \(0.0549011\pi\) | ||||
−0.985163 | + | 0.171623i | \(0.945099\pi\) | |||||||
\(542\) | 1.03940e7 | 1.51980 | ||||||||
\(543\) | −7.59341e6 | −1.10519 | ||||||||
\(544\) | −2.72950e6 | + | 9.28774e6i | −0.395445 | + | 1.34559i | ||||
\(545\) | 5.94343e6 | 0.857129 | ||||||||
\(546\) | 3.77407e6 | 0.541787 | ||||||||
\(547\) | − | 1.26927e7i | − | 1.81378i | −0.421364 | − | 0.906891i | \(-0.638449\pi\) | ||
0.421364 | − | 0.906891i | \(-0.361551\pi\) | |||||||
\(548\) | −2.28326e6 | −0.324791 | ||||||||
\(549\) | − | 447793.i | − | 0.0634084i | ||||||
\(550\) | 1.94556e7i | 2.74245i | ||||||||
\(551\) | 4.87180e6i | 0.683613i | ||||||||
\(552\) | 164343. | 0.0229564 | ||||||||
\(553\) | −4.33879e6 | −0.603331 | ||||||||
\(554\) | 6.90566e6i | 0.955940i | ||||||||
\(555\) | − | 1.77305e7i | − | 2.44337i | ||||||
\(556\) | − | 7.22617e6i | − | 0.991337i | ||||||
\(557\) | −398976. | −0.0544890 | −0.0272445 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272445 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(558\) | − | 4.60048e6i | − | 0.625485i | ||||||
\(559\) | −8.90353e6 | −1.20513 | ||||||||
\(560\) | 3.32611e6 | 0.448195 | ||||||||
\(561\) | −1.78409e6 | + | 6.07076e6i | −0.239337 | + | 0.814397i | ||||
\(562\) | 1.05417e7 | 1.40789 | ||||||||
\(563\) | 4.81547e6 | 0.640277 | 0.320138 | − | 0.947371i | \(-0.396271\pi\) | ||||
0.320138 | + | 0.947371i | \(0.396271\pi\) | |||||||
\(564\) | 5.39236e6i | 0.713808i | ||||||||
\(565\) | 9.36336e6 | 1.23399 | ||||||||
\(566\) | − | 1.68195e7i | − | 2.20685i | ||||||
\(567\) | − | 1.56730e6i | − | 0.204736i | ||||||
\(568\) | 2.70967e6i | 0.352408i | ||||||||
\(569\) | −7.56736e6 | −0.979860 | −0.489930 | − | 0.871762i | \(-0.662978\pi\) | ||||
−0.489930 | + | 0.871762i | \(0.662978\pi\) | |||||||
\(570\) | −1.87836e7 | −2.42154 | ||||||||
\(571\) | 4.23691e6i | 0.543825i | 0.962322 | + | 0.271912i | \(0.0876561\pi\) | ||||
−0.962322 | + | 0.271912i | \(0.912344\pi\) | |||||||
\(572\) | − | 1.17120e7i | − | 1.49673i | ||||||
\(573\) | 2.09426e6i | 0.266467i | ||||||||
\(574\) | −964535. | −0.122191 | ||||||||
\(575\) | 1.00798e6i | 0.127140i | ||||||||
\(576\) | −4.12046e6 | −0.517476 | ||||||||
\(577\) | 3.56144e6 | 0.445334 | 0.222667 | − | 0.974895i | \(-0.428524\pi\) | ||||
0.222667 | + | 0.974895i | \(0.428524\pi\) | |||||||
\(578\) | 1.01510e7 | + | 6.53039e6i | 1.26383 | + | 0.813055i | ||||
\(579\) | 8.51441e6 | 1.05550 | ||||||||
\(580\) | −9.39628e6 | −1.15981 | ||||||||
\(581\) | 1.24650e6i | 0.153197i | ||||||||
\(582\) | −915703. | −0.112059 | ||||||||
\(583\) | − | 8.05967e6i | − | 0.982077i | ||||||
\(584\) | − | 1.52803e6i | − | 0.185396i | ||||||
\(585\) | − | 5.52073e6i | − | 0.666971i | ||||||
\(586\) | 9.20194e6 | 1.10697 | ||||||||
\(587\) | −9.70530e6 | −1.16256 | −0.581278 | − | 0.813705i | \(-0.697447\pi\) | ||||
−0.581278 | + | 0.813705i | \(0.697447\pi\) | |||||||
\(588\) | − | 7.06401e6i | − | 0.842574i | ||||||
\(589\) | 1.18641e7i | 1.40911i | ||||||||
\(590\) | − | 1.96886e6i | − | 0.232855i | ||||||
\(591\) | 3.36072e6 | 0.395789 | ||||||||
\(592\) | 1.06717e7i | 1.25150i | ||||||||
\(593\) | 2.04380e6 | 0.238672 | 0.119336 | − | 0.992854i | \(-0.461923\pi\) | ||||
0.119336 | + | 0.992854i | \(0.461923\pi\) | |||||||
\(594\) | −1.49315e7 | −1.73635 | ||||||||
\(595\) | 1.61685e6 | − | 5.50168e6i | 0.187231 | − | 0.637093i | ||||
\(596\) | 921638. | 0.106278 | ||||||||
\(597\) | −1.21122e7 | −1.39087 | ||||||||
\(598\) | − | 1.08901e6i | − | 0.124532i | ||||||
\(599\) | −5.77410e6 | −0.657532 | −0.328766 | − | 0.944411i | \(-0.606633\pi\) | ||||
−0.328766 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(600\) | − | 4.70123e6i | − | 0.533131i | ||||||
\(601\) | 365716.i | 0.0413007i | 0.999787 | + | 0.0206503i | \(0.00657368\pi\) | ||||
−0.999787 | + | 0.0206503i | \(0.993426\pi\) | |||||||
\(602\) | − | 5.79088e6i | − | 0.651259i | ||||||
\(603\) | 3.50584e6 | 0.392644 | ||||||||
\(604\) | 1.48801e7 | 1.65963 | ||||||||
\(605\) | − | 1.89892e6i | − | 0.210921i | ||||||
\(606\) | − | 3.68415e6i | − | 0.407526i | ||||||
\(607\) | 275964.i | 0.0304005i | 0.999884 | + | 0.0152002i | \(0.00483858\pi\) | ||||
−0.999884 | + | 0.0152002i | \(0.995161\pi\) | |||||||
\(608\) | 1.56324e7 | 1.71501 | ||||||||
\(609\) | 1.64707e6i | 0.179957i | ||||||||
\(610\) | −3.99733e6 | −0.434956 | ||||||||
\(611\) | 7.33539e6 | 0.794914 | ||||||||
\(612\) | −1.18740e6 | + | 4.04040e6i | −0.128150 | + | 0.436059i | ||||
\(613\) | −8.74854e6 | −0.940339 | −0.470170 | − | 0.882576i | \(-0.655807\pi\) | ||||
−0.470170 | + | 0.882576i | \(0.655807\pi\) | |||||||
\(614\) | 2.26657e6 | 0.242632 | ||||||||
\(615\) | − | 2.49533e6i | − | 0.266035i | ||||||
\(616\) | 1.56379e6 | 0.166045 | ||||||||
\(617\) | − | 4.86898e6i | − | 0.514902i | −0.966291 | − | 0.257451i | \(-0.917117\pi\) | ||
0.966291 | − | 0.257451i | \(-0.0828827\pi\) | |||||||
\(618\) | 5.75101e6i | 0.605721i | ||||||||
\(619\) | 1.32188e7i | 1.38665i | 0.720625 | + | 0.693325i | \(0.243855\pi\) | ||||
−0.720625 | + | 0.693325i | \(0.756145\pi\) | |||||||
\(620\) | −2.28824e7 | −2.39068 | ||||||||
\(621\) | −773587. | −0.0804971 | ||||||||
\(622\) | − | 7.29737e6i | − | 0.756293i | ||||||
\(623\) | 6.93761e6i | 0.716126i | ||||||||
\(624\) | − | 5.87669e6i | − | 0.604186i | ||||||
\(625\) | 2.28828e6 | 0.234320 | ||||||||
\(626\) | − | 1.88588e7i | − | 1.92344i | ||||||
\(627\) | 1.02178e7 | 1.03798 | ||||||||
\(628\) | −5.21771e6 | −0.527936 | ||||||||
\(629\) | 1.76519e7 | + | 5.18760e6i | 1.77896 | + | 0.522805i | ||||
\(630\) | 3.59070e6 | 0.360436 | ||||||||
\(631\) | −8.33370e6 | −0.833229 | −0.416615 | − | 0.909083i | \(-0.636784\pi\) | ||||
−0.416615 | + | 0.909083i | \(0.636784\pi\) | |||||||
\(632\) | − | 5.83918e6i | − | 0.581513i | ||||||
\(633\) | −6.67126e6 | −0.661757 | ||||||||
\(634\) | 2.64770e7i | 2.61605i | ||||||||
\(635\) | 5.91861e6i | 0.582486i | ||||||||
\(636\) | 9.48683e6i | 0.929990i | ||||||||
\(637\) | −9.60937e6 | −0.938310 | ||||||||
\(638\) | 9.17340e6 | 0.892233 | ||||||||
\(639\) | − | 3.38452e6i | − | 0.327903i | ||||||
\(640\) | 1.28215e7i | 1.23734i | ||||||||
\(641\) | − | 1.18813e7i | − | 1.14214i | −0.820901 | − | 0.571070i | \(-0.806528\pi\) | ||
0.820901 | − | 0.571070i | \(-0.193472\pi\) | |||||||
\(642\) | 3.57052e6 | 0.341896 | ||||||||
\(643\) | − | 1.89814e7i | − | 1.81051i | −0.424870 | − | 0.905254i | \(-0.639680\pi\) | ||
0.424870 | − | 0.905254i | \(-0.360320\pi\) | |||||||
\(644\) | 394658. | 0.0374978 | ||||||||
\(645\) | 1.49815e7 | 1.41793 | ||||||||
\(646\) | 5.49572e6 | − | 1.87004e7i | 0.518135 | − | 1.76307i | ||||
\(647\) | 5.13716e6 | 0.482461 | 0.241231 | − | 0.970468i | \(-0.422449\pi\) | ||||
0.241231 | + | 0.970468i | \(0.422449\pi\) | |||||||
\(648\) | 2.10929e6 | 0.197332 | ||||||||
\(649\) | 1.07101e6i | 0.0998121i | ||||||||
\(650\) | −3.11525e7 | −2.89208 | ||||||||
\(651\) | 4.01104e6i | 0.370941i | ||||||||
\(652\) | 979816.i | 0.0902663i | ||||||||
\(653\) | − | 3.66473e6i | − | 0.336325i | −0.985759 | − | 0.168162i | \(-0.946217\pi\) | ||
0.985759 | − | 0.168162i | \(-0.0537833\pi\) | |||||||
\(654\) | 6.82992e6 | 0.624412 | ||||||||
\(655\) | −4.12344e6 | −0.375540 | ||||||||
\(656\) | 1.50190e6i | 0.136264i | ||||||||
\(657\) | 1.90859e6i | 0.172504i | ||||||||
\(658\) | 4.77096e6i | 0.429577i | ||||||||
\(659\) | −1.74894e7 | −1.56878 | −0.784390 | − | 0.620268i | \(-0.787024\pi\) | ||||
−0.784390 | + | 0.620268i | \(0.787024\pi\) | |||||||
\(660\) | 1.97072e7i | 1.76102i | ||||||||
\(661\) | 1.01514e7 | 0.903696 | 0.451848 | − | 0.892095i | \(-0.350765\pi\) | ||||
0.451848 | + | 0.892095i | \(0.350765\pi\) | |||||||
\(662\) | 5.63510e6 | 0.499755 | ||||||||
\(663\) | −9.72055e6 | − | 2.85670e6i | −0.858830 | − | 0.252395i | ||||
\(664\) | −1.67755e6 | −0.147657 | ||||||||
\(665\) | −9.25999e6 | −0.812001 | ||||||||
\(666\) | 1.15206e7i | 1.00645i | ||||||||
\(667\) | 475265. | 0.0413639 | ||||||||
\(668\) | 2.00460e7i | 1.73815i | ||||||||
\(669\) | − | 1.17104e7i | − | 1.01160i | ||||||
\(670\) | − | 3.12958e7i | − | 2.69339i | ||||||
\(671\) | 2.17445e6 | 0.186442 | ||||||||
\(672\) | 5.28504e6 | 0.451466 | ||||||||
\(673\) | 1.29476e7i | 1.10193i | 0.834530 | + | 0.550963i | \(0.185739\pi\) | ||||
−0.834530 | + | 0.550963i | \(0.814261\pi\) | |||||||
\(674\) | − | 4.59905e6i | − | 0.389958i | ||||||
\(675\) | 2.21294e7i | 1.86943i | ||||||||
\(676\) | 3.80289e6 | 0.320072 | ||||||||
\(677\) | − | 3.01652e6i | − | 0.252950i | −0.991970 | − | 0.126475i | \(-0.959634\pi\) | ||
0.991970 | − | 0.126475i | \(-0.0403664\pi\) | |||||||
\(678\) | 1.07599e7 | 0.898950 | ||||||||
\(679\) | −451426. | −0.0375761 | ||||||||
\(680\) | 7.40422e6 | + | 2.17597e6i | 0.614055 | + | 0.180460i | ||||
\(681\) | −8.99940e6 | −0.743611 | ||||||||
\(682\) | 2.23396e7 | 1.83914 | ||||||||
\(683\) | 1.18964e7i | 0.975810i | 0.872897 | + | 0.487905i | \(0.162239\pi\) | ||||
−0.872897 | + | 0.487905i | \(0.837761\pi\) | |||||||
\(684\) | 6.80047e6 | 0.555775 | ||||||||
\(685\) | − | 5.22626e6i | − | 0.425563i | ||||||
\(686\) | − | 1.37100e7i | − | 1.11232i | ||||||
\(687\) | 7.32356e6i | 0.592012i | ||||||||
\(688\) | −9.01711e6 | −0.726267 | ||||||||
\(689\) | 1.29052e7 | 1.03566 | ||||||||
\(690\) | 1.83242e6i | 0.146522i | ||||||||
\(691\) | 5.11208e6i | 0.407289i | 0.979045 | + | 0.203644i | \(0.0652786\pi\) | ||||
−0.979045 | + | 0.203644i | \(0.934721\pi\) | |||||||
\(692\) | 1.92100e7i | 1.52497i | ||||||||
\(693\) | −1.95325e6 | −0.154499 | ||||||||
\(694\) | 1.94232e7i | 1.53081i | ||||||||
\(695\) | 1.65403e7 | 1.29892 | ||||||||
\(696\) | −2.21665e6 | −0.173450 | ||||||||
\(697\) | 2.48427e6 | + | 730084.i | 0.193694 | + | 0.0569234i | ||||
\(698\) | −2.72707e7 | −2.11864 | ||||||||
\(699\) | 4.70938e6 | 0.364562 | ||||||||
\(700\) | − | 1.12897e7i | − | 0.870836i | ||||||
\(701\) | 3.63687e6 | 0.279533 | 0.139767 | − | 0.990184i | \(-0.455365\pi\) | ||||
0.139767 | + | 0.990184i | \(0.455365\pi\) | |||||||
\(702\) | − | 2.39085e7i | − | 1.83109i | ||||||
\(703\) | − | 2.97103e7i | − | 2.26735i | ||||||
\(704\) | − | 2.00087e7i | − | 1.52155i | ||||||
\(705\) | −1.23428e7 | −0.935282 | ||||||||
\(706\) | −1.29249e7 | −0.975922 | ||||||||
\(707\) | − | 1.81622e6i | − | 0.136653i | ||||||
\(708\) | − | 1.26066e6i | − | 0.0945182i | ||||||
\(709\) | − | 1.16176e7i | − | 0.867966i | −0.900921 | − | 0.433983i | \(-0.857108\pi\) | ||
0.900921 | − | 0.433983i | \(-0.142892\pi\) | |||||||
\(710\) | −3.02127e7 | −2.24928 | ||||||||
\(711\) | 7.29345e6i | 0.541077i | ||||||||
\(712\) | −9.33670e6 | −0.690229 | ||||||||
\(713\) | 1.15739e6 | 0.0852622 | ||||||||
\(714\) | 1.85801e6 | − | 6.32228e6i | 0.136396 | − | 0.464118i | ||||
\(715\) | 2.68083e7 | 1.96112 | ||||||||
\(716\) | 872025. | 0.0635692 | ||||||||
\(717\) | 5.42766e6i | 0.394289i | ||||||||
\(718\) | −1.97991e7 | −1.43329 | ||||||||
\(719\) | − | 5.78331e6i | − | 0.417210i | −0.978000 | − | 0.208605i | \(-0.933108\pi\) | ||
0.978000 | − | 0.208605i | \(-0.0668923\pi\) | |||||||
\(720\) | − | 5.59116e6i | − | 0.401949i | ||||||
\(721\) | 2.83515e6i | 0.203113i | ||||||||
\(722\) | −1.04258e7 | −0.744330 | ||||||||
\(723\) | 1.02985e7 | 0.732700 | ||||||||
\(724\) | − | 2.45409e7i | − | 1.73998i | ||||||
\(725\) | − | 1.35955e7i | − | 0.960619i | ||||||
\(726\) | − | 2.18215e6i | − | 0.153654i | ||||||
\(727\) | −1.80894e7 | −1.26937 | −0.634684 | − | 0.772772i | \(-0.718870\pi\) | ||||
−0.634684 | + | 0.772772i | \(0.718870\pi\) | |||||||
\(728\) | 2.50395e6i | 0.175104i | ||||||||
\(729\) | −1.51115e7 | −1.05315 | ||||||||
\(730\) | 1.70375e7 | 1.18331 | ||||||||
\(731\) | −4.38328e6 | + | 1.49151e7i | −0.303393 | + | 1.03236i | ||||
\(732\) | −2.55949e6 | −0.176553 | ||||||||
\(733\) | −5.16718e6 | −0.355217 | −0.177608 | − | 0.984101i | \(-0.556836\pi\) | ||||
−0.177608 | + | 0.984101i | \(0.556836\pi\) | |||||||
\(734\) | − | 1.91142e7i | − | 1.30953i | ||||||
\(735\) | 1.61691e7 | 1.10400 | ||||||||
\(736\) | − | 1.52501e6i | − | 0.103771i | ||||||
\(737\) | 1.70241e7i | 1.15451i | ||||||||
\(738\) | 1.62137e6i | 0.109583i | ||||||||
\(739\) | −9.97913e6 | −0.672174 | −0.336087 | − | 0.941831i | \(-0.609104\pi\) | ||||
−0.336087 | + | 0.941831i | \(0.609104\pi\) | |||||||
\(740\) | 5.73026e7 | 3.84676 | ||||||||
\(741\) | 1.63609e7i | 1.09461i | ||||||||
\(742\) | 8.39359e6i | 0.559677i | ||||||||
\(743\) | 1.59724e6i | 0.106145i | 0.998591 | + | 0.0530725i | \(0.0169014\pi\) | ||||
−0.998591 | + | 0.0530725i | \(0.983099\pi\) | |||||||
\(744\) | −5.39810e6 | −0.357527 | ||||||||
\(745\) | 2.10958e6i | 0.139253i | ||||||||
\(746\) | 3.28110e7 | 2.15860 | ||||||||
\(747\) | 2.09535e6 | 0.137390 | ||||||||
\(748\) | −1.96199e7 | − | 5.76594e6i | −1.28216 | − | 0.376805i | ||||
\(749\) | 1.76021e6 | 0.114646 | ||||||||
\(750\) | 2.19130e7 | 1.42249 | ||||||||
\(751\) | 1.64962e7i | 1.06730i | 0.845707 | + | 0.533648i | \(0.179179\pi\) | ||||
−0.845707 | + | 0.533648i | \(0.820821\pi\) | |||||||
\(752\) | 7.42896e6 | 0.479053 | ||||||||
\(753\) | − | 1.84748e7i | − | 1.18739i | ||||||
\(754\) | 1.46885e7i | 0.940913i | ||||||||
\(755\) | 3.40597e7i | 2.17457i | ||||||||
\(756\) | 8.66442e6 | 0.551360 | ||||||||
\(757\) | −2.15408e7 | −1.36623 | −0.683114 | − | 0.730312i | \(-0.739375\pi\) | ||||
−0.683114 | + | 0.730312i | \(0.739375\pi\) | |||||||
\(758\) | 3.22685e7i | 2.03989i | ||||||||
\(759\) | − | 996792.i | − | 0.0628059i | ||||||
\(760\) | − | 1.24622e7i | − | 0.782637i | ||||||
\(761\) | −1.75451e7 | −1.09823 | −0.549116 | − | 0.835746i | \(-0.685036\pi\) | ||||
−0.549116 | + | 0.835746i | \(0.685036\pi\) | |||||||
\(762\) | 6.80140e6i | 0.424337i | ||||||||
\(763\) | 3.36703e6 | 0.209380 | ||||||||
\(764\) | −6.76836e6 | −0.419517 | ||||||||
\(765\) | −9.24826e6 | − | 2.71790e6i | −0.571356 | − | 0.167912i | ||||
\(766\) | −3.73377e7 | −2.29920 | ||||||||
\(767\) | −1.71491e6 | −0.105258 | ||||||||
\(768\) | − | 3.98297e6i | − | 0.243671i | ||||||
\(769\) | 8.55838e6 | 0.521886 | 0.260943 | − | 0.965354i | \(-0.415967\pi\) | ||||
0.260943 | + | 0.965354i | \(0.415967\pi\) | |||||||
\(770\) | 1.74362e7i | 1.05980i | ||||||||
\(771\) | 2.28881e7i | 1.38667i | ||||||||
\(772\) | 2.75174e7i | 1.66174i | ||||||||
\(773\) | 1.26354e7 | 0.760573 | 0.380287 | − | 0.924869i | \(-0.375825\pi\) | ||||
0.380287 | + | 0.924869i | \(0.375825\pi\) | |||||||
\(774\) | −9.73441e6 | −0.584060 | ||||||||
\(775\) | − | 3.31086e7i | − | 1.98010i | ||||||
\(776\) | − | 607533.i | − | 0.0362173i | ||||||
\(777\) | − | 1.00446e7i | − | 0.596868i | ||||||
\(778\) | 3.20926e7 | 1.90089 | ||||||||
\(779\) | − | 4.18132e6i | − | 0.246871i | ||||||
\(780\) | −3.15553e7 | −1.85710 | ||||||||
\(781\) | 1.64350e7 | 0.964144 | ||||||||
\(782\) | −1.82430e6 | − | 536131.i | −0.106679 | − | 0.0313512i | ||||
\(783\) | 1.04341e7 | 0.608205 | ||||||||
\(784\) | −9.73196e6 | −0.565471 | ||||||||
\(785\) | − | 1.19431e7i | − | 0.691739i | ||||||
\(786\) | −4.73847e6 | −0.273578 | ||||||||
\(787\) | 2.82263e7i | 1.62449i | 0.583317 | + | 0.812244i | \(0.301754\pi\) | ||||
−0.583317 | + | 0.812244i | \(0.698246\pi\) | |||||||
\(788\) | 1.08614e7i | 0.623118i | ||||||||
\(789\) | − | 2.56207e7i | − | 1.46521i | ||||||
\(790\) | 6.51067e7 | 3.71158 | ||||||||
\(791\) | 5.30446e6 | 0.301440 | ||||||||
\(792\) | − | 2.62871e6i | − | 0.148912i | ||||||
\(793\) | 3.48175e6i | 0.196614i | ||||||||
\(794\) | − | 7.58754e6i | − | 0.427120i | ||||||
\(795\) | −2.17149e7 | −1.21854 | ||||||||
\(796\) | − | 3.91451e7i | − | 2.18975i | ||||||
\(797\) | 8.07435e6 | 0.450258 | 0.225129 | − | 0.974329i | \(-0.427720\pi\) | ||||
0.225129 | + | 0.974329i | \(0.427720\pi\) | |||||||
\(798\) | −1.06412e7 | −0.591536 | ||||||||
\(799\) | 3.61128e6 | − | 1.22882e7i | 0.200122 | − | 0.680957i | ||||
\(800\) | −4.36246e7 | −2.40994 | ||||||||
\(801\) | 1.16620e7 | 0.642234 | ||||||||
\(802\) | 215330.i | 0.0118214i | ||||||||
\(803\) | −9.26798e6 | −0.507220 | ||||||||
\(804\) | − | 2.00387e7i | − | 1.09327i | ||||||
\(805\) | 903352.i | 0.0491323i | ||||||||
\(806\) | 3.57703e7i | 1.93948i | ||||||||
\(807\) | 6.49846e6 | 0.351258 | ||||||||
\(808\) | 2.44429e6 | 0.131712 | ||||||||
\(809\) | − | 3.17376e7i | − | 1.70491i | −0.522798 | − | 0.852456i | \(-0.675112\pi\) | ||
0.522798 | − | 0.852456i | \(-0.324888\pi\) | |||||||
\(810\) | 2.35185e7i | 1.25950i | ||||||||
\(811\) | − | 1.43905e7i | − | 0.768286i | −0.923274 | − | 0.384143i | \(-0.874497\pi\) | ||
0.923274 | − | 0.384143i | \(-0.125503\pi\) | |||||||
\(812\) | −5.32311e6 | −0.283319 | ||||||||
\(813\) | 1.52336e7i | 0.808308i | ||||||||
\(814\) | −5.59433e7 | −2.95929 | ||||||||
\(815\) | −2.24275e6 | −0.118273 | ||||||||
\(816\) | −9.84456e6 | − | 2.89314e6i | −0.517572 | − | 0.152105i | ||||
\(817\) | 2.51039e7 | 1.31579 | ||||||||
\(818\) | 3.59933e7 | 1.88078 | ||||||||
\(819\) | − | 3.12757e6i | − | 0.162928i | ||||||
\(820\) | 8.06456e6 | 0.418838 | ||||||||
\(821\) | − | 2.24839e7i | − | 1.16416i | −0.813131 | − | 0.582081i | \(-0.802239\pi\) | ||
0.813131 | − | 0.582081i | \(-0.197761\pi\) | |||||||
\(822\) | − | 6.00577e6i | − | 0.310020i | ||||||
\(823\) | − | 3.28688e7i | − | 1.69155i | −0.533543 | − | 0.845773i | \(-0.679140\pi\) | ||
0.533543 | − | 0.845773i | \(-0.320860\pi\) | |||||||
\(824\) | −3.81557e6 | −0.195768 | ||||||||
\(825\) | −2.85144e7 | −1.45858 | ||||||||
\(826\) | − | 1.11539e6i | − | 0.0568820i | ||||||
\(827\) | − | 2.64779e7i | − | 1.34623i | −0.739537 | − | 0.673116i | \(-0.764955\pi\) | ||
0.739537 | − | 0.673116i | \(-0.235045\pi\) | |||||||
\(828\) | − | 663416.i | − | 0.0336287i | ||||||
\(829\) | −1.20532e6 | −0.0609140 | −0.0304570 | − | 0.999536i | \(-0.509696\pi\) | ||||
−0.0304570 | + | 0.999536i | \(0.509696\pi\) | |||||||
\(830\) | − | 1.87046e7i | − | 0.942441i | ||||||
\(831\) | −1.01210e7 | −0.508419 | ||||||||
\(832\) | 3.20380e7 | 1.60457 | ||||||||
\(833\) | −4.73078e6 | + | 1.60975e7i | −0.236222 | + | 0.803797i | ||||
\(834\) | 1.90074e7 | 0.946253 | ||||||||
\(835\) | −4.58843e7 | −2.27745 | ||||||||
\(836\) | 3.30226e7i | 1.63416i | ||||||||
\(837\) | 2.54097e7 | 1.25368 | ||||||||
\(838\) | 2.09721e6i | 0.103165i | ||||||||
\(839\) | 1.82466e7i | 0.894904i | 0.894308 | + | 0.447452i | \(0.147669\pi\) | ||||
−0.894308 | + | 0.447452i | \(0.852331\pi\) | |||||||
\(840\) | − | 4.21325e6i | − | 0.206025i | ||||||
\(841\) | 1.41008e7 | 0.687471 | ||||||||
\(842\) | −1.15014e7 | −0.559073 | ||||||||
\(843\) | 1.54500e7i | 0.748789i | ||||||||
\(844\) | − | 2.15606e7i | − | 1.04185i | ||||||
\(845\) | 8.70462e6i | 0.419380i | ||||||||
\(846\) | 8.01993e6 | 0.385252 | ||||||||
\(847\) | − | 1.07576e6i | − | 0.0515239i | ||||||
\(848\) | 1.30698e7 | 0.624138 | ||||||||
\(849\) | 2.46509e7 | 1.17372 | ||||||||
\(850\) | −1.53367e7 | + | 5.21864e7i | −0.728088 | + | 2.47748i | ||||
\(851\) | −2.89837e6 | −0.137192 | ||||||||
\(852\) | −1.93452e7 | −0.913008 | ||||||||
\(853\) | − | 7.11178e6i | − | 0.334662i | −0.985901 | − | 0.167331i | \(-0.946485\pi\) | ||
0.985901 | − | 0.167331i | \(-0.0535148\pi\) | |||||||
\(854\) | −2.26454e6 | −0.106252 | ||||||||
\(855\) | 1.55659e7i | 0.728215i | ||||||||
\(856\) | 2.36890e6i | 0.110500i | ||||||||
\(857\) | − | 3.32856e7i | − | 1.54812i | −0.633113 | − | 0.774059i | \(-0.718223\pi\) | ||
0.633113 | − | 0.774059i | \(-0.281777\pi\) | |||||||
\(858\) | 3.08068e7 | 1.42866 | ||||||||
\(859\) | 1.87077e7 | 0.865044 | 0.432522 | − | 0.901623i | \(-0.357624\pi\) | ||||
0.432522 | + | 0.901623i | \(0.357624\pi\) | |||||||
\(860\) | 4.84181e7i | 2.23234i | ||||||||
\(861\) | − | 1.41363e6i | − | 0.0649874i | ||||||
\(862\) | 3.54718e7i | 1.62598i | ||||||||
\(863\) | 1.74479e7 | 0.797471 | 0.398736 | − | 0.917066i | \(-0.369449\pi\) | ||||
0.398736 | + | 0.917066i | \(0.369449\pi\) | |||||||
\(864\) | − | 3.34803e7i | − | 1.52583i | ||||||
\(865\) | −4.39707e7 | −1.99813 | ||||||||
\(866\) | −4.26737e6 | −0.193359 | ||||||||
\(867\) | −9.57103e6 | + | 1.48774e7i | −0.432425 | + | 0.672169i | ||||
\(868\) | −1.29631e7 | −0.583998 | ||||||||
\(869\) | −3.54165e7 | −1.59095 | ||||||||
\(870\) | − | 2.47155e7i | − | 1.10706i | ||||||
\(871\) | −2.72592e7 | −1.21750 | ||||||||
\(872\) | 4.53138e6i | 0.201809i | ||||||||
\(873\) | 758841.i | 0.0336989i | ||||||||
\(874\) | 3.07052e6i | 0.135967i | ||||||||
\(875\) | 1.08027e7 | 0.476995 | ||||||||
\(876\) | 1.09091e7 | 0.480318 | ||||||||
\(877\) | 1.68743e7i | 0.740845i | 0.928863 | + | 0.370422i | \(0.120787\pi\) | ||||
−0.928863 | + | 0.370422i | \(0.879213\pi\) | |||||||
\(878\) | − | 1.28898e7i | − | 0.564302i | ||||||
\(879\) | 1.34865e7i | 0.588744i | ||||||||
\(880\) | 2.71503e7 | 1.18186 | ||||||||
\(881\) | 1.24244e7i | 0.539305i | 0.962958 | + | 0.269652i | \(0.0869088\pi\) | ||||
−0.962958 | + | 0.269652i | \(0.913091\pi\) | |||||||
\(882\) | −1.05061e7 | −0.454748 | ||||||||
\(883\) | 1.23060e7 | 0.531148 | 0.265574 | − | 0.964091i | \(-0.414439\pi\) | ||||
0.265574 | + | 0.964091i | \(0.414439\pi\) | |||||||
\(884\) | 9.23248e6 | − | 3.14155e7i | 0.397363 | − | 1.35211i | ||||
\(885\) | 2.88559e6 | 0.123844 | ||||||||
\(886\) | 3.10218e7 | 1.32765 | ||||||||
\(887\) | 6.21137e6i | 0.265081i | 0.991178 | + | 0.132540i | \(0.0423134\pi\) | ||||
−0.991178 | + | 0.132540i | \(0.957687\pi\) | |||||||
\(888\) | 1.35181e7 | 0.575284 | ||||||||
\(889\) | 3.35297e6i | 0.142290i | ||||||||
\(890\) | − | 1.04104e8i | − | 4.40547i | ||||||
\(891\) | − | 1.27935e7i | − | 0.539877i | ||||||
\(892\) | 3.78466e7 | 1.59263 | ||||||||
\(893\) | −2.06824e7 | −0.867907 | ||||||||
\(894\) | 2.42423e6i | 0.101445i | ||||||||
\(895\) | 1.99602e6i | 0.0832928i | ||||||||
\(896\) | 7.26354e6i | 0.302258i | ||||||||
\(897\) | 1.59607e6 | 0.0662325 | ||||||||
\(898\) | 5.05115e7i | 2.09025i | ||||||||
\(899\) | −1.56108e7 | −0.644208 | ||||||||
\(900\) | −1.89778e7 | −0.780980 | ||||||||
\(901\) | 6.35335e6 | − | 2.16186e7i | 0.260730 | − | 0.887190i | ||||
\(902\) | −7.87326e6 | −0.322210 | ||||||||
\(903\) | 8.48719e6 | 0.346373 | ||||||||
\(904\) | 7.13880e6i | 0.290539i | ||||||||
\(905\) | 5.61728e7 | 2.27984 | ||||||||
\(906\) | 3.91398e7i | 1.58416i | ||||||||
\(907\) | 3.64815e7i | 1.47250i | 0.676712 | + | 0.736248i | \(0.263404\pi\) | ||||
−0.676712 | + | 0.736248i | \(0.736596\pi\) | |||||||
\(908\) | − | 2.90849e7i | − | 1.17072i | ||||||
\(909\) | −3.05305e6 | −0.122553 | ||||||||
\(910\) | −2.79190e7 | −1.11762 | ||||||||
\(911\) | − | 3.38686e7i | − | 1.35207i | −0.736867 | − | 0.676037i | \(-0.763696\pi\) | ||
0.736867 | − | 0.676037i | \(-0.236304\pi\) | |||||||
\(912\) | 1.65696e7i | 0.659666i | ||||||||
\(913\) | 1.01749e7i | 0.403972i | ||||||||
\(914\) | −4.42500e7 | −1.75206 | ||||||||
\(915\) | − | 5.85854e6i | − | 0.231333i | ||||||
\(916\) | −2.36688e7 | −0.932045 | ||||||||
\(917\) | −2.33598e6 | −0.0917374 | ||||||||
\(918\) | −4.00512e7 | − | 1.17703e7i | −1.56859 | − | 0.460980i | ||||
\(919\) | 3.90947e7 | 1.52696 | 0.763482 | − | 0.645829i | \(-0.223488\pi\) | ||||
0.763482 | + | 0.645829i | \(0.223488\pi\) | |||||||
\(920\) | −1.21574e6 | −0.0473556 | ||||||||
\(921\) | 3.32191e6i | 0.129044i | ||||||||
\(922\) | −6.00116e7 | −2.32492 | ||||||||
\(923\) | 2.63158e7i | 1.01675i | ||||||||
\(924\) | 1.11644e7i | 0.430184i | ||||||||
\(925\) | 8.29114e7i | 3.18610i | ||||||||
\(926\) | −1.21604e7 | −0.466037 | ||||||||
\(927\) | 4.76585e6 | 0.182155 | ||||||||
\(928\) | 2.05691e7i | 0.784054i | ||||||||
\(929\) | 4.50805e7i | 1.71376i | 0.515517 | + | 0.856880i | \(0.327600\pi\) | ||||
−0.515517 | + | 0.856880i | \(0.672400\pi\) | |||||||
\(930\) | − | 6.01887e7i | − | 2.28196i | ||||||
\(931\) | 2.70940e7 | 1.02447 | ||||||||
\(932\) | 1.52201e7i | 0.573954i | ||||||||
\(933\) | 1.06951e7 | 0.402236 | ||||||||
\(934\) | 6.24161e6 | 0.234115 | ||||||||
\(935\) | 1.31979e7 | − | 4.49089e7i | 0.493716 | − | 1.67998i | ||||
\(936\) | 4.20911e6 | 0.157036 | ||||||||
\(937\) | 2.58502e7 | 0.961868 | 0.480934 | − | 0.876757i | \(-0.340298\pi\) | ||||
0.480934 | + | 0.876757i | \(0.340298\pi\) | |||||||
\(938\) | − | 1.77295e7i | − | 0.657943i | ||||||
\(939\) | 2.76397e7 | 1.02299 | ||||||||
\(940\) | − | 3.98904e7i | − | 1.47248i | ||||||
\(941\) | 8.12617e6i | 0.299166i | 0.988749 | + | 0.149583i | \(0.0477931\pi\) | ||||
−0.988749 | + | 0.149583i | \(0.952207\pi\) | |||||||
\(942\) | − | 1.37244e7i | − | 0.503926i | ||||||
\(943\) | −407906. | −0.0149376 | ||||||||
\(944\) | −1.73679e6 | −0.0634334 | ||||||||
\(945\) | 1.98324e7i | 0.722430i | ||||||||
\(946\) | − | 4.72696e7i | − | 1.71733i | ||||||
\(947\) | − | 2.98990e7i | − | 1.08338i | −0.840578 | − | 0.541691i | \(-0.817784\pi\) | ||
0.840578 | − | 0.541691i | \(-0.182216\pi\) | |||||||
\(948\) | 4.16878e7 | 1.50657 | ||||||||
\(949\) | − | 1.48400e7i | − | 0.534893i | ||||||
\(950\) | 8.78359e7 | 3.15764 | ||||||||
\(951\) | −3.88050e7 | −1.39135 | ||||||||
\(952\) | 4.19459e6 | + | 1.23272e6i | 0.150002 | + | 0.0440830i | ||||
\(953\) | −5.53260e7 | −1.97332 | −0.986659 | − | 0.162799i | \(-0.947948\pi\) | ||||
−0.986659 | + | 0.162799i | \(0.947948\pi\) | |||||||
\(954\) | 1.41095e7 | 0.501928 | ||||||||
\(955\) | − | 1.54924e7i | − | 0.549681i | ||||||
\(956\) | −1.75415e7 | −0.620757 | ||||||||
\(957\) | 1.34446e7i | 0.474536i | ||||||||
\(958\) | 1.46529e7i | 0.515835i | ||||||||
\(959\) | − | 2.96074e6i | − | 0.103957i | ||||||
\(960\) | −5.39086e7 | −1.88790 | ||||||||
\(961\) | −9.38715e6 | −0.327888 | ||||||||
\(962\) | − | 8.95769e7i | − | 3.12075i | ||||||
\(963\) | − | 2.95889e6i | − | 0.102816i | ||||||
\(964\) | 3.32832e7i | 1.15354i | ||||||||
\(965\) | −6.29859e7 | −2.17734 | ||||||||
\(966\) | 1.03809e6i | 0.0357925i | ||||||||
\(967\) | −489793. | −0.0168440 | −0.00842202 | − | 0.999965i | \(-0.502681\pi\) | ||||
−0.00842202 | + | 0.999965i | \(0.502681\pi\) | |||||||
\(968\) | 1.44777e6 | 0.0496607 | ||||||||
\(969\) | 2.74075e7 | + | 8.05459e6i | 0.937692 | + | 0.275571i | ||||
\(970\) | 6.77398e6 | 0.231161 | ||||||||
\(971\) | −2.62829e6 | −0.0894593 | −0.0447296 | − | 0.998999i | \(-0.514243\pi\) | ||||
−0.0447296 | + | 0.998999i | \(0.514243\pi\) | |||||||
\(972\) | − | 2.52648e7i | − | 0.857728i | ||||||
\(973\) | 9.37031e6 | 0.317301 | ||||||||
\(974\) | − | 2.74027e7i | − | 0.925540i | ||||||
\(975\) | − | 4.56576e7i | − | 1.53816i | ||||||
\(976\) | 3.52616e6i | 0.118489i | ||||||||
\(977\) | −2.96424e7 | −0.993520 | −0.496760 | − | 0.867888i | \(-0.665477\pi\) | ||||
−0.496760 | + | 0.867888i | \(0.665477\pi\) | |||||||
\(978\) | −2.57726e6 | −0.0861612 | ||||||||
\(979\) | 5.66300e7i | 1.88838i | ||||||||
\(980\) | 5.22565e7i | 1.73810i | ||||||||
\(981\) | − | 5.65994e6i | − | 0.187776i | ||||||
\(982\) | 3.00393e7 | 0.994055 | ||||||||
\(983\) | 2.21240e7i | 0.730263i | 0.930956 | + | 0.365131i | \(0.118976\pi\) | ||||
−0.930956 | + | 0.365131i | \(0.881024\pi\) | |||||||
\(984\) | 1.90248e6 | 0.0626373 | ||||||||
\(985\) | −2.48612e7 | −0.816452 | ||||||||
\(986\) | 2.46060e7 | + | 7.23129e6i | 0.806026 | + | 0.236877i | ||||
\(987\) | −6.99238e6 | −0.228472 | ||||||||
\(988\) | −5.28761e7 | −1.72332 | ||||||||
\(989\) | − | 2.44899e6i | − | 0.0796153i | ||||||
\(990\) | 2.93100e7 | 0.950448 | ||||||||
\(991\) | − | 5.22482e7i | − | 1.69000i | −0.534764 | − | 0.845001i | \(-0.679599\pi\) | ||
0.534764 | − | 0.845001i | \(-0.320401\pi\) | |||||||
\(992\) | 5.00911e7i | 1.61615i | ||||||||
\(993\) | 8.25888e6i | 0.265796i | ||||||||
\(994\) | −1.71159e7 | −0.549457 | ||||||||
\(995\) | 8.96010e7 | 2.86916 | ||||||||
\(996\) | − | 1.19766e7i | − | 0.382546i | ||||||
\(997\) | − | 2.19323e7i | − | 0.698790i | −0.936975 | − | 0.349395i | \(-0.886387\pi\) | ||
0.936975 | − | 0.349395i | \(-0.113613\pi\) | |||||||
\(998\) | 3.71788e7i | 1.18160i | ||||||||
\(999\) | −6.36315e7 | −2.01724 |
(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 | 17.6.b.a.16.1 | ✓ | 6 | |
3.2 | odd | 2 | 153.6.d.b.118.5 | 6 | |||
4.3 | odd | 2 | 272.6.b.c.33.4 | 6 | |||
17.4 | even | 4 | 289.6.a.f.1.5 | 6 | |||
17.13 | even | 4 | 289.6.a.f.1.6 | 6 | |||
17.16 | even | 2 | inner | 17.6.b.a.16.2 | yes | 6 | |
51.50 | odd | 2 | 153.6.d.b.118.6 | 6 | |||
68.67 | odd | 2 | 272.6.b.c.33.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.6.b.a.16.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
17.6.b.a.16.2 | yes | 6 | 17.16 | even | 2 | inner | |
153.6.d.b.118.5 | 6 | 3.2 | odd | 2 | |||
153.6.d.b.118.6 | 6 | 51.50 | odd | 2 | |||
272.6.b.c.33.3 | 6 | 68.67 | odd | 2 | |||
272.6.b.c.33.4 | 6 | 4.3 | odd | 2 | |||
289.6.a.f.1.5 | 6 | 17.4 | even | 4 | |||
289.6.a.f.1.6 | 6 | 17.13 | even | 4 |