Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\), degree \(2\), 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: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 252 x^{14} + 27174 x^{12} - 1635700 x^{10} + 60061815 x^{8} - 1376564028 x^{6} + \cdots + 498214340649 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{8}\cdot 5^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.3 | ||
Root | \(3.79037 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.107 |
Dual form | 450.6.f.g.143.3 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | + | 2.82843i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 16.0000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 140.653 | + | 140.653i | 1.08494 | + | 1.08494i | 0.996041 | + | 0.0888972i | \(0.0283343\pi\) |
0.0888972 | + | 0.996041i | \(0.471666\pi\) | |||||||
\(8\) | 45.2548 | + | 45.2548i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 540.947i | 1.34795i | 0.738755 | + | 0.673974i | \(0.235414\pi\) | ||||
−0.738755 | + | 0.673974i | \(0.764586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −798.801 | + | 798.801i | −1.31093 | + | 1.31093i | −0.390205 | + | 0.920728i | \(0.627596\pi\) |
−0.920728 | + | 0.390205i | \(0.872404\pi\) | |||||||
\(14\) | −795.655 | −1.08494 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | −598.220 | + | 598.220i | −0.502041 | + | 0.502041i | −0.912072 | − | 0.410031i | \(-0.865518\pi\) |
0.410031 | + | 0.912072i | \(0.365518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1784.25i | − | 1.13389i | −0.823755 | − | 0.566946i | \(-0.808125\pi\) | ||
0.823755 | − | 0.566946i | \(-0.191875\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1530.03 | − | 1530.03i | −0.673974 | − | 0.673974i | ||||
\(23\) | 718.106 | + | 718.106i | 0.283054 | + | 0.283054i | 0.834326 | − | 0.551272i | \(-0.185857\pi\) |
−0.551272 | + | 0.834326i | \(0.685857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4518.70i | − | 1.31093i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2250.45 | − | 2250.45i | 0.542469 | − | 0.542469i | ||||
\(29\) | −5380.98 | −1.18814 | −0.594068 | − | 0.804415i | \(-0.702479\pi\) | ||||
−0.594068 | + | 0.804415i | \(0.702479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1803.17 | 0.337002 | 0.168501 | − | 0.985702i | \(-0.446107\pi\) | ||||
0.168501 | + | 0.985702i | \(0.446107\pi\) | |||||||
\(32\) | 724.077 | − | 724.077i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3384.05i | − | 0.502041i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7344.12 | + | 7344.12i | 0.881932 | + | 0.881932i | 0.993731 | − | 0.111799i | \(-0.0356612\pi\) |
−0.111799 | + | 0.993731i | \(0.535661\pi\) | |||||||
\(38\) | 5046.62 | + | 5046.62i | 0.566946 | + | 0.566946i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12486.0i | 1.16002i | 0.814610 | + | 0.580009i | \(0.196951\pi\) | ||||
−0.814610 | + | 0.580009i | \(0.803049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9900.97 | − | 9900.97i | 0.816594 | − | 0.816594i | −0.169018 | − | 0.985613i | \(-0.554060\pi\) |
0.985613 | + | 0.169018i | \(0.0540598\pi\) | |||||||
\(44\) | 8655.16 | 0.673974 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4062.22 | −0.283054 | ||||||||
\(47\) | 1821.38 | − | 1821.38i | 0.120270 | − | 0.120270i | −0.644410 | − | 0.764680i | \(-0.722897\pi\) |
0.764680 | + | 0.644410i | \(0.222897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22759.7i | 1.35418i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12780.8 | + | 12780.8i | 0.655466 | + | 0.655466i | ||||
\(53\) | −16089.2 | − | 16089.2i | −0.786764 | − | 0.786764i | 0.194199 | − | 0.980962i | \(-0.437789\pi\) |
−0.980962 | + | 0.194199i | \(0.937789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12730.5i | 0.542469i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15219.7 | − | 15219.7i | 0.594068 | − | 0.594068i | ||||
\(59\) | −45243.7 | −1.69211 | −0.846054 | − | 0.533096i | \(-0.821028\pi\) | ||||
−0.846054 | + | 0.533096i | \(0.821028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 605.793 | 0.0208449 | 0.0104224 | − | 0.999946i | \(-0.496682\pi\) | ||||
0.0104224 | + | 0.999946i | \(0.496682\pi\) | |||||||
\(62\) | −5100.13 | + | 5100.13i | −0.168501 | + | 0.168501i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23073.5 | − | 23073.5i | −0.627951 | − | 0.627951i | 0.319601 | − | 0.947552i | \(-0.396451\pi\) |
−0.947552 | + | 0.319601i | \(0.896451\pi\) | |||||||
\(68\) | 9571.53 | + | 9571.53i | 0.251020 | + | 0.251020i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11301.7i | − | 0.266072i | −0.991111 | − | 0.133036i | \(-0.957527\pi\) | ||
0.991111 | − | 0.133036i | \(-0.0424727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41883.4 | − | 41883.4i | 0.919889 | − | 0.919889i | −0.0771322 | − | 0.997021i | \(-0.524576\pi\) |
0.997021 | + | 0.0771322i | \(0.0245764\pi\) | |||||||
\(74\) | −41544.6 | −0.881932 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28548.0 | −0.566946 | ||||||||
\(77\) | −76086.0 | + | 76086.0i | −1.46244 | + | 1.46244i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 61935.6i | − | 1.11654i | −0.829661 | − | 0.558268i | \(-0.811466\pi\) | ||
0.829661 | − | 0.558268i | \(-0.188534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −35315.9 | − | 35315.9i | −0.580009 | − | 0.580009i | ||||
\(83\) | 82133.1 | + | 82133.1i | 1.30865 | + | 1.30865i | 0.922391 | + | 0.386258i | \(0.126233\pi\) |
0.386258 | + | 0.922391i | \(0.373767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 56008.3i | 0.816594i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24480.5 | + | 24480.5i | −0.336987 | + | 0.336987i | ||||
\(89\) | 10787.0 | 0.144353 | 0.0721765 | − | 0.997392i | \(-0.477005\pi\) | ||||
0.0721765 | + | 0.997392i | \(0.477005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −224708. | −2.84456 | ||||||||
\(92\) | 11489.7 | − | 11489.7i | 0.141527 | − | 0.141527i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10303.3i | 0.120270i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51439.5 | + | 51439.5i | 0.555096 | + | 0.555096i | 0.927907 | − | 0.372812i | \(-0.121606\pi\) |
−0.372812 | + | 0.927907i | \(0.621606\pi\) | |||||||
\(98\) | −64374.2 | − | 64374.2i | −0.677091 | − | 0.677091i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 183902.i | 1.79384i | 0.442194 | + | 0.896919i | \(0.354200\pi\) | ||||
−0.442194 | + | 0.896919i | \(0.645800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 84524.9 | − | 84524.9i | 0.785039 | − | 0.785039i | −0.195637 | − | 0.980676i | \(-0.562677\pi\) |
0.980676 | + | 0.195637i | \(0.0626774\pi\) | |||||||
\(104\) | −72299.3 | −0.655466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 91014.2 | 0.786764 | ||||||||
\(107\) | 21138.5 | − | 21138.5i | 0.178491 | − | 0.178491i | −0.612207 | − | 0.790698i | \(-0.709718\pi\) |
0.790698 | + | 0.612207i | \(0.209718\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 52674.2i | − | 0.424651i | −0.977199 | − | 0.212325i | \(-0.931896\pi\) | ||
0.977199 | − | 0.212325i | \(-0.0681037\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −36007.3 | − | 36007.3i | −0.271235 | − | 0.271235i | ||||
\(113\) | −171149. | − | 171149.i | −1.26089 | − | 1.26089i | −0.950661 | − | 0.310230i | \(-0.899594\pi\) |
−0.310230 | − | 0.950661i | \(-0.600406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 86095.6i | 0.594068i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 127969. | − | 127969.i | 0.846054 | − | 0.846054i | ||||
\(119\) | −168283. | −1.08937 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −131573. | −0.816965 | ||||||||
\(122\) | −1713.44 | + | 1713.44i | −0.0104224 | + | 0.0104224i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 28850.7i | − | 0.168501i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −80016.7 | − | 80016.7i | −0.440222 | − | 0.440222i | 0.451865 | − | 0.892086i | \(-0.350759\pi\) |
−0.892086 | + | 0.451865i | \(0.850759\pi\) | |||||||
\(128\) | −11585.2 | − | 11585.2i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 185291.i | − | 0.943357i | −0.881771 | − | 0.471678i | \(-0.843648\pi\) | ||
0.881771 | − | 0.471678i | \(-0.156352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 250961. | − | 250961.i | 1.23020 | − | 1.23020i | ||||
\(134\) | 130523. | 0.627951 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −54144.7 | −0.251020 | ||||||||
\(137\) | 30362.4 | − | 30362.4i | 0.138209 | − | 0.138209i | −0.634618 | − | 0.772826i | \(-0.718842\pi\) |
0.772826 | + | 0.634618i | \(0.218842\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 75341.5i | − | 0.330748i | −0.986231 | − | 0.165374i | \(-0.947117\pi\) | ||
0.986231 | − | 0.165374i | \(-0.0528831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 31966.2 | + | 31966.2i | 0.133036 | + | 0.133036i | ||||
\(143\) | −432110. | − | 432110.i | −1.76707 | − | 1.76707i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 236929.i | 0.919889i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 117506. | − | 117506.i | 0.440966 | − | 0.440966i | ||||
\(149\) | 125123. | 0.461713 | 0.230857 | − | 0.972988i | \(-0.425847\pi\) | ||||
0.230857 | + | 0.972988i | \(0.425847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −419846. | −1.49847 | −0.749234 | − | 0.662306i | \(-0.769578\pi\) | ||||
−0.749234 | + | 0.662306i | \(0.769578\pi\) | |||||||
\(152\) | 80745.9 | − | 80745.9i | 0.283473 | − | 0.283473i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 430408.i | − | 1.46244i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 149608. | + | 149608.i | 0.484400 | + | 0.484400i | 0.906534 | − | 0.422133i | \(-0.138719\pi\) |
−0.422133 | + | 0.906534i | \(0.638719\pi\) | |||||||
\(158\) | 175180. | + | 175180.i | 0.558268 | + | 0.558268i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 202008.i | 0.614192i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −231571. | + | 231571.i | −0.682677 | + | 0.682677i | −0.960603 | − | 0.277925i | \(-0.910353\pi\) |
0.277925 | + | 0.960603i | \(0.410353\pi\) | |||||||
\(164\) | 199777. | 0.580009 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −464615. | −1.30865 | ||||||||
\(167\) | −175238. | + | 175238.i | −0.486224 | + | 0.486224i | −0.907112 | − | 0.420889i | \(-0.861718\pi\) |
0.420889 | + | 0.907112i | \(0.361718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 904875.i | − | 2.43709i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −158415. | − | 158415.i | −0.408297 | − | 0.408297i | ||||
\(173\) | −173263. | − | 173263.i | −0.440139 | − | 0.440139i | 0.451919 | − | 0.892059i | \(-0.350739\pi\) |
−0.892059 | + | 0.451919i | \(0.850739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 138483.i | − | 0.336987i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −30510.3 | + | 30510.3i | −0.0721765 | + | 0.0721765i | ||||
\(179\) | −819035. | −1.91060 | −0.955301 | − | 0.295636i | \(-0.904468\pi\) | ||||
−0.955301 | + | 0.295636i | \(0.904468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −268935. | −0.610169 | −0.305085 | − | 0.952325i | \(-0.598685\pi\) | ||||
−0.305085 | + | 0.952325i | \(0.598685\pi\) | |||||||
\(182\) | 635571. | − | 635571.i | 1.42228 | − | 1.42228i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 64995.5i | 0.141527i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −323606. | − | 323606.i | −0.676725 | − | 0.676725i | ||||
\(188\) | −29142.1 | − | 29142.1i | −0.0601348 | − | 0.0601348i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 513760.i | 1.01901i | 0.860469 | + | 0.509503i | \(0.170171\pi\) | ||||
−0.860469 | + | 0.509503i | \(0.829829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −187981. | + | 187981.i | −0.363263 | + | 0.363263i | −0.865013 | − | 0.501750i | \(-0.832690\pi\) |
0.501750 | + | 0.865013i | \(0.332690\pi\) | |||||||
\(194\) | −290986. | −0.555096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 364156. | 0.677091 | ||||||||
\(197\) | −745856. | + | 745856.i | −1.36927 | + | 1.36927i | −0.507790 | + | 0.861481i | \(0.669538\pi\) |
−0.861481 | + | 0.507790i | \(0.830462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 411062.i | 0.735825i | 0.929860 | + | 0.367913i | \(0.119927\pi\) | ||||
−0.929860 | + | 0.367913i | \(0.880073\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −520154. | − | 520154.i | −0.896919 | − | 0.896919i | ||||
\(203\) | −756852. | − | 756852.i | −1.28905 | − | 1.28905i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 478145.i | 0.785039i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 204493. | − | 204493.i | 0.327733 | − | 0.327733i | ||||
\(209\) | 965185. | 1.52843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −243588. | −0.376660 | −0.188330 | − | 0.982106i | \(-0.560307\pi\) | ||||
−0.188330 | + | 0.982106i | \(0.560307\pi\) | |||||||
\(212\) | −257427. | + | 257427.i | −0.393382 | + | 0.393382i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 119578.i | 0.178491i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 253622. | + | 253622.i | 0.365626 | + | 0.365626i | ||||
\(218\) | 148985. | + | 148985.i | 0.212325 | + | 0.212325i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 955719.i | − | 1.31628i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 438788. | − | 438788.i | 0.590871 | − | 0.590871i | −0.346995 | − | 0.937867i | \(-0.612798\pi\) |
0.937867 | + | 0.346995i | \(0.112798\pi\) | |||||||
\(224\) | 203688. | 0.271235 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 968164. | 1.26089 | ||||||||
\(227\) | 584859. | − | 584859.i | 0.753332 | − | 0.753332i | −0.221767 | − | 0.975100i | \(-0.571183\pi\) |
0.975100 | + | 0.221767i | \(0.0711825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28534.6i | 0.0359570i | 0.999838 | + | 0.0179785i | \(0.00572304\pi\) | ||||
−0.999838 | + | 0.0179785i | \(0.994277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −243515. | − | 243515.i | −0.297034 | − | 0.297034i | ||||
\(233\) | 479688. | + | 479688.i | 0.578854 | + | 0.578854i | 0.934587 | − | 0.355734i | \(-0.115769\pi\) |
−0.355734 | + | 0.934587i | \(0.615769\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 723900.i | 0.846054i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 475977. | − | 475977.i | 0.544683 | − | 0.544683i | ||||
\(239\) | 794921. | 0.900180 | 0.450090 | − | 0.892983i | \(-0.351392\pi\) | ||||
0.450090 | + | 0.892983i | \(0.351392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.58233e6 | −1.75491 | −0.877455 | − | 0.479660i | \(-0.840760\pi\) | ||||
−0.877455 | + | 0.479660i | \(0.840760\pi\) | |||||||
\(242\) | 372145. | − | 372145.i | 0.408482 | − | 0.408482i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9692.69i | − | 0.0104224i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.42526e6 | + | 1.42526e6i | 1.48646 | + | 1.48646i | ||||
\(248\) | 81602.1 | + | 81602.1i | 0.0842504 | + | 0.0842504i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.37423e6i | − | 1.37682i | −0.725323 | − | 0.688408i | \(-0.758310\pi\) | ||
0.725323 | − | 0.688408i | \(-0.241690\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −388458. | + | 388458.i | −0.381542 | + | 0.381542i | ||||
\(254\) | 452643. | 0.440222 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −353875. | + | 353875.i | −0.334209 | + | 0.334209i | −0.854182 | − | 0.519974i | \(-0.825942\pi\) |
0.519974 | + | 0.854182i | \(0.325942\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.06595e6i | 1.91368i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 524082. | + | 524082.i | 0.471678 | + | 0.471678i | ||||
\(263\) | 877240. | + | 877240.i | 0.782040 | + | 0.782040i | 0.980175 | − | 0.198135i | \(-0.0634884\pi\) |
−0.198135 | + | 0.980175i | \(0.563488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.41965e6i | 1.23020i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −369176. | + | 369176.i | −0.313976 | + | 0.313976i | ||||
\(269\) | −1.98017e6 | −1.66849 | −0.834243 | − | 0.551398i | \(-0.814095\pi\) | ||||
−0.834243 | + | 0.551398i | \(0.814095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 678161. | 0.560931 | 0.280466 | − | 0.959864i | \(-0.409511\pi\) | ||||
0.280466 | + | 0.959864i | \(0.409511\pi\) | |||||||
\(272\) | 153144. | − | 153144.i | 0.125510 | − | 0.125510i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 171756.i | 0.138209i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −747103. | − | 747103.i | −0.585034 | − | 0.585034i | 0.351248 | − | 0.936282i | \(-0.385757\pi\) |
−0.936282 | + | 0.351248i | \(0.885757\pi\) | |||||||
\(278\) | 213098. | + | 213098.i | 0.165374 | + | 0.165374i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.28008e6i | − | 1.72260i | −0.508100 | − | 0.861298i | \(-0.669652\pi\) | ||
0.508100 | − | 0.861298i | \(-0.330348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −433565. | + | 433565.i | −0.321801 | + | 0.321801i | −0.849458 | − | 0.527656i | \(-0.823071\pi\) |
0.527656 | + | 0.849458i | \(0.323071\pi\) | |||||||
\(284\) | −180828. | −0.133036 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.44438e6 | 1.76707 | ||||||||
\(287\) | −1.75620e6 | + | 1.75620e6i | −1.25855 | + | 1.25855i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 704122.i | 0.495910i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −670135. | − | 670135.i | −0.459944 | − | 0.459944i | ||||
\(293\) | 233140. | + | 233140.i | 0.158653 | + | 0.158653i | 0.781970 | − | 0.623317i | \(-0.214215\pi\) |
−0.623317 | + | 0.781970i | \(0.714215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 664713.i | 0.440966i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −353902. | + | 353902.i | −0.230857 | + | 0.230857i | ||||
\(299\) | −1.14725e6 | −0.742129 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.78521e6 | 1.77191 | ||||||||
\(302\) | 1.18750e6 | − | 1.18750e6i | 0.749234 | − | 0.749234i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 456768.i | 0.283473i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 667932. | + | 667932.i | 0.404470 | + | 0.404470i | 0.879805 | − | 0.475335i | \(-0.157673\pi\) |
−0.475335 | + | 0.879805i | \(0.657673\pi\) | |||||||
\(308\) | 1.21738e6 | + | 1.21738e6i | 0.731220 | + | 0.731220i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.00168e6i | − | 0.587259i | −0.955919 | − | 0.293630i | \(-0.905137\pi\) | ||
0.955919 | − | 0.293630i | \(-0.0948632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.80630e6 | + | 1.80630e6i | −1.04215 | + | 1.04215i | −0.0430780 | + | 0.999072i | \(0.513716\pi\) |
−0.999072 | + | 0.0430780i | \(0.986284\pi\) | |||||||
\(314\) | −846308. | −0.484400 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −990970. | −0.558268 | ||||||||
\(317\) | −1.09346e6 | + | 1.09346e6i | −0.611158 | + | 0.611158i | −0.943248 | − | 0.332090i | \(-0.892246\pi\) |
0.332090 | + | 0.943248i | \(0.392246\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.91082e6i | − | 1.60155i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −571365. | − | 571365.i | −0.307096 | − | 0.307096i | ||||
\(323\) | 1.06737e6 | + | 1.06737e6i | 0.569260 | + | 0.569260i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.30996e6i | − | 0.682677i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −565054. | + | 565054.i | −0.290005 | + | 0.290005i | ||||
\(329\) | 512366. | 0.260970 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.52662e6 | 1.26757 | 0.633783 | − | 0.773511i | \(-0.281501\pi\) | ||||
0.633783 | + | 0.773511i | \(0.281501\pi\) | |||||||
\(332\) | 1.31413e6 | − | 1.31413e6i | 0.654325 | − | 0.654325i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 991294.i | − | 0.486224i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.55352e6 | + | 2.55352e6i | 1.22480 | + | 1.22480i | 0.965906 | + | 0.258893i | \(0.0833578\pi\) |
0.258893 | + | 0.965906i | \(0.416642\pi\) | |||||||
\(338\) | 2.55937e6 | + | 2.55937e6i | 1.21855 | + | 1.21855i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 975419.i | 0.454261i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −837270. | + | 837270.i | −0.384265 | + | 0.384265i | ||||
\(344\) | 896133. | 0.408297 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 980123. | 0.440139 | ||||||||
\(347\) | −847128. | + | 847128.i | −0.377681 | + | 0.377681i | −0.870265 | − | 0.492584i | \(-0.836052\pi\) |
0.492584 | + | 0.870265i | \(0.336052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.05487e6i | 1.78202i | 0.453981 | + | 0.891011i | \(0.350003\pi\) | ||||
−0.453981 | + | 0.891011i | \(0.649997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 391688. | + | 391688.i | 0.168494 | + | 0.168494i | ||||
\(353\) | −659897. | − | 659897.i | −0.281864 | − | 0.281864i | 0.551988 | − | 0.833852i | \(-0.313869\pi\) |
−0.833852 | + | 0.551988i | \(0.813869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 172592.i | − | 0.0721765i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.31658e6 | − | 2.31658e6i | 0.955301 | − | 0.955301i | ||||
\(359\) | 3.58684e6 | 1.46884 | 0.734422 | − | 0.678693i | \(-0.237453\pi\) | ||||
0.734422 | + | 0.678693i | \(0.237453\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −707445. | −0.285709 | ||||||||
\(362\) | 760662. | − | 760662.i | 0.305085 | − | 0.305085i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.59533e6i | 1.42228i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.33916e6 | + | 1.33916e6i | 0.519001 | + | 0.519001i | 0.917269 | − | 0.398268i | \(-0.130389\pi\) |
−0.398268 | + | 0.917269i | \(0.630389\pi\) | |||||||
\(368\) | −183835. | − | 183835.i | −0.0707635 | − | 0.0707635i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.52599e6i | − | 1.70718i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.26970e6 | + | 2.26970e6i | −0.844689 | + | 0.844689i | −0.989464 | − | 0.144776i | \(-0.953754\pi\) |
0.144776 | + | 0.989464i | \(0.453754\pi\) | |||||||
\(374\) | 1.83059e6 | 0.676725 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 164852. | 0.0601348 | ||||||||
\(377\) | 4.29833e6 | − | 4.29833e6i | 1.55757 | − | 1.55757i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.67739e6i | 1.67265i | 0.548232 | + | 0.836326i | \(0.315301\pi\) | ||||
−0.548232 | + | 0.836326i | \(0.684699\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.45313e6 | − | 1.45313e6i | −0.509503 | − | 0.509503i | ||||
\(383\) | 1.60463e6 | + | 1.60463e6i | 0.558957 | + | 0.558957i | 0.929010 | − | 0.370054i | \(-0.120661\pi\) |
−0.370054 | + | 0.929010i | \(0.620661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.06338e6i | − | 0.363263i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 823033. | − | 823033.i | 0.277548 | − | 0.277548i | ||||
\(389\) | −1.68645e6 | −0.565067 | −0.282533 | − | 0.959257i | \(-0.591175\pi\) | ||||
−0.282533 | + | 0.959257i | \(0.591175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −859171. | −0.284209 | ||||||||
\(392\) | −1.02999e6 | + | 1.02999e6i | −0.338545 | + | 0.338545i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 4.21920e6i | − | 1.36927i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.40797e6 | − | 1.40797e6i | −0.448349 | − | 0.448349i | 0.446456 | − | 0.894805i | \(-0.352686\pi\) |
−0.894805 | + | 0.446456i | \(0.852686\pi\) | |||||||
\(398\) | −1.16266e6 | − | 1.16266e6i | −0.367913 | − | 0.367913i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.35644e6i | − | 0.421251i | −0.977567 | − | 0.210625i | \(-0.932450\pi\) | ||
0.977567 | − | 0.210625i | \(-0.0675500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.44037e6 | + | 1.44037e6i | −0.441787 | + | 0.441787i | ||||
\(404\) | 2.94243e6 | 0.896919 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.28140e6 | 1.28905 | ||||||||
\(407\) | −3.97278e6 | + | 3.97278e6i | −1.18880 | + | 1.18880i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.99089e6i | 0.884082i | 0.896995 | + | 0.442041i | \(0.145746\pi\) | ||||
−0.896995 | + | 0.442041i | \(0.854254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.35240e6 | − | 1.35240e6i | −0.392520 | − | 0.392520i | ||||
\(413\) | −6.36368e6 | − | 6.36368e6i | −1.83583 | − | 1.83583i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.15679e6i | 0.327733i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.72995e6 | + | 2.72995e6i | −0.764213 | + | 0.764213i | ||||
\(419\) | 1.50892e6 | 0.419887 | 0.209944 | − | 0.977714i | \(-0.432672\pi\) | ||||
0.209944 | + | 0.977714i | \(0.432672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.92470e6 | 1.62915 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(422\) | 688971. | − | 688971.i | 0.188330 | − | 0.188330i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 1.45623e6i | − | 0.393382i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 85206.8 | + | 85206.8i | 0.0226154 | + | 0.0226154i | ||||
\(428\) | −338216. | − | 338216.i | −0.0892453 | − | 0.0892453i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.78110e6i | 0.721148i | 0.932731 | + | 0.360574i | \(0.117419\pi\) | ||||
−0.932731 | + | 0.360574i | \(0.882581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −674431. | + | 674431.i | −0.172869 | + | 0.172869i | −0.788239 | − | 0.615369i | \(-0.789007\pi\) |
0.615369 | + | 0.788239i | \(0.289007\pi\) | |||||||
\(434\) | −1.43470e6 | −0.365626 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −842788. | −0.212325 | ||||||||
\(437\) | 1.28128e6 | − | 1.28128e6i | 0.320952 | − | 0.320952i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.04061e6i | − | 1.49596i | −0.663722 | − | 0.747980i | \(-0.731024\pi\) | ||
0.663722 | − | 0.747980i | \(-0.268976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.70318e6 | + | 2.70318e6i | 0.658142 | + | 0.658142i | ||||
\(443\) | 1.88878e6 | + | 1.88878e6i | 0.457269 | + | 0.457269i | 0.897758 | − | 0.440489i | \(-0.145195\pi\) |
−0.440489 | + | 0.897758i | \(0.645195\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.48216e6i | 0.590871i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −576116. | + | 576116.i | −0.135617 | + | 0.135617i | ||||
\(449\) | 2.99443e6 | 0.700969 | 0.350485 | − | 0.936569i | \(-0.386017\pi\) | ||||
0.350485 | + | 0.936569i | \(0.386017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.75429e6 | −1.56365 | ||||||||
\(452\) | −2.73838e6 | + | 2.73838e6i | −0.630446 | + | 0.630446i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.30846e6i | 0.753332i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.15779e6 | − | 4.15779e6i | −0.931263 | − | 0.931263i | 0.0665219 | − | 0.997785i | \(-0.478810\pi\) |
−0.997785 | + | 0.0665219i | \(0.978810\pi\) | |||||||
\(458\) | −80708.1 | − | 80708.1i | −0.0179785 | − | 0.0179785i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.95742e6i | − | 1.30559i | −0.757535 | − | 0.652794i | \(-0.773597\pi\) | ||
0.757535 | − | 0.652794i | \(-0.226403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.41469e6 | + | 1.41469e6i | −0.306697 | + | 0.306697i | −0.843627 | − | 0.536930i | \(-0.819584\pi\) |
0.536930 | + | 0.843627i | \(0.319584\pi\) | |||||||
\(464\) | 1.37753e6 | 0.297034 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.71352e6 | −0.578854 | ||||||||
\(467\) | 1.26542e6 | − | 1.26542e6i | 0.268500 | − | 0.268500i | −0.559996 | − | 0.828495i | \(-0.689197\pi\) |
0.828495 | + | 0.559996i | \(0.189197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.49072e6i | − | 1.36258i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.04750e6 | − | 2.04750e6i | −0.423027 | − | 0.423027i | ||||
\(473\) | 5.35590e6 | + | 5.35590e6i | 1.10073 | + | 1.10073i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.69253e6i | 0.544683i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.24838e6 | + | 2.24838e6i | −0.450090 | + | 0.450090i | ||||
\(479\) | 433242. | 0.0862764 | 0.0431382 | − | 0.999069i | \(-0.486264\pi\) | ||||
0.0431382 | + | 0.999069i | \(0.486264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.17330e7 | −2.31231 | ||||||||
\(482\) | 4.47551e6 | − | 4.47551e6i | 0.877455 | − | 0.877455i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.10517e6i | 0.408482i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.57807e6 | − | 1.57807e6i | −0.301511 | − | 0.301511i | 0.540094 | − | 0.841605i | \(-0.318389\pi\) |
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(488\) | 27415.1 | + | 27415.1i | 0.00521122 | + | 0.00521122i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.51329e6i | 1.40646i | 0.710964 | + | 0.703228i | \(0.248259\pi\) | ||||
−0.710964 | + | 0.703228i | \(0.751741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.21901e6 | − | 3.21901e6i | 0.596492 | − | 0.596492i | ||||
\(494\) | −8.06249e6 | −1.48646 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −461611. | −0.0842504 | ||||||||
\(497\) | 1.58963e6 | − | 1.58963e6i | 0.288672 | − | 0.288672i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7.36148e6i | − | 1.32347i | −0.749738 | − | 0.661735i | \(-0.769821\pi\) | ||
0.749738 | − | 0.661735i | \(-0.230179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.88692e6 | + | 3.88692e6i | 0.688408 | + | 0.688408i | ||||
\(503\) | −617251. | − | 617251.i | −0.108778 | − | 0.108778i | 0.650623 | − | 0.759401i | \(-0.274508\pi\) |
−0.759401 | + | 0.650623i | \(0.774508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.19745e6i | − | 0.381542i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.28027e6 | + | 1.28027e6i | −0.220111 | + | 0.220111i | ||||
\(509\) | 6.12846e6 | 1.04847 | 0.524236 | − | 0.851573i | \(-0.324351\pi\) | ||||
0.524236 | + | 0.851573i | \(0.324351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.17821e7 | 1.99604 | ||||||||
\(512\) | −185364. | + | 185364.i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.00182e6i | − | 0.334209i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 985270. | + | 985270.i | 0.162117 | + | 0.162117i | ||||
\(518\) | −5.84338e6 | − | 5.84338e6i | −0.956842 | − | 0.956842i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.64518e6i | − | 0.911137i | −0.890201 | − | 0.455568i | \(-0.849436\pi\) | ||
0.890201 | − | 0.455568i | \(-0.150564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.09740e6 | − | 6.09740e6i | 0.974744 | − | 0.974744i | −0.0249444 | − | 0.999689i | \(-0.507941\pi\) |
0.999689 | + | 0.0249444i | \(0.00794089\pi\) | |||||||
\(524\) | −2.96465e6 | −0.471678 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.96242e6 | −0.782040 | ||||||||
\(527\) | −1.07869e6 | + | 1.07869e6i | −0.169189 | + | 0.169189i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 5.40499e6i | − | 0.839761i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.01537e6 | − | 4.01537e6i | −0.615101 | − | 0.615101i | ||||
\(533\) | −9.97387e6 | − | 9.97387e6i | −1.52071 | − | 1.52071i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.08837e6i | − | 0.313976i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.60077e6 | − | 5.60077e6i | 0.834243 | − | 0.834243i | ||||
\(539\) | −1.23118e7 | −1.82537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −311432. | −0.0457477 | −0.0228739 | − | 0.999738i | \(-0.507282\pi\) | ||||
−0.0228739 | + | 0.999738i | \(0.507282\pi\) | |||||||
\(542\) | −1.91813e6 | + | 1.91813e6i | −0.280466 | + | 0.280466i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 866316.i | 0.125510i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.47279e6 | − | 1.47279e6i | −0.210461 | − | 0.210461i | 0.594002 | − | 0.804463i | \(-0.297547\pi\) |
−0.804463 | + | 0.594002i | \(0.797547\pi\) | |||||||
\(548\) | −485799. | − | 485799.i | −0.0691043 | − | 0.0691043i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.60100e6i | 1.34722i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71145e6 | − | 8.71145e6i | 1.21137 | − | 1.21137i | ||||
\(554\) | 4.22625e6 | 0.585034 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.20546e6 | −0.165374 | ||||||||
\(557\) | −254284. | + | 254284.i | −0.0347281 | + | 0.0347281i | −0.724258 | − | 0.689530i | \(-0.757817\pi\) |
0.689530 | + | 0.724258i | \(0.257817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.58178e7i | 2.14100i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.44903e6 | + | 6.44903e6i | 0.861298 | + | 0.861298i | ||||
\(563\) | −4.03909e6 | − | 4.03909e6i | −0.537047 | − | 0.537047i | 0.385613 | − | 0.922660i | \(-0.373990\pi\) |
−0.922660 | + | 0.385613i | \(0.873990\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 2.45261e6i | − | 0.321801i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 511459. | − | 511459.i | 0.0665181 | − | 0.0665181i | ||||
\(569\) | 2.72030e6 | 0.352238 | 0.176119 | − | 0.984369i | \(-0.443646\pi\) | ||||
0.176119 | + | 0.984369i | \(0.443646\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.34348e6 | −0.300796 | −0.150398 | − | 0.988626i | \(-0.548055\pi\) | ||||
−0.150398 | + | 0.988626i | \(0.548055\pi\) | |||||||
\(572\) | −6.91375e6 | + | 6.91375e6i | −0.883535 | + | 0.883535i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 9.93458e6i | − | 1.25855i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.80678e6 | + | 5.80678e6i | 0.726099 | + | 0.726099i | 0.969840 | − | 0.243741i | \(-0.0783748\pi\) |
−0.243741 | + | 0.969840i | \(0.578375\pi\) | |||||||
\(578\) | −1.99156e6 | − | 1.99156e6i | −0.247955 | − | 0.247955i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.31046e7i | 2.83961i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.70340e6 | − | 8.70340e6i | 1.06052 | − | 1.06052i | ||||
\(584\) | 3.79086e6 | 0.459944 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.31884e6 | −0.158653 | ||||||||
\(587\) | 7.26783e6 | − | 7.26783e6i | 0.870581 | − | 0.870581i | −0.121954 | − | 0.992536i | \(-0.538916\pi\) |
0.992536 | + | 0.121954i | \(0.0389162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.21730e6i | − | 0.382123i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.88009e6 | − | 1.88009e6i | −0.220483 | − | 0.220483i | ||||
\(593\) | 8.83276e6 | + | 8.83276e6i | 1.03148 | + | 1.03148i | 0.999488 | + | 0.0319896i | \(0.0101844\pi\) |
0.0319896 | + | 0.999488i | \(0.489816\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.00197e6i | − | 0.230857i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.24491e6 | − | 3.24491e6i | 0.371065 | − | 0.371065i | ||||
\(599\) | −1.64552e7 | −1.87386 | −0.936928 | − | 0.349522i | \(-0.886344\pi\) | ||||
−0.936928 | + | 0.349522i | \(0.886344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.36957e7 | −1.54668 | −0.773338 | − | 0.633994i | \(-0.781414\pi\) | ||||
−0.773338 | + | 0.633994i | \(0.781414\pi\) | |||||||
\(602\) | −7.87776e6 | + | 7.87776e6i | −0.885954 | + | 0.885954i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.71753e6i | 0.749234i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.85652e6 | + | 2.85652e6i | 0.314677 | + | 0.314677i | 0.846718 | − | 0.532041i | \(-0.178575\pi\) |
−0.532041 | + | 0.846718i | \(0.678575\pi\) | |||||||
\(608\) | −1.29193e6 | − | 1.29193e6i | −0.141736 | − | 0.141736i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.90984e6i | 0.315331i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.97843e6 | + | 8.97843e6i | −0.965049 | + | 0.965049i | −0.999409 | − | 0.0343607i | \(-0.989061\pi\) |
0.0343607 | + | 0.999409i | \(0.489061\pi\) | |||||||
\(614\) | −3.77839e6 | −0.404470 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.88652e6 | −0.731220 | ||||||||
\(617\) | −3.16198e6 | + | 3.16198e6i | −0.334385 | + | 0.334385i | −0.854249 | − | 0.519864i | \(-0.825983\pi\) |
0.519864 | + | 0.854249i | \(0.325983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.02582e6i | 0.212508i | 0.994339 | + | 0.106254i | \(0.0338856\pi\) | ||||
−0.994339 | + | 0.106254i | \(0.966114\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.83319e6 | + | 2.83319e6i | 0.293630 | + | 0.293630i | ||||
\(623\) | 1.51723e6 | + | 1.51723e6i | 0.156614 | + | 0.156614i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1.02180e7i | − | 1.04215i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.39372e6 | − | 2.39372e6i | 0.242200 | − | 0.242200i | ||||
\(629\) | −8.78680e6 | −0.885532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.08365e7 | −1.08347 | −0.541734 | − | 0.840550i | \(-0.682232\pi\) | ||||
−0.541734 | + | 0.840550i | \(0.682232\pi\) | |||||||
\(632\) | 2.80289e6 | − | 2.80289e6i | 0.279134 | − | 0.279134i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 6.18553e6i | − | 0.611158i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.81805e7 | − | 1.81805e7i | −1.77524 | − | 1.77524i | ||||
\(638\) | 8.23305e6 | + | 8.23305e6i | 0.800773 | + | 0.800773i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.19747e7i | 1.15112i | 0.817760 | + | 0.575559i | \(0.195215\pi\) | ||||
−0.817760 | + | 0.575559i | \(0.804785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.52742e6 | − | 6.52742e6i | 0.622607 | − | 0.622607i | −0.323590 | − | 0.946197i | \(-0.604890\pi\) |
0.946197 | + | 0.323590i | \(0.104890\pi\) | |||||||
\(644\) | 3.23213e6 | 0.307096 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.03798e6 | −0.569260 | ||||||||
\(647\) | 7.04412e6 | − | 7.04412e6i | 0.661555 | − | 0.661555i | −0.294191 | − | 0.955747i | \(-0.595050\pi\) |
0.955747 | + | 0.294191i | \(0.0950503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.44745e7i | − | 2.28088i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.70514e6 | + | 3.70514e6i | 0.341339 | + | 0.341339i | ||||
\(653\) | −1.42497e6 | − | 1.42497e6i | −0.130774 | − | 0.130774i | 0.638690 | − | 0.769464i | \(-0.279477\pi\) |
−0.769464 | + | 0.638690i | \(0.779477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3.19643e6i | − | 0.290005i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.44919e6 | + | 1.44919e6i | −0.130485 | + | 0.130485i | ||||
\(659\) | −8.38442e6 | −0.752072 | −0.376036 | − | 0.926605i | \(-0.622713\pi\) | ||||
−0.376036 | + | 0.926605i | \(0.622713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.38637e6 | 0.746569 | 0.373285 | − | 0.927717i | \(-0.378231\pi\) | ||||
0.373285 | + | 0.927717i | \(0.378231\pi\) | |||||||
\(662\) | −7.14637e6 | + | 7.14637e6i | −0.633783 | + | 0.633783i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.43384e6i | 0.654325i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.86411e6 | − | 3.86411e6i | −0.336306 | − | 0.336306i | ||||
\(668\) | 2.80380e6 | + | 2.80380e6i | 0.243112 | + | 0.243112i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 327702.i | 0.0280978i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.15707e6 | − | 7.15707e6i | 0.609113 | − | 0.609113i | −0.333602 | − | 0.942714i | \(-0.608264\pi\) |
0.942714 | + | 0.333602i | \(0.108264\pi\) | |||||||
\(674\) | −1.44449e7 | −1.22480 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.44780e7 | −1.21855 | ||||||||
\(677\) | −1.19723e6 | + | 1.19723e6i | −0.100393 | + | 0.100393i | −0.755519 | − | 0.655126i | \(-0.772615\pi\) |
0.655126 | + | 0.755519i | \(0.272615\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.44703e7i | 1.20449i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.75890e6 | − | 2.75890e6i | −0.227130 | − | 0.227130i | ||||
\(683\) | 6.40752e6 | + | 6.40752e6i | 0.525580 | + | 0.525580i | 0.919251 | − | 0.393672i | \(-0.128795\pi\) |
−0.393672 | + | 0.919251i | \(0.628795\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 4.73632e6i | − | 0.384265i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.53465e6 | + | 2.53465e6i | −0.204149 | + | 0.204149i | ||||
\(689\) | 2.57041e7 | 2.06279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.04957e7 | 0.836214 | 0.418107 | − | 0.908398i | \(-0.362694\pi\) | ||||
0.418107 | + | 0.908398i | \(0.362694\pi\) | |||||||
\(692\) | −2.77221e6 | + | 2.77221e6i | −0.220070 | + | 0.220070i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4.79208e6i | − | 0.377681i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.46940e6 | − | 7.46940e6i | −0.582377 | − | 0.582377i | ||||
\(698\) | −1.14689e7 | − | 1.14689e7i | −0.891011 | − | 0.891011i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.30048e7i | 0.999560i | 0.866152 | + | 0.499780i | \(0.166586\pi\) | ||||
−0.866152 | + | 0.499780i | \(0.833414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31037e7 | − | 1.31037e7i | 1.00002 | − | 1.00002i | ||||
\(704\) | −2.21572e6 | −0.168494 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.73294e6 | 0.281864 | ||||||||
\(707\) | −2.58665e7 | + | 2.58665e7i | −1.94620 | + | 1.94620i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.36809e6i | − | 0.401056i | −0.979688 | − | 0.200528i | \(-0.935734\pi\) | ||
0.979688 | − | 0.200528i | \(-0.0642657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 488164. | + | 488164.i | 0.0360883 | + | 0.0360883i | ||||
\(713\) | 1.29487e6 | + | 1.29487e6i | 0.0953896 | + | 0.0953896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.31046e7i | 0.955301i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.01451e7 | + | 1.01451e7i | −0.734422 | + | 0.734422i | ||||
\(719\) | −4.98201e6 | −0.359403 | −0.179702 | − | 0.983721i | \(-0.557513\pi\) | ||||
−0.179702 | + | 0.983721i | \(0.557513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.37774e7 | 1.70344 | ||||||||
\(722\) | 2.00096e6 | − | 2.00096e6i | 0.142855 | − | 0.142855i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.30296e6i | 0.305085i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.33509e6 | − | 2.33509e6i | −0.163858 | − | 0.163858i | 0.620416 | − | 0.784273i | \(-0.286964\pi\) |
−0.784273 | + | 0.620416i | \(0.786964\pi\) | |||||||
\(728\) | −1.01691e7 | − | 1.01691e7i | −0.711141 | − | 0.711141i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.18459e7i | 0.819927i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.25922e7 | + | 1.25922e7i | −0.865650 | + | 0.865650i | −0.991987 | − | 0.126337i | \(-0.959678\pi\) |
0.126337 | + | 0.991987i | \(0.459678\pi\) | |||||||
\(734\) | −7.57545e6 | −0.519001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.03993e6 | 0.0707635 | ||||||||
\(737\) | 1.24815e7 | − | 1.24815e7i | 0.846446 | − | 0.846446i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.79608e6i | 0.255696i | 0.991794 | + | 0.127848i | \(0.0408070\pi\) | ||||
−0.991794 | + | 0.127848i | \(0.959193\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.28014e7 | + | 1.28014e7i | 0.853590 | + | 0.853590i | ||||
\(743\) | 1.26035e7 | + | 1.26035e7i | 0.837563 | + | 0.837563i | 0.988538 | − | 0.150974i | \(-0.0482411\pi\) |
−0.150974 | + | 0.988538i | \(0.548241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 1.28394e7i | − | 0.844689i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.17769e6 | + | 5.17769e6i | −0.338362 | + | 0.338362i | ||||
\(749\) | 5.94641e6 | 0.387302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.62657e7 | −1.05238 | −0.526190 | − | 0.850367i | \(-0.676380\pi\) | ||||
−0.526190 | + | 0.850367i | \(0.676380\pi\) | |||||||
\(752\) | −466273. | + | 466273.i | −0.0300674 | + | 0.0300674i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.43150e7i | 1.55757i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.96785e7 | + | 1.96785e7i | 1.24811 | + | 1.24811i | 0.956554 | + | 0.291555i | \(0.0941727\pi\) |
0.291555 | + | 0.956554i | \(0.405827\pi\) | |||||||
\(758\) | −1.32297e7 | − | 1.32297e7i | −0.836326 | − | 0.836326i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.76431e7i | − | 1.10437i | −0.833723 | − | 0.552183i | \(-0.813795\pi\) | ||
0.833723 | − | 0.552183i | \(-0.186205\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.40881e6 | − | 7.40881e6i | 0.460720 | − | 0.460720i | ||||
\(764\) | 8.22016e6 | 0.509503 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.07717e6 | −0.558957 | ||||||||
\(767\) | 3.61408e7 | − | 3.61408e7i | 2.21824 | − | 2.21824i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.37152e6i | 0.205594i | 0.994702 | + | 0.102797i | \(0.0327791\pi\) | ||||
−0.994702 | + | 0.102797i | \(0.967221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.00770e6 | + | 3.00770e6i | 0.181631 | + | 0.181631i | ||||
\(773\) | −1.91448e7 | − | 1.91448e7i | −1.15240 | − | 1.15240i | −0.986071 | − | 0.166324i | \(-0.946810\pi\) |
−0.166324 | − | 0.986071i | \(-0.553190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.65578e6i | 0.277548i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.77000e6 | − | 4.77000e6i | 0.282533 | − | 0.282533i | ||||
\(779\) | 2.22782e7 | 1.31534 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.11365e6 | 0.358652 | ||||||||
\(782\) | 2.43010e6 | − | 2.43010e6i | 0.142105 | − | 0.142105i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.82649e6i | − | 0.338545i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.34689e6 | + | 6.34689e6i | 0.365279 | + | 0.365279i | 0.865752 | − | 0.500473i | \(-0.166841\pi\) |
−0.500473 | + | 0.865752i | \(0.666841\pi\) | |||||||
\(788\) | 1.19337e7 | + | 1.19337e7i | 0.684635 | + | 0.684635i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.81453e7i | − | 2.73598i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −483908. | + | 483908.i | −0.0273263 | + | 0.0273263i | ||||
\(794\) | 7.96467e6 | 0.448349 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.57699e6 | 0.367913 | ||||||||
\(797\) | 1.07553e7 | − | 1.07553e7i | 0.599758 | − | 0.599758i | −0.340490 | − | 0.940248i | \(-0.610593\pi\) |
0.940248 | + | 0.340490i | \(0.110593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.17917e6i | 0.120760i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.83660e6 | + | 3.83660e6i | 0.210625 | + | 0.210625i | ||||
\(803\) | 2.26567e7 | + | 2.26567e7i | 1.23996 | + | 1.23996i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 8.14798e6i | − | 0.441787i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.32246e6 | + | 8.32246e6i | −0.448460 | + | 0.448460i | ||||
\(809\) | 1.62013e7 | 0.870320 | 0.435160 | − | 0.900353i | \(-0.356692\pi\) | ||||
0.435160 | + | 0.900353i | \(0.356692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −826427. | −0.0441217 | −0.0220609 | − | 0.999757i | \(-0.507023\pi\) | ||||
−0.0220609 | + | 0.999757i | \(0.507023\pi\) | |||||||
\(812\) | −1.21096e7 | + | 1.21096e7i | −0.644527 | + | 0.644527i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 2.24734e7i | − | 1.18880i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.76658e7 | − | 1.76658e7i | −0.925929 | − | 0.925929i | ||||
\(818\) | −8.45953e6 | − | 8.45953e6i | −0.442041 | − | 0.442041i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.76364e6i | 0.453761i | 0.973923 | + | 0.226880i | \(0.0728526\pi\) | ||||
−0.973923 | + | 0.226880i | \(0.927147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.62027e7 | + | 1.62027e7i | −0.833849 | + | 0.833849i | −0.988041 | − | 0.154192i | \(-0.950723\pi\) |
0.154192 | + | 0.988041i | \(0.450723\pi\) | |||||||
\(824\) | 7.65032e6 | 0.392520 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.59984e7 | 1.83583 | ||||||||
\(827\) | 5.28656e6 | − | 5.28656e6i | 0.268788 | − | 0.268788i | −0.559824 | − | 0.828612i | \(-0.689131\pi\) |
0.828612 | + | 0.559824i | \(0.189131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.49472e6i | − | 0.176614i | −0.996093 | − | 0.0883072i | \(-0.971854\pi\) | ||
0.996093 | − | 0.0883072i | \(-0.0281457\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.27189e6 | − | 3.27189e6i | −0.163867 | − | 0.163867i | ||||
\(833\) | −1.36153e7 | − | 1.36153e7i | −0.679854 | − | 0.679854i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 1.54430e7i | − | 0.764213i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.26788e6 | + | 4.26788e6i | −0.209944 | + | 0.209944i | ||||
\(839\) | −2.31902e7 | −1.13737 | −0.568683 | − | 0.822557i | \(-0.692547\pi\) | ||||
−0.568683 | + | 0.822557i | \(0.692547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.44375e6 | 0.411666 | ||||||||
\(842\) | −1.67576e7 | + | 1.67576e7i | −0.814576 | + | 0.814576i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.89741e6i | 0.188330i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.85062e7 | − | 1.85062e7i | −0.886356 | − | 0.886356i | ||||
\(848\) | 4.11883e6 | + | 4.11883e6i | 0.196691 | + | 0.196691i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05477e7i | 0.499269i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.30682e7 | + | 2.30682e7i | −1.08553 | + | 1.08553i | −0.0895430 | + | 0.995983i | \(0.528541\pi\) |
−0.995983 | + | 0.0895430i | \(0.971459\pi\) | |||||||
\(854\) | −482003. | −0.0226154 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.91324e6 | 0.0892453 | ||||||||
\(857\) | 7.59368e6 | − | 7.59368e6i | 0.353183 | − | 0.353183i | −0.508109 | − | 0.861293i | \(-0.669655\pi\) |
0.861293 | + | 0.508109i | \(0.169655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.42112e6i | − | 0.0657127i | −0.999460 | − | 0.0328563i | \(-0.989540\pi\) | ||
0.999460 | − | 0.0328563i | \(-0.0104604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.86615e6 | − | 7.86615e6i | −0.360574 | − | 0.360574i | ||||
\(863\) | 1.78343e7 | + | 1.78343e7i | 0.815133 | + | 0.815133i | 0.985398 | − | 0.170266i | \(-0.0544626\pi\) |
−0.170266 | + | 0.985398i | \(0.554463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 3.81516e6i | − | 0.172869i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.05795e6 | − | 4.05795e6i | 0.182813 | − | 0.182813i | ||||
\(869\) | 3.35039e7 | 1.50503 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.68623e7 | 1.64640 | ||||||||
\(872\) | 2.38376e6 | − | 2.38376e6i | 0.106163 | − | 0.106163i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.24801e6i | 0.320952i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.43434e6 | + | 6.43434e6i | 0.282491 | + | 0.282491i | 0.834102 | − | 0.551611i | \(-0.185987\pi\) |
−0.551611 | + | 0.834102i | \(0.685987\pi\) | |||||||
\(878\) | 1.70854e7 | + | 1.70854e7i | 0.747980 | + | 0.747980i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.64210e7i | − | 1.14686i | −0.819256 | − | 0.573428i | \(-0.805613\pi\) | ||
0.819256 | − | 0.573428i | \(-0.194387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.32206e7 | + | 1.32206e7i | −0.570622 | + | 0.570622i | −0.932302 | − | 0.361680i | \(-0.882203\pi\) |
0.361680 | + | 0.932302i | \(0.382203\pi\) | |||||||
\(884\) | −1.52915e7 | −0.658142 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.06846e7 | −0.457269 | ||||||||
\(887\) | −3.04269e7 | + | 3.04269e7i | −1.29852 | + | 1.29852i | −0.369150 | + | 0.929370i | \(0.620351\pi\) |
−0.929370 | + | 0.369150i | \(0.879649\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.25092e7i | − | 0.955226i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.02061e6 | − | 7.02061e6i | −0.295436 | − | 0.295436i | ||||
\(893\) | −3.24979e6 | − | 3.24979e6i | −0.136373 | − | 0.136373i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 3.25900e6i | − | 0.135617i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.46954e6 | + | 8.46954e6i | −0.350485 | + | 0.350485i | ||||
\(899\) | −9.70280e6 | −0.400404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.92498e7 | 0.789975 | ||||||||
\(902\) | 1.91040e7 | − | 1.91040e7i | 0.781823 | − | 0.781823i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.54906e7i | − | 0.630446i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.23326e7 | + | 2.23326e7i | 0.901408 | + | 0.901408i | 0.995558 | − | 0.0941500i | \(-0.0300133\pi\) |
−0.0941500 | + | 0.995558i | \(0.530013\pi\) | |||||||
\(908\) | −9.35775e6 | − | 9.35775e6i | −0.376666 | − | 0.376666i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.60012e7i | 1.03800i | 0.854775 | + | 0.518999i | \(0.173695\pi\) | ||||
−0.854775 | + | 0.518999i | \(0.826305\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.44297e7 | + | 4.44297e7i | −1.76399 | + | 1.76399i | ||||
\(914\) | 2.35200e7 | 0.931263 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 456554. | 0.0179785 | ||||||||
\(917\) | 2.60618e7 | − | 2.60618e7i | 1.02348 | − | 1.02348i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.80057e7i | 0.703268i | 0.936138 | + | 0.351634i | \(0.114374\pi\) | ||||
−0.936138 | + | 0.351634i | \(0.885626\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.68501e7 | + | 1.68501e7i | 0.652794 | + | 0.652794i | ||||
\(923\) | 9.02785e6 | + | 9.02785e6i | 0.348803 | + | 0.348803i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 8.00270e6i | − | 0.306697i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.89624e6 | + | 3.89624e6i | −0.148517 | + | 0.148517i | ||||
\(929\) | −4.92761e6 | −0.187326 | −0.0936628 | − | 0.995604i | \(-0.529858\pi\) | ||||
−0.0936628 | + | 0.995604i | \(0.529858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.06090e7 | 1.53549 | ||||||||
\(932\) | 7.67501e6 | − | 7.67501e6i | 0.289427 | − | 0.289427i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.15832e6i | 0.268500i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.59273e6 | + | 2.59273e6i | 0.0964737 | + | 0.0964737i | 0.753696 | − | 0.657223i | \(-0.228269\pi\) |
−0.657223 | + | 0.753696i | \(0.728269\pi\) | |||||||
\(938\) | 1.83585e7 | + | 1.83585e7i | 0.681288 | + | 0.681288i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.69862e6i | 0.357056i | 0.983935 | + | 0.178528i | \(0.0571335\pi\) | ||||
−0.983935 | + | 0.178528i | \(0.942867\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.96630e6 | + | 8.96630e6i | −0.328348 | + | 0.328348i | ||||
\(944\) | 1.15824e7 | 0.423027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.02975e7 | −1.10073 | ||||||||
\(947\) | −2.70302e7 | + | 2.70302e7i | −0.979431 | + | 0.979431i | −0.999793 | − | 0.0203616i | \(-0.993518\pi\) |
0.0203616 | + | 0.999793i | \(0.493518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.69131e7i | 2.41182i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.61564e6 | − | 7.61564e6i | −0.272342 | − | 0.272342i | ||||
\(953\) | −1.51028e7 | − | 1.51028e7i | −0.538674 | − | 0.538674i | 0.384466 | − | 0.923139i | \(-0.374386\pi\) |
−0.923139 | + | 0.384466i | \(0.874386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.27187e7i | − | 0.450090i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.22539e6 | + | 1.22539e6i | −0.0431382 | + | 0.0431382i | ||||
\(959\) | 8.54115e6 | 0.299895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.53777e7 | −0.886430 | ||||||||
\(962\) | 3.31859e7 | − | 3.31859e7i | 1.15615 | − | 1.15615i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.53173e7i | 0.877455i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.69949e6 | − | 2.69949e6i | −0.0928360 | − | 0.0928360i | 0.659164 | − | 0.752000i | \(-0.270910\pi\) |
−0.752000 | + | 0.659164i | \(0.770910\pi\) | |||||||
\(968\) | −5.95431e6 | − | 5.95431e6i | −0.204241 | − | 0.204241i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.74219e6i | 0.195447i | 0.995214 | + | 0.0977235i | \(0.0311561\pi\) | ||||
−0.995214 | + | 0.0977235i | \(0.968844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.05970e7 | − | 1.05970e7i | 0.358841 | − | 0.358841i | ||||
\(974\) | 8.92690e6 | 0.301511 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −155083. | −0.00521122 | ||||||||
\(977\) | −3.62050e6 | + | 3.62050e6i | −0.121348 | + | 0.121348i | −0.765173 | − | 0.643825i | \(-0.777346\pi\) |
0.643825 | + | 0.765173i | \(0.277346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.83520e6i | 0.194581i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.12508e7 | − | 2.12508e7i | −0.703228 | − | 0.703228i | ||||
\(983\) | 9.59647e6 | + | 9.59647e6i | 0.316758 | + | 0.316758i | 0.847521 | − | 0.530762i | \(-0.178094\pi\) |
−0.530762 | + | 0.847521i | \(0.678094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.82095e7i | 0.596492i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.28042e7 | − | 2.28042e7i | 0.743228 | − | 0.743228i | ||||
\(989\) | 1.42199e7 | 0.462280 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.21393e7 | 1.03956 | 0.519782 | − | 0.854299i | \(-0.326013\pi\) | ||||
0.519782 | + | 0.854299i | \(0.326013\pi\) | |||||||
\(992\) | 1.30563e6 | − | 1.30563e6i | 0.0421252 | − | 0.0421252i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.99230e6i | 0.288672i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.23317e6 | − | 3.23317e6i | −0.103013 | − | 0.103013i | 0.653722 | − | 0.756735i | \(-0.273207\pi\) |
−0.756735 | + | 0.653722i | \(0.773207\pi\) | |||||||
\(998\) | 2.08214e7 | + | 2.08214e7i | 0.661735 | + | 0.661735i | ||||
\(999\) | 0 | 0 |
(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 | 450.6.f.g.107.3 | yes | 16 | |
3.2 | odd | 2 | inner | 450.6.f.g.107.7 | yes | 16 | |
5.2 | odd | 4 | 450.6.f.f.143.2 | yes | 16 | ||
5.3 | odd | 4 | inner | 450.6.f.g.143.7 | yes | 16 | |
5.4 | even | 2 | 450.6.f.f.107.6 | yes | 16 | ||
15.2 | even | 4 | 450.6.f.f.143.6 | yes | 16 | ||
15.8 | even | 4 | inner | 450.6.f.g.143.3 | yes | 16 | |
15.14 | odd | 2 | 450.6.f.f.107.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.f.f.107.2 | ✓ | 16 | 15.14 | odd | 2 | ||
450.6.f.f.107.6 | yes | 16 | 5.4 | even | 2 | ||
450.6.f.f.143.2 | yes | 16 | 5.2 | odd | 4 | ||
450.6.f.f.143.6 | yes | 16 | 15.2 | even | 4 | ||
450.6.f.g.107.3 | yes | 16 | 1.1 | even | 1 | trivial | |
450.6.f.g.107.7 | yes | 16 | 3.2 | odd | 2 | inner | |
450.6.f.g.143.3 | yes | 16 | 15.8 | even | 4 | inner | |
450.6.f.g.143.7 | yes | 16 | 5.3 | odd | 4 | inner |