Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,5,Mod(91,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.91");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.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: | \(14.2650549056\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1428 x^{14} - 600 x^{13} + 788282 x^{12} - 529464 x^{11} + 213396724 x^{10} + \cdots + 274129967370817 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.12 | ||
Root | \(0.707107 - 1.47108i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 138.91 |
Dual form | 138.5.b.a.91.9 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843 | 0.707107 | ||||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 19.9722i | 0.798887i | 0.916758 | + | 0.399443i | \(0.130797\pi\) | ||||
−0.916758 | + | 0.399443i | \(0.869203\pi\) | |||||||
\(6\) | −14.6969 | −0.408248 | ||||||||
\(7\) | − | 58.9751i | − | 1.20357i | −0.798656 | − | 0.601787i | \(-0.794456\pi\) | ||
0.798656 | − | 0.601787i | \(-0.205544\pi\) | |||||||
\(8\) | 22.6274 | 0.353553 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 56.4898i | 0.564898i | ||||||||
\(11\) | 168.627i | 1.39361i | 0.717260 | + | 0.696806i | \(0.245396\pi\) | ||||
−0.717260 | + | 0.696806i | \(0.754604\pi\) | |||||||
\(12\) | −41.5692 | −0.288675 | ||||||||
\(13\) | 288.481 | 1.70699 | 0.853495 | − | 0.521101i | \(-0.174478\pi\) | ||||
0.853495 | + | 0.521101i | \(0.174478\pi\) | |||||||
\(14\) | − | 166.807i | − | 0.851056i | ||||||
\(15\) | − | 103.778i | − | 0.461238i | ||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 311.477i | 1.07778i | 0.842377 | + | 0.538888i | \(0.181155\pi\) | ||||
−0.842377 | + | 0.538888i | \(0.818845\pi\) | |||||||
\(18\) | 76.3675 | 0.235702 | ||||||||
\(19\) | 118.278i | 0.327640i | 0.986490 | + | 0.163820i | \(0.0523816\pi\) | ||||
−0.986490 | + | 0.163820i | \(0.947618\pi\) | |||||||
\(20\) | 159.777i | 0.399443i | ||||||||
\(21\) | 306.444i | 0.694884i | ||||||||
\(22\) | 476.949i | 0.985432i | ||||||||
\(23\) | −383.722 | + | 364.140i | −0.725373 | + | 0.688356i | ||||
\(24\) | −117.576 | −0.204124 | ||||||||
\(25\) | 226.112 | 0.361780 | ||||||||
\(26\) | 815.949 | 1.20702 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | − | 471.801i | − | 0.601787i | ||||||
\(29\) | 991.638 | 1.17912 | 0.589559 | − | 0.807725i | \(-0.299302\pi\) | ||||
0.589559 | + | 0.807725i | \(0.299302\pi\) | |||||||
\(30\) | − | 293.530i | − | 0.326144i | ||||||
\(31\) | 827.898 | 0.861496 | 0.430748 | − | 0.902472i | \(-0.358250\pi\) | ||||
0.430748 | + | 0.902472i | \(0.358250\pi\) | |||||||
\(32\) | 181.019 | 0.176777 | ||||||||
\(33\) | − | 876.212i | − | 0.804602i | ||||||
\(34\) | 880.991i | 0.762103i | ||||||||
\(35\) | 1177.86 | 0.961520 | ||||||||
\(36\) | 216.000 | 0.166667 | ||||||||
\(37\) | 80.7914i | 0.0590149i | 0.999565 | + | 0.0295074i | \(0.00939387\pi\) | ||||
−0.999565 | + | 0.0295074i | \(0.990606\pi\) | |||||||
\(38\) | 334.541i | 0.231677i | ||||||||
\(39\) | −1498.99 | −0.985531 | ||||||||
\(40\) | 451.919i | 0.282449i | ||||||||
\(41\) | 187.684 | 0.111650 | 0.0558251 | − | 0.998441i | \(-0.482221\pi\) | ||||
0.0558251 | + | 0.998441i | \(0.482221\pi\) | |||||||
\(42\) | 866.754i | 0.491357i | ||||||||
\(43\) | 331.510i | 0.179292i | 0.995974 | + | 0.0896458i | \(0.0285735\pi\) | ||||
−0.995974 | + | 0.0896458i | \(0.971426\pi\) | |||||||
\(44\) | 1349.02i | 0.696806i | ||||||||
\(45\) | 539.249i | 0.266296i | ||||||||
\(46\) | −1085.33 | + | 1029.94i | −0.512916 | + | 0.486741i | ||||
\(47\) | −1896.65 | −0.858603 | −0.429302 | − | 0.903161i | \(-0.641240\pi\) | ||||
−0.429302 | + | 0.903161i | \(0.641240\pi\) | |||||||
\(48\) | −332.554 | −0.144338 | ||||||||
\(49\) | −1077.07 | −0.448591 | ||||||||
\(50\) | 639.542 | 0.255817 | ||||||||
\(51\) | − | 1618.48i | − | 0.622254i | ||||||
\(52\) | 2307.85 | 0.853495 | ||||||||
\(53\) | − | 4190.84i | − | 1.49193i | −0.665984 | − | 0.745966i | \(-0.731988\pi\) | ||
0.665984 | − | 0.745966i | \(-0.268012\pi\) | |||||||
\(54\) | −396.817 | −0.136083 | ||||||||
\(55\) | −3367.85 | −1.11334 | ||||||||
\(56\) | − | 1334.46i | − | 0.425528i | ||||||
\(57\) | − | 614.591i | − | 0.189163i | ||||||
\(58\) | 2804.78 | 0.833762 | ||||||||
\(59\) | −4961.39 | −1.42528 | −0.712638 | − | 0.701532i | \(-0.752500\pi\) | ||||
−0.712638 | + | 0.701532i | \(0.752500\pi\) | |||||||
\(60\) | − | 830.228i | − | 0.230619i | ||||||
\(61\) | − | 5565.38i | − | 1.49567i | −0.663886 | − | 0.747834i | \(-0.731094\pi\) | ||
0.663886 | − | 0.747834i | \(-0.268906\pi\) | |||||||
\(62\) | 2341.65 | 0.609170 | ||||||||
\(63\) | − | 1592.33i | − | 0.401191i | ||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 5761.60i | 1.36369i | ||||||||
\(66\) | − | 2478.30i | − | 0.568940i | ||||||
\(67\) | 6833.36i | 1.52225i | 0.648608 | + | 0.761123i | \(0.275351\pi\) | ||||
−0.648608 | + | 0.761123i | \(0.724649\pi\) | |||||||
\(68\) | 2491.82i | 0.538888i | ||||||||
\(69\) | 1993.88 | − | 1892.13i | 0.418794 | − | 0.397422i | ||||
\(70\) | 3331.50 | 0.679897 | ||||||||
\(71\) | 1911.46 | 0.379183 | 0.189592 | − | 0.981863i | \(-0.439284\pi\) | ||||
0.189592 | + | 0.981863i | \(0.439284\pi\) | |||||||
\(72\) | 610.940 | 0.117851 | ||||||||
\(73\) | −6606.73 | −1.23977 | −0.619885 | − | 0.784693i | \(-0.712821\pi\) | ||||
−0.619885 | + | 0.784693i | \(0.712821\pi\) | |||||||
\(74\) | 228.512i | 0.0417298i | ||||||||
\(75\) | −1174.91 | −0.208874 | ||||||||
\(76\) | 946.225i | 0.163820i | ||||||||
\(77\) | 9944.80 | 1.67732 | ||||||||
\(78\) | −4239.79 | −0.696876 | ||||||||
\(79\) | − | 11343.7i | − | 1.81761i | −0.417226 | − | 0.908803i | \(-0.636998\pi\) | ||
0.417226 | − | 0.908803i | \(-0.363002\pi\) | |||||||
\(80\) | 1278.22i | 0.199722i | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 530.850 | 0.0789486 | ||||||||
\(83\) | 3573.28i | 0.518694i | 0.965784 | + | 0.259347i | \(0.0835073\pi\) | ||||
−0.965784 | + | 0.259347i | \(0.916493\pi\) | |||||||
\(84\) | 2451.55i | 0.347442i | ||||||||
\(85\) | −6220.88 | −0.861021 | ||||||||
\(86\) | 937.652i | 0.126778i | ||||||||
\(87\) | −5152.70 | −0.680764 | ||||||||
\(88\) | 3815.59i | 0.492716i | ||||||||
\(89\) | 3641.31i | 0.459703i | 0.973226 | + | 0.229851i | \(0.0738240\pi\) | ||||
−0.973226 | + | 0.229851i | \(0.926176\pi\) | |||||||
\(90\) | 1525.23i | 0.188299i | ||||||||
\(91\) | − | 17013.2i | − | 2.05449i | ||||||
\(92\) | −3069.78 | + | 2913.12i | −0.362687 | + | 0.344178i | ||||
\(93\) | −4301.88 | −0.497385 | ||||||||
\(94\) | −5364.55 | −0.607124 | ||||||||
\(95\) | −2362.27 | −0.261747 | ||||||||
\(96\) | −940.604 | −0.102062 | ||||||||
\(97\) | 9509.93i | 1.01073i | 0.862907 | + | 0.505363i | \(0.168642\pi\) | ||||
−0.862907 | + | 0.505363i | \(0.831358\pi\) | |||||||
\(98\) | −3046.41 | −0.317202 | ||||||||
\(99\) | 4552.93i | 0.464537i | ||||||||
\(100\) | 1808.90 | 0.180890 | ||||||||
\(101\) | 7894.84 | 0.773928 | 0.386964 | − | 0.922095i | \(-0.373524\pi\) | ||||
0.386964 | + | 0.922095i | \(0.373524\pi\) | |||||||
\(102\) | − | 4577.76i | − | 0.440000i | ||||||
\(103\) | − | 9239.82i | − | 0.870942i | −0.900203 | − | 0.435471i | \(-0.856582\pi\) | ||
0.900203 | − | 0.435471i | \(-0.143418\pi\) | |||||||
\(104\) | 6527.59 | 0.603512 | ||||||||
\(105\) | −6120.35 | −0.555134 | ||||||||
\(106\) | − | 11853.5i | − | 1.05496i | ||||||
\(107\) | − | 18393.4i | − | 1.60655i | −0.595607 | − | 0.803276i | \(-0.703089\pi\) | ||
0.595607 | − | 0.803276i | \(-0.296911\pi\) | |||||||
\(108\) | −1122.37 | −0.0962250 | ||||||||
\(109\) | 1577.05i | 0.132737i | 0.997795 | + | 0.0663687i | \(0.0211414\pi\) | ||||
−0.997795 | + | 0.0663687i | \(0.978859\pi\) | |||||||
\(110\) | −9525.71 | −0.787249 | ||||||||
\(111\) | − | 419.804i | − | 0.0340723i | ||||||
\(112\) | − | 3774.41i | − | 0.300894i | ||||||
\(113\) | 12500.1i | 0.978942i | 0.872020 | + | 0.489471i | \(0.162810\pi\) | ||||
−0.872020 | + | 0.489471i | \(0.837190\pi\) | |||||||
\(114\) | − | 1738.33i | − | 0.133759i | ||||||
\(115\) | −7272.67 | − | 7663.77i | −0.549918 | − | 0.579491i | ||||
\(116\) | 7933.10 | 0.589559 | ||||||||
\(117\) | 7789.00 | 0.568997 | ||||||||
\(118\) | −14032.9 | −1.00782 | ||||||||
\(119\) | 18369.4 | 1.29718 | ||||||||
\(120\) | − | 2348.24i | − | 0.163072i | ||||||
\(121\) | −13794.1 | −0.942153 | ||||||||
\(122\) | − | 15741.3i | − | 1.05760i | ||||||
\(123\) | −975.234 | −0.0644612 | ||||||||
\(124\) | 6623.18 | 0.430748 | ||||||||
\(125\) | 16998.6i | 1.08791i | ||||||||
\(126\) | − | 4503.79i | − | 0.283685i | ||||||
\(127\) | −26262.9 | −1.62830 | −0.814152 | − | 0.580652i | \(-0.802798\pi\) | ||||
−0.814152 | + | 0.580652i | \(0.802798\pi\) | |||||||
\(128\) | 1448.15 | 0.0883883 | ||||||||
\(129\) | − | 1722.58i | − | 0.103514i | ||||||
\(130\) | 16296.3i | 0.964276i | ||||||||
\(131\) | 18959.4 | 1.10479 | 0.552397 | − | 0.833581i | \(-0.313713\pi\) | ||||
0.552397 | + | 0.833581i | \(0.313713\pi\) | |||||||
\(132\) | − | 7009.69i | − | 0.402301i | ||||||
\(133\) | 6975.47 | 0.394339 | ||||||||
\(134\) | 19327.7i | 1.07639i | ||||||||
\(135\) | − | 2802.02i | − | 0.153746i | ||||||
\(136\) | 7047.93i | 0.381051i | ||||||||
\(137\) | 10213.0i | 0.544140i | 0.962277 | + | 0.272070i | \(0.0877082\pi\) | ||||
−0.962277 | + | 0.272070i | \(0.912292\pi\) | |||||||
\(138\) | 5639.55 | − | 5351.75i | 0.296132 | − | 0.281020i | ||||
\(139\) | 19685.0 | 1.01884 | 0.509420 | − | 0.860518i | \(-0.329860\pi\) | ||||
0.509420 | + | 0.860518i | \(0.329860\pi\) | |||||||
\(140\) | 9422.90 | 0.480760 | ||||||||
\(141\) | 9855.30 | 0.495715 | ||||||||
\(142\) | 5406.43 | 0.268123 | ||||||||
\(143\) | 48645.8i | 2.37888i | ||||||||
\(144\) | 1728.00 | 0.0833333 | ||||||||
\(145\) | 19805.2i | 0.941982i | ||||||||
\(146\) | −18686.7 | −0.876650 | ||||||||
\(147\) | 5596.61 | 0.258994 | ||||||||
\(148\) | 646.331i | 0.0295074i | ||||||||
\(149\) | − | 18845.6i | − | 0.848864i | −0.905460 | − | 0.424432i | \(-0.860474\pi\) | ||
0.905460 | − | 0.424432i | \(-0.139526\pi\) | |||||||
\(150\) | −3323.16 | −0.147696 | ||||||||
\(151\) | −6343.55 | −0.278214 | −0.139107 | − | 0.990277i | \(-0.544423\pi\) | ||||
−0.139107 | + | 0.990277i | \(0.544423\pi\) | |||||||
\(152\) | 2676.33i | 0.115838i | ||||||||
\(153\) | 8409.89i | 0.359259i | ||||||||
\(154\) | 28128.1 | 1.18604 | ||||||||
\(155\) | 16534.9i | 0.688238i | ||||||||
\(156\) | −11991.9 | −0.492766 | ||||||||
\(157\) | − | 26439.6i | − | 1.07264i | −0.844014 | − | 0.536321i | \(-0.819814\pi\) | ||
0.844014 | − | 0.536321i | \(-0.180186\pi\) | |||||||
\(158\) | − | 32084.8i | − | 1.28524i | ||||||
\(159\) | 21776.2i | 0.861367i | ||||||||
\(160\) | 3615.35i | 0.141225i | ||||||||
\(161\) | 21475.2 | + | 22630.1i | 0.828487 | + | 0.873041i | ||||
\(162\) | 2061.92 | 0.0785674 | ||||||||
\(163\) | 11346.9 | 0.427072 | 0.213536 | − | 0.976935i | \(-0.431502\pi\) | ||||
0.213536 | + | 0.976935i | \(0.431502\pi\) | |||||||
\(164\) | 1501.47 | 0.0558251 | ||||||||
\(165\) | 17499.9 | 0.642786 | ||||||||
\(166\) | 10106.8i | 0.366772i | ||||||||
\(167\) | 6625.97 | 0.237584 | 0.118792 | − | 0.992919i | \(-0.462098\pi\) | ||||
0.118792 | + | 0.992919i | \(0.462098\pi\) | |||||||
\(168\) | 6934.03i | 0.245679i | ||||||||
\(169\) | 54660.5 | 1.91382 | ||||||||
\(170\) | −17595.3 | −0.608834 | ||||||||
\(171\) | 3193.51i | 0.109213i | ||||||||
\(172\) | 2652.08i | 0.0896458i | ||||||||
\(173\) | 27706.0 | 0.925725 | 0.462863 | − | 0.886430i | \(-0.346822\pi\) | ||||
0.462863 | + | 0.886430i | \(0.346822\pi\) | |||||||
\(174\) | −14574.0 | −0.481373 | ||||||||
\(175\) | − | 13335.0i | − | 0.435429i | ||||||
\(176\) | 10792.1i | 0.348403i | ||||||||
\(177\) | 25780.1 | 0.822884 | ||||||||
\(178\) | 10299.2i | 0.325059i | ||||||||
\(179\) | −22956.0 | −0.716457 | −0.358228 | − | 0.933634i | \(-0.616619\pi\) | ||||
−0.358228 | + | 0.933634i | \(0.616619\pi\) | |||||||
\(180\) | 4313.99i | 0.133148i | ||||||||
\(181\) | 19018.6i | 0.580526i | 0.956947 | + | 0.290263i | \(0.0937427\pi\) | ||||
−0.956947 | + | 0.290263i | \(0.906257\pi\) | |||||||
\(182\) | − | 48120.7i | − | 1.45274i | ||||||
\(183\) | 28918.6i | 0.863524i | ||||||||
\(184\) | −8682.65 | + | 8239.55i | −0.256458 | + | 0.243371i | ||||
\(185\) | −1613.58 | −0.0471462 | ||||||||
\(186\) | −12167.6 | −0.351704 | ||||||||
\(187\) | −52523.5 | −1.50200 | ||||||||
\(188\) | −15173.2 | −0.429302 | ||||||||
\(189\) | 8273.98i | 0.231628i | ||||||||
\(190\) | −6681.51 | −0.185083 | ||||||||
\(191\) | − | 70888.2i | − | 1.94315i | −0.236726 | − | 0.971576i | \(-0.576074\pi\) | ||
0.236726 | − | 0.971576i | \(-0.423926\pi\) | |||||||
\(192\) | −2660.43 | −0.0721688 | ||||||||
\(193\) | 23342.4 | 0.626658 | 0.313329 | − | 0.949645i | \(-0.398556\pi\) | ||||
0.313329 | + | 0.949645i | \(0.398556\pi\) | |||||||
\(194\) | 26898.1i | 0.714692i | ||||||||
\(195\) | − | 29938.2i | − | 0.787328i | ||||||
\(196\) | −8616.54 | −0.224296 | ||||||||
\(197\) | −51130.3 | −1.31749 | −0.658743 | − | 0.752368i | \(-0.728911\pi\) | ||||
−0.658743 | + | 0.752368i | \(0.728911\pi\) | |||||||
\(198\) | 12877.6i | 0.328477i | ||||||||
\(199\) | 68616.0i | 1.73268i | 0.499452 | + | 0.866342i | \(0.333535\pi\) | ||||
−0.499452 | + | 0.866342i | \(0.666465\pi\) | |||||||
\(200\) | 5116.34 | 0.127908 | ||||||||
\(201\) | − | 35507.2i | − | 0.878869i | ||||||
\(202\) | 22330.0 | 0.547250 | ||||||||
\(203\) | − | 58482.0i | − | 1.41916i | ||||||
\(204\) | − | 12947.9i | − | 0.311127i | ||||||
\(205\) | 3748.45i | 0.0891958i | ||||||||
\(206\) | − | 26134.2i | − | 0.615849i | ||||||
\(207\) | −10360.5 | + | 9831.79i | −0.241791 | + | 0.229452i | ||||
\(208\) | 18462.8 | 0.426748 | ||||||||
\(209\) | −19944.9 | −0.456603 | ||||||||
\(210\) | −17311.0 | −0.392539 | ||||||||
\(211\) | −59489.3 | −1.33621 | −0.668104 | − | 0.744068i | \(-0.732894\pi\) | ||||
−0.668104 | + | 0.744068i | \(0.732894\pi\) | |||||||
\(212\) | − | 33526.7i | − | 0.745966i | ||||||
\(213\) | −9932.25 | −0.218922 | ||||||||
\(214\) | − | 52024.4i | − | 1.13600i | ||||||
\(215\) | −6620.98 | −0.143234 | ||||||||
\(216\) | −3174.54 | −0.0680414 | ||||||||
\(217\) | − | 48825.4i | − | 1.03687i | ||||||
\(218\) | 4460.58i | 0.0938595i | ||||||||
\(219\) | 34329.6 | 0.715781 | ||||||||
\(220\) | −26942.8 | −0.556669 | ||||||||
\(221\) | 89855.4i | 1.83975i | ||||||||
\(222\) | − | 1187.39i | − | 0.0240927i | ||||||
\(223\) | 59731.0 | 1.20113 | 0.600565 | − | 0.799576i | \(-0.294942\pi\) | ||||
0.600565 | + | 0.799576i | \(0.294942\pi\) | |||||||
\(224\) | − | 10675.6i | − | 0.212764i | ||||||
\(225\) | 6105.03 | 0.120593 | ||||||||
\(226\) | 35355.7i | 0.692217i | ||||||||
\(227\) | − | 36166.2i | − | 0.701860i | −0.936402 | − | 0.350930i | \(-0.885865\pi\) | ||
0.936402 | − | 0.350930i | \(-0.114135\pi\) | |||||||
\(228\) | − | 4916.73i | − | 0.0945816i | ||||||
\(229\) | − | 45527.5i | − | 0.868165i | −0.900873 | − | 0.434083i | \(-0.857073\pi\) | ||
0.900873 | − | 0.434083i | \(-0.142927\pi\) | |||||||
\(230\) | −20570.2 | − | 21676.4i | −0.388851 | − | 0.409762i | ||||
\(231\) | −51674.7 | −0.968398 | ||||||||
\(232\) | 22438.2 | 0.416881 | ||||||||
\(233\) | −34923.6 | −0.643291 | −0.321645 | − | 0.946860i | \(-0.604236\pi\) | ||||
−0.321645 | + | 0.946860i | \(0.604236\pi\) | |||||||
\(234\) | 22030.6 | 0.402342 | ||||||||
\(235\) | − | 37880.3i | − | 0.685927i | ||||||
\(236\) | −39691.1 | −0.712638 | ||||||||
\(237\) | 58943.5i | 1.04939i | ||||||||
\(238\) | 51956.6 | 0.917247 | ||||||||
\(239\) | −87697.7 | −1.53530 | −0.767649 | − | 0.640871i | \(-0.778573\pi\) | ||||
−0.767649 | + | 0.640871i | \(0.778573\pi\) | |||||||
\(240\) | − | 6641.82i | − | 0.115309i | ||||||
\(241\) | 78064.1i | 1.34406i | 0.740526 | + | 0.672028i | \(0.234577\pi\) | ||||
−0.740526 | + | 0.672028i | \(0.765423\pi\) | |||||||
\(242\) | −39015.5 | −0.666203 | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | − | 44523.0i | − | 0.747834i | ||||||
\(245\) | − | 21511.4i | − | 0.358374i | ||||||
\(246\) | −2758.38 | −0.0455810 | ||||||||
\(247\) | 34121.0i | 0.559279i | ||||||||
\(248\) | 18733.2 | 0.304585 | ||||||||
\(249\) | − | 18567.3i | − | 0.299468i | ||||||
\(250\) | 48079.2i | 0.769267i | ||||||||
\(251\) | − | 51539.5i | − | 0.818075i | −0.912518 | − | 0.409037i | \(-0.865865\pi\) | ||
0.912518 | − | 0.409037i | \(-0.134135\pi\) | |||||||
\(252\) | − | 12738.6i | − | 0.200596i | ||||||
\(253\) | −61403.9 | − | 64706.0i | −0.959301 | − | 1.01089i | ||||
\(254\) | −74282.7 | −1.15138 | ||||||||
\(255\) | 32324.6 | 0.497111 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −44584.2 | −0.675016 | −0.337508 | − | 0.941323i | \(-0.609584\pi\) | ||||
−0.337508 | + | 0.941323i | \(0.609584\pi\) | |||||||
\(258\) | − | 4872.18i | − | 0.0731955i | ||||||
\(259\) | 4764.68 | 0.0710288 | ||||||||
\(260\) | 46092.8i | 0.681846i | ||||||||
\(261\) | 26774.2 | 0.393039 | ||||||||
\(262\) | 53625.1 | 0.781207 | ||||||||
\(263\) | − | 100390.i | − | 1.45138i | −0.688023 | − | 0.725688i | \(-0.741521\pi\) | ||
0.688023 | − | 0.725688i | \(-0.258479\pi\) | |||||||
\(264\) | − | 19826.4i | − | 0.284470i | ||||||
\(265\) | 83700.1 | 1.19188 | ||||||||
\(266\) | 19729.6 | 0.278840 | ||||||||
\(267\) | − | 18920.8i | − | 0.265410i | ||||||
\(268\) | 54666.9i | 0.761123i | ||||||||
\(269\) | 89798.2 | 1.24097 | 0.620487 | − | 0.784216i | \(-0.286935\pi\) | ||||
0.620487 | + | 0.784216i | \(0.286935\pi\) | |||||||
\(270\) | − | 7925.30i | − | 0.108715i | ||||||
\(271\) | −9946.27 | −0.135432 | −0.0677161 | − | 0.997705i | \(-0.521571\pi\) | ||||
−0.0677161 | + | 0.997705i | \(0.521571\pi\) | |||||||
\(272\) | 19934.5i | 0.269444i | ||||||||
\(273\) | 88403.4i | 1.18616i | ||||||||
\(274\) | 28886.6i | 0.384765i | ||||||||
\(275\) | 38128.6i | 0.504180i | ||||||||
\(276\) | 15951.0 | − | 15137.0i | 0.209397 | − | 0.198711i | ||||
\(277\) | −137747. | −1.79524 | −0.897620 | − | 0.440770i | \(-0.854705\pi\) | ||||
−0.897620 | + | 0.440770i | \(0.854705\pi\) | |||||||
\(278\) | 55677.6 | 0.720428 | ||||||||
\(279\) | 22353.2 | 0.287165 | ||||||||
\(280\) | 26652.0 | 0.339949 | ||||||||
\(281\) | − | 144672.i | − | 1.83220i | −0.400952 | − | 0.916099i | \(-0.631321\pi\) | ||
0.400952 | − | 0.916099i | \(-0.368679\pi\) | |||||||
\(282\) | 27875.0 | 0.350523 | ||||||||
\(283\) | − | 11368.5i | − | 0.141948i | −0.997478 | − | 0.0709740i | \(-0.977389\pi\) | ||
0.997478 | − | 0.0709740i | \(-0.0226107\pi\) | |||||||
\(284\) | 15291.7 | 0.189592 | ||||||||
\(285\) | 12274.7 | 0.151120 | ||||||||
\(286\) | 137591.i | 1.68212i | ||||||||
\(287\) | − | 11068.7i | − | 0.134379i | ||||||
\(288\) | 4887.52 | 0.0589256 | ||||||||
\(289\) | −13497.1 | −0.161601 | ||||||||
\(290\) | 56017.5i | 0.666082i | ||||||||
\(291\) | − | 49415.0i | − | 0.583543i | ||||||
\(292\) | −52853.9 | −0.619885 | ||||||||
\(293\) | − | 16897.0i | − | 0.196823i | −0.995146 | − | 0.0984113i | \(-0.968624\pi\) | ||
0.995146 | − | 0.0984113i | \(-0.0313761\pi\) | |||||||
\(294\) | 15829.6 | 0.183137 | ||||||||
\(295\) | − | 99089.7i | − | 1.13863i | ||||||
\(296\) | 1828.10i | 0.0208649i | ||||||||
\(297\) | − | 23657.7i | − | 0.268201i | ||||||
\(298\) | − | 53303.5i | − | 0.600237i | ||||||
\(299\) | −110697. | + | 105048.i | −1.23821 | + | 1.17502i | ||||
\(300\) | −9399.31 | −0.104437 | ||||||||
\(301\) | 19550.9 | 0.215791 | ||||||||
\(302\) | −17942.3 | −0.196727 | ||||||||
\(303\) | −41022.8 | −0.446828 | ||||||||
\(304\) | 7569.80i | 0.0819100i | ||||||||
\(305\) | 111153. | 1.19487 | ||||||||
\(306\) | 23786.8i | 0.254034i | ||||||||
\(307\) | −61670.7 | −0.654338 | −0.327169 | − | 0.944966i | \(-0.606095\pi\) | ||||
−0.327169 | + | 0.944966i | \(0.606095\pi\) | |||||||
\(308\) | 79558.4 | 0.838658 | ||||||||
\(309\) | 48011.5i | 0.502839i | ||||||||
\(310\) | 46767.8i | 0.486658i | ||||||||
\(311\) | 94648.6 | 0.978574 | 0.489287 | − | 0.872123i | \(-0.337257\pi\) | ||||
0.489287 | + | 0.872123i | \(0.337257\pi\) | |||||||
\(312\) | −33918.3 | −0.348438 | ||||||||
\(313\) | 64314.1i | 0.656474i | 0.944595 | + | 0.328237i | \(0.106454\pi\) | ||||
−0.944595 | + | 0.328237i | \(0.893546\pi\) | |||||||
\(314\) | − | 74782.4i | − | 0.758473i | ||||||
\(315\) | 31802.3 | 0.320507 | ||||||||
\(316\) | − | 90749.4i | − | 0.908803i | ||||||
\(317\) | −41158.9 | −0.409586 | −0.204793 | − | 0.978805i | \(-0.565652\pi\) | ||||
−0.204793 | + | 0.978805i | \(0.565652\pi\) | |||||||
\(318\) | 61592.5i | 0.609079i | ||||||||
\(319\) | 167217.i | 1.64323i | ||||||||
\(320\) | 10225.8i | 0.0998609i | ||||||||
\(321\) | 95575.0i | 0.927543i | ||||||||
\(322\) | 60741.1 | + | 64007.6i | 0.585829 | + | 0.617333i | ||||
\(323\) | −36840.9 | −0.353123 | ||||||||
\(324\) | 5832.00 | 0.0555556 | ||||||||
\(325\) | 65229.2 | 0.617554 | ||||||||
\(326\) | 32093.8 | 0.301986 | ||||||||
\(327\) | − | 8194.61i | − | 0.0766360i | ||||||
\(328\) | 4246.80 | 0.0394743 | ||||||||
\(329\) | 111855.i | 1.03339i | ||||||||
\(330\) | 49497.1 | 0.454518 | ||||||||
\(331\) | 114900. | 1.04873 | 0.524366 | − | 0.851493i | \(-0.324302\pi\) | ||||
0.524366 | + | 0.851493i | \(0.324302\pi\) | |||||||
\(332\) | 28586.3i | 0.259347i | ||||||||
\(333\) | 2181.37i | 0.0196716i | ||||||||
\(334\) | 18741.1 | 0.167997 | ||||||||
\(335\) | −136477. | −1.21610 | ||||||||
\(336\) | 19612.4i | 0.173721i | ||||||||
\(337\) | − | 93546.8i | − | 0.823701i | −0.911252 | − | 0.411850i | \(-0.864883\pi\) | ||
0.911252 | − | 0.411850i | \(-0.135117\pi\) | |||||||
\(338\) | 154603. | 1.35327 | ||||||||
\(339\) | − | 64952.5i | − | 0.565192i | ||||||
\(340\) | −49767.0 | −0.430511 | ||||||||
\(341\) | 139606.i | 1.20059i | ||||||||
\(342\) | 9032.60i | 0.0772255i | ||||||||
\(343\) | − | 78079.1i | − | 0.663661i | ||||||
\(344\) | 7501.22i | 0.0633892i | ||||||||
\(345\) | 37789.9 | + | 39822.1i | 0.317496 | + | 0.334569i | ||||
\(346\) | 78364.5 | 0.654587 | ||||||||
\(347\) | −30832.5 | −0.256064 | −0.128032 | − | 0.991770i | \(-0.540866\pi\) | ||||
−0.128032 | + | 0.991770i | \(0.540866\pi\) | |||||||
\(348\) | −41221.6 | −0.340382 | ||||||||
\(349\) | 33514.4 | 0.275157 | 0.137578 | − | 0.990491i | \(-0.456068\pi\) | ||||
0.137578 | + | 0.990491i | \(0.456068\pi\) | |||||||
\(350\) | − | 37717.1i | − | 0.307895i | ||||||
\(351\) | −40472.8 | −0.328510 | ||||||||
\(352\) | 30524.7i | 0.246358i | ||||||||
\(353\) | 111286. | 0.893082 | 0.446541 | − | 0.894763i | \(-0.352656\pi\) | ||||
0.446541 | + | 0.894763i | \(0.352656\pi\) | |||||||
\(354\) | 72917.2 | 0.581867 | ||||||||
\(355\) | 38176.1i | 0.302925i | ||||||||
\(356\) | 29130.4i | 0.229851i | ||||||||
\(357\) | −95450.3 | −0.748929 | ||||||||
\(358\) | −64929.4 | −0.506611 | ||||||||
\(359\) | − | 90598.3i | − | 0.702961i | −0.936195 | − | 0.351480i | \(-0.885678\pi\) | ||
0.936195 | − | 0.351480i | \(-0.114322\pi\) | |||||||
\(360\) | 12201.8i | 0.0941497i | ||||||||
\(361\) | 116331. | 0.892652 | ||||||||
\(362\) | 53792.7i | 0.410494i | ||||||||
\(363\) | 71676.1 | 0.543952 | ||||||||
\(364\) | − | 136106.i | − | 1.02725i | ||||||
\(365\) | − | 131951.i | − | 0.990436i | ||||||
\(366\) | 81794.1i | 0.610604i | ||||||||
\(367\) | − | 120673.i | − | 0.895936i | −0.894049 | − | 0.447968i | \(-0.852148\pi\) | ||
0.894049 | − | 0.447968i | \(-0.147852\pi\) | |||||||
\(368\) | −24558.2 | + | 23305.0i | −0.181343 | + | 0.172089i | ||||
\(369\) | 5067.46 | 0.0372167 | ||||||||
\(370\) | −4563.89 | −0.0333374 | ||||||||
\(371\) | −247155. | −1.79565 | ||||||||
\(372\) | −34415.1 | −0.248693 | ||||||||
\(373\) | − | 67722.9i | − | 0.486763i | −0.969931 | − | 0.243382i | \(-0.921743\pi\) | ||
0.969931 | − | 0.243382i | \(-0.0782567\pi\) | |||||||
\(374\) | −148559. | −1.06208 | ||||||||
\(375\) | − | 88327.1i | − | 0.628104i | ||||||
\(376\) | −42916.4 | −0.303562 | ||||||||
\(377\) | 286069. | 2.01274 | ||||||||
\(378\) | 23402.4i | 0.163786i | ||||||||
\(379\) | 82059.4i | 0.571281i | 0.958337 | + | 0.285641i | \(0.0922064\pi\) | ||||
−0.958337 | + | 0.285641i | \(0.907794\pi\) | |||||||
\(380\) | −18898.2 | −0.130874 | ||||||||
\(381\) | 136466. | 0.940101 | ||||||||
\(382\) | − | 200502.i | − | 1.37402i | ||||||
\(383\) | 137181.i | 0.935181i | 0.883945 | + | 0.467590i | \(0.154878\pi\) | ||||
−0.883945 | + | 0.467590i | \(0.845122\pi\) | |||||||
\(384\) | −7524.83 | −0.0510310 | ||||||||
\(385\) | 198619.i | 1.33999i | ||||||||
\(386\) | 66022.3 | 0.443114 | ||||||||
\(387\) | 8950.78i | 0.0597639i | ||||||||
\(388\) | 76079.4i | 0.505363i | ||||||||
\(389\) | 8522.96i | 0.0563237i | 0.999603 | + | 0.0281619i | \(0.00896538\pi\) | ||||
−0.999603 | + | 0.0281619i | \(0.991035\pi\) | |||||||
\(390\) | − | 84677.9i | − | 0.556725i | ||||||
\(391\) | −113421. | − | 119521.i | −0.741893 | − | 0.781790i | ||||
\(392\) | −24371.3 | −0.158601 | ||||||||
\(393\) | −98515.7 | −0.637853 | ||||||||
\(394\) | −144618. | −0.931603 | ||||||||
\(395\) | 226558. | 1.45206 | ||||||||
\(396\) | 36423.4i | 0.232269i | ||||||||
\(397\) | −187463. | −1.18942 | −0.594708 | − | 0.803942i | \(-0.702732\pi\) | ||||
−0.594708 | + | 0.803942i | \(0.702732\pi\) | |||||||
\(398\) | 194075.i | 1.22519i | ||||||||
\(399\) | −36245.6 | −0.227672 | ||||||||
\(400\) | 14471.2 | 0.0904449 | ||||||||
\(401\) | − | 113907.i | − | 0.708374i | −0.935175 | − | 0.354187i | \(-0.884758\pi\) | ||
0.935175 | − | 0.354187i | \(-0.115242\pi\) | |||||||
\(402\) | − | 100429.i | − | 0.621454i | ||||||
\(403\) | 238833. | 1.47057 | ||||||||
\(404\) | 63158.7 | 0.386964 | ||||||||
\(405\) | 14559.7i | 0.0887652i | ||||||||
\(406\) | − | 165412.i | − | 1.00349i | ||||||
\(407\) | −13623.6 | −0.0822438 | ||||||||
\(408\) | − | 36622.1i | − | 0.220000i | ||||||
\(409\) | −260370. | −1.55649 | −0.778243 | − | 0.627964i | \(-0.783889\pi\) | ||||
−0.778243 | + | 0.627964i | \(0.783889\pi\) | |||||||
\(410\) | 10602.2i | 0.0630710i | ||||||||
\(411\) | − | 53068.1i | − | 0.314159i | ||||||
\(412\) | − | 73918.6i | − | 0.435471i | ||||||
\(413\) | 292598.i | 1.71543i | ||||||||
\(414\) | −29303.9 | + | 27808.5i | −0.170972 | + | 0.162247i | ||||
\(415\) | −71366.2 | −0.414378 | ||||||||
\(416\) | 52220.7 | 0.301756 | ||||||||
\(417\) | −102286. | −0.588227 | ||||||||
\(418\) | −56412.6 | −0.322867 | ||||||||
\(419\) | 93509.6i | 0.532633i | 0.963886 | + | 0.266317i | \(0.0858067\pi\) | ||||
−0.963886 | + | 0.266317i | \(0.914193\pi\) | |||||||
\(420\) | −48962.8 | −0.277567 | ||||||||
\(421\) | 41315.4i | 0.233103i | 0.993185 | + | 0.116552i | \(0.0371840\pi\) | ||||
−0.993185 | + | 0.116552i | \(0.962816\pi\) | |||||||
\(422\) | −168261. | −0.944841 | ||||||||
\(423\) | −51209.7 | −0.286201 | ||||||||
\(424\) | − | 94827.8i | − | 0.527478i | ||||||
\(425\) | 70428.8i | 0.389917i | ||||||||
\(426\) | −28092.6 | −0.154801 | ||||||||
\(427\) | −328219. | −1.80015 | ||||||||
\(428\) | − | 147147.i | − | 0.803276i | ||||||
\(429\) | − | 252771.i | − | 1.37345i | ||||||
\(430\) | −18727.0 | −0.101282 | ||||||||
\(431\) | 106474.i | 0.573178i | 0.958054 | + | 0.286589i | \(0.0925215\pi\) | ||||
−0.958054 | + | 0.286589i | \(0.907479\pi\) | |||||||
\(432\) | −8978.95 | −0.0481125 | ||||||||
\(433\) | 147335.i | 0.785832i | 0.919574 | + | 0.392916i | \(0.128534\pi\) | ||||
−0.919574 | + | 0.392916i | \(0.871466\pi\) | |||||||
\(434\) | − | 138099.i | − | 0.733181i | ||||||
\(435\) | − | 102911.i | − | 0.543853i | ||||||
\(436\) | 12616.4i | 0.0663687i | ||||||||
\(437\) | −43069.8 | − | 45386.0i | −0.225533 | − | 0.237661i | ||||
\(438\) | 97098.7 | 0.506134 | ||||||||
\(439\) | 277220. | 1.43845 | 0.719227 | − | 0.694775i | \(-0.244496\pi\) | ||||
0.719227 | + | 0.694775i | \(0.244496\pi\) | |||||||
\(440\) | −76205.7 | −0.393624 | ||||||||
\(441\) | −29080.8 | −0.149530 | ||||||||
\(442\) | 254149.i | 1.30090i | ||||||||
\(443\) | 17965.1 | 0.0915425 | 0.0457712 | − | 0.998952i | \(-0.485425\pi\) | ||||
0.0457712 | + | 0.998952i | \(0.485425\pi\) | |||||||
\(444\) | − | 3358.43i | − | 0.0170361i | ||||||
\(445\) | −72724.8 | −0.367251 | ||||||||
\(446\) | 168945. | 0.849327 | ||||||||
\(447\) | 97924.7i | 0.490092i | ||||||||
\(448\) | − | 30195.3i | − | 0.150447i | ||||||
\(449\) | 186125. | 0.923235 | 0.461617 | − | 0.887079i | \(-0.347269\pi\) | ||||
0.461617 | + | 0.887079i | \(0.347269\pi\) | |||||||
\(450\) | 17267.6 | 0.0852723 | ||||||||
\(451\) | 31648.6i | 0.155597i | ||||||||
\(452\) | 100001.i | 0.489471i | ||||||||
\(453\) | 32962.1 | 0.160627 | ||||||||
\(454\) | − | 102293.i | − | 0.496290i | ||||||
\(455\) | 339791. | 1.64131 | ||||||||
\(456\) | − | 13906.6i | − | 0.0668793i | ||||||
\(457\) | − | 356339.i | − | 1.70621i | −0.521743 | − | 0.853103i | \(-0.674718\pi\) | ||
0.521743 | − | 0.853103i | \(-0.325282\pi\) | |||||||
\(458\) | − | 128771.i | − | 0.613886i | ||||||
\(459\) | − | 43699.1i | − | 0.207418i | ||||||
\(460\) | −58181.4 | − | 61310.2i | −0.274959 | − | 0.289746i | ||||
\(461\) | −107546. | −0.506046 | −0.253023 | − | 0.967460i | \(-0.581425\pi\) | ||||
−0.253023 | + | 0.967460i | \(0.581425\pi\) | |||||||
\(462\) | −146158. | −0.684761 | ||||||||
\(463\) | 71300.2 | 0.332605 | 0.166303 | − | 0.986075i | \(-0.446817\pi\) | ||||
0.166303 | + | 0.986075i | \(0.446817\pi\) | |||||||
\(464\) | 63464.8 | 0.294779 | ||||||||
\(465\) | − | 85918.0i | − | 0.397354i | ||||||
\(466\) | −98778.9 | −0.454875 | ||||||||
\(467\) | − | 297142.i | − | 1.36248i | −0.732059 | − | 0.681241i | \(-0.761441\pi\) | ||
0.732059 | − | 0.681241i | \(-0.238559\pi\) | |||||||
\(468\) | 62312.0 | 0.284498 | ||||||||
\(469\) | 402998. | 1.83214 | ||||||||
\(470\) | − | 107142.i | − | 0.485024i | ||||||
\(471\) | 137384.i | 0.619291i | ||||||||
\(472\) | −112263. | −0.503911 | ||||||||
\(473\) | −55901.6 | −0.249863 | ||||||||
\(474\) | 166717.i | 0.742034i | ||||||||
\(475\) | 26744.1i | 0.118534i | ||||||||
\(476\) | 146955. | 0.648592 | ||||||||
\(477\) | − | 113153.i | − | 0.497311i | ||||||
\(478\) | −248047. | −1.08562 | ||||||||
\(479\) | 9251.37i | 0.0403213i | 0.999797 | + | 0.0201607i | \(0.00641778\pi\) | ||||
−0.999797 | + | 0.0201607i | \(0.993582\pi\) | |||||||
\(480\) | − | 18785.9i | − | 0.0815361i | ||||||
\(481\) | 23306.8i | 0.100738i | ||||||||
\(482\) | 220799.i | 0.950391i | ||||||||
\(483\) | −111589. | − | 117589.i | −0.478327 | − | 0.504050i | ||||
\(484\) | −110353. | −0.471077 | ||||||||
\(485\) | −189934. | −0.807456 | ||||||||
\(486\) | −10714.1 | −0.0453609 | ||||||||
\(487\) | 404796. | 1.70678 | 0.853391 | − | 0.521271i | \(-0.174542\pi\) | ||||
0.853391 | + | 0.521271i | \(0.174542\pi\) | |||||||
\(488\) | − | 125930.i | − | 0.528799i | ||||||
\(489\) | −58960.1 | −0.246570 | ||||||||
\(490\) | − | 60843.4i | − | 0.253409i | ||||||
\(491\) | −156227. | −0.648029 | −0.324014 | − | 0.946052i | \(-0.605033\pi\) | ||||
−0.324014 | + | 0.946052i | \(0.605033\pi\) | |||||||
\(492\) | −7801.87 | −0.0322306 | ||||||||
\(493\) | 308873.i | 1.27082i | ||||||||
\(494\) | 96508.8i | 0.395470i | ||||||||
\(495\) | −90931.9 | −0.371113 | ||||||||
\(496\) | 52985.5 | 0.215374 | ||||||||
\(497\) | − | 112729.i | − | 0.456375i | ||||||
\(498\) | − | 52516.3i | − | 0.211756i | ||||||
\(499\) | −272853. | −1.09579 | −0.547896 | − | 0.836547i | \(-0.684571\pi\) | ||||
−0.547896 | + | 0.836547i | \(0.684571\pi\) | |||||||
\(500\) | 135988.i | 0.543954i | ||||||||
\(501\) | −34429.6 | −0.137169 | ||||||||
\(502\) | − | 145776.i | − | 0.578466i | ||||||
\(503\) | 25089.1i | 0.0991631i | 0.998770 | + | 0.0495815i | \(0.0157888\pi\) | ||||
−0.998770 | + | 0.0495815i | \(0.984211\pi\) | |||||||
\(504\) | − | 36030.3i | − | 0.141843i | ||||||
\(505\) | 157677.i | 0.618281i | ||||||||
\(506\) | −173676. | − | 183016.i | −0.678328 | − | 0.714806i | ||||
\(507\) | −284024. | −1.10494 | ||||||||
\(508\) | −210103. | −0.814152 | ||||||||
\(509\) | −208154. | −0.803432 | −0.401716 | − | 0.915764i | \(-0.631586\pi\) | ||||
−0.401716 | + | 0.915764i | \(0.631586\pi\) | |||||||
\(510\) | 91427.9 | 0.351510 | ||||||||
\(511\) | 389633.i | 1.49216i | ||||||||
\(512\) | 11585.2 | 0.0441942 | ||||||||
\(513\) | − | 16594.0i | − | 0.0630544i | ||||||
\(514\) | −126103. | −0.477309 | ||||||||
\(515\) | 184539. | 0.695784 | ||||||||
\(516\) | − | 13780.6i | − | 0.0517570i | ||||||
\(517\) | − | 319827.i | − | 1.19656i | ||||||
\(518\) | 13476.6 | 0.0502249 | ||||||||
\(519\) | −143965. | −0.534468 | ||||||||
\(520\) | 130370.i | 0.482138i | ||||||||
\(521\) | 318213.i | 1.17231i | 0.810200 | + | 0.586154i | \(0.199359\pi\) | ||||
−0.810200 | + | 0.586154i | \(0.800641\pi\) | |||||||
\(522\) | 75728.9 | 0.277921 | ||||||||
\(523\) | 266854.i | 0.975596i | 0.872957 | + | 0.487798i | \(0.162200\pi\) | ||||
−0.872957 | + | 0.487798i | \(0.837800\pi\) | |||||||
\(524\) | 151675. | 0.552397 | ||||||||
\(525\) | 69290.7i | 0.251395i | ||||||||
\(526\) | − | 283947.i | − | 1.02628i | ||||||
\(527\) | 257871.i | 0.928500i | ||||||||
\(528\) | − | 56077.5i | − | 0.201151i | ||||||
\(529\) | 14644.8 | − | 279458.i | 0.0523326 | − | 0.998630i | ||||
\(530\) | 236740. | 0.842790 | ||||||||
\(531\) | −133957. | −0.475092 | ||||||||
\(532\) | 55803.7 | 0.197170 | ||||||||
\(533\) | 54143.3 | 0.190586 | ||||||||
\(534\) | − | 53516.0i | − | 0.187673i | ||||||
\(535\) | 367356. | 1.28345 | ||||||||
\(536\) | 154621.i | 0.538195i | ||||||||
\(537\) | 119283. | 0.413647 | ||||||||
\(538\) | 253988. | 0.877502 | ||||||||
\(539\) | − | 181623.i | − | 0.625162i | ||||||
\(540\) | − | 22416.1i | − | 0.0768729i | ||||||
\(541\) | 385497. | 1.31712 | 0.658562 | − | 0.752526i | \(-0.271165\pi\) | ||||
0.658562 | + | 0.752526i | \(0.271165\pi\) | |||||||
\(542\) | −28132.3 | −0.0957650 | ||||||||
\(543\) | − | 98823.6i | − | 0.335167i | ||||||
\(544\) | 56383.4i | 0.190526i | ||||||||
\(545\) | −31497.2 | −0.106042 | ||||||||
\(546\) | 250042.i | 0.838742i | ||||||||
\(547\) | 366081. | 1.22350 | 0.611748 | − | 0.791053i | \(-0.290467\pi\) | ||||
0.611748 | + | 0.791053i | \(0.290467\pi\) | |||||||
\(548\) | 81703.7i | 0.272070i | ||||||||
\(549\) | − | 150265.i | − | 0.498556i | ||||||
\(550\) | 107844.i | 0.356509i | ||||||||
\(551\) | 117289.i | 0.386326i | ||||||||
\(552\) | 45116.4 | − | 42814.0i | 0.148066 | − | 0.140510i | ||||
\(553\) | −668995. | −2.18762 | ||||||||
\(554\) | −389607. | −1.26943 | ||||||||
\(555\) | 8384.40 | 0.0272199 | ||||||||
\(556\) | 157480. | 0.509420 | ||||||||
\(557\) | 28811.7i | 0.0928665i | 0.998921 | + | 0.0464333i | \(0.0147855\pi\) | ||||
−0.998921 | + | 0.0464333i | \(0.985215\pi\) | |||||||
\(558\) | 63224.5 | 0.203057 | ||||||||
\(559\) | 95634.5i | 0.306049i | ||||||||
\(560\) | 75383.2 | 0.240380 | ||||||||
\(561\) | 272920. | 0.867181 | ||||||||
\(562\) | − | 409195.i | − | 1.29556i | ||||||
\(563\) | − | 137155.i | − | 0.432708i | −0.976315 | − | 0.216354i | \(-0.930583\pi\) | ||
0.976315 | − | 0.216354i | \(-0.0694166\pi\) | |||||||
\(564\) | 78842.4 | 0.247857 | ||||||||
\(565\) | −249654. | −0.782064 | ||||||||
\(566\) | − | 32154.9i | − | 0.100372i | ||||||
\(567\) | − | 42992.9i | − | 0.133730i | ||||||
\(568\) | 43251.5 | 0.134062 | ||||||||
\(569\) | − | 451318.i | − | 1.39399i | −0.717078 | − | 0.696993i | \(-0.754521\pi\) | ||
0.717078 | − | 0.696993i | \(-0.245479\pi\) | |||||||
\(570\) | 34718.1 | 0.106858 | ||||||||
\(571\) | − | 143304.i | − | 0.439528i | −0.975553 | − | 0.219764i | \(-0.929471\pi\) | ||
0.975553 | − | 0.219764i | \(-0.0705287\pi\) | |||||||
\(572\) | 389166.i | 1.18944i | ||||||||
\(573\) | 368346.i | 1.12188i | ||||||||
\(574\) | − | 31307.0i | − | 0.0950205i | ||||||
\(575\) | −86764.4 | + | 82336.6i | −0.262425 | + | 0.249033i | ||||
\(576\) | 13824.0 | 0.0416667 | ||||||||
\(577\) | −467347. | −1.40374 | −0.701871 | − | 0.712304i | \(-0.747652\pi\) | ||||
−0.701871 | + | 0.712304i | \(0.747652\pi\) | |||||||
\(578\) | −38175.6 | −0.114269 | ||||||||
\(579\) | −121291. | −0.361801 | ||||||||
\(580\) | 158441.i | 0.470991i | ||||||||
\(581\) | 210735. | 0.624287 | ||||||||
\(582\) | − | 139767.i | − | 0.412627i | ||||||
\(583\) | 706688. | 2.07917 | ||||||||
\(584\) | −149493. | −0.438325 | ||||||||
\(585\) | 155563.i | 0.454564i | ||||||||
\(586\) | − | 47792.0i | − | 0.139175i | ||||||
\(587\) | 13978.2 | 0.0405672 | 0.0202836 | − | 0.999794i | \(-0.493543\pi\) | ||||
0.0202836 | + | 0.999794i | \(0.493543\pi\) | |||||||
\(588\) | 44772.9 | 0.129497 | ||||||||
\(589\) | 97922.2i | 0.282261i | ||||||||
\(590\) | − | 280268.i | − | 0.805136i | ||||||
\(591\) | 265681. | 0.760651 | ||||||||
\(592\) | 5170.65i | 0.0147537i | ||||||||
\(593\) | 485533. | 1.38073 | 0.690365 | − | 0.723461i | \(-0.257450\pi\) | ||||
0.690365 | + | 0.723461i | \(0.257450\pi\) | |||||||
\(594\) | − | 66914.1i | − | 0.189647i | ||||||
\(595\) | 366877.i | 1.03630i | ||||||||
\(596\) | − | 150765.i | − | 0.424432i | ||||||
\(597\) | − | 356539.i | − | 1.00037i | ||||||
\(598\) | −313098. | + | 297120.i | −0.875543 | + | 0.830862i | ||||
\(599\) | −473979. | −1.32101 | −0.660503 | − | 0.750823i | \(-0.729657\pi\) | ||||
−0.660503 | + | 0.750823i | \(0.729657\pi\) | |||||||
\(600\) | −26585.3 | −0.0738480 | ||||||||
\(601\) | 275818. | 0.763615 | 0.381807 | − | 0.924242i | \(-0.375302\pi\) | ||||
0.381807 | + | 0.924242i | \(0.375302\pi\) | |||||||
\(602\) | 55298.2 | 0.152587 | ||||||||
\(603\) | 184501.i | 0.507415i | ||||||||
\(604\) | −50748.4 | −0.139107 | ||||||||
\(605\) | − | 275497.i | − | 0.752674i | ||||||
\(606\) | −116030. | −0.315955 | ||||||||
\(607\) | 351708. | 0.954564 | 0.477282 | − | 0.878750i | \(-0.341622\pi\) | ||||
0.477282 | + | 0.878750i | \(0.341622\pi\) | |||||||
\(608\) | 21410.6i | 0.0579191i | ||||||||
\(609\) | 303881.i | 0.819350i | ||||||||
\(610\) | 314387. | 0.844900 | ||||||||
\(611\) | −547149. | −1.46563 | ||||||||
\(612\) | 67279.1i | 0.179629i | ||||||||
\(613\) | − | 178842.i | − | 0.475935i | −0.971273 | − | 0.237968i | \(-0.923519\pi\) | ||
0.971273 | − | 0.237968i | \(-0.0764812\pi\) | |||||||
\(614\) | −174431. | −0.462687 | ||||||||
\(615\) | − | 19477.5i | − | 0.0514972i | ||||||
\(616\) | 225025. | 0.593021 | ||||||||
\(617\) | 223536.i | 0.587189i | 0.955930 | + | 0.293594i | \(0.0948515\pi\) | ||||
−0.955930 | + | 0.293594i | \(0.905148\pi\) | |||||||
\(618\) | 135797.i | 0.355561i | ||||||||
\(619\) | 332661.i | 0.868200i | 0.900865 | + | 0.434100i | \(0.142934\pi\) | ||||
−0.900865 | + | 0.434100i | \(0.857066\pi\) | |||||||
\(620\) | 132279.i | 0.344119i | ||||||||
\(621\) | 53834.8 | − | 51087.5i | 0.139598 | − | 0.132474i | ||||
\(622\) | 267707. | 0.691956 | ||||||||
\(623\) | 214747. | 0.553287 | ||||||||
\(624\) | −95935.6 | −0.246383 | ||||||||
\(625\) | −198178. | −0.507336 | ||||||||
\(626\) | 181908.i | 0.464197i | ||||||||
\(627\) | 103637. | 0.263620 | ||||||||
\(628\) | − | 211517.i | − | 0.536321i | ||||||
\(629\) | −25164.7 | −0.0636048 | ||||||||
\(630\) | 89950.4 | 0.226632 | ||||||||
\(631\) | 664444.i | 1.66878i | 0.551173 | + | 0.834391i | \(0.314180\pi\) | ||||
−0.551173 | + | 0.834391i | \(0.685820\pi\) | |||||||
\(632\) | − | 256678.i | − | 0.642620i | ||||||
\(633\) | 309115. | 0.771459 | ||||||||
\(634\) | −116415. | −0.289621 | ||||||||
\(635\) | − | 524527.i | − | 1.30083i | ||||||
\(636\) | 174210.i | 0.430684i | ||||||||
\(637\) | −310714. | −0.765741 | ||||||||
\(638\) | 472961.i | 1.16194i | ||||||||
\(639\) | 51609.5 | 0.126394 | ||||||||
\(640\) | 28922.8i | 0.0706123i | ||||||||
\(641\) | 338234.i | 0.823191i | 0.911367 | + | 0.411596i | \(0.135028\pi\) | ||||
−0.911367 | + | 0.411596i | \(0.864972\pi\) | |||||||
\(642\) | 270327.i | 0.655872i | ||||||||
\(643\) | − | 262721.i | − | 0.635438i | −0.948185 | − | 0.317719i | \(-0.897083\pi\) | ||
0.948185 | − | 0.317719i | \(-0.102917\pi\) | |||||||
\(644\) | 171802. | + | 181041.i | 0.414244 | + | 0.436520i | ||||
\(645\) | 34403.6 | 0.0826960 | ||||||||
\(646\) | −104202. | −0.249695 | ||||||||
\(647\) | 348233. | 0.831881 | 0.415941 | − | 0.909392i | \(-0.363452\pi\) | ||||
0.415941 | + | 0.909392i | \(0.363452\pi\) | |||||||
\(648\) | 16495.4 | 0.0392837 | ||||||||
\(649\) | − | 836624.i | − | 1.98628i | ||||||
\(650\) | 184496. | 0.436677 | ||||||||
\(651\) | 253704.i | 0.598640i | ||||||||
\(652\) | 90775.1 | 0.213536 | ||||||||
\(653\) | −592841. | −1.39031 | −0.695155 | − | 0.718859i | \(-0.744664\pi\) | ||||
−0.695155 | + | 0.718859i | \(0.744664\pi\) | |||||||
\(654\) | − | 23177.9i | − | 0.0541898i | ||||||
\(655\) | 378659.i | 0.882605i | ||||||||
\(656\) | 12011.8 | 0.0279125 | ||||||||
\(657\) | −178382. | −0.413257 | ||||||||
\(658\) | 316375.i | 0.730719i | ||||||||
\(659\) | 377415.i | 0.869058i | 0.900658 | + | 0.434529i | \(0.143085\pi\) | ||||
−0.900658 | + | 0.434529i | \(0.856915\pi\) | |||||||
\(660\) | 139999. | 0.321393 | ||||||||
\(661\) | − | 547932.i | − | 1.25408i | −0.778988 | − | 0.627038i | \(-0.784267\pi\) | ||
0.778988 | − | 0.627038i | \(-0.215733\pi\) | |||||||
\(662\) | 324986. | 0.741565 | ||||||||
\(663\) | − | 466902.i | − | 1.06218i | ||||||
\(664\) | 80854.2i | 0.183386i | ||||||||
\(665\) | 139315.i | 0.315032i | ||||||||
\(666\) | 6169.84i | 0.0139099i | ||||||||
\(667\) | −380514. | + | 361095.i | −0.855300 | + | 0.811652i | ||||
\(668\) | 53007.8 | 0.118792 | ||||||||
\(669\) | −310371. | −0.693473 | ||||||||
\(670\) | −386015. | −0.859914 | ||||||||
\(671\) | 938473. | 2.08438 | ||||||||
\(672\) | 55472.3i | 0.122839i | ||||||||
\(673\) | −776783. | −1.71502 | −0.857511 | − | 0.514466i | \(-0.827990\pi\) | ||||
−0.857511 | + | 0.514466i | \(0.827990\pi\) | |||||||
\(674\) | − | 264590.i | − | 0.582444i | ||||||
\(675\) | −31722.7 | −0.0696245 | ||||||||
\(676\) | 437284. | 0.956908 | ||||||||
\(677\) | − | 377606.i | − | 0.823876i | −0.911212 | − | 0.411938i | \(-0.864852\pi\) | ||
0.911212 | − | 0.411938i | \(-0.135148\pi\) | |||||||
\(678\) | − | 183713.i | − | 0.399651i | ||||||
\(679\) | 560849. | 1.21648 | ||||||||
\(680\) | −140762. | −0.304417 | ||||||||
\(681\) | 187925.i | 0.405219i | ||||||||
\(682\) | 394865.i | 0.848946i | ||||||||
\(683\) | −67277.0 | −0.144220 | −0.0721099 | − | 0.997397i | \(-0.522973\pi\) | ||||
−0.0721099 | + | 0.997397i | \(0.522973\pi\) | |||||||
\(684\) | 25548.1i | 0.0546067i | ||||||||
\(685\) | −203975. | −0.434706 | ||||||||
\(686\) | − | 220841.i | − | 0.469279i | ||||||
\(687\) | 236568.i | 0.501235i | ||||||||
\(688\) | 21216.7i | 0.0448229i | ||||||||
\(689\) | − | 1.20898e6i | − | 2.54671i | ||||||
\(690\) | 106886. | + | 112634.i | 0.224503 | + | 0.236576i | ||||
\(691\) | 540961. | 1.13295 | 0.566474 | − | 0.824080i | \(-0.308307\pi\) | ||||
0.566474 | + | 0.824080i | \(0.308307\pi\) | |||||||
\(692\) | 221648. | 0.462863 | ||||||||
\(693\) | 268510. | 0.559105 | ||||||||
\(694\) | −87207.4 | −0.181065 | ||||||||
\(695\) | 393152.i | 0.813938i | ||||||||
\(696\) | −116592. | −0.240686 | ||||||||
\(697\) | 58459.3i | 0.120334i | ||||||||
\(698\) | 94792.9 | 0.194565 | ||||||||
\(699\) | 181468. | 0.371404 | ||||||||
\(700\) | − | 106680.i | − | 0.217714i | ||||||
\(701\) | − | 356596.i | − | 0.725671i | −0.931853 | − | 0.362836i | \(-0.881809\pi\) | ||
0.931853 | − | 0.362836i | \(-0.118191\pi\) | |||||||
\(702\) | −114474. | −0.232292 | ||||||||
\(703\) | −9555.85 | −0.0193356 | ||||||||
\(704\) | 86337.0i | 0.174201i | ||||||||
\(705\) | 196832.i | 0.396020i | ||||||||
\(706\) | 314764. | 0.631504 | ||||||||
\(707\) | − | 465600.i | − | 0.931480i | ||||||
\(708\) | 206241. | 0.411442 | ||||||||
\(709\) | 608246.i | 1.21000i | 0.796224 | + | 0.605002i | \(0.206828\pi\) | ||||
−0.796224 | + | 0.605002i | \(0.793172\pi\) | |||||||
\(710\) | 107978.i | 0.214200i | ||||||||
\(711\) | − | 306279.i | − | 0.605868i | ||||||
\(712\) | 82393.3i | 0.162529i | ||||||||
\(713\) | −317683. | + | 301471.i | −0.624906 | + | 0.593016i | ||||
\(714\) | −269974. | −0.529573 | ||||||||
\(715\) | −971561. | −1.90046 | ||||||||
\(716\) | −183648. | −0.358228 | ||||||||
\(717\) | 455691. | 0.886405 | ||||||||
\(718\) | − | 256251.i | − | 0.497068i | ||||||
\(719\) | −770910. | −1.49123 | −0.745617 | − | 0.666374i | \(-0.767845\pi\) | ||||
−0.745617 | + | 0.666374i | \(0.767845\pi\) | |||||||
\(720\) | 34511.9i | 0.0665739i | ||||||||
\(721\) | −544920. | −1.04824 | ||||||||
\(722\) | 329035. | 0.631200 | ||||||||
\(723\) | − | 405633.i | − | 0.775991i | ||||||
\(724\) | 152149.i | 0.290263i | ||||||||
\(725\) | 224222. | 0.426581 | ||||||||
\(726\) | 202731. | 0.384632 | ||||||||
\(727\) | − | 53283.8i | − | 0.100815i | −0.998729 | − | 0.0504076i | \(-0.983948\pi\) | ||
0.998729 | − | 0.0504076i | \(-0.0160520\pi\) | |||||||
\(728\) | − | 384966.i | − | 0.726372i | ||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | − | 373213.i | − | 0.700344i | ||||||
\(731\) | −103258. | −0.193236 | ||||||||
\(732\) | 231349.i | 0.431762i | ||||||||
\(733\) | − | 865807.i | − | 1.61144i | −0.592299 | − | 0.805718i | \(-0.701780\pi\) | ||
0.592299 | − | 0.805718i | \(-0.298220\pi\) | |||||||
\(734\) | − | 341314.i | − | 0.633523i | ||||||
\(735\) | 111776.i | 0.206907i | ||||||||
\(736\) | −69461.2 | + | 65916.4i | −0.128229 | + | 0.121685i | ||||
\(737\) | −1.15229e6 | −2.12142 | ||||||||
\(738\) | 14333.0 | 0.0263162 | ||||||||
\(739\) | 227470. | 0.416520 | 0.208260 | − | 0.978074i | \(-0.433220\pi\) | ||||
0.208260 | + | 0.978074i | \(0.433220\pi\) | |||||||
\(740\) | −12908.6 | −0.0235731 | ||||||||
\(741\) | − | 177298.i | − | 0.322900i | ||||||
\(742\) | −699060. | −1.26972 | ||||||||
\(743\) | − | 101640.i | − | 0.184114i | −0.995754 | − | 0.0920568i | \(-0.970656\pi\) | ||
0.995754 | − | 0.0920568i | \(-0.0293441\pi\) | |||||||
\(744\) | −97340.5 | −0.175852 | ||||||||
\(745\) | 376388. | 0.678146 | ||||||||
\(746\) | − | 191549.i | − | 0.344194i | ||||||
\(747\) | 96478.7i | 0.172898i | ||||||||
\(748\) | −420188. | −0.751001 | ||||||||
\(749\) | −1.08475e6 | −1.93360 | ||||||||
\(750\) | − | 249827.i | − | 0.444137i | ||||||
\(751\) | − | 699200.i | − | 1.23971i | −0.784715 | − | 0.619857i | \(-0.787191\pi\) | ||
0.784715 | − | 0.619857i | \(-0.212809\pi\) | |||||||
\(752\) | −121386. | −0.214651 | ||||||||
\(753\) | 267807.i | 0.472316i | ||||||||
\(754\) | 809126. | 1.42322 | ||||||||
\(755\) | − | 126695.i | − | 0.222261i | ||||||
\(756\) | 66191.9i | 0.115814i | ||||||||
\(757\) | − | 420292.i | − | 0.733430i | −0.930333 | − | 0.366715i | \(-0.880482\pi\) | ||
0.930333 | − | 0.366715i | \(-0.119518\pi\) | |||||||
\(758\) | 232099.i | 0.403957i | ||||||||
\(759\) | 319064. | + | 336222.i | 0.553852 | + | 0.583637i | ||||
\(760\) | −53452.1 | −0.0925417 | ||||||||
\(761\) | −557730. | −0.963063 | −0.481531 | − | 0.876429i | \(-0.659919\pi\) | ||||
−0.481531 | + | 0.876429i | \(0.659919\pi\) | |||||||
\(762\) | 385984. | 0.664752 | ||||||||
\(763\) | 93007.0 | 0.159759 | ||||||||
\(764\) | − | 567105.i | − | 0.971576i | ||||||
\(765\) | −167964. | −0.287007 | ||||||||
\(766\) | 388006.i | 0.661273i | ||||||||
\(767\) | −1.43127e6 | −2.43293 | ||||||||
\(768\) | −21283.4 | −0.0360844 | ||||||||
\(769\) | − | 521694.i | − | 0.882192i | −0.897460 | − | 0.441096i | \(-0.854590\pi\) | ||
0.897460 | − | 0.441096i | \(-0.145410\pi\) | |||||||
\(770\) | 561780.i | 0.947513i | ||||||||
\(771\) | 231666. | 0.389721 | ||||||||
\(772\) | 186739. | 0.313329 | ||||||||
\(773\) | 769723.i | 1.28818i | 0.764951 | + | 0.644089i | \(0.222763\pi\) | ||||
−0.764951 | + | 0.644089i | \(0.777237\pi\) | |||||||
\(774\) | 25316.6i | 0.0422594i | ||||||||
\(775\) | 187198. | 0.311672 | ||||||||
\(776\) | 215185.i | 0.357346i | ||||||||
\(777\) | −24758.0 | −0.0410085 | ||||||||
\(778\) | 24106.6i | 0.0398269i | ||||||||
\(779\) | 22198.9i | 0.0365811i | ||||||||
\(780\) | − | 239505.i | − | 0.393664i | ||||||
\(781\) | 322324.i | 0.528434i | ||||||||
\(782\) | −320804. | − | 338056.i | −0.524598 | − | 0.552809i | ||||
\(783\) | −139123. | −0.226921 | ||||||||
\(784\) | −68932.4 | −0.112148 | ||||||||
\(785\) | 528056. | 0.856920 | ||||||||
\(786\) | −278644. | −0.451030 | ||||||||
\(787\) | 65163.1i | 0.105209i | 0.998615 | + | 0.0526044i | \(0.0167522\pi\) | ||||
−0.998615 | + | 0.0526044i | \(0.983248\pi\) | |||||||
\(788\) | −409042. | −0.658743 | ||||||||
\(789\) | 521643.i | 0.837953i | ||||||||
\(790\) | 640802. | 1.02676 | ||||||||
\(791\) | 737196. | 1.17823 | ||||||||
\(792\) | 103021.i | 0.164239i | ||||||||
\(793\) | − | 1.60551e6i | − | 2.55309i | ||||||
\(794\) | −530225. | −0.841044 | ||||||||
\(795\) | −434919. | −0.688135 | ||||||||
\(796\) | 548928.i | 0.866342i | ||||||||
\(797\) | 322367.i | 0.507498i | 0.967270 | + | 0.253749i | \(0.0816637\pi\) | ||||
−0.967270 | + | 0.253749i | \(0.918336\pi\) | |||||||
\(798\) | −102518. | −0.160988 | ||||||||
\(799\) | − | 590765.i | − | 0.925382i | ||||||
\(800\) | 40930.7 | 0.0639542 | ||||||||
\(801\) | 98315.3i | 0.153234i | ||||||||
\(802\) | − | 322178.i | − | 0.500896i | ||||||
\(803\) | − | 1.11407e6i | − | 1.72776i | ||||||
\(804\) | − | 284057.i | − | 0.439434i | ||||||
\(805\) | −451972. | + | 428907.i | −0.697461 | + | 0.661868i | ||||
\(806\) | 675522. | 1.03985 | ||||||||
\(807\) | −466605. | −0.716477 | ||||||||
\(808\) | 178640. | 0.273625 | ||||||||
\(809\) | 498598. | 0.761822 | 0.380911 | − | 0.924612i | \(-0.375610\pi\) | ||||
0.380911 | + | 0.924612i | \(0.375610\pi\) | |||||||
\(810\) | 41181.1i | 0.0627665i | ||||||||
\(811\) | −572320. | −0.870156 | −0.435078 | − | 0.900393i | \(-0.643279\pi\) | ||||
−0.435078 | + | 0.900393i | \(0.643279\pi\) | |||||||
\(812\) | − | 467856.i | − | 0.709578i | ||||||
\(813\) | 51682.4 | 0.0781918 | ||||||||
\(814\) | −38533.4 | −0.0581552 | ||||||||
\(815\) | 226622.i | 0.341182i | ||||||||
\(816\) | − | 103583.i | − | 0.155564i | ||||||
\(817\) | −39210.4 | −0.0587431 | ||||||||
\(818\) | −736439. | −1.10060 | ||||||||
\(819\) | − | 459357.i | − | 0.684830i | ||||||
\(820\) | 29987.6i | 0.0445979i | ||||||||
\(821\) | 710376. | 1.05391 | 0.526953 | − | 0.849894i | \(-0.323334\pi\) | ||||
0.526953 | + | 0.849894i | \(0.323334\pi\) | |||||||
\(822\) | − | 150099.i | − | 0.222144i | ||||||
\(823\) | −219640. | −0.324273 | −0.162137 | − | 0.986768i | \(-0.551839\pi\) | ||||
−0.162137 | + | 0.986768i | \(0.551839\pi\) | |||||||
\(824\) | − | 209073.i | − | 0.307925i | ||||||
\(825\) | − | 198122.i | − | 0.291089i | ||||||
\(826\) | 827593.i | 1.21299i | ||||||||
\(827\) | − | 771580.i | − | 1.12816i | −0.825721 | − | 0.564079i | \(-0.809231\pi\) | ||
0.825721 | − | 0.564079i | \(-0.190769\pi\) | |||||||
\(828\) | −82884.0 | + | 78654.3i | −0.120896 | + | 0.114726i | ||||
\(829\) | 1.08700e6 | 1.58169 | 0.790844 | − | 0.612018i | \(-0.209642\pi\) | ||||
0.790844 | + | 0.612018i | \(0.209642\pi\) | |||||||
\(830\) | −201854. | −0.293009 | ||||||||
\(831\) | 715754. | 1.03648 | ||||||||
\(832\) | 147702. | 0.213374 | ||||||||
\(833\) | − | 335482.i | − | 0.483481i | ||||||
\(834\) | −289309. | −0.415940 | ||||||||
\(835\) | 132335.i | 0.189802i | ||||||||
\(836\) | −159559. | −0.228302 | ||||||||
\(837\) | −116151. | −0.165795 | ||||||||
\(838\) | 264485.i | 0.376629i | ||||||||
\(839\) | 331804.i | 0.471365i | 0.971830 | + | 0.235683i | \(0.0757326\pi\) | ||||
−0.971830 | + | 0.235683i | \(0.924267\pi\) | |||||||
\(840\) | −138488. | −0.196269 | ||||||||
\(841\) | 276065. | 0.390318 | ||||||||
\(842\) | 116858.i | 0.164829i | ||||||||
\(843\) | 751739.i | 1.05782i | ||||||||
\(844\) | −475914. | −0.668104 | ||||||||
\(845\) | 1.09169e6i | 1.52892i | ||||||||
\(846\) | −144843. | −0.202375 | ||||||||
\(847\) | 813507.i | 1.13395i | ||||||||
\(848\) | − | 268214.i | − | 0.372983i | ||||||
\(849\) | 59072.3i | 0.0819537i | ||||||||
\(850\) | 199203.i | 0.275713i | ||||||||
\(851\) | −29419.4 | − | 31001.5i | −0.0406232 | − | 0.0428078i | ||||
\(852\) | −79458.0 | −0.109461 | ||||||||
\(853\) | 126462. | 0.173805 | 0.0869024 | − | 0.996217i | \(-0.472303\pi\) | ||||
0.0869024 | + | 0.996217i | \(0.472303\pi\) | |||||||
\(854\) | −928344. | −1.27290 | ||||||||
\(855\) | −63781.3 | −0.0872491 | ||||||||
\(856\) | − | 416195.i | − | 0.568002i | ||||||
\(857\) | −80673.1 | −0.109842 | −0.0549208 | − | 0.998491i | \(-0.517491\pi\) | ||||
−0.0549208 | + | 0.998491i | \(0.517491\pi\) | |||||||
\(858\) | − | 714944.i | − | 0.971174i | ||||||
\(859\) | 672529. | 0.911433 | 0.455717 | − | 0.890125i | \(-0.349383\pi\) | ||||
0.455717 | + | 0.890125i | \(0.349383\pi\) | |||||||
\(860\) | −52967.8 | −0.0716169 | ||||||||
\(861\) | 57514.6i | 0.0775839i | ||||||||
\(862\) | 301154.i | 0.405298i | ||||||||
\(863\) | 993649. | 1.33417 | 0.667086 | − | 0.744981i | \(-0.267542\pi\) | ||||
0.667086 | + | 0.744981i | \(0.267542\pi\) | |||||||
\(864\) | −25396.3 | −0.0340207 | ||||||||
\(865\) | 553350.i | 0.739550i | ||||||||
\(866\) | 416726.i | 0.555667i | ||||||||
\(867\) | 70133.0 | 0.0933006 | ||||||||
\(868\) | − | 390603.i | − | 0.518437i | ||||||
\(869\) | 1.91285e6 | 2.53304 | ||||||||
\(870\) | − | 291075.i | − | 0.384562i | ||||||
\(871\) | 1.97130e6i | 2.59846i | ||||||||
\(872\) | 35684.6i | 0.0469298i | ||||||||
\(873\) | 256768.i | 0.336909i | ||||||||
\(874\) | −121820. | − | 128371.i | −0.159476 | − | 0.168052i | ||||
\(875\) | 1.00249e6 | 1.30938 | ||||||||
\(876\) | 274637. | 0.357891 | ||||||||
\(877\) | −416237. | −0.541180 | −0.270590 | − | 0.962695i | \(-0.587219\pi\) | ||||
−0.270590 | + | 0.962695i | \(0.587219\pi\) | |||||||
\(878\) | 784098. | 1.01714 | ||||||||
\(879\) | 87799.5i | 0.113636i | ||||||||
\(880\) | −215542. | −0.278335 | ||||||||
\(881\) | 636344.i | 0.819861i | 0.912117 | + | 0.409930i | \(0.134447\pi\) | ||||
−0.912117 | + | 0.409930i | \(0.865553\pi\) | |||||||
\(882\) | −82253.0 | −0.105734 | ||||||||
\(883\) | 125554. | 0.161031 | 0.0805153 | − | 0.996753i | \(-0.474343\pi\) | ||||
0.0805153 | + | 0.996753i | \(0.474343\pi\) | |||||||
\(884\) | 718843.i | 0.919877i | ||||||||
\(885\) | 514885.i | 0.657391i | ||||||||
\(886\) | 50813.0 | 0.0647303 | ||||||||
\(887\) | −299033. | −0.380077 | −0.190039 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190039 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(888\) | − | 9499.09i | − | 0.0120464i | ||||||
\(889\) | 1.54886e6i | 1.95978i | ||||||||
\(890\) | −205697. | −0.259685 | ||||||||
\(891\) | 122929.i | 0.154846i | ||||||||
\(892\) | 477848. | 0.600565 | ||||||||
\(893\) | − | 224333.i | − | 0.281313i | ||||||
\(894\) | 276973.i | 0.346547i | ||||||||
\(895\) | − | 458481.i | − | 0.572368i | ||||||
\(896\) | − | 85405.1i | − | 0.106382i | ||||||
\(897\) | 575197. | − | 545844.i | 0.714878 | − | 0.678396i | ||||
\(898\) | 526441. | 0.652826 | ||||||||
\(899\) | 820975. | 1.01581 | ||||||||
\(900\) | 48840.3 | 0.0602966 | ||||||||
\(901\) | 1.30535e6 | 1.60797 | ||||||||
\(902\) | 89515.7i | 0.110024i | ||||||||
\(903\) | −101589. | −0.124587 | ||||||||
\(904\) | 282845.i | 0.346108i | ||||||||
\(905\) | −379843. | −0.463774 | ||||||||
\(906\) | 93230.8 | 0.113580 | ||||||||
\(907\) | − | 237752.i | − | 0.289008i | −0.989504 | − | 0.144504i | \(-0.953841\pi\) | ||
0.989504 | − | 0.144504i | \(-0.0461587\pi\) | |||||||
\(908\) | − | 289329.i | − | 0.350930i | ||||||
\(909\) | 213161. | 0.257976 | ||||||||
\(910\) | 961075. | 1.16058 | ||||||||
\(911\) | 1.18670e6i | 1.42990i | 0.699176 | + | 0.714950i | \(0.253550\pi\) | ||||
−0.699176 | + | 0.714950i | \(0.746450\pi\) | |||||||
\(912\) | − | 39333.8i | − | 0.0472908i | ||||||
\(913\) | −602552. | −0.722858 | ||||||||
\(914\) | − | 1.00788e6i | − | 1.20647i | ||||||
\(915\) | −577567. | −0.689858 | ||||||||
\(916\) | − | 364220.i | − | 0.434083i | ||||||
\(917\) | − | 1.11813e6i | − | 1.32970i | ||||||
\(918\) | − | 123600.i | − | 0.146667i | ||||||
\(919\) | 1.42655e6i | 1.68910i | 0.535477 | + | 0.844550i | \(0.320132\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(920\) | −164562. | − | 173411.i | −0.194426 | − | 0.204881i | ||||
\(921\) | 320450. | 0.377782 | ||||||||
\(922\) | −304185. | −0.357829 | ||||||||
\(923\) | 551421. | 0.647262 | ||||||||
\(924\) | −413398. | −0.484199 | ||||||||
\(925\) | 18267.9i | 0.0213504i | ||||||||
\(926\) | 201667. | 0.235187 | ||||||||
\(927\) | − | 249475.i | − | 0.290314i | ||||||
\(928\) | 179506. | 0.208441 | ||||||||
\(929\) | 194050. | 0.224845 | 0.112423 | − | 0.993660i | \(-0.464139\pi\) | ||||
0.112423 | + | 0.993660i | \(0.464139\pi\) | |||||||
\(930\) | − | 243013.i | − | 0.280972i | ||||||
\(931\) | − | 127394.i | − | 0.146977i | ||||||
\(932\) | −279389. | −0.321645 | ||||||||
\(933\) | −491809. | −0.564980 | ||||||||
\(934\) | − | 840445.i | − | 0.963420i | ||||||
\(935\) | − | 1.04901e6i | − | 1.19993i | ||||||
\(936\) | 176245. | 0.201171 | ||||||||
\(937\) | 330519.i | 0.376459i | 0.982125 | + | 0.188229i | \(0.0602748\pi\) | ||||
−0.982125 | + | 0.188229i | \(0.939725\pi\) | |||||||
\(938\) | 1.13985e6 | 1.29552 | ||||||||
\(939\) | − | 334186.i | − | 0.379015i | ||||||
\(940\) | − | 303042.i | − | 0.342963i | ||||||
\(941\) | 1.47447e6i | 1.66517i | 0.553900 | + | 0.832583i | \(0.313139\pi\) | ||||
−0.553900 | + | 0.832583i | \(0.686861\pi\) | |||||||
\(942\) | 388581.i | 0.437905i | ||||||||
\(943\) | −72018.5 | + | 68343.2i | −0.0809880 | + | 0.0768550i | ||||
\(944\) | −317529. | −0.356319 | ||||||||
\(945\) | −165249. | −0.185045 | ||||||||
\(946\) | −158114. | −0.176680 | ||||||||
\(947\) | −494341. | −0.551222 | −0.275611 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275611 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(948\) | 471548.i | 0.524697i | ||||||||
\(949\) | −1.90592e6 | −2.11627 | ||||||||
\(950\) | 75643.8i | 0.0838159i | ||||||||
\(951\) | 213868. | 0.236475 | ||||||||
\(952\) | 415653. | 0.458624 | ||||||||
\(953\) | 1.71443e6i | 1.88771i | 0.330367 | + | 0.943853i | \(0.392828\pi\) | ||||
−0.330367 | + | 0.943853i | \(0.607172\pi\) | |||||||
\(954\) | − | 320044.i | − | 0.351652i | ||||||
\(955\) | 1.41579e6 | 1.55236 | ||||||||
\(956\) | −701582. | −0.767649 | ||||||||
\(957\) | − | 868885.i | − | 0.948720i | ||||||
\(958\) | 26166.8i | 0.0285115i | ||||||||
\(959\) | 602311. | 0.654913 | ||||||||
\(960\) | − | 53134.6i | − | 0.0576547i | ||||||
\(961\) | −238106. | −0.257824 | ||||||||
\(962\) | 65921.6i | 0.0712324i | ||||||||
\(963\) | − | 496622.i | − | 0.535517i | ||||||
\(964\) | 624513.i | 0.672028i | ||||||||
\(965\) | 466198.i | 0.500629i | ||||||||
\(966\) | −315620. | − | 332593.i | −0.338229 | − | 0.356417i | ||||
\(967\) | −1.20027e6 | −1.28359 | −0.641795 | − | 0.766877i | \(-0.721810\pi\) | ||||
−0.641795 | + | 0.766877i | \(0.721810\pi\) | |||||||
\(968\) | −312124. | −0.333101 | ||||||||
\(969\) | 191431. | 0.203875 | ||||||||
\(970\) | −537214. | −0.570958 | ||||||||
\(971\) | 1.61911e6i | 1.71727i | 0.512589 | + | 0.858634i | \(0.328687\pi\) | ||||
−0.512589 | + | 0.858634i | \(0.671313\pi\) | |||||||
\(972\) | −30304.0 | −0.0320750 | ||||||||
\(973\) | − | 1.16093e6i | − | 1.22625i | ||||||
\(974\) | 1.14494e6 | 1.20688 | ||||||||
\(975\) | −338941. | −0.356545 | ||||||||
\(976\) | − | 356184.i | − | 0.373917i | ||||||
\(977\) | − | 109801.i | − | 0.115032i | −0.998345 | − | 0.0575158i | \(-0.981682\pi\) | ||
0.998345 | − | 0.0575158i | \(-0.0183179\pi\) | |||||||
\(978\) | −166764. | −0.174352 | ||||||||
\(979\) | −614022. | −0.640647 | ||||||||
\(980\) | − | 172091.i | − | 0.179187i | ||||||
\(981\) | 42580.4i | 0.0442458i | ||||||||
\(982\) | −441878. | −0.458225 | ||||||||
\(983\) | 1.29774e6i | 1.34301i | 0.741000 | + | 0.671505i | \(0.234352\pi\) | ||||
−0.741000 | + | 0.671505i | \(0.765648\pi\) | |||||||
\(984\) | −22067.0 | −0.0227905 | ||||||||
\(985\) | − | 1.02118e6i | − | 1.05252i | ||||||
\(986\) | 873624.i | 0.898609i | ||||||||
\(987\) | − | 581218.i | − | 0.596630i | ||||||
\(988\) | 272968.i | 0.279639i | ||||||||
\(989\) | −120716. | − | 127208.i | −0.123416 | − | 0.130053i | ||||
\(990\) | −257194. | −0.262416 | ||||||||
\(991\) | −569407. | −0.579797 | −0.289898 | − | 0.957057i | \(-0.593621\pi\) | ||||
−0.289898 | + | 0.957057i | \(0.593621\pi\) | |||||||
\(992\) | 149866. | 0.152292 | ||||||||
\(993\) | −597038. | −0.605485 | ||||||||
\(994\) | − | 318845.i | − | 0.322706i | ||||||
\(995\) | −1.37041e6 | −1.38422 | ||||||||
\(996\) | − | 148539.i | − | 0.149734i | ||||||
\(997\) | 1.02559e6 | 1.03178 | 0.515888 | − | 0.856656i | \(-0.327462\pi\) | ||||
0.515888 | + | 0.856656i | \(0.327462\pi\) | |||||||
\(998\) | −771745. | −0.774842 | ||||||||
\(999\) | − | 11334.7i | − | 0.0113574i |
(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 | 138.5.b.a.91.12 | yes | 16 | |
3.2 | odd | 2 | 414.5.b.b.91.2 | 16 | |||
4.3 | odd | 2 | 1104.5.c.a.1057.14 | 16 | |||
23.22 | odd | 2 | inner | 138.5.b.a.91.9 | ✓ | 16 | |
69.68 | even | 2 | 414.5.b.b.91.7 | 16 | |||
92.91 | even | 2 | 1104.5.c.a.1057.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.5.b.a.91.9 | ✓ | 16 | 23.22 | odd | 2 | inner | |
138.5.b.a.91.12 | yes | 16 | 1.1 | even | 1 | trivial | |
414.5.b.b.91.2 | 16 | 3.2 | odd | 2 | |||
414.5.b.b.91.7 | 16 | 69.68 | even | 2 | |||
1104.5.c.a.1057.11 | 16 | 92.91 | even | 2 | |||
1104.5.c.a.1057.14 | 16 | 4.3 | odd | 2 |