Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,5,Mod(13,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.o (of order \(30\), degree \(8\), 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: | \(12.8178754224\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{30})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 13.7 | ||
Character | \(\chi\) | \(=\) | 124.13 |
Dual form | 124.5.o.a.105.7 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{11}{30}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72821 | + | 3.88162i | 0.192023 | + | 0.431291i | 0.983740 | − | 0.179597i | \(-0.0574794\pi\) |
−0.791717 | + | 0.610888i | \(0.790813\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.33763 | + | 12.7091i | 0.293505 | + | 0.508366i | 0.974636 | − | 0.223796i | \(-0.0718449\pi\) |
−0.681131 | + | 0.732162i | \(0.738512\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −56.6769 | − | 62.9461i | −1.15667 | − | 1.28461i | −0.952108 | − | 0.305761i | \(-0.901089\pi\) |
−0.204564 | − | 0.978853i | \(-0.565578\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 42.1193 | − | 46.7783i | 0.519992 | − | 0.577509i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.3674 | − | 128.753i | −0.226177 | − | 1.06408i | −0.933885 | − | 0.357573i | \(-0.883604\pi\) |
0.707708 | − | 0.706505i | \(-0.249729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 286.317 | + | 30.0931i | 1.69418 | + | 0.178066i | 0.901857 | − | 0.432034i | \(-0.142204\pi\) |
0.792325 | + | 0.610100i | \(0.208871\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −36.6511 | + | 50.4459i | −0.162894 | + | 0.224204i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −42.0787 | + | 197.965i | −0.145601 | + | 0.685000i | 0.843424 | + | 0.537249i | \(0.180537\pi\) |
−0.989025 | + | 0.147750i | \(0.952797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.62881 | − | 44.0402i | −0.0128222 | − | 0.121995i | 0.986238 | − | 0.165329i | \(-0.0528686\pi\) |
−0.999061 | + | 0.0433342i | \(0.986202\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 146.383 | − | 328.782i | 0.331935 | − | 0.745537i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 492.853 | − | 160.138i | 0.931669 | − | 0.302718i | 0.196424 | − | 0.980519i | \(-0.437067\pi\) |
0.735245 | + | 0.677801i | \(0.237067\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 204.818 | − | 354.756i | 0.327710 | − | 0.567610i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 581.687 | + | 189.002i | 0.797925 | + | 0.259261i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −285.727 | − | 393.270i | −0.339747 | − | 0.467622i | 0.604620 | − | 0.796514i | \(-0.293325\pi\) |
−0.944368 | + | 0.328892i | \(0.893325\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −323.087 | − | 905.061i | −0.336198 | − | 0.941791i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 452.475 | − | 328.742i | 0.415496 | − | 0.301875i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 384.117 | − | 1182.19i | 0.313565 | − | 0.965053i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1336.70 | + | 771.741i | 0.976403 | + | 0.563726i | 0.901182 | − | 0.433441i | \(-0.142701\pi\) |
0.0752205 | + | 0.997167i | \(0.476034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 378.005 | + | 1163.38i | 0.248524 | + | 0.764878i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2144.71 | − | 954.886i | −1.27585 | − | 0.568046i | −0.346781 | − | 0.937946i | \(-0.612725\pi\) |
−0.929072 | + | 0.369900i | \(0.879392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1196.64 | − | 125.771i | 0.647180 | − | 0.0680213i | 0.224749 | − | 0.974417i | \(-0.427844\pi\) |
0.422430 | + | 0.906395i | \(0.361177\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 903.567 | + | 192.059i | 0.446206 | + | 0.0948440i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −653.336 | − | 474.676i | −0.295761 | − | 0.214883i | 0.430002 | − | 0.902828i | \(-0.358513\pi\) |
−0.725763 | + | 0.687945i | \(0.758513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −498.965 | + | 4747.34i | −0.207816 | + | 1.97723i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −841.144 | + | 178.791i | −0.323393 | + | 0.0687392i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3356.62 | − | 3022.31i | −1.19495 | − | 1.07594i | −0.995376 | − | 0.0960557i | \(-0.969377\pi\) |
−0.199575 | − | 0.979883i | \(-0.563956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1435.53 | − | 1292.56i | 0.474557 | − | 0.427293i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 162.948 | − | 94.0778i | 0.0501532 | − | 0.0289559i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2633.61 | − | 1172.56i | 0.756567 | − | 0.336845i | 0.00805565 | − | 0.999968i | \(-0.497436\pi\) |
0.748511 | + | 0.663122i | \(0.230769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1953.56i | − | 0.525009i | −0.964931 | − | 0.262505i | \(-0.915452\pi\) | ||
0.964931 | − | 0.262505i | \(-0.0845485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5331.70 | −1.34334 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1718.43 | + | 3859.65i | 0.406729 | + | 0.913527i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1871.10 | − | 3240.84i | −0.416818 | − | 0.721950i | 0.578799 | − | 0.815470i | \(-0.303522\pi\) |
−0.995617 | + | 0.0935197i | \(0.970188\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1473.34 | + | 1636.32i | 0.309461 | + | 0.343692i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6104.64 | + | 6779.89i | −1.21100 | + | 1.34495i | −0.289203 | + | 0.957268i | \(0.593390\pi\) |
−0.921794 | + | 0.387681i | \(0.873276\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1624.55 | + | 7642.89i | 0.304850 | + | 1.43421i | 0.817658 | + | 0.575704i | \(0.195272\pi\) |
−0.512808 | + | 0.858503i | \(0.671395\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1731.00 | + | 181.935i | 0.307733 | + | 0.0323440i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6553.43 | + | 9020.02i | −1.10532 | + | 1.52134i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1532.51 | + | 7209.92i | −0.245556 | + | 1.15525i | 0.666603 | + | 0.745413i | \(0.267748\pi\) |
−0.912159 | + | 0.409837i | \(0.865586\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −261.311 | − | 2486.20i | −0.0398279 | − | 0.378937i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 388.781 | − | 873.218i | 0.0564351 | − | 0.126755i | −0.883127 | − | 0.469134i | \(-0.844566\pi\) |
0.939562 | + | 0.342379i | \(0.111233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2824.72 | + | 917.808i | −0.390965 | + | 0.127032i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1032.73 | − | 1788.74i | 0.136442 | − | 0.236324i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13606.0 | + | 4420.86i | 1.71771 | + | 0.558118i | 0.991587 | − | 0.129444i | \(-0.0413193\pi\) |
0.726125 | + | 0.687563i | \(0.241319\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14333.3 | − | 19728.1i | −1.73087 | − | 2.38233i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2954.74 | − | 2818.23i | 0.341628 | − | 0.325845i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 525.749 | − | 381.979i | 0.0582547 | − | 0.0423245i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2835.75 | − | 8727.54i | 0.301387 | − | 0.927574i | −0.679614 | − | 0.733570i | \(-0.737853\pi\) |
0.981001 | − | 0.194004i | \(-0.0621474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7175.56 | − | 4142.81i | −0.732125 | − | 0.422693i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4079.90 | + | 12556.6i | 0.399951 | + | 1.23092i | 0.925038 | + | 0.379873i | \(0.124032\pi\) |
−0.525088 | + | 0.851048i | \(0.675968\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9290.54 | − | 4136.42i | −0.875723 | − | 0.389897i | −0.0808883 | − | 0.996723i | \(-0.525776\pi\) |
−0.794834 | + | 0.606826i | \(0.792442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5252.64 | − | 552.075i | 0.476430 | − | 0.0500748i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6342.76 | + | 1348.20i | 0.554001 | + | 0.117757i | 0.476401 | − | 0.879228i | \(-0.341941\pi\) |
0.0776000 | + | 0.996985i | \(0.475274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1123.57 | − | 816.322i | −0.0945687 | − | 0.0687082i | 0.539496 | − | 0.841988i | \(-0.318615\pi\) |
−0.634065 | + | 0.773280i | \(0.718615\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −685.518 | + | 6522.27i | −0.0556382 | + | 0.529362i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17964.8 | + | 3818.54i | −1.40691 | + | 0.299048i | −0.847919 | − | 0.530126i | \(-0.822144\pi\) |
−0.558990 | + | 0.829174i | \(0.688811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5651.58 | + | 5088.71i | 0.427341 | + | 0.384779i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13467.2 | − | 12125.9i | 0.983795 | − | 0.885813i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14846.0 | − | 8571.35i | 1.04837 | − | 0.605278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2453.26 | + | 1092.26i | −0.167561 | + | 0.0746029i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 9975.18i | − | 0.659341i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15183.6 | 0.971748 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4787.78 | − | 10753.5i | −0.296843 | − | 0.666721i | 0.702129 | − | 0.712050i | \(-0.252233\pi\) |
−0.998972 | + | 0.0453292i | \(0.985566\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2556.23 | + | 4427.52i | 0.153610 | + | 0.266061i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12711.2 | + | 14117.2i | 0.740700 | + | 0.822631i | 0.989288 | − | 0.145978i | \(-0.0466330\pi\) |
−0.248587 | + | 0.968609i | \(0.579966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2509.81 | + | 2787.43i | −0.141885 | + | 0.157580i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1866.15 | + | 8779.57i | 0.102395 | + | 0.481732i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7885.23 | + | 828.771i | 0.420120 | + | 0.0441564i | 0.312230 | − | 0.950006i | \(-0.398924\pi\) |
0.107890 | + | 0.994163i | \(0.465591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11800.8 | − | 16242.4i | 0.610775 | − | 0.840659i | −0.385866 | − | 0.922555i | \(-0.626097\pi\) |
0.996641 | + | 0.0818953i | \(0.0260973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 713.411 | − | 3356.34i | 0.0358841 | − | 0.168821i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3961.15 | − | 37687.8i | −0.193709 | − | 1.84302i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2901.56 | − | 6517.02i | 0.138005 | − | 0.309965i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19289.7 | + | 6267.59i | −0.892668 | + | 0.290045i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9589.56 | + | 16609.6i | −0.431943 | + | 0.748146i | −0.997041 | − | 0.0768774i | \(-0.975505\pi\) |
0.565098 | + | 0.825024i | \(0.308838\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 31638.2 | + | 10279.9i | 1.38758 | + | 0.450852i | 0.905154 | − | 0.425084i | \(-0.139755\pi\) |
0.482427 | + | 0.875936i | \(0.339755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7488.12 | + | 10306.5i | 0.319882 | + | 0.440280i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9131.86 | − | 10747.2i | 0.380098 | − | 0.447332i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3451.58 | + | 2507.72i | −0.140029 | + | 0.101737i | −0.655595 | − | 0.755113i | \(-0.727582\pi\) |
0.515565 | + | 0.856850i | \(0.327582\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5930.52 | − | 18252.3i | 0.234584 | − | 0.721976i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −38013.4 | − | 21947.1i | −1.46651 | − | 0.846691i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7264.17 | − | 22356.8i | −0.273408 | − | 0.841462i | −0.989636 | − | 0.143596i | \(-0.954133\pi\) |
0.716229 | − | 0.697866i | \(-0.245867\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7498.13 | + | 3338.38i | 0.275413 | + | 0.122622i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14989.5 | + | 1575.46i | −0.537470 | + | 0.0564904i | −0.369375 | − | 0.929280i | \(-0.620428\pi\) |
−0.168095 | + | 0.985771i | \(0.553762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 53134.8 | + | 11294.2i | 1.86040 | + | 0.395440i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2255.09 | − | 1638.42i | −0.0771207 | − | 0.0560315i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2489.09 | + | 23682.1i | −0.0831665 | + | 0.791276i | 0.870855 | + | 0.491539i | \(0.163566\pi\) |
−0.954022 | + | 0.299737i | \(0.903101\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33939.0 | + | 7213.95i | −1.10821 | + | 0.235558i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9102.84 | + | 8196.23i | 0.290556 | + | 0.261618i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −39033.6 | + | 35146.0i | −1.21824 | + | 1.09691i | −0.225799 | + | 0.974174i | \(0.572499\pi\) |
−0.992440 | + | 0.122733i | \(0.960834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −145.497 | + | 84.0030i | −0.00444118 | + | 0.00256411i | −0.502219 | − | 0.864740i | \(-0.667483\pi\) |
0.497778 | + | 0.867305i | \(0.334150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7582.97 | − | 3376.15i | 0.226432 | − | 0.100814i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22651.0i | 0.661826i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26640.2 | 0.761825 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21071.3 | − | 47327.0i | −0.589886 | − | 1.32491i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7131.85 | + | 12352.7i | 0.195495 | + | 0.338607i | 0.947063 | − | 0.321049i | \(-0.104035\pi\) |
−0.751568 | + | 0.659656i | \(0.770702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −28453.0 | − | 31600.3i | −0.763859 | − | 0.848352i | 0.228266 | − | 0.973599i | \(-0.426694\pi\) |
−0.992126 | + | 0.125247i | \(0.960028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12011.9 | + | 13340.6i | −0.315895 | + | 0.350836i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5680.15 | + | 26723.0i | 0.146362 | + | 0.688577i | 0.988734 | + | 0.149682i | \(0.0478249\pi\) |
−0.842373 | + | 0.538895i | \(0.818842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15954.1 | − | 1676.84i | −0.402871 | − | 0.0423435i | −0.0990738 | − | 0.995080i | \(-0.531588\pi\) |
−0.303798 | + | 0.952737i | \(0.598255\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9346.04 | − | 12863.7i | 0.231332 | − | 0.318401i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8560.67 | + | 40274.8i | −0.207738 | + | 0.977329i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3601.29 | − | 34264.0i | −0.0856940 | − | 0.815324i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13267.7 | − | 29799.7i | 0.309638 | − | 0.695458i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5543.65 | + | 1801.24i | −0.126912 | + | 0.0412362i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23342.2 | + | 40429.9i | −0.524297 | + | 0.908109i | 0.475303 | + | 0.879822i | \(0.342339\pi\) |
−0.999600 | + | 0.0282868i | \(0.990995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −36867.0 | − | 11978.8i | −0.812603 | − | 0.264031i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10378.9 | + | 14285.3i | 0.224530 | + | 0.309039i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38658.5 | + | 71633.1i | −0.820967 | + | 1.52123i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26859.2 | + | 19514.4i | −0.560022 | + | 0.406880i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18005.2 | + | 55414.4i | −0.368650 | + | 1.13459i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 71962.4 | + | 41547.5i | 1.44709 | + | 0.835478i | 0.998307 | − | 0.0581625i | \(-0.0185242\pi\) |
0.448783 | + | 0.893641i | \(0.351857\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7968.05 | − | 24523.1i | −0.157394 | − | 0.484408i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 31271.6 | + | 13923.0i | 0.606873 | + | 0.270197i | 0.687081 | − | 0.726581i | \(-0.258892\pi\) |
−0.0802080 | + | 0.996778i | \(0.525558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −55340.5 | + | 5816.52i | −1.05529 | + | 0.110916i | −0.616249 | − | 0.787551i | \(-0.711349\pi\) |
−0.439041 | + | 0.898467i | \(0.644682\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −46337.9 | − | 9849.43i | −0.868386 | − | 0.184581i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 55205.1 | + | 40108.8i | 1.01687 | + | 0.738802i | 0.965640 | − | 0.259885i | \(-0.0836845\pi\) |
0.0512342 | + | 0.998687i | \(0.483685\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1238.79 | − | 11786.3i | 0.0224317 | − | 0.213424i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30634.6 | + | 6511.59i | −0.545401 | + | 0.115929i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24868.9 | + | 22392.1i | 0.435372 | + | 0.392011i | 0.857466 | − | 0.514541i | \(-0.172038\pi\) |
−0.422093 | + | 0.906552i | \(0.638704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 56981.3 | − | 51306.2i | 0.981066 | − | 0.883356i | −0.0121164 | − | 0.999927i | \(-0.503857\pi\) |
0.993182 | + | 0.116571i | \(0.0371902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 52103.0 | − | 30081.7i | 0.882369 | − | 0.509436i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −63995.8 | + | 28492.8i | −1.06615 | + | 0.474682i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12748.7i | − | 0.208965i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4061.39 | 0.0655052 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13057.9 | + | 29328.6i | 0.207265 | + | 0.465525i | 0.987028 | − | 0.160550i | \(-0.0513268\pi\) |
−0.779762 | + | 0.626076i | \(0.784660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34106.4 | − | 59074.0i | −0.532837 | − | 0.922901i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8444.28 | − | 9378.33i | −0.129862 | − | 0.144226i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 34406.4 | − | 38212.1i | 0.520922 | − | 0.578542i | −0.424073 | − | 0.905628i | \(-0.639400\pi\) |
0.944995 | + | 0.327086i | \(0.106067\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27181.7 | − | 127880.i | −0.405207 | − | 1.90635i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30431.1 | − | 3198.44i | −0.446722 | − | 0.0469524i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11211.8 | + | 15431.7i | −0.162093 | + | 0.223101i | −0.882336 | − | 0.470620i | \(-0.844030\pi\) |
0.720243 | + | 0.693722i | \(0.244030\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13781.4 | − | 64836.3i | 0.196246 | − | 0.923265i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6353.91 | + | 60453.4i | 0.0891289 | + | 0.848005i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10720.4 | + | 24078.4i | −0.148152 | + | 0.332754i | −0.972343 | − | 0.233557i | \(-0.924963\pi\) |
0.824191 | + | 0.566311i | \(0.191630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −34992.7 | + | 11369.8i | −0.476474 | + | 0.154816i | −0.537402 | − | 0.843326i | \(-0.680594\pi\) |
0.0609277 | + | 0.998142i | \(0.480594\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 51806.0 | − | 89730.7i | 0.695112 | − | 1.20397i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −51281.4 | − | 16662.3i | −0.678101 | − | 0.220328i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 40007.7 | + | 55065.9i | 0.521415 | + | 0.717667i | 0.985792 | − | 0.167971i | \(-0.0537215\pi\) |
−0.464376 | + | 0.885638i | \(0.653722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −55945.4 | − | 23007.2i | −0.718714 | − | 0.295566i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 106420. | − | 77318.4i | 1.34775 | − | 0.979197i | 0.348628 | − | 0.937261i | \(-0.386648\pi\) |
0.999120 | − | 0.0419356i | \(-0.0133524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2982.39 | + | 9178.86i | −0.0372385 | + | 0.114608i | −0.967948 | − | 0.251151i | \(-0.919191\pi\) |
0.930709 | + | 0.365760i | \(0.119191\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2391.30 | + | 1380.62i | 0.0294404 | + | 0.0169974i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 61449.1 | + | 189121.i | 0.746023 | + | 2.29602i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38880.8 | + | 17310.8i | 0.465521 | + | 0.207263i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38777.7 | − | 4075.71i | 0.457927 | − | 0.0481301i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 58974.3 | + | 12535.4i | 0.686954 | + | 0.146017i | 0.538149 | − | 0.842850i | \(-0.319124\pi\) |
0.148806 | + | 0.988866i | \(0.452457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34226.6 | + | 24867.1i | 0.393297 | + | 0.285747i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8415.35 | − | 80066.7i | 0.0954024 | − | 0.907693i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 145931. | − | 31018.6i | 1.63232 | − | 0.346960i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −75738.4 | − | 68195.2i | −0.835956 | − | 0.752698i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −41689.1 | + | 37537.0i | −0.454085 | + | 0.408860i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24828.1 | − | 14334.5i | 0.266897 | − | 0.154093i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 132289. | − | 58898.9i | 1.40361 | − | 0.624929i | 0.441421 | − | 0.897300i | \(-0.354474\pi\) |
0.962192 | + | 0.272371i | \(0.0878078\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 43210.9i | − | 0.452560i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −132941. | −1.37448 | −0.687242 | − | 0.726428i | \(-0.741179\pi\) | ||||
−0.687242 | + | 0.726428i | \(0.741179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22496.1 | + | 50527.1i | 0.229625 | + | 0.515745i | 0.991207 | − | 0.132323i | \(-0.0422437\pi\) |
−0.761582 | + | 0.648069i | \(0.775577\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −39122.0 | − | 67761.4i | −0.394276 | − | 0.682906i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −119220. | − | 132407.i | −1.18640 | − | 1.31763i | −0.937040 | − | 0.349221i | \(-0.886446\pi\) |
−0.249360 | − | 0.968411i | \(-0.580220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42815.3 | + | 47551.2i | −0.420743 | + | 0.467283i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5728.43 | + | 26950.1i | 0.0555937 | + | 0.261548i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8913.19 | + | 936.814i | 0.0854334 | + | 0.00897942i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 69318.7 | − | 95409.0i | 0.656271 | − | 0.903280i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1226.89 | − | 5772.04i | 0.0114738 | − | 0.0539801i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7150.04 | + | 68028.1i | 0.0660567 | + | 0.628487i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14483.3 | + | 32529.9i | −0.132194 | + | 0.296911i | −0.967499 | − | 0.252874i | \(-0.918624\pi\) |
0.835306 | + | 0.549786i | \(0.185291\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 92401.4 | − | 30023.0i | 0.833279 | − | 0.270749i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27458.8 | − | 47560.1i | 0.244677 | − | 0.423792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −78467.8 | − | 25495.7i | −0.690926 | − | 0.224496i | −0.0575534 | − | 0.998342i | \(-0.518330\pi\) |
−0.633373 | + | 0.773847i | \(0.718330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45869.0 | − | 63133.3i | −0.399135 | − | 0.549363i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −107688. | + | 66367.7i | −0.926099 | + | 0.570753i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 162576. | − | 118118.i | 1.38187 | − | 1.00399i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9985.31 | + | 30731.6i | −0.0838925 | + | 0.258195i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 112129. | + | 64737.9i | 0.931238 | + | 0.537650i | 0.887203 | − | 0.461380i | \(-0.152645\pi\) |
0.0440349 | + | 0.999030i | \(0.485979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7736.70 | + | 23811.1i | 0.0635192 | + | 0.195492i | 0.977780 | − | 0.209635i | \(-0.0672275\pi\) |
−0.914261 | + | 0.405127i | \(0.867227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 160859. | + | 71619.1i | 1.30566 | + | 0.581319i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12119.2 | − | 1273.78i | 0.0972575 | − | 0.0102222i | −0.0557747 | − | 0.998443i | \(-0.517763\pi\) |
0.153032 | + | 0.988221i | \(0.451096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −130960. | − | 27836.4i | −1.03916 | − | 0.220880i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 58927.7 | + | 42813.5i | 0.462363 | + | 0.335926i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1551.81 | + | 14764.5i | −0.0120406 | + | 0.114559i | −0.998891 | − | 0.0470755i | \(-0.985010\pi\) |
0.986851 | + | 0.161634i | \(0.0516765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 125555. | − | 26687.6i | 0.963429 | − | 0.204783i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8479.48 | − | 7634.96i | −0.0643511 | − | 0.0579420i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −85214.3 | + | 76727.3i | −0.639627 | + | 0.575923i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −50861.1 | + | 29364.7i | −0.377619 | + | 0.218018i | −0.676782 | − | 0.736184i | \(-0.736626\pi\) |
0.299163 | + | 0.954202i | \(0.403293\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −135002. | + | 60106.6i | −0.991485 | + | 0.441438i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 382581.i | 2.77956i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −179222. | −1.28817 | −0.644086 | − | 0.764953i | \(-0.722762\pi\) | ||||
−0.644086 | + | 0.764953i | \(0.722762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 26240.3 | + | 58936.8i | 0.186598 | + | 0.419106i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −69973.8 | − | 121198.i | −0.492326 | − | 0.852734i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 48747.4 | + | 54139.5i | 0.339370 | + | 0.376909i | 0.888538 | − | 0.458804i | \(-0.151722\pi\) |
−0.549168 | + | 0.835712i | \(0.685055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33466.8 | − | 37168.7i | 0.230550 | − | 0.256051i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35531.2 | − | 167161.i | −0.242221 | − | 1.13956i | −0.916172 | − | 0.400786i | \(-0.868737\pi\) |
0.673951 | − | 0.738776i | \(-0.264596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −162723. | − | 17102.9i | −1.09781 | − | 0.115385i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 44518.1 | − | 61273.9i | 0.297245 | − | 0.409123i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10878.8 | + | 51180.6i | −0.0718921 | + | 0.338226i | −0.999364 | − | 0.0356679i | \(-0.988644\pi\) |
0.927472 | + | 0.373894i | \(0.121977\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10963.0 | + | 104306.i | 0.0717094 | + | 0.682269i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32829.9 | + | 73737.2i | −0.212562 | + | 0.477421i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −102877. | + | 33426.7i | −0.659361 | + | 0.214240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −108321. | + | 187617.i | −0.687275 | + | 1.19040i | 0.285441 | + | 0.958396i | \(0.407860\pi\) |
−0.972716 | + | 0.231999i | \(0.925473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15157.2 | − | 4924.87i | −0.0952080 | − | 0.0309349i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8151.98 | + | 11220.2i | 0.0506961 | + | 0.0697772i | 0.833612 | − | 0.552350i | \(-0.186269\pi\) |
−0.782916 | + | 0.622127i | \(0.786269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −65269.0 | − | 268857.i | −0.401880 | − | 1.65543i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29680.1 | − | 21563.9i | 0.180949 | − | 0.131467i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 62782.5 | − | 193225.i | 0.379009 | − | 1.16647i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28054.2 | + | 16197.1i | 0.167707 | + | 0.0968256i | 0.581504 | − | 0.813543i | \(-0.302464\pi\) |
−0.413797 | + | 0.910369i | \(0.635798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10410.3 | + | 32039.7i | 0.0616285 | + | 0.189673i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −223073. | − | 99318.4i | −1.30782 | − | 0.582277i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13950.6 | − | 1466.26i | 0.0810021 | − | 0.00851366i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 83440.9 | + | 17735.9i | 0.479851 | + | 0.101996i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 49044.5 | + | 35633.0i | 0.279359 | + | 0.202966i | 0.718638 | − | 0.695385i | \(-0.244766\pi\) |
−0.439279 | + | 0.898351i | \(0.644766\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18714.5 | − | 178056.i | 0.105588 | − | 1.00460i | −0.805558 | − | 0.592517i | \(-0.798134\pi\) |
0.911146 | − | 0.412084i | \(-0.135199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −49722.6 | + | 10568.9i | −0.277890 | + | 0.0590673i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 61610.7 | + | 55474.5i | 0.341097 | + | 0.307126i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −122969. | + | 110722.i | −0.674434 | + | 0.607263i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 139444. | − | 80508.1i | 0.757679 | − | 0.437446i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −243437. | + | 108385.i | −1.31048 | + | 0.583465i | −0.938662 | − | 0.344840i | \(-0.887933\pi\) |
−0.371821 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 114033.i | − | 0.608211i | −0.952638 | − | 0.304106i | \(-0.901642\pi\) | ||
0.952638 | − | 0.304106i | \(-0.0983576\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30311.1 | 0.160185 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9333.82 | − | 20964.1i | −0.0488761 | − | 0.109777i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 82062.8 | + | 142137.i | 0.425811 | + | 0.737527i | 0.996496 | − | 0.0836424i | \(-0.0266553\pi\) |
−0.570684 | + | 0.821170i | \(0.693322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 201056. | + | 223295.i | 1.03381 | + | 1.14816i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −201201. | + | 223456.i | −1.02523 | + | 1.13863i | −0.0349733 | + | 0.999388i | \(0.511135\pi\) |
−0.990258 | + | 0.139246i | \(0.955532\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43650.4 | + | 205359.i | 0.220429 | + | 1.03704i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −81044.8 | − | 8518.15i | −0.405611 | − | 0.0426315i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5341.56 | − | 7352.03i | 0.0264957 | − | 0.0364682i | −0.795564 | − | 0.605870i | \(-0.792825\pi\) |
0.822059 | + | 0.569402i | \(0.192825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −64249.8 | + | 302271.i | −0.315877 | + | 1.48609i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14774.8 | + | 140573.i | 0.0719990 | + | 0.685025i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 145555. | − | 326922.i | 0.703079 | − | 1.57914i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 67030.8 | − | 21779.6i | 0.320954 | − | 0.104284i | −0.144109 | − | 0.989562i | \(-0.546032\pi\) |
0.465063 | + | 0.885278i | \(0.346032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −61892.3 | + | 107201.i | −0.293773 | + | 0.508829i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −91792.7 | − | 29825.3i | −0.431923 | − | 0.140340i | 0.0849831 | − | 0.996382i | \(-0.472916\pi\) |
−0.516906 | + | 0.856042i | \(0.672916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −155498. | − | 214025.i | −0.725378 | − | 0.998397i | −0.999328 | − | 0.0366527i | \(-0.988330\pi\) |
0.273951 | − | 0.961744i | \(-0.411670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 57498.1 | + | 16873.1i | 0.265918 | + | 0.0780348i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 62454.3 | − | 45375.7i | 0.286371 | − | 0.208060i | −0.435321 | − | 0.900275i | \(-0.643365\pi\) |
0.721691 | + | 0.692215i | \(0.243365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −97949.9 | + | 301459.i | −0.445306 | + | 1.37051i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15699.1 | − | 9063.86i | −0.0707672 | − | 0.0408574i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48942.3 | − | 150629.i | −0.218757 | − | 0.673265i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16571.6 | − | 7378.15i | −0.0734475 | − | 0.0327009i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −282757. | + | 29718.9i | −1.24273 | + | 0.130616i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 307049. | + | 65265.3i | 1.33825 | + | 0.284453i | 0.820778 | − | 0.571248i | \(-0.193540\pi\) |
0.517470 | + | 0.855701i | \(0.326874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 359494. | + | 261188.i | 1.55382 | + | 1.12892i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19495.0 | − | 185483.i | 0.0835659 | − | 0.795077i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 131727. | − | 27999.5i | 0.560005 | − | 0.119033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −125581. | − | 113073.i | −0.529499 | − | 0.476763i | 0.360479 | − | 0.932768i | \(-0.382613\pi\) |
−0.889977 | + | 0.456005i | \(0.849280\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 74226.6 | − | 66833.9i | 0.310414 | − | 0.279498i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −82998.1 | + | 47919.0i | −0.344275 | + | 0.198767i | −0.662161 | − | 0.749362i | \(-0.730360\pi\) |
0.317886 | + | 0.948129i | \(0.397027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 89876.7 | − | 40015.7i | 0.369788 | − | 0.164640i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 121594.i | − | 0.496250i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 772759. | 3.12847 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −191080. | − | 429174.i | −0.767388 | − | 1.72358i | −0.686814 | − | 0.726833i | \(-0.740991\pi\) |
−0.0805743 | − | 0.996749i | \(-0.525675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32020.3 | − | 55460.8i | −0.127570 | − | 0.220958i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −281835. | − | 313009.i | −1.11393 | − | 1.23715i | −0.968829 | − | 0.247730i | \(-0.920315\pi\) |
−0.145103 | − | 0.989417i | \(-0.546351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −129647. | + | 143988.i | −0.508371 | + | 0.564603i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 47988.4 | + | 225768.i | 0.186690 | + | 0.878306i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9981.34 | − | 1049.08i | −0.0385260 | − | 0.00404924i | 0.0852459 | − | 0.996360i | \(-0.472832\pi\) |
−0.123772 | + | 0.992311i | \(0.539499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 389016. | − | 535434.i | 1.48979 | − | 2.05052i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5631.15 | − | 26492.5i | 0.0213975 | − | 0.100667i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15600.2 | − | 148426.i | −0.0588189 | − | 0.559624i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43236.1 | + | 97109.9i | −0.161758 | + | 0.363314i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −96226.5 | + | 31265.9i | −0.357240 | + | 0.116074i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3078.02 | + | 5331.29i | −0.0113396 | + | 0.0196407i | −0.871640 | − | 0.490147i | \(-0.836943\pi\) |
0.860300 | + | 0.509788i | \(0.170276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17689.5 | − | 5747.66i | −0.0646713 | − | 0.0210130i | 0.276503 | − | 0.961013i | \(-0.410825\pi\) |
−0.341174 | + | 0.940000i | \(0.610825\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −86655.4 | − | 119271.i | −0.314396 | − | 0.432729i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 192765. | − | 25876.0i | 0.694077 | − | 0.0931699i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9136.12 | + | 6637.78i | −0.0326476 | + | 0.0237198i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 56075.6 | − | 172583.i | 0.198877 | − | 0.612081i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −585330. | − | 337941.i | −2.06038 | − | 1.18956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29406.4 | + | 90503.6i | 0.102739 | + | 0.316197i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −203881. | − | 90773.9i | −0.707016 | − | 0.314784i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 624891. | − | 65678.7i | 2.15093 | − | 0.226072i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 277728. | + | 59033.0i | 0.948911 | + | 0.201697i | 0.656271 | − | 0.754525i | \(-0.272133\pi\) |
0.292640 | + | 0.956223i | \(0.405466\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −577.517 | − | 419.591i | −0.00195869 | − | 0.00142307i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2130.41 | − | 20269.5i | 0.00717249 | − | 0.0682417i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −194284. | + | 41296.3i | −0.649325 | + | 0.138018i | −0.520787 | − | 0.853686i | \(-0.674362\pi\) |
−0.128538 | + | 0.991705i | \(0.541028\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −91384.1 | − | 82282.6i | −0.303198 | − | 0.273000i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15997.1 | + | 14403.9i | −0.0526912 | + | 0.0474434i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 540694. | − | 312170.i | 1.76808 | − | 1.02080i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −87922.5 | + | 39145.6i | −0.285439 | + | 0.127086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 455378.i | 1.46778i | 0.679267 | + | 0.733891i | \(0.262298\pi\) | ||||
−0.679267 | + | 0.733891i | \(0.737702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 346402. | 1.10855 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 46039.9 | + | 103407.i | 0.146288 | + | 0.328568i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 134219. | + | 232475.i | 0.423446 | + | 0.733430i | 0.996274 | − | 0.0862455i | \(-0.0274870\pi\) |
−0.572828 | + | 0.819676i | \(0.694154\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −180350. | − | 200298.i | −0.564961 | − | 0.627452i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −141687. | + | 157359.i | −0.440720 | + | 0.489469i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 82263.1 | + | 387017.i | 0.254086 | + | 1.19538i | 0.901342 | + | 0.433107i | \(0.142583\pi\) |
−0.647257 | + | 0.762272i | \(0.724084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −82043.3 | − | 8623.10i | −0.251635 | − | 0.0264479i | −0.0221289 | − | 0.999755i | \(-0.507044\pi\) |
−0.229506 | + | 0.973307i | \(0.573711\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35623.2 | + | 49031.2i | −0.108499 | + | 0.149336i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44135.6 | − | 207642.i | 0.133491 | − | 0.628028i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6155.44 | + | 58565.1i | 0.0184887 | + | 0.175909i | 0.999869 | − | 0.0161646i | \(-0.00514558\pi\) |
−0.981381 | + | 0.192073i | \(0.938479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 73487.4 | − | 165055.i | 0.219208 | − | 0.492348i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −77000.6 | + | 25019.0i | −0.228109 | + | 0.0741170i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −297271. | + | 514889.i | −0.874612 | + | 1.51487i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 252927. | + | 82180.9i | 0.739066 | + | 0.240137i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −272099. | − | 374512.i | −0.789678 | − | 1.08690i | −0.994148 | − | 0.108026i | \(-0.965547\pi\) |
0.204470 | − | 0.978873i | \(-0.434453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38363.6 | + | 18418.2i | −0.110583 | + | 0.0530903i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −93911.9 | + | 68231.0i | −0.268872 | + | 0.195347i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 114330. | − | 351871.i | 0.325125 | − | 1.00063i | −0.646259 | − | 0.763118i | \(-0.723667\pi\) |
0.971384 | − | 0.237514i | \(-0.0763326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 217869. | + | 125787.i | 0.615406 | + | 0.355305i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21063.1 | − | 64825.7i | −0.0590982 | − | 0.181886i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 223616. | + | 99560.2i | 0.623231 | + | 0.277480i | 0.693958 | − | 0.720015i | \(-0.255865\pi\) |
−0.0707271 | + | 0.997496i | \(0.522532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 124049. | − | 13038.1i | 0.343434 | − | 0.0360964i | 0.0687586 | − | 0.997633i | \(-0.478096\pi\) |
0.274676 | + | 0.961537i | \(0.411430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −230410. | − | 48975.2i | −0.633675 | − | 0.134692i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31882.8 | − | 23164.2i | −0.0871055 | − | 0.0632859i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −66506.3 | + | 632765.i | −0.180503 | + | 1.71738i | 0.411475 | + | 0.911421i | \(0.365014\pi\) |
−0.591978 | + | 0.805954i | \(0.701653\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −171126. | + | 36373.9i | −0.461404 | + | 0.0980743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −172776. | − | 155569.i | −0.462809 | − | 0.416715i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 437817. | − | 394213.i | 1.16512 | − | 1.04908i | 0.167120 | − | 0.985937i | \(-0.446553\pi\) |
0.998004 | − | 0.0631457i | \(-0.0201133\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 126776. | − | 73194.1i | 0.335187 | − | 0.193520i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −128974. | + | 57422.8i | −0.338790 | + | 0.150839i | −0.569078 | − | 0.822283i | \(-0.692700\pi\) |
0.230288 | + | 0.973123i | \(0.426033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 675106.i | − | 1.76194i | −0.473174 | − | 0.880969i | \(-0.656892\pi\) | ||
0.473174 | − | 0.880969i | \(-0.343108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 316953. | 0.821885 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −492870. | − | 1.10700e6i | −1.26986 | − | 2.85216i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16600.3 | − | 28752.5i | −0.0424966 | − | 0.0736064i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16572.3 | − | 18405.4i | −0.0421549 | − | 0.0468177i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −209024. | + | 232145.i | −0.528318 | + | 0.586756i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 124706. | + | 586697.i | 0.313206 | + | 1.47352i | 0.800000 | + | 0.600000i | \(0.204833\pi\) |
−0.486794 | + | 0.873517i | \(0.661834\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −197274. | − | 20734.3i | −0.492336 | − | 0.0517466i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 101537. | − | 139754.i | 0.251813 | − | 0.346591i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −285724. | + | 1.34423e6i | −0.704155 | + | 3.31279i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 60028.0 | + | 571128.i | 0.147012 | + | 1.39872i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −269259. | + | 604765.i | −0.655321 | + | 1.47187i | 0.213599 | + | 0.976921i | \(0.431481\pi\) |
−0.868920 | + | 0.494953i | \(0.835185\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −134558. | + | 43720.6i | −0.325453 | + | 0.105746i | −0.467187 | − | 0.884159i | \(-0.654732\pi\) |
0.141734 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37513.3 | + | 64975.0i | −0.0901708 | + | 0.156180i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −230663. | − | 74946.8i | −0.551021 | − | 0.179038i | 0.0202559 | − | 0.999795i | \(-0.493552\pi\) |
−0.571277 | + | 0.820757i | \(0.693552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −223046. | − | 306996.i | −0.529547 | − | 0.728859i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −344862. | − | 26260.7i | −0.813736 | − | 0.0619647i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 600060. | − | 435969.i | 1.40724 | − | 1.02242i | 0.413524 | − | 0.910493i | \(-0.364298\pi\) |
0.993716 | − | 0.111927i | \(-0.0357022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −86147.4 | + | 265134.i | −0.200798 | + | 0.617993i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 425946. | + | 245920.i | 0.986788 | + | 0.569722i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 139528. | + | 429422.i | 0.321284 | + | 0.988810i | 0.973090 | + | 0.230425i | \(0.0740116\pi\) |
−0.651806 | + | 0.758386i | \(0.725988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −173963. | − | 77453.5i | −0.398158 | − | 0.177271i | 0.197883 | − | 0.980226i | \(-0.436593\pi\) |
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −246214. | + | 25878.1i | −0.560126 | + | 0.0588716i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −53841.9 | − | 11444.4i | −0.121752 | − | 0.0258792i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −203799. | − | 148069.i | −0.458089 | − | 0.332821i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36905.6 | + | 351133.i | −0.0824593 | + | 0.784548i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −251527. | + | 53463.8i | −0.558651 | + | 0.118745i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 65982.3 | + | 59410.7i | 0.145679 | + | 0.131170i | 0.738748 | − | 0.673982i | \(-0.235417\pi\) |
−0.593069 | + | 0.805152i | \(0.702084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 186190. | − | 167646.i | 0.408647 | − | 0.367947i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −179014. | + | 103354.i | −0.390579 | + | 0.225501i | −0.682411 | − | 0.730969i | \(-0.739068\pi\) |
0.291832 | + | 0.956470i | \(0.405735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −710087. | + | 316151.i | −1.54018 | + | 0.685733i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 145446.i | 0.313623i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 610583. | 1.30889 | 0.654445 | − | 0.756110i | \(-0.272902\pi\) | ||||
0.654445 | + | 0.756110i | \(0.272902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 47325.9 | + | 106296.i | 0.100860 | + | 0.226535i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −118217. | − | 204758.i | −0.250477 | − | 0.433839i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −870105. | − | 966349.i | −1.83288 | − | 2.03561i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −394330. | + | 437948.i | −0.825855 | + | 0.917205i | −0.997691 | − | 0.0679209i | \(-0.978363\pi\) |
0.171836 | + | 0.985126i | \(0.445030\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 145915. | + | 686475.i | 0.303832 | + | 1.42942i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 293016. | + | 30797.3i | 0.606628 | + | 0.0637592i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 279280. | − | 384397.i | 0.574877 | − | 0.791250i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −60281.3 | + | 283601.i | −0.123375 | + | 0.580435i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −83111.8 | − | 790756.i | −0.169132 | − | 1.60919i | −0.669121 | − | 0.743154i | \(-0.733329\pi\) |
0.499988 | − | 0.866032i | \(-0.333338\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27800.3 | − | 62440.6i | 0.0562522 | − | 0.126344i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 47890.9 | − | 15560.7i | 0.0963551 | − | 0.0313077i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 559155. | − | 968485.i | 1.11865 | − | 1.93755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −267771. | − | 87004.2i | −0.532686 | − | 0.173080i | 0.0303087 | − | 0.999541i | \(-0.490351\pi\) |
−0.562995 | + | 0.826460i | \(0.690351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 272719. | + | 375365.i | 0.539481 | + | 0.742531i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −304169. | − | 394324.i | −0.598322 | − | 0.775665i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 449915. | − | 326882.i | 0.880072 | − | 0.639410i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43938.8 | + | 135230.i | −0.0854692 | + | 0.263047i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −400512. | − | 231236.i | −0.774743 | − | 0.447298i | 0.0598209 | − | 0.998209i | \(-0.480947\pi\) |
−0.834564 | + | 0.550911i | \(0.814280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 266188. | + | 819243.i | 0.512057 | + | 1.57595i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 297626. | + | 132512.i | 0.569370 | + | 0.253500i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −198037. | + | 20814.5i | −0.376765 | + | 0.0395996i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −98889.9 | − | 21019.7i | −0.187104 | − | 0.0397702i | 0.113407 | − | 0.993549i | \(-0.463824\pi\) |
−0.300511 | + | 0.953778i | \(0.597157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 42991.0 | + | 31234.8i | 0.0808951 | + | 0.0587737i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25454.6 | + | 242184.i | −0.0476355 | + | 0.453222i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 645989. | − | 137309.i | 1.20231 | − | 0.255559i | 0.437145 | − | 0.899391i | \(-0.355990\pi\) |
0.765167 | + | 0.643832i | \(0.222656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −221196. | − | 199166.i | −0.409451 | − | 0.368672i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −366062. | + | 329603.i | −0.673937 | + | 0.606816i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −242080. | + | 139765.i | −0.443271 | + | 0.255923i | −0.704984 | − | 0.709223i | \(-0.749046\pi\) |
0.261713 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49485.7 | − | 22032.5i | 0.0901246 | − | 0.0401261i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 809492.i | 1.46634i | 0.680045 | + | 0.733170i | \(0.261960\pi\) | ||||
−0.680045 | + | 0.733170i | \(0.738040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −281458. | −0.507109 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24472.4 | − | 54965.9i | −0.0438566 | − | 0.0985035i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −274625. | − | 475664.i | −0.489526 | − | 0.847884i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 341205. | + | 378947.i | 0.604973 | + | 0.671890i | 0.965363 | − | 0.260911i | \(-0.0840231\pi\) |
−0.360390 | + | 0.932802i | \(0.617356\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −91275.5 | + | 101372.i | −0.160977 | + | 0.178783i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 101501. | + | 477525.i | 0.178064 | + | 0.837726i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −844916. | − | 88804.3i | −1.47442 | − | 0.154968i | −0.667051 | − | 0.745012i | \(-0.732444\pi\) |
−0.807371 | + | 0.590044i | \(0.799110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 170360. | − | 234480.i | 0.295722 | − | 0.407026i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −110698. | + | 520793.i | −0.191148 | + | 0.899281i | 0.773101 | + | 0.634283i | \(0.218705\pi\) |
−0.964249 | + | 0.264998i | \(0.914629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12296.2 | + | 116991.i | 0.0211214 | + | 0.200957i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −76042.0 | + | 170793.i | −0.129936 | + | 0.291842i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 789332. | − | 256470.i | 1.34174 | − | 0.435958i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 442983. | − | 767269.i | 0.749090 | − | 1.29746i | −0.199169 | − | 0.979965i | \(-0.563824\pi\) |
0.948259 | − | 0.317498i | \(-0.102843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 207786. | + | 67513.8i | 0.349549 | + | 0.113575i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −615805. | − | 847583.i | −1.03059 | − | 1.41848i | −0.904507 | − | 0.426460i | \(-0.859761\pi\) |
−0.126079 | − | 0.992020i | \(-0.540239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −387250. | − | 70756.4i | −0.644745 | − | 0.117805i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 449404. | − | 326511.i | 0.744381 | − | 0.540824i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32125.9 | + | 98873.4i | −0.0529396 | + | 0.162931i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.04000e6 | + | 600445.i | 1.70503 | + | 0.984399i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −91875.3 | − | 282763.i | −0.149856 | − | 0.461210i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −57197.4 | − | 25465.9i | −0.0928190 | − | 0.0413257i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −160961. | + | 16917.7i | −0.259879 | + | 0.0273144i | −0.233572 | − | 0.972340i | \(-0.575041\pi\) |
−0.0263071 | + | 0.999654i | \(0.508375\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −79276.2 | − | 16850.7i | −0.127347 | − | 0.0270684i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.25855e6 | + | 914392.i | 2.01149 | + | 1.46144i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58788.7 | − | 559337.i | 0.0934861 | − | 0.889461i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 275487. | − | 58556.5i | 0.435879 | − | 0.0926490i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −170383. | − | 153414.i | −0.268232 | − | 0.241517i | 0.524028 | − | 0.851701i | \(-0.324429\pi\) |
−0.792260 | + | 0.610184i | \(0.791095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 121461. | − | 109364.i | 0.190258 | − | 0.171309i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 779875. | − | 450261.i | 1.21551 | − | 0.701778i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 939589. | − | 418332.i | 1.45716 | − | 0.648769i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 644157.i | − | 0.994032i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −111990. | −0.171962 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −62168.6 | − | 139633.i | −0.0949892 | − | 0.213349i | 0.859801 | − | 0.510629i | \(-0.170587\pi\) |
−0.954790 | + | 0.297280i | \(0.903921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 178097. | + | 308474.i | 0.270780 | + | 0.469004i | 0.969062 | − | 0.246819i | \(-0.0793852\pi\) |
−0.698282 | + | 0.715823i | \(0.746052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −104608. | − | 116179.i | −0.158265 | − | 0.175771i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 230834. | − | 256367.i | 0.347524 | − | 0.385964i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11078.0 | − | 52117.9i | −0.0165965 | − | 0.0780805i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52656e6 | − | 160447.i | −2.27586 | − | 0.239202i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −137382. | + | 189090.i | −0.203819 | + | 0.280532i | −0.898674 | − | 0.438617i | \(-0.855468\pi\) |
0.694855 | + | 0.719150i | \(0.255468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12882.3 | − | 60606.2i | 0.0190192 | − | 0.0894783i | −0.967614 | − | 0.252433i | \(-0.918769\pi\) |
0.986634 | + | 0.162955i | \(0.0521025\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23948.1 | − | 227851.i | −0.0351854 | − | 0.334767i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −75065.9 | + | 168601.i | −0.109757 | + | 0.246518i | −0.960070 | − | 0.279758i | \(-0.909746\pi\) |
0.850314 | + | 0.526276i | \(0.176412\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −178024. | + | 57843.4i | −0.259041 | + | 0.0841676i | −0.435659 | − | 0.900112i | \(-0.643484\pi\) |
0.176617 | + | 0.984280i | \(0.443484\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −144603. | + | 250460.i | −0.209399 | + | 0.362690i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −918810. | − | 298539.i | −1.32415 | − | 0.430241i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −130010. | − | 178944.i | −0.186468 | − | 0.256651i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16877.3 | − | 587526.i | −0.0240908 | − | 0.838642i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 543230. | − | 394679.i | 0.771720 | − | 0.560687i | −0.130763 | − | 0.991414i | \(-0.541743\pi\) |
0.902482 | + | 0.430727i | \(0.141743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 145541. | − | 447928.i | 0.205775 | − | 0.633310i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 484035. | + | 279458.i | 0.681117 | + | 0.393243i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 246344. | + | 758170.i | 0.345008 | + | 1.06183i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 207797. | + | 92517.1i | 0.289649 | + | 0.128960i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40783.0 | + | 4286.47i | −0.0565801 | + | 0.00594681i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 782379. | + | 166300.i | 1.08033 | + | 0.229632i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −246636. | − | 179191.i | −0.338968 | − | 0.246274i | 0.405258 | − | 0.914202i | \(-0.367182\pi\) |
−0.744226 | + | 0.667928i | \(0.767182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4275.88 | − | 40682.3i | 0.00584916 | − | 0.0556510i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.07960e6 | − | 229477.i | 1.46995 | − | 0.312447i | 0.597784 | − | 0.801658i | \(-0.296048\pi\) |
0.872166 | + | 0.489210i | \(0.162715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 377549. | + | 339946.i | 0.511666 | + | 0.460706i | 0.884063 | − | 0.467367i | \(-0.154797\pi\) |
−0.372397 | + | 0.928073i | \(0.621464\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −627898. | + | 565362.i | −0.846999 | + | 0.762642i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 659445. | − | 380731.i | 0.885436 | − | 0.511207i | 0.0129890 | − | 0.999916i | \(-0.495865\pi\) |
0.872447 | + | 0.488709i | \(0.162532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −319243. | + | 142136.i | −0.426667 | + | 0.189965i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 180837.i | 0.240574i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 970242. | 1.28482 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −438200. | − | 984213.i | −0.577611 | − | 1.29734i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −288819. | − | 500250.i | −0.378964 | − | 0.656385i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −860557. | − | 955746.i | −1.12399 | − | 1.24832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 578849. | − | 642877.i | 0.752603 | − | 0.835850i | −0.238192 | − | 0.971218i | \(-0.576555\pi\) |
0.990795 | + | 0.135368i | \(0.0432215\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 53262.3 | + | 250580.i | 0.0689354 | + | 0.324316i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.24686e6 | − | 131050.i | −1.60645 | − | 0.168844i | −0.741586 | − | 0.670857i | \(-0.765926\pi\) |
−0.864860 | + | 0.502013i | \(0.832593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 377249. | − | 519239.i | 0.483846 | − | 0.665956i | −0.495393 | − | 0.868669i | \(-0.664976\pi\) |
0.979238 | + | 0.202713i | \(0.0649758\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −37373.9 | + | 175830.i | −0.0477179 | + | 0.224495i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 125471. | + | 1.19377e6i | 0.159476 | + | 1.51731i | 0.722789 | + | 0.691069i | \(0.242860\pi\) |
−0.563313 | + | 0.826243i | \(0.690474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −405536. | + | 910850.i | −0.513129 | + | 1.15251i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −312956. | + | 101686.i | −0.394210 | + | 0.128087i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17880.7 | + | 30970.2i | −0.0224223 | + | 0.0388366i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −733090. | − | 238195.i | −0.915189 | − | 0.297363i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 372602. | + | 512842.i | 0.463084 | + | 0.637380i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −263619. | + | 385661.i | −0.326180 | + | 0.477185i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 739554. | − | 537317.i | 0.911003 | − | 0.661883i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 133816. | − | 411843.i | 0.164109 | − | 0.505075i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2135.21 | − | 1232.76i | −0.00260702 | − | 0.00150516i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 274583. | + | 845079.i | 0.333779 | + | 1.02727i | 0.967320 | + | 0.253557i | \(0.0816006\pi\) |
−0.633541 | + | 0.773709i | \(0.718399\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 759220. | + | 338026.i | 0.918840 | + | 0.409094i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −83140.5 | + | 8738.42i | −0.100179 | + | 0.0105292i | −0.154485 | − | 0.987995i | \(-0.549372\pi\) |
0.0543064 | + | 0.998524i | \(0.482705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −123070. | − | 26159.3i | −0.147642 | − | 0.0313823i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 98549.0 | + | 71600.1i | 0.117709 | + | 0.0855207i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 168192. | − | 1.60024e6i | 0.200016 | − | 1.90303i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 96939.9 | − | 20605.2i | 0.114781 | − | 0.0243975i | −0.150163 | − | 0.988661i | \(-0.547980\pi\) |
0.264944 | + | 0.964264i | \(0.414646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 457246. | + | 411706.i | 0.539052 | + | 0.485365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.95189e6 | + | 1.75749e6i | −2.29114 | + | 2.06295i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 547560. | − | 316134.i | 0.639953 | − | 0.369477i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −584806. | + | 260372.i | −0.680538 | + | 0.302995i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 483398.i | 0.560110i | 0.959984 | + | 0.280055i | \(0.0903527\pi\) | ||||
−0.959984 | + | 0.280055i | \(0.909647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 211383. | 0.243877 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −229750. | − | 516028.i | −0.263933 | − | 0.592802i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 195476. | + | 338575.i | 0.223599 | + | 0.387286i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11621.2 | − | 12906.7i | −0.0132365 | − | 0.0147006i | 0.736490 | − | 0.676448i | \(-0.236482\pi\) |
−0.749727 | + | 0.661748i | \(0.769815\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −157249. | + | 174642.i | −0.178343 | + | 0.198070i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −262529. | − | 1.23510e6i | −0.296482 | − | 1.39484i | −0.834084 | − | 0.551638i | \(-0.814003\pi\) |
0.537602 | − | 0.843199i | \(-0.319330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.20994e6 | − | 127170.i | −1.36063 | − | 0.143008i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 446872. | − | 615066.i | 0.500402 | − | 0.688745i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −200340. | + | 942526.i | −0.223392 | + | 1.05098i | 0.713309 | + | 0.700849i | \(0.247195\pi\) |
−0.936702 | + | 0.350129i | \(0.886138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 235137. | + | 2.23718e6i | 0.261089 | + | 2.48409i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 307918. | − | 691595.i | 0.340466 | − | 0.764699i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 269633. | − | 87609.2i | 0.296885 | − | 0.0964637i | −0.156787 | − | 0.987632i | \(-0.550114\pi\) |
0.453672 | + | 0.891169i | \(0.350114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −104662. | + | 181279.i | −0.114758 | + | 0.198766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −258569. | − | 84014.2i | −0.282327 | − | 0.0917337i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −394743. | − | 543317.i | −0.429217 | − | 0.590767i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −714751. | + | 584826.i | −0.773941 | + | 0.633257i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 330219. | − | 239918.i | 0.356082 | − | 0.258708i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 192835. | − | 593484.i | 0.207076 | − | 0.637315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −558541. | − | 322474.i | −0.597313 | − | 0.344859i | 0.170671 | − | 0.985328i | \(-0.445406\pi\) |
−0.767984 | + | 0.640469i | \(0.778740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11767.5 | + | 36216.6i | 0.0125324 | + | 0.0385709i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −262626. | − | 116929.i | −0.278548 | − | 0.124018i | 0.262708 | − | 0.964875i | \(-0.415384\pi\) |
−0.541256 | + | 0.840858i | \(0.682051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.69123e6 | + | 177755.i | −1.78639 | + | 0.187757i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 490138. | + | 104182.i | 0.515596 | + | 0.109593i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 727060. | + | 528240.i | 0.761695 | + | 0.553404i | 0.899430 | − | 0.437065i | \(-0.143982\pi\) |
−0.137735 | + | 0.990469i | \(0.543982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 196840. | − | 1.87281e6i | 0.205375 | − | 1.95401i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −85510.1 | + | 18175.7i | −0.0888545 | + | 0.0188866i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 153998. | + | 138660.i | 0.159370 | + | 0.143498i | 0.744958 | − | 0.667111i | \(-0.232469\pi\) |
−0.585588 | + | 0.810609i | \(0.699136\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −297948. | + | 268273.i | −0.307091 | + | 0.276506i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −251702. | + | 145320.i | −0.258376 | + | 0.149174i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 569624. | − | 253613.i | 0.582366 | − | 0.259286i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 632201.i | 0.643736i | 0.946785 | + | 0.321868i | \(0.104311\pi\) | ||||
−0.946785 | + | 0.321868i | \(0.895689\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −151299. | −0.153439 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −95754.0 | − | 215067.i | −0.0967188 | − | 0.217234i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 902937. | + | 1.56393e6i | 0.908379 | + | 1.57336i | 0.816316 | + | 0.577605i | \(0.196013\pi\) |
0.0920626 | + | 0.995753i | \(0.470654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 631678. | + | 701550.i | 0.632943 | + | 0.702955i |
(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 | 124.5.o.a.13.7 | ✓ | 88 | |
31.12 | odd | 30 | inner | 124.5.o.a.105.7 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.5.o.a.13.7 | ✓ | 88 | 1.1 | even | 1 | trivial | |
124.5.o.a.105.7 | yes | 88 | 31.12 | odd | 30 | inner |