Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3900,2,Mod(1357,3900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3900.1357");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3900.r (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.1416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 780) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1357.8 | ||
Character | \(\chi\) | \(=\) | 3900.1357 |
Dual form | 3900.2.r.b.3193.8 |
$q$-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 \(\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1951\) | \(3277\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.69969i | − | 1.77631i | −0.459539 | − | 0.888157i | \(-0.651986\pi\) | ||
0.459539 | − | 0.888157i | \(-0.348014\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.315352 | + | 0.315352i | 0.0950822 | + | 0.0950822i | 0.753048 | − | 0.657966i | \(-0.228583\pi\) |
−0.657966 | + | 0.753048i | \(0.728583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.87788 | − | 2.17205i | −0.798181 | − | 0.602418i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.07992 | + | 1.07992i | −0.261918 | + | 0.261918i | −0.825833 | − | 0.563915i | \(-0.809295\pi\) |
0.563915 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.49017 | − | 3.49017i | −0.800700 | − | 0.800700i | 0.182505 | − | 0.983205i | \(-0.441579\pi\) |
−0.983205 | + | 0.182505i | \(0.941579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.32318 | − | 3.32318i | −0.725177 | − | 0.725177i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.48094 | + | 3.48094i | 0.725827 | + | 0.725827i | 0.969786 | − | 0.243959i | \(-0.0784462\pi\) |
−0.243959 | + | 0.969786i | \(0.578446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.87828i | 0.534483i | 0.963630 | + | 0.267241i | \(0.0861121\pi\) | ||||
−0.963630 | + | 0.267241i | \(0.913888\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.13365 | + | 1.13365i | −0.203610 | + | 0.203610i | −0.801545 | − | 0.597935i | \(-0.795988\pi\) |
0.597935 | + | 0.801545i | \(0.295988\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.445975 | 0.0776343 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.92799i | − | 1.46775i | −0.679283 | − | 0.733876i | \(-0.737709\pi\) | ||
0.679283 | − | 0.733876i | \(-0.262291\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.57084 | + | 0.499101i | −0.571792 | + | 0.0799202i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.10267 | − | 6.10267i | 0.953078 | − | 0.953078i | −0.0458697 | − | 0.998947i | \(-0.514606\pi\) |
0.998947 | + | 0.0458697i | \(0.0146059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.557675 | + | 0.557675i | 0.0850447 | + | 0.0850447i | 0.748349 | − | 0.663305i | \(-0.230847\pi\) |
−0.663305 | + | 0.748349i | \(0.730847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.16002i | − | 0.898531i | −0.893398 | − | 0.449265i | \(-0.851686\pi\) | ||
0.893398 | − | 0.449265i | \(-0.148314\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.0871 | −2.15529 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.52723i | 0.213855i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.42127 | + | 8.42127i | −1.15675 | + | 1.15675i | −0.171581 | + | 0.985170i | \(0.554887\pi\) |
−0.985170 | + | 0.171581i | \(0.945113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.93584 | −0.653769 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.44238 | + | 1.44238i | −0.187782 | + | 0.187782i | −0.794736 | − | 0.606955i | \(-0.792391\pi\) |
0.606955 | + | 0.794736i | \(0.292391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.80499 | −0.743253 | −0.371626 | − | 0.928382i | \(-0.621200\pi\) | ||||
−0.371626 | + | 0.928382i | \(0.621200\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.69969 | −0.592105 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.05741 | −0.495691 | −0.247846 | − | 0.968800i | \(-0.579723\pi\) | ||||
−0.247846 | + | 0.968800i | \(0.579723\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.92280 | 0.592635 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.68803 | + | 6.68803i | −0.793723 | + | 0.793723i | −0.982097 | − | 0.188374i | \(-0.939678\pi\) |
0.188374 | + | 0.982097i | \(0.439678\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.734212 | −0.0859330 | −0.0429665 | − | 0.999077i | \(-0.513681\pi\) | ||||
−0.0429665 | + | 0.999077i | \(0.513681\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.48205 | − | 1.48205i | 0.168896 | − | 0.168896i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9137i | 1.45290i | 0.687218 | + | 0.726451i | \(0.258832\pi\) | ||||
−0.687218 | + | 0.726451i | \(0.741168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.05600i | − | 0.115911i | −0.998319 | − | 0.0579553i | \(-0.981542\pi\) | ||
0.998319 | − | 0.0579553i | \(-0.0184581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.03525 | + | 2.03525i | 0.218202 | + | 0.218202i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.36534 | − | 5.36534i | 0.568725 | − | 0.568725i | −0.363046 | − | 0.931771i | \(-0.618263\pi\) |
0.931771 | + | 0.363046i | \(0.118263\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2079 | + | 13.5251i | −1.07008 | + | 1.41782i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.60322i | 0.166246i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.56277 | 0.463279 | 0.231640 | − | 0.972802i | \(-0.425591\pi\) | ||||
0.231640 | + | 0.972802i | \(0.425591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.315352 | − | 0.315352i | 0.0316941 | − | 0.0316941i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.68921i | − | 0.864609i | −0.901728 | − | 0.432304i | \(-0.857701\pi\) | ||
0.901728 | − | 0.432304i | \(-0.142299\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.72580 | − | 3.72580i | −0.367114 | − | 0.367114i | 0.499310 | − | 0.866424i | \(-0.333587\pi\) |
−0.866424 | + | 0.499310i | \(0.833587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4478 | + | 12.4478i | 1.20337 | + | 1.20337i | 0.973134 | + | 0.230240i | \(0.0739512\pi\) |
0.230240 | + | 0.973134i | \(0.426049\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0020 | + | 12.0020i | 1.14958 | + | 1.14958i | 0.986635 | + | 0.162949i | \(0.0521006\pi\) |
0.162949 | + | 0.986635i | \(0.447899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.31304 | − | 6.31304i | −0.599207 | − | 0.599207i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3426 | + | 11.3426i | −1.06702 | + | 1.06702i | −0.0694367 | + | 0.997586i | \(0.522120\pi\) |
−0.997586 | + | 0.0694367i | \(0.977880\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.17205 | + | 2.87788i | −0.200806 | + | 0.266060i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.07526 | + | 5.07526i | 0.465249 | + | 0.465249i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.8011i | − | 0.981919i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.63049i | − | 0.778185i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.73937 | − | 6.73937i | 0.598022 | − | 0.598022i | −0.341764 | − | 0.939786i | \(-0.611024\pi\) |
0.939786 | + | 0.341764i | \(0.111024\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.788672 | 0.0694387 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.18022 | −0.452598 | −0.226299 | − | 0.974058i | \(-0.572663\pi\) | ||||
−0.226299 | + | 0.974058i | \(0.572663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.4027 | + | 16.4027i | −1.42229 | + | 1.42229i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.8964i | − | 1.44356i | −0.692124 | − | 0.721778i | \(-0.743325\pi\) | ||
0.692124 | − | 0.721778i | \(-0.256675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.05422i | − | 0.259056i | −0.991576 | − | 0.129528i | \(-0.958654\pi\) | ||
0.991576 | − | 0.129528i | \(-0.0413462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.35579 | − | 4.35579i | −0.366824 | − | 0.366824i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.222587 | − | 1.59250i | −0.0186136 | − | 0.133172i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.6682 | + | 10.6682i | −0.879895 | + | 0.879895i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.623594 | − | 0.623594i | −0.0510868 | − | 0.0510868i | 0.681102 | − | 0.732189i | \(-0.261501\pi\) |
−0.732189 | + | 0.681102i | \(0.761501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.84579 | + | 5.84579i | 0.475724 | + | 0.475724i | 0.903761 | − | 0.428037i | \(-0.140795\pi\) |
−0.428037 | + | 0.903761i | \(0.640795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.07992 | + | 1.07992i | 0.0873060 | + | 0.0873060i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2125 | − | 10.2125i | −0.815046 | − | 0.815046i | 0.170339 | − | 0.985385i | \(-0.445514\pi\) |
−0.985385 | + | 0.170339i | \(0.945514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.9095i | 0.944483i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3593 | − | 16.3593i | 1.28930 | − | 1.28930i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.2373 | −1.82009 | −0.910044 | − | 0.414511i | \(-0.863953\pi\) | ||||
−0.910044 | + | 0.414511i | \(0.863953\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.5054i | 0.967697i | 0.875152 | + | 0.483848i | \(0.160761\pi\) | ||||
−0.875152 | + | 0.483848i | \(0.839239\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.56442 | + | 12.5018i | 0.274186 | + | 0.961677i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.49017 | + | 3.49017i | −0.266900 | + | 0.266900i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.3381 | − | 18.3381i | −1.39422 | − | 1.39422i | −0.815599 | − | 0.578618i | \(-0.803592\pi\) |
−0.578618 | − | 0.815599i | \(-0.696408\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.03983i | 0.153323i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.9880 | 1.04552 | 0.522758 | − | 0.852481i | \(-0.324903\pi\) | ||||
0.522758 | + | 0.852481i | \(0.324903\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6342i | 1.08775i | 0.839165 | + | 0.543877i | \(0.183044\pi\) | ||||
−0.839165 | + | 0.543877i | \(0.816956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.10475 | + | 4.10475i | −0.303432 | + | 0.303432i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.681107 | −0.0498074 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.32318 | + | 3.32318i | −0.241726 | + | 0.241726i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6896 | −0.990548 | −0.495274 | − | 0.868737i | \(-0.664932\pi\) | ||||
−0.495274 | + | 0.868737i | \(0.664932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3452 | 0.816647 | 0.408323 | − | 0.912837i | \(-0.366114\pi\) | ||||
0.408323 | + | 0.912837i | \(0.366114\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7625 | −0.909294 | −0.454647 | − | 0.890672i | \(-0.650234\pi\) | ||||
−0.454647 | + | 0.890672i | \(0.650234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.52762 | −0.179178 | −0.0895892 | − | 0.995979i | \(-0.528555\pi\) | ||||
−0.0895892 | + | 0.995979i | \(0.528555\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.86902 | + | 2.86902i | −0.202365 | + | 0.202365i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.5270 | 0.949409 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.48094 | − | 3.48094i | 0.241942 | − | 0.241942i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.20126i | − | 0.152265i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4839 | 0.721738 | 0.360869 | − | 0.932616i | \(-0.382480\pi\) | ||||
0.360869 | + | 0.932616i | \(0.382480\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.45830i | 0.648072i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.32780 | + | 5.32780i | 0.361675 | + | 0.361675i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.519166 | + | 0.519166i | −0.0350820 | + | 0.0350820i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.45350 | − | 0.762243i | 0.366842 | − | 0.0512740i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.90938i | 0.127861i | 0.997954 | + | 0.0639306i | \(0.0203636\pi\) | ||||
−0.997954 | + | 0.0639306i | \(0.979636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.0353 | −1.86077 | −0.930385 | − | 0.366584i | \(-0.880527\pi\) | ||||
−0.930385 | + | 0.366584i | \(0.880527\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.80903 | − | 5.80903i | 0.383871 | − | 0.383871i | −0.488623 | − | 0.872495i | \(-0.662501\pi\) |
0.872495 | + | 0.488623i | \(0.162501\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.09594i | − | 0.137903i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.4654 | − | 10.4654i | −0.685613 | − | 0.685613i | 0.275646 | − | 0.961259i | \(-0.411108\pi\) |
−0.961259 | + | 0.275646i | \(0.911108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.13135 | + | 9.13135i | 0.593145 | + | 0.593145i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.358095 | + | 0.358095i | 0.0231633 | + | 0.0231633i | 0.718594 | − | 0.695430i | \(-0.244786\pi\) |
−0.695430 | + | 0.718594i | \(0.744786\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.96339 | − | 8.96339i | −0.577383 | − | 0.577383i | 0.356799 | − | 0.934181i | \(-0.383868\pi\) |
−0.934181 | + | 0.356799i | \(0.883868\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.46349 | + | 17.6251i | 0.156748 | + | 1.12146i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.746702 | − | 0.746702i | −0.0473203 | − | 0.0473203i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3022i | 0.650272i | 0.945667 | + | 0.325136i | \(0.105410\pi\) | ||||
−0.945667 | + | 0.325136i | \(0.894590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.19544i | 0.138026i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2281 | − | 20.2281i | 1.26179 | − | 1.26179i | 0.311572 | − | 0.950222i | \(-0.399144\pi\) |
0.950222 | − | 0.311572i | \(-0.100856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.9587 | −2.60719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.87828 | 0.178161 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.83060 | − | 5.83060i | 0.359530 | − | 0.359530i | −0.504110 | − | 0.863640i | \(-0.668179\pi\) |
0.863640 | + | 0.504110i | \(0.168179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7.58774i | − | 0.464362i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.2933i | − | 1.60313i | −0.597906 | − | 0.801566i | \(-0.704001\pi\) | ||
0.597906 | − | 0.801566i | \(-0.295999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.5497 | − | 21.5497i | −1.30905 | − | 1.30905i | −0.922100 | − | 0.386953i | \(-0.873528\pi\) |
−0.386953 | − | 0.922100i | \(-0.626472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.34562 | + | 16.7818i | 0.141963 | + | 1.01568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0701 | + | 11.0701i | −0.665137 | + | 0.665137i | −0.956586 | − | 0.291449i | \(-0.905863\pi\) |
0.291449 | + | 0.956586i | \(0.405863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.13365 | + | 1.13365i | 0.0678698 | + | 0.0678698i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6165 | + | 13.6165i | 0.812291 | + | 0.812291i | 0.984977 | − | 0.172686i | \(-0.0552446\pi\) |
−0.172686 | + | 0.984977i | \(0.555245\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6708 | − | 12.6708i | −0.753204 | − | 0.753204i | 0.221872 | − | 0.975076i | \(-0.428783\pi\) |
−0.975076 | + | 0.221872i | \(0.928783\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.6807 | − | 28.6807i | −1.69297 | − | 1.69297i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.6676i | 0.862798i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.22637 | − | 3.22637i | 0.189133 | − | 0.189133i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.1560 | 1.82015 | 0.910077 | − | 0.414439i | \(-0.136022\pi\) | ||||
0.910077 | + | 0.414439i | \(0.136022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.445975i | − | 0.0258781i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.45697 | − | 17.5785i | −0.142090 | − | 1.01659i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.62090 | − | 2.62090i | 0.151066 | − | 0.151066i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.14420 | − | 6.14420i | −0.352975 | − | 0.352975i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.0732i | − | 1.60222i | −0.598517 | − | 0.801110i | \(-0.704243\pi\) | ||
0.598517 | − | 0.801110i | \(-0.295757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.26907 | −0.299747 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7252i | 0.721579i | 0.932647 | + | 0.360789i | \(0.117493\pi\) | ||||
−0.932647 | + | 0.360789i | \(0.882507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1806 | − | 14.1806i | 0.801534 | − | 0.801534i | −0.181801 | − | 0.983335i | \(-0.558193\pi\) |
0.983335 | + | 0.181801i | \(0.0581928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.64077 | −0.429148 | −0.214574 | − | 0.976708i | \(-0.568836\pi\) | ||||
−0.214574 | + | 0.976708i | \(0.568836\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.907670 | + | 0.907670i | −0.0508198 | + | 0.0508198i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6038 | 0.982551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.53817 | 0.419435 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.9734 | 0.938631 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.9502 | −1.59607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0162 | − | 15.0162i | 0.825365 | − | 0.825365i | −0.161507 | − | 0.986872i | \(-0.551635\pi\) |
0.986872 | + | 0.161507i | \(0.0516354\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.92799 | −0.489251 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.44617 | − | 9.44617i | 0.514566 | − | 0.514566i | −0.401356 | − | 0.915922i | \(-0.631461\pi\) |
0.915922 | + | 0.401356i | \(0.131461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0409i | 0.871221i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.714997 | −0.0387193 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 38.0066i | 2.05217i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.5249 | − | 20.5249i | −1.10183 | − | 1.10183i | −0.994190 | − | 0.107642i | \(-0.965670\pi\) |
−0.107642 | − | 0.994190i | \(-0.534330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.54929 | + | 1.54929i | −0.0829316 | + | 0.0829316i | −0.747356 | − | 0.664424i | \(-0.768677\pi\) |
0.664424 | + | 0.747356i | \(0.268677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.499101 | + | 3.57084i | 0.0266401 | + | 0.190597i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.75270i | 0.519084i | 0.965732 | + | 0.259542i | \(0.0835716\pi\) | ||||
−0.965732 | + | 0.259542i | \(0.916428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.17751 | 0.379874 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.81152 | − | 2.81152i | 0.148387 | − | 0.148387i | −0.629010 | − | 0.777397i | \(-0.716540\pi\) |
0.777397 | + | 0.629010i | \(0.216540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.36257i | 0.282240i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.63754 | − | 7.63754i | −0.400867 | − | 0.400867i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.2265 | + | 23.2265i | 1.21241 | + | 1.21241i | 0.970230 | + | 0.242184i | \(0.0778636\pi\) |
0.242184 | + | 0.970230i | \(0.422136\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.10267 | − | 6.10267i | −0.317693 | − | 0.317693i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.5773 | + | 39.5773i | 2.05475 | + | 2.05475i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.06758 | − | 3.06758i | 0.158833 | − | 0.158833i | −0.623216 | − | 0.782050i | \(-0.714174\pi\) |
0.782050 | + | 0.623216i | \(0.214174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.25175 | − | 8.28334i | 0.321982 | − | 0.426614i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7416 | + | 16.7416i | 0.859959 | + | 0.859959i | 0.991333 | − | 0.131374i | \(-0.0419387\pi\) |
−0.131374 | + | 0.991333i | \(0.541939\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 9.53091i | − | 0.488283i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.16648i | − | 0.263995i | −0.991250 | − | 0.131997i | \(-0.957861\pi\) | ||
0.991250 | − | 0.131997i | \(-0.0421390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.557675 | − | 0.557675i | 0.0283482 | − | 0.0283482i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.92391 | −0.249652 | −0.124826 | − | 0.992179i | \(-0.539837\pi\) | ||||
−0.124826 | + | 0.992179i | \(0.539837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.51825 | −0.380214 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.66297 | + | 3.66297i | −0.184772 | + | 0.184772i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.9445i | 1.35231i | 0.736760 | + | 0.676154i | \(0.236355\pi\) | ||||
−0.736760 | + | 0.676154i | \(0.763645\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.1969i | 1.16130i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.1188 | − | 25.1188i | −1.25437 | − | 1.25437i | −0.953739 | − | 0.300635i | \(-0.902801\pi\) |
−0.300635 | − | 0.953739i | \(-0.597199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.72485 | − | 0.800171i | 0.285175 | − | 0.0398593i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.81546 | − | 2.81546i | 0.139557 | − | 0.139557i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.765296 | + | 0.765296i | 0.0378414 | + | 0.0378414i | 0.725774 | − | 0.687933i | \(-0.241482\pi\) |
−0.687933 | + | 0.725774i | \(0.741482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9476 | − | 11.9476i | −0.589330 | − | 0.589330i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.77873 | + | 6.77873i | 0.333559 | + | 0.333559i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.15966 | − | 2.15966i | −0.105759 | − | 0.105759i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.89257i | − | 0.336724i | −0.985725 | − | 0.168362i | \(-0.946152\pi\) | ||
0.985725 | − | 0.168362i | \(-0.0538477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8483 | − | 19.8483i | 0.967349 | − | 0.967349i | −0.0321346 | − | 0.999484i | \(-0.510231\pi\) |
0.999484 | + | 0.0321346i | \(0.0102305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.16002 | −0.299510 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.2816i | 1.32025i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.28346 | − | 0.968678i | −0.0619662 | − | 0.0467682i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3880 | + | 18.3880i | −0.885718 | + | 0.885718i | −0.994108 | − | 0.108391i | \(-0.965430\pi\) |
0.108391 | + | 0.994108i | \(0.465430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.17848 | − | 6.17848i | −0.296919 | − | 0.296919i | 0.542887 | − | 0.839806i | \(-0.317331\pi\) |
−0.839806 | + | 0.542887i | \(0.817331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 24.2982i | − | 1.16234i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.7983 | 0.754013 | 0.377006 | − | 0.926211i | \(-0.376954\pi\) | ||||
0.377006 | + | 0.926211i | \(0.376954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.0871i | 0.718431i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.28734 | − | 7.28734i | 0.346232 | − | 0.346232i | −0.512472 | − | 0.858704i | \(-0.671270\pi\) |
0.858704 | + | 0.512472i | \(0.171270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.881895 | −0.0417122 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.9047 | + | 11.9047i | −0.561819 | + | 0.561819i | −0.929824 | − | 0.368005i | \(-0.880041\pi\) |
0.368005 | + | 0.929824i | \(0.380041\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.84898 | 0.181241 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.26719 | 0.388427 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4884 | 0.490628 | 0.245314 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245314 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.52723 | 0.0712850 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.4899 | + | 17.4899i | −0.814587 | + | 0.814587i | −0.985318 | − | 0.170731i | \(-0.945387\pi\) |
0.170731 | + | 0.985318i | \(0.445387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3159 | −0.758266 | −0.379133 | − | 0.925342i | \(-0.623778\pi\) | ||||
−0.379133 | + | 0.925342i | \(0.623778\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5684 | − | 13.5684i | 0.627870 | − | 0.627870i | −0.319662 | − | 0.947532i | \(-0.603569\pi\) |
0.947532 | + | 0.319662i | \(0.103569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.0686i | 0.880504i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.4427 | −0.665482 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.351728i | 0.0161725i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.42127 | + | 8.42127i | 0.385584 | + | 0.385584i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.7533 | − | 17.7533i | 0.811171 | − | 0.811171i | −0.173639 | − | 0.984809i | \(-0.555552\pi\) |
0.984809 | + | 0.173639i | \(0.0555524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.3920 | + | 25.6937i | −0.884200 | + | 1.17153i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 23.1356i | − | 1.05271i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.7675 | −1.53015 | −0.765075 | − | 0.643941i | \(-0.777298\pi\) | ||||
−0.765075 | + | 0.643941i | \(0.777298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.4313 | + | 16.4313i | −0.743048 | + | 0.743048i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.9938i | − | 1.03770i | −0.854866 | − | 0.518849i | \(-0.826361\pi\) | ||
0.854866 | − | 0.518849i | \(-0.173639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.10830 | − | 3.10830i | −0.139991 | − | 0.139991i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.4317 | + | 31.4317i | 1.40990 | + | 1.40990i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.02065 | − | 6.02065i | −0.269521 | − | 0.269521i | 0.559386 | − | 0.828907i | \(-0.311037\pi\) |
−0.828907 | + | 0.559386i | \(0.811037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.84265 | + | 8.84265i | 0.395060 | + | 0.395060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.3721 | − | 10.3721i | 0.462470 | − | 0.462470i | −0.436995 | − | 0.899464i | \(-0.643957\pi\) |
0.899464 | + | 0.436995i | \(0.143957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.3605 | + | 6.31968i | 0.504539 | + | 0.280667i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.39148 | + | 5.39148i | 0.238973 | + | 0.238973i | 0.816425 | − | 0.577452i | \(-0.195953\pi\) |
−0.577452 | + | 0.816425i | \(0.695953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.45057i | 0.152644i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.93584i | 0.217923i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.94257 | − | 1.94257i | 0.0854343 | − | 0.0854343i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.9339 | −1.13837 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.1874 | 1.84826 | 0.924131 | − | 0.382076i | \(-0.124791\pi\) | ||||
0.924131 | + | 0.382076i | \(0.124791\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3298 | + | 11.3298i | −0.495417 | + | 0.495417i | −0.910008 | − | 0.414591i | \(-0.863925\pi\) |
0.414591 | + | 0.910008i | \(0.363925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.44849i | − | 0.106658i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.23393i | 0.0536492i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.44238 | + | 1.44238i | 0.0625939 | + | 0.0625939i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.8181 | + | 4.30749i | −1.33488 | + | 0.186578i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.89104 | − | 9.89104i | 0.426830 | − | 0.426830i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.75773 | − | 4.75773i | −0.204930 | − | 0.204930i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3903 | − | 11.3903i | −0.489709 | − | 0.489709i | 0.418506 | − | 0.908214i | \(-0.362554\pi\) |
−0.908214 | + | 0.418506i | \(0.862554\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3480 | + | 10.3480i | 0.444074 | + | 0.444074i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.3855 | − | 11.3855i | −0.486809 | − | 0.486809i | 0.420489 | − | 0.907298i | \(-0.361859\pi\) |
−0.907298 | + | 0.420489i | \(0.861859\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.80499i | 0.247751i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0457 | − | 10.0457i | 0.427960 | − | 0.427960i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.6902 | 2.58081 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 34.1016i | − | 1.44493i | −0.691408 | − | 0.722465i | \(-0.743009\pi\) | ||
0.691408 | − | 0.722465i | \(-0.256991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.393627 | − | 2.81622i | −0.0166487 | − | 0.119113i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.481615 | + | 0.481615i | −0.0203338 | + | 0.0203338i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7769 | + | 25.7769i | 1.08637 | + | 1.08637i | 0.995899 | + | 0.0904666i | \(0.0288358\pi\) |
0.0904666 | + | 0.995899i | \(0.471164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.69969i | 0.197368i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.2934 | 1.10228 | 0.551138 | − | 0.834414i | \(-0.314194\pi\) | ||||
0.551138 | + | 0.834414i | \(0.314194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 14.6838i | − | 0.614496i | −0.951629 | − | 0.307248i | \(-0.900592\pi\) | ||
0.951629 | − | 0.307248i | \(-0.0994082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.68004 | + | 9.68004i | −0.404389 | + | 0.404389i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.1978 | −0.965735 | −0.482868 | − | 0.875693i | \(-0.660405\pi\) | ||||
−0.482868 | + | 0.875693i | \(0.660405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.02228 | − | 8.02228i | 0.333395 | − | 0.333395i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.96285 | −0.205894 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.31133 | −0.219973 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.91675 | −0.326759 | −0.163380 | − | 0.986563i | \(-0.552240\pi\) | ||||
−0.163380 | + | 0.986563i | \(0.552240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.91326 | 0.326060 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.02448 | + | 9.02448i | −0.371218 | + | 0.371218i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.6618 | 1.79297 | 0.896487 | − | 0.443071i | \(-0.146111\pi\) | ||||
0.896487 | + | 0.443071i | \(0.146111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.78730 | + | 1.78730i | −0.0731492 | + | 0.0731492i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 15.5444i | − | 0.635126i | −0.948237 | − | 0.317563i | \(-0.897136\pi\) | ||
0.948237 | − | 0.317563i | \(-0.102864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.39443 | −0.301625 | −0.150813 | − | 0.988562i | \(-0.548189\pi\) | ||||
−0.150813 | + | 0.988562i | \(0.548189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.05741i | 0.165230i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.2174 | + | 29.2174i | 1.18590 | + | 1.18590i | 0.978192 | + | 0.207705i | \(0.0665994\pi\) |
0.207705 | + | 0.978192i | \(0.433401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.56503 | − | 9.56503i | 0.387595 | − | 0.387595i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.3798 | + | 17.7278i | −0.541291 | + | 0.717190i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.5039i | 1.59555i | 0.602957 | + | 0.797774i | \(0.293989\pi\) | ||||
−0.602957 | + | 0.797774i | \(0.706011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.88852 | −0.116288 | −0.0581438 | − | 0.998308i | \(-0.518518\pi\) | ||||
−0.0581438 | + | 0.998308i | \(0.518518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1526 | − | 13.1526i | 0.528649 | − | 0.528649i | −0.391520 | − | 0.920169i | \(-0.628051\pi\) |
0.920169 | + | 0.391520i | \(0.128051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.92280i | − | 0.197545i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.2154 | − | 25.2154i | −1.01023 | − | 1.01023i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.55653 | − | 1.55653i | −0.0621617 | − | 0.0621617i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.64147 | + | 9.64147i | 0.384431 | + | 0.384431i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9044 | − | 26.9044i | −1.07105 | − | 1.07105i | −0.997275 | − | 0.0737713i | \(-0.976497\pi\) |
−0.0737713 | − | 0.997275i | \(-0.523503\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.41320 | − | 7.41320i | 0.294648 | − | 0.294648i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.4188 | + | 32.7698i | 1.72032 | + | 1.29839i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.68803 | + | 6.68803i | 0.264574 | + | 0.264574i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.72592i | 0.305156i | 0.988291 | + | 0.152578i | \(0.0487575\pi\) | ||||
−0.988291 | + | 0.152578i | \(0.951243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.3325i | − | 0.683528i | −0.939786 | − | 0.341764i | \(-0.888976\pi\) | ||
0.939786 | − | 0.341764i | \(-0.111024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.2911 | + | 11.2911i | −0.443898 | + | 0.443898i | −0.893320 | − | 0.449421i | \(-0.851630\pi\) |
0.449421 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.909714 | −0.0357094 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.53465 | 0.295306 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.3452 | − | 19.3452i | 0.757037 | − | 0.757037i | −0.218745 | − | 0.975782i | \(-0.570196\pi\) |
0.975782 | + | 0.218745i | \(0.0701963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.734212i | 0.0286443i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 41.8280i | − | 1.62939i | −0.579890 | − | 0.814695i | \(-0.696905\pi\) | ||
0.579890 | − | 0.814695i | \(-0.303095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9894 | − | 14.9894i | −0.583022 | − | 0.583022i | 0.352711 | − | 0.935732i | \(-0.385260\pi\) |
−0.935732 | + | 0.352711i | \(0.885260\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.31722 | − | 4.39519i | 0.128830 | − | 0.170695i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0191 | + | 10.0191i | −0.387942 | + | 0.387942i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.35013 | + | 1.35013i | 0.0521991 | + | 0.0521991i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.83061 | − | 1.83061i | −0.0706701 | − | 0.0706701i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.3096 | − | 11.3096i | −0.435952 | − | 0.435952i | 0.454695 | − | 0.890647i | \(-0.349748\pi\) |
−0.890647 | + | 0.454695i | \(0.849748\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2625 | + | 14.2625i | 0.548153 | + | 0.548153i | 0.925906 | − | 0.377753i | \(-0.123303\pi\) |
−0.377753 | + | 0.925906i | \(0.623303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 21.4436i | − | 0.822930i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.8240 | + | 19.8240i | −0.759656 | + | 0.759656i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.2502 | −0.927910 | −0.463955 | − | 0.885859i | \(-0.653570\pi\) | ||||
−0.463955 | + | 0.885859i | \(0.653570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 8.21520i | − | 0.313430i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.5268 | − | 5.94404i | 1.62014 | − | 0.226450i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8507 | − | 18.8507i | 0.717116 | − | 0.717116i | −0.250898 | − | 0.968014i | \(-0.580726\pi\) |
0.968014 | + | 0.250898i | \(0.0807257\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.48205 | − | 1.48205i | −0.0562986 | − | 0.0562986i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.1807i | 0.499256i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.8003 | −0.559800 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.7436i | − | 0.896783i | −0.893837 | − | 0.448392i | \(-0.851997\pi\) | ||
0.893837 | − | 0.448392i | \(-0.148003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.1602 | + | 31.1602i | −1.17523 | + | 1.17523i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.8366 | −1.53582 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.02523 | − | 6.02523i | 0.226282 | − | 0.226282i | −0.584855 | − | 0.811138i | \(-0.698849\pi\) |
0.811138 | + | 0.584855i | \(0.198849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.9137 | 0.484301 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.89234 | −0.295571 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.506423 | 0.0189127 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.39301 | 0.201125 | 0.100563 | − | 0.994931i | \(-0.467936\pi\) | ||||
0.100563 | + | 0.994931i | \(0.467936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5101 | + | 17.5101i | −0.652109 | + | 0.652109i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.6761 | −0.471431 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4677 | + | 27.4677i | −1.01872 | + | 1.01872i | −0.0188979 | + | 0.999821i | \(0.506016\pi\) |
−0.999821 | + | 0.0188979i | \(0.993984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.20448 | −0.0445495 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.5951i | − | 1.49941i | −0.661770 | − | 0.749707i | \(-0.730194\pi\) | ||
0.661770 | − | 0.749707i | \(-0.269806\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.27951 | − | 1.27951i | −0.0471314 | − | 0.0471314i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5815 | − | 19.5815i | 0.720315 | − | 0.720315i | −0.248354 | − | 0.968669i | \(-0.579890\pi\) |
0.968669 | + | 0.248354i | \(0.0798896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.2048 | + | 10.7209i | 0.521826 | + | 0.393842i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.1542i | 1.21631i | 0.793818 | + | 0.608155i | \(0.208090\pi\) | ||||
−0.793818 | + | 0.608155i | \(0.791910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.05600 | −0.0386369 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 58.5008 | − | 58.5008i | 2.13757 | − | 2.13757i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.49285i | 0.346399i | 0.984887 | + | 0.173200i | \(0.0554105\pi\) | ||||
−0.984887 | + | 0.173200i | \(0.944589\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.28479 | + | 7.28479i | 0.265472 | + | 0.265472i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.84463 | − | 2.84463i | −0.103390 | − | 0.103390i | 0.653520 | − | 0.756909i | \(-0.273292\pi\) |
−0.756909 | + | 0.653520i | \(0.773292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.55241 | + | 1.55241i | 0.0563490 | + | 0.0563490i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.6477 | + | 33.6477i | 1.21973 | + | 1.21973i | 0.967727 | + | 0.252002i | \(0.0810888\pi\) |
0.252002 | + | 0.967727i | \(0.418911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.4057 | − | 56.4057i | 2.04202 | − | 2.04202i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.28391 | − | 1.01808i | 0.263007 | − | 0.0367608i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.09238 | − | 2.09238i | −0.0754532 | − | 0.0754532i | 0.668373 | − | 0.743826i | \(-0.266991\pi\) |
−0.743826 | + | 0.668373i | \(0.766991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 28.6069i | − | 1.03025i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 33.8949i | − | 1.21911i | −0.792742 | − | 0.609557i | \(-0.791347\pi\) | ||
0.792742 | − | 0.609557i | \(-0.208653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29.6693 | + | 29.6693i | −1.06438 | + | 1.06438i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.5987 | −1.52626 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.21817 | −0.150938 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.03525 | − | 2.03525i | 0.0727339 | − | 0.0727339i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 13.3356i | − | 0.475363i | −0.971343 | − | 0.237682i | \(-0.923612\pi\) | ||
0.971343 | − | 0.237682i | \(-0.0763875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 8.24571i | − | 0.293555i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53.3067 | + | 53.3067i | 1.89537 | + | 1.89537i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.7061 | + | 12.6087i | 0.593250 | + | 0.447748i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.21618 | − | 2.21618i | 0.0785012 | − | 0.0785012i | −0.666766 | − | 0.745267i | \(-0.732322\pi\) |
0.745267 | + | 0.666766i | \(0.232322\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.65230 | + | 6.65230i | 0.235341 | + | 0.235341i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.36534 | − | 5.36534i | −0.189575 | − | 0.189575i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.231535 | − | 0.231535i | −0.00817069 | − | 0.00817069i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5922 | − | 18.5922i | −0.654476 | − | 0.654476i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10.3854i | − | 0.365131i | −0.983194 | − | 0.182565i | \(-0.941560\pi\) | ||
0.983194 | − | 0.182565i | \(-0.0584401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.72201 | + | 2.72201i | −0.0955825 | + | 0.0955825i | −0.753281 | − | 0.657699i | \(-0.771530\pi\) |
0.657699 | + | 0.753281i | \(0.271530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.4759 | −1.06884 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.89276i | − | 0.136191i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.5251 | + | 10.2079i | 0.472607 | + | 0.356694i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.79821 | − | 3.79821i | 0.132558 | − | 0.132558i | −0.637714 | − | 0.770273i | \(-0.720120\pi\) |
0.770273 | + | 0.637714i | \(0.220120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.2441 | − | 36.2441i | −1.26339 | − | 1.26339i | −0.949439 | − | 0.313951i | \(-0.898347\pi\) |
−0.313951 | − | 0.949439i | \(-0.601653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.2770i | 1.26147i | 0.775996 | + | 0.630737i | \(0.217247\pi\) | ||||
−0.775996 | + | 0.630737i | \(0.782753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.4935 | 0.399185 | 0.199592 | − | 0.979879i | \(-0.436038\pi\) | ||||
0.199592 | + | 0.979879i | \(0.436038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.6555i | 0.543082i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.2927 | − | 16.2927i | 0.564510 | − | 0.564510i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.60322 | 0.0554155 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.5056 | − | 20.5056i | 0.707931 | − | 0.707931i | −0.258169 | − | 0.966100i | \(-0.583119\pi\) |
0.966100 | + | 0.258169i | \(0.0831191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.7155 | 0.714328 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.2566 | 0.663233 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.7618 | −1.74420 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.9193 | −0.614988 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.0778 | − | 31.0778i | 1.06533 | − | 1.06533i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6968 | 0.366253 | 0.183126 | − | 0.983089i | \(-0.441378\pi\) | ||||
0.183126 | + | 0.983089i | \(0.441378\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.4311 | − | 20.4311i | 0.697912 | − | 0.697912i | −0.266048 | − | 0.963960i | \(-0.585718\pi\) |
0.963960 | + | 0.266048i | \(0.0857178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.0854i | − | 1.06062i | −0.847803 | − | 0.530311i | \(-0.822075\pi\) | ||
0.847803 | − | 0.530311i | \(-0.177925\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −40.5606 | −1.38230 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 32.6466i | − | 1.11130i | −0.831415 | − | 0.555651i | \(-0.812469\pi\) | ||
0.831415 | − | 0.555651i | \(-0.187531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.3715 | + | 10.3715i | 0.352236 | + | 0.352236i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.07235 | + | 4.07235i | −0.138145 | + | 0.138145i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6768 | + | 8.81289i | 0.395652 | + | 0.298613i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.56277i | − | 0.154426i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.8946 | 0.840629 | 0.420315 | − | 0.907378i | \(-0.361920\pi\) | ||||
0.420315 | + | 0.907378i | \(0.361920\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.0306 | − | 22.0306i | 0.743075 | − | 0.743075i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 57.1910i | − | 1.92681i | −0.268046 | − | 0.963406i | \(-0.586378\pi\) | ||
0.268046 | − | 0.963406i | \(-0.413622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8928 | + | 18.8928i | 0.635793 | + | 0.635793i | 0.949515 | − | 0.313722i | \(-0.101576\pi\) |
−0.313722 | + | 0.949515i | \(0.601576\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.5287 | + | 14.5287i | 0.487826 | + | 0.487826i | 0.907620 | − | 0.419794i | \(-0.137898\pi\) |
−0.419794 | + | 0.907620i | \(0.637898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.6729 | − | 31.6729i | −1.06228 | − | 1.06228i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.315352 | − | 0.315352i | −0.0105647 | − | 0.0105647i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.4995 | + | 21.4995i | −0.719454 | + | 0.719454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.1672 | − | 10.6925i | −0.473030 | − | 0.357014i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.26296 | − | 3.26296i | −0.108826 | − | 0.108826i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 18.1885i | − | 0.605948i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3.70651i | − | 0.123345i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.2325 | − | 14.2325i | 0.472583 | − | 0.472583i | −0.430166 | − | 0.902750i | \(-0.641545\pi\) |
0.902750 | + | 0.430166i | \(0.141545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.68921 | −0.288203 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2436 | 1.06828 | 0.534139 | − | 0.845397i | \(-0.320636\pi\) | ||||
0.534139 | + | 0.845397i | \(0.320636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.333010 | − | 0.333010i | 0.0110210 | − | 0.0110210i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.3454i | 0.803956i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.73620i | 0.321168i | 0.987022 | + | 0.160584i | \(0.0513377\pi\) | ||||
−0.987022 | + | 0.160584i | \(0.948662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.8507 | − | 19.8507i | −0.654103 | − | 0.654103i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.7741 | − | 4.72065i | 1.11169 | − | 0.155382i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.72580 | + | 3.72580i | −0.122371 | + | 0.122371i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.82032 | + | 9.82032i | 0.322194 | + | 0.322194i | 0.849608 | − | 0.527414i | \(-0.176838\pi\) |
−0.527414 | + | 0.849608i | \(0.676838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52.6564 | + | 52.6564i | 1.72574 | + | 1.72574i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.99806 | + | 8.99806i | 0.294583 | + | 0.294583i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.29485 | + | 6.29485i | 0.205644 | + | 0.205644i | 0.802413 | − | 0.596769i | \(-0.203549\pi\) |
−0.596769 | + | 0.802413i | \(0.703549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 20.0544i | − | 0.654450i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.4276 | − | 32.4276i | 1.05711 | − | 1.05711i | 0.0588409 | − | 0.998267i | \(-0.481260\pi\) |
0.998267 | − | 0.0588409i | \(-0.0187405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.4861 | 1.38354 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.1923i | 1.33857i | 0.743006 | + | 0.669285i | \(0.233399\pi\) | ||||
−0.743006 | + | 0.669285i | \(0.766601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.11298 | + | 1.59474i | 0.0685901 | + | 0.0517675i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.40284 | + | 5.40284i | −0.175199 | + | 0.175199i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.0574 | + | 33.0574i | 1.07083 | + | 1.07083i | 0.997292 | + | 0.0735423i | \(0.0234304\pi\) |
0.0735423 | + | 0.997292i | \(0.476570\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.28364i | 0.0414942i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −79.4078 | −2.56421 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4297i | 0.917086i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.4478 | − | 12.4478i | 0.401125 | − | 0.401125i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.2975 | −1.74609 | −0.873045 | − | 0.487640i | \(-0.837858\pi\) | ||||
−0.873045 | + | 0.487640i | \(0.837858\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.33029 | − | 5.33029i | 0.171234 | − | 0.171234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.8468 | −1.56757 | −0.783785 | − | 0.621033i | \(-0.786713\pi\) | ||||
−0.783785 | + | 0.621033i | \(0.786713\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3539 | −0.460165 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.8534 | 1.81890 | 0.909451 | − | 0.415811i | \(-0.136502\pi\) | ||||
0.909451 | + | 0.415811i | \(0.136502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.38394 | 0.108151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0020 | − | 12.0020i | 0.383194 | − | 0.383194i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.7995 | 0.503924 | 0.251962 | − | 0.967737i | \(-0.418924\pi\) | ||||
0.251962 | + | 0.967737i | \(0.418924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.4709 | + | 20.4709i | −0.651594 | + | 0.651594i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.88247i | 0.123455i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.8662 | −0.567538 | −0.283769 | − | 0.958893i | \(-0.591585\pi\) | ||||
−0.283769 | + | 0.958893i | \(0.591585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 21.2361i | − | 0.673907i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.03661 | − | 5.03661i | −0.159511 | − | 0.159511i | 0.622839 | − | 0.782350i | \(-0.285979\pi\) |
−0.782350 | + | 0.622839i | \(0.785979\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.31304 | + | 6.31304i | −0.199736 | + | 0.199736i |
(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 | 3900.2.r.b.1357.8 | 28 | ||
5.2 | odd | 4 | 780.2.bm.a.733.1 | yes | 28 | ||
5.3 | odd | 4 | 3900.2.bm.b.2293.8 | 28 | |||
5.4 | even | 2 | 780.2.r.a.577.4 | yes | 28 | ||
13.8 | odd | 4 | 3900.2.bm.b.2257.8 | 28 | |||
15.2 | even | 4 | 2340.2.bp.i.1513.14 | 28 | |||
15.14 | odd | 2 | 2340.2.u.i.577.7 | 28 | |||
65.8 | even | 4 | inner | 3900.2.r.b.3193.8 | 28 | ||
65.34 | odd | 4 | 780.2.bm.a.697.1 | yes | 28 | ||
65.47 | even | 4 | 780.2.r.a.73.4 | ✓ | 28 | ||
195.47 | odd | 4 | 2340.2.u.i.73.7 | 28 | |||
195.164 | even | 4 | 2340.2.bp.i.1477.14 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
780.2.r.a.73.4 | ✓ | 28 | 65.47 | even | 4 | ||
780.2.r.a.577.4 | yes | 28 | 5.4 | even | 2 | ||
780.2.bm.a.697.1 | yes | 28 | 65.34 | odd | 4 | ||
780.2.bm.a.733.1 | yes | 28 | 5.2 | odd | 4 | ||
2340.2.u.i.73.7 | 28 | 195.47 | odd | 4 | |||
2340.2.u.i.577.7 | 28 | 15.14 | odd | 2 | |||
2340.2.bp.i.1477.14 | 28 | 195.164 | even | 4 | |||
2340.2.bp.i.1513.14 | 28 | 15.2 | even | 4 | |||
3900.2.r.b.1357.8 | 28 | 1.1 | even | 1 | trivial | ||
3900.2.r.b.3193.8 | 28 | 65.8 | even | 4 | inner | ||
3900.2.bm.b.2257.8 | 28 | 13.8 | odd | 4 | |||
3900.2.bm.b.2293.8 | 28 | 5.3 | odd | 4 |