Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 729.9 | ||
Character | \(\chi\) | \(=\) | 1148.729 |
Dual form | 1148.2.k.b.337.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −0.197445 | + | 0.197445i | −0.113995 | + | 0.113995i | −0.761803 | − | 0.647809i | \(-0.775686\pi\) |
0.647809 | + | 0.761803i | \(0.275686\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.12585i | 1.39792i | 0.715159 | + | 0.698962i | \(0.246354\pi\) | ||||
−0.715159 | + | 0.698962i | \(0.753646\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.92203i | 0.974010i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0441522 | + | 0.0441522i | −0.0133124 | + | 0.0133124i | −0.713732 | − | 0.700419i | \(-0.752996\pi\) |
0.700419 | + | 0.713732i | \(0.252996\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.40539 | + | 3.40539i | −0.944485 | + | 0.944485i | −0.998538 | − | 0.0540535i | \(-0.982786\pi\) |
0.0540535 | + | 0.998538i | \(0.482786\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.617183 | − | 0.617183i | −0.159356 | − | 0.159356i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.97395 | + | 2.97395i | 0.721290 | + | 0.721290i | 0.968868 | − | 0.247578i | \(-0.0796347\pi\) |
−0.247578 | + | 0.968868i | \(0.579635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.33738 | − | 5.33738i | −1.22448 | − | 1.22448i | −0.966023 | − | 0.258455i | \(-0.916787\pi\) |
−0.258455 | − | 0.966023i | \(-0.583213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.279229i | 0.0609327i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.780656 | −0.162778 | −0.0813890 | − | 0.996682i | \(-0.525936\pi\) | ||||
−0.0813890 | + | 0.996682i | \(0.525936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77096 | −0.954193 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.16927 | − | 1.16927i | −0.225027 | − | 0.225027i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24444 | − | 4.24444i | 0.788172 | − | 0.788172i | −0.193022 | − | 0.981194i | \(-0.561829\pi\) |
0.981194 | + | 0.193022i | \(0.0618289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.87513 | −0.875598 | −0.437799 | − | 0.899073i | \(-0.644242\pi\) | ||||
−0.437799 | + | 0.899073i | \(0.644242\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.0174352i | − | 0.00303509i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.21031 | + | 2.21031i | 0.373611 | + | 0.373611i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50079 | −0.246729 | −0.123364 | − | 0.992361i | \(-0.539368\pi\) | ||||
−0.123364 | + | 0.992361i | \(0.539368\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.34475i | − | 0.215332i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.85343 | + | 5.11381i | 0.601805 | + | 0.798643i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.42062i | 0.369141i | 0.982819 | + | 0.184571i | \(0.0590894\pi\) | ||||
−0.982819 | + | 0.184571i | \(0.940911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.13384 | −1.36159 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.29984 | − | 4.29984i | −0.627196 | − | 0.627196i | 0.320166 | − | 0.947361i | \(-0.396261\pi\) |
−0.947361 | + | 0.320166i | \(0.896261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.17438 | −0.164446 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.07903 | + | 4.07903i | −0.560298 | + | 0.560298i | −0.929392 | − | 0.369094i | \(-0.879668\pi\) |
0.369094 | + | 0.929392i | \(0.379668\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.138013 | − | 0.138013i | −0.0186097 | − | 0.0186097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.10767 | 0.279168 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.85555 | −0.762328 | −0.381164 | − | 0.924507i | \(-0.624477\pi\) | ||||
−0.381164 | + | 0.924507i | \(0.624477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.77946i | 1.12409i | 0.827105 | + | 0.562047i | \(0.189986\pi\) | ||||
−0.827105 | + | 0.562047i | \(0.810014\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.06619 | + | 2.06619i | 0.260315 | + | 0.260315i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.6447 | − | 10.6447i | −1.32032 | − | 1.32032i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.81463 | + | 7.81463i | 0.954709 | + | 0.954709i | 0.999018 | − | 0.0443091i | \(-0.0141086\pi\) |
−0.0443091 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.154136 | − | 0.154136i | 0.0185558 | − | 0.0185558i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.22855 | − | 6.22855i | 0.739193 | − | 0.739193i | −0.233229 | − | 0.972422i | \(-0.574929\pi\) |
0.972422 | + | 0.233229i | \(0.0749292\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.3469i | − | 1.56213i | −0.624447 | − | 0.781067i | \(-0.714676\pi\) | ||
0.624447 | − | 0.781067i | \(-0.285324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.942001 | − | 0.942001i | 0.108773 | − | 0.108773i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0624407i | 0.00711578i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.78541 | + | 5.78541i | −0.650910 | + | 0.650910i | −0.953212 | − | 0.302302i | \(-0.902245\pi\) |
0.302302 | + | 0.953212i | \(0.402245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.30436 | −0.922707 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.21760 | −0.792234 | −0.396117 | − | 0.918200i | \(-0.629643\pi\) | ||||
−0.396117 | + | 0.918200i | \(0.629643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.29615 | + | 9.29615i | −1.00831 | + | 1.00831i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.67608i | 0.179695i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.01579 | + | 9.01579i | −0.955672 | + | 0.955672i | −0.999058 | − | 0.0433862i | \(-0.986185\pi\) |
0.0433862 | + | 0.999058i | \(0.486185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.81595i | 0.504848i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.962567 | − | 0.962567i | 0.0998136 | − | 0.0998136i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.6839 | − | 16.6839i | 1.71173 | − | 1.71173i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0205 | + | 11.0205i | 1.11896 | + | 1.11896i | 0.991895 | + | 0.127063i | \(0.0405552\pi\) |
0.127063 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.129014 | − | 0.129014i | −0.0129664 | − | 0.0129664i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6473 | − | 10.6473i | −1.05945 | − | 1.05945i | −0.998117 | − | 0.0613309i | \(-0.980466\pi\) |
−0.0613309 | − | 0.998117i | \(-0.519534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.6105i | 1.93228i | 0.258026 | + | 0.966138i | \(0.416928\pi\) | ||||
−0.258026 | + | 0.966138i | \(0.583072\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.872829 | −0.0851794 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.95499 | 0.188996 | 0.0944980 | − | 0.995525i | \(-0.469875\pi\) | ||||
0.0944980 | + | 0.995525i | \(0.469875\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.08789 | − | 4.08789i | −0.391549 | − | 0.391549i | 0.483690 | − | 0.875239i | \(-0.339296\pi\) |
−0.875239 | + | 0.483690i | \(0.839296\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.296323 | − | 0.296323i | 0.0281258 | − | 0.0281258i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.31266 | 0.593845 | 0.296922 | − | 0.954902i | \(-0.404040\pi\) | ||||
0.296922 | + | 0.954902i | \(0.404040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.44022i | − | 0.227551i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.95065 | − | 9.95065i | −0.919938 | − | 0.919938i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.20581 | 0.385546 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9961i | 0.999646i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.77053 | − | 0.248855i | −0.159644 | − | 0.0224385i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.715936i | 0.0640353i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0950 | 0.895783 | 0.447892 | − | 0.894088i | \(-0.352175\pi\) | ||||
0.447892 | + | 0.894088i | \(0.352175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.477939 | − | 0.477939i | −0.0420801 | − | 0.0420801i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.491225i | 0.0429185i | 0.999770 | + | 0.0214592i | \(0.00683121\pi\) | ||||
−0.999770 | + | 0.0214592i | \(0.993169\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.54819 | −0.654511 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.65498 | − | 3.65498i | 0.314570 | − | 0.314570i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8411 | + | 11.8411i | 1.01165 | + | 1.01165i | 0.999931 | + | 0.0117200i | \(0.00373069\pi\) |
0.0117200 | + | 0.999931i | \(0.496269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0107 | 1.69729 | 0.848644 | − | 0.528964i | \(-0.177420\pi\) | ||||
0.848644 | + | 0.528964i | \(0.177420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.69796 | 0.142994 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.300711i | − | 0.0251467i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.2675 | + | 13.2675i | 1.10181 | + | 1.10181i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.197445 | + | 0.197445i | 0.0162850 | + | 0.0162850i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.08115 | + | 4.08115i | 0.334341 | + | 0.334341i | 0.854232 | − | 0.519891i | \(-0.174028\pi\) |
−0.519891 | + | 0.854232i | \(0.674028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.52725 | − | 6.52725i | 0.531180 | − | 0.531180i | −0.389743 | − | 0.920923i | \(-0.627436\pi\) |
0.920923 | + | 0.389743i | \(0.127436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.68999 | + | 8.68999i | −0.702544 | + | 0.702544i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 15.2389i | − | 1.22402i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.69698 | − | 3.69698i | 0.295051 | − | 0.295051i | −0.544021 | − | 0.839072i | \(-0.683099\pi\) |
0.839072 | + | 0.544021i | \(0.183099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.61076i | − | 0.127742i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.552007 | + | 0.552007i | −0.0435042 | + | 0.0435042i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.6546 | −1.53947 | −0.769734 | − | 0.638365i | \(-0.779611\pi\) | ||||
−0.769734 | + | 0.638365i | \(0.779611\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0545000 | 0.00424282 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.13425 | + | 5.13425i | −0.397300 | + | 0.397300i | −0.877280 | − | 0.479980i | \(-0.840644\pi\) |
0.479980 | + | 0.877280i | \(0.340644\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.1933i | − | 0.784102i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.5960 | − | 15.5960i | 1.19265 | − | 1.19265i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.93744i | − | 0.299358i | −0.988735 | − | 0.149679i | \(-0.952176\pi\) | ||
0.988735 | − | 0.149679i | \(-0.0478241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37358 | + | 3.37358i | −0.255019 | + | 0.255019i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.15615 | − | 1.15615i | 0.0869013 | − | 0.0869013i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7303 | + | 11.7303i | 0.876765 | + | 0.876765i | 0.993198 | − | 0.116434i | \(-0.0371463\pi\) |
−0.116434 | + | 0.993198i | \(0.537146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0472 | − | 11.0472i | −0.821134 | − | 0.821134i | 0.165136 | − | 0.986271i | \(-0.447194\pi\) |
−0.986271 | + | 0.165136i | \(0.947194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.73346 | − | 1.73346i | −0.128141 | − | 0.128141i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.69126i | − | 0.344908i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.262613 | −0.0192042 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.65360 | −0.120282 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8724 | + | 10.8724i | 0.786697 | + | 0.786697i | 0.980951 | − | 0.194254i | \(-0.0622286\pi\) |
−0.194254 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6058 | − | 14.6058i | 1.05135 | − | 1.05135i | 0.0527383 | − | 0.998608i | \(-0.483205\pi\) |
0.998608 | − | 0.0527383i | \(-0.0167949\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.20350 | 0.301019 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 25.8248i | − | 1.83994i | −0.391985 | − | 0.919972i | \(-0.628211\pi\) | ||
0.391985 | − | 0.919972i | \(-0.371789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4368 | + | 16.4368i | 1.16517 | + | 1.16517i | 0.983327 | + | 0.181847i | \(0.0582076\pi\) |
0.181847 | + | 0.983327i | \(0.441792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.08591 | −0.217664 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.00254i | − | 0.421296i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.9850 | + | 12.0453i | −1.11644 | + | 0.841278i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.28110i | − | 0.158547i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.471314 | 0.0326015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.17726 | − | 9.17726i | −0.631788 | − | 0.631788i | 0.316728 | − | 0.948516i | \(-0.397416\pi\) |
−0.948516 | + | 0.316728i | \(0.897416\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.45959i | 0.168528i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.56651 | −0.516031 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.44723 | + | 3.44723i | −0.234013 | + | 0.234013i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.63527 | + | 2.63527i | 0.178075 | + | 0.178075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.2549 | −1.36249 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.6366 | −0.712279 | −0.356140 | − | 0.934433i | \(-0.615907\pi\) | ||||
−0.356140 | + | 0.934433i | \(0.615907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 13.9409i | − | 0.929394i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.181481 | − | 0.181481i | −0.0120453 | − | 0.0120453i | 0.701058 | − | 0.713104i | \(-0.252711\pi\) |
−0.713104 | + | 0.701058i | \(0.752711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8821 | + | 14.8821i | 0.983438 | + | 0.983438i | 0.999865 | − | 0.0164271i | \(-0.00522915\pi\) |
−0.0164271 | + | 0.999865i | \(0.505229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0123286 | − | 0.0123286i | −0.000811161 | − | 0.000811161i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.8210 | − | 13.8210i | 0.905441 | − | 0.905441i | −0.0904593 | − | 0.995900i | \(-0.528834\pi\) |
0.995900 | + | 0.0904593i | \(0.0288335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.4407 | − | 13.4407i | 0.876772 | − | 0.876772i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.28460i | − | 0.148401i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.24022 | − | 1.24022i | 0.0802230 | − | 0.0802230i | −0.665857 | − | 0.746080i | \(-0.731934\pi\) |
0.746080 | + | 0.665857i | \(0.231934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.11244i | 0.329321i | 0.986350 | + | 0.164661i | \(0.0526529\pi\) | ||||
−0.986350 | + | 0.164661i | \(0.947347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.14747 | − | 5.14747i | 0.330210 | − | 0.330210i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.12585 | 0.199703 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.3517 | 2.31300 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.42508 | − | 1.42508i | 0.0903105 | − | 0.0903105i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.33802i | 0.400052i | 0.979791 | + | 0.200026i | \(0.0641027\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0344677 | − | 0.0344677i | 0.00216697 | − | 0.00216697i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 3.67095i | − | 0.229884i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1608 | − | 18.1608i | 1.13284 | − | 1.13284i | 0.143135 | − | 0.989703i | \(-0.454282\pi\) |
0.989703 | − | 0.143135i | \(-0.0457182\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.06122 | + | 1.06122i | −0.0659410 | + | 0.0659410i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4024 | + | 12.4024i | 0.767688 | + | 0.767688i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.59438 | − | 8.59438i | −0.529952 | − | 0.529952i | 0.390606 | − | 0.920558i | \(-0.372266\pi\) |
−0.920558 | + | 0.390606i | \(0.872266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.7504 | − | 12.7504i | −0.783254 | − | 0.783254i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.56024i | − | 0.217883i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.49990 | −0.152422 | −0.0762108 | − | 0.997092i | \(-0.524282\pi\) | ||||
−0.0762108 | + | 0.997092i | \(0.524282\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.9761 | −1.27420 | −0.637102 | − | 0.770779i | \(-0.719867\pi\) | ||||
−0.637102 | + | 0.770779i | \(0.719867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.950883 | − | 0.950883i | −0.0575500 | − | 0.0575500i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.210649 | − | 0.210649i | 0.0127026 | − | 0.0127026i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.54775 | 0.0929953 | 0.0464977 | − | 0.998918i | \(-0.485194\pi\) | ||||
0.0464977 | + | 0.998918i | \(0.485194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 14.2453i | − | 0.852842i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.574366 | − | 0.574366i | −0.0342638 | − | 0.0342638i | 0.689767 | − | 0.724031i | \(-0.257713\pi\) |
−0.724031 | + | 0.689767i | \(0.757713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4316 | 1.27397 | 0.636987 | − | 0.770875i | \(-0.280180\pi\) | ||||
0.636987 | + | 0.770875i | \(0.280180\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.58828i | 0.390256i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.34080 | + | 0.891222i | 0.374285 | + | 0.0526072i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.688802i | 0.0405178i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.35186 | −0.255111 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.66303 | + | 2.66303i | 0.155576 | + | 0.155576i | 0.780603 | − | 0.625027i | \(-0.214912\pi\) |
−0.625027 | + | 0.780603i | \(0.714912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 18.3036i | − | 1.06568i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.103252 | 0.00599129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.65844 | − | 2.65844i | 0.153741 | − | 0.153741i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.71164 | + | 1.71164i | 0.0986571 | + | 0.0986571i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.20451 | 0.241543 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.4433 | −1.57140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.9715i | 0.854466i | 0.904141 | + | 0.427233i | \(0.140512\pi\) | ||||
−0.904141 | + | 0.427233i | \(0.859488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.87198 | − | 3.87198i | −0.220269 | − | 0.220269i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4001 | + | 22.4001i | 1.27019 | + | 1.27019i | 0.945987 | + | 0.324205i | \(0.105097\pi\) |
0.324205 | + | 0.945987i | \(0.394903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5977 | + | 16.5977i | 0.938155 | + | 0.938155i | 0.998196 | − | 0.0600412i | \(-0.0191232\pi\) |
−0.0600412 | + | 0.998196i | \(0.519123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.45860 | + | 6.45860i | −0.363901 | + | 0.363901i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.17288 | − | 3.17288i | 0.178207 | − | 0.178207i | −0.612367 | − | 0.790574i | \(-0.709783\pi\) |
0.790574 | + | 0.612367i | \(0.209783\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.374803i | 0.0209849i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.386002 | + | 0.386002i | −0.0215445 | + | 0.0215445i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 31.7462i | − | 1.76641i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.2470 | − | 16.2470i | 0.901220 | − | 0.901220i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.61427 | 0.0892691 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.08089 | −0.335250 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.432919 | − | 0.432919i | 0.0237954 | − | 0.0237954i | −0.695109 | − | 0.718904i | \(-0.744644\pi\) |
0.718904 | + | 0.695109i | \(0.244644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4.38536i | − | 0.240316i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.4274 | + | 24.4274i | −1.33461 | + | 1.33461i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6117i | 0.795948i | 0.917397 | + | 0.397974i | \(0.130287\pi\) | ||||
−0.917397 | + | 0.397974i | \(0.869713\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.24640 | + | 1.24640i | −0.0676952 | + | 0.0676952i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.215248 | − | 0.215248i | 0.0116563 | − | 0.0116563i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.481807 | + | 0.481807i | 0.0259396 | + | 0.0259396i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.944092 | − | 0.944092i | −0.0506815 | − | 0.0506815i | 0.681312 | − | 0.731993i | \(-0.261410\pi\) |
−0.731993 | + | 0.681312i | \(0.761410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.79145i | 0.470596i | 0.971923 | + | 0.235298i | \(0.0756066\pi\) | ||||
−0.971923 | + | 0.235298i | \(0.924393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.96366 | 0.425069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.42474 | 0.182280 | 0.0911401 | − | 0.995838i | \(-0.470949\pi\) | ||||
0.0911401 | + | 0.995838i | \(0.470949\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4695 | + | 19.4695i | 1.03334 | + | 1.03334i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.830414 | + | 0.830414i | −0.0439502 | + | 0.0439502i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.293669 | −0.0154992 | −0.00774962 | − | 0.999970i | \(-0.502467\pi\) | ||||
−0.00774962 | + | 0.999970i | \(0.502467\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.9752i | 1.99870i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.17112 | − | 2.17112i | −0.113954 | − | 0.113954i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.7204 | 2.18375 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.2960i | − | 1.42484i | −0.701754 | − | 0.712419i | \(-0.747600\pi\) | ||
0.701754 | − | 0.712419i | \(-0.252400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.9427 | + | 11.2599i | −0.777887 | + | 0.586164i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.76862i | 0.299492i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.02826 | −0.415688 | −0.207844 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207844 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.141358 | − | 0.141358i | −0.00729968 | − | 0.00729968i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.9079i | 1.48883i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.1054 | 0.519080 | 0.259540 | − | 0.965732i | \(-0.416429\pi\) | ||||
0.259540 | + | 0.965732i | \(0.416429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.99320 | + | 1.99320i | −0.102115 | + | 0.102115i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.77147 | + | 3.77147i | 0.192713 | + | 0.192713i | 0.796867 | − | 0.604154i | \(-0.206489\pi\) |
−0.604154 | + | 0.796867i | \(0.706489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.195180 | −0.00994732 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.07313 | −0.359547 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.68798i | 0.186988i | 0.995620 | + | 0.0934940i | \(0.0298036\pi\) | ||||
−0.995620 | + | 0.0934940i | \(0.970196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.32163 | − | 2.32163i | −0.117410 | − | 0.117410i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0969897 | − | 0.0969897i | −0.00489248 | − | 0.00489248i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.0844 | − | 18.0844i | −0.909923 | − | 0.909923i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.4075 | + | 25.4075i | −1.27517 | + | 1.27517i | −0.331824 | + | 0.943341i | \(0.607664\pi\) |
−0.943341 | + | 0.331824i | \(0.892336\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.49035 | − | 1.49035i | 0.0746108 | − | 0.0746108i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5249i | 0.725337i | 0.931918 | + | 0.362669i | \(0.118134\pi\) | ||||
−0.931918 | + | 0.362669i | \(0.881866\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6017 | − | 16.6017i | 0.826989 | − | 0.826989i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 25.9582i | − | 1.28987i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0662633 | − | 0.0662633i | 0.00328455 | − | 0.00328455i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.302043 | −0.0149351 | −0.00746754 | − | 0.999972i | \(-0.502377\pi\) | ||||
−0.00746754 | + | 0.999972i | \(0.502377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.67591 | −0.230646 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.14050 | + | 4.14050i | −0.203741 | + | 0.203741i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 22.5612i | − | 1.10748i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.95101 | + | 3.95101i | −0.193482 | + | 0.193482i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.1732i | 1.62062i | 0.586002 | + | 0.810309i | \(0.300701\pi\) | ||||
−0.586002 | + | 0.810309i | \(0.699299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.15792 | + | 4.15792i | −0.202645 | + | 0.202645i | −0.801132 | − | 0.598488i | \(-0.795769\pi\) |
0.598488 | + | 0.801132i | \(0.295769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.5643 | − | 12.5643i | 0.610895 | − | 0.610895i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.1886 | − | 14.1886i | −0.688249 | − | 0.688249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.20801 | + | 6.20801i | 0.300427 | + | 0.300427i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0593738 | + | 0.0593738i | 0.00286659 | + | 0.00286659i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.0184i | − | 0.627074i | −0.949576 | − | 0.313537i | \(-0.898486\pi\) | ||
0.949576 | − | 0.313537i | \(-0.101514\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3433 | 1.21792 | 0.608961 | − | 0.793200i | \(-0.291587\pi\) | ||||
0.608961 | + | 0.793200i | \(0.291587\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.23919 | −0.251200 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.16665 | + | 4.16665i | 0.199318 | + | 0.199318i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.34677 | − | 7.34677i | 0.350642 | − | 0.350642i | −0.509706 | − | 0.860348i | \(-0.670246\pi\) |
0.860348 | + | 0.509706i | \(0.170246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.92203 | 0.139144 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.7528i | − | 0.700929i | −0.936576 | − | 0.350464i | \(-0.886024\pi\) | ||
0.936576 | − | 0.350464i | \(-0.113976\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.1821 | − | 28.1821i | −1.33596 | − | 1.33596i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.61160 | −0.0762262 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.6232i | − | 1.25643i | −0.778040 | − | 0.628214i | \(-0.783786\pi\) | ||
0.778040 | − | 0.628214i | \(-0.216214\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.395924 | − | 0.0556485i | −0.0186433 | − | 0.00262039i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.57754i | 0.121103i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.0539 | −0.705740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.826739 | + | 0.826739i | 0.0386732 | + | 0.0386732i | 0.726179 | − | 0.687506i | \(-0.241294\pi\) |
−0.687506 | + | 0.726179i | \(0.741294\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 6.95473i | − | 0.324619i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.4479 | −1.04550 | −0.522751 | − | 0.852485i | \(-0.675094\pi\) | ||||
−0.522751 | + | 0.852485i | \(0.675094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0147 | + | 10.0147i | −0.465421 | + | 0.465421i | −0.900427 | − | 0.435006i | \(-0.856746\pi\) |
0.435006 | + | 0.900427i | \(0.356746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.00884 | + | 3.00884i | 0.139532 | + | 0.139532i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.21327 | −0.194967 | −0.0974835 | − | 0.995237i | \(-0.531079\pi\) | ||||
−0.0974835 | + | 0.995237i | \(0.531079\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0516 | 0.510313 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.45990i | 0.0672685i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.106876 | − | 0.106876i | −0.00491415 | − | 0.00491415i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.4644 | + | 25.4644i | 1.16839 | + | 1.16839i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.9190 | − | 11.9190i | −0.545736 | − | 0.545736i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.8672 | − | 10.8672i | 0.496536 | − | 0.496536i | −0.413822 | − | 0.910358i | \(-0.635806\pi\) |
0.910358 | + | 0.413822i | \(0.135806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.11078 | − | 5.11078i | 0.233032 | − | 0.233032i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.217982i | − | 0.00991851i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.4483 | + | 34.4483i | −1.56422 | + | 1.56422i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.9944i | − | 0.588833i | −0.955677 | − | 0.294416i | \(-0.904875\pi\) | ||
0.955677 | − | 0.294416i | \(-0.0951252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.88070 | − | 3.88070i | 0.175491 | − | 0.175491i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.3827 | −1.73219 | −0.866094 | − | 0.499880i | \(-0.833377\pi\) | ||||
−0.866094 | + | 0.499880i | \(0.833377\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.2455 | 1.13700 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.403280 | − | 0.403280i | 0.0181261 | − | 0.0181261i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.80850i | − | 0.395115i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.8653 | + | 22.8653i | −1.02359 | + | 1.02359i | −0.0238770 | + | 0.999715i | \(0.507601\pi\) |
−0.999715 | + | 0.0238770i | \(0.992399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 2.02746i | − | 0.0905802i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.1861 | + | 27.1861i | −1.21217 | + | 1.21217i | −0.241853 | + | 0.970313i | \(0.577755\pi\) |
−0.970313 | + | 0.241853i | \(0.922245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.2820 | − | 33.2820i | 1.48103 | − | 1.48103i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.01262 | + | 2.01262i | 0.0893835 | + | 0.0893835i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.86448 | + | 2.86448i | 0.126966 | + | 0.126966i | 0.767734 | − | 0.640768i | \(-0.221384\pi\) |
−0.640768 | + | 0.767734i | \(0.721384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.43767 | − | 9.43767i | −0.417498 | − | 0.417498i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.4817i | 0.551081i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −61.2994 | −2.70118 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.379695 | 0.0166990 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.777427 | + | 0.777427i | 0.0341253 | + | 0.0341253i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.47356 | − | 6.47356i | 0.283612 | − | 0.283612i | −0.550936 | − | 0.834548i | \(-0.685729\pi\) |
0.834548 | + | 0.550936i | \(0.185729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.07244 | 0.221802 | 0.110901 | − | 0.993831i | \(-0.464626\pi\) | ||||
0.110901 | + | 0.993831i | \(0.464626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.33219i | − | 0.0581416i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.4984 | − | 14.4984i | −0.631560 | − | 0.631560i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3906 | −0.973503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 17.1101i | − | 0.742515i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.5369 | − | 4.29208i | −1.32270 | − | 0.185910i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.11101i | 0.264202i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.63217 | −0.199893 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0441522 | + | 0.0441522i | 0.00190177 | + | 0.00190177i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.3720i | 1.00484i | 0.864623 | + | 0.502421i | \(0.167557\pi\) | ||||
−0.864623 | + | 0.502421i | \(0.832443\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.36243 | 0.187210 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.7782 | − | 12.7782i | 0.547356 | − | 0.547356i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.86406 | + | 4.86406i | 0.207972 | + | 0.207972i | 0.803405 | − | 0.595433i | \(-0.203019\pi\) |
−0.595433 | + | 0.803405i | \(0.703019\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.6538 | −1.09488 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.3083 | −1.93020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.18181i | 0.347926i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.926264 | + | 0.926264i | 0.0393177 | + | 0.0393177i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.76253 | − | 3.76253i | −0.159424 | − | 0.159424i | 0.622888 | − | 0.782311i | \(-0.285959\pi\) |
−0.782311 | + | 0.622888i | \(0.785959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.24315 | − | 8.24315i | −0.348648 | − | 0.348648i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0518516 | − | 0.0518516i | 0.00218918 | − | 0.00218918i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.0660 | + | 14.0660i | −0.592809 | + | 0.592809i | −0.938389 | − | 0.345580i | \(-0.887682\pi\) |
0.345580 | + | 0.938389i | \(0.387682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.7324i | 0.830150i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.87207 | + | 5.87207i | −0.246604 | + | 0.246604i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 15.8567i | − | 0.664747i | −0.943148 | − | 0.332374i | \(-0.892151\pi\) | ||
0.943148 | − | 0.332374i | \(-0.107849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.86553 | + | 5.86553i | −0.245465 | + | 0.245465i | −0.819106 | − | 0.573642i | \(-0.805530\pi\) |
0.573642 | + | 0.819106i | \(0.305530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.29338 | −0.179359 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.72448 | 0.155322 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9767 | − | 14.9767i | 0.623489 | − | 0.623489i | −0.322933 | − | 0.946422i | \(-0.604669\pi\) |
0.946422 | + | 0.322933i | \(0.104669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.76766i | 0.239696i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.10361 | + | 5.10361i | −0.211733 | + | 0.211733i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.360196i | − | 0.0149178i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.1043 | − | 31.1043i | 1.28600 | − | 1.28600i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3988 | − | 17.3988i | 0.718123 | − | 0.718123i | −0.250097 | − | 0.968221i | \(-0.580463\pi\) |
0.968221 | + | 0.250097i | \(0.0804626\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.0204 | + | 26.0204i | 1.07215 | + | 1.07215i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.09898 | + | 5.09898i | 0.209744 | + | 0.209744i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0399 | + | 26.0399i | 1.06933 | + | 1.06933i | 0.997410 | + | 0.0719204i | \(0.0229128\pi\) |
0.0719204 | + | 0.997410i | \(0.477087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1467i | 0.538964i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.49072 | −0.265647 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.2062 | 1.31591 | 0.657956 | − | 0.753057i | \(-0.271421\pi\) | ||||
0.657956 | + | 0.753057i | \(0.271421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.54445 | − | 5.54445i | −0.226163 | − | 0.226163i | 0.584925 | − | 0.811088i | \(-0.301124\pi\) |
−0.811088 | + | 0.584925i | \(0.801124\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.8346 | + | 22.8346i | −0.929896 | + | 0.929896i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −34.3722 | −1.39743 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.212677i | 0.00863230i | 0.999991 | + | 0.00431615i | \(0.00137388\pi\) | ||||
−0.999991 | + | 0.00431615i | \(0.998626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.18517 | + | 1.18517i | 0.0480255 | + | 0.0480255i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.2852 | 1.18475 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.2498i | 1.62568i | 0.582490 | + | 0.812838i | \(0.302079\pi\) | ||||
−0.582490 | + | 0.812838i | \(0.697921\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.777884 | − | 5.53443i | 0.0313673 | − | 0.223170i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 41.6968i | − | 1.67865i | −0.543631 | − | 0.839324i | \(-0.682951\pi\) | ||
0.543631 | − | 0.839324i | \(-0.317049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.7221 | −1.47599 | −0.737993 | − | 0.674809i | \(-0.764226\pi\) | ||||
−0.737993 | + | 0.674809i | \(0.764226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.912800 | + | 0.912800i | 0.0366294 | + | 0.0366294i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7503i | 0.510828i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.0927 | −1.04371 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0930585 | + | 0.0930585i | −0.00371640 | + | 0.00371640i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.46329 | − | 4.46329i | −0.177963 | − | 0.177963i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.01872 | −0.359030 | −0.179515 | − | 0.983755i | \(-0.557453\pi\) | ||||
−0.179515 | + | 0.983755i | \(0.557453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.62400 | 0.144041 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.5554i | 1.25224i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.40539 | + | 3.40539i | 0.134926 | + | 0.134926i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.2000 | + | 18.2000i | 0.719982 | + | 0.719982i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.3192 | + | 27.3192i | 1.07904 | + | 1.07904i | 0.996595 | + | 0.0824465i | \(0.0262734\pi\) |
0.0824465 | + | 0.996595i | \(0.473727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.8634 | − | 27.8634i | 1.09882 | − | 1.09882i | 0.104275 | − | 0.994548i | \(-0.466748\pi\) |
0.994548 | − | 0.104275i | \(-0.0332524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.49397 | − | 1.49397i | 0.0588249 | − | 0.0588249i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6332i | 0.968430i | 0.874949 | + | 0.484215i | \(0.160895\pi\) | ||||
−0.874949 | + | 0.484215i | \(0.839105\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.258536 | − | 0.258536i | 0.0101484 | − | 0.0101484i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.36128i | − | 0.0533526i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.70523 | − | 6.70523i | 0.262396 | − | 0.262396i | −0.563631 | − | 0.826027i | \(-0.690596\pi\) |
0.826027 | + | 0.563631i | \(0.190596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.53550 | −0.0599968 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 39.0000 | 1.52154 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5120 | − | 13.5120i | 0.526351 | − | 0.526351i | −0.393131 | − | 0.919482i | \(-0.628608\pi\) |
0.919482 | + | 0.393131i | \(0.128608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.4896i | 1.80823i | 0.427285 | + | 0.904117i | \(0.359470\pi\) | ||||
−0.427285 | + | 0.904117i | \(0.640530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.99923 | − | 3.99923i | 0.155317 | − | 0.155317i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 23.5945i | − | 0.914957i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.31344 | + | 3.31344i | −0.128297 | + | 0.128297i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.10014 | − | 2.10014i | 0.0811961 | − | 0.0811961i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.387633 | − | 0.387633i | −0.0149644 | − | 0.0149644i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.17202 | + | 7.17202i | 0.276461 | + | 0.276461i | 0.831695 | − | 0.555233i | \(-0.187371\pi\) |
−0.555233 | + | 0.831695i | \(0.687371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.57856 | + | 5.57856i | 0.214719 | + | 0.214719i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 17.3396i | − | 0.666415i | −0.942854 | − | 0.333208i | \(-0.891869\pi\) | ||
0.942854 | − | 0.333208i | \(-0.108131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.5853 | 0.598108 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0716649 | 0.00274621 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.30935 | + | 9.30935i | 0.356212 | + | 0.356212i | 0.862415 | − | 0.506202i | \(-0.168951\pi\) |
−0.506202 | + | 0.862415i | \(0.668951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.0135 | + | 37.0135i | −1.41421 | + | 1.41421i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.87679 | −0.224213 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 27.7813i | − | 1.05838i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1097 | − | 22.1097i | −0.841094 | − | 0.841094i | 0.147908 | − | 0.989001i | \(-0.452746\pi\) |
−0.989001 | + | 0.147908i | \(0.952746\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.182454 | −0.00693084 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 62.5506i | 2.37268i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.74831 | + | 26.6682i | −0.141977 | + | 1.01013i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.45775i | 0.206431i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.47646 | −0.282382 | −0.141191 | − | 0.989982i | \(-0.545093\pi\) | ||||
−0.141191 | + | 0.989982i | \(0.545093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.01030 | + | 8.01030i | 0.302114 | + | 0.302114i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.30757i | 0.199895i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.0576 | −0.566299 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.87895 | − | 1.87895i | 0.0705656 | − | 0.0705656i | −0.670943 | − | 0.741509i | \(-0.734111\pi\) |
0.741509 | + | 0.670943i | \(0.234111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.9052 | − | 16.9052i | −0.633993 | − | 0.633993i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.80579 | 0.142528 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.939978 | 0.0351532 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.489748i | 0.0182900i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.9733 | − | 33.9733i | −1.26699 | − | 1.26699i | −0.947636 | − | 0.319353i | \(-0.896534\pi\) |
−0.319353 | − | 0.947636i | \(-0.603466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8667 | + | 13.8667i | 0.516422 | + | 0.516422i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00942 | − | 1.00942i | −0.0375409 | − | 0.0375409i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.2501 | + | 20.2501i | −0.752068 | + | 0.752068i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.5286 | + | 25.5286i | −0.946802 | + | 0.946802i | −0.998655 | − | 0.0518532i | \(-0.983487\pi\) |
0.0518532 | + | 0.998655i | \(0.483487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 22.8804i | − | 0.847422i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.19881 | + | 7.19881i | −0.266258 | + | 0.266258i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3586i | 0.936639i | 0.883559 | + | 0.468320i | \(0.155140\pi\) | ||||
−0.883559 | + | 0.468320i | \(0.844860\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.617183 | + | 0.617183i | −0.0227651 | + | 0.0227651i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.690067 | −0.0254189 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.2470 | 1.11265 | 0.556327 | − | 0.830964i | \(-0.312210\pi\) | ||||
0.556327 | + | 0.830964i | \(0.312210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.17744 | + | 7.17744i | −0.263670 | + | 0.263670i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.3795i | 1.48138i | 0.671848 | + | 0.740689i | \(0.265501\pi\) | ||||
−0.671848 | + | 0.740689i | \(0.734499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7571 | + | 12.7571i | −0.467383 | + | 0.467383i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 21.0900i | − | 0.771644i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.38239 | − | 1.38239i | 0.0505113 | − | 0.0505113i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.1052 | + | 22.1052i | −0.806628 | + | 0.806628i | −0.984122 | − | 0.177494i | \(-0.943201\pi\) |
0.177494 | + | 0.984122i | \(0.443201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.25141 | − | 1.25141i | −0.0456039 | − | 0.0456039i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.4032 | + | 20.4032i | 0.742549 | + | 0.742549i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.38191 | − | 2.38191i | −0.0865719 | − | 0.0865719i | 0.662495 | − | 0.749067i | \(-0.269498\pi\) |
−0.749067 | + | 0.662495i | \(0.769498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0136109i | 0.000494045i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.9273 | −0.831114 | −0.415557 | − | 0.909567i | \(-0.636413\pi\) | ||||
−0.415557 | + | 0.909567i | \(0.636413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.78115 | −0.209292 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.1636 | − | 27.1636i | −0.982103 | − | 0.982103i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.9404 | − | 19.9404i | 0.720007 | − | 0.720007i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.07809 | −0.219182 | −0.109591 | − | 0.993977i | \(-0.534954\pi\) | ||||
−0.109591 | + | 0.993977i | \(0.534954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.17149i | 0.258275i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.7106 | − | 32.7106i | −1.17652 | − | 1.17652i | −0.980625 | − | 0.195894i | \(-0.937239\pi\) |
−0.195894 | − | 0.980625i | \(-0.562761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.2590 | 0.835489 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.419065i | − | 0.0150339i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.72711 | − | 47.8616i | 0.241024 | − | 1.71482i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.550009i | 0.0196809i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.92582 | −0.354720 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.5562 | + | 11.5562i | 0.412459 | + | 0.412459i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.5774i | 0.840442i | 0.907422 | + | 0.420221i | \(0.138047\pi\) | ||||
−0.907422 | + | 0.420221i | \(0.861953\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.39383 | 0.120823 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.46372 | − | 4.46372i | 0.158712 | − | 0.158712i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.8975 | − | 29.8975i | −1.06169 | − | 1.06169i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.03501 | 0.178574 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.77084 | 0.204414 | 0.102207 | − | 0.994763i | \(-0.467410\pi\) | ||||
0.102207 | + | 0.994763i | \(0.467410\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 25.5750i | − | 0.904779i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.3444 | − | 26.3444i | −0.930835 | − | 0.930835i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.589295 | + | 0.589295i | 0.0207958 | + | 0.0207958i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.72549 | − | 1.72549i | −0.0608156 | − | 0.0608156i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.493592 | − | 0.493592i | 0.0173753 | − | 0.0173753i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.8270 | − | 21.8270i | 0.767398 | − | 0.767398i | −0.210250 | − | 0.977648i | \(-0.567428\pi\) |
0.977648 | + | 0.210250i | \(0.0674278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.60631i | 0.267094i | 0.991042 | + | 0.133547i | \(0.0426367\pi\) | ||||
−0.991042 | + | 0.133547i | \(0.957363\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.14161 | − | 4.14161i | 0.145253 | − | 0.145253i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 61.4374i | − | 2.15206i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9198 | − | 12.9198i | 0.452005 | − | 0.452005i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.0723 | −0.491727 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.66749 | 0.197797 | 0.0988983 | − | 0.995098i | \(-0.468468\pi\) | ||||
0.0988983 | + | 0.995098i | \(0.468468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.33364 | − | 5.33364i | 0.185919 | − | 0.185919i | −0.608010 | − | 0.793929i | \(-0.708032\pi\) |
0.793929 | + | 0.608010i | \(0.208032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0831829i | 0.00289606i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.4764 | − | 37.4764i | 1.30318 | − | 1.30318i | 0.376949 | − | 0.926234i | \(-0.376973\pi\) |
0.926234 | − | 0.376949i | \(-0.123027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.4575i | − | 0.849444i | −0.905324 | − | 0.424722i | \(-0.860372\pi\) | ||
0.905324 | − | 0.424722i | \(-0.139628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.305595 | + | 0.305595i | −0.0106010 | + | 0.0106010i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.97395 | − | 2.97395i | 0.103041 | − | 0.103041i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0489 | − | 16.0489i | −0.555396 | − | 0.555396i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.70035 | + | 5.70035i | 0.197033 | + | 0.197033i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.8896 | − | 40.8896i | −1.41167 | − | 1.41167i | −0.748248 | − | 0.663419i | \(-0.769105\pi\) |
−0.663419 | − | 0.748248i | \(-0.730895\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.03050i | − | 0.242431i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.226811 | 0.00781178 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.8629 | 1.09612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.77542 | + | 7.77542i | 0.267167 | + | 0.267167i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.23155 | + | 4.23155i | −0.145226 | + | 0.145226i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17160 | 0.0401620 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.3034i | − | 0.832134i | −0.909334 | − | 0.416067i | \(-0.863408\pi\) | ||
0.909334 | − | 0.416067i | \(-0.136592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48.7508 | + | 48.7508i | 1.66724 | + | 1.66724i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.3674 | 1.13981 | 0.569905 | − | 0.821711i | \(-0.306980\pi\) | ||||
0.569905 | + | 0.821711i | \(0.306980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.59218i | − | 0.327281i | −0.986520 | − | 0.163640i | \(-0.947676\pi\) | ||
0.986520 | − | 0.163640i | \(-0.0523237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.42792 | + | 1.07599i | −0.0486635 | + | 0.0366696i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 9.45642i | − | 0.321900i | −0.986963 | − | 0.160950i | \(-0.948544\pi\) | ||
0.986963 | − | 0.160950i | \(-0.0514558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3079 | 0.418480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.136000 | − | 0.136000i | −0.00461881 | − | 0.00461881i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.510878i | − | 0.0173303i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.2237 | −1.80342 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.2021 | + | 32.2021i | −1.08988 | + | 1.08988i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.506243 | + | 0.506243i | 0.0171141 | + | 0.0171141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.7642 | 0.937531 | 0.468766 | − | 0.883323i | \(-0.344699\pi\) | ||||
0.468766 | + | 0.883323i | \(0.344699\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.05160 | −0.0354696 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 11.5441i | − | 0.388930i | −0.980909 | − | 0.194465i | \(-0.937703\pi\) | ||
0.980909 | − | 0.194465i | \(-0.0622971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0676 | − | 11.0676i | −0.372453 | − | 0.372453i | 0.495917 | − | 0.868370i | \(-0.334832\pi\) |
−0.868370 | + | 0.495917i | \(0.834832\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.61395 | + | 3.61395i | 0.121482 | + | 0.121482i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.9764 | + | 31.9764i | 1.07366 | + | 1.07366i | 0.997062 | + | 0.0766007i | \(0.0244067\pi\) |
0.0766007 | + | 0.997062i | \(0.475593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.13822 | − | 7.13822i | 0.239408 | − | 0.239408i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.366656 | − | 0.366656i | 0.0122834 | − | 0.0122834i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.8997i | 1.53598i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.6672 | + | 36.6672i | −1.22565 | + | 1.22565i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.04979i | 0.0350514i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.6922 | + | 20.6922i | −0.690122 | + | 0.690122i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.2617 | −0.808274 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.675907 | −0.0224928 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.5320 | − | 34.5320i | 1.14788 | − | 1.14788i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 12.2822i | − | 0.407825i | −0.978989 | − | 0.203912i | \(-0.934634\pi\) | ||
0.978989 | − | 0.203912i | \(-0.0653658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.1118 | − | 31.1118i | 1.03191 | − | 1.03191i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3599i | 0.608291i | 0.952626 | + | 0.304146i | \(0.0983709\pi\) | ||||
−0.952626 | + | 0.304146i | \(0.901629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.318673 | − | 0.318673i | 0.0105465 | − | 0.0105465i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.41853 | − | 5.41853i | 0.179131 | − | 0.179131i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.347348 | + | 0.347348i | 0.0114704 | + | 0.0114704i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2017 | + | 10.2017i | 0.336524 | + | 0.336524i | 0.855057 | − | 0.518534i | \(-0.173522\pi\) |
−0.518534 | + | 0.855057i | \(0.673522\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.95603 | − | 2.95603i | −0.0974046 | − | 0.0974046i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.4213i | 1.39631i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.16023 | 0.235427 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −57.3024 | −1.88206 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.2565 | − | 35.2565i | −1.15673 | − | 1.15673i | −0.985175 | − | 0.171555i | \(-0.945121\pi\) |
−0.171555 | − | 0.985175i | \(-0.554879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.33738 | + | 5.33738i | −0.174926 | + | 0.174926i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.84555 | −0.289590 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.820891i | − | 0.0268460i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0764 | − | 27.0764i | −0.884548 | − | 0.884548i | 0.109445 | − | 0.993993i | \(-0.465093\pi\) |
−0.993993 | + | 0.109445i | \(0.965093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.55423 | −0.213889 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 53.8999i | − | 1.75709i | −0.477664 | − | 0.878543i | \(-0.658516\pi\) | ||
0.477664 | − | 0.878543i | \(-0.341484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.00820 | − | 3.99213i | −0.0979606 | − | 0.130001i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 5.16892i | − | 0.168145i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.7842 | 1.32531 | 0.662654 | − | 0.748925i | \(-0.269430\pi\) | ||||
0.662654 | + | 0.748925i | \(0.269430\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.4513 | + | 45.4513i | 1.47541 | + | 1.47541i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.25293i | 0.0406292i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.3796 | 0.984092 | 0.492046 | − | 0.870569i | \(-0.336249\pi\) | ||||
0.492046 | + | 0.870569i | \(0.336249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.9854 | + | 33.9854i | −1.09974 | + | 1.09974i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0740028 | − | 0.0740028i | −0.00239217 | − | 0.00239217i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.7458 | 0.540750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.23316 | −0.233328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.71254i | 0.184084i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.6555 | + | 45.6555i | 1.46970 | + | 1.46970i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0024 | + | 17.0024i | 0.546761 | + | 0.546761i | 0.925503 | − | 0.378741i | \(-0.123643\pi\) |
−0.378741 | + | 0.925503i | \(0.623643\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.26812 | + | 6.26812i | 0.201361 | + | 0.201361i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.7973 | − | 12.7973i | 0.410685 | − | 0.410685i | −0.471292 | − | 0.881977i | \(-0.656212\pi\) |
0.881977 | + | 0.471292i | \(0.156212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1497 | − | 14.1497i | 0.453619 | − | 0.453619i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.41576i | 0.205469i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.6468 | − | 43.6468i | 1.39639 | − | 1.39639i | 0.586267 | − | 0.810118i | \(-0.300597\pi\) |
0.810118 | − | 0.586267i | \(-0.199403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.796135i | − | 0.0254446i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.9450 | − | 11.9450i | 0.381373 | − | 0.381373i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3898 | 0.873598 | 0.436799 | − | 0.899559i | \(-0.356112\pi\) | ||||
0.436799 | + | 0.899559i | \(0.356112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 80.7247 | 2.57210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.20064 | − | 1.20064i | 0.0382167 | − | 0.0382167i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.88967i | − | 0.0600880i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.8514 | + | 34.8514i | −1.10709 | + | 1.10709i | −0.113559 | + | 0.993531i | \(0.536225\pi\) |
−0.993531 | + | 0.113559i | \(0.963775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.170955i | 0.00542509i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.3790 | + | 51.3790i | −1.62883 | + | 1.62883i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.5574 | − | 21.5574i | 0.682729 | − | 0.682729i | −0.277886 | − | 0.960614i | \(-0.589634\pi\) |
0.960614 | + | 0.277886i | \(0.0896336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.75484 | + | 1.75484i | 0.0555206 | + | 0.0555206i |
(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 | 1148.2.k.b.729.9 | yes | 36 | |
41.9 | even | 4 | inner | 1148.2.k.b.337.9 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.9 | ✓ | 36 | 41.9 | even | 4 | inner | |
1148.2.k.b.729.9 | yes | 36 | 1.1 | even | 1 | trivial |