Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.40 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.38 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 4.99818 | − | 0.134731i | 0.999637 | − | 0.0269461i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −11.0735 | −1.58193 | −0.790966 | − | 0.611860i | \(-0.790422\pi\) | ||||
−0.790966 | + | 0.611860i | \(0.790422\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0.190538 | + | 7.06850i | 0.0190538 | + | 0.706850i | ||||
\(11\) | − | 9.44141i | − | 0.858310i | −0.903231 | − | 0.429155i | \(-0.858811\pi\) | ||
0.903231 | − | 0.429155i | \(-0.141189\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | − | 22.3707i | − | 1.72082i | −0.509599 | − | 0.860412i | \(-0.670206\pi\) | ||
0.509599 | − | 0.860412i | \(-0.329794\pi\) | |||||||
\(14\) | − | 15.6603i | − | 1.11859i | ||||||
\(15\) | 0.233360 | + | 8.65711i | 0.0155574 | + | 0.577141i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 29.3065 | 1.72391 | 0.861957 | − | 0.506982i | \(-0.169239\pi\) | ||||
0.861957 | + | 0.506982i | \(0.169239\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | 31.8609i | 1.67689i | 0.544985 | + | 0.838446i | \(0.316535\pi\) | ||||
−0.544985 | + | 0.838446i | \(0.683465\pi\) | |||||||
\(20\) | −9.99637 | + | 0.269461i | −0.499818 | + | 0.0134731i | ||||
\(21\) | − | 19.1799i | − | 0.913329i | ||||||
\(22\) | 13.3522 | 0.606917 | ||||||||
\(23\) | 20.6810 | − | 10.0645i | 0.899176 | − | 0.437588i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | 24.9637 | − | 1.34682i | 0.998548 | − | 0.0538727i | ||||
\(26\) | 31.6370 | 1.21681 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 22.1470 | 0.790966 | ||||||||
\(29\) | 21.8003 | 0.751733 | 0.375867 | − | 0.926674i | \(-0.377345\pi\) | ||||
0.375867 | + | 0.926674i | \(0.377345\pi\) | |||||||
\(30\) | −12.2430 | + | 0.330021i | −0.408100 | + | 0.0110007i | ||||
\(31\) | −33.9150 | −1.09403 | −0.547016 | − | 0.837122i | \(-0.684236\pi\) | ||||
−0.547016 | + | 0.837122i | \(0.684236\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 16.3530 | 0.495545 | ||||||||
\(34\) | 41.4457i | 1.21899i | ||||||||
\(35\) | −55.3475 | + | 1.49194i | −1.58136 | + | 0.0426269i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 7.59191 | 0.205187 | 0.102593 | − | 0.994723i | \(-0.467286\pi\) | ||||
0.102593 | + | 0.994723i | \(0.467286\pi\) | |||||||
\(38\) | −45.0582 | −1.18574 | ||||||||
\(39\) | 38.7472 | 0.993518 | ||||||||
\(40\) | −0.381076 | − | 14.1370i | −0.00952689 | − | 0.353425i | ||||
\(41\) | 55.7647 | 1.36011 | 0.680057 | − | 0.733159i | \(-0.261955\pi\) | ||||
0.680057 | + | 0.733159i | \(0.261955\pi\) | |||||||
\(42\) | 27.1245 | 0.645821 | ||||||||
\(43\) | −22.0768 | −0.513413 | −0.256707 | − | 0.966489i | \(-0.582637\pi\) | ||||
−0.256707 | + | 0.966489i | \(0.582637\pi\) | |||||||
\(44\) | 18.8828i | 0.429155i | ||||||||
\(45\) | −14.9946 | + | 0.404192i | −0.333212 | + | 0.00898204i | ||||
\(46\) | 14.2334 | + | 29.2474i | 0.309421 | + | 0.635813i | ||||
\(47\) | − | 77.2646i | − | 1.64393i | −0.569539 | − | 0.821964i | \(-0.692878\pi\) | ||
0.569539 | − | 0.821964i | \(-0.307122\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 73.6229 | 1.50251 | ||||||||
\(50\) | 1.90469 | + | 35.3040i | 0.0380937 | + | 0.706080i | ||||
\(51\) | 50.7604i | 0.995302i | ||||||||
\(52\) | 44.7414i | 0.860412i | ||||||||
\(53\) | −39.1954 | −0.739535 | −0.369768 | − | 0.929124i | \(-0.620563\pi\) | ||||
−0.369768 | + | 0.929124i | \(0.620563\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | −1.27205 | − | 47.1899i | −0.0231281 | − | 0.857998i | ||||
\(56\) | 31.3207i | 0.559297i | ||||||||
\(57\) | −55.1848 | −0.968154 | ||||||||
\(58\) | 30.8302i | 0.531556i | ||||||||
\(59\) | 70.2950 | 1.19144 | 0.595720 | − | 0.803192i | \(-0.296867\pi\) | ||||
0.595720 | + | 0.803192i | \(0.296867\pi\) | |||||||
\(60\) | −0.466721 | − | 17.3142i | −0.00777868 | − | 0.288570i | ||||
\(61\) | − | 31.9143i | − | 0.523185i | −0.965178 | − | 0.261592i | \(-0.915752\pi\) | ||
0.965178 | − | 0.261592i | \(-0.0842476\pi\) | |||||||
\(62\) | − | 47.9630i | − | 0.773597i | ||||||
\(63\) | 33.2206 | 0.527311 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −3.01402 | − | 111.813i | −0.0463695 | − | 1.72020i | ||||
\(66\) | 23.1266i | 0.350403i | ||||||||
\(67\) | 21.9858 | 0.328147 | 0.164073 | − | 0.986448i | \(-0.447537\pi\) | ||||
0.164073 | + | 0.986448i | \(0.447537\pi\) | |||||||
\(68\) | −58.6131 | −0.861957 | ||||||||
\(69\) | 17.4322 | + | 35.8206i | 0.252641 | + | 0.519139i | ||||
\(70\) | −2.10993 | − | 78.2732i | −0.0301418 | − | 1.11819i | ||||
\(71\) | −31.2687 | −0.440404 | −0.220202 | − | 0.975454i | \(-0.570672\pi\) | ||||
−0.220202 | + | 0.975454i | \(0.570672\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | − | 64.0595i | − | 0.877527i | −0.898602 | − | 0.438764i | \(-0.855417\pi\) | ||
0.898602 | − | 0.438764i | \(-0.144583\pi\) | |||||||
\(74\) | 10.7366i | 0.145089i | ||||||||
\(75\) | 2.33276 | + | 43.2384i | 0.0311034 | + | 0.576512i | ||||
\(76\) | − | 63.7219i | − | 0.838446i | ||||||
\(77\) | 104.550i | 1.35779i | ||||||||
\(78\) | 54.7968i | 0.702524i | ||||||||
\(79\) | − | 8.93982i | − | 0.113162i | −0.998398 | − | 0.0565812i | \(-0.981980\pi\) | ||
0.998398 | − | 0.0565812i | \(-0.0180200\pi\) | |||||||
\(80\) | 19.9927 | − | 0.538922i | 0.249909 | − | 0.00673653i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 78.8632i | 0.961746i | ||||||||
\(83\) | 6.63429 | 0.0799312 | 0.0399656 | − | 0.999201i | \(-0.487275\pi\) | ||||
0.0399656 | + | 0.999201i | \(0.487275\pi\) | |||||||
\(84\) | 38.3598i | 0.456664i | ||||||||
\(85\) | 146.479 | − | 3.94849i | 1.72329 | − | 0.0464528i | ||||
\(86\) | − | 31.2213i | − | 0.363038i | ||||||
\(87\) | 37.7592i | 0.434013i | ||||||||
\(88\) | −26.7043 | −0.303458 | ||||||||
\(89\) | 153.281i | 1.72226i | 0.508383 | + | 0.861131i | \(0.330243\pi\) | ||||
−0.508383 | + | 0.861131i | \(0.669757\pi\) | |||||||
\(90\) | −0.571614 | − | 21.2055i | −0.00635126 | − | 0.235617i | ||||
\(91\) | 247.723i | 2.72223i | ||||||||
\(92\) | −41.3621 | + | 20.1290i | −0.449588 | + | 0.218794i | ||||
\(93\) | − | 58.7425i | − | 0.631639i | ||||||
\(94\) | 109.269 | 1.16243 | ||||||||
\(95\) | 4.29264 | + | 159.247i | 0.0451857 | + | 1.67628i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 71.0282 | 0.732249 | 0.366125 | − | 0.930566i | \(-0.380684\pi\) | ||||
0.366125 | + | 0.930566i | \(0.380684\pi\) | |||||||
\(98\) | 104.119i | 1.06243i | ||||||||
\(99\) | 28.3242i | 0.286103i | ||||||||
\(100\) | −49.9274 | + | 2.69363i | −0.499274 | + | 0.0269363i | ||||
\(101\) | −138.006 | −1.36639 | −0.683196 | − | 0.730235i | \(-0.739410\pi\) | ||||
−0.683196 | + | 0.730235i | \(0.739410\pi\) | |||||||
\(102\) | −71.7860 | −0.703785 | ||||||||
\(103\) | 14.2828 | 0.138668 | 0.0693338 | − | 0.997594i | \(-0.477913\pi\) | ||||
0.0693338 | + | 0.997594i | \(0.477913\pi\) | |||||||
\(104\) | −63.2739 | −0.608403 | ||||||||
\(105\) | −2.58412 | − | 95.8647i | −0.0246107 | − | 0.912997i | ||||
\(106\) | − | 55.4306i | − | 0.522930i | ||||||
\(107\) | 175.517 | 1.64035 | 0.820173 | − | 0.572116i | \(-0.193877\pi\) | ||||
0.820173 | + | 0.572116i | \(0.193877\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | − | 162.959i | − | 1.49503i | −0.664243 | − | 0.747517i | \(-0.731246\pi\) | ||
0.664243 | − | 0.747517i | \(-0.268754\pi\) | |||||||
\(110\) | 66.7366 | − | 1.79895i | 0.606696 | − | 0.0163540i | ||||
\(111\) | 13.1496i | 0.118465i | ||||||||
\(112\) | −44.2941 | −0.395483 | ||||||||
\(113\) | −66.7137 | −0.590387 | −0.295194 | − | 0.955437i | \(-0.595384\pi\) | ||||
−0.295194 | + | 0.955437i | \(0.595384\pi\) | |||||||
\(114\) | − | 78.0431i | − | 0.684588i | ||||||
\(115\) | 102.012 | − | 53.0907i | 0.887058 | − | 0.461658i | ||||
\(116\) | −43.6005 | −0.375867 | ||||||||
\(117\) | 67.1121i | 0.573608i | ||||||||
\(118\) | 99.4121i | 0.842476i | ||||||||
\(119\) | −324.527 | −2.72711 | ||||||||
\(120\) | 24.4860 | − | 0.660042i | 0.204050 | − | 0.00550035i | ||||
\(121\) | 31.8598 | 0.263304 | ||||||||
\(122\) | 45.1336 | 0.369948 | ||||||||
\(123\) | 96.5873i | 0.785262i | ||||||||
\(124\) | 67.8299 | 0.547016 | ||||||||
\(125\) | 124.592 | − | 10.0950i | 0.996734 | − | 0.0807601i | ||||
\(126\) | 46.9810i | 0.372865i | ||||||||
\(127\) | − | 32.5760i | − | 0.256504i | −0.991742 | − | 0.128252i | \(-0.959063\pi\) | ||
0.991742 | − | 0.128252i | \(-0.0409366\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | − | 38.2381i | − | 0.296419i | ||||||
\(130\) | 158.127 | − | 4.26247i | 1.21636 | − | 0.0327882i | ||||
\(131\) | 120.875 | 0.922708 | 0.461354 | − | 0.887216i | \(-0.347364\pi\) | ||||
0.461354 | + | 0.887216i | \(0.347364\pi\) | |||||||
\(132\) | −32.7060 | −0.247773 | ||||||||
\(133\) | − | 352.813i | − | 2.65273i | ||||||
\(134\) | 31.0926i | 0.232035i | ||||||||
\(135\) | −0.700081 | − | 25.9713i | −0.00518578 | − | 0.192380i | ||||
\(136\) | − | 82.8914i | − | 0.609495i | ||||||
\(137\) | −17.4362 | −0.127271 | −0.0636356 | − | 0.997973i | \(-0.520270\pi\) | ||||
−0.0636356 | + | 0.997973i | \(0.520270\pi\) | |||||||
\(138\) | −50.6580 | + | 24.6529i | −0.367087 | + | 0.178644i | ||||
\(139\) | −140.316 | −1.00947 | −0.504734 | − | 0.863275i | \(-0.668409\pi\) | ||||
−0.504734 | + | 0.863275i | \(0.668409\pi\) | |||||||
\(140\) | 110.695 | − | 2.98388i | 0.790679 | − | 0.0213135i | ||||
\(141\) | 133.826 | 0.949122 | ||||||||
\(142\) | − | 44.2206i | − | 0.311413i | ||||||
\(143\) | −211.211 | −1.47700 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 108.962 | − | 2.93716i | 0.751460 | − | 0.0202563i | ||||
\(146\) | 90.5938 | 0.620506 | ||||||||
\(147\) | 127.519i | 0.867474i | ||||||||
\(148\) | −15.1838 | −0.102593 | ||||||||
\(149\) | 32.9711i | 0.221283i | 0.993860 | + | 0.110641i | \(0.0352905\pi\) | ||||
−0.993860 | + | 0.110641i | \(0.964710\pi\) | |||||||
\(150\) | −61.1483 | + | 3.29901i | −0.407655 | + | 0.0219934i | ||||
\(151\) | 241.409 | 1.59873 | 0.799366 | − | 0.600844i | \(-0.205169\pi\) | ||||
0.799366 | + | 0.600844i | \(0.205169\pi\) | |||||||
\(152\) | 90.1164 | 0.592871 | ||||||||
\(153\) | −87.9196 | −0.574638 | ||||||||
\(154\) | −147.856 | −0.960101 | ||||||||
\(155\) | −169.513 | + | 4.56938i | −1.09363 | + | 0.0294799i | ||||
\(156\) | −77.4944 | −0.496759 | ||||||||
\(157\) | 67.8434 | 0.432123 | 0.216062 | − | 0.976380i | \(-0.430679\pi\) | ||||
0.216062 | + | 0.976380i | \(0.430679\pi\) | |||||||
\(158\) | 12.6428 | 0.0800178 | ||||||||
\(159\) | − | 67.8884i | − | 0.426971i | ||||||
\(160\) | 0.762151 | + | 28.2740i | 0.00476345 | + | 0.176713i | ||||
\(161\) | −229.012 | + | 111.450i | −1.42243 | + | 0.692234i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | − | 222.059i | − | 1.36232i | −0.732133 | − | 0.681162i | \(-0.761475\pi\) | ||
0.732133 | − | 0.681162i | \(-0.238525\pi\) | |||||||
\(164\) | −111.529 | −0.680057 | ||||||||
\(165\) | 81.7353 | − | 2.20325i | 0.495365 | − | 0.0133530i | ||||
\(166\) | 9.38230i | 0.0565199i | ||||||||
\(167\) | − | 223.321i | − | 1.33725i | −0.743599 | − | 0.668626i | \(-0.766883\pi\) | ||
0.743599 | − | 0.668626i | \(-0.233117\pi\) | |||||||
\(168\) | −54.2490 | −0.322910 | ||||||||
\(169\) | −331.449 | −1.96124 | ||||||||
\(170\) | 5.58400 | + | 207.153i | 0.0328471 | + | 1.21855i | ||||
\(171\) | − | 95.5828i | − | 0.558964i | ||||||
\(172\) | 44.1536 | 0.256707 | ||||||||
\(173\) | − | 30.8477i | − | 0.178310i | −0.996018 | − | 0.0891551i | \(-0.971583\pi\) | ||
0.996018 | − | 0.0891551i | \(-0.0284167\pi\) | |||||||
\(174\) | −53.3995 | −0.306894 | ||||||||
\(175\) | −276.436 | + | 14.9140i | −1.57963 | + | 0.0852229i | ||||
\(176\) | − | 37.7656i | − | 0.214577i | ||||||
\(177\) | 121.755i | 0.687879i | ||||||||
\(178\) | −216.773 | −1.21782 | ||||||||
\(179\) | 55.2209 | 0.308497 | 0.154248 | − | 0.988032i | \(-0.450704\pi\) | ||||
0.154248 | + | 0.988032i | \(0.450704\pi\) | |||||||
\(180\) | 29.9891 | − | 0.808384i | 0.166606 | − | 0.00449102i | ||||
\(181\) | 45.7487i | 0.252755i | 0.991982 | + | 0.126378i | \(0.0403351\pi\) | ||||
−0.991982 | + | 0.126378i | \(0.959665\pi\) | |||||||
\(182\) | −350.333 | −1.92491 | ||||||||
\(183\) | 55.2771 | 0.302061 | ||||||||
\(184\) | −28.4667 | − | 58.4948i | −0.154711 | − | 0.317907i | ||||
\(185\) | 37.9458 | − | 1.02286i | 0.205112 | − | 0.00552899i | ||||
\(186\) | 83.0744 | 0.446636 | ||||||||
\(187\) | − | 276.695i | − | 1.47965i | ||||||
\(188\) | 154.529i | 0.821964i | ||||||||
\(189\) | 57.5397i | 0.304443i | ||||||||
\(190\) | −225.209 | + | 6.07072i | −1.18531 | + | 0.0319511i | ||||
\(191\) | − | 140.527i | − | 0.735745i | −0.929876 | − | 0.367873i | \(-0.880086\pi\) | ||
0.929876 | − | 0.367873i | \(-0.119914\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | − | 171.323i | − | 0.887683i | −0.896105 | − | 0.443842i | \(-0.853615\pi\) | ||
0.896105 | − | 0.443842i | \(-0.146385\pi\) | |||||||
\(194\) | 100.449i | 0.517779i | ||||||||
\(195\) | 193.666 | − | 5.22044i | 0.993158 | − | 0.0267715i | ||||
\(196\) | −147.246 | −0.751254 | ||||||||
\(197\) | 47.7742i | 0.242509i | 0.992621 | + | 0.121254i | \(0.0386916\pi\) | ||||
−0.992621 | + | 0.121254i | \(0.961308\pi\) | |||||||
\(198\) | −40.0565 | −0.202306 | ||||||||
\(199\) | 45.4098i | 0.228190i | 0.993470 | + | 0.114095i | \(0.0363968\pi\) | ||||
−0.993470 | + | 0.114095i | \(0.963603\pi\) | |||||||
\(200\) | −3.80937 | − | 70.6080i | −0.0190469 | − | 0.353040i | ||||
\(201\) | 38.0806i | 0.189456i | ||||||||
\(202\) | − | 195.169i | − | 0.966185i | ||||||
\(203\) | −241.406 | −1.18919 | ||||||||
\(204\) | − | 101.521i | − | 0.497651i | ||||||
\(205\) | 278.722 | − | 7.51321i | 1.35962 | − | 0.0366498i | ||||
\(206\) | 20.1989i | 0.0980528i | ||||||||
\(207\) | −62.0431 | + | 30.1935i | −0.299725 | + | 0.145863i | ||||
\(208\) | − | 89.4829i | − | 0.430206i | ||||||
\(209\) | 300.812 | 1.43929 | ||||||||
\(210\) | 135.573 | − | 3.65450i | 0.645586 | − | 0.0174024i | ||||
\(211\) | −125.035 | −0.592585 | −0.296293 | − | 0.955097i | \(-0.595750\pi\) | ||||
−0.296293 | + | 0.955097i | \(0.595750\pi\) | |||||||
\(212\) | 78.3907 | 0.369768 | ||||||||
\(213\) | − | 54.1589i | − | 0.254267i | ||||||
\(214\) | 248.219i | 1.15990i | ||||||||
\(215\) | −110.344 | + | 2.97442i | −0.513227 | + | 0.0138345i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 375.558 | 1.73068 | ||||||||
\(218\) | 230.458 | 1.05715 | ||||||||
\(219\) | 110.954 | 0.506641 | ||||||||
\(220\) | 2.54409 | + | 94.3798i | 0.0115641 | + | 0.428999i | ||||
\(221\) | − | 655.608i | − | 2.96655i | ||||||
\(222\) | −18.5963 | −0.0837672 | ||||||||
\(223\) | 398.218i | 1.78573i | 0.450324 | + | 0.892865i | \(0.351308\pi\) | ||||
−0.450324 | + | 0.892865i | \(0.648692\pi\) | |||||||
\(224\) | − | 62.6413i | − | 0.279649i | ||||||
\(225\) | −74.8911 | + | 4.04045i | −0.332849 | + | 0.0179576i | ||||
\(226\) | − | 94.3475i | − | 0.417467i | ||||||
\(227\) | 120.751 | 0.531945 | 0.265972 | − | 0.963981i | \(-0.414307\pi\) | ||||
0.265972 | + | 0.963981i | \(0.414307\pi\) | |||||||
\(228\) | 110.370 | 0.484077 | ||||||||
\(229\) | 2.35749i | 0.0102947i | 0.999987 | + | 0.00514735i | \(0.00163846\pi\) | ||||
−0.999987 | + | 0.00514735i | \(0.998362\pi\) | |||||||
\(230\) | 75.0815 | + | 144.266i | 0.326441 | + | 0.627245i | ||||
\(231\) | −181.085 | −0.783919 | ||||||||
\(232\) | − | 61.6605i | − | 0.265778i | ||||||
\(233\) | − | 80.4920i | − | 0.345459i | −0.984969 | − | 0.172730i | \(-0.944741\pi\) | ||
0.984969 | − | 0.172730i | \(-0.0552587\pi\) | |||||||
\(234\) | −94.9109 | −0.405602 | ||||||||
\(235\) | −10.4099 | − | 386.183i | −0.0442975 | − | 1.64333i | ||||
\(236\) | −140.590 | −0.595720 | ||||||||
\(237\) | 15.4842 | 0.0653343 | ||||||||
\(238\) | − | 458.950i | − | 1.92836i | ||||||
\(239\) | −177.239 | −0.741584 | −0.370792 | − | 0.928716i | \(-0.620914\pi\) | ||||
−0.370792 | + | 0.928716i | \(0.620914\pi\) | |||||||
\(240\) | 0.933441 | + | 34.6284i | 0.00388934 | + | 0.144285i | ||||
\(241\) | 373.299i | 1.54896i | 0.632600 | + | 0.774479i | \(0.281988\pi\) | ||||
−0.632600 | + | 0.774479i | \(0.718012\pi\) | |||||||
\(242\) | 45.0566i | 0.186184i | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 63.8285i | 0.261592i | ||||||||
\(245\) | 367.981 | − | 9.91926i | 1.50196 | − | 0.0404868i | ||||
\(246\) | −136.595 | −0.555264 | ||||||||
\(247\) | 712.752 | 2.88564 | ||||||||
\(248\) | 95.9260i | 0.386798i | ||||||||
\(249\) | 11.4909i | 0.0461483i | ||||||||
\(250\) | 14.2765 | + | 176.199i | 0.0571060 | + | 0.704797i | ||||
\(251\) | − | 78.0057i | − | 0.310780i | −0.987853 | − | 0.155390i | \(-0.950337\pi\) | ||
0.987853 | − | 0.155390i | \(-0.0496633\pi\) | |||||||
\(252\) | −66.4411 | −0.263655 | ||||||||
\(253\) | −95.0232 | − | 195.258i | −0.375586 | − | 0.771771i | ||||
\(254\) | 46.0694 | 0.181375 | ||||||||
\(255\) | 6.83898 | + | 253.710i | 0.0268195 | + | 0.994940i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 163.162i | − | 0.634872i | −0.948280 | − | 0.317436i | \(-0.897178\pi\) | ||
0.948280 | − | 0.317436i | \(-0.102822\pi\) | |||||||
\(258\) | 54.0768 | 0.209600 | ||||||||
\(259\) | −84.0692 | −0.324592 | ||||||||
\(260\) | 6.02804 | + | 223.626i | 0.0231848 | + | 0.860100i | ||||
\(261\) | −65.4008 | −0.250578 | ||||||||
\(262\) | 170.943i | 0.652453i | ||||||||
\(263\) | 40.0337 | 0.152219 | 0.0761097 | − | 0.997099i | \(-0.475750\pi\) | ||||
0.0761097 | + | 0.997099i | \(0.475750\pi\) | |||||||
\(264\) | − | 46.2533i | − | 0.175202i | ||||||
\(265\) | −195.906 | + | 5.28082i | −0.739267 | + | 0.0199276i | ||||
\(266\) | 498.953 | 1.87576 | ||||||||
\(267\) | −265.491 | −0.994348 | ||||||||
\(268\) | −43.9716 | −0.164073 | ||||||||
\(269\) | −284.506 | −1.05764 | −0.528822 | − | 0.848733i | \(-0.677366\pi\) | ||||
−0.528822 | + | 0.848733i | \(0.677366\pi\) | |||||||
\(270\) | 36.7290 | − | 0.990064i | 0.136033 | − | 0.00366690i | ||||
\(271\) | −443.178 | −1.63534 | −0.817671 | − | 0.575685i | \(-0.804735\pi\) | ||||
−0.817671 | + | 0.575685i | \(0.804735\pi\) | |||||||
\(272\) | 117.226 | 0.430978 | ||||||||
\(273\) | −429.068 | −1.57168 | ||||||||
\(274\) | − | 24.6585i | − | 0.0899944i | ||||||
\(275\) | −12.7158 | − | 235.692i | −0.0462394 | − | 0.857063i | ||||
\(276\) | −34.8645 | − | 71.6412i | −0.126321 | − | 0.259570i | ||||
\(277\) | 314.272i | 1.13456i | 0.823526 | + | 0.567279i | \(0.192004\pi\) | ||||
−0.823526 | + | 0.567279i | \(0.807996\pi\) | |||||||
\(278\) | − | 198.437i | − | 0.713802i | ||||||
\(279\) | 101.745 | 0.364677 | ||||||||
\(280\) | 4.21985 | + | 156.546i | 0.0150709 | + | 0.559094i | ||||
\(281\) | 71.4214i | 0.254169i | 0.991892 | + | 0.127084i | \(0.0405619\pi\) | ||||
−0.991892 | + | 0.127084i | \(0.959438\pi\) | |||||||
\(282\) | 189.259i | 0.671131i | ||||||||
\(283\) | −203.792 | −0.720113 | −0.360057 | − | 0.932930i | \(-0.617243\pi\) | ||||
−0.360057 | + | 0.932930i | \(0.617243\pi\) | |||||||
\(284\) | 62.5373 | 0.220202 | ||||||||
\(285\) | −275.824 | + | 7.43508i | −0.967802 | + | 0.0260880i | ||||
\(286\) | − | 298.697i | − | 1.04440i | ||||||
\(287\) | −617.512 | −2.15161 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 569.873 | 1.97188 | ||||||||
\(290\) | 4.15378 | + | 154.095i | 0.0143234 | + | 0.531363i | ||||
\(291\) | 123.024i | 0.422764i | ||||||||
\(292\) | 128.119i | 0.438764i | ||||||||
\(293\) | −36.5407 | −0.124712 | −0.0623562 | − | 0.998054i | \(-0.519861\pi\) | ||||
−0.0623562 | + | 0.998054i | \(0.519861\pi\) | |||||||
\(294\) | −180.339 | −0.613397 | ||||||||
\(295\) | 351.347 | − | 9.47089i | 1.19101 | − | 0.0321047i | ||||
\(296\) | − | 21.4732i | − | 0.0725445i | ||||||
\(297\) | −49.0590 | −0.165182 | ||||||||
\(298\) | −46.6282 | −0.156470 | ||||||||
\(299\) | −225.150 | − | 462.650i | −0.753011 | − | 1.54732i | ||||
\(300\) | −4.66551 | − | 86.4768i | −0.0155517 | − | 0.288256i | ||||
\(301\) | 244.468 | 0.812185 | ||||||||
\(302\) | 341.403i | 1.13047i | ||||||||
\(303\) | − | 239.033i | − | 0.788887i | ||||||
\(304\) | 127.444i | 0.419223i | ||||||||
\(305\) | −4.29983 | − | 159.513i | −0.0140978 | − | 0.522995i | ||||
\(306\) | − | 124.337i | − | 0.406330i | ||||||
\(307\) | 128.731i | 0.419319i | 0.977774 | + | 0.209659i | \(0.0672355\pi\) | ||||
−0.977774 | + | 0.209659i | \(0.932764\pi\) | |||||||
\(308\) | − | 209.099i | − | 0.678894i | ||||||
\(309\) | 24.7385i | 0.0800598i | ||||||||
\(310\) | −6.46209 | − | 239.728i | −0.0208454 | − | 0.773316i | ||||
\(311\) | −480.481 | −1.54495 | −0.772477 | − | 0.635043i | \(-0.780982\pi\) | ||||
−0.772477 | + | 0.635043i | \(0.780982\pi\) | |||||||
\(312\) | − | 109.594i | − | 0.351262i | ||||||
\(313\) | −262.271 | −0.837926 | −0.418963 | − | 0.908003i | \(-0.637606\pi\) | ||||
−0.418963 | + | 0.908003i | \(0.637606\pi\) | |||||||
\(314\) | 95.9450i | 0.305557i | ||||||||
\(315\) | 166.043 | − | 4.47583i | 0.527119 | − | 0.0142090i | ||||
\(316\) | 17.8796i | 0.0565812i | ||||||||
\(317\) | 361.397i | 1.14005i | 0.821626 | + | 0.570027i | \(0.193067\pi\) | ||||
−0.821626 | + | 0.570027i | \(0.806933\pi\) | |||||||
\(318\) | 96.0086 | 0.301914 | ||||||||
\(319\) | − | 205.825i | − | 0.645220i | ||||||
\(320\) | −39.9855 | + | 1.07784i | −0.124955 | + | 0.00336827i | ||||
\(321\) | 304.004i | 0.947054i | ||||||||
\(322\) | −157.614 | − | 323.872i | −0.489483 | − | 1.00581i | ||||
\(323\) | 933.734i | 2.89082i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | −30.1293 | − | 558.456i | −0.0927054 | − | 1.71833i | ||||
\(326\) | 314.039 | 0.963309 | ||||||||
\(327\) | 282.253 | 0.863158 | ||||||||
\(328\) | − | 157.726i | − | 0.480873i | ||||||
\(329\) | 855.592i | 2.60058i | ||||||||
\(330\) | 3.11586 | + | 115.591i | 0.00944201 | + | 0.350276i | ||||
\(331\) | 219.463 | 0.663032 | 0.331516 | − | 0.943450i | \(-0.392440\pi\) | ||||
0.331516 | + | 0.943450i | \(0.392440\pi\) | |||||||
\(332\) | −13.2686 | −0.0399656 | ||||||||
\(333\) | −22.7757 | −0.0683956 | ||||||||
\(334\) | 315.824 | 0.945580 | ||||||||
\(335\) | 109.889 | − | 2.96216i | 0.328027 | − | 0.00884228i | ||||
\(336\) | − | 76.7196i | − | 0.228332i | ||||||
\(337\) | −477.616 | −1.41726 | −0.708629 | − | 0.705581i | \(-0.750686\pi\) | ||||
−0.708629 | + | 0.705581i | \(0.750686\pi\) | |||||||
\(338\) | − | 468.740i | − | 1.38680i | ||||||
\(339\) | − | 115.552i | − | 0.340860i | ||||||
\(340\) | −292.959 | + | 7.89697i | −0.861644 | + | 0.0232264i | ||||
\(341\) | 320.205i | 0.939018i | ||||||||
\(342\) | 135.175 | 0.395247 | ||||||||
\(343\) | −272.662 | −0.794934 | ||||||||
\(344\) | 62.4426i | 0.181519i | ||||||||
\(345\) | 91.9557 | + | 176.689i | 0.266538 | + | 0.512143i | ||||
\(346\) | 43.6252 | 0.126084 | ||||||||
\(347\) | 333.470i | 0.961008i | 0.876993 | + | 0.480504i | \(0.159546\pi\) | ||||
−0.876993 | + | 0.480504i | \(0.840454\pi\) | |||||||
\(348\) | − | 75.5183i | − | 0.217007i | ||||||
\(349\) | −106.304 | −0.304596 | −0.152298 | − | 0.988335i | \(-0.548667\pi\) | ||||
−0.152298 | + | 0.988335i | \(0.548667\pi\) | |||||||
\(350\) | −21.0916 | − | 390.940i | −0.0602617 | − | 1.11697i | ||||
\(351\) | −116.242 | −0.331173 | ||||||||
\(352\) | 53.4087 | 0.151729 | ||||||||
\(353\) | − | 365.647i | − | 1.03583i | −0.855433 | − | 0.517914i | \(-0.826709\pi\) | ||
0.855433 | − | 0.517914i | \(-0.173291\pi\) | |||||||
\(354\) | −172.187 | −0.486404 | ||||||||
\(355\) | −156.287 | + | 4.21285i | −0.440244 | + | 0.0118672i | ||||
\(356\) | − | 306.563i | − | 0.861131i | ||||||
\(357\) | − | 562.096i | − | 1.57450i | ||||||
\(358\) | 78.0942i | 0.218140i | ||||||||
\(359\) | 654.287i | 1.82253i | 0.411823 | + | 0.911264i | \(0.364892\pi\) | ||||
−0.411823 | + | 0.911264i | \(0.635108\pi\) | |||||||
\(360\) | 1.14323 | + | 42.4110i | 0.00317563 | + | 0.117808i | ||||
\(361\) | −654.120 | −1.81197 | ||||||||
\(362\) | −64.6984 | −0.178725 | ||||||||
\(363\) | 55.1829i | 0.152019i | ||||||||
\(364\) | − | 495.445i | − | 1.36111i | ||||||
\(365\) | −8.63078 | − | 320.181i | −0.0236460 | − | 0.877209i | ||||
\(366\) | 78.1737i | 0.213589i | ||||||||
\(367\) | −368.184 | −1.00323 | −0.501613 | − | 0.865092i | \(-0.667260\pi\) | ||||
−0.501613 | + | 0.865092i | \(0.667260\pi\) | |||||||
\(368\) | 82.7242 | − | 40.2581i | 0.224794 | − | 0.109397i | ||||
\(369\) | −167.294 | −0.453371 | ||||||||
\(370\) | 1.44655 | + | 53.6634i | 0.00390959 | + | 0.145036i | ||||
\(371\) | 434.031 | 1.16989 | ||||||||
\(372\) | 117.485i | 0.315820i | ||||||||
\(373\) | −91.4071 | −0.245059 | −0.122530 | − | 0.992465i | \(-0.539101\pi\) | ||||
−0.122530 | + | 0.992465i | \(0.539101\pi\) | |||||||
\(374\) | 391.306 | 1.04627 | ||||||||
\(375\) | 17.4851 | + | 215.799i | 0.0466269 | + | 0.575464i | ||||
\(376\) | −218.537 | −0.581216 | ||||||||
\(377\) | − | 487.687i | − | 1.29360i | ||||||
\(378\) | −81.3734 | −0.215274 | ||||||||
\(379\) | − | 203.934i | − | 0.538084i | −0.963128 | − | 0.269042i | \(-0.913293\pi\) | ||
0.963128 | − | 0.269042i | \(-0.0867070\pi\) | |||||||
\(380\) | −8.58529 | − | 318.494i | −0.0225929 | − | 0.838141i | ||||
\(381\) | 56.4232 | 0.148092 | ||||||||
\(382\) | 198.736 | 0.520251 | ||||||||
\(383\) | 398.715 | 1.04103 | 0.520516 | − | 0.853852i | \(-0.325740\pi\) | ||||
0.520516 | + | 0.853852i | \(0.325740\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | 14.0860 | + | 522.558i | 0.0365871 | + | 1.35729i | ||||
\(386\) | 242.287 | 0.627687 | ||||||||
\(387\) | 66.2303 | 0.171138 | ||||||||
\(388\) | −142.056 | −0.366125 | ||||||||
\(389\) | 39.2823i | 0.100983i | 0.998724 | + | 0.0504914i | \(0.0160788\pi\) | ||||
−0.998724 | + | 0.0504914i | \(0.983921\pi\) | |||||||
\(390\) | 7.38281 | + | 273.885i | 0.0189303 | + | 0.702268i | ||||
\(391\) | 606.090 | − | 294.956i | 1.55010 | − | 0.754363i | ||||
\(392\) | − | 208.237i | − | 0.531217i | ||||||
\(393\) | 209.361i | 0.532726i | ||||||||
\(394\) | −67.5629 | −0.171479 | ||||||||
\(395\) | −1.20447 | − | 44.6829i | −0.00304929 | − | 0.113121i | ||||
\(396\) | − | 56.6484i | − | 0.143052i | ||||||
\(397\) | − | 6.66240i | − | 0.0167819i | −0.999965 | − | 0.00839094i | \(-0.997329\pi\) | ||
0.999965 | − | 0.00839094i | \(-0.00267095\pi\) | |||||||
\(398\) | −64.2192 | −0.161355 | ||||||||
\(399\) | 611.090 | 1.53155 | ||||||||
\(400\) | 99.8548 | − | 5.38727i | 0.249637 | − | 0.0134682i | ||||
\(401\) | − | 88.5787i | − | 0.220895i | −0.993882 | − | 0.110447i | \(-0.964772\pi\) | ||
0.993882 | − | 0.110447i | \(-0.0352283\pi\) | |||||||
\(402\) | −53.8540 | −0.133965 | ||||||||
\(403\) | 758.702i | 1.88264i | ||||||||
\(404\) | 276.011 | 0.683196 | ||||||||
\(405\) | 44.9837 | − | 1.21258i | 0.111071 | − | 0.00299401i | ||||
\(406\) | − | 341.399i | − | 0.840885i | ||||||
\(407\) | − | 71.6783i | − | 0.176114i | ||||||
\(408\) | 143.572 | 0.351892 | ||||||||
\(409\) | 140.829 | 0.344325 | 0.172162 | − | 0.985069i | \(-0.444925\pi\) | ||||
0.172162 | + | 0.985069i | \(0.444925\pi\) | |||||||
\(410\) | 10.6253 | + | 394.173i | 0.0259153 | + | 0.961397i | ||||
\(411\) | − | 30.2003i | − | 0.0734801i | ||||||
\(412\) | −28.5655 | −0.0693338 | ||||||||
\(413\) | −778.413 | −1.88478 | ||||||||
\(414\) | −42.7001 | − | 87.7422i | −0.103140 | − | 0.211938i | ||||
\(415\) | 33.1594 | − | 0.893842i | 0.0799021 | − | 0.00215383i | ||||
\(416\) | 126.548 | 0.304202 | ||||||||
\(417\) | − | 243.035i | − | 0.582817i | ||||||
\(418\) | 425.413i | 1.01773i | ||||||||
\(419\) | − | 607.946i | − | 1.45095i | −0.688251 | − | 0.725473i | \(-0.741621\pi\) | ||
0.688251 | − | 0.725473i | \(-0.258379\pi\) | |||||||
\(420\) | 5.16824 | + | 191.729i | 0.0123053 | + | 0.456499i | ||||
\(421\) | 197.430i | 0.468955i | 0.972122 | + | 0.234477i | \(0.0753379\pi\) | ||||
−0.972122 | + | 0.234477i | \(0.924662\pi\) | |||||||
\(422\) | − | 176.827i | − | 0.419021i | ||||||
\(423\) | 231.794i | 0.547976i | ||||||||
\(424\) | 110.861i | 0.261465i | ||||||||
\(425\) | 731.599 | − | 39.4705i | 1.72141 | − | 0.0928718i | ||||
\(426\) | 76.5923 | 0.179794 | ||||||||
\(427\) | 353.403i | 0.827643i | ||||||||
\(428\) | −351.034 | −0.820173 | ||||||||
\(429\) | − | 365.828i | − | 0.852746i | ||||||
\(430\) | −4.20646 | − | 156.050i | −0.00978247 | − | 0.362906i | ||||
\(431\) | 495.113i | 1.14875i | 0.818591 | + | 0.574377i | \(0.194755\pi\) | ||||
−0.818591 | + | 0.574377i | \(0.805245\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | −49.7031 | −0.114788 | −0.0573939 | − | 0.998352i | \(-0.518279\pi\) | ||||
−0.0573939 | + | 0.998352i | \(0.518279\pi\) | |||||||
\(434\) | 531.120i | 1.22378i | ||||||||
\(435\) | 5.08731 | + | 188.727i | 0.0116950 | + | 0.433856i | ||||
\(436\) | 325.917i | 0.747517i | ||||||||
\(437\) | 320.665 | + | 658.918i | 0.733787 | + | 1.50782i | ||||
\(438\) | 156.913i | 0.358249i | ||||||||
\(439\) | 275.213 | 0.626910 | 0.313455 | − | 0.949603i | \(-0.398514\pi\) | ||||
0.313455 | + | 0.949603i | \(0.398514\pi\) | |||||||
\(440\) | −133.473 | + | 3.59789i | −0.303348 | + | 0.00817702i | ||||
\(441\) | −220.869 | −0.500836 | ||||||||
\(442\) | 927.170 | 2.09767 | ||||||||
\(443\) | − | 322.324i | − | 0.727594i | −0.931478 | − | 0.363797i | \(-0.881480\pi\) | ||
0.931478 | − | 0.363797i | \(-0.118520\pi\) | |||||||
\(444\) | − | 26.2992i | − | 0.0592323i | ||||||
\(445\) | 20.6517 | + | 766.128i | 0.0464083 | + | 1.72164i | ||||
\(446\) | −563.165 | −1.26270 | ||||||||
\(447\) | −57.1076 | −0.127758 | ||||||||
\(448\) | 88.5882 | 0.197741 | ||||||||
\(449\) | 159.589 | 0.355432 | 0.177716 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177716 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(450\) | −5.71406 | − | 105.912i | −0.0126979 | − | 0.235360i | ||||
\(451\) | − | 526.497i | − | 1.16740i | ||||||
\(452\) | 133.427 | 0.295194 | ||||||||
\(453\) | 418.132i | 0.923029i | ||||||||
\(454\) | 170.768i | 0.376142i | ||||||||
\(455\) | 33.3758 | + | 1238.16i | 0.0733535 | + | 2.72124i | ||||
\(456\) | 156.086i | 0.342294i | ||||||||
\(457\) | 698.342 | 1.52810 | 0.764051 | − | 0.645156i | \(-0.223208\pi\) | ||||
0.764051 | + | 0.645156i | \(0.223208\pi\) | |||||||
\(458\) | −3.33399 | −0.00727946 | ||||||||
\(459\) | − | 152.281i | − | 0.331767i | ||||||
\(460\) | −204.023 | + | 106.181i | −0.443529 | + | 0.230829i | ||||
\(461\) | 808.968 | 1.75481 | 0.877405 | − | 0.479750i | \(-0.159273\pi\) | ||||
0.877405 | + | 0.479750i | \(0.159273\pi\) | |||||||
\(462\) | − | 256.093i | − | 0.554314i | ||||||
\(463\) | − | 490.949i | − | 1.06036i | −0.847884 | − | 0.530182i | \(-0.822124\pi\) | ||
0.847884 | − | 0.530182i | \(-0.177876\pi\) | |||||||
\(464\) | 87.2011 | 0.187933 | ||||||||
\(465\) | −7.91441 | − | 293.606i | −0.0170202 | − | 0.631410i | ||||
\(466\) | 113.833 | 0.244277 | ||||||||
\(467\) | 363.574 | 0.778532 | 0.389266 | − | 0.921125i | \(-0.372729\pi\) | ||||
0.389266 | + | 0.921125i | \(0.372729\pi\) | |||||||
\(468\) | − | 134.224i | − | 0.286804i | ||||||
\(469\) | −243.461 | −0.519106 | ||||||||
\(470\) | 546.145 | − | 14.7218i | 1.16201 | − | 0.0313231i | ||||
\(471\) | 117.508i | 0.249487i | ||||||||
\(472\) | − | 198.824i | − | 0.421238i | ||||||
\(473\) | 208.436i | 0.440668i | ||||||||
\(474\) | 21.8980i | 0.0461983i | ||||||||
\(475\) | 42.9109 | + | 795.367i | 0.0903386 | + | 1.67446i | ||||
\(476\) | 649.053 | 1.36356 | ||||||||
\(477\) | 117.586 | 0.246512 | ||||||||
\(478\) | − | 250.653i | − | 0.524379i | ||||||
\(479\) | 231.968i | 0.484275i | 0.970242 | + | 0.242138i | \(0.0778486\pi\) | ||||
−0.970242 | + | 0.242138i | \(0.922151\pi\) | |||||||
\(480\) | −48.9720 | + | 1.32008i | −0.102025 | + | 0.00275018i | ||||
\(481\) | − | 169.836i | − | 0.353090i | ||||||
\(482\) | −527.924 | −1.09528 | ||||||||
\(483\) | −193.036 | − | 396.660i | −0.399661 | − | 0.821243i | ||||
\(484\) | −63.7197 | −0.131652 | ||||||||
\(485\) | 355.012 | − | 9.56967i | 0.731984 | − | 0.0197313i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 126.084i | 0.258898i | 0.991586 | + | 0.129449i | \(0.0413209\pi\) | ||||
−0.991586 | + | 0.129449i | \(0.958679\pi\) | |||||||
\(488\) | −90.2672 | −0.184974 | ||||||||
\(489\) | 384.617 | 0.786538 | ||||||||
\(490\) | 14.0280 | + | 520.404i | 0.0286285 | + | 1.06205i | ||||
\(491\) | 18.6259 | 0.0379346 | 0.0189673 | − | 0.999820i | \(-0.493962\pi\) | ||||
0.0189673 | + | 0.999820i | \(0.493962\pi\) | |||||||
\(492\) | − | 193.175i | − | 0.392631i | ||||||
\(493\) | 638.890 | 1.29592 | ||||||||
\(494\) | 1007.98i | 2.04045i | ||||||||
\(495\) | 3.81614 | + | 141.570i | 0.00770937 | + | 0.285999i | ||||
\(496\) | −135.660 | −0.273508 | ||||||||
\(497\) | 346.254 | 0.696689 | ||||||||
\(498\) | −16.2506 | −0.0326318 | ||||||||
\(499\) | 835.929 | 1.67521 | 0.837604 | − | 0.546277i | \(-0.183955\pi\) | ||||
0.837604 | + | 0.546277i | \(0.183955\pi\) | |||||||
\(500\) | −249.183 | + | 20.1900i | −0.498367 | + | 0.0403801i | ||||
\(501\) | 386.803 | 0.772062 | ||||||||
\(502\) | 110.317 | 0.219754 | ||||||||
\(503\) | −455.945 | −0.906452 | −0.453226 | − | 0.891396i | \(-0.649727\pi\) | ||||
−0.453226 | + | 0.891396i | \(0.649727\pi\) | |||||||
\(504\) | − | 93.9620i | − | 0.186432i | ||||||
\(505\) | −689.777 | + | 18.5936i | −1.36590 | + | 0.0368190i | ||||
\(506\) | 276.137 | − | 134.383i | 0.545725 | − | 0.265579i | ||||
\(507\) | − | 574.086i | − | 1.13232i | ||||||
\(508\) | 65.1519i | 0.128252i | ||||||||
\(509\) | −546.234 | −1.07315 | −0.536576 | − | 0.843852i | \(-0.680283\pi\) | ||||
−0.536576 | + | 0.843852i | \(0.680283\pi\) | |||||||
\(510\) | −358.800 | + | 9.67178i | −0.703529 | + | 0.0189643i | ||||
\(511\) | 709.364i | 1.38819i | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 165.554 | 0.322718 | ||||||||
\(514\) | 230.746 | 0.448922 | ||||||||
\(515\) | 71.3879 | − | 1.92433i | 0.138617 | − | 0.00373655i | ||||
\(516\) | 76.4762i | 0.148210i | ||||||||
\(517\) | −729.487 | −1.41100 | ||||||||
\(518\) | − | 118.892i | − | 0.229521i | ||||||
\(519\) | 53.4297 | 0.102947 | ||||||||
\(520\) | −316.255 | + | 8.52494i | −0.608182 | + | 0.0163941i | ||||
\(521\) | − | 468.515i | − | 0.899261i | −0.893215 | − | 0.449631i | \(-0.851556\pi\) | ||
0.893215 | − | 0.449631i | \(-0.148444\pi\) | |||||||
\(522\) | − | 92.4907i | − | 0.177185i | ||||||
\(523\) | −780.495 | −1.49234 | −0.746171 | − | 0.665754i | \(-0.768110\pi\) | ||||
−0.746171 | + | 0.665754i | \(0.768110\pi\) | |||||||
\(524\) | −241.749 | −0.461354 | ||||||||
\(525\) | −25.8318 | − | 478.801i | −0.0492035 | − | 0.912002i | ||||
\(526\) | 56.6162i | 0.107635i | ||||||||
\(527\) | −993.930 | −1.88602 | ||||||||
\(528\) | 65.4120 | 0.123886 | ||||||||
\(529\) | 326.411 | − | 416.289i | 0.617034 | − | 0.786936i | ||||
\(530\) | −7.46820 | − | 277.052i | −0.0140909 | − | 0.522740i | ||||
\(531\) | −210.885 | −0.397147 | ||||||||
\(532\) | 705.626i | 1.32636i | ||||||||
\(533\) | − | 1247.50i | − | 2.34052i | ||||||
\(534\) | − | 375.461i | − | 0.703111i | ||||||
\(535\) | 877.266 | − | 23.6475i | 1.63975 | − | 0.0442010i | ||||
\(536\) | − | 62.1853i | − | 0.116017i | ||||||
\(537\) | 95.6455i | 0.178111i | ||||||||
\(538\) | − | 402.353i | − | 0.747867i | ||||||
\(539\) | − | 695.104i | − | 1.28962i | ||||||
\(540\) | 1.40016 | + | 51.9427i | 0.00259289 | + | 0.0961901i | ||||
\(541\) | −190.214 | −0.351597 | −0.175799 | − | 0.984426i | \(-0.556251\pi\) | ||||
−0.175799 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(542\) | − | 626.748i | − | 1.15636i | ||||||
\(543\) | −79.2390 | −0.145928 | ||||||||
\(544\) | 165.783i | 0.304748i | ||||||||
\(545\) | −21.9555 | − | 814.497i | −0.0402854 | − | 1.49449i | ||||
\(546\) | − | 606.794i | − | 1.11134i | ||||||
\(547\) | 285.722i | 0.522344i | 0.965292 | + | 0.261172i | \(0.0841090\pi\) | ||||
−0.965292 | + | 0.261172i | \(0.915891\pi\) | |||||||
\(548\) | 34.8723 | 0.0636356 | ||||||||
\(549\) | 95.7428i | 0.174395i | ||||||||
\(550\) | 333.319 | − | 17.9829i | 0.606035 | − | 0.0326962i | ||||
\(551\) | 694.577i | 1.26058i | ||||||||
\(552\) | 101.316 | − | 49.3058i | 0.183543 | − | 0.0893222i | ||||
\(553\) | 98.9953i | 0.179015i | ||||||||
\(554\) | −444.448 | −0.802253 | ||||||||
\(555\) | 1.77165 | + | 65.7240i | 0.00319216 | + | 0.118422i | ||||
\(556\) | 280.632 | 0.504734 | ||||||||
\(557\) | 65.8064 | 0.118144 | 0.0590721 | − | 0.998254i | \(-0.481186\pi\) | ||||
0.0590721 | + | 0.998254i | \(0.481186\pi\) | |||||||
\(558\) | 143.889i | 0.257866i | ||||||||
\(559\) | 493.873i | 0.883494i | ||||||||
\(560\) | −221.390 | + | 5.96777i | −0.395339 | + | 0.0106567i | ||||
\(561\) | 479.250 | 0.854277 | ||||||||
\(562\) | −101.005 | −0.179724 | ||||||||
\(563\) | 206.928 | 0.367545 | 0.183772 | − | 0.982969i | \(-0.441169\pi\) | ||||
0.183772 | + | 0.982969i | \(0.441169\pi\) | |||||||
\(564\) | −267.652 | −0.474561 | ||||||||
\(565\) | −333.448 | + | 8.98838i | −0.590173 | + | 0.0159086i | ||||
\(566\) | − | 288.206i | − | 0.509197i | ||||||
\(567\) | −99.6617 | −0.175770 | ||||||||
\(568\) | 88.4412i | 0.155706i | ||||||||
\(569\) | 60.5855i | 0.106477i | 0.998582 | + | 0.0532386i | \(0.0169544\pi\) | ||||
−0.998582 | + | 0.0532386i | \(0.983046\pi\) | |||||||
\(570\) | −10.5148 | − | 390.074i | −0.0184470 | − | 0.684340i | ||||
\(571\) | 810.739i | 1.41986i | 0.704273 | + | 0.709929i | \(0.251273\pi\) | ||||
−0.704273 | + | 0.709929i | \(0.748727\pi\) | |||||||
\(572\) | 422.422 | 0.738500 | ||||||||
\(573\) | 243.401 | 0.424783 | ||||||||
\(574\) | − | 873.293i | − | 1.52142i | ||||||
\(575\) | 502.720 | − | 279.101i | 0.874296 | − | 0.485393i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 1016.03i | 1.76088i | 0.474159 | + | 0.880439i | \(0.342752\pi\) | ||||
−0.474159 | + | 0.880439i | \(0.657248\pi\) | |||||||
\(578\) | 805.922i | 1.39433i | ||||||||
\(579\) | 296.740 | 0.512504 | ||||||||
\(580\) | −217.923 | + | 5.87433i | −0.375730 | + | 0.0101281i | ||||
\(581\) | −73.4649 | −0.126446 | ||||||||
\(582\) | −173.983 | −0.298940 | ||||||||
\(583\) | 370.059i | 0.634750i | ||||||||
\(584\) | −181.188 | −0.310253 | ||||||||
\(585\) | 9.04206 | + | 335.439i | 0.0154565 | + | 0.573400i | ||||
\(586\) | − | 51.6764i | − | 0.0881850i | ||||||
\(587\) | 962.245i | 1.63926i | 0.572894 | + | 0.819629i | \(0.305821\pi\) | ||||
−0.572894 | + | 0.819629i | \(0.694179\pi\) | |||||||
\(588\) | − | 255.037i | − | 0.433737i | ||||||
\(589\) | − | 1080.56i | − | 1.83457i | ||||||
\(590\) | 13.3939 | + | 496.880i | 0.0227015 | + | 0.842170i | ||||
\(591\) | −82.7473 | −0.140012 | ||||||||
\(592\) | 30.3676 | 0.0512967 | ||||||||
\(593\) | 234.132i | 0.394826i | 0.980320 | + | 0.197413i | \(0.0632539\pi\) | ||||
−0.980320 | + | 0.197413i | \(0.936746\pi\) | |||||||
\(594\) | − | 69.3799i | − | 0.116801i | ||||||
\(595\) | −1622.04 | + | 43.7237i | −2.72612 | + | 0.0734851i | ||||
\(596\) | − | 65.9422i | − | 0.110641i | ||||||
\(597\) | −78.6521 | −0.131746 | ||||||||
\(598\) | 654.286 | − | 318.411i | 1.09412 | − | 0.532459i | ||||
\(599\) | −129.460 | −0.216127 | −0.108063 | − | 0.994144i | \(-0.534465\pi\) | ||||
−0.108063 | + | 0.994144i | \(0.534465\pi\) | |||||||
\(600\) | 122.297 | − | 6.59803i | 0.203828 | − | 0.0109967i | ||||
\(601\) | −109.440 | −0.182097 | −0.0910483 | − | 0.995846i | \(-0.529022\pi\) | ||||
−0.0910483 | + | 0.995846i | \(0.529022\pi\) | |||||||
\(602\) | 345.730i | 0.574302i | ||||||||
\(603\) | −65.9575 | −0.109382 | ||||||||
\(604\) | −482.817 | −0.799366 | ||||||||
\(605\) | 159.241 | − | 4.29250i | 0.263209 | − | 0.00709503i | ||||
\(606\) | 338.043 | 0.557827 | ||||||||
\(607\) | 643.634i | 1.06035i | 0.847887 | + | 0.530176i | \(0.177874\pi\) | ||||
−0.847887 | + | 0.530176i | \(0.822126\pi\) | |||||||
\(608\) | −180.233 | −0.296435 | ||||||||
\(609\) | − | 418.127i | − | 0.686580i | ||||||
\(610\) | 225.586 | − | 6.08088i | 0.369813 | − | 0.00996865i | ||||
\(611\) | −1728.46 | −2.82891 | ||||||||
\(612\) | 175.839 | 0.287319 | ||||||||
\(613\) | 837.840 | 1.36679 | 0.683393 | − | 0.730050i | \(-0.260503\pi\) | ||||
0.683393 | + | 0.730050i | \(0.260503\pi\) | |||||||
\(614\) | −182.053 | −0.296503 | ||||||||
\(615\) | 13.0133 | + | 482.761i | 0.0211598 | + | 0.784977i | ||||
\(616\) | 295.711 | 0.480050 | ||||||||
\(617\) | −249.042 | −0.403634 | −0.201817 | − | 0.979423i | \(-0.564685\pi\) | ||||
−0.201817 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(618\) | −34.9855 | −0.0566108 | ||||||||
\(619\) | 128.268i | 0.207218i | 0.994618 | + | 0.103609i | \(0.0330391\pi\) | ||||
−0.994618 | + | 0.103609i | \(0.966961\pi\) | |||||||
\(620\) | 339.027 | − | 9.13877i | 0.546817 | − | 0.0147400i | ||||
\(621\) | −52.2967 | − | 107.462i | −0.0842138 | − | 0.173046i | ||||
\(622\) | − | 679.502i | − | 1.09245i | ||||||
\(623\) | − | 1697.36i | − | 2.72450i | ||||||
\(624\) | 154.989 | 0.248380 | ||||||||
\(625\) | 621.372 | − | 67.2430i | 0.994195 | − | 0.107589i | ||||
\(626\) | − | 370.907i | − | 0.592503i | ||||||
\(627\) | 521.022i | 0.830976i | ||||||||
\(628\) | −135.687 | −0.216062 | ||||||||
\(629\) | 222.493 | 0.353724 | ||||||||
\(630\) | 6.32978 | + | 234.820i | 0.0100473 | + | 0.372730i | ||||
\(631\) | 927.605i | 1.47006i | 0.678037 | + | 0.735028i | \(0.262831\pi\) | ||||
−0.678037 | + | 0.735028i | \(0.737169\pi\) | |||||||
\(632\) | −25.2856 | −0.0400089 | ||||||||
\(633\) | − | 216.568i | − | 0.342129i | ||||||
\(634\) | −511.093 | −0.806140 | ||||||||
\(635\) | −4.38898 | − | 162.821i | −0.00691178 | − | 0.256410i | ||||
\(636\) | 135.777i | 0.213485i | ||||||||
\(637\) | − | 1647.00i | − | 2.58555i | ||||||
\(638\) | 291.081 | 0.456239 | ||||||||
\(639\) | 93.8060 | 0.146801 | ||||||||
\(640\) | −1.52430 | − | 56.5480i | −0.00238172 | − | 0.0883563i | ||||
\(641\) | 722.264i | 1.12678i | 0.826192 | + | 0.563388i | \(0.190503\pi\) | ||||
−0.826192 | + | 0.563388i | \(0.809497\pi\) | |||||||
\(642\) | −429.927 | −0.669668 | ||||||||
\(643\) | −601.221 | −0.935025 | −0.467513 | − | 0.883986i | \(-0.654850\pi\) | ||||
−0.467513 | + | 0.883986i | \(0.654850\pi\) | |||||||
\(644\) | 458.024 | − | 222.899i | 0.711217 | − | 0.346117i | ||||
\(645\) | −5.15184 | − | 191.121i | −0.00798735 | − | 0.296312i | ||||
\(646\) | −1320.50 | −2.04412 | ||||||||
\(647\) | 330.745i | 0.511198i | 0.966783 | + | 0.255599i | \(0.0822727\pi\) | ||||
−0.966783 | + | 0.255599i | \(0.917727\pi\) | |||||||
\(648\) | − | 25.4558i | − | 0.0392837i | ||||||
\(649\) | − | 663.684i | − | 1.02263i | ||||||
\(650\) | 789.776 | − | 42.6092i | 1.21504 | − | 0.0655526i | ||||
\(651\) | 650.486i | 0.999210i | ||||||||
\(652\) | 444.118i | 0.681162i | ||||||||
\(653\) | − | 903.860i | − | 1.38417i | −0.721818 | − | 0.692083i | \(-0.756693\pi\) | ||
0.721818 | − | 0.692083i | \(-0.243307\pi\) | |||||||
\(654\) | 399.166i | 0.610345i | ||||||||
\(655\) | 604.154 | − | 16.2855i | 0.922373 | − | 0.0248634i | ||||
\(656\) | 223.059 | 0.340029 | ||||||||
\(657\) | 192.178i | 0.292509i | ||||||||
\(658\) | −1209.99 | −1.83889 | ||||||||
\(659\) | − | 897.167i | − | 1.36141i | −0.732559 | − | 0.680703i | \(-0.761674\pi\) | ||
0.732559 | − | 0.680703i | \(-0.238326\pi\) | |||||||
\(660\) | −163.471 | + | 4.40650i | −0.247683 | + | 0.00667651i | ||||
\(661\) | 154.770i | 0.234145i | 0.993123 | + | 0.117072i | \(0.0373510\pi\) | ||||
−0.993123 | + | 0.117072i | \(0.962649\pi\) | |||||||
\(662\) | 310.368i | 0.468834i | ||||||||
\(663\) | 1135.55 | 1.71274 | ||||||||
\(664\) | − | 18.7646i | − | 0.0282599i | ||||||
\(665\) | −47.5347 | − | 1763.42i | −0.0714807 | − | 2.65177i | ||||
\(666\) | − | 32.2098i | − | 0.0483630i | ||||||
\(667\) | 450.852 | − | 219.409i | 0.675940 | − | 0.328949i | ||||
\(668\) | 446.642i | 0.668626i | ||||||||
\(669\) | −689.733 | −1.03099 | ||||||||
\(670\) | 4.18913 | + | 155.407i | 0.00625244 | + | 0.231950i | ||||
\(671\) | −301.316 | −0.449055 | ||||||||
\(672\) | 108.498 | 0.161455 | ||||||||
\(673\) | 274.578i | 0.407991i | 0.978972 | + | 0.203996i | \(0.0653929\pi\) | ||||
−0.978972 | + | 0.203996i | \(0.934607\pi\) | |||||||
\(674\) | − | 675.451i | − | 1.00215i | ||||||
\(675\) | −6.99827 | − | 129.715i | −0.0103678 | − | 0.192171i | ||||
\(676\) | 662.898 | 0.980618 | ||||||||
\(677\) | −32.5312 | −0.0480520 | −0.0240260 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240260 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(678\) | 163.415 | 0.241024 | ||||||||
\(679\) | −786.532 | −1.15837 | ||||||||
\(680\) | −11.1680 | − | 414.306i | −0.0164235 | − | 0.609274i | ||||
\(681\) | 209.148i | 0.307119i | ||||||||
\(682\) | −452.838 | −0.663986 | ||||||||
\(683\) | 1033.83i | 1.51367i | 0.653608 | + | 0.756834i | \(0.273255\pi\) | ||||
−0.653608 | + | 0.756834i | \(0.726745\pi\) | |||||||
\(684\) | 191.166i | 0.279482i | ||||||||
\(685\) | −87.1491 | + | 2.34918i | −0.127225 | + | 0.00342947i | ||||
\(686\) | − | 385.603i | − | 0.562103i | ||||||
\(687\) | −4.08329 | −0.00594365 | ||||||||
\(688\) | −88.3071 | −0.128353 | ||||||||
\(689\) | 876.828i | 1.27261i | ||||||||
\(690\) | −249.877 | + | 130.045i | −0.362140 | + | 0.188471i | ||||
\(691\) | 529.831 | 0.766760 | 0.383380 | − | 0.923591i | \(-0.374760\pi\) | ||||
0.383380 | + | 0.923591i | \(0.374760\pi\) | |||||||
\(692\) | 61.6953i | 0.0891551i | ||||||||
\(693\) | − | 313.649i | − | 0.452596i | ||||||
\(694\) | −471.598 | −0.679535 | ||||||||
\(695\) | −701.326 | + | 18.9049i | −1.00910 | + | 0.0272013i | ||||
\(696\) | 106.799 | 0.153447 | ||||||||
\(697\) | 1634.27 | 2.34472 | ||||||||
\(698\) | − | 150.337i | − | 0.215382i | ||||||
\(699\) | 139.416 | 0.199451 | ||||||||
\(700\) | 552.872 | − | 29.8280i | 0.789817 | − | 0.0426114i | ||||
\(701\) | 105.986i | 0.151193i | 0.997138 | + | 0.0755965i | \(0.0240861\pi\) | ||||
−0.997138 | + | 0.0755965i | \(0.975914\pi\) | |||||||
\(702\) | − | 164.391i | − | 0.234175i | ||||||
\(703\) | 241.885i | 0.344076i | ||||||||
\(704\) | 75.5313i | 0.107289i | ||||||||
\(705\) | 668.888 | − | 18.0305i | 0.948778 | − | 0.0255752i | ||||
\(706\) | 517.103 | 0.732441 | ||||||||
\(707\) | 1528.21 | 2.16154 | ||||||||
\(708\) | − | 243.509i | − | 0.343939i | ||||||
\(709\) | 62.3237i | 0.0879036i | 0.999034 | + | 0.0439518i | \(0.0139948\pi\) | ||||
−0.999034 | + | 0.0439518i | \(0.986005\pi\) | |||||||
\(710\) | −5.95787 | − | 221.023i | −0.00839136 | − | 0.311299i | ||||
\(711\) | 26.8195i | 0.0377208i | ||||||||
\(712\) | 433.545 | 0.608912 | ||||||||
\(713\) | −701.397 | + | 341.338i | −0.983727 | + | 0.478734i | ||||
\(714\) | 794.924 | 1.11334 | ||||||||
\(715\) | −1055.67 | + | 28.4566i | −1.47646 | + | 0.0397994i | ||||
\(716\) | −110.442 | −0.154248 | ||||||||
\(717\) | − | 306.986i | − | 0.428154i | ||||||
\(718\) | −925.302 | −1.28872 | ||||||||
\(719\) | 138.262 | 0.192297 | 0.0961486 | − | 0.995367i | \(-0.469348\pi\) | ||||
0.0961486 | + | 0.995367i | \(0.469348\pi\) | |||||||
\(720\) | −59.9782 | + | 1.61677i | −0.0833031 | + | 0.00224551i | ||||
\(721\) | −158.160 | −0.219363 | ||||||||
\(722\) | − | 925.065i | − | 1.28125i | ||||||
\(723\) | −646.572 | −0.894291 | ||||||||
\(724\) | − | 91.4974i | − | 0.126378i | ||||||
\(725\) | 544.215 | − | 29.3610i | 0.750642 | − | 0.0404979i | ||||
\(726\) | −78.0404 | −0.107494 | ||||||||
\(727\) | −1156.59 | −1.59090 | −0.795452 | − | 0.606016i | \(-0.792767\pi\) | ||||
−0.795452 | + | 0.606016i | \(0.792767\pi\) | |||||||
\(728\) | 700.665 | 0.962453 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 452.805 | − | 12.2058i | 0.620280 | − | 0.0167202i | ||||
\(731\) | −646.994 | −0.885080 | ||||||||
\(732\) | −110.554 | −0.151030 | ||||||||
\(733\) | 562.996 | 0.768071 | 0.384036 | − | 0.923318i | \(-0.374534\pi\) | ||||
0.384036 | + | 0.923318i | \(0.374534\pi\) | |||||||
\(734\) | − | 520.691i | − | 0.709388i | ||||||
\(735\) | 17.1807 | + | 637.362i | 0.0233751 | + | 0.867159i | ||||
\(736\) | 56.9335 | + | 116.990i | 0.0773553 | + | 0.158953i | ||||
\(737\) | − | 207.577i | − | 0.281651i | ||||||
\(738\) | − | 236.590i | − | 0.320582i | ||||||
\(739\) | −487.116 | −0.659155 | −0.329578 | − | 0.944128i | \(-0.606906\pi\) | ||||
−0.329578 | + | 0.944128i | \(0.606906\pi\) | |||||||
\(740\) | −75.8915 | + | 2.04573i | −0.102556 | + | 0.00276449i | ||||
\(741\) | 1234.52i | 1.66602i | ||||||||
\(742\) | 613.812i | 0.827240i | ||||||||
\(743\) | 884.971 | 1.19108 | 0.595539 | − | 0.803326i | \(-0.296938\pi\) | ||||
0.595539 | + | 0.803326i | \(0.296938\pi\) | |||||||
\(744\) | −166.149 | −0.223318 | ||||||||
\(745\) | 4.44222 | + | 164.796i | 0.00596271 | + | 0.221202i | ||||
\(746\) | − | 129.269i | − | 0.173283i | ||||||
\(747\) | −19.9029 | −0.0266437 | ||||||||
\(748\) | 553.390i | 0.739826i | ||||||||
\(749\) | −1943.59 | −2.59492 | ||||||||
\(750\) | −305.186 | + | 24.7276i | −0.406915 | + | 0.0329702i | ||||
\(751\) | − | 1213.24i | − | 1.61550i | −0.589528 | − | 0.807748i | \(-0.700686\pi\) | ||
0.589528 | − | 0.807748i | \(-0.299314\pi\) | |||||||
\(752\) | − | 309.058i | − | 0.410982i | ||||||
\(753\) | 135.110 | 0.179429 | ||||||||
\(754\) | 689.694 | 0.914714 | ||||||||
\(755\) | 1206.60 | − | 32.5251i | 1.59815 | − | 0.0430796i | ||||
\(756\) | − | 115.079i | − | 0.152221i | ||||||
\(757\) | −193.250 | −0.255284 | −0.127642 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127642 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(758\) | 288.406 | 0.380483 | ||||||||
\(759\) | 338.197 | − | 164.585i | 0.445582 | − | 0.216844i | ||||
\(760\) | 450.418 | − | 12.1414i | 0.592656 | − | 0.0159756i | ||||
\(761\) | −418.741 | −0.550251 | −0.275125 | − | 0.961408i | \(-0.588719\pi\) | ||||
−0.275125 | + | 0.961408i | \(0.588719\pi\) | |||||||
\(762\) | 79.7945i | 0.104717i | ||||||||
\(763\) | 1804.53i | 2.36504i | ||||||||
\(764\) | 281.055i | 0.367873i | ||||||||
\(765\) | −439.438 | + | 11.8455i | −0.574429 | + | 0.0154843i | ||||
\(766\) | 563.868i | 0.736120i | ||||||||
\(767\) | − | 1572.55i | − | 2.05026i | ||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 557.012i | 0.724333i | 0.932113 | + | 0.362167i | \(0.117963\pi\) | ||||
−0.932113 | + | 0.362167i | \(0.882037\pi\) | |||||||
\(770\) | −739.009 | + | 19.9207i | −0.959752 | + | 0.0258710i | ||||
\(771\) | 282.605 | 0.366543 | ||||||||
\(772\) | 342.646i | 0.443842i | ||||||||
\(773\) | −1116.13 | −1.44390 | −0.721948 | − | 0.691947i | \(-0.756753\pi\) | ||||
−0.721948 | + | 0.691947i | \(0.756753\pi\) | |||||||
\(774\) | 93.6638i | 0.121013i | ||||||||
\(775\) | −846.643 | + | 45.6773i | −1.09244 | + | 0.0589384i | ||||
\(776\) | − | 200.898i | − | 0.258889i | ||||||
\(777\) | − | 145.612i | − | 0.187403i | ||||||
\(778\) | −55.5536 | −0.0714057 | ||||||||
\(779\) | 1776.72i | 2.28076i | ||||||||
\(780\) | −387.331 | + | 10.4409i | −0.496579 | + | 0.0133857i | ||||
\(781\) | 295.220i | 0.378003i | ||||||||
\(782\) | 417.131 | + | 857.140i | 0.533415 | + | 1.09609i | ||||
\(783\) | − | 113.277i | − | 0.144671i | ||||||
\(784\) | 294.492 | 0.375627 | ||||||||
\(785\) | 339.094 | − | 9.14058i | 0.431966 | − | 0.0116440i | ||||
\(786\) | −296.081 | −0.376694 | ||||||||
\(787\) | 795.293 | 1.01054 | 0.505269 | − | 0.862962i | \(-0.331393\pi\) | ||||
0.505269 | + | 0.862962i | \(0.331393\pi\) | |||||||
\(788\) | − | 95.5484i | − | 0.121254i | ||||||
\(789\) | 69.3404i | 0.0878840i | ||||||||
\(790\) | 63.1911 | − | 1.70337i | 0.0799888 | − | 0.00215617i | ||||
\(791\) | 738.756 | 0.933952 | ||||||||
\(792\) | 80.1130 | 0.101153 | ||||||||
\(793\) | −713.945 | −0.900309 | ||||||||
\(794\) | 9.42206 | 0.0118666 | ||||||||
\(795\) | −9.14664 | − | 339.319i | −0.0115052 | − | 0.426816i | ||||
\(796\) | − | 90.8196i | − | 0.114095i | ||||||
\(797\) | −1372.56 | −1.72216 | −0.861080 | − | 0.508470i | \(-0.830211\pi\) | ||||
−0.861080 | + | 0.508470i | \(0.830211\pi\) | |||||||
\(798\) | 864.212i | 1.08297i | ||||||||
\(799\) | − | 2264.36i | − | 2.83399i | ||||||
\(800\) | 7.61875 | + | 141.216i | 0.00952343 | + | 0.176520i | ||||
\(801\) | − | 459.844i | − | 0.574087i | ||||||
\(802\) | 125.269 | 0.156196 | ||||||||
\(803\) | −604.812 | −0.753190 | ||||||||
\(804\) | − | 76.1611i | − | 0.0947278i | ||||||
\(805\) | −1129.63 | + | 587.901i | −1.40327 | + | 0.730311i | ||||
\(806\) | −1072.97 | −1.33122 | ||||||||
\(807\) | − | 492.779i | − | 0.610631i | ||||||
\(808\) | 390.339i | 0.483092i | ||||||||
\(809\) | 1416.49 | 1.75091 | 0.875454 | − | 0.483301i | \(-0.160562\pi\) | ||||
0.875454 | + | 0.483301i | \(0.160562\pi\) | |||||||
\(810\) | 1.71484 | + | 63.6165i | 0.00211709 | + | 0.0785389i | ||||
\(811\) | 268.418 | 0.330972 | 0.165486 | − | 0.986212i | \(-0.447081\pi\) | ||||
0.165486 | + | 0.986212i | \(0.447081\pi\) | |||||||
\(812\) | 482.811 | 0.594595 | ||||||||
\(813\) | − | 767.607i | − | 0.944166i | ||||||
\(814\) | 101.368 | 0.124531 | ||||||||
\(815\) | −29.9181 | − | 1109.89i | −0.0367094 | − | 1.36183i | ||||
\(816\) | 203.042i | 0.248825i | ||||||||
\(817\) | − | 703.387i | − | 0.860939i | ||||||
\(818\) | 199.162i | 0.243475i | ||||||||
\(819\) | − | 743.168i | − | 0.907409i | ||||||
\(820\) | −557.444 | + | 15.0264i | −0.679810 | + | 0.0183249i | ||||
\(821\) | −1148.66 | −1.39910 | −0.699549 | − | 0.714584i | \(-0.746616\pi\) | ||||
−0.699549 | + | 0.714584i | \(0.746616\pi\) | |||||||
\(822\) | 42.7097 | 0.0519583 | ||||||||
\(823\) | − | 1510.42i | − | 1.83527i | −0.397429 | − | 0.917633i | \(-0.630098\pi\) | ||
0.397429 | − | 0.917633i | \(-0.369902\pi\) | |||||||
\(824\) | − | 40.3977i | − | 0.0490264i | ||||||
\(825\) | 408.231 | − | 22.0245i | 0.494826 | − | 0.0266964i | ||||
\(826\) | − | 1100.84i | − | 1.33274i | ||||||
\(827\) | −578.500 | −0.699516 | −0.349758 | − | 0.936840i | \(-0.613736\pi\) | ||||
−0.349758 | + | 0.936840i | \(0.613736\pi\) | |||||||
\(828\) | 124.086 | − | 60.3871i | 0.149863 | − | 0.0729313i | ||||
\(829\) | 1007.46 | 1.21527 | 0.607636 | − | 0.794216i | \(-0.292118\pi\) | ||||
0.607636 | + | 0.794216i | \(0.292118\pi\) | |||||||
\(830\) | 1.26408 | + | 46.8945i | 0.00152299 | + | 0.0564993i | ||||
\(831\) | −544.336 | −0.655037 | ||||||||
\(832\) | 178.966i | 0.215103i | ||||||||
\(833\) | 2157.63 | 2.59019 | ||||||||
\(834\) | 343.703 | 0.412114 | ||||||||
\(835\) | −30.0882 | − | 1116.20i | −0.0360337 | − | 1.33677i | ||||
\(836\) | −601.624 | −0.719646 | ||||||||
\(837\) | 176.227i | 0.210546i | ||||||||
\(838\) | 859.766 | 1.02597 | ||||||||
\(839\) | − | 128.132i | − | 0.152720i | −0.997080 | − | 0.0763601i | \(-0.975670\pi\) | ||
0.997080 | − | 0.0763601i | \(-0.0243299\pi\) | |||||||
\(840\) | −271.146 | + | 7.30900i | −0.322793 | + | 0.00870119i | ||||
\(841\) | −365.749 | −0.434897 | ||||||||
\(842\) | −279.208 | −0.331601 | ||||||||
\(843\) | −123.706 | −0.146744 | ||||||||
\(844\) | 250.071 | 0.296293 | ||||||||
\(845\) | −1656.64 | + | 44.6563i | −1.96052 | + | 0.0528477i | ||||
\(846\) | −327.806 | −0.387478 | ||||||||
\(847\) | −352.801 | −0.416530 | ||||||||
\(848\) | −156.781 | −0.184884 | ||||||||
\(849\) | − | 352.978i | − | 0.415758i | ||||||
\(850\) | 55.8198 | + | 1034.64i | 0.0656703 | + | 1.21722i | ||||
\(851\) | 157.009 | − | 76.4089i | 0.184499 | − | 0.0897872i | ||||
\(852\) | 108.318i | 0.127134i | ||||||||
\(853\) | 928.585i | 1.08861i | 0.838887 | + | 0.544305i | \(0.183207\pi\) | ||||
−0.838887 | + | 0.544305i | \(0.816793\pi\) | |||||||
\(854\) | −499.788 | −0.585232 | ||||||||
\(855\) | −12.8779 | − | 477.741i | −0.0150619 | − | 0.558761i | ||||
\(856\) | − | 496.437i | − | 0.579950i | ||||||
\(857\) | − | 1165.78i | − | 1.36030i | −0.733072 | − | 0.680151i | \(-0.761914\pi\) | ||
0.733072 | − | 0.680151i | \(-0.238086\pi\) | |||||||
\(858\) | 517.359 | 0.602983 | ||||||||
\(859\) | 894.893 | 1.04178 | 0.520892 | − | 0.853622i | \(-0.325599\pi\) | ||||
0.520892 | + | 0.853622i | \(0.325599\pi\) | |||||||
\(860\) | 220.688 | − | 5.94883i | 0.256613 | − | 0.00691725i | ||||
\(861\) | − | 1069.56i | − | 1.24223i | ||||||
\(862\) | −700.195 | −0.812291 | ||||||||
\(863\) | 314.462i | 0.364382i | 0.983263 | + | 0.182191i | \(0.0583189\pi\) | ||||
−0.983263 | + | 0.182191i | \(0.941681\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | −4.15612 | − | 154.182i | −0.00480477 | − | 0.178245i | ||||
\(866\) | − | 70.2909i | − | 0.0811673i | ||||||
\(867\) | 987.048i | 1.13846i | ||||||||
\(868\) | −751.116 | −0.865342 | ||||||||
\(869\) | −84.4045 | −0.0971283 | ||||||||
\(870\) | −266.901 | + | 7.19455i | −0.306782 | + | 0.00826960i | ||||
\(871\) | − | 491.839i | − | 0.564683i | ||||||
\(872\) | −460.917 | −0.528574 | ||||||||
\(873\) | −213.085 | −0.244083 | ||||||||
\(874\) | −931.850 | + | 453.489i | −1.06619 | + | 0.518866i | ||||
\(875\) | −1379.67 | + | 111.787i | −1.57676 | + | 0.127757i | ||||
\(876\) | −221.909 | −0.253320 | ||||||||
\(877\) | − | 543.927i | − | 0.620213i | −0.950702 | − | 0.310107i | \(-0.899635\pi\) | ||
0.950702 | − | 0.310107i | \(-0.100365\pi\) | |||||||
\(878\) | 389.211i | 0.443292i | ||||||||
\(879\) | − | 63.2904i | − | 0.0720027i | ||||||
\(880\) | −5.08819 | − | 188.760i | −0.00578203 | − | 0.214500i | ||||
\(881\) | − | 1012.21i | − | 1.14893i | −0.818530 | − | 0.574464i | \(-0.805211\pi\) | ||
0.818530 | − | 0.574464i | \(-0.194789\pi\) | |||||||
\(882\) | − | 312.356i | − | 0.354145i | ||||||
\(883\) | 1113.87i | 1.26146i | 0.776004 | + | 0.630729i | \(0.217244\pi\) | ||||
−0.776004 | + | 0.630729i | \(0.782756\pi\) | |||||||
\(884\) | 1311.22i | 1.48328i | ||||||||
\(885\) | 16.4041 | + | 608.552i | 0.0185357 | + | 0.687629i | ||||
\(886\) | 455.835 | 0.514487 | ||||||||
\(887\) | 142.275i | 0.160400i | 0.996779 | + | 0.0801999i | \(0.0255559\pi\) | ||||
−0.996779 | + | 0.0801999i | \(0.974444\pi\) | |||||||
\(888\) | 37.1926 | 0.0418836 | ||||||||
\(889\) | 360.731i | 0.405771i | ||||||||
\(890\) | −1083.47 | + | 29.2059i | −1.21738 | + | 0.0328156i | ||||
\(891\) | − | 84.9727i | − | 0.0953677i | ||||||
\(892\) | − | 796.436i | − | 0.892865i | ||||||
\(893\) | 2461.72 | 2.75669 | ||||||||
\(894\) | − | 80.7624i | − | 0.0903382i | ||||||
\(895\) | 276.004 | − | 7.43995i | 0.308385 | − | 0.00831279i | ||||
\(896\) | 125.283i | 0.139824i | ||||||||
\(897\) | 801.333 | − | 389.972i | 0.893348 | − | 0.434751i | ||||
\(898\) | 225.693i | 0.251328i | ||||||||
\(899\) | −739.355 | −0.822420 | ||||||||
\(900\) | 149.782 | − | 8.08090i | 0.166425 | − | 0.00897878i | ||||
\(901\) | −1148.68 | −1.27489 | ||||||||
\(902\) | 744.579 | 0.825476 | ||||||||
\(903\) | 423.430i | 0.468915i | ||||||||
\(904\) | 188.695i | 0.208733i | ||||||||
\(905\) | 6.16375 | + | 228.660i | 0.00681077 | + | 0.252663i | ||||
\(906\) | −591.328 | −0.652680 | ||||||||
\(907\) | −1352.97 | −1.49169 | −0.745847 | − | 0.666117i | \(-0.767955\pi\) | ||||
−0.745847 | + | 0.666117i | \(0.767955\pi\) | |||||||
\(908\) | −241.503 | −0.265972 | ||||||||
\(909\) | 414.017 | 0.455464 | ||||||||
\(910\) | −1751.03 | + | 47.2005i | −1.92421 | + | 0.0518687i | ||||
\(911\) | − | 1639.29i | − | 1.79944i | −0.436473 | − | 0.899718i | \(-0.643772\pi\) | ||
0.436473 | − | 0.899718i | \(-0.356228\pi\) | |||||||
\(912\) | −220.739 | −0.242038 | ||||||||
\(913\) | − | 62.6370i | − | 0.0686057i | ||||||
\(914\) | 987.605i | 1.08053i | ||||||||
\(915\) | 276.285 | − | 7.44752i | 0.301951 | − | 0.00813937i | ||||
\(916\) | − | 4.71498i | − | 0.00514735i | ||||||
\(917\) | −1338.51 | −1.45966 | ||||||||
\(918\) | 215.358 | 0.234595 | ||||||||
\(919\) | 1680.00i | 1.82807i | 0.405633 | + | 0.914036i | \(0.367051\pi\) | ||||
−0.405633 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(920\) | −150.163 | − | 288.533i | −0.163221 | − | 0.313622i | ||||
\(921\) | −222.968 | −0.242094 | ||||||||
\(922\) | 1144.05i | 1.24084i | ||||||||
\(923\) | 699.503i | 0.757858i | ||||||||
\(924\) | 362.171 | 0.391959 | ||||||||
\(925\) | 189.522 | − | 10.2249i | 0.204889 | − | 0.0110540i | ||||
\(926\) | 694.306 | 0.749791 | ||||||||
\(927\) | −42.8483 | −0.0462225 | ||||||||
\(928\) | 123.321i | 0.132889i | ||||||||
\(929\) | −193.633 | −0.208431 | −0.104216 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104216 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(930\) | 415.221 | − | 11.1927i | 0.446474 | − | 0.0120351i | ||||
\(931\) | 2345.70i | 2.51954i | ||||||||
\(932\) | 160.984i | 0.172730i | ||||||||
\(933\) | − | 832.217i | − | 0.891979i | ||||||
\(934\) | 514.172i | 0.550505i | ||||||||
\(935\) | −37.2793 | − | 1382.97i | −0.0398709 | − | 1.47911i | ||||
\(936\) | 189.822 | 0.202801 | ||||||||
\(937\) | −128.669 | −0.137320 | −0.0686599 | − | 0.997640i | \(-0.521872\pi\) | ||||
−0.0686599 | + | 0.997640i | \(0.521872\pi\) | |||||||
\(938\) | − | 344.305i | − | 0.367063i | ||||||
\(939\) | − | 454.267i | − | 0.483777i | ||||||
\(940\) | 20.8198 | + | 772.366i | 0.0221487 | + | 0.821666i | ||||
\(941\) | 1506.94i | 1.60142i | 0.599051 | + | 0.800711i | \(0.295545\pi\) | ||||
−0.599051 | + | 0.800711i | \(0.704455\pi\) | |||||||
\(942\) | −166.182 | −0.176414 | ||||||||
\(943\) | 1153.27 | − | 561.244i | 1.22298 | − | 0.595169i | ||||
\(944\) | 281.180 | 0.297860 | ||||||||
\(945\) | 7.75236 | + | 287.594i | 0.00820356 | + | 0.304332i | ||||
\(946\) | −294.773 | −0.311599 | ||||||||
\(947\) | − | 296.571i | − | 0.313169i | −0.987665 | − | 0.156585i | \(-0.949952\pi\) | ||
0.987665 | − | 0.156585i | \(-0.0500484\pi\) | |||||||
\(948\) | −30.9685 | −0.0326671 | ||||||||
\(949\) | −1433.06 | −1.51007 | ||||||||
\(950\) | −1124.82 | + | 60.6851i | −1.18402 | + | 0.0638791i | ||||
\(951\) | −625.958 | −0.658210 | ||||||||
\(952\) | 917.900i | 0.964180i | ||||||||
\(953\) | 648.066 | 0.680028 | 0.340014 | − | 0.940420i | \(-0.389568\pi\) | ||||
0.340014 | + | 0.940420i | \(0.389568\pi\) | |||||||
\(954\) | 166.292i | 0.174310i | ||||||||
\(955\) | −18.9333 | − | 702.382i | −0.0198255 | − | 0.735478i | ||||
\(956\) | 354.477 | 0.370792 | ||||||||
\(957\) | 356.500 | 0.372518 | ||||||||
\(958\) | −328.052 | −0.342434 | ||||||||
\(959\) | 193.080 | 0.201334 | ||||||||
\(960\) | −1.86688 | − | 69.2569i | −0.00194467 | − | 0.0721426i | ||||
\(961\) | 189.225 | 0.196905 | ||||||||
\(962\) | 240.185 | 0.249673 | ||||||||
\(963\) | −526.551 | −0.546782 | ||||||||
\(964\) | − | 746.597i | − | 0.774479i | ||||||
\(965\) | −23.0824 | − | 856.303i | −0.0239196 | − | 0.887361i | ||||
\(966\) | 560.963 | − | 272.995i | 0.580707 | − | 0.282603i | ||||
\(967\) | 847.812i | 0.876745i | 0.898793 | + | 0.438372i | \(0.144445\pi\) | ||||
−0.898793 | + | 0.438372i | \(0.855555\pi\) | |||||||
\(968\) | − | 90.1132i | − | 0.0930922i | ||||||
\(969\) | −1617.27 | −1.66901 | ||||||||
\(970\) | 13.5336 | + | 502.063i | 0.0139521 | + | 0.517591i | ||||
\(971\) | − | 968.123i | − | 0.997037i | −0.866879 | − | 0.498519i | \(-0.833878\pi\) | ||
0.866879 | − | 0.498519i | \(-0.166122\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | 1553.79 | 1.59691 | ||||||||
\(974\) | −178.309 | −0.183069 | ||||||||
\(975\) | 967.274 | − | 52.1854i | 0.992076 | − | 0.0535235i | ||||
\(976\) | − | 127.657i | − | 0.130796i | ||||||
\(977\) | −741.921 | −0.759387 | −0.379693 | − | 0.925112i | \(-0.623970\pi\) | ||||
−0.379693 | + | 0.925112i | \(0.623970\pi\) | |||||||
\(978\) | 543.931i | 0.556166i | ||||||||
\(979\) | 1447.19 | 1.47823 | ||||||||
\(980\) | −735.962 | + | 19.8385i | −0.750981 | + | 0.0202434i | ||||
\(981\) | 488.876i | 0.498345i | ||||||||
\(982\) | 26.3410i | 0.0268238i | ||||||||
\(983\) | 1287.65 | 1.30992 | 0.654959 | − | 0.755665i | \(-0.272686\pi\) | ||||
0.654959 | + | 0.755665i | \(0.272686\pi\) | |||||||
\(984\) | 273.190 | 0.277632 | ||||||||
\(985\) | 6.43665 | + | 238.784i | 0.00653467 | + | 0.242421i | ||||
\(986\) | 903.527i | 0.916356i | ||||||||
\(987\) | −1481.93 | −1.50145 | ||||||||
\(988\) | −1425.50 | −1.44282 | ||||||||
\(989\) | −456.571 | + | 222.192i | −0.461649 | + | 0.224663i | ||||
\(990\) | −200.210 | + | 5.39684i | −0.202232 | + | 0.00545135i | ||||
\(991\) | −122.228 | −0.123338 | −0.0616689 | − | 0.998097i | \(-0.519642\pi\) | ||||
−0.0616689 | + | 0.998097i | \(0.519642\pi\) | |||||||
\(992\) | − | 191.852i | − | 0.193399i | ||||||
\(993\) | 380.122i | 0.382801i | ||||||||
\(994\) | 489.678i | 0.492633i | ||||||||
\(995\) | 6.11809 | + | 226.967i | 0.00614884 | + | 0.228107i | ||||
\(996\) | − | 22.9818i | − | 0.0230741i | ||||||
\(997\) | 1953.85i | 1.95973i | 0.199660 | + | 0.979865i | \(0.436016\pi\) | ||||
−0.199660 | + | 0.979865i | \(0.563984\pi\) | |||||||
\(998\) | 1182.18i | 1.18455i | ||||||||
\(999\) | − | 39.4487i | − | 0.0394882i |
(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 | 690.3.f.a.229.40 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.37 | ✓ | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.39 | yes | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.38 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.37 | ✓ | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.38 | yes | 48 | 115.114 | odd | 2 | inner | |
690.3.f.a.229.39 | yes | 48 | 23.22 | odd | 2 | inner | |
690.3.f.a.229.40 | yes | 48 | 1.1 | even | 1 | trivial |