Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.8 | ||
Character | \(\chi\) | \(=\) | 108.29 |
Dual form | 108.5.k.a.41.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.39288 | + | 7.85510i | 0.488098 | + | 0.872789i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.32074 | + | 7.53276i | 0.252829 | + | 0.301310i | 0.877499 | − | 0.479579i | \(-0.159211\pi\) |
−0.624669 | + | 0.780889i | \(0.714766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 66.1128 | − | 24.0631i | 1.34924 | − | 0.491084i | 0.436531 | − | 0.899689i | \(-0.356207\pi\) |
0.912711 | + | 0.408606i | \(0.133985\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −42.4052 | + | 69.0131i | −0.523521 | + | 0.852013i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 90.1574 | − | 107.445i | 0.745103 | − | 0.887979i | −0.251706 | − | 0.967804i | \(-0.580992\pi\) |
0.996809 | + | 0.0798249i | \(0.0254361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.0033 | + | 209.856i | 0.218954 | + | 1.24175i | 0.873912 | + | 0.486085i | \(0.161575\pi\) |
−0.654957 | + | 0.755666i | \(0.727313\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.4043 | + | 82.7405i | −0.139575 | + | 0.367736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −45.6573 | + | 26.3602i | −0.157984 | + | 0.0912119i | −0.576908 | − | 0.816809i | \(-0.695741\pi\) |
0.418924 | + | 0.908021i | \(0.362407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −163.587 | + | 283.340i | −0.453148 | + | 0.784876i | −0.998580 | − | 0.0532795i | \(-0.983033\pi\) |
0.545431 | + | 0.838156i | \(0.316366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 479.444 | + | 413.617i | 1.08717 | + | 0.937906i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −193.229 | + | 530.892i | −0.365272 | + | 1.00358i | 0.611864 | + | 0.790963i | \(0.290420\pi\) |
−0.977136 | + | 0.212614i | \(0.931802\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 91.7393 | − | 520.280i | 0.146783 | − | 0.832447i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −728.385 | − | 29.9305i | −0.999157 | − | 0.0410569i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 109.946 | + | 19.3864i | 0.130732 | + | 0.0230516i | 0.238631 | − | 0.971110i | \(-0.423301\pi\) |
−0.107899 | + | 0.994162i | \(0.534412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 868.674 | + | 316.171i | 0.903927 | + | 0.329002i | 0.751825 | − | 0.659362i | \(-0.229174\pi\) |
0.152102 | + | 0.988365i | \(0.451396\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1240.05 | + | 236.200i | 1.13870 | + | 0.216897i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 599.143 | + | 345.916i | 0.489097 | + | 0.282380i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 154.394 | + | 267.419i | 0.112779 | + | 0.195339i | 0.916890 | − | 0.399141i | \(-0.130691\pi\) |
−0.804111 | + | 0.594480i | \(0.797358\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1485.89 | + | 1212.54i | −0.976915 | + | 0.797197i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −478.016 | + | 84.2871i | −0.284364 | + | 0.0501411i | −0.314011 | − | 0.949419i | \(-0.601673\pi\) |
0.0296468 | + | 0.999560i | \(0.490562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1943.12 | + | 1630.47i | 1.05090 | + | 0.881813i | 0.993188 | − | 0.116521i | \(-0.0371741\pi\) |
0.0577150 | + | 0.998333i | \(0.481619\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −787.891 | + | 116.785i | −0.389082 | + | 0.0576718i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1391.66 | − | 3823.56i | −0.629997 | − | 1.73090i | −0.681081 | − | 0.732208i | \(-0.738490\pi\) |
0.0510841 | − | 0.998694i | \(-0.483732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1952.60 | − | 1638.43i | 0.813245 | − | 0.682394i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −407.629 | − | 242.845i | −0.156720 | − | 0.0933660i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4272.88i | − | 1.52114i | −0.649256 | − | 0.760570i | \(-0.724920\pi\) | ||
0.649256 | − | 0.760570i | \(-0.275080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1379.22 | 0.455941 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2944.28 | − | 40.3082i | −0.906212 | − | 0.0124064i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3174.41 | − | 3783.11i | −0.911924 | − | 1.08679i | −0.995913 | − | 0.0903222i | \(-0.971210\pi\) |
0.0839884 | − | 0.996467i | \(-0.473234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1472.97 | + | 536.118i | −0.395854 | + | 0.144079i | −0.532274 | − | 0.846572i | \(-0.678662\pi\) |
0.136420 | + | 0.990651i | \(0.456440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1142.86 | + | 5583.05i | −0.287946 | + | 1.40666i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1346.91 | + | 1605.18i | −0.318794 | + | 0.379924i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −527.119 | − | 2989.44i | −0.117425 | − | 0.665948i | −0.985521 | − | 0.169553i | \(-0.945768\pi\) |
0.868097 | − | 0.496395i | \(-0.165343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5019.04 | + | 814.314i | −1.05420 | + | 0.171039i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5046.35 | + | 2913.51i | −1.00106 | + | 0.577963i | −0.908562 | − | 0.417750i | \(-0.862819\pi\) |
−0.0924992 | + | 0.995713i | \(0.529486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3497.66 | − | 6058.12i | 0.656344 | − | 1.13682i | −0.325211 | − | 0.945642i | \(-0.605435\pi\) |
0.981555 | − | 0.191180i | \(-0.0612314\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4489.85 | − | 1564.91i | 0.798195 | − | 0.278206i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3375.09 | − | 9272.99i | 0.569252 | − | 1.56401i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54.1811 | − | 307.276i | 0.00868148 | − | 0.0492351i | −0.980159 | − | 0.198211i | \(-0.936487\pi\) |
0.988841 | + | 0.148976i | \(0.0475978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2964.60 | − | 5853.02i | −0.451852 | − | 0.892093i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11818.7 | + | 2083.95i | 1.71559 | + | 0.302504i | 0.943096 | − | 0.332521i | \(-0.107899\pi\) |
0.772491 | + | 0.635025i | \(0.219010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −487.153 | − | 177.309i | −0.0674260 | − | 0.0245411i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 330.697 | + | 948.798i | 0.0436910 | + | 0.125353i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8394.50 | − | 4846.57i | −1.05978 | − | 0.611863i | −0.134407 | − | 0.990926i | \(-0.542913\pi\) |
−0.925371 | + | 0.379063i | \(0.876246\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7496.17 | + | 12983.8i | 0.905226 | + | 1.56790i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1332.42 | + | 8212.42i | 0.154055 | + | 0.949523i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3168.32 | + | 558.661i | −0.351061 | + | 0.0619015i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3647.23 | + | 3060.39i | 0.387632 | + | 0.325262i | 0.815690 | − | 0.578490i | \(-0.196358\pi\) |
−0.428058 | + | 0.903751i | \(0.640802\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3592.00 | + | 10778.3i | 0.366493 | + | 1.09971i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3495.98 | − | 9605.13i | −0.342710 | − | 0.941587i | −0.984605 | − | 0.174795i | \(-0.944074\pi\) |
0.641895 | − | 0.766792i | \(-0.278148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1825.20 | − | 1531.53i | 0.172043 | − | 0.144361i | −0.552701 | − | 0.833380i | \(-0.686403\pi\) |
0.724743 | + | 0.689019i | \(0.241958\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −85.2347 | + | 6225.90i | −0.00773104 | + | 0.564707i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15855.4i | 1.38487i | 0.721479 | + | 0.692436i | \(0.243462\pi\) | ||||
−0.721479 | + | 0.692436i | \(0.756538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18526.7 | 1.55935 | 0.779676 | − | 0.626183i | \(-0.215384\pi\) | ||||
0.779676 | + | 0.626183i | \(0.215384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1422.37 | + | 2387.52i | −0.115442 | + | 0.193777i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4943.81 | − | 5891.80i | −0.387173 | − | 0.461415i | 0.536892 | − | 0.843651i | \(-0.319598\pi\) |
−0.924064 | + | 0.382237i | \(0.875154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5220.43 | + | 1900.08i | −0.394740 | + | 0.143673i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16051.9 | − | 6345.26i | −1.17261 | − | 0.463530i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2384.22 | + | 2841.41i | −0.168365 | + | 0.200650i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −873.777 | − | 4955.44i | −0.0596801 | − | 0.338463i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2761.95 | − | 3384.60i | −0.182560 | − | 0.223716i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9821.44 | − | 5670.41i | 0.628572 | − | 0.362906i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1907.85 | + | 3304.49i | −0.118287 | + | 0.204879i | −0.919089 | − | 0.394050i | \(-0.871074\pi\) |
0.800802 | + | 0.598929i | \(0.204407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4271.62 | + | 22425.9i | −0.256692 | + | 1.34763i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4284.95 | + | 11772.8i | −0.249691 | + | 0.686021i | 0.750006 | + | 0.661430i | \(0.230050\pi\) |
−0.999698 | + | 0.0245903i | \(0.992172\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3997.13 | + | 22668.8i | −0.225967 | + | 1.28152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4378.47 | − | 5675.93i | −0.240245 | − | 0.311437i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9048.16 | + | 1595.44i | 0.482080 | + | 0.0850038i | 0.409407 | − | 0.912352i | \(-0.365736\pi\) |
0.0726736 | + | 0.997356i | \(0.476847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 38.1456 | + | 13.8839i | 0.00197431 | + | 0.000718590i | 0.343007 | − | 0.939333i | \(-0.388555\pi\) |
−0.341033 | + | 0.940051i | \(0.610777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23921.1 | − | 27728.1i | 1.20321 | − | 1.39470i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25884.2 | + | 14944.2i | 1.26579 | + | 0.730805i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 548.906 | + | 950.732i | 0.0261073 | + | 0.0452191i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21447.6 | + | 8140.46i | 0.992529 | + | 0.376716i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6325.77 | + | 1115.40i | −0.284932 | + | 0.0502412i | −0.314287 | − | 0.949328i | \(-0.601766\pi\) |
0.0293557 | + | 0.999569i | \(0.490654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −33859.8 | − | 28411.8i | −1.48501 | − | 1.24608i | −0.900621 | − | 0.434605i | \(-0.856888\pi\) |
−0.584394 | − | 0.811470i | \(-0.698668\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 116.903 | − | 4268.76i | 0.00499395 | − | 0.182355i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3109.01 | + | 8541.94i | 0.129407 | + | 0.355544i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9697.94 | − | 8137.54i | 0.393442 | − | 0.330137i | −0.424511 | − | 0.905423i | \(-0.639554\pi\) |
0.817952 | + | 0.575286i | \(0.195109\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 33563.9 | − | 18770.3i | 1.32763 | − | 0.742465i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 39748.5i | 1.53345i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −34222.6 | −1.28806 | −0.644032 | − | 0.764999i | \(-0.722740\pi\) | ||||
−0.644032 | + | 0.764999i | \(0.722740\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6058.76 | + | 10833.9i | 0.222544 | + | 0.397940i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −26227.0 | − | 31256.2i | −0.940407 | − | 1.12073i | −0.992519 | − | 0.122093i | \(-0.961039\pi\) |
0.0521112 | − | 0.998641i | \(-0.483405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15831.7 | + | 5762.26i | −0.554311 | + | 0.201753i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12617.3 | − | 23304.7i | −0.431492 | − | 0.796987i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 26785.1 | − | 31921.3i | 0.894956 | − | 1.06657i | −0.102461 | − | 0.994737i | \(-0.532672\pi\) |
0.997417 | − | 0.0718297i | \(-0.0228838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6454.40 | − | 36604.7i | −0.210756 | − | 1.19526i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15771.9 | − | 41554.1i | 0.503429 | − | 1.32638i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −31745.4 | + | 18328.2i | −0.990773 | + | 0.572023i | −0.905505 | − | 0.424335i | \(-0.860508\pi\) |
−0.0852679 | + | 0.996358i | \(0.527175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1763.07 | + | 3053.72i | −0.0538160 | + | 0.0932121i | −0.891678 | − | 0.452669i | \(-0.850472\pi\) |
0.837862 | + | 0.545881i | \(0.183805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10681.8 | − | 9215.23i | −0.318966 | − | 0.275172i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1038.52 | + | 2853.30i | −0.0303438 | + | 0.0833689i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1284.05 | + | 7282.23i | −0.0367198 | + | 0.208248i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −48875.8 | + | 15548.4i | −1.36827 | + | 0.435274i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 43588.6 | + | 7685.85i | 1.19483 | + | 0.210681i | 0.735462 | − | 0.677565i | \(-0.236965\pi\) |
0.459368 | + | 0.888246i | \(0.348076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −47996.6 | − | 17469.3i | −1.28853 | − | 0.468988i | −0.395288 | − | 0.918557i | \(-0.629355\pi\) |
−0.893245 | + | 0.449570i | \(0.851577\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18525.6 | − | 3528.71i | −0.487197 | − | 0.0927998i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17477.7 | − | 10090.8i | −0.450353 | − | 0.260011i | 0.257626 | − | 0.966245i | \(-0.417060\pi\) |
−0.707979 | + | 0.706233i | \(0.750393\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14185.5 | + | 24570.0i | 0.358211 | + | 0.620439i | 0.987662 | − | 0.156601i | \(-0.0500536\pi\) |
−0.629451 | + | 0.777040i | \(0.716720\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21166.8 | − | 17272.8i | 0.523917 | − | 0.427535i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7735.33 | − | 1363.95i | 0.187710 | − | 0.0330983i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3656.33 | − | 3068.02i | −0.0870036 | − | 0.0730047i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −28444.6 | − | 35847.9i | −0.663833 | − | 0.836610i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15695.1 | + | 43121.9i | 0.359311 | + | 0.987200i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2986.01 | − | 2505.56i | 0.0670697 | − | 0.0562782i | −0.608637 | − | 0.793449i | \(-0.708283\pi\) |
0.675706 | + | 0.737171i | \(0.263839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −45053.9 | − | 26840.9i | −0.993056 | − | 0.591612i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24942.8i | 0.539596i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 65038.5 | 1.38118 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 62951.9 | + | 861.834i | 1.31257 | + | 0.0179695i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7221.32 | − | 8606.03i | −0.147854 | − | 0.176205i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −87864.5 | + | 31980.1i | −1.76687 | + | 0.643087i | −0.766867 | + | 0.641806i | \(0.778186\pi\) |
−0.999999 | + | 0.00128111i | \(0.999592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32015.9 | + | 28393.8i | 0.632412 | + | 0.560864i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28076.5 | − | 33460.3i | 0.544868 | − | 0.649349i | −0.421404 | − | 0.906873i | \(-0.638462\pi\) |
0.966272 | + | 0.257525i | \(0.0829069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11334.4 | − | 64280.4i | −0.216136 | − | 1.22577i | −0.878925 | − | 0.476961i | \(-0.841738\pi\) |
0.662789 | − | 0.748806i | \(-0.269373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 87666.6 | − | 14223.5i | 1.64290 | − | 0.266552i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −65540.1 | + | 37839.6i | −1.20724 | + | 0.697003i | −0.962156 | − | 0.272498i | \(-0.912150\pi\) |
−0.245088 | + | 0.969501i | \(0.578817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20005.6 | − | 34650.8i | 0.362257 | − | 0.627448i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2651.70 | − | 924.231i | 0.0472093 | − | 0.0164545i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10375.8 | + | 28507.3i | −0.181646 | + | 0.499069i | −0.996778 | − | 0.0802063i | \(-0.974442\pi\) |
0.815132 | + | 0.579275i | \(0.196664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15861.1 | + | 89953.0i | −0.273087 | + | 1.54875i | 0.471888 | + | 0.881659i | \(0.343573\pi\) |
−0.744975 | + | 0.667093i | \(0.767538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 32952.9 | − | 48998.9i | 0.558060 | − | 0.829801i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24683.8 | + | 4352.41i | 0.411225 | + | 0.0725100i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −65513.9 | − | 23845.1i | −1.07384 | − | 0.390846i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35548.4 | + | 101991.i | 0.573352 | + | 1.64500i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 67801.8 | + | 39145.4i | 1.07620 | + | 0.621346i | 0.929869 | − | 0.367890i | \(-0.119920\pi\) |
0.146333 | + | 0.989235i | \(0.453253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39620.9 | + | 68625.4i | 0.618990 | + | 1.07212i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −747.224 | − | 4605.53i | −0.0114913 | − | 0.0708271i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5822.68 | − | 1026.70i | 0.0881570 | − | 0.0155445i | −0.129396 | − | 0.991593i | \(-0.541304\pi\) |
0.217553 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16642.4 | + | 13964.6i | 0.248094 | + | 0.208175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6000.19 | + | 6765.62i | −0.0880814 | + | 0.0993176i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 42306.2 | + | 116235.i | 0.611635 | + | 1.68045i | 0.726581 | + | 0.687081i | \(0.241108\pi\) |
−0.114946 | + | 0.993372i | \(0.536670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32186.6 | − | 27007.8i | 0.458335 | − | 0.384589i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1194.21 | − | 87230.0i | 0.0167517 | − | 1.22361i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31192.9i | 0.431073i | 0.976496 | + | 0.215536i | \(0.0691500\pi\) | ||||
−0.976496 | + | 0.215536i | \(0.930850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 49482.4 | 0.673770 | 0.336885 | − | 0.941546i | \(-0.390627\pi\) | ||||
0.336885 | + | 0.941546i | \(0.390627\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −69058.9 | + | 115919.i | −0.926604 | + | 1.55536i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −47630.7 | − | 56764.0i | −0.629827 | − | 0.750599i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −53816.5 | + | 19587.6i | −0.701385 | + | 0.255283i | −0.668002 | − | 0.744160i | \(-0.732850\pi\) |
−0.0333826 | + | 0.999443i | \(0.510628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −58656.2 | + | 46542.5i | −0.753539 | + | 0.597918i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 68511.2 | − | 81648.5i | 0.867659 | − | 1.03404i | −0.131429 | − | 0.991326i | \(-0.541956\pi\) |
0.999088 | − | 0.0427098i | \(-0.0135991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8701.95 | − | 49351.2i | −0.108654 | − | 0.616205i | −0.989698 | − | 0.143171i | \(-0.954270\pi\) |
0.881044 | − | 0.473034i | \(-0.156841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18306.4 | − | 22433.4i | −0.225379 | − | 0.276188i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29574.8 | + | 17075.0i | −0.359052 | + | 0.207299i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −40370.8 | + | 69924.2i | −0.483361 | + | 0.837205i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8017.80 | + | 42093.3i | −0.0946824 | + | 0.497080i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32359.9 | − | 88908.2i | 0.376940 | − | 1.03563i | −0.595677 | − | 0.803224i | \(-0.703116\pi\) |
0.972618 | − | 0.232411i | \(-0.0746614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8432.68 | − | 47824.1i | 0.0968995 | − | 0.549544i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −68885.2 | + | 75563.2i | −0.780932 | + | 0.856638i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −118561. | − | 20905.5i | −1.32617 | − | 0.233840i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 167699. | + | 61037.6i | 1.85097 | + | 0.673697i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 60091.8 | − | 69655.5i | 0.654531 | − | 0.758700i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13348.7 | − | 7706.88i | −0.143496 | − | 0.0828474i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −39692.4 | − | 68749.2i | −0.421143 | − | 0.729442i | 0.574908 | − | 0.818218i | \(-0.305038\pi\) |
−0.996052 | + | 0.0887760i | \(0.971704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20048.2 | + | 7609.33i | 0.209970 | + | 0.0796947i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7118.06 | − | 1255.11i | 0.0735937 | − | 0.0129766i | −0.136730 | − | 0.990608i | \(-0.543659\pi\) |
0.210324 | + | 0.977632i | \(0.432548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 63912.8 | + | 53629.2i | 0.652378 | + | 0.547410i | 0.907791 | − | 0.419422i | \(-0.137767\pi\) |
−0.255414 | + | 0.966832i | \(0.582212\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −49279.5 | + | 26680.1i | −0.496644 | + | 0.268885i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34347.7 | − | 94369.5i | −0.341805 | − | 0.939103i | −0.984871 | − | 0.173291i | \(-0.944560\pi\) |
0.643065 | − | 0.765811i | \(-0.277662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11995.4 | − | 10065.4i | 0.117878 | − | 0.0989117i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −124546. | + | 69650.9i | −1.20870 | + | 0.675953i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17248.7i | − | 0.165330i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 112578. | 1.06583 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 81385.5 | + | 145529.i | 0.761117 | + | 1.36099i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −184014. | − | 219299.i | −1.70004 | − | 2.02602i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 52213.1 | − | 19004.0i | 0.476567 | − | 0.173456i | −0.0925579 | − | 0.995707i | \(-0.529504\pi\) |
0.569125 | + | 0.822251i | \(0.307282\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25002.5 | − | 684.714i | −0.225473 | − | 0.00617477i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19187.0 | − | 22866.1i | 0.170969 | − | 0.203752i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22332.3 | + | 126653.i | 0.196641 | + | 1.11520i | 0.910063 | + | 0.414470i | \(0.136033\pi\) |
−0.713422 | + | 0.700734i | \(0.752856\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24563.1 | − | 64716.1i | 0.213739 | − | 0.563136i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 112289. | − | 64829.8i | 0.965665 | − | 0.557527i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5204.24 | − | 9014.01i | 0.0442353 | − | 0.0766178i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −37858.1 | − | 32660.2i | −0.318068 | − | 0.274398i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −73160.9 | + | 201008.i | −0.607603 | + | 1.66938i | 0.127844 | + | 0.991794i | \(0.459194\pi\) |
−0.735447 | + | 0.677582i | \(0.763028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35289.9 | − | 200139.i | 0.289734 | − | 1.64316i | −0.398135 | − | 0.917327i | \(-0.630343\pi\) |
0.687869 | − | 0.725835i | \(-0.258546\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20671.5 | − | 153963.i | −0.167787 | − | 1.24969i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 72699.0 | + | 12818.8i | 0.583417 | + | 0.102872i | 0.457564 | − | 0.889177i | \(-0.348722\pi\) |
0.125853 | + | 0.992049i | \(0.459833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −53843.4 | − | 19597.4i | −0.427244 | − | 0.155504i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −32793.1 | − | 6246.34i | −0.257304 | − | 0.0490105i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −40092.8 | − | 23147.6i | −0.311084 | − | 0.179605i | 0.336327 | − | 0.941745i | \(-0.390815\pi\) |
−0.647412 | + | 0.762141i | \(0.724148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11639.4 | + | 20160.0i | 0.0893130 | + | 0.154695i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 35087.0 | − | 28632.3i | 0.266277 | − | 0.217291i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 67742.1 | − | 11944.8i | 0.508479 | − | 0.0896586i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −71661.3 | − | 60131.0i | −0.532050 | − | 0.446443i | 0.336758 | − | 0.941591i | \(-0.390669\pi\) |
−0.868809 | + | 0.495148i | \(0.835114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14453.4 | − | 36563.6i | 0.106150 | − | 0.268532i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −102819. | − | 282492.i | −0.747007 | − | 2.05238i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 62546.6 | − | 52482.8i | 0.449558 | − | 0.377224i | −0.389714 | − | 0.920936i | \(-0.627426\pi\) |
0.839272 | + | 0.543712i | \(0.182982\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 87686.1 | + | 52238.9i | 0.623546 | + | 0.371477i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23790.2i | 0.167384i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38147.7 | −0.265577 | −0.132788 | − | 0.991144i | \(-0.542393\pi\) | ||||
−0.132788 | + | 0.991144i | \(0.542393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34338.0 | − | 470.100i | −0.236551 | − | 0.00323847i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14867.8 | + | 17718.8i | 0.101356 | + | 0.120792i | 0.814338 | − | 0.580391i | \(-0.197100\pi\) |
−0.712982 | + | 0.701183i | \(0.752656\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 91184.3 | − | 33188.4i | 0.615175 | − | 0.223905i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −194922. | + | 64960.3i | −1.30149 | + | 0.433736i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −95185.9 | + | 113438.i | −0.629033 | + | 0.749652i | −0.982595 | − | 0.185759i | \(-0.940526\pi\) |
0.353563 | + | 0.935411i | \(0.384970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5172.14 | − | 29332.6i | −0.0338311 | − | 0.191866i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −111300. | + | 18057.8i | −0.720625 | + | 0.116918i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2657.10 | − | 1534.08i | 0.0170300 | − | 0.00983227i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39001.3 | − | 67552.2i | 0.247456 | − | 0.428606i | −0.715363 | − | 0.698753i | \(-0.753739\pi\) |
0.962819 | + | 0.270146i | \(0.0870721\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −195625. | + | 68183.7i | −1.22879 | + | 0.428287i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28243.3 | + | 77597.8i | −0.175641 | + | 0.482570i | −0.996008 | − | 0.0892678i | \(-0.971547\pi\) |
0.820366 | + | 0.571838i | \(0.193770\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34206.7 | + | 193996.i | −0.210620 | + | 1.19449i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25350.9 | − | 59327.0i | 0.154555 | − | 0.361695i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42652.7 | + | 7520.83i | 0.257489 | + | 0.0454022i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −61270.7 | − | 22300.7i | −0.366274 | − | 0.133313i | 0.152325 | − | 0.988330i | \(-0.451324\pi\) |
−0.518599 | + | 0.855018i | \(0.673546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27215.2 | + | 78082.8i | 0.161112 | + | 0.462244i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −300903. | − | 173726.i | −1.76411 | − | 1.01851i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 59004.8 | + | 102199.i | 0.342603 | + | 0.593406i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 58.5101 | + | 360.628i | 0.000336479 | + | 0.00207390i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 269322. | − | 47488.7i | 1.53406 | − | 0.270497i | 0.658121 | − | 0.752912i | \(-0.271352\pi\) |
0.875943 | + | 0.482415i | \(0.160240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18999.3 | − | 15942.3i | −0.107195 | − | 0.0899471i | 0.587615 | − | 0.809141i | \(-0.300067\pi\) |
−0.694810 | + | 0.719194i | \(0.744511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 322890. | + | 66095.9i | 1.80457 | + | 0.369397i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9526.13 | + | 26172.8i | 0.0527398 | + | 0.144901i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −84481.7 | + | 70888.5i | −0.463347 | + | 0.388795i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3682.31 | + | 268971.i | −0.0200081 | + | 1.46147i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 124866.i | − | 0.672186i | −0.941829 | − | 0.336093i | \(-0.890894\pi\) | ||
0.941829 | − | 0.336093i | \(-0.109106\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 125519. | 0.669475 | 0.334738 | − | 0.942311i | \(-0.391352\pi\) | ||||
0.334738 | + | 0.942311i | \(0.391352\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5056.82 | + | 8488.16i | −0.0267238 | + | 0.0448575i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −118813. | − | 141596.i | −0.622161 | − | 0.741463i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 156512. | − | 56965.8i | 0.812118 | − | 0.295587i | 0.0976196 | − | 0.995224i | \(-0.468877\pi\) |
0.714498 | + | 0.699637i | \(0.246655\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30272.5 | + | 204233.i | 0.155658 | + | 1.05014i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −94109.7 | + | 112156.i | −0.479542 | + | 0.571496i | −0.950526 | − | 0.310646i | \(-0.899455\pi\) |
0.470983 | + | 0.882142i | \(0.343899\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16551.4 | − | 93867.6i | −0.0835824 | − | 0.474019i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36550.0 | − | 44789.7i | −0.182925 | − | 0.224163i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 146812. | − | 84762.1i | 0.728231 | − | 0.420445i | −0.0895434 | − | 0.995983i | \(-0.528541\pi\) |
0.817775 | + | 0.575538i | \(0.195207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34040.4 | + | 58959.7i | −0.167356 | + | 0.289869i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 74435.0 | − | 390782.i | 0.362728 | − | 1.90431i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −50422.2 | + | 138534.i | −0.243556 | + | 0.669164i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −58409.4 | + | 331256.i | −0.279673 | + | 1.58610i | 0.444044 | + | 0.896005i | \(0.353543\pi\) |
−0.723717 | + | 0.690097i | \(0.757568\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34045.1 | − | 17833.9i | 0.161595 | − | 0.0846486i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 97008.3 | + | 17105.2i | 0.456465 | + | 0.0804870i | 0.397153 | − | 0.917752i | \(-0.369998\pi\) |
0.0593118 | + | 0.998240i | \(0.481109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 312412. | + | 113709.i | 1.45736 | + | 0.530434i | 0.944635 | − | 0.328122i | \(-0.106416\pi\) |
0.512720 | + | 0.858556i | \(0.328638\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −53440.3 | + | 61945.4i | −0.247151 | + | 0.286486i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 311347. | + | 179756.i | 1.42761 | + | 0.824233i | 0.996932 | − | 0.0782717i | \(-0.0249402\pi\) |
0.430681 | + | 0.902504i | \(0.358273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −106785. | − | 184956.i | −0.485470 | − | 0.840859i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 106523. | + | 40431.0i | 0.480178 | + | 0.182252i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 350373. | − | 61780.3i | 1.56606 | − | 0.276139i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 132409. | + | 111104.i | 0.586854 | + | 0.492429i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 294885. | + | 181192.i | 1.29603 | + | 0.796348i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 100143. | + | 275140.i | 0.436464 | + | 1.19917i | 0.941777 | + | 0.336238i | \(0.109155\pi\) |
−0.505313 | + | 0.862936i | \(0.668623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −50406.3 | + | 42295.9i | −0.217869 | + | 0.182814i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −312228. | + | 174610.i | −1.33838 | + | 0.748472i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46817.6i | 0.199033i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −468342. | −1.97472 | −0.987359 | − | 0.158502i | \(-0.949334\pi\) | ||||
−0.987359 | + | 0.158502i | \(0.949334\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −150336. | − | 268822.i | −0.628701 | − | 1.12421i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 122177. | + | 145605.i | 0.506788 | + | 0.603967i | 0.957404 | − | 0.288751i | \(-0.0932400\pi\) |
−0.450616 | + | 0.892718i | \(0.648796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5530.86 | + | 2013.07i | −0.0227561 | + | 0.00828256i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −58486.1 | + | 95184.3i | −0.238695 | + | 0.388468i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −263520. | + | 314051.i | −1.06685 | + | 1.27142i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 71474.9 | + | 405354.i | 0.287047 | + | 1.62792i | 0.697882 | + | 0.716213i | \(0.254126\pi\) |
−0.410836 | + | 0.911709i | \(0.634763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 130308. | − | 343320.i | 0.519153 | − | 1.36781i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −254905. | + | 147169.i | −1.00749 | + | 0.581676i | −0.910457 | − | 0.413605i | \(-0.864270\pi\) |
−0.0970362 | + | 0.995281i | \(0.530936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50256.0 | − | 87045.9i | 0.197063 | − | 0.341323i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −114810. | − | 99046.5i | −0.446646 | − | 0.385321i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −91361.9 | + | 251015.i | −0.352638 | + | 0.968866i | 0.628881 | + | 0.777502i | \(0.283513\pi\) |
−0.981519 | + | 0.191364i | \(0.938709\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 85462.9 | − | 484684.i | 0.327292 | − | 1.85617i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 127635. | − | 201485.i | 0.484991 | − | 0.765609i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23073.2 | + | 4068.44i | 0.0869950 | + | 0.0153396i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −536293. | − | 195195.i | −2.00642 | − | 0.730276i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 368409. | + | 70173.4i | 1.36771 | + | 0.260518i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32279.1 | − | 18636.3i | −0.118918 | − | 0.0686571i | 0.439361 | − | 0.898310i | \(-0.355205\pi\) |
−0.558279 | + | 0.829653i | \(0.688538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −237983. | − | 412199.i | −0.870048 | − | 1.50697i | −0.861946 | − | 0.507000i | \(-0.830754\pi\) |
−0.00810215 | − | 0.999967i | \(-0.502579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 259180. | − | 211500.i | 0.940336 | − | 0.767347i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47995.6 | + | 8462.92i | −0.172815 | + | 0.0304719i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −30138.4 | − | 25289.1i | −0.107698 | − | 0.0903695i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 395695. | − | 58652.1i | 1.40337 | − | 0.208015i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −35376.3 | − | 97195.6i | −0.124525 | − | 0.342131i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −119435. | + | 100218.i | −0.417276 | + | 0.350136i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −283423. | − | 168849.i | −0.982850 | − | 0.585532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 357515.i | − | 1.23060i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −312630. | −1.06816 | −0.534081 | − | 0.845434i | \(-0.679342\pi\) | ||||
−0.534081 | + | 0.845434i | \(0.679342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31732.2 | − | 434.425i | −0.107622 | − | 0.00147338i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 117102. | + | 139557.i | 0.394250 | + | 0.469849i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 92448.8 | − | 33648.6i | 0.308977 | − | 0.112459i | −0.182878 | − | 0.983136i | \(-0.558541\pi\) |
0.491855 | + | 0.870677i | \(0.336319\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25462.5 | − | 124388.i | 0.0844804 | − | 0.412701i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23478.6 | + | 27980.7i | −0.0773338 | + | 0.0921629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3811.96 | − | 21618.7i | −0.0124652 | − | 0.0706934i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26975.0 | + | 4376.56i | −0.0875742 | + | 0.0142085i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13215.8 | − | 7630.14i | 0.0425973 | − | 0.0245936i | −0.478550 | − | 0.878060i | \(-0.658837\pi\) |
0.521147 | + | 0.853467i | \(0.325504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −270262. | + | 468108.i | −0.864892 | + | 1.49804i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −62843.4 | + | 21903.6i | −0.199680 | + | 0.0695970i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −207977. | + | 571412.i | −0.656143 | + | 1.80274i | −0.0624470 | + | 0.998048i | \(0.519890\pi\) |
−0.593696 | + | 0.804690i | \(0.702332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13133.0 | − | 74481.1i | 0.0411403 | − | 0.233318i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −336840. | − | 315622.i | −1.04775 | − | 0.981751i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −232026. | − | 40912.4i | −0.716658 | − | 0.126366i | −0.196584 | − | 0.980487i | \(-0.562985\pi\) |
−0.520074 | + | 0.854121i | \(0.674096\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 462951. | + | 168501.i | 1.41992 | + | 0.516808i | 0.934024 | − | 0.357210i | \(-0.116272\pi\) |
0.485894 | + | 0.874018i | \(0.338494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 131107. | + | 376156.i | 0.399314 | + | 1.14567i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 258486. | + | 149237.i | 0.781809 | + | 0.451378i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 92113.0 | + | 159544.i | 0.276675 | + | 0.479214i | 0.970556 | − | 0.240875i | \(-0.0774343\pi\) |
−0.693882 | + | 0.720089i | \(0.744101\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −73620.0 | − | 453759.i | −0.219603 | − | 1.35353i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 831513. | − | 146618.i | 2.46330 | − | 0.434346i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −459102. | − | 385232.i | −1.35074 | − | 1.13341i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −53662.6 | − | 161022.i | −0.156805 | − | 0.470515i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −172208. | − | 473138.i | −0.499779 | − | 1.37313i | −0.891489 | − | 0.453042i | \(-0.850339\pi\) |
0.391710 | − | 0.920089i | \(-0.371884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −231687. | + | 194409.i | −0.667839 | + | 0.560384i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2486.40 | − | 181617.i | 0.00711862 | − | 0.519974i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 427298.i | − | 1.21513i | −0.794271 | − | 0.607563i | \(-0.792147\pi\) | ||
0.794271 | − | 0.607563i | \(-0.207853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36473.7 | −0.103026 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −130685. | + | 219362.i | −0.366670 | + | 0.615478i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −142612. | − | 169958.i | −0.397467 | − | 0.473683i | 0.529779 | − | 0.848136i | \(-0.322275\pi\) |
−0.927246 | + | 0.374453i | \(0.877831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 196054. | − | 71357.7i | 0.542783 | − | 0.197557i | −0.0560543 | − | 0.998428i | \(-0.517852\pi\) |
0.598837 | + | 0.800871i | \(0.295630\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 228663. | + | 90389.6i | 0.628870 | + | 0.248590i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31805.2 | − | 37904.0i | 0.0868935 | − | 0.103556i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37410.2 | + | 212164.i | 0.101534 | + | 0.575830i | 0.992548 | + | 0.121853i | \(0.0388838\pi\) |
−0.891014 | + | 0.453976i | \(0.850005\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 44694.4 | + | 54770.1i | 0.120509 | + | 0.147676i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 750901. | − | 433533.i | 2.01141 | − | 1.16129i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 275443. | − | 477081.i | 0.733011 | − | 1.26961i | −0.222579 | − | 0.974915i | \(-0.571447\pi\) |
0.955590 | − | 0.294698i | \(-0.0952192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8037.81 | − | 42198.3i | 0.0212514 | − | 0.111569i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −236748. | + | 650459.i | −0.621892 | + | 1.70863i | 0.0804154 | + | 0.996761i | \(0.474375\pi\) |
−0.702308 | + | 0.711874i | \(0.747847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 116854. | − | 662713.i | 0.304974 | − | 1.72959i | −0.318652 | − | 0.947872i | \(-0.603230\pi\) |
0.623626 | − | 0.781723i | \(-0.285659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 156635. | − | 380911.i | 0.406168 | − | 0.987734i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −671608. | − | 118423.i | −1.73037 | − | 0.305111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −205486. | − | 74790.6i | −0.526043 | − | 0.191464i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −269780. | + | 312716.i | −0.686238 | + | 0.795453i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14098.5 | − | 8139.74i | −0.0356345 | − | 0.0205736i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −196798. | − | 340864.i | −0.494268 | − | 0.856097i | 0.505710 | − | 0.862703i | \(-0.331230\pi\) |
−0.999978 | + | 0.00660642i | \(0.997897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32798.6 | + | 12448.8i | 0.0818556 | + | 0.0310684i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36950.9 | + | 6515.45i | −0.0916385 | + | 0.0161583i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 416086. | + | 349138.i | 1.02543 | + | 0.860435i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12921.0 | − | 471812.i | 0.0316441 | − | 1.15549i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 240188. | + | 659912.i | 0.584569 | + | 1.60609i | 0.780282 | + | 0.625428i | \(0.215076\pi\) |
−0.195713 | + | 0.980661i | \(0.562702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −208490. | + | 174944.i | −0.504270 | + | 0.423133i | −0.859107 | − | 0.511795i | \(-0.828981\pi\) |
0.354837 | + | 0.934928i | \(0.384536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −195928. | + | 109571.i | −0.470954 | + | 0.263376i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 337710.i | 0.806743i | 0.915036 | + | 0.403372i | \(0.132162\pi\) | ||||
−0.915036 | + | 0.403372i | \(0.867838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −692675. | −1.64452 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 285707. | + | 510884.i | 0.674153 | + | 1.20548i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −88035.2 | − | 104916.i | −0.206457 | − | 0.246046i | 0.652873 | − | 0.757468i | \(-0.273564\pi\) |
−0.859330 | + | 0.511421i | \(0.829119\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −115766. | + | 42135.3i | −0.269834 | + | 0.0982117i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 269771. | + | 498280.i | 0.624977 | + | 1.15436i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 82186.9 | − | 97946.5i | 0.189248 | − | 0.225537i | −0.663075 | − | 0.748553i | \(-0.730749\pi\) |
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 59270.9 | + | 336142.i | 0.135656 | + | 0.769343i | 0.974401 | + | 0.224818i | \(0.0721788\pi\) |
−0.838745 | + | 0.544525i | \(0.816710\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35878.8 | − | 94529.4i | 0.0816227 | − | 0.215050i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −196024. | + | 113174.i | −0.443267 | + | 0.255920i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31536.8 | + | 54623.4i | −0.0708870 | + | 0.122780i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −637185. | − | 549700.i | −1.42368 | − | 1.22821i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −75195.9 | + | 206599.i | −0.167013 | + | 0.458863i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34575.4 | − | 196087.i | 0.0763375 | − | 0.432931i | −0.922554 | − | 0.385867i | \(-0.873902\pi\) |
0.998892 | − | 0.0470642i | \(-0.0149865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −82393.8 | + | 376218.i | −0.180837 | + | 0.825719i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −261985. | − | 46195.1i | −0.571609 | − | 0.100790i | −0.119630 | − | 0.992819i | \(-0.538171\pi\) |
−0.451979 | + | 0.892028i | \(0.649282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 314771. | + | 114567.i | 0.682740 | + | 0.248497i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 386171. | + | 73556.7i | 0.832693 | + | 0.158609i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −228548. | − | 131952.i | −0.489933 | − | 0.282863i | 0.234614 | − | 0.972089i | \(-0.424617\pi\) |
−0.724547 | + | 0.689226i | \(0.757951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45173.0 | + | 78242.0i | 0.0962716 | + | 0.166747i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 455139. | − | 371409.i | 0.964340 | − | 0.786935i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 896689. | − | 158110.i | 1.88888 | − | 0.333060i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 508520. | + | 426699.i | 1.06501 | + | 0.893646i | 0.994591 | − | 0.103872i | \(-0.0331233\pi\) |
0.0704147 | + | 0.997518i | \(0.477568\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 496836. | + | 626148.i | 1.03454 | + | 1.30380i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 136.525 | + | 375.098i | 0.000282645 | + | 0.000776560i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19603.1 | − | 16448.9i | 0.0403514 | − | 0.0338588i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −585144. | − | 348599.i | −1.19759 | − | 0.713464i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 214146.i | 0.435788i | 0.975972 | + | 0.217894i | \(0.0699186\pi\) | ||||
−0.975972 | + | 0.217894i | \(0.930081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −101027. | −0.204422 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 360068. | + | 4929.45i | 0.724446 | + | 0.00991792i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −462259. | − | 550898.i | −0.924797 | − | 1.10213i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −283230. | + | 103087.i | −0.563438 | + | 0.205075i | −0.608007 | − | 0.793932i | \(-0.708031\pi\) |
0.0445691 | + | 0.999006i | \(0.485809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18908.5 | + | 16769.3i | 0.0374040 | + | 0.0331723i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −335706. | + | 400079.i | −0.660358 | + | 0.786984i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 51035.7 | + | 289438.i | 0.0998302 | + | 0.566165i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −269508. | + | 43726.2i | −0.524243 | + | 0.0850558i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 249436. | − | 144012.i | 0.482505 | − | 0.278574i | −0.238955 | − | 0.971031i | \(-0.576805\pi\) |
0.721460 | + | 0.692456i | \(0.243472\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 83816.0 | − | 145174.i | 0.161234 | − | 0.279265i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −776266. | + | 270562.i | −1.48503 | + | 0.517596i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20172.7 | − | 55424.1i | 0.0383786 | − | 0.105444i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −64865.9 | + | 367873.i | −0.122729 | + | 0.696032i | 0.859901 | + | 0.510460i | \(0.170525\pi\) |
−0.982631 | + | 0.185572i | \(0.940586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 529649. | + | 43601.9i | 0.996629 | + | 0.0820446i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −131697. | − | 23221.8i | −0.246457 | − | 0.0434571i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 88629.6 | + | 32258.5i | 0.164957 | + | 0.0600394i | 0.423179 | − | 0.906046i | \(-0.360914\pi\) |
−0.258222 | + | 0.966086i | \(0.583136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 74244.2 | + | 213013.i | 0.137432 | + | 0.394304i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −368725. | − | 212884.i | −0.678841 | − | 0.391929i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 419686. | + | 726918.i | 0.768486 | + | 1.33106i | 0.938384 | + | 0.345595i | \(0.112323\pi\) |
−0.169898 | + | 0.985462i | \(0.554344\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −100489. | − | 619367.i | −0.183013 | − | 1.12801i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 565336. | − | 99684.0i | 1.02407 | − | 0.180571i | 0.363703 | − | 0.931515i | \(-0.381512\pi\) |
0.660366 | + | 0.750944i | \(0.270401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48385.6 | − | 40600.3i | −0.0871773 | − | 0.0731505i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −644993. | + | 727273.i | −1.15588 | + | 1.30334i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 381530. | + | 1.04825e6i | 0.680088 | + | 1.86853i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 719252. | − | 603524.i | 1.27527 | − | 1.07008i | 0.281388 | − | 0.959594i | \(-0.409205\pi\) |
0.993878 | − | 0.110482i | \(-0.0352394\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9645.55 | + | 704551.i | −0.0170113 | + | 1.24257i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 434641.i | − | 0.762495i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 980425. | 1.71089 | 0.855446 | − | 0.517891i | \(-0.173283\pi\) | ||||
0.855446 | + | 0.517891i | \(0.173283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −365010. | + | 612690.i | −0.633608 | + | 1.06355i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −326111. | − | 388644.i | −0.563113 | − | 0.671092i | 0.407089 | − | 0.913388i | \(-0.366544\pi\) |
−0.970202 | + | 0.242296i | \(0.922099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.22485e6 | − | 445809.i | 2.10394 | − | 0.765773i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32894.4 | − | 26101.1i | 0.0562082 | − | 0.0446001i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 676445. | − | 806156.i | 1.14985 | − | 1.37034i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −63373.5 | − | 359409.i | −0.107166 | − | 0.607766i | −0.990333 | − | 0.138709i | \(-0.955705\pi\) |
0.883168 | − | 0.469057i | \(-0.155406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33643.2 | + | 41227.6i | 0.0565963 | + | 0.0693553i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −629772. | + | 363599.i | −1.05396 | + | 0.608504i | −0.923755 | − | 0.382983i | \(-0.874897\pi\) |
−0.130205 | + | 0.991487i | \(0.541563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 244189. | − | 422948.i | 0.406558 | − | 0.704180i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36585.4 | + | 192072.i | −0.0605991 | + | 0.318144i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54315.1 | − | 149229.i | 0.0895046 | − | 0.245912i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −141922. | + | 804882.i | −0.232675 | + | 1.31956i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −79502.7 | − | 17411.5i | −0.129676 | − | 0.0283997i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 122596. | + | 21617.0i | 0.198947 | + | 0.0350798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 342474. | + | 124650.i | 0.552940 | + | 0.201254i | 0.603352 | − | 0.797475i | \(-0.293831\pi\) |
−0.0504125 | + | 0.998728i | \(0.516054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −727193. | + | 842927.i | −1.16814 | + | 1.35405i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −468624. | − | 270560.i | −0.748983 | − | 0.432425i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −167012. | − | 289274.i | −0.265584 | − | 0.460005i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 353540. | + | 134187.i | 0.559377 | + | 0.212313i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −291577. | + | 51412.9i | −0.459025 | + | 0.0809386i | −0.398379 | − | 0.917221i | \(-0.630427\pi\) |
−0.0606461 | + | 0.998159i | \(0.519316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 164330. | + | 137889.i | 0.257408 | + | 0.215991i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 690447. | − | 373811.i | 1.07613 | − | 0.582622i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −335578. | − | 921992.i | −0.520429 | − | 1.42987i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −299416. | + | 251240.i | −0.462043 | + | 0.387700i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −245023. | + | 137027.i | −0.376236 | + | 0.210406i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 494809.i | − | 0.756033i | −0.925799 | − | 0.378017i | \(-0.876606\pi\) | ||
0.925799 | − | 0.378017i | \(-0.123394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 466081. | 0.708631 | 0.354315 | − | 0.935126i | \(-0.384714\pi\) | ||||
0.354315 | + | 0.935126i | \(0.384714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 217370. | + | 388689.i | 0.328866 | + | 0.588059i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −216312. | − | 257790.i | −0.325660 | − | 0.388107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −779847. | + | 283841.i | −1.16833 | + | 0.425237i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.21393e6 | − | 33244.3i | −1.80977 | − | 0.0495621i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 105926. | − | 126237.i | 0.157150 | − | 0.187284i | −0.681724 | − | 0.731609i | \(-0.738770\pi\) |
0.838874 | + | 0.544325i | \(0.183214\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21965.1 | − | 124571.i | −0.0324291 | − | 0.183914i | 0.964291 | − | 0.264847i | \(-0.0853214\pi\) |
−0.996720 | + | 0.0809323i | \(0.974210\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 236651. | − | 623502.i | 0.347697 | − | 0.916072i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 776147. | − | 448109.i | 1.13484 | − | 0.655198i | 0.189689 | − | 0.981844i | \(-0.439252\pi\) |
0.945147 | + | 0.326646i | \(0.105919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −195237. | + | 338161.i | −0.284089 | + | 0.492056i | −0.972388 | − | 0.233371i | \(-0.925024\pi\) |
0.688299 | + | 0.725427i | \(0.258358\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −390272. | − | 336688.i | −0.565153 | − | 0.487557i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −45961.1 | + | 126277.i | −0.0662370 | + | 0.181985i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 69671.0 | − | 395124.i | 0.0999261 | − | 0.566709i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −623266. | − | 256294.i | −0.889657 | − | 0.365837i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −955631. | − | 168504.i | −1.35758 | − | 0.239378i | −0.552981 | − | 0.833194i | \(-0.686510\pi\) |
−0.804601 | + | 0.593815i | \(0.797621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −652914. | − | 237641.i | −0.923133 | − | 0.335993i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 942318. | + | 179490.i | 1.32600 | + | 0.252572i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −143474. | − | 82834.5i | −0.200936 | − | 0.116011i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −177011. | − | 306592.i | −0.246737 | − | 0.427360i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 349432. | − | 285149.i | 0.484783 | − | 0.395600i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −171804. | + | 30293.7i | −0.237233 | + | 0.0418305i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −578870. | − | 485730.i | −0.795579 | − | 0.667570i | 0.151541 | − | 0.988451i | \(-0.451577\pi\) |
−0.947119 | + | 0.320881i | \(0.896021\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 95798.3 | − | 242346.i | 0.131047 | − | 0.331515i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −248575. | − | 682955.i | −0.338452 | − | 0.929888i | −0.985834 | − | 0.167723i | \(-0.946359\pi\) |
0.647383 | − | 0.762165i | \(-0.275864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −284896. | + | 239056.i | −0.386101 | + | 0.323977i | −0.815092 | − | 0.579332i | \(-0.803314\pi\) |
0.428991 | + | 0.903309i | \(0.358869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −264044. | − | 157304.i | −0.356181 | − | 0.212195i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 175442.i | 0.235565i | 0.993039 | + | 0.117783i | \(0.0375786\pi\) | ||||
−0.993039 | + | 0.117783i | \(0.962421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 409757. | 0.547639 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −726606. | − | 9947.48i | −0.966631 | − | 0.0132335i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28130.6 | − | 33524.8i | −0.0372511 | − | 0.0443942i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 607846. | − | 221238.i | 0.801231 | − | 0.291624i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −365868. | + | 121930.i | −0.480061 | + | 0.159986i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 512876. | − | 611221.i | 0.669878 | − | 0.798330i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −191527. | − | 1.08620e6i | −0.249018 | − | 1.41225i | −0.810974 | − | 0.585083i | \(-0.801062\pi\) |
0.561956 | − | 0.827167i | \(-0.310049\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 840536. | − | 136373.i | 1.08787 | − | 0.176502i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −564401. | + | 325857.i | −0.727171 | + | 0.419832i | −0.817386 | − | 0.576090i | \(-0.804578\pi\) |
0.0902156 | + | 0.995922i | \(0.471244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −437795. | + | 758282.i | −0.561499 | + | 0.972545i | 0.435867 | + | 0.900011i | \(0.356442\pi\) |
−0.997366 | + | 0.0725337i | \(0.976892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 412707. | − | 143846.i | 0.526933 | − | 0.183659i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −500450. | + | 1.37498e6i | −0.636083 | + | 1.74762i | 0.0276111 | + | 0.999619i | \(0.491210\pi\) |
−0.663694 | + | 0.748004i | \(0.731012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46617.0 | + | 264378.i | −0.0589848 | + | 0.334520i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −896161. | − | 209160.i | −1.12884 | − | 0.263465i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.31103e6 | + | 231169.i | 1.64403 | + | 0.289886i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −338716. | − | 123283.i | −0.422853 | − | 0.153906i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −356610. | − | 1.02314e6i | −0.443208 | − | 1.27160i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 89377.7 | + | 51602.2i | 0.110588 | + | 0.0638482i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 112634. | + | 195088.i | 0.138746 | + | 0.240315i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 257227. | + | 1.58543e6i | 0.315458 | + | 1.94433i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34146.8 | + | 6021.01i | −0.0416921 | + | 0.00735144i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −369828. | − | 310322.i | −0.449557 | − | 0.377223i | 0.389715 | − | 0.920936i | \(-0.372574\pi\) |
−0.839271 | + | 0.543713i | \(0.817018\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 811127. | + | 166039.i | 0.981660 | + | 0.200947i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −106730. | − | 293238.i | −0.128602 | − | 0.353332i | 0.858635 | − | 0.512587i | \(-0.171313\pi\) |
−0.987237 | + | 0.159255i | \(0.949091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.28945e6 | − | 1.08198e6i | 1.54691 | − | 1.29801i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1899.00 | − | 138711.i | 0.00226821 | − | 0.165679i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 881443.i | 1.04823i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −527904. | −0.625063 | −0.312532 | − | 0.949907i | \(-0.601177\pi\) | ||||
−0.312532 | + | 0.949907i | \(0.601177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 365668. | − | 613794.i | 0.431089 | − | 0.723609i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −798149. | − | 951197.i | −0.936873 | − | 1.11652i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 153297. | − | 55795.4i | 0.179163 | − | 0.0652101i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28297.3 | + | 190907.i | 0.0329296 | + | 0.222159i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −332213. | + | 395916.i | −0.384933 | + | 0.458745i | −0.923365 | − | 0.383924i | \(-0.874572\pi\) |
0.538432 | + | 0.842669i | \(0.319017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 144813. | + | 821276.i | 0.167074 | + | 0.947522i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41127.8 | + | 50399.5i | 0.0472468 | + | 0.0578980i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −62971.5 | + | 36356.6i | −0.0720312 | + | 0.0415872i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 383203. | − | 663727.i | 0.436465 | − | 0.755980i | −0.560949 | − | 0.827851i | \(-0.689564\pi\) |
0.997414 | + | 0.0718706i | \(0.0228969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −140501. | + | 737628.i | −0.159349 | + | 0.836578i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 279218. | − | 767146.i | 0.315329 | − | 0.866361i | −0.676228 | − | 0.736692i | \(-0.736387\pi\) |
0.991557 | − | 0.129668i | \(-0.0413912\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47619.2 | − | 270062.i | 0.0535498 | − | 0.303696i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −426054. | − | 269892.i | −0.477091 | − | 0.302223i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 845700. | + | 149120.i | 0.943010 | + | 0.166278i | 0.623957 | − | 0.781459i | \(-0.285524\pi\) |
0.319053 | + | 0.947737i | \(0.396635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.40076e6 | + | 509834.i | 1.55536 | + | 0.566104i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 590396. | − | 684359.i | 0.652804 | − | 0.756698i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.27474e6 | + | 735974.i | 1.40358 | + | 0.810358i | 0.994758 | − | 0.102256i | \(-0.0326061\pi\) |
0.408823 | + | 0.912614i | \(0.365939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 217616. | + | 376923.i | 0.238608 | + | 0.413281i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 131759. | + | 50009.3i | 0.143865 | + | 0.0546043i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 636591. | − | 112248.i | 0.692187 | − | 0.122051i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −52828.6 | − | 44328.5i | −0.0572035 | − | 0.0479994i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.09423e6 | − | 672351.i | −1.17993 | − | 0.725009i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −171781. | − | 471966.i | −0.184468 | − | 0.506822i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −194589. | + | 163280.i | −0.208097 | + | 0.174614i | −0.740879 | − | 0.671638i | \(-0.765591\pi\) |
0.532782 | + | 0.846252i | \(0.321147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 135490. | − | 75771.6i | 0.144298 | − | 0.0806973i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 114390.i | 0.121325i | 0.998158 | + | 0.0606625i | \(0.0193213\pi\) | ||||
−0.998158 | + | 0.0606625i | \(0.980679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2856.00 | 0.00301671 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 494544. | + | 884314.i | 0.520230 | + | 0.930245i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −887683. | − | 1.05790e6i | −0.929969 | − | 1.10829i | −0.993894 | − | 0.110339i | \(-0.964806\pi\) |
0.0639248 | − | 0.997955i | \(-0.479638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.27757e6 | + | 464997.i | −1.33296 | + | 0.485160i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −785627. | + | 1.27858e6i | −0.816353 | + | 1.32859i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −867499. | + | 1.03385e6i | −0.897764 | + | 1.06991i | 0.0994294 | + | 0.995045i | \(0.468298\pi\) |
−0.997193 | + | 0.0748689i | \(0.976146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34460.8 | − | 195437.i | −0.0355183 | − | 0.201434i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 914264. | − | 2.40880e6i | 0.938507 | − | 2.47267i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.24107e6 | + | 716533.i | −1.26883 | + | 0.732561i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −290755. | + | 503602.i | −0.296060 | + | 0.512791i | −0.975231 | − | 0.221189i | \(-0.929006\pi\) |
0.679171 | + | 0.733980i | \(0.262339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 378645. | + | 326657.i | 0.384002 | + | 0.331279i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −95417.2 | + | 262157.i | −0.0963786 | + | 0.264798i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −201359. | + | 1.14196e6i | −0.202572 | + | 1.14884i | 0.698642 | + | 0.715471i | \(0.253788\pi\) |
−0.901214 | + | 0.433374i | \(0.857323\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −104455. | − | 199405.i | −0.104664 | − | 0.199805i |
(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 | 108.5.k.a.29.8 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.89.5 | 72 | |||
27.13 | even | 9 | 324.5.k.a.233.5 | 72 | |||
27.14 | odd | 18 | inner | 108.5.k.a.41.8 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.29.8 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.41.8 | yes | 72 | 27.14 | odd | 18 | inner | |
324.5.k.a.89.5 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.233.5 | 72 | 27.13 | even | 9 |