Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(71,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.e (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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.11 | ||
Root | \(1.35489 - 0.405301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.71 |
Dual form | 252.2.e.a.71.12 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35489 | − | 0.405301i | 0.958053 | − | 0.286591i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.67146 | − | 1.09828i | 0.835731 | − | 0.549139i | ||||
\(5\) | 3.31339i | 1.48179i | 0.671618 | + | 0.740897i | \(0.265600\pi\) | ||||
−0.671618 | + | 0.740897i | \(0.734400\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 1.81951 | − | 2.16549i | 0.643296 | − | 0.765618i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.34292 | + | 4.48929i | 0.424670 | + | 1.41964i | ||||
\(11\) | 4.72761 | 1.42543 | 0.712714 | − | 0.701455i | \(-0.247466\pi\) | ||||
0.712714 | + | 0.701455i | \(0.247466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.97858 | −1.38081 | −0.690404 | − | 0.723424i | \(-0.742567\pi\) | ||||
−0.690404 | + | 0.723424i | \(0.742567\pi\) | |||||||
\(14\) | −0.405301 | − | 1.35489i | −0.108321 | − | 0.362110i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.58757 | − | 3.67146i | 0.396892 | − | 0.917865i | ||||
\(17\) | 0.484966i | 0.117622i | 0.998269 | + | 0.0588108i | \(0.0187309\pi\) | ||||
−0.998269 | + | 0.0588108i | \(0.981269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.29273i | − | 0.525989i | −0.964797 | − | 0.262994i | \(-0.915290\pi\) | ||
0.964797 | − | 0.262994i | \(-0.0847100\pi\) | |||||||
\(20\) | 3.63903 | + | 5.53821i | 0.813712 | + | 1.23838i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.40539 | − | 1.91611i | 1.36563 | − | 0.408515i | ||||
\(23\) | −7.97002 | −1.66186 | −0.830932 | − | 0.556374i | \(-0.812192\pi\) | ||||
−0.830932 | + | 0.556374i | \(0.812192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.97858 | −1.19572 | ||||||||
\(26\) | −6.74543 | + | 2.01782i | −1.32289 | + | 0.395728i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.09828 | − | 1.67146i | −0.207555 | − | 0.315877i | ||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.66442i | − | 1.37657i | −0.725440 | − | 0.688286i | \(-0.758364\pi\) | ||
0.725440 | − | 0.688286i | \(-0.241636\pi\) | |||||||
\(32\) | 0.662933 | − | 5.61788i | 0.117191 | − | 0.993109i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.196558 | + | 0.657077i | 0.0337093 | + | 0.112688i | ||||
\(35\) | 3.31339 | 0.560066 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.39312 | −0.393426 | −0.196713 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196713 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(38\) | −0.929247 | − | 3.10640i | −0.150744 | − | 0.503925i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.17513 | + | 6.02877i | 1.13449 | + | 0.953232i | ||||
\(41\) | 6.55580i | 1.02384i | 0.859032 | + | 0.511922i | \(0.171066\pi\) | ||||
−0.859032 | + | 0.511922i | \(0.828934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.37169i | 0.819175i | 0.912271 | + | 0.409588i | \(0.134327\pi\) | ||||
−0.912271 | + | 0.409588i | \(0.865673\pi\) | |||||||
\(44\) | 7.90201 | − | 5.19223i | 1.19127 | − | 0.782758i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.7985 | + | 3.23026i | −1.59215 | + | 0.476276i | ||||
\(47\) | −6.21280 | −0.906230 | −0.453115 | − | 0.891452i | \(-0.649687\pi\) | ||||
−0.453115 | + | 0.891452i | \(0.649687\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −8.10032 | + | 2.42313i | −1.14556 | + | 0.342682i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.32150 | + | 5.46787i | −1.15398 | + | 0.758257i | ||||
\(53\) | − | 1.00023i | − | 0.137392i | −0.997638 | − | 0.0686960i | \(-0.978116\pi\) | ||
0.997638 | − | 0.0686960i | \(-0.0218839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.6644i | 2.11219i | ||||||||
\(56\) | −2.16549 | − | 1.81951i | −0.289376 | − | 0.243143i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.573183 | + | 1.91611i | 0.0752626 | + | 0.251597i | ||||
\(59\) | −1.38392 | −0.180171 | −0.0900853 | − | 0.995934i | \(-0.528714\pi\) | ||||
−0.0900853 | + | 0.995934i | \(0.528714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6644 | 1.74955 | 0.874775 | − | 0.484529i | \(-0.161009\pi\) | ||||
0.874775 | + | 0.484529i | \(0.161009\pi\) | |||||||
\(62\) | −3.10640 | − | 10.3845i | −0.394513 | − | 1.31883i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.37873 | − | 7.88030i | −0.172341 | − | 0.985037i | ||||
\(65\) | − | 16.4960i | − | 2.04608i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.27131i | 0.399654i | 0.979831 | + | 0.199827i | \(0.0640380\pi\) | ||||
−0.979831 | + | 0.199827i | \(0.935962\pi\) | |||||||
\(68\) | 0.532628 | + | 0.810603i | 0.0645907 | + | 0.0983000i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.48929 | − | 1.34292i | 0.536573 | − | 0.160510i | ||||
\(71\) | −3.34369 | −0.396823 | −0.198412 | − | 0.980119i | \(-0.563578\pi\) | ||||
−0.198412 | + | 0.980119i | \(0.563578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.10038 | −0.245831 | −0.122916 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122916 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(74\) | −3.24241 | + | 0.969933i | −0.376923 | + | 0.112752i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.51806 | − | 3.83221i | −0.288841 | − | 0.439585i | ||||
\(77\) | − | 4.72761i | − | 0.538761i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.0575i | − | 1.35658i | −0.734795 | − | 0.678290i | \(-0.762722\pi\) | ||
0.734795 | − | 0.678290i | \(-0.237278\pi\) | |||||||
\(80\) | 12.1650 | + | 5.26024i | 1.36009 | + | 0.588112i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.65708 | + | 8.88240i | 0.293425 | + | 0.980897i | ||||
\(83\) | 3.24241 | 0.355901 | 0.177950 | − | 0.984039i | \(-0.443053\pi\) | ||||
0.177950 | + | 0.984039i | \(0.443053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.60688 | −0.174291 | ||||||||
\(86\) | 2.17715 | + | 7.27806i | 0.234769 | + | 0.784813i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.60195 | − | 10.2376i | 0.916971 | − | 1.09133i | ||||
\(89\) | 5.72784i | 0.607149i | 0.952808 | + | 0.303575i | \(0.0981802\pi\) | ||||
−0.952808 | + | 0.303575i | \(0.901820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.97858i | 0.521897i | ||||||||
\(92\) | −13.3216 | + | 8.75330i | −1.38887 | + | 0.912595i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.41767 | + | 2.51806i | −0.868217 | + | 0.259718i | ||||
\(95\) | 7.59672 | 0.779407 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0575 | 1.22426 | 0.612129 | − | 0.790758i | \(-0.290313\pi\) | ||||
0.612129 | + | 0.790758i | \(0.290313\pi\) | |||||||
\(98\) | −1.35489 | + | 0.405301i | −0.136865 | + | 0.0409416i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.99296 | + | 6.56614i | −0.999296 | + | 0.656614i | ||||
\(101\) | − | 14.5665i | − | 1.44942i | −0.689053 | − | 0.724711i | \(-0.741973\pi\) | ||
0.689053 | − | 0.724711i | \(-0.258027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.70727i | 0.562354i | 0.959656 | + | 0.281177i | \(0.0907248\pi\) | ||||
−0.959656 | + | 0.281177i | \(0.909275\pi\) | |||||||
\(104\) | −9.05860 | + | 10.7811i | −0.888268 | + | 1.05717i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.405394 | − | 1.35520i | −0.0393754 | − | 0.131629i | ||||
\(107\) | 16.0413 | 1.55077 | 0.775386 | − | 0.631487i | \(-0.217555\pi\) | ||||
0.775386 | + | 0.631487i | \(0.217555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.37169 | 0.131384 | 0.0656921 | − | 0.997840i | \(-0.479074\pi\) | ||||
0.0656921 | + | 0.997840i | \(0.479074\pi\) | |||||||
\(110\) | 6.34881 | + | 21.2236i | 0.605336 | + | 2.02359i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.67146 | − | 1.58757i | −0.346921 | − | 0.150011i | ||||
\(113\) | 11.2834i | 1.06145i | 0.847543 | + | 0.530727i | \(0.178081\pi\) | ||||
−0.847543 | + | 0.530727i | \(0.821919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 26.4078i | − | 2.46254i | ||||||
\(116\) | 1.55320 | + | 2.36380i | 0.144211 | + | 0.219474i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.87506 | + | 0.560904i | −0.172613 | + | 0.0516354i | ||||
\(119\) | 0.484966 | 0.0444568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3503 | 1.03184 | ||||||||
\(122\) | 18.5138 | − | 5.53821i | 1.67616 | − | 0.501406i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.41767 | − | 12.8108i | −0.755929 | − | 1.15044i | ||||
\(125\) | − | 3.24241i | − | 0.290010i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6430i | 1.47683i | 0.674348 | + | 0.738414i | \(0.264425\pi\) | ||||
−0.674348 | + | 0.738414i | \(0.735575\pi\) | |||||||
\(128\) | −5.06193 | − | 10.1181i | −0.447415 | − | 0.894326i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.68585 | − | 22.3503i | −0.586387 | − | 1.96025i | ||||
\(131\) | −7.59672 | −0.663729 | −0.331864 | − | 0.943327i | \(-0.607678\pi\) | ||||
−0.331864 | + | 0.943327i | \(0.607678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.29273 | −0.198805 | ||||||||
\(134\) | 1.32587 | + | 4.43227i | 0.114537 | + | 0.382890i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.05019 | + | 0.882404i | 0.0900532 | + | 0.0756655i | ||||
\(137\) | − | 9.42492i | − | 0.805225i | −0.915370 | − | 0.402613i | \(-0.868102\pi\) | ||
0.915370 | − | 0.402613i | \(-0.131898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.0000i | − | 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 5.53821 | − | 3.63903i | 0.468064 | − | 0.307554i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.53034 | + | 1.35520i | −0.380177 | + | 0.113726i | ||||
\(143\) | −23.5368 | −1.96824 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.68585 | −0.389138 | ||||||||
\(146\) | −2.84579 | + | 0.851289i | −0.235519 | + | 0.0704532i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | + | 2.62831i | −0.328798 | + | 0.216046i | ||||
\(149\) | 18.4661i | 1.51281i | 0.654106 | + | 0.756403i | \(0.273045\pi\) | ||||
−0.654106 | + | 0.756403i | \(0.726955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.3288i | 1.89847i | 0.314561 | + | 0.949237i | \(0.398143\pi\) | ||||
−0.314561 | + | 0.949237i | \(0.601857\pi\) | |||||||
\(152\) | −4.96490 | − | 4.17166i | −0.402706 | − | 0.338366i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.91611 | − | 6.40539i | −0.154404 | − | 0.516161i | ||||
\(155\) | 25.3953 | 2.03980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.2499 | 1.77573 | 0.887867 | − | 0.460100i | \(-0.152186\pi\) | ||||
0.887867 | + | 0.460100i | \(0.152186\pi\) | |||||||
\(158\) | −4.88694 | − | 16.3367i | −0.388784 | − | 1.29967i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.6142 | + | 2.19656i | 1.47158 | + | 0.173653i | ||||
\(161\) | 7.97002i | 0.628125i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.6430i | − | 1.30358i | −0.758399 | − | 0.651790i | \(-0.774018\pi\) | ||
0.758399 | − | 0.651790i | \(-0.225982\pi\) | |||||||
\(164\) | 7.20010 | + | 10.9578i | 0.562233 | + | 0.855659i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.39312 | − | 1.31415i | 0.340972 | − | 0.101998i | ||||
\(167\) | 8.98064 | 0.694943 | 0.347471 | − | 0.937691i | \(-0.387040\pi\) | ||||
0.347471 | + | 0.937691i | \(0.387040\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7862 | 0.906633 | ||||||||
\(170\) | −2.17715 | + | 0.651273i | −0.166980 | + | 0.0499503i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.89962 | + | 8.97858i | 0.449841 | + | 0.684610i | ||||
\(173\) | 2.75744i | 0.209645i | 0.994491 | + | 0.104822i | \(0.0334274\pi\) | ||||
−0.994491 | + | 0.104822i | \(0.966573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.97858i | 0.451938i | ||||||||
\(176\) | 7.50539 | − | 17.3572i | 0.565740 | − | 1.30835i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.32150 | + | 7.76060i | 0.174004 | + | 0.581681i | ||||
\(179\) | 4.72761 | 0.353358 | 0.176679 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176679 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.39312 | −0.623855 | −0.311928 | − | 0.950106i | \(-0.600975\pi\) | ||||
−0.311928 | + | 0.950106i | \(0.600975\pi\) | |||||||
\(182\) | 2.01782 | + | 6.74543i | 0.149571 | + | 0.500005i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.5016 | + | 17.2590i | −1.06907 | + | 1.27235i | ||||
\(185\) | − | 7.92933i | − | 0.582976i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29273i | 0.167661i | ||||||||
\(188\) | −10.3845 | + | 6.82339i | −0.757365 | + | 0.497647i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.2927 | − | 3.07896i | 0.746713 | − | 0.223371i | ||||
\(191\) | −1.48520 | −0.107465 | −0.0537325 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537325 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.35027 | −0.601066 | −0.300533 | − | 0.953771i | \(-0.597164\pi\) | ||||
−0.300533 | + | 0.953771i | \(0.597164\pi\) | |||||||
\(194\) | 16.3367 | − | 4.88694i | 1.17290 | − | 0.350862i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.67146 | + | 1.09828i | −0.119390 | + | 0.0784485i | ||||
\(197\) | − | 3.82866i | − | 0.272780i | −0.990655 | − | 0.136390i | \(-0.956450\pi\) | ||
0.990655 | − | 0.136390i | \(-0.0435501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.04285i | 0.428366i | 0.976794 | + | 0.214183i | \(0.0687089\pi\) | ||||
−0.976794 | + | 0.214183i | \(0.931291\pi\) | |||||||
\(200\) | −10.8781 | + | 12.9466i | −0.769199 | + | 0.915461i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.90383 | − | 19.7360i | −0.415392 | − | 1.38862i | ||||
\(203\) | 1.41421 | 0.0992583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.7220 | −1.51713 | ||||||||
\(206\) | 2.31316 | + | 7.73273i | 0.161166 | + | 0.538765i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.90383 | + | 18.2787i | −0.548032 | + | 1.26740i | ||||
\(209\) | − | 10.8391i | − | 0.749758i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.95715i | 0.685479i | 0.939431 | + | 0.342739i | \(0.111355\pi\) | ||||
−0.939431 | + | 0.342739i | \(0.888645\pi\) | |||||||
\(212\) | −1.09853 | − | 1.67185i | −0.0754474 | − | 0.114823i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.7342 | − | 6.50157i | 1.48572 | − | 0.444438i | ||||
\(215\) | −17.7985 | −1.21385 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.66442 | −0.520295 | ||||||||
\(218\) | 1.85849 | − | 0.555949i | 0.125873 | − | 0.0376536i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.2039 | + | 26.1825i | 1.15989 | + | 1.76522i | ||||
\(221\) | − | 2.41444i | − | 0.162413i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.786230i | 0.0526499i | 0.999653 | + | 0.0263249i | \(0.00838046\pi\) | ||||
−0.999653 | + | 0.0263249i | \(0.991620\pi\) | |||||||
\(224\) | −5.61788 | − | 0.662933i | −0.375360 | − | 0.0442941i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.57318 | + | 15.2878i | 0.304204 | + | 1.01693i | ||||
\(227\) | −20.2943 | −1.34698 | −0.673492 | − | 0.739195i | \(-0.735206\pi\) | ||||
−0.673492 | + | 0.739195i | \(0.735206\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.97858 | −0.328994 | −0.164497 | − | 0.986378i | \(-0.552600\pi\) | ||||
−0.164497 | + | 0.986378i | \(0.552600\pi\) | |||||||
\(230\) | −10.7031 | − | 35.7797i | −0.705743 | − | 2.35924i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.06247 | + | 2.57318i | 0.201061 | + | 0.168938i | ||||
\(233\) | 0.383688i | 0.0251362i | 0.999921 | + | 0.0125681i | \(0.00400066\pi\) | ||||
−0.999921 | + | 0.0125681i | \(0.995999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 20.5855i | − | 1.34285i | ||||||
\(236\) | −2.31316 | + | 1.51993i | −0.150574 | + | 0.0989388i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.657077 | − | 0.196558i | 0.0425920 | − | 0.0127409i | ||||
\(239\) | 1.48520 | 0.0960693 | 0.0480347 | − | 0.998846i | \(-0.484704\pi\) | ||||
0.0480347 | + | 0.998846i | \(0.484704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.4721 | −1.51197 | −0.755985 | − | 0.654589i | \(-0.772842\pi\) | ||||
−0.755985 | + | 0.654589i | \(0.772842\pi\) | |||||||
\(242\) | 15.3784 | − | 4.60028i | 0.988560 | − | 0.295717i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.8396 | − | 15.0073i | 1.46215 | − | 0.960747i | ||||
\(245\) | − | 3.31339i | − | 0.211685i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4145i | 0.726290i | ||||||||
\(248\) | −16.5973 | − | 13.9455i | −1.05393 | − | 0.885542i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.31415 | − | 4.39312i | −0.0831144 | − | 0.277845i | ||||
\(251\) | −4.62633 | −0.292011 | −0.146006 | − | 0.989284i | \(-0.546642\pi\) | ||||
−0.146006 | + | 0.989284i | \(0.546642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.6791 | −2.36887 | ||||||||
\(254\) | 6.74543 | + | 22.5495i | 0.423246 | + | 1.41488i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9593 | − | 11.6574i | −0.684954 | − | 0.728587i | ||||
\(257\) | − | 3.78797i | − | 0.236287i | −0.992997 | − | 0.118144i | \(-0.962306\pi\) | ||
0.992997 | − | 0.118144i | \(-0.0376943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.39312i | 0.148701i | ||||||||
\(260\) | −18.1172 | − | 27.5724i | −1.12358 | − | 1.70997i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.2927 | + | 3.07896i | −0.635887 | + | 0.190219i | ||||
\(263\) | −12.7989 | −0.789214 | −0.394607 | − | 0.918850i | \(-0.629119\pi\) | ||||
−0.394607 | + | 0.918850i | \(0.629119\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.31415 | 0.203587 | ||||||||
\(266\) | −3.10640 | + | 0.929247i | −0.190466 | + | 0.0569758i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.59281 | + | 5.46787i | 0.219466 | + | 0.334003i | ||||
\(269\) | 25.4662i | 1.55270i | 0.630300 | + | 0.776352i | \(0.282932\pi\) | ||||
−0.630300 | + | 0.776352i | \(0.717068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 21.0361i | − | 1.27785i | −0.769268 | − | 0.638927i | \(-0.779379\pi\) | ||
0.769268 | − | 0.638927i | \(-0.220621\pi\) | |||||||
\(272\) | 1.78054 | + | 0.769917i | 0.107961 | + | 0.0466831i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.81993 | − | 12.7697i | −0.230771 | − | 0.771448i | ||||
\(275\) | −28.2644 | −1.70441 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.39312 | 0.504293 | 0.252147 | − | 0.967689i | \(-0.418863\pi\) | ||||
0.252147 | + | 0.967689i | \(0.418863\pi\) | |||||||
\(278\) | −6.48482 | − | 21.6783i | −0.388934 | − | 1.30018i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.02877 | − | 7.17513i | 0.360288 | − | 0.428796i | ||||
\(281\) | − | 0.111668i | − | 0.00666157i | −0.999994 | − | 0.00333078i | \(-0.998940\pi\) | ||
0.999994 | − | 0.00333078i | \(-0.00106022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 11.4637i | − | 0.681444i | −0.940164 | − | 0.340722i | \(-0.889329\pi\) | ||
0.940164 | − | 0.340722i | \(-0.110671\pi\) | |||||||
\(284\) | −5.58885 | + | 3.67230i | −0.331637 | + | 0.217911i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.8898 | + | 9.53948i | −1.88568 | + | 0.564081i | ||||
\(287\) | 6.55580 | 0.386977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7648 | 0.986165 | ||||||||
\(290\) | −6.34881 | + | 1.89918i | −0.372815 | + | 0.111524i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.51071 | + | 2.30681i | −0.205449 | + | 0.134996i | ||||
\(293\) | 17.8089i | 1.04041i | 0.854042 | + | 0.520204i | \(0.174144\pi\) | ||||
−0.854042 | + | 0.520204i | \(0.825856\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.58546i | − | 0.266976i | ||||||
\(296\) | −4.35431 | + | 5.18228i | −0.253089 | + | 0.301214i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.48436 | + | 25.0196i | 0.433557 | + | 1.44935i | ||||
\(299\) | 39.6794 | 2.29472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.37169 | 0.309619 | ||||||||
\(302\) | 9.45521 | + | 31.6081i | 0.544086 | + | 1.81884i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.41767 | − | 3.63986i | −0.482787 | − | 0.208761i | ||||
\(305\) | 45.2756i | 2.59247i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2499i | 1.15572i | 0.816135 | + | 0.577861i | \(0.196112\pi\) | ||||
−0.816135 | + | 0.577861i | \(0.803888\pi\) | |||||||
\(308\) | −5.19223 | − | 7.90201i | −0.295855 | − | 0.450259i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 34.4078 | − | 10.2927i | 1.95423 | − | 0.584588i | ||||
\(311\) | 1.38392 | 0.0784747 | 0.0392374 | − | 0.999230i | \(-0.487507\pi\) | ||||
0.0392374 | + | 0.999230i | \(0.487507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.1151 | −1.70220 | −0.851102 | − | 0.525000i | \(-0.824065\pi\) | ||||
−0.851102 | + | 0.525000i | \(0.824065\pi\) | |||||||
\(314\) | 30.1462 | − | 9.01791i | 1.70125 | − | 0.508910i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.2425 | − | 20.1537i | −0.744951 | − | 1.13373i | ||||
\(317\) | 5.27317i | 0.296171i | 0.988975 | + | 0.148085i | \(0.0473110\pi\) | ||||
−0.988975 | + | 0.148085i | \(0.952689\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.68585i | 0.374336i | ||||||||
\(320\) | 26.1105 | − | 4.56828i | 1.45962 | − | 0.255374i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.23026 | + | 10.7985i | 0.180015 | + | 0.601777i | ||||
\(323\) | 1.11190 | 0.0618676 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.7648 | 1.65105 | ||||||||
\(326\) | −6.74543 | − | 22.5495i | −0.373595 | − | 1.24890i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.1966 | + | 11.9284i | 0.783874 | + | 0.658635i | ||||
\(329\) | 6.21280i | 0.342523i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.95715i | 0.547295i | 0.961830 | + | 0.273647i | \(0.0882301\pi\) | ||||
−0.961830 | + | 0.273647i | \(0.911770\pi\) | |||||||
\(332\) | 5.41957 | − | 3.56107i | 0.297437 | − | 0.195439i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1678 | − | 3.63986i | 0.665792 | − | 0.199165i | ||||
\(335\) | −10.8391 | −0.592205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3717 | −0.728402 | −0.364201 | − | 0.931320i | \(-0.618658\pi\) | ||||
−0.364201 | + | 0.931320i | \(0.618658\pi\) | |||||||
\(338\) | 15.9691 | − | 4.77698i | 0.868602 | − | 0.259833i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.68585 | + | 1.76481i | −0.145660 | + | 0.0957101i | ||||
\(341\) | − | 36.2344i | − | 1.96220i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 11.6324 | + | 9.77387i | 0.627175 | + | 0.526972i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.11760 | + | 3.73604i | 0.0600823 | + | 0.200851i | ||||
\(347\) | 11.2124 | 0.601915 | 0.300957 | − | 0.953638i | \(-0.402694\pi\) | ||||
0.300957 | + | 0.953638i | \(0.402694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.29273 | −0.229785 | −0.114892 | − | 0.993378i | \(-0.536652\pi\) | ||||
−0.114892 | + | 0.993378i | \(0.536652\pi\) | |||||||
\(350\) | 2.42313 | + | 8.10032i | 0.129522 | + | 0.432980i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.13409 | − | 26.5591i | 0.167047 | − | 1.41561i | ||||
\(353\) | − | 1.78751i | − | 0.0951397i | −0.998868 | − | 0.0475698i | \(-0.984852\pi\) | ||
0.998868 | − | 0.0475698i | \(-0.0151477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.0790i | − | 0.588010i | ||||||
\(356\) | 6.29076 | + | 9.57386i | 0.333410 | + | 0.507413i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.40539 | − | 1.91611i | 0.338536 | − | 0.101269i | ||||
\(359\) | −12.7989 | −0.675500 | −0.337750 | − | 0.941236i | \(-0.609666\pi\) | ||||
−0.337750 | + | 0.941236i | \(0.609666\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7434 | 0.723336 | ||||||||
\(362\) | −11.3718 | + | 3.40174i | −0.597686 | + | 0.178792i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.46787 | + | 8.32150i | 0.286594 | + | 0.436165i | ||||
\(365\) | − | 6.95940i | − | 0.364272i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.1579i | − | 1.57423i | −0.616806 | − | 0.787115i | \(-0.711574\pi\) | ||
0.616806 | − | 0.787115i | \(-0.288426\pi\) | |||||||
\(368\) | −12.6529 | + | 29.2616i | −0.659580 | + | 1.52537i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.21377 | − | 10.7434i | −0.167076 | − | 0.558522i | ||||
\(371\) | −1.00023 | −0.0519293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.21377 | 0.269959 | 0.134979 | − | 0.990848i | \(-0.456903\pi\) | ||||
0.134979 | + | 0.990848i | \(0.456903\pi\) | |||||||
\(374\) | 0.929247 | + | 3.10640i | 0.0480502 | + | 0.160628i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.3043 | + | 13.4538i | −0.582974 | + | 0.693826i | ||||
\(377\) | − | 7.04077i | − | 0.362618i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.7862i | − | 0.862251i | −0.902292 | − | 0.431125i | \(-0.858117\pi\) | ||
0.902292 | − | 0.431125i | \(-0.141883\pi\) | |||||||
\(380\) | 12.6976 | − | 8.34332i | 0.651374 | − | 0.428003i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.01228 | + | 0.601952i | −0.102957 | + | 0.0307985i | ||||
\(383\) | 23.7393 | 1.21302 | 0.606511 | − | 0.795075i | \(-0.292569\pi\) | ||||
0.606511 | + | 0.795075i | \(0.292569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.6644 | 0.798333 | ||||||||
\(386\) | −11.3137 | + | 3.38438i | −0.575853 | + | 0.172260i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.1537 | − | 13.2425i | 1.02315 | − | 0.672288i | ||||
\(389\) | − | 17.7682i | − | 0.900885i | −0.892805 | − | 0.450443i | \(-0.851266\pi\) | ||
0.892805 | − | 0.450443i | \(-0.148734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.86519i | − | 0.195471i | ||||||
\(392\) | −1.81951 | + | 2.16549i | −0.0918994 | + | 0.109374i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.55176 | − | 5.18741i | −0.0781765 | − | 0.261338i | ||||
\(395\) | 39.9514 | 2.01017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4078 | 1.22499 | 0.612496 | − | 0.790473i | \(-0.290165\pi\) | ||||
0.612496 | + | 0.790473i | \(0.290165\pi\) | |||||||
\(398\) | 2.44917 | + | 8.18740i | 0.122766 | + | 0.410397i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.49139 | + | 21.9501i | −0.474570 | + | 1.09751i | ||||
\(401\) | − | 29.1633i | − | 1.45635i | −0.685393 | − | 0.728173i | \(-0.740370\pi\) | ||
0.685393 | − | 0.728173i | \(-0.259630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.1579i | 1.90078i | ||||||||
\(404\) | −15.9981 | − | 24.3474i | −0.795935 | − | 1.21133i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.91611 | − | 0.573183i | 0.0950947 | − | 0.0284466i | ||||
\(407\) | −11.3137 | −0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4851 | −0.518454 | −0.259227 | − | 0.965816i | \(-0.583468\pi\) | ||||
−0.259227 | + | 0.965816i | \(0.583468\pi\) | |||||||
\(410\) | −29.4309 | + | 8.80394i | −1.45349 | + | 0.434796i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.26817 | + | 9.53948i | 0.308811 | + | 0.469976i | ||||
\(413\) | 1.38392i | 0.0680981i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.7434i | 0.527372i | ||||||||
\(416\) | −3.30046 | + | 27.9690i | −0.161818 | + | 1.37129i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.39312 | − | 14.6858i | −0.214874 | − | 0.718308i | ||||
\(419\) | 31.1335 | 1.52097 | 0.760485 | − | 0.649356i | \(-0.224961\pi\) | ||||
0.760485 | + | 0.649356i | \(0.224961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2646 | 1.47501 | 0.737503 | − | 0.675344i | \(-0.236005\pi\) | ||||
0.737503 | + | 0.675344i | \(0.236005\pi\) | |||||||
\(422\) | 4.03565 | + | 13.4909i | 0.196452 | + | 0.656725i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.16599 | − | 1.81993i | −0.105190 | − | 0.0883837i | ||||
\(425\) | − | 2.89941i | − | 0.140642i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.6644i | − | 0.661268i | ||||||
\(428\) | 26.8124 | − | 17.6178i | 1.29603 | − | 0.851590i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.1151 | + | 7.21377i | −1.16293 | + | 0.347879i | ||||
\(431\) | 2.23179 | 0.107502 | 0.0537508 | − | 0.998554i | \(-0.482882\pi\) | ||||
0.0537508 | + | 0.998554i | \(0.482882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.54262 | −0.410532 | −0.205266 | − | 0.978706i | \(-0.565806\pi\) | ||||
−0.205266 | + | 0.978706i | \(0.565806\pi\) | |||||||
\(434\) | −10.3845 | + | 3.10640i | −0.498470 | + | 0.149112i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.29273 | − | 1.50650i | 0.109802 | − | 0.0721483i | ||||
\(437\) | 18.2731i | 0.874121i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.17092i | 0.0558851i | 0.999610 | + | 0.0279426i | \(0.00889556\pi\) | ||||
−0.999610 | + | 0.0279426i | \(0.991104\pi\) | |||||||
\(440\) | 33.9212 | + | 28.5017i | 1.61713 | + | 1.35876i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.978577 | − | 3.27131i | −0.0465462 | − | 0.155600i | ||||
\(443\) | −6.58610 | −0.312915 | −0.156458 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156458 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.9786 | −0.899671 | ||||||||
\(446\) | 0.318660 | + | 1.06526i | 0.0150890 | + | 0.0504414i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.88030 | + | 1.37873i | −0.372309 | + | 0.0651389i | ||||
\(449\) | − | 11.2228i | − | 0.529638i | −0.964298 | − | 0.264819i | \(-0.914688\pi\) | ||
0.964298 | − | 0.264819i | \(-0.0853121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.9933i | 1.45942i | ||||||||
\(452\) | 12.3923 | + | 18.8598i | 0.582886 | + | 0.887090i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.4966 | + | 8.22533i | −1.29048 | + | 0.386034i | ||||
\(455\) | −16.4960 | −0.773344 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9143 | 0.557328 | 0.278664 | − | 0.960389i | \(-0.410108\pi\) | ||||
0.278664 | + | 0.960389i | \(0.410108\pi\) | |||||||
\(458\) | −6.74543 | + | 2.01782i | −0.315193 | + | 0.0942867i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −29.0031 | − | 44.1396i | −1.35228 | − | 2.05802i | ||||
\(461\) | − | 18.4255i | − | 0.858159i | −0.903267 | − | 0.429080i | \(-0.858838\pi\) | ||
0.903267 | − | 0.429080i | \(-0.141162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.47208i | − | 0.347257i | −0.984811 | − | 0.173628i | \(-0.944451\pi\) | ||
0.984811 | − | 0.173628i | \(-0.0555492\pi\) | |||||||
\(464\) | 5.19223 | + | 2.24516i | 0.241043 | + | 0.104229i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.155509 | + | 0.519855i | 0.00720382 | + | 0.0240818i | ||||
\(467\) | −5.57548 | −0.258003 | −0.129001 | − | 0.991644i | \(-0.541177\pi\) | ||||
−0.129001 | + | 0.991644i | \(0.541177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.27131 | 0.151055 | ||||||||
\(470\) | −8.34332 | − | 27.8911i | −0.384849 | − | 1.28652i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.51806 | + | 2.99686i | −0.115903 | + | 0.137942i | ||||
\(473\) | 25.3953i | 1.16767i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7073i | 0.628933i | ||||||||
\(476\) | 0.810603 | − | 0.532628i | 0.0371539 | − | 0.0244130i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.01228 | − | 0.601952i | 0.0920395 | − | 0.0275326i | ||||
\(479\) | 15.9400 | 0.728319 | 0.364159 | − | 0.931337i | \(-0.381356\pi\) | ||||
0.364159 | + | 0.931337i | \(0.381356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9143 | 0.543246 | ||||||||
\(482\) | −31.8021 | + | 9.51327i | −1.44855 | + | 0.433317i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.9715 | − | 12.4658i | 0.862343 | − | 0.566625i | ||||
\(485\) | 39.9514i | 1.81410i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.0722i | − | 1.54396i | −0.635647 | − | 0.771980i | \(-0.719266\pi\) | ||
0.635647 | − | 0.771980i | \(-0.280734\pi\) | |||||||
\(488\) | 24.8626 | − | 29.5902i | 1.12548 | − | 1.33949i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.34292 | − | 4.48929i | −0.0606671 | − | 0.202805i | ||||
\(491\) | −34.0026 | −1.53452 | −0.767258 | − | 0.641339i | \(-0.778379\pi\) | ||||
−0.767258 | + | 0.641339i | \(0.778379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.685846 | −0.0308890 | ||||||||
\(494\) | 4.62633 | + | 15.4655i | 0.208148 | + | 0.695824i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.1396 | − | 12.1678i | −1.26351 | − | 0.546350i | ||||
\(497\) | 3.34369i | 0.149985i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.37169i | 0.240470i | 0.992745 | + | 0.120235i | \(0.0383648\pi\) | ||||
−0.992745 | + | 0.120235i | \(0.961635\pi\) | |||||||
\(500\) | −3.56107 | − | 5.41957i | −0.159256 | − | 0.242370i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.26817 | + | 1.87506i | −0.279762 | + | 0.0836879i | ||||
\(503\) | −37.3463 | −1.66519 | −0.832594 | − | 0.553884i | \(-0.813145\pi\) | ||||
−0.832594 | + | 0.553884i | \(0.813145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.2646 | 2.14775 | ||||||||
\(506\) | −51.0511 | + | 15.2714i | −2.26950 | + | 0.678896i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.2787 | + | 27.8181i | 0.810984 | + | 1.23423i | ||||
\(509\) | 0.403595i | 0.0178890i | 0.999960 | + | 0.00894451i | \(0.00284716\pi\) | ||||
−0.999960 | + | 0.00894451i | \(0.997153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.10038i | 0.0929155i | ||||||||
\(512\) | −19.5734 | − | 11.3527i | −0.865029 | − | 0.501723i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.53527 | − | 5.13229i | −0.0677179 | − | 0.226376i | ||||
\(515\) | −18.9104 | −0.833293 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.3717 | −1.29177 | ||||||||
\(518\) | 0.969933 | + | 3.24241i | 0.0426164 | + | 0.142463i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −35.7220 | − | 30.0147i | −1.56651 | − | 1.31623i | ||||
\(521\) | − | 42.9927i | − | 1.88355i | −0.336249 | − | 0.941773i | \(-0.609158\pi\) | ||
0.336249 | − | 0.941773i | \(-0.390842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0000i | − | 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | −12.6976 | + | 8.34332i | −0.554698 | + | 0.364479i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3411 | + | 5.18741i | −0.756109 | + | 0.226182i | ||||
\(527\) | 3.71699 | 0.161915 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.5212 | 1.76179 | ||||||||
\(530\) | 4.49032 | − | 1.34323i | 0.195047 | − | 0.0583462i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.83221 | + | 2.51806i | −0.166147 | + | 0.109172i | ||||
\(533\) | − | 32.6386i | − | 1.41373i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.1512i | 2.29793i | ||||||||
\(536\) | 7.08400 | + | 5.95219i | 0.305982 | + | 0.257096i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.3215 | + | 34.5040i | 0.444991 | + | 1.48757i | ||||
\(539\) | −4.72761 | −0.203632 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1365 | 0.822742 | 0.411371 | − | 0.911468i | \(-0.365050\pi\) | ||||
0.411371 | + | 0.911468i | \(0.365050\pi\) | |||||||
\(542\) | −8.52597 | − | 28.5017i | −0.366222 | − | 1.22425i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.72448 | + | 0.321500i | 0.116811 | + | 0.0137842i | ||||
\(545\) | 4.54496i | 0.194685i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.14323i | 0.348179i | 0.984730 | + | 0.174090i | \(0.0556983\pi\) | ||||
−0.984730 | + | 0.174090i | \(0.944302\pi\) | |||||||
\(548\) | −10.3512 | − | 15.7534i | −0.442181 | − | 0.672951i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −38.2951 | + | 11.4556i | −1.63291 | + | 0.488468i | ||||
\(551\) | 3.24241 | 0.138131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0575 | −0.512739 | ||||||||
\(554\) | 11.3718 | − | 3.40174i | 0.483140 | − | 0.144526i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.5725 | − | 26.7434i | −0.745238 | − | 1.13417i | ||||
\(557\) | − | 39.0931i | − | 1.65643i | −0.560412 | − | 0.828214i | \(-0.689357\pi\) | ||
0.560412 | − | 0.828214i | \(-0.310643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 26.7434i | − | 1.13112i | ||||||
\(560\) | 5.26024 | − | 12.1650i | 0.222286 | − | 0.514065i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0452593 | − | 0.151298i | −0.00190915 | − | 0.00638213i | ||||
\(563\) | −13.6468 | −0.575143 | −0.287572 | − | 0.957759i | \(-0.592848\pi\) | ||||
−0.287572 | + | 0.957759i | \(0.592848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.3864 | −1.57286 | ||||||||
\(566\) | −4.64624 | − | 15.5320i | −0.195296 | − | 0.652859i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.08389 | + | 7.24074i | −0.255275 | + | 0.303815i | ||||
\(569\) | 2.32355i | 0.0974084i | 0.998813 | + | 0.0487042i | \(0.0155092\pi\) | ||||
−0.998813 | + | 0.0487042i | \(0.984491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 2.88661i | − | 0.120801i | −0.998174 | − | 0.0604005i | \(-0.980762\pi\) | ||
0.998174 | − | 0.0604005i | \(-0.0192378\pi\) | |||||||
\(572\) | −39.3408 | + | 25.8499i | −1.64492 | + | 1.08084i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.88240 | − | 2.65708i | 0.370744 | − | 0.110904i | ||||
\(575\) | 47.6494 | 1.98712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5855 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(578\) | 22.7145 | − | 6.79480i | 0.944798 | − | 0.282626i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.83221 | + | 5.14637i | −0.325215 | + | 0.213691i | ||||
\(581\) | − | 3.24241i | − | 0.134518i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.72869i | − | 0.195842i | ||||||
\(584\) | −3.82168 | + | 4.54837i | −0.158142 | + | 0.188213i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.21798 | + | 24.1292i | 0.298172 | + | 0.996766i | ||||
\(587\) | 9.92979 | 0.409846 | 0.204923 | − | 0.978778i | \(-0.434306\pi\) | ||||
0.204923 | + | 0.978778i | \(0.434306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.5725 | −0.724061 | ||||||||
\(590\) | −1.85849 | − | 6.21280i | −0.0765130 | − | 0.255777i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.79923 | + | 8.78623i | −0.156147 | + | 0.361112i | ||||
\(593\) | − | 24.0823i | − | 0.988942i | −0.869194 | − | 0.494471i | \(-0.835362\pi\) | ||
0.869194 | − | 0.494471i | \(-0.164638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.60688i | 0.0658759i | ||||||||
\(596\) | 20.2810 | + | 30.8655i | 0.830741 | + | 1.26430i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 53.7612 | − | 16.0821i | 2.19846 | − | 0.657646i | ||||
\(599\) | −19.2837 | −0.787912 | −0.393956 | − | 0.919129i | \(-0.628894\pi\) | ||||
−0.393956 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.5855 | 0.431790 | 0.215895 | − | 0.976417i | \(-0.430733\pi\) | ||||
0.215895 | + | 0.976417i | \(0.430733\pi\) | |||||||
\(602\) | 7.27806 | − | 2.17715i | 0.296632 | − | 0.0887342i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25.6216 | + | 38.9933i | 1.04253 | + | 1.58661i | ||||
\(605\) | 37.6079i | 1.52898i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.0722i | 1.38295i | 0.722401 | + | 0.691475i | \(0.243039\pi\) | ||||
−0.722401 | + | 0.691475i | \(0.756961\pi\) | |||||||
\(608\) | −12.8803 | − | 1.51993i | −0.522364 | − | 0.0616412i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.3503 | + | 61.3435i | 0.742981 | + | 2.48373i | ||||
\(611\) | 30.9309 | 1.25133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3288 | −0.699906 | −0.349953 | − | 0.936767i | \(-0.613802\pi\) | ||||
−0.349953 | + | 0.936767i | \(0.613802\pi\) | |||||||
\(614\) | 8.20731 | + | 27.4364i | 0.331220 | + | 1.10724i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.2376 | − | 8.60195i | −0.412485 | − | 0.346583i | ||||
\(617\) | − | 1.76760i | − | 0.0711611i | −0.999367 | − | 0.0355805i | \(-0.988672\pi\) | ||
0.999367 | − | 0.0355805i | \(-0.0113280\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.0424i | 1.89079i | 0.325922 | + | 0.945397i | \(0.394325\pi\) | ||||
−0.325922 | + | 0.945397i | \(0.605675\pi\) | |||||||
\(620\) | 42.4472 | − | 27.8911i | 1.70472 | − | 1.12013i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.87506 | − | 0.560904i | 0.0751830 | − | 0.0224902i | ||||
\(623\) | 5.72784 | 0.229481 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.1495 | −0.765980 | ||||||||
\(626\) | −40.8027 | + | 12.2057i | −1.63080 | + | 0.487837i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.1898 | − | 24.4366i | 1.48404 | − | 0.975126i | ||||
\(629\) | − | 1.16058i | − | 0.0462754i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.0147i | − | 0.557916i | −0.960303 | − | 0.278958i | \(-0.910011\pi\) | ||
0.960303 | − | 0.278958i | \(-0.0899890\pi\) | |||||||
\(632\) | −26.1105 | − | 21.9389i | −1.03862 | − | 0.872681i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.13722 | + | 7.14457i | 0.0848799 | + | 0.283747i | ||||
\(635\) | −55.1448 | −2.18836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.97858 | 0.197258 | ||||||||
\(638\) | 2.70978 | + | 9.05860i | 0.107281 | + | 0.358633i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.5254 | − | 16.7722i | 1.32521 | − | 0.662978i | ||||
\(641\) | 8.92956i | 0.352696i | 0.984328 | + | 0.176348i | \(0.0564285\pi\) | ||||
−0.984328 | + | 0.176348i | \(0.943572\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.53635i | 0.178896i | 0.995991 | + | 0.0894480i | \(0.0285103\pi\) | ||||
−0.995991 | + | 0.0894480i | \(0.971490\pi\) | |||||||
\(644\) | 8.75330 | + | 13.3216i | 0.344928 | + | 0.524944i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50650 | − | 0.450654i | 0.0592725 | − | 0.0177307i | ||||
\(647\) | −5.10091 | −0.200537 | −0.100269 | − | 0.994960i | \(-0.531970\pi\) | ||||
−0.100269 | + | 0.994960i | \(0.531970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.54262 | −0.256820 | ||||||||
\(650\) | 40.3281 | − | 12.0637i | 1.58180 | − | 0.473178i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.2787 | − | 27.8181i | −0.715847 | − | 1.08944i | ||||
\(653\) | − | 26.2535i | − | 1.02738i | −0.857976 | − | 0.513690i | \(-0.828278\pi\) | ||
0.857976 | − | 0.513690i | \(-0.171722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 25.1709i | − | 0.983509i | ||||||
\(656\) | 24.0694 | + | 10.4078i | 0.939752 | + | 0.406356i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.51806 | + | 8.41767i | 0.0981641 | + | 0.328155i | ||||
\(659\) | −16.0413 | −0.624881 | −0.312440 | − | 0.949937i | \(-0.601146\pi\) | ||||
−0.312440 | + | 0.949937i | \(0.601146\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8652 | 1.16162 | 0.580811 | − | 0.814039i | \(-0.302736\pi\) | ||||
0.580811 | + | 0.814039i | \(0.302736\pi\) | |||||||
\(662\) | 4.03565 | + | 13.4909i | 0.156850 | + | 0.524337i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.89962 | − | 7.02142i | 0.228949 | − | 0.272484i | ||||
\(665\) | − | 7.59672i | − | 0.294588i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.2713i | − | 0.436427i | ||||||
\(668\) | 15.0108 | − | 9.86324i | 0.580785 | − | 0.381620i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.6858 | + | 4.39312i | −0.567364 | + | 0.169721i | ||||
\(671\) | 64.6000 | 2.49386 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0080 | −1.34946 | −0.674729 | − | 0.738066i | \(-0.735739\pi\) | ||||
−0.674729 | + | 0.738066i | \(0.735739\pi\) | |||||||
\(674\) | −18.1172 | + | 5.41957i | −0.697848 | + | 0.208754i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.7002 | − | 12.9446i | 0.757701 | − | 0.497868i | ||||
\(677\) | 37.6893i | 1.44852i | 0.689529 | + | 0.724258i | \(0.257818\pi\) | ||||
−0.689529 | + | 0.724258i | \(0.742182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12.0575i | − | 0.462726i | ||||||
\(680\) | −2.92375 | + | 3.47970i | −0.112121 | + | 0.133440i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.6858 | − | 49.0937i | −0.562350 | − | 1.87989i | ||||
\(683\) | −21.5770 | −0.825620 | −0.412810 | − | 0.910817i | \(-0.635453\pi\) | ||||
−0.412810 | + | 0.910817i | \(0.635453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.2285 | 1.19318 | ||||||||
\(686\) | 0.405301 | + | 1.35489i | 0.0154745 | + | 0.0517300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.7220 | + | 8.52792i | 0.751893 | + | 0.325124i | ||||
\(689\) | 4.97972i | 0.189712i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0428i | 0.534215i | 0.963667 | + | 0.267108i | \(0.0860679\pi\) | ||||
−0.963667 | + | 0.267108i | \(0.913932\pi\) | |||||||
\(692\) | 3.02844 | + | 4.60896i | 0.115124 | + | 0.175206i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.1916 | − | 4.54441i | 0.576666 | − | 0.172504i | ||||
\(695\) | 53.0143 | 2.01095 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.17935 | −0.120426 | ||||||||
\(698\) | −5.81618 | + | 1.73985i | −0.220146 | + | 0.0658543i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.56614 | + | 9.99296i | 0.248177 | + | 0.377698i | ||||
\(701\) | 27.9214i | 1.05458i | 0.849687 | + | 0.527288i | \(0.176791\pi\) | ||||
−0.849687 | + | 0.527288i | \(0.823209\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48677i | 0.206937i | ||||||||
\(704\) | −6.51810 | − | 37.2550i | −0.245660 | − | 1.40410i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.724481 | − | 2.42188i | −0.0272662 | − | 0.0911488i | ||||
\(707\) | −14.5665 | −0.547830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5426 | −0.395936 | −0.197968 | − | 0.980208i | \(-0.563434\pi\) | ||||
−0.197968 | + | 0.980208i | \(0.563434\pi\) | |||||||
\(710\) | −4.49032 | − | 15.0108i | −0.168519 | − | 0.563345i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.4036 | + | 10.4219i | 0.464844 | + | 0.390577i | ||||
\(713\) | 61.0856i | 2.28767i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 77.9865i | − | 2.91653i | ||||||
\(716\) | 7.90201 | − | 5.19223i | 0.295312 | − | 0.194043i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.3411 | + | 5.18741i | −0.647165 | + | 0.193593i | ||||
\(719\) | 31.8801 | 1.18893 | 0.594463 | − | 0.804123i | \(-0.297365\pi\) | ||||
0.594463 | + | 0.804123i | \(0.297365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.70727 | 0.212550 | ||||||||
\(722\) | 18.6208 | − | 5.57021i | 0.692994 | − | 0.207302i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.0288 | + | 9.21798i | −0.521375 | + | 0.342584i | ||||
\(725\) | − | 8.45498i | − | 0.314010i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 46.2070i | − | 1.71372i | −0.515546 | − | 0.856862i | \(-0.672411\pi\) | ||
0.515546 | − | 0.856862i | \(-0.327589\pi\) | |||||||
\(728\) | 10.7811 | + | 9.05860i | 0.399573 | + | 0.335734i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.82065 | − | 9.42923i | −0.104397 | − | 0.348991i | ||||
\(731\) | −2.60509 | −0.0963528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.4360 | 0.828691 | 0.414346 | − | 0.910120i | \(-0.364010\pi\) | ||||
0.414346 | + | 0.910120i | \(0.364010\pi\) | |||||||
\(734\) | −12.2230 | − | 40.8607i | −0.451161 | − | 1.50820i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.28359 | + | 44.7746i | −0.194756 | + | 1.65041i | ||||
\(737\) | 15.4655i | 0.569678i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 14.0147i | − | 0.515539i | −0.966206 | − | 0.257769i | \(-0.917013\pi\) | ||
0.966206 | − | 0.257769i | \(-0.0829875\pi\) | |||||||
\(740\) | −8.70862 | − | 13.2536i | −0.320135 | − | 0.487211i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.35520 | + | 0.405394i | −0.0497510 | + | 0.0148825i | ||||
\(743\) | −25.9313 | −0.951327 | −0.475663 | − | 0.879627i | \(-0.657792\pi\) | ||||
−0.475663 | + | 0.879627i | \(0.657792\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −61.1856 | −2.24167 | ||||||||
\(746\) | 7.06409 | − | 2.11315i | 0.258635 | − | 0.0773679i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.51806 | + | 3.83221i | 0.0920693 | + | 0.140120i | ||||
\(749\) | − | 16.0413i | − | 0.586137i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.74338i | 0.100108i | 0.998747 | + | 0.0500538i | \(0.0159393\pi\) | ||||
−0.998747 | + | 0.0500538i | \(0.984061\pi\) | |||||||
\(752\) | −9.86324 | + | 22.8101i | −0.359675 | + | 0.831798i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.85363 | − | 9.53948i | −0.103923 | − | 0.347407i | ||||
\(755\) | −77.2977 | −2.81315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7992 | −0.574233 | −0.287116 | − | 0.957896i | \(-0.592697\pi\) | ||||
−0.287116 | + | 0.957896i | \(0.592697\pi\) | |||||||
\(758\) | −6.80348 | − | 22.7435i | −0.247114 | − | 0.826082i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.8223 | − | 16.4507i | 0.501389 | − | 0.596728i | ||||
\(761\) | 27.0527i | 0.980660i | 0.871537 | + | 0.490330i | \(0.163124\pi\) | ||||
−0.871537 | + | 0.490330i | \(0.836876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.37169i | − | 0.0496586i | ||||||
\(764\) | −2.48245 | + | 1.63116i | −0.0898118 | + | 0.0590133i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.1642 | − | 9.62158i | 1.16214 | − | 0.347642i | ||||
\(767\) | 6.88994 | 0.248781 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.8715 | 1.43780 | 0.718901 | − | 0.695113i | \(-0.244646\pi\) | ||||
0.718901 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(770\) | 21.2236 | − | 6.34881i | 0.764845 | − | 0.228795i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.9572 | + | 9.17092i | −0.502329 | + | 0.330069i | ||||
\(773\) | 34.4261i | 1.23822i | 0.785304 | + | 0.619110i | \(0.212507\pi\) | ||||
−0.785304 | + | 0.619110i | \(0.787493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.8223i | 1.64599i | ||||||||
\(776\) | 21.9389 | − | 26.1105i | 0.787560 | − | 0.937313i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.20149 | − | 24.0740i | −0.258186 | − | 0.863096i | ||||
\(779\) | 15.0307 | 0.538531 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8077 | −0.565642 | ||||||||
\(782\) | −1.56657 | − | 5.23692i | −0.0560203 | − | 0.187272i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.58757 | + | 3.67146i | −0.0566988 | + | 0.131124i | ||||
\(785\) | 73.7226i | 2.63127i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1151i | 0.859610i | 0.902922 | + | 0.429805i | \(0.141418\pi\) | ||||
−0.902922 | + | 0.429805i | \(0.858582\pi\) | |||||||
\(788\) | −4.20493 | − | 6.39945i | −0.149795 | − | 0.227971i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 54.1298 | − | 16.1923i | 1.92585 | − | 0.576098i | ||||
\(791\) | 11.2834 | 0.401192 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.0294 | −2.41579 | ||||||||
\(794\) | 33.0699 | − | 9.89252i | 1.17361 | − | 0.351072i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.63673 | + | 10.1004i | 0.235233 | + | 0.357999i | ||||
\(797\) | − | 35.0634i | − | 1.24201i | −0.783807 | − | 0.621005i | \(-0.786725\pi\) | ||
0.783807 | − | 0.621005i | \(-0.213275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.01300i | − | 0.106592i | ||||||
\(800\) | −3.96340 | + | 33.5869i | −0.140127 | + | 1.18748i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.8199 | − | 39.5131i | −0.417376 | − | 1.39526i | ||||
\(803\) | −9.92979 | −0.350415 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.4078 | −0.930753 | ||||||||
\(806\) | 15.4655 | + | 51.6998i | 0.544748 | + | 1.82105i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −31.5437 | − | 26.5040i | −1.10970 | − | 0.932407i | ||||
\(809\) | − | 21.9806i | − | 0.772796i | −0.922332 | − | 0.386398i | \(-0.873719\pi\) | ||
0.922332 | − | 0.386398i | \(-0.126281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 44.7005i | − | 1.56965i | −0.619719 | − | 0.784824i | \(-0.712753\pi\) | ||
0.619719 | − | 0.784824i | \(-0.287247\pi\) | |||||||
\(812\) | 2.36380 | − | 1.55320i | 0.0829532 | − | 0.0545067i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.3288 | + | 4.58546i | −0.537276 | + | 0.160720i | ||||
\(815\) | 55.1448 | 1.93164 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3158 | 0.430877 | ||||||||
\(818\) | −14.2061 | + | 4.24962i | −0.496706 | + | 0.148584i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.3074 | + | 23.8568i | −1.26791 | + | 0.833115i | ||||
\(821\) | 39.3651i | 1.37385i | 0.726727 | + | 0.686926i | \(0.241040\pi\) | ||||
−0.726727 | + | 0.686926i | \(0.758960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 31.9718i | − | 1.11447i | −0.830355 | − | 0.557234i | \(-0.811863\pi\) | ||
0.830355 | − | 0.557234i | \(-0.188137\pi\) | |||||||
\(824\) | 12.3591 | + | 10.3845i | 0.430548 | + | 0.361760i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.560904 | + | 1.87506i | 0.0195163 | + | 0.0652416i | ||||
\(827\) | −20.8702 | −0.725728 | −0.362864 | − | 0.931842i | \(-0.618201\pi\) | ||||
−0.362864 | + | 0.931842i | \(0.618201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.2217 | −1.11911 | −0.559554 | − | 0.828794i | \(-0.689027\pi\) | ||||
−0.559554 | + | 0.828794i | \(0.689027\pi\) | |||||||
\(830\) | 4.35431 | + | 14.5561i | 0.151140 | + | 0.505250i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.86412 | + | 39.2327i | 0.237970 | + | 1.36015i | ||||
\(833\) | − | 0.484966i | − | 0.0168031i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.7564i | 1.02976i | ||||||||
\(836\) | −11.9044 | − | 18.1172i | −0.411722 | − | 0.626596i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42.1825 | − | 12.6184i | 1.45717 | − | 0.435897i | ||||
\(839\) | −48.9320 | −1.68932 | −0.844660 | − | 0.535303i | \(-0.820198\pi\) | ||||
−0.844660 | + | 0.535303i | \(0.820198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 41.0052 | − | 12.2663i | 1.41313 | − | 0.422724i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.9357 | + | 16.6430i | 0.376423 | + | 0.572876i | ||||
\(845\) | 39.0524i | 1.34344i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.3503i | − | 0.390000i | ||||||
\(848\) | −3.67230 | − | 1.58793i | −0.126107 | − | 0.0545298i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.17513 | − | 3.92839i | −0.0403068 | − | 0.134742i | ||||
\(851\) | 19.0732 | 0.653820 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2927 | 0.420895 | 0.210448 | − | 0.977605i | \(-0.432508\pi\) | ||||
0.210448 | + | 0.977605i | \(0.432508\pi\) | |||||||
\(854\) | −5.53821 | − | 18.5138i | −0.189514 | − | 0.633530i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.1874 | − | 34.7374i | 0.997605 | − | 1.18730i | ||||
\(857\) | − | 57.1349i | − | 1.95169i | −0.218463 | − | 0.975845i | \(-0.570104\pi\) | ||
0.218463 | − | 0.975845i | \(-0.429896\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.8223i | 0.744569i | 0.928119 | + | 0.372284i | \(0.121425\pi\) | ||||
−0.928119 | + | 0.372284i | \(0.878575\pi\) | |||||||
\(860\) | −29.7496 | + | 19.5477i | −1.01445 | + | 0.666573i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.02384 | − | 0.904549i | 0.102992 | − | 0.0308090i | ||||
\(863\) | 42.2764 | 1.43911 | 0.719553 | − | 0.694437i | \(-0.244347\pi\) | ||||
0.719553 | + | 0.694437i | \(0.244347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.13650 | −0.310650 | ||||||||
\(866\) | −11.5743 | + | 3.46233i | −0.393311 | + | 0.117655i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.8108 | + | 8.41767i | −0.434827 | + | 0.285714i | ||||
\(869\) | − | 57.0033i | − | 1.93370i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 16.2865i | − | 0.551846i | ||||||
\(872\) | 2.49581 | − | 2.97039i | 0.0845190 | − | 0.100590i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.40612 | + | 24.7581i | 0.250516 | + | 0.837454i | ||||
\(875\) | −3.24241 | −0.109614 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.2008 | 0.884737 | 0.442369 | − | 0.896833i | \(-0.354138\pi\) | ||||
0.442369 | + | 0.896833i | \(0.354138\pi\) | |||||||
\(878\) | 0.474577 | + | 1.58647i | 0.0160162 | + | 0.0535409i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 57.5113 | + | 24.8683i | 1.93871 | + | 0.838311i | ||||
\(881\) | − | 47.4165i | − | 1.59750i | −0.601661 | − | 0.798752i | \(-0.705494\pi\) | ||
0.601661 | − | 0.798752i | \(-0.294506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.6283i | 0.896114i | 0.894005 | + | 0.448057i | \(0.147884\pi\) | ||||
−0.894005 | + | 0.448057i | \(0.852116\pi\) | |||||||
\(884\) | −2.65173 | − | 4.03565i | −0.0891874 | − | 0.135734i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.92345 | + | 2.66936i | −0.299789 | + | 0.0896788i | ||||
\(887\) | 6.75684 | 0.226873 | 0.113436 | − | 0.993545i | \(-0.463814\pi\) | ||||
0.113436 | + | 0.993545i | \(0.463814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.6430 | 0.558188 | ||||||||
\(890\) | −25.7139 | + | 7.69204i | −0.861932 | + | 0.257838i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.863500 | + | 1.31415i | 0.0289121 | + | 0.0440011i | ||||
\(893\) | 14.2443i | 0.476667i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.6644i | 0.523604i | ||||||||
\(896\) | −10.1181 | + | 5.06193i | −0.338024 | + | 0.169107i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.54862 | − | 15.2057i | −0.151790 | − | 0.507421i | ||||
\(899\) | 10.8391 | 0.361505 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.485078 | 0.0161603 | ||||||||
\(902\) | 12.5616 | + | 41.9925i | 0.418256 | + | 1.39820i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.4342 | + | 20.5303i | 0.812668 | + | 0.682829i | ||||
\(905\) | − | 27.8097i | − | 0.924426i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 25.2860i | − | 0.839608i | −0.907615 | − | 0.419804i | \(-0.862099\pi\) | ||
0.907615 | − | 0.419804i | \(-0.137901\pi\) | |||||||
\(908\) | −33.9212 | + | 22.2888i | −1.12572 | + | 0.739681i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.3503 | + | 6.68585i | −0.740904 | + | 0.221634i | ||||
\(911\) | −21.3050 | −0.705865 | −0.352932 | − | 0.935649i | \(-0.614815\pi\) | ||||
−0.352932 | + | 0.935649i | \(0.614815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3288 | 0.507311 | ||||||||
\(914\) | 16.1426 | − | 4.82889i | 0.533950 | − | 0.159725i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.32150 | + | 5.46787i | −0.274950 | + | 0.180663i | ||||
\(917\) | 7.59672i | 0.250866i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.4998i | 1.59986i | 0.600093 | + | 0.799930i | \(0.295130\pi\) | ||||
−0.600093 | + | 0.799930i | \(0.704870\pi\) | |||||||
\(920\) | −57.1860 | − | 48.0494i | −1.88537 | − | 1.58414i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.46787 | − | 24.9645i | −0.245941 | − | 0.822162i | ||||
\(923\) | 16.6468 | 0.547937 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.3074 | 0.470425 | ||||||||
\(926\) | −3.02844 | − | 10.1239i | −0.0995208 | − | 0.332690i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.94488 | + | 0.937529i | 0.260803 | + | 0.0307759i | ||||
\(929\) | − | 10.5567i | − | 0.346355i | −0.984891 | − | 0.173177i | \(-0.944597\pi\) | ||
0.984891 | − | 0.173177i | \(-0.0554034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29273i | 0.0751412i | ||||||||
\(932\) | 0.421396 | + | 0.641319i | 0.0138033 | + | 0.0210071i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.55417 | + | 2.25975i | −0.247180 | + | 0.0739413i | ||||
\(935\) | −7.59672 | −0.248439 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.5296 | −0.964690 | −0.482345 | − | 0.875981i | \(-0.660215\pi\) | ||||
−0.482345 | + | 0.875981i | \(0.660215\pi\) | |||||||
\(938\) | 4.43227 | − | 1.32587i | 0.144719 | − | 0.0432911i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −22.6086 | − | 34.4078i | −0.737410 | − | 1.12226i | ||||
\(941\) | 6.53503i | 0.213036i | 0.994311 | + | 0.106518i | \(0.0339701\pi\) | ||||
−0.994311 | + | 0.106518i | \(0.966030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 52.2499i | − | 1.70149i | ||||||
\(944\) | −2.19706 | + | 5.08100i | −0.0715083 | + | 0.165372i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.2927 | + | 34.4078i | 0.334646 | + | 1.11869i | ||||
\(947\) | −43.2951 | −1.40690 | −0.703450 | − | 0.710745i | \(-0.748358\pi\) | ||||
−0.703450 | + | 0.710745i | \(0.748358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4569 | 0.339446 | ||||||||
\(950\) | 5.55558 | + | 18.5719i | 0.180247 | + | 0.602551i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.882404 | − | 1.05019i | 0.0285989 | − | 0.0340369i | ||||
\(953\) | 19.4848i | 0.631173i | 0.948897 | + | 0.315587i | \(0.102201\pi\) | ||||
−0.948897 | + | 0.315587i | \(0.897799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.92104i | − | 0.159241i | ||||||
\(956\) | 2.48245 | − | 1.63116i | 0.0802881 | − | 0.0527555i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.5970 | − | 6.46052i | 0.697768 | − | 0.208730i | ||||
\(959\) | −9.42492 | −0.304346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.7434 | −0.894948 | ||||||||
\(962\) | 16.1426 | − | 4.82889i | 0.520458 | − | 0.155690i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −39.2327 | + | 25.7789i | −1.26360 | + | 0.830282i | ||||
\(965\) | − | 27.6677i | − | 0.890656i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4422i | 0.914641i | 0.889302 | + | 0.457320i | \(0.151191\pi\) | ||||
−0.889302 | + | 0.457320i | \(0.848809\pi\) | |||||||
\(968\) | 20.6520 | − | 24.5789i | 0.663780 | − | 0.789997i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.1923 | + | 54.1298i | 0.519905 | + | 1.73800i | ||||
\(971\) | 8.61534 | 0.276479 | 0.138240 | − | 0.990399i | \(-0.455856\pi\) | ||||
0.138240 | + | 0.990399i | \(0.455856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.0000 | −0.512936 | ||||||||
\(974\) | −13.8095 | − | 46.1642i | −0.442486 | − | 1.47920i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.6932 | − | 50.1684i | 0.694382 | − | 1.60585i | ||||
\(977\) | − | 35.8715i | − | 1.14763i | −0.818985 | − | 0.573815i | \(-0.805463\pi\) | ||
0.818985 | − | 0.573815i | \(-0.194537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0790i | 0.865447i | ||||||||
\(980\) | −3.63903 | − | 5.53821i | −0.116245 | − | 0.176912i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −46.0698 | + | 13.7813i | −1.47015 | + | 0.439779i | ||||
\(983\) | 41.0633 | 1.30971 | 0.654857 | − | 0.755752i | \(-0.272729\pi\) | ||||
0.654857 | + | 0.755752i | \(0.272729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.6858 | 0.404205 | ||||||||
\(986\) | −0.929247 | + | 0.277974i | −0.0295933 | + | 0.00885251i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.5363 | + | 19.0790i | 0.398834 | + | 0.606983i | ||||
\(989\) | − | 42.8125i | − | 1.36136i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6707i | 0.815456i | 0.913103 | + | 0.407728i | \(0.133679\pi\) | ||||
−0.913103 | + | 0.407728i | \(0.866321\pi\) | |||||||
\(992\) | −43.0578 | − | 5.08100i | −1.36709 | − | 0.161322i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.35520 | + | 4.53034i | 0.0429844 | + | 0.143694i | ||||
\(995\) | −20.0223 | −0.634750 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.45065 | −0.0776130 | −0.0388065 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388065 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(998\) | 2.17715 | + | 7.27806i | 0.0689166 | + | 0.230383i | ||||
\(999\) | 0 | 0 |
(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 | 252.2.e.a.71.11 | yes | 12 | |
3.2 | odd | 2 | inner | 252.2.e.a.71.2 | yes | 12 | |
4.3 | odd | 2 | inner | 252.2.e.a.71.1 | ✓ | 12 | |
7.6 | odd | 2 | 1764.2.e.g.1079.11 | 12 | |||
8.3 | odd | 2 | 4032.2.h.h.575.2 | 12 | |||
8.5 | even | 2 | 4032.2.h.h.575.1 | 12 | |||
12.11 | even | 2 | inner | 252.2.e.a.71.12 | yes | 12 | |
21.20 | even | 2 | 1764.2.e.g.1079.2 | 12 | |||
24.5 | odd | 2 | 4032.2.h.h.575.11 | 12 | |||
24.11 | even | 2 | 4032.2.h.h.575.12 | 12 | |||
28.27 | even | 2 | 1764.2.e.g.1079.1 | 12 | |||
84.83 | odd | 2 | 1764.2.e.g.1079.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.e.a.71.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
252.2.e.a.71.2 | yes | 12 | 3.2 | odd | 2 | inner | |
252.2.e.a.71.11 | yes | 12 | 1.1 | even | 1 | trivial | |
252.2.e.a.71.12 | yes | 12 | 12.11 | even | 2 | inner | |
1764.2.e.g.1079.1 | 12 | 28.27 | even | 2 | |||
1764.2.e.g.1079.2 | 12 | 21.20 | even | 2 | |||
1764.2.e.g.1079.11 | 12 | 7.6 | odd | 2 | |||
1764.2.e.g.1079.12 | 12 | 84.83 | odd | 2 | |||
4032.2.h.h.575.1 | 12 | 8.5 | even | 2 | |||
4032.2.h.h.575.2 | 12 | 8.3 | odd | 2 | |||
4032.2.h.h.575.11 | 12 | 24.5 | odd | 2 | |||
4032.2.h.h.575.12 | 12 | 24.11 | even | 2 |