Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(95,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bz (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 9 x^{12} + 3 x^{11} - 46 x^{10} + 141 x^{9} - 266 x^{8} + \cdots + 6561 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Root | \(-0.0741962 + 1.73046i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.95 |
Dual form | 624.2.bz.h.335.4 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0741962 | + | 1.73046i | −0.0428372 | + | 0.999082i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.88845 | −0.844540 | −0.422270 | − | 0.906470i | \(-0.638767\pi\) | ||||
−0.422270 | + | 0.906470i | \(0.638767\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.897962 | + | 1.55532i | 0.339398 | + | 0.587854i | 0.984320 | − | 0.176394i | \(-0.0564434\pi\) |
−0.644922 | + | 0.764249i | \(0.723110\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98899 | − | 0.256787i | −0.996330 | − | 0.0855958i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56534 | − | 1.48110i | −0.773481 | − | 0.446569i | 0.0606343 | − | 0.998160i | \(-0.480688\pi\) |
−0.834115 | + | 0.551591i | \(0.814021\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.29809 | − | 1.45691i | −0.914727 | − | 0.404073i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.140116 | − | 3.26789i | 0.0361778 | − | 0.843765i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00651 | + | 1.15846i | −0.486650 | + | 0.280967i | −0.723183 | − | 0.690656i | \(-0.757322\pi\) |
0.236534 | + | 0.971623i | \(0.423989\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.897962 | + | 1.55532i | 0.206007 | + | 0.356814i | 0.950453 | − | 0.310868i | \(-0.100620\pi\) |
−0.744446 | + | 0.667682i | \(0.767286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.75804 | + | 1.43849i | −0.601853 | + | 0.313904i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.56534 | − | 4.44331i | 0.534911 | − | 0.926494i | −0.464256 | − | 0.885701i | \(-0.653678\pi\) |
0.999168 | − | 0.0407927i | \(-0.0129883\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.43376 | −0.286752 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.666132 | − | 5.15328i | 0.128197 | − | 0.991749i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.08236 | − | 0.624903i | −0.200990 | − | 0.116041i | 0.396127 | − | 0.918196i | \(-0.370354\pi\) |
−0.597117 | + | 0.802154i | \(0.703687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65910 | 0.477589 | 0.238794 | − | 0.971070i | \(-0.423248\pi\) | ||||
0.238794 | + | 0.971070i | \(0.423248\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.75333 | − | 4.32934i | 0.479293 | − | 0.753641i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.69576 | − | 2.93714i | −0.286635 | − | 0.496466i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.01497 | − | 2.89540i | −0.824457 | − | 0.476000i | 0.0274943 | − | 0.999622i | \(-0.491247\pi\) |
−0.851951 | + | 0.523622i | \(0.824581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.76583 | − | 5.59913i | 0.442887 | − | 0.896578i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.74408 | + | 9.94904i | −0.897075 | + | 1.55378i | −0.0658595 | + | 0.997829i | \(0.520979\pi\) |
−0.831215 | + | 0.555950i | \(0.812354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.00651 | + | 5.19991i | −1.37348 | + | 0.792979i | −0.991364 | − | 0.131136i | \(-0.958138\pi\) |
−0.382115 | + | 0.924115i | \(0.624804\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.64456 | + | 0.484930i | 0.841441 | + | 0.0722891i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.667511i | − | 0.0973664i | −0.998814 | − | 0.0486832i | \(-0.984498\pi\) | ||
0.998814 | − | 0.0486832i | \(-0.0155025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.88733 | − | 3.26895i | 0.269618 | − | 0.466993i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.85579 | − | 3.55814i | −0.259863 | − | 0.498239i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.67049i | − | 0.504181i | −0.967704 | − | 0.252090i | \(-0.918882\pi\) | ||
0.967704 | − | 0.252090i | \(-0.0811180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.84452 | + | 2.79699i | 0.653235 | + | 0.377146i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.75804 | + | 1.43849i | −0.365311 | + | 0.190533i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.14343 | + | 1.81486i | −0.409239 | + | 0.236274i | −0.690463 | − | 0.723368i | \(-0.742593\pi\) |
0.281224 | + | 0.959642i | \(0.409260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.68542 | − | 8.11539i | −0.599907 | − | 1.03907i | −0.992834 | − | 0.119500i | \(-0.961871\pi\) |
0.392927 | − | 0.919570i | \(-0.371462\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.28461 | − | 4.87941i | −0.287834 | − | 0.614748i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.22828 | + | 2.75129i | 0.772523 | + | 0.341256i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.306114 | − | 0.530205i | 0.0373978 | − | 0.0647749i | −0.846721 | − | 0.532038i | \(-0.821426\pi\) |
0.884118 | + | 0.467263i | \(0.154760\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.49863 | + | 4.76891i | 0.902729 | + | 0.574109i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.23069 | − | 4.75199i | 0.976804 | − | 0.563958i | 0.0755000 | − | 0.997146i | \(-0.475945\pi\) |
0.901304 | + | 0.433188i | \(0.142611\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.90142i | 1.04183i | 0.853608 | + | 0.520916i | \(0.174410\pi\) | ||||
−0.853608 | + | 0.520916i | \(0.825590\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.106379 | − | 2.48106i | 0.0122836 | − | 0.286489i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.31989i | − | 0.606258i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.22126i | 0.699947i | 0.936760 | + | 0.349973i | \(0.113809\pi\) | ||||
−0.936760 | + | 0.349973i | \(0.886191\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86812 | + | 1.53507i | 0.985347 | + | 0.170563i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.7231i | 1.94536i | 0.232146 | + | 0.972681i | \(0.425425\pi\) | ||||
−0.232146 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.78919 | − | 2.18769i | 0.410995 | − | 0.237288i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.16168 | − | 1.82662i | 0.124545 | − | 0.195834i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.75804 | − | 4.77706i | 0.292351 | − | 0.506368i | −0.682014 | − | 0.731339i | \(-0.738896\pi\) |
0.974365 | + | 0.224972i | \(0.0722290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.695613 | − | 6.43782i | −0.0729200 | − | 0.674867i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.197295 | + | 4.60147i | −0.0204586 | + | 0.477150i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69576 | − | 2.93714i | −0.173981 | − | 0.301344i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.54976 | + | 5.51356i | −0.969631 | + | 0.559817i | −0.899124 | − | 0.437695i | \(-0.855795\pi\) |
−0.0705073 | + | 0.997511i | \(0.522462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.28746 | + | 5.08575i | 0.732417 | + | 0.511137i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6428 | − | 6.14460i | −1.05899 | − | 0.611410i | −0.133840 | − | 0.991003i | \(-0.542731\pi\) |
−0.925154 | + | 0.379593i | \(0.876064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.1044i | 1.88242i | 0.337829 | + | 0.941208i | \(0.390308\pi\) | ||||
−0.337829 | + | 0.941208i | \(0.609692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.20842 | − | 2.71651i | 0.508289 | − | 0.265105i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.57676 | + | 14.8554i | −0.829146 | + | 1.43612i | 0.0695624 | + | 0.997578i | \(0.477840\pi\) |
−0.898709 | + | 0.438546i | \(0.855494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2885i | 1.17703i | 0.808487 | + | 0.588514i | \(0.200287\pi\) | ||||
−0.808487 | + | 0.588514i | \(0.799713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.38246 | − | 8.46339i | 0.510881 | − | 0.803309i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.32579 | − | 4.22955i | 0.689153 | − | 0.397882i | −0.114142 | − | 0.993464i | \(-0.536412\pi\) |
0.803295 | + | 0.595582i | \(0.203079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.84452 | + | 8.39096i | −0.451754 | + | 0.782461i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.48385 | + | 5.20159i | 0.876783 | + | 0.480887i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.60353 | − | 2.08050i | −0.330335 | − | 0.190719i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.11267 | − | 1.92720i | −0.101152 | − | 0.175200i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.7902 | − | 10.6781i | −1.51392 | − | 0.962811i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1498 | 1.08671 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.54976 | + | 2.04945i | 0.314990 | + | 0.181860i | 0.649157 | − | 0.760654i | \(-0.275122\pi\) |
−0.334167 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.32999 | − | 15.9712i | −0.733415 | − | 1.40619i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9535 | 0.957012 | 0.478506 | − | 0.878084i | \(-0.341178\pi\) | ||||
0.478506 | + | 0.878084i | \(0.341178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.61267 | + | 2.79323i | −0.139836 | + | 0.242204i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.25796 | + | 9.73170i | −0.108268 | + | 0.837572i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.35869 | − | 9.28153i | −0.457824 | − | 0.792975i | 0.541022 | − | 0.841009i | \(-0.318038\pi\) |
−0.998846 | + | 0.0480340i | \(0.984704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.849362 | − | 0.490379i | 0.0720420 | − | 0.0415934i | −0.463546 | − | 0.886073i | \(-0.653423\pi\) |
0.535588 | + | 0.844479i | \(0.320090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.15510 | + | 0.0495268i | 0.0972771 | + | 0.00417091i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.30292 | + | 8.62228i | 0.527077 | + | 0.721031i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.04399 | + | 1.18010i | 0.169744 | + | 0.0980017i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.51676 | + | 3.50849i | 0.455014 | + | 0.289376i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.94290 | + | 15.4896i | 0.732631 | + | 1.26895i | 0.955755 | + | 0.294164i | \(0.0950412\pi\) |
−0.223124 | + | 0.974790i | \(0.571626\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3036 | −1.40815 | −0.704073 | − | 0.710127i | \(-0.748637\pi\) | ||||
−0.704073 | + | 0.710127i | \(0.748637\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.29491 | − | 2.94737i | 0.508913 | − | 0.238281i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.02158 | −0.403343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.04687 | −0.562402 | −0.281201 | − | 0.959649i | \(-0.590733\pi\) | ||||
−0.281201 | + | 0.959649i | \(0.590733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.35164 | + | 0.272337i | 0.503718 | + | 0.0215977i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.21433 | 0.726191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.49154 | + | 4.31547i | 0.195152 | + | 0.338014i | 0.946950 | − | 0.321380i | \(-0.104147\pi\) |
−0.751798 | + | 0.659393i | \(0.770813\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.19952 | + | 8.17573i | −0.404782 | + | 0.636480i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.14343 | + | 1.81486i | 0.243246 | + | 0.140438i | 0.616668 | − | 0.787224i | \(-0.288482\pi\) |
−0.373422 | + | 0.927662i | \(0.621816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.75485 | + | 9.61003i | 0.673450 | + | 0.739233i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.28461 | − | 4.87941i | −0.174709 | − | 0.373138i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.1424 | − | 9.89716i | 1.30331 | − | 0.752467i | 0.322340 | − | 0.946624i | \(-0.395530\pi\) |
0.980970 | + | 0.194157i | \(0.0621971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.28746 | − | 2.22995i | −0.0973229 | − | 0.168568i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.90731 | − | 5.57423i | −0.218527 | − | 0.418985i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.64898 | − | 11.5164i | 0.496968 | − | 0.860774i | −0.503026 | − | 0.864272i | \(-0.667780\pi\) |
0.999994 | + | 0.00349718i | \(0.00111319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9371 | 0.887277 | 0.443638 | − | 0.896206i | \(-0.353687\pi\) | ||||
0.443638 | + | 0.896206i | \(0.353687\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.3910 | − | 7.50581i | 1.06381 | − | 0.554845i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.47052 | + | 5.46781i | 0.696287 | + | 0.402001i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.86318 | 0.501885 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.61313 | − | 3.59140i | 0.626513 | − | 0.261236i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2725 | − | 17.7925i | −0.743293 | − | 1.28742i | −0.950988 | − | 0.309227i | \(-0.899930\pi\) |
0.207695 | − | 0.978194i | \(-0.433404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84090 | − | 1.06284i | −0.132511 | − | 0.0765051i | 0.432279 | − | 0.901740i | \(-0.357709\pi\) |
−0.564790 | + | 0.825235i | \(0.691043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.22312 | + | 10.5737i | −0.374036 | + | 0.757196i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5870 | + | 20.0692i | −0.825538 | + | 1.42987i | 0.0759694 | + | 0.997110i | \(0.475795\pi\) |
−0.901507 | + | 0.432764i | \(0.857538\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.39428 | − | 1.38234i | 0.169726 | − | 0.0979914i | −0.412731 | − | 0.910853i | \(-0.635425\pi\) |
0.582457 | + | 0.812862i | \(0.302092\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.894787 | + | 0.569058i | 0.0631134 | + | 0.0401383i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.24455i | − | 0.157537i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.8474 | − | 18.7883i | 0.757616 | − | 1.31223i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.80877 | + | 12.6223i | −0.612252 | + | 0.877307i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.31989i | − | 0.367985i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5498 | − | 7.24561i | −0.863961 | − | 0.498808i | 0.00137575 | − | 0.999999i | \(-0.499562\pi\) |
−0.865337 | + | 0.501191i | \(0.832895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.61245 | + | 14.5955i | 0.521597 | + | 1.00007i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.0083 | − | 9.81977i | 1.15996 | − | 0.669703i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.38777 | + | 4.13574i | 0.162092 | + | 0.280752i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.4036 | − | 0.660452i | −1.04088 | − | 0.0446292i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.30541 | − | 0.897408i | 0.558683 | − | 0.0603662i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.36606 | − | 9.29429i | 0.359338 | − | 0.622392i | −0.628512 | − | 0.777800i | \(-0.716336\pi\) |
0.987850 | + | 0.155408i | \(0.0496692\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.28549 | + | 0.368171i | 0.285699 | + | 0.0245447i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.60353 | + | 2.08050i | −0.239175 | + | 0.138088i | −0.614797 | − | 0.788685i | \(-0.710762\pi\) |
0.375623 | + | 0.926773i | \(0.377429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 16.5809i | − | 1.09570i | −0.836577 | − | 0.547849i | \(-0.815447\pi\) | ||
0.836577 | − | 0.547849i | \(-0.184553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.20587 | + | 0.394716i | 0.605702 | + | 0.0259704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.9386i | − | 0.913148i | −0.889685 | − | 0.456574i | \(-0.849076\pi\) | ||
0.889685 | − | 0.456574i | \(-0.150924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26056i | 0.0822299i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.7657 | − | 0.461594i | −0.699304 | − | 0.0299838i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.69044i | 0.497453i | 0.968574 | + | 0.248727i | \(0.0800121\pi\) | ||||
−0.968574 | + | 0.248727i | \(0.919988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.13083 | + | 4.11698i | −0.459337 | + | 0.265198i | −0.711765 | − | 0.702417i | \(-0.752104\pi\) |
0.252428 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.31436 | + | 15.2320i | −0.212616 | + | 0.977136i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.56412 | + | 6.17325i | −0.227704 | + | 0.394394i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.695613 | − | 6.43782i | −0.0442608 | − | 0.409629i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.6691 | − | 1.31499i | −1.94358 | − | 0.0833339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.79736 | − | 4.84517i | −0.176568 | − | 0.305825i | 0.764135 | − | 0.645057i | \(-0.223166\pi\) |
−0.940703 | + | 0.339232i | \(0.889833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1620 | + | 7.59908i | −0.827487 | + | 0.477750i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.50457 | + | 6.71936i | 0.219464 | + | 0.420783i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.1005 | − | 15.0691i | −1.62811 | − | 0.939987i | −0.984658 | − | 0.174497i | \(-0.944170\pi\) |
−0.643447 | − | 0.765490i | \(-0.722496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 10.3998i | − | 0.646213i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.07470 | + | 2.14576i | 0.190319 | + | 0.132819i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0545556 | − | 0.0944930i | 0.00336404 | − | 0.00582669i | −0.864338 | − | 0.502911i | \(-0.832263\pi\) |
0.867703 | + | 0.497084i | \(0.165596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.93153i | 0.425801i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.06188 | + | 5.12712i | 0.493379 | + | 0.313775i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.3567 | + | 15.2171i | −1.60700 | + | 0.927800i | −0.616959 | + | 0.786995i | \(0.711636\pi\) |
−0.990037 | + | 0.140805i | \(0.955031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.33433 | − | 16.1675i | 0.567020 | − | 0.982108i | −0.429838 | − | 0.902906i | \(-0.641429\pi\) |
0.996859 | − | 0.0792022i | \(-0.0252373\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.1920 | − | 0.726069i | 0.677372 | − | 0.0439437i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.67808 | + | 2.12354i | 0.221797 | + | 0.128054i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.95764 | − | 17.2471i | −0.598296 | − | 1.03628i | −0.993073 | − | 0.117503i | \(-0.962511\pi\) |
0.394776 | − | 0.918777i | \(-0.370822\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.94803 | − | 0.682824i | −0.475836 | − | 0.0408796i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.5507 | −0.868020 | −0.434010 | − | 0.900908i | \(-0.642902\pi\) | ||||
−0.434010 | + | 0.900908i | \(0.642902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.682537 | − | 0.394063i | −0.0405726 | − | 0.0234246i | 0.479576 | − | 0.877500i | \(-0.340790\pi\) |
−0.520149 | + | 0.854075i | \(0.674124\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.20842 | − | 2.71651i | 0.308520 | − | 0.160912i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.6319 | −1.21786 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.81595 | + | 10.0735i | −0.342115 | + | 0.592560i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.83244 | − | 16.9346i | −0.517767 | − | 0.992722i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.28284 | − | 10.8822i | −0.367047 | − | 0.635745i | 0.622055 | − | 0.782973i | \(-0.286298\pi\) |
−0.989102 | + | 0.147229i | \(0.952965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.93620 | − | 3.42727i | 0.345619 | − | 0.199543i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.34139 | + | 12.2333i | −0.542042 | + | 0.709849i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.9342 | + | 10.9170i | −0.863669 | + | 0.631345i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.1750 | − | 9.33864i | −0.932312 | − | 0.538270i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4226 | − | 17.9610i | 0.656213 | − | 1.03183i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.84818 | + | 15.3255i | 0.506646 | + | 0.877536i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.1125 | 1.09081 | 0.545405 | − | 0.838173i | \(-0.316376\pi\) | ||||
0.545405 | + | 0.838173i | \(0.316376\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.0595 | − | 1.41748i | −1.88069 | − | 0.0806374i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8882 | 0.900939 | 0.450470 | − | 0.892792i | \(-0.351257\pi\) | ||||
0.450470 | + | 0.892792i | \(0.351257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.4008 | 1.20964 | 0.604822 | − | 0.796361i | \(-0.293244\pi\) | ||||
0.604822 | + | 0.796361i | \(0.293244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.31438 | + | 9.21452i | 0.243088 | + | 0.519179i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.504196 | −0.0283185 | −0.0141592 | − | 0.999900i | \(-0.504507\pi\) | ||||
−0.0141592 | + | 0.999900i | \(0.504507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.85109 | + | 3.20618i | 0.103641 | + | 0.179512i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.0703 | − | 15.9440i | −1.39929 | − | 0.889905i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.60353 | − | 2.08050i | −0.200506 | − | 0.115762i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.72867 | + | 2.08885i | 0.262299 | + | 0.115869i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.2648 | − | 0.911762i | −1.17595 | − | 0.0504206i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.03819 | − | 0.599399i | 0.0572373 | − | 0.0330459i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50846 | + | 11.2730i | 0.357737 | + | 0.619620i | 0.987582 | − | 0.157101i | \(-0.0502149\pi\) |
−0.629845 | + | 0.776721i | \(0.716882\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.2462 | + | 9.94209i | 0.780687 | + | 0.544823i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.578081 | + | 1.00127i | −0.0315840 | + | 0.0547050i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0995 | 1.09489 | 0.547445 | − | 0.836842i | \(-0.315600\pi\) | ||||
0.547445 | + | 0.836842i | \(0.315600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.77552 | + | 12.9908i | 0.367996 | + | 0.705564i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.82151 | − | 3.93840i | −0.369406 | − | 0.213276i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3505 | 1.04483 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.1608 | − | 9.00584i | −0.762391 | − | 0.484858i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5898 | − | 21.8061i | −0.675854 | − | 1.17061i | −0.976218 | − | 0.216789i | \(-0.930442\pi\) |
0.300364 | − | 0.953825i | \(-0.402892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.849362 | + | 0.490379i | 0.0454653 | + | 0.0262494i | 0.522560 | − | 0.852602i | \(-0.324977\pi\) |
−0.477095 | + | 0.878852i | \(0.658310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.70481 | + | 16.0255i | −0.518004 | + | 0.855378i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.7300 | + | 27.2452i | −0.837225 | + | 1.45012i | 0.0549818 | + | 0.998487i | \(0.482490\pi\) |
−0.892206 | + | 0.451628i | \(0.850843\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.5432 | + | 8.97390i | −0.824950 | + | 0.476285i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.86760 | − | 6.08141i | 0.204695 | − | 0.321862i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3045i | 0.966075i | 0.875600 | + | 0.483038i | \(0.160467\pi\) | ||||
−0.875600 | + | 0.483038i | \(0.839533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.88733 | − | 13.6613i | 0.415123 | − | 0.719013i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.41751 | − | 1.78244i | 0.179373 | − | 0.0935540i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 16.8099i | − | 0.879870i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.6956 | − | 12.5259i | −1.13250 | − | 0.653849i | −0.187937 | − | 0.982181i | \(-0.560180\pi\) |
−0.944562 | + | 0.328333i | \(0.893513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.7238 | − | 28.2626i | 1.02678 | − | 1.47129i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.70877 | − | 3.29596i | 0.296385 | − | 0.171118i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.18209 | + | 3.77950i | 0.112985 | + | 0.195695i | 0.916972 | − | 0.398951i | \(-0.130626\pi\) |
−0.803988 | + | 0.594646i | \(0.797292\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.901472 | + | 21.0248i | −0.0465518 | + | 1.08572i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.65931 | + | 3.63789i | 0.136961 | + | 0.187361i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3756 | − | 31.8275i | 0.943893 | − | 1.63487i | 0.185939 | − | 0.982561i | \(-0.440467\pi\) |
0.757953 | − | 0.652309i | \(-0.226199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.80988 | + | 5.99066i | −0.195186 | + | 0.306911i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.2486 | + | 7.07176i | −0.625876 | + | 0.361350i | −0.779153 | − | 0.626833i | \(-0.784351\pi\) |
0.153277 | + | 0.988183i | \(0.451017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0464i | 0.512009i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.2556 | − | 13.2297i | 1.43631 | − | 0.672505i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.8039i | 0.547781i | 0.961761 | + | 0.273891i | \(0.0883106\pi\) | ||||
−0.961761 | + | 0.273891i | \(0.911689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8874i | 0.601170i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.812709 | + | 18.9546i | −0.0409957 | + | 0.956134i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.7485i | − | 0.591133i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7928 | − | 10.8500i | 0.943184 | − | 0.544548i | 0.0522272 | − | 0.998635i | \(-0.483368\pi\) |
0.890957 | + | 0.454088i | \(0.150035\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.71392 | − | 2.99791i | −0.235991 | − | 0.150083i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1170 | + | 24.4514i | −0.704970 | + | 1.22104i | 0.261733 | + | 0.965140i | \(0.415706\pi\) |
−0.966702 | + | 0.255903i | \(0.917627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.76997 | − | 3.87406i | −0.436863 | − | 0.192981i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.7470 | − | 2.89890i | −0.832165 | − | 0.144048i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.57676 | + | 14.8554i | 0.425134 | + | 0.736354i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.32242 | − | 3.07290i | 0.263177 | − | 0.151945i | −0.362606 | − | 0.931942i | \(-0.618113\pi\) |
0.625783 | + | 0.779997i | \(0.284780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.4589 | − | 8.58436i | 0.811859 | − | 0.423435i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.64535 | − | 3.25935i | −0.277790 | − | 0.160382i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 33.4692i | − | 1.64294i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.785563 | + | 1.50617i | 0.0384692 | + | 0.0737576i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.79736 | − | 4.84517i | 0.136660 | − | 0.236702i | −0.789570 | − | 0.613660i | \(-0.789697\pi\) |
0.926230 | + | 0.376958i | \(0.123030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.6161i | − | 0.956029i | −0.878352 | − | 0.478015i | \(-0.841357\pi\) | ||
0.878352 | − | 0.478015i | \(-0.158643\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.171408 | + | 1.99518i | −0.00833416 | + | 0.0970091i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.87685 | − | 1.66095i | 0.139548 | − | 0.0805678i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.41466 | − | 14.5746i | 0.407214 | − | 0.705315i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.3882 | + | 10.2672i | −0.742948 | + | 0.495706i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.8355 | − | 20.1123i | −1.67797 | − | 0.968774i | −0.962955 | − | 0.269661i | \(-0.913088\pi\) |
−0.715011 | − | 0.699113i | \(-0.753578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2473 | + | 19.4808i | 0.540509 | + | 0.936189i | 0.998875 | + | 0.0474257i | \(0.0151017\pi\) |
−0.458366 | + | 0.888764i | \(0.651565\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.19377 | + | 3.44948i | −0.105183 | + | 0.165390i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.21433 | 0.440781 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4694 | − | 11.2407i | −0.929225 | − | 0.536488i | −0.0426587 | − | 0.999090i | \(-0.513583\pi\) |
−0.886566 | + | 0.462601i | \(0.846916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.48063 | + | 9.28621i | −0.308601 | + | 0.442201i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.1424 | 1.14704 | 0.573519 | − | 0.819192i | \(-0.305578\pi\) | ||||
0.573519 | + | 0.819192i | \(0.305578\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.20842 | + | 9.02124i | −0.246903 | + | 0.427648i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.4676 | + | 14.3261i | −1.29917 | + | 0.677600i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.8669 | − | 29.2144i | −0.796000 | − | 1.37871i | −0.922202 | − | 0.386708i | \(-0.873612\pi\) |
0.126202 | − | 0.992005i | \(-0.459721\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.4711 | − | 17.0151i | 1.38774 | − | 0.801212i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.28386 | − | 29.9432i | 0.0603211 | − | 1.40685i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.31363 | + | 12.1575i | 0.0615839 | + | 0.569953i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7957 | − | 9.11965i | −0.738892 | − | 0.426599i | 0.0827746 | − | 0.996568i | \(-0.473622\pi\) |
−0.821666 | + | 0.569969i | \(0.806955\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.63325 | + | 11.1118i | 0.216262 | + | 0.518653i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.04833 | + | 7.01191i | 0.188549 | + | 0.326577i | 0.944767 | − | 0.327743i | \(-0.106288\pi\) |
−0.756217 | + | 0.654320i | \(0.772955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.2470 | −1.91691 | −0.958456 | − | 0.285239i | \(-0.907927\pi\) | ||||
−0.958456 | + | 0.285239i | \(0.907927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.372582 | − | 8.68964i | 0.0172781 | − | 0.402973i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.7233 | 1.79190 | 0.895951 | − | 0.444153i | \(-0.146495\pi\) | ||||
0.895951 | + | 0.444153i | \(0.146495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.09952 | 0.0507709 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.522851 | − | 12.1943i | 0.0240917 | − | 0.561885i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.8064 | 1.41648 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.28746 | − | 2.22995i | −0.0590727 | − | 0.102317i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.942535 | + | 10.9711i | −0.0431557 | + | 0.502330i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.56011 | + | 2.05543i | 0.162666 | + | 0.0939151i | 0.579123 | − | 0.815240i | \(-0.303395\pi\) |
−0.416457 | + | 0.909155i | \(0.636728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.3215 | + | 16.8556i | 0.561813 | + | 0.768551i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.683668 | + | 15.9450i | −0.0311080 | + | 0.725524i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.0342 | − | 10.4121i | 0.818892 | − | 0.472788i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4933 | + | 21.6390i | 0.566124 | + | 0.980555i | 0.996944 | + | 0.0781175i | \(0.0248909\pi\) |
−0.430820 | + | 0.902438i | \(0.641776\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.65261 | + | 3.99132i | −0.346063 | + | 0.180494i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.53131 | − | 9.58051i | 0.249624 | − | 0.432362i | −0.713797 | − | 0.700352i | \(-0.753026\pi\) |
0.963422 | + | 0.267990i | \(0.0863595\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.89569 | 0.130415 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.7620 | − | 9.60418i | −0.618556 | − | 0.431676i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.7817 | + | 8.53422i | 0.663050 | + | 0.382812i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.3108 | −1.17784 | −0.588918 | − | 0.808193i | \(-0.700446\pi\) | ||||
−0.588918 | + | 0.808193i | \(0.700446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.37377 | + | 5.30492i | −0.150729 | + | 0.237006i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.76696 | + | 11.7207i | 0.301724 | + | 0.522601i | 0.976526 | − | 0.215397i | \(-0.0691047\pi\) |
−0.674803 | + | 0.737998i | \(0.735771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0983 | + | 11.6038i | 0.894363 | + | 0.516361i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.2794 | + | 14.4369i | −0.767403 | + | 0.641165i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.14083 | − | 14.1003i | 0.360836 | − | 0.624986i | −0.627263 | − | 0.778808i | \(-0.715825\pi\) |
0.988099 | + | 0.153822i | \(0.0491582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8445 | + | 7.99314i | −0.612446 | + | 0.353596i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.61313 | − | 3.59140i | 0.380279 | − | 0.158564i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 36.0777i | − | 1.58978i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.988652 | + | 1.71239i | −0.0434809 | + | 0.0753110i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.8547 | + | 30.3985i | 0.695946 | + | 1.33435i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.40258i | − | 0.149070i | −0.997218 | − | 0.0745348i | \(-0.976253\pi\) | ||
0.997218 | − | 0.0745348i | \(-0.0237472\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.605718 | − | 0.349712i | −0.0264862 | − | 0.0152918i | 0.486698 | − | 0.873570i | \(-0.338201\pi\) |
−0.513185 | + | 0.858278i | \(0.671534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.95436 | − | 2.06245i | 0.172582 | − | 0.0900126i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.33551 | + | 3.08046i | −0.232418 | + | 0.134187i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.66199 | − | 2.87864i | −0.0722603 | − | 0.125158i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.86170 | − | 4.61740i | 0.427961 | − | 0.200378i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.4393 | − | 24.4443i | 1.44842 | − | 1.05880i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1968 | − | 28.0536i | 0.700247 | − | 1.21286i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.4353 | + | 12.3603i | 0.838695 | + | 0.533385i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.68330 | + | 5.59065i | −0.417089 | + | 0.240807i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.25977i | − | 0.140148i | −0.997542 | − | 0.0700742i | \(-0.977676\pi\) | ||
0.997542 | − | 0.0700742i | \(-0.0223236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.885687 | + | 20.6567i | −0.0380085 | + | 0.886462i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 23.2063i | − | 0.994047i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3786i | 1.12787i | 0.825820 | + | 0.563933i | \(0.190713\pi\) | ||||
−0.825820 | + | 0.563933i | \(0.809287\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9208 | + | 25.4600i | 0.508765 | + | 1.08661i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.24455i | − | 0.0956212i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.67603 | + | 5.58646i | −0.411467 | + | 0.237560i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.1645 | + | 15.9827i | −0.431459 | + | 0.678427i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.59684 | + | 14.8902i | −0.364260 | + | 0.630916i | −0.988657 | − | 0.150191i | \(-0.952011\pi\) |
0.624397 | + | 0.781107i | \(0.285345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.2801 | − | 4.02815i | 1.57678 | − | 0.170373i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.509222 | + | 11.8765i | −0.0214994 | + | 0.501425i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.7963 | + | 29.0921i | 0.707880 | + | 1.22608i | 0.965642 | + | 0.259876i | \(0.0836817\pi\) |
−0.257762 | + | 0.966209i | \(0.582985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8344 | + | 7.98729i | −0.582017 | + | 0.336028i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.57572 | + | 15.1712i | 0.234158 | + | 0.637129i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.42743 | + | 2.55618i | 0.185607 | + | 0.107161i | 0.589925 | − | 0.807458i | \(-0.299157\pi\) |
−0.404317 | + | 0.914619i | \(0.632491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 13.5901i | − | 0.568728i | −0.958716 | − | 0.284364i | \(-0.908218\pi\) | ||
0.958716 | − | 0.284364i | \(-0.0917825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.5514 | − | 16.4560i | 1.31808 | − | 0.687461i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.67808 | + | 6.37063i | −0.153387 | + | 0.265674i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.8884i | 1.03612i | 0.855345 | + | 0.518058i | \(0.173345\pi\) | ||||
−0.855345 | + | 0.518058i | \(0.826655\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.97580 | − | 3.10674i | 0.0821113 | − | 0.129112i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.5650 | + | 15.9147i | −1.14359 | + | 0.660251i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.43637 | + | 9.41607i | −0.225151 | + | 0.389974i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.9098 | − | 9.82294i | −0.740478 | − | 0.406128i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.11795 | − | 4.10955i | −0.293789 | − | 0.169619i | 0.345860 | − | 0.938286i | \(-0.387587\pi\) |
−0.639650 | + | 0.768667i | \(0.720920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.38777 | + | 4.13574i | 0.0983864 | + | 0.170410i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.8693 | − | 21.5399i | −1.39320 | − | 0.886032i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.6118 | 1.66773 | 0.833863 | − | 0.551972i | \(-0.186124\pi\) | ||||
0.833863 | + | 0.551972i | \(0.186124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.80509 | + | 3.92892i | 0.278982 | + | 0.161070i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.21444 | + | 4.24577i | 0.0906309 | + | 0.173768i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.9719 | −0.816029 | −0.408014 | − | 0.912975i | \(-0.633779\pi\) | ||||
−0.408014 | + | 0.912975i | \(0.633779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5299 | − | 26.8987i | 0.633480 | − | 1.09722i | −0.353355 | − | 0.935489i | \(-0.614959\pi\) |
0.986835 | − | 0.161730i | \(-0.0517073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.05112 | + | 1.50617i | −0.0428050 | + | 0.0613361i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.10122 | + | 3.63943i | 0.0854269 | + | 0.147964i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3864 | − | 6.57397i | 0.462161 | − | 0.266829i | −0.250791 | − | 0.968041i | \(-0.580691\pi\) |
0.712953 | + | 0.701212i | \(0.247357\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.88411 | + | 0.166538i | 0.157392 | + | 0.00674844i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.972501 | + | 2.20151i | −0.0393432 | + | 0.0890637i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.05460 | − | 0.608871i | −0.0425947 | − | 0.0245921i | 0.478551 | − | 0.878060i | \(-0.341162\pi\) |
−0.521146 | + | 0.853467i | \(0.674495\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.7075 | + | 20.1650i | 1.27857 | + | 0.813133i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.04423 | − | 7.00481i | −0.162815 | − | 0.282003i | 0.773063 | − | 0.634330i | \(-0.218724\pi\) |
−0.935877 | + | 0.352327i | \(0.885391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5019 | −0.502494 | −0.251247 | − | 0.967923i | \(-0.580841\pi\) | ||||
−0.251247 | + | 0.967923i | \(0.580841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.1887 | − | 16.1798i | −0.850275 | − | 0.649272i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.90645 | 0.396894 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.7755 | −0.631022 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.20587 | + | 0.394716i | 0.367647 | + | 0.0157634i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4168 | 0.534962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.62836 | + | 8.01655i | 0.184252 | + | 0.319134i | 0.943324 | − | 0.331873i | \(-0.107680\pi\) |
−0.759072 | + | 0.651006i | \(0.774347\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.4694 | − | 21.1793i | 0.535360 | − | 0.841800i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.70354 | − | 3.87029i | −0.266022 | − | 0.153588i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9871 | + | 8.03164i | −0.435326 | + | 0.318225i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.8217 | + | 12.0901i | −1.02149 | + | 0.478278i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8264 | + | 6.25063i | −0.427618 | + | 0.246885i | −0.698331 | − | 0.715775i | \(-0.746074\pi\) |
0.270714 | + | 0.962660i | \(0.412740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.7894 | + | 34.2762i | 0.780416 | + | 1.35172i | 0.931700 | + | 0.363230i | \(0.118326\pi\) |
−0.151283 | + | 0.988490i | \(0.548341\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7308 | + | 30.1609i | 0.619399 | + | 1.18758i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.1294 | + | 22.7407i | −0.516169 | + | 0.894030i | 0.483655 | + | 0.875259i | \(0.339309\pi\) |
−0.999824 | + | 0.0187716i | \(0.994024\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.7520 | 0.422051 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.33390 | + | 3.82509i | −0.287438 | + | 0.149917i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.9639 | + | 13.8356i | 0.937779 | + | 0.541427i | 0.889264 | − | 0.457395i | \(-0.151218\pi\) |
0.0485159 | + | 0.998822i | \(0.484551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6851 | −0.808235 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.28577 | − | 26.6063i | 0.0891765 | − | 1.03801i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7623 | + | 34.2293i | 0.769829 | + | 1.33338i | 0.937655 | + | 0.347567i | \(0.112992\pi\) |
−0.167826 | + | 0.985817i | \(0.553675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.92681 | + | 3.42184i | 0.230526 | + | 0.133094i | 0.610815 | − | 0.791774i | \(-0.290842\pi\) |
−0.380289 | + | 0.924868i | \(0.624175\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.936699 | + | 14.4388i | 0.0363784 | + | 0.560756i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04545 | − | 5.27487i | 0.118097 | − | 0.204551i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.55327 | + | 3.20618i | −0.215023 | + | 0.124144i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.6853 | + | 9.97536i | 0.606428 | + | 0.385670i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.7584i | 1.07160i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.60509 | + | 16.6365i | −0.370249 | + | 0.641290i | −0.989604 | − | 0.143821i | \(-0.954061\pi\) |
0.619355 | + | 0.785111i | \(0.287394\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.955073 | + | 7.38856i | −0.0367608 | + | 0.284386i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 31.2564i | − | 1.20128i | −0.799519 | − | 0.600640i | \(-0.794912\pi\) | ||
0.799519 | − | 0.600640i | \(-0.205088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.1506 | − | 9.90193i | −0.658181 | − | 0.380001i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.33286 | − | 6.39014i | −0.127715 | − | 0.244871i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1522 | + | 14.5216i | −0.962422 | + | 0.555654i | −0.896918 | − | 0.442198i | \(-0.854199\pi\) |
−0.0655042 | + | 0.997852i | \(0.520866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1196 | + | 17.5277i | 0.386651 | + | 0.669699i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.6926 | + | 1.23024i | 1.09469 | + | 0.0469367i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.34756 | + | 12.1056i | −0.203726 | + | 0.461187i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.2202 | + | 40.2185i | −0.883336 | + | 1.52998i | −0.0357274 | + | 0.999362i | \(0.511375\pi\) |
−0.847609 | + | 0.530622i | \(0.821959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.36608 | + | 15.9011i | −0.0518932 | + | 0.604033i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.60398 | + | 0.926057i | −0.0608423 | + | 0.0351273i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 26.6171i | − | 1.00819i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.1202 | + | 1.03419i | 0.912310 | + | 0.0391167i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.03343i | − | 0.190110i | −0.995472 | − | 0.0950550i | \(-0.969697\pi\) | ||
0.995472 | − | 0.0950550i | \(-0.0303027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 10.3998i | − | 0.392237i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.18135 | − | 0.0935288i | −0.0821544 | − | 0.00352250i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 22.0705i | − | 0.830045i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8731 | − | 21.2887i | 1.38480 | − | 0.799514i | 0.392075 | − | 0.919933i | \(-0.371757\pi\) |
0.992723 | + | 0.120419i | \(0.0384239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.59754 | − | 18.5953i | 0.0599125 | − | 0.697378i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.82151 | − | 11.8152i | 0.255468 | − | 0.442483i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9027 | − | 16.2827i | −0.445137 | − | 0.608940i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.3080 | − | 0.570602i | −0.496997 | − | 0.0213095i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.48789 | − | 9.50530i | −0.204664 | − | 0.354488i | 0.745362 | − | 0.666660i | \(-0.232277\pi\) |
−0.950026 | + | 0.312172i | \(0.898943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.7134 | + | 17.1550i | −1.10659 | + | 0.638887i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.59520 | − | 12.6451i | −0.245278 | − | 0.470276i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.55185 | + | 0.895959i | 0.0576342 | + | 0.0332751i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.642323i | 0.0238224i | 0.999929 | + | 0.0119112i | \(0.00379155\pi\) | ||||
−0.999929 | + | 0.0119112i | \(0.996208\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.1125 | − | 6.86553i | −0.967131 | − | 0.254279i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0478 | − | 20.8673i | 0.445602 | − | 0.771806i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1122i | 1.03835i | 0.854669 | + | 0.519173i | \(0.173760\pi\) | ||||
−0.854669 | + | 0.519173i | \(0.826240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.4181 | − | 6.62561i | −0.384278 | − | 0.244389i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.57058 | + | 0.906773i | −0.0578529 | + | 0.0334014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7724 | − | 32.5148i | 0.690555 | − | 1.19608i | −0.281101 | − | 0.959678i | \(-0.590700\pi\) |
0.971656 | − | 0.236398i | \(-0.0759670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1920 | − | 0.726069i | 0.411149 | − | 0.0266728i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2637 | − | 5.92572i | −0.376537 | − | 0.217394i | 0.299774 | − | 0.954010i | \(-0.403089\pi\) |
−0.676310 | + | 0.736617i | \(0.736422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.8882 | − | 29.2512i | −0.618736 | − | 1.07168i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.55107 | − | 52.9741i | 0.166515 | − | 1.93822i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.8064 | −1.12564 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.4467 | + | 10.6502i | 0.673131 | + | 0.388632i | 0.797262 | − | 0.603634i | \(-0.206281\pi\) |
−0.124131 | + | 0.992266i | \(0.539614\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.59194 | − | 4.48123i | 0.313108 | − | 0.163305i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.6770 | 1.18924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.7008 | − | 20.2664i | 0.425274 | − | 0.736597i | −0.571172 | − | 0.820831i | \(-0.693511\pi\) |
0.996446 | + | 0.0842340i | \(0.0268443\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.1733 | − | 23.3401i | −0.441864 | − | 0.847193i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.86026 | + | 3.22206i | 0.0674343 | + | 0.116800i | 0.897771 | − | 0.440462i | \(-0.145185\pi\) |
−0.830337 | + | 0.557262i | \(0.811852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.1125 | + | 11.0346i | −0.691920 | + | 0.399480i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.8876 | + | 5.56596i | −0.429798 | + | 0.201238i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.0114 | − | 1.40589i | 0.469814 | − | 0.0507639i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.4463 | + | 14.6914i | 0.917618 | + | 0.529787i | 0.882874 | − | 0.469609i | \(-0.155605\pi\) |
0.0347439 | + | 0.999396i | \(0.488938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0131 | − | 44.0478i | 1.00887 | − | 1.58634i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.287410 | + | 0.497808i | 0.0103374 | + | 0.0179049i | 0.871148 | − | 0.491021i | \(-0.163376\pi\) |
−0.860810 | + | 0.508926i | \(0.830043\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.81251 | −0.136949 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.9965 | + | 0.771628i | 0.645620 | + | 0.0276820i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.6319 | −0.739213 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.1528 | −1.00738 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.94129 | + | 5.16145i | −0.140850 | + | 0.184455i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.3077 | 0.474971 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.29304 | + | 5.70371i | 0.117384 | + | 0.203315i | 0.918730 | − | 0.394886i | \(-0.129216\pi\) |
−0.801346 | + | 0.598201i | \(0.795882\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.159469 | + | 0.101417i | 0.00567724 | + | 0.00361055i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1566 | + | 7.59595i | 0.467794 | + | 0.270081i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.62960 | + | 33.5915i | 0.128891 | + | 1.19287i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.9947 | − | 0.514294i | −0.425410 | − | 0.0182401i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.0021 | + | 14.4350i | −0.885619 | + | 0.511312i | −0.872507 | − | 0.488602i | \(-0.837507\pi\) |
−0.0131121 | + | 0.999914i | \(0.504174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.773283 | + | 1.33937i | 0.0273568 | + | 0.0473833i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.47044 | + | 13.5704i | −0.334621 | + | 0.479485i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.1839 | − | 22.8352i | 0.465250 | − | 0.805837i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.4008 | −0.613297 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3769 | − | 46.7383i | −0.858109 | − | 1.64527i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.13144 | − | 2.96264i | −0.180412 | − | 0.104161i | 0.407074 | − | 0.913395i | \(-0.366549\pi\) |
−0.587486 | + | 0.809234i | \(0.699882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.5845 | 1.49534 | 0.747672 | − | 0.664068i | \(-0.231172\pi\) | ||||
0.747672 | + | 0.664068i | \(0.231172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.2847 | + | 17.3523i | 0.956917 | + | 0.608571i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.70514 | − | 8.14954i | −0.164814 | − | 0.285466i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1750 | − | 9.33864i | −0.565892 | − | 0.326718i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.426028 | + | 19.4212i | 0.0148866 | + | 0.678632i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.4101 | + | 28.4231i | −0.572716 | + | 0.991973i | 0.423569 | + | 0.905864i | \(0.360777\pi\) |
−0.996286 | + | 0.0861099i | \(0.972556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.4135 | + | 26.7968i | −1.61787 | + | 0.934079i | −0.630402 | + | 0.776269i | \(0.717110\pi\) |
−0.987469 | + | 0.157810i | \(0.949557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.94761 | + | 6.20722i | −0.137438 | + | 0.216108i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.5894i | − | 1.20279i | −0.798951 | − | 0.601396i | \(-0.794612\pi\) | ||
0.798951 | − | 0.601396i | \(-0.205388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.41879 | − | 14.5818i | 0.292397 | − | 0.506446i | −0.681979 | − | 0.731371i | \(-0.738881\pi\) |
0.974376 | + | 0.224926i | \(0.0722140\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.5843 | − | 15.9516i | 1.06096 | − | 0.553356i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.74556i | 0.303016i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.93620 | − | 3.42727i | −0.205431 | − | 0.118605i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.77131 | − | 13.7031i | 0.0612255 | − | 0.473648i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.5443 | − | 23.4082i | 1.39974 | − | 0.808142i | 0.405378 | − | 0.914149i | \(-0.367140\pi\) |
0.994365 | + | 0.106007i | \(0.0338066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7190 | − | 23.7620i | −0.473069 | − | 0.819379i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.07960 | − | 25.1794i | 0.0371836 | − | 0.867223i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.5331 | − | 18.1481i | −0.568755 | − | 0.624312i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.99827 | − | 3.46111i | 0.0686615 | − | 0.118925i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.732553 | − | 1.15187i | 0.0251411 | − | 0.0395320i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7303 | + | 14.8554i | −0.882022 | + | 0.509236i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 50.6867i | − | 1.73548i | −0.497019 | − | 0.867739i | \(-0.665572\pi\) | ||
0.497019 | − | 0.867739i | \(-0.334428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.31438 | + | 9.21452i | 0.147549 | + | 0.315130i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.9765i | 1.29725i | 0.761107 | + | 0.648626i | \(0.224656\pi\) | ||||
−0.761107 | + | 0.648626i | \(0.775344\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.6738i | 1.31953i | 0.751471 | + | 0.659766i | \(0.229345\pi\) | ||||
−0.751471 | + | 0.659766i | \(0.770655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.53081 | − | 35.7026i | 0.0521698 | − | 1.21674i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.0860835i | − | 0.00293032i | −0.999999 | − | 0.00146516i | \(-0.999534\pi\) | ||
0.999999 | − | 0.00146516i | \(-0.000466374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.3725 | + | 18.6903i | −1.10070 | + | 0.635489i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0003 | − | 10.8117i | −0.577361 | − | 0.367184i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.21433 | − | 15.9597i | 0.312575 | − | 0.541395i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78205 | + | 1.30269i | −0.0603826 | + | 0.0441399i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.9599 | − | 14.0277i | 1.01399 | − | 0.474766i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9101 | + | 18.8968i | 0.368828 | + | 0.638829i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.4044 | + | 18.7087i | −1.09422 | + | 0.631748i | −0.934697 | − | 0.355446i | \(-0.884329\pi\) |
−0.159523 | + | 0.987194i | \(0.550996\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2974 | − | 10.0648i | 0.650884 | − | 0.339477i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6895 | − | 17.1412i | −1.00026 | − | 0.577503i | −0.0919376 | − | 0.995765i | \(-0.529306\pi\) |
−0.908326 | + | 0.418262i | \(0.862639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.37789i | 0.248286i | 0.992264 | + | 0.124143i | \(0.0396181\pi\) | ||||
−0.992264 | + | 0.124143i | \(0.960382\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.49031 | + | 10.5267i | 0.184555 | + | 0.353850i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.79576 | − | 8.30650i | 0.161026 | − | 0.278905i | −0.774211 | − | 0.632928i | \(-0.781853\pi\) |
0.935237 | + | 0.354023i | \(0.115186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.36133i | 0.246891i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.4762 | − | 17.0726i | −0.685978 | − | 0.571953i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.03819 | − | 0.599399i | 0.0347417 | − | 0.0200581i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.5563 | + | 21.7481i | −0.419710 | + | 0.726959i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.7833 | − | 26.6531i | −0.593768 | − | 0.889921i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.87811 | − | 1.66168i | −0.0959904 | − | 0.0554201i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.25211 | + | 7.36487i | 0.141658 | + | 0.245359i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.3603 | − | 27.2973i | 0.577714 | − | 0.908398i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.5426 | −0.749341 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.8624 | − | 12.6223i | −0.725928 | − | 0.419115i | 0.0910023 | − | 0.995851i | \(-0.470993\pi\) |
−0.816931 | + | 0.576736i | \(0.804326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.2332 | + | 21.0991i | 1.00277 | + | 0.699812i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.6403 | −1.44587 | −0.722934 | − | 0.690917i | \(-0.757207\pi\) | ||||
−0.722934 | + | 0.690917i | \(0.757207\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2497 | − | 45.4658i | 0.868739 | − | 1.50470i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.1767 | + | 14.1743i | −0.898434 | + | 0.468589i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.83583 | + | 17.0362i | 0.324808 | + | 0.562584i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.9505 | − | 13.8279i | 0.790056 | − | 0.456139i | −0.0499264 | − | 0.998753i | \(-0.515899\pi\) |
0.839982 | + | 0.542614i | \(0.182565\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.41808 | + | 33.0735i | −0.0467273 | + | 1.08981i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.0688 | + | 3.68117i | −1.12139 | + | 0.121167i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.19026 | + | 4.15130i | 0.236414 | + | 0.136494i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.90578 | − | 57.1029i | 0.161127 | − | 1.87551i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.5733 | − | 23.5097i | −0.445326 | − | 0.771328i | 0.552749 | − | 0.833348i | \(-0.313579\pi\) |
−0.998075 | + | 0.0620204i | \(0.980246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.77900 | 0.222173 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.17885 | + | 27.4940i | −0.0385937 | + | 0.900112i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.9608 | −0.423862 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5163 | −0.408891 | −0.204446 | − | 0.978878i | \(-0.565539\pi\) | ||||
−0.204446 | + | 0.978878i | \(0.565539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.58786 | + | 37.0332i | −0.0518178 | + | 1.20853i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.8824 | −1.52832 | −0.764161 | − | 0.645025i | \(-0.776847\pi\) | ||||
−0.764161 | + | 0.645025i | \(0.776847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.4711 | + | 51.0454i | 0.959711 | + | 1.66227i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.2655 | + | 6.78218i | −0.529116 | + | 0.220624i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.2693 | − | 8.23839i | −0.463690 | − | 0.267712i | 0.249904 | − | 0.968270i | \(-0.419601\pi\) |
−0.713595 | + | 0.700559i | \(0.752934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9685 | − | 29.3577i | 0.420977 | − | 0.952992i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.0374095 | − | 0.872492i | 0.00121309 | − | 0.0282925i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.4608 | + | 6.61690i | −0.371252 | + | 0.214342i | −0.674005 | − | 0.738727i | \(-0.735428\pi\) |
0.302753 | + | 0.953069i | \(0.402094\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3991 | + | 33.6003i | 0.627741 | + | 1.08728i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.68551 | + | 2.96535i | −0.183787 | + | 0.0958562i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.62381 | − | 16.6689i | 0.310769 | − | 0.538268i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9292 | −0.771909 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.4505 | − | 42.2002i | 0.949029 | − | 1.35988i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.47644 | + | 2.00713i | 0.111911 | + | 0.0646117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.89544 | −0.0931111 | −0.0465555 | − | 0.998916i | \(-0.514824\pi\) | ||||
−0.0465555 | + | 0.998916i | \(0.514824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.86760 | − | 6.08141i | 0.124245 | − | 0.195363i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.8072 | + | 18.7186i | 0.346819 | + | 0.600707i | 0.985682 | − | 0.168612i | \(-0.0539286\pi\) |
−0.638864 | + | 0.769320i | \(0.720595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52539 | + | 0.880684i | 0.0489017 | + | 0.0282334i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.96553 | + | 8.02779i | −0.126999 | + | 0.257095i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.32579 | + | 12.6886i | −0.234373 | + | 0.405946i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.724717 | + | 0.689046i | \(0.241970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1506 | + | 8.16987i | −0.452256 | + | 0.261110i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.15554 | − | 36.7303i | 0.100749 | − | 1.17271i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.6123i | 1.32723i | 0.748075 | + | 0.663614i | \(0.230978\pi\) | ||||
−0.748075 | + | 0.663614i | \(0.769022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8814 | − | 37.8997i | 0.697200 | − | 1.20759i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.960207 | + | 1.84102i | 0.0305637 | + | 0.0586003i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.3583i | 1.69669i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.8946 | + | 25.9199i | 1.42612 | + | 0.823373i | 0.996812 | − | 0.0797837i | \(-0.0254230\pi\) |
0.429311 | + | 0.903157i | \(0.358756\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.9904 | + | 10.4262i | −0.634375 | + | 0.330866i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.52148 | + | 2.61048i | −0.143341 | + | 0.0827577i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.909879 | + | 1.57596i | 0.0288162 | + | 0.0499111i | 0.880074 | − | 0.474837i | \(-0.157493\pi\) |
−0.851258 | + | 0.524748i | \(0.824160\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.2614 | + | 23.9148i | −0.577766 | + | 0.756632i |
(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 | 624.2.bz.h.95.4 | yes | 16 | |
3.2 | odd | 2 | inner | 624.2.bz.h.95.7 | yes | 16 | |
4.3 | odd | 2 | 624.2.bz.g.95.5 | yes | 16 | ||
12.11 | even | 2 | 624.2.bz.g.95.2 | ✓ | 16 | ||
13.10 | even | 6 | 624.2.bz.g.335.2 | yes | 16 | ||
39.23 | odd | 6 | 624.2.bz.g.335.5 | yes | 16 | ||
52.23 | odd | 6 | inner | 624.2.bz.h.335.7 | yes | 16 | |
156.23 | even | 6 | inner | 624.2.bz.h.335.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.bz.g.95.2 | ✓ | 16 | 12.11 | even | 2 | ||
624.2.bz.g.95.5 | yes | 16 | 4.3 | odd | 2 | ||
624.2.bz.g.335.2 | yes | 16 | 13.10 | even | 6 | ||
624.2.bz.g.335.5 | yes | 16 | 39.23 | odd | 6 | ||
624.2.bz.h.95.4 | yes | 16 | 1.1 | even | 1 | trivial | |
624.2.bz.h.95.7 | yes | 16 | 3.2 | odd | 2 | inner | |
624.2.bz.h.335.4 | yes | 16 | 156.23 | even | 6 | inner | |
624.2.bz.h.335.7 | yes | 16 | 52.23 | odd | 6 | inner |