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 | 335.4 | ||
Root | \(-0.0741962 - 1.73046i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.335 |
Dual form | 624.2.bz.h.95.4 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | −0.644922 | − | 0.764249i | \(-0.723110\pi\) |
0.984320 | + | 0.176394i | \(0.0564434\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98899 | + | 0.256787i | −0.996330 | + | 0.0855958i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56534 | + | 1.48110i | −0.773481 | + | 0.446569i | −0.834115 | − | 0.551591i | \(-0.814021\pi\) |
0.0606343 | + | 0.998160i | \(0.480688\pi\) | |||||||
\(12\) | 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 | 0.236534 | − | 0.971623i | \(-0.423989\pi\) |
−0.723183 | + | 0.690656i | \(0.757322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.897962 | − | 1.55532i | 0.206007 | − | 0.356814i | −0.744446 | − | 0.667682i | \(-0.767286\pi\) |
0.950453 | + | 0.310868i | \(0.100620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.75804 | − | 1.43849i | −0.601853 | − | 0.313904i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.56534 | + | 4.44331i | 0.534911 | + | 0.926494i | 0.999168 | + | 0.0407927i | \(0.0129883\pi\) |
−0.464256 | + | 0.885701i | \(0.653678\pi\) | |||||||
\(24\) | 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 | −0.597117 | − | 0.802154i | \(-0.703687\pi\) |
0.396127 | + | 0.918196i | \(0.370354\pi\) | |||||||
\(30\) | 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 | −0.851951 | − | 0.523622i | \(-0.824581\pi\) |
0.0274943 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.76583 | + | 5.59913i | 0.442887 | + | 0.896578i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.74408 | − | 9.94904i | −0.897075 | − | 1.55378i | −0.831215 | − | 0.555950i | \(-0.812354\pi\) |
−0.0658595 | − | 0.997829i | \(-0.520979\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.00651 | − | 5.19991i | −1.37348 | − | 0.792979i | −0.382115 | − | 0.924115i | \(-0.624804\pi\) |
−0.991364 | + | 0.131136i | \(0.958138\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.64456 | − | 0.484930i | 0.841441 | − | 0.0722891i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.667511i | 0.0973664i | 0.998814 | + | 0.0486832i | \(0.0155025\pi\) | ||||
−0.998814 | + | 0.0486832i | \(0.984498\pi\) | |||||||
\(48\) | 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 | \(0.0811180\pi\) | ||||
−0.967704 | + | 0.252090i | \(0.918882\pi\) | |||||||
\(54\) | 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 | 0.281224 | − | 0.959642i | \(-0.409260\pi\) |
−0.690463 | + | 0.723368i | \(0.742593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.68542 | + | 8.11539i | −0.599907 | + | 1.03907i | 0.392927 | + | 0.919570i | \(0.371462\pi\) |
−0.992834 | + | 0.119500i | \(0.961871\pi\) | |||||||
\(62\) | 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 | 0.884118 | − | 0.467263i | \(-0.154760\pi\) |
−0.846721 | + | 0.532038i | \(0.821426\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.49863 | − | 4.76891i | 0.902729 | − | 0.574109i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.23069 | + | 4.75199i | 0.976804 | + | 0.563958i | 0.901304 | − | 0.433188i | \(-0.142611\pi\) |
0.0755000 | + | 0.997146i | \(0.475945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.90142i | − | 1.04183i | −0.853608 | − | 0.520916i | \(-0.825590\pi\) | ||
0.853608 | − | 0.520916i | \(-0.174410\pi\) | |||||||
\(74\) | 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 | \(-0.886191\pi\) | ||
0.936760 | − | 0.349973i | \(-0.113809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86812 | − | 1.53507i | 0.985347 | − | 0.170563i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.7231i | − | 1.94536i | −0.232146 | − | 0.972681i | \(-0.574575\pi\) | ||
0.232146 | − | 0.972681i | \(-0.425425\pi\) | |||||||
\(84\) | 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 | 0.974365 | − | 0.224972i | \(-0.0722290\pi\) |
−0.682014 | + | 0.731339i | \(0.738896\pi\) | |||||||
\(90\) | 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 | −0.0705073 | − | 0.997511i | \(-0.522462\pi\) |
−0.899124 | + | 0.437695i | \(0.855795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.28746 | − | 5.08575i | 0.732417 | − | 0.511137i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6428 | + | 6.14460i | −1.05899 | + | 0.611410i | −0.925154 | − | 0.379593i | \(-0.876064\pi\) |
−0.133840 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.1044i | − | 1.88242i | −0.337829 | − | 0.941208i | \(-0.609692\pi\) | ||
0.337829 | − | 0.941208i | \(-0.390308\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.20842 | + | 2.71651i | 0.508289 | + | 0.265105i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.57676 | − | 14.8554i | −0.829146 | − | 1.43612i | −0.898709 | − | 0.438546i | \(-0.855494\pi\) |
0.0695624 | − | 0.997578i | \(-0.477840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.2885i | − | 1.17703i | −0.808487 | − | 0.588514i | \(-0.799713\pi\) | ||
0.808487 | − | 0.588514i | \(-0.200287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.38246 | + | 8.46339i | 0.510881 | + | 0.803309i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.32579 | + | 4.22955i | 0.689153 | + | 0.397882i | 0.803295 | − | 0.595582i | \(-0.203079\pi\) |
−0.114142 | + | 0.993464i | \(0.536412\pi\) | |||||||
\(114\) | 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 | −0.334167 | − | 0.942514i | \(-0.608455\pi\) |
0.649157 | + | 0.760654i | \(0.275122\pi\) | |||||||
\(128\) | 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 | −0.998846 | − | 0.0480340i | \(-0.984704\pi\) |
0.541022 | + | 0.841009i | \(0.318038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.849362 | + | 0.490379i | 0.0720420 | + | 0.0415934i | 0.535588 | − | 0.844479i | \(-0.320090\pi\) |
−0.463546 | + | 0.886073i | \(0.653423\pi\) | |||||||
\(140\) | 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 | −0.223124 | − | 0.974790i | \(-0.571626\pi\) |
0.955755 | − | 0.294164i | \(-0.0950412\pi\) | |||||||
\(150\) | 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 | −0.751798 | − | 0.659393i | \(-0.770813\pi\) |
0.946950 | + | 0.321380i | \(0.104147\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.19952 | − | 8.17573i | −0.404782 | − | 0.636480i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.14343 | − | 1.81486i | 0.243246 | − | 0.140438i | −0.373422 | − | 0.927662i | \(-0.621816\pi\) |
0.616668 | + | 0.787224i | \(0.288482\pi\) | |||||||
\(168\) | 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 | 0.980970 | − | 0.194157i | \(-0.0621971\pi\) |
0.322340 | + | 0.946624i | \(0.395530\pi\) | |||||||
\(174\) | 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 | 0.999994 | − | 0.00349718i | \(-0.00111319\pi\) |
−0.503026 | + | 0.864272i | \(0.667780\pi\) | |||||||
\(180\) | 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 | 0.207695 | + | 0.978194i | \(0.433404\pi\) |
−0.950988 | + | 0.309227i | \(0.899930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84090 | + | 1.06284i | −0.132511 | + | 0.0765051i | −0.564790 | − | 0.825235i | \(-0.691043\pi\) |
0.432279 | + | 0.901740i | \(0.357709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.22312 | − | 10.5737i | −0.374036 | − | 0.757196i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5870 | − | 20.0692i | −0.825538 | − | 1.42987i | −0.901507 | − | 0.432764i | \(-0.857538\pi\) |
0.0759694 | − | 0.997110i | \(-0.475795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.39428 | + | 1.38234i | 0.169726 | + | 0.0979914i | 0.582457 | − | 0.812862i | \(-0.302092\pi\) |
−0.412731 | + | 0.910853i | \(0.635425\pi\) | |||||||
\(200\) | 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 | −0.865337 | − | 0.501191i | \(-0.832895\pi\) |
0.00137575 | + | 0.999999i | \(0.499562\pi\) | |||||||
\(212\) | 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 | 0.987850 | − | 0.155408i | \(-0.0496692\pi\) |
−0.628512 | + | 0.777800i | \(0.716336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.28549 | − | 0.368171i | 0.285699 | − | 0.0245447i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.60353 | − | 2.08050i | −0.239175 | − | 0.138088i | 0.375623 | − | 0.926773i | \(-0.377429\pi\) |
−0.614797 | + | 0.788685i | \(0.710762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5809i | 1.09570i | 0.836577 | + | 0.547849i | \(0.184553\pi\) | ||||
−0.836577 | + | 0.547849i | \(0.815447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.20587 | − | 0.394716i | 0.605702 | − | 0.0259704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.9386i | 0.913148i | 0.889685 | + | 0.456574i | \(0.150924\pi\) | ||||
−0.889685 | + | 0.456574i | \(0.849076\pi\) | |||||||
\(234\) | 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 | \(-0.919988\pi\) | ||
0.968574 | − | 0.248727i | \(-0.0800121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.13083 | − | 4.11698i | −0.459337 | − | 0.265198i | 0.252428 | − | 0.967616i | \(-0.418771\pi\) |
−0.711765 | + | 0.702417i | \(0.752104\pi\) | |||||||
\(242\) | 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 | −0.940703 | − | 0.339232i | \(-0.889833\pi\) |
0.764135 | + | 0.645057i | \(0.223166\pi\) | |||||||
\(252\) | 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 | −0.643447 | + | 0.765490i | \(0.722496\pi\) |
−0.984658 | + | 0.174497i | \(0.944170\pi\) | |||||||
\(258\) | 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 | 0.867703 | − | 0.497084i | \(-0.165596\pi\) |
−0.864338 | + | 0.502911i | \(0.832263\pi\) | |||||||
\(264\) | 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 | −0.990037 | − | 0.140805i | \(-0.955031\pi\) |
−0.616959 | − | 0.786995i | \(-0.711636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.33433 | + | 16.1675i | 0.567020 | + | 0.982108i | 0.996859 | + | 0.0792022i | \(0.0252373\pi\) |
−0.429838 | + | 0.902906i | \(0.641429\pi\) | |||||||
\(272\) | 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 | 0.394776 | + | 0.918777i | \(0.370822\pi\) |
−0.993073 | + | 0.117503i | \(0.962511\pi\) | |||||||
\(278\) | 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 | −0.520149 | − | 0.854075i | \(-0.674124\pi\) |
0.479576 | + | 0.877500i | \(0.340790\pi\) | |||||||
\(284\) | 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 | −0.989102 | − | 0.147229i | \(-0.952965\pi\) |
0.622055 | + | 0.782973i | \(0.286298\pi\) | |||||||
\(294\) | 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 | −0.629845 | − | 0.776721i | \(-0.716882\pi\) |
0.987582 | + | 0.157101i | \(0.0502149\pi\) | |||||||
\(332\) | 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 | 0.300364 | + | 0.953825i | \(0.402892\pi\) |
−0.976218 | + | 0.216789i | \(0.930442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.849362 | − | 0.490379i | 0.0454653 | − | 0.0262494i | −0.477095 | − | 0.878852i | \(-0.658310\pi\) |
0.522560 | + | 0.852602i | \(0.324977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.70481 | − | 16.0255i | −0.518004 | − | 0.855378i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.7300 | − | 27.2452i | −0.837225 | − | 1.45012i | −0.892206 | − | 0.451628i | \(-0.850843\pi\) |
0.0549818 | − | 0.998487i | \(-0.482490\pi\) | |||||||
\(354\) | 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 | \(-0.839533\pi\) | ||
0.875600 | − | 0.483038i | \(-0.160467\pi\) | |||||||
\(360\) | 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 | −0.944562 | − | 0.328333i | \(-0.893513\pi\) |
−0.187937 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(368\) | 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 | −0.803988 | − | 0.594646i | \(-0.797292\pi\) |
0.916972 | + | 0.398951i | \(0.130626\pi\) | |||||||
\(374\) | 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 | 0.757953 | + | 0.652309i | \(0.226199\pi\) |
0.185939 | + | 0.982561i | \(0.440467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.80988 | − | 5.99066i | −0.195186 | − | 0.306911i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.2486 | − | 7.07176i | −0.625876 | − | 0.361350i | 0.153277 | − | 0.988183i | \(-0.451017\pi\) |
−0.779153 | + | 0.626833i | \(0.784351\pi\) | |||||||
\(384\) | 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 | \(-0.911689\pi\) | ||
0.961761 | − | 0.273891i | \(-0.0883106\pi\) | |||||||
\(390\) | 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 | 0.890957 | − | 0.454088i | \(-0.150035\pi\) |
0.0522272 | + | 0.998635i | \(0.483368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.71392 | + | 2.99791i | −0.235991 | + | 0.150083i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1170 | − | 24.4514i | −0.704970 | − | 1.22104i | −0.966702 | − | 0.255903i | \(-0.917627\pi\) |
0.261733 | − | 0.965140i | \(-0.415706\pi\) | |||||||
\(402\) | 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 | 0.625783 | − | 0.779997i | \(-0.284780\pi\) |
−0.362606 | + | 0.931942i | \(0.618113\pi\) | |||||||
\(410\) | 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 | 0.926230 | − | 0.376958i | \(-0.123030\pi\) |
−0.789570 | + | 0.613660i | \(0.789697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.6161i | 0.956029i | 0.878352 | + | 0.478015i | \(0.158643\pi\) | ||||
−0.878352 | + | 0.478015i | \(0.841357\pi\) | |||||||
\(422\) | 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 | −0.715011 | + | 0.699113i | \(0.753578\pi\) |
−0.962955 | + | 0.269661i | \(0.913088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2473 | − | 19.4808i | 0.540509 | − | 0.936189i | −0.458366 | − | 0.888764i | \(-0.651565\pi\) |
0.998875 | − | 0.0474257i | \(-0.0151017\pi\) | |||||||
\(434\) | 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 | −0.886566 | − | 0.462601i | \(-0.846916\pi\) |
−0.0426587 | + | 0.999090i | \(0.513583\pi\) | |||||||
\(440\) | 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 | 0.126202 | + | 0.992005i | \(0.459721\pi\) |
−0.922202 | + | 0.386708i | \(0.873612\pi\) | |||||||
\(450\) | 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 | −0.821666 | − | 0.569969i | \(-0.806955\pi\) |
0.0827746 | + | 0.996568i | \(0.473622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.63325 | − | 11.1118i | 0.216262 | − | 0.518653i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.04833 | − | 7.01191i | 0.188549 | − | 0.326577i | −0.756217 | − | 0.654320i | \(-0.772955\pi\) |
0.944767 | + | 0.327743i | \(0.106288\pi\) | |||||||
\(462\) | 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 | −0.416457 | − | 0.909155i | \(-0.636728\pi\) |
0.579123 | + | 0.815240i | \(0.303395\pi\) | |||||||
\(480\) | 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 | −0.430820 | − | 0.902438i | \(-0.641776\pi\) |
0.996944 | − | 0.0781175i | \(-0.0248909\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.65261 | − | 3.99132i | −0.346063 | − | 0.180494i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.53131 | + | 9.58051i | 0.249624 | + | 0.432362i | 0.963422 | − | 0.267990i | \(-0.0863595\pi\) |
−0.713797 | + | 0.700352i | \(0.753026\pi\) | |||||||
\(492\) | 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 | −0.674803 | − | 0.737998i | \(-0.735771\pi\) |
0.976526 | + | 0.215397i | \(0.0691047\pi\) | |||||||
\(504\) | 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 | 0.988099 | − | 0.153822i | \(-0.0491582\pi\) |
−0.627263 | + | 0.778808i | \(0.715825\pi\) | |||||||
\(510\) | 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 | \(0.0237472\pi\) | ||||
−0.997218 | + | 0.0745348i | \(0.976253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.605718 | + | 0.349712i | −0.0264862 | + | 0.0152918i | −0.513185 | − | 0.858278i | \(-0.671534\pi\) |
0.486698 | + | 0.873570i | \(0.338201\pi\) | |||||||
\(524\) | 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 | \(0.0223236\pi\) | ||||
−0.997542 | + | 0.0700742i | \(0.977676\pi\) | |||||||
\(542\) | 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 | \(-0.809287\pi\) | ||
0.825820 | − | 0.563933i | \(-0.190713\pi\) | |||||||
\(548\) | 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 | 0.624397 | − | 0.781107i | \(-0.285345\pi\) |
−0.988657 | + | 0.150191i | \(0.952011\pi\) | |||||||
\(558\) | 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 | −0.257762 | − | 0.966209i | \(-0.582985\pi\) |
0.965642 | − | 0.259876i | \(-0.0836817\pi\) | |||||||
\(564\) | 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 | −0.404317 | − | 0.914619i | \(-0.632491\pi\) |
0.589925 | + | 0.807458i | \(0.299157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5901i | 0.568728i | 0.958716 | + | 0.284364i | \(0.0917825\pi\) | ||||
−0.958716 | + | 0.284364i | \(0.908218\pi\) | |||||||
\(572\) | 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 | \(-0.826655\pi\) | ||
0.855345 | − | 0.518058i | \(-0.173345\pi\) | |||||||
\(578\) | 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 | −0.639650 | − | 0.768667i | \(-0.720920\pi\) |
0.345860 | + | 0.938286i | \(0.387587\pi\) | |||||||
\(588\) | 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 | 0.986835 | + | 0.161730i | \(0.0517073\pi\) |
−0.353355 | + | 0.935489i | \(0.614959\pi\) | |||||||
\(602\) | 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 | 0.712953 | − | 0.701212i | \(-0.247357\pi\) |
−0.250791 | + | 0.968041i | \(0.580691\pi\) | |||||||
\(608\) | 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 | −0.521146 | − | 0.853467i | \(-0.674495\pi\) |
0.478551 | + | 0.878060i | \(0.341162\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.7075 | − | 20.1650i | 1.27857 | − | 0.813133i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.04423 | + | 7.00481i | −0.162815 | + | 0.282003i | −0.935877 | − | 0.352327i | \(-0.885391\pi\) |
0.773063 | + | 0.634330i | \(0.218724\pi\) | |||||||
\(618\) | 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 | −0.759072 | − | 0.651006i | \(-0.774347\pi\) |
0.943324 | + | 0.331873i | \(0.107680\pi\) | |||||||
\(632\) | 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 | 0.270714 | − | 0.962660i | \(-0.412740\pi\) |
−0.698331 | + | 0.715775i | \(0.746074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.7894 | − | 34.2762i | 0.780416 | − | 1.35172i | −0.151283 | − | 0.988490i | \(-0.548341\pi\) |
0.931700 | − | 0.363230i | \(-0.118326\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7308 | − | 30.1609i | 0.619399 | − | 1.18758i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.1294 | − | 22.7407i | −0.516169 | − | 0.894030i | −0.999824 | − | 0.0187716i | \(-0.994024\pi\) |
0.483655 | − | 0.875259i | \(-0.339309\pi\) | |||||||
\(648\) | 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 | 0.0485159 | − | 0.998822i | \(-0.484551\pi\) |
0.889264 | + | 0.457395i | \(0.151218\pi\) | |||||||
\(654\) | 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 | −0.167826 | − | 0.985817i | \(-0.553675\pi\) |
0.937655 | − | 0.347567i | \(-0.112992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.92681 | − | 3.42184i | 0.230526 | − | 0.133094i | −0.380289 | − | 0.924868i | \(-0.624175\pi\) |
0.610815 | + | 0.791774i | \(0.290842\pi\) | |||||||
\(662\) | 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 | 0.619355 | − | 0.785111i | \(-0.287394\pi\) |
−0.989604 | + | 0.143821i | \(0.954061\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.955073 | − | 7.38856i | −0.0367608 | − | 0.284386i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2564i | 1.20128i | 0.799519 | + | 0.600640i | \(0.205088\pi\) | ||||
−0.799519 | + | 0.600640i | \(0.794912\pi\) | |||||||
\(678\) | 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 | −0.0655042 | − | 0.997852i | \(-0.520866\pi\) |
−0.896918 | + | 0.442198i | \(0.854199\pi\) | |||||||
\(684\) | 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 | −0.847609 | − | 0.530622i | \(-0.821959\pi\) |
−0.0357274 | − | 0.999362i | \(-0.511375\pi\) | |||||||
\(692\) | 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 | \(0.0303027\pi\) | ||||
−0.995472 | + | 0.0950550i | \(0.969697\pi\) | |||||||
\(702\) | 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 | 0.992723 | − | 0.120419i | \(-0.0384239\pi\) |
0.392075 | + | 0.919933i | \(0.371757\pi\) | |||||||
\(710\) | 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 | −0.950026 | − | 0.312172i | \(-0.898943\pi\) |
0.745362 | + | 0.666660i | \(0.232277\pi\) | |||||||
\(720\) | 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 | \(-0.996208\pi\) | ||
0.999929 | − | 0.0119112i | \(-0.00379155\pi\) | |||||||
\(728\) | 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 | \(-0.826240\pi\) | ||
0.854669 | − | 0.519173i | \(-0.173760\pi\) | |||||||
\(734\) | 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 | 0.971656 | + | 0.236398i | \(0.0759670\pi\) |
−0.281101 | + | 0.959678i | \(0.590700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1920 | + | 0.726069i | 0.411149 | + | 0.0266728i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2637 | + | 5.92572i | −0.376537 | + | 0.217394i | −0.676310 | − | 0.736617i | \(-0.736422\pi\) |
0.299774 | + | 0.954010i | \(0.403089\pi\) | |||||||
\(744\) | 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 | −0.124131 | − | 0.992266i | \(-0.539614\pi\) |
0.797262 | + | 0.603634i | \(0.206281\pi\) | |||||||
\(752\) | 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 | 0.996446 | − | 0.0842340i | \(-0.0268443\pi\) |
−0.571172 | + | 0.820831i | \(0.693511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.1733 | + | 23.3401i | −0.441864 | + | 0.847193i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.86026 | − | 3.22206i | 0.0674343 | − | 0.116800i | −0.830337 | − | 0.557262i | \(-0.811852\pi\) |
0.897771 | + | 0.440462i | \(0.145185\pi\) | |||||||
\(762\) | 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 | 0.0347439 | − | 0.999396i | \(-0.488938\pi\) |
0.882874 | + | 0.469609i | \(0.155605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0131 | + | 44.0478i | 1.00887 | + | 1.58634i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.287410 | − | 0.497808i | 0.0103374 | − | 0.0179049i | −0.860810 | − | 0.508926i | \(-0.830043\pi\) |
0.871148 | + | 0.491021i | \(0.163376\pi\) | |||||||
\(774\) | 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 | −0.801346 | − | 0.598201i | \(-0.795882\pi\) |
0.918730 | + | 0.394886i | \(0.129216\pi\) | |||||||
\(788\) | 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 | −0.0131121 | − | 0.999914i | \(-0.504174\pi\) |
−0.872507 | + | 0.488602i | \(0.837507\pi\) | |||||||
\(798\) | 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 | −0.587486 | − | 0.809234i | \(-0.699882\pi\) |
0.407074 | + | 0.913395i | \(0.366549\pi\) | |||||||
\(810\) | 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 | −0.996286 | − | 0.0861099i | \(-0.972556\pi\) |
0.423569 | − | 0.905864i | \(-0.360777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.4135 | − | 26.7968i | −1.61787 | − | 0.934079i | −0.987469 | − | 0.157810i | \(-0.949557\pi\) |
−0.630402 | − | 0.776269i | \(-0.717110\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.94761 | − | 6.20722i | −0.137438 | − | 0.216108i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5894i | 1.20279i | 0.798951 | + | 0.601396i | \(0.205388\pi\) | ||||
−0.798951 | + | 0.601396i | \(0.794612\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.41879 | + | 14.5818i | 0.292397 | + | 0.506446i | 0.974376 | − | 0.224926i | \(-0.0722140\pi\) |
−0.681979 | + | 0.731371i | \(0.738881\pi\) | |||||||
\(830\) | 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 | 0.994365 | − | 0.106007i | \(-0.0338066\pi\) |
0.405378 | + | 0.914149i | \(0.367140\pi\) | |||||||
\(840\) | 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 | \(0.334428\pi\) | ||||
−0.497019 | + | 0.867739i | \(0.665572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.31438 | − | 9.21452i | 0.147549 | − | 0.315130i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 37.9765i | − | 1.29725i | −0.761107 | − | 0.648626i | \(-0.775344\pi\) | ||
0.761107 | − | 0.648626i | \(-0.224656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 38.6738i | − | 1.31953i | −0.751471 | − | 0.659766i | \(-0.770655\pi\) | ||
0.751471 | − | 0.659766i | \(-0.229345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.53081 | + | 35.7026i | 0.0521698 | + | 1.21674i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.0860835i | 0.00293032i | 0.999999 | + | 0.00146516i | \(0.000466374\pi\) | ||||
−0.999999 | + | 0.00146516i | \(0.999534\pi\) | |||||||
\(864\) | 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 | −0.159523 | − | 0.987194i | \(-0.550996\pi\) |
−0.934697 | + | 0.355446i | \(0.884329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2974 | + | 10.0648i | 0.650884 | + | 0.339477i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6895 | + | 17.1412i | −1.00026 | + | 0.577503i | −0.908326 | − | 0.418262i | \(-0.862639\pi\) |
−0.0919376 | + | 0.995765i | \(0.529306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.37789i | − | 0.248286i | −0.992264 | − | 0.124143i | \(-0.960382\pi\) | ||
0.992264 | − | 0.124143i | \(-0.0396181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.49031 | − | 10.5267i | 0.184555 | − | 0.353850i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.79576 | + | 8.30650i | 0.161026 | + | 0.278905i | 0.935237 | − | 0.354023i | \(-0.115186\pi\) |
−0.774211 | + | 0.632928i | \(0.781853\pi\) | |||||||
\(888\) | 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 | −0.816931 | − | 0.576736i | \(-0.804326\pi\) |
0.0910023 | + | 0.995851i | \(0.470993\pi\) | |||||||
\(908\) | 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 | 0.839982 | − | 0.542614i | \(-0.182565\pi\) |
−0.0499264 | + | 0.998753i | \(0.515899\pi\) | |||||||
\(920\) | 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 | −0.998075 | − | 0.0620204i | \(-0.980246\pi\) |
0.552749 | + | 0.833348i | \(0.313579\pi\) | |||||||
\(930\) | 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 | −0.713595 | − | 0.700559i | \(-0.752934\pi\) |
0.249904 | + | 0.968270i | \(0.419601\pi\) | |||||||
\(948\) | 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 | 0.302753 | − | 0.953069i | \(-0.402094\pi\) |
−0.674005 | + | 0.738727i | \(0.735428\pi\) | |||||||
\(954\) | 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 | −0.638864 | − | 0.769320i | \(-0.720595\pi\) |
0.985682 | + | 0.168612i | \(0.0539286\pi\) | |||||||
\(972\) | 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 | 0.724717 | − | 0.689046i | \(-0.241970\pi\) |
−0.959090 | + | 0.283101i | \(0.908637\pi\) | |||||||
\(978\) | 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 | \(-0.769022\pi\) | ||
0.748075 | − | 0.663614i | \(-0.230978\pi\) | |||||||
\(984\) | 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 | 0.429311 | − | 0.903157i | \(-0.358756\pi\) |
0.996812 | + | 0.0797837i | \(0.0254230\pi\) | |||||||
\(992\) | 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 | −0.851258 | − | 0.524748i | \(-0.824160\pi\) |
0.880074 | + | 0.474837i | \(0.157493\pi\) | |||||||
\(998\) | 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.335.4 | yes | 16 | |
3.2 | odd | 2 | inner | 624.2.bz.h.335.7 | yes | 16 | |
4.3 | odd | 2 | 624.2.bz.g.335.5 | yes | 16 | ||
12.11 | even | 2 | 624.2.bz.g.335.2 | yes | 16 | ||
13.4 | even | 6 | 624.2.bz.g.95.2 | ✓ | 16 | ||
39.17 | odd | 6 | 624.2.bz.g.95.5 | yes | 16 | ||
52.43 | odd | 6 | inner | 624.2.bz.h.95.7 | yes | 16 | |
156.95 | even | 6 | inner | 624.2.bz.h.95.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.bz.g.95.2 | ✓ | 16 | 13.4 | even | 6 | ||
624.2.bz.g.95.5 | yes | 16 | 39.17 | odd | 6 | ||
624.2.bz.g.335.2 | yes | 16 | 12.11 | even | 2 | ||
624.2.bz.g.335.5 | yes | 16 | 4.3 | odd | 2 | ||
624.2.bz.h.95.4 | yes | 16 | 156.95 | even | 6 | inner | |
624.2.bz.h.95.7 | yes | 16 | 52.43 | odd | 6 | inner | |
624.2.bz.h.335.4 | yes | 16 | 1.1 | even | 1 | trivial | |
624.2.bz.h.335.7 | yes | 16 | 3.2 | odd | 2 | inner |