Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(656,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.656");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.s (of order \(6\), degree \(2\), not 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 962.3 | ||
Character | \(\chi\) | \(=\) | 1323.962 |
Dual form | 1323.2.s.d.656.3 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05485 | − | 1.18637i | −1.45300 | − | 0.838890i | −0.454350 | − | 0.890823i | \(-0.650129\pi\) |
−0.998651 | + | 0.0519328i | \(0.983462\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.81495 | + | 3.14358i | 0.907474 | + | 1.57179i | ||||
\(5\) | −3.43548 | −1.53640 | −0.768198 | − | 0.640213i | \(-0.778846\pi\) | ||||
−0.768198 | + | 0.640213i | \(0.778846\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 3.86732i | − | 1.36730i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.05942 | + | 4.07576i | 2.23238 | + | 1.28887i | ||||
\(11\) | − | 0.313957i | − | 0.0946617i | −0.998879 | − | 0.0473309i | \(-0.984928\pi\) | ||
0.998879 | − | 0.0473309i | \(-0.0150715\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.09882 | − | 2.94381i | −1.41416 | − | 0.816465i | −0.418383 | − | 0.908271i | \(-0.637403\pi\) |
−0.995777 | + | 0.0918054i | \(0.970736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.958178 | + | 1.65961i | −0.239545 | + | 0.414903i | ||||
\(17\) | 0.476712 | − | 0.825689i | 0.115620 | − | 0.200259i | −0.802408 | − | 0.596776i | \(-0.796448\pi\) |
0.918027 | + | 0.396517i | \(0.129781\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09214 | + | 0.630546i | −0.250553 | + | 0.144657i | −0.620018 | − | 0.784588i | \(-0.712875\pi\) |
0.369464 | + | 0.929245i | \(0.379541\pi\) | |||||||
\(20\) | −6.23523 | − | 10.7997i | −1.39424 | − | 2.41489i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.372470 | + | 0.645137i | −0.0794108 | + | 0.137544i | ||||
\(23\) | − | 6.82815i | − | 1.42377i | −0.702297 | − | 0.711884i | \(-0.747842\pi\) | ||
0.702297 | − | 0.711884i | \(-0.252158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.80255 | 1.36051 | ||||||||
\(26\) | 6.98489 | + | 12.0982i | 1.36985 | + | 2.37265i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.43518 | + | 1.98330i | −0.637897 | + | 0.368290i | −0.783804 | − | 0.621008i | \(-0.786723\pi\) |
0.145907 | + | 0.989298i | \(0.453390\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.53388 | + | 2.61764i | −0.814309 | + | 0.470141i | −0.848450 | − | 0.529276i | \(-0.822464\pi\) |
0.0341412 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(32\) | −2.76057 | + | 1.59381i | −0.488004 | + | 0.281749i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.95915 | + | 1.13111i | −0.335991 | + | 0.193984i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.68802 | − | 4.65579i | −0.441908 | − | 0.765407i | 0.555923 | − | 0.831234i | \(-0.312365\pi\) |
−0.997831 | + | 0.0658264i | \(0.979032\pi\) | |||||||
\(38\) | 2.99224 | 0.485406 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.2861i | 2.10072i | ||||||||
\(41\) | −0.0699627 | + | 0.121179i | −0.0109263 | + | 0.0189250i | −0.871437 | − | 0.490508i | \(-0.836811\pi\) |
0.860511 | + | 0.509433i | \(0.170145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.44078 | + | 2.49550i | 0.219716 | + | 0.380560i | 0.954721 | − | 0.297502i | \(-0.0961535\pi\) |
−0.735005 | + | 0.678062i | \(0.762820\pi\) | |||||||
\(44\) | 0.986951 | − | 0.569817i | 0.148788 | − | 0.0859031i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.10072 | + | 14.0309i | −1.19439 | + | 2.06874i | ||||
\(47\) | 1.00695 | − | 1.74409i | 0.146879 | − | 0.254402i | −0.783193 | − | 0.621778i | \(-0.786411\pi\) |
0.930072 | + | 0.367376i | \(0.119744\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −13.9783 | − | 8.07035i | −1.97682 | − | 1.14132i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 21.3714i | − | 2.96369i | ||||||
\(53\) | 10.3749 | + | 5.98997i | 1.42511 | + | 0.822786i | 0.996729 | − | 0.0808132i | \(-0.0257517\pi\) |
0.428378 | + | 0.903599i | \(0.359085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.07860i | 0.145438i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.41172 | 1.23582 | ||||||||
\(59\) | −0.824459 | − | 1.42801i | −0.107335 | − | 0.185910i | 0.807355 | − | 0.590067i | \(-0.200899\pi\) |
−0.914690 | + | 0.404156i | \(0.867565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.57423 | − | 1.48623i | −0.329597 | − | 0.190293i | 0.326065 | − | 0.945347i | \(-0.394277\pi\) |
−0.655662 | + | 0.755055i | \(0.727610\pi\) | |||||||
\(62\) | 12.4219 | 1.57759 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.3961 | 1.42452 | ||||||||
\(65\) | 17.5169 | + | 10.1134i | 2.17271 | + | 1.25441i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.934059 | + | 1.61784i | 0.114113 | + | 0.197650i | 0.917425 | − | 0.397909i | \(-0.130264\pi\) |
−0.803312 | + | 0.595559i | \(0.796931\pi\) | |||||||
\(68\) | 3.46083 | 0.419687 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9981i | 1.30524i | 0.757686 | + | 0.652619i | \(0.226330\pi\) | ||||
−0.757686 | + | 0.652619i | \(0.773670\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.354655 | − | 0.204760i | −0.0415092 | − | 0.0239653i | 0.479102 | − | 0.877759i | \(-0.340962\pi\) |
−0.520611 | + | 0.853794i | \(0.674296\pi\) | |||||||
\(74\) | 12.7560i | 1.48285i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.96435 | − | 2.28882i | −0.454742 | − | 0.262545i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.23325 | + | 9.06426i | −0.588787 | + | 1.01981i | 0.405605 | + | 0.914049i | \(0.367061\pi\) |
−0.994392 | + | 0.105760i | \(0.966272\pi\) | |||||||
\(80\) | 3.29181 | − | 5.70158i | 0.368035 | − | 0.637456i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.287526 | − | 0.166003i | 0.0317519 | − | 0.0183320i | ||||
\(83\) | 4.00094 | + | 6.92984i | 0.439161 | + | 0.760649i | 0.997625 | − | 0.0688800i | \(-0.0219426\pi\) |
−0.558464 | + | 0.829529i | \(0.688609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.63774 | + | 2.83664i | −0.177637 | + | 0.307677i | ||||
\(86\) | − | 6.83718i | − | 0.737272i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.21417 | −0.129431 | ||||||||
\(89\) | −1.05931 | − | 1.83478i | −0.112287 | − | 0.194487i | 0.804405 | − | 0.594081i | \(-0.202484\pi\) |
−0.916692 | + | 0.399595i | \(0.869151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 21.4649 | − | 12.3927i | 2.23787 | − | 1.29203i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.13828 | + | 2.38924i | −0.426831 | + | 0.246431i | ||||
\(95\) | 3.75202 | − | 2.16623i | 0.384949 | − | 0.222251i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5054 | − | 6.06531i | 1.06666 | − | 0.615839i | 0.139396 | − | 0.990237i | \(-0.455484\pi\) |
0.927268 | + | 0.374398i | \(0.122150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.3463 | + | 21.3844i | 1.23463 | + | 2.13844i | ||||
\(101\) | −12.5208 | −1.24586 | −0.622932 | − | 0.782276i | \(-0.714059\pi\) | ||||
−0.622932 | + | 0.782276i | \(0.714059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.0179i | 1.77536i | 0.460461 | + | 0.887680i | \(0.347684\pi\) | ||||
−0.460461 | + | 0.887680i | \(0.652316\pi\) | |||||||
\(104\) | −11.3847 | + | 19.7188i | −1.11636 | + | 1.93359i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.2127 | − | 24.6170i | −1.38046 | − | 2.39102i | ||||
\(107\) | 3.11610 | − | 1.79908i | 0.301245 | − | 0.173924i | −0.341757 | − | 0.939788i | \(-0.611022\pi\) |
0.643002 | + | 0.765864i | \(0.277689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.28109 | − | 5.68302i | 0.314271 | − | 0.544334i | −0.665011 | − | 0.746834i | \(-0.731573\pi\) |
0.979282 | + | 0.202499i | \(0.0649064\pi\) | |||||||
\(110\) | 1.27961 | − | 2.21636i | 0.122006 | − | 0.211321i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.87912 | + | 1.08491i | 0.176773 | + | 0.102060i | 0.585775 | − | 0.810473i | \(-0.300790\pi\) |
−0.409003 | + | 0.912533i | \(0.634123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.4580i | 2.18747i | ||||||||
\(116\) | −12.4694 | − | 7.19918i | −1.15775 | − | 0.668427i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.91246i | 0.360171i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9014 | 0.991039 | ||||||||
\(122\) | 3.52645 | + | 6.10798i | 0.319269 | + | 0.552991i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.4575 | − | 9.50175i | −1.47793 | − | 0.853282i | ||||
\(125\) | −6.19265 | −0.553887 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.34967 | 0.208499 | 0.104250 | − | 0.994551i | \(-0.466756\pi\) | ||||
0.104250 | + | 0.994551i | \(0.466756\pi\) | |||||||
\(128\) | −17.8962 | − | 10.3324i | −1.58182 | − | 0.913263i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −23.9965 | − | 41.5631i | −2.10463 | − | 3.64533i | ||||
\(131\) | 9.49188 | 0.829309 | 0.414655 | − | 0.909979i | \(-0.363902\pi\) | ||||
0.414655 | + | 0.909979i | \(0.363902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 4.43256i | − | 0.382915i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.19320 | − | 1.84360i | −0.273815 | − | 0.158087i | ||||
\(137\) | − | 10.2244i | − | 0.873527i | −0.899576 | − | 0.436763i | \(-0.856125\pi\) | ||
0.899576 | − | 0.436763i | \(-0.143875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.56556 | + | 2.63593i | 0.387246 | + | 0.223577i | 0.680966 | − | 0.732315i | \(-0.261560\pi\) |
−0.293720 | + | 0.955891i | \(0.594893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.0479 | − | 22.5996i | 1.09495 | − | 1.89651i | ||||
\(143\) | −0.924230 | + | 1.60081i | −0.0772880 | + | 0.133867i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.8015 | − | 6.81361i | 0.980062 | − | 0.565839i | ||||
\(146\) | 0.485842 | + | 0.841504i | 0.0402086 | + | 0.0696433i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.75724 | − | 16.9000i | 0.802040 | − | 1.38917i | ||||
\(149\) | 18.2617i | 1.49606i | 0.663666 | + | 0.748029i | \(0.269000\pi\) | ||||
−0.663666 | + | 0.748029i | \(0.731000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.1102 | 1.88068 | 0.940340 | − | 0.340236i | \(-0.110507\pi\) | ||||
0.940340 | + | 0.340236i | \(0.110507\pi\) | |||||||
\(152\) | 2.43852 | + | 4.22365i | 0.197790 | + | 0.342583i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.5761 | − | 8.99285i | 1.25110 | − | 0.722323i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.65459 | − | 3.26468i | 0.451286 | − | 0.260550i | −0.257087 | − | 0.966388i | \(-0.582763\pi\) |
0.708373 | + | 0.705838i | \(0.249430\pi\) | |||||||
\(158\) | 21.5071 | − | 12.4172i | 1.71102 | − | 0.987855i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.48388 | − | 5.47552i | 0.749767 | − | 0.432878i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2623 | − | 21.2389i | −0.960457 | − | 1.66356i | −0.721354 | − | 0.692566i | \(-0.756480\pi\) |
−0.239103 | − | 0.970994i | \(-0.576853\pi\) | |||||||
\(164\) | −0.507915 | −0.0396615 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 18.9864i | − | 1.47363i | ||||||
\(167\) | −6.99871 | + | 12.1221i | −0.541576 | + | 0.938037i | 0.457238 | + | 0.889345i | \(0.348839\pi\) |
−0.998814 | + | 0.0486928i | \(0.984494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8320 | + | 18.7616i | 0.833232 | + | 1.44320i | ||||
\(170\) | 6.73061 | − | 3.88592i | 0.516214 | − | 0.298037i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.22987 | + | 9.05840i | −0.398774 | + | 0.690697i | ||||
\(173\) | 5.44974 | − | 9.43923i | 0.414336 | − | 0.717651i | −0.581022 | − | 0.813888i | \(-0.697347\pi\) |
0.995359 | + | 0.0962363i | \(0.0306805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.521048 | + | 0.300827i | 0.0392755 | + | 0.0226757i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.02695i | 0.376786i | ||||||||
\(179\) | 1.38517 | + | 0.799726i | 0.103532 | + | 0.0597743i | 0.550872 | − | 0.834590i | \(-0.314295\pi\) |
−0.447340 | + | 0.894364i | \(0.647629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.5088i | 1.30142i | 0.759326 | + | 0.650710i | \(0.225529\pi\) | ||||
−0.759326 | + | 0.650710i | \(0.774471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −26.4067 | −1.94673 | ||||||||
\(185\) | 9.23466 | + | 15.9949i | 0.678946 | + | 1.17597i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.259231 | − | 0.149667i | −0.0189569 | − | 0.0109447i | ||||
\(188\) | 7.31027 | 0.533156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.2798 | −0.745775 | ||||||||
\(191\) | −13.9107 | − | 8.03138i | −1.00655 | − | 0.581130i | −0.0963679 | − | 0.995346i | \(-0.530723\pi\) |
−0.910179 | + | 0.414216i | \(0.864056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.44196 | + | 9.42575i | 0.391721 | + | 0.678480i | 0.992677 | − | 0.120802i | \(-0.0385467\pi\) |
−0.600956 | + | 0.799282i | \(0.705213\pi\) | |||||||
\(194\) | −28.7828 | −2.06649 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.50777i | − | 0.463660i | −0.972756 | − | 0.231830i | \(-0.925529\pi\) | ||
0.972756 | − | 0.231830i | \(-0.0744712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4217 | + | 8.90372i | 1.09321 | + | 0.631168i | 0.934431 | − | 0.356145i | \(-0.115909\pi\) |
0.158784 | + | 0.987313i | \(0.449243\pi\) | |||||||
\(200\) | − | 26.3077i | − | 1.86023i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.7284 | + | 14.8543i | 1.81024 | + | 1.04514i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.240356 | − | 0.416308i | 0.0167872 | − | 0.0290762i | ||||
\(206\) | 21.3759 | − | 37.0242i | 1.48933 | − | 2.57960i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.77117 | − | 5.64139i | 0.677508 | − | 0.391160i | ||||
\(209\) | 0.197965 | + | 0.342885i | 0.0136935 | + | 0.0237178i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.282402 | + | 0.489135i | −0.0194414 | + | 0.0336735i | −0.875582 | − | 0.483069i | \(-0.839522\pi\) |
0.856141 | + | 0.516742i | \(0.172855\pi\) | |||||||
\(212\) | 43.4860i | 2.98663i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.53751 | −0.583612 | ||||||||
\(215\) | −4.94977 | − | 8.57325i | −0.337571 | − | 0.584691i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.4843 | + | 7.78518i | −0.913273 | + | 0.527279i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.39066 | + | 1.95760i | −0.228598 | + | 0.131981i | ||||
\(221\) | −4.86134 | + | 2.80670i | −0.327009 | + | 0.188799i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.61261 | + | 4.39514i | −0.509778 | + | 0.294321i | −0.732742 | − | 0.680506i | \(-0.761760\pi\) |
0.222964 | + | 0.974827i | \(0.428427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.57421 | − | 4.45866i | −0.171234 | − | 0.296586i | ||||
\(227\) | −16.9066 | −1.12213 | −0.561065 | − | 0.827772i | \(-0.689608\pi\) | ||||
−0.561065 | + | 0.827772i | \(0.689608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.5618i | − | 1.29268i | −0.763050 | − | 0.646339i | \(-0.776299\pi\) | ||
0.763050 | − | 0.646339i | \(-0.223701\pi\) | |||||||
\(230\) | 27.8299 | − | 48.2028i | 1.83505 | − | 3.17840i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.67007 | + | 13.2849i | 0.503565 | + | 0.872200i | ||||
\(233\) | 17.0926 | − | 9.86840i | 1.11977 | − | 0.646500i | 0.178428 | − | 0.983953i | \(-0.442899\pi\) |
0.941342 | + | 0.337453i | \(0.109565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.45937 | + | 5.99180i | −0.225664 | + | 0.390862i | ||||
\(236\) | 2.99270 | − | 5.18351i | 0.194808 | − | 0.337418i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9761 | + | 9.80118i | 1.09809 | + | 0.633985i | 0.935720 | − | 0.352744i | \(-0.114751\pi\) |
0.162375 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.9540i | − | 1.02769i | −0.857883 | − | 0.513845i | \(-0.828221\pi\) | ||
0.857883 | − | 0.513845i | \(-0.171779\pi\) | |||||||
\(242\) | −22.4008 | − | 12.9331i | −1.43998 | − | 0.831373i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 10.7897i | − | 0.690743i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.42482 | 0.472430 | ||||||||
\(248\) | 10.1232 | + | 17.5340i | 0.642826 | + | 1.11341i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.7250 | + | 7.34677i | 0.804798 | + | 0.464651i | ||||
\(251\) | −0.976065 | −0.0616087 | −0.0308044 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308044 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.14375 | −0.134776 | ||||||||
\(254\) | −4.82822 | − | 2.78758i | −0.302950 | − | 0.174908i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.1200 | + | 22.7244i | 0.819998 | + | 1.42028i | ||||
\(257\) | 12.2389 | 0.763444 | 0.381722 | − | 0.924277i | \(-0.375331\pi\) | ||||
0.381722 | + | 0.924277i | \(0.375331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 73.4212i | 4.55339i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.5044 | − | 11.2609i | −1.20499 | − | 0.695700i | ||||
\(263\) | 4.20815i | 0.259486i | 0.991548 | + | 0.129743i | \(0.0414152\pi\) | ||||
−0.991548 | + | 0.129743i | \(0.958585\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.6429 | − | 20.5785i | −2.18953 | − | 1.26413i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.39054 | + | 5.87258i | −0.207110 | + | 0.358725i | ||||
\(269\) | −10.8299 | + | 18.7579i | −0.660309 | + | 1.14369i | 0.320225 | + | 0.947341i | \(0.396241\pi\) |
−0.980534 | + | 0.196348i | \(0.937092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8987 | + | 10.3338i | −1.08727 | + | 0.627736i | −0.932849 | − | 0.360268i | \(-0.882685\pi\) |
−0.154423 | + | 0.988005i | \(0.549352\pi\) | |||||||
\(272\) | 0.913549 | + | 1.58231i | 0.0553921 | + | 0.0959419i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.1299 | + | 21.0096i | −0.732793 | + | 1.26923i | ||||
\(275\) | − | 2.13571i | − | 0.128788i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.8897 | −1.67573 | −0.837864 | − | 0.545879i | \(-0.816196\pi\) | ||||
−0.837864 | + | 0.545879i | \(0.816196\pi\) | |||||||
\(278\) | −6.25437 | − | 10.8329i | −0.375112 | − | 0.649714i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7176 | + | 9.65190i | −0.997287 | + | 0.575784i | −0.907444 | − | 0.420172i | \(-0.861970\pi\) |
−0.0898425 | + | 0.995956i | \(0.528636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2703 | − | 8.81631i | 0.907725 | − | 0.524075i | 0.0280263 | − | 0.999607i | \(-0.491078\pi\) |
0.879698 | + | 0.475532i | \(0.157744\pi\) | |||||||
\(284\) | −34.5735 | + | 19.9610i | −2.05156 | + | 1.18447i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.79832 | − | 2.19296i | 0.224599 | − | 0.129672i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.04549 | + | 13.9352i | 0.473264 | + | 0.819718i | ||||
\(290\) | −32.3338 | −1.89871 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 1.48652i | − | 0.0869917i | ||||||
\(293\) | −14.1138 | + | 24.4458i | −0.824536 | + | 1.42814i | 0.0777369 | + | 0.996974i | \(0.475231\pi\) |
−0.902273 | + | 0.431165i | \(0.858103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.83242 | + | 4.90589i | 0.164910 | + | 0.285632i | ||||
\(296\) | −18.0054 | + | 10.3954i | −1.04655 | + | 0.604223i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.6651 | − | 37.5251i | 1.25503 | − | 2.17377i | ||||
\(299\) | −20.1008 | + | 34.8156i | −1.16246 | + | 2.01344i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −47.4880 | − | 27.4172i | −2.73263 | − | 1.57768i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2.41670i | − | 0.138607i | ||||||
\(305\) | 8.84374 | + | 5.10593i | 0.506391 | + | 0.292365i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.56651i | 0.488917i | 0.969660 | + | 0.244458i | \(0.0786102\pi\) | ||||
−0.969660 | + | 0.244458i | \(0.921390\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −42.6754 | −2.42380 | ||||||||
\(311\) | −9.67914 | − | 16.7648i | −0.548854 | − | 0.950642i | −0.998353 | − | 0.0573619i | \(-0.981731\pi\) |
0.449500 | − | 0.893280i | \(-0.351602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9507 | + | 13.2506i | 1.29725 | + | 0.748967i | 0.979928 | − | 0.199352i | \(-0.0638836\pi\) |
0.317321 | + | 0.948318i | \(0.397217\pi\) | |||||||
\(314\) | −15.4925 | −0.874291 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −37.9923 | −2.13724 | ||||||||
\(317\) | −7.50458 | − | 4.33277i | −0.421499 | − | 0.243353i | 0.274219 | − | 0.961667i | \(-0.411581\pi\) |
−0.695719 | + | 0.718314i | \(0.744914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.622673 | + | 1.07850i | 0.0348630 | + | 0.0603844i | ||||
\(320\) | −39.1512 | −2.18862 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20235i | 0.0669008i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.6850 | − | 20.0254i | −1.92398 | − | 1.11081i | ||||
\(326\) | 58.1905i | 3.22287i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.468638 | + | 0.270568i | 0.0258762 | + | 0.0149396i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.66912 | + | 16.7474i | −0.531463 | + | 0.920521i | 0.467863 | + | 0.883801i | \(0.345024\pi\) |
−0.999326 | + | 0.0367197i | \(0.988309\pi\) | |||||||
\(332\) | −14.5230 | + | 25.1546i | −0.797054 | + | 1.38054i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.7626 | − | 16.6061i | 1.57382 | − | 0.908646i | ||||
\(335\) | −3.20894 | − | 5.55805i | −0.175323 | − | 0.303669i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4451 | + | 21.5556i | −0.677930 | + | 1.17421i | 0.297673 | + | 0.954668i | \(0.403790\pi\) |
−0.975603 | + | 0.219542i | \(0.929544\pi\) | |||||||
\(338\) | − | 51.4031i | − | 2.79596i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.8896 | −0.644805 | ||||||||
\(341\) | 0.821826 | + | 1.42345i | 0.0445044 | + | 0.0770839i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.65090 | − | 5.57195i | 0.520341 | − | 0.300419i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.3968 | + | 12.9308i | −1.20406 | + | 0.695165i | ||||
\(347\) | 5.01728 | − | 2.89673i | 0.269342 | − | 0.155505i | −0.359247 | − | 0.933243i | \(-0.616966\pi\) |
0.628588 | + | 0.777738i | \(0.283633\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3430 | + | 7.70360i | −0.714236 | + | 0.412364i | −0.812627 | − | 0.582784i | \(-0.801963\pi\) |
0.0983918 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500390 | + | 0.866700i | 0.0266709 | + | 0.0461953i | ||||
\(353\) | 17.7453 | 0.944485 | 0.472243 | − | 0.881469i | \(-0.343445\pi\) | ||||
0.472243 | + | 0.881469i | \(0.343445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 37.7839i | − | 2.00536i | ||||||
\(356\) | 3.84519 | − | 6.66007i | 0.203795 | − | 0.352983i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.89754 | − | 3.28664i | −0.100288 | − | 0.173704i | ||||
\(359\) | −19.8490 | + | 11.4599i | −1.04759 | + | 0.604828i | −0.921974 | − | 0.387251i | \(-0.873425\pi\) |
−0.125618 | + | 0.992079i | \(0.540091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.70482 | + | 15.0772i | −0.458149 | + | 0.793537i | ||||
\(362\) | 20.7719 | − | 35.9781i | 1.09175 | − | 1.89096i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.21841 | + | 0.703450i | 0.0637745 | + | 0.0368203i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00277i | 0.261143i | 0.991439 | + | 0.130571i | \(0.0416811\pi\) | ||||
−0.991439 | + | 0.130571i | \(0.958319\pi\) | |||||||
\(368\) | 11.3321 | + | 6.54259i | 0.590726 | + | 0.341056i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 43.8229i | − | 2.27824i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.52560 | 0.493217 | 0.246608 | − | 0.969115i | \(-0.420684\pi\) | ||||
0.246608 | + | 0.969115i | \(0.420684\pi\) | |||||||
\(374\) | 0.355121 | + | 0.615088i | 0.0183629 | + | 0.0318055i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.74497 | − | 3.89421i | −0.347845 | − | 0.200828i | ||||
\(377\) | 23.3538 | 1.20278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.8369 | −0.710756 | −0.355378 | − | 0.934723i | \(-0.615648\pi\) | ||||
−0.355378 | + | 0.934723i | \(0.615648\pi\) | |||||||
\(380\) | 13.6194 | + | 7.86319i | 0.698663 | + | 0.403373i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.0564 | + | 33.0066i | 0.975009 | + | 1.68876i | ||||
\(383\) | 21.2320 | 1.08490 | 0.542452 | − | 0.840087i | \(-0.317496\pi\) | ||||
0.542452 | + | 0.840087i | \(0.317496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 25.8247i | − | 1.31444i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 38.1336 | + | 22.0165i | 1.93594 | + | 1.11772i | ||||
\(389\) | 4.51972i | 0.229159i | 0.993414 | + | 0.114579i | \(0.0365521\pi\) | ||||
−0.993414 | + | 0.114579i | \(0.963448\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.63793 | − | 3.25506i | −0.285122 | − | 0.164616i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.72063 | + | 13.3725i | −0.388960 | + | 0.673698i | ||||
\(395\) | 17.9788 | − | 31.1401i | 0.904610 | − | 1.56683i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.5830 | + | 7.84214i | −0.681710 | + | 0.393586i | −0.800499 | − | 0.599334i | \(-0.795432\pi\) |
0.118789 | + | 0.992920i | \(0.462099\pi\) | |||||||
\(398\) | −21.1262 | − | 36.5917i | −1.05896 | − | 1.83417i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.51806 | + | 11.2896i | −0.325903 | + | 0.564480i | ||||
\(401\) | 10.7883i | 0.538741i | 0.963037 | + | 0.269370i | \(0.0868156\pi\) | ||||
−0.963037 | + | 0.269370i | \(0.913184\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.8233 | 1.53542 | ||||||||
\(404\) | −22.7246 | − | 39.3601i | −1.13059 | − | 1.95824i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.46172 | + | 0.843925i | −0.0724548 | + | 0.0418318i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9860 | − | 9.80689i | 0.839906 | − | 0.484920i | −0.0173265 | − | 0.999850i | \(-0.505515\pi\) |
0.857232 | + | 0.514930i | \(0.172182\pi\) | |||||||
\(410\) | −0.987791 | + | 0.570302i | −0.0487835 | + | 0.0281652i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −56.6409 | + | 32.7016i | −2.79050 | + | 1.61109i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7452 | − | 23.8074i | −0.674724 | − | 1.16866i | ||||
\(416\) | 18.7675 | 0.920154 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 0.939437i | − | 0.0459494i | ||||||
\(419\) | 8.83829 | − | 15.3084i | 0.431779 | − | 0.747862i | −0.565248 | − | 0.824921i | \(-0.691220\pi\) |
0.997027 | + | 0.0770586i | \(0.0245528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9507 | − | 29.3594i | −0.826124 | − | 1.43089i | −0.901057 | − | 0.433701i | \(-0.857208\pi\) |
0.0749327 | − | 0.997189i | \(-0.476126\pi\) | |||||||
\(422\) | 1.16059 | − | 0.670068i | 0.0564967 | − | 0.0326184i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.1652 | − | 40.1232i | 1.12500 | − | 1.94856i | ||||
\(425\) | 3.24286 | − | 5.61679i | 0.157302 | − | 0.272454i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.3111 | + | 6.53048i | 0.546744 | + | 0.315663i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.4890i | 1.13274i | ||||||||
\(431\) | −12.2317 | − | 7.06195i | −0.589178 | − | 0.340162i | 0.175594 | − | 0.984463i | \(-0.443815\pi\) |
−0.764772 | + | 0.644300i | \(0.777149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.10088i | − | 0.437360i | −0.975797 | − | 0.218680i | \(-0.929825\pi\) | ||
0.975797 | − | 0.218680i | \(-0.0701752\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.8200 | 1.14077 | ||||||||
\(437\) | 4.30546 | + | 7.45728i | 0.205958 | + | 0.356730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1520 | + | 5.86126i | 0.484529 | + | 0.279743i | 0.722302 | − | 0.691578i | \(-0.243084\pi\) |
−0.237773 | + | 0.971321i | \(0.576417\pi\) | |||||||
\(440\) | 4.17128 | 0.198858 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.3191 | 0.633526 | ||||||||
\(443\) | −6.17796 | − | 3.56685i | −0.293524 | − | 0.169466i | 0.346006 | − | 0.938232i | \(-0.387538\pi\) |
−0.639530 | + | 0.768766i | \(0.720871\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.63925 | + | 6.30337i | 0.172517 | + | 0.298808i | ||||
\(446\) | 20.8571 | 0.987611 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.17445i | 0.149811i | 0.997191 | + | 0.0749057i | \(0.0238656\pi\) | ||||
−0.997191 | + | 0.0749057i | \(0.976134\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0380450 | + | 0.0219653i | 0.00179147 | + | 0.00103431i | ||||
\(452\) | 7.87622i | 0.370466i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.7406 | + | 20.0575i | 1.63045 | + | 0.941344i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0745 | + | 20.9137i | −0.564821 | + | 0.978299i | 0.432245 | + | 0.901756i | \(0.357722\pi\) |
−0.997066 | + | 0.0765431i | \(0.975612\pi\) | |||||||
\(458\) | −23.2075 | + | 40.1966i | −1.08442 | + | 1.87826i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −73.7422 | + | 42.5751i | −3.43825 | + | 1.98507i | ||||
\(461\) | −6.87281 | − | 11.9041i | −0.320099 | − | 0.554427i | 0.660409 | − | 0.750906i | \(-0.270383\pi\) |
−0.980508 | + | 0.196478i | \(0.937049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3157 | − | 17.8673i | 0.479411 | − | 0.830364i | −0.520310 | − | 0.853977i | \(-0.674184\pi\) |
0.999721 | + | 0.0236135i | \(0.00751711\pi\) | |||||||
\(464\) | − | 7.60143i | − | 0.352887i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −46.8303 | −2.16937 | ||||||||
\(467\) | −0.465894 | − | 0.806952i | −0.0215590 | − | 0.0373413i | 0.855045 | − | 0.518554i | \(-0.173530\pi\) |
−0.876604 | + | 0.481213i | \(0.840196\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 14.2170 | − | 8.20819i | 0.655781 | − | 0.378615i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.52256 | + | 3.18845i | −0.254196 | + | 0.146760i | ||||
\(473\) | 0.783481 | − | 0.452343i | 0.0360245 | − | 0.0207987i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.42932 | + | 4.28932i | −0.340881 | + | 0.196808i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.2556 | − | 40.2800i | −1.06369 | − | 1.84236i | ||||
\(479\) | 32.4063 | 1.48068 | 0.740340 | − | 0.672232i | \(-0.234664\pi\) | ||||
0.740340 | + | 0.672232i | \(0.234664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.6521i | 1.44321i | ||||||||
\(482\) | −18.9274 | + | 32.7832i | −0.862120 | + | 1.49324i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.7855 | + | 34.2695i | 0.899342 | + | 1.55771i | ||||
\(485\) | −36.0912 | + | 20.8373i | −1.63882 | + | 0.946172i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1867 | − | 29.7682i | 0.778802 | − | 1.34892i | −0.153830 | − | 0.988097i | \(-0.549161\pi\) |
0.932633 | − | 0.360828i | \(-0.117506\pi\) | |||||||
\(488\) | −5.74774 | + | 9.95538i | −0.260188 | + | 0.450659i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.31048 | + | 4.22071i | 0.329917 | + | 0.190478i | 0.655804 | − | 0.754931i | \(-0.272330\pi\) |
−0.325887 | + | 0.945409i | \(0.605663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.78185i | 0.170326i | ||||||||
\(494\) | −15.2569 | − | 8.80859i | −0.686441 | − | 0.396317i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 10.0326i | − | 0.450479i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.4080 | −0.510692 | −0.255346 | − | 0.966850i | \(-0.582189\pi\) | ||||
−0.255346 | + | 0.966850i | \(0.582189\pi\) | |||||||
\(500\) | −11.2393 | − | 19.4671i | −0.502638 | − | 0.870595i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.00567 | + | 1.15797i | 0.0895175 | + | 0.0516830i | ||||
\(503\) | 32.8028 | 1.46261 | 0.731303 | − | 0.682053i | \(-0.238913\pi\) | ||||
0.731303 | + | 0.682053i | \(0.238913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.0149 | 1.91414 | ||||||||
\(506\) | 4.40509 | + | 2.54328i | 0.195830 | + | 0.113063i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.26453 | + | 7.38638i | 0.189208 | + | 0.327717i | ||||
\(509\) | −19.5166 | −0.865056 | −0.432528 | − | 0.901621i | \(-0.642378\pi\) | ||||
−0.432528 | + | 0.901621i | \(0.642378\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 20.9310i | − | 0.925027i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.1492 | − | 14.5199i | −1.10928 | − | 0.640446i | ||||
\(515\) | − | 61.9003i | − | 2.72765i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.547571 | − | 0.316140i | −0.0240821 | − | 0.0139038i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 39.1118 | − | 67.7436i | 1.71517 | − | 2.97075i | ||||
\(521\) | 9.93108 | − | 17.2011i | 0.435088 | − | 0.753595i | −0.562215 | − | 0.826991i | \(-0.690050\pi\) |
0.997303 | + | 0.0733964i | \(0.0233838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.71478 | + | 3.87678i | −0.293617 | + | 0.169520i | −0.639572 | − | 0.768731i | \(-0.720888\pi\) |
0.345955 | + | 0.938251i | \(0.387555\pi\) | |||||||
\(524\) | 17.2273 | + | 29.8385i | 0.752577 | + | 1.30350i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.99242 | − | 8.64713i | 0.217680 | − | 0.377033i | ||||
\(527\) | 4.99143i | 0.217430i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.6237 | −1.02712 | ||||||||
\(530\) | 48.8274 | + | 84.5715i | 2.12092 | + | 3.67355i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.713455 | − | 0.411913i | 0.0309032 | − | 0.0178419i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7053 | + | 6.18072i | −0.462831 | + | 0.267216i | ||||
\(536\) | 6.25670 | − | 3.61231i | 0.270248 | − | 0.156028i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 44.5076 | − | 25.6965i | 1.91886 | − | 1.10785i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.04616 | + | 15.6684i | 0.388925 | + | 0.673638i | 0.992305 | − | 0.123816i | \(-0.0395133\pi\) |
−0.603380 | + | 0.797454i | \(0.706180\pi\) | |||||||
\(542\) | 49.0391 | 2.10641 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.03916i | 0.130303i | ||||||||
\(545\) | −11.2721 | + | 19.5239i | −0.482845 | + | 0.836313i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.46839 | + | 6.00743i | 0.148298 | + | 0.256859i | 0.930598 | − | 0.366042i | \(-0.119287\pi\) |
−0.782301 | + | 0.622901i | \(0.785954\pi\) | |||||||
\(548\) | 32.1411 | − | 18.5567i | 1.37300 | − | 0.792703i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.53375 | + | 4.38858i | −0.108039 | + | 0.187130i | ||||
\(551\) | 2.50113 | − | 4.33208i | 0.106552 | − | 0.184553i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 57.3092 | + | 33.0875i | 2.43483 | + | 1.40575i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.1363i | 0.811560i | ||||||||
\(557\) | 13.6993 | + | 7.90931i | 0.580459 | + | 0.335128i | 0.761316 | − | 0.648381i | \(-0.224554\pi\) |
−0.180857 | + | 0.983509i | \(0.557887\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.9655i | − | 0.717563i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 45.8029 | 1.93208 | ||||||||
\(563\) | 16.0561 | + | 27.8101i | 0.676686 | + | 1.17205i | 0.975973 | + | 0.217891i | \(0.0699178\pi\) |
−0.299287 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.45568 | − | 3.72719i | −0.271593 | − | 0.156804i | ||||
\(566\) | −41.8376 | −1.75857 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.5333 | 1.78466 | ||||||||
\(569\) | 31.3107 | + | 18.0772i | 1.31261 | + | 0.757837i | 0.982528 | − | 0.186114i | \(-0.0595894\pi\) |
0.330084 | + | 0.943951i | \(0.392923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1792 | − | 24.5590i | −0.593380 | − | 1.02776i | −0.993773 | − | 0.111421i | \(-0.964460\pi\) |
0.400393 | − | 0.916343i | \(-0.368873\pi\) | |||||||
\(572\) | −6.70972 | −0.280548 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 46.4489i | − | 1.93705i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3589 | − | 20.9918i | −1.51364 | − | 0.873901i | −0.999872 | − | 0.0159713i | \(-0.994916\pi\) |
−0.513768 | − | 0.857929i | \(-0.671751\pi\) | |||||||
\(578\) | − | 38.1797i | − | 1.58807i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 42.8383 | + | 24.7327i | 1.77876 | + | 1.02697i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.88060 | − | 3.25729i | 0.0778864 | − | 0.134903i | ||||
\(584\) | −0.791873 | + | 1.37156i | −0.0327679 | + | 0.0567557i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 58.0035 | − | 33.4884i | 2.39610 | − | 1.38339i | ||||
\(587\) | −9.79227 | − | 16.9607i | −0.404170 | − | 0.700043i | 0.590054 | − | 0.807364i | \(-0.299106\pi\) |
−0.994225 | + | 0.107320i | \(0.965773\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.30108 | − | 5.71764i | 0.136019 | − | 0.235591i | ||||
\(590\) | − | 13.4412i | − | 0.553365i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.3024 | 0.423427 | ||||||||
\(593\) | 9.96374 | + | 17.2577i | 0.409162 | + | 0.708689i | 0.994796 | − | 0.101886i | \(-0.0324878\pi\) |
−0.585634 | + | 0.810575i | \(0.699154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −57.4072 | + | 33.1441i | −2.35149 | + | 1.35763i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 82.6083 | − | 47.6939i | 3.37810 | − | 1.95035i | ||||
\(599\) | 0.0267639 | − | 0.0154521i | 0.00109354 | − | 0.000631357i | −0.499453 | − | 0.866341i | \(-0.666466\pi\) |
0.500547 | + | 0.865710i | \(0.333132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8633 | − | 14.9322i | 1.05499 | − | 0.609097i | 0.130945 | − | 0.991390i | \(-0.458199\pi\) |
0.924041 | + | 0.382293i | \(0.124865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 41.9438 | + | 72.6488i | 1.70667 | + | 2.95604i | ||||
\(605\) | −37.4517 | −1.52263 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.3960i | − | 1.27433i | −0.770729 | − | 0.637163i | \(-0.780108\pi\) | ||
0.770729 | − | 0.637163i | \(-0.219892\pi\) | |||||||
\(608\) | 2.00994 | − | 3.48133i | 0.0815140 | − | 0.141186i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1151 | − | 20.9839i | −0.490524 | − | 0.849613i | ||||
\(611\) | −10.2685 | + | 5.92855i | −0.415421 | + | 0.239843i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.23146 | − | 3.86500i | 0.0901278 | − | 0.156106i | −0.817437 | − | 0.576018i | \(-0.804606\pi\) |
0.907565 | + | 0.419912i | \(0.137939\pi\) | |||||||
\(614\) | 10.1631 | − | 17.6029i | 0.410148 | − | 0.710396i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.9685 | − | 15.5703i | −1.08571 | − | 0.626835i | −0.153279 | − | 0.988183i | \(-0.548983\pi\) |
−0.932431 | + | 0.361348i | \(0.882317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.31050i | 0.0526736i | 0.999653 | + | 0.0263368i | \(0.00838424\pi\) | ||||
−0.999653 | + | 0.0263368i | \(0.991616\pi\) | |||||||
\(620\) | 56.5395 | + | 32.6431i | 2.27068 | + | 1.31098i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 45.9322i | 1.84171i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.7380 | −0.509521 | ||||||||
\(626\) | −31.4402 | − | 54.4560i | −1.25660 | − | 2.17650i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.5256 | + | 11.8505i | 0.819060 | + | 0.472884i | ||||
\(629\) | −5.12565 | −0.204373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8892 | −1.15006 | −0.575030 | − | 0.818132i | \(-0.695010\pi\) | ||||
−0.575030 | + | 0.818132i | \(0.695010\pi\) | |||||||
\(632\) | 35.0544 | + | 20.2387i | 1.39439 | + | 0.805051i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.2805 | + | 17.8064i | 0.408293 | + | 0.707183i | ||||
\(635\) | −8.07225 | −0.320337 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.95488i | − | 0.116985i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 61.4822 | + | 35.4968i | 2.43030 | + | 1.40313i | ||||
\(641\) | − | 2.78658i | − | 0.110063i | −0.998485 | − | 0.0550316i | \(-0.982474\pi\) | ||
0.998485 | − | 0.0550316i | \(-0.0175260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.324584 | − | 0.187399i | −0.0128004 | − | 0.00739029i | 0.493586 | − | 0.869697i | \(-0.335686\pi\) |
−0.506387 | + | 0.862307i | \(0.669019\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.42644 | − | 2.47066i | 0.0561224 | − | 0.0972069i | ||||
\(647\) | 25.1608 | − | 43.5798i | 0.989172 | − | 1.71330i | 0.367490 | − | 0.930027i | \(-0.380217\pi\) |
0.621682 | − | 0.783270i | \(-0.286450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.448333 | + | 0.258845i | −0.0175986 | + | 0.0101606i | ||||
\(650\) | 47.5151 | + | 82.2986i | 1.86370 | + | 3.22802i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 44.5109 | − | 77.0951i | 1.74318 | − | 3.01928i | ||||
\(653\) | − | 28.9270i | − | 1.13200i | −0.824405 | − | 0.566000i | \(-0.808490\pi\) | ||
0.824405 | − | 0.566000i | \(-0.191510\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.6092 | −1.27415 | ||||||||
\(656\) | −0.134073 | − | 0.232222i | −0.00523469 | − | 0.00906674i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.8449 | − | 13.1895i | 0.889910 | − | 0.513790i | 0.0159971 | − | 0.999872i | \(-0.494908\pi\) |
0.873913 | + | 0.486082i | \(0.161574\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0533 | + | 5.80428i | −0.391028 | + | 0.225760i | −0.682606 | − | 0.730787i | \(-0.739153\pi\) |
0.291577 | + | 0.956547i | \(0.405820\pi\) | |||||||
\(662\) | 39.7373 | − | 22.9423i | 1.54443 | − | 0.891678i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.7999 | − | 15.4729i | 1.04004 | − | 0.600466i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5423 | + | 23.4559i | 0.524360 | + | 0.908218i | ||||
\(668\) | −50.8092 | −1.96587 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.2280i | 0.588308i | ||||||||
\(671\) | −0.466614 | + | 0.808199i | −0.0180134 | + | 0.0312002i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7692 | − | 23.8490i | −0.530764 | − | 0.919310i | −0.999356 | − | 0.0358949i | \(-0.988572\pi\) |
0.468592 | − | 0.883415i | \(-0.344761\pi\) | |||||||
\(674\) | 51.1459 | − | 29.5291i | 1.97007 | − | 1.13742i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −39.3191 | + | 68.1026i | −1.51227 | + | 2.61933i | ||||
\(677\) | −2.31563 | + | 4.01080i | −0.0889970 | + | 0.154147i | −0.907087 | − | 0.420942i | \(-0.861700\pi\) |
0.818090 | + | 0.575090i | \(0.195033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.9702 | + | 6.33365i | 0.420688 | + | 0.242884i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 3.89996i | − | 0.149337i | ||||||
\(683\) | 12.0197 | + | 6.93959i | 0.459922 | + | 0.265536i | 0.712012 | − | 0.702168i | \(-0.247784\pi\) |
−0.252089 | + | 0.967704i | \(0.581118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.1257i | 1.34208i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.52208 | −0.210527 | ||||||||
\(689\) | −35.2667 | − | 61.0837i | −1.34355 | − | 2.32710i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.6168 | + | 11.3258i | 0.746258 | + | 0.430852i | 0.824340 | − | 0.566095i | \(-0.191546\pi\) |
−0.0780825 | + | 0.996947i | \(0.524880\pi\) | |||||||
\(692\) | 39.5640 | 1.50400 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.7464 | −0.521805 | ||||||||
\(695\) | −15.6849 | − | 9.05569i | −0.594963 | − | 0.343502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0667040 | + | 0.115535i | 0.00252660 | + | 0.00437619i | ||||
\(698\) | 36.5573 | 1.38371 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16.3485i | − | 0.617474i | −0.951147 | − | 0.308737i | \(-0.900094\pi\) | ||
0.951147 | − | 0.308737i | \(-0.0999063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.87138 | + | 3.38984i | 0.221443 | + | 0.127850i | ||||
\(704\) | − | 3.57790i | − | 0.134847i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.4639 | − | 21.0525i | −1.37234 | − | 0.792320i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.65356 | + | 13.2564i | −0.287435 | + | 0.497853i | −0.973197 | − | 0.229974i | \(-0.926136\pi\) |
0.685761 | + | 0.727826i | \(0.259469\pi\) | |||||||
\(710\) | −44.8257 | + | 77.6404i | −1.68228 | + | 2.91379i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.09569 | + | 4.09670i | −0.265922 | + | 0.153530i | ||||
\(713\) | 17.8736 | + | 30.9580i | 0.669372 | + | 1.15939i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.17518 | − | 5.49957i | 0.118745 | − | 0.205672i | ||||
\(716\) | 5.80585i | 0.216975i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 54.3825 | 2.02954 | ||||||||
\(719\) | −7.46359 | − | 12.9273i | −0.278345 | − | 0.482108i | 0.692629 | − | 0.721294i | \(-0.256453\pi\) |
−0.970974 | + | 0.239187i | \(0.923119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 35.7743 | − | 20.6543i | 1.33138 | − | 0.768673i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −55.0404 | + | 31.7776i | −2.04556 | + | 1.18101i | ||||
\(725\) | −23.3680 | + | 13.4915i | −0.867866 | + | 0.501063i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.62968 | + | 2.67295i | −0.171705 | + | 0.0991341i | −0.583390 | − | 0.812192i | \(-0.698274\pi\) |
0.411684 | + | 0.911326i | \(0.364941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.66910 | − | 2.89097i | −0.0617763 | − | 0.107000i | ||||
\(731\) | 2.74734 | 0.101614 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.9486i | − | 0.699881i | −0.936772 | − | 0.349941i | \(-0.886202\pi\) | ||
0.936772 | − | 0.349941i | \(-0.113798\pi\) | |||||||
\(734\) | 5.93514 | − | 10.2800i | 0.219070 | − | 0.379440i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.8828 | + | 18.8496i | 0.401145 | + | 0.694804i | ||||
\(737\) | 0.507932 | − | 0.293255i | 0.0187099 | − | 0.0108022i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.8430 | + | 39.5653i | −0.840295 | + | 1.45543i | 0.0493510 | + | 0.998781i | \(0.484285\pi\) |
−0.889646 | + | 0.456651i | \(0.849049\pi\) | |||||||
\(740\) | −33.5209 | + | 58.0598i | −1.23225 | + | 2.13432i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.0448 | + | 14.4596i | 0.918804 | + | 0.530472i | 0.883253 | − | 0.468896i | \(-0.155348\pi\) |
0.0355508 | + | 0.999368i | \(0.488681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 62.7378i | − | 2.29854i | ||||||
\(746\) | −19.5737 | − | 11.3009i | −0.716644 | − | 0.413755i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.08655i | − | 0.0397283i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.2014 | 1.61293 | 0.806465 | − | 0.591281i | \(-0.201378\pi\) | ||||
0.806465 | + | 0.591281i | \(0.201378\pi\) | |||||||
\(752\) | 1.92968 | + | 3.34230i | 0.0703682 | + | 0.121881i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −47.9887 | − | 27.7063i | −1.74765 | − | 1.00900i | ||||
\(755\) | −79.3947 | −2.88947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.5029 | −0.999611 | −0.499805 | − | 0.866138i | \(-0.666595\pi\) | ||||
−0.499805 | + | 0.866138i | \(0.666595\pi\) | |||||||
\(758\) | 28.4329 | + | 16.4157i | 1.03273 | + | 0.596246i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.37751 | − | 14.5103i | −0.303884 | − | 0.526343i | ||||
\(761\) | 5.09302 | 0.184622 | 0.0923109 | − | 0.995730i | \(-0.470575\pi\) | ||||
0.0923109 | + | 0.995730i | \(0.470575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 58.3061i | − | 2.10944i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.6286 | − | 25.1890i | −1.57637 | − | 0.910115i | ||||
\(767\) | 9.70820i | 0.350543i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.4505 | + | 19.3126i | 1.20626 | + | 0.696432i | 0.961939 | − | 0.273264i | \(-0.0881031\pi\) |
0.244316 | + | 0.969696i | \(0.421436\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.7537 | + | 34.2145i | −0.710953 | + | 1.23141i | ||||
\(773\) | −17.1754 | + | 29.7486i | −0.617754 | + | 1.06998i | 0.372140 | + | 0.928177i | \(0.378624\pi\) |
−0.989895 | + | 0.141806i | \(0.954709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.8420 | + | 17.8066i | −1.10788 | + | 0.639632i | ||||
\(776\) | −23.4565 | − | 40.6279i | −0.842040 | − | 1.45846i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.36206 | − | 9.28736i | 0.192239 | − | 0.332968i | ||||
\(779\) | − | 0.176459i | − | 0.00632229i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.45295 | 0.123556 | ||||||||
\(782\) | 7.72341 | + | 13.3773i | 0.276189 | + | 0.478373i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.4263 | + | 11.2158i | −0.693353 | + | 0.400308i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.3343 | − | 11.7400i | 0.724839 | − | 0.418486i | −0.0916921 | − | 0.995787i | \(-0.529228\pi\) |
0.816531 | + | 0.577301i | \(0.195894\pi\) | |||||||
\(788\) | 20.4577 | − | 11.8113i | 0.728776 | − | 0.420759i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −73.8874 | + | 42.6589i | −2.62880 | + | 1.51774i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.75037 | + | 15.1561i | 0.310735 | + | 0.538209i | ||||
\(794\) | 37.2147 | 1.32070 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 64.6392i | 2.29107i | ||||||||
\(797\) | 5.82399 | − | 10.0875i | 0.206296 | − | 0.357316i | −0.744249 | − | 0.667903i | \(-0.767192\pi\) |
0.950545 | + | 0.310587i | \(0.100526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.960052 | − | 1.66286i | −0.0339642 | − | 0.0588277i | ||||
\(800\) | −18.7789 | + | 10.8420i | −0.663934 | + | 0.383323i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.7989 | − | 22.1683i | 0.451945 | − | 0.782791i | ||||
\(803\) | −0.0642859 | + | 0.111347i | −0.00226860 | + | 0.00392933i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −63.3373 | − | 36.5678i | −2.23096 | − | 1.28805i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48.4219i | 1.70348i | ||||||||
\(809\) | −13.7723 | − | 7.95147i | −0.484210 | − | 0.279559i | 0.237959 | − | 0.971275i | \(-0.423521\pi\) |
−0.722169 | + | 0.691716i | \(0.756855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.56109i | − | 0.125047i | −0.998044 | − | 0.0625233i | \(-0.980085\pi\) | ||
0.998044 | − | 0.0625233i | \(-0.0199148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00483 | 0.140369 | ||||||||
\(815\) | 42.1269 | + | 72.9660i | 1.47564 | + | 2.55589i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.14705 | − | 1.81695i | −0.110101 | − | 0.0635671i | ||||
\(818\) | −46.5384 | −1.62718 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.74493 | 0.0609357 | ||||||||
\(821\) | −0.113440 | − | 0.0654949i | −0.00395910 | − | 0.00228579i | 0.498019 | − | 0.867166i | \(-0.334061\pi\) |
−0.501978 | + | 0.864880i | \(0.667394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0144 | − | 39.8621i | −0.802231 | − | 1.38950i | −0.918145 | − | 0.396245i | \(-0.870313\pi\) |
0.115914 | − | 0.993259i | \(-0.463020\pi\) | |||||||
\(824\) | 69.6811 | 2.42746 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.5836i | 1.41123i | 0.708595 | + | 0.705615i | \(0.249329\pi\) | ||||
−0.708595 | + | 0.705615i | \(0.750671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0930 | + | 15.0648i | 0.906248 | + | 0.523223i | 0.879222 | − | 0.476412i | \(-0.158063\pi\) |
0.0270260 | + | 0.999635i | \(0.491396\pi\) | |||||||
\(830\) | 65.2275i | 2.26408i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −58.1068 | − | 33.5480i | −2.01449 | − | 1.16307i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0439 | − | 41.6453i | 0.832075 | − | 1.44120i | ||||
\(836\) | −0.718591 | + | 1.24464i | −0.0248530 | + | 0.0430466i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36.3228 | + | 20.9710i | −1.25475 | + | 0.724430i | ||||
\(839\) | −5.81551 | − | 10.0728i | −0.200774 | − | 0.347750i | 0.748004 | − | 0.663694i | \(-0.231012\pi\) |
−0.948778 | + | 0.315944i | \(0.897679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.63302 | + | 11.4887i | −0.228725 | + | 0.396163i | ||||
\(842\) | 80.4390i | 2.77211i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.05018 | −0.0705702 | ||||||||
\(845\) | −37.2132 | − | 64.4552i | −1.28017 | − | 2.21732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.8821 | + | 11.4789i | −0.682754 | + | 0.394188i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.3272 | + | 7.69446i | −0.457119 | + | 0.263918i | ||||
\(851\) | −31.7905 | + | 18.3542i | −1.08976 | + | 0.629175i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6854 | − | 11.9427i | 0.708254 | − | 0.408911i | −0.102160 | − | 0.994768i | \(-0.532575\pi\) |
0.810414 | + | 0.585857i | \(0.199242\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.95763 | − | 12.0510i | −0.237807 | − | 0.411894i | ||||
\(857\) | −34.6724 | −1.18439 | −0.592193 | − | 0.805796i | \(-0.701738\pi\) | ||||
−0.592193 | + | 0.805796i | \(0.701738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.4763i | 1.03984i | 0.854216 | + | 0.519918i | \(0.174038\pi\) | ||||
−0.854216 | + | 0.519918i | \(0.825962\pi\) | |||||||
\(860\) | 17.9671 | − | 31.1200i | 0.612674 | − | 1.06118i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.7562 | + | 29.0225i | 0.570717 | + | 0.988512i | ||||
\(863\) | 28.9298 | − | 16.7026i | 0.984781 | − | 0.568564i | 0.0810708 | − | 0.996708i | \(-0.474166\pi\) |
0.903710 | + | 0.428145i | \(0.140833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7225 | + | 32.4283i | −0.636584 | + | 1.10260i | ||||
\(866\) | −10.7970 | + | 18.7010i | −0.366898 | + | 0.635485i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.84579 | + | 1.64302i | 0.0965369 | + | 0.0557356i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.9988i | − | 0.372679i | ||||||
\(872\) | −21.9780 | − | 12.6890i | −0.744271 | − | 0.429705i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20.4315i | − | 0.691106i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.5200 | −1.87478 | −0.937389 | − | 0.348285i | \(-0.886764\pi\) | ||||
−0.937389 | + | 0.348285i | \(0.886764\pi\) | |||||||
\(878\) | −13.9073 | − | 24.0881i | −0.469347 | − | 0.812933i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.79005 | − | 1.03349i | −0.0603426 | − | 0.0348388i | ||||
\(881\) | 19.9850 | 0.673313 | 0.336656 | − | 0.941628i | \(-0.390704\pi\) | ||||
0.336656 | + | 0.941628i | \(0.390704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5837 | 1.19749 | 0.598743 | − | 0.800941i | \(-0.295667\pi\) | ||||
0.598743 | + | 0.800941i | \(0.295667\pi\) | |||||||
\(884\) | −17.6462 | − | 10.1880i | −0.593504 | − | 0.342660i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.46321 | + | 14.6587i | 0.284327 | + | 0.492469i | ||||
\(887\) | 35.6633 | 1.19746 | 0.598729 | − | 0.800952i | \(-0.295673\pi\) | ||||
0.598729 | + | 0.800952i | \(0.295673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 17.2700i | − | 0.578892i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.6330 | − | 15.9539i | −0.925221 | − | 0.534177i | ||||
\(893\) | 2.53972i | 0.0849884i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.75872 | − | 2.74745i | −0.159066 | − | 0.0918370i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.76607 | − | 6.52302i | 0.125675 | − | 0.217676i | ||||
\(899\) | 10.3831 | − | 17.9841i | 0.346297 | − | 0.599804i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.89171 | − | 5.71098i | 0.329541 | − | 0.190260i | ||||
\(902\) | −0.0521180 | − | 0.0902710i | −0.00173534 | − | 0.00300569i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.19569 | − | 7.26715i | 0.139547 | − | 0.241702i | ||||
\(905\) | − | 60.1513i | − | 1.99950i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.2429 | 1.23663 | 0.618315 | − | 0.785930i | \(-0.287815\pi\) | ||||
0.618315 | + | 0.785930i | \(0.287815\pi\) | |||||||
\(908\) | −30.6846 | − | 53.1472i | −1.01830 | − | 1.76375i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8068 | − | 10.8581i | 0.623098 | − | 0.359746i | −0.154976 | − | 0.987918i | \(-0.549530\pi\) |
0.778074 | + | 0.628172i | \(0.216197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.17567 | − | 1.25613i | 0.0720043 | − | 0.0415717i | ||||
\(914\) | 49.6227 | − | 28.6497i | 1.64137 | − | 0.947647i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 61.4940 | − | 35.5036i | 2.03182 | − | 1.17307i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.1023 | − | 29.6220i | −0.564153 | − | 0.977141i | −0.997128 | − | 0.0757353i | \(-0.975870\pi\) |
0.432975 | − | 0.901406i | \(-0.357464\pi\) | |||||||
\(920\) | 90.7197 | 2.99094 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.6148i | 1.07411i | ||||||||
\(923\) | 32.3764 | − | 56.0776i | 1.06568 | − | 1.84582i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.2854 | − | 31.6713i | −0.601221 | − | 1.04135i | ||||
\(926\) | −42.3945 | + | 24.4764i | −1.39317 | + | 0.804346i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.32203 | − | 10.9501i | 0.207531 | − | 0.359454i | ||||
\(929\) | −23.4757 | + | 40.6611i | −0.770213 | + | 1.33405i | 0.167233 | + | 0.985917i | \(0.446517\pi\) |
−0.937446 | + | 0.348131i | \(0.886816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 62.0442 | + | 35.8213i | 2.03233 | + | 1.17336i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.21089i | 0.0723425i | ||||||||
\(935\) | 0.890585 | + | 0.514179i | 0.0291252 | + | 0.0168155i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.8826i | 0.943555i | 0.881718 | + | 0.471777i | \(0.156387\pi\) | ||||
−0.881718 | + | 0.471777i | \(0.843613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −25.1143 | −0.819138 | ||||||||
\(941\) | −0.727044 | − | 1.25928i | −0.0237009 | − | 0.0410512i | 0.853932 | − | 0.520385i | \(-0.174212\pi\) |
−0.877633 | + | 0.479334i | \(0.840878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.827428 | + | 0.477716i | 0.0269448 | + | 0.0155566i | ||||
\(944\) | 3.15992 | 0.102847 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.14658 | −0.0697914 | ||||||||
\(947\) | −36.9596 | − | 21.3386i | −1.20102 | − | 0.693412i | −0.240241 | − | 0.970713i | \(-0.577227\pi\) |
−0.960783 | + | 0.277301i | \(0.910560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20555 | + | 2.08807i | 0.0391338 | + | 0.0677817i | ||||
\(950\) | 20.3549 | 0.660400 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.8171i | 0.350401i | 0.984533 | + | 0.175200i | \(0.0560574\pi\) | ||||
−0.984533 | + | 0.175200i | \(0.943943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.7902 | + | 27.5917i | 1.54645 | + | 0.892845i | ||||
\(956\) | 71.1545i | 2.30130i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −66.5902 | − | 38.4458i | −2.15143 | − | 1.24213i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.79596 | + | 3.11070i | −0.0579342 | + | 0.100345i | ||||
\(962\) | 37.5511 | − | 65.0404i | 1.21070 | − | 2.09699i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 50.1529 | − | 28.9558i | 1.61532 | − | 0.932603i | ||||
\(965\) | −18.6958 | − | 32.3820i | −0.601838 | − | 1.04241i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4942 | + | 38.9611i | −0.723365 | + | 1.25290i | 0.236279 | + | 0.971685i | \(0.424072\pi\) |
−0.959643 | + | 0.281219i | \(0.909261\pi\) | |||||||
\(968\) | − | 42.1593i | − | 1.35505i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 98.8829 | 3.17494 | ||||||||
\(971\) | 3.40171 | + | 5.89194i | 0.109166 | + | 0.189081i | 0.915433 | − | 0.402471i | \(-0.131849\pi\) |
−0.806267 | + | 0.591552i | \(0.798515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −70.6321 | + | 40.7795i | −2.26320 | + | 1.30666i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.93315 | − | 2.84815i | 0.157906 | − | 0.0911672i | ||||
\(977\) | −29.2645 | + | 16.8959i | −0.936254 | + | 0.540546i | −0.888784 | − | 0.458326i | \(-0.848449\pi\) |
−0.0474698 | + | 0.998873i | \(0.515116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.576044 | + | 0.332579i | −0.0184104 | + | 0.0106293i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.0146 | − | 17.3459i | −0.319580 | − | 0.553529i | ||||
\(983\) | 46.9826 | 1.49851 | 0.749256 | − | 0.662280i | \(-0.230411\pi\) | ||||
0.749256 | + | 0.662280i | \(0.230411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3573i | 0.712364i | ||||||||
\(986\) | 4.48668 | − | 7.77116i | 0.142885 | − | 0.247484i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.4757 | + | 23.3405i | 0.428718 | + | 0.742562i | ||||
\(989\) | 17.0397 | − | 9.83785i | 0.541829 | − | 0.312825i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.300449 | + | 0.520392i | −0.00954406 | + | 0.0165308i | −0.870758 | − | 0.491712i | \(-0.836371\pi\) |
0.861214 | + | 0.508243i | \(0.169705\pi\) | |||||||
\(992\) | 8.34405 | − | 14.4523i | 0.264924 | − | 0.458861i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52.9810 | − | 30.5886i | −1.67961 | − | 0.969723i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.4267i | 1.53369i | 0.641834 | + | 0.766844i | \(0.278174\pi\) | ||||
−0.641834 | + | 0.766844i | \(0.721826\pi\) | |||||||
\(998\) | 23.4418 | + | 13.5341i | 0.742036 | + | 0.428415i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1323.2.s.d.962.3 | 48 | ||
3.2 | odd | 2 | 441.2.s.d.374.21 | 48 | |||
7.2 | even | 3 | 1323.2.i.d.1097.24 | 48 | |||
7.3 | odd | 6 | 1323.2.o.e.881.22 | 48 | |||
7.4 | even | 3 | 1323.2.o.e.881.21 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.1097.4 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.s.d.962.4 | 48 | ||
9.2 | odd | 6 | 1323.2.i.d.521.4 | 48 | |||
9.7 | even | 3 | 441.2.i.d.227.21 | 48 | |||
21.2 | odd | 6 | 441.2.i.d.68.4 | 48 | |||
21.5 | even | 6 | 441.2.i.d.68.3 | 48 | |||
21.11 | odd | 6 | 441.2.o.e.293.3 | yes | 48 | ||
21.17 | even | 6 | 441.2.o.e.293.4 | yes | 48 | ||
21.20 | even | 2 | 441.2.s.d.374.22 | 48 | |||
63.2 | odd | 6 | inner | 1323.2.s.d.656.4 | 48 | ||
63.11 | odd | 6 | 1323.2.o.e.440.22 | 48 | |||
63.16 | even | 3 | 441.2.s.d.362.22 | 48 | |||
63.20 | even | 6 | 1323.2.i.d.521.24 | 48 | |||
63.25 | even | 3 | 441.2.o.e.146.4 | yes | 48 | ||
63.34 | odd | 6 | 441.2.i.d.227.22 | 48 | |||
63.38 | even | 6 | 1323.2.o.e.440.21 | 48 | |||
63.47 | even | 6 | inner | 1323.2.s.d.656.3 | 48 | ||
63.52 | odd | 6 | 441.2.o.e.146.3 | ✓ | 48 | ||
63.61 | odd | 6 | 441.2.s.d.362.21 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.3 | 48 | 21.5 | even | 6 | |||
441.2.i.d.68.4 | 48 | 21.2 | odd | 6 | |||
441.2.i.d.227.21 | 48 | 9.7 | even | 3 | |||
441.2.i.d.227.22 | 48 | 63.34 | odd | 6 | |||
441.2.o.e.146.3 | ✓ | 48 | 63.52 | odd | 6 | ||
441.2.o.e.146.4 | yes | 48 | 63.25 | even | 3 | ||
441.2.o.e.293.3 | yes | 48 | 21.11 | odd | 6 | ||
441.2.o.e.293.4 | yes | 48 | 21.17 | even | 6 | ||
441.2.s.d.362.21 | 48 | 63.61 | odd | 6 | |||
441.2.s.d.362.22 | 48 | 63.16 | even | 3 | |||
441.2.s.d.374.21 | 48 | 3.2 | odd | 2 | |||
441.2.s.d.374.22 | 48 | 21.20 | even | 2 | |||
1323.2.i.d.521.4 | 48 | 9.2 | odd | 6 | |||
1323.2.i.d.521.24 | 48 | 63.20 | even | 6 | |||
1323.2.i.d.1097.4 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.1097.24 | 48 | 7.2 | even | 3 | |||
1323.2.o.e.440.21 | 48 | 63.38 | even | 6 | |||
1323.2.o.e.440.22 | 48 | 63.11 | odd | 6 | |||
1323.2.o.e.881.21 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.881.22 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.656.3 | 48 | 63.47 | even | 6 | inner | ||
1323.2.s.d.656.4 | 48 | 63.2 | odd | 6 | inner | ||
1323.2.s.d.962.3 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.s.d.962.4 | 48 | 7.6 | odd | 2 | inner |