Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.8 | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.l.961.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.04208 | + | 1.38350i | 0.601647 | + | 0.798762i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0619693 | −0.0277135 | −0.0138567 | − | 0.999904i | \(-0.504411\pi\) | ||||
−0.0138567 | + | 0.999904i | \(0.504411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63689 | + | 2.07860i | 0.618688 | + | 0.785637i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.828124 | + | 2.88344i | −0.276041 | + | 0.961146i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.18053 | 0.958967 | 0.479483 | − | 0.877551i | \(-0.340824\pi\) | ||||
0.479483 | + | 0.877551i | \(0.340824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.252417 | + | 0.437198i | −0.0700078 | + | 0.121257i | −0.898904 | − | 0.438145i | \(-0.855636\pi\) |
0.828897 | + | 0.559402i | \(0.188969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0645772 | − | 0.0857342i | −0.0166737 | − | 0.0221365i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.554700 | + | 0.960769i | −0.134535 | + | 0.233021i | −0.925420 | − | 0.378944i | \(-0.876287\pi\) |
0.790885 | + | 0.611965i | \(0.209621\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.933573 | − | 1.61700i | −0.214176 | − | 0.370964i | 0.738841 | − | 0.673880i | \(-0.235373\pi\) |
−0.953017 | + | 0.302915i | \(0.902040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.16996 | + | 4.43071i | −0.255305 | + | 0.966860i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.20496 | 1.29382 | 0.646912 | − | 0.762565i | \(-0.276060\pi\) | ||||
0.646912 | + | 0.762565i | \(0.276060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99616 | −0.999232 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.85220 | + | 1.85908i | −0.933806 | + | 0.357779i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39645 | + | 4.15077i | 0.445010 | + | 0.770779i | 0.998053 | − | 0.0623731i | \(-0.0198669\pi\) |
−0.553043 | + | 0.833153i | \(0.686534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.26858 | − | 2.19724i | −0.227843 | − | 0.394636i | 0.729325 | − | 0.684167i | \(-0.239834\pi\) |
−0.957169 | + | 0.289531i | \(0.906501\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.31438 | + | 4.40026i | 0.576960 | + | 0.765986i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.101437 | − | 0.128809i | −0.0171460 | − | 0.0217728i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26085 | − | 7.38001i | −0.700479 | − | 1.21327i | −0.968298 | − | 0.249797i | \(-0.919636\pi\) |
0.267819 | − | 0.963469i | \(-0.413697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.867902 | + | 0.106380i | −0.138976 | + | 0.0170344i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.94516 | + | 8.56527i | −0.772305 | + | 1.33767i | 0.163992 | + | 0.986462i | \(0.447563\pi\) |
−0.936297 | + | 0.351210i | \(0.885770\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.95574 | + | 6.85154i | 0.603244 | + | 1.04485i | 0.992326 | + | 0.123646i | \(0.0394589\pi\) |
−0.389082 | + | 0.921203i | \(0.627208\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0513182 | − | 0.178684i | 0.00765007 | − | 0.0266367i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.29168 | − | 5.70136i | 0.480141 | − | 0.831628i | −0.519600 | − | 0.854410i | \(-0.673919\pi\) |
0.999740 | + | 0.0227816i | \(0.00725224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.64116 | + | 6.80489i | −0.234451 | + | 0.972128i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.90726 | + | 0.233776i | −0.267070 | + | 0.0327352i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.58258 | + | 2.74112i | −0.217385 | + | 0.376521i | −0.954008 | − | 0.299782i | \(-0.903086\pi\) |
0.736623 | + | 0.676304i | \(0.236419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.197095 | −0.0265763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.26425 | − | 2.97664i | 0.167454 | − | 0.394266i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50652 | + | 7.80552i | 0.586699 | + | 1.01619i | 0.994661 | + | 0.103194i | \(0.0329062\pi\) |
−0.407962 | + | 0.912999i | \(0.633760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.94094 | − | 12.0221i | 0.888697 | − | 1.53927i | 0.0472794 | − | 0.998882i | \(-0.484945\pi\) |
0.841417 | − | 0.540386i | \(-0.181722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.34906 | + | 2.99854i | −0.925895 | + | 0.377781i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0156421 | − | 0.0270929i | 0.00194016 | − | 0.00336046i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.66642 | + | 2.88632i | 0.203585 | + | 0.352620i | 0.949681 | − | 0.313219i | \(-0.101407\pi\) |
−0.746096 | + | 0.665839i | \(0.768074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.46609 | + | 8.58454i | 0.778425 | + | 1.03346i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.25651 | −0.267798 | −0.133899 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133899 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.07503 | − | 3.59406i | 0.242864 | − | 0.420652i | −0.718665 | − | 0.695356i | \(-0.755247\pi\) |
0.961529 | + | 0.274704i | \(0.0885799\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.20642 | − | 6.91217i | −0.601185 | − | 0.798148i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.20619 | + | 6.61106i | 0.593301 | + | 0.753400i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.48925 | + | 2.57946i | −0.167554 | + | 0.290211i | −0.937559 | − | 0.347826i | \(-0.886920\pi\) |
0.770006 | + | 0.638037i | \(0.220253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.62842 | − | 4.77569i | −0.847602 | − | 0.530632i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.17289 | − | 3.76355i | −0.238506 | − | 0.413104i | 0.721780 | − | 0.692122i | \(-0.243324\pi\) |
−0.960286 | + | 0.279019i | \(0.909991\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0343744 | − | 0.0595381i | 0.00372842 | − | 0.00645782i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.24528 | + | 7.64093i | −0.347930 | + | 0.819194i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.30077 | − | 7.44915i | −0.455880 | − | 0.789608i | 0.542858 | − | 0.839824i | \(-0.317342\pi\) |
−0.998738 | + | 0.0502166i | \(0.984009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32194 | + | 0.190974i | −0.138577 | + | 0.0200195i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.71791 | − | 4.04478i | 0.178139 | − | 0.419424i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0578528 | + | 0.100204i | 0.00593558 | + | 0.0102807i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.27671 | − | 5.67542i | −0.332699 | − | 0.576252i | 0.650341 | − | 0.759642i | \(-0.274626\pi\) |
−0.983040 | + | 0.183391i | \(0.941293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.63388 | + | 9.17087i | −0.264714 | + | 0.921707i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.51654 | 0.648420 | 0.324210 | − | 0.945985i | \(-0.394902\pi\) | ||||
0.324210 | + | 0.945985i | \(0.394902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.0196 | −1.67699 | −0.838494 | − | 0.544911i | \(-0.816563\pi\) | ||||
−0.838494 | + | 0.544911i | \(0.816563\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0725013 | − | 0.274568i | 0.00707540 | − | 0.0267951i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.86075 | + | 15.3473i | 0.856601 | + | 1.48368i | 0.875152 | + | 0.483848i | \(0.160761\pi\) |
−0.0185508 | + | 0.999828i | \(0.505905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.62928 | − | 11.4822i | 0.634970 | − | 1.09980i | −0.351552 | − | 0.936168i | \(-0.614346\pi\) |
0.986522 | − | 0.163631i | \(-0.0523208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.77005 | − | 13.5855i | 0.547669 | − | 1.28947i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.10094 | − | 1.90689i | 0.103568 | − | 0.179385i | −0.809584 | − | 0.587004i | \(-0.800307\pi\) |
0.913152 | + | 0.407619i | \(0.133641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.384517 | −0.0358564 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.05160 | − | 1.08988i | −0.0972207 | − | 0.100760i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.90504 | + | 0.419676i | −0.266305 | + | 0.0384717i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.884207 | −0.0803825 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.0033 | + | 2.08412i | −1.53314 | + | 0.187918i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.619455 | 0.0554057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.61290 | 0.409329 | 0.204664 | − | 0.978832i | \(-0.434390\pi\) | ||||
0.204664 | + | 0.978832i | \(0.434390\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.35687 | + | 12.6126i | −0.471646 | + | 1.11048i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.152139 | 0.0132925 | 0.00664623 | − | 0.999978i | \(-0.497884\pi\) | ||||
0.00664623 | + | 0.999978i | \(0.497884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.83293 | − | 4.58738i | 0.158935 | − | 0.397776i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.300687 | − | 0.115206i | 0.0258790 | − | 0.00991532i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.55540 | −0.303759 | −0.151879 | − | 0.988399i | \(-0.548533\pi\) | ||||
−0.151879 | + | 0.988399i | \(0.548533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.60945 | − | 13.1800i | 0.645425 | − | 1.11791i | −0.338778 | − | 0.940866i | \(-0.610013\pi\) |
0.984203 | − | 0.177043i | \(-0.0566532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3180 | − | 1.38726i | 0.953148 | − | 0.116829i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.802820 | + | 1.39052i | −0.0671352 | + | 0.116281i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.148506 | − | 0.257220i | −0.0123328 | − | 0.0213610i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.1248 | + | 4.82073i | −0.917556 | + | 0.397607i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.366914 | 0.0300588 | 0.0150294 | − | 0.999887i | \(-0.495216\pi\) | ||||
0.0150294 | + | 0.999887i | \(0.495216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5832 | 1.02401 | 0.512005 | − | 0.858983i | \(-0.328903\pi\) | ||||
0.512005 | + | 0.858983i | \(0.328903\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.31096 | − | 2.39508i | −0.186830 | − | 0.193631i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0786128 | + | 0.136161i | 0.00631434 | + | 0.0109368i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.72734 | + | 4.72389i | 0.217666 | + | 0.377008i | 0.954094 | − | 0.299508i | \(-0.0968225\pi\) |
−0.736428 | + | 0.676516i | \(0.763489\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.44151 | + | 0.666973i | −0.431540 | + | 0.0528944i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.1569 | + | 12.8976i | 0.800473 | + | 1.01648i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.83559 | − | 6.64343i | −0.300426 | − | 0.520354i | 0.675806 | − | 0.737079i | \(-0.263796\pi\) |
−0.976233 | + | 0.216726i | \(0.930462\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.205390 | − | 0.272681i | −0.0159896 | − | 0.0212282i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.47493 | − | 16.4111i | 0.733192 | − | 1.26993i | −0.222320 | − | 0.974974i | \(-0.571363\pi\) |
0.955512 | − | 0.294952i | \(-0.0953037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.37257 | + | 11.0376i | 0.490198 | + | 0.849048i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.43562 | − | 1.35283i | 0.415672 | − | 0.103453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9959 | − | 20.7776i | 0.912034 | − | 1.57969i | 0.100846 | − | 0.994902i | \(-0.467845\pi\) |
0.811187 | − | 0.584787i | \(-0.198822\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.17818 | − | 10.3850i | −0.618212 | − | 0.785034i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.10274 | + | 14.3688i | −0.458710 | + | 1.08002i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.27901 | − | 7.41146i | 0.319828 | − | 0.553959i | −0.660624 | − | 0.750717i | \(-0.729708\pi\) |
0.980452 | + | 0.196758i | \(0.0630415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.632669 | 0.0470259 | 0.0235130 | − | 0.999724i | \(-0.492515\pi\) | ||||
0.0235130 | + | 0.999724i | \(0.492515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.8655 | − | 2.92523i | 1.76419 | − | 0.216239i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.264042 | + | 0.457334i | 0.0194127 | + | 0.0336238i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.76424 | + | 3.05576i | −0.129014 | + | 0.223459i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.8068 | − | 7.04267i | −0.858819 | − | 0.512279i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7915 | − | 20.4235i | 0.853205 | − | 1.47780i | −0.0250944 | − | 0.999685i | \(-0.507989\pi\) |
0.878300 | − | 0.478110i | \(-0.158678\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8030 | − | 22.1754i | −0.921577 | − | 1.59622i | −0.796976 | − | 0.604011i | \(-0.793568\pi\) |
−0.124600 | − | 0.992207i | \(-0.539765\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0537832 | − | 0.00659228i | 0.00385150 | − | 0.000472083i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.45810 | 0.673862 | 0.336931 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336931 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.15133 | + | 7.19032i | −0.294280 | + | 0.509708i | −0.974817 | − | 0.223005i | \(-0.928413\pi\) |
0.680537 | + | 0.732714i | \(0.261747\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.25666 | + | 5.31327i | −0.159173 | + | 0.374769i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.70507 | + | 11.7756i | −0.330231 | + | 0.826488i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.306448 | − | 0.530784i | 0.0214033 | − | 0.0370715i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.13848 | + | 17.8916i | −0.357149 | + | 1.24355i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.96926 | − | 5.14291i | −0.205388 | − | 0.355742i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1164 | − | 17.5222i | 0.696444 | − | 1.20628i | −0.273247 | − | 0.961944i | \(-0.588098\pi\) |
0.969691 | − | 0.244333i | \(-0.0785689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.35147 | − | 3.12187i | −0.161120 | − | 0.213907i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.245134 | − | 0.424585i | −0.0167180 | − | 0.0289564i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.49066 | − | 6.23352i | 0.169077 | − | 0.423159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.13472 | − | 0.874512i | 0.482120 | − | 0.0590940i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.280031 | − | 0.485028i | −0.0188369 | − | 0.0326265i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.41918 | + | 4.19014i | 0.162000 | + | 0.280593i | 0.935586 | − | 0.353099i | \(-0.114872\pi\) |
−0.773586 | + | 0.633692i | \(0.781539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.13744 | − | 14.4061i | 0.275829 | − | 0.960408i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.672213 | −0.0446163 | −0.0223082 | − | 0.999751i | \(-0.507101\pi\) | ||||
−0.0223082 | + | 0.999751i | \(0.507101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.13553 | −0.405447 | −0.202724 | − | 0.979236i | \(-0.564979\pi\) | ||||
−0.202724 | + | 0.979236i | \(0.564979\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.72108 | + | 14.0920i | −0.244829 | + | 0.927187i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1492 | + | 21.0431i | 0.795922 | + | 1.37858i | 0.922252 | + | 0.386589i | \(0.126347\pi\) |
−0.126330 | + | 0.991988i | \(0.540320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.203983 | + | 0.353309i | −0.0133064 | + | 0.0230473i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.12059 | + | 0.627637i | −0.332618 | + | 0.0407694i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5978 | + | 23.5521i | −0.879569 | + | 1.52346i | −0.0277545 | + | 0.999615i | \(0.508836\pi\) |
−0.851815 | + | 0.523843i | \(0.824498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.8054 | −1.66227 | −0.831135 | − | 0.556070i | \(-0.812309\pi\) | ||||
−0.831135 | + | 0.556070i | \(0.812309\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.34231 | − | 15.5306i | −0.0861092 | − | 0.996286i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.101701 | − | 0.421694i | 0.00649747 | − | 0.0269411i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.942598 | 0.0599760 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.94253 | − | 6.92812i | 0.186475 | − | 0.439052i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0741 | 1.70890 | 0.854450 | − | 0.519533i | \(-0.173894\pi\) | ||||
0.854450 | + | 0.519533i | \(0.173894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7351 | 1.24073 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.118192 | − | 0.0144869i | 0.00740146 | − | 0.000907206i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5215 | −0.843445 | −0.421723 | − | 0.906725i | \(-0.638574\pi\) | ||||
−0.421723 | + | 0.906725i | \(0.638574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.36553 | − | 20.9369i | 0.519809 | − | 1.30096i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.9531 | + | 3.47266i | −0.863672 | + | 0.214952i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3745 | 0.824710 | 0.412355 | − | 0.911023i | \(-0.364706\pi\) | ||||
0.412355 | + | 0.911023i | \(0.364706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0980716 | − | 0.169865i | 0.00602449 | − | 0.0104347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.82411 | − | 13.7127i | 0.356430 | − | 0.839205i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.91594 | − | 6.78261i | 0.238759 | − | 0.413543i | −0.721599 | − | 0.692311i | \(-0.756593\pi\) |
0.960359 | + | 0.278768i | \(0.0899260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.1737 | − | 26.2816i | −0.921735 | − | 1.59649i | −0.796730 | − | 0.604335i | \(-0.793439\pi\) |
−0.125005 | − | 0.992156i | \(-0.539895\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.64178 | − | 1.62989i | −0.0993653 | − | 0.0986453i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.8905 | −0.958230 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.6924 | −1.36346 | −0.681728 | − | 0.731606i | \(-0.738771\pi\) | ||||
−0.681728 | + | 0.731606i | \(0.738771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.38615 | − | 1.83828i | 0.442197 | − | 0.110055i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0826 | − | 17.4635i | −0.601475 | − | 1.04179i | −0.992598 | − | 0.121447i | \(-0.961246\pi\) |
0.391122 | − | 0.920339i | \(-0.372087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.45297 | − | 14.6410i | −0.502477 | − | 0.870316i | −0.999996 | − | 0.00286255i | \(-0.999089\pi\) |
0.497519 | − | 0.867453i | \(-0.334245\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0783444 | + | 0.184460i | −0.00464072 | + | 0.0109265i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.8985 | + | 3.74142i | −1.52874 | + | 0.220849i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.88462 | + | 13.6566i | 0.463801 | + | 0.803327i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.43732 | − | 10.4476i | 0.260120 | − | 0.612448i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.40597 | − | 4.16727i | 0.140558 | − | 0.243454i | −0.787149 | − | 0.616763i | \(-0.788444\pi\) |
0.927707 | + | 0.373309i | \(0.121777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.279266 | − | 0.483703i | −0.0162595 | − | 0.0281623i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.4326 | + | 5.91286i | −0.895489 | + | 0.343099i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.56624 | + | 2.71280i | −0.0905777 | + | 0.156885i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.76649 | + | 19.4376i | −0.447653 | + | 1.12037i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.79078 | + | 9.01561i | 0.390120 | + | 0.517933i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.430125 | + | 0.744999i | −0.0246289 | + | 0.0426585i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.9188 | −0.908534 | −0.454267 | − | 0.890866i | \(-0.650099\pi\) | ||||
−0.454267 | + | 0.890866i | \(0.650099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.7358 | − | 23.5465i | −1.00896 | − | 1.33951i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.131435 | − | 0.227651i | −0.00745297 | − | 0.0129089i | 0.862275 | − | 0.506441i | \(-0.169039\pi\) |
−0.869728 | + | 0.493532i | \(0.835706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.12534 | − | 5.41325i | 0.176655 | − | 0.305975i | −0.764078 | − | 0.645124i | \(-0.776806\pi\) |
0.940733 | + | 0.339149i | \(0.110139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.455416 | − | 0.185817i | 0.0256598 | − | 0.0104696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.83961 | − | 17.0427i | 0.552648 | − | 0.957214i | −0.445435 | − | 0.895314i | \(-0.646951\pi\) |
0.998082 | − | 0.0618994i | \(-0.0197158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.62199 | + | 13.2017i | 0.426750 | + | 0.739152i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9992 | + | 28.2519i | −0.669733 | + | 1.57687i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.07141 | 0.115256 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.26111 | − | 2.18431i | 0.0699540 | − | 0.121164i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.7939 | − | 2.79388i | 1.26051 | − | 0.154502i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2390 | − | 2.49043i | 0.950415 | − | 0.137302i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2669 | − | 21.2469i | 0.674249 | − | 1.16783i | −0.302439 | − | 0.953169i | \(-0.597801\pi\) |
0.976688 | − | 0.214665i | \(-0.0688659\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.8083 | − | 6.17433i | 1.35949 | − | 0.338351i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.103267 | − | 0.178863i | −0.00564206 | − | 0.00977233i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.89471 | + | 11.9420i | −0.375579 | + | 0.650521i | −0.990413 | − | 0.138135i | \(-0.955889\pi\) |
0.614835 | + | 0.788656i | \(0.289223\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.78545 | − | 0.463988i | 0.205598 | − | 0.0252004i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.03475 | − | 6.98840i | −0.218494 | − | 0.378443i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8311 | + | 7.72757i | −0.908792 | + | 0.417250i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.400699 | − | 0.531978i | −0.0215729 | − | 0.0286407i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.84786 | − | 17.0570i | −0.528661 | − | 0.915667i | −0.999441 | − | 0.0334170i | \(-0.989361\pi\) |
0.470781 | − | 0.882250i | \(-0.343972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.34712 | + | 9.26149i | 0.286225 | + | 0.495756i | 0.972905 | − | 0.231203i | \(-0.0742662\pi\) |
−0.686681 | + | 0.726959i | \(0.740933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.411990 | − | 2.59064i | 0.0219904 | − | 0.138278i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.6615 | −0.620677 | −0.310338 | − | 0.950626i | \(-0.600442\pi\) | ||||
−0.310338 | + | 0.950626i | \(0.600442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.139834 | 0.00742162 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.60792 | − | 3.58177i | −0.190951 | − | 0.189568i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.82159 | + | 15.2794i | 0.465586 | + | 0.806418i | 0.999228 | − | 0.0392925i | \(-0.0125104\pi\) |
−0.533642 | + | 0.845710i | \(0.679177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.75688 | − | 13.4353i | 0.408257 | − | 0.707122i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.921418 | − | 1.22330i | −0.0483619 | − | 0.0642064i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.128588 | + | 0.222721i | −0.00673061 | + | 0.0116578i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.38292 | −0.176587 | −0.0882934 | − | 0.996095i | \(-0.528141\pi\) | ||||
−0.0882934 | + | 0.996095i | \(0.528141\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.6022 | − | 21.3522i | −1.07251 | − | 1.11155i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.28821 | + | 1.19736i | −0.430302 | + | 0.0621636i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3902 | 0.693320 | 0.346660 | − | 0.937991i | \(-0.387316\pi\) | ||||
0.346660 | + | 0.937991i | \(0.387316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.645524 | + | 0.857013i | 0.0333347 | + | 0.0442560i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.41962 | −0.124617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.6131 | 1.41839 | 0.709194 | − | 0.705013i | \(-0.249059\pi\) | ||||
0.709194 | + | 0.705013i | \(0.249059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.80703 | + | 6.38193i | 0.246271 | + | 0.326956i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.0040 | −1.27764 | −0.638822 | − | 0.769354i | \(-0.720578\pi\) | ||||
−0.638822 | + | 0.769354i | \(0.720578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.322624 | − | 0.409682i | −0.0164424 | − | 0.0208793i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.0318 | + | 5.73220i | −1.17077 | + | 0.291384i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.136646 | −0.00692821 | −0.00346411 | − | 0.999994i | \(-0.501103\pi\) | ||||
−0.00346411 | + | 0.999994i | \(0.501103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.44189 | + | 5.96153i | −0.174064 | + | 0.301488i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.158542 | + | 0.210484i | 0.00799737 | + | 0.0106175i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0922877 | − | 0.159847i | 0.00464350 | − | 0.00804277i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.91030 | + | 13.7010i | 0.397006 | + | 0.687635i | 0.993355 | − | 0.115090i | \(-0.0367157\pi\) |
−0.596349 | + | 0.802726i | \(0.703382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.25668 | − | 2.24458i | 0.413351 | − | 0.112369i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0549 | −0.552055 | −0.276028 | − | 0.961150i | \(-0.589018\pi\) | ||||
−0.276028 | + | 0.961150i | \(0.589018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.28084 | 0.0638032 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.472728 | + | 0.295946i | 0.0234900 | + | 0.0147057i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.5518 | − | 23.4724i | −0.671737 | − | 1.16348i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0064 | + | 31.1880i | 0.890358 | + | 1.54215i | 0.839446 | + | 0.543443i | \(0.182880\pi\) |
0.0509122 | + | 0.998703i | \(0.483787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.70503 | − | 4.91889i | −0.182756 | − | 0.242631i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.84787 | + | 22.1441i | −0.435375 | + | 1.08964i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.134652 | + | 0.233225i | 0.00660982 | + | 0.0114485i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.1641 | − | 3.20697i | 1.28126 | − | 0.157046i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.4877 | + | 28.5576i | −0.805477 | + | 1.39513i | 0.110491 | + | 0.993877i | \(0.464758\pi\) |
−0.915968 | + | 0.401251i | \(0.868576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9800 | + | 25.9461i | 0.730080 | + | 1.26454i | 0.956849 | + | 0.290587i | \(0.0938505\pi\) |
−0.226769 | + | 0.973949i | \(0.572816\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.7136 | + | 14.2128i | 0.666777 | + | 0.691049i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.77137 | − | 4.80016i | 0.134431 | − | 0.232842i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.3507 | − | 5.25139i | 1.75913 | − | 0.254133i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.76039 | + | 0.338345i | −0.133273 | + | 0.0163354i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4021 | − | 21.4811i | 0.597389 | − | 1.03471i | −0.395816 | − | 0.918330i | \(-0.629538\pi\) |
0.993205 | − | 0.116379i | \(-0.0371286\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00906 | −0.240720 | −0.120360 | − | 0.992730i | \(-0.538405\pi\) | ||||
−0.120360 | + | 0.992730i | \(0.538405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.201108 | − | 0.473503i | 0.00964237 | − | 0.0227027i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.79278 | − | 10.0334i | −0.277106 | − | 0.479962i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.2918 | + | 35.1464i | −0.968475 | + | 1.67745i | −0.268502 | + | 0.963279i | \(0.586529\pi\) |
−0.699973 | + | 0.714169i | \(0.746805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.2624 | − | 10.3675i | −0.869638 | − | 0.493689i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1332 | + | 24.4795i | −0.671490 | + | 1.16305i | 0.305992 | + | 0.952034i | \(0.401012\pi\) |
−0.977482 | + | 0.211021i | \(0.932321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.266515 | + | 0.461618i | 0.0126340 | + | 0.0218828i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.382355 | + | 0.507624i | 0.0180848 | + | 0.0240098i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.6443 | 1.72935 | 0.864676 | − | 0.502329i | \(-0.167523\pi\) | ||||
0.864676 | + | 0.502329i | \(0.167523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.7283 | + | 27.2421i | −0.740615 | + | 1.28278i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.1128 | + | 17.4089i | 0.616092 | + | 0.817939i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0819197 | − | 0.0118345i | 0.00384045 | − | 0.000554811i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.19154 | − | 5.52791i | 0.149294 | − | 0.258585i | −0.781673 | − | 0.623689i | \(-0.785633\pi\) |
0.930967 | + | 0.365104i | \(0.118967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.905373 | − | 5.69307i | 0.0422592 | − | 0.265730i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.24366 | + | 12.5464i | 0.337371 | + | 0.584343i | 0.983937 | − | 0.178514i | \(-0.0571291\pi\) |
−0.646567 | + | 0.762858i | \(0.723796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2527 | + | 22.9544i | −0.615907 | + | 1.06678i | 0.374317 | + | 0.927301i | \(0.377877\pi\) |
−0.990225 | + | 0.139482i | \(0.955456\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.106458 | + | 0.250652i | −0.00493686 | + | 0.0116237i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6879 | + | 20.2440i | 0.540851 | + | 0.936782i | 0.998855 | + | 0.0478318i | \(0.0152311\pi\) |
−0.458004 | + | 0.888950i | \(0.651436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.27176 | + | 8.18841i | −0.151076 | + | 0.378106i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.69337 | + | 8.69596i | −0.170182 | + | 0.400689i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.5814 | + | 21.7915i | 0.578491 | + | 1.00198i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.66428 | + | 8.07877i | 0.214012 | + | 0.370679i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.59326 | − | 6.83327i | −0.301885 | − | 0.312874i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.29606 | −0.424748 | −0.212374 | − | 0.977188i | \(-0.568119\pi\) | ||||
−0.212374 | + | 0.977188i | \(0.568119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.30204 | 0.196156 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.25953 | + | 27.4924i | −0.330320 | + | 1.25095i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.203055 | + | 0.351702i | 0.00922026 | + | 0.0159700i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.04947 | + | 3.54979i | −0.0928704 | + | 0.160856i | −0.908718 | − | 0.417411i | \(-0.862938\pi\) |
0.815847 | + | 0.578267i | \(0.196271\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.19416 | − | 12.2295i | 0.234888 | − | 0.553038i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.98703 | + | 8.63778i | −0.225061 | + | 0.389818i | −0.956338 | − | 0.292264i | \(-0.905592\pi\) |
0.731277 | + | 0.682081i | \(0.238925\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.31725 | −0.239477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.163219 | − | 0.568312i | 0.00733616 | − | 0.0255437i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.69366 | − | 4.69037i | −0.165683 | − | 0.210392i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2083 | 0.501752 | 0.250876 | − | 0.968019i | \(-0.419281\pi\) | ||||
0.250876 | + | 0.968019i | \(0.419281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.5783 | − | 3.99317i | 1.45549 | − | 0.178402i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.69350 | 0.0755094 | 0.0377547 | − | 0.999287i | \(-0.487979\pi\) | ||||
0.0377547 | + | 0.999287i | \(0.487979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.403825 | −0.0179700 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.62975 | + | 20.3185i | −0.383261 | + | 0.902378i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.9555 | −1.81532 | −0.907659 | − | 0.419707i | \(-0.862133\pi\) | ||||
−0.907659 | + | 0.419707i | \(0.862133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8672 | − | 1.56993i | 0.480737 | − | 0.0694496i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.53600 | + | 6.11040i | 0.332723 | + | 0.269781i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.05469 | 0.0464752 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4693 | − | 18.1334i | 0.460439 | − | 0.797504i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.2464 | − | 5.05563i | 1.81052 | − | 0.221918i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.5075 | − | 26.8598i | 0.679396 | − | 1.17675i | −0.295767 | − | 0.955260i | \(-0.595575\pi\) |
0.975163 | − | 0.221488i | \(-0.0710914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.67840 | + | 6.37117i | 0.160845 | + | 0.278592i | 0.935172 | − | 0.354194i | \(-0.115245\pi\) |
−0.774327 | + | 0.632786i | \(0.781911\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.84529 | − | 22.1365i | 0.255109 | − | 0.966118i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.81472 | 0.122611 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.5015 | 0.673980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.2387 | + | 6.53033i | −1.13866 | + | 0.283392i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.49648 | − | 4.32404i | −0.108135 | − | 0.187295i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.549094 | − | 0.951059i | −0.0237394 | − | 0.0411179i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7128 | − | 1.80337i | 0.634905 | − | 0.0778211i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.21976 | + | 21.6432i | −0.224831 | + | 0.932238i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4735 | − | 25.0688i | −0.622262 | − | 1.07779i | −0.989063 | − | 0.147491i | \(-0.952880\pi\) |
0.366801 | − | 0.930299i | \(-0.380453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.659294 | + | 0.875295i | 0.0282930 | + | 0.0375625i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.410812 | + | 0.711546i | −0.0175972 | + | 0.0304793i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.34891 | − | 16.1928i | −0.399731 | − | 0.692354i | 0.593962 | − | 0.804493i | \(-0.297563\pi\) |
−0.993692 | + | 0.112140i | \(0.964230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 28.9169 | + | 29.9695i | 1.23414 | + | 1.27907i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.47452 | − | 7.75010i | 0.190621 | − | 0.330165i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.79940 | + | 1.12674i | −0.331664 | + | 0.0479138i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.357566 | + | 0.841881i | −0.0151778 | + | 0.0357358i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.1787 | + | 29.7544i | −0.727886 | + | 1.26074i | 0.229889 | + | 0.973217i | \(0.426164\pi\) |
−0.957775 | + | 0.287519i | \(0.907170\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.99397 | −0.168927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.06612 | + | 0.743532i | −0.256112 | + | 0.0313919i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.37355 | − | 12.7714i | −0.310758 | − | 0.538249i | 0.667769 | − | 0.744369i | \(-0.267250\pi\) |
−0.978527 | + | 0.206120i | \(0.933916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0682247 | + | 0.118169i | −0.00287024 | + | 0.00497139i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.56017 | − | 23.6737i | −0.107517 | − | 0.994203i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.66821 | + | 2.88942i | −0.0699349 | + | 0.121131i | −0.898872 | − | 0.438210i | \(-0.855613\pi\) |
0.828938 | + | 0.559341i | \(0.188946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.40360 | + | 16.2875i | 0.393528 | + | 0.681611i | 0.992912 | − | 0.118851i | \(-0.0379210\pi\) |
−0.599384 | + | 0.800462i | \(0.704588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.5437 | − | 4.96949i | 1.69374 | − | 0.207603i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.0010 | −1.29283 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.6961 | + | 30.6505i | −0.736697 | + | 1.27600i | 0.217277 | + | 0.976110i | \(0.430282\pi\) |
−0.953975 | + | 0.299887i | \(0.903051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.3378 | − | 40.8214i | 0.720534 | − | 1.69648i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.26614 | − | 10.6771i | 0.176989 | − | 0.442961i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.03346 | + | 8.71821i | −0.208465 | + | 0.361072i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0651670 | + | 0.0675392i | 0.00269432 | + | 0.00279240i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2921 | + | 29.9508i | 0.713722 | + | 1.23620i | 0.963450 | + | 0.267887i | \(0.0863256\pi\) |
−0.249728 | + | 0.968316i | \(0.580341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.36862 | + | 4.10257i | −0.0975973 | + | 0.169043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.85613 | + | 13.0852i | 0.405427 | + | 0.538255i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.9787 | − | 27.6759i | −0.656166 | − | 1.13651i | −0.981600 | − | 0.190949i | \(-0.938844\pi\) |
0.325434 | − | 0.945565i | \(-0.394490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.180023 | − | 0.0260070i | 0.00738023 | − | 0.00106618i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.2738 | + | 1.74956i | −0.584188 | + | 0.0716047i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.92476 | − | 8.52993i | −0.201220 | − | 0.348524i | 0.747702 | − | 0.664035i | \(-0.231157\pi\) |
−0.948922 | + | 0.315511i | \(0.897824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.77340 | − | 6.53572i | −0.153920 | − | 0.266598i | 0.778745 | − | 0.627340i | \(-0.215857\pi\) |
−0.932665 | + | 0.360743i | \(0.882523\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.70252 | + | 2.41478i | −0.395117 | + | 0.0983374i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0547937 | 0.00222768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8584 | −0.440730 | −0.220365 | − | 0.975417i | \(-0.570725\pi\) | ||||
−0.220365 | + | 0.975417i | \(0.570725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.1946 | + | 5.76176i | −0.858850 | + | 0.233478i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.66175 | + | 2.87823i | 0.0672272 | + | 0.116441i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.8823 | + | 41.3653i | −0.964596 | + | 1.67073i | −0.253899 | + | 0.967231i | \(0.581713\pi\) |
−0.710697 | + | 0.703499i | \(0.751620\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.05368 | − | 0.129151i | 0.0424886 | − | 0.00520788i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.7769 | + | 32.5225i | −0.755929 | + | 1.30931i | 0.188982 | + | 0.981980i | \(0.439481\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.9657 | −1.44558 | −0.722792 | − | 0.691065i | \(-0.757142\pi\) | ||||
−0.722792 | + | 0.691065i | \(0.757142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.1077 | + | 11.5355i | −1.20818 | + | 0.462904i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.44390 | − | 21.1330i | 0.338298 | − | 0.846677i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9424 | 0.997696 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.02098 | − | 9.46730i | 0.160582 | − | 0.378088i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.45398 | 0.376955 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.8848 | 1.26931 | 0.634656 | − | 0.772794i | \(-0.281142\pi\) | ||||
0.634656 | + | 0.772794i | \(0.281142\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.7840 | − | 4.26353i | 1.38254 | − | 0.169460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.285858 | −0.0113439 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.56083 | − | 2.43518i | −0.101464 | − | 0.0964854i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.86867 | − | 6.50649i | 0.0739233 | − | 0.257393i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6788 | 0.658772 | 0.329386 | − | 0.944195i | \(-0.393158\pi\) | ||||
0.329386 | + | 0.944195i | \(0.393158\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.5295 | + | 40.7544i | −0.927915 | + | 1.60720i | −0.141109 | + | 0.989994i | \(0.545067\pi\) |
−0.786805 | + | 0.617201i | \(0.788266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.331961 | − | 0.781595i | 0.0130710 | − | 0.0307753i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2324 | − | 21.1872i | 0.480906 | − | 0.832954i | −0.518854 | − | 0.854863i | \(-0.673641\pi\) |
0.999760 | + | 0.0219091i | \(0.00697444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.3331 | + | 24.8257i | 0.562625 | + | 0.974495i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.2195 | − | 3.05003i | 0.439728 | − | 0.119540i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8261 | −0.462792 | −0.231396 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231396 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.00942795 | −0.000368380 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.64486 | + | 8.95954i | 0.337268 | + | 0.349545i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.51539 | − | 6.08883i | −0.136940 | − | 0.237187i | 0.789397 | − | 0.613883i | \(-0.210393\pi\) |
−0.926337 | + | 0.376696i | \(0.877060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.43024 | − | 12.8696i | −0.289003 | − | 0.500568i | 0.684569 | − | 0.728948i | \(-0.259990\pi\) |
−0.973572 | + | 0.228380i | \(0.926657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.379219 | − | 0.892862i | 0.0147276 | − | 0.0346759i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.113585 | + | 0.284276i | −0.00440465 | + | 0.0110238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8699 | + | 25.7554i | 0.575764 | + | 0.997253i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.27606 | + | 7.71341i | −0.126660 | + | 0.298218i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.0759 | − | 38.2366i | 0.852231 | − | 1.47611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.81679 | + | 13.5391i | 0.301315 | + | 0.521893i | 0.976434 | − | 0.215816i | \(-0.0692411\pi\) |
−0.675119 | + | 0.737709i | \(0.735908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.2424 | − | 9.28824i | 0.933089 | − | 0.357505i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.3561 | + | 21.4014i | −0.474883 | + | 0.822522i | −0.999586 | − | 0.0287634i | \(-0.990843\pi\) |
0.524703 | + | 0.851285i | \(0.324176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.43332 | − | 16.1010i | 0.246888 | − | 0.617901i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.700502 | − | 0.930004i | −0.0268433 | − | 0.0356378i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7467 | − | 29.0061i | 0.640794 | − | 1.10989i | −0.344462 | − | 0.938800i | \(-0.611939\pi\) |
0.985256 | − | 0.171087i | \(-0.0547279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.220326 | 0.00841821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.39373 | − | 8.48848i | −0.243936 | − | 0.323856i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.798941 | − | 1.38381i | −0.0304372 | − | 0.0527189i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.33836 | + | 2.31811i | −0.0509137 | + | 0.0881851i | −0.890359 | − | 0.455259i | \(-0.849547\pi\) |
0.839445 | + | 0.543444i | \(0.182880\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.3739 | + | 9.53696i | −0.887903 | + | 0.362279i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.471552 | + | 0.816752i | −0.0178870 | + | 0.0309812i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.48617 | − | 9.50232i | −0.207803 | − | 0.359926i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.4525 | + | 38.7370i | −0.622291 | + | 1.46517i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.3715 | −1.37373 | −0.686866 | − | 0.726784i | \(-0.741014\pi\) | ||||
−0.686866 | + | 0.726784i | \(0.741014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.95563 | + | 13.7796i | −0.300052 | + | 0.519706i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.701369 | + | 0.0859677i | −0.0264151 | + | 0.00323773i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.6669 | + | 13.5453i | 0.401169 | + | 0.509423i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.95369 | − | 10.3121i | 0.223596 | − | 0.387279i | −0.732302 | − | 0.680980i | \(-0.761554\pi\) |
0.955897 | + | 0.293702i | \(0.0948872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.20442 | − | 6.43027i | −0.232684 | − | 0.241154i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.87148 | − | 13.6338i | −0.294789 | − | 0.510590i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0497501 | − | 0.0861698i | 0.00186055 | − | 0.00322257i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.7543 | + | 5.73073i | −1.74607 | + | 0.214018i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.44050 | − | 14.6194i | −0.314778 | − | 0.545211i | 0.664613 | − | 0.747188i | \(-0.268597\pi\) |
−0.979390 | + | 0.201977i | \(0.935263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.8592 | − | 35.3769i | −1.03753 | − | 1.31750i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.8914 | − | 35.7016i | −1.00010 | − | 1.32776i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.9731 | − | 20.7379i | −0.444668 | − | 0.770187i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.24570 | − | 2.15762i | −0.0462006 | − | 0.0800218i | 0.842000 | − | 0.539477i | \(-0.181378\pi\) |
−0.888201 | + | 0.459455i | \(0.848045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0877 | − | 18.0412i | 0.743988 | − | 0.668193i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.77699 | −0.324629 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5131 | −0.462181 | −0.231090 | − | 0.972932i | \(-0.574229\pi\) | ||||
−0.231090 | + | 0.972932i | \(0.574229\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.689394 | − | 0.298737i | 0.0254287 | − | 0.0110191i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.30009 | + | 9.18003i | 0.195231 | + | 0.338151i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.0051 | − | 17.3294i | 0.368044 | − | 0.637472i | −0.621215 | − | 0.783640i | \(-0.713361\pi\) |
0.989260 | + | 0.146168i | \(0.0466941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.982265 | + | 1.30408i | 0.0360844 | + | 0.0479066i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.49879 | + | 9.52419i | −0.201731 | + | 0.349408i | −0.949086 | − | 0.315016i | \(-0.897990\pi\) |
0.747355 | + | 0.664425i | \(0.231323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0227374 | −0.000833034 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.6514 | − | 3.14870i | 0.462890 | − | 0.115205i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.3967 | + | 43.5398i | −0.635663 | + | 1.59091i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.8670 | −1.05337 | −0.526686 | − | 0.850060i | \(-0.676566\pi\) | ||||
−0.526686 | + | 0.850060i | \(0.676566\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.2135 | + | 37.4569i | 1.02816 | + | 1.36500i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.779774 | −0.0283789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3626 | −0.631053 | −0.315527 | − | 0.948917i | \(-0.602181\pi\) | ||||
−0.315527 | + | 0.948917i | \(0.602181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.5656 | + | 27.3034i | 0.746484 | + | 0.991051i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.0039 | −1.88514 | −0.942571 | − | 0.334006i | \(-0.891599\pi\) | ||||
−0.942571 | + | 0.334006i | \(0.891599\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.7184 | − | 5.01559i | 1.25689 | − | 0.181577i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.143208 | + | 0.148421i | 0.00517771 | + | 0.00536618i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.55008 | −0.164294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5839 | − | 23.5280i | 0.489849 | − | 0.848443i | −0.510083 | − | 0.860125i | \(-0.670385\pi\) |
0.999932 | + | 0.0116822i | \(0.00371865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0905 | − | 18.7069i | −0.507457 | − | 0.673712i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2452 | − | 21.2093i | 0.440428 | − | 0.762845i | −0.557293 | − | 0.830316i | \(-0.688160\pi\) |
0.997721 | + | 0.0674716i | \(0.0214932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.33802 | + | 10.9778i | 0.227668 | + | 0.394333i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37.6837 | − | 10.2443i | 1.35189 | − | 0.367513i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.4667 | 0.661638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.17689 | −0.256809 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.3447 | − | 15.6852i | −0.691322 | − | 0.560543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.169011 | − | 0.292736i | −0.00603227 | − | 0.0104482i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.939312 | + | 1.62694i | 0.0334828 | + | 0.0579940i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848798 | + | 0.528717i | \(0.822673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.9374 | + | 18.5036i | 0.496184 | + | 0.658747i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.76579 | − | 0.832955i | 0.205008 | − | 0.0296165i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.50402 | + | 6.06914i | 0.124431 | + | 0.215521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.337206 | − | 0.0413318i | 0.0119595 | − | 0.00146589i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.6067 | − | 30.4957i | 0.623662 | − | 1.08021i | −0.365137 | − | 0.930954i | \(-0.618978\pi\) |
0.988798 | − | 0.149259i | \(-0.0476890\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.65179 | + | 6.32509i | 0.129191 | + | 0.223765i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.0407 | − | 6.23218i | 0.884770 | − | 0.220203i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.59970 | − | 11.4310i | 0.232898 | − | 0.403392i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.629413 | − | 0.799257i | −0.0221839 | − | 0.0281701i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.4645 | − | 1.65036i | 0.473971 | − | 0.0580953i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.53614 | − | 2.66067i | 0.0540077 | − | 0.0935441i | −0.837758 | − | 0.546042i | \(-0.816134\pi\) |
0.891765 | + | 0.452498i | \(0.149467\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8034 | 0.519818 | 0.259909 | − | 0.965633i | \(-0.416307\pi\) | ||||
0.259909 | + | 0.965633i | \(0.416307\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.5482 | − | 48.3803i | 0.720657 | − | 1.69677i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.237688 | + | 0.411689i | 0.00832586 | + | 0.0144208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.38594 | − | 12.7928i | 0.258401 | − | 0.447564i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.544069 | − | 3.96988i | 0.0190113 | − | 0.138719i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5061 | + | 21.6612i | −0.436467 | + | 0.755982i | −0.997414 | − | 0.0718690i | \(-0.977104\pi\) |
0.560947 | + | 0.827851i | \(0.310437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.7480 | + | 34.2046i | 0.688374 | + | 1.19230i | 0.972364 | + | 0.233471i | \(0.0750084\pi\) |
−0.283990 | + | 0.958827i | \(0.591658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.5592 | − | 21.9844i | −0.576517 | − | 0.765398i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4528 | −0.433026 | −0.216513 | − | 0.976280i | \(-0.569468\pi\) | ||||
−0.216513 | + | 0.976280i | \(0.569468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.2995 | + | 24.7675i | −0.496643 | + | 0.860211i | −0.999993 | − | 0.00387209i | \(-0.998767\pi\) |
0.503350 | + | 0.864083i | \(0.332101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.6474 | − | 31.3949i | −0.820320 | − | 1.08908i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.62758 | − | 5.35145i | −0.194984 | − | 0.185417i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.587154 | + | 1.01698i | −0.0203193 | + | 0.0351941i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.2402 | + | 8.30307i | 0.353954 | + | 0.286996i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0794 | − | 36.5107i | −0.727743 | − | 1.26049i | −0.957835 | − | 0.287319i | \(-0.907236\pi\) |
0.230092 | − | 0.973169i | \(-0.426097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.01405 | − | 5.22048i | 0.103933 | − | 0.180017i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.6538 | − | 32.1476i | 0.470263 | − | 1.10722i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.394904 | − | 0.683993i | −0.0135851 | − | 0.0235301i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.44735 | − | 1.83791i | −0.0497316 | − | 0.0631514i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.4470 | − | 26.9518i | 0.392861 | − | 0.924983i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.4384 | − | 45.7927i | −0.906297 | − | 1.56975i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.6206 | − | 44.3761i | −0.877232 | − | 1.51941i | −0.854366 | − | 0.519671i | \(-0.826054\pi\) |
−0.0228654 | − | 0.999739i | \(-0.507279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.336841 | + | 0.0838337i | −0.0115197 | + | 0.00286705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.8058 | −1.29142 | −0.645710 | − | 0.763582i | \(-0.723439\pi\) | ||||
−0.645710 | + | 0.763582i | \(0.723439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.6224 | 1.52250 | 0.761249 | − | 0.648460i | \(-0.224587\pi\) | ||||
0.761249 | + | 0.648460i | \(0.224587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.1646 | − | 31.9316i | −1.09617 | − | 1.08823i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.4848 | + | 26.8205i | 0.527109 | + | 0.912980i | 0.999501 | + | 0.0315912i | \(0.0100575\pi\) |
−0.472392 | + | 0.881389i | \(0.656609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.743379 | + | 1.28757i | −0.0252756 | + | 0.0437787i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.6774 | + | 25.1396i | −0.362622 | + | 0.853786i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.73661 | + | 8.20405i | −0.160678 | + | 0.278303i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.68253 | −0.0570102 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.0782 | − | 4.74823i | 0.645701 | − | 0.160703i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.01398 | + | 1.28760i | 0.0342788 | + | 0.0435288i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1686 | 0.782347 | 0.391174 | − | 0.920317i | \(-0.372069\pi\) | ||||
0.391174 | + | 0.920317i | \(0.372069\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.27263 | − | 1.01399i | 0.279029 | − | 0.0342009i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0143 | 0.472155 | 0.236077 | − | 0.971734i | \(-0.424138\pi\) | ||||
0.236077 | + | 0.971734i | \(0.424138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.9269 | 1.34365 | 0.671824 | − | 0.740711i | \(-0.265511\pi\) | ||||
0.671824 | + | 0.740711i | \(0.265511\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.378182 | − | 0.890422i | 0.0127125 | − | 0.0299312i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8441 | 0.901338 | 0.450669 | − | 0.892691i | \(-0.351186\pi\) | ||||
0.450669 | + | 0.892691i | \(0.351186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.55082 | + | 9.58837i | 0.253246 | + | 0.321584i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.2625 | − | 15.1892i | −0.812823 | − | 0.508858i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.2921 | −0.411339 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.265167 | + | 0.459283i | −0.00886356 | + | 0.0153521i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.38530 | + | 0.660083i | −0.179810 | + | 0.0220395i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.08017 | − | 10.5312i | 0.202785 | − | 0.351234i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.75572 | − | 3.04100i | −0.0584915 | − | 0.101310i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.9852 | + | 9.51073i | −1.16424 | + | 0.316497i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0392060 | −0.00130325 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.7617 | −1.25386 | −0.626928 | − | 0.779077i | \(-0.715688\pi\) | ||||
−0.626928 | + | 0.779077i | \(0.715688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.39650 | + | 18.7900i | −0.178991 | + | 0.623226i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.93650 | − | 13.7464i | −0.262948 | − | 0.455439i | 0.704076 | − | 0.710125i | \(-0.251361\pi\) |
−0.967024 | + | 0.254685i | \(0.918028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.91094 | − | 11.9701i | −0.228719 | − | 0.396153i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.47893 | + | 0.181274i | −0.0488919 | + | 0.00599274i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.249035 | + | 0.316236i | 0.00822388 | + | 0.0104430i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.22203 | − | 9.04482i | −0.172259 | − | 0.298361i | 0.766950 | − | 0.641706i | \(-0.221773\pi\) |
−0.939209 | + | 0.343345i | \(0.888440\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.5887 | − | 22.0236i | −0.546617 | − | 0.725702i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.569580 | − | 0.986541i | 0.0187479 | − | 0.0324724i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.2879 | + | 36.8717i | 0.699941 | + | 1.21233i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.0943 | − | 49.0749i | 0.462918 | − | 1.61183i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.58169 | − | 16.5960i | 0.314365 | − | 0.544496i | −0.664937 | − | 0.746899i | \(-0.731542\pi\) |
0.979302 | + | 0.202403i | \(0.0648751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5356 | − | 3.69912i | 0.410839 | − | 0.121234i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.177989 | − | 0.419071i | 0.00582710 | − | 0.0137198i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.109329 | − | 0.189363i | 0.00357543 | − | 0.00619283i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.09451 | 0.101093 | 0.0505467 | − | 0.998722i | \(-0.483904\pi\) | ||||
0.0505467 | + | 0.998722i | \(0.483904\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.7461 | − | 1.31716i | 0.350685 | − | 0.0429839i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.65564 | − | 13.2600i | −0.249567 | − | 0.432262i | 0.713839 | − | 0.700310i | \(-0.246955\pi\) |
−0.963406 | + | 0.268048i | \(0.913622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.6845 | + | 53.1472i | −0.999226 | + | 1.73071i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.731659 | + | 0.436429i | 0.0238009 | + | 0.0141970i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.507747 | − | 0.879443i | 0.0164995 | − | 0.0285781i | −0.857658 | − | 0.514221i | \(-0.828081\pi\) |
0.874157 | + | 0.485643i | \(0.161414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.04754 | + | 1.81440i | 0.0340047 | + | 0.0588979i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.8322 | − | 4.14686i | 1.09708 | − | 0.134471i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.4930 | −1.14973 | −0.574865 | − | 0.818248i | \(-0.694945\pi\) | ||||
−0.574865 | + | 0.818248i | \(0.694945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.730713 | + | 1.26563i | −0.0236453 | + | 0.0409549i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.3217 | + | 24.3022i | −0.333654 | + | 0.785580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.81982 | − | 7.39026i | −0.187932 | − | 0.238644i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2814 | − | 21.2720i | 0.396175 | − | 0.686195i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.5907 | + | 12.8400i | −1.66249 | + | 0.413763i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.793390 | + | 1.37419i | 0.0255401 | + | 0.0442368i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.87762 | + | 11.9124i | −0.221169 | + | 0.383077i | −0.955163 | − | 0.296079i | \(-0.904321\pi\) |
0.733994 | + | 0.679156i | \(0.237654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.15859 | + | 2.86579i | 0.0693437 | + | 0.0920625i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6567 | + | 37.5104i | 0.694995 | + | 1.20377i | 0.970182 | + | 0.242376i | \(0.0779269\pi\) |
−0.275187 | + | 0.961391i | \(0.588740\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.8517 | − | 5.75718i | 1.27759 | − | 0.184567i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.33618 | − | 0.531491i | 0.138869 | − | 0.0170213i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.78420 | + | 8.28648i | 0.153060 | + | 0.265108i | 0.932351 | − | 0.361554i | \(-0.117754\pi\) |
−0.779291 | + | 0.626662i | \(0.784421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.6787 | − | 23.6923i | −0.437174 | − | 0.757208i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.6185 | + | 28.6238i | 0.881790 | + | 0.913889i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1329 | −0.546454 | −0.273227 | − | 0.961950i | \(-0.588091\pi\) | ||||
−0.273227 | + | 0.961950i | \(0.588091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.586111 | −0.0186751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.4099 | + | 21.2548i | 0.681486 | + | 0.676548i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.5452 | + | 42.5135i | 0.780492 | + | 1.35185i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.32891 | + | 10.9620i | −0.201044 | + | 0.348219i | −0.948865 | − | 0.315682i | \(-0.897767\pi\) |
0.747821 | + | 0.663901i | \(0.231100\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.1781 | − | 5.16982i | 1.33848 | − | 0.164059i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.257255 | − | 0.445579i | 0.00815553 | − | 0.0141258i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.6704 | −0.812989 | −0.406495 | − | 0.913653i | \(-0.633249\pi\) | ||||
−0.406495 | + | 0.913653i | \(0.633249\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.3945 | + | 27.8880i | 1.08819 | + | 0.882338i |
(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 | 1008.2.t.l.193.8 | 22 | ||
3.2 | odd | 2 | 3024.2.t.k.1873.6 | 22 | |||
4.3 | odd | 2 | 504.2.t.c.193.4 | yes | 22 | ||
7.2 | even | 3 | 1008.2.q.l.625.1 | 22 | |||
9.2 | odd | 6 | 3024.2.q.l.2881.6 | 22 | |||
9.7 | even | 3 | 1008.2.q.l.529.1 | 22 | |||
12.11 | even | 2 | 1512.2.t.c.361.6 | 22 | |||
21.2 | odd | 6 | 3024.2.q.l.2305.6 | 22 | |||
28.23 | odd | 6 | 504.2.q.c.121.11 | yes | 22 | ||
36.7 | odd | 6 | 504.2.q.c.25.11 | ✓ | 22 | ||
36.11 | even | 6 | 1512.2.q.d.1369.6 | 22 | |||
63.2 | odd | 6 | 3024.2.t.k.289.6 | 22 | |||
63.16 | even | 3 | inner | 1008.2.t.l.961.8 | 22 | ||
84.23 | even | 6 | 1512.2.q.d.793.6 | 22 | |||
252.79 | odd | 6 | 504.2.t.c.457.4 | yes | 22 | ||
252.191 | even | 6 | 1512.2.t.c.289.6 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.11 | ✓ | 22 | 36.7 | odd | 6 | ||
504.2.q.c.121.11 | yes | 22 | 28.23 | odd | 6 | ||
504.2.t.c.193.4 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.c.457.4 | yes | 22 | 252.79 | odd | 6 | ||
1008.2.q.l.529.1 | 22 | 9.7 | even | 3 | |||
1008.2.q.l.625.1 | 22 | 7.2 | even | 3 | |||
1008.2.t.l.193.8 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.l.961.8 | 22 | 63.16 | even | 3 | inner | ||
1512.2.q.d.793.6 | 22 | 84.23 | even | 6 | |||
1512.2.q.d.1369.6 | 22 | 36.11 | even | 6 | |||
1512.2.t.c.289.6 | 22 | 252.191 | even | 6 | |||
1512.2.t.c.361.6 | 22 | 12.11 | even | 2 | |||
3024.2.q.l.2305.6 | 22 | 21.2 | odd | 6 | |||
3024.2.q.l.2881.6 | 22 | 9.2 | odd | 6 | |||
3024.2.t.k.289.6 | 22 | 63.2 | odd | 6 | |||
3024.2.t.k.1873.6 | 22 | 3.2 | odd | 2 |