Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.c.1349.3 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.189469 | + | 2.63896i | 0.0716124 | + | 0.997433i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.32697 | + | 0.766125i | 0.400096 | + | 0.230995i | 0.686525 | − | 0.727106i | \(-0.259135\pi\) |
−0.286430 | + | 0.958101i | \(0.592468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.48236 | −0.411133 | −0.205567 | − | 0.978643i | \(-0.565904\pi\) | ||||
−0.205567 | + | 0.978643i | \(0.565904\pi\) | |||||||
\(14\) | 2.19067 | − | 1.48356i | 0.585481 | − | 0.396499i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.10342 | − | 1.21441i | −0.510155 | − | 0.294538i | 0.222742 | − | 0.974877i | \(-0.428499\pi\) |
−0.732898 | + | 0.680339i | \(0.761833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.21209 | + | 2.43185i | −0.966320 | + | 0.557905i | −0.898112 | − | 0.439766i | \(-0.855061\pi\) |
−0.0682075 | + | 0.997671i | \(0.521728\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.53225i | − | 0.326677i | ||||||
\(23\) | 0.133975 | + | 0.232051i | 0.0279356 | + | 0.0483859i | 0.879655 | − | 0.475612i | \(-0.157773\pi\) |
−0.851720 | + | 0.523998i | \(0.824440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.741181 | + | 1.28376i | 0.145358 | + | 0.251767i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.38014 | − | 1.15539i | −0.449804 | − | 0.218349i | ||||
\(29\) | 0.898979i | 0.166936i | 0.996510 | + | 0.0834681i | \(0.0265997\pi\) | ||||
−0.996510 | + | 0.0834681i | \(0.973400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.717439 | − | 0.414214i | −0.128856 | − | 0.0743950i | 0.434187 | − | 0.900823i | \(-0.357036\pi\) |
−0.563042 | + | 0.826428i | \(0.690369\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.42883i | 0.416540i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.74786 | + | 2.74118i | −0.780544 | + | 0.450647i | −0.836623 | − | 0.547779i | \(-0.815473\pi\) |
0.0560790 | + | 0.998426i | \(0.482140\pi\) | |||||||
\(38\) | 4.21209 | + | 2.43185i | 0.683291 | + | 0.394498i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.76028 | 1.36813 | 0.684063 | − | 0.729423i | \(-0.260211\pi\) | ||||
0.684063 | + | 0.729423i | \(0.260211\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.86370i | − | 0.284212i | −0.989851 | − | 0.142106i | \(-0.954613\pi\) | ||
0.989851 | − | 0.142106i | \(-0.0453874\pi\) | |||||||
\(44\) | −1.32697 | + | 0.766125i | −0.200048 | + | 0.115498i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.133975 | − | 0.232051i | 0.0197535 | − | 0.0342140i | ||||
\(47\) | −6.46008 | + | 3.72973i | −0.942299 | + | 0.544037i | −0.890680 | − | 0.454630i | \(-0.849771\pi\) |
−0.0516191 | + | 0.998667i | \(0.516438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92820 | + | 1.00000i | −0.989743 | + | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.741181 | − | 1.28376i | 0.102783 | − | 0.178026i | ||||
\(53\) | −1.73508 | + | 3.00524i | −0.238331 | + | 0.412802i | −0.960236 | − | 0.279191i | \(-0.909934\pi\) |
0.721904 | + | 0.691993i | \(0.243267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.189469 | + | 2.63896i | 0.0253188 | + | 0.352646i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.778539 | − | 0.449490i | 0.102227 | − | 0.0590209i | ||||
\(59\) | 3.12837 | − | 5.41849i | 0.407279 | − | 0.705428i | −0.587305 | − | 0.809366i | \(-0.699811\pi\) |
0.994584 | + | 0.103938i | \(0.0331444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.73445 | − | 3.31079i | 0.734222 | − | 0.423903i | −0.0857429 | − | 0.996317i | \(-0.527326\pi\) |
0.819965 | + | 0.572414i | \(0.193993\pi\) | |||||||
\(62\) | 0.828427i | 0.105210i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.8859 | − | 8.01702i | −1.69643 | − | 0.979434i | −0.949097 | − | 0.314985i | \(-0.898000\pi\) |
−0.747334 | − | 0.664449i | \(-0.768666\pi\) | |||||||
\(68\) | 2.10342 | − | 1.21441i | 0.255078 | − | 0.147269i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.7627i | − | 1.51465i | −0.653037 | − | 0.757326i | \(-0.726505\pi\) | ||
0.653037 | − | 0.757326i | \(-0.273495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.171573 | − | 0.297173i | 0.0200811 | − | 0.0347815i | −0.855810 | − | 0.517290i | \(-0.826941\pi\) |
0.875891 | + | 0.482508i | \(0.160274\pi\) | |||||||
\(74\) | 4.74786 | + | 2.74118i | 0.551928 | + | 0.318656i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.86370i | − | 0.557905i | ||||||
\(77\) | −1.77035 | + | 3.64697i | −0.201750 | + | 0.415611i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.22438 | − | 9.04889i | −0.587789 | − | 1.01808i | −0.994521 | − | 0.104533i | \(-0.966665\pi\) |
0.406733 | − | 0.913547i | \(-0.366668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.38014 | − | 7.58662i | −0.483705 | − | 0.837802i | ||||
\(83\) | − | 5.45001i | − | 0.598216i | −0.954219 | − | 0.299108i | \(-0.903311\pi\) | ||
0.954219 | − | 0.299108i | \(-0.0966891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.61401 | + | 0.931852i | −0.174044 | + | 0.100484i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.32697 | + | 0.766125i | 0.141455 | + | 0.0816692i | ||||
\(89\) | 7.98502 | + | 13.8305i | 0.846411 | + | 1.46603i | 0.884390 | + | 0.466748i | \(0.154574\pi\) |
−0.0379795 | + | 0.999279i | \(0.512092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.280861 | − | 3.91189i | −0.0294423 | − | 0.410078i | ||||
\(92\) | −0.267949 | −0.0279356 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.46008 | + | 3.72973i | 0.666306 | + | 0.384692i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.9481 | −1.51775 | −0.758877 | − | 0.651234i | \(-0.774252\pi\) | ||||
−0.758877 | + | 0.651234i | \(0.774252\pi\) | |||||||
\(98\) | 4.33013 | + | 5.50000i | 0.437409 | + | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.36773 | − | 2.36897i | 0.136094 | − | 0.235721i | −0.789921 | − | 0.613209i | \(-0.789878\pi\) |
0.926015 | + | 0.377487i | \(0.123212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.08845 | + | 5.34935i | 0.304314 | + | 0.527087i | 0.977108 | − | 0.212742i | \(-0.0682395\pi\) |
−0.672794 | + | 0.739829i | \(0.734906\pi\) | |||||||
\(104\) | −1.48236 | −0.145358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.47015 | 0.337051 | ||||||||
\(107\) | −2.28497 | − | 3.95768i | −0.220896 | − | 0.382603i | 0.734184 | − | 0.678950i | \(-0.237565\pi\) |
−0.955080 | + | 0.296347i | \(0.904231\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.97934 | + | 5.16036i | −0.285369 | + | 0.494273i | −0.972699 | − | 0.232072i | \(-0.925449\pi\) |
0.687330 | + | 0.726345i | \(0.258783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.19067 | − | 1.48356i | 0.206999 | − | 0.140184i | ||||
\(113\) | −19.8977 | −1.87182 | −0.935911 | − | 0.352237i | \(-0.885421\pi\) | ||||
−0.935911 | + | 0.352237i | \(0.885421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.778539 | − | 0.449490i | −0.0722855 | − | 0.0417341i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.25674 | −0.575979 | ||||||||
\(119\) | 2.80625 | − | 5.78094i | 0.257249 | − | 0.529938i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.32611 | − | 7.49303i | −0.393282 | − | 0.681185i | ||||
\(122\) | −5.73445 | − | 3.31079i | −0.519173 | − | 0.299745i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.717439 | − | 0.414214i | 0.0644279 | − | 0.0371975i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21.2025i | − | 1.88142i | −0.339219 | − | 0.940708i | \(-0.610163\pi\) | ||
0.339219 | − | 0.940708i | \(-0.389837\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.73085 | − | 6.46202i | −0.325966 | − | 0.564589i | 0.655742 | − | 0.754985i | \(-0.272356\pi\) |
−0.981707 | + | 0.190396i | \(0.939023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.21561 | − | 10.6548i | −0.625673 | − | 0.923886i | ||||
\(134\) | 16.0340i | 1.38513i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.10342 | − | 1.21441i | −0.180367 | − | 0.104135i | ||||
\(137\) | −0.310789 | + | 0.538302i | −0.0265525 | + | 0.0459903i | −0.878996 | − | 0.476829i | \(-0.841786\pi\) |
0.852444 | + | 0.522819i | \(0.175120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5334i | 1.57198i | 0.618237 | + | 0.785992i | \(0.287847\pi\) | ||||
−0.618237 | + | 0.785992i | \(0.712153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.0528 | + | 6.38134i | −0.927531 | + | 0.535510i | ||||
\(143\) | −1.96705 | − | 1.13567i | −0.164493 | − | 0.0949699i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.343146 | −0.0283989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.48236i | − | 0.450647i | ||||||
\(149\) | 12.1100 | − | 6.99171i | 0.992089 | − | 0.572783i | 0.0861911 | − | 0.996279i | \(-0.472530\pi\) |
0.905898 | + | 0.423496i | \(0.139197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.83839 | + | 17.0406i | −0.800637 | + | 1.38674i | 0.118560 | + | 0.992947i | \(0.462172\pi\) |
−0.919197 | + | 0.393797i | \(0.871161\pi\) | |||||||
\(152\) | −4.21209 | + | 2.43185i | −0.341646 | + | 0.197249i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.04354 | − | 0.290313i | 0.325838 | − | 0.0233941i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.53005 | − | 7.84628i | 0.361538 | − | 0.626201i | −0.626677 | − | 0.779279i | \(-0.715585\pi\) |
0.988214 | + | 0.153078i | \(0.0489186\pi\) | |||||||
\(158\) | −5.22438 | + | 9.04889i | −0.415629 | + | 0.719891i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.586988 | + | 0.397520i | −0.0462612 | + | 0.0313289i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2368 | + | 5.91019i | −0.801804 | + | 0.462922i | −0.844102 | − | 0.536183i | \(-0.819866\pi\) |
0.0422974 | + | 0.999105i | \(0.486532\pi\) | |||||||
\(164\) | −4.38014 | + | 7.58662i | −0.342031 | + | 0.592416i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.71984 | + | 2.72500i | −0.366331 | + | 0.211501i | ||||
\(167\) | 15.7778i | 1.22092i | 0.792046 | + | 0.610462i | \(0.209016\pi\) | ||||
−0.792046 | + | 0.610462i | \(0.790984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8026 | −0.830969 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.61401 | + | 0.931852i | 0.123067 | + | 0.0710530i | ||||
\(173\) | −17.5129 | + | 10.1111i | −1.33148 | + | 0.768730i | −0.985527 | − | 0.169521i | \(-0.945778\pi\) |
−0.345954 | + | 0.938252i | \(0.612445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.53225i | − | 0.115498i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.98502 | − | 13.8305i | 0.598503 | − | 1.03664i | ||||
\(179\) | 5.94667 | + | 3.43331i | 0.444475 | + | 0.256618i | 0.705494 | − | 0.708716i | \(-0.250725\pi\) |
−0.261019 | + | 0.965334i | \(0.584059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.3066i | − | 1.21206i | −0.795441 | − | 0.606031i | \(-0.792761\pi\) | ||
0.795441 | − | 0.606031i | \(-0.207239\pi\) | |||||||
\(182\) | −3.24737 | + | 2.19918i | −0.240711 | + | 0.163014i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.133975 | + | 0.232051i | 0.00987674 | + | 0.0171070i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.86078 | − | 3.22297i | −0.136074 | − | 0.235687i | ||||
\(188\) | − | 7.45946i | − | 0.544037i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8630 | + | 8.58114i | −1.07545 | + | 0.620910i | −0.929665 | − | 0.368407i | \(-0.879903\pi\) |
−0.145782 | + | 0.989317i | \(0.546570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.84204 | + | 4.52761i | 0.564483 | + | 0.325904i | 0.754943 | − | 0.655791i | \(-0.227665\pi\) |
−0.190460 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(194\) | 7.47407 | + | 12.9455i | 0.536607 | + | 0.929430i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.59808 | − | 6.50000i | 0.185577 | − | 0.464286i | ||||
\(197\) | 21.7379 | 1.54876 | 0.774380 | − | 0.632720i | \(-0.218062\pi\) | ||||
0.774380 | + | 0.632720i | \(0.218062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.21101 | + | 4.16328i | 0.511175 | + | 0.295127i | 0.733317 | − | 0.679887i | \(-0.237971\pi\) |
−0.222141 | + | 0.975014i | \(0.571305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.73545 | −0.192466 | ||||||||
\(203\) | −2.37237 | + | 0.170328i | −0.166508 | + | 0.0119547i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.08845 | − | 5.34935i | 0.215182 | − | 0.372707i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.741181 | + | 1.28376i | 0.0513917 | + | 0.0890130i | ||||
\(209\) | −7.45241 | −0.515494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9330 | −1.37225 | −0.686123 | − | 0.727486i | \(-0.740689\pi\) | ||||
−0.686123 | + | 0.727486i | \(0.740689\pi\) | |||||||
\(212\) | −1.73508 | − | 3.00524i | −0.119166 | − | 0.206401i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.28497 | + | 3.95768i | −0.156197 | + | 0.270541i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.957160 | − | 1.97177i | 0.0649763 | − | 0.133853i | ||||
\(218\) | 5.95867 | 0.403572 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.11804 | + | 1.80020i | 0.209742 | + | 0.121094i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.16604 | −0.479873 | −0.239937 | − | 0.970789i | \(-0.577127\pi\) | ||||
−0.239937 | + | 0.970789i | \(0.577127\pi\) | |||||||
\(224\) | −2.38014 | − | 1.15539i | −0.159030 | − | 0.0771980i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.94887 | + | 17.2319i | 0.661789 | + | 1.14625i | ||||
\(227\) | −13.7303 | − | 7.92721i | −0.911314 | − | 0.526147i | −0.0304601 | − | 0.999536i | \(-0.509697\pi\) |
−0.880854 | + | 0.473389i | \(0.843031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4371 | + | 14.1087i | −1.61485 | + | 0.932332i | −0.626622 | + | 0.779323i | \(0.715563\pi\) |
−0.988225 | + | 0.153009i | \(0.951104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.898979i | 0.0590209i | ||||||||
\(233\) | 12.1487 | + | 21.0421i | 0.795886 | + | 1.37851i | 0.922275 | + | 0.386534i | \(0.126328\pi\) |
−0.126390 | + | 0.991981i | \(0.540339\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.12837 | + | 5.41849i | 0.203639 | + | 0.352714i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.40957 | + | 0.460186i | −0.415471 | + | 0.0298295i | ||||
\(239\) | − | 19.9081i | − | 1.28774i | −0.765133 | − | 0.643872i | \(-0.777327\pi\) | ||
0.765133 | − | 0.643872i | \(-0.222673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7755 | + | 10.2627i | 1.14502 | + | 0.661078i | 0.947669 | − | 0.319255i | \(-0.103433\pi\) |
0.197351 | + | 0.980333i | \(0.436766\pi\) | |||||||
\(242\) | −4.32611 | + | 7.49303i | −0.278093 | + | 0.481670i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.62158i | 0.423903i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.24384 | − | 3.60488i | 0.397286 | − | 0.229373i | ||||
\(248\) | −0.717439 | − | 0.414214i | −0.0455574 | − | 0.0263026i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.86787 | 0.370376 | 0.185188 | − | 0.982703i | \(-0.440711\pi\) | ||||
0.185188 | + | 0.982703i | \(0.440711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.410565i | 0.0258120i | ||||||||
\(254\) | −18.3619 | + | 10.6012i | −1.15213 | + | 0.665181i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.63519 | + | 3.83083i | −0.413892 | + | 0.238961i | −0.692461 | − | 0.721456i | \(-0.743473\pi\) |
0.278569 | + | 0.960416i | \(0.410140\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.13343 | − | 12.0100i | −0.505387 | − | 0.746268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.73085 | + | 6.46202i | −0.230493 | + | 0.399225i | ||||
\(263\) | 4.23143 | − | 7.32905i | 0.260921 | − | 0.451929i | −0.705566 | − | 0.708644i | \(-0.749307\pi\) |
0.966487 | + | 0.256716i | \(0.0826404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.61950 | + | 11.5763i | −0.344553 | + | 0.709788i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.8859 | − | 8.01702i | 0.848215 | − | 0.489717i | ||||
\(269\) | 8.52155 | − | 14.7598i | 0.519568 | − | 0.899919i | −0.480173 | − | 0.877174i | \(-0.659426\pi\) |
0.999741 | − | 0.0227449i | \(-0.00724054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.12436 | + | 5.26795i | −0.554265 | + | 0.320005i | −0.750840 | − | 0.660484i | \(-0.770351\pi\) |
0.196575 | + | 0.980489i | \(0.437018\pi\) | |||||||
\(272\) | 2.42883i | 0.147269i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.621578 | 0.0375509 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00720 | + | 4.04561i | 0.421022 | + | 0.243077i | 0.695514 | − | 0.718512i | \(-0.255177\pi\) |
−0.274493 | + | 0.961589i | \(0.588510\pi\) | |||||||
\(278\) | 16.0504 | − | 9.26670i | 0.962639 | − | 0.555780i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.1684i | 0.666253i | 0.942882 | + | 0.333127i | \(0.108104\pi\) | ||||
−0.942882 | + | 0.333127i | \(0.891896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.60796 | + | 6.24917i | −0.214471 | + | 0.371475i | −0.953109 | − | 0.302628i | \(-0.902136\pi\) |
0.738638 | + | 0.674103i | \(0.235469\pi\) | |||||||
\(284\) | 11.0528 | + | 6.38134i | 0.655863 | + | 0.378663i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.27135i | 0.134308i | ||||||||
\(287\) | 1.65980 | + | 23.1180i | 0.0979748 | + | 1.36461i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.55040 | − | 9.61358i | −0.326494 | − | 0.565505i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.171573 | + | 0.297173i | 0.0100405 | + | 0.0173907i | ||||
\(293\) | − | 18.2573i | − | 1.06660i | −0.845926 | − | 0.533300i | \(-0.820952\pi\) | ||
0.845926 | − | 0.533300i | \(-0.179048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.74786 | + | 2.74118i | −0.275964 | + | 0.159328i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.1100 | − | 6.99171i | −0.701513 | − | 0.405019i | ||||
\(299\) | −0.198599 | − | 0.343983i | −0.0114853 | − | 0.0198931i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.91824 | − | 0.353113i | 0.283482 | − | 0.0203531i | ||||
\(302\) | 19.6768 | 1.13227 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.21209 | + | 2.43185i | 0.241580 | + | 0.139476i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.42078 | 0.195234 | 0.0976172 | − | 0.995224i | \(-0.468878\pi\) | ||||
0.0976172 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(308\) | −2.27319 | − | 3.35666i | −0.129527 | − | 0.191263i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.84544 | + | 4.92845i | −0.161350 | + | 0.279467i | −0.935353 | − | 0.353715i | \(-0.884918\pi\) |
0.774003 | + | 0.633182i | \(0.218252\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.67335 | + | 11.5586i | 0.377200 | + | 0.653330i | 0.990654 | − | 0.136401i | \(-0.0435535\pi\) |
−0.613453 | + | 0.789731i | \(0.710220\pi\) | |||||||
\(314\) | −9.06010 | −0.511291 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4488 | 0.587789 | ||||||||
\(317\) | −6.26330 | − | 10.8484i | −0.351782 | − | 0.609305i | 0.634780 | − | 0.772693i | \(-0.281091\pi\) |
−0.986562 | + | 0.163389i | \(0.947758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.688731 | + | 1.19292i | −0.0385615 | + | 0.0667905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.637756 | + | 0.309587i | 0.0355408 | + | 0.0172526i | ||||
\(323\) | 11.8131 | 0.657298 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.2368 | + | 5.91019i | 0.566961 | + | 0.327335i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.76028 | 0.483705 | ||||||||
\(329\) | −11.0666 | − | 16.3412i | −0.610120 | − | 0.900920i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.640916 | + | 1.11010i | 0.0352279 | + | 0.0610166i | 0.883102 | − | 0.469181i | \(-0.155451\pi\) |
−0.847874 | + | 0.530198i | \(0.822118\pi\) | |||||||
\(332\) | 4.71984 | + | 2.72500i | 0.259035 | + | 0.149554i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.6640 | − | 7.88891i | 0.747660 | − | 0.431662i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.1058i | − | 0.713920i | −0.934120 | − | 0.356960i | \(-0.883813\pi\) | ||
0.934120 | − | 0.356960i | \(-0.116187\pi\) | |||||||
\(338\) | 5.40130 | + | 9.35533i | 0.293792 | + | 0.508863i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.634679 | − | 1.09930i | −0.0343698 | − | 0.0595302i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.95164 | − | 18.0938i | −0.213368 | − | 0.976972i | ||||
\(344\) | − | 1.86370i | − | 0.100484i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.5129 | + | 10.1111i | 0.941499 | + | 0.543574i | ||||
\(347\) | −7.14262 | + | 12.3714i | −0.383436 | + | 0.664130i | −0.991551 | − | 0.129719i | \(-0.958593\pi\) |
0.608115 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2713i | 0.710399i | 0.934791 | + | 0.355200i | \(0.115587\pi\) | ||||
−0.934791 | + | 0.355200i | \(0.884413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.32697 | + | 0.766125i | −0.0707276 | + | 0.0408346i | ||||
\(353\) | −28.2725 | − | 16.3232i | −1.50480 | − | 0.868794i | −0.999985 | − | 0.00556437i | \(-0.998229\pi\) |
−0.504811 | − | 0.863230i | \(-0.668438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.9700 | −0.846411 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 6.86662i | − | 0.362912i | ||||||
\(359\) | −5.40692 | + | 3.12168i | −0.285366 | + | 0.164756i | −0.635850 | − | 0.771812i | \(-0.719350\pi\) |
0.350484 | + | 0.936569i | \(0.386017\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.32780 | − | 4.03188i | 0.122516 | − | 0.212204i | ||||
\(362\) | −14.1220 | + | 8.15331i | −0.742233 | + | 0.428529i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.52823 | + | 1.71271i | 0.184929 | + | 0.0897705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.29461 | + | 10.9026i | −0.328576 | + | 0.569110i | −0.982230 | − | 0.187684i | \(-0.939902\pi\) |
0.653654 | + | 0.756794i | \(0.273235\pi\) | |||||||
\(368\) | 0.133975 | − | 0.232051i | 0.00698391 | − | 0.0120965i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.25945 | − | 4.00940i | −0.428809 | − | 0.208158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.1408 | + | 17.9791i | −1.61241 | + | 0.930924i | −0.623598 | + | 0.781745i | \(0.714330\pi\) |
−0.988810 | + | 0.149179i | \(0.952337\pi\) | |||||||
\(374\) | −1.86078 | + | 3.22297i | −0.0962188 | + | 0.166656i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.46008 | + | 3.72973i | −0.333153 | + | 0.192346i | ||||
\(377\) | − | 1.33261i | − | 0.0686331i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.5899 | 0.595331 | 0.297666 | − | 0.954670i | \(-0.403792\pi\) | ||||
0.297666 | + | 0.954670i | \(0.403792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.8630 | + | 8.58114i | 0.760456 | + | 0.439049i | ||||
\(383\) | 3.86897 | − | 2.23375i | 0.197695 | − | 0.114139i | −0.397885 | − | 0.917435i | \(-0.630256\pi\) |
0.595580 | + | 0.803296i | \(0.296922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.05521i | − | 0.460898i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.47407 | − | 12.9455i | 0.379438 | − | 0.657207i | ||||
\(389\) | 11.2197 | + | 6.47772i | 0.568863 | + | 0.328433i | 0.756695 | − | 0.653768i | \(-0.226813\pi\) |
−0.187832 | + | 0.982201i | \(0.560146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.650802i | − | 0.0329125i | ||||||
\(392\) | −6.92820 | + | 1.00000i | −0.349927 | + | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.8689 | − | 18.8256i | −0.547570 | − | 0.948418i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.63995 | + | 8.03664i | 0.232873 | + | 0.403347i | 0.958652 | − | 0.284580i | \(-0.0918541\pi\) |
−0.725780 | + | 0.687927i | \(0.758521\pi\) | |||||||
\(398\) | − | 8.32656i | − | 0.417373i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.44260 | + | 3.71964i | −0.321728 | + | 0.185750i | −0.652163 | − | 0.758079i | \(-0.726138\pi\) |
0.330434 | + | 0.943829i | \(0.392805\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.06350 | + | 0.614014i | 0.0529769 | + | 0.0305862i | ||||
\(404\) | 1.36773 | + | 2.36897i | 0.0680469 | + | 0.117861i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.33369 | + | 1.96937i | 0.0661901 | + | 0.0977381i | ||||
\(407\) | −8.40035 | −0.416390 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8647 | + | 8.00481i | 0.685567 | + | 0.395812i | 0.801949 | − | 0.597392i | \(-0.203796\pi\) |
−0.116382 | + | 0.993204i | \(0.537130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.17690 | −0.304314 | ||||||||
\(413\) | 14.8919 | + | 7.22900i | 0.732783 | + | 0.355716i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.741181 | − | 1.28376i | 0.0363394 | − | 0.0629417i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.72620 | + | 6.45398i | 0.182255 | + | 0.315674i | ||||
\(419\) | −28.4419 | −1.38948 | −0.694738 | − | 0.719263i | \(-0.744480\pi\) | ||||
−0.694738 | + | 0.719263i | \(0.744480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8345 | 0.869199 | 0.434600 | − | 0.900624i | \(-0.356890\pi\) | ||||
0.434600 | + | 0.900624i | \(0.356890\pi\) | |||||||
\(422\) | 9.96651 | + | 17.2625i | 0.485162 | + | 0.840325i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.73508 | + | 3.00524i | −0.0842628 | + | 0.145947i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.82353 | + | 14.5057i | 0.475394 | + | 0.701980i | ||||
\(428\) | 4.56993 | 0.220896 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.7539 | − | 15.4464i | −1.28869 | − | 0.744025i | −0.310268 | − | 0.950649i | \(-0.600419\pi\) |
−0.978420 | + | 0.206624i | \(0.933752\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2207 | 0.731462 | 0.365731 | − | 0.930721i | \(-0.380819\pi\) | ||||
0.365731 | + | 0.930721i | \(0.380819\pi\) | |||||||
\(434\) | −2.18618 | + | 0.156961i | −0.104940 | + | 0.00753437i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.97934 | − | 5.16036i | −0.142684 | − | 0.247136i | ||||
\(437\) | −1.12863 | − | 0.651613i | −0.0539895 | − | 0.0311709i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4054 | + | 7.16228i | −0.592079 | + | 0.341837i | −0.765919 | − | 0.642937i | \(-0.777716\pi\) |
0.173840 | + | 0.984774i | \(0.444382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 3.60040i | − | 0.171253i | ||||||
\(443\) | 2.57874 | + | 4.46651i | 0.122520 | + | 0.212210i | 0.920761 | − | 0.390128i | \(-0.127569\pi\) |
−0.798241 | + | 0.602338i | \(0.794236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.58302 | + | 6.20597i | 0.169661 | + | 0.293861i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.189469 | + | 2.63896i | 0.00895155 | + | 0.124679i | ||||
\(449\) | − | 19.9377i | − | 0.940918i | −0.882422 | − | 0.470459i | \(-0.844088\pi\) | ||
0.882422 | − | 0.470459i | \(-0.155912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6246 | + | 6.71147i | 0.547381 | + | 0.316031i | ||||
\(452\) | 9.94887 | − | 17.2319i | 0.467955 | − | 0.810522i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.8544i | 0.744085i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.82065 | − | 5.66995i | 0.459391 | − | 0.265229i | −0.252397 | − | 0.967624i | \(-0.581219\pi\) |
0.711788 | + | 0.702394i | \(0.247886\pi\) | |||||||
\(458\) | 24.4371 | + | 14.1087i | 1.14187 | + | 0.659258i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.01890 | 0.0940298 | 0.0470149 | − | 0.998894i | \(-0.485029\pi\) | ||||
0.0470149 | + | 0.998894i | \(0.485029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.2844i | 1.26801i | 0.773327 | + | 0.634007i | \(0.218591\pi\) | ||||
−0.773327 | + | 0.634007i | \(0.781409\pi\) | |||||||
\(464\) | 0.778539 | − | 0.449490i | 0.0361428 | − | 0.0208670i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.1487 | − | 21.0421i | 0.562776 | − | 0.974757i | ||||
\(467\) | 0.599403 | − | 0.346065i | 0.0277370 | − | 0.0160140i | −0.486067 | − | 0.873921i | \(-0.661569\pi\) |
0.513804 | + | 0.857907i | \(0.328236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.5256 | − | 38.1632i | 0.855434 | − | 1.76221i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.12837 | − | 5.41849i | 0.143995 | − | 0.249406i | ||||
\(473\) | 1.42783 | − | 2.47307i | 0.0656517 | − | 0.113712i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.60332 | + | 5.32076i | 0.165158 | + | 0.243876i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.2409 | + | 9.95403i | −0.788580 | + | 0.455287i | ||||
\(479\) | 7.95403 | − | 13.7768i | 0.363429 | − | 0.629477i | −0.625094 | − | 0.780550i | \(-0.714939\pi\) |
0.988523 | + | 0.151072i | \(0.0482727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.03805 | − | 4.06342i | 0.320908 | − | 0.185276i | ||||
\(482\) | − | 20.5254i | − | 0.934905i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.65221 | 0.393282 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8981 | + | 14.3749i | 1.12824 | + | 0.651390i | 0.943492 | − | 0.331396i | \(-0.107520\pi\) |
0.184749 | + | 0.982786i | \(0.440853\pi\) | |||||||
\(488\) | 5.73445 | − | 3.31079i | 0.259587 | − | 0.149872i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.45753i | − | 0.246295i | −0.992388 | − | 0.123148i | \(-0.960701\pi\) | ||
0.992388 | − | 0.123148i | \(-0.0392988\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.09173 | − | 1.89094i | 0.0491691 | − | 0.0851635i | ||||
\(494\) | −6.24384 | − | 3.60488i | −0.280924 | − | 0.162191i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.828427i | 0.0371975i | ||||||||
\(497\) | 33.6802 | − | 2.41813i | 1.51076 | − | 0.108468i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.43148 | − | 7.67555i | −0.198380 | − | 0.343605i | 0.749623 | − | 0.661865i | \(-0.230235\pi\) |
−0.948003 | + | 0.318260i | \(0.896901\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.93393 | − | 5.08172i | −0.130948 | − | 0.226808i | ||||
\(503\) | 9.36536i | 0.417581i | 0.977960 | + | 0.208790i | \(0.0669526\pi\) | ||||
−0.977960 | + | 0.208790i | \(0.933047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.355560 | − | 0.205283i | 0.0158066 | − | 0.00912592i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.3619 | + | 10.6012i | 0.814677 | + | 0.470354i | ||||
\(509\) | 17.5164 | + | 30.3393i | 0.776400 | + | 1.34477i | 0.934004 | + | 0.357263i | \(0.116290\pi\) |
−0.157603 | + | 0.987502i | \(0.550377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.816735 | + | 0.396469i | 0.0361302 | + | 0.0175387i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.63519 | + | 3.83083i | 0.292666 | + | 0.168971i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.4298 | −0.502680 | ||||||||
\(518\) | −6.33429 | + | 13.0488i | −0.278313 | + | 0.573331i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.99807 | − | 17.3172i | 0.438023 | − | 0.758679i | −0.559514 | − | 0.828821i | \(-0.689012\pi\) |
0.997537 | + | 0.0701424i | \(0.0223454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7515 | + | 29.0144i | 0.732491 | + | 1.26871i | 0.955816 | + | 0.293967i | \(0.0949756\pi\) |
−0.223325 | + | 0.974744i | \(0.571691\pi\) | |||||||
\(524\) | 7.46170 | 0.325966 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.46286 | −0.368998 | ||||||||
\(527\) | 1.00605 | + | 1.74253i | 0.0438243 | + | 0.0759060i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4641 | − | 19.8564i | 0.498439 | − | 0.863322i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.8351 | − | 0.921519i | 0.556473 | − | 0.0399529i | ||||
\(533\) | −12.9859 | −0.562482 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.8859 | − | 8.01702i | −0.599779 | − | 0.346282i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.0431 | −0.734781 | ||||||||
\(539\) | −9.95962 | − | 3.98090i | −0.428991 | − | 0.171470i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.8766 | − | 32.6952i | −0.811568 | − | 1.40568i | −0.911766 | − | 0.410710i | \(-0.865281\pi\) |
0.100198 | − | 0.994967i | \(-0.468052\pi\) | |||||||
\(542\) | 9.12436 | + | 5.26795i | 0.391925 | + | 0.226278i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.10342 | − | 1.21441i | 0.0901836 | − | 0.0520675i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.07130i | 0.216833i | 0.994106 | + | 0.108417i | \(0.0345780\pi\) | ||||
−0.994106 | + | 0.108417i | \(0.965422\pi\) | |||||||
\(548\) | −0.310789 | − | 0.538302i | −0.0132762 | − | 0.0229951i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.18618 | − | 3.78658i | −0.0931346 | − | 0.161314i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.8898 | − | 15.5014i | 0.973373 | − | 0.659187i | ||||
\(554\) | − | 8.09122i | − | 0.343763i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.0504 | − | 9.26670i | −0.680689 | − | 0.392996i | ||||
\(557\) | 17.1778 | − | 29.7528i | 0.727846 | − | 1.26067i | −0.229946 | − | 0.973203i | \(-0.573855\pi\) |
0.957792 | − | 0.287463i | \(-0.0928118\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.76268i | 0.116849i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.67215 | − | 5.58422i | 0.407995 | − | 0.235556i | ||||
\(563\) | −40.7539 | − | 23.5293i | −1.71757 | − | 0.991641i | −0.923300 | − | 0.384079i | \(-0.874519\pi\) |
−0.794272 | − | 0.607562i | \(-0.792148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.21592 | 0.303308 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12.7627i | − | 0.535510i | ||||||
\(569\) | −38.2670 | + | 22.0934i | −1.60424 | + | 0.926206i | −0.613608 | + | 0.789611i | \(0.710283\pi\) |
−0.990627 | + | 0.136595i | \(0.956384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5804 | + | 35.6463i | −0.861263 | + | 1.49175i | 0.00944654 | + | 0.999955i | \(0.496993\pi\) |
−0.870710 | + | 0.491797i | \(0.836340\pi\) | |||||||
\(572\) | 1.96705 | − | 1.13567i | 0.0822463 | − | 0.0474849i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.1909 | − | 12.9964i | 0.801012 | − | 0.542461i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.06058 | + | 12.2293i | −0.293936 | + | 0.509112i | −0.974737 | − | 0.223357i | \(-0.928299\pi\) |
0.680801 | + | 0.732469i | \(0.261632\pi\) | |||||||
\(578\) | −5.55040 | + | 9.61358i | −0.230866 | + | 0.399872i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.3823 | − | 1.03261i | 0.596680 | − | 0.0428397i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.60478 | + | 2.65857i | −0.190711 | + | 0.110107i | ||||
\(584\) | 0.171573 | − | 0.297173i | 0.00709974 | − | 0.0122971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.8112 | + | 9.12863i | −0.653156 | + | 0.377100i | ||||
\(587\) | − | 37.7819i | − | 1.55942i | −0.626138 | − | 0.779712i | \(-0.715365\pi\) | ||
0.626138 | − | 0.779712i | \(-0.284635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.02922 | 0.166021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.74786 | + | 2.74118i | 0.195136 | + | 0.112662i | ||||
\(593\) | 22.6865 | − | 13.0981i | 0.931623 | − | 0.537873i | 0.0442982 | − | 0.999018i | \(-0.485895\pi\) |
0.887324 | + | 0.461146i | \(0.152562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.9834i | 0.572783i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.198599 | + | 0.343983i | −0.00812131 | + | 0.0140665i | ||||
\(599\) | −4.15712 | − | 2.40012i | −0.169856 | − | 0.0980661i | 0.412662 | − | 0.910884i | \(-0.364599\pi\) |
−0.582518 | + | 0.812818i | \(0.697932\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.3722i | 1.52444i | 0.647317 | + | 0.762221i | \(0.275891\pi\) | ||||
−0.647317 | + | 0.762221i | \(0.724109\pi\) | |||||||
\(602\) | −2.76492 | − | 4.08276i | −0.112690 | − | 0.166401i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.83839 | − | 17.0406i | −0.400319 | − | 0.693372i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.6195 | + | 32.2499i | 0.755742 | + | 1.30898i | 0.945005 | + | 0.327057i | \(0.106057\pi\) |
−0.189263 | + | 0.981927i | \(0.560610\pi\) | |||||||
\(608\) | − | 4.86370i | − | 0.197249i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.57618 | − | 5.52881i | 0.387411 | − | 0.223672i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.53861 | − | 4.92977i | −0.344871 | − | 0.199112i | 0.317553 | − | 0.948241i | \(-0.397139\pi\) |
−0.662424 | + | 0.749129i | \(0.730472\pi\) | |||||||
\(614\) | −1.71039 | − | 2.96248i | −0.0690258 | − | 0.119556i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.77035 | + | 3.64697i | −0.0713296 | + | 0.146941i | ||||
\(617\) | 31.3545 | 1.26229 | 0.631143 | − | 0.775666i | \(-0.282586\pi\) | ||||
0.631143 | + | 0.775666i | \(0.282586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1943 | + | 7.61774i | 0.530325 | + | 0.306183i | 0.741149 | − | 0.671341i | \(-0.234281\pi\) |
−0.210824 | + | 0.977524i | \(0.567615\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.69089 | 0.228184 | ||||||||
\(623\) | −34.9851 | + | 23.6926i | −1.40165 | + | 0.949223i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.67335 | − | 11.5586i | 0.266721 | − | 0.461974i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.53005 | + | 7.84628i | 0.180769 | + | 0.313101i | ||||
\(629\) | 13.3157 | 0.530932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00406 | −0.0399710 | −0.0199855 | − | 0.999800i | \(-0.506362\pi\) | ||||
−0.0199855 | + | 0.999800i | \(0.506362\pi\) | |||||||
\(632\) | −5.22438 | − | 9.04889i | −0.207815 | − | 0.359946i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.26330 | + | 10.8484i | −0.248748 | + | 0.430844i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.2701 | − | 1.48236i | 0.406916 | − | 0.0587333i | ||||
\(638\) | 1.37746 | 0.0545342 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.2689 | + | 11.7023i | 0.800574 | + | 0.462211i | 0.843672 | − | 0.536860i | \(-0.180389\pi\) |
−0.0430981 | + | 0.999071i | \(0.513723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.4475 | 1.31904 | 0.659521 | − | 0.751686i | \(-0.270759\pi\) | ||||
0.659521 | + | 0.751686i | \(0.270759\pi\) | |||||||
\(644\) | −0.0507680 | − | 0.707107i | −0.00200054 | − | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.90654 | − | 10.2304i | −0.232390 | − | 0.402511i | ||||
\(647\) | 14.3507 | + | 8.28540i | 0.564185 | + | 0.325733i | 0.754824 | − | 0.655928i | \(-0.227722\pi\) |
−0.190638 | + | 0.981660i | \(0.561056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.30249 | − | 4.79344i | 0.325901 | − | 0.188159i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 11.8204i | − | 0.462922i | ||||||
\(653\) | 3.01453 | + | 5.22132i | 0.117968 | + | 0.204326i | 0.918962 | − | 0.394346i | \(-0.129029\pi\) |
−0.800994 | + | 0.598672i | \(0.795695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.38014 | − | 7.58662i | −0.171016 | − | 0.296208i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.61862 | + | 17.7545i | −0.335989 | + | 0.692144i | ||||
\(659\) | − | 36.3672i | − | 1.41666i | −0.705880 | − | 0.708332i | \(-0.749448\pi\) | ||
0.705880 | − | 0.708332i | \(-0.250552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.90289 | − | 5.71744i | −0.385178 | − | 0.222383i | 0.294891 | − | 0.955531i | \(-0.404717\pi\) |
−0.680069 | + | 0.733148i | \(0.738050\pi\) | |||||||
\(662\) | 0.640916 | − | 1.11010i | 0.0249099 | − | 0.0431452i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 5.45001i | − | 0.211501i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.208609 | + | 0.120440i | −0.00807737 | + | 0.00466347i | ||||
\(668\) | −13.6640 | − | 7.88891i | −0.528675 | − | 0.305231i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1459 | 0.391679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.8070i | − | 0.416581i | −0.978067 | − | 0.208290i | \(-0.933210\pi\) | ||
0.978067 | − | 0.208290i | \(-0.0667899\pi\) | |||||||
\(674\) | −11.3500 | + | 6.55291i | −0.437185 | + | 0.252409i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.40130 | − | 9.35533i | 0.207742 | − | 0.359820i | ||||
\(677\) | 12.1638 | − | 7.02280i | 0.467494 | − | 0.269908i | −0.247696 | − | 0.968838i | \(-0.579673\pi\) |
0.715190 | + | 0.698930i | \(0.246340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.83220 | − | 39.4475i | −0.108690 | − | 1.51386i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.634679 | + | 1.09930i | −0.0243031 | + | 0.0420942i | ||||
\(683\) | 18.2385 | − | 31.5900i | 0.697877 | − | 1.20876i | −0.271324 | − | 0.962488i | \(-0.587461\pi\) |
0.969201 | − | 0.246271i | \(-0.0792052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.6938 | + | 12.4691i | −0.522834 | + | 0.476073i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.61401 | + | 0.931852i | −0.0615337 | + | 0.0355265i | ||||
\(689\) | 2.57201 | − | 4.45486i | 0.0979859 | − | 0.169716i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5831 | + | 11.8836i | −0.783017 | + | 0.452075i | −0.837498 | − | 0.546440i | \(-0.815983\pi\) |
0.0544816 | + | 0.998515i | \(0.482649\pi\) | |||||||
\(692\) | − | 20.2221i | − | 0.768730i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2852 | 0.542260 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.4266 | − | 10.6386i | −0.697957 | − | 0.402965i | ||||
\(698\) | 11.4933 | − | 6.63567i | 0.435029 | − | 0.251164i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.74502i | − | 0.0659086i | −0.999457 | − | 0.0329543i | \(-0.989508\pi\) | ||
0.999457 | − | 0.0329543i | \(-0.0104916\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3323 | − | 23.0922i | 0.502837 | − | 0.870939i | ||||
\(704\) | 1.32697 | + | 0.766125i | 0.0500120 | + | 0.0288744i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.6463i | 1.22866i | ||||||||
\(707\) | 6.51075 | + | 3.16052i | 0.244862 | + | 0.118864i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.06162 | − | 10.4990i | −0.227649 | − | 0.394299i | 0.729462 | − | 0.684021i | \(-0.239770\pi\) |
−0.957111 | + | 0.289722i | \(0.906437\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.98502 | + | 13.8305i | 0.299251 | + | 0.518319i | ||||
\(713\) | − | 0.221976i | − | 0.00831308i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.94667 | + | 3.43331i | −0.222237 | + | 0.128309i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.40692 | + | 3.12168i | 0.201784 | + | 0.116500i | ||||
\(719\) | −0.893176 | − | 1.54703i | −0.0333098 | − | 0.0576943i | 0.848890 | − | 0.528570i | \(-0.177271\pi\) |
−0.882200 | + | 0.470875i | \(0.843938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5315 | + | 9.16382i | −0.503941 | + | 0.341279i | ||||
\(722\) | −4.65561 | −0.173264 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.1220 | + | 8.15331i | 0.524838 | + | 0.303015i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.8785 | 1.10813 | 0.554066 | − | 0.832472i | \(-0.313075\pi\) | ||||
0.554066 | + | 0.832472i | \(0.313075\pi\) | |||||||
\(728\) | −0.280861 | − | 3.91189i | −0.0104094 | − | 0.144984i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.26330 | + | 3.92016i | −0.0837114 | + | 0.144992i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.89554 | + | 11.9434i | 0.254692 | + | 0.441140i | 0.964812 | − | 0.262941i | \(-0.0846924\pi\) |
−0.710119 | + | 0.704081i | \(0.751359\pi\) | |||||||
\(734\) | 12.5892 | 0.464677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.267949 | −0.00987674 | ||||||||
\(737\) | −12.2841 | − | 21.2766i | −0.452490 | − | 0.783735i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.68349 | − | 6.37999i | 0.135499 | − | 0.234692i | −0.790289 | − | 0.612735i | \(-0.790069\pi\) |
0.925788 | + | 0.378043i | \(0.123403\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.657486 | + | 9.15759i | 0.0241371 | + | 0.336186i | ||||
\(743\) | 11.0774 | 0.406389 | 0.203194 | − | 0.979138i | \(-0.434868\pi\) | ||||
0.203194 | + | 0.979138i | \(0.434868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.1408 | + | 17.9791i | 1.14014 | + | 0.658263i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.72157 | 0.136074 | ||||||||
\(749\) | 10.0112 | − | 6.77978i | 0.365802 | − | 0.247728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1879 | − | 21.1100i | −0.444741 | − | 0.770315i | 0.553293 | − | 0.832987i | \(-0.313371\pi\) |
−0.998034 | + | 0.0626722i | \(0.980038\pi\) | |||||||
\(752\) | 6.46008 | + | 3.72973i | 0.235575 | + | 0.136009i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.15408 | + | 0.666306i | −0.0420290 | + | 0.0242655i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6761i | 0.715139i | 0.933887 | + | 0.357569i | \(0.116394\pi\) | ||||
−0.933887 | + | 0.357569i | \(0.883606\pi\) | |||||||
\(758\) | −5.79493 | − | 10.0371i | −0.210481 | − | 0.364565i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.9168 | + | 43.1572i | 0.903234 | + | 1.56445i | 0.823270 | + | 0.567650i | \(0.192147\pi\) |
0.0799647 | + | 0.996798i | \(0.474519\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1825 | − | 6.88462i | −0.513440 | − | 0.249240i | ||||
\(764\) | − | 17.1623i | − | 0.620910i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.86897 | − | 2.23375i | −0.139792 | − | 0.0807087i | ||||
\(767\) | −4.63737 | + | 8.03217i | −0.167446 | + | 0.290025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.0584i | − | 1.12000i | −0.828494 | − | 0.559998i | \(-0.810802\pi\) | ||
0.828494 | − | 0.559998i | \(-0.189198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.84204 | + | 4.52761i | −0.282241 | + | 0.162952i | ||||
\(773\) | −3.43855 | − | 1.98525i | −0.123676 | − | 0.0714043i | 0.436886 | − | 0.899517i | \(-0.356081\pi\) |
−0.560562 | + | 0.828113i | \(0.689415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.9481 | −0.536607 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 12.9554i | − | 0.464475i | ||||||
\(779\) | −36.8991 | + | 21.3037i | −1.32205 | + | 0.763284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.77781 | − | 16.9357i | 0.349878 | − | 0.606006i | ||||
\(782\) | −0.563611 | + | 0.325401i | −0.0201547 | + | 0.0116363i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.33013 | + | 5.50000i | 0.154647 | + | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.4013 | + | 38.8001i | −0.798519 | + | 1.38308i | 0.122061 | + | 0.992523i | \(0.461050\pi\) |
−0.920580 | + | 0.390553i | \(0.872284\pi\) | |||||||
\(788\) | −10.8689 | + | 18.8256i | −0.387190 | + | 0.670633i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.77000 | − | 52.5093i | −0.134046 | − | 1.86702i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.50054 | + | 4.90779i | −0.301863 | + | 0.174281i | ||||
\(794\) | 4.63995 | − | 8.03664i | 0.164666 | − | 0.285210i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.21101 | + | 4.16328i | −0.255588 | + | 0.147564i | ||||
\(797\) | − | 38.4813i | − | 1.36308i | −0.731781 | − | 0.681539i | \(-0.761311\pi\) | ||
0.731781 | − | 0.681539i | \(-0.238689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1177 | 0.640959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.44260 | + | 3.71964i | 0.227496 | + | 0.131345i | ||||
\(803\) | 0.455343 | − | 0.262893i | 0.0160687 | − | 0.00927728i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1.22803i | − | 0.0432555i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.36773 | − | 2.36897i | 0.0481164 | − | 0.0833401i | ||||
\(809\) | −15.0298 | − | 8.67748i | −0.528421 | − | 0.305084i | 0.211952 | − | 0.977280i | \(-0.432018\pi\) |
−0.740373 | + | 0.672196i | \(0.765351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 32.7270i | − | 1.14920i | −0.818434 | − | 0.574601i | \(-0.805157\pi\) | ||
0.818434 | − | 0.574601i | \(-0.194843\pi\) | |||||||
\(812\) | 1.03868 | − | 2.13970i | 0.0364504 | − | 0.0750886i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.20017 | + | 7.27492i | 0.147216 | + | 0.254986i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.53225 | + | 7.85009i | 0.158563 | + | 0.274640i | ||||
\(818\) | − | 16.0096i | − | 0.559763i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.4093 | − | 8.89658i | 0.537789 | − | 0.310493i | −0.206393 | − | 0.978469i | \(-0.566173\pi\) |
0.744182 | + | 0.667976i | \(0.232839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.50579 | + | 4.91082i | 0.296493 | + | 0.171181i | 0.640867 | − | 0.767652i | \(-0.278575\pi\) |
−0.344373 | + | 0.938833i | \(0.611909\pi\) | |||||||
\(824\) | 3.08845 | + | 5.34935i | 0.107591 | + | 0.186353i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.18546 | − | 16.5113i | −0.0412473 | − | 0.574501i | ||||
\(827\) | −7.78482 | −0.270705 | −0.135352 | − | 0.990798i | \(-0.543217\pi\) | ||||
−0.135352 | + | 0.990798i | \(0.543217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.1015 | + | 7.56413i | 0.455032 | + | 0.262713i | 0.709953 | − | 0.704249i | \(-0.248716\pi\) |
−0.254921 | + | 0.966962i | \(0.582049\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.48236 | −0.0513917 | ||||||||
\(833\) | 15.7874 | + | 6.31027i | 0.547000 | + | 0.218638i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.72620 | − | 6.45398i | 0.128873 | − | 0.223215i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.2209 | + | 24.6314i | 0.491254 | + | 0.850877i | ||||
\(839\) | 25.2077 | 0.870265 | 0.435133 | − | 0.900366i | \(-0.356701\pi\) | ||||
0.435133 | + | 0.900366i | \(0.356701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1918 | 0.972132 | ||||||||
\(842\) | −8.91724 | − | 15.4451i | −0.307308 | − | 0.532274i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.96651 | − | 17.2625i | 0.343061 | − | 0.594200i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9541 | − | 12.8361i | 0.651272 | − | 0.441054i | ||||
\(848\) | 3.47015 | 0.119166 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.27219 | − | 0.734497i | −0.0436100 | − | 0.0251782i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3020 | 0.797846 | 0.398923 | − | 0.916984i | \(-0.369384\pi\) | ||||
0.398923 | + | 0.916984i | \(0.369384\pi\) | |||||||
\(854\) | 7.65053 | − | 15.7603i | 0.261796 | − | 0.539306i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.28497 | − | 3.95768i | −0.0780985 | − | 0.135271i | ||||
\(857\) | −23.0414 | − | 13.3030i | −0.787080 | − | 0.454421i | 0.0518534 | − | 0.998655i | \(-0.483487\pi\) |
−0.838934 | + | 0.544234i | \(0.816820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.0044 | + | 28.2927i | −1.67201 | + | 0.965334i | −0.705495 | + | 0.708714i | \(0.749275\pi\) |
−0.966512 | + | 0.256620i | \(0.917391\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.8927i | 1.05221i | ||||||||
\(863\) | 17.0283 | + | 29.4939i | 0.579650 | + | 1.00398i | 0.995519 | + | 0.0945593i | \(0.0301442\pi\) |
−0.415869 | + | 0.909425i | \(0.636522\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.61037 | − | 13.1815i | −0.258611 | − | 0.447927i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.22902 | + | 1.81481i | 0.0417158 | + | 0.0615987i | ||||
\(869\) | − | 16.0101i | − | 0.543106i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.5839 | + | 11.8841i | 0.697459 | + | 0.402678i | ||||
\(872\) | −2.97934 | + | 5.16036i | −0.100893 | + | 0.174752i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.30323i | 0.0440823i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.9043 | − | 12.0691i | 0.705888 | − | 0.407545i | −0.103649 | − | 0.994614i | \(-0.533052\pi\) |
0.809537 | + | 0.587069i | \(0.199718\pi\) | |||||||
\(878\) | 12.4054 | + | 7.16228i | 0.418663 | + | 0.241715i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.2609 | 1.25535 | 0.627676 | − | 0.778475i | \(-0.284006\pi\) | ||||
0.627676 | + | 0.778475i | \(0.284006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.5544i | − | 1.63398i | −0.576648 | − | 0.816992i | \(-0.695640\pi\) | ||
0.576648 | − | 0.816992i | \(-0.304360\pi\) | |||||||
\(884\) | −3.11804 | + | 1.80020i | −0.104871 | + | 0.0605472i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.57874 | − | 4.46651i | 0.0866344 | − | 0.150055i | ||||
\(887\) | −15.1302 | + | 8.73545i | −0.508024 | + | 0.293308i | −0.732021 | − | 0.681282i | \(-0.761423\pi\) |
0.223997 | + | 0.974590i | \(0.428089\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.9524 | − | 4.01720i | 1.87658 | − | 0.134733i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.58302 | − | 6.20597i | 0.119968 | − | 0.207791i | ||||
\(893\) | 18.1403 | − | 31.4199i | 0.607042 | − | 1.05143i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.19067 | − | 1.48356i | 0.0731852 | − | 0.0495624i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2665 | + | 9.96885i | −0.576192 | + | 0.332665i | ||||
\(899\) | 0.372369 | − | 0.644963i | 0.0124192 | − | 0.0215107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.29921 | − | 4.21420i | 0.243172 | − | 0.140395i | ||||
\(902\) | − | 13.4229i | − | 0.446935i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.8977 | −0.661789 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5780 | + | 10.7260i | 0.616872 | + | 0.356151i | 0.775650 | − | 0.631163i | \(-0.217422\pi\) |
−0.158778 | + | 0.987314i | \(0.550756\pi\) | |||||||
\(908\) | 13.7303 | − | 7.92721i | 0.455657 | − | 0.263074i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2281i | 1.39908i | 0.714593 | + | 0.699540i | \(0.246612\pi\) | ||||
−0.714593 | + | 0.699540i | \(0.753388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.17539 | − | 7.23198i | 0.138185 | − | 0.239344i | ||||
\(914\) | −9.82065 | − | 5.66995i | −0.324838 | − | 0.187545i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 28.2175i | − | 0.932332i | ||||||
\(917\) | 16.3461 | − | 11.0699i | 0.539797 | − | 0.365560i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0816 | − | 48.6387i | −0.926325 | − | 1.60444i | −0.789416 | − | 0.613858i | \(-0.789617\pi\) |
−0.136908 | − | 0.990584i | \(-0.543717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.00945 | − | 1.74842i | −0.0332445 | − | 0.0575812i | ||||
\(923\) | 18.9189i | 0.622724i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.6290 | − | 13.6422i | 0.776497 | − | 0.448311i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.778539 | − | 0.449490i | −0.0255568 | − | 0.0147552i | ||||
\(929\) | 9.26942 | + | 16.0551i | 0.304120 | + | 0.526751i | 0.977065 | − | 0.212941i | \(-0.0683044\pi\) |
−0.672945 | + | 0.739692i | \(0.734971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.7504 | − | 21.0605i | 0.876708 | − | 0.690228i | ||||
\(932\) | −24.2973 | −0.795886 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.599403 | − | 0.346065i | −0.0196131 | − | 0.0113236i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.5337 | −1.29151 | −0.645755 | − | 0.763545i | \(-0.723457\pi\) | ||||
−0.645755 | + | 0.763545i | \(0.723457\pi\) | |||||||
\(938\) | −42.3131 | + | 3.03795i | −1.38157 | + | 0.0991925i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.2474 | + | 43.7299i | −0.823043 | + | 1.42555i | 0.0803623 | + | 0.996766i | \(0.474392\pi\) |
−0.903406 | + | 0.428787i | \(0.858941\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.17365 | + | 2.03283i | 0.0382195 | + | 0.0661980i | ||||
\(944\) | −6.25674 | −0.203639 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.85566 | −0.0928455 | ||||||||
\(947\) | 19.5814 | + | 33.9160i | 0.636310 | + | 1.10212i | 0.986236 | + | 0.165344i | \(0.0528735\pi\) |
−0.349926 | + | 0.936777i | \(0.613793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.254333 | + | 0.440518i | −0.00825600 | + | 0.0142998i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.80625 | − | 5.78094i | 0.0909511 | − | 0.187361i | ||||
\(953\) | 52.9933 | 1.71662 | 0.858311 | − | 0.513130i | \(-0.171514\pi\) | ||||
0.858311 | + | 0.513130i | \(0.171514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.2409 | + | 9.95403i | 0.557610 | + | 0.321936i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.9081 | −0.513966 | ||||||||
\(959\) | −1.47944 | − | 0.718168i | −0.0477737 | − | 0.0231909i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1569 | − | 26.2524i | −0.488931 | − | 0.846853i | ||||
\(962\) | −7.03805 | − | 4.06342i | −0.226916 | − | 0.131010i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.7755 | + | 10.2627i | −0.572510 | + | 0.330539i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6208i | 0.984700i | 0.870397 | + | 0.492350i | \(0.163862\pi\) | ||||
−0.870397 | + | 0.492350i | \(0.836138\pi\) | |||||||
\(968\) | −4.32611 | − | 7.49303i | −0.139046 | − | 0.240835i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.03548 | − | 10.4538i | −0.193688 | − | 0.335477i | 0.752782 | − | 0.658270i | \(-0.228712\pi\) |
−0.946470 | + | 0.322793i | \(0.895378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.9089 | + | 3.51150i | −1.56795 | + | 0.112574i | ||||
\(974\) | − | 28.7498i | − | 0.921205i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.73445 | − | 3.31079i | −0.183555 | − | 0.105976i | ||||
\(977\) | −5.61642 | + | 9.72792i | −0.179685 | + | 0.311224i | −0.941773 | − | 0.336250i | \(-0.890841\pi\) |
0.762088 | + | 0.647474i | \(0.224175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.4701i | 0.782068i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.72636 | + | 2.72877i | −0.150824 | + | 0.0870784i | ||||
\(983\) | −19.7385 | − | 11.3960i | −0.629561 | − | 0.363477i | 0.151021 | − | 0.988531i | \(-0.451744\pi\) |
−0.780582 | + | 0.625053i | \(0.785077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.18346 | −0.0695357 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.20977i | 0.229373i | ||||||||
\(989\) | 0.432474 | − | 0.249689i | 0.0137519 | − | 0.00793965i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.41057 | − | 7.63932i | 0.140106 | − | 0.242671i | −0.787430 | − | 0.616404i | \(-0.788589\pi\) |
0.927536 | + | 0.373733i | \(0.121922\pi\) | |||||||
\(992\) | 0.717439 | − | 0.414214i | 0.0227787 | − | 0.0131513i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.9343 | − | 27.9588i | −0.600558 | − | 0.886800i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.2381 | − | 40.2497i | 0.735960 | − | 1.27472i | −0.218342 | − | 0.975872i | \(-0.570065\pi\) |
0.954301 | − | 0.298847i | \(-0.0966020\pi\) | |||||||
\(998\) | −4.43148 | + | 7.67555i | −0.140276 | + | 0.242965i | ||||
\(999\) | 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 | 3150.2.bp.c.899.3 | 8 | ||
3.2 | odd | 2 | 3150.2.bp.d.899.3 | 8 | |||
5.2 | odd | 4 | 3150.2.bf.c.1151.3 | 8 | |||
5.3 | odd | 4 | 630.2.be.b.521.2 | yes | 8 | ||
5.4 | even | 2 | 3150.2.bp.f.899.2 | 8 | |||
7.5 | odd | 6 | 3150.2.bp.a.1349.2 | 8 | |||
15.2 | even | 4 | 3150.2.bf.b.1151.1 | 8 | |||
15.8 | even | 4 | 630.2.be.a.521.4 | yes | 8 | ||
15.14 | odd | 2 | 3150.2.bp.a.899.2 | 8 | |||
21.5 | even | 6 | 3150.2.bp.f.1349.2 | 8 | |||
35.3 | even | 12 | 4410.2.b.e.881.2 | 8 | |||
35.12 | even | 12 | 3150.2.bf.b.1601.1 | 8 | |||
35.18 | odd | 12 | 4410.2.b.b.881.2 | 8 | |||
35.19 | odd | 6 | 3150.2.bp.d.1349.3 | 8 | |||
35.33 | even | 12 | 630.2.be.a.341.4 | ✓ | 8 | ||
105.38 | odd | 12 | 4410.2.b.b.881.7 | 8 | |||
105.47 | odd | 12 | 3150.2.bf.c.1601.3 | 8 | |||
105.53 | even | 12 | 4410.2.b.e.881.7 | 8 | |||
105.68 | odd | 12 | 630.2.be.b.341.2 | yes | 8 | ||
105.89 | even | 6 | inner | 3150.2.bp.c.1349.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.4 | ✓ | 8 | 35.33 | even | 12 | ||
630.2.be.a.521.4 | yes | 8 | 15.8 | even | 4 | ||
630.2.be.b.341.2 | yes | 8 | 105.68 | odd | 12 | ||
630.2.be.b.521.2 | yes | 8 | 5.3 | odd | 4 | ||
3150.2.bf.b.1151.1 | 8 | 15.2 | even | 4 | |||
3150.2.bf.b.1601.1 | 8 | 35.12 | even | 12 | |||
3150.2.bf.c.1151.3 | 8 | 5.2 | odd | 4 | |||
3150.2.bf.c.1601.3 | 8 | 105.47 | odd | 12 | |||
3150.2.bp.a.899.2 | 8 | 15.14 | odd | 2 | |||
3150.2.bp.a.1349.2 | 8 | 7.5 | odd | 6 | |||
3150.2.bp.c.899.3 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bp.c.1349.3 | 8 | 105.89 | even | 6 | inner | ||
3150.2.bp.d.899.3 | 8 | 3.2 | odd | 2 | |||
3150.2.bp.d.1349.3 | 8 | 35.19 | odd | 6 | |||
3150.2.bp.f.899.2 | 8 | 5.4 | even | 2 | |||
3150.2.bp.f.1349.2 | 8 | 21.5 | even | 6 | |||
4410.2.b.b.881.2 | 8 | 35.18 | odd | 12 | |||
4410.2.b.b.881.7 | 8 | 105.38 | odd | 12 | |||
4410.2.b.e.881.2 | 8 | 35.3 | even | 12 | |||
4410.2.b.e.881.7 | 8 | 105.53 | even | 12 |