Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
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.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
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 | 1601.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1601 |
Dual form | 3150.2.bf.b.1151.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63896 | − | 0.189469i | −0.997433 | − | 0.0716124i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.32697 | + | 0.766125i | −0.400096 | + | 0.230995i | −0.686525 | − | 0.727106i | \(-0.740865\pi\) |
0.286430 | + | 0.958101i | \(0.407532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.48236i | − | 0.411133i | −0.978643 | − | 0.205567i | \(-0.934096\pi\) | ||
0.978643 | − | 0.205567i | \(-0.0659037\pi\) | |||||||
\(14\) | 2.19067 | + | 1.48356i | 0.585481 | + | 0.396499i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.21441 | − | 2.10342i | −0.294538 | − | 0.510155i | 0.680339 | − | 0.732898i | \(-0.261833\pi\) |
−0.974877 | + | 0.222742i | \(0.928499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.21209 | + | 2.43185i | 0.966320 | + | 0.557905i | 0.898112 | − | 0.439766i | \(-0.144939\pi\) |
0.0682075 | + | 0.997671i | \(0.478272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.53225 | 0.326677 | ||||||||
\(23\) | −0.232051 | − | 0.133975i | −0.0483859 | − | 0.0279356i | 0.475612 | − | 0.879655i | \(-0.342227\pi\) |
−0.523998 | + | 0.851720i | \(0.675560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.741181 | + | 1.28376i | −0.145358 | + | 0.251767i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.15539 | − | 2.38014i | −0.218349 | − | 0.449804i | ||||
\(29\) | − | 0.898979i | − | 0.166936i | −0.996510 | − | 0.0834681i | \(-0.973400\pi\) | ||
0.996510 | − | 0.0834681i | \(-0.0265997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.717439 | + | 0.414214i | −0.128856 | + | 0.0743950i | −0.563042 | − | 0.826428i | \(-0.690369\pi\) |
0.434187 | + | 0.900823i | \(0.357036\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.42883i | 0.416540i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.74118 | + | 4.74786i | −0.450647 | + | 0.780544i | −0.998426 | − | 0.0560790i | \(-0.982140\pi\) |
0.547779 | + | 0.836623i | \(0.315473\pi\) | |||||||
\(38\) | −2.43185 | − | 4.21209i | −0.394498 | − | 0.683291i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.76028 | −1.36813 | −0.684063 | − | 0.729423i | \(-0.739789\pi\) | ||||
−0.684063 | + | 0.729423i | \(0.739789\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.86370 | −0.284212 | −0.142106 | − | 0.989851i | \(-0.545387\pi\) | ||||
−0.142106 | + | 0.989851i | \(0.545387\pi\) | |||||||
\(44\) | −1.32697 | − | 0.766125i | −0.200048 | − | 0.115498i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.133975 | + | 0.232051i | 0.0197535 | + | 0.0342140i | ||||
\(47\) | 3.72973 | − | 6.46008i | 0.544037 | − | 0.942299i | −0.454630 | − | 0.890680i | \(-0.650229\pi\) |
0.998667 | − | 0.0516191i | \(-0.0164382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | + | 1.00000i | 0.989743 | + | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.28376 | − | 0.741181i | 0.178026 | − | 0.102783i | ||||
\(53\) | −3.00524 | + | 1.73508i | −0.412802 | + | 0.238331i | −0.691993 | − | 0.721904i | \(-0.743267\pi\) |
0.279191 | + | 0.960236i | \(0.409934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.189469 | + | 2.63896i | −0.0253188 | + | 0.352646i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.449490 | + | 0.778539i | −0.0590209 | + | 0.102227i | ||||
\(59\) | 3.12837 | + | 5.41849i | 0.407279 | + | 0.705428i | 0.994584 | − | 0.103938i | \(-0.0331444\pi\) |
−0.587305 | + | 0.809366i | \(0.699811\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.73445 | + | 3.31079i | 0.734222 | + | 0.423903i | 0.819965 | − | 0.572414i | \(-0.193993\pi\) |
−0.0857429 | + | 0.996317i | \(0.527326\pi\) | |||||||
\(62\) | 0.828427 | 0.105210 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.01702 | + | 13.8859i | 0.979434 | + | 1.69643i | 0.664449 | + | 0.747334i | \(0.268666\pi\) |
0.314985 | + | 0.949097i | \(0.398000\pi\) | |||||||
\(68\) | 1.21441 | − | 2.10342i | 0.147269 | − | 0.255078i | ||||
\(69\) | 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 | ||||||||
\(73\) | −0.297173 | + | 0.171573i | −0.0347815 | + | 0.0200811i | −0.517290 | − | 0.855810i | \(-0.673059\pi\) |
0.482508 | + | 0.875891i | \(0.339726\pi\) | |||||||
\(74\) | 4.74786 | − | 2.74118i | 0.551928 | − | 0.318656i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.86370i | 0.557905i | ||||||||
\(77\) | 3.64697 | − | 1.77035i | 0.415611 | − | 0.201750i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.22438 | − | 9.04889i | 0.587789 | − | 1.01808i | −0.406733 | − | 0.913547i | \(-0.633332\pi\) |
0.994521 | − | 0.104533i | \(-0.0333347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.58662 | + | 4.38014i | 0.837802 | + | 0.483705i | ||||
\(83\) | 5.45001 | 0.598216 | 0.299108 | − | 0.954219i | \(-0.403311\pi\) | ||||
0.299108 | + | 0.954219i | \(0.403311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.61401 | + | 0.931852i | 0.174044 | + | 0.100484i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.766125 | + | 1.32697i | 0.0816692 | + | 0.141455i | ||||
\(89\) | 7.98502 | − | 13.8305i | 0.846411 | − | 1.46603i | −0.0379795 | − | 0.999279i | \(-0.512092\pi\) |
0.884390 | − | 0.466748i | \(-0.154574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.280861 | + | 3.91189i | −0.0294423 | + | 0.410078i | ||||
\(92\) | − | 0.267949i | − | 0.0279356i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.46008 | + | 3.72973i | −0.666306 | + | 0.384692i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9481i | 1.51775i | 0.651234 | + | 0.758877i | \(0.274252\pi\) | ||||
−0.651234 | + | 0.758877i | \(0.725748\pi\) | |||||||
\(98\) | −5.50000 | − | 4.33013i | −0.555584 | − | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.36773 | − | 2.36897i | −0.136094 | − | 0.235721i | 0.789921 | − | 0.613209i | \(-0.210122\pi\) |
−0.926015 | + | 0.377487i | \(0.876788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.34935 | + | 3.08845i | 0.527087 | + | 0.304314i | 0.739829 | − | 0.672794i | \(-0.234906\pi\) |
−0.212742 | + | 0.977108i | \(0.568240\pi\) | |||||||
\(104\) | −1.48236 | −0.145358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.47015 | 0.337051 | ||||||||
\(107\) | −3.95768 | − | 2.28497i | −0.382603 | − | 0.220896i | 0.296347 | − | 0.955080i | \(-0.404231\pi\) |
−0.678950 | + | 0.734184i | \(0.737565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.97934 | + | 5.16036i | 0.285369 | + | 0.494273i | 0.972699 | − | 0.232072i | \(-0.0745506\pi\) |
−0.687330 | + | 0.726345i | \(0.741217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.48356 | − | 2.19067i | 0.140184 | − | 0.206999i | ||||
\(113\) | 19.8977i | 1.87182i | 0.352237 | + | 0.935911i | \(0.385421\pi\) | ||||
−0.352237 | + | 0.935911i | \(0.614579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.778539 | − | 0.449490i | 0.0722855 | − | 0.0417341i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.25674i | − | 0.575979i | ||||||
\(119\) | 2.80625 | + | 5.78094i | 0.257249 | + | 0.529938i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.32611 | + | 7.49303i | −0.393282 | + | 0.681185i | ||||
\(122\) | −3.31079 | − | 5.73445i | −0.299745 | − | 0.519173i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.717439 | − | 0.414214i | −0.0644279 | − | 0.0371975i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2025 | 1.88142 | 0.940708 | − | 0.339219i | \(-0.110163\pi\) | ||||
0.940708 | + | 0.339219i | \(0.110163\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.73085 | − | 6.46202i | 0.325966 | − | 0.564589i | −0.655742 | − | 0.754985i | \(-0.727644\pi\) |
0.981707 | + | 0.190396i | \(0.0609772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.6548 | − | 7.21561i | −0.923886 | − | 0.625673i | ||||
\(134\) | − | 16.0340i | − | 1.38513i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.10342 | + | 1.21441i | −0.180367 | + | 0.104135i | ||||
\(137\) | 0.538302 | − | 0.310789i | 0.0459903 | − | 0.0265525i | −0.476829 | − | 0.878996i | \(-0.658214\pi\) |
0.522819 | + | 0.852444i | \(0.324880\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −6.38134 | + | 11.0528i | −0.535510 | + | 0.927531i | ||||
\(143\) | 1.13567 | + | 1.96705i | 0.0949699 | + | 0.164493i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.343146 | 0.0283989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.48236 | −0.450647 | ||||||||
\(149\) | 12.1100 | + | 6.99171i | 0.992089 | + | 0.572783i | 0.905898 | − | 0.423496i | \(-0.139197\pi\) |
0.0861911 | + | 0.996279i | \(0.472530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.83839 | − | 17.0406i | −0.800637 | − | 1.38674i | −0.919197 | − | 0.393797i | \(-0.871161\pi\) |
0.118560 | − | 0.992947i | \(-0.462172\pi\) | |||||||
\(152\) | 2.43185 | − | 4.21209i | 0.197249 | − | 0.341646i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.04354 | − | 0.290313i | −0.325838 | − | 0.0233941i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.84628 | − | 4.53005i | 0.626201 | − | 0.361538i | −0.153078 | − | 0.988214i | \(-0.548919\pi\) |
0.779279 | + | 0.626677i | \(0.215585\pi\) | |||||||
\(158\) | −9.04889 | + | 5.22438i | −0.719891 | + | 0.415629i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.586988 | + | 0.397520i | 0.0462612 | + | 0.0313289i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.91019 | − | 10.2368i | 0.462922 | − | 0.801804i | −0.536183 | − | 0.844102i | \(-0.680134\pi\) |
0.999105 | + | 0.0422974i | \(0.0134677\pi\) | |||||||
\(164\) | −4.38014 | − | 7.58662i | −0.342031 | − | 0.592416i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.71984 | − | 2.72500i | −0.366331 | − | 0.211501i | ||||
\(167\) | 15.7778 | 1.22092 | 0.610462 | − | 0.792046i | \(-0.290984\pi\) | ||||
0.610462 | + | 0.792046i | \(0.290984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8026 | 0.830969 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.931852 | − | 1.61401i | −0.0710530 | − | 0.123067i | ||||
\(173\) | −10.1111 | + | 17.5129i | −0.768730 | + | 1.33148i | 0.169521 | + | 0.985527i | \(0.445778\pi\) |
−0.938252 | + | 0.345954i | \(0.887555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.53225i | − | 0.115498i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.8305 | + | 7.98502i | −1.03664 | + | 0.598503i | ||||
\(179\) | 5.94667 | − | 3.43331i | 0.444475 | − | 0.256618i | −0.261019 | − | 0.965334i | \(-0.584059\pi\) |
0.705494 | + | 0.708716i | \(0.250725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3066i | 1.21206i | 0.795441 | + | 0.606031i | \(0.207239\pi\) | ||||
−0.795441 | + | 0.606031i | \(0.792761\pi\) | |||||||
\(182\) | 2.19918 | − | 3.24737i | 0.163014 | − | 0.240711i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.133975 | + | 0.232051i | −0.00987674 | + | 0.0171070i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.22297 | + | 1.86078i | 0.235687 | + | 0.136074i | ||||
\(188\) | 7.45946 | 0.544037 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8630 | + | 8.58114i | 1.07545 | + | 0.620910i | 0.929665 | − | 0.368407i | \(-0.120097\pi\) |
0.145782 | + | 0.989317i | \(0.453430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.52761 | + | 7.84204i | 0.325904 | + | 0.564483i | 0.981695 | − | 0.190460i | \(-0.0609980\pi\) |
−0.655791 | + | 0.754943i | \(0.727665\pi\) | |||||||
\(194\) | 7.47407 | − | 12.9455i | 0.536607 | − | 0.929430i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.59808 | + | 6.50000i | 0.185577 | + | 0.464286i | ||||
\(197\) | 21.7379i | 1.54876i | 0.632720 | + | 0.774380i | \(0.281938\pi\) | ||||
−0.632720 | + | 0.774380i | \(0.718062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.21101 | + | 4.16328i | −0.511175 | + | 0.295127i | −0.733317 | − | 0.679887i | \(-0.762029\pi\) |
0.222141 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.73545i | 0.192466i | ||||||||
\(203\) | −0.170328 | + | 2.37237i | −0.0119547 | + | 0.166508i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.08845 | − | 5.34935i | −0.215182 | − | 0.372707i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.28376 | + | 0.741181i | 0.0890130 | + | 0.0513917i | ||||
\(209\) | −7.45241 | −0.515494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9330 | −1.37225 | −0.686123 | − | 0.727486i | \(-0.740689\pi\) | ||||
−0.686123 | + | 0.727486i | \(0.740689\pi\) | |||||||
\(212\) | −3.00524 | − | 1.73508i | −0.206401 | − | 0.119166i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.28497 | + | 3.95768i | 0.156197 | + | 0.270541i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.97177 | − | 0.957160i | 0.133853 | − | 0.0649763i | ||||
\(218\) | − | 5.95867i | − | 0.403572i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.11804 | + | 1.80020i | −0.209742 | + | 0.121094i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.16604i | − | 0.479873i | −0.970789 | − | 0.239937i | \(-0.922873\pi\) | ||
0.970789 | − | 0.239937i | \(-0.0771267\pi\) | |||||||
\(224\) | −2.38014 | + | 1.15539i | −0.159030 | + | 0.0771980i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.94887 | − | 17.2319i | 0.661789 | − | 1.14625i | ||||
\(227\) | −7.92721 | − | 13.7303i | −0.526147 | − | 0.911314i | −0.999536 | − | 0.0304601i | \(-0.990303\pi\) |
0.473389 | − | 0.880854i | \(-0.343031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4371 | + | 14.1087i | 1.61485 | + | 0.932332i | 0.988225 | + | 0.153009i | \(0.0488964\pi\) |
0.626622 | + | 0.779323i | \(0.284437\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.898979 | −0.0590209 | ||||||||
\(233\) | −21.0421 | − | 12.1487i | −1.37851 | − | 0.795886i | −0.386534 | − | 0.922275i | \(-0.626328\pi\) |
−0.991981 | + | 0.126390i | \(0.959661\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.12837 | + | 5.41849i | −0.203639 | + | 0.352714i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.460186 | − | 6.40957i | 0.0298295 | − | 0.415471i | ||||
\(239\) | 19.9081i | 1.28774i | 0.765133 | + | 0.643872i | \(0.222673\pi\) | ||||
−0.765133 | + | 0.643872i | \(0.777327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7755 | − | 10.2627i | 1.14502 | − | 0.661078i | 0.197351 | − | 0.980333i | \(-0.436766\pi\) |
0.947669 | + | 0.319255i | \(0.103433\pi\) | |||||||
\(242\) | 7.49303 | − | 4.32611i | 0.481670 | − | 0.278093i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.62158i | 0.423903i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.60488 | − | 6.24384i | 0.229373 | − | 0.397286i | ||||
\(248\) | 0.414214 | + | 0.717439i | 0.0263026 | + | 0.0455574i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.86787 | −0.370376 | −0.185188 | − | 0.982703i | \(-0.559289\pi\) | ||||
−0.185188 | + | 0.982703i | \(0.559289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.410565 | 0.0258120 | ||||||||
\(254\) | −18.3619 | − | 10.6012i | −1.15213 | − | 0.665181i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.83083 | − | 6.63519i | 0.238961 | − | 0.413892i | −0.721456 | − | 0.692461i | \(-0.756527\pi\) |
0.960416 | + | 0.278569i | \(0.0898600\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.13343 | − | 12.0100i | 0.505387 | − | 0.746268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.46202 | + | 3.73085i | −0.399225 | + | 0.230493i | ||||
\(263\) | 7.32905 | − | 4.23143i | 0.451929 | − | 0.260921i | −0.256716 | − | 0.966487i | \(-0.582640\pi\) |
0.708644 | + | 0.705566i | \(0.249307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.61950 | + | 11.5763i | 0.344553 | + | 0.709788i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.01702 | + | 13.8859i | −0.489717 | + | 0.848215i | ||||
\(269\) | 8.52155 | + | 14.7598i | 0.519568 | + | 0.899919i | 0.999741 | + | 0.0227449i | \(0.00724054\pi\) |
−0.480173 | + | 0.877174i | \(0.659426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.12436 | − | 5.26795i | −0.554265 | − | 0.320005i | 0.196575 | − | 0.980489i | \(-0.437018\pi\) |
−0.750840 | + | 0.660484i | \(0.770351\pi\) | |||||||
\(272\) | 2.42883 | 0.147269 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.621578 | −0.0375509 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.04561 | − | 7.00720i | −0.243077 | − | 0.421022i | 0.718512 | − | 0.695514i | \(-0.244823\pi\) |
−0.961589 | + | 0.274493i | \(0.911490\pi\) | |||||||
\(278\) | 9.26670 | − | 16.0504i | 0.555780 | − | 0.962639i | ||||
\(279\) | 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 | ||||||||
\(283\) | 6.24917 | − | 3.60796i | 0.371475 | − | 0.214471i | −0.302628 | − | 0.953109i | \(-0.597864\pi\) |
0.674103 | + | 0.738638i | \(0.264531\pi\) | |||||||
\(284\) | 11.0528 | − | 6.38134i | 0.655863 | − | 0.378663i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.27135i | − | 0.134308i | ||||||
\(287\) | 23.1180 | + | 1.65980i | 1.36461 | + | 0.0979748i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.55040 | − | 9.61358i | 0.326494 | − | 0.565505i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.297173 | − | 0.171573i | −0.0173907 | − | 0.0100405i | ||||
\(293\) | 18.2573 | 1.06660 | 0.533300 | − | 0.845926i | \(-0.320952\pi\) | ||||
0.533300 | + | 0.845926i | \(0.320952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.74786 | + | 2.74118i | 0.275964 | + | 0.159328i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.99171 | − | 12.1100i | −0.405019 | − | 0.701513i | ||||
\(299\) | −0.198599 | + | 0.343983i | −0.0114853 | + | 0.0198931i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.91824 | + | 0.353113i | 0.283482 | + | 0.0203531i | ||||
\(302\) | 19.6768i | 1.13227i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.21209 | + | 2.43185i | −0.241580 | + | 0.139476i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.42078i | − | 0.195234i | −0.995224 | − | 0.0976172i | \(-0.968878\pi\) | ||
0.995224 | − | 0.0976172i | \(-0.0311221\pi\) | |||||||
\(308\) | 3.35666 | + | 2.27319i | 0.191263 | + | 0.129527i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.84544 | + | 4.92845i | 0.161350 | + | 0.279467i | 0.935353 | − | 0.353715i | \(-0.115082\pi\) |
−0.774003 | + | 0.633182i | \(0.781748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5586 | + | 6.67335i | 0.653330 | + | 0.377200i | 0.789731 | − | 0.613453i | \(-0.210220\pi\) |
−0.136401 | + | 0.990654i | \(0.543553\pi\) | |||||||
\(314\) | −9.06010 | −0.511291 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4488 | 0.587789 | ||||||||
\(317\) | −10.8484 | − | 6.26330i | −0.609305 | − | 0.351782i | 0.163389 | − | 0.986562i | \(-0.447758\pi\) |
−0.772693 | + | 0.634780i | \(0.781091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.688731 | + | 1.19292i | 0.0385615 | + | 0.0667905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.309587 | − | 0.637756i | −0.0172526 | − | 0.0355408i | ||||
\(323\) | − | 11.8131i | − | 0.657298i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.2368 | + | 5.91019i | −0.566961 | + | 0.327335i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.76028i | 0.483705i | ||||||||
\(329\) | −11.0666 | + | 16.3412i | −0.610120 | + | 0.900920i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.640916 | − | 1.11010i | 0.0352279 | − | 0.0610166i | −0.847874 | − | 0.530198i | \(-0.822118\pi\) |
0.883102 | + | 0.469181i | \(0.155451\pi\) | |||||||
\(332\) | 2.72500 | + | 4.71984i | 0.149554 | + | 0.259035i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.6640 | − | 7.88891i | −0.747660 | − | 0.431662i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.1058 | 0.713920 | 0.356960 | − | 0.934120i | \(-0.383813\pi\) | ||||
0.356960 | + | 0.934120i | \(0.383813\pi\) | |||||||
\(338\) | −9.35533 | − | 5.40130i | −0.508863 | − | 0.293792i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.634679 | − | 1.09930i | 0.0343698 | − | 0.0595302i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | − | 3.95164i | −0.976972 | − | 0.213368i | ||||
\(344\) | 1.86370i | 0.100484i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.5129 | − | 10.1111i | 0.941499 | − | 0.543574i | ||||
\(347\) | 12.3714 | − | 7.14262i | 0.664130 | − | 0.383436i | −0.129719 | − | 0.991551i | \(-0.541407\pi\) |
0.793849 | + | 0.608115i | \(0.208074\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | −0.766125 | + | 1.32697i | −0.0408346 | + | 0.0707276i | ||||
\(353\) | 16.3232 | + | 28.2725i | 0.868794 | + | 1.50480i | 0.863230 | + | 0.504811i | \(0.168438\pi\) |
0.00556437 | + | 0.999985i | \(0.498229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.9700 | 0.846411 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.86662 | −0.362912 | ||||||||
\(359\) | −5.40692 | − | 3.12168i | −0.285366 | − | 0.164756i | 0.350484 | − | 0.936569i | \(-0.386017\pi\) |
−0.635850 | + | 0.771812i | \(0.719350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.32780 | + | 4.03188i | 0.122516 | + | 0.212204i | ||||
\(362\) | 8.15331 | − | 14.1220i | 0.428529 | − | 0.742233i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.52823 | + | 1.71271i | −0.184929 | + | 0.0897705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9026 | + | 6.29461i | −0.569110 | + | 0.328576i | −0.756794 | − | 0.653654i | \(-0.773235\pi\) |
0.187684 | + | 0.982230i | \(0.439902\pi\) | |||||||
\(368\) | 0.232051 | − | 0.133975i | 0.0120965 | − | 0.00698391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.25945 | − | 4.00940i | 0.428809 | − | 0.208158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9791 | − | 31.1408i | 0.930924 | − | 1.61241i | 0.149179 | − | 0.988810i | \(-0.452337\pi\) |
0.781745 | − | 0.623598i | \(-0.214330\pi\) | |||||||
\(374\) | −1.86078 | − | 3.22297i | −0.0962188 | − | 0.166656i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.46008 | − | 3.72973i | −0.333153 | − | 0.192346i | ||||
\(377\) | −1.33261 | −0.0686331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.5899 | −0.595331 | −0.297666 | − | 0.954670i | \(-0.596208\pi\) | ||||
−0.297666 | + | 0.954670i | \(0.596208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.58114 | − | 14.8630i | −0.439049 | − | 0.760456i | ||||
\(383\) | 2.23375 | − | 3.86897i | 0.114139 | − | 0.197695i | −0.803296 | − | 0.595580i | \(-0.796922\pi\) |
0.917435 | + | 0.397885i | \(0.130256\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.05521i | − | 0.460898i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.9455 | + | 7.47407i | −0.657207 | + | 0.379438i | ||||
\(389\) | 11.2197 | − | 6.47772i | 0.568863 | − | 0.328433i | −0.187832 | − | 0.982201i | \(-0.560146\pi\) |
0.756695 | + | 0.653768i | \(0.226813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.650802i | 0.0329125i | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.8689 | − | 18.8256i | 0.547570 | − | 0.948418i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.03664 | − | 4.63995i | −0.403347 | − | 0.232873i | 0.284580 | − | 0.958652i | \(-0.408146\pi\) |
−0.687927 | + | 0.725780i | \(0.741479\pi\) | |||||||
\(398\) | 8.32656 | 0.417373 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.44260 | + | 3.71964i | 0.321728 | + | 0.185750i | 0.652163 | − | 0.758079i | \(-0.273862\pi\) |
−0.330434 | + | 0.943829i | \(0.607195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.614014 | + | 1.06350i | 0.0305862 | + | 0.0529769i | ||||
\(404\) | 1.36773 | − | 2.36897i | 0.0680469 | − | 0.117861i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.33369 | − | 1.96937i | 0.0661901 | − | 0.0977381i | ||||
\(407\) | − | 8.40035i | − | 0.416390i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.8647 | + | 8.00481i | −0.685567 | + | 0.395812i | −0.801949 | − | 0.597392i | \(-0.796204\pi\) |
0.116382 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.17690i | 0.304314i | ||||||||
\(413\) | −7.22900 | − | 14.8919i | −0.355716 | − | 0.732783i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.741181 | − | 1.28376i | −0.0363394 | − | 0.0629417i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.45398 | + | 3.72620i | 0.315674 | + | 0.182255i | ||||
\(419\) | −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 | \(0.356890\pi\) | |||||||
\(422\) | 17.2625 | + | 9.96651i | 0.840325 | + | 0.485162i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.73508 | + | 3.00524i | 0.0842628 | + | 0.145947i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5057 | − | 9.82353i | −0.701980 | − | 0.475394i | ||||
\(428\) | − | 4.56993i | − | 0.220896i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.7539 | − | 15.4464i | 1.28869 | − | 0.744025i | 0.310268 | − | 0.950649i | \(-0.399581\pi\) |
0.978420 | + | 0.206624i | \(0.0662477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2207i | 0.731462i | 0.930721 | + | 0.365731i | \(0.119181\pi\) | ||||
−0.930721 | + | 0.365731i | \(0.880819\pi\) | |||||||
\(434\) | −2.18618 | − | 0.156961i | −0.104940 | − | 0.00753437i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.97934 | + | 5.16036i | −0.142684 | + | 0.247136i | ||||
\(437\) | −0.651613 | − | 1.12863i | −0.0311709 | − | 0.0539895i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4054 | + | 7.16228i | 0.592079 | + | 0.341837i | 0.765919 | − | 0.642937i | \(-0.222284\pi\) |
−0.173840 | + | 0.984774i | \(0.555618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.60040 | 0.171253 | ||||||||
\(443\) | −4.46651 | − | 2.57874i | −0.212210 | − | 0.122520i | 0.390128 | − | 0.920761i | \(-0.372431\pi\) |
−0.602338 | + | 0.798241i | \(0.705764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.58302 | + | 6.20597i | −0.169661 | + | 0.293861i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.63896 | + | 0.189469i | 0.124679 | + | 0.00895155i | ||||
\(449\) | 19.9377i | 0.940918i | 0.882422 | + | 0.470459i | \(0.155912\pi\) | ||||
−0.882422 | + | 0.470459i | \(0.844088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6246 | − | 6.71147i | 0.547381 | − | 0.316031i | ||||
\(452\) | −17.2319 | + | 9.94887i | −0.810522 | + | 0.467955i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.8544i | 0.744085i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.66995 | − | 9.82065i | 0.265229 | − | 0.459391i | −0.702394 | − | 0.711788i | \(-0.747886\pi\) |
0.967624 | + | 0.252397i | \(0.0812190\pi\) | |||||||
\(458\) | −14.1087 | − | 24.4371i | −0.659258 | − | 1.14187i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.01890 | −0.0940298 | −0.0470149 | − | 0.998894i | \(-0.514971\pi\) | ||||
−0.0470149 | + | 0.998894i | \(0.514971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.2844 | 1.26801 | 0.634007 | − | 0.773327i | \(-0.281409\pi\) | ||||
0.634007 | + | 0.773327i | \(0.281409\pi\) | |||||||
\(464\) | 0.778539 | + | 0.449490i | 0.0361428 | + | 0.0208670i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.1487 | + | 21.0421i | 0.562776 | + | 0.974757i | ||||
\(467\) | −0.346065 | + | 0.599403i | −0.0160140 | + | 0.0277370i | −0.873921 | − | 0.486067i | \(-0.838431\pi\) |
0.857907 | + | 0.513804i | \(0.171764\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.5256 | − | 38.1632i | −0.855434 | − | 1.76221i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.41849 | − | 3.12837i | 0.249406 | − | 0.143995i | ||||
\(473\) | 2.47307 | − | 1.42783i | 0.113712 | − | 0.0656517i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.60332 | + | 5.32076i | −0.165158 | + | 0.243876i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.95403 | − | 17.2409i | 0.455287 | − | 0.788580i | ||||
\(479\) | 7.95403 | + | 13.7768i | 0.363429 | + | 0.629477i | 0.988523 | − | 0.151072i | \(-0.0482727\pi\) |
−0.625094 | + | 0.780550i | \(0.714939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.03805 | + | 4.06342i | 0.320908 | + | 0.185276i | ||||
\(482\) | −20.5254 | −0.934905 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.65221 | −0.393282 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3749 | − | 24.8981i | −0.651390 | − | 1.12824i | −0.982786 | − | 0.184749i | \(-0.940853\pi\) |
0.331396 | − | 0.943492i | \(-0.392480\pi\) | |||||||
\(488\) | 3.31079 | − | 5.73445i | 0.149872 | − | 0.259587i | ||||
\(489\) | 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 | ||||||||
\(493\) | −1.89094 | + | 1.09173i | −0.0851635 | + | 0.0491691i | ||||
\(494\) | −6.24384 | + | 3.60488i | −0.280924 | + | 0.162191i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.828427i | − | 0.0371975i | ||||||
\(497\) | −2.41813 | + | 33.6802i | −0.108468 | + | 1.51076i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.43148 | − | 7.67555i | 0.198380 | − | 0.343605i | −0.749623 | − | 0.661865i | \(-0.769765\pi\) |
0.948003 | + | 0.318260i | \(0.103099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.08172 | + | 2.93393i | 0.226808 | + | 0.130948i | ||||
\(503\) | −9.36536 | −0.417581 | −0.208790 | − | 0.977960i | \(-0.566953\pi\) | ||||
−0.208790 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.355560 | − | 0.205283i | −0.0158066 | − | 0.00912592i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.6012 | + | 18.3619i | 0.470354 | + | 0.814677i | ||||
\(509\) | 17.5164 | − | 30.3393i | 0.776400 | − | 1.34477i | −0.157603 | − | 0.987502i | \(-0.550377\pi\) |
0.934004 | − | 0.357263i | \(-0.116290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.816735 | − | 0.396469i | 0.0361302 | − | 0.0175387i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.63519 | + | 3.83083i | −0.292666 | + | 0.168971i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4298i | 0.502680i | ||||||||
\(518\) | −13.0488 | + | 6.33429i | −0.573331 | + | 0.278313i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.99807 | − | 17.3172i | −0.438023 | − | 0.758679i | 0.559514 | − | 0.828821i | \(-0.310988\pi\) |
−0.997537 | + | 0.0701424i | \(0.977655\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0144 | + | 16.7515i | 1.26871 | + | 0.732491i | 0.974744 | − | 0.223325i | \(-0.0716911\pi\) |
0.293967 | + | 0.955816i | \(0.405024\pi\) | |||||||
\(524\) | 7.46170 | 0.325966 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.46286 | −0.368998 | ||||||||
\(527\) | 1.74253 | + | 1.00605i | 0.0759060 | + | 0.0438243i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4641 | − | 19.8564i | −0.498439 | − | 0.863322i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.921519 | − | 12.8351i | 0.0399529 | − | 0.556473i | ||||
\(533\) | 12.9859i | 0.562482i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.8859 | − | 8.01702i | 0.599779 | − | 0.346282i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 17.0431i | − | 0.734781i | ||||||
\(539\) | −9.95962 | + | 3.98090i | −0.428991 | + | 0.171470i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.8766 | + | 32.6952i | −0.811568 | + | 1.40568i | 0.100198 | + | 0.994967i | \(0.468052\pi\) |
−0.911766 | + | 0.410710i | \(0.865281\pi\) | |||||||
\(542\) | 5.26795 | + | 9.12436i | 0.226278 | + | 0.391925i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.10342 | − | 1.21441i | −0.0901836 | − | 0.0520675i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.07130 | −0.216833 | −0.108417 | − | 0.994106i | \(-0.534578\pi\) | ||||
−0.108417 | + | 0.994106i | \(0.534578\pi\) | |||||||
\(548\) | 0.538302 | + | 0.310789i | 0.0229951 | + | 0.0132762i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.18618 | − | 3.78658i | 0.0931346 | − | 0.161314i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.5014 | + | 22.8898i | −0.659187 | + | 0.973373i | ||||
\(554\) | 8.09122i | 0.343763i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.0504 | + | 9.26670i | −0.680689 | + | 0.392996i | ||||
\(557\) | −29.7528 | + | 17.1778i | −1.26067 | + | 0.727846i | −0.973203 | − | 0.229946i | \(-0.926145\pi\) |
−0.287463 | + | 0.957792i | \(0.592812\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.76268i | 0.116849i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.58422 | − | 9.67215i | 0.235556 | − | 0.407995i | ||||
\(563\) | 23.5293 | + | 40.7539i | 0.991641 | + | 1.71757i | 0.607562 | + | 0.794272i | \(0.292148\pi\) |
0.384079 | + | 0.923300i | \(0.374519\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.21592 | −0.303308 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7627 | −0.535510 | ||||||||
\(569\) | −38.2670 | − | 22.0934i | −1.60424 | − | 0.926206i | −0.990627 | − | 0.136595i | \(-0.956384\pi\) |
−0.613608 | − | 0.789611i | \(-0.710283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5804 | − | 35.6463i | −0.861263 | − | 1.49175i | −0.870710 | − | 0.491797i | \(-0.836340\pi\) |
0.00944654 | − | 0.999955i | \(-0.496993\pi\) | |||||||
\(572\) | −1.13567 | + | 1.96705i | −0.0474849 | + | 0.0822463i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.1909 | − | 12.9964i | −0.801012 | − | 0.542461i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.2293 | + | 7.06058i | −0.509112 | + | 0.293936i | −0.732469 | − | 0.680801i | \(-0.761632\pi\) |
0.223357 | + | 0.974737i | \(0.428299\pi\) | |||||||
\(578\) | −9.61358 | + | 5.55040i | −0.399872 | + | 0.230866i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.3823 | − | 1.03261i | −0.596680 | − | 0.0428397i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.65857 | − | 4.60478i | 0.110107 | − | 0.190711i | ||||
\(584\) | 0.171573 | + | 0.297173i | 0.00709974 | + | 0.0122971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.8112 | − | 9.12863i | −0.653156 | − | 0.377100i | ||||
\(587\) | −37.7819 | −1.55942 | −0.779712 | − | 0.626138i | \(-0.784635\pi\) | ||||
−0.779712 | + | 0.626138i | \(0.784635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.02922 | −0.166021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.74118 | − | 4.74786i | −0.112662 | − | 0.195136i | ||||
\(593\) | 13.0981 | − | 22.6865i | 0.537873 | − | 0.931623i | −0.461146 | − | 0.887324i | \(-0.652562\pi\) |
0.999018 | − | 0.0442982i | \(-0.0141052\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.9834i | 0.572783i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.343983 | − | 0.198599i | 0.0140665 | − | 0.00812131i | ||||
\(599\) | −4.15712 | + | 2.40012i | −0.169856 | + | 0.0980661i | −0.582518 | − | 0.812818i | \(-0.697932\pi\) |
0.412662 | + | 0.910884i | \(0.364599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.3722i | − | 1.52444i | −0.647317 | − | 0.762221i | \(-0.724109\pi\) | ||
0.647317 | − | 0.762221i | \(-0.275891\pi\) | |||||||
\(602\) | −4.08276 | − | 2.76492i | −0.166401 | − | 0.112690i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.83839 | − | 17.0406i | 0.400319 | − | 0.693372i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.2499 | − | 18.6195i | −1.30898 | − | 0.755742i | −0.327057 | − | 0.945005i | \(-0.606057\pi\) |
−0.981927 | + | 0.189263i | \(0.939390\pi\) | |||||||
\(608\) | 4.86370 | 0.197249 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.57618 | − | 5.52881i | −0.387411 | − | 0.223672i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.92977 | − | 8.53861i | −0.199112 | − | 0.344871i | 0.749129 | − | 0.662424i | \(-0.230472\pi\) |
−0.948241 | + | 0.317553i | \(0.897139\pi\) | |||||||
\(614\) | −1.71039 | + | 2.96248i | −0.0690258 | + | 0.119556i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.77035 | − | 3.64697i | −0.0713296 | − | 0.146941i | ||||
\(617\) | 31.3545i | 1.26229i | 0.775666 | + | 0.631143i | \(0.217414\pi\) | ||||
−0.775666 | + | 0.631143i | \(0.782586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1943 | + | 7.61774i | −0.530325 | + | 0.306183i | −0.741149 | − | 0.671341i | \(-0.765719\pi\) |
0.210824 | + | 0.977524i | \(0.432385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 5.69089i | − | 0.228184i | ||||||
\(623\) | −23.6926 | + | 34.9851i | −0.949223 | + | 1.40165i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.67335 | − | 11.5586i | −0.266721 | − | 0.461974i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.84628 | + | 4.53005i | 0.313101 | + | 0.180769i | ||||
\(629\) | 13.3157 | 0.530932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00406 | −0.0399710 | −0.0199855 | − | 0.999800i | \(-0.506362\pi\) | ||||
−0.0199855 | + | 0.999800i | \(0.506362\pi\) | |||||||
\(632\) | −9.04889 | − | 5.22438i | −0.359946 | − | 0.207815i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.26330 | + | 10.8484i | 0.248748 | + | 0.430844i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.48236 | − | 10.2701i | 0.0587333 | − | 0.406916i | ||||
\(638\) | − | 1.37746i | − | 0.0545342i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.2689 | + | 11.7023i | −0.800574 | + | 0.462211i | −0.843672 | − | 0.536860i | \(-0.819611\pi\) |
0.0430981 | + | 0.999071i | \(0.486277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.4475i | 1.31904i | 0.751686 | + | 0.659521i | \(0.229241\pi\) | ||||
−0.751686 | + | 0.659521i | \(0.770759\pi\) | |||||||
\(644\) | −0.0507680 | + | 0.707107i | −0.00200054 | + | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.90654 | + | 10.2304i | −0.232390 | + | 0.402511i | ||||
\(647\) | 8.28540 | + | 14.3507i | 0.325733 | + | 0.564185i | 0.981660 | − | 0.190638i | \(-0.0610557\pi\) |
−0.655928 | + | 0.754824i | \(0.727722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.30249 | − | 4.79344i | −0.325901 | − | 0.188159i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.8204 | 0.462922 | ||||||||
\(653\) | −5.22132 | − | 3.01453i | −0.204326 | − | 0.117968i | 0.394346 | − | 0.918962i | \(-0.370971\pi\) |
−0.598672 | + | 0.800994i | \(0.704305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.38014 | − | 7.58662i | 0.171016 | − | 0.296208i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.7545 | − | 8.61862i | 0.692144 | − | 0.335989i | ||||
\(659\) | 36.3672i | 1.41666i | 0.705880 | + | 0.708332i | \(0.250552\pi\) | ||||
−0.705880 | + | 0.708332i | \(0.749448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.90289 | + | 5.71744i | −0.385178 | + | 0.222383i | −0.680069 | − | 0.733148i | \(-0.738050\pi\) |
0.294891 | + | 0.955531i | \(0.404717\pi\) | |||||||
\(662\) | −1.11010 | + | 0.640916i | −0.0431452 | + | 0.0249099i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 5.45001i | − | 0.211501i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.120440 | + | 0.208609i | −0.00466347 | + | 0.00807737i | ||||
\(668\) | 7.88891 | + | 13.6640i | 0.305231 | + | 0.528675i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1459 | −0.391679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8070 | −0.416581 | −0.208290 | − | 0.978067i | \(-0.566790\pi\) | ||||
−0.208290 | + | 0.978067i | \(0.566790\pi\) | |||||||
\(674\) | −11.3500 | − | 6.55291i | −0.437185 | − | 0.252409i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.40130 | + | 9.35533i | 0.207742 | + | 0.359820i | ||||
\(677\) | −7.02280 | + | 12.1638i | −0.269908 | + | 0.467494i | −0.968838 | − | 0.247696i | \(-0.920327\pi\) |
0.698930 | + | 0.715190i | \(0.253660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.83220 | − | 39.4475i | 0.108690 | − | 1.51386i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.09930 | + | 0.634679i | −0.0420942 | + | 0.0243031i | ||||
\(683\) | 31.5900 | − | 18.2385i | 1.20876 | − | 0.697877i | 0.246271 | − | 0.969201i | \(-0.420795\pi\) |
0.962488 | + | 0.271324i | \(0.0874614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.6938 | + | 12.4691i | 0.522834 | + | 0.476073i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.931852 | − | 1.61401i | 0.0355265 | − | 0.0615337i | ||||
\(689\) | 2.57201 | + | 4.45486i | 0.0979859 | + | 0.169716i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5831 | − | 11.8836i | −0.783017 | − | 0.452075i | 0.0544816 | − | 0.998515i | \(-0.482649\pi\) |
−0.837498 | + | 0.546440i | \(0.815983\pi\) | |||||||
\(692\) | −20.2221 | −0.768730 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.2852 | −0.542260 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6386 | + | 18.4266i | 0.402965 | + | 0.697957i | ||||
\(698\) | 6.63567 | − | 11.4933i | 0.251164 | − | 0.435029i | ||||
\(699\) | 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 | ||||||||
\(703\) | −23.0922 | + | 13.3323i | −0.870939 | + | 0.502837i | ||||
\(704\) | 1.32697 | − | 0.766125i | 0.0500120 | − | 0.0288744i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 32.6463i | − | 1.22866i | ||||||
\(707\) | 3.16052 | + | 6.51075i | 0.118864 | + | 0.244862i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.06162 | − | 10.4990i | 0.227649 | − | 0.394299i | −0.729462 | − | 0.684021i | \(-0.760230\pi\) |
0.957111 | + | 0.289722i | \(0.0935629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.8305 | − | 7.98502i | −0.518319 | − | 0.299251i | ||||
\(713\) | 0.221976 | 0.00831308 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.94667 | + | 3.43331i | 0.222237 | + | 0.128309i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.12168 | + | 5.40692i | 0.116500 | + | 0.201784i | ||||
\(719\) | −0.893176 | + | 1.54703i | −0.0333098 | + | 0.0576943i | −0.882200 | − | 0.470875i | \(-0.843938\pi\) |
0.848890 | + | 0.528570i | \(0.177271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5315 | − | 9.16382i | −0.503941 | − | 0.341279i | ||||
\(722\) | − | 4.65561i | − | 0.173264i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.1220 | + | 8.15331i | −0.524838 | + | 0.303015i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.8785i | − | 1.10813i | −0.832472 | − | 0.554066i | \(-0.813075\pi\) | ||
0.832472 | − | 0.554066i | \(-0.186925\pi\) | |||||||
\(728\) | 3.91189 | + | 0.280861i | 0.144984 | + | 0.0104094i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.26330 | + | 3.92016i | 0.0837114 | + | 0.144992i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.9434 | + | 6.89554i | 0.441140 | + | 0.254692i | 0.704081 | − | 0.710119i | \(-0.251359\pi\) |
−0.262941 | + | 0.964812i | \(0.584692\pi\) | |||||||
\(734\) | 12.5892 | 0.464677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.267949 | −0.00987674 | ||||||||
\(737\) | −21.2766 | − | 12.2841i | −0.783735 | − | 0.452490i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.68349 | − | 6.37999i | −0.135499 | − | 0.234692i | 0.790289 | − | 0.612735i | \(-0.209931\pi\) |
−0.925788 | + | 0.378043i | \(0.876597\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.15759 | − | 0.657486i | −0.336186 | − | 0.0241371i | ||||
\(743\) | − | 11.0774i | − | 0.406389i | −0.979138 | − | 0.203194i | \(-0.934868\pi\) | ||
0.979138 | − | 0.203194i | \(-0.0651323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31.1408 | + | 17.9791i | −1.14014 | + | 0.658263i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.72157i | 0.136074i | ||||||||
\(749\) | 10.0112 | + | 6.77978i | 0.365802 | + | 0.247728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1879 | + | 21.1100i | −0.444741 | + | 0.770315i | −0.998034 | − | 0.0626722i | \(-0.980038\pi\) |
0.553293 | + | 0.832987i | \(0.313371\pi\) | |||||||
\(752\) | 3.72973 | + | 6.46008i | 0.136009 | + | 0.235575i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.15408 | + | 0.666306i | 0.0420290 | + | 0.0242655i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6761 | −0.715139 | −0.357569 | − | 0.933887i | \(-0.616394\pi\) | ||||
−0.357569 | + | 0.933887i | \(0.616394\pi\) | |||||||
\(758\) | 10.0371 | + | 5.79493i | 0.364565 | + | 0.210481i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9168 | + | 43.1572i | −0.903234 | + | 1.56445i | −0.0799647 | + | 0.996798i | \(0.525481\pi\) |
−0.823270 | + | 0.567650i | \(0.807853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.88462 | − | 14.1825i | −0.249240 | − | 0.513440i | ||||
\(764\) | 17.1623i | 0.620910i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.86897 | + | 2.23375i | −0.139792 | + | 0.0807087i | ||||
\(767\) | 8.03217 | − | 4.63737i | 0.290025 | − | 0.167446i | ||||
\(768\) | 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 | ||||||||
\(772\) | −4.52761 | + | 7.84204i | −0.162952 | + | 0.282241i | ||||
\(773\) | 1.98525 | + | 3.43855i | 0.0714043 | + | 0.123676i | 0.899517 | − | 0.436886i | \(-0.143919\pi\) |
−0.828113 | + | 0.560562i | \(0.810585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.9481 | 0.536607 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.9554 | −0.464475 | ||||||||
\(779\) | −36.8991 | − | 21.3037i | −1.32205 | − | 0.763284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.77781 | + | 16.9357i | 0.349878 | + | 0.606006i | ||||
\(782\) | 0.325401 | − | 0.563611i | 0.0116363 | − | 0.0201547i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.33013 | + | 5.50000i | −0.154647 | + | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.8001 | + | 22.4013i | −1.38308 | + | 0.798519i | −0.992523 | − | 0.122061i | \(-0.961050\pi\) |
−0.390553 | + | 0.920580i | \(0.627716\pi\) | |||||||
\(788\) | −18.8256 | + | 10.8689i | −0.670633 | + | 0.387190i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.77000 | − | 52.5093i | 0.134046 | − | 1.86702i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.90779 | − | 8.50054i | 0.174281 | − | 0.301863i | ||||
\(794\) | 4.63995 | + | 8.03664i | 0.164666 | + | 0.285210i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.21101 | − | 4.16328i | −0.255588 | − | 0.147564i | ||||
\(797\) | −38.4813 | −1.36308 | −0.681539 | − | 0.731781i | \(-0.738689\pi\) | ||||
−0.681539 | + | 0.731781i | \(0.738689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.1177 | −0.640959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.71964 | − | 6.44260i | −0.131345 | − | 0.227496i | ||||
\(803\) | 0.262893 | − | 0.455343i | 0.00927728 | − | 0.0160687i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1.22803i | − | 0.0432555i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.36897 | + | 1.36773i | −0.0833401 | + | 0.0481164i | ||||
\(809\) | −15.0298 | + | 8.67748i | −0.528421 | + | 0.305084i | −0.740373 | − | 0.672196i | \(-0.765351\pi\) |
0.211952 | + | 0.977280i | \(0.432018\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7270i | 1.14920i | 0.818434 | + | 0.574601i | \(0.194843\pi\) | ||||
−0.818434 | + | 0.574601i | \(0.805157\pi\) | |||||||
\(812\) | −2.13970 | + | 1.03868i | −0.0750886 | + | 0.0364504i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.20017 | + | 7.27492i | −0.147216 | + | 0.254986i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.85009 | − | 4.53225i | −0.274640 | − | 0.158563i | ||||
\(818\) | 16.0096 | 0.559763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4093 | − | 8.89658i | −0.537789 | − | 0.310493i | 0.206393 | − | 0.978469i | \(-0.433827\pi\) |
−0.744182 | + | 0.667976i | \(0.767161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.91082 | + | 8.50579i | 0.171181 | + | 0.296493i | 0.938833 | − | 0.344373i | \(-0.111909\pi\) |
−0.767652 | + | 0.640867i | \(0.778575\pi\) | |||||||
\(824\) | 3.08845 | − | 5.34935i | 0.107591 | − | 0.186353i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.18546 | + | 16.5113i | −0.0412473 | + | 0.574501i | ||||
\(827\) | − | 7.78482i | − | 0.270705i | −0.990798 | − | 0.135352i | \(-0.956783\pi\) | ||
0.990798 | − | 0.135352i | \(-0.0432167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.1015 | + | 7.56413i | −0.455032 | + | 0.262713i | −0.709953 | − | 0.704249i | \(-0.751284\pi\) |
0.254921 | + | 0.966962i | \(0.417951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.48236i | 0.0513917i | ||||||||
\(833\) | −6.31027 | − | 15.7874i | −0.218638 | − | 0.547000i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.72620 | − | 6.45398i | −0.128873 | − | 0.223215i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.6314 | + | 14.2209i | 0.850877 | + | 0.491254i | ||||
\(839\) | 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 | ||||||||
\(842\) | −15.4451 | − | 8.91724i | −0.532274 | − | 0.307308i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.96651 | − | 17.2625i | −0.343061 | − | 0.594200i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8361 | − | 18.9541i | 0.441054 | − | 0.651272i | ||||
\(848\) | − | 3.47015i | − | 0.119166i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.27219 | − | 0.734497i | 0.0436100 | − | 0.0251782i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3020i | 0.797846i | 0.916984 | + | 0.398923i | \(0.130616\pi\) | ||||
−0.916984 | + | 0.398923i | \(0.869384\pi\) | |||||||
\(854\) | 7.65053 | + | 15.7603i | 0.261796 | + | 0.539306i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.28497 | + | 3.95768i | −0.0780985 | + | 0.135271i | ||||
\(857\) | −13.3030 | − | 23.0414i | −0.454421 | − | 0.787080i | 0.544234 | − | 0.838934i | \(-0.316820\pi\) |
−0.998655 | + | 0.0518534i | \(0.983487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.0044 | + | 28.2927i | 1.67201 | + | 0.965334i | 0.966512 | + | 0.256620i | \(0.0826088\pi\) |
0.705495 | + | 0.708714i | \(0.250725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.8927 | −1.05221 | ||||||||
\(863\) | −29.4939 | − | 17.0283i | −1.00398 | − | 0.579650i | −0.0945593 | − | 0.995519i | \(-0.530144\pi\) |
−0.909425 | + | 0.415869i | \(0.863478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.61037 | − | 13.1815i | 0.258611 | − | 0.447927i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.81481 | + | 1.22902i | 0.0615987 | + | 0.0417158i | ||||
\(869\) | 16.0101i | 0.543106i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.5839 | − | 11.8841i | 0.697459 | − | 0.402678i | ||||
\(872\) | 5.16036 | − | 2.97934i | 0.174752 | − | 0.100893i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.30323i | 0.0440823i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0691 | − | 20.9043i | 0.407545 | − | 0.705888i | −0.587069 | − | 0.809537i | \(-0.699718\pi\) |
0.994614 | + | 0.103649i | \(0.0330518\pi\) | |||||||
\(878\) | −7.16228 | − | 12.4054i | −0.241715 | − | 0.418663i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.2609 | −1.25535 | −0.627676 | − | 0.778475i | \(-0.715994\pi\) | ||||
−0.627676 | + | 0.778475i | \(0.715994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.5544 | −1.63398 | −0.816992 | − | 0.576648i | \(-0.804360\pi\) | ||||
−0.816992 | + | 0.576648i | \(0.804360\pi\) | |||||||
\(884\) | −3.11804 | − | 1.80020i | −0.104871 | − | 0.0605472i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.57874 | + | 4.46651i | 0.0866344 | + | 0.150055i | ||||
\(887\) | 8.73545 | − | 15.1302i | 0.293308 | − | 0.508024i | −0.681282 | − | 0.732021i | \(-0.738577\pi\) |
0.974590 | + | 0.223997i | \(0.0719106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −55.9524 | − | 4.01720i | −1.87658 | − | 0.134733i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.20597 | − | 3.58302i | 0.207791 | − | 0.119968i | ||||
\(893\) | 31.4199 | − | 18.1403i | 1.05143 | − | 0.607042i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.19067 | − | 1.48356i | −0.0731852 | − | 0.0495624i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.96885 | − | 17.2665i | 0.332665 | − | 0.576192i | ||||
\(899\) | 0.372369 | + | 0.644963i | 0.0124192 | + | 0.0215107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.29921 | + | 4.21420i | 0.243172 | + | 0.140395i | ||||
\(902\) | −13.4229 | −0.446935 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.8977 | 0.661789 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.7260 | − | 18.5780i | −0.356151 | − | 0.616872i | 0.631163 | − | 0.775650i | \(-0.282578\pi\) |
−0.987314 | + | 0.158778i | \(0.949244\pi\) | |||||||
\(908\) | 7.92721 | − | 13.7303i | 0.263074 | − | 0.455657i | ||||
\(909\) | 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 | ||||||||
\(913\) | −7.23198 | + | 4.17539i | −0.239344 | + | 0.138185i | ||||
\(914\) | −9.82065 | + | 5.66995i | −0.324838 | + | 0.187545i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.2175i | 0.932332i | ||||||||
\(917\) | −11.0699 | + | 16.3461i | −0.365560 | + | 0.539797i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.0816 | − | 48.6387i | 0.926325 | − | 1.60444i | 0.136908 | − | 0.990584i | \(-0.456283\pi\) |
0.789416 | − | 0.613858i | \(-0.210383\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.74842 | + | 1.00945i | 0.0575812 | + | 0.0332445i | ||||
\(923\) | −18.9189 | −0.622724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.6290 | − | 13.6422i | −0.776497 | − | 0.448311i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.449490 | − | 0.778539i | −0.0147552 | − | 0.0255568i | ||||
\(929\) | 9.26942 | − | 16.0551i | 0.304120 | − | 0.526751i | −0.672945 | − | 0.739692i | \(-0.734971\pi\) |
0.977065 | + | 0.212941i | \(0.0683044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.7504 | + | 21.0605i | 0.876708 | + | 0.690228i | ||||
\(932\) | − | 24.2973i | − | 0.795886i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.599403 | − | 0.346065i | 0.0196131 | − | 0.0113236i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.5337i | 1.29151i | 0.763545 | + | 0.645755i | \(0.223457\pi\) | ||||
−0.763545 | + | 0.645755i | \(0.776543\pi\) | |||||||
\(938\) | −3.03795 | + | 42.3131i | −0.0991925 | + | 1.38157i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2474 | + | 43.7299i | 0.823043 | + | 1.42555i | 0.903406 | + | 0.428787i | \(0.141059\pi\) |
−0.0803623 | + | 0.996766i | \(0.525608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.03283 | + | 1.17365i | 0.0661980 | + | 0.0382195i | ||||
\(944\) | −6.25674 | −0.203639 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.85566 | −0.0928455 | ||||||||
\(947\) | 33.9160 | + | 19.5814i | 1.10212 | + | 0.636310i | 0.936777 | − | 0.349926i | \(-0.113793\pi\) |
0.165344 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.254333 | + | 0.440518i | 0.00825600 | + | 0.0142998i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.78094 | − | 2.80625i | 0.187361 | − | 0.0909511i | ||||
\(953\) | − | 52.9933i | − | 1.71662i | −0.513130 | − | 0.858311i | \(-0.671514\pi\) | ||
0.513130 | − | 0.858311i | \(-0.328486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.2409 | + | 9.95403i | −0.557610 | + | 0.321936i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 15.9081i | − | 0.513966i | ||||||
\(959\) | −1.47944 | + | 0.718168i | −0.0477737 | + | 0.0231909i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1569 | + | 26.2524i | −0.488931 | + | 0.846853i | ||||
\(962\) | −4.06342 | − | 7.03805i | −0.131010 | − | 0.226916i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.7755 | + | 10.2627i | 0.572510 | + | 0.330539i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.6208 | −0.984700 | −0.492350 | − | 0.870397i | \(-0.663862\pi\) | ||||
−0.492350 | + | 0.870397i | \(0.663862\pi\) | |||||||
\(968\) | 7.49303 | + | 4.32611i | 0.240835 | + | 0.139046i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.03548 | − | 10.4538i | 0.193688 | − | 0.335477i | −0.752782 | − | 0.658270i | \(-0.771288\pi\) |
0.946470 | + | 0.322793i | \(0.104622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.51150 | − | 48.9089i | 0.112574 | − | 1.56795i | ||||
\(974\) | 28.7498i | 0.921205i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.73445 | + | 3.31079i | −0.183555 | + | 0.105976i | ||||
\(977\) | 9.72792 | − | 5.61642i | 0.311224 | − | 0.179685i | −0.336250 | − | 0.941773i | \(-0.609159\pi\) |
0.647474 | + | 0.762088i | \(0.275825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.4701i | 0.782068i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.72877 | + | 4.72636i | −0.0870784 | + | 0.150824i | ||||
\(983\) | 11.3960 | + | 19.7385i | 0.363477 | + | 0.629561i | 0.988531 | − | 0.151021i | \(-0.0482562\pi\) |
−0.625053 | + | 0.780582i | \(0.714923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.18346 | 0.0695357 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.20977 | 0.229373 | ||||||||
\(989\) | 0.432474 | + | 0.249689i | 0.0137519 | + | 0.00793965i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.41057 | + | 7.63932i | 0.140106 | + | 0.242671i | 0.927536 | − | 0.373733i | \(-0.121922\pi\) |
−0.787430 | + | 0.616404i | \(0.788589\pi\) | |||||||
\(992\) | −0.414214 | + | 0.717439i | −0.0131513 | + | 0.0227787i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.9343 | − | 27.9588i | 0.600558 | − | 0.886800i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.2497 | − | 23.2381i | 1.27472 | − | 0.735960i | 0.298847 | − | 0.954301i | \(-0.403398\pi\) |
0.975872 | + | 0.218342i | \(0.0700647\pi\) | |||||||
\(998\) | −7.67555 | + | 4.43148i | −0.242965 | + | 0.140276i | ||||
\(999\) | 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.bf.b.1601.1 | 8 | ||
3.2 | odd | 2 | 3150.2.bf.c.1601.3 | 8 | |||
5.2 | odd | 4 | 3150.2.bp.d.1349.3 | 8 | |||
5.3 | odd | 4 | 3150.2.bp.a.1349.2 | 8 | |||
5.4 | even | 2 | 630.2.be.a.341.4 | ✓ | 8 | ||
7.3 | odd | 6 | 3150.2.bf.c.1151.3 | 8 | |||
15.2 | even | 4 | 3150.2.bp.c.1349.3 | 8 | |||
15.8 | even | 4 | 3150.2.bp.f.1349.2 | 8 | |||
15.14 | odd | 2 | 630.2.be.b.341.2 | yes | 8 | ||
21.17 | even | 6 | inner | 3150.2.bf.b.1151.1 | 8 | ||
35.3 | even | 12 | 3150.2.bp.c.899.3 | 8 | |||
35.9 | even | 6 | 4410.2.b.e.881.2 | 8 | |||
35.17 | even | 12 | 3150.2.bp.f.899.2 | 8 | |||
35.19 | odd | 6 | 4410.2.b.b.881.2 | 8 | |||
35.24 | odd | 6 | 630.2.be.b.521.2 | yes | 8 | ||
105.17 | odd | 12 | 3150.2.bp.a.899.2 | 8 | |||
105.38 | odd | 12 | 3150.2.bp.d.899.3 | 8 | |||
105.44 | odd | 6 | 4410.2.b.b.881.7 | 8 | |||
105.59 | even | 6 | 630.2.be.a.521.4 | yes | 8 | ||
105.89 | even | 6 | 4410.2.b.e.881.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.4 | ✓ | 8 | 5.4 | even | 2 | ||
630.2.be.a.521.4 | yes | 8 | 105.59 | even | 6 | ||
630.2.be.b.341.2 | yes | 8 | 15.14 | odd | 2 | ||
630.2.be.b.521.2 | yes | 8 | 35.24 | odd | 6 | ||
3150.2.bf.b.1151.1 | 8 | 21.17 | even | 6 | inner | ||
3150.2.bf.b.1601.1 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bf.c.1151.3 | 8 | 7.3 | odd | 6 | |||
3150.2.bf.c.1601.3 | 8 | 3.2 | odd | 2 | |||
3150.2.bp.a.899.2 | 8 | 105.17 | odd | 12 | |||
3150.2.bp.a.1349.2 | 8 | 5.3 | odd | 4 | |||
3150.2.bp.c.899.3 | 8 | 35.3 | even | 12 | |||
3150.2.bp.c.1349.3 | 8 | 15.2 | even | 4 | |||
3150.2.bp.d.899.3 | 8 | 105.38 | odd | 12 | |||
3150.2.bp.d.1349.3 | 8 | 5.2 | odd | 4 | |||
3150.2.bp.f.899.2 | 8 | 35.17 | even | 12 | |||
3150.2.bp.f.1349.2 | 8 | 15.8 | even | 4 | |||
4410.2.b.b.881.2 | 8 | 35.19 | odd | 6 | |||
4410.2.b.b.881.7 | 8 | 105.44 | odd | 6 | |||
4410.2.b.e.881.2 | 8 | 35.9 | even | 6 | |||
4410.2.b.e.881.7 | 8 | 105.89 | even | 6 |