Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1949.3 | ||
Character | \(\chi\) | \(=\) | 2100.1949 |
Dual form | 2100.2.bo.i.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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.56849 | − | 0.734734i | −0.905569 | − | 0.424199i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.156656 | − | 2.64111i | 0.0592104 | − | 0.998246i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.92033 | + | 2.30485i | 0.640111 | + | 0.768282i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.92449 | + | 2.84316i | 1.48479 | + | 0.857244i | 0.999850 | − | 0.0173038i | \(-0.00550823\pi\) |
0.484940 | + | 0.874548i | \(0.338842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.43616 | −0.398318 | −0.199159 | − | 0.979967i | \(-0.563821\pi\) | ||||
−0.199159 | + | 0.979967i | \(0.563821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.81310 | + | 1.62414i | 0.682277 | + | 0.393913i | 0.800712 | − | 0.599049i | \(-0.204455\pi\) |
−0.118435 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.43583 | + | 3.13838i | −1.24707 | + | 0.719994i | −0.970523 | − | 0.241008i | \(-0.922522\pi\) |
−0.276543 | + | 0.961002i | \(0.589189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.18623 | + | 4.02746i | −0.477074 | + | 0.878863i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.510633 | + | 0.884443i | 0.106474 | + | 0.184419i | 0.914340 | − | 0.404948i | \(-0.132710\pi\) |
−0.807865 | + | 0.589367i | \(0.799377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.31858 | − | 5.02607i | −0.253760 | − | 0.967267i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.95680i | 0.920456i | 0.887801 | + | 0.460228i | \(0.152232\pi\) | ||||
−0.887801 | + | 0.460228i | \(0.847768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.28384 | − | 1.31858i | −0.410190 | − | 0.236823i | 0.280681 | − | 0.959801i | \(-0.409440\pi\) |
−0.690871 | + | 0.722978i | \(0.742773\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.63506 | − | 8.07766i | −0.980938 | − | 1.40614i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.88253 | + | 4.55098i | −1.29588 | + | 0.748176i | −0.979690 | − | 0.200520i | \(-0.935737\pi\) |
−0.316190 | + | 0.948696i | \(0.602404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.25260 | + | 1.05519i | 0.360704 | + | 0.168966i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.203153 | 0.0317271 | 0.0158636 | − | 0.999874i | \(-0.494950\pi\) | ||||
0.0158636 | + | 0.999874i | \(0.494950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.91245i | 0.596642i | 0.954466 | + | 0.298321i | \(0.0964267\pi\) | ||||
−0.954466 | + | 0.298321i | \(0.903573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.98660 | − | 5.76577i | 1.45670 | − | 0.841024i | 0.457849 | − | 0.889030i | \(-0.348620\pi\) |
0.998847 | + | 0.0480062i | \(0.0152867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95092 | − | 0.827492i | −0.992988 | − | 0.118213i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.21901 | − | 4.61434i | −0.450752 | − | 0.646136i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.32156 | + | 9.21721i | −0.730972 | + | 1.26608i | 0.225496 | + | 0.974244i | \(0.427600\pi\) |
−0.956468 | + | 0.291837i | \(0.905734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.8319 | − | 0.928633i | 1.43472 | − | 0.123000i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.739701 | + | 1.28120i | −0.0963009 | + | 0.166798i | −0.910151 | − | 0.414277i | \(-0.864034\pi\) |
0.813850 | + | 0.581075i | \(0.197368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.62492 | − | 4.40225i | 0.976271 | − | 0.563650i | 0.0751289 | − | 0.997174i | \(-0.476063\pi\) |
0.901142 | + | 0.433523i | \(0.142730\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.38819 | − | 4.71074i | 0.804836 | − | 0.593498i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.05487 | + | 2.34108i | 0.495381 | + | 0.286008i | 0.726804 | − | 0.686845i | \(-0.241005\pi\) |
−0.231423 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.151094 | − | 1.76242i | −0.0181896 | − | 0.212171i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.08138i | − | 0.128336i | −0.997939 | − | 0.0641680i | \(-0.979561\pi\) | ||
0.997939 | − | 0.0641680i | \(-0.0204394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.51983 | + | 7.82857i | −0.529006 | + | 0.916265i | 0.470422 | + | 0.882442i | \(0.344102\pi\) |
−0.999428 | + | 0.0338235i | \(0.989232\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.28054 | − | 12.5607i | 0.943655 | − | 1.43143i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.80981 | + | 10.0629i | 0.653655 | + | 1.13216i | 0.982229 | + | 0.187685i | \(0.0600984\pi\) |
−0.328575 | + | 0.944478i | \(0.606568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.62464 | + | 8.85215i | −0.180516 | + | 0.983572i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.1512i | − | 1.11424i | −0.830433 | − | 0.557118i | \(-0.811907\pi\) | ||
0.830433 | − | 0.557118i | \(-0.188093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.64193 | − | 7.77471i | 0.390456 | − | 0.833536i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.53465 | + | 13.0504i | 0.798672 | + | 1.38334i | 0.920481 | + | 0.390787i | \(0.127797\pi\) |
−0.121810 | + | 0.992553i | \(0.538870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.224982 | + | 3.79304i | −0.0235846 | + | 0.397619i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.61339 | + | 3.74619i | 0.270995 | + | 0.388462i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5540 | 1.07159 | 0.535797 | − | 0.844347i | \(-0.320011\pi\) | ||||
0.535797 | + | 0.844347i | \(0.320011\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.90362 | + | 16.8100i | 0.291825 | + | 1.68947i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.49149 | + | 12.9756i | −0.745431 | + | 1.29112i | 0.204562 | + | 0.978854i | \(0.434423\pi\) |
−0.949993 | + | 0.312271i | \(0.898910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.98195 | − | 3.43283i | −0.195287 | − | 0.338247i | 0.751708 | − | 0.659497i | \(-0.229231\pi\) |
−0.946995 | + | 0.321249i | \(0.895897\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.78087 | + | 8.28071i | 0.462184 | + | 0.800526i | 0.999070 | − | 0.0431288i | \(-0.0137326\pi\) |
−0.536885 | + | 0.843655i | \(0.680399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.03847 | − | 12.1910i | 0.674163 | − | 1.16769i | −0.302549 | − | 0.953134i | \(-0.597838\pi\) |
0.976713 | − | 0.214551i | \(-0.0688290\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.7074 | − | 1.34661i | 1.49088 | − | 0.127815i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.91796 | −0.556715 | −0.278357 | − | 0.960478i | \(-0.589790\pi\) | ||||
−0.278357 | + | 0.960478i | \(0.589790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.75790 | − | 3.31012i | −0.254968 | − | 0.306021i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.73023 | − | 7.17527i | 0.433620 | − | 0.657756i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6671 | + | 18.4759i | 0.969734 | + | 1.67963i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.318643 | − | 0.149263i | −0.0287311 | − | 0.0134586i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.35916i | 0.741756i | 0.928682 | + | 0.370878i | \(0.120943\pi\) | ||||
−0.928682 | + | 0.370878i | \(0.879057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.87461 | − | 6.13664i | 0.253095 | − | 0.540301i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.27436 | + | 14.3316i | 0.722934 | + | 1.25216i | 0.959819 | + | 0.280620i | \(0.0905402\pi\) |
−0.236885 | + | 0.971538i | \(0.576126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.43725 | + | 14.8483i | 0.644891 | + | 1.28751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.17568 | − | 8.96454i | 0.442188 | − | 0.765892i | −0.555663 | − | 0.831407i | \(-0.687536\pi\) |
0.997852 | + | 0.0655150i | \(0.0208690\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.17498i | − | 0.778212i | −0.921193 | − | 0.389106i | \(-0.872784\pi\) | ||
0.921193 | − | 0.389106i | \(-0.127216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.9002 | + | 1.70607i | −1.67590 | + | 0.143677i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.07233 | − | 4.08321i | −0.591418 | − | 0.341455i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.2945 | + | 6.40499i | 0.849074 | + | 0.528274i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.71301 | − | 2.14370i | 0.304181 | − | 0.175619i | −0.340138 | − | 0.940375i | \(-0.610474\pi\) |
0.644320 | + | 0.764756i | \(0.277141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06606 | − | 10.5067i | 0.493649 | − | 0.855025i | −0.506324 | − | 0.862343i | \(-0.668996\pi\) |
0.999973 | + | 0.00731794i | \(0.00232939\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.65868 | + | 9.60266i | 0.134097 | + | 0.776329i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.19593 | + | 10.7317i | −0.494489 | + | 0.856480i | −0.999980 | − | 0.00635192i | \(-0.997978\pi\) |
0.505491 | + | 0.862832i | \(0.331311\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.1190 | − | 10.5472i | 1.19902 | − | 0.836447i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.41590 | − | 1.21009i | 0.190400 | − | 0.0953681i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8074 | − | 10.2811i | 1.39478 | − | 0.805279i | 0.400944 | − | 0.916103i | \(-0.368682\pi\) |
0.993840 | + | 0.110824i | \(0.0353488\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.95678i | − | 0.306185i | −0.988212 | − | 0.153093i | \(-0.951077\pi\) | ||
0.988212 | − | 0.153093i | \(-0.0489232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9375 | −0.841343 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.6721 | − | 6.50203i | −1.35142 | − | 0.497223i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2678 | + | 6.50547i | −0.856675 | + | 0.494602i | −0.862898 | − | 0.505379i | \(-0.831353\pi\) |
0.00622220 | + | 0.999981i | \(0.498019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.10156 | − | 1.46607i | 0.157963 | − | 0.110196i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.2033 | + | 11.6644i | 1.51007 | + | 0.871837i | 0.999931 | + | 0.0117426i | \(0.00373787\pi\) |
0.510135 | + | 0.860094i | \(0.329595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.770872i | − | 0.0572984i | −0.999590 | − | 0.0286492i | \(-0.990879\pi\) | ||
0.999590 | − | 0.0286492i | \(-0.00912058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.1941 | + | 1.30261i | −1.12318 | + | 0.0962915i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.23539 | + | 15.9962i | 0.675359 | + | 1.16976i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.4810 | + | 2.69514i | −0.980595 | + | 0.196043i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.02156 | + | 1.16715i | −0.146275 | + | 0.0844517i | −0.571351 | − | 0.820706i | \(-0.693581\pi\) |
0.425076 | + | 0.905157i | \(0.360247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.607965 | − | 0.351009i | −0.0437623 | − | 0.0252662i | 0.477959 | − | 0.878382i | \(-0.341377\pi\) |
−0.521722 | + | 0.853116i | \(0.674710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.3932 | −1.38171 | −0.690855 | − | 0.722993i | \(-0.742766\pi\) | ||||
−0.690855 | + | 0.722993i | \(0.742766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0457 | − | 9.26397i | −1.13745 | − | 0.656706i | −0.191650 | − | 0.981463i | \(-0.561384\pi\) |
−0.945797 | + | 0.324758i | \(0.894717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.63996 | − | 6.65121i | −0.327277 | − | 0.469140i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.0915 | + | 0.776514i | 0.918841 | + | 0.0545006i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.05792 | + | 2.87536i | −0.0735305 | + | 0.199851i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.6916 | −2.46884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5538 | 1.55267 | 0.776335 | − | 0.630321i | \(-0.217077\pi\) | ||||
0.776335 | + | 0.630321i | \(0.217077\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.794525 | + | 1.69613i | −0.0544400 | + | 0.116217i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.84028 | + | 5.82532i | −0.260696 | + | 0.395448i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8412 | − | 8.95818i | 0.867730 | − | 0.605338i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.04005 | − | 2.33252i | −0.271763 | − | 0.156902i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7072 | −0.984868 | −0.492434 | − | 0.870350i | \(-0.663893\pi\) | ||||
−0.492434 | + | 0.870350i | \(0.663893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6835 | + | 8.47751i | 0.974577 | + | 0.562672i | 0.900628 | − | 0.434590i | \(-0.143107\pi\) |
0.0739481 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4690 | − | 11.2404i | 1.28655 | − | 0.742789i | 0.308511 | − | 0.951221i | \(-0.400169\pi\) |
0.978037 | + | 0.208432i | \(0.0668360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.2167 | + | 13.6174i | −1.46175 | + | 0.895959i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8315 | + | 22.2249i | 0.840621 | + | 1.45600i | 0.889370 | + | 0.457188i | \(0.151143\pi\) |
−0.0487486 | + | 0.998811i | \(0.515523\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.71910 | − | 20.0522i | −0.111667 | − | 1.30253i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.58286i | 0.490494i | 0.969461 | + | 0.245247i | \(0.0788691\pi\) | ||||
−0.969461 | + | 0.245247i | \(0.921131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.34408 | + | 4.24011i | 0.473074 | + | 0.273129i | 0.717526 | − | 0.696532i | \(-0.245275\pi\) |
−0.244452 | + | 0.969661i | \(0.578608\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.05221 | − | 12.6908i | 0.580700 | − | 0.814118i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.80670 | − | 4.50720i | 0.496729 | − | 0.286786i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.45841 | + | 15.9220i | −0.472657 | + | 1.00902i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.17721 | −0.0743051 | −0.0371526 | − | 0.999310i | \(-0.511829\pi\) | ||||
−0.0371526 | + | 0.999310i | \(0.511829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.80724i | 0.365098i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.62211 | + | 2.66857i | −0.288319 | + | 0.166461i | −0.637184 | − | 0.770712i | \(-0.719901\pi\) |
0.348864 | + | 0.937173i | \(0.386567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7848 | + | 21.5316i | 0.670134 | + | 1.33791i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4247 | + | 9.51871i | −0.707170 | + | 0.589194i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.65408 | − | 13.2573i | 0.471971 | − | 0.817478i | −0.527515 | − | 0.849546i | \(-0.676876\pi\) |
0.999486 | + | 0.0320683i | \(0.0102094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.22947 | − | 26.0054i | −0.136441 | − | 1.59151i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.50096 | − | 6.06384i | 0.213457 | − | 0.369719i | −0.739337 | − | 0.673336i | \(-0.764861\pi\) |
0.952794 | + | 0.303617i | \(0.0981943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1722 | − | 6.45029i | 0.678665 | − | 0.391827i | −0.120687 | − | 0.992691i | \(-0.538510\pi\) |
0.799352 | + | 0.600863i | \(0.205176\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.13976 | − | 5.78405i | 0.190027 | − | 0.350067i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.64261 | − | 5.56717i | −0.579369 | − | 0.334499i | 0.181514 | − | 0.983388i | \(-0.441900\pi\) |
−0.760882 | + | 0.648890i | \(0.775234\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.34662 | − | 7.79602i | −0.0806200 | − | 0.466735i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.5391i | − | 1.34457i | −0.740291 | − | 0.672286i | \(-0.765312\pi\) | ||
0.740291 | − | 0.672286i | \(-0.234688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.14640 | + | 15.8420i | −0.543697 | + | 0.941710i | 0.454991 | + | 0.890496i | \(0.349643\pi\) |
−0.998688 | + | 0.0512144i | \(0.983691\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0318251 | − | 0.536549i | 0.00187858 | − | 0.0316715i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.22431 | − | 5.58467i | −0.189665 | − | 0.328510i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.5538 | − | 7.75436i | −0.970402 | − | 0.454568i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 17.0413i | − | 0.995566i | −0.867302 | − | 0.497783i | \(-0.834148\pi\) | ||
0.867302 | − | 0.497783i | \(-0.165852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.79657 | − | 28.4997i | 0.452403 | − | 1.65372i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.733349 | − | 1.27020i | −0.0424106 | − | 0.0734574i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3332 | + | 0.612909i | 0.595596 | + | 0.0353275i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.2840 | − | 14.8479i | 1.22273 | − | 0.852992i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9629 | −0.968124 | −0.484062 | − | 0.875034i | \(-0.660839\pi\) | ||||
−0.484062 | + | 0.875034i | \(0.660839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.586450 | + | 6.84058i | 0.0333620 | + | 0.389147i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.7519 | − | 29.0151i | 0.949911 | − | 1.64529i | 0.204305 | − | 0.978907i | \(-0.434507\pi\) |
0.745606 | − | 0.666387i | \(-0.232160\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.42235 | − | 5.92768i | −0.193443 | − | 0.335052i | 0.752946 | − | 0.658082i | \(-0.228632\pi\) |
−0.946389 | + | 0.323030i | \(0.895299\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.51876 | + | 11.2908i | 0.366130 | + | 0.634156i | 0.988957 | − | 0.148204i | \(-0.0473492\pi\) |
−0.622827 | + | 0.782360i | \(0.714016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.0930 | + | 24.4097i | −0.789055 | + | 1.36668i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.41464 | − | 16.5009i | −0.0789574 | − | 0.920990i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.3887 | −1.13446 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.9969 | + | 13.9501i | −1.10583 | + | 0.771440i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.6636 | − | 27.2790i | −0.753297 | − | 1.50394i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.35727 | + | 5.81496i | 0.184532 | + | 0.319619i | 0.943419 | − | 0.331604i | \(-0.107590\pi\) |
−0.758887 | + | 0.651223i | \(0.774256\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.6264 | − | 9.42863i | −1.40432 | − | 0.516686i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.0783052i | 0.00426556i | 0.999998 | + | 0.00213278i | \(0.000678885\pi\) | ||||
−0.999998 | + | 0.00213278i | \(0.999321\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.28227 | + | 4.34812i | 0.504144 | + | 0.236158i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.49784 | − | 12.9866i | −0.406031 | − | 0.703266i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.27440 | + | 18.2285i | −0.176801 | + | 0.984247i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.9669 | + | 24.1913i | −0.749780 | + | 1.29866i | 0.198148 | + | 0.980172i | \(0.436507\pi\) |
−0.947928 | + | 0.318485i | \(0.896826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.8292i | 1.00790i | 0.863732 | + | 0.503952i | \(0.168121\pi\) | ||||
−0.863732 | + | 0.503952i | \(0.831879\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.89368 | + | 7.21821i | 0.101077 | + | 0.385280i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0565 | + | 13.8890i | 1.28040 | + | 0.739239i | 0.976921 | − | 0.213600i | \(-0.0685190\pi\) |
0.303477 | + | 0.952839i | \(0.401852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.6912 | + | 7.77890i | −0.671692 | + | 0.411703i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.6446 | − | 14.2286i | 1.30069 | − | 0.750954i | 0.320168 | − | 0.947361i | \(-0.396260\pi\) |
0.980523 | + | 0.196406i | \(0.0629271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.1989 | − | 17.6650i | 0.536782 | − | 0.929734i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.15634 | − | 36.8168i | −0.165665 | − | 1.93238i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.84147 | + | 13.5818i | −0.409321 | + | 0.708966i | −0.994814 | − | 0.101712i | \(-0.967568\pi\) |
0.585492 | + | 0.810678i | \(0.300901\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.390121 | + | 0.468236i | 0.0203089 | + | 0.0243754i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.5100 | + | 15.4988i | 1.22058 | + | 0.804655i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.28231 | − | 1.31769i | 0.118173 | − | 0.0682274i | −0.439748 | − | 0.898121i | \(-0.644932\pi\) |
0.557922 | + | 0.829894i | \(0.311599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.11874i | − | 0.366634i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.3684 | −1.35445 | −0.677227 | − | 0.735774i | \(-0.736819\pi\) | ||||
−0.677227 | + | 0.735774i | \(0.736819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.14176 | − | 13.1113i | 0.314652 | − | 0.671711i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.5116 | − | 8.95565i | 0.792607 | − | 0.457612i | −0.0482722 | − | 0.998834i | \(-0.515372\pi\) |
0.840880 | + | 0.541222i | \(0.182038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.01759 | + | 7.51320i | −0.458390 | + | 0.381917i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6243 | − | 10.1754i | −0.893590 | − | 0.515914i | −0.0184749 | − | 0.999829i | \(-0.505881\pi\) |
−0.875115 | + | 0.483915i | \(0.839214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31737i | 0.167767i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.44835 | − | 28.5585i | −0.123503 | − | 1.44058i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.25692 | + | 14.3014i | 0.414403 | + | 0.717767i | 0.995366 | − | 0.0961632i | \(-0.0306571\pi\) |
−0.580963 | + | 0.813930i | \(0.697324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.755733 | − | 28.7538i | −0.0378340 | − | 1.43949i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.0643 | + | 15.0482i | −1.30159 | + | 0.751473i | −0.980677 | − | 0.195636i | \(-0.937323\pi\) |
−0.320912 | + | 0.947109i | \(0.603990\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.27995 | + | 1.89368i | 0.163386 | + | 0.0943310i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −51.7566 | −2.56548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.1623 | − | 11.0634i | −0.947515 | − | 0.547048i | −0.0552067 | − | 0.998475i | \(-0.517582\pi\) |
−0.892308 | + | 0.451427i | \(0.850915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7046 | + | 10.2581i | −0.725322 | + | 0.505993i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.26791 | + | 2.15434i | 0.160803 | + | 0.106008i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.74117 | + | 14.3909i | −0.330116 | + | 0.704724i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.3632 | −1.19022 | −0.595111 | − | 0.803643i | \(-0.702892\pi\) | ||||
−0.595111 | + | 0.803643i | \(0.702892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6655 | −0.666018 | −0.333009 | − | 0.942924i | \(-0.608064\pi\) | ||||
−0.333009 | + | 0.942924i | \(0.608064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 32.4668 | + | 11.9454i | 1.57859 | + | 0.580805i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.4323 | − | 20.8279i | −0.504856 | − | 1.00793i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.09282 | + | 11.6008i | 0.390725 | + | 0.560090i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2369 | − | 10.5291i | −0.878439 | − | 0.507167i | −0.00829574 | − | 0.999966i | \(-0.502641\pi\) |
−0.870143 | + | 0.492798i | \(0.835974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.13627 | −0.102663 | −0.0513313 | − | 0.998682i | \(-0.516346\pi\) | ||||
−0.0513313 | + | 0.998682i | \(0.516346\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.55144 | − | 3.20512i | −0.265561 | − | 0.153322i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0942 | + | 7.55996i | −0.624954 | + | 0.360817i | −0.778795 | − | 0.627278i | \(-0.784169\pi\) |
0.153841 | + | 0.988096i | \(0.450836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.4408 | − | 17.6099i | −0.544802 | − | 0.838565i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.39238 | − | 12.8040i | −0.351223 | − | 0.608335i | 0.635241 | − | 0.772314i | \(-0.280901\pi\) |
−0.986464 | + | 0.163978i | \(0.947567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.39887 | + | 0.634313i | −0.349955 | + | 0.0300020i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2040i | 1.14226i | 0.820860 | + | 0.571130i | \(0.193495\pi\) | ||||
−0.820860 | + | 0.571130i | \(0.806505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00042 | + | 0.577595i | 0.0471081 | + | 0.0271979i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.2342 | + | 12.0228i | −0.809734 | + | 0.564879i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.7314 | + | 6.19577i | −0.501993 | + | 0.289826i | −0.729536 | − | 0.683942i | \(-0.760264\pi\) |
0.227543 | + | 0.973768i | \(0.426931\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.45377 | − | 16.2804i | 0.207884 | − | 0.759904i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.34732 | 0.155900 | 0.0779502 | − | 0.996957i | \(-0.475162\pi\) | ||||
0.0779502 | + | 0.996957i | \(0.475162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8360i | 0.596542i | 0.954481 | + | 0.298271i | \(0.0964099\pi\) | ||||
−0.954481 | + | 0.298271i | \(0.903590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.9359 | + | 14.9741i | −1.20017 | + | 0.692918i | −0.960593 | − | 0.277959i | \(-0.910342\pi\) |
−0.239576 | + | 0.970878i | \(0.577009\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.81827 | − | 10.3426i | 0.314838 | − | 0.477577i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.6032 | − | 12.2802i | 0.811112 | − | 0.565840i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.1237 | + | 19.2668i | −0.511468 | + | 0.885889i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.4634 | + | 5.43473i | −1.44061 | + | 0.248839i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0585 | − | 17.4218i | 0.459584 | − | 0.796023i | −0.539355 | − | 0.842079i | \(-0.681332\pi\) |
0.998939 | + | 0.0460557i | \(0.0146652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3205 | − | 6.53591i | 0.516172 | − | 0.298012i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.67842 | + | 0.122962i | −0.212875 | + | 0.00559498i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5981 | − | 12.4697i | −0.978704 | − | 0.565055i | −0.0768256 | − | 0.997045i | \(-0.524478\pi\) |
−0.901879 | + | 0.431989i | \(0.857812\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.4847 | + | 3.04214i | −1.60467 | + | 0.137570i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.2524i | − | 0.507814i | −0.967229 | − | 0.253907i | \(-0.918284\pi\) | ||
0.967229 | − | 0.253907i | \(-0.0817157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.05057 | + | 13.9440i | −0.362579 | + | 0.628006i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.85604 | − | 0.169405i | −0.128111 | − | 0.00759883i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.84476 | − | 4.92727i | −0.127349 | − | 0.220575i | 0.795300 | − | 0.606216i | \(-0.207313\pi\) |
−0.922649 | + | 0.385642i | \(0.873980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.90718 | + | 6.20618i | −0.129883 | + | 0.277272i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 22.7975i | − | 1.01649i | −0.861212 | − | 0.508245i | \(-0.830294\pi\) | ||
0.861212 | − | 0.508245i | \(-0.169706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.1553 | + | 8.03612i | 0.761894 | + | 0.356897i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.17913 | − | 14.1667i | −0.362534 | − | 0.627927i | 0.625843 | − | 0.779949i | \(-0.284755\pi\) |
−0.988377 | + | 0.152022i | \(0.951422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.9681 | + | 13.1638i | 0.883335 | + | 0.582330i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.9413 | + | 23.1827i | 1.01288 | + | 1.02354i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 65.5719 | 2.88385 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.4532 | − | 1.92494i | 0.985588 | − | 0.0844955i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.67177 | + | 15.0199i | −0.379917 | + | 0.658036i | −0.991050 | − | 0.133492i | \(-0.957381\pi\) |
0.611133 | + | 0.791528i | \(0.290714\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.44905 | − | 11.1701i | −0.281997 | − | 0.488433i | 0.689879 | − | 0.723924i | \(-0.257664\pi\) |
−0.971877 | + | 0.235491i | \(0.924330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.28312 | − | 7.41858i | −0.186576 | − | 0.323158i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.9785 | − | 19.0153i | 0.477326 | − | 0.826754i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.37344 | + | 0.755432i | −0.189791 | + | 0.0327830i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.291759 | −0.0126375 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.1185 | − | 33.1395i | −0.997637 | − | 1.43008i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.8770 | − | 23.8375i | −1.37304 | − | 1.02675i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.22594 | − | 3.85543i | −0.0957004 | − | 0.165758i | 0.814200 | − | 0.580584i | \(-0.197176\pi\) |
−0.909901 | + | 0.414826i | \(0.863842\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.566385 | + | 1.20911i | −0.0243059 | + | 0.0518877i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.58754i | − | 0.238906i | −0.992840 | − | 0.119453i | \(-0.961886\pi\) | ||
0.992840 | − | 0.119453i | \(-0.0381141\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.7889 | + | 9.12050i | 1.05796 | + | 0.389253i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.5563 | − | 26.9444i | −0.662722 | − | 1.14787i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.4873 | − | 13.7679i | 1.16888 | − | 0.585472i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.4844 | + | 18.1594i | −0.444236 | + | 0.769440i | −0.997999 | − | 0.0632348i | \(-0.979858\pi\) |
0.553762 | + | 0.832675i | \(0.313192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.61888i | − | 0.237653i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.73271 | − | 31.8754i | −0.115375 | − | 1.34578i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6432 | − | 6.14487i | −0.448559 | − | 0.258975i | 0.258663 | − | 0.965968i | \(-0.416718\pi\) |
−0.707221 | + | 0.706992i | \(0.750052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.1250 | + | 5.67760i | 0.971158 | + | 0.238437i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.1989 | − | 21.4768i | 1.55946 | − | 0.900355i | 0.562153 | − | 0.827033i | \(-0.309973\pi\) |
0.997308 | − | 0.0733217i | \(-0.0233600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.24932 | + | 5.62799i | −0.135980 | + | 0.235524i | −0.925971 | − | 0.377594i | \(-0.876752\pi\) |
0.789991 | + | 0.613118i | \(0.210085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.02834 | − | 0.345353i | 0.168286 | − | 0.0144273i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.667135 | − | 1.15551i | 0.0277732 | − | 0.0481046i | −0.851805 | − | 0.523859i | \(-0.824492\pi\) |
0.879578 | + | 0.475755i | \(0.157825\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.695690 | + | 0.997247i | 0.0289119 | + | 0.0414442i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.8104 | − | 1.59024i | −1.11228 | − | 0.0659744i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.4119 | + | 30.2600i | −2.17068 | + | 1.25324i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.5791i | − | 0.849391i | −0.905336 | − | 0.424696i | \(-0.860381\pi\) | ||
0.905336 | − | 0.424696i | \(-0.139619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5528 | 0.682046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.4181 | + | 14.2489i | 1.25123 | + | 0.586120i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.36894 | − | 4.83181i | 0.343671 | − | 0.198419i | −0.318223 | − | 0.948016i | \(-0.603086\pi\) |
0.661894 | + | 0.749597i | \(0.269753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.3610 | + | 26.3198i | 0.751464 | + | 1.07720i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.3444 | + | 21.5608i | 1.52585 | + | 0.880951i | 0.999530 | + | 0.0306663i | \(0.00976291\pi\) |
0.526323 | + | 0.850285i | \(0.323570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0495i | 0.980999i | 0.871442 | + | 0.490499i | \(0.163186\pi\) | ||||
−0.871442 | + | 0.490499i | \(0.836814\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.39087 | + | 13.8415i | 0.0973636 | + | 0.563670i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.78982 | + | 6.56417i | 0.153824 | + | 0.266431i | 0.932630 | − | 0.360833i | \(-0.117508\pi\) |
−0.778806 | + | 0.627265i | \(0.784174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.9633 | − | 10.8367i | −0.808955 | − | 0.439125i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.3423 | + | 8.28054i | −0.580228 | + | 0.334995i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.1812 | + | 23.1986i | 1.62290 | + | 0.936983i | 0.986138 | + | 0.165925i | \(0.0530609\pi\) |
0.636764 | + | 0.771058i | \(0.280272\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.36960 | 0.0551380 | 0.0275690 | − | 0.999620i | \(-0.491223\pi\) | ||||
0.0275690 | + | 0.999620i | \(0.491223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0178 | + | 7.51581i | 0.523228 | + | 0.302086i | 0.738255 | − | 0.674522i | \(-0.235650\pi\) |
−0.215026 | + | 0.976608i | \(0.568984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.77196 | − | 3.73268i | 0.151364 | − | 0.149787i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.6479 | − | 17.8554i | 1.42820 | − | 0.715362i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.9820 | + | 26.2238i | 2.23571 | + | 1.04728i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.5658 | −1.17886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.30638 | 0.171434 | 0.0857172 | − | 0.996320i | \(-0.472682\pi\) | ||||
0.0857172 | + | 0.996320i | \(0.472682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.3755 | − | 16.5711i | −1.40605 | − | 0.658640i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.98260 | + | 1.18841i | 0.395525 | + | 0.0470864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.49241 | − | 2.07661i | 0.0985983 | − | 0.0821493i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9310 | − | 6.31100i | −0.431747 | − | 0.249270i | 0.268343 | − | 0.963323i | \(-0.413524\pi\) |
−0.700091 | + | 0.714054i | \(0.746857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2411 | 1.15316 | 0.576578 | − | 0.817042i | \(-0.304388\pi\) | ||||
0.576578 | + | 0.817042i | \(0.304388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.6985 | − | 7.33150i | −0.499231 | − | 0.288231i | 0.229165 | − | 0.973388i | \(-0.426400\pi\) |
−0.728396 | + | 0.685157i | \(0.759734\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.28531 | + | 4.20617i | −0.285973 | + | 0.165107i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.3035 | − | 6.31537i | 0.403826 | − | 0.247519i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.0248 | + | 27.7557i | 0.627098 | + | 1.08617i | 0.988131 | + | 0.153613i | \(0.0490910\pi\) |
−0.361033 | + | 0.932553i | \(0.617576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.7232 | + | 4.61595i | −1.04257 | + | 0.180085i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.0951i | 1.71770i | 0.512225 | + | 0.858851i | \(0.328821\pi\) | ||||
−0.512225 | + | 0.858851i | \(0.671179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9096 | − | 17.2683i | −1.16335 | − | 0.671660i | −0.211245 | − | 0.977433i | \(-0.567752\pi\) |
−0.952104 | + | 0.305773i | \(0.901085\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.62300 | + | 6.62690i | 0.179542 | + | 0.257368i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.38401 | + | 2.53111i | −0.169750 | + | 0.0980050i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.0681 | + | 10.8059i | 0.891866 | + | 0.417780i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.0651 | 1.93274 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0196i | 0.424773i | 0.977186 | + | 0.212386i | \(0.0681235\pi\) | ||||
−0.977186 | + | 0.212386i | \(0.931876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.55993 | + | 3.78738i | −0.252119 | + | 0.145561i | −0.620734 | − | 0.784021i | \(-0.713165\pi\) |
0.368615 | + | 0.929582i | \(0.379832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.65334 | − | 27.8742i | 0.0634495 | − | 1.06971i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8022 | − | 24.0853i | −0.643862 | − | 0.922952i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6985 | − | 21.9945i | 0.485896 | − | 0.841596i | −0.513973 | − | 0.857807i | \(-0.671827\pi\) |
0.999869 | + | 0.0162102i | \(0.00516008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.7957 | + | 3.32600i | −1.48015 | + | 0.126895i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.64258 | − | 13.2373i | 0.291159 | − | 0.504303i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.43241 | + | 1.40435i | −0.0925332 | + | 0.0534241i | −0.545553 | − | 0.838077i | \(-0.683680\pi\) |
0.453019 | + | 0.891501i | \(0.350347\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.8519 | − | 5.03539i | 1.70378 | − | 0.191279i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.571489 | + | 0.329949i | 0.0216467 | + | 0.0124977i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.79679 | − | 44.2873i | −0.143608 | − | 1.67510i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 18.1659i | − | 0.686115i | −0.939314 | − | 0.343058i | \(-0.888537\pi\) | ||
0.939314 | − | 0.343058i | \(-0.111463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.5654 | − | 49.4767i | 1.07736 | − | 1.86605i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.0965 | + | 21.8186i | 1.24472 | + | 0.820571i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0139 | + | 26.0048i | 0.563858 | + | 0.976631i | 0.997155 | + | 0.0753797i | \(0.0240169\pi\) |
−0.433297 | + | 0.901251i | \(0.642650\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0366 | + | 32.7148i | −0.451409 | + | 1.22690i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.69324i | − | 0.100863i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.57138 | − | 11.8936i | 0.208067 | − | 0.444176i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.687643 | + | 1.19103i | 0.0256447 | + | 0.0444180i | 0.878563 | − | 0.477627i | \(-0.158503\pi\) |
−0.852918 | + | 0.522045i | \(0.825169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.37697 | + | 4.69677i | −0.349217 | + | 0.174917i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.40378 | − | 12.0465i | −0.312540 | − | 0.448015i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.6733 | −1.24887 | −0.624436 | − | 0.781076i | \(-0.714671\pi\) | ||||
−0.624436 | + | 0.781076i | \(0.714671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.5227 | + | 13.2545i | −0.871211 | + | 0.490908i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.35438 | + | 11.0061i | −0.235025 | + | 0.407075i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.37999 | + | 14.5146i | 0.309522 | + | 0.536108i | 0.978258 | − | 0.207392i | \(-0.0664977\pi\) |
−0.668736 | + | 0.743500i | \(0.733164\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.3121 | + | 23.0572i | 0.490358 | + | 0.849325i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.3091 | − | 33.4444i | 0.710298 | − | 1.23027i | −0.254448 | − | 0.967087i | \(-0.581894\pi\) |
0.964745 | − | 0.263185i | \(-0.0847730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.5563 | + | 1.33366i | −0.571476 | + | 0.0489933i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.3068 | −1.07516 | −0.537582 | − | 0.843212i | \(-0.680662\pi\) | ||||
−0.537582 | + | 0.843212i | \(0.680662\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.3969 | − | 19.4936i | 0.856048 | − | 0.713234i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.6192 | − | 11.3296i | 0.826488 | − | 0.413974i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.94534 | − | 10.2976i | −0.216949 | − | 0.375766i | 0.736925 | − | 0.675974i | \(-0.236277\pi\) |
−0.953874 | + | 0.300209i | \(0.902944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.84645 | + | 0.864939i | 0.0672884 | + | 0.0315201i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.9755i | 1.63466i | 0.576167 | + | 0.817332i | \(0.304548\pi\) | ||||
−0.576167 | + | 0.817332i | \(0.695452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.26678 | − | 9.10861i | 0.154874 | − | 0.330622i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.22673 | + | 2.12476i | 0.0444690 | + | 0.0770226i | 0.887403 | − | 0.460994i | \(-0.152507\pi\) |
−0.842934 | + | 0.538017i | \(0.819174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.0951 | − | 20.4992i | −1.12572 | − | 0.742120i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.06233 | − | 1.84000i | 0.0383584 | − | 0.0664386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 18.4658i | − | 0.665894i | −0.942946 | − | 0.332947i | \(-0.891957\pi\) | ||
0.942946 | − | 0.332947i | \(-0.108043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.21043 | − | 0.789620i | 0.331705 | − | 0.0284375i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.53190 | + | 0.884443i | 0.0550986 | + | 0.0318112i | 0.527296 | − | 0.849682i | \(-0.323206\pi\) |
−0.472198 | + | 0.881493i | \(0.656539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.09589 | − | 41.6960i | −0.0393149 | − | 1.49584i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.10430 | + | 0.637571i | −0.0395658 | + | 0.0228433i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.07453 | − | 5.32524i | 0.110015 | − | 0.190552i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.9132 | − | 6.53593i | 0.890326 | − | 0.233575i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.5888 | + | 46.0531i | −0.947788 | + | 1.64162i | −0.197718 | + | 0.980259i | \(0.563353\pi\) |
−0.750070 | + | 0.661358i | \(0.769980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.7459 | + | 15.1702i | −0.774175 | + | 0.540073i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.927084 | + | 15.6300i | −0.0329633 | + | 0.555738i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9506 | + | 6.32231i | −0.388866 | + | 0.224512i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.8237i | − | 1.19810i | −0.800713 | − | 0.599049i | \(-0.795546\pi\) | ||
0.800713 | − | 0.599049i | \(-0.204454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.4578 | 1.32516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.6101 | + | 42.4273i | −0.551557 | + | 1.49910i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −44.5157 | + | 25.7012i | −1.57093 | + | 0.906974i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.94653 | + | 6.93881i | −0.350135 | + | 0.244258i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.8866 | − | 13.7909i | −0.839807 | − | 0.484863i | 0.0173917 | − | 0.999849i | \(-0.494464\pi\) |
−0.857199 | + | 0.514986i | \(0.827797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.97378i | 0.139538i | 0.997563 | + | 0.0697692i | \(0.0222263\pi\) | ||||
−0.997563 | + | 0.0697692i | \(0.977774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.2628 | + | 1.90861i | −0.780790 | + | 0.0669380i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.2787 | − | 21.2674i | −0.429579 | − | 0.744052i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.17443 | + | 6.76535i | −0.320580 | + | 0.236401i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.8143 | − | 26.4509i | 1.59893 | − | 0.923143i | 0.607237 | − | 0.794521i | \(-0.292278\pi\) |
0.991694 | − | 0.128623i | \(-0.0410556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.98823 | − | 5.18936i | −0.313310 | − | 0.180890i | 0.335097 | − | 0.942184i | \(-0.391231\pi\) |
−0.648407 | + | 0.761294i | \(0.724564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.8249 | 1.76736 | 0.883678 | − | 0.468095i | \(-0.155059\pi\) | ||||
0.883678 | + | 0.468095i | \(0.155059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.33850 | + | 0.772785i | 0.0464881 | + | 0.0268399i | 0.523064 | − | 0.852293i | \(-0.324789\pi\) |
−0.476576 | + | 0.879133i | \(0.658122\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0340 | + | 15.8168i | 0.382764 | + | 0.548679i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.2097 | − | 13.6171i | −0.630927 | − | 0.471805i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.61584 | + | 13.2174i | −0.124982 | + | 0.456860i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0738 | −0.831118 | −0.415559 | − | 0.909566i | \(-0.636414\pi\) | ||||
−0.415559 | + | 0.909566i | \(0.636414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.43009 | 0.152762 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.5603 | + | 35.3525i | −0.570366 | + | 1.21760i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.4680 | − | 25.2785i | 1.73410 | − | 0.868581i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.9857 | − | 18.1279i | 0.891827 | − | 0.622148i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.05016 | − | 4.64776i | −0.275956 | − | 0.159323i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.6929 | −0.571555 | −0.285777 | − | 0.958296i | \(-0.592252\pi\) | ||||
−0.285777 | + | 0.958296i | \(0.592252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.3974 | − | 14.0858i | −0.833398 | − | 0.481163i | 0.0216164 | − | 0.999766i | \(-0.493119\pi\) |
−0.855015 | + | 0.518604i | \(0.826452\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.0897 | + | 27.7646i | −1.64080 | + | 0.947315i | −0.660248 | + | 0.751048i | \(0.729549\pi\) |
−0.980550 | + | 0.196268i | \(0.937118\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.444138 | + | 0.818189i | −0.0151362 | + | 0.0278838i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.6517 | + | 25.3774i | 0.498748 | + | 0.863857i | 0.999999 | − | 0.00144510i | \(-0.000459991\pi\) |
−0.501251 | + | 0.865302i | \(0.667127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.954060 | + | 11.1285i | 0.0324016 | + | 0.377944i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.0728i | 2.24137i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.82342 | − | 3.36215i | −0.197319 | − | 0.113922i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.2671 | + | 24.3253i | 0.685939 | + | 0.823286i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.2276 | − | 24.9574i | 1.45969 | − | 0.842753i | 0.460695 | − | 0.887558i | \(-0.347600\pi\) |
0.998996 | + | 0.0448051i | \(0.0142667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.5209 | + | 26.7292i | −0.422318 | + | 0.901554i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.0594 | 1.92238 | 0.961191 | − | 0.275885i | \(-0.0889709\pi\) | ||||
0.961191 | + | 0.275885i | \(0.0889709\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.2846i | − | 1.32203i | −0.750371 | − | 0.661017i | \(-0.770125\pi\) | ||
0.750371 | − | 0.661017i | \(-0.229875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6684 | + | 7.89144i | −0.458939 | + | 0.264969i | −0.711598 | − | 0.702587i | \(-0.752028\pi\) |
0.252659 | + | 0.967555i | \(0.418695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.0775 | + | 1.30951i | 0.740454 | + | 0.0439197i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.1686 | + | 38.9732i | −1.11119 | + | 1.30565i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.1904 | + | 62.6835i | −1.21106 | + | 2.09762i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.216995 | + | 2.53111i | 0.00724524 | + | 0.0845113i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.53593 | − | 11.3206i | 0.217985 | − | 0.377562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.9402 | + | 17.2860i | −0.997451 | + | 0.575879i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.7572 | − | 8.55349i | −0.524367 | − | 0.284642i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.8965 | − | 23.0343i | −1.32474 | − | 0.764840i | −0.340261 | − | 0.940331i | \(-0.610516\pi\) |
−0.984481 | + | 0.175490i | \(0.943849\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44.2930 | + | 7.65081i | −1.46911 | + | 0.253761i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6500i | 0.882953i | 0.897273 | + | 0.441477i | \(0.145545\pi\) | ||||
−0.897273 | + | 0.441477i | \(0.854455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.8614 | − | 49.9893i | 0.955172 | − | 1.65441i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.1476 | − | 19.6083i | 1.29277 | − | 0.647525i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.65362 | + | 2.86415i | 0.0545478 | + | 0.0944795i | 0.892010 | − | 0.452016i | \(-0.149295\pi\) |
−0.837462 | + | 0.546495i | \(0.815962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.6062 | + | 12.4632i | 0.876704 | + | 0.410677i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.55303i | 0.0511185i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.10616 | − | 11.1603i | 0.134864 | − | 0.366551i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3962 | + | 19.7388i | 0.373898 | + | 0.647610i | 0.990161 | − | 0.139930i | \(-0.0446878\pi\) |
−0.616264 | + | 0.787540i | \(0.711354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.3810 | − | 17.3165i | 1.32343 | − | 0.567526i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.5935 | + | 33.2018i | −1.55814 | + | 1.08698i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.2636 | 1.08667 | 0.543336 | − | 0.839515i | \(-0.317161\pi\) | ||||
0.543336 | + | 0.839515i | \(0.317161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.01266 | + | 11.8120i | 0.0330468 | + | 0.385471i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.1677 | + | 40.1277i | −0.755246 | + | 1.30812i | 0.190006 | + | 0.981783i | \(0.439149\pi\) |
−0.945252 | + | 0.326341i | \(0.894184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.103737 | + | 0.179677i | 0.00337813 | + | 0.00585109i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.8743 | + | 36.1553i | 0.678322 | + | 1.17489i | 0.975486 | + | 0.220062i | \(0.0706259\pi\) |
−0.297164 | + | 0.954826i | \(0.596041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.49117 | − | 11.2430i | 0.210712 | − | 0.364965i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.92887 | − | 22.4991i | −0.0625480 | − | 0.729584i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.47667 | −0.177407 | −0.0887034 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887034 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.0394 | − | 27.9319i | 1.29429 | − | 0.902910i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.8655 | − | 15.0739i | −0.738366 | − | 0.486761i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0227 | − | 20.8239i | −0.387829 | − | 0.671740i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.90491 | + | 26.9209i | −0.319181 | + | 0.867514i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 60.2148i | − | 1.93638i | −0.250223 | − | 0.968188i | \(-0.580504\pi\) | ||
0.250223 | − | 0.968188i | \(-0.419496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.9796 | + | 14.9803i | 1.02733 | + | 0.481236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.2636 | + | 22.9732i | 0.425650 | + | 0.737247i | 0.996481 | − | 0.0838207i | \(-0.0267123\pi\) |
−0.570831 | + | 0.821067i | \(0.693379\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.2321 | − | 1.43732i | −0.776846 | − | 0.0460782i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.07480 | + | 5.32572i | −0.0983717 | + | 0.170385i | −0.911011 | − | 0.412383i | \(-0.864697\pi\) |
0.812639 | + | 0.582767i | \(0.198030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 85.6888i | 2.73863i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.6146 | − | 7.18816i | 1.32865 | − | 0.229500i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.4877 | + | 22.7982i | 1.25946 | + | 0.727150i | 0.972970 | − | 0.230932i | \(-0.0741776\pi\) |
0.286492 | + | 0.958083i | \(0.407511\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.38842 | + | 52.8259i | 0.0441938 | + | 1.68147i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.46033 | + | 1.99783i | −0.110032 | + | 0.0635271i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0880 | − | 19.2049i | 0.352221 | − | 0.610065i | −0.634417 | − | 0.772991i | \(-0.718760\pi\) |
0.986638 | + | 0.162926i | \(0.0520931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.993401 | − | 11.5874i | −0.0315246 | − | 0.367715i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.84211 | + | 10.1188i | −0.185021 | + | 0.320466i | −0.943584 | − | 0.331134i | \(-0.892569\pi\) |
0.758562 | + | 0.651600i | \(0.225902\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.2672 | + | 33.6173i | 1.05253 | + | 1.06360i |
(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 | 2100.2.bo.i.1949.3 | 32 | ||
3.2 | odd | 2 | inner | 2100.2.bo.i.1949.12 | 32 | ||
5.2 | odd | 4 | 2100.2.bi.m.101.2 | yes | 16 | ||
5.3 | odd | 4 | 2100.2.bi.l.101.7 | yes | 16 | ||
5.4 | even | 2 | inner | 2100.2.bo.i.1949.14 | 32 | ||
7.5 | odd | 6 | inner | 2100.2.bo.i.1349.5 | 32 | ||
15.2 | even | 4 | 2100.2.bi.m.101.6 | yes | 16 | ||
15.8 | even | 4 | 2100.2.bi.l.101.3 | ✓ | 16 | ||
15.14 | odd | 2 | inner | 2100.2.bo.i.1949.5 | 32 | ||
21.5 | even | 6 | inner | 2100.2.bo.i.1349.14 | 32 | ||
35.12 | even | 12 | 2100.2.bi.m.1601.6 | yes | 16 | ||
35.19 | odd | 6 | inner | 2100.2.bo.i.1349.12 | 32 | ||
35.33 | even | 12 | 2100.2.bi.l.1601.3 | yes | 16 | ||
105.47 | odd | 12 | 2100.2.bi.m.1601.2 | yes | 16 | ||
105.68 | odd | 12 | 2100.2.bi.l.1601.7 | yes | 16 | ||
105.89 | even | 6 | inner | 2100.2.bo.i.1349.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.3 | ✓ | 16 | 15.8 | even | 4 | ||
2100.2.bi.l.101.7 | yes | 16 | 5.3 | odd | 4 | ||
2100.2.bi.l.1601.3 | yes | 16 | 35.33 | even | 12 | ||
2100.2.bi.l.1601.7 | yes | 16 | 105.68 | odd | 12 | ||
2100.2.bi.m.101.2 | yes | 16 | 5.2 | odd | 4 | ||
2100.2.bi.m.101.6 | yes | 16 | 15.2 | even | 4 | ||
2100.2.bi.m.1601.2 | yes | 16 | 105.47 | odd | 12 | ||
2100.2.bi.m.1601.6 | yes | 16 | 35.12 | even | 12 | ||
2100.2.bo.i.1349.3 | 32 | 105.89 | even | 6 | inner | ||
2100.2.bo.i.1349.5 | 32 | 7.5 | odd | 6 | inner | ||
2100.2.bo.i.1349.12 | 32 | 35.19 | odd | 6 | inner | ||
2100.2.bo.i.1349.14 | 32 | 21.5 | even | 6 | inner | ||
2100.2.bo.i.1949.3 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.bo.i.1949.5 | 32 | 15.14 | odd | 2 | inner | ||
2100.2.bo.i.1949.12 | 32 | 3.2 | odd | 2 | inner | ||
2100.2.bo.i.1949.14 | 32 | 5.4 | even | 2 | inner |