Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(626,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.626");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 626.14 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.a.626.13 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.42582 | −1.00821 | −0.504104 | − | 0.863643i | \(-0.668177\pi\) | ||||
−0.504104 | + | 0.863643i | \(0.668177\pi\) | |||||||
\(3\) | − | 1.05301i | − | 0.607954i | −0.952679 | − | 0.303977i | \(-0.901685\pi\) | ||
0.952679 | − | 0.303977i | \(-0.0983146\pi\) | |||||||
\(4\) | 0.0329672 | 0.0164836 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.50140i | 0.612944i | ||||||||
\(7\) | − | 0.901840i | − | 0.340863i | −0.985369 | − | 0.170432i | \(-0.945484\pi\) | ||
0.985369 | − | 0.170432i | \(-0.0545162\pi\) | |||||||
\(8\) | 2.80464 | 0.991589 | ||||||||
\(9\) | 1.89118 | 0.630392 | ||||||||
\(10\) | 1.42582 | 0.450884 | ||||||||
\(11\) | 2.88768 | + | 1.63135i | 0.870668 | + | 0.491871i | ||||
\(12\) | − | 0.0347147i | − | 0.0100213i | ||||||
\(13\) | −5.62988 | −1.56145 | −0.780724 | − | 0.624876i | \(-0.785149\pi\) | ||||
−0.780724 | + | 0.624876i | \(0.785149\pi\) | |||||||
\(14\) | 1.28586i | 0.343661i | ||||||||
\(15\) | 1.05301i | 0.271885i | ||||||||
\(16\) | −4.06485 | −1.01621 | ||||||||
\(17\) | 2.98133i | 0.723079i | 0.932357 | + | 0.361540i | \(0.117749\pi\) | ||||
−0.932357 | + | 0.361540i | \(0.882251\pi\) | |||||||
\(18\) | −2.69648 | −0.635566 | ||||||||
\(19\) | −0.563246 | + | 4.32236i | −0.129218 | + | 0.991616i | ||||
\(20\) | −0.0329672 | −0.00737169 | ||||||||
\(21\) | −0.949644 | −0.207229 | ||||||||
\(22\) | −4.11732 | − | 2.32602i | −0.877815 | − | 0.495908i | ||||
\(23\) | −5.84146 | −1.21803 | −0.609014 | − | 0.793159i | \(-0.708435\pi\) | ||||
−0.609014 | + | 0.793159i | \(0.708435\pi\) | |||||||
\(24\) | − | 2.95330i | − | 0.602841i | ||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.02721 | 1.57426 | ||||||||
\(27\) | − | 5.15044i | − | 0.991203i | ||||||
\(28\) | − | 0.0297311i | − | 0.00561866i | ||||||
\(29\) | 2.10889 | 0.391610 | 0.195805 | − | 0.980643i | \(-0.437268\pi\) | ||||
0.195805 | + | 0.980643i | \(0.437268\pi\) | |||||||
\(30\) | − | 1.50140i | − | 0.274117i | ||||||
\(31\) | − | 9.55444i | − | 1.71603i | −0.513626 | − | 0.858014i | \(-0.671698\pi\) | ||
0.513626 | − | 0.858014i | \(-0.328302\pi\) | |||||||
\(32\) | 0.186472 | 0.0329639 | ||||||||
\(33\) | 1.71783 | − | 3.04075i | 0.299035 | − | 0.529326i | ||||
\(34\) | − | 4.25085i | − | 0.729014i | ||||||
\(35\) | 0.901840i | 0.152439i | ||||||||
\(36\) | 0.0623468 | 0.0103911 | ||||||||
\(37\) | 8.43084i | 1.38602i | 0.720927 | + | 0.693011i | \(0.243716\pi\) | ||||
−0.720927 | + | 0.693011i | \(0.756284\pi\) | |||||||
\(38\) | 0.803089 | − | 6.16291i | 0.130278 | − | 0.999756i | ||||
\(39\) | 5.92831i | 0.949289i | ||||||||
\(40\) | −2.80464 | −0.443452 | ||||||||
\(41\) | −4.89924 | −0.765132 | −0.382566 | − | 0.923928i | \(-0.624960\pi\) | ||||
−0.382566 | + | 0.923928i | \(0.624960\pi\) | |||||||
\(42\) | 1.35402 | 0.208930 | ||||||||
\(43\) | 10.7286i | 1.63610i | 0.575150 | + | 0.818048i | \(0.304944\pi\) | ||||
−0.575150 | + | 0.818048i | \(0.695056\pi\) | |||||||
\(44\) | 0.0951988 | + | 0.0537811i | 0.0143518 | + | 0.00810781i | ||||
\(45\) | −1.89118 | −0.281920 | ||||||||
\(46\) | 8.32888 | 1.22803 | ||||||||
\(47\) | 6.27493 | 0.915292 | 0.457646 | − | 0.889134i | \(-0.348693\pi\) | ||||
0.457646 | + | 0.889134i | \(0.348693\pi\) | |||||||
\(48\) | 4.28032i | 0.617810i | ||||||||
\(49\) | 6.18669 | 0.883812 | ||||||||
\(50\) | −1.42582 | −0.201642 | ||||||||
\(51\) | 3.13937 | 0.439599 | ||||||||
\(52\) | −0.185602 | −0.0257383 | ||||||||
\(53\) | 0.813546i | 0.111749i | 0.998438 | + | 0.0558746i | \(0.0177947\pi\) | ||||
−0.998438 | + | 0.0558746i | \(0.982205\pi\) | |||||||
\(54\) | 7.34361i | 0.999339i | ||||||||
\(55\) | −2.88768 | − | 1.63135i | −0.389375 | − | 0.219971i | ||||
\(56\) | − | 2.52933i | − | 0.337996i | ||||||
\(57\) | 4.55147 | + | 0.593103i | 0.602857 | + | 0.0785584i | ||||
\(58\) | −3.00690 | −0.394825 | ||||||||
\(59\) | 13.9409i | 1.81494i | 0.420112 | + | 0.907472i | \(0.361991\pi\) | ||||
−0.420112 | + | 0.907472i | \(0.638009\pi\) | |||||||
\(60\) | 0.0347147i | 0.00448165i | ||||||||
\(61\) | 11.3812i | 1.45722i | 0.684930 | + | 0.728609i | \(0.259833\pi\) | ||||
−0.684930 | + | 0.728609i | \(0.740167\pi\) | |||||||
\(62\) | 13.6229i | 1.73011i | ||||||||
\(63\) | − | 1.70554i | − | 0.214877i | ||||||
\(64\) | 7.86382 | 0.982977 | ||||||||
\(65\) | 5.62988 | 0.698301 | ||||||||
\(66\) | −2.44931 | + | 4.33556i | −0.301490 | + | 0.533671i | ||||
\(67\) | 5.05376i | 0.617415i | 0.951157 | + | 0.308707i | \(0.0998964\pi\) | ||||
−0.951157 | + | 0.308707i | \(0.900104\pi\) | |||||||
\(68\) | 0.0982862i | 0.0119190i | ||||||||
\(69\) | 6.15110i | 0.740506i | ||||||||
\(70\) | − | 1.28586i | − | 0.153690i | ||||||
\(71\) | − | 2.36569i | − | 0.280756i | −0.990098 | − | 0.140378i | \(-0.955168\pi\) | ||
0.990098 | − | 0.140378i | \(-0.0448317\pi\) | |||||||
\(72\) | 5.30406 | 0.625090 | ||||||||
\(73\) | − | 4.24232i | − | 0.496526i | −0.968693 | − | 0.248263i | \(-0.920140\pi\) | ||
0.968693 | − | 0.248263i | \(-0.0798598\pi\) | |||||||
\(74\) | − | 12.0209i | − | 1.39740i | ||||||
\(75\) | − | 1.05301i | − | 0.121591i | ||||||
\(76\) | −0.0185687 | + | 0.142496i | −0.00212997 | + | 0.0163454i | ||||
\(77\) | 1.47122 | − | 2.60422i | 0.167661 | − | 0.296779i | ||||
\(78\) | − | 8.45271i | − | 0.957081i | ||||||
\(79\) | 5.64937 | 0.635604 | 0.317802 | − | 0.948157i | \(-0.397055\pi\) | ||||
0.317802 | + | 0.948157i | \(0.397055\pi\) | |||||||
\(80\) | 4.06485 | 0.454464 | ||||||||
\(81\) | 0.250069 | 0.0277855 | ||||||||
\(82\) | 6.98544 | 0.771413 | ||||||||
\(83\) | − | 14.6416i | − | 1.60712i | −0.595223 | − | 0.803561i | \(-0.702936\pi\) | ||
0.595223 | − | 0.803561i | \(-0.297064\pi\) | |||||||
\(84\) | −0.0313071 | −0.00341589 | ||||||||
\(85\) | − | 2.98133i | − | 0.323371i | ||||||
\(86\) | − | 15.2971i | − | 1.64953i | ||||||
\(87\) | − | 2.22067i | − | 0.238081i | ||||||
\(88\) | 8.09889 | + | 4.57535i | 0.863345 | + | 0.487734i | ||||
\(89\) | 13.7701i | 1.45962i | 0.683648 | + | 0.729812i | \(0.260393\pi\) | ||||
−0.683648 | + | 0.729812i | \(0.739607\pi\) | |||||||
\(90\) | 2.69648 | 0.284234 | ||||||||
\(91\) | 5.07725i | 0.532240i | ||||||||
\(92\) | −0.192577 | −0.0200775 | ||||||||
\(93\) | −10.0609 | −1.04327 | ||||||||
\(94\) | −8.94693 | −0.922805 | ||||||||
\(95\) | 0.563246 | − | 4.32236i | 0.0577879 | − | 0.443464i | ||||
\(96\) | − | 0.196356i | − | 0.0200405i | ||||||
\(97\) | 9.17901i | 0.931987i | 0.884788 | + | 0.465994i | \(0.154303\pi\) | ||||
−0.884788 | + | 0.465994i | \(0.845697\pi\) | |||||||
\(98\) | −8.82111 | −0.891067 | ||||||||
\(99\) | 5.46111 | + | 3.08517i | 0.548862 | + | 0.310071i | ||||
\(100\) | 0.0329672 | 0.00329672 | ||||||||
\(101\) | 4.14181i | 0.412126i | 0.978539 | + | 0.206063i | \(0.0660652\pi\) | ||||
−0.978539 | + | 0.206063i | \(0.933935\pi\) | |||||||
\(102\) | −4.47617 | −0.443207 | ||||||||
\(103\) | 4.07026i | 0.401054i | 0.979688 | + | 0.200527i | \(0.0642655\pi\) | ||||
−0.979688 | + | 0.200527i | \(0.935735\pi\) | |||||||
\(104\) | −15.7898 | −1.54831 | ||||||||
\(105\) | 0.949644 | 0.0926758 | ||||||||
\(106\) | − | 1.15997i | − | 0.112666i | ||||||
\(107\) | −4.87597 | −0.471378 | −0.235689 | − | 0.971829i | \(-0.575735\pi\) | ||||
−0.235689 | + | 0.971829i | \(0.575735\pi\) | |||||||
\(108\) | − | 0.169796i | − | 0.0163386i | ||||||
\(109\) | 19.4459 | 1.86258 | 0.931289 | − | 0.364281i | \(-0.118685\pi\) | ||||
0.931289 | + | 0.364281i | \(0.118685\pi\) | |||||||
\(110\) | 4.11732 | + | 2.32602i | 0.392571 | + | 0.221777i | ||||
\(111\) | 8.87774 | 0.842637 | ||||||||
\(112\) | 3.66584i | 0.346389i | ||||||||
\(113\) | − | 7.25680i | − | 0.682662i | −0.939943 | − | 0.341331i | \(-0.889122\pi\) | ||
0.939943 | − | 0.341331i | \(-0.110878\pi\) | |||||||
\(114\) | −6.48959 | − | 0.845659i | −0.607806 | − | 0.0792032i | ||||
\(115\) | 5.84146 | 0.544719 | ||||||||
\(116\) | 0.0695241 | 0.00645515 | ||||||||
\(117\) | −10.6471 | −0.984324 | ||||||||
\(118\) | − | 19.8772i | − | 1.82984i | ||||||
\(119\) | 2.68868 | 0.246471 | ||||||||
\(120\) | 2.95330i | 0.269599i | ||||||||
\(121\) | 5.67738 | + | 9.42164i | 0.516126 | + | 0.856513i | ||||
\(122\) | − | 16.2276i | − | 1.46918i | ||||||
\(123\) | 5.15893i | 0.465165i | ||||||||
\(124\) | − | 0.314983i | − | 0.0282863i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.43179i | 0.216641i | ||||||||
\(127\) | 3.03121 | 0.268976 | 0.134488 | − | 0.990915i | \(-0.457061\pi\) | ||||
0.134488 | + | 0.990915i | \(0.457061\pi\) | |||||||
\(128\) | −11.5853 | −1.02401 | ||||||||
\(129\) | 11.2973 | 0.994672 | ||||||||
\(130\) | −8.02721 | −0.704032 | ||||||||
\(131\) | − | 5.47883i | − | 0.478687i | −0.970935 | − | 0.239344i | \(-0.923068\pi\) | ||
0.970935 | − | 0.239344i | \(-0.0769323\pi\) | |||||||
\(132\) | 0.0566319 | − | 0.100245i | 0.00492918 | − | 0.00872521i | ||||
\(133\) | 3.89807 | + | 0.507958i | 0.338006 | + | 0.0440455i | ||||
\(134\) | − | 7.20576i | − | 0.622483i | ||||||
\(135\) | 5.15044i | 0.443280i | ||||||||
\(136\) | 8.36156i | 0.716998i | ||||||||
\(137\) | −1.26081 | −0.107718 | −0.0538590 | − | 0.998549i | \(-0.517152\pi\) | ||||
−0.0538590 | + | 0.998549i | \(0.517152\pi\) | |||||||
\(138\) | − | 8.77037i | − | 0.746584i | ||||||
\(139\) | 16.3563i | 1.38733i | 0.720300 | + | 0.693663i | \(0.244004\pi\) | ||||
−0.720300 | + | 0.693663i | \(0.755996\pi\) | |||||||
\(140\) | 0.0297311i | 0.00251274i | ||||||||
\(141\) | − | 6.60755i | − | 0.556456i | ||||||
\(142\) | 3.37305i | 0.283060i | ||||||||
\(143\) | −16.2573 | − | 9.18432i | −1.35950 | − | 0.768031i | ||||
\(144\) | −7.68734 | −0.640612 | ||||||||
\(145\) | −2.10889 | −0.175134 | ||||||||
\(146\) | 6.04880i | 0.500602i | ||||||||
\(147\) | − | 6.51463i | − | 0.537317i | ||||||
\(148\) | 0.277941i | 0.0228466i | ||||||||
\(149\) | − | 18.0379i | − | 1.47772i | −0.673858 | − | 0.738860i | \(-0.735364\pi\) | ||
0.673858 | − | 0.738860i | \(-0.264636\pi\) | |||||||
\(150\) | 1.50140i | 0.122589i | ||||||||
\(151\) | 8.10849 | 0.659860 | 0.329930 | − | 0.944005i | \(-0.392975\pi\) | ||||
0.329930 | + | 0.944005i | \(0.392975\pi\) | |||||||
\(152\) | −1.57970 | + | 12.1226i | −0.128131 | + | 0.983276i | ||||
\(153\) | 5.63822i | 0.455823i | ||||||||
\(154\) | −2.09769 | + | 3.71316i | −0.169037 | + | 0.299215i | ||||
\(155\) | 9.55444i | 0.767431i | ||||||||
\(156\) | 0.195440i | 0.0156477i | ||||||||
\(157\) | −12.7219 | −1.01532 | −0.507659 | − | 0.861558i | \(-0.669489\pi\) | ||||
−0.507659 | + | 0.861558i | \(0.669489\pi\) | |||||||
\(158\) | −8.05500 | −0.640821 | ||||||||
\(159\) | 0.856670 | 0.0679383 | ||||||||
\(160\) | −0.186472 | −0.0147419 | ||||||||
\(161\) | 5.26806i | 0.415181i | ||||||||
\(162\) | −0.356554 | −0.0280135 | ||||||||
\(163\) | 24.4172 | 1.91250 | 0.956250 | − | 0.292550i | \(-0.0945036\pi\) | ||||
0.956250 | + | 0.292550i | \(0.0945036\pi\) | |||||||
\(164\) | −0.161514 | −0.0126121 | ||||||||
\(165\) | −1.71783 | + | 3.04075i | −0.133733 | + | 0.236722i | ||||
\(166\) | 20.8763i | 1.62031i | ||||||||
\(167\) | −1.19788 | −0.0926946 | −0.0463473 | − | 0.998925i | \(-0.514758\pi\) | ||||
−0.0463473 | + | 0.998925i | \(0.514758\pi\) | |||||||
\(168\) | −2.66341 | −0.205486 | ||||||||
\(169\) | 18.6956 | 1.43812 | ||||||||
\(170\) | 4.25085i | 0.326025i | ||||||||
\(171\) | −1.06520 | + | 8.17433i | −0.0814577 | + | 0.625107i | ||||
\(172\) | 0.353692i | 0.0269688i | ||||||||
\(173\) | 5.36104 | 0.407592 | 0.203796 | − | 0.979013i | \(-0.434672\pi\) | ||||
0.203796 | + | 0.979013i | \(0.434672\pi\) | |||||||
\(174\) | 3.16628i | 0.240035i | ||||||||
\(175\) | − | 0.901840i | − | 0.0681727i | ||||||
\(176\) | −11.7380 | − | 6.63120i | −0.884783 | − | 0.499845i | ||||
\(177\) | 14.6798 | 1.10340 | ||||||||
\(178\) | − | 19.6337i | − | 1.47161i | ||||||
\(179\) | 6.25624i | 0.467613i | 0.972283 | + | 0.233807i | \(0.0751183\pi\) | ||||
−0.972283 | + | 0.233807i | \(0.924882\pi\) | |||||||
\(180\) | −0.0623468 | −0.00464706 | ||||||||
\(181\) | 6.39099i | 0.475039i | 0.971383 | + | 0.237519i | \(0.0763343\pi\) | ||||
−0.971383 | + | 0.237519i | \(0.923666\pi\) | |||||||
\(182\) | − | 7.23925i | − | 0.536609i | ||||||
\(183\) | 11.9845 | 0.885922 | ||||||||
\(184\) | −16.3832 | −1.20778 | ||||||||
\(185\) | − | 8.43084i | − | 0.619848i | ||||||
\(186\) | 14.3450 | 1.05183 | ||||||||
\(187\) | −4.86360 | + | 8.60913i | −0.355662 | + | 0.629562i | ||||
\(188\) | 0.206867 | 0.0150873 | ||||||||
\(189\) | −4.64487 | −0.337865 | ||||||||
\(190\) | −0.803089 | + | 6.16291i | −0.0582622 | + | 0.447104i | ||||
\(191\) | −11.7414 | −0.849581 | −0.424791 | − | 0.905292i | \(-0.639652\pi\) | ||||
−0.424791 | + | 0.905292i | \(0.639652\pi\) | |||||||
\(192\) | − | 8.28066i | − | 0.597605i | ||||||
\(193\) | −19.0146 | −1.36870 | −0.684351 | − | 0.729152i | \(-0.739915\pi\) | ||||
−0.684351 | + | 0.729152i | \(0.739915\pi\) | |||||||
\(194\) | − | 13.0876i | − | 0.939637i | ||||||
\(195\) | − | 5.92831i | − | 0.424535i | ||||||
\(196\) | 0.203958 | 0.0145684 | ||||||||
\(197\) | 9.02300i | 0.642862i | 0.946933 | + | 0.321431i | \(0.104164\pi\) | ||||
−0.946933 | + | 0.321431i | \(0.895836\pi\) | |||||||
\(198\) | −7.78656 | − | 4.39891i | −0.553367 | − | 0.312617i | ||||
\(199\) | −21.1949 | −1.50247 | −0.751235 | − | 0.660035i | \(-0.770541\pi\) | ||||
−0.751235 | + | 0.660035i | \(0.770541\pi\) | |||||||
\(200\) | 2.80464 | 0.198318 | ||||||||
\(201\) | 5.32164 | 0.375360 | ||||||||
\(202\) | − | 5.90549i | − | 0.415509i | ||||||
\(203\) | − | 1.90188i | − | 0.133486i | ||||||
\(204\) | 0.103496 | 0.00724618 | ||||||||
\(205\) | 4.89924 | 0.342178 | ||||||||
\(206\) | − | 5.80346i | − | 0.404346i | ||||||
\(207\) | −11.0472 | −0.767835 | ||||||||
\(208\) | 22.8846 | 1.58676 | ||||||||
\(209\) | −8.67776 | + | 11.5627i | −0.600253 | + | 0.799810i | ||||
\(210\) | −1.35402 | −0.0934365 | ||||||||
\(211\) | 7.76779 | 0.534757 | 0.267378 | − | 0.963592i | \(-0.413843\pi\) | ||||
0.267378 | + | 0.963592i | \(0.413843\pi\) | |||||||
\(212\) | 0.0268203i | 0.00184203i | ||||||||
\(213\) | −2.49109 | −0.170687 | ||||||||
\(214\) | 6.95226 | 0.475247 | ||||||||
\(215\) | − | 10.7286i | − | 0.731685i | ||||||
\(216\) | − | 14.4451i | − | 0.982867i | ||||||
\(217\) | −8.61657 | −0.584931 | ||||||||
\(218\) | −27.7264 | −1.87787 | ||||||||
\(219\) | −4.46720 | −0.301865 | ||||||||
\(220\) | −0.0951988 | − | 0.0537811i | −0.00641830 | − | 0.00362592i | ||||
\(221\) | − | 16.7845i | − | 1.12905i | ||||||
\(222\) | −12.6581 | −0.849554 | ||||||||
\(223\) | 11.8143i | 0.791146i | 0.918435 | + | 0.395573i | \(0.129454\pi\) | ||||
−0.918435 | + | 0.395573i | \(0.870546\pi\) | |||||||
\(224\) | − | 0.168168i | − | 0.0112362i | ||||||
\(225\) | 1.89118 | 0.126078 | ||||||||
\(226\) | 10.3469i | 0.688265i | ||||||||
\(227\) | 9.22668 | 0.612396 | 0.306198 | − | 0.951968i | \(-0.400943\pi\) | ||||
0.306198 | + | 0.951968i | \(0.400943\pi\) | |||||||
\(228\) | 0.150049 | + | 0.0195529i | 0.00993726 | + | 0.00129493i | ||||
\(229\) | −14.4401 | −0.954227 | −0.477113 | − | 0.878842i | \(-0.658317\pi\) | ||||
−0.477113 | + | 0.878842i | \(0.658317\pi\) | |||||||
\(230\) | −8.32888 | −0.549190 | ||||||||
\(231\) | −2.74227 | − | 1.54920i | −0.180428 | − | 0.101930i | ||||
\(232\) | 5.91466 | 0.388317 | ||||||||
\(233\) | − | 19.4161i | − | 1.27199i | −0.771693 | − | 0.635995i | \(-0.780590\pi\) | ||
0.771693 | − | 0.635995i | \(-0.219410\pi\) | |||||||
\(234\) | 15.1809 | 0.992403 | ||||||||
\(235\) | −6.27493 | −0.409331 | ||||||||
\(236\) | 0.459591i | 0.0299168i | ||||||||
\(237\) | − | 5.94883i | − | 0.386418i | ||||||
\(238\) | −3.83358 | −0.248494 | ||||||||
\(239\) | 14.2248i | 0.920123i | 0.887887 | + | 0.460062i | \(0.152173\pi\) | ||||
−0.887887 | + | 0.460062i | \(0.847827\pi\) | |||||||
\(240\) | − | 4.28032i | − | 0.276293i | ||||||
\(241\) | −22.9488 | −1.47826 | −0.739132 | − | 0.673560i | \(-0.764764\pi\) | ||||
−0.739132 | + | 0.673560i | \(0.764764\pi\) | |||||||
\(242\) | −8.09493 | − | 13.4336i | −0.520362 | − | 0.863543i | ||||
\(243\) | − | 15.7147i | − | 1.00810i | ||||||
\(244\) | 0.375208i | 0.0240202i | ||||||||
\(245\) | −6.18669 | −0.395253 | ||||||||
\(246\) | − | 7.35572i | − | 0.468984i | ||||||
\(247\) | 3.17101 | − | 24.3343i | 0.201767 | − | 1.54836i | ||||
\(248\) | − | 26.7967i | − | 1.70159i | ||||||
\(249\) | −15.4177 | −0.977056 | ||||||||
\(250\) | 1.42582 | 0.0901769 | ||||||||
\(251\) | 15.0672 | 0.951031 | 0.475516 | − | 0.879707i | \(-0.342261\pi\) | ||||
0.475516 | + | 0.879707i | \(0.342261\pi\) | |||||||
\(252\) | − | 0.0562268i | − | 0.00354196i | ||||||
\(253\) | −16.8683 | − | 9.52948i | −1.06050 | − | 0.599113i | ||||
\(254\) | −4.32196 | −0.271184 | ||||||||
\(255\) | −3.13937 | −0.196595 | ||||||||
\(256\) | 0.790999 | 0.0494375 | ||||||||
\(257\) | 19.8073i | 1.23554i | 0.786358 | + | 0.617771i | \(0.211964\pi\) | ||||
−0.786358 | + | 0.617771i | \(0.788036\pi\) | |||||||
\(258\) | −16.1079 | −1.00284 | ||||||||
\(259\) | 7.60327 | 0.472444 | ||||||||
\(260\) | 0.185602 | 0.0115105 | ||||||||
\(261\) | 3.98827 | 0.246868 | ||||||||
\(262\) | 7.81183i | 0.482617i | ||||||||
\(263\) | − | 5.72534i | − | 0.353040i | −0.984297 | − | 0.176520i | \(-0.943516\pi\) | ||
0.984297 | − | 0.176520i | \(-0.0564840\pi\) | |||||||
\(264\) | 4.81788 | − | 8.52820i | 0.296520 | − | 0.524874i | ||||
\(265\) | − | 0.813546i | − | 0.0499757i | ||||||
\(266\) | −5.55795 | − | 0.724257i | −0.340780 | − | 0.0444071i | ||||
\(267\) | 14.5000 | 0.887385 | ||||||||
\(268\) | 0.166608i | 0.0101772i | ||||||||
\(269\) | − | 20.6199i | − | 1.25722i | −0.777723 | − | 0.628608i | \(-0.783625\pi\) | ||
0.777723 | − | 0.628608i | \(-0.216375\pi\) | |||||||
\(270\) | − | 7.34361i | − | 0.446918i | ||||||
\(271\) | 18.9246i | 1.14959i | 0.818297 | + | 0.574795i | \(0.194918\pi\) | ||||
−0.818297 | + | 0.574795i | \(0.805082\pi\) | |||||||
\(272\) | − | 12.1187i | − | 0.734802i | ||||||
\(273\) | 5.34638 | 0.323578 | ||||||||
\(274\) | 1.79769 | 0.108602 | ||||||||
\(275\) | 2.88768 | + | 1.63135i | 0.174134 | + | 0.0983742i | ||||
\(276\) | 0.202785i | 0.0122062i | ||||||||
\(277\) | − | 2.96097i | − | 0.177907i | −0.996036 | − | 0.0889537i | \(-0.971648\pi\) | ||
0.996036 | − | 0.0889537i | \(-0.0283523\pi\) | |||||||
\(278\) | − | 23.3212i | − | 1.39871i | ||||||
\(279\) | − | 18.0691i | − | 1.08177i | ||||||
\(280\) | 2.52933i | 0.151157i | ||||||||
\(281\) | −22.1209 | −1.31962 | −0.659810 | − | 0.751433i | \(-0.729363\pi\) | ||||
−0.659810 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(282\) | 9.42118i | 0.561023i | ||||||||
\(283\) | − | 11.3104i | − | 0.672333i | −0.941803 | − | 0.336166i | \(-0.890870\pi\) | ||
0.941803 | − | 0.336166i | \(-0.109130\pi\) | |||||||
\(284\) | − | 0.0779902i | − | 0.00462787i | ||||||
\(285\) | −4.55147 | − | 0.593103i | −0.269606 | − | 0.0351324i | ||||
\(286\) | 23.1800 | + | 13.0952i | 1.37066 | + | 0.774335i | ||||
\(287\) | 4.41833i | 0.260806i | ||||||||
\(288\) | 0.352651 | 0.0207802 | ||||||||
\(289\) | 8.11166 | 0.477156 | ||||||||
\(290\) | 3.00690 | 0.176571 | ||||||||
\(291\) | 9.66557 | 0.566606 | ||||||||
\(292\) | − | 0.139858i | − | 0.00818455i | ||||||
\(293\) | −12.3218 | −0.719846 | −0.359923 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359923 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(294\) | 9.28869i | 0.541728i | ||||||||
\(295\) | − | 13.9409i | − | 0.811668i | ||||||
\(296\) | 23.6454i | 1.37436i | ||||||||
\(297\) | 8.40219 | − | 14.8728i | 0.487544 | − | 0.863009i | ||||
\(298\) | 25.7188i | 1.48985i | ||||||||
\(299\) | 32.8867 | 1.90189 | ||||||||
\(300\) | − | 0.0347147i | − | 0.00200426i | ||||||
\(301\) | 9.67548 | 0.557685 | ||||||||
\(302\) | −11.5613 | −0.665276 | ||||||||
\(303\) | 4.36136 | 0.250554 | ||||||||
\(304\) | 2.28951 | − | 17.5697i | 0.131312 | − | 1.00769i | ||||
\(305\) | − | 11.3812i | − | 0.651688i | ||||||
\(306\) | − | 8.03910i | − | 0.459565i | ||||||
\(307\) | 26.9323 | 1.53711 | 0.768553 | − | 0.639786i | \(-0.220977\pi\) | ||||
0.768553 | + | 0.639786i | \(0.220977\pi\) | |||||||
\(308\) | 0.0485020 | − | 0.0858540i | 0.00276366 | − | 0.00489199i | ||||
\(309\) | 4.28601 | 0.243823 | ||||||||
\(310\) | − | 13.6229i | − | 0.773730i | ||||||
\(311\) | −12.1912 | −0.691301 | −0.345651 | − | 0.938363i | \(-0.612342\pi\) | ||||
−0.345651 | + | 0.938363i | \(0.612342\pi\) | |||||||
\(312\) | 16.6268i | 0.941304i | ||||||||
\(313\) | −8.18206 | −0.462477 | −0.231239 | − | 0.972897i | \(-0.574278\pi\) | ||||
−0.231239 | + | 0.972897i | \(0.574278\pi\) | |||||||
\(314\) | 18.1392 | 1.02365 | ||||||||
\(315\) | 1.70554i | 0.0960961i | ||||||||
\(316\) | 0.186244 | 0.0104770 | ||||||||
\(317\) | 19.3644i | 1.08762i | 0.839210 | + | 0.543808i | \(0.183018\pi\) | ||||
−0.839210 | + | 0.543808i | \(0.816982\pi\) | |||||||
\(318\) | −1.22146 | −0.0684960 | ||||||||
\(319\) | 6.08979 | + | 3.44034i | 0.340963 | + | 0.192622i | ||||
\(320\) | −7.86382 | −0.439601 | ||||||||
\(321\) | 5.13443i | 0.286576i | ||||||||
\(322\) | − | 7.51132i | − | 0.418589i | ||||||
\(323\) | −12.8864 | − | 1.67922i | −0.717017 | − | 0.0934345i | ||||
\(324\) | 0.00824409 | 0.000458005 | ||||||||
\(325\) | −5.62988 | −0.312290 | ||||||||
\(326\) | −34.8145 | −1.92820 | ||||||||
\(327\) | − | 20.4767i | − | 1.13236i | ||||||
\(328\) | −13.7406 | −0.758697 | ||||||||
\(329\) | − | 5.65898i | − | 0.311990i | ||||||
\(330\) | 2.44931 | − | 4.33556i | 0.134830 | − | 0.238665i | ||||
\(331\) | 10.1969i | 0.560473i | 0.959931 | + | 0.280237i | \(0.0904129\pi\) | ||||
−0.959931 | + | 0.280237i | \(0.909587\pi\) | |||||||
\(332\) | − | 0.482692i | − | 0.0264912i | ||||||
\(333\) | 15.9442i | 0.873736i | ||||||||
\(334\) | 1.70796 | 0.0934554 | ||||||||
\(335\) | − | 5.05376i | − | 0.276116i | ||||||
\(336\) | 3.86016 | 0.210589 | ||||||||
\(337\) | 19.1076 | 1.04086 | 0.520428 | − | 0.853906i | \(-0.325772\pi\) | ||||
0.520428 | + | 0.853906i | \(0.325772\pi\) | |||||||
\(338\) | −26.6565 | −1.44992 | ||||||||
\(339\) | −7.64146 | −0.415027 | ||||||||
\(340\) | − | 0.0982862i | − | 0.00533032i | ||||||
\(341\) | 15.5867 | − | 27.5902i | 0.844065 | − | 1.49409i | ||||
\(342\) | 1.51878 | − | 11.6551i | 0.0821263 | − | 0.630238i | ||||
\(343\) | − | 11.8923i | − | 0.642123i | ||||||
\(344\) | 30.0898i | 1.62234i | ||||||||
\(345\) | − | 6.15110i | − | 0.331164i | ||||||
\(346\) | −7.64389 | −0.410938 | ||||||||
\(347\) | 5.65842i | 0.303760i | 0.988399 | + | 0.151880i | \(0.0485328\pi\) | ||||
−0.988399 | + | 0.151880i | \(0.951467\pi\) | |||||||
\(348\) | − | 0.0732094i | − | 0.00392444i | ||||||
\(349\) | − | 19.1660i | − | 1.02593i | −0.858409 | − | 0.512967i | \(-0.828546\pi\) | ||
0.858409 | − | 0.512967i | \(-0.171454\pi\) | |||||||
\(350\) | 1.28586i | 0.0687322i | ||||||||
\(351\) | 28.9964i | 1.54771i | ||||||||
\(352\) | 0.538471 | + | 0.304201i | 0.0287006 | + | 0.0162140i | ||||
\(353\) | −26.1542 | −1.39205 | −0.696025 | − | 0.718017i | \(-0.745050\pi\) | ||||
−0.696025 | + | 0.718017i | \(0.745050\pi\) | |||||||
\(354\) | −20.9308 | −1.11246 | ||||||||
\(355\) | 2.36569i | 0.125558i | ||||||||
\(356\) | 0.453961i | 0.0240599i | ||||||||
\(357\) | − | 2.83120i | − | 0.149843i | ||||||
\(358\) | − | 8.92028i | − | 0.471451i | ||||||
\(359\) | 14.9692i | 0.790043i | 0.918672 | + | 0.395022i | \(0.129263\pi\) | ||||
−0.918672 | + | 0.395022i | \(0.870737\pi\) | |||||||
\(360\) | −5.30406 | −0.279549 | ||||||||
\(361\) | −18.3655 | − | 4.86910i | −0.966606 | − | 0.256269i | ||||
\(362\) | − | 9.11242i | − | 0.478938i | ||||||
\(363\) | 9.92106 | − | 5.97833i | 0.520721 | − | 0.313781i | ||||
\(364\) | 0.167383i | 0.00877324i | ||||||||
\(365\) | 4.24232i | 0.222053i | ||||||||
\(366\) | −17.0878 | −0.893193 | ||||||||
\(367\) | 32.8273 | 1.71357 | 0.856785 | − | 0.515674i | \(-0.172459\pi\) | ||||
0.856785 | + | 0.515674i | \(0.172459\pi\) | |||||||
\(368\) | 23.7446 | 1.23778 | ||||||||
\(369\) | −9.26532 | −0.482333 | ||||||||
\(370\) | 12.0209i | 0.624935i | ||||||||
\(371\) | 0.733688 | 0.0380912 | ||||||||
\(372\) | −0.331680 | −0.0171968 | ||||||||
\(373\) | −0.160453 | −0.00830792 | −0.00415396 | − | 0.999991i | \(-0.501322\pi\) | ||||
−0.00415396 | + | 0.999991i | \(0.501322\pi\) | |||||||
\(374\) | 6.93463 | − | 12.2751i | 0.358581 | − | 0.634729i | ||||
\(375\) | 1.05301i | 0.0543771i | ||||||||
\(376\) | 17.5989 | 0.907594 | ||||||||
\(377\) | −11.8728 | −0.611479 | ||||||||
\(378\) | 6.62276 | 0.340638 | ||||||||
\(379\) | − | 4.85119i | − | 0.249189i | −0.992208 | − | 0.124595i | \(-0.960237\pi\) | ||
0.992208 | − | 0.124595i | \(-0.0397630\pi\) | |||||||
\(380\) | 0.0185687 | − | 0.142496i | 0.000952552 | − | 0.00730989i | ||||
\(381\) | − | 3.19188i | − | 0.163525i | ||||||
\(382\) | 16.7412 | 0.856555 | ||||||||
\(383\) | 21.5584i | 1.10158i | 0.834642 | + | 0.550792i | \(0.185674\pi\) | ||||
−0.834642 | + | 0.550792i | \(0.814326\pi\) | |||||||
\(384\) | 12.1995i | 0.622551i | ||||||||
\(385\) | −1.47122 | + | 2.60422i | −0.0749802 | + | 0.132724i | ||||
\(386\) | 27.1115 | 1.37994 | ||||||||
\(387\) | 20.2897i | 1.03138i | ||||||||
\(388\) | 0.302607i | 0.0153625i | ||||||||
\(389\) | −1.78194 | −0.0903478 | −0.0451739 | − | 0.998979i | \(-0.514384\pi\) | ||||
−0.0451739 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(390\) | 8.45271i | 0.428019i | ||||||||
\(391\) | − | 17.4153i | − | 0.880731i | ||||||
\(392\) | 17.3514 | 0.876379 | ||||||||
\(393\) | −5.76925 | −0.291020 | ||||||||
\(394\) | − | 12.8652i | − | 0.648139i | ||||||
\(395\) | −5.64937 | −0.284251 | ||||||||
\(396\) | 0.180038 | + | 0.101710i | 0.00904723 | + | 0.00511110i | ||||
\(397\) | −24.5140 | −1.23032 | −0.615161 | − | 0.788402i | \(-0.710909\pi\) | ||||
−0.615161 | + | 0.788402i | \(0.710909\pi\) | |||||||
\(398\) | 30.2202 | 1.51480 | ||||||||
\(399\) | 0.534883 | − | 4.10470i | 0.0267777 | − | 0.205492i | ||||
\(400\) | −4.06485 | −0.203242 | ||||||||
\(401\) | − | 13.5931i | − | 0.678808i | −0.940641 | − | 0.339404i | \(-0.889775\pi\) | ||
0.940641 | − | 0.339404i | \(-0.110225\pi\) | |||||||
\(402\) | −7.58772 | −0.378441 | ||||||||
\(403\) | 53.7903i | 2.67949i | ||||||||
\(404\) | 0.136544i | 0.00679332i | ||||||||
\(405\) | −0.250069 | −0.0124260 | ||||||||
\(406\) | 2.71174i | 0.134581i | ||||||||
\(407\) | −13.7537 | + | 24.3456i | −0.681744 | + | 1.20676i | ||||
\(408\) | 8.80478 | 0.435902 | ||||||||
\(409\) | −24.0687 | −1.19012 | −0.595059 | − | 0.803682i | \(-0.702871\pi\) | ||||
−0.595059 | + | 0.803682i | \(0.702871\pi\) | |||||||
\(410\) | −6.98544 | −0.344986 | ||||||||
\(411\) | 1.32764i | 0.0654876i | ||||||||
\(412\) | 0.134185i | 0.00661082i | ||||||||
\(413\) | 12.5724 | 0.618648 | ||||||||
\(414\) | 15.7514 | 0.774138 | ||||||||
\(415\) | 14.6416i | 0.718726i | ||||||||
\(416\) | −1.04981 | −0.0514714 | ||||||||
\(417\) | 17.2233 | 0.843431 | ||||||||
\(418\) | 12.3729 | − | 16.4864i | 0.605180 | − | 0.806375i | ||||
\(419\) | 36.7457 | 1.79515 | 0.897573 | − | 0.440865i | \(-0.145328\pi\) | ||||
0.897573 | + | 0.440865i | \(0.145328\pi\) | |||||||
\(420\) | 0.0313071 | 0.00152763 | ||||||||
\(421\) | − | 5.19903i | − | 0.253385i | −0.991942 | − | 0.126693i | \(-0.959564\pi\) | ||
0.991942 | − | 0.126693i | \(-0.0404362\pi\) | |||||||
\(422\) | −11.0755 | −0.539146 | ||||||||
\(423\) | 11.8670 | 0.576993 | ||||||||
\(424\) | 2.28170i | 0.110809i | ||||||||
\(425\) | 2.98133i | 0.144616i | ||||||||
\(426\) | 3.55185 | 0.172088 | ||||||||
\(427\) | 10.2640 | 0.496712 | ||||||||
\(428\) | −0.160747 | −0.00777001 | ||||||||
\(429\) | −9.67115 | + | 17.1190i | −0.466928 | + | 0.826515i | ||||
\(430\) | 15.2971i | 0.737690i | ||||||||
\(431\) | −16.2337 | −0.781949 | −0.390974 | − | 0.920402i | \(-0.627862\pi\) | ||||
−0.390974 | + | 0.920402i | \(0.627862\pi\) | |||||||
\(432\) | 20.9358i | 1.00727i | ||||||||
\(433\) | 38.7358i | 1.86153i | 0.365624 | + | 0.930763i | \(0.380856\pi\) | ||||
−0.365624 | + | 0.930763i | \(0.619144\pi\) | |||||||
\(434\) | 12.2857 | 0.589732 | ||||||||
\(435\) | 2.22067i | 0.106473i | ||||||||
\(436\) | 0.641077 | 0.0307020 | ||||||||
\(437\) | 3.29018 | − | 25.2489i | 0.157391 | − | 1.20782i | ||||
\(438\) | 6.36943 | 0.304343 | ||||||||
\(439\) | −33.5838 | −1.60287 | −0.801434 | − | 0.598083i | \(-0.795929\pi\) | ||||
−0.801434 | + | 0.598083i | \(0.795929\pi\) | |||||||
\(440\) | −8.09889 | − | 4.57535i | −0.386100 | − | 0.218121i | ||||
\(441\) | 11.7001 | 0.557148 | ||||||||
\(442\) | 23.9318i | 1.13832i | ||||||||
\(443\) | 21.4260 | 1.01798 | 0.508991 | − | 0.860772i | \(-0.330019\pi\) | ||||
0.508991 | + | 0.860772i | \(0.330019\pi\) | |||||||
\(444\) | 0.292674 | 0.0138897 | ||||||||
\(445\) | − | 13.7701i | − | 0.652764i | ||||||
\(446\) | − | 16.8451i | − | 0.797640i | ||||||
\(447\) | −18.9940 | −0.898387 | ||||||||
\(448\) | − | 7.09190i | − | 0.335061i | ||||||
\(449\) | 2.20285i | 0.103959i | 0.998648 | + | 0.0519795i | \(0.0165531\pi\) | ||||
−0.998648 | + | 0.0519795i | \(0.983447\pi\) | |||||||
\(450\) | −2.69648 | −0.127113 | ||||||||
\(451\) | −14.1474 | − | 7.99238i | −0.666176 | − | 0.376347i | ||||
\(452\) | − | 0.239236i | − | 0.0112527i | ||||||
\(453\) | − | 8.53830i | − | 0.401164i | ||||||
\(454\) | −13.1556 | −0.617423 | ||||||||
\(455\) | − | 5.07725i | − | 0.238025i | ||||||
\(456\) | 12.7652 | + | 1.66344i | 0.597787 | + | 0.0778976i | ||||
\(457\) | 7.87683i | 0.368463i | 0.982883 | + | 0.184231i | \(0.0589796\pi\) | ||||
−0.982883 | + | 0.184231i | \(0.941020\pi\) | |||||||
\(458\) | 20.5890 | 0.962059 | ||||||||
\(459\) | 15.3552 | 0.716719 | ||||||||
\(460\) | 0.192577 | 0.00897894 | ||||||||
\(461\) | − | 11.1537i | − | 0.519481i | −0.965678 | − | 0.259741i | \(-0.916363\pi\) | ||
0.965678 | − | 0.259741i | \(-0.0836371\pi\) | |||||||
\(462\) | 3.90998 | + | 2.20889i | 0.181909 | + | 0.102767i | ||||
\(463\) | −0.272621 | −0.0126698 | −0.00633488 | − | 0.999980i | \(-0.502016\pi\) | ||||
−0.00633488 | + | 0.999980i | \(0.502016\pi\) | |||||||
\(464\) | −8.57230 | −0.397959 | ||||||||
\(465\) | 10.0609 | 0.466563 | ||||||||
\(466\) | 27.6839i | 1.28243i | ||||||||
\(467\) | −34.0388 | −1.57513 | −0.787564 | − | 0.616233i | \(-0.788658\pi\) | ||||
−0.787564 | + | 0.616233i | \(0.788658\pi\) | |||||||
\(468\) | −0.351005 | −0.0162252 | ||||||||
\(469\) | 4.55768 | 0.210454 | ||||||||
\(470\) | 8.94693 | 0.412691 | ||||||||
\(471\) | 13.3963i | 0.617267i | ||||||||
\(472\) | 39.0990i | 1.79968i | ||||||||
\(473\) | −17.5021 | + | 30.9808i | −0.804749 | + | 1.42450i | ||||
\(474\) | 8.48197i | 0.389590i | ||||||||
\(475\) | −0.563246 | + | 4.32236i | −0.0258435 | + | 0.198323i | ||||
\(476\) | 0.0886384 | 0.00406274 | ||||||||
\(477\) | 1.53856i | 0.0704457i | ||||||||
\(478\) | − | 20.2820i | − | 0.927676i | ||||||
\(479\) | − | 20.1960i | − | 0.922778i | −0.887198 | − | 0.461389i | \(-0.847351\pi\) | ||
0.887198 | − | 0.461389i | \(-0.152649\pi\) | |||||||
\(480\) | 0.196356i | 0.00896240i | ||||||||
\(481\) | − | 47.4646i | − | 2.16420i | ||||||
\(482\) | 32.7209 | 1.49040 | ||||||||
\(483\) | 5.54731 | 0.252411 | ||||||||
\(484\) | 0.187167 | + | 0.310605i | 0.00850761 | + | 0.0141184i | ||||
\(485\) | − | 9.17901i | − | 0.416797i | ||||||
\(486\) | 22.4063i | 1.01637i | ||||||||
\(487\) | 5.97405i | 0.270710i | 0.990797 | + | 0.135355i | \(0.0432175\pi\) | ||||
−0.990797 | + | 0.135355i | \(0.956783\pi\) | |||||||
\(488\) | 31.9202i | 1.44496i | ||||||||
\(489\) | − | 25.7115i | − | 1.16271i | ||||||
\(490\) | 8.82111 | 0.398497 | ||||||||
\(491\) | 0.729652i | 0.0329287i | 0.999864 | + | 0.0164644i | \(0.00524101\pi\) | ||||
−0.999864 | + | 0.0164644i | \(0.994759\pi\) | |||||||
\(492\) | 0.170076i | 0.00766761i | ||||||||
\(493\) | 6.28729i | 0.283165i | ||||||||
\(494\) | −4.52129 | + | 34.6964i | −0.203423 | + | 1.56107i | ||||
\(495\) | −5.46111 | − | 3.08517i | −0.245459 | − | 0.138668i | ||||
\(496\) | 38.8373i | 1.74385i | ||||||||
\(497\) | −2.13347 | −0.0956994 | ||||||||
\(498\) | 21.9829 | 0.985076 | ||||||||
\(499\) | −24.6032 | −1.10139 | −0.550695 | − | 0.834706i | \(-0.685637\pi\) | ||||
−0.550695 | + | 0.834706i | \(0.685637\pi\) | |||||||
\(500\) | −0.0329672 | −0.00147434 | ||||||||
\(501\) | 1.26137i | 0.0563541i | ||||||||
\(502\) | −21.4831 | −0.958838 | ||||||||
\(503\) | − | 8.17919i | − | 0.364692i | −0.983234 | − | 0.182346i | \(-0.941631\pi\) | ||
0.983234 | − | 0.182346i | \(-0.0583691\pi\) | |||||||
\(504\) | − | 4.78341i | − | 0.213070i | ||||||
\(505\) | − | 4.14181i | − | 0.184308i | ||||||
\(506\) | 24.0511 | + | 13.5873i | 1.06920 | + | 0.604031i | ||||
\(507\) | − | 19.6866i | − | 0.874311i | ||||||
\(508\) | 0.0999304 | 0.00443370 | ||||||||
\(509\) | 12.7190i | 0.563758i | 0.959450 | + | 0.281879i | \(0.0909577\pi\) | ||||
−0.959450 | + | 0.281879i | \(0.909042\pi\) | |||||||
\(510\) | 4.47617 | 0.198208 | ||||||||
\(511\) | −3.82589 | −0.169248 | ||||||||
\(512\) | 22.0429 | 0.974166 | ||||||||
\(513\) | 22.2620 | + | 2.90097i | 0.982893 | + | 0.128081i | ||||
\(514\) | − | 28.2416i | − | 1.24568i | ||||||
\(515\) | − | 4.07026i | − | 0.179357i | ||||||
\(516\) | 0.372440 | 0.0163958 | ||||||||
\(517\) | 18.1200 | + | 10.2366i | 0.796916 | + | 0.450206i | ||||
\(518\) | −10.8409 | −0.476322 | ||||||||
\(519\) | − | 5.64522i | − | 0.247798i | ||||||
\(520\) | 15.7898 | 0.692427 | ||||||||
\(521\) | 6.53428i | 0.286272i | 0.989703 | + | 0.143136i | \(0.0457186\pi\) | ||||
−0.989703 | + | 0.143136i | \(0.954281\pi\) | |||||||
\(522\) | −5.68657 | −0.248894 | ||||||||
\(523\) | 0.662002 | 0.0289473 | 0.0144737 | − | 0.999895i | \(-0.495393\pi\) | ||||
0.0144737 | + | 0.999895i | \(0.495393\pi\) | |||||||
\(524\) | − | 0.180622i | − | 0.00789050i | ||||||
\(525\) | −0.949644 | −0.0414459 | ||||||||
\(526\) | 8.16332i | 0.355938i | ||||||||
\(527\) | 28.4850 | 1.24082 | ||||||||
\(528\) | −6.98270 | + | 12.3602i | −0.303883 | + | 0.537908i | ||||
\(529\) | 11.1227 | 0.483594 | ||||||||
\(530\) | 1.15997i | 0.0503859i | ||||||||
\(531\) | 26.3646i | 1.14413i | ||||||||
\(532\) | 0.128509 | + | 0.0167460i | 0.00557155 | + | 0.000726029i | ||||
\(533\) | 27.5821 | 1.19471 | ||||||||
\(534\) | −20.6744 | −0.894669 | ||||||||
\(535\) | 4.87597 | 0.210806 | ||||||||
\(536\) | 14.1740i | 0.612222i | ||||||||
\(537\) | 6.58787 | 0.284287 | ||||||||
\(538\) | 29.4002i | 1.26753i | ||||||||
\(539\) | 17.8652 | + | 10.0927i | 0.769507 | + | 0.434722i | ||||
\(540\) | 0.169796i | 0.00730685i | ||||||||
\(541\) | 3.82889i | 0.164617i | 0.996607 | + | 0.0823085i | \(0.0262293\pi\) | ||||
−0.996607 | + | 0.0823085i | \(0.973771\pi\) | |||||||
\(542\) | − | 26.9832i | − | 1.15903i | ||||||
\(543\) | 6.72976 | 0.288802 | ||||||||
\(544\) | 0.555935i | 0.0238355i | ||||||||
\(545\) | −19.4459 | −0.832970 | ||||||||
\(546\) | −7.62299 | −0.326234 | ||||||||
\(547\) | −14.7797 | −0.631936 | −0.315968 | − | 0.948770i | \(-0.602329\pi\) | ||||
−0.315968 | + | 0.948770i | \(0.602329\pi\) | |||||||
\(548\) | −0.0415653 | −0.00177558 | ||||||||
\(549\) | 21.5239i | 0.918618i | ||||||||
\(550\) | −4.11732 | − | 2.32602i | −0.175563 | − | 0.0991817i | ||||
\(551\) | −1.18782 | + | 9.11536i | −0.0506029 | + | 0.388327i | ||||
\(552\) | 17.2516i | 0.734277i | ||||||||
\(553\) | − | 5.09483i | − | 0.216654i | ||||||
\(554\) | 4.22181i | 0.179368i | ||||||||
\(555\) | −8.87774 | −0.376839 | ||||||||
\(556\) | 0.539223i | 0.0228681i | ||||||||
\(557\) | − | 33.4642i | − | 1.41792i | −0.705247 | − | 0.708962i | \(-0.749164\pi\) | ||
0.705247 | − | 0.708962i | \(-0.250836\pi\) | |||||||
\(558\) | 25.7633i | 1.09065i | ||||||||
\(559\) | − | 60.4007i | − | 2.55468i | ||||||
\(560\) | − | 3.66584i | − | 0.154910i | ||||||
\(561\) | 9.06548 | + | 5.12141i | 0.382745 | + | 0.216226i | ||||
\(562\) | 31.5404 | 1.33045 | ||||||||
\(563\) | −15.6241 | −0.658476 | −0.329238 | − | 0.944247i | \(-0.606792\pi\) | ||||
−0.329238 | + | 0.944247i | \(0.606792\pi\) | |||||||
\(564\) | − | 0.217832i | − | 0.00917240i | ||||||
\(565\) | 7.25680i | 0.305296i | ||||||||
\(566\) | 16.1266i | 0.677851i | ||||||||
\(567\) | − | 0.225522i | − | 0.00947105i | ||||||
\(568\) | − | 6.63490i | − | 0.278394i | ||||||
\(569\) | −2.66835 | −0.111863 | −0.0559316 | − | 0.998435i | \(-0.517813\pi\) | ||||
−0.0559316 | + | 0.998435i | \(0.517813\pi\) | |||||||
\(570\) | 6.48959 | + | 0.845659i | 0.271819 | + | 0.0354207i | ||||
\(571\) | 35.7601i | 1.49651i | 0.663410 | + | 0.748256i | \(0.269109\pi\) | ||||
−0.663410 | + | 0.748256i | \(0.730891\pi\) | |||||||
\(572\) | −0.535958 | − | 0.302781i | −0.0224095 | − | 0.0126599i | ||||
\(573\) | 12.3638i | 0.516507i | ||||||||
\(574\) | − | 6.29975i | − | 0.262946i | ||||||
\(575\) | −5.84146 | −0.243606 | ||||||||
\(576\) | 14.8719 | 0.619661 | ||||||||
\(577\) | 23.8081 | 0.991143 | 0.495571 | − | 0.868567i | \(-0.334959\pi\) | ||||
0.495571 | + | 0.868567i | \(0.334959\pi\) | |||||||
\(578\) | −11.5658 | −0.481073 | ||||||||
\(579\) | 20.0225i | 0.832108i | ||||||||
\(580\) | −0.0695241 | −0.00288683 | ||||||||
\(581\) | −13.2044 | −0.547809 | ||||||||
\(582\) | −13.7814 | −0.571256 | ||||||||
\(583\) | −1.32718 | + | 2.34926i | −0.0549662 | + | 0.0972964i | ||||
\(584\) | − | 11.8982i | − | 0.492350i | ||||||
\(585\) | 10.6471 | 0.440203 | ||||||||
\(586\) | 17.5686 | 0.725754 | ||||||||
\(587\) | 4.18900 | 0.172898 | 0.0864492 | − | 0.996256i | \(-0.472448\pi\) | ||||
0.0864492 | + | 0.996256i | \(0.472448\pi\) | |||||||
\(588\) | − | 0.214769i | − | 0.00885693i | ||||||
\(589\) | 41.2977 | + | 5.38150i | 1.70164 | + | 0.221741i | ||||
\(590\) | 19.8772i | 0.818330i | ||||||||
\(591\) | 9.50128 | 0.390831 | ||||||||
\(592\) | − | 34.2701i | − | 1.40849i | ||||||
\(593\) | − | 38.4621i | − | 1.57945i | −0.613461 | − | 0.789725i | \(-0.710223\pi\) | ||
0.613461 | − | 0.789725i | \(-0.289777\pi\) | |||||||
\(594\) | −11.9800 | + | 21.2060i | −0.491546 | + | 0.870093i | ||||
\(595\) | −2.68868 | −0.110225 | ||||||||
\(596\) | − | 0.594659i | − | 0.0243582i | ||||||
\(597\) | 22.3184i | 0.913432i | ||||||||
\(598\) | −46.8906 | −1.91750 | ||||||||
\(599\) | − | 42.1022i | − | 1.72025i | −0.510086 | − | 0.860124i | \(-0.670386\pi\) | ||
0.510086 | − | 0.860124i | \(-0.329614\pi\) | |||||||
\(600\) | − | 2.95330i | − | 0.120568i | ||||||
\(601\) | 25.0134 | 1.02032 | 0.510159 | − | 0.860080i | \(-0.329587\pi\) | ||||
0.510159 | + | 0.860080i | \(0.329587\pi\) | |||||||
\(602\) | −13.7955 | −0.562263 | ||||||||
\(603\) | 9.55754i | 0.389213i | ||||||||
\(604\) | 0.267314 | 0.0108769 | ||||||||
\(605\) | −5.67738 | − | 9.42164i | −0.230818 | − | 0.383044i | ||||
\(606\) | −6.21852 | −0.252610 | ||||||||
\(607\) | −22.1188 | −0.897775 | −0.448887 | − | 0.893588i | \(-0.648180\pi\) | ||||
−0.448887 | + | 0.893588i | \(0.648180\pi\) | |||||||
\(608\) | −0.105030 | + | 0.805998i | −0.00425951 | + | 0.0326875i | ||||
\(609\) | −2.00269 | −0.0811532 | ||||||||
\(610\) | 16.2276i | 0.657037i | ||||||||
\(611\) | −35.3271 | −1.42918 | ||||||||
\(612\) | 0.185876i | 0.00751361i | ||||||||
\(613\) | 17.6194i | 0.711642i | 0.934554 | + | 0.355821i | \(0.115799\pi\) | ||||
−0.934554 | + | 0.355821i | \(0.884201\pi\) | |||||||
\(614\) | −38.4006 | −1.54972 | ||||||||
\(615\) | − | 5.15893i | − | 0.208028i | ||||||
\(616\) | 4.12623 | − | 7.30390i | 0.166251 | − | 0.294283i | ||||
\(617\) | 0.650912 | 0.0262047 | 0.0131024 | − | 0.999914i | \(-0.495829\pi\) | ||||
0.0131024 | + | 0.999914i | \(0.495829\pi\) | |||||||
\(618\) | −6.11108 | −0.245824 | ||||||||
\(619\) | 4.52383 | 0.181828 | 0.0909140 | − | 0.995859i | \(-0.471021\pi\) | ||||
0.0909140 | + | 0.995859i | \(0.471021\pi\) | |||||||
\(620\) | 0.314983i | 0.0126500i | ||||||||
\(621\) | 30.0861i | 1.20731i | ||||||||
\(622\) | 17.3825 | 0.696976 | ||||||||
\(623\) | 12.4184 | 0.497533 | ||||||||
\(624\) | − | 24.0977i | − | 0.964679i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.6662 | 0.466273 | ||||||||
\(627\) | 12.1756 | + | 9.13774i | 0.486248 | + | 0.364926i | ||||
\(628\) | −0.419405 | −0.0167361 | ||||||||
\(629\) | −25.1351 | −1.00220 | ||||||||
\(630\) | − | 2.43179i | − | 0.0968849i | ||||||
\(631\) | 30.6552 | 1.22036 | 0.610182 | − | 0.792261i | \(-0.291096\pi\) | ||||
0.610182 | + | 0.792261i | \(0.291096\pi\) | |||||||
\(632\) | 15.8444 | 0.630258 | ||||||||
\(633\) | − | 8.17954i | − | 0.325108i | ||||||
\(634\) | − | 27.6102i | − | 1.09654i | ||||||
\(635\) | −3.03121 | −0.120290 | ||||||||
\(636\) | 0.0282420 | 0.00111987 | ||||||||
\(637\) | −34.8303 | −1.38003 | ||||||||
\(638\) | −8.68295 | − | 4.90531i | −0.343761 | − | 0.194203i | ||||
\(639\) | − | 4.47393i | − | 0.176986i | ||||||
\(640\) | 11.5853 | 0.457951 | ||||||||
\(641\) | − | 20.0450i | − | 0.791732i | −0.918308 | − | 0.395866i | \(-0.870445\pi\) | ||
0.918308 | − | 0.395866i | \(-0.129555\pi\) | |||||||
\(642\) | − | 7.32078i | − | 0.288928i | ||||||
\(643\) | 4.54366 | 0.179185 | 0.0895923 | − | 0.995979i | \(-0.471444\pi\) | ||||
0.0895923 | + | 0.995979i | \(0.471444\pi\) | |||||||
\(644\) | 0.173673i | 0.00684369i | ||||||||
\(645\) | −11.2973 | −0.444831 | ||||||||
\(646\) | 18.3737 | + | 2.39427i | 0.722903 | + | 0.0942015i | ||||
\(647\) | −37.3454 | −1.46820 | −0.734099 | − | 0.679042i | \(-0.762395\pi\) | ||||
−0.734099 | + | 0.679042i | \(0.762395\pi\) | |||||||
\(648\) | 0.701354 | 0.0275518 | ||||||||
\(649\) | −22.7424 | + | 40.2567i | −0.892719 | + | 1.58021i | ||||
\(650\) | 8.02721 | 0.314853 | ||||||||
\(651\) | 9.07331i | 0.355611i | ||||||||
\(652\) | 0.804966 | 0.0315249 | ||||||||
\(653\) | 20.7486 | 0.811957 | 0.405978 | − | 0.913883i | \(-0.366931\pi\) | ||||
0.405978 | + | 0.913883i | \(0.366931\pi\) | |||||||
\(654\) | 29.1961i | 1.14166i | ||||||||
\(655\) | 5.47883i | 0.214076i | ||||||||
\(656\) | 19.9147 | 0.777537 | ||||||||
\(657\) | − | 8.02298i | − | 0.313006i | ||||||
\(658\) | 8.06870i | 0.314551i | ||||||||
\(659\) | 21.3264 | 0.830759 | 0.415380 | − | 0.909648i | \(-0.363649\pi\) | ||||
0.415380 | + | 0.909648i | \(0.363649\pi\) | |||||||
\(660\) | −0.0566319 | + | 0.100245i | −0.00220440 | + | 0.00390203i | ||||
\(661\) | − | 47.0683i | − | 1.83075i | −0.402608 | − | 0.915373i | \(-0.631896\pi\) | ||
0.402608 | − | 0.915373i | \(-0.368104\pi\) | |||||||
\(662\) | − | 14.5390i | − | 0.565074i | ||||||
\(663\) | −17.6743 | −0.686411 | ||||||||
\(664\) | − | 41.0643i | − | 1.59360i | ||||||
\(665\) | −3.89807 | − | 0.507958i | −0.151161 | − | 0.0196978i | ||||
\(666\) | − | 22.7336i | − | 0.880908i | ||||||
\(667\) | −12.3190 | −0.476993 | ||||||||
\(668\) | −0.0394907 | −0.00152794 | ||||||||
\(669\) | 12.4406 | 0.480981 | ||||||||
\(670\) | 7.20576i | 0.278383i | ||||||||
\(671\) | −18.5668 | + | 32.8654i | −0.716763 | + | 1.26875i | ||||
\(672\) | −0.177082 | −0.00683108 | ||||||||
\(673\) | 15.2046 | 0.586094 | 0.293047 | − | 0.956098i | \(-0.405331\pi\) | ||||
0.293047 | + | 0.956098i | \(0.405331\pi\) | |||||||
\(674\) | −27.2440 | −1.04940 | ||||||||
\(675\) | − | 5.15044i | − | 0.198241i | ||||||
\(676\) | 0.616340 | 0.0237054 | ||||||||
\(677\) | −16.5878 | −0.637522 | −0.318761 | − | 0.947835i | \(-0.603267\pi\) | ||||
−0.318761 | + | 0.947835i | \(0.603267\pi\) | |||||||
\(678\) | 10.8954 | 0.418434 | ||||||||
\(679\) | 8.27800 | 0.317680 | ||||||||
\(680\) | − | 8.36156i | − | 0.320651i | ||||||
\(681\) | − | 9.71577i | − | 0.372309i | ||||||
\(682\) | −22.2238 | + | 39.3386i | −0.850993 | + | 1.50635i | ||||
\(683\) | − | 11.8388i | − | 0.452998i | −0.974011 | − | 0.226499i | \(-0.927272\pi\) | ||
0.974011 | − | 0.226499i | \(-0.0727280\pi\) | |||||||
\(684\) | −0.0351166 | + | 0.269485i | −0.00134272 | + | 0.0103040i | ||||
\(685\) | 1.26081 | 0.0481730 | ||||||||
\(686\) | 16.9563i | 0.647393i | ||||||||
\(687\) | 15.2055i | 0.580126i | ||||||||
\(688\) | − | 43.6101i | − | 1.66262i | ||||||
\(689\) | − | 4.58017i | − | 0.174490i | ||||||
\(690\) | 8.77037i | 0.333882i | ||||||||
\(691\) | 32.1810 | 1.22422 | 0.612112 | − | 0.790771i | \(-0.290320\pi\) | ||||
0.612112 | + | 0.790771i | \(0.290320\pi\) | |||||||
\(692\) | 0.176739 | 0.00671859 | ||||||||
\(693\) | 2.78233 | − | 4.92504i | 0.105692 | − | 0.187087i | ||||
\(694\) | − | 8.06790i | − | 0.306253i | ||||||
\(695\) | − | 16.3563i | − | 0.620431i | ||||||
\(696\) | − | 6.22818i | − | 0.236079i | ||||||
\(697\) | − | 14.6063i | − | 0.553251i | ||||||
\(698\) | 27.3273i | 1.03435i | ||||||||
\(699\) | −20.4453 | −0.773312 | ||||||||
\(700\) | − | 0.0297311i | − | 0.00112373i | ||||||
\(701\) | − | 4.01817i | − | 0.151764i | −0.997117 | − | 0.0758820i | \(-0.975823\pi\) | ||
0.997117 | − | 0.0758820i | \(-0.0241772\pi\) | |||||||
\(702\) | − | 41.3437i | − | 1.56042i | ||||||
\(703\) | −36.4411 | − | 4.74864i | −1.37440 | − | 0.179098i | ||||
\(704\) | 22.7082 | + | 12.8287i | 0.855847 | + | 0.483498i | ||||
\(705\) | 6.60755i | 0.248855i | ||||||||
\(706\) | 37.2913 | 1.40348 | ||||||||
\(707\) | 3.73525 | 0.140479 | ||||||||
\(708\) | 0.483953 | 0.0181881 | ||||||||
\(709\) | 4.15961 | 0.156218 | 0.0781088 | − | 0.996945i | \(-0.475112\pi\) | ||||
0.0781088 | + | 0.996945i | \(0.475112\pi\) | |||||||
\(710\) | − | 3.37305i | − | 0.126588i | ||||||
\(711\) | 10.6840 | 0.400679 | ||||||||
\(712\) | 38.6201i | 1.44735i | ||||||||
\(713\) | 55.8119i | 2.09017i | ||||||||
\(714\) | 4.03679i | 0.151073i | ||||||||
\(715\) | 16.2573 | + | 9.18432i | 0.607988 | + | 0.343474i | ||||
\(716\) | 0.206251i | 0.00770795i | ||||||||
\(717\) | 14.9788 | 0.559393 | ||||||||
\(718\) | − | 21.3434i | − | 0.796528i | ||||||
\(719\) | 34.8816 | 1.30086 | 0.650432 | − | 0.759565i | \(-0.274588\pi\) | ||||
0.650432 | + | 0.759565i | \(0.274588\pi\) | |||||||
\(720\) | 7.68734 | 0.286490 | ||||||||
\(721\) | 3.67072 | 0.136705 | ||||||||
\(722\) | 26.1859 | + | 6.94247i | 0.974540 | + | 0.258372i | ||||
\(723\) | 24.1653i | 0.898717i | ||||||||
\(724\) | 0.210693i | 0.00783035i | ||||||||
\(725\) | 2.10889 | 0.0783221 | ||||||||
\(726\) | −14.1457 | + | 8.52403i | −0.524995 | + | 0.316356i | ||||
\(727\) | −4.49125 | −0.166571 | −0.0832856 | − | 0.996526i | \(-0.526541\pi\) | ||||
−0.0832856 | + | 0.996526i | \(0.526541\pi\) | |||||||
\(728\) | 14.2398i | 0.527764i | ||||||||
\(729\) | −15.7974 | −0.585091 | ||||||||
\(730\) | − | 6.04880i | − | 0.223876i | ||||||
\(731\) | −31.9855 | −1.18303 | ||||||||
\(732\) | 0.395096 | 0.0146032 | ||||||||
\(733\) | 32.7845i | 1.21092i | 0.795874 | + | 0.605462i | \(0.207012\pi\) | ||||
−0.795874 | + | 0.605462i | \(0.792988\pi\) | |||||||
\(734\) | −46.8058 | −1.72763 | ||||||||
\(735\) | 6.51463i | 0.240296i | ||||||||
\(736\) | −1.08927 | −0.0401510 | ||||||||
\(737\) | −8.24446 | + | 14.5936i | −0.303689 | + | 0.537563i | ||||
\(738\) | 13.2107 | 0.486292 | ||||||||
\(739\) | 40.4424i | 1.48770i | 0.668348 | + | 0.743849i | \(0.267002\pi\) | ||||
−0.668348 | + | 0.743849i | \(0.732998\pi\) | |||||||
\(740\) | − | 0.277941i | − | 0.0102173i | ||||||
\(741\) | −25.6242 | − | 3.33910i | −0.941330 | − | 0.122665i | ||||
\(742\) | −1.04611 | −0.0384038 | ||||||||
\(743\) | 28.7094 | 1.05325 | 0.526623 | − | 0.850099i | \(-0.323458\pi\) | ||||
0.526623 | + | 0.850099i | \(0.323458\pi\) | |||||||
\(744\) | −28.2172 | −1.03449 | ||||||||
\(745\) | 18.0379i | 0.660857i | ||||||||
\(746\) | 0.228777 | 0.00837611 | ||||||||
\(747\) | − | 27.6898i | − | 1.01312i | ||||||
\(748\) | −0.160339 | + | 0.283819i | −0.00586259 | + | 0.0103775i | ||||
\(749\) | 4.39734i | 0.160675i | ||||||||
\(750\) | − | 1.50140i | − | 0.0548234i | ||||||
\(751\) | − | 1.48823i | − | 0.0543064i | −0.999631 | − | 0.0271532i | \(-0.991356\pi\) | ||
0.999631 | − | 0.0271532i | \(-0.00864420\pi\) | |||||||
\(752\) | −25.5066 | −0.930131 | ||||||||
\(753\) | − | 15.8658i | − | 0.578184i | ||||||
\(754\) | 16.9285 | 0.616498 | ||||||||
\(755\) | −8.10849 | −0.295098 | ||||||||
\(756\) | −0.153129 | −0.00556923 | ||||||||
\(757\) | 16.7554 | 0.608987 | 0.304493 | − | 0.952514i | \(-0.401513\pi\) | ||||
0.304493 | + | 0.952514i | \(0.401513\pi\) | |||||||
\(758\) | 6.91694i | 0.251234i | ||||||||
\(759\) | −10.0346 | + | 17.7624i | −0.364233 | + | 0.644735i | ||||
\(760\) | 1.57970 | − | 12.1226i | 0.0573018 | − | 0.439734i | ||||
\(761\) | − | 13.9024i | − | 0.503962i | −0.967732 | − | 0.251981i | \(-0.918918\pi\) | ||
0.967732 | − | 0.251981i | \(-0.0810820\pi\) | |||||||
\(762\) | 4.55105i | 0.164867i | ||||||||
\(763\) | − | 17.5371i | − | 0.634885i | ||||||
\(764\) | −0.387083 | −0.0140042 | ||||||||
\(765\) | − | 5.63822i | − | 0.203850i | ||||||
\(766\) | − | 30.7385i | − | 1.11063i | ||||||
\(767\) | − | 78.4853i | − | 2.83394i | ||||||
\(768\) | − | 0.832928i | − | 0.0300557i | ||||||
\(769\) | − | 31.5810i | − | 1.13884i | −0.822047 | − | 0.569420i | \(-0.807168\pi\) | ||
0.822047 | − | 0.569420i | \(-0.192832\pi\) | |||||||
\(770\) | 2.09769 | − | 3.71316i | 0.0755957 | − | 0.133813i | ||||
\(771\) | 20.8572 | 0.751153 | ||||||||
\(772\) | −0.626859 | −0.0225612 | ||||||||
\(773\) | − | 43.0045i | − | 1.54677i | −0.633939 | − | 0.773383i | \(-0.718563\pi\) | ||
0.633939 | − | 0.773383i | \(-0.281437\pi\) | |||||||
\(774\) | − | 28.9294i | − | 1.03985i | ||||||
\(775\) | − | 9.55444i | − | 0.343206i | ||||||
\(776\) | 25.7438i | 0.924149i | ||||||||
\(777\) | − | 8.00630i | − | 0.287224i | ||||||
\(778\) | 2.54073 | 0.0910894 | ||||||||
\(779\) | 2.75948 | − | 21.1762i | 0.0988686 | − | 0.758718i | ||||
\(780\) | − | 0.195440i | − | 0.00699787i | ||||||
\(781\) | 3.85927 | − | 6.83135i | 0.138096 | − | 0.244445i | ||||
\(782\) | 24.8312i | 0.887960i | ||||||||
\(783\) | − | 10.8617i | − | 0.388166i | ||||||
\(784\) | −25.1479 | −0.898140 | ||||||||
\(785\) | 12.7219 | 0.454064 | ||||||||
\(786\) | 8.22592 | 0.293409 | ||||||||
\(787\) | 37.5328 | 1.33790 | 0.668950 | − | 0.743307i | \(-0.266744\pi\) | ||||
0.668950 | + | 0.743307i | \(0.266744\pi\) | |||||||
\(788\) | 0.297463i | 0.0105967i | ||||||||
\(789\) | −6.02883 | −0.214632 | ||||||||
\(790\) | 8.05500 | 0.286584 | ||||||||
\(791\) | −6.54447 | −0.232694 | ||||||||
\(792\) | 15.3164 | + | 8.65279i | 0.544246 | + | 0.307464i | ||||
\(793\) | − | 64.0750i | − | 2.27537i | ||||||
\(794\) | 34.9526 | 1.24042 | ||||||||
\(795\) | −0.856670 | −0.0303830 | ||||||||
\(796\) | −0.698738 | −0.0247661 | ||||||||
\(797\) | 0.454063i | 0.0160837i | 0.999968 | + | 0.00804187i | \(0.00255984\pi\) | ||||
−0.999968 | + | 0.00804187i | \(0.997440\pi\) | |||||||
\(798\) | −0.762648 | + | 5.85257i | −0.0269975 | + | 0.207179i | ||||
\(799\) | 18.7076i | 0.661829i | ||||||||
\(800\) | 0.186472 | 0.00659278 | ||||||||
\(801\) | 26.0416i | 0.920135i | ||||||||
\(802\) | 19.3814i | 0.684380i | ||||||||
\(803\) | 6.92072 | − | 12.2505i | 0.244227 | − | 0.432310i | ||||
\(804\) | 0.175440 | 0.00618729 | ||||||||
\(805\) | − | 5.26806i | − | 0.185675i | ||||||
\(806\) | − | 76.6954i | − | 2.70148i | ||||||
\(807\) | −21.7129 | −0.764329 | ||||||||
\(808\) | 11.6163i | 0.408660i | ||||||||
\(809\) | 2.11976i | 0.0745266i | 0.999305 | + | 0.0372633i | \(0.0118640\pi\) | ||||
−0.999305 | + | 0.0372633i | \(0.988136\pi\) | |||||||
\(810\) | 0.356554 | 0.0125280 | ||||||||
\(811\) | −54.9435 | −1.92933 | −0.964663 | − | 0.263486i | \(-0.915128\pi\) | ||||
−0.964663 | + | 0.263486i | \(0.915128\pi\) | |||||||
\(812\) | − | 0.0626996i | − | 0.00220033i | ||||||
\(813\) | 19.9278 | 0.698898 | ||||||||
\(814\) | 19.6103 | − | 34.7124i | 0.687340 | − | 1.21667i | ||||
\(815\) | −24.4172 | −0.855296 | ||||||||
\(816\) | −12.7610 | −0.446726 | ||||||||
\(817\) | −46.3728 | − | 6.04285i | −1.62238 | − | 0.211412i | ||||
\(818\) | 34.3176 | 1.19989 | ||||||||
\(819\) | 9.60197i | 0.335520i | ||||||||
\(820\) | 0.161514 | 0.00564032 | ||||||||
\(821\) | − | 45.3581i | − | 1.58301i | −0.611163 | − | 0.791505i | \(-0.709298\pi\) | ||
0.611163 | − | 0.791505i | \(-0.290702\pi\) | |||||||
\(822\) | − | 1.89298i | − | 0.0660252i | ||||||
\(823\) | 18.0345 | 0.628642 | 0.314321 | − | 0.949317i | \(-0.398223\pi\) | ||||
0.314321 | + | 0.949317i | \(0.398223\pi\) | |||||||
\(824\) | 11.4156i | 0.397681i | ||||||||
\(825\) | 1.71783 | − | 3.04075i | 0.0598070 | − | 0.105865i | ||||
\(826\) | −17.9260 | −0.623726 | ||||||||
\(827\) | −1.68723 | −0.0586707 | −0.0293353 | − | 0.999570i | \(-0.509339\pi\) | ||||
−0.0293353 | + | 0.999570i | \(0.509339\pi\) | |||||||
\(828\) | −0.364196 | −0.0126567 | ||||||||
\(829\) | − | 29.3844i | − | 1.02056i | −0.860008 | − | 0.510280i | \(-0.829542\pi\) | ||
0.860008 | − | 0.510280i | \(-0.170458\pi\) | |||||||
\(830\) | − | 20.8763i | − | 0.724626i | ||||||
\(831\) | −3.11792 | −0.108160 | ||||||||
\(832\) | −44.2724 | −1.53487 | ||||||||
\(833\) | 18.4446i | 0.639066i | ||||||||
\(834\) | −24.5574 | −0.850354 | ||||||||
\(835\) | 1.19788 | 0.0414543 | ||||||||
\(836\) | −0.286082 | + | 0.381191i | −0.00989434 | + | 0.0131838i | ||||
\(837\) | −49.2096 | −1.70093 | ||||||||
\(838\) | −52.3929 | −1.80988 | ||||||||
\(839\) | 16.3384i | 0.564066i | 0.959405 | + | 0.282033i | \(0.0910087\pi\) | ||||
−0.959405 | + | 0.282033i | \(0.908991\pi\) | |||||||
\(840\) | 2.66341 | 0.0918963 | ||||||||
\(841\) | −24.5526 | −0.846641 | ||||||||
\(842\) | 7.41289i | 0.255465i | ||||||||
\(843\) | 23.2934i | 0.802268i | ||||||||
\(844\) | 0.256082 | 0.00881472 | ||||||||
\(845\) | −18.6956 | −0.643147 | ||||||||
\(846\) | −16.9202 | −0.581729 | ||||||||
\(847\) | 8.49681 | − | 5.12009i | 0.291954 | − | 0.175928i | ||||
\(848\) | − | 3.30694i | − | 0.113561i | ||||||
\(849\) | −11.9099 | −0.408748 | ||||||||
\(850\) | − | 4.25085i | − | 0.145803i | ||||||
\(851\) | − | 49.2484i | − | 1.68821i | ||||||
\(852\) | −0.0821243 | −0.00281353 | ||||||||
\(853\) | 13.4324i | 0.459915i | 0.973201 | + | 0.229957i | \(0.0738587\pi\) | ||||
−0.973201 | + | 0.229957i | \(0.926141\pi\) | |||||||
\(854\) | −14.6347 | −0.500789 | ||||||||
\(855\) | 1.06520 | − | 8.17433i | 0.0364290 | − | 0.279556i | ||||
\(856\) | −13.6753 | −0.467413 | ||||||||
\(857\) | −35.7851 | −1.22240 | −0.611198 | − | 0.791478i | \(-0.709312\pi\) | ||||
−0.611198 | + | 0.791478i | \(0.709312\pi\) | |||||||
\(858\) | 13.7893 | − | 24.4087i | 0.470760 | − | 0.833300i | ||||
\(859\) | 2.41890 | 0.0825317 | 0.0412658 | − | 0.999148i | \(-0.486861\pi\) | ||||
0.0412658 | + | 0.999148i | \(0.486861\pi\) | |||||||
\(860\) | − | 0.353692i | − | 0.0120608i | ||||||
\(861\) | 4.65253 | 0.158558 | ||||||||
\(862\) | 23.1463 | 0.788367 | ||||||||
\(863\) | 33.1469i | 1.12833i | 0.825661 | + | 0.564167i | \(0.190803\pi\) | ||||
−0.825661 | + | 0.564167i | \(0.809197\pi\) | |||||||
\(864\) | − | 0.960413i | − | 0.0326739i | ||||||
\(865\) | −5.36104 | −0.182281 | ||||||||
\(866\) | − | 55.2304i | − | 1.87680i | ||||||
\(867\) | − | 8.54164i | − | 0.290089i | ||||||
\(868\) | −0.284064 | −0.00964177 | ||||||||
\(869\) | 16.3136 | + | 9.21611i | 0.553400 | + | 0.312635i | ||||
\(870\) | − | 3.16628i | − | 0.107347i | ||||||
\(871\) | − | 28.4521i | − | 0.964061i | ||||||
\(872\) | 54.5387 | 1.84691 | ||||||||
\(873\) | 17.3591i | 0.587517i | ||||||||
\(874\) | −4.69121 | + | 36.0004i | −0.158683 | + | 1.21773i | ||||
\(875\) | 0.901840i | 0.0304877i | ||||||||
\(876\) | −0.147271 | −0.00497583 | ||||||||
\(877\) | −23.3683 | −0.789090 | −0.394545 | − | 0.918877i | \(-0.629098\pi\) | ||||
−0.394545 | + | 0.918877i | \(0.629098\pi\) | |||||||
\(878\) | 47.8846 | 1.61603 | ||||||||
\(879\) | 12.9749i | 0.437633i | ||||||||
\(880\) | 11.7380 | + | 6.63120i | 0.395687 | + | 0.223538i | ||||
\(881\) | −27.6215 | −0.930590 | −0.465295 | − | 0.885156i | \(-0.654052\pi\) | ||||
−0.465295 | + | 0.885156i | \(0.654052\pi\) | |||||||
\(882\) | −16.6823 | −0.561721 | ||||||||
\(883\) | 19.3375 | 0.650758 | 0.325379 | − | 0.945584i | \(-0.394508\pi\) | ||||
0.325379 | + | 0.945584i | \(0.394508\pi\) | |||||||
\(884\) | − | 0.553340i | − | 0.0186108i | ||||||
\(885\) | −14.6798 | −0.493457 | ||||||||
\(886\) | −30.5497 | −1.02634 | ||||||||
\(887\) | 57.9130 | 1.94453 | 0.972263 | − | 0.233888i | \(-0.0751451\pi\) | ||||
0.972263 | + | 0.233888i | \(0.0751451\pi\) | |||||||
\(888\) | 24.8988 | 0.835550 | ||||||||
\(889\) | − | 2.73366i | − | 0.0916841i | ||||||
\(890\) | 19.6337i | 0.658122i | ||||||||
\(891\) | 0.722120 | + | 0.407951i | 0.0241919 | + | 0.0136669i | ||||
\(892\) | 0.389486i | 0.0130409i | ||||||||
\(893\) | −3.53433 | + | 27.1225i | −0.118272 | + | 0.907619i | ||||
\(894\) | 27.0821 | 0.905761 | ||||||||
\(895\) | − | 6.25624i | − | 0.209123i | ||||||
\(896\) | 10.4481i | 0.349047i | ||||||||
\(897\) | − | 34.6300i | − | 1.15626i | ||||||
\(898\) | − | 3.14088i | − | 0.104812i | ||||||
\(899\) | − | 20.1492i | − | 0.672014i | ||||||
\(900\) | 0.0623468 | 0.00207823 | ||||||||
\(901\) | −2.42545 | −0.0808035 | ||||||||
\(902\) | 20.1717 | + | 11.3957i | 0.671644 | + | 0.379436i | ||||
\(903\) | − | 10.1884i | − | 0.339047i | ||||||
\(904\) | − | 20.3527i | − | 0.676920i | ||||||
\(905\) | − | 6.39099i | − | 0.212444i | ||||||
\(906\) | 12.1741i | 0.404457i | ||||||||
\(907\) | 2.95496i | 0.0981179i | 0.998796 | + | 0.0490590i | \(0.0156222\pi\) | ||||
−0.998796 | + | 0.0490590i | \(0.984378\pi\) | |||||||
\(908\) | 0.304178 | 0.0100945 | ||||||||
\(909\) | 7.83290i | 0.259801i | ||||||||
\(910\) | 7.23925i | 0.239979i | ||||||||
\(911\) | 58.9818i | 1.95415i | 0.212888 | + | 0.977077i | \(0.431713\pi\) | ||||
−0.212888 | + | 0.977077i | \(0.568287\pi\) | |||||||
\(912\) | −18.5010 | − | 2.41087i | −0.612631 | − | 0.0798319i | ||||
\(913\) | 23.8856 | − | 42.2802i | 0.790497 | − | 1.39927i | ||||
\(914\) | − | 11.2310i | − | 0.371487i | ||||||
\(915\) | −11.9845 | −0.396196 | ||||||||
\(916\) | −0.476049 | −0.0157291 | ||||||||
\(917\) | −4.94102 | −0.163167 | ||||||||
\(918\) | −21.8938 | −0.722602 | ||||||||
\(919\) | 7.25820i | 0.239426i | 0.992809 | + | 0.119713i | \(0.0381974\pi\) | ||||
−0.992809 | + | 0.119713i | \(0.961803\pi\) | |||||||
\(920\) | 16.3832 | 0.540138 | ||||||||
\(921\) | − | 28.3599i | − | 0.934490i | ||||||
\(922\) | 15.9032i | 0.523745i | ||||||||
\(923\) | 13.3186i | 0.438386i | ||||||||
\(924\) | −0.0904049 | − | 0.0510729i | −0.00297410 | − | 0.00168018i | ||||
\(925\) | 8.43084i | 0.277204i | ||||||||
\(926\) | 0.388708 | 0.0127737 | ||||||||
\(927\) | 7.69757i | 0.252821i | ||||||||
\(928\) | 0.393248 | 0.0129090 | ||||||||
\(929\) | −39.9341 | −1.31020 | −0.655098 | − | 0.755544i | \(-0.727373\pi\) | ||||
−0.655098 | + | 0.755544i | \(0.727373\pi\) | |||||||
\(930\) | −14.3450 | −0.470392 | ||||||||
\(931\) | −3.48463 | + | 26.7411i | −0.114204 | + | 0.876403i | ||||
\(932\) | − | 0.640095i | − | 0.0209670i | ||||||
\(933\) | 12.8375i | 0.420280i | ||||||||
\(934\) | 48.5332 | 1.58806 | ||||||||
\(935\) | 4.86360 | − | 8.60913i | 0.159057 | − | 0.281549i | ||||
\(936\) | −29.8612 | −0.976045 | ||||||||
\(937\) | − | 36.7081i | − | 1.19920i | −0.800299 | − | 0.599601i | \(-0.795326\pi\) | ||
0.800299 | − | 0.599601i | \(-0.204674\pi\) | |||||||
\(938\) | −6.49844 | −0.212182 | ||||||||
\(939\) | 8.61577i | 0.281165i | ||||||||
\(940\) | −0.206867 | −0.00674726 | ||||||||
\(941\) | 22.2948 | 0.726790 | 0.363395 | − | 0.931635i | \(-0.381618\pi\) | ||||
0.363395 | + | 0.931635i | \(0.381618\pi\) | |||||||
\(942\) | − | 19.1007i | − | 0.622333i | ||||||
\(943\) | 28.6187 | 0.931953 | ||||||||
\(944\) | − | 56.6674i | − | 1.84437i | ||||||
\(945\) | 4.64487 | 0.151098 | ||||||||
\(946\) | 24.9549 | − | 44.1730i | 0.811354 | − | 1.43619i | ||||
\(947\) | −50.9261 | −1.65487 | −0.827437 | − | 0.561558i | \(-0.810202\pi\) | ||||
−0.827437 | + | 0.561558i | \(0.810202\pi\) | |||||||
\(948\) | − | 0.196116i | − | 0.00636956i | ||||||
\(949\) | 23.8838i | 0.775300i | ||||||||
\(950\) | 0.803089 | − | 6.16291i | 0.0260556 | − | 0.199951i | ||||
\(951\) | 20.3909 | 0.661220 | ||||||||
\(952\) | 7.54078 | 0.244398 | ||||||||
\(953\) | −41.5830 | −1.34701 | −0.673504 | − | 0.739184i | \(-0.735211\pi\) | ||||
−0.673504 | + | 0.739184i | \(0.735211\pi\) | |||||||
\(954\) | − | 2.19371i | − | 0.0710240i | ||||||
\(955\) | 11.7414 | 0.379944 | ||||||||
\(956\) | 0.468951i | 0.0151669i | ||||||||
\(957\) | 3.62270 | − | 6.41259i | 0.117105 | − | 0.207290i | ||||
\(958\) | 28.7959i | 0.930353i | ||||||||
\(959\) | 1.13705i | 0.0367171i | ||||||||
\(960\) | 8.28066i | 0.267257i | ||||||||
\(961\) | −60.2873 | −1.94475 | ||||||||
\(962\) | 67.6761i | 2.18196i | ||||||||
\(963\) | −9.22131 | −0.297153 | ||||||||
\(964\) | −0.756559 | −0.0243671 | ||||||||
\(965\) | 19.0146 | 0.612102 | ||||||||
\(966\) | −7.90947 | −0.254483 | ||||||||
\(967\) | 33.7443i | 1.08514i | 0.840010 | + | 0.542571i | \(0.182549\pi\) | ||||
−0.840010 | + | 0.542571i | \(0.817451\pi\) | |||||||
\(968\) | 15.9230 | + | 26.4243i | 0.511785 | + | 0.849309i | ||||
\(969\) | −1.76824 | + | 13.5695i | −0.0568039 | + | 0.435914i | ||||
\(970\) | 13.0876i | 0.420219i | ||||||||
\(971\) | − | 56.8920i | − | 1.82575i | −0.408239 | − | 0.912875i | \(-0.633857\pi\) | ||
0.408239 | − | 0.912875i | \(-0.366143\pi\) | |||||||
\(972\) | − | 0.518069i | − | 0.0166171i | ||||||
\(973\) | 14.7508 | 0.472889 | ||||||||
\(974\) | − | 8.51792i | − | 0.272932i | ||||||
\(975\) | 5.92831i | 0.189858i | ||||||||
\(976\) | − | 46.2630i | − | 1.48084i | ||||||
\(977\) | 43.1130i | 1.37931i | 0.724140 | + | 0.689653i | \(0.242237\pi\) | ||||
−0.724140 | + | 0.689653i | \(0.757763\pi\) | |||||||
\(978\) | 36.6600i | 1.17226i | ||||||||
\(979\) | −22.4638 | + | 39.7635i | −0.717947 | + | 1.27085i | ||||
\(980\) | −0.203958 | −0.00651519 | ||||||||
\(981\) | 36.7756 | 1.17415 | ||||||||
\(982\) | − | 1.04035i | − | 0.0331990i | ||||||
\(983\) | 17.8759i | 0.570154i | 0.958505 | + | 0.285077i | \(0.0920191\pi\) | ||||
−0.958505 | + | 0.285077i | \(0.907981\pi\) | |||||||
\(984\) | 14.4689i | 0.461253i | ||||||||
\(985\) | − | 9.02300i | − | 0.287497i | ||||||
\(986\) | − | 8.96456i | − | 0.285490i | ||||||
\(987\) | −5.95895 | −0.189675 | ||||||||
\(988\) | 0.104539 | − | 0.802236i | 0.00332584 | − | 0.0255225i | ||||
\(989\) | − | 62.6707i | − | 1.99281i | ||||||
\(990\) | 7.78656 | + | 4.39891i | 0.247473 | + | 0.139806i | ||||
\(991\) | − | 42.8471i | − | 1.36108i | −0.732710 | − | 0.680541i | \(-0.761745\pi\) | ||
0.732710 | − | 0.680541i | \(-0.238255\pi\) | |||||||
\(992\) | − | 1.78163i | − | 0.0565669i | ||||||
\(993\) | 10.7374 | 0.340742 | ||||||||
\(994\) | 3.04195 | 0.0964849 | ||||||||
\(995\) | 21.1949 | 0.671925 | ||||||||
\(996\) | −0.508278 | −0.0161054 | ||||||||
\(997\) | − | 31.9958i | − | 1.01332i | −0.862147 | − | 0.506658i | \(-0.830881\pi\) | ||
0.862147 | − | 0.506658i | \(-0.169119\pi\) | |||||||
\(998\) | 35.0798 | 1.11043 | ||||||||
\(999\) | 43.4226 | 1.37383 |
(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 | 1045.2.f.a.626.14 | yes | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.a.626.28 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.a.626.27 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.a.626.13 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.a.626.13 | ✓ | 40 | 209.208 | even | 2 | inner | |
1045.2.f.a.626.14 | yes | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.a.626.27 | yes | 40 | 19.18 | odd | 2 | inner | |
1045.2.f.a.626.28 | yes | 40 | 11.10 | odd | 2 | inner |