Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,3,Mod(91,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.b (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: | \(3.76022764817\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1358954496.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 8x^{6} + 20x^{4} + 16x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.8 | ||
Root | \(1.98289i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 138.91 |
Dual form | 138.3.b.a.91.7 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 4.92225i | 0.984450i | 0.870468 | + | 0.492225i | \(0.163816\pi\) | ||||
−0.870468 | + | 0.492225i | \(0.836184\pi\) | |||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 5.13851i | 0.734073i | 0.930206 | + | 0.367037i | \(0.119628\pi\) | ||||
−0.930206 | + | 0.367037i | \(0.880372\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 6.96111i | 0.696111i | ||||||||
\(11\) | − | 7.71925i | − | 0.701750i | −0.936422 | − | 0.350875i | \(-0.885884\pi\) | ||
0.936422 | − | 0.350875i | \(-0.114116\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | 0.944060 | 0.0726200 | 0.0363100 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363100 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(14\) | 7.26695i | 0.519068i | ||||||||
\(15\) | 8.52559i | 0.568372i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 27.6556i | − | 1.62680i | −0.581703 | − | 0.813401i | \(-0.697613\pi\) | ||
0.581703 | − | 0.813401i | \(-0.302387\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | − | 9.08137i | − | 0.477967i | −0.971024 | − | 0.238983i | \(-0.923186\pi\) | ||
0.971024 | − | 0.238983i | \(-0.0768141\pi\) | |||||||
\(20\) | 9.84450i | 0.492225i | ||||||||
\(21\) | 8.90017i | 0.423817i | ||||||||
\(22\) | − | 10.9167i | − | 0.496212i | ||||||
\(23\) | −20.0652 | + | 11.2423i | −0.872399 | + | 0.488794i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | 0.771456 | 0.0308582 | ||||||||
\(26\) | 1.33510 | 0.0513501 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 10.2770i | 0.367037i | ||||||||
\(29\) | −14.4550 | −0.498449 | −0.249225 | − | 0.968446i | \(-0.580176\pi\) | ||||
−0.249225 | + | 0.968446i | \(0.580176\pi\) | |||||||
\(30\) | 12.0570i | 0.401900i | ||||||||
\(31\) | −0.830916 | −0.0268037 | −0.0134019 | − | 0.999910i | \(-0.504266\pi\) | ||||
−0.0134019 | + | 0.999910i | \(0.504266\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 13.3701i | − | 0.405155i | ||||||
\(34\) | − | 39.1110i | − | 1.15032i | ||||||
\(35\) | −25.2930 | −0.722658 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 23.8369i | 0.644241i | 0.946699 | + | 0.322120i | \(0.104396\pi\) | ||||
−0.946699 | + | 0.322120i | \(0.895604\pi\) | |||||||
\(38\) | − | 12.8430i | − | 0.337973i | ||||||
\(39\) | 1.63516 | 0.0419272 | ||||||||
\(40\) | 13.9222i | 0.348056i | ||||||||
\(41\) | −26.8431 | −0.654709 | −0.327354 | − | 0.944902i | \(-0.606157\pi\) | ||||
−0.327354 | + | 0.944902i | \(0.606157\pi\) | |||||||
\(42\) | 12.5867i | 0.299684i | ||||||||
\(43\) | − | 26.7736i | − | 0.622642i | −0.950305 | − | 0.311321i | \(-0.899229\pi\) | ||
0.950305 | − | 0.311321i | \(-0.100771\pi\) | |||||||
\(44\) | − | 15.4385i | − | 0.350875i | ||||||
\(45\) | 14.7667i | 0.328150i | ||||||||
\(46\) | −28.3764 | + | 15.8990i | −0.616879 | + | 0.345630i | ||||
\(47\) | −38.2280 | −0.813363 | −0.406681 | − | 0.913570i | \(-0.633314\pi\) | ||||
−0.406681 | + | 0.913570i | \(0.633314\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 22.5957 | 0.461136 | ||||||||
\(50\) | 1.09100 | 0.0218201 | ||||||||
\(51\) | − | 47.9010i | − | 0.939235i | ||||||
\(52\) | 1.88812 | 0.0363100 | ||||||||
\(53\) | − | 92.3727i | − | 1.74288i | −0.490502 | − | 0.871440i | \(-0.663186\pi\) | ||
0.490502 | − | 0.871440i | \(-0.336814\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | 37.9961 | 0.690837 | ||||||||
\(56\) | 14.5339i | 0.259534i | ||||||||
\(57\) | − | 15.7294i | − | 0.275954i | ||||||
\(58\) | −20.4425 | −0.352457 | ||||||||
\(59\) | −47.8457 | −0.810944 | −0.405472 | − | 0.914108i | \(-0.632893\pi\) | ||||
−0.405472 | + | 0.914108i | \(0.632893\pi\) | |||||||
\(60\) | 17.0512i | 0.284186i | ||||||||
\(61\) | 121.824i | 1.99711i | 0.0537398 | + | 0.998555i | \(0.482886\pi\) | ||||
−0.0537398 | + | 0.998555i | \(0.517114\pi\) | |||||||
\(62\) | −1.17509 | −0.0189531 | ||||||||
\(63\) | 15.4155i | 0.244691i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 4.64690i | 0.0714907i | ||||||||
\(66\) | − | 18.9082i | − | 0.286488i | ||||||
\(67\) | 8.10477i | 0.120967i | 0.998169 | + | 0.0604834i | \(0.0192642\pi\) | ||||
−0.998169 | + | 0.0604834i | \(0.980736\pi\) | |||||||
\(68\) | − | 55.3113i | − | 0.813401i | ||||||
\(69\) | −34.7539 | + | 19.4722i | −0.503680 | + | 0.282205i | ||||
\(70\) | −35.7698 | −0.510997 | ||||||||
\(71\) | −23.8139 | −0.335407 | −0.167704 | − | 0.985837i | \(-0.553635\pi\) | ||||
−0.167704 | + | 0.985837i | \(0.553635\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | 98.1035 | 1.34388 | 0.671942 | − | 0.740604i | \(-0.265460\pi\) | ||||
0.671942 | + | 0.740604i | \(0.265460\pi\) | |||||||
\(74\) | 33.7105i | 0.455547i | ||||||||
\(75\) | 1.33620 | 0.0178160 | ||||||||
\(76\) | − | 18.1627i | − | 0.238983i | ||||||
\(77\) | 39.6654 | 0.515136 | ||||||||
\(78\) | 2.31246 | 0.0296470 | ||||||||
\(79\) | − | 70.0030i | − | 0.886114i | −0.896493 | − | 0.443057i | \(-0.853894\pi\) | ||
0.896493 | − | 0.443057i | \(-0.146106\pi\) | |||||||
\(80\) | 19.6890i | 0.246112i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −37.9618 | −0.462949 | ||||||||
\(83\) | 50.7347i | 0.611261i | 0.952150 | + | 0.305631i | \(0.0988672\pi\) | ||||
−0.952150 | + | 0.305631i | \(0.901133\pi\) | |||||||
\(84\) | 17.8003i | 0.211909i | ||||||||
\(85\) | 136.128 | 1.60151 | ||||||||
\(86\) | − | 37.8636i | − | 0.440274i | ||||||
\(87\) | −25.0368 | −0.287780 | ||||||||
\(88\) | − | 21.8333i | − | 0.248106i | ||||||
\(89\) | 87.6727i | 0.985086i | 0.870288 | + | 0.492543i | \(0.163933\pi\) | ||||
−0.870288 | + | 0.492543i | \(0.836067\pi\) | |||||||
\(90\) | 20.8833i | 0.232037i | ||||||||
\(91\) | 4.85106i | 0.0533084i | ||||||||
\(92\) | −40.1304 | + | 22.4845i | −0.436200 | + | 0.244397i | ||||
\(93\) | −1.43919 | −0.0154751 | ||||||||
\(94\) | −54.0626 | −0.575134 | ||||||||
\(95\) | 44.7008 | 0.470534 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 36.7344i | 0.378705i | 0.981909 | + | 0.189353i | \(0.0606390\pi\) | ||||
−0.981909 | + | 0.189353i | \(0.939361\pi\) | |||||||
\(98\) | 31.9551 | 0.326073 | ||||||||
\(99\) | − | 23.1577i | − | 0.233917i | ||||||
\(100\) | 1.54291 | 0.0154291 | ||||||||
\(101\) | 189.428 | 1.87553 | 0.937764 | − | 0.347273i | \(-0.112892\pi\) | ||||
0.937764 | + | 0.347273i | \(0.112892\pi\) | |||||||
\(102\) | − | 67.7422i | − | 0.664139i | ||||||
\(103\) | 85.5225i | 0.830316i | 0.909749 | + | 0.415158i | \(0.136274\pi\) | ||||
−0.909749 | + | 0.415158i | \(0.863726\pi\) | |||||||
\(104\) | 2.67020 | 0.0256750 | ||||||||
\(105\) | −43.8088 | −0.417227 | ||||||||
\(106\) | − | 130.635i | − | 1.23240i | ||||||
\(107\) | − | 138.422i | − | 1.29366i | −0.762634 | − | 0.646830i | \(-0.776094\pi\) | ||
0.762634 | − | 0.646830i | \(-0.223906\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | 49.7589i | 0.456503i | 0.973602 | + | 0.228252i | \(0.0733009\pi\) | ||||
−0.973602 | + | 0.228252i | \(0.926699\pi\) | |||||||
\(110\) | 53.7345 | 0.488496 | ||||||||
\(111\) | 41.2867i | 0.371952i | ||||||||
\(112\) | 20.5541i | 0.183518i | ||||||||
\(113\) | 189.178i | 1.67414i | 0.547096 | + | 0.837070i | \(0.315733\pi\) | ||||
−0.547096 | + | 0.837070i | \(0.684267\pi\) | |||||||
\(114\) | − | 22.2447i | − | 0.195129i | ||||||
\(115\) | −55.3373 | − | 98.7658i | −0.481193 | − | 0.858833i | ||||
\(116\) | −28.9101 | −0.249225 | ||||||||
\(117\) | 2.83218 | 0.0242067 | ||||||||
\(118\) | −67.6640 | −0.573424 | ||||||||
\(119\) | 142.109 | 1.19419 | ||||||||
\(120\) | 24.1140i | 0.200950i | ||||||||
\(121\) | 61.4133 | 0.507548 | ||||||||
\(122\) | 172.285i | 1.41217i | ||||||||
\(123\) | −46.4935 | −0.377996 | ||||||||
\(124\) | −1.66183 | −0.0134019 | ||||||||
\(125\) | 126.854i | 1.01483i | ||||||||
\(126\) | 21.8009i | 0.173023i | ||||||||
\(127\) | −32.2016 | −0.253556 | −0.126778 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126778 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 46.3733i | − | 0.359483i | ||||||
\(130\) | 6.57170i | 0.0505516i | ||||||||
\(131\) | 88.6957 | 0.677066 | 0.338533 | − | 0.940954i | \(-0.390069\pi\) | ||||
0.338533 | + | 0.940954i | \(0.390069\pi\) | |||||||
\(132\) | − | 26.7402i | − | 0.202578i | ||||||
\(133\) | 46.6647 | 0.350863 | ||||||||
\(134\) | 11.4619i | 0.0855364i | ||||||||
\(135\) | 25.5768i | 0.189457i | ||||||||
\(136\) | − | 78.2220i | − | 0.575162i | ||||||
\(137\) | − | 88.3772i | − | 0.645089i | −0.946554 | − | 0.322544i | \(-0.895462\pi\) | ||
0.946554 | − | 0.322544i | \(-0.104538\pi\) | |||||||
\(138\) | −49.1495 | + | 27.5378i | −0.356155 | + | 0.199549i | ||||
\(139\) | −183.605 | −1.32090 | −0.660449 | − | 0.750871i | \(-0.729634\pi\) | ||||
−0.660449 | + | 0.750871i | \(0.729634\pi\) | |||||||
\(140\) | −50.5861 | −0.361329 | ||||||||
\(141\) | −66.2129 | −0.469595 | ||||||||
\(142\) | −33.6780 | −0.237169 | ||||||||
\(143\) | − | 7.28743i | − | 0.0509610i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | − | 71.1513i | − | 0.490698i | ||||||
\(146\) | 138.739 | 0.950269 | ||||||||
\(147\) | 39.1369 | 0.266237 | ||||||||
\(148\) | 47.6738i | 0.322120i | ||||||||
\(149\) | − | 86.5480i | − | 0.580859i | −0.956896 | − | 0.290430i | \(-0.906202\pi\) | ||
0.956896 | − | 0.290430i | \(-0.0937982\pi\) | |||||||
\(150\) | 1.88967 | 0.0125978 | ||||||||
\(151\) | −263.765 | −1.74679 | −0.873393 | − | 0.487016i | \(-0.838085\pi\) | ||||
−0.873393 | + | 0.487016i | \(0.838085\pi\) | |||||||
\(152\) | − | 25.6860i | − | 0.168987i | ||||||
\(153\) | − | 82.9669i | − | 0.542268i | ||||||
\(154\) | 56.0954 | 0.364256 | ||||||||
\(155\) | − | 4.08998i | − | 0.0263869i | ||||||
\(156\) | 3.27032 | 0.0209636 | ||||||||
\(157\) | − | 83.4996i | − | 0.531845i | −0.963994 | − | 0.265922i | \(-0.914324\pi\) | ||
0.963994 | − | 0.265922i | \(-0.0856765\pi\) | |||||||
\(158\) | − | 98.9992i | − | 0.626577i | ||||||
\(159\) | − | 159.994i | − | 1.00625i | ||||||
\(160\) | 27.8445i | 0.174028i | ||||||||
\(161\) | −57.7685 | − | 103.105i | −0.358811 | − | 0.640405i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −178.643 | −1.09597 | −0.547986 | − | 0.836487i | \(-0.684605\pi\) | ||||
−0.547986 | + | 0.836487i | \(0.684605\pi\) | |||||||
\(164\) | −53.6861 | −0.327354 | ||||||||
\(165\) | 65.8111 | 0.398855 | ||||||||
\(166\) | 71.7497i | 0.432227i | ||||||||
\(167\) | −125.596 | −0.752072 | −0.376036 | − | 0.926605i | \(-0.622713\pi\) | ||||
−0.376036 | + | 0.926605i | \(0.622713\pi\) | |||||||
\(168\) | 25.1735i | 0.149842i | ||||||||
\(169\) | −168.109 | −0.994726 | ||||||||
\(170\) | 192.514 | 1.13244 | ||||||||
\(171\) | − | 27.2441i | − | 0.159322i | ||||||
\(172\) | − | 53.5472i | − | 0.311321i | ||||||
\(173\) | 145.986 | 0.843849 | 0.421925 | − | 0.906631i | \(-0.361355\pi\) | ||||
0.421925 | + | 0.906631i | \(0.361355\pi\) | |||||||
\(174\) | −35.4074 | −0.203491 | ||||||||
\(175\) | 3.96414i | 0.0226522i | ||||||||
\(176\) | − | 30.8770i | − | 0.175437i | ||||||
\(177\) | −82.8712 | −0.468199 | ||||||||
\(178\) | 123.988i | 0.696561i | ||||||||
\(179\) | −152.764 | −0.853428 | −0.426714 | − | 0.904387i | \(-0.640329\pi\) | ||||
−0.426714 | + | 0.904387i | \(0.640329\pi\) | |||||||
\(180\) | 29.5335i | 0.164075i | ||||||||
\(181\) | − | 133.516i | − | 0.737658i | −0.929497 | − | 0.368829i | \(-0.879759\pi\) | ||
0.929497 | − | 0.368829i | \(-0.120241\pi\) | |||||||
\(182\) | 6.86044i | 0.0376947i | ||||||||
\(183\) | 211.005i | 1.15303i | ||||||||
\(184\) | −56.7529 | + | 31.7979i | −0.308440 | + | 0.172815i | ||||
\(185\) | −117.331 | −0.634223 | ||||||||
\(186\) | −2.03532 | −0.0109426 | ||||||||
\(187\) | −213.481 | −1.14161 | ||||||||
\(188\) | −76.4561 | −0.406681 | ||||||||
\(189\) | 26.7005i | 0.141272i | ||||||||
\(190\) | 63.2164 | 0.332718 | ||||||||
\(191\) | 271.502i | 1.42148i | 0.703456 | + | 0.710739i | \(0.251639\pi\) | ||||
−0.703456 | + | 0.710739i | \(0.748361\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | 242.088 | 1.25434 | 0.627172 | − | 0.778881i | \(-0.284212\pi\) | ||||
0.627172 | + | 0.778881i | \(0.284212\pi\) | |||||||
\(194\) | 51.9503i | 0.267785i | ||||||||
\(195\) | 8.04866i | 0.0412752i | ||||||||
\(196\) | 45.1914 | 0.230568 | ||||||||
\(197\) | −251.316 | −1.27571 | −0.637857 | − | 0.770155i | \(-0.720179\pi\) | ||||
−0.637857 | + | 0.770155i | \(0.720179\pi\) | |||||||
\(198\) | − | 32.7500i | − | 0.165404i | ||||||
\(199\) | − | 176.314i | − | 0.885999i | −0.896522 | − | 0.443000i | \(-0.853914\pi\) | ||
0.896522 | − | 0.443000i | \(-0.146086\pi\) | |||||||
\(200\) | 2.18201 | 0.0109100 | ||||||||
\(201\) | 14.0379i | 0.0698402i | ||||||||
\(202\) | 267.892 | 1.32620 | ||||||||
\(203\) | − | 74.2773i | − | 0.365898i | ||||||
\(204\) | − | 95.8020i | − | 0.469617i | ||||||
\(205\) | − | 132.128i | − | 0.644528i | ||||||
\(206\) | 120.947i | 0.587122i | ||||||||
\(207\) | −60.1955 | + | 33.7268i | −0.290800 | + | 0.162931i | ||||
\(208\) | 3.77624 | 0.0181550 | ||||||||
\(209\) | −70.1013 | −0.335413 | ||||||||
\(210\) | −61.9551 | −0.295024 | ||||||||
\(211\) | 215.285 | 1.02031 | 0.510155 | − | 0.860082i | \(-0.329588\pi\) | ||||
0.510155 | + | 0.860082i | \(0.329588\pi\) | |||||||
\(212\) | − | 184.745i | − | 0.871440i | ||||||
\(213\) | −41.2469 | −0.193647 | ||||||||
\(214\) | − | 195.758i | − | 0.914756i | ||||||
\(215\) | 131.786 | 0.612960 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | − | 4.26967i | − | 0.0196759i | ||||||
\(218\) | 70.3697i | 0.322797i | ||||||||
\(219\) | 169.920 | 0.775892 | ||||||||
\(220\) | 75.9921 | 0.345419 | ||||||||
\(221\) | − | 26.1086i | − | 0.118138i | ||||||
\(222\) | 58.3882i | 0.263010i | ||||||||
\(223\) | 237.892 | 1.06678 | 0.533391 | − | 0.845869i | \(-0.320918\pi\) | ||||
0.533391 | + | 0.845869i | \(0.320918\pi\) | |||||||
\(224\) | 29.0678i | 0.129767i | ||||||||
\(225\) | 2.31437 | 0.0102861 | ||||||||
\(226\) | 267.538i | 1.18380i | ||||||||
\(227\) | − | 1.80104i | − | 0.00793410i | −0.999992 | − | 0.00396705i | \(-0.998737\pi\) | ||
0.999992 | − | 0.00396705i | \(-0.00126275\pi\) | |||||||
\(228\) | − | 31.4588i | − | 0.137977i | ||||||
\(229\) | 230.994i | 1.00871i | 0.863497 | + | 0.504353i | \(0.168269\pi\) | ||||
−0.863497 | + | 0.504353i | \(0.831731\pi\) | |||||||
\(230\) | −78.2587 | − | 139.676i | −0.340255 | − | 0.607287i | ||||
\(231\) | 68.7026 | 0.297414 | ||||||||
\(232\) | −40.8850 | −0.176228 | ||||||||
\(233\) | −50.0293 | −0.214718 | −0.107359 | − | 0.994220i | \(-0.534239\pi\) | ||||
−0.107359 | + | 0.994220i | \(0.534239\pi\) | |||||||
\(234\) | 4.00531 | 0.0171167 | ||||||||
\(235\) | − | 188.168i | − | 0.800715i | ||||||
\(236\) | −95.6914 | −0.405472 | ||||||||
\(237\) | − | 121.249i | − | 0.511598i | ||||||
\(238\) | 200.972 | 0.844422 | ||||||||
\(239\) | 405.258 | 1.69564 | 0.847820 | − | 0.530284i | \(-0.177915\pi\) | ||||
0.847820 | + | 0.530284i | \(0.177915\pi\) | |||||||
\(240\) | 34.1023i | 0.142093i | ||||||||
\(241\) | 348.532i | 1.44619i | 0.690748 | + | 0.723095i | \(0.257281\pi\) | ||||
−0.690748 | + | 0.723095i | \(0.742719\pi\) | |||||||
\(242\) | 86.8515 | 0.358890 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 243.647i | 0.998555i | ||||||||
\(245\) | 111.222i | 0.453966i | ||||||||
\(246\) | −65.7518 | −0.267284 | ||||||||
\(247\) | − | 8.57335i | − | 0.0347099i | ||||||
\(248\) | −2.35019 | −0.00947655 | ||||||||
\(249\) | 87.8750i | 0.352912i | ||||||||
\(250\) | 179.398i | 0.717592i | ||||||||
\(251\) | − | 5.76047i | − | 0.0229501i | −0.999934 | − | 0.0114750i | \(-0.996347\pi\) | ||
0.999934 | − | 0.0114750i | \(-0.00365270\pi\) | |||||||
\(252\) | 30.8311i | 0.122346i | ||||||||
\(253\) | 86.7818 | + | 154.888i | 0.343011 | + | 0.612206i | ||||
\(254\) | −45.5399 | −0.179291 | ||||||||
\(255\) | 235.781 | 0.924630 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 26.3305 | 0.102453 | 0.0512267 | − | 0.998687i | \(-0.483687\pi\) | ||||
0.0512267 | + | 0.998687i | \(0.483687\pi\) | |||||||
\(258\) | − | 65.5817i | − | 0.254193i | ||||||
\(259\) | −122.486 | −0.472920 | ||||||||
\(260\) | 9.29379i | 0.0357454i | ||||||||
\(261\) | −43.3651 | −0.166150 | ||||||||
\(262\) | 125.435 | 0.478758 | ||||||||
\(263\) | − | 61.0826i | − | 0.232253i | −0.993234 | − | 0.116127i | \(-0.962952\pi\) | ||
0.993234 | − | 0.116127i | \(-0.0370478\pi\) | |||||||
\(264\) | − | 37.8164i | − | 0.143244i | ||||||
\(265\) | 454.681 | 1.71578 | ||||||||
\(266\) | 65.9939 | 0.248097 | ||||||||
\(267\) | 151.853i | 0.568740i | ||||||||
\(268\) | 16.2095i | 0.0604834i | ||||||||
\(269\) | −8.00773 | −0.0297685 | −0.0148843 | − | 0.999889i | \(-0.504738\pi\) | ||||
−0.0148843 | + | 0.999889i | \(0.504738\pi\) | |||||||
\(270\) | 36.1710i | 0.133967i | ||||||||
\(271\) | 347.677 | 1.28294 | 0.641470 | − | 0.767148i | \(-0.278325\pi\) | ||||
0.641470 | + | 0.767148i | \(0.278325\pi\) | |||||||
\(272\) | − | 110.623i | − | 0.406701i | ||||||
\(273\) | 8.40229i | 0.0307776i | ||||||||
\(274\) | − | 124.984i | − | 0.456147i | ||||||
\(275\) | − | 5.95506i | − | 0.0216547i | ||||||
\(276\) | −69.5078 | + | 38.9444i | −0.251840 | + | 0.141103i | ||||
\(277\) | −320.160 | −1.15581 | −0.577907 | − | 0.816103i | \(-0.696130\pi\) | ||||
−0.577907 | + | 0.816103i | \(0.696130\pi\) | |||||||
\(278\) | −259.657 | −0.934017 | ||||||||
\(279\) | −2.49275 | −0.00893458 | ||||||||
\(280\) | −71.5395 | −0.255498 | ||||||||
\(281\) | 77.6750i | 0.276424i | 0.990403 | + | 0.138212i | \(0.0441355\pi\) | ||||
−0.990403 | + | 0.138212i | \(0.955865\pi\) | |||||||
\(282\) | −93.6392 | −0.332054 | ||||||||
\(283\) | 449.812i | 1.58944i | 0.606974 | + | 0.794721i | \(0.292383\pi\) | ||||
−0.606974 | + | 0.794721i | \(0.707617\pi\) | |||||||
\(284\) | −47.6278 | −0.167704 | ||||||||
\(285\) | 77.4240 | 0.271663 | ||||||||
\(286\) | − | 10.3060i | − | 0.0360349i | ||||||
\(287\) | − | 137.933i | − | 0.480604i | ||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −475.835 | −1.64649 | ||||||||
\(290\) | − | 100.623i | − | 0.346976i | ||||||
\(291\) | 63.6259i | 0.218646i | ||||||||
\(292\) | 196.207 | 0.671942 | ||||||||
\(293\) | − | 437.459i | − | 1.49304i | −0.665366 | − | 0.746518i | \(-0.731724\pi\) | ||
0.665366 | − | 0.746518i | \(-0.268276\pi\) | |||||||
\(294\) | 55.3479 | 0.188258 | ||||||||
\(295\) | − | 235.508i | − | 0.798334i | ||||||
\(296\) | 67.4209i | 0.227773i | ||||||||
\(297\) | − | 40.1104i | − | 0.135052i | ||||||
\(298\) | − | 122.397i | − | 0.410729i | ||||||
\(299\) | −18.9427 | + | 10.6134i | −0.0633536 | + | 0.0354962i | ||||
\(300\) | 2.67240 | 0.00890800 | ||||||||
\(301\) | 137.577 | 0.457065 | ||||||||
\(302\) | −373.020 | −1.23516 | ||||||||
\(303\) | 328.100 | 1.08284 | ||||||||
\(304\) | − | 36.3255i | − | 0.119492i | ||||||
\(305\) | −599.647 | −1.96605 | ||||||||
\(306\) | − | 117.333i | − | 0.383441i | ||||||
\(307\) | −465.359 | −1.51583 | −0.757914 | − | 0.652354i | \(-0.773781\pi\) | ||||
−0.757914 | + | 0.652354i | \(0.773781\pi\) | |||||||
\(308\) | 79.3309 | 0.257568 | ||||||||
\(309\) | 148.129i | 0.479383i | ||||||||
\(310\) | − | 5.78410i | − | 0.0186584i | ||||||
\(311\) | 596.299 | 1.91736 | 0.958679 | − | 0.284489i | \(-0.0918238\pi\) | ||||
0.958679 | + | 0.284489i | \(0.0918238\pi\) | |||||||
\(312\) | 4.62493 | 0.0148235 | ||||||||
\(313\) | − | 411.536i | − | 1.31481i | −0.753536 | − | 0.657406i | \(-0.771654\pi\) | ||
0.753536 | − | 0.657406i | \(-0.228346\pi\) | |||||||
\(314\) | − | 118.086i | − | 0.376071i | ||||||
\(315\) | −75.8791 | −0.240886 | ||||||||
\(316\) | − | 140.006i | − | 0.443057i | ||||||
\(317\) | −348.576 | −1.09961 | −0.549804 | − | 0.835293i | \(-0.685298\pi\) | ||||
−0.549804 | + | 0.835293i | \(0.685298\pi\) | |||||||
\(318\) | − | 226.266i | − | 0.711528i | ||||||
\(319\) | 111.582i | 0.349786i | ||||||||
\(320\) | 39.3780i | 0.123056i | ||||||||
\(321\) | − | 239.753i | − | 0.746895i | ||||||
\(322\) | −81.6970 | − | 145.813i | −0.253718 | − | 0.452835i | ||||
\(323\) | −251.151 | −0.777558 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0.728300 | 0.00224092 | ||||||||
\(326\) | −252.640 | −0.774969 | ||||||||
\(327\) | 86.1849i | 0.263562i | ||||||||
\(328\) | −75.9236 | −0.231474 | ||||||||
\(329\) | − | 196.435i | − | 0.597068i | ||||||
\(330\) | 93.0709 | 0.282033 | ||||||||
\(331\) | −62.3646 | −0.188413 | −0.0942064 | − | 0.995553i | \(-0.530031\pi\) | ||||
−0.0942064 | + | 0.995553i | \(0.530031\pi\) | |||||||
\(332\) | 101.469i | 0.305631i | ||||||||
\(333\) | 71.5107i | 0.214747i | ||||||||
\(334\) | −177.620 | −0.531795 | ||||||||
\(335\) | −39.8937 | −0.119086 | ||||||||
\(336\) | 35.6007i | 0.105954i | ||||||||
\(337\) | 106.990i | 0.317477i | 0.987321 | + | 0.158738i | \(0.0507427\pi\) | ||||
−0.987321 | + | 0.158738i | \(0.949257\pi\) | |||||||
\(338\) | −237.742 | −0.703378 | ||||||||
\(339\) | 327.666i | 0.966565i | ||||||||
\(340\) | 272.256 | 0.800753 | ||||||||
\(341\) | 6.41404i | 0.0188095i | ||||||||
\(342\) | − | 38.5290i | − | 0.112658i | ||||||
\(343\) | 367.895i | 1.07258i | ||||||||
\(344\) | − | 75.7272i | − | 0.220137i | ||||||
\(345\) | −95.8469 | − | 171.067i | −0.277817 | − | 0.495848i | ||||
\(346\) | 206.455 | 0.596692 | ||||||||
\(347\) | −319.649 | −0.921177 | −0.460589 | − | 0.887614i | \(-0.652362\pi\) | ||||
−0.460589 | + | 0.887614i | \(0.652362\pi\) | |||||||
\(348\) | −50.0737 | −0.143890 | ||||||||
\(349\) | −156.934 | −0.449667 | −0.224834 | − | 0.974397i | \(-0.572184\pi\) | ||||
−0.224834 | + | 0.974397i | \(0.572184\pi\) | |||||||
\(350\) | 5.60613i | 0.0160175i | ||||||||
\(351\) | 4.90548 | 0.0139757 | ||||||||
\(352\) | − | 43.6666i | − | 0.124053i | ||||||
\(353\) | 157.767 | 0.446933 | 0.223466 | − | 0.974712i | \(-0.428263\pi\) | ||||
0.223466 | + | 0.974712i | \(0.428263\pi\) | |||||||
\(354\) | −117.198 | −0.331066 | ||||||||
\(355\) | − | 117.218i | − | 0.330192i | ||||||
\(356\) | 175.345i | 0.492543i | ||||||||
\(357\) | 246.140 | 0.689467 | ||||||||
\(358\) | −216.040 | −0.603465 | ||||||||
\(359\) | 149.911i | 0.417580i | 0.977961 | + | 0.208790i | \(0.0669525\pi\) | ||||
−0.977961 | + | 0.208790i | \(0.933047\pi\) | |||||||
\(360\) | 41.7667i | 0.116019i | ||||||||
\(361\) | 278.529 | 0.771548 | ||||||||
\(362\) | − | 188.820i | − | 0.521603i | ||||||
\(363\) | 106.371 | 0.293033 | ||||||||
\(364\) | 9.70212i | 0.0266542i | ||||||||
\(365\) | 482.890i | 1.32299i | ||||||||
\(366\) | 298.406i | 0.815317i | ||||||||
\(367\) | − | 643.183i | − | 1.75254i | −0.481818 | − | 0.876271i | \(-0.660023\pi\) | ||
0.481818 | − | 0.876271i | \(-0.339977\pi\) | |||||||
\(368\) | −80.2607 | + | 44.9691i | −0.218100 | + | 0.122199i | ||||
\(369\) | −80.5292 | −0.218236 | ||||||||
\(370\) | −165.931 | −0.448463 | ||||||||
\(371\) | 474.658 | 1.27940 | ||||||||
\(372\) | −2.87838 | −0.00773757 | ||||||||
\(373\) | − | 240.542i | − | 0.644884i | −0.946589 | − | 0.322442i | \(-0.895496\pi\) | ||
0.946589 | − | 0.322442i | \(-0.104504\pi\) | |||||||
\(374\) | −301.907 | −0.807239 | ||||||||
\(375\) | 219.717i | 0.585911i | ||||||||
\(376\) | −108.125 | −0.287567 | ||||||||
\(377\) | −13.6464 | −0.0361974 | ||||||||
\(378\) | 37.7602i | 0.0998947i | ||||||||
\(379\) | − | 690.895i | − | 1.82294i | −0.411364 | − | 0.911471i | \(-0.634948\pi\) | ||
0.411364 | − | 0.911471i | \(-0.365052\pi\) | |||||||
\(380\) | 89.4015 | 0.235267 | ||||||||
\(381\) | −55.7747 | −0.146390 | ||||||||
\(382\) | 383.962i | 1.00514i | ||||||||
\(383\) | 249.591i | 0.651674i | 0.945426 | + | 0.325837i | \(0.105646\pi\) | ||||
−0.945426 | + | 0.325837i | \(0.894354\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | 195.243i | 0.507125i | ||||||||
\(386\) | 342.365 | 0.886955 | ||||||||
\(387\) | − | 80.3208i | − | 0.207547i | ||||||
\(388\) | 73.4689i | 0.189353i | ||||||||
\(389\) | − | 515.323i | − | 1.32474i | −0.749177 | − | 0.662369i | \(-0.769551\pi\) | ||
0.749177 | − | 0.662369i | \(-0.230449\pi\) | |||||||
\(390\) | 11.3825i | 0.0291860i | ||||||||
\(391\) | 310.912 | + | 554.915i | 0.795172 | + | 1.41922i | ||||
\(392\) | 63.9103 | 0.163036 | ||||||||
\(393\) | 153.625 | 0.390904 | ||||||||
\(394\) | −355.414 | −0.902066 | ||||||||
\(395\) | 344.572 | 0.872335 | ||||||||
\(396\) | − | 46.3155i | − | 0.116958i | ||||||
\(397\) | −219.200 | −0.552140 | −0.276070 | − | 0.961138i | \(-0.589032\pi\) | ||||
−0.276070 | + | 0.961138i | \(0.589032\pi\) | |||||||
\(398\) | − | 249.345i | − | 0.626496i | ||||||
\(399\) | 80.8257 | 0.202571 | ||||||||
\(400\) | 3.08582 | 0.00771456 | ||||||||
\(401\) | − | 110.690i | − | 0.276034i | −0.990430 | − | 0.138017i | \(-0.955927\pi\) | ||
0.990430 | − | 0.138017i | \(-0.0440729\pi\) | |||||||
\(402\) | 19.8525i | 0.0493844i | ||||||||
\(403\) | −0.784434 | −0.00194649 | ||||||||
\(404\) | 378.857 | 0.937764 | ||||||||
\(405\) | 44.3002i | 0.109383i | ||||||||
\(406\) | − | 105.044i | − | 0.258729i | ||||||
\(407\) | 184.003 | 0.452096 | ||||||||
\(408\) | − | 135.484i | − | 0.332070i | ||||||
\(409\) | 632.891 | 1.54741 | 0.773706 | − | 0.633545i | \(-0.218401\pi\) | ||||
0.773706 | + | 0.633545i | \(0.218401\pi\) | |||||||
\(410\) | − | 186.858i | − | 0.455750i | ||||||
\(411\) | − | 153.074i | − | 0.372442i | ||||||
\(412\) | 171.045i | 0.415158i | ||||||||
\(413\) | − | 245.856i | − | 0.595292i | ||||||
\(414\) | −85.1293 | + | 47.6969i | −0.205626 | + | 0.115210i | ||||
\(415\) | −249.729 | −0.601756 | ||||||||
\(416\) | 5.34041 | 0.0128375 | ||||||||
\(417\) | −318.013 | −0.762621 | ||||||||
\(418\) | −99.1382 | −0.237173 | ||||||||
\(419\) | 655.862i | 1.56530i | 0.622461 | + | 0.782651i | \(0.286133\pi\) | ||||
−0.622461 | + | 0.782651i | \(0.713867\pi\) | |||||||
\(420\) | −87.6177 | −0.208614 | ||||||||
\(421\) | − | 257.748i | − | 0.612228i | −0.951995 | − | 0.306114i | \(-0.900971\pi\) | ||
0.951995 | − | 0.306114i | \(-0.0990288\pi\) | |||||||
\(422\) | 304.460 | 0.721468 | ||||||||
\(423\) | −114.684 | −0.271121 | ||||||||
\(424\) | − | 261.269i | − | 0.616201i | ||||||
\(425\) | − | 21.3351i | − | 0.0502003i | ||||||
\(426\) | −58.3319 | −0.136929 | ||||||||
\(427\) | −625.993 | −1.46603 | ||||||||
\(428\) | − | 276.843i | − | 0.646830i | ||||||
\(429\) | − | 12.6222i | − | 0.0294224i | ||||||
\(430\) | 186.374 | 0.433428 | ||||||||
\(431\) | 703.840i | 1.63304i | 0.577317 | + | 0.816520i | \(0.304100\pi\) | ||||
−0.577317 | + | 0.816520i | \(0.695900\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 621.176i | 1.43459i | 0.696772 | + | 0.717293i | \(0.254619\pi\) | ||||
−0.696772 | + | 0.717293i | \(0.745381\pi\) | |||||||
\(434\) | − | 6.03823i | − | 0.0139130i | ||||||
\(435\) | − | 123.238i | − | 0.283305i | ||||||
\(436\) | 99.5177i | 0.228252i | ||||||||
\(437\) | 102.095 | + | 182.219i | 0.233627 | + | 0.416978i | ||||
\(438\) | 240.304 | 0.548638 | ||||||||
\(439\) | −292.224 | −0.665659 | −0.332830 | − | 0.942987i | \(-0.608003\pi\) | ||||
−0.332830 | + | 0.942987i | \(0.608003\pi\) | |||||||
\(440\) | 107.469 | 0.244248 | ||||||||
\(441\) | 67.7871 | 0.153712 | ||||||||
\(442\) | − | 36.9231i | − | 0.0835364i | ||||||
\(443\) | −541.206 | −1.22168 | −0.610842 | − | 0.791753i | \(-0.709169\pi\) | ||||
−0.610842 | + | 0.791753i | \(0.709169\pi\) | |||||||
\(444\) | 82.5734i | 0.185976i | ||||||||
\(445\) | −431.547 | −0.969768 | ||||||||
\(446\) | 336.430 | 0.754328 | ||||||||
\(447\) | − | 149.906i | − | 0.335359i | ||||||
\(448\) | 41.1081i | 0.0917592i | ||||||||
\(449\) | 554.320 | 1.23457 | 0.617283 | − | 0.786741i | \(-0.288233\pi\) | ||||
0.617283 | + | 0.786741i | \(0.288233\pi\) | |||||||
\(450\) | 3.27301 | 0.00727335 | ||||||||
\(451\) | 207.208i | 0.459442i | ||||||||
\(452\) | 378.356i | 0.837070i | ||||||||
\(453\) | −456.854 | −1.00851 | ||||||||
\(454\) | − | 2.54706i | − | 0.00561026i | ||||||
\(455\) | −23.8781 | −0.0524794 | ||||||||
\(456\) | − | 44.4894i | − | 0.0975645i | ||||||
\(457\) | − | 740.778i | − | 1.62096i | −0.585767 | − | 0.810480i | \(-0.699207\pi\) | ||
0.585767 | − | 0.810480i | \(-0.300793\pi\) | |||||||
\(458\) | 326.674i | 0.713263i | ||||||||
\(459\) | − | 143.703i | − | 0.313078i | ||||||
\(460\) | −110.675 | − | 197.532i | −0.240597 | − | 0.429417i | ||||
\(461\) | 74.1009 | 0.160739 | 0.0803697 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803697 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(462\) | 97.1601 | 0.210303 | ||||||||
\(463\) | 704.351 | 1.52128 | 0.760638 | − | 0.649176i | \(-0.224886\pi\) | ||||
0.760638 | + | 0.649176i | \(0.224886\pi\) | |||||||
\(464\) | −57.8201 | −0.124612 | ||||||||
\(465\) | − | 7.08405i | − | 0.0152345i | ||||||
\(466\) | −70.7520 | −0.151828 | ||||||||
\(467\) | − | 584.754i | − | 1.25215i | −0.779763 | − | 0.626075i | \(-0.784660\pi\) | ||
0.779763 | − | 0.626075i | \(-0.215340\pi\) | |||||||
\(468\) | 5.66436 | 0.0121033 | ||||||||
\(469\) | −41.6465 | −0.0887984 | ||||||||
\(470\) | − | 266.110i | − | 0.566191i | ||||||
\(471\) | − | 144.626i | − | 0.307061i | ||||||
\(472\) | −135.328 | −0.286712 | ||||||||
\(473\) | −206.672 | −0.436939 | ||||||||
\(474\) | − | 171.472i | − | 0.361755i | ||||||
\(475\) | − | 7.00587i | − | 0.0147492i | ||||||
\(476\) | 284.218 | 0.597096 | ||||||||
\(477\) | − | 277.118i | − | 0.580960i | ||||||
\(478\) | 573.122 | 1.19900 | ||||||||
\(479\) | 586.758i | 1.22496i | 0.790485 | + | 0.612482i | \(0.209829\pi\) | ||||
−0.790485 | + | 0.612482i | \(0.790171\pi\) | |||||||
\(480\) | 48.2280i | 0.100475i | ||||||||
\(481\) | 22.5035i | 0.0467847i | ||||||||
\(482\) | 492.899i | 1.02261i | ||||||||
\(483\) | −100.058 | − | 178.583i | −0.207160 | − | 0.369738i | ||||
\(484\) | 122.827 | 0.253774 | ||||||||
\(485\) | −180.816 | −0.372817 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −143.981 | −0.295650 | −0.147825 | − | 0.989014i | \(-0.547227\pi\) | ||||
−0.147825 | + | 0.989014i | \(0.547227\pi\) | |||||||
\(488\) | 344.569i | 0.706085i | ||||||||
\(489\) | −309.420 | −0.632760 | ||||||||
\(490\) | 157.291i | 0.321002i | ||||||||
\(491\) | 672.591 | 1.36984 | 0.684920 | − | 0.728618i | \(-0.259837\pi\) | ||||
0.684920 | + | 0.728618i | \(0.259837\pi\) | |||||||
\(492\) | −92.9871 | −0.188998 | ||||||||
\(493\) | 399.763i | 0.810879i | ||||||||
\(494\) | − | 12.1245i | − | 0.0245436i | ||||||
\(495\) | 113.988 | 0.230279 | ||||||||
\(496\) | −3.32366 | −0.00670094 | ||||||||
\(497\) | − | 122.368i | − | 0.246213i | ||||||
\(498\) | 124.274i | 0.249546i | ||||||||
\(499\) | 110.196 | 0.220834 | 0.110417 | − | 0.993885i | \(-0.464781\pi\) | ||||
0.110417 | + | 0.993885i | \(0.464781\pi\) | |||||||
\(500\) | 253.707i | 0.507414i | ||||||||
\(501\) | −217.539 | −0.434209 | ||||||||
\(502\) | − | 8.14653i | − | 0.0162281i | ||||||
\(503\) | − | 697.316i | − | 1.38631i | −0.720786 | − | 0.693157i | \(-0.756219\pi\) | ||
0.720786 | − | 0.693157i | \(-0.243781\pi\) | |||||||
\(504\) | 43.6017i | 0.0865114i | ||||||||
\(505\) | 932.414i | 1.84636i | ||||||||
\(506\) | 122.728 | + | 219.045i | 0.242546 | + | 0.432895i | ||||
\(507\) | −291.173 | −0.574306 | ||||||||
\(508\) | −64.4031 | −0.126778 | ||||||||
\(509\) | 702.717 | 1.38058 | 0.690292 | − | 0.723531i | \(-0.257482\pi\) | ||||
0.690292 | + | 0.723531i | \(0.257482\pi\) | |||||||
\(510\) | 333.444 | 0.653812 | ||||||||
\(511\) | 504.106i | 0.986509i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 47.1882i | − | 0.0919847i | ||||||
\(514\) | 37.2370 | 0.0724454 | ||||||||
\(515\) | −420.963 | −0.817405 | ||||||||
\(516\) | − | 92.7465i | − | 0.179741i | ||||||
\(517\) | 295.092i | 0.570777i | ||||||||
\(518\) | −173.222 | −0.334405 | ||||||||
\(519\) | 252.855 | 0.487197 | ||||||||
\(520\) | 13.1434i | 0.0252758i | ||||||||
\(521\) | 130.216i | 0.249935i | 0.992161 | + | 0.124968i | \(0.0398827\pi\) | ||||
−0.992161 | + | 0.124968i | \(0.960117\pi\) | |||||||
\(522\) | −61.3275 | −0.117486 | ||||||||
\(523\) | − | 966.051i | − | 1.84713i | −0.383436 | − | 0.923567i | \(-0.625259\pi\) | ||
0.383436 | − | 0.923567i | \(-0.374741\pi\) | |||||||
\(524\) | 177.391 | 0.338533 | ||||||||
\(525\) | 6.86608i | 0.0130783i | ||||||||
\(526\) | − | 86.3838i | − | 0.164228i | ||||||
\(527\) | 22.9795i | 0.0436044i | ||||||||
\(528\) | − | 53.4805i | − | 0.101289i | ||||||
\(529\) | 276.223 | − | 451.156i | 0.522160 | − | 0.852847i | ||||
\(530\) | 643.017 | 1.21324 | ||||||||
\(531\) | −143.537 | −0.270315 | ||||||||
\(532\) | 93.3294 | 0.175431 | ||||||||
\(533\) | −25.3414 | −0.0475449 | ||||||||
\(534\) | 214.753i | 0.402160i | ||||||||
\(535\) | 681.346 | 1.27354 | ||||||||
\(536\) | 22.9237i | 0.0427682i | ||||||||
\(537\) | −264.594 | −0.492727 | ||||||||
\(538\) | −11.3246 | −0.0210495 | ||||||||
\(539\) | − | 174.422i | − | 0.323602i | ||||||
\(540\) | 51.1535i | 0.0947287i | ||||||||
\(541\) | 250.233 | 0.462539 | 0.231269 | − | 0.972890i | \(-0.425712\pi\) | ||||
0.231269 | + | 0.972890i | \(0.425712\pi\) | |||||||
\(542\) | 491.689 | 0.907175 | ||||||||
\(543\) | − | 231.257i | − | 0.425887i | ||||||
\(544\) | − | 156.444i | − | 0.287581i | ||||||
\(545\) | −244.926 | −0.449405 | ||||||||
\(546\) | 11.8826i | 0.0217631i | ||||||||
\(547\) | 226.518 | 0.414109 | 0.207055 | − | 0.978329i | \(-0.433612\pi\) | ||||
0.207055 | + | 0.978329i | \(0.433612\pi\) | |||||||
\(548\) | − | 176.754i | − | 0.322544i | ||||||
\(549\) | 365.471i | 0.665703i | ||||||||
\(550\) | − | 8.42172i | − | 0.0153122i | ||||||
\(551\) | 131.271i | 0.238242i | ||||||||
\(552\) | −98.2989 | + | 55.0756i | −0.178078 | + | 0.0997747i | ||||
\(553\) | 359.711 | 0.650473 | ||||||||
\(554\) | −452.775 | −0.817284 | ||||||||
\(555\) | −203.224 | −0.366169 | ||||||||
\(556\) | −367.210 | −0.660449 | ||||||||
\(557\) | − | 693.109i | − | 1.24436i | −0.782874 | − | 0.622181i | \(-0.786247\pi\) | ||
0.782874 | − | 0.622181i | \(-0.213753\pi\) | |||||||
\(558\) | −3.52528 | −0.00631770 | ||||||||
\(559\) | − | 25.2759i | − | 0.0452162i | ||||||
\(560\) | −101.172 | −0.180665 | ||||||||
\(561\) | −369.759 | −0.659108 | ||||||||
\(562\) | 109.849i | 0.195461i | ||||||||
\(563\) | − | 232.265i | − | 0.412549i | −0.978494 | − | 0.206275i | \(-0.933866\pi\) | ||
0.978494 | − | 0.206275i | \(-0.0661340\pi\) | |||||||
\(564\) | −132.426 | −0.234798 | ||||||||
\(565\) | −931.180 | −1.64811 | ||||||||
\(566\) | 636.131i | 1.12391i | ||||||||
\(567\) | 46.2466i | 0.0815637i | ||||||||
\(568\) | −67.3559 | −0.118584 | ||||||||
\(569\) | 285.831i | 0.502340i | 0.967943 | + | 0.251170i | \(0.0808153\pi\) | ||||
−0.967943 | + | 0.251170i | \(0.919185\pi\) | |||||||
\(570\) | 109.494 | 0.192095 | ||||||||
\(571\) | − | 572.347i | − | 1.00236i | −0.865344 | − | 0.501179i | \(-0.832900\pi\) | ||
0.865344 | − | 0.501179i | \(-0.167100\pi\) | |||||||
\(572\) | − | 14.5749i | − | 0.0254805i | ||||||
\(573\) | 470.255i | 0.820690i | ||||||||
\(574\) | − | 195.067i | − | 0.339838i | ||||||
\(575\) | −15.4794 | + | 8.67291i | −0.0269207 | + | 0.0150833i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 157.233 | 0.272501 | 0.136251 | − | 0.990674i | \(-0.456495\pi\) | ||||
0.136251 | + | 0.990674i | \(0.456495\pi\) | |||||||
\(578\) | −672.932 | −1.16424 | ||||||||
\(579\) | 419.310 | 0.724196 | ||||||||
\(580\) | − | 142.303i | − | 0.245349i | ||||||
\(581\) | −260.701 | −0.448710 | ||||||||
\(582\) | 89.9806i | 0.154606i | ||||||||
\(583\) | −713.047 | −1.22307 | ||||||||
\(584\) | 277.479 | 0.475135 | ||||||||
\(585\) | 13.9407i | 0.0238302i | ||||||||
\(586\) | − | 618.661i | − | 1.05574i | ||||||
\(587\) | −212.520 | −0.362044 | −0.181022 | − | 0.983479i | \(-0.557941\pi\) | ||||
−0.181022 | + | 0.983479i | \(0.557941\pi\) | |||||||
\(588\) | 78.2738 | 0.133119 | ||||||||
\(589\) | 7.54585i | 0.0128113i | ||||||||
\(590\) | − | 333.059i | − | 0.564507i | ||||||
\(591\) | −435.292 | −0.736534 | ||||||||
\(592\) | 95.3476i | 0.161060i | ||||||||
\(593\) | −937.090 | −1.58025 | −0.790127 | − | 0.612944i | \(-0.789985\pi\) | ||||
−0.790127 | + | 0.612944i | \(0.789985\pi\) | |||||||
\(594\) | − | 56.7246i | − | 0.0954960i | ||||||
\(595\) | 699.495i | 1.17562i | ||||||||
\(596\) | − | 173.096i | − | 0.290430i | ||||||
\(597\) | − | 305.385i | − | 0.511532i | ||||||
\(598\) | −26.7891 | + | 15.0096i | −0.0447978 | + | 0.0250996i | ||||
\(599\) | −318.493 | −0.531708 | −0.265854 | − | 0.964013i | \(-0.585654\pi\) | ||||
−0.265854 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(600\) | 3.77935 | 0.00629891 | ||||||||
\(601\) | 799.628 | 1.33050 | 0.665248 | − | 0.746623i | \(-0.268326\pi\) | ||||
0.665248 | + | 0.746623i | \(0.268326\pi\) | |||||||
\(602\) | 194.563 | 0.323194 | ||||||||
\(603\) | 24.3143i | 0.0403222i | ||||||||
\(604\) | −527.529 | −0.873393 | ||||||||
\(605\) | 302.291i | 0.499655i | ||||||||
\(606\) | 464.003 | 0.765681 | ||||||||
\(607\) | −185.298 | −0.305268 | −0.152634 | − | 0.988283i | \(-0.548776\pi\) | ||||
−0.152634 | + | 0.988283i | \(0.548776\pi\) | |||||||
\(608\) | − | 51.3720i | − | 0.0844934i | ||||||
\(609\) | − | 128.652i | − | 0.211251i | ||||||
\(610\) | −848.029 | −1.39021 | ||||||||
\(611\) | −36.0896 | −0.0590664 | ||||||||
\(612\) | − | 165.934i | − | 0.271134i | ||||||
\(613\) | − | 399.963i | − | 0.652469i | −0.945289 | − | 0.326234i | \(-0.894220\pi\) | ||
0.945289 | − | 0.326234i | \(-0.105780\pi\) | |||||||
\(614\) | −658.117 | −1.07185 | ||||||||
\(615\) | − | 228.853i | − | 0.372118i | ||||||
\(616\) | 112.191 | 0.182128 | ||||||||
\(617\) | 308.392i | 0.499826i | 0.968268 | + | 0.249913i | \(0.0804020\pi\) | ||||
−0.968268 | + | 0.249913i | \(0.919598\pi\) | |||||||
\(618\) | 209.487i | 0.338975i | ||||||||
\(619\) | 659.561i | 1.06553i | 0.846264 | + | 0.532763i | \(0.178846\pi\) | ||||
−0.846264 | + | 0.532763i | \(0.821154\pi\) | |||||||
\(620\) | − | 8.17995i | − | 0.0131935i | ||||||
\(621\) | −104.262 | + | 58.4165i | −0.167893 | + | 0.0940685i | ||||
\(622\) | 843.294 | 1.35578 | ||||||||
\(623\) | −450.507 | −0.723125 | ||||||||
\(624\) | 6.54064 | 0.0104818 | ||||||||
\(625\) | −605.118 | −0.968190 | ||||||||
\(626\) | − | 582.000i | − | 0.929713i | ||||||
\(627\) | −121.419 | −0.193651 | ||||||||
\(628\) | − | 166.999i | − | 0.265922i | ||||||
\(629\) | 659.225 | 1.04805 | ||||||||
\(630\) | −107.309 | −0.170332 | ||||||||
\(631\) | 102.663i | 0.162699i | 0.996686 | + | 0.0813497i | \(0.0259231\pi\) | ||||
−0.996686 | + | 0.0813497i | \(0.974077\pi\) | |||||||
\(632\) | − | 197.998i | − | 0.313289i | ||||||
\(633\) | 372.885 | 0.589076 | ||||||||
\(634\) | −492.961 | −0.777541 | ||||||||
\(635\) | − | 158.504i | − | 0.249613i | ||||||
\(636\) | − | 319.988i | − | 0.503126i | ||||||
\(637\) | 21.3317 | 0.0334877 | ||||||||
\(638\) | 157.801i | 0.247336i | ||||||||
\(639\) | −71.4417 | −0.111802 | ||||||||
\(640\) | 55.6889i | 0.0870139i | ||||||||
\(641\) | − | 721.856i | − | 1.12614i | −0.826409 | − | 0.563070i | \(-0.809620\pi\) | ||
0.826409 | − | 0.563070i | \(-0.190380\pi\) | |||||||
\(642\) | − | 339.062i | − | 0.528135i | ||||||
\(643\) | − | 177.237i | − | 0.275641i | −0.990457 | − | 0.137821i | \(-0.955990\pi\) | ||
0.990457 | − | 0.137821i | \(-0.0440097\pi\) | |||||||
\(644\) | −115.537 | − | 206.210i | −0.179405 | − | 0.320202i | ||||
\(645\) | 228.261 | 0.353893 | ||||||||
\(646\) | −355.181 | −0.549816 | ||||||||
\(647\) | 568.014 | 0.877920 | 0.438960 | − | 0.898507i | \(-0.355347\pi\) | ||||
0.438960 | + | 0.898507i | \(0.355347\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 369.333i | 0.569079i | ||||||||
\(650\) | 1.02997 | 0.00158457 | ||||||||
\(651\) | − | 7.39529i | − | 0.0113599i | ||||||
\(652\) | −357.287 | −0.547986 | ||||||||
\(653\) | −550.970 | −0.843752 | −0.421876 | − | 0.906653i | \(-0.638628\pi\) | ||||
−0.421876 | + | 0.906653i | \(0.638628\pi\) | |||||||
\(654\) | 121.884i | 0.186367i | ||||||||
\(655\) | 436.582i | 0.666538i | ||||||||
\(656\) | −107.372 | −0.163677 | ||||||||
\(657\) | 294.311 | 0.447961 | ||||||||
\(658\) | − | 277.801i | − | 0.422191i | ||||||
\(659\) | − | 663.157i | − | 1.00631i | −0.864197 | − | 0.503154i | \(-0.832173\pi\) | ||
0.864197 | − | 0.503154i | \(-0.167827\pi\) | |||||||
\(660\) | 131.622 | 0.199428 | ||||||||
\(661\) | − | 893.783i | − | 1.35217i | −0.736825 | − | 0.676084i | \(-0.763676\pi\) | ||
0.736825 | − | 0.676084i | \(-0.236324\pi\) | |||||||
\(662\) | −88.1969 | −0.133228 | ||||||||
\(663\) | − | 45.2214i | − | 0.0682072i | ||||||
\(664\) | 143.499i | 0.216113i | ||||||||
\(665\) | 229.695i | 0.345407i | ||||||||
\(666\) | 101.131i | 0.151849i | ||||||||
\(667\) | 290.043 | − | 162.507i | 0.434847 | − | 0.243639i | ||||
\(668\) | −251.192 | −0.376036 | ||||||||
\(669\) | 412.041 | 0.615906 | ||||||||
\(670\) | −56.4182 | −0.0842063 | ||||||||
\(671\) | 940.387 | 1.40147 | ||||||||
\(672\) | 50.3469i | 0.0749210i | ||||||||
\(673\) | 1201.94 | 1.78594 | 0.892969 | − | 0.450118i | \(-0.148618\pi\) | ||||
0.892969 | + | 0.450118i | \(0.148618\pi\) | |||||||
\(674\) | 151.306i | 0.224490i | ||||||||
\(675\) | 4.00860 | 0.00593867 | ||||||||
\(676\) | −336.218 | −0.497363 | ||||||||
\(677\) | 338.932i | 0.500639i | 0.968163 | + | 0.250319i | \(0.0805356\pi\) | ||||
−0.968163 | + | 0.250319i | \(0.919464\pi\) | |||||||
\(678\) | 463.389i | 0.683465i | ||||||||
\(679\) | −188.760 | −0.277998 | ||||||||
\(680\) | 385.028 | 0.566218 | ||||||||
\(681\) | − | 3.11949i | − | 0.00458076i | ||||||
\(682\) | 9.07083i | 0.0133003i | ||||||||
\(683\) | −951.288 | −1.39281 | −0.696404 | − | 0.717650i | \(-0.745218\pi\) | ||||
−0.696404 | + | 0.717650i | \(0.745218\pi\) | |||||||
\(684\) | − | 54.4882i | − | 0.0796611i | ||||||
\(685\) | 435.015 | 0.635058 | ||||||||
\(686\) | 520.283i | 0.758429i | ||||||||
\(687\) | 400.093i | 0.582377i | ||||||||
\(688\) | − | 107.094i | − | 0.155661i | ||||||
\(689\) | − | 87.2053i | − | 0.126568i | ||||||
\(690\) | −135.548 | − | 241.926i | −0.196446 | − | 0.350617i | ||||
\(691\) | −407.739 | −0.590071 | −0.295036 | − | 0.955486i | \(-0.595332\pi\) | ||||
−0.295036 | + | 0.955486i | \(0.595332\pi\) | |||||||
\(692\) | 291.972 | 0.421925 | ||||||||
\(693\) | 118.996 | 0.171712 | ||||||||
\(694\) | −452.051 | −0.651371 | ||||||||
\(695\) | − | 903.749i | − | 1.30036i | ||||||
\(696\) | −70.8149 | −0.101746 | ||||||||
\(697\) | 742.362i | 1.06508i | ||||||||
\(698\) | −221.938 | −0.317963 | ||||||||
\(699\) | −86.6532 | −0.123967 | ||||||||
\(700\) | 7.92827i | 0.0113261i | ||||||||
\(701\) | 1016.66i | 1.45029i | 0.688594 | + | 0.725147i | \(0.258228\pi\) | ||||
−0.688594 | + | 0.725147i | \(0.741772\pi\) | |||||||
\(702\) | 6.93739 | 0.00988233 | ||||||||
\(703\) | 216.472 | 0.307926 | ||||||||
\(704\) | − | 61.7540i | − | 0.0877187i | ||||||
\(705\) | − | 325.917i | − | 0.462293i | ||||||
\(706\) | 223.117 | 0.316029 | ||||||||
\(707\) | 973.380i | 1.37678i | ||||||||
\(708\) | −165.742 | −0.234099 | ||||||||
\(709\) | − | 121.061i | − | 0.170749i | −0.996349 | − | 0.0853744i | \(-0.972791\pi\) | ||
0.996349 | − | 0.0853744i | \(-0.0272086\pi\) | |||||||
\(710\) | − | 165.771i | − | 0.233481i | ||||||
\(711\) | − | 210.009i | − | 0.295371i | ||||||
\(712\) | 247.976i | 0.348281i | ||||||||
\(713\) | 16.6725 | − | 9.34138i | 0.0233836 | − | 0.0131015i | ||||
\(714\) | 348.094 | 0.487527 | ||||||||
\(715\) | 35.8705 | 0.0501686 | ||||||||
\(716\) | −305.527 | −0.426714 | ||||||||
\(717\) | 701.928 | 0.978979 | ||||||||
\(718\) | 212.006i | 0.295274i | ||||||||
\(719\) | 160.481 | 0.223200 | 0.111600 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111600 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(720\) | 59.0670i | 0.0820375i | ||||||||
\(721\) | −439.459 | −0.609513 | ||||||||
\(722\) | 393.899 | 0.545567 | ||||||||
\(723\) | 603.675i | 0.834959i | ||||||||
\(724\) | − | 267.032i | − | 0.368829i | ||||||
\(725\) | −11.1514 | −0.0153813 | ||||||||
\(726\) | 150.431 | 0.207205 | ||||||||
\(727\) | − | 328.928i | − | 0.452446i | −0.974076 | − | 0.226223i | \(-0.927362\pi\) | ||
0.974076 | − | 0.226223i | \(-0.0726378\pi\) | |||||||
\(728\) | 13.7209i | 0.0188474i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 682.910i | 0.935493i | ||||||||
\(731\) | −740.441 | −1.01292 | ||||||||
\(732\) | 422.010i | 0.576516i | ||||||||
\(733\) | 528.441i | 0.720929i | 0.932773 | + | 0.360465i | \(0.117382\pi\) | ||||
−0.932773 | + | 0.360465i | \(0.882618\pi\) | |||||||
\(734\) | − | 909.598i | − | 1.23923i | ||||||
\(735\) | 192.641i | 0.262097i | ||||||||
\(736\) | −113.506 | + | 63.5959i | −0.154220 | + | 0.0864074i | ||||
\(737\) | 62.5627 | 0.0848883 | ||||||||
\(738\) | −113.885 | −0.154316 | ||||||||
\(739\) | 816.397 | 1.10473 | 0.552366 | − | 0.833602i | \(-0.313725\pi\) | ||||
0.552366 | + | 0.833602i | \(0.313725\pi\) | |||||||
\(740\) | −234.662 | −0.317111 | ||||||||
\(741\) | − | 14.8495i | − | 0.0200398i | ||||||
\(742\) | 671.268 | 0.904674 | ||||||||
\(743\) | 501.473i | 0.674930i | 0.941338 | + | 0.337465i | \(0.109570\pi\) | ||||
−0.941338 | + | 0.337465i | \(0.890430\pi\) | |||||||
\(744\) | −4.07064 | −0.00547129 | ||||||||
\(745\) | 426.011 | 0.571827 | ||||||||
\(746\) | − | 340.177i | − | 0.456002i | ||||||
\(747\) | 152.204i | 0.203754i | ||||||||
\(748\) | −426.961 | −0.570804 | ||||||||
\(749\) | 711.281 | 0.949641 | ||||||||
\(750\) | 310.726i | 0.414302i | ||||||||
\(751\) | 706.401i | 0.940614i | 0.882503 | + | 0.470307i | \(0.155857\pi\) | ||||
−0.882503 | + | 0.470307i | \(0.844143\pi\) | |||||||
\(752\) | −152.912 | −0.203341 | ||||||||
\(753\) | − | 9.97742i | − | 0.0132502i | ||||||
\(754\) | −19.2989 | −0.0255954 | ||||||||
\(755\) | − | 1298.32i | − | 1.71962i | ||||||
\(756\) | 53.4010i | 0.0706362i | ||||||||
\(757\) | − | 1154.74i | − | 1.52542i | −0.646740 | − | 0.762711i | \(-0.723868\pi\) | ||
0.646740 | − | 0.762711i | \(-0.276132\pi\) | |||||||
\(758\) | − | 977.073i | − | 1.28901i | ||||||
\(759\) | 150.311 | + | 268.274i | 0.198038 | + | 0.353457i | ||||
\(760\) | 126.433 | 0.166359 | ||||||||
\(761\) | 834.803 | 1.09698 | 0.548491 | − | 0.836157i | \(-0.315203\pi\) | ||||
0.548491 | + | 0.836157i | \(0.315203\pi\) | |||||||
\(762\) | −78.8774 | −0.103514 | ||||||||
\(763\) | −255.687 | −0.335107 | ||||||||
\(764\) | 543.004i | 0.710739i | ||||||||
\(765\) | 408.384 | 0.533835 | ||||||||
\(766\) | 352.975i | 0.460803i | ||||||||
\(767\) | −45.1692 | −0.0588907 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | 154.214i | 0.200538i | 0.994960 | + | 0.100269i | \(0.0319703\pi\) | ||||
−0.994960 | + | 0.100269i | \(0.968030\pi\) | |||||||
\(770\) | 276.116i | 0.358592i | ||||||||
\(771\) | 45.6058 | 0.0591515 | ||||||||
\(772\) | 484.177 | 0.627172 | ||||||||
\(773\) | 487.995i | 0.631301i | 0.948876 | + | 0.315650i | \(0.102223\pi\) | ||||
−0.948876 | + | 0.315650i | \(0.897777\pi\) | |||||||
\(774\) | − | 113.591i | − | 0.146758i | ||||||
\(775\) | −0.641015 | −0.000827116 | ||||||||
\(776\) | 103.901i | 0.133893i | ||||||||
\(777\) | −212.152 | −0.273040 | ||||||||
\(778\) | − | 728.777i | − | 0.936732i | ||||||
\(779\) | 243.772i | 0.312929i | ||||||||
\(780\) | 16.0973i | 0.0206376i | ||||||||
\(781\) | 183.825i | 0.235372i | ||||||||
\(782\) | 439.696 | + | 784.769i | 0.562271 | + | 1.00354i | ||||
\(783\) | −75.1105 | −0.0959266 | ||||||||
\(784\) | 90.3827 | 0.115284 | ||||||||
\(785\) | 411.006 | 0.523574 | ||||||||
\(786\) | 217.259 | 0.276411 | ||||||||
\(787\) | − | 193.960i | − | 0.246455i | −0.992378 | − | 0.123228i | \(-0.960675\pi\) | ||
0.992378 | − | 0.123228i | \(-0.0393246\pi\) | |||||||
\(788\) | −502.631 | −0.637857 | ||||||||
\(789\) | − | 105.798i | − | 0.134091i | ||||||
\(790\) | 487.299 | 0.616834 | ||||||||
\(791\) | −972.092 | −1.22894 | ||||||||
\(792\) | − | 65.5000i | − | 0.0827020i | ||||||
\(793\) | 115.009i | 0.145030i | ||||||||
\(794\) | −309.995 | −0.390422 | ||||||||
\(795\) | 787.531 | 0.990605 | ||||||||
\(796\) | − | 352.628i | − | 0.443000i | ||||||
\(797\) | 916.068i | 1.14939i | 0.818366 | + | 0.574697i | \(0.194880\pi\) | ||||
−0.818366 | + | 0.574697i | \(0.805120\pi\) | |||||||
\(798\) | 114.305 | 0.143239 | ||||||||
\(799\) | 1057.22i | 1.32318i | ||||||||
\(800\) | 4.36401 | 0.00545502 | ||||||||
\(801\) | 263.018i | 0.328362i | ||||||||
\(802\) | − | 156.539i | − | 0.195186i | ||||||
\(803\) | − | 757.285i | − | 0.943070i | ||||||
\(804\) | 28.0757i | 0.0349201i | ||||||||
\(805\) | 507.509 | − | 284.351i | 0.630447 | − | 0.353231i | ||||
\(806\) | −1.10936 | −0.00137637 | ||||||||
\(807\) | −13.8698 | −0.0171869 | ||||||||
\(808\) | 535.784 | 0.663099 | ||||||||
\(809\) | −81.4166 | −0.100639 | −0.0503193 | − | 0.998733i | \(-0.516024\pi\) | ||||
−0.0503193 | + | 0.998733i | \(0.516024\pi\) | |||||||
\(810\) | 62.6500i | 0.0773457i | ||||||||
\(811\) | 1503.38 | 1.85374 | 0.926870 | − | 0.375382i | \(-0.122489\pi\) | ||||
0.926870 | + | 0.375382i | \(0.122489\pi\) | |||||||
\(812\) | − | 148.555i | − | 0.182949i | ||||||
\(813\) | 602.193 | 0.740705 | ||||||||
\(814\) | 260.219 | 0.319680 | ||||||||
\(815\) | − | 879.328i | − | 1.07893i | ||||||
\(816\) | − | 191.604i | − | 0.234809i | ||||||
\(817\) | −243.141 | −0.297602 | ||||||||
\(818\) | 895.044 | 1.09419 | ||||||||
\(819\) | 14.5532i | 0.0177695i | ||||||||
\(820\) | − | 264.256i | − | 0.322264i | ||||||
\(821\) | −136.557 | −0.166330 | −0.0831651 | − | 0.996536i | \(-0.526503\pi\) | ||||
−0.0831651 | + | 0.996536i | \(0.526503\pi\) | |||||||
\(822\) | − | 216.479i | − | 0.263356i | ||||||
\(823\) | −134.188 | −0.163048 | −0.0815239 | − | 0.996671i | \(-0.525979\pi\) | ||||
−0.0815239 | + | 0.996671i | \(0.525979\pi\) | |||||||
\(824\) | 241.894i | 0.293561i | ||||||||
\(825\) | − | 10.3145i | − | 0.0125024i | ||||||
\(826\) | − | 347.692i | − | 0.420935i | ||||||
\(827\) | 1190.70i | 1.43979i | 0.694085 | + | 0.719893i | \(0.255809\pi\) | ||||
−0.694085 | + | 0.719893i | \(0.744191\pi\) | |||||||
\(828\) | −120.391 | + | 67.4536i | −0.145400 | + | 0.0814657i | ||||
\(829\) | 167.849 | 0.202471 | 0.101236 | − | 0.994862i | \(-0.467720\pi\) | ||||
0.101236 | + | 0.994862i | \(0.467720\pi\) | |||||||
\(830\) | −353.170 | −0.425506 | ||||||||
\(831\) | −554.534 | −0.667309 | ||||||||
\(832\) | 7.55248 | 0.00907750 | ||||||||
\(833\) | − | 624.898i | − | 0.750178i | ||||||
\(834\) | −449.738 | −0.539255 | ||||||||
\(835\) | − | 618.215i | − | 0.740378i | ||||||
\(836\) | −140.203 | −0.167706 | ||||||||
\(837\) | −4.31757 | −0.00515838 | ||||||||
\(838\) | 927.528i | 1.10684i | ||||||||
\(839\) | 620.476i | 0.739542i | 0.929123 | + | 0.369771i | \(0.120564\pi\) | ||||
−0.929123 | + | 0.369771i | \(0.879436\pi\) | |||||||
\(840\) | −123.910 | −0.147512 | ||||||||
\(841\) | −632.052 | −0.751548 | ||||||||
\(842\) | − | 364.511i | − | 0.432910i | ||||||
\(843\) | 134.537i | 0.159593i | ||||||||
\(844\) | 430.571 | 0.510155 | ||||||||
\(845\) | − | 827.473i | − | 0.979258i | ||||||
\(846\) | −162.188 | −0.191711 | ||||||||
\(847\) | 315.573i | 0.372577i | ||||||||
\(848\) | − | 369.491i | − | 0.435720i | ||||||
\(849\) | 779.098i | 0.917665i | ||||||||
\(850\) | − | 30.1724i | − | 0.0354969i | ||||||
\(851\) | −267.981 | − | 478.292i | −0.314901 | − | 0.562035i | ||||
\(852\) | −82.4938 | −0.0968237 | ||||||||
\(853\) | 639.619 | 0.749846 | 0.374923 | − | 0.927056i | \(-0.377669\pi\) | ||||
0.374923 | + | 0.927056i | \(0.377669\pi\) | |||||||
\(854\) | −885.287 | −1.03664 | ||||||||
\(855\) | 134.102 | 0.156845 | ||||||||
\(856\) | − | 391.516i | − | 0.457378i | ||||||
\(857\) | 351.336 | 0.409960 | 0.204980 | − | 0.978766i | \(-0.434287\pi\) | ||||
0.204980 | + | 0.978766i | \(0.434287\pi\) | |||||||
\(858\) | − | 17.8505i | − | 0.0208048i | ||||||
\(859\) | −1548.57 | −1.80276 | −0.901382 | − | 0.433024i | \(-0.857446\pi\) | ||||
−0.901382 | + | 0.433024i | \(0.857446\pi\) | |||||||
\(860\) | 263.573 | 0.306480 | ||||||||
\(861\) | − | 238.908i | − | 0.277477i | ||||||
\(862\) | 995.381i | 1.15473i | ||||||||
\(863\) | −1502.94 | −1.74153 | −0.870763 | − | 0.491703i | \(-0.836375\pi\) | ||||
−0.870763 | + | 0.491703i | \(0.836375\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | 718.579i | 0.830727i | ||||||||
\(866\) | 878.475i | 1.01441i | ||||||||
\(867\) | −824.170 | −0.950600 | ||||||||
\(868\) | − | 8.53934i | − | 0.00983795i | ||||||
\(869\) | −540.370 | −0.621830 | ||||||||
\(870\) | − | 174.284i | − | 0.200327i | ||||||
\(871\) | 7.65138i | 0.00878460i | ||||||||
\(872\) | 140.739i | 0.161398i | ||||||||
\(873\) | 110.203i | 0.126235i | ||||||||
\(874\) | 144.384 | + | 257.697i | 0.165200 | + | 0.294848i | ||||
\(875\) | −651.839 | −0.744958 | ||||||||
\(876\) | 339.841 | 0.387946 | ||||||||
\(877\) | −474.173 | −0.540676 | −0.270338 | − | 0.962765i | \(-0.587135\pi\) | ||||
−0.270338 | + | 0.962765i | \(0.587135\pi\) | |||||||
\(878\) | −413.268 | −0.470692 | ||||||||
\(879\) | − | 757.702i | − | 0.862004i | ||||||
\(880\) | 151.984 | 0.172709 | ||||||||
\(881\) | − | 727.978i | − | 0.826309i | −0.910661 | − | 0.413154i | \(-0.864427\pi\) | ||
0.910661 | − | 0.413154i | \(-0.135573\pi\) | |||||||
\(882\) | 95.8654 | 0.108691 | ||||||||
\(883\) | 134.373 | 0.152178 | 0.0760890 | − | 0.997101i | \(-0.475757\pi\) | ||||
0.0760890 | + | 0.997101i | \(0.475757\pi\) | |||||||
\(884\) | − | 52.2172i | − | 0.0590692i | ||||||
\(885\) | − | 407.913i | − | 0.460918i | ||||||
\(886\) | −765.381 | −0.863861 | ||||||||
\(887\) | 510.194 | 0.575190 | 0.287595 | − | 0.957752i | \(-0.407144\pi\) | ||||
0.287595 | + | 0.957752i | \(0.407144\pi\) | |||||||
\(888\) | 116.776i | 0.131505i | ||||||||
\(889\) | − | 165.468i | − | 0.186128i | ||||||
\(890\) | −610.299 | −0.685729 | ||||||||
\(891\) | − | 69.4732i | − | 0.0779722i | ||||||
\(892\) | 475.784 | 0.533391 | ||||||||
\(893\) | 347.163i | 0.388760i | ||||||||
\(894\) | − | 211.998i | − | 0.237135i | ||||||
\(895\) | − | 751.941i | − | 0.840157i | ||||||
\(896\) | 58.1356i | 0.0648835i | ||||||||
\(897\) | −32.8098 | + | 18.3829i | −0.0365772 | + | 0.0204938i | ||||
\(898\) | 783.927 | 0.872970 | ||||||||
\(899\) | 12.0109 | 0.0133603 | ||||||||
\(900\) | 4.62873 | 0.00514304 | ||||||||
\(901\) | −2554.63 | −2.83532 | ||||||||
\(902\) | 293.037i | 0.324874i | ||||||||
\(903\) | 238.290 | 0.263887 | ||||||||
\(904\) | 535.076i | 0.591898i | ||||||||
\(905\) | 657.199 | 0.726187 | ||||||||
\(906\) | −646.089 | −0.713122 | ||||||||
\(907\) | − | 594.907i | − | 0.655907i | −0.944694 | − | 0.327953i | \(-0.893641\pi\) | ||
0.944694 | − | 0.327953i | \(-0.106359\pi\) | |||||||
\(908\) | − | 3.60208i | − | 0.00396705i | ||||||
\(909\) | 568.285 | 0.625176 | ||||||||
\(910\) | −33.7688 | −0.0371086 | ||||||||
\(911\) | − | 1025.46i | − | 1.12564i | −0.826579 | − | 0.562821i | \(-0.809716\pi\) | ||
0.826579 | − | 0.562821i | \(-0.190284\pi\) | |||||||
\(912\) | − | 62.9176i | − | 0.0689886i | ||||||
\(913\) | 391.633 | 0.428952 | ||||||||
\(914\) | − | 1047.62i | − | 1.14619i | ||||||
\(915\) | −1038.62 | −1.13510 | ||||||||
\(916\) | 461.987i | 0.504353i | ||||||||
\(917\) | 455.764i | 0.497016i | ||||||||
\(918\) | − | 203.227i | − | 0.221380i | ||||||
\(919\) | − | 1333.78i | − | 1.45133i | −0.688046 | − | 0.725667i | \(-0.741531\pi\) | ||
0.688046 | − | 0.725667i | \(-0.258469\pi\) | |||||||
\(920\) | −156.517 | − | 279.352i | −0.170128 | − | 0.303643i | ||||
\(921\) | −806.026 | −0.875164 | ||||||||
\(922\) | 104.794 | 0.113660 | ||||||||
\(923\) | −22.4817 | −0.0243573 | ||||||||
\(924\) | 137.405 | 0.148707 | ||||||||
\(925\) | 18.3891i | 0.0198801i | ||||||||
\(926\) | 996.103 | 1.07570 | ||||||||
\(927\) | 256.568i | 0.276772i | ||||||||
\(928\) | −81.7700 | −0.0881142 | ||||||||
\(929\) | −1146.22 | −1.23382 | −0.616911 | − | 0.787033i | \(-0.711616\pi\) | ||||
−0.616911 | + | 0.787033i | \(0.711616\pi\) | |||||||
\(930\) | − | 10.0184i | − | 0.0107724i | ||||||
\(931\) | − | 205.200i | − | 0.220408i | ||||||
\(932\) | −100.059 | −0.107359 | ||||||||
\(933\) | 1032.82 | 1.10699 | ||||||||
\(934\) | − | 826.968i | − | 0.885404i | ||||||
\(935\) | − | 1050.81i | − | 1.12386i | ||||||
\(936\) | 8.01061 | 0.00855834 | ||||||||
\(937\) | 1095.51i | 1.16916i | 0.811334 | + | 0.584582i | \(0.198742\pi\) | ||||
−0.811334 | + | 0.584582i | \(0.801258\pi\) | |||||||
\(938\) | −58.8970 | −0.0627900 | ||||||||
\(939\) | − | 712.802i | − | 0.759107i | ||||||
\(940\) | − | 376.336i | − | 0.400357i | ||||||
\(941\) | 422.732i | 0.449237i | 0.974447 | + | 0.224618i | \(0.0721135\pi\) | ||||
−0.974447 | + | 0.224618i | \(0.927886\pi\) | |||||||
\(942\) | − | 204.531i | − | 0.217125i | ||||||
\(943\) | 538.611 | − | 301.777i | 0.571167 | − | 0.320018i | ||||
\(944\) | −191.383 | −0.202736 | ||||||||
\(945\) | −131.427 | −0.139076 | ||||||||
\(946\) | −292.278 | −0.308962 | ||||||||
\(947\) | 823.217 | 0.869289 | 0.434645 | − | 0.900602i | \(-0.356874\pi\) | ||||
0.434645 | + | 0.900602i | \(0.356874\pi\) | |||||||
\(948\) | − | 242.498i | − | 0.255799i | ||||||
\(949\) | 92.6156 | 0.0975928 | ||||||||
\(950\) | − | 9.90780i | − | 0.0104293i | ||||||
\(951\) | −603.751 | −0.634859 | ||||||||
\(952\) | 401.945 | 0.422211 | ||||||||
\(953\) | 397.062i | 0.416644i | 0.978060 | + | 0.208322i | \(0.0668002\pi\) | ||||
−0.978060 | + | 0.208322i | \(0.933200\pi\) | |||||||
\(954\) | − | 391.904i | − | 0.410801i | ||||||
\(955\) | −1336.40 | −1.39937 | ||||||||
\(956\) | 810.516 | 0.847820 | ||||||||
\(957\) | 193.266i | 0.201949i | ||||||||
\(958\) | 829.801i | 0.866180i | ||||||||
\(959\) | 454.127 | 0.473543 | ||||||||
\(960\) | 68.2047i | 0.0710466i | ||||||||
\(961\) | −960.310 | −0.999282 | ||||||||
\(962\) | 31.8247i | 0.0330818i | ||||||||
\(963\) | − | 415.265i | − | 0.431220i | ||||||
\(964\) | 697.064i | 0.723095i | ||||||||
\(965\) | 1191.62i | 1.23484i | ||||||||
\(966\) | −141.503 | − | 252.555i | −0.146484 | − | 0.261444i | ||||
\(967\) | −981.927 | −1.01544 | −0.507718 | − | 0.861523i | \(-0.669511\pi\) | ||||
−0.507718 | + | 0.861523i | \(0.669511\pi\) | |||||||
\(968\) | 173.703 | 0.179445 | ||||||||
\(969\) | −435.006 | −0.448923 | ||||||||
\(970\) | −255.713 | −0.263621 | ||||||||
\(971\) | 985.395i | 1.01483i | 0.861703 | + | 0.507413i | \(0.169398\pi\) | ||||
−0.861703 | + | 0.507413i | \(0.830602\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | − | 943.456i | − | 0.969637i | ||||||
\(974\) | −203.620 | −0.209056 | ||||||||
\(975\) | 1.26145 | 0.00129380 | ||||||||
\(976\) | 487.295i | 0.499277i | ||||||||
\(977\) | − | 1772.59i | − | 1.81432i | −0.420783 | − | 0.907161i | \(-0.638245\pi\) | ||
0.420783 | − | 0.907161i | \(-0.361755\pi\) | |||||||
\(978\) | −437.585 | −0.447429 | ||||||||
\(979\) | 676.767 | 0.691284 | ||||||||
\(980\) | 222.443i | 0.226983i | ||||||||
\(981\) | 149.277i | 0.152168i | ||||||||
\(982\) | 951.188 | 0.968623 | ||||||||
\(983\) | − | 1328.52i | − | 1.35149i | −0.737135 | − | 0.675746i | \(-0.763822\pi\) | ||
0.737135 | − | 0.675746i | \(-0.236178\pi\) | |||||||
\(984\) | −131.504 | −0.133642 | ||||||||
\(985\) | − | 1237.04i | − | 1.25588i | ||||||
\(986\) | 565.350i | 0.573378i | ||||||||
\(987\) | − | 340.236i | − | 0.344717i | ||||||
\(988\) | − | 17.1467i | − | 0.0173550i | ||||||
\(989\) | 300.996 | + | 537.217i | 0.304344 | + | 0.543192i | ||||
\(990\) | 161.204 | 0.162832 | ||||||||
\(991\) | −274.330 | −0.276821 | −0.138411 | − | 0.990375i | \(-0.544199\pi\) | ||||
−0.138411 | + | 0.990375i | \(0.544199\pi\) | |||||||
\(992\) | −4.70037 | −0.00473828 | ||||||||
\(993\) | −108.019 | −0.108780 | ||||||||
\(994\) | − | 173.055i | − | 0.174099i | ||||||
\(995\) | 867.861 | 0.872222 | ||||||||
\(996\) | 175.750i | 0.176456i | ||||||||
\(997\) | −1081.51 | −1.08476 | −0.542380 | − | 0.840133i | \(-0.682477\pi\) | ||||
−0.542380 | + | 0.840133i | \(0.682477\pi\) | |||||||
\(998\) | 155.841 | 0.156153 | ||||||||
\(999\) | 123.860i | 0.123984i |
(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 | 138.3.b.a.91.8 | yes | 8 | |
3.2 | odd | 2 | 414.3.b.c.91.2 | 8 | |||
4.3 | odd | 2 | 1104.3.c.c.1057.4 | 8 | |||
23.22 | odd | 2 | inner | 138.3.b.a.91.7 | ✓ | 8 | |
69.68 | even | 2 | 414.3.b.c.91.3 | 8 | |||
92.91 | even | 2 | 1104.3.c.c.1057.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.3.b.a.91.7 | ✓ | 8 | 23.22 | odd | 2 | inner | |
138.3.b.a.91.8 | yes | 8 | 1.1 | even | 1 | trivial | |
414.3.b.c.91.2 | 8 | 3.2 | odd | 2 | |||
414.3.b.c.91.3 | 8 | 69.68 | even | 2 | |||
1104.3.c.c.1057.1 | 8 | 92.91 | even | 2 | |||
1104.3.c.c.1057.4 | 8 | 4.3 | odd | 2 |