Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.18 | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.b.449.17 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −2.98306 | + | 0.318317i | −0.994355 | + | 0.106106i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.21869 | + | 0.450168i | −0.703115 | + | 0.0750280i | ||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 8.79735 | − | 1.89912i | 0.977483 | − | 0.211013i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.46124i | − | 0.223749i | −0.993722 | − | 0.111874i | \(-0.964315\pi\) | ||
0.993722 | − | 0.111874i | \(-0.0356854\pi\) | |||||||
\(12\) | −5.96613 | + | 0.636634i | −0.497177 | + | 0.0530528i | ||||
\(13\) | 5.95665i | 0.458204i | 0.973402 | + | 0.229102i | \(0.0735789\pi\) | ||||
−0.973402 | + | 0.229102i | \(0.926421\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −17.1483 | −1.00873 | −0.504363 | − | 0.863492i | \(-0.668273\pi\) | ||||
−0.504363 | + | 0.863492i | \(0.668273\pi\) | |||||||
\(18\) | 12.4413 | − | 2.68576i | 0.691185 | − | 0.149209i | ||||
\(19\) | 10.3642 | 0.545486 | 0.272743 | − | 0.962087i | \(-0.412069\pi\) | ||||
0.272743 | + | 0.962087i | \(0.412069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.842187 | − | 7.89245i | −0.0401042 | − | 0.375831i | ||||
\(22\) | − | 3.48072i | − | 0.158214i | ||||||
\(23\) | 25.4573 | 1.10684 | 0.553420 | − | 0.832902i | \(-0.313322\pi\) | ||||
0.553420 | + | 0.832902i | \(0.313322\pi\) | |||||||
\(24\) | −8.43738 | + | 0.900336i | −0.351558 | + | 0.0375140i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.42398i | 0.323999i | ||||||||
\(27\) | −25.6385 | + | 8.46554i | −0.949575 | + | 0.313539i | ||||
\(28\) | 5.29150i | 0.188982i | ||||||||
\(29\) | 2.22108i | 0.0765890i | 0.999266 | + | 0.0382945i | \(0.0121925\pi\) | ||||
−0.999266 | + | 0.0382945i | \(0.987807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.60441 | 0.277562 | 0.138781 | − | 0.990323i | \(-0.455682\pi\) | ||||
0.138781 | + | 0.990323i | \(0.455682\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0.783453 | + | 7.34203i | 0.0237410 | + | 0.222486i | ||||
\(34\) | −24.2514 | −0.713277 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 17.5947 | − | 3.79824i | 0.488742 | − | 0.105507i | ||||
\(37\) | 24.2274i | 0.654796i | 0.944887 | + | 0.327398i | \(0.106172\pi\) | ||||
−0.944887 | + | 0.327398i | \(0.893828\pi\) | |||||||
\(38\) | 14.6572 | 0.385717 | ||||||||
\(39\) | −1.89610 | − | 17.7691i | −0.0486180 | − | 0.455617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9247i | 0.266455i | 0.991085 | + | 0.133228i | \(0.0425342\pi\) | ||||
−0.991085 | + | 0.133228i | \(0.957466\pi\) | |||||||
\(42\) | −1.19103 | − | 11.1616i | −0.0283579 | − | 0.265753i | ||||
\(43\) | 63.9354i | 1.48687i | 0.668808 | + | 0.743435i | \(0.266805\pi\) | ||||
−0.668808 | + | 0.743435i | \(0.733195\pi\) | |||||||
\(44\) | − | 4.92247i | − | 0.111874i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 36.0021 | 0.782654 | ||||||||
\(47\) | −53.3023 | −1.13409 | −0.567046 | − | 0.823686i | \(-0.691914\pi\) | ||||
−0.567046 | + | 0.823686i | \(0.691914\pi\) | |||||||
\(48\) | −11.9323 | + | 1.27327i | −0.248589 | + | 0.0265264i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 51.1546 | − | 5.45861i | 1.00303 | − | 0.107031i | ||||
\(52\) | 11.9133i | 0.229102i | ||||||||
\(53\) | 64.5180 | 1.21732 | 0.608660 | − | 0.793431i | \(-0.291707\pi\) | ||||
0.608660 | + | 0.793431i | \(0.291707\pi\) | |||||||
\(54\) | −36.2584 | + | 11.9721i | −0.671451 | + | 0.221705i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | −30.9172 | + | 3.29911i | −0.542406 | + | 0.0578791i | ||||
\(58\) | 3.14108i | 0.0541566i | ||||||||
\(59\) | − | 25.0383i | − | 0.424378i | −0.977229 | − | 0.212189i | \(-0.931941\pi\) | ||
0.977229 | − | 0.212189i | \(-0.0680593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.3424 | 1.18594 | 0.592970 | − | 0.805224i | \(-0.297955\pi\) | ||||
0.592970 | + | 0.805224i | \(0.297955\pi\) | |||||||
\(62\) | 12.1685 | 0.196266 | ||||||||
\(63\) | 5.02460 | + | 23.2756i | 0.0797555 | + | 0.369454i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.10797 | + | 10.3832i | 0.0167874 | + | 0.157321i | ||||
\(67\) | 76.9249i | 1.14813i | 0.818809 | + | 0.574067i | \(0.194635\pi\) | ||||
−0.818809 | + | 0.574067i | \(0.805365\pi\) | |||||||
\(68\) | −34.2967 | −0.504363 | ||||||||
\(69\) | −75.9409 | + | 8.10350i | −1.10059 | + | 0.117442i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 43.1374i | 0.607569i | 0.952741 | + | 0.303784i | \(0.0982503\pi\) | ||||
−0.952741 | + | 0.303784i | \(0.901750\pi\) | |||||||
\(72\) | 24.8827 | − | 5.37152i | 0.345592 | − | 0.0746045i | ||||
\(73\) | 96.2952i | 1.31911i | 0.751655 | + | 0.659556i | \(0.229256\pi\) | ||||
−0.751655 | + | 0.659556i | \(0.770744\pi\) | |||||||
\(74\) | 34.2628i | 0.463011i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.7284 | 0.272743 | ||||||||
\(77\) | 6.51182 | 0.0845691 | ||||||||
\(78\) | −2.68149 | − | 25.1293i | −0.0343781 | − | 0.322170i | ||||
\(79\) | 56.4860 | 0.715013 | 0.357506 | − | 0.933911i | \(-0.383627\pi\) | ||||
0.357506 | + | 0.933911i | \(0.383627\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 73.7867 | − | 33.4144i | 0.910947 | − | 0.412524i | ||||
\(82\) | 15.4498i | 0.188412i | ||||||||
\(83\) | 10.9616 | 0.132067 | 0.0660337 | − | 0.997817i | \(-0.478965\pi\) | ||||
0.0660337 | + | 0.997817i | \(0.478965\pi\) | |||||||
\(84\) | −1.68437 | − | 15.7849i | −0.0200521 | − | 0.187915i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 90.4183i | 1.05138i | ||||||||
\(87\) | −0.707008 | − | 6.62563i | −0.00812652 | − | 0.0761567i | ||||
\(88\) | − | 6.96143i | − | 0.0791072i | ||||||
\(89\) | 161.438i | 1.81391i | 0.421223 | + | 0.906957i | \(0.361601\pi\) | ||||
−0.421223 | + | 0.906957i | \(0.638399\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.7598 | −0.173185 | ||||||||
\(92\) | 50.9147 | 0.553420 | ||||||||
\(93\) | −25.6675 | + | 2.73893i | −0.275995 | + | 0.0294508i | ||||
\(94\) | −75.3809 | −0.801924 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −16.8748 | + | 1.80067i | −0.175779 | + | 0.0187570i | ||||
\(97\) | 167.772i | 1.72960i | 0.502113 | + | 0.864802i | \(0.332556\pi\) | ||||
−0.502113 | + | 0.864802i | \(0.667444\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | −4.67418 | − | 21.6524i | −0.0472140 | − | 0.218711i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 113.437i | 1.12314i | 0.827429 | + | 0.561570i | \(0.189802\pi\) | ||||
−0.827429 | + | 0.561570i | \(0.810198\pi\) | |||||||
\(102\) | 72.3435 | − | 7.71963i | 0.709250 | − | 0.0756827i | ||||
\(103\) | 11.0672i | 0.107448i | 0.998556 | + | 0.0537242i | \(0.0171092\pi\) | ||||
−0.998556 | + | 0.0537242i | \(0.982891\pi\) | |||||||
\(104\) | 16.8480i | 0.162000i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 91.2422 | 0.860776 | ||||||||
\(107\) | 19.2928 | 0.180307 | 0.0901534 | − | 0.995928i | \(-0.471264\pi\) | ||||
0.0901534 | + | 0.995928i | \(0.471264\pi\) | |||||||
\(108\) | −51.2771 | + | 16.9311i | −0.474788 | + | 0.156769i | ||||
\(109\) | −29.3391 | −0.269166 | −0.134583 | − | 0.990902i | \(-0.542970\pi\) | ||||
−0.134583 | + | 0.990902i | \(0.542970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.71200 | − | 72.2720i | −0.0694775 | − | 0.651099i | ||||
\(112\) | 10.5830i | 0.0944911i | ||||||||
\(113\) | −33.2693 | −0.294418 | −0.147209 | − | 0.989105i | \(-0.547029\pi\) | ||||
−0.147209 | + | 0.989105i | \(0.547029\pi\) | |||||||
\(114\) | −43.7235 | + | 4.66564i | −0.383539 | + | 0.0409267i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.44216i | 0.0382945i | ||||||||
\(117\) | 11.3124 | + | 52.4027i | 0.0966871 | + | 0.447887i | ||||
\(118\) | − | 35.4095i | − | 0.300081i | ||||||
\(119\) | − | 45.3702i | − | 0.381263i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.942 | 0.949936 | ||||||||
\(122\) | 102.308 | 0.838587 | ||||||||
\(123\) | −3.47751 | − | 32.5890i | −0.0282724 | − | 0.264951i | ||||
\(124\) | 17.2088 | 0.138781 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.10585 | + | 32.9167i | 0.0563957 | + | 0.261243i | ||||
\(127\) | − | 154.615i | − | 1.21744i | −0.793386 | − | 0.608719i | \(-0.791684\pi\) | ||
0.793386 | − | 0.608719i | \(-0.208316\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −20.3517 | − | 190.723i | −0.157765 | − | 1.47848i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 191.400i | − | 1.46107i | −0.682875 | − | 0.730535i | \(-0.739271\pi\) | ||
0.682875 | − | 0.730535i | \(-0.260729\pi\) | |||||||
\(132\) | 1.56691 | + | 14.6841i | 0.0118705 | + | 0.111243i | ||||
\(133\) | 27.4212i | 0.206174i | ||||||||
\(134\) | 108.788i | 0.811853i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −48.5028 | −0.356638 | ||||||||
\(137\) | 30.7427 | 0.224399 | 0.112199 | − | 0.993686i | \(-0.464210\pi\) | ||||
0.112199 | + | 0.993686i | \(0.464210\pi\) | |||||||
\(138\) | −107.397 | + | 11.4601i | −0.778236 | + | 0.0830440i | ||||
\(139\) | −26.4077 | −0.189983 | −0.0949917 | − | 0.995478i | \(-0.530282\pi\) | ||||
−0.0949917 | + | 0.995478i | \(0.530282\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 159.004 | − | 16.9670i | 1.12769 | − | 0.120334i | ||||
\(142\) | 61.0055i | 0.429616i | ||||||||
\(143\) | 14.6607 | 0.102523 | ||||||||
\(144\) | 35.1894 | − | 7.59648i | 0.244371 | − | 0.0527533i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 136.182i | 0.932753i | ||||||||
\(147\) | 20.8815 | − | 2.22822i | 0.142051 | − | 0.0151579i | ||||
\(148\) | 48.4549i | 0.327398i | ||||||||
\(149\) | 0.905723i | 0.00607868i | 0.999995 | + | 0.00303934i | \(0.000967453\pi\) | ||||
−0.999995 | + | 0.00303934i | \(0.999033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −93.4124 | −0.618625 | −0.309313 | − | 0.950960i | \(-0.600099\pi\) | ||||
−0.309313 | + | 0.950960i | \(0.600099\pi\) | |||||||
\(152\) | 29.3145 | 0.192858 | ||||||||
\(153\) | −150.860 | + | 32.5667i | −0.986013 | + | 0.212855i | ||||
\(154\) | 9.20911 | 0.0597994 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.79220 | − | 35.5381i | −0.0243090 | − | 0.227809i | ||||
\(157\) | − | 32.6815i | − | 0.208162i | −0.994569 | − | 0.104081i | \(-0.966810\pi\) | ||
0.994569 | − | 0.104081i | \(-0.0331902\pi\) | |||||||
\(158\) | 79.8832 | 0.505590 | ||||||||
\(159\) | −192.461 | + | 20.5372i | −1.21045 | + | 0.129165i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.3538i | 0.418346i | ||||||||
\(162\) | 104.350 | − | 47.2551i | 0.644137 | − | 0.291698i | ||||
\(163\) | − | 124.070i | − | 0.761167i | −0.924747 | − | 0.380584i | \(-0.875723\pi\) | ||
0.924747 | − | 0.380584i | \(-0.124277\pi\) | |||||||
\(164\) | 21.8493i | 0.133228i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.5020 | 0.0933858 | ||||||||
\(167\) | −183.213 | −1.09708 | −0.548542 | − | 0.836123i | \(-0.684817\pi\) | ||||
−0.548542 | + | 0.836123i | \(0.684817\pi\) | |||||||
\(168\) | −2.38207 | − | 22.3232i | −0.0141790 | − | 0.132876i | ||||
\(169\) | 133.518 | 0.790049 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.1777 | − | 19.6829i | 0.533203 | − | 0.115105i | ||||
\(172\) | 127.871i | 0.743435i | ||||||||
\(173\) | 70.8439 | 0.409502 | 0.204751 | − | 0.978814i | \(-0.434361\pi\) | ||||
0.204751 | + | 0.978814i | \(0.434361\pi\) | |||||||
\(174\) | −0.999860 | − | 9.37005i | −0.00574632 | − | 0.0538509i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 9.84495i | − | 0.0559372i | ||||||
\(177\) | 7.97012 | + | 74.6909i | 0.0450289 | + | 0.421983i | ||||
\(178\) | 228.308i | 1.28263i | ||||||||
\(179\) | − | 305.073i | − | 1.70432i | −0.523282 | − | 0.852160i | \(-0.675293\pi\) | ||
0.523282 | − | 0.852160i | \(-0.324707\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −69.3954 | −0.383400 | −0.191700 | − | 0.981454i | \(-0.561400\pi\) | ||||
−0.191700 | + | 0.981454i | \(0.561400\pi\) | |||||||
\(182\) | −22.2877 | −0.122460 | ||||||||
\(183\) | −215.802 | + | 23.0278i | −1.17925 | + | 0.125835i | ||||
\(184\) | 72.0042 | 0.391327 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −36.2993 | + | 3.87343i | −0.195158 | + | 0.0208249i | ||||
\(187\) | 42.2061i | 0.225701i | ||||||||
\(188\) | −106.605 | −0.567046 | ||||||||
\(189\) | −22.3977 | − | 67.8332i | −0.118506 | − | 0.358906i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 165.339i | − | 0.865648i | −0.901478 | − | 0.432824i | \(-0.857517\pi\) | ||
0.901478 | − | 0.432824i | \(-0.142483\pi\) | |||||||
\(192\) | −23.8645 | + | 2.54653i | −0.124294 | + | 0.0132632i | ||||
\(193\) | 321.908i | 1.66792i | 0.551828 | + | 0.833958i | \(0.313930\pi\) | ||||
−0.551828 | + | 0.833958i | \(0.686070\pi\) | |||||||
\(194\) | 237.265i | 1.22301i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −354.728 | −1.80065 | −0.900325 | − | 0.435218i | \(-0.856671\pi\) | ||||
−0.900325 | + | 0.435218i | \(0.856671\pi\) | |||||||
\(198\) | −6.61029 | − | 30.6211i | −0.0333853 | − | 0.154652i | ||||
\(199\) | 252.929 | 1.27100 | 0.635501 | − | 0.772100i | \(-0.280794\pi\) | ||||
0.635501 | + | 0.772100i | \(0.280794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.4865 | − | 229.472i | −0.121823 | − | 1.14165i | ||||
\(202\) | 160.424i | 0.794180i | ||||||||
\(203\) | −5.87643 | −0.0289479 | ||||||||
\(204\) | 102.309 | − | 10.9172i | 0.501516 | − | 0.0535157i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6514i | 0.0759774i | ||||||||
\(207\) | 223.957 | − | 48.3465i | 1.08192 | − | 0.233558i | ||||
\(208\) | 23.8266i | 0.114551i | ||||||||
\(209\) | − | 25.5088i | − | 0.122052i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40.9685 | 0.194163 | 0.0970817 | − | 0.995276i | \(-0.469049\pi\) | ||||
0.0970817 | + | 0.995276i | \(0.469049\pi\) | |||||||
\(212\) | 129.036 | 0.608660 | ||||||||
\(213\) | −13.7314 | − | 128.682i | −0.0644665 | − | 0.604139i | ||||
\(214\) | 27.2842 | 0.127496 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −72.5167 | + | 23.9442i | −0.335726 | + | 0.110853i | ||||
\(217\) | 22.7651i | 0.104908i | ||||||||
\(218\) | −41.4918 | −0.190329 | ||||||||
\(219\) | −30.6524 | − | 287.255i | −0.139965 | − | 1.31167i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 102.147i | − | 0.462202i | ||||||
\(222\) | −10.9064 | − | 102.208i | −0.0491280 | − | 0.460397i | ||||
\(223\) | − | 217.935i | − | 0.977289i | −0.872483 | − | 0.488645i | \(-0.837491\pi\) | ||
0.872483 | − | 0.488645i | \(-0.162509\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −47.0499 | −0.208185 | ||||||||
\(227\) | −130.607 | −0.575361 | −0.287680 | − | 0.957726i | \(-0.592884\pi\) | ||||
−0.287680 | + | 0.957726i | \(0.592884\pi\) | |||||||
\(228\) | −61.8343 | + | 6.59821i | −0.271203 | + | 0.0289395i | ||||
\(229\) | −176.250 | −0.769652 | −0.384826 | − | 0.922989i | \(-0.625739\pi\) | ||||
−0.384826 | + | 0.922989i | \(0.625739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.4252 | + | 2.07282i | −0.0840917 | + | 0.00897326i | ||||
\(232\) | 6.28217i | 0.0270783i | ||||||||
\(233\) | 383.463 | 1.64576 | 0.822882 | − | 0.568213i | \(-0.192365\pi\) | ||||
0.822882 | + | 0.568213i | \(0.192365\pi\) | |||||||
\(234\) | 15.9981 | + | 74.1087i | 0.0683681 | + | 0.316704i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 50.0767i | − | 0.212189i | ||||||
\(237\) | −168.501 | + | 17.9804i | −0.710976 | + | 0.0758668i | ||||
\(238\) | − | 64.1632i | − | 0.269593i | ||||||
\(239\) | 157.348i | 0.658361i | 0.944267 | + | 0.329181i | \(0.106772\pi\) | ||||
−0.944267 | + | 0.329181i | \(0.893228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.975 | 0.435580 | 0.217790 | − | 0.975996i | \(-0.430115\pi\) | ||||
0.217790 | + | 0.975996i | \(0.430115\pi\) | |||||||
\(242\) | 162.553 | 0.671707 | ||||||||
\(243\) | −209.474 | + | 123.165i | −0.862033 | + | 0.506852i | ||||
\(244\) | 144.685 | 0.592970 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.91794 | − | 46.0878i | −0.0199916 | − | 0.187349i | ||||
\(247\) | 61.7361i | 0.249944i | ||||||||
\(248\) | 24.3369 | 0.0981328 | ||||||||
\(249\) | −32.6992 | + | 3.48926i | −0.131322 | + | 0.0140131i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 85.3203i | 0.339921i | 0.985451 | + | 0.169961i | \(0.0543641\pi\) | ||||
−0.985451 | + | 0.169961i | \(0.945636\pi\) | |||||||
\(252\) | 10.0492 | + | 46.5512i | 0.0398778 | + | 0.184727i | ||||
\(253\) | − | 62.6565i | − | 0.247654i | ||||||
\(254\) | − | 218.658i | − | 0.860858i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −342.067 | −1.33100 | −0.665499 | − | 0.746398i | \(-0.731781\pi\) | ||||
−0.665499 | + | 0.746398i | \(0.731781\pi\) | |||||||
\(258\) | −28.7817 | − | 269.724i | −0.111557 | − | 1.04544i | ||||
\(259\) | −64.0998 | −0.247490 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.21810 | + | 19.5396i | 0.0161613 | + | 0.0748645i | ||||
\(262\) | − | 270.681i | − | 1.03313i | ||||||
\(263\) | 491.050 | 1.86711 | 0.933555 | − | 0.358433i | \(-0.116689\pi\) | ||||
0.933555 | + | 0.358433i | \(0.116689\pi\) | |||||||
\(264\) | 2.21594 | + | 20.7664i | 0.00839371 | + | 0.0786606i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 38.7794i | 0.145787i | ||||||||
\(267\) | −51.3885 | − | 481.581i | −0.192466 | − | 1.80367i | ||||
\(268\) | 153.850i | 0.574067i | ||||||||
\(269\) | − | 77.8232i | − | 0.289305i | −0.989482 | − | 0.144653i | \(-0.953793\pi\) | ||
0.989482 | − | 0.144653i | \(-0.0462065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −395.316 | −1.45873 | −0.729366 | − | 0.684124i | \(-0.760185\pi\) | ||||
−0.729366 | + | 0.684124i | \(0.760185\pi\) | |||||||
\(272\) | −68.5934 | −0.252181 | ||||||||
\(273\) | 47.0125 | − | 5.01661i | 0.172207 | − | 0.0183759i | ||||
\(274\) | 43.4767 | 0.158674 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −151.882 | + | 16.2070i | −0.550296 | + | 0.0587210i | ||||
\(277\) | − | 544.962i | − | 1.96737i | −0.179896 | − | 0.983686i | \(-0.557576\pi\) | ||
0.179896 | − | 0.983686i | \(-0.442424\pi\) | |||||||
\(278\) | −37.3461 | −0.134339 | ||||||||
\(279\) | 75.6960 | − | 16.3408i | 0.271312 | − | 0.0585692i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 239.047i | 0.850703i | 0.905028 | + | 0.425351i | \(0.139849\pi\) | ||||
−0.905028 | + | 0.425351i | \(0.860151\pi\) | |||||||
\(282\) | 224.866 | − | 23.9950i | 0.797397 | − | 0.0850887i | ||||
\(283\) | − | 409.774i | − | 1.44796i | −0.689819 | − | 0.723982i | \(-0.742310\pi\) | ||
0.689819 | − | 0.723982i | \(-0.257690\pi\) | |||||||
\(284\) | 86.2748i | 0.303784i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.7334 | 0.0724944 | ||||||||
\(287\) | −28.9040 | −0.100711 | ||||||||
\(288\) | 49.7653 | − | 10.7430i | 0.172796 | − | 0.0373022i | ||||
\(289\) | 5.06559 | 0.0175280 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −53.4045 | − | 500.473i | −0.183521 | − | 1.71984i | ||||
\(292\) | 192.590i | 0.659556i | ||||||||
\(293\) | 253.198 | 0.864158 | 0.432079 | − | 0.901836i | \(-0.357780\pi\) | ||||
0.432079 | + | 0.901836i | \(0.357780\pi\) | |||||||
\(294\) | 29.5308 | − | 3.15118i | 0.100445 | − | 0.0107183i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 68.5256i | 0.231505i | ||||||||
\(297\) | 20.8357 | + | 63.1025i | 0.0701539 | + | 0.212466i | ||||
\(298\) | 1.28089i | 0.00429827i | ||||||||
\(299\) | 151.640i | 0.507159i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −169.157 | −0.561984 | ||||||||
\(302\) | −132.105 | −0.437434 | ||||||||
\(303\) | −36.1089 | − | 338.390i | −0.119171 | − | 1.11680i | ||||
\(304\) | 41.4569 | 0.136371 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −213.348 | + | 46.0563i | −0.697216 | + | 0.150511i | ||||
\(307\) | − | 107.521i | − | 0.350230i | −0.984548 | − | 0.175115i | \(-0.943970\pi\) | ||
0.984548 | − | 0.175115i | \(-0.0560298\pi\) | |||||||
\(308\) | 13.0236 | 0.0422846 | ||||||||
\(309\) | −3.52287 | − | 33.0141i | −0.0114009 | − | 0.106842i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 164.570i | 0.529162i | 0.964363 | + | 0.264581i | \(0.0852337\pi\) | ||||
−0.964363 | + | 0.264581i | \(0.914766\pi\) | |||||||
\(312\) | −5.36299 | − | 50.2585i | −0.0171891 | − | 0.161085i | ||||
\(313\) | − | 558.672i | − | 1.78489i | −0.451153 | − | 0.892447i | \(-0.648987\pi\) | ||
0.451153 | − | 0.892447i | \(-0.351013\pi\) | |||||||
\(314\) | − | 46.2186i | − | 0.147193i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 112.972 | 0.357506 | ||||||||
\(317\) | −183.286 | −0.578190 | −0.289095 | − | 0.957300i | \(-0.593354\pi\) | ||||
−0.289095 | + | 0.957300i | \(0.593354\pi\) | |||||||
\(318\) | −272.181 | + | 29.0439i | −0.855917 | + | 0.0913331i | ||||
\(319\) | 5.46661 | 0.0171367 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −57.5517 | + | 6.14123i | −0.179289 | + | 0.0191316i | ||||
\(322\) | 95.2526i | 0.295816i | ||||||||
\(323\) | −177.729 | −0.550245 | ||||||||
\(324\) | 147.573 | − | 66.8289i | 0.455473 | − | 0.206262i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 175.462i | − | 0.538227i | ||||||
\(327\) | 87.5205 | − | 9.33913i | 0.267647 | − | 0.0285600i | ||||
\(328\) | 30.8996i | 0.0942062i | ||||||||
\(329\) | − | 141.025i | − | 0.428647i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −566.039 | −1.71009 | −0.855043 | − | 0.518557i | \(-0.826469\pi\) | ||||
−0.855043 | + | 0.518557i | \(0.826469\pi\) | |||||||
\(332\) | 21.9232 | 0.0660337 | ||||||||
\(333\) | 46.0108 | + | 213.137i | 0.138171 | + | 0.640052i | ||||
\(334\) | −259.102 | −0.775756 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.36875 | − | 31.5698i | −0.0100260 | − | 0.0939577i | ||||
\(337\) | − | 533.027i | − | 1.58168i | −0.612022 | − | 0.790841i | \(-0.709643\pi\) | ||
0.612022 | − | 0.790841i | \(-0.290357\pi\) | |||||||
\(338\) | 188.823 | 0.558649 | ||||||||
\(339\) | 99.2444 | − | 10.5902i | 0.292756 | − | 0.0312394i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 21.1775i | − | 0.0621041i | ||||||
\(342\) | 128.945 | − | 27.8358i | 0.377031 | − | 0.0813913i | ||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | 180.837i | 0.525688i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 100.188 | 0.289562 | ||||||||
\(347\) | 390.990 | 1.12677 | 0.563386 | − | 0.826194i | \(-0.309499\pi\) | ||||
0.563386 | + | 0.826194i | \(0.309499\pi\) | |||||||
\(348\) | −1.41402 | − | 13.2513i | −0.00406326 | − | 0.0380783i | ||||
\(349\) | −283.402 | −0.812041 | −0.406021 | − | 0.913864i | \(-0.633084\pi\) | ||||
−0.406021 | + | 0.913864i | \(0.633084\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −50.4263 | − | 152.720i | −0.143665 | − | 0.435099i | ||||
\(352\) | − | 13.9229i | − | 0.0395536i | ||||||
\(353\) | 580.549 | 1.64461 | 0.822307 | − | 0.569044i | \(-0.192686\pi\) | ||||
0.822307 | + | 0.569044i | \(0.192686\pi\) | |||||||
\(354\) | 11.2715 | + | 105.629i | 0.0318403 | + | 0.298387i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 322.877i | 0.906957i | ||||||||
\(357\) | 14.4421 | + | 135.342i | 0.0404541 | + | 0.379110i | ||||
\(358\) | − | 431.439i | − | 1.20514i | ||||||
\(359\) | 465.159i | 1.29571i | 0.761765 | + | 0.647854i | \(0.224333\pi\) | ||||
−0.761765 | + | 0.647854i | \(0.775667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −253.583 | −0.702446 | ||||||||
\(362\) | −98.1399 | −0.271105 | ||||||||
\(363\) | −342.880 | + | 36.5881i | −0.944574 | + | 0.100794i | ||||
\(364\) | −31.5196 | −0.0865924 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −305.190 | + | 32.5662i | −0.833853 | + | 0.0889788i | ||||
\(367\) | − | 486.978i | − | 1.32691i | −0.748214 | − | 0.663457i | \(-0.769088\pi\) | ||
0.748214 | − | 0.663457i | \(-0.230912\pi\) | |||||||
\(368\) | 101.829 | 0.276710 | ||||||||
\(369\) | 20.7473 | + | 96.1081i | 0.0562256 | + | 0.260456i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 170.699i | 0.460104i | ||||||||
\(372\) | −51.3350 | + | 5.47786i | −0.137997 | + | 0.0147254i | ||||
\(373\) | − | 90.3262i | − | 0.242161i | −0.992643 | − | 0.121081i | \(-0.961364\pi\) | ||
0.992643 | − | 0.121081i | \(-0.0386360\pi\) | |||||||
\(374\) | 59.6885i | 0.159595i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −150.762 | −0.400962 | ||||||||
\(377\) | −13.2302 | −0.0350934 | ||||||||
\(378\) | −31.6752 | − | 95.9306i | −0.0837967 | − | 0.253785i | ||||
\(379\) | 580.355 | 1.53128 | 0.765640 | − | 0.643269i | \(-0.222422\pi\) | ||||
0.765640 | + | 0.643269i | \(0.222422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.2164 | + | 461.225i | 0.129177 | + | 1.21056i | ||||
\(382\) | − | 233.824i | − | 0.612106i | ||||||
\(383\) | 106.999 | 0.279371 | 0.139685 | − | 0.990196i | \(-0.455391\pi\) | ||||
0.139685 | + | 0.990196i | \(0.455391\pi\) | |||||||
\(384\) | −33.7495 | + | 3.60134i | −0.0878894 | + | 0.00937850i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 455.246i | 1.17939i | ||||||||
\(387\) | 121.421 | + | 562.462i | 0.313749 | + | 1.45339i | ||||
\(388\) | 335.543i | 0.864802i | ||||||||
\(389\) | 474.997i | 1.22107i | 0.791988 | + | 0.610536i | \(0.209046\pi\) | ||||
−0.791988 | + | 0.610536i | \(0.790954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −436.551 | −1.11650 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | 60.9259 | + | 570.959i | 0.155028 | + | 1.45282i | ||||
\(394\) | −501.661 | −1.27325 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.34837 | − | 43.3047i | −0.0236070 | − | 0.109355i | ||||
\(397\) | 543.180i | 1.36821i | 0.729383 | + | 0.684106i | \(0.239807\pi\) | ||||
−0.729383 | + | 0.684106i | \(0.760193\pi\) | |||||||
\(398\) | 357.696 | 0.898734 | ||||||||
\(399\) | −8.72862 | − | 81.7991i | −0.0218762 | − | 0.205010i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 113.348i | − | 0.282662i | −0.989962 | − | 0.141331i | \(-0.954862\pi\) | ||
0.989962 | − | 0.141331i | \(-0.0451382\pi\) | |||||||
\(402\) | −34.6291 | − | 324.522i | −0.0861421 | − | 0.807270i | ||||
\(403\) | 51.2535i | 0.127180i | ||||||||
\(404\) | 226.874i | 0.561570i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.31053 | −0.0204693 | ||||||||
\(407\) | 59.6295 | 0.146510 | ||||||||
\(408\) | 144.687 | − | 15.4393i | 0.354625 | − | 0.0378413i | ||||
\(409\) | 507.919 | 1.24186 | 0.620928 | − | 0.783867i | \(-0.286756\pi\) | ||||
0.620928 | + | 0.783867i | \(0.286756\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −91.7073 | + | 9.78590i | −0.223132 | + | 0.0238100i | ||||
\(412\) | 22.1344i | 0.0537242i | ||||||||
\(413\) | 66.2452 | 0.160400 | ||||||||
\(414\) | 316.723 | − | 68.3723i | 0.765031 | − | 0.165150i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 33.6959i | 0.0809998i | ||||||||
\(417\) | 78.7758 | − | 8.40601i | 0.188911 | − | 0.0201583i | ||||
\(418\) | − | 36.0749i | − | 0.0863036i | ||||||
\(419\) | − | 8.79015i | − | 0.0209789i | −0.999945 | − | 0.0104894i | \(-0.996661\pi\) | ||
0.999945 | − | 0.0104894i | \(-0.00333895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 182.651 | 0.433851 | 0.216926 | − | 0.976188i | \(-0.430397\pi\) | ||||
0.216926 | + | 0.976188i | \(0.430397\pi\) | |||||||
\(422\) | 57.9382 | 0.137294 | ||||||||
\(423\) | −468.919 | + | 101.228i | −1.10856 | + | 0.239309i | ||||
\(424\) | 182.484 | 0.430388 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −19.4191 | − | 181.983i | −0.0455847 | − | 0.427191i | ||||
\(427\) | 191.400i | 0.448244i | ||||||||
\(428\) | 38.5857 | 0.0901534 | ||||||||
\(429\) | −43.7339 | + | 4.66676i | −0.101944 | + | 0.0108782i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 109.256i | 0.253493i | 0.991935 | + | 0.126747i | \(0.0404535\pi\) | ||||
−0.991935 | + | 0.126747i | \(0.959546\pi\) | |||||||
\(432\) | −102.554 | + | 33.8622i | −0.237394 | + | 0.0783846i | ||||
\(433\) | − | 241.349i | − | 0.557387i | −0.960380 | − | 0.278694i | \(-0.910099\pi\) | ||
0.960380 | − | 0.278694i | \(-0.0899014\pi\) | |||||||
\(434\) | 32.1947i | 0.0741815i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −58.6782 | −0.134583 | ||||||||
\(437\) | 263.845 | 0.603765 | ||||||||
\(438\) | −43.3490 | − | 406.240i | −0.0989704 | − | 0.927488i | ||||
\(439\) | 78.9565 | 0.179855 | 0.0899277 | − | 0.995948i | \(-0.471336\pi\) | ||||
0.0899277 | + | 0.995948i | \(0.471336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −61.5814 | + | 13.2938i | −0.139640 | + | 0.0301448i | ||||
\(442\) | − | 144.457i | − | 0.326826i | ||||||
\(443\) | −348.992 | −0.787791 | −0.393896 | − | 0.919155i | \(-0.628873\pi\) | ||||
−0.393896 | + | 0.919155i | \(0.628873\pi\) | |||||||
\(444\) | −15.4240 | − | 144.544i | −0.0347388 | − | 0.325550i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 308.207i | − | 0.691048i | ||||||
\(447\) | −0.288307 | − | 2.70183i | −0.000644982 | − | 0.00604436i | ||||
\(448\) | 21.1660i | 0.0472456i | ||||||||
\(449\) | 401.895i | 0.895088i | 0.894262 | + | 0.447544i | \(0.147701\pi\) | ||||
−0.894262 | + | 0.447544i | \(0.852299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.8882 | 0.0596191 | ||||||||
\(452\) | −66.5385 | −0.147209 | ||||||||
\(453\) | 278.655 | − | 29.7347i | 0.615133 | − | 0.0656396i | ||||
\(454\) | −184.706 | −0.406842 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −87.4469 | + | 9.33128i | −0.191770 | + | 0.0204633i | ||||
\(457\) | 80.5571i | 0.176274i | 0.996108 | + | 0.0881369i | \(0.0280913\pi\) | ||||
−0.996108 | + | 0.0881369i | \(0.971909\pi\) | |||||||
\(458\) | −249.256 | −0.544226 | ||||||||
\(459\) | 439.658 | − | 145.170i | 0.957861 | − | 0.316274i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 670.208i | 1.45381i | 0.686736 | + | 0.726907i | \(0.259043\pi\) | ||||
−0.686736 | + | 0.726907i | \(0.740957\pi\) | |||||||
\(462\) | −27.4714 | + | 2.93141i | −0.0594618 | + | 0.00634505i | ||||
\(463\) | 384.490i | 0.830433i | 0.909723 | + | 0.415216i | \(0.136294\pi\) | ||||
−0.909723 | + | 0.415216i | \(0.863706\pi\) | |||||||
\(464\) | 8.88433i | 0.0191473i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 542.298 | 1.16373 | ||||||||
\(467\) | 524.245 | 1.12258 | 0.561290 | − | 0.827619i | \(-0.310305\pi\) | ||||
0.561290 | + | 0.827619i | \(0.310305\pi\) | |||||||
\(468\) | 22.6248 | + | 104.805i | 0.0483435 | + | 0.223943i | ||||
\(469\) | −203.524 | −0.433953 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4031 | + | 97.4910i | 0.0220872 | + | 0.206987i | ||||
\(472\) | − | 70.8191i | − | 0.150040i | ||||||
\(473\) | 157.360 | 0.332685 | ||||||||
\(474\) | −238.297 | + | 25.4282i | −0.502736 | + | 0.0536460i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 90.7405i | − | 0.190631i | ||||||
\(477\) | 567.587 | − | 122.527i | 1.18991 | − | 0.256871i | ||||
\(478\) | 222.524i | 0.465532i | ||||||||
\(479\) | − | 238.920i | − | 0.498790i | −0.968402 | − | 0.249395i | \(-0.919768\pi\) | ||
0.968402 | − | 0.249395i | \(-0.0802317\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −144.314 | −0.300030 | ||||||||
\(482\) | 148.457 | 0.308002 | ||||||||
\(483\) | −21.4398 | − | 200.921i | −0.0443889 | − | 0.415985i | ||||
\(484\) | 229.885 | 0.474968 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −296.241 | + | 174.182i | −0.609550 | + | 0.358398i | ||||
\(487\) | 109.180i | 0.224188i | 0.993698 | + | 0.112094i | \(0.0357558\pi\) | ||||
−0.993698 | + | 0.112094i | \(0.964244\pi\) | |||||||
\(488\) | 204.615 | 0.419293 | ||||||||
\(489\) | 39.4937 | + | 370.110i | 0.0807641 | + | 0.756870i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 418.094i | − | 0.851515i | −0.904837 | − | 0.425758i | \(-0.860008\pi\) | ||
0.904837 | − | 0.425758i | \(-0.139992\pi\) | |||||||
\(492\) | −6.95501 | − | 65.1780i | −0.0141362 | − | 0.132476i | ||||
\(493\) | − | 38.0879i | − | 0.0772573i | ||||||
\(494\) | 87.3080i | 0.176737i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.4176 | 0.0693904 | ||||||||
\(497\) | −114.131 | −0.229639 | ||||||||
\(498\) | −46.2436 | + | 4.93456i | −0.0928586 | + | 0.00990876i | ||||
\(499\) | −288.979 | −0.579115 | −0.289558 | − | 0.957161i | \(-0.593508\pi\) | ||||
−0.289558 | + | 0.957161i | \(0.593508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 546.536 | − | 58.3198i | 1.09089 | − | 0.116407i | ||||
\(502\) | 120.661i | 0.240361i | ||||||||
\(503\) | −868.307 | −1.72626 | −0.863128 | − | 0.504986i | \(-0.831498\pi\) | ||||
−0.863128 | + | 0.504986i | \(0.831498\pi\) | |||||||
\(504\) | 14.2117 | + | 65.8333i | 0.0281978 | + | 0.130622i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 88.6097i | − | 0.175118i | ||||||
\(507\) | −398.294 | + | 42.5011i | −0.785589 | + | 0.0838287i | ||||
\(508\) | − | 309.229i | − | 0.608719i | ||||||
\(509\) | − | 125.512i | − | 0.246586i | −0.992370 | − | 0.123293i | \(-0.960654\pi\) | ||
0.992370 | − | 0.123293i | \(-0.0393455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −254.773 | −0.498578 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −265.724 | + | 87.7388i | −0.517980 | + | 0.171031i | ||||
\(514\) | −483.755 | −0.941158 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −40.7034 | − | 381.447i | −0.0788826 | − | 0.739238i | ||||
\(517\) | 131.190i | 0.253752i | ||||||||
\(518\) | −90.6508 | −0.175002 | ||||||||
\(519\) | −211.332 | + | 22.5508i | −0.407191 | + | 0.0434505i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 238.393i | 0.457569i | 0.973477 | + | 0.228784i | \(0.0734751\pi\) | ||||
−0.973477 | + | 0.228784i | \(0.926525\pi\) | |||||||
\(522\) | 5.96529 | + | 27.6332i | 0.0114278 | + | 0.0529372i | ||||
\(523\) | − | 554.925i | − | 1.06104i | −0.847672 | − | 0.530521i | \(-0.821996\pi\) | ||
0.847672 | − | 0.530521i | \(-0.178004\pi\) | |||||||
\(524\) | − | 382.800i | − | 0.730535i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 694.450 | 1.32025 | ||||||||
\(527\) | −147.551 | −0.279984 | ||||||||
\(528\) | 3.13381 | + | 29.3681i | 0.00593525 | + | 0.0556214i | ||||
\(529\) | 119.076 | 0.225096 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −47.5508 | − | 220.271i | −0.0895495 | − | 0.414823i | ||||
\(532\) | 54.8423i | 0.103087i | ||||||||
\(533\) | −65.0744 | −0.122091 | ||||||||
\(534\) | −72.6744 | − | 681.058i | −0.136094 | − | 1.27539i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 217.577i | 0.405926i | ||||||||
\(537\) | 97.1099 | + | 910.053i | 0.180838 | + | 1.69470i | ||||
\(538\) | − | 110.059i | − | 0.204570i | ||||||
\(539\) | 17.2287i | 0.0319641i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −271.258 | −0.501401 | −0.250701 | − | 0.968065i | \(-0.580661\pi\) | ||||
−0.250701 | + | 0.968065i | \(0.580661\pi\) | |||||||
\(542\) | −559.062 | −1.03148 | ||||||||
\(543\) | 207.011 | − | 22.0897i | 0.381236 | − | 0.0406809i | ||||
\(544\) | −97.0057 | −0.178319 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 66.4858 | − | 7.09456i | 0.121769 | − | 0.0129937i | ||||
\(547\) | − | 1053.10i | − | 1.92523i | −0.270873 | − | 0.962615i | \(-0.587312\pi\) | ||
0.270873 | − | 0.962615i | \(-0.412688\pi\) | |||||||
\(548\) | 61.4853 | 0.112199 | ||||||||
\(549\) | 636.421 | − | 137.387i | 1.15924 | − | 0.250249i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.0198i | 0.0417782i | ||||||||
\(552\) | −214.793 | + | 22.9201i | −0.389118 | + | 0.0415220i | ||||
\(553\) | 149.448i | 0.270249i | ||||||||
\(554\) | − | 770.692i | − | 1.39114i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −52.8154 | −0.0949917 | ||||||||
\(557\) | 198.443 | 0.356271 | 0.178136 | − | 0.984006i | \(-0.442993\pi\) | ||||
0.178136 | + | 0.984006i | \(0.442993\pi\) | |||||||
\(558\) | 107.050 | − | 23.1094i | 0.191846 | − | 0.0414147i | ||||
\(559\) | −380.841 | −0.681290 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.4349 | − | 125.904i | −0.0239482 | − | 0.224427i | ||||
\(562\) | 338.064i | 0.601538i | ||||||||
\(563\) | −22.4619 | −0.0398968 | −0.0199484 | − | 0.999801i | \(-0.506350\pi\) | ||||
−0.0199484 | + | 0.999801i | \(0.506350\pi\) | |||||||
\(564\) | 318.009 | − | 33.9341i | 0.563845 | − | 0.0601668i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 579.508i | − | 1.02387i | ||||||
\(567\) | 88.4063 | + | 195.221i | 0.155919 | + | 0.344306i | ||||
\(568\) | 122.011i | 0.214808i | ||||||||
\(569\) | 1019.36i | 1.79150i | 0.444562 | + | 0.895748i | \(0.353359\pi\) | ||||
−0.444562 | + | 0.895748i | \(0.646641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 162.612 | 0.284784 | 0.142392 | − | 0.989810i | \(-0.454521\pi\) | ||||
0.142392 | + | 0.989810i | \(0.454521\pi\) | |||||||
\(572\) | 29.3215 | 0.0512613 | ||||||||
\(573\) | 52.6301 | + | 493.216i | 0.0918501 | + | 0.860761i | ||||
\(574\) | −40.8764 | −0.0712132 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 70.3788 | − | 15.1930i | 0.122185 | − | 0.0263767i | ||||
\(577\) | − | 589.353i | − | 1.02141i | −0.859756 | − | 0.510704i | \(-0.829385\pi\) | ||
0.859756 | − | 0.510704i | \(-0.170615\pi\) | |||||||
\(578\) | 7.16383 | 0.0123942 | ||||||||
\(579\) | −102.469 | − | 960.271i | −0.176975 | − | 1.65850i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.0017i | 0.0499168i | ||||||||
\(582\) | −75.5254 | − | 707.776i | −0.129769 | − | 1.21611i | ||||
\(583\) | − | 158.794i | − | 0.272374i | ||||||
\(584\) | 272.364i | 0.466377i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 358.076 | 0.611052 | ||||||||
\(587\) | −529.888 | −0.902705 | −0.451352 | − | 0.892346i | \(-0.649058\pi\) | ||||
−0.451352 | + | 0.892346i | \(0.649058\pi\) | |||||||
\(588\) | 41.7629 | − | 4.45644i | 0.0710253 | − | 0.00757897i | ||||
\(589\) | 89.1780 | 0.151406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1058.18 | − | 112.916i | 1.79049 | − | 0.191059i | ||||
\(592\) | 96.9098i | 0.163699i | ||||||||
\(593\) | 471.654 | 0.795369 | 0.397684 | − | 0.917522i | \(-0.369814\pi\) | ||||
0.397684 | + | 0.917522i | \(0.369814\pi\) | |||||||
\(594\) | 29.4661 | + | 89.2404i | 0.0496063 | + | 0.150236i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.81145i | 0.00303934i | ||||||||
\(597\) | −754.505 | + | 80.5117i | −1.26383 | + | 0.134860i | ||||
\(598\) | 214.452i | 0.358615i | ||||||||
\(599\) | − | 477.503i | − | 0.797167i | −0.917132 | − | 0.398583i | \(-0.869502\pi\) | ||
0.917132 | − | 0.398583i | \(-0.130498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −731.782 | −1.21761 | −0.608804 | − | 0.793321i | \(-0.708350\pi\) | ||||
−0.608804 | + | 0.793321i | \(0.708350\pi\) | |||||||
\(602\) | −239.224 | −0.397383 | ||||||||
\(603\) | 146.090 | + | 676.735i | 0.242271 | + | 1.12228i | ||||
\(604\) | −186.825 | −0.309313 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −51.0658 | − | 478.556i | −0.0842669 | − | 0.789697i | ||||
\(607\) | 659.688i | 1.08680i | 0.839474 | + | 0.543401i | \(0.182864\pi\) | ||||
−0.839474 | + | 0.543401i | \(0.817136\pi\) | |||||||
\(608\) | 58.6289 | 0.0964291 | ||||||||
\(609\) | 17.5298 | − | 1.87057i | 0.0287845 | − | 0.00307154i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 317.503i | − | 0.519646i | ||||||
\(612\) | −301.720 | + | 65.1335i | −0.493006 | + | 0.106427i | ||||
\(613\) | − | 214.842i | − | 0.350476i | −0.984526 | − | 0.175238i | \(-0.943931\pi\) | ||
0.984526 | − | 0.175238i | \(-0.0560694\pi\) | |||||||
\(614\) | − | 152.057i | − | 0.247650i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.4182 | 0.0298997 | ||||||||
\(617\) | −72.1435 | −0.116926 | −0.0584631 | − | 0.998290i | \(-0.518620\pi\) | ||||
−0.0584631 | + | 0.998290i | \(0.518620\pi\) | |||||||
\(618\) | −4.98209 | − | 46.6890i | −0.00806163 | − | 0.0755485i | ||||
\(619\) | 166.270 | 0.268610 | 0.134305 | − | 0.990940i | \(-0.457120\pi\) | ||||
0.134305 | + | 0.990940i | \(0.457120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −652.689 | + | 215.510i | −1.05103 | + | 0.347037i | ||||
\(622\) | 232.736i | 0.374174i | ||||||||
\(623\) | −427.126 | −0.685595 | ||||||||
\(624\) | −7.58441 | − | 71.0763i | −0.0121545 | − | 0.113904i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 790.081i | − | 1.26211i | ||||||
\(627\) | 8.11989 | + | 76.0944i | 0.0129504 | + | 0.121363i | ||||
\(628\) | − | 65.3630i | − | 0.104081i | ||||||
\(629\) | − | 415.460i | − | 0.660509i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 948.332 | 1.50290 | 0.751451 | − | 0.659788i | \(-0.229354\pi\) | ||||
0.751451 | + | 0.659788i | \(0.229354\pi\) | |||||||
\(632\) | 159.766 | 0.252795 | ||||||||
\(633\) | −122.212 | + | 13.0410i | −0.193067 | + | 0.0206018i | ||||
\(634\) | −259.206 | −0.408842 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −384.923 | + | 41.0743i | −0.605224 | + | 0.0645823i | ||||
\(637\) | − | 41.6966i | − | 0.0654577i | ||||||
\(638\) | 7.73095 | 0.0121175 | ||||||||
\(639\) | 81.9231 | + | 379.495i | 0.128205 | + | 0.593888i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.6929i | − | 0.0182417i | −0.999958 | − | 0.00912085i | \(-0.997097\pi\) | ||
0.999958 | − | 0.00912085i | \(-0.00290330\pi\) | |||||||
\(642\) | −81.3905 | + | 8.68501i | −0.126776 | + | 0.0135281i | ||||
\(643\) | 515.459i | 0.801647i | 0.916155 | + | 0.400823i | \(0.131276\pi\) | ||||
−0.916155 | + | 0.400823i | \(0.868724\pi\) | |||||||
\(644\) | 134.708i | 0.209173i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −251.347 | −0.389082 | ||||||||
\(647\) | 1235.46 | 1.90951 | 0.954757 | − | 0.297387i | \(-0.0961153\pi\) | ||||
0.954757 | + | 0.297387i | \(0.0961153\pi\) | |||||||
\(648\) | 208.700 | − | 94.5103i | 0.322068 | − | 0.145849i | ||||
\(649\) | −61.6253 | −0.0949542 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.24652 | − | 67.9098i | −0.0111314 | − | 0.104316i | ||||
\(652\) | − | 248.141i | − | 0.380584i | ||||||
\(653\) | −414.510 | −0.634778 | −0.317389 | − | 0.948295i | \(-0.602806\pi\) | ||||
−0.317389 | + | 0.948295i | \(0.602806\pi\) | |||||||
\(654\) | 123.773 | − | 13.2075i | 0.189255 | − | 0.0201950i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.6987i | 0.0666138i | ||||||||
\(657\) | 182.876 | + | 847.142i | 0.278350 | + | 1.28941i | ||||
\(658\) | − | 199.439i | − | 0.303099i | ||||||
\(659\) | − | 433.365i | − | 0.657609i | −0.944398 | − | 0.328805i | \(-0.893354\pi\) | ||
0.944398 | − | 0.328805i | \(-0.106646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 979.636 | 1.48205 | 0.741025 | − | 0.671477i | \(-0.234340\pi\) | ||||
0.741025 | + | 0.671477i | \(0.234340\pi\) | |||||||
\(662\) | −800.499 | −1.20921 | ||||||||
\(663\) | 32.5150 | + | 304.710i | 0.0490422 | + | 0.459593i | ||||
\(664\) | 31.0041 | 0.0466929 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 65.0691 | + | 301.422i | 0.0977014 | + | 0.452585i | ||||
\(667\) | 56.5428i | 0.0847718i | ||||||||
\(668\) | −366.426 | −0.548542 | ||||||||
\(669\) | 69.3725 | + | 650.116i | 0.103696 | + | 0.971772i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 178.052i | − | 0.265353i | ||||||
\(672\) | −4.76413 | − | 44.6464i | −0.00708948 | − | 0.0664381i | ||||
\(673\) | 654.898i | 0.973103i | 0.873652 | + | 0.486551i | \(0.161745\pi\) | ||||
−0.873652 | + | 0.486551i | \(0.838255\pi\) | |||||||
\(674\) | − | 753.814i | − | 1.11842i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 267.037 | 0.395025 | ||||||||
\(677\) | 314.756 | 0.464928 | 0.232464 | − | 0.972605i | \(-0.425321\pi\) | ||||
0.232464 | + | 0.972605i | \(0.425321\pi\) | |||||||
\(678\) | 140.353 | − | 14.9768i | 0.207010 | − | 0.0220896i | ||||
\(679\) | −443.882 | −0.653729 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 389.609 | − | 41.5744i | 0.572113 | − | 0.0610490i | ||||
\(682\) | − | 29.9495i | − | 0.0439142i | ||||||
\(683\) | −978.165 | −1.43216 | −0.716079 | − | 0.698019i | \(-0.754065\pi\) | ||||
−0.716079 | + | 0.698019i | \(0.754065\pi\) | |||||||
\(684\) | 182.355 | − | 39.3658i | 0.266601 | − | 0.0575523i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | 525.766 | − | 56.1035i | 0.765308 | − | 0.0816644i | ||||
\(688\) | 255.742i | 0.371718i | ||||||||
\(689\) | 384.311i | 0.557781i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 928.182 | 1.34325 | 0.671623 | − | 0.740893i | \(-0.265598\pi\) | ||||
0.671623 | + | 0.740893i | \(0.265598\pi\) | |||||||
\(692\) | 141.688 | 0.204751 | ||||||||
\(693\) | 57.2868 | − | 12.3667i | 0.0826649 | − | 0.0178452i | ||||
\(694\) | 552.943 | 0.796748 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.99972 | − | 18.7401i | −0.00287316 | − | 0.0269254i | ||||
\(697\) | − | 187.340i | − | 0.268780i | ||||||
\(698\) | −400.792 | −0.574200 | ||||||||
\(699\) | −1143.89 | + | 122.063i | −1.63647 | + | 0.174625i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1177.79i | 1.68015i | 0.542468 | + | 0.840077i | \(0.317490\pi\) | ||||
−0.542468 | + | 0.840077i | \(0.682510\pi\) | |||||||
\(702\) | −71.3135 | − | 215.978i | −0.101586 | − | 0.307662i | ||||
\(703\) | 251.099i | 0.357182i | ||||||||
\(704\) | − | 19.6899i | − | 0.0279686i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 821.020 | 1.16292 | ||||||||
\(707\) | −300.126 | −0.424507 | ||||||||
\(708\) | 15.9402 | + | 149.382i | 0.0225145 | + | 0.210991i | ||||
\(709\) | −1177.46 | −1.66074 | −0.830369 | − | 0.557214i | \(-0.811870\pi\) | ||||
−0.830369 | + | 0.557214i | \(0.811870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 496.927 | − | 107.274i | 0.698913 | − | 0.150877i | ||||
\(712\) | 456.617i | 0.641315i | ||||||||
\(713\) | 219.045 | 0.307216 | ||||||||
\(714\) | 20.4242 | + | 191.403i | 0.0286054 | + | 0.268071i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 610.146i | − | 0.852160i | ||||||
\(717\) | −50.0866 | − | 469.380i | −0.0698558 | − | 0.654645i | ||||
\(718\) | 657.834i | 0.916203i | ||||||||
\(719\) | − | 862.273i | − | 1.19927i | −0.800275 | − | 0.599634i | \(-0.795313\pi\) | ||
0.800275 | − | 0.599634i | \(-0.204687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.2810 | −0.0406116 | ||||||||
\(722\) | −358.620 | −0.496704 | ||||||||
\(723\) | −313.147 | + | 33.4152i | −0.433121 | + | 0.0462175i | ||||
\(724\) | −138.791 | −0.191700 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −484.906 | + | 51.7433i | −0.667915 | + | 0.0712718i | ||||
\(727\) | 1195.80i | 1.64484i | 0.568882 | + | 0.822419i | \(0.307376\pi\) | ||||
−0.568882 | + | 0.822419i | \(0.692624\pi\) | |||||||
\(728\) | −44.5755 | −0.0612301 | ||||||||
\(729\) | 585.669 | − | 434.088i | 0.803387 | − | 0.595457i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1096.39i | − | 1.49984i | ||||||
\(732\) | −431.604 | + | 46.0556i | −0.589623 | + | 0.0629175i | ||||
\(733\) | − | 1037.50i | − | 1.41541i | −0.706506 | − | 0.707707i | \(-0.749730\pi\) | ||
0.706506 | − | 0.707707i | \(-0.250270\pi\) | |||||||
\(734\) | − | 688.690i | − | 0.938270i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 144.008 | 0.195664 | ||||||||
\(737\) | 189.330 | 0.256893 | ||||||||
\(738\) | 29.3410 | + | 135.917i | 0.0397575 | + | 0.184170i | ||||
\(739\) | −333.738 | −0.451608 | −0.225804 | − | 0.974173i | \(-0.572501\pi\) | ||||
−0.225804 | + | 0.974173i | \(0.572501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.6516 | − | 184.163i | −0.0265204 | − | 0.248533i | ||||
\(742\) | 241.404i | 0.325343i | ||||||||
\(743\) | −746.025 | −1.00407 | −0.502036 | − | 0.864847i | \(-0.667415\pi\) | ||||
−0.502036 | + | 0.864847i | \(0.667415\pi\) | |||||||
\(744\) | −72.5987 | + | 7.74686i | −0.0975789 | + | 0.0104124i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 127.740i | − | 0.171234i | ||||||
\(747\) | 96.4330 | − | 20.8174i | 0.129094 | − | 0.0278680i | ||||
\(748\) | 84.4123i | 0.112851i | ||||||||
\(749\) | 51.0440i | 0.0681496i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 518.562 | 0.690495 | 0.345248 | − | 0.938512i | \(-0.387795\pi\) | ||||
0.345248 | + | 0.938512i | \(0.387795\pi\) | |||||||
\(752\) | −213.209 | −0.283523 | ||||||||
\(753\) | −27.1589 | − | 254.516i | −0.0360676 | − | 0.338002i | ||||
\(754\) | −18.7103 | −0.0248148 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −44.7954 | − | 135.666i | −0.0592532 | − | 0.179453i | ||||
\(757\) | − | 1172.19i | − | 1.54846i | −0.632903 | − | 0.774231i | \(-0.718137\pi\) | ||
0.632903 | − | 0.774231i | \(-0.281863\pi\) | |||||||
\(758\) | 820.746 | 1.08278 | ||||||||
\(759\) | 19.9446 | + | 186.908i | 0.0262775 | + | 0.246256i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 682.033i | 0.896233i | 0.893975 | + | 0.448116i | \(0.147905\pi\) | ||||
−0.893975 | + | 0.448116i | \(0.852095\pi\) | |||||||
\(762\) | 69.6025 | + | 652.271i | 0.0913419 | + | 0.855998i | ||||
\(763\) | − | 77.6240i | − | 0.101735i | ||||||
\(764\) | − | 330.678i | − | 0.432824i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 151.319 | 0.197545 | ||||||||
\(767\) | 149.145 | 0.194452 | ||||||||
\(768\) | −47.7290 | + | 5.09307i | −0.0621472 | + | 0.00663160i | ||||
\(769\) | −711.176 | −0.924807 | −0.462403 | − | 0.886670i | \(-0.653013\pi\) | ||||
−0.462403 | + | 0.886670i | \(0.653013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1020.41 | − | 108.886i | 1.32348 | − | 0.141226i | ||||
\(772\) | 643.815i | 0.833958i | ||||||||
\(773\) | 657.862 | 0.851050 | 0.425525 | − | 0.904947i | \(-0.360089\pi\) | ||||
0.425525 | + | 0.904947i | \(0.360089\pi\) | |||||||
\(774\) | 171.715 | + | 795.442i | 0.221854 | + | 1.02770i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 474.530i | 0.611507i | ||||||||
\(777\) | 191.214 | − | 20.4040i | 0.246092 | − | 0.0262600i | ||||
\(778\) | 671.747i | 0.863428i | ||||||||
\(779\) | 113.226i | 0.145348i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 106.171 | 0.135943 | ||||||||
\(782\) | −617.376 | −0.789484 | ||||||||
\(783\) | −18.8027 | − | 56.9453i | −0.0240136 | − | 0.0727270i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 86.1622 | + | 807.458i | 0.109621 | + | 1.02730i | ||||
\(787\) | 1054.23i | 1.33955i | 0.742565 | + | 0.669775i | \(0.233609\pi\) | ||||
−0.742565 | + | 0.669775i | \(0.766391\pi\) | |||||||
\(788\) | −709.456 | −0.900325 | ||||||||
\(789\) | −1464.83 | + | 156.310i | −1.85657 | + | 0.198111i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 88.0222i | − | 0.111280i | ||||||
\(792\) | −13.2206 | − | 61.2421i | −0.0166927 | − | 0.0773259i | ||||
\(793\) | 430.918i | 0.543403i | ||||||||
\(794\) | 768.173i | 0.967472i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 505.859 | 0.635501 | ||||||||
\(797\) | 284.062 | 0.356414 | 0.178207 | − | 0.983993i | \(-0.442970\pi\) | ||||
0.178207 | + | 0.983993i | \(0.442970\pi\) | |||||||
\(798\) | −12.3441 | − | 115.681i | −0.0154688 | − | 0.144964i | ||||
\(799\) | 914.047 | 1.14399 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 306.591 | + | 1420.23i | 0.382760 | + | 1.77307i | ||||
\(802\) | − | 160.298i | − | 0.199872i | ||||||
\(803\) | 237.005 | 0.295150 | ||||||||
\(804\) | −48.9730 | − | 458.944i | −0.0609117 | − | 0.570826i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 72.4833i | 0.0899297i | ||||||||
\(807\) | 24.7724 | + | 232.152i | 0.0306969 | + | 0.287672i | ||||
\(808\) | 320.849i | 0.397090i | ||||||||
\(809\) | 736.234i | 0.910054i | 0.890478 | + | 0.455027i | \(0.150370\pi\) | ||||
−0.890478 | + | 0.455027i | \(0.849630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −537.651 | −0.662948 | −0.331474 | − | 0.943464i | \(-0.607546\pi\) | ||||
−0.331474 | + | 0.943464i | \(0.607546\pi\) | |||||||
\(812\) | −11.7529 | −0.0144740 | ||||||||
\(813\) | 1179.25 | − | 125.836i | 1.45050 | − | 0.154780i | ||||
\(814\) | 84.3288 | 0.103598 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 204.618 | − | 21.8344i | 0.250758 | − | 0.0267579i | ||||
\(817\) | 662.641i | 0.811066i | ||||||||
\(818\) | 718.307 | 0.878125 | ||||||||
\(819\) | −138.645 | + | 29.9298i | −0.169285 | + | 0.0365443i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 616.599i | − | 0.751034i | −0.926816 | − | 0.375517i | \(-0.877465\pi\) | ||
0.926816 | − | 0.375517i | \(-0.122535\pi\) | |||||||
\(822\) | −129.694 | + | 13.8394i | −0.157778 | + | 0.0168362i | ||||
\(823\) | 1135.48i | 1.37968i | 0.723962 | + | 0.689839i | \(0.242319\pi\) | ||||
−0.723962 | + | 0.689839i | \(0.757681\pi\) | |||||||
\(824\) | 31.3027i | 0.0379887i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 93.6848 | 0.113420 | ||||||||
\(827\) | 912.460 | 1.10334 | 0.551669 | − | 0.834063i | \(-0.313991\pi\) | ||||
0.551669 | + | 0.834063i | \(0.313991\pi\) | |||||||
\(828\) | 447.914 | − | 96.6930i | 0.540959 | − | 0.116779i | ||||
\(829\) | −199.050 | −0.240108 | −0.120054 | − | 0.992767i | \(-0.538307\pi\) | ||||
−0.120054 | + | 0.992767i | \(0.538307\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 173.471 | + | 1625.66i | 0.208749 | + | 1.95627i | ||||
\(832\) | 47.6532i | 0.0572755i | ||||||||
\(833\) | 120.038 | 0.144104 | ||||||||
\(834\) | 111.406 | − | 11.8879i | 0.133580 | − | 0.0142541i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 51.0176i | − | 0.0610259i | ||||||
\(837\) | −220.604 | + | 72.8410i | −0.263566 | + | 0.0870262i | ||||
\(838\) | − | 12.4312i | − | 0.0148343i | ||||||
\(839\) | − | 28.6559i | − | 0.0341548i | −0.999854 | − | 0.0170774i | \(-0.994564\pi\) | ||
0.999854 | − | 0.0170774i | \(-0.00543617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 836.067 | 0.994134 | ||||||||
\(842\) | 258.308 | 0.306779 | ||||||||
\(843\) | −76.0928 | − | 713.094i | −0.0902643 | − | 0.845900i | ||||
\(844\) | 81.9370 | 0.0970817 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −663.152 | + | 143.157i | −0.783868 | + | 0.169217i | ||||
\(847\) | 304.109i | 0.359042i | ||||||||
\(848\) | 258.072 | 0.304330 | ||||||||
\(849\) | 130.438 | + | 1222.38i | 0.153637 | + | 1.43979i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 616.766i | 0.724754i | ||||||||
\(852\) | −27.4627 | − | 257.363i | −0.0322332 | − | 0.302070i | ||||
\(853\) | − | 1093.16i | − | 1.28154i | −0.767731 | − | 0.640772i | \(-0.778614\pi\) | ||
0.767731 | − | 0.640772i | \(-0.221386\pi\) | |||||||
\(854\) | 270.680i | 0.316956i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54.5684 | 0.0637481 | ||||||||
\(857\) | 407.107 | 0.475037 | 0.237519 | − | 0.971383i | \(-0.423666\pi\) | ||||
0.237519 | + | 0.971383i | \(0.423666\pi\) | |||||||
\(858\) | −61.8491 | + | 6.59979i | −0.0720852 | + | 0.00769206i | ||||
\(859\) | 1041.16 | 1.21206 | 0.606032 | − | 0.795440i | \(-0.292760\pi\) | ||||
0.606032 | + | 0.795440i | \(0.292760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 86.2224 | − | 9.20062i | 0.100142 | − | 0.0106860i | ||||
\(862\) | 154.511i | 0.179247i | ||||||||
\(863\) | −1485.61 | −1.72145 | −0.860727 | − | 0.509067i | \(-0.829991\pi\) | ||||
−0.860727 | + | 0.509067i | \(0.829991\pi\) | |||||||
\(864\) | −145.033 | + | 47.8883i | −0.167863 | + | 0.0554263i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 341.319i | − | 0.394132i | ||||||
\(867\) | −15.1110 | + | 1.61246i | −0.0174291 | + | 0.00185982i | ||||
\(868\) | 45.5303i | 0.0524542i | ||||||||
\(869\) | − | 139.025i | − | 0.159983i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −458.215 | −0.526079 | ||||||||
\(872\) | −82.9835 | −0.0951646 | ||||||||
\(873\) | 318.618 | + | 1475.95i | 0.364969 | + | 1.69066i | ||||
\(874\) | 373.134 | 0.426927 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −61.3048 | − | 574.510i | −0.0699826 | − | 0.655833i | ||||
\(877\) | − | 285.779i | − | 0.325860i | −0.986638 | − | 0.162930i | \(-0.947906\pi\) | ||
0.986638 | − | 0.162930i | \(-0.0520944\pi\) | |||||||
\(878\) | 111.661 | 0.127177 | ||||||||
\(879\) | −755.307 | + | 80.5973i | −0.859279 | + | 0.0916920i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 134.739i | 0.152938i | 0.997072 | + | 0.0764692i | \(0.0243647\pi\) | ||||
−0.997072 | + | 0.0764692i | \(0.975635\pi\) | |||||||
\(882\) | −87.0893 | + | 18.8003i | −0.0987407 | + | 0.0213156i | ||||
\(883\) | 49.4924i | 0.0560503i | 0.999607 | + | 0.0280252i | \(0.00892185\pi\) | ||||
−0.999607 | + | 0.0280252i | \(0.991078\pi\) | |||||||
\(884\) | − | 204.293i | − | 0.231101i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −493.549 | −0.557053 | ||||||||
\(887\) | 1334.66 | 1.50469 | 0.752345 | − | 0.658769i | \(-0.228923\pi\) | ||||
0.752345 | + | 0.658769i | \(0.228923\pi\) | |||||||
\(888\) | −21.8128 | − | 204.416i | −0.0245640 | − | 0.230198i | ||||
\(889\) | 409.072 | 0.460148 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −82.2408 | − | 181.607i | −0.0923017 | − | 0.203823i | ||||
\(892\) | − | 435.871i | − | 0.488645i | ||||||
\(893\) | −552.437 | −0.618631 | ||||||||
\(894\) | −0.407728 | − | 3.82097i | −0.000456071 | − | 0.00427401i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | −48.2697 | − | 452.353i | −0.0538124 | − | 0.504296i | ||||
\(898\) | 568.365i | 0.632923i | ||||||||
\(899\) | 19.1111i | 0.0212582i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1106.38 | −1.22794 | ||||||||
\(902\) | 38.0257 | 0.0421571 | ||||||||
\(903\) | 504.607 | − | 53.8456i | 0.558812 | − | 0.0596297i | ||||
\(904\) | −94.0997 | −0.104093 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 394.078 | − | 42.0513i | 0.434965 | − | 0.0464142i | ||||
\(907\) | − | 368.808i | − | 0.406624i | −0.979114 | − | 0.203312i | \(-0.934829\pi\) | ||
0.979114 | − | 0.203312i | \(-0.0651706\pi\) | |||||||
\(908\) | −261.214 | −0.287680 | ||||||||
\(909\) | 215.431 | + | 997.946i | 0.236997 | + | 1.09785i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 371.365i | 0.407645i | 0.979008 | + | 0.203822i | \(0.0653365\pi\) | ||||
−0.979008 | + | 0.203822i | \(0.934663\pi\) | |||||||
\(912\) | −123.669 | + | 13.1964i | −0.135602 | + | 0.0144698i | ||||
\(913\) | − | 26.9791i | − | 0.0295499i | ||||||
\(914\) | 113.925i | 0.124644i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −352.501 | −0.384826 | ||||||||
\(917\) | 506.397 | 0.552232 | ||||||||
\(918\) | 621.771 | − | 205.301i | 0.677310 | − | 0.223640i | ||||
\(919\) | 4.28269 | 0.00466017 | 0.00233008 | − | 0.999997i | \(-0.499258\pi\) | ||||
0.00233008 | + | 0.999997i | \(0.499258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.2256 | + | 320.741i | 0.0371614 | + | 0.348253i | ||||
\(922\) | 947.817i | 1.02800i | ||||||||
\(923\) | −256.954 | −0.278390 | ||||||||
\(924\) | −38.8504 | + | 4.14564i | −0.0420459 | + | 0.00448663i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 543.752i | 0.587205i | ||||||||
\(927\) | 21.0179 | + | 97.3618i | 0.0226730 | + | 0.105029i | ||||
\(928\) | 12.5643i | 0.0135392i | ||||||||
\(929\) | − | 1323.53i | − | 1.42468i | −0.701833 | − | 0.712341i | \(-0.747635\pi\) | ||
0.701833 | − | 0.712341i | \(-0.252365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −72.5496 | −0.0779265 | ||||||||
\(932\) | 766.926 | 0.822882 | ||||||||
\(933\) | −52.3852 | − | 490.921i | −0.0561471 | − | 0.526175i | ||||
\(934\) | 741.394 | 0.793784 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.9963 | + | 148.217i | 0.0341841 | + | 0.158352i | ||||
\(937\) | 1514.47i | 1.61630i | 0.588977 | + | 0.808150i | \(0.299531\pi\) | ||||
−0.588977 | + | 0.808150i | \(0.700469\pi\) | |||||||
\(938\) | −287.827 | −0.306851 | ||||||||
\(939\) | 177.835 | + | 1666.55i | 0.189387 | + | 1.77482i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1235.73i | − | 1.31320i | −0.754237 | − | 0.656602i | \(-0.771993\pi\) | ||
0.754237 | − | 0.656602i | \(-0.228007\pi\) | |||||||
\(942\) | 14.7122 | + | 137.873i | 0.0156180 | + | 0.146362i | ||||
\(943\) | 278.113i | 0.294924i | ||||||||
\(944\) | − | 100.153i | − | 0.106095i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 222.541 | 0.235244 | ||||||||
\(947\) | −1424.36 | −1.50407 | −0.752036 | − | 0.659122i | \(-0.770928\pi\) | ||||
−0.752036 | + | 0.659122i | \(0.770928\pi\) | |||||||
\(948\) | −337.003 | + | 35.9609i | −0.355488 | + | 0.0379334i | ||||
\(949\) | −573.597 | −0.604422 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 546.755 | − | 58.3431i | 0.574927 | − | 0.0613493i | ||||
\(952\) | − | 128.326i | − | 0.134797i | ||||||
\(953\) | −544.301 | −0.571145 | −0.285573 | − | 0.958357i | \(-0.592184\pi\) | ||||
−0.285573 | + | 0.958357i | \(0.592184\pi\) | |||||||
\(954\) | 802.690 | − | 173.280i | 0.841394 | − | 0.181635i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 314.697i | 0.329181i | ||||||||
\(957\) | −16.3072 | + | 1.74011i | −0.0170400 | + | 0.00181830i | ||||
\(958\) | − | 337.884i | − | 0.352698i | ||||||
\(959\) | 81.3374i | 0.0848148i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −886.964 | −0.922960 | ||||||||
\(962\) | −204.091 | −0.212153 | ||||||||
\(963\) | 169.726 | − | 36.6394i | 0.176247 | − | 0.0380471i | ||||
\(964\) | 209.950 | 0.217790 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −30.3205 | − | 284.145i | −0.0313877 | − | 0.294146i | ||||
\(967\) | − | 1312.39i | − | 1.35718i | −0.734518 | − | 0.678590i | \(-0.762591\pi\) | ||
0.734518 | − | 0.678590i | \(-0.237409\pi\) | |||||||
\(968\) | 325.106 | 0.335853 | ||||||||
\(969\) | 530.178 | − | 56.5742i | 0.547139 | − | 0.0583841i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 194.087i | − | 0.199884i | −0.994993 | − | 0.0999419i | \(-0.968134\pi\) | ||
0.994993 | − | 0.0999419i | \(-0.0318657\pi\) | |||||||
\(972\) | −418.948 | + | 246.330i | −0.431017 | + | 0.253426i | ||||
\(973\) | − | 69.8682i | − | 0.0718070i | ||||||
\(974\) | 154.403i | 0.158525i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 289.370 | 0.296485 | ||||||||
\(977\) | −1340.42 | −1.37198 | −0.685989 | − | 0.727612i | \(-0.740630\pi\) | ||||
−0.685989 | + | 0.727612i | \(0.740630\pi\) | |||||||
\(978\) | 55.8525 | + | 523.414i | 0.0571089 | + | 0.535188i | ||||
\(979\) | 397.338 | 0.405861 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −258.106 | + | 55.7185i | −0.263105 | + | 0.0567976i | ||||
\(982\) | − | 591.274i | − | 0.602112i | ||||||
\(983\) | 508.734 | 0.517532 | 0.258766 | − | 0.965940i | \(-0.416684\pi\) | ||||
0.258766 | + | 0.965940i | \(0.416684\pi\) | |||||||
\(984\) | −9.83587 | − | 92.1756i | −0.00999581 | − | 0.0936744i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 53.8644i | − | 0.0546292i | ||||||
\(987\) | 44.8906 | + | 420.686i | 0.0454818 | + | 0.426227i | ||||
\(988\) | 123.472i | 0.124972i | ||||||||
\(989\) | 1627.62i | 1.64573i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1087.94 | −1.09782 | −0.548912 | − | 0.835880i | \(-0.684958\pi\) | ||||
−0.548912 | + | 0.835880i | \(0.684958\pi\) | |||||||
\(992\) | 48.6739 | 0.0490664 | ||||||||
\(993\) | 1688.53 | − | 180.180i | 1.70043 | − | 0.181450i | ||||
\(994\) | −161.405 | −0.162380 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −65.3983 | + | 6.97853i | −0.0656610 | + | 0.00700655i | ||||
\(997\) | − | 1221.50i | − | 1.22518i | −0.790402 | − | 0.612588i | \(-0.790128\pi\) | ||
0.790402 | − | 0.612588i | \(-0.209872\pi\) | |||||||
\(998\) | −408.677 | −0.409496 | ||||||||
\(999\) | −205.098 | − | 621.156i | −0.205304 | − | 0.621778i |
(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 | 1050.3.c.b.449.18 | 32 | ||
3.2 | odd | 2 | inner | 1050.3.c.b.449.16 | 32 | ||
5.2 | odd | 4 | 1050.3.e.c.701.12 | yes | 16 | ||
5.3 | odd | 4 | 1050.3.e.b.701.5 | ✓ | 16 | ||
5.4 | even | 2 | inner | 1050.3.c.b.449.15 | 32 | ||
15.2 | even | 4 | 1050.3.e.c.701.4 | yes | 16 | ||
15.8 | even | 4 | 1050.3.e.b.701.13 | yes | 16 | ||
15.14 | odd | 2 | inner | 1050.3.c.b.449.17 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.c.b.449.15 | 32 | 5.4 | even | 2 | inner | ||
1050.3.c.b.449.16 | 32 | 3.2 | odd | 2 | inner | ||
1050.3.c.b.449.17 | 32 | 15.14 | odd | 2 | inner | ||
1050.3.c.b.449.18 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.e.b.701.5 | ✓ | 16 | 5.3 | odd | 4 | ||
1050.3.e.b.701.13 | yes | 16 | 15.8 | even | 4 | ||
1050.3.e.c.701.4 | yes | 16 | 15.2 | even | 4 | ||
1050.3.e.c.701.12 | yes | 16 | 5.2 | odd | 4 |