Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(3,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([8, 8, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.s (of order \(16\), degree \(8\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{16}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.11 |
Dual form | 136.4.s.a.99.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{16}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61313 | − | 1.08239i | −0.923880 | − | 0.382683i | ||||
\(3\) | −1.54267 | − | 7.75551i | −0.296887 | − | 1.49255i | −0.784850 | − | 0.619685i | \(-0.787260\pi\) |
0.487964 | − | 0.872864i | \(-0.337740\pi\) | |||||||
\(4\) | 5.65685 | + | 5.65685i | 0.707107 | + | 0.707107i | ||||
\(5\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(6\) | −4.36332 | + | 21.9359i | −0.296887 | + | 1.49255i | ||||
\(7\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(8\) | −8.65914 | − | 20.9050i | −0.382683 | − | 0.923880i | ||||
\(9\) | −32.8234 | + | 13.5959i | −1.21568 | + | 0.503552i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −71.4636 | − | 14.2150i | −1.95883 | − | 0.389635i | −0.989731 | − | 0.142943i | \(-0.954343\pi\) |
−0.969094 | − | 0.246691i | \(-0.920657\pi\) | |||||||
\(12\) | 35.1452 | − | 52.5985i | 0.845461 | − | 1.26532i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000i | 1.00000i | ||||||||
\(17\) | 21.0091 | + | 66.8701i | 0.299733 | + | 0.954023i | ||||
\(18\) | 100.488 | 1.31585 | ||||||||
\(19\) | 13.9013 | + | 5.75812i | 0.167852 | + | 0.0695264i | 0.465027 | − | 0.885296i | \(-0.346045\pi\) |
−0.297175 | + | 0.954823i | \(0.596045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 171.357 | + | 114.497i | 1.66061 | + | 1.10959i | ||||
\(23\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(24\) | −148.771 | + | 99.4055i | −1.26532 | + | 0.845461i | ||||
\(25\) | 47.8354 | + | 115.485i | 0.382683 | + | 0.923880i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 37.4640 | + | 56.0688i | 0.267035 | + | 0.399646i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(32\) | 69.2731 | − | 167.240i | 0.382683 | − | 0.923880i | ||||
\(33\) | 576.166i | 3.03932i | ||||||||
\(34\) | 17.4802 | − | 197.480i | 0.0881716 | − | 0.996105i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −262.587 | − | 108.767i | −1.21568 | − | 0.503552i | ||||
\(37\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(38\) | −30.0934 | − | 30.0934i | −0.128468 | − | 0.128468i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −416.511 | + | 278.304i | −1.58654 | + | 1.06009i | −0.626809 | + | 0.779173i | \(0.715639\pi\) |
−0.959731 | + | 0.280919i | \(0.909361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −76.5305 | + | 31.7000i | −0.271414 | + | 0.112423i | −0.514239 | − | 0.857647i | \(-0.671926\pi\) |
0.242826 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(44\) | −323.847 | − | 484.671i | −1.10959 | − | 1.66061i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 496.353 | − | 98.7307i | 1.49255 | − | 0.296887i | ||||
\(49\) | 131.260 | − | 316.891i | 0.382683 | − | 0.923880i | ||||
\(50\) | − | 353.553i | − | 1.00000i | ||||||
\(51\) | 486.202 | − | 266.095i | 1.33494 | − | 0.730603i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(54\) | −37.2096 | − | 187.065i | −0.0937702 | − | 0.471415i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 23.2120 | − | 116.695i | 0.0539387 | − | 0.271168i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −251.472 | − | 607.106i | −0.554895 | − | 1.33964i | −0.913763 | − | 0.406247i | \(-0.866837\pi\) |
0.358868 | − | 0.933388i | \(-0.383163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −362.039 | + | 362.039i | −0.707107 | + | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 623.637 | − | 1505.59i | 1.16310 | − | 2.80797i | ||||
\(67\) | 984.492i | 1.79515i | 0.440865 | + | 0.897573i | \(0.354672\pi\) | ||||
−0.440865 | + | 0.897573i | \(0.645328\pi\) | |||||||
\(68\) | −259.429 | + | 497.120i | −0.462653 | + | 0.886539i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(72\) | 568.445 | + | 568.445i | 0.930443 | + | 0.930443i | ||||
\(73\) | −1024.67 | − | 684.661i | −1.64285 | − | 1.09772i | −0.907515 | − | 0.420021i | \(-0.862023\pi\) |
−0.735339 | − | 0.677699i | \(-0.762977\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 821.851 | − | 549.143i | 1.26532 | − | 0.845461i | ||||
\(76\) | 46.0649 | + | 111.211i | 0.0695264 | + | 0.167852i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −301.245 | + | 301.245i | −0.413231 | + | 0.413231i | ||||
\(82\) | 1389.63 | − | 276.415i | 1.87145 | − | 0.372255i | ||||
\(83\) | 43.2971 | − | 104.528i | 0.0572587 | − | 0.138235i | −0.892661 | − | 0.450728i | \(-0.851164\pi\) |
0.949920 | + | 0.312494i | \(0.101164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 234.296 | 0.293776 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 321.648 | + | 1617.04i | 0.389635 | + | 1.95883i | ||||
\(89\) | −1029.99 | − | 1029.99i | −1.22673 | − | 1.22673i | −0.965195 | − | 0.261531i | \(-0.915773\pi\) |
−0.261531 | − | 0.965195i | \(-0.584227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1403.90 | − | 279.253i | −1.49255 | − | 0.296887i | ||||
\(97\) | −866.591 | + | 1296.94i | −0.907103 | + | 1.35757i | 0.0266459 | + | 0.999645i | \(0.491517\pi\) |
−0.933748 | + | 0.357930i | \(0.883483\pi\) | |||||||
\(98\) | −686.000 | + | 686.000i | −0.707107 | + | 0.707107i | ||||
\(99\) | 2538.94 | − | 505.028i | 2.57751 | − | 0.512699i | ||||
\(100\) | −382.683 | + | 923.880i | −0.382683 | + | 0.923880i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | −1558.53 | + | 169.078i | −1.51291 | + | 0.164130i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1831.56 | − | 1223.81i | −1.65480 | − | 1.10570i | −0.882311 | − | 0.470667i | \(-0.844013\pi\) |
−0.772486 | − | 0.635032i | \(-0.780987\pi\) | |||||||
\(108\) | −105.245 | + | 529.101i | −0.0937702 | + | 0.471415i | ||||
\(109\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1080.59 | − | 214.942i | −0.899584 | − | 0.178938i | −0.276427 | − | 0.961035i | \(-0.589150\pi\) |
−0.623157 | + | 0.782097i | \(0.714150\pi\) | |||||||
\(114\) | −186.965 | + | 279.814i | −0.153605 | + | 0.229885i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1858.64i | 1.45001i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3675.29 | + | 1522.36i | 2.76130 | + | 1.14377i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2800.93 | + | 2800.93i | 2.05326 | + | 2.05326i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(128\) | 1337.92 | − | 554.185i | 0.923880 | − | 0.382683i | ||||
\(129\) | 363.911 | + | 544.631i | 0.248376 | + | 0.371721i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 380.926 | − | 570.097i | 0.254059 | − | 0.380226i | −0.682414 | − | 0.730966i | \(-0.739070\pi\) |
0.936473 | + | 0.350740i | \(0.114070\pi\) | |||||||
\(132\) | −3259.29 | + | 3259.29i | −2.14912 | + | 2.14912i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1065.61 | − | 2572.60i | 0.686973 | − | 1.65850i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1216.00 | − | 1018.23i | 0.766700 | − | 0.642006i | ||||
\(137\) | 3206.99 | 1.99994 | 0.999970 | − | 0.00779827i | \(-0.00248229\pi\) | ||||
0.999970 | + | 0.00779827i | \(0.00248229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −556.393 | − | 2797.17i | −0.339515 | − | 1.70686i | −0.653078 | − | 0.757291i | \(-0.726523\pi\) |
0.313563 | − | 0.949567i | \(-0.398477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −870.138 | − | 2100.70i | −0.503552 | − | 1.21568i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1936.51 | + | 2898.20i | 1.09772 | + | 1.64285i | ||||
\(147\) | −2660.14 | − | 529.135i | −1.49255 | − | 0.296887i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(150\) | −2741.99 | + | 545.415i | −1.49255 | + | 0.296887i | ||||
\(151\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(152\) | − | 340.468i | − | 0.181681i | ||||||
\(153\) | −1598.75 | − | 1909.27i | −0.844781 | − | 1.00886i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1113.26 | − | 461.126i | 0.539912 | − | 0.223639i | ||||
\(163\) | −801.206 | − | 1199.09i | −0.385002 | − | 0.576196i | 0.587461 | − | 0.809252i | \(-0.300127\pi\) |
−0.972463 | + | 0.233056i | \(0.925127\pi\) | |||||||
\(164\) | −3930.47 | − | 781.819i | −1.87145 | − | 0.372255i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −226.281 | + | 226.281i | −0.105800 | + | 0.105800i | ||||
\(167\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2197.00i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −534.576 | −0.239065 | ||||||||
\(172\) | −612.244 | − | 253.600i | −0.271414 | − | 0.112423i | ||||
\(173\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 909.759 | − | 4573.67i | 0.389635 | − | 1.95883i | ||||
\(177\) | −4320.48 | + | 2886.85i | −1.83473 | + | 1.22593i | ||||
\(178\) | 1576.64 | + | 3806.34i | 0.663899 | + | 1.60280i | ||||
\(179\) | −629.206 | + | 260.626i | −0.262732 | + | 0.108827i | −0.510161 | − | 0.860079i | \(-0.670414\pi\) |
0.247429 | + | 0.968906i | \(0.420414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −550.829 | − | 5077.42i | −0.215404 | − | 1.98555i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | 3366.30 | + | 2249.29i | 1.26532 | + | 0.845461i | ||||
\(193\) | −574.544 | + | 2888.43i | −0.214283 | + | 1.07727i | 0.712499 | + | 0.701673i | \(0.247563\pi\) |
−0.926782 | + | 0.375600i | \(0.877437\pi\) | |||||||
\(194\) | 3668.31 | − | 2451.09i | 1.35757 | − | 0.907103i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2535.13 | − | 1050.08i | 0.923880 | − | 0.382683i | ||||
\(197\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(198\) | −7181.22 | − | 1428.43i | −2.57751 | − | 0.512699i | ||||
\(199\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(200\) | 2000.00 | − | 2000.00i | 0.707107 | − | 0.707107i | ||||
\(201\) | 7635.24 | − | 1518.74i | 2.67935 | − | 0.532955i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4255.64 | + | 1245.11i | 1.46056 | + | 0.427331i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −911.586 | − | 609.103i | −0.301702 | − | 0.201591i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −681.025 | + | 455.046i | −0.222198 | + | 0.148468i | −0.661687 | − | 0.749780i | \(-0.730159\pi\) |
0.439490 | + | 0.898248i | \(0.355159\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3461.45 | + | 5180.42i | 1.10570 | + | 1.65480i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 847.713 | − | 1268.69i | 0.267035 | − | 0.399646i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3729.18 | + | 9003.03i | −1.15066 | + | 2.77794i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3140.25 | − | 3140.25i | −0.930443 | − | 0.930443i | ||||
\(226\) | 2591.06 | + | 1731.29i | 0.762631 | + | 0.509574i | ||||
\(227\) | −1272.05 | + | 6395.02i | −0.371933 | + | 1.86983i | 0.110464 | + | 0.993880i | \(0.464766\pi\) |
−0.482397 | + | 0.875953i | \(0.660234\pi\) | |||||||
\(228\) | 791.432 | − | 528.818i | 0.229885 | − | 0.153605i | ||||
\(229\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3604.16 | − | 5394.01i | 1.01338 | − | 1.51662i | 0.165654 | − | 0.986184i | \(-0.447026\pi\) |
0.847722 | − | 0.530441i | \(-0.177974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2011.77 | − | 4856.85i | 0.554895 | − | 1.33964i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −514.788 | − | 2588.01i | −0.137595 | − | 0.691737i | −0.986575 | − | 0.163311i | \(-0.947783\pi\) |
0.848980 | − | 0.528426i | \(-0.177217\pi\) | |||||||
\(242\) | −7956.21 | − | 7956.21i | −2.11341 | − | 2.11341i | ||||
\(243\) | 4314.89 | + | 2883.12i | 1.13910 | + | 0.761120i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4287.48 | − | 10350.9i | −1.11122 | − | 2.68272i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −877.464 | − | 174.539i | −0.223321 | − | 0.0444214i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5534.06 | + | 5534.06i | −1.39166 | + | 1.39166i | −0.570054 | + | 0.821607i | \(0.693078\pi\) |
−0.821607 | + | 0.570054i | \(0.806922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4096.00 | −1.00000 | ||||||||
\(257\) | 7577.61 | + | 3138.75i | 1.83922 | + | 0.761828i | 0.956366 | + | 0.292170i | \(0.0943774\pi\) |
0.882849 | + | 0.469658i | \(0.155623\pi\) | |||||||
\(258\) | −361.440 | − | 1817.08i | −0.0872182 | − | 0.438475i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1612.48 | + | 1077.42i | −0.380226 | + | 0.254059i | ||||
\(263\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(264\) | 12044.7 | − | 4989.10i | 2.80797 | − | 1.16310i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6399.16 | + | 9577.03i | −1.46675 | + | 2.19515i | ||||
\(268\) | −5569.13 | + | 5569.13i | −1.26936 | + | 1.26936i | ||||
\(269\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | −4279.69 | + | 1344.58i | −0.954023 | + | 0.299733i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8380.27 | − | 3471.22i | −1.84770 | − | 0.765344i | ||||
\(275\) | −1776.87 | − | 8932.95i | −0.389635 | − | 1.95883i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(278\) | −1573.72 | + | 7911.61i | −0.339515 | + | 1.70686i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6897.49 | + | 2857.03i | −1.46431 | + | 0.606535i | −0.965552 | − | 0.260209i | \(-0.916209\pi\) |
−0.498753 | + | 0.866744i | \(0.666209\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8703.40 | + | 1731.21i | 1.82814 | + | 0.363640i | 0.984793 | − | 0.173731i | \(-0.0555824\pi\) |
0.843346 | + | 0.537371i | \(0.180582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6431.22i | 1.31585i | ||||||||
\(289\) | −4030.23 | + | 2809.77i | −0.820320 | + | 0.571905i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11395.3 | + | 4720.10i | 2.29555 | + | 0.950850i | ||||
\(292\) | −1923.37 | − | 9669.43i | −0.385468 | − | 1.93788i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 6378.55 | + | 4262.01i | 1.26532 | + | 0.845461i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1880.29 | − | 4539.42i | −0.367359 | − | 0.886883i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7755.51 | + | 1542.67i | 1.49255 | + | 0.296887i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −368.519 | + | 889.685i | −0.0695264 | + | 0.167852i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2111.16 | + | 6719.64i | 0.394402 | + | 1.25535i | ||||
\(307\) | −7204.00 | −1.33926 | −0.669632 | − | 0.742693i | \(-0.733548\pi\) | ||||
−0.669632 | + | 0.742693i | \(0.733548\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8873.70 | − | 5929.22i | 1.60246 | − | 1.07073i | 0.652769 | − | 0.757557i | \(-0.273607\pi\) |
0.949695 | − | 0.313175i | \(-0.101393\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6665.77 | + | 16092.6i | −1.15902 | + | 2.79813i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −92.9914 | + | 1050.56i | −0.0160191 | + | 0.180974i | ||||
\(324\) | −3408.20 | −0.584397 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 795.767 | + | 4000.59i | 0.135195 | + | 0.679670i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9424.58 | + | 6297.30i | 1.58654 | + | 1.06009i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4312.01 | − | 10410.1i | −0.716041 | − | 1.72868i | −0.684322 | − | 0.729180i | \(-0.739902\pi\) |
−0.0317191 | − | 0.999497i | \(-0.510098\pi\) | |||||||
\(332\) | 836.227 | − | 346.377i | 0.138235 | − | 0.0572587i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6697.07 | − | 1332.13i | 1.08253 | − | 0.215329i | 0.378574 | − | 0.925571i | \(-0.376415\pi\) |
0.703957 | + | 0.710242i | \(0.251415\pi\) | |||||||
\(338\) | −2378.02 | + | 5741.04i | −0.382683 | + | 0.923880i | ||||
\(339\) | 8712.09i | 1.39580i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1396.91 | + | 578.621i | 0.220867 | + | 0.0914860i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1325.38 | + | 1325.38i | 0.207731 | + | 0.207731i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6772.37 | + | 4525.15i | −1.04772 | + | 0.700066i | −0.955295 | − | 0.295654i | \(-0.904463\pi\) |
−0.0924274 | + | 0.995719i | \(0.529463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7327.82 | + | 10966.9i | −1.10959 | + | 1.66061i | ||||
\(353\) | 6465.40 | − | 6465.40i | 0.974840 | − | 0.974840i | −0.0248514 | − | 0.999691i | \(-0.507911\pi\) |
0.999691 | + | 0.0248514i | \(0.00791128\pi\) | |||||||
\(354\) | 14414.7 | − | 2867.26i | 2.16421 | − | 0.430489i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11653.0i | − | 1.73485i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1926.29 | 0.284379 | ||||||||
\(359\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4689.95 | − | 4689.95i | −0.683767 | − | 0.683767i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6136.90 | − | 30852.3i | 0.887338 | − | 4.46095i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9887.53 | − | 14797.7i | 1.39492 | − | 2.08764i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | −4056.38 | + | 13864.2i | −0.560830 | + | 1.91684i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10979.4 | − | 7336.21i | −1.48806 | − | 0.994290i | −0.992032 | − | 0.125984i | \(-0.959791\pi\) |
−0.496028 | − | 0.868306i | \(-0.665209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(384\) | −6361.95 | − | 9521.34i | −0.845461 | − | 1.26532i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4627.77 | − | 6925.94i | 0.610226 | − | 0.913268i | ||||
\(387\) | 2081.00 | − | 2081.00i | 0.273342 | − | 0.273342i | ||||
\(388\) | −12238.8 | + | 2434.45i | −1.60137 | + | 0.318532i | ||||
\(389\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7761.20 | −1.00000 | ||||||||
\(393\) | −5009.04 | − | 2074.81i | −0.642932 | − | 0.266311i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 17219.3 | + | 11505.6i | 2.18511 | + | 1.46004i | ||||
\(397\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7391.04 | + | 3061.47i | −0.923880 | + | 0.382683i | ||||
\(401\) | 8837.76 | + | 13226.6i | 1.10059 | + | 1.64715i | 0.664601 | + | 0.747198i | \(0.268601\pi\) |
0.435989 | + | 0.899952i | \(0.356399\pi\) | |||||||
\(402\) | −21595.7 | − | 4295.66i | −2.67935 | − | 0.532955i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9772.81 | − | 7859.91i | −1.18585 | − | 0.953734i | ||||
\(409\) | 3903.53 | 0.471925 | 0.235962 | − | 0.971762i | \(-0.424176\pi\) | ||||
0.235962 | + | 0.971762i | \(0.424176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4947.32 | − | 24871.9i | −0.593755 | − | 2.98501i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20835.2 | + | 8630.22i | −2.44677 | + | 1.01349i | ||||
\(418\) | 1722.80 | + | 2578.36i | 0.201591 | + | 0.301702i | ||||
\(419\) | 11792.0 | + | 2345.58i | 1.37489 | + | 0.273482i | 0.826591 | − | 0.562803i | \(-0.190277\pi\) |
0.548296 | + | 0.836285i | \(0.315277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | 2272.14 | − | 451.957i | 0.262100 | − | 0.0521349i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6717.51 | + | 5625.00i | −0.766700 | + | 0.642006i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3437.95 | − | 17283.7i | −0.388270 | − | 1.95197i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(432\) | −3588.40 | + | 2397.69i | −0.399646 | + | 0.267035i | ||||
\(433\) | −3151.72 | − | 7608.93i | −0.349797 | − | 0.844484i | −0.996644 | − | 0.0818641i | \(-0.973913\pi\) |
0.646847 | − | 0.762620i | \(-0.276087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 19489.6 | − | 19489.6i | 2.12614 | − | 2.12614i | ||||
\(439\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12186.0i | 1.31585i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15449.4 | 1.65694 | 0.828471 | − | 0.560032i | \(-0.189211\pi\) | ||||
0.828471 | + | 0.560032i | \(0.189211\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8671.90 | − | 5794.38i | 0.911475 | − | 0.609028i | −0.00894477 | − | 0.999960i | \(-0.502847\pi\) |
0.920420 | + | 0.390932i | \(0.127847\pi\) | |||||||
\(450\) | 4806.88 | + | 11604.8i | 0.503552 | + | 1.21568i | ||||
\(451\) | 33721.5 | − | 13967.9i | 3.52080 | − | 1.45836i | ||||
\(452\) | −4896.82 | − | 7328.62i | −0.509574 | − | 0.762631i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10245.9 | − | 15334.1i | 1.05918 | − | 1.58517i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2640.50 | + | 525.228i | −0.271168 | + | 0.0539387i | ||||
\(457\) | −2878.32 | + | 6948.89i | −0.294622 | + | 0.711280i | 0.705375 | + | 0.708834i | \(0.250779\pi\) |
−0.999997 | + | 0.00244611i | \(0.999221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2962.24 | + | 3683.18i | −0.301232 | + | 0.374545i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15256.6 | + | 10194.1i | −1.51662 | + | 1.01338i | ||||
\(467\) | 7712.53 | + | 18619.7i | 0.764226 | + | 1.84500i | 0.432546 | + | 0.901612i | \(0.357615\pi\) |
0.331679 | + | 0.943392i | \(0.392385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10514.0 | + | 10514.0i | −1.02531 | + | 1.02531i | ||||
\(473\) | 5919.76 | − | 1177.51i | 0.575456 | − | 0.114465i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1880.84i | 0.181681i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1456.04 | + | 7320.00i | −0.137595 | + | 0.691737i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12178.8 | + | 29402.3i | 1.14377 | + | 2.76130i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8154.69 | − | 12204.4i | −0.761120 | − | 1.13910i | ||||
\(487\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8063.57 | + | 8063.57i | −0.745699 | + | 0.745699i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8178.81 | + | 19745.4i | −0.751740 | + | 1.81486i | −0.202311 | + | 0.979321i | \(0.564845\pi\) |
−0.549429 | + | 0.835540i | \(0.685155\pi\) | |||||||
\(492\) | 31688.9i | 2.90375i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2104.01 | + | 1405.85i | 0.189323 | + | 0.126501i | ||||
\(499\) | 2995.83 | − | 15061.0i | 0.268761 | − | 1.35115i | −0.576631 | − | 0.817005i | \(-0.695633\pi\) |
0.845392 | − | 0.534147i | \(-0.179367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20451.2 | − | 8471.18i | 1.81829 | − | 0.753162i | ||||
\(503\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17038.9 | + | 3389.24i | −1.49255 | + | 0.296887i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10703.4 | + | 4433.48i | 0.923880 | + | 0.382683i | ||||
\(513\) | 197.948 | + | 995.152i | 0.0170363 | + | 0.0856472i | ||||
\(514\) | −16403.9 | − | 16403.9i | −1.40767 | − | 1.40767i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1022.31 | + | 5139.49i | −0.0872182 | + | 0.438475i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19360.2 | − | 3850.97i | −1.62799 | − | 0.323828i | −0.705165 | − | 0.709043i | \(-0.749127\pi\) |
−0.922827 | + | 0.385215i | \(0.874127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9447.21 | + | 9447.21i | −0.789862 | + | 0.789862i | −0.981471 | − | 0.191609i | \(-0.938629\pi\) |
0.191609 | + | 0.981471i | \(0.438629\pi\) | |||||||
\(524\) | 5379.80 | − | 1070.11i | 0.448507 | − | 0.0892136i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −36874.6 | −3.03932 | ||||||||
\(529\) | −11240.8 | − | 4656.11i | −0.923880 | − | 0.382683i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16508.3 | + | 16508.3i | 1.34915 | + | 1.34915i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 27087.9 | − | 18099.6i | 2.19515 | − | 1.46675i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20580.8 | − | 8524.85i | 1.65850 | − | 0.686973i | ||||
\(537\) | 2991.94 | + | 4477.76i | 0.240432 | + | 0.359831i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13884.9 | + | 20780.3i | −1.10959 | + | 1.66061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12638.7 | + | 1118.73i | 0.996105 | + | 0.0881716i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2101.33 | + | 10564.1i | 0.164253 | + | 0.825757i | 0.971773 | + | 0.235917i | \(0.0758092\pi\) |
−0.807520 | + | 0.589840i | \(0.799191\pi\) | |||||||
\(548\) | 18141.5 | + | 18141.5i | 1.41417 | + | 1.41417i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5025.76 | + | 25266.2i | −0.389635 | + | 1.95883i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12675.8 | − | 18970.6i | 0.966857 | − | 1.44700i | ||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38528.3 | + | 12104.7i | −2.89958 | + | 0.910985i | ||||
\(562\) | 21116.4 | 1.58495 | ||||||||
\(563\) | −18945.3 | − | 7847.39i | −1.41820 | − | 0.587439i | −0.463795 | − | 0.885943i | \(-0.653512\pi\) |
−0.954408 | + | 0.298504i | \(0.903512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20869.2 | − | 13944.4i | −1.54982 | − | 1.03556i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9209.41 | + | 22233.5i | 0.678521 | + | 1.63809i | 0.766712 | + | 0.641991i | \(0.221891\pi\) |
−0.0881913 | + | 0.996104i | \(0.528109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4941.81 | − | 7395.94i | −0.362186 | − | 0.542050i | 0.604965 | − | 0.796252i | \(-0.293187\pi\) |
−0.967151 | + | 0.254202i | \(0.918187\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6961.11 | − | 16805.6i | 0.503552 | − | 1.21568i | ||||
\(577\) | − | 19651.9i | − | 1.41789i | −0.705266 | − | 0.708943i | \(-0.749173\pi\) | ||
0.705266 | − | 0.708943i | \(-0.250827\pi\) | |||||||
\(578\) | 13572.8 | − | 2979.98i | 0.976735 | − | 0.214448i | ||||
\(579\) | 23287.6 | 1.67150 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −24668.4 | − | 24668.4i | −1.75694 | − | 1.75694i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5440.11 | + | 27349.3i | −0.385468 | + | 1.93788i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9562.15 | − | 3960.77i | 0.672355 | − | 0.278498i | −0.0202721 | − | 0.999795i | \(-0.506453\pi\) |
0.692627 | + | 0.721296i | \(0.256453\pi\) | |||||||
\(588\) | −12054.8 | − | 18041.3i | −0.845461 | − | 1.26532i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8139.44 | − | 19650.3i | 0.563654 | − | 1.36078i | −0.343171 | − | 0.939273i | \(-0.611501\pi\) |
0.906825 | − | 0.421507i | \(-0.138499\pi\) | |||||||
\(594\) | 13897.3i | 0.959955i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(600\) | −18596.4 | − | 12425.7i | −1.26532 | − | 0.845461i | ||||
\(601\) | −2609.98 | + | 13121.3i | −0.177144 | + | 0.890561i | 0.785307 | + | 0.619106i | \(0.212505\pi\) |
−0.962451 | + | 0.271455i | \(0.912495\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13385.1 | − | 32314.4i | −0.903950 | − | 2.18233i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(608\) | 1925.98 | − | 1925.98i | 0.128468 | − | 0.128468i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1756.55 | − | 19844.4i | 0.116020 | − | 1.31072i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 18825.0 | + | 7797.56i | 1.23732 | + | 0.512514i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21448.2 | − | 14331.3i | −1.39947 | − | 0.935097i | −0.999830 | − | 0.0184247i | \(-0.994135\pi\) |
−0.399641 | − | 0.916672i | \(-0.630865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22345.5 | − | 14930.8i | 1.45095 | − | 0.969495i | 0.454039 | − | 0.890982i | \(-0.349983\pi\) |
0.996913 | − | 0.0785136i | \(-0.0250174\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11048.5 | + | 11048.5i | −0.707107 | + | 0.707107i | ||||
\(626\) | −29605.8 | + | 5888.97i | −1.89024 | + | 0.375991i | ||||
\(627\) | −3317.63 | + | 8009.46i | −0.211313 | + | 0.510155i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4579.71 | + | 4579.71i | 0.287563 | + | 0.287563i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18031.4 | − | 26986.0i | 1.11107 | − | 1.66284i | 0.546495 | − | 0.837462i | \(-0.315962\pi\) |
0.564580 | − | 0.825378i | \(-0.309038\pi\) | |||||||
\(642\) | 34837.0 | − | 34837.0i | 2.14160 | − | 2.14160i | ||||
\(643\) | 9694.64 | − | 1928.38i | 0.594587 | − | 0.118271i | 0.111381 | − | 0.993778i | \(-0.464472\pi\) |
0.483205 | + | 0.875507i | \(0.339472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1380.11 | − | 2644.58i | 0.0840554 | − | 0.161068i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 8906.06 | + | 3689.01i | 0.539912 | + | 0.223639i | ||||
\(649\) | 9341.05 | + | 46960.6i | 0.564974 | + | 2.84032i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2250.77 | − | 11315.4i | 0.135195 | − | 0.679670i | ||||
\(653\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17811.5 | − | 26656.7i | −1.06009 | − | 1.58654i | ||||
\(657\) | 42941.7 | + | 8541.64i | 2.54995 | + | 0.507216i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21039.3 | + | 21039.3i | −1.24366 | + | 1.24366i | −0.285191 | + | 0.958471i | \(0.592057\pi\) |
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(662\) | 31870.2i | 1.87111i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2560.08 | −0.149624 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7294.65 | + | 10917.2i | 0.417813 | + | 0.625301i | 0.979355 | − | 0.202147i | \(-0.0647919\pi\) |
−0.561542 | + | 0.827448i | \(0.689792\pi\) | |||||||
\(674\) | −18942.2 | − | 3767.83i | −1.08253 | − | 0.215329i | ||||
\(675\) | −4683.00 | + | 7008.60i | −0.267035 | + | 0.399646i | ||||
\(676\) | 12428.1 | − | 12428.1i | 0.707107 | − | 0.707107i | ||||
\(677\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(678\) | 9429.89 | − | 22765.8i | 0.534149 | − | 1.28955i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 51559.0 | 2.90124 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3570.43 | + | 17949.8i | 0.200028 | + | 1.00561i | 0.942112 | + | 0.335300i | \(0.108838\pi\) |
−0.742084 | + | 0.670307i | \(0.766162\pi\) | |||||||
\(684\) | −3024.02 | − | 3024.02i | −0.169044 | − | 0.169044i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2028.80 | − | 4897.95i | −0.112423 | − | 0.271414i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8843.56 | + | 1759.09i | 0.486867 | + | 0.0968438i | 0.432419 | − | 0.901673i | \(-0.357660\pi\) |
0.0544477 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22595.0 | − | 4494.43i | 1.23587 | − | 0.245830i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27360.8 | − | 22005.3i | −1.48689 | − | 1.19585i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −47393.4 | − | 19631.0i | −2.56450 | − | 1.06225i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 31018.9 | − | 20726.2i | 1.66061 | − | 1.10959i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23893.0 | + | 9896.80i | −1.27369 | + | 0.527579i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −40770.9 | − | 8109.83i | −2.16421 | − | 0.430489i | ||||
\(709\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12613.1 | + | 30450.8i | −0.663899 | + | 1.60280i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5033.65 | − | 2085.00i | −0.262732 | − | 0.108827i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7179.07 | + | 17331.8i | 0.370052 | + | 0.893384i | ||||
\(723\) | −19277.2 | + | 7984.89i | −0.991601 | + | 0.410735i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −49430.7 | + | 73978.3i | −2.52692 | + | 3.78181i | ||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11301.7 | − | 27284.8i | 0.574187 | − | 1.38621i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3727.62 | − | 4451.62i | −0.188606 | − | 0.225238i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13994.5 | − | 70355.3i | 0.699451 | − | 3.51638i | ||||
\(738\) | −41854.3 | + | 27966.2i | −2.08764 | + | 1.39492i | ||||
\(739\) | −6770.36 | − | 16345.1i | −0.337012 | − | 0.813619i | −0.997999 | − | 0.0632220i | \(-0.979862\pi\) |
0.660988 | − | 0.750397i | \(-0.270138\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4019.64i | 0.196882i | ||||||||
\(748\) | 25606.3 | − | 31838.2i | 1.25168 | − | 1.55631i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51456.7 | + | 34382.3i | 2.49029 | + | 1.66396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(758\) | 20749.9 | + | 31054.5i | 0.994290 | + | 1.48806i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29281.5 | + | 29281.5i | −1.39482 | + | 1.39482i | −0.580691 | + | 0.814124i | \(0.697218\pi\) |
−0.814124 | + | 0.580691i | \(0.802782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 6318.77 | + | 31766.6i | 0.296887 | + | 1.49255i | ||||
\(769\) | −27307.9 | − | 27307.9i | −1.28056 | − | 1.28056i | −0.940351 | − | 0.340207i | \(-0.889503\pi\) |
−0.340207 | − | 0.940351i | \(-0.610497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12652.9 | − | 63610.3i | 0.591027 | − | 2.97130i | ||||
\(772\) | −19589.5 | + | 13089.3i | −0.913268 | + | 0.610226i | ||||
\(773\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(774\) | −7690.38 | + | 3185.46i | −0.357138 | + | 0.147932i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 34616.6 | + | 6885.66i | 1.60137 | + | 0.318532i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7392.56 | + | 1470.47i | −0.340008 | + | 0.0676318i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20281.0 | + | 8400.67i | 0.923880 | + | 0.382683i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10843.5 | + | 10843.5i | 0.492079 | + | 0.492079i | ||||
\(787\) | −33357.0 | − | 22288.5i | −1.51086 | − | 1.00953i | −0.987536 | − | 0.157396i | \(-0.949690\pi\) |
−0.523328 | − | 0.852131i | \(-0.675310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −32542.7 | − | 48703.6i | −1.46004 | − | 2.18511i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 22627.4 | 1.00000 | ||||||||
\(801\) | 47811.4 | + | 19804.1i | 2.10903 | + | 0.873589i | ||||
\(802\) | −8777.77 | − | 44128.8i | −0.386476 | − | 1.94295i | ||||
\(803\) | 63494.0 | + | 63494.0i | 2.79035 | + | 2.79035i | ||||
\(804\) | 51782.8 | + | 34600.1i | 2.27144 | + | 1.51773i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15771.5 | − | 23603.6i | −0.685408 | − | 1.02578i | −0.997137 | − | 0.0756140i | \(-0.975908\pi\) |
0.311730 | − | 0.950171i | \(-0.399092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −805.820 | + | 1205.99i | −0.0348905 | + | 0.0522173i | −0.848505 | − | 0.529188i | \(-0.822497\pi\) |
0.813614 | + | 0.581405i | \(0.197497\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17030.1 | + | 31116.9i | 0.730603 | + | 1.33494i | ||||
\(817\) | −1246.41 | −0.0533736 | ||||||||
\(818\) | −10200.4 | − | 4225.15i | −0.436001 | − | 0.180598i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(822\) | −13993.1 | + | 70348.2i | −0.593755 | + | 2.98501i | ||||
\(823\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −66538.5 | + | 27561.1i | −2.80797 | + | 1.16310i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46528.5 | − | 9255.09i | −1.95641 | − | 0.389155i | −0.992345 | − | 0.123496i | \(-0.960589\pi\) |
−0.964067 | − | 0.265658i | \(-0.914411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23948.2 | + | 2119.81i | 0.996105 | + | 0.0881716i | ||||
\(834\) | 63786.3 | 2.64837 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1711.11 | − | 8602.32i | −0.0707893 | − | 0.355882i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28275.2 | − | 18892.9i | −1.16557 | − | 0.778811i | ||||
\(839\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9333.27 | − | 22532.5i | −0.382683 | − | 0.923880i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32798.3 | + | 49086.1i | 1.34002 | + | 2.00548i | ||||
\(844\) | −6426.59 | − | 1278.33i | −0.262100 | − | 0.0521349i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 70170.0i | − | 2.83655i | ||||||
\(850\) | 23642.2 | − | 7427.85i | 0.954023 | − | 0.299733i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9723.99 | + | 48885.8i | −0.388270 | + | 1.95197i | ||||
\(857\) | 34971.7 | − | 23367.3i | 1.39394 | − | 0.931404i | 0.394020 | − | 0.919102i | \(-0.371084\pi\) |
0.999924 | − | 0.0123023i | \(-0.00391605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31446.3 | + | 13025.5i | −1.24905 | + | 0.517373i | −0.906532 | − | 0.422138i | \(-0.861280\pi\) |
−0.342518 | + | 0.939511i | \(0.611280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 11972.2 | − | 2381.42i | 0.471415 | − | 0.0937702i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23294.5i | 0.914063i | ||||||||
\(867\) | 28008.5 | + | 26922.0i | 1.09714 | + | 1.05458i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10811.3 | − | 54352.3i | 0.419139 | − | 2.10715i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −72024.3 | + | 29833.4i | −2.77794 | + | 1.15066i | ||||
\(877\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38296.4 | + | 7617.63i | −1.46452 | + | 0.291311i | −0.862046 | − | 0.506830i | \(-0.830817\pi\) |
−0.602471 | + | 0.798141i | \(0.705817\pi\) | |||||||
\(882\) | 13190.1 | − | 31843.7i | 0.503552 | − | 1.21568i | ||||
\(883\) | 24867.2i | 0.947733i | 0.880597 | + | 0.473866i | \(0.157142\pi\) | ||||
−0.880597 | + | 0.473866i | \(0.842858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40371.3 | − | 16722.4i | −1.53081 | − | 0.634084i | ||||
\(887\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25810.3 | − | 17245.9i | 0.970456 | − | 0.648438i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28932.6 | + | 5755.04i | −1.07516 | + | 0.213862i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | − | 35527.8i | − | 1.31585i | ||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −103237. | −3.81089 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4863.58 | + | 24450.9i | 0.178938 | + | 0.899584i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8174.09 | + | 41093.9i | −0.299246 | + | 1.50441i | 0.479762 | + | 0.877399i | \(0.340723\pi\) |
−0.779008 | + | 0.627013i | \(0.784277\pi\) | |||||||
\(908\) | −43371.5 | + | 28979.9i | −1.58517 | + | 1.05918i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(912\) | 7468.46 | + | 1485.57i | 0.271168 | + | 0.0539387i | ||||
\(913\) | −4580.03 | + | 6854.50i | −0.166021 | + | 0.248468i | ||||
\(914\) | 15042.8 | − | 15042.8i | 0.544390 | − | 0.544390i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11727.4 | − | 6418.30i | 0.421634 | − | 0.230757i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11113.4 | + | 55870.8i | 0.397610 | + | 1.99892i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42035.7 | + | 8361.41i | 1.48455 | + | 0.295295i | 0.869791 | − | 0.493421i | \(-0.164254\pi\) |
0.614758 | + | 0.788716i | \(0.289254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3649.39 | − | 3649.39i | 0.128468 | − | 0.128468i | ||||
\(932\) | 50901.4 | − | 10124.9i | 1.78898 | − | 0.355850i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 57003.6i | − | 1.99702i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10300.9 | + | 4266.79i | 0.359143 | + | 0.148762i | 0.554957 | − | 0.831879i | \(-0.312735\pi\) |
−0.195814 | + | 0.980641i | \(0.562735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −59673.3 | − | 59673.3i | −2.07387 | − | 2.07387i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 38854.8 | − | 16094.2i | 1.33964 | − | 0.554895i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16743.6 | − | 3330.51i | −0.575456 | − | 0.114465i | ||||
\(947\) | −19139.9 | + | 28644.9i | −0.656773 | + | 0.982931i | 0.342287 | + | 0.939595i | \(0.388798\pi\) |
−0.999061 | + | 0.0433353i | \(0.986202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2035.80 | − | 4914.86i | 0.0695264 | − | 0.167852i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28444.1 | −0.966836 | −0.483418 | − | 0.875390i | \(-0.660605\pi\) | ||||
−0.483418 | + | 0.875390i | \(0.660605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27523.3 | − | 11400.5i | 0.923880 | − | 0.382683i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 76756.7 | + | 15267.9i | 2.56848 | + | 0.510903i | ||||
\(964\) | 11727.9 | − | 17552.1i | 0.391837 | − | 0.586426i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(968\) | − | 90014.3i | − | 2.98881i | ||||||
\(969\) | 8291.06 | − | 899.463i | 0.274868 | − | 0.0298193i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21256.7 | − | 8804.82i | −0.702534 | − | 0.290999i | 0.00267705 | − | 0.999996i | \(-0.499148\pi\) |
−0.705211 | + | 0.708997i | \(0.749148\pi\) | |||||||
\(972\) | 8099.33 | + | 40718.1i | 0.267270 | + | 1.34366i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2433.83 | + | 5875.78i | 0.0796981 | + | 0.192408i | 0.958706 | − | 0.284399i | \(-0.0917940\pi\) |
−0.879008 | + | 0.476807i | \(0.841794\pi\) | |||||||
\(978\) | 29799.1 | − | 12343.2i | 0.974303 | − | 0.403570i | ||||
\(979\) | 58965.4 | + | 88248.0i | 1.92497 | + | 2.88092i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42744.5 | − | 42744.5i | 1.38904 | − | 1.38904i | ||||
\(983\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(984\) | 34299.8 | − | 82807.1i | 1.11122 | − | 2.68272i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −74083.8 | + | 49501.2i | −2.36755 | + | 1.58195i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3976.35 | − | 5951.03i | −0.126501 | − | 0.189323i | ||||
\(997\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(998\) | −24130.4 | + | 36113.7i | −0.765366 | + | 1.14545i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 136.4.s.a.11.1 | ✓ | 8 | |
8.3 | odd | 2 | CM | 136.4.s.a.11.1 | ✓ | 8 | |
17.14 | odd | 16 | inner | 136.4.s.a.99.1 | yes | 8 | |
136.99 | even | 16 | inner | 136.4.s.a.99.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.s.a.11.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
136.4.s.a.11.1 | ✓ | 8 | 8.3 | odd | 2 | CM | |
136.4.s.a.99.1 | yes | 8 | 17.14 | odd | 16 | inner | |
136.4.s.a.99.1 | yes | 8 | 136.99 | even | 16 | inner |