Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), 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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(-3.50329 - 6.06788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.163 |
Dual form | 378.4.g.e.109.2 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.21575 | + | 3.83779i | −0.198183 | + | 0.343263i | −0.947939 | − | 0.318451i | \(-0.896837\pi\) |
0.749756 | + | 0.661714i | \(0.230171\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.5959 | + | 14.4407i | −0.626121 | + | 0.779726i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.43150 | + | 7.67558i | 0.140136 | + | 0.242723i | ||||
\(11\) | −19.8193 | − | 34.3281i | −0.543251 | − | 0.940938i | −0.998715 | − | 0.0506835i | \(-0.983860\pi\) |
0.455464 | − | 0.890254i | \(-0.349473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.4863 | 0.799757 | 0.399878 | − | 0.916568i | \(-0.369052\pi\) | ||||
0.399878 | + | 0.916568i | \(0.369052\pi\) | |||||||
\(14\) | 13.4162 | + | 34.5255i | 0.256116 | + | 0.659094i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 57.0112 | + | 98.7463i | 0.813367 | + | 1.40879i | 0.910494 | + | 0.413521i | \(0.135701\pi\) |
−0.0971273 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67.5634 | − | 117.023i | 0.815796 | − | 1.41300i | −0.0929597 | − | 0.995670i | \(-0.529633\pi\) |
0.908755 | − | 0.417329i | \(-0.137034\pi\) | |||||||
\(20\) | 17.7260 | 0.198183 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −79.2774 | −0.768272 | ||||||||
\(23\) | 96.1989 | − | 166.621i | 0.872124 | − | 1.51056i | 0.0123284 | − | 0.999924i | \(-0.496076\pi\) |
0.859795 | − | 0.510639i | \(-0.170591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.6809 | + | 91.2460i | 0.421447 | + | 0.729968i | ||||
\(26\) | 37.4863 | − | 64.9282i | 0.282757 | − | 0.489749i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 73.2160 | + | 11.2880i | 0.494161 | + | 0.0761867i | ||||
\(29\) | 129.302 | 0.827957 | 0.413978 | − | 0.910287i | \(-0.364139\pi\) | ||||
0.413978 | + | 0.910287i | \(0.364139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 122.291 | + | 211.813i | 0.708517 | + | 1.22719i | 0.965407 | + | 0.260747i | \(0.0839687\pi\) |
−0.256890 | + | 0.966441i | \(0.582698\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 228.045 | 1.15027 | ||||||||
\(35\) | −29.7269 | − | 76.4998i | −0.143564 | − | 0.369452i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −136.629 | + | 236.649i | −0.607073 | + | 1.05148i | 0.384647 | + | 0.923064i | \(0.374323\pi\) |
−0.991720 | + | 0.128418i | \(0.959010\pi\) | |||||||
\(38\) | −135.127 | − | 234.047i | −0.576855 | − | 0.999141i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 17.7260 | − | 30.7023i | 0.0700682 | − | 0.121362i | ||||
\(41\) | 365.448 | 1.39203 | 0.696017 | − | 0.718025i | \(-0.254954\pi\) | ||||
0.696017 | + | 0.718025i | \(0.254954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.2537 | 0.203049 | 0.101525 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101525 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(44\) | −79.2774 | + | 137.312i | −0.271625 | + | 0.470469i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −192.398 | − | 333.243i | −0.616685 | − | 1.06813i | ||||
\(47\) | 172.495 | − | 298.771i | 0.535341 | − | 0.927238i | −0.463805 | − | 0.885937i | \(-0.653516\pi\) |
0.999147 | − | 0.0413012i | \(-0.0131503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −74.0693 | − | 334.907i | −0.215946 | − | 0.976405i | ||||
\(50\) | 210.724 | 0.596016 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −74.9727 | − | 129.856i | −0.199939 | − | 0.346305i | ||||
\(53\) | −300.911 | − | 521.193i | −0.779874 | − | 1.35078i | −0.932014 | − | 0.362422i | \(-0.881950\pi\) |
0.152140 | − | 0.988359i | \(-0.451384\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 175.659 | 0.430652 | ||||||||
\(56\) | 92.7674 | − | 115.526i | 0.221367 | − | 0.275675i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 129.302 | − | 223.957i | 0.292727 | − | 0.507018i | ||||
\(59\) | 15.7631 | + | 27.3024i | 0.0347827 | + | 0.0602454i | 0.882893 | − | 0.469575i | \(-0.155593\pi\) |
−0.848110 | + | 0.529820i | \(0.822259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −431.259 | + | 746.963i | −0.905199 | + | 1.56785i | −0.0845483 | + | 0.996419i | \(0.526945\pi\) |
−0.820650 | + | 0.571431i | \(0.806389\pi\) | |||||||
\(62\) | 489.162 | 1.00199 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −83.0604 | + | 143.865i | −0.158498 | + | 0.274527i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 341.295 | + | 591.141i | 0.622326 | + | 1.07790i | 0.989051 | + | 0.147571i | \(0.0471456\pi\) |
−0.366725 | + | 0.930329i | \(0.619521\pi\) | |||||||
\(68\) | 228.045 | − | 394.985i | 0.406684 | − | 0.704397i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −162.228 | − | 25.0114i | −0.277000 | − | 0.0427061i | ||||
\(71\) | 664.860 | 1.11133 | 0.555665 | − | 0.831406i | \(-0.312464\pi\) | ||||
0.555665 | + | 0.831406i | \(0.312464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −471.122 | − | 816.007i | −0.755351 | − | 1.30831i | −0.945199 | − | 0.326494i | \(-0.894133\pi\) |
0.189848 | − | 0.981813i | \(-0.439200\pi\) | |||||||
\(74\) | 273.259 | + | 473.298i | 0.429266 | + | 0.743510i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −540.507 | −0.815796 | ||||||||
\(77\) | 725.546 | + | 111.860i | 1.07381 | + | 0.165554i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.66271 | − | 2.87990i | 0.00236797 | − | 0.00410145i | −0.864839 | − | 0.502049i | \(-0.832580\pi\) |
0.867207 | + | 0.497948i | \(0.165913\pi\) | |||||||
\(80\) | −35.4520 | − | 61.4047i | −0.0495457 | − | 0.0858156i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 365.448 | − | 632.975i | 0.492159 | − | 0.852444i | ||||
\(83\) | −54.0900 | −0.0715319 | −0.0357660 | − | 0.999360i | \(-0.511387\pi\) | ||||
−0.0357660 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −505.290 | −0.644781 | ||||||||
\(86\) | 57.2537 | − | 99.1664i | 0.0717887 | − | 0.124342i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 158.555 | + | 274.625i | 0.192068 | + | 0.332672i | ||||
\(89\) | 142.700 | − | 247.163i | 0.169957 | − | 0.294374i | −0.768448 | − | 0.639913i | \(-0.778971\pi\) |
0.938404 | + | 0.345539i | \(0.112304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −434.689 | + | 541.330i | −0.500744 | + | 0.623591i | ||||
\(92\) | −769.591 | −0.872124 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −344.991 | − | 597.542i | −0.378543 | − | 0.655656i | ||||
\(95\) | 299.407 | + | 518.589i | 0.323353 | + | 0.560064i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 240.309 | 0.251543 | 0.125771 | − | 0.992059i | \(-0.459859\pi\) | ||||
0.125771 | + | 0.992059i | \(0.459859\pi\) | |||||||
\(98\) | −654.145 | − | 206.615i | −0.674272 | − | 0.212972i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 210.724 | − | 364.984i | 0.210724 | − | 0.364984i | ||||
\(101\) | −222.821 | − | 385.937i | −0.219520 | − | 0.380220i | 0.735141 | − | 0.677914i | \(-0.237116\pi\) |
−0.954661 | + | 0.297694i | \(0.903782\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 423.094 | − | 732.821i | 0.404745 | − | 0.701039i | −0.589547 | − | 0.807734i | \(-0.700694\pi\) |
0.994292 | + | 0.106695i | \(0.0340270\pi\) | |||||||
\(104\) | −299.891 | −0.282757 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1203.64 | −1.10291 | ||||||||
\(107\) | −281.156 | + | 486.976i | −0.254022 | + | 0.439979i | −0.964629 | − | 0.263610i | \(-0.915087\pi\) |
0.710607 | + | 0.703589i | \(0.248420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 557.817 | + | 966.168i | 0.490176 | + | 0.849010i | 0.999936 | − | 0.0113064i | \(-0.00359902\pi\) |
−0.509760 | + | 0.860317i | \(0.670266\pi\) | |||||||
\(110\) | 175.659 | − | 304.250i | 0.152258 | − | 0.263719i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −107.329 | − | 276.204i | −0.0905506 | − | 0.233025i | ||||
\(113\) | 1518.31 | 1.26399 | 0.631995 | − | 0.774972i | \(-0.282236\pi\) | ||||
0.631995 | + | 0.774972i | \(0.282236\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 426.305 | + | 738.382i | 0.345680 | + | 0.598735i | ||||
\(116\) | −258.604 | − | 447.915i | −0.206989 | − | 0.358516i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 63.0523 | 0.0491901 | ||||||||
\(119\) | −2087.06 | − | 321.771i | −1.60774 | − | 0.247871i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.113 | + | 208.041i | −0.0902423 | + | 0.156304i | ||||
\(122\) | 862.519 | + | 1493.93i | 0.640072 | + | 1.10864i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 489.162 | − | 847.253i | 0.354258 | − | 0.613594i | ||||
\(125\) | −1020.85 | −0.730460 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −803.079 | −0.561116 | −0.280558 | − | 0.959837i | \(-0.590519\pi\) | ||||
−0.280558 | + | 0.959837i | \(0.590519\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 166.121 | + | 287.730i | 0.112075 | + | 0.194120i | ||||
\(131\) | −445.107 | + | 770.948i | −0.296864 | + | 0.514183i | −0.975417 | − | 0.220368i | \(-0.929274\pi\) |
0.678553 | + | 0.734552i | \(0.262607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 906.442 | + | 2332.66i | 0.590966 | + | 1.52081i | ||||
\(134\) | 1365.18 | 0.880102 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −456.089 | − | 789.970i | −0.287569 | − | 0.498084i | ||||
\(137\) | −1022.28 | − | 1770.64i | −0.637514 | − | 1.10421i | −0.985976 | − | 0.166884i | \(-0.946629\pi\) |
0.348462 | − | 0.937323i | \(-0.386704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 587.471 | 0.358479 | 0.179240 | − | 0.983805i | \(-0.442636\pi\) | ||||
0.179240 | + | 0.983805i | \(0.442636\pi\) | |||||||
\(140\) | −205.549 | + | 255.976i | −0.124086 | + | 0.154528i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 664.860 | − | 1151.57i | 0.392914 | − | 0.680547i | ||||
\(143\) | −742.955 | − | 1286.84i | −0.434468 | − | 0.752521i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −286.501 | + | 496.233i | −0.164087 | + | 0.284207i | ||||
\(146\) | −1884.49 | −1.06823 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1093.03 | 0.607073 | ||||||||
\(149\) | −1356.66 | + | 2349.80i | −0.745918 | + | 1.29197i | 0.203847 | + | 0.979003i | \(0.434655\pi\) |
−0.949765 | + | 0.312964i | \(0.898678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 83.2159 | + | 144.134i | 0.0448478 | + | 0.0776786i | 0.887578 | − | 0.460658i | \(-0.152386\pi\) |
−0.842730 | + | 0.538336i | \(0.819053\pi\) | |||||||
\(152\) | −540.507 | + | 936.186i | −0.288427 | + | 0.499571i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 919.294 | − | 1144.82i | 0.481031 | − | 0.599042i | ||||
\(155\) | −1083.86 | −0.561663 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 267.786 | + | 463.819i | 0.136125 | + | 0.235776i | 0.926027 | − | 0.377458i | \(-0.123202\pi\) |
−0.789901 | + | 0.613234i | \(0.789868\pi\) | |||||||
\(158\) | −3.32542 | − | 5.75980i | −0.00167441 | − | 0.00290016i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −141.808 | −0.0700682 | ||||||||
\(161\) | 1290.62 | + | 3321.31i | 0.631770 | + | 1.62581i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −601.378 | + | 1041.62i | −0.288979 | + | 0.500526i | −0.973566 | − | 0.228404i | \(-0.926649\pi\) |
0.684587 | + | 0.728931i | \(0.259982\pi\) | |||||||
\(164\) | −730.896 | − | 1265.95i | −0.348009 | − | 0.602769i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −54.0900 | + | 93.6866i | −0.0252903 | + | 0.0438042i | ||||
\(167\) | 3467.14 | 1.60656 | 0.803279 | − | 0.595604i | \(-0.203087\pi\) | ||||
0.803279 | + | 0.595604i | \(0.203087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −791.774 | −0.360389 | ||||||||
\(170\) | −505.290 | + | 875.188i | −0.227965 | + | 0.394846i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −114.507 | − | 198.333i | −0.0507623 | − | 0.0879229i | ||||
\(173\) | −208.096 | + | 360.433i | −0.0914524 | + | 0.158400i | −0.908122 | − | 0.418705i | \(-0.862484\pi\) |
0.816670 | + | 0.577105i | \(0.195818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1928.54 | − | 297.331i | −0.833052 | − | 0.128435i | ||||
\(176\) | 634.219 | 0.271625 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −285.400 | − | 494.327i | −0.120178 | − | 0.208154i | ||||
\(179\) | −187.817 | − | 325.309i | −0.0784251 | − | 0.135836i | 0.824145 | − | 0.566378i | \(-0.191656\pi\) |
−0.902571 | + | 0.430542i | \(0.858322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2201.29 | 0.903981 | 0.451990 | − | 0.892023i | \(-0.350714\pi\) | ||||
0.451990 | + | 0.892023i | \(0.350714\pi\) | |||||||
\(182\) | 502.923 | + | 1294.23i | 0.204830 | + | 0.527115i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −769.591 | + | 1332.97i | −0.308342 | + | 0.534065i | ||||
\(185\) | −605.473 | − | 1048.71i | −0.240623 | − | 0.416771i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2259.85 | − | 3914.17i | 0.883724 | − | 1.53066i | ||||
\(188\) | −1379.96 | −0.535341 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1197.63 | 0.457290 | ||||||||
\(191\) | −2176.64 | + | 3770.05i | −0.824587 | + | 1.42823i | 0.0776467 | + | 0.996981i | \(0.475259\pi\) |
−0.902234 | + | 0.431246i | \(0.858074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1113.21 | + | 1928.14i | 0.415184 | + | 0.719121i | 0.995448 | − | 0.0953083i | \(-0.0303837\pi\) |
−0.580263 | + | 0.814429i | \(0.697050\pi\) | |||||||
\(194\) | 240.309 | − | 416.227i | 0.0889339 | − | 0.154038i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1012.01 | + | 926.398i | −0.368810 | + | 0.337609i | ||||
\(197\) | −3746.39 | −1.35492 | −0.677460 | − | 0.735559i | \(-0.736919\pi\) | ||||
−0.677460 | + | 0.735559i | \(0.736919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1432.02 | + | 2480.33i | 0.510116 | + | 0.883547i | 0.999931 | + | 0.0117211i | \(0.00373101\pi\) |
−0.489815 | + | 0.871826i | \(0.662936\pi\) | |||||||
\(200\) | −421.447 | − | 729.968i | −0.149004 | − | 0.258083i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −891.284 | −0.310448 | ||||||||
\(203\) | −1499.37 | + | 1867.21i | −0.518401 | + | 0.645579i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −809.742 | + | 1402.51i | −0.275877 | + | 0.477833i | ||||
\(206\) | −846.189 | − | 1465.64i | −0.286198 | − | 0.495709i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −299.891 | + | 519.426i | −0.0999696 | + | 0.173152i | ||||
\(209\) | −5356.25 | −1.77273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3729.13 | 1.21670 | 0.608350 | − | 0.793669i | \(-0.291832\pi\) | ||||
0.608350 | + | 0.793669i | \(0.291832\pi\) | |||||||
\(212\) | −1203.64 | + | 2084.77i | −0.389937 | + | 0.675391i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 562.311 | + | 973.952i | 0.179621 | + | 0.311112i | ||||
\(215\) | −126.860 | + | 219.728i | −0.0402408 | + | 0.0696992i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4476.81 | − | 690.207i | −1.40049 | − | 0.215918i | ||||
\(218\) | 2231.27 | 0.693214 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −351.318 | − | 608.500i | −0.107663 | − | 0.186478i | ||||
\(221\) | 2137.14 | + | 3701.64i | 0.650496 | + | 1.12669i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 152.890 | 0.0459115 | 0.0229557 | − | 0.999736i | \(-0.492692\pi\) | ||||
0.0229557 | + | 0.999736i | \(0.492692\pi\) | |||||||
\(224\) | −585.728 | − | 90.3039i | −0.174712 | − | 0.0269361i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1518.31 | − | 2629.80i | 0.446888 | − | 0.774033i | ||||
\(227\) | −1693.04 | − | 2932.43i | −0.495027 | − | 0.857411i | 0.504957 | − | 0.863144i | \(-0.331508\pi\) |
−0.999984 | + | 0.00573340i | \(0.998175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 386.178 | − | 668.880i | 0.111438 | − | 0.193017i | −0.804912 | − | 0.593394i | \(-0.797788\pi\) |
0.916350 | + | 0.400377i | \(0.131121\pi\) | |||||||
\(230\) | 1705.22 | 0.488865 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1034.41 | −0.292727 | ||||||||
\(233\) | 1781.93 | − | 3086.39i | 0.501021 | − | 0.867794i | −0.498978 | − | 0.866614i | \(-0.666291\pi\) |
0.999999 | − | 0.00117935i | \(-0.000375398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 764.413 | + | 1324.00i | 0.212191 | + | 0.367525i | ||||
\(236\) | 63.0523 | − | 109.210i | 0.0173913 | − | 0.0301227i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2644.39 | + | 3293.13i | −0.720211 | + | 0.896899i | ||||
\(239\) | 5832.92 | 1.57866 | 0.789331 | − | 0.613968i | \(-0.210428\pi\) | ||||
0.789331 | + | 0.613968i | \(0.210428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1846.61 | − | 3198.42i | −0.493570 | − | 0.854889i | 0.506402 | − | 0.862297i | \(-0.330975\pi\) |
−0.999973 | + | 0.00740841i | \(0.997642\pi\) | |||||||
\(242\) | 240.225 | + | 416.082i | 0.0638110 | + | 0.110524i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3450.08 | 0.905199 | ||||||||
\(245\) | 1449.42 | + | 457.808i | 0.377960 | + | 0.119381i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2532.71 | − | 4386.78i | 0.652438 | − | 1.13006i | ||||
\(248\) | −978.324 | − | 1694.51i | −0.250499 | − | 0.433876i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1020.85 | + | 1768.16i | −0.258257 | + | 0.447313i | ||||
\(251\) | −1571.78 | −0.395259 | −0.197630 | − | 0.980277i | \(-0.563324\pi\) | ||||
−0.197630 | + | 0.980277i | \(0.563324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7626.39 | −1.89513 | ||||||||
\(254\) | −803.079 | + | 1390.97i | −0.198384 | + | 0.343612i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1826.14 | − | 3162.97i | 0.443236 | − | 0.767707i | −0.554692 | − | 0.832056i | \(-0.687164\pi\) |
0.997927 | + | 0.0643490i | \(0.0204971\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1833.04 | − | 4717.19i | −0.439767 | − | 1.13171i | ||||
\(260\) | 664.483 | 0.158498 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 890.214 | + | 1541.90i | 0.209914 | + | 0.363582i | ||||
\(263\) | −355.268 | − | 615.342i | −0.0832956 | − | 0.144272i | 0.821368 | − | 0.570399i | \(-0.193211\pi\) |
−0.904664 | + | 0.426126i | \(0.859878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2666.98 | 0.618230 | ||||||||
\(266\) | 4946.72 | + | 762.655i | 1.14024 | + | 0.175795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1365.18 | − | 2364.56i | 0.311163 | − | 0.538950i | ||||
\(269\) | 4.13321 | + | 7.15894i | 0.000936827 | + | 0.00162263i | 0.866493 | − | 0.499188i | \(-0.166368\pi\) |
−0.865557 | + | 0.500811i | \(0.833035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1361.85 | − | 2358.79i | 0.305264 | − | 0.528732i | −0.672056 | − | 0.740500i | \(-0.734589\pi\) |
0.977320 | + | 0.211768i | \(0.0679221\pi\) | |||||||
\(272\) | −1824.36 | −0.406684 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4089.13 | −0.901581 | ||||||||
\(275\) | 2088.20 | − | 3616.87i | 0.457903 | − | 0.793111i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −620.284 | − | 1074.36i | −0.134546 | − | 0.233041i | 0.790878 | − | 0.611974i | \(-0.209624\pi\) |
−0.925424 | + | 0.378933i | \(0.876291\pi\) | |||||||
\(278\) | 587.471 | − | 1017.53i | 0.126742 | − | 0.219523i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 237.815 | + | 611.998i | 0.0507577 | + | 0.130621i | ||||
\(281\) | 7346.62 | 1.55965 | 0.779826 | − | 0.625996i | \(-0.215307\pi\) | ||||
0.779826 | + | 0.625996i | \(0.215307\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2058.87 | − | 3566.06i | −0.432462 | − | 0.749047i | 0.564622 | − | 0.825349i | \(-0.309022\pi\) |
−0.997085 | + | 0.0763025i | \(0.975689\pi\) | |||||||
\(284\) | −1329.72 | − | 2303.14i | −0.277832 | − | 0.481220i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2971.82 | −0.614431 | ||||||||
\(287\) | −4237.71 | + | 5277.34i | −0.871582 | + | 1.08541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4044.05 | + | 7004.50i | −0.823132 | + | 1.42571i | ||||
\(290\) | 573.001 | + | 992.467i | 0.116027 | + | 0.200964i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1884.49 | + | 3264.03i | −0.377676 | + | 0.654154i | ||||
\(293\) | −2410.10 | −0.480545 | −0.240273 | − | 0.970705i | \(-0.577237\pi\) | ||||
−0.240273 | + | 0.970705i | \(0.577237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −139.708 | −0.0275733 | ||||||||
\(296\) | 1093.03 | − | 1893.19i | 0.214633 | − | 0.371755i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2713.32 | + | 4699.60i | 0.527443 | + | 0.913559i | ||||
\(299\) | 3606.14 | − | 6246.02i | 0.697487 | − | 1.20808i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −663.910 | + | 826.786i | −0.127133 | + | 0.158323i | ||||
\(302\) | 332.864 | 0.0634244 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1081.01 | + | 1872.37i | 0.203949 | + | 0.353250i | ||||
\(305\) | −1911.13 | − | 3310.17i | −0.358789 | − | 0.621442i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5172.84 | −0.961661 | −0.480830 | − | 0.876814i | \(-0.659665\pi\) | ||||
−0.480830 | + | 0.876814i | \(0.659665\pi\) | |||||||
\(308\) | −1063.60 | − | 2737.09i | −0.196767 | − | 0.506364i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1083.86 | + | 1877.30i | −0.198578 | + | 0.343947i | ||||
\(311\) | −1714.23 | − | 2969.14i | −0.312557 | − | 0.541365i | 0.666358 | − | 0.745632i | \(-0.267852\pi\) |
−0.978915 | + | 0.204267i | \(0.934519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2292.03 | − | 3969.91i | 0.413908 | − | 0.716909i | −0.581406 | − | 0.813614i | \(-0.697497\pi\) |
0.995313 | + | 0.0967050i | \(0.0308303\pi\) | |||||||
\(314\) | 1071.14 | 0.192510 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.3017 | −0.00236797 | ||||||||
\(317\) | −74.0671 | + | 128.288i | −0.0131231 | + | 0.0227299i | −0.872512 | − | 0.488592i | \(-0.837511\pi\) |
0.859389 | + | 0.511322i | \(0.170844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2562.68 | − | 4438.69i | −0.449788 | − | 0.779055i | ||||
\(320\) | −141.808 | + | 245.619i | −0.0247728 | + | 0.0429078i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7043.29 | + | 1085.89i | 1.21897 | + | 0.187933i | ||||
\(323\) | 15407.5 | 2.65417 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1974.81 | + | 3420.48i | 0.337055 | + | 0.583797i | ||||
\(326\) | 1202.76 | + | 2083.24i | 0.204339 | + | 0.353926i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2923.59 | −0.492159 | ||||||||
\(329\) | 2314.23 | + | 5955.48i | 0.387804 | + | 0.997983i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3893.30 | − | 6743.40i | 0.646512 | − | 1.11979i | −0.337438 | − | 0.941348i | \(-0.609560\pi\) |
0.983950 | − | 0.178444i | \(-0.0571062\pi\) | |||||||
\(332\) | 108.180 | + | 187.373i | 0.0178830 | + | 0.0309742i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3467.14 | − | 6005.26i | 0.568004 | − | 0.983811i | ||||
\(335\) | −3024.90 | −0.493337 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 906.591 | 0.146544 | 0.0732718 | − | 0.997312i | \(-0.476656\pi\) | ||||
0.0732718 | + | 0.997312i | \(0.476656\pi\) | |||||||
\(338\) | −791.774 | + | 1371.39i | −0.127417 | + | 0.220692i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1010.58 | + | 1750.38i | 0.161195 | + | 0.279199i | ||||
\(341\) | 4847.43 | − | 8396.00i | 0.769804 | − | 1.33334i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5695.20 | + | 2813.94i | 0.896537 | + | 0.442969i | ||||
\(344\) | −458.030 | −0.0717887 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 416.192 | + | 720.866i | 0.0646666 | + | 0.112006i | ||||
\(347\) | −2098.16 | − | 3634.12i | −0.324597 | − | 0.562219i | 0.656834 | − | 0.754036i | \(-0.271895\pi\) |
−0.981431 | + | 0.191817i | \(0.938562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5970.17 | −0.915690 | −0.457845 | − | 0.889032i | \(-0.651379\pi\) | ||||
−0.457845 | + | 0.889032i | \(0.651379\pi\) | |||||||
\(350\) | −2443.53 | + | 3043.00i | −0.373178 | + | 0.464729i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 634.219 | − | 1098.50i | 0.0960340 | − | 0.166336i | ||||
\(353\) | −5523.89 | − | 9567.65i | −0.832880 | − | 1.44259i | −0.895745 | − | 0.444569i | \(-0.853357\pi\) |
0.0628644 | − | 0.998022i | \(-0.479976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1473.16 | + | 2551.60i | −0.220246 | + | 0.381478i | ||||
\(356\) | −1141.60 | −0.169957 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −751.268 | −0.110910 | ||||||||
\(359\) | −3781.82 | + | 6550.31i | −0.555980 | + | 0.962986i | 0.441846 | + | 0.897091i | \(0.354324\pi\) |
−0.997827 | + | 0.0658953i | \(0.979010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5700.14 | − | 9872.93i | −0.831045 | − | 1.43941i | ||||
\(362\) | 2201.29 | − | 3812.74i | 0.319605 | − | 0.553573i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2744.60 | + | 423.145i | 0.395209 | + | 0.0609309i | ||||
\(365\) | 4175.55 | 0.598790 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1716.04 | + | 2972.26i | 0.244077 | + | 0.422754i | 0.961872 | − | 0.273501i | \(-0.0881816\pi\) |
−0.717794 | + | 0.696255i | \(0.754848\pi\) | |||||||
\(368\) | 1539.18 | + | 2665.94i | 0.218031 | + | 0.377641i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2421.89 | −0.340292 | ||||||||
\(371\) | 11015.8 | + | 1698.34i | 1.54153 | + | 0.237664i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2636.84 | − | 4567.15i | 0.366034 | − | 0.633989i | −0.622908 | − | 0.782295i | \(-0.714049\pi\) |
0.988941 | + | 0.148306i | \(0.0473822\pi\) | |||||||
\(374\) | −4519.70 | − | 7828.34i | −0.624887 | − | 1.08234i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1379.96 | + | 2390.17i | −0.189272 | + | 0.327828i | ||||
\(377\) | 4847.05 | 0.662164 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8856.92 | 1.20039 | 0.600197 | − | 0.799852i | \(-0.295089\pi\) | ||||
0.600197 | + | 0.799852i | \(0.295089\pi\) | |||||||
\(380\) | 1197.63 | − | 2074.36i | 0.161677 | − | 0.280032i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4353.28 | + | 7540.10i | 0.583071 | + | 1.00991i | ||||
\(383\) | −520.852 | + | 902.142i | −0.0694890 | + | 0.120358i | −0.898676 | − | 0.438612i | \(-0.855470\pi\) |
0.829187 | + | 0.558971i | \(0.188804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2036.93 | + | 2536.64i | −0.269640 | + | 0.335790i | ||||
\(386\) | 4452.84 | 0.587160 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −480.618 | − | 832.454i | −0.0628857 | − | 0.108921i | ||||
\(389\) | 4666.34 | + | 8082.33i | 0.608207 | + | 1.05345i | 0.991536 | + | 0.129834i | \(0.0414445\pi\) |
−0.383328 | + | 0.923612i | \(0.625222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21937.6 | 2.83743 | ||||||||
\(392\) | 592.555 | + | 2679.26i | 0.0763483 | + | 0.345211i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3746.39 | + | 6488.94i | −0.479037 | + | 0.829716i | ||||
\(395\) | 7.36831 | + | 12.7623i | 0.000938582 | + | 0.00162567i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3411.16 | + | 5908.31i | −0.431238 | + | 0.746926i | −0.996980 | − | 0.0776562i | \(-0.975256\pi\) |
0.565742 | + | 0.824582i | \(0.308590\pi\) | |||||||
\(398\) | 5728.08 | 0.721414 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1685.79 | −0.210724 | ||||||||
\(401\) | −4054.97 | + | 7023.42i | −0.504977 | + | 0.874646i | 0.495007 | + | 0.868889i | \(0.335166\pi\) |
−0.999983 | + | 0.00575638i | \(0.998168\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4584.22 | + | 7940.11i | 0.566641 | + | 0.981452i | ||||
\(404\) | −891.284 | + | 1543.75i | −0.109760 | + | 0.190110i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1734.73 | + | 4464.20i | 0.212053 | + | 0.545701i | ||||
\(407\) | 10831.6 | 1.31917 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2216.52 | − | 3839.13i | −0.267970 | − | 0.464138i | 0.700367 | − | 0.713783i | \(-0.253020\pi\) |
−0.968338 | + | 0.249644i | \(0.919686\pi\) | |||||||
\(410\) | 1619.48 | + | 2805.03i | 0.195075 | + | 0.337879i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3384.76 | −0.404745 | ||||||||
\(413\) | −577.055 | − | 88.9667i | −0.0687530 | − | 0.0105999i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 119.850 | − | 207.586i | 0.0141764 | − | 0.0245542i | ||||
\(416\) | 599.781 | + | 1038.85i | 0.0706892 | + | 0.122437i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5356.25 | + | 9277.30i | −0.626753 | + | 1.08557i | ||||
\(419\) | −6782.36 | −0.790787 | −0.395394 | − | 0.918512i | \(-0.629392\pi\) | ||||
−0.395394 | + | 0.918512i | \(0.629392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4798.62 | −0.555512 | −0.277756 | − | 0.960652i | \(-0.589591\pi\) | ||||
−0.277756 | + | 0.960652i | \(0.589591\pi\) | |||||||
\(422\) | 3729.13 | − | 6459.04i | 0.430168 | − | 0.745073i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2407.29 | + | 4169.55i | 0.275727 | + | 0.477573i | ||||
\(425\) | −6006.80 | + | 10404.1i | −0.685583 | + | 1.18746i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5785.85 | − | 14889.4i | −0.655730 | − | 1.68747i | ||||
\(428\) | 2249.25 | 0.254022 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 253.720 | + | 439.456i | 0.0284546 | + | 0.0492848i | ||||
\(431\) | −6474.64 | − | 11214.4i | −0.723602 | − | 1.25332i | −0.959547 | − | 0.281549i | \(-0.909152\pi\) |
0.235945 | − | 0.971766i | \(-0.424182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 937.240 | 0.104020 | 0.0520102 | − | 0.998647i | \(-0.483437\pi\) | ||||
0.0520102 | + | 0.998647i | \(0.483437\pi\) | |||||||
\(434\) | −5672.28 | + | 7063.86i | −0.627369 | + | 0.781281i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2231.27 | − | 3864.67i | 0.245088 | − | 0.424505i | ||||
\(437\) | −12999.1 | − | 22515.0i | −1.42295 | − | 2.46462i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6800.15 | − | 11778.2i | 0.739302 | − | 1.28051i | −0.213509 | − | 0.976941i | \(-0.568489\pi\) |
0.952810 | − | 0.303567i | \(-0.0981775\pi\) | |||||||
\(440\) | −1405.27 | −0.152258 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8548.56 | 0.919940 | ||||||||
\(443\) | −2316.24 | + | 4011.84i | −0.248415 | + | 0.430267i | −0.963086 | − | 0.269193i | \(-0.913243\pi\) |
0.714671 | + | 0.699460i | \(0.246576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 632.374 | + | 1095.30i | 0.0673650 | + | 0.116680i | ||||
\(446\) | 152.890 | − | 264.813i | 0.0162322 | − | 0.0281149i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −742.139 | + | 924.207i | −0.0782651 | + | 0.0974658i | ||||
\(449\) | −254.426 | −0.0267419 | −0.0133709 | − | 0.999911i | \(-0.504256\pi\) | ||||
−0.0133709 | + | 0.999911i | \(0.504256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7242.94 | − | 12545.1i | −0.756224 | − | 1.30982i | ||||
\(452\) | −3036.63 | − | 5259.59i | −0.315998 | − | 0.547324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6772.16 | −0.700073 | ||||||||
\(455\) | −1114.35 | − | 2867.70i | −0.114817 | − | 0.295472i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8205.25 | + | 14211.9i | −0.839881 | + | 1.45472i | 0.0501133 | + | 0.998744i | \(0.484042\pi\) |
−0.889994 | + | 0.455972i | \(0.849292\pi\) | |||||||
\(458\) | −772.356 | − | 1337.76i | −0.0787988 | − | 0.136483i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1705.22 | − | 2953.53i | 0.172840 | − | 0.299367i | ||||
\(461\) | 5842.56 | 0.590272 | 0.295136 | − | 0.955455i | \(-0.404635\pi\) | ||||
0.295136 | + | 0.955455i | \(0.404635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6699.12 | 0.672429 | 0.336215 | − | 0.941785i | \(-0.390853\pi\) | ||||
0.336215 | + | 0.941785i | \(0.390853\pi\) | |||||||
\(464\) | −1034.41 | + | 1791.66i | −0.103495 | + | 0.179258i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3563.85 | − | 6172.77i | −0.354275 | − | 0.613623i | ||||
\(467\) | −912.817 | + | 1581.05i | −0.0904500 | + | 0.156664i | −0.907701 | − | 0.419619i | \(-0.862164\pi\) |
0.817251 | + | 0.576282i | \(0.195497\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12494.1 | − | 1926.27i | −1.23012 | − | 0.189652i | ||||
\(470\) | 3057.65 | 0.300083 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −126.105 | − | 218.420i | −0.0122975 | − | 0.0212999i | ||||
\(473\) | −1134.73 | − | 1965.41i | −0.110307 | − | 0.191057i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14237.2 | 1.37526 | ||||||||
\(476\) | 3059.48 | + | 7873.35i | 0.294603 | + | 0.758139i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5832.92 | − | 10102.9i | 0.558141 | − | 0.966729i | ||||
\(479\) | 5518.07 | + | 9557.58i | 0.526362 | + | 0.911685i | 0.999528 | + | 0.0307121i | \(0.00977749\pi\) |
−0.473167 | + | 0.880973i | \(0.656889\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5121.73 | + | 8871.10i | −0.485511 | + | 0.840930i | ||||
\(482\) | −7386.43 | −0.698014 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 960.900 | 0.0902423 | ||||||||
\(485\) | −532.464 | + | 922.255i | −0.0498515 | + | 0.0863453i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4092.78 | − | 7088.90i | −0.380824 | − | 0.659607i | 0.610356 | − | 0.792127i | \(-0.291026\pi\) |
−0.991180 | + | 0.132520i | \(0.957693\pi\) | |||||||
\(488\) | 3450.08 | − | 5975.71i | 0.320036 | − | 0.554319i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2242.37 | − | 2052.67i | 0.206735 | − | 0.189245i | ||||
\(491\) | −19006.2 | −1.74692 | −0.873459 | − | 0.486897i | \(-0.838129\pi\) | ||||
−0.873459 | + | 0.486897i | \(0.838129\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7371.65 | + | 12768.1i | 0.673433 | + | 1.16642i | ||||
\(494\) | −5065.41 | − | 8773.55i | −0.461343 | − | 0.799070i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3913.30 | −0.354258 | ||||||||
\(497\) | −7709.66 | + | 9601.07i | −0.695826 | + | 0.866533i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8246.79 | + | 14283.9i | −0.739834 | + | 1.28143i | 0.212736 | + | 0.977110i | \(0.431763\pi\) |
−0.952570 | + | 0.304320i | \(0.901571\pi\) | |||||||
\(500\) | 2041.70 | + | 3536.32i | 0.182615 | + | 0.316298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1571.78 | + | 2722.41i | −0.139745 | + | 0.242046i | ||||
\(503\) | −10368.0 | −0.919059 | −0.459530 | − | 0.888162i | \(-0.651982\pi\) | ||||
−0.459530 | + | 0.888162i | \(0.651982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1974.86 | 0.174020 | ||||||||
\(506\) | −7626.39 | + | 13209.3i | −0.670029 | + | 1.16052i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1606.16 | + | 2781.95i | 0.140279 | + | 0.242970i | ||||
\(509\) | 3254.37 | − | 5636.74i | 0.283394 | − | 0.490853i | −0.688825 | − | 0.724928i | \(-0.741873\pi\) |
0.972218 | + | 0.234075i | \(0.0752063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17246.8 | + | 2659.01i | 1.49306 | + | 0.230191i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3652.28 | − | 6325.94i | −0.313415 | − | 0.542851i | ||||
\(515\) | 1874.94 | + | 3247.50i | 0.160427 | + | 0.277868i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13675.0 | −1.16330 | ||||||||
\(518\) | −10003.4 | − | 1542.27i | −0.848506 | − | 0.130817i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 664.483 | − | 1150.92i | 0.0560375 | − | 0.0970598i | ||||
\(521\) | 6759.54 | + | 11707.9i | 0.568409 | + | 0.984513i | 0.996724 | + | 0.0808831i | \(0.0257741\pi\) |
−0.428315 | + | 0.903630i | \(0.640893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −929.020 | + | 1609.11i | −0.0776734 | + | 0.134534i | −0.902246 | − | 0.431222i | \(-0.858082\pi\) |
0.824572 | + | 0.565757i | \(0.191416\pi\) | |||||||
\(524\) | 3560.85 | 0.296864 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1421.07 | −0.117798 | ||||||||
\(527\) | −13943.9 | + | 24151.5i | −1.15257 | + | 1.99631i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12424.9 | − | 21520.6i | −1.02120 | − | 1.76877i | ||||
\(530\) | 2666.98 | − | 4619.34i | 0.218577 | − | 0.378587i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6267.68 | − | 7805.32i | 0.510787 | − | 0.636097i | ||||
\(533\) | 13699.3 | 1.11329 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1245.94 | − | 2158.03i | −0.100686 | − | 0.174392i | ||||
\(536\) | −2730.36 | − | 4729.13i | −0.220026 | − | 0.381095i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.5329 | 0.00132487 | ||||||||
\(539\) | −10028.7 | + | 9180.30i | −0.801424 | + | 0.733624i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6846.27 | + | 11858.1i | −0.544075 | + | 0.942365i | 0.454590 | + | 0.890701i | \(0.349786\pi\) |
−0.998665 | + | 0.0516640i | \(0.983548\pi\) | |||||||
\(542\) | −2723.70 | − | 4717.58i | −0.215854 | − | 0.373870i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1824.36 | + | 3159.88i | −0.143784 | + | 0.249042i | ||||
\(545\) | −4943.94 | −0.388578 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9054.00 | −0.707717 | −0.353858 | − | 0.935299i | \(-0.615131\pi\) | ||||
−0.353858 | + | 0.935299i | \(0.615131\pi\) | |||||||
\(548\) | −4089.13 | + | 7082.58i | −0.318757 | + | 0.552104i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4176.40 | − | 7233.74i | −0.323786 | − | 0.560814i | ||||
\(551\) | 8736.07 | − | 15131.3i | 0.675443 | − | 1.16990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.3072 | + | 57.4059i | 0.00171537 | + | 0.00441437i | ||||
\(554\) | −2481.14 | −0.190277 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1174.94 | − | 2035.06i | −0.0896198 | − | 0.155226i | ||||
\(557\) | 4717.22 | + | 8170.46i | 0.358842 | + | 0.621533i | 0.987768 | − | 0.155933i | \(-0.0498383\pi\) |
−0.628926 | + | 0.777465i | \(0.716505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2146.23 | 0.162390 | ||||||||
\(560\) | 1297.83 | + | 200.091i | 0.0979343 | + | 0.0150989i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7346.62 | − | 12724.7i | 0.551421 | − | 0.955088i | ||||
\(563\) | −3205.10 | − | 5551.39i | −0.239927 | − | 0.415565i | 0.720766 | − | 0.693178i | \(-0.243790\pi\) |
−0.960693 | + | 0.277613i | \(0.910457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3364.20 | + | 5826.97i | −0.250501 | + | 0.433880i | ||||
\(566\) | −8235.46 | −0.611594 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5318.88 | −0.392914 | ||||||||
\(569\) | −2432.99 | + | 4214.06i | −0.179255 | + | 0.310479i | −0.941626 | − | 0.336662i | \(-0.890702\pi\) |
0.762370 | + | 0.647141i | \(0.224035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9349.38 | − | 16193.6i | −0.685218 | − | 1.18683i | −0.973368 | − | 0.229247i | \(-0.926374\pi\) |
0.288150 | − | 0.957585i | \(-0.406960\pi\) | |||||||
\(572\) | −2971.82 | + | 5147.34i | −0.217234 | + | 0.376261i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4902.91 | + | 12617.3i | 0.356522 | + | 0.917482i | ||||
\(575\) | 20271.4 | 1.47022 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9174.11 | + | 15890.0i | 0.661912 | + | 1.14647i | 0.980113 | + | 0.198442i | \(0.0635882\pi\) |
−0.318200 | + | 0.948023i | \(0.603079\pi\) | |||||||
\(578\) | 8088.10 | + | 14009.0i | 0.582042 | + | 1.00813i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2292.00 | 0.164087 | ||||||||
\(581\) | 627.223 | − | 781.099i | 0.0447876 | − | 0.0557753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11927.7 | + | 20659.4i | −0.847334 | + | 1.46763i | ||||
\(584\) | 3768.98 | + | 6528.06i | 0.267057 | + | 0.462556i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2410.10 | + | 4174.42i | −0.169898 | + | 0.294273i | ||||
\(587\) | −17246.6 | −1.21268 | −0.606340 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606340 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33049.5 | 2.31202 | ||||||||
\(590\) | −139.708 | + | 241.982i | −0.00974863 | + | 0.0168851i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2186.07 | − | 3786.38i | −0.151768 | − | 0.262870i | ||||
\(593\) | −8806.40 | + | 15253.1i | −0.609841 | + | 1.05628i | 0.381426 | + | 0.924400i | \(0.375433\pi\) |
−0.991266 | + | 0.131875i | \(0.957900\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5859.30 | − | 7296.76i | 0.403711 | − | 0.502753i | ||||
\(596\) | 10853.3 | 0.745918 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7212.29 | − | 12492.0i | −0.493198 | − | 0.854244i | ||||
\(599\) | −6533.22 | − | 11315.9i | −0.445643 | − | 0.771876i | 0.552454 | − | 0.833544i | \(-0.313692\pi\) |
−0.998097 | + | 0.0616672i | \(0.980358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10232.8 | −0.694516 | −0.347258 | − | 0.937770i | \(-0.612887\pi\) | ||||
−0.347258 | + | 0.937770i | \(0.612887\pi\) | |||||||
\(602\) | 768.125 | + | 1976.71i | 0.0520041 | + | 0.133828i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 332.864 | − | 576.537i | 0.0224239 | − | 0.0388393i | ||||
\(605\) | −532.279 | − | 921.934i | −0.0357689 | − | 0.0619536i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5116.84 | − | 8862.63i | 0.342152 | − | 0.592625i | −0.642680 | − | 0.766135i | \(-0.722178\pi\) |
0.984832 | + | 0.173510i | \(0.0555109\pi\) | |||||||
\(608\) | 4324.06 | 0.288427 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7644.51 | −0.507405 | ||||||||
\(611\) | 6466.22 | − | 11199.8i | 0.428143 | − | 0.741565i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1435.08 | + | 2485.63i | 0.0945550 | + | 0.163774i | 0.909423 | − | 0.415873i | \(-0.136524\pi\) |
−0.814868 | + | 0.579647i | \(0.803191\pi\) | |||||||
\(614\) | −5172.84 | + | 8959.63i | −0.339998 | + | 0.588894i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5804.37 | − | 894.882i | −0.379651 | − | 0.0585322i | ||||
\(617\) | 743.774 | 0.0485304 | 0.0242652 | − | 0.999706i | \(-0.492275\pi\) | ||||
0.0242652 | + | 0.999706i | \(0.492275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11435.6 | + | 19807.0i | 0.742543 | + | 1.28612i | 0.951334 | + | 0.308162i | \(0.0997140\pi\) |
−0.208790 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(620\) | 2167.72 | + | 3754.60i | 0.140416 | + | 0.243207i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6856.94 | −0.442023 | ||||||||
\(623\) | 1914.48 | + | 4926.78i | 0.123117 | + | 0.316833i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4323.17 | + | 7487.95i | −0.276683 | + | 0.479228i | ||||
\(626\) | −4584.06 | − | 7939.82i | −0.292677 | − | 0.506931i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1071.14 | − | 1855.28i | 0.0680626 | − | 0.117888i | ||||
\(629\) | −31157.6 | −1.97509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16861.8 | −1.06380 | −0.531901 | − | 0.846807i | \(-0.678522\pi\) | ||||
−0.531901 | + | 0.846807i | \(0.678522\pi\) | |||||||
\(632\) | −13.3017 | + | 23.0392i | −0.000837204 | + | 0.00145008i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 148.134 | + | 256.576i | 0.00927943 | + | 0.0160724i | ||||
\(635\) | 1779.42 | − | 3082.05i | 0.111203 | − | 0.192610i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2776.59 | − | 12554.4i | −0.172704 | − | 0.780887i | ||||
\(638\) | −10250.7 | −0.636096 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 283.616 | + | 491.237i | 0.0175170 | + | 0.0303404i | ||||
\(641\) | −4259.46 | − | 7377.61i | −0.262463 | − | 0.454599i | 0.704433 | − | 0.709771i | \(-0.251201\pi\) |
−0.966896 | + | 0.255172i | \(0.917868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12045.2 | −0.738748 | −0.369374 | − | 0.929281i | \(-0.620428\pi\) | ||||
−0.369374 | + | 0.929281i | \(0.620428\pi\) | |||||||
\(644\) | 8924.11 | − | 11113.5i | 0.546055 | − | 0.680018i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15407.5 | − | 26686.5i | 0.938389 | − | 1.62534i | ||||
\(647\) | −2078.82 | − | 3600.63i | −0.126317 | − | 0.218787i | 0.795930 | − | 0.605389i | \(-0.206982\pi\) |
−0.922247 | + | 0.386601i | \(0.873649\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 624.828 | − | 1082.23i | 0.0377914 | − | 0.0654566i | ||||
\(650\) | 7899.26 | 0.476668 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4811.03 | 0.288979 | ||||||||
\(653\) | −15174.8 | + | 26283.5i | −0.909394 | + | 1.57512i | −0.0944872 | + | 0.995526i | \(0.530121\pi\) |
−0.814907 | + | 0.579591i | \(0.803212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1972.49 | − | 3416.45i | −0.117667 | − | 0.203804i | ||||
\(656\) | −2923.59 | + | 5063.80i | −0.174004 | + | 0.301384i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12629.4 | + | 1947.13i | 0.748246 | + | 0.115360i | ||||
\(659\) | −14482.7 | −0.856093 | −0.428046 | − | 0.903757i | \(-0.640798\pi\) | ||||
−0.428046 | + | 0.903757i | \(0.640798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3262.70 | + | 5651.16i | 0.191988 | + | 0.332533i | 0.945909 | − | 0.324432i | \(-0.105173\pi\) |
−0.753921 | + | 0.656965i | \(0.771840\pi\) | |||||||
\(662\) | −7786.61 | − | 13486.8i | −0.457153 | − | 0.791812i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 432.720 | 0.0252903 | ||||||||
\(665\) | −10960.7 | − | 1689.85i | −0.639155 | − | 0.0985409i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12438.7 | − | 21544.4i | 0.722081 | − | 1.25068i | ||||
\(668\) | −6934.27 | − | 12010.5i | −0.401639 | − | 0.695660i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3024.90 | + | 5239.28i | −0.174421 | + | 0.302106i | ||||
\(671\) | 34189.1 | 1.96700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1453.70 | 0.0832629 | 0.0416314 | − | 0.999133i | \(-0.486744\pi\) | ||||
0.0416314 | + | 0.999133i | \(0.486744\pi\) | |||||||
\(674\) | 906.591 | − | 1570.26i | 0.0518110 | − | 0.0897392i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1583.55 | + | 2742.79i | 0.0900972 | + | 0.156053i | ||||
\(677\) | 7385.35 | − | 12791.8i | 0.419265 | − | 0.726187i | −0.576601 | − | 0.817026i | \(-0.695621\pi\) |
0.995866 | + | 0.0908383i | \(0.0289546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2786.60 | + | 3470.23i | −0.157496 | + | 0.196135i | ||||
\(680\) | 4042.32 | 0.227965 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9694.87 | − | 16792.0i | −0.544334 | − | 0.942814i | ||||
\(683\) | 4539.15 | + | 7862.04i | 0.254298 | + | 0.440457i | 0.964705 | − | 0.263334i | \(-0.0848222\pi\) |
−0.710406 | + | 0.703792i | \(0.751489\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9060.49 | 0.505377 | ||||||||
\(686\) | 10569.1 | − | 7050.44i | 0.588236 | − | 0.392401i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −458.030 | + | 793.331i | −0.0253811 | + | 0.0439614i | ||||
\(689\) | −11280.1 | − | 19537.6i | −0.623710 | − | 1.08030i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2234.84 | + | 3870.86i | −0.123035 | + | 0.213104i | −0.920963 | − | 0.389649i | \(-0.872596\pi\) |
0.797928 | + | 0.602753i | \(0.205930\pi\) | |||||||
\(692\) | 1664.77 | 0.0914524 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8392.65 | −0.459050 | ||||||||
\(695\) | −1301.69 | + | 2254.59i | −0.0710444 | + | 0.123053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20834.6 | + | 36086.6i | 1.13224 | + | 1.96109i | ||||
\(698\) | −5970.17 | + | 10340.6i | −0.323745 | + | 0.560743i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2827.10 | + | 7275.33i | 0.152649 | + | 0.392831i | ||||
\(701\) | 29024.1 | 1.56380 | 0.781901 | − | 0.623403i | \(-0.214250\pi\) | ||||
0.781901 | + | 0.623403i | \(0.214250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18462.3 | + | 31977.6i | 0.990496 | + | 1.71559i | ||||
\(704\) | −1268.44 | − | 2197.00i | −0.0679063 | − | 0.117617i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22095.5 | −1.17787 | ||||||||
\(707\) | 8157.03 | + | 1257.60i | 0.433913 | + | 0.0668980i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.0540 | − | 57.2511i | 0.00175087 | − | 0.00303260i | −0.865149 | − | 0.501516i | \(-0.832776\pi\) |
0.866900 | + | 0.498483i | \(0.166109\pi\) | |||||||
\(710\) | 2946.33 | + | 5103.19i | 0.155738 | + | 0.269746i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1141.60 | + | 1977.31i | −0.0600888 | + | 0.104077i | ||||
\(713\) | 47056.8 | 2.47166 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6584.81 | 0.344417 | ||||||||
\(716\) | −751.268 | + | 1301.23i | −0.0392126 | + | 0.0679182i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7563.64 | + | 13100.6i | 0.393137 | + | 0.680934i | ||||
\(719\) | 14833.0 | − | 25691.4i | 0.769368 | − | 1.33259i | −0.168537 | − | 0.985695i | \(-0.553904\pi\) |
0.937906 | − | 0.346890i | \(-0.112762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5676.30 | + | 14607.5i | 0.293199 | + | 0.754525i | ||||
\(722\) | −22800.5 | −1.17527 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4402.58 | − | 7625.49i | −0.225995 | − | 0.391435i | ||||
\(725\) | 6811.74 | + | 11798.3i | 0.348940 | + | 0.604382i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23619.7 | 1.20496 | 0.602481 | − | 0.798133i | \(-0.294179\pi\) | ||||
0.602481 | + | 0.798133i | \(0.294179\pi\) | |||||||
\(728\) | 3477.51 | − | 4330.64i | 0.177040 | − | 0.220473i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4175.55 | − | 7232.27i | 0.211704 | − | 0.366683i | ||||
\(731\) | 3264.10 | + | 5653.59i | 0.165154 | + | 0.286054i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10767.9 | + | 18650.5i | −0.542593 | + | 0.939798i | 0.456161 | + | 0.889897i | \(0.349224\pi\) |
−0.998754 | + | 0.0499012i | \(0.984109\pi\) | |||||||
\(734\) | 6864.15 | 0.345177 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6156.73 | 0.308342 | ||||||||
\(737\) | 13528.5 | − | 23432.0i | 0.676158 | − | 1.17114i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5373.78 | − | 9307.66i | −0.267494 | − | 0.463312i | 0.700720 | − | 0.713436i | \(-0.252862\pi\) |
−0.968214 | + | 0.250124i | \(0.919529\pi\) | |||||||
\(740\) | −2421.89 | + | 4194.84i | −0.120311 | + | 0.208386i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13957.4 | − | 17381.5i | 0.690554 | − | 0.859966i | ||||
\(743\) | −19106.9 | −0.943426 | −0.471713 | − | 0.881752i | \(-0.656364\pi\) | ||||
−0.471713 | + | 0.881752i | \(0.656364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6012.03 | − | 10413.1i | −0.295656 | − | 0.512091i | ||||
\(746\) | −5273.69 | − | 9134.29i | −0.258825 | − | 0.448298i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18078.8 | −0.883724 | ||||||||
\(749\) | −3772.03 | − | 9707.03i | −0.184015 | − | 0.473547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2371.18 | − | 4107.00i | 0.115214 | − | 0.199556i | −0.802651 | − | 0.596448i | \(-0.796578\pi\) |
0.917865 | + | 0.396892i | \(0.129911\pi\) | |||||||
\(752\) | 2759.93 | + | 4780.33i | 0.133835 | + | 0.231810i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4847.05 | − | 8395.34i | 0.234110 | − | 0.405491i | ||||
\(755\) | −737.543 | −0.0355522 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3717.28 | −0.178476 | −0.0892382 | − | 0.996010i | \(-0.528443\pi\) | ||||
−0.0892382 | + | 0.996010i | \(0.528443\pi\) | |||||||
\(758\) | 8856.92 | − | 15340.6i | 0.424403 | − | 0.735088i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2395.26 | − | 4148.71i | −0.114323 | − | 0.198013i | ||||
\(761\) | 2047.43 | − | 3546.26i | 0.0975288 | − | 0.168925i | −0.813132 | − | 0.582079i | \(-0.802240\pi\) |
0.910661 | + | 0.413154i | \(0.135573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20420.6 | − | 3148.32i | −0.968905 | − | 0.149380i | ||||
\(764\) | 17413.1 | 0.824587 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1041.70 | + | 1804.28i | 0.0491361 | + | 0.0851063i | ||||
\(767\) | 590.900 | + | 1023.47i | 0.0278177 | + | 0.0481816i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16871.2 | 0.791145 | 0.395573 | − | 0.918435i | \(-0.370546\pi\) | ||||
0.395573 | + | 0.918435i | \(0.370546\pi\) | |||||||
\(770\) | 2356.67 | + | 6064.70i | 0.110297 | + | 0.283840i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4452.84 | − | 7712.54i | 0.207592 | − | 0.359560i | ||||
\(773\) | 14015.1 | + | 24274.9i | 0.652121 | + | 1.12951i | 0.982607 | + | 0.185696i | \(0.0594538\pi\) |
−0.330487 | + | 0.943811i | \(0.607213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12884.7 | + | 22317.0i | −0.597205 | + | 1.03439i | ||||
\(776\) | −1922.47 | −0.0889339 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18665.4 | 0.860135 | ||||||||
\(779\) | 24690.9 | − | 42766.0i | 1.13562 | − | 1.96694i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13177.1 | − | 22823.4i | −0.603730 | − | 1.04569i | ||||
\(782\) | 21937.6 | − | 37997.1i | 1.00318 | − | 1.73756i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5233.16 | + | 1652.92i | 0.238391 | + | 0.0752971i | ||||
\(785\) | −2373.39 | −0.107911 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2603.42 | − | 4509.26i | −0.117919 | − | 0.204241i | 0.801024 | − | 0.598632i | \(-0.204289\pi\) |
−0.918943 | + | 0.394391i | \(0.870956\pi\) | |||||||
\(788\) | 7492.78 | + | 12977.9i | 0.338730 | + | 0.586698i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 29.4732 | 0.00132736 | ||||||||
\(791\) | −17606.2 | + | 21925.5i | −0.791410 | + | 0.985566i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16166.3 | + | 28000.9i | −0.723939 | + | 1.25390i | ||||
\(794\) | 6822.33 | + | 11816.6i | 0.304931 | + | 0.528156i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5728.08 | − | 9921.32i | 0.255058 | − | 0.441774i | ||||
\(797\) | −4553.19 | −0.202362 | −0.101181 | − | 0.994868i | \(-0.532262\pi\) | ||||
−0.101181 | + | 0.994868i | \(0.532262\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39336.7 | 1.74172 | ||||||||
\(800\) | −1685.79 | + | 2919.87i | −0.0745020 | + | 0.129041i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8109.95 | + | 14046.8i | 0.357073 | + | 0.618468i | ||||
\(803\) | −18674.7 | + | 32345.4i | −0.820690 | + | 1.42148i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15606.2 | − | 2406.06i | −0.683287 | − | 0.105345i | ||||
\(806\) | 18336.9 | 0.801352 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1782.57 | + | 3087.50i | 0.0776120 | + | 0.134428i | ||||
\(809\) | −17523.7 | − | 30351.9i | −0.761557 | − | 1.31906i | −0.942048 | − | 0.335479i | \(-0.891102\pi\) |
0.180490 | − | 0.983577i | \(-0.442232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36540.6 | 1.58214 | 0.791069 | − | 0.611727i | \(-0.209525\pi\) | ||||
0.791069 | + | 0.611727i | \(0.209525\pi\) | |||||||
\(812\) | 9466.96 | + | 1459.56i | 0.409144 | + | 0.0630793i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10831.6 | − | 18760.9i | 0.466398 | − | 0.807824i | ||||
\(815\) | −2665.01 | − | 4615.93i | −0.114541 | − | 0.198391i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3868.26 | − | 6700.02i | 0.165647 | − | 0.286908i | ||||
\(818\) | −8866.08 | −0.378967 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6477.94 | 0.275877 | ||||||||
\(821\) | −4052.84 | + | 7019.73i | −0.172284 | + | 0.298405i | −0.939218 | − | 0.343321i | \(-0.888448\pi\) |
0.766934 | + | 0.641726i | \(0.221781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8980.10 | − | 15554.0i | −0.380348 | − | 0.658783i | 0.610764 | − | 0.791813i | \(-0.290863\pi\) |
−0.991112 | + | 0.133030i | \(0.957529\pi\) | |||||||
\(824\) | −3384.76 | + | 5862.57i | −0.143099 | + | 0.247855i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −731.149 | + | 910.521i | −0.0307990 | + | 0.0383548i | ||||
\(827\) | −527.061 | −0.0221617 | −0.0110808 | − | 0.999939i | \(-0.503527\pi\) | ||||
−0.0110808 | + | 0.999939i | \(0.503527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14390.3 | − | 24924.7i | −0.602888 | − | 1.04423i | −0.992381 | − | 0.123204i | \(-0.960683\pi\) |
0.389493 | − | 0.921029i | \(-0.372650\pi\) | |||||||
\(830\) | −239.700 | − | 415.172i | −0.0100242 | − | 0.0173625i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2399.13 | 0.0999696 | ||||||||
\(833\) | 28848.0 | − | 26407.5i | 1.19991 | − | 1.09840i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7682.31 | + | 13306.1i | −0.318392 | + | 0.551471i | ||||
\(836\) | 10712.5 | + | 18554.6i | 0.443181 | + | 0.767613i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6782.36 | + | 11747.4i | −0.279585 | + | 0.484256i | ||||
\(839\) | −2811.89 | −0.115706 | −0.0578530 | − | 0.998325i | \(-0.518425\pi\) | ||||
−0.0578530 | + | 0.998325i | \(0.518425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7670.04 | −0.314488 | ||||||||
\(842\) | −4798.62 | + | 8311.46i | −0.196403 | + | 0.340180i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7458.25 | − | 12918.1i | −0.304175 | − | 0.526846i | ||||
\(845\) | 1754.37 | − | 3038.67i | 0.0714228 | − | 0.123708i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1611.45 | − | 4146.94i | −0.0653719 | − | 0.168230i | ||||
\(848\) | 9629.15 | 0.389937 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12013.6 | + | 20808.2i | 0.484780 | + | 0.839664i | ||||
\(851\) | 26287.2 | + | 45530.7i | 1.05889 | + | 1.83404i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26873.5 | −1.07870 | −0.539351 | − | 0.842081i | \(-0.681330\pi\) | ||||
−0.539351 | + | 0.842081i | \(0.681330\pi\) | |||||||
\(854\) | −31575.1 | − | 4868.05i | −1.26520 | − | 0.195060i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2249.25 | − | 3895.81i | 0.0898103 | − | 0.155556i | ||||
\(857\) | −10187.0 | − | 17644.4i | −0.406045 | − | 0.703290i | 0.588398 | − | 0.808572i | \(-0.299759\pi\) |
−0.994442 | + | 0.105282i | \(0.966426\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19982.8 | + | 34611.3i | −0.793720 | + | 1.37476i | 0.129929 | + | 0.991523i | \(0.458525\pi\) |
−0.923649 | + | 0.383240i | \(0.874808\pi\) | |||||||
\(860\) | 1014.88 | 0.0402408 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25898.6 | −1.02333 | ||||||||
\(863\) | 21047.6 | − | 36455.6i | 0.830208 | − | 1.43796i | −0.0676645 | − | 0.997708i | \(-0.521555\pi\) |
0.897873 | − | 0.440255i | \(-0.145112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −922.179 | − | 1597.26i | −0.0362486 | − | 0.0627844i | ||||
\(866\) | 937.240 | − | 1623.35i | 0.0367768 | − | 0.0636993i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6562.67 | + | 16888.5i | 0.256626 | + | 0.660408i | ||||
\(869\) | −131.815 | −0.00514561 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12793.9 | + | 22159.7i | 0.497710 | + | 0.862058i | ||||
\(872\) | −4462.54 | − | 7729.35i | −0.173304 | − | 0.300171i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −51996.2 | −2.01235 | ||||||||
\(875\) | 11837.7 | − | 14741.8i | 0.457356 | − | 0.569559i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6378.94 | + | 11048.6i | −0.245612 | + | 0.425412i | −0.962303 | − | 0.271978i | \(-0.912322\pi\) |
0.716692 | + | 0.697390i | \(0.245655\pi\) | |||||||
\(878\) | −13600.3 | − | 23556.4i | −0.522765 | − | 0.905456i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1405.27 | + | 2434.00i | −0.0538314 | + | 0.0932388i | ||||
\(881\) | 21457.2 | 0.820557 | 0.410278 | − | 0.911960i | \(-0.365432\pi\) | ||||
0.410278 | + | 0.911960i | \(0.365432\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20778.9 | 0.791920 | 0.395960 | − | 0.918268i | \(-0.370412\pi\) | ||||
0.395960 | + | 0.918268i | \(0.370412\pi\) | |||||||
\(884\) | 8548.56 | − | 14806.5i | 0.325248 | − | 0.563346i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4632.47 | + | 8023.68i | 0.175656 | + | 0.304245i | ||||
\(887\) | −8337.09 | + | 14440.3i | −0.315594 | + | 0.546625i | −0.979564 | − | 0.201135i | \(-0.935537\pi\) |
0.663969 | + | 0.747760i | \(0.268870\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9312.43 | − | 11597.0i | 0.351326 | − | 0.437517i | ||||
\(890\) | 2529.50 | 0.0952685 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −305.780 | − | 529.626i | −0.0114779 | − | 0.0198803i | ||||
\(893\) | −23308.8 | − | 40372.0i | −0.873458 | − | 1.51287i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1664.62 | 0.0621700 | ||||||||
\(896\) | 858.634 | + | 2209.63i | 0.0320145 | + | 0.0823867i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −254.426 | + | 440.679i | −0.00945468 | + | 0.0163760i | ||||
\(899\) | 15812.4 | + | 27387.8i | 0.586621 | + | 1.01606i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34310.6 | − | 59427.7i | 1.26865 | − | 2.19736i | ||||
\(902\) | −28971.8 | −1.06946 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12146.5 | −0.446888 | ||||||||
\(905\) | −4877.51 | + | 8448.09i | −0.179153 | + | 0.310303i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9844.63 | − | 17051.4i | −0.360403 | − | 0.624237i | 0.627624 | − | 0.778517i | \(-0.284028\pi\) |
−0.988027 | + | 0.154280i | \(0.950694\pi\) | |||||||
\(908\) | −6772.16 | + | 11729.7i | −0.247513 | + | 0.428706i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6081.35 | − | 937.584i | −0.221533 | − | 0.0341545i | ||||
\(911\) | 110.121 | 0.00400492 | 0.00200246 | − | 0.999998i | \(-0.499363\pi\) | ||||
0.00200246 | + | 0.999998i | \(0.499363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1072.03 | + | 1856.81i | 0.0388597 | + | 0.0673071i | ||||
\(914\) | 16410.5 | + | 28423.8i | 0.593885 | + | 1.02864i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3089.42 | −0.111438 | ||||||||
\(917\) | −5971.62 | − | 15367.5i | −0.215049 | − | 0.553413i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −57.8619 | + | 100.220i | −0.00207692 | + | 0.00359733i | −0.867062 | − | 0.498200i | \(-0.833994\pi\) |
0.864985 | + | 0.501798i | \(0.167328\pi\) | |||||||
\(920\) | −3410.44 | − | 5907.06i | −0.122216 | − | 0.211685i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5842.56 | − | 10119.6i | 0.208693 | − | 0.361466i | ||||
\(923\) | 24923.2 | 0.888793 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28791.0 | −1.02340 | ||||||||
\(926\) | 6699.12 | − | 11603.2i | 0.237740 | − | 0.411777i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2068.83 | + | 3583.32i | 0.0731817 | + | 0.126754i | ||||
\(929\) | −9408.07 | + | 16295.3i | −0.332259 | + | 0.575490i | −0.982954 | − | 0.183849i | \(-0.941144\pi\) |
0.650695 | + | 0.759339i | \(0.274478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44196.3 | − | 13959.6i | −1.55583 | − | 0.491416i | ||||
\(932\) | −14255.4 | −0.501021 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1825.63 | + | 3162.09i | 0.0639578 | + | 0.110778i | ||||
\(935\) | 10014.5 | + | 17345.7i | 0.350278 | + | 0.606699i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6981.55 | 0.243412 | 0.121706 | − | 0.992566i | \(-0.461163\pi\) | ||||
0.121706 | + | 0.992566i | \(0.461163\pi\) | |||||||
\(938\) | −15830.5 | + | 19714.2i | −0.551050 | + | 0.686239i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3057.65 | − | 5296.01i | 0.106095 | − | 0.183763i | ||||
\(941\) | 14876.6 | + | 25767.1i | 0.515372 | + | 0.892650i | 0.999841 | + | 0.0178417i | \(0.00567949\pi\) |
−0.484469 | + | 0.874808i | \(0.660987\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35155.7 | − | 60891.5i | 1.21403 | − | 2.10276i | ||||
\(944\) | −504.418 | −0.0173913 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4538.93 | −0.155997 | ||||||||
\(947\) | 13793.6 | − | 23891.2i | 0.473317 | − | 0.819809i | −0.526217 | − | 0.850351i | \(-0.676390\pi\) |
0.999533 | + | 0.0305416i | \(0.00972319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17660.6 | − | 30589.1i | −0.604098 | − | 1.04633i | ||||
\(950\) | 14237.2 | − | 24659.6i | 0.486227 | − | 0.842171i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16696.5 | + | 2574.16i | 0.568422 | + | 0.0876357i | ||||
\(953\) | −53424.4 | −1.81593 | −0.907967 | − | 0.419042i | \(-0.862366\pi\) | ||||
−0.907967 | + | 0.419042i | \(0.862366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9645.79 | − | 16707.0i | −0.326838 | − | 0.566100i | ||||
\(956\) | −11665.8 | − | 20205.8i | −0.394666 | − | 0.683581i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22072.3 | 0.744388 | ||||||||
\(959\) | 37423.7 | + | 5769.75i | 1.26014 | + | 0.194281i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15014.4 | + | 26005.8i | −0.503992 | + | 0.872940i | ||||
\(962\) | 10243.5 | + | 17742.2i | 0.343308 | + | 0.594627i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7386.43 | + | 12793.7i | −0.246785 | + | 0.427445i | ||||
\(965\) | −9866.38 | −0.329130 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55913.3 | −1.85941 | −0.929705 | − | 0.368305i | \(-0.879938\pi\) | ||||
−0.929705 | + | 0.368305i | \(0.879938\pi\) | |||||||
\(968\) | 960.900 | − | 1664.33i | 0.0319055 | − | 0.0552619i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1064.93 | + | 1844.51i | 0.0352503 | + | 0.0610553i | ||||
\(971\) | 1286.67 | − | 2228.58i | 0.0425244 | − | 0.0736544i | −0.843980 | − | 0.536375i | \(-0.819793\pi\) |
0.886504 | + | 0.462720i | \(0.153127\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6812.27 | + | 8483.51i | −0.224451 | + | 0.279516i | ||||
\(974\) | −16371.1 | −0.538567 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6900.15 | − | 11951.4i | −0.226300 | − | 0.391963i | ||||
\(977\) | 13958.3 | + | 24176.5i | 0.457078 | + | 0.791683i | 0.998805 | − | 0.0488718i | \(-0.0155626\pi\) |
−0.541727 | + | 0.840555i | \(0.682229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11312.9 | −0.369316 | ||||||||
\(980\) | −1312.95 | − | 5936.56i | −0.0427967 | − | 0.193507i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19006.2 | + | 32919.7i | −0.617629 | + | 1.06976i | ||||
\(983\) | −19945.8 | − | 34547.2i | −0.647175 | − | 1.12094i | −0.983794 | − | 0.179300i | \(-0.942617\pi\) |
0.336619 | − | 0.941641i | \(-0.390717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8301.07 | − | 14377.9i | 0.268522 | − | 0.465094i | ||||
\(986\) | 29486.6 | 0.952378 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20261.6 | −0.652438 | ||||||||
\(989\) | 5507.74 | − | 9539.69i | 0.177084 | − | 0.306719i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3506.45 | + | 6073.36i | 0.112398 | + | 0.194679i | 0.916737 | − | 0.399492i | \(-0.130814\pi\) |
−0.804339 | + | 0.594171i | \(0.797480\pi\) | |||||||
\(992\) | −3913.30 | + | 6778.03i | −0.125249 | + | 0.216938i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8919.87 | + | 22954.6i | 0.284629 | + | 0.732470i | ||||
\(995\) | −12692.0 | −0.404385 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8436.08 | + | 14611.7i | 0.267977 | + | 0.464150i | 0.968339 | − | 0.249638i | \(-0.0803115\pi\) |
−0.700362 | + | 0.713788i | \(0.746978\pi\) | |||||||
\(998\) | 16493.6 | + | 28567.7i | 0.523142 | + | 0.906108i | ||||
\(999\) | 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 | 378.4.g.e.163.2 | yes | 8 | |
3.2 | odd | 2 | 378.4.g.d.163.3 | yes | 8 | ||
7.4 | even | 3 | inner | 378.4.g.e.109.2 | yes | 8 | |
21.11 | odd | 6 | 378.4.g.d.109.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.d.109.3 | ✓ | 8 | 21.11 | odd | 6 | ||
378.4.g.d.163.3 | yes | 8 | 3.2 | odd | 2 | ||
378.4.g.e.109.2 | yes | 8 | 7.4 | even | 3 | inner | |
378.4.g.e.163.2 | yes | 8 | 1.1 | even | 1 | trivial |