Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(85,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.85");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.j (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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 7 x^{17} + 81 x^{16} - 470 x^{15} + 2687 x^{14} - 12243 x^{13} + 43732 x^{12} - 169303 x^{11} + 166449 x^{10} - 57172 x^{9} - 3758051 x^{8} + \cdots + 5500612092612 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.3 | ||
Root | \(2.54993 - 4.95961i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.169 |
Dual form | 252.4.j.b.85.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.54993 | − | 4.95961i | −0.298284 | − | 0.954477i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.85902 | + | 6.68401i | 0.345161 | + | 0.597836i | 0.985383 | − | 0.170354i | \(-0.0544910\pi\) |
−0.640222 | + | 0.768190i | \(0.721158\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.50000 | + | 6.06218i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −22.1955 | + | 15.3741i | −0.822054 | + | 0.569410i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.9501 | − | 36.2866i | 0.574244 | − | 0.994620i | −0.421879 | − | 0.906652i | \(-0.638629\pi\) |
0.996123 | − | 0.0879680i | \(-0.0280373\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.8256 | − | 34.3390i | −0.422972 | − | 0.732609i | 0.573257 | − | 0.819376i | \(-0.305680\pi\) |
−0.996229 | + | 0.0867670i | \(0.972346\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 27.1689 | − | 29.4989i | 0.467665 | − | 0.507773i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −68.0598 | −0.970996 | −0.485498 | − | 0.874238i | \(-0.661362\pi\) | ||||
−0.485498 | + | 0.874238i | \(0.661362\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −104.181 | −1.25793 | −0.628965 | − | 0.777434i | \(-0.716521\pi\) | ||||
−0.628965 | + | 0.777434i | \(0.716521\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.4908 | + | 7.96270i | 0.368796 | + | 0.0827430i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −72.9636 | − | 126.377i | −0.661477 | − | 1.14571i | −0.980228 | − | 0.197873i | \(-0.936597\pi\) |
0.318751 | − | 0.947839i | \(-0.396737\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 32.7160 | − | 56.6658i | 0.261728 | − | 0.453326i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 110.651 | + | 86.2521i | 0.788694 | + | 0.614786i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −145.615 | + | 252.213i | −0.932417 | + | 1.61499i | −0.153240 | + | 0.988189i | \(0.548971\pi\) |
−0.779177 | + | 0.626804i | \(0.784363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 133.567 | + | 231.344i | 0.773847 | + | 1.34034i | 0.935440 | + | 0.353485i | \(0.115003\pi\) |
−0.161593 | + | 0.986857i | \(0.551663\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −212.438 | − | 47.6626i | −1.12063 | − | 0.251424i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −54.0262 | −0.260917 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −341.523 | −1.51746 | −0.758731 | − | 0.651404i | \(-0.774180\pi\) | ||||
−0.758731 | + | 0.651404i | \(0.774180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −139.580 | + | 151.550i | −0.573093 | + | 0.622242i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −116.552 | − | 201.874i | −0.443960 | − | 0.768962i | 0.554019 | − | 0.832504i | \(-0.313094\pi\) |
−0.997979 | + | 0.0635423i | \(0.979760\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.6831 | − | 35.8241i | 0.0733521 | − | 0.127050i | −0.827016 | − | 0.562178i | \(-0.809964\pi\) |
0.900368 | + | 0.435128i | \(0.143297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −188.413 | − | 89.0259i | −0.624155 | − | 0.294916i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120.893 | + | 209.392i | −0.375192 | + | 0.649851i | −0.990356 | − | 0.138548i | \(-0.955756\pi\) |
0.615164 | + | 0.788399i | \(0.289090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 105.488 | + | 337.550i | 0.289632 | + | 0.926793i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −505.372 | −1.30978 | −0.654889 | − | 0.755725i | \(-0.727285\pi\) | ||||
−0.654889 | + | 0.755725i | \(0.727285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 323.387 | 0.792826 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 161.472 | + | 516.695i | 0.375220 | + | 1.20067i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −90.6191 | − | 156.957i | −0.199959 | − | 0.346340i | 0.748556 | − | 0.663072i | \(-0.230748\pi\) |
−0.948515 | + | 0.316732i | \(0.897414\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 339.158 | − | 587.439i | 0.711881 | − | 1.23301i | −0.252270 | − | 0.967657i | \(-0.581177\pi\) |
0.964150 | − | 0.265356i | \(-0.0854896\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.5162 | − | 188.362i | −0.0310295 | − | 0.376689i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 153.015 | − | 265.029i | 0.291987 | − | 0.505736i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −443.394 | − | 767.980i | −0.808495 | − | 1.40035i | −0.913906 | − | 0.405925i | \(-0.866949\pi\) |
0.105412 | − | 0.994429i | \(-0.466384\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −513.691 | + | 557.746i | −0.896248 | + | 0.973112i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 594.531 | 0.993773 | 0.496886 | − | 0.867816i | \(-0.334477\pi\) | ||||
0.496886 | + | 0.867816i | \(0.334477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 704.964 | 1.13027 | 0.565136 | − | 0.824998i | \(-0.308824\pi\) | ||||
0.565136 | + | 0.824998i | \(0.308824\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −331.747 | − | 74.4308i | −0.510759 | − | 0.114594i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 146.651 | + | 254.006i | 0.217044 | + | 0.375931i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 287.818 | − | 498.516i | 0.409900 | − | 0.709967i | −0.584978 | − | 0.811049i | \(-0.698897\pi\) |
0.994878 | + | 0.101082i | \(0.0322304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 256.276 | − | 682.469i | 0.351545 | − | 0.936171i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −170.316 | + | 294.997i | −0.225237 | + | 0.390122i | −0.956390 | − | 0.292091i | \(-0.905649\pi\) |
0.731154 | + | 0.682213i | \(0.238982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −262.644 | − | 454.912i | −0.335150 | − | 0.580496i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1476.57 | + | 331.283i | 1.81960 | + | 0.408245i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1427.89 | −1.70063 | −0.850317 | − | 0.526272i | \(-0.823590\pi\) | ||||
−0.850317 | + | 0.526272i | \(0.823590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 277.559 | 0.319737 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 940.358 | − | 1021.00i | 1.04850 | − | 1.13842i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −402.034 | − | 696.344i | −0.434188 | − | 0.752036i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 76.5670 | − | 132.618i | 0.0801464 | − | 0.138818i | −0.823166 | − | 0.567800i | \(-0.807795\pi\) |
0.903313 | + | 0.428983i | \(0.141128\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 92.8760 | + | 1127.49i | 0.0942868 | + | 1.14461i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −512.568 | + | 887.793i | −0.504974 | + | 0.874641i | 0.495009 | + | 0.868888i | \(0.335165\pi\) |
−0.999983 | + | 0.00575325i | \(0.998169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 876.289 | + | 1517.78i | 0.838284 | + | 1.45195i | 0.891328 | + | 0.453359i | \(0.149774\pi\) |
−0.0530438 | + | 0.998592i | \(0.516892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 83.7367 | + | 267.949i | 0.0778273 | + | 0.249039i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −247.500 | −0.223614 | −0.111807 | − | 0.993730i | \(-0.535664\pi\) | ||||
−0.111807 | + | 0.993730i | \(0.535664\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1257.29 | 1.10483 | 0.552416 | − | 0.833568i | \(-0.313706\pi\) | ||||
0.552416 | + | 0.833568i | \(0.313706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 529.336 | + | 1693.82i | 0.452634 | + | 1.44838i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −249.452 | − | 432.064i | −0.207668 | − | 0.359692i | 0.743311 | − | 0.668946i | \(-0.233254\pi\) |
−0.950980 | + | 0.309254i | \(0.899921\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 563.136 | − | 975.380i | 0.456632 | − | 0.790910i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 967.968 | + | 457.369i | 0.764860 | + | 0.361400i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 238.209 | − | 412.591i | 0.183501 | − | 0.317833i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −212.311 | − | 367.734i | −0.159513 | − | 0.276284i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −820.569 | + | 890.943i | −0.601531 | + | 0.653119i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1469.76 | 1.05167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 491.102 | 0.343136 | 0.171568 | − | 0.985172i | \(-0.445117\pi\) | ||||
0.171568 | + | 0.985172i | \(0.445117\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −209.731 | − | 47.0552i | −0.143146 | − | 0.0321161i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 109.506 | + | 189.670i | 0.0730349 | + | 0.126500i | 0.900230 | − | 0.435415i | \(-0.143398\pi\) |
−0.827195 | + | 0.561915i | \(0.810065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 364.632 | − | 631.561i | 0.237726 | − | 0.411754i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −149.507 | + | 1072.44i | −0.0953151 | + | 0.683710i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 530.907 | − | 919.558i | 0.331084 | − | 0.573454i | −0.651641 | − | 0.758528i | \(-0.725919\pi\) |
0.982725 | + | 0.185074i | \(0.0592524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −71.3339 | − | 123.554i | −0.0435285 | − | 0.0753936i | 0.843440 | − | 0.537223i | \(-0.180527\pi\) |
−0.886969 | + | 0.461829i | \(0.847193\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1225.88 | + | 275.038i | 0.732181 | + | 0.164272i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1661.39 | −0.971557 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2247.73 | −1.28734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −172.489 | + | 187.282i | −0.0967800 | + | 0.105080i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1293.63 | − | 2240.63i | −0.711262 | − | 1.23194i | −0.964384 | − | 0.264508i | \(-0.914790\pi\) |
0.253121 | − | 0.967435i | \(-0.418543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 879.334 | − | 1523.05i | 0.473902 | − | 0.820822i | −0.525652 | − | 0.850700i | \(-0.676178\pi\) |
0.999554 | + | 0.0298777i | \(0.00951178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1510.62 | − | 1046.36i | 0.798211 | − | 0.552894i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1030.87 | + | 1785.52i | −0.534203 | + | 0.925267i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −240.519 | − | 416.591i | −0.122264 | − | 0.211768i | 0.798396 | − | 0.602133i | \(-0.205682\pi\) |
−0.920660 | + | 0.390365i | \(0.872349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 783.290 | + | 2506.45i | 0.390685 | + | 1.25015i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1021.49 | 0.500030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2967.97 | 1.42619 | 0.713097 | − | 0.701066i | \(-0.247292\pi\) | ||||
0.713097 | + | 0.701066i | \(0.247292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −501.226 | − | 1603.87i | −0.236487 | − | 0.756735i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −460.641 | − | 797.854i | −0.213446 | − | 0.369699i | 0.739345 | − | 0.673327i | \(-0.235135\pi\) |
−0.952791 | + | 0.303628i | \(0.901802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 312.390 | − | 541.076i | 0.142190 | − | 0.246279i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2312.33 | − | 1601.68i | 1.03409 | − | 0.716277i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −524.992 | + | 909.313i | −0.230719 | + | 0.399617i | −0.958020 | − | 0.286702i | \(-0.907441\pi\) |
0.727301 | + | 0.686319i | \(0.240774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 229.012 | + | 396.660i | 0.0989239 | + | 0.171341i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −637.992 | + | 692.707i | −0.270929 | + | 0.294164i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1435.40 | 0.599367 | 0.299683 | − | 0.954039i | \(-0.403119\pi\) | ||||
0.299683 | + | 0.954039i | \(0.403119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 845.711 | 0.347300 | 0.173650 | − | 0.984807i | \(-0.444444\pi\) | ||||
0.173650 | + | 0.984807i | \(0.444444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3439.14 | − | 771.604i | −1.38923 | − | 0.311686i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1317.94 | − | 2282.75i | −0.523769 | − | 0.907194i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1425.86 | + | 2469.66i | −0.557589 | + | 0.965772i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −910.153 | + | 368.902i | −0.350285 | + | 0.141977i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1289.40 | + | 2233.30i | −0.488468 | + | 0.846052i | −0.999912 | − | 0.0132651i | \(-0.995777\pi\) |
0.511444 | + | 0.859317i | \(0.329111\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2276.19 | − | 3942.47i | −0.848930 | − | 1.47039i | −0.882164 | − | 0.470942i | \(-0.843914\pi\) |
0.0332344 | − | 0.999448i | \(-0.489419\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1551.60 | − | 348.117i | −0.569808 | − | 0.127842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2802.02 | −1.01338 | −0.506690 | − | 0.862129i | \(-0.669131\pi\) | ||||
−0.506690 | + | 0.862129i | \(0.669131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 346.315 | 0.123365 | 0.0616825 | − | 0.998096i | \(-0.480353\pi\) | ||||
0.0616825 | + | 0.998096i | \(0.480353\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3121.65 | + | 3389.37i | −1.09545 | + | 1.18939i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1019.31 | − | 1765.49i | −0.352420 | − | 0.610410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 899.552 | − | 1558.07i | 0.306475 | − | 0.530831i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3562.38 | + | 1683.24i | 1.19615 | + | 0.565185i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2182.59 | + | 3780.36i | −0.722359 | + | 1.25116i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −861.334 | − | 1491.87i | −0.281027 | − | 0.486753i | 0.690611 | − | 0.723226i | \(-0.257342\pi\) |
−0.971638 | + | 0.236473i | \(0.924008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −921.480 | − | 2948.64i | −0.296426 | − | 0.948534i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 319.265 | 0.101273 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1869.93 | −0.584973 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1092.64 | − | 3496.35i | −0.337141 | − | 1.07882i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1349.33 | + | 2337.10i | 0.410704 | + | 0.711360i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2103.45 | + | 3643.29i | −0.631648 | + | 1.09405i | 0.355566 | + | 0.934651i | \(0.384288\pi\) |
−0.987215 | + | 0.159396i | \(0.949045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 145.037 | + | 1760.70i | 0.0429739 | + | 0.521689i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1044.04 | − | 1808.33i | 0.305266 | − | 0.528736i | −0.672055 | − | 0.740502i | \(-0.734588\pi\) |
0.977321 | + | 0.211765i | \(0.0679213\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2036.30 | + | 3526.97i | 0.587609 | + | 1.01777i | 0.994545 | + | 0.104311i | \(0.0332638\pi\) |
−0.406936 | + | 0.913457i | \(0.633403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1032.47 | − | 1121.02i | 0.294077 | − | 0.319298i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3431.73 | 0.964894 | 0.482447 | − | 0.875925i | \(-0.339748\pi\) | ||||
0.482447 | + | 0.875925i | \(0.339748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1866.11 | −0.518006 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2918.54 | − | 654.803i | −0.799914 | − | 0.179468i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 766.959 | + | 1328.41i | 0.207575 | + | 0.359530i | 0.950950 | − | 0.309344i | \(-0.100110\pi\) |
−0.743375 | + | 0.668875i | \(0.766776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2131.97 | + | 3692.67i | −0.569842 | + | 0.986996i | 0.426739 | + | 0.904375i | \(0.359662\pi\) |
−0.996581 | + | 0.0826208i | \(0.973671\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3781.99 | − | 213.254i | −0.998414 | − | 0.0562973i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 189.092 | − | 327.517i | 0.0493087 | − | 0.0854052i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2065.44 | + | 3577.45i | 0.532069 | + | 0.921570i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1727.05 | + | 387.480i | 0.439547 | + | 0.0986165i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 221.139 | 0.0556102 | 0.0278051 | − | 0.999613i | \(-0.491148\pi\) | ||||
0.0278051 | + | 0.999613i | \(0.491148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6114.37 | −1.51940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1849.11 | + | 2007.69i | −0.454101 | + | 0.493045i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1192.69 | + | 2065.80i | 0.289487 | + | 0.501406i | 0.973687 | − | 0.227888i | \(-0.0731821\pi\) |
−0.684201 | + | 0.729294i | \(0.739849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1195.33 | − | 2070.38i | 0.286773 | − | 0.496706i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −645.543 | − | 7836.68i | −0.153096 | − | 1.85854i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1103.18 | − | 1910.77i | 0.258651 | − | 0.447996i | −0.707230 | − | 0.706984i | \(-0.750055\pi\) |
0.965881 | + | 0.258987i | \(0.0833888\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1950.24 | − | 3377.92i | −0.452084 | − | 0.783033i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2213.13 | + | 7081.79i | 0.507271 | + | 1.62322i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4084.22 | 0.925722 | 0.462861 | − | 0.886431i | \(-0.346823\pi\) | ||||
0.462861 | + | 0.886431i | \(0.346823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2734.83 | 0.613022 | 0.306511 | − | 0.951867i | \(-0.400838\pi\) | ||||
0.306511 | + | 0.951867i | \(0.400838\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −430.195 | − | 1376.58i | −0.0953722 | − | 0.305181i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1370.81 | − | 2374.30i | −0.300591 | − | 0.520640i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 72.9088 | − | 126.282i | 0.0158147 | − | 0.0273918i | −0.858010 | − | 0.513633i | \(-0.828299\pi\) |
0.873824 | + | 0.486242i | \(0.161632\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6521.27 | − | 3081.32i | −1.39935 | − | 0.661197i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3716.57 | + | 6437.30i | −0.789012 | + | 1.36661i | 0.137561 | + | 0.990493i | \(0.456074\pi\) |
−0.926573 | + | 0.376115i | \(0.877260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2721.28 | − | 4713.39i | −0.571601 | − | 0.990043i | −0.996402 | − | 0.0847557i | \(-0.972989\pi\) |
0.424800 | − | 0.905287i | \(-0.360344\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2830.47 | + | 3073.22i | −0.588290 | + | 0.638743i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1631.73 | 0.335602 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −280.864 | −0.0571675 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −776.406 | − | 174.194i | −0.156405 | − | 0.0350909i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1390.00 | − | 2407.55i | −0.277149 | − | 0.480035i | 0.693526 | − | 0.720431i | \(-0.256056\pi\) |
−0.970675 | + | 0.240396i | \(0.922723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 699.401 | − | 1211.40i | 0.138036 | − | 0.239086i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5447.94 | − | 2208.15i | 1.06438 | − | 0.431413i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2893.10 | + | 5010.99i | −0.559572 | + | 0.969208i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 144.782 | + | 250.769i | 0.0277245 | + | 0.0480202i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5197.55 | + | 1166.12i | 0.985450 | + | 0.221095i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5235.26 | 0.982853 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2464.61 | 0.458184 | 0.229092 | − | 0.973405i | \(-0.426424\pi\) | ||||
0.229092 | + | 0.973405i | \(0.426424\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6169.40 | − | 6698.49i | 1.13581 | − | 1.23322i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1694.23 | − | 2934.49i | −0.308910 | − | 0.535047i | 0.669214 | − | 0.743069i | \(-0.266631\pi\) |
−0.978124 | + | 0.208022i | \(0.933297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5288.19 | + | 9159.42i | −0.954972 | + | 1.65406i | −0.220540 | + | 0.975378i | \(0.570782\pi\) |
−0.734432 | + | 0.678682i | \(0.762551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1199.14 | − | 830.603i | 0.214488 | − | 0.148569i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4723.53 | − | 8181.40i | 0.836909 | − | 1.44957i | −0.0555582 | − | 0.998455i | \(-0.517694\pi\) |
0.892467 | − | 0.451113i | \(-0.148973\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6101.30 | + | 10567.8i | 1.07087 | + | 1.85480i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 383.607 | + | 1227.50i | 0.0667005 | + | 0.213435i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7090.51 | 1.22144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2594.46 | −0.442814 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1948.71 | − | 6235.68i | −0.329554 | − | 1.05454i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −846.248 | − | 1465.75i | −0.141809 | − | 0.245621i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2643.85 | + | 4579.28i | −0.439031 | + | 0.760423i | −0.997615 | − | 0.0690245i | \(-0.978011\pi\) |
0.558584 | + | 0.829448i | \(0.311345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7580.27 | − | 5250.60i | 1.24744 | − | 0.864058i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3422.13 | − | 5927.30i | 0.558121 | − | 0.966695i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 261.033 | + | 452.122i | 0.0421940 | + | 0.0730821i | 0.886351 | − | 0.463014i | \(-0.153232\pi\) |
−0.844157 | + | 0.536096i | \(0.819899\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1756.24 | + | 1906.86i | −0.281374 | + | 0.305505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11192.9 | 1.77751 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5710.32 | − | 1281.17i | −0.891111 | − | 0.199929i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4089.91 | − | 7083.93i | −0.632731 | − | 1.09592i | −0.986991 | − | 0.160776i | \(-0.948600\pi\) |
0.354260 | − | 0.935147i | \(-0.384733\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3972.34 | + | 6880.30i | −0.609268 | + | 1.05528i | 0.382093 | + | 0.924124i | \(0.375203\pi\) |
−0.991361 | + | 0.131160i | \(0.958130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 768.091 | − | 5509.63i | 0.116802 | − | 0.837841i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3647.98 | + | 6318.48i | −0.550035 | + | 0.952688i | 0.448237 | + | 0.893915i | \(0.352052\pi\) |
−0.998271 | + | 0.0587729i | \(0.981281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2294.31 | + | 3973.85i | 0.343011 | + | 0.594113i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2415.50 | − | 541.940i | −0.358100 | − | 0.0803431i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5008.17 | 0.736271 | 0.368136 | − | 0.929772i | \(-0.379996\pi\) | ||||
0.368136 | + | 0.929772i | \(0.379996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3994.59 | 0.582386 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1494.75 | + | 1622.94i | −0.216127 | + | 0.234662i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2720.47 | + | 4711.99i | 0.390125 | + | 0.675717i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6583.34 | − | 11402.7i | 0.936370 | − | 1.62184i | 0.164196 | − | 0.986428i | \(-0.447497\pi\) |
0.772173 | − | 0.635412i | \(-0.219170\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5690.55 | + | 2688.81i | 0.802814 | + | 0.379333i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1768.80 | − | 3063.66i | 0.247525 | − | 0.428726i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4393.91 | − | 7610.47i | −0.609941 | − | 1.05645i | −0.991250 | − | 0.132001i | \(-0.957860\pi\) |
0.381309 | − | 0.924448i | \(-0.375473\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2278.02 | − | 7289.44i | −0.313697 | − | 1.00380i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11547.7 | 1.57754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −687.994 | −0.0932451 | −0.0466226 | − | 0.998913i | \(-0.514846\pi\) | ||||
−0.0466226 | + | 0.998913i | \(0.514846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −761.173 | − | 2435.68i | −0.102352 | − | 0.327516i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2311.60 | − | 4003.81i | −0.308401 | − | 0.534165i | 0.669612 | − | 0.742711i | \(-0.266460\pi\) |
−0.978013 | + | 0.208546i | \(0.933127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1131.85 | + | 1960.43i | −0.149830 | + | 0.259513i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 91.6924 | + | 1113.12i | 0.0120439 | + | 0.146209i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3383.44 | + | 5860.30i | −0.440996 | + | 0.763827i | −0.997764 | − | 0.0668410i | \(-0.978708\pi\) |
0.556768 | + | 0.830668i | \(0.312041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4965.89 | + | 8601.17i | 0.642291 | + | 1.11248i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 770.961 | − | 837.080i | 0.0989564 | − | 0.107443i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4442.78 | 0.565925 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10230.5 | −1.29334 | −0.646669 | − | 0.762771i | \(-0.723839\pi\) | ||||
−0.646669 | + | 0.762771i | \(0.723839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3697.45 | − | 829.559i | −0.463920 | − | 0.104085i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5795.59 | + | 10038.3i | 0.721741 | + | 1.25009i | 0.960302 | + | 0.278964i | \(0.0899910\pi\) |
−0.238561 | + | 0.971128i | \(0.576676\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5296.08 | − | 9173.07i | 0.654631 | − | 1.13385i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5550.60 | − | 920.704i | 0.681016 | − | 0.112963i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7154.94 | + | 12392.7i | −0.871394 | + | 1.50930i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2924.72 | + | 5065.76i | 0.353589 | + | 0.612435i | 0.986875 | − | 0.161483i | \(-0.0516277\pi\) |
−0.633286 | + | 0.773918i | \(0.718294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5383.52 | − | 1207.84i | −0.646106 | − | 0.144960i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1268.67 | 0.151155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2629.01 | −0.310972 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −502.217 | + | 545.288i | −0.0589776 | + | 0.0640356i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1540.92 | − | 2668.95i | −0.179663 | − | 0.311185i | 0.762102 | − | 0.647457i | \(-0.224167\pi\) |
−0.941765 | + | 0.336272i | \(0.890834\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3806.37 | + | 6592.83i | −0.440644 | + | 0.763218i | −0.997737 | − | 0.0672317i | \(-0.978583\pi\) |
0.557093 | + | 0.830450i | \(0.311917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −535.942 | − | 6506.17i | −0.0616038 | − | 0.747850i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2226.64 | + | 3856.66i | −0.254137 | + | 0.440178i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2374.10 | + | 4112.07i | 0.269066 | + | 0.466035i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2575.04 | + | 8239.86i | 0.289799 | + | 0.927329i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4831.62 | 0.539979 | 0.269989 | − | 0.962863i | \(-0.412980\pi\) | ||||
0.269989 | + | 0.962863i | \(0.412980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5173.85 | 0.574225 | 0.287112 | − | 0.957897i | \(-0.407305\pi\) | ||||
0.287112 | + | 0.957897i | \(0.407305\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3483.81 | + | 11147.8i | 0.383991 | + | 1.22873i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7601.39 | + | 13166.0i | 0.832091 | + | 1.44122i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −220.798 | + | 382.433i | −0.0240048 | + | 0.0415775i | −0.877778 | − | 0.479067i | \(-0.840975\pi\) |
0.853773 | + | 0.520645i | \(0.174308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1196.19 | + | 565.205i | 0.129164 | + | 0.0610307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5812.33 | − | 10067.2i | 0.623368 | − | 1.07971i | −0.365486 | − | 0.930817i | \(-0.619097\pi\) |
0.988854 | − | 0.148888i | \(-0.0475695\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5510.26 | − | 9544.05i | −0.586992 | − | 1.01670i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9107.61 | + | 9888.70i | −0.963703 | + | 1.04635i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11833.8 | −1.24381 | −0.621906 | − | 0.783092i | \(-0.713641\pi\) | ||||
−0.621906 | + | 0.783092i | \(0.713641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9767.10 | −1.01977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8916.64 | − | 2000.54i | −0.924813 | − | 0.207491i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1071.10 | + | 1855.20i | 0.110361 | + | 0.191150i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −147.660 | + | 255.754i | −0.0151143 | + | 0.0261787i | −0.873484 | − | 0.486854i | \(-0.838145\pi\) |
0.858369 | + | 0.513032i | \(0.171478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7530.86 | − | 5870.30i | −0.765818 | − | 0.596955i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5995.26 | − | 10384.1i | 0.605698 | − | 1.04910i | −0.386242 | − | 0.922397i | \(-0.626227\pi\) |
0.991941 | − | 0.126703i | \(-0.0404395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5320.43 | − | 9215.25i | −0.534042 | − | 0.924987i | −0.999209 | − | 0.0397645i | \(-0.987339\pi\) |
0.465167 | − | 0.885223i | \(-0.345994\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10453.3 | + | 2345.29i | 1.04249 | + | 0.233893i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2566.48 | 0.254309 | 0.127155 | − | 0.991883i | \(-0.459416\pi\) | ||||
0.127155 | + | 0.991883i | \(0.459416\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6207.51 | 0.611165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1693.34 | + | 1838.56i | −0.165658 | + | 0.179865i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −866.624 | − | 1501.04i | −0.0842440 | − | 0.145915i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3408.37 | + | 5903.47i | −0.329235 | + | 0.570252i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11217.0 | − | 7769.63i | 1.07671 | − | 0.745801i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2200.37 | + | 3811.15i | −0.209890 | + | 0.363540i | −0.951680 | − | 0.307092i | \(-0.900644\pi\) |
0.741790 | + | 0.670633i | \(0.233977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6770.91 | + | 11727.6i | 0.641844 | + | 1.11171i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1583.24 | − | 5066.20i | −0.149151 | − | 0.477267i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1181.89 | 0.110654 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15244.7 | −1.41849 | −0.709243 | − | 0.704964i | \(-0.750963\pi\) | ||||
−0.709243 | + | 0.704964i | \(0.750963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4600.14 | − | 14720.0i | −0.425410 | − | 1.36127i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8684.08 | − | 15041.3i | −0.798182 | − | 1.38249i | −0.920799 | − | 0.390037i | \(-0.872462\pi\) |
0.122617 | − | 0.992454i | \(-0.460871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9910.55 | − | 17165.6i | 0.905373 | − | 1.56815i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7177.71 | + | 4971.77i | −0.651746 | + | 0.451443i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2080.86 | + | 3604.15i | −0.187805 | + | 0.325288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1475.23 | − | 2555.17i | −0.132345 | − | 0.229229i | 0.792235 | − | 0.610216i | \(-0.208917\pi\) |
−0.924580 | + | 0.380987i | \(0.875584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3243.08 | + | 3521.22i | −0.289202 | + | 0.314005i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13169.6 | −1.16740 | −0.583701 | − | 0.811968i | \(-0.698396\pi\) | ||||
−0.583701 | + | 0.811968i | \(0.698396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7912.03 | −0.697189 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3167.71 | − | 710.706i | −0.277481 | − | 0.0622555i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4467.78 | − | 7738.42i | −0.389059 | − | 0.673869i | 0.603265 | − | 0.797541i | \(-0.293866\pi\) |
−0.992323 | + | 0.123672i | \(0.960533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2467.37 | + | 4273.62i | −0.213601 | + | 0.369968i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11527.7 | − | 8985.79i | −0.992121 | − | 0.773358i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6763.22 | + | 11714.2i | −0.578686 | + | 1.00231i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5065.42 | + | 8773.56i | 0.430903 | + | 0.746346i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5323.53 | + | 1194.39i | 0.450245 | + | 0.101017i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4285.65 | −0.360380 | −0.180190 | − | 0.983632i | \(-0.557671\pi\) | ||||
−0.180190 | + | 0.983632i | \(0.557671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17587.3 | 1.47044 | 0.735220 | − | 0.677828i | \(-0.237079\pi\) | ||||
0.735220 | + | 0.677828i | \(0.237079\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1612.33 | − | 1750.60i | 0.134034 | − | 0.145529i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9090.51 | − | 15745.2i | −0.751402 | − | 1.30147i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4563.88 | + | 7904.88i | −0.375103 | + | 0.649698i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4424.40 | + | 2090.54i | 0.361587 | + | 0.170851i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4621.43 | + | 8004.55i | −0.375565 | + | 0.650499i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −955.107 | − | 1654.29i | −0.0771829 | − | 0.133685i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2224.76 | − | 7119.01i | −0.178781 | − | 0.572082i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2053.11 | −0.164070 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11196.4 | 0.889780 | 0.444890 | − | 0.895585i | \(-0.353243\pi\) | ||||
0.444890 | + | 0.895585i | \(0.353243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1310.79 | − | 4194.40i | −0.103594 | − | 0.331490i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4851.91 | + | 8403.76i | 0.381345 | + | 0.660509i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10695.6 | − | 18525.4i | 0.836036 | − | 1.44806i | −0.0571474 | − | 0.998366i | \(-0.518200\pi\) |
0.893184 | − | 0.449692i | \(-0.148466\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1503.56 | + | 18252.7i | 0.116886 | + | 1.41895i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15170.3 | − | 26275.7i | 1.17291 | − | 2.03155i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2014.73 | + | 3489.61i | 0.154928 | + | 0.268342i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9278.82 | + | 10074.6i | −0.709665 | + | 0.770526i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13798.3 | −1.04964 | −0.524822 | − | 0.851212i | \(-0.675868\pi\) | ||||
−0.524822 | + | 0.851212i | \(0.675868\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1640.22 | −0.124103 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14458.5 | + | 3243.91i | 1.08813 | + | 0.244132i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1977.64 | − | 3425.37i | −0.148042 | − | 0.256416i | 0.782462 | − | 0.622698i | \(-0.213964\pi\) |
−0.930504 | + | 0.366283i | \(0.880630\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1925.28 | − | 3334.69i | 0.143358 | − | 0.248303i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3240.28 | + | 3942.23i | 0.239998 | + | 0.291990i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6488.75 | + | 11238.9i | −0.478072 | + | 0.828044i | −0.999684 | − | 0.0251383i | \(-0.991997\pi\) |
0.521612 | + | 0.853183i | \(0.325331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7591.71 | − | 13149.2i | −0.556398 | − | 0.963710i | −0.997793 | − | 0.0663968i | \(-0.978850\pi\) |
0.441395 | − | 0.897313i | \(-0.354484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13074.8 | + | 2933.45i | 0.953239 | + | 0.213868i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9548.31 | −0.692508 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18148.1 | −1.30938 | −0.654691 | − | 0.755897i | \(-0.727201\pi\) | ||||
−0.654691 | + | 0.755897i | \(0.727201\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16025.2 | + | 17399.5i | −1.15023 | + | 1.24888i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1192.21 | − | 2064.98i | −0.0851315 | − | 0.147452i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10587.6 | + | 18338.2i | −0.752132 | + | 1.30273i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 678.346 | + | 8234.90i | 0.0479421 | + | 0.582002i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12047.6 | + | 20867.1i | −0.847119 | + | 1.46725i | 0.0366501 | + | 0.999328i | \(0.488331\pi\) |
−0.883769 | + | 0.467924i | \(0.845002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13915.0 | − | 24101.5i | −0.973445 | − | 1.68606i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4342.93 | + | 13896.9i | 0.302274 | + | 0.967247i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10618.6 | −0.735333 | −0.367666 | − | 0.929958i | \(-0.619843\pi\) | ||||
−0.367666 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3677.01 | 0.253349 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −536.763 | − | 1717.59i | −0.0367978 | − | 0.117749i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12015.6 | − | 20811.6i | −0.819606 | − | 1.41960i | −0.905973 | − | 0.423335i | \(-0.860859\pi\) |
0.0863674 | − | 0.996263i | \(-0.472474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 430.072 | − | 744.907i | 0.0291897 | − | 0.0505580i | −0.851062 | − | 0.525066i | \(-0.824041\pi\) |
0.880251 | + | 0.474508i | \(0.157374\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21648.3 | + | 10228.9i | 1.46200 | + | 0.690801i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1638.63 | − | 2838.18i | 0.110115 | − | 0.190725i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3506.39 | − | 6073.24i | −0.234464 | − | 0.406104i | 0.724653 | − | 0.689114i | \(-0.242000\pi\) |
−0.959117 | + | 0.283010i | \(0.908667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7176.30 | + | 7791.75i | −0.477501 | + | 0.518453i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9587.08 | 0.634782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10045.8 | 0.661903 | 0.330952 | − | 0.943648i | \(-0.392630\pi\) | ||||
0.330952 | + | 0.943648i | \(0.392630\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9121.66 | − | 2046.53i | −0.598083 | − | 0.134186i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9874.66 | + | 17103.4i | 0.644309 | + | 1.11598i | 0.984461 | + | 0.175605i | \(0.0561883\pi\) |
−0.340152 | + | 0.940371i | \(0.610478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8995.65 | + | 15580.9i | −0.584112 | + | 1.01171i | 0.410873 | + | 0.911693i | \(0.365224\pi\) |
−0.994985 | + | 0.100020i | \(0.968109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2826.78 | − | 20276.9i | 0.182665 | − | 1.31028i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4997.62 | − | 8656.14i | 0.321389 | − | 0.556663i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1582.33 | + | 2740.67i | 0.101269 | + | 0.175403i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22132.0 | + | 4965.52i | 1.40967 | + | 0.316274i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23244.0 | 1.47345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14458.5 | 0.912175 | 0.456087 | − | 0.889935i | \(-0.349250\pi\) | ||||
0.456087 | + | 0.889935i | \(0.349250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6064.11 | + | 6584.18i | −0.380769 | + | 0.413424i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1895.17 | + | 3282.53i | 0.118437 | + | 0.205139i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −971.455 | + | 1682.61i | −0.0604246 | + | 0.104658i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13195.9 | + | 9140.36i | −0.816935 | + | 0.565864i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10467.4 | + | 18130.0i | −0.644985 | + | 1.11715i | 0.339320 | + | 0.940671i | \(0.389803\pi\) |
−0.984305 | + | 0.176476i | \(0.943530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 855.505 | + | 1481.78i | 0.0524694 | + | 0.0908797i | 0.891067 | − | 0.453871i | \(-0.149957\pi\) |
−0.838598 | + | 0.544751i | \(0.816624\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −494.838 | − | 1583.43i | −0.0302081 | − | 0.0966628i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20098.7 | −1.22127 | −0.610636 | − | 0.791912i | \(-0.709086\pi\) | ||||
−0.610636 | + | 0.791912i | \(0.709086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7593.91 | −0.459302 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2898.26 | + | 9274.13i | 0.174488 | + | 0.558344i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3901.88 | − | 6758.26i | −0.233832 | − | 0.405010i | 0.725100 | − | 0.688643i | \(-0.241793\pi\) |
−0.958933 | + | 0.283634i | \(0.908460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −845.169 | + | 1463.88i | −0.0504176 | + | 0.0873258i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15647.0 | + | 10838.2i | −0.929144 | + | 0.643588i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14784.9 | + | 25608.2i | −0.873958 | + | 1.51374i | −0.0160894 | + | 0.999871i | \(0.505122\pi\) |
−0.857869 | + | 0.513869i | \(0.828212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10529.2 | − | 18237.1i | −0.619575 | − | 1.07313i | −0.989563 | − | 0.144099i | \(-0.953972\pi\) |
0.369989 | − | 0.929036i | \(-0.379362\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9499.76 | − | 10314.5i | 0.556471 | − | 0.604195i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5628.48 | 0.328215 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42498.5 | 2.46709 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21329.5 | + | 4785.47i | 1.23265 | + | 0.276558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14210.8 | − | 24613.8i | −0.817586 | − | 1.41610i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12119.1 | − | 20990.8i | 0.694139 | − | 1.20228i | −0.276331 | − | 0.961063i | \(-0.589119\pi\) |
0.970470 | − | 0.241222i | \(-0.0775481\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8507.59 | − | 3448.28i | 0.485122 | − | 0.196629i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10950.2 | − | 18966.4i | 0.621642 | − | 1.07672i | −0.367538 | − | 0.930008i | \(-0.619799\pi\) |
0.989180 | − | 0.146707i | \(-0.0468674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 535.969 | + | 928.325i | 0.0302925 | + | 0.0524681i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10586.8 | − | 2375.25i | −0.595723 | − | 0.133656i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7529.77 | −0.421843 | −0.210921 | − | 0.977503i | \(-0.567646\pi\) | ||||
−0.210921 | + | 0.977503i | \(0.567646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8195.12 | 0.457109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14336.3 | − | 15565.8i | 0.796162 | − | 0.864443i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10019.3 | + | 17354.0i | 0.553999 | + | 0.959555i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14569.6 | − | 25235.3i | 0.802105 | − | 1.38929i | −0.116123 | − | 0.993235i | \(-0.537047\pi\) |
0.918228 | − | 0.396052i | \(-0.129620\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7160.08 | − | 3383.17i | −0.392481 | − | 0.185449i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 550.557 | − | 953.593i | 0.0300487 | − | 0.0520458i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7932.51 | + | 13739.5i | 0.431084 | + | 0.746659i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5318.94 | − | 17020.1i | −0.287812 | − | 0.920970i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23973.7 | −1.29169 | −0.645844 | − | 0.763470i | \(-0.723494\pi\) | ||||
−0.645844 | + | 0.763470i | \(0.723494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35580.1 | 1.90886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2892.33 | + | 9255.16i | 0.154513 | + | 0.494425i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3587.97 | − | 6214.55i | −0.190862 | − | 0.330583i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5860.85 | + | 10151.3i | −0.310450 | + | 0.537714i | −0.978460 | − | 0.206438i | \(-0.933813\pi\) |
0.668010 | + | 0.744152i | \(0.267146\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1275.96 | + | 15489.7i | 0.0673026 | + | 0.817032i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19491.0 | − | 33759.4i | 1.02376 | − | 1.77321i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6411.34 | − | 11104.8i | −0.335343 | − | 0.580832i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5399.67 | − | 5862.75i | 0.281247 | − | 0.305368i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28287.7 | 1.46725 | 0.733625 | − | 0.679554i | \(-0.237827\pi\) | ||||
0.733625 | + | 0.679554i | \(0.237827\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12268.0 | −0.633683 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21618.6 | + | 4850.34i | 1.11204 | + | 0.249497i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9527.90 | + | 16502.8i | 0.488079 | + | 0.845378i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16094.2 | − | 27876.0i | 0.821048 | − | 1.42210i | −0.0838538 | − | 0.996478i | \(-0.526723\pi\) |
0.904902 | − | 0.425619i | \(-0.139944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4804.15 | + | 19087.7i | 0.244076 | + | 0.969756i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1407.69 | + | 2438.18i | −0.0712245 | + | 0.123365i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3176.49 | + | 5501.85i | 0.160063 | + | 0.277238i | 0.934891 | − | 0.354934i | \(-0.115497\pi\) |
−0.774828 | + | 0.632172i | \(0.782163\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1917.43 | − | 430.195i | −0.0962253 | − | 0.0215891i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37156.5 | −1.85709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12283.6 | −0.611447 | −0.305723 | − | 0.952120i | \(-0.598898\pi\) | ||||
−0.305723 | + | 0.952120i | \(0.598898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14541.5 | − | 15788.6i | 0.720910 | − | 0.782737i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8697.39 | + | 15064.3i | 0.429443 | + | 0.743818i | 0.996824 | − | 0.0796381i | \(-0.0253765\pi\) |
−0.567381 | + | 0.823456i | \(0.692043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9984.26 | − | 17293.2i | 0.491000 | − | 0.850437i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −755.048 | − | 9166.04i | −0.0369823 | − | 0.448953i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 866.250 | − | 1500.39i | 0.0422591 | − | 0.0731950i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5029.77 | + | 8711.82i | 0.244393 | + | 0.423301i | 0.961961 | − | 0.273188i | \(-0.0880780\pi\) |
−0.717568 | + | 0.696489i | \(0.754745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −342.749 | − | 1096.76i | −0.0165876 | − | 0.0530787i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13573.5 | 0.654290 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6358.99 | 0.305312 | 0.152656 | − | 0.988279i | \(-0.451217\pi\) | ||||
0.152656 | + | 0.988279i | \(0.451217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9476.83 | + | 30324.9i | 0.453211 | + | 1.45023i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15869.3 | − | 27486.5i | −0.755930 | − | 1.30931i | −0.944911 | − | 0.327329i | \(-0.893852\pi\) |
0.188980 | − | 0.981981i | \(-0.439482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4400.52 | + | 7621.93i | −0.208794 | + | 0.361641i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12823.4 | + | 6059.09i | 0.606051 | + | 0.286362i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3593.16 | + | 6223.53i | −0.169154 | + | 0.292984i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13354.6 | + | 23130.9i | 0.626242 | + | 1.08468i | 0.988299 | + | 0.152527i | \(0.0487410\pi\) |
−0.362058 | + | 0.932156i | \(0.617926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8396.99 | − | 9117.13i | 0.392231 | − | 0.425870i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26220.5 | −1.22003 | −0.610017 | − | 0.792388i | \(-0.708837\pi\) | ||||
−0.610017 | + | 0.792388i | \(0.708837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17479.0 | 0.810150 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12120.9 | − | 2719.45i | −0.559635 | − | 0.125559i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12142.5 | + | 21031.4i | 0.558471 | + | 0.967300i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12455.5 | − | 21573.5i | 0.570668 | − | 0.988426i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37866.3 | + | 15347.9i | −1.72827 | + | 0.700498i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1856.33 | − | 3215.26i | 0.0844017 | − | 0.146188i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11280.8 | − | 19538.9i | −0.510949 | − | 0.884989i | −0.999919 | − | 0.0126892i | \(-0.995961\pi\) |
0.488971 | − | 0.872300i | \(-0.337373\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11186.5 | − | 2509.80i | −0.504753 | − | 0.113246i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3492.33 | 0.156982 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26896.0 | −1.20442 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13730.4 | + | 14908.0i | −0.612538 | + | 0.665070i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5165.99 | − | 8947.76i | −0.229597 | − | 0.397674i | 0.728092 | − | 0.685480i | \(-0.240408\pi\) |
−0.957689 | + | 0.287806i | \(0.907074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8227.93 | − | 14251.2i | 0.364309 | − | 0.631002i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31692.7 | − | 21952.5i | 1.39801 | − | 0.968357i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14769.1 | − | 25580.7i | 0.649052 | − | 1.12419i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3941.95 | + | 6827.66i | 0.172591 | + | 0.298936i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6330.24 | − | 20256.1i | −0.276128 | − | 0.883581i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19586.3 | 0.851194 | 0.425597 | − | 0.904913i | \(-0.360064\pi\) | ||||
0.425597 | + | 0.904913i | \(0.360064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5057.68 | −0.218988 | −0.109494 | − | 0.993987i | \(-0.534923\pi\) | ||||
−0.109494 | + | 0.993987i | \(0.534923\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4238.78 | − | 13563.7i | −0.182854 | − | 0.585116i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11453.5 | + | 19838.0i | 0.492266 | + | 0.852630i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2154.77 | + | 3732.18i | −0.0922717 | + | 0.159819i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6160.54 | + | 4267.20i | −0.262841 | + | 0.182061i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7583.11 | + | 13134.3i | −0.322354 | + | 0.558333i | −0.980973 | − | 0.194143i | \(-0.937807\pi\) |
0.658619 | + | 0.752476i | \(0.271141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14526.0 | + | 25159.7i | 0.615242 | + | 1.06563i | 0.990342 | + | 0.138646i | \(0.0442749\pi\) |
−0.375100 | + | 0.926984i | \(0.622392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9650.97 | + | 10478.7i | −0.407277 | + | 0.442206i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4623.53 | −0.194409 | −0.0972044 | − | 0.995264i | \(-0.530990\pi\) | ||||
−0.0972044 | + | 0.995264i | \(0.530990\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26368.0 | −1.10470 | −0.552350 | − | 0.833612i | \(-0.686269\pi\) | ||||
−0.552350 | + | 0.833612i | \(0.686269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −739.311 | − | 165.872i | −0.0308621 | − | 0.00692422i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1667.47 | + | 2888.13i | 0.0693568 | + | 0.120130i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3555.24 | − | 6157.86i | 0.147346 | − | 0.255212i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5174.68 | + | 37118.8i | −0.213695 | + | 1.53287i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4781.51 | − | 8281.81i | 0.196753 | − | 0.340787i | −0.750721 | − | 0.660620i | \(-0.770294\pi\) |
0.947474 | + | 0.319833i | \(0.103627\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30213.1 | − | 52330.7i | −1.23880 | − | 2.14567i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37686.9 | + | 8455.42i | 1.53975 | + | 0.345457i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4822.08 | 0.196313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2972.36 | 0.120580 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19158.8 | + | 20801.9i | −0.774474 | + | 0.840894i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24918.8 | + | 43160.6i | 1.00377 | + | 1.73857i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4274.68 | − | 7403.96i | 0.171585 | − | 0.297194i | −0.767389 | − | 0.641182i | \(-0.778444\pi\) |
0.938974 | + | 0.343987i | \(0.111778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19629.0 | + | 9274.77i | 0.785142 | + | 0.370983i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −969.021 | + | 1678.39i | −0.0386244 | + | 0.0668995i | −0.884691 | − | 0.466177i | \(-0.845631\pi\) |
0.846067 | + | 0.533077i | \(0.178964\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14860.6 | + | 25739.3i | 0.590263 | + | 1.02237i | 0.994197 | + | 0.107578i | \(0.0343095\pi\) |
−0.403933 | + | 0.914788i | \(0.632357\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2529.06 | − | 8092.74i | −0.100105 | − | 0.320325i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28125.2 | 1.10938 | 0.554688 | − | 0.832058i | \(-0.312838\pi\) | ||||
0.554688 | + | 0.832058i | \(0.312838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8103.81 | −0.318541 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 435.318 | + | 1392.97i | 0.0170521 | + | 0.0545650i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12059.6 | − | 20887.9i | −0.470765 | − | 0.815389i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17581.1 | + | 30451.4i | −0.683941 | + | 1.18462i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 339.437 | + | 4120.66i | 0.0131595 | + | 0.159752i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5144.16 | + | 8909.95i | −0.198748 | + | 0.344241i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10763.2 | + | 18642.3i | 0.414419 | + | 0.717796i | 0.995367 | − | 0.0961452i | \(-0.0306513\pi\) |
−0.580948 | + | 0.813941i | \(0.697318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9786.10 | + | 10625.4i | −0.375514 | + | 0.407719i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41820.1 | −1.59927 | −0.799634 | − | 0.600488i | \(-0.794973\pi\) | ||||
−0.799634 | + | 0.600488i | \(0.794973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28659.1 | −1.09225 | −0.546124 | − | 0.837704i | \(-0.683897\pi\) | ||||
−0.546124 | + | 0.837704i | \(0.683897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7092.08 | − | 1591.18i | −0.269376 | − | 0.0604371i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 813.010 | + | 1408.18i | 0.0307759 | + | 0.0533054i | 0.881003 | − | 0.473110i | \(-0.156869\pi\) |
−0.850227 | + | 0.526416i | \(0.823536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1718.86 | + | 2977.15i | −0.0648466 | + | 0.112318i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19395.5 | − | 23597.2i | −0.729262 | − | 0.887244i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12594.7 | − | 21814.6i | 0.471964 | − | 0.817466i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5539.22 | + | 9594.22i | 0.206878 | + | 0.358323i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29336.6 | + | 6581.96i | 1.09200 | + | 0.245000i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −77797.3 | −2.88619 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34395.5 | 1.27179 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1019.32 | − | 1106.73i | 0.0375644 | − | 0.0407860i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3263.61 | + | 5652.74i | 0.119874 | + | 0.207628i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12888.7 | + | 22323.8i | −0.471843 | + | 0.817256i | −0.999481 | − | 0.0322135i | \(-0.989744\pi\) |
0.527638 | + | 0.849469i | \(0.323078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2272.32 | − | 27585.2i | −0.0829132 | − | 1.00654i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7520.47 | + | 13025.8i | −0.273506 | + | 0.473727i | −0.969757 | − | 0.244072i | \(-0.921517\pi\) |
0.696251 | + | 0.717799i | \(0.254850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7136.28 | + | 12360.4i | 0.258682 | + | 0.448050i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8114.27 | − | 25964.9i | −0.293169 | − | 0.938111i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1533.08 | −0.0552092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5117.68 | −0.183696 | −0.0918480 | − | 0.995773i | \(-0.529277\pi\) | ||||
−0.0918480 | + | 0.995773i | \(0.529277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3819.96 | − | 12223.5i | −0.136669 | − | 0.437326i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11786.9 | − | 20415.6i | −0.420338 | − | 0.728047i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11173.3 | + | 19352.7i | −0.397162 | + | 0.687905i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42784.0 | − | 20215.6i | −1.51587 | − | 0.716255i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18761.3 | − | 32495.5i | 0.662581 | − | 1.14762i | −0.317353 | − | 0.948307i | \(-0.602794\pi\) |
0.979935 | − | 0.199317i | \(-0.0638725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2552.42 | + | 4420.93i | 0.0898521 | + | 0.155628i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11928.0 | + | 12951.0i | −0.418548 | + | 0.454443i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22009.6 | −0.769831 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1480.05 | −0.0516019 | −0.0258010 | − | 0.999667i | \(-0.508214\pi\) | ||||
−0.0258010 | + | 0.999667i | \(0.508214\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 53623.4 | + | 12030.9i | 1.86362 | + | 0.418120i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8643.42 | + | 14970.8i | 0.299434 | + | 0.518635i | 0.976007 | − | 0.217741i | \(-0.0698688\pi\) |
−0.676573 | + | 0.736376i | \(0.736536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17008.1 | + | 29458.9i | −0.587339 | + | 1.01730i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5978.04 | − | 4659.88i | −0.205784 | − | 0.160408i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11234.6 | − | 19458.9i | 0.385508 | − | 0.667720i | −0.606331 | − | 0.795212i | \(-0.707359\pi\) |
0.991840 | + | 0.127492i | \(0.0406928\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13976.3 | − | 24207.7i | −0.478073 | − | 0.828047i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47897.7 | − | 10746.3i | −1.63322 | − | 0.366428i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26138.5 | 0.888468 | 0.444234 | − | 0.895911i | \(-0.353476\pi\) | ||||
0.444234 | + | 0.895911i | \(0.353476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19903.2 | −0.674400 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42955.4 | − | 46639.4i | 1.45094 | − | 1.57538i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3716.35 | + | 6436.91i | 0.125138 | + | 0.216745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20784.5 | + | 35999.9i | −0.697678 | + | 1.20841i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5493.38 | − | 3805.08i | 0.183823 | − | 0.127328i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17567.7 | − | 30428.1i | 0.586035 | − | 1.01504i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19505.6 | − | 33784.6i | −0.648662 | − | 1.12352i | −0.983443 | − | 0.181220i | \(-0.941995\pi\) |
0.334780 | − | 0.942296i | \(-0.391338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10989.8 | − | 35166.1i | −0.364337 | − | 1.16584i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6211.92 | 0.205304 | 0.102652 | − | 0.994717i | \(-0.467267\pi\) | ||||
0.102652 | + | 0.994717i | \(0.467267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 998.675 | 0.0329045 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4021.22 | + | 12867.5i | 0.132084 | + | 0.422656i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9656.01 | + | 16724.7i | 0.316195 | + | 0.547667i | 0.979691 | − | 0.200514i | \(-0.0642611\pi\) |
−0.663495 | + | 0.748180i | \(0.730928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29914.5 | + | 51813.4i | −0.976579 | + | 1.69148i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27906.2 | + | 19329.7i | −0.908232 | + | 0.629103i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7520.24 | + | 13025.4i | −0.244006 | + | 0.422631i | −0.961852 | − | 0.273571i | \(-0.911795\pi\) |
0.717845 | + | 0.696203i | \(0.245128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10813.0 | − | 18728.7i | −0.349779 | − | 0.605835i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5957.90 | + | 6468.86i | −0.192140 | + | 0.208618i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6036.45 | −0.194083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16045.6 | −0.514333 | −0.257166 | − | 0.966367i | \(-0.582789\pi\) | ||||
−0.257166 | + | 0.966367i | \(0.582789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26809.2 | + | 6014.91i | 0.856762 | + | 0.192223i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1336.44 | + | 2314.78i | 0.0425808 | + | 0.0737521i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7021.12 | − | 12160.9i | 0.223030 | − | 0.386300i | −0.732696 | − | 0.680556i | \(-0.761738\pi\) |
0.955727 | + | 0.294256i | \(0.0950718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37789.8 | − | 29457.1i | −1.19681 | − | 0.932915i |
(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 | 252.4.j.b.169.3 | yes | 18 | |
3.2 | odd | 2 | 756.4.j.b.505.3 | 18 | |||
9.2 | odd | 6 | 2268.4.a.h.1.7 | 9 | |||
9.4 | even | 3 | inner | 252.4.j.b.85.3 | ✓ | 18 | |
9.5 | odd | 6 | 756.4.j.b.253.3 | 18 | |||
9.7 | even | 3 | 2268.4.a.i.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.j.b.85.3 | ✓ | 18 | 9.4 | even | 3 | inner | |
252.4.j.b.169.3 | yes | 18 | 1.1 | even | 1 | trivial | |
756.4.j.b.253.3 | 18 | 9.5 | odd | 6 | |||
756.4.j.b.505.3 | 18 | 3.2 | odd | 2 | |||
2268.4.a.h.1.7 | 9 | 9.2 | odd | 6 | |||
2268.4.a.i.1.3 | 9 | 9.7 | even | 3 |