Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.12 | ||
Root | \(-1.85197 - 2.13780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.5.c.a.31.11 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28004 | + | 3.78966i | 0.320009 | + | 0.947415i | ||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | −12.7230 | + | 9.70180i | −0.795189 | + | 0.606362i | ||||
\(5\) | 11.1803 | 0.447214 | ||||||||
\(6\) | 19.6916 | − | 6.65126i | 0.546990 | − | 0.184757i | ||||
\(7\) | 89.0673i | 1.81770i | 0.417124 | + | 0.908850i | \(0.363038\pi\) | ||||
−0.417124 | + | 0.908850i | \(0.636962\pi\) | |||||||
\(8\) | −53.0524 | − | 35.7972i | −0.828944 | − | 0.559332i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 14.3112 | + | 42.3697i | 0.143112 | + | 0.423697i | ||||
\(11\) | 174.486i | 1.44203i | 0.692918 | + | 0.721017i | \(0.256325\pi\) | ||||
−0.692918 | + | 0.721017i | \(0.743675\pi\) | |||||||
\(12\) | 50.4120 | + | 66.1107i | 0.350083 | + | 0.459102i | ||||
\(13\) | −22.9919 | −0.136047 | −0.0680235 | − | 0.997684i | \(-0.521669\pi\) | ||||
−0.0680235 | + | 0.997684i | \(0.521669\pi\) | |||||||
\(14\) | −337.534 | + | 114.009i | −1.72211 | + | 0.581680i | ||||
\(15\) | − | 58.0948i | − | 0.258199i | ||||||
\(16\) | 67.7503 | − | 246.872i | 0.264650 | − | 0.964345i | ||||
\(17\) | 69.2339 | 0.239563 | 0.119782 | − | 0.992800i | \(-0.461781\pi\) | ||||
0.119782 | + | 0.992800i | \(0.461781\pi\) | |||||||
\(18\) | −34.5610 | − | 102.321i | −0.106670 | − | 0.315805i | ||||
\(19\) | − | 341.023i | − | 0.944662i | −0.881421 | − | 0.472331i | \(-0.843413\pi\) | ||
0.881421 | − | 0.472331i | \(-0.156587\pi\) | |||||||
\(20\) | −142.248 | + | 108.469i | −0.355619 | + | 0.271173i | ||||
\(21\) | 462.807 | 1.04945 | ||||||||
\(22\) | −661.242 | + | 223.348i | −1.36620 | + | 0.461464i | ||||
\(23\) | 319.580i | 0.604120i | 0.953289 | + | 0.302060i | \(0.0976743\pi\) | ||||
−0.953289 | + | 0.302060i | \(0.902326\pi\) | |||||||
\(24\) | −186.008 | + | 275.668i | −0.322930 | + | 0.478591i | ||||
\(25\) | 125.000 | 0.200000 | ||||||||
\(26\) | −29.4305 | − | 87.1316i | −0.0435362 | − | 0.128893i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | −864.112 | − | 1133.20i | −1.10218 | − | 1.44541i | ||||
\(29\) | 679.276 | 0.807701 | 0.403850 | − | 0.914825i | \(-0.367672\pi\) | ||||
0.403850 | + | 0.914825i | \(0.367672\pi\) | |||||||
\(30\) | 220.159 | − | 74.3634i | 0.244621 | − | 0.0826260i | ||||
\(31\) | − | 72.5397i | − | 0.0754835i | −0.999288 | − | 0.0377418i | \(-0.987984\pi\) | ||
0.999288 | − | 0.0377418i | \(-0.0120164\pi\) | |||||||
\(32\) | 1022.28 | − | 59.2548i | 0.998324 | − | 0.0578660i | ||||
\(33\) | 906.656 | 0.832558 | ||||||||
\(34\) | 88.6218 | + | 262.373i | 0.0766625 | + | 0.226966i | ||||
\(35\) | 995.802i | 0.812900i | ||||||||
\(36\) | 343.521 | − | 261.948i | 0.265063 | − | 0.202121i | ||||
\(37\) | 2373.44 | 1.73371 | 0.866853 | − | 0.498564i | \(-0.166139\pi\) | ||||
0.866853 | + | 0.498564i | \(0.166139\pi\) | |||||||
\(38\) | 1292.36 | − | 436.521i | 0.894986 | − | 0.302300i | ||||
\(39\) | 119.470i | 0.0785467i | ||||||||
\(40\) | −593.144 | − | 400.225i | −0.370715 | − | 0.250141i | ||||
\(41\) | −762.724 | −0.453732 | −0.226866 | − | 0.973926i | \(-0.572848\pi\) | ||||
−0.226866 | + | 0.973926i | \(0.572848\pi\) | |||||||
\(42\) | 592.410 | + | 1753.88i | 0.335833 | + | 0.994263i | ||||
\(43\) | − | 3111.55i | − | 1.68283i | −0.540390 | − | 0.841415i | \(-0.681723\pi\) | ||
0.540390 | − | 0.841415i | \(-0.318277\pi\) | |||||||
\(44\) | −1692.83 | − | 2219.99i | −0.874395 | − | 1.14669i | ||||
\(45\) | −301.869 | −0.149071 | ||||||||
\(46\) | −1211.10 | + | 409.073i | −0.572352 | + | 0.193324i | ||||
\(47\) | − | 315.636i | − | 0.142886i | −0.997445 | − | 0.0714432i | \(-0.977240\pi\) | ||
0.997445 | − | 0.0714432i | \(-0.0227605\pi\) | |||||||
\(48\) | −1282.79 | − | 352.041i | −0.556765 | − | 0.152796i | ||||
\(49\) | −5531.98 | −2.30403 | ||||||||
\(50\) | 160.004 | + | 473.707i | 0.0640018 | + | 0.189483i | ||||
\(51\) | − | 359.750i | − | 0.138312i | ||||||
\(52\) | 292.527 | − | 223.063i | 0.108183 | − | 0.0824937i | ||||
\(53\) | 3385.94 | 1.20539 | 0.602695 | − | 0.797972i | \(-0.294094\pi\) | ||||
0.602695 | + | 0.797972i | \(0.294094\pi\) | |||||||
\(54\) | −531.674 | + | 179.584i | −0.182330 | + | 0.0615858i | ||||
\(55\) | 1950.81i | 0.644897i | ||||||||
\(56\) | 3188.36 | − | 4725.23i | 1.01670 | − | 1.50677i | ||||
\(57\) | −1772.01 | −0.545401 | ||||||||
\(58\) | 869.498 | + | 2574.22i | 0.258471 | + | 0.765227i | ||||
\(59\) | 6683.46i | 1.91998i | 0.280032 | + | 0.959991i | \(0.409655\pi\) | ||||
−0.280032 | + | 0.959991i | \(0.590345\pi\) | |||||||
\(60\) | 563.623 | + | 739.140i | 0.156562 | + | 0.205317i | ||||
\(61\) | −5316.04 | −1.42866 | −0.714330 | − | 0.699809i | \(-0.753268\pi\) | ||||
−0.714330 | + | 0.699809i | \(0.753268\pi\) | |||||||
\(62\) | 274.901 | − | 92.8534i | 0.0715142 | − | 0.0241554i | ||||
\(63\) | − | 2404.82i | − | 0.605900i | ||||||
\(64\) | 1533.12 | + | 3798.26i | 0.374296 | + | 0.927309i | ||||
\(65\) | −257.058 | −0.0608420 | ||||||||
\(66\) | 1160.55 | + | 3435.92i | 0.266426 | + | 0.788778i | ||||
\(67\) | − | 4015.09i | − | 0.894429i | −0.894427 | − | 0.447215i | \(-0.852416\pi\) | ||
0.894427 | − | 0.447215i | \(-0.147584\pi\) | |||||||
\(68\) | −880.863 | + | 671.693i | −0.190498 | + | 0.145262i | ||||
\(69\) | 1660.58 | 0.348789 | ||||||||
\(70\) | −3773.75 | + | 1274.66i | −0.770153 | + | 0.260135i | ||||
\(71\) | − | 2954.05i | − | 0.586005i | −0.956112 | − | 0.293002i | \(-0.905346\pi\) | ||
0.956112 | − | 0.293002i | \(-0.0946544\pi\) | |||||||
\(72\) | 1432.41 | + | 966.525i | 0.276315 | + | 0.186444i | ||||
\(73\) | 5741.92 | 1.07749 | 0.538743 | − | 0.842470i | \(-0.318899\pi\) | ||||
0.538743 | + | 0.842470i | \(0.318899\pi\) | |||||||
\(74\) | 3038.09 | + | 8994.54i | 0.554801 | + | 1.64254i | ||||
\(75\) | − | 649.519i | − | 0.115470i | ||||||
\(76\) | 3308.53 | + | 4338.84i | 0.572807 | + | 0.751184i | ||||
\(77\) | −15541.0 | −2.62118 | ||||||||
\(78\) | −452.749 | + | 152.925i | −0.0744163 | + | 0.0251357i | ||||
\(79\) | − | 414.704i | − | 0.0664484i | −0.999448 | − | 0.0332242i | \(-0.989422\pi\) | ||
0.999448 | − | 0.0332242i | \(-0.0105775\pi\) | |||||||
\(80\) | 757.472 | − | 2760.12i | 0.118355 | − | 0.431268i | ||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −976.314 | − | 2890.46i | −0.145198 | − | 0.429873i | ||||
\(83\) | 9738.88i | 1.41368i | 0.707371 | + | 0.706842i | \(0.249881\pi\) | ||||
−0.707371 | + | 0.706842i | \(0.750119\pi\) | |||||||
\(84\) | −5888.30 | + | 4490.06i | −0.834510 | + | 0.636346i | ||||
\(85\) | 774.058 | 0.107136 | ||||||||
\(86\) | 11791.7 | − | 3982.90i | 1.59434 | − | 0.538521i | ||||
\(87\) | − | 3529.62i | − | 0.466326i | ||||||
\(88\) | 6246.12 | − | 9256.90i | 0.806575 | − | 1.19536i | ||||
\(89\) | −8192.42 | −1.03427 | −0.517133 | − | 0.855905i | \(-0.673001\pi\) | ||||
−0.517133 | + | 0.855905i | \(0.673001\pi\) | |||||||
\(90\) | −386.403 | − | 1143.98i | −0.0477041 | − | 0.141232i | ||||
\(91\) | − | 2047.83i | − | 0.247292i | ||||||
\(92\) | −3100.50 | − | 4066.02i | −0.366316 | − | 0.480389i | ||||
\(93\) | −376.927 | −0.0435804 | ||||||||
\(94\) | 1196.15 | − | 404.025i | 0.135373 | − | 0.0457249i | ||||
\(95\) | − | 3812.75i | − | 0.422466i | ||||||
\(96\) | −307.897 | − | 5311.94i | −0.0334089 | − | 0.576383i | ||||
\(97\) | 9564.24 | 1.01650 | 0.508250 | − | 0.861210i | \(-0.330293\pi\) | ||||
0.508250 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(98\) | −7081.13 | − | 20964.3i | −0.737310 | − | 2.18287i | ||||
\(99\) | − | 4711.12i | − | 0.480678i | ||||||
\(100\) | −1590.38 | + | 1212.72i | −0.159038 | + | 0.121272i | ||||
\(101\) | −1386.95 | −0.135962 | −0.0679809 | − | 0.997687i | \(-0.521656\pi\) | ||||
−0.0679809 | + | 0.997687i | \(0.521656\pi\) | |||||||
\(102\) | 1363.33 | − | 460.492i | 0.131039 | − | 0.0442611i | ||||
\(103\) | − | 627.330i | − | 0.0591318i | −0.999563 | − | 0.0295659i | \(-0.990588\pi\) | ||
0.999563 | − | 0.0295659i | \(-0.00941250\pi\) | |||||||
\(104\) | 1219.78 | + | 823.048i | 0.112775 | + | 0.0760954i | ||||
\(105\) | 5174.34 | 0.469328 | ||||||||
\(106\) | 4334.12 | + | 12831.5i | 0.385735 | + | 1.14200i | ||||
\(107\) | 2988.95i | 0.261067i | 0.991444 | + | 0.130533i | \(0.0416689\pi\) | ||||
−0.991444 | + | 0.130533i | \(0.958331\pi\) | |||||||
\(108\) | −1361.12 | − | 1784.99i | −0.116694 | − | 0.153034i | ||||
\(109\) | 15704.4 | 1.32181 | 0.660905 | − | 0.750469i | \(-0.270173\pi\) | ||||
0.660905 | + | 0.750469i | \(0.270173\pi\) | |||||||
\(110\) | −7392.92 | + | 2497.11i | −0.610985 | + | 0.206373i | ||||
\(111\) | − | 12332.8i | − | 1.00096i | ||||||
\(112\) | 21988.2 | + | 6034.33i | 1.75289 | + | 0.481053i | ||||
\(113\) | 19067.1 | 1.49323 | 0.746616 | − | 0.665255i | \(-0.231677\pi\) | ||||
0.746616 | + | 0.665255i | \(0.231677\pi\) | |||||||
\(114\) | −2268.23 | − | 6715.30i | −0.174533 | − | 0.516720i | ||||
\(115\) | 3573.01i | 0.270171i | ||||||||
\(116\) | −8642.44 | + | 6590.20i | −0.642274 | + | 0.489759i | ||||
\(117\) | 620.782 | 0.0453490 | ||||||||
\(118\) | −25328.0 | + | 8555.06i | −1.81902 | + | 0.614411i | ||||
\(119\) | 6166.47i | 0.435454i | ||||||||
\(120\) | −2079.63 | + | 3082.07i | −0.144419 | + | 0.214032i | ||||
\(121\) | −15804.4 | −1.07946 | ||||||||
\(122\) | −6804.72 | − | 20146.0i | −0.457184 | − | 1.35353i | ||||
\(123\) | 3963.23i | 0.261962i | ||||||||
\(124\) | 703.765 | + | 922.924i | 0.0457704 | + | 0.0600237i | ||||
\(125\) | 1397.54 | 0.0894427 | ||||||||
\(126\) | 9113.43 | − | 3078.25i | 0.574038 | − | 0.193893i | ||||
\(127\) | − | 375.889i | − | 0.0233052i | −0.999932 | − | 0.0116526i | \(-0.996291\pi\) | ||
0.999932 | − | 0.0116526i | \(-0.00370922\pi\) | |||||||
\(128\) | −12431.7 | + | 10671.9i | −0.758768 | + | 0.651361i | ||||
\(129\) | −16168.1 | −0.971582 | ||||||||
\(130\) | −329.043 | − | 974.160i | −0.0194700 | − | 0.0576426i | ||||
\(131\) | 11766.3i | 0.685639i | 0.939401 | + | 0.342820i | \(0.111382\pi\) | ||||
−0.939401 | + | 0.342820i | \(0.888618\pi\) | |||||||
\(132\) | −11535.4 | + | 8796.19i | −0.662041 | + | 0.504832i | ||||
\(133\) | 30374.0 | 1.71711 | ||||||||
\(134\) | 15215.8 | − | 5139.46i | 0.847395 | − | 0.286225i | ||||
\(135\) | 1568.56i | 0.0860663i | ||||||||
\(136\) | −3673.02 | − | 2478.38i | −0.198585 | − | 0.133995i | ||||
\(137\) | 1889.31 | 0.100661 | 0.0503306 | − | 0.998733i | \(-0.483973\pi\) | ||||
0.0503306 | + | 0.998733i | \(0.483973\pi\) | |||||||
\(138\) | 2125.61 | + | 6293.04i | 0.111616 | + | 0.330448i | ||||
\(139\) | 15093.1i | 0.781174i | 0.920566 | + | 0.390587i | \(0.127728\pi\) | ||||
−0.920566 | + | 0.390587i | \(0.872272\pi\) | |||||||
\(140\) | −9661.07 | − | 12669.6i | −0.492912 | − | 0.646409i | ||||
\(141\) | −1640.09 | −0.0824955 | ||||||||
\(142\) | 11194.8 | − | 3781.29i | 0.555189 | − | 0.187527i | ||||
\(143\) | − | 4011.77i | − | 0.196184i | ||||||
\(144\) | −1829.26 | + | 6665.55i | −0.0882166 | + | 0.321448i | ||||
\(145\) | 7594.54 | 0.361215 | ||||||||
\(146\) | 7349.87 | + | 21759.9i | 0.344805 | + | 1.02083i | ||||
\(147\) | 28745.0i | 1.33023i | ||||||||
\(148\) | −30197.3 | + | 23026.7i | −1.37862 | + | 1.05125i | ||||
\(149\) | 29887.1 | 1.34621 | 0.673103 | − | 0.739549i | \(-0.264961\pi\) | ||||
0.673103 | + | 0.739549i | \(0.264961\pi\) | |||||||
\(150\) | 2461.46 | − | 831.408i | 0.109398 | − | 0.0369515i | ||||
\(151\) | − | 15818.0i | − | 0.693741i | −0.937913 | − | 0.346871i | \(-0.887244\pi\) | ||
0.937913 | − | 0.346871i | \(-0.112756\pi\) | |||||||
\(152\) | −12207.7 | + | 18092.1i | −0.528379 | + | 0.783071i | ||||
\(153\) | −1869.31 | −0.0798545 | ||||||||
\(154\) | −19893.0 | − | 58895.0i | −0.838802 | − | 2.48335i | ||||
\(155\) | − | 811.018i | − | 0.0337573i | ||||||
\(156\) | −1159.07 | − | 1520.01i | −0.0476278 | − | 0.0624595i | ||||
\(157\) | −32589.5 | −1.32214 | −0.661071 | − | 0.750324i | \(-0.729898\pi\) | ||||
−0.661071 | + | 0.750324i | \(0.729898\pi\) | |||||||
\(158\) | 1571.59 | − | 530.836i | 0.0629541 | − | 0.0212641i | ||||
\(159\) | − | 17593.9i | − | 0.695932i | ||||||
\(160\) | 11429.5 | − | 662.488i | 0.446464 | − | 0.0258784i | ||||
\(161\) | −28464.1 | −1.09811 | ||||||||
\(162\) | 933.146 | + | 2762.66i | 0.0355565 | + | 0.105268i | ||||
\(163\) | 19528.4i | 0.735008i | 0.930022 | + | 0.367504i | \(0.119788\pi\) | ||||
−0.930022 | + | 0.367504i | \(0.880212\pi\) | |||||||
\(164\) | 9704.15 | − | 7399.79i | 0.360803 | − | 0.275126i | ||||
\(165\) | 10136.7 | 0.372331 | ||||||||
\(166\) | −36907.0 | + | 12466.1i | −1.33935 | + | 0.452392i | ||||
\(167\) | − | 20882.0i | − | 0.748755i | −0.927276 | − | 0.374377i | \(-0.877856\pi\) | ||
0.927276 | − | 0.374377i | \(-0.122144\pi\) | |||||||
\(168\) | −24553.0 | − | 16567.2i | −0.869934 | − | 0.586990i | ||||
\(169\) | −28032.4 | −0.981491 | ||||||||
\(170\) | 990.822 | + | 2933.42i | 0.0342845 | + | 0.101502i | ||||
\(171\) | 9207.62i | 0.314887i | ||||||||
\(172\) | 30187.6 | + | 39588.3i | 1.02040 | + | 1.33817i | ||||
\(173\) | −5278.82 | −0.176378 | −0.0881891 | − | 0.996104i | \(-0.528108\pi\) | ||||
−0.0881891 | + | 0.996104i | \(0.528108\pi\) | |||||||
\(174\) | 13376.1 | − | 4518.04i | 0.441804 | − | 0.149229i | ||||
\(175\) | 11133.4i | 0.363540i | ||||||||
\(176\) | 43075.8 | + | 11821.5i | 1.39062 | + | 0.381634i | ||||
\(177\) | 34728.3 | 1.10850 | ||||||||
\(178\) | −10486.6 | − | 31046.5i | −0.330974 | − | 0.979878i | ||||
\(179\) | − | 47041.6i | − | 1.46817i | −0.679058 | − | 0.734084i | \(-0.737612\pi\) | ||
0.679058 | − | 0.734084i | \(-0.262388\pi\) | |||||||
\(180\) | 3840.69 | − | 2928.67i | 0.118540 | − | 0.0903911i | ||||
\(181\) | −16396.0 | −0.500472 | −0.250236 | − | 0.968185i | \(-0.580508\pi\) | ||||
−0.250236 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(182\) | 7760.57 | − | 2621.29i | 0.234288 | − | 0.0791358i | ||||
\(183\) | 27623.0i | 0.824837i | ||||||||
\(184\) | 11440.1 | − | 16954.5i | 0.337904 | − | 0.500782i | ||||
\(185\) | 26535.9 | 0.775337 | ||||||||
\(186\) | −482.480 | − | 1428.43i | −0.0139461 | − | 0.0412887i | ||||
\(187\) | 12080.3i | 0.345459i | ||||||||
\(188\) | 3062.23 | + | 4015.84i | 0.0866409 | + | 0.113622i | ||||
\(189\) | −12495.8 | −0.349816 | ||||||||
\(190\) | 14449.0 | − | 4880.46i | 0.400250 | − | 0.135193i | ||||
\(191\) | − | 32485.2i | − | 0.890469i | −0.895414 | − | 0.445235i | \(-0.853120\pi\) | ||
0.895414 | − | 0.445235i | \(-0.146880\pi\) | |||||||
\(192\) | 19736.3 | − | 7966.30i | 0.535382 | − | 0.216100i | ||||
\(193\) | −10400.5 | −0.279215 | −0.139607 | − | 0.990207i | \(-0.544584\pi\) | ||||
−0.139607 | + | 0.990207i | \(0.544584\pi\) | |||||||
\(194\) | 12242.6 | + | 36245.2i | 0.325289 | + | 0.963046i | ||||
\(195\) | 1335.71i | 0.0351272i | ||||||||
\(196\) | 70383.4 | − | 53670.1i | 1.83214 | − | 1.39708i | ||||
\(197\) | −47175.4 | −1.21558 | −0.607790 | − | 0.794098i | \(-0.707944\pi\) | ||||
−0.607790 | + | 0.794098i | \(0.707944\pi\) | |||||||
\(198\) | 17853.5 | − | 6030.41i | 0.455401 | − | 0.153821i | ||||
\(199\) | − | 57145.1i | − | 1.44302i | −0.692403 | − | 0.721511i | \(-0.743448\pi\) | ||
0.692403 | − | 0.721511i | \(-0.256552\pi\) | |||||||
\(200\) | −6631.55 | − | 4474.65i | −0.165789 | − | 0.111866i | ||||
\(201\) | −20863.0 | −0.516399 | ||||||||
\(202\) | −1775.34 | − | 5256.05i | −0.0435090 | − | 0.128812i | ||||
\(203\) | 60501.3i | 1.46816i | ||||||||
\(204\) | 3490.22 | + | 4577.10i | 0.0838672 | + | 0.109984i | ||||
\(205\) | −8527.51 | −0.202915 | ||||||||
\(206\) | 2377.36 | − | 803.004i | 0.0560224 | − | 0.0189227i | ||||
\(207\) | − | 8628.65i | − | 0.201373i | ||||||
\(208\) | −1557.71 | + | 5676.07i | −0.0360048 | + | 0.131196i | ||||
\(209\) | 59503.7 | 1.36223 | ||||||||
\(210\) | 6623.34 | + | 19609.0i | 0.150189 | + | 0.444648i | ||||
\(211\) | 24560.7i | 0.551666i | 0.961206 | + | 0.275833i | \(0.0889536\pi\) | ||||
−0.961206 | + | 0.275833i | \(0.911046\pi\) | |||||||
\(212\) | −43079.3 | + | 32849.7i | −0.958512 | + | 0.730902i | ||||
\(213\) | −15349.7 | −0.338330 | ||||||||
\(214\) | −11327.1 | + | 3825.96i | −0.247338 | + | 0.0835436i | ||||
\(215\) | − | 34788.2i | − | 0.752584i | ||||||
\(216\) | 5022.21 | − | 7443.05i | 0.107643 | − | 0.159530i | ||||
\(217\) | 6460.91 | 0.137206 | ||||||||
\(218\) | 20102.2 | + | 59514.4i | 0.422991 | + | 1.25230i | ||||
\(219\) | − | 29835.9i | − | 0.622087i | ||||||
\(220\) | −18926.4 | − | 24820.2i | −0.391041 | − | 0.512815i | ||||
\(221\) | −1591.82 | −0.0325919 | ||||||||
\(222\) | 46737.0 | − | 15786.4i | 0.948319 | − | 0.320315i | ||||
\(223\) | − | 71260.5i | − | 1.43298i | −0.697599 | − | 0.716489i | \(-0.745748\pi\) | ||
0.697599 | − | 0.716489i | \(-0.254252\pi\) | |||||||
\(224\) | 5277.66 | + | 91052.0i | 0.105183 | + | 1.81465i | ||||
\(225\) | −3375.00 | −0.0666667 | ||||||||
\(226\) | 24406.6 | + | 72257.7i | 0.477848 | + | 1.41471i | ||||
\(227\) | − | 73287.1i | − | 1.42225i | −0.703066 | − | 0.711125i | \(-0.748186\pi\) | ||
0.703066 | − | 0.711125i | \(-0.251814\pi\) | |||||||
\(228\) | 22545.3 | − | 17191.6i | 0.433696 | − | 0.330710i | ||||
\(229\) | −37103.1 | −0.707520 | −0.353760 | − | 0.935336i | \(-0.615097\pi\) | ||||
−0.353760 | + | 0.935336i | \(0.615097\pi\) | |||||||
\(230\) | −13540.5 | + | 4573.58i | −0.255964 | + | 0.0864570i | ||||
\(231\) | 80753.4i | 1.51334i | ||||||||
\(232\) | −36037.2 | − | 24316.2i | −0.669538 | − | 0.451773i | ||||
\(233\) | 21001.4 | 0.386844 | 0.193422 | − | 0.981116i | \(-0.438041\pi\) | ||||
0.193422 | + | 0.981116i | \(0.438041\pi\) | |||||||
\(234\) | 794.623 | + | 2352.55i | 0.0145121 | + | 0.0429643i | ||||
\(235\) | − | 3528.92i | − | 0.0639007i | ||||||
\(236\) | −64841.5 | − | 85033.7i | −1.16420 | − | 1.52675i | ||||
\(237\) | −2154.87 | −0.0383640 | ||||||||
\(238\) | −23368.8 | + | 7893.30i | −0.412556 | + | 0.139349i | ||||
\(239\) | 8886.00i | 0.155565i | 0.996970 | + | 0.0777823i | \(0.0247839\pi\) | ||||
−0.996970 | + | 0.0777823i | \(0.975216\pi\) | |||||||
\(240\) | −14342.0 | − | 3935.94i | −0.248993 | − | 0.0683322i | ||||
\(241\) | −11033.8 | −0.189973 | −0.0949864 | − | 0.995479i | \(-0.530281\pi\) | ||||
−0.0949864 | + | 0.995479i | \(0.530281\pi\) | |||||||
\(242\) | −20230.2 | − | 59893.2i | −0.345437 | − | 1.02270i | ||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | 67636.1 | − | 51575.1i | 1.13605 | − | 0.866285i | ||||
\(245\) | −61849.4 | −1.03039 | ||||||||
\(246\) | −15019.3 | + | 5073.08i | −0.248187 | + | 0.0838303i | ||||
\(247\) | 7840.77i | 0.128518i | ||||||||
\(248\) | −2596.72 | + | 3848.41i | −0.0422204 | + | 0.0625716i | ||||
\(249\) | 50604.7 | 0.816191 | ||||||||
\(250\) | 1788.90 | + | 5296.21i | 0.0286225 | + | 0.0847393i | ||||
\(251\) | 51472.3i | 0.817008i | 0.912756 | + | 0.408504i | \(0.133949\pi\) | ||||
−0.912756 | + | 0.408504i | \(0.866051\pi\) | |||||||
\(252\) | 23331.0 | + | 30596.5i | 0.367395 | + | 0.481804i | ||||
\(253\) | −55762.2 | −0.871161 | ||||||||
\(254\) | 1424.49 | − | 481.152i | 0.0220797 | − | 0.00745787i | ||||
\(255\) | − | 4022.12i | − | 0.0618550i | ||||||
\(256\) | −56355.8 | − | 33451.3i | −0.859921 | − | 0.510427i | ||||
\(257\) | −42550.6 | −0.644227 | −0.322114 | − | 0.946701i | \(-0.604393\pi\) | ||||
−0.322114 | + | 0.946701i | \(0.604393\pi\) | |||||||
\(258\) | −20695.7 | − | 61271.6i | −0.310915 | − | 0.920491i | ||||
\(259\) | 211396.i | 3.15135i | ||||||||
\(260\) | 3270.55 | − | 2493.92i | 0.0483809 | − | 0.0368923i | ||||
\(261\) | −18340.5 | −0.269234 | ||||||||
\(262\) | −44590.1 | + | 15061.2i | −0.649585 | + | 0.219411i | ||||
\(263\) | − | 5761.02i | − | 0.0832891i | −0.999132 | − | 0.0416445i | \(-0.986740\pi\) | ||
0.999132 | − | 0.0416445i | \(-0.0132597\pi\) | |||||||
\(264\) | −48100.3 | − | 32455.8i | −0.690144 | − | 0.465676i | ||||
\(265\) | 37855.9 | 0.539066 | ||||||||
\(266\) | 38879.8 | + | 115107.i | 0.549491 | + | 1.62682i | ||||
\(267\) | 42569.0i | 0.597133i | ||||||||
\(268\) | 38953.6 | + | 51084.1i | 0.542348 | + | 0.711240i | ||||
\(269\) | 19772.4 | 0.273247 | 0.136623 | − | 0.990623i | \(-0.456375\pi\) | ||||
0.136623 | + | 0.990623i | \(0.456375\pi\) | |||||||
\(270\) | −5944.30 | + | 2007.81i | −0.0815405 | + | 0.0275420i | ||||
\(271\) | − | 60381.3i | − | 0.822174i | −0.911596 | − | 0.411087i | \(-0.865149\pi\) | ||
0.911596 | − | 0.411087i | \(-0.134851\pi\) | |||||||
\(272\) | 4690.62 | − | 17091.9i | 0.0634004 | − | 0.231022i | ||||
\(273\) | −10640.8 | −0.142774 | ||||||||
\(274\) | 2418.38 | + | 7159.84i | 0.0322125 | + | 0.0953679i | ||||
\(275\) | 21810.8i | 0.288407i | ||||||||
\(276\) | −21127.6 | + | 16110.6i | −0.277353 | + | 0.211492i | ||||
\(277\) | 137089. | 1.78666 | 0.893332 | − | 0.449398i | \(-0.148362\pi\) | ||||
0.893332 | + | 0.449398i | \(0.148362\pi\) | |||||||
\(278\) | −57197.5 | + | 19319.6i | −0.740095 | + | 0.249983i | ||||
\(279\) | 1958.57i | 0.0251612i | ||||||||
\(280\) | 35647.0 | − | 52829.7i | 0.454681 | − | 0.673848i | ||||
\(281\) | 68276.4 | 0.864685 | 0.432343 | − | 0.901709i | \(-0.357687\pi\) | ||||
0.432343 | + | 0.901709i | \(0.357687\pi\) | |||||||
\(282\) | −2099.38 | − | 6215.39i | −0.0263993 | − | 0.0781574i | ||||
\(283\) | − | 46455.4i | − | 0.580047i | −0.957019 | − | 0.290024i | \(-0.906337\pi\) | ||
0.957019 | − | 0.290024i | \(-0.0936632\pi\) | |||||||
\(284\) | 28659.6 | + | 37584.4i | 0.355331 | + | 0.465984i | ||||
\(285\) | −19811.6 | −0.243911 | ||||||||
\(286\) | 15203.2 | − | 5135.21i | 0.185868 | − | 0.0627807i | ||||
\(287\) | − | 67933.7i | − | 0.824749i | ||||||
\(288\) | −27601.7 | + | 1599.88i | −0.332775 | + | 0.0192887i | ||||
\(289\) | −78727.7 | −0.942609 | ||||||||
\(290\) | 9721.28 | + | 28780.7i | 0.115592 | + | 0.342220i | ||||
\(291\) | − | 49697.3i | − | 0.586876i | ||||||
\(292\) | −73054.6 | + | 55707.0i | −0.856805 | + | 0.653347i | ||||
\(293\) | 75824.8 | 0.883234 | 0.441617 | − | 0.897204i | \(-0.354405\pi\) | ||||
0.441617 | + | 0.897204i | \(0.354405\pi\) | |||||||
\(294\) | −108934. | + | 36794.6i | −1.26028 | + | 0.425686i | ||||
\(295\) | 74723.3i | 0.858642i | ||||||||
\(296\) | −125917. | − | 84962.7i | −1.43714 | − | 0.969717i | ||||
\(297\) | −24479.7 | −0.277519 | ||||||||
\(298\) | 38256.6 | + | 113262.i | 0.430798 | + | 1.27542i | ||||
\(299\) | − | 7347.75i | − | 0.0821887i | ||||||
\(300\) | 6301.50 | + | 8263.84i | 0.0700167 | + | 0.0918205i | ||||
\(301\) | 277137. | 3.05888 | ||||||||
\(302\) | 59944.8 | − | 20247.6i | 0.657261 | − | 0.222003i | ||||
\(303\) | 7206.79i | 0.0784976i | ||||||||
\(304\) | −84189.1 | − | 23104.4i | −0.910979 | − | 0.250004i | ||||
\(305\) | −59435.1 | −0.638916 | ||||||||
\(306\) | −2392.79 | − | 7084.06i | −0.0255542 | − | 0.0756553i | ||||
\(307\) | 115095.i | 1.22118i | 0.791947 | + | 0.610590i | \(0.209068\pi\) | ||||
−0.791947 | + | 0.610590i | \(0.790932\pi\) | |||||||
\(308\) | 197728. | − | 150776.i | 2.08433 | − | 1.58939i | ||||
\(309\) | −3259.70 | −0.0341398 | ||||||||
\(310\) | 3073.48 | − | 1038.13i | 0.0319821 | − | 0.0108026i | ||||
\(311\) | − | 45164.1i | − | 0.466953i | −0.972362 | − | 0.233476i | \(-0.924990\pi\) | ||
0.972362 | − | 0.233476i | \(-0.0750102\pi\) | |||||||
\(312\) | 4276.68 | − | 6338.15i | 0.0439337 | − | 0.0651108i | ||||
\(313\) | 27892.1 | 0.284704 | 0.142352 | − | 0.989816i | \(-0.454534\pi\) | ||||
0.142352 | + | 0.989816i | \(0.454534\pi\) | |||||||
\(314\) | −41715.7 | − | 123503.i | −0.423097 | − | 1.25262i | ||||
\(315\) | − | 26886.7i | − | 0.270967i | ||||||
\(316\) | 4023.38 | + | 5276.29i | 0.0402918 | + | 0.0528390i | ||||
\(317\) | 90168.8 | 0.897300 | 0.448650 | − | 0.893708i | \(-0.351905\pi\) | ||||
0.448650 | + | 0.893708i | \(0.351905\pi\) | |||||||
\(318\) | 66674.7 | − | 22520.8i | 0.659336 | − | 0.222704i | ||||
\(319\) | 118524.i | 1.16473i | ||||||||
\(320\) | 17140.8 | + | 42465.8i | 0.167390 | + | 0.414705i | ||||
\(321\) | 15531.0 | 0.150727 | ||||||||
\(322\) | −36435.0 | − | 107869.i | −0.351405 | − | 1.04036i | ||||
\(323\) | − | 23610.3i | − | 0.226306i | ||||||
\(324\) | −9275.08 | + | 7072.61i | −0.0883543 | + | 0.0673736i | ||||
\(325\) | −2873.99 | −0.0272094 | ||||||||
\(326\) | −74006.1 | + | 24997.1i | −0.696357 | + | 0.235209i | ||||
\(327\) | − | 81602.6i | − | 0.763148i | ||||||
\(328\) | 40464.3 | + | 27303.4i | 0.376119 | + | 0.253787i | ||||
\(329\) | 28112.8 | 0.259724 | ||||||||
\(330\) | 12975.4 | + | 38414.7i | 0.119149 | + | 0.352752i | ||||
\(331\) | − | 135944.i | − | 1.24081i | −0.784283 | − | 0.620403i | \(-0.786969\pi\) | ||
0.784283 | − | 0.620403i | \(-0.213031\pi\) | |||||||
\(332\) | −94484.6 | − | 123908.i | −0.857205 | − | 1.12415i | ||||
\(333\) | −64082.9 | −0.577902 | ||||||||
\(334\) | 79135.7 | − | 26729.7i | 0.709381 | − | 0.239608i | ||||
\(335\) | − | 44890.1i | − | 0.400001i | ||||||
\(336\) | 31355.3 | − | 114254.i | 0.277736 | − | 1.01203i | ||||
\(337\) | −83154.4 | −0.732193 | −0.366096 | − | 0.930577i | \(-0.619306\pi\) | ||||
−0.366096 | + | 0.930577i | \(0.619306\pi\) | |||||||
\(338\) | −35882.4 | − | 106233.i | −0.314086 | − | 0.929879i | ||||
\(339\) | − | 99075.5i | − | 0.862118i | ||||||
\(340\) | −9848.35 | + | 7509.75i | −0.0851934 | + | 0.0649633i | ||||
\(341\) | 12657.2 | 0.108850 | ||||||||
\(342\) | −34893.7 | + | 11786.1i | −0.298329 | + | 0.100767i | ||||
\(343\) | − | 278867.i | − | 2.37033i | ||||||
\(344\) | −111385. | + | 165075.i | −0.941260 | + | 1.39497i | ||||
\(345\) | 18565.9 | 0.155983 | ||||||||
\(346\) | −6757.08 | − | 20004.9i | −0.0564426 | − | 0.167103i | ||||
\(347\) | 119011.i | 0.988391i | 0.869351 | + | 0.494195i | \(0.164537\pi\) | ||||
−0.869351 | + | 0.494195i | \(0.835463\pi\) | |||||||
\(348\) | 34243.7 | + | 44907.5i | 0.282763 | + | 0.370817i | ||||
\(349\) | −101177. | −0.830673 | −0.415337 | − | 0.909668i | \(-0.636336\pi\) | ||||
−0.415337 | + | 0.909668i | \(0.636336\pi\) | |||||||
\(350\) | −42191.8 | + | 14251.2i | −0.344423 | + | 0.116336i | ||||
\(351\) | − | 3225.68i | − | 0.0261822i | ||||||
\(352\) | 10339.1 | + | 178374.i | 0.0834447 | + | 1.43962i | ||||
\(353\) | −204510. | −1.64121 | −0.820606 | − | 0.571495i | \(-0.806364\pi\) | ||||
−0.820606 | + | 0.571495i | \(0.806364\pi\) | |||||||
\(354\) | 44453.4 | + | 131608.i | 0.354730 | + | 1.05021i | ||||
\(355\) | − | 33027.3i | − | 0.262069i | ||||||
\(356\) | 104232. | − | 79481.2i | 0.822436 | − | 0.627140i | ||||
\(357\) | 32041.9 | 0.251410 | ||||||||
\(358\) | 178272. | − | 60214.9i | 1.39096 | − | 0.469827i | ||||
\(359\) | 45291.4i | 0.351420i | 0.984442 | + | 0.175710i | \(0.0562222\pi\) | ||||
−0.984442 | + | 0.175710i | \(0.943778\pi\) | |||||||
\(360\) | 16014.9 | + | 10806.1i | 0.123572 | + | 0.0833803i | ||||
\(361\) | 14024.4 | 0.107615 | ||||||||
\(362\) | −20987.4 | − | 62135.1i | −0.160155 | − | 0.474154i | ||||
\(363\) | 82122.0i | 0.623227i | ||||||||
\(364\) | 19867.6 | + | 26054.6i | 0.149949 | + | 0.196644i | ||||
\(365\) | 64196.7 | 0.481867 | ||||||||
\(366\) | −104682. | + | 35358.4i | −0.781462 | + | 0.263955i | ||||
\(367\) | 17522.8i | 0.130098i | 0.997882 | + | 0.0650490i | \(0.0207204\pi\) | ||||
−0.997882 | + | 0.0650490i | \(0.979280\pi\) | |||||||
\(368\) | 78895.3 | + | 21651.6i | 0.582580 | + | 0.159880i | ||||
\(369\) | 20593.5 | 0.151244 | ||||||||
\(370\) | 33966.9 | + | 100562.i | 0.248115 | + | 0.734565i | ||||
\(371\) | 301576.i | 2.19103i | ||||||||
\(372\) | 4795.65 | − | 3656.87i | 0.0346547 | − | 0.0264255i | ||||
\(373\) | −16535.7 | −0.118852 | −0.0594258 | − | 0.998233i | \(-0.518927\pi\) | ||||
−0.0594258 | + | 0.998233i | \(0.518927\pi\) | |||||||
\(374\) | −45780.4 | + | 15463.3i | −0.327292 | + | 0.110550i | ||||
\(375\) | − | 7261.84i | − | 0.0516398i | ||||||
\(376\) | −11298.9 | + | 16745.2i | −0.0799209 | + | 0.118445i | ||||
\(377\) | −15617.9 | −0.109885 | ||||||||
\(378\) | −15995.1 | − | 47354.8i | −0.111944 | − | 0.331421i | ||||
\(379\) | − | 63835.5i | − | 0.444410i | −0.975000 | − | 0.222205i | \(-0.928675\pi\) | ||
0.975000 | − | 0.222205i | \(-0.0713255\pi\) | |||||||
\(380\) | 36990.5 | + | 48509.7i | 0.256167 | + | 0.335940i | ||||
\(381\) | −1953.18 | −0.0134553 | ||||||||
\(382\) | 123108. | − | 41582.2i | 0.843643 | − | 0.284958i | ||||
\(383\) | 79806.3i | 0.544051i | 0.962290 | + | 0.272025i | \(0.0876935\pi\) | ||||
−0.962290 | + | 0.272025i | \(0.912307\pi\) | |||||||
\(384\) | 55452.8 | + | 64596.8i | 0.376063 | + | 0.438075i | ||||
\(385\) | −173754. | −1.17223 | ||||||||
\(386\) | −13313.0 | − | 39414.2i | −0.0893512 | − | 0.264532i | ||||
\(387\) | 84011.9i | 0.560943i | ||||||||
\(388\) | −121686. | + | 92790.3i | −0.808309 | + | 0.616367i | ||||
\(389\) | −159539. | −1.05431 | −0.527153 | − | 0.849770i | \(-0.676741\pi\) | ||||
−0.527153 | + | 0.849770i | \(0.676741\pi\) | |||||||
\(390\) | −5061.89 | + | 1709.76i | −0.0332800 | + | 0.0112410i | ||||
\(391\) | 22125.7i | 0.144725i | ||||||||
\(392\) | 293485. | + | 198029.i | 1.90991 | + | 1.28872i | ||||
\(393\) | 61139.3 | 0.395854 | ||||||||
\(394\) | −60386.2 | − | 178779.i | −0.388996 | − | 1.15166i | ||||
\(395\) | − | 4636.53i | − | 0.0297166i | ||||||
\(396\) | 45706.4 | + | 59939.7i | 0.291465 | + | 0.382229i | ||||
\(397\) | 147558. | 0.936231 | 0.468115 | − | 0.883667i | \(-0.344933\pi\) | ||||
0.468115 | + | 0.883667i | \(0.344933\pi\) | |||||||
\(398\) | 216561. | − | 73147.8i | 1.36714 | − | 0.461780i | ||||
\(399\) | − | 157828.i | − | 0.991374i | ||||||
\(400\) | 8468.79 | − | 30859.0i | 0.0529299 | − | 0.192869i | ||||
\(401\) | −47897.3 | −0.297867 | −0.148934 | − | 0.988847i | \(-0.547584\pi\) | ||||
−0.148934 | + | 0.988847i | \(0.547584\pi\) | |||||||
\(402\) | −26705.4 | − | 79063.8i | −0.165252 | − | 0.489244i | ||||
\(403\) | 1667.83i | 0.0102693i | ||||||||
\(404\) | 17646.2 | − | 13455.9i | 0.108115 | − | 0.0824421i | ||||
\(405\) | 8150.47 | 0.0496904 | ||||||||
\(406\) | −229279. | + | 77443.8i | −1.39095 | + | 0.469823i | ||||
\(407\) | 414133.i | 2.50006i | ||||||||
\(408\) | −12878.0 | + | 19085.6i | −0.0773623 | + | 0.114653i | ||||
\(409\) | 25189.0 | 0.150579 | 0.0752894 | − | 0.997162i | \(-0.476012\pi\) | ||||
0.0752894 | + | 0.997162i | \(0.476012\pi\) | |||||||
\(410\) | −10915.5 | − | 32316.4i | −0.0649347 | − | 0.192245i | ||||
\(411\) | − | 9817.14i | − | 0.0581168i | ||||||
\(412\) | 6086.22 | + | 7981.53i | 0.0358553 | + | 0.0470210i | ||||
\(413\) | −595277. | −3.48995 | ||||||||
\(414\) | 32699.6 | − | 11045.0i | 0.190784 | − | 0.0644413i | ||||
\(415\) | 108884.i | 0.632219i | ||||||||
\(416\) | −23504.3 | + | 1362.38i | −0.135819 | + | 0.00787249i | ||||
\(417\) | 78425.8 | 0.451011 | ||||||||
\(418\) | 76166.9 | + | 225499.i | 0.435927 | + | 1.29060i | ||||
\(419\) | − | 180642.i | − | 1.02894i | −0.857508 | − | 0.514470i | \(-0.827989\pi\) | ||
0.857508 | − | 0.514470i | \(-0.172011\pi\) | |||||||
\(420\) | −65833.2 | + | 50200.4i | −0.373204 | + | 0.284583i | ||||
\(421\) | −139551. | −0.787354 | −0.393677 | − | 0.919249i | \(-0.628797\pi\) | ||||
−0.393677 | + | 0.919249i | \(0.628797\pi\) | |||||||
\(422\) | −93076.7 | + | 31438.6i | −0.522656 | + | 0.176538i | ||||
\(423\) | 8522.17i | 0.0476288i | ||||||||
\(424\) | −179632. | − | 121207.i | −0.999200 | − | 0.674213i | ||||
\(425\) | 8654.23 | 0.0479127 | ||||||||
\(426\) | −19648.2 | − | 58170.1i | −0.108269 | − | 0.320539i | ||||
\(427\) | − | 473485.i | − | 2.59687i | ||||||
\(428\) | −28998.2 | − | 38028.5i | −0.158301 | − | 0.207597i | ||||
\(429\) | −20845.8 | −0.113267 | ||||||||
\(430\) | 131835. | − | 44530.2i | 0.713009 | − | 0.240834i | ||||
\(431\) | − | 165053.i | − | 0.888523i | −0.895897 | − | 0.444261i | \(-0.853466\pi\) | ||
0.895897 | − | 0.444261i | \(-0.146534\pi\) | |||||||
\(432\) | 34635.2 | + | 9505.11i | 0.185588 | + | 0.0509319i | ||||
\(433\) | 26213.4 | 0.139813 | 0.0699065 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699065 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(434\) | 8270.20 | + | 24484.6i | 0.0439073 | + | 0.129991i | ||||
\(435\) | − | 39462.4i | − | 0.208547i | ||||||
\(436\) | −199808. | + | 152361.i | −1.05109 | + | 0.801496i | ||||
\(437\) | 108984. | 0.570689 | ||||||||
\(438\) | 113068. | − | 38191.0i | 0.589374 | − | 0.199073i | ||||
\(439\) | 355921.i | 1.84682i | 0.383813 | + | 0.923411i | \(0.374611\pi\) | ||||
−0.383813 | + | 0.923411i | \(0.625389\pi\) | |||||||
\(440\) | 69833.7 | − | 103495.i | 0.360711 | − | 0.534583i | ||||
\(441\) | 149363. | 0.768010 | ||||||||
\(442\) | −2037.59 | − | 6032.45i | −0.0104297 | − | 0.0308780i | ||||
\(443\) | − | 114260.i | − | 0.582220i | −0.956690 | − | 0.291110i | \(-0.905975\pi\) | ||
0.956690 | − | 0.291110i | \(-0.0940246\pi\) | |||||||
\(444\) | 119650. | + | 156910.i | 0.606941 | + | 0.795948i | ||||
\(445\) | −91594.0 | −0.462538 | ||||||||
\(446\) | 270053. | − | 91216.0i | 1.35762 | − | 0.458566i | ||||
\(447\) | − | 155298.i | − | 0.777232i | ||||||
\(448\) | −338301. | + | 136550.i | −1.68557 | + | 0.680357i | ||||
\(449\) | 85579.1 | 0.424497 | 0.212249 | − | 0.977216i | \(-0.431921\pi\) | ||||
0.212249 | + | 0.977216i | \(0.431921\pi\) | |||||||
\(450\) | −4320.12 | − | 12790.1i | −0.0213339 | − | 0.0631610i | ||||
\(451\) | − | 133085.i | − | 0.654297i | ||||||
\(452\) | −242591. | + | 184985.i | −1.18740 | + | 0.905440i | ||||
\(453\) | −82192.7 | −0.400532 | ||||||||
\(454\) | 277733. | − | 93810.1i | 1.34746 | − | 0.455133i | ||||
\(455\) | − | 22895.4i | − | 0.110593i | ||||||
\(456\) | 94009.2 | + | 63432.9i | 0.452106 | + | 0.305060i | ||||
\(457\) | −388386. | −1.85965 | −0.929826 | − | 0.368000i | \(-0.880042\pi\) | ||||
−0.929826 | + | 0.368000i | \(0.880042\pi\) | |||||||
\(458\) | −47493.3 | − | 140608.i | −0.226413 | − | 0.670315i | ||||
\(459\) | 9713.24i | 0.0461040i | ||||||||
\(460\) | −34664.6 | − | 45459.4i | −0.163821 | − | 0.214837i | ||||
\(461\) | 322691. | 1.51840 | 0.759198 | − | 0.650860i | \(-0.225591\pi\) | ||||
0.759198 | + | 0.650860i | \(0.225591\pi\) | |||||||
\(462\) | −306028. | + | 103367.i | −1.43376 | + | 0.484283i | ||||
\(463\) | − | 186325.i | − | 0.869181i | −0.900628 | − | 0.434591i | \(-0.856893\pi\) | ||
0.900628 | − | 0.434591i | \(-0.143107\pi\) | |||||||
\(464\) | 46021.2 | − | 167694.i | 0.213758 | − | 0.778902i | ||||
\(465\) | −4214.18 | −0.0194898 | ||||||||
\(466\) | 26882.5 | + | 79588.0i | 0.123793 | + | 0.366501i | ||||
\(467\) | − | 119419.i | − | 0.547572i | −0.961791 | − | 0.273786i | \(-0.911724\pi\) | ||
0.961791 | − | 0.273786i | \(-0.0882760\pi\) | |||||||
\(468\) | −7898.22 | + | 6022.70i | −0.0360610 | + | 0.0274979i | ||||
\(469\) | 357613. | 1.62580 | ||||||||
\(470\) | 13373.4 | − | 4517.14i | 0.0605405 | − | 0.0204488i | ||||
\(471\) | 169340.i | 0.763339i | ||||||||
\(472\) | 239249. | − | 354573.i | 1.07391 | − | 1.59156i | ||||
\(473\) | 542922. | 2.42670 | ||||||||
\(474\) | −2758.31 | − | 8166.21i | −0.0122768 | − | 0.0363466i | ||||
\(475\) | − | 42627.9i | − | 0.188932i | ||||||
\(476\) | −59825.8 | − | 78456.1i | −0.264043 | − | 0.346268i | ||||
\(477\) | −91420.3 | −0.401796 | ||||||||
\(478\) | −33674.9 | + | 11374.4i | −0.147384 | + | 0.0497820i | ||||
\(479\) | 91602.7i | 0.399243i | 0.979873 | + | 0.199622i | \(0.0639713\pi\) | ||||
−0.979873 | + | 0.199622i | \(0.936029\pi\) | |||||||
\(480\) | −3442.39 | − | 59389.3i | −0.0149409 | − | 0.257766i | ||||
\(481\) | −54570.0 | −0.235865 | ||||||||
\(482\) | −14123.7 | − | 41814.4i | −0.0607930 | − | 0.179983i | ||||
\(483\) | 147904.i | 0.633993i | ||||||||
\(484\) | 201079. | − | 153331.i | 0.858375 | − | 0.654544i | ||||
\(485\) | 106931. | 0.454592 | ||||||||
\(486\) | 14355.2 | − | 4848.77i | 0.0607767 | − | 0.0205286i | ||||
\(487\) | − | 204150.i | − | 0.860778i | −0.902644 | − | 0.430389i | \(-0.858376\pi\) | ||
0.902644 | − | 0.430389i | \(-0.141624\pi\) | |||||||
\(488\) | 282029. | + | 190300.i | 1.18428 | + | 0.799095i | ||||
\(489\) | 101473. | 0.424357 | ||||||||
\(490\) | −79169.4 | − | 234388.i | −0.329735 | − | 0.976210i | ||||
\(491\) | 191987.i | 0.796360i | 0.917307 | + | 0.398180i | \(0.130358\pi\) | ||||
−0.917307 | + | 0.398180i | \(0.869642\pi\) | |||||||
\(492\) | −38450.5 | − | 50424.2i | −0.158844 | − | 0.208310i | ||||
\(493\) | 47028.9 | 0.193496 | ||||||||
\(494\) | −29713.9 | + | 10036.5i | −0.121760 | + | 0.0411270i | ||||
\(495\) | − | 52672.0i | − | 0.214966i | ||||||
\(496\) | −17908.0 | − | 4914.59i | −0.0727922 | − | 0.0199767i | ||||
\(497\) | 263109. | 1.06518 | ||||||||
\(498\) | 64775.8 | + | 191774.i | 0.261189 | + | 0.773272i | ||||
\(499\) | 86859.0i | 0.348830i | 0.984672 | + | 0.174415i | \(0.0558034\pi\) | ||||
−0.984672 | + | 0.174415i | \(0.944197\pi\) | |||||||
\(500\) | −17781.0 | + | 13558.7i | −0.0711238 | + | 0.0542347i | ||||
\(501\) | −108506. | −0.432294 | ||||||||
\(502\) | −195063. | + | 65886.4i | −0.774046 | + | 0.261450i | ||||
\(503\) | 351571.i | 1.38956i | 0.719222 | + | 0.694780i | \(0.244498\pi\) | ||||
−0.719222 | + | 0.694780i | \(0.755502\pi\) | |||||||
\(504\) | −86085.8 | + | 127581.i | −0.338899 | + | 0.502257i | ||||
\(505\) | −15506.5 | −0.0608040 | ||||||||
\(506\) | −71377.6 | − | 211320.i | −0.278779 | − | 0.825351i | ||||
\(507\) | 145660.i | 0.566664i | ||||||||
\(508\) | 3646.80 | + | 4782.45i | 0.0141314 | + | 0.0185320i | ||||
\(509\) | −50040.2 | −0.193145 | −0.0965725 | − | 0.995326i | \(-0.530788\pi\) | ||||
−0.0965725 | + | 0.995326i | \(0.530788\pi\) | |||||||
\(510\) | 15242.5 | − | 5148.46i | 0.0586024 | − | 0.0197942i | ||||
\(511\) | 511417.i | 1.95855i | ||||||||
\(512\) | 54631.7 | − | 256388.i | 0.208403 | − | 0.978043i | ||||
\(513\) | 47844.2 | 0.181800 | ||||||||
\(514\) | −54466.3 | − | 161252.i | −0.206159 | − | 0.610350i | ||||
\(515\) | − | 7013.76i | − | 0.0264446i | ||||||
\(516\) | 205707. | − | 156860.i | 0.772591 | − | 0.589131i | ||||
\(517\) | 55074.1 | 0.206047 | ||||||||
\(518\) | −801119. | + | 270594.i | −2.98564 | + | 1.00846i | ||||
\(519\) | 27429.6i | 0.101832i | ||||||||
\(520\) | 13637.5 | + | 9201.95i | 0.0504346 | + | 0.0340309i | ||||
\(521\) | −149074. | −0.549195 | −0.274598 | − | 0.961559i | \(-0.588545\pi\) | ||||
−0.274598 | + | 0.961559i | \(0.588545\pi\) | |||||||
\(522\) | −23476.4 | − | 69504.1i | −0.0861571 | − | 0.255076i | ||||
\(523\) | − | 109372.i | − | 0.399854i | −0.979811 | − | 0.199927i | \(-0.935930\pi\) | ||
0.979811 | − | 0.199927i | \(-0.0640705\pi\) | |||||||
\(524\) | −114154. | − | 149702.i | −0.415746 | − | 0.545213i | ||||
\(525\) | 57850.9 | 0.209890 | ||||||||
\(526\) | 21832.3 | − | 7374.31i | 0.0789093 | − | 0.0266532i | ||||
\(527\) | − | 5022.20i | − | 0.0180831i | ||||||
\(528\) | 61426.2 | − | 223828.i | 0.220336 | − | 0.802873i | ||||
\(529\) | 177710. | 0.635039 | ||||||||
\(530\) | 48457.0 | + | 143461.i | 0.172506 | + | 0.510719i | ||||
\(531\) | − | 180453.i | − | 0.639994i | ||||||
\(532\) | −386448. | + | 294682.i | −1.36543 | + | 1.04119i | ||||
\(533\) | 17536.5 | 0.0617289 | ||||||||
\(534\) | −161322. | + | 54489.9i | −0.565733 | + | 0.191088i | ||||
\(535\) | 33417.5i | 0.116753i | ||||||||
\(536\) | −143729. | + | 213010.i | −0.500283 | + | 0.741432i | ||||
\(537\) | −244435. | −0.847648 | ||||||||
\(538\) | 25309.4 | + | 74930.7i | 0.0874414 | + | 0.258878i | ||||
\(539\) | − | 965252.i | − | 3.32249i | ||||||
\(540\) | −15217.8 | − | 19956.8i | −0.0521874 | − | 0.0684389i | ||||
\(541\) | 102538. | 0.350340 | 0.175170 | − | 0.984538i | \(-0.443953\pi\) | ||||
0.175170 | + | 0.984538i | \(0.443953\pi\) | |||||||
\(542\) | 228825. | − | 77290.2i | 0.778940 | − | 0.263103i | ||||
\(543\) | 85195.9i | 0.288947i | ||||||||
\(544\) | 70776.7 | − | 4102.43i | 0.239162 | − | 0.0138626i | ||||
\(545\) | 175581. | 0.591132 | ||||||||
\(546\) | −13620.6 | − | 40325.1i | −0.0456891 | − | 0.135266i | ||||
\(547\) | 388547.i | 1.29858i | 0.760541 | + | 0.649290i | \(0.224934\pi\) | ||||
−0.760541 | + | 0.649290i | \(0.775066\pi\) | |||||||
\(548\) | −24037.7 | + | 18329.7i | −0.0800446 | + | 0.0610371i | ||||
\(549\) | 143533. | 0.476220 | ||||||||
\(550\) | −82655.3 | + | 27918.5i | −0.273241 | + | 0.0922927i | ||||
\(551\) | − | 231649.i | − | 0.763004i | ||||||
\(552\) | −88098.0 | − | 59444.3i | −0.289126 | − | 0.195089i | ||||
\(553\) | 36936.6 | 0.120783 | ||||||||
\(554\) | 175479. | + | 519520.i | 0.571748 | + | 1.69271i | ||||
\(555\) | − | 137885.i | − | 0.447641i | ||||||
\(556\) | −146430. | − | 192029.i | −0.473674 | − | 0.621180i | ||||
\(557\) | −24464.5 | −0.0788544 | −0.0394272 | − | 0.999222i | \(-0.512553\pi\) | ||||
−0.0394272 | + | 0.999222i | \(0.512553\pi\) | |||||||
\(558\) | −7422.32 | + | 2507.04i | −0.0238381 | + | 0.00805180i | ||||
\(559\) | 71540.6i | 0.228944i | ||||||||
\(560\) | 245836. | + | 67465.9i | 0.783915 | + | 0.215134i | ||||
\(561\) | 62771.3 | 0.199451 | ||||||||
\(562\) | 87396.3 | + | 258744.i | 0.276707 | + | 0.819216i | ||||
\(563\) | 534256.i | 1.68551i | 0.538294 | + | 0.842757i | \(0.319069\pi\) | ||||
−0.538294 | + | 0.842757i | \(0.680931\pi\) | |||||||
\(564\) | 20866.9 | − | 15911.8i | 0.0655994 | − | 0.0500221i | ||||
\(565\) | 213177. | 0.667794 | ||||||||
\(566\) | 176050. | − | 59464.6i | 0.549545 | − | 0.185620i | ||||
\(567\) | 64930.0i | 0.201967i | ||||||||
\(568\) | −105747. | + | 156719.i | −0.327771 | + | 0.485765i | ||||
\(569\) | −264769. | −0.817792 | −0.408896 | − | 0.912581i | \(-0.634086\pi\) | ||||
−0.408896 | + | 0.912581i | \(0.634086\pi\) | |||||||
\(570\) | −25359.6 | − | 75079.3i | −0.0780536 | − | 0.231084i | ||||
\(571\) | − | 159329.i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(572\) | 38921.4 | + | 51041.8i | 0.118959 | + | 0.156003i | ||||
\(573\) | −168798. | −0.514113 | ||||||||
\(574\) | 257446. | − | 86957.6i | 0.781379 | − | 0.263927i | ||||
\(575\) | 39947.4i | 0.120824i | ||||||||
\(576\) | −41394.1 | − | 102553.i | −0.124765 | − | 0.309103i | ||||
\(577\) | 244978. | 0.735827 | 0.367913 | − | 0.929860i | \(-0.380072\pi\) | ||||
0.367913 | + | 0.929860i | \(0.380072\pi\) | |||||||
\(578\) | −100774. | − | 298351.i | −0.301643 | − | 0.893042i | ||||
\(579\) | 54042.4i | 0.161205i | ||||||||
\(580\) | −96625.5 | + | 73680.7i | −0.287234 | + | 0.219027i | ||||
\(581\) | −867415. | −2.56965 | ||||||||
\(582\) | 188336. | − | 63614.3i | 0.556015 | − | 0.187806i | ||||
\(583\) | 590799.i | 1.73821i | ||||||||
\(584\) | −304623. | − | 205545.i | −0.893176 | − | 0.602672i | ||||
\(585\) | 6940.56 | 0.0202807 | ||||||||
\(586\) | 97058.4 | + | 287350.i | 0.282643 | + | 0.836789i | ||||
\(587\) | − | 415608.i | − | 1.20617i | −0.797678 | − | 0.603084i | \(-0.793938\pi\) | ||
0.797678 | − | 0.603084i | \(-0.206062\pi\) | |||||||
\(588\) | −278878. | − | 365723.i | −0.806603 | − | 1.05779i | ||||
\(589\) | −24737.7 | −0.0713064 | ||||||||
\(590\) | −283176. | + | 95648.5i | −0.813490 | + | 0.274773i | ||||
\(591\) | 245131.i | 0.701815i | ||||||||
\(592\) | 160801. | − | 585937.i | 0.458825 | − | 1.67189i | ||||
\(593\) | −149847. | −0.426128 | −0.213064 | − | 0.977038i | \(-0.568344\pi\) | ||||
−0.213064 | + | 0.977038i | \(0.568344\pi\) | |||||||
\(594\) | −31334.9 | − | 92769.7i | −0.0888087 | − | 0.262926i | ||||
\(595\) | 68943.2i | 0.194741i | ||||||||
\(596\) | −380254. | + | 289959.i | −1.07049 | + | 0.816289i | ||||
\(597\) | −296935. | −0.833129 | ||||||||
\(598\) | 27845.5 | − | 9405.38i | 0.0778668 | − | 0.0263011i | ||||
\(599\) | − | 34050.6i | − | 0.0949011i | −0.998874 | − | 0.0474505i | \(-0.984890\pi\) | ||
0.998874 | − | 0.0474505i | \(-0.0151096\pi\) | |||||||
\(600\) | −23251.0 | + | 34458.5i | −0.0645861 | + | 0.0957182i | ||||
\(601\) | −618647. | −1.71275 | −0.856375 | − | 0.516355i | \(-0.827288\pi\) | ||||
−0.856375 | + | 0.516355i | \(0.827288\pi\) | |||||||
\(602\) | 354746. | + | 1.05026e6i | 0.978868 | + | 2.89803i | ||||
\(603\) | 108408.i | 0.298143i | ||||||||
\(604\) | 153463. | + | 201253.i | 0.420659 | + | 0.551655i | ||||
\(605\) | −176698. | −0.482749 | ||||||||
\(606\) | −27311.3 | + | 9224.95i | −0.0743698 | + | 0.0251199i | ||||
\(607\) | 35350.6i | 0.0959444i | 0.998849 | + | 0.0479722i | \(0.0152759\pi\) | ||||
−0.998849 | + | 0.0479722i | \(0.984724\pi\) | |||||||
\(608\) | −20207.2 | − | 348622.i | −0.0546638 | − | 0.943079i | ||||
\(609\) | 314374. | 0.847641 | ||||||||
\(610\) | −76079.1 | − | 225239.i | −0.204459 | − | 0.605318i | ||||
\(611\) | 7257.08i | 0.0194392i | ||||||||
\(612\) | 23783.3 | − | 18135.7i | 0.0634994 | − | 0.0484208i | ||||
\(613\) | 690354. | 1.83718 | 0.918588 | − | 0.395215i | \(-0.129330\pi\) | ||||
0.918588 | + | 0.395215i | \(0.129330\pi\) | |||||||
\(614\) | −436171. | + | 147326.i | −1.15696 | + | 0.390789i | ||||
\(615\) | 44310.3i | 0.117153i | ||||||||
\(616\) | 824487. | + | 556325.i | 2.17281 | + | 1.46611i | ||||
\(617\) | −94309.0 | −0.247732 | −0.123866 | − | 0.992299i | \(-0.539529\pi\) | ||||
−0.123866 | + | 0.992299i | \(0.539529\pi\) | |||||||
\(618\) | −4172.53 | − | 12353.2i | −0.0109250 | − | 0.0323445i | ||||
\(619\) | − | 107669.i | − | 0.281002i | −0.990081 | − | 0.140501i | \(-0.955129\pi\) | ||
0.990081 | − | 0.140501i | \(-0.0448713\pi\) | |||||||
\(620\) | 7868.33 | + | 10318.6i | 0.0204691 | + | 0.0268434i | ||||
\(621\) | −44835.8 | −0.116263 | ||||||||
\(622\) | 171157. | − | 57811.7i | 0.442398 | − | 0.149429i | ||||
\(623\) | − | 729676.i | − | 1.87998i | ||||||
\(624\) | 29493.7 | + | 8094.10i | 0.0757461 | + | 0.0207874i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 35702.9 | + | 105702.i | 0.0911077 | + | 0.269732i | ||||
\(627\) | − | 309190.i | − | 0.786486i | ||||||
\(628\) | 414636. | − | 316176.i | 1.05135 | − | 0.801697i | ||||
\(629\) | 164323. | 0.415332 | ||||||||
\(630\) | 101891. | − | 34415.9i | 0.256718 | − | 0.0867117i | ||||
\(631\) | − | 489941.i | − | 1.23051i | −0.788329 | − | 0.615254i | \(-0.789053\pi\) | ||
0.788329 | − | 0.615254i | \(-0.210947\pi\) | |||||||
\(632\) | −14845.3 | + | 22001.1i | −0.0371667 | + | 0.0550820i | ||||
\(633\) | 127621. | 0.318504 | ||||||||
\(634\) | 115419. | + | 341709.i | 0.287144 | + | 0.850115i | ||||
\(635\) | − | 4202.57i | − | 0.0104224i | ||||||
\(636\) | 170692. | + | 223847.i | 0.421987 | + | 0.553397i | ||||
\(637\) | 127191. | 0.313456 | ||||||||
\(638\) | −449166. | + | 151715.i | −1.10348 | + | 0.372724i | ||||
\(639\) | 79759.3i | 0.195335i | ||||||||
\(640\) | −138990. | + | 119315.i | −0.339332 | + | 0.291297i | ||||
\(641\) | 593431. | 1.44429 | 0.722145 | − | 0.691742i | \(-0.243156\pi\) | ||||
0.722145 | + | 0.691742i | \(0.243156\pi\) | |||||||
\(642\) | 19880.3 | + | 58857.3i | 0.0482339 | + | 0.142801i | ||||
\(643\) | − | 263108.i | − | 0.636372i | −0.948028 | − | 0.318186i | \(-0.896926\pi\) | ||
0.948028 | − | 0.318186i | \(-0.103074\pi\) | |||||||
\(644\) | 362149. | − | 276153.i | 0.873203 | − | 0.665851i | ||||
\(645\) | −180765. | −0.434505 | ||||||||
\(646\) | 89475.1 | − | 30222.1i | 0.214406 | − | 0.0724201i | ||||
\(647\) | 640998.i | 1.53126i | 0.643282 | + | 0.765629i | \(0.277572\pi\) | ||||
−0.643282 | + | 0.765629i | \(0.722428\pi\) | |||||||
\(648\) | −38675.2 | − | 26096.2i | −0.0921049 | − | 0.0621480i | ||||
\(649\) | −1.16617e6 | −2.76868 | ||||||||
\(650\) | −3678.81 | − | 10891.4i | −0.00870725 | − | 0.0257786i | ||||
\(651\) | − | 33571.9i | − | 0.0792161i | ||||||
\(652\) | −189461. | − | 248461.i | −0.445681 | − | 0.584470i | ||||
\(653\) | 453024. | 1.06242 | 0.531208 | − | 0.847241i | \(-0.321738\pi\) | ||||
0.531208 | + | 0.847241i | \(0.321738\pi\) | |||||||
\(654\) | 309246. | − | 104454.i | 0.723017 | − | 0.244214i | ||||
\(655\) | 131551.i | 0.306627i | ||||||||
\(656\) | −51674.8 | + | 188295.i | −0.120080 | + | 0.437554i | ||||
\(657\) | −155032. | −0.359162 | ||||||||
\(658\) | 35985.4 | + | 106538.i | 0.0831141 | + | 0.246067i | ||||
\(659\) | − | 16332.5i | − | 0.0376081i | −0.999823 | − | 0.0188040i | \(-0.994014\pi\) | ||
0.999823 | − | 0.0188040i | \(-0.00598586\pi\) | |||||||
\(660\) | −128970. | + | 98344.4i | −0.296074 | + | 0.225768i | ||||
\(661\) | 143631. | 0.328735 | 0.164367 | − | 0.986399i | \(-0.447442\pi\) | ||||
0.164367 | + | 0.986399i | \(0.447442\pi\) | |||||||
\(662\) | 515181. | − | 174013.i | 1.17556 | − | 0.397069i | ||||
\(663\) | 8271.34i | 0.0188169i | ||||||||
\(664\) | 348625. | − | 516671.i | 0.790719 | − | 1.17187i | ||||
\(665\) | 339591. | 0.767915 | ||||||||
\(666\) | −82028.5 | − | 242852.i | −0.184934 | − | 0.547513i | ||||
\(667\) | 217083.i | 0.487948i | ||||||||
\(668\) | 202593. | + | 265682.i | 0.454017 | + | 0.595401i | ||||
\(669\) | −370281. | −0.827330 | ||||||||
\(670\) | 170118. | − | 57460.9i | 0.378967 | − | 0.128004i | ||||
\(671\) | − | 927575.i | − | 2.06017i | ||||||
\(672\) | 473120. | − | 27423.5i | 1.04769 | − | 0.0607274i | ||||
\(673\) | −331571. | −0.732058 | −0.366029 | − | 0.930603i | \(-0.619283\pi\) | ||||
−0.366029 | + | 0.930603i | \(0.619283\pi\) | |||||||
\(674\) | −106441. | − | 315127.i | −0.234308 | − | 0.693690i | ||||
\(675\) | 17537.0i | 0.0384900i | ||||||||
\(676\) | 356656. | − | 271964.i | 0.780471 | − | 0.595139i | ||||
\(677\) | −495629. | −1.08138 | −0.540691 | − | 0.841221i | \(-0.681837\pi\) | ||||
−0.540691 | + | 0.841221i | \(0.681837\pi\) | |||||||
\(678\) | 375462. | − | 126820.i | 0.816783 | − | 0.275886i | ||||
\(679\) | 851861.i | 1.84769i | ||||||||
\(680\) | −41065.6 | − | 27709.1i | −0.0888098 | − | 0.0599246i | ||||
\(681\) | −380811. | −0.821136 | ||||||||
\(682\) | 16201.6 | + | 47966.3i | 0.0348329 | + | 0.103126i | ||||
\(683\) | − | 490413.i | − | 1.05128i | −0.850706 | − | 0.525642i | \(-0.823825\pi\) | ||
0.850706 | − | 0.525642i | \(-0.176175\pi\) | |||||||
\(684\) | −89330.4 | − | 117149.i | −0.190936 | − | 0.250395i | ||||
\(685\) | 21123.1 | 0.0450170 | ||||||||
\(686\) | 1.05681e6 | − | 356960.i | 2.24569 | − | 0.758528i | ||||
\(687\) | 192793.i | 0.408487i | ||||||||
\(688\) | −768156. | − | 210809.i | −1.62283 | − | 0.445360i | ||||
\(689\) | −77849.3 | −0.163990 | ||||||||
\(690\) | 23765.0 | + | 70358.4i | 0.0499160 | + | 0.147781i | ||||
\(691\) | 157915.i | 0.330725i | 0.986233 | + | 0.165363i | \(0.0528794\pi\) | ||||
−0.986233 | + | 0.165363i | \(0.947121\pi\) | |||||||
\(692\) | 67162.6 | − | 51214.1i | 0.140254 | − | 0.106949i | ||||
\(693\) | 419607. | 0.873728 | ||||||||
\(694\) | −451012. | + | 152339.i | −0.936416 | + | 0.316294i | ||||
\(695\) | 168745.i | 0.349351i | ||||||||
\(696\) | −126351. | + | 187255.i | −0.260831 | + | 0.386558i | ||||
\(697\) | −52806.3 | −0.108698 | ||||||||
\(698\) | −129510. | − | 383425.i | −0.265823 | − | 0.786992i | ||||
\(699\) | − | 109126.i | − | 0.223344i | ||||||
\(700\) | −108014. | − | 141651.i | −0.220437 | − | 0.289083i | ||||
\(701\) | −125021. | −0.254418 | −0.127209 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127209 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(702\) | 12224.2 | − | 4128.98i | 0.0248054 | − | 0.00837855i | ||||
\(703\) | − | 809398.i | − | 1.63776i | ||||||
\(704\) | −662743. | + | 267507.i | −1.33721 | + | 0.539747i | ||||
\(705\) | −18336.8 | −0.0368931 | ||||||||
\(706\) | −261780. | − | 775022.i | −0.525202 | − | 1.55491i | ||||
\(707\) | − | 123532.i | − | 0.247138i | ||||||
\(708\) | −441848. | + | 336926.i | −0.881468 | + | 0.672154i | ||||
\(709\) | −223380. | −0.444377 | −0.222189 | − | 0.975004i | \(-0.571320\pi\) | ||||
−0.222189 | + | 0.975004i | \(0.571320\pi\) | |||||||
\(710\) | 125162. | − | 42276.1i | 0.248288 | − | 0.0838645i | ||||
\(711\) | 11197.0i | 0.0221495i | ||||||||
\(712\) | 434627. | + | 293266.i | 0.857348 | + | 0.578498i | ||||
\(713\) | 23182.2 | 0.0456011 | ||||||||
\(714\) | 41014.8 | + | 121428.i | 0.0804533 | + | 0.238189i | ||||
\(715\) | − | 44853.0i | − | 0.0877363i | ||||||
\(716\) | 456388. | + | 598511.i | 0.890242 | + | 1.16747i | ||||
\(717\) | 46173.0 | 0.0898152 | ||||||||
\(718\) | −171639. | + | 57974.6i | −0.332941 | + | 0.112458i | ||||
\(719\) | 839679.i | 1.62426i | 0.583477 | + | 0.812130i | \(0.301692\pi\) | ||||
−0.583477 | + | 0.812130i | \(0.698308\pi\) | |||||||
\(720\) | −20451.7 | + | 74523.1i | −0.0394516 | + | 0.143756i | ||||
\(721\) | 55874.5 | 0.107484 | ||||||||
\(722\) | 17951.8 | + | 53147.8i | 0.0344376 | + | 0.101956i | ||||
\(723\) | 57333.4i | 0.109681i | ||||||||
\(724\) | 208606. | − | 159070.i | 0.397969 | − | 0.303467i | ||||
\(725\) | 84909.5 | 0.161540 | ||||||||
\(726\) | −311214. | + | 105119.i | −0.590454 | + | 0.199438i | ||||
\(727\) | − | 244897.i | − | 0.463355i | −0.972793 | − | 0.231678i | \(-0.925579\pi\) | ||
0.972793 | − | 0.231678i | \(-0.0744214\pi\) | |||||||
\(728\) | −73306.6 | + | 108642.i | −0.138319 | + | 0.204991i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 82174.0 | + | 243283.i | 0.154202 | + | 0.456527i | ||||
\(731\) | − | 215425.i | − | 0.403145i | ||||||
\(732\) | −267992. | − | 351447.i | −0.500150 | − | 0.655901i | ||||
\(733\) | 370157. | 0.688935 | 0.344467 | − | 0.938798i | \(-0.388060\pi\) | ||||
0.344467 | + | 0.938798i | \(0.388060\pi\) | |||||||
\(734\) | −66405.3 | + | 22429.8i | −0.123257 | + | 0.0416325i | ||||
\(735\) | 321379.i | 0.594898i | ||||||||
\(736\) | 18936.6 | + | 326701.i | 0.0349580 | + | 0.603108i | ||||
\(737\) | 700578. | 1.28980 | ||||||||
\(738\) | 26360.5 | + | 78042.5i | 0.0483995 | + | 0.143291i | ||||
\(739\) | − | 555878.i | − | 1.01787i | −0.860806 | − | 0.508933i | \(-0.830040\pi\) | ||
0.860806 | − | 0.508933i | \(-0.169960\pi\) | |||||||
\(740\) | −337617. | + | 257446.i | −0.616539 | + | 0.470135i | ||||
\(741\) | 40741.9 | 0.0742001 | ||||||||
\(742\) | −1.14287e6 | + | 386028.i | −2.07582 | + | 0.701151i | ||||
\(743\) | − | 282516.i | − | 0.511759i | −0.966709 | − | 0.255880i | \(-0.917635\pi\) | ||
0.966709 | − | 0.255880i | \(-0.0823650\pi\) | |||||||
\(744\) | 19996.9 | + | 13493.0i | 0.0361257 | + | 0.0243759i | ||||
\(745\) | 334148. | 0.602042 | ||||||||
\(746\) | −21166.3 | − | 62664.7i | −0.0380336 | − | 0.112602i | ||||
\(747\) | − | 262950.i | − | 0.471228i | ||||||
\(748\) | −117201. | − | 153698.i | −0.209473 | − | 0.274705i | ||||
\(749\) | −266218. | −0.474540 | ||||||||
\(750\) | 27519.9 | − | 9295.42i | 0.0489243 | − | 0.0165252i | ||||
\(751\) | − | 406925.i | − | 0.721498i | −0.932663 | − | 0.360749i | \(-0.882521\pi\) | ||
0.932663 | − | 0.360749i | \(-0.117479\pi\) | |||||||
\(752\) | −77921.7 | − | 21384.4i | −0.137792 | − | 0.0378148i | ||||
\(753\) | 267458. | 0.471700 | ||||||||
\(754\) | −19991.4 | − | 59186.4i | −0.0351642 | − | 0.104107i | ||||
\(755\) | − | 176851.i | − | 0.310251i | ||||||
\(756\) | 158984. | − | 121232.i | 0.278170 | − | 0.212115i | ||||
\(757\) | −973008. | −1.69795 | −0.848974 | − | 0.528434i | \(-0.822779\pi\) | ||||
−0.848974 | + | 0.528434i | \(0.822779\pi\) | |||||||
\(758\) | 241915. | − | 81711.8i | 0.421041 | − | 0.142215i | ||||
\(759\) | 289749.i | 0.502965i | ||||||||
\(760\) | −136486. | + | 202276.i | −0.236298 | + | 0.350200i | ||||
\(761\) | −457654. | −0.790255 | −0.395128 | − | 0.918626i | \(-0.629300\pi\) | ||||
−0.395128 | + | 0.918626i | \(0.629300\pi\) | |||||||
\(762\) | −2500.14 | − | 7401.88i | −0.00430580 | − | 0.0127477i | ||||
\(763\) | 1.39875e6i | 2.40265i | ||||||||
\(764\) | 315165. | + | 413310.i | 0.539947 | + | 0.708091i | ||||
\(765\) | −20899.6 | −0.0357120 | ||||||||
\(766\) | −302439. | + | 102155.i | −0.515442 | + | 0.174101i | ||||
\(767\) | − | 153666.i | − | 0.261208i | ||||||
\(768\) | −173818. | + | 292833.i | −0.294695 | + | 0.496476i | ||||
\(769\) | 449424. | 0.759982 | 0.379991 | − | 0.924990i | \(-0.375927\pi\) | ||||
0.379991 | + | 0.924990i | \(0.375927\pi\) | |||||||
\(770\) | −222411. | − | 658467.i | −0.375124 | − | 1.11059i | ||||
\(771\) | 221099.i | 0.371945i | ||||||||
\(772\) | 132325. | − | 100903.i | 0.222028 | − | 0.169305i | ||||
\(773\) | 842657. | 1.41024 | 0.705118 | − | 0.709090i | \(-0.250894\pi\) | ||||
0.705118 | + | 0.709090i | \(0.250894\pi\) | |||||||
\(774\) | −318376. | + | 107538.i | −0.531446 | + | 0.179507i | ||||
\(775\) | − | 9067.46i | − | 0.0150967i | ||||||
\(776\) | −507406. | − | 342373.i | −0.842621 | − | 0.568560i | ||||
\(777\) | 1.09845e6 | 1.81944 | ||||||||
\(778\) | −204215. | − | 604597.i | −0.337387 | − | 0.998865i | ||||
\(779\) | 260106.i | 0.428623i | ||||||||
\(780\) | −12958.8 | − | 16994.3i | −0.0212998 | − | 0.0279327i | ||||
\(781\) | 515440. | 0.845038 | ||||||||
\(782\) | −83848.9 | + | 28321.7i | −0.137115 | + | 0.0463133i | ||||
\(783\) | 95299.8i | 0.155442i | ||||||||
\(784\) | −374793. | + | 1.36569e6i | −0.609761 | + | 2.22188i | ||||
\(785\) | −364361. | −0.591280 | ||||||||
\(786\) | 78260.4 | + | 231697.i | 0.126677 | + | 0.375038i | ||||
\(787\) | 370408.i | 0.598041i | 0.954247 | + | 0.299021i | \(0.0966600\pi\) | ||||
−0.954247 | + | 0.299021i | \(0.903340\pi\) | |||||||
\(788\) | 600214. | − | 457686.i | 0.966615 | − | 0.737081i | ||||
\(789\) | −29935.1 | −0.0480870 | ||||||||
\(790\) | 17570.9 | − | 5934.93i | 0.0281539 | − | 0.00950958i | ||||
\(791\) | 1.69825e6i | 2.71425i | ||||||||
\(792\) | −168645. | + | 249936.i | −0.268858 | + | 0.398455i | ||||
\(793\) | 122226. | 0.194365 | ||||||||
\(794\) | 188880. | + | 559196.i | 0.299602 | + | 0.886999i | ||||
\(795\) | − | 196705.i | − | 0.311230i | ||||||
\(796\) | 554410. | + | 727058.i | 0.874994 | + | 1.14747i | ||||
\(797\) | −321175. | −0.505621 | −0.252810 | − | 0.967516i | \(-0.581355\pi\) | ||||
−0.252810 | + | 0.967516i | \(0.581355\pi\) | |||||||
\(798\) | 598113. | − | 202025.i | 0.939242 | − | 0.317249i | ||||
\(799\) | − | 21852.7i | − | 0.0342303i | ||||||
\(800\) | 127786. | − | 7406.84i | 0.199665 | − | 0.0115732i | ||||
\(801\) | 221195. | 0.344755 | ||||||||
\(802\) | −61310.3 | − | 181514.i | −0.0953201 | − | 0.282204i | ||||
\(803\) | 1.00189e6i | 1.55377i | ||||||||
\(804\) | 265441. | − | 202409.i | 0.410635 | − | 0.313125i | ||||
\(805\) | −318238. | −0.491089 | ||||||||
\(806\) | −6320.50 | + | 2134.88i | −0.00972929 | + | 0.00328627i | ||||
\(807\) | − | 102740.i | − | 0.157759i | ||||||
\(808\) | 73580.9 | + | 49648.9i | 0.112705 | + | 0.0760478i | ||||
\(809\) | 596798. | 0.911864 | 0.455932 | − | 0.890015i | \(-0.349306\pi\) | ||||
0.455932 | + | 0.890015i | \(0.349306\pi\) | |||||||
\(810\) | 10432.9 | + | 30887.5i | 0.0159014 | + | 0.0470774i | ||||
\(811\) | − | 479347.i | − | 0.728800i | −0.931243 | − | 0.364400i | \(-0.881274\pi\) | ||
0.931243 | − | 0.364400i | \(-0.118726\pi\) | |||||||
\(812\) | −586971. | − | 769759.i | −0.890235 | − | 1.16746i | ||||
\(813\) | −313750. | −0.474683 | ||||||||
\(814\) | −1.56942e6 | + | 530105.i | −2.36859 | + | 0.800042i | ||||
\(815\) | 218334.i | 0.328706i | ||||||||
\(816\) | −88812.2 | − | 24373.2i | −0.133380 | − | 0.0366042i | ||||
\(817\) | −1.06111e6 | −1.58970 | ||||||||
\(818\) | 32242.8 | + | 95457.7i | 0.0481866 | + | 0.142661i | ||||
\(819\) | 55291.4i | 0.0824308i | ||||||||
\(820\) | 108496. | − | 82732.2i | 0.161356 | − | 0.123040i | ||||
\(821\) | 84958.2 | 0.126043 | 0.0630215 | − | 0.998012i | \(-0.479926\pi\) | ||||
0.0630215 | + | 0.998012i | \(0.479926\pi\) | |||||||
\(822\) | 37203.6 | − | 12566.3i | 0.0550607 | − | 0.0185979i | ||||
\(823\) | 67392.6i | 0.0994975i | 0.998762 | + | 0.0497488i | \(0.0158421\pi\) | ||||
−0.998762 | + | 0.0497488i | \(0.984158\pi\) | |||||||
\(824\) | −22456.7 | + | 33281.3i | −0.0330743 | + | 0.0490170i | ||||
\(825\) | 113332. | 0.166512 | ||||||||
\(826\) | −761976. | − | 2.25590e6i | −1.11681 | − | 3.30643i | ||||
\(827\) | − | 433061.i | − | 0.633196i | −0.948560 | − | 0.316598i | \(-0.897459\pi\) | ||
0.948560 | − | 0.316598i | \(-0.102541\pi\) | |||||||
\(828\) | 83713.4 | + | 109782.i | 0.122105 | + | 0.160130i | ||||
\(829\) | 1.14798e6 | 1.67043 | 0.835213 | − | 0.549927i | \(-0.185345\pi\) | ||||
0.835213 | + | 0.549927i | \(0.185345\pi\) | |||||||
\(830\) | −412633. | + | 139375.i | −0.598974 | + | 0.202316i | ||||
\(831\) | − | 712335.i | − | 1.03153i | ||||||
\(832\) | −35249.3 | − | 87329.3i | −0.0509218 | − | 0.126158i | ||||
\(833\) | −383000. | −0.551961 | ||||||||
\(834\) | 100388. | + | 297207.i | 0.144327 | + | 0.427294i | ||||
\(835\) | − | 233468.i | − | 0.334853i | ||||||
\(836\) | −757067. | + | 577293.i | −1.08323 | + | 0.826007i | ||||
\(837\) | 10177.0 | 0.0145268 | ||||||||
\(838\) | 684570. | − | 231228.i | 0.974832 | − | 0.329270i | ||||
\(839\) | 499869.i | 0.710121i | 0.934843 | + | 0.355060i | \(0.115540\pi\) | ||||
−0.934843 | + | 0.355060i | \(0.884460\pi\) | |||||||
\(840\) | −274511. | − | 185227.i | −0.389046 | − | 0.262510i | ||||
\(841\) | −245865. | −0.347620 | ||||||||
\(842\) | −178631. | − | 528852.i | −0.251960 | − | 0.745950i | ||||
\(843\) | − | 354775.i | − | 0.499226i | ||||||
\(844\) | −238283. | − | 312486.i | −0.334509 | − | 0.438678i | ||||
\(845\) | −313411. | −0.438936 | ||||||||
\(846\) | −32296.1 | + | 10908.7i | −0.0451242 | + | 0.0152416i | ||||
\(847\) | − | 1.40765e6i | − | 1.96213i | ||||||
\(848\) | 229398. | − | 835894.i | 0.319006 | − | 1.16241i | ||||
\(849\) | −241389. | −0.334890 | ||||||||
\(850\) | 11077.7 | + | 32796.6i | 0.0153325 | + | 0.0453932i | ||||
\(851\) | 758504.i | 1.04737i | ||||||||
\(852\) | 195294. | − | 148920.i | 0.269036 | − | 0.205151i | ||||
\(853\) | 490741. | 0.674457 | 0.337228 | − | 0.941423i | \(-0.390511\pi\) | ||||
0.337228 | + | 0.941423i | \(0.390511\pi\) | |||||||
\(854\) | 1.79435e6 | − | 606078.i | 2.46031 | − | 0.831022i | ||||
\(855\) | 102944.i | 0.140822i | ||||||||
\(856\) | 106996. | − | 158571.i | 0.146023 | − | 0.216410i | ||||
\(857\) | 920396. | 1.25318 | 0.626590 | − | 0.779349i | \(-0.284450\pi\) | ||||
0.626590 | + | 0.779349i | \(0.284450\pi\) | |||||||
\(858\) | −26683.3 | − | 78998.4i | −0.0362465 | − | 0.107311i | ||||
\(859\) | − | 1.31521e6i | − | 1.78242i | −0.453595 | − | 0.891208i | \(-0.649859\pi\) | ||
0.453595 | − | 0.891208i | \(-0.350141\pi\) | |||||||
\(860\) | 337508. | + | 442611.i | 0.456339 | + | 0.598446i | ||||
\(861\) | −352994. | −0.476169 | ||||||||
\(862\) | 625494. | − | 211274.i | 0.841799 | − | 0.284335i | ||||
\(863\) | 68287.4i | 0.0916894i | 0.998949 | + | 0.0458447i | \(0.0145979\pi\) | ||||
−0.998949 | + | 0.0458447i | \(0.985402\pi\) | |||||||
\(864\) | 8313.21 | + | 143422.i | 0.0111363 | + | 0.192128i | ||||
\(865\) | −59019.1 | −0.0788787 | ||||||||
\(866\) | 33554.1 | + | 99339.8i | 0.0447414 | + | 0.132461i | ||||
\(867\) | 409081.i | 0.544216i | ||||||||
\(868\) | −82202.3 | + | 62682.4i | −0.109105 | + | 0.0831968i | ||||
\(869\) | 72360.1 | 0.0958208 | ||||||||
\(870\) | 149549. | − | 50513.3i | 0.197581 | − | 0.0667370i | ||||
\(871\) | 92314.8i | 0.121684i | ||||||||
\(872\) | −833158. | − | 562175.i | −1.09571 | − | 0.739331i | ||||
\(873\) | −258235. | −0.338833 | ||||||||
\(874\) | 139503. | + | 413012.i | 0.182626 | + | 0.540679i | ||||
\(875\) | 124475.i | 0.162580i | ||||||||
\(876\) | 289462. | + | 379603.i | 0.377210 | + | 0.494676i | ||||
\(877\) | 1.14924e6 | 1.49421 | 0.747104 | − | 0.664707i | \(-0.231444\pi\) | ||||
0.747104 | + | 0.664707i | \(0.231444\pi\) | |||||||
\(878\) | −1.34882e6 | + | 455592.i | −1.74971 | + | 0.591000i | ||||
\(879\) | − | 393997.i | − | 0.509935i | ||||||
\(880\) | 481602. | + | 132168.i | 0.621903 | + | 0.170672i | ||||
\(881\) | −79533.6 | −0.102470 | −0.0512352 | − | 0.998687i | \(-0.516316\pi\) | ||||
−0.0512352 | + | 0.998687i | \(0.516316\pi\) | |||||||
\(882\) | 191190. | + | 566036.i | 0.245770 | + | 0.727624i | ||||
\(883\) | − | 226846.i | − | 0.290945i | −0.989362 | − | 0.145472i | \(-0.953530\pi\) | ||
0.989362 | − | 0.145472i | \(-0.0464702\pi\) | |||||||
\(884\) | 20252.8 | − | 15443.5i | 0.0259167 | − | 0.0197625i | ||||
\(885\) | 388274. | 0.495737 | ||||||||
\(886\) | 433007. | − | 146257.i | 0.551604 | − | 0.186316i | ||||
\(887\) | − | 421203.i | − | 0.535358i | −0.963508 | − | 0.267679i | \(-0.913743\pi\) | ||
0.963508 | − | 0.267679i | \(-0.0862567\pi\) | |||||||
\(888\) | −441479. | + | 654283.i | −0.559866 | + | 0.829736i | ||||
\(889\) | 33479.4 | 0.0423618 | ||||||||
\(890\) | −117244. | − | 347110.i | −0.148016 | − | 0.438215i | ||||
\(891\) | 127200.i | 0.160226i | ||||||||
\(892\) | 691355. | + | 906649.i | 0.868904 | + | 1.13949i | ||||
\(893\) | −107639. | −0.134979 | ||||||||
\(894\) | 588526. | − | 198787.i | 0.736361 | − | 0.248721i | ||||
\(895\) | − | 525941.i | − | 0.656585i | ||||||
\(896\) | −950516. | − | 1.10725e6i | −1.18398 | − | 1.37921i | ||||
\(897\) | −38180.0 | −0.0474517 | ||||||||
\(898\) | 109544. | + | 324316.i | 0.135843 | + | 0.402175i | ||||
\(899\) | − | 49274.5i | − | 0.0609681i | ||||||
\(900\) | 42940.2 | − | 32743.6i | 0.0530126 | − | 0.0404241i | ||||
\(901\) | 234422. | 0.288767 | ||||||||
\(902\) | 504346. | − | 170353.i | 0.619891 | − | 0.209381i | ||||
\(903\) | − | 1.44005e6i | − | 1.76604i | ||||||
\(904\) | −1.01155e6 | − | 682549.i | −1.23781 | − | 0.835213i | ||||
\(905\) | −183312. | −0.223818 | ||||||||
\(906\) | −105210. | − | 311482.i | −0.128174 | − | 0.379470i | ||||
\(907\) | 743335.i | 0.903587i | 0.892123 | + | 0.451793i | \(0.149216\pi\) | ||||
−0.892123 | + | 0.451793i | \(0.850784\pi\) | |||||||
\(908\) | 711016. | + | 932433.i | 0.862398 | + | 1.13096i | ||||
\(909\) | 37447.6 | 0.0453206 | ||||||||
\(910\) | 86765.8 | − | 29307.0i | 0.104777 | − | 0.0353906i | ||||
\(911\) | − | 460545.i | − | 0.554927i | −0.960736 | − | 0.277463i | \(-0.910506\pi\) | ||
0.960736 | − | 0.277463i | \(-0.0894937\pi\) | |||||||
\(912\) | −120054. | + | 437459.i | −0.144340 | + | 0.525954i | ||||
\(913\) | −1.69930e6 | −2.03858 | ||||||||
\(914\) | −497148. | − | 1.47185e6i | −0.595105 | − | 1.76186i | ||||
\(915\) | 308834.i | 0.368878i | ||||||||
\(916\) | 472063. | − | 359966.i | 0.562612 | − | 0.429014i | ||||
\(917\) | −1.04799e6 | −1.24629 | ||||||||
\(918\) | −36809.9 | + | 12433.3i | −0.0436796 | + | 0.0147537i | ||||
\(919\) | 398036.i | 0.471293i | 0.971839 | + | 0.235647i | \(0.0757208\pi\) | ||||
−0.971839 | + | 0.235647i | \(0.924279\pi\) | |||||||
\(920\) | 127904. | − | 189557.i | 0.151115 | − | 0.223956i | ||||
\(921\) | 598052. | 0.705049 | ||||||||
\(922\) | 413056. | + | 1.22289e6i | 0.485900 | + | 1.43855i | ||||
\(923\) | 67919.3i | 0.0797241i | ||||||||
\(924\) | −783453. | − | 1.02743e6i | −0.917633 | − | 1.20339i | ||||
\(925\) | 296680. | 0.346741 | ||||||||
\(926\) | 706110. | − | 238503.i | 0.823475 | − | 0.278146i | ||||
\(927\) | 16937.9i | 0.0197106i | ||||||||
\(928\) | 694413. | − | 40250.3i | 0.806347 | − | 0.0467384i | ||||
\(929\) | −1.29517e6 | −1.50070 | −0.750352 | − | 0.661039i | \(-0.770116\pi\) | ||||
−0.750352 | + | 0.661039i | \(0.770116\pi\) | |||||||
\(930\) | −5394.29 | − | 15970.3i | −0.00623690 | − | 0.0184649i | ||||
\(931\) | 1.88653e6i | 2.17653i | ||||||||
\(932\) | −267201. | + | 203751.i | −0.307614 | + | 0.234567i | ||||
\(933\) | −234680. | −0.269595 | ||||||||
\(934\) | 452559. | − | 152861.i | 0.518778 | − | 0.175228i | ||||
\(935\) | 135062.i | 0.154494i | ||||||||
\(936\) | −32934.0 | − | 22222.3i | −0.0375918 | − | 0.0253651i | ||||
\(937\) | 567776. | 0.646693 | 0.323347 | − | 0.946281i | \(-0.395192\pi\) | ||||
0.323347 | + | 0.946281i | \(0.395192\pi\) | |||||||
\(938\) | 457758. | + | 1.35523e6i | 0.520272 | + | 1.54031i | ||||
\(939\) | − | 144932.i | − | 0.164374i | ||||||
\(940\) | 34236.8 | + | 44898.5i | 0.0387470 | + | 0.0508131i | ||||
\(941\) | 595092. | 0.672055 | 0.336027 | − | 0.941852i | \(-0.390917\pi\) | ||||
0.336027 | + | 0.941852i | \(0.390917\pi\) | |||||||
\(942\) | −641740. | + | 216761.i | −0.723198 | + | 0.244275i | ||||
\(943\) | − | 243751.i | − | 0.274109i | ||||||
\(944\) | 1.64996e6 | + | 452806.i | 1.85152 | + | 0.508122i | ||||
\(945\) | −139707. | −0.156443 | ||||||||
\(946\) | 694960. | + | 2.05749e6i | 0.776565 | + | 2.29909i | ||||
\(947\) | 847579.i | 0.945105i | 0.881303 | + | 0.472552i | \(0.156667\pi\) | ||||
−0.881303 | + | 0.472552i | \(0.843333\pi\) | |||||||
\(948\) | 27416.4 | − | 20906.1i | 0.0305066 | − | 0.0232625i | ||||
\(949\) | −132018. | −0.146589 | ||||||||
\(950\) | 161545. | − | 54565.2i | 0.178997 | − | 0.0604600i | ||||
\(951\) | − | 468531.i | − | 0.518056i | ||||||
\(952\) | 220743. | − | 327146.i | 0.243563 | − | 0.360967i | ||||
\(953\) | −705705. | −0.777030 | −0.388515 | − | 0.921442i | \(-0.627012\pi\) | ||||
−0.388515 | + | 0.921442i | \(0.627012\pi\) | |||||||
\(954\) | −117021. | − | 346452.i | −0.128578 | − | 0.380668i | ||||
\(955\) | − | 363196.i | − | 0.398230i | ||||||
\(956\) | −86210.2 | − | 113057.i | −0.0943285 | − | 0.123703i | ||||
\(957\) | 615870. | 0.672458 | ||||||||
\(958\) | −347143. | + | 117255.i | −0.378249 | + | 0.127761i | ||||
\(959\) | 168276.i | 0.182972i | ||||||||
\(960\) | 220659. | − | 89066.0i | 0.239430 | − | 0.0966428i | ||||
\(961\) | 918259. | 0.994302 | ||||||||
\(962\) | −69851.6 | − | 206802.i | −0.0754790 | − | 0.223462i | ||||
\(963\) | − | 80701.7i | − | 0.0870222i | ||||||
\(964\) | 140383. | − | 107048.i | 0.151064 | − | 0.115192i | ||||
\(965\) | −116281. | −0.124869 | ||||||||
\(966\) | −560504. | + | 189322.i | −0.600654 | + | 0.202883i | ||||
\(967\) | 1.51802e6i | 1.62339i | 0.584079 | + | 0.811697i | \(0.301456\pi\) | ||||
−0.584079 | + | 0.811697i | \(0.698544\pi\) | |||||||
\(968\) | 838460. | + | 565753.i | 0.894812 | + | 0.603777i | ||||
\(969\) | −122683. | −0.130658 | ||||||||
\(970\) | 136876. | + | 405234.i | 0.145474 | + | 0.430687i | ||||
\(971\) | − | 697559.i | − | 0.739848i | −0.929062 | − | 0.369924i | \(-0.879384\pi\) | ||
0.929062 | − | 0.369924i | \(-0.120616\pi\) | |||||||
\(972\) | 36750.4 | + | 48194.7i | 0.0388982 | + | 0.0510114i | ||||
\(973\) | −1.34430e6 | −1.41994 | ||||||||
\(974\) | 773658. | − | 261319.i | 0.815513 | − | 0.275457i | ||||
\(975\) | 14933.7i | 0.0157093i | ||||||||
\(976\) | −360163. | + | 1.31238e6i | −0.378094 | + | 1.37772i | ||||
\(977\) | −1.31716e6 | −1.37990 | −0.689952 | − | 0.723856i | \(-0.742368\pi\) | ||||
−0.689952 | + | 0.723856i | \(0.742368\pi\) | |||||||
\(978\) | 129889. | + | 384547.i | 0.135798 | + | 0.402042i | ||||
\(979\) | − | 1.42946e6i | − | 1.49145i | ||||||
\(980\) | 786910. | − | 600050.i | 0.819357 | − | 0.624792i | ||||
\(981\) | −424020. | −0.440603 | ||||||||
\(982\) | −727566. | + | 245751.i | −0.754483 | + | 0.254842i | ||||
\(983\) | − | 1.38061e6i | − | 1.42878i | −0.699749 | − | 0.714389i | \(-0.746705\pi\) | ||
0.699749 | − | 0.714389i | \(-0.253295\pi\) | |||||||
\(984\) | 141873. | − | 210259.i | 0.146524 | − | 0.217152i | ||||
\(985\) | −527437. | −0.543624 | ||||||||
\(986\) | 60198.7 | + | 178223.i | 0.0619203 | + | 0.183321i | ||||
\(987\) | − | 146078.i | − | 0.149952i | ||||||
\(988\) | −76069.6 | − | 99758.3i | −0.0779287 | − | 0.102196i | ||||
\(989\) | 994388. | 1.01663 | ||||||||
\(990\) | 199609. | − | 67422.0i | 0.203662 | − | 0.0687909i | ||||
\(991\) | 183725.i | 0.187077i | 0.995616 | + | 0.0935385i | \(0.0298178\pi\) | ||||
−0.995616 | + | 0.0935385i | \(0.970182\pi\) | |||||||
\(992\) | −4298.32 | − | 74156.2i | −0.00436793 | − | 0.0753571i | ||||
\(993\) | −706385. | −0.716379 | ||||||||
\(994\) | 336789. | + | 997093.i | 0.340867 | + | 1.00917i | ||||
\(995\) | − | 638902.i | − | 0.645339i | ||||||
\(996\) | −643844. | + | 490956.i | −0.649026 | + | 0.494908i | ||||
\(997\) | 547047. | 0.550344 | 0.275172 | − | 0.961395i | \(-0.411265\pi\) | ||||
0.275172 | + | 0.961395i | \(0.411265\pi\) | |||||||
\(998\) | −329166. | + | 111183.i | −0.330486 | + | 0.111629i | ||||
\(999\) | 332985.i | 0.333652i |
(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 | 60.5.c.a.31.12 | yes | 16 | |
3.2 | odd | 2 | 180.5.c.c.91.5 | 16 | |||
4.3 | odd | 2 | inner | 60.5.c.a.31.11 | ✓ | 16 | |
5.2 | odd | 4 | 300.5.f.b.199.4 | 32 | |||
5.3 | odd | 4 | 300.5.f.b.199.29 | 32 | |||
5.4 | even | 2 | 300.5.c.d.151.5 | 16 | |||
8.3 | odd | 2 | 960.5.e.f.511.1 | 16 | |||
8.5 | even | 2 | 960.5.e.f.511.12 | 16 | |||
12.11 | even | 2 | 180.5.c.c.91.6 | 16 | |||
20.3 | even | 4 | 300.5.f.b.199.3 | 32 | |||
20.7 | even | 4 | 300.5.f.b.199.30 | 32 | |||
20.19 | odd | 2 | 300.5.c.d.151.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.c.a.31.11 | ✓ | 16 | 4.3 | odd | 2 | inner | |
60.5.c.a.31.12 | yes | 16 | 1.1 | even | 1 | trivial | |
180.5.c.c.91.5 | 16 | 3.2 | odd | 2 | |||
180.5.c.c.91.6 | 16 | 12.11 | even | 2 | |||
300.5.c.d.151.5 | 16 | 5.4 | even | 2 | |||
300.5.c.d.151.6 | 16 | 20.19 | odd | 2 | |||
300.5.f.b.199.3 | 32 | 20.3 | even | 4 | |||
300.5.f.b.199.4 | 32 | 5.2 | odd | 4 | |||
300.5.f.b.199.29 | 32 | 5.3 | odd | 4 | |||
300.5.f.b.199.30 | 32 | 20.7 | even | 4 | |||
960.5.e.f.511.1 | 16 | 8.3 | odd | 2 | |||
960.5.e.f.511.12 | 16 | 8.5 | even | 2 |