Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(41,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.b (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: | \(6.19520055060\) |
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: | \( x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.15 | ||
Root | \(4.61386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.41 |
Dual form | 105.4.b.a.41.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.61386i | 1.63125i | 0.578583 | + | 0.815623i | \(0.303606\pi\) | ||||
−0.578583 | + | 0.815623i | \(0.696394\pi\) | |||||||
\(3\) | −3.98691 | + | 3.33234i | −0.767282 | + | 0.641310i | ||||
\(4\) | −13.2877 | −1.66097 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −15.3750 | − | 18.3951i | −1.04613 | − | 1.25163i | ||||
\(7\) | 0.582685 | − | 18.5111i | 0.0314620 | − | 0.999505i | ||||
\(8\) | − | 24.3969i | − | 1.07820i | ||||||
\(9\) | 4.79097 | − | 26.5715i | 0.177444 | − | 0.984131i | ||||
\(10\) | − | 23.0693i | − | 0.729516i | ||||||
\(11\) | 65.3963i | 1.79252i | 0.443528 | + | 0.896260i | \(0.353727\pi\) | ||||
−0.443528 | + | 0.896260i | \(0.646273\pi\) | |||||||
\(12\) | 52.9770 | − | 44.2793i | 1.27443 | − | 1.06519i | ||||
\(13\) | − | 30.9388i | − | 0.660067i | −0.943969 | − | 0.330033i | \(-0.892940\pi\) | ||
0.943969 | − | 0.330033i | \(-0.107060\pi\) | |||||||
\(14\) | 85.4076 | + | 2.68843i | 1.63044 | + | 0.0513223i | ||||
\(15\) | 19.9346 | − | 16.6617i | 0.343139 | − | 0.286802i | ||||
\(16\) | 6.26191 | 0.0978423 | ||||||||
\(17\) | −85.8927 | −1.22541 | −0.612707 | − | 0.790310i | \(-0.709919\pi\) | ||||
−0.612707 | + | 0.790310i | \(0.709919\pi\) | |||||||
\(18\) | 122.597 | + | 22.1049i | 1.60536 | + | 0.289454i | ||||
\(19\) | 6.24097i | 0.0753567i | 0.999290 | + | 0.0376783i | \(0.0119962\pi\) | ||||
−0.999290 | + | 0.0376783i | \(0.988004\pi\) | |||||||
\(20\) | 66.4386 | 0.742807 | ||||||||
\(21\) | 59.3622 | + | 75.7438i | 0.616852 | + | 0.787079i | ||||
\(22\) | −301.730 | −2.92404 | ||||||||
\(23\) | − | 193.142i | − | 1.75099i | −0.483224 | − | 0.875497i | \(-0.660534\pi\) | ||
0.483224 | − | 0.875497i | \(-0.339466\pi\) | |||||||
\(24\) | 81.2987 | + | 97.2682i | 0.691459 | + | 0.827283i | ||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 142.747 | 1.07673 | ||||||||
\(27\) | 69.4443 | + | 121.904i | 0.494984 | + | 0.868902i | ||||
\(28\) | −7.74256 | + | 245.970i | −0.0522574 | + | 1.66014i | ||||
\(29\) | − | 30.7085i | − | 0.196635i | −0.995155 | − | 0.0983176i | \(-0.968654\pi\) | ||
0.995155 | − | 0.0983176i | \(-0.0313461\pi\) | |||||||
\(30\) | 76.8749 | + | 91.9754i | 0.467846 | + | 0.559744i | ||||
\(31\) | 61.0950i | 0.353967i | 0.984214 | + | 0.176984i | \(0.0566339\pi\) | ||||
−0.984214 | + | 0.176984i | \(0.943366\pi\) | |||||||
\(32\) | − | 166.283i | − | 0.918594i | ||||||
\(33\) | −217.923 | − | 260.730i | −1.14956 | − | 1.37537i | ||||
\(34\) | − | 396.297i | − | 1.99895i | ||||||
\(35\) | −2.91342 | + | 92.5555i | −0.0140702 | + | 0.446992i | ||||
\(36\) | −63.6612 | + | 353.075i | −0.294728 | + | 1.63461i | ||||
\(37\) | −8.71591 | −0.0387267 | −0.0193633 | − | 0.999813i | \(-0.506164\pi\) | ||||
−0.0193633 | + | 0.999813i | \(0.506164\pi\) | |||||||
\(38\) | −28.7950 | −0.122925 | ||||||||
\(39\) | 103.099 | + | 123.350i | 0.423307 | + | 0.506457i | ||||
\(40\) | 121.984i | 0.482185i | ||||||||
\(41\) | −387.588 | −1.47637 | −0.738183 | − | 0.674600i | \(-0.764316\pi\) | ||||
−0.738183 | + | 0.674600i | \(0.764316\pi\) | |||||||
\(42\) | −349.472 | + | 273.889i | −1.28392 | + | 1.00624i | ||||
\(43\) | −281.233 | −0.997388 | −0.498694 | − | 0.866778i | \(-0.666187\pi\) | ||||
−0.498694 | + | 0.866778i | \(0.666187\pi\) | |||||||
\(44\) | − | 868.968i | − | 2.97732i | ||||||
\(45\) | −23.9549 | + | 132.858i | −0.0793551 | + | 0.440117i | ||||
\(46\) | 891.130 | 2.85630 | ||||||||
\(47\) | −208.528 | −0.647169 | −0.323585 | − | 0.946199i | \(-0.604888\pi\) | ||||
−0.323585 | + | 0.946199i | \(0.604888\pi\) | |||||||
\(48\) | −24.9657 | + | 20.8668i | −0.0750727 | + | 0.0627472i | ||||
\(49\) | −342.321 | − | 21.5723i | −0.998020 | − | 0.0628929i | ||||
\(50\) | 115.347i | 0.326249i | ||||||||
\(51\) | 342.447 | − | 286.224i | 0.940238 | − | 0.785870i | ||||
\(52\) | 411.106i | 1.09635i | ||||||||
\(53\) | 211.802i | 0.548929i | 0.961597 | + | 0.274464i | \(0.0885005\pi\) | ||||
−0.961597 | + | 0.274464i | \(0.911499\pi\) | |||||||
\(54\) | −562.447 | + | 320.406i | −1.41739 | + | 0.807440i | ||||
\(55\) | − | 326.982i | − | 0.801640i | ||||||
\(56\) | −451.612 | − | 14.2157i | −1.07767 | − | 0.0339223i | ||||
\(57\) | −20.7971 | − | 24.8822i | −0.0483270 | − | 0.0578198i | ||||
\(58\) | 141.685 | 0.320760 | ||||||||
\(59\) | −213.993 | −0.472195 | −0.236097 | − | 0.971729i | \(-0.575868\pi\) | ||||
−0.236097 | + | 0.971729i | \(0.575868\pi\) | |||||||
\(60\) | −264.885 | + | 221.396i | −0.569942 | + | 0.476369i | ||||
\(61\) | 673.667i | 1.41400i | 0.707212 | + | 0.707001i | \(0.249953\pi\) | ||||
−0.707212 | + | 0.707001i | \(0.750047\pi\) | |||||||
\(62\) | −281.884 | −0.577408 | ||||||||
\(63\) | −489.076 | − | 104.169i | −0.978061 | − | 0.208318i | ||||
\(64\) | 817.303 | 1.59630 | ||||||||
\(65\) | 154.694i | 0.295191i | ||||||||
\(66\) | 1202.97 | − | 1005.47i | 2.24357 | − | 1.87522i | ||||
\(67\) | −500.399 | −0.912440 | −0.456220 | − | 0.889867i | \(-0.650797\pi\) | ||||
−0.456220 | + | 0.889867i | \(0.650797\pi\) | |||||||
\(68\) | 1141.32 | 2.03537 | ||||||||
\(69\) | 643.615 | + | 770.040i | 1.12293 | + | 1.34351i | ||||
\(70\) | −427.038 | − | 13.4421i | −0.729155 | − | 0.0229520i | ||||
\(71\) | 319.460i | 0.533984i | 0.963699 | + | 0.266992i | \(0.0860298\pi\) | ||||
−0.963699 | + | 0.266992i | \(0.913970\pi\) | |||||||
\(72\) | −648.262 | − | 116.885i | −1.06109 | − | 0.191319i | ||||
\(73\) | 555.337i | 0.890374i | 0.895438 | + | 0.445187i | \(0.146863\pi\) | ||||
−0.895438 | + | 0.445187i | \(0.853137\pi\) | |||||||
\(74\) | − | 40.2140i | − | 0.0631728i | ||||||
\(75\) | −99.6729 | + | 83.3086i | −0.153456 | + | 0.128262i | ||||
\(76\) | − | 82.9283i | − | 0.125165i | ||||||
\(77\) | 1210.56 | + | 38.1054i | 1.79163 | + | 0.0563963i | ||||
\(78\) | −569.121 | + | 475.683i | −0.826157 | + | 0.690518i | ||||
\(79\) | 842.582 | 1.19997 | 0.599987 | − | 0.800010i | \(-0.295173\pi\) | ||||
0.599987 | + | 0.800010i | \(0.295173\pi\) | |||||||
\(80\) | −31.3095 | −0.0437564 | ||||||||
\(81\) | −683.093 | − | 254.607i | −0.937028 | − | 0.349255i | ||||
\(82\) | − | 1788.28i | − | 2.40832i | ||||||
\(83\) | 887.665 | 1.17390 | 0.586951 | − | 0.809622i | \(-0.300328\pi\) | ||||
0.586951 | + | 0.809622i | \(0.300328\pi\) | |||||||
\(84\) | −788.789 | − | 1006.46i | −1.02457 | − | 1.30731i | ||||
\(85\) | 429.463 | 0.548022 | ||||||||
\(86\) | − | 1297.57i | − | 1.62699i | ||||||
\(87\) | 102.331 | + | 122.432i | 0.126104 | + | 0.150875i | ||||
\(88\) | 1595.46 | 1.93269 | ||||||||
\(89\) | −480.245 | −0.571976 | −0.285988 | − | 0.958233i | \(-0.592322\pi\) | ||||
−0.285988 | + | 0.958233i | \(0.592322\pi\) | |||||||
\(90\) | −612.987 | − | 110.524i | −0.717939 | − | 0.129448i | ||||
\(91\) | −572.710 | − | 18.0275i | −0.659740 | − | 0.0207670i | ||||
\(92\) | 2566.42i | 2.90834i | ||||||||
\(93\) | −203.589 | − | 243.580i | −0.227003 | − | 0.271593i | ||||
\(94\) | − | 962.120i | − | 1.05569i | ||||||
\(95\) | − | 31.2048i | − | 0.0337005i | ||||||
\(96\) | 554.113 | + | 662.957i | 0.589103 | + | 0.704821i | ||||
\(97\) | 477.578i | 0.499904i | 0.968258 | + | 0.249952i | \(0.0804149\pi\) | ||||
−0.968258 | + | 0.249952i | \(0.919585\pi\) | |||||||
\(98\) | 99.5315 | − | 1579.42i | 0.102594 | − | 1.62802i | ||||
\(99\) | 1737.68 | + | 313.312i | 1.76408 | + | 0.318071i | ||||
\(100\) | −332.193 | −0.332193 | ||||||||
\(101\) | −1177.46 | −1.16002 | −0.580009 | − | 0.814610i | \(-0.696951\pi\) | ||||
−0.580009 | + | 0.814610i | \(0.696951\pi\) | |||||||
\(102\) | 1320.60 | + | 1580.00i | 1.28195 | + | 1.53376i | ||||
\(103\) | − | 236.191i | − | 0.225948i | −0.993598 | − | 0.112974i | \(-0.963962\pi\) | ||
0.993598 | − | 0.112974i | \(-0.0360376\pi\) | |||||||
\(104\) | −754.808 | −0.711683 | ||||||||
\(105\) | −296.811 | − | 378.719i | −0.275865 | − | 0.351992i | ||||
\(106\) | −977.225 | −0.895438 | ||||||||
\(107\) | − | 381.844i | − | 0.344993i | −0.985010 | − | 0.172497i | \(-0.944817\pi\) | ||
0.985010 | − | 0.172497i | \(-0.0551834\pi\) | |||||||
\(108\) | −922.757 | − | 1619.82i | −0.822151 | − | 1.44322i | ||||
\(109\) | −66.2128 | −0.0581838 | −0.0290919 | − | 0.999577i | \(-0.509262\pi\) | ||||
−0.0290919 | + | 0.999577i | \(0.509262\pi\) | |||||||
\(110\) | 1508.65 | 1.30767 | ||||||||
\(111\) | 34.7496 | − | 29.0444i | 0.0297143 | − | 0.0248358i | ||||
\(112\) | 3.64872 | − | 115.915i | 0.00307832 | − | 0.0977939i | ||||
\(113\) | − | 1640.52i | − | 1.36573i | −0.730545 | − | 0.682864i | \(-0.760734\pi\) | ||
0.730545 | − | 0.682864i | \(-0.239266\pi\) | |||||||
\(114\) | 114.803 | − | 95.9547i | 0.0943184 | − | 0.0788332i | ||||
\(115\) | 965.709i | 0.783068i | ||||||||
\(116\) | 408.046i | 0.326604i | ||||||||
\(117\) | −822.090 | − | 148.227i | −0.649592 | − | 0.117125i | ||||
\(118\) | − | 987.333i | − | 0.770266i | ||||||
\(119\) | −50.0484 | + | 1589.97i | −0.0385540 | + | 1.22481i | ||||
\(120\) | −406.494 | − | 486.341i | −0.309230 | − | 0.369972i | ||||
\(121\) | −2945.68 | −2.21313 | ||||||||
\(122\) | −3108.20 | −2.30659 | ||||||||
\(123\) | 1545.28 | − | 1291.58i | 1.13279 | − | 0.946809i | ||||
\(124\) | − | 811.813i | − | 0.587927i | ||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 480.621 | − | 2256.53i | 0.339819 | − | 1.59546i | ||||
\(127\) | 405.224 | 0.283133 | 0.141566 | − | 0.989929i | \(-0.454786\pi\) | ||||
0.141566 | + | 0.989929i | \(0.454786\pi\) | |||||||
\(128\) | 2440.66i | 1.68536i | ||||||||
\(129\) | 1121.25 | − | 937.166i | 0.765278 | − | 0.639635i | ||||
\(130\) | −713.736 | −0.481529 | ||||||||
\(131\) | 2002.74 | 1.33573 | 0.667865 | − | 0.744283i | \(-0.267208\pi\) | ||||
0.667865 | + | 0.744283i | \(0.267208\pi\) | |||||||
\(132\) | 2895.70 | + | 3464.50i | 1.90938 | + | 2.28444i | ||||
\(133\) | 115.527 | + | 3.63652i | 0.0753194 | + | 0.00237087i | ||||
\(134\) | − | 2308.77i | − | 1.48841i | ||||||
\(135\) | −347.221 | − | 609.518i | −0.221363 | − | 0.388585i | ||||
\(136\) | 2095.51i | 1.32124i | ||||||||
\(137\) | 2374.19i | 1.48059i | 0.672281 | + | 0.740296i | \(0.265315\pi\) | ||||
−0.672281 | + | 0.740296i | \(0.734685\pi\) | |||||||
\(138\) | −3552.86 | + | 2969.55i | −2.19159 | + | 1.83178i | ||||
\(139\) | − | 1018.72i | − | 0.621631i | −0.950470 | − | 0.310815i | \(-0.899398\pi\) | ||
0.950470 | − | 0.310815i | \(-0.100602\pi\) | |||||||
\(140\) | 38.7128 | − | 1229.85i | 0.0233702 | − | 0.742439i | ||||
\(141\) | 831.384 | − | 694.887i | 0.496561 | − | 0.415036i | ||||
\(142\) | −1473.94 | −0.871060 | ||||||||
\(143\) | 2023.28 | 1.18318 | ||||||||
\(144\) | 30.0006 | − | 166.389i | 0.0173615 | − | 0.0962897i | ||||
\(145\) | 153.542i | 0.0879379i | ||||||||
\(146\) | −2562.25 | −1.45242 | ||||||||
\(147\) | 1436.69 | − | 1054.72i | 0.806097 | − | 0.591784i | ||||
\(148\) | 115.815 | 0.0643237 | ||||||||
\(149\) | 1957.03i | 1.07601i | 0.842941 | + | 0.538007i | \(0.180822\pi\) | ||||
−0.842941 | + | 0.538007i | \(0.819178\pi\) | |||||||
\(150\) | −384.374 | − | 459.877i | −0.209227 | − | 0.250325i | ||||
\(151\) | 965.606 | 0.520397 | 0.260198 | − | 0.965555i | \(-0.416212\pi\) | ||||
0.260198 | + | 0.965555i | \(0.416212\pi\) | |||||||
\(152\) | 152.260 | 0.0812495 | ||||||||
\(153\) | −411.510 | + | 2282.30i | −0.217442 | + | 1.20597i | ||||
\(154\) | −175.813 | + | 5585.34i | −0.0919964 | + | 2.92260i | ||||
\(155\) | − | 305.475i | − | 0.158299i | ||||||
\(156\) | −1369.95 | − | 1639.04i | −0.703099 | − | 0.841208i | ||||
\(157\) | 1279.67i | 0.650501i | 0.945628 | + | 0.325250i | \(0.105449\pi\) | ||||
−0.945628 | + | 0.325250i | \(0.894551\pi\) | |||||||
\(158\) | 3887.56i | 1.95745i | ||||||||
\(159\) | −705.797 | − | 844.436i | −0.352033 | − | 0.421183i | ||||
\(160\) | 831.416i | 0.410808i | ||||||||
\(161\) | −3575.27 | − | 112.541i | −1.75013 | − | 0.0550898i | ||||
\(162\) | 1174.72 | − | 3151.70i | 0.569722 | − | 1.52852i | ||||
\(163\) | −1558.78 | −0.749039 | −0.374520 | − | 0.927219i | \(-0.622192\pi\) | ||||
−0.374520 | + | 0.927219i | \(0.622192\pi\) | |||||||
\(164\) | 5150.16 | 2.45220 | ||||||||
\(165\) | 1089.61 | + | 1303.65i | 0.514099 | + | 0.615084i | ||||
\(166\) | 4095.57i | 1.91492i | ||||||||
\(167\) | −428.816 | −0.198699 | −0.0993495 | − | 0.995053i | \(-0.531676\pi\) | ||||
−0.0993495 | + | 0.995053i | \(0.531676\pi\) | |||||||
\(168\) | 1847.91 | − | 1448.25i | 0.848628 | − | 0.665089i | ||||
\(169\) | 1239.79 | 0.564312 | ||||||||
\(170\) | 1981.49i | 0.893959i | ||||||||
\(171\) | 165.832 | + | 29.9003i | 0.0741608 | + | 0.0133716i | ||||
\(172\) | 3736.95 | 1.65663 | ||||||||
\(173\) | −1708.89 | −0.751010 | −0.375505 | − | 0.926820i | \(-0.622531\pi\) | ||||
−0.375505 | + | 0.926820i | \(0.622531\pi\) | |||||||
\(174\) | −564.885 | + | 472.142i | −0.246114 | + | 0.205707i | ||||
\(175\) | 14.5671 | − | 462.777i | 0.00629241 | − | 0.199901i | ||||
\(176\) | 409.506i | 0.175384i | ||||||||
\(177\) | 853.171 | − | 713.097i | 0.362306 | − | 0.302823i | ||||
\(178\) | − | 2215.78i | − | 0.933034i | ||||||
\(179\) | 1129.27i | 0.471541i | 0.971809 | + | 0.235770i | \(0.0757613\pi\) | ||||
−0.971809 | + | 0.235770i | \(0.924239\pi\) | |||||||
\(180\) | 318.306 | − | 1765.38i | 0.131806 | − | 0.731019i | ||||
\(181\) | − | 3997.53i | − | 1.64162i | −0.571198 | − | 0.820812i | \(-0.693521\pi\) | ||
0.571198 | − | 0.820812i | \(-0.306479\pi\) | |||||||
\(182\) | 83.1766 | − | 2642.41i | 0.0338762 | − | 1.07620i | ||||
\(183\) | −2244.89 | − | 2685.85i | −0.906814 | − | 1.08494i | ||||
\(184\) | −4712.05 | −1.88792 | ||||||||
\(185\) | 43.5796 | 0.0173191 | ||||||||
\(186\) | 1123.85 | − | 939.334i | 0.443035 | − | 0.370297i | ||||
\(187\) | − | 5617.06i | − | 2.19658i | ||||||
\(188\) | 2770.87 | 1.07493 | ||||||||
\(189\) | 2297.03 | − | 1214.46i | 0.884045 | − | 0.467401i | ||||
\(190\) | 143.975 | 0.0549739 | ||||||||
\(191\) | 544.334i | 0.206213i | 0.994670 | + | 0.103106i | \(0.0328782\pi\) | ||||
−0.994670 | + | 0.103106i | \(0.967122\pi\) | |||||||
\(192\) | −3258.52 | + | 2723.54i | −1.22481 | + | 1.02372i | ||||
\(193\) | −4438.14 | −1.65526 | −0.827628 | − | 0.561276i | \(-0.810310\pi\) | ||||
−0.827628 | + | 0.561276i | \(0.810310\pi\) | |||||||
\(194\) | −2203.48 | −0.815467 | ||||||||
\(195\) | −515.493 | − | 616.751i | −0.189309 | − | 0.226495i | ||||
\(196\) | 4548.67 | + | 286.646i | 1.65768 | + | 0.104463i | ||||
\(197\) | − | 1163.82i | − | 0.420906i | −0.977604 | − | 0.210453i | \(-0.932506\pi\) | ||
0.977604 | − | 0.210453i | \(-0.0674939\pi\) | |||||||
\(198\) | −1445.58 | + | 8017.42i | −0.518853 | + | 2.87764i | ||||
\(199\) | − | 2295.86i | − | 0.817837i | −0.912571 | − | 0.408918i | \(-0.865906\pi\) | ||
0.912571 | − | 0.408918i | \(-0.134094\pi\) | |||||||
\(200\) | − | 609.921i | − | 0.215640i | ||||||
\(201\) | 1995.05 | − | 1667.50i | 0.700099 | − | 0.585156i | ||||
\(202\) | − | 5432.65i | − | 1.89228i | ||||||
\(203\) | −568.447 | − | 17.8934i | −0.196538 | − | 0.00618654i | ||||
\(204\) | −4550.34 | + | 3803.27i | −1.56170 | + | 1.30530i | ||||
\(205\) | 1937.94 | 0.660251 | ||||||||
\(206\) | 1089.75 | 0.368576 | ||||||||
\(207\) | −5132.08 | − | 925.338i | −1.72321 | − | 0.310702i | ||||
\(208\) | − | 193.736i | − | 0.0645825i | ||||||
\(209\) | −408.136 | −0.135078 | ||||||||
\(210\) | 1747.36 | − | 1369.45i | 0.574187 | − | 0.450003i | ||||
\(211\) | 1364.52 | 0.445200 | 0.222600 | − | 0.974910i | \(-0.428546\pi\) | ||||
0.222600 | + | 0.974910i | \(0.428546\pi\) | |||||||
\(212\) | − | 2814.37i | − | 0.911752i | ||||||
\(213\) | −1064.55 | − | 1273.66i | −0.342449 | − | 0.409717i | ||||
\(214\) | 1761.78 | 0.562769 | ||||||||
\(215\) | 1406.17 | 0.446046 | ||||||||
\(216\) | 2974.06 | − | 1694.22i | 0.936849 | − | 0.533691i | ||||
\(217\) | 1130.93 | + | 35.5991i | 0.353792 | + | 0.0111365i | ||||
\(218\) | − | 305.497i | − | 0.0949121i | ||||||
\(219\) | −1850.57 | − | 2214.08i | −0.571005 | − | 0.683168i | ||||
\(220\) | 4344.84i | 1.33150i | ||||||||
\(221\) | 2657.41i | 0.808855i | ||||||||
\(222\) | 134.007 | + | 160.330i | 0.0405133 | + | 0.0484713i | ||||
\(223\) | − | 782.650i | − | 0.235023i | −0.993072 | − | 0.117511i | \(-0.962508\pi\) | ||
0.993072 | − | 0.117511i | \(-0.0374917\pi\) | |||||||
\(224\) | −3078.08 | − | 96.8907i | −0.918139 | − | 0.0289008i | ||||
\(225\) | 119.774 | − | 664.288i | 0.0354887 | − | 0.196826i | ||||
\(226\) | 7569.14 | 2.22784 | ||||||||
\(227\) | 431.312 | 0.126111 | 0.0630555 | − | 0.998010i | \(-0.479915\pi\) | ||||
0.0630555 | + | 0.998010i | \(0.479915\pi\) | |||||||
\(228\) | 276.346 | + | 330.628i | 0.0802695 | + | 0.0960368i | ||||
\(229\) | 5093.80i | 1.46990i | 0.678119 | + | 0.734952i | \(0.262795\pi\) | ||||
−0.678119 | + | 0.734952i | \(0.737205\pi\) | |||||||
\(230\) | −4455.65 | −1.27738 | ||||||||
\(231\) | −4953.37 | + | 3882.07i | −1.41086 | + | 1.10572i | ||||
\(232\) | −749.190 | −0.212012 | ||||||||
\(233\) | − | 3844.93i | − | 1.08107i | −0.841321 | − | 0.540536i | \(-0.818222\pi\) | ||
0.841321 | − | 0.540536i | \(-0.181778\pi\) | |||||||
\(234\) | 683.898 | − | 3793.01i | 0.191059 | − | 1.05964i | ||||
\(235\) | 1042.64 | 0.289423 | ||||||||
\(236\) | 2843.48 | 0.784299 | ||||||||
\(237\) | −3359.30 | + | 2807.77i | −0.920718 | + | 0.769555i | ||||
\(238\) | −7335.89 | − | 230.916i | −1.99796 | − | 0.0628911i | ||||
\(239\) | 1426.08i | 0.385964i | 0.981202 | + | 0.192982i | \(0.0618159\pi\) | ||||
−0.981202 | + | 0.192982i | \(0.938184\pi\) | |||||||
\(240\) | 124.828 | − | 104.334i | 0.0335735 | − | 0.0280614i | ||||
\(241\) | 5231.73i | 1.39836i | 0.714945 | + | 0.699181i | \(0.246452\pi\) | ||||
−0.714945 | + | 0.699181i | \(0.753548\pi\) | |||||||
\(242\) | − | 13591.0i | − | 3.61016i | ||||||
\(243\) | 3571.87 | − | 1261.20i | 0.942945 | − | 0.332948i | ||||
\(244\) | − | 8951.50i | − | 2.34861i | ||||||
\(245\) | 1711.60 | + | 107.861i | 0.446328 | + | 0.0281266i | ||||
\(246\) | 5959.15 | + | 7129.71i | 1.54448 | + | 1.84786i | ||||
\(247\) | 193.088 | 0.0497404 | ||||||||
\(248\) | 1490.53 | 0.381647 | ||||||||
\(249\) | −3539.05 | + | 2958.01i | −0.900714 | + | 0.752835i | ||||
\(250\) | − | 576.733i | − | 0.145903i | ||||||
\(251\) | 2122.49 | 0.533746 | 0.266873 | − | 0.963732i | \(-0.414010\pi\) | ||||
0.266873 | + | 0.963732i | \(0.414010\pi\) | |||||||
\(252\) | 6498.72 | + | 1384.17i | 1.62453 | + | 0.346010i | ||||
\(253\) | 12630.8 | 3.13869 | ||||||||
\(254\) | 1869.65i | 0.461859i | ||||||||
\(255\) | −1712.23 | + | 1431.12i | −0.420487 | + | 0.351452i | ||||
\(256\) | −4722.44 | −1.15294 | ||||||||
\(257\) | 6347.65 | 1.54068 | 0.770341 | − | 0.637632i | \(-0.220086\pi\) | ||||
0.770341 | + | 0.637632i | \(0.220086\pi\) | |||||||
\(258\) | 4323.96 | + | 5173.31i | 1.04340 | + | 1.24836i | ||||
\(259\) | −5.07863 | + | 161.341i | −0.00121842 | + | 0.0387075i | ||||
\(260\) | − | 2055.53i | − | 0.490302i | ||||||
\(261\) | −815.971 | − | 147.123i | −0.193515 | − | 0.0348916i | ||||
\(262\) | 9240.39i | 2.17890i | ||||||||
\(263\) | − | 931.743i | − | 0.218455i | −0.994017 | − | 0.109228i | \(-0.965162\pi\) | ||
0.994017 | − | 0.109228i | \(-0.0348378\pi\) | |||||||
\(264\) | −6360.98 | + | 5316.64i | −1.48292 | + | 1.23946i | ||||
\(265\) | − | 1059.01i | − | 0.245488i | ||||||
\(266\) | −16.7784 | + | 533.026i | −0.00386748 | + | 0.122864i | ||||
\(267\) | 1914.70 | − | 1600.34i | 0.438867 | − | 0.366814i | ||||
\(268\) | 6649.16 | 1.51553 | ||||||||
\(269\) | 3245.79 | 0.735685 | 0.367843 | − | 0.929888i | \(-0.380097\pi\) | ||||
0.367843 | + | 0.929888i | \(0.380097\pi\) | |||||||
\(270\) | 2812.23 | − | 1602.03i | 0.633878 | − | 0.361098i | ||||
\(271\) | − | 2735.96i | − | 0.613276i | −0.951826 | − | 0.306638i | \(-0.900796\pi\) | ||
0.951826 | − | 0.306638i | \(-0.0992041\pi\) | |||||||
\(272\) | −537.852 | −0.119897 | ||||||||
\(273\) | 2343.42 | − | 1836.59i | 0.519525 | − | 0.407163i | ||||
\(274\) | −10954.2 | −2.41521 | ||||||||
\(275\) | 1634.91i | 0.358504i | ||||||||
\(276\) | −8552.18 | − | 10232.1i | −1.86515 | − | 2.23152i | ||||
\(277\) | −2982.49 | −0.646934 | −0.323467 | − | 0.946239i | \(-0.604848\pi\) | ||||
−0.323467 | + | 0.946239i | \(0.604848\pi\) | |||||||
\(278\) | 4700.23 | 1.01403 | ||||||||
\(279\) | 1623.39 | + | 292.704i | 0.348350 | + | 0.0628092i | ||||
\(280\) | 2258.06 | + | 71.0784i | 0.481946 | + | 0.0151705i | ||||
\(281\) | 2595.38i | 0.550987i | 0.961303 | + | 0.275494i | \(0.0888413\pi\) | ||||
−0.961303 | + | 0.275494i | \(0.911159\pi\) | |||||||
\(282\) | 3206.12 | + | 3835.89i | 0.677026 | + | 0.810014i | ||||
\(283\) | − | 6717.96i | − | 1.41110i | −0.708660 | − | 0.705550i | \(-0.750700\pi\) | ||
0.708660 | − | 0.705550i | \(-0.249300\pi\) | |||||||
\(284\) | − | 4244.89i | − | 0.886930i | ||||||
\(285\) | 103.985 | + | 124.411i | 0.0216125 | + | 0.0258578i | ||||
\(286\) | 9335.14i | 1.93006i | ||||||||
\(287\) | −225.842 | + | 7174.67i | −0.0464495 | + | 1.47564i | ||||
\(288\) | −4418.40 | − | 796.659i | −0.904017 | − | 0.162999i | ||||
\(289\) | 2464.55 | 0.501639 | ||||||||
\(290\) | −708.423 | −0.143448 | ||||||||
\(291\) | −1591.45 | − | 1904.06i | −0.320594 | − | 0.383568i | ||||
\(292\) | − | 7379.17i | − | 1.47888i | ||||||
\(293\) | −7321.08 | −1.45973 | −0.729867 | − | 0.683589i | \(-0.760418\pi\) | ||||
−0.729867 | + | 0.683589i | \(0.760418\pi\) | |||||||
\(294\) | 4866.35 | + | 6628.69i | 0.965345 | + | 1.31494i | ||||
\(295\) | 1069.96 | 0.211172 | ||||||||
\(296\) | 212.641i | 0.0417551i | ||||||||
\(297\) | −7972.05 | + | 4541.40i | −1.55753 | + | 0.887269i | ||||
\(298\) | −9029.46 | −1.75524 | ||||||||
\(299\) | −5975.57 | −1.15577 | ||||||||
\(300\) | 1324.43 | − | 1106.98i | 0.254886 | − | 0.213039i | ||||
\(301\) | −163.870 | + | 5205.94i | −0.0313799 | + | 0.996894i | ||||
\(302\) | 4455.17i | 0.848895i | ||||||||
\(303\) | 4694.44 | − | 3923.71i | 0.890061 | − | 0.743931i | ||||
\(304\) | 39.0804i | 0.00737307i | ||||||||
\(305\) | − | 3368.33i | − | 0.632361i | ||||||
\(306\) | −10530.2 | − | 1898.65i | −1.96723 | − | 0.354701i | ||||
\(307\) | 7027.37i | 1.30643i | 0.757173 | + | 0.653214i | \(0.226580\pi\) | ||||
−0.757173 | + | 0.653214i | \(0.773420\pi\) | |||||||
\(308\) | −16085.6 | − | 506.335i | −2.97584 | − | 0.0936724i | ||||
\(309\) | 787.070 | + | 941.674i | 0.144902 | + | 0.173365i | ||||
\(310\) | 1409.42 | 0.258225 | ||||||||
\(311\) | 8857.75 | 1.61504 | 0.807520 | − | 0.589841i | \(-0.200809\pi\) | ||||
0.807520 | + | 0.589841i | \(0.200809\pi\) | |||||||
\(312\) | 3009.36 | − | 2515.28i | 0.546062 | − | 0.456409i | ||||
\(313\) | 8152.90i | 1.47230i | 0.676820 | + | 0.736148i | \(0.263357\pi\) | ||||
−0.676820 | + | 0.736148i | \(0.736643\pi\) | |||||||
\(314\) | −5904.21 | −1.06113 | ||||||||
\(315\) | 2445.38 | + | 520.845i | 0.437402 | + | 0.0931628i | ||||
\(316\) | −11196.0 | −1.99312 | ||||||||
\(317\) | − | 8636.70i | − | 1.53024i | −0.643889 | − | 0.765119i | \(-0.722680\pi\) | ||
0.643889 | − | 0.765119i | \(-0.277320\pi\) | |||||||
\(318\) | 3896.11 | − | 3256.45i | 0.687054 | − | 0.574253i | ||||
\(319\) | 2008.22 | 0.352473 | ||||||||
\(320\) | −4086.52 | −0.713885 | ||||||||
\(321\) | 1272.44 | + | 1522.38i | 0.221247 | + | 0.264707i | ||||
\(322\) | 519.248 | − | 16495.8i | 0.0898651 | − | 2.85489i | ||||
\(323\) | − | 536.054i | − | 0.0923431i | ||||||
\(324\) | 9076.76 | + | 3383.15i | 1.55637 | + | 0.580101i | ||||
\(325\) | − | 773.469i | − | 0.132013i | ||||||
\(326\) | − | 7192.02i | − | 1.22187i | ||||||
\(327\) | 263.985 | − | 220.644i | 0.0446434 | − | 0.0373138i | ||||
\(328\) | 9455.92i | 1.59182i | ||||||||
\(329\) | −121.506 | + | 3860.08i | −0.0203613 | + | 0.646849i | ||||
\(330\) | −6014.85 | + | 5027.33i | −1.00335 | + | 0.838623i | ||||
\(331\) | −8444.88 | −1.40233 | −0.701167 | − | 0.712997i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(332\) | −11795.1 | −1.94981 | ||||||||
\(333\) | −41.7577 | + | 231.595i | −0.00687180 | + | 0.0381121i | ||||
\(334\) | − | 1978.50i | − | 0.324127i | ||||||
\(335\) | 2501.99 | 0.408055 | ||||||||
\(336\) | 371.721 | + | 474.301i | 0.0603542 | + | 0.0770097i | ||||
\(337\) | −2136.69 | −0.345380 | −0.172690 | − | 0.984976i | \(-0.555246\pi\) | ||||
−0.172690 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(338\) | 5720.24i | 0.920532i | ||||||||
\(339\) | 5466.78 | + | 6540.62i | 0.875855 | + | 1.04790i | ||||
\(340\) | −5706.59 | −0.910245 | ||||||||
\(341\) | −3995.39 | −0.634493 | ||||||||
\(342\) | −137.956 | + | 765.127i | −0.0218123 | + | 0.120975i | ||||
\(343\) | −598.791 | + | 6324.16i | −0.0942615 | + | 0.995547i | ||||
\(344\) | 6861.21i | 1.07538i | ||||||||
\(345\) | −3218.07 | − | 3850.20i | −0.502189 | − | 0.600834i | ||||
\(346\) | − | 7884.60i | − | 1.22508i | ||||||
\(347\) | 7751.53i | 1.19920i | 0.800298 | + | 0.599602i | \(0.204674\pi\) | ||||
−0.800298 | + | 0.599602i | \(0.795326\pi\) | |||||||
\(348\) | −1359.75 | − | 1626.84i | −0.209455 | − | 0.250598i | ||||
\(349\) | − | 8211.51i | − | 1.25946i | −0.776814 | − | 0.629731i | \(-0.783165\pi\) | ||
0.776814 | − | 0.629731i | \(-0.216835\pi\) | |||||||
\(350\) | 2135.19 | + | 67.2107i | 0.326088 | + | 0.0102645i | ||||
\(351\) | 3771.55 | − | 2148.52i | 0.573533 | − | 0.326722i | ||||
\(352\) | 10874.3 | 1.64660 | ||||||||
\(353\) | −5500.56 | −0.829364 | −0.414682 | − | 0.909966i | \(-0.636107\pi\) | ||||
−0.414682 | + | 0.909966i | \(0.636107\pi\) | |||||||
\(354\) | 3290.13 | + | 3936.41i | 0.493979 | + | 0.591011i | ||||
\(355\) | − | 1597.30i | − | 0.238805i | ||||||
\(356\) | 6381.37 | 0.950033 | ||||||||
\(357\) | −5098.78 | − | 6505.84i | −0.755899 | − | 0.964498i | ||||
\(358\) | −5210.31 | −0.769200 | ||||||||
\(359\) | − | 7487.50i | − | 1.10077i | −0.834912 | − | 0.550383i | \(-0.814482\pi\) | ||
0.834912 | − | 0.550383i | \(-0.185518\pi\) | |||||||
\(360\) | 3241.31 | + | 584.424i | 0.474533 | + | 0.0855606i | ||||
\(361\) | 6820.05 | 0.994321 | ||||||||
\(362\) | 18444.1 | 2.67790 | ||||||||
\(363\) | 11744.2 | − | 9816.01i | 1.69810 | − | 1.41930i | ||||
\(364\) | 7610.02 | + | 239.545i | 1.09581 | + | 0.0344933i | ||||
\(365\) | − | 2776.69i | − | 0.398187i | ||||||
\(366\) | 12392.1 | − | 10357.6i | 1.76980 | − | 1.47924i | ||||
\(367\) | − | 2158.05i | − | 0.306946i | −0.988153 | − | 0.153473i | \(-0.950954\pi\) | ||
0.988153 | − | 0.153473i | \(-0.0490458\pi\) | |||||||
\(368\) | − | 1209.44i | − | 0.171321i | ||||||
\(369\) | −1856.92 | + | 10298.8i | −0.261972 | + | 1.45294i | ||||
\(370\) | 201.070i | 0.0282517i | ||||||||
\(371\) | 3920.68 | + | 123.414i | 0.548657 | + | 0.0172704i | ||||
\(372\) | 2705.24 | + | 3236.63i | 0.377044 | + | 0.451106i | ||||
\(373\) | 3989.15 | 0.553755 | 0.276877 | − | 0.960905i | \(-0.410700\pi\) | ||||
0.276877 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(374\) | 25916.4 | 3.58316 | ||||||||
\(375\) | 498.364 | − | 416.543i | 0.0686278 | − | 0.0573605i | ||||
\(376\) | 5087.43i | 0.697777i | ||||||||
\(377\) | −950.082 | −0.129792 | ||||||||
\(378\) | 5603.34 | + | 10598.2i | 0.762447 | + | 1.44210i | ||||
\(379\) | −6120.41 | −0.829510 | −0.414755 | − | 0.909933i | \(-0.636133\pi\) | ||||
−0.414755 | + | 0.909933i | \(0.636133\pi\) | |||||||
\(380\) | 414.642i | 0.0559754i | ||||||||
\(381\) | −1615.60 | + | 1350.35i | −0.217243 | + | 0.181576i | ||||
\(382\) | −2511.48 | −0.336384 | ||||||||
\(383\) | −7418.34 | −0.989711 | −0.494856 | − | 0.868975i | \(-0.664779\pi\) | ||||
−0.494856 | + | 0.868975i | \(0.664779\pi\) | |||||||
\(384\) | −8133.12 | − | 9730.70i | −1.08084 | − | 1.29315i | ||||
\(385\) | −6052.79 | − | 190.527i | −0.801243 | − | 0.0252212i | ||||
\(386\) | − | 20477.0i | − | 2.70013i | ||||||
\(387\) | −1347.38 | + | 7472.80i | −0.176980 | + | 0.981561i | ||||
\(388\) | − | 6345.93i | − | 0.830324i | ||||||
\(389\) | − | 10680.3i | − | 1.39206i | −0.718012 | − | 0.696031i | \(-0.754948\pi\) | ||
0.718012 | − | 0.696031i | \(-0.245052\pi\) | |||||||
\(390\) | 2845.60 | − | 2378.41i | 0.369469 | − | 0.308809i | ||||
\(391\) | 16589.5i | 2.14569i | ||||||||
\(392\) | −526.295 | + | 8351.55i | −0.0678111 | + | 1.07606i | ||||
\(393\) | −7984.77 | + | 6673.83i | −1.02488 | + | 0.856616i | ||||
\(394\) | 5369.69 | 0.686601 | ||||||||
\(395\) | −4212.91 | −0.536644 | ||||||||
\(396\) | −23089.8 | − | 4163.21i | −2.93007 | − | 0.528305i | ||||
\(397\) | 7169.57i | 0.906374i | 0.891415 | + | 0.453187i | \(0.149713\pi\) | ||||
−0.891415 | + | 0.453187i | \(0.850287\pi\) | |||||||
\(398\) | 10592.8 | 1.33409 | ||||||||
\(399\) | −472.715 | + | 370.478i | −0.0593117 | + | 0.0464839i | ||||
\(400\) | 156.548 | 0.0195685 | ||||||||
\(401\) | 3463.68i | 0.431341i | 0.976466 | + | 0.215671i | \(0.0691938\pi\) | ||||
−0.976466 | + | 0.215671i | \(0.930806\pi\) | |||||||
\(402\) | 7693.62 | + | 9204.88i | 0.954535 | + | 1.14203i | ||||
\(403\) | 1890.20 | 0.233642 | ||||||||
\(404\) | 15645.8 | 1.92675 | ||||||||
\(405\) | 3415.47 | + | 1273.04i | 0.419051 | + | 0.156192i | ||||
\(406\) | 82.5575 | − | 2622.74i | 0.0100918 | − | 0.320602i | ||||
\(407\) | − | 569.989i | − | 0.0694184i | ||||||
\(408\) | −6982.96 | − | 8354.62i | −0.847324 | − | 1.01376i | ||||
\(409\) | − | 12770.9i | − | 1.54396i | −0.635646 | − | 0.771980i | \(-0.719266\pi\) | ||
0.635646 | − | 0.771980i | \(-0.280734\pi\) | |||||||
\(410\) | 8941.38i | 1.07703i | ||||||||
\(411\) | −7911.63 | − | 9465.71i | −0.949518 | − | 1.13603i | ||||
\(412\) | 3138.44i | 0.375291i | ||||||||
\(413\) | −124.690 | + | 3961.24i | −0.0148562 | + | 0.471961i | ||||
\(414\) | 4269.38 | − | 23678.7i | 0.506832 | − | 2.81098i | ||||
\(415\) | −4438.33 | −0.524985 | ||||||||
\(416\) | −5144.60 | −0.606333 | ||||||||
\(417\) | 3394.72 | + | 4061.55i | 0.398658 | + | 0.476966i | ||||
\(418\) | − | 1883.09i | − | 0.220346i | ||||||
\(419\) | −15235.0 | −1.77632 | −0.888159 | − | 0.459536i | \(-0.848016\pi\) | ||||
−0.888159 | + | 0.459536i | \(0.848016\pi\) | |||||||
\(420\) | 3943.94 | + | 5032.32i | 0.458202 | + | 0.584648i | ||||
\(421\) | −7109.57 | −0.823039 | −0.411519 | − | 0.911401i | \(-0.635002\pi\) | ||||
−0.411519 | + | 0.911401i | \(0.635002\pi\) | |||||||
\(422\) | 6295.70i | 0.726232i | ||||||||
\(423\) | −999.053 | + | 5540.91i | −0.114836 | + | 0.636899i | ||||
\(424\) | 5167.30 | 0.591854 | ||||||||
\(425\) | −2147.32 | −0.245083 | ||||||||
\(426\) | 5876.48 | − | 4911.68i | 0.668349 | − | 0.558619i | ||||
\(427\) | 12470.3 | + | 392.535i | 1.41330 | + | 0.0444874i | ||||
\(428\) | 5073.84i | 0.573022i | ||||||||
\(429\) | −8066.65 | + | 6742.27i | −0.907835 | + | 0.758787i | ||||
\(430\) | 6487.86i | 0.727610i | ||||||||
\(431\) | 6091.94i | 0.680832i | 0.940275 | + | 0.340416i | \(0.110568\pi\) | ||||
−0.940275 | + | 0.340416i | \(0.889432\pi\) | |||||||
\(432\) | 434.854 | + | 763.349i | 0.0484304 | + | 0.0850154i | ||||
\(433\) | 1238.51i | 0.137457i | 0.997635 | + | 0.0687285i | \(0.0218942\pi\) | ||||
−0.997635 | + | 0.0687285i | \(0.978106\pi\) | |||||||
\(434\) | −164.249 | + | 5217.98i | −0.0181664 | + | 0.577122i | ||||
\(435\) | −511.656 | − | 612.160i | −0.0563954 | − | 0.0674732i | ||||
\(436\) | 879.817 | 0.0966413 | ||||||||
\(437\) | 1205.39 | 0.131949 | ||||||||
\(438\) | 10215.5 | − | 8538.29i | 1.11442 | − | 0.931451i | ||||
\(439\) | − | 2934.43i | − | 0.319027i | −0.987196 | − | 0.159513i | \(-0.949007\pi\) | ||
0.987196 | − | 0.159513i | \(-0.0509925\pi\) | |||||||
\(440\) | −7977.32 | −0.864327 | ||||||||
\(441\) | −2213.26 | + | 8992.64i | −0.238987 | + | 0.971023i | ||||
\(442\) | −12260.9 | −1.31944 | ||||||||
\(443\) | 1995.37i | 0.214002i | 0.994259 | + | 0.107001i | \(0.0341247\pi\) | ||||
−0.994259 | + | 0.107001i | \(0.965875\pi\) | |||||||
\(444\) | −461.743 | + | 385.934i | −0.0493544 | + | 0.0412514i | ||||
\(445\) | 2401.23 | 0.255795 | ||||||||
\(446\) | 3611.04 | 0.383380 | ||||||||
\(447\) | −6521.49 | − | 7802.50i | −0.690058 | − | 0.825606i | ||||
\(448\) | 476.230 | − | 15129.2i | 0.0502227 | − | 1.59551i | ||||
\(449\) | 8336.05i | 0.876175i | 0.898932 | + | 0.438088i | \(0.144344\pi\) | ||||
−0.898932 | + | 0.438088i | \(0.855656\pi\) | |||||||
\(450\) | 3064.94 | + | 552.622i | 0.321072 | + | 0.0578908i | ||||
\(451\) | − | 25346.8i | − | 2.64642i | ||||||
\(452\) | 21798.8i | 2.26843i | ||||||||
\(453\) | −3849.79 | + | 3217.73i | −0.399291 | + | 0.333735i | ||||
\(454\) | 1990.02i | 0.205718i | ||||||||
\(455\) | 2863.55 | + | 90.1377i | 0.295045 | + | 0.00928730i | ||||
\(456\) | −607.048 | + | 507.383i | −0.0623413 | + | 0.0521061i | ||||
\(457\) | −4202.63 | −0.430177 | −0.215088 | − | 0.976595i | \(-0.569004\pi\) | ||||
−0.215088 | + | 0.976595i | \(0.569004\pi\) | |||||||
\(458\) | −23502.1 | −2.39778 | ||||||||
\(459\) | −5964.76 | − | 10470.6i | −0.606560 | − | 1.06476i | ||||
\(460\) | − | 12832.1i | − | 1.30065i | ||||||
\(461\) | 2079.74 | 0.210116 | 0.105058 | − | 0.994466i | \(-0.466497\pi\) | ||||
0.105058 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(462\) | −17911.3 | − | 22854.2i | −1.80370 | − | 2.30145i | ||||
\(463\) | 18876.0 | 1.89469 | 0.947344 | − | 0.320219i | \(-0.103757\pi\) | ||||
0.947344 | + | 0.320219i | \(0.103757\pi\) | |||||||
\(464\) | − | 192.294i | − | 0.0192392i | ||||||
\(465\) | 1017.95 | + | 1217.90i | 0.101519 | + | 0.121460i | ||||
\(466\) | 17740.0 | 1.76349 | ||||||||
\(467\) | 13053.4 | 1.29345 | 0.646725 | − | 0.762723i | \(-0.276138\pi\) | ||||
0.646725 | + | 0.762723i | \(0.276138\pi\) | |||||||
\(468\) | 10923.7 | + | 1969.60i | 1.07895 | + | 0.194540i | ||||
\(469\) | −291.575 | + | 9262.93i | −0.0287072 | + | 0.911988i | ||||
\(470\) | 4810.60i | 0.472120i | ||||||||
\(471\) | −4264.29 | − | 5101.93i | −0.417172 | − | 0.499118i | ||||
\(472\) | 5220.75i | 0.509120i | ||||||||
\(473\) | − | 18391.6i | − | 1.78784i | ||||||
\(474\) | −12954.7 | − | 15499.4i | −1.25533 | − | 1.50192i | ||||
\(475\) | 156.024i | 0.0150713i | ||||||||
\(476\) | 665.029 | − | 21127.1i | 0.0640369 | − | 2.03436i | ||||
\(477\) | 5627.90 | + | 1014.74i | 0.540218 | + | 0.0974039i | ||||
\(478\) | −6579.73 | −0.629602 | ||||||||
\(479\) | −17589.1 | −1.67780 | −0.838898 | − | 0.544289i | \(-0.816800\pi\) | ||||
−0.838898 | + | 0.544289i | \(0.816800\pi\) | |||||||
\(480\) | −2770.56 | − | 3314.79i | −0.263455 | − | 0.315205i | ||||
\(481\) | 269.659i | 0.0255622i | ||||||||
\(482\) | −24138.5 | −2.28107 | ||||||||
\(483\) | 14629.3 | − | 11465.3i | 1.37817 | − | 1.08010i | ||||
\(484\) | 39141.4 | 3.67594 | ||||||||
\(485\) | − | 2387.89i | − | 0.223564i | ||||||
\(486\) | 5819.02 | + | 16480.1i | 0.543120 | + | 1.53818i | ||||
\(487\) | −13335.6 | −1.24085 | −0.620426 | − | 0.784265i | \(-0.713040\pi\) | ||||
−0.620426 | + | 0.784265i | \(0.713040\pi\) | |||||||
\(488\) | 16435.3 | 1.52458 | ||||||||
\(489\) | 6214.74 | − | 5194.40i | 0.574724 | − | 0.480366i | ||||
\(490\) | −497.657 | + | 7897.11i | −0.0458814 | + | 0.728072i | ||||
\(491\) | 5242.11i | 0.481819i | 0.970548 | + | 0.240910i | \(0.0774457\pi\) | ||||
−0.970548 | + | 0.240910i | \(0.922554\pi\) | |||||||
\(492\) | −20533.3 | + | 17162.1i | −1.88153 | + | 1.57262i | ||||
\(493\) | 2637.63i | 0.240959i | ||||||||
\(494\) | 890.881i | 0.0811389i | ||||||||
\(495\) | −8688.40 | − | 1566.56i | −0.788919 | − | 0.142246i | ||||
\(496\) | 382.571i | 0.0346330i | ||||||||
\(497\) | 5913.55 | + | 186.144i | 0.533720 | + | 0.0168002i | ||||
\(498\) | −13647.8 | − | 16328.7i | −1.22806 | − | 1.46929i | ||||
\(499\) | −2586.43 | −0.232033 | −0.116017 | − | 0.993247i | \(-0.537013\pi\) | ||||
−0.116017 | + | 0.993247i | \(0.537013\pi\) | |||||||
\(500\) | 1660.97 | 0.148561 | ||||||||
\(501\) | 1709.65 | − | 1428.96i | 0.152458 | − | 0.127428i | ||||
\(502\) | 9792.87i | 0.870671i | ||||||||
\(503\) | 11209.5 | 0.993648 | 0.496824 | − | 0.867851i | \(-0.334499\pi\) | ||||
0.496824 | + | 0.867851i | \(0.334499\pi\) | |||||||
\(504\) | −2541.40 | + | 11931.9i | −0.224609 | + | 1.05454i | ||||
\(505\) | 5887.31 | 0.518776 | ||||||||
\(506\) | 58276.6i | 5.11998i | ||||||||
\(507\) | −4942.95 | + | 4131.42i | −0.432987 | + | 0.361899i | ||||
\(508\) | −5384.51 | −0.470274 | ||||||||
\(509\) | 7789.54 | 0.678321 | 0.339160 | − | 0.940729i | \(-0.389857\pi\) | ||||
0.339160 | + | 0.940729i | \(0.389857\pi\) | |||||||
\(510\) | −6602.99 | − | 7900.01i | −0.573304 | − | 0.685918i | ||||
\(511\) | 10279.9 | + | 323.587i | 0.889933 | + | 0.0280130i | ||||
\(512\) | − | 2263.42i | − | 0.195371i | ||||||
\(513\) | −760.797 | + | 433.400i | −0.0654776 | + | 0.0373003i | ||||
\(514\) | 29287.2i | 2.51323i | ||||||||
\(515\) | 1180.96i | 0.101047i | ||||||||
\(516\) | −14898.9 | + | 12452.8i | −1.27110 | + | 1.06241i | ||||
\(517\) | − | 13637.0i | − | 1.16006i | ||||||
\(518\) | −744.406 | − | 23.4321i | −0.0631415 | − | 0.00198754i | ||||
\(519\) | 6813.21 | − | 5694.62i | 0.576236 | − | 0.481630i | ||||
\(520\) | 3774.04 | 0.318274 | ||||||||
\(521\) | −11342.0 | −0.953749 | −0.476874 | − | 0.878971i | \(-0.658230\pi\) | ||||
−0.476874 | + | 0.878971i | \(0.658230\pi\) | |||||||
\(522\) | 678.808 | − | 3764.78i | 0.0569169 | − | 0.315670i | ||||
\(523\) | 13306.6i | 1.11254i | 0.831003 | + | 0.556269i | \(0.187767\pi\) | ||||
−0.831003 | + | 0.556269i | \(0.812233\pi\) | |||||||
\(524\) | −26611.9 | −2.21860 | ||||||||
\(525\) | 1484.05 | + | 1893.60i | 0.123370 | + | 0.157416i | ||||
\(526\) | 4298.94 | 0.356355 | ||||||||
\(527\) | − | 5247.61i | − | 0.433756i | ||||||
\(528\) | −1364.61 | − | 1632.66i | −0.112476 | − | 0.134569i | ||||
\(529\) | −25136.8 | −2.06598 | ||||||||
\(530\) | 4886.12 | 0.400452 | ||||||||
\(531\) | −1025.23 | + | 5686.12i | −0.0837879 | + | 0.464701i | ||||
\(532\) | −1535.09 | − | 48.3211i | −0.125103 | − | 0.00393794i | ||||
\(533\) | 11991.5i | 0.974501i | ||||||||
\(534\) | 7383.76 | + | 8834.14i | 0.598364 | + | 0.715900i | ||||
\(535\) | 1909.22i | 0.154286i | ||||||||
\(536\) | 12208.2i | 0.983791i | ||||||||
\(537\) | −3763.12 | − | 4502.31i | −0.302404 | − | 0.361805i | ||||
\(538\) | 14975.6i | 1.20008i | ||||||||
\(539\) | 1410.75 | − | 22386.5i | 0.112737 | − | 1.78897i | ||||
\(540\) | 4613.78 | + | 8099.11i | 0.367677 | + | 0.645426i | ||||
\(541\) | −11369.5 | −0.903533 | −0.451767 | − | 0.892136i | \(-0.649206\pi\) | ||||
−0.451767 | + | 0.892136i | \(0.649206\pi\) | |||||||
\(542\) | 12623.4 | 1.00040 | ||||||||
\(543\) | 13321.1 | + | 15937.8i | 1.05279 | + | 1.25959i | ||||
\(544\) | 14282.5i | 1.12566i | ||||||||
\(545\) | 331.064 | 0.0260206 | ||||||||
\(546\) | 8473.78 | + | 10812.2i | 0.664184 | + | 0.847473i | ||||
\(547\) | −15590.8 | −1.21867 | −0.609336 | − | 0.792912i | \(-0.708564\pi\) | ||||
−0.609336 | + | 0.792912i | \(0.708564\pi\) | |||||||
\(548\) | − | 31547.6i | − | 2.45921i | ||||||
\(549\) | 17900.4 | + | 3227.52i | 1.39156 | + | 0.250906i | ||||
\(550\) | −7543.24 | −0.584809 | ||||||||
\(551\) | 191.651 | 0.0148178 | ||||||||
\(552\) | 18786.6 | − | 15702.2i | 1.44857 | − | 1.21074i | ||||
\(553\) | 490.960 | − | 15597.1i | 0.0377536 | − | 1.19938i | ||||
\(554\) | − | 13760.8i | − | 1.05531i | ||||||
\(555\) | −173.748 | + | 145.222i | −0.0132886 | + | 0.0111069i | ||||
\(556\) | 13536.5i | 1.03251i | ||||||||
\(557\) | − | 6966.49i | − | 0.529946i | −0.964256 | − | 0.264973i | \(-0.914637\pi\) | ||
0.964256 | − | 0.264973i | \(-0.0853630\pi\) | |||||||
\(558\) | −1350.50 | + | 7490.09i | −0.102457 | + | 0.568245i | ||||
\(559\) | 8701.01i | 0.658343i | ||||||||
\(560\) | −18.2436 | + | 579.574i | −0.00137667 | + | 0.0437348i | ||||
\(561\) | 18718.0 | + | 22394.8i | 1.40869 | + | 1.68540i | ||||
\(562\) | −11974.7 | −0.898796 | ||||||||
\(563\) | 13867.2 | 1.03807 | 0.519035 | − | 0.854753i | \(-0.326291\pi\) | ||||
0.519035 | + | 0.854753i | \(0.326291\pi\) | |||||||
\(564\) | −11047.2 | + | 9233.48i | −0.824772 | + | 0.689361i | ||||
\(565\) | 8202.61i | 0.610772i | ||||||||
\(566\) | 30995.8 | 2.30185 | ||||||||
\(567\) | −5111.08 | + | 12496.4i | −0.378563 | + | 0.925575i | ||||
\(568\) | 7793.81 | 0.575741 | ||||||||
\(569\) | − | 14357.4i | − | 1.05781i | −0.848680 | − | 0.528906i | \(-0.822602\pi\) | ||
0.848680 | − | 0.528906i | \(-0.177398\pi\) | |||||||
\(570\) | −574.016 | + | 479.774i | −0.0421805 | + | 0.0352553i | ||||
\(571\) | 15732.7 | 1.15305 | 0.576526 | − | 0.817079i | \(-0.304408\pi\) | ||||
0.576526 | + | 0.817079i | \(0.304408\pi\) | |||||||
\(572\) | −26884.8 | −1.96523 | ||||||||
\(573\) | −1813.91 | − | 2170.21i | −0.132246 | − | 0.158223i | ||||
\(574\) | −33103.0 | − | 1042.00i | −2.40713 | − | 0.0757706i | ||||
\(575\) | − | 4828.55i | − | 0.350199i | ||||||
\(576\) | 3915.68 | − | 21717.0i | 0.283252 | − | 1.57096i | ||||
\(577\) | − | 15847.2i | − | 1.14337i | −0.820472 | − | 0.571686i | \(-0.806290\pi\) | ||
0.820472 | − | 0.571686i | \(-0.193710\pi\) | |||||||
\(578\) | 11371.1i | 0.818297i | ||||||||
\(579\) | 17694.5 | − | 14789.4i | 1.27005 | − | 1.06153i | ||||
\(580\) | − | 2040.23i | − | 0.146062i | ||||||
\(581\) | 517.229 | − | 16431.7i | 0.0369334 | − | 1.17332i | ||||
\(582\) | 8785.09 | − | 7342.75i | 0.625694 | − | 0.522967i | ||||
\(583\) | −13851.1 | −0.983966 | ||||||||
\(584\) | 13548.5 | 0.960000 | ||||||||
\(585\) | 4110.45 | + | 741.134i | 0.290506 | + | 0.0523797i | ||||
\(586\) | − | 33778.5i | − | 2.38119i | ||||||
\(587\) | 18831.4 | 1.32411 | 0.662055 | − | 0.749455i | \(-0.269684\pi\) | ||||
0.662055 | + | 0.749455i | \(0.269684\pi\) | |||||||
\(588\) | −19090.4 | + | 14014.9i | −1.33890 | + | 0.982932i | ||||
\(589\) | −381.292 | −0.0266738 | ||||||||
\(590\) | 4936.66i | 0.344473i | ||||||||
\(591\) | 3878.23 | + | 4640.03i | 0.269931 | + | 0.322953i | ||||
\(592\) | −54.5783 | −0.00378911 | ||||||||
\(593\) | −1882.77 | −0.130381 | −0.0651905 | − | 0.997873i | \(-0.520766\pi\) | ||||
−0.0651905 | + | 0.997873i | \(0.520766\pi\) | |||||||
\(594\) | −20953.4 | − | 36781.9i | −1.44735 | − | 2.54071i | ||||
\(595\) | 250.242 | − | 7949.84i | 0.0172419 | − | 0.547750i | ||||
\(596\) | − | 26004.5i | − | 1.78722i | ||||||
\(597\) | 7650.61 | + | 9153.42i | 0.524487 | + | 0.627511i | ||||
\(598\) | − | 27570.4i | − | 1.88535i | ||||||
\(599\) | 11287.0i | 0.769906i | 0.922936 | + | 0.384953i | \(0.125782\pi\) | ||||
−0.922936 | + | 0.384953i | \(0.874218\pi\) | |||||||
\(600\) | 2032.47 | + | 2431.70i | 0.138292 | + | 0.165457i | ||||
\(601\) | − | 1723.22i | − | 0.116958i | −0.998289 | − | 0.0584789i | \(-0.981375\pi\) | ||
0.998289 | − | 0.0584789i | \(-0.0186250\pi\) | |||||||
\(602\) | −24019.5 | − | 756.076i | −1.62618 | − | 0.0511883i | ||||
\(603\) | −2397.40 | + | 13296.4i | −0.161906 | + | 0.897960i | ||||
\(604\) | −12830.7 | −0.864361 | ||||||||
\(605\) | 14728.4 | 0.989742 | ||||||||
\(606\) | 18103.4 | + | 21659.5i | 1.21353 | + | 1.45191i | ||||
\(607\) | 12098.5i | 0.808997i | 0.914539 | + | 0.404498i | \(0.132554\pi\) | ||||
−0.914539 | + | 0.404498i | \(0.867446\pi\) | |||||||
\(608\) | 1037.77 | 0.0692222 | ||||||||
\(609\) | 2325.98 | − | 1822.92i | 0.154767 | − | 0.121295i | ||||
\(610\) | 15541.0 | 1.03154 | ||||||||
\(611\) | 6451.60i | 0.427175i | ||||||||
\(612\) | 5468.03 | − | 30326.6i | 0.361163 | − | 2.00307i | ||||
\(613\) | 5440.08 | 0.358438 | 0.179219 | − | 0.983809i | \(-0.442643\pi\) | ||||
0.179219 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(614\) | −32423.3 | −2.13111 | ||||||||
\(615\) | −7726.40 | + | 6457.88i | −0.506599 | + | 0.423426i | ||||
\(616\) | 929.653 | − | 29533.8i | 0.0608065 | − | 1.93174i | ||||
\(617\) | − | 4755.92i | − | 0.310318i | −0.987890 | − | 0.155159i | \(-0.950411\pi\) | ||
0.987890 | − | 0.155159i | \(-0.0495890\pi\) | |||||||
\(618\) | −4344.75 | + | 3631.43i | −0.282802 | + | 0.236372i | ||||
\(619\) | − | 1077.63i | − | 0.0699734i | −0.999388 | − | 0.0349867i | \(-0.988861\pi\) | ||
0.999388 | − | 0.0349867i | \(-0.0111389\pi\) | |||||||
\(620\) | 4059.07i | 0.262929i | ||||||||
\(621\) | 23544.7 | − | 13412.6i | 1.52144 | − | 0.866713i | ||||
\(622\) | 40868.5i | 2.63453i | ||||||||
\(623\) | −279.832 | + | 8889.86i | −0.0179955 | + | 0.571693i | ||||
\(624\) | 645.594 | + | 772.408i | 0.0414174 | + | 0.0495530i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −37616.3 | −2.40168 | ||||||||
\(627\) | 1627.20 | − | 1360.05i | 0.103643 | − | 0.0866271i | ||||
\(628\) | − | 17003.9i | − | 1.08046i | ||||||
\(629\) | 748.633 | 0.0474562 | ||||||||
\(630\) | −2403.11 | + | 11282.7i | −0.151972 | + | 0.713511i | ||||
\(631\) | −9647.56 | −0.608658 | −0.304329 | − | 0.952567i | \(-0.598432\pi\) | ||||
−0.304329 | + | 0.952567i | \(0.598432\pi\) | |||||||
\(632\) | − | 20556.4i | − | 1.29381i | ||||||
\(633\) | −5440.22 | + | 4547.04i | −0.341594 | + | 0.285511i | ||||
\(634\) | 39848.5 | 2.49619 | ||||||||
\(635\) | −2026.12 | −0.126621 | ||||||||
\(636\) | 9378.43 | + | 11220.6i | 0.584716 | + | 0.699571i | ||||
\(637\) | −667.419 | + | 10591.0i | −0.0415135 | + | 0.658760i | ||||
\(638\) | 9265.65i | 0.574970i | ||||||||
\(639\) | 8488.53 | + | 1530.52i | 0.525510 | + | 0.0947520i | ||||
\(640\) | − | 12203.3i | − | 0.753715i | ||||||
\(641\) | − | 5927.19i | − | 0.365226i | −0.983185 | − | 0.182613i | \(-0.941544\pi\) | ||
0.983185 | − | 0.182613i | \(-0.0584555\pi\) | |||||||
\(642\) | −7024.05 | + | 5870.84i | −0.431803 | + | 0.360909i | ||||
\(643\) | 431.199i | 0.0264460i | 0.999913 | + | 0.0132230i | \(0.00420914\pi\) | ||||
−0.999913 | + | 0.0132230i | \(0.995791\pi\) | |||||||
\(644\) | 47507.2 | + | 1495.41i | 2.90690 | + | 0.0915023i | ||||
\(645\) | −5606.27 | + | 4685.83i | −0.342243 | + | 0.286053i | ||||
\(646\) | 2473.28 | 0.150634 | ||||||||
\(647\) | 5165.60 | 0.313881 | 0.156940 | − | 0.987608i | \(-0.449837\pi\) | ||||
0.156940 | + | 0.987608i | \(0.449837\pi\) | |||||||
\(648\) | −6211.61 | + | 16665.3i | −0.376567 | + | 1.01030i | ||||
\(649\) | − | 13994.3i | − | 0.846419i | ||||||
\(650\) | 3568.68 | 0.215346 | ||||||||
\(651\) | −4627.57 | + | 3626.73i | −0.278600 | + | 0.218345i | ||||
\(652\) | 20712.7 | 1.24413 | ||||||||
\(653\) | 9518.46i | 0.570423i | 0.958465 | + | 0.285211i | \(0.0920638\pi\) | ||||
−0.958465 | + | 0.285211i | \(0.907936\pi\) | |||||||
\(654\) | 1018.02 | + | 1217.99i | 0.0608681 | + | 0.0728244i | ||||
\(655\) | −10013.7 | −0.597356 | ||||||||
\(656\) | −2427.04 | −0.144451 | ||||||||
\(657\) | 14756.2 | + | 2660.61i | 0.876244 | + | 0.157991i | ||||
\(658\) | −17809.9 | − | 560.613i | −1.05517 | − | 0.0332142i | ||||
\(659\) | 21188.2i | 1.25247i | 0.779636 | + | 0.626233i | \(0.215404\pi\) | ||||
−0.779636 | + | 0.626233i | \(0.784596\pi\) | |||||||
\(660\) | −14478.5 | − | 17322.5i | −0.853902 | − | 1.02163i | ||||
\(661\) | 9084.73i | 0.534577i | 0.963617 | + | 0.267288i | \(0.0861276\pi\) | ||||
−0.963617 | + | 0.267288i | \(0.913872\pi\) | |||||||
\(662\) | − | 38963.5i | − | 2.28755i | ||||||
\(663\) | −8855.41 | − | 10594.9i | −0.518726 | − | 0.620620i | ||||
\(664\) | − | 21656.2i | − | 1.26570i | ||||||
\(665\) | −577.636 | − | 18.1826i | −0.0336838 | − | 0.00106029i | ||||
\(666\) | −1068.55 | − | 192.664i | −0.0621703 | − | 0.0112096i | ||||
\(667\) | −5931.09 | −0.344307 | ||||||||
\(668\) | 5697.99 | 0.330032 | ||||||||
\(669\) | 2608.06 | + | 3120.36i | 0.150723 | + | 0.180329i | ||||
\(670\) | 11543.9i | 0.665639i | ||||||||
\(671\) | −44055.3 | −2.53463 | ||||||||
\(672\) | 12594.9 | − | 9870.94i | 0.723006 | − | 0.566637i | ||||
\(673\) | −27912.6 | −1.59874 | −0.799369 | − | 0.600841i | \(-0.794833\pi\) | ||||
−0.799369 | + | 0.600841i | \(0.794833\pi\) | |||||||
\(674\) | − | 9858.41i | − | 0.563400i | ||||||
\(675\) | 1736.11 | + | 3047.59i | 0.0989967 | + | 0.173780i | ||||
\(676\) | −16474.0 | −0.937303 | ||||||||
\(677\) | 6051.62 | 0.343549 | 0.171774 | − | 0.985136i | \(-0.445050\pi\) | ||||
0.171774 | + | 0.985136i | \(0.445050\pi\) | |||||||
\(678\) | −30177.5 | + | 25223.0i | −1.70938 | + | 1.42874i | ||||
\(679\) | 8840.50 | + | 278.278i | 0.499657 | + | 0.0157280i | ||||
\(680\) | − | 10477.6i | − | 0.590876i | ||||||
\(681\) | −1719.61 | + | 1437.28i | −0.0967627 | + | 0.0808762i | ||||
\(682\) | − | 18434.2i | − | 1.03502i | ||||||
\(683\) | − | 13395.7i | − | 0.750470i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) | ||
0.926930 | − | 0.375235i | \(-0.122438\pi\) | |||||||
\(684\) | −2203.53 | − | 397.307i | −0.123179 | − | 0.0222097i | ||||
\(685\) | − | 11871.0i | − | 0.662141i | ||||||
\(686\) | −29178.8 | − | 2762.74i | −1.62398 | − | 0.153764i | ||||
\(687\) | −16974.3 | − | 20308.6i | −0.942664 | − | 1.12783i | ||||
\(688\) | −1761.06 | −0.0975868 | ||||||||
\(689\) | 6552.89 | 0.362330 | ||||||||
\(690\) | 17764.3 | − | 14847.8i | 0.980109 | − | 0.819195i | ||||
\(691\) | 11208.4i | 0.617057i | 0.951215 | + | 0.308528i | \(0.0998365\pi\) | ||||
−0.951215 | + | 0.308528i | \(0.900164\pi\) | |||||||
\(692\) | 22707.3 | 1.24740 | ||||||||
\(693\) | 6812.27 | − | 31983.8i | 0.373415 | − | 1.75319i | ||||
\(694\) | −35764.5 | −1.95620 | ||||||||
\(695\) | 5093.60i | 0.278002i | ||||||||
\(696\) | 2986.96 | − | 2496.56i | 0.162673 | − | 0.135965i | ||||
\(697\) | 33291.0 | 1.80916 | ||||||||
\(698\) | 37886.8 | 2.05449 | ||||||||
\(699\) | 12812.6 | + | 15329.4i | 0.693302 | + | 0.829487i | ||||
\(700\) | −193.564 | + | 6149.26i | −0.0104515 | + | 0.332029i | ||||
\(701\) | − | 23842.7i | − | 1.28463i | −0.766440 | − | 0.642316i | \(-0.777974\pi\) | ||
0.766440 | − | 0.642316i | \(-0.222026\pi\) | |||||||
\(702\) | 9912.97 | + | 17401.4i | 0.532964 | + | 0.935575i | ||||
\(703\) | − | 54.3958i | − | 0.00291831i | ||||||
\(704\) | 53448.6i | 2.86139i | ||||||||
\(705\) | −4156.92 | + | 3474.44i | −0.222069 | + | 0.185610i | ||||
\(706\) | − | 25378.8i | − | 1.35290i | ||||||
\(707\) | −686.089 | + | 21796.1i | −0.0364965 | + | 1.15944i | ||||
\(708\) | −11336.7 | + | 9475.44i | −0.601779 | + | 0.502979i | ||||
\(709\) | −18980.0 | −1.00537 | −0.502686 | − | 0.864469i | \(-0.667655\pi\) | ||||
−0.502686 | + | 0.864469i | \(0.667655\pi\) | |||||||
\(710\) | 7369.71 | 0.389550 | ||||||||
\(711\) | 4036.79 | − | 22388.7i | 0.212928 | − | 1.18093i | ||||
\(712\) | 11716.5i | 0.616704i | ||||||||
\(713\) | 11800.0 | 0.619794 | ||||||||
\(714\) | 30017.1 | − | 23525.1i | 1.57333 | − | 1.23306i | ||||
\(715\) | −10116.4 | −0.529136 | ||||||||
\(716\) | − | 15005.5i | − | 0.783213i | ||||||
\(717\) | −4752.18 | − | 5685.65i | −0.247522 | − | 0.296143i | ||||
\(718\) | 34546.3 | 1.79562 | ||||||||
\(719\) | 8691.86 | 0.450837 | 0.225419 | − | 0.974262i | \(-0.427625\pi\) | ||||
0.225419 | + | 0.974262i | \(0.427625\pi\) | |||||||
\(720\) | −150.003 | + | 831.943i | −0.00776429 | + | 0.0430620i | ||||
\(721\) | −4372.15 | − | 137.625i | −0.225836 | − | 0.00710877i | ||||
\(722\) | 31466.8i | 1.62198i | ||||||||
\(723\) | −17433.9 | − | 20858.4i | −0.896783 | − | 1.07294i | ||||
\(724\) | 53118.1i | 2.72668i | ||||||||
\(725\) | − | 767.712i | − | 0.0393270i | ||||||
\(726\) | 45289.7 | + | 54186.0i | 2.31523 | + | 2.77001i | ||||
\(727\) | − | 3749.84i | − | 0.191298i | −0.995415 | − | 0.0956492i | \(-0.969507\pi\) | ||
0.995415 | − | 0.0956492i | \(-0.0304927\pi\) | |||||||
\(728\) | −439.815 | + | 13972.3i | −0.0223910 | + | 0.711331i | ||||
\(729\) | −10038.0 | + | 16931.0i | −0.509982 | + | 0.860185i | ||||
\(730\) | 12811.2 | 0.649542 | ||||||||
\(731\) | 24155.9 | 1.22221 | ||||||||
\(732\) | 29829.5 | + | 35688.9i | 1.50619 | + | 1.80205i | ||||
\(733\) | 18593.5i | 0.936924i | 0.883484 | + | 0.468462i | \(0.155192\pi\) | ||||
−0.883484 | + | 0.468462i | \(0.844808\pi\) | |||||||
\(734\) | 9956.93 | 0.500704 | ||||||||
\(735\) | −7183.45 | + | 5273.62i | −0.360497 | + | 0.264654i | ||||
\(736\) | −32116.3 | −1.60845 | ||||||||
\(737\) | − | 32724.2i | − | 1.63557i | ||||||
\(738\) | −47517.3 | − | 8567.59i | −2.37010 | − | 0.427341i | ||||
\(739\) | 33391.6 | 1.66215 | 0.831077 | − | 0.556158i | \(-0.187725\pi\) | ||||
0.831077 | + | 0.556158i | \(0.187725\pi\) | |||||||
\(740\) | −579.073 | −0.0287664 | ||||||||
\(741\) | −769.825 | + | 643.435i | −0.0381649 | + | 0.0318990i | ||||
\(742\) | −569.414 | + | 18089.5i | −0.0281723 | + | 0.894995i | ||||
\(743\) | − | 7117.50i | − | 0.351434i | −0.984441 | − | 0.175717i | \(-0.943776\pi\) | ||
0.984441 | − | 0.175717i | \(-0.0562244\pi\) | |||||||
\(744\) | −5942.60 | + | 4966.94i | −0.292831 | + | 0.244754i | ||||
\(745\) | − | 9785.14i | − | 0.481208i | ||||||
\(746\) | 18405.4i | 0.903311i | ||||||||
\(747\) | 4252.78 | − | 23586.6i | 0.208301 | − | 1.15527i | ||||
\(748\) | 74638.0i | 3.64844i | ||||||||
\(749\) | −7068.35 | − | 222.495i | −0.344822 | − | 0.0108542i | ||||
\(750\) | 1921.87 | + | 2299.38i | 0.0935691 | + | 0.111949i | ||||
\(751\) | 17029.8 | 0.827465 | 0.413733 | − | 0.910398i | \(-0.364225\pi\) | ||||
0.413733 | + | 0.910398i | \(0.364225\pi\) | |||||||
\(752\) | −1305.78 | −0.0633206 | ||||||||
\(753\) | −8462.18 | + | 7072.86i | −0.409534 | + | 0.342297i | ||||
\(754\) | − | 4383.55i | − | 0.211723i | ||||||
\(755\) | −4828.03 | −0.232728 | ||||||||
\(756\) | −30522.4 | + | 16137.4i | −1.46837 | + | 0.776337i | ||||
\(757\) | 27250.9 | 1.30839 | 0.654195 | − | 0.756326i | \(-0.273008\pi\) | ||||
0.654195 | + | 0.756326i | \(0.273008\pi\) | |||||||
\(758\) | − | 28238.7i | − | 1.35313i | ||||||
\(759\) | −50357.8 | + | 42090.0i | −2.40826 | + | 2.01287i | ||||
\(760\) | −761.300 | −0.0363359 | ||||||||
\(761\) | 13216.0 | 0.629537 | 0.314769 | − | 0.949168i | \(-0.398073\pi\) | ||||
0.314769 | + | 0.949168i | \(0.398073\pi\) | |||||||
\(762\) | −6230.32 | − | 7454.14i | −0.296195 | − | 0.354376i | ||||
\(763\) | −38.5812 | + | 1225.67i | −0.00183058 | + | 0.0581550i | ||||
\(764\) | − | 7232.97i | − | 0.342513i | ||||||
\(765\) | 2057.55 | − | 11411.5i | 0.0972429 | − | 0.539325i | ||||
\(766\) | − | 34227.2i | − | 1.61446i | ||||||
\(767\) | 6620.67i | 0.311680i | ||||||||
\(768\) | 18828.0 | − | 15736.8i | 0.884630 | − | 0.739392i | ||||
\(769\) | − | 5595.39i | − | 0.262386i | −0.991357 | − | 0.131193i | \(-0.958119\pi\) | ||
0.991357 | − | 0.131193i | \(-0.0418808\pi\) | |||||||
\(770\) | 879.066 | − | 27926.7i | 0.0411420 | − | 1.30702i | ||||
\(771\) | −25307.5 | + | 21152.5i | −1.18214 | + | 0.988055i | ||||
\(772\) | 58972.8 | 2.74933 | ||||||||
\(773\) | −21363.7 | −0.994046 | −0.497023 | − | 0.867737i | \(-0.665573\pi\) | ||||
−0.497023 | + | 0.867737i | \(0.665573\pi\) | |||||||
\(774\) | −34478.5 | − | 6216.64i | −1.60117 | − | 0.288698i | ||||
\(775\) | 1527.37i | 0.0707934i | ||||||||
\(776\) | 11651.4 | 0.538996 | ||||||||
\(777\) | −517.396 | − | 660.177i | −0.0238886 | − | 0.0304810i | ||||
\(778\) | 49277.4 | 2.27080 | ||||||||
\(779\) | − | 2418.92i | − | 0.111254i | ||||||
\(780\) | 6849.73 | + | 8195.22i | 0.314435 | + | 0.376200i | ||||
\(781\) | −20891.5 | −0.957178 | ||||||||
\(782\) | −76541.5 | −3.50015 | ||||||||
\(783\) | 3743.47 | − | 2132.53i | 0.170857 | − | 0.0973312i | ||||
\(784\) | −2143.58 | − | 135.084i | −0.0976486 | − | 0.00615359i | ||||
\(785\) | − | 6398.34i | − | 0.290913i | ||||||
\(786\) | −30792.1 | − | 36840.6i | −1.39735 | − | 1.67183i | ||||
\(787\) | − | 9648.50i | − | 0.437017i | −0.975835 | − | 0.218508i | \(-0.929881\pi\) | ||
0.975835 | − | 0.218508i | \(-0.0701191\pi\) | |||||||
\(788\) | 15464.5i | 0.699110i | ||||||||
\(789\) | 3104.89 | + | 3714.78i | 0.140098 | + | 0.167617i | ||||
\(790\) | − | 19437.8i | − | 0.875400i | ||||||
\(791\) | −30367.8 | − | 955.907i | −1.36505 | − | 0.0429686i | ||||
\(792\) | 7643.83 | − | 42393.9i | 0.342944 | − | 1.90202i | ||||
\(793\) | 20842.4 | 0.933336 | ||||||||
\(794\) | −33079.4 | −1.47852 | ||||||||
\(795\) | 3528.98 | + | 4222.18i | 0.157434 | + | 0.188359i | ||||
\(796\) | 30506.8i | 1.35840i | ||||||||
\(797\) | −37706.0 | −1.67580 | −0.837901 | − | 0.545822i | \(-0.816217\pi\) | ||||
−0.837901 | + | 0.545822i | \(0.816217\pi\) | |||||||
\(798\) | −1709.33 | − | 2181.04i | −0.0758267 | − | 0.0967519i | ||||
\(799\) | 17911.0 | 0.793050 | ||||||||
\(800\) | − | 4157.08i | − | 0.183719i | ||||||
\(801\) | −2300.84 | + | 12760.8i | −0.101493 | + | 0.562899i | ||||
\(802\) | −15980.9 | −0.703624 | ||||||||
\(803\) | −36317.0 | −1.59601 | ||||||||
\(804\) | −26509.7 | + | 22157.3i | −1.16284 | + | 0.971925i | ||||
\(805\) | 17876.3 | + | 562.704i | 0.782681 | + | 0.0246369i | ||||
\(806\) | 8721.13i | 0.381128i | ||||||||
\(807\) | −12940.7 | + | 10816.1i | −0.564478 | + | 0.471802i | ||||
\(808\) | 28726.4i | 1.25073i | ||||||||
\(809\) | − | 31780.0i | − | 1.38112i | −0.723275 | − | 0.690560i | \(-0.757364\pi\) | ||
0.723275 | − | 0.690560i | \(-0.242636\pi\) | |||||||
\(810\) | −5873.61 | + | 15758.5i | −0.254787 | + | 0.683576i | ||||
\(811\) | 16076.8i | 0.696096i | 0.937477 | + | 0.348048i | \(0.113155\pi\) | ||||
−0.937477 | + | 0.348048i | \(0.886845\pi\) | |||||||
\(812\) | 7553.37 | + | 237.762i | 0.326443 | + | 0.0102756i | ||||
\(813\) | 9117.16 | + | 10908.0i | 0.393300 | + | 0.470556i | ||||
\(814\) | 2629.85 | 0.113239 | ||||||||
\(815\) | 7793.92 | 0.334981 | ||||||||
\(816\) | 2144.37 | − | 1792.31i | 0.0919951 | − | 0.0768913i | ||||
\(817\) | − | 1755.17i | − | 0.0751599i | ||||||
\(818\) | 58923.1 | 2.51858 | ||||||||
\(819\) | −3222.86 | + | 15131.4i | −0.137504 | + | 0.645585i | ||||
\(820\) | −25750.8 | −1.09666 | ||||||||
\(821\) | 2584.08i | 0.109848i | 0.998491 | + | 0.0549239i | \(0.0174916\pi\) | ||||
−0.998491 | + | 0.0549239i | \(0.982508\pi\) | |||||||
\(822\) | 43673.5 | − | 36503.2i | 1.85315 | − | 1.54890i | ||||
\(823\) | −28772.6 | −1.21865 | −0.609326 | − | 0.792920i | \(-0.708560\pi\) | ||||
−0.609326 | + | 0.792920i | \(0.708560\pi\) | |||||||
\(824\) | −5762.32 | −0.243616 | ||||||||
\(825\) | −5448.07 | − | 6518.24i | −0.229912 | − | 0.275074i | ||||
\(826\) | −18276.6 | − | 575.304i | −0.769884 | − | 0.0242341i | ||||
\(827\) | 37901.7i | 1.59368i | 0.604192 | + | 0.796839i | \(0.293496\pi\) | ||||
−0.604192 | + | 0.796839i | \(0.706504\pi\) | |||||||
\(828\) | 68193.6 | + | 12295.6i | 2.86219 | + | 0.516066i | ||||
\(829\) | − | 28711.1i | − | 1.20287i | −0.798922 | − | 0.601435i | \(-0.794596\pi\) | ||
0.798922 | − | 0.601435i | \(-0.205404\pi\) | |||||||
\(830\) | − | 20477.8i | − | 0.856380i | ||||||
\(831\) | 11890.9 | − | 9938.69i | 0.496381 | − | 0.414885i | ||||
\(832\) | − | 25286.3i | − | 1.05366i | ||||||
\(833\) | 29402.9 | + | 1852.90i | 1.22299 | + | 0.0770698i | ||||
\(834\) | −18739.4 | + | 15662.8i | −0.778049 | + | 0.650309i | ||||
\(835\) | 2144.08 | 0.0888609 | ||||||||
\(836\) | 5423.21 | 0.224361 | ||||||||
\(837\) | −7447.70 | + | 4242.70i | −0.307563 | + | 0.175208i | ||||
\(838\) | − | 70292.1i | − | 2.89761i | ||||||
\(839\) | −15203.4 | −0.625602 | −0.312801 | − | 0.949819i | \(-0.601267\pi\) | ||||
−0.312801 | + | 0.949819i | \(0.601267\pi\) | |||||||
\(840\) | −9239.56 | + | 7241.25i | −0.379518 | + | 0.297437i | ||||
\(841\) | 23446.0 | 0.961335 | ||||||||
\(842\) | − | 32802.6i | − | 1.34258i | ||||||
\(843\) | −8648.70 | − | 10347.6i | −0.353354 | − | 0.422763i | ||||
\(844\) | −18131.3 | −0.739463 | ||||||||
\(845\) | −6198.97 | −0.252368 | ||||||||
\(846\) | −25565.0 | − | 4609.49i | −1.03894 | − | 0.187326i | ||||
\(847\) | −1716.40 | + | 54527.7i | −0.0696296 | + | 2.21204i | ||||
\(848\) | 1326.28i | 0.0537085i | ||||||||
\(849\) | 22386.6 | + | 26783.9i | 0.904952 | + | 1.08271i | ||||
\(850\) | − | 9907.43i | − | 0.399790i | ||||||
\(851\) | 1683.41i | 0.0678102i | ||||||||
\(852\) | 14145.4 | + | 16924.0i | 0.568797 | + | 0.680525i | ||||
\(853\) | − | 33912.6i | − | 1.36125i | −0.732633 | − | 0.680624i | \(-0.761709\pi\) | ||
0.732633 | − | 0.680624i | \(-0.238291\pi\) | |||||||
\(854\) | −1811.10 | + | 57536.3i | −0.0725699 | + | 2.30545i | ||||
\(855\) | −829.161 | − | 149.502i | −0.0331657 | − | 0.00597994i | ||||
\(856\) | −9315.80 | −0.371971 | ||||||||
\(857\) | 39113.6 | 1.55904 | 0.779519 | − | 0.626379i | \(-0.215464\pi\) | ||||
0.779519 | + | 0.626379i | \(0.215464\pi\) | |||||||
\(858\) | −31107.9 | − | 37218.4i | −1.23777 | − | 1.48090i | ||||
\(859\) | − | 40537.5i | − | 1.61015i | −0.593171 | − | 0.805076i | \(-0.702124\pi\) | ||
0.593171 | − | 0.805076i | \(-0.297876\pi\) | |||||||
\(860\) | −18684.8 | −0.740867 | ||||||||
\(861\) | −23008.1 | − | 29357.4i | −0.910700 | − | 1.16202i | ||||
\(862\) | −28107.4 | −1.11060 | ||||||||
\(863\) | 11206.6i | 0.442034i | 0.975270 | + | 0.221017i | \(0.0709377\pi\) | ||||
−0.975270 | + | 0.221017i | \(0.929062\pi\) | |||||||
\(864\) | 20270.5 | − | 11547.4i | 0.798168 | − | 0.454689i | ||||
\(865\) | 8544.46 | 0.335862 | ||||||||
\(866\) | −5714.31 | −0.224226 | ||||||||
\(867\) | −9825.96 | + | 8212.73i | −0.384899 | + | 0.321706i | ||||
\(868\) | −15027.6 | − | 473.031i | −0.587636 | − | 0.0184974i | ||||
\(869\) | 55101.8i | 2.15098i | ||||||||
\(870\) | 2824.42 | − | 2360.71i | 0.110065 | − | 0.0919949i | ||||
\(871\) | 15481.7i | 0.602271i | ||||||||
\(872\) | 1615.38i | 0.0627337i | ||||||||
\(873\) | 12690.0 | + | 2288.07i | 0.491971 | + | 0.0887048i | ||||
\(874\) | 5561.51i | 0.215241i | ||||||||
\(875\) | −72.8356 | + | 2313.89i | −0.00281405 | + | 0.0893984i | ||||
\(876\) | 24589.9 | + | 29420.1i | 0.948421 | + | 1.13472i | ||||
\(877\) | 13067.0 | 0.503124 | 0.251562 | − | 0.967841i | \(-0.419056\pi\) | ||||
0.251562 | + | 0.967841i | \(0.419056\pi\) | |||||||
\(878\) | 13539.1 | 0.520412 | ||||||||
\(879\) | 29188.5 | − | 24396.4i | 1.12003 | − | 0.936142i | ||||
\(880\) | − | 2047.53i | − | 0.0784343i | ||||||
\(881\) | −12147.0 | −0.464521 | −0.232261 | − | 0.972654i | \(-0.574612\pi\) | ||||
−0.232261 | + | 0.972654i | \(0.574612\pi\) | |||||||
\(882\) | −41490.8 | − | 10211.7i | −1.58398 | − | 0.389847i | ||||
\(883\) | −30946.6 | −1.17943 | −0.589715 | − | 0.807611i | \(-0.700760\pi\) | ||||
−0.589715 | + | 0.807611i | \(0.700760\pi\) | |||||||
\(884\) | − | 35311.0i | − | 1.34348i | ||||||
\(885\) | −4265.85 | + | 3565.49i | −0.162028 | + | 0.135427i | ||||
\(886\) | −9206.35 | −0.349089 | ||||||||
\(887\) | −46378.4 | −1.75562 | −0.877810 | − | 0.479009i | \(-0.840996\pi\) | ||||
−0.877810 | + | 0.479009i | \(0.840996\pi\) | |||||||
\(888\) | −708.592 | − | 847.781i | −0.0267779 | − | 0.0320379i | ||||
\(889\) | 236.118 | − | 7501.15i | 0.00890793 | − | 0.282993i | ||||
\(890\) | 11078.9i | 0.417266i | ||||||||
\(891\) | 16650.4 | − | 44671.8i | 0.626047 | − | 1.67964i | ||||
\(892\) | 10399.6i | 0.390365i | ||||||||
\(893\) | − | 1301.42i | − | 0.0487685i | ||||||
\(894\) | 35999.7 | − | 30089.3i | 1.34677 | − | 1.12565i | ||||
\(895\) | − | 5646.36i | − | 0.210879i | ||||||
\(896\) | 45179.3 | + | 1422.14i | 1.68452 | + | 0.0530248i | ||||
\(897\) | 23824.1 | − | 19912.6i | 0.886804 | − | 0.741208i | ||||
\(898\) | −38461.4 | −1.42926 | ||||||||
\(899\) | 1876.13 | 0.0696024 | ||||||||
\(900\) | −1591.53 | + | 8826.88i | −0.0589455 | + | 0.326922i | ||||
\(901\) | − | 18192.2i | − | 0.672665i | ||||||
\(902\) | 116947. | 4.31696 | ||||||||
\(903\) | −16694.6 | − | 21301.7i | −0.615241 | − | 0.785023i | ||||
\(904\) | −40023.6 | −1.47253 | ||||||||
\(905\) | 19987.7i | 0.734157i | ||||||||
\(906\) | −14846.2 | − | 17762.4i | −0.544405 | − | 0.651342i | ||||
\(907\) | 6560.02 | 0.240157 | 0.120078 | − | 0.992764i | \(-0.461685\pi\) | ||||
0.120078 | + | 0.992764i | \(0.461685\pi\) | |||||||
\(908\) | −5731.16 | −0.209466 | ||||||||
\(909\) | −5641.19 | + | 31287.0i | −0.205838 | + | 1.14161i | ||||
\(910\) | −415.883 | + | 13212.0i | −0.0151499 | + | 0.481291i | ||||
\(911\) | − | 26129.2i | − | 0.950274i | −0.879912 | − | 0.475137i | \(-0.842399\pi\) | ||
0.879912 | − | 0.475137i | \(-0.157601\pi\) | |||||||
\(912\) | −130.229 | − | 155.810i | −0.00472842 | − | 0.00565723i | ||||
\(913\) | 58050.0i | 2.10424i | ||||||||
\(914\) | − | 19390.4i | − | 0.701724i | ||||||
\(915\) | 11224.4 | + | 13429.3i | 0.405539 | + | 0.485199i | ||||
\(916\) | − | 67685.1i | − | 2.44146i | ||||||
\(917\) | 1166.97 | − | 37073.0i | 0.0420248 | − | 1.33507i | ||||
\(918\) | 48310.0 | − | 27520.6i | 1.73689 | − | 0.989449i | ||||
\(919\) | −7234.60 | −0.259682 | −0.129841 | − | 0.991535i | \(-0.541447\pi\) | ||||
−0.129841 | + | 0.991535i | \(0.541447\pi\) | |||||||
\(920\) | 23560.3 | 0.844303 | ||||||||
\(921\) | −23417.6 | − | 28017.5i | −0.837825 | − | 1.00240i | ||||
\(922\) | 9595.65i | 0.342751i | ||||||||
\(923\) | 9883.68 | 0.352465 | ||||||||
\(924\) | 65819.0 | − | 51583.9i | 2.34338 | − | 1.83656i | ||||
\(925\) | −217.898 | −0.00774534 | ||||||||
\(926\) | 87091.1i | 3.09070i | ||||||||
\(927\) | −6275.96 | − | 1131.59i | −0.222362 | − | 0.0400929i | ||||
\(928\) | −5106.30 | −0.180628 | ||||||||
\(929\) | −26897.8 | −0.949934 | −0.474967 | − | 0.880004i | \(-0.657540\pi\) | ||||
−0.474967 | + | 0.880004i | \(0.657540\pi\) | |||||||
\(930\) | −5619.23 | + | 4696.67i | −0.198131 | + | 0.165602i | ||||
\(931\) | 134.632 | − | 2136.41i | 0.00473940 | − | 0.0752075i | ||||
\(932\) | 51090.4i | 1.79562i | ||||||||
\(933\) | −35315.1 | + | 29517.1i | −1.23919 | + | 1.03574i | ||||
\(934\) | 60226.8i | 2.10994i | ||||||||
\(935\) | 28085.3i | 0.982340i | ||||||||
\(936\) | −3616.27 | + | 20056.4i | −0.126284 | + | 0.700389i | ||||
\(937\) | 29633.3i | 1.03317i | 0.856237 | + | 0.516583i | \(0.172796\pi\) | ||||
−0.856237 | + | 0.516583i | \(0.827204\pi\) | |||||||
\(938\) | −42737.9 | − | 1345.29i | −1.48768 | − | 0.0468285i | ||||
\(939\) | −27168.2 | − | 32504.9i | −0.944198 | − | 1.12967i | ||||
\(940\) | −13854.3 | −0.480722 | ||||||||
\(941\) | 52426.3 | 1.81621 | 0.908103 | − | 0.418747i | \(-0.137531\pi\) | ||||
0.908103 | + | 0.418747i | \(0.137531\pi\) | |||||||
\(942\) | 23539.6 | − | 19674.9i | 0.814184 | − | 0.680511i | ||||
\(943\) | 74859.4i | 2.58511i | ||||||||
\(944\) | −1340.00 | −0.0462006 | ||||||||
\(945\) | −11485.2 | + | 6072.29i | −0.395357 | + | 0.209028i | ||||
\(946\) | 84856.5 | 2.91641 | ||||||||
\(947\) | − | 5941.91i | − | 0.203893i | −0.994790 | − | 0.101946i | \(-0.967493\pi\) | ||
0.994790 | − | 0.101946i | \(-0.0325070\pi\) | |||||||
\(948\) | 44637.5 | − | 37308.9i | 1.52928 | − | 1.27820i | ||||
\(949\) | 17181.4 | 0.587706 | ||||||||
\(950\) | −719.874 | −0.0245851 | ||||||||
\(951\) | 28780.4 | + | 34433.8i | 0.981356 | + | 1.17412i | ||||
\(952\) | 38790.2 | + | 1221.02i | 1.32059 | + | 0.0415689i | ||||
\(953\) | 15418.4i | 0.524082i | 0.965057 | + | 0.262041i | \(0.0843956\pi\) | ||||
−0.965057 | + | 0.262041i | \(0.915604\pi\) | |||||||
\(954\) | −4681.86 | + | 25966.4i | −0.158890 | + | 0.881229i | ||||
\(955\) | − | 2721.67i | − | 0.0922212i | ||||||
\(956\) | − | 18949.3i | − | 0.641073i | ||||||
\(957\) | −8006.60 | + | 6692.08i | −0.270446 | + | 0.226044i | ||||
\(958\) | − | 81153.5i | − | 2.73690i | ||||||
\(959\) | 43948.9 | + | 1383.41i | 1.47986 | + | 0.0465824i | ||||
\(960\) | 16292.6 | − | 13617.7i | 0.547751 | − | 0.457822i | ||||
\(961\) | 26058.4 | 0.874707 | ||||||||
\(962\) | −1244.17 | −0.0416982 | ||||||||
\(963\) | −10146.2 | − | 1829.41i | −0.339518 | − | 0.0612168i | ||||
\(964\) | − | 69517.7i | − | 2.32263i | ||||||
\(965\) | 22190.7 | 0.740253 | ||||||||
\(966\) | 52899.4 | + | 67497.6i | 1.76192 | + | 2.24814i | ||||
\(967\) | −25966.2 | −0.863512 | −0.431756 | − | 0.901991i | \(-0.642106\pi\) | ||||
−0.431756 | + | 0.901991i | \(0.642106\pi\) | |||||||
\(968\) | 71865.3i | 2.38620i | ||||||||
\(969\) | 1786.31 | + | 2137.20i | 0.0592205 | + | 0.0708532i | ||||
\(970\) | 11017.4 | 0.364688 | ||||||||
\(971\) | 9776.28 | 0.323106 | 0.161553 | − | 0.986864i | \(-0.448350\pi\) | ||||
0.161553 | + | 0.986864i | \(0.448350\pi\) | |||||||
\(972\) | −47462.1 | + | 16758.5i | −1.56620 | + | 0.553015i | ||||
\(973\) | −18857.6 | − | 593.592i | −0.621323 | − | 0.0195578i | ||||
\(974\) | − | 61528.7i | − | 2.02414i | ||||||
\(975\) | 2577.46 | + | 3083.75i | 0.0846614 | + | 0.101291i | ||||
\(976\) | 4218.44i | 0.138349i | ||||||||
\(977\) | − | 11309.1i | − | 0.370328i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) | ||
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(978\) | 23966.3 | + | 28674.0i | 0.783596 | + | 0.937517i | ||||
\(979\) | − | 31406.3i | − | 1.02528i | ||||||
\(980\) | −22743.3 | − | 1433.23i | −0.741336 | − | 0.0467173i | ||||
\(981\) | −317.224 | + | 1759.37i | −0.0103243 | + | 0.0572605i | ||||
\(982\) | −24186.4 | −0.785966 | ||||||||
\(983\) | −42744.9 | −1.38693 | −0.693464 | − | 0.720492i | \(-0.743916\pi\) | ||||
−0.693464 | + | 0.720492i | \(0.743916\pi\) | |||||||
\(984\) | −31510.4 | − | 37700.0i | −1.02085 | − | 1.22137i | ||||
\(985\) | 5819.08i | 0.188235i | ||||||||
\(986\) | −12169.7 | −0.393064 | ||||||||
\(987\) | −12378.7 | − | 15794.7i | −0.399208 | − | 0.509374i | ||||
\(988\) | −2565.70 | −0.0826171 | ||||||||
\(989\) | 54317.9i | 1.74642i | ||||||||
\(990\) | 7227.89 | − | 40087.1i | 0.232038 | − | 1.28692i | ||||
\(991\) | −1645.30 | −0.0527392 | −0.0263696 | − | 0.999652i | \(-0.508395\pi\) | ||||
−0.0263696 | + | 0.999652i | \(0.508395\pi\) | |||||||
\(992\) | 10159.1 | 0.325152 | ||||||||
\(993\) | 33669.0 | − | 28141.2i | 1.07599 | − | 0.899331i | ||||
\(994\) | −858.844 | + | 27284.3i | −0.0274053 | + | 0.870629i | ||||
\(995\) | 11479.3i | 0.365748i | ||||||||
\(996\) | 47025.9 | − | 39305.2i | 1.49606 | − | 1.25043i | ||||
\(997\) | − | 37031.8i | − | 1.17634i | −0.808738 | − | 0.588169i | \(-0.799849\pi\) | ||
0.808738 | − | 0.588169i | \(-0.200151\pi\) | |||||||
\(998\) | − | 11933.5i | − | 0.378504i | ||||||
\(999\) | −605.270 | − | 1062.50i | −0.0191691 | − | 0.0336497i |
(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 | 105.4.b.a.41.15 | yes | 16 | |
3.2 | odd | 2 | 105.4.b.b.41.2 | yes | 16 | ||
7.6 | odd | 2 | 105.4.b.b.41.15 | yes | 16 | ||
21.20 | even | 2 | inner | 105.4.b.a.41.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.b.a.41.2 | ✓ | 16 | 21.20 | even | 2 | inner | |
105.4.b.a.41.15 | yes | 16 | 1.1 | even | 1 | trivial | |
105.4.b.b.41.2 | yes | 16 | 3.2 | odd | 2 | ||
105.4.b.b.41.15 | yes | 16 | 7.6 | odd | 2 |