Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (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: | \(11.1639560131\) |
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: | \( x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + \cdots + 2924100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.8 | ||
Root | \(3.07345 - 2.03963i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.a.55.7 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35962 | + | 3.76184i | −0.339904 | + | 0.940460i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −12.3029 | − | 10.2293i | −0.768930 | − | 0.639333i | ||||
\(5\) | 2.66014 | 0.106406 | 0.0532029 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532029 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 88.8835i | 1.81395i | 0.421186 | + | 0.906974i | \(0.361614\pi\) | ||||
−0.421186 | + | 0.906974i | \(0.638386\pi\) | |||||||
\(8\) | 55.2083 | − | 32.3735i | 0.862630 | − | 0.505836i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.61678 | + | 10.0070i | −0.0361678 | + | 0.100070i | ||||
\(11\) | − | 72.9595i | − | 0.602971i | −0.953471 | − | 0.301486i | \(-0.902517\pi\) | ||
0.953471 | − | 0.301486i | \(-0.0974825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −173.728 | −1.02797 | −0.513987 | − | 0.857798i | \(-0.671832\pi\) | ||||
−0.513987 | + | 0.857798i | \(0.671832\pi\) | |||||||
\(14\) | −334.365 | − | 120.848i | −1.70595 | − | 0.616569i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 46.7216 | + | 251.700i | 0.182506 | + | 0.983205i | ||||
\(17\) | −423.661 | −1.46595 | −0.732977 | − | 0.680253i | \(-0.761870\pi\) | ||||
−0.732977 | + | 0.680253i | \(0.761870\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 153.339i | − | 0.424761i | −0.977187 | − | 0.212381i | \(-0.931878\pi\) | ||
0.977187 | − | 0.212381i | \(-0.0681216\pi\) | |||||||
\(20\) | −32.7274 | − | 27.2115i | −0.0818186 | − | 0.0680287i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 274.462 | + | 99.1971i | 0.567070 | + | 0.204953i | ||||
\(23\) | − | 723.430i | − | 1.36754i | −0.729696 | − | 0.683771i | \(-0.760339\pi\) | ||
0.729696 | − | 0.683771i | \(-0.239661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −617.924 | −0.988678 | ||||||||
\(26\) | 236.203 | − | 653.536i | 0.349413 | − | 0.966769i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 909.218 | − | 1093.52i | 1.15972 | − | 1.39480i | ||||
\(29\) | 366.864 | 0.436223 | 0.218112 | − | 0.975924i | \(-0.430010\pi\) | ||||
0.218112 | + | 0.975924i | \(0.430010\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 642.635i | 0.668715i | 0.942446 | + | 0.334357i | \(0.108519\pi\) | ||||
−0.942446 | + | 0.334357i | \(0.891481\pi\) | |||||||
\(32\) | −1010.38 | − | 166.457i | −0.986699 | − | 0.162556i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 576.017 | − | 1593.74i | 0.498284 | − | 1.37867i | ||||
\(35\) | 236.443i | 0.193015i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −535.717 | −0.391320 | −0.195660 | − | 0.980672i | \(-0.562685\pi\) | ||||
−0.195660 | + | 0.980672i | \(0.562685\pi\) | |||||||
\(38\) | 576.836 | + | 208.482i | 0.399471 | + | 0.144378i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 146.862 | − | 86.1181i | 0.0917888 | − | 0.0538238i | ||||
\(41\) | −2141.50 | −1.27394 | −0.636972 | − | 0.770887i | \(-0.719813\pi\) | ||||
−0.636972 | + | 0.770887i | \(0.719813\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 615.945i | 0.333123i | 0.986031 | + | 0.166562i | \(0.0532665\pi\) | ||||
−0.986031 | + | 0.166562i | \(0.946734\pi\) | |||||||
\(44\) | −746.327 | + | 897.612i | −0.385499 | + | 0.463643i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2721.43 | + | 983.589i | 1.28612 | + | 0.464834i | ||||
\(47\) | − | 330.667i | − | 0.149691i | −0.997195 | − | 0.0748454i | \(-0.976154\pi\) | ||
0.997195 | − | 0.0748454i | \(-0.0238463\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5499.27 | −2.29041 | ||||||||
\(50\) | 840.140 | − | 2324.53i | 0.336056 | − | 0.929812i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2137.35 | + | 1777.12i | 0.790440 | + | 0.657218i | ||||
\(53\) | 4628.97 | 1.64791 | 0.823953 | − | 0.566659i | \(-0.191764\pi\) | ||||
0.823953 | + | 0.566659i | \(0.191764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 194.083i | − | 0.0641596i | ||||||
\(56\) | 2877.47 | + | 4907.11i | 0.917560 | + | 1.56477i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −498.795 | + | 1380.08i | −0.148274 | + | 0.410250i | ||||
\(59\) | 3469.85i | 0.996797i | 0.866948 | + | 0.498399i | \(0.166078\pi\) | ||||
−0.866948 | + | 0.498399i | \(0.833922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4646.40 | −1.24870 | −0.624348 | − | 0.781146i | \(-0.714635\pi\) | ||||
−0.624348 | + | 0.781146i | \(0.714635\pi\) | |||||||
\(62\) | −2417.49 | − | 873.738i | −0.628899 | − | 0.227299i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1999.92 | − | 3574.57i | 0.488261 | − | 0.872698i | ||||
\(65\) | −462.141 | −0.109382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6670.10i | 1.48588i | 0.669360 | + | 0.742938i | \(0.266568\pi\) | ||||
−0.669360 | + | 0.742938i | \(0.733432\pi\) | |||||||
\(68\) | 5212.25 | + | 4333.77i | 1.12722 | + | 0.937233i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −889.460 | − | 321.472i | −0.181522 | − | 0.0656065i | ||||
\(71\) | 6445.22i | 1.27856i | 0.768974 | + | 0.639280i | \(0.220768\pi\) | ||||
−0.768974 | + | 0.639280i | \(0.779232\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4735.78 | 0.888682 | 0.444341 | − | 0.895858i | \(-0.353438\pi\) | ||||
0.444341 | + | 0.895858i | \(0.353438\pi\) | |||||||
\(74\) | 728.370 | − | 2015.28i | 0.133011 | − | 0.368021i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1568.55 | + | 1886.51i | −0.271564 | + | 0.326611i | ||||
\(77\) | 6484.89 | 1.09376 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2085.24i | 0.334119i | 0.985947 | + | 0.167059i | \(0.0534272\pi\) | ||||
−0.985947 | + | 0.167059i | \(0.946573\pi\) | |||||||
\(80\) | 124.286 | + | 669.559i | 0.0194197 | + | 0.104619i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2911.62 | − | 8055.98i | 0.433019 | − | 1.19809i | ||||
\(83\) | − | 9294.47i | − | 1.34917i | −0.738195 | − | 0.674587i | \(-0.764322\pi\) | ||
0.738195 | − | 0.674587i | \(-0.235678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1127.00 | −0.155986 | ||||||||
\(86\) | −2317.09 | − | 837.450i | −0.313289 | − | 0.113230i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2361.95 | − | 4027.97i | −0.305004 | − | 0.520141i | ||||
\(89\) | −5704.72 | −0.720202 | −0.360101 | − | 0.932913i | \(-0.617258\pi\) | ||||
−0.360101 | + | 0.932913i | \(0.617258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15441.5i | − | 1.86469i | ||||||
\(92\) | −7400.21 | + | 8900.27i | −0.874315 | + | 1.05154i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1243.92 | + | 449.581i | 0.140778 | + | 0.0508805i | ||||
\(95\) | − | 407.903i | − | 0.0451970i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6975.60 | 0.741376 | 0.370688 | − | 0.928758i | \(-0.379122\pi\) | ||||
0.370688 | + | 0.928758i | \(0.379122\pi\) | |||||||
\(98\) | 7476.91 | − | 20687.4i | 0.778520 | − | 2.15404i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7602.24 | + | 6320.94i | 0.760224 | + | 0.632094i | ||||
\(101\) | −14821.3 | −1.45293 | −0.726463 | − | 0.687206i | \(-0.758837\pi\) | ||||
−0.726463 | + | 0.687206i | \(0.758837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8686.29i | − | 0.818766i | −0.912363 | − | 0.409383i | \(-0.865744\pi\) | ||
0.912363 | − | 0.409383i | \(-0.134256\pi\) | |||||||
\(104\) | −9591.21 | + | 5624.17i | −0.886761 | + | 0.519986i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6293.62 | + | 17413.4i | −0.560130 | + | 1.54979i | ||||
\(107\) | 10919.9i | 0.953790i | 0.878960 | + | 0.476895i | \(0.158238\pi\) | ||||
−0.878960 | + | 0.476895i | \(0.841762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12531.6 | 1.05476 | 0.527379 | − | 0.849630i | \(-0.323175\pi\) | ||||
0.527379 | + | 0.849630i | \(0.323175\pi\) | |||||||
\(110\) | 730.108 | + | 263.878i | 0.0603395 | + | 0.0218081i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −22372.0 | + | 4152.78i | −1.78348 | + | 0.331057i | ||||
\(113\) | 12299.0 | 0.963194 | 0.481597 | − | 0.876393i | \(-0.340057\pi\) | ||||
0.481597 | + | 0.876393i | \(0.340057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1924.43i | − | 0.145514i | ||||||
\(116\) | −4513.48 | − | 3752.77i | −0.335425 | − | 0.278892i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13053.0 | − | 4717.67i | −0.937448 | − | 0.338816i | ||||
\(119\) | − | 37656.4i | − | 2.65916i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9317.91 | 0.636426 | ||||||||
\(122\) | 6317.33 | − | 17479.0i | 0.424438 | − | 1.17435i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6573.72 | − | 7906.26i | 0.427532 | − | 0.514195i | ||||
\(125\) | −3306.36 | −0.211607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22807.9i | 1.41409i | 0.707167 | + | 0.707047i | \(0.249973\pi\) | ||||
−0.707167 | + | 0.707047i | \(0.750027\pi\) | |||||||
\(128\) | 10727.8 | + | 12383.4i | 0.654775 | + | 0.755824i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 628.335 | − | 1738.50i | 0.0371796 | − | 0.102870i | ||||
\(131\) | 6242.75i | 0.363775i | 0.983319 | + | 0.181888i | \(0.0582207\pi\) | ||||
−0.983319 | + | 0.181888i | \(0.941779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13629.3 | 0.770495 | ||||||||
\(134\) | −25091.8 | − | 9068.78i | −1.39741 | − | 0.505056i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23389.6 | + | 13715.4i | −1.26458 | + | 0.741532i | ||||
\(137\) | −9530.74 | −0.507791 | −0.253896 | − | 0.967232i | \(-0.581712\pi\) | ||||
−0.253896 | + | 0.967232i | \(0.581712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11582.2i | 0.599462i | 0.954024 | + | 0.299731i | \(0.0968970\pi\) | ||||
−0.954024 | + | 0.299731i | \(0.903103\pi\) | |||||||
\(140\) | 2418.65 | − | 2908.93i | 0.123401 | − | 0.148415i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24245.9 | − | 8763.04i | −1.20243 | − | 0.434588i | ||||
\(143\) | 12675.1i | 0.619839i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 975.910 | 0.0464167 | ||||||||
\(146\) | −6438.86 | + | 17815.3i | −0.302067 | + | 0.835769i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6590.86 | + | 5480.03i | 0.300898 | + | 0.250184i | ||||
\(149\) | −38532.6 | −1.73562 | −0.867811 | − | 0.496894i | \(-0.834474\pi\) | ||||
−0.867811 | + | 0.496894i | \(0.834474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22912.5i | − | 1.00489i | −0.864610 | − | 0.502444i | \(-0.832434\pi\) | ||
0.864610 | − | 0.502444i | \(-0.167566\pi\) | |||||||
\(152\) | −4964.11 | − | 8465.57i | −0.214859 | − | 0.366412i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8816.98 | + | 24395.1i | −0.371773 | + | 1.02864i | ||||
\(155\) | 1709.50i | 0.0711551i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25755.8 | 1.04490 | 0.522451 | − | 0.852669i | \(-0.325018\pi\) | ||||
0.522451 | + | 0.852669i | \(0.325018\pi\) | |||||||
\(158\) | −7844.33 | − | 2835.12i | −0.314226 | − | 0.113569i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2687.76 | − | 442.800i | −0.104990 | − | 0.0172969i | ||||
\(161\) | 64301.0 | 2.48065 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21920.6i | − | 0.825045i | −0.910947 | − | 0.412522i | \(-0.864648\pi\) | ||
0.910947 | − | 0.412522i | \(-0.135352\pi\) | |||||||
\(164\) | 26346.6 | + | 21906.1i | 0.979573 | + | 0.814474i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 34964.3 | + | 12636.9i | 1.26884 | + | 0.458591i | ||||
\(167\) | − | 3716.35i | − | 0.133255i | −0.997778 | − | 0.0666275i | \(-0.978776\pi\) | ||
0.997778 | − | 0.0666275i | \(-0.0212239\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1620.29 | 0.0567309 | ||||||||
\(170\) | 1532.29 | − | 4239.59i | 0.0530203 | − | 0.146699i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6300.71 | − | 7577.90i | 0.212977 | − | 0.256148i | ||||
\(173\) | 23829.7 | 0.796208 | 0.398104 | − | 0.917340i | \(-0.369668\pi\) | ||||
0.398104 | + | 0.917340i | \(0.369668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 54923.2i | − | 1.79341i | ||||||
\(176\) | 18363.9 | − | 3408.79i | 0.592844 | − | 0.110046i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7756.24 | − | 21460.3i | 0.244800 | − | 0.677322i | ||||
\(179\) | 53055.1i | 1.65585i | 0.560838 | + | 0.827926i | \(0.310479\pi\) | ||||
−0.560838 | + | 0.827926i | \(0.689521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −38125.2 | −1.16374 | −0.581869 | − | 0.813283i | \(-0.697678\pi\) | ||||
−0.581869 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(182\) | 58088.5 | + | 20994.6i | 1.75367 | + | 0.633817i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −23419.9 | − | 39939.4i | −0.691752 | − | 1.17968i | ||||
\(185\) | −1425.08 | −0.0416387 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30910.1i | 0.883928i | ||||||||
\(188\) | −3382.50 | + | 4068.15i | −0.0957022 | + | 0.115102i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1534.47 | + | 554.592i | 0.0425060 | + | 0.0153627i | ||||
\(191\) | − | 19578.7i | − | 0.536683i | −0.963324 | − | 0.268341i | \(-0.913525\pi\) | ||
0.963324 | − | 0.268341i | \(-0.0864755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10489.3 | 0.281600 | 0.140800 | − | 0.990038i | \(-0.455033\pi\) | ||||
0.140800 | + | 0.990038i | \(0.455033\pi\) | |||||||
\(194\) | −9484.15 | + | 26241.1i | −0.251997 | + | 0.697234i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 67656.9 | + | 56253.9i | 1.76116 | + | 1.46433i | ||||
\(197\) | −18533.1 | −0.477547 | −0.238773 | − | 0.971075i | \(-0.576745\pi\) | ||||
−0.238773 | + | 0.971075i | \(0.576745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 66138.9i | 1.67013i | 0.550150 | + | 0.835066i | \(0.314570\pi\) | ||||
−0.550150 | + | 0.835066i | \(0.685430\pi\) | |||||||
\(200\) | −34114.5 | + | 20004.3i | −0.852863 | + | 0.500108i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20151.3 | − | 55755.4i | 0.493856 | − | 1.36642i | ||||
\(203\) | 32608.1i | 0.791286i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5696.69 | −0.135555 | ||||||||
\(206\) | 32676.4 | + | 11810.0i | 0.770017 | + | 0.278302i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8116.84 | − | 43727.3i | −0.187612 | − | 1.01071i | ||||
\(209\) | −11187.5 | −0.256119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25222.6i | 0.566533i | 0.959041 | + | 0.283267i | \(0.0914182\pi\) | ||||
−0.959041 | + | 0.283267i | \(0.908582\pi\) | |||||||
\(212\) | −56949.6 | − | 47351.2i | −1.26712 | − | 1.05356i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −41079.1 | − | 14846.9i | −0.897001 | − | 0.324198i | ||||
\(215\) | 1638.50i | 0.0354462i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −57119.6 | −1.21301 | ||||||||
\(218\) | −17038.2 | + | 47141.8i | −0.358517 | + | 0.991958i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1985.34 | + | 2387.78i | −0.0410194 | + | 0.0493342i | ||||
\(221\) | 73601.6 | 1.50696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14958.0i | 0.300791i | 0.988626 | + | 0.150395i | \(0.0480547\pi\) | ||||
−0.988626 | + | 0.150395i | \(0.951945\pi\) | |||||||
\(224\) | 14795.3 | − | 89806.1i | 0.294868 | − | 1.78982i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16722.0 | + | 46267.0i | −0.327394 | + | 0.905845i | ||||
\(227\) | − | 26750.1i | − | 0.519126i | −0.965726 | − | 0.259563i | \(-0.916421\pi\) | ||
0.965726 | − | 0.259563i | \(-0.0835785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −54043.1 | −1.03055 | −0.515275 | − | 0.857025i | \(-0.672310\pi\) | ||||
−0.515275 | + | 0.857025i | \(0.672310\pi\) | |||||||
\(230\) | 7239.39 | + | 2616.49i | 0.136850 | + | 0.0494610i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20253.9 | − | 11876.7i | 0.376299 | − | 0.220657i | ||||
\(233\) | −89436.5 | −1.64742 | −0.823708 | − | 0.567015i | \(-0.808098\pi\) | ||||
−0.823708 | + | 0.567015i | \(0.808098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 879.621i | − | 0.0159280i | ||||||
\(236\) | 35494.2 | − | 42689.2i | 0.637285 | − | 0.766467i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 141657. | + | 51198.4i | 2.50084 | + | 0.903862i | ||||
\(239\) | − | 64893.0i | − | 1.13606i | −0.823007 | − | 0.568031i | \(-0.807705\pi\) | ||
0.823007 | − | 0.568031i | \(-0.192295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −93131.9 | −1.60348 | −0.801742 | − | 0.597671i | \(-0.796093\pi\) | ||||
−0.801742 | + | 0.597671i | \(0.796093\pi\) | |||||||
\(242\) | −12668.8 | + | 35052.5i | −0.216324 | + | 0.598533i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 57164.1 | + | 47529.6i | 0.960160 | + | 0.798333i | ||||
\(245\) | −14628.9 | −0.243713 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26639.2i | 0.436643i | ||||||||
\(248\) | 20804.3 | + | 35478.8i | 0.338260 | + | 0.576853i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4495.38 | − | 12438.0i | 0.0719261 | − | 0.199008i | ||||
\(251\) | 13729.0i | 0.217917i | 0.994046 | + | 0.108958i | \(0.0347515\pi\) | ||||
−0.994046 | + | 0.108958i | \(0.965249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −52781.1 | −0.824589 | ||||||||
\(254\) | −85799.7 | − | 31010.1i | −1.32990 | − | 0.480657i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −61170.2 | + | 23519.7i | −0.933383 | + | 0.358882i | ||||
\(257\) | −24255.6 | −0.367237 | −0.183618 | − | 0.982998i | \(-0.558781\pi\) | ||||
−0.183618 | + | 0.982998i | \(0.558781\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 47616.4i | − | 0.709834i | ||||||
\(260\) | 5685.66 | + | 4727.39i | 0.0841074 | + | 0.0699318i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −23484.2 | − | 8487.75i | −0.342116 | − | 0.123649i | ||||
\(263\) | − | 34613.8i | − | 0.500423i | −0.968191 | − | 0.250212i | \(-0.919500\pi\) | ||
0.968191 | − | 0.250212i | \(-0.0805002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12313.7 | 0.175347 | ||||||||
\(266\) | −18530.6 | + | 51271.2i | −0.261895 | + | 0.724619i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 68230.6 | − | 82061.4i | 0.949970 | − | 1.14253i | ||||
\(269\) | 67272.9 | 0.929684 | 0.464842 | − | 0.885394i | \(-0.346111\pi\) | ||||
0.464842 | + | 0.885394i | \(0.346111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7814.00i | 0.106398i | 0.998584 | + | 0.0531992i | \(0.0169418\pi\) | ||||
−0.998584 | + | 0.0531992i | \(0.983058\pi\) | |||||||
\(272\) | −19794.1 | − | 106636.i | −0.267546 | − | 1.44133i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12958.2 | − | 35853.1i | 0.172601 | − | 0.477557i | ||||
\(275\) | 45083.4i | 0.596144i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 50559.4 | 0.658935 | 0.329467 | − | 0.944167i | \(-0.393131\pi\) | ||||
0.329467 | + | 0.944167i | \(0.393131\pi\) | |||||||
\(278\) | −43570.4 | − | 15747.4i | −0.563770 | − | 0.203760i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7654.48 | + | 13053.6i | 0.0976336 | + | 0.166500i | ||||
\(281\) | −81351.4 | −1.03027 | −0.515136 | − | 0.857108i | \(-0.672259\pi\) | ||||
−0.515136 | + | 0.857108i | \(0.672259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2795.45i | 0.0349043i | 0.999848 | + | 0.0174522i | \(0.00555548\pi\) | ||||
−0.999848 | + | 0.0174522i | \(0.994445\pi\) | |||||||
\(284\) | 65930.3 | − | 79294.8i | 0.817426 | − | 0.983123i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −47681.6 | − | 17233.3i | −0.582934 | − | 0.210686i | ||||
\(287\) | − | 190344.i | − | 2.31087i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 95967.4 | 1.14902 | ||||||||
\(290\) | −1326.87 | + | 3671.22i | −0.0157772 | + | 0.0436530i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −58263.8 | − | 48443.9i | −0.683334 | − | 0.568164i | ||||
\(293\) | −48302.8 | −0.562648 | −0.281324 | − | 0.959613i | \(-0.590774\pi\) | ||||
−0.281324 | + | 0.959613i | \(0.590774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9230.30i | 0.106065i | ||||||||
\(296\) | −29576.0 | + | 17343.0i | −0.337564 | + | 0.197944i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 52389.6 | − | 144953.i | 0.589946 | − | 1.63228i | ||||
\(299\) | 125680.i | 1.40580i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −54747.3 | −0.604269 | ||||||||
\(302\) | 86193.0 | + | 31152.2i | 0.945057 | + | 0.341566i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 38595.4 | − | 7164.23i | 0.417627 | − | 0.0775216i | ||||
\(305\) | −12360.1 | −0.132869 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1578.26i | 0.0167457i | 0.999965 | + | 0.00837284i | \(0.00266519\pi\) | ||||
−0.999965 | + | 0.00837284i | \(0.997335\pi\) | |||||||
\(308\) | −79782.9 | − | 66336.1i | −0.841024 | − | 0.699276i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6430.87 | − | 2324.27i | −0.0669185 | − | 0.0241859i | ||||
\(311\) | 2640.95i | 0.0273049i | 0.999907 | + | 0.0136524i | \(0.00434584\pi\) | ||||
−0.999907 | + | 0.0136524i | \(0.995654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 52927.9 | 0.540252 | 0.270126 | − | 0.962825i | \(-0.412935\pi\) | ||||
0.270126 | + | 0.962825i | \(0.412935\pi\) | |||||||
\(314\) | −35018.1 | + | 96889.2i | −0.355167 | + | 0.982689i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21330.6 | − | 25654.4i | 0.213613 | − | 0.256914i | ||||
\(317\) | 40687.1 | 0.404891 | 0.202446 | − | 0.979293i | \(-0.435111\pi\) | ||||
0.202446 | + | 0.979293i | \(0.435111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 26766.2i | − | 0.263030i | ||||||
\(320\) | 5320.06 | − | 9508.87i | 0.0519538 | − | 0.0928601i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −87424.8 | + | 241890.i | −0.843185 | + | 2.33295i | ||||
\(323\) | 64963.6i | 0.622680i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 107350. | 1.01634 | ||||||||
\(326\) | 82461.8 | + | 29803.7i | 0.775922 | + | 0.280436i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −118229. | + | 69327.8i | −1.09894 | + | 0.644406i | ||||
\(329\) | 29390.8 | 0.271531 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 44484.1i | 0.406021i | 0.979177 | + | 0.203011i | \(0.0650726\pi\) | ||||
−0.979177 | + | 0.203011i | \(0.934927\pi\) | |||||||
\(332\) | −95076.2 | + | 114349.i | −0.862572 | + | 1.03742i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13980.3 | + | 5052.82i | 0.125321 | + | 0.0452940i | ||||
\(335\) | 17743.4i | 0.158106i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1175.77 | −0.0103529 | −0.00517645 | − | 0.999987i | \(-0.501648\pi\) | ||||
−0.00517645 | + | 0.999987i | \(0.501648\pi\) | |||||||
\(338\) | −2202.98 | + | 6095.27i | −0.0192831 | + | 0.0533531i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13865.3 | + | 11528.4i | 0.119942 | + | 0.0997270i | ||||
\(341\) | 46886.3 | 0.403216 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 275385.i | − | 2.34073i | ||||||
\(344\) | 19940.3 | + | 34005.3i | 0.168506 | + | 0.287362i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −32399.3 | + | 89643.6i | −0.270635 | + | 0.748802i | ||||
\(347\) | 80258.8i | 0.666551i | 0.942829 | + | 0.333276i | \(0.108154\pi\) | ||||
−0.942829 | + | 0.333276i | \(0.891846\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11160.8 | −0.0916318 | −0.0458159 | − | 0.998950i | \(-0.514589\pi\) | ||||
−0.0458159 | + | 0.998950i | \(0.514589\pi\) | |||||||
\(350\) | 206612. | + | 74674.6i | 1.68663 | + | 0.609588i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12144.6 | + | 73716.8i | −0.0980164 | + | 0.594951i | ||||
\(353\) | 235353. | 1.88873 | 0.944366 | − | 0.328895i | \(-0.106676\pi\) | ||||
0.944366 | + | 0.328895i | \(0.106676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17145.2i | 0.136046i | ||||||||
\(356\) | 70184.5 | + | 58355.5i | 0.553785 | + | 0.460449i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −199585. | − | 72134.7i | −1.55726 | − | 0.562831i | ||||
\(359\) | − | 141216.i | − | 1.09571i | −0.836573 | − | 0.547855i | \(-0.815444\pi\) | ||
0.836573 | − | 0.547855i | \(-0.184556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 106808. | 0.819578 | ||||||||
\(362\) | 51835.7 | − | 143421.i | 0.395560 | − | 1.09445i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −157956. | + | 189975.i | −1.19216 | + | 1.43382i | ||||
\(365\) | 12597.9 | 0.0945608 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 63764.0i | 0.473417i | 0.971581 | + | 0.236708i | \(0.0760686\pi\) | ||||
−0.971581 | + | 0.236708i | \(0.923931\pi\) | |||||||
\(368\) | 182088. | − | 33799.8i | 1.34457 | − | 0.249585i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1937.57 | − | 5360.94i | 0.0141532 | − | 0.0391595i | ||||
\(371\) | 411438.i | 2.98921i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 119610. | 0.859708 | 0.429854 | − | 0.902898i | \(-0.358565\pi\) | ||||
0.429854 | + | 0.902898i | \(0.358565\pi\) | |||||||
\(374\) | −116279. | − | 42025.9i | −0.831299 | − | 0.300451i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10704.8 | − | 18255.6i | −0.0757189 | − | 0.129128i | ||||
\(377\) | −63734.4 | −0.448426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 40019.5i | 0.278608i | 0.990250 | + | 0.139304i | \(0.0444865\pi\) | ||||
−0.990250 | + | 0.139304i | \(0.955514\pi\) | |||||||
\(380\) | −4172.58 | + | 5018.38i | −0.0288960 | + | 0.0347533i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 73652.0 | + | 26619.6i | 0.504729 | + | 0.182421i | ||||
\(383\) | − | 195988.i | − | 1.33608i | −0.744125 | − | 0.668040i | \(-0.767133\pi\) | ||
0.744125 | − | 0.668040i | \(-0.232867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17250.8 | 0.116382 | ||||||||
\(386\) | −14261.4 | + | 39459.1i | −0.0957170 | + | 0.264833i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −85820.0 | − | 71355.7i | −0.570066 | − | 0.473986i | ||||
\(389\) | −29348.7 | −0.193950 | −0.0969751 | − | 0.995287i | \(-0.530917\pi\) | ||||
−0.0969751 | + | 0.995287i | \(0.530917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 306489.i | 2.00475i | ||||||||
\(392\) | −303605. | + | 178031.i | −1.97577 | + | 1.15857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25198.0 | − | 69718.6i | 0.162320 | − | 0.449114i | ||||
\(395\) | 5547.03i | 0.0355522i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 190863. | 1.21099 | 0.605495 | − | 0.795849i | \(-0.292975\pi\) | ||||
0.605495 | + | 0.795849i | \(0.292975\pi\) | |||||||
\(398\) | −248804. | − | 89923.6i | −1.57069 | − | 0.567685i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −28870.4 | − | 155532.i | −0.180440 | − | 0.972073i | ||||
\(401\) | −35070.1 | −0.218096 | −0.109048 | − | 0.994036i | \(-0.534780\pi\) | ||||
−0.109048 | + | 0.994036i | \(0.534780\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 111643.i | − | 0.687422i | ||||||
\(404\) | 182345. | + | 151612.i | 1.11720 | + | 0.928904i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −122667. | − | 44334.6i | −0.744173 | − | 0.268962i | ||||
\(407\) | 39085.7i | 0.235955i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −106623. | −0.637388 | −0.318694 | − | 0.947858i | \(-0.603244\pi\) | ||||
−0.318694 | + | 0.947858i | \(0.603244\pi\) | |||||||
\(410\) | 7745.33 | − | 21430.1i | 0.0460757 | − | 0.127484i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −88855.0 | + | 106866.i | −0.523465 | + | 0.629574i | ||||
\(413\) | −308412. | −1.80814 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 24724.6i | − | 0.143560i | ||||||
\(416\) | 175531. | + | 28918.2i | 1.01430 | + | 0.167103i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15210.8 | − | 42085.7i | 0.0870559 | − | 0.240869i | ||||
\(419\) | − | 150952.i | − | 0.859826i | −0.902870 | − | 0.429913i | \(-0.858544\pi\) | ||
0.902870 | − | 0.429913i | \(-0.141456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 188580. | 1.06397 | 0.531987 | − | 0.846752i | \(-0.321445\pi\) | ||||
0.531987 | + | 0.846752i | \(0.321445\pi\) | |||||||
\(422\) | −94883.5 | − | 34293.1i | −0.532802 | − | 0.192567i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 255557. | − | 149856.i | 1.42153 | − | 0.833569i | ||||
\(425\) | 261790. | 1.44936 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 412988.i | − | 2.26507i | ||||||
\(428\) | 111704. | − | 134347.i | 0.609790 | − | 0.733398i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6163.78 | − | 2227.74i | −0.0333358 | − | 0.0120483i | ||||
\(431\) | − | 111824.i | − | 0.601975i | −0.953628 | − | 0.300988i | \(-0.902684\pi\) | ||
0.953628 | − | 0.300988i | \(-0.0973163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 86904.0 | 0.463515 | 0.231758 | − | 0.972774i | \(-0.425552\pi\) | ||||
0.231758 | + | 0.972774i | \(0.425552\pi\) | |||||||
\(434\) | 77660.9 | − | 214875.i | 0.412309 | − | 1.14079i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −154175. | − | 128190.i | −0.811035 | − | 0.674342i | ||||
\(437\) | −110930. | −0.580879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 200474.i | − | 1.04023i | −0.854096 | − | 0.520115i | \(-0.825889\pi\) | ||
0.854096 | − | 0.520115i | \(-0.174111\pi\) | |||||||
\(440\) | −6283.14 | − | 10715.0i | −0.0324542 | − | 0.0553460i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −100070. | + | 276877.i | −0.512223 | + | 1.41724i | ||||
\(443\) | 40063.7i | 0.204147i | 0.994777 | + | 0.102074i | \(0.0325477\pi\) | ||||
−0.994777 | + | 0.102074i | \(0.967452\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15175.4 | −0.0766337 | ||||||||
\(446\) | −56269.7 | − | 20337.2i | −0.282882 | − | 0.102240i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 317720. | + | 177759.i | 1.58303 | + | 0.885680i | ||||
\(449\) | 95081.8 | 0.471634 | 0.235817 | − | 0.971798i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971798i | \(0.424223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 156243.i | 0.768151i | ||||||||
\(452\) | −151313. | − | 125811.i | −0.740629 | − | 0.615802i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 100629. | + | 36369.8i | 0.488217 | + | 0.176453i | ||||
\(455\) | − | 41076.7i | − | 0.198414i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −132420. | −0.634047 | −0.317024 | − | 0.948418i | \(-0.602683\pi\) | ||||
−0.317024 | + | 0.948418i | \(0.602683\pi\) | |||||||
\(458\) | 73477.9 | − | 203301.i | 0.350289 | − | 0.969191i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −19685.6 | + | 23676.0i | −0.0930322 | + | 0.111890i | ||||
\(461\) | −85031.6 | −0.400109 | −0.200055 | − | 0.979785i | \(-0.564112\pi\) | ||||
−0.200055 | + | 0.979785i | \(0.564112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23890.7i | 0.111447i | 0.998446 | + | 0.0557234i | \(0.0177465\pi\) | ||||
−0.998446 | + | 0.0557234i | \(0.982254\pi\) | |||||||
\(464\) | 17140.5 | + | 92339.7i | 0.0796135 | + | 0.428897i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 121599. | − | 336446.i | 0.559964 | − | 1.54933i | ||||
\(467\) | − | 233452.i | − | 1.07044i | −0.844712 | − | 0.535221i | \(-0.820228\pi\) | ||
0.844712 | − | 0.535221i | \(-0.179772\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −592861. | −2.69530 | ||||||||
\(470\) | 3308.99 | + | 1195.95i | 0.0149796 | + | 0.00541398i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 112331. | + | 191565.i | 0.504215 | + | 0.859867i | ||||
\(473\) | 44939.1 | 0.200864 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 94751.6i | 0.419952i | ||||||||
\(476\) | −385200. | + | 463283.i | −1.70009 | + | 2.04471i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 244117. | + | 88229.7i | 1.06842 | + | 0.386153i | ||||
\(479\) | − | 97384.4i | − | 0.424442i | −0.977222 | − | 0.212221i | \(-0.931930\pi\) | ||
0.977222 | − | 0.212221i | \(-0.0680696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 93068.8 | 0.402267 | ||||||||
\(482\) | 126624. | − | 350347.i | 0.545031 | − | 1.50801i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −114637. | − | 95316.0i | −0.489367 | − | 0.406888i | ||||
\(485\) | 18556.1 | 0.0788866 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 42812.3i | − | 0.180514i | −0.995919 | − | 0.0902570i | \(-0.971231\pi\) | ||
0.995919 | − | 0.0902570i | \(-0.0287689\pi\) | |||||||
\(488\) | −256520. | + | 150420.i | −1.07716 | + | 0.631635i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19889.6 | − | 55031.4i | 0.0828390 | − | 0.229202i | ||||
\(491\) | 376010.i | 1.55968i | 0.625976 | + | 0.779842i | \(0.284701\pi\) | ||||
−0.625976 | + | 0.779842i | \(0.715299\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −155426. | −0.639483 | ||||||||
\(494\) | −100212. | − | 36219.1i | −0.410646 | − | 0.148417i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −161751. | + | 30024.9i | −0.657484 | + | 0.122045i | ||||
\(497\) | −572874. | −2.31924 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 239303.i | 0.961051i | 0.876981 | + | 0.480525i | \(0.159554\pi\) | ||||
−0.876981 | + | 0.480525i | \(0.840446\pi\) | |||||||
\(500\) | 40677.7 | + | 33821.8i | 0.162711 | + | 0.135287i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −51646.1 | − | 18666.1i | −0.204942 | − | 0.0740708i | ||||
\(503\) | − | 297365.i | − | 1.17531i | −0.809111 | − | 0.587656i | \(-0.800051\pi\) | ||
0.809111 | − | 0.587656i | \(-0.199949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39426.8 | −0.154600 | ||||||||
\(506\) | 71762.1 | − | 198554.i | 0.280281 | − | 0.775493i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 233310. | − | 280603.i | 0.904077 | − | 1.08734i | ||||
\(509\) | −189362. | −0.730897 | −0.365449 | − | 0.930831i | \(-0.619084\pi\) | ||||
−0.365449 | + | 0.930831i | \(0.619084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 420933.i | 1.61202i | ||||||||
\(512\) | −5309.28 | − | 262090.i | −0.0202533 | − | 0.999795i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32978.4 | − | 91245.8i | 0.124825 | − | 0.345372i | ||||
\(515\) | − | 23106.8i | − | 0.0871215i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24125.3 | −0.0902592 | ||||||||
\(518\) | 179125. | + | 64740.1i | 0.667571 | + | 0.241276i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25514.0 | + | 14961.1i | −0.0943565 | + | 0.0553295i | ||||
\(521\) | 347810. | 1.28135 | 0.640673 | − | 0.767814i | \(-0.278655\pi\) | ||||
0.640673 | + | 0.767814i | \(0.278655\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 465334.i | 1.70122i | 0.525794 | + | 0.850612i | \(0.323768\pi\) | ||||
−0.525794 | + | 0.850612i | \(0.676232\pi\) | |||||||
\(524\) | 63859.1 | − | 76803.7i | 0.232573 | − | 0.279718i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 130212. | + | 47061.5i | 0.470628 | + | 0.170096i | ||||
\(527\) | − | 272259.i | − | 0.980305i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −243510. | −0.870173 | ||||||||
\(530\) | −16741.9 | + | 46322.2i | −0.0596011 | + | 0.164906i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −167679. | − | 139418.i | −0.592456 | − | 0.492603i | ||||
\(533\) | 372038. | 1.30958 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29048.6i | 0.101489i | ||||||||
\(536\) | 215934. | + | 368245.i | 0.751609 | + | 1.28176i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −91465.4 | + | 253070.i | −0.316004 | + | 0.874331i | ||||
\(539\) | 401224.i | 1.38105i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −340727. | −1.16416 | −0.582080 | − | 0.813132i | \(-0.697761\pi\) | ||||
−0.582080 | + | 0.813132i | \(0.697761\pi\) | |||||||
\(542\) | −29395.0 | − | 10624.1i | −0.100063 | − | 0.0361653i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 428058. | + | 70521.3i | 1.44646 | + | 0.238299i | ||||
\(545\) | 33335.8 | 0.112232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 87443.4i | − | 0.292248i | −0.989266 | − | 0.146124i | \(-0.953320\pi\) | ||
0.989266 | − | 0.146124i | \(-0.0466799\pi\) | |||||||
\(548\) | 117255. | + | 97493.1i | 0.390456 | + | 0.324648i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −169597. | − | 61296.2i | −0.560650 | − | 0.202632i | ||||
\(551\) | − | 56254.4i | − | 0.185291i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −185343. | −0.606075 | ||||||||
\(554\) | −68741.5 | + | 190196.i | −0.223975 | + | 0.619702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 118478. | − | 142495.i | 0.383256 | − | 0.460944i | ||||
\(557\) | 82261.1 | 0.265146 | 0.132573 | − | 0.991173i | \(-0.457676\pi\) | ||||
0.132573 | + | 0.991173i | \(0.457676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 107007.i | − | 0.342442i | ||||||
\(560\) | −59512.8 | + | 11047.0i | −0.189773 | + | 0.0352264i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 110607. | − | 306031.i | 0.350194 | − | 0.968930i | ||||
\(563\) | 440276.i | 1.38902i | 0.719483 | + | 0.694510i | \(0.244379\pi\) | ||||
−0.719483 | + | 0.694510i | \(0.755621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32717.2 | 0.102489 | ||||||||
\(566\) | −10516.0 | − | 3800.75i | −0.0328261 | − | 0.0118641i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 208654. | + | 355830.i | 0.646741 | + | 1.10292i | ||||
\(569\) | −124980. | −0.386026 | −0.193013 | − | 0.981196i | \(-0.561826\pi\) | ||||
−0.193013 | + | 0.981196i | \(0.561826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 404239.i | − | 1.23984i | −0.784665 | − | 0.619921i | \(-0.787165\pi\) | ||
0.784665 | − | 0.619921i | \(-0.212835\pi\) | |||||||
\(572\) | 129658. | − | 155940.i | 0.396283 | − | 0.476613i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 716043. | + | 258795.i | 2.17328 | + | 0.785474i | ||||
\(575\) | 447025.i | 1.35206i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −118286. | −0.355290 | −0.177645 | − | 0.984095i | \(-0.556848\pi\) | ||||
−0.177645 | + | 0.984095i | \(0.556848\pi\) | |||||||
\(578\) | −130479. | + | 361014.i | −0.390558 | + | 1.08061i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12006.5 | − | 9982.91i | −0.0356912 | − | 0.0296757i | ||||
\(581\) | 826124. | 2.44733 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 337727.i | − | 0.993639i | ||||||
\(584\) | 261455. | − | 153314.i | 0.766603 | − | 0.449527i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 65673.3 | − | 181707.i | 0.191247 | − | 0.529148i | ||||
\(587\) | 47852.6i | 0.138877i | 0.997586 | + | 0.0694383i | \(0.0221207\pi\) | ||||
−0.997586 | + | 0.0694383i | \(0.977879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 98540.8 | 0.284044 | ||||||||
\(590\) | −34722.9 | − | 12549.7i | −0.0997498 | − | 0.0360520i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25029.6 | − | 134840.i | −0.0714184 | − | 0.384748i | ||||
\(593\) | −633658. | −1.80196 | −0.900981 | − | 0.433859i | \(-0.857152\pi\) | ||||
−0.900981 | + | 0.433859i | \(0.857152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 100172.i | − | 0.282950i | ||||||
\(596\) | 474061. | + | 394162.i | 1.33457 | + | 1.10964i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −472787. | − | 170877.i | −1.32210 | − | 0.477837i | ||||
\(599\) | − | 158241.i | − | 0.441027i | −0.975384 | − | 0.220513i | \(-0.929227\pi\) | ||
0.975384 | − | 0.220513i | \(-0.0707733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −84042.2 | −0.232674 | −0.116337 | − | 0.993210i | \(-0.537115\pi\) | ||||
−0.116337 | + | 0.993210i | \(0.537115\pi\) | |||||||
\(602\) | 74435.5 | − | 205951.i | 0.205394 | − | 0.568290i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −234379. | + | 281889.i | −0.642458 | + | 0.772689i | ||||
\(605\) | 24787.0 | 0.0677194 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 504787.i | − | 1.37003i | −0.728528 | − | 0.685016i | \(-0.759795\pi\) | ||
0.728528 | − | 0.685016i | \(-0.240205\pi\) | |||||||
\(608\) | −25524.3 | + | 154930.i | −0.0690474 | + | 0.419111i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16805.0 | − | 46496.7i | 0.0451626 | − | 0.124958i | ||||
\(611\) | 57446.0i | 0.153878i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30449.3 | −0.0810320 | −0.0405160 | − | 0.999179i | \(-0.512900\pi\) | ||||
−0.0405160 | + | 0.999179i | \(0.512900\pi\) | |||||||
\(614\) | −5937.18 | − | 2145.84i | −0.0157486 | − | 0.00569193i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 358020. | − | 209939.i | 0.943509 | − | 0.553262i | ||||
\(617\) | 147465. | 0.387364 | 0.193682 | − | 0.981064i | \(-0.437957\pi\) | ||||
0.193682 | + | 0.981064i | \(0.437957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 264366.i | 0.689960i | 0.938610 | + | 0.344980i | \(0.112114\pi\) | ||||
−0.938610 | + | 0.344980i | \(0.887886\pi\) | |||||||
\(620\) | 17487.1 | − | 21031.8i | 0.0454918 | − | 0.0547133i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9934.84 | − | 3590.69i | −0.0256791 | − | 0.00928104i | ||||
\(623\) | − | 507056.i | − | 1.30641i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 377407. | 0.966162 | ||||||||
\(626\) | −71961.8 | + | 199106.i | −0.183634 | + | 0.508085i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −316871. | − | 263465.i | −0.803457 | − | 0.668041i | ||||
\(629\) | 226962. | 0.573657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 455734.i | 1.14460i | 0.820045 | + | 0.572299i | \(0.193948\pi\) | ||||
−0.820045 | + | 0.572299i | \(0.806052\pi\) | |||||||
\(632\) | 67506.4 | + | 115122.i | 0.169009 | + | 0.288221i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −55318.9 | + | 153058.i | −0.137624 | + | 0.380784i | ||||
\(635\) | 60672.3i | 0.150468i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 955375. | 2.35448 | ||||||||
\(638\) | 100690. | + | 36391.8i | 0.247369 | + | 0.0894051i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 28537.6 | + | 32941.7i | 0.0696719 | + | 0.0804240i | ||||
\(641\) | 42568.5 | 0.103603 | 0.0518015 | − | 0.998657i | \(-0.483504\pi\) | ||||
0.0518015 | + | 0.998657i | \(0.483504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 397515.i | 0.961461i | 0.876868 | + | 0.480730i | \(0.159628\pi\) | ||||
−0.876868 | + | 0.480730i | \(0.840372\pi\) | |||||||
\(644\) | −791087. | − | 657756.i | −1.90745 | − | 1.58596i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −244383. | − | 88325.7i | −0.585606 | − | 0.211652i | ||||
\(647\) | 454122.i | 1.08483i | 0.840109 | + | 0.542417i | \(0.182491\pi\) | ||||
−0.840109 | + | 0.542417i | \(0.817509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 253159. | 0.601040 | ||||||||
\(650\) | −145956. | + | 403835.i | −0.345457 | + | 0.955823i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −224233. | + | 269687.i | −0.527478 | + | 0.634402i | ||||
\(653\) | −351238. | −0.823712 | −0.411856 | − | 0.911249i | \(-0.635119\pi\) | ||||
−0.411856 | + | 0.911249i | \(0.635119\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16606.6i | 0.0387078i | ||||||||
\(656\) | −100054. | − | 539016.i | −0.232503 | − | 1.25255i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −39960.3 | + | 110564.i | −0.0922947 | + | 0.255364i | ||||
\(659\) | − | 636361.i | − | 1.46532i | −0.680595 | − | 0.732660i | \(-0.738279\pi\) | ||
0.680595 | − | 0.732660i | \(-0.261721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −194949. | −0.446188 | −0.223094 | − | 0.974797i | \(-0.571616\pi\) | ||||
−0.223094 | + | 0.974797i | \(0.571616\pi\) | |||||||
\(662\) | −167342. | − | 60481.4i | −0.381847 | − | 0.138009i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −300894. | − | 513132.i | −0.682461 | − | 1.16384i | ||||
\(665\) | 36255.8 | 0.0819851 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 265400.i | − | 0.596554i | ||||||
\(668\) | −38015.8 | + | 45721.8i | −0.0851944 | + | 0.102464i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −66747.9 | − | 24124.3i | −0.148692 | − | 0.0537409i | ||||
\(671\) | 338999.i | 0.752928i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −771557. | −1.70348 | −0.851742 | − | 0.523962i | \(-0.824453\pi\) | ||||
−0.851742 | + | 0.523962i | \(0.824453\pi\) | |||||||
\(674\) | 1598.59 | − | 4423.05i | 0.00351899 | − | 0.00973648i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19934.2 | − | 16574.5i | −0.0436220 | − | 0.0362699i | ||||
\(677\) | −334198. | −0.729166 | −0.364583 | − | 0.931171i | \(-0.618788\pi\) | ||||
−0.364583 | + | 0.931171i | \(0.618788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 620016.i | 1.34482i | ||||||||
\(680\) | −62219.7 | + | 36484.9i | −0.134558 | + | 0.0789032i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −63747.5 | + | 176379.i | −0.137055 | + | 0.379208i | ||||
\(683\) | 452549.i | 0.970117i | 0.874482 | + | 0.485059i | \(0.161202\pi\) | ||||
−0.874482 | + | 0.485059i | \(0.838798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25353.1 | −0.0540319 | ||||||||
\(686\) | 1.03595e6 | + | 374418.i | 2.20137 | + | 0.795626i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −155034. | + | 28778.0i | −0.327528 | + | 0.0607971i | ||||
\(689\) | −804179. | −1.69400 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 864703.i | − | 1.81097i | −0.424379 | − | 0.905485i | \(-0.639508\pi\) | ||
0.424379 | − | 0.905485i | \(-0.360492\pi\) | |||||||
\(692\) | −293174. | − | 243762.i | −0.612228 | − | 0.509042i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −301921. | − | 109121.i | −0.626865 | − | 0.226564i | ||||
\(695\) | 30810.3i | 0.0637862i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 907269. | 1.86754 | ||||||||
\(698\) | 15174.5 | − | 41985.3i | 0.0311461 | − | 0.0861761i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −561827. | + | 675713.i | −1.14659 | + | 1.37901i | ||||
\(701\) | 576160. | 1.17249 | 0.586243 | − | 0.810136i | \(-0.300607\pi\) | ||||
0.586243 | + | 0.810136i | \(0.300607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 82146.2i | 0.166217i | ||||||||
\(704\) | −260799. | − | 145913.i | −0.526212 | − | 0.294407i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −319990. | + | 885361.i | −0.641989 | + | 1.77628i | ||||
\(707\) | − | 1.31737e6i | − | 2.63553i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 506535. | 1.00767 | 0.503834 | − | 0.863801i | \(-0.331922\pi\) | ||||
0.503834 | + | 0.863801i | \(0.331922\pi\) | |||||||
\(710\) | −64497.6 | − | 23310.9i | −0.127946 | − | 0.0462427i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −314948. | + | 184682.i | −0.621268 | + | 0.364304i | ||||
\(713\) | 464901. | 0.914496 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33717.5i | 0.0659544i | ||||||||
\(716\) | 542719. | − | 652731.i | 1.05864 | − | 1.27323i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 531233. | + | 192000.i | 1.03047 | + | 0.372437i | ||||
\(719\) | − | 521745.i | − | 1.00925i | −0.863338 | − | 0.504627i | \(-0.831630\pi\) | ||
0.863338 | − | 0.504627i | \(-0.168370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 772068. | 1.48520 | ||||||||
\(722\) | −145218. | + | 401795.i | −0.278578 | + | 0.770780i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 469050. | + | 389995.i | 0.894833 | + | 0.744016i | ||||
\(725\) | −226694. | −0.431284 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26945.2i | 0.0509815i | 0.999675 | + | 0.0254908i | \(0.00811484\pi\) | ||||
−0.999675 | + | 0.0254908i | \(0.991885\pi\) | |||||||
\(728\) | −499896. | − | 852500.i | −0.943228 | − | 1.60854i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17128.3 | + | 47391.2i | −0.0321417 | + | 0.0889307i | ||||
\(731\) | − | 260952.i | − | 0.488344i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −672594. | −1.25183 | −0.625914 | − | 0.779892i | \(-0.715274\pi\) | ||||
−0.625914 | + | 0.779892i | \(0.715274\pi\) | |||||||
\(734\) | −239870. | − | 86694.7i | −0.445229 | − | 0.160916i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −120420. | + | 730939.i | −0.222302 | + | 1.34935i | ||||
\(737\) | 486647. | 0.895940 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 846279.i | − | 1.54962i | −0.632196 | − | 0.774809i | \(-0.717846\pi\) | ||
0.632196 | − | 0.774809i | \(-0.282154\pi\) | |||||||
\(740\) | 17532.6 | + | 14577.7i | 0.0320172 | + | 0.0266210i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.54777e6 | − | 559399.i | −2.81124 | − | 1.01605i | ||||
\(743\) | 713156.i | 1.29183i | 0.763407 | + | 0.645917i | \(0.223525\pi\) | ||||
−0.763407 | + | 0.645917i | \(0.776475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −102502. | −0.184680 | ||||||||
\(746\) | −162624. | + | 449955.i | −0.292219 | + | 0.808521i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 316189. | − | 380283.i | 0.565124 | − | 0.679679i | ||||
\(749\) | −970602. | −1.73013 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.09057e6i | − | 1.93364i | −0.255461 | − | 0.966819i | \(-0.582227\pi\) | ||
0.255461 | − | 0.966819i | \(-0.417773\pi\) | |||||||
\(752\) | 83229.0 | − | 15449.3i | 0.147177 | − | 0.0273195i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 86654.4 | − | 239758.i | 0.152422 | − | 0.421727i | ||||
\(755\) | − | 60950.4i | − | 0.106926i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 727090. | 1.26881 | 0.634405 | − | 0.773001i | \(-0.281245\pi\) | ||||
0.634405 | + | 0.773001i | \(0.281245\pi\) | |||||||
\(758\) | −150547. | − | 54411.2i | −0.262019 | − | 0.0947000i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13205.2 | − | 22519.6i | −0.0228623 | − | 0.0389883i | ||||
\(761\) | −377157. | −0.651258 | −0.325629 | − | 0.945498i | \(-0.605576\pi\) | ||||
−0.325629 | + | 0.945498i | \(0.605576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.11385e6i | 1.91328i | ||||||||
\(764\) | −200277. | + | 240875.i | −0.343119 | + | 0.412671i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 737276. | + | 266469.i | 1.25653 | + | 0.454140i | ||||
\(767\) | − | 602809.i | − | 1.02468i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −508831. | −0.860440 | −0.430220 | − | 0.902724i | \(-0.641564\pi\) | ||||
−0.430220 | + | 0.902724i | \(0.641564\pi\) | |||||||
\(770\) | −23454.4 | + | 64894.6i | −0.0395588 | + | 0.109453i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −129049. | − | 107299.i | −0.216530 | − | 0.180036i | ||||
\(773\) | −569650. | −0.953344 | −0.476672 | − | 0.879081i | \(-0.658157\pi\) | ||||
−0.476672 | + | 0.879081i | \(0.658157\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 397099.i | − | 0.661143i | ||||||
\(776\) | 385111. | − | 225825.i | 0.639533 | − | 0.375014i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39903.1 | − | 110405.i | 0.0659246 | − | 0.182402i | ||||
\(779\) | 328375.i | 0.541122i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 470240. | 0.770935 | ||||||||
\(782\) | −1.15296e6 | − | 416708.i | −1.88539 | − | 0.681425i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −256935. | − | 1.38417e6i | −0.418014 | − | 2.25194i | ||||
\(785\) | 68514.2 | 0.111184 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 911291.i | 1.47132i | 0.677350 | + | 0.735661i | \(0.263128\pi\) | ||||
−0.677350 | + | 0.735661i | \(0.736872\pi\) | |||||||
\(788\) | 228011. | + | 189581.i | 0.367200 | + | 0.305312i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20867.0 | − | 7541.84i | −0.0334354 | − | 0.0120843i | ||||
\(791\) | 1.09318e6i | 1.74718i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 807208. | 1.28363 | ||||||||
\(794\) | −259500. | + | 717995.i | −0.411621 | + | 1.13889i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 676556. | − | 813699.i | 1.06777 | − | 1.28421i | ||||
\(797\) | −229990. | −0.362069 | −0.181035 | − | 0.983477i | \(-0.557945\pi\) | ||||
−0.181035 | + | 0.983477i | \(0.557945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 140091.i | 0.219440i | ||||||||
\(800\) | 624338. | + | 102858.i | 0.975528 | + | 0.160715i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 47682.0 | − | 131928.i | 0.0741320 | − | 0.205111i | ||||
\(803\) | − | 345521.i | − | 0.535849i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 171050. | 0.263956 | ||||||||
\(806\) | 419985. | + | 151792.i | 0.646492 | + | 0.233658i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −818259. | + | 479817.i | −1.25334 | + | 0.734942i | ||||
\(809\) | 642259. | 0.981326 | 0.490663 | − | 0.871350i | \(-0.336755\pi\) | ||||
0.490663 | + | 0.871350i | \(0.336755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 878969.i | − | 1.33639i | −0.743988 | − | 0.668193i | \(-0.767068\pi\) | ||
0.743988 | − | 0.668193i | \(-0.232932\pi\) | |||||||
\(812\) | 333559. | − | 401174.i | 0.505896 | − | 0.608444i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −147034. | − | 53141.6i | −0.221906 | − | 0.0802020i | ||||
\(815\) | − | 58312.0i | − | 0.0877895i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 94448.2 | 0.141498 | ||||||||
\(818\) | 144966. | − | 401098.i | 0.216651 | − | 0.599438i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 70085.7 | + | 58273.4i | 0.104232 | + | 0.0866647i | ||||
\(821\) | 322494. | 0.478448 | 0.239224 | − | 0.970964i | \(-0.423107\pi\) | ||||
0.239224 | + | 0.970964i | \(0.423107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 172131.i | 0.254133i | 0.991894 | + | 0.127066i | \(0.0405561\pi\) | ||||
−0.991894 | + | 0.127066i | \(0.959444\pi\) | |||||||
\(824\) | −281206. | − | 479556.i | −0.414161 | − | 0.706292i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 419323. | − | 1.16020e6i | 0.614594 | − | 1.70048i | ||||
\(827\) | − | 25110.9i | − | 0.0367156i | −0.999831 | − | 0.0183578i | \(-0.994156\pi\) | ||
0.999831 | − | 0.0183578i | \(-0.00584381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −757576. | −1.10234 | −0.551172 | − | 0.834392i | \(-0.685819\pi\) | ||||
−0.551172 | + | 0.834392i | \(0.685819\pi\) | |||||||
\(830\) | 93010.0 | + | 33616.0i | 0.135012 | + | 0.0487967i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −347441. | + | 621002.i | −0.501919 | + | 0.897111i | ||||
\(833\) | 2.32983e6 | 3.35763 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9886.03i | − | 0.0141791i | ||||||
\(836\) | 137639. | + | 114441.i | 0.196937 | + | 0.163745i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 567857. | + | 205237.i | 0.808632 | + | 0.292259i | ||||
\(839\) | 224257.i | 0.318583i | 0.987232 | + | 0.159292i | \(0.0509210\pi\) | ||||
−0.987232 | + | 0.159292i | \(0.949079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −572692. | −0.809709 | ||||||||
\(842\) | −256397. | + | 709408.i | −0.361650 | + | 1.00063i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 258011. | − | 310311.i | 0.362204 | − | 0.435624i | ||||
\(845\) | 4310.20 | 0.00603649 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 828208.i | 1.15444i | ||||||||
\(848\) | 216273. | + | 1.16511e6i | 0.300753 | + | 1.62023i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −355934. | + | 984812.i | −0.492643 | + | 1.36306i | ||||
\(851\) | 387554.i | 0.535147i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −337460. | −0.463794 | −0.231897 | − | 0.972740i | \(-0.574493\pi\) | ||||
−0.231897 | + | 0.972740i | \(0.574493\pi\) | |||||||
\(854\) | 1.55360e6 | + | 561506.i | 2.13021 | + | 0.769908i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 353517. | + | 602872.i | 0.482461 | + | 0.822768i | ||||
\(857\) | −370777. | −0.504837 | −0.252418 | − | 0.967618i | \(-0.581226\pi\) | ||||
−0.252418 | + | 0.967618i | \(0.581226\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 240459.i | 0.325877i | 0.986636 | + | 0.162939i | \(0.0520973\pi\) | ||||
−0.986636 | + | 0.162939i | \(0.947903\pi\) | |||||||
\(860\) | 16760.8 | − | 20158.3i | 0.0226620 | − | 0.0272557i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 420662. | + | 152037.i | 0.566134 | + | 0.204614i | ||||
\(863\) | 5184.93i | 0.00696179i | 0.999994 | + | 0.00348090i | \(0.00110801\pi\) | ||||
−0.999994 | + | 0.00348090i | \(0.998892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 63390.5 | 0.0847211 | ||||||||
\(866\) | −118156. | + | 326919.i | −0.157551 | + | 0.435917i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 702736. | + | 584295.i | 0.932723 | + | 0.775520i | ||||
\(869\) | 152138. | 0.201464 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.15878e6i | − | 1.52744i | ||||||
\(872\) | 691848. | − | 405691.i | 0.909866 | − | 0.533534i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 150822. | − | 417300.i | 0.197443 | − | 0.546293i | ||||
\(875\) | − | 293880.i | − | 0.383844i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 261506. | 0.340003 | 0.170001 | − | 0.985444i | \(-0.445623\pi\) | ||||
0.170001 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(878\) | 754152. | + | 272568.i | 0.978295 | + | 0.353579i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 48850.7 | − | 9067.86i | 0.0630820 | − | 0.0117095i | ||||
\(881\) | −1.02303e6 | −1.31807 | −0.659035 | − | 0.752113i | \(-0.729035\pi\) | ||||
−0.659035 | + | 0.752113i | \(0.729035\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 223764.i | 0.286991i | 0.989651 | + | 0.143496i | \(0.0458343\pi\) | ||||
−0.989651 | + | 0.143496i | \(0.954166\pi\) | |||||||
\(884\) | −905511. | − | 752895.i | −1.15875 | − | 0.963451i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −150713. | − | 54471.3i | −0.191992 | − | 0.0693906i | ||||
\(887\) | 1.14417e6i | 1.45426i | 0.686500 | + | 0.727129i | \(0.259146\pi\) | ||||
−0.686500 | + | 0.727129i | \(0.740854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.02725e6 | −2.56509 | ||||||||
\(890\) | 20632.7 | − | 57087.4i | 0.0260481 | − | 0.0720709i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 153011. | − | 184027.i | 0.192306 | − | 0.231287i | ||||
\(893\) | −50704.0 | −0.0635828 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 141134.i | 0.176192i | ||||||||
\(896\) | −1.10068e6 | + | 953528.i | −1.37102 | + | 1.18773i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −129275. | + | 357683.i | −0.160310 | + | 0.443553i | ||||
\(899\) | 235759.i | 0.291709i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.96111e6 | −2.41575 | ||||||||
\(902\) | −587760. | − | 212430.i | −0.722415 | − | 0.261098i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 679008. | − | 398162.i | 0.830880 | − | 0.487218i | ||||
\(905\) | −101419. | −0.123828 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 326996.i | − | 0.397492i | −0.980051 | − | 0.198746i | \(-0.936313\pi\) | ||
0.980051 | − | 0.198746i | \(-0.0636868\pi\) | |||||||
\(908\) | −273635. | + | 329103.i | −0.331895 | + | 0.399172i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 154524. | + | 55848.6i | 0.186600 | + | 0.0674418i | ||||
\(911\) | 1.40153e6i | 1.68875i | 0.535752 | + | 0.844375i | \(0.320028\pi\) | ||||
−0.535752 | + | 0.844375i | \(0.679972\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −678120. | −0.813514 | ||||||||
\(914\) | 180041. | − | 498143.i | 0.215515 | − | 0.596296i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 664885. | + | 552824.i | 0.792421 | + | 0.658865i | ||||
\(917\) | −554877. | −0.659869 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.18092e6i | 1.39826i | 0.714995 | + | 0.699130i | \(0.246429\pi\) | ||||
−0.714995 | + | 0.699130i | \(0.753571\pi\) | |||||||
\(920\) | −62300.4 | − | 106244.i | −0.0736064 | − | 0.125525i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 115610. | − | 319875.i | 0.135999 | − | 0.376287i | ||||
\(923\) | − | 1.11971e6i | − | 1.31433i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 331032. | 0.386889 | ||||||||
\(926\) | −89873.1 | − | 32482.3i | −0.104811 | − | 0.0378812i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −370672. | − | 61067.1i | −0.430421 | − | 0.0709106i | ||||
\(929\) | 569778. | 0.660198 | 0.330099 | − | 0.943946i | \(-0.392918\pi\) | ||||
0.330099 | + | 0.943946i | \(0.392918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 843251.i | 0.972876i | ||||||||
\(932\) | 1.10033e6 | + | 914876.i | 1.26675 | + | 1.05325i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 878208. | + | 317405.i | 1.00671 | + | 0.363848i | ||||
\(935\) | 82225.3i | 0.0940550i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.25337e6 | 1.42758 | 0.713791 | − | 0.700359i | \(-0.246977\pi\) | ||||
0.713791 | + | 0.700359i | \(0.246977\pi\) | |||||||
\(938\) | 806065. | − | 2.23025e6i | 0.916145 | − | 2.53482i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8997.94 | + | 10821.9i | −0.0101833 | + | 0.0122475i | ||||
\(941\) | 1.13681e6 | 1.28383 | 0.641914 | − | 0.766776i | \(-0.278140\pi\) | ||||
0.641914 | + | 0.766776i | \(0.278140\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.54922e6i | 1.74217i | ||||||||
\(944\) | −873363. | + | 162117.i | −0.980056 | + | 0.181922i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −61099.9 | + | 169054.i | −0.0682745 | + | 0.188904i | ||||
\(947\) | − | 939587.i | − | 1.04770i | −0.851811 | − | 0.523850i | \(-0.824495\pi\) | ||
0.851811 | − | 0.523850i | \(-0.175505\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −822737. | −0.913542 | ||||||||
\(950\) | −356440. | − | 128826.i | −0.394948 | − | 0.142744i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.21907e6 | − | 2.07895e6i | −1.34510 | − | 2.29388i | ||||
\(953\) | −103408. | −0.113859 | −0.0569296 | − | 0.998378i | \(-0.518131\pi\) | ||||
−0.0569296 | + | 0.998378i | \(0.518131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 52082.2i | − | 0.0571061i | ||||||
\(956\) | −663812. | + | 798371.i | −0.726322 | + | 0.873552i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 366344. | + | 132406.i | 0.399171 | + | 0.144270i | ||||
\(959\) | − | 847125.i | − | 0.921107i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 510541. | 0.552821 | ||||||||
\(962\) | −126538. | + | 350110.i | −0.136732 | + | 0.378316i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.14579e6 | + | 952677.i | 1.23297 | + | 1.02516i | ||||
\(965\) | 27903.1 | 0.0299638 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 568578.i | − | 0.608047i | −0.952665 | − | 0.304023i | \(-0.901670\pi\) | ||
0.952665 | − | 0.304023i | \(-0.0983301\pi\) | |||||||
\(968\) | 514426. | − | 301653.i | 0.549000 | − | 0.321927i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25229.2 | + | 69805.1i | −0.0268139 | + | 0.0741897i | ||||
\(971\) | − | 1.25649e6i | − | 1.33267i | −0.745653 | − | 0.666334i | \(-0.767863\pi\) | ||
0.745653 | − | 0.666334i | \(-0.232137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.02947e6 | −1.08739 | ||||||||
\(974\) | 161053. | + | 58208.4i | 0.169766 | + | 0.0613575i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −217087. | − | 1.16950e6i | −0.227895 | − | 1.22772i | ||||
\(977\) | −1.34062e6 | −1.40448 | −0.702241 | − | 0.711939i | \(-0.747817\pi\) | ||||
−0.702241 | + | 0.711939i | \(0.747817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 416214.i | 0.434261i | ||||||||
\(980\) | 179977. | + | 149643.i | 0.187398 | + | 0.155814i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.41449e6 | − | 511230.i | −1.46682 | − | 0.530144i | ||||
\(983\) | 1.08955e6i | 1.12757i | 0.825923 | + | 0.563783i | \(0.190654\pi\) | ||||
−0.825923 | + | 0.563783i | \(0.809346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49300.8 | −0.0508137 | ||||||||
\(986\) | 211320. | − | 584687.i | 0.217363 | − | 0.601408i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 272501. | − | 327739.i | 0.279161 | − | 0.335748i | ||||
\(989\) | 445593. | 0.455560 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 114312.i | − | 0.116398i | −0.998305 | − | 0.0581990i | \(-0.981464\pi\) | ||
0.998305 | − | 0.0581990i | \(-0.0185358\pi\) | |||||||
\(992\) | 106971. | − | 649306.i | 0.108703 | − | 0.659820i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 778889. | − | 2.15506e6i | 0.788321 | − | 2.18115i | ||||
\(995\) | 175939.i | 0.177712i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.31273e6 | 1.32065 | 0.660323 | − | 0.750981i | \(-0.270419\pi\) | ||||
0.660323 | + | 0.750981i | \(0.270419\pi\) | |||||||
\(998\) | −900218. | − | 325360.i | −0.903830 | − | 0.326666i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.d.a.55.8 | yes | 16 | |
3.2 | odd | 2 | inner | 108.5.d.a.55.9 | yes | 16 | |
4.3 | odd | 2 | inner | 108.5.d.a.55.7 | ✓ | 16 | |
12.11 | even | 2 | inner | 108.5.d.a.55.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.a.55.7 | ✓ | 16 | 4.3 | odd | 2 | inner | |
108.5.d.a.55.8 | yes | 16 | 1.1 | even | 1 | trivial | |
108.5.d.a.55.9 | yes | 16 | 3.2 | odd | 2 | inner | |
108.5.d.a.55.10 | yes | 16 | 12.11 | even | 2 | inner |