Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(64,105)]
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([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.7 | ||
Root | \(-1.35311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.64 |
Dual form | 105.4.d.b.64.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.20666i | 0.780172i | 0.920778 | + | 0.390086i | \(0.127555\pi\) | ||||
−0.920778 | + | 0.390086i | \(0.872445\pi\) | |||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 3.13065 | 0.391332 | ||||||||
\(5\) | −1.50045 | + | 11.0792i | −0.134204 | + | 0.990954i | ||||
\(6\) | 6.61998 | 0.450432 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 24.5616i | 1.08548i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | −24.4480 | − | 3.31098i | −0.773114 | − | 0.104702i | ||||
\(11\) | 56.2010 | 1.54048 | 0.770238 | − | 0.637757i | \(-0.220138\pi\) | ||||
0.770238 | + | 0.637757i | \(0.220138\pi\) | |||||||
\(12\) | − | 9.39196i | − | 0.225936i | ||||||
\(13\) | 38.9026i | 0.829972i | 0.909828 | + | 0.414986i | \(0.136214\pi\) | ||||
−0.909828 | + | 0.414986i | \(0.863786\pi\) | |||||||
\(14\) | 15.4466 | 0.294877 | ||||||||
\(15\) | 33.2376 | + | 4.50134i | 0.572127 | + | 0.0774828i | ||||
\(16\) | −29.1538 | −0.455528 | ||||||||
\(17\) | 119.322i | 1.70235i | 0.524886 | + | 0.851173i | \(0.324108\pi\) | ||||
−0.524886 | + | 0.851173i | \(0.675892\pi\) | |||||||
\(18\) | − | 19.8599i | − | 0.260057i | ||||||
\(19\) | 13.0045 | 0.157023 | 0.0785113 | − | 0.996913i | \(-0.474983\pi\) | ||||
0.0785113 | + | 0.996913i | \(0.474983\pi\) | |||||||
\(20\) | −4.69738 | + | 34.6851i | −0.0525183 | + | 0.387792i | ||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 124.016i | 1.20184i | ||||||||
\(23\) | − | 130.565i | − | 1.18368i | −0.806055 | − | 0.591840i | \(-0.798402\pi\) | ||
0.806055 | − | 0.591840i | \(-0.201598\pi\) | |||||||
\(24\) | 73.6847 | 0.626701 | ||||||||
\(25\) | −120.497 | − | 33.2475i | −0.963979 | − | 0.265980i | ||||
\(26\) | −85.8448 | −0.647521 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − | 21.9146i | − | 0.147910i | ||||||
\(29\) | −77.9925 | −0.499408 | −0.249704 | − | 0.968322i | \(-0.580333\pi\) | ||||
−0.249704 | + | 0.968322i | \(0.580333\pi\) | |||||||
\(30\) | −9.93293 | + | 73.3441i | −0.0604499 | + | 0.446358i | ||||
\(31\) | 61.0660 | 0.353799 | 0.176900 | − | 0.984229i | \(-0.443393\pi\) | ||||
0.176900 | + | 0.984229i | \(0.443393\pi\) | |||||||
\(32\) | 132.160i | 0.730088i | ||||||||
\(33\) | − | 168.603i | − | 0.889394i | ||||||
\(34\) | −263.303 | −1.32812 | ||||||||
\(35\) | 77.5544 | + | 10.5031i | 0.374545 | + | 0.0507244i | ||||
\(36\) | −28.1759 | −0.130444 | ||||||||
\(37\) | − | 167.391i | − | 0.743757i | −0.928282 | − | 0.371878i | \(-0.878714\pi\) | ||
0.928282 | − | 0.371878i | \(-0.121286\pi\) | |||||||
\(38\) | 28.6964i | 0.122505i | ||||||||
\(39\) | 116.708 | 0.479185 | ||||||||
\(40\) | −272.122 | − | 36.8533i | −1.07566 | − | 0.145676i | ||||
\(41\) | 436.142 | 1.66132 | 0.830658 | − | 0.556783i | \(-0.187964\pi\) | ||||
0.830658 | + | 0.556783i | \(0.187964\pi\) | |||||||
\(42\) | − | 46.3398i | − | 0.170247i | ||||||
\(43\) | − | 393.030i | − | 1.39387i | −0.717134 | − | 0.696936i | \(-0.754546\pi\) | ||
0.717134 | − | 0.696936i | \(-0.245454\pi\) | |||||||
\(44\) | 175.946 | 0.602837 | ||||||||
\(45\) | 13.5040 | − | 99.7128i | 0.0447347 | − | 0.330318i | ||||
\(46\) | 288.112 | 0.923474 | ||||||||
\(47\) | − | 365.271i | − | 1.13362i | −0.823848 | − | 0.566811i | \(-0.808177\pi\) | ||
0.823848 | − | 0.566811i | \(-0.191823\pi\) | |||||||
\(48\) | 87.4613i | 0.262999i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 73.3659 | − | 265.897i | 0.207510 | − | 0.752069i | ||||
\(51\) | 357.966 | 0.982849 | ||||||||
\(52\) | 121.791i | 0.324794i | ||||||||
\(53\) | − | 282.048i | − | 0.730987i | −0.930814 | − | 0.365494i | \(-0.880900\pi\) | ||
0.930814 | − | 0.365494i | \(-0.119100\pi\) | |||||||
\(54\) | −59.5798 | −0.150144 | ||||||||
\(55\) | −84.3266 | + | 622.662i | −0.206738 | + | 1.52654i | ||||
\(56\) | 171.931 | 0.410272 | ||||||||
\(57\) | − | 39.0134i | − | 0.0906570i | ||||||
\(58\) | − | 172.103i | − | 0.389624i | ||||||
\(59\) | −414.842 | −0.915388 | −0.457694 | − | 0.889110i | \(-0.651324\pi\) | ||||
−0.457694 | + | 0.889110i | \(0.651324\pi\) | |||||||
\(60\) | 104.055 | + | 14.0921i | 0.223892 | + | 0.0303215i | ||||
\(61\) | −563.802 | −1.18340 | −0.591701 | − | 0.806158i | \(-0.701543\pi\) | ||||
−0.591701 | + | 0.806158i | \(0.701543\pi\) | |||||||
\(62\) | 134.752i | 0.276024i | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | −524.862 | −1.02512 | ||||||||
\(65\) | −431.009 | − | 58.3713i | −0.822464 | − | 0.111386i | ||||
\(66\) | 372.049 | 0.693880 | ||||||||
\(67\) | − | 395.230i | − | 0.720673i | −0.932822 | − | 0.360336i | \(-0.882662\pi\) | ||
0.932822 | − | 0.360336i | \(-0.117338\pi\) | |||||||
\(68\) | 373.556i | 0.666182i | ||||||||
\(69\) | −391.694 | −0.683398 | ||||||||
\(70\) | −23.1768 | + | 171.136i | −0.0395737 | + | 0.292210i | ||||
\(71\) | 103.990 | 0.173821 | 0.0869107 | − | 0.996216i | \(-0.472301\pi\) | ||||
0.0869107 | + | 0.996216i | \(0.472301\pi\) | |||||||
\(72\) | − | 221.054i | − | 0.361826i | ||||||
\(73\) | − | 128.026i | − | 0.205264i | −0.994719 | − | 0.102632i | \(-0.967274\pi\) | ||
0.994719 | − | 0.102632i | \(-0.0327264\pi\) | |||||||
\(74\) | 369.376 | 0.580258 | ||||||||
\(75\) | −99.7426 | + | 361.492i | −0.153564 | + | 0.556553i | ||||
\(76\) | 40.7125 | 0.0614479 | ||||||||
\(77\) | − | 393.407i | − | 0.582245i | ||||||
\(78\) | 257.534i | 0.373846i | ||||||||
\(79\) | 641.999 | 0.914310 | 0.457155 | − | 0.889387i | \(-0.348868\pi\) | ||||
0.457155 | + | 0.889387i | \(0.348868\pi\) | |||||||
\(80\) | 43.7437 | − | 323.000i | 0.0611337 | − | 0.451407i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 962.417i | 1.29611i | ||||||||
\(83\) | 512.010i | 0.677113i | 0.940946 | + | 0.338557i | \(0.109939\pi\) | ||||
−0.940946 | + | 0.338557i | \(0.890061\pi\) | |||||||
\(84\) | −65.7437 | −0.0853956 | ||||||||
\(85\) | −1321.99 | − | 179.037i | −1.68695 | − | 0.228462i | ||||
\(86\) | 867.283 | 1.08746 | ||||||||
\(87\) | 233.977i | 0.288333i | ||||||||
\(88\) | 1380.38i | 1.67215i | ||||||||
\(89\) | −1225.10 | −1.45911 | −0.729554 | − | 0.683923i | \(-0.760272\pi\) | ||||
−0.729554 | + | 0.683923i | \(0.760272\pi\) | |||||||
\(90\) | 220.032 | + | 29.7988i | 0.257705 | + | 0.0349008i | ||||
\(91\) | 272.318 | 0.313700 | ||||||||
\(92\) | − | 408.753i | − | 0.463212i | ||||||
\(93\) | − | 183.198i | − | 0.204266i | ||||||
\(94\) | 806.028 | 0.884420 | ||||||||
\(95\) | −19.5125 | + | 144.079i | −0.0210731 | + | 0.155602i | ||||
\(96\) | 396.480 | 0.421517 | ||||||||
\(97\) | − | 186.760i | − | 0.195491i | −0.995211 | − | 0.0977454i | \(-0.968837\pi\) | ||
0.995211 | − | 0.0977454i | \(-0.0311631\pi\) | |||||||
\(98\) | − | 108.126i | − | 0.111453i | ||||||
\(99\) | −505.809 | −0.513492 | ||||||||
\(100\) | −377.235 | − | 104.086i | −0.377235 | − | 0.104086i | ||||
\(101\) | 1650.68 | 1.62623 | 0.813114 | − | 0.582104i | \(-0.197770\pi\) | ||||
0.813114 | + | 0.582104i | \(0.197770\pi\) | |||||||
\(102\) | 789.910i | 0.766792i | ||||||||
\(103\) | − | 72.1876i | − | 0.0690568i | −0.999404 | − | 0.0345284i | \(-0.989007\pi\) | ||
0.999404 | − | 0.0345284i | \(-0.0109929\pi\) | |||||||
\(104\) | −955.508 | −0.900916 | ||||||||
\(105\) | 31.5094 | − | 232.663i | 0.0292857 | − | 0.216244i | ||||
\(106\) | 622.385 | 0.570296 | ||||||||
\(107\) | 1202.55i | 1.08649i | 0.839574 | + | 0.543246i | \(0.182805\pi\) | ||||
−0.839574 | + | 0.543246i | \(0.817195\pi\) | |||||||
\(108\) | 84.5277i | 0.0753118i | ||||||||
\(109\) | 1551.36 | 1.36324 | 0.681622 | − | 0.731704i | \(-0.261275\pi\) | ||||
0.681622 | + | 0.731704i | \(0.261275\pi\) | |||||||
\(110\) | −1374.00 | − | 186.080i | −1.19096 | − | 0.161291i | ||||
\(111\) | −502.174 | −0.429408 | ||||||||
\(112\) | 204.076i | 0.172173i | ||||||||
\(113\) | 2080.90i | 1.73234i | 0.499749 | + | 0.866170i | \(0.333426\pi\) | ||||
−0.499749 | + | 0.866170i | \(0.666574\pi\) | |||||||
\(114\) | 86.0893 | 0.0707281 | ||||||||
\(115\) | 1446.55 | + | 195.906i | 1.17297 | + | 0.158855i | ||||
\(116\) | −244.167 | −0.195434 | ||||||||
\(117\) | − | 350.123i | − | 0.276657i | ||||||
\(118\) | − | 915.416i | − | 0.714160i | ||||||
\(119\) | 835.255 | 0.643426 | ||||||||
\(120\) | −110.560 | + | 816.367i | −0.0841059 | + | 0.621032i | ||||
\(121\) | 1827.55 | 1.37306 | ||||||||
\(122\) | − | 1244.12i | − | 0.923257i | ||||||
\(123\) | − | 1308.43i | − | 0.959161i | ||||||
\(124\) | 191.177 | 0.138453 | ||||||||
\(125\) | 549.156 | − | 1285.13i | 0.392944 | − | 0.919562i | ||||
\(126\) | −139.020 | −0.0982924 | ||||||||
\(127\) | − | 1414.70i | − | 0.988461i | −0.869331 | − | 0.494231i | \(-0.835450\pi\) | ||
0.869331 | − | 0.494231i | \(-0.164550\pi\) | |||||||
\(128\) | − | 100.912i | − | 0.0696832i | ||||||
\(129\) | −1179.09 | −0.804752 | ||||||||
\(130\) | 128.806 | − | 951.091i | 0.0869000 | − | 0.641663i | ||||
\(131\) | −2472.51 | −1.64904 | −0.824520 | − | 0.565833i | \(-0.808555\pi\) | ||||
−0.824520 | + | 0.565833i | \(0.808555\pi\) | |||||||
\(132\) | − | 527.837i | − | 0.348048i | ||||||
\(133\) | − | 91.0313i | − | 0.0593490i | ||||||
\(134\) | 872.139 | 0.562249 | ||||||||
\(135\) | −299.138 | − | 40.5121i | −0.190709 | − | 0.0258276i | ||||
\(136\) | −2930.74 | −1.84786 | ||||||||
\(137\) | 214.391i | 0.133698i | 0.997763 | + | 0.0668491i | \(0.0212946\pi\) | ||||
−0.997763 | + | 0.0668491i | \(0.978705\pi\) | |||||||
\(138\) | − | 864.336i | − | 0.533168i | ||||||
\(139\) | −942.774 | −0.575288 | −0.287644 | − | 0.957737i | \(-0.592872\pi\) | ||||
−0.287644 | + | 0.957737i | \(0.592872\pi\) | |||||||
\(140\) | 242.796 | + | 32.8817i | 0.146571 | + | 0.0198501i | ||||
\(141\) | −1095.81 | −0.654497 | ||||||||
\(142\) | 229.470i | 0.135611i | ||||||||
\(143\) | 2186.36i | 1.27855i | ||||||||
\(144\) | 262.384 | 0.151843 | ||||||||
\(145\) | 117.024 | − | 864.094i | 0.0670226 | − | 0.494890i | ||||
\(146\) | 282.509 | 0.160141 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | − | 524.045i | − | 0.291056i | ||||||
\(149\) | −1693.07 | −0.930882 | −0.465441 | − | 0.885079i | \(-0.654104\pi\) | ||||
−0.465441 | + | 0.885079i | \(0.654104\pi\) | |||||||
\(150\) | −797.690 | − | 220.098i | −0.434207 | − | 0.119806i | ||||
\(151\) | 2519.69 | 1.35795 | 0.678973 | − | 0.734163i | \(-0.262425\pi\) | ||||
0.678973 | + | 0.734163i | \(0.262425\pi\) | |||||||
\(152\) | 319.410i | 0.170445i | ||||||||
\(153\) | − | 1073.90i | − | 0.567448i | ||||||
\(154\) | 868.115 | 0.454251 | ||||||||
\(155\) | −91.6263 | + | 676.562i | −0.0474813 | + | 0.350599i | ||||
\(156\) | 365.372 | 0.187520 | ||||||||
\(157\) | − | 1621.48i | − | 0.824258i | −0.911125 | − | 0.412129i | \(-0.864785\pi\) | ||
0.911125 | − | 0.412129i | \(-0.135215\pi\) | |||||||
\(158\) | 1416.67i | 0.713319i | ||||||||
\(159\) | −846.145 | −0.422036 | ||||||||
\(160\) | −1464.23 | − | 198.299i | −0.723484 | − | 0.0979808i | ||||
\(161\) | −913.954 | −0.447389 | ||||||||
\(162\) | 178.739i | 0.0866858i | ||||||||
\(163\) | 925.194i | 0.444582i | 0.974980 | + | 0.222291i | \(0.0713534\pi\) | ||||
−0.974980 | + | 0.222291i | \(0.928647\pi\) | |||||||
\(164\) | 1365.41 | 0.650126 | ||||||||
\(165\) | 1867.98 | + | 252.980i | 0.881348 | + | 0.119360i | ||||
\(166\) | −1129.83 | −0.528265 | ||||||||
\(167\) | − | 2681.55i | − | 1.24254i | −0.783596 | − | 0.621271i | \(-0.786617\pi\) | ||
0.783596 | − | 0.621271i | \(-0.213383\pi\) | |||||||
\(168\) | − | 515.793i | − | 0.236871i | ||||||
\(169\) | 683.589 | 0.311147 | ||||||||
\(170\) | 395.073 | − | 2917.19i | 0.178239 | − | 1.31611i | ||||
\(171\) | −117.040 | −0.0523409 | ||||||||
\(172\) | − | 1230.44i | − | 0.545466i | ||||||
\(173\) | 287.591i | 0.126388i | 0.998001 | + | 0.0631940i | \(0.0201287\pi\) | ||||
−0.998001 | + | 0.0631940i | \(0.979871\pi\) | |||||||
\(174\) | −516.308 | −0.224950 | ||||||||
\(175\) | −232.733 | + | 843.481i | −0.100531 | + | 0.364350i | ||||
\(176\) | −1638.47 | −0.701729 | ||||||||
\(177\) | 1244.53i | 0.528499i | ||||||||
\(178\) | − | 2703.38i | − | 1.13835i | ||||||
\(179\) | −3683.47 | −1.53808 | −0.769038 | − | 0.639203i | \(-0.779265\pi\) | ||||
−0.769038 | + | 0.639203i | \(0.779265\pi\) | |||||||
\(180\) | 42.2764 | − | 312.166i | 0.0175061 | − | 0.129264i | ||||
\(181\) | 3132.65 | 1.28645 | 0.643227 | − | 0.765676i | \(-0.277595\pi\) | ||||
0.643227 | + | 0.765676i | \(0.277595\pi\) | |||||||
\(182\) | 600.913i | 0.244740i | ||||||||
\(183\) | 1691.41i | 0.683237i | ||||||||
\(184\) | 3206.88 | 1.28486 | ||||||||
\(185\) | 1854.56 | + | 251.162i | 0.737028 | + | 0.0998152i | ||||
\(186\) | 404.256 | 0.159363 | ||||||||
\(187\) | 6706.02i | 2.62242i | ||||||||
\(188\) | − | 1143.54i | − | 0.443622i | ||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −317.933 | − | 43.0575i | −0.121396 | − | 0.0164406i | ||||
\(191\) | 1586.93 | 0.601184 | 0.300592 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300592 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(192\) | 1574.59i | 0.591854i | ||||||||
\(193\) | − | 5179.00i | − | 1.93157i | −0.259352 | − | 0.965783i | \(-0.583509\pi\) | ||
0.259352 | − | 0.965783i | \(-0.416491\pi\) | |||||||
\(194\) | 412.116 | 0.152516 | ||||||||
\(195\) | −175.114 | + | 1293.03i | −0.0643085 | + | 0.474850i | ||||
\(196\) | −153.402 | −0.0559045 | ||||||||
\(197\) | − | 903.798i | − | 0.326868i | −0.986554 | − | 0.163434i | \(-0.947743\pi\) | ||
0.986554 | − | 0.163434i | \(-0.0522570\pi\) | |||||||
\(198\) | − | 1116.15i | − | 0.400612i | ||||||
\(199\) | 1171.51 | 0.417317 | 0.208659 | − | 0.977989i | \(-0.433090\pi\) | ||||
0.208659 | + | 0.977989i | \(0.433090\pi\) | |||||||
\(200\) | 816.611 | − | 2959.60i | 0.288716 | − | 1.04638i | ||||
\(201\) | −1185.69 | −0.416081 | ||||||||
\(202\) | 3642.50i | 1.26874i | ||||||||
\(203\) | 545.947i | 0.188759i | ||||||||
\(204\) | 1120.67 | 0.384620 | ||||||||
\(205\) | −654.409 | + | 4832.11i | −0.222955 | + | 1.64629i | ||||
\(206\) | 159.293 | 0.0538762 | ||||||||
\(207\) | 1175.08i | 0.394560i | ||||||||
\(208\) | − | 1134.16i | − | 0.378075i | ||||||
\(209\) | 730.864 | 0.241889 | ||||||||
\(210\) | 513.408 | + | 69.5305i | 0.168707 | + | 0.0228479i | ||||
\(211\) | −1103.16 | −0.359928 | −0.179964 | − | 0.983673i | \(-0.557598\pi\) | ||||
−0.179964 | + | 0.983673i | \(0.557598\pi\) | |||||||
\(212\) | − | 882.996i | − | 0.286059i | ||||||
\(213\) | − | 311.969i | − | 0.100356i | ||||||
\(214\) | −2653.61 | −0.847651 | ||||||||
\(215\) | 4354.45 | + | 589.721i | 1.38126 | + | 0.187063i | ||||
\(216\) | −663.162 | −0.208900 | ||||||||
\(217\) | − | 427.462i | − | 0.133724i | ||||||
\(218\) | 3423.33i | 1.06357i | ||||||||
\(219\) | −384.077 | −0.118509 | ||||||||
\(220\) | −263.997 | + | 1949.34i | −0.0809032 | + | 0.597383i | ||||
\(221\) | −4641.94 | −1.41290 | ||||||||
\(222\) | − | 1108.13i | − | 0.335012i | ||||||
\(223\) | 4079.95i | 1.22517i | 0.790404 | + | 0.612586i | \(0.209871\pi\) | ||||
−0.790404 | + | 0.612586i | \(0.790129\pi\) | |||||||
\(224\) | 925.120 | 0.275947 | ||||||||
\(225\) | 1084.48 | + | 299.228i | 0.321326 | + | 0.0886600i | ||||
\(226\) | −4591.83 | −1.35152 | ||||||||
\(227\) | − | 931.964i | − | 0.272496i | −0.990675 | − | 0.136248i | \(-0.956496\pi\) | ||
0.990675 | − | 0.136248i | \(-0.0435044\pi\) | |||||||
\(228\) | − | 122.137i | − | 0.0354770i | ||||||
\(229\) | 1471.55 | 0.424641 | 0.212321 | − | 0.977200i | \(-0.431898\pi\) | ||||
0.212321 | + | 0.977200i | \(0.431898\pi\) | |||||||
\(230\) | −432.297 | + | 3192.05i | −0.123934 | + | 0.915120i | ||||
\(231\) | −1180.22 | −0.336159 | ||||||||
\(232\) | − | 1915.62i | − | 0.542097i | ||||||
\(233\) | 2479.06i | 0.697034i | 0.937303 | + | 0.348517i | \(0.113315\pi\) | ||||
−0.937303 | + | 0.348517i | \(0.886685\pi\) | |||||||
\(234\) | 772.603 | 0.215840 | ||||||||
\(235\) | 4046.91 | + | 548.070i | 1.12337 | + | 0.152137i | ||||
\(236\) | −1298.73 | −0.358220 | ||||||||
\(237\) | − | 1926.00i | − | 0.527877i | ||||||
\(238\) | 1843.12i | 0.501983i | ||||||||
\(239\) | 954.068 | 0.258216 | 0.129108 | − | 0.991631i | \(-0.458789\pi\) | ||||
0.129108 | + | 0.991631i | \(0.458789\pi\) | |||||||
\(240\) | −969.001 | − | 131.231i | −0.260620 | − | 0.0352956i | ||||
\(241\) | −5297.02 | −1.41581 | −0.707906 | − | 0.706306i | \(-0.750360\pi\) | ||||
−0.707906 | + | 0.706306i | \(0.750360\pi\) | |||||||
\(242\) | 4032.77i | 1.07123i | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | −1765.07 | −0.463103 | ||||||||
\(245\) | 73.5219 | − | 542.881i | 0.0191720 | − | 0.141565i | ||||
\(246\) | 2887.25 | 0.748311 | ||||||||
\(247\) | 505.907i | 0.130324i | ||||||||
\(248\) | 1499.88i | 0.384041i | ||||||||
\(249\) | 1536.03 | 0.390931 | ||||||||
\(250\) | 2835.84 | + | 1211.80i | 0.717417 | + | 0.306564i | ||||
\(251\) | 1855.17 | 0.466524 | 0.233262 | − | 0.972414i | \(-0.425060\pi\) | ||||
0.233262 | + | 0.972414i | \(0.425060\pi\) | |||||||
\(252\) | 197.231i | 0.0493032i | ||||||||
\(253\) | − | 7337.87i | − | 1.82343i | ||||||
\(254\) | 3121.77 | 0.771170 | ||||||||
\(255\) | −537.110 | + | 3965.98i | −0.131902 | + | 0.973958i | ||||
\(256\) | −3976.22 | −0.970757 | ||||||||
\(257\) | − | 6233.09i | − | 1.51288i | −0.654065 | − | 0.756438i | \(-0.726938\pi\) | ||
0.654065 | − | 0.756438i | \(-0.273062\pi\) | |||||||
\(258\) | − | 2601.85i | − | 0.627845i | ||||||
\(259\) | −1171.74 | −0.281114 | ||||||||
\(260\) | −1349.34 | − | 182.740i | −0.321856 | − | 0.0435887i | ||||
\(261\) | 701.932 | 0.166469 | ||||||||
\(262\) | − | 5455.99i | − | 1.28653i | ||||||
\(263\) | 1184.50i | 0.277716i | 0.990312 | + | 0.138858i | \(0.0443432\pi\) | ||||
−0.990312 | + | 0.138858i | \(0.955657\pi\) | |||||||
\(264\) | 4141.15 | 0.965417 | ||||||||
\(265\) | 3124.87 | + | 423.199i | 0.724375 | + | 0.0981015i | ||||
\(266\) | 200.875 | 0.0463024 | ||||||||
\(267\) | 3675.31i | 0.842416i | ||||||||
\(268\) | − | 1237.33i | − | 0.282022i | ||||||
\(269\) | 1916.03 | 0.434283 | 0.217141 | − | 0.976140i | \(-0.430327\pi\) | ||||
0.217141 | + | 0.976140i | \(0.430327\pi\) | |||||||
\(270\) | 89.3964 | − | 660.097i | 0.0201500 | − | 0.148786i | ||||
\(271\) | −1168.95 | −0.262025 | −0.131013 | − | 0.991381i | \(-0.541823\pi\) | ||||
−0.131013 | + | 0.991381i | \(0.541823\pi\) | |||||||
\(272\) | − | 3478.69i | − | 0.775465i | ||||||
\(273\) | − | 816.954i | − | 0.181115i | ||||||
\(274\) | −473.088 | −0.104308 | ||||||||
\(275\) | −6772.06 | − | 1868.54i | −1.48498 | − | 0.409736i | ||||
\(276\) | −1226.26 | −0.267435 | ||||||||
\(277\) | 7269.54i | 1.57684i | 0.615138 | + | 0.788419i | \(0.289100\pi\) | ||||
−0.615138 | + | 0.788419i | \(0.710900\pi\) | |||||||
\(278\) | − | 2080.38i | − | 0.448824i | ||||||
\(279\) | −549.594 | −0.117933 | ||||||||
\(280\) | −257.973 | + | 1904.86i | −0.0550602 | + | 0.406561i | ||||
\(281\) | 298.126 | 0.0632908 | 0.0316454 | − | 0.999499i | \(-0.489925\pi\) | ||||
0.0316454 | + | 0.999499i | \(0.489925\pi\) | |||||||
\(282\) | − | 2418.09i | − | 0.510620i | ||||||
\(283\) | 4496.30i | 0.944444i | 0.881480 | + | 0.472222i | \(0.156548\pi\) | ||||
−0.881480 | + | 0.472222i | \(0.843452\pi\) | |||||||
\(284\) | 325.556 | 0.0680218 | ||||||||
\(285\) | 432.237 | + | 58.5376i | 0.0898369 | + | 0.0121665i | ||||
\(286\) | −4824.56 | −0.997490 | ||||||||
\(287\) | − | 3053.00i | − | 0.627919i | ||||||
\(288\) | − | 1189.44i | − | 0.243363i | ||||||
\(289\) | −9324.77 | −1.89798 | ||||||||
\(290\) | 1906.76 | + | 258.231i | 0.386100 | + | 0.0522892i | ||||
\(291\) | −560.280 | −0.112867 | ||||||||
\(292\) | − | 400.804i | − | 0.0803264i | ||||||
\(293\) | 1644.33i | 0.327859i | 0.986472 | + | 0.163929i | \(0.0524169\pi\) | ||||
−0.986472 | + | 0.163929i | \(0.947583\pi\) | |||||||
\(294\) | −324.379 | −0.0643475 | ||||||||
\(295\) | 622.449 | − | 4596.12i | 0.122849 | − | 0.907107i | ||||
\(296\) | 4111.40 | 0.807331 | ||||||||
\(297\) | 1517.43i | 0.296465i | ||||||||
\(298\) | − | 3736.02i | − | 0.726248i | ||||||
\(299\) | 5079.31 | 0.982421 | ||||||||
\(300\) | −312.259 | + | 1131.71i | −0.0600944 | + | 0.217797i | ||||
\(301\) | −2751.21 | −0.526834 | ||||||||
\(302\) | 5560.11i | 1.05943i | ||||||||
\(303\) | − | 4952.05i | − | 0.938904i | ||||||
\(304\) | −379.129 | −0.0715281 | ||||||||
\(305\) | 845.956 | − | 6246.48i | 0.158817 | − | 1.17270i | ||||
\(306\) | 2369.73 | 0.442707 | ||||||||
\(307\) | − | 4726.18i | − | 0.878623i | −0.898335 | − | 0.439312i | \(-0.855222\pi\) | ||
0.898335 | − | 0.439312i | \(-0.144778\pi\) | |||||||
\(308\) | − | 1231.62i | − | 0.227851i | ||||||
\(309\) | −216.563 | −0.0398700 | ||||||||
\(310\) | −1492.94 | − | 202.188i | −0.273527 | − | 0.0370436i | ||||
\(311\) | −4853.99 | −0.885031 | −0.442515 | − | 0.896761i | \(-0.645914\pi\) | ||||
−0.442515 | + | 0.896761i | \(0.645914\pi\) | |||||||
\(312\) | 2866.52i | 0.520144i | ||||||||
\(313\) | − | 1690.87i | − | 0.305348i | −0.988277 | − | 0.152674i | \(-0.951212\pi\) | ||
0.988277 | − | 0.152674i | \(-0.0487884\pi\) | |||||||
\(314\) | 3578.06 | 0.643063 | ||||||||
\(315\) | −697.990 | − | 94.5282i | −0.124848 | − | 0.0169081i | ||||
\(316\) | 2009.88 | 0.357799 | ||||||||
\(317\) | − | 3878.38i | − | 0.687166i | −0.939122 | − | 0.343583i | \(-0.888359\pi\) | ||
0.939122 | − | 0.343583i | \(-0.111641\pi\) | |||||||
\(318\) | − | 1867.15i | − | 0.329260i | ||||||
\(319\) | −4383.25 | −0.769326 | ||||||||
\(320\) | 787.529 | − | 5815.06i | 0.137576 | − | 1.01585i | ||||
\(321\) | 3607.64 | 0.627286 | ||||||||
\(322\) | − | 2016.78i | − | 0.349040i | ||||||
\(323\) | 1551.72i | 0.267307i | ||||||||
\(324\) | 253.583 | 0.0434813 | ||||||||
\(325\) | 1293.41 | − | 4687.66i | 0.220756 | − | 0.800075i | ||||
\(326\) | −2041.59 | −0.346850 | ||||||||
\(327\) | − | 4654.09i | − | 0.787070i | ||||||
\(328\) | 10712.3i | 1.80332i | ||||||||
\(329\) | −2556.90 | −0.428469 | ||||||||
\(330\) | −558.240 | + | 4122.01i | −0.0931215 | + | 0.687603i | ||||
\(331\) | 9927.71 | 1.64857 | 0.824284 | − | 0.566176i | \(-0.191578\pi\) | ||||
0.824284 | + | 0.566176i | \(0.191578\pi\) | |||||||
\(332\) | 1602.93i | 0.264976i | ||||||||
\(333\) | 1506.52i | 0.247919i | ||||||||
\(334\) | 5917.26 | 0.969396 | ||||||||
\(335\) | 4378.84 | + | 593.023i | 0.714153 | + | 0.0967173i | ||||
\(336\) | 612.229 | 0.0994043 | ||||||||
\(337\) | − | 5283.88i | − | 0.854099i | −0.904228 | − | 0.427050i | \(-0.859553\pi\) | ||
0.904228 | − | 0.427050i | \(-0.140447\pi\) | |||||||
\(338\) | 1508.45i | 0.242748i | ||||||||
\(339\) | 6242.70 | 1.00017 | ||||||||
\(340\) | −4138.71 | − | 560.502i | −0.660155 | − | 0.0894043i | ||||
\(341\) | 3431.97 | 0.545019 | ||||||||
\(342\) | − | 258.268i | − | 0.0408349i | ||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 9653.42 | 1.51302 | ||||||||
\(345\) | 587.717 | − | 4339.66i | 0.0917148 | − | 0.677216i | ||||
\(346\) | −634.615 | −0.0986044 | ||||||||
\(347\) | 10548.3i | 1.63188i | 0.578137 | + | 0.815940i | \(0.303780\pi\) | ||||
−0.578137 | + | 0.815940i | \(0.696220\pi\) | |||||||
\(348\) | 732.502i | 0.112834i | ||||||||
\(349\) | −628.411 | −0.0963841 | −0.0481921 | − | 0.998838i | \(-0.515346\pi\) | ||||
−0.0481921 | + | 0.998838i | \(0.515346\pi\) | |||||||
\(350\) | −1861.28 | − | 513.562i | −0.284255 | − | 0.0784315i | ||||
\(351\) | −1050.37 | −0.159728 | ||||||||
\(352\) | 7427.52i | 1.12468i | ||||||||
\(353\) | 2548.17i | 0.384209i | 0.981375 | + | 0.192104i | \(0.0615312\pi\) | ||||
−0.981375 | + | 0.192104i | \(0.938469\pi\) | |||||||
\(354\) | −2746.25 | −0.412320 | ||||||||
\(355\) | −156.031 | + | 1152.12i | −0.0233275 | + | 0.172249i | ||||
\(356\) | −3835.37 | −0.570995 | ||||||||
\(357\) | − | 2505.76i | − | 0.371482i | ||||||
\(358\) | − | 8128.17i | − | 1.19996i | ||||||
\(359\) | −13046.3 | −1.91799 | −0.958996 | − | 0.283420i | \(-0.908531\pi\) | ||||
−0.958996 | + | 0.283420i | \(0.908531\pi\) | |||||||
\(360\) | 2449.10 | + | 331.680i | 0.358553 | + | 0.0485585i | ||||
\(361\) | −6689.88 | −0.975344 | ||||||||
\(362\) | 6912.69i | 1.00366i | ||||||||
\(363\) | − | 5482.64i | − | 0.792738i | ||||||
\(364\) | 852.534 | 0.122761 | ||||||||
\(365\) | 1418.42 | + | 192.096i | 0.203407 | + | 0.0275473i | ||||
\(366\) | −3732.36 | −0.533043 | ||||||||
\(367\) | − | 8068.23i | − | 1.14757i | −0.819006 | − | 0.573785i | \(-0.805475\pi\) | ||
0.819006 | − | 0.573785i | \(-0.194525\pi\) | |||||||
\(368\) | 3806.46i | 0.539199i | ||||||||
\(369\) | −3925.28 | −0.553772 | ||||||||
\(370\) | −554.229 | + | 4092.39i | −0.0778730 | + | 0.575009i | ||||
\(371\) | −1974.34 | −0.276287 | ||||||||
\(372\) | − | 573.530i | − | 0.0799358i | ||||||
\(373\) | − | 3623.32i | − | 0.502972i | −0.967861 | − | 0.251486i | \(-0.919081\pi\) | ||
0.967861 | − | 0.251486i | \(-0.0809193\pi\) | |||||||
\(374\) | −14797.9 | −2.04594 | ||||||||
\(375\) | −3855.38 | − | 1647.47i | −0.530910 | − | 0.226866i | ||||
\(376\) | 8971.62 | 1.23052 | ||||||||
\(377\) | − | 3034.11i | − | 0.414495i | ||||||
\(378\) | 417.059i | 0.0567492i | ||||||||
\(379\) | −7486.58 | −1.01467 | −0.507335 | − | 0.861749i | \(-0.669369\pi\) | ||||
−0.507335 | + | 0.861749i | \(0.669369\pi\) | |||||||
\(380\) | −61.0870 | + | 451.062i | −0.00824657 | + | 0.0608921i | ||||
\(381\) | −4244.11 | −0.570688 | ||||||||
\(382\) | 3501.81i | 0.469027i | ||||||||
\(383\) | 8926.58i | 1.19093i | 0.803381 | + | 0.595466i | \(0.203033\pi\) | ||||
−0.803381 | + | 0.595466i | \(0.796967\pi\) | |||||||
\(384\) | −302.736 | −0.0402316 | ||||||||
\(385\) | 4358.63 | + | 590.286i | 0.576978 | + | 0.0781397i | ||||
\(386\) | 11428.3 | 1.50695 | ||||||||
\(387\) | 3537.27i | 0.464624i | ||||||||
\(388\) | − | 584.681i | − | 0.0765018i | ||||||
\(389\) | 12600.1 | 1.64228 | 0.821141 | − | 0.570725i | \(-0.193338\pi\) | ||||
0.821141 | + | 0.570725i | \(0.193338\pi\) | |||||||
\(390\) | −2853.27 | − | 386.417i | −0.370464 | − | 0.0501717i | ||||
\(391\) | 15579.3 | 2.01503 | ||||||||
\(392\) | − | 1203.52i | − | 0.155068i | ||||||
\(393\) | 7417.53i | 0.952074i | ||||||||
\(394\) | 1994.37 | 0.255013 | ||||||||
\(395\) | −963.286 | + | 7112.83i | −0.122704 | + | 0.906039i | ||||
\(396\) | −1583.51 | −0.200946 | ||||||||
\(397\) | 12713.4i | 1.60722i | 0.595154 | + | 0.803612i | \(0.297091\pi\) | ||||
−0.595154 | + | 0.803612i | \(0.702909\pi\) | |||||||
\(398\) | 2585.12i | 0.325579i | ||||||||
\(399\) | −273.094 | −0.0342651 | ||||||||
\(400\) | 3512.95 | + | 969.290i | 0.439119 | + | 0.121161i | ||||
\(401\) | −6133.51 | −0.763822 | −0.381911 | − | 0.924199i | \(-0.624734\pi\) | ||||
−0.381911 | + | 0.924199i | \(0.624734\pi\) | |||||||
\(402\) | − | 2616.42i | − | 0.324614i | ||||||
\(403\) | 2375.62i | 0.293643i | ||||||||
\(404\) | 5167.72 | 0.636395 | ||||||||
\(405\) | −121.536 | + | 897.415i | −0.0149116 | + | 0.110106i | ||||
\(406\) | −1204.72 | −0.147264 | ||||||||
\(407\) | − | 9407.56i | − | 1.14574i | ||||||
\(408\) | 8792.21i | 1.06686i | ||||||||
\(409\) | −10600.3 | −1.28154 | −0.640769 | − | 0.767733i | \(-0.721385\pi\) | ||||
−0.640769 | + | 0.767733i | \(0.721385\pi\) | |||||||
\(410\) | −10662.8 | − | 1444.06i | −1.28439 | − | 0.173944i | ||||
\(411\) | 643.173 | 0.0771907 | ||||||||
\(412\) | − | 225.994i | − | 0.0270241i | ||||||
\(413\) | 2903.90i | 0.345984i | ||||||||
\(414\) | −2593.01 | −0.307825 | ||||||||
\(415\) | −5672.66 | − | 768.244i | −0.670988 | − | 0.0908714i | ||||
\(416\) | −5141.37 | −0.605953 | ||||||||
\(417\) | 2828.32i | 0.332143i | ||||||||
\(418\) | 1612.77i | 0.188715i | ||||||||
\(419\) | −4296.43 | −0.500941 | −0.250470 | − | 0.968124i | \(-0.580585\pi\) | ||||
−0.250470 | + | 0.968124i | \(0.580585\pi\) | |||||||
\(420\) | 98.6450 | − | 728.388i | 0.0114604 | − | 0.0846231i | ||||
\(421\) | 3916.78 | 0.453425 | 0.226713 | − | 0.973962i | \(-0.427202\pi\) | ||||
0.226713 | + | 0.973962i | \(0.427202\pi\) | |||||||
\(422\) | − | 2434.30i | − | 0.280806i | ||||||
\(423\) | 3287.44i | 0.377874i | ||||||||
\(424\) | 6927.55 | 0.793471 | ||||||||
\(425\) | 3967.16 | − | 14378.0i | 0.452790 | − | 1.64102i | ||||
\(426\) | 688.410 | 0.0782948 | ||||||||
\(427\) | 3946.62i | 0.447284i | ||||||||
\(428\) | 3764.76i | 0.425179i | ||||||||
\(429\) | 6559.09 | 0.738172 | ||||||||
\(430\) | −1301.31 | + | 9608.80i | −0.145942 | + | 1.07762i | ||||
\(431\) | 13408.9 | 1.49857 | 0.749287 | − | 0.662246i | \(-0.230396\pi\) | ||||
0.749287 | + | 0.662246i | \(0.230396\pi\) | |||||||
\(432\) | − | 787.152i | − | 0.0876663i | ||||||
\(433\) | 7792.31i | 0.864837i | 0.901673 | + | 0.432419i | \(0.142340\pi\) | ||||
−0.901673 | + | 0.432419i | \(0.857660\pi\) | |||||||
\(434\) | 943.263 | 0.104327 | ||||||||
\(435\) | −2592.28 | − | 351.071i | −0.285725 | − | 0.0386955i | ||||
\(436\) | 4856.78 | 0.533481 | ||||||||
\(437\) | − | 1697.93i | − | 0.185865i | ||||||
\(438\) | − | 847.528i | − | 0.0924576i | ||||||
\(439\) | −1039.29 | −0.112990 | −0.0564948 | − | 0.998403i | \(-0.517992\pi\) | ||||
−0.0564948 | + | 0.998403i | \(0.517992\pi\) | |||||||
\(440\) | −15293.5 | − | 2071.19i | −1.65702 | − | 0.224410i | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − | 10243.2i | − | 1.10230i | ||||||
\(443\) | − | 2846.33i | − | 0.305267i | −0.988283 | − | 0.152633i | \(-0.951225\pi\) | ||
0.988283 | − | 0.152633i | \(-0.0487754\pi\) | |||||||
\(444\) | −1572.13 | −0.168041 | ||||||||
\(445\) | 1838.20 | − | 13573.2i | 0.195818 | − | 1.44591i | ||||
\(446\) | −9003.05 | −0.955845 | ||||||||
\(447\) | 5079.20i | 0.537445i | ||||||||
\(448\) | 3674.04i | 0.387460i | ||||||||
\(449\) | −7472.64 | −0.785425 | −0.392713 | − | 0.919661i | \(-0.628463\pi\) | ||||
−0.392713 | + | 0.919661i | \(0.628463\pi\) | |||||||
\(450\) | −660.294 | + | 2393.07i | −0.0691701 | + | 0.250690i | ||||
\(451\) | 24511.6 | 2.55922 | ||||||||
\(452\) | 6514.57i | 0.677920i | ||||||||
\(453\) | − | 7559.08i | − | 0.784010i | ||||||
\(454\) | 2056.53 | 0.212594 | ||||||||
\(455\) | −408.599 | + | 3017.07i | −0.0420998 | + | 0.310862i | ||||
\(456\) | 958.230 | 0.0984062 | ||||||||
\(457\) | 11014.3i | 1.12742i | 0.825974 | + | 0.563708i | \(0.190626\pi\) | ||||
−0.825974 | + | 0.563708i | \(0.809374\pi\) | |||||||
\(458\) | 3247.21i | 0.331293i | ||||||||
\(459\) | −3221.70 | −0.327616 | ||||||||
\(460\) | 4528.66 | + | 613.313i | 0.459021 | + | 0.0621649i | ||||
\(461\) | 7944.67 | 0.802647 | 0.401323 | − | 0.915936i | \(-0.368550\pi\) | ||||
0.401323 | + | 0.915936i | \(0.368550\pi\) | |||||||
\(462\) | − | 2604.34i | − | 0.262262i | ||||||
\(463\) | − | 7627.25i | − | 0.765591i | −0.923833 | − | 0.382795i | \(-0.874961\pi\) | ||
0.923833 | − | 0.382795i | \(-0.125039\pi\) | |||||||
\(464\) | 2273.77 | 0.227494 | ||||||||
\(465\) | 2029.69 | + | 274.879i | 0.202418 | + | 0.0274133i | ||||
\(466\) | −5470.45 | −0.543806 | ||||||||
\(467\) | 3284.28i | 0.325436i | 0.986673 | + | 0.162718i | \(0.0520260\pi\) | ||||
−0.986673 | + | 0.162718i | \(0.947974\pi\) | |||||||
\(468\) | − | 1096.11i | − | 0.108265i | ||||||
\(469\) | −2766.61 | −0.272389 | ||||||||
\(470\) | −1209.40 | + | 8930.15i | −0.118693 | + | 0.876419i | ||||
\(471\) | −4864.45 | −0.475886 | ||||||||
\(472\) | − | 10189.2i | − | 0.993633i | ||||||
\(473\) | − | 22088.6i | − | 2.14722i | ||||||
\(474\) | 4250.02 | 0.411835 | ||||||||
\(475\) | −1567.00 | − | 432.366i | −0.151366 | − | 0.0417649i | ||||
\(476\) | 2614.89 | 0.251793 | ||||||||
\(477\) | 2538.44i | 0.243662i | ||||||||
\(478\) | 2105.30i | 0.201453i | ||||||||
\(479\) | 2909.45 | 0.277528 | 0.138764 | − | 0.990325i | \(-0.455687\pi\) | ||||
0.138764 | + | 0.990325i | \(0.455687\pi\) | |||||||
\(480\) | −594.898 | + | 4392.68i | −0.0565693 | + | 0.417703i | ||||
\(481\) | 6511.96 | 0.617297 | ||||||||
\(482\) | − | 11688.7i | − | 1.10458i | ||||||
\(483\) | 2741.86i | 0.258300i | ||||||||
\(484\) | 5721.42 | 0.537323 | ||||||||
\(485\) | 2069.15 | + | 280.224i | 0.193722 | + | 0.0262357i | ||||
\(486\) | 536.218 | 0.0500481 | ||||||||
\(487\) | 2201.84i | 0.204876i | 0.994739 | + | 0.102438i | \(0.0326644\pi\) | ||||
−0.994739 | + | 0.102438i | \(0.967336\pi\) | |||||||
\(488\) | − | 13847.9i | − | 1.28456i | ||||||
\(489\) | 2775.58 | 0.256679 | ||||||||
\(490\) | 1197.95 | + | 162.238i | 0.110445 | + | 0.0149575i | ||||
\(491\) | −11827.6 | −1.08711 | −0.543556 | − | 0.839373i | \(-0.682922\pi\) | ||||
−0.543556 | + | 0.839373i | \(0.682922\pi\) | |||||||
\(492\) | − | 4096.23i | − | 0.375350i | ||||||
\(493\) | − | 9306.23i | − | 0.850165i | ||||||
\(494\) | −1116.37 | −0.101675 | ||||||||
\(495\) | 758.939 | − | 5603.95i | 0.0689127 | − | 0.508846i | ||||
\(496\) | −1780.30 | −0.161165 | ||||||||
\(497\) | − | 727.928i | − | 0.0656983i | ||||||
\(498\) | 3389.49i | 0.304994i | ||||||||
\(499\) | −1408.66 | −0.126374 | −0.0631868 | − | 0.998002i | \(-0.520126\pi\) | ||||
−0.0631868 | + | 0.998002i | \(0.520126\pi\) | |||||||
\(500\) | 1719.22 | − | 4023.29i | 0.153771 | − | 0.359854i | ||||
\(501\) | −8044.65 | −0.717382 | ||||||||
\(502\) | 4093.74i | 0.363969i | ||||||||
\(503\) | − | 11018.9i | − | 0.976758i | −0.872632 | − | 0.488379i | \(-0.837588\pi\) | ||
0.872632 | − | 0.488379i | \(-0.162412\pi\) | |||||||
\(504\) | −1547.38 | −0.136757 | ||||||||
\(505\) | −2476.76 | + | 18288.2i | −0.218247 | + | 1.61152i | ||||
\(506\) | 16192.2 | 1.42259 | ||||||||
\(507\) | − | 2050.77i | − | 0.179641i | ||||||
\(508\) | − | 4428.95i | − | 0.386816i | ||||||
\(509\) | −7032.93 | −0.612434 | −0.306217 | − | 0.951962i | \(-0.599063\pi\) | ||||
−0.306217 | + | 0.951962i | \(0.599063\pi\) | |||||||
\(510\) | −8751.57 | − | 1185.22i | −0.759855 | − | 0.102907i | ||||
\(511\) | −896.180 | −0.0775825 | ||||||||
\(512\) | − | 9581.46i | − | 0.827041i | ||||||
\(513\) | 351.121i | 0.0302190i | ||||||||
\(514\) | 13754.3 | 1.18030 | ||||||||
\(515\) | 799.781 | + | 108.314i | 0.0684321 | + | 0.00926771i | ||||
\(516\) | −3691.32 | −0.314925 | ||||||||
\(517\) | − | 20528.6i | − | 1.74632i | ||||||
\(518\) | − | 2585.63i | − | 0.219317i | ||||||
\(519\) | 862.773 | 0.0729702 | ||||||||
\(520\) | 1433.69 | − | 10586.3i | 0.120907 | − | 0.892766i | ||||
\(521\) | 3049.04 | 0.256394 | 0.128197 | − | 0.991749i | \(-0.459081\pi\) | ||||
0.128197 | + | 0.991749i | \(0.459081\pi\) | |||||||
\(522\) | 1548.93i | 0.129875i | ||||||||
\(523\) | 8714.06i | 0.728564i | 0.931289 | + | 0.364282i | \(0.118686\pi\) | ||||
−0.931289 | + | 0.364282i | \(0.881314\pi\) | |||||||
\(524\) | −7740.58 | −0.645322 | ||||||||
\(525\) | 2530.44 | + | 698.198i | 0.210357 | + | 0.0580416i | ||||
\(526\) | −2613.79 | −0.216666 | ||||||||
\(527\) | 7286.52i | 0.602288i | ||||||||
\(528\) | 4915.41i | 0.405143i | ||||||||
\(529\) | −4880.17 | −0.401099 | ||||||||
\(530\) | −933.856 | + | 6895.53i | −0.0765361 | + | 0.565137i | ||||
\(531\) | 3733.58 | 0.305129 | ||||||||
\(532\) | − | 284.987i | − | 0.0232251i | ||||||
\(533\) | 16967.1i | 1.37885i | ||||||||
\(534\) | −8110.15 | −0.657230 | ||||||||
\(535\) | −13323.3 | − | 1804.36i | −1.07666 | − | 0.145812i | ||||
\(536\) | 9707.48 | 0.782275 | ||||||||
\(537\) | 11050.4i | 0.888009i | ||||||||
\(538\) | 4228.02i | 0.338815i | ||||||||
\(539\) | −2753.85 | −0.220068 | ||||||||
\(540\) | −936.499 | − | 126.829i | −0.0746305 | − | 0.0101072i | ||||
\(541\) | −5999.45 | −0.476778 | −0.238389 | − | 0.971170i | \(-0.576619\pi\) | ||||
−0.238389 | + | 0.971170i | \(0.576619\pi\) | |||||||
\(542\) | − | 2579.48i | − | 0.204425i | ||||||
\(543\) | − | 9397.95i | − | 0.742734i | ||||||
\(544\) | −15769.6 | −1.24286 | ||||||||
\(545\) | −2327.74 | + | 17187.9i | −0.182953 | + | 1.35091i | ||||
\(546\) | 1802.74 | 0.141301 | ||||||||
\(547\) | − | 7759.95i | − | 0.606566i | −0.952901 | − | 0.303283i | \(-0.901917\pi\) | ||
0.952901 | − | 0.303283i | \(-0.0980828\pi\) | |||||||
\(548\) | 671.184i | 0.0523203i | ||||||||
\(549\) | 5074.22 | 0.394467 | ||||||||
\(550\) | 4123.24 | − | 14943.6i | 0.319664 | − | 1.15854i | ||||
\(551\) | −1014.25 | −0.0784184 | ||||||||
\(552\) | − | 9620.63i | − | 0.741814i | ||||||
\(553\) | − | 4493.99i | − | 0.345577i | ||||||
\(554\) | −16041.4 | −1.23021 | ||||||||
\(555\) | 753.487 | − | 5563.69i | 0.0576283 | − | 0.425523i | ||||
\(556\) | −2951.50 | −0.225128 | ||||||||
\(557\) | 6392.82i | 0.486306i | 0.969988 | + | 0.243153i | \(0.0781817\pi\) | ||||
−0.969988 | + | 0.243153i | \(0.921818\pi\) | |||||||
\(558\) | − | 1212.77i | − | 0.0920081i | ||||||
\(559\) | 15289.9 | 1.15687 | ||||||||
\(560\) | −2261.00 | − | 306.206i | −0.170616 | − | 0.0231064i | ||||
\(561\) | 20118.1 | 1.51406 | ||||||||
\(562\) | 657.863i | 0.0493777i | ||||||||
\(563\) | − | 7682.70i | − | 0.575111i | −0.957764 | − | 0.287555i | \(-0.907157\pi\) | ||
0.957764 | − | 0.287555i | \(-0.0928425\pi\) | |||||||
\(564\) | −3430.61 | −0.256125 | ||||||||
\(565\) | −23054.7 | − | 3122.28i | −1.71667 | − | 0.232487i | ||||
\(566\) | −9921.81 | −0.736828 | ||||||||
\(567\) | − | 567.000i | − | 0.0419961i | ||||||
\(568\) | 2554.15i | 0.188679i | ||||||||
\(569\) | −143.175 | −0.0105487 | −0.00527434 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527434 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(570\) | −129.172 | + | 953.800i | −0.00949200 | + | 0.0700883i | ||||
\(571\) | 1077.72 | 0.0789863 | 0.0394932 | − | 0.999220i | \(-0.487426\pi\) | ||||
0.0394932 | + | 0.999220i | \(0.487426\pi\) | |||||||
\(572\) | 6844.74i | 0.500338i | ||||||||
\(573\) | − | 4760.78i | − | 0.347094i | ||||||
\(574\) | 6736.92 | 0.489884 | ||||||||
\(575\) | −4340.96 | + | 15732.7i | −0.314835 | + | 1.14104i | ||||
\(576\) | 4723.76 | 0.341707 | ||||||||
\(577\) | 12651.7i | 0.912818i | 0.889770 | + | 0.456409i | \(0.150865\pi\) | ||||
−0.889770 | + | 0.456409i | \(0.849135\pi\) | |||||||
\(578\) | − | 20576.6i | − | 1.48075i | ||||||
\(579\) | −15537.0 | −1.11519 | ||||||||
\(580\) | 366.361 | − | 2705.18i | 0.0262281 | − | 0.193666i | ||||
\(581\) | 3584.07 | 0.255925 | ||||||||
\(582\) | − | 1236.35i | − | 0.0880554i | ||||||
\(583\) | − | 15851.4i | − | 1.12607i | ||||||
\(584\) | 3144.51 | 0.222810 | ||||||||
\(585\) | 3879.09 | + | 525.342i | 0.274155 | + | 0.0371286i | ||||
\(586\) | −3628.47 | −0.255786 | ||||||||
\(587\) | 2920.89i | 0.205380i | 0.994713 | + | 0.102690i | \(0.0327450\pi\) | ||||
−0.994713 | + | 0.102690i | \(0.967255\pi\) | |||||||
\(588\) | 460.206i | 0.0322765i | ||||||||
\(589\) | 794.131 | 0.0555545 | ||||||||
\(590\) | 10142.1 | + | 1373.53i | 0.707699 | + | 0.0958432i | ||||
\(591\) | −2711.39 | −0.188717 | ||||||||
\(592\) | 4880.09i | 0.338802i | ||||||||
\(593\) | − | 9801.70i | − | 0.678765i | −0.940648 | − | 0.339382i | \(-0.889782\pi\) | ||
0.940648 | − | 0.339382i | \(-0.110218\pi\) | |||||||
\(594\) | −3348.44 | −0.231293 | ||||||||
\(595\) | −1253.26 | + | 9253.96i | −0.0863504 | + | 0.637605i | ||||
\(596\) | −5300.41 | −0.364284 | ||||||||
\(597\) | − | 3514.53i | − | 0.240938i | ||||||
\(598\) | 11208.3i | 0.766458i | ||||||||
\(599\) | 6992.54 | 0.476974 | 0.238487 | − | 0.971146i | \(-0.423349\pi\) | ||||
0.238487 | + | 0.971146i | \(0.423349\pi\) | |||||||
\(600\) | −8878.81 | − | 2449.83i | −0.604126 | − | 0.166690i | ||||
\(601\) | −26159.1 | −1.77546 | −0.887730 | − | 0.460364i | \(-0.847719\pi\) | ||||
−0.887730 | + | 0.460364i | \(0.847719\pi\) | |||||||
\(602\) | − | 6070.98i | − | 0.411021i | ||||||
\(603\) | 3557.07i | 0.240224i | ||||||||
\(604\) | 7888.29 | 0.531407 | ||||||||
\(605\) | −2742.14 | + | 20247.8i | −0.184271 | + | 1.36064i | ||||
\(606\) | 10927.5 | 0.732506 | ||||||||
\(607\) | − | 264.526i | − | 0.0176883i | −0.999961 | − | 0.00884415i | \(-0.997185\pi\) | ||
0.999961 | − | 0.00884415i | \(-0.00281522\pi\) | |||||||
\(608\) | 1718.67i | 0.114640i | ||||||||
\(609\) | 1637.84 | 0.108980 | ||||||||
\(610\) | 13783.9 | + | 1866.74i | 0.914905 | + | 0.123905i | ||||
\(611\) | 14210.0 | 0.940875 | ||||||||
\(612\) | − | 3362.01i | − | 0.222061i | ||||||
\(613\) | 29371.1i | 1.93521i | 0.252461 | + | 0.967607i | \(0.418760\pi\) | ||||
−0.252461 | + | 0.967607i | \(0.581240\pi\) | |||||||
\(614\) | 10429.1 | 0.685477 | ||||||||
\(615\) | 14496.3 | + | 1963.23i | 0.950485 | + | 0.128723i | ||||
\(616\) | 9662.68 | 0.632014 | ||||||||
\(617\) | 26226.1i | 1.71122i | 0.517622 | + | 0.855609i | \(0.326817\pi\) | ||||
−0.517622 | + | 0.855609i | \(0.673183\pi\) | |||||||
\(618\) | − | 477.880i | − | 0.0311054i | ||||||
\(619\) | 8903.12 | 0.578105 | 0.289052 | − | 0.957313i | \(-0.406660\pi\) | ||||
0.289052 | + | 0.957313i | \(0.406660\pi\) | |||||||
\(620\) | −286.850 | + | 2118.08i | −0.0185809 | + | 0.137200i | ||||
\(621\) | 3525.25 | 0.227799 | ||||||||
\(622\) | − | 10711.1i | − | 0.690476i | ||||||
\(623\) | 8575.72i | 0.551491i | ||||||||
\(624\) | −3402.47 | −0.218282 | ||||||||
\(625\) | 13414.2 | + | 8012.47i | 0.858509 | + | 0.512798i | ||||
\(626\) | 3731.18 | 0.238224 | ||||||||
\(627\) | − | 2192.59i | − | 0.139655i | ||||||
\(628\) | − | 5076.31i | − | 0.322558i | ||||||
\(629\) | 19973.5 | 1.26613 | ||||||||
\(630\) | 208.592 | − | 1540.23i | 0.0131912 | − | 0.0974032i | ||||
\(631\) | −14136.0 | −0.891832 | −0.445916 | − | 0.895075i | \(-0.647122\pi\) | ||||
−0.445916 | + | 0.895075i | \(0.647122\pi\) | |||||||
\(632\) | 15768.5i | 0.992464i | ||||||||
\(633\) | 3309.49i | 0.207805i | ||||||||
\(634\) | 8558.27 | 0.536108 | ||||||||
\(635\) | 15673.8 | + | 2122.69i | 0.979519 | + | 0.132656i | ||||
\(636\) | −2648.99 | −0.165156 | ||||||||
\(637\) | − | 1906.23i | − | 0.118567i | ||||||
\(638\) | − | 9672.34i | − | 0.600206i | ||||||
\(639\) | −935.908 | −0.0579404 | ||||||||
\(640\) | 1118.02 | + | 151.413i | 0.0690528 | + | 0.00935177i | ||||
\(641\) | 17665.7 | 1.08854 | 0.544270 | − | 0.838910i | \(-0.316807\pi\) | ||||
0.544270 | + | 0.838910i | \(0.316807\pi\) | |||||||
\(642\) | 7960.84i | 0.489391i | ||||||||
\(643\) | 10890.0i | 0.667901i | 0.942591 | + | 0.333951i | \(0.108382\pi\) | ||||
−0.942591 | + | 0.333951i | \(0.891618\pi\) | |||||||
\(644\) | −2861.27 | −0.175078 | ||||||||
\(645\) | 1769.16 | − | 13063.4i | 0.108001 | − | 0.797472i | ||||
\(646\) | −3424.12 | −0.208545 | ||||||||
\(647\) | − | 24281.0i | − | 1.47540i | −0.675128 | − | 0.737701i | \(-0.735911\pi\) | ||
0.675128 | − | 0.737701i | \(-0.264089\pi\) | |||||||
\(648\) | 1989.49i | 0.120609i | ||||||||
\(649\) | −23314.5 | −1.41013 | ||||||||
\(650\) | 10344.1 | + | 2854.12i | 0.624196 | + | 0.172228i | ||||
\(651\) | −1282.39 | −0.0772053 | ||||||||
\(652\) | 2896.46i | 0.173979i | ||||||||
\(653\) | 1865.16i | 0.111776i | 0.998437 | + | 0.0558878i | \(0.0177989\pi\) | ||||
−0.998437 | + | 0.0558878i | \(0.982201\pi\) | |||||||
\(654\) | 10270.0 | 0.614050 | ||||||||
\(655\) | 3709.87 | − | 27393.4i | 0.221308 | − | 1.63412i | ||||
\(656\) | −12715.2 | −0.756775 | ||||||||
\(657\) | 1152.23i | 0.0684214i | ||||||||
\(658\) | − | 5642.20i | − | 0.334279i | ||||||
\(659\) | 8327.14 | 0.492230 | 0.246115 | − | 0.969241i | \(-0.420846\pi\) | ||||
0.246115 | + | 0.969241i | \(0.420846\pi\) | |||||||
\(660\) | 5848.01 | + | 791.992i | 0.344899 | + | 0.0467095i | ||||
\(661\) | −20665.7 | −1.21604 | −0.608021 | − | 0.793921i | \(-0.708036\pi\) | ||||
−0.608021 | + | 0.793921i | \(0.708036\pi\) | |||||||
\(662\) | 21907.1i | 1.28617i | ||||||||
\(663\) | 13925.8i | 0.815737i | ||||||||
\(664\) | −12575.8 | −0.734991 | ||||||||
\(665\) | 1008.55 | + | 136.588i | 0.0588121 | + | 0.00796488i | ||||
\(666\) | −3324.38 | −0.193419 | ||||||||
\(667\) | 10183.1i | 0.591140i | ||||||||
\(668\) | − | 8395.00i | − | 0.486246i | ||||||
\(669\) | 12239.8 | 0.707353 | ||||||||
\(670\) | −1308.60 | + | 9662.60i | −0.0754561 | + | 0.557163i | ||||
\(671\) | −31686.2 | −1.82300 | ||||||||
\(672\) | − | 2775.36i | − | 0.159318i | ||||||
\(673\) | − | 1283.48i | − | 0.0735136i | −0.999324 | − | 0.0367568i | \(-0.988297\pi\) | ||
0.999324 | − | 0.0367568i | \(-0.0117027\pi\) | |||||||
\(674\) | 11659.7 | 0.666344 | ||||||||
\(675\) | 897.683 | − | 3253.43i | 0.0511879 | − | 0.185518i | ||||
\(676\) | 2140.08 | 0.121762 | ||||||||
\(677\) | 13783.2i | 0.782467i | 0.920291 | + | 0.391234i | \(0.127952\pi\) | ||||
−0.920291 | + | 0.391234i | \(0.872048\pi\) | |||||||
\(678\) | 13775.5i | 0.780302i | ||||||||
\(679\) | −1307.32 | −0.0738886 | ||||||||
\(680\) | 4397.42 | − | 32470.2i | 0.247990 | − | 1.83114i | ||||
\(681\) | −2795.89 | −0.157326 | ||||||||
\(682\) | 7573.18i | 0.425208i | ||||||||
\(683\) | 10796.5i | 0.604856i | 0.953172 | + | 0.302428i | \(0.0977972\pi\) | ||||
−0.953172 | + | 0.302428i | \(0.902203\pi\) | |||||||
\(684\) | −366.412 | −0.0204826 | ||||||||
\(685\) | −2375.28 | − | 321.682i | −0.132489 | − | 0.0179428i | ||||
\(686\) | −756.884 | −0.0421253 | ||||||||
\(687\) | − | 4414.66i | − | 0.245167i | ||||||
\(688\) | 11458.3i | 0.634947i | ||||||||
\(689\) | 10972.4 | 0.606699 | ||||||||
\(690\) | 9576.15 | + | 1296.89i | 0.528345 | + | 0.0715533i | ||||
\(691\) | −12082.4 | −0.665173 | −0.332587 | − | 0.943073i | \(-0.607921\pi\) | ||||
−0.332587 | + | 0.943073i | \(0.607921\pi\) | |||||||
\(692\) | 900.348i | 0.0494597i | ||||||||
\(693\) | 3540.66i | 0.194082i | ||||||||
\(694\) | −23276.5 | −1.27315 | ||||||||
\(695\) | 1414.58 | − | 10445.2i | 0.0772060 | − | 0.570084i | ||||
\(696\) | −5746.85 | −0.312980 | ||||||||
\(697\) | 52041.4i | 2.82813i | ||||||||
\(698\) | − | 1386.69i | − | 0.0751962i | ||||||
\(699\) | 7437.19 | 0.402433 | ||||||||
\(700\) | −728.605 | + | 2640.65i | −0.0393410 | + | 0.142582i | ||||
\(701\) | −28753.5 | −1.54922 | −0.774610 | − | 0.632439i | \(-0.782054\pi\) | ||||
−0.774610 | + | 0.632439i | \(0.782054\pi\) | |||||||
\(702\) | − | 2317.81i | − | 0.124615i | ||||||
\(703\) | − | 2176.84i | − | 0.116787i | ||||||
\(704\) | −29497.8 | −1.57917 | ||||||||
\(705\) | 1644.21 | − | 12140.7i | 0.0878362 | − | 0.648576i | ||||
\(706\) | −5622.95 | −0.299749 | ||||||||
\(707\) | − | 11554.8i | − | 0.614657i | ||||||
\(708\) | 3896.18i | 0.206819i | ||||||||
\(709\) | −4577.21 | −0.242455 | −0.121228 | − | 0.992625i | \(-0.538683\pi\) | ||||
−0.121228 | + | 0.992625i | \(0.538683\pi\) | |||||||
\(710\) | −2542.34 | − | 344.308i | −0.134384 | − | 0.0181995i | ||||
\(711\) | −5777.99 | −0.304770 | ||||||||
\(712\) | − | 30090.4i | − | 1.58383i | ||||||
\(713\) | − | 7973.07i | − | 0.418785i | ||||||
\(714\) | 5529.37 | 0.289820 | ||||||||
\(715\) | −24223.1 | − | 3280.52i | −1.26698 | − | 0.171587i | ||||
\(716\) | −11531.7 | −0.601898 | ||||||||
\(717\) | − | 2862.20i | − | 0.149081i | ||||||
\(718\) | − | 28788.8i | − | 1.49636i | ||||||
\(719\) | −30875.9 | −1.60150 | −0.800749 | − | 0.599000i | \(-0.795565\pi\) | ||||
−0.800749 | + | 0.599000i | \(0.795565\pi\) | |||||||
\(720\) | −393.693 | + | 2907.00i | −0.0203779 | + | 0.150469i | ||||
\(721\) | −505.313 | −0.0261010 | ||||||||
\(722\) | − | 14762.3i | − | 0.760936i | ||||||
\(723\) | 15891.1i | 0.817420i | ||||||||
\(724\) | 9807.25 | 0.503430 | ||||||||
\(725\) | 9397.88 | + | 2593.06i | 0.481419 | + | 0.132833i | ||||
\(726\) | 12098.3 | 0.618472 | ||||||||
\(727\) | 520.090i | 0.0265324i | 0.999912 | + | 0.0132662i | \(0.00422289\pi\) | ||||
−0.999912 | + | 0.0132662i | \(0.995777\pi\) | |||||||
\(728\) | 6688.56i | 0.340514i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −423.890 | + | 3129.98i | −0.0214916 | + | 0.158693i | ||||
\(731\) | 46897.1 | 2.37285 | ||||||||
\(732\) | 5295.21i | 0.267372i | ||||||||
\(733\) | 393.396i | 0.0198232i | 0.999951 | + | 0.00991160i | \(0.00315501\pi\) | ||||
−0.999951 | + | 0.00991160i | \(0.996845\pi\) | |||||||
\(734\) | 17803.8 | 0.895301 | ||||||||
\(735\) | −1628.64 | − | 220.566i | −0.0817325 | − | 0.0110690i | ||||
\(736\) | 17255.5 | 0.864191 | ||||||||
\(737\) | − | 22212.3i | − | 1.11018i | ||||||
\(738\) | − | 8661.76i | − | 0.432037i | ||||||
\(739\) | 9348.92 | 0.465366 | 0.232683 | − | 0.972553i | \(-0.425250\pi\) | ||||
0.232683 | + | 0.972553i | \(0.425250\pi\) | |||||||
\(740\) | 5806.00 | + | 786.302i | 0.288423 | + | 0.0390609i | ||||
\(741\) | 1517.72 | 0.0752428 | ||||||||
\(742\) | − | 4356.69i | − | 0.215552i | ||||||
\(743\) | − | 33710.8i | − | 1.66451i | −0.554394 | − | 0.832254i | \(-0.687050\pi\) | ||
0.554394 | − | 0.832254i | \(-0.312950\pi\) | |||||||
\(744\) | 4499.63 | 0.221726 | ||||||||
\(745\) | 2540.36 | − | 18757.8i | 0.124928 | − | 0.922461i | ||||
\(746\) | 7995.44 | 0.392405 | ||||||||
\(747\) | − | 4608.09i | − | 0.225704i | ||||||
\(748\) | 20994.2i | 1.02624i | ||||||||
\(749\) | 8417.83 | 0.410655 | ||||||||
\(750\) | 3635.40 | − | 8507.52i | 0.176995 | − | 0.414201i | ||||
\(751\) | −21116.6 | −1.02604 | −0.513019 | − | 0.858377i | \(-0.671473\pi\) | ||||
−0.513019 | + | 0.858377i | \(0.671473\pi\) | |||||||
\(752\) | 10649.0i | 0.516396i | ||||||||
\(753\) | − | 5565.52i | − | 0.269348i | ||||||
\(754\) | 6695.24 | 0.323377 | ||||||||
\(755\) | −3780.67 | + | 27916.2i | −0.182242 | + | 1.34566i | ||||
\(756\) | 591.694 | 0.0284652 | ||||||||
\(757\) | − | 7385.25i | − | 0.354586i | −0.984158 | − | 0.177293i | \(-0.943266\pi\) | ||
0.984158 | − | 0.177293i | \(-0.0567340\pi\) | |||||||
\(758\) | − | 16520.3i | − | 0.791616i | ||||||
\(759\) | −22013.6 | −1.05276 | ||||||||
\(760\) | −3538.81 | − | 479.258i | −0.168903 | − | 0.0228744i | ||||
\(761\) | −27682.0 | −1.31862 | −0.659311 | − | 0.751871i | \(-0.729152\pi\) | ||||
−0.659311 | + | 0.751871i | \(0.729152\pi\) | |||||||
\(762\) | − | 9365.30i | − | 0.445235i | ||||||
\(763\) | − | 10859.5i | − | 0.515258i | ||||||
\(764\) | 4968.12 | 0.235262 | ||||||||
\(765\) | 11897.9 | + | 1611.33i | 0.562315 | + | 0.0761539i | ||||
\(766\) | −19697.9 | −0.929132 | ||||||||
\(767\) | − | 16138.4i | − | 0.759746i | ||||||
\(768\) | 11928.7i | 0.560467i | ||||||||
\(769\) | 22248.6 | 1.04331 | 0.521654 | − | 0.853157i | \(-0.325315\pi\) | ||||
0.521654 | + | 0.853157i | \(0.325315\pi\) | |||||||
\(770\) | −1302.56 | + | 9618.01i | −0.0609624 | + | 0.450142i | ||||
\(771\) | −18699.3 | −0.873460 | ||||||||
\(772\) | − | 16213.6i | − | 0.755883i | ||||||
\(773\) | 11372.3i | 0.529152i | 0.964365 | + | 0.264576i | \(0.0852321\pi\) | ||||
−0.964365 | + | 0.264576i | \(0.914768\pi\) | |||||||
\(774\) | −7805.54 | −0.362486 | ||||||||
\(775\) | −7358.29 | − | 2030.29i | −0.341055 | − | 0.0941036i | ||||
\(776\) | 4587.12 | 0.212201 | ||||||||
\(777\) | 3515.22i | 0.162301i | ||||||||
\(778\) | 27804.0i | 1.28126i | ||||||||
\(779\) | 5671.80 | 0.260864 | ||||||||
\(780\) | −548.221 | + | 4048.02i | −0.0251660 | + | 0.185824i | ||||
\(781\) | 5844.32 | 0.267767 | ||||||||
\(782\) | 34378.1i | 1.57207i | ||||||||
\(783\) | − | 2105.80i | − | 0.0961112i | ||||||
\(784\) | 1428.53 | 0.0650754 | ||||||||
\(785\) | 17964.7 | + | 2432.95i | 0.816802 | + | 0.110619i | ||||
\(786\) | −16368.0 | −0.742781 | ||||||||
\(787\) | − | 36561.9i | − | 1.65602i | −0.560710 | − | 0.828012i | \(-0.689472\pi\) | ||
0.560710 | − | 0.828012i | \(-0.310528\pi\) | |||||||
\(788\) | − | 2829.48i | − | 0.127914i | ||||||
\(789\) | 3553.50 | 0.160339 | ||||||||
\(790\) | −15695.6 | − | 2125.64i | −0.706866 | − | 0.0957304i | ||||
\(791\) | 14566.3 | 0.654763 | ||||||||
\(792\) | − | 12423.4i | − | 0.557384i | ||||||
\(793\) | − | 21933.4i | − | 0.982190i | ||||||
\(794\) | −28054.2 | −1.25391 | ||||||||
\(795\) | 1269.60 | − | 9374.61i | 0.0566389 | − | 0.418218i | ||||
\(796\) | 3667.59 | 0.163309 | ||||||||
\(797\) | − | 7436.80i | − | 0.330521i | −0.986250 | − | 0.165260i | \(-0.947154\pi\) | ||
0.986250 | − | 0.165260i | \(-0.0528465\pi\) | |||||||
\(798\) | − | 602.625i | − | 0.0267327i | ||||||
\(799\) | 43584.9 | 1.92982 | ||||||||
\(800\) | 4393.99 | − | 15924.9i | 0.194189 | − | 0.703789i | ||||
\(801\) | 11025.9 | 0.486369 | ||||||||
\(802\) | − | 13534.6i | − | 0.595913i | ||||||
\(803\) | − | 7195.17i | − | 0.316204i | ||||||
\(804\) | −3711.99 | −0.162826 | ||||||||
\(805\) | 1371.34 | − | 10125.9i | 0.0600415 | − | 0.443342i | ||||
\(806\) | −5242.20 | −0.229092 | ||||||||
\(807\) | − | 5748.08i | − | 0.250733i | ||||||
\(808\) | 40543.4i | 1.76524i | ||||||||
\(809\) | 30585.4 | 1.32920 | 0.664601 | − | 0.747198i | \(-0.268601\pi\) | ||||
0.664601 | + | 0.747198i | \(0.268601\pi\) | |||||||
\(810\) | −1980.29 | − | 268.189i | −0.0859016 | − | 0.0116336i | ||||
\(811\) | 23756.0 | 1.02859 | 0.514294 | − | 0.857614i | \(-0.328054\pi\) | ||||
0.514294 | + | 0.857614i | \(0.328054\pi\) | |||||||
\(812\) | 1709.17i | 0.0738672i | ||||||||
\(813\) | 3506.86i | 0.151280i | ||||||||
\(814\) | 20759.3 | 0.893873 | ||||||||
\(815\) | −10250.4 | − | 1388.21i | −0.440560 | − | 0.0596647i | ||||
\(816\) | −10436.1 | −0.447715 | ||||||||
\(817\) | − | 5111.14i | − | 0.218869i | ||||||
\(818\) | − | 23391.2i | − | 0.999821i | ||||||
\(819\) | −2450.86 | −0.104567 | ||||||||
\(820\) | −2048.73 | + | 15127.7i | −0.0872496 | + | 0.644245i | ||||
\(821\) | −33842.2 | −1.43861 | −0.719306 | − | 0.694694i | \(-0.755540\pi\) | ||||
−0.719306 | + | 0.694694i | \(0.755540\pi\) | |||||||
\(822\) | 1419.26i | 0.0602220i | ||||||||
\(823\) | 18730.9i | 0.793340i | 0.917961 | + | 0.396670i | \(0.129834\pi\) | ||||
−0.917961 | + | 0.396670i | \(0.870166\pi\) | |||||||
\(824\) | 1773.04 | 0.0749597 | ||||||||
\(825\) | −5605.63 | + | 20316.2i | −0.236561 | + | 0.857356i | ||||
\(826\) | −6407.91 | −0.269927 | ||||||||
\(827\) | − | 19107.1i | − | 0.803409i | −0.915769 | − | 0.401705i | \(-0.868418\pi\) | ||
0.915769 | − | 0.401705i | \(-0.131582\pi\) | |||||||
\(828\) | 3678.78i | 0.154404i | ||||||||
\(829\) | −9942.59 | −0.416551 | −0.208275 | − | 0.978070i | \(-0.566785\pi\) | ||||
−0.208275 | + | 0.978070i | \(0.566785\pi\) | |||||||
\(830\) | 1695.25 | − | 12517.6i | 0.0708953 | − | 0.523486i | ||||
\(831\) | 21808.6 | 0.910388 | ||||||||
\(832\) | − | 20418.5i | − | 0.850822i | ||||||
\(833\) | − | 5846.78i | − | 0.243192i | ||||||
\(834\) | −6241.14 | −0.259128 | ||||||||
\(835\) | 29709.4 | + | 4023.52i | 1.23130 | + | 0.166754i | ||||
\(836\) | 2288.08 | 0.0946590 | ||||||||
\(837\) | 1648.78i | 0.0680887i | ||||||||
\(838\) | − | 9480.75i | − | 0.390820i | ||||||
\(839\) | −37144.9 | −1.52847 | −0.764233 | − | 0.644940i | \(-0.776882\pi\) | ||||
−0.764233 | + | 0.644940i | \(0.776882\pi\) | |||||||
\(840\) | 5714.57 | + | 773.920i | 0.234728 | + | 0.0317890i | ||||
\(841\) | −18306.2 | −0.750591 | ||||||||
\(842\) | 8642.99i | 0.353750i | ||||||||
\(843\) | − | 894.379i | − | 0.0365410i | ||||||
\(844\) | −3453.62 | −0.140851 | ||||||||
\(845\) | −1025.69 | + | 7573.62i | −0.0417572 | + | 0.308332i | ||||
\(846\) | −7254.26 | −0.294807 | ||||||||
\(847\) | − | 12792.8i | − | 0.518969i | ||||||
\(848\) | 8222.78i | 0.332985i | ||||||||
\(849\) | 13488.9 | 0.545275 | ||||||||
\(850\) | 31727.3 | + | 8754.18i | 1.28028 | + | 0.353254i | ||||
\(851\) | −21855.4 | −0.880370 | ||||||||
\(852\) | − | 976.668i | − | 0.0392724i | ||||||
\(853\) | 31377.2i | 1.25948i | 0.776807 | + | 0.629739i | \(0.216838\pi\) | ||||
−0.776807 | + | 0.629739i | \(0.783162\pi\) | |||||||
\(854\) | −8708.84 | −0.348958 | ||||||||
\(855\) | 175.613 | − | 1296.71i | 0.00702436 | − | 0.0518674i | ||||
\(856\) | −29536.4 | −1.17936 | ||||||||
\(857\) | − | 24561.3i | − | 0.978993i | −0.872005 | − | 0.489496i | \(-0.837181\pi\) | ||
0.872005 | − | 0.489496i | \(-0.162819\pi\) | |||||||
\(858\) | 14473.7i | 0.575901i | ||||||||
\(859\) | 39819.1 | 1.58162 | 0.790809 | − | 0.612063i | \(-0.209660\pi\) | ||||
0.790809 | + | 0.612063i | \(0.209660\pi\) | |||||||
\(860\) | 13632.3 | + | 1846.21i | 0.540532 | + | 0.0732038i | ||||
\(861\) | −9158.99 | −0.362529 | ||||||||
\(862\) | 29588.9i | 1.16914i | ||||||||
\(863\) | − | 14702.2i | − | 0.579919i | −0.957039 | − | 0.289959i | \(-0.906358\pi\) | ||
0.957039 | − | 0.289959i | \(-0.0936418\pi\) | |||||||
\(864\) | −3568.32 | −0.140506 | ||||||||
\(865\) | −3186.28 | − | 431.515i | −0.125245 | − | 0.0169618i | ||||
\(866\) | −17195.0 | −0.674722 | ||||||||
\(867\) | 27974.3i | 1.09580i | ||||||||
\(868\) | − | 1338.24i | − | 0.0523303i | ||||||
\(869\) | 36081.0 | 1.40847 | ||||||||
\(870\) | 774.694 | − | 5720.28i | 0.0301892 | − | 0.222915i | ||||
\(871\) | 15375.5 | 0.598138 | ||||||||
\(872\) | 38103.9i | 1.47977i | ||||||||
\(873\) | 1680.84i | 0.0651636i | ||||||||
\(874\) | 3746.74 | 0.145006 | ||||||||
\(875\) | −8995.89 | − | 3844.09i | −0.347562 | − | 0.148519i | ||||
\(876\) | −1202.41 | −0.0463764 | ||||||||
\(877\) | 7208.31i | 0.277546i | 0.990324 | + | 0.138773i | \(0.0443158\pi\) | ||||
−0.990324 | + | 0.138773i | \(0.955684\pi\) | |||||||
\(878\) | − | 2293.35i | − | 0.0881512i | ||||||
\(879\) | 4932.98 | 0.189289 | ||||||||
\(880\) | 2458.44 | − | 18152.9i | 0.0941749 | − | 0.695381i | ||||
\(881\) | 3789.00 | 0.144898 | 0.0724488 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724488 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(882\) | 973.137i | 0.0371510i | ||||||||
\(883\) | 26953.7i | 1.02725i | 0.858014 | + | 0.513626i | \(0.171698\pi\) | ||||
−0.858014 | + | 0.513626i | \(0.828302\pi\) | |||||||
\(884\) | −14532.3 | −0.552912 | ||||||||
\(885\) | −13788.4 | − | 1867.35i | −0.523718 | − | 0.0709268i | ||||
\(886\) | 6280.88 | 0.238160 | ||||||||
\(887\) | − | 37869.8i | − | 1.43353i | −0.697314 | − | 0.716766i | \(-0.745621\pi\) | ||
0.697314 | − | 0.716766i | \(-0.254379\pi\) | |||||||
\(888\) | − | 12334.2i | − | 0.466113i | ||||||
\(889\) | −9902.92 | −0.373603 | ||||||||
\(890\) | 29951.3 | + | 4056.29i | 1.12806 | + | 0.152772i | ||||
\(891\) | 4552.28 | 0.171164 | ||||||||
\(892\) | 12772.9i | 0.479449i | ||||||||
\(893\) | − | 4750.15i | − | 0.178004i | ||||||
\(894\) | −11208.1 | −0.419300 | ||||||||
\(895\) | 5526.86 | − | 40809.9i | 0.206416 | − | 1.52416i | ||||
\(896\) | −706.385 | −0.0263378 | ||||||||
\(897\) | − | 15237.9i | − | 0.567201i | ||||||
\(898\) | − | 16489.6i | − | 0.612767i | ||||||
\(899\) | −4762.69 | −0.176690 | ||||||||
\(900\) | 3395.12 | + | 936.778i | 0.125745 | + | 0.0346955i | ||||
\(901\) | 33654.6 | 1.24439 | ||||||||
\(902\) | 54088.8i | 1.99663i | ||||||||
\(903\) | 8253.62i | 0.304168i | ||||||||
\(904\) | −51110.1 | −1.88042 | ||||||||
\(905\) | −4700.38 | + | 34707.3i | −0.172647 | + | 1.27482i | ||||
\(906\) | 16680.3 | 0.611663 | ||||||||
\(907\) | 11717.5i | 0.428968i | 0.976728 | + | 0.214484i | \(0.0688070\pi\) | ||||
−0.976728 | + | 0.214484i | \(0.931193\pi\) | |||||||
\(908\) | − | 2917.66i | − | 0.106636i | ||||||
\(909\) | −14856.1 | −0.542076 | ||||||||
\(910\) | −6657.64 | − | 901.639i | −0.242526 | − | 0.0328451i | ||||
\(911\) | −15909.2 | −0.578589 | −0.289294 | − | 0.957240i | \(-0.593421\pi\) | ||||
−0.289294 | + | 0.957240i | \(0.593421\pi\) | |||||||
\(912\) | 1137.39i | 0.0412968i | ||||||||
\(913\) | 28775.4i | 1.04308i | ||||||||
\(914\) | −24304.9 | −0.879578 | ||||||||
\(915\) | −18739.4 | − | 2537.87i | −0.677056 | − | 0.0916933i | ||||
\(916\) | 4606.92 | 0.166176 | ||||||||
\(917\) | 17307.6i | 0.623279i | ||||||||
\(918\) | − | 7109.19i | − | 0.255597i | ||||||
\(919\) | 32933.3 | 1.18212 | 0.591060 | − | 0.806628i | \(-0.298710\pi\) | ||||
0.591060 | + | 0.806628i | \(0.298710\pi\) | |||||||
\(920\) | −4811.75 | + | 35529.6i | −0.172433 | + | 1.27324i | ||||
\(921\) | −14178.5 | −0.507273 | ||||||||
\(922\) | 17531.2i | 0.626203i | ||||||||
\(923\) | 4045.47i | 0.144267i | ||||||||
\(924\) | −3694.86 | −0.131550 | ||||||||
\(925\) | −5565.35 | + | 20170.2i | −0.197824 | + | 0.716965i | ||||
\(926\) | 16830.7 | 0.597292 | ||||||||
\(927\) | 649.688i | 0.0230189i | ||||||||
\(928\) | − | 10307.5i | − | 0.364612i | ||||||
\(929\) | 30912.6 | 1.09172 | 0.545861 | − | 0.837876i | \(-0.316203\pi\) | ||||
0.545861 | + | 0.837876i | \(0.316203\pi\) | |||||||
\(930\) | −606.564 | + | 4478.83i | −0.0213871 | + | 0.157921i | ||||
\(931\) | −637.219 | −0.0224318 | ||||||||
\(932\) | 7761.09i | 0.272771i | ||||||||
\(933\) | 14562.0i | 0.510973i | ||||||||
\(934\) | −7247.29 | −0.253896 | ||||||||
\(935\) | −74297.3 | − | 10062.0i | −2.59870 | − | 0.351940i | ||||
\(936\) | 8599.57 | 0.300305 | ||||||||
\(937\) | − | 45737.6i | − | 1.59465i | −0.603553 | − | 0.797323i | \(-0.706249\pi\) | ||
0.603553 | − | 0.797323i | \(-0.293751\pi\) | |||||||
\(938\) | − | 6104.97i | − | 0.212510i | ||||||
\(939\) | −5072.62 | −0.176293 | ||||||||
\(940\) | 12669.5 | + | 1715.82i | 0.439609 | + | 0.0595359i | ||||
\(941\) | −2137.79 | −0.0740595 | −0.0370297 | − | 0.999314i | \(-0.511790\pi\) | ||||
−0.0370297 | + | 0.999314i | \(0.511790\pi\) | |||||||
\(942\) | − | 10734.2i | − | 0.371273i | ||||||
\(943\) | − | 56944.8i | − | 1.96647i | ||||||
\(944\) | 12094.2 | 0.416984 | ||||||||
\(945\) | −283.585 | + | 2093.97i | −0.00976191 | + | 0.0720813i | ||||
\(946\) | 48742.1 | 1.67520 | ||||||||
\(947\) | 42513.2i | 1.45881i | 0.684082 | + | 0.729405i | \(0.260203\pi\) | ||||
−0.684082 | + | 0.729405i | \(0.739797\pi\) | |||||||
\(948\) | − | 6029.63i | − | 0.206575i | ||||||
\(949\) | 4980.53 | 0.170363 | ||||||||
\(950\) | 954.085 | − | 3457.84i | 0.0325838 | − | 0.118092i | ||||
\(951\) | −11635.2 | −0.396736 | ||||||||
\(952\) | 20515.2i | 0.698425i | ||||||||
\(953\) | 9012.85i | 0.306353i | 0.988199 | + | 0.153177i | \(0.0489504\pi\) | ||||
−0.988199 | + | 0.153177i | \(0.951050\pi\) | |||||||
\(954\) | −5601.46 | −0.190099 | ||||||||
\(955\) | −2381.10 | + | 17581.9i | −0.0806813 | + | 0.595745i | ||||
\(956\) | 2986.86 | 0.101048 | ||||||||
\(957\) | 13149.8i | 0.444171i | ||||||||
\(958\) | 6420.15i | 0.216520i | ||||||||
\(959\) | 1500.74 | 0.0505332 | ||||||||
\(960\) | −17445.2 | − | 2362.59i | −0.586500 | − | 0.0794293i | ||||
\(961\) | −26061.9 | −0.874826 | ||||||||
\(962\) | 14369.7i | 0.481598i | ||||||||
\(963\) | − | 10822.9i | − | 0.362164i | ||||||
\(964\) | −16583.1 | −0.554053 | ||||||||
\(965\) | 57379.1 | + | 7770.81i | 1.91409 | + | 0.259224i | ||||
\(966\) | −6050.35 | −0.201519 | ||||||||
\(967\) | 29024.2i | 0.965207i | 0.875839 | + | 0.482604i | \(0.160309\pi\) | ||||
−0.875839 | + | 0.482604i | \(0.839691\pi\) | |||||||
\(968\) | 44887.4i | 1.49043i | ||||||||
\(969\) | 4655.16 | 0.154330 | ||||||||
\(970\) | −618.358 | + | 4565.91i | −0.0204683 | + | 0.151137i | ||||
\(971\) | 12874.4 | 0.425498 | 0.212749 | − | 0.977107i | \(-0.431758\pi\) | ||||
0.212749 | + | 0.977107i | \(0.431758\pi\) | |||||||
\(972\) | − | 760.749i | − | 0.0251039i | ||||||
\(973\) | 6599.42i | 0.217438i | ||||||||
\(974\) | −4858.70 | −0.159839 | ||||||||
\(975\) | −14063.0 | − | 3880.24i | −0.461924 | − | 0.127454i | ||||
\(976\) | 16437.0 | 0.539072 | ||||||||
\(977\) | − | 15195.8i | − | 0.497600i | −0.968555 | − | 0.248800i | \(-0.919964\pi\) | ||
0.968555 | − | 0.248800i | \(-0.0800362\pi\) | |||||||
\(978\) | 6124.77i | 0.200254i | ||||||||
\(979\) | −68851.9 | −2.24772 | ||||||||
\(980\) | 230.172 | − | 1699.57i | 0.00750262 | − | 0.0553988i | ||||
\(981\) | −13962.3 | −0.454415 | ||||||||
\(982\) | − | 26099.5i | − | 0.848134i | ||||||
\(983\) | − | 12042.2i | − | 0.390728i | −0.980731 | − | 0.195364i | \(-0.937411\pi\) | ||
0.980731 | − | 0.195364i | \(-0.0625888\pi\) | |||||||
\(984\) | 32137.0 | 1.04115 | ||||||||
\(985\) | 10013.4 | + | 1356.10i | 0.323911 | + | 0.0438670i | ||||
\(986\) | 20535.7 | 0.663275 | ||||||||
\(987\) | 7670.69i | 0.247377i | ||||||||
\(988\) | 1583.82i | 0.0510001i | ||||||||
\(989\) | −51315.8 | −1.64990 | ||||||||
\(990\) | 12366.0 | + | 1674.72i | 0.396988 | + | 0.0537638i | ||||
\(991\) | 11490.7 | 0.368330 | 0.184165 | − | 0.982895i | \(-0.441042\pi\) | ||||
0.184165 | + | 0.982895i | \(0.441042\pi\) | |||||||
\(992\) | 8070.49i | 0.258305i | ||||||||
\(993\) | − | 29783.1i | − | 0.951801i | ||||||
\(994\) | 1606.29 | 0.0512560 | ||||||||
\(995\) | −1757.79 | + | 12979.4i | −0.0560057 | + | 0.413542i | ||||
\(996\) | 4808.78 | 0.152984 | ||||||||
\(997\) | 4076.85i | 0.129504i | 0.997901 | + | 0.0647518i | \(0.0206256\pi\) | ||||
−0.997901 | + | 0.0647518i | \(0.979374\pi\) | |||||||
\(998\) | − | 3108.44i | − | 0.0985931i | ||||||
\(999\) | 4519.57 | 0.143136 |
(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.d.b.64.7 | yes | 10 | |
3.2 | odd | 2 | 315.4.d.b.64.4 | 10 | |||
5.2 | odd | 4 | 525.4.a.x.1.2 | 5 | |||
5.3 | odd | 4 | 525.4.a.w.1.4 | 5 | |||
5.4 | even | 2 | inner | 105.4.d.b.64.4 | ✓ | 10 | |
15.2 | even | 4 | 1575.4.a.bo.1.4 | 5 | |||
15.8 | even | 4 | 1575.4.a.bp.1.2 | 5 | |||
15.14 | odd | 2 | 315.4.d.b.64.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.b.64.4 | ✓ | 10 | 5.4 | even | 2 | inner | |
105.4.d.b.64.7 | yes | 10 | 1.1 | even | 1 | trivial | |
315.4.d.b.64.4 | 10 | 3.2 | odd | 2 | |||
315.4.d.b.64.7 | 10 | 15.14 | odd | 2 | |||
525.4.a.w.1.4 | 5 | 5.3 | odd | 4 | |||
525.4.a.x.1.2 | 5 | 5.2 | odd | 4 | |||
1575.4.a.bo.1.4 | 5 | 15.2 | even | 4 | |||
1575.4.a.bp.1.2 | 5 | 15.8 | even | 4 |