Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.a (trivial) |
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: | yes |
Analytic conductor: | \(109.684550701\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + 941923 x^{9} - 2799440 x^{8} - 6021311 x^{7} + 15765187 x^{6} + \cdots + 2596992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.61453\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.61453 | −1.63148 | −0.815741 | − | 0.578417i | \(-0.803671\pi\) | ||||
−0.815741 | + | 0.578417i | \(0.803671\pi\) | |||||||
\(3\) | 3.68758 | 0.709676 | 0.354838 | − | 0.934928i | \(-0.384536\pi\) | ||||
0.354838 | + | 0.934928i | \(0.384536\pi\) | |||||||
\(4\) | 13.2939 | 1.66173 | ||||||||
\(5\) | 19.7910 | 1.77016 | 0.885079 | − | 0.465442i | \(-0.154104\pi\) | ||||
0.885079 | + | 0.465442i | \(0.154104\pi\) | |||||||
\(6\) | −17.0165 | −1.15782 | ||||||||
\(7\) | −18.7869 | −1.01440 | −0.507199 | − | 0.861829i | \(-0.669319\pi\) | ||||
−0.507199 | + | 0.861829i | \(0.669319\pi\) | |||||||
\(8\) | −24.4287 | −1.07961 | ||||||||
\(9\) | −13.4017 | −0.496360 | ||||||||
\(10\) | −91.3259 | −2.88798 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 49.0223 | 1.17929 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 86.6927 | 1.65497 | ||||||||
\(15\) | 72.9808 | 1.25624 | ||||||||
\(16\) | 6.37610 | 0.0996265 | ||||||||
\(17\) | 67.7750 | 0.966933 | 0.483466 | − | 0.875363i | \(-0.339378\pi\) | ||||
0.483466 | + | 0.875363i | \(0.339378\pi\) | |||||||
\(18\) | 61.8427 | 0.809803 | ||||||||
\(19\) | 129.430 | 1.56280 | 0.781401 | − | 0.624029i | \(-0.214505\pi\) | ||||
0.781401 | + | 0.624029i | \(0.214505\pi\) | |||||||
\(20\) | 263.099 | 2.94153 | ||||||||
\(21\) | −69.2783 | −0.719893 | ||||||||
\(22\) | 50.7598 | 0.491910 | ||||||||
\(23\) | −103.682 | −0.939966 | −0.469983 | − | 0.882676i | \(-0.655740\pi\) | ||||
−0.469983 | + | 0.882676i | \(0.655740\pi\) | |||||||
\(24\) | −90.0830 | −0.766171 | ||||||||
\(25\) | 266.682 | 2.13346 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −148.985 | −1.06193 | ||||||||
\(28\) | −249.751 | −1.68566 | ||||||||
\(29\) | 269.826 | 1.72778 | 0.863888 | − | 0.503684i | \(-0.168022\pi\) | ||||
0.863888 | + | 0.503684i | \(0.168022\pi\) | |||||||
\(30\) | −336.772 | −2.04953 | ||||||||
\(31\) | 75.1728 | 0.435530 | 0.217765 | − | 0.976001i | \(-0.430123\pi\) | ||||
0.217765 | + | 0.976001i | \(0.430123\pi\) | |||||||
\(32\) | 166.007 | 0.917069 | ||||||||
\(33\) | −40.5634 | −0.213975 | ||||||||
\(34\) | −312.750 | −1.57753 | ||||||||
\(35\) | −371.811 | −1.79564 | ||||||||
\(36\) | −178.161 | −0.824819 | ||||||||
\(37\) | −9.87062 | −0.0438573 | −0.0219286 | − | 0.999760i | \(-0.506981\pi\) | ||||
−0.0219286 | + | 0.999760i | \(0.506981\pi\) | |||||||
\(38\) | −597.258 | −2.54968 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −483.468 | −1.91108 | ||||||||
\(41\) | 162.811 | 0.620168 | 0.310084 | − | 0.950709i | \(-0.399643\pi\) | ||||
0.310084 | + | 0.950709i | \(0.399643\pi\) | |||||||
\(42\) | 319.687 | 1.17449 | ||||||||
\(43\) | −231.244 | −0.820101 | −0.410051 | − | 0.912063i | \(-0.634489\pi\) | ||||
−0.410051 | + | 0.912063i | \(0.634489\pi\) | |||||||
\(44\) | −146.233 | −0.501032 | ||||||||
\(45\) | −265.233 | −0.878636 | ||||||||
\(46\) | 478.444 | 1.53354 | ||||||||
\(47\) | 42.7253 | 0.132598 | 0.0662991 | − | 0.997800i | \(-0.478881\pi\) | ||||
0.0662991 | + | 0.997800i | \(0.478881\pi\) | |||||||
\(48\) | 23.5124 | 0.0707025 | ||||||||
\(49\) | 9.94786 | 0.0290025 | ||||||||
\(50\) | −1230.61 | −3.48070 | ||||||||
\(51\) | 249.926 | 0.686209 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −717.060 | −1.85841 | −0.929205 | − | 0.369564i | \(-0.879507\pi\) | ||||
−0.929205 | + | 0.369564i | \(0.879507\pi\) | |||||||
\(54\) | 687.494 | 1.73252 | ||||||||
\(55\) | −217.701 | −0.533722 | ||||||||
\(56\) | 458.940 | 1.09515 | ||||||||
\(57\) | 477.283 | 1.10908 | ||||||||
\(58\) | −1245.12 | −2.81884 | ||||||||
\(59\) | 583.309 | 1.28712 | 0.643562 | − | 0.765394i | \(-0.277456\pi\) | ||||
0.643562 | + | 0.765394i | \(0.277456\pi\) | |||||||
\(60\) | 970.198 | 2.08753 | ||||||||
\(61\) | −341.669 | −0.717152 | −0.358576 | − | 0.933501i | \(-0.616738\pi\) | ||||
−0.358576 | + | 0.933501i | \(0.616738\pi\) | |||||||
\(62\) | −346.887 | −0.710559 | ||||||||
\(63\) | 251.777 | 0.503507 | ||||||||
\(64\) | −817.054 | −1.59581 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 187.181 | 0.349097 | ||||||||
\(67\) | −697.923 | −1.27261 | −0.636305 | − | 0.771438i | \(-0.719538\pi\) | ||||
−0.636305 | + | 0.771438i | \(0.719538\pi\) | |||||||
\(68\) | 900.993 | 1.60679 | ||||||||
\(69\) | −382.336 | −0.667071 | ||||||||
\(70\) | 1715.73 | 2.92956 | ||||||||
\(71\) | 620.263 | 1.03678 | 0.518392 | − | 0.855143i | \(-0.326531\pi\) | ||||
0.518392 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(72\) | 327.387 | 0.535875 | ||||||||
\(73\) | 790.345 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(74\) | 45.5483 | 0.0715524 | ||||||||
\(75\) | 983.412 | 1.51406 | ||||||||
\(76\) | 1720.62 | 2.59696 | ||||||||
\(77\) | 206.656 | 0.305852 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −119.274 | −0.169866 | −0.0849328 | − | 0.996387i | \(-0.527068\pi\) | ||||
−0.0849328 | + | 0.996387i | \(0.527068\pi\) | |||||||
\(80\) | 126.189 | 0.176355 | ||||||||
\(81\) | −187.547 | −0.257266 | ||||||||
\(82\) | −751.298 | −1.01179 | ||||||||
\(83\) | 98.6344 | 0.130440 | 0.0652201 | − | 0.997871i | \(-0.479225\pi\) | ||||
0.0652201 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(84\) | −920.977 | −1.19627 | ||||||||
\(85\) | 1341.33 | 1.71162 | ||||||||
\(86\) | 1067.08 | 1.33798 | ||||||||
\(87\) | 995.007 | 1.22616 | ||||||||
\(88\) | 268.716 | 0.325514 | ||||||||
\(89\) | 455.102 | 0.542030 | 0.271015 | − | 0.962575i | \(-0.412641\pi\) | ||||
0.271015 | + | 0.962575i | \(0.412641\pi\) | |||||||
\(90\) | 1223.93 | 1.43348 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1378.34 | −1.56197 | ||||||||
\(93\) | 277.206 | 0.309085 | ||||||||
\(94\) | −197.157 | −0.216332 | ||||||||
\(95\) | 2561.54 | 2.76641 | ||||||||
\(96\) | 612.165 | 0.650821 | ||||||||
\(97\) | 346.559 | 0.362761 | 0.181380 | − | 0.983413i | \(-0.441943\pi\) | ||||
0.181380 | + | 0.983413i | \(0.441943\pi\) | |||||||
\(98\) | −45.9047 | −0.0473171 | ||||||||
\(99\) | 147.419 | 0.149658 | ||||||||
\(100\) | 3545.24 | 3.54524 | ||||||||
\(101\) | 1584.30 | 1.56083 | 0.780414 | − | 0.625264i | \(-0.215009\pi\) | ||||
0.780414 | + | 0.625264i | \(0.215009\pi\) | |||||||
\(102\) | −1153.29 | −1.11954 | ||||||||
\(103\) | −430.743 | −0.412062 | −0.206031 | − | 0.978546i | \(-0.566055\pi\) | ||||
−0.206031 | + | 0.978546i | \(0.566055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1371.08 | −1.27432 | ||||||||
\(106\) | 3308.89 | 3.03196 | ||||||||
\(107\) | 446.381 | 0.403302 | 0.201651 | − | 0.979457i | \(-0.435369\pi\) | ||||
0.201651 | + | 0.979457i | \(0.435369\pi\) | |||||||
\(108\) | −1980.58 | −1.76465 | ||||||||
\(109\) | −1219.62 | −1.07173 | −0.535865 | − | 0.844303i | \(-0.680015\pi\) | ||||
−0.535865 | + | 0.844303i | \(0.680015\pi\) | |||||||
\(110\) | 1004.59 | 0.870759 | ||||||||
\(111\) | −36.3987 | −0.0311245 | ||||||||
\(112\) | −119.787 | −0.101061 | ||||||||
\(113\) | −509.751 | −0.424366 | −0.212183 | − | 0.977230i | \(-0.568057\pi\) | ||||
−0.212183 | + | 0.977230i | \(0.568057\pi\) | |||||||
\(114\) | −2202.44 | −1.80945 | ||||||||
\(115\) | −2051.97 | −1.66389 | ||||||||
\(116\) | 3587.04 | 2.87110 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2691.69 | −2.09992 | ||||||||
\(119\) | −1273.28 | −0.980854 | ||||||||
\(120\) | −1782.83 | −1.35624 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1576.64 | 1.17002 | ||||||||
\(123\) | 600.381 | 0.440118 | ||||||||
\(124\) | 999.337 | 0.723735 | ||||||||
\(125\) | 2804.02 | 2.00640 | ||||||||
\(126\) | −1161.83 | −0.821463 | ||||||||
\(127\) | 796.850 | 0.556764 | 0.278382 | − | 0.960470i | \(-0.410202\pi\) | ||||
0.278382 | + | 0.960470i | \(0.410202\pi\) | |||||||
\(128\) | 2442.26 | 1.68646 | ||||||||
\(129\) | −852.731 | −0.582006 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1834.53 | 1.22354 | 0.611770 | − | 0.791035i | \(-0.290458\pi\) | ||||
0.611770 | + | 0.791035i | \(0.290458\pi\) | |||||||
\(132\) | −539.245 | −0.355570 | ||||||||
\(133\) | −2431.59 | −1.58530 | ||||||||
\(134\) | 3220.58 | 2.07624 | ||||||||
\(135\) | −2948.55 | −1.87978 | ||||||||
\(136\) | −1655.66 | −1.04391 | ||||||||
\(137\) | −387.717 | −0.241788 | −0.120894 | − | 0.992665i | \(-0.538576\pi\) | ||||
−0.120894 | + | 0.992665i | \(0.538576\pi\) | |||||||
\(138\) | 1764.30 | 1.08831 | ||||||||
\(139\) | −2736.11 | −1.66960 | −0.834798 | − | 0.550556i | \(-0.814416\pi\) | ||||
−0.834798 | + | 0.550556i | \(0.814416\pi\) | |||||||
\(140\) | −4942.81 | −2.98388 | ||||||||
\(141\) | 157.553 | 0.0941018 | ||||||||
\(142\) | −2862.22 | −1.69149 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −85.4508 | −0.0494507 | ||||||||
\(145\) | 5340.12 | 3.05843 | ||||||||
\(146\) | −3647.07 | −2.06735 | ||||||||
\(147\) | 36.6835 | 0.0205824 | ||||||||
\(148\) | −131.219 | −0.0728792 | ||||||||
\(149\) | 1496.72 | 0.822929 | 0.411465 | − | 0.911426i | \(-0.365017\pi\) | ||||
0.411465 | + | 0.911426i | \(0.365017\pi\) | |||||||
\(150\) | −4537.98 | −2.47017 | ||||||||
\(151\) | −2527.52 | −1.36216 | −0.681080 | − | 0.732209i | \(-0.738490\pi\) | ||||
−0.681080 | + | 0.732209i | \(0.738490\pi\) | |||||||
\(152\) | −3161.81 | −1.68721 | ||||||||
\(153\) | −908.303 | −0.479947 | ||||||||
\(154\) | −953.620 | −0.498993 | ||||||||
\(155\) | 1487.74 | 0.770956 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1946.37 | 0.989408 | 0.494704 | − | 0.869061i | \(-0.335276\pi\) | ||||
0.494704 | + | 0.869061i | \(0.335276\pi\) | |||||||
\(158\) | 550.394 | 0.277133 | ||||||||
\(159\) | −2644.22 | −1.31887 | ||||||||
\(160\) | 3285.44 | 1.62336 | ||||||||
\(161\) | 1947.87 | 0.953499 | ||||||||
\(162\) | 865.440 | 0.419725 | ||||||||
\(163\) | 962.612 | 0.462562 | 0.231281 | − | 0.972887i | \(-0.425708\pi\) | ||||
0.231281 | + | 0.972887i | \(0.425708\pi\) | |||||||
\(164\) | 2164.40 | 1.03055 | ||||||||
\(165\) | −802.789 | −0.378770 | ||||||||
\(166\) | −455.151 | −0.212811 | ||||||||
\(167\) | −1302.91 | −0.603727 | −0.301863 | − | 0.953351i | \(-0.597609\pi\) | ||||
−0.301863 | + | 0.953351i | \(0.597609\pi\) | |||||||
\(168\) | 1692.38 | 0.777202 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6189.62 | −2.79248 | ||||||||
\(171\) | −1734.58 | −0.775713 | ||||||||
\(172\) | −3074.13 | −1.36279 | ||||||||
\(173\) | 1703.21 | 0.748514 | 0.374257 | − | 0.927325i | \(-0.377898\pi\) | ||||
0.374257 | + | 0.927325i | \(0.377898\pi\) | |||||||
\(174\) | −4591.49 | −2.00046 | ||||||||
\(175\) | −5010.13 | −2.16417 | ||||||||
\(176\) | −70.1371 | −0.0300385 | ||||||||
\(177\) | 2151.00 | 0.913441 | ||||||||
\(178\) | −2100.08 | −0.884313 | ||||||||
\(179\) | 959.537 | 0.400666 | 0.200333 | − | 0.979728i | \(-0.435798\pi\) | ||||
0.200333 | + | 0.979728i | \(0.435798\pi\) | |||||||
\(180\) | −3525.98 | −1.46006 | ||||||||
\(181\) | 3296.59 | 1.35378 | 0.676888 | − | 0.736086i | \(-0.263328\pi\) | ||||
0.676888 | + | 0.736086i | \(0.263328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1259.93 | −0.508945 | ||||||||
\(184\) | 2532.82 | 1.01479 | ||||||||
\(185\) | −195.349 | −0.0776343 | ||||||||
\(186\) | −1279.17 | −0.504267 | ||||||||
\(187\) | −745.525 | −0.291541 | ||||||||
\(188\) | 567.984 | 0.220343 | ||||||||
\(189\) | 2798.96 | 1.07722 | ||||||||
\(190\) | −11820.3 | −4.51334 | ||||||||
\(191\) | 1052.02 | 0.398543 | 0.199271 | − | 0.979944i | \(-0.436143\pi\) | ||||
0.199271 | + | 0.979944i | \(0.436143\pi\) | |||||||
\(192\) | −3012.95 | −1.13251 | ||||||||
\(193\) | 1543.16 | 0.575540 | 0.287770 | − | 0.957700i | \(-0.407086\pi\) | ||||
0.287770 | + | 0.957700i | \(0.407086\pi\) | |||||||
\(194\) | −1599.21 | −0.591838 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 132.246 | 0.0481944 | ||||||||
\(197\) | −2564.36 | −0.927427 | −0.463713 | − | 0.885985i | \(-0.653483\pi\) | ||||
−0.463713 | + | 0.885985i | \(0.653483\pi\) | |||||||
\(198\) | −680.269 | −0.244165 | ||||||||
\(199\) | 618.993 | 0.220499 | 0.110249 | − | 0.993904i | \(-0.464835\pi\) | ||||
0.110249 | + | 0.993904i | \(0.464835\pi\) | |||||||
\(200\) | −6514.70 | −2.30330 | ||||||||
\(201\) | −2573.65 | −0.903140 | ||||||||
\(202\) | −7310.79 | −2.54646 | ||||||||
\(203\) | −5069.20 | −1.75265 | ||||||||
\(204\) | 3322.49 | 1.14030 | ||||||||
\(205\) | 3222.20 | 1.09779 | ||||||||
\(206\) | 1987.68 | 0.672271 | ||||||||
\(207\) | 1389.52 | 0.466562 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1423.73 | −0.471203 | ||||||||
\(210\) | 6326.90 | 2.07904 | ||||||||
\(211\) | −102.673 | −0.0334990 | −0.0167495 | − | 0.999860i | \(-0.505332\pi\) | ||||
−0.0167495 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(212\) | −9532.51 | −3.08818 | ||||||||
\(213\) | 2287.27 | 0.735780 | ||||||||
\(214\) | −2059.84 | −0.657980 | ||||||||
\(215\) | −4576.54 | −1.45171 | ||||||||
\(216\) | 3639.51 | 1.14647 | ||||||||
\(217\) | −1412.26 | −0.441800 | ||||||||
\(218\) | 5627.98 | 1.74851 | ||||||||
\(219\) | 2914.46 | 0.899274 | ||||||||
\(220\) | −2894.08 | −0.886905 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 167.963 | 0.0507790 | ||||||||
\(223\) | 4471.33 | 1.34270 | 0.671350 | − | 0.741140i | \(-0.265715\pi\) | ||||
0.671350 | + | 0.741140i | \(0.265715\pi\) | |||||||
\(224\) | −3118.76 | −0.930272 | ||||||||
\(225\) | −3574.00 | −1.05896 | ||||||||
\(226\) | 2352.26 | 0.692345 | ||||||||
\(227\) | 310.802 | 0.0908752 | 0.0454376 | − | 0.998967i | \(-0.485532\pi\) | ||||
0.0454376 | + | 0.998967i | \(0.485532\pi\) | |||||||
\(228\) | 6344.94 | 1.84300 | ||||||||
\(229\) | 4163.95 | 1.20158 | 0.600789 | − | 0.799408i | \(-0.294853\pi\) | ||||
0.600789 | + | 0.799408i | \(0.294853\pi\) | |||||||
\(230\) | 9468.86 | 2.71460 | ||||||||
\(231\) | 762.061 | 0.217056 | ||||||||
\(232\) | −6591.52 | −1.86532 | ||||||||
\(233\) | −1678.18 | −0.471849 | −0.235925 | − | 0.971771i | \(-0.575812\pi\) | ||||
−0.235925 | + | 0.971771i | \(0.575812\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 845.574 | 0.234720 | ||||||||
\(236\) | 7754.43 | 2.13886 | ||||||||
\(237\) | −439.833 | −0.120549 | ||||||||
\(238\) | 5875.60 | 1.60025 | ||||||||
\(239\) | 6855.31 | 1.85537 | 0.927685 | − | 0.373364i | \(-0.121796\pi\) | ||||
0.927685 | + | 0.373364i | \(0.121796\pi\) | |||||||
\(240\) | 465.333 | 0.125155 | ||||||||
\(241\) | 2819.47 | 0.753602 | 0.376801 | − | 0.926294i | \(-0.377024\pi\) | ||||
0.376801 | + | 0.926294i | \(0.377024\pi\) | |||||||
\(242\) | −558.358 | −0.148317 | ||||||||
\(243\) | 3330.99 | 0.879355 | ||||||||
\(244\) | −4542.11 | −1.19172 | ||||||||
\(245\) | 196.878 | 0.0513390 | ||||||||
\(246\) | −2770.47 | −0.718045 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1836.38 | −0.470201 | ||||||||
\(249\) | 363.723 | 0.0925702 | ||||||||
\(250\) | −12939.2 | −3.27340 | ||||||||
\(251\) | −2693.44 | −0.677325 | −0.338662 | − | 0.940908i | \(-0.609974\pi\) | ||||
−0.338662 | + | 0.940908i | \(0.609974\pi\) | |||||||
\(252\) | 3347.09 | 0.836695 | ||||||||
\(253\) | 1140.50 | 0.283410 | ||||||||
\(254\) | −3677.09 | −0.908351 | ||||||||
\(255\) | 4946.28 | 1.21470 | ||||||||
\(256\) | −4733.45 | −1.15563 | ||||||||
\(257\) | 1225.71 | 0.297500 | 0.148750 | − | 0.988875i | \(-0.452475\pi\) | ||||
0.148750 | + | 0.988875i | \(0.452475\pi\) | |||||||
\(258\) | 3934.95 | 0.949532 | ||||||||
\(259\) | 185.438 | 0.0444887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3616.14 | −0.857600 | ||||||||
\(262\) | −8465.50 | −1.99619 | ||||||||
\(263\) | 2300.15 | 0.539291 | 0.269646 | − | 0.962960i | \(-0.413093\pi\) | ||||
0.269646 | + | 0.962960i | \(0.413093\pi\) | |||||||
\(264\) | 990.913 | 0.231009 | ||||||||
\(265\) | −14191.3 | −3.28968 | ||||||||
\(266\) | 11220.6 | 2.58639 | ||||||||
\(267\) | 1678.23 | 0.384666 | ||||||||
\(268\) | −9278.10 | −2.11474 | ||||||||
\(269\) | −4183.92 | −0.948321 | −0.474160 | − | 0.880438i | \(-0.657248\pi\) | ||||
−0.474160 | + | 0.880438i | \(0.657248\pi\) | |||||||
\(270\) | 13606.2 | 3.06683 | ||||||||
\(271\) | −3308.84 | −0.741689 | −0.370845 | − | 0.928695i | \(-0.620932\pi\) | ||||
−0.370845 | + | 0.928695i | \(0.620932\pi\) | |||||||
\(272\) | 432.140 | 0.0963322 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1789.13 | 0.394473 | ||||||||
\(275\) | −2933.50 | −0.643261 | ||||||||
\(276\) | −5082.73 | −1.10849 | ||||||||
\(277\) | 656.952 | 0.142500 | 0.0712499 | − | 0.997458i | \(-0.477301\pi\) | ||||
0.0712499 | + | 0.997458i | \(0.477301\pi\) | |||||||
\(278\) | 12625.9 | 2.72392 | ||||||||
\(279\) | −1007.45 | −0.216180 | ||||||||
\(280\) | 9082.87 | 1.93859 | ||||||||
\(281\) | 7566.29 | 1.60629 | 0.803144 | − | 0.595785i | \(-0.203159\pi\) | ||||
0.803144 | + | 0.595785i | \(0.203159\pi\) | |||||||
\(282\) | −727.033 | −0.153525 | ||||||||
\(283\) | 2773.07 | 0.582479 | 0.291240 | − | 0.956650i | \(-0.405932\pi\) | ||||
0.291240 | + | 0.956650i | \(0.405932\pi\) | |||||||
\(284\) | 8245.70 | 1.72286 | ||||||||
\(285\) | 9445.89 | 1.96325 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3058.72 | −0.629097 | ||||||||
\(288\) | −2224.78 | −0.455197 | ||||||||
\(289\) | −319.546 | −0.0650409 | ||||||||
\(290\) | −24642.1 | −4.98978 | ||||||||
\(291\) | 1277.97 | 0.257442 | ||||||||
\(292\) | 10506.7 | 2.10569 | ||||||||
\(293\) | 4758.11 | 0.948709 | 0.474354 | − | 0.880334i | \(-0.342682\pi\) | ||||
0.474354 | + | 0.880334i | \(0.342682\pi\) | |||||||
\(294\) | −169.277 | −0.0335798 | ||||||||
\(295\) | 11544.2 | 2.27841 | ||||||||
\(296\) | 241.127 | 0.0473487 | ||||||||
\(297\) | 1638.83 | 0.320184 | ||||||||
\(298\) | −6906.68 | −1.34259 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13073.4 | 2.51597 | ||||||||
\(301\) | 4344.36 | 0.831909 | ||||||||
\(302\) | 11663.3 | 2.22234 | ||||||||
\(303\) | 5842.23 | 1.10768 | ||||||||
\(304\) | 825.257 | 0.155697 | ||||||||
\(305\) | −6761.96 | −1.26947 | ||||||||
\(306\) | 4191.39 | 0.783025 | ||||||||
\(307\) | 769.035 | 0.142968 | 0.0714840 | − | 0.997442i | \(-0.477227\pi\) | ||||
0.0714840 | + | 0.997442i | \(0.477227\pi\) | |||||||
\(308\) | 2747.26 | 0.508245 | ||||||||
\(309\) | −1588.40 | −0.292430 | ||||||||
\(310\) | −6865.22 | −1.25780 | ||||||||
\(311\) | 804.126 | 0.146617 | 0.0733084 | − | 0.997309i | \(-0.476644\pi\) | ||||
0.0733084 | + | 0.997309i | \(0.476644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7233.90 | 1.30634 | 0.653170 | − | 0.757211i | \(-0.273439\pi\) | ||||
0.653170 | + | 0.757211i | \(0.273439\pi\) | |||||||
\(314\) | −8981.57 | −1.61420 | ||||||||
\(315\) | 4982.91 | 0.891286 | ||||||||
\(316\) | −1585.61 | −0.282271 | ||||||||
\(317\) | −2161.28 | −0.382932 | −0.191466 | − | 0.981499i | \(-0.561324\pi\) | ||||
−0.191466 | + | 0.981499i | \(0.561324\pi\) | |||||||
\(318\) | 12201.8 | 2.15171 | ||||||||
\(319\) | −2968.09 | −0.520944 | ||||||||
\(320\) | −16170.3 | −2.82483 | ||||||||
\(321\) | 1646.07 | 0.286214 | ||||||||
\(322\) | −8988.48 | −1.55562 | ||||||||
\(323\) | 8772.11 | 1.51112 | ||||||||
\(324\) | −2493.22 | −0.427507 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4442.00 | −0.754661 | ||||||||
\(327\) | −4497.46 | −0.760581 | ||||||||
\(328\) | −3977.28 | −0.669538 | ||||||||
\(329\) | −802.675 | −0.134507 | ||||||||
\(330\) | 3704.49 | 0.617956 | ||||||||
\(331\) | −3564.76 | −0.591955 | −0.295978 | − | 0.955195i | \(-0.595645\pi\) | ||||
−0.295978 | + | 0.955195i | \(0.595645\pi\) | |||||||
\(332\) | 1311.23 | 0.216757 | ||||||||
\(333\) | 132.283 | 0.0217690 | ||||||||
\(334\) | 6012.33 | 0.984970 | ||||||||
\(335\) | −13812.6 | −2.25272 | ||||||||
\(336\) | −441.725 | −0.0717205 | ||||||||
\(337\) | 9469.23 | 1.53063 | 0.765315 | − | 0.643656i | \(-0.222583\pi\) | ||||
0.765315 | + | 0.643656i | \(0.222583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1879.75 | −0.301162 | ||||||||
\(340\) | 17831.5 | 2.84426 | ||||||||
\(341\) | −826.900 | −0.131317 | ||||||||
\(342\) | 8004.29 | 1.26556 | ||||||||
\(343\) | 6257.02 | 0.984978 | ||||||||
\(344\) | 5648.99 | 0.885388 | ||||||||
\(345\) | −7566.80 | −1.18082 | ||||||||
\(346\) | −7859.53 | −1.22119 | ||||||||
\(347\) | 3030.03 | 0.468763 | 0.234381 | − | 0.972145i | \(-0.424694\pi\) | ||||
0.234381 | + | 0.972145i | \(0.424694\pi\) | |||||||
\(348\) | 13227.5 | 2.03755 | ||||||||
\(349\) | 11320.6 | 1.73633 | 0.868165 | − | 0.496276i | \(-0.165300\pi\) | ||||
0.868165 | + | 0.496276i | \(0.165300\pi\) | |||||||
\(350\) | 23119.4 | 3.53081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1826.08 | −0.276507 | ||||||||
\(353\) | −9960.80 | −1.50187 | −0.750935 | − | 0.660376i | \(-0.770397\pi\) | ||||
−0.750935 | + | 0.660376i | \(0.770397\pi\) | |||||||
\(354\) | −9925.85 | −1.49026 | ||||||||
\(355\) | 12275.6 | 1.83527 | ||||||||
\(356\) | 6050.07 | 0.900710 | ||||||||
\(357\) | −4695.34 | −0.696088 | ||||||||
\(358\) | −4427.81 | −0.653679 | ||||||||
\(359\) | −9822.94 | −1.44411 | −0.722054 | − | 0.691837i | \(-0.756802\pi\) | ||||
−0.722054 | + | 0.691837i | \(0.756802\pi\) | |||||||
\(360\) | 6479.31 | 0.948582 | ||||||||
\(361\) | 9893.08 | 1.44235 | ||||||||
\(362\) | −15212.2 | −2.20866 | ||||||||
\(363\) | 446.198 | 0.0645160 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15641.7 | 2.24308 | ||||||||
\(366\) | 5814.00 | 0.830335 | ||||||||
\(367\) | −2451.62 | −0.348701 | −0.174351 | − | 0.984684i | \(-0.555783\pi\) | ||||
−0.174351 | + | 0.984684i | \(0.555783\pi\) | |||||||
\(368\) | −661.087 | −0.0936455 | ||||||||
\(369\) | −2181.96 | −0.307827 | ||||||||
\(370\) | 901.444 | 0.126659 | ||||||||
\(371\) | 13471.3 | 1.88517 | ||||||||
\(372\) | 3685.14 | 0.513617 | ||||||||
\(373\) | 7431.12 | 1.03155 | 0.515776 | − | 0.856724i | \(-0.327504\pi\) | ||||
0.515776 | + | 0.856724i | \(0.327504\pi\) | |||||||
\(374\) | 3440.25 | 0.475644 | ||||||||
\(375\) | 10340.1 | 1.42389 | ||||||||
\(376\) | −1043.72 | −0.143154 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −12915.9 | −1.75747 | ||||||||
\(379\) | −6225.63 | −0.843771 | −0.421886 | − | 0.906649i | \(-0.638632\pi\) | ||||
−0.421886 | + | 0.906649i | \(0.638632\pi\) | |||||||
\(380\) | 34052.8 | 4.59703 | ||||||||
\(381\) | 2938.45 | 0.395122 | ||||||||
\(382\) | −4854.58 | −0.650215 | ||||||||
\(383\) | 5098.87 | 0.680261 | 0.340131 | − | 0.940378i | \(-0.389529\pi\) | ||||
0.340131 | + | 0.940378i | \(0.389529\pi\) | |||||||
\(384\) | 9006.04 | 1.19684 | ||||||||
\(385\) | 4089.92 | 0.541407 | ||||||||
\(386\) | −7120.96 | −0.938983 | ||||||||
\(387\) | 3099.07 | 0.407066 | ||||||||
\(388\) | 4607.12 | 0.602812 | ||||||||
\(389\) | −2672.32 | −0.348308 | −0.174154 | − | 0.984718i | \(-0.555719\pi\) | ||||
−0.174154 | + | 0.984718i | \(0.555719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7027.06 | −0.908884 | ||||||||
\(392\) | −243.014 | −0.0313113 | ||||||||
\(393\) | 6764.99 | 0.868317 | ||||||||
\(394\) | 11833.3 | 1.51308 | ||||||||
\(395\) | −2360.55 | −0.300689 | ||||||||
\(396\) | 1959.77 | 0.248692 | ||||||||
\(397\) | −400.284 | −0.0506038 | −0.0253019 | − | 0.999680i | \(-0.508055\pi\) | ||||
−0.0253019 | + | 0.999680i | \(0.508055\pi\) | |||||||
\(398\) | −2856.36 | −0.359740 | ||||||||
\(399\) | −8966.68 | −1.12505 | ||||||||
\(400\) | 1700.39 | 0.212549 | ||||||||
\(401\) | −8939.46 | −1.11325 | −0.556627 | − | 0.830762i | \(-0.687905\pi\) | ||||
−0.556627 | + | 0.830762i | \(0.687905\pi\) | |||||||
\(402\) | 11876.2 | 1.47346 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 21061.5 | 2.59368 | ||||||||
\(405\) | −3711.73 | −0.455401 | ||||||||
\(406\) | 23392.0 | 2.85942 | ||||||||
\(407\) | 108.577 | 0.0132235 | ||||||||
\(408\) | −6105.38 | −0.740836 | ||||||||
\(409\) | −9481.18 | −1.14624 | −0.573122 | − | 0.819470i | \(-0.694268\pi\) | ||||
−0.573122 | + | 0.819470i | \(0.694268\pi\) | |||||||
\(410\) | −14868.9 | −1.79103 | ||||||||
\(411\) | −1429.74 | −0.171591 | ||||||||
\(412\) | −5726.24 | −0.684737 | ||||||||
\(413\) | −10958.6 | −1.30566 | ||||||||
\(414\) | −6411.98 | −0.761187 | ||||||||
\(415\) | 1952.07 | 0.230900 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10089.6 | −1.18487 | ||||||||
\(418\) | 6569.83 | 0.768759 | ||||||||
\(419\) | 12413.7 | 1.44737 | 0.723687 | − | 0.690128i | \(-0.242446\pi\) | ||||
0.723687 | + | 0.690128i | \(0.242446\pi\) | |||||||
\(420\) | −18227.0 | −2.11759 | ||||||||
\(421\) | 13243.0 | 1.53307 | 0.766536 | − | 0.642201i | \(-0.221979\pi\) | ||||
0.766536 | + | 0.642201i | \(0.221979\pi\) | |||||||
\(422\) | 473.786 | 0.0546529 | ||||||||
\(423\) | −572.592 | −0.0658165 | ||||||||
\(424\) | 17516.9 | 2.00635 | ||||||||
\(425\) | 18074.4 | 2.06291 | ||||||||
\(426\) | −10554.7 | −1.20041 | ||||||||
\(427\) | 6418.91 | 0.727477 | ||||||||
\(428\) | 5934.14 | 0.670181 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21118.6 | 2.36844 | ||||||||
\(431\) | −6005.50 | −0.671171 | −0.335585 | − | 0.942010i | \(-0.608934\pi\) | ||||
−0.335585 | + | 0.942010i | \(0.608934\pi\) | |||||||
\(432\) | −949.941 | −0.105796 | ||||||||
\(433\) | −9921.49 | −1.10115 | −0.550573 | − | 0.834787i | \(-0.685591\pi\) | ||||
−0.550573 | + | 0.834787i | \(0.685591\pi\) | |||||||
\(434\) | 6516.93 | 0.720790 | ||||||||
\(435\) | 19692.1 | 2.17050 | ||||||||
\(436\) | −16213.5 | −1.78093 | ||||||||
\(437\) | −13419.6 | −1.46898 | ||||||||
\(438\) | −13448.9 | −1.46715 | ||||||||
\(439\) | −4889.28 | −0.531555 | −0.265777 | − | 0.964034i | \(-0.585629\pi\) | ||||
−0.265777 | + | 0.964034i | \(0.585629\pi\) | |||||||
\(440\) | 5318.15 | 0.576211 | ||||||||
\(441\) | −133.319 | −0.0143957 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10568.8 | −1.13349 | −0.566747 | − | 0.823892i | \(-0.691798\pi\) | ||||
−0.566747 | + | 0.823892i | \(0.691798\pi\) | |||||||
\(444\) | −483.880 | −0.0517206 | ||||||||
\(445\) | 9006.90 | 0.959479 | ||||||||
\(446\) | −20633.1 | −2.19059 | ||||||||
\(447\) | 5519.30 | 0.584013 | ||||||||
\(448\) | 15349.9 | 1.61878 | ||||||||
\(449\) | −15760.7 | −1.65656 | −0.828280 | − | 0.560315i | \(-0.810680\pi\) | ||||
−0.828280 | + | 0.560315i | \(0.810680\pi\) | |||||||
\(450\) | 16492.3 | 1.72768 | ||||||||
\(451\) | −1790.93 | −0.186988 | ||||||||
\(452\) | −6776.56 | −0.705183 | ||||||||
\(453\) | −9320.42 | −0.966692 | ||||||||
\(454\) | −1434.21 | −0.148261 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11659.4 | −1.19737 | ||||||||
\(457\) | 1098.13 | 0.112404 | 0.0562018 | − | 0.998419i | \(-0.482101\pi\) | ||||
0.0562018 | + | 0.998419i | \(0.482101\pi\) | |||||||
\(458\) | −19214.7 | −1.96035 | ||||||||
\(459\) | −10097.4 | −1.02682 | ||||||||
\(460\) | −27278.6 | −2.76494 | ||||||||
\(461\) | −257.041 | −0.0259687 | −0.0129843 | − | 0.999916i | \(-0.504133\pi\) | ||||
−0.0129843 | + | 0.999916i | \(0.504133\pi\) | |||||||
\(462\) | −3516.55 | −0.354123 | ||||||||
\(463\) | −14489.1 | −1.45435 | −0.727177 | − | 0.686450i | \(-0.759168\pi\) | ||||
−0.727177 | + | 0.686450i | \(0.759168\pi\) | |||||||
\(464\) | 1720.44 | 0.172132 | ||||||||
\(465\) | 5486.17 | 0.547129 | ||||||||
\(466\) | 7743.99 | 0.769814 | ||||||||
\(467\) | 8855.29 | 0.877461 | 0.438730 | − | 0.898619i | \(-0.355428\pi\) | ||||
0.438730 | + | 0.898619i | \(0.355428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13111.8 | 1.29093 | ||||||||
\(470\) | −3901.92 | −0.382941 | ||||||||
\(471\) | 7177.40 | 0.702159 | ||||||||
\(472\) | −14249.5 | −1.38959 | ||||||||
\(473\) | 2543.68 | 0.247270 | ||||||||
\(474\) | 2029.62 | 0.196674 | ||||||||
\(475\) | 34516.6 | 3.33417 | ||||||||
\(476\) | −16926.9 | −1.62992 | ||||||||
\(477\) | 9609.85 | 0.922442 | ||||||||
\(478\) | −31634.0 | −3.02700 | ||||||||
\(479\) | 13509.7 | 1.28867 | 0.644336 | − | 0.764743i | \(-0.277134\pi\) | ||||
0.644336 | + | 0.764743i | \(0.277134\pi\) | |||||||
\(480\) | 12115.3 | 1.15206 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13010.5 | −1.22949 | ||||||||
\(483\) | 7182.92 | 0.676675 | ||||||||
\(484\) | 1608.56 | 0.151067 | ||||||||
\(485\) | 6858.74 | 0.642143 | ||||||||
\(486\) | −15371.0 | −1.43465 | ||||||||
\(487\) | 16750.5 | 1.55860 | 0.779298 | − | 0.626654i | \(-0.215576\pi\) | ||||
0.779298 | + | 0.626654i | \(0.215576\pi\) | |||||||
\(488\) | 8346.55 | 0.774243 | ||||||||
\(489\) | 3549.71 | 0.328269 | ||||||||
\(490\) | −908.497 | −0.0837586 | ||||||||
\(491\) | 4829.42 | 0.443888 | 0.221944 | − | 0.975059i | \(-0.428760\pi\) | ||||
0.221944 | + | 0.975059i | \(0.428760\pi\) | |||||||
\(492\) | 7981.39 | 0.731359 | ||||||||
\(493\) | 18287.5 | 1.67064 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2917.56 | 0.264919 | ||||||||
\(496\) | 479.309 | 0.0433903 | ||||||||
\(497\) | −11652.8 | −1.05171 | ||||||||
\(498\) | −1678.41 | −0.151027 | ||||||||
\(499\) | 8964.56 | 0.804226 | 0.402113 | − | 0.915590i | \(-0.368276\pi\) | ||||
0.402113 | + | 0.915590i | \(0.368276\pi\) | |||||||
\(500\) | 37276.3 | 3.33410 | ||||||||
\(501\) | −4804.60 | −0.428450 | ||||||||
\(502\) | 12429.0 | 1.10504 | ||||||||
\(503\) | 12006.7 | 1.06432 | 0.532158 | − | 0.846645i | \(-0.321381\pi\) | ||||
0.532158 | + | 0.846645i | \(0.321381\pi\) | |||||||
\(504\) | −6150.60 | −0.543590 | ||||||||
\(505\) | 31354.8 | 2.76291 | ||||||||
\(506\) | −5262.88 | −0.462379 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10593.2 | 0.925194 | ||||||||
\(509\) | 13634.7 | 1.18733 | 0.593663 | − | 0.804714i | \(-0.297681\pi\) | ||||
0.593663 | + | 0.804714i | \(0.297681\pi\) | |||||||
\(510\) | −22824.7 | −1.98176 | ||||||||
\(511\) | −14848.1 | −1.28541 | ||||||||
\(512\) | 2304.56 | 0.198922 | ||||||||
\(513\) | −19283.1 | −1.65959 | ||||||||
\(514\) | −5656.06 | −0.485366 | ||||||||
\(515\) | −8524.81 | −0.729414 | ||||||||
\(516\) | −11336.1 | −0.967139 | ||||||||
\(517\) | −469.978 | −0.0399799 | ||||||||
\(518\) | −855.711 | −0.0725826 | ||||||||
\(519\) | 6280.74 | 0.531202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16044.5 | 1.34918 | 0.674591 | − | 0.738192i | \(-0.264320\pi\) | ||||
0.674591 | + | 0.738192i | \(0.264320\pi\) | |||||||
\(522\) | 16686.8 | 1.39916 | ||||||||
\(523\) | −6594.48 | −0.551351 | −0.275675 | − | 0.961251i | \(-0.588901\pi\) | ||||
−0.275675 | + | 0.961251i | \(0.588901\pi\) | |||||||
\(524\) | 24388.0 | 2.03320 | ||||||||
\(525\) | −18475.3 | −1.53586 | ||||||||
\(526\) | −10614.1 | −0.879844 | ||||||||
\(527\) | 5094.84 | 0.421128 | ||||||||
\(528\) | −258.636 | −0.0213176 | ||||||||
\(529\) | −1417.03 | −0.116465 | ||||||||
\(530\) | 65486.2 | 5.36705 | ||||||||
\(531\) | −7817.35 | −0.638878 | ||||||||
\(532\) | −32325.2 | −2.63435 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7744.22 | −0.627575 | ||||||||
\(535\) | 8834.31 | 0.713908 | ||||||||
\(536\) | 17049.4 | 1.37392 | ||||||||
\(537\) | 3538.37 | 0.284343 | ||||||||
\(538\) | 19306.8 | 1.54717 | ||||||||
\(539\) | −109.426 | −0.00874458 | ||||||||
\(540\) | −39197.7 | −3.12370 | ||||||||
\(541\) | −6092.77 | −0.484193 | −0.242097 | − | 0.970252i | \(-0.577835\pi\) | ||||
−0.242097 | + | 0.970252i | \(0.577835\pi\) | |||||||
\(542\) | 15268.7 | 1.21005 | ||||||||
\(543\) | 12156.4 | 0.960742 | ||||||||
\(544\) | 11251.1 | 0.886744 | ||||||||
\(545\) | −24137.5 | −1.89713 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1980.28 | 0.154791 | 0.0773954 | − | 0.997000i | \(-0.475340\pi\) | ||||
0.0773954 | + | 0.997000i | \(0.475340\pi\) | |||||||
\(548\) | −5154.27 | −0.401787 | ||||||||
\(549\) | 4578.96 | 0.355966 | ||||||||
\(550\) | 13536.7 | 1.04947 | ||||||||
\(551\) | 34923.6 | 2.70017 | ||||||||
\(552\) | 9339.99 | 0.720175 | ||||||||
\(553\) | 2240.79 | 0.172311 | ||||||||
\(554\) | −3031.52 | −0.232486 | ||||||||
\(555\) | −720.366 | −0.0550952 | ||||||||
\(556\) | −36373.5 | −2.77442 | ||||||||
\(557\) | 4042.44 | 0.307511 | 0.153756 | − | 0.988109i | \(-0.450863\pi\) | ||||
0.153756 | + | 0.988109i | \(0.450863\pi\) | |||||||
\(558\) | 4648.88 | 0.352694 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2370.70 | −0.178894 | ||||||||
\(561\) | −2749.19 | −0.206900 | ||||||||
\(562\) | −34914.8 | −2.62063 | ||||||||
\(563\) | 195.731 | 0.0146520 | 0.00732601 | − | 0.999973i | \(-0.497668\pi\) | ||||
0.00732601 | + | 0.999973i | \(0.497668\pi\) | |||||||
\(564\) | 2094.49 | 0.156372 | ||||||||
\(565\) | −10088.5 | −0.751194 | ||||||||
\(566\) | −12796.4 | −0.950305 | ||||||||
\(567\) | 3523.42 | 0.260970 | ||||||||
\(568\) | −15152.2 | −1.11932 | ||||||||
\(569\) | −5398.85 | −0.397771 | −0.198885 | − | 0.980023i | \(-0.563732\pi\) | ||||
−0.198885 | + | 0.980023i | \(0.563732\pi\) | |||||||
\(570\) | −43588.3 | −3.20301 | ||||||||
\(571\) | −11551.6 | −0.846618 | −0.423309 | − | 0.905985i | \(-0.639132\pi\) | ||||
−0.423309 | + | 0.905985i | \(0.639132\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3879.42 | 0.282836 | ||||||||
\(574\) | 14114.6 | 1.02636 | ||||||||
\(575\) | −27650.1 | −2.00538 | ||||||||
\(576\) | 10949.9 | 0.792096 | ||||||||
\(577\) | 4928.61 | 0.355599 | 0.177800 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177800 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(578\) | 1474.55 | 0.106113 | ||||||||
\(579\) | 5690.54 | 0.408447 | ||||||||
\(580\) | 70990.9 | 5.08231 | ||||||||
\(581\) | −1853.04 | −0.132318 | ||||||||
\(582\) | −5897.21 | −0.420013 | ||||||||
\(583\) | 7887.66 | 0.560332 | ||||||||
\(584\) | −19307.1 | −1.36804 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21956.4 | −1.54780 | ||||||||
\(587\) | −22142.3 | −1.55692 | −0.778459 | − | 0.627696i | \(-0.783998\pi\) | ||||
−0.778459 | + | 0.627696i | \(0.783998\pi\) | |||||||
\(588\) | 487.666 | 0.0342024 | ||||||||
\(589\) | 9729.60 | 0.680647 | ||||||||
\(590\) | −53271.2 | −3.71719 | ||||||||
\(591\) | −9456.29 | −0.658172 | ||||||||
\(592\) | −62.9361 | −0.00436935 | ||||||||
\(593\) | 6962.36 | 0.482141 | 0.241071 | − | 0.970508i | \(-0.422501\pi\) | ||||
0.241071 | + | 0.970508i | \(0.422501\pi\) | |||||||
\(594\) | −7562.44 | −0.522375 | ||||||||
\(595\) | −25199.5 | −1.73627 | ||||||||
\(596\) | 19897.3 | 1.36749 | ||||||||
\(597\) | 2282.59 | 0.156482 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4050.44 | −0.276288 | −0.138144 | − | 0.990412i | \(-0.544114\pi\) | ||||
−0.138144 | + | 0.990412i | \(0.544114\pi\) | |||||||
\(600\) | −24023.5 | −1.63459 | ||||||||
\(601\) | 5193.94 | 0.352521 | 0.176261 | − | 0.984344i | \(-0.443600\pi\) | ||||
0.176261 | + | 0.984344i | \(0.443600\pi\) | |||||||
\(602\) | −20047.2 | −1.35724 | ||||||||
\(603\) | 9353.37 | 0.631673 | ||||||||
\(604\) | −33600.5 | −2.26355 | ||||||||
\(605\) | 2394.71 | 0.160923 | ||||||||
\(606\) | −26959.1 | −1.80716 | ||||||||
\(607\) | −11147.8 | −0.745428 | −0.372714 | − | 0.927946i | \(-0.621573\pi\) | ||||
−0.372714 | + | 0.927946i | \(0.621573\pi\) | |||||||
\(608\) | 21486.3 | 1.43320 | ||||||||
\(609\) | −18693.1 | −1.24381 | ||||||||
\(610\) | 31203.3 | 2.07112 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12074.9 | −0.797545 | ||||||||
\(613\) | 26142.9 | 1.72251 | 0.861257 | − | 0.508170i | \(-0.169678\pi\) | ||||
0.861257 | + | 0.508170i | \(0.169678\pi\) | |||||||
\(614\) | −3548.73 | −0.233250 | ||||||||
\(615\) | 11882.1 | 0.779078 | ||||||||
\(616\) | −5048.34 | −0.330201 | ||||||||
\(617\) | 8866.64 | 0.578537 | 0.289269 | − | 0.957248i | \(-0.406588\pi\) | ||||
0.289269 | + | 0.957248i | \(0.406588\pi\) | |||||||
\(618\) | 7329.72 | 0.477095 | ||||||||
\(619\) | 14375.9 | 0.933464 | 0.466732 | − | 0.884399i | \(-0.345431\pi\) | ||||
0.466732 | + | 0.884399i | \(0.345431\pi\) | |||||||
\(620\) | 19777.8 | 1.28112 | ||||||||
\(621\) | 15447.0 | 0.998178 | ||||||||
\(622\) | −3710.66 | −0.239203 | ||||||||
\(623\) | −8549.96 | −0.549834 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22159.1 | 1.41818 | ||||||||
\(626\) | −33381.1 | −2.13127 | ||||||||
\(627\) | −5250.12 | −0.334401 | ||||||||
\(628\) | 25874.8 | 1.64413 | ||||||||
\(629\) | −668.982 | −0.0424071 | ||||||||
\(630\) | −22993.8 | −1.45412 | ||||||||
\(631\) | −16861.7 | −1.06379 | −0.531897 | − | 0.846809i | \(-0.678521\pi\) | ||||
−0.531897 | + | 0.846809i | \(0.678521\pi\) | |||||||
\(632\) | 2913.71 | 0.183388 | ||||||||
\(633\) | −378.614 | −0.0237734 | ||||||||
\(634\) | 9973.28 | 0.624747 | ||||||||
\(635\) | 15770.4 | 0.985560 | ||||||||
\(636\) | −35151.9 | −2.19161 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13696.3 | 0.849911 | ||||||||
\(639\) | −8312.60 | −0.514618 | ||||||||
\(640\) | 48334.7 | 2.98531 | ||||||||
\(641\) | 17281.8 | 1.06488 | 0.532442 | − | 0.846467i | \(-0.321275\pi\) | ||||
0.532442 | + | 0.846467i | \(0.321275\pi\) | |||||||
\(642\) | −7595.83 | −0.466952 | ||||||||
\(643\) | −5058.54 | −0.310248 | −0.155124 | − | 0.987895i | \(-0.549578\pi\) | ||||
−0.155124 | + | 0.987895i | \(0.549578\pi\) | |||||||
\(644\) | 25894.7 | 1.58446 | ||||||||
\(645\) | −16876.4 | −1.03024 | ||||||||
\(646\) | −40479.2 | −2.46537 | ||||||||
\(647\) | 4595.03 | 0.279211 | 0.139605 | − | 0.990207i | \(-0.455417\pi\) | ||||
0.139605 | + | 0.990207i | \(0.455417\pi\) | |||||||
\(648\) | 4581.53 | 0.277746 | ||||||||
\(649\) | −6416.40 | −0.388083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5207.84 | −0.313535 | ||||||||
\(652\) | 12796.8 | 0.768655 | ||||||||
\(653\) | −11986.5 | −0.718326 | −0.359163 | − | 0.933275i | \(-0.616938\pi\) | ||||
−0.359163 | + | 0.933275i | \(0.616938\pi\) | |||||||
\(654\) | 20753.7 | 1.24088 | ||||||||
\(655\) | 36307.2 | 2.16586 | ||||||||
\(656\) | 1038.10 | 0.0617852 | ||||||||
\(657\) | −10592.0 | −0.628969 | ||||||||
\(658\) | 3703.97 | 0.219446 | ||||||||
\(659\) | −27151.2 | −1.60495 | −0.802475 | − | 0.596686i | \(-0.796484\pi\) | ||||
−0.802475 | + | 0.596686i | \(0.796484\pi\) | |||||||
\(660\) | −10672.2 | −0.629415 | ||||||||
\(661\) | 9477.81 | 0.557707 | 0.278853 | − | 0.960334i | \(-0.410046\pi\) | ||||
0.278853 | + | 0.960334i | \(0.410046\pi\) | |||||||
\(662\) | 16449.7 | 0.965765 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2409.51 | −0.140824 | ||||||||
\(665\) | −48123.4 | −2.80623 | ||||||||
\(666\) | −610.426 | −0.0355158 | ||||||||
\(667\) | −27976.2 | −1.62405 | ||||||||
\(668\) | −17320.8 | −1.00323 | ||||||||
\(669\) | 16488.4 | 0.952882 | ||||||||
\(670\) | 63738.4 | 3.67527 | ||||||||
\(671\) | 3758.36 | 0.216229 | ||||||||
\(672\) | −11500.7 | −0.660192 | ||||||||
\(673\) | −12835.8 | −0.735192 | −0.367596 | − | 0.929986i | \(-0.619819\pi\) | ||||
−0.367596 | + | 0.929986i | \(0.619819\pi\) | |||||||
\(674\) | −43696.1 | −2.49719 | ||||||||
\(675\) | −39731.6 | −2.26558 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25666.5 | −1.45708 | −0.728541 | − | 0.685002i | \(-0.759801\pi\) | ||||
−0.728541 | + | 0.685002i | \(0.759801\pi\) | |||||||
\(678\) | 8674.15 | 0.491340 | ||||||||
\(679\) | −6510.78 | −0.367984 | ||||||||
\(680\) | −32767.1 | −1.84788 | ||||||||
\(681\) | 1146.11 | 0.0644919 | ||||||||
\(682\) | 3815.76 | 0.214242 | ||||||||
\(683\) | −34230.6 | −1.91771 | −0.958856 | − | 0.283892i | \(-0.908374\pi\) | ||||
−0.958856 | + | 0.283892i | \(0.908374\pi\) | |||||||
\(684\) | −23059.3 | −1.28903 | ||||||||
\(685\) | −7673.30 | −0.428003 | ||||||||
\(686\) | −28873.2 | −1.60697 | ||||||||
\(687\) | 15354.9 | 0.852731 | ||||||||
\(688\) | −1474.43 | −0.0817039 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 34917.2 | 1.92649 | ||||||||
\(691\) | 31496.4 | 1.73398 | 0.866988 | − | 0.498328i | \(-0.166053\pi\) | ||||
0.866988 | + | 0.498328i | \(0.166053\pi\) | |||||||
\(692\) | 22642.3 | 1.24383 | ||||||||
\(693\) | −2769.55 | −0.151813 | ||||||||
\(694\) | −13982.2 | −0.764778 | ||||||||
\(695\) | −54150.2 | −2.95545 | ||||||||
\(696\) | −24306.8 | −1.32377 | ||||||||
\(697\) | 11034.6 | 0.599661 | ||||||||
\(698\) | −52239.3 | −2.83279 | ||||||||
\(699\) | −6188.41 | −0.334860 | ||||||||
\(700\) | −66604.0 | −3.59628 | ||||||||
\(701\) | −27292.4 | −1.47050 | −0.735249 | − | 0.677797i | \(-0.762935\pi\) | ||||
−0.735249 | + | 0.677797i | \(0.762935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1277.55 | −0.0685403 | ||||||||
\(704\) | 8987.59 | 0.481154 | ||||||||
\(705\) | 3118.12 | 0.166575 | ||||||||
\(706\) | 45964.4 | 2.45027 | ||||||||
\(707\) | −29764.1 | −1.58330 | ||||||||
\(708\) | 28595.1 | 1.51790 | ||||||||
\(709\) | −9950.79 | −0.527094 | −0.263547 | − | 0.964647i | \(-0.584892\pi\) | ||||
−0.263547 | + | 0.964647i | \(0.584892\pi\) | |||||||
\(710\) | −56646.1 | −2.99421 | ||||||||
\(711\) | 1598.48 | 0.0843146 | ||||||||
\(712\) | −11117.6 | −0.585180 | ||||||||
\(713\) | −7794.07 | −0.409383 | ||||||||
\(714\) | 21666.8 | 1.13566 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12756.0 | 0.665800 | ||||||||
\(717\) | 25279.5 | 1.31671 | ||||||||
\(718\) | 45328.2 | 2.35604 | ||||||||
\(719\) | 18426.3 | 0.955753 | 0.477876 | − | 0.878427i | \(-0.341407\pi\) | ||||
0.477876 | + | 0.878427i | \(0.341407\pi\) | |||||||
\(720\) | −1691.15 | −0.0875355 | ||||||||
\(721\) | 8092.32 | 0.417994 | ||||||||
\(722\) | −45651.9 | −2.35317 | ||||||||
\(723\) | 10397.0 | 0.534813 | ||||||||
\(724\) | 43824.4 | 2.24962 | ||||||||
\(725\) | 71957.8 | 3.68613 | ||||||||
\(726\) | −2058.99 | −0.105257 | ||||||||
\(727\) | −18460.9 | −0.941781 | −0.470891 | − | 0.882192i | \(-0.656067\pi\) | ||||
−0.470891 | + | 0.882192i | \(0.656067\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17347.1 | 0.881323 | ||||||||
\(730\) | −72179.0 | −3.65954 | ||||||||
\(731\) | −15672.6 | −0.792983 | ||||||||
\(732\) | −16749.4 | −0.845732 | ||||||||
\(733\) | 24975.1 | 1.25849 | 0.629247 | − | 0.777205i | \(-0.283363\pi\) | ||||
0.629247 | + | 0.777205i | \(0.283363\pi\) | |||||||
\(734\) | 11313.1 | 0.568900 | ||||||||
\(735\) | 726.003 | 0.0364340 | ||||||||
\(736\) | −17212.0 | −0.862013 | ||||||||
\(737\) | 7677.15 | 0.383706 | ||||||||
\(738\) | 10068.7 | 0.502214 | ||||||||
\(739\) | −8876.13 | −0.441832 | −0.220916 | − | 0.975293i | \(-0.570905\pi\) | ||||
−0.220916 | + | 0.975293i | \(0.570905\pi\) | |||||||
\(740\) | −2596.95 | −0.129008 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −62163.9 | −3.07562 | ||||||||
\(743\) | −35601.7 | −1.75788 | −0.878938 | − | 0.476937i | \(-0.841747\pi\) | ||||
−0.878938 | + | 0.476937i | \(0.841747\pi\) | |||||||
\(744\) | −6771.79 | −0.333691 | ||||||||
\(745\) | 29621.6 | 1.45671 | ||||||||
\(746\) | −34291.1 | −1.68296 | ||||||||
\(747\) | −1321.87 | −0.0647454 | ||||||||
\(748\) | −9910.92 | −0.484464 | ||||||||
\(749\) | −8386.12 | −0.409109 | ||||||||
\(750\) | −47714.5 | −2.32305 | ||||||||
\(751\) | 37294.6 | 1.81212 | 0.906058 | − | 0.423153i | \(-0.139077\pi\) | ||||
0.906058 | + | 0.423153i | \(0.139077\pi\) | |||||||
\(752\) | 272.420 | 0.0132103 | ||||||||
\(753\) | −9932.29 | −0.480681 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50021.9 | −2.41124 | ||||||||
\(756\) | 37209.1 | 1.79005 | ||||||||
\(757\) | 2656.35 | 0.127538 | 0.0637692 | − | 0.997965i | \(-0.479688\pi\) | ||||
0.0637692 | + | 0.997965i | \(0.479688\pi\) | |||||||
\(758\) | 28728.4 | 1.37660 | ||||||||
\(759\) | 4205.70 | 0.201129 | ||||||||
\(760\) | −62575.2 | −2.98663 | ||||||||
\(761\) | 13669.7 | 0.651152 | 0.325576 | − | 0.945516i | \(-0.394442\pi\) | ||||
0.325576 | + | 0.945516i | \(0.394442\pi\) | |||||||
\(762\) | −13559.6 | −0.644634 | ||||||||
\(763\) | 22912.9 | 1.08716 | ||||||||
\(764\) | 13985.4 | 0.662272 | ||||||||
\(765\) | −17976.2 | −0.849582 | ||||||||
\(766\) | −23528.9 | −1.10983 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −17455.0 | −0.820121 | ||||||||
\(769\) | 624.543 | 0.0292868 | 0.0146434 | − | 0.999893i | \(-0.495339\pi\) | ||||
0.0146434 | + | 0.999893i | \(0.495339\pi\) | |||||||
\(770\) | −18873.1 | −0.883296 | ||||||||
\(771\) | 4519.89 | 0.211128 | ||||||||
\(772\) | 20514.6 | 0.956394 | ||||||||
\(773\) | −17576.4 | −0.817826 | −0.408913 | − | 0.912573i | \(-0.634092\pi\) | ||||
−0.408913 | + | 0.912573i | \(0.634092\pi\) | |||||||
\(774\) | −14300.7 | −0.664121 | ||||||||
\(775\) | 20047.2 | 0.929184 | ||||||||
\(776\) | −8466.01 | −0.391639 | ||||||||
\(777\) | 683.820 | 0.0315726 | ||||||||
\(778\) | 12331.5 | 0.568259 | ||||||||
\(779\) | 21072.7 | 0.969200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6822.89 | −0.312602 | ||||||||
\(782\) | 32426.5 | 1.48283 | ||||||||
\(783\) | −40200.0 | −1.83478 | ||||||||
\(784\) | 63.4285 | 0.00288942 | ||||||||
\(785\) | 38520.5 | 1.75141 | ||||||||
\(786\) | −31217.2 | −1.41664 | ||||||||
\(787\) | 21207.3 | 0.960557 | 0.480279 | − | 0.877116i | \(-0.340536\pi\) | ||||
0.480279 | + | 0.877116i | \(0.340536\pi\) | |||||||
\(788\) | −34090.3 | −1.54114 | ||||||||
\(789\) | 8482.01 | 0.382722 | ||||||||
\(790\) | 10892.8 | 0.490568 | ||||||||
\(791\) | 9576.64 | 0.430475 | ||||||||
\(792\) | −3601.26 | −0.161572 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1847.12 | 0.0825591 | ||||||||
\(795\) | −52331.6 | −2.33461 | ||||||||
\(796\) | 8228.81 | 0.366410 | ||||||||
\(797\) | 21481.3 | 0.954712 | 0.477356 | − | 0.878710i | \(-0.341595\pi\) | ||||
0.477356 | + | 0.878710i | \(0.341595\pi\) | |||||||
\(798\) | 41377.0 | 1.83550 | ||||||||
\(799\) | 2895.71 | 0.128214 | ||||||||
\(800\) | 44271.1 | 1.95653 | ||||||||
\(801\) | −6099.15 | −0.269042 | ||||||||
\(802\) | 41251.4 | 1.81626 | ||||||||
\(803\) | −8693.79 | −0.382064 | ||||||||
\(804\) | −34213.7 | −1.50078 | ||||||||
\(805\) | 38550.1 | 1.68784 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15428.6 | −0.673000 | ||||||||
\(808\) | −38702.4 | −1.68508 | ||||||||
\(809\) | −4674.16 | −0.203133 | −0.101566 | − | 0.994829i | \(-0.532385\pi\) | ||||
−0.101566 | + | 0.994829i | \(0.532385\pi\) | |||||||
\(810\) | 17127.9 | 0.742979 | ||||||||
\(811\) | 10381.5 | 0.449499 | 0.224749 | − | 0.974417i | \(-0.427844\pi\) | ||||
0.224749 | + | 0.974417i | \(0.427844\pi\) | |||||||
\(812\) | −67389.3 | −2.91244 | ||||||||
\(813\) | −12201.6 | −0.526359 | ||||||||
\(814\) | −501.031 | −0.0215739 | ||||||||
\(815\) | 19051.0 | 0.818807 | ||||||||
\(816\) | 1593.55 | 0.0683646 | ||||||||
\(817\) | −29929.8 | −1.28166 | ||||||||
\(818\) | 43751.2 | 1.87008 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 42835.5 | 1.82424 | ||||||||
\(821\) | 41246.0 | 1.75335 | 0.876673 | − | 0.481087i | \(-0.159758\pi\) | ||||
0.876673 | + | 0.481087i | \(0.159758\pi\) | |||||||
\(822\) | 6597.58 | 0.279948 | ||||||||
\(823\) | −22899.1 | −0.969882 | −0.484941 | − | 0.874547i | \(-0.661159\pi\) | ||||
−0.484941 | + | 0.874547i | \(0.661159\pi\) | |||||||
\(824\) | 10522.5 | 0.444865 | ||||||||
\(825\) | −10817.5 | −0.456507 | ||||||||
\(826\) | 50568.6 | 2.13015 | ||||||||
\(827\) | 18630.2 | 0.783358 | 0.391679 | − | 0.920102i | \(-0.371894\pi\) | ||||
0.391679 | + | 0.920102i | \(0.371894\pi\) | |||||||
\(828\) | 18472.1 | 0.775302 | ||||||||
\(829\) | −17105.3 | −0.716638 | −0.358319 | − | 0.933599i | \(-0.616650\pi\) | ||||
−0.358319 | + | 0.933599i | \(0.616650\pi\) | |||||||
\(830\) | −9007.88 | −0.376709 | ||||||||
\(831\) | 2422.57 | 0.101129 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 674.216 | 0.0280435 | ||||||||
\(834\) | 46558.9 | 1.93310 | ||||||||
\(835\) | −25785.9 | −1.06869 | ||||||||
\(836\) | −18926.9 | −0.783013 | ||||||||
\(837\) | −11199.6 | −0.462503 | ||||||||
\(838\) | −57283.5 | −2.36137 | ||||||||
\(839\) | −16211.0 | −0.667065 | −0.333532 | − | 0.942739i | \(-0.608241\pi\) | ||||
−0.333532 | + | 0.942739i | \(0.608241\pi\) | |||||||
\(840\) | 33493.8 | 1.37577 | ||||||||
\(841\) | 48417.3 | 1.98521 | ||||||||
\(842\) | −61110.1 | −2.50118 | ||||||||
\(843\) | 27901.3 | 1.13994 | ||||||||
\(844\) | −1364.92 | −0.0556664 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2642.24 | 0.107379 | ||||||||
\(847\) | −2273.22 | −0.0922180 | ||||||||
\(848\) | −4572.05 | −0.185147 | ||||||||
\(849\) | 10225.9 | 0.413371 | ||||||||
\(850\) | −83404.8 | −3.36560 | ||||||||
\(851\) | 1023.41 | 0.0412244 | ||||||||
\(852\) | 30406.7 | 1.22267 | ||||||||
\(853\) | 25403.3 | 1.01969 | 0.509843 | − | 0.860267i | \(-0.329703\pi\) | ||||
0.509843 | + | 0.860267i | \(0.329703\pi\) | |||||||
\(854\) | −29620.2 | −1.18687 | ||||||||
\(855\) | −34329.1 | −1.37313 | ||||||||
\(856\) | −10904.5 | −0.435408 | ||||||||
\(857\) | 26314.5 | 1.04887 | 0.524437 | − | 0.851449i | \(-0.324276\pi\) | ||||
0.524437 | + | 0.851449i | \(0.324276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37876.6 | 1.50446 | 0.752231 | − | 0.658900i | \(-0.228978\pi\) | ||||
0.752231 | + | 0.658900i | \(0.228978\pi\) | |||||||
\(860\) | −60839.9 | −2.41235 | ||||||||
\(861\) | −11279.3 | −0.446455 | ||||||||
\(862\) | 27712.5 | 1.09500 | ||||||||
\(863\) | −7130.65 | −0.281263 | −0.140632 | − | 0.990062i | \(-0.544913\pi\) | ||||
−0.140632 | + | 0.990062i | \(0.544913\pi\) | |||||||
\(864\) | −24732.5 | −0.973863 | ||||||||
\(865\) | 33708.2 | 1.32499 | ||||||||
\(866\) | 45783.0 | 1.79650 | ||||||||
\(867\) | −1178.35 | −0.0461579 | ||||||||
\(868\) | −18774.5 | −0.734155 | ||||||||
\(869\) | 1312.01 | 0.0512164 | ||||||||
\(870\) | −90870.0 | −3.54113 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 29793.8 | 1.15705 | ||||||||
\(873\) | −4644.50 | −0.180060 | ||||||||
\(874\) | 61924.9 | 2.39661 | ||||||||
\(875\) | −52678.9 | −2.03528 | ||||||||
\(876\) | 38744.5 | 1.49435 | ||||||||
\(877\) | 498.556 | 0.0191962 | 0.00959809 | − | 0.999954i | \(-0.496945\pi\) | ||||
0.00959809 | + | 0.999954i | \(0.496945\pi\) | |||||||
\(878\) | 22561.7 | 0.867222 | ||||||||
\(879\) | 17545.9 | 0.673275 | ||||||||
\(880\) | −1388.08 | −0.0531729 | ||||||||
\(881\) | 2371.51 | 0.0906903 | 0.0453452 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453452 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(882\) | 615.202 | 0.0234863 | ||||||||
\(883\) | −32108.2 | −1.22370 | −0.611849 | − | 0.790974i | \(-0.709574\pi\) | ||||
−0.611849 | + | 0.790974i | \(0.709574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 42570.3 | 1.61693 | ||||||||
\(886\) | 48769.9 | 1.84927 | ||||||||
\(887\) | −24899.9 | −0.942566 | −0.471283 | − | 0.881982i | \(-0.656209\pi\) | ||||
−0.471283 | + | 0.881982i | \(0.656209\pi\) | |||||||
\(888\) | 889.175 | 0.0336022 | ||||||||
\(889\) | −14970.4 | −0.564780 | ||||||||
\(890\) | −41562.6 | −1.56537 | ||||||||
\(891\) | 2063.01 | 0.0775686 | ||||||||
\(892\) | 59441.3 | 2.23121 | ||||||||
\(893\) | 5529.92 | 0.207225 | ||||||||
\(894\) | −25469.0 | −0.952807 | ||||||||
\(895\) | 18990.1 | 0.709241 | ||||||||
\(896\) | −45882.5 | −1.71074 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 72728.4 | 2.70265 | ||||||||
\(899\) | 20283.6 | 0.752498 | ||||||||
\(900\) | −47512.3 | −1.75972 | ||||||||
\(901\) | −48598.8 | −1.79696 | ||||||||
\(902\) | 8264.28 | 0.305067 | ||||||||
\(903\) | 16020.2 | 0.590385 | ||||||||
\(904\) | 12452.6 | 0.458148 | ||||||||
\(905\) | 65242.7 | 2.39640 | ||||||||
\(906\) | 43009.4 | 1.57714 | ||||||||
\(907\) | −15807.4 | −0.578696 | −0.289348 | − | 0.957224i | \(-0.593438\pi\) | ||||
−0.289348 | + | 0.957224i | \(0.593438\pi\) | |||||||
\(908\) | 4131.77 | 0.151011 | ||||||||
\(909\) | −21232.3 | −0.774733 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6529.29 | 0.237459 | 0.118729 | − | 0.992927i | \(-0.462118\pi\) | ||||
0.118729 | + | 0.992927i | \(0.462118\pi\) | |||||||
\(912\) | 3043.21 | 0.110494 | ||||||||
\(913\) | −1084.98 | −0.0393292 | ||||||||
\(914\) | −5067.36 | −0.183385 | ||||||||
\(915\) | −24935.3 | −0.900913 | ||||||||
\(916\) | 55355.0 | 1.99670 | ||||||||
\(917\) | −34465.2 | −1.24116 | ||||||||
\(918\) | 46594.9 | 1.67523 | ||||||||
\(919\) | −592.657 | −0.0212731 | −0.0106365 | − | 0.999943i | \(-0.503386\pi\) | ||||
−0.0106365 | + | 0.999943i | \(0.503386\pi\) | |||||||
\(920\) | 50127.0 | 1.79634 | ||||||||
\(921\) | 2835.88 | 0.101461 | ||||||||
\(922\) | 1186.12 | 0.0423675 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 10130.7 | 0.360689 | ||||||||
\(925\) | −2632.32 | −0.0935676 | ||||||||
\(926\) | 66860.4 | 2.37275 | ||||||||
\(927\) | 5772.70 | 0.204531 | ||||||||
\(928\) | 44793.1 | 1.58449 | ||||||||
\(929\) | 6338.23 | 0.223843 | 0.111922 | − | 0.993717i | \(-0.464299\pi\) | ||||
0.111922 | + | 0.993717i | \(0.464299\pi\) | |||||||
\(930\) | −25316.1 | −0.892631 | ||||||||
\(931\) | 1287.55 | 0.0453252 | ||||||||
\(932\) | −22309.4 | −0.784088 | ||||||||
\(933\) | 2965.28 | 0.104050 | ||||||||
\(934\) | −40863.0 | −1.43156 | ||||||||
\(935\) | −14754.7 | −0.516074 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19414.2 | −0.676877 | −0.338438 | − | 0.940989i | \(-0.609899\pi\) | ||||
−0.338438 | + | 0.940989i | \(0.609899\pi\) | |||||||
\(938\) | −60504.8 | −2.10613 | ||||||||
\(939\) | 26675.6 | 0.927078 | ||||||||
\(940\) | 11241.0 | 0.390042 | ||||||||
\(941\) | 29467.4 | 1.02084 | 0.510419 | − | 0.859926i | \(-0.329490\pi\) | ||||
0.510419 | + | 0.859926i | \(0.329490\pi\) | |||||||
\(942\) | −33120.3 | −1.14556 | ||||||||
\(943\) | −16880.6 | −0.582936 | ||||||||
\(944\) | 3719.23 | 0.128232 | ||||||||
\(945\) | 55394.1 | 1.90685 | ||||||||
\(946\) | −11737.9 | −0.403416 | ||||||||
\(947\) | 36382.4 | 1.24844 | 0.624218 | − | 0.781250i | \(-0.285418\pi\) | ||||
0.624218 | + | 0.781250i | \(0.285418\pi\) | |||||||
\(948\) | −5847.08 | −0.200321 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −159278. | −5.43964 | ||||||||
\(951\) | −7969.90 | −0.271758 | ||||||||
\(952\) | 31104.7 | 1.05894 | ||||||||
\(953\) | 15865.6 | 0.539284 | 0.269642 | − | 0.962961i | \(-0.413095\pi\) | ||||
0.269642 | + | 0.962961i | \(0.413095\pi\) | |||||||
\(954\) | −44344.9 | −1.50495 | ||||||||
\(955\) | 20820.5 | 0.705483 | ||||||||
\(956\) | 91133.7 | 3.08313 | ||||||||
\(957\) | −10945.1 | −0.369701 | ||||||||
\(958\) | −62340.9 | −2.10245 | ||||||||
\(959\) | 7284.01 | 0.245269 | ||||||||
\(960\) | −59629.2 | −2.00471 | ||||||||
\(961\) | −24140.1 | −0.810314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5982.28 | −0.200183 | ||||||||
\(964\) | 37481.7 | 1.25229 | ||||||||
\(965\) | 30540.6 | 1.01880 | ||||||||
\(966\) | −33145.8 | −1.10398 | ||||||||
\(967\) | −54819.1 | −1.82302 | −0.911512 | − | 0.411273i | \(-0.865084\pi\) | ||||
−0.911512 | + | 0.411273i | \(0.865084\pi\) | |||||||
\(968\) | −2955.88 | −0.0981462 | ||||||||
\(969\) | 32347.9 | 1.07241 | ||||||||
\(970\) | −31649.9 | −1.04765 | ||||||||
\(971\) | 18825.3 | 0.622177 | 0.311088 | − | 0.950381i | \(-0.399306\pi\) | ||||
0.311088 | + | 0.950381i | \(0.399306\pi\) | |||||||
\(972\) | 44281.8 | 1.46125 | ||||||||
\(973\) | 51403.0 | 1.69363 | ||||||||
\(974\) | −77295.5 | −2.54282 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2178.52 | −0.0714474 | ||||||||
\(977\) | −33592.0 | −1.10000 | −0.550002 | − | 0.835163i | \(-0.685373\pi\) | ||||
−0.550002 | + | 0.835163i | \(0.685373\pi\) | |||||||
\(978\) | −16380.2 | −0.535565 | ||||||||
\(979\) | −5006.12 | −0.163428 | ||||||||
\(980\) | 2617.27 | 0.0853117 | ||||||||
\(981\) | 16345.1 | 0.531965 | ||||||||
\(982\) | −22285.5 | −0.724195 | ||||||||
\(983\) | −52254.5 | −1.69548 | −0.847741 | − | 0.530411i | \(-0.822038\pi\) | ||||
−0.847741 | + | 0.530411i | \(0.822038\pi\) | |||||||
\(984\) | −14666.5 | −0.475155 | ||||||||
\(985\) | −50751.2 | −1.64169 | ||||||||
\(986\) | −84388.1 | −2.72562 | ||||||||
\(987\) | −2959.93 | −0.0954566 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23975.8 | 0.770867 | ||||||||
\(990\) | −13463.2 | −0.432210 | ||||||||
\(991\) | −11333.3 | −0.363285 | −0.181642 | − | 0.983365i | \(-0.558141\pi\) | ||||
−0.181642 | + | 0.983365i | \(0.558141\pi\) | |||||||
\(992\) | 12479.2 | 0.399411 | ||||||||
\(993\) | −13145.4 | −0.420096 | ||||||||
\(994\) | 53772.3 | 1.71585 | ||||||||
\(995\) | 12250.5 | 0.390317 | ||||||||
\(996\) | 4835.28 | 0.153827 | ||||||||
\(997\) | 2785.34 | 0.0884781 | 0.0442390 | − | 0.999021i | \(-0.485914\pi\) | ||||
0.0442390 | + | 0.999021i | \(0.485914\pi\) | |||||||
\(998\) | −41367.2 | −1.31208 | ||||||||
\(999\) | 1470.57 | 0.0465734 |
(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 | 1859.4.a.i.1.2 | 17 | ||
13.3 | even | 3 | 143.4.e.a.100.16 | ✓ | 34 | ||
13.9 | even | 3 | 143.4.e.a.133.16 | yes | 34 | ||
13.12 | even | 2 | 1859.4.a.f.1.16 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.e.a.100.16 | ✓ | 34 | 13.3 | even | 3 | ||
143.4.e.a.133.16 | yes | 34 | 13.9 | even | 3 | ||
1859.4.a.f.1.16 | 17 | 13.12 | even | 2 | |||
1859.4.a.i.1.2 | 17 | 1.1 | even | 1 | trivial |