Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 13x^{2} + 14x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.170498\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.12311 | −1.45774 | −0.728869 | − | 0.684653i | \(-0.759954\pi\) | ||||
−0.728869 | + | 0.684653i | \(0.759954\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 9.00000 | 1.12500 | ||||||||
\(5\) | 13.4424 | 1.20232 | 0.601161 | − | 0.799128i | \(-0.294705\pi\) | ||||
0.601161 | + | 0.799128i | \(0.294705\pi\) | |||||||
\(6\) | 12.3693 | 0.841625 | ||||||||
\(7\) | −31.4219 | −1.69662 | −0.848311 | − | 0.529498i | \(-0.822380\pi\) | ||||
−0.848311 | + | 0.529498i | \(0.822380\pi\) | |||||||
\(8\) | −4.12311 | −0.182217 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −55.4243 | −1.75267 | ||||||||
\(11\) | 40.4962 | 1.11001 | 0.555003 | − | 0.831849i | \(-0.312717\pi\) | ||||
0.555003 | + | 0.831849i | \(0.312717\pi\) | |||||||
\(12\) | −27.0000 | −0.649519 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 129.556 | 2.47323 | ||||||||
\(15\) | −40.3271 | −0.694161 | ||||||||
\(16\) | −55.0000 | −0.859375 | ||||||||
\(17\) | −43.1414 | −0.615490 | −0.307745 | − | 0.951469i | \(-0.599574\pi\) | ||||
−0.307745 | + | 0.951469i | \(0.599574\pi\) | |||||||
\(18\) | −37.1080 | −0.485913 | ||||||||
\(19\) | −26.9779 | −0.325745 | −0.162873 | − | 0.986647i | \(-0.552076\pi\) | ||||
−0.162873 | + | 0.986647i | \(0.552076\pi\) | |||||||
\(20\) | 120.981 | 1.35261 | ||||||||
\(21\) | 94.2656 | 0.979545 | ||||||||
\(22\) | −166.970 | −1.61810 | ||||||||
\(23\) | −19.0100 | −0.172342 | −0.0861709 | − | 0.996280i | \(-0.527463\pi\) | ||||
−0.0861709 | + | 0.996280i | \(0.527463\pi\) | |||||||
\(24\) | 12.3693 | 0.105203 | ||||||||
\(25\) | 55.6971 | 0.445577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −282.797 | −1.90870 | ||||||||
\(29\) | −154.111 | −0.986820 | −0.493410 | − | 0.869797i | \(-0.664250\pi\) | ||||
−0.493410 | + | 0.869797i | \(0.664250\pi\) | |||||||
\(30\) | 166.273 | 1.01190 | ||||||||
\(31\) | 308.270 | 1.78603 | 0.893016 | − | 0.450025i | \(-0.148585\pi\) | ||||
0.893016 | + | 0.450025i | \(0.148585\pi\) | |||||||
\(32\) | 259.756 | 1.43496 | ||||||||
\(33\) | −121.489 | −0.640862 | ||||||||
\(34\) | 177.877 | 0.897223 | ||||||||
\(35\) | −422.384 | −2.03988 | ||||||||
\(36\) | 81.0000 | 0.375000 | ||||||||
\(37\) | 43.5116 | 0.193331 | 0.0966657 | − | 0.995317i | \(-0.469182\pi\) | ||||
0.0966657 | + | 0.995317i | \(0.469182\pi\) | |||||||
\(38\) | 111.233 | 0.474851 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −55.4243 | −0.219084 | ||||||||
\(41\) | 47.8384 | 0.182222 | 0.0911110 | − | 0.995841i | \(-0.470958\pi\) | ||||
0.0911110 | + | 0.995841i | \(0.470958\pi\) | |||||||
\(42\) | −388.667 | −1.42792 | ||||||||
\(43\) | 342.121 | 1.21333 | 0.606663 | − | 0.794959i | \(-0.292508\pi\) | ||||
0.606663 | + | 0.794959i | \(0.292508\pi\) | |||||||
\(44\) | 364.466 | 1.24876 | ||||||||
\(45\) | 120.981 | 0.400774 | ||||||||
\(46\) | 78.3802 | 0.251229 | ||||||||
\(47\) | 133.468 | 0.414218 | 0.207109 | − | 0.978318i | \(-0.433594\pi\) | ||||
0.207109 | + | 0.978318i | \(0.433594\pi\) | |||||||
\(48\) | 165.000 | 0.496160 | ||||||||
\(49\) | 644.334 | 1.87853 | ||||||||
\(50\) | −229.645 | −0.649535 | ||||||||
\(51\) | 129.424 | 0.355353 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −438.454 | −1.13635 | −0.568173 | − | 0.822909i | \(-0.692350\pi\) | ||||
−0.568173 | + | 0.822909i | \(0.692350\pi\) | |||||||
\(54\) | 111.324 | 0.280542 | ||||||||
\(55\) | 544.364 | 1.33458 | ||||||||
\(56\) | 129.556 | 0.309154 | ||||||||
\(57\) | 80.9338 | 0.188069 | ||||||||
\(58\) | 635.418 | 1.43852 | ||||||||
\(59\) | 590.553 | 1.30311 | 0.651555 | − | 0.758601i | \(-0.274117\pi\) | ||||
0.651555 | + | 0.758601i | \(0.274117\pi\) | |||||||
\(60\) | −362.944 | −0.780931 | ||||||||
\(61\) | −541.304 | −1.13618 | −0.568089 | − | 0.822967i | \(-0.692317\pi\) | ||||
−0.568089 | + | 0.822967i | \(0.692317\pi\) | |||||||
\(62\) | −1271.03 | −2.60357 | ||||||||
\(63\) | −282.797 | −0.565541 | ||||||||
\(64\) | −631.000 | −1.23242 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 500.910 | 0.934208 | ||||||||
\(67\) | −230.345 | −0.420018 | −0.210009 | − | 0.977700i | \(-0.567349\pi\) | ||||
−0.210009 | + | 0.977700i | \(0.567349\pi\) | |||||||
\(68\) | −388.273 | −0.692426 | ||||||||
\(69\) | 57.0300 | 0.0995015 | ||||||||
\(70\) | 1741.54 | 2.97362 | ||||||||
\(71\) | 449.412 | 0.751203 | 0.375601 | − | 0.926781i | \(-0.377436\pi\) | ||||
0.375601 | + | 0.926781i | \(0.377436\pi\) | |||||||
\(72\) | −37.1080 | −0.0607391 | ||||||||
\(73\) | −389.711 | −0.624826 | −0.312413 | − | 0.949946i | \(-0.601137\pi\) | ||||
−0.312413 | + | 0.949946i | \(0.601137\pi\) | |||||||
\(74\) | −179.403 | −0.281826 | ||||||||
\(75\) | −167.091 | −0.257254 | ||||||||
\(76\) | −242.801 | −0.366464 | ||||||||
\(77\) | −1272.47 | −1.88326 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −897.820 | −1.27864 | −0.639321 | − | 0.768940i | \(-0.720784\pi\) | ||||
−0.639321 | + | 0.768940i | \(0.720784\pi\) | |||||||
\(80\) | −739.330 | −1.03325 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −197.243 | −0.265632 | ||||||||
\(83\) | −1300.24 | −1.71952 | −0.859759 | − | 0.510700i | \(-0.829386\pi\) | ||||
−0.859759 | + | 0.510700i | \(0.829386\pi\) | |||||||
\(84\) | 848.391 | 1.10199 | ||||||||
\(85\) | −579.923 | −0.740017 | ||||||||
\(86\) | −1410.60 | −1.76871 | ||||||||
\(87\) | 462.334 | 0.569741 | ||||||||
\(88\) | −166.970 | −0.202262 | ||||||||
\(89\) | −925.045 | −1.10174 | −0.550869 | − | 0.834592i | \(-0.685703\pi\) | ||||
−0.550869 | + | 0.834592i | \(0.685703\pi\) | |||||||
\(90\) | −498.819 | −0.584223 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −171.090 | −0.193884 | ||||||||
\(93\) | −924.811 | −1.03117 | ||||||||
\(94\) | −550.301 | −0.603822 | ||||||||
\(95\) | −362.647 | −0.391651 | ||||||||
\(96\) | −779.267 | −0.828475 | ||||||||
\(97\) | −1560.49 | −1.63344 | −0.816722 | − | 0.577031i | \(-0.804211\pi\) | ||||
−0.816722 | + | 0.577031i | \(0.804211\pi\) | |||||||
\(98\) | −2656.66 | −2.73840 | ||||||||
\(99\) | 364.466 | 0.370002 | ||||||||
\(100\) | 501.274 | 0.501274 | ||||||||
\(101\) | 958.840 | 0.944635 | 0.472318 | − | 0.881428i | \(-0.343418\pi\) | ||||
0.472318 | + | 0.881428i | \(0.343418\pi\) | |||||||
\(102\) | −533.630 | −0.518012 | ||||||||
\(103\) | 635.153 | 0.607606 | 0.303803 | − | 0.952735i | \(-0.401743\pi\) | ||||
0.303803 | + | 0.952735i | \(0.401743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1267.15 | 1.17773 | ||||||||
\(106\) | 1807.79 | 1.65649 | ||||||||
\(107\) | −1448.32 | −1.30855 | −0.654275 | − | 0.756257i | \(-0.727026\pi\) | ||||
−0.654275 | + | 0.756257i | \(0.727026\pi\) | |||||||
\(108\) | −243.000 | −0.216506 | ||||||||
\(109\) | −331.084 | −0.290937 | −0.145468 | − | 0.989363i | \(-0.546469\pi\) | ||||
−0.145468 | + | 0.989363i | \(0.546469\pi\) | |||||||
\(110\) | −2244.47 | −1.94547 | ||||||||
\(111\) | −130.535 | −0.111620 | ||||||||
\(112\) | 1728.20 | 1.45803 | ||||||||
\(113\) | 695.204 | 0.578755 | 0.289378 | − | 0.957215i | \(-0.406552\pi\) | ||||
0.289378 | + | 0.957215i | \(0.406552\pi\) | |||||||
\(114\) | −333.699 | −0.274156 | ||||||||
\(115\) | −255.539 | −0.207210 | ||||||||
\(116\) | −1387.00 | −1.11017 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2434.91 | −1.89959 | ||||||||
\(119\) | 1355.58 | 1.04425 | ||||||||
\(120\) | 166.273 | 0.126488 | ||||||||
\(121\) | 308.940 | 0.232111 | ||||||||
\(122\) | 2231.85 | 1.65625 | ||||||||
\(123\) | −143.515 | −0.105206 | ||||||||
\(124\) | 2774.43 | 2.00929 | ||||||||
\(125\) | −931.594 | −0.666595 | ||||||||
\(126\) | 1166.00 | 0.824410 | ||||||||
\(127\) | 247.154 | 0.172688 | 0.0863441 | − | 0.996265i | \(-0.472482\pi\) | ||||
0.0863441 | + | 0.996265i | \(0.472482\pi\) | |||||||
\(128\) | 523.634 | 0.361587 | ||||||||
\(129\) | −1026.36 | −0.700514 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 472.243 | 0.314962 | 0.157481 | − | 0.987522i | \(-0.449663\pi\) | ||||
0.157481 | + | 0.987522i | \(0.449663\pi\) | |||||||
\(132\) | −1093.40 | −0.720969 | ||||||||
\(133\) | 847.697 | 0.552667 | ||||||||
\(134\) | 949.739 | 0.612275 | ||||||||
\(135\) | −362.944 | −0.231387 | ||||||||
\(136\) | 177.877 | 0.112153 | ||||||||
\(137\) | −1830.70 | −1.14166 | −0.570829 | − | 0.821069i | \(-0.693378\pi\) | ||||
−0.570829 | + | 0.821069i | \(0.693378\pi\) | |||||||
\(138\) | −235.141 | −0.145047 | ||||||||
\(139\) | −100.000 | −0.0610208 | −0.0305104 | − | 0.999534i | \(-0.509713\pi\) | ||||
−0.0305104 | + | 0.999534i | \(0.509713\pi\) | |||||||
\(140\) | −3801.46 | −2.29487 | ||||||||
\(141\) | −400.403 | −0.239149 | ||||||||
\(142\) | −1852.97 | −1.09506 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −495.000 | −0.286458 | ||||||||
\(145\) | −2071.62 | −1.18647 | ||||||||
\(146\) | 1606.82 | 0.910832 | ||||||||
\(147\) | −1933.00 | −1.08457 | ||||||||
\(148\) | 391.604 | 0.217498 | ||||||||
\(149\) | 149.557 | 0.0822293 | 0.0411147 | − | 0.999154i | \(-0.486909\pi\) | ||||
0.0411147 | + | 0.999154i | \(0.486909\pi\) | |||||||
\(150\) | 688.936 | 0.375009 | ||||||||
\(151\) | −800.032 | −0.431163 | −0.215582 | − | 0.976486i | \(-0.569165\pi\) | ||||
−0.215582 | + | 0.976486i | \(0.569165\pi\) | |||||||
\(152\) | 111.233 | 0.0593564 | ||||||||
\(153\) | −388.273 | −0.205163 | ||||||||
\(154\) | 5246.51 | 2.74530 | ||||||||
\(155\) | 4143.88 | 2.14739 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2706.16 | −1.37564 | −0.687818 | − | 0.725884i | \(-0.741431\pi\) | ||||
−0.687818 | + | 0.725884i | \(0.741431\pi\) | |||||||
\(158\) | 3701.81 | 1.86392 | ||||||||
\(159\) | 1315.36 | 0.656070 | ||||||||
\(160\) | 3491.73 | 1.72528 | ||||||||
\(161\) | 597.330 | 0.292399 | ||||||||
\(162\) | −333.972 | −0.161971 | ||||||||
\(163\) | 3678.25 | 1.76750 | 0.883750 | − | 0.467959i | \(-0.155010\pi\) | ||||
0.883750 | + | 0.467959i | \(0.155010\pi\) | |||||||
\(164\) | 430.546 | 0.205000 | ||||||||
\(165\) | −1633.09 | −0.770522 | ||||||||
\(166\) | 5361.03 | 2.50661 | ||||||||
\(167\) | −3223.11 | −1.49348 | −0.746742 | − | 0.665114i | \(-0.768383\pi\) | ||||
−0.746742 | + | 0.665114i | \(0.768383\pi\) | |||||||
\(168\) | −388.667 | −0.178490 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2391.08 | 1.07875 | ||||||||
\(171\) | −242.801 | −0.108582 | ||||||||
\(172\) | 3079.09 | 1.36499 | ||||||||
\(173\) | −2689.54 | −1.18198 | −0.590988 | − | 0.806680i | \(-0.701262\pi\) | ||||
−0.590988 | + | 0.806680i | \(0.701262\pi\) | |||||||
\(174\) | −1906.25 | −0.830533 | ||||||||
\(175\) | −1750.11 | −0.755976 | ||||||||
\(176\) | −2227.29 | −0.953911 | ||||||||
\(177\) | −1771.66 | −0.752351 | ||||||||
\(178\) | 3814.06 | 1.60604 | ||||||||
\(179\) | −1524.04 | −0.636381 | −0.318191 | − | 0.948027i | \(-0.603075\pi\) | ||||
−0.318191 | + | 0.948027i | \(0.603075\pi\) | |||||||
\(180\) | 1088.83 | 0.450871 | ||||||||
\(181\) | 476.881 | 0.195836 | 0.0979180 | − | 0.995194i | \(-0.468782\pi\) | ||||
0.0979180 | + | 0.995194i | \(0.468782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1623.91 | 0.655973 | ||||||||
\(184\) | 78.3802 | 0.0314036 | ||||||||
\(185\) | 584.899 | 0.232446 | ||||||||
\(186\) | 3813.09 | 1.50317 | ||||||||
\(187\) | −1747.06 | −0.683197 | ||||||||
\(188\) | 1201.21 | 0.465996 | ||||||||
\(189\) | 848.391 | 0.326515 | ||||||||
\(190\) | 1495.23 | 0.570924 | ||||||||
\(191\) | −1369.74 | −0.518906 | −0.259453 | − | 0.965756i | \(-0.583542\pi\) | ||||
−0.259453 | + | 0.965756i | \(0.583542\pi\) | |||||||
\(192\) | 1893.00 | 0.711539 | ||||||||
\(193\) | −2144.72 | −0.799898 | −0.399949 | − | 0.916537i | \(-0.630972\pi\) | ||||
−0.399949 | + | 0.916537i | \(0.630972\pi\) | |||||||
\(194\) | 6434.08 | 2.38113 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5799.01 | 2.11334 | ||||||||
\(197\) | −239.739 | −0.0867040 | −0.0433520 | − | 0.999060i | \(-0.513804\pi\) | ||||
−0.0433520 | + | 0.999060i | \(0.513804\pi\) | |||||||
\(198\) | −1502.73 | −0.539365 | ||||||||
\(199\) | −1589.94 | −0.566371 | −0.283185 | − | 0.959065i | \(-0.591391\pi\) | ||||
−0.283185 | + | 0.959065i | \(0.591391\pi\) | |||||||
\(200\) | −229.645 | −0.0811918 | ||||||||
\(201\) | 691.036 | 0.242497 | ||||||||
\(202\) | −3953.40 | −1.37703 | ||||||||
\(203\) | 4842.47 | 1.67426 | ||||||||
\(204\) | 1164.82 | 0.399773 | ||||||||
\(205\) | 643.061 | 0.219090 | ||||||||
\(206\) | −2618.80 | −0.885731 | ||||||||
\(207\) | −171.090 | −0.0574472 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1092.50 | −0.361579 | ||||||||
\(210\) | −5224.61 | −1.71682 | ||||||||
\(211\) | −1872.85 | −0.611055 | −0.305527 | − | 0.952183i | \(-0.598833\pi\) | ||||
−0.305527 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(212\) | −3946.09 | −1.27839 | ||||||||
\(213\) | −1348.24 | −0.433707 | ||||||||
\(214\) | 5971.59 | 1.90752 | ||||||||
\(215\) | 4598.92 | 1.45881 | ||||||||
\(216\) | 111.324 | 0.0350677 | ||||||||
\(217\) | −9686.43 | −3.03022 | ||||||||
\(218\) | 1365.09 | 0.424109 | ||||||||
\(219\) | 1169.13 | 0.360743 | ||||||||
\(220\) | 4899.28 | 1.50141 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 538.209 | 0.162713 | ||||||||
\(223\) | −56.1283 | −0.0168548 | −0.00842742 | − | 0.999964i | \(-0.502683\pi\) | ||||
−0.00842742 | + | 0.999964i | \(0.502683\pi\) | |||||||
\(224\) | −8162.01 | −2.43459 | ||||||||
\(225\) | 501.274 | 0.148526 | ||||||||
\(226\) | −2866.40 | −0.843673 | ||||||||
\(227\) | −667.390 | −0.195137 | −0.0975687 | − | 0.995229i | \(-0.531107\pi\) | ||||
−0.0975687 | + | 0.995229i | \(0.531107\pi\) | |||||||
\(228\) | 728.404 | 0.211578 | ||||||||
\(229\) | 723.299 | 0.208720 | 0.104360 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104360 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(230\) | 1053.62 | 0.302058 | ||||||||
\(231\) | 3817.40 | 1.08730 | ||||||||
\(232\) | 635.418 | 0.179816 | ||||||||
\(233\) | −275.451 | −0.0774482 | −0.0387241 | − | 0.999250i | \(-0.512329\pi\) | ||||
−0.0387241 | + | 0.999250i | \(0.512329\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1794.12 | 0.498024 | ||||||||
\(236\) | 5314.98 | 1.46600 | ||||||||
\(237\) | 2693.46 | 0.738224 | ||||||||
\(238\) | −5589.22 | −1.52225 | ||||||||
\(239\) | −1529.39 | −0.413925 | −0.206963 | − | 0.978349i | \(-0.566358\pi\) | ||||
−0.206963 | + | 0.978349i | \(0.566358\pi\) | |||||||
\(240\) | 2217.99 | 0.596544 | ||||||||
\(241\) | 975.526 | 0.260743 | 0.130372 | − | 0.991465i | \(-0.458383\pi\) | ||||
0.130372 | + | 0.991465i | \(0.458383\pi\) | |||||||
\(242\) | −1273.79 | −0.338357 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −4871.74 | −1.27820 | ||||||||
\(245\) | 8661.38 | 2.25859 | ||||||||
\(246\) | 591.729 | 0.153363 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1271.03 | −0.325446 | ||||||||
\(249\) | 3900.72 | 0.992765 | ||||||||
\(250\) | 3841.06 | 0.971720 | ||||||||
\(251\) | −1874.14 | −0.471294 | −0.235647 | − | 0.971839i | \(-0.575721\pi\) | ||||
−0.235647 | + | 0.971839i | \(0.575721\pi\) | |||||||
\(252\) | −2545.17 | −0.636233 | ||||||||
\(253\) | −769.832 | −0.191300 | ||||||||
\(254\) | −1019.04 | −0.251734 | ||||||||
\(255\) | 1739.77 | 0.427249 | ||||||||
\(256\) | 2889.00 | 0.705322 | ||||||||
\(257\) | −1818.19 | −0.441305 | −0.220653 | − | 0.975352i | \(-0.570819\pi\) | ||||
−0.220653 | + | 0.975352i | \(0.570819\pi\) | |||||||
\(258\) | 4231.81 | 1.02117 | ||||||||
\(259\) | −1367.22 | −0.328010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1387.00 | −0.328940 | ||||||||
\(262\) | −1947.11 | −0.459132 | ||||||||
\(263\) | 673.799 | 0.157978 | 0.0789890 | − | 0.996875i | \(-0.474831\pi\) | ||||
0.0789890 | + | 0.996875i | \(0.474831\pi\) | |||||||
\(264\) | 500.910 | 0.116776 | ||||||||
\(265\) | −5893.86 | −1.36625 | ||||||||
\(266\) | −3495.14 | −0.805643 | ||||||||
\(267\) | 2775.14 | 0.636088 | ||||||||
\(268\) | −2073.11 | −0.472520 | ||||||||
\(269\) | −3356.40 | −0.760756 | −0.380378 | − | 0.924831i | \(-0.624206\pi\) | ||||
−0.380378 | + | 0.924831i | \(0.624206\pi\) | |||||||
\(270\) | 1496.46 | 0.337301 | ||||||||
\(271\) | 8915.55 | 1.99845 | 0.999227 | − | 0.0393133i | \(-0.0125170\pi\) | ||||
0.999227 | + | 0.0393133i | \(0.0125170\pi\) | |||||||
\(272\) | 2372.78 | 0.528937 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7548.16 | 1.66424 | ||||||||
\(275\) | 2255.52 | 0.494593 | ||||||||
\(276\) | 513.270 | 0.111939 | ||||||||
\(277\) | 4017.31 | 0.871396 | 0.435698 | − | 0.900093i | \(-0.356502\pi\) | ||||
0.435698 | + | 0.900093i | \(0.356502\pi\) | |||||||
\(278\) | 412.311 | 0.0889523 | ||||||||
\(279\) | 2774.43 | 0.595344 | ||||||||
\(280\) | 1741.54 | 0.371702 | ||||||||
\(281\) | 1841.12 | 0.390860 | 0.195430 | − | 0.980718i | \(-0.437390\pi\) | ||||
0.195430 | + | 0.980718i | \(0.437390\pi\) | |||||||
\(282\) | 1650.90 | 0.348617 | ||||||||
\(283\) | 4849.40 | 1.01861 | 0.509305 | − | 0.860586i | \(-0.329902\pi\) | ||||
0.509305 | + | 0.860586i | \(0.329902\pi\) | |||||||
\(284\) | 4044.71 | 0.845103 | ||||||||
\(285\) | 1087.94 | 0.226120 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1503.17 | −0.309162 | ||||||||
\(288\) | 2337.80 | 0.478320 | ||||||||
\(289\) | −3051.82 | −0.621172 | ||||||||
\(290\) | 8541.52 | 1.72957 | ||||||||
\(291\) | 4681.48 | 0.943070 | ||||||||
\(292\) | −3507.40 | −0.702929 | ||||||||
\(293\) | −1413.85 | −0.281905 | −0.140953 | − | 0.990016i | \(-0.545017\pi\) | ||||
−0.140953 | + | 0.990016i | \(0.545017\pi\) | |||||||
\(294\) | 7969.97 | 1.58101 | ||||||||
\(295\) | 7938.43 | 1.56676 | ||||||||
\(296\) | −179.403 | −0.0352283 | ||||||||
\(297\) | −1093.40 | −0.213621 | ||||||||
\(298\) | −616.639 | −0.119869 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1503.82 | −0.289411 | ||||||||
\(301\) | −10750.1 | −2.05856 | ||||||||
\(302\) | 3298.62 | 0.628523 | ||||||||
\(303\) | −2876.52 | −0.545385 | ||||||||
\(304\) | 1483.79 | 0.279937 | ||||||||
\(305\) | −7276.41 | −1.36605 | ||||||||
\(306\) | 1600.89 | 0.299074 | ||||||||
\(307\) | −4625.64 | −0.859932 | −0.429966 | − | 0.902845i | \(-0.641474\pi\) | ||||
−0.429966 | + | 0.902845i | \(0.641474\pi\) | |||||||
\(308\) | −11452.2 | −2.11867 | ||||||||
\(309\) | −1905.46 | −0.350802 | ||||||||
\(310\) | −17085.7 | −3.13032 | ||||||||
\(311\) | −6060.79 | −1.10507 | −0.552534 | − | 0.833490i | \(-0.686339\pi\) | ||||
−0.552534 | + | 0.833490i | \(0.686339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 969.946 | 0.175158 | 0.0875792 | − | 0.996158i | \(-0.472087\pi\) | ||||
0.0875792 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(314\) | 11157.8 | 2.00532 | ||||||||
\(315\) | −3801.46 | −0.679962 | ||||||||
\(316\) | −8080.38 | −1.43847 | ||||||||
\(317\) | 8741.63 | 1.54883 | 0.774414 | − | 0.632679i | \(-0.218045\pi\) | ||||
0.774414 | + | 0.632679i | \(0.218045\pi\) | |||||||
\(318\) | −5423.38 | −0.956378 | ||||||||
\(319\) | −6240.92 | −1.09537 | ||||||||
\(320\) | −8482.13 | −1.48177 | ||||||||
\(321\) | 4344.97 | 0.755491 | ||||||||
\(322\) | −2462.85 | −0.426241 | ||||||||
\(323\) | 1163.87 | 0.200493 | ||||||||
\(324\) | 729.000 | 0.125000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15165.8 | −2.57655 | ||||||||
\(327\) | 993.252 | 0.167972 | ||||||||
\(328\) | −197.243 | −0.0332040 | ||||||||
\(329\) | −4193.81 | −0.702772 | ||||||||
\(330\) | 6733.41 | 1.12322 | ||||||||
\(331\) | 6987.76 | 1.16037 | 0.580184 | − | 0.814485i | \(-0.302981\pi\) | ||||
0.580184 | + | 0.814485i | \(0.302981\pi\) | |||||||
\(332\) | −11702.2 | −1.93446 | ||||||||
\(333\) | 391.604 | 0.0644438 | ||||||||
\(334\) | 13289.2 | 2.17711 | ||||||||
\(335\) | −3096.39 | −0.504996 | ||||||||
\(336\) | −5184.61 | −0.841797 | ||||||||
\(337\) | −4156.59 | −0.671881 | −0.335940 | − | 0.941883i | \(-0.609054\pi\) | ||||
−0.335940 | + | 0.941883i | \(0.609054\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2085.61 | −0.334144 | ||||||||
\(340\) | −5219.30 | −0.832519 | ||||||||
\(341\) | 12483.8 | 1.98250 | ||||||||
\(342\) | 1001.10 | 0.158284 | ||||||||
\(343\) | −9468.49 | −1.49053 | ||||||||
\(344\) | −1410.60 | −0.221089 | ||||||||
\(345\) | 766.618 | 0.119633 | ||||||||
\(346\) | 11089.3 | 1.72301 | ||||||||
\(347\) | −312.513 | −0.0483475 | −0.0241737 | − | 0.999708i | \(-0.507695\pi\) | ||||
−0.0241737 | + | 0.999708i | \(0.507695\pi\) | |||||||
\(348\) | 4161.01 | 0.640958 | ||||||||
\(349\) | −4458.75 | −0.683872 | −0.341936 | − | 0.939723i | \(-0.611083\pi\) | ||||
−0.341936 | + | 0.939723i | \(0.611083\pi\) | |||||||
\(350\) | 7215.88 | 1.10201 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10519.1 | 1.59281 | ||||||||
\(353\) | −2249.17 | −0.339126 | −0.169563 | − | 0.985519i | \(-0.554236\pi\) | ||||
−0.169563 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(354\) | 7304.74 | 1.09673 | ||||||||
\(355\) | 6041.16 | 0.903187 | ||||||||
\(356\) | −8325.41 | −1.23945 | ||||||||
\(357\) | −4066.75 | −0.602900 | ||||||||
\(358\) | 6283.78 | 0.927677 | ||||||||
\(359\) | −7842.79 | −1.15300 | −0.576499 | − | 0.817098i | \(-0.695582\pi\) | ||||
−0.576499 | + | 0.817098i | \(0.695582\pi\) | |||||||
\(360\) | −498.819 | −0.0730279 | ||||||||
\(361\) | −6131.19 | −0.893890 | ||||||||
\(362\) | −1966.23 | −0.285478 | ||||||||
\(363\) | −926.820 | −0.134009 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5238.64 | −0.751241 | ||||||||
\(366\) | −6695.56 | −0.956237 | ||||||||
\(367\) | 6660.24 | 0.947307 | 0.473653 | − | 0.880711i | \(-0.342935\pi\) | ||||
0.473653 | + | 0.880711i | \(0.342935\pi\) | |||||||
\(368\) | 1045.55 | 0.148106 | ||||||||
\(369\) | 430.546 | 0.0607407 | ||||||||
\(370\) | −2411.60 | −0.338846 | ||||||||
\(371\) | 13777.1 | 1.92795 | ||||||||
\(372\) | −8323.30 | −1.16006 | ||||||||
\(373\) | −36.9873 | −0.00513439 | −0.00256720 | − | 0.999997i | \(-0.500817\pi\) | ||||
−0.00256720 | + | 0.999997i | \(0.500817\pi\) | |||||||
\(374\) | 7203.32 | 0.995923 | ||||||||
\(375\) | 2794.78 | 0.384859 | ||||||||
\(376\) | −550.301 | −0.0754777 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3498.00 | −0.475973 | ||||||||
\(379\) | 12079.9 | 1.63721 | 0.818603 | − | 0.574360i | \(-0.194749\pi\) | ||||
0.818603 | + | 0.574360i | \(0.194749\pi\) | |||||||
\(380\) | −3263.82 | −0.440607 | ||||||||
\(381\) | −741.463 | −0.0997015 | ||||||||
\(382\) | 5647.59 | 0.756429 | ||||||||
\(383\) | −10567.4 | −1.40984 | −0.704919 | − | 0.709287i | \(-0.749017\pi\) | ||||
−0.704919 | + | 0.709287i | \(0.749017\pi\) | |||||||
\(384\) | −1570.90 | −0.208763 | ||||||||
\(385\) | −17104.9 | −2.26428 | ||||||||
\(386\) | 8842.90 | 1.16604 | ||||||||
\(387\) | 3079.09 | 0.404442 | ||||||||
\(388\) | −14044.4 | −1.83763 | ||||||||
\(389\) | −9757.49 | −1.27179 | −0.635893 | − | 0.771778i | \(-0.719368\pi\) | ||||
−0.635893 | + | 0.771778i | \(0.719368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 820.119 | 0.106075 | ||||||||
\(392\) | −2656.66 | −0.342300 | ||||||||
\(393\) | −1416.73 | −0.181844 | ||||||||
\(394\) | 988.469 | 0.126392 | ||||||||
\(395\) | −12068.8 | −1.53734 | ||||||||
\(396\) | 3280.19 | 0.416252 | ||||||||
\(397\) | −14200.5 | −1.79522 | −0.897612 | − | 0.440786i | \(-0.854700\pi\) | ||||
−0.897612 | + | 0.440786i | \(0.854700\pi\) | |||||||
\(398\) | 6555.48 | 0.825620 | ||||||||
\(399\) | −2543.09 | −0.319082 | ||||||||
\(400\) | −3063.34 | −0.382918 | ||||||||
\(401\) | −12676.4 | −1.57863 | −0.789313 | − | 0.613992i | \(-0.789563\pi\) | ||||
−0.789313 | + | 0.613992i | \(0.789563\pi\) | |||||||
\(402\) | −2849.22 | −0.353497 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8629.56 | 1.06271 | ||||||||
\(405\) | 1088.83 | 0.133591 | ||||||||
\(406\) | −19966.0 | −2.44063 | ||||||||
\(407\) | 1762.05 | 0.214599 | ||||||||
\(408\) | −533.630 | −0.0647515 | ||||||||
\(409\) | 1533.68 | 0.185417 | 0.0927083 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927083 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(410\) | −2651.41 | −0.319375 | ||||||||
\(411\) | 5492.09 | 0.659136 | ||||||||
\(412\) | 5716.38 | 0.683557 | ||||||||
\(413\) | −18556.3 | −2.21089 | ||||||||
\(414\) | 705.422 | 0.0837430 | ||||||||
\(415\) | −17478.3 | −2.06741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 300.000 | 0.0352304 | ||||||||
\(418\) | 4504.50 | 0.527087 | ||||||||
\(419\) | −2165.89 | −0.252532 | −0.126266 | − | 0.991996i | \(-0.540299\pi\) | ||||
−0.126266 | + | 0.991996i | \(0.540299\pi\) | |||||||
\(420\) | 11404.4 | 1.32494 | ||||||||
\(421\) | 734.575 | 0.0850380 | 0.0425190 | − | 0.999096i | \(-0.486462\pi\) | ||||
0.0425190 | + | 0.999096i | \(0.486462\pi\) | |||||||
\(422\) | 7721.98 | 0.890758 | ||||||||
\(423\) | 1201.21 | 0.138073 | ||||||||
\(424\) | 1807.79 | 0.207062 | ||||||||
\(425\) | −2402.85 | −0.274248 | ||||||||
\(426\) | 5558.92 | 0.632231 | ||||||||
\(427\) | 17008.8 | 1.92767 | ||||||||
\(428\) | −13034.9 | −1.47212 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18961.8 | −2.12656 | ||||||||
\(431\) | −13709.3 | −1.53215 | −0.766073 | − | 0.642754i | \(-0.777792\pi\) | ||||
−0.766073 | + | 0.642754i | \(0.777792\pi\) | |||||||
\(432\) | 1485.00 | 0.165387 | ||||||||
\(433\) | 10049.9 | 1.11540 | 0.557701 | − | 0.830042i | \(-0.311684\pi\) | ||||
0.557701 | + | 0.830042i | \(0.311684\pi\) | |||||||
\(434\) | 39938.2 | 4.41727 | ||||||||
\(435\) | 6214.87 | 0.685011 | ||||||||
\(436\) | −2979.76 | −0.327304 | ||||||||
\(437\) | 512.850 | 0.0561395 | ||||||||
\(438\) | −4820.46 | −0.525869 | ||||||||
\(439\) | −8133.47 | −0.884258 | −0.442129 | − | 0.896951i | \(-0.645777\pi\) | ||||
−0.442129 | + | 0.896951i | \(0.645777\pi\) | |||||||
\(440\) | −2244.47 | −0.243184 | ||||||||
\(441\) | 5799.01 | 0.626175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2370.78 | −0.254264 | −0.127132 | − | 0.991886i | \(-0.540577\pi\) | ||||
−0.127132 | + | 0.991886i | \(0.540577\pi\) | |||||||
\(444\) | −1174.81 | −0.125572 | ||||||||
\(445\) | −12434.8 | −1.32464 | ||||||||
\(446\) | 231.423 | 0.0245699 | ||||||||
\(447\) | −448.670 | −0.0474751 | ||||||||
\(448\) | 19827.2 | 2.09095 | ||||||||
\(449\) | 12923.2 | 1.35832 | 0.679158 | − | 0.733992i | \(-0.262345\pi\) | ||||
0.679158 | + | 0.733992i | \(0.262345\pi\) | |||||||
\(450\) | −2066.81 | −0.216512 | ||||||||
\(451\) | 1937.27 | 0.202267 | ||||||||
\(452\) | 6256.84 | 0.651099 | ||||||||
\(453\) | 2400.10 | 0.248932 | ||||||||
\(454\) | 2751.72 | 0.284459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −333.699 | −0.0342694 | ||||||||
\(457\) | 8401.26 | 0.859944 | 0.429972 | − | 0.902842i | \(-0.358523\pi\) | ||||
0.429972 | + | 0.902842i | \(0.358523\pi\) | |||||||
\(458\) | −2982.24 | −0.304260 | ||||||||
\(459\) | 1164.82 | 0.118451 | ||||||||
\(460\) | −2299.85 | −0.233111 | ||||||||
\(461\) | 17627.3 | 1.78088 | 0.890441 | − | 0.455098i | \(-0.150396\pi\) | ||||
0.890441 | + | 0.455098i | \(0.150396\pi\) | |||||||
\(462\) | −15739.5 | −1.58500 | ||||||||
\(463\) | −5461.81 | −0.548233 | −0.274116 | − | 0.961697i | \(-0.588385\pi\) | ||||
−0.274116 | + | 0.961697i | \(0.588385\pi\) | |||||||
\(464\) | 8476.13 | 0.848048 | ||||||||
\(465\) | −12431.6 | −1.23979 | ||||||||
\(466\) | 1135.72 | 0.112899 | ||||||||
\(467\) | 8262.19 | 0.818691 | 0.409345 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409345 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7237.89 | 0.712611 | ||||||||
\(470\) | −7397.35 | −0.725988 | ||||||||
\(471\) | 8118.47 | 0.794223 | ||||||||
\(472\) | −2434.91 | −0.237449 | ||||||||
\(473\) | 13854.6 | 1.34680 | ||||||||
\(474\) | −11105.4 | −1.07614 | ||||||||
\(475\) | −1502.59 | −0.145145 | ||||||||
\(476\) | 12200.3 | 1.17479 | ||||||||
\(477\) | −3946.09 | −0.378782 | ||||||||
\(478\) | 6305.84 | 0.603395 | ||||||||
\(479\) | −1575.87 | −0.150320 | −0.0751601 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751601 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(480\) | −10475.2 | −0.996093 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4022.20 | −0.380095 | ||||||||
\(483\) | −1791.99 | −0.168816 | ||||||||
\(484\) | 2780.46 | 0.261125 | ||||||||
\(485\) | −20976.7 | −1.96393 | ||||||||
\(486\) | 1001.91 | 0.0935139 | ||||||||
\(487\) | −12595.7 | −1.17200 | −0.586001 | − | 0.810310i | \(-0.699299\pi\) | ||||
−0.586001 | + | 0.810310i | \(0.699299\pi\) | |||||||
\(488\) | 2231.85 | 0.207031 | ||||||||
\(489\) | −11034.7 | −1.02047 | ||||||||
\(490\) | −35711.8 | −3.29244 | ||||||||
\(491\) | −1071.21 | −0.0984586 | −0.0492293 | − | 0.998788i | \(-0.515677\pi\) | ||||
−0.0492293 | + | 0.998788i | \(0.515677\pi\) | |||||||
\(492\) | −1291.64 | −0.118357 | ||||||||
\(493\) | 6648.59 | 0.607378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4899.28 | 0.444861 | ||||||||
\(496\) | −16954.9 | −1.53487 | ||||||||
\(497\) | −14121.4 | −1.27451 | ||||||||
\(498\) | −16083.1 | −1.44719 | ||||||||
\(499\) | −1422.30 | −0.127597 | −0.0637985 | − | 0.997963i | \(-0.520322\pi\) | ||||
−0.0637985 | + | 0.997963i | \(0.520322\pi\) | |||||||
\(500\) | −8384.35 | −0.749919 | ||||||||
\(501\) | 9669.33 | 0.862263 | ||||||||
\(502\) | 7727.28 | 0.687022 | ||||||||
\(503\) | −9349.34 | −0.828760 | −0.414380 | − | 0.910104i | \(-0.636002\pi\) | ||||
−0.414380 | + | 0.910104i | \(0.636002\pi\) | |||||||
\(504\) | 1166.00 | 0.103051 | ||||||||
\(505\) | 12889.1 | 1.13576 | ||||||||
\(506\) | 3174.10 | 0.278866 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2224.39 | 0.194274 | ||||||||
\(509\) | 13736.3 | 1.19617 | 0.598086 | − | 0.801432i | \(-0.295928\pi\) | ||||
0.598086 | + | 0.801432i | \(0.295928\pi\) | |||||||
\(510\) | −7173.25 | −0.622817 | ||||||||
\(511\) | 12245.5 | 1.06009 | ||||||||
\(512\) | −16100.7 | −1.38976 | ||||||||
\(513\) | 728.404 | 0.0626897 | ||||||||
\(514\) | 7496.58 | 0.643307 | ||||||||
\(515\) | 8537.96 | 0.730538 | ||||||||
\(516\) | −9237.28 | −0.788079 | ||||||||
\(517\) | 5404.93 | 0.459785 | ||||||||
\(518\) | 5637.17 | 0.478153 | ||||||||
\(519\) | 8068.62 | 0.682414 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11052.3 | 0.929386 | 0.464693 | − | 0.885472i | \(-0.346165\pi\) | ||||
0.464693 | + | 0.885472i | \(0.346165\pi\) | |||||||
\(522\) | 5718.76 | 0.479508 | ||||||||
\(523\) | 6477.04 | 0.541532 | 0.270766 | − | 0.962645i | \(-0.412723\pi\) | ||||
0.270766 | + | 0.962645i | \(0.412723\pi\) | |||||||
\(524\) | 4250.19 | 0.354332 | ||||||||
\(525\) | 5250.33 | 0.436463 | ||||||||
\(526\) | −2778.14 | −0.230290 | ||||||||
\(527\) | −13299.2 | −1.09929 | ||||||||
\(528\) | 6681.87 | 0.550741 | ||||||||
\(529\) | −11805.6 | −0.970298 | ||||||||
\(530\) | 24301.0 | 1.99164 | ||||||||
\(531\) | 5314.98 | 0.434370 | ||||||||
\(532\) | 7629.27 | 0.621750 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −11442.2 | −0.927250 | ||||||||
\(535\) | −19468.9 | −1.57330 | ||||||||
\(536\) | 949.739 | 0.0765344 | ||||||||
\(537\) | 4572.12 | 0.367415 | ||||||||
\(538\) | 13838.8 | 1.10898 | ||||||||
\(539\) | 26093.1 | 2.08517 | ||||||||
\(540\) | −3266.49 | −0.260310 | ||||||||
\(541\) | 18341.5 | 1.45761 | 0.728803 | − | 0.684723i | \(-0.240077\pi\) | ||||
0.728803 | + | 0.684723i | \(0.240077\pi\) | |||||||
\(542\) | −36759.7 | −2.91322 | ||||||||
\(543\) | −1430.64 | −0.113066 | ||||||||
\(544\) | −11206.2 | −0.883204 | ||||||||
\(545\) | −4450.55 | −0.349799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18943.1 | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(548\) | −16476.3 | −1.28436 | ||||||||
\(549\) | −4871.74 | −0.378726 | ||||||||
\(550\) | −9299.75 | −0.720987 | ||||||||
\(551\) | 4157.61 | 0.321452 | ||||||||
\(552\) | −235.141 | −0.0181309 | ||||||||
\(553\) | 28211.2 | 2.16937 | ||||||||
\(554\) | −16563.8 | −1.27027 | ||||||||
\(555\) | −1754.70 | −0.134203 | ||||||||
\(556\) | −900.000 | −0.0686484 | ||||||||
\(557\) | 415.532 | 0.0316098 | 0.0158049 | − | 0.999875i | \(-0.494969\pi\) | ||||
0.0158049 | + | 0.999875i | \(0.494969\pi\) | |||||||
\(558\) | −11439.3 | −0.867856 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 23231.1 | 1.75303 | ||||||||
\(561\) | 5241.19 | 0.394444 | ||||||||
\(562\) | −7591.12 | −0.569772 | ||||||||
\(563\) | 18291.8 | 1.36929 | 0.684643 | − | 0.728879i | \(-0.259958\pi\) | ||||
0.684643 | + | 0.728879i | \(0.259958\pi\) | |||||||
\(564\) | −3603.63 | −0.269043 | ||||||||
\(565\) | 9345.19 | 0.695850 | ||||||||
\(566\) | −19994.6 | −1.48487 | ||||||||
\(567\) | −2545.17 | −0.188514 | ||||||||
\(568\) | −1852.97 | −0.136882 | ||||||||
\(569\) | 4347.47 | 0.320308 | 0.160154 | − | 0.987092i | \(-0.448801\pi\) | ||||
0.160154 | + | 0.987092i | \(0.448801\pi\) | |||||||
\(570\) | −4485.70 | −0.329623 | ||||||||
\(571\) | −16756.0 | −1.22805 | −0.614024 | − | 0.789288i | \(-0.710450\pi\) | ||||
−0.614024 | + | 0.789288i | \(0.710450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4109.23 | 0.299591 | ||||||||
\(574\) | 6197.74 | 0.450677 | ||||||||
\(575\) | −1058.80 | −0.0767915 | ||||||||
\(576\) | −5679.00 | −0.410807 | ||||||||
\(577\) | 19974.7 | 1.44117 | 0.720587 | − | 0.693364i | \(-0.243872\pi\) | ||||
0.720587 | + | 0.693364i | \(0.243872\pi\) | |||||||
\(578\) | 12583.0 | 0.905506 | ||||||||
\(579\) | 6434.16 | 0.461821 | ||||||||
\(580\) | −18644.6 | −1.33478 | ||||||||
\(581\) | 40856.0 | 2.91737 | ||||||||
\(582\) | −19302.2 | −1.37475 | ||||||||
\(583\) | −17755.7 | −1.26135 | ||||||||
\(584\) | 1606.82 | 0.113854 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5829.47 | 0.410944 | ||||||||
\(587\) | −15748.7 | −1.10735 | −0.553677 | − | 0.832732i | \(-0.686776\pi\) | ||||
−0.553677 | + | 0.832732i | \(0.686776\pi\) | |||||||
\(588\) | −17397.0 | −1.22014 | ||||||||
\(589\) | −8316.50 | −0.581792 | ||||||||
\(590\) | −32731.0 | −2.28392 | ||||||||
\(591\) | 719.217 | 0.0500586 | ||||||||
\(592\) | −2393.14 | −0.166144 | ||||||||
\(593\) | 13318.4 | 0.922297 | 0.461148 | − | 0.887323i | \(-0.347438\pi\) | ||||
0.461148 | + | 0.887323i | \(0.347438\pi\) | |||||||
\(594\) | 4508.19 | 0.311403 | ||||||||
\(595\) | 18222.3 | 1.25553 | ||||||||
\(596\) | 1346.01 | 0.0925080 | ||||||||
\(597\) | 4769.82 | 0.326994 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2970.80 | 0.202644 | 0.101322 | − | 0.994854i | \(-0.467693\pi\) | ||||
0.101322 | + | 0.994854i | \(0.467693\pi\) | |||||||
\(600\) | 688.936 | 0.0468761 | ||||||||
\(601\) | 10632.6 | 0.721654 | 0.360827 | − | 0.932633i | \(-0.382495\pi\) | ||||
0.360827 | + | 0.932633i | \(0.382495\pi\) | |||||||
\(602\) | 44323.8 | 3.00083 | ||||||||
\(603\) | −2073.11 | −0.140006 | ||||||||
\(604\) | −7200.29 | −0.485059 | ||||||||
\(605\) | 4152.88 | 0.279072 | ||||||||
\(606\) | 11860.2 | 0.795029 | ||||||||
\(607\) | 11587.9 | 0.774856 | 0.387428 | − | 0.921900i | \(-0.373364\pi\) | ||||
0.387428 | + | 0.921900i | \(0.373364\pi\) | |||||||
\(608\) | −7007.67 | −0.467432 | ||||||||
\(609\) | −14527.4 | −0.966634 | ||||||||
\(610\) | 30001.4 | 1.99135 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3494.46 | −0.230809 | ||||||||
\(613\) | 20792.3 | 1.36998 | 0.684988 | − | 0.728555i | \(-0.259808\pi\) | ||||
0.684988 | + | 0.728555i | \(0.259808\pi\) | |||||||
\(614\) | 19072.0 | 1.25356 | ||||||||
\(615\) | −1929.18 | −0.126491 | ||||||||
\(616\) | 5246.51 | 0.343162 | ||||||||
\(617\) | −1562.78 | −0.101969 | −0.0509846 | − | 0.998699i | \(-0.516236\pi\) | ||||
−0.0509846 | + | 0.998699i | \(0.516236\pi\) | |||||||
\(618\) | 7856.41 | 0.511377 | ||||||||
\(619\) | 758.406 | 0.0492454 | 0.0246227 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246227 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(620\) | 37294.9 | 2.41581 | ||||||||
\(621\) | 513.270 | 0.0331672 | ||||||||
\(622\) | 24989.3 | 1.61090 | ||||||||
\(623\) | 29066.7 | 1.86923 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19485.0 | −1.24704 | ||||||||
\(626\) | −3999.19 | −0.255335 | ||||||||
\(627\) | 3277.51 | 0.208758 | ||||||||
\(628\) | −24355.4 | −1.54759 | ||||||||
\(629\) | −1877.15 | −0.118994 | ||||||||
\(630\) | 15673.8 | 0.991206 | ||||||||
\(631\) | −14265.2 | −0.899981 | −0.449990 | − | 0.893033i | \(-0.648573\pi\) | ||||
−0.449990 | + | 0.893033i | \(0.648573\pi\) | |||||||
\(632\) | 3701.81 | 0.232990 | ||||||||
\(633\) | 5618.56 | 0.352793 | ||||||||
\(634\) | −36042.7 | −2.25779 | ||||||||
\(635\) | 3322.34 | 0.207627 | ||||||||
\(636\) | 11838.3 | 0.738078 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 25732.0 | 1.59677 | ||||||||
\(639\) | 4044.71 | 0.250401 | ||||||||
\(640\) | 7038.88 | 0.434744 | ||||||||
\(641\) | 3985.64 | 0.245590 | 0.122795 | − | 0.992432i | \(-0.460814\pi\) | ||||
0.122795 | + | 0.992432i | \(0.460814\pi\) | |||||||
\(642\) | −17914.8 | −1.10131 | ||||||||
\(643\) | −8156.55 | −0.500254 | −0.250127 | − | 0.968213i | \(-0.580472\pi\) | ||||
−0.250127 | + | 0.968213i | \(0.580472\pi\) | |||||||
\(644\) | 5375.97 | 0.328949 | ||||||||
\(645\) | −13796.8 | −0.842243 | ||||||||
\(646\) | −4798.74 | −0.292266 | ||||||||
\(647\) | 11279.2 | 0.685368 | 0.342684 | − | 0.939451i | \(-0.388664\pi\) | ||||
0.342684 | + | 0.939451i | \(0.388664\pi\) | |||||||
\(648\) | −333.972 | −0.0202464 | ||||||||
\(649\) | 23915.2 | 1.44646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29059.3 | 1.74950 | ||||||||
\(652\) | 33104.2 | 1.98844 | ||||||||
\(653\) | 6565.75 | 0.393473 | 0.196736 | − | 0.980456i | \(-0.436966\pi\) | ||||
0.196736 | + | 0.980456i | \(0.436966\pi\) | |||||||
\(654\) | −4095.28 | −0.244860 | ||||||||
\(655\) | 6348.06 | 0.378686 | ||||||||
\(656\) | −2631.11 | −0.156597 | ||||||||
\(657\) | −3507.40 | −0.208275 | ||||||||
\(658\) | 17291.5 | 1.02446 | ||||||||
\(659\) | 4799.35 | 0.283696 | 0.141848 | − | 0.989888i | \(-0.454696\pi\) | ||||
0.141848 | + | 0.989888i | \(0.454696\pi\) | |||||||
\(660\) | −14697.8 | −0.866837 | ||||||||
\(661\) | 15593.6 | 0.917581 | 0.458790 | − | 0.888545i | \(-0.348283\pi\) | ||||
0.458790 | + | 0.888545i | \(0.348283\pi\) | |||||||
\(662\) | −28811.3 | −1.69151 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5361.03 | 0.313326 | ||||||||
\(665\) | 11395.1 | 0.664483 | ||||||||
\(666\) | −1614.63 | −0.0939422 | ||||||||
\(667\) | 2929.66 | 0.170070 | ||||||||
\(668\) | −29008.0 | −1.68017 | ||||||||
\(669\) | 168.385 | 0.00973115 | ||||||||
\(670\) | 12766.7 | 0.736152 | ||||||||
\(671\) | −21920.8 | −1.26116 | ||||||||
\(672\) | 24486.0 | 1.40561 | ||||||||
\(673\) | −2205.54 | −0.126326 | −0.0631630 | − | 0.998003i | \(-0.520119\pi\) | ||||
−0.0631630 | + | 0.998003i | \(0.520119\pi\) | |||||||
\(674\) | 17138.1 | 0.979426 | ||||||||
\(675\) | −1503.82 | −0.0857514 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15046.4 | −0.854182 | −0.427091 | − | 0.904209i | \(-0.640462\pi\) | ||||
−0.427091 | + | 0.904209i | \(0.640462\pi\) | |||||||
\(678\) | 8599.20 | 0.487095 | ||||||||
\(679\) | 49033.6 | 2.77134 | ||||||||
\(680\) | 2391.08 | 0.134844 | ||||||||
\(681\) | 2002.17 | 0.112663 | ||||||||
\(682\) | −51471.9 | −2.88997 | ||||||||
\(683\) | 30632.5 | 1.71614 | 0.858068 | − | 0.513537i | \(-0.171665\pi\) | ||||
0.858068 | + | 0.513537i | \(0.171665\pi\) | |||||||
\(684\) | −2185.21 | −0.122155 | ||||||||
\(685\) | −24608.9 | −1.37264 | ||||||||
\(686\) | 39039.6 | 2.17280 | ||||||||
\(687\) | −2169.90 | −0.120505 | ||||||||
\(688\) | −18816.7 | −1.04270 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3160.85 | −0.174393 | ||||||||
\(691\) | 2175.72 | 0.119780 | 0.0598901 | − | 0.998205i | \(-0.480925\pi\) | ||||
0.0598901 | + | 0.998205i | \(0.480925\pi\) | |||||||
\(692\) | −24205.9 | −1.32972 | ||||||||
\(693\) | −11452.2 | −0.627753 | ||||||||
\(694\) | 1288.52 | 0.0704780 | ||||||||
\(695\) | −1344.24 | −0.0733666 | ||||||||
\(696\) | −1906.25 | −0.103817 | ||||||||
\(697\) | −2063.82 | −0.112156 | ||||||||
\(698\) | 18383.9 | 0.996906 | ||||||||
\(699\) | 826.354 | 0.0447147 | ||||||||
\(700\) | −15751.0 | −0.850473 | ||||||||
\(701\) | −32718.2 | −1.76284 | −0.881419 | − | 0.472335i | \(-0.843411\pi\) | ||||
−0.881419 | + | 0.472335i | \(0.843411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1173.85 | −0.0629768 | ||||||||
\(704\) | −25553.1 | −1.36799 | ||||||||
\(705\) | −5382.36 | −0.287534 | ||||||||
\(706\) | 9273.58 | 0.494356 | ||||||||
\(707\) | −30128.6 | −1.60269 | ||||||||
\(708\) | −15944.9 | −0.846395 | ||||||||
\(709\) | −25219.7 | −1.33589 | −0.667945 | − | 0.744211i | \(-0.732826\pi\) | ||||
−0.667945 | + | 0.744211i | \(0.732826\pi\) | |||||||
\(710\) | −24908.3 | −1.31661 | ||||||||
\(711\) | −8080.38 | −0.426214 | ||||||||
\(712\) | 3814.06 | 0.200756 | ||||||||
\(713\) | −5860.22 | −0.307808 | ||||||||
\(714\) | 16767.7 | 0.878871 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13716.4 | −0.715929 | ||||||||
\(717\) | 4588.18 | 0.238980 | ||||||||
\(718\) | 32336.6 | 1.68077 | ||||||||
\(719\) | −35466.2 | −1.83959 | −0.919796 | − | 0.392398i | \(-0.871646\pi\) | ||||
−0.919796 | + | 0.392398i | \(0.871646\pi\) | |||||||
\(720\) | −6653.97 | −0.344415 | ||||||||
\(721\) | −19957.7 | −1.03088 | ||||||||
\(722\) | 25279.5 | 1.30306 | ||||||||
\(723\) | −2926.58 | −0.150540 | ||||||||
\(724\) | 4291.93 | 0.220315 | ||||||||
\(725\) | −8583.57 | −0.439704 | ||||||||
\(726\) | 3821.38 | 0.195351 | ||||||||
\(727\) | −14262.2 | −0.727588 | −0.363794 | − | 0.931479i | \(-0.618519\pi\) | ||||
−0.363794 | + | 0.931479i | \(0.618519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 21599.5 | 1.09511 | ||||||||
\(731\) | −14759.6 | −0.746790 | ||||||||
\(732\) | 14615.2 | 0.737970 | ||||||||
\(733\) | 16022.5 | 0.807371 | 0.403685 | − | 0.914898i | \(-0.367729\pi\) | ||||
0.403685 | + | 0.914898i | \(0.367729\pi\) | |||||||
\(734\) | −27460.9 | −1.38093 | ||||||||
\(735\) | −25984.1 | −1.30400 | ||||||||
\(736\) | −4937.96 | −0.247304 | ||||||||
\(737\) | −9328.11 | −0.466222 | ||||||||
\(738\) | −1775.19 | −0.0885440 | ||||||||
\(739\) | 3796.21 | 0.188966 | 0.0944830 | − | 0.995526i | \(-0.469880\pi\) | ||||
0.0944830 | + | 0.995526i | \(0.469880\pi\) | |||||||
\(740\) | 5264.09 | 0.261502 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −56804.3 | −2.81044 | ||||||||
\(743\) | −30329.3 | −1.49754 | −0.748772 | − | 0.662827i | \(-0.769356\pi\) | ||||
−0.748772 | + | 0.662827i | \(0.769356\pi\) | |||||||
\(744\) | 3813.09 | 0.187896 | ||||||||
\(745\) | 2010.40 | 0.0988661 | ||||||||
\(746\) | 152.502 | 0.00748460 | ||||||||
\(747\) | −11702.2 | −0.573173 | ||||||||
\(748\) | −15723.6 | −0.768597 | ||||||||
\(749\) | 45509.1 | 2.22011 | ||||||||
\(750\) | −11523.2 | −0.561023 | ||||||||
\(751\) | 21551.9 | 1.04719 | 0.523595 | − | 0.851967i | \(-0.324591\pi\) | ||||
0.523595 | + | 0.851967i | \(0.324591\pi\) | |||||||
\(752\) | −7340.72 | −0.355969 | ||||||||
\(753\) | 5622.42 | 0.272101 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10754.3 | −0.518397 | ||||||||
\(756\) | 7635.52 | 0.367329 | ||||||||
\(757\) | −20417.6 | −0.980306 | −0.490153 | − | 0.871637i | \(-0.663059\pi\) | ||||
−0.490153 | + | 0.871637i | \(0.663059\pi\) | |||||||
\(758\) | −49806.5 | −2.38662 | ||||||||
\(759\) | 2309.50 | 0.110447 | ||||||||
\(760\) | 1495.23 | 0.0713655 | ||||||||
\(761\) | −31375.4 | −1.49456 | −0.747278 | − | 0.664512i | \(-0.768640\pi\) | ||||
−0.747278 | + | 0.664512i | \(0.768640\pi\) | |||||||
\(762\) | 3057.13 | 0.145339 | ||||||||
\(763\) | 10403.3 | 0.493609 | ||||||||
\(764\) | −12327.7 | −0.583770 | ||||||||
\(765\) | −5219.30 | −0.246672 | ||||||||
\(766\) | 43570.5 | 2.05518 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8667.00 | −0.407218 | ||||||||
\(769\) | 12452.7 | 0.583946 | 0.291973 | − | 0.956427i | \(-0.405688\pi\) | ||||
0.291973 | + | 0.956427i | \(0.405688\pi\) | |||||||
\(770\) | 70525.5 | 3.30073 | ||||||||
\(771\) | 5454.56 | 0.254788 | ||||||||
\(772\) | −19302.5 | −0.899885 | ||||||||
\(773\) | −37449.8 | −1.74253 | −0.871264 | − | 0.490815i | \(-0.836699\pi\) | ||||
−0.871264 | + | 0.490815i | \(0.836699\pi\) | |||||||
\(774\) | −12695.4 | −0.589571 | ||||||||
\(775\) | 17169.8 | 0.795815 | ||||||||
\(776\) | 6434.08 | 0.297642 | ||||||||
\(777\) | 4101.65 | 0.189377 | ||||||||
\(778\) | 40231.2 | 1.85393 | ||||||||
\(779\) | −1290.58 | −0.0593580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18199.5 | 0.833839 | ||||||||
\(782\) | −3381.44 | −0.154629 | ||||||||
\(783\) | 4161.01 | 0.189914 | ||||||||
\(784\) | −35438.4 | −1.61436 | ||||||||
\(785\) | −36377.1 | −1.65396 | ||||||||
\(786\) | 5841.32 | 0.265080 | ||||||||
\(787\) | −26460.2 | −1.19848 | −0.599240 | − | 0.800570i | \(-0.704530\pi\) | ||||
−0.599240 | + | 0.800570i | \(0.704530\pi\) | |||||||
\(788\) | −2157.65 | −0.0975420 | ||||||||
\(789\) | −2021.40 | −0.0912086 | ||||||||
\(790\) | 49761.0 | 2.24104 | ||||||||
\(791\) | −21844.6 | −0.981928 | ||||||||
\(792\) | −1502.73 | −0.0674207 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 58550.3 | 2.61697 | ||||||||
\(795\) | 17681.6 | 0.788807 | ||||||||
\(796\) | −14309.4 | −0.637167 | ||||||||
\(797\) | 4749.47 | 0.211085 | 0.105543 | − | 0.994415i | \(-0.466342\pi\) | ||||
0.105543 | + | 0.994415i | \(0.466342\pi\) | |||||||
\(798\) | 10485.4 | 0.465138 | ||||||||
\(799\) | −5757.99 | −0.254947 | ||||||||
\(800\) | 14467.6 | 0.639386 | ||||||||
\(801\) | −8325.41 | −0.367246 | ||||||||
\(802\) | 52266.1 | 2.30122 | ||||||||
\(803\) | −15781.8 | −0.693560 | ||||||||
\(804\) | 6219.33 | 0.272809 | ||||||||
\(805\) | 8029.53 | 0.351557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10069.2 | 0.439223 | ||||||||
\(808\) | −3953.40 | −0.172129 | ||||||||
\(809\) | −4464.04 | −0.194002 | −0.0970009 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0970009 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(810\) | −4489.37 | −0.194741 | ||||||||
\(811\) | −20774.6 | −0.899499 | −0.449749 | − | 0.893155i | \(-0.648487\pi\) | ||||
−0.449749 | + | 0.893155i | \(0.648487\pi\) | |||||||
\(812\) | 43582.2 | 1.88354 | ||||||||
\(813\) | −26746.6 | −1.15381 | ||||||||
\(814\) | −7265.13 | −0.312829 | ||||||||
\(815\) | 49444.3 | 2.12510 | ||||||||
\(816\) | −7118.34 | −0.305382 | ||||||||
\(817\) | −9229.73 | −0.395235 | ||||||||
\(818\) | −6323.51 | −0.270289 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5787.55 | 0.246476 | ||||||||
\(821\) | 35769.2 | 1.52053 | 0.760264 | − | 0.649614i | \(-0.225070\pi\) | ||||
0.760264 | + | 0.649614i | \(0.225070\pi\) | |||||||
\(822\) | −22644.5 | −0.960848 | ||||||||
\(823\) | 2945.44 | 0.124753 | 0.0623764 | − | 0.998053i | \(-0.480132\pi\) | ||||
0.0623764 | + | 0.998053i | \(0.480132\pi\) | |||||||
\(824\) | −2618.80 | −0.110716 | ||||||||
\(825\) | −6766.56 | −0.285553 | ||||||||
\(826\) | 76509.6 | 3.22289 | ||||||||
\(827\) | 17878.6 | 0.751753 | 0.375877 | − | 0.926670i | \(-0.377342\pi\) | ||||
0.375877 | + | 0.926670i | \(0.377342\pi\) | |||||||
\(828\) | −1539.81 | −0.0646281 | ||||||||
\(829\) | 13423.8 | 0.562398 | 0.281199 | − | 0.959649i | \(-0.409268\pi\) | ||||
0.281199 | + | 0.959649i | \(0.409268\pi\) | |||||||
\(830\) | 72065.0 | 3.01375 | ||||||||
\(831\) | −12051.9 | −0.503101 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27797.5 | −1.15621 | ||||||||
\(834\) | −1236.93 | −0.0513566 | ||||||||
\(835\) | −43326.2 | −1.79565 | ||||||||
\(836\) | −9832.53 | −0.406776 | ||||||||
\(837\) | −8323.30 | −0.343722 | ||||||||
\(838\) | 8930.21 | 0.368125 | ||||||||
\(839\) | 31542.7 | 1.29794 | 0.648971 | − | 0.760813i | \(-0.275200\pi\) | ||||
0.648971 | + | 0.760813i | \(0.275200\pi\) | |||||||
\(840\) | −5224.61 | −0.214602 | ||||||||
\(841\) | −638.669 | −0.0261867 | ||||||||
\(842\) | −3028.73 | −0.123963 | ||||||||
\(843\) | −5523.35 | −0.225663 | ||||||||
\(844\) | −16855.7 | −0.687437 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4952.71 | −0.201274 | ||||||||
\(847\) | −9707.47 | −0.393805 | ||||||||
\(848\) | 24115.0 | 0.976547 | ||||||||
\(849\) | −14548.2 | −0.588095 | ||||||||
\(850\) | 9907.22 | 0.399782 | ||||||||
\(851\) | −827.155 | −0.0333191 | ||||||||
\(852\) | −12134.1 | −0.487920 | ||||||||
\(853\) | −21810.6 | −0.875476 | −0.437738 | − | 0.899103i | \(-0.644220\pi\) | ||||
−0.437738 | + | 0.899103i | \(0.644220\pi\) | |||||||
\(854\) | −70129.1 | −2.81003 | ||||||||
\(855\) | −3263.82 | −0.130550 | ||||||||
\(856\) | 5971.59 | 0.238440 | ||||||||
\(857\) | 33234.6 | 1.32470 | 0.662352 | − | 0.749193i | \(-0.269558\pi\) | ||||
0.662352 | + | 0.749193i | \(0.269558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42697.7 | 1.69596 | 0.847978 | − | 0.530032i | \(-0.177820\pi\) | ||||
0.847978 | + | 0.530032i | \(0.177820\pi\) | |||||||
\(860\) | 41390.3 | 1.64116 | ||||||||
\(861\) | 4509.52 | 0.178495 | ||||||||
\(862\) | 56525.0 | 2.23347 | ||||||||
\(863\) | 27419.2 | 1.08153 | 0.540765 | − | 0.841174i | \(-0.318135\pi\) | ||||
0.540765 | + | 0.841174i | \(0.318135\pi\) | |||||||
\(864\) | −7013.40 | −0.276158 | ||||||||
\(865\) | −36153.8 | −1.42112 | ||||||||
\(866\) | −41437.0 | −1.62596 | ||||||||
\(867\) | 9155.45 | 0.358634 | ||||||||
\(868\) | −87177.9 | −3.40900 | ||||||||
\(869\) | −36358.3 | −1.41930 | ||||||||
\(870\) | −25624.5 | −0.998567 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1365.09 | 0.0530137 | ||||||||
\(873\) | −14044.4 | −0.544482 | ||||||||
\(874\) | −2114.54 | −0.0818367 | ||||||||
\(875\) | 29272.4 | 1.13096 | ||||||||
\(876\) | 10522.2 | 0.405836 | ||||||||
\(877\) | 42604.2 | 1.64041 | 0.820206 | − | 0.572068i | \(-0.193859\pi\) | ||||
0.820206 | + | 0.572068i | \(0.193859\pi\) | |||||||
\(878\) | 33535.2 | 1.28902 | ||||||||
\(879\) | 4241.56 | 0.162758 | ||||||||
\(880\) | −29940.0 | −1.14691 | ||||||||
\(881\) | −4699.40 | −0.179712 | −0.0898562 | − | 0.995955i | \(-0.528641\pi\) | ||||
−0.0898562 | + | 0.995955i | \(0.528641\pi\) | |||||||
\(882\) | −23909.9 | −0.912799 | ||||||||
\(883\) | 22233.5 | 0.847358 | 0.423679 | − | 0.905812i | \(-0.360738\pi\) | ||||
0.423679 | + | 0.905812i | \(0.360738\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23815.3 | −0.904568 | ||||||||
\(886\) | 9774.98 | 0.370651 | ||||||||
\(887\) | −8852.46 | −0.335103 | −0.167552 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167552 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(888\) | 538.209 | 0.0203391 | ||||||||
\(889\) | −7766.05 | −0.292986 | ||||||||
\(890\) | 51270.0 | 1.93098 | ||||||||
\(891\) | 3280.19 | 0.123334 | ||||||||
\(892\) | −505.155 | −0.0189617 | ||||||||
\(893\) | −3600.68 | −0.134930 | ||||||||
\(894\) | 1849.92 | 0.0692063 | ||||||||
\(895\) | −20486.7 | −0.765135 | ||||||||
\(896\) | −16453.6 | −0.613477 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −53283.7 | −1.98007 | ||||||||
\(899\) | −47508.0 | −1.76249 | ||||||||
\(900\) | 4511.47 | 0.167091 | ||||||||
\(901\) | 18915.5 | 0.699410 | ||||||||
\(902\) | −7987.58 | −0.294853 | ||||||||
\(903\) | 32250.3 | 1.18851 | ||||||||
\(904\) | −2866.40 | −0.105459 | ||||||||
\(905\) | 6410.41 | 0.235458 | ||||||||
\(906\) | −9895.85 | −0.362878 | ||||||||
\(907\) | 37172.4 | 1.36085 | 0.680424 | − | 0.732818i | \(-0.261795\pi\) | ||||
0.680424 | + | 0.732818i | \(0.261795\pi\) | |||||||
\(908\) | −6006.51 | −0.219530 | ||||||||
\(909\) | 8629.56 | 0.314878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38035.1 | 1.38327 | 0.691635 | − | 0.722247i | \(-0.256891\pi\) | ||||
0.691635 | + | 0.722247i | \(0.256891\pi\) | |||||||
\(912\) | −4451.36 | −0.161622 | ||||||||
\(913\) | −52654.8 | −1.90867 | ||||||||
\(914\) | −34639.3 | −1.25357 | ||||||||
\(915\) | 21829.2 | 0.788691 | ||||||||
\(916\) | 6509.70 | 0.234810 | ||||||||
\(917\) | −14838.8 | −0.534372 | ||||||||
\(918\) | −4802.67 | −0.172671 | ||||||||
\(919\) | −8352.27 | −0.299800 | −0.149900 | − | 0.988701i | \(-0.547895\pi\) | ||||
−0.149900 | + | 0.988701i | \(0.547895\pi\) | |||||||
\(920\) | 1053.62 | 0.0377573 | ||||||||
\(921\) | 13876.9 | 0.496482 | ||||||||
\(922\) | −72679.4 | −2.59606 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 34356.6 | 1.22321 | ||||||||
\(925\) | 2423.47 | 0.0861440 | ||||||||
\(926\) | 22519.6 | 0.799179 | ||||||||
\(927\) | 5716.38 | 0.202535 | ||||||||
\(928\) | −40031.3 | −1.41605 | ||||||||
\(929\) | 20232.1 | 0.714524 | 0.357262 | − | 0.934004i | \(-0.383710\pi\) | ||||
0.357262 | + | 0.934004i | \(0.383710\pi\) | |||||||
\(930\) | 51257.0 | 1.80729 | ||||||||
\(931\) | −17382.8 | −0.611921 | ||||||||
\(932\) | −2479.06 | −0.0871292 | ||||||||
\(933\) | 18182.4 | 0.638011 | ||||||||
\(934\) | −34065.9 | −1.19344 | ||||||||
\(935\) | −23484.7 | −0.821423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27766.9 | −0.968095 | −0.484048 | − | 0.875042i | \(-0.660834\pi\) | ||||
−0.484048 | + | 0.875042i | \(0.660834\pi\) | |||||||
\(938\) | −29842.6 | −1.03880 | ||||||||
\(939\) | −2909.84 | −0.101128 | ||||||||
\(940\) | 16147.1 | 0.560277 | ||||||||
\(941\) | −400.765 | −0.0138837 | −0.00694185 | − | 0.999976i | \(-0.502210\pi\) | ||||
−0.00694185 | + | 0.999976i | \(0.502210\pi\) | |||||||
\(942\) | −33473.3 | −1.15777 | ||||||||
\(943\) | −909.408 | −0.0314045 | ||||||||
\(944\) | −32480.4 | −1.11986 | ||||||||
\(945\) | 11404.4 | 0.392576 | ||||||||
\(946\) | −57124.0 | −1.96328 | ||||||||
\(947\) | 21804.4 | 0.748201 | 0.374101 | − | 0.927388i | \(-0.377951\pi\) | ||||
0.374101 | + | 0.927388i | \(0.377951\pi\) | |||||||
\(948\) | 24241.1 | 0.830502 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6195.35 | 0.211583 | ||||||||
\(951\) | −26224.9 | −0.894217 | ||||||||
\(952\) | −5589.22 | −0.190281 | ||||||||
\(953\) | 30480.4 | 1.03605 | 0.518026 | − | 0.855365i | \(-0.326667\pi\) | ||||
0.518026 | + | 0.855365i | \(0.326667\pi\) | |||||||
\(954\) | 16270.1 | 0.552165 | ||||||||
\(955\) | −18412.6 | −0.623892 | ||||||||
\(956\) | −13764.5 | −0.465666 | ||||||||
\(957\) | 18722.8 | 0.632415 | ||||||||
\(958\) | 6497.48 | 0.219127 | ||||||||
\(959\) | 57524.0 | 1.93696 | ||||||||
\(960\) | 25446.4 | 0.855499 | ||||||||
\(961\) | 65239.6 | 2.18991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13034.9 | −0.436183 | ||||||||
\(964\) | 8779.73 | 0.293336 | ||||||||
\(965\) | −28830.1 | −0.961734 | ||||||||
\(966\) | 7388.56 | 0.246090 | ||||||||
\(967\) | 23864.1 | 0.793608 | 0.396804 | − | 0.917903i | \(-0.370119\pi\) | ||||
0.396804 | + | 0.917903i | \(0.370119\pi\) | |||||||
\(968\) | −1273.79 | −0.0422947 | ||||||||
\(969\) | −3491.60 | −0.115755 | ||||||||
\(970\) | 86489.2 | 2.86289 | ||||||||
\(971\) | −14010.3 | −0.463040 | −0.231520 | − | 0.972830i | \(-0.574370\pi\) | ||||
−0.231520 | + | 0.972830i | \(0.574370\pi\) | |||||||
\(972\) | −2187.00 | −0.0721688 | ||||||||
\(973\) | 3142.19 | 0.103529 | ||||||||
\(974\) | 51933.3 | 1.70847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29771.7 | 0.976404 | ||||||||
\(977\) | −25448.2 | −0.833326 | −0.416663 | − | 0.909061i | \(-0.636800\pi\) | ||||
−0.416663 | + | 0.909061i | \(0.636800\pi\) | |||||||
\(978\) | 45497.4 | 1.48757 | ||||||||
\(979\) | −37460.8 | −1.22293 | ||||||||
\(980\) | 77952.4 | 2.54092 | ||||||||
\(981\) | −2979.76 | −0.0969789 | ||||||||
\(982\) | 4416.72 | 0.143527 | ||||||||
\(983\) | 52479.9 | 1.70280 | 0.851399 | − | 0.524519i | \(-0.175755\pi\) | ||||
0.851399 | + | 0.524519i | \(0.175755\pi\) | |||||||
\(984\) | 591.729 | 0.0191703 | ||||||||
\(985\) | −3222.66 | −0.104246 | ||||||||
\(986\) | −27412.8 | −0.885398 | ||||||||
\(987\) | 12581.4 | 0.405746 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6503.73 | −0.209107 | ||||||||
\(990\) | −20200.2 | −0.648491 | ||||||||
\(991\) | 38048.5 | 1.21963 | 0.609814 | − | 0.792545i | \(-0.291244\pi\) | ||||
0.609814 | + | 0.792545i | \(0.291244\pi\) | |||||||
\(992\) | 80075.0 | 2.56289 | ||||||||
\(993\) | −20963.3 | −0.669939 | ||||||||
\(994\) | 58223.9 | 1.85790 | ||||||||
\(995\) | −21372.5 | −0.680960 | ||||||||
\(996\) | 35106.5 | 1.11686 | ||||||||
\(997\) | −31236.6 | −0.992251 | −0.496125 | − | 0.868251i | \(-0.665244\pi\) | ||||
−0.496125 | + | 0.868251i | \(0.665244\pi\) | |||||||
\(998\) | 5864.30 | 0.186003 | ||||||||
\(999\) | −1174.81 | −0.0372066 |
(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 | 507.4.a.k.1.2 | 4 | ||
3.2 | odd | 2 | 1521.4.a.z.1.3 | 4 | |||
13.2 | odd | 12 | 39.4.j.b.4.1 | ✓ | 4 | ||
13.5 | odd | 4 | 507.4.b.e.337.3 | 4 | |||
13.7 | odd | 12 | 39.4.j.b.10.1 | yes | 4 | ||
13.8 | odd | 4 | 507.4.b.e.337.2 | 4 | |||
13.12 | even | 2 | inner | 507.4.a.k.1.3 | 4 | ||
39.2 | even | 12 | 117.4.q.d.82.2 | 4 | |||
39.20 | even | 12 | 117.4.q.d.10.2 | 4 | |||
39.38 | odd | 2 | 1521.4.a.z.1.2 | 4 | |||
52.7 | even | 12 | 624.4.bv.c.49.2 | 4 | |||
52.15 | even | 12 | 624.4.bv.c.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.b.4.1 | ✓ | 4 | 13.2 | odd | 12 | ||
39.4.j.b.10.1 | yes | 4 | 13.7 | odd | 12 | ||
117.4.q.d.10.2 | 4 | 39.20 | even | 12 | |||
117.4.q.d.82.2 | 4 | 39.2 | even | 12 | |||
507.4.a.k.1.2 | 4 | 1.1 | even | 1 | trivial | ||
507.4.a.k.1.3 | 4 | 13.12 | even | 2 | inner | ||
507.4.b.e.337.2 | 4 | 13.8 | odd | 4 | |||
507.4.b.e.337.3 | 4 | 13.5 | odd | 4 | |||
624.4.bv.c.49.2 | 4 | 52.7 | even | 12 | |||
624.4.bv.c.433.1 | 4 | 52.15 | even | 12 | |||
1521.4.a.z.1.2 | 4 | 39.38 | odd | 2 | |||
1521.4.a.z.1.3 | 4 | 3.2 | odd | 2 |