Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,4,Mod(1,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, 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("725.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.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: | \(42.7763847542\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.328194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24125 | −0.792400 | −0.396200 | − | 0.918164i | \(-0.629671\pi\) | ||||
−0.396200 | + | 0.918164i | \(0.629671\pi\) | |||||||
\(3\) | −1.84328 | −0.354739 | −0.177369 | − | 0.984144i | \(-0.556759\pi\) | ||||
−0.177369 | + | 0.984144i | \(0.556759\pi\) | |||||||
\(4\) | −2.97681 | −0.372101 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.13124 | 0.281095 | ||||||||
\(7\) | 16.8583 | 0.910262 | 0.455131 | − | 0.890425i | \(-0.349592\pi\) | ||||
0.455131 | + | 0.890425i | \(0.349592\pi\) | |||||||
\(8\) | 24.6017 | 1.08725 | ||||||||
\(9\) | −23.6023 | −0.874160 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 52.4385 | 1.43735 | 0.718673 | − | 0.695348i | \(-0.244750\pi\) | ||||
0.718673 | + | 0.695348i | \(0.244750\pi\) | |||||||
\(12\) | 5.48709 | 0.131999 | ||||||||
\(13\) | 87.5580 | 1.86802 | 0.934008 | − | 0.357252i | \(-0.116286\pi\) | ||||
0.934008 | + | 0.357252i | \(0.116286\pi\) | |||||||
\(14\) | −37.7836 | −0.721292 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.3241 | −0.489439 | ||||||||
\(17\) | −15.4072 | −0.219812 | −0.109906 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109906 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(18\) | 52.8987 | 0.692685 | ||||||||
\(19\) | 67.0156 | 0.809181 | 0.404591 | − | 0.914498i | \(-0.367414\pi\) | ||||
0.404591 | + | 0.914498i | \(0.367414\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −31.0745 | −0.322905 | ||||||||
\(22\) | −117.528 | −1.13895 | ||||||||
\(23\) | −132.679 | −1.20285 | −0.601423 | − | 0.798931i | \(-0.705399\pi\) | ||||
−0.601423 | + | 0.798931i | \(0.705399\pi\) | |||||||
\(24\) | −45.3478 | −0.385691 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −196.239 | −1.48022 | ||||||||
\(27\) | 93.2741 | 0.664837 | ||||||||
\(28\) | −50.1839 | −0.338710 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 90.2221 | 0.522721 | 0.261361 | − | 0.965241i | \(-0.415829\pi\) | ||||
0.261361 | + | 0.965241i | \(0.415829\pi\) | |||||||
\(32\) | −126.609 | −0.699422 | ||||||||
\(33\) | −96.6587 | −0.509882 | ||||||||
\(34\) | 34.5314 | 0.174179 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 70.2597 | 0.325276 | ||||||||
\(37\) | −11.1247 | −0.0494296 | −0.0247148 | − | 0.999695i | \(-0.507868\pi\) | ||||
−0.0247148 | + | 0.999695i | \(0.507868\pi\) | |||||||
\(38\) | −150.199 | −0.641196 | ||||||||
\(39\) | −161.394 | −0.662658 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.8392 | −0.0717608 | −0.0358804 | − | 0.999356i | \(-0.511424\pi\) | ||||
−0.0358804 | + | 0.999356i | \(0.511424\pi\) | |||||||
\(42\) | 69.6456 | 0.255870 | ||||||||
\(43\) | 147.756 | 0.524013 | 0.262007 | − | 0.965066i | \(-0.415616\pi\) | ||||
0.262007 | + | 0.965066i | \(0.415616\pi\) | |||||||
\(44\) | −156.100 | −0.534839 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 297.366 | 0.953136 | ||||||||
\(47\) | −21.0963 | −0.0654726 | −0.0327363 | − | 0.999464i | \(-0.510422\pi\) | ||||
−0.0327363 | + | 0.999464i | \(0.510422\pi\) | |||||||
\(48\) | 57.7390 | 0.173623 | ||||||||
\(49\) | −58.7983 | −0.171424 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.3997 | 0.0779757 | ||||||||
\(52\) | −260.644 | −0.695092 | ||||||||
\(53\) | 290.454 | 0.752772 | 0.376386 | − | 0.926463i | \(-0.377167\pi\) | ||||
0.376386 | + | 0.926463i | \(0.377167\pi\) | |||||||
\(54\) | −209.050 | −0.526817 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 414.743 | 0.989686 | ||||||||
\(57\) | −123.528 | −0.287048 | ||||||||
\(58\) | 64.9962 | 0.147145 | ||||||||
\(59\) | −337.343 | −0.744379 | −0.372190 | − | 0.928157i | \(-0.621393\pi\) | ||||
−0.372190 | + | 0.928157i | \(0.621393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 84.0147 | 0.176344 | 0.0881720 | − | 0.996105i | \(-0.471897\pi\) | ||||
0.0881720 | + | 0.996105i | \(0.471897\pi\) | |||||||
\(62\) | −202.210 | −0.414205 | ||||||||
\(63\) | −397.895 | −0.795715 | ||||||||
\(64\) | 534.355 | 1.04366 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 216.636 | 0.404031 | ||||||||
\(67\) | −330.821 | −0.603228 | −0.301614 | − | 0.953430i | \(-0.597525\pi\) | ||||
−0.301614 | + | 0.953430i | \(0.597525\pi\) | |||||||
\(68\) | 45.8644 | 0.0817922 | ||||||||
\(69\) | 244.564 | 0.426696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 492.420 | 0.823092 | 0.411546 | − | 0.911389i | \(-0.364989\pi\) | ||||
0.411546 | + | 0.911389i | \(0.364989\pi\) | |||||||
\(72\) | −580.659 | −0.950434 | ||||||||
\(73\) | 347.053 | 0.556431 | 0.278216 | − | 0.960519i | \(-0.410257\pi\) | ||||
0.278216 | + | 0.960519i | \(0.410257\pi\) | |||||||
\(74\) | 24.9333 | 0.0391681 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −199.493 | −0.301098 | ||||||||
\(77\) | 884.023 | 1.30836 | ||||||||
\(78\) | 361.723 | 0.525090 | ||||||||
\(79\) | −986.297 | −1.40465 | −0.702324 | − | 0.711858i | \(-0.747854\pi\) | ||||
−0.702324 | + | 0.711858i | \(0.747854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 465.333 | 0.638317 | ||||||||
\(82\) | 42.2234 | 0.0568633 | ||||||||
\(83\) | −594.382 | −0.786048 | −0.393024 | − | 0.919528i | \(-0.628571\pi\) | ||||
−0.393024 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(84\) | 92.5029 | 0.120153 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −331.157 | −0.415228 | ||||||||
\(87\) | 53.4550 | 0.0658733 | ||||||||
\(88\) | 1290.08 | 1.56276 | ||||||||
\(89\) | 1387.04 | 1.65197 | 0.825987 | − | 0.563689i | \(-0.190618\pi\) | ||||
0.825987 | + | 0.563689i | \(0.190618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1476.08 | 1.70038 | ||||||||
\(92\) | 394.960 | 0.447581 | ||||||||
\(93\) | −166.304 | −0.185430 | ||||||||
\(94\) | 47.2820 | 0.0518805 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 233.375 | 0.248112 | ||||||||
\(97\) | 334.003 | 0.349617 | 0.174808 | − | 0.984602i | \(-0.444069\pi\) | ||||
0.174808 | + | 0.984602i | \(0.444069\pi\) | |||||||
\(98\) | 131.781 | 0.135836 | ||||||||
\(99\) | −1237.67 | −1.25647 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −245.919 | −0.242276 | −0.121138 | − | 0.992636i | \(-0.538654\pi\) | ||||
−0.121138 | + | 0.992636i | \(0.538654\pi\) | |||||||
\(102\) | −63.6508 | −0.0617880 | ||||||||
\(103\) | 531.298 | 0.508255 | 0.254128 | − | 0.967171i | \(-0.418212\pi\) | ||||
0.254128 | + | 0.967171i | \(0.418212\pi\) | |||||||
\(104\) | 2154.08 | 2.03101 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −650.979 | −0.596497 | ||||||||
\(107\) | 429.030 | 0.387625 | 0.193812 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193812 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(108\) | −277.659 | −0.247387 | ||||||||
\(109\) | −967.263 | −0.849972 | −0.424986 | − | 0.905200i | \(-0.639721\pi\) | ||||
−0.424986 | + | 0.905200i | \(0.639721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.5060 | 0.0175346 | ||||||||
\(112\) | −528.070 | −0.445518 | ||||||||
\(113\) | 1705.23 | 1.41960 | 0.709798 | − | 0.704405i | \(-0.248786\pi\) | ||||
0.709798 | + | 0.704405i | \(0.248786\pi\) | |||||||
\(114\) | 276.858 | 0.227457 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 86.3275 | 0.0690975 | ||||||||
\(117\) | −2066.57 | −1.63295 | ||||||||
\(118\) | 756.070 | 0.589846 | ||||||||
\(119\) | −259.739 | −0.200086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1418.80 | 1.06596 | ||||||||
\(122\) | −188.298 | −0.139735 | ||||||||
\(123\) | 34.7259 | 0.0254563 | ||||||||
\(124\) | −268.574 | −0.194505 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 891.781 | 0.630525 | ||||||||
\(127\) | 2670.28 | 1.86574 | 0.932870 | − | 0.360213i | \(-0.117296\pi\) | ||||
0.932870 | + | 0.360213i | \(0.117296\pi\) | |||||||
\(128\) | −184.749 | −0.127576 | ||||||||
\(129\) | −272.355 | −0.185888 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 879.993 | 0.586911 | 0.293455 | − | 0.955973i | \(-0.405195\pi\) | ||||
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(132\) | 287.735 | 0.189728 | ||||||||
\(133\) | 1129.77 | 0.736567 | ||||||||
\(134\) | 741.452 | 0.477998 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −379.044 | −0.238991 | ||||||||
\(137\) | −2064.15 | −1.28724 | −0.643620 | − | 0.765345i | \(-0.722568\pi\) | ||||
−0.643620 | + | 0.765345i | \(0.722568\pi\) | |||||||
\(138\) | −548.128 | −0.338114 | ||||||||
\(139\) | 605.130 | 0.369255 | 0.184628 | − | 0.982809i | \(-0.440892\pi\) | ||||
0.184628 | + | 0.982809i | \(0.440892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 38.8863 | 0.0232257 | ||||||||
\(142\) | −1103.63 | −0.652218 | ||||||||
\(143\) | 4591.41 | 2.68499 | ||||||||
\(144\) | 739.322 | 0.427848 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −777.832 | −0.440917 | ||||||||
\(147\) | 108.381 | 0.0608106 | ||||||||
\(148\) | 33.1163 | 0.0183928 | ||||||||
\(149\) | −775.322 | −0.426287 | −0.213144 | − | 0.977021i | \(-0.568370\pi\) | ||||
−0.213144 | + | 0.977021i | \(0.568370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 427.925 | 0.230623 | 0.115311 | − | 0.993329i | \(-0.463213\pi\) | ||||
0.115311 | + | 0.993329i | \(0.463213\pi\) | |||||||
\(152\) | 1648.70 | 0.879785 | ||||||||
\(153\) | 363.646 | 0.192151 | ||||||||
\(154\) | −1981.31 | −1.03675 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 480.438 | 0.246576 | ||||||||
\(157\) | 1680.93 | 0.854474 | 0.427237 | − | 0.904140i | \(-0.359487\pi\) | ||||
0.427237 | + | 0.904140i | \(0.359487\pi\) | |||||||
\(158\) | 2210.54 | 1.11304 | ||||||||
\(159\) | −535.387 | −0.267037 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2236.74 | −1.09490 | ||||||||
\(162\) | −1042.93 | −0.505803 | ||||||||
\(163\) | −2038.68 | −0.979645 | −0.489822 | − | 0.871822i | \(-0.662938\pi\) | ||||
−0.489822 | + | 0.871822i | \(0.662938\pi\) | |||||||
\(164\) | 56.0808 | 0.0267023 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1332.16 | 0.622865 | ||||||||
\(167\) | −2543.12 | −1.17840 | −0.589199 | − | 0.807988i | \(-0.700557\pi\) | ||||
−0.589199 | + | 0.807988i | \(0.700557\pi\) | |||||||
\(168\) | −764.486 | −0.351080 | ||||||||
\(169\) | 5469.40 | 2.48949 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1581.73 | −0.707354 | ||||||||
\(172\) | −439.842 | −0.194986 | ||||||||
\(173\) | 306.031 | 0.134492 | 0.0672460 | − | 0.997736i | \(-0.478579\pi\) | ||||
0.0672460 | + | 0.997736i | \(0.478579\pi\) | |||||||
\(174\) | −119.806 | −0.0521981 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1642.59 | −0.703493 | ||||||||
\(177\) | 621.817 | 0.264060 | ||||||||
\(178\) | −3108.69 | −1.30903 | ||||||||
\(179\) | −478.797 | −0.199927 | −0.0999635 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999635 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −478.433 | −0.196473 | −0.0982367 | − | 0.995163i | \(-0.531320\pi\) | ||||
−0.0982367 | + | 0.995163i | \(0.531320\pi\) | |||||||
\(182\) | −3308.25 | −1.34739 | ||||||||
\(183\) | −154.862 | −0.0625560 | ||||||||
\(184\) | −3264.13 | −1.30780 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 372.729 | 0.146934 | ||||||||
\(187\) | −807.931 | −0.315945 | ||||||||
\(188\) | 62.7998 | 0.0243625 | ||||||||
\(189\) | 1572.44 | 0.605176 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 833.106 | 0.315610 | 0.157805 | − | 0.987470i | \(-0.449558\pi\) | ||||
0.157805 | + | 0.987470i | \(0.449558\pi\) | |||||||
\(192\) | −984.963 | −0.370227 | ||||||||
\(193\) | 1449.88 | 0.540751 | 0.270376 | − | 0.962755i | \(-0.412852\pi\) | ||||
0.270376 | + | 0.962755i | \(0.412852\pi\) | |||||||
\(194\) | −748.582 | −0.277037 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 175.031 | 0.0637870 | ||||||||
\(197\) | 1993.27 | 0.720886 | 0.360443 | − | 0.932781i | \(-0.382626\pi\) | ||||
0.360443 | + | 0.932781i | \(0.382626\pi\) | |||||||
\(198\) | 2773.93 | 0.995628 | ||||||||
\(199\) | −356.359 | −0.126943 | −0.0634714 | − | 0.997984i | \(-0.520217\pi\) | ||||
−0.0634714 | + | 0.997984i | \(0.520217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 609.795 | 0.213988 | ||||||||
\(202\) | 551.165 | 0.191979 | ||||||||
\(203\) | −488.890 | −0.169031 | ||||||||
\(204\) | −84.5407 | −0.0290149 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1190.77 | −0.402742 | ||||||||
\(207\) | 3131.53 | 1.05148 | ||||||||
\(208\) | −2742.67 | −0.914280 | ||||||||
\(209\) | 3514.20 | 1.16307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4131.66 | 1.34803 | 0.674017 | − | 0.738716i | \(-0.264567\pi\) | ||||
0.674017 | + | 0.738716i | \(0.264567\pi\) | |||||||
\(212\) | −864.626 | −0.280107 | ||||||||
\(213\) | −907.666 | −0.291982 | ||||||||
\(214\) | −961.562 | −0.307154 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2294.71 | 0.722847 | ||||||||
\(217\) | 1520.99 | 0.475813 | ||||||||
\(218\) | 2167.87 | 0.673518 | ||||||||
\(219\) | −639.715 | −0.197388 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1349.02 | −0.410612 | ||||||||
\(222\) | −45.9590 | −0.0138944 | ||||||||
\(223\) | −1332.32 | −0.400086 | −0.200043 | − | 0.979787i | \(-0.564108\pi\) | ||||
−0.200043 | + | 0.979787i | \(0.564108\pi\) | |||||||
\(224\) | −2134.41 | −0.636657 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3821.84 | −1.12489 | ||||||||
\(227\) | 1329.33 | 0.388681 | 0.194340 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194340 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(228\) | 367.721 | 0.106811 | ||||||||
\(229\) | 5455.47 | 1.57427 | 0.787135 | − | 0.616780i | \(-0.211563\pi\) | ||||
0.787135 | + | 0.616780i | \(0.211563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1629.50 | −0.464126 | ||||||||
\(232\) | −713.451 | −0.201898 | ||||||||
\(233\) | 591.158 | 0.166215 | 0.0831075 | − | 0.996541i | \(-0.473516\pi\) | ||||
0.0831075 | + | 0.996541i | \(0.473516\pi\) | |||||||
\(234\) | 4631.70 | 1.29395 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1004.21 | 0.276985 | ||||||||
\(237\) | 1818.02 | 0.498283 | ||||||||
\(238\) | 582.139 | 0.158548 | ||||||||
\(239\) | 6946.01 | 1.87992 | 0.939959 | − | 0.341289i | \(-0.110863\pi\) | ||||
0.939959 | + | 0.341289i | \(0.110863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7105.62 | 1.89923 | 0.949613 | − | 0.313426i | \(-0.101477\pi\) | ||||
0.949613 | + | 0.313426i | \(0.101477\pi\) | |||||||
\(242\) | −3179.88 | −0.844670 | ||||||||
\(243\) | −3376.14 | −0.891273 | ||||||||
\(244\) | −250.096 | −0.0656179 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −77.8293 | −0.0201716 | ||||||||
\(247\) | 5867.75 | 1.51156 | ||||||||
\(248\) | 2219.62 | 0.568331 | ||||||||
\(249\) | 1095.61 | 0.278842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4874.53 | −1.22581 | −0.612904 | − | 0.790158i | \(-0.709999\pi\) | ||||
−0.612904 | + | 0.790158i | \(0.709999\pi\) | |||||||
\(252\) | 1184.46 | 0.296087 | ||||||||
\(253\) | −6957.49 | −1.72891 | ||||||||
\(254\) | −5984.75 | −1.47841 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3860.77 | −0.942570 | ||||||||
\(257\) | −2488.22 | −0.603934 | −0.301967 | − | 0.953318i | \(-0.597643\pi\) | ||||
−0.301967 | + | 0.953318i | \(0.597643\pi\) | |||||||
\(258\) | 610.415 | 0.147298 | ||||||||
\(259\) | −187.544 | −0.0449939 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 684.468 | 0.162328 | ||||||||
\(262\) | −1972.28 | −0.465068 | ||||||||
\(263\) | 2812.52 | 0.659419 | 0.329709 | − | 0.944082i | \(-0.393049\pi\) | ||||
0.329709 | + | 0.944082i | \(0.393049\pi\) | |||||||
\(264\) | −2377.97 | −0.554372 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2532.09 | −0.583656 | ||||||||
\(267\) | −2556.69 | −0.586019 | ||||||||
\(268\) | 984.793 | 0.224462 | ||||||||
\(269\) | −5554.63 | −1.25900 | −0.629501 | − | 0.777000i | \(-0.716741\pi\) | ||||
−0.629501 | + | 0.777000i | \(0.716741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3168.41 | −0.710211 | −0.355105 | − | 0.934826i | \(-0.615555\pi\) | ||||
−0.355105 | + | 0.934826i | \(0.615555\pi\) | |||||||
\(272\) | 482.617 | 0.107584 | ||||||||
\(273\) | −2720.82 | −0.603192 | ||||||||
\(274\) | 4626.26 | 1.02001 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −728.021 | −0.158774 | ||||||||
\(277\) | −3965.64 | −0.860189 | −0.430095 | − | 0.902784i | \(-0.641520\pi\) | ||||
−0.430095 | + | 0.902784i | \(0.641520\pi\) | |||||||
\(278\) | −1356.25 | −0.292598 | ||||||||
\(279\) | −2129.45 | −0.456942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1655.16 | 0.351383 | 0.175692 | − | 0.984445i | \(-0.443784\pi\) | ||||
0.175692 | + | 0.984445i | \(0.443784\pi\) | |||||||
\(282\) | −87.1539 | −0.0184040 | ||||||||
\(283\) | −7786.09 | −1.63546 | −0.817730 | − | 0.575602i | \(-0.804768\pi\) | ||||
−0.817730 | + | 0.575602i | \(0.804768\pi\) | |||||||
\(284\) | −1465.84 | −0.306274 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10290.5 | −2.12758 | ||||||||
\(287\) | −317.597 | −0.0653211 | ||||||||
\(288\) | 2988.27 | 0.611407 | ||||||||
\(289\) | −4675.62 | −0.951683 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −615.659 | −0.124023 | ||||||||
\(292\) | −1033.11 | −0.207049 | ||||||||
\(293\) | −8090.80 | −1.61321 | −0.806603 | − | 0.591094i | \(-0.798696\pi\) | ||||
−0.806603 | + | 0.591094i | \(0.798696\pi\) | |||||||
\(294\) | −242.910 | −0.0481863 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −273.688 | −0.0537426 | ||||||||
\(297\) | 4891.16 | 0.955601 | ||||||||
\(298\) | 1737.69 | 0.337790 | ||||||||
\(299\) | −11617.1 | −2.24694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2490.91 | 0.476989 | ||||||||
\(302\) | −959.086 | −0.182746 | ||||||||
\(303\) | 453.297 | 0.0859446 | ||||||||
\(304\) | −2099.20 | −0.396045 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −815.020 | −0.152260 | ||||||||
\(307\) | 6129.49 | 1.13951 | 0.569753 | − | 0.821816i | \(-0.307039\pi\) | ||||
0.569753 | + | 0.821816i | \(0.307039\pi\) | |||||||
\(308\) | −2631.57 | −0.486843 | ||||||||
\(309\) | −979.328 | −0.180298 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8167.93 | −1.48926 | −0.744632 | − | 0.667476i | \(-0.767375\pi\) | ||||
−0.744632 | + | 0.667476i | \(0.767375\pi\) | |||||||
\(312\) | −3970.56 | −0.720477 | ||||||||
\(313\) | −1877.25 | −0.339005 | −0.169502 | − | 0.985530i | \(-0.554216\pi\) | ||||
−0.169502 | + | 0.985530i | \(0.554216\pi\) | |||||||
\(314\) | −3767.37 | −0.677086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2936.02 | 0.522671 | ||||||||
\(317\) | −1222.93 | −0.216677 | −0.108338 | − | 0.994114i | \(-0.534553\pi\) | ||||
−0.108338 | + | 0.994114i | \(0.534553\pi\) | |||||||
\(318\) | 1199.93 | 0.211600 | ||||||||
\(319\) | −1520.72 | −0.266908 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −790.820 | −0.137506 | ||||||||
\(322\) | 5013.08 | 0.867603 | ||||||||
\(323\) | −1032.52 | −0.177867 | ||||||||
\(324\) | −1385.21 | −0.237519 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4569.20 | 0.776271 | ||||||||
\(327\) | 1782.93 | 0.301518 | ||||||||
\(328\) | −463.478 | −0.0780222 | ||||||||
\(329\) | −355.648 | −0.0595972 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3769.03 | 0.625876 | 0.312938 | − | 0.949774i | \(-0.398687\pi\) | ||||
0.312938 | + | 0.949774i | \(0.398687\pi\) | |||||||
\(332\) | 1769.36 | 0.292489 | ||||||||
\(333\) | 262.570 | 0.0432094 | ||||||||
\(334\) | 5699.76 | 0.933763 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 973.380 | 0.158042 | ||||||||
\(337\) | 10900.2 | 1.76193 | 0.880967 | − | 0.473179i | \(-0.156893\pi\) | ||||
0.880967 | + | 0.473179i | \(0.156893\pi\) | |||||||
\(338\) | −12258.3 | −1.97267 | ||||||||
\(339\) | −3143.21 | −0.503586 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4731.11 | 0.751332 | ||||||||
\(342\) | 3545.04 | 0.560508 | ||||||||
\(343\) | −6773.63 | −1.06630 | ||||||||
\(344\) | 3635.05 | 0.569735 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −685.892 | −0.106572 | ||||||||
\(347\) | 8542.30 | 1.32154 | 0.660771 | − | 0.750588i | \(-0.270230\pi\) | ||||
0.660771 | + | 0.750588i | \(0.270230\pi\) | |||||||
\(348\) | −159.126 | −0.0245116 | ||||||||
\(349\) | −993.823 | −0.152430 | −0.0762151 | − | 0.997091i | \(-0.524284\pi\) | ||||
−0.0762151 | + | 0.997091i | \(0.524284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8166.89 | 1.24193 | ||||||||
\(352\) | −6639.19 | −1.00531 | ||||||||
\(353\) | −8191.10 | −1.23504 | −0.617519 | − | 0.786556i | \(-0.711862\pi\) | ||||
−0.617519 | + | 0.786556i | \(0.711862\pi\) | |||||||
\(354\) | −1393.65 | −0.209241 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4128.95 | −0.614702 | ||||||||
\(357\) | 478.771 | 0.0709783 | ||||||||
\(358\) | 1073.10 | 0.158422 | ||||||||
\(359\) | −4703.71 | −0.691510 | −0.345755 | − | 0.938325i | \(-0.612377\pi\) | ||||
−0.345755 | + | 0.938325i | \(0.612377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2367.90 | −0.345226 | ||||||||
\(362\) | 1072.29 | 0.155686 | ||||||||
\(363\) | −2615.24 | −0.378139 | ||||||||
\(364\) | −4394.00 | −0.632715 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 347.085 | 0.0495694 | ||||||||
\(367\) | −9431.88 | −1.34153 | −0.670763 | − | 0.741672i | \(-0.734033\pi\) | ||||
−0.670763 | + | 0.741672i | \(0.734033\pi\) | |||||||
\(368\) | 4156.05 | 0.588720 | ||||||||
\(369\) | 444.650 | 0.0627305 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4896.55 | 0.685219 | ||||||||
\(372\) | 495.056 | 0.0689986 | ||||||||
\(373\) | 8281.46 | 1.14959 | 0.574796 | − | 0.818297i | \(-0.305081\pi\) | ||||
0.574796 | + | 0.818297i | \(0.305081\pi\) | |||||||
\(374\) | 1810.77 | 0.250355 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −519.006 | −0.0711854 | ||||||||
\(377\) | −2539.18 | −0.346882 | ||||||||
\(378\) | −3524.23 | −0.479542 | ||||||||
\(379\) | 6875.50 | 0.931848 | 0.465924 | − | 0.884825i | \(-0.345722\pi\) | ||||
0.465924 | + | 0.884825i | \(0.345722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4922.06 | −0.661850 | ||||||||
\(382\) | −1867.20 | −0.250089 | ||||||||
\(383\) | 4826.61 | 0.643938 | 0.321969 | − | 0.946750i | \(-0.395655\pi\) | ||||
0.321969 | + | 0.946750i | \(0.395655\pi\) | |||||||
\(384\) | 340.544 | 0.0452560 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3249.55 | −0.428492 | ||||||||
\(387\) | −3487.38 | −0.458072 | ||||||||
\(388\) | −994.263 | −0.130093 | ||||||||
\(389\) | 4970.57 | 0.647861 | 0.323930 | − | 0.946081i | \(-0.394996\pi\) | ||||
0.323930 | + | 0.946081i | \(0.394996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2044.21 | 0.264400 | ||||||||
\(392\) | −1446.54 | −0.186381 | ||||||||
\(393\) | −1622.07 | −0.208200 | ||||||||
\(394\) | −4467.41 | −0.571230 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3684.31 | 0.467535 | ||||||||
\(397\) | 12288.8 | 1.55355 | 0.776774 | − | 0.629779i | \(-0.216855\pi\) | ||||
0.776774 | + | 0.629779i | \(0.216855\pi\) | |||||||
\(398\) | 798.689 | 0.100590 | ||||||||
\(399\) | −2082.48 | −0.261289 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11971.7 | −1.49086 | −0.745432 | − | 0.666581i | \(-0.767757\pi\) | ||||
−0.745432 | + | 0.666581i | \(0.767757\pi\) | |||||||
\(402\) | −1366.70 | −0.169564 | ||||||||
\(403\) | 7899.66 | 0.976452 | ||||||||
\(404\) | 732.055 | 0.0901512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1095.72 | 0.133941 | ||||||||
\(407\) | −583.365 | −0.0710475 | ||||||||
\(408\) | 698.683 | 0.0847794 | ||||||||
\(409\) | 11147.7 | 1.34772 | 0.673861 | − | 0.738858i | \(-0.264635\pi\) | ||||
0.673861 | + | 0.738858i | \(0.264635\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3804.79 | 0.456634 | ||||||||
\(412\) | −1581.57 | −0.189123 | ||||||||
\(413\) | −5687.03 | −0.677580 | ||||||||
\(414\) | −7018.54 | −0.833194 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11085.6 | −1.30653 | ||||||||
\(417\) | −1115.42 | −0.130989 | ||||||||
\(418\) | −7876.19 | −0.921620 | ||||||||
\(419\) | 11557.3 | 1.34752 | 0.673762 | − | 0.738949i | \(-0.264677\pi\) | ||||
0.673762 | + | 0.738949i | \(0.264677\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12874.4 | −1.49040 | −0.745201 | − | 0.666840i | \(-0.767647\pi\) | ||||
−0.745201 | + | 0.666840i | \(0.767647\pi\) | |||||||
\(422\) | −9260.07 | −1.06818 | ||||||||
\(423\) | 497.922 | 0.0572336 | ||||||||
\(424\) | 7145.67 | 0.818454 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2034.30 | 0.231367 | ||||||||
\(427\) | 1416.34 | 0.160519 | ||||||||
\(428\) | −1277.14 | −0.144236 | ||||||||
\(429\) | −8463.24 | −0.952469 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4088.31 | −0.456907 | −0.228454 | − | 0.973555i | \(-0.573367\pi\) | ||||
−0.228454 | + | 0.973555i | \(0.573367\pi\) | |||||||
\(432\) | −2921.73 | −0.325397 | ||||||||
\(433\) | 3865.90 | 0.429060 | 0.214530 | − | 0.976717i | \(-0.431178\pi\) | ||||
0.214530 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(434\) | −3408.91 | −0.377035 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2879.36 | 0.316276 | ||||||||
\(437\) | −8891.56 | −0.973320 | ||||||||
\(438\) | 1433.76 | 0.156410 | ||||||||
\(439\) | 10662.4 | 1.15920 | 0.579600 | − | 0.814901i | \(-0.303209\pi\) | ||||
0.579600 | + | 0.814901i | \(0.303209\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1387.78 | 0.149852 | ||||||||
\(442\) | 3023.50 | 0.325369 | ||||||||
\(443\) | −10288.9 | −1.10347 | −0.551736 | − | 0.834019i | \(-0.686034\pi\) | ||||
−0.551736 | + | 0.834019i | \(0.686034\pi\) | |||||||
\(444\) | −61.0424 | −0.00652465 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2986.07 | 0.317028 | ||||||||
\(447\) | 1429.13 | 0.151221 | ||||||||
\(448\) | 9008.30 | 0.950005 | ||||||||
\(449\) | 12426.2 | 1.30608 | 0.653041 | − | 0.757323i | \(-0.273493\pi\) | ||||
0.653041 | + | 0.757323i | \(0.273493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −987.901 | −0.103145 | ||||||||
\(452\) | −5076.14 | −0.528234 | ||||||||
\(453\) | −788.784 | −0.0818108 | ||||||||
\(454\) | −2979.35 | −0.307991 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3039.01 | −0.312094 | ||||||||
\(457\) | 10657.8 | 1.09092 | 0.545462 | − | 0.838136i | \(-0.316354\pi\) | ||||
0.545462 | + | 0.838136i | \(0.316354\pi\) | |||||||
\(458\) | −12227.1 | −1.24745 | ||||||||
\(459\) | −1437.09 | −0.146139 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9819.21 | 0.992031 | 0.496016 | − | 0.868314i | \(-0.334796\pi\) | ||||
0.496016 | + | 0.868314i | \(0.334796\pi\) | |||||||
\(462\) | 3652.11 | 0.367774 | ||||||||
\(463\) | 19210.5 | 1.92827 | 0.964135 | − | 0.265412i | \(-0.0855081\pi\) | ||||
0.964135 | + | 0.265412i | \(0.0855081\pi\) | |||||||
\(464\) | 908.399 | 0.0908865 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1324.93 | −0.131709 | ||||||||
\(467\) | 345.566 | 0.0342417 | 0.0171208 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171208 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(468\) | 6151.80 | 0.607622 | ||||||||
\(469\) | −5577.08 | −0.549095 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3098.41 | −0.303115 | ||||||||
\(472\) | −8299.24 | −0.809329 | ||||||||
\(473\) | 7748.10 | 0.753188 | ||||||||
\(474\) | −4074.63 | −0.394839 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 773.194 | 0.0744523 | ||||||||
\(477\) | −6855.39 | −0.658043 | ||||||||
\(478\) | −15567.7 | −1.48965 | ||||||||
\(479\) | −253.709 | −0.0242009 | −0.0121005 | − | 0.999927i | \(-0.503852\pi\) | ||||
−0.0121005 | + | 0.999927i | \(0.503852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −974.060 | −0.0923354 | ||||||||
\(482\) | −15925.5 | −1.50495 | ||||||||
\(483\) | 4122.93 | 0.388405 | ||||||||
\(484\) | −4223.50 | −0.396647 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7566.76 | 0.706245 | ||||||||
\(487\) | 13255.1 | 1.23336 | 0.616680 | − | 0.787214i | \(-0.288477\pi\) | ||||
0.616680 | + | 0.787214i | \(0.288477\pi\) | |||||||
\(488\) | 2066.91 | 0.191731 | ||||||||
\(489\) | 3757.86 | 0.347518 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6454.57 | −0.593260 | −0.296630 | − | 0.954993i | \(-0.595863\pi\) | ||||
−0.296630 | + | 0.954993i | \(0.595863\pi\) | |||||||
\(492\) | −103.372 | −0.00947234 | ||||||||
\(493\) | 446.809 | 0.0408180 | ||||||||
\(494\) | −13151.1 | −1.19776 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2826.12 | −0.255840 | ||||||||
\(497\) | 8301.36 | 0.749229 | ||||||||
\(498\) | −2455.54 | −0.220954 | ||||||||
\(499\) | 8090.41 | 0.725805 | 0.362902 | − | 0.931827i | \(-0.381786\pi\) | ||||
0.362902 | + | 0.931827i | \(0.381786\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4687.67 | 0.418023 | ||||||||
\(502\) | 10925.0 | 0.971330 | ||||||||
\(503\) | 18897.4 | 1.67513 | 0.837567 | − | 0.546334i | \(-0.183977\pi\) | ||||
0.837567 | + | 0.546334i | \(0.183977\pi\) | |||||||
\(504\) | −9788.91 | −0.865144 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15593.4 | 1.36999 | ||||||||
\(507\) | −10081.6 | −0.883117 | ||||||||
\(508\) | −7948.92 | −0.694245 | ||||||||
\(509\) | 4265.15 | 0.371413 | 0.185707 | − | 0.982605i | \(-0.440543\pi\) | ||||
0.185707 | + | 0.982605i | \(0.440543\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5850.72 | 0.506498 | ||||||||
\(512\) | 10130.9 | 0.874469 | ||||||||
\(513\) | 6250.82 | 0.537974 | ||||||||
\(514\) | 5576.72 | 0.478558 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 810.750 | 0.0691691 | ||||||||
\(517\) | −1106.26 | −0.0941068 | ||||||||
\(518\) | 420.333 | 0.0356532 | ||||||||
\(519\) | −564.100 | −0.0477096 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3324.96 | −0.279595 | −0.139798 | − | 0.990180i | \(-0.544645\pi\) | ||||
−0.139798 | + | 0.990180i | \(0.544645\pi\) | |||||||
\(522\) | −1534.06 | −0.128628 | ||||||||
\(523\) | −13017.6 | −1.08838 | −0.544188 | − | 0.838964i | \(-0.683162\pi\) | ||||
−0.544188 | + | 0.838964i | \(0.683162\pi\) | |||||||
\(524\) | −2619.57 | −0.218390 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6303.54 | −0.522524 | ||||||||
\(527\) | −1390.07 | −0.114900 | ||||||||
\(528\) | 3027.75 | 0.249556 | ||||||||
\(529\) | 5436.69 | 0.446839 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7962.09 | 0.650707 | ||||||||
\(532\) | −3363.11 | −0.274078 | ||||||||
\(533\) | −1649.52 | −0.134050 | ||||||||
\(534\) | 5730.18 | 0.464362 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8138.78 | −0.655862 | ||||||||
\(537\) | 882.555 | 0.0709219 | ||||||||
\(538\) | 12449.3 | 0.997634 | ||||||||
\(539\) | −3083.29 | −0.246395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17906.8 | −1.42305 | −0.711527 | − | 0.702658i | \(-0.751996\pi\) | ||||
−0.711527 | + | 0.702658i | \(0.751996\pi\) | |||||||
\(542\) | 7101.19 | 0.562771 | ||||||||
\(543\) | 881.885 | 0.0696967 | ||||||||
\(544\) | 1950.69 | 0.153741 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6098.03 | 0.477970 | ||||||||
\(547\) | −1612.94 | −0.126078 | −0.0630389 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630389 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(548\) | 6144.58 | 0.478984 | ||||||||
\(549\) | −1982.94 | −0.154153 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1943.45 | −0.150261 | ||||||||
\(552\) | 6016.70 | 0.463927 | ||||||||
\(553\) | −16627.3 | −1.27860 | ||||||||
\(554\) | 8887.99 | 0.681614 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1801.36 | −0.137400 | ||||||||
\(557\) | 7803.94 | 0.593651 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(558\) | 4772.63 | 0.362081 | ||||||||
\(559\) | 12937.2 | 0.978865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1489.24 | 0.112078 | ||||||||
\(562\) | −3709.63 | −0.278436 | ||||||||
\(563\) | 12329.5 | 0.922958 | 0.461479 | − | 0.887151i | \(-0.347319\pi\) | ||||
0.461479 | + | 0.887151i | \(0.347319\pi\) | |||||||
\(564\) | −115.757 | −0.00864231 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17450.6 | 1.29594 | ||||||||
\(567\) | 7844.72 | 0.581035 | ||||||||
\(568\) | 12114.4 | 0.894910 | ||||||||
\(569\) | 1554.46 | 0.114528 | 0.0572640 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572640 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15951.8 | 1.16911 | 0.584556 | − | 0.811353i | \(-0.301269\pi\) | ||||
0.584556 | + | 0.811353i | \(0.301269\pi\) | |||||||
\(572\) | −13667.8 | −0.999087 | ||||||||
\(573\) | −1535.64 | −0.111959 | ||||||||
\(574\) | 711.813 | 0.0517605 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12612.0 | −0.912328 | ||||||||
\(577\) | −10491.7 | −0.756975 | −0.378488 | − | 0.925606i | \(-0.623556\pi\) | ||||
−0.378488 | + | 0.925606i | \(0.623556\pi\) | |||||||
\(578\) | 10479.2 | 0.754114 | ||||||||
\(579\) | −2672.54 | −0.191825 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10020.3 | −0.715509 | ||||||||
\(582\) | 1379.84 | 0.0982756 | ||||||||
\(583\) | 15231.0 | 1.08199 | ||||||||
\(584\) | 8538.11 | 0.604982 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18133.5 | 1.27831 | ||||||||
\(587\) | −6437.47 | −0.452645 | −0.226323 | − | 0.974052i | \(-0.572670\pi\) | ||||
−0.226323 | + | 0.974052i | \(0.572670\pi\) | |||||||
\(588\) | −322.631 | −0.0226277 | ||||||||
\(589\) | 6046.29 | 0.422976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3674.15 | −0.255726 | ||||||||
\(592\) | 348.473 | 0.0241928 | ||||||||
\(593\) | −11240.6 | −0.778411 | −0.389205 | − | 0.921151i | \(-0.627250\pi\) | ||||
−0.389205 | + | 0.921151i | \(0.627250\pi\) | |||||||
\(594\) | −10962.3 | −0.757219 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2307.99 | 0.158622 | ||||||||
\(597\) | 656.869 | 0.0450316 | ||||||||
\(598\) | 26036.8 | 1.78047 | ||||||||
\(599\) | 15903.5 | 1.08481 | 0.542405 | − | 0.840117i | \(-0.317514\pi\) | ||||
0.542405 | + | 0.840117i | \(0.317514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 117.190 | 0.00795385 | 0.00397692 | − | 0.999992i | \(-0.498734\pi\) | ||||
0.00397692 | + | 0.999992i | \(0.498734\pi\) | |||||||
\(602\) | −5582.75 | −0.377966 | ||||||||
\(603\) | 7808.16 | 0.527318 | ||||||||
\(604\) | −1273.85 | −0.0858151 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1015.95 | −0.0681025 | ||||||||
\(607\) | 22047.8 | 1.47429 | 0.737143 | − | 0.675737i | \(-0.236175\pi\) | ||||
0.737143 | + | 0.675737i | \(0.236175\pi\) | |||||||
\(608\) | −8484.78 | −0.565959 | ||||||||
\(609\) | 901.160 | 0.0599620 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1847.15 | −0.122304 | ||||||||
\(612\) | −1082.51 | −0.0714995 | ||||||||
\(613\) | 12719.2 | 0.838050 | 0.419025 | − | 0.907975i | \(-0.362372\pi\) | ||||
0.419025 | + | 0.907975i | \(0.362372\pi\) | |||||||
\(614\) | −13737.7 | −0.902945 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21748.5 | 1.42252 | ||||||||
\(617\) | −12736.9 | −0.831064 | −0.415532 | − | 0.909578i | \(-0.636405\pi\) | ||||
−0.415532 | + | 0.909578i | \(0.636405\pi\) | |||||||
\(618\) | 2194.92 | 0.142868 | ||||||||
\(619\) | 28083.4 | 1.82353 | 0.911767 | − | 0.410709i | \(-0.134719\pi\) | ||||
0.911767 | + | 0.410709i | \(0.134719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12375.5 | −0.799697 | ||||||||
\(622\) | 18306.4 | 1.18009 | ||||||||
\(623\) | 23383.1 | 1.50373 | ||||||||
\(624\) | 5055.51 | 0.324331 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4207.38 | 0.268628 | ||||||||
\(627\) | −6477.64 | −0.412587 | ||||||||
\(628\) | −5003.80 | −0.317951 | ||||||||
\(629\) | 171.401 | 0.0108652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 281.496 | 0.0177594 | 0.00887969 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00887969 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(632\) | −24264.6 | −1.52721 | ||||||||
\(633\) | −7615.79 | −0.478200 | ||||||||
\(634\) | 2740.89 | 0.171695 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1593.75 | 0.0993650 | ||||||||
\(637\) | −5148.26 | −0.320222 | ||||||||
\(638\) | 3408.30 | 0.211498 | ||||||||
\(639\) | −11622.3 | −0.719514 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8440.98 | −0.520123 | −0.260061 | − | 0.965592i | \(-0.583743\pi\) | ||||
−0.260061 | + | 0.965592i | \(0.583743\pi\) | |||||||
\(642\) | 1772.42 | 0.108959 | ||||||||
\(643\) | 1173.61 | 0.0719792 | 0.0359896 | − | 0.999352i | \(-0.488542\pi\) | ||||
0.0359896 | + | 0.999352i | \(0.488542\pi\) | |||||||
\(644\) | 6658.35 | 0.407416 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2314.14 | 0.140942 | ||||||||
\(647\) | 10845.7 | 0.659025 | 0.329513 | − | 0.944151i | \(-0.393116\pi\) | ||||
0.329513 | + | 0.944151i | \(0.393116\pi\) | |||||||
\(648\) | 11448.0 | 0.694012 | ||||||||
\(649\) | −17689.8 | −1.06993 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2803.60 | −0.168789 | ||||||||
\(652\) | 6068.78 | 0.364527 | ||||||||
\(653\) | 5282.40 | 0.316564 | 0.158282 | − | 0.987394i | \(-0.449404\pi\) | ||||
0.158282 | + | 0.987394i | \(0.449404\pi\) | |||||||
\(654\) | −3995.99 | −0.238923 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 590.122 | 0.0351225 | ||||||||
\(657\) | −8191.26 | −0.486410 | ||||||||
\(658\) | 797.094 | 0.0472249 | ||||||||
\(659\) | −19243.7 | −1.13752 | −0.568761 | − | 0.822503i | \(-0.692577\pi\) | ||||
−0.568761 | + | 0.822503i | \(0.692577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29196.9 | 1.71804 | 0.859021 | − | 0.511940i | \(-0.171073\pi\) | ||||
0.859021 | + | 0.511940i | \(0.171073\pi\) | |||||||
\(662\) | −8447.34 | −0.495944 | ||||||||
\(663\) | 2486.62 | 0.145660 | ||||||||
\(664\) | −14622.8 | −0.854633 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −588.484 | −0.0342392 | ||||||||
\(667\) | 3847.69 | 0.223363 | ||||||||
\(668\) | 7570.39 | 0.438484 | ||||||||
\(669\) | 2455.84 | 0.141926 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4405.61 | 0.253467 | ||||||||
\(672\) | 3934.31 | 0.225847 | ||||||||
\(673\) | −19924.5 | −1.14121 | −0.570605 | − | 0.821224i | \(-0.693291\pi\) | ||||
−0.570605 | + | 0.821224i | \(0.693291\pi\) | |||||||
\(674\) | −24430.0 | −1.39616 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16281.4 | −0.926341 | ||||||||
\(677\) | 4980.43 | 0.282738 | 0.141369 | − | 0.989957i | \(-0.454850\pi\) | ||||
0.141369 | + | 0.989957i | \(0.454850\pi\) | |||||||
\(678\) | 7044.70 | 0.399041 | ||||||||
\(679\) | 5630.71 | 0.318243 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2450.32 | −0.137880 | ||||||||
\(682\) | −10603.6 | −0.595355 | ||||||||
\(683\) | −29295.8 | −1.64125 | −0.820624 | − | 0.571468i | \(-0.806374\pi\) | ||||
−0.820624 | + | 0.571468i | \(0.806374\pi\) | |||||||
\(684\) | 4708.50 | 0.263208 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15181.4 | 0.844938 | ||||||||
\(687\) | −10055.9 | −0.558455 | ||||||||
\(688\) | −4628.32 | −0.256472 | ||||||||
\(689\) | 25431.5 | 1.40619 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32759.8 | −1.80353 | −0.901766 | − | 0.432225i | \(-0.857729\pi\) | ||||
−0.901766 | + | 0.432225i | \(0.857729\pi\) | |||||||
\(692\) | −910.998 | −0.0500447 | ||||||||
\(693\) | −20865.0 | −1.14372 | ||||||||
\(694\) | −19145.4 | −1.04719 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1315.09 | 0.0716210 | ||||||||
\(697\) | 290.260 | 0.0157739 | ||||||||
\(698\) | 2227.40 | 0.120786 | ||||||||
\(699\) | −1089.67 | −0.0589629 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27958.5 | 1.50639 | 0.753195 | − | 0.657797i | \(-0.228512\pi\) | ||||
0.753195 | + | 0.657797i | \(0.228512\pi\) | |||||||
\(702\) | −18304.0 | −0.984104 | ||||||||
\(703\) | −745.532 | −0.0399975 | ||||||||
\(704\) | 28020.8 | 1.50010 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18358.3 | 0.978644 | ||||||||
\(707\) | −4145.77 | −0.220534 | ||||||||
\(708\) | −1851.03 | −0.0982572 | ||||||||
\(709\) | −31863.5 | −1.68781 | −0.843906 | − | 0.536492i | \(-0.819749\pi\) | ||||
−0.843906 | + | 0.536492i | \(0.819749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23278.9 | 1.22789 | ||||||||
\(712\) | 34123.6 | 1.79612 | ||||||||
\(713\) | −11970.6 | −0.628753 | ||||||||
\(714\) | −1073.04 | −0.0562432 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1425.29 | 0.0743931 | ||||||||
\(717\) | −12803.4 | −0.666879 | ||||||||
\(718\) | 10542.2 | 0.547953 | ||||||||
\(719\) | 7944.76 | 0.412085 | 0.206043 | − | 0.978543i | \(-0.433941\pi\) | ||||
0.206043 | + | 0.978543i | \(0.433941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8956.76 | 0.462645 | ||||||||
\(722\) | 5307.06 | 0.273557 | ||||||||
\(723\) | −13097.6 | −0.673729 | ||||||||
\(724\) | 1424.21 | 0.0731080 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5861.39 | 0.299637 | ||||||||
\(727\) | −28640.3 | −1.46109 | −0.730543 | − | 0.682866i | \(-0.760733\pi\) | ||||
−0.730543 | + | 0.682866i | \(0.760733\pi\) | |||||||
\(728\) | 36314.1 | 1.84875 | ||||||||
\(729\) | −6340.84 | −0.322148 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2276.51 | −0.115184 | ||||||||
\(732\) | 460.996 | 0.0232772 | ||||||||
\(733\) | −11852.7 | −0.597258 | −0.298629 | − | 0.954369i | \(-0.596529\pi\) | ||||
−0.298629 | + | 0.954369i | \(0.596529\pi\) | |||||||
\(734\) | 21139.2 | 1.06303 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16798.3 | 0.841297 | ||||||||
\(737\) | −17347.8 | −0.867047 | ||||||||
\(738\) | −996.570 | −0.0497076 | ||||||||
\(739\) | −24052.5 | −1.19727 | −0.598636 | − | 0.801021i | \(-0.704290\pi\) | ||||
−0.598636 | + | 0.801021i | \(0.704290\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10815.9 | −0.536210 | ||||||||
\(742\) | −10974.4 | −0.542968 | ||||||||
\(743\) | 12530.4 | 0.618704 | 0.309352 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309352 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(744\) | −4091.37 | −0.201609 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18560.8 | −0.910937 | ||||||||
\(747\) | 14028.8 | 0.687132 | ||||||||
\(748\) | 2405.06 | 0.117564 | ||||||||
\(749\) | 7232.71 | 0.352840 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30921.6 | 1.50246 | 0.751229 | − | 0.660042i | \(-0.229461\pi\) | ||||
0.751229 | + | 0.660042i | \(0.229461\pi\) | |||||||
\(752\) | 660.823 | 0.0320449 | ||||||||
\(753\) | 8985.11 | 0.434841 | ||||||||
\(754\) | 5690.93 | 0.274869 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4680.86 | −0.225187 | ||||||||
\(757\) | 6257.40 | 0.300435 | 0.150217 | − | 0.988653i | \(-0.452003\pi\) | ||||
0.150217 | + | 0.988653i | \(0.452003\pi\) | |||||||
\(758\) | −15409.7 | −0.738397 | ||||||||
\(759\) | 12824.6 | 0.613310 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20094.8 | −0.957211 | −0.478605 | − | 0.878030i | \(-0.658858\pi\) | ||||
−0.478605 | + | 0.878030i | \(0.658858\pi\) | |||||||
\(762\) | 11031.6 | 0.524450 | ||||||||
\(763\) | −16306.4 | −0.773697 | ||||||||
\(764\) | −2480.00 | −0.117439 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10817.6 | −0.510257 | ||||||||
\(767\) | −29537.1 | −1.39051 | ||||||||
\(768\) | 7116.46 | 0.334366 | ||||||||
\(769\) | −26647.8 | −1.24960 | −0.624801 | − | 0.780784i | \(-0.714820\pi\) | ||||
−0.624801 | + | 0.780784i | \(0.714820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4586.48 | 0.214239 | ||||||||
\(772\) | −4316.03 | −0.201214 | ||||||||
\(773\) | 18513.2 | 0.861414 | 0.430707 | − | 0.902492i | \(-0.358264\pi\) | ||||
0.430707 | + | 0.902492i | \(0.358264\pi\) | |||||||
\(774\) | 7816.09 | 0.362976 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8217.05 | 0.380122 | ||||||||
\(777\) | 345.696 | 0.0159611 | ||||||||
\(778\) | −11140.3 | −0.513365 | ||||||||
\(779\) | −1262.52 | −0.0580675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25821.8 | 1.18307 | ||||||||
\(782\) | −4581.58 | −0.209510 | ||||||||
\(783\) | −2704.95 | −0.123457 | ||||||||
\(784\) | 1841.80 | 0.0839014 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3635.46 | 0.164978 | ||||||||
\(787\) | 29524.5 | 1.33727 | 0.668636 | − | 0.743590i | \(-0.266878\pi\) | ||||
0.668636 | + | 0.743590i | \(0.266878\pi\) | |||||||
\(788\) | −5933.59 | −0.268243 | ||||||||
\(789\) | −5184.25 | −0.233921 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28747.2 | 1.29220 | ||||||||
\(792\) | −30448.9 | −1.36610 | ||||||||
\(793\) | 7356.16 | 0.329413 | ||||||||
\(794\) | −27542.3 | −1.23103 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1060.81 | 0.0472356 | ||||||||
\(797\) | −38789.4 | −1.72395 | −0.861976 | − | 0.506949i | \(-0.830773\pi\) | ||||
−0.861976 | + | 0.506949i | \(0.830773\pi\) | |||||||
\(798\) | 4667.34 | 0.207045 | ||||||||
\(799\) | 325.035 | 0.0143916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32737.3 | −1.44409 | ||||||||
\(802\) | 26831.5 | 1.18136 | ||||||||
\(803\) | 18199.0 | 0.799785 | ||||||||
\(804\) | −1815.25 | −0.0796254 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17705.1 | −0.773741 | ||||||||
\(807\) | 10238.7 | 0.446617 | ||||||||
\(808\) | −6050.04 | −0.263415 | ||||||||
\(809\) | −11552.0 | −0.502037 | −0.251018 | − | 0.967982i | \(-0.580765\pi\) | ||||
−0.251018 | + | 0.967982i | \(0.580765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26939.1 | 1.16641 | 0.583205 | − | 0.812325i | \(-0.301798\pi\) | ||||
0.583205 | + | 0.812325i | \(0.301798\pi\) | |||||||
\(812\) | 1455.33 | 0.0628968 | ||||||||
\(813\) | 5840.25 | 0.251939 | ||||||||
\(814\) | 1307.47 | 0.0562981 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −889.596 | −0.0381643 | ||||||||
\(817\) | 9901.96 | 0.424022 | ||||||||
\(818\) | −24984.8 | −1.06794 | ||||||||
\(819\) | −34838.9 | −1.48641 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7558.67 | −0.321315 | −0.160657 | − | 0.987010i | \(-0.551361\pi\) | ||||
−0.160657 | + | 0.987010i | \(0.551361\pi\) | |||||||
\(822\) | −8527.48 | −0.361837 | ||||||||
\(823\) | 3201.90 | 0.135615 | 0.0678076 | − | 0.997698i | \(-0.478400\pi\) | ||||
0.0678076 | + | 0.997698i | \(0.478400\pi\) | |||||||
\(824\) | 13070.8 | 0.552603 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12746.0 | 0.536915 | ||||||||
\(827\) | 11479.1 | 0.482670 | 0.241335 | − | 0.970442i | \(-0.422415\pi\) | ||||
0.241335 | + | 0.970442i | \(0.422415\pi\) | |||||||
\(828\) | −9321.98 | −0.391257 | ||||||||
\(829\) | −1667.94 | −0.0698794 | −0.0349397 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349397 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7309.78 | 0.305142 | ||||||||
\(832\) | 46787.0 | 1.94958 | ||||||||
\(833\) | 905.917 | 0.0376809 | ||||||||
\(834\) | 2499.94 | 0.103796 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10461.1 | −0.432781 | ||||||||
\(837\) | 8415.38 | 0.347525 | ||||||||
\(838\) | −25902.8 | −1.06778 | ||||||||
\(839\) | 15210.3 | 0.625884 | 0.312942 | − | 0.949772i | \(-0.398685\pi\) | ||||
0.312942 | + | 0.949772i | \(0.398685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 28854.7 | 1.18100 | ||||||||
\(843\) | −3050.92 | −0.124649 | ||||||||
\(844\) | −12299.2 | −0.501606 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1115.97 | −0.0453519 | ||||||||
\(847\) | 23918.5 | 0.970306 | ||||||||
\(848\) | −9098.20 | −0.368436 | ||||||||
\(849\) | 14351.9 | 0.580161 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1476.02 | 0.0594563 | ||||||||
\(852\) | 2701.95 | 0.108647 | ||||||||
\(853\) | 18281.2 | 0.733805 | 0.366902 | − | 0.930259i | \(-0.380418\pi\) | ||||
0.366902 | + | 0.930259i | \(0.380418\pi\) | |||||||
\(854\) | −3174.38 | −0.127195 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10554.9 | 0.421447 | ||||||||
\(857\) | −585.415 | −0.0233342 | −0.0116671 | − | 0.999932i | \(-0.503714\pi\) | ||||
−0.0116671 | + | 0.999932i | \(0.503714\pi\) | |||||||
\(858\) | 18968.2 | 0.754737 | ||||||||
\(859\) | −935.611 | −0.0371626 | −0.0185813 | − | 0.999827i | \(-0.505915\pi\) | ||||
−0.0185813 | + | 0.999827i | \(0.505915\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 585.419 | 0.0231719 | ||||||||
\(862\) | 9162.92 | 0.362054 | ||||||||
\(863\) | 12110.7 | 0.477696 | 0.238848 | − | 0.971057i | \(-0.423230\pi\) | ||||
0.238848 | + | 0.971057i | \(0.423230\pi\) | |||||||
\(864\) | −11809.3 | −0.465002 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8664.43 | −0.339988 | ||||||||
\(867\) | 8618.46 | 0.337599 | ||||||||
\(868\) | −4527.70 | −0.177051 | ||||||||
\(869\) | −51720.0 | −2.01896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28966.1 | −1.12684 | ||||||||
\(872\) | −23796.4 | −0.924136 | ||||||||
\(873\) | −7883.24 | −0.305621 | ||||||||
\(874\) | 19928.2 | 0.771260 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1904.31 | 0.0734483 | ||||||||
\(877\) | −5841.41 | −0.224915 | −0.112458 | − | 0.993657i | \(-0.535872\pi\) | ||||
−0.112458 | + | 0.993657i | \(0.535872\pi\) | |||||||
\(878\) | −23897.1 | −0.918551 | ||||||||
\(879\) | 14913.6 | 0.572267 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47826.2 | −1.82895 | −0.914476 | − | 0.404641i | \(-0.867397\pi\) | ||||
−0.914476 | + | 0.404641i | \(0.867397\pi\) | |||||||
\(882\) | −3110.35 | −0.118743 | ||||||||
\(883\) | −17337.5 | −0.660761 | −0.330381 | − | 0.943848i | \(-0.607177\pi\) | ||||
−0.330381 | + | 0.943848i | \(0.607177\pi\) | |||||||
\(884\) | 4015.79 | 0.152789 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23059.9 | 0.874392 | ||||||||
\(887\) | −35181.5 | −1.33177 | −0.665885 | − | 0.746055i | \(-0.731946\pi\) | ||||
−0.665885 | + | 0.746055i | \(0.731946\pi\) | |||||||
\(888\) | 504.483 | 0.0190646 | ||||||||
\(889\) | 45016.3 | 1.69831 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24401.4 | 0.917482 | ||||||||
\(892\) | 3966.08 | 0.148872 | ||||||||
\(893\) | −1413.78 | −0.0529792 | ||||||||
\(894\) | −3203.04 | −0.119827 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3114.56 | −0.116127 | ||||||||
\(897\) | 21413.5 | 0.797075 | ||||||||
\(898\) | −27850.3 | −1.03494 | ||||||||
\(899\) | −2616.44 | −0.0970669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4475.08 | −0.165468 | ||||||||
\(902\) | 2214.13 | 0.0817322 | ||||||||
\(903\) | −4591.44 | −0.169207 | ||||||||
\(904\) | 41951.6 | 1.54346 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1767.86 | 0.0648270 | ||||||||
\(907\) | 28184.4 | 1.03180 | 0.515902 | − | 0.856648i | \(-0.327457\pi\) | ||||
0.515902 | + | 0.856648i | \(0.327457\pi\) | |||||||
\(908\) | −3957.15 | −0.144629 | ||||||||
\(909\) | 5804.26 | 0.211788 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34136.6 | −1.24149 | −0.620745 | − | 0.784013i | \(-0.713170\pi\) | ||||
−0.620745 | + | 0.784013i | \(0.713170\pi\) | |||||||
\(912\) | 3869.41 | 0.140492 | ||||||||
\(913\) | −31168.5 | −1.12982 | ||||||||
\(914\) | −23886.8 | −0.864448 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16239.9 | −0.585788 | ||||||||
\(917\) | 14835.2 | 0.534242 | ||||||||
\(918\) | 3220.88 | 0.115801 | ||||||||
\(919\) | 15512.0 | 0.556794 | 0.278397 | − | 0.960466i | \(-0.410197\pi\) | ||||
0.278397 | + | 0.960466i | \(0.410197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11298.3 | −0.404227 | ||||||||
\(922\) | −22007.3 | −0.786086 | ||||||||
\(923\) | 43115.3 | 1.53755 | ||||||||
\(924\) | 4850.71 | 0.172702 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −43055.5 | −1.52796 | ||||||||
\(927\) | −12539.9 | −0.444297 | ||||||||
\(928\) | 3671.66 | 0.129879 | ||||||||
\(929\) | −3100.72 | −0.109506 | −0.0547531 | − | 0.998500i | \(-0.517437\pi\) | ||||
−0.0547531 | + | 0.998500i | \(0.517437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3940.40 | −0.138713 | ||||||||
\(932\) | −1759.77 | −0.0618488 | ||||||||
\(933\) | 15055.8 | 0.528299 | ||||||||
\(934\) | −774.498 | −0.0271331 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −50841.3 | −1.77543 | ||||||||
\(937\) | 19638.8 | 0.684708 | 0.342354 | − | 0.939571i | \(-0.388776\pi\) | ||||
0.342354 | + | 0.939571i | \(0.388776\pi\) | |||||||
\(938\) | 12499.6 | 0.435103 | ||||||||
\(939\) | 3460.29 | 0.120258 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50033.6 | −1.73332 | −0.866658 | − | 0.498903i | \(-0.833736\pi\) | ||||
−0.866658 | + | 0.498903i | \(0.833736\pi\) | |||||||
\(942\) | 6944.30 | 0.240189 | ||||||||
\(943\) | 2499.57 | 0.0863172 | ||||||||
\(944\) | 10567.0 | 0.364328 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17365.4 | −0.596827 | ||||||||
\(947\) | −19758.4 | −0.677994 | −0.338997 | − | 0.940787i | \(-0.610088\pi\) | ||||
−0.338997 | + | 0.940787i | \(0.610088\pi\) | |||||||
\(948\) | −5411.90 | −0.185412 | ||||||||
\(949\) | 30387.3 | 1.03942 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2254.20 | 0.0768636 | ||||||||
\(952\) | −6390.03 | −0.217544 | ||||||||
\(953\) | −33843.4 | −1.15036 | −0.575180 | − | 0.818027i | \(-0.695068\pi\) | ||||
−0.575180 | + | 0.818027i | \(0.695068\pi\) | |||||||
\(954\) | 15364.6 | 0.521434 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20677.0 | −0.699520 | ||||||||
\(957\) | 2803.10 | 0.0946828 | ||||||||
\(958\) | 568.624 | 0.0191768 | ||||||||
\(959\) | −34798.0 | −1.17173 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21651.0 | −0.726762 | ||||||||
\(962\) | 2183.11 | 0.0731666 | ||||||||
\(963\) | −10126.1 | −0.338846 | ||||||||
\(964\) | −21152.1 | −0.706705 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9240.50 | −0.307772 | ||||||||
\(967\) | −35236.9 | −1.17181 | −0.585906 | − | 0.810379i | \(-0.699261\pi\) | ||||
−0.585906 | + | 0.810379i | \(0.699261\pi\) | |||||||
\(968\) | 34904.9 | 1.15897 | ||||||||
\(969\) | 1903.23 | 0.0630964 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4505.40 | −0.148903 | −0.0744517 | − | 0.997225i | \(-0.523721\pi\) | ||||
−0.0744517 | + | 0.997225i | \(0.523721\pi\) | |||||||
\(972\) | 10050.1 | 0.331644 | ||||||||
\(973\) | 10201.5 | 0.336119 | ||||||||
\(974\) | −29708.0 | −0.977314 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2631.69 | −0.0863096 | ||||||||
\(977\) | 15167.4 | 0.496671 | 0.248336 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248336 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(978\) | −8422.29 | −0.275373 | ||||||||
\(979\) | 72734.2 | 2.37446 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22829.7 | 0.743012 | ||||||||
\(982\) | 14466.3 | 0.470099 | ||||||||
\(983\) | −25342.5 | −0.822278 | −0.411139 | − | 0.911573i | \(-0.634869\pi\) | ||||
−0.411139 | + | 0.911573i | \(0.634869\pi\) | |||||||
\(984\) | 854.318 | 0.0276775 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1001.41 | −0.0323442 | ||||||||
\(987\) | 655.557 | 0.0211414 | ||||||||
\(988\) | −17467.2 | −0.562455 | ||||||||
\(989\) | −19604.1 | −0.630307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40576.1 | 1.30065 | 0.650324 | − | 0.759657i | \(-0.274633\pi\) | ||||
0.650324 | + | 0.759657i | \(0.274633\pi\) | |||||||
\(992\) | −11422.9 | −0.365603 | ||||||||
\(993\) | −6947.37 | −0.222022 | ||||||||
\(994\) | −18605.4 | −0.593689 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3261.43 | −0.103757 | ||||||||
\(997\) | −7442.49 | −0.236415 | −0.118208 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118208 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(998\) | −18132.6 | −0.575128 | ||||||||
\(999\) | −1037.65 | −0.0328627 |
(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 | 725.4.a.c.1.2 | 5 | ||
5.4 | even | 2 | 29.4.a.b.1.4 | ✓ | 5 | ||
15.14 | odd | 2 | 261.4.a.f.1.2 | 5 | |||
20.19 | odd | 2 | 464.4.a.l.1.3 | 5 | |||
35.34 | odd | 2 | 1421.4.a.e.1.4 | 5 | |||
40.19 | odd | 2 | 1856.4.a.bb.1.3 | 5 | |||
40.29 | even | 2 | 1856.4.a.y.1.3 | 5 | |||
145.144 | even | 2 | 841.4.a.b.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.4 | ✓ | 5 | 5.4 | even | 2 | ||
261.4.a.f.1.2 | 5 | 15.14 | odd | 2 | |||
464.4.a.l.1.3 | 5 | 20.19 | odd | 2 | |||
725.4.a.c.1.2 | 5 | 1.1 | even | 1 | trivial | ||
841.4.a.b.1.2 | 5 | 145.144 | even | 2 | |||
1421.4.a.e.1.4 | 5 | 35.34 | odd | 2 | |||
1856.4.a.y.1.3 | 5 | 40.29 | even | 2 | |||
1856.4.a.bb.1.3 | 5 | 40.19 | odd | 2 |