Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,4,Mod(274,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1756207519\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.274 |
Dual form | 325.4.b.e.274.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155i | 0.905646i | 0.891601 | + | 0.452823i | \(0.149583\pi\) | ||||
−0.891601 | + | 0.452823i | \(0.850417\pi\) | |||||||
\(3\) | 3.68466i | 0.709113i | 0.935035 | + | 0.354556i | \(0.115368\pi\) | ||||
−0.935035 | + | 0.354556i | \(0.884632\pi\) | |||||||
\(4\) | 1.43845 | 0.179806 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −9.43845 | −0.642205 | ||||||||
\(7\) | 18.1771i | 0.981470i | 0.871309 | + | 0.490735i | \(0.163272\pi\) | ||||
−0.871309 | + | 0.490735i | \(0.836728\pi\) | |||||||
\(8\) | 24.1771i | 1.06849i | ||||||||
\(9\) | 13.4233 | 0.497159 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.7386 | 1.77449 | 0.887247 | − | 0.461295i | \(-0.152615\pi\) | ||||
0.887247 | + | 0.461295i | \(0.152615\pi\) | |||||||
\(12\) | 5.30019i | 0.127503i | ||||||||
\(13\) | 13.0000i | 0.277350i | ||||||||
\(14\) | −46.5616 | −0.888864 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | − 25.5464i | − 0.364465i | −0.983255 | − | 0.182233i | \(-0.941668\pi\) | ||||
0.983255 | − | 0.182233i | \(-0.0583324\pi\) | |||||||
\(18\) | 34.3845i | 0.450250i | ||||||||
\(19\) | 107.970 | 1.30368 | 0.651841 | − | 0.758356i | \(-0.273997\pi\) | ||||
0.651841 | + | 0.758356i | \(0.273997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −66.9763 | −0.695973 | ||||||||
\(22\) | 165.831i | 1.60706i | ||||||||
\(23\) | − 73.2614i | − 0.664176i | −0.943248 | − | 0.332088i | \(-0.892247\pi\) | ||||
0.943248 | − | 0.332088i | \(-0.107753\pi\) | |||||||
\(24\) | −89.0843 | −0.757677 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −33.3002 | −0.251181 | ||||||||
\(27\) | 148.946i | 1.06165i | ||||||||
\(28\) | 26.1468i | 0.176474i | ||||||||
\(29\) | −175.909 | −1.12640 | −0.563198 | − | 0.826322i | \(-0.690429\pi\) | ||||
−0.563198 | + | 0.826322i | \(0.690429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −113.093 | −0.655228 | −0.327614 | − | 0.944812i | \(-0.606245\pi\) | ||||
−0.327614 | + | 0.944812i | \(0.606245\pi\) | |||||||
\(32\) | 64.2547i | 0.354961i | ||||||||
\(33\) | 238.540i | 1.25832i | ||||||||
\(34\) | 65.4384 | 0.330077 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.3087 | 0.0893921 | ||||||||
\(37\) | 114.808i | 0.510116i | 0.966926 | + | 0.255058i | \(0.0820945\pi\) | ||||
−0.966926 | + | 0.255058i | \(0.917905\pi\) | |||||||
\(38\) | 276.570i | 1.18067i | ||||||||
\(39\) | −47.9006 | −0.196673 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −69.6458 | −0.265289 | −0.132645 | − | 0.991164i | \(-0.542347\pi\) | ||||
−0.132645 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(42\) | − 171.563i | − 0.630305i | ||||||||
\(43\) | − 438.302i | − 1.55443i | −0.629236 | − | 0.777214i | \(-0.716632\pi\) | ||||
0.629236 | − | 0.777214i | \(-0.283368\pi\) | |||||||
\(44\) | 93.1231 | 0.319064 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 187.663 | 0.601508 | ||||||||
\(47\) | − 31.9479i | − 0.0991506i | −0.998770 | − | 0.0495753i | \(-0.984213\pi\) | ||||
0.998770 | − | 0.0495753i | \(-0.0157868\pi\) | |||||||
\(48\) | − 185.793i | − 0.558684i | ||||||||
\(49\) | 12.5937 | 0.0367164 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 94.1298 | 0.258447 | ||||||||
\(52\) | 18.6998i | 0.0498692i | ||||||||
\(53\) | − 2.84658i | − 0.00737752i | −0.999993 | − | 0.00368876i | \(-0.998826\pi\) | ||||
0.999993 | − | 0.00368876i | \(-0.00117417\pi\) | |||||||
\(54\) | −381.533 | −0.961483 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −439.469 | −1.04869 | ||||||||
\(57\) | 397.831i | 0.924457i | ||||||||
\(58\) | − 450.600i | − 1.02012i | ||||||||
\(59\) | −71.6325 | −0.158064 | −0.0790319 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790319 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −920.695 | −1.93251 | −0.966253 | − | 0.257593i | \(-0.917071\pi\) | ||||
−0.966253 | + | 0.257593i | \(0.917071\pi\) | |||||||
\(62\) | − 289.693i | − 0.593404i | ||||||||
\(63\) | 243.996i | 0.487947i | ||||||||
\(64\) | −567.978 | −1.10933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −611.032 | −1.13959 | ||||||||
\(67\) | − 444.280i | − 0.810112i | −0.914292 | − | 0.405056i | \(-0.867252\pi\) | ||||
0.914292 | − | 0.405056i | \(-0.132748\pi\) | |||||||
\(68\) | − 36.7471i | − 0.0655330i | ||||||||
\(69\) | 269.943 | 0.470976 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −541.719 | −0.905496 | −0.452748 | − | 0.891639i | \(-0.649556\pi\) | ||||
−0.452748 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(72\) | 324.536i | 0.531207i | ||||||||
\(73\) | − 764.004i | − 1.22493i | −0.790498 | − | 0.612465i | \(-0.790178\pi\) | ||||
0.790498 | − | 0.612465i | \(-0.209822\pi\) | |||||||
\(74\) | −294.086 | −0.461984 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 155.309 | 0.234410 | ||||||||
\(77\) | 1176.76i | 1.74161i | ||||||||
\(78\) | − 122.700i | − 0.178116i | ||||||||
\(79\) | 421.538 | 0.600338 | 0.300169 | − | 0.953886i | \(-0.402957\pi\) | ||||
0.300169 | + | 0.953886i | \(0.402957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −186.386 | −0.255674 | ||||||||
\(82\) | − 178.401i | − 0.240258i | ||||||||
\(83\) | − 603.797i | − 0.798498i | −0.916842 | − | 0.399249i | \(-0.869271\pi\) | ||||
0.916842 | − | 0.399249i | \(-0.130729\pi\) | |||||||
\(84\) | −96.3419 | −0.125140 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1122.73 | 1.40776 | ||||||||
\(87\) | − 648.165i | − 0.798742i | ||||||||
\(88\) | 1565.19i | 1.89602i | ||||||||
\(89\) | 1159.88 | 1.38143 | 0.690715 | − | 0.723127i | \(-0.257296\pi\) | ||||
0.690715 | + | 0.723127i | \(0.257296\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −236.302 | −0.272211 | ||||||||
\(92\) | − 105.383i | − 0.119423i | ||||||||
\(93\) | − 416.708i | − 0.464631i | ||||||||
\(94\) | 81.8362 | 0.0897953 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −236.757 | −0.251707 | ||||||||
\(97\) | 583.269i | 0.610536i | 0.952267 | + | 0.305268i | \(0.0987460\pi\) | ||||
−0.952267 | + | 0.305268i | \(0.901254\pi\) | |||||||
\(98\) | 32.2595i | 0.0332521i | ||||||||
\(99\) | 869.006 | 0.882206 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 921.740 | 0.908085 | 0.454043 | − | 0.890980i | \(-0.349981\pi\) | ||||
0.454043 | + | 0.890980i | \(0.349981\pi\) | |||||||
\(102\) | 241.118i | 0.234061i | ||||||||
\(103\) | 930.712i | 0.890347i | 0.895444 | + | 0.445174i | \(0.146858\pi\) | ||||
−0.895444 | + | 0.445174i | \(0.853142\pi\) | |||||||
\(104\) | −314.302 | −0.296345 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.29168 | 0.00668142 | ||||||||
\(107\) | 857.383i | 0.774638i | 0.921946 | + | 0.387319i | \(0.126599\pi\) | ||||
−0.921946 | + | 0.387319i | \(0.873401\pi\) | |||||||
\(108\) | 214.251i | 0.190892i | ||||||||
\(109\) | −671.853 | −0.590384 | −0.295192 | − | 0.955438i | \(-0.595384\pi\) | ||||
−0.295192 | + | 0.955438i | \(0.595384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −423.027 | −0.361730 | ||||||||
\(112\) | − 916.548i | − 0.773265i | ||||||||
\(113\) | − 641.474i | − 0.534024i | −0.963693 | − | 0.267012i | \(-0.913964\pi\) | ||||
0.963693 | − | 0.267012i | \(-0.0860364\pi\) | |||||||
\(114\) | −1019.07 | −0.837231 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −253.036 | −0.202533 | ||||||||
\(117\) | 174.503i | 0.137887i | ||||||||
\(118\) | − 183.491i | − 0.143150i | ||||||||
\(119\) | 464.359 | 0.357712 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2860.09 | 2.14883 | ||||||||
\(122\) | − 2358.41i | − 1.75017i | ||||||||
\(123\) | − 256.621i | − 0.188120i | ||||||||
\(124\) | −162.678 | −0.117814 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −625.009 | −0.441907 | ||||||||
\(127\) | − 553.174i | − 0.386506i | −0.981149 | − | 0.193253i | \(-0.938096\pi\) | ||||
0.981149 | − | 0.193253i | \(-0.0619038\pi\) | |||||||
\(128\) | − 940.868i | − 0.649702i | ||||||||
\(129\) | 1614.99 | 1.10227 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2056.40 | 1.37152 | 0.685758 | − | 0.727830i | \(-0.259471\pi\) | ||||
0.685758 | + | 0.727830i | \(0.259471\pi\) | |||||||
\(132\) | 343.127i | 0.226253i | ||||||||
\(133\) | 1962.57i | 1.27952i | ||||||||
\(134\) | 1138.05 | 0.733674 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 617.637 | 0.389426 | ||||||||
\(137\) | − 1808.57i | − 1.12786i | −0.825824 | − | 0.563928i | \(-0.809290\pi\) | ||||
0.825824 | − | 0.563928i | \(-0.190710\pi\) | |||||||
\(138\) | 691.474i | 0.426537i | ||||||||
\(139\) | −1493.64 | −0.911428 | −0.455714 | − | 0.890126i | \(-0.650616\pi\) | ||||
−0.455714 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 117.717 | 0.0703090 | ||||||||
\(142\) | − 1387.64i | − 0.820058i | ||||||||
\(143\) | 841.602i | 0.492156i | ||||||||
\(144\) | −676.847 | −0.391694 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1957.04 | 1.10935 | ||||||||
\(147\) | 46.4036i | 0.0260361i | ||||||||
\(148\) | 165.145i | 0.0917218i | ||||||||
\(149\) | 2759.02 | 1.51696 | 0.758482 | − | 0.651694i | \(-0.225941\pi\) | ||||
0.758482 | + | 0.651694i | \(0.225941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −976.355 | −0.526190 | −0.263095 | − | 0.964770i | \(-0.584743\pi\) | ||||
−0.263095 | + | 0.964770i | \(0.584743\pi\) | |||||||
\(152\) | 2610.39i | 1.39297i | ||||||||
\(153\) | − 342.917i | − 0.181197i | ||||||||
\(154\) | −3014.33 | −1.57728 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −68.9024 | −0.0353629 | ||||||||
\(157\) | − 564.875i | − 0.287146i | −0.989640 | − | 0.143573i | \(-0.954141\pi\) | ||||
0.989640 | − | 0.143573i | \(-0.0458592\pi\) | |||||||
\(158\) | 1079.79i | 0.543694i | ||||||||
\(159\) | 10.4887 | 0.00523149 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1331.68 | 0.651869 | ||||||||
\(162\) | − 477.438i | − 0.231550i | ||||||||
\(163\) | − 1508.53i | − 0.724892i | −0.932005 | − | 0.362446i | \(-0.881942\pi\) | ||||
0.932005 | − | 0.362446i | \(-0.118058\pi\) | |||||||
\(164\) | −100.182 | −0.0477005 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1546.66 | 0.723157 | ||||||||
\(167\) | 592.521i | 0.274555i | 0.990533 | + | 0.137277i | \(0.0438351\pi\) | ||||
−0.990533 | + | 0.137277i | \(0.956165\pi\) | |||||||
\(168\) | − 1619.29i | − 0.743638i | ||||||||
\(169\) | −169.000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1449.31 | 0.648137 | ||||||||
\(172\) | − 630.474i | − 0.279495i | ||||||||
\(173\) | 4495.57i | 1.97568i | 0.155488 | + | 0.987838i | \(0.450305\pi\) | ||||
−0.155488 | + | 0.987838i | \(0.549695\pi\) | |||||||
\(174\) | 1660.31 | 0.723377 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3264.34 | −1.39806 | ||||||||
\(177\) | − 263.941i | − 0.112085i | ||||||||
\(178\) | 2971.10i | 1.25109i | ||||||||
\(179\) | 154.285 | 0.0644235 | 0.0322117 | − | 0.999481i | \(-0.489745\pi\) | ||||
0.0322117 | + | 0.999481i | \(0.489745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1071.35 | 0.439959 | 0.219979 | − | 0.975505i | \(-0.429401\pi\) | ||||
0.219979 | + | 0.975505i | \(0.429401\pi\) | |||||||
\(182\) | − 605.300i | − 0.246527i | ||||||||
\(183\) | − 3392.45i | − 1.37037i | ||||||||
\(184\) | 1771.25 | 0.709663 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1067.42 | 0.420791 | ||||||||
\(187\) | − 1653.84i | − 0.646742i | ||||||||
\(188\) | − 45.9554i | − 0.0178279i | ||||||||
\(189\) | −2707.40 | −1.04198 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 677.203 | 0.256548 | 0.128274 | − | 0.991739i | \(-0.459056\pi\) | ||||
0.128274 | + | 0.991739i | \(0.459056\pi\) | |||||||
\(192\) | − 2092.81i | − 0.786642i | ||||||||
\(193\) | − 1321.68i | − 0.492936i | −0.969151 | − | 0.246468i | \(-0.920730\pi\) | ||||
0.969151 | − | 0.246468i | \(-0.0792700\pi\) | |||||||
\(194\) | −1494.07 | −0.552929 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.1154 | 0.00660183 | ||||||||
\(197\) | 1267.37i | 0.458356i | 0.973385 | + | 0.229178i | \(0.0736038\pi\) | ||||
−0.973385 | + | 0.229178i | \(0.926396\pi\) | |||||||
\(198\) | 2226.00i | 0.798966i | ||||||||
\(199\) | −2396.24 | −0.853593 | −0.426796 | − | 0.904348i | \(-0.640358\pi\) | ||||
−0.426796 | + | 0.904348i | \(0.640358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1637.02 | 0.574460 | ||||||||
\(202\) | 2361.09i | 0.822403i | ||||||||
\(203\) | − 3197.51i | − 1.10552i | ||||||||
\(204\) | 135.401 | 0.0464703 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2384.07 | −0.806339 | ||||||||
\(207\) | − 983.409i | − 0.330201i | ||||||||
\(208\) | − 655.503i | − 0.218514i | ||||||||
\(209\) | 6989.81 | 2.31337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −91.5539 | −0.0298712 | −0.0149356 | − | 0.999888i | \(-0.504754\pi\) | ||||
−0.0149356 | + | 0.999888i | \(0.504754\pi\) | |||||||
\(212\) | − 4.09466i | − 0.00132652i | ||||||||
\(213\) | − 1996.05i | − 0.642099i | ||||||||
\(214\) | −2196.23 | −0.701548 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3601.08 | −1.13436 | ||||||||
\(217\) | − 2055.70i | − 0.643087i | ||||||||
\(218\) | − 1720.99i | − 0.534679i | ||||||||
\(219\) | 2815.09 | 0.868613 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 332.103 | 0.101085 | ||||||||
\(222\) | − 1083.61i | − 0.327599i | ||||||||
\(223\) | − 1235.42i | − 0.370985i | −0.982646 | − | 0.185493i | \(-0.940612\pi\) | ||||
0.982646 | − | 0.185493i | \(-0.0593880\pi\) | |||||||
\(224\) | −1167.96 | −0.348383 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1643.17 | 0.483637 | ||||||||
\(227\) | 3301.66i | 0.965370i | 0.875794 | + | 0.482685i | \(0.160338\pi\) | ||||
−0.875794 | + | 0.482685i | \(0.839662\pi\) | |||||||
\(228\) | 572.260i | 0.166223i | ||||||||
\(229\) | −211.283 | −0.0609694 | −0.0304847 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304847 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4335.96 | −1.23500 | ||||||||
\(232\) | − 4252.97i | − 1.20354i | ||||||||
\(233\) | 256.724i | 0.0721827i | 0.999348 | + | 0.0360913i | \(0.0114907\pi\) | ||||
−0.999348 | + | 0.0360913i | \(0.988509\pi\) | |||||||
\(234\) | −446.998 | −0.124877 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −103.040 | −0.0284208 | ||||||||
\(237\) | 1553.22i | 0.425708i | ||||||||
\(238\) | 1189.48i | 0.323960i | ||||||||
\(239\) | 3549.62 | 0.960694 | 0.480347 | − | 0.877078i | \(-0.340511\pi\) | ||||
0.480347 | + | 0.877078i | \(0.340511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5030.10 | −1.34447 | −0.672235 | − | 0.740338i | \(-0.734665\pi\) | ||||
−0.672235 | + | 0.740338i | \(0.734665\pi\) | |||||||
\(242\) | 7326.27i | 1.94608i | ||||||||
\(243\) | 3334.77i | 0.880353i | ||||||||
\(244\) | −1324.37 | −0.347476 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 657.349 | 0.170370 | ||||||||
\(247\) | 1403.61i | 0.361576i | ||||||||
\(248\) | − 2734.25i | − 0.700102i | ||||||||
\(249\) | 2224.79 | 0.566226 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −718.784 | −0.180754 | −0.0903770 | − | 0.995908i | \(-0.528807\pi\) | ||||
−0.0903770 | + | 0.995908i | \(0.528807\pi\) | |||||||
\(252\) | 350.976i | 0.0877357i | ||||||||
\(253\) | − 4742.84i | − 1.17858i | ||||||||
\(254\) | 1416.98 | 0.350038 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | 1280.79i | 0.310871i | 0.987846 | + | 0.155435i | \(0.0496780\pi\) | ||||
−0.987846 | + | 0.155435i | \(0.950322\pi\) | |||||||
\(258\) | 4136.89i | 0.998262i | ||||||||
\(259\) | −2086.87 | −0.500663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2361.28 | −0.559998 | ||||||||
\(262\) | 5267.58i | 1.24211i | ||||||||
\(263\) | − 5225.55i | − 1.22517i | −0.790403 | − | 0.612587i | \(-0.790129\pi\) | ||||
0.790403 | − | 0.612587i | \(-0.209871\pi\) | |||||||
\(264\) | −5767.19 | −1.34449 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5027.24 | −1.15880 | ||||||||
\(267\) | 4273.77i | 0.979590i | ||||||||
\(268\) | − 639.074i | − 0.145663i | ||||||||
\(269\) | −6443.80 | −1.46054 | −0.730270 | − | 0.683158i | \(-0.760606\pi\) | ||||
−0.730270 | + | 0.683158i | \(0.760606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3929.93 | −0.880909 | −0.440455 | − | 0.897775i | \(-0.645183\pi\) | ||||
−0.440455 | + | 0.897775i | \(0.645183\pi\) | |||||||
\(272\) | 1288.13i | 0.287149i | ||||||||
\(273\) | − 870.692i | − 0.193028i | ||||||||
\(274\) | 4632.74 | 1.02144 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 388.299 | 0.0846842 | ||||||||
\(277\) | − 5884.40i | − 1.27639i | −0.769876 | − | 0.638194i | \(-0.779682\pi\) | ||||
0.769876 | − | 0.638194i | \(-0.220318\pi\) | |||||||
\(278\) | − 3826.03i | − 0.825431i | ||||||||
\(279\) | −1518.08 | −0.325752 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3529.79 | 0.749358 | 0.374679 | − | 0.927155i | \(-0.377753\pi\) | ||||
0.374679 | + | 0.927155i | \(0.377753\pi\) | |||||||
\(282\) | 301.538i | 0.0636750i | ||||||||
\(283\) | 2611.00i | 0.548438i | 0.961667 | + | 0.274219i | \(0.0884193\pi\) | ||||
−0.961667 | + | 0.274219i | \(0.911581\pi\) | |||||||
\(284\) | −779.234 | −0.162813 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2155.81 | −0.445719 | ||||||||
\(287\) | − 1265.96i | − 0.260373i | ||||||||
\(288\) | 862.510i | 0.176472i | ||||||||
\(289\) | 4260.38 | 0.867165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2149.15 | −0.432939 | ||||||||
\(292\) | − 1098.98i | − 0.220250i | ||||||||
\(293\) | 5491.03i | 1.09484i | 0.836857 | + | 0.547422i | \(0.184391\pi\) | ||||
−0.836857 | + | 0.547422i | \(0.815609\pi\) | |||||||
\(294\) | −118.865 | −0.0235795 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2775.72 | −0.545052 | ||||||||
\(297\) | 9642.56i | 1.88390i | ||||||||
\(298\) | 7067.37i | 1.37383i | ||||||||
\(299\) | 952.398 | 0.184209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7967.05 | 1.52563 | ||||||||
\(302\) | − 2500.99i | − 0.476542i | ||||||||
\(303\) | 3396.30i | 0.643935i | ||||||||
\(304\) | −5444.19 | −1.02712 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 878.399 | 0.164100 | ||||||||
\(307\) | − 7307.59i | − 1.35852i | −0.733897 | − | 0.679261i | \(-0.762300\pi\) | ||||
0.733897 | − | 0.679261i | \(-0.237700\pi\) | |||||||
\(308\) | 1692.71i | 0.313152i | ||||||||
\(309\) | −3429.36 | −0.631357 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7904.92 | 1.44131 | 0.720654 | − | 0.693295i | \(-0.243842\pi\) | ||||
0.720654 | + | 0.693295i | \(0.243842\pi\) | |||||||
\(312\) | − 1158.10i | − 0.210142i | ||||||||
\(313\) | − 10002.4i | − 1.80629i | −0.429336 | − | 0.903145i | \(-0.641252\pi\) | ||||
0.429336 | − | 0.903145i | \(-0.358748\pi\) | |||||||
\(314\) | 1446.96 | 0.260053 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 606.360 | 0.107944 | ||||||||
\(317\) | − 6230.81i | − 1.10397i | −0.833856 | − | 0.551983i | \(-0.813871\pi\) | ||||
0.833856 | − | 0.551983i | \(-0.186129\pi\) | |||||||
\(318\) | 26.8673i | 0.00473788i | ||||||||
\(319\) | −11388.1 | −1.99878 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3159.16 | −0.549306 | ||||||||
\(322\) | 3411.16i | 0.590362i | ||||||||
\(323\) | − 2758.24i | − 0.475147i | ||||||||
\(324\) | −268.107 | −0.0459717 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3864.19 | 0.656495 | ||||||||
\(327\) | − 2475.55i | − 0.418649i | ||||||||
\(328\) | − 1683.83i | − 0.283458i | ||||||||
\(329\) | 580.719 | 0.0973134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4634.51 | −0.769594 | −0.384797 | − | 0.923001i | \(-0.625729\pi\) | ||||
−0.384797 | + | 0.923001i | \(0.625729\pi\) | |||||||
\(332\) | − 868.531i | − 0.143575i | ||||||||
\(333\) | 1541.10i | 0.253609i | ||||||||
\(334\) | −1517.77 | −0.248649 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3377.17 | 0.548332 | ||||||||
\(337\) | 3029.82i | 0.489747i | 0.969555 | + | 0.244874i | \(0.0787464\pi\) | ||||
−0.969555 | + | 0.244874i | \(0.921254\pi\) | |||||||
\(338\) | − 432.902i | − 0.0696651i | ||||||||
\(339\) | 2363.61 | 0.378684 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7321.47 | −1.16270 | ||||||||
\(342\) | 3712.48i | 0.586982i | ||||||||
\(343\) | 6463.66i | 1.01751i | ||||||||
\(344\) | 10596.9 | 1.66089 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11515.6 | −1.78926 | ||||||||
\(347\) | 2841.60i | 0.439611i | 0.975544 | + | 0.219805i | \(0.0705423\pi\) | ||||
−0.975544 | + | 0.219805i | \(0.929458\pi\) | |||||||
\(348\) | − 932.351i | − 0.143619i | ||||||||
\(349\) | −7565.68 | −1.16040 | −0.580202 | − | 0.814472i | \(-0.697027\pi\) | ||||
−0.580202 | + | 0.814472i | \(0.697027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1936.30 | −0.294450 | ||||||||
\(352\) | 4159.76i | 0.629875i | ||||||||
\(353\) | 2339.44i | 0.352736i | 0.984324 | + | 0.176368i | \(0.0564348\pi\) | ||||
−0.984324 | + | 0.176368i | \(0.943565\pi\) | |||||||
\(354\) | 676.100 | 0.101509 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1668.43 | 0.248389 | ||||||||
\(357\) | 1711.00i | 0.253658i | ||||||||
\(358\) | 395.209i | 0.0583449i | ||||||||
\(359\) | 2531.68 | 0.372192 | 0.186096 | − | 0.982532i | \(-0.440417\pi\) | ||||
0.186096 | + | 0.982532i | \(0.440417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4798.45 | 0.699585 | ||||||||
\(362\) | 2744.31i | 0.398447i | ||||||||
\(363\) | 10538.5i | 1.52376i | ||||||||
\(364\) | −339.908 | −0.0489451 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8689.93 | 1.24107 | ||||||||
\(367\) | 6577.81i | 0.935583i | 0.883839 | + | 0.467792i | \(0.154950\pi\) | ||||
−0.883839 | + | 0.467792i | \(0.845050\pi\) | |||||||
\(368\) | 3694.08i | 0.523280i | ||||||||
\(369\) | −934.876 | −0.131891 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 51.7426 | 0.00724081 | ||||||||
\(372\) | − 599.413i | − 0.0835433i | ||||||||
\(373\) | − 2902.72i | − 0.402942i | −0.979495 | − | 0.201471i | \(-0.935428\pi\) | ||||
0.979495 | − | 0.201471i | \(-0.0645721\pi\) | |||||||
\(374\) | 4236.40 | 0.585719 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 772.407 | 0.105941 | ||||||||
\(377\) | − 2286.82i | − 0.312406i | ||||||||
\(378\) | − 6935.16i | − 0.943667i | ||||||||
\(379\) | 1865.73 | 0.252866 | 0.126433 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126433 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2038.26 | 0.274076 | ||||||||
\(382\) | 1734.69i | 0.232342i | ||||||||
\(383\) | − 10836.0i | − 1.44567i | −0.691019 | − | 0.722837i | \(-0.742838\pi\) | ||||
0.691019 | − | 0.722837i | \(-0.257162\pi\) | |||||||
\(384\) | 3466.78 | 0.460712 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3385.55 | 0.446425 | ||||||||
\(387\) | − 5883.46i | − 0.772798i | ||||||||
\(388\) | 839.001i | 0.109778i | ||||||||
\(389\) | 9520.34 | 1.24088 | 0.620438 | − | 0.784256i | \(-0.286955\pi\) | ||||
0.620438 | + | 0.784256i | \(0.286955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1871.56 | −0.242069 | ||||||||
\(392\) | 304.480i | 0.0392310i | ||||||||
\(393\) | 7577.13i | 0.972559i | ||||||||
\(394\) | −3246.43 | −0.415108 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1250.02 | 0.158626 | ||||||||
\(397\) | − 10108.8i | − 1.27796i | −0.769225 | − | 0.638978i | \(-0.779358\pi\) | ||||
0.769225 | − | 0.638978i | \(-0.220642\pi\) | |||||||
\(398\) | − 6138.10i | − 0.773053i | ||||||||
\(399\) | −7231.41 | −0.907327 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2084.38 | 0.259573 | 0.129787 | − | 0.991542i | \(-0.458571\pi\) | ||||
0.129787 | + | 0.991542i | \(0.458571\pi\) | |||||||
\(402\) | 4193.32i | 0.520258i | ||||||||
\(403\) | − 1470.21i | − 0.181728i | ||||||||
\(404\) | 1325.88 | 0.163279 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8190.60 | 1.00121 | ||||||||
\(407\) | 7432.50i | 0.905197i | ||||||||
\(408\) | 2275.78i | 0.276147i | ||||||||
\(409\) | 9716.53 | 1.17470 | 0.587349 | − | 0.809334i | \(-0.300172\pi\) | ||||
0.587349 | + | 0.809334i | \(0.300172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6663.95 | 0.799777 | ||||||||
\(412\) | 1338.78i | 0.160090i | ||||||||
\(413\) | − 1302.07i | − 0.155135i | ||||||||
\(414\) | 2519.05 | 0.299045 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −835.311 | −0.0984483 | ||||||||
\(417\) | − 5503.54i | − 0.646305i | ||||||||
\(418\) | 17904.8i | 2.09510i | ||||||||
\(419\) | −13381.9 | −1.56026 | −0.780129 | − | 0.625619i | \(-0.784847\pi\) | ||||
−0.780129 | + | 0.625619i | \(0.784847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9463.37 | −1.09553 | −0.547763 | − | 0.836633i | \(-0.684521\pi\) | ||||
−0.547763 | + | 0.836633i | \(0.684521\pi\) | |||||||
\(422\) | − 234.520i | − 0.0270527i | ||||||||
\(423\) | − 428.846i | − 0.0492936i | ||||||||
\(424\) | 68.8221 | 0.00788278 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5112.98 | 0.581514 | ||||||||
\(427\) | − 16735.5i | − 1.89670i | ||||||||
\(428\) | 1233.30i | 0.139285i | ||||||||
\(429\) | −3101.02 | −0.348994 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4852.28 | 0.542288 | 0.271144 | − | 0.962539i | \(-0.412598\pi\) | ||||
0.271144 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(432\) | − 7510.35i | − 0.836439i | ||||||||
\(433\) | 8208.00i | 0.910973i | 0.890243 | + | 0.455486i | \(0.150535\pi\) | ||||
−0.890243 | + | 0.455486i | \(0.849465\pi\) | |||||||
\(434\) | 5265.78 | 0.582409 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −966.425 | −0.106155 | ||||||||
\(437\) | − 7910.01i | − 0.865874i | ||||||||
\(438\) | 7211.01i | 0.786656i | ||||||||
\(439\) | 2993.80 | 0.325481 | 0.162741 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162741 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 169.049 | 0.0182539 | ||||||||
\(442\) | 850.700i | 0.0915468i | ||||||||
\(443\) | − 9743.67i | − 1.04500i | −0.852639 | − | 0.522501i | \(-0.824999\pi\) | ||||
0.852639 | − | 0.522501i | \(-0.175001\pi\) | |||||||
\(444\) | −608.503 | −0.0650411 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3164.59 | 0.335981 | ||||||||
\(447\) | 10166.0i | 1.07570i | ||||||||
\(448\) | − 10324.2i | − 1.08878i | ||||||||
\(449\) | 561.459 | 0.0590131 | 0.0295065 | − | 0.999565i | \(-0.490606\pi\) | ||||
0.0295065 | + | 0.999565i | \(0.490606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4508.78 | −0.470754 | ||||||||
\(452\) | − 922.726i | − 0.0960207i | ||||||||
\(453\) | − 3597.54i | − 0.373128i | ||||||||
\(454\) | −8457.38 | −0.874283 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9618.40 | −0.987770 | ||||||||
\(457\) | 13758.4i | 1.40830i | 0.710054 | + | 0.704148i | \(0.248671\pi\) | ||||
−0.710054 | + | 0.704148i | \(0.751329\pi\) | |||||||
\(458\) | − 541.213i | − 0.0552166i | ||||||||
\(459\) | 3805.03 | 0.386936 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12009.2 | 1.21329 | 0.606644 | − | 0.794974i | \(-0.292515\pi\) | ||||
0.606644 | + | 0.794974i | \(0.292515\pi\) | |||||||
\(462\) | − 11106.8i | − 1.11847i | ||||||||
\(463\) | − 13635.7i | − 1.36870i | −0.729156 | − | 0.684348i | \(-0.760087\pi\) | ||||
0.729156 | − | 0.684348i | \(-0.239913\pi\) | |||||||
\(464\) | 8869.91 | 0.887447 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −657.613 | −0.0653719 | ||||||||
\(467\) | 8821.95i | 0.874157i | 0.899423 | + | 0.437079i | \(0.143987\pi\) | ||||
−0.899423 | + | 0.437079i | \(0.856013\pi\) | |||||||
\(468\) | 251.013i | 0.0247929i | ||||||||
\(469\) | 8075.72 | 0.795100 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2081.37 | 0.203619 | ||||||||
\(472\) | − 1731.87i | − 0.168889i | ||||||||
\(473\) | − 28375.1i | − 2.75832i | ||||||||
\(474\) | −3978.66 | −0.385540 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 667.956 | 0.0643187 | ||||||||
\(477\) | − 38.2105i | − 0.00366780i | ||||||||
\(478\) | 9092.54i | 0.870049i | ||||||||
\(479\) | 14620.0 | 1.39459 | 0.697293 | − | 0.716786i | \(-0.254388\pi\) | ||||
0.697293 | + | 0.716786i | \(0.254388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1492.50 | −0.141481 | ||||||||
\(482\) | − 12884.9i | − 1.21761i | ||||||||
\(483\) | 4906.78i | 0.462249i | ||||||||
\(484\) | 4114.09 | 0.386372 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8542.20 | −0.797288 | ||||||||
\(487\) | − 9798.86i | − 0.911763i | −0.890040 | − | 0.455882i | \(-0.849324\pi\) | ||||
0.890040 | − | 0.455882i | \(-0.150676\pi\) | |||||||
\(488\) | − 22259.7i | − 2.06486i | ||||||||
\(489\) | 5558.43 | 0.514030 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10836.1 | −0.995977 | −0.497989 | − | 0.867184i | \(-0.665928\pi\) | ||||
−0.497989 | + | 0.867184i | \(0.665928\pi\) | |||||||
\(492\) | − 369.136i | − 0.0338251i | ||||||||
\(493\) | 4493.84i | 0.410532i | ||||||||
\(494\) | −3595.41 | −0.327460 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5702.51 | 0.516230 | ||||||||
\(497\) | − 9846.86i | − 0.888717i | ||||||||
\(498\) | 5698.91i | 0.512800i | ||||||||
\(499\) | −2589.96 | −0.232349 | −0.116175 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116175 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2183.24 | −0.194690 | ||||||||
\(502\) | − 1841.20i | − 0.163699i | ||||||||
\(503\) | 17067.5i | 1.51292i | 0.654038 | + | 0.756462i | \(0.273074\pi\) | ||||
−0.654038 | + | 0.756462i | \(0.726926\pi\) | |||||||
\(504\) | −5899.12 | −0.521364 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12149.0 | 1.06737 | ||||||||
\(507\) | − 622.707i | − 0.0545471i | ||||||||
\(508\) | − 795.712i | − 0.0694961i | ||||||||
\(509\) | 1012.89 | 0.0882038 | 0.0441019 | − | 0.999027i | \(-0.485957\pi\) | ||||
0.0441019 | + | 0.999027i | \(0.485957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13887.4 | 1.20223 | ||||||||
\(512\) | − 12992.6i | − 1.12148i | ||||||||
\(513\) | 16081.7i | 1.38406i | ||||||||
\(514\) | −3280.82 | −0.281539 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2323.08 | 0.198194 | ||||||||
\(517\) | − 2068.26i | − 0.175942i | ||||||||
\(518\) | − 5345.63i | − 0.453424i | ||||||||
\(519\) | −16564.6 | −1.40098 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14367.7 | −1.20818 | −0.604089 | − | 0.796917i | \(-0.706463\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(522\) | − 6048.54i | − 0.507160i | ||||||||
\(523\) | 16219.9i | 1.35611i | 0.735010 | + | 0.678057i | \(0.237178\pi\) | ||||
−0.735010 | + | 0.678057i | \(0.762822\pi\) | |||||||
\(524\) | 2958.02 | 0.246607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13385.5 | 1.10957 | ||||||||
\(527\) | 2889.11i | 0.238808i | ||||||||
\(528\) | − 12028.0i | − 0.991382i | ||||||||
\(529\) | 6799.77 | 0.558870 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −961.545 | −0.0785828 | ||||||||
\(532\) | 2823.06i | 0.230066i | ||||||||
\(533\) | − 905.396i | − 0.0735780i | ||||||||
\(534\) | −10947.5 | −0.887161 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10741.4 | 0.865593 | ||||||||
\(537\) | 568.488i | 0.0456835i | ||||||||
\(538\) | − 16506.1i | − 1.32273i | ||||||||
\(539\) | 815.301 | 0.0651530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17592.2 | 1.39806 | 0.699029 | − | 0.715094i | \(-0.253616\pi\) | ||||
0.699029 | + | 0.715094i | \(0.253616\pi\) | |||||||
\(542\) | − 10066.7i | − 0.797792i | ||||||||
\(543\) | 3947.55i | 0.311980i | ||||||||
\(544\) | 1641.48 | 0.129371 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2230.32 | 0.174815 | ||||||||
\(547\) | 10504.6i | 0.821103i | 0.911837 | + | 0.410552i | \(0.134664\pi\) | ||||
−0.911837 | + | 0.410552i | \(0.865336\pi\) | |||||||
\(548\) | − 2601.53i | − 0.202795i | ||||||||
\(549\) | −12358.8 | −0.960763 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18992.8 | −1.46846 | ||||||||
\(552\) | 6526.44i | 0.503231i | ||||||||
\(553\) | 7662.33i | 0.589214i | ||||||||
\(554\) | 15073.2 | 1.15596 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2148.52 | −0.163880 | ||||||||
\(557\) | − 507.558i | − 0.0386102i | −0.999814 | − | 0.0193051i | \(-0.993855\pi\) | ||||
0.999814 | − | 0.0193051i | \(-0.00614539\pi\) | |||||||
\(558\) | − 3888.64i | − 0.295016i | ||||||||
\(559\) | 5697.93 | 0.431121 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6093.83 | 0.458613 | ||||||||
\(562\) | 9041.75i | 0.678653i | ||||||||
\(563\) | 3443.14i | 0.257746i | 0.991661 | + | 0.128873i | \(0.0411360\pi\) | ||||
−0.991661 | + | 0.128873i | \(0.958864\pi\) | |||||||
\(564\) | 169.330 | 0.0126420 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6688.21 | −0.496690 | ||||||||
\(567\) | − 3387.96i | − 0.250936i | ||||||||
\(568\) | − 13097.2i | − 0.967509i | ||||||||
\(569\) | −23972.2 | −1.76620 | −0.883098 | − | 0.469189i | \(-0.844546\pi\) | ||||
−0.883098 | + | 0.469189i | \(0.844546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7458.32 | −0.546622 | −0.273311 | − | 0.961926i | \(-0.588119\pi\) | ||||
−0.273311 | + | 0.961926i | \(0.588119\pi\) | |||||||
\(572\) | 1210.60i | 0.0884926i | ||||||||
\(573\) | 2495.26i | 0.181922i | ||||||||
\(574\) | 3242.82 | 0.235806 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7624.14 | −0.551515 | ||||||||
\(577\) | 5669.57i | 0.409059i | 0.978860 | + | 0.204530i | \(0.0655665\pi\) | ||||
−0.978860 | + | 0.204530i | \(0.934434\pi\) | |||||||
\(578\) | 10913.2i | 0.785344i | ||||||||
\(579\) | 4869.94 | 0.349547 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10975.3 | 0.783702 | ||||||||
\(582\) | − 5505.15i | − 0.392089i | ||||||||
\(583\) | − 184.284i | − 0.0130914i | ||||||||
\(584\) | 18471.4 | 1.30882 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14065.6 | −0.991541 | ||||||||
\(587\) | 1017.39i | 0.0715371i | 0.999360 | + | 0.0357685i | \(0.0113879\pi\) | ||||
−0.999360 | + | 0.0357685i | \(0.988612\pi\) | |||||||
\(588\) | 66.7491i | 0.00468144i | ||||||||
\(589\) | −12210.6 | −0.854208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4669.81 | −0.325026 | ||||||||
\(592\) | − 5788.99i | − 0.401902i | ||||||||
\(593\) | 10198.2i | 0.706221i | 0.935582 | + | 0.353111i | \(0.114876\pi\) | ||||
−0.935582 | + | 0.353111i | \(0.885124\pi\) | |||||||
\(594\) | −24699.9 | −1.70615 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3968.70 | 0.272759 | ||||||||
\(597\) | − 8829.33i | − 0.605294i | ||||||||
\(598\) | 2439.62i | 0.166828i | ||||||||
\(599\) | −12516.3 | −0.853763 | −0.426881 | − | 0.904308i | \(-0.640388\pi\) | ||||
−0.426881 | + | 0.904308i | \(0.640388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9627.46 | 0.653431 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(602\) | 20408.0i | 1.38168i | ||||||||
\(603\) | − 5963.70i | − 0.402754i | ||||||||
\(604\) | −1404.44 | −0.0946120 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8699.80 | −0.583177 | ||||||||
\(607\) | 6667.20i | 0.445821i | 0.974839 | + | 0.222910i | \(0.0715557\pi\) | ||||
−0.974839 | + | 0.222910i | \(0.928444\pi\) | |||||||
\(608\) | 6937.56i | 0.462755i | ||||||||
\(609\) | 11781.7 | 0.783942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 415.323 | 0.0274994 | ||||||||
\(612\) | − 493.268i | − 0.0325803i | ||||||||
\(613\) | 23085.4i | 1.52106i | 0.649302 | + | 0.760530i | \(0.275061\pi\) | ||||
−0.649302 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(614\) | 18718.8 | 1.23034 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28450.6 | −1.86089 | ||||||||
\(617\) | 3049.24i | 0.198959i | 0.995040 | + | 0.0994796i | \(0.0317178\pi\) | ||||
−0.995040 | + | 0.0994796i | \(0.968282\pi\) | |||||||
\(618\) | − 8784.48i | − 0.571786i | ||||||||
\(619\) | −7296.58 | −0.473787 | −0.236894 | − | 0.971536i | \(-0.576129\pi\) | ||||
−0.236894 | + | 0.971536i | \(0.576129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10912.0 | 0.705126 | ||||||||
\(622\) | 20248.9i | 1.30531i | ||||||||
\(623\) | 21083.3i | 1.35583i | ||||||||
\(624\) | 2415.30 | 0.154951 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25621.7 | 1.63586 | ||||||||
\(627\) | 25755.1i | 1.64044i | ||||||||
\(628\) | − 812.543i | − 0.0516305i | ||||||||
\(629\) | 2932.92 | 0.185920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23829.5 | −1.50339 | −0.751694 | − | 0.659512i | \(-0.770763\pi\) | ||||
−0.751694 | + | 0.659512i | \(0.770763\pi\) | |||||||
\(632\) | 10191.6i | 0.641453i | ||||||||
\(633\) | − 337.345i | − 0.0211821i | ||||||||
\(634\) | 15960.5 | 0.999801 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.0874 | 0.000940653 0 | ||||||||
\(637\) | 163.718i | 0.0101833i | ||||||||
\(638\) | − 29171.3i | − 1.81019i | ||||||||
\(639\) | −7271.65 | −0.450175 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13405.3 | 0.826016 | 0.413008 | − | 0.910727i | \(-0.364478\pi\) | ||||
0.413008 | + | 0.910727i | \(0.364478\pi\) | |||||||
\(642\) | − 8092.36i | − 0.497477i | ||||||||
\(643\) | − 5251.51i | − 0.322083i | −0.986948 | − | 0.161042i | \(-0.948515\pi\) | ||||
0.986948 | − | 0.161042i | \(-0.0514853\pi\) | |||||||
\(644\) | 1915.55 | 0.117210 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7065.37 | 0.430315 | ||||||||
\(647\) | 21611.4i | 1.31319i | 0.754244 | + | 0.656595i | \(0.228004\pi\) | ||||
−0.754244 | + | 0.656595i | \(0.771996\pi\) | |||||||
\(648\) | − 4506.28i | − 0.273184i | ||||||||
\(649\) | −4637.39 | −0.280483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7574.54 | 0.456021 | ||||||||
\(652\) | − 2169.94i | − 0.130340i | ||||||||
\(653\) | 21595.8i | 1.29420i | 0.762406 | + | 0.647099i | \(0.224018\pi\) | ||||
−0.762406 | + | 0.647099i | \(0.775982\pi\) | |||||||
\(654\) | 6341.25 | 0.379148 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3511.77 | 0.209012 | ||||||||
\(657\) | − 10255.4i | − 0.608985i | ||||||||
\(658\) | 1487.54i | 0.0881314i | ||||||||
\(659\) | 16642.6 | 0.983768 | 0.491884 | − | 0.870661i | \(-0.336308\pi\) | ||||
0.491884 | + | 0.870661i | \(0.336308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26981.1 | 1.58766 | 0.793831 | − | 0.608139i | \(-0.208084\pi\) | ||||
0.793831 | + | 0.608139i | \(0.208084\pi\) | |||||||
\(662\) | − 11871.5i | − 0.696980i | ||||||||
\(663\) | 1223.69i | 0.0716803i | ||||||||
\(664\) | 14598.1 | 0.853185 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3947.60 | −0.229680 | ||||||||
\(667\) | 12887.3i | 0.748126i | ||||||||
\(668\) | 852.310i | 0.0493665i | ||||||||
\(669\) | 4552.09 | 0.263070 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −59604.5 | −3.42922 | ||||||||
\(672\) | − 4303.55i | − 0.247043i | ||||||||
\(673\) | − 11149.2i | − 0.638591i | −0.947655 | − | 0.319296i | \(-0.896554\pi\) | ||||
0.947655 | − | 0.319296i | \(-0.103446\pi\) | |||||||
\(674\) | −7761.04 | −0.443537 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −243.098 | −0.0138312 | ||||||||
\(677\) | 3314.33i | 0.188154i | 0.995565 | + | 0.0940769i | \(0.0299900\pi\) | ||||
−0.995565 | + | 0.0940769i | \(0.970010\pi\) | |||||||
\(678\) | 6054.51i | 0.342953i | ||||||||
\(679\) | −10602.1 | −0.599223 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12165.5 | −0.684556 | ||||||||
\(682\) | − 18754.3i | − 1.05299i | ||||||||
\(683\) | − 24505.2i | − 1.37287i | −0.727193 | − | 0.686433i | \(-0.759176\pi\) | ||||
0.727193 | − | 0.686433i | \(-0.240824\pi\) | |||||||
\(684\) | 2084.75 | 0.116539 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16557.0 | −0.921500 | ||||||||
\(687\) | − 778.506i | − 0.0432342i | ||||||||
\(688\) | 22100.6i | 1.22468i | ||||||||
\(689\) | 37.0056 | 0.00204616 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21752.8 | −1.19756 | −0.598782 | − | 0.800912i | \(-0.704348\pi\) | ||||
−0.598782 | + | 0.800912i | \(0.704348\pi\) | |||||||
\(692\) | 6466.64i | 0.355238i | ||||||||
\(693\) | 15796.0i | 0.865858i | ||||||||
\(694\) | −7278.90 | −0.398132 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15670.7 | 0.853445 | ||||||||
\(697\) | 1779.20i | 0.0966887i | ||||||||
\(698\) | − 19379.9i | − 1.05092i | ||||||||
\(699\) | −945.941 | −0.0511857 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34250.9 | 1.84542 | 0.922709 | − | 0.385496i | \(-0.125970\pi\) | ||||
0.922709 | + | 0.385496i | \(0.125970\pi\) | |||||||
\(702\) | − 4959.93i | − 0.266667i | ||||||||
\(703\) | 12395.8i | 0.665028i | ||||||||
\(704\) | −36770.1 | −1.96850 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5992.59 | −0.319454 | ||||||||
\(707\) | 16754.6i | 0.891259i | ||||||||
\(708\) | − 379.666i | − 0.0201536i | ||||||||
\(709\) | 5527.11 | 0.292771 | 0.146386 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146386 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5658.43 | 0.298464 | ||||||||
\(712\) | 28042.6i | 1.47604i | ||||||||
\(713\) | 8285.33i | 0.435187i | ||||||||
\(714\) | −4382.83 | −0.229724 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 221.931 | 0.0115837 | ||||||||
\(717\) | 13079.1i | 0.681241i | ||||||||
\(718\) | 6485.02i | 0.337074i | ||||||||
\(719\) | 3777.78 | 0.195949 | 0.0979745 | − | 0.995189i | \(-0.468764\pi\) | ||||
0.0979745 | + | 0.995189i | \(0.468764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16917.6 | −0.873849 | ||||||||
\(722\) | 12291.5i | 0.633576i | ||||||||
\(723\) | − 18534.2i | − 0.953380i | ||||||||
\(724\) | 1541.08 | 0.0791072 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26994.8 | −1.37999 | ||||||||
\(727\) | 19076.8i | 0.973204i | 0.873624 | + | 0.486602i | \(0.161764\pi\) | ||||
−0.873624 | + | 0.486602i | \(0.838236\pi\) | |||||||
\(728\) | − 5713.09i | − 0.290853i | ||||||||
\(729\) | −17319.9 | −0.879944 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11197.0 | −0.566535 | ||||||||
\(732\) | − 4879.86i | − 0.246400i | ||||||||
\(733\) | − 7997.30i | − 0.402984i | −0.979490 | − | 0.201492i | \(-0.935421\pi\) | ||||
0.979490 | − | 0.201492i | \(-0.0645790\pi\) | |||||||
\(734\) | −16849.4 | −0.847307 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4707.39 | 0.235756 | ||||||||
\(737\) | − 28762.1i | − 1.43754i | ||||||||
\(738\) | − 2394.74i | − 0.119446i | ||||||||
\(739\) | −28983.6 | −1.44273 | −0.721367 | − | 0.692553i | \(-0.756486\pi\) | ||||
−0.721367 | + | 0.692553i | \(0.756486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5171.81 | −0.256398 | ||||||||
\(742\) | 132.541i | 0.00655761i | ||||||||
\(743\) | 19145.4i | 0.945324i | 0.881244 | + | 0.472662i | \(0.156707\pi\) | ||||
−0.881244 | + | 0.472662i | \(0.843293\pi\) | |||||||
\(744\) | 10074.8 | 0.496451 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7435.47 | 0.364922 | ||||||||
\(747\) | − 8104.95i | − 0.396981i | ||||||||
\(748\) | − 2378.96i | − 0.116288i | ||||||||
\(749\) | −15584.7 | −0.760284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25516.9 | −1.23985 | −0.619923 | − | 0.784663i | \(-0.712836\pi\) | ||||
−0.619923 | + | 0.784663i | \(0.712836\pi\) | |||||||
\(752\) | 1610.92i | 0.0781172i | ||||||||
\(753\) | − 2648.47i | − 0.128175i | ||||||||
\(754\) | 5857.80 | 0.282929 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3894.46 | −0.187355 | ||||||||
\(757\) | − 17230.6i | − 0.827289i | −0.910438 | − | 0.413645i | \(-0.864256\pi\) | ||||
0.910438 | − | 0.413645i | \(-0.135744\pi\) | |||||||
\(758\) | 4779.17i | 0.229007i | ||||||||
\(759\) | 17475.7 | 0.835744 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2343.06 | −0.111611 | −0.0558053 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558053 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(762\) | 5221.11i | 0.248216i | ||||||||
\(763\) | − 12212.3i | − 0.579444i | ||||||||
\(764\) | 974.121 | 0.0461289 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27756.9 | 1.30927 | ||||||||
\(767\) | − 931.223i | − 0.0438390i | ||||||||
\(768\) | − 7862.11i | − 0.369400i | ||||||||
\(769\) | 7100.18 | 0.332950 | 0.166475 | − | 0.986046i | \(-0.446761\pi\) | ||||
0.166475 | + | 0.986046i | \(0.446761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4719.29 | −0.220442 | ||||||||
\(772\) | − 1901.17i | − 0.0886328i | ||||||||
\(773\) | − 12270.4i | − 0.570940i | −0.958388 | − | 0.285470i | \(-0.907850\pi\) | ||||
0.958388 | − | 0.285470i | \(-0.0921498\pi\) | |||||||
\(774\) | 15070.8 | 0.699881 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14101.7 | −0.652349 | ||||||||
\(777\) | − 7689.40i | − 0.355027i | ||||||||
\(778\) | 24386.9i | 1.12379i | ||||||||
\(779\) | −7519.64 | −0.345852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35070.1 | −1.60680 | ||||||||
\(782\) | − 4794.11i | − 0.219229i | ||||||||
\(783\) | − 26201.0i | − 1.19584i | ||||||||
\(784\) | −635.017 | −0.0289275 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19409.2 | −0.880794 | ||||||||
\(787\) | 3425.04i | 0.155133i | 0.996987 | + | 0.0775663i | \(0.0247150\pi\) | ||||
−0.996987 | + | 0.0775663i | \(0.975285\pi\) | |||||||
\(788\) | 1823.04i | 0.0824151i | ||||||||
\(789\) | 19254.3 | 0.868787 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11660.1 | 0.524129 | ||||||||
\(792\) | 21010.0i | 0.942624i | ||||||||
\(793\) | − 11969.0i | − 0.535981i | ||||||||
\(794\) | 25894.3 | 1.15737 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3446.87 | −0.153481 | ||||||||
\(797\) | − 11781.1i | − 0.523600i | −0.965122 | − | 0.261800i | \(-0.915684\pi\) | ||||
0.965122 | − | 0.261800i | \(-0.0843160\pi\) | |||||||
\(798\) | − 18523.6i | − 0.821717i | ||||||||
\(799\) | −816.154 | −0.0361370 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15569.4 | 0.686790 | ||||||||
\(802\) | 5339.24i | 0.235081i | ||||||||
\(803\) | − 49460.6i | − 2.17363i | ||||||||
\(804\) | 2354.77 | 0.103291 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3766.01 | 0.164581 | ||||||||
\(807\) | − 23743.2i | − 1.03569i | ||||||||
\(808\) | 22285.0i | 0.970276i | ||||||||
\(809\) | −18910.1 | −0.821810 | −0.410905 | − | 0.911678i | \(-0.634787\pi\) | ||||
−0.410905 | + | 0.911678i | \(0.634787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12803.3 | 0.554359 | 0.277180 | − | 0.960818i | \(-0.410600\pi\) | ||||
0.277180 | + | 0.960818i | \(0.410600\pi\) | |||||||
\(812\) | − 4599.45i | − 0.198780i | ||||||||
\(813\) | − 14480.5i | − 0.624664i | ||||||||
\(814\) | −19038.7 | −0.819788 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4746.33 | −0.203621 | ||||||||
\(817\) | − 47323.3i | − 2.02648i | ||||||||
\(818\) | 24889.4i | 1.06386i | ||||||||
\(819\) | −3171.95 | −0.135332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19335.1 | 0.821923 | 0.410962 | − | 0.911653i | \(-0.365193\pi\) | ||||
0.410962 | + | 0.911653i | \(0.365193\pi\) | |||||||
\(822\) | 17070.1i | 0.724315i | ||||||||
\(823\) | 2125.90i | 0.0900417i | 0.998986 | + | 0.0450209i | \(0.0143354\pi\) | ||||
−0.998986 | + | 0.0450209i | \(0.985665\pi\) | |||||||
\(824\) | −22501.9 | −0.951324 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3335.32 | 0.140497 | ||||||||
\(827\) | − 6989.24i | − 0.293881i | −0.989145 | − | 0.146941i | \(-0.953057\pi\) | ||||
0.989145 | − | 0.146941i | \(-0.0469426\pi\) | |||||||
\(828\) | − 1414.58i | − 0.0593721i | ||||||||
\(829\) | 32649.7 | 1.36788 | 0.683938 | − | 0.729540i | \(-0.260266\pi\) | ||||
0.683938 | + | 0.729540i | \(0.260266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21682.0 | 0.905103 | ||||||||
\(832\) | − 7383.72i | − 0.307673i | ||||||||
\(833\) | − 321.724i | − 0.0133819i | ||||||||
\(834\) | 14097.6 | 0.585324 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10054.5 | 0.415958 | ||||||||
\(837\) | − 16844.7i | − 0.695626i | ||||||||
\(838\) | − 34278.4i | − 1.41304i | ||||||||
\(839\) | 4038.23 | 0.166168 | 0.0830841 | − | 0.996543i | \(-0.473523\pi\) | ||||
0.0830841 | + | 0.996543i | \(0.473523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6555.00 | 0.268769 | ||||||||
\(842\) | − 24240.9i | − 0.992159i | ||||||||
\(843\) | 13006.1i | 0.531380i | ||||||||
\(844\) | −131.695 | −0.00537102 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1098.51 | 0.0446426 | ||||||||
\(847\) | 51988.1i | 2.10901i | ||||||||
\(848\) | 143.534i | 0.00581248i | ||||||||
\(849\) | −9620.64 | −0.388904 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8410.97 | 0.338807 | ||||||||
\(852\) | − 2871.21i | − 0.115453i | ||||||||
\(853\) | − 8114.12i | − 0.325700i | −0.986651 | − | 0.162850i | \(-0.947931\pi\) | ||||
0.986651 | − | 0.162850i | \(-0.0520687\pi\) | |||||||
\(854\) | 42869.0 | 1.71774 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20729.0 | −0.827690 | ||||||||
\(857\) | − 22298.1i | − 0.888786i | −0.895832 | − | 0.444393i | \(-0.853419\pi\) | ||||
0.895832 | − | 0.444393i | \(-0.146581\pi\) | |||||||
\(858\) | − 7943.42i | − 0.316065i | ||||||||
\(859\) | −33550.5 | −1.33263 | −0.666315 | − | 0.745670i | \(-0.732130\pi\) | ||||
−0.666315 | + | 0.745670i | \(0.732130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4664.62 | 0.184634 | ||||||||
\(862\) | 12429.4i | 0.491121i | ||||||||
\(863\) | 14120.5i | 0.556972i | 0.960440 | + | 0.278486i | \(0.0898326\pi\) | ||||
−0.960440 | + | 0.278486i | \(0.910167\pi\) | |||||||
\(864\) | −9570.49 | −0.376846 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21025.2 | −0.825018 | ||||||||
\(867\) | 15698.1i | 0.614918i | ||||||||
\(868\) | − 2957.01i | − 0.115631i | ||||||||
\(869\) | 27289.8 | 1.06530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5775.64 | 0.224685 | ||||||||
\(872\) | − 16243.4i | − 0.630817i | ||||||||
\(873\) | 7829.39i | 0.303533i | ||||||||
\(874\) | 20261.9 | 0.784175 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4049.36 | 0.156182 | ||||||||
\(877\) | − 1941.69i | − 0.0747619i | −0.999301 | − | 0.0373809i | \(-0.988099\pi\) | ||||
0.999301 | − | 0.0373809i | \(-0.0119015\pi\) | |||||||
\(878\) | 7668.78i | 0.294771i | ||||||||
\(879\) | −20232.6 | −0.776368 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −790.231 | −0.0302197 | −0.0151099 | − | 0.999886i | \(-0.504810\pi\) | ||||
−0.0151099 | + | 0.999886i | \(0.504810\pi\) | |||||||
\(882\) | 433.029i | 0.0165316i | ||||||||
\(883\) | 36638.6i | 1.39636i | 0.715922 | + | 0.698180i | \(0.246007\pi\) | ||||
−0.715922 | + | 0.698180i | \(0.753993\pi\) | |||||||
\(884\) | 477.713 | 0.0181756 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24958.9 | 0.946401 | ||||||||
\(887\) | − 40686.3i | − 1.54015i | −0.637954 | − | 0.770075i | \(-0.720219\pi\) | ||||
0.637954 | − | 0.770075i | \(-0.279781\pi\) | |||||||
\(888\) | − 10227.6i | − 0.386503i | ||||||||
\(889\) | 10055.1 | 0.379344 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12066.4 | −0.453692 | ||||||||
\(892\) | − 1777.08i | − 0.0667053i | ||||||||
\(893\) | − 3449.40i | − 0.129261i | ||||||||
\(894\) | −26040.9 | −0.974202 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17102.2 | 0.637663 | ||||||||
\(897\) | 3509.26i | 0.130625i | ||||||||
\(898\) | 1438.21i | 0.0534449i | ||||||||
\(899\) | 19894.0 | 0.738046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −72.7200 | −0.00268885 | ||||||||
\(902\) | − 11549.5i | − 0.426336i | ||||||||
\(903\) | 29355.9i | 1.08184i | ||||||||
\(904\) | 15509.0 | 0.570598 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9215.28 | 0.337922 | ||||||||
\(907\) | − 10464.4i | − 0.383093i | −0.981484 | − | 0.191547i | \(-0.938650\pi\) | ||||
0.981484 | − | 0.191547i | \(-0.0613503\pi\) | |||||||
\(908\) | 4749.26i | 0.173579i | ||||||||
\(909\) | 12372.8 | 0.451463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35611.5 | −1.29513 | −0.647563 | − | 0.762011i | \(-0.724212\pi\) | ||||
−0.647563 | + | 0.762011i | \(0.724212\pi\) | |||||||
\(912\) | − 20060.0i | − 0.728346i | ||||||||
\(913\) | − 39089.0i | − 1.41693i | ||||||||
\(914\) | −35242.9 | −1.27542 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −303.920 | −0.0109627 | ||||||||
\(917\) | 37379.4i | 1.34610i | ||||||||
\(918\) | 9746.80i | 0.350427i | ||||||||
\(919\) | −1077.25 | −0.0386674 | −0.0193337 | − | 0.999813i | \(-0.506154\pi\) | ||||
−0.0193337 | + | 0.999813i | \(0.506154\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26926.0 | 0.963346 | ||||||||
\(922\) | 30762.3i | 1.09881i | ||||||||
\(923\) | − 7042.34i | − 0.251139i | ||||||||
\(924\) | −6237.04 | −0.222060 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34928.6 | 1.23955 | ||||||||
\(927\) | 12493.2i | 0.442644i | ||||||||
\(928\) | − 11303.0i | − 0.399826i | ||||||||
\(929\) | −55733.8 | −1.96832 | −0.984159 | − | 0.177290i | \(-0.943267\pi\) | ||||
−0.984159 | + | 0.177290i | \(0.943267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1359.74 | 0.0478665 | ||||||||
\(932\) | 369.284i | 0.0129789i | ||||||||
\(933\) | 29126.9i | 1.02205i | ||||||||
\(934\) | −22597.9 | −0.791677 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4218.97 | −0.147330 | ||||||||
\(937\) | − 3198.60i | − 0.111519i | −0.998444 | − | 0.0557596i | \(-0.982242\pi\) | ||||
0.998444 | − | 0.0557596i | \(-0.0177581\pi\) | |||||||
\(938\) | 20686.4i | 0.720079i | ||||||||
\(939\) | 36855.4 | 1.28086 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8823.35 | 0.305667 | 0.152834 | − | 0.988252i | \(-0.451160\pi\) | ||||
0.152834 | + | 0.988252i | \(0.451160\pi\) | |||||||
\(942\) | 5331.54i | 0.184407i | ||||||||
\(943\) | 5102.35i | 0.176199i | ||||||||
\(944\) | 3611.95 | 0.124533 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 72684.3 | 2.49806 | ||||||||
\(947\) | 28290.4i | 0.970766i | 0.874301 | + | 0.485383i | \(0.161320\pi\) | ||||
−0.874301 | + | 0.485383i | \(0.838680\pi\) | |||||||
\(948\) | 2234.23i | 0.0765447i | ||||||||
\(949\) | 9932.05 | 0.339734 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22958.4 | 0.782836 | ||||||||
\(952\) | 11226.8i | 0.382210i | ||||||||
\(953\) | 12399.0i | 0.421452i | 0.977545 | + | 0.210726i | \(0.0675828\pi\) | ||||
−0.977545 | + | 0.210726i | \(0.932417\pi\) | |||||||
\(954\) | 97.8783 | 0.00332173 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5105.94 | 0.172739 | ||||||||
\(957\) | − 41961.3i | − 1.41736i | ||||||||
\(958\) | 37450.0i | 1.26300i | ||||||||
\(959\) | 32874.5 | 1.10696 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17001.0 | −0.570676 | ||||||||
\(962\) | − 3823.12i | − 0.128131i | ||||||||
\(963\) | 11508.9i | 0.385118i | ||||||||
\(964\) | −7235.53 | −0.241744 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12569.0 | −0.418634 | ||||||||
\(967\) | − 26667.1i | − 0.886820i | −0.896319 | − | 0.443410i | \(-0.853769\pi\) | ||||
0.896319 | − | 0.443410i | \(-0.146231\pi\) | |||||||
\(968\) | 69148.6i | 2.29599i | ||||||||
\(969\) | 10163.2 | 0.336933 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49420.7 | 1.63335 | 0.816676 | − | 0.577096i | \(-0.195814\pi\) | ||||
0.816676 | + | 0.577096i | \(0.195814\pi\) | |||||||
\(972\) | 4796.89i | 0.158293i | ||||||||
\(973\) | − 27149.9i | − 0.894539i | ||||||||
\(974\) | 25100.3 | 0.825735 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46424.5 | 1.52255 | ||||||||
\(977\) | 778.759i | 0.0255012i | 0.999919 | + | 0.0127506i | \(0.00405876\pi\) | ||||
−0.999919 | + | 0.0127506i | \(0.995941\pi\) | |||||||
\(978\) | 14238.2i | 0.465529i | ||||||||
\(979\) | 75089.2 | 2.45134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9018.48 | −0.293515 | ||||||||
\(982\) | − 27757.2i | − 0.902003i | ||||||||
\(983\) | − 5997.90i | − 0.194612i | −0.995255 | − | 0.0973059i | \(-0.968977\pi\) | ||||
0.995255 | − | 0.0973059i | \(-0.0310225\pi\) | |||||||
\(984\) | 6204.35 | 0.201004 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11511.2 | −0.371797 | ||||||||
\(987\) | 2139.75i | 0.0690062i | ||||||||
\(988\) | 2019.01i | 0.0650135i | ||||||||
\(989\) | −32110.6 | −1.03241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8974.94 | 0.287688 | 0.143844 | − | 0.989600i | \(-0.454054\pi\) | ||||
0.143844 | + | 0.989600i | \(0.454054\pi\) | |||||||
\(992\) | − 7266.75i | − 0.232580i | ||||||||
\(993\) | − 17076.6i | − 0.545729i | ||||||||
\(994\) | 25223.3 | 0.804863 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3200.24 | 0.101811 | ||||||||
\(997\) | 28530.2i | 0.906280i | 0.891439 | + | 0.453140i | \(0.149696\pi\) | ||||
−0.891439 | + | 0.453140i | \(0.850304\pi\) | |||||||
\(998\) | − 6634.31i | − 0.210426i | ||||||||
\(999\) | −17100.2 | −0.541567 |
(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 | 325.4.b.e.274.4 | 4 | ||
5.2 | odd | 4 | 325.4.a.f.1.1 | 2 | |||
5.3 | odd | 4 | 13.4.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 325.4.b.e.274.1 | 4 | ||
15.8 | even | 4 | 117.4.a.d.1.1 | 2 | |||
20.3 | even | 4 | 208.4.a.h.1.2 | 2 | |||
35.13 | even | 4 | 637.4.a.b.1.2 | 2 | |||
40.3 | even | 4 | 832.4.a.z.1.1 | 2 | |||
40.13 | odd | 4 | 832.4.a.s.1.2 | 2 | |||
55.43 | even | 4 | 1573.4.a.b.1.1 | 2 | |||
60.23 | odd | 4 | 1872.4.a.bb.1.1 | 2 | |||
65.3 | odd | 12 | 169.4.c.g.22.1 | 4 | |||
65.8 | even | 4 | 169.4.b.f.168.4 | 4 | |||
65.18 | even | 4 | 169.4.b.f.168.1 | 4 | |||
65.23 | odd | 12 | 169.4.c.j.22.2 | 4 | |||
65.28 | even | 12 | 169.4.e.f.147.4 | 8 | |||
65.33 | even | 12 | 169.4.e.f.23.4 | 8 | |||
65.38 | odd | 4 | 169.4.a.g.1.1 | 2 | |||
65.43 | odd | 12 | 169.4.c.j.146.2 | 4 | |||
65.48 | odd | 12 | 169.4.c.g.146.1 | 4 | |||
65.58 | even | 12 | 169.4.e.f.23.1 | 8 | |||
65.63 | even | 12 | 169.4.e.f.147.1 | 8 | |||
195.38 | even | 4 | 1521.4.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
117.4.a.d.1.1 | 2 | 15.8 | even | 4 | |||
169.4.a.g.1.1 | 2 | 65.38 | odd | 4 | |||
169.4.b.f.168.1 | 4 | 65.18 | even | 4 | |||
169.4.b.f.168.4 | 4 | 65.8 | even | 4 | |||
169.4.c.g.22.1 | 4 | 65.3 | odd | 12 | |||
169.4.c.g.146.1 | 4 | 65.48 | odd | 12 | |||
169.4.c.j.22.2 | 4 | 65.23 | odd | 12 | |||
169.4.c.j.146.2 | 4 | 65.43 | odd | 12 | |||
169.4.e.f.23.1 | 8 | 65.58 | even | 12 | |||
169.4.e.f.23.4 | 8 | 65.33 | even | 12 | |||
169.4.e.f.147.1 | 8 | 65.63 | even | 12 | |||
169.4.e.f.147.4 | 8 | 65.28 | even | 12 | |||
208.4.a.h.1.2 | 2 | 20.3 | even | 4 | |||
325.4.a.f.1.1 | 2 | 5.2 | odd | 4 | |||
325.4.b.e.274.1 | 4 | 5.4 | even | 2 | inner | ||
325.4.b.e.274.4 | 4 | 1.1 | even | 1 | trivial | ||
637.4.a.b.1.2 | 2 | 35.13 | even | 4 | |||
832.4.a.s.1.2 | 2 | 40.13 | odd | 4 | |||
832.4.a.z.1.1 | 2 | 40.3 | even | 4 | |||
1521.4.a.r.1.2 | 2 | 195.38 | even | 4 | |||
1573.4.a.b.1.1 | 2 | 55.43 | even | 4 | |||
1872.4.a.bb.1.1 | 2 | 60.23 | odd | 4 |