Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} + 54x^{6} + 889x^{4} + 4584x^{2} + 5776 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 13^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.8 | ||
Root | \(4.33039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.h.337.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.33039i | 1.88458i | 0.334800 | + | 0.942289i | \(0.391331\pi\) | ||||
−0.334800 | + | 0.942289i | \(0.608669\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −20.4131 | −2.55164 | ||||||||
\(5\) | − 16.4131i | − 1.46803i | −0.679132 | − | 0.734016i | \(-0.737644\pi\) | ||||
0.679132 | − | 0.734016i | \(-0.262356\pi\) | |||||||
\(6\) | − 15.9912i | − 1.08806i | ||||||||
\(7\) | − 9.67968i | − 0.522654i | −0.965250 | − | 0.261327i | \(-0.915840\pi\) | ||||
0.965250 | − | 0.261327i | \(-0.0841601\pi\) | |||||||
\(8\) | − 66.1667i | − 2.92418i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 87.4882 | 2.76662 | ||||||||
\(11\) | − 27.5882i | − 0.756195i | −0.925766 | − | 0.378098i | \(-0.876578\pi\) | ||||
0.925766 | − | 0.378098i | \(-0.123422\pi\) | |||||||
\(12\) | 61.2393 | 1.47319 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 51.5965 | 0.984982 | ||||||||
\(15\) | 49.2393i | 0.847568i | ||||||||
\(16\) | 189.390 | 2.95921 | ||||||||
\(17\) | −107.928 | −1.53979 | −0.769895 | − | 0.638171i | \(-0.779691\pi\) | ||||
−0.769895 | + | 0.638171i | \(0.779691\pi\) | |||||||
\(18\) | 47.9735i | 0.628193i | ||||||||
\(19\) | − 2.24723i | − 0.0271342i | −0.999908 | − | 0.0135671i | \(-0.995681\pi\) | ||||
0.999908 | − | 0.0135671i | \(-0.00431868\pi\) | |||||||
\(20\) | 335.042i | 3.74588i | ||||||||
\(21\) | 29.0391i | 0.301754i | ||||||||
\(22\) | 147.056 | 1.42511 | ||||||||
\(23\) | −41.8090 | −0.379034 | −0.189517 | − | 0.981877i | \(-0.560692\pi\) | ||||
−0.189517 | + | 0.981877i | \(0.560692\pi\) | |||||||
\(24\) | 198.500i | 1.68828i | ||||||||
\(25\) | −144.390 | −1.15512 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 197.592i | 1.33362i | ||||||||
\(29\) | 61.6213 | 0.394579 | 0.197289 | − | 0.980345i | \(-0.436786\pi\) | ||||
0.197289 | + | 0.980345i | \(0.436786\pi\) | |||||||
\(30\) | −262.465 | −1.59731 | ||||||||
\(31\) | 191.932i | 1.11200i | 0.831182 | + | 0.556000i | \(0.187665\pi\) | ||||
−0.831182 | + | 0.556000i | \(0.812335\pi\) | |||||||
\(32\) | 480.187i | 2.65269i | ||||||||
\(33\) | 82.7645i | 0.436589i | ||||||||
\(34\) | − 575.300i | − 2.90185i | ||||||||
\(35\) | −158.874 | −0.767272 | ||||||||
\(36\) | −183.718 | −0.850545 | ||||||||
\(37\) | − 98.4236i | − 0.437317i | −0.975801 | − | 0.218659i | \(-0.929832\pi\) | ||||
0.975801 | − | 0.218659i | \(-0.0701681\pi\) | |||||||
\(38\) | 11.9786 | 0.0511366 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1086.00 | −4.29279 | ||||||||
\(41\) | − 30.7452i | − 0.117112i | −0.998284 | − | 0.0585561i | \(-0.981350\pi\) | ||||
0.998284 | − | 0.0585561i | \(-0.0186496\pi\) | |||||||
\(42\) | −154.790 | −0.568680 | ||||||||
\(43\) | −238.325 | −0.845216 | −0.422608 | − | 0.906313i | \(-0.638885\pi\) | ||||
−0.422608 | + | 0.906313i | \(0.638885\pi\) | |||||||
\(44\) | 563.160i | 1.92953i | ||||||||
\(45\) | − 147.718i | − 0.489344i | ||||||||
\(46\) | − 222.858i | − 0.714319i | ||||||||
\(47\) | 511.482i | 1.58739i | 0.608316 | + | 0.793695i | \(0.291845\pi\) | ||||
−0.608316 | + | 0.793695i | \(0.708155\pi\) | |||||||
\(48\) | −568.169 | −1.70850 | ||||||||
\(49\) | 249.304 | 0.726833 | ||||||||
\(50\) | − 769.653i | − 2.17691i | ||||||||
\(51\) | 323.785 | 0.888998 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 492.825 | 1.27726 | 0.638630 | − | 0.769514i | \(-0.279502\pi\) | ||||
0.638630 | + | 0.769514i | \(0.279502\pi\) | |||||||
\(54\) | − 143.921i | − 0.362687i | ||||||||
\(55\) | −452.807 | −1.11012 | ||||||||
\(56\) | −640.472 | −1.52833 | ||||||||
\(57\) | 6.74170i | 0.0156660i | ||||||||
\(58\) | 328.466i | 0.743615i | ||||||||
\(59\) | − 484.179i | − 1.06838i | −0.845363 | − | 0.534192i | \(-0.820616\pi\) | ||||
0.845363 | − | 0.534192i | \(-0.179384\pi\) | |||||||
\(60\) | − 1005.13i | − 2.16269i | ||||||||
\(61\) | −444.021 | −0.931985 | −0.465993 | − | 0.884789i | \(-0.654303\pi\) | ||||
−0.465993 | + | 0.884789i | \(0.654303\pi\) | |||||||
\(62\) | −1023.07 | −2.09565 | ||||||||
\(63\) | − 87.1172i | − 0.174218i | ||||||||
\(64\) | −1044.47 | −2.03998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −441.167 | −0.822787 | ||||||||
\(67\) | 190.114i | 0.346658i | 0.984864 | + | 0.173329i | \(0.0554524\pi\) | ||||
−0.984864 | + | 0.173329i | \(0.944548\pi\) | |||||||
\(68\) | 2203.15 | 3.92898 | ||||||||
\(69\) | 125.427 | 0.218835 | ||||||||
\(70\) | − 846.858i | − 1.44598i | ||||||||
\(71\) | 484.785i | 0.810329i | 0.914244 | + | 0.405164i | \(0.132786\pi\) | ||||
−0.914244 | + | 0.405164i | \(0.867214\pi\) | |||||||
\(72\) | − 595.500i | − 0.974727i | ||||||||
\(73\) | 957.780i | 1.53561i | 0.640683 | + | 0.767806i | \(0.278651\pi\) | ||||
−0.640683 | + | 0.767806i | \(0.721349\pi\) | |||||||
\(74\) | 524.636 | 0.824159 | ||||||||
\(75\) | 433.169 | 0.666907 | ||||||||
\(76\) | 45.8729i | 0.0692367i | ||||||||
\(77\) | −267.045 | −0.395228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −375.216 | −0.534368 | −0.267184 | − | 0.963646i | \(-0.586093\pi\) | ||||
−0.267184 | + | 0.963646i | \(0.586093\pi\) | |||||||
\(80\) | − 3108.47i | − 4.34422i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 163.884 | 0.220707 | ||||||||
\(83\) | − 715.765i | − 0.946571i | −0.880909 | − | 0.473286i | \(-0.843068\pi\) | ||||
0.880909 | − | 0.473286i | \(-0.156932\pi\) | |||||||
\(84\) | − 592.777i | − 0.769967i | ||||||||
\(85\) | 1771.43i | 2.26046i | ||||||||
\(86\) | − 1270.37i | − 1.59288i | ||||||||
\(87\) | −184.864 | −0.227810 | ||||||||
\(88\) | −1825.42 | −2.21125 | ||||||||
\(89\) | 1038.15i | 1.23645i | 0.786002 | + | 0.618224i | \(0.212148\pi\) | ||||
−0.786002 | + | 0.618224i | \(0.787852\pi\) | |||||||
\(90\) | 787.394 | 0.922207 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 853.451 | 0.967157 | ||||||||
\(93\) | − 575.796i | − 0.642013i | ||||||||
\(94\) | −2726.40 | −2.99156 | ||||||||
\(95\) | −36.8840 | −0.0398339 | ||||||||
\(96\) | − 1440.56i | − 1.53153i | ||||||||
\(97\) | 65.5636i | 0.0686286i | 0.999411 | + | 0.0343143i | \(0.0109247\pi\) | ||||
−0.999411 | + | 0.0343143i | \(0.989075\pi\) | |||||||
\(98\) | 1328.89i | 1.36977i | ||||||||
\(99\) | − 248.293i | − 0.252065i | ||||||||
\(100\) | 2947.44 | 2.94744 | ||||||||
\(101\) | −531.798 | −0.523920 | −0.261960 | − | 0.965079i | \(-0.584369\pi\) | ||||
−0.261960 | + | 0.965079i | \(0.584369\pi\) | |||||||
\(102\) | 1725.90i | 1.67539i | ||||||||
\(103\) | 735.984 | 0.704064 | 0.352032 | − | 0.935988i | \(-0.385491\pi\) | ||||
0.352032 | + | 0.935988i | \(0.385491\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 476.621 | 0.442985 | ||||||||
\(106\) | 2626.95i | 2.40710i | ||||||||
\(107\) | −783.265 | −0.707673 | −0.353837 | − | 0.935307i | \(-0.615123\pi\) | ||||
−0.353837 | + | 0.935307i | \(0.615123\pi\) | |||||||
\(108\) | 551.153 | 0.491063 | ||||||||
\(109\) | − 532.339i | − 0.467788i | −0.972262 | − | 0.233894i | \(-0.924853\pi\) | ||||
0.972262 | − | 0.233894i | \(-0.0751468\pi\) | |||||||
\(110\) | − 2413.64i | − 2.09210i | ||||||||
\(111\) | 295.271i | 0.252485i | ||||||||
\(112\) | − 1833.23i | − 1.54664i | ||||||||
\(113\) | −180.589 | −0.150340 | −0.0751699 | − | 0.997171i | \(-0.523950\pi\) | ||||
−0.0751699 | + | 0.997171i | \(0.523950\pi\) | |||||||
\(114\) | −35.9359 | −0.0295237 | ||||||||
\(115\) | 686.215i | 0.556434i | ||||||||
\(116\) | −1257.88 | −1.00682 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2580.86 | 2.01346 | ||||||||
\(119\) | 1044.71i | 0.804777i | ||||||||
\(120\) | 3258.00 | 2.47844 | ||||||||
\(121\) | 569.893 | 0.428169 | ||||||||
\(122\) | − 2366.81i | − 1.75640i | ||||||||
\(123\) | 92.2357i | 0.0676147i | ||||||||
\(124\) | − 3917.92i | − 2.83742i | ||||||||
\(125\) | 318.242i | 0.227716i | ||||||||
\(126\) | 464.369 | 0.328327 | ||||||||
\(127\) | −1431.63 | −1.00029 | −0.500146 | − | 0.865941i | \(-0.666720\pi\) | ||||
−0.500146 | + | 0.865941i | \(0.666720\pi\) | |||||||
\(128\) | − 1725.94i | − 1.19182i | ||||||||
\(129\) | 714.976 | 0.487986 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2067.32 | 1.37880 | 0.689400 | − | 0.724381i | \(-0.257874\pi\) | ||||
0.689400 | + | 0.724381i | \(0.257874\pi\) | |||||||
\(132\) | − 1689.48i | − 1.11402i | ||||||||
\(133\) | −21.7525 | −0.0141818 | ||||||||
\(134\) | −1013.38 | −0.653304 | ||||||||
\(135\) | 443.153i | 0.282523i | ||||||||
\(136\) | 7141.25i | 4.50262i | ||||||||
\(137\) | 387.512i | 0.241660i | 0.992673 | + | 0.120830i | \(0.0385555\pi\) | ||||
−0.992673 | + | 0.120830i | \(0.961444\pi\) | |||||||
\(138\) | 668.575i | 0.412412i | ||||||||
\(139\) | 752.568 | 0.459223 | 0.229611 | − | 0.973282i | \(-0.426254\pi\) | ||||
0.229611 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(140\) | 3243.10 | 1.95780 | ||||||||
\(141\) | − 1534.45i | − 0.916480i | ||||||||
\(142\) | −2584.09 | −1.52713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1704.51 | 0.986404 | ||||||||
\(145\) | − 1011.40i | − 0.579254i | ||||||||
\(146\) | −5105.34 | −2.89398 | ||||||||
\(147\) | −747.911 | −0.419637 | ||||||||
\(148\) | 2009.13i | 1.11587i | ||||||||
\(149\) | − 2636.72i | − 1.44972i | −0.688895 | − | 0.724862i | \(-0.741904\pi\) | ||||
0.688895 | − | 0.724862i | \(-0.258096\pi\) | |||||||
\(150\) | 2308.96i | 1.25684i | ||||||||
\(151\) | 3332.42i | 1.79595i | 0.440046 | + | 0.897975i | \(0.354962\pi\) | ||||
−0.440046 | + | 0.897975i | \(0.645038\pi\) | |||||||
\(152\) | −148.692 | −0.0793454 | ||||||||
\(153\) | −971.354 | −0.513263 | ||||||||
\(154\) | − 1423.45i | − 0.744839i | ||||||||
\(155\) | 3150.20 | 1.63245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1625.26 | −0.826179 | −0.413089 | − | 0.910690i | \(-0.635550\pi\) | ||||
−0.413089 | + | 0.910690i | \(0.635550\pi\) | |||||||
\(158\) | − 2000.05i | − 1.00706i | ||||||||
\(159\) | −1478.48 | −0.737426 | ||||||||
\(160\) | 7881.36 | 3.89423 | ||||||||
\(161\) | 404.698i | 0.198104i | ||||||||
\(162\) | 431.762i | 0.209398i | ||||||||
\(163\) | 1835.37i | 0.881944i | 0.897521 | + | 0.440972i | \(0.145366\pi\) | ||||
−0.897521 | + | 0.440972i | \(0.854634\pi\) | |||||||
\(164\) | 627.605i | 0.298828i | ||||||||
\(165\) | 1358.42 | 0.640927 | ||||||||
\(166\) | 3815.31 | 1.78389 | ||||||||
\(167\) | − 1945.00i | − 0.901248i | −0.892714 | − | 0.450624i | \(-0.851202\pi\) | ||||
0.892714 | − | 0.450624i | \(-0.148798\pi\) | |||||||
\(168\) | 1921.42 | 0.882384 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9442.44 | −4.26001 | ||||||||
\(171\) | − 20.2251i | − 0.00904474i | ||||||||
\(172\) | 4864.96 | 2.15668 | ||||||||
\(173\) | −2531.63 | −1.11258 | −0.556289 | − | 0.830989i | \(-0.687775\pi\) | ||||
−0.556289 | + | 0.830989i | \(0.687775\pi\) | |||||||
\(174\) | − 985.397i | − 0.429326i | ||||||||
\(175\) | 1397.65i | 0.603726i | ||||||||
\(176\) | − 5224.91i | − 2.23774i | ||||||||
\(177\) | 1452.54i | 0.616832i | ||||||||
\(178\) | −5533.76 | −2.33018 | ||||||||
\(179\) | −4263.01 | −1.78007 | −0.890035 | − | 0.455892i | \(-0.849320\pi\) | ||||
−0.890035 | + | 0.455892i | \(0.849320\pi\) | |||||||
\(180\) | 3015.38i | 1.24863i | ||||||||
\(181\) | −3944.61 | −1.61989 | −0.809946 | − | 0.586504i | \(-0.800504\pi\) | ||||
−0.809946 | + | 0.586504i | \(0.800504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1332.06 | 0.538082 | ||||||||
\(184\) | 2766.36i | 1.10836i | ||||||||
\(185\) | −1615.43 | −0.641995 | ||||||||
\(186\) | 3069.22 | 1.20992 | ||||||||
\(187\) | 2977.54i | 1.16438i | ||||||||
\(188\) | − 10440.9i | − 4.05044i | ||||||||
\(189\) | 261.351i | 0.100585i | ||||||||
\(190\) | − 196.606i | − 0.0750701i | ||||||||
\(191\) | −214.109 | −0.0811119 | −0.0405559 | − | 0.999177i | \(-0.512913\pi\) | ||||
−0.0405559 | + | 0.999177i | \(0.512913\pi\) | |||||||
\(192\) | 3133.42 | 1.17779 | ||||||||
\(193\) | 1207.19i | 0.450234i | 0.974332 | + | 0.225117i | \(0.0722764\pi\) | ||||
−0.974332 | + | 0.225117i | \(0.927724\pi\) | |||||||
\(194\) | −349.480 | −0.129336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5089.06 | −1.85461 | ||||||||
\(197\) | − 927.631i | − 0.335487i | −0.985831 | − | 0.167744i | \(-0.946352\pi\) | ||||
0.985831 | − | 0.167744i | \(-0.0536481\pi\) | |||||||
\(198\) | 1323.50 | 0.475036 | ||||||||
\(199\) | −478.951 | −0.170613 | −0.0853064 | − | 0.996355i | \(-0.527187\pi\) | ||||
−0.0853064 | + | 0.996355i | \(0.527187\pi\) | |||||||
\(200\) | 9553.77i | 3.37777i | ||||||||
\(201\) | − 570.341i | − 0.200143i | ||||||||
\(202\) | − 2834.69i | − 0.987368i | ||||||||
\(203\) | − 596.474i | − 0.206228i | ||||||||
\(204\) | −6609.44 | −2.26840 | ||||||||
\(205\) | −504.624 | −0.171924 | ||||||||
\(206\) | 3923.08i | 1.32686i | ||||||||
\(207\) | −376.281 | −0.126345 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −61.9970 | −0.0205188 | ||||||||
\(210\) | 2540.58i | 0.834840i | ||||||||
\(211\) | −1450.95 | −0.473402 | −0.236701 | − | 0.971583i | \(-0.576066\pi\) | ||||
−0.236701 | + | 0.971583i | \(0.576066\pi\) | |||||||
\(212\) | −10060.1 | −3.25910 | ||||||||
\(213\) | − 1454.35i | − 0.467843i | ||||||||
\(214\) | − 4175.11i | − 1.33367i | ||||||||
\(215\) | 3911.66i | 1.24080i | ||||||||
\(216\) | 1786.50i | 0.562759i | ||||||||
\(217\) | 1857.84 | 0.581191 | ||||||||
\(218\) | 2837.58 | 0.881583 | ||||||||
\(219\) | − 2873.34i | − 0.886586i | ||||||||
\(220\) | 9243.19 | 2.83262 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1573.91 | −0.475828 | ||||||||
\(223\) | − 2059.79i | − 0.618536i | −0.950975 | − | 0.309268i | \(-0.899916\pi\) | ||||
0.950975 | − | 0.309268i | \(-0.100084\pi\) | |||||||
\(224\) | 4648.06 | 1.38644 | ||||||||
\(225\) | −1299.51 | −0.385039 | ||||||||
\(226\) | − 962.612i | − 0.283327i | ||||||||
\(227\) | 4482.46i | 1.31062i | 0.755359 | + | 0.655311i | \(0.227463\pi\) | ||||
−0.755359 | + | 0.655311i | \(0.772537\pi\) | |||||||
\(228\) | − 137.619i | − 0.0399738i | ||||||||
\(229\) | 1630.39i | 0.470477i | 0.971938 | + | 0.235239i | \(0.0755872\pi\) | ||||
−0.971938 | + | 0.235239i | \(0.924413\pi\) | |||||||
\(230\) | −3657.80 | −1.04864 | ||||||||
\(231\) | 801.134 | 0.228185 | ||||||||
\(232\) | − 4077.27i | − 1.15382i | ||||||||
\(233\) | 1903.69 | 0.535258 | 0.267629 | − | 0.963522i | \(-0.413760\pi\) | ||||
0.267629 | + | 0.963522i | \(0.413760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8395.00 | 2.33034 | ||||||||
\(236\) | 9883.58i | 2.72613i | ||||||||
\(237\) | 1125.65 | 0.308517 | ||||||||
\(238\) | −5568.72 | −1.51667 | ||||||||
\(239\) | 3763.79i | 1.01866i | 0.860572 | + | 0.509328i | \(0.170106\pi\) | ||||
−0.860572 | + | 0.509328i | \(0.829894\pi\) | |||||||
\(240\) | 9325.40i | 2.50813i | ||||||||
\(241\) | 3614.74i | 0.966166i | 0.875575 | + | 0.483083i | \(0.160483\pi\) | ||||
−0.875575 | + | 0.483083i | \(0.839517\pi\) | |||||||
\(242\) | 3037.75i | 0.806918i | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 9063.85 | 2.37809 | ||||||||
\(245\) | − 4091.84i | − 1.06701i | ||||||||
\(246\) | −491.652 | −0.127425 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12699.5 | 3.25169 | ||||||||
\(249\) | 2147.30i | 0.546503i | ||||||||
\(250\) | −1696.36 | −0.429148 | ||||||||
\(251\) | 5729.77 | 1.44088 | 0.720438 | − | 0.693520i | \(-0.243941\pi\) | ||||
0.720438 | + | 0.693520i | \(0.243941\pi\) | |||||||
\(252\) | 1778.33i | 0.444541i | ||||||||
\(253\) | 1153.43i | 0.286624i | ||||||||
\(254\) | − 7631.18i | − 1.88513i | ||||||||
\(255\) | − 5314.30i | − 1.30508i | ||||||||
\(256\) | 844.191 | 0.206101 | ||||||||
\(257\) | 5525.79 | 1.34120 | 0.670602 | − | 0.741818i | \(-0.266036\pi\) | ||||
0.670602 | + | 0.741818i | \(0.266036\pi\) | |||||||
\(258\) | 3811.10i | 0.919647i | ||||||||
\(259\) | −952.709 | −0.228565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 554.591 | 0.131526 | ||||||||
\(262\) | 11019.6i | 2.59846i | ||||||||
\(263\) | 5223.21 | 1.22463 | 0.612313 | − | 0.790615i | \(-0.290239\pi\) | ||||
0.612313 | + | 0.790615i | \(0.290239\pi\) | |||||||
\(264\) | 5476.25 | 1.27667 | ||||||||
\(265\) | − 8088.78i | − 1.87506i | ||||||||
\(266\) | − 115.949i | − 0.0267267i | ||||||||
\(267\) | − 3114.46i | − 0.713864i | ||||||||
\(268\) | − 3880.81i | − 0.884545i | ||||||||
\(269\) | 7203.88 | 1.63282 | 0.816410 | − | 0.577473i | \(-0.195961\pi\) | ||||
0.816410 | + | 0.577473i | \(0.195961\pi\) | |||||||
\(270\) | −2362.18 | −0.532436 | ||||||||
\(271\) | 8577.69i | 1.92272i | 0.275293 | + | 0.961360i | \(0.411225\pi\) | ||||
−0.275293 | + | 0.961360i | \(0.588775\pi\) | |||||||
\(272\) | −20440.5 | −4.55656 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2065.59 | −0.455427 | ||||||||
\(275\) | 3983.44i | 0.873493i | ||||||||
\(276\) | −2560.35 | −0.558388 | ||||||||
\(277\) | −7169.19 | −1.55507 | −0.777536 | − | 0.628838i | \(-0.783531\pi\) | ||||
−0.777536 | + | 0.628838i | \(0.783531\pi\) | |||||||
\(278\) | 4011.48i | 0.865442i | ||||||||
\(279\) | 1727.39i | 0.370667i | ||||||||
\(280\) | 10512.1i | 2.24364i | ||||||||
\(281\) | − 849.157i | − 0.180272i | −0.995929 | − | 0.0901360i | \(-0.971270\pi\) | ||||
0.995929 | − | 0.0901360i | \(-0.0287302\pi\) | |||||||
\(282\) | 8179.20 | 1.72718 | ||||||||
\(283\) | −1115.37 | −0.234283 | −0.117141 | − | 0.993115i | \(-0.537373\pi\) | ||||
−0.117141 | + | 0.993115i | \(0.537373\pi\) | |||||||
\(284\) | − 9895.95i | − 2.06766i | ||||||||
\(285\) | 110.652 | 0.0229981 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −297.604 | −0.0612091 | ||||||||
\(288\) | 4321.69i | 0.884229i | ||||||||
\(289\) | 6735.49 | 1.37095 | ||||||||
\(290\) | 5391.14 | 1.09165 | ||||||||
\(291\) | − 196.691i | − 0.0396227i | ||||||||
\(292\) | − 19551.2i | − 3.91832i | ||||||||
\(293\) | 1863.53i | 0.371565i | 0.982591 | + | 0.185782i | \(0.0594819\pi\) | ||||
−0.982591 | + | 0.185782i | \(0.940518\pi\) | |||||||
\(294\) | − 3986.66i | − 0.790839i | ||||||||
\(295\) | −7946.87 | −1.56842 | ||||||||
\(296\) | −6512.36 | −1.27879 | ||||||||
\(297\) | 744.880i | 0.145530i | ||||||||
\(298\) | 14054.8 | 2.73212 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −8842.31 | −1.70170 | ||||||||
\(301\) | 2306.91i | 0.441755i | ||||||||
\(302\) | −17763.1 | −3.38461 | ||||||||
\(303\) | 1595.39 | 0.302485 | ||||||||
\(304\) | − 425.602i | − 0.0802959i | ||||||||
\(305\) | 7287.76i | 1.36818i | ||||||||
\(306\) | − 5177.70i | − 0.967285i | ||||||||
\(307\) | 6387.50i | 1.18747i | 0.804660 | + | 0.593736i | \(0.202348\pi\) | ||||
−0.804660 | + | 0.593736i | \(0.797652\pi\) | |||||||
\(308\) | 5451.21 | 1.00848 | ||||||||
\(309\) | −2207.95 | −0.406492 | ||||||||
\(310\) | 16791.8i | 3.07648i | ||||||||
\(311\) | 3492.59 | 0.636806 | 0.318403 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318403 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5912.01 | −1.06762 | −0.533812 | − | 0.845603i | \(-0.679241\pi\) | ||||
−0.533812 | + | 0.845603i | \(0.679241\pi\) | |||||||
\(314\) | − 8663.29i | − 1.55700i | ||||||||
\(315\) | −1429.86 | −0.255757 | ||||||||
\(316\) | 7659.31 | 1.36351 | ||||||||
\(317\) | − 1677.54i | − 0.297224i | −0.988896 | − | 0.148612i | \(-0.952519\pi\) | ||||
0.988896 | − | 0.148612i | \(-0.0474805\pi\) | |||||||
\(318\) | − 7880.86i | − 1.38974i | ||||||||
\(319\) | − 1700.02i | − 0.298378i | ||||||||
\(320\) | 17143.0i | 2.99476i | ||||||||
\(321\) | 2349.79 | 0.408575 | ||||||||
\(322\) | −2157.20 | −0.373342 | ||||||||
\(323\) | 242.540i | 0.0417810i | ||||||||
\(324\) | −1653.46 | −0.283515 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9783.22 | −1.66209 | ||||||||
\(327\) | 1597.02i | 0.270077i | ||||||||
\(328\) | −2034.31 | −0.342457 | ||||||||
\(329\) | 4950.98 | 0.829655 | ||||||||
\(330\) | 7240.92i | 1.20788i | ||||||||
\(331\) | 2010.31i | 0.333827i | 0.985972 | + | 0.166913i | \(0.0533800\pi\) | ||||
−0.985972 | + | 0.166913i | \(0.946620\pi\) | |||||||
\(332\) | 14611.0i | 2.41531i | ||||||||
\(333\) | − 885.812i | − 0.145772i | ||||||||
\(334\) | 10367.6 | 1.69847 | ||||||||
\(335\) | 3120.35 | 0.508905 | ||||||||
\(336\) | 5499.69i | 0.892955i | ||||||||
\(337\) | −7139.24 | −1.15400 | −0.577002 | − | 0.816743i | \(-0.695778\pi\) | ||||
−0.577002 | + | 0.816743i | \(0.695778\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 541.768 | 0.0867988 | ||||||||
\(340\) | − 36160.5i | − 5.76787i | ||||||||
\(341\) | 5295.05 | 0.840889 | ||||||||
\(342\) | 107.808 | 0.0170455 | ||||||||
\(343\) | − 5733.31i | − 0.902536i | ||||||||
\(344\) | 15769.2i | 2.47156i | ||||||||
\(345\) | − 2058.64i | − 0.321257i | ||||||||
\(346\) | − 13494.6i | − 2.09674i | ||||||||
\(347\) | 1.13990 | 0.000176349 0 | 8.81743e−5 | − | 1.00000i | \(-0.499972\pi\) | ||||
8.81743e−5 | 1.00000i | \(0.499972\pi\) | ||||||||
\(348\) | 3773.64 | 0.581289 | ||||||||
\(349\) | − 12199.1i | − 1.87107i | −0.353235 | − | 0.935535i | \(-0.614918\pi\) | ||||
0.353235 | − | 0.935535i | \(-0.385082\pi\) | |||||||
\(350\) | −7450.00 | −1.13777 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13247.5 | 2.00595 | ||||||||
\(353\) | − 10892.3i | − 1.64232i | −0.570698 | − | 0.821160i | \(-0.693327\pi\) | ||||
0.570698 | − | 0.821160i | \(-0.306673\pi\) | |||||||
\(354\) | −7742.59 | −1.16247 | ||||||||
\(355\) | 7956.81 | 1.18959 | ||||||||
\(356\) | − 21191.9i | − 3.15497i | ||||||||
\(357\) | − 3134.13i | − 0.464638i | ||||||||
\(358\) | − 22723.5i | − 3.35468i | ||||||||
\(359\) | 3525.78i | 0.518339i | 0.965832 | + | 0.259169i | \(0.0834488\pi\) | ||||
−0.965832 | + | 0.259169i | \(0.916551\pi\) | |||||||
\(360\) | −9773.99 | −1.43093 | ||||||||
\(361\) | 6853.95 | 0.999264 | ||||||||
\(362\) | − 21026.3i | − 3.05281i | ||||||||
\(363\) | −1709.68 | −0.247204 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15720.1 | 2.25433 | ||||||||
\(366\) | 7100.42i | 1.01406i | ||||||||
\(367\) | 2383.75 | 0.339049 | 0.169525 | − | 0.985526i | \(-0.445777\pi\) | ||||
0.169525 | + | 0.985526i | \(0.445777\pi\) | |||||||
\(368\) | −7918.19 | −1.12164 | ||||||||
\(369\) | − 276.707i | − 0.0390374i | ||||||||
\(370\) | − 8610.90i | − 1.20989i | ||||||||
\(371\) | − 4770.39i | − 0.667564i | ||||||||
\(372\) | 11753.8i | 1.63818i | ||||||||
\(373\) | −13282.2 | −1.84377 | −0.921885 | − | 0.387463i | \(-0.873352\pi\) | ||||
−0.921885 | + | 0.387463i | \(0.873352\pi\) | |||||||
\(374\) | −15871.5 | −2.19437 | ||||||||
\(375\) | − 954.727i | − 0.131472i | ||||||||
\(376\) | 33843.1 | 4.64181 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1393.11 | −0.189560 | ||||||||
\(379\) | − 4436.73i | − 0.601318i | −0.953732 | − | 0.300659i | \(-0.902793\pi\) | ||||
0.953732 | − | 0.300659i | \(-0.0972065\pi\) | |||||||
\(380\) | 752.917 | 0.101642 | ||||||||
\(381\) | 4294.90 | 0.577519 | ||||||||
\(382\) | − 1141.28i | − 0.152862i | ||||||||
\(383\) | − 810.412i | − 0.108120i | −0.998538 | − | 0.0540602i | \(-0.982784\pi\) | ||||
0.998538 | − | 0.0540602i | \(-0.0172163\pi\) | |||||||
\(384\) | 5177.83i | 0.688100i | ||||||||
\(385\) | 4383.03i | 0.580207i | ||||||||
\(386\) | −6434.78 | −0.848501 | ||||||||
\(387\) | −2144.93 | −0.281739 | ||||||||
\(388\) | − 1338.35i | − 0.175115i | ||||||||
\(389\) | −3463.79 | −0.451469 | −0.225734 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225734 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4512.37 | 0.583633 | ||||||||
\(392\) | − 16495.6i | − 2.12539i | ||||||||
\(393\) | −6201.96 | −0.796050 | ||||||||
\(394\) | 4944.64 | 0.632252 | ||||||||
\(395\) | 6158.45i | 0.784469i | ||||||||
\(396\) | 5068.44i | 0.643178i | ||||||||
\(397\) | − 425.405i | − 0.0537796i | −0.999638 | − | 0.0268898i | \(-0.991440\pi\) | ||||
0.999638 | − | 0.0268898i | \(-0.00856031\pi\) | |||||||
\(398\) | − 2553.00i | − 0.321533i | ||||||||
\(399\) | 65.2575 | 0.00818787 | ||||||||
\(400\) | −27345.9 | −3.41823 | ||||||||
\(401\) | 1186.85i | 0.147801i | 0.997266 | + | 0.0739007i | \(0.0235448\pi\) | ||||
−0.997266 | + | 0.0739007i | \(0.976455\pi\) | |||||||
\(402\) | 3040.14 | 0.377185 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10855.6 | 1.33685 | ||||||||
\(405\) | − 1329.46i | − 0.163115i | ||||||||
\(406\) | 3179.44 | 0.388653 | ||||||||
\(407\) | −2715.33 | −0.330697 | ||||||||
\(408\) | − 21423.7i | − 2.59959i | ||||||||
\(409\) | 8007.42i | 0.968071i | 0.875048 | + | 0.484036i | \(0.160830\pi\) | ||||
−0.875048 | + | 0.484036i | \(0.839170\pi\) | |||||||
\(410\) | − 2689.84i | − 0.324005i | ||||||||
\(411\) | − 1162.54i | − 0.139522i | ||||||||
\(412\) | −15023.7 | −1.79652 | ||||||||
\(413\) | −4686.70 | −0.558395 | ||||||||
\(414\) | − 2005.73i | − 0.238106i | ||||||||
\(415\) | −11747.9 | −1.38960 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2257.70 | −0.265132 | ||||||||
\(418\) | − 330.468i | − 0.0386692i | ||||||||
\(419\) | 6832.46 | 0.796629 | 0.398314 | − | 0.917249i | \(-0.369595\pi\) | ||||
0.398314 | + | 0.917249i | \(0.369595\pi\) | |||||||
\(420\) | −9729.30 | −1.13034 | ||||||||
\(421\) | 10739.6i | 1.24326i | 0.783309 | + | 0.621632i | \(0.213530\pi\) | ||||
−0.783309 | + | 0.621632i | \(0.786470\pi\) | |||||||
\(422\) | − 7734.16i | − 0.892163i | ||||||||
\(423\) | 4603.34i | 0.529130i | ||||||||
\(424\) | − 32608.6i | − 3.73494i | ||||||||
\(425\) | 15583.7 | 1.77864 | ||||||||
\(426\) | 7752.28 | 0.881688 | ||||||||
\(427\) | 4297.99i | 0.487106i | ||||||||
\(428\) | 15988.9 | 1.80573 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20850.7 | −2.33839 | ||||||||
\(431\) | 5214.45i | 0.582763i | 0.956607 | + | 0.291382i | \(0.0941150\pi\) | ||||
−0.956607 | + | 0.291382i | \(0.905885\pi\) | |||||||
\(432\) | −5113.52 | −0.569501 | ||||||||
\(433\) | −8642.24 | −0.959168 | −0.479584 | − | 0.877496i | \(-0.659212\pi\) | ||||
−0.479584 | + | 0.877496i | \(0.659212\pi\) | |||||||
\(434\) | 9903.02i | 1.09530i | ||||||||
\(435\) | 3034.19i | 0.334432i | ||||||||
\(436\) | 10866.7i | 1.19362i | ||||||||
\(437\) | 93.9545i | 0.0102848i | ||||||||
\(438\) | 15316.0 | 1.67084 | ||||||||
\(439\) | 13026.2 | 1.41619 | 0.708097 | − | 0.706116i | \(-0.249554\pi\) | ||||
0.708097 | + | 0.706116i | \(0.249554\pi\) | |||||||
\(440\) | 29960.7i | 3.24619i | ||||||||
\(441\) | 2243.73 | 0.242278 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11533.0 | −1.23690 | −0.618450 | − | 0.785824i | \(-0.712239\pi\) | ||||
−0.618450 | + | 0.785824i | \(0.712239\pi\) | |||||||
\(444\) | − 6027.39i | − 0.644250i | ||||||||
\(445\) | 17039.3 | 1.81515 | ||||||||
\(446\) | 10979.5 | 1.16568 | ||||||||
\(447\) | 7910.17i | 0.836998i | ||||||||
\(448\) | 10110.2i | 1.06621i | ||||||||
\(449\) | − 9882.75i | − 1.03874i | −0.854548 | − | 0.519372i | \(-0.826166\pi\) | ||||
0.854548 | − | 0.519372i | \(-0.173834\pi\) | |||||||
\(450\) | − 6926.88i | − 0.725636i | ||||||||
\(451\) | −848.204 | −0.0885596 | ||||||||
\(452\) | 3686.38 | 0.383613 | ||||||||
\(453\) | − 9997.26i | − 1.03689i | ||||||||
\(454\) | −23893.3 | −2.46997 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 446.075 | 0.0458101 | ||||||||
\(457\) | − 15628.1i | − 1.59967i | −0.600218 | − | 0.799836i | \(-0.704920\pi\) | ||||
0.600218 | − | 0.799836i | \(-0.295080\pi\) | |||||||
\(458\) | −8690.63 | −0.886652 | ||||||||
\(459\) | 2914.06 | 0.296333 | ||||||||
\(460\) | − 14007.8i | − 1.41982i | ||||||||
\(461\) | − 7747.46i | − 0.782723i | −0.920237 | − | 0.391361i | \(-0.872004\pi\) | ||||
0.920237 | − | 0.391361i | \(-0.127996\pi\) | |||||||
\(462\) | 4270.36i | 0.430033i | ||||||||
\(463\) | 333.422i | 0.0334675i | 0.999860 | + | 0.0167337i | \(0.00532676\pi\) | ||||
−0.999860 | + | 0.0167337i | \(0.994673\pi\) | |||||||
\(464\) | 11670.4 | 1.16764 | ||||||||
\(465\) | −9450.59 | −0.942496 | ||||||||
\(466\) | 10147.4i | 1.00874i | ||||||||
\(467\) | −8198.33 | −0.812363 | −0.406182 | − | 0.913792i | \(-0.633140\pi\) | ||||
−0.406182 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1840.24 | 0.181182 | ||||||||
\(470\) | 44748.7i | 4.39171i | ||||||||
\(471\) | 4875.79 | 0.476995 | ||||||||
\(472\) | −32036.5 | −3.12415 | ||||||||
\(473\) | 6574.96i | 0.639148i | ||||||||
\(474\) | 6000.14i | 0.581425i | ||||||||
\(475\) | 324.477i | 0.0313432i | ||||||||
\(476\) | − 21325.8i | − 2.05350i | ||||||||
\(477\) | 4435.43 | 0.425753 | ||||||||
\(478\) | −20062.5 | −1.91974 | ||||||||
\(479\) | 6435.88i | 0.613910i | 0.951724 | + | 0.306955i | \(0.0993101\pi\) | ||||
−0.951724 | + | 0.306955i | \(0.900690\pi\) | |||||||
\(480\) | −23644.1 | −2.24833 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −19268.0 | −1.82082 | ||||||||
\(483\) | − 1214.09i | − 0.114375i | ||||||||
\(484\) | −11633.3 | −1.09253 | ||||||||
\(485\) | 1076.10 | 0.100749 | ||||||||
\(486\) | − 1295.29i | − 0.120896i | ||||||||
\(487\) | 8095.37i | 0.753257i | 0.926364 | + | 0.376629i | \(0.122917\pi\) | ||||
−0.926364 | + | 0.376629i | \(0.877083\pi\) | |||||||
\(488\) | 29379.4i | 2.72529i | ||||||||
\(489\) | − 5506.10i | − 0.509191i | ||||||||
\(490\) | 21811.1 | 2.01087 | ||||||||
\(491\) | −5116.46 | −0.470270 | −0.235135 | − | 0.971963i | \(-0.575553\pi\) | ||||
−0.235135 | + | 0.971963i | \(0.575553\pi\) | |||||||
\(492\) | − 1882.82i | − 0.172528i | ||||||||
\(493\) | −6650.67 | −0.607568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4075.26 | −0.370039 | ||||||||
\(496\) | 36349.9i | 3.29064i | ||||||||
\(497\) | 4692.56 | 0.423521 | ||||||||
\(498\) | −11445.9 | −1.02993 | ||||||||
\(499\) | − 18050.7i | − 1.61936i | −0.586870 | − | 0.809682i | \(-0.699640\pi\) | ||||
0.586870 | − | 0.809682i | \(-0.300360\pi\) | |||||||
\(500\) | − 6496.31i | − 0.581047i | ||||||||
\(501\) | 5834.99i | 0.520336i | ||||||||
\(502\) | 30541.9i | 2.71544i | ||||||||
\(503\) | 10531.1 | 0.933512 | 0.466756 | − | 0.884386i | \(-0.345423\pi\) | ||||
0.466756 | + | 0.884386i | \(0.345423\pi\) | |||||||
\(504\) | −5764.25 | −0.509445 | ||||||||
\(505\) | 8728.45i | 0.769131i | ||||||||
\(506\) | −6148.25 | −0.540165 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29224.1 | 2.55238 | ||||||||
\(509\) | − 1963.31i | − 0.170967i | −0.996340 | − | 0.0854834i | \(-0.972757\pi\) | ||||
0.996340 | − | 0.0854834i | \(-0.0272435\pi\) | |||||||
\(510\) | 28327.3 | 2.45952 | ||||||||
\(511\) | 9271.00 | 0.802593 | ||||||||
\(512\) | − 9307.69i | − 0.803409i | ||||||||
\(513\) | 60.6753i | 0.00522198i | ||||||||
\(514\) | 29454.6i | 2.52760i | ||||||||
\(515\) | − 12079.8i | − 1.03359i | ||||||||
\(516\) | −14594.9 | −1.24516 | ||||||||
\(517\) | 14110.9 | 1.20038 | ||||||||
\(518\) | − 5078.31i | − 0.430750i | ||||||||
\(519\) | 7594.89 | 0.642348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7044.93 | −0.592407 | −0.296203 | − | 0.955125i | \(-0.595721\pi\) | ||||
−0.296203 | + | 0.955125i | \(0.595721\pi\) | |||||||
\(522\) | 2956.19i | 0.247872i | ||||||||
\(523\) | −3213.29 | −0.268657 | −0.134328 | − | 0.990937i | \(-0.542888\pi\) | ||||
−0.134328 | + | 0.990937i | \(0.542888\pi\) | |||||||
\(524\) | −42200.4 | −3.51819 | ||||||||
\(525\) | − 4192.94i | − 0.348561i | ||||||||
\(526\) | 27841.7i | 2.30790i | ||||||||
\(527\) | − 20714.9i | − 1.71225i | ||||||||
\(528\) | 15674.7i | 1.29196i | ||||||||
\(529\) | −10419.0 | −0.856333 | ||||||||
\(530\) | 43116.4 | 3.53369 | ||||||||
\(531\) | − 4357.61i | − 0.356128i | ||||||||
\(532\) | 444.036 | 0.0361868 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 16601.3 | 1.34533 | ||||||||
\(535\) | 12855.8i | 1.03889i | ||||||||
\(536\) | 12579.2 | 1.01369 | ||||||||
\(537\) | 12789.0 | 1.02772 | ||||||||
\(538\) | 38399.5i | 3.07718i | ||||||||
\(539\) | − 6877.83i | − 0.549627i | ||||||||
\(540\) | − 9046.13i | − 0.720895i | ||||||||
\(541\) | − 11251.4i | − 0.894150i | −0.894497 | − | 0.447075i | \(-0.852466\pi\) | ||||
0.894497 | − | 0.447075i | \(-0.147534\pi\) | |||||||
\(542\) | −45722.4 | −3.62352 | ||||||||
\(543\) | 11833.8 | 0.935245 | ||||||||
\(544\) | − 51825.8i | − 4.08458i | ||||||||
\(545\) | −8737.33 | −0.686727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1533.54 | 0.119871 | 0.0599353 | − | 0.998202i | \(-0.480911\pi\) | ||||
0.0599353 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(548\) | − 7910.31i | − 0.616628i | ||||||||
\(549\) | −3996.19 | −0.310662 | ||||||||
\(550\) | −21233.3 | −1.64617 | ||||||||
\(551\) | − 138.477i | − 0.0107066i | ||||||||
\(552\) | − 8299.08i | − 0.639914i | ||||||||
\(553\) | 3631.97i | 0.279289i | ||||||||
\(554\) | − 38214.6i | − 2.93066i | ||||||||
\(555\) | 4846.30 | 0.370656 | ||||||||
\(556\) | −15362.2 | −1.17177 | ||||||||
\(557\) | − 16845.7i | − 1.28146i | −0.767766 | − | 0.640731i | \(-0.778631\pi\) | ||||
0.767766 | − | 0.640731i | \(-0.221369\pi\) | |||||||
\(558\) | −9207.65 | −0.698550 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −30089.0 | −2.27052 | ||||||||
\(561\) | − 8932.62i | − 0.672256i | ||||||||
\(562\) | 4526.34 | 0.339737 | ||||||||
\(563\) | 20820.1 | 1.55855 | 0.779273 | − | 0.626685i | \(-0.215589\pi\) | ||||
0.779273 | + | 0.626685i | \(0.215589\pi\) | |||||||
\(564\) | 31322.8i | 2.33852i | ||||||||
\(565\) | 2964.03i | 0.220704i | ||||||||
\(566\) | − 5945.37i | − 0.441524i | ||||||||
\(567\) | − 784.054i | − 0.0580726i | ||||||||
\(568\) | 32076.6 | 2.36955 | ||||||||
\(569\) | −23636.6 | −1.74147 | −0.870735 | − | 0.491752i | \(-0.836357\pi\) | ||||
−0.870735 | + | 0.491752i | \(0.836357\pi\) | |||||||
\(570\) | 589.819i | 0.0433417i | ||||||||
\(571\) | 26955.1 | 1.97554 | 0.987771 | − | 0.155913i | \(-0.0498319\pi\) | ||||
0.987771 | + | 0.155913i | \(0.0498319\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 642.326 | 0.0468300 | ||||||||
\(574\) | − 1586.35i | − 0.115353i | ||||||||
\(575\) | 6036.78 | 0.437828 | ||||||||
\(576\) | −9400.25 | −0.679995 | ||||||||
\(577\) | 23499.8i | 1.69551i | 0.530388 | + | 0.847755i | \(0.322046\pi\) | ||||
−0.530388 | + | 0.847755i | \(0.677954\pi\) | |||||||
\(578\) | 35902.8i | 2.58367i | ||||||||
\(579\) | − 3621.56i | − 0.259943i | ||||||||
\(580\) | 20645.7i | 1.47805i | ||||||||
\(581\) | −6928.38 | −0.494729 | ||||||||
\(582\) | 1048.44 | 0.0746721 | ||||||||
\(583\) | − 13596.1i | − 0.965857i | ||||||||
\(584\) | 63373.1 | 4.49040 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9933.33 | −0.700243 | ||||||||
\(587\) | 4637.50i | 0.326082i | 0.986619 | + | 0.163041i | \(0.0521303\pi\) | ||||
−0.986619 | + | 0.163041i | \(0.947870\pi\) | |||||||
\(588\) | 15267.2 | 1.07076 | ||||||||
\(589\) | 431.316 | 0.0301733 | ||||||||
\(590\) | − 42359.9i | − 2.95582i | ||||||||
\(591\) | 2782.89i | 0.193694i | ||||||||
\(592\) | − 18640.4i | − 1.29411i | ||||||||
\(593\) | − 12633.5i | − 0.874869i | −0.899250 | − | 0.437434i | \(-0.855887\pi\) | ||||
0.899250 | − | 0.437434i | \(-0.144113\pi\) | |||||||
\(594\) | −3970.51 | −0.274262 | ||||||||
\(595\) | 17146.9 | 1.18144 | ||||||||
\(596\) | 53823.7i | 3.69917i | ||||||||
\(597\) | 1436.85 | 0.0985033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18757.1 | −1.27946 | −0.639730 | − | 0.768600i | \(-0.720954\pi\) | ||||
−0.639730 | + | 0.768600i | \(0.720954\pi\) | |||||||
\(600\) | − 28661.3i | − 1.95016i | ||||||||
\(601\) | −3632.98 | −0.246576 | −0.123288 | − | 0.992371i | \(-0.539344\pi\) | ||||
−0.123288 | + | 0.992371i | \(0.539344\pi\) | |||||||
\(602\) | −12296.8 | −0.832522 | ||||||||
\(603\) | 1711.02i | 0.115553i | ||||||||
\(604\) | − 68025.0i | − 4.58261i | ||||||||
\(605\) | − 9353.71i | − 0.628566i | ||||||||
\(606\) | 8504.08i | 0.570057i | ||||||||
\(607\) | −12700.0 | −0.849219 | −0.424610 | − | 0.905377i | \(-0.639589\pi\) | ||||
−0.424610 | + | 0.905377i | \(0.639589\pi\) | |||||||
\(608\) | 1079.09 | 0.0719786 | ||||||||
\(609\) | 1789.42i | 0.119066i | ||||||||
\(610\) | −38846.6 | −2.57845 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 19828.3 | 1.30966 | ||||||||
\(613\) | 21640.1i | 1.42584i | 0.701248 | + | 0.712918i | \(0.252627\pi\) | ||||
−0.701248 | + | 0.712918i | \(0.747373\pi\) | |||||||
\(614\) | −34047.9 | −2.23788 | ||||||||
\(615\) | 1513.87 | 0.0992605 | ||||||||
\(616\) | 17669.5i | 1.15572i | ||||||||
\(617\) | − 16541.7i | − 1.07933i | −0.841881 | − | 0.539663i | \(-0.818552\pi\) | ||||
0.841881 | − | 0.539663i | \(-0.181448\pi\) | |||||||
\(618\) | − 11769.2i | − 0.766066i | ||||||||
\(619\) | 21138.9i | 1.37261i | 0.727316 | + | 0.686303i | \(0.240767\pi\) | ||||
−0.727316 | + | 0.686303i | \(0.759233\pi\) | |||||||
\(620\) | −64305.2 | −4.16542 | ||||||||
\(621\) | 1128.84 | 0.0729451 | ||||||||
\(622\) | 18616.9i | 1.20011i | ||||||||
\(623\) | 10049.0 | 0.646235 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12825.4 | −0.820823 | ||||||||
\(626\) | − 31513.3i | − 2.01202i | ||||||||
\(627\) | 185.991 | 0.0118465 | ||||||||
\(628\) | 33176.6 | 2.10811 | ||||||||
\(629\) | 10622.7i | 0.673377i | ||||||||
\(630\) | − 7621.73i | − 0.481995i | ||||||||
\(631\) | − 5489.80i | − 0.346348i | −0.984891 | − | 0.173174i | \(-0.944598\pi\) | ||||
0.984891 | − | 0.173174i | \(-0.0554023\pi\) | |||||||
\(632\) | 24826.8i | 1.56259i | ||||||||
\(633\) | 4352.86 | 0.273319 | ||||||||
\(634\) | 8941.94 | 0.560141 | ||||||||
\(635\) | 23497.5i | 1.46846i | ||||||||
\(636\) | 30180.3 | 1.88164 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9061.76 | 0.562318 | ||||||||
\(639\) | 4363.06i | 0.270110i | ||||||||
\(640\) | −28328.1 | −1.74963 | ||||||||
\(641\) | −4297.04 | −0.264778 | −0.132389 | − | 0.991198i | \(-0.542265\pi\) | ||||
−0.132389 | + | 0.991198i | \(0.542265\pi\) | |||||||
\(642\) | 12525.3i | 0.769993i | ||||||||
\(643\) | 25696.9i | 1.57603i | 0.615655 | + | 0.788016i | \(0.288892\pi\) | ||||
−0.615655 | + | 0.788016i | \(0.711108\pi\) | |||||||
\(644\) | − 8261.14i | − 0.505488i | ||||||||
\(645\) | − 11735.0i | − 0.716378i | ||||||||
\(646\) | −1292.83 | −0.0787396 | ||||||||
\(647\) | −2174.98 | −0.132160 | −0.0660798 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660798 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(648\) | − 5359.50i | − 0.324909i | ||||||||
\(649\) | −13357.6 | −0.807907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5573.52 | −0.335551 | ||||||||
\(652\) | − 37465.5i | − 2.25040i | ||||||||
\(653\) | −15454.5 | −0.926160 | −0.463080 | − | 0.886316i | \(-0.653256\pi\) | ||||
−0.463080 | + | 0.886316i | \(0.653256\pi\) | |||||||
\(654\) | −8512.73 | −0.508982 | ||||||||
\(655\) | − 33931.1i | − 2.02412i | ||||||||
\(656\) | − 5822.82i | − 0.346560i | ||||||||
\(657\) | 8620.02i | 0.511870i | ||||||||
\(658\) | 26390.7i | 1.56355i | ||||||||
\(659\) | −3148.77 | −0.186129 | −0.0930643 | − | 0.995660i | \(-0.529666\pi\) | ||||
−0.0930643 | + | 0.995660i | \(0.529666\pi\) | |||||||
\(660\) | −27729.6 | −1.63541 | ||||||||
\(661\) | 2099.70i | 0.123553i | 0.998090 | + | 0.0617767i | \(0.0196767\pi\) | ||||
−0.998090 | + | 0.0617767i | \(0.980323\pi\) | |||||||
\(662\) | −10715.7 | −0.629122 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47359.8 | −2.76795 | ||||||||
\(665\) | 357.026i | 0.0208193i | ||||||||
\(666\) | 4721.73 | 0.274720 | ||||||||
\(667\) | −2576.32 | −0.149559 | ||||||||
\(668\) | 39703.4i | 2.29966i | ||||||||
\(669\) | 6179.36i | 0.357112i | ||||||||
\(670\) | 16632.7i | 0.959071i | ||||||||
\(671\) | 12249.7i | 0.704763i | ||||||||
\(672\) | −13944.2 | −0.800460 | ||||||||
\(673\) | −30970.8 | −1.77390 | −0.886950 | − | 0.461865i | \(-0.847181\pi\) | ||||
−0.886950 | + | 0.461865i | \(0.847181\pi\) | |||||||
\(674\) | − 38055.0i | − 2.17481i | ||||||||
\(675\) | 3898.52 | 0.222302 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14640.6 | 0.831141 | 0.415570 | − | 0.909561i | \(-0.363582\pi\) | ||||
0.415570 | + | 0.909561i | \(0.363582\pi\) | |||||||
\(678\) | 2887.83i | 0.163579i | ||||||||
\(679\) | 634.635 | 0.0358690 | ||||||||
\(680\) | 117210. | 6.60999 | ||||||||
\(681\) | − 13447.4i | − 0.756688i | ||||||||
\(682\) | 28224.7i | 1.58472i | ||||||||
\(683\) | 6685.83i | 0.374563i | 0.982306 | + | 0.187281i | \(0.0599676\pi\) | ||||
−0.982306 | + | 0.187281i | \(0.940032\pi\) | |||||||
\(684\) | 412.856i | 0.0230789i | ||||||||
\(685\) | 6360.27 | 0.354764 | ||||||||
\(686\) | 30560.8 | 1.70090 | ||||||||
\(687\) | − 4891.18i | − 0.271630i | ||||||||
\(688\) | −45136.3 | −2.50117 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 10973.4 | 0.605434 | ||||||||
\(691\) | − 30194.1i | − 1.66228i | −0.556062 | − | 0.831141i | \(-0.687688\pi\) | ||||
0.556062 | − | 0.831141i | \(-0.312312\pi\) | |||||||
\(692\) | 51678.4 | 2.83890 | ||||||||
\(693\) | −2403.40 | −0.131743 | ||||||||
\(694\) | 6.07611i | 0 0.000332343i | ||||||||
\(695\) | − 12352.0i | − 0.674154i | ||||||||
\(696\) | 12231.8i | 0.666158i | ||||||||
\(697\) | 3318.28i | 0.180328i | ||||||||
\(698\) | 65026.0 | 3.52618 | ||||||||
\(699\) | −5711.08 | −0.309031 | ||||||||
\(700\) | − 28530.3i | − 1.54049i | ||||||||
\(701\) | 30300.9 | 1.63260 | 0.816298 | − | 0.577631i | \(-0.196023\pi\) | ||||
0.816298 | + | 0.577631i | \(0.196023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −221.181 | −0.0118663 | ||||||||
\(704\) | 28815.1i | 1.54263i | ||||||||
\(705\) | −25185.0 | −1.34542 | ||||||||
\(706\) | 58060.3 | 3.09508 | ||||||||
\(707\) | 5147.64i | 0.273829i | ||||||||
\(708\) | − 29650.8i | − 1.57393i | ||||||||
\(709\) | − 26123.2i | − 1.38375i | −0.722017 | − | 0.691875i | \(-0.756785\pi\) | ||||
0.722017 | − | 0.691875i | \(-0.243215\pi\) | |||||||
\(710\) | 42412.9i | 2.24187i | ||||||||
\(711\) | −3376.94 | −0.178123 | ||||||||
\(712\) | 68691.1 | 3.61560 | ||||||||
\(713\) | − 8024.48i | − 0.421486i | ||||||||
\(714\) | 16706.2 | 0.875647 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 87021.3 | 4.54209 | ||||||||
\(717\) | − 11291.4i | − 0.588122i | ||||||||
\(718\) | −18793.8 | −0.976850 | ||||||||
\(719\) | −19325.7 | −1.00240 | −0.501200 | − | 0.865331i | \(-0.667108\pi\) | ||||
−0.501200 | + | 0.865331i | \(0.667108\pi\) | |||||||
\(720\) | − 27976.2i | − 1.44807i | ||||||||
\(721\) | − 7124.09i | − 0.367982i | ||||||||
\(722\) | 36534.2i | 1.88319i | ||||||||
\(723\) | − 10844.2i | − 0.557816i | ||||||||
\(724\) | 80521.7 | 4.13338 | ||||||||
\(725\) | −8897.47 | −0.455784 | ||||||||
\(726\) | − 9113.26i | − 0.465875i | ||||||||
\(727\) | −26065.8 | −1.32975 | −0.664875 | − | 0.746954i | \(-0.731515\pi\) | ||||
−0.664875 | + | 0.746954i | \(0.731515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 83794.4i | 4.24845i | ||||||||
\(731\) | 25722.0 | 1.30145 | ||||||||
\(732\) | −27191.5 | −1.37299 | ||||||||
\(733\) | 1055.45i | 0.0531843i | 0.999646 | + | 0.0265921i | \(0.00846554\pi\) | ||||
−0.999646 | + | 0.0265921i | \(0.991534\pi\) | |||||||
\(734\) | 12706.4i | 0.638965i | ||||||||
\(735\) | 12275.5i | 0.616041i | ||||||||
\(736\) | − 20076.2i | − 1.00546i | ||||||||
\(737\) | 5244.89 | 0.262141 | ||||||||
\(738\) | 1474.96 | 0.0735690 | ||||||||
\(739\) | − 9410.40i | − 0.468426i | −0.972185 | − | 0.234213i | \(-0.924749\pi\) | ||||
0.972185 | − | 0.234213i | \(-0.0752514\pi\) | |||||||
\(740\) | 32976.0 | 1.63814 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25428.1 | 1.25808 | ||||||||
\(743\) | − 7523.70i | − 0.371491i | −0.982598 | − | 0.185746i | \(-0.940530\pi\) | ||||
0.982598 | − | 0.185746i | \(-0.0594700\pi\) | |||||||
\(744\) | −38098.5 | −1.87736 | ||||||||
\(745\) | −43276.8 | −2.12824 | ||||||||
\(746\) | − 70799.4i | − 3.47473i | ||||||||
\(747\) | − 6441.89i | − 0.315524i | ||||||||
\(748\) | − 60780.8i | − 2.97108i | ||||||||
\(749\) | 7581.76i | 0.369868i | ||||||||
\(750\) | 5089.07 | 0.247769 | ||||||||
\(751\) | 12984.1 | 0.630886 | 0.315443 | − | 0.948945i | \(-0.397847\pi\) | ||||
0.315443 | + | 0.948945i | \(0.397847\pi\) | |||||||
\(752\) | 96869.3i | 4.69742i | ||||||||
\(753\) | −17189.3 | −0.831890 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54695.3 | 2.63651 | ||||||||
\(756\) | − 5334.99i | − 0.256656i | ||||||||
\(757\) | −27934.6 | −1.34122 | −0.670609 | − | 0.741811i | \(-0.733967\pi\) | ||||
−0.670609 | + | 0.741811i | \(0.733967\pi\) | |||||||
\(758\) | 23649.5 | 1.13323 | ||||||||
\(759\) | − 3460.30i | − 0.165482i | ||||||||
\(760\) | 2440.49i | 0.116482i | ||||||||
\(761\) | 15519.3i | 0.739255i | 0.929180 | + | 0.369627i | \(0.120515\pi\) | ||||
−0.929180 | + | 0.369627i | \(0.879485\pi\) | |||||||
\(762\) | 22893.5i | 1.08838i | ||||||||
\(763\) | −5152.88 | −0.244491 | ||||||||
\(764\) | 4370.62 | 0.206968 | ||||||||
\(765\) | 15942.9i | 0.753487i | ||||||||
\(766\) | 4319.82 | 0.203761 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2532.57 | −0.118993 | ||||||||
\(769\) | 12885.2i | 0.604228i | 0.953272 | + | 0.302114i | \(0.0976924\pi\) | ||||
−0.953272 | + | 0.302114i | \(0.902308\pi\) | |||||||
\(770\) | −23363.3 | −1.09345 | ||||||||
\(771\) | −16577.4 | −0.774344 | ||||||||
\(772\) | − 24642.4i | − 1.14883i | ||||||||
\(773\) | 5892.04i | 0.274155i | 0.990560 | + | 0.137078i | \(0.0437710\pi\) | ||||
−0.990560 | + | 0.137078i | \(0.956229\pi\) | |||||||
\(774\) | − 11433.3i | − 0.530958i | ||||||||
\(775\) | − 27713.0i | − 1.28449i | ||||||||
\(776\) | 4338.12 | 0.200682 | ||||||||
\(777\) | 2858.13 | 0.131962 | ||||||||
\(778\) | − 18463.4i | − 0.850828i | ||||||||
\(779\) | −69.0916 | −0.00317775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13374.3 | 0.612766 | ||||||||
\(782\) | 24052.7i | 1.09990i | ||||||||
\(783\) | −1663.77 | −0.0759367 | ||||||||
\(784\) | 47215.5 | 2.15085 | ||||||||
\(785\) | 26675.6i | 1.21286i | ||||||||
\(786\) | − 33058.9i | − 1.50022i | ||||||||
\(787\) | 21020.4i | 0.952091i | 0.879421 | + | 0.476045i | \(0.157930\pi\) | ||||
−0.879421 | + | 0.476045i | \(0.842070\pi\) | |||||||
\(788\) | 18935.8i | 0.856042i | ||||||||
\(789\) | −15669.6 | −0.707038 | ||||||||
\(790\) | −32827.0 | −1.47839 | ||||||||
\(791\) | 1748.05i | 0.0785757i | ||||||||
\(792\) | −16428.7 | −0.737084 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2267.58 | 0.101352 | ||||||||
\(795\) | 24266.4i | 1.08256i | ||||||||
\(796\) | 9776.87 | 0.435342 | ||||||||
\(797\) | −31355.6 | −1.39356 | −0.696782 | − | 0.717283i | \(-0.745386\pi\) | ||||
−0.696782 | + | 0.717283i | \(0.745386\pi\) | |||||||
\(798\) | 347.848i | 0.0154307i | ||||||||
\(799\) | − 55203.3i | − 2.44425i | ||||||||
\(800\) | − 69334.0i | − 3.06416i | ||||||||
\(801\) | 9343.37i | 0.412150i | ||||||||
\(802\) | −6326.37 | −0.278543 | ||||||||
\(803\) | 26423.4 | 1.16122 | ||||||||
\(804\) | 11642.4i | 0.510692i | ||||||||
\(805\) | 6642.34 | 0.290822 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21611.7 | −0.942709 | ||||||||
\(808\) | 35187.3i | 1.53204i | ||||||||
\(809\) | −18132.5 | −0.788017 | −0.394009 | − | 0.919107i | \(-0.628912\pi\) | ||||
−0.394009 | + | 0.919107i | \(0.628912\pi\) | |||||||
\(810\) | 7086.55 | 0.307402 | ||||||||
\(811\) | − 24755.3i | − 1.07186i | −0.844263 | − | 0.535928i | \(-0.819962\pi\) | ||||
0.844263 | − | 0.535928i | \(-0.180038\pi\) | |||||||
\(812\) | 12175.9i | 0.526219i | ||||||||
\(813\) | − 25733.1i | − 1.11008i | ||||||||
\(814\) | − 14473.8i | − 0.623225i | ||||||||
\(815\) | 30124.0 | 1.29472 | ||||||||
\(816\) | 61321.4 | 2.63073 | ||||||||
\(817\) | 535.572i | 0.0229343i | ||||||||
\(818\) | −42682.7 | −1.82441 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10300.9 | 0.438688 | ||||||||
\(821\) | 4082.65i | 0.173551i | 0.996228 | + | 0.0867755i | \(0.0276563\pi\) | ||||
−0.996228 | + | 0.0867755i | \(0.972344\pi\) | |||||||
\(822\) | 6196.77 | 0.262941 | ||||||||
\(823\) | 34327.0 | 1.45391 | 0.726954 | − | 0.686687i | \(-0.240935\pi\) | ||||
0.726954 | + | 0.686687i | \(0.240935\pi\) | |||||||
\(824\) | − 48697.6i | − 2.05881i | ||||||||
\(825\) | − 11950.3i | − 0.504312i | ||||||||
\(826\) | − 24981.9i | − 1.05234i | ||||||||
\(827\) | − 3228.87i | − 0.135767i | −0.997693 | − | 0.0678833i | \(-0.978375\pi\) | ||||
0.997693 | − | 0.0678833i | \(-0.0216245\pi\) | |||||||
\(828\) | 7681.06 | 0.322386 | ||||||||
\(829\) | 10452.4 | 0.437908 | 0.218954 | − | 0.975735i | \(-0.429735\pi\) | ||||
0.218954 | + | 0.975735i | \(0.429735\pi\) | |||||||
\(830\) | − 62621.0i | − 2.61880i | ||||||||
\(831\) | 21507.6 | 0.897821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26906.9 | −1.11917 | ||||||||
\(834\) | − 12034.5i | − 0.499663i | ||||||||
\(835\) | −31923.4 | −1.32306 | ||||||||
\(836\) | 1265.55 | 0.0523564 | ||||||||
\(837\) | − 5182.16i | − 0.214004i | ||||||||
\(838\) | 36419.7i | 1.50131i | ||||||||
\(839\) | 28289.0i | 1.16406i | 0.813169 | + | 0.582028i | \(0.197741\pi\) | ||||
−0.813169 | + | 0.582028i | \(0.802259\pi\) | |||||||
\(840\) | − 31536.4i | − 1.29537i | ||||||||
\(841\) | −20591.8 | −0.844308 | ||||||||
\(842\) | −57246.1 | −2.34303 | ||||||||
\(843\) | 2547.47i | 0.104080i | ||||||||
\(844\) | 29618.5 | 1.20795 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −24537.6 | −0.997187 | ||||||||
\(847\) | − 5516.39i | − 0.223784i | ||||||||
\(848\) | 93335.9 | 3.77968 | ||||||||
\(849\) | 3346.12 | 0.135263 | ||||||||
\(850\) | 83067.2i | 3.35198i | ||||||||
\(851\) | 4114.99i | 0.165758i | ||||||||
\(852\) | 29687.8i | 1.19377i | ||||||||
\(853\) | 26631.8i | 1.06900i | 0.845170 | + | 0.534498i | \(0.179499\pi\) | ||||
−0.845170 | + | 0.534498i | \(0.820501\pi\) | |||||||
\(854\) | −22910.0 | −0.917989 | ||||||||
\(855\) | −331.956 | −0.0132780 | ||||||||
\(856\) | 51826.0i | 2.06936i | ||||||||
\(857\) | −11796.7 | −0.470209 | −0.235104 | − | 0.971970i | \(-0.575543\pi\) | ||||
−0.235104 | + | 0.971970i | \(0.575543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22672.8 | −0.900567 | −0.450283 | − | 0.892886i | \(-0.648677\pi\) | ||||
−0.450283 | + | 0.892886i | \(0.648677\pi\) | |||||||
\(860\) | − 79849.0i | − 3.16608i | ||||||||
\(861\) | 892.812 | 0.0353391 | ||||||||
\(862\) | −27795.0 | −1.09826 | ||||||||
\(863\) | 21421.1i | 0.844940i | 0.906377 | + | 0.422470i | \(0.138837\pi\) | ||||
−0.906377 | + | 0.422470i | \(0.861163\pi\) | |||||||
\(864\) | − 12965.1i | − 0.510510i | ||||||||
\(865\) | 41551.9i | 1.63330i | ||||||||
\(866\) | − 46066.6i | − 1.80763i | ||||||||
\(867\) | −20206.5 | −0.791520 | ||||||||
\(868\) | −37924.3 | −1.48299 | ||||||||
\(869\) | 10351.5i | 0.404086i | ||||||||
\(870\) | −16173.4 | −0.630264 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −35223.1 | −1.36790 | ||||||||
\(873\) | 590.072i | 0.0228762i | ||||||||
\(874\) | −500.814 | −0.0193825 | ||||||||
\(875\) | 3080.48 | 0.119016 | ||||||||
\(876\) | 58653.7i | 2.26224i | ||||||||
\(877\) | − 5155.20i | − 0.198493i | −0.995063 | − | 0.0992466i | \(-0.968357\pi\) | ||||
0.995063 | − | 0.0992466i | \(-0.0316433\pi\) | |||||||
\(878\) | 69435.0i | 2.66893i | ||||||||
\(879\) | − 5590.58i | − 0.214523i | ||||||||
\(880\) | −85756.9 | −3.28507 | ||||||||
\(881\) | −23692.2 | −0.906027 | −0.453013 | − | 0.891504i | \(-0.649651\pi\) | ||||
−0.453013 | + | 0.891504i | \(0.649651\pi\) | |||||||
\(882\) | 11960.0i | 0.456591i | ||||||||
\(883\) | 14591.5 | 0.556108 | 0.278054 | − | 0.960565i | \(-0.410311\pi\) | ||||
0.278054 | + | 0.960565i | \(0.410311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23840.6 | 0.905529 | ||||||||
\(886\) | − 61475.2i | − 2.33104i | ||||||||
\(887\) | −9722.26 | −0.368029 | −0.184014 | − | 0.982924i | \(-0.558909\pi\) | ||||
−0.184014 | + | 0.982924i | \(0.558909\pi\) | |||||||
\(888\) | 19537.1 | 0.738312 | ||||||||
\(889\) | 13857.8i | 0.522806i | ||||||||
\(890\) | 90826.1i | 3.42078i | ||||||||
\(891\) | − 2234.64i | − 0.0840217i | ||||||||
\(892\) | 42046.6i | 1.57828i | ||||||||
\(893\) | 1149.42 | 0.0430726 | ||||||||
\(894\) | −42164.3 | −1.57739 | ||||||||
\(895\) | 69969.2i | 2.61320i | ||||||||
\(896\) | −16706.6 | −0.622911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52678.9 | 1.95759 | ||||||||
\(899\) | 11827.1i | 0.438771i | ||||||||
\(900\) | 26526.9 | 0.982479 | ||||||||
\(901\) | −53189.7 | −1.96671 | ||||||||
\(902\) | − 4521.26i | − 0.166898i | ||||||||
\(903\) | − 6920.74i | − 0.255048i | ||||||||
\(904\) | 11949.0i | 0.439621i | ||||||||
\(905\) | 64743.2i | 2.37805i | ||||||||
\(906\) | 53289.3 | 1.95411 | ||||||||
\(907\) | −11799.0 | −0.431951 | −0.215975 | − | 0.976399i | \(-0.569293\pi\) | ||||
−0.215975 | + | 0.976399i | \(0.569293\pi\) | |||||||
\(908\) | − 91500.9i | − 3.34423i | ||||||||
\(909\) | −4786.18 | −0.174640 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43012.4 | −1.56429 | −0.782143 | − | 0.623099i | \(-0.785873\pi\) | ||||
−0.782143 | + | 0.623099i | \(0.785873\pi\) | |||||||
\(912\) | 1276.81i | 0.0463589i | ||||||||
\(913\) | −19746.6 | −0.715793 | ||||||||
\(914\) | 83303.8 | 3.01471 | ||||||||
\(915\) | − 21863.3i | − 0.789921i | ||||||||
\(916\) | − 33281.3i | − 1.20049i | ||||||||
\(917\) | − 20011.0i | − 0.720635i | ||||||||
\(918\) | 15533.1i | 0.558462i | ||||||||
\(919\) | −4951.41 | −0.177728 | −0.0888639 | − | 0.996044i | \(-0.528324\pi\) | ||||
−0.0888639 | + | 0.996044i | \(0.528324\pi\) | |||||||
\(920\) | 45404.5 | 1.62711 | ||||||||
\(921\) | − 19162.5i | − 0.685587i | ||||||||
\(922\) | 41297.0 | 1.47510 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16353.6 | −0.582245 | ||||||||
\(925\) | 14211.3i | 0.505152i | ||||||||
\(926\) | −1777.27 | −0.0630721 | ||||||||
\(927\) | 6623.85 | 0.234688 | ||||||||
\(928\) | 29589.8i | 1.04669i | ||||||||
\(929\) | − 8934.86i | − 0.315547i | −0.987475 | − | 0.157774i | \(-0.949568\pi\) | ||||
0.987475 | − | 0.157774i | \(-0.0504316\pi\) | |||||||
\(930\) | − 50375.4i | − 1.77621i | ||||||||
\(931\) | − 560.243i | − 0.0197221i | ||||||||
\(932\) | −38860.2 | −1.36578 | ||||||||
\(933\) | −10477.8 | −0.367660 | ||||||||
\(934\) | − 43700.3i | − 1.53096i | ||||||||
\(935\) | 48870.6 | 1.70935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13182.8 | −0.459620 | −0.229810 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229810 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(938\) | 9809.20i | 0.341452i | ||||||||
\(939\) | 17736.0 | 0.616393 | ||||||||
\(940\) | −171368. | −5.94618 | ||||||||
\(941\) | − 21693.7i | − 0.751536i | −0.926714 | − | 0.375768i | \(-0.877379\pi\) | ||||
0.926714 | − | 0.375768i | \(-0.122621\pi\) | |||||||
\(942\) | 25989.9i | 0.898934i | ||||||||
\(943\) | 1285.43i | 0.0443895i | ||||||||
\(944\) | − 91698.4i | − 3.16158i | ||||||||
\(945\) | 4289.59 | 0.147662 | ||||||||
\(946\) | −35047.1 | −1.20452 | ||||||||
\(947\) | 49790.0i | 1.70851i | 0.519856 | + | 0.854254i | \(0.325986\pi\) | ||||
−0.519856 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(948\) | −22977.9 | −0.787224 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1729.59 | −0.0590687 | ||||||||
\(951\) | 5032.61i | 0.171602i | ||||||||
\(952\) | 69125.0 | 2.35331 | ||||||||
\(953\) | −4217.93 | −0.143371 | −0.0716853 | − | 0.997427i | \(-0.522838\pi\) | ||||
−0.0716853 | + | 0.997427i | \(0.522838\pi\) | |||||||
\(954\) | 23642.6i | 0.802365i | ||||||||
\(955\) | 3514.19i | 0.119075i | ||||||||
\(956\) | − 76830.5i | − 2.59924i | ||||||||
\(957\) | 5100.05i | 0.172269i | ||||||||
\(958\) | −34305.8 | −1.15696 | ||||||||
\(959\) | 3750.99 | 0.126304 | ||||||||
\(960\) | − 51429.0i | − 1.72903i | ||||||||
\(961\) | −7046.87 | −0.236544 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7049.38 | −0.235891 | ||||||||
\(964\) | − 73788.1i | − 2.46530i | ||||||||
\(965\) | 19813.7 | 0.660958 | ||||||||
\(966\) | 6471.60 | 0.215549 | ||||||||
\(967\) | − 40927.9i | − 1.36107i | −0.732717 | − | 0.680534i | \(-0.761748\pi\) | ||||
0.732717 | − | 0.680534i | \(-0.238252\pi\) | |||||||
\(968\) | − 37707.9i | − 1.25204i | ||||||||
\(969\) | − 727.619i | − 0.0241223i | ||||||||
\(970\) | 5736.04i | 0.189869i | ||||||||
\(971\) | −17114.8 | −0.565645 | −0.282822 | − | 0.959172i | \(-0.591271\pi\) | ||||
−0.282822 | + | 0.959172i | \(0.591271\pi\) | |||||||
\(972\) | 4960.38 | 0.163688 | ||||||||
\(973\) | − 7284.62i | − 0.240015i | ||||||||
\(974\) | −43151.5 | −1.41957 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −84093.0 | −2.75794 | ||||||||
\(977\) | − 118.470i | − 0.00387940i | −0.999998 | − | 0.00193970i | \(-0.999383\pi\) | ||||
0.999998 | − | 0.00193970i | \(-0.000617427\pi\) | |||||||
\(978\) | 29349.7 | 0.959610 | ||||||||
\(979\) | 28640.7 | 0.934996 | ||||||||
\(980\) | 83527.2i | 2.72263i | ||||||||
\(981\) | − 4791.05i | − 0.155929i | ||||||||
\(982\) | − 27272.8i | − 0.886261i | ||||||||
\(983\) | − 26002.8i | − 0.843705i | −0.906665 | − | 0.421852i | \(-0.861380\pi\) | ||||
0.906665 | − | 0.421852i | \(-0.138620\pi\) | |||||||
\(984\) | 6102.93 | 0.197718 | ||||||||
\(985\) | −15225.3 | −0.492506 | ||||||||
\(986\) | − 35450.7i | − 1.14501i | ||||||||
\(987\) | −14853.0 | −0.479002 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9964.14 | 0.320365 | ||||||||
\(990\) | − 21722.8i | − 0.697368i | ||||||||
\(991\) | −16062.0 | −0.514860 | −0.257430 | − | 0.966297i | \(-0.582876\pi\) | ||||
−0.257430 | + | 0.966297i | \(0.582876\pi\) | |||||||
\(992\) | −92163.3 | −2.94979 | ||||||||
\(993\) | − 6030.93i | − 0.192735i | ||||||||
\(994\) | 25013.2i | 0.798159i | ||||||||
\(995\) | 7861.07i | 0.250465i | ||||||||
\(996\) | − 43832.9i | − 1.39448i | ||||||||
\(997\) | 1361.54 | 0.0432503 | 0.0216251 | − | 0.999766i | \(-0.493116\pi\) | ||||
0.0216251 | + | 0.999766i | \(0.493116\pi\) | |||||||
\(998\) | 96217.5 | 3.05182 | ||||||||
\(999\) | 2657.44i | 0.0841617i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 507.4.b.h.337.8 | 8 | ||
13.2 | odd | 12 | 39.4.e.c.22.1 | yes | 8 | ||
13.5 | odd | 4 | 507.4.a.m.1.4 | 4 | |||
13.6 | odd | 12 | 39.4.e.c.16.1 | ✓ | 8 | ||
13.8 | odd | 4 | 507.4.a.i.1.1 | 4 | |||
13.12 | even | 2 | inner | 507.4.b.h.337.1 | 8 | ||
39.2 | even | 12 | 117.4.g.e.100.4 | 8 | |||
39.5 | even | 4 | 1521.4.a.v.1.1 | 4 | |||
39.8 | even | 4 | 1521.4.a.bb.1.4 | 4 | |||
39.32 | even | 12 | 117.4.g.e.55.4 | 8 | |||
52.15 | even | 12 | 624.4.q.i.529.1 | 8 | |||
52.19 | even | 12 | 624.4.q.i.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.1 | ✓ | 8 | 13.6 | odd | 12 | ||
39.4.e.c.22.1 | yes | 8 | 13.2 | odd | 12 | ||
117.4.g.e.55.4 | 8 | 39.32 | even | 12 | |||
117.4.g.e.100.4 | 8 | 39.2 | even | 12 | |||
507.4.a.i.1.1 | 4 | 13.8 | odd | 4 | |||
507.4.a.m.1.4 | 4 | 13.5 | odd | 4 | |||
507.4.b.h.337.1 | 8 | 13.12 | even | 2 | inner | ||
507.4.b.h.337.8 | 8 | 1.1 | even | 1 | trivial | ||
624.4.q.i.289.1 | 8 | 52.19 | even | 12 | |||
624.4.q.i.529.1 | 8 | 52.15 | even | 12 | |||
1521.4.a.v.1.1 | 4 | 39.5 | even | 4 | |||
1521.4.a.bb.1.4 | 4 | 39.8 | even | 4 |