Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.8521965066\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 107x^{3} - 3x^{2} + 2151x - 2916 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.53483\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0.534830 | 0.102928 | 0.0514640 | − | 0.998675i | \(-0.483611\pi\) | ||||
0.0514640 | + | 0.998675i | \(0.483611\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.06966 | −0.0727812 | ||||||||
\(7\) | 28.9380 | 1.56250 | 0.781252 | − | 0.624215i | \(-0.214581\pi\) | ||||
0.781252 | + | 0.624215i | \(0.214581\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −26.7140 | −0.989406 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.5234 | 0.918880 | 0.459440 | − | 0.888209i | \(-0.348050\pi\) | ||||
0.459440 | + | 0.888209i | \(0.348050\pi\) | |||||||
\(12\) | 2.13932 | 0.0514640 | ||||||||
\(13\) | −10.2917 | −0.219570 | −0.109785 | − | 0.993955i | \(-0.535016\pi\) | ||||
−0.109785 | + | 0.993955i | \(0.535016\pi\) | |||||||
\(14\) | −57.8760 | −1.10486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −56.5854 | −0.807293 | −0.403646 | − | 0.914915i | \(-0.632257\pi\) | ||||
−0.403646 | + | 0.914915i | \(0.632257\pi\) | |||||||
\(18\) | 53.4279 | 0.699616 | ||||||||
\(19\) | −5.26405 | −0.0635608 | −0.0317804 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317804 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.4769 | 0.160826 | ||||||||
\(22\) | −67.0468 | −0.649747 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −4.27864 | −0.0363906 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 20.5834 | 0.155259 | ||||||||
\(27\) | −28.7278 | −0.204766 | ||||||||
\(28\) | 115.752 | 0.781252 | ||||||||
\(29\) | −162.334 | −1.03947 | −0.519737 | − | 0.854327i | \(-0.673970\pi\) | ||||
−0.519737 | + | 0.854327i | \(0.673970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.556 | −0.930218 | −0.465109 | − | 0.885253i | \(-0.653985\pi\) | ||||
−0.465109 | + | 0.885253i | \(0.653985\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 17.9293 | 0.0945786 | ||||||||
\(34\) | 113.171 | 0.570842 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −106.856 | −0.494703 | ||||||||
\(37\) | 16.9178 | 0.0751694 | 0.0375847 | − | 0.999293i | \(-0.488034\pi\) | ||||
0.0375847 | + | 0.999293i | \(0.488034\pi\) | |||||||
\(38\) | 10.5281 | 0.0449443 | ||||||||
\(39\) | −5.50431 | −0.0225999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.7758 | 0.0867557 | 0.0433779 | − | 0.999059i | \(-0.486188\pi\) | ||||
0.0433779 | + | 0.999059i | \(0.486188\pi\) | |||||||
\(42\) | −30.9538 | −0.113721 | ||||||||
\(43\) | −333.620 | −1.18318 | −0.591589 | − | 0.806240i | \(-0.701499\pi\) | ||||
−0.591589 | + | 0.806240i | \(0.701499\pi\) | |||||||
\(44\) | 134.094 | 0.459440 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −130.383 | −0.404645 | −0.202322 | − | 0.979319i | \(-0.564849\pi\) | ||||
−0.202322 | + | 0.979319i | \(0.564849\pi\) | |||||||
\(48\) | 8.55728 | 0.0257320 | ||||||||
\(49\) | 494.408 | 1.44142 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −30.2636 | −0.0830931 | ||||||||
\(52\) | −41.1668 | −0.109785 | ||||||||
\(53\) | −673.206 | −1.74475 | −0.872376 | − | 0.488835i | \(-0.837422\pi\) | ||||
−0.872376 | + | 0.488835i | \(0.837422\pi\) | |||||||
\(54\) | 57.4557 | 0.144791 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −231.504 | −0.552429 | ||||||||
\(57\) | −2.81537 | −0.00654219 | ||||||||
\(58\) | 324.669 | 0.735019 | ||||||||
\(59\) | 291.958 | 0.644233 | 0.322116 | − | 0.946700i | \(-0.395606\pi\) | ||||
0.322116 | + | 0.946700i | \(0.395606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 454.587 | 0.954162 | 0.477081 | − | 0.878859i | \(-0.341695\pi\) | ||||
0.477081 | + | 0.878859i | \(0.341695\pi\) | |||||||
\(62\) | 321.113 | 0.657764 | ||||||||
\(63\) | −773.048 | −1.54595 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −35.8586 | −0.0668772 | ||||||||
\(67\) | −132.389 | −0.241401 | −0.120701 | − | 0.992689i | \(-0.538514\pi\) | ||||
−0.120701 | + | 0.992689i | \(0.538514\pi\) | |||||||
\(68\) | −226.342 | −0.403646 | ||||||||
\(69\) | −12.3011 | −0.0214620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 121.326 | 0.202799 | 0.101399 | − | 0.994846i | \(-0.467668\pi\) | ||||
0.101399 | + | 0.994846i | \(0.467668\pi\) | |||||||
\(72\) | 213.712 | 0.349808 | ||||||||
\(73\) | −176.482 | −0.282955 | −0.141477 | − | 0.989942i | \(-0.545185\pi\) | ||||
−0.141477 | + | 0.989942i | \(0.545185\pi\) | |||||||
\(74\) | −33.8356 | −0.0531528 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.0562 | −0.0317804 | ||||||||
\(77\) | 970.100 | 1.43576 | ||||||||
\(78\) | 11.0086 | 0.0159805 | ||||||||
\(79\) | 563.082 | 0.801920 | 0.400960 | − | 0.916096i | \(-0.368677\pi\) | ||||
0.400960 | + | 0.916096i | \(0.368677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 705.912 | 0.968330 | ||||||||
\(82\) | −45.5516 | −0.0613456 | ||||||||
\(83\) | −809.068 | −1.06996 | −0.534981 | − | 0.844864i | \(-0.679681\pi\) | ||||
−0.534981 | + | 0.844864i | \(0.679681\pi\) | |||||||
\(84\) | 61.9076 | 0.0804128 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 667.241 | 0.836633 | ||||||||
\(87\) | −86.8213 | −0.106991 | ||||||||
\(88\) | −268.187 | −0.324873 | ||||||||
\(89\) | −702.417 | −0.836585 | −0.418293 | − | 0.908312i | \(-0.637371\pi\) | ||||
−0.418293 | + | 0.908312i | \(0.637371\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −297.821 | −0.343079 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −85.8703 | −0.0957456 | ||||||||
\(94\) | 260.766 | 0.286127 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −17.1146 | −0.0181953 | ||||||||
\(97\) | −342.945 | −0.358977 | −0.179489 | − | 0.983760i | \(-0.557444\pi\) | ||||
−0.179489 | + | 0.983760i | \(0.557444\pi\) | |||||||
\(98\) | −988.815 | −1.01924 | ||||||||
\(99\) | −895.543 | −0.909146 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1719.68 | 1.69420 | 0.847102 | − | 0.531431i | \(-0.178345\pi\) | ||||
0.847102 | + | 0.531431i | \(0.178345\pi\) | |||||||
\(102\) | 60.5272 | 0.0587557 | ||||||||
\(103\) | −387.872 | −0.371050 | −0.185525 | − | 0.982640i | \(-0.559399\pi\) | ||||
−0.185525 | + | 0.982640i | \(0.559399\pi\) | |||||||
\(104\) | 82.3337 | 0.0776296 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1346.41 | 1.23373 | ||||||||
\(107\) | −31.3904 | −0.0283610 | −0.0141805 | − | 0.999899i | \(-0.504514\pi\) | ||||
−0.0141805 | + | 0.999899i | \(0.504514\pi\) | |||||||
\(108\) | −114.911 | −0.102383 | ||||||||
\(109\) | 686.159 | 0.602955 | 0.301478 | − | 0.953473i | \(-0.402520\pi\) | ||||
0.301478 | + | 0.953473i | \(0.402520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.04814 | 0.00773704 | ||||||||
\(112\) | 463.008 | 0.390626 | ||||||||
\(113\) | 42.2350 | 0.0351605 | 0.0175802 | − | 0.999845i | \(-0.494404\pi\) | ||||
0.0175802 | + | 0.999845i | \(0.494404\pi\) | |||||||
\(114\) | 5.63074 | 0.00462603 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −649.337 | −0.519737 | ||||||||
\(117\) | 274.932 | 0.217244 | ||||||||
\(118\) | −583.917 | −0.455541 | ||||||||
\(119\) | −1637.47 | −1.26140 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −207.182 | −0.155659 | ||||||||
\(122\) | −909.173 | −0.674694 | ||||||||
\(123\) | 12.1812 | 0.00892960 | ||||||||
\(124\) | −642.225 | −0.465109 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1546.10 | 1.09315 | ||||||||
\(127\) | −1234.48 | −0.862538 | −0.431269 | − | 0.902223i | \(-0.641934\pi\) | ||||
−0.431269 | + | 0.902223i | \(0.641934\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −178.430 | −0.121782 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2216.74 | −1.47846 | −0.739228 | − | 0.673455i | \(-0.764809\pi\) | ||||
−0.739228 | + | 0.673455i | \(0.764809\pi\) | |||||||
\(132\) | 71.7173 | 0.0472893 | ||||||||
\(133\) | −152.331 | −0.0993140 | ||||||||
\(134\) | 264.778 | 0.170697 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 452.683 | 0.285421 | ||||||||
\(137\) | 1179.48 | 0.735545 | 0.367773 | − | 0.929916i | \(-0.380120\pi\) | ||||
0.367773 | + | 0.929916i | \(0.380120\pi\) | |||||||
\(138\) | 24.6022 | 0.0151759 | ||||||||
\(139\) | 241.224 | 0.147197 | 0.0735983 | − | 0.997288i | \(-0.476552\pi\) | ||||
0.0735983 | + | 0.997288i | \(0.476552\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −69.7327 | −0.0416493 | ||||||||
\(142\) | −242.651 | −0.143400 | ||||||||
\(143\) | −345.013 | −0.201758 | ||||||||
\(144\) | −427.423 | −0.247351 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 352.964 | 0.200079 | ||||||||
\(147\) | 264.424 | 0.148363 | ||||||||
\(148\) | 67.6711 | 0.0375847 | ||||||||
\(149\) | −1028.14 | −0.565294 | −0.282647 | − | 0.959224i | \(-0.591212\pi\) | ||||
−0.282647 | + | 0.959224i | \(0.591212\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1511.24 | 0.814456 | 0.407228 | − | 0.913327i | \(-0.366495\pi\) | ||||
0.407228 | + | 0.913327i | \(0.366495\pi\) | |||||||
\(152\) | 42.1124 | 0.0224721 | ||||||||
\(153\) | 1511.62 | 0.798740 | ||||||||
\(154\) | −1940.20 | −1.01523 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −22.0173 | −0.0112999 | ||||||||
\(157\) | 2097.04 | 1.06600 | 0.532999 | − | 0.846116i | \(-0.321065\pi\) | ||||
0.532999 | + | 0.846116i | \(0.321065\pi\) | |||||||
\(158\) | −1126.16 | −0.567043 | ||||||||
\(159\) | −360.051 | −0.179584 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −665.574 | −0.325805 | ||||||||
\(162\) | −1411.82 | −0.684712 | ||||||||
\(163\) | −703.046 | −0.337833 | −0.168917 | − | 0.985630i | \(-0.554027\pi\) | ||||
−0.168917 | + | 0.985630i | \(0.554027\pi\) | |||||||
\(164\) | 91.1033 | 0.0433779 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1618.14 | 0.756577 | ||||||||
\(167\) | −3063.04 | −1.41931 | −0.709656 | − | 0.704549i | \(-0.751150\pi\) | ||||
−0.709656 | + | 0.704549i | \(0.751150\pi\) | |||||||
\(168\) | −123.815 | −0.0568605 | ||||||||
\(169\) | −2091.08 | −0.951789 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 140.624 | 0.0628874 | ||||||||
\(172\) | −1334.48 | −0.591589 | ||||||||
\(173\) | −2810.34 | −1.23506 | −0.617531 | − | 0.786546i | \(-0.711867\pi\) | ||||
−0.617531 | + | 0.786546i | \(0.711867\pi\) | |||||||
\(174\) | 173.643 | 0.0756541 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 536.374 | 0.229720 | ||||||||
\(177\) | 156.148 | 0.0663096 | ||||||||
\(178\) | 1404.83 | 0.591555 | ||||||||
\(179\) | −2516.53 | −1.05081 | −0.525403 | − | 0.850853i | \(-0.676086\pi\) | ||||
−0.525403 | + | 0.850853i | \(0.676086\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1085.01 | 0.445570 | 0.222785 | − | 0.974868i | \(-0.428485\pi\) | ||||
0.222785 | + | 0.974868i | \(0.428485\pi\) | |||||||
\(182\) | 595.643 | 0.242593 | ||||||||
\(183\) | 243.127 | 0.0982100 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 171.741 | 0.0677024 | ||||||||
\(187\) | −1896.94 | −0.741806 | ||||||||
\(188\) | −521.532 | −0.202322 | ||||||||
\(189\) | −831.326 | −0.319947 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2081.87 | −0.788683 | −0.394342 | − | 0.918964i | \(-0.629027\pi\) | ||||
−0.394342 | + | 0.918964i | \(0.629027\pi\) | |||||||
\(192\) | 34.2291 | 0.0128660 | ||||||||
\(193\) | −648.493 | −0.241863 | −0.120931 | − | 0.992661i | \(-0.538588\pi\) | ||||
−0.120931 | + | 0.992661i | \(0.538588\pi\) | |||||||
\(194\) | 685.890 | 0.253835 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1977.63 | 0.720711 | ||||||||
\(197\) | 1250.92 | 0.452409 | 0.226205 | − | 0.974080i | \(-0.427368\pi\) | ||||
0.226205 | + | 0.974080i | \(0.427368\pi\) | |||||||
\(198\) | 1791.09 | 0.642863 | ||||||||
\(199\) | 3135.54 | 1.11695 | 0.558473 | − | 0.829523i | \(-0.311387\pi\) | ||||
0.558473 | + | 0.829523i | \(0.311387\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −70.8056 | −0.0248470 | ||||||||
\(202\) | −3439.36 | −1.19798 | ||||||||
\(203\) | −4697.63 | −1.62418 | ||||||||
\(204\) | −121.054 | −0.0415466 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 775.743 | 0.262372 | ||||||||
\(207\) | 614.421 | 0.206305 | ||||||||
\(208\) | −164.667 | −0.0548924 | ||||||||
\(209\) | −176.469 | −0.0584048 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −844.189 | −0.275433 | −0.137716 | − | 0.990472i | \(-0.543976\pi\) | ||||
−0.137716 | + | 0.990472i | \(0.543976\pi\) | |||||||
\(212\) | −2692.82 | −0.872376 | ||||||||
\(213\) | 64.8886 | 0.0208737 | ||||||||
\(214\) | 62.7808 | 0.0200542 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 229.823 | 0.0723956 | ||||||||
\(217\) | −4646.18 | −1.45347 | ||||||||
\(218\) | −1372.32 | −0.426354 | ||||||||
\(219\) | −94.3880 | −0.0291240 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 582.360 | 0.177257 | ||||||||
\(222\) | −18.0963 | −0.00547091 | ||||||||
\(223\) | −5648.57 | −1.69622 | −0.848108 | − | 0.529824i | \(-0.822258\pi\) | ||||
−0.848108 | + | 0.529824i | \(0.822258\pi\) | |||||||
\(224\) | −926.016 | −0.276214 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −84.4700 | −0.0248622 | ||||||||
\(227\) | 3914.91 | 1.14468 | 0.572338 | − | 0.820018i | \(-0.306036\pi\) | ||||
0.572338 | + | 0.820018i | \(0.306036\pi\) | |||||||
\(228\) | −11.2615 | −0.00327110 | ||||||||
\(229\) | −550.992 | −0.158998 | −0.0794990 | − | 0.996835i | \(-0.525332\pi\) | ||||
−0.0794990 | + | 0.996835i | \(0.525332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 518.839 | 0.147780 | ||||||||
\(232\) | 1298.67 | 0.367509 | ||||||||
\(233\) | −5785.67 | −1.62675 | −0.813373 | − | 0.581742i | \(-0.802371\pi\) | ||||
−0.813373 | + | 0.581742i | \(0.802371\pi\) | |||||||
\(234\) | −549.864 | −0.153614 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1167.83 | 0.322116 | ||||||||
\(237\) | 301.153 | 0.0825400 | ||||||||
\(238\) | 3274.94 | 0.891944 | ||||||||
\(239\) | −4525.71 | −1.22487 | −0.612435 | − | 0.790521i | \(-0.709810\pi\) | ||||
−0.612435 | + | 0.790521i | \(0.709810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 517.292 | 0.138264 | 0.0691322 | − | 0.997608i | \(-0.477977\pi\) | ||||
0.0691322 | + | 0.997608i | \(0.477977\pi\) | |||||||
\(242\) | 414.363 | 0.110067 | ||||||||
\(243\) | 1153.19 | 0.304434 | ||||||||
\(244\) | 1818.35 | 0.477081 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.3624 | −0.00631418 | ||||||||
\(247\) | 54.1760 | 0.0139560 | ||||||||
\(248\) | 1284.45 | 0.328882 | ||||||||
\(249\) | −432.714 | −0.110129 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7039.00 | −1.77011 | −0.885055 | − | 0.465486i | \(-0.845879\pi\) | ||||
−0.885055 | + | 0.465486i | \(0.845879\pi\) | |||||||
\(252\) | −3092.19 | −0.772976 | ||||||||
\(253\) | −771.038 | −0.191600 | ||||||||
\(254\) | 2468.96 | 0.609906 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4250.94 | 1.03177 | 0.515887 | − | 0.856656i | \(-0.327462\pi\) | ||||
0.515887 | + | 0.856656i | \(0.327462\pi\) | |||||||
\(258\) | 356.860 | 0.0861130 | ||||||||
\(259\) | 489.567 | 0.117453 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4336.59 | 1.02846 | ||||||||
\(262\) | 4433.49 | 1.04543 | ||||||||
\(263\) | −3598.83 | −0.843778 | −0.421889 | − | 0.906648i | \(-0.638633\pi\) | ||||
−0.421889 | + | 0.906648i | \(0.638633\pi\) | |||||||
\(264\) | −143.435 | −0.0334386 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 304.662 | 0.0702256 | ||||||||
\(267\) | −375.674 | −0.0861081 | ||||||||
\(268\) | −529.556 | −0.120701 | ||||||||
\(269\) | −5062.52 | −1.14746 | −0.573731 | − | 0.819044i | \(-0.694505\pi\) | ||||
−0.573731 | + | 0.819044i | \(0.694505\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1854.58 | 0.415712 | 0.207856 | − | 0.978159i | \(-0.433352\pi\) | ||||
0.207856 | + | 0.978159i | \(0.433352\pi\) | |||||||
\(272\) | −905.366 | −0.201823 | ||||||||
\(273\) | −159.284 | −0.0353124 | ||||||||
\(274\) | −2358.96 | −0.520109 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −49.2044 | −0.0107310 | ||||||||
\(277\) | −8747.91 | −1.89751 | −0.948756 | − | 0.316009i | \(-0.897657\pi\) | ||||
−0.948756 | + | 0.316009i | \(0.897657\pi\) | |||||||
\(278\) | −482.447 | −0.104084 | ||||||||
\(279\) | 4289.09 | 0.920363 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4046.88 | 0.859134 | 0.429567 | − | 0.903035i | \(-0.358666\pi\) | ||||
0.429567 | + | 0.903035i | \(0.358666\pi\) | |||||||
\(282\) | 139.465 | 0.0294505 | ||||||||
\(283\) | −1598.52 | −0.335766 | −0.167883 | − | 0.985807i | \(-0.553693\pi\) | ||||
−0.167883 | + | 0.985807i | \(0.553693\pi\) | |||||||
\(284\) | 485.303 | 0.101399 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 690.026 | 0.142665 | ||||||||
\(287\) | 659.086 | 0.135556 | ||||||||
\(288\) | 854.847 | 0.174904 | ||||||||
\(289\) | −1711.09 | −0.348278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −183.417 | −0.0369488 | ||||||||
\(292\) | −705.929 | −0.141477 | ||||||||
\(293\) | 4542.62 | 0.905742 | 0.452871 | − | 0.891576i | \(-0.350400\pi\) | ||||
0.452871 | + | 0.891576i | \(0.350400\pi\) | |||||||
\(294\) | −528.848 | −0.104908 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −135.342 | −0.0265764 | ||||||||
\(297\) | −963.055 | −0.188155 | ||||||||
\(298\) | 2056.29 | 0.399723 | ||||||||
\(299\) | 236.709 | 0.0457834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9654.31 | −1.84872 | ||||||||
\(302\) | −3022.48 | −0.575907 | ||||||||
\(303\) | 919.736 | 0.174381 | ||||||||
\(304\) | −84.2247 | −0.0158902 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3023.24 | −0.564795 | ||||||||
\(307\) | 2366.39 | 0.439925 | 0.219963 | − | 0.975508i | \(-0.429406\pi\) | ||||
0.219963 | + | 0.975508i | \(0.429406\pi\) | |||||||
\(308\) | 3880.40 | 0.717878 | ||||||||
\(309\) | −207.445 | −0.0381914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 830.158 | 0.151363 | 0.0756816 | − | 0.997132i | \(-0.475887\pi\) | ||||
0.0756816 | + | 0.997132i | \(0.475887\pi\) | |||||||
\(312\) | 44.0345 | 0.00799027 | ||||||||
\(313\) | 7182.03 | 1.29697 | 0.648486 | − | 0.761226i | \(-0.275402\pi\) | ||||
0.648486 | + | 0.761226i | \(0.275402\pi\) | |||||||
\(314\) | −4194.07 | −0.753775 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2252.33 | 0.400960 | ||||||||
\(317\) | −1910.06 | −0.338422 | −0.169211 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169211 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(318\) | 720.101 | 0.126985 | ||||||||
\(319\) | −5442.00 | −0.955152 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.7885 | −0.00291914 | ||||||||
\(322\) | 1331.15 | 0.230379 | ||||||||
\(323\) | 297.868 | 0.0513122 | ||||||||
\(324\) | 2823.65 | 0.484165 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1406.09 | 0.238884 | ||||||||
\(327\) | 366.979 | 0.0620610 | ||||||||
\(328\) | −182.207 | −0.0306728 | ||||||||
\(329\) | −3773.02 | −0.632260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7540.40 | 1.25214 | 0.626069 | − | 0.779767i | \(-0.284663\pi\) | ||||
0.626069 | + | 0.779767i | \(0.284663\pi\) | |||||||
\(332\) | −3236.27 | −0.534981 | ||||||||
\(333\) | −451.941 | −0.0743730 | ||||||||
\(334\) | 6126.08 | 1.00360 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 247.631 | 0.0402064 | ||||||||
\(337\) | 10069.4 | 1.62764 | 0.813822 | − | 0.581114i | \(-0.197383\pi\) | ||||
0.813822 | + | 0.581114i | \(0.197383\pi\) | |||||||
\(338\) | 4182.16 | 0.673017 | ||||||||
\(339\) | 22.5885 | 0.00361900 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5382.39 | −0.854759 | ||||||||
\(342\) | −281.247 | −0.0444681 | ||||||||
\(343\) | 4381.43 | 0.689723 | ||||||||
\(344\) | 2668.96 | 0.418316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5620.67 | 0.873321 | ||||||||
\(347\) | −6031.06 | −0.933039 | −0.466519 | − | 0.884511i | \(-0.654492\pi\) | ||||
−0.466519 | + | 0.884511i | \(0.654492\pi\) | |||||||
\(348\) | −347.285 | −0.0534955 | ||||||||
\(349\) | −11352.0 | −1.74114 | −0.870569 | − | 0.492047i | \(-0.836249\pi\) | ||||
−0.870569 | + | 0.492047i | \(0.836249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 295.659 | 0.0449604 | ||||||||
\(352\) | −1072.75 | −0.162437 | ||||||||
\(353\) | 4864.81 | 0.733506 | 0.366753 | − | 0.930318i | \(-0.380469\pi\) | ||||
0.366753 | + | 0.930318i | \(0.380469\pi\) | |||||||
\(354\) | −312.296 | −0.0468880 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2809.67 | −0.418293 | ||||||||
\(357\) | −875.767 | −0.129833 | ||||||||
\(358\) | 5033.06 | 0.743032 | ||||||||
\(359\) | −5809.49 | −0.854076 | −0.427038 | − | 0.904234i | \(-0.640443\pi\) | ||||
−0.427038 | + | 0.904234i | \(0.640443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6831.29 | −0.995960 | ||||||||
\(362\) | −2170.02 | −0.315066 | ||||||||
\(363\) | −110.807 | −0.0160216 | ||||||||
\(364\) | −1191.29 | −0.171539 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −486.253 | −0.0694450 | ||||||||
\(367\) | −6984.38 | −0.993410 | −0.496705 | − | 0.867919i | \(-0.665457\pi\) | ||||
−0.496705 | + | 0.867919i | \(0.665457\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −608.432 | −0.0858366 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19481.2 | −2.72618 | ||||||||
\(372\) | −343.481 | −0.0478728 | ||||||||
\(373\) | −8551.53 | −1.18708 | −0.593541 | − | 0.804804i | \(-0.702270\pi\) | ||||
−0.593541 | + | 0.804804i | \(0.702270\pi\) | |||||||
\(374\) | 3793.87 | 0.524536 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1043.06 | 0.143064 | ||||||||
\(377\) | 1670.70 | 0.228237 | ||||||||
\(378\) | 1662.65 | 0.226237 | ||||||||
\(379\) | 9933.40 | 1.34629 | 0.673145 | − | 0.739510i | \(-0.264943\pi\) | ||||
0.673145 | + | 0.739510i | \(0.264943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −660.236 | −0.0887794 | ||||||||
\(382\) | 4163.73 | 0.557683 | ||||||||
\(383\) | −9748.52 | −1.30059 | −0.650295 | − | 0.759682i | \(-0.725355\pi\) | ||||
−0.650295 | + | 0.759682i | \(0.725355\pi\) | |||||||
\(384\) | −68.4582 | −0.00909764 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1296.99 | 0.171023 | ||||||||
\(387\) | 8912.32 | 1.17064 | ||||||||
\(388\) | −1371.78 | −0.179489 | ||||||||
\(389\) | −10517.0 | −1.37078 | −0.685391 | − | 0.728175i | \(-0.740369\pi\) | ||||
−0.685391 | + | 0.728175i | \(0.740369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1301.46 | 0.168332 | ||||||||
\(392\) | −3955.26 | −0.509619 | ||||||||
\(393\) | −1185.58 | −0.152175 | ||||||||
\(394\) | −2501.85 | −0.319902 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3582.17 | −0.454573 | ||||||||
\(397\) | −4117.94 | −0.520588 | −0.260294 | − | 0.965529i | \(-0.583819\pi\) | ||||
−0.260294 | + | 0.965529i | \(0.583819\pi\) | |||||||
\(398\) | −6271.07 | −0.789800 | ||||||||
\(399\) | −81.4712 | −0.0102222 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7374.29 | −0.918340 | −0.459170 | − | 0.888348i | \(-0.651853\pi\) | ||||
−0.459170 | + | 0.888348i | \(0.651853\pi\) | |||||||
\(402\) | 141.611 | 0.0175695 | ||||||||
\(403\) | 1652.40 | 0.204248 | ||||||||
\(404\) | 6878.72 | 0.847102 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9395.26 | 1.14847 | ||||||||
\(407\) | 567.142 | 0.0690717 | ||||||||
\(408\) | 242.109 | 0.0293778 | ||||||||
\(409\) | 12941.5 | 1.56459 | 0.782296 | − | 0.622907i | \(-0.214049\pi\) | ||||
0.782296 | + | 0.622907i | \(0.214049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 630.821 | 0.0757083 | ||||||||
\(412\) | −1551.49 | −0.185525 | ||||||||
\(413\) | 8448.69 | 1.00662 | ||||||||
\(414\) | −1228.84 | −0.145880 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 329.335 | 0.0388148 | ||||||||
\(417\) | 129.014 | 0.0151507 | ||||||||
\(418\) | 352.937 | 0.0412984 | ||||||||
\(419\) | 5633.46 | 0.656832 | 0.328416 | − | 0.944533i | \(-0.393485\pi\) | ||||
0.328416 | + | 0.944533i | \(0.393485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4205.49 | −0.486848 | −0.243424 | − | 0.969920i | \(-0.578271\pi\) | ||||
−0.243424 | + | 0.969920i | \(0.578271\pi\) | |||||||
\(422\) | 1688.38 | 0.194761 | ||||||||
\(423\) | 3483.04 | 0.400358 | ||||||||
\(424\) | 5385.64 | 0.616863 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −129.777 | −0.0147599 | ||||||||
\(427\) | 13154.8 | 1.49088 | ||||||||
\(428\) | −125.562 | −0.0141805 | ||||||||
\(429\) | −184.523 | −0.0207666 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15075.7 | 1.68486 | 0.842428 | − | 0.538809i | \(-0.181125\pi\) | ||||
0.842428 | + | 0.538809i | \(0.181125\pi\) | |||||||
\(432\) | −459.645 | −0.0511914 | ||||||||
\(433\) | −3098.05 | −0.343840 | −0.171920 | − | 0.985111i | \(-0.554997\pi\) | ||||
−0.171920 | + | 0.985111i | \(0.554997\pi\) | |||||||
\(434\) | 9292.36 | 1.02776 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2744.64 | 0.301478 | ||||||||
\(437\) | 121.073 | 0.0132533 | ||||||||
\(438\) | 188.776 | 0.0205938 | ||||||||
\(439\) | 6867.74 | 0.746649 | 0.373325 | − | 0.927701i | \(-0.378218\pi\) | ||||
0.373325 | + | 0.927701i | \(0.378218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13207.6 | −1.42615 | ||||||||
\(442\) | −1164.72 | −0.125340 | ||||||||
\(443\) | 5878.29 | 0.630442 | 0.315221 | − | 0.949018i | \(-0.397921\pi\) | ||||
0.315221 | + | 0.949018i | \(0.397921\pi\) | |||||||
\(444\) | 36.1926 | 0.00386852 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11297.1 | 1.19941 | ||||||||
\(447\) | −549.882 | −0.0581846 | ||||||||
\(448\) | 1852.03 | 0.195313 | ||||||||
\(449\) | 13670.7 | 1.43689 | 0.718443 | − | 0.695586i | \(-0.244855\pi\) | ||||
0.718443 | + | 0.695586i | \(0.244855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 763.523 | 0.0797182 | ||||||||
\(452\) | 168.940 | 0.0175802 | ||||||||
\(453\) | 808.256 | 0.0838304 | ||||||||
\(454\) | −7829.81 | −0.809408 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.5230 | 0.00231301 | ||||||||
\(457\) | 16947.2 | 1.73470 | 0.867349 | − | 0.497700i | \(-0.165822\pi\) | ||||
0.867349 | + | 0.497700i | \(0.165822\pi\) | |||||||
\(458\) | 1101.98 | 0.112429 | ||||||||
\(459\) | 1625.58 | 0.165306 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5583.33 | −0.564081 | −0.282041 | − | 0.959402i | \(-0.591011\pi\) | ||||
−0.282041 | + | 0.959402i | \(0.591011\pi\) | |||||||
\(462\) | −1037.68 | −0.104496 | ||||||||
\(463\) | 5858.02 | 0.588003 | 0.294001 | − | 0.955805i | \(-0.405013\pi\) | ||||
0.294001 | + | 0.955805i | \(0.405013\pi\) | |||||||
\(464\) | −2597.35 | −0.259868 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11571.3 | 1.15028 | ||||||||
\(467\) | 13949.8 | 1.38227 | 0.691136 | − | 0.722725i | \(-0.257111\pi\) | ||||
0.691136 | + | 0.722725i | \(0.257111\pi\) | |||||||
\(468\) | 1099.73 | 0.108622 | ||||||||
\(469\) | −3831.07 | −0.377191 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1121.56 | 0.109721 | ||||||||
\(472\) | −2335.67 | −0.227771 | ||||||||
\(473\) | −11184.1 | −1.08720 | ||||||||
\(474\) | −602.306 | −0.0583646 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6549.87 | −0.630699 | ||||||||
\(477\) | 17984.0 | 1.72627 | ||||||||
\(478\) | 9051.43 | 0.866114 | ||||||||
\(479\) | 7154.84 | 0.682491 | 0.341245 | − | 0.939974i | \(-0.389151\pi\) | ||||
0.341245 | + | 0.939974i | \(0.389151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −174.113 | −0.0165049 | ||||||||
\(482\) | −1034.58 | −0.0977677 | ||||||||
\(483\) | −355.969 | −0.0335345 | ||||||||
\(484\) | −828.727 | −0.0778293 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2306.39 | −0.215267 | ||||||||
\(487\) | 14811.9 | 1.37821 | 0.689106 | − | 0.724661i | \(-0.258004\pi\) | ||||
0.689106 | + | 0.724661i | \(0.258004\pi\) | |||||||
\(488\) | −3636.69 | −0.337347 | ||||||||
\(489\) | −376.010 | −0.0347725 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3092.94 | 0.284282 | 0.142141 | − | 0.989846i | \(-0.454601\pi\) | ||||
0.142141 | + | 0.989846i | \(0.454601\pi\) | |||||||
\(492\) | 48.7248 | 0.00446480 | ||||||||
\(493\) | 9185.75 | 0.839159 | ||||||||
\(494\) | −108.352 | −0.00986840 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2568.90 | −0.232555 | ||||||||
\(497\) | 3510.92 | 0.316874 | ||||||||
\(498\) | 865.428 | 0.0778730 | ||||||||
\(499\) | 17250.6 | 1.54758 | 0.773790 | − | 0.633443i | \(-0.218359\pi\) | ||||
0.773790 | + | 0.633443i | \(0.218359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1638.21 | −0.146087 | ||||||||
\(502\) | 14078.0 | 1.25166 | ||||||||
\(503\) | 5534.20 | 0.490572 | 0.245286 | − | 0.969451i | \(-0.421118\pi\) | ||||
0.245286 | + | 0.969451i | \(0.421118\pi\) | |||||||
\(504\) | 6184.39 | 0.546576 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1542.08 | 0.135482 | ||||||||
\(507\) | −1118.37 | −0.0979658 | ||||||||
\(508\) | −4937.91 | −0.431269 | ||||||||
\(509\) | 21995.5 | 1.91539 | 0.957693 | − | 0.287791i | \(-0.0929208\pi\) | ||||
0.957693 | + | 0.287791i | \(0.0929208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5107.04 | −0.442118 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 151.225 | 0.0130151 | ||||||||
\(514\) | −8501.87 | −0.729575 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −713.721 | −0.0608911 | ||||||||
\(517\) | −4370.88 | −0.371820 | ||||||||
\(518\) | −979.134 | −0.0830515 | ||||||||
\(519\) | −1503.05 | −0.127123 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 150.733 | 0.0126751 | 0.00633756 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633756 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(522\) | −8673.18 | −0.727232 | ||||||||
\(523\) | 21831.2 | 1.82526 | 0.912630 | − | 0.408787i | \(-0.134048\pi\) | ||||
0.912630 | + | 0.408787i | \(0.134048\pi\) | |||||||
\(524\) | −8866.97 | −0.739228 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7197.67 | 0.596641 | ||||||||
\(527\) | 9085.14 | 0.750958 | ||||||||
\(528\) | 286.869 | 0.0236447 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7799.36 | −0.637408 | ||||||||
\(532\) | −609.324 | −0.0496570 | ||||||||
\(533\) | −234.402 | −0.0190489 | ||||||||
\(534\) | 751.348 | 0.0608877 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1059.11 | 0.0853483 | ||||||||
\(537\) | −1345.92 | −0.108158 | ||||||||
\(538\) | 10125.0 | 0.811379 | ||||||||
\(539\) | 16574.2 | 1.32449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5796.22 | 0.460627 | 0.230313 | − | 0.973117i | \(-0.426025\pi\) | ||||
0.230313 | + | 0.973117i | \(0.426025\pi\) | |||||||
\(542\) | −3709.16 | −0.293952 | ||||||||
\(543\) | 580.297 | 0.0458617 | ||||||||
\(544\) | 1810.73 | 0.142711 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 318.568 | 0.0249697 | ||||||||
\(547\) | −9736.32 | −0.761051 | −0.380526 | − | 0.924770i | \(-0.624257\pi\) | ||||
−0.380526 | + | 0.924770i | \(0.624257\pi\) | |||||||
\(548\) | 4717.92 | 0.367773 | ||||||||
\(549\) | −12143.8 | −0.944053 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 854.535 | 0.0660698 | ||||||||
\(552\) | 98.4087 | 0.00758796 | ||||||||
\(553\) | 16294.5 | 1.25300 | ||||||||
\(554\) | 17495.8 | 1.34174 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 964.895 | 0.0735983 | ||||||||
\(557\) | −5064.36 | −0.385249 | −0.192625 | − | 0.981273i | \(-0.561700\pi\) | ||||
−0.192625 | + | 0.981273i | \(0.561700\pi\) | |||||||
\(558\) | −8578.19 | −0.650795 | ||||||||
\(559\) | 3433.52 | 0.259790 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1014.54 | −0.0763526 | ||||||||
\(562\) | −8093.76 | −0.607499 | ||||||||
\(563\) | −3091.61 | −0.231431 | −0.115716 | − | 0.993282i | \(-0.536916\pi\) | ||||
−0.115716 | + | 0.993282i | \(0.536916\pi\) | |||||||
\(564\) | −278.931 | −0.0208247 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3197.03 | 0.237423 | ||||||||
\(567\) | 20427.7 | 1.51302 | ||||||||
\(568\) | −970.605 | −0.0717002 | ||||||||
\(569\) | 8120.51 | 0.598294 | 0.299147 | − | 0.954207i | \(-0.403298\pi\) | ||||
0.299147 | + | 0.954207i | \(0.403298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5547.16 | −0.406552 | −0.203276 | − | 0.979121i | \(-0.565159\pi\) | ||||
−0.203276 | + | 0.979121i | \(0.565159\pi\) | |||||||
\(572\) | −1380.05 | −0.100879 | ||||||||
\(573\) | −1113.44 | −0.0811777 | ||||||||
\(574\) | −1318.17 | −0.0958527 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1709.69 | −0.123676 | ||||||||
\(577\) | −23746.0 | −1.71327 | −0.856636 | − | 0.515922i | \(-0.827450\pi\) | ||||
−0.856636 | + | 0.515922i | \(0.827450\pi\) | |||||||
\(578\) | 3422.18 | 0.246270 | ||||||||
\(579\) | −346.833 | −0.0248945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23412.8 | −1.67182 | ||||||||
\(582\) | 366.835 | 0.0261268 | ||||||||
\(583\) | −22568.1 | −1.60322 | ||||||||
\(584\) | 1411.86 | 0.100040 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9085.23 | −0.640456 | ||||||||
\(587\) | −17023.6 | −1.19700 | −0.598500 | − | 0.801123i | \(-0.704237\pi\) | ||||
−0.598500 | + | 0.801123i | \(0.704237\pi\) | |||||||
\(588\) | 1057.70 | 0.0741814 | ||||||||
\(589\) | 845.176 | 0.0591254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 669.032 | 0.0465656 | ||||||||
\(592\) | 270.685 | 0.0187923 | ||||||||
\(593\) | −2675.31 | −0.185264 | −0.0926321 | − | 0.995700i | \(-0.529528\pi\) | ||||
−0.0926321 | + | 0.995700i | \(0.529528\pi\) | |||||||
\(594\) | 1926.11 | 0.133046 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4112.57 | −0.282647 | ||||||||
\(597\) | 1676.98 | 0.114965 | ||||||||
\(598\) | −473.419 | −0.0323738 | ||||||||
\(599\) | 15350.4 | 1.04708 | 0.523538 | − | 0.852002i | \(-0.324612\pi\) | ||||
0.523538 | + | 0.852002i | \(0.324612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15429.3 | −1.04721 | −0.523604 | − | 0.851962i | \(-0.675413\pi\) | ||||
−0.523604 | + | 0.851962i | \(0.675413\pi\) | |||||||
\(602\) | 19308.6 | 1.30724 | ||||||||
\(603\) | 3536.63 | 0.238844 | ||||||||
\(604\) | 6044.95 | 0.407228 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1839.47 | −0.123306 | ||||||||
\(607\) | 6027.74 | 0.403061 | 0.201531 | − | 0.979482i | \(-0.435408\pi\) | ||||
0.201531 | + | 0.979482i | \(0.435408\pi\) | |||||||
\(608\) | 168.449 | 0.0112361 | ||||||||
\(609\) | −2512.43 | −0.167174 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1341.86 | 0.0888478 | ||||||||
\(612\) | 6046.48 | 0.399370 | ||||||||
\(613\) | 21260.9 | 1.40085 | 0.700423 | − | 0.713728i | \(-0.252995\pi\) | ||||
0.700423 | + | 0.713728i | \(0.252995\pi\) | |||||||
\(614\) | −4732.78 | −0.311074 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7760.80 | −0.507616 | ||||||||
\(617\) | −20739.7 | −1.35324 | −0.676621 | − | 0.736332i | \(-0.736556\pi\) | ||||
−0.676621 | + | 0.736332i | \(0.736556\pi\) | |||||||
\(618\) | 414.891 | 0.0270054 | ||||||||
\(619\) | −17994.4 | −1.16843 | −0.584214 | − | 0.811600i | \(-0.698597\pi\) | ||||
−0.584214 | + | 0.811600i | \(0.698597\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 660.740 | 0.0426966 | ||||||||
\(622\) | −1660.32 | −0.107030 | ||||||||
\(623\) | −20326.6 | −1.30717 | ||||||||
\(624\) | −88.0690 | −0.00564997 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14364.1 | −0.917098 | ||||||||
\(627\) | −94.3808 | −0.00601149 | ||||||||
\(628\) | 8388.15 | 0.532999 | ||||||||
\(629\) | −957.300 | −0.0606837 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22242.4 | 1.40326 | 0.701630 | − | 0.712542i | \(-0.252456\pi\) | ||||
0.701630 | + | 0.712542i | \(0.252456\pi\) | |||||||
\(632\) | −4504.65 | −0.283521 | ||||||||
\(633\) | −451.498 | −0.0283498 | ||||||||
\(634\) | 3820.13 | 0.239301 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1440.20 | −0.0897920 | ||||||||
\(637\) | −5088.30 | −0.316492 | ||||||||
\(638\) | 10884.0 | 0.675394 | ||||||||
\(639\) | −3241.09 | −0.200650 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12480.7 | 0.769046 | 0.384523 | − | 0.923115i | \(-0.374366\pi\) | ||||
0.384523 | + | 0.923115i | \(0.374366\pi\) | |||||||
\(642\) | 33.5771 | 0.00206415 | ||||||||
\(643\) | 3063.19 | 0.187870 | 0.0939352 | − | 0.995578i | \(-0.470055\pi\) | ||||
0.0939352 | + | 0.995578i | \(0.470055\pi\) | |||||||
\(644\) | −2662.30 | −0.162902 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −595.736 | −0.0362832 | ||||||||
\(647\) | −20052.9 | −1.21849 | −0.609243 | − | 0.792984i | \(-0.708526\pi\) | ||||
−0.609243 | + | 0.792984i | \(0.708526\pi\) | |||||||
\(648\) | −5647.30 | −0.342356 | ||||||||
\(649\) | 9787.43 | 0.591973 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2484.92 | −0.149603 | ||||||||
\(652\) | −2812.18 | −0.168917 | ||||||||
\(653\) | 16978.6 | 1.01749 | 0.508746 | − | 0.860917i | \(-0.330109\pi\) | ||||
0.508746 | + | 0.860917i | \(0.330109\pi\) | |||||||
\(654\) | −733.957 | −0.0438838 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 364.413 | 0.0216889 | ||||||||
\(657\) | 4714.54 | 0.279957 | ||||||||
\(658\) | 7546.04 | 0.447075 | ||||||||
\(659\) | −15608.4 | −0.922637 | −0.461319 | − | 0.887235i | \(-0.652623\pi\) | ||||
−0.461319 | + | 0.887235i | \(0.652623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3744.26 | 0.220325 | 0.110163 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110163 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(662\) | −15080.8 | −0.885396 | ||||||||
\(663\) | 311.464 | 0.0182447 | ||||||||
\(664\) | 6472.55 | 0.378288 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 903.882 | 0.0525897 | ||||||||
\(667\) | 3733.69 | 0.216745 | ||||||||
\(668\) | −12252.2 | −0.709656 | ||||||||
\(669\) | −3021.02 | −0.174588 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15239.3 | 0.876761 | ||||||||
\(672\) | −495.261 | −0.0284302 | ||||||||
\(673\) | −8962.72 | −0.513355 | −0.256677 | − | 0.966497i | \(-0.582628\pi\) | ||||
−0.256677 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(674\) | −20138.8 | −1.15092 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8364.32 | −0.475895 | ||||||||
\(677\) | −30864.5 | −1.75217 | −0.876086 | − | 0.482155i | \(-0.839854\pi\) | ||||
−0.876086 | + | 0.482155i | \(0.839854\pi\) | |||||||
\(678\) | −45.1771 | −0.00255902 | ||||||||
\(679\) | −9924.14 | −0.560904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2093.81 | 0.117819 | ||||||||
\(682\) | 10764.8 | 0.604406 | ||||||||
\(683\) | −2135.02 | −0.119611 | −0.0598055 | − | 0.998210i | \(-0.519048\pi\) | ||||
−0.0598055 | + | 0.998210i | \(0.519048\pi\) | |||||||
\(684\) | 562.494 | 0.0314437 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8762.86 | −0.487708 | ||||||||
\(687\) | −294.687 | −0.0163654 | ||||||||
\(688\) | −5337.93 | −0.295794 | ||||||||
\(689\) | 6928.44 | 0.383095 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14271.3 | −0.785680 | −0.392840 | − | 0.919607i | \(-0.628507\pi\) | ||||
−0.392840 | + | 0.919607i | \(0.628507\pi\) | |||||||
\(692\) | −11241.3 | −0.617531 | ||||||||
\(693\) | −25915.2 | −1.42054 | ||||||||
\(694\) | 12062.1 | 0.659758 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 694.570 | 0.0378270 | ||||||||
\(697\) | −1288.78 | −0.0700373 | ||||||||
\(698\) | 22703.9 | 1.23117 | ||||||||
\(699\) | −3094.35 | −0.167438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13473.5 | −0.725945 | −0.362973 | − | 0.931800i | \(-0.618238\pi\) | ||||
−0.362973 | + | 0.931800i | \(0.618238\pi\) | |||||||
\(702\) | −591.317 | −0.0317918 | ||||||||
\(703\) | −89.0560 | −0.00477782 | ||||||||
\(704\) | 2145.50 | 0.114860 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9729.61 | −0.518667 | ||||||||
\(707\) | 49764.1 | 2.64720 | ||||||||
\(708\) | 624.592 | 0.0331548 | ||||||||
\(709\) | −8117.53 | −0.429986 | −0.214993 | − | 0.976616i | \(-0.568973\pi\) | ||||
−0.214993 | + | 0.976616i | \(0.568973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15042.1 | −0.793424 | ||||||||
\(712\) | 5619.34 | 0.295778 | ||||||||
\(713\) | 3692.80 | 0.193964 | ||||||||
\(714\) | 1751.53 | 0.0918061 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10066.1 | −0.525403 | ||||||||
\(717\) | −2420.49 | −0.126074 | ||||||||
\(718\) | 11619.0 | 0.603923 | ||||||||
\(719\) | −34187.5 | −1.77327 | −0.886634 | − | 0.462471i | \(-0.846963\pi\) | ||||
−0.886634 | + | 0.462471i | \(0.846963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11224.2 | −0.579767 | ||||||||
\(722\) | 13662.6 | 0.704250 | ||||||||
\(723\) | 276.663 | 0.0142313 | ||||||||
\(724\) | 4340.04 | 0.222785 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 221.614 | 0.0113290 | ||||||||
\(727\) | −26638.2 | −1.35895 | −0.679476 | − | 0.733698i | \(-0.737793\pi\) | ||||
−0.679476 | + | 0.733698i | \(0.737793\pi\) | |||||||
\(728\) | 2382.57 | 0.121297 | ||||||||
\(729\) | −18442.9 | −0.936995 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18878.0 | 0.955171 | ||||||||
\(732\) | 972.507 | 0.0491050 | ||||||||
\(733\) | 26875.8 | 1.35427 | 0.677135 | − | 0.735858i | \(-0.263221\pi\) | ||||
0.677135 | + | 0.735858i | \(0.263221\pi\) | |||||||
\(734\) | 13968.8 | 0.702447 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −4438.13 | −0.221819 | ||||||||
\(738\) | 1216.86 | 0.0606957 | ||||||||
\(739\) | 5873.86 | 0.292386 | 0.146193 | − | 0.989256i | \(-0.453298\pi\) | ||||
0.146193 | + | 0.989256i | \(0.453298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.9750 | 0.00143647 | ||||||||
\(742\) | 38962.4 | 1.92770 | ||||||||
\(743\) | 16863.9 | 0.832673 | 0.416337 | − | 0.909210i | \(-0.363314\pi\) | ||||
0.416337 | + | 0.909210i | \(0.363314\pi\) | |||||||
\(744\) | 686.963 | 0.0338512 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17103.1 | 0.839394 | ||||||||
\(747\) | 21613.4 | 1.05863 | ||||||||
\(748\) | −7587.74 | −0.370903 | ||||||||
\(749\) | −908.376 | −0.0443142 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24885.3 | 1.20916 | 0.604578 | − | 0.796546i | \(-0.293342\pi\) | ||||
0.604578 | + | 0.796546i | \(0.293342\pi\) | |||||||
\(752\) | −2086.13 | −0.101161 | ||||||||
\(753\) | −3764.67 | −0.182194 | ||||||||
\(754\) | −3341.39 | −0.161388 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3325.30 | −0.159974 | ||||||||
\(757\) | 14692.8 | 0.705442 | 0.352721 | − | 0.935728i | \(-0.385256\pi\) | ||||
0.352721 | + | 0.935728i | \(0.385256\pi\) | |||||||
\(758\) | −19866.8 | −0.951971 | ||||||||
\(759\) | −412.374 | −0.0197210 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7531.01 | −0.358737 | −0.179369 | − | 0.983782i | \(-0.557405\pi\) | ||||
−0.179369 | + | 0.983782i | \(0.557405\pi\) | |||||||
\(762\) | 1320.47 | 0.0627765 | ||||||||
\(763\) | 19856.1 | 0.942121 | ||||||||
\(764\) | −8327.46 | −0.394342 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19497.0 | 0.919656 | ||||||||
\(767\) | −3004.75 | −0.141454 | ||||||||
\(768\) | 136.916 | 0.00643301 | ||||||||
\(769\) | 20747.5 | 0.972916 | 0.486458 | − | 0.873704i | \(-0.338289\pi\) | ||||
0.486458 | + | 0.873704i | \(0.338289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2273.53 | 0.106199 | ||||||||
\(772\) | −2593.97 | −0.120931 | ||||||||
\(773\) | 940.128 | 0.0437439 | 0.0218720 | − | 0.999761i | \(-0.493037\pi\) | ||||
0.0218720 | + | 0.999761i | \(0.493037\pi\) | |||||||
\(774\) | −17824.6 | −0.827769 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2743.56 | 0.126918 | ||||||||
\(777\) | 261.835 | 0.0120892 | ||||||||
\(778\) | 21034.1 | 0.969290 | ||||||||
\(779\) | −119.893 | −0.00551426 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4067.25 | 0.186348 | ||||||||
\(782\) | −2602.93 | −0.119029 | ||||||||
\(783\) | 4663.51 | 0.212849 | ||||||||
\(784\) | 7910.52 | 0.360355 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2371.16 | 0.107604 | ||||||||
\(787\) | 6072.14 | 0.275030 | 0.137515 | − | 0.990500i | \(-0.456088\pi\) | ||||
0.137515 | + | 0.990500i | \(0.456088\pi\) | |||||||
\(788\) | 5003.70 | 0.226205 | ||||||||
\(789\) | −1924.76 | −0.0868484 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1222.20 | 0.0549384 | ||||||||
\(792\) | 7164.34 | 0.321432 | ||||||||
\(793\) | −4678.47 | −0.209505 | ||||||||
\(794\) | 8235.88 | 0.368111 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12542.1 | 0.558473 | ||||||||
\(797\) | −5424.76 | −0.241098 | −0.120549 | − | 0.992707i | \(-0.538465\pi\) | ||||
−0.120549 | + | 0.992707i | \(0.538465\pi\) | |||||||
\(798\) | 162.942 | 0.00722819 | ||||||||
\(799\) | 7377.77 | 0.326667 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18764.4 | 0.827723 | ||||||||
\(802\) | 14748.6 | 0.649365 | ||||||||
\(803\) | −5916.28 | −0.260001 | ||||||||
\(804\) | −283.223 | −0.0124235 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3304.80 | −0.144425 | ||||||||
\(807\) | −2707.59 | −0.118106 | ||||||||
\(808\) | −13757.4 | −0.598991 | ||||||||
\(809\) | −13646.3 | −0.593051 | −0.296526 | − | 0.955025i | \(-0.595828\pi\) | ||||
−0.296526 | + | 0.955025i | \(0.595828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10015.4 | −0.433647 | −0.216823 | − | 0.976211i | \(-0.569570\pi\) | ||||
−0.216823 | + | 0.976211i | \(0.569570\pi\) | |||||||
\(812\) | −18790.5 | −0.812091 | ||||||||
\(813\) | 991.886 | 0.0427884 | ||||||||
\(814\) | −1134.28 | −0.0488410 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −484.217 | −0.0207733 | ||||||||
\(817\) | 1756.19 | 0.0752037 | ||||||||
\(818\) | −25883.1 | −1.10633 | ||||||||
\(819\) | 7955.99 | 0.339444 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6525.48 | 0.277394 | 0.138697 | − | 0.990335i | \(-0.455709\pi\) | ||||
0.138697 | + | 0.990335i | \(0.455709\pi\) | |||||||
\(822\) | −1261.64 | −0.0535338 | ||||||||
\(823\) | −42874.0 | −1.81591 | −0.907954 | − | 0.419069i | \(-0.862356\pi\) | ||||
−0.907954 | + | 0.419069i | \(0.862356\pi\) | |||||||
\(824\) | 3102.97 | 0.131186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16897.4 | −0.711785 | ||||||||
\(827\) | 21654.4 | 0.910517 | 0.455259 | − | 0.890359i | \(-0.349547\pi\) | ||||
0.455259 | + | 0.890359i | \(0.349547\pi\) | |||||||
\(828\) | 2457.68 | 0.103153 | ||||||||
\(829\) | −22392.7 | −0.938153 | −0.469077 | − | 0.883158i | \(-0.655413\pi\) | ||||
−0.469077 | + | 0.883158i | \(0.655413\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4678.64 | −0.195307 | ||||||||
\(832\) | −658.669 | −0.0274462 | ||||||||
\(833\) | −27976.2 | −1.16365 | ||||||||
\(834\) | −258.027 | −0.0107131 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −705.875 | −0.0292024 | ||||||||
\(837\) | 4612.44 | 0.190477 | ||||||||
\(838\) | −11266.9 | −0.464450 | ||||||||
\(839\) | 21335.4 | 0.877926 | 0.438963 | − | 0.898505i | \(-0.355346\pi\) | ||||
0.438963 | + | 0.898505i | \(0.355346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1963.43 | 0.0805049 | ||||||||
\(842\) | 8410.97 | 0.344253 | ||||||||
\(843\) | 2164.39 | 0.0884290 | ||||||||
\(844\) | −3376.76 | −0.137716 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6966.09 | −0.283096 | ||||||||
\(847\) | −5995.42 | −0.243217 | ||||||||
\(848\) | −10771.3 | −0.436188 | ||||||||
\(849\) | −854.934 | −0.0345598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −389.109 | −0.0156739 | ||||||||
\(852\) | 259.554 | 0.0104368 | ||||||||
\(853\) | 11610.2 | 0.466034 | 0.233017 | − | 0.972473i | \(-0.425140\pi\) | ||||
0.233017 | + | 0.972473i | \(0.425140\pi\) | |||||||
\(854\) | −26309.7 | −1.05421 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 251.123 | 0.0100271 | ||||||||
\(857\) | −27905.6 | −1.11230 | −0.556148 | − | 0.831084i | \(-0.687721\pi\) | ||||
−0.556148 | + | 0.831084i | \(0.687721\pi\) | |||||||
\(858\) | 369.047 | 0.0146842 | ||||||||
\(859\) | 4529.52 | 0.179913 | 0.0899565 | − | 0.995946i | \(-0.471327\pi\) | ||||
0.0899565 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 352.499 | 0.0139525 | ||||||||
\(862\) | −30151.5 | −1.19137 | ||||||||
\(863\) | 10511.6 | 0.414622 | 0.207311 | − | 0.978275i | \(-0.433529\pi\) | ||||
0.207311 | + | 0.978275i | \(0.433529\pi\) | |||||||
\(864\) | 919.291 | 0.0361978 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6196.11 | 0.243132 | ||||||||
\(867\) | −915.143 | −0.0358476 | ||||||||
\(868\) | −18584.7 | −0.726735 | ||||||||
\(869\) | 18876.4 | 0.736868 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1362.51 | 0.0530044 | ||||||||
\(872\) | −5489.27 | −0.213177 | ||||||||
\(873\) | 9161.42 | 0.355174 | ||||||||
\(874\) | −242.146 | −0.00937153 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −377.552 | −0.0145620 | ||||||||
\(877\) | −20949.8 | −0.806643 | −0.403321 | − | 0.915058i | \(-0.632144\pi\) | ||||
−0.403321 | + | 0.915058i | \(0.632144\pi\) | |||||||
\(878\) | −13735.5 | −0.527961 | ||||||||
\(879\) | 2429.53 | 0.0932263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39907.1 | 1.52611 | 0.763057 | − | 0.646332i | \(-0.223698\pi\) | ||||
0.763057 | + | 0.646332i | \(0.223698\pi\) | |||||||
\(882\) | 26415.2 | 1.00844 | ||||||||
\(883\) | 16565.2 | 0.631329 | 0.315665 | − | 0.948871i | \(-0.397773\pi\) | ||||
0.315665 | + | 0.948871i | \(0.397773\pi\) | |||||||
\(884\) | 2329.44 | 0.0886285 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11756.6 | −0.445790 | ||||||||
\(887\) | −8217.44 | −0.311065 | −0.155532 | − | 0.987831i | \(-0.549709\pi\) | ||||
−0.155532 | + | 0.987831i | \(0.549709\pi\) | |||||||
\(888\) | −72.3851 | −0.00273546 | ||||||||
\(889\) | −35723.3 | −1.34772 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23664.6 | 0.889779 | ||||||||
\(892\) | −22594.3 | −0.848108 | ||||||||
\(893\) | 686.342 | 0.0257195 | ||||||||
\(894\) | 1099.76 | 0.0411427 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3704.06 | −0.138107 | ||||||||
\(897\) | 126.599 | 0.00471240 | ||||||||
\(898\) | −27341.5 | −1.01603 | ||||||||
\(899\) | 26063.8 | 0.966937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38093.6 | 1.40853 | ||||||||
\(902\) | −1527.05 | −0.0563692 | ||||||||
\(903\) | −5163.41 | −0.190285 | ||||||||
\(904\) | −337.880 | −0.0124311 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1616.51 | −0.0592770 | ||||||||
\(907\) | −25129.0 | −0.919952 | −0.459976 | − | 0.887931i | \(-0.652142\pi\) | ||||
−0.459976 | + | 0.887931i | \(0.652142\pi\) | |||||||
\(908\) | 15659.6 | 0.572338 | ||||||||
\(909\) | −45939.5 | −1.67625 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9275.75 | −0.337343 | −0.168671 | − | 0.985672i | \(-0.553948\pi\) | ||||
−0.168671 | + | 0.985672i | \(0.553948\pi\) | |||||||
\(912\) | −45.0459 | −0.00163555 | ||||||||
\(913\) | −27122.7 | −0.983166 | ||||||||
\(914\) | −33894.4 | −1.22662 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2203.97 | −0.0794990 | ||||||||
\(917\) | −64148.1 | −2.31010 | ||||||||
\(918\) | −3251.15 | −0.116889 | ||||||||
\(919\) | −47822.1 | −1.71655 | −0.858273 | − | 0.513194i | \(-0.828462\pi\) | ||||
−0.858273 | + | 0.513194i | \(0.828462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1265.62 | 0.0452807 | ||||||||
\(922\) | 11166.7 | 0.398866 | ||||||||
\(923\) | −1248.65 | −0.0445285 | ||||||||
\(924\) | 2075.35 | 0.0738898 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11716.0 | −0.415781 | ||||||||
\(927\) | 10361.6 | 0.367119 | ||||||||
\(928\) | 5194.70 | 0.183755 | ||||||||
\(929\) | −447.878 | −0.0158175 | −0.00790873 | − | 0.999969i | \(-0.502517\pi\) | ||||
−0.00790873 | + | 0.999969i | \(0.502517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2602.58 | −0.0916179 | ||||||||
\(932\) | −23142.7 | −0.813373 | ||||||||
\(933\) | 443.994 | 0.0155795 | ||||||||
\(934\) | −27899.6 | −0.977414 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2199.46 | −0.0768072 | ||||||||
\(937\) | 3402.08 | 0.118614 | 0.0593069 | − | 0.998240i | \(-0.481111\pi\) | ||||
0.0593069 | + | 0.998240i | \(0.481111\pi\) | |||||||
\(938\) | 7662.15 | 0.266714 | ||||||||
\(939\) | 3841.17 | 0.133495 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14084.0 | 0.487912 | 0.243956 | − | 0.969786i | \(-0.421555\pi\) | ||||
0.243956 | + | 0.969786i | \(0.421555\pi\) | |||||||
\(942\) | −2243.12 | −0.0775846 | ||||||||
\(943\) | −523.844 | −0.0180898 | ||||||||
\(944\) | 4671.33 | 0.161058 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22368.2 | 0.768766 | ||||||||
\(947\) | 10020.6 | 0.343850 | 0.171925 | − | 0.985110i | \(-0.445001\pi\) | ||||
0.171925 | + | 0.985110i | \(0.445001\pi\) | |||||||
\(948\) | 1204.61 | 0.0412700 | ||||||||
\(949\) | 1816.30 | 0.0621283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1021.56 | −0.0348331 | ||||||||
\(952\) | 13099.7 | 0.445972 | ||||||||
\(953\) | 45482.6 | 1.54599 | 0.772993 | − | 0.634415i | \(-0.218759\pi\) | ||||
0.772993 | + | 0.634415i | \(0.218759\pi\) | |||||||
\(954\) | −35968.0 | −1.22066 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18102.9 | −0.612435 | ||||||||
\(957\) | −2910.54 | −0.0983120 | ||||||||
\(958\) | −14309.7 | −0.482594 | ||||||||
\(959\) | 34131.8 | 1.14929 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4012.67 | −0.134694 | ||||||||
\(962\) | 348.226 | 0.0116707 | ||||||||
\(963\) | 838.562 | 0.0280605 | ||||||||
\(964\) | 2069.17 | 0.0691322 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 711.938 | 0.0237124 | ||||||||
\(967\) | −50955.7 | −1.69455 | −0.847273 | − | 0.531158i | \(-0.821757\pi\) | ||||
−0.847273 | + | 0.531158i | \(0.821757\pi\) | |||||||
\(968\) | 1657.45 | 0.0550336 | ||||||||
\(969\) | 159.309 | 0.00528146 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38192.3 | −1.26226 | −0.631128 | − | 0.775679i | \(-0.717408\pi\) | ||||
−0.631128 | + | 0.775679i | \(0.717408\pi\) | |||||||
\(972\) | 4612.78 | 0.152217 | ||||||||
\(973\) | 6980.53 | 0.229995 | ||||||||
\(974\) | −29623.7 | −0.974543 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7273.39 | 0.238540 | ||||||||
\(977\) | 28889.6 | 0.946018 | 0.473009 | − | 0.881058i | \(-0.343168\pi\) | ||||
0.473009 | + | 0.881058i | \(0.343168\pi\) | |||||||
\(978\) | 752.020 | 0.0245879 | ||||||||
\(979\) | −23547.4 | −0.768722 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18330.0 | −0.596568 | ||||||||
\(982\) | −6185.88 | −0.201018 | ||||||||
\(983\) | −51725.2 | −1.67831 | −0.839154 | − | 0.543894i | \(-0.816949\pi\) | ||||
−0.839154 | + | 0.543894i | \(0.816949\pi\) | |||||||
\(984\) | −97.4495 | −0.00315709 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18371.5 | −0.593375 | ||||||||
\(987\) | −2017.93 | −0.0650773 | ||||||||
\(988\) | 216.704 | 0.00697801 | ||||||||
\(989\) | 7673.27 | 0.246710 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24851.8 | 0.796613 | 0.398307 | − | 0.917252i | \(-0.369598\pi\) | ||||
0.398307 | + | 0.917252i | \(0.369598\pi\) | |||||||
\(992\) | 5137.80 | 0.164441 | ||||||||
\(993\) | 4032.83 | 0.128880 | ||||||||
\(994\) | −7021.84 | −0.224064 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1730.86 | −0.0550645 | ||||||||
\(997\) | −2537.99 | −0.0806209 | −0.0403104 | − | 0.999187i | \(-0.512835\pi\) | ||||
−0.0403104 | + | 0.999187i | \(0.512835\pi\) | |||||||
\(998\) | −34501.2 | −1.09430 | ||||||||
\(999\) | −486.011 | −0.0153921 |
(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 | 1150.4.a.q.1.3 | ✓ | 5 | |
5.2 | odd | 4 | 1150.4.b.r.599.3 | 10 | |||
5.3 | odd | 4 | 1150.4.b.r.599.8 | 10 | |||
5.4 | even | 2 | 1150.4.a.v.1.3 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.4.a.q.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1150.4.a.v.1.3 | yes | 5 | 5.4 | even | 2 | ||
1150.4.b.r.599.3 | 10 | 5.2 | odd | 4 | |||
1150.4.b.r.599.8 | 10 | 5.3 | odd | 4 |