Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(149,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.5 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.149 |
Dual form | 150.3.b.b.149.6 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −2.94317 | − | 0.581139i | −0.981058 | − | 0.193713i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.16228 | − | 0.821854i | −0.693713 | − | 0.136976i | ||||
\(7\) | − | 11.4868i | − | 1.64098i | −0.571664 | − | 0.820488i | \(-0.693702\pi\) | ||
0.571664 | − | 0.820488i | \(-0.306298\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 8.32456 | + | 3.42079i | 0.924951 | + | 0.380087i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.48528i | − | 0.771389i | −0.922627 | − | 0.385695i | \(-0.873962\pi\) | ||
0.922627 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(12\) | −5.88635 | − | 1.16228i | −0.490529 | − | 0.0968565i | ||||
\(13\) | − | 10.0000i | − | 0.769231i | −0.923077 | − | 0.384615i | \(-0.874334\pi\) | ||
0.923077 | − | 0.384615i | \(-0.125666\pi\) | |||||||
\(14\) | − | 16.2448i | − | 1.16035i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 3.55415 | 0.209068 | 0.104534 | − | 0.994521i | \(-0.466665\pi\) | ||||
0.104534 | + | 0.994521i | \(0.466665\pi\) | |||||||
\(18\) | 11.7727 | + | 4.83772i | 0.654039 | + | 0.268762i | ||||
\(19\) | 10.9737 | 0.577561 | 0.288781 | − | 0.957395i | \(-0.406750\pi\) | ||||
0.288781 | + | 0.957395i | \(0.406750\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.67544 | + | 33.8078i | −0.317878 | + | 1.60989i | ||||
\(22\) | − | 12.0000i | − | 0.545455i | ||||||
\(23\) | −17.6590 | −0.767785 | −0.383892 | − | 0.923378i | \(-0.625417\pi\) | ||||
−0.383892 | + | 0.923378i | \(0.625417\pi\) | |||||||
\(24\) | −8.32456 | − | 1.64371i | −0.346856 | − | 0.0684879i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 14.1421i | − | 0.543928i | ||||||
\(27\) | −22.5127 | − | 14.9057i | −0.833803 | − | 0.552063i | ||||
\(28\) | − | 22.9737i | − | 0.820488i | ||||||
\(29\) | 26.8328i | 0.925270i | 0.886549 | + | 0.462635i | \(0.153096\pi\) | ||||
−0.886549 | + | 0.462635i | \(0.846904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 0.258065 | 0.129032 | − | 0.991640i | \(-0.458813\pi\) | ||||
0.129032 | + | 0.991640i | \(0.458813\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | −4.93113 | + | 24.9737i | −0.149428 | + | 0.756778i | ||||
\(34\) | 5.02633 | 0.147833 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.6491 | + | 6.84157i | 0.462475 | + | 0.190044i | ||||
\(37\) | 59.9473i | 1.62020i | 0.586293 | + | 0.810099i | \(0.300587\pi\) | ||||
−0.586293 | + | 0.810099i | \(0.699413\pi\) | |||||||
\(38\) | 15.5191 | 0.408398 | ||||||||
\(39\) | −5.81139 | + | 29.4317i | −0.149010 | + | 0.754660i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 20.5247i | − | 0.500603i | −0.968168 | − | 0.250301i | \(-0.919470\pi\) | ||
0.968168 | − | 0.250301i | \(-0.0805297\pi\) | |||||||
\(42\) | −9.44050 | + | 47.8114i | −0.224774 | + | 1.13837i | ||||
\(43\) | 42.4605i | 0.987453i | 0.869617 | + | 0.493727i | \(0.164366\pi\) | ||||
−0.869617 | + | 0.493727i | \(0.835634\pi\) | |||||||
\(44\) | − | 16.9706i | − | 0.385695i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24.9737 | −0.542906 | ||||||||
\(47\) | 88.2952 | 1.87862 | 0.939311 | − | 0.343067i | \(-0.111466\pi\) | ||||
0.939311 | + | 0.343067i | \(0.111466\pi\) | |||||||
\(48\) | −11.7727 | − | 2.32456i | −0.245265 | − | 0.0484282i | ||||
\(49\) | −82.9473 | −1.69280 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4605 | − | 2.06546i | −0.205108 | − | 0.0404992i | ||||
\(52\) | − | 20.0000i | − | 0.384615i | ||||||
\(53\) | −3.55415 | −0.0670595 | −0.0335298 | − | 0.999438i | \(-0.510675\pi\) | ||||
−0.0335298 | + | 0.999438i | \(0.510675\pi\) | |||||||
\(54\) | −31.8377 | − | 21.0798i | −0.589587 | − | 0.390367i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 32.4897i | − | 0.580173i | ||||||
\(57\) | −32.2974 | − | 6.37722i | −0.566621 | − | 0.111881i | ||||
\(58\) | 37.9473i | 0.654264i | ||||||||
\(59\) | − | 77.7445i | − | 1.31770i | −0.752273 | − | 0.658852i | \(-0.771042\pi\) | ||
0.752273 | − | 0.658852i | \(-0.228958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21.9473 | 0.359792 | 0.179896 | − | 0.983686i | \(-0.442424\pi\) | ||||
0.179896 | + | 0.983686i | \(0.442424\pi\) | |||||||
\(62\) | 11.3137 | 0.182479 | ||||||||
\(63\) | 39.2940 | − | 95.6228i | 0.623714 | − | 1.51782i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.97367 | + | 35.3181i | −0.105662 | + | 0.535123i | ||||
\(67\) | 53.5395i | 0.799097i | 0.916712 | + | 0.399549i | \(0.130833\pi\) | ||||
−0.916712 | + | 0.399549i | \(0.869167\pi\) | |||||||
\(68\) | 7.10831 | 0.104534 | ||||||||
\(69\) | 51.9737 | + | 10.2624i | 0.753242 | + | 0.148730i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 69.2592i | − | 0.975482i | −0.872988 | − | 0.487741i | \(-0.837821\pi\) | ||
0.872988 | − | 0.487741i | \(-0.162179\pi\) | |||||||
\(72\) | 23.5454 | + | 9.67544i | 0.327019 | + | 0.134381i | ||||
\(73\) | 12.0527i | 0.165105i | 0.996587 | + | 0.0825525i | \(0.0263072\pi\) | ||||
−0.996587 | + | 0.0825525i | \(0.973693\pi\) | |||||||
\(74\) | 84.7783i | 1.14565i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 21.9473 | 0.288781 | ||||||||
\(77\) | −97.4690 | −1.26583 | ||||||||
\(78\) | −8.21854 | + | 41.6228i | −0.105366 | + | 0.533625i | ||||
\(79\) | 9.02633 | 0.114257 | 0.0571287 | − | 0.998367i | \(-0.481805\pi\) | ||||
0.0571287 | + | 0.998367i | \(0.481805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 57.5964 | + | 56.9530i | 0.711067 | + | 0.703124i | ||||
\(82\) | − | 29.0263i | − | 0.353980i | ||||||
\(83\) | −0.688486 | −0.00829501 | −0.00414750 | − | 0.999991i | \(-0.501320\pi\) | ||||
−0.00414750 | + | 0.999991i | \(0.501320\pi\) | |||||||
\(84\) | −13.3509 | + | 67.6155i | −0.158939 | + | 0.804947i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 60.0482i | 0.698235i | ||||||||
\(87\) | 15.5936 | − | 78.9737i | 0.179237 | − | 0.907743i | ||||
\(88\) | − | 24.0000i | − | 0.272727i | ||||||
\(89\) | 7.10831i | 0.0798686i | 0.999202 | + | 0.0399343i | \(0.0127149\pi\) | ||||
−0.999202 | + | 0.0399343i | \(0.987285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −114.868 | −1.26229 | ||||||||
\(92\) | −35.3181 | −0.383892 | ||||||||
\(93\) | −23.5454 | − | 4.64911i | −0.253176 | − | 0.0499904i | ||||
\(94\) | 124.868 | 1.32839 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −16.6491 | − | 3.28742i | −0.173428 | − | 0.0342439i | ||||
\(97\) | − | 111.947i | − | 1.15410i | −0.816710 | − | 0.577048i | \(-0.804205\pi\) | ||
0.816710 | − | 0.577048i | \(-0.195795\pi\) | |||||||
\(98\) | −117.305 | −1.19699 | ||||||||
\(99\) | 29.0263 | − | 70.6362i | 0.293195 | − | 0.713497i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 155.489i | 1.53950i | 0.638348 | + | 0.769748i | \(0.279618\pi\) | ||||
−0.638348 | + | 0.769748i | \(0.720382\pi\) | |||||||
\(102\) | −14.7934 | − | 2.92100i | −0.145033 | − | 0.0286372i | ||||
\(103\) | 7.59217i | 0.0737104i | 0.999321 | + | 0.0368552i | \(0.0117340\pi\) | ||||
−0.999321 | + | 0.0368552i | \(0.988266\pi\) | |||||||
\(104\) | − | 28.2843i | − | 0.271964i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.02633 | −0.0474182 | ||||||||
\(107\) | 16.2821 | 0.152169 | 0.0760845 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760845 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(108\) | −45.0253 | − | 29.8114i | −0.416901 | − | 0.276031i | ||||
\(109\) | 93.8420 | 0.860936 | 0.430468 | − | 0.902606i | \(-0.358349\pi\) | ||||
0.430468 | + | 0.902606i | \(0.358349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.8377 | − | 176.435i | 0.313853 | − | 1.58951i | ||||
\(112\) | − | 45.9473i | − | 0.410244i | ||||||
\(113\) | 195.738 | 1.73220 | 0.866098 | − | 0.499874i | \(-0.166620\pi\) | ||||
0.866098 | + | 0.499874i | \(0.166620\pi\) | |||||||
\(114\) | −45.6754 | − | 9.01876i | −0.400662 | − | 0.0791119i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 53.6656i | 0.462635i | ||||||||
\(117\) | 34.2079 | − | 83.2456i | 0.292375 | − | 0.711500i | ||||
\(118\) | − | 109.947i | − | 0.931757i | ||||||
\(119\) | − | 40.8260i | − | 0.343075i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 31.0382 | 0.254412 | ||||||||
\(123\) | −11.9277 | + | 60.4078i | −0.0969733 | + | 0.491121i | ||||
\(124\) | 16.0000 | 0.129032 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 55.5701 | − | 135.231i | 0.441033 | − | 1.07326i | ||||
\(127\) | 77.5395i | 0.610547i | 0.952265 | + | 0.305274i | \(0.0987479\pi\) | ||||
−0.952265 | + | 0.305274i | \(0.901252\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 24.6754 | − | 124.969i | 0.191283 | − | 0.968749i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 101.600i | − | 0.775572i | −0.921749 | − | 0.387786i | \(-0.873240\pi\) | ||
0.921749 | − | 0.387786i | \(-0.126760\pi\) | |||||||
\(132\) | −9.86225 | + | 49.9473i | −0.0747140 | + | 0.378389i | ||||
\(133\) | − | 126.053i | − | 0.947764i | ||||||
\(134\) | 75.7163i | 0.565047i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.0527 | 0.0739167 | ||||||||
\(137\) | −176.014 | −1.28477 | −0.642386 | − | 0.766381i | \(-0.722055\pi\) | ||||
−0.642386 | + | 0.766381i | \(0.722055\pi\) | |||||||
\(138\) | 73.5019 | + | 14.5132i | 0.532622 | + | 0.105168i | ||||
\(139\) | −188.816 | −1.35839 | −0.679193 | − | 0.733960i | \(-0.737670\pi\) | ||||
−0.679193 | + | 0.733960i | \(0.737670\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −259.868 | − | 51.3118i | −1.84304 | − | 0.363913i | ||||
\(142\) | − | 97.9473i | − | 0.689770i | ||||||
\(143\) | −84.8528 | −0.593376 | ||||||||
\(144\) | 33.2982 | + | 13.6831i | 0.231238 | + | 0.0950218i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.0450i | 0.116747i | ||||||||
\(147\) | 244.128 | + | 48.2039i | 1.66074 | + | 0.327918i | ||||
\(148\) | 119.895i | 0.810099i | ||||||||
\(149\) | 72.5899i | 0.487181i | 0.969878 | + | 0.243590i | \(0.0783252\pi\) | ||||
−0.969878 | + | 0.243590i | \(0.921675\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 93.9473 | 0.622168 | 0.311084 | − | 0.950382i | \(-0.399308\pi\) | ||||
0.311084 | + | 0.950382i | \(0.399308\pi\) | |||||||
\(152\) | 31.0382 | 0.204199 | ||||||||
\(153\) | 29.5868 | + | 12.1580i | 0.193378 | + | 0.0794641i | ||||
\(154\) | −137.842 | −0.895078 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.6228 | + | 58.8635i | −0.0745050 | + | 0.377330i | ||||
\(157\) | 123.842i | 0.788803i | 0.918938 | + | 0.394401i | \(0.129048\pi\) | ||||
−0.918938 | + | 0.394401i | \(0.870952\pi\) | |||||||
\(158\) | 12.7652 | 0.0807922 | ||||||||
\(159\) | 10.4605 | + | 2.06546i | 0.0657893 | + | 0.0129903i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 202.847i | 1.25992i | ||||||||
\(162\) | 81.4537 | + | 80.5438i | 0.502800 | + | 0.497184i | ||||
\(163\) | 159.381i | 0.977801i | 0.872340 | + | 0.488900i | \(0.162602\pi\) | ||||
−0.872340 | + | 0.488900i | \(0.837398\pi\) | |||||||
\(164\) | − | 41.0494i | − | 0.250301i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.973666 | −0.00586546 | ||||||||
\(167\) | −10.7742 | −0.0645161 | −0.0322581 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322581 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(168\) | −18.8810 | + | 95.6228i | −0.112387 | + | 0.569183i | ||||
\(169\) | 69.0000 | 0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.3509 | + | 37.5386i | 0.534216 | + | 0.219524i | ||||
\(172\) | 84.9210i | 0.493727i | ||||||||
\(173\) | −283.345 | −1.63783 | −0.818916 | − | 0.573913i | \(-0.805425\pi\) | ||||
−0.818916 | + | 0.573913i | \(0.805425\pi\) | |||||||
\(174\) | 22.0527 | − | 111.686i | 0.126739 | − | 0.641871i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 33.9411i | − | 0.192847i | ||||||
\(177\) | −45.1804 | + | 228.816i | −0.255256 | + | 1.29274i | ||||
\(178\) | 10.0527i | 0.0564757i | ||||||||
\(179\) | 306.624i | 1.71298i | 0.516163 | + | 0.856491i | \(0.327360\pi\) | ||||
−0.516163 | + | 0.856491i | \(0.672640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 265.684 | 1.46787 | 0.733934 | − | 0.679221i | \(-0.237682\pi\) | ||||
0.733934 | + | 0.679221i | \(0.237682\pi\) | |||||||
\(182\) | −162.448 | −0.892573 | ||||||||
\(183\) | −64.5948 | − | 12.7544i | −0.352977 | − | 0.0696964i | ||||
\(184\) | −49.9473 | −0.271453 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −33.2982 | − | 6.57484i | −0.179023 | − | 0.0353486i | ||||
\(187\) | − | 30.1580i | − | 0.161273i | ||||||
\(188\) | 176.590 | 0.939311 | ||||||||
\(189\) | −171.219 | + | 258.599i | −0.905922 | + | 1.36825i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 159.620i | 0.835706i | 0.908515 | + | 0.417853i | \(0.137217\pi\) | ||||
−0.908515 | + | 0.417853i | \(0.862783\pi\) | |||||||
\(192\) | −23.5454 | − | 4.64911i | −0.122632 | − | 0.0242141i | ||||
\(193\) | − | 92.0527i | − | 0.476957i | −0.971148 | − | 0.238478i | \(-0.923351\pi\) | ||
0.971148 | − | 0.238478i | \(-0.0766486\pi\) | |||||||
\(194\) | − | 158.317i | − | 0.816069i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −165.895 | −0.846401 | ||||||||
\(197\) | 69.8360 | 0.354497 | 0.177249 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177249 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(198\) | 41.0494 | − | 99.8947i | 0.207320 | − | 0.504519i | ||||
\(199\) | −148.921 | −0.748347 | −0.374173 | − | 0.927359i | \(-0.622074\pi\) | ||||
−0.374173 | + | 0.927359i | \(0.622074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.1139 | − | 157.576i | 0.154795 | − | 0.783961i | ||||
\(202\) | 219.895i | 1.08859i | ||||||||
\(203\) | 308.224 | 1.51835 | ||||||||
\(204\) | −20.9210 | − | 4.13091i | −0.102554 | − | 0.0202496i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.7369i | 0.0521211i | ||||||||
\(207\) | −147.004 | − | 60.4078i | −0.710163 | − | 0.291825i | ||||
\(208\) | − | 40.0000i | − | 0.192308i | ||||||
\(209\) | − | 93.1146i | − | 0.445525i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −285.842 | −1.35470 | −0.677351 | − | 0.735660i | \(-0.736872\pi\) | ||||
−0.677351 | + | 0.735660i | \(0.736872\pi\) | |||||||
\(212\) | −7.10831 | −0.0335298 | ||||||||
\(213\) | −40.2492 | + | 203.842i | −0.188963 | + | 0.957005i | ||||
\(214\) | 23.0263 | 0.107600 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −63.6754 | − | 42.1597i | −0.294794 | − | 0.195184i | ||||
\(217\) | − | 91.8947i | − | 0.423478i | ||||||
\(218\) | 132.713 | 0.608774 | ||||||||
\(219\) | 7.00427 | − | 35.4731i | 0.0319830 | − | 0.161978i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 35.5415i | − | 0.160821i | ||||||
\(222\) | 49.2680 | − | 249.517i | 0.221928 | − | 1.12395i | ||||
\(223\) | − | 71.3815i | − | 0.320096i | −0.987109 | − | 0.160048i | \(-0.948835\pi\) | ||
0.987109 | − | 0.160048i | \(-0.0511650\pi\) | |||||||
\(224\) | − | 64.9793i | − | 0.290086i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 276.816 | 1.22485 | ||||||||
\(227\) | 29.1217 | 0.128290 | 0.0641448 | − | 0.997941i | \(-0.479568\pi\) | ||||
0.0641448 | + | 0.997941i | \(0.479568\pi\) | |||||||
\(228\) | −64.5948 | − | 12.7544i | −0.283311 | − | 0.0559406i | ||||
\(229\) | 129.684 | 0.566306 | 0.283153 | − | 0.959075i | \(-0.408620\pi\) | ||||
0.283153 | + | 0.959075i | \(0.408620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 286.868 | + | 56.6430i | 1.24185 | + | 0.245208i | ||||
\(232\) | 75.8947i | 0.327132i | ||||||||
\(233\) | −185.876 | −0.797751 | −0.398875 | − | 0.917005i | \(-0.630599\pi\) | ||||
−0.398875 | + | 0.917005i | \(0.630599\pi\) | |||||||
\(234\) | 48.3772 | − | 117.727i | 0.206740 | − | 0.503107i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 155.489i | − | 0.658852i | ||||||
\(237\) | −26.5661 | − | 5.24555i | −0.112093 | − | 0.0221331i | ||||
\(238\) | − | 57.7367i | − | 0.242591i | ||||||
\(239\) | − | 302.716i | − | 1.26659i | −0.773908 | − | 0.633297i | \(-0.781701\pi\) | ||
0.773908 | − | 0.633297i | \(-0.218299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −237.526 | −0.985585 | −0.492793 | − | 0.870147i | \(-0.664024\pi\) | ||||
−0.492793 | + | 0.870147i | \(0.664024\pi\) | |||||||
\(242\) | 69.2965 | 0.286349 | ||||||||
\(243\) | −136.419 | − | 201.094i | −0.561394 | − | 0.827549i | ||||
\(244\) | 43.8947 | 0.179896 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.8683 | + | 85.4296i | −0.0685704 | + | 0.347275i | ||||
\(247\) | − | 109.737i | − | 0.444278i | ||||||
\(248\) | 22.6274 | 0.0912396 | ||||||||
\(249\) | 2.02633 | + | 0.400106i | 0.00813789 | + | 0.00160685i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 84.6294i | − | 0.337169i | −0.985687 | − | 0.168584i | \(-0.946080\pi\) | ||
0.985687 | − | 0.168584i | \(-0.0539196\pi\) | |||||||
\(252\) | 78.5880 | − | 191.246i | 0.311857 | − | 0.758911i | ||||
\(253\) | 149.842i | 0.592261i | ||||||||
\(254\) | 109.657i | 0.431722i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 292.054 | 1.13640 | 0.568198 | − | 0.822892i | \(-0.307641\pi\) | ||||
0.568198 | + | 0.822892i | \(0.307641\pi\) | |||||||
\(258\) | 34.8963 | − | 176.732i | 0.135257 | − | 0.685009i | ||||
\(259\) | 688.605 | 2.65871 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −91.7893 | + | 223.371i | −0.351683 | + | 0.855829i | ||||
\(262\) | − | 143.684i | − | 0.548412i | ||||||
\(263\) | −277.725 | −1.05599 | −0.527995 | − | 0.849247i | \(-0.677056\pi\) | ||||
−0.527995 | + | 0.849247i | \(0.677056\pi\) | |||||||
\(264\) | −13.9473 | + | 70.6362i | −0.0528308 | + | 0.267561i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 178.265i | − | 0.670171i | ||||||
\(267\) | 4.13091 | − | 20.9210i | 0.0154716 | − | 0.0783558i | ||||
\(268\) | 107.079i | 0.399549i | ||||||||
\(269\) | 286.546i | 1.06523i | 0.846359 | + | 0.532613i | \(0.178790\pi\) | ||||
−0.846359 | + | 0.532613i | \(0.821210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −324.105 | −1.19596 | −0.597980 | − | 0.801511i | \(-0.704030\pi\) | ||||
−0.597980 | + | 0.801511i | \(0.704030\pi\) | |||||||
\(272\) | 14.2166 | 0.0522670 | ||||||||
\(273\) | 338.078 | + | 66.7544i | 1.23838 | + | 0.244522i | ||||
\(274\) | −248.921 | −0.908471 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 103.947 | + | 20.5247i | 0.376621 | + | 0.0743649i | ||||
\(277\) | − | 415.842i | − | 1.50123i | −0.660737 | − | 0.750617i | \(-0.729756\pi\) | ||
0.660737 | − | 0.750617i | \(-0.270244\pi\) | |||||||
\(278\) | −267.026 | −0.960524 | ||||||||
\(279\) | 66.5964 | + | 27.3663i | 0.238697 | + | 0.0980871i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 431.726i | − | 1.53639i | −0.640216 | − | 0.768195i | \(-0.721155\pi\) | ||
0.640216 | − | 0.768195i | \(-0.278845\pi\) | |||||||
\(282\) | −367.509 | − | 72.5658i | −1.30322 | − | 0.257326i | ||||
\(283\) | 141.540i | 0.500140i | 0.968228 | + | 0.250070i | \(0.0804536\pi\) | ||||
−0.968228 | + | 0.250070i | \(0.919546\pi\) | |||||||
\(284\) | − | 138.518i | − | 0.487741i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −120.000 | −0.419580 | ||||||||
\(287\) | −235.764 | −0.821477 | ||||||||
\(288\) | 47.0908 | + | 19.3509i | 0.163510 | + | 0.0671906i | ||||
\(289\) | −276.368 | −0.956291 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −65.0569 | + | 329.481i | −0.223563 | + | 1.13224i | ||||
\(292\) | 24.1053i | 0.0825525i | ||||||||
\(293\) | 164.998 | 0.563133 | 0.281566 | − | 0.959542i | \(-0.409146\pi\) | ||||
0.281566 | + | 0.959542i | \(0.409146\pi\) | |||||||
\(294\) | 345.250 | + | 68.1706i | 1.17432 | + | 0.231873i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 169.557i | 0.572827i | ||||||||
\(297\) | −126.479 | + | 191.026i | −0.425855 | + | 0.643186i | ||||
\(298\) | 102.658i | 0.344489i | ||||||||
\(299\) | 176.590i | 0.590604i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 487.737 | 1.62039 | ||||||||
\(302\) | 132.862 | 0.439939 | ||||||||
\(303\) | 90.3607 | − | 457.631i | 0.298220 | − | 1.51033i | ||||
\(304\) | 43.8947 | 0.144390 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 41.8420 | + | 17.1940i | 0.136739 | + | 0.0561896i | ||||
\(307\) | − | 159.381i | − | 0.519158i | −0.965722 | − | 0.259579i | \(-0.916416\pi\) | ||
0.965722 | − | 0.259579i | \(-0.0835838\pi\) | |||||||
\(308\) | −194.938 | −0.632916 | ||||||||
\(309\) | 4.41210 | − | 22.3451i | 0.0142787 | − | 0.0723142i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 143.096i | − | 0.460117i | −0.973177 | − | 0.230058i | \(-0.926108\pi\) | ||
0.973177 | − | 0.230058i | \(-0.0738917\pi\) | |||||||
\(312\) | −16.4371 | + | 83.2456i | −0.0526830 | + | 0.266813i | ||||
\(313\) | − | 501.684i | − | 1.60282i | −0.598113 | − | 0.801412i | \(-0.704082\pi\) | ||
0.598113 | − | 0.801412i | \(-0.295918\pi\) | |||||||
\(314\) | 175.139i | 0.557768i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0527 | 0.0571287 | ||||||||
\(317\) | 334.257 | 1.05444 | 0.527219 | − | 0.849730i | \(-0.323235\pi\) | ||||
0.527219 | + | 0.849730i | \(0.323235\pi\) | |||||||
\(318\) | 14.7934 | + | 2.92100i | 0.0465201 | + | 0.00918553i | ||||
\(319\) | 227.684 | 0.713743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.9210 | − | 9.46215i | −0.149287 | − | 0.0294771i | ||||
\(322\) | 286.868i | 0.890895i | ||||||||
\(323\) | 39.0021 | 0.120750 | ||||||||
\(324\) | 115.193 | + | 113.906i | 0.355534 | + | 0.351562i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 225.399i | 0.691409i | ||||||||
\(327\) | −276.193 | − | 54.5352i | −0.844628 | − | 0.166774i | ||||
\(328\) | − | 58.0527i | − | 0.176990i | ||||||
\(329\) | − | 1014.23i | − | 3.08277i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 389.421 | 1.17650 | 0.588249 | − | 0.808680i | \(-0.299818\pi\) | ||||
0.588249 | + | 0.808680i | \(0.299818\pi\) | |||||||
\(332\) | −1.37697 | −0.00414750 | ||||||||
\(333\) | −205.067 | + | 499.035i | −0.615817 | + | 1.49860i | ||||
\(334\) | −15.2370 | −0.0456198 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −26.7018 | + | 135.231i | −0.0794696 | + | 0.402473i | ||||
\(337\) | 129.684i | 0.384819i | 0.981315 | + | 0.192409i | \(0.0616302\pi\) | ||||
−0.981315 | + | 0.192409i | \(0.938370\pi\) | |||||||
\(338\) | 97.5807 | 0.288700 | ||||||||
\(339\) | −576.092 | − | 113.751i | −1.69939 | − | 0.335549i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 67.8823i | − | 0.199068i | ||||||
\(342\) | 129.190 | + | 53.0875i | 0.377748 | + | 0.155227i | ||||
\(343\) | 389.947i | 1.13687i | ||||||||
\(344\) | 120.096i | 0.349118i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −400.710 | −1.15812 | ||||||||
\(347\) | −346.985 | −0.999956 | −0.499978 | − | 0.866038i | \(-0.666659\pi\) | ||||
−0.499978 | + | 0.866038i | \(0.666659\pi\) | |||||||
\(348\) | 31.1872 | − | 157.947i | 0.0896183 | − | 0.453872i | ||||
\(349\) | −509.579 | −1.46011 | −0.730055 | − | 0.683388i | \(-0.760506\pi\) | ||||
−0.730055 | + | 0.683388i | \(0.760506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −149.057 | + | 225.127i | −0.424664 | + | 0.641387i | ||||
\(352\) | − | 48.0000i | − | 0.136364i | ||||||
\(353\) | 637.679 | 1.80646 | 0.903229 | − | 0.429159i | \(-0.141190\pi\) | ||||
0.903229 | + | 0.429159i | \(0.141190\pi\) | |||||||
\(354\) | −63.8947 | + | 323.594i | −0.180493 | + | 0.914108i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.2166i | 0.0399343i | ||||||||
\(357\) | −23.7256 | + | 120.158i | −0.0664582 | + | 0.336577i | ||||
\(358\) | 433.631i | 1.21126i | ||||||||
\(359\) | 166.952i | 0.465046i | 0.972591 | + | 0.232523i | \(0.0746982\pi\) | ||||
−0.972591 | + | 0.232523i | \(0.925302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.579 | −0.666423 | ||||||||
\(362\) | 375.734 | 1.03794 | ||||||||
\(363\) | −144.216 | − | 28.4758i | −0.397288 | − | 0.0784457i | ||||
\(364\) | −229.737 | −0.631145 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −91.3509 | − | 18.0375i | −0.249593 | − | 0.0492828i | ||||
\(367\) | 505.828i | 1.37828i | 0.724629 | + | 0.689140i | \(0.242011\pi\) | ||||
−0.724629 | + | 0.689140i | \(0.757989\pi\) | |||||||
\(368\) | −70.6362 | −0.191946 | ||||||||
\(369\) | 70.2107 | − | 170.859i | 0.190273 | − | 0.463033i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.8260i | 0.110043i | ||||||||
\(372\) | −47.0908 | − | 9.29822i | −0.126588 | − | 0.0249952i | ||||
\(373\) | − | 416.053i | − | 1.11542i | −0.830035 | − | 0.557711i | \(-0.811680\pi\) | ||
0.830035 | − | 0.557711i | \(-0.188320\pi\) | |||||||
\(374\) | − | 42.6499i | − | 0.114037i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 249.737 | 0.664193 | ||||||||
\(377\) | 268.328 | 0.711746 | ||||||||
\(378\) | −242.141 | + | 365.715i | −0.640583 | + | 0.967499i | ||||
\(379\) | −82.7630 | −0.218372 | −0.109186 | − | 0.994021i | \(-0.534824\pi\) | ||||
−0.109186 | + | 0.994021i | \(0.534824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 45.0612 | − | 228.212i | 0.118271 | − | 0.598982i | ||||
\(382\) | 225.737i | 0.590934i | ||||||||
\(383\) | 334.592 | 0.873608 | 0.436804 | − | 0.899557i | \(-0.356110\pi\) | ||||
0.436804 | + | 0.899557i | \(0.356110\pi\) | |||||||
\(384\) | −33.2982 | − | 6.57484i | −0.0867141 | − | 0.0171220i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 130.182i | − | 0.337259i | ||||||
\(387\) | −145.248 | + | 353.465i | −0.375319 | + | 0.913346i | ||||
\(388\) | − | 223.895i | − | 0.577048i | ||||||
\(389\) | 542.964i | 1.39580i | 0.716197 | + | 0.697898i | \(0.245881\pi\) | ||||
−0.716197 | + | 0.697898i | \(0.754119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −62.7630 | −0.160519 | ||||||||
\(392\) | −234.610 | −0.598496 | ||||||||
\(393\) | −59.0437 | + | 299.026i | −0.150238 | + | 0.760881i | ||||
\(394\) | 98.7630 | 0.250667 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 58.0527 | − | 141.272i | 0.146598 | − | 0.356748i | ||||
\(397\) | 214.000i | 0.539043i | 0.962994 | + | 0.269521i | \(0.0868655\pi\) | ||||
−0.962994 | + | 0.269521i | \(0.913135\pi\) | |||||||
\(398\) | −210.606 | −0.529161 | ||||||||
\(399\) | −73.2541 | + | 370.995i | −0.183594 | + | 0.929812i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 726.086i | − | 1.81069i | −0.424677 | − | 0.905345i | \(-0.639613\pi\) | ||
0.424677 | − | 0.905345i | \(-0.360387\pi\) | |||||||
\(402\) | 44.0017 | − | 222.846i | 0.109457 | − | 0.554344i | ||||
\(403\) | − | 80.0000i | − | 0.198511i | ||||||
\(404\) | 310.978i | 0.769748i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 435.895 | 1.07363 | ||||||||
\(407\) | 508.670 | 1.24980 | ||||||||
\(408\) | −29.5868 | − | 5.84200i | −0.0725166 | − | 0.0143186i | ||||
\(409\) | 346.158 | 0.846352 | 0.423176 | − | 0.906047i | \(-0.360915\pi\) | ||||
0.423176 | + | 0.906047i | \(0.360915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 518.039 | + | 102.288i | 1.26044 | + | 0.248877i | ||||
\(412\) | 15.1843i | 0.0368552i | ||||||||
\(413\) | −893.038 | −2.16232 | ||||||||
\(414\) | −207.895 | − | 85.4296i | −0.502161 | − | 0.206352i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 56.5685i | − | 0.135982i | ||||||
\(417\) | 555.717 | + | 109.728i | 1.33266 | + | 0.263137i | ||||
\(418\) | − | 131.684i | − | 0.315033i | ||||||
\(419\) | − | 580.907i | − | 1.38641i | −0.720740 | − | 0.693206i | \(-0.756198\pi\) | ||
0.720740 | − | 0.693206i | \(-0.243802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −269.315 | −0.639704 | −0.319852 | − | 0.947468i | \(-0.603633\pi\) | ||||
−0.319852 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(422\) | −404.242 | −0.957919 | ||||||||
\(423\) | 735.019 | + | 302.039i | 1.73763 | + | 0.714041i | ||||
\(424\) | −10.0527 | −0.0237091 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −56.9210 | + | 288.276i | −0.133617 | + | 0.676704i | ||||
\(427\) | − | 252.105i | − | 0.590411i | ||||||
\(428\) | 32.5642 | 0.0760845 | ||||||||
\(429\) | 249.737 | + | 49.3113i | 0.582137 | + | 0.114945i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 776.068i | 1.80062i | 0.435247 | + | 0.900311i | \(0.356661\pi\) | ||||
−0.435247 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(432\) | −90.0507 | − | 59.6228i | −0.208451 | − | 0.138016i | ||||
\(433\) | − | 195.526i | − | 0.451561i | −0.974178 | − | 0.225781i | \(-0.927507\pi\) | ||
0.974178 | − | 0.225781i | \(-0.0724932\pi\) | |||||||
\(434\) | − | 129.959i | − | 0.299444i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 187.684 | 0.430468 | ||||||||
\(437\) | −193.785 | −0.443443 | ||||||||
\(438\) | 9.90554 | − | 50.1666i | 0.0226154 | − | 0.114536i | ||||
\(439\) | −598.763 | −1.36392 | −0.681962 | − | 0.731387i | \(-0.738873\pi\) | ||||
−0.681962 | + | 0.731387i | \(0.738873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −690.500 | − | 283.745i | −1.56576 | − | 0.643413i | ||||
\(442\) | − | 50.2633i | − | 0.113718i | ||||||
\(443\) | −216.728 | −0.489228 | −0.244614 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244614 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(444\) | 69.6754 | − | 352.871i | 0.156927 | − | 0.794754i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 100.949i | − | 0.226342i | ||||||
\(447\) | 42.1848 | − | 213.645i | 0.0943732 | − | 0.477953i | ||||
\(448\) | − | 91.8947i | − | 0.205122i | ||||||
\(449\) | − | 246.203i | − | 0.548336i | −0.961682 | − | 0.274168i | \(-0.911598\pi\) | ||
0.961682 | − | 0.274168i | \(-0.0884025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −174.158 | −0.386160 | ||||||||
\(452\) | 391.476 | 0.866098 | ||||||||
\(453\) | −276.503 | − | 54.5964i | −0.610383 | − | 0.120522i | ||||
\(454\) | 41.1843 | 0.0907144 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −91.3509 | − | 18.0375i | −0.200331 | − | 0.0395559i | ||||
\(457\) | − | 553.052i | − | 1.21018i | −0.796157 | − | 0.605090i | \(-0.793137\pi\) | ||
0.796157 | − | 0.605090i | \(-0.206863\pi\) | |||||||
\(458\) | 183.401 | 0.400439 | ||||||||
\(459\) | −80.0135 | − | 52.9771i | −0.174321 | − | 0.115419i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 124.749i | 0.270605i | 0.990804 | + | 0.135302i | \(0.0432006\pi\) | ||||
−0.990804 | + | 0.135302i | \(0.956799\pi\) | |||||||
\(462\) | 405.693 | + | 80.1053i | 0.878124 | + | 0.173388i | ||||
\(463\) | 669.723i | 1.44649i | 0.690593 | + | 0.723243i | \(0.257349\pi\) | ||||
−0.690593 | + | 0.723243i | \(0.742651\pi\) | |||||||
\(464\) | 107.331i | 0.231317i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −262.868 | −0.564095 | ||||||||
\(467\) | −486.880 | −1.04257 | −0.521285 | − | 0.853383i | \(-0.674547\pi\) | ||||
−0.521285 | + | 0.853383i | \(0.674547\pi\) | |||||||
\(468\) | 68.4157 | − | 166.491i | 0.146187 | − | 0.355750i | ||||
\(469\) | 614.999 | 1.31130 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.9694 | − | 364.489i | 0.152801 | − | 0.773861i | ||||
\(472\) | − | 219.895i | − | 0.465879i | ||||||
\(473\) | 360.289 | 0.761711 | ||||||||
\(474\) | −37.5701 | − | 7.41833i | −0.0792618 | − | 0.0156505i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 81.6520i | − | 0.171538i | ||||||
\(477\) | −29.5868 | − | 12.1580i | −0.0620267 | − | 0.0254885i | ||||
\(478\) | − | 428.105i | − | 0.895618i | ||||||
\(479\) | 520.580i | 1.08680i | 0.839472 | + | 0.543402i | \(0.182864\pi\) | ||||
−0.839472 | + | 0.543402i | \(0.817136\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 599.473 | 1.24631 | ||||||||
\(482\) | −335.912 | −0.696914 | ||||||||
\(483\) | 117.882 | − | 597.013i | 0.244062 | − | 1.23605i | ||||
\(484\) | 98.0000 | 0.202479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −192.925 | − | 284.390i | −0.396966 | − | 0.585165i | ||||
\(487\) | 263.381i | 0.540824i | 0.962745 | + | 0.270412i | \(0.0871600\pi\) | ||||
−0.962745 | + | 0.270412i | \(0.912840\pi\) | |||||||
\(488\) | 62.0764 | 0.127206 | ||||||||
\(489\) | 92.6228 | − | 469.088i | 0.189413 | − | 0.959279i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 711.646i | 1.44938i | 0.689074 | + | 0.724691i | \(0.258017\pi\) | ||||
−0.689074 | + | 0.724691i | \(0.741983\pi\) | |||||||
\(492\) | −23.8554 | + | 120.816i | −0.0484866 | + | 0.245560i | ||||
\(493\) | 95.3680i | 0.193444i | ||||||||
\(494\) | − | 155.191i | − | 0.314152i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 0.0645161 | ||||||||
\(497\) | −795.569 | −1.60074 | ||||||||
\(498\) | 2.86567 | + | 0.565835i | 0.00575436 | + | 0.00113622i | ||||
\(499\) | −23.0790 | −0.0462505 | −0.0231253 | − | 0.999733i | \(-0.507362\pi\) | ||||
−0.0231253 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.7103 | + | 6.26130i | 0.0632941 | + | 0.0124976i | ||||
\(502\) | − | 119.684i | − | 0.238414i | ||||||
\(503\) | 40.5844 | 0.0806847 | 0.0403423 | − | 0.999186i | \(-0.487155\pi\) | ||||
0.0403423 | + | 0.999186i | \(0.487155\pi\) | |||||||
\(504\) | 111.140 | − | 270.462i | 0.220516 | − | 0.536631i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 211.909i | 0.418792i | ||||||||
\(507\) | −203.079 | − | 40.0986i | −0.400550 | − | 0.0790899i | ||||
\(508\) | 155.079i | 0.305274i | ||||||||
\(509\) | 484.591i | 0.952045i | 0.879433 | + | 0.476023i | \(0.157922\pi\) | ||||
−0.879433 | + | 0.476023i | \(0.842078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 138.447 | 0.270933 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −247.047 | − | 163.570i | −0.481572 | − | 0.318850i | ||||
\(514\) | 413.026 | 0.803553 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 49.3509 | − | 249.937i | 0.0956413 | − | 0.484375i | ||||
\(517\) | − | 749.210i | − | 1.44915i | ||||||
\(518\) | 973.835 | 1.87999 | ||||||||
\(519\) | 833.934 | + | 164.663i | 1.60681 | + | 0.317269i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 539.857i | 1.03619i | 0.855322 | + | 0.518097i | \(0.173359\pi\) | ||||
−0.855322 | + | 0.518097i | \(0.826641\pi\) | |||||||
\(522\) | −129.810 | + | 315.895i | −0.248678 | + | 0.605162i | ||||
\(523\) | − | 266.644i | − | 0.509836i | −0.966963 | − | 0.254918i | \(-0.917952\pi\) | ||
0.966963 | − | 0.254918i | \(-0.0820485\pi\) | |||||||
\(524\) | − | 203.200i | − | 0.387786i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −392.763 | −0.746698 | ||||||||
\(527\) | 28.4332 | 0.0539530 | ||||||||
\(528\) | −19.7245 | + | 99.8947i | −0.0373570 | + | 0.189194i | ||||
\(529\) | −217.158 | −0.410507 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 265.947 | − | 647.188i | 0.500842 | − | 1.21881i | ||||
\(532\) | − | 252.105i | − | 0.473882i | ||||||
\(533\) | −205.247 | −0.385079 | ||||||||
\(534\) | 5.84200 | − | 29.5868i | 0.0109401 | − | 0.0554059i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 151.433i | 0.282523i | ||||||||
\(537\) | 178.191 | − | 902.447i | 0.331827 | − | 1.68053i | ||||
\(538\) | 405.237i | 0.753229i | ||||||||
\(539\) | 703.831i | 1.30581i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −337.895 | −0.624574 | −0.312287 | − | 0.949988i | \(-0.601095\pi\) | ||||
−0.312287 | + | 0.949988i | \(0.601095\pi\) | |||||||
\(542\) | −458.354 | −0.845672 | ||||||||
\(543\) | −781.954 | − | 154.399i | −1.44006 | − | 0.284345i | ||||
\(544\) | 20.1053 | 0.0369583 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 478.114 | + | 94.4050i | 0.875666 | + | 0.172903i | ||||
\(547\) | 214.566i | 0.392259i | 0.980578 | + | 0.196130i | \(0.0628373\pi\) | ||||
−0.980578 | + | 0.196130i | \(0.937163\pi\) | |||||||
\(548\) | −352.027 | −0.642386 | ||||||||
\(549\) | 182.702 | + | 75.0771i | 0.332790 | + | 0.136753i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 294.454i | 0.534400i | ||||||||
\(552\) | 147.004 | + | 29.0263i | 0.266311 | + | 0.0525839i | ||||
\(553\) | − | 103.684i | − | 0.187494i | ||||||
\(554\) | − | 588.089i | − | 1.06153i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −377.631 | −0.679193 | ||||||||
\(557\) | 674.821 | 1.21153 | 0.605764 | − | 0.795644i | \(-0.292867\pi\) | ||||
0.605764 | + | 0.795644i | \(0.292867\pi\) | |||||||
\(558\) | 94.1816 | + | 38.7018i | 0.168784 | + | 0.0693580i | ||||
\(559\) | 424.605 | 0.759580 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.5260 | + | 88.7603i | −0.0312406 | + | 0.158218i | ||||
\(562\) | − | 610.552i | − | 1.08639i | ||||||
\(563\) | −718.513 | −1.27622 | −0.638111 | − | 0.769944i | \(-0.720284\pi\) | ||||
−0.638111 | + | 0.769944i | \(0.720284\pi\) | |||||||
\(564\) | −519.737 | − | 102.624i | −0.921519 | − | 0.181957i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 200.167i | 0.353652i | ||||||||
\(567\) | 654.210 | − | 661.601i | 1.15381 | − | 1.16684i | ||||
\(568\) | − | 195.895i | − | 0.344885i | ||||||
\(569\) | 183.122i | 0.321831i | 0.986968 | + | 0.160916i | \(0.0514447\pi\) | ||||
−0.986968 | + | 0.160916i | \(0.948555\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −295.895 | −0.518204 | −0.259102 | − | 0.965850i | \(-0.583427\pi\) | ||||
−0.259102 | + | 0.965850i | \(0.583427\pi\) | |||||||
\(572\) | −169.706 | −0.296688 | ||||||||
\(573\) | 92.7613 | − | 469.789i | 0.161887 | − | 0.819877i | ||||
\(574\) | −333.421 | −0.580872 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 66.5964 | + | 27.3663i | 0.115619 | + | 0.0475109i | ||||
\(577\) | 984.947i | 1.70701i | 0.521082 | + | 0.853507i | \(0.325529\pi\) | ||||
−0.521082 | + | 0.853507i | \(0.674471\pi\) | |||||||
\(578\) | −390.843 | −0.676200 | ||||||||
\(579\) | −53.4954 | + | 270.927i | −0.0923927 | + | 0.467922i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.90852i | 0.0136119i | ||||||||
\(582\) | −92.0044 | + | 465.956i | −0.158083 | + | 0.800611i | ||||
\(583\) | 30.1580i | 0.0517290i | ||||||||
\(584\) | 34.0901i | 0.0583734i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 233.342 | 0.398195 | ||||||||
\(587\) | −378.172 | −0.644245 | −0.322122 | − | 0.946698i | \(-0.604396\pi\) | ||||
−0.322122 | + | 0.946698i | \(0.604396\pi\) | |||||||
\(588\) | 488.257 | + | 96.4078i | 0.830369 | + | 0.163959i | ||||
\(589\) | 87.7893 | 0.149048 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −205.540 | − | 40.5844i | −0.347783 | − | 0.0686707i | ||||
\(592\) | 239.789i | 0.405050i | ||||||||
\(593\) | 265.221 | 0.447253 | 0.223626 | − | 0.974675i | \(-0.428210\pi\) | ||||
0.223626 | + | 0.974675i | \(0.428210\pi\) | |||||||
\(594\) | −178.868 | + | 270.152i | −0.301125 | + | 0.454801i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 145.180i | 0.243590i | ||||||||
\(597\) | 438.301 | + | 86.5438i | 0.734172 | + | 0.144964i | ||||
\(598\) | 249.737i | 0.417620i | ||||||||
\(599\) | − | 382.061i | − | 0.637832i | −0.947783 | − | 0.318916i | \(-0.896681\pi\) | ||
0.947783 | − | 0.318916i | \(-0.103319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1021.53 | 1.69971 | 0.849855 | − | 0.527016i | \(-0.176689\pi\) | ||||
0.849855 | + | 0.527016i | \(0.176689\pi\) | |||||||
\(602\) | 689.764 | 1.14579 | ||||||||
\(603\) | −183.147 | + | 445.693i | −0.303727 | + | 0.739125i | ||||
\(604\) | 187.895 | 0.311084 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 127.789 | − | 647.188i | 0.210873 | − | 1.06797i | ||||
\(607\) | 835.487i | 1.37642i | 0.725512 | + | 0.688210i | \(0.241603\pi\) | ||||
−0.725512 | + | 0.688210i | \(0.758397\pi\) | |||||||
\(608\) | 62.0764 | 0.102099 | ||||||||
\(609\) | −907.157 | − | 179.121i | −1.48959 | − | 0.294123i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 882.952i | − | 1.44509i | ||||||
\(612\) | 59.1735 | + | 24.3160i | 0.0966888 | + | 0.0397320i | ||||
\(613\) | 833.263i | 1.35932i | 0.733528 | + | 0.679660i | \(0.237872\pi\) | ||||
−0.733528 | + | 0.679660i | \(0.762128\pi\) | |||||||
\(614\) | − | 225.399i | − | 0.367100i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −275.684 | −0.447539 | ||||||||
\(617\) | −455.098 | −0.737598 | −0.368799 | − | 0.929509i | \(-0.620231\pi\) | ||||
−0.368799 | + | 0.929509i | \(0.620231\pi\) | |||||||
\(618\) | 6.23966 | − | 31.6007i | 0.0100965 | − | 0.0511338i | ||||
\(619\) | −336.710 | −0.543959 | −0.271979 | − | 0.962303i | \(-0.587678\pi\) | ||||
−0.271979 | + | 0.962303i | \(0.587678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 397.552 | + | 263.220i | 0.640181 | + | 0.423865i | ||||
\(622\) | − | 202.369i | − | 0.325352i | ||||||
\(623\) | 81.6520 | 0.131063 | ||||||||
\(624\) | −23.2456 | + | 117.727i | −0.0372525 | + | 0.188665i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 709.488i | − | 1.13337i | ||||||
\(627\) | −54.1125 | + | 274.053i | −0.0863039 | + | 0.437086i | ||||
\(628\) | 247.684i | 0.394401i | ||||||||
\(629\) | 213.062i | 0.338731i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1100.89 | −1.74468 | −0.872341 | − | 0.488898i | \(-0.837399\pi\) | ||||
−0.872341 | + | 0.488898i | \(0.837399\pi\) | |||||||
\(632\) | 25.5303 | 0.0403961 | ||||||||
\(633\) | 841.283 | + | 166.114i | 1.32904 | + | 0.262423i | ||||
\(634\) | 472.710 | 0.745600 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 20.9210 | + | 4.13091i | 0.0328947 | + | 0.00649515i | ||||
\(637\) | 829.473i | 1.30216i | ||||||||
\(638\) | 321.994 | 0.504692 | ||||||||
\(639\) | 236.921 | − | 576.552i | 0.370768 | − | 0.902273i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 337.011i | − | 0.525758i | −0.964829 | − | 0.262879i | \(-0.915328\pi\) | ||
0.964829 | − | 0.262879i | \(-0.0846719\pi\) | |||||||
\(642\) | −67.7705 | − | 13.3815i | −0.105562 | − | 0.0208435i | ||||
\(643\) | − | 599.381i | − | 0.932164i | −0.884742 | − | 0.466082i | \(-0.845665\pi\) | ||
0.884742 | − | 0.466082i | \(-0.154335\pi\) | |||||||
\(644\) | 405.693i | 0.629958i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 55.1573 | 0.0853828 | ||||||||
\(647\) | 47.0224 | 0.0726775 | 0.0363388 | − | 0.999340i | \(-0.488430\pi\) | ||||
0.0363388 | + | 0.999340i | \(0.488430\pi\) | |||||||
\(648\) | 162.907 | + | 161.088i | 0.251400 | + | 0.248592i | ||||
\(649\) | −659.684 | −1.01646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.4036 | + | 270.462i | −0.0820331 | + | 0.415456i | ||||
\(652\) | 318.763i | 0.488900i | ||||||||
\(653\) | 559.228 | 0.856399 | 0.428199 | − | 0.903684i | \(-0.359148\pi\) | ||||
0.428199 | + | 0.903684i | \(0.359148\pi\) | |||||||
\(654\) | −390.596 | − | 77.1245i | −0.597242 | − | 0.117927i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 82.0989i | − | 0.125151i | ||||||
\(657\) | −41.2296 | + | 100.333i | −0.0627543 | + | 0.152714i | ||||
\(658\) | − | 1434.34i | − | 2.17985i | ||||||
\(659\) | − | 665.759i | − | 1.01026i | −0.863044 | − | 0.505129i | \(-0.831445\pi\) | ||
0.863044 | − | 0.505129i | \(-0.168555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −557.947 | −0.844096 | −0.422048 | − | 0.906574i | \(-0.638689\pi\) | ||||
−0.422048 | + | 0.906574i | \(0.638689\pi\) | |||||||
\(662\) | 550.724 | 0.831909 | ||||||||
\(663\) | −20.6546 | + | 104.605i | −0.0311532 | + | 0.157775i | ||||
\(664\) | −1.94733 | −0.00293273 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −290.009 | + | 705.742i | −0.435448 | + | 1.05967i | ||||
\(667\) | − | 473.842i | − | 0.710408i | ||||||
\(668\) | −21.5484 | −0.0322581 | ||||||||
\(669\) | −41.4826 | + | 210.088i | −0.0620068 | + | 0.314033i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 186.229i | − | 0.277540i | ||||||
\(672\) | −37.7620 | + | 191.246i | −0.0561935 | + | 0.284592i | ||||
\(673\) | 1019.42i | 1.51474i | 0.652985 | + | 0.757370i | \(0.273516\pi\) | ||||
−0.652985 | + | 0.757370i | \(0.726484\pi\) | |||||||
\(674\) | 183.401i | 0.272108i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 138.000 | 0.204142 | ||||||||
\(677\) | −624.616 | −0.922624 | −0.461312 | − | 0.887238i | \(-0.652621\pi\) | ||||
−0.461312 | + | 0.887238i | \(0.652621\pi\) | |||||||
\(678\) | −814.717 | − | 160.868i | −1.20165 | − | 0.237269i | ||||
\(679\) | −1285.92 | −1.89384 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −85.7103 | − | 16.9238i | −0.125860 | − | 0.0248513i | ||||
\(682\) | − | 96.0000i | − | 0.140762i | ||||||
\(683\) | 525.882 | 0.769959 | 0.384980 | − | 0.922925i | \(-0.374208\pi\) | ||||
0.384980 | + | 0.922925i | \(0.374208\pi\) | |||||||
\(684\) | 182.702 | + | 75.0771i | 0.267108 | + | 0.109762i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 551.469i | 0.803890i | ||||||||
\(687\) | −381.683 | − | 75.3644i | −0.555579 | − | 0.109701i | ||||
\(688\) | 169.842i | 0.246863i | ||||||||
\(689\) | 35.5415i | 0.0515843i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 932.000 | 1.34877 | 0.674385 | − | 0.738380i | \(-0.264409\pi\) | ||||
0.674385 | + | 0.738380i | \(0.264409\pi\) | |||||||
\(692\) | −566.690 | −0.818916 | ||||||||
\(693\) | −811.386 | − | 333.421i | −1.17083 | − | 0.481126i | ||||
\(694\) | −490.710 | −0.707075 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 44.1053 | − | 223.371i | 0.0633697 | − | 0.320936i | ||||
\(697\) | − | 72.9480i | − | 0.104660i | ||||||
\(698\) | −720.653 | −1.03245 | ||||||||
\(699\) | 547.065 | + | 108.020i | 0.782640 | + | 0.154535i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 606.045i | 0.864544i | 0.901743 | + | 0.432272i | \(0.142288\pi\) | ||||
−0.901743 | + | 0.432272i | \(0.857712\pi\) | |||||||
\(702\) | −210.798 | + | 318.377i | −0.300283 | + | 0.453529i | ||||
\(703\) | 657.842i | 0.935764i | ||||||||
\(704\) | − | 67.8823i | − | 0.0964237i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 901.815 | 1.27736 | ||||||||
\(707\) | 1786.08 | 2.52627 | ||||||||
\(708\) | −90.3607 | + | 457.631i | −0.127628 | + | 0.646372i | ||||
\(709\) | −489.473 | −0.690371 | −0.345186 | − | 0.938534i | \(-0.612184\pi\) | ||||
−0.345186 | + | 0.938534i | \(0.612184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 75.1402 | + | 30.8772i | 0.105682 | + | 0.0434278i | ||||
\(712\) | 20.1053i | 0.0282378i | ||||||||
\(713\) | −141.272 | −0.198138 | ||||||||
\(714\) | −33.5530 | + | 169.929i | −0.0469930 | + | 0.237996i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 613.247i | 0.856491i | ||||||||
\(717\) | −175.920 | + | 890.947i | −0.245356 | + | 1.24260i | ||||
\(718\) | 236.105i | 0.328838i | ||||||||
\(719\) | − | 107.778i | − | 0.149900i | −0.997187 | − | 0.0749500i | \(-0.976120\pi\) | ||
0.997187 | − | 0.0749500i | \(-0.0238797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 87.2100 | 0.120957 | ||||||||
\(722\) | −340.230 | −0.471232 | ||||||||
\(723\) | 699.080 | + | 138.036i | 0.966916 | + | 0.190921i | ||||
\(724\) | 531.368 | 0.733934 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −203.952 | − | 40.2709i | −0.280925 | − | 0.0554695i | ||||
\(727\) | 150.172i | 0.206563i | 0.994652 | + | 0.103282i | \(0.0329343\pi\) | ||||
−0.994652 | + | 0.103282i | \(0.967066\pi\) | |||||||
\(728\) | −324.897 | −0.446287 | ||||||||
\(729\) | 284.641 | + | 671.134i | 0.390453 | + | 0.920623i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 150.911i | 0.206445i | ||||||||
\(732\) | −129.190 | − | 25.5089i | −0.176489 | − | 0.0348482i | ||||
\(733\) | − | 675.526i | − | 0.921591i | −0.887506 | − | 0.460795i | \(-0.847564\pi\) | ||
0.887506 | − | 0.460795i | \(-0.152436\pi\) | |||||||
\(734\) | 715.349i | 0.974591i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −99.8947 | −0.135726 | ||||||||
\(737\) | 454.298 | 0.616415 | ||||||||
\(738\) | 99.2929 | − | 241.631i | 0.134543 | − | 0.327414i | ||||
\(739\) | 936.921 | 1.26782 | 0.633911 | − | 0.773406i | \(-0.281448\pi\) | ||||
0.633911 | + | 0.773406i | \(0.281448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −63.7722 | + | 322.974i | −0.0860624 | + | 0.435863i | ||||
\(742\) | 57.7367i | 0.0778122i | ||||||||
\(743\) | 452.939 | 0.609608 | 0.304804 | − | 0.952415i | \(-0.401409\pi\) | ||||
0.304804 | + | 0.952415i | \(0.401409\pi\) | |||||||
\(744\) | −66.5964 | − | 13.1497i | −0.0895113 | − | 0.0176743i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 588.387i | − | 0.788723i | ||||||
\(747\) | −5.73134 | − | 2.35516i | −0.00767247 | − | 0.00315283i | ||||
\(748\) | − | 60.3160i | − | 0.0806364i | ||||||
\(749\) | − | 187.029i | − | 0.249706i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 654.369 | 0.871330 | 0.435665 | − | 0.900109i | \(-0.356513\pi\) | ||||
0.435665 | + | 0.900109i | \(0.356513\pi\) | |||||||
\(752\) | 353.181 | 0.469656 | ||||||||
\(753\) | −49.1814 | + | 249.079i | −0.0653140 | + | 0.330782i | ||||
\(754\) | 379.473 | 0.503280 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −342.438 | + | 517.199i | −0.452961 | + | 0.684125i | ||||
\(757\) | − | 123.315i | − | 0.162900i | −0.996677 | − | 0.0814500i | \(-0.974045\pi\) | ||
0.996677 | − | 0.0814500i | \(-0.0259551\pi\) | |||||||
\(758\) | −117.045 | −0.154412 | ||||||||
\(759\) | 87.0790 | − | 441.011i | 0.114729 | − | 0.581042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 502.715i | 0.660598i | 0.943876 | + | 0.330299i | \(0.107150\pi\) | ||||
−0.943876 | + | 0.330299i | \(0.892850\pi\) | |||||||
\(762\) | 63.7262 | − | 322.741i | 0.0836302 | − | 0.423545i | ||||
\(763\) | − | 1077.95i | − | 1.41278i | ||||||
\(764\) | 319.240i | 0.417853i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 473.184 | 0.617734 | ||||||||
\(767\) | −777.445 | −1.01362 | ||||||||
\(768\) | −47.0908 | − | 9.29822i | −0.0613161 | − | 0.0121071i | ||||
\(769\) | 286.316 | 0.372323 | 0.186161 | − | 0.982519i | \(-0.440395\pi\) | ||||
0.186161 | + | 0.982519i | \(0.440395\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −859.565 | − | 169.724i | −1.11487 | − | 0.220135i | ||||
\(772\) | − | 184.105i | − | 0.238478i | ||||||
\(773\) | −972.030 | −1.25748 | −0.628739 | − | 0.777617i | \(-0.716428\pi\) | ||||
−0.628739 | + | 0.777617i | \(0.716428\pi\) | |||||||
\(774\) | −205.412 | + | 499.875i | −0.265390 | + | 0.645833i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 316.635i | − | 0.408035i | ||||||
\(777\) | −2026.68 | − | 400.175i | −2.60835 | − | 0.515026i | ||||
\(778\) | 767.868i | 0.986976i | ||||||||
\(779\) | − | 225.231i | − | 0.289129i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −587.684 | −0.752476 | ||||||||
\(782\) | −88.7603 | −0.113504 | ||||||||
\(783\) | 399.962 | − | 604.078i | 0.510807 | − | 0.771492i | ||||
\(784\) | −331.789 | −0.423201 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −83.5003 | + | 422.887i | −0.106235 | + | 0.538024i | ||||
\(787\) | − | 1492.70i | − | 1.89669i | −0.317237 | − | 0.948346i | \(-0.602755\pi\) | ||
0.317237 | − | 0.948346i | \(-0.397245\pi\) | |||||||
\(788\) | 139.672 | 0.177249 | ||||||||
\(789\) | 817.394 | + | 161.397i | 1.03599 | + | 0.204559i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2248.41i | − | 2.84249i | ||||||
\(792\) | 82.0989 | − | 199.789i | 0.103660 | − | 0.252259i | ||||
\(793\) | − | 219.473i | − | 0.276763i | ||||||
\(794\) | 302.642i | 0.381161i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −297.842 | −0.374173 | ||||||||
\(797\) | 94.3618 | 0.118396 | 0.0591981 | − | 0.998246i | \(-0.481146\pi\) | ||||
0.0591981 | + | 0.998246i | \(0.481146\pi\) | |||||||
\(798\) | −103.597 | + | 524.666i | −0.129821 | + | 0.657476i | ||||
\(799\) | 313.815 | 0.392760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.3160 | + | 59.1735i | −0.0303571 | + | 0.0738746i | ||||
\(802\) | − | 1026.84i | − | 1.28035i | ||||||
\(803\) | 102.270 | 0.127360 | ||||||||
\(804\) | 62.2278 | − | 315.152i | 0.0773977 | − | 0.391980i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 113.137i | − | 0.140369i | ||||||
\(807\) | 166.523 | − | 843.354i | 0.206348 | − | 1.04505i | ||||
\(808\) | 439.789i | 0.544294i | ||||||||
\(809\) | − | 1103.35i | − | 1.36384i | −0.731427 | − | 0.681920i | \(-0.761145\pi\) | ||
0.731427 | − | 0.681920i | \(-0.238855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1580 | −0.0125253 | −0.00626264 | − | 0.999980i | \(-0.501993\pi\) | ||||
−0.00626264 | + | 0.999980i | \(0.501993\pi\) | |||||||
\(812\) | 616.448 | 0.759173 | ||||||||
\(813\) | 953.899 | + | 188.350i | 1.17331 | + | 0.231673i | ||||
\(814\) | 719.368 | 0.883744 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −41.8420 | − | 8.26183i | −0.0512770 | − | 0.0101248i | ||||
\(817\) | 465.947i | 0.570315i | ||||||||
\(818\) | 489.541 | 0.598461 | ||||||||
\(819\) | −956.228 | − | 392.940i | −1.16756 | − | 0.479780i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 337.011i | − | 0.410488i | −0.978711 | − | 0.205244i | \(-0.934201\pi\) | ||
0.978711 | − | 0.205244i | \(-0.0657988\pi\) | |||||||
\(822\) | 732.618 | + | 144.658i | 0.891263 | + | 0.175983i | ||||
\(823\) | − | 901.512i | − | 1.09540i | −0.836675 | − | 0.547699i | \(-0.815504\pi\) | ||
0.836675 | − | 0.547699i | \(-0.184496\pi\) | |||||||
\(824\) | 21.4739i | 0.0260606i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1262.95 | −1.52899 | ||||||||
\(827\) | 531.354 | 0.642508 | 0.321254 | − | 0.946993i | \(-0.395896\pi\) | ||||
0.321254 | + | 0.946993i | \(0.395896\pi\) | |||||||
\(828\) | −294.007 | − | 120.816i | −0.355081 | − | 0.145913i | ||||
\(829\) | 197.631 | 0.238397 | 0.119199 | − | 0.992870i | \(-0.461967\pi\) | ||||
0.119199 | + | 0.992870i | \(0.461967\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −241.662 | + | 1223.90i | −0.290809 | + | 1.47280i | ||||
\(832\) | − | 80.0000i | − | 0.0961538i | ||||||
\(833\) | −294.808 | −0.353911 | ||||||||
\(834\) | 785.903 | + | 155.179i | 0.942330 | + | 0.186066i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 186.229i | − | 0.222762i | ||||||
\(837\) | −180.101 | − | 119.246i | −0.215175 | − | 0.142468i | ||||
\(838\) | − | 821.526i | − | 0.980341i | ||||||
\(839\) | − | 943.950i | − | 1.12509i | −0.826767 | − | 0.562545i | \(-0.809822\pi\) | ||
0.826767 | − | 0.562545i | \(-0.190178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 121.000 | 0.143876 | ||||||||
\(842\) | −380.869 | −0.452339 | ||||||||
\(843\) | −250.893 | + | 1270.64i | −0.297619 | + | 1.50729i | ||||
\(844\) | −571.684 | −0.677351 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1039.47 | + | 427.148i | 1.22869 | + | 0.504903i | ||||
\(847\) | − | 562.855i | − | 0.664528i | ||||||
\(848\) | −14.2166 | −0.0167649 | ||||||||
\(849\) | 82.2541 | − | 416.575i | 0.0968835 | − | 0.490666i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1058.61i | − | 1.24396i | ||||||
\(852\) | −80.4984 | + | 407.684i | −0.0944817 | + | 0.478502i | ||||
\(853\) | − | 1196.42i | − | 1.40260i | −0.712865 | − | 0.701301i | \(-0.752603\pi\) | ||
0.712865 | − | 0.701301i | \(-0.247397\pi\) | |||||||
\(854\) | − | 356.531i | − | 0.417483i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46.0527 | 0.0537998 | ||||||||
\(857\) | 1266.04 | 1.47729 | 0.738645 | − | 0.674095i | \(-0.235466\pi\) | ||||
0.738645 | + | 0.674095i | \(0.235466\pi\) | |||||||
\(858\) | 353.181 | + | 69.7367i | 0.411633 | + | 0.0812782i | ||||
\(859\) | 470.868 | 0.548159 | 0.274079 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274079 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 693.895 | + | 137.012i | 0.805917 | + | 0.159131i | ||||
\(862\) | 1097.53i | 1.27323i | ||||||||
\(863\) | −285.057 | −0.330310 | −0.165155 | − | 0.986268i | \(-0.552812\pi\) | ||||
−0.165155 | + | 0.986268i | \(0.552812\pi\) | |||||||
\(864\) | −127.351 | − | 84.3193i | −0.147397 | − | 0.0975918i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 276.516i | − | 0.319302i | ||||||
\(867\) | 813.399 | + | 160.608i | 0.938177 | + | 0.185246i | ||||
\(868\) | − | 183.789i | − | 0.211739i | ||||||
\(869\) | − | 76.5910i | − | 0.0881369i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 535.395 | 0.614690 | ||||||||
\(872\) | 265.425 | 0.304387 | ||||||||
\(873\) | 382.948 | − | 931.912i | 0.438657 | − | 1.06748i | ||||
\(874\) | −274.053 | −0.313561 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0085 | − | 70.9462i | 0.0159915 | − | 0.0809888i | ||||
\(877\) | − | 244.579i | − | 0.278882i | −0.990230 | − | 0.139441i | \(-0.955469\pi\) | ||
0.990230 | − | 0.139441i | \(-0.0445305\pi\) | |||||||
\(878\) | −846.779 | −0.964440 | ||||||||
\(879\) | −485.618 | − | 95.8867i | −0.552466 | − | 0.109086i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 137.271i | 0.155813i | 0.996961 | + | 0.0779065i | \(0.0248236\pi\) | ||||
−0.996961 | + | 0.0779065i | \(0.975176\pi\) | |||||||
\(882\) | −976.514 | − | 401.276i | −1.10716 | − | 0.454962i | ||||
\(883\) | 1647.75i | 1.86608i | 0.359772 | + | 0.933040i | \(0.382854\pi\) | ||||
−0.359772 | + | 0.933040i | \(0.617146\pi\) | |||||||
\(884\) | − | 71.0831i | − | 0.0804107i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −306.500 | −0.345936 | ||||||||
\(887\) | −514.419 | −0.579954 | −0.289977 | − | 0.957034i | \(-0.593648\pi\) | ||||
−0.289977 | + | 0.957034i | \(0.593648\pi\) | |||||||
\(888\) | 98.5360 | − | 499.035i | 0.110964 | − | 0.561976i | ||||
\(889\) | 890.683 | 1.00189 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 483.263 | − | 488.722i | 0.542382 | − | 0.548510i | ||||
\(892\) | − | 142.763i | − | 0.160048i | ||||||
\(893\) | 968.923 | 1.08502 | ||||||||
\(894\) | 59.6584 | − | 302.139i | 0.0667319 | − | 0.337964i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 129.959i | − | 0.145043i | ||||||
\(897\) | 102.624 | − | 519.737i | 0.114408 | − | 0.579417i | ||||
\(898\) | − | 348.184i | − | 0.387732i | ||||||
\(899\) | 214.663i | 0.238779i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6320 | −0.0140200 | ||||||||
\(902\) | −246.297 | −0.273056 | ||||||||
\(903\) | −1435.49 | − | 283.443i | −1.58969 | − | 0.313890i | ||||
\(904\) | 553.631 | 0.612424 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −391.035 | − | 77.2110i | −0.431606 | − | 0.0852219i | ||||
\(907\) | − | 347.303i | − | 0.382914i | −0.981501 | − | 0.191457i | \(-0.938679\pi\) | ||
0.981501 | − | 0.191457i | \(-0.0613213\pi\) | |||||||
\(908\) | 58.2434 | 0.0641448 | ||||||||
\(909\) | −531.895 | + | 1294.38i | −0.585143 | + | 1.42396i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 304.540i | − | 0.334292i | −0.985932 | − | 0.167146i | \(-0.946545\pi\) | ||
0.985932 | − | 0.167146i | \(-0.0534551\pi\) | |||||||
\(912\) | −129.190 | − | 25.5089i | −0.141655 | − | 0.0279703i | ||||
\(913\) | 5.84200i | 0.00639868i | ||||||||
\(914\) | − | 782.134i | − | 0.855726i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 259.368 | 0.283153 | ||||||||
\(917\) | −1167.06 | −1.27270 | ||||||||
\(918\) | −113.156 | − | 74.9210i | −0.123264 | − | 0.0816133i | ||||
\(919\) | −244.289 | −0.265820 | −0.132910 | − | 0.991128i | \(-0.542432\pi\) | ||||
−0.132910 | + | 0.991128i | \(0.542432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −92.6228 | + | 469.088i | −0.100568 | + | 0.509324i | ||||
\(922\) | 176.421i | 0.191346i | ||||||||
\(923\) | −692.592 | −0.750371 | ||||||||
\(924\) | 573.737 | + | 113.286i | 0.620927 | + | 0.122604i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 947.132i | 1.02282i | ||||||||
\(927\) | −25.9712 | + | 63.2014i | −0.0280164 | + | 0.0681785i | ||||
\(928\) | 151.789i | 0.163566i | ||||||||
\(929\) | 1025.96i | 1.10437i | 0.833723 | + | 0.552183i | \(0.186205\pi\) | ||||
−0.833723 | + | 0.552183i | \(0.813795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −910.236 | −0.977697 | ||||||||
\(932\) | −371.752 | −0.398875 | ||||||||
\(933\) | −83.1588 | + | 421.157i | −0.0891305 | + | 0.451401i | ||||
\(934\) | −688.552 | −0.737208 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 96.7544 | − | 235.454i | 0.103370 | − | 0.251553i | ||||
\(937\) | 332.053i | 0.354379i | 0.984177 | + | 0.177189i | \(0.0567005\pi\) | ||||
−0.984177 | + | 0.177189i | \(0.943300\pi\) | |||||||
\(938\) | 869.740 | 0.927229 | ||||||||
\(939\) | −291.548 | + | 1476.54i | −0.310488 | + | 1.57246i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1636.99i | 1.73963i | 0.493381 | + | 0.869813i | \(0.335761\pi\) | ||||
−0.493381 | + | 0.869813i | \(0.664239\pi\) | |||||||
\(942\) | 101.780 | − | 515.465i | 0.108047 | − | 0.547203i | ||||
\(943\) | 362.447i | 0.384355i | ||||||||
\(944\) | − | 310.978i | − | 0.329426i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 509.526 | 0.538611 | ||||||||
\(947\) | 1209.32 | 1.27700 | 0.638500 | − | 0.769622i | \(-0.279555\pi\) | ||||
0.638500 | + | 0.769622i | \(0.279555\pi\) | |||||||
\(948\) | −53.1322 | − | 10.4911i | −0.0560466 | − | 0.0110666i | ||||
\(949\) | 120.527 | 0.127004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −983.776 | − | 194.250i | −1.03446 | − | 0.204258i | ||||
\(952\) | − | 115.473i | − | 0.121296i | ||||||
\(953\) | 1205.26 | 1.26470 | 0.632352 | − | 0.774681i | \(-0.282090\pi\) | ||||
0.632352 | + | 0.774681i | \(0.282090\pi\) | |||||||
\(954\) | −41.8420 | − | 17.1940i | −0.0438595 | − | 0.0180231i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 605.432i | − | 0.633297i | ||||||
\(957\) | −670.114 | − | 132.316i | −0.700223 | − | 0.138261i | ||||
\(958\) | 736.211i | 0.768487i | ||||||||
\(959\) | 2021.84i | 2.10828i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −897.000 | −0.933403 | ||||||||
\(962\) | 847.783 | 0.881272 | ||||||||
\(963\) | 135.541 | + | 55.6975i | 0.140749 | + | 0.0578375i | ||||
\(964\) | −475.052 | −0.492793 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 166.710 | − | 844.304i | 0.172578 | − | 0.874020i | ||||
\(967\) | 1845.93i | 1.90893i | 0.298325 | + | 0.954464i | \(0.403572\pi\) | ||||
−0.298325 | + | 0.954464i | \(0.596428\pi\) | |||||||
\(968\) | 138.593 | 0.143175 | ||||||||
\(969\) | −114.790 | − | 22.6656i | −0.118462 | − | 0.0233908i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1057.91i | 1.08950i | 0.838598 | + | 0.544751i | \(0.183376\pi\) | ||||
−0.838598 | + | 0.544751i | \(0.816624\pi\) | |||||||
\(972\) | −272.838 | − | 402.189i | −0.280697 | − | 0.413774i | ||||
\(973\) | 2168.89i | 2.22908i | ||||||||
\(974\) | 372.478i | 0.382421i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 87.7893 | 0.0899481 | ||||||||
\(977\) | −964.028 | −0.986722 | −0.493361 | − | 0.869825i | \(-0.664232\pi\) | ||||
−0.493361 | + | 0.869825i | \(0.664232\pi\) | |||||||
\(978\) | 130.988 | − | 663.390i | 0.133935 | − | 0.678313i | ||||
\(979\) | 60.3160 | 0.0616098 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 781.193 | + | 321.013i | 0.796323 | + | 0.327231i | ||||
\(982\) | 1006.42i | 1.02487i | ||||||||
\(983\) | −460.718 | −0.468685 | −0.234343 | − | 0.972154i | \(-0.575294\pi\) | ||||
−0.234343 | + | 0.972154i | \(0.575294\pi\) | |||||||
\(984\) | −33.7367 | + | 170.859i | −0.0342852 | + | 0.173637i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 134.871i | 0.136786i | ||||||||
\(987\) | −589.410 | + | 2985.06i | −0.597173 | + | 3.02438i | ||||
\(988\) | − | 219.473i | − | 0.222139i | ||||||
\(989\) | − | 749.812i | − | 0.758152i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1237.89 | 1.24914 | 0.624568 | − | 0.780971i | \(-0.285275\pi\) | ||||
0.624568 | + | 0.780971i | \(0.285275\pi\) | |||||||
\(992\) | 45.2548 | 0.0456198 | ||||||||
\(993\) | −1146.13 | − | 226.307i | −1.15421 | − | 0.227903i | ||||
\(994\) | −1125.10 | −1.13190 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.05267 | + | 0.800212i | 0.00406894 | + | 0.000803425i | ||||
\(997\) | 9.36798i | 0.00939617i | 0.999989 | + | 0.00469809i | \(0.00149545\pi\) | ||||
−0.999989 | + | 0.00469809i | \(0.998505\pi\) | |||||||
\(998\) | −32.6386 | −0.0327040 | ||||||||
\(999\) | 893.557 | − | 1349.57i | 0.894451 | − | 1.35093i |
(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 | 150.3.b.b.149.5 | 8 | ||
3.2 | odd | 2 | inner | 150.3.b.b.149.3 | 8 | ||
4.3 | odd | 2 | 1200.3.c.k.449.8 | 8 | |||
5.2 | odd | 4 | 30.3.d.a.11.3 | yes | 4 | ||
5.3 | odd | 4 | 150.3.d.c.101.2 | 4 | |||
5.4 | even | 2 | inner | 150.3.b.b.149.4 | 8 | ||
12.11 | even | 2 | 1200.3.c.k.449.2 | 8 | |||
15.2 | even | 4 | 30.3.d.a.11.1 | ✓ | 4 | ||
15.8 | even | 4 | 150.3.d.c.101.4 | 4 | |||
15.14 | odd | 2 | inner | 150.3.b.b.149.6 | 8 | ||
20.3 | even | 4 | 1200.3.l.u.401.2 | 4 | |||
20.7 | even | 4 | 240.3.l.c.161.3 | 4 | |||
20.19 | odd | 2 | 1200.3.c.k.449.1 | 8 | |||
40.27 | even | 4 | 960.3.l.f.641.2 | 4 | |||
40.37 | odd | 4 | 960.3.l.e.641.3 | 4 | |||
45.2 | even | 12 | 810.3.h.a.701.1 | 8 | |||
45.7 | odd | 12 | 810.3.h.a.701.4 | 8 | |||
45.22 | odd | 12 | 810.3.h.a.431.1 | 8 | |||
45.32 | even | 12 | 810.3.h.a.431.4 | 8 | |||
60.23 | odd | 4 | 1200.3.l.u.401.1 | 4 | |||
60.47 | odd | 4 | 240.3.l.c.161.4 | 4 | |||
60.59 | even | 2 | 1200.3.c.k.449.7 | 8 | |||
120.77 | even | 4 | 960.3.l.e.641.4 | 4 | |||
120.107 | odd | 4 | 960.3.l.f.641.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.3.d.a.11.1 | ✓ | 4 | 15.2 | even | 4 | ||
30.3.d.a.11.3 | yes | 4 | 5.2 | odd | 4 | ||
150.3.b.b.149.3 | 8 | 3.2 | odd | 2 | inner | ||
150.3.b.b.149.4 | 8 | 5.4 | even | 2 | inner | ||
150.3.b.b.149.5 | 8 | 1.1 | even | 1 | trivial | ||
150.3.b.b.149.6 | 8 | 15.14 | odd | 2 | inner | ||
150.3.d.c.101.2 | 4 | 5.3 | odd | 4 | |||
150.3.d.c.101.4 | 4 | 15.8 | even | 4 | |||
240.3.l.c.161.3 | 4 | 20.7 | even | 4 | |||
240.3.l.c.161.4 | 4 | 60.47 | odd | 4 | |||
810.3.h.a.431.1 | 8 | 45.22 | odd | 12 | |||
810.3.h.a.431.4 | 8 | 45.32 | even | 12 | |||
810.3.h.a.701.1 | 8 | 45.2 | even | 12 | |||
810.3.h.a.701.4 | 8 | 45.7 | odd | 12 | |||
960.3.l.e.641.3 | 4 | 40.37 | odd | 4 | |||
960.3.l.e.641.4 | 4 | 120.77 | even | 4 | |||
960.3.l.f.641.1 | 4 | 120.107 | odd | 4 | |||
960.3.l.f.641.2 | 4 | 40.27 | even | 4 | |||
1200.3.c.k.449.1 | 8 | 20.19 | odd | 2 | |||
1200.3.c.k.449.2 | 8 | 12.11 | even | 2 | |||
1200.3.c.k.449.7 | 8 | 60.59 | even | 2 | |||
1200.3.c.k.449.8 | 8 | 4.3 | odd | 2 | |||
1200.3.l.u.401.1 | 4 | 60.23 | odd | 4 | |||
1200.3.l.u.401.2 | 4 | 20.3 | even | 4 |