Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), 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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.g.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 3.00000 | − | 5.19615i | 0.268328 | − | 0.464758i | −0.700102 | − | 0.714043i | \(-0.746862\pi\) |
0.968430 | + | 0.249285i | \(0.0801955\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | + | 10.3923i | 0.189737 | + | 0.328634i | ||||
\(11\) | −15.0000 | − | 25.9808i | −0.411152 | − | 0.712136i | 0.583864 | − | 0.811851i | \(-0.301540\pi\) |
−0.995016 | + | 0.0997155i | \(0.968207\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −53.0000 | −1.13074 | −0.565368 | − | 0.824839i | \(-0.691266\pi\) | ||||
−0.565368 | + | 0.824839i | \(0.691266\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 42.0000 | + | 72.7461i | 0.599206 | + | 1.03785i | 0.992939 | + | 0.118630i | \(0.0378502\pi\) |
−0.393733 | + | 0.919225i | \(0.628817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −48.5000 | + | 84.0045i | −0.585614 | + | 1.01431i | 0.409185 | + | 0.912452i | \(0.365813\pi\) |
−0.994799 | + | 0.101861i | \(0.967520\pi\) | |||||||
\(20\) | −24.0000 | −0.268328 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.0000 | 0.581456 | ||||||||
\(23\) | 42.0000 | − | 72.7461i | 0.380765 | − | 0.659505i | −0.610406 | − | 0.792088i | \(-0.708994\pi\) |
0.991172 | + | 0.132583i | \(0.0423272\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.5000 | + | 77.0763i | 0.356000 | + | 0.616610i | ||||
\(26\) | 53.0000 | − | 91.7987i | 0.399775 | − | 0.692431i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 180.000 | 1.15259 | 0.576296 | − | 0.817241i | \(-0.304498\pi\) | ||||
0.576296 | + | 0.817241i | \(0.304498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 89.5000 | + | 155.019i | 0.518538 | + | 0.898134i | 0.999768 | + | 0.0215397i | \(0.00685682\pi\) |
−0.481230 | + | 0.876594i | \(0.659810\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −168.000 | −0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 72.5000 | − | 125.574i | 0.322133 | − | 0.557951i | −0.658795 | − | 0.752323i | \(-0.728933\pi\) |
0.980928 | + | 0.194372i | \(0.0622668\pi\) | |||||||
\(38\) | −97.0000 | − | 168.009i | −0.414092 | − | 0.717228i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.0000 | − | 41.5692i | 0.0948683 | − | 0.164317i | ||||
\(41\) | 126.000 | 0.479949 | 0.239974 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239974 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −325.000 | −1.15261 | −0.576303 | − | 0.817236i | \(-0.695505\pi\) | ||||
−0.576303 | + | 0.817236i | \(0.695505\pi\) | |||||||
\(44\) | −60.0000 | + | 103.923i | −0.205576 | + | 0.356068i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 84.0000 | + | 145.492i | 0.269242 | + | 0.466341i | ||||
\(47\) | 183.000 | − | 316.965i | 0.567942 | − | 0.983705i | −0.428827 | − | 0.903387i | \(-0.641073\pi\) |
0.996769 | − | 0.0803184i | \(-0.0255937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −178.000 | −0.503460 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 106.000 | + | 183.597i | 0.282684 | + | 0.489623i | ||||
\(53\) | −384.000 | − | 665.108i | −0.995216 | − | 1.72376i | −0.582217 | − | 0.813034i | \(-0.697814\pi\) |
−0.413000 | − | 0.910731i | \(-0.635519\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −180.000 | −0.441294 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −180.000 | + | 311.769i | −0.407503 | + | 0.705815i | ||||
\(59\) | 132.000 | + | 228.631i | 0.291270 | + | 0.504495i | 0.974110 | − | 0.226073i | \(-0.0725888\pi\) |
−0.682840 | + | 0.730568i | \(0.739255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 409.000 | − | 708.409i | 0.858477 | − | 1.48693i | −0.0149048 | − | 0.999889i | \(-0.504745\pi\) |
0.873382 | − | 0.487036i | \(-0.161922\pi\) | |||||||
\(62\) | −358.000 | −0.733323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −159.000 | + | 275.396i | −0.303408 | + | 0.525518i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 261.500 | + | 452.931i | 0.476826 | + | 0.825886i | 0.999647 | − | 0.0265560i | \(-0.00845402\pi\) |
−0.522822 | + | 0.852442i | \(0.675121\pi\) | |||||||
\(68\) | 168.000 | − | 290.985i | 0.299603 | − | 0.518927i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 342.000 | 0.571661 | 0.285831 | − | 0.958280i | \(-0.407731\pi\) | ||||
0.285831 | + | 0.958280i | \(0.407731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.5000 | − | 37.2391i | −0.0344710 | − | 0.0597056i | 0.848275 | − | 0.529556i | \(-0.177641\pi\) |
−0.882746 | + | 0.469850i | \(0.844308\pi\) | |||||||
\(74\) | 145.000 | + | 251.147i | 0.227783 | + | 0.394531i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 388.000 | 0.585614 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 585.500 | − | 1014.12i | 0.833847 | − | 1.44427i | −0.0611191 | − | 0.998130i | \(-0.519467\pi\) |
0.894966 | − | 0.446135i | \(-0.147200\pi\) | |||||||
\(80\) | 48.0000 | + | 83.1384i | 0.0670820 | + | 0.116190i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −126.000 | + | 218.238i | −0.169687 | + | 0.293907i | ||||
\(83\) | −810.000 | −1.07119 | −0.535597 | − | 0.844474i | \(-0.679913\pi\) | ||||
−0.535597 | + | 0.844474i | \(0.679913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 504.000 | 0.643135 | ||||||||
\(86\) | 325.000 | − | 562.917i | 0.407508 | − | 0.705824i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −120.000 | − | 207.846i | −0.145364 | − | 0.251778i | ||||
\(89\) | 300.000 | − | 519.615i | 0.357303 | − | 0.618866i | −0.630207 | − | 0.776428i | \(-0.717030\pi\) |
0.987509 | + | 0.157561i | \(0.0503631\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −336.000 | −0.380765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 366.000 | + | 633.931i | 0.401596 | + | 0.695585i | ||||
\(95\) | 291.000 | + | 504.027i | 0.314273 | + | 0.544337i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −386.000 | −0.404045 | −0.202022 | − | 0.979381i | \(-0.564751\pi\) | ||||
−0.202022 | + | 0.979381i | \(0.564751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 178.000 | − | 308.305i | 0.178000 | − | 0.308305i | ||||
\(101\) | −309.000 | − | 535.204i | −0.304422 | − | 0.527275i | 0.672710 | − | 0.739906i | \(-0.265130\pi\) |
−0.977133 | + | 0.212631i | \(0.931797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 737.500 | − | 1277.39i | 0.705515 | − | 1.22199i | −0.260991 | − | 0.965341i | \(-0.584049\pi\) |
0.966505 | − | 0.256646i | \(-0.0826175\pi\) | |||||||
\(104\) | −424.000 | −0.399775 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1536.00 | 1.40745 | ||||||||
\(107\) | 942.000 | − | 1631.59i | 0.851090 | − | 1.47413i | −0.0291364 | − | 0.999575i | \(-0.509276\pi\) |
0.880226 | − | 0.474555i | \(-0.157391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −206.500 | − | 357.668i | −0.181460 | − | 0.314298i | 0.760918 | − | 0.648848i | \(-0.224749\pi\) |
−0.942378 | + | 0.334550i | \(0.891416\pi\) | |||||||
\(110\) | 180.000 | − | 311.769i | 0.156021 | − | 0.270237i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 882.000 | 0.734262 | 0.367131 | − | 0.930169i | \(-0.380340\pi\) | ||||
0.367131 | + | 0.930169i | \(0.380340\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −252.000 | − | 436.477i | −0.204340 | − | 0.353928i | ||||
\(116\) | −360.000 | − | 623.538i | −0.288148 | − | 0.499087i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −528.000 | −0.411918 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 215.500 | − | 373.257i | 0.161908 | − | 0.280433i | ||||
\(122\) | 818.000 | + | 1416.82i | 0.607035 | + | 1.05142i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 358.000 | − | 620.074i | 0.259269 | − | 0.449067i | ||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2483.00 | 1.73489 | 0.867443 | − | 0.497536i | \(-0.165762\pi\) | ||||
0.867443 | + | 0.497536i | \(0.165762\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −318.000 | − | 550.792i | −0.214542 | − | 0.371597i | ||||
\(131\) | −1059.00 | + | 1834.24i | −0.706300 | + | 1.22335i | 0.259921 | + | 0.965630i | \(0.416304\pi\) |
−0.966220 | + | 0.257717i | \(0.917030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1046.00 | −0.674333 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 336.000 | + | 581.969i | 0.211851 | + | 0.366937i | ||||
\(137\) | 1506.00 | + | 2608.47i | 0.939170 | + | 1.62669i | 0.767024 | + | 0.641618i | \(0.221737\pi\) |
0.172146 | + | 0.985071i | \(0.444930\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37.0000 | 0.0225777 | 0.0112888 | − | 0.999936i | \(-0.496407\pi\) | ||||
0.0112888 | + | 0.999936i | \(0.496407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −342.000 | + | 592.361i | −0.202113 | + | 0.350069i | ||||
\(143\) | 795.000 | + | 1376.98i | 0.464904 | + | 0.805237i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 540.000 | − | 935.307i | 0.309273 | − | 0.535676i | ||||
\(146\) | 86.0000 | 0.0487494 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −580.000 | −0.322133 | ||||||||
\(149\) | −822.000 | + | 1423.75i | −0.451952 | + | 0.782804i | −0.998507 | − | 0.0546191i | \(-0.982606\pi\) |
0.546555 | + | 0.837423i | \(0.315939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −544.000 | − | 942.236i | −0.293179 | − | 0.507802i | 0.681380 | − | 0.731930i | \(-0.261380\pi\) |
−0.974560 | + | 0.224128i | \(0.928047\pi\) | |||||||
\(152\) | −388.000 | + | 672.036i | −0.207046 | + | 0.358614i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1074.00 | 0.556553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 253.000 | + | 438.209i | 0.128609 | + | 0.222757i | 0.923138 | − | 0.384469i | \(-0.125615\pi\) |
−0.794529 | + | 0.607226i | \(0.792282\pi\) | |||||||
\(158\) | 1171.00 | + | 2028.23i | 0.589619 | + | 1.02125i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −192.000 | −0.0948683 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −922.000 | + | 1596.95i | −0.443047 | + | 0.767379i | −0.997914 | − | 0.0645596i | \(-0.979436\pi\) |
0.554867 | + | 0.831939i | \(0.312769\pi\) | |||||||
\(164\) | −252.000 | − | 436.477i | −0.119987 | − | 0.207824i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 810.000 | − | 1402.96i | 0.378724 | − | 0.655969i | ||||
\(167\) | 162.000 | 0.0750655 | 0.0375327 | − | 0.999295i | \(-0.488050\pi\) | ||||
0.0375327 | + | 0.999295i | \(0.488050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 612.000 | 0.278562 | ||||||||
\(170\) | −504.000 | + | 872.954i | −0.227383 | + | 0.393838i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 650.000 | + | 1125.83i | 0.288151 | + | 0.499093i | ||||
\(173\) | 1362.00 | − | 2359.05i | 0.598560 | − | 1.03674i | −0.394473 | − | 0.918907i | \(-0.629073\pi\) |
0.993034 | − | 0.117830i | \(-0.0375937\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 480.000 | 0.205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 600.000 | + | 1039.23i | 0.252651 | + | 0.437605i | ||||
\(179\) | −627.000 | − | 1086.00i | −0.261811 | − | 0.453470i | 0.704912 | − | 0.709295i | \(-0.250986\pi\) |
−0.966723 | + | 0.255825i | \(0.917653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1807.00 | 0.742062 | 0.371031 | − | 0.928620i | \(-0.379004\pi\) | ||||
0.371031 | + | 0.928620i | \(0.379004\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 336.000 | − | 581.969i | 0.134621 | − | 0.233170i | ||||
\(185\) | −435.000 | − | 753.442i | −0.172875 | − | 0.299428i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1260.00 | − | 2182.38i | 0.492729 | − | 0.853432i | ||||
\(188\) | −1464.00 | −0.567942 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1164.00 | −0.444450 | ||||||||
\(191\) | 357.000 | − | 618.342i | 0.135244 | − | 0.234250i | −0.790447 | − | 0.612531i | \(-0.790151\pi\) |
0.925691 | + | 0.378281i | \(0.123485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1854.50 | + | 3212.09i | 0.691657 | + | 1.19799i | 0.971295 | + | 0.237880i | \(0.0764524\pi\) |
−0.279637 | + | 0.960106i | \(0.590214\pi\) | |||||||
\(194\) | 386.000 | − | 668.572i | 0.142851 | − | 0.247426i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1044.00 | 0.377573 | 0.188787 | − | 0.982018i | \(-0.439545\pi\) | ||||
0.188787 | + | 0.982018i | \(0.439545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −68.0000 | − | 117.779i | −0.0242231 | − | 0.0419556i | 0.853660 | − | 0.520831i | \(-0.174378\pi\) |
−0.877883 | + | 0.478875i | \(0.841045\pi\) | |||||||
\(200\) | 356.000 | + | 616.610i | 0.125865 | + | 0.218005i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1236.00 | 0.430518 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 378.000 | − | 654.715i | 0.128784 | − | 0.223060i | ||||
\(206\) | 1475.00 | + | 2554.77i | 0.498874 | + | 0.864076i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 424.000 | − | 734.390i | 0.141342 | − | 0.244811i | ||||
\(209\) | 2910.00 | 0.963105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1484.00 | 0.484184 | 0.242092 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242092 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(212\) | −1536.00 | + | 2660.43i | −0.497608 | + | 0.861882i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1884.00 | + | 3263.18i | 0.601811 | + | 1.04237i | ||||
\(215\) | −975.000 | + | 1688.75i | −0.309277 | + | 0.535683i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 826.000 | 0.256623 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 360.000 | + | 623.538i | 0.110324 | + | 0.191086i | ||||
\(221\) | −2226.00 | − | 3855.55i | −0.677543 | − | 1.17354i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2032.00 | 0.610192 | 0.305096 | − | 0.952322i | \(-0.401311\pi\) | ||||
0.305096 | + | 0.952322i | \(0.401311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −882.000 | + | 1527.67i | −0.259601 | + | 0.449642i | ||||
\(227\) | −3099.00 | − | 5367.63i | −0.906114 | − | 1.56944i | −0.819415 | − | 0.573201i | \(-0.805702\pi\) |
−0.0866989 | − | 0.996235i | \(-0.527632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2295.50 | + | 3975.92i | −0.662406 | + | 1.14732i | 0.317576 | + | 0.948233i | \(0.397131\pi\) |
−0.979982 | + | 0.199088i | \(0.936202\pi\) | |||||||
\(230\) | 1008.00 | 0.288981 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1440.00 | 0.407503 | ||||||||
\(233\) | 2265.00 | − | 3923.10i | 0.636846 | − | 1.10305i | −0.349275 | − | 0.937020i | \(-0.613572\pi\) |
0.986121 | − | 0.166029i | \(-0.0530946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1098.00 | − | 1901.79i | −0.304790 | − | 0.527912i | ||||
\(236\) | 528.000 | − | 914.523i | 0.145635 | − | 0.252247i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1530.00 | −0.414090 | −0.207045 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207045 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2767.00 | + | 4792.58i | 0.739577 | + | 1.28099i | 0.952686 | + | 0.303957i | \(0.0983079\pi\) |
−0.213108 | + | 0.977029i | \(0.568359\pi\) | |||||||
\(242\) | 431.000 | + | 746.514i | 0.114486 | + | 0.198296i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3272.00 | −0.858477 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2570.50 | − | 4452.24i | 0.662174 | − | 1.14692i | ||||
\(248\) | 716.000 | + | 1240.15i | 0.183331 | + | 0.317538i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1284.00 | + | 2223.95i | −0.324829 | + | 0.562621i | ||||
\(251\) | −468.000 | −0.117689 | −0.0588444 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588444 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2520.00 | −0.626210 | ||||||||
\(254\) | −2483.00 | + | 4300.68i | −0.613375 | + | 1.06240i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1245.00 | − | 2156.40i | 0.302183 | − | 0.523396i | −0.674447 | − | 0.738323i | \(-0.735618\pi\) |
0.976630 | + | 0.214927i | \(0.0689514\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1272.00 | 0.303408 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2118.00 | − | 3668.48i | −0.499429 | − | 0.865037i | ||||
\(263\) | 786.000 | + | 1361.39i | 0.184285 | + | 0.319190i | 0.943335 | − | 0.331841i | \(-0.107670\pi\) |
−0.759051 | + | 0.651032i | \(0.774337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4608.00 | −1.06818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1046.00 | − | 1811.73i | 0.238413 | − | 0.412943i | ||||
\(269\) | −903.000 | − | 1564.04i | −0.204672 | − | 0.354503i | 0.745356 | − | 0.666667i | \(-0.232280\pi\) |
−0.950028 | + | 0.312164i | \(0.898946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3056.00 | + | 5293.15i | −0.685014 | + | 1.18648i | 0.288418 | + | 0.957504i | \(0.406871\pi\) |
−0.973432 | + | 0.228975i | \(0.926463\pi\) | |||||||
\(272\) | −1344.00 | −0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6024.00 | −1.32819 | ||||||||
\(275\) | 1335.00 | − | 2312.29i | 0.292740 | − | 0.507041i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2115.50 | + | 3664.15i | 0.458874 | + | 0.794793i | 0.998902 | − | 0.0468542i | \(-0.0149196\pi\) |
−0.540028 | + | 0.841647i | \(0.681586\pi\) | |||||||
\(278\) | −37.0000 | + | 64.0859i | −0.00798242 | + | 0.0138260i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3816.00 | 0.810119 | 0.405060 | − | 0.914290i | \(-0.367251\pi\) | ||||
0.405060 | + | 0.914290i | \(0.367251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1998.50 | − | 3461.50i | −0.419783 | − | 0.727085i | 0.576135 | − | 0.817355i | \(-0.304560\pi\) |
−0.995917 | + | 0.0902699i | \(0.971227\pi\) | |||||||
\(284\) | −684.000 | − | 1184.72i | −0.142915 | − | 0.247536i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3180.00 | −0.657473 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | 1080.00 | + | 1870.61i | 0.218689 | + | 0.378780i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −86.0000 | + | 148.956i | −0.0172355 | + | 0.0298528i | ||||
\(293\) | 4608.00 | 0.918779 | 0.459389 | − | 0.888235i | \(-0.348068\pi\) | ||||
0.459389 | + | 0.888235i | \(0.348068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1584.00 | 0.312624 | ||||||||
\(296\) | 580.000 | − | 1004.59i | 0.113891 | − | 0.197265i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1644.00 | − | 2847.49i | −0.319578 | − | 0.553526i | ||||
\(299\) | −2226.00 | + | 3855.55i | −0.430545 | + | 0.745726i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2176.00 | 0.414618 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −776.000 | − | 1344.07i | −0.146403 | − | 0.253578i | ||||
\(305\) | −2454.00 | − | 4250.45i | −0.460707 | − | 0.797968i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 631.000 | 0.117306 | 0.0586532 | − | 0.998278i | \(-0.481319\pi\) | ||||
0.0586532 | + | 0.998278i | \(0.481319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1074.00 | + | 1860.22i | −0.196771 | + | 0.340818i | ||||
\(311\) | −1947.00 | − | 3372.30i | −0.354998 | − | 0.614874i | 0.632120 | − | 0.774871i | \(-0.282185\pi\) |
−0.987118 | + | 0.159997i | \(0.948852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1092.50 | + | 1892.27i | −0.197290 | + | 0.341716i | −0.947649 | − | 0.319314i | \(-0.896547\pi\) |
0.750359 | + | 0.661031i | \(0.229881\pi\) | |||||||
\(314\) | −1012.00 | −0.181880 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4684.00 | −0.833847 | ||||||||
\(317\) | 1752.00 | − | 3034.55i | 0.310417 | − | 0.537658i | −0.668036 | − | 0.744129i | \(-0.732865\pi\) |
0.978453 | + | 0.206471i | \(0.0661981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2700.00 | − | 4676.54i | −0.473890 | − | 0.820802i | ||||
\(320\) | 192.000 | − | 332.554i | 0.0335410 | − | 0.0580948i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8148.00 | −1.40361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2358.50 | − | 4085.04i | −0.402542 | − | 0.697223i | ||||
\(326\) | −1844.00 | − | 3193.90i | −0.313281 | − | 0.542619i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1008.00 | 0.169687 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1472.50 | + | 2550.44i | −0.244519 | + | 0.423520i | −0.961996 | − | 0.273062i | \(-0.911964\pi\) |
0.717477 | + | 0.696582i | \(0.245297\pi\) | |||||||
\(332\) | 1620.00 | + | 2805.92i | 0.267798 | + | 0.463840i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −162.000 | + | 280.592i | −0.0265397 | + | 0.0459680i | ||||
\(335\) | 3138.00 | 0.511783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4277.00 | 0.691344 | 0.345672 | − | 0.938355i | \(-0.387651\pi\) | ||||
0.345672 | + | 0.938355i | \(0.387651\pi\) | |||||||
\(338\) | −612.000 | + | 1060.02i | −0.0984864 | + | 0.170583i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1008.00 | − | 1745.91i | −0.160784 | − | 0.278486i | ||||
\(341\) | 2685.00 | − | 4650.56i | 0.426396 | − | 0.738539i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2600.00 | −0.407508 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2724.00 | + | 4718.11i | 0.423246 | + | 0.733084i | ||||
\(347\) | 3594.00 | + | 6224.99i | 0.556012 | + | 0.963040i | 0.997824 | + | 0.0659329i | \(0.0210023\pi\) |
−0.441812 | + | 0.897107i | \(0.645664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9406.00 | 1.44267 | 0.721335 | − | 0.692587i | \(-0.243529\pi\) | ||||
0.721335 | + | 0.692587i | \(0.243529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −480.000 | + | 831.384i | −0.0726821 | + | 0.125889i | ||||
\(353\) | −1695.00 | − | 2935.83i | −0.255569 | − | 0.442658i | 0.709481 | − | 0.704724i | \(-0.248929\pi\) |
−0.965050 | + | 0.262066i | \(0.915596\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1026.00 | − | 1777.08i | 0.153393 | − | 0.265684i | ||||
\(356\) | −2400.00 | −0.357303 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2508.00 | 0.370257 | ||||||||
\(359\) | −2406.00 | + | 4167.31i | −0.353715 | + | 0.612653i | −0.986897 | − | 0.161350i | \(-0.948415\pi\) |
0.633182 | + | 0.774003i | \(0.281749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1275.00 | − | 2208.36i | −0.185887 | − | 0.321966i | ||||
\(362\) | −1807.00 | + | 3129.82i | −0.262359 | + | 0.454418i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −258.000 | −0.0369982 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3549.50 | − | 6147.91i | −0.504857 | − | 0.874437i | −0.999984 | − | 0.00561709i | \(-0.998212\pi\) |
0.495128 | − | 0.868820i | \(-0.335121\pi\) | |||||||
\(368\) | 672.000 | + | 1163.94i | 0.0951914 | + | 0.164876i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1740.00 | 0.244482 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1481.50 | + | 2566.03i | −0.205655 | + | 0.356204i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) |
0.744687 | + | 0.667414i | \(0.232599\pi\) | |||||||
\(374\) | 2520.00 | + | 4364.77i | 0.348412 | + | 0.603467i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1464.00 | − | 2535.72i | 0.200798 | − | 0.347792i | ||||
\(377\) | −9540.00 | −1.30328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11899.0 | −1.61269 | −0.806346 | − | 0.591444i | \(-0.798558\pi\) | ||||
−0.806346 | + | 0.591444i | \(0.798558\pi\) | |||||||
\(380\) | 1164.00 | − | 2016.11i | 0.157137 | − | 0.272169i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 714.000 | + | 1236.68i | 0.0956320 | + | 0.165639i | ||||
\(383\) | −1284.00 | + | 2223.95i | −0.171304 | + | 0.296707i | −0.938876 | − | 0.344256i | \(-0.888131\pi\) |
0.767572 | + | 0.640963i | \(0.221465\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7418.00 | −0.978151 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 772.000 | + | 1337.14i | 0.101011 | + | 0.174957i | ||||
\(389\) | −5073.00 | − | 8786.69i | −0.661212 | − | 1.14525i | −0.980298 | − | 0.197526i | \(-0.936709\pi\) |
0.319086 | − | 0.947726i | \(-0.396624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1044.00 | + | 1808.26i | −0.133492 | + | 0.231215i | ||||
\(395\) | −3513.00 | − | 6084.69i | −0.447489 | − | 0.775074i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3114.50 | + | 5394.47i | −0.393734 | + | 0.681967i | −0.992939 | − | 0.118629i | \(-0.962150\pi\) |
0.599205 | + | 0.800596i | \(0.295483\pi\) | |||||||
\(398\) | 272.000 | 0.0342566 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1424.00 | −0.178000 | ||||||||
\(401\) | −1236.00 | + | 2140.81i | −0.153922 | + | 0.266601i | −0.932666 | − | 0.360741i | \(-0.882524\pi\) |
0.778744 | + | 0.627342i | \(0.215857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4743.50 | − | 8215.98i | −0.586329 | − | 1.01555i | ||||
\(404\) | −1236.00 | + | 2140.81i | −0.152211 | + | 0.263637i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4350.00 | −0.529783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3537.50 | − | 6127.13i | −0.427673 | − | 0.740751i | 0.568993 | − | 0.822342i | \(-0.307333\pi\) |
−0.996666 | + | 0.0815915i | \(0.974000\pi\) | |||||||
\(410\) | 756.000 | + | 1309.43i | 0.0910639 | + | 0.157727i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5900.00 | −0.705515 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2430.00 | + | 4208.88i | −0.287431 | + | 0.497846i | ||||
\(416\) | 848.000 | + | 1468.78i | 0.0999438 | + | 0.173108i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2910.00 | + | 5040.27i | −0.340509 | + | 0.589779i | ||||
\(419\) | −4158.00 | −0.484801 | −0.242400 | − | 0.970176i | \(-0.577935\pi\) | ||||
−0.242400 | + | 0.970176i | \(0.577935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6595.00 | −0.763469 | −0.381735 | − | 0.924272i | \(-0.624673\pi\) | ||||
−0.381735 | + | 0.924272i | \(0.624673\pi\) | |||||||
\(422\) | −1484.00 | + | 2570.36i | −0.171185 | + | 0.296501i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3072.00 | − | 5320.86i | −0.351862 | − | 0.609443i | ||||
\(425\) | −3738.00 | + | 6474.41i | −0.426634 | + | 0.738953i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7536.00 | −0.851090 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1950.00 | − | 3377.50i | −0.218692 | − | 0.378785i | ||||
\(431\) | 759.000 | + | 1314.63i | 0.0848254 | + | 0.146922i | 0.905317 | − | 0.424737i | \(-0.139633\pi\) |
−0.820491 | + | 0.571659i | \(0.806300\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8567.00 | −0.950817 | −0.475408 | − | 0.879765i | \(-0.657700\pi\) | ||||
−0.475408 | + | 0.879765i | \(0.657700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −826.000 | + | 1430.67i | −0.0907299 | + | 0.157149i | ||||
\(437\) | 4074.00 | + | 7056.37i | 0.445963 | + | 0.772431i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5320.00 | − | 9214.51i | 0.578382 | − | 1.00179i | −0.417283 | − | 0.908777i | \(-0.637018\pi\) |
0.995665 | − | 0.0930106i | \(-0.0296491\pi\) | |||||||
\(440\) | −1440.00 | −0.156021 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8904.00 | 0.958190 | ||||||||
\(443\) | 3516.00 | − | 6089.89i | 0.377088 | − | 0.653136i | −0.613549 | − | 0.789657i | \(-0.710259\pi\) |
0.990637 | + | 0.136520i | \(0.0435919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1800.00 | − | 3117.69i | −0.191749 | − | 0.332119i | ||||
\(446\) | −2032.00 | + | 3519.53i | −0.215735 | + | 0.373665i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14814.0 | 1.55705 | 0.778525 | − | 0.627613i | \(-0.215968\pi\) | ||||
0.778525 | + | 0.627613i | \(0.215968\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1890.00 | − | 3273.58i | −0.197332 | − | 0.341789i | ||||
\(452\) | −1764.00 | − | 3055.34i | −0.183565 | − | 0.317945i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12396.0 | 1.28144 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5625.50 | − | 9743.65i | 0.575820 | − | 0.997350i | −0.420132 | − | 0.907463i | \(-0.638016\pi\) |
0.995952 | − | 0.0898866i | \(-0.0286505\pi\) | |||||||
\(458\) | −4591.00 | − | 7951.85i | −0.468392 | − | 0.811278i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1008.00 | + | 1745.91i | −0.102170 | + | 0.176964i | ||||
\(461\) | −3852.00 | −0.389166 | −0.194583 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194583 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −475.000 | −0.0476784 | −0.0238392 | − | 0.999716i | \(-0.507589\pi\) | ||||
−0.0238392 | + | 0.999716i | \(0.507589\pi\) | |||||||
\(464\) | −1440.00 | + | 2494.15i | −0.144074 | + | 0.249543i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4530.00 | + | 7846.19i | 0.450318 | + | 0.779974i | ||||
\(467\) | −2967.00 | + | 5138.99i | −0.293997 | + | 0.509217i | −0.974751 | − | 0.223295i | \(-0.928319\pi\) |
0.680754 | + | 0.732512i | \(0.261652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4392.00 | 0.431038 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1056.00 | + | 1829.05i | 0.102980 | + | 0.178366i | ||||
\(473\) | 4875.00 | + | 8443.75i | 0.473896 | + | 0.820812i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8633.00 | −0.833914 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1530.00 | − | 2650.04i | 0.146403 | − | 0.253577i | ||||
\(479\) | 6684.00 | + | 11577.0i | 0.637578 | + | 1.10432i | 0.985963 | + | 0.166966i | \(0.0533969\pi\) |
−0.348385 | + | 0.937352i | \(0.613270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3842.50 | + | 6655.41i | −0.364247 | + | 0.630895i | ||||
\(482\) | −11068.0 | −1.04592 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1724.00 | −0.161908 | ||||||||
\(485\) | −1158.00 | + | 2005.71i | −0.108417 | + | 0.187783i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3326.50 | − | 5761.67i | −0.309524 | − | 0.536111i | 0.668734 | − | 0.743501i | \(-0.266836\pi\) |
−0.978258 | + | 0.207390i | \(0.933503\pi\) | |||||||
\(488\) | 3272.00 | − | 5667.27i | 0.303517 | − | 0.525708i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15444.0 | −1.41951 | −0.709754 | − | 0.704450i | \(-0.751194\pi\) | ||||
−0.709754 | + | 0.704450i | \(0.751194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7560.00 | + | 13094.3i | 0.690640 | + | 1.19622i | ||||
\(494\) | 5141.00 | + | 8904.47i | 0.468228 | + | 0.810994i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2864.00 | −0.259269 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −341.500 | + | 591.495i | −0.0306366 | + | 0.0530641i | −0.880937 | − | 0.473233i | \(-0.843087\pi\) |
0.850301 | + | 0.526297i | \(0.176420\pi\) | |||||||
\(500\) | −2568.00 | − | 4447.91i | −0.229689 | − | 0.397833i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 468.000 | − | 810.600i | 0.0416093 | − | 0.0720694i | ||||
\(503\) | 9882.00 | 0.875977 | 0.437989 | − | 0.898980i | \(-0.355691\pi\) | ||||
0.437989 | + | 0.898980i | \(0.355691\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3708.00 | −0.326740 | ||||||||
\(506\) | 2520.00 | − | 4364.77i | 0.221399 | − | 0.383474i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4966.00 | − | 8601.36i | −0.433722 | − | 0.751228i | ||||
\(509\) | −2103.00 | + | 3642.50i | −0.183131 | + | 0.317193i | −0.942945 | − | 0.332948i | \(-0.891957\pi\) |
0.759814 | + | 0.650141i | \(0.225290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2490.00 | + | 4312.81i | 0.213675 | + | 0.370097i | ||||
\(515\) | −4425.00 | − | 7664.32i | −0.378619 | − | 0.655787i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10980.0 | −0.934042 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1272.00 | + | 2203.17i | −0.107271 | + | 0.185799i | ||||
\(521\) | −4530.00 | − | 7846.19i | −0.380927 | − | 0.659785i | 0.610268 | − | 0.792195i | \(-0.291062\pi\) |
−0.991195 | + | 0.132410i | \(0.957728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7839.50 | + | 13578.4i | −0.655444 | + | 1.13526i | 0.326338 | + | 0.945253i | \(0.394185\pi\) |
−0.981782 | + | 0.190010i | \(0.939148\pi\) | |||||||
\(524\) | 8472.00 | 0.706300 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3144.00 | −0.260618 | ||||||||
\(527\) | −7518.00 | + | 13021.6i | −0.621422 | + | 1.07633i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | 4608.00 | − | 7981.29i | 0.377658 | − | 0.654123i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6678.00 | −0.542695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5652.00 | − | 9789.55i | −0.456743 | − | 0.791101i | ||||
\(536\) | 2092.00 | + | 3623.45i | 0.168583 | + | 0.291995i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3612.00 | 0.289451 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3855.50 | − | 6677.92i | 0.306397 | − | 0.530696i | −0.671174 | − | 0.741300i | \(-0.734210\pi\) |
0.977571 | + | 0.210604i | \(0.0675431\pi\) | |||||||
\(542\) | −6112.00 | − | 10586.3i | −0.484378 | − | 0.838967i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1344.00 | − | 2327.88i | 0.105926 | − | 0.183469i | ||||
\(545\) | −2478.00 | −0.194763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4292.00 | 0.335489 | 0.167745 | − | 0.985830i | \(-0.446352\pi\) | ||||
0.167745 | + | 0.985830i | \(0.446352\pi\) | |||||||
\(548\) | 6024.00 | − | 10433.9i | 0.469585 | − | 0.813345i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2670.00 | + | 4624.58i | 0.206999 | + | 0.358532i | ||||
\(551\) | −8730.00 | + | 15120.8i | −0.674974 | + | 1.16909i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8462.00 | −0.648946 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −74.0000 | − | 128.172i | −0.00564442 | − | 0.00977643i | ||||
\(557\) | −4929.00 | − | 8537.28i | −0.374952 | − | 0.649436i | 0.615368 | − | 0.788240i | \(-0.289008\pi\) |
−0.990320 | + | 0.138804i | \(0.955674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17225.0 | 1.30329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3816.00 | + | 6609.51i | −0.286420 | + | 0.496095i | ||||
\(563\) | 6945.00 | + | 12029.1i | 0.519888 | + | 0.900472i | 0.999733 | + | 0.0231188i | \(0.00735960\pi\) |
−0.479845 | + | 0.877353i | \(0.659307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2646.00 | − | 4583.01i | 0.197023 | − | 0.341254i | ||||
\(566\) | 7994.00 | 0.593662 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2736.00 | 0.202113 | ||||||||
\(569\) | 9519.00 | − | 16487.4i | 0.701331 | − | 1.21474i | −0.266669 | − | 0.963788i | \(-0.585923\pi\) |
0.967999 | − | 0.250952i | \(-0.0807437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4026.50 | + | 6974.10i | 0.295103 | + | 0.511133i | 0.975009 | − | 0.222166i | \(-0.0713127\pi\) |
−0.679906 | + | 0.733299i | \(0.737979\pi\) | |||||||
\(572\) | 3180.00 | − | 5507.92i | 0.232452 | − | 0.402618i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7476.00 | 0.542210 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8568.50 | − | 14841.1i | −0.618217 | − | 1.07078i | −0.989811 | − | 0.142388i | \(-0.954522\pi\) |
0.371594 | − | 0.928395i | \(-0.378811\pi\) | |||||||
\(578\) | −2143.00 | − | 3711.78i | −0.154216 | − | 0.267111i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4320.00 | −0.309273 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11520.0 | + | 19953.2i | −0.818370 | + | 1.41746i | ||||
\(584\) | −172.000 | − | 297.913i | −0.0121873 | − | 0.0211091i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4608.00 | + | 7981.29i | −0.324837 | + | 0.562635i | ||||
\(587\) | 18144.0 | 1.27578 | 0.637890 | − | 0.770127i | \(-0.279807\pi\) | ||||
0.637890 | + | 0.770127i | \(0.279807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17363.0 | −1.21465 | ||||||||
\(590\) | −1584.00 | + | 2743.57i | −0.110529 | + | 0.191442i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1160.00 | + | 2009.18i | 0.0805333 | + | 0.139488i | ||||
\(593\) | 12351.0 | − | 21392.6i | 0.855303 | − | 1.48143i | −0.0210603 | − | 0.999778i | \(-0.506704\pi\) |
0.876363 | − | 0.481650i | \(-0.159962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6576.00 | 0.451952 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4452.00 | − | 7711.09i | −0.304441 | − | 0.527308i | ||||
\(599\) | −1086.00 | − | 1881.01i | −0.0740781 | − | 0.128307i | 0.826607 | − | 0.562780i | \(-0.190268\pi\) |
−0.900685 | + | 0.434473i | \(0.856935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4175.00 | −0.283364 | −0.141682 | − | 0.989912i | \(-0.545251\pi\) | ||||
−0.141682 | + | 0.989912i | \(0.545251\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2176.00 | + | 3768.94i | −0.146590 | + | 0.253901i | ||||
\(605\) | −1293.00 | − | 2239.54i | −0.0868891 | − | 0.150496i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1130.50 | − | 1958.08i | 0.0755940 | − | 0.130933i | −0.825750 | − | 0.564036i | \(-0.809248\pi\) |
0.901344 | + | 0.433103i | \(0.142581\pi\) | |||||||
\(608\) | 3104.00 | 0.207046 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9816.00 | 0.651538 | ||||||||
\(611\) | −9699.00 | + | 16799.2i | −0.642192 | + | 1.11231i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8159.00 | + | 14131.8i | 0.537584 | + | 0.931123i | 0.999033 | + | 0.0439561i | \(0.0139962\pi\) |
−0.461450 | + | 0.887166i | \(0.652670\pi\) | |||||||
\(614\) | −631.000 | + | 1092.92i | −0.0414741 | + | 0.0718352i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26550.0 | 1.73235 | 0.866177 | − | 0.499737i | \(-0.166570\pi\) | ||||
0.866177 | + | 0.499737i | \(0.166570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9962.50 | + | 17255.6i | 0.646893 | + | 1.12045i | 0.983861 | + | 0.178935i | \(0.0572652\pi\) |
−0.336968 | + | 0.941516i | \(0.609401\pi\) | |||||||
\(620\) | −2148.00 | − | 3720.45i | −0.139138 | − | 0.240995i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7788.00 | 0.502042 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1710.50 | + | 2962.67i | −0.109472 | + | 0.189611i | ||||
\(626\) | −2185.00 | − | 3784.53i | −0.139505 | − | 0.241630i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1012.00 | − | 1752.84i | 0.0643045 | − | 0.111379i | ||||
\(629\) | 12180.0 | 0.772096 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6832.00 | −0.431026 | −0.215513 | − | 0.976501i | \(-0.569142\pi\) | ||||
−0.215513 | + | 0.976501i | \(0.569142\pi\) | |||||||
\(632\) | 4684.00 | − | 8112.93i | 0.294809 | − | 0.510625i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3504.00 | + | 6069.11i | 0.219498 | + | 0.380181i | ||||
\(635\) | 7449.00 | − | 12902.0i | 0.465519 | − | 0.806303i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10800.0 | 0.670182 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 384.000 | + | 665.108i | 0.0237171 | + | 0.0410792i | ||||
\(641\) | 5106.00 | + | 8843.85i | 0.314625 | + | 0.544947i | 0.979358 | − | 0.202134i | \(-0.0647878\pi\) |
−0.664732 | + | 0.747082i | \(0.731454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3779.00 | −0.231772 | −0.115886 | − | 0.993263i | \(-0.536971\pi\) | ||||
−0.115886 | + | 0.993263i | \(0.536971\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8148.00 | − | 14112.7i | 0.496252 | − | 0.859534i | ||||
\(647\) | −8499.00 | − | 14720.7i | −0.516430 | − | 0.894483i | −0.999818 | − | 0.0190767i | \(-0.993927\pi\) |
0.483388 | − | 0.875406i | \(-0.339406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3960.00 | − | 6858.92i | 0.239512 | − | 0.414848i | ||||
\(650\) | 9434.00 | 0.569280 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7376.00 | 0.443047 | ||||||||
\(653\) | −10875.0 | + | 18836.1i | −0.651718 | + | 1.12881i | 0.330988 | + | 0.943635i | \(0.392618\pi\) |
−0.982706 | + | 0.185173i | \(0.940715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6354.00 | + | 11005.5i | 0.379040 | + | 0.656517i | ||||
\(656\) | −1008.00 | + | 1745.91i | −0.0599936 | + | 0.103912i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10944.0 | 0.646916 | 0.323458 | − | 0.946243i | \(-0.395155\pi\) | ||||
0.323458 | + | 0.946243i | \(0.395155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5477.50 | + | 9487.31i | 0.322315 | + | 0.558266i | 0.980965 | − | 0.194184i | \(-0.0622057\pi\) |
−0.658650 | + | 0.752449i | \(0.728872\pi\) | |||||||
\(662\) | −2945.00 | − | 5100.89i | −0.172901 | − | 0.299474i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6480.00 | −0.378724 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7560.00 | − | 13094.3i | 0.438867 | − | 0.760140i | ||||
\(668\) | −324.000 | − | 561.184i | −0.0187664 | − | 0.0325043i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3138.00 | + | 5435.18i | −0.180943 | + | 0.313402i | ||||
\(671\) | −24540.0 | −1.41186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25103.0 | 1.43782 | 0.718908 | − | 0.695106i | \(-0.244642\pi\) | ||||
0.718908 | + | 0.695106i | \(0.244642\pi\) | |||||||
\(674\) | −4277.00 | + | 7407.98i | −0.244427 | + | 0.423360i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1224.00 | − | 2120.03i | −0.0696404 | − | 0.120621i | ||||
\(677\) | 2802.00 | − | 4853.21i | 0.159069 | − | 0.275515i | −0.775464 | − | 0.631391i | \(-0.782484\pi\) |
0.934533 | + | 0.355876i | \(0.115817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4032.00 | 0.227383 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5370.00 | + | 9301.11i | 0.301507 | + | 0.522226i | ||||
\(683\) | 5484.00 | + | 9498.57i | 0.307232 | + | 0.532141i | 0.977756 | − | 0.209747i | \(-0.0672639\pi\) |
−0.670524 | + | 0.741888i | \(0.733931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18072.0 | 1.00802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2600.00 | − | 4503.33i | 0.144076 | − | 0.249546i | ||||
\(689\) | 20352.0 | + | 35250.7i | 1.12533 | + | 1.94912i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4202.50 | − | 7278.94i | 0.231361 | − | 0.400729i | −0.726848 | − | 0.686799i | \(-0.759015\pi\) |
0.958209 | + | 0.286069i | \(0.0923487\pi\) | |||||||
\(692\) | −10896.0 | −0.598560 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14376.0 | −0.786319 | ||||||||
\(695\) | 111.000 | − | 192.258i | 0.00605823 | − | 0.0104932i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5292.00 | + | 9166.01i | 0.287588 | + | 0.498117i | ||||
\(698\) | −9406.00 | + | 16291.7i | −0.510061 | + | 0.883451i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −468.000 | −0.0252156 | −0.0126078 | − | 0.999921i | \(-0.504013\pi\) | ||||
−0.0126078 | + | 0.999921i | \(0.504013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7032.50 | + | 12180.6i | 0.377291 | + | 0.653488i | ||||
\(704\) | −960.000 | − | 1662.77i | −0.0513940 | − | 0.0890170i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6780.00 | 0.361429 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12533.0 | − | 21707.8i | 0.663874 | − | 1.14986i | −0.315715 | − | 0.948854i | \(-0.602244\pi\) |
0.979589 | − | 0.201010i | \(-0.0644222\pi\) | |||||||
\(710\) | 2052.00 | + | 3554.17i | 0.108465 | + | 0.187867i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2400.00 | − | 4156.92i | 0.126326 | − | 0.218802i | ||||
\(713\) | 15036.0 | 0.789765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9540.00 | 0.498987 | ||||||||
\(716\) | −2508.00 | + | 4343.98i | −0.130906 | + | 0.226735i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4812.00 | − | 8334.63i | −0.250115 | − | 0.433211i | ||||
\(719\) | −5541.00 | + | 9597.29i | −0.287405 | + | 0.497801i | −0.973190 | − | 0.230004i | \(-0.926126\pi\) |
0.685784 | + | 0.727805i | \(0.259459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5100.00 | 0.262884 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3614.00 | − | 6259.63i | −0.185516 | − | 0.321322i | ||||
\(725\) | 8010.00 | + | 13873.7i | 0.410323 | + | 0.710700i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13481.0 | −0.687734 | −0.343867 | − | 0.939018i | \(-0.611737\pi\) | ||||
−0.343867 | + | 0.939018i | \(0.611737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 258.000 | − | 446.869i | 0.0130808 | − | 0.0226567i | ||||
\(731\) | −13650.0 | − | 23642.5i | −0.690648 | − | 1.19624i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12158.5 | − | 21059.1i | 0.612666 | − | 1.06117i | −0.378123 | − | 0.925755i | \(-0.623430\pi\) |
0.990789 | − | 0.135414i | \(-0.0432364\pi\) | |||||||
\(734\) | 14198.0 | 0.713975 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2688.00 | −0.134621 | ||||||||
\(737\) | 7845.00 | − | 13587.9i | 0.392095 | − | 0.679129i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9108.50 | + | 15776.4i | 0.453399 | + | 0.785309i | 0.998595 | − | 0.0529992i | \(-0.0168781\pi\) |
−0.545196 | + | 0.838309i | \(0.683545\pi\) | |||||||
\(740\) | −1740.00 | + | 3013.77i | −0.0864374 | + | 0.149714i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19782.0 | −0.976758 | −0.488379 | − | 0.872632i | \(-0.662412\pi\) | ||||
−0.488379 | + | 0.872632i | \(0.662412\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4932.00 | + | 8542.47i | 0.242543 | + | 0.420097i | ||||
\(746\) | −2963.00 | − | 5132.07i | −0.145420 | − | 0.251874i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10080.0 | −0.492729 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2460.50 | − | 4261.71i | 0.119554 | − | 0.207073i | −0.800037 | − | 0.599951i | \(-0.795187\pi\) |
0.919591 | + | 0.392877i | \(0.128520\pi\) | |||||||
\(752\) | 2928.00 | + | 5071.44i | 0.141986 | + | 0.245926i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9540.00 | − | 16523.8i | 0.460778 | − | 0.798090i | ||||
\(755\) | −6528.00 | −0.314673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18098.0 | 0.868934 | 0.434467 | − | 0.900688i | \(-0.356937\pi\) | ||||
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(758\) | 11899.0 | − | 20609.7i | 0.570173 | − | 0.987569i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2328.00 | + | 4032.21i | 0.111112 | + | 0.192452i | ||||
\(761\) | 12234.0 | − | 21189.9i | 0.582762 | − | 1.00937i | −0.412388 | − | 0.911008i | \(-0.635305\pi\) |
0.995150 | − | 0.0983657i | \(-0.0313615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2856.00 | −0.135244 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2568.00 | − | 4447.91i | −0.121130 | − | 0.209803i | ||||
\(767\) | −6996.00 | − | 12117.4i | −0.329349 | − | 0.570450i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21719.0 | −1.01847 | −0.509237 | − | 0.860626i | \(-0.670072\pi\) | ||||
−0.509237 | + | 0.860626i | \(0.670072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7418.00 | − | 12848.4i | 0.345829 | − | 0.598993i | ||||
\(773\) | 15153.0 | + | 26245.8i | 0.705065 | + | 1.22121i | 0.966668 | + | 0.256033i | \(0.0824157\pi\) |
−0.261603 | + | 0.965176i | \(0.584251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7965.50 | + | 13796.7i | −0.369199 | + | 0.639471i | ||||
\(776\) | −3088.00 | −0.142851 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20292.0 | 0.935094 | ||||||||
\(779\) | −6111.00 | + | 10584.6i | −0.281065 | + | 0.486818i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5130.00 | − | 8885.42i | −0.235039 | − | 0.407100i | ||||
\(782\) | −7056.00 | + | 12221.4i | −0.322662 | + | 0.558868i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3036.00 | 0.138038 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13648.0 | + | 23639.0i | 0.618169 | + | 1.07070i | 0.989820 | + | 0.142327i | \(0.0454584\pi\) |
−0.371651 | + | 0.928372i | \(0.621208\pi\) | |||||||
\(788\) | −2088.00 | − | 3616.52i | −0.0943933 | − | 0.163494i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14052.0 | 0.632845 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21677.0 | + | 37545.7i | −0.970710 | + | 1.68132i | ||||
\(794\) | −6229.00 | − | 10788.9i | −0.278412 | − | 0.482223i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −272.000 | + | 471.118i | −0.0121115 | + | 0.0209778i | ||||
\(797\) | −35100.0 | −1.55998 | −0.779991 | − | 0.625791i | \(-0.784776\pi\) | ||||
−0.779991 | + | 0.625791i | \(0.784776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30744.0 | 1.36126 | ||||||||
\(800\) | 1424.00 | − | 2466.44i | 0.0629325 | − | 0.109002i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2472.00 | − | 4281.63i | −0.108840 | − | 0.188516i | ||||
\(803\) | −645.000 | + | 1117.17i | −0.0283456 | + | 0.0490961i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18974.0 | 0.829194 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2472.00 | − | 4281.63i | −0.107630 | − | 0.186420i | ||||
\(809\) | 22197.0 | + | 38446.3i | 0.964654 | + | 1.67083i | 0.710542 | + | 0.703655i | \(0.248450\pi\) |
0.254112 | + | 0.967175i | \(0.418217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8584.00 | 0.371671 | 0.185835 | − | 0.982581i | \(-0.440501\pi\) | ||||
0.185835 | + | 0.982581i | \(0.440501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4350.00 | − | 7534.42i | 0.187306 | − | 0.324424i | ||||
\(815\) | 5532.00 | + | 9581.71i | 0.237764 | + | 0.411819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15762.5 | − | 27301.5i | 0.674982 | − | 1.16910i | ||||
\(818\) | 14150.0 | 0.604820 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3024.00 | −0.128784 | ||||||||
\(821\) | −4917.00 | + | 8516.49i | −0.209019 | + | 0.362031i | −0.951406 | − | 0.307940i | \(-0.900360\pi\) |
0.742387 | + | 0.669971i | \(0.233694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21928.0 | − | 37980.4i | −0.928751 | − | 1.60864i | −0.785415 | − | 0.618970i | \(-0.787550\pi\) |
−0.143336 | − | 0.989674i | \(-0.545783\pi\) | |||||||
\(824\) | 5900.00 | − | 10219.1i | 0.249437 | − | 0.432038i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13266.0 | −0.557804 | −0.278902 | − | 0.960320i | \(-0.589970\pi\) | ||||
−0.278902 | + | 0.960320i | \(0.589970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8726.50 | + | 15114.7i | 0.365602 | + | 0.633241i | 0.988873 | − | 0.148765i | \(-0.0475299\pi\) |
−0.623271 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(830\) | −4860.00 | − | 8417.77i | −0.203245 | − | 0.352030i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3392.00 | −0.141342 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 486.000 | − | 841.777i | 0.0201422 | − | 0.0348873i | ||||
\(836\) | −5820.00 | − | 10080.5i | −0.240776 | − | 0.417037i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4158.00 | − | 7201.87i | 0.171403 | − | 0.296879i | ||||
\(839\) | −35172.0 | −1.44729 | −0.723643 | − | 0.690175i | \(-0.757534\pi\) | ||||
−0.723643 | + | 0.690175i | \(0.757534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8011.00 | 0.328468 | ||||||||
\(842\) | 6595.00 | − | 11422.9i | 0.269927 | − | 0.467528i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2968.00 | − | 5140.73i | −0.121046 | − | 0.209658i | ||||
\(845\) | 1836.00 | − | 3180.05i | 0.0747459 | − | 0.129464i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12288.0 | 0.497608 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7476.00 | − | 12948.8i | −0.301676 | − | 0.522518i | ||||
\(851\) | −6090.00 | − | 10548.2i | −0.245314 | − | 0.424897i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3503.00 | −0.140610 | −0.0703051 | − | 0.997526i | \(-0.522397\pi\) | ||||
−0.0703051 | + | 0.997526i | \(0.522397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7536.00 | − | 13052.7i | 0.300906 | − | 0.521184i | ||||
\(857\) | −11424.0 | − | 19786.9i | −0.455352 | − | 0.788692i | 0.543357 | − | 0.839502i | \(-0.317153\pi\) |
−0.998708 | + | 0.0508097i | \(0.983820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6728.00 | + | 11653.2i | −0.267237 | + | 0.462868i | −0.968147 | − | 0.250382i | \(-0.919444\pi\) |
0.700910 | + | 0.713249i | \(0.252777\pi\) | |||||||
\(860\) | 7800.00 | 0.309277 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3036.00 | −0.119961 | ||||||||
\(863\) | 20355.0 | − | 35255.9i | 0.802888 | − | 1.39064i | −0.114820 | − | 0.993386i | \(-0.536629\pi\) |
0.917708 | − | 0.397256i | \(-0.130038\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8172.00 | − | 14154.3i | −0.321221 | − | 0.556371i | ||||
\(866\) | 8567.00 | − | 14838.5i | 0.336165 | − | 0.582254i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35130.0 | −1.37135 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13859.5 | − | 24005.4i | −0.539163 | − | 0.933858i | ||||
\(872\) | −1652.00 | − | 2861.35i | −0.0641557 | − | 0.111121i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16296.0 | −0.630687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1453.00 | + | 2516.67i | −0.0559456 | + | 0.0969007i | −0.892642 | − | 0.450767i | \(-0.851151\pi\) |
0.836696 | + | 0.547667i | \(0.184484\pi\) | |||||||
\(878\) | 10640.0 | + | 18429.0i | 0.408978 | + | 0.708371i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1440.00 | − | 2494.15i | 0.0551618 | − | 0.0955431i | ||||
\(881\) | −19188.0 | −0.733780 | −0.366890 | − | 0.930264i | \(-0.619577\pi\) | ||||
−0.366890 | + | 0.930264i | \(0.619577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17251.0 | −0.657466 | −0.328733 | − | 0.944423i | \(-0.606622\pi\) | ||||
−0.328733 | + | 0.944423i | \(0.606622\pi\) | |||||||
\(884\) | −8904.00 | + | 15422.2i | −0.338771 | + | 0.586769i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7032.00 | + | 12179.8i | 0.266642 | + | 0.461837i | ||||
\(887\) | 1047.00 | − | 1813.46i | 0.0396334 | − | 0.0686471i | −0.845528 | − | 0.533931i | \(-0.820714\pi\) |
0.885162 | + | 0.465284i | \(0.154048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7200.00 | 0.271174 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4064.00 | − | 7039.05i | −0.152548 | − | 0.264221i | ||||
\(893\) | 17751.0 | + | 30745.6i | 0.665190 | + | 1.15214i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7524.00 | −0.281005 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14814.0 | + | 25658.6i | −0.550501 | + | 0.953495i | ||||
\(899\) | 16110.0 | + | 27903.3i | 0.597662 | + | 1.03518i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32256.0 | − | 55869.0i | 1.19268 | − | 2.06578i | ||||
\(902\) | 7560.00 | 0.279069 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7056.00 | 0.259601 | ||||||||
\(905\) | 5421.00 | − | 9389.45i | 0.199116 | − | 0.344879i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20133.5 | + | 34872.2i | 0.737069 | + | 1.27664i | 0.953809 | + | 0.300412i | \(0.0971242\pi\) |
−0.216740 | + | 0.976229i | \(0.569542\pi\) | |||||||
\(908\) | −12396.0 | + | 21470.5i | −0.453057 | + | 0.784718i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17604.0 | −0.640227 | −0.320113 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320113 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12150.0 | + | 21044.4i | 0.440423 | + | 0.762835i | ||||
\(914\) | 11251.0 | + | 19487.3i | 0.407166 | + | 0.705233i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18364.0 | 0.662406 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1754.50 | + | 3038.88i | −0.0629767 | + | 0.109079i | −0.895795 | − | 0.444468i | \(-0.853393\pi\) |
0.832818 | + | 0.553547i | \(0.186726\pi\) | |||||||
\(920\) | −2016.00 | − | 3491.81i | −0.0722452 | − | 0.125132i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3852.00 | − | 6671.86i | 0.137591 | − | 0.238315i | ||||
\(923\) | −18126.0 | −0.646397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12905.0 | 0.458718 | ||||||||
\(926\) | 475.000 | − | 822.724i | 0.0168569 | − | 0.0291970i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2880.00 | − | 4988.31i | −0.101876 | − | 0.176454i | ||||
\(929\) | 17319.0 | − | 29997.4i | 0.611645 | − | 1.05940i | −0.379319 | − | 0.925266i | \(-0.623842\pi\) |
0.990963 | − | 0.134134i | \(-0.0428251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18120.0 | −0.636846 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5934.00 | − | 10278.0i | −0.207887 | − | 0.360071i | ||||
\(935\) | −7560.00 | − | 13094.3i | −0.264426 | − | 0.458000i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17353.0 | 0.605014 | 0.302507 | − | 0.953147i | \(-0.402176\pi\) | ||||
0.302507 | + | 0.953147i | \(0.402176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4392.00 | + | 7607.17i | −0.152395 | + | 0.263956i | ||||
\(941\) | 23460.0 | + | 40633.9i | 0.812725 | + | 1.40768i | 0.910950 | + | 0.412517i | \(0.135350\pi\) |
−0.0982252 | + | 0.995164i | \(0.531317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5292.00 | − | 9166.01i | 0.182748 | − | 0.316529i | ||||
\(944\) | −4224.00 | −0.145635 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19500.0 | −0.670190 | ||||||||
\(947\) | 9177.00 | − | 15895.0i | 0.314902 | − | 0.545427i | −0.664514 | − | 0.747275i | \(-0.731362\pi\) |
0.979417 | + | 0.201849i | \(0.0646949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1139.50 | + | 1973.67i | 0.0389776 | + | 0.0675112i | ||||
\(950\) | 8633.00 | − | 14952.8i | 0.294833 | − | 0.510666i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35568.0 | −1.20898 | −0.604491 | − | 0.796612i | \(-0.706624\pi\) | ||||
−0.604491 | + | 0.796612i | \(0.706624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2142.00 | − | 3710.05i | −0.0725796 | − | 0.125712i | ||||
\(956\) | 3060.00 | + | 5300.08i | 0.103522 | + | 0.179306i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26736.0 | −0.901671 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1125.00 | + | 1948.56i | −0.0377631 | + | 0.0654076i | ||||
\(962\) | −7685.00 | − | 13310.8i | −0.257562 | − | 0.446110i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11068.0 | − | 19170.3i | 0.369789 | − | 0.640493i | ||||
\(965\) | 22254.0 | 0.742364 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27343.0 | −0.909298 | −0.454649 | − | 0.890671i | \(-0.650235\pi\) | ||||
−0.454649 | + | 0.890671i | \(0.650235\pi\) | |||||||
\(968\) | 1724.00 | − | 2986.06i | 0.0572432 | − | 0.0991482i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2316.00 | − | 4011.43i | −0.0766621 | − | 0.132783i | ||||
\(971\) | −25512.0 | + | 44188.1i | −0.843171 | + | 1.46042i | 0.0440291 | + | 0.999030i | \(0.485981\pi\) |
−0.887200 | + | 0.461385i | \(0.847353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13306.0 | 0.437733 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6544.00 | + | 11334.5i | 0.214619 | + | 0.371731i | ||||
\(977\) | −1113.00 | − | 1927.77i | −0.0364463 | − | 0.0631268i | 0.847227 | − | 0.531231i | \(-0.178270\pi\) |
−0.883673 | + | 0.468104i | \(0.844937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18000.0 | −0.587623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15444.0 | − | 26749.8i | 0.501872 | − | 0.869267i | ||||
\(983\) | −17652.0 | − | 30574.2i | −0.572748 | − | 0.992029i | −0.996282 | − | 0.0861487i | \(-0.972544\pi\) |
0.423534 | − | 0.905880i | \(-0.360789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3132.00 | − | 5424.78i | 0.101314 | − | 0.175480i | ||||
\(986\) | −30240.0 | −0.976712 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20564.0 | −0.662174 | ||||||||
\(989\) | −13650.0 | + | 23642.5i | −0.438872 | + | 0.760149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1170.50 | + | 2027.37i | 0.0375198 | + | 0.0649863i | 0.884176 | − | 0.467155i | \(-0.154721\pi\) |
−0.846656 | + | 0.532141i | \(0.821388\pi\) | |||||||
\(992\) | 2864.00 | − | 4960.59i | 0.0916654 | − | 0.158769i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −816.000 | −0.0259989 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14507.5 | + | 25127.7i | 0.460840 | + | 0.798198i | 0.999003 | − | 0.0446429i | \(-0.0142150\pi\) |
−0.538163 | + | 0.842841i | \(0.680882\pi\) | |||||||
\(998\) | −683.000 | − | 1182.99i | −0.0216633 | − | 0.0375220i | ||||
\(999\) | 0 | 0 |
(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 | 882.4.g.g.667.1 | 2 | ||
3.2 | odd | 2 | 294.4.e.i.79.1 | 2 | |||
7.2 | even | 3 | 882.4.a.l.1.1 | 1 | |||
7.3 | odd | 6 | 126.4.g.b.109.1 | 2 | |||
7.4 | even | 3 | inner | 882.4.g.g.361.1 | 2 | ||
7.5 | odd | 6 | 882.4.a.o.1.1 | 1 | |||
7.6 | odd | 2 | 126.4.g.b.37.1 | 2 | |||
21.2 | odd | 6 | 294.4.a.c.1.1 | 1 | |||
21.5 | even | 6 | 294.4.a.d.1.1 | 1 | |||
21.11 | odd | 6 | 294.4.e.i.67.1 | 2 | |||
21.17 | even | 6 | 42.4.e.a.25.1 | ✓ | 2 | ||
21.20 | even | 2 | 42.4.e.a.37.1 | yes | 2 | ||
84.23 | even | 6 | 2352.4.a.bf.1.1 | 1 | |||
84.47 | odd | 6 | 2352.4.a.f.1.1 | 1 | |||
84.59 | odd | 6 | 336.4.q.f.193.1 | 2 | |||
84.83 | odd | 2 | 336.4.q.f.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.a.25.1 | ✓ | 2 | 21.17 | even | 6 | ||
42.4.e.a.37.1 | yes | 2 | 21.20 | even | 2 | ||
126.4.g.b.37.1 | 2 | 7.6 | odd | 2 | |||
126.4.g.b.109.1 | 2 | 7.3 | odd | 6 | |||
294.4.a.c.1.1 | 1 | 21.2 | odd | 6 | |||
294.4.a.d.1.1 | 1 | 21.5 | even | 6 | |||
294.4.e.i.67.1 | 2 | 21.11 | odd | 6 | |||
294.4.e.i.79.1 | 2 | 3.2 | odd | 2 | |||
336.4.q.f.193.1 | 2 | 84.59 | odd | 6 | |||
336.4.q.f.289.1 | 2 | 84.83 | odd | 2 | |||
882.4.a.l.1.1 | 1 | 7.2 | even | 3 | |||
882.4.a.o.1.1 | 1 | 7.5 | odd | 6 | |||
882.4.g.g.361.1 | 2 | 7.4 | even | 3 | inner | ||
882.4.g.g.667.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.f.1.1 | 1 | 84.47 | odd | 6 | |||
2352.4.a.bf.1.1 | 1 | 84.23 | even | 6 |