Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (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: | \(26.0198423125\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.e.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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | −0.940775 | − | 0.339032i | \(-0.889900\pi\) |
0.763998 | + | 0.645219i | \(0.223234\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.50000 | + | 6.06218i | 0.437500 | + | 0.757772i | ||||
\(5\) | −8.00000 | + | 13.8564i | −0.715542 | + | 1.23935i | 0.247208 | + | 0.968962i | \(0.420487\pi\) |
−0.962750 | + | 0.270392i | \(0.912847\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −15.0000 | −0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.00000 | − | 13.8564i | −0.252982 | − | 0.438178i | ||||
\(11\) | −4.00000 | − | 6.92820i | −0.109640 | − | 0.189903i | 0.805984 | − | 0.591937i | \(-0.201637\pi\) |
−0.915625 | + | 0.402034i | \(0.868303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20.5000 | + | 35.5070i | −0.320312 | + | 0.554798i | ||||
\(17\) | −27.0000 | − | 46.7654i | −0.385204 | − | 0.667192i | 0.606594 | − | 0.795012i | \(-0.292535\pi\) |
−0.991797 | + | 0.127820i | \(0.959202\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −55.0000 | + | 95.2628i | −0.664098 | + | 1.15025i | 0.315431 | + | 0.948949i | \(0.397851\pi\) |
−0.979529 | + | 0.201303i | \(0.935482\pi\) | |||||||
\(20\) | −112.000 | −1.25220 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.00000 | 0.0775275 | ||||||||
\(23\) | 24.0000 | − | 41.5692i | 0.217580 | − | 0.376860i | −0.736487 | − | 0.676451i | \(-0.763517\pi\) |
0.954068 | + | 0.299591i | \(0.0968503\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −65.5000 | − | 113.449i | −0.524000 | − | 0.907595i | ||||
\(26\) | 14.0000 | − | 24.2487i | 0.105601 | − | 0.182906i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 110.000 | 0.704362 | 0.352181 | − | 0.935932i | \(-0.385440\pi\) | ||||
0.352181 | + | 0.935932i | \(0.385440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | + | 10.3923i | 0.0347623 | + | 0.0602101i | 0.882883 | − | 0.469593i | \(-0.155599\pi\) |
−0.848121 | + | 0.529803i | \(0.822266\pi\) | |||||||
\(32\) | −80.5000 | − | 139.430i | −0.444704 | − | 0.770250i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 54.0000 | 0.272380 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 123.000 | − | 213.042i | 0.546516 | − | 0.946593i | −0.451994 | − | 0.892021i | \(-0.649287\pi\) |
0.998510 | − | 0.0545719i | \(-0.0173794\pi\) | |||||||
\(38\) | −55.0000 | − | 95.2628i | −0.234794 | − | 0.406675i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 120.000 | − | 207.846i | 0.474342 | − | 0.821584i | ||||
\(41\) | 182.000 | 0.693259 | 0.346630 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346630 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 128.000 | 0.453949 | 0.226975 | − | 0.973901i | \(-0.427117\pi\) | ||||
0.226975 | + | 0.973901i | \(0.427117\pi\) | |||||||
\(44\) | 28.0000 | − | 48.4974i | 0.0959354 | − | 0.166165i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 24.0000 | + | 41.5692i | 0.0769262 | + | 0.133240i | ||||
\(47\) | −162.000 | + | 280.592i | −0.502769 | + | 0.870821i | 0.497226 | + | 0.867621i | \(0.334352\pi\) |
−0.999995 | + | 0.00319997i | \(0.998981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 131.000 | 0.370524 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −98.0000 | − | 169.741i | −0.261349 | − | 0.452670i | ||||
\(53\) | −81.0000 | − | 140.296i | −0.209928 | − | 0.363607i | 0.741763 | − | 0.670662i | \(-0.233990\pi\) |
−0.951692 | + | 0.307055i | \(0.900656\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 128.000 | 0.313809 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −55.0000 | + | 95.2628i | −0.124515 | + | 0.215666i | ||||
\(59\) | −405.000 | − | 701.481i | −0.893670 | − | 1.54788i | −0.835442 | − | 0.549578i | \(-0.814789\pi\) |
−0.0582271 | − | 0.998303i | \(-0.518545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −244.000 | + | 422.620i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | −12.0000 | −0.0245807 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 224.000 | − | 387.979i | 0.427443 | − | 0.740353i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −122.000 | − | 211.310i | −0.222458 | − | 0.385308i | 0.733096 | − | 0.680125i | \(-0.238075\pi\) |
−0.955554 | + | 0.294817i | \(0.904741\pi\) | |||||||
\(68\) | 189.000 | − | 327.358i | 0.337053 | − | 0.583793i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 768.000 | 1.28373 | 0.641865 | − | 0.766818i | \(-0.278161\pi\) | ||||
0.641865 | + | 0.766818i | \(0.278161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −351.000 | − | 607.950i | −0.562759 | − | 0.974728i | −0.997254 | − | 0.0740537i | \(-0.976406\pi\) |
0.434495 | − | 0.900674i | \(-0.356927\pi\) | |||||||
\(74\) | 123.000 | + | 213.042i | 0.193222 | + | 0.334671i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −770.000 | −1.16217 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −220.000 | + | 381.051i | −0.313316 | + | 0.542679i | −0.979078 | − | 0.203485i | \(-0.934773\pi\) |
0.665762 | + | 0.746164i | \(0.268106\pi\) | |||||||
\(80\) | −328.000 | − | 568.113i | −0.458394 | − | 0.793962i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −91.0000 | + | 157.617i | −0.122552 | + | 0.212266i | ||||
\(83\) | −1302.00 | −1.72184 | −0.860922 | − | 0.508737i | \(-0.830113\pi\) | ||||
−0.860922 | + | 0.508737i | \(0.830113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 864.000 | 1.10252 | ||||||||
\(86\) | −64.0000 | + | 110.851i | −0.0802476 | + | 0.138993i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 60.0000 | + | 103.923i | 0.0726821 | + | 0.125889i | ||||
\(89\) | −365.000 | + | 632.199i | −0.434718 | + | 0.752954i | −0.997273 | − | 0.0738062i | \(-0.976485\pi\) |
0.562554 | + | 0.826760i | \(0.309819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 336.000 | 0.380765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −162.000 | − | 280.592i | −0.177756 | − | 0.307882i | ||||
\(95\) | −880.000 | − | 1524.20i | −0.950380 | − | 1.64611i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −294.000 | −0.307744 | −0.153872 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153872 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 458.500 | − | 794.145i | 0.458500 | − | 0.794145i | ||||
\(101\) | 344.000 | + | 595.825i | 0.338904 | + | 0.586999i | 0.984227 | − | 0.176911i | \(-0.0566106\pi\) |
−0.645323 | + | 0.763910i | \(0.723277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 694.000 | − | 1202.04i | 0.663901 | − | 1.14991i | −0.315680 | − | 0.948866i | \(-0.602233\pi\) |
0.979582 | − | 0.201046i | \(-0.0644339\pi\) | |||||||
\(104\) | 420.000 | 0.396004 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 162.000 | 0.148442 | ||||||||
\(107\) | 122.000 | − | 211.310i | 0.110226 | − | 0.190917i | −0.805635 | − | 0.592412i | \(-0.798176\pi\) |
0.915861 | + | 0.401495i | \(0.131509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −45.0000 | − | 77.9423i | −0.0395433 | − | 0.0684910i | 0.845576 | − | 0.533854i | \(-0.179257\pi\) |
−0.885120 | + | 0.465363i | \(0.845924\pi\) | |||||||
\(110\) | −64.0000 | + | 110.851i | −0.0554742 | + | 0.0960841i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1318.00 | −1.09723 | −0.548615 | − | 0.836075i | \(-0.684845\pi\) | ||||
−0.548615 | + | 0.836075i | \(0.684845\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 384.000 | + | 665.108i | 0.311376 | + | 0.539318i | ||||
\(116\) | 385.000 | + | 666.840i | 0.308158 | + | 0.533746i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 810.000 | 0.631920 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 633.500 | − | 1097.25i | 0.475958 | − | 0.824383i | ||||
\(122\) | −244.000 | − | 422.620i | −0.181071 | − | 0.313625i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −42.0000 | + | 72.7461i | −0.0304170 | + | 0.0526838i | ||||
\(125\) | 96.0000 | 0.0686920 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1776.00 | −1.24090 | −0.620451 | − | 0.784245i | \(-0.713050\pi\) | ||||
−0.620451 | + | 0.784245i | \(0.713050\pi\) | |||||||
\(128\) | 727.500 | − | 1260.07i | 0.502363 | − | 0.870119i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 224.000 | + | 387.979i | 0.151124 | + | 0.261754i | ||||
\(131\) | 559.000 | − | 968.216i | 0.372825 | − | 0.645752i | −0.617174 | − | 0.786827i | \(-0.711723\pi\) |
0.989999 | + | 0.141075i | \(0.0450559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 244.000 | 0.157301 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 405.000 | + | 701.481i | 0.255356 | + | 0.442290i | ||||
\(137\) | 1137.00 | + | 1969.34i | 0.709054 | + | 1.22812i | 0.965208 | + | 0.261482i | \(0.0842113\pi\) |
−0.256154 | + | 0.966636i | \(0.582455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 210.000 | 0.128144 | 0.0640718 | − | 0.997945i | \(-0.479591\pi\) | ||||
0.0640718 | + | 0.997945i | \(0.479591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −384.000 | + | 665.108i | −0.226934 | + | 0.393060i | ||||
\(143\) | 112.000 | + | 193.990i | 0.0654959 | + | 0.113442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −880.000 | + | 1524.20i | −0.504000 | + | 0.872954i | ||||
\(146\) | 702.000 | 0.397931 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1722.00 | 0.956402 | ||||||||
\(149\) | −1005.00 | + | 1740.71i | −0.552569 | + | 0.957078i | 0.445519 | + | 0.895272i | \(0.353019\pi\) |
−0.998088 | + | 0.0618054i | \(0.980314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −556.000 | − | 963.020i | −0.299647 | − | 0.519003i | 0.676408 | − | 0.736527i | \(-0.263535\pi\) |
−0.976055 | + | 0.217524i | \(0.930202\pi\) | |||||||
\(152\) | 825.000 | − | 1428.94i | 0.440239 | − | 0.762516i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −192.000 | −0.0994956 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 62.0000 | + | 107.387i | 0.0315168 | + | 0.0545887i | 0.881354 | − | 0.472457i | \(-0.156633\pi\) |
−0.849837 | + | 0.527046i | \(0.823300\pi\) | |||||||
\(158\) | −220.000 | − | 381.051i | −0.110774 | − | 0.191866i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2576.00 | 1.27282 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1004.00 | + | 1738.98i | −0.482450 | + | 0.835628i | −0.999797 | − | 0.0201478i | \(-0.993586\pi\) |
0.517347 | + | 0.855776i | \(0.326920\pi\) | |||||||
\(164\) | 637.000 | + | 1103.32i | 0.303301 | + | 0.525333i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 651.000 | − | 1127.57i | 0.304382 | − | 0.527205i | ||||
\(167\) | 2884.00 | 1.33635 | 0.668176 | − | 0.744004i | \(-0.267076\pi\) | ||||
0.668176 | + | 0.744004i | \(0.267076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | −432.000 | + | 748.246i | −0.194899 | + | 0.337576i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 448.000 | + | 775.959i | 0.198603 | + | 0.343990i | ||||
\(173\) | −1114.00 | + | 1929.50i | −0.489571 | + | 0.847963i | −0.999928 | − | 0.0120003i | \(-0.996180\pi\) |
0.510357 | + | 0.859963i | \(0.329513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 328.000 | 0.140477 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −365.000 | − | 632.199i | −0.153696 | − | 0.266209i | ||||
\(179\) | −410.000 | − | 710.141i | −0.171200 | − | 0.296527i | 0.767640 | − | 0.640882i | \(-0.221431\pi\) |
−0.938840 | + | 0.344354i | \(0.888098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3892.00 | −1.59829 | −0.799144 | − | 0.601140i | \(-0.794713\pi\) | ||||
−0.799144 | + | 0.601140i | \(0.794713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −360.000 | + | 623.538i | −0.144237 | + | 0.249825i | ||||
\(185\) | 1968.00 | + | 3408.68i | 0.782109 | + | 1.35465i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −216.000 | + | 374.123i | −0.0844678 | + | 0.146303i | ||||
\(188\) | −2268.00 | −0.879845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1760.00 | 0.672020 | ||||||||
\(191\) | −2524.00 | + | 4371.70i | −0.956179 | + | 1.65615i | −0.224533 | + | 0.974466i | \(0.572086\pi\) |
−0.731646 | + | 0.681684i | \(0.761248\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1481.00 | + | 2565.17i | 0.552356 | + | 0.956709i | 0.998104 | + | 0.0615502i | \(0.0196044\pi\) |
−0.445748 | + | 0.895159i | \(0.647062\pi\) | |||||||
\(194\) | 147.000 | − | 254.611i | 0.0544020 | − | 0.0942270i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3334.00 | −1.20577 | −0.602887 | − | 0.797826i | \(-0.705983\pi\) | ||||
−0.602887 | + | 0.797826i | \(0.705983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 930.000 | + | 1610.81i | 0.331286 | + | 0.573805i | 0.982764 | − | 0.184863i | \(-0.0591841\pi\) |
−0.651478 | + | 0.758667i | \(0.725851\pi\) | |||||||
\(200\) | 982.500 | + | 1701.74i | 0.347366 | + | 0.601656i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −688.000 | −0.239641 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1456.00 | + | 2521.87i | −0.496056 | + | 0.859194i | ||||
\(206\) | 694.000 | + | 1202.04i | 0.234725 | + | 0.406555i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 574.000 | − | 994.197i | 0.191345 | − | 0.331419i | ||||
\(209\) | 880.000 | 0.291248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4268.00 | −1.39252 | −0.696259 | − | 0.717791i | \(-0.745153\pi\) | ||||
−0.696259 | + | 0.717791i | \(0.745153\pi\) | |||||||
\(212\) | 567.000 | − | 982.073i | 0.183687 | − | 0.318156i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 122.000 | + | 211.310i | 0.0389708 | + | 0.0674994i | ||||
\(215\) | −1024.00 | + | 1773.62i | −0.324820 | + | 0.562604i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 90.0000 | 0.0279613 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 448.000 | + | 775.959i | 0.137292 | + | 0.237796i | ||||
\(221\) | 756.000 | + | 1309.43i | 0.230109 | + | 0.398560i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5432.00 | 1.63118 | 0.815591 | − | 0.578629i | \(-0.196412\pi\) | ||||
0.815591 | + | 0.578629i | \(0.196412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 659.000 | − | 1141.42i | 0.193965 | − | 0.335957i | ||||
\(227\) | 1023.00 | + | 1771.89i | 0.299114 | + | 0.518081i | 0.975934 | − | 0.218068i | \(-0.0699756\pi\) |
−0.676819 | + | 0.736149i | \(0.736642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1490.00 | + | 2580.76i | −0.429965 | + | 0.744721i | −0.996870 | − | 0.0790622i | \(-0.974807\pi\) |
0.566905 | + | 0.823783i | \(0.308141\pi\) | |||||||
\(230\) | −768.000 | −0.220176 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1650.00 | −0.466930 | ||||||||
\(233\) | 2229.00 | − | 3860.74i | 0.626724 | − | 1.08552i | −0.361481 | − | 0.932379i | \(-0.617729\pi\) |
0.988205 | − | 0.153138i | \(-0.0489379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2592.00 | − | 4489.48i | −0.719504 | − | 1.24622i | ||||
\(236\) | 2835.00 | − | 4910.36i | 0.781961 | − | 1.35440i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4440.00 | −1.20167 | −0.600836 | − | 0.799372i | \(-0.705166\pi\) | ||||
−0.600836 | + | 0.799372i | \(0.705166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1651.00 | + | 2859.62i | 0.441287 | + | 0.764332i | 0.997785 | − | 0.0665168i | \(-0.0211886\pi\) |
−0.556498 | + | 0.830849i | \(0.687855\pi\) | |||||||
\(242\) | 633.500 | + | 1097.25i | 0.168277 | + | 0.291464i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3416.00 | −0.896258 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1540.00 | − | 2667.36i | 0.396712 | − | 0.687125i | ||||
\(248\) | −90.0000 | − | 155.885i | −0.0230444 | − | 0.0399140i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −48.0000 | + | 83.1384i | −0.0121431 | + | 0.0210325i | ||||
\(251\) | 1582.00 | 0.397829 | 0.198914 | − | 0.980017i | \(-0.436258\pi\) | ||||
0.198914 | + | 0.980017i | \(0.436258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −384.000 | −0.0954224 | ||||||||
\(254\) | 888.000 | − | 1538.06i | 0.219363 | − | 0.379947i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 59.5000 | + | 103.057i | 0.0145264 | + | 0.0251604i | ||||
\(257\) | −1177.00 | + | 2038.62i | −0.285678 | + | 0.494809i | −0.972773 | − | 0.231758i | \(-0.925552\pi\) |
0.687095 | + | 0.726567i | \(0.258885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3136.00 | 0.748025 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 559.000 | + | 968.216i | 0.131813 | + | 0.228308i | ||||
\(263\) | −1936.00 | − | 3353.25i | −0.453912 | − | 0.786199i | 0.544713 | − | 0.838623i | \(-0.316639\pi\) |
−0.998625 | + | 0.0524239i | \(0.983305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2592.00 | 0.600850 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 854.000 | − | 1479.17i | 0.194651 | − | 0.337145i | ||||
\(269\) | −90.0000 | − | 155.885i | −0.0203992 | − | 0.0353325i | 0.855646 | − | 0.517562i | \(-0.173160\pi\) |
−0.876045 | + | 0.482230i | \(0.839827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1016.00 | − | 1759.76i | 0.227740 | − | 0.394458i | −0.729398 | − | 0.684090i | \(-0.760200\pi\) |
0.957138 | + | 0.289632i | \(0.0935330\pi\) | |||||||
\(272\) | 2214.00 | 0.493542 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2274.00 | −0.501377 | ||||||||
\(275\) | −524.000 | + | 907.595i | −0.114903 | + | 0.199018i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2713.00 | + | 4699.05i | 0.588478 | + | 1.01927i | 0.994432 | + | 0.105380i | \(0.0336059\pi\) |
−0.405954 | + | 0.913893i | \(0.633061\pi\) | |||||||
\(278\) | −105.000 | + | 181.865i | −0.0226528 | + | 0.0392358i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −842.000 | −0.178753 | −0.0893764 | − | 0.995998i | \(-0.528487\pi\) | ||||
−0.0893764 | + | 0.995998i | \(0.528487\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1891.00 | − | 3275.31i | −0.397202 | − | 0.687975i | 0.596177 | − | 0.802853i | \(-0.296686\pi\) |
−0.993380 | + | 0.114878i | \(0.963352\pi\) | |||||||
\(284\) | 2688.00 | + | 4655.75i | 0.561632 | + | 0.972775i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −224.000 | −0.0463126 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 998.500 | − | 1729.45i | 0.203236 | − | 0.352016i | ||||
\(290\) | −880.000 | − | 1524.20i | −0.178191 | − | 0.308636i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2457.00 | − | 4255.65i | 0.492415 | − | 0.852887i | ||||
\(293\) | −4312.00 | −0.859760 | −0.429880 | − | 0.902886i | \(-0.641444\pi\) | ||||
−0.429880 | + | 0.902886i | \(0.641444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12960.0 | 2.55783 | ||||||||
\(296\) | −1845.00 | + | 3195.63i | −0.362292 | + | 0.627508i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1005.00 | − | 1740.71i | −0.195363 | − | 0.338378i | ||||
\(299\) | −672.000 | + | 1163.94i | −0.129976 | + | 0.225125i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1112.00 | 0.211882 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2255.00 | − | 3905.77i | −0.425438 | − | 0.736880i | ||||
\(305\) | −3904.00 | − | 6761.93i | −0.732926 | − | 1.26946i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2674.00 | −0.497112 | −0.248556 | − | 0.968618i | \(-0.579956\pi\) | ||||
−0.248556 | + | 0.968618i | \(0.579956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 96.0000 | − | 166.277i | 0.0175885 | − | 0.0304642i | ||||
\(311\) | 1884.00 | + | 3263.18i | 0.343511 | + | 0.594978i | 0.985082 | − | 0.172085i | \(-0.0550505\pi\) |
−0.641571 | + | 0.767063i | \(0.721717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1219.00 | − | 2111.37i | 0.220134 | − | 0.381283i | −0.734714 | − | 0.678376i | \(-0.762684\pi\) |
0.954849 | + | 0.297093i | \(0.0960172\pi\) | |||||||
\(314\) | −124.000 | −0.0222857 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3080.00 | −0.548302 | ||||||||
\(317\) | −1593.00 | + | 2759.16i | −0.282245 | + | 0.488863i | −0.971937 | − | 0.235239i | \(-0.924413\pi\) |
0.689692 | + | 0.724103i | \(0.257746\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −440.000 | − | 762.102i | −0.0772266 | − | 0.133760i | ||||
\(320\) | 1336.00 | − | 2314.02i | 0.233390 | − | 0.404243i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5940.00 | 1.02325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1834.00 | + | 3176.58i | 0.313022 | + | 0.542169i | ||||
\(326\) | −1004.00 | − | 1738.98i | −0.170572 | − | 0.295439i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2730.00 | −0.459570 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4336.00 | + | 7510.17i | −0.720025 | + | 1.24712i | 0.240965 | + | 0.970534i | \(0.422536\pi\) |
−0.960989 | + | 0.276585i | \(0.910797\pi\) | |||||||
\(332\) | −4557.00 | − | 7892.96i | −0.753307 | − | 1.30477i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1442.00 | + | 2497.62i | −0.236236 | + | 0.409172i | ||||
\(335\) | 3904.00 | 0.636711 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 814.000 | 0.131577 | 0.0657884 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657884 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(338\) | 706.500 | − | 1223.69i | 0.113694 | − | 0.196924i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3024.00 | + | 5237.72i | 0.482351 | + | 0.835457i | ||||
\(341\) | 48.0000 | − | 83.1384i | 0.00762271 | − | 0.0132029i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1920.00 | −0.300929 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1114.00 | − | 1929.50i | −0.173090 | − | 0.299800i | ||||
\(347\) | 4672.00 | + | 8092.14i | 0.722784 | + | 1.25190i | 0.959880 | + | 0.280413i | \(0.0904713\pi\) |
−0.237095 | + | 0.971486i | \(0.576195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5180.00 | 0.794496 | 0.397248 | − | 0.917711i | \(-0.369965\pi\) | ||||
0.397248 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −644.000 | + | 1115.44i | −0.0975151 | + | 0.168901i | ||||
\(353\) | −6089.00 | − | 10546.5i | −0.918087 | − | 1.59017i | −0.802317 | − | 0.596898i | \(-0.796400\pi\) |
−0.115770 | − | 0.993276i | \(-0.536933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6144.00 | + | 10641.7i | −0.918562 | + | 1.59100i | ||||
\(356\) | −5110.00 | −0.760757 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 820.000 | 0.121057 | ||||||||
\(359\) | 220.000 | − | 381.051i | 0.0323431 | − | 0.0560198i | −0.849401 | − | 0.527748i | \(-0.823036\pi\) |
0.881744 | + | 0.471729i | \(0.156370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2620.50 | − | 4538.84i | −0.382053 | − | 0.661735i | ||||
\(362\) | 1946.00 | − | 3370.57i | 0.282540 | − | 0.489374i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11232.0 | 1.61071 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4908.00 | − | 8500.91i | −0.698080 | − | 1.20911i | −0.969131 | − | 0.246546i | \(-0.920704\pi\) |
0.271051 | − | 0.962565i | \(-0.412629\pi\) | |||||||
\(368\) | 984.000 | + | 1704.34i | 0.139387 | + | 0.241426i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3936.00 | −0.553035 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 221.000 | − | 382.783i | 0.0306781 | − | 0.0531361i | −0.850279 | − | 0.526333i | \(-0.823567\pi\) |
0.880957 | + | 0.473197i | \(0.156900\pi\) | |||||||
\(374\) | −216.000 | − | 374.123i | −0.0298639 | − | 0.0517258i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2430.00 | − | 4208.88i | 0.333292 | − | 0.577278i | ||||
\(377\) | −3080.00 | −0.420764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3960.00 | −0.536706 | −0.268353 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268353 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(380\) | 6160.00 | − | 10669.4i | 0.831582 | − | 1.44034i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2524.00 | − | 4371.70i | −0.338060 | − | 0.585538i | ||||
\(383\) | −3354.00 | + | 5809.30i | −0.447471 | + | 0.775043i | −0.998221 | − | 0.0596280i | \(-0.981009\pi\) |
0.550750 | + | 0.834670i | \(0.314342\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2962.00 | −0.390575 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1029.00 | − | 1782.28i | −0.134638 | − | 0.233200i | ||||
\(389\) | −6675.00 | − | 11561.4i | −0.870015 | − | 1.50691i | −0.861980 | − | 0.506943i | \(-0.830775\pi\) |
−0.00803563 | − | 0.999968i | \(-0.502558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2592.00 | −0.335251 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1667.00 | − | 2887.33i | 0.213153 | − | 0.369192i | ||||
\(395\) | −3520.00 | − | 6096.82i | −0.448381 | − | 0.776618i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −678.000 | + | 1174.33i | −0.0857125 | + | 0.148458i | −0.905695 | − | 0.423931i | \(-0.860650\pi\) |
0.819982 | + | 0.572389i | \(0.193983\pi\) | |||||||
\(398\) | −1860.00 | −0.234255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5371.00 | 0.671375 | ||||||||
\(401\) | 3111.00 | − | 5388.41i | 0.387421 | − | 0.671033i | −0.604681 | − | 0.796468i | \(-0.706699\pi\) |
0.992102 | + | 0.125435i | \(0.0400326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −168.000 | − | 290.985i | −0.0207659 | − | 0.0359677i | ||||
\(404\) | −2408.00 | + | 4170.78i | −0.296541 | + | 0.513624i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1968.00 | −0.239681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2575.00 | + | 4460.03i | 0.311309 | + | 0.539204i | 0.978646 | − | 0.205552i | \(-0.0658991\pi\) |
−0.667337 | + | 0.744756i | \(0.732566\pi\) | |||||||
\(410\) | −1456.00 | − | 2521.87i | −0.175382 | − | 0.303771i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9716.00 | 1.16183 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10416.0 | − | 18041.0i | 1.23205 | − | 2.13398i | ||||
\(416\) | 2254.00 | + | 3904.04i | 0.265653 | + | 0.460124i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −440.000 | + | 762.102i | −0.0514859 | + | 0.0891762i | ||||
\(419\) | 2310.00 | 0.269334 | 0.134667 | − | 0.990891i | \(-0.457004\pi\) | ||||
0.134667 | + | 0.990891i | \(0.457004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1262.00 | 0.146095 | 0.0730476 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730476 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(422\) | 2134.00 | − | 3696.20i | 0.246165 | − | 0.426370i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1215.00 | + | 2104.44i | 0.139164 | + | 0.241039i | ||||
\(425\) | −3537.00 | + | 6126.26i | −0.403693 | + | 0.699218i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1708.00 | 0.192896 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1024.00 | − | 1773.62i | −0.114841 | − | 0.198911i | ||||
\(431\) | −2244.00 | − | 3886.72i | −0.250788 | − | 0.434378i | 0.712955 | − | 0.701210i | \(-0.247356\pi\) |
−0.963743 | + | 0.266832i | \(0.914023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17038.0 | −1.89098 | −0.945490 | − | 0.325652i | \(-0.894416\pi\) | ||||
−0.945490 | + | 0.325652i | \(0.894416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 315.000 | − | 545.596i | 0.0346004 | − | 0.0599296i | ||||
\(437\) | 2640.00 | + | 4572.61i | 0.288989 | + | 0.500544i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8100.00 | − | 14029.6i | 0.880619 | − | 1.52528i | 0.0299658 | − | 0.999551i | \(-0.490460\pi\) |
0.850654 | − | 0.525727i | \(-0.176206\pi\) | |||||||
\(440\) | −1920.00 | −0.208028 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1512.00 | −0.162712 | ||||||||
\(443\) | −4386.00 | + | 7596.77i | −0.470395 | + | 0.814749i | −0.999427 | − | 0.0338535i | \(-0.989222\pi\) |
0.529031 | + | 0.848602i | \(0.322555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5840.00 | − | 10115.2i | −0.622118 | − | 1.07754i | ||||
\(446\) | −2716.00 | + | 4704.25i | −0.288355 | + | 0.499446i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2130.00 | −0.223877 | −0.111939 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111939 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −728.000 | − | 1260.93i | −0.0760093 | − | 0.131652i | ||||
\(452\) | −4613.00 | − | 7989.95i | −0.480038 | − | 0.831451i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2046.00 | −0.211506 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5267.00 | + | 9122.71i | −0.539124 | + | 0.933791i | 0.459827 | + | 0.888009i | \(0.347911\pi\) |
−0.998951 | + | 0.0457824i | \(0.985422\pi\) | |||||||
\(458\) | −1490.00 | − | 2580.76i | −0.152016 | − | 0.263299i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2688.00 | + | 4655.75i | −0.272454 | + | 0.471903i | ||||
\(461\) | −9268.00 | −0.936342 | −0.468171 | − | 0.883638i | \(-0.655087\pi\) | ||||
−0.468171 | + | 0.883638i | \(0.655087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9392.00 | −0.942728 | −0.471364 | − | 0.881939i | \(-0.656238\pi\) | ||||
−0.471364 | + | 0.881939i | \(0.656238\pi\) | |||||||
\(464\) | −2255.00 | + | 3905.77i | −0.225616 | + | 0.390778i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2229.00 | + | 3860.74i | 0.221580 | + | 0.383788i | ||||
\(467\) | 5403.00 | − | 9358.27i | 0.535377 | − | 0.927300i | −0.463768 | − | 0.885957i | \(-0.653503\pi\) |
0.999145 | − | 0.0413434i | \(-0.0131638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5184.00 | 0.508766 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6075.00 | + | 10522.2i | 0.592425 | + | 1.02611i | ||||
\(473\) | −512.000 | − | 886.810i | −0.0497712 | − | 0.0862063i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14410.0 | 1.39195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2220.00 | − | 3845.15i | 0.212428 | − | 0.367936i | ||||
\(479\) | −2470.00 | − | 4278.17i | −0.235610 | − | 0.408088i | 0.723840 | − | 0.689968i | \(-0.242375\pi\) |
−0.959450 | + | 0.281880i | \(0.909042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3444.00 | + | 5965.18i | −0.326472 | + | 0.565466i | ||||
\(482\) | −3302.00 | −0.312037 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8869.00 | 0.832926 | ||||||||
\(485\) | 2352.00 | − | 4073.78i | 0.220204 | − | 0.381404i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2608.00 | + | 4517.19i | 0.242669 | + | 0.420315i | 0.961474 | − | 0.274897i | \(-0.0886438\pi\) |
−0.718805 | + | 0.695212i | \(0.755310\pi\) | |||||||
\(488\) | 3660.00 | − | 6339.31i | 0.339509 | − | 0.588047i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4412.00 | −0.405521 | −0.202760 | − | 0.979228i | \(-0.564991\pi\) | ||||
−0.202760 | + | 0.979228i | \(0.564991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2970.00 | − | 5144.19i | −0.271323 | − | 0.469945i | ||||
\(494\) | 1540.00 | + | 2667.36i | 0.140259 | + | 0.242935i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −492.000 | −0.0445392 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9530.00 | + | 16506.4i | −0.854953 | + | 1.48082i | 0.0217362 | + | 0.999764i | \(0.493081\pi\) |
−0.876689 | + | 0.481058i | \(0.840253\pi\) | |||||||
\(500\) | 336.000 | + | 581.969i | 0.0300528 | + | 0.0520529i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −791.000 | + | 1370.05i | −0.0703268 | + | 0.121810i | ||||
\(503\) | 12768.0 | 1.13180 | 0.565902 | − | 0.824473i | \(-0.308528\pi\) | ||||
0.565902 | + | 0.824473i | \(0.308528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11008.0 | −0.969999 | ||||||||
\(506\) | 192.000 | − | 332.554i | 0.0168685 | − | 0.0292170i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6216.00 | − | 10766.4i | −0.542894 | − | 0.940321i | ||||
\(509\) | 2750.00 | − | 4763.14i | 0.239473 | − | 0.414779i | −0.721090 | − | 0.692841i | \(-0.756359\pi\) |
0.960563 | + | 0.278062i | \(0.0896921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11521.0 | 0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1177.00 | − | 2038.62i | −0.101002 | − | 0.174941i | ||||
\(515\) | 11104.0 | + | 19232.7i | 0.950098 | + | 1.64562i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2592.00 | 0.220495 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3360.00 | + | 5819.69i | −0.283357 | + | 0.490789i | ||||
\(521\) | 3669.00 | + | 6354.89i | 0.308526 | + | 0.534382i | 0.978040 | − | 0.208417i | \(-0.0668311\pi\) |
−0.669514 | + | 0.742799i | \(0.733498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8791.00 | + | 15226.5i | −0.734997 | + | 1.27305i | 0.219727 | + | 0.975561i | \(0.429483\pi\) |
−0.954725 | + | 0.297491i | \(0.903850\pi\) | |||||||
\(524\) | 7826.00 | 0.652444 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3872.00 | 0.320964 | ||||||||
\(527\) | 324.000 | − | 561.184i | 0.0267811 | − | 0.0463863i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4931.50 | + | 8541.61i | 0.405318 | + | 0.702031i | ||||
\(530\) | −1296.00 | + | 2244.74i | −0.106216 | + | 0.183972i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5096.00 | −0.414132 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1952.00 | + | 3380.96i | 0.157743 | + | 0.273218i | ||||
\(536\) | 1830.00 | + | 3169.65i | 0.147470 | + | 0.255426i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 180.000 | 0.0144244 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 809.000 | − | 1401.23i | 0.0642914 | − | 0.111356i | −0.832088 | − | 0.554644i | \(-0.812855\pi\) |
0.896379 | + | 0.443288i | \(0.146188\pi\) | |||||||
\(542\) | 1016.00 | + | 1759.76i | 0.0805183 | + | 0.139462i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4347.00 | + | 7529.22i | −0.342603 | + | 0.593406i | ||||
\(545\) | 1440.00 | 0.113179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16144.0 | 1.26192 | 0.630958 | − | 0.775817i | \(-0.282662\pi\) | ||||
0.630958 | + | 0.775817i | \(0.282662\pi\) | |||||||
\(548\) | −7959.00 | + | 13785.4i | −0.620423 | + | 1.07460i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −524.000 | − | 907.595i | −0.0406244 | − | 0.0703636i | ||||
\(551\) | −6050.00 | + | 10478.9i | −0.467765 | + | 0.810193i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5426.00 | −0.416117 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 735.000 | + | 1273.06i | 0.0560628 | + | 0.0971037i | ||||
\(557\) | 2327.00 | + | 4030.48i | 0.177016 | + | 0.306601i | 0.940857 | − | 0.338803i | \(-0.110022\pi\) |
−0.763841 | + | 0.645405i | \(0.776689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3584.00 | −0.271175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 421.000 | − | 729.193i | 0.0315993 | − | 0.0547316i | ||||
\(563\) | −5039.00 | − | 8727.80i | −0.377209 | − | 0.653345i | 0.613446 | − | 0.789736i | \(-0.289783\pi\) |
−0.990655 | + | 0.136392i | \(0.956449\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10544.0 | − | 18262.7i | 0.785114 | − | 1.35986i | ||||
\(566\) | 3782.00 | 0.280865 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11520.0 | −0.851001 | ||||||||
\(569\) | −2965.00 | + | 5135.53i | −0.218452 | + | 0.378370i | −0.954335 | − | 0.298739i | \(-0.903434\pi\) |
0.735883 | + | 0.677109i | \(0.236767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9524.00 | + | 16496.1i | 0.698016 | + | 1.20900i | 0.969153 | + | 0.246458i | \(0.0792668\pi\) |
−0.271138 | + | 0.962541i | \(0.587400\pi\) | |||||||
\(572\) | −784.000 | + | 1357.93i | −0.0573089 | + | 0.0992619i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6288.00 | −0.456048 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7183.00 | − | 12441.3i | −0.518253 | − | 0.897641i | −0.999775 | − | 0.0212070i | \(-0.993249\pi\) |
0.481522 | − | 0.876434i | \(-0.340084\pi\) | |||||||
\(578\) | 998.500 | + | 1729.45i | 0.0718549 | + | 0.124456i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12320.0 | −0.882000 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −648.000 | + | 1122.37i | −0.0460333 | + | 0.0797320i | ||||
\(584\) | 5265.00 | + | 9119.25i | 0.373060 | + | 0.646159i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2156.00 | − | 3734.30i | 0.151986 | − | 0.263247i | ||||
\(587\) | −3626.00 | −0.254959 | −0.127480 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127480 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1320.00 | −0.0923424 | ||||||||
\(590\) | −6480.00 | + | 11223.7i | −0.452165 | + | 0.783173i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5043.00 | + | 8734.73i | 0.350112 | + | 0.606411i | ||||
\(593\) | 531.000 | − | 919.719i | 0.0367716 | − | 0.0636903i | −0.847054 | − | 0.531507i | \(-0.821626\pi\) |
0.883826 | + | 0.467817i | \(0.154959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14070.0 | −0.966996 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −672.000 | − | 1163.94i | −0.0459534 | − | 0.0795936i | ||||
\(599\) | −5100.00 | − | 8833.46i | −0.347880 | − | 0.602547i | 0.637992 | − | 0.770043i | \(-0.279765\pi\) |
−0.985873 | + | 0.167496i | \(0.946432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25158.0 | 1.70751 | 0.853757 | − | 0.520671i | \(-0.174318\pi\) | ||||
0.853757 | + | 0.520671i | \(0.174318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3892.00 | − | 6741.14i | 0.262191 | − | 0.454128i | ||||
\(605\) | 10136.0 | + | 17556.1i | 0.681136 | + | 1.17976i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12832.0 | − | 22225.7i | 0.858047 | − | 1.48618i | −0.0157413 | − | 0.999876i | \(-0.505011\pi\) |
0.873789 | − | 0.486306i | \(-0.161656\pi\) | |||||||
\(608\) | 17710.0 | 1.18131 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7808.00 | 0.518257 | ||||||||
\(611\) | 4536.00 | − | 7856.58i | 0.300339 | − | 0.520202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9509.00 | − | 16470.1i | −0.626533 | − | 1.08519i | −0.988242 | − | 0.152896i | \(-0.951140\pi\) |
0.361709 | − | 0.932291i | \(-0.382193\pi\) | |||||||
\(614\) | 1337.00 | − | 2315.75i | 0.0878777 | − | 0.152209i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17334.0 | −1.13102 | −0.565511 | − | 0.824741i | \(-0.691321\pi\) | ||||
−0.565511 | + | 0.824741i | \(0.691321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9365.00 | + | 16220.7i | 0.608096 | + | 1.05325i | 0.991554 | + | 0.129694i | \(0.0413996\pi\) |
−0.383459 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(620\) | −672.000 | − | 1163.94i | −0.0435293 | − | 0.0753950i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3768.00 | −0.242899 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7419.50 | − | 12851.0i | 0.474848 | − | 0.822461i | ||||
\(626\) | 1219.00 | + | 2111.37i | 0.0778291 | + | 0.134804i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −434.000 | + | 751.710i | −0.0275772 | + | 0.0477651i | ||||
\(629\) | −13284.0 | −0.842079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6928.00 | −0.437083 | −0.218541 | − | 0.975828i | \(-0.570130\pi\) | ||||
−0.218541 | + | 0.975828i | \(0.570130\pi\) | |||||||
\(632\) | 3300.00 | − | 5715.77i | 0.207701 | − | 0.359748i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1593.00 | − | 2759.16i | −0.0997888 | − | 0.172839i | ||||
\(635\) | 14208.0 | − | 24609.0i | 0.887917 | − | 1.53792i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 880.000 | 0.0546074 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11640.0 | + | 20161.1i | 0.718924 | + | 1.24521i | ||||
\(641\) | 8151.00 | + | 14117.9i | 0.502255 | + | 0.869930i | 0.999997 | + | 0.00260525i | \(0.000829277\pi\) |
−0.497742 | + | 0.867325i | \(0.665837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4718.00 | −0.289362 | −0.144681 | − | 0.989478i | \(-0.546216\pi\) | ||||
−0.144681 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2970.00 | + | 5144.19i | −0.180887 | + | 0.313306i | ||||
\(647\) | 10718.0 | + | 18564.1i | 0.651264 | + | 1.12802i | 0.982816 | + | 0.184586i | \(0.0590944\pi\) |
−0.331552 | + | 0.943437i | \(0.607572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3240.00 | + | 5611.84i | −0.195965 | + | 0.339421i | ||||
\(650\) | −3668.00 | −0.221340 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14056.0 | −0.844287 | ||||||||
\(653\) | 2229.00 | − | 3860.74i | 0.133580 | − | 0.231367i | −0.791474 | − | 0.611202i | \(-0.790686\pi\) |
0.925054 | + | 0.379836i | \(0.124019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8944.00 | + | 15491.5i | 0.533544 | + | 0.924124i | ||||
\(656\) | −3731.00 | + | 6462.28i | −0.222060 | + | 0.384618i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26640.0 | 1.57473 | 0.787365 | − | 0.616487i | \(-0.211445\pi\) | ||||
0.787365 | + | 0.616487i | \(0.211445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3716.00 | + | 6436.30i | 0.218662 | + | 0.378734i | 0.954399 | − | 0.298533i | \(-0.0964974\pi\) |
−0.735737 | + | 0.677267i | \(0.763164\pi\) | |||||||
\(662\) | −4336.00 | − | 7510.17i | −0.254567 | − | 0.440923i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19530.0 | 1.14143 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2640.00 | − | 4572.61i | 0.153255 | − | 0.265446i | ||||
\(668\) | 10094.0 | + | 17483.3i | 0.584654 | + | 1.01265i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1952.00 | + | 3380.96i | −0.112556 | + | 0.194952i | ||||
\(671\) | 3904.00 | 0.224608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 58.0000 | 0.00332204 | 0.00166102 | − | 0.999999i | \(-0.499471\pi\) | ||||
0.00166102 | + | 0.999999i | \(0.499471\pi\) | |||||||
\(674\) | −407.000 | + | 704.945i | −0.0232597 | + | 0.0402870i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4945.50 | − | 8565.86i | −0.281378 | − | 0.487361i | ||||
\(677\) | 10758.0 | − | 18633.4i | 0.610729 | − | 1.05781i | −0.380389 | − | 0.924827i | \(-0.624210\pi\) |
0.991118 | − | 0.132987i | \(-0.0424568\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12960.0 | −0.730873 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48.0000 | + | 83.1384i | 0.00269504 | + | 0.00466794i | ||||
\(683\) | 9054.00 | + | 15682.0i | 0.507235 | + | 0.878557i | 0.999965 | + | 0.00837480i | \(0.00266581\pi\) |
−0.492730 | + | 0.870182i | \(0.664001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36384.0 | −2.02943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2624.00 | + | 4544.90i | −0.145406 | + | 0.251850i | ||||
\(689\) | 2268.00 | + | 3928.29i | 0.125405 | + | 0.217208i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5039.00 | + | 8727.80i | −0.277413 | + | 0.480494i | −0.970741 | − | 0.240128i | \(-0.922810\pi\) |
0.693328 | + | 0.720622i | \(0.256144\pi\) | |||||||
\(692\) | −15596.0 | −0.856750 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9344.00 | −0.511086 | ||||||||
\(695\) | −1680.00 | + | 2909.85i | −0.0916921 | + | 0.158815i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4914.00 | − | 8511.30i | −0.267046 | − | 0.462537i | ||||
\(698\) | −2590.00 | + | 4486.01i | −0.140448 | + | 0.243264i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18762.0 | −1.01089 | −0.505443 | − | 0.862860i | \(-0.668671\pi\) | ||||
−0.505443 | + | 0.862860i | \(0.668671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13530.0 | + | 23434.6i | 0.725880 | + | 1.25726i | ||||
\(704\) | 668.000 | + | 1157.01i | 0.0357616 | + | 0.0619410i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12178.0 | 0.649186 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3405.00 | + | 5897.63i | −0.180363 | + | 0.312398i | −0.942004 | − | 0.335601i | \(-0.891061\pi\) |
0.761641 | + | 0.647999i | \(0.224394\pi\) | |||||||
\(710\) | −6144.00 | − | 10641.7i | −0.324761 | − | 0.562502i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5475.00 | − | 9482.98i | 0.288180 | − | 0.499143i | ||||
\(713\) | 576.000 | 0.0302544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3584.00 | −0.187460 | ||||||||
\(716\) | 2870.00 | − | 4970.99i | 0.149800 | − | 0.259462i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 220.000 | + | 381.051i | 0.0114350 | + | 0.0198060i | ||||
\(719\) | −2430.00 | + | 4208.88i | −0.126041 | + | 0.218310i | −0.922140 | − | 0.386858i | \(-0.873561\pi\) |
0.796098 | + | 0.605167i | \(0.206894\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5241.00 | 0.270152 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13622.0 | − | 23594.0i | −0.699251 | − | 1.21114i | ||||
\(725\) | −7205.00 | − | 12479.4i | −0.369085 | − | 0.639275i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13636.0 | 0.695641 | 0.347821 | − | 0.937561i | \(-0.386922\pi\) | ||||
0.347821 | + | 0.937561i | \(0.386922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5616.00 | + | 9727.20i | −0.284736 | + | 0.493178i | ||||
\(731\) | −3456.00 | − | 5985.97i | −0.174863 | − | 0.302871i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1044.00 | − | 1808.26i | 0.0526071 | − | 0.0911182i | −0.838523 | − | 0.544867i | \(-0.816580\pi\) |
0.891130 | + | 0.453749i | \(0.149914\pi\) | |||||||
\(734\) | 9816.00 | 0.493617 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7728.00 | −0.387035 | ||||||||
\(737\) | −976.000 | + | 1690.48i | −0.0487808 | + | 0.0844908i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2580.00 | + | 4468.69i | 0.128426 | + | 0.222440i | 0.923067 | − | 0.384639i | \(-0.125674\pi\) |
−0.794641 | + | 0.607080i | \(0.792341\pi\) | |||||||
\(740\) | −13776.0 | + | 23860.7i | −0.684346 | + | 1.18532i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28152.0 | 1.39004 | 0.695018 | − | 0.718992i | \(-0.255396\pi\) | ||||
0.695018 | + | 0.718992i | \(0.255396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16080.0 | − | 27851.4i | −0.790773 | − | 1.36966i | ||||
\(746\) | 221.000 | + | 382.783i | 0.0108464 | + | 0.0187864i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3024.00 | −0.147819 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8404.00 | − | 14556.2i | 0.408344 | − | 0.707272i | −0.586360 | − | 0.810050i | \(-0.699440\pi\) |
0.994704 | + | 0.102778i | \(0.0327731\pi\) | |||||||
\(752\) | −6642.00 | − | 11504.3i | −0.322086 | − | 0.557870i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1540.00 | − | 2667.36i | 0.0743813 | − | 0.128832i | ||||
\(755\) | 17792.0 | 0.857639 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21674.0 | 1.04063 | 0.520314 | − | 0.853975i | \(-0.325815\pi\) | ||||
0.520314 | + | 0.853975i | \(0.325815\pi\) | |||||||
\(758\) | 1980.00 | − | 3429.46i | 0.0948771 | − | 0.164332i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13200.0 | + | 22863.1i | 0.630019 | + | 1.09122i | ||||
\(761\) | −3711.00 | + | 6427.64i | −0.176772 | + | 0.306178i | −0.940773 | − | 0.339037i | \(-0.889899\pi\) |
0.764001 | + | 0.645215i | \(0.223232\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35336.0 | −1.67331 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3354.00 | − | 5809.30i | −0.158205 | − | 0.274019i | ||||
\(767\) | 11340.0 | + | 19641.5i | 0.533851 | + | 0.924657i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13790.0 | −0.646658 | −0.323329 | − | 0.946287i | \(-0.604802\pi\) | ||||
−0.323329 | + | 0.946287i | \(0.604802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10367.0 | + | 17956.2i | −0.483312 | + | 0.837120i | ||||
\(773\) | 3116.00 | + | 5397.07i | 0.144987 | + | 0.251124i | 0.929368 | − | 0.369155i | \(-0.120353\pi\) |
−0.784381 | + | 0.620279i | \(0.787019\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 786.000 | − | 1361.39i | 0.0364309 | − | 0.0631002i | ||||
\(776\) | 4410.00 | 0.204007 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13350.0 | 0.615194 | ||||||||
\(779\) | −10010.0 | + | 17337.8i | −0.460392 | + | 0.797423i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3072.00 | − | 5320.86i | −0.140749 | − | 0.243784i | ||||
\(782\) | 1296.00 | − | 2244.74i | 0.0592645 | − | 0.102649i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1984.00 | −0.0902064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −883.000 | − | 1529.40i | −0.0399943 | − | 0.0692722i | 0.845335 | − | 0.534236i | \(-0.179401\pi\) |
−0.885330 | + | 0.464964i | \(0.846067\pi\) | |||||||
\(788\) | −11669.0 | − | 20211.3i | −0.527527 | − | 0.913703i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7040.00 | 0.317053 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6832.00 | − | 11833.4i | 0.305941 | − | 0.529906i | ||||
\(794\) | −678.000 | − | 1174.33i | −0.0303039 | − | 0.0524879i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6510.00 | + | 11275.7i | −0.289875 | + | 0.502079i | ||||
\(797\) | 1204.00 | 0.0535105 | 0.0267552 | − | 0.999642i | \(-0.491483\pi\) | ||||
0.0267552 | + | 0.999642i | \(0.491483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17496.0 | 0.774673 | ||||||||
\(800\) | −10545.5 | + | 18265.3i | −0.466050 | + | 0.807222i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3111.00 | + | 5388.41i | 0.136974 | + | 0.237246i | ||||
\(803\) | −2808.00 | + | 4863.60i | −0.123402 | + | 0.213739i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 336.000 | 0.0146837 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5160.00 | − | 8937.38i | −0.224664 | − | 0.389129i | ||||
\(809\) | −3525.00 | − | 6105.48i | −0.153192 | − | 0.265336i | 0.779207 | − | 0.626766i | \(-0.215622\pi\) |
−0.932399 | + | 0.361430i | \(0.882289\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23282.0 | −1.00807 | −0.504033 | − | 0.863684i | \(-0.668151\pi\) | ||||
−0.504033 | + | 0.863684i | \(0.668151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 984.000 | − | 1704.34i | 0.0423700 | − | 0.0733870i | ||||
\(815\) | −16064.0 | − | 27823.7i | −0.690426 | − | 1.19585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7040.00 | + | 12193.6i | −0.301467 | + | 0.522156i | ||||
\(818\) | −5150.00 | −0.220129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20384.0 | −0.868098 | ||||||||
\(821\) | 5071.00 | − | 8783.23i | 0.215565 | − | 0.373370i | −0.737882 | − | 0.674930i | \(-0.764174\pi\) |
0.953447 | + | 0.301560i | \(0.0975073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4596.00 | + | 7960.51i | 0.194662 | + | 0.337164i | 0.946790 | − | 0.321853i | \(-0.104306\pi\) |
−0.752128 | + | 0.659017i | \(0.770972\pi\) | |||||||
\(824\) | −10410.0 | + | 18030.6i | −0.440109 | + | 0.762291i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46716.0 | 1.96430 | 0.982149 | − | 0.188104i | \(-0.0602344\pi\) | ||||
0.982149 | + | 0.188104i | \(0.0602344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5620.00 | + | 9734.13i | 0.235453 | + | 0.407817i | 0.959404 | − | 0.282034i | \(-0.0910092\pi\) |
−0.723951 | + | 0.689851i | \(0.757676\pi\) | |||||||
\(830\) | 10416.0 | + | 18041.0i | 0.435596 | + | 0.754474i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4676.00 | 0.194845 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23072.0 | + | 39961.9i | −0.956215 | + | 1.65621i | ||||
\(836\) | 3080.00 | + | 5334.72i | 0.127421 | + | 0.220700i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1155.00 | + | 2000.52i | −0.0476119 | + | 0.0824663i | ||||
\(839\) | 700.000 | 0.0288042 | 0.0144021 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0144021 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12289.0 | −0.503875 | ||||||||
\(842\) | −631.000 | + | 1092.92i | −0.0258262 | + | 0.0447324i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14938.0 | − | 25873.4i | −0.609226 | − | 1.05521i | ||||
\(845\) | 11304.0 | − | 19579.1i | 0.460200 | − | 0.797091i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6642.00 | 0.268971 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3537.00 | − | 6126.26i | −0.142727 | − | 0.247211i | ||||
\(851\) | −5904.00 | − | 10226.0i | −0.237822 | − | 0.411920i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37492.0 | 1.50493 | 0.752463 | − | 0.658635i | \(-0.228866\pi\) | ||||
0.752463 | + | 0.658635i | \(0.228866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1830.00 | + | 3169.65i | −0.0730702 | + | 0.126561i | ||||
\(857\) | −14447.0 | − | 25022.9i | −0.575846 | − | 0.997395i | −0.995949 | − | 0.0899183i | \(-0.971339\pi\) |
0.420103 | − | 0.907476i | \(-0.361994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1385.00 | + | 2398.89i | −0.0550123 | + | 0.0952841i | −0.892220 | − | 0.451601i | \(-0.850853\pi\) |
0.837208 | + | 0.546885i | \(0.184186\pi\) | |||||||
\(860\) | −14336.0 | −0.568434 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4488.00 | 0.177334 | ||||||||
\(863\) | 8844.00 | − | 15318.3i | 0.348845 | − | 0.604217i | −0.637200 | − | 0.770699i | \(-0.719907\pi\) |
0.986045 | + | 0.166482i | \(0.0532406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17824.0 | − | 30872.1i | −0.700618 | − | 1.21351i | ||||
\(866\) | 8519.00 | − | 14755.3i | 0.334281 | − | 0.578992i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3520.00 | 0.137408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3416.00 | + | 5916.69i | 0.132889 | + | 0.230171i | ||||
\(872\) | 675.000 | + | 1169.13i | 0.0262137 | + | 0.0454035i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5280.00 | −0.204346 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16783.0 | − | 29069.0i | 0.646205 | − | 1.11926i | −0.337817 | − | 0.941212i | \(-0.609688\pi\) |
0.984022 | − | 0.178048i | \(-0.0569782\pi\) | |||||||
\(878\) | 8100.00 | + | 14029.6i | 0.311346 | + | 0.539267i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2624.00 | + | 4544.90i | −0.100517 | + | 0.174101i | ||||
\(881\) | −16758.0 | −0.640853 | −0.320426 | − | 0.947273i | \(-0.603826\pi\) | ||||
−0.320426 | + | 0.947273i | \(0.603826\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11468.0 | 0.437066 | 0.218533 | − | 0.975830i | \(-0.429873\pi\) | ||||
0.218533 | + | 0.975830i | \(0.429873\pi\) | |||||||
\(884\) | −5292.00 | + | 9166.01i | −0.201345 | + | 0.348740i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4386.00 | − | 7596.77i | −0.166310 | − | 0.288057i | ||||
\(887\) | 25178.0 | − | 43609.6i | 0.953094 | − | 1.65081i | 0.214424 | − | 0.976741i | \(-0.431213\pi\) |
0.738670 | − | 0.674067i | \(-0.235454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11680.0 | 0.439904 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19012.0 | + | 32929.7i | 0.713642 | + | 1.23606i | ||||
\(893\) | −17820.0 | − | 30865.1i | −0.667776 | − | 1.15662i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13120.0 | 0.490004 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1065.00 | − | 1844.63i | 0.0395763 | − | 0.0685481i | ||||
\(899\) | 660.000 | + | 1143.15i | 0.0244852 | + | 0.0424097i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4374.00 | + | 7575.99i | −0.161730 | + | 0.280125i | ||||
\(902\) | 1456.00 | 0.0537467 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19770.0 | 0.727368 | ||||||||
\(905\) | 31136.0 | − | 53929.1i | 1.14364 | − | 1.98085i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4358.00 | + | 7548.28i | 0.159542 | + | 0.276336i | 0.934704 | − | 0.355428i | \(-0.115665\pi\) |
−0.775161 | + | 0.631763i | \(0.782331\pi\) | |||||||
\(908\) | −7161.00 | + | 12403.2i | −0.261725 | + | 0.453321i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7632.00 | −0.277563 | −0.138781 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138781 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5208.00 | + | 9020.52i | 0.188784 | + | 0.326983i | ||||
\(914\) | −5267.00 | − | 9122.71i | −0.190609 | − | 0.330145i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20860.0 | −0.752439 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11540.0 | − | 19987.9i | 0.414221 | − | 0.717453i | −0.581125 | − | 0.813814i | \(-0.697387\pi\) |
0.995346 | + | 0.0963618i | \(0.0307206\pi\) | |||||||
\(920\) | −5760.00 | − | 9976.61i | −0.206415 | − | 0.357521i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4634.00 | − | 8026.32i | 0.165523 | − | 0.286695i | ||||
\(923\) | −21504.0 | −0.766861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32226.0 | −1.14550 | ||||||||
\(926\) | 4696.00 | − | 8133.71i | 0.166652 | − | 0.288650i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8855.00 | − | 15337.3i | −0.313232 | − | 0.542534i | ||||
\(929\) | −22555.0 | + | 39066.4i | −0.796561 | + | 1.37968i | 0.125282 | + | 0.992121i | \(0.460017\pi\) |
−0.921843 | + | 0.387564i | \(0.873317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 31206.0 | 1.09677 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5403.00 | + | 9358.27i | 0.189284 | + | 0.327850i | ||||
\(935\) | −3456.00 | − | 5985.97i | −0.120881 | − | 0.209371i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16674.0 | −0.581340 | −0.290670 | − | 0.956823i | \(-0.593878\pi\) | ||||
−0.290670 | + | 0.956823i | \(0.593878\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18144.0 | − | 31426.3i | 0.629566 | − | 1.09044i | ||||
\(941\) | −21916.0 | − | 37959.6i | −0.759236 | − | 1.31504i | −0.943241 | − | 0.332110i | \(-0.892239\pi\) |
0.184005 | − | 0.982925i | \(-0.441094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4368.00 | − | 7565.60i | 0.150840 | − | 0.261262i | ||||
\(944\) | 33210.0 | 1.14501 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1024.00 | 0.0351936 | ||||||||
\(947\) | −368.000 | + | 637.395i | −0.0126277 | + | 0.0218717i | −0.872270 | − | 0.489024i | \(-0.837353\pi\) |
0.859643 | + | 0.510896i | \(0.170686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9828.00 | + | 17022.6i | 0.336175 | + | 0.582273i | ||||
\(950\) | −7205.00 | + | 12479.4i | −0.246064 | + | 0.426196i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38138.0 | −1.29634 | −0.648169 | − | 0.761496i | \(-0.724465\pi\) | ||||
−0.648169 | + | 0.761496i | \(0.724465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40384.0 | − | 69947.1i | −1.36837 | − | 2.37009i | ||||
\(956\) | −15540.0 | − | 26916.1i | −0.525732 | − | 0.910594i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4940.00 | 0.166601 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14823.5 | − | 25675.1i | 0.497583 | − | 0.861839i | ||||
\(962\) | −3444.00 | − | 5965.18i | −0.115425 | − | 0.199922i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11557.0 | + | 20017.3i | −0.386126 | + | 0.668791i | ||||
\(965\) | −47392.0 | −1.58094 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26224.0 | 0.872086 | 0.436043 | − | 0.899926i | \(-0.356380\pi\) | ||||
0.436043 | + | 0.899926i | \(0.356380\pi\) | |||||||
\(968\) | −9502.50 | + | 16458.8i | −0.315519 | + | 0.546494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2352.00 | + | 4073.78i | 0.0778538 | + | 0.134847i | ||||
\(971\) | −9381.00 | + | 16248.4i | −0.310042 | + | 0.537008i | −0.978371 | − | 0.206857i | \(-0.933676\pi\) |
0.668329 | + | 0.743866i | \(0.267010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5216.00 | −0.171593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10004.0 | − | 17327.4i | −0.328095 | − | 0.568276i | ||||
\(977\) | 19197.0 | + | 33250.2i | 0.628625 | + | 1.08881i | 0.987828 | + | 0.155551i | \(0.0497152\pi\) |
−0.359203 | + | 0.933259i | \(0.616951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5840.00 | 0.190651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2206.00 | − | 3820.90i | 0.0716866 | − | 0.124165i | ||||
\(983\) | −2694.00 | − | 4666.14i | −0.0874112 | − | 0.151401i | 0.819005 | − | 0.573787i | \(-0.194526\pi\) |
−0.906416 | + | 0.422386i | \(0.861193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26672.0 | − | 46197.3i | 0.862782 | − | 1.49438i | ||||
\(986\) | 5940.00 | 0.191854 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21560.0 | 0.694246 | ||||||||
\(989\) | 3072.00 | − | 5320.86i | 0.0987704 | − | 0.171075i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12736.0 | − | 22059.4i | −0.408247 | − | 0.707104i | 0.586447 | − | 0.809988i | \(-0.300526\pi\) |
−0.994693 | + | 0.102884i | \(0.967193\pi\) | |||||||
\(992\) | 966.000 | − | 1673.16i | 0.0309179 | − | 0.0535513i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29760.0 | −0.948196 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8548.00 | − | 14805.6i | −0.271532 | − | 0.470308i | 0.697722 | − | 0.716369i | \(-0.254197\pi\) |
−0.969254 | + | 0.246061i | \(0.920864\pi\) | |||||||
\(998\) | −9530.00 | − | 16506.4i | −0.302271 | − | 0.523549i | ||||
\(999\) | 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 | 441.4.e.e.226.1 | 2 | ||
3.2 | odd | 2 | 49.4.c.b.30.1 | 2 | |||
7.2 | even | 3 | 441.4.a.i.1.1 | 1 | |||
7.3 | odd | 6 | 441.4.e.h.361.1 | 2 | |||
7.4 | even | 3 | inner | 441.4.e.e.361.1 | 2 | ||
7.5 | odd | 6 | 63.4.a.b.1.1 | 1 | |||
7.6 | odd | 2 | 441.4.e.h.226.1 | 2 | |||
21.2 | odd | 6 | 49.4.a.b.1.1 | 1 | |||
21.5 | even | 6 | 7.4.a.a.1.1 | ✓ | 1 | ||
21.11 | odd | 6 | 49.4.c.b.18.1 | 2 | |||
21.17 | even | 6 | 49.4.c.c.18.1 | 2 | |||
21.20 | even | 2 | 49.4.c.c.30.1 | 2 | |||
28.19 | even | 6 | 1008.4.a.c.1.1 | 1 | |||
35.19 | odd | 6 | 1575.4.a.e.1.1 | 1 | |||
84.23 | even | 6 | 784.4.a.g.1.1 | 1 | |||
84.47 | odd | 6 | 112.4.a.f.1.1 | 1 | |||
105.44 | odd | 6 | 1225.4.a.j.1.1 | 1 | |||
105.47 | odd | 12 | 175.4.b.b.99.1 | 2 | |||
105.68 | odd | 12 | 175.4.b.b.99.2 | 2 | |||
105.89 | even | 6 | 175.4.a.b.1.1 | 1 | |||
168.5 | even | 6 | 448.4.a.i.1.1 | 1 | |||
168.131 | odd | 6 | 448.4.a.e.1.1 | 1 | |||
231.131 | odd | 6 | 847.4.a.b.1.1 | 1 | |||
273.194 | even | 6 | 1183.4.a.b.1.1 | 1 | |||
357.152 | even | 6 | 2023.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.a.a.1.1 | ✓ | 1 | 21.5 | even | 6 | ||
49.4.a.b.1.1 | 1 | 21.2 | odd | 6 | |||
49.4.c.b.18.1 | 2 | 21.11 | odd | 6 | |||
49.4.c.b.30.1 | 2 | 3.2 | odd | 2 | |||
49.4.c.c.18.1 | 2 | 21.17 | even | 6 | |||
49.4.c.c.30.1 | 2 | 21.20 | even | 2 | |||
63.4.a.b.1.1 | 1 | 7.5 | odd | 6 | |||
112.4.a.f.1.1 | 1 | 84.47 | odd | 6 | |||
175.4.a.b.1.1 | 1 | 105.89 | even | 6 | |||
175.4.b.b.99.1 | 2 | 105.47 | odd | 12 | |||
175.4.b.b.99.2 | 2 | 105.68 | odd | 12 | |||
441.4.a.i.1.1 | 1 | 7.2 | even | 3 | |||
441.4.e.e.226.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.e.361.1 | 2 | 7.4 | even | 3 | inner | ||
441.4.e.h.226.1 | 2 | 7.6 | odd | 2 | |||
441.4.e.h.361.1 | 2 | 7.3 | odd | 6 | |||
448.4.a.e.1.1 | 1 | 168.131 | odd | 6 | |||
448.4.a.i.1.1 | 1 | 168.5 | even | 6 | |||
784.4.a.g.1.1 | 1 | 84.23 | even | 6 | |||
847.4.a.b.1.1 | 1 | 231.131 | odd | 6 | |||
1008.4.a.c.1.1 | 1 | 28.19 | even | 6 | |||
1183.4.a.b.1.1 | 1 | 273.194 | even | 6 | |||
1225.4.a.j.1.1 | 1 | 105.44 | odd | 6 | |||
1575.4.a.e.1.1 | 1 | 35.19 | odd | 6 | |||
2023.4.a.a.1.1 | 1 | 357.152 | even | 6 |