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: | \(\Z[a_1, \ldots, a_{5}]\) |
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.k.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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | −0.633316 | − | 0.773893i | \(-0.718307\pi\) |
0.986869 | + | 0.161521i | \(0.0516399\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | + | 3.46410i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.50000 | + | 6.06218i | −0.313050 | + | 0.542218i | −0.979021 | − | 0.203760i | \(-0.934684\pi\) |
0.665971 | + | 0.745977i | \(0.268017\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.0000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.00000 | + | 12.1244i | 0.221359 | + | 0.383406i | ||||
\(11\) | −2.50000 | − | 4.33013i | −0.0685253 | − | 0.118689i | 0.829727 | − | 0.558169i | \(-0.188496\pi\) |
−0.898252 | + | 0.439480i | \(0.855163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.0000 | 0.298685 | 0.149342 | − | 0.988786i | \(-0.452284\pi\) | ||||
0.149342 | + | 0.988786i | \(0.452284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.00000 | − | 13.8564i | 0.125000 | − | 0.216506i | ||||
\(17\) | 10.5000 | + | 18.1865i | 0.149801 | + | 0.259464i | 0.931154 | − | 0.364626i | \(-0.118803\pi\) |
−0.781353 | + | 0.624090i | \(0.785470\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.5000 | − | 42.4352i | 0.295826 | − | 0.512385i | −0.679351 | − | 0.733813i | \(-0.737739\pi\) |
0.975177 | + | 0.221429i | \(0.0710720\pi\) | |||||||
\(20\) | −28.0000 | −0.313050 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.0000 | −0.0969094 | ||||||||
\(23\) | −79.5000 | + | 137.698i | −0.720735 | + | 1.24835i | 0.239971 | + | 0.970780i | \(0.422862\pi\) |
−0.960706 | + | 0.277569i | \(0.910471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38.0000 | + | 65.8179i | 0.304000 | + | 0.526543i | ||||
\(26\) | 14.0000 | − | 24.2487i | 0.105601 | − | 0.182906i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 73.5000 | + | 127.306i | 0.425838 | + | 0.737574i | 0.996498 | − | 0.0836128i | \(-0.0266459\pi\) |
−0.570660 | + | 0.821186i | \(0.693313\pi\) | |||||||
\(32\) | 80.0000 | + | 138.564i | 0.441942 | + | 0.765466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 42.0000 | 0.211851 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −109.500 | + | 189.660i | −0.486532 | + | 0.842698i | −0.999880 | − | 0.0154821i | \(-0.995072\pi\) |
0.513348 | + | 0.858181i | \(0.328405\pi\) | |||||||
\(38\) | −49.0000 | − | 84.8705i | −0.209180 | − | 0.362311i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −84.0000 | + | 145.492i | −0.332039 | + | 0.575109i | ||||
\(41\) | 350.000 | 1.33319 | 0.666595 | − | 0.745420i | \(-0.267751\pi\) | ||||
0.666595 | + | 0.745420i | \(0.267751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −124.000 | −0.439763 | −0.219882 | − | 0.975527i | \(-0.570567\pi\) | ||||
−0.219882 | + | 0.975527i | \(0.570567\pi\) | |||||||
\(44\) | 10.0000 | − | 17.3205i | 0.0342627 | − | 0.0593447i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 159.000 | + | 275.396i | 0.509636 | + | 0.882716i | ||||
\(47\) | −262.500 | + | 454.663i | −0.814671 | + | 1.41105i | 0.0948921 | + | 0.995488i | \(0.469749\pi\) |
−0.909564 | + | 0.415565i | \(0.863584\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 152.000 | 0.429921 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 28.0000 | + | 48.4974i | 0.0746712 | + | 0.129334i | ||||
\(53\) | 151.500 | + | 262.406i | 0.392644 | + | 0.680079i | 0.992797 | − | 0.119806i | \(-0.0382272\pi\) |
−0.600153 | + | 0.799885i | \(0.704894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35.0000 | 0.0858073 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −58.0000 | + | 100.459i | −0.131306 | + | 0.227429i | ||||
\(59\) | 52.5000 | + | 90.9327i | 0.115846 | + | 0.200651i | 0.918118 | − | 0.396308i | \(-0.129709\pi\) |
−0.802272 | + | 0.596959i | \(0.796375\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −206.500 | + | 357.668i | −0.433436 | + | 0.750734i | −0.997167 | − | 0.0752252i | \(-0.976032\pi\) |
0.563730 | + | 0.825959i | \(0.309366\pi\) | |||||||
\(62\) | 294.000 | 0.602226 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 448.000 | 0.875000 | ||||||||
\(65\) | −49.0000 | + | 84.8705i | −0.0935031 | + | 0.161952i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −207.500 | − | 359.401i | −0.378361 | − | 0.655340i | 0.612463 | − | 0.790499i | \(-0.290179\pi\) |
−0.990824 | + | 0.135159i | \(0.956845\pi\) | |||||||
\(68\) | −42.0000 | + | 72.7461i | −0.0749007 | + | 0.129732i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 432.000 | 0.722098 | 0.361049 | − | 0.932547i | \(-0.382419\pi\) | ||||
0.361049 | + | 0.932547i | \(0.382419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −556.500 | − | 963.886i | −0.892238 | − | 1.54540i | −0.837186 | − | 0.546919i | \(-0.815801\pi\) |
−0.0550526 | − | 0.998483i | \(-0.517533\pi\) | |||||||
\(74\) | 219.000 | + | 379.319i | 0.344030 | + | 0.595878i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 196.000 | 0.295826 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51.5000 | − | 89.2006i | 0.0733443 | − | 0.127036i | −0.827021 | − | 0.562171i | \(-0.809966\pi\) |
0.900365 | + | 0.435135i | \(0.143299\pi\) | |||||||
\(80\) | 56.0000 | + | 96.9948i | 0.0782624 | + | 0.135554i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 350.000 | − | 606.218i | 0.471354 | − | 0.816409i | ||||
\(83\) | 1092.00 | 1.44413 | 0.722064 | − | 0.691827i | \(-0.243194\pi\) | ||||
0.722064 | + | 0.691827i | \(0.243194\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −147.000 | −0.187581 | ||||||||
\(86\) | −124.000 | + | 214.774i | −0.155480 | + | 0.269299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −60.0000 | − | 103.923i | −0.0726821 | − | 0.125889i | ||||
\(89\) | 164.500 | − | 284.922i | 0.195921 | − | 0.339345i | −0.751281 | − | 0.659982i | \(-0.770564\pi\) |
0.947202 | + | 0.320637i | \(0.103897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −636.000 | −0.720735 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 525.000 | + | 909.327i | 0.576060 | + | 0.997765i | ||||
\(95\) | 171.500 | + | 297.047i | 0.185216 | + | 0.320804i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 882.000 | 0.923232 | 0.461616 | − | 0.887080i | \(-0.347270\pi\) | ||||
0.461616 | + | 0.887080i | \(0.347270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −152.000 | + | 263.272i | −0.152000 | + | 0.263272i | ||||
\(101\) | −689.500 | − | 1194.25i | −0.679285 | − | 1.17656i | −0.975196 | − | 0.221341i | \(-0.928957\pi\) |
0.295911 | − | 0.955215i | \(-0.404377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −339.500 | + | 588.031i | −0.324776 | + | 0.562529i | −0.981467 | − | 0.191631i | \(-0.938622\pi\) |
0.656691 | + | 0.754160i | \(0.271956\pi\) | |||||||
\(104\) | 336.000 | 0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 606.000 | 0.555282 | ||||||||
\(107\) | 228.500 | − | 395.774i | 0.206448 | − | 0.357578i | −0.744145 | − | 0.668018i | \(-0.767143\pi\) |
0.950593 | + | 0.310440i | \(0.100476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 562.500 | + | 974.279i | 0.494291 | + | 0.856137i | 0.999978 | − | 0.00657959i | \(-0.00209436\pi\) |
−0.505687 | + | 0.862717i | \(0.668761\pi\) | |||||||
\(110\) | 35.0000 | − | 60.6218i | 0.0303374 | − | 0.0525460i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1538.00 | 1.28038 | 0.640190 | − | 0.768217i | \(-0.278856\pi\) | ||||
0.640190 | + | 0.768217i | \(0.278856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −556.500 | − | 963.886i | −0.451251 | − | 0.781590i | ||||
\(116\) | −116.000 | − | 200.918i | −0.0928477 | − | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 210.000 | 0.163831 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.000 | − | 1131.03i | 0.490609 | − | 0.849759i | ||||
\(122\) | 413.000 | + | 715.337i | 0.306486 | + | 0.530849i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −294.000 | + | 509.223i | −0.212919 | + | 0.368787i | ||||
\(125\) | −1407.00 | −1.00677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 72.0000 | 0.0503068 | 0.0251534 | − | 0.999684i | \(-0.491993\pi\) | ||||
0.0251534 | + | 0.999684i | \(0.491993\pi\) | |||||||
\(128\) | −192.000 | + | 332.554i | −0.132583 | + | 0.229640i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 98.0000 | + | 169.741i | 0.0661167 | + | 0.114517i | ||||
\(131\) | −1074.50 | + | 1861.09i | −0.716637 | + | 1.24125i | 0.245687 | + | 0.969349i | \(0.420986\pi\) |
−0.962325 | + | 0.271903i | \(0.912347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −830.000 | −0.535083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 252.000 | + | 436.477i | 0.158888 | + | 0.275203i | ||||
\(137\) | −562.500 | − | 974.279i | −0.350786 | − | 0.607578i | 0.635602 | − | 0.772017i | \(-0.280752\pi\) |
−0.986387 | + | 0.164439i | \(0.947419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −252.000 | −0.153772 | −0.0768862 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768862 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 432.000 | − | 748.246i | 0.255300 | − | 0.442193i | ||||
\(143\) | −35.0000 | − | 60.6218i | −0.0204675 | − | 0.0354507i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 203.000 | − | 351.606i | 0.116264 | − | 0.201375i | ||||
\(146\) | −2226.00 | −1.26182 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −876.000 | −0.486532 | ||||||||
\(149\) | −100.500 | + | 174.071i | −0.0552569 | + | 0.0957078i | −0.892331 | − | 0.451382i | \(-0.850931\pi\) |
0.837074 | + | 0.547090i | \(0.184264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −809.500 | − | 1402.10i | −0.436266 | − | 0.755635i | 0.561132 | − | 0.827726i | \(-0.310366\pi\) |
−0.997398 | + | 0.0720914i | \(0.977033\pi\) | |||||||
\(152\) | 588.000 | − | 1018.45i | 0.313770 | − | 0.543466i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1029.00 | −0.533234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 339.500 | + | 588.031i | 0.172580 | + | 0.298917i | 0.939321 | − | 0.343039i | \(-0.111456\pi\) |
−0.766741 | + | 0.641956i | \(0.778123\pi\) | |||||||
\(158\) | −103.000 | − | 178.401i | −0.0518623 | − | 0.0898281i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1120.00 | −0.553399 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 233.500 | − | 404.434i | 0.112203 | − | 0.194342i | −0.804455 | − | 0.594014i | \(-0.797543\pi\) |
0.916658 | + | 0.399672i | \(0.130876\pi\) | |||||||
\(164\) | 700.000 | + | 1212.44i | 0.333298 | + | 0.577288i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1092.00 | − | 1891.40i | 0.510576 | − | 0.884344i | ||||
\(167\) | 1204.00 | 0.557894 | 0.278947 | − | 0.960306i | \(-0.410015\pi\) | ||||
0.278947 | + | 0.960306i | \(0.410015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2001.00 | −0.910787 | ||||||||
\(170\) | −147.000 | + | 254.611i | −0.0663199 | + | 0.114869i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −248.000 | − | 429.549i | −0.109941 | − | 0.190423i | ||||
\(173\) | 1410.50 | − | 2443.06i | 0.619875 | − | 1.07365i | −0.369633 | − | 0.929178i | \(-0.620517\pi\) |
0.989508 | − | 0.144477i | \(-0.0461499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −80.0000 | −0.0342627 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −329.000 | − | 569.845i | −0.138537 | − | 0.239953i | ||||
\(179\) | −1626.50 | − | 2817.18i | −0.679164 | − | 1.17635i | −0.975233 | − | 0.221180i | \(-0.929009\pi\) |
0.296069 | − | 0.955166i | \(-0.404324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1582.00 | −0.649664 | −0.324832 | − | 0.945772i | \(-0.605308\pi\) | ||||
−0.324832 | + | 0.945772i | \(0.605308\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1908.00 | + | 3304.75i | −0.764454 | + | 1.32407i | ||||
\(185\) | −766.500 | − | 1327.62i | −0.304617 | − | 0.527613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52.5000 | − | 90.9327i | 0.0205304 | − | 0.0355597i | ||||
\(188\) | −2100.00 | −0.814671 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 686.000 | 0.261935 | ||||||||
\(191\) | 1278.50 | − | 2214.43i | 0.484340 | − | 0.838902i | −0.515498 | − | 0.856891i | \(-0.672393\pi\) |
0.999838 | + | 0.0179887i | \(0.00572630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 198.500 | + | 343.812i | 0.0740329 | + | 0.128229i | 0.900665 | − | 0.434514i | \(-0.143080\pi\) |
−0.826632 | + | 0.562742i | \(0.809746\pi\) | |||||||
\(194\) | 882.000 | − | 1527.67i | 0.326412 | − | 0.565362i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2914.00 | −1.05388 | −0.526939 | − | 0.849903i | \(-0.676660\pi\) | ||||
−0.526939 | + | 0.849903i | \(0.676660\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1669.50 | + | 2891.66i | 0.594712 | + | 1.03007i | 0.993587 | + | 0.113066i | \(0.0360673\pi\) |
−0.398875 | + | 0.917005i | \(0.630599\pi\) | |||||||
\(200\) | 912.000 | + | 1579.63i | 0.322441 | + | 0.558484i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2758.00 | −0.960654 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1225.00 | + | 2121.76i | −0.417355 | + | 0.722880i | ||||
\(206\) | 679.000 | + | 1176.06i | 0.229651 | + | 0.397768i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 112.000 | − | 193.990i | 0.0373356 | − | 0.0646671i | ||||
\(209\) | −245.000 | −0.0810861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1780.00 | 0.580759 | 0.290380 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290380 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(212\) | −606.000 | + | 1049.62i | −0.196322 | + | 0.340040i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −457.000 | − | 791.547i | −0.145981 | − | 0.252846i | ||||
\(215\) | 434.000 | − | 751.710i | 0.137668 | − | 0.238447i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2250.00 | 0.699033 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 70.0000 | + | 121.244i | 0.0214518 | + | 0.0371556i | ||||
\(221\) | 147.000 | + | 254.611i | 0.0447434 | + | 0.0774978i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1400.00 | 0.420408 | 0.210204 | − | 0.977658i | \(-0.432587\pi\) | ||||
0.210204 | + | 0.977658i | \(0.432587\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1538.00 | − | 2663.89i | 0.452682 | − | 0.784069i | ||||
\(227\) | 1102.50 | + | 1909.59i | 0.322359 | + | 0.558342i | 0.980974 | − | 0.194138i | \(-0.0621908\pi\) |
−0.658615 | + | 0.752480i | \(0.728858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 143.500 | − | 248.549i | 0.0414094 | − | 0.0717231i | −0.844578 | − | 0.535433i | \(-0.820149\pi\) |
0.885987 | + | 0.463710i | \(0.153482\pi\) | |||||||
\(230\) | −2226.00 | −0.638166 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1392.00 | −0.393919 | ||||||||
\(233\) | 2293.50 | − | 3972.46i | 0.644859 | − | 1.11693i | −0.339475 | − | 0.940615i | \(-0.610249\pi\) |
0.984334 | − | 0.176314i | \(-0.0564173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1837.50 | − | 3182.64i | −0.510065 | − | 0.883459i | ||||
\(236\) | −210.000 | + | 363.731i | −0.0579230 | + | 0.100326i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1668.00 | −0.451439 | −0.225720 | − | 0.974192i | \(-0.572473\pi\) | ||||
−0.225720 | + | 0.974192i | \(0.572473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1704.50 | − | 2952.28i | −0.455587 | − | 0.789100i | 0.543135 | − | 0.839646i | \(-0.317237\pi\) |
−0.998722 | + | 0.0505456i | \(0.983904\pi\) | |||||||
\(242\) | −1306.00 | − | 2262.06i | −0.346913 | − | 0.600870i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1652.00 | −0.433436 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 343.000 | − | 594.093i | 0.0883586 | − | 0.153042i | ||||
\(248\) | 1764.00 | + | 3055.34i | 0.451670 | + | 0.782315i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1407.00 | + | 2437.00i | −0.355946 | + | 0.616517i | ||||
\(251\) | −4760.00 | −1.19701 | −0.598503 | − | 0.801121i | \(-0.704238\pi\) | ||||
−0.598503 | + | 0.801121i | \(0.704238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 795.000 | 0.197554 | ||||||||
\(254\) | 72.0000 | − | 124.708i | 0.0177861 | − | 0.0308065i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2176.00 | + | 3768.94i | 0.531250 | + | 0.920152i | ||||
\(257\) | 402.500 | − | 697.150i | 0.0976936 | − | 0.169210i | −0.813036 | − | 0.582213i | \(-0.802187\pi\) |
0.910730 | + | 0.413003i | \(0.135520\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −392.000 | −0.0935031 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2149.00 | + | 3722.18i | 0.506739 | + | 0.877698i | ||||
\(263\) | −128.500 | − | 222.569i | −0.0301279 | − | 0.0521831i | 0.850568 | − | 0.525865i | \(-0.176258\pi\) |
−0.880696 | + | 0.473681i | \(0.842925\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2121.00 | −0.491668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 830.000 | − | 1437.60i | 0.189180 | − | 0.327670i | ||||
\(269\) | −1795.50 | − | 3109.90i | −0.406965 | − | 0.704884i | 0.587583 | − | 0.809164i | \(-0.300080\pi\) |
−0.994548 | + | 0.104280i | \(0.966746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 696.500 | − | 1206.37i | 0.156123 | − | 0.270413i | −0.777344 | − | 0.629075i | \(-0.783434\pi\) |
0.933467 | + | 0.358662i | \(0.116767\pi\) | |||||||
\(272\) | 336.000 | 0.0749007 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2250.00 | −0.496086 | ||||||||
\(275\) | 190.000 | − | 329.090i | 0.0416634 | − | 0.0721631i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −207.500 | − | 359.401i | −0.0450089 | − | 0.0779577i | 0.842643 | − | 0.538472i | \(-0.180998\pi\) |
−0.887652 | + | 0.460514i | \(0.847665\pi\) | |||||||
\(278\) | −252.000 | + | 436.477i | −0.0543667 | + | 0.0941660i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4954.00 | 1.05171 | 0.525856 | − | 0.850574i | \(-0.323745\pi\) | ||||
0.525856 | + | 0.850574i | \(0.323745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2138.50 | − | 3703.99i | −0.449190 | − | 0.778019i | 0.549144 | − | 0.835728i | \(-0.314954\pi\) |
−0.998333 | + | 0.0577087i | \(0.981621\pi\) | |||||||
\(284\) | 864.000 | + | 1496.49i | 0.180525 | + | 0.312678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −140.000 | −0.0289454 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2236.00 | − | 3872.87i | 0.455119 | − | 0.788289i | ||||
\(290\) | −406.000 | − | 703.213i | −0.0822108 | − | 0.142393i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2226.00 | − | 3855.55i | 0.446119 | − | 0.772701i | ||||
\(293\) | 7742.00 | 1.54366 | 0.771830 | − | 0.635829i | \(-0.219342\pi\) | ||||
0.771830 | + | 0.635829i | \(0.219342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −735.000 | −0.145062 | ||||||||
\(296\) | −2628.00 | + | 4551.83i | −0.516045 | + | 0.893817i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 201.000 | + | 348.142i | 0.0390725 | + | 0.0676756i | ||||
\(299\) | −1113.00 | + | 1927.77i | −0.215272 | + | 0.372863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3238.00 | −0.616973 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −392.000 | − | 678.964i | −0.0739564 | − | 0.128096i | ||||
\(305\) | −1445.50 | − | 2503.68i | −0.271374 | − | 0.470034i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7364.00 | 1.36901 | 0.684504 | − | 0.729009i | \(-0.260019\pi\) | ||||
0.684504 | + | 0.729009i | \(0.260019\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1029.00 | + | 1782.28i | −0.188527 | + | 0.326538i | ||||
\(311\) | −4987.50 | − | 8638.60i | −0.909374 | − | 1.57508i | −0.814936 | − | 0.579550i | \(-0.803228\pi\) |
−0.0944372 | − | 0.995531i | \(-0.530105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2376.50 | + | 4116.22i | −0.429162 | + | 0.743330i | −0.996799 | − | 0.0799485i | \(-0.974524\pi\) |
0.567637 | + | 0.823279i | \(0.307858\pi\) | |||||||
\(314\) | 1358.00 | 0.244065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 412.000 | 0.0733443 | ||||||||
\(317\) | −1738.50 | + | 3011.17i | −0.308025 | + | 0.533515i | −0.977930 | − | 0.208932i | \(-0.933001\pi\) |
0.669905 | + | 0.742447i | \(0.266335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 145.000 | + | 251.147i | 0.0254497 | + | 0.0440801i | ||||
\(320\) | −1568.00 | + | 2715.86i | −0.273918 | + | 0.474440i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1029.00 | 0.177260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 532.000 | + | 921.451i | 0.0908002 | + | 0.157270i | ||||
\(326\) | −467.000 | − | 808.868i | −0.0793397 | − | 0.137420i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8400.00 | 1.41406 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1670.50 | + | 2893.39i | −0.277399 | + | 0.480469i | −0.970738 | − | 0.240143i | \(-0.922806\pi\) |
0.693339 | + | 0.720612i | \(0.256139\pi\) | |||||||
\(332\) | 2184.00 | + | 3782.80i | 0.361032 | + | 0.625325i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1204.00 | − | 2085.39i | 0.197245 | − | 0.341639i | ||||
\(335\) | 2905.00 | 0.473782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7366.00 | 1.19066 | 0.595329 | − | 0.803482i | \(-0.297022\pi\) | ||||
0.595329 | + | 0.803482i | \(0.297022\pi\) | |||||||
\(338\) | −2001.00 | + | 3465.83i | −0.322012 | + | 0.557741i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −294.000 | − | 509.223i | −0.0468953 | − | 0.0812250i | ||||
\(341\) | 367.500 | − | 636.529i | 0.0583614 | − | 0.101085i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2976.00 | −0.466439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2821.00 | − | 4886.12i | −0.438318 | − | 0.759188i | ||||
\(347\) | 3707.50 | + | 6421.58i | 0.573571 | + | 0.993454i | 0.996195 | + | 0.0871487i | \(0.0277755\pi\) |
−0.422625 | + | 0.906305i | \(0.638891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3878.00 | 0.594798 | 0.297399 | − | 0.954753i | \(-0.403881\pi\) | ||||
0.297399 | + | 0.954753i | \(0.403881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 400.000 | − | 692.820i | 0.0605684 | − | 0.104908i | ||||
\(353\) | −633.500 | − | 1097.25i | −0.0955179 | − | 0.165442i | 0.814307 | − | 0.580435i | \(-0.197117\pi\) |
−0.909825 | + | 0.414993i | \(0.863784\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1512.00 | + | 2618.86i | −0.226052 | + | 0.391534i | ||||
\(356\) | 1316.00 | 0.195921 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6506.00 | −0.960483 | ||||||||
\(359\) | 2342.50 | − | 4057.33i | 0.344380 | − | 0.596484i | −0.640861 | − | 0.767657i | \(-0.721422\pi\) |
0.985241 | + | 0.171173i | \(0.0547558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2229.00 | + | 3860.74i | 0.324974 | + | 0.562872i | ||||
\(362\) | −1582.00 | + | 2740.10i | −0.229691 | + | 0.397836i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7791.00 | 1.11726 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2320.50 | − | 4019.22i | −0.330052 | − | 0.571667i | 0.652470 | − | 0.757815i | \(-0.273733\pi\) |
−0.982522 | + | 0.186148i | \(0.940400\pi\) | |||||||
\(368\) | 1272.00 | + | 2203.17i | 0.180184 | + | 0.312087i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3066.00 | −0.430794 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4398.50 | − | 7618.43i | 0.610578 | − | 1.05755i | −0.380565 | − | 0.924754i | \(-0.624270\pi\) |
0.991143 | − | 0.132798i | \(-0.0423963\pi\) | |||||||
\(374\) | −105.000 | − | 181.865i | −0.0145172 | − | 0.0251445i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6300.00 | + | 10911.9i | −0.864090 | + | 1.49665i | ||||
\(377\) | −812.000 | −0.110929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13680.0 | 1.85407 | 0.927037 | − | 0.374969i | \(-0.122347\pi\) | ||||
0.927037 | + | 0.374969i | \(0.122347\pi\) | |||||||
\(380\) | −686.000 | + | 1188.19i | −0.0926080 | + | 0.160402i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2557.00 | − | 4428.85i | −0.342480 | − | 0.593193i | ||||
\(383\) | −4882.50 | + | 8456.74i | −0.651395 | + | 1.12825i | 0.331390 | + | 0.943494i | \(0.392482\pi\) |
−0.982785 | + | 0.184755i | \(0.940851\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 794.000 | 0.104698 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1764.00 | + | 3055.34i | 0.230808 | + | 0.399771i | ||||
\(389\) | 865.500 | + | 1499.09i | 0.112809 | + | 0.195390i | 0.916902 | − | 0.399113i | \(-0.130682\pi\) |
−0.804093 | + | 0.594504i | \(0.797349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3339.00 | −0.431868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2914.00 | + | 5047.20i | −0.372602 | + | 0.645366i | ||||
\(395\) | 360.500 | + | 624.404i | 0.0459208 | + | 0.0795372i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5491.50 | − | 9511.56i | 0.694233 | − | 1.20245i | −0.276206 | − | 0.961099i | \(-0.589077\pi\) |
0.970439 | − | 0.241348i | \(-0.0775896\pi\) | |||||||
\(398\) | 6678.00 | 0.841050 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1216.00 | 0.152000 | ||||||||
\(401\) | 3301.50 | − | 5718.37i | 0.411145 | − | 0.712124i | −0.583870 | − | 0.811847i | \(-0.698462\pi\) |
0.995015 | + | 0.0997232i | \(0.0317957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1029.00 | + | 1782.28i | 0.127191 | + | 0.220302i | ||||
\(404\) | 2758.00 | − | 4777.00i | 0.339643 | − | 0.588278i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1095.00 | 0.133359 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5477.50 | + | 9487.31i | 0.662213 | + | 1.14699i | 0.980033 | + | 0.198835i | \(0.0637158\pi\) |
−0.317820 | + | 0.948151i | \(0.602951\pi\) | |||||||
\(410\) | 2450.00 | + | 4243.52i | 0.295114 | + | 0.511153i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2716.00 | −0.324776 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3822.00 | + | 6619.90i | −0.452083 | + | 0.783031i | ||||
\(416\) | 1120.00 | + | 1939.90i | 0.132001 | + | 0.228633i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −245.000 | + | 424.352i | −0.0286683 | + | 0.0496549i | ||||
\(419\) | 6636.00 | 0.773723 | 0.386861 | − | 0.922138i | \(-0.373559\pi\) | ||||
0.386861 | + | 0.922138i | \(0.373559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16630.0 | −1.92517 | −0.962585 | − | 0.270980i | \(-0.912652\pi\) | ||||
−0.962585 | + | 0.270980i | \(0.912652\pi\) | |||||||
\(422\) | 1780.00 | − | 3083.05i | 0.205329 | − | 0.355641i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3636.00 | + | 6297.74i | 0.416462 | + | 0.721333i | ||||
\(425\) | −798.000 | + | 1382.18i | −0.0910793 | + | 0.157754i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1828.00 | 0.206448 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −868.000 | − | 1503.42i | −0.0973458 | − | 0.168608i | ||||
\(431\) | 2461.50 | + | 4263.44i | 0.275096 | + | 0.476480i | 0.970159 | − | 0.242468i | \(-0.0779571\pi\) |
−0.695064 | + | 0.718948i | \(0.744624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8974.00 | −0.995988 | −0.497994 | − | 0.867180i | \(-0.665930\pi\) | ||||
−0.497994 | + | 0.867180i | \(0.665930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2250.00 | + | 3897.11i | −0.247146 | + | 0.428069i | ||||
\(437\) | 3895.50 | + | 6747.20i | 0.426423 | + | 0.738587i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2089.50 | + | 3619.12i | −0.227167 | + | 0.393465i | −0.956967 | − | 0.290195i | \(-0.906280\pi\) |
0.729800 | + | 0.683660i | \(0.239613\pi\) | |||||||
\(440\) | 840.000 | 0.0910123 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 588.000 | 0.0632767 | ||||||||
\(443\) | −6463.50 | + | 11195.1i | −0.693206 | + | 1.20067i | 0.277576 | + | 0.960704i | \(0.410469\pi\) |
−0.970782 | + | 0.239964i | \(0.922864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1151.50 | + | 1994.46i | 0.122666 | + | 0.212464i | ||||
\(446\) | 1400.00 | − | 2424.87i | 0.148637 | − | 0.257446i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2826.00 | 0.297032 | 0.148516 | − | 0.988910i | \(-0.452550\pi\) | ||||
0.148516 | + | 0.988910i | \(0.452550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −875.000 | − | 1515.54i | −0.0913573 | − | 0.158235i | ||||
\(452\) | 3076.00 | + | 5327.79i | 0.320095 | + | 0.554421i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4410.00 | 0.455884 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4239.50 | + | 7343.03i | −0.433951 | + | 0.751625i | −0.997209 | − | 0.0746560i | \(-0.976214\pi\) |
0.563259 | + | 0.826281i | \(0.309547\pi\) | |||||||
\(458\) | −287.000 | − | 497.099i | −0.0292808 | − | 0.0507159i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2226.00 | − | 3855.55i | 0.225626 | − | 0.390795i | ||||
\(461\) | 9338.00 | 0.943414 | 0.471707 | − | 0.881755i | \(-0.343638\pi\) | ||||
0.471707 | + | 0.881755i | \(0.343638\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4016.00 | −0.403109 | −0.201554 | − | 0.979477i | \(-0.564599\pi\) | ||||
−0.201554 | + | 0.979477i | \(0.564599\pi\) | |||||||
\(464\) | −464.000 | + | 803.672i | −0.0464238 | + | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4587.00 | − | 7944.92i | −0.455984 | − | 0.789788i | ||||
\(467\) | 2929.50 | − | 5074.04i | 0.290281 | − | 0.502781i | −0.683595 | − | 0.729861i | \(-0.739585\pi\) |
0.973876 | + | 0.227080i | \(0.0729180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7350.00 | −0.721341 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1260.00 | + | 2182.38i | 0.122873 | + | 0.212823i | ||||
\(473\) | 310.000 | + | 536.936i | 0.0301349 | + | 0.0521952i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3724.00 | 0.359724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1668.00 | + | 2889.06i | −0.159608 | + | 0.276449i | ||||
\(479\) | −3251.50 | − | 5631.76i | −0.310156 | − | 0.537206i | 0.668240 | − | 0.743946i | \(-0.267048\pi\) |
−0.978396 | + | 0.206740i | \(0.933715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1533.00 | + | 2655.23i | −0.145320 | + | 0.251701i | ||||
\(482\) | −6818.00 | −0.644297 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5224.00 | 0.490609 | ||||||||
\(485\) | −3087.00 | + | 5346.84i | −0.289017 | + | 0.500593i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8024.50 | + | 13898.8i | 0.746663 | + | 1.29326i | 0.949414 | + | 0.314028i | \(0.101678\pi\) |
−0.202751 | + | 0.979230i | \(0.564988\pi\) | |||||||
\(488\) | −4956.00 | + | 8584.04i | −0.459729 | + | 0.796273i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8864.00 | −0.814718 | −0.407359 | − | 0.913268i | \(-0.633550\pi\) | ||||
−0.407359 | + | 0.913268i | \(0.633550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −609.000 | − | 1054.82i | −0.0556348 | − | 0.0963624i | ||||
\(494\) | −686.000 | − | 1188.19i | −0.0624789 | − | 0.108217i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2352.00 | 0.212919 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5105.50 | − | 8842.99i | 0.458023 | − | 0.793319i | −0.540833 | − | 0.841130i | \(-0.681891\pi\) |
0.998856 | + | 0.0478104i | \(0.0152243\pi\) | |||||||
\(500\) | −2814.00 | − | 4873.99i | −0.251692 | − | 0.435943i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4760.00 | + | 8244.56i | −0.423206 | + | 0.733014i | ||||
\(503\) | −1680.00 | −0.148921 | −0.0744607 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744607 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9653.00 | 0.850600 | ||||||||
\(506\) | 795.000 | − | 1376.98i | 0.0698460 | − | 0.120977i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 144.000 | + | 249.415i | 0.0125767 | + | 0.0217835i | ||||
\(509\) | 4728.50 | − | 8190.00i | 0.411762 | − | 0.713193i | −0.583320 | − | 0.812242i | \(-0.698247\pi\) |
0.995083 | + | 0.0990489i | \(0.0315800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5632.00 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −805.000 | − | 1394.30i | −0.0690798 | − | 0.119650i | ||||
\(515\) | −2376.50 | − | 4116.22i | −0.203342 | − | 0.352199i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2625.00 | 0.223302 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1176.00 | + | 2036.89i | −0.0991750 | + | 0.171776i | ||||
\(521\) | 9040.50 | + | 15658.6i | 0.760214 | + | 1.31673i | 0.942740 | + | 0.333528i | \(0.108239\pi\) |
−0.182526 | + | 0.983201i | \(0.558427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10188.5 | − | 17647.0i | 0.851839 | − | 1.47543i | −0.0277071 | − | 0.999616i | \(-0.508821\pi\) |
0.879546 | − | 0.475813i | \(-0.157846\pi\) | |||||||
\(524\) | −8596.00 | −0.716637 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −514.000 | −0.0426073 | ||||||||
\(527\) | −1543.50 | + | 2673.42i | −0.127582 | + | 0.220979i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6557.00 | − | 11357.1i | −0.538917 | − | 0.933431i | ||||
\(530\) | −2121.00 | + | 3673.68i | −0.173831 | + | 0.301084i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4900.00 | 0.398204 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1599.50 | + | 2770.42i | 0.129257 | + | 0.223879i | ||||
\(536\) | −4980.00 | − | 8625.61i | −0.401312 | − | 0.695093i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7182.00 | −0.575535 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3096.50 | − | 5363.30i | 0.246079 | − | 0.426222i | −0.716355 | − | 0.697736i | \(-0.754191\pi\) |
0.962435 | + | 0.271514i | \(0.0875243\pi\) | |||||||
\(542\) | −1393.00 | − | 2412.75i | −0.110396 | − | 0.191211i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1680.00 | + | 2909.85i | −0.132407 | + | 0.229336i | ||||
\(545\) | −7875.00 | −0.618950 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18464.0 | −1.44326 | −0.721630 | − | 0.692279i | \(-0.756607\pi\) | ||||
−0.721630 | + | 0.692279i | \(0.756607\pi\) | |||||||
\(548\) | 2250.00 | − | 3897.11i | 0.175393 | − | 0.303789i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −380.000 | − | 658.179i | −0.0294605 | − | 0.0510270i | ||||
\(551\) | −1421.00 | + | 2461.24i | −0.109867 | + | 0.190295i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −830.000 | −0.0636522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −504.000 | − | 872.954i | −0.0384431 | − | 0.0665854i | ||||
\(557\) | −4706.50 | − | 8151.90i | −0.358027 | − | 0.620120i | 0.629604 | − | 0.776916i | \(-0.283217\pi\) |
−0.987631 | + | 0.156796i | \(0.949884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1736.00 | −0.131351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4954.00 | − | 8580.58i | 0.371836 | − | 0.644039i | ||||
\(563\) | −1599.50 | − | 2770.42i | −0.119735 | − | 0.207387i | 0.799928 | − | 0.600097i | \(-0.204871\pi\) |
−0.919663 | + | 0.392709i | \(0.871538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5383.00 | + | 9323.63i | −0.400822 | + | 0.694244i | ||||
\(566\) | −8554.00 | −0.635250 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10368.0 | 0.765901 | ||||||||
\(569\) | 10791.5 | − | 18691.4i | 0.795085 | − | 1.37713i | −0.127701 | − | 0.991813i | \(-0.540760\pi\) |
0.922785 | − | 0.385314i | \(-0.125907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10133.5 | − | 17551.7i | −0.742686 | − | 1.28637i | −0.951268 | − | 0.308365i | \(-0.900218\pi\) |
0.208582 | − | 0.978005i | \(-0.433115\pi\) | |||||||
\(572\) | 140.000 | − | 242.487i | 0.0102337 | − | 0.0177253i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12084.0 | −0.876413 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6975.50 | + | 12081.9i | 0.503282 | + | 0.871710i | 0.999993 | + | 0.00379418i | \(0.00120773\pi\) |
−0.496711 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(578\) | −4472.00 | − | 7745.73i | −0.321818 | − | 0.557405i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1624.00 | 0.116264 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 757.500 | − | 1312.03i | 0.0538121 | − | 0.0932053i | ||||
\(584\) | −13356.0 | − | 23133.3i | −0.946362 | − | 1.63915i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7742.00 | − | 13409.5i | 0.545766 | − | 0.945295i | ||||
\(587\) | −20972.0 | −1.47463 | −0.737314 | − | 0.675550i | \(-0.763906\pi\) | ||||
−0.737314 | + | 0.675550i | \(0.763906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7203.00 | 0.503895 | ||||||||
\(590\) | −735.000 | + | 1273.06i | −0.0512872 | + | 0.0888321i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1752.00 | + | 3034.55i | 0.121633 | + | 0.210675i | ||||
\(593\) | 94.5000 | − | 163.679i | 0.00654410 | − | 0.0113347i | −0.862735 | − | 0.505657i | \(-0.831250\pi\) |
0.869279 | + | 0.494322i | \(0.164584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −804.000 | −0.0552569 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2226.00 | + | 3855.55i | 0.152221 | + | 0.263654i | ||||
\(599\) | −5140.50 | − | 8903.61i | −0.350643 | − | 0.607331i | 0.635719 | − | 0.771920i | \(-0.280704\pi\) |
−0.986362 | + | 0.164589i | \(0.947370\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6090.00 | 0.413338 | 0.206669 | − | 0.978411i | \(-0.433738\pi\) | ||||
0.206669 | + | 0.978411i | \(0.433738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3238.00 | − | 5608.38i | 0.218133 | − | 0.377817i | ||||
\(605\) | 4571.00 | + | 7917.20i | 0.307170 | + | 0.532033i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2474.50 | − | 4285.96i | 0.165464 | − | 0.286593i | −0.771356 | − | 0.636404i | \(-0.780421\pi\) |
0.936820 | + | 0.349812i | \(0.113754\pi\) | |||||||
\(608\) | 7840.00 | 0.522951 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5782.00 | −0.383781 | ||||||||
\(611\) | −3675.00 | + | 6365.29i | −0.243330 | + | 0.421460i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7898.50 | + | 13680.6i | 0.520420 | + | 0.901394i | 0.999718 | + | 0.0237416i | \(0.00755791\pi\) |
−0.479298 | + | 0.877652i | \(0.659109\pi\) | |||||||
\(614\) | 7364.00 | − | 12754.8i | 0.484018 | − | 0.838343i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9378.00 | 0.611903 | 0.305951 | − | 0.952047i | \(-0.401025\pi\) | ||||
0.305951 | + | 0.952047i | \(0.401025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12176.5 | − | 21090.3i | −0.790654 | − | 1.36945i | −0.925562 | − | 0.378595i | \(-0.876407\pi\) |
0.134908 | − | 0.990858i | \(-0.456926\pi\) | |||||||
\(620\) | −2058.00 | − | 3564.56i | −0.133308 | − | 0.230897i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19950.0 | −1.28605 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 174.500 | − | 302.243i | 0.0111680 | − | 0.0193435i | ||||
\(626\) | 4753.00 | + | 8232.44i | 0.303463 | + | 0.525614i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1358.00 | + | 2352.12i | −0.0862900 | + | 0.149459i | ||||
\(629\) | −4599.00 | −0.291533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12640.0 | −0.797449 | −0.398725 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398725 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(632\) | 1236.00 | − | 2140.81i | 0.0777934 | − | 0.134742i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3477.00 | + | 6022.34i | 0.217806 | + | 0.377252i | ||||
\(635\) | −252.000 | + | 436.477i | −0.0157485 | + | 0.0272772i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 580.000 | 0.0359913 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1344.00 | − | 2327.88i | −0.0830098 | − | 0.143777i | ||||
\(641\) | −520.500 | − | 901.532i | −0.0320726 | − | 0.0555513i | 0.849544 | − | 0.527518i | \(-0.176877\pi\) |
−0.881616 | + | 0.471967i | \(0.843544\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9548.00 | −0.585593 | −0.292797 | − | 0.956175i | \(-0.594586\pi\) | ||||
−0.292797 | + | 0.956175i | \(0.594586\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1029.00 | − | 1782.28i | 0.0626710 | − | 0.108549i | ||||
\(647\) | 1620.50 | + | 2806.79i | 0.0984674 | + | 0.170551i | 0.911050 | − | 0.412295i | \(-0.135273\pi\) |
−0.812583 | + | 0.582845i | \(0.801939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 262.500 | − | 454.663i | 0.0158768 | − | 0.0274994i | ||||
\(650\) | 2128.00 | 0.128411 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1868.00 | 0.112203 | ||||||||
\(653\) | −4426.50 | + | 7666.92i | −0.265272 | + | 0.459464i | −0.967635 | − | 0.252355i | \(-0.918795\pi\) |
0.702363 | + | 0.711819i | \(0.252128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7521.50 | − | 13027.6i | −0.448686 | − | 0.777147i | ||||
\(656\) | 2800.00 | − | 4849.74i | 0.166649 | − | 0.288644i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7044.00 | −0.416381 | −0.208191 | − | 0.978088i | \(-0.566757\pi\) | ||||
−0.208191 | + | 0.978088i | \(0.566757\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6044.50 | − | 10469.4i | −0.355679 | − | 0.616054i | 0.631555 | − | 0.775331i | \(-0.282417\pi\) |
−0.987234 | + | 0.159277i | \(0.949084\pi\) | |||||||
\(662\) | 3341.00 | + | 5786.78i | 0.196151 | + | 0.339743i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26208.0 | 1.53173 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4611.00 | − | 7986.49i | 0.267674 | − | 0.463625i | ||||
\(668\) | 2408.00 | + | 4170.78i | 0.139474 | + | 0.241575i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2905.00 | − | 5031.61i | 0.167507 | − | 0.290131i | ||||
\(671\) | 2065.00 | 0.118805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 982.000 | 0.0562456 | 0.0281228 | − | 0.999604i | \(-0.491047\pi\) | ||||
0.0281228 | + | 0.999604i | \(0.491047\pi\) | |||||||
\(674\) | 7366.00 | − | 12758.3i | 0.420961 | − | 0.729126i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4002.00 | − | 6931.67i | −0.227697 | − | 0.394383i | ||||
\(677\) | 15256.5 | − | 26425.0i | 0.866108 | − | 1.50014i | 0.000164659 | − | 1.00000i | \(-0.499948\pi\) |
0.865943 | − | 0.500143i | \(-0.166719\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3528.00 | −0.198960 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −735.000 | − | 1273.06i | −0.0412677 | − | 0.0714778i | ||||
\(683\) | 5737.50 | + | 9937.64i | 0.321434 | + | 0.556740i | 0.980784 | − | 0.195096i | \(-0.0625019\pi\) |
−0.659350 | + | 0.751836i | \(0.729169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7875.00 | 0.439253 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −992.000 | + | 1718.19i | −0.0549704 | + | 0.0952116i | ||||
\(689\) | 2121.00 | + | 3673.68i | 0.117277 | + | 0.203129i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14157.5 | + | 24521.5i | −0.779416 | + | 1.34999i | 0.152862 | + | 0.988248i | \(0.451151\pi\) |
−0.932279 | + | 0.361741i | \(0.882182\pi\) | |||||||
\(692\) | 11284.0 | 0.619875 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14830.0 | 0.811151 | ||||||||
\(695\) | 882.000 | − | 1527.67i | 0.0481384 | − | 0.0833781i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3675.00 | + | 6365.29i | 0.199714 | + | 0.345915i | ||||
\(698\) | 3878.00 | − | 6716.89i | 0.210293 | − | 0.364238i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10614.0 | −0.571876 | −0.285938 | − | 0.958248i | \(-0.592305\pi\) | ||||
−0.285938 | + | 0.958248i | \(0.592305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5365.50 | + | 9293.32i | 0.287857 | + | 0.498583i | ||||
\(704\) | −1120.00 | − | 1939.90i | −0.0599596 | − | 0.103853i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2534.00 | −0.135083 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5149.50 | + | 8919.20i | −0.272769 | + | 0.472451i | −0.969570 | − | 0.244814i | \(-0.921273\pi\) |
0.696801 | + | 0.717265i | \(0.254606\pi\) | |||||||
\(710\) | 3024.00 | + | 5237.72i | 0.159843 | + | 0.276857i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3948.00 | − | 6838.14i | 0.207806 | − | 0.359930i | ||||
\(713\) | −23373.0 | −1.22767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 490.000 | 0.0256293 | ||||||||
\(716\) | 6506.00 | − | 11268.7i | 0.339582 | − | 0.588173i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4685.00 | − | 8114.66i | −0.243513 | − | 0.421778i | ||||
\(719\) | −16264.5 | + | 28170.9i | −0.843621 | + | 1.46119i | 0.0431924 | + | 0.999067i | \(0.486247\pi\) |
−0.886813 | + | 0.462128i | \(0.847086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8916.00 | 0.459583 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3164.00 | − | 5480.21i | −0.162416 | − | 0.281313i | ||||
\(725\) | −2204.00 | − | 3817.44i | −0.112903 | − | 0.195553i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29456.0 | −1.50270 | −0.751350 | − | 0.659904i | \(-0.770597\pi\) | ||||
−0.751350 | + | 0.659904i | \(0.770597\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7791.00 | − | 13494.4i | 0.395011 | − | 0.684179i | ||||
\(731\) | −1302.00 | − | 2255.13i | −0.0658772 | − | 0.114103i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13933.5 | − | 24133.5i | 0.702109 | − | 1.21609i | −0.265616 | − | 0.964079i | \(-0.585575\pi\) |
0.967725 | − | 0.252009i | \(-0.0810912\pi\) | |||||||
\(734\) | −9282.00 | −0.466764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25440.0 | −1.27409 | ||||||||
\(737\) | −1037.50 | + | 1797.00i | −0.0518546 | + | 0.0898147i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9769.50 | − | 16921.3i | −0.486302 | − | 0.842299i | 0.513574 | − | 0.858045i | \(-0.328321\pi\) |
−0.999876 | + | 0.0157460i | \(0.994988\pi\) | |||||||
\(740\) | 3066.00 | − | 5310.47i | 0.152309 | − | 0.263806i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1248.00 | −0.0616214 | −0.0308107 | − | 0.999525i | \(-0.509809\pi\) | ||||
−0.0308107 | + | 0.999525i | \(0.509809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −703.500 | − | 1218.50i | −0.0345963 | − | 0.0599226i | ||||
\(746\) | −8797.00 | − | 15236.9i | −0.431744 | − | 0.747803i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 420.000 | 0.0205304 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14046.5 | + | 24329.3i | −0.682509 | + | 1.18214i | 0.291704 | + | 0.956509i | \(0.405778\pi\) |
−0.974213 | + | 0.225631i | \(0.927556\pi\) | |||||||
\(752\) | 4200.00 | + | 7274.61i | 0.203668 | + | 0.352763i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −812.000 | + | 1406.43i | −0.0392192 | + | 0.0679297i | ||||
\(755\) | 11333.0 | 0.546292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35954.0 | 1.72625 | 0.863124 | − | 0.504991i | \(-0.168504\pi\) | ||||
0.863124 | + | 0.504991i | \(0.168504\pi\) | |||||||
\(758\) | 13680.0 | − | 23694.5i | 0.655514 | − | 1.13538i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4116.00 | + | 7129.12i | 0.196451 | + | 0.340264i | ||||
\(761\) | 430.500 | − | 745.648i | 0.0205067 | − | 0.0355187i | −0.855590 | − | 0.517654i | \(-0.826805\pi\) |
0.876097 | + | 0.482136i | \(0.160139\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10228.0 | 0.484340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9765.00 | + | 16913.5i | 0.460605 | + | 0.797792i | ||||
\(767\) | 735.000 | + | 1273.06i | 0.0346014 | + | 0.0599315i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24710.0 | −1.15873 | −0.579366 | − | 0.815067i | \(-0.696700\pi\) | ||||
−0.579366 | + | 0.815067i | \(0.696700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −794.000 | + | 1375.25i | −0.0370164 | + | 0.0641143i | ||||
\(773\) | −8249.50 | − | 14288.6i | −0.383847 | − | 0.664843i | 0.607761 | − | 0.794120i | \(-0.292068\pi\) |
−0.991609 | + | 0.129277i | \(0.958734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5586.00 | + | 9675.24i | −0.258910 | + | 0.448445i | ||||
\(776\) | 21168.0 | 0.979236 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3462.00 | 0.159536 | ||||||||
\(779\) | 8575.00 | − | 14852.3i | 0.394392 | − | 0.683107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1080.00 | − | 1870.61i | −0.0494820 | − | 0.0857053i | ||||
\(782\) | −3339.00 | + | 5783.32i | −0.152688 | + | 0.264464i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4753.00 | −0.216104 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8235.50 | + | 14264.3i | 0.373016 | + | 0.646083i | 0.990028 | − | 0.140871i | \(-0.0449902\pi\) |
−0.617012 | + | 0.786954i | \(0.711657\pi\) | |||||||
\(788\) | −5828.00 | − | 10094.4i | −0.263469 | − | 0.456342i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1442.00 | 0.0649418 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2891.00 | + | 5007.36i | −0.129461 | + | 0.224233i | ||||
\(794\) | −10983.0 | − | 19023.1i | −0.490897 | − | 0.850258i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6678.00 | + | 11566.6i | −0.297356 | + | 0.515036i | ||||
\(797\) | −36470.0 | −1.62087 | −0.810435 | − | 0.585828i | \(-0.800769\pi\) | ||||
−0.810435 | + | 0.585828i | \(0.800769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11025.0 | −0.488156 | ||||||||
\(800\) | −6080.00 | + | 10530.9i | −0.268701 | + | 0.465403i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6603.00 | − | 11436.7i | −0.290723 | − | 0.503547i | ||||
\(803\) | −2782.50 | + | 4819.43i | −0.122282 | + | 0.211798i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4116.00 | 0.179876 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16548.0 | − | 28662.0i | −0.720491 | − | 1.24793i | ||||
\(809\) | 17875.5 | + | 30961.3i | 0.776847 | + | 1.34554i | 0.933751 | + | 0.357924i | \(0.116515\pi\) |
−0.156904 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16492.0 | 0.714072 | 0.357036 | − | 0.934091i | \(-0.383787\pi\) | ||||
0.357036 | + | 0.934091i | \(0.383787\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1095.00 | − | 1896.60i | 0.0471495 | − | 0.0816654i | ||||
\(815\) | 1634.50 | + | 2831.04i | 0.0702504 | + | 0.121677i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3038.00 | + | 5261.97i | −0.130093 | + | 0.225328i | ||||
\(818\) | 21910.0 | 0.936510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9800.00 | −0.417355 | ||||||||
\(821\) | −20736.5 | + | 35916.7i | −0.881497 | + | 1.52680i | −0.0318198 | + | 0.999494i | \(0.510130\pi\) |
−0.849677 | + | 0.527304i | \(0.823203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12532.5 | + | 21706.9i | 0.530809 | + | 0.919387i | 0.999354 | + | 0.0359479i | \(0.0114450\pi\) |
−0.468545 | + | 0.883440i | \(0.655222\pi\) | |||||||
\(824\) | −8148.00 | + | 14112.7i | −0.344477 | + | 0.596652i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9732.00 | −0.409208 | −0.204604 | − | 0.978845i | \(-0.565591\pi\) | ||||
−0.204604 | + | 0.978845i | \(0.565591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13877.5 | + | 24036.5i | 0.581406 | + | 1.00702i | 0.995313 | + | 0.0967055i | \(0.0308305\pi\) |
−0.413907 | + | 0.910319i | \(0.635836\pi\) | |||||||
\(830\) | 7644.00 | + | 13239.8i | 0.319671 | + | 0.553687i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6272.00 | 0.261349 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4214.00 | + | 7298.86i | −0.174648 | + | 0.302500i | ||||
\(836\) | −490.000 | − | 848.705i | −0.0202715 | − | 0.0351113i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6636.00 | − | 11493.9i | 0.273552 | − | 0.473806i | ||||
\(839\) | 21112.0 | 0.868733 | 0.434367 | − | 0.900736i | \(-0.356972\pi\) | ||||
0.434367 | + | 0.900736i | \(0.356972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | −16630.0 | + | 28804.0i | −0.680650 | + | 1.17892i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3560.00 | + | 6166.10i | 0.145190 | + | 0.251476i | ||||
\(845\) | 7003.50 | − | 12130.4i | 0.285122 | − | 0.493845i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4848.00 | 0.196322 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1596.00 | + | 2764.35i | 0.0644028 | + | 0.111549i | ||||
\(851\) | −17410.5 | − | 30155.9i | −0.701321 | − | 1.21472i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21238.0 | 0.852492 | 0.426246 | − | 0.904607i | \(-0.359836\pi\) | ||||
0.426246 | + | 0.904607i | \(0.359836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5484.00 | − | 9498.57i | 0.218971 | − | 0.379269i | ||||
\(857\) | 17804.5 | + | 30838.3i | 0.709673 | + | 1.22919i | 0.964978 | + | 0.262330i | \(0.0844908\pi\) |
−0.255305 | + | 0.966861i | \(0.582176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1088.50 | − | 1885.34i | 0.0432353 | − | 0.0748858i | −0.843598 | − | 0.536975i | \(-0.819567\pi\) |
0.886833 | + | 0.462090i | \(0.152900\pi\) | |||||||
\(860\) | 3472.00 | 0.137668 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9846.00 | 0.389044 | ||||||||
\(863\) | −16123.5 | + | 27926.7i | −0.635980 | + | 1.10155i | 0.350327 | + | 0.936627i | \(0.386070\pi\) |
−0.986307 | + | 0.164921i | \(0.947263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9873.50 | + | 17101.4i | 0.388103 | + | 0.672214i | ||||
\(866\) | −8974.00 | + | 15543.4i | −0.352135 | + | 0.609916i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −515.000 | −0.0201038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2905.00 | − | 5031.61i | −0.113011 | − | 0.195740i | ||||
\(872\) | 13500.0 | + | 23382.7i | 0.524275 | + | 0.908071i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 15582.0 | 0.603054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13815.5 | + | 23929.1i | −0.531946 | + | 0.921357i | 0.467359 | + | 0.884068i | \(0.345206\pi\) |
−0.999305 | + | 0.0372891i | \(0.988128\pi\) | |||||||
\(878\) | 4179.00 | + | 7238.24i | 0.160631 | + | 0.278222i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 280.000 | − | 484.974i | 0.0107259 | − | 0.0185778i | ||||
\(881\) | 24402.0 | 0.933172 | 0.466586 | − | 0.884476i | \(-0.345484\pi\) | ||||
0.466586 | + | 0.884476i | \(0.345484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19612.0 | −0.747448 | −0.373724 | − | 0.927540i | \(-0.621919\pi\) | ||||
−0.373724 | + | 0.927540i | \(0.621919\pi\) | |||||||
\(884\) | −588.000 | + | 1018.45i | −0.0223717 | + | 0.0387489i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12927.0 | + | 22390.2i | 0.490170 | + | 0.849000i | ||||
\(887\) | −1130.50 | + | 1958.08i | −0.0427942 | + | 0.0741218i | −0.886629 | − | 0.462481i | \(-0.846959\pi\) |
0.843835 | + | 0.536603i | \(0.180293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4606.00 | 0.173476 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2800.00 | + | 4849.74i | 0.105102 | + | 0.182042i | ||||
\(893\) | 12862.5 | + | 22278.5i | 0.482001 | + | 0.834851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22771.0 | 0.850448 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2826.00 | − | 4894.78i | 0.105017 | − | 0.181894i | ||||
\(899\) | −4263.00 | − | 7383.73i | −0.158152 | − | 0.273928i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3181.50 | + | 5510.52i | −0.117637 | + | 0.203754i | ||||
\(902\) | −3500.00 | −0.129199 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36912.0 | 1.35805 | ||||||||
\(905\) | 5537.00 | − | 9590.37i | 0.203377 | − | 0.352259i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11916.5 | + | 20640.0i | 0.436252 | + | 0.755611i | 0.997397 | − | 0.0721066i | \(-0.0229722\pi\) |
−0.561145 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(908\) | −4410.00 | + | 7638.34i | −0.161180 | + | 0.279171i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31824.0 | −1.15738 | −0.578692 | − | 0.815546i | \(-0.696437\pi\) | ||||
−0.578692 | + | 0.815546i | \(0.696437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2730.00 | − | 4728.50i | −0.0989593 | − | 0.171402i | ||||
\(914\) | 8479.00 | + | 14686.1i | 0.306849 | + | 0.531479i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1148.00 | 0.0414094 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8409.50 | − | 14565.7i | 0.301854 | − | 0.522826i | −0.674702 | − | 0.738090i | \(-0.735728\pi\) |
0.976556 | + | 0.215264i | \(0.0690612\pi\) | |||||||
\(920\) | −13356.0 | − | 23133.3i | −0.478624 | − | 0.829001i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9338.00 | − | 16173.9i | 0.333547 | − | 0.577721i | ||||
\(923\) | 6048.00 | 0.215680 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16644.0 | −0.591623 | ||||||||
\(926\) | −4016.00 | + | 6955.92i | −0.142520 | + | 0.246853i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4640.00 | − | 8036.72i | −0.164133 | − | 0.284287i | ||||
\(929\) | −899.500 | + | 1557.98i | −0.0317671 | + | 0.0550222i | −0.881472 | − | 0.472237i | \(-0.843447\pi\) |
0.849705 | + | 0.527259i | \(0.176780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18348.0 | 0.644859 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5859.00 | − | 10148.1i | −0.205259 | − | 0.355520i | ||||
\(935\) | 367.500 | + | 636.529i | 0.0128540 | + | 0.0222639i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14154.0 | −0.493480 | −0.246740 | − | 0.969082i | \(-0.579359\pi\) | ||||
−0.246740 | + | 0.969082i | \(0.579359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7350.00 | − | 12730.6i | 0.255033 | − | 0.441729i | ||||
\(941\) | −6023.50 | − | 10433.0i | −0.208672 | − | 0.361431i | 0.742624 | − | 0.669708i | \(-0.233581\pi\) |
−0.951296 | + | 0.308277i | \(0.900247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27825.0 | + | 48194.3i | −0.960877 | + | 1.66429i | ||||
\(944\) | 1680.00 | 0.0579230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1240.00 | 0.0426172 | ||||||||
\(947\) | −12189.5 | + | 21112.8i | −0.418274 | + | 0.724472i | −0.995766 | − | 0.0919245i | \(-0.970698\pi\) |
0.577492 | + | 0.816396i | \(0.304031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7791.00 | − | 13494.4i | −0.266498 | − | 0.461588i | ||||
\(950\) | 3724.00 | − | 6450.16i | 0.127182 | − | 0.220285i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52330.0 | 1.77874 | 0.889368 | − | 0.457192i | \(-0.151145\pi\) | ||||
0.889368 | + | 0.457192i | \(0.151145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8949.50 | + | 15501.0i | 0.303245 | + | 0.525236i | ||||
\(956\) | −3336.00 | − | 5778.12i | −0.112860 | − | 0.195479i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13006.0 | −0.438627 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4091.00 | − | 7085.82i | 0.137323 | − | 0.237851i | ||||
\(962\) | 3066.00 | + | 5310.47i | 0.102757 | + | 0.177980i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6818.00 | − | 11809.1i | 0.227794 | − | 0.394550i | ||||
\(965\) | −2779.00 | −0.0927038 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12416.0 | −0.412897 | −0.206449 | − | 0.978457i | \(-0.566191\pi\) | ||||
−0.206449 | + | 0.978457i | \(0.566191\pi\) | |||||||
\(968\) | 15672.0 | − | 27144.7i | 0.520369 | − | 0.901305i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6174.00 | + | 10693.7i | 0.204366 | + | 0.353973i | ||||
\(971\) | −18406.5 | + | 31881.0i | −0.608334 | + | 1.05367i | 0.383181 | + | 0.923673i | \(0.374829\pi\) |
−0.991515 | + | 0.129993i | \(0.958505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32098.0 | 1.05594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3304.00 | + | 5722.70i | 0.108359 | + | 0.187683i | ||||
\(977\) | 17497.5 | + | 30306.6i | 0.572973 | + | 0.992418i | 0.996259 | + | 0.0864221i | \(0.0275434\pi\) |
−0.423286 | + | 0.905996i | \(0.639123\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1645.00 | −0.0537022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8864.00 | + | 15352.9i | −0.288046 | + | 0.498911i | ||||
\(983\) | 7150.50 | + | 12385.0i | 0.232010 | + | 0.401853i | 0.958399 | − | 0.285430i | \(-0.0921366\pi\) |
−0.726390 | + | 0.687283i | \(0.758803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10199.0 | − | 17665.2i | 0.329916 | − | 0.571431i | ||||
\(986\) | −2436.00 | −0.0786796 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2744.00 | 0.0883586 | ||||||||
\(989\) | 9858.00 | − | 17074.6i | 0.316953 | − | 0.548978i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1332.50 | + | 2307.96i | 0.0427127 | + | 0.0739805i | 0.886591 | − | 0.462553i | \(-0.153067\pi\) |
−0.843879 | + | 0.536534i | \(0.819733\pi\) | |||||||
\(992\) | −11760.0 | + | 20368.9i | −0.376392 | + | 0.651929i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23373.0 | −0.744697 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12435.5 | + | 21538.9i | 0.395021 | + | 0.684197i | 0.993104 | − | 0.117237i | \(-0.0374039\pi\) |
−0.598083 | + | 0.801434i | \(0.704071\pi\) | |||||||
\(998\) | −10211.0 | − | 17686.0i | −0.323871 | − | 0.560962i | ||||
\(999\) | 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.k.226.1 | 2 | ||
3.2 | odd | 2 | 49.4.c.a.30.1 | 2 | |||
7.2 | even | 3 | 441.4.a.e.1.1 | 1 | |||
7.3 | odd | 6 | 63.4.e.b.46.1 | 2 | |||
7.4 | even | 3 | inner | 441.4.e.k.361.1 | 2 | ||
7.5 | odd | 6 | 441.4.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 63.4.e.b.37.1 | 2 | |||
21.2 | odd | 6 | 49.4.a.c.1.1 | 1 | |||
21.5 | even | 6 | 49.4.a.d.1.1 | 1 | |||
21.11 | odd | 6 | 49.4.c.a.18.1 | 2 | |||
21.17 | even | 6 | 7.4.c.a.4.1 | yes | 2 | ||
21.20 | even | 2 | 7.4.c.a.2.1 | ✓ | 2 | ||
84.23 | even | 6 | 784.4.a.r.1.1 | 1 | |||
84.47 | odd | 6 | 784.4.a.b.1.1 | 1 | |||
84.59 | odd | 6 | 112.4.i.c.81.1 | 2 | |||
84.83 | odd | 2 | 112.4.i.c.65.1 | 2 | |||
105.17 | odd | 12 | 175.4.k.a.74.2 | 4 | |||
105.38 | odd | 12 | 175.4.k.a.74.1 | 4 | |||
105.44 | odd | 6 | 1225.4.a.d.1.1 | 1 | |||
105.59 | even | 6 | 175.4.e.a.151.1 | 2 | |||
105.62 | odd | 4 | 175.4.k.a.149.1 | 4 | |||
105.83 | odd | 4 | 175.4.k.a.149.2 | 4 | |||
105.89 | even | 6 | 1225.4.a.c.1.1 | 1 | |||
105.104 | even | 2 | 175.4.e.a.51.1 | 2 | |||
168.59 | odd | 6 | 448.4.i.a.193.1 | 2 | |||
168.83 | odd | 2 | 448.4.i.a.65.1 | 2 | |||
168.101 | even | 6 | 448.4.i.f.193.1 | 2 | |||
168.125 | even | 2 | 448.4.i.f.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.c.a.2.1 | ✓ | 2 | 21.20 | even | 2 | ||
7.4.c.a.4.1 | yes | 2 | 21.17 | even | 6 | ||
49.4.a.c.1.1 | 1 | 21.2 | odd | 6 | |||
49.4.a.d.1.1 | 1 | 21.5 | even | 6 | |||
49.4.c.a.18.1 | 2 | 21.11 | odd | 6 | |||
49.4.c.a.30.1 | 2 | 3.2 | odd | 2 | |||
63.4.e.b.37.1 | 2 | 7.6 | odd | 2 | |||
63.4.e.b.46.1 | 2 | 7.3 | odd | 6 | |||
112.4.i.c.65.1 | 2 | 84.83 | odd | 2 | |||
112.4.i.c.81.1 | 2 | 84.59 | odd | 6 | |||
175.4.e.a.51.1 | 2 | 105.104 | even | 2 | |||
175.4.e.a.151.1 | 2 | 105.59 | even | 6 | |||
175.4.k.a.74.1 | 4 | 105.38 | odd | 12 | |||
175.4.k.a.74.2 | 4 | 105.17 | odd | 12 | |||
175.4.k.a.149.1 | 4 | 105.62 | odd | 4 | |||
175.4.k.a.149.2 | 4 | 105.83 | odd | 4 | |||
441.4.a.d.1.1 | 1 | 7.5 | odd | 6 | |||
441.4.a.e.1.1 | 1 | 7.2 | even | 3 | |||
441.4.e.k.226.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.k.361.1 | 2 | 7.4 | even | 3 | inner | ||
448.4.i.a.65.1 | 2 | 168.83 | odd | 2 | |||
448.4.i.a.193.1 | 2 | 168.59 | odd | 6 | |||
448.4.i.f.65.1 | 2 | 168.125 | even | 2 | |||
448.4.i.f.193.1 | 2 | 168.101 | even | 6 | |||
784.4.a.b.1.1 | 1 | 84.47 | odd | 6 | |||
784.4.a.r.1.1 | 1 | 84.23 | even | 6 | |||
1225.4.a.c.1.1 | 1 | 105.89 | even | 6 | |||
1225.4.a.d.1.1 | 1 | 105.44 | odd | 6 |