Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{1345})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(9.41856 + 16.3134i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.bf.667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −10.4186 | − | 18.0455i | −0.931864 | − | 1.61404i | −0.780132 | − | 0.625615i | \(-0.784848\pi\) |
−0.151732 | − | 0.988422i | \(-0.548485\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 20.8371 | − | 36.0910i | 0.658928 | − | 1.14130i | ||||
\(11\) | 7.58144 | − | 13.1314i | 0.207808 | − | 0.359934i | −0.743216 | − | 0.669052i | \(-0.766700\pi\) |
0.951024 | + | 0.309118i | \(0.100034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.16288 | −0.0461442 | −0.0230721 | − | 0.999734i | \(-0.507345\pi\) | ||||
−0.0230721 | + | 0.999734i | \(0.507345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 59.6742 | − | 103.359i | 0.851361 | − | 1.47460i | −0.0286202 | − | 0.999590i | \(-0.509111\pi\) |
0.879981 | − | 0.475009i | \(-0.157555\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.7557 | − | 29.0217i | −0.202317 | − | 0.350423i | 0.746958 | − | 0.664871i | \(-0.231514\pi\) |
−0.949274 | + | 0.314449i | \(0.898180\pi\) | |||||||
\(20\) | 83.3485 | 0.931864 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 30.3258 | 0.293885 | ||||||||
\(23\) | 0.325758 | + | 0.564230i | 0.00295327 | + | 0.00511522i | 0.867498 | − | 0.497440i | \(-0.165727\pi\) |
−0.864545 | + | 0.502555i | \(0.832393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −154.593 | + | 267.763i | −1.23674 | + | 2.14210i | ||||
\(26\) | −2.16288 | − | 3.74622i | −0.0163144 | − | 0.0282574i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 163.208 | 1.04507 | 0.522535 | − | 0.852618i | \(-0.324986\pi\) | ||||
0.522535 | + | 0.852618i | \(0.324986\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −111.663 | + | 193.406i | −0.646943 | + | 1.12054i | 0.336906 | + | 0.941538i | \(0.390620\pi\) |
−0.983849 | + | 0.179000i | \(0.942714\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 238.697 | 1.20401 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −84.2670 | − | 145.955i | −0.374417 | − | 0.648509i | 0.615823 | − | 0.787885i | \(-0.288824\pi\) |
−0.990240 | + | 0.139376i | \(0.955490\pi\) | |||||||
\(38\) | 33.5114 | − | 58.0434i | 0.143059 | − | 0.247786i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 83.3485 | + | 144.364i | 0.329464 | + | 0.570648i | ||||
\(41\) | −323.023 | −1.23043 | −0.615216 | − | 0.788359i | \(-0.710931\pi\) | ||||
−0.615216 | + | 0.788359i | \(0.710931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 221.557 | 0.785746 | 0.392873 | − | 0.919593i | \(-0.371481\pi\) | ||||
0.392873 | + | 0.919593i | \(0.371481\pi\) | |||||||
\(44\) | 30.3258 | + | 52.5258i | 0.103904 | + | 0.179967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.651517 | + | 1.12846i | −0.00208828 | + | 0.00361701i | ||||
\(47\) | −254.023 | − | 439.980i | −0.788362 | − | 1.36548i | −0.926970 | − | 0.375136i | \(-0.877596\pi\) |
0.138608 | − | 0.990347i | \(-0.455737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −618.371 | −1.74902 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.32576 | − | 7.49243i | 0.0115361 | − | 0.0199810i | ||||
\(53\) | −88.2557 | + | 152.863i | −0.228733 | + | 0.396177i | −0.957433 | − | 0.288656i | \(-0.906792\pi\) |
0.728700 | + | 0.684833i | \(0.240125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −315.951 | −0.774596 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 163.208 | + | 282.685i | 0.369488 | + | 0.639972i | ||||
\(59\) | −227.464 | + | 393.979i | −0.501920 | + | 0.869351i | 0.498077 | + | 0.867133i | \(0.334040\pi\) |
−0.999998 | + | 0.00221868i | \(0.999294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19.3258 | + | 33.4732i | 0.0405641 | + | 0.0702591i | 0.885595 | − | 0.464459i | \(-0.153751\pi\) |
−0.845031 | + | 0.534718i | \(0.820418\pi\) | |||||||
\(62\) | −446.652 | −0.914916 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 22.5341 | + | 39.0302i | 0.0430001 | + | 0.0744784i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −70.8958 | + | 122.795i | −0.129273 | + | 0.223908i | −0.923395 | − | 0.383851i | \(-0.874598\pi\) |
0.794122 | + | 0.607758i | \(0.207931\pi\) | |||||||
\(68\) | 238.697 | + | 413.435i | 0.425680 | + | 0.737300i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −602.742 | −1.00750 | −0.503749 | − | 0.863850i | \(-0.668046\pi\) | ||||
−0.503749 | + | 0.863850i | \(0.668046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −551.150 | + | 954.619i | −0.883660 | + | 1.53054i | −0.0364183 | + | 0.999337i | \(0.511595\pi\) |
−0.847242 | + | 0.531207i | \(0.821738\pi\) | |||||||
\(74\) | 168.534 | − | 291.910i | 0.264753 | − | 0.458565i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 134.045 | 0.202317 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.1515 | + | 100.721i | 0.0828172 | + | 0.143444i | 0.904459 | − | 0.426561i | \(-0.140275\pi\) |
−0.821642 | + | 0.570004i | \(0.806942\pi\) | |||||||
\(80\) | −166.697 | + | 288.728i | −0.232966 | + | 0.403509i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −323.023 | − | 559.492i | −0.435023 | − | 0.753482i | ||||
\(83\) | −568.928 | −0.752385 | −0.376193 | − | 0.926542i | \(-0.622767\pi\) | ||||
−0.376193 | + | 0.926542i | \(0.622767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2486.88 | −3.17341 | ||||||||
\(86\) | 221.557 | + | 383.748i | 0.277803 | + | 0.481169i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −60.6515 | + | 105.052i | −0.0734713 | + | 0.127256i | ||||
\(89\) | 191.580 | + | 331.825i | 0.228173 | + | 0.395207i | 0.957267 | − | 0.289207i | \(-0.0933915\pi\) |
−0.729094 | + | 0.684414i | \(0.760058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.60607 | −0.00295327 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 508.045 | − | 879.961i | 0.557456 | − | 0.965543i | ||||
\(95\) | −349.140 | + | 604.728i | −0.377063 | + | 0.653093i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −334.701 | −0.350348 | −0.175174 | − | 0.984538i | \(-0.556049\pi\) | ||||
−0.175174 | + | 0.984538i | \(0.556049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −618.371 | − | 1071.05i | −0.618371 | − | 1.07105i | ||||
\(101\) | 7.37121 | − | 12.7673i | 0.00726201 | − | 0.0125782i | −0.862372 | − | 0.506276i | \(-0.831022\pi\) |
0.869634 | + | 0.493698i | \(0.164355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −420.710 | − | 728.691i | −0.402464 | − | 0.697088i | 0.591559 | − | 0.806262i | \(-0.298513\pi\) |
−0.994023 | + | 0.109174i | \(0.965180\pi\) | |||||||
\(104\) | 17.3030 | 0.0163144 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −353.023 | −0.323477 | ||||||||
\(107\) | −357.835 | − | 619.789i | −0.323301 | − | 0.559974i | 0.657866 | − | 0.753135i | \(-0.271459\pi\) |
−0.981167 | + | 0.193161i | \(0.938126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −300.009 | + | 519.632i | −0.263630 | + | 0.456621i | −0.967204 | − | 0.254001i | \(-0.918253\pi\) |
0.703574 | + | 0.710622i | \(0.251587\pi\) | |||||||
\(110\) | −315.951 | − | 547.243i | −0.273861 | − | 0.474341i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −622.644 | −0.518349 | −0.259174 | − | 0.965831i | \(-0.583450\pi\) | ||||
−0.259174 | + | 0.965831i | \(0.583450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.78787 | − | 11.7569i | 0.00550410 | − | 0.00953339i | ||||
\(116\) | −326.417 | + | 565.370i | −0.261267 | + | 0.452529i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −909.856 | −0.709822 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 550.544 | + | 953.569i | 0.413632 | + | 0.716431i | ||||
\(122\) | −38.6515 | + | 66.9464i | −0.0286831 | + | 0.0496807i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −446.652 | − | 773.623i | −0.323472 | − | 0.560269i | ||||
\(125\) | 3837.90 | 2.74618 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −180.076 | −0.125820 | −0.0629100 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629100 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −45.0682 | + | 78.0604i | −0.0304057 | + | 0.0526642i | ||||
\(131\) | −108.930 | − | 188.672i | −0.0726508 | − | 0.125835i | 0.827411 | − | 0.561596i | \(-0.189813\pi\) |
−0.900062 | + | 0.435761i | \(0.856479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −283.583 | −0.182820 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −477.394 | + | 826.871i | −0.301001 | + | 0.521350i | ||||
\(137\) | −1300.93 | + | 2253.27i | −0.811283 | + | 1.40518i | 0.100683 | + | 0.994919i | \(0.467897\pi\) |
−0.911966 | + | 0.410265i | \(0.865436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2651.55 | 1.61800 | 0.808998 | − | 0.587811i | \(-0.200010\pi\) | ||||
0.808998 | + | 0.587811i | \(0.200010\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −602.742 | − | 1043.98i | −0.356204 | − | 0.616964i | ||||
\(143\) | −16.3977 | + | 28.4017i | −0.00958914 | + | 0.0166089i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1700.40 | − | 2945.17i | −0.973863 | − | 1.68678i | ||||
\(146\) | −2204.60 | −1.24968 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 674.136 | 0.374417 | ||||||||
\(149\) | 290.511 | + | 503.180i | 0.159729 | + | 0.276659i | 0.934771 | − | 0.355251i | \(-0.115605\pi\) |
−0.775042 | + | 0.631910i | \(0.782271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 307.695 | − | 532.943i | 0.165827 | − | 0.287221i | −0.771122 | − | 0.636688i | \(-0.780304\pi\) |
0.936949 | + | 0.349467i | \(0.113637\pi\) | |||||||
\(152\) | 134.045 | + | 232.174i | 0.0715297 | + | 0.123893i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4653.47 | 2.41145 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −153.466 | + | 265.811i | −0.0780122 | + | 0.135121i | −0.902392 | − | 0.430916i | \(-0.858191\pi\) |
0.824380 | + | 0.566037i | \(0.191524\pi\) | |||||||
\(158\) | −116.303 | + | 201.443i | −0.0585606 | + | 0.101430i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −666.788 | −0.329464 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1757.25 | − | 3043.65i | −0.844408 | − | 1.46256i | −0.886135 | − | 0.463428i | \(-0.846619\pi\) |
0.0417271 | − | 0.999129i | \(-0.486714\pi\) | |||||||
\(164\) | 646.045 | − | 1118.98i | 0.307608 | − | 0.532792i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −568.928 | − | 985.412i | −0.266008 | − | 0.460740i | ||||
\(167\) | 1123.30 | 0.520502 | 0.260251 | − | 0.965541i | \(-0.416195\pi\) | ||||
0.260251 | + | 0.965541i | \(0.416195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2192.32 | −0.997871 | ||||||||
\(170\) | −2486.88 | − | 4307.40i | −1.12197 | − | 1.94331i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −443.114 | + | 767.495i | −0.196437 | + | 0.340238i | ||||
\(173\) | −765.299 | − | 1325.54i | −0.336327 | − | 0.582536i | 0.647412 | − | 0.762141i | \(-0.275852\pi\) |
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −242.606 | −0.103904 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −383.159 | + | 663.651i | −0.161343 | + | 0.279454i | ||||
\(179\) | 1706.72 | − | 2956.12i | 0.712659 | − | 1.23436i | −0.251197 | − | 0.967936i | \(-0.580824\pi\) |
0.963856 | − | 0.266425i | \(-0.0858426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1286.71 | −0.528399 | −0.264200 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264200 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.60607 | − | 4.51384i | −0.00104414 | − | 0.00180850i | ||||
\(185\) | −1755.88 | + | 3041.28i | −0.697811 | + | 1.20864i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −904.833 | − | 1567.22i | −0.353839 | − | 0.612868i | ||||
\(188\) | 2032.18 | 0.788362 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1396.56 | −0.533248 | ||||||||
\(191\) | 527.648 | + | 913.913i | 0.199891 | + | 0.346222i | 0.948493 | − | 0.316798i | \(-0.102608\pi\) |
−0.748602 | + | 0.663020i | \(0.769274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2385.42 | − | 4131.67i | 0.889670 | − | 1.54095i | 0.0494044 | − | 0.998779i | \(-0.484268\pi\) |
0.840266 | − | 0.542175i | \(-0.182399\pi\) | |||||||
\(194\) | −334.701 | − | 579.719i | −0.123867 | − | 0.214543i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1622.31 | −0.586725 | −0.293363 | − | 0.956001i | \(-0.594774\pi\) | ||||
−0.293363 | + | 0.956001i | \(0.594774\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1775.07 | + | 3074.51i | −0.632318 | + | 1.09521i | 0.354759 | + | 0.934958i | \(0.384563\pi\) |
−0.987077 | + | 0.160249i | \(0.948770\pi\) | |||||||
\(200\) | 1236.74 | − | 2142.10i | 0.437254 | − | 0.757347i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 29.4848 | 0.0102700 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3365.43 | + | 5829.10i | 1.14659 | + | 1.98596i | ||||
\(206\) | 841.420 | − | 1457.38i | 0.284585 | − | 0.492916i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.3030 | + | 29.9697i | 0.00576803 | + | 0.00999051i | ||||
\(209\) | −508.129 | −0.168172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4653.39 | 1.51826 | 0.759129 | − | 0.650941i | \(-0.225625\pi\) | ||||
0.759129 | + | 0.650941i | \(0.225625\pi\) | |||||||
\(212\) | −353.023 | − | 611.453i | −0.114367 | − | 0.198089i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 715.670 | − | 1239.58i | 0.228609 | − | 0.395962i | ||||
\(215\) | −2308.30 | − | 3998.10i | −0.732209 | − | 1.26822i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1200.04 | −0.372829 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 631.901 | − | 1094.49i | 0.193649 | − | 0.335410i | ||||
\(221\) | −129.068 | + | 223.553i | −0.0392854 | + | 0.0680442i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4649.53 | 1.39621 | 0.698107 | − | 0.715993i | \(-0.254026\pi\) | ||||
0.698107 | + | 0.715993i | \(0.254026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −622.644 | − | 1078.45i | −0.183264 | − | 0.317423i | ||||
\(227\) | −2075.86 | + | 3595.49i | −0.606958 | + | 1.05128i | 0.384780 | + | 0.923008i | \(0.374277\pi\) |
−0.991739 | + | 0.128274i | \(0.959056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2131.82 | + | 3692.41i | 0.615172 | + | 1.06551i | 0.990354 | + | 0.138558i | \(0.0442468\pi\) |
−0.375182 | + | 0.926951i | \(0.622420\pi\) | |||||||
\(230\) | 27.1515 | 0.00778398 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1305.67 | −0.369488 | ||||||||
\(233\) | 1524.95 | + | 2641.29i | 0.428768 | + | 0.742647i | 0.996764 | − | 0.0803838i | \(-0.0256146\pi\) |
−0.567996 | + | 0.823031i | \(0.692281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5293.10 | + | 9167.92i | −1.46929 | + | 2.54489i | ||||
\(236\) | −909.856 | − | 1575.92i | −0.250960 | − | 0.434676i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3987.20 | −1.07912 | −0.539562 | − | 0.841946i | \(-0.681410\pi\) | ||||
−0.539562 | + | 0.841946i | \(0.681410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −312.324 | + | 540.961i | −0.0834795 | + | 0.144591i | −0.904742 | − | 0.425959i | \(-0.859937\pi\) |
0.821263 | + | 0.570550i | \(0.193270\pi\) | |||||||
\(242\) | −1101.09 | + | 1907.14i | −0.292482 | + | 0.506593i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −154.606 | −0.0405641 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.2405 | + | 62.7704i | 0.00933574 | + | 0.0161700i | ||||
\(248\) | 893.303 | − | 1547.25i | 0.228729 | − | 0.396170i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3837.90 | + | 6647.43i | 0.970920 | + | 1.68168i | ||||
\(251\) | −1328.78 | −0.334152 | −0.167076 | − | 0.985944i | \(-0.553432\pi\) | ||||
−0.167076 | + | 0.985944i | \(0.553432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.87887 | 0.00245486 | ||||||||
\(254\) | −180.076 | − | 311.900i | −0.0444841 | − | 0.0770487i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1613.09 | + | 2793.96i | 0.391525 | + | 0.678141i | 0.992651 | − | 0.121013i | \(-0.0386144\pi\) |
−0.601126 | + | 0.799154i | \(0.705281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −180.273 | −0.0430001 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 217.860 | − | 377.344i | 0.0513719 | − | 0.0889787i | ||||
\(263\) | 1625.31 | − | 2815.11i | 0.381067 | − | 0.660028i | −0.610148 | − | 0.792288i | \(-0.708890\pi\) |
0.991215 | + | 0.132260i | \(0.0422233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3677.99 | 0.852593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −283.583 | − | 491.181i | −0.0646366 | − | 0.111954i | ||||
\(269\) | −1413.02 | + | 2447.42i | −0.320273 | + | 0.554729i | −0.980544 | − | 0.196298i | \(-0.937108\pi\) |
0.660271 | + | 0.751027i | \(0.270441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1198.38 | − | 2075.66i | −0.268622 | − | 0.465268i | 0.699884 | − | 0.714257i | \(-0.253235\pi\) |
−0.968506 | + | 0.248989i | \(0.919902\pi\) | |||||||
\(272\) | −1909.58 | −0.425680 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5203.71 | −1.14733 | ||||||||
\(275\) | 2344.07 | + | 4060.05i | 0.514010 | + | 0.890292i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −910.233 | + | 1576.57i | −0.197439 | + | 0.341974i | −0.947697 | − | 0.319170i | \(-0.896596\pi\) |
0.750258 | + | 0.661145i | \(0.229929\pi\) | |||||||
\(278\) | 2651.55 | + | 4592.62i | 0.572048 | + | 0.990816i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3083.81 | −0.654679 | −0.327339 | − | 0.944907i | \(-0.606152\pi\) | ||||
−0.327339 | + | 0.944907i | \(0.606152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1277.38 | − | 2212.49i | 0.268313 | − | 0.464732i | −0.700113 | − | 0.714032i | \(-0.746867\pi\) |
0.968426 | + | 0.249300i | \(0.0802005\pi\) | |||||||
\(284\) | 1205.48 | − | 2087.96i | 0.251875 | − | 0.436259i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −65.5910 | −0.0135611 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4665.53 | − | 8080.94i | −0.949630 | − | 1.64481i | ||||
\(290\) | 3400.79 | − | 5890.34i | 0.688625 | − | 1.19273i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2204.60 | − | 3818.48i | −0.441830 | − | 0.765272i | ||||
\(293\) | −1846.47 | −0.368163 | −0.184081 | − | 0.982911i | \(-0.558931\pi\) | ||||
−0.184081 | + | 0.982911i | \(0.558931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9479.39 | 1.87089 | ||||||||
\(296\) | 674.136 | + | 1167.64i | 0.132376 | + | 0.229282i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −581.023 | + | 1006.36i | −0.112945 | + | 0.195627i | ||||
\(299\) | −0.704576 | − | 1.22036i | −0.000136277 | − | 0.000236038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1230.78 | 0.234515 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −268.091 | + | 464.347i | −0.0505792 | + | 0.0876057i | ||||
\(305\) | 402.693 | − | 697.485i | 0.0756005 | − | 0.130944i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7041.50 | −1.30905 | −0.654527 | − | 0.756039i | \(-0.727132\pi\) | ||||
−0.654527 | + | 0.756039i | \(0.727132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4653.47 | + | 8060.04i | 0.852578 | + | 1.47671i | ||||
\(311\) | 1343.00 | − | 2326.14i | 0.244869 | − | 0.424126i | −0.717226 | − | 0.696841i | \(-0.754588\pi\) |
0.962095 | + | 0.272715i | \(0.0879216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1109.59 | + | 1921.87i | 0.200377 | + | 0.347063i | 0.948650 | − | 0.316328i | \(-0.102450\pi\) |
−0.748273 | + | 0.663391i | \(0.769117\pi\) | |||||||
\(314\) | −613.864 | −0.110326 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −465.212 | −0.0828172 | ||||||||
\(317\) | 1110.63 | + | 1923.67i | 0.196780 | + | 0.340833i | 0.947483 | − | 0.319807i | \(-0.103618\pi\) |
−0.750703 | + | 0.660640i | \(0.770285\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1237.35 | − | 2143.16i | 0.217174 | − | 0.376157i | ||||
\(320\) | −666.788 | − | 1154.91i | −0.116483 | − | 0.201755i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3999.53 | −0.688978 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 334.366 | − | 579.138i | 0.0570685 | − | 0.0988455i | ||||
\(326\) | 3514.50 | − | 6087.29i | 0.597086 | − | 1.03418i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2584.18 | 0.435023 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2077.03 | − | 3597.52i | −0.344906 | − | 0.597394i | 0.640431 | − | 0.768016i | \(-0.278756\pi\) |
−0.985337 | + | 0.170622i | \(0.945422\pi\) | |||||||
\(332\) | 1137.86 | − | 1970.82i | 0.188096 | − | 0.325792i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1123.30 | + | 1945.62i | 0.184025 | + | 0.318741i | ||||
\(335\) | 2954.53 | 0.481860 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −254.167 | −0.0410841 | −0.0205420 | − | 0.999789i | \(-0.506539\pi\) | ||||
−0.0205420 | + | 0.999789i | \(0.506539\pi\) | |||||||
\(338\) | −2192.32 | − | 3797.21i | −0.352801 | − | 0.611069i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4973.76 | − | 8614.80i | 0.793353 | − | 1.37413i | ||||
\(341\) | 1693.13 | + | 2932.59i | 0.268880 | + | 0.465714i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1772.45 | −0.277803 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1530.60 | − | 2651.07i | 0.237819 | − | 0.411915i | ||||
\(347\) | −3112.32 | + | 5390.69i | −0.481493 | + | 0.833970i | −0.999774 | − | 0.0212401i | \(-0.993239\pi\) |
0.518282 | + | 0.855210i | \(0.326572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9732.21 | −1.49270 | −0.746352 | − | 0.665552i | \(-0.768196\pi\) | ||||
−0.746352 | + | 0.665552i | \(0.768196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −242.606 | − | 420.206i | −0.0367356 | − | 0.0636280i | ||||
\(353\) | −712.807 | + | 1234.62i | −0.107476 | + | 0.186153i | −0.914747 | − | 0.404027i | \(-0.867610\pi\) |
0.807271 | + | 0.590180i | \(0.200943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6279.71 | + | 10876.8i | 0.938852 | + | 1.62614i | ||||
\(356\) | −1532.64 | −0.228173 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6826.86 | 1.00785 | ||||||||
\(359\) | −2883.25 | − | 4993.93i | −0.423877 | − | 0.734177i | 0.572438 | − | 0.819948i | \(-0.305998\pi\) |
−0.996315 | + | 0.0857714i | \(0.972665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2867.99 | − | 4967.51i | 0.418136 | − | 0.724233i | ||||
\(362\) | −1286.71 | − | 2228.64i | −0.186817 | − | 0.323577i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22968.7 | 3.29381 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5772.67 | − | 9998.56i | 0.821065 | − | 1.42213i | −0.0838244 | − | 0.996481i | \(-0.526713\pi\) |
0.904890 | − | 0.425646i | \(-0.139953\pi\) | |||||||
\(368\) | 5.21213 | − | 9.02768i | 0.000738319 | − | 0.00127881i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7023.53 | −0.986854 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3239.79 | + | 5611.47i | 0.449731 | + | 0.778957i | 0.998368 | − | 0.0571033i | \(-0.0181864\pi\) |
−0.548637 | + | 0.836061i | \(0.684853\pi\) | |||||||
\(374\) | 1809.67 | − | 3134.43i | 0.250202 | − | 0.433363i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2032.18 | + | 3519.84i | 0.278728 | + | 0.482771i | ||||
\(377\) | −353.000 | −0.0482239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 611.996 | 0.0829449 | 0.0414725 | − | 0.999140i | \(-0.486795\pi\) | ||||
0.0414725 | + | 0.999140i | \(0.486795\pi\) | |||||||
\(380\) | −1396.56 | − | 2418.91i | −0.188532 | − | 0.326546i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1055.30 | + | 1827.83i | −0.141345 | + | 0.244816i | ||||
\(383\) | −2180.41 | − | 3776.57i | −0.290897 | − | 0.503848i | 0.683125 | − | 0.730301i | \(-0.260620\pi\) |
−0.974022 | + | 0.226453i | \(0.927287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9541.68 | 1.25818 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 669.402 | − | 1159.44i | 0.0875869 | − | 0.151705i | ||||
\(389\) | −6573.46 | + | 11385.6i | −0.856781 | + | 1.48399i | 0.0182021 | + | 0.999834i | \(0.494206\pi\) |
−0.874983 | + | 0.484154i | \(0.839128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 77.7575 | 0.0100572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1622.31 | − | 2809.92i | −0.207439 | − | 0.359294i | ||||
\(395\) | 1211.71 | − | 2098.74i | 0.154349 | − | 0.267340i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4239.02 | − | 7342.20i | −0.535895 | − | 0.928198i | −0.999119 | − | 0.0419565i | \(-0.986641\pi\) |
0.463224 | − | 0.886241i | \(-0.346692\pi\) | |||||||
\(398\) | −7100.27 | −0.894232 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4946.97 | 0.618371 | ||||||||
\(401\) | 1401.50 | + | 2427.47i | 0.174533 | + | 0.302299i | 0.939999 | − | 0.341176i | \(-0.110825\pi\) |
−0.765467 | + | 0.643475i | \(0.777492\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 241.513 | − | 418.313i | 0.0298527 | − | 0.0517064i | ||||
\(404\) | 29.4848 | + | 51.0692i | 0.00363100 | + | 0.00628908i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2555.46 | −0.311227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3192.69 | + | 5529.91i | −0.385987 | + | 0.668548i | −0.991906 | − | 0.126978i | \(-0.959472\pi\) |
0.605919 | + | 0.795526i | \(0.292806\pi\) | |||||||
\(410\) | −6730.86 | + | 11658.2i | −0.810765 | + | 1.40429i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3365.68 | 0.402464 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5927.41 | + | 10266.6i | 0.701121 | + | 1.21438i | ||||
\(416\) | −34.6061 | + | 59.9395i | −0.00407861 | + | 0.00706436i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −508.129 | − | 880.105i | −0.0594579 | − | 0.102984i | ||||
\(419\) | 4831.66 | 0.563346 | 0.281673 | − | 0.959510i | \(-0.409111\pi\) | ||||
0.281673 | + | 0.959510i | \(0.409111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7475.37 | 0.865385 | 0.432693 | − | 0.901542i | \(-0.357564\pi\) | ||||
0.432693 | + | 0.901542i | \(0.357564\pi\) | |||||||
\(422\) | 4653.39 | + | 8059.90i | 0.536785 | + | 0.929739i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 706.045 | − | 1222.91i | 0.0808693 | − | 0.140070i | ||||
\(425\) | 18450.4 | + | 31957.1i | 2.10583 | + | 3.64740i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2862.68 | 0.323301 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4616.61 | − | 7996.20i | 0.517750 | − | 0.896769i | ||||
\(431\) | 3495.97 | − | 6055.19i | 0.390707 | − | 0.676725i | −0.601836 | − | 0.798620i | \(-0.705564\pi\) |
0.992543 | + | 0.121895i | \(0.0388972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7699.26 | 0.854510 | 0.427255 | − | 0.904131i | \(-0.359481\pi\) | ||||
0.427255 | + | 0.904131i | \(0.359481\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1200.04 | − | 2078.53i | −0.131815 | − | 0.228310i | ||||
\(437\) | 10.9166 | − | 18.9081i | 0.00119499 | − | 0.00206979i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4706.16 | + | 8151.31i | 0.511646 | + | 0.886198i | 0.999909 | + | 0.0135008i | \(0.00429758\pi\) |
−0.488262 | + | 0.872697i | \(0.662369\pi\) | |||||||
\(440\) | 2527.61 | 0.273861 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −516.273 | −0.0555579 | ||||||||
\(443\) | −3129.09 | − | 5419.74i | −0.335593 | − | 0.581263i | 0.648006 | − | 0.761635i | \(-0.275603\pi\) |
−0.983598 | + | 0.180372i | \(0.942270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3991.97 | − | 6914.29i | 0.425252 | − | 0.736559i | ||||
\(446\) | 4649.53 | + | 8053.23i | 0.493636 | + | 0.855003i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11633.8 | 1.22279 | 0.611396 | − | 0.791325i | \(-0.290608\pi\) | ||||
0.611396 | + | 0.791325i | \(0.290608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2448.98 | + | 4241.75i | −0.255694 | + | 0.442874i | ||||
\(452\) | 1245.29 | − | 2156.90i | 0.129587 | − | 0.224452i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8303.43 | −0.858369 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6552.31 | + | 11348.9i | 0.670688 | + | 1.16167i | 0.977709 | + | 0.209963i | \(0.0673343\pi\) |
−0.307022 | + | 0.951703i | \(0.599332\pi\) | |||||||
\(458\) | −4263.63 | + | 7384.83i | −0.434992 | + | 0.753429i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 27.1515 | + | 47.0277i | 0.00275205 | + | 0.00476669i | ||||
\(461\) | −2594.63 | −0.262134 | −0.131067 | − | 0.991373i | \(-0.541840\pi\) | ||||
−0.131067 | + | 0.991373i | \(0.541840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14136.2 | −1.41893 | −0.709465 | − | 0.704741i | \(-0.751063\pi\) | ||||
−0.709465 | + | 0.704741i | \(0.751063\pi\) | |||||||
\(464\) | −1305.67 | − | 2261.48i | −0.130634 | − | 0.226264i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3049.90 | + | 5282.58i | −0.303184 | + | 0.525131i | ||||
\(467\) | −7795.12 | − | 13501.5i | −0.772409 | − | 1.33785i | −0.936239 | − | 0.351363i | \(-0.885718\pi\) |
0.163830 | − | 0.986489i | \(-0.447615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −21172.4 | −2.07789 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1819.71 | − | 3151.83i | 0.177456 | − | 0.307362i | ||||
\(473\) | 1679.72 | − | 2909.36i | 0.163285 | − | 0.282817i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10361.2 | 1.00085 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3987.20 | − | 6906.04i | −0.381528 | − | 0.660826i | ||||
\(479\) | 4226.75 | − | 7320.95i | 0.403184 | − | 0.698336i | −0.590924 | − | 0.806727i | \(-0.701237\pi\) |
0.994108 | + | 0.108391i | \(0.0345700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 182.259 | + | 315.683i | 0.0172772 | + | 0.0299249i | ||||
\(482\) | −1249.30 | −0.118058 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4404.35 | −0.413632 | ||||||||
\(485\) | 3487.10 | + | 6039.83i | 0.326476 | + | 0.565474i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2005.53 | − | 3473.69i | 0.186611 | − | 0.323219i | −0.757507 | − | 0.652827i | \(-0.773583\pi\) |
0.944118 | + | 0.329607i | \(0.106916\pi\) | |||||||
\(488\) | −154.606 | − | 267.786i | −0.0143416 | − | 0.0248403i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13927.9 | −1.28016 | −0.640079 | − | 0.768309i | \(-0.721098\pi\) | ||||
−0.640079 | + | 0.768309i | \(0.721098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9739.33 | − | 16869.0i | 0.889731 | − | 1.54106i | ||||
\(494\) | −72.4810 | + | 125.541i | −0.00660137 | + | 0.0114339i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3573.21 | 0.323472 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1973.77 | + | 3418.68i | 0.177071 | + | 0.306695i | 0.940876 | − | 0.338751i | \(-0.110005\pi\) |
−0.763805 | + | 0.645447i | \(0.776671\pi\) | |||||||
\(500\) | −7675.80 | + | 13294.9i | −0.686544 | + | 1.18913i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1328.78 | − | 2301.52i | −0.118141 | − | 0.204625i | ||||
\(503\) | −13725.3 | −1.21666 | −0.608331 | − | 0.793684i | \(-0.708161\pi\) | ||||
−0.608331 | + | 0.793684i | \(0.708161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −307.190 | −0.0270688 | ||||||||
\(506\) | 9.87887 | + | 17.1107i | 0.000867924 | + | 0.00150329i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 360.152 | − | 623.801i | 0.0314550 | − | 0.0544817i | ||||
\(509\) | −3915.05 | − | 6781.07i | −0.340926 | − | 0.590502i | 0.643679 | − | 0.765296i | \(-0.277407\pi\) |
−0.984605 | + | 0.174794i | \(0.944074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3226.18 | + | 5587.91i | −0.276850 | + | 0.479518i | ||||
\(515\) | −8766.39 | + | 15183.8i | −0.750084 | + | 1.29918i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7703.43 | −0.655312 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −180.273 | − | 312.241i | −0.0152028 | − | 0.0263321i | ||||
\(521\) | 2953.69 | − | 5115.95i | 0.248376 | − | 0.430199i | −0.714700 | − | 0.699431i | \(-0.753437\pi\) |
0.963075 | + | 0.269232i | \(0.0867700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3954.03 | + | 6848.58i | 0.330588 | + | 0.572595i | 0.982627 | − | 0.185590i | \(-0.0594196\pi\) |
−0.652039 | + | 0.758185i | \(0.726086\pi\) | |||||||
\(524\) | 871.439 | 0.0726508 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6501.23 | 0.538911 | ||||||||
\(527\) | 13326.8 | + | 23082.7i | 1.10156 | + | 1.90797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6083.29 | − | 10536.6i | 0.499983 | − | 0.865995i | ||||
\(530\) | 3677.99 | + | 6370.46i | 0.301437 | + | 0.522104i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 698.659 | 0.0567773 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7456.26 | + | 12914.6i | −0.602546 | + | 1.04364i | ||||
\(536\) | 567.167 | − | 982.362i | 0.0457050 | − | 0.0791633i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5652.08 | −0.452934 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1970.52 | + | 3413.04i | 0.156598 | + | 0.271235i | 0.933640 | − | 0.358214i | \(-0.116614\pi\) |
−0.777042 | + | 0.629449i | \(0.783281\pi\) | |||||||
\(542\) | 2396.77 | − | 4151.33i | 0.189945 | − | 0.328994i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1909.58 | − | 3307.48i | −0.150501 | − | 0.260675i | ||||
\(545\) | 12502.7 | 0.982670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1828.71 | −0.142943 | −0.0714717 | − | 0.997443i | \(-0.522770\pi\) | ||||
−0.0714717 | + | 0.997443i | \(0.522770\pi\) | |||||||
\(548\) | −5203.71 | − | 9013.09i | −0.405642 | − | 0.702592i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4688.14 | + | 8120.10i | −0.363460 | + | 0.629532i | ||||
\(551\) | −2734.67 | − | 4736.58i | −0.211435 | − | 0.366216i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3640.93 | −0.279221 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5303.10 | + | 9185.24i | −0.404499 | + | 0.700613i | ||||
\(557\) | 11266.0 | − | 19513.3i | 0.857011 | − | 1.48439i | −0.0177556 | − | 0.999842i | \(-0.505652\pi\) |
0.874767 | − | 0.484544i | \(-0.161015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −479.201 | −0.0362577 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3083.81 | − | 5341.32i | −0.231464 | − | 0.400907i | ||||
\(563\) | −11677.9 | + | 20226.6i | −0.874179 | + | 1.51412i | −0.0165446 | + | 0.999863i | \(0.505267\pi\) |
−0.857635 | + | 0.514260i | \(0.828067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6487.05 | + | 11235.9i | 0.483031 | + | 0.836634i | ||||
\(566\) | 5109.54 | 0.379452 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4821.94 | 0.356204 | ||||||||
\(569\) | −10443.8 | − | 18089.2i | −0.769468 | − | 1.33276i | −0.937852 | − | 0.347036i | \(-0.887188\pi\) |
0.168384 | − | 0.985721i | \(-0.446145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11872.6 | + | 20564.0i | −0.870147 | + | 1.50714i | −0.00830301 | + | 0.999966i | \(0.502643\pi\) |
−0.861844 | + | 0.507173i | \(0.830690\pi\) | |||||||
\(572\) | −65.5910 | − | 113.607i | −0.00479457 | − | 0.00830444i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −201.440 | −0.0146098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1227.20 | − | 2125.57i | 0.0885422 | − | 0.153360i | −0.818353 | − | 0.574716i | \(-0.805113\pi\) |
0.906895 | + | 0.421356i | \(0.138446\pi\) | |||||||
\(578\) | 9331.06 | − | 16161.9i | 0.671490 | − | 1.16305i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13603.2 | 0.973863 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1338.21 | + | 2317.85i | 0.0950652 | + | 0.164658i | ||||
\(584\) | 4409.20 | − | 7636.95i | 0.312421 | − | 0.541129i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1846.47 | − | 3198.17i | −0.130165 | − | 0.225453i | ||||
\(587\) | 18567.5 | 1.30556 | 0.652780 | − | 0.757547i | \(-0.273603\pi\) | ||||
0.652780 | + | 0.757547i | \(0.273603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7483.95 | 0.523550 | ||||||||
\(590\) | 9479.39 | + | 16418.8i | 0.661458 | + | 1.14568i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1348.27 | + | 2335.28i | −0.0936042 | + | 0.162127i | ||||
\(593\) | −8556.47 | − | 14820.2i | −0.592533 | − | 1.02630i | −0.993890 | − | 0.110375i | \(-0.964795\pi\) |
0.401357 | − | 0.915922i | \(-0.368539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2324.09 | −0.159729 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.40915 | − | 2.44072i | 9.63621e−5 | − | 0.000166904i | ||||
\(599\) | 11632.4 | − | 20147.9i | 0.793469 | − | 1.37433i | −0.130338 | − | 0.991470i | \(-0.541606\pi\) |
0.923807 | − | 0.382859i | \(-0.125060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25322.3 | −1.71867 | −0.859334 | − | 0.511416i | \(-0.829121\pi\) | ||||
−0.859334 | + | 0.511416i | \(0.829121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1230.78 | + | 2131.77i | 0.0829135 | + | 0.143610i | ||||
\(605\) | 11471.7 | − | 19869.6i | 0.770897 | − | 1.33523i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10867.2 | − | 18822.5i | −0.726665 | − | 1.25862i | −0.958285 | − | 0.285814i | \(-0.907736\pi\) |
0.231620 | − | 0.972806i | \(-0.425597\pi\) | |||||||
\(608\) | −1072.36 | −0.0715297 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1610.77 | 0.106915 | ||||||||
\(611\) | 549.420 | + | 951.624i | 0.0363784 | + | 0.0630092i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6786.19 | − | 11754.0i | 0.447131 | − | 0.774454i | −0.551067 | − | 0.834461i | \(-0.685779\pi\) |
0.998198 | + | 0.0600072i | \(0.0191124\pi\) | |||||||
\(614\) | −7041.50 | − | 12196.2i | −0.462820 | − | 0.801628i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8497.12 | 0.554427 | 0.277213 | − | 0.960808i | \(-0.410589\pi\) | ||||
0.277213 | + | 0.960808i | \(0.410589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11491.5 | + | 19903.8i | −0.746173 | + | 1.29241i | 0.203472 | + | 0.979081i | \(0.434777\pi\) |
−0.949645 | + | 0.313329i | \(0.898556\pi\) | |||||||
\(620\) | −9306.93 | + | 16120.1i | −0.602863 | + | 1.04419i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5371.98 | 0.346297 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20661.3 | − | 35786.4i | −1.32232 | − | 2.29033i | ||||
\(626\) | −2219.19 | + | 3843.75i | −0.141688 | + | 0.245411i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −613.864 | − | 1063.24i | −0.0390061 | − | 0.0675605i | ||||
\(629\) | −20114.3 | −1.27505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15717.9 | −0.991635 | −0.495817 | − | 0.868427i | \(-0.665131\pi\) | ||||
−0.495817 | + | 0.868427i | \(0.665131\pi\) | |||||||
\(632\) | −465.212 | − | 805.771i | −0.0292803 | − | 0.0507150i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2221.26 | + | 3847.34i | −0.139144 | + | 0.241005i | ||||
\(635\) | 1876.13 | + | 3249.55i | 0.117247 | + | 0.203078i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4949.42 | 0.307131 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1333.58 | − | 2309.82i | 0.0823660 | − | 0.142662i | ||||
\(641\) | 14553.7 | − | 25207.7i | 0.896780 | − | 1.55327i | 0.0651930 | − | 0.997873i | \(-0.479234\pi\) |
0.831587 | − | 0.555395i | \(-0.187433\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3112.26 | 0.190880 | 0.0954398 | − | 0.995435i | \(-0.469574\pi\) | ||||
0.0954398 | + | 0.995435i | \(0.469574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3999.53 | − | 6927.39i | −0.243590 | − | 0.421911i | ||||
\(647\) | 3928.80 | − | 6804.87i | 0.238728 | − | 0.413489i | −0.721622 | − | 0.692288i | \(-0.756603\pi\) |
0.960349 | + | 0.278799i | \(0.0899363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3449.01 | + | 5973.86i | 0.208606 | + | 0.361317i | ||||
\(650\) | 1337.46 | 0.0807071 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14058.0 | 0.844408 | ||||||||
\(653\) | −9761.01 | − | 16906.6i | −0.584958 | − | 1.01318i | −0.994881 | − | 0.101057i | \(-0.967778\pi\) |
0.409923 | − | 0.912120i | \(-0.365556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2269.79 | + | 3931.38i | −0.135401 | + | 0.234522i | ||||
\(656\) | 2584.18 | + | 4475.93i | 0.153804 | + | 0.266396i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −664.061 | −0.0392536 | −0.0196268 | − | 0.999807i | \(-0.506248\pi\) | ||||
−0.0196268 | + | 0.999807i | \(0.506248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7960.82 | − | 13788.5i | 0.468442 | − | 0.811365i | −0.530908 | − | 0.847430i | \(-0.678149\pi\) |
0.999349 | + | 0.0360650i | \(0.0114823\pi\) | |||||||
\(662\) | 4154.06 | − | 7195.04i | 0.243885 | − | 0.422422i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4551.42 | 0.266008 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.1665 | + | 92.0870i | 0.00308638 | + | 0.00534576i | ||||
\(668\) | −2246.61 | + | 3891.24i | −0.130125 | + | 0.225384i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2954.53 | + | 5117.40i | 0.170363 | + | 0.295078i | ||||
\(671\) | 586.068 | 0.0337182 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24631.0 | 1.41078 | 0.705391 | − | 0.708819i | \(-0.250771\pi\) | ||||
0.705391 | + | 0.708819i | \(0.250771\pi\) | |||||||
\(674\) | −254.167 | − | 440.230i | −0.0145254 | − | 0.0251588i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4384.64 | − | 7594.43i | 0.249468 | − | 0.432091i | ||||
\(677\) | −8546.39 | − | 14802.8i | −0.485177 | − | 0.840350i | 0.514678 | − | 0.857383i | \(-0.327911\pi\) |
−0.999855 | + | 0.0170329i | \(0.994578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 19895.0 | 1.12197 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3386.26 | + | 5865.18i | −0.190127 | + | 0.329310i | ||||
\(683\) | −9581.79 | + | 16596.1i | −0.536804 | + | 0.929771i | 0.462270 | + | 0.886739i | \(0.347035\pi\) |
−0.999074 | + | 0.0430322i | \(0.986298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54215.2 | 3.02402 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1772.45 | − | 3069.98i | −0.0982183 | − | 0.170119i | ||||
\(689\) | 190.886 | − | 330.625i | 0.0105547 | − | 0.0182813i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4047.94 | + | 7011.23i | 0.222852 | + | 0.385991i | 0.955673 | − | 0.294431i | \(-0.0951300\pi\) |
−0.732821 | + | 0.680422i | \(0.761797\pi\) | |||||||
\(692\) | 6122.39 | 0.336327 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12449.3 | −0.680934 | ||||||||
\(695\) | −27625.3 | − | 47848.5i | −1.50775 | − | 2.61150i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19276.1 | + | 33387.2i | −1.04754 | + | 1.81439i | ||||
\(698\) | −9732.21 | − | 16856.7i | −0.527750 | − | 0.914090i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12354.7 | −0.665664 | −0.332832 | − | 0.942986i | \(-0.608004\pi\) | ||||
−0.332832 | + | 0.942986i | \(0.608004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2823.90 | + | 4891.14i | −0.151501 | + | 0.262408i | ||||
\(704\) | 485.212 | − | 840.412i | 0.0259760 | − | 0.0449918i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2851.23 | −0.151993 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1914.41 | − | 3315.85i | −0.101406 | − | 0.175641i | 0.810858 | − | 0.585243i | \(-0.199001\pi\) |
−0.912264 | + | 0.409602i | \(0.865668\pi\) | |||||||
\(710\) | −12559.4 | + | 21753.5i | −0.663868 | + | 1.14985i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1532.64 | − | 2654.60i | −0.0806713 | − | 0.139727i | ||||
\(713\) | −145.500 | −0.00764241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 683.363 | 0.0357431 | ||||||||
\(716\) | 6826.86 | + | 11824.5i | 0.356329 | + | 0.617181i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5766.49 | − | 9987.86i | 0.299726 | − | 0.519141i | ||||
\(719\) | −611.500 | − | 1059.15i | −0.0317178 | − | 0.0549368i | 0.849731 | − | 0.527217i | \(-0.176764\pi\) |
−0.881449 | + | 0.472280i | \(0.843431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11472.0 | 0.591333 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2573.42 | − | 4457.29i | 0.132100 | − | 0.228804i | ||||
\(725\) | −25230.8 | + | 43701.1i | −1.29248 | + | 2.23864i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6368.21 | −0.324875 | −0.162437 | − | 0.986719i | \(-0.551936\pi\) | ||||
−0.162437 | + | 0.986719i | \(0.551936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22968.7 | + | 39783.0i | 1.16454 | + | 2.01704i | ||||
\(731\) | 13221.2 | − | 22899.9i | 0.668954 | − | 1.15866i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12577.0 | − | 21784.0i | −0.633753 | − | 1.09769i | −0.986778 | − | 0.162079i | \(-0.948180\pi\) |
0.353024 | − | 0.935614i | \(-0.385153\pi\) | |||||||
\(734\) | 23090.7 | 1.16116 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8485 | 0.00104414 | ||||||||
\(737\) | 1074.98 | + | 1861.93i | 0.0537281 | + | 0.0930597i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5369.55 | − | 9300.34i | 0.267283 | − | 0.462948i | −0.700876 | − | 0.713283i | \(-0.747207\pi\) |
0.968159 | + | 0.250335i | \(0.0805408\pi\) | |||||||
\(740\) | −7023.53 | − | 12165.1i | −0.348906 | − | 0.604322i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28166.3 | −1.39074 | −0.695370 | − | 0.718652i | \(-0.744760\pi\) | ||||
−0.695370 | + | 0.718652i | \(0.744760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6053.42 | − | 10484.8i | 0.297691 | − | 0.515617i | ||||
\(746\) | −6479.57 | + | 11222.9i | −0.318008 | + | 0.550806i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7238.67 | 0.353839 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14328.5 | − | 24817.7i | −0.696211 | − | 1.20587i | −0.969771 | − | 0.244018i | \(-0.921534\pi\) |
0.273559 | − | 0.961855i | \(-0.411799\pi\) | |||||||
\(752\) | −4064.36 | + | 7039.68i | −0.197091 | + | 0.341371i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −353.000 | − | 611.414i | −0.0170497 | − | 0.0295310i | ||||
\(755\) | −12823.0 | −0.618113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23604.1 | −1.13330 | −0.566648 | − | 0.823960i | \(-0.691760\pi\) | ||||
−0.566648 | + | 0.823960i | \(0.691760\pi\) | |||||||
\(758\) | 611.996 | + | 1060.01i | 0.0293255 | + | 0.0507932i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2793.12 | − | 4837.83i | 0.133312 | − | 0.230903i | ||||
\(761\) | −2315.48 | − | 4010.54i | −0.110297 | − | 0.191041i | 0.805593 | − | 0.592470i | \(-0.201847\pi\) |
−0.915890 | + | 0.401429i | \(0.868514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4221.18 | −0.199891 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4360.81 | − | 7553.15i | 0.205695 | − | 0.356274i | ||||
\(767\) | 491.977 | − | 852.129i | 0.0231607 | − | 0.0401155i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33276.8 | −1.56046 | −0.780228 | − | 0.625495i | \(-0.784897\pi\) | ||||
−0.780228 | + | 0.625495i | \(0.784897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9541.68 | + | 16526.7i | 0.444835 | + | 0.770477i | ||||
\(773\) | 11469.4 | − | 19865.6i | 0.533668 | − | 0.924340i | −0.465558 | − | 0.885017i | \(-0.654147\pi\) |
0.999227 | − | 0.0393231i | \(-0.0125202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34524.6 | − | 59798.3i | −1.60020 | − | 2.77164i | ||||
\(776\) | 2677.61 | 0.123867 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26293.8 | −1.21167 | ||||||||
\(779\) | 5412.47 | + | 9374.67i | 0.248937 | + | 0.431171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4569.66 | + | 7914.88i | −0.209366 | + | 0.362633i | ||||
\(782\) | 77.7575 | + | 134.680i | 0.00355576 | + | 0.00615876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6395.58 | 0.290787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6757.23 | + | 11703.9i | −0.306060 | + | 0.530112i | −0.977497 | − | 0.210950i | \(-0.932344\pi\) |
0.671437 | + | 0.741062i | \(0.265678\pi\) | |||||||
\(788\) | 3244.62 | − | 5619.85i | 0.146681 | − | 0.254059i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4846.84 | 0.218282 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.7993 | − | 72.3985i | −0.00187180 | − | 0.00324205i | ||||
\(794\) | 8478.04 | − | 14684.4i | 0.378935 | − | 0.656335i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7100.27 | − | 12298.0i | −0.316159 | − | 0.547603i | ||||
\(797\) | 10473.4 | 0.465480 | 0.232740 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232740 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60634.5 | −2.68472 | ||||||||
\(800\) | 4946.97 | + | 8568.40i | 0.218627 | + | 0.378673i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2803.00 | + | 4854.94i | −0.123413 | + | 0.213758i | ||||
\(803\) | 8357.02 | + | 14474.8i | 0.367264 | + | 0.636119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 966.053 | 0.0422181 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −58.9697 | + | 102.138i | −0.00256751 | + | 0.00444705i | ||||
\(809\) | 11784.0 | − | 20410.5i | 0.512117 | − | 0.887013i | −0.487784 | − | 0.872964i | \(-0.662195\pi\) |
0.999901 | − | 0.0140486i | \(-0.00447194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6704.22 | 0.290280 | 0.145140 | − | 0.989411i | \(-0.453637\pi\) | ||||
0.145140 | + | 0.989411i | \(0.453637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2555.46 | − | 4426.19i | −0.110035 | − | 0.190587i | ||||
\(815\) | −36616.0 | + | 63420.8i | −1.57375 | + | 2.72581i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3712.34 | − | 6429.95i | −0.158970 | − | 0.275343i | ||||
\(818\) | −12770.8 | −0.545867 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26923.5 | −1.14659 | ||||||||
\(821\) | 12269.7 | + | 21251.8i | 0.521579 | + | 0.903401i | 0.999685 | + | 0.0250988i | \(0.00799003\pi\) |
−0.478106 | + | 0.878302i | \(0.658677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15558.5 | − | 26948.1i | 0.658973 | − | 1.14137i | −0.321909 | − | 0.946771i | \(-0.604325\pi\) |
0.980882 | − | 0.194604i | \(-0.0623421\pi\) | |||||||
\(824\) | 3365.68 | + | 5829.53i | 0.142293 | + | 0.246458i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31244.9 | −1.31377 | −0.656887 | − | 0.753989i | \(-0.728127\pi\) | ||||
−0.656887 | + | 0.753989i | \(0.728127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2115.75 | − | 3664.58i | 0.0886405 | − | 0.153530i | −0.818296 | − | 0.574797i | \(-0.805081\pi\) |
0.906937 | + | 0.421267i | \(0.138414\pi\) | |||||||
\(830\) | −11854.8 | + | 20533.2i | −0.495767 | + | 0.858694i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −138.424 | −0.00576803 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11703.2 | − | 20270.5i | −0.485037 | − | 0.840109i | ||||
\(836\) | 1016.26 | − | 1760.21i | 0.0420431 | − | 0.0728207i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4831.66 | + | 8368.68i | 0.199173 | + | 0.344978i | ||||
\(839\) | −38670.4 | −1.59124 | −0.795621 | − | 0.605795i | \(-0.792855\pi\) | ||||
−0.795621 | + | 0.605795i | \(0.792855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2247.96 | 0.0921710 | ||||||||
\(842\) | 7475.37 | + | 12947.7i | 0.305960 | + | 0.529938i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9306.77 | + | 16119.8i | −0.379564 | + | 0.657425i | ||||
\(845\) | 22840.8 | + | 39561.5i | 0.929880 | + | 1.61060i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2824.18 | 0.114367 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −36900.8 | + | 63914.1i | −1.48904 | + | 2.57910i | ||||
\(851\) | 54.9014 | − | 95.0920i | 0.00221151 | − | 0.00383045i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19944.4 | 0.800565 | 0.400282 | − | 0.916392i | \(-0.368912\pi\) | ||||
0.400282 | + | 0.916392i | \(0.368912\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2862.68 | + | 4958.31i | 0.114304 | + | 0.197981i | ||||
\(857\) | −6941.10 | + | 12022.3i | −0.276667 | + | 0.479201i | −0.970554 | − | 0.240882i | \(-0.922563\pi\) |
0.693887 | + | 0.720084i | \(0.255897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2078.58 | − | 3600.21i | −0.0825614 | − | 0.143000i | 0.821788 | − | 0.569793i | \(-0.192977\pi\) |
−0.904349 | + | 0.426793i | \(0.859643\pi\) | |||||||
\(860\) | 18466.4 | 0.732209 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13983.9 | 0.552543 | ||||||||
\(863\) | −8118.96 | − | 14062.5i | −0.320246 | − | 0.554683i | 0.660292 | − | 0.751009i | \(-0.270432\pi\) |
−0.980539 | + | 0.196326i | \(0.937099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15946.6 | + | 27620.4i | −0.626823 | + | 1.08569i | ||||
\(866\) | 7699.26 | + | 13335.5i | 0.302115 | + | 0.523278i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1763.49 | 0.0688403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 153.339 | − | 265.591i | 0.00596521 | − | 0.0103320i | ||||
\(872\) | 2400.08 | − | 4157.05i | 0.0932074 | − | 0.161440i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 43.6664 | 0.00168998 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8244.70 | + | 14280.2i | 0.317450 | + | 0.549840i | 0.979955 | − | 0.199218i | \(-0.0638401\pi\) |
−0.662505 | + | 0.749057i | \(0.730507\pi\) | |||||||
\(878\) | −9412.32 | + | 16302.6i | −0.361789 | + | 0.626636i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2527.61 | + | 4377.94i | 0.0968245 | + | 0.167705i | ||||
\(881\) | 45411.7 | 1.73662 | 0.868309 | − | 0.496023i | \(-0.165207\pi\) | ||||
0.868309 | + | 0.496023i | \(0.165207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2206.85 | −0.0841070 | −0.0420535 | − | 0.999115i | \(-0.513390\pi\) | ||||
−0.0420535 | + | 0.999115i | \(0.513390\pi\) | |||||||
\(884\) | −516.273 | − | 894.211i | −0.0196427 | − | 0.0340221i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6258.18 | − | 10839.5i | 0.237300 | − | 0.411015i | ||||
\(887\) | −14073.1 | − | 24375.3i | −0.532727 | − | 0.922710i | −0.999270 | − | 0.0382111i | \(-0.987834\pi\) |
0.466543 | − | 0.884498i | \(-0.345499\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15967.9 | 0.601398 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9299.07 | + | 16106.5i | −0.349054 | + | 0.604579i | ||||
\(893\) | −8512.65 | + | 14744.3i | −0.318998 | + | 0.552520i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71126.1 | −2.65641 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11633.8 | + | 20150.4i | 0.432322 | + | 0.748804i | ||||
\(899\) | −18224.3 | + | 31565.4i | −0.676101 | + | 1.17104i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10533.2 | + | 18244.0i | 0.389469 | + | 0.674579i | ||||
\(902\) | −9795.91 | −0.361605 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4981.15 | 0.183264 | ||||||||
\(905\) | 13405.6 | + | 23219.3i | 0.492396 | + | 0.852856i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2521.12 | − | 4366.71i | 0.0922960 | − | 0.159861i | −0.816181 | − | 0.577797i | \(-0.803913\pi\) |
0.908477 | + | 0.417935i | \(0.137246\pi\) | |||||||
\(908\) | −8303.43 | − | 14382.0i | −0.303479 | − | 0.525641i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29647.3 | −1.07822 | −0.539110 | − | 0.842235i | \(-0.681239\pi\) | ||||
−0.539110 | + | 0.842235i | \(0.681239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4313.29 | + | 7470.84i | −0.156352 | + | 0.270809i | ||||
\(914\) | −13104.6 | + | 22697.9i | −0.474248 | + | 0.821421i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17054.5 | −0.615172 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5945.64 | + | 10298.1i | 0.213415 | + | 0.369646i | 0.952781 | − | 0.303658i | \(-0.0982080\pi\) |
−0.739366 | + | 0.673304i | \(0.764875\pi\) | |||||||
\(920\) | −54.3029 | + | 94.0554i | −0.00194599 | + | 0.00337056i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2594.63 | − | 4494.03i | −0.0926785 | − | 0.160524i | ||||
\(923\) | 1303.66 | 0.0464902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 52108.3 | 1.85223 | ||||||||
\(926\) | −14136.2 | − | 24484.6i | −0.501667 | − | 0.868913i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2611.33 | − | 4522.96i | 0.0923720 | − | 0.159993i | ||||
\(929\) | 19594.3 | + | 33938.3i | 0.691999 | + | 1.19858i | 0.971182 | + | 0.238340i | \(0.0766032\pi\) |
−0.279183 | + | 0.960238i | \(0.590063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12199.6 | −0.428768 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15590.2 | − | 27003.1i | 0.546176 | − | 0.946004i | ||||
\(935\) | −18854.1 | + | 32656.3i | −0.659461 | + | 1.14222i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9716.23 | −0.338757 | −0.169379 | − | 0.985551i | \(-0.554176\pi\) | ||||
−0.169379 | + | 0.985551i | \(0.554176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21172.4 | − | 36671.7i | −0.734647 | − | 1.27245i | ||||
\(941\) | 3497.93 | − | 6058.60i | 0.121179 | − | 0.209888i | −0.799054 | − | 0.601259i | \(-0.794666\pi\) |
0.920233 | + | 0.391371i | \(0.127999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −105.227 | − | 182.259i | −0.00363380 | − | 0.00629393i | ||||
\(944\) | 7278.85 | 0.250960 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6718.88 | 0.230919 | ||||||||
\(947\) | 7489.62 | + | 12972.4i | 0.257001 | + | 0.445139i | 0.965437 | − | 0.260636i | \(-0.0839323\pi\) |
−0.708436 | + | 0.705775i | \(0.750599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1192.07 | − | 2064.73i | 0.0407758 | − | 0.0706258i | ||||
\(950\) | 10361.2 | + | 17946.2i | 0.353855 | + | 0.612896i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29393.3 | −0.999100 | −0.499550 | − | 0.866285i | \(-0.666501\pi\) | ||||
−0.499550 | + | 0.866285i | \(0.666501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10994.7 | − | 19043.3i | 0.372543 | − | 0.645264i | ||||
\(956\) | 7974.41 | − | 13812.1i | 0.269781 | − | 0.467275i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16907.0 | 0.570189 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10041.7 | − | 17392.7i | −0.337072 | − | 0.583825i | ||||
\(962\) | −364.519 | + | 631.365i | −0.0122168 | + | 0.0211601i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1249.30 | − | 2163.84i | −0.0417397 | − | 0.0722953i | ||||
\(965\) | −99410.6 | −3.31621 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7133.95 | −0.237241 | −0.118621 | − | 0.992940i | \(-0.537847\pi\) | ||||
−0.118621 | + | 0.992940i | \(0.537847\pi\) | |||||||
\(968\) | −4404.35 | − | 7628.56i | −0.146241 | − | 0.253297i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6974.20 | + | 12079.7i | −0.230854 | + | 0.399850i | ||||
\(971\) | 4844.06 | + | 8390.16i | 0.160096 | + | 0.277295i | 0.934903 | − | 0.354903i | \(-0.115486\pi\) |
−0.774807 | + | 0.632198i | \(0.782153\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8022.14 | 0.263907 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 309.212 | − | 535.571i | 0.0101410 | − | 0.0175648i | ||||
\(977\) | 10652.8 | − | 18451.3i | 0.348838 | − | 0.604205i | −0.637205 | − | 0.770694i | \(-0.719910\pi\) |
0.986043 | + | 0.166489i | \(0.0532431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5809.79 | 0.189665 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13927.9 | − | 24123.8i | −0.452604 | − | 0.783933i | ||||
\(983\) | 18640.4 | − | 32286.1i | 0.604818 | − | 1.04758i | −0.387262 | − | 0.921970i | \(-0.626579\pi\) |
0.992080 | − | 0.125606i | \(-0.0400874\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16902.1 | + | 29275.4i | 0.546748 | + | 0.946996i | ||||
\(986\) | 38957.3 | 1.25827 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −289.924 | −0.00933574 | ||||||||
\(989\) | 72.1740 | + | 125.009i | 0.00232052 | + | 0.00401927i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25698.5 | − | 44511.2i | 0.823755 | − | 1.42678i | −0.0791128 | − | 0.996866i | \(-0.525209\pi\) |
0.902867 | − | 0.429919i | \(-0.141458\pi\) | |||||||
\(992\) | 3573.21 | + | 6188.98i | 0.114365 | + | 0.198085i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73974.6 | 2.35694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17186.9 | + | 29768.6i | −0.545953 | + | 0.945618i | 0.452594 | + | 0.891717i | \(0.350499\pi\) |
−0.998546 | + | 0.0539007i | \(0.982835\pi\) | |||||||
\(998\) | −3947.55 | + | 6837.36i | −0.125208 | + | 0.216866i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.4.g.bf.361.1 | 4 | ||
3.2 | odd | 2 | 294.4.e.l.67.2 | 4 | |||
7.2 | even | 3 | inner | 882.4.g.bf.667.1 | 4 | ||
7.3 | odd | 6 | 882.4.a.v.1.1 | 2 | |||
7.4 | even | 3 | 882.4.a.z.1.2 | 2 | |||
7.5 | odd | 6 | 126.4.g.g.37.2 | 4 | |||
7.6 | odd | 2 | 126.4.g.g.109.2 | 4 | |||
21.2 | odd | 6 | 294.4.e.l.79.2 | 4 | |||
21.5 | even | 6 | 42.4.e.c.37.1 | yes | 4 | ||
21.11 | odd | 6 | 294.4.a.m.1.1 | 2 | |||
21.17 | even | 6 | 294.4.a.n.1.2 | 2 | |||
21.20 | even | 2 | 42.4.e.c.25.1 | ✓ | 4 | ||
84.11 | even | 6 | 2352.4.a.ca.1.1 | 2 | |||
84.47 | odd | 6 | 336.4.q.j.289.1 | 4 | |||
84.59 | odd | 6 | 2352.4.a.bq.1.2 | 2 | |||
84.83 | odd | 2 | 336.4.q.j.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.1 | ✓ | 4 | 21.20 | even | 2 | ||
42.4.e.c.37.1 | yes | 4 | 21.5 | even | 6 | ||
126.4.g.g.37.2 | 4 | 7.5 | odd | 6 | |||
126.4.g.g.109.2 | 4 | 7.6 | odd | 2 | |||
294.4.a.m.1.1 | 2 | 21.11 | odd | 6 | |||
294.4.a.n.1.2 | 2 | 21.17 | even | 6 | |||
294.4.e.l.67.2 | 4 | 3.2 | odd | 2 | |||
294.4.e.l.79.2 | 4 | 21.2 | odd | 6 | |||
336.4.q.j.193.1 | 4 | 84.83 | odd | 2 | |||
336.4.q.j.289.1 | 4 | 84.47 | odd | 6 | |||
882.4.a.v.1.1 | 2 | 7.3 | odd | 6 | |||
882.4.a.z.1.2 | 2 | 7.4 | even | 3 | |||
882.4.g.bf.361.1 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bf.667.1 | 4 | 7.2 | even | 3 | inner | ||
2352.4.a.bq.1.2 | 2 | 84.59 | odd | 6 | |||
2352.4.a.ca.1.1 | 2 | 84.11 | even | 6 |