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: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.2 | ||
Root | \(-3.22311 + 5.58259i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.z.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.72311 | − | 2.98452i | 0.154120 | − | 0.266943i | −0.778618 | − | 0.627498i | \(-0.784079\pi\) |
0.932738 | + | 0.360554i | \(0.117413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.44622 | + | 5.96903i | 0.108979 | + | 0.188757i | ||||
\(11\) | 18.0618 | + | 31.2839i | 0.495076 | + | 0.857496i | 0.999984 | − | 0.00567700i | \(-0.00180706\pi\) |
−0.504908 | + | 0.863173i | \(0.668474\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.2311 | −0.218277 | −0.109138 | − | 0.994027i | \(-0.534809\pi\) | ||||
−0.109138 | + | 0.994027i | \(0.534809\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −59.2311 | − | 102.591i | −0.845038 | − | 1.46365i | −0.885588 | − | 0.464472i | \(-0.846244\pi\) |
0.0405493 | − | 0.999178i | \(-0.487089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.3307 | + | 33.4817i | −0.233408 | + | 0.404275i | −0.958809 | − | 0.284052i | \(-0.908321\pi\) |
0.725401 | + | 0.688327i | \(0.241655\pi\) | |||||||
\(20\) | −13.7849 | −0.154120 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −72.2471 | −0.700143 | ||||||||
\(23\) | −18.1236 | + | 31.3909i | −0.164305 | + | 0.284585i | −0.936408 | − | 0.350912i | \(-0.885872\pi\) |
0.772103 | + | 0.635497i | \(0.219205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56.5618 | + | 97.9679i | 0.452494 | + | 0.783743i | ||||
\(26\) | 10.2311 | − | 17.7208i | 0.0771725 | − | 0.133667i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 12.1236 | 0.0776306 | 0.0388153 | − | 0.999246i | \(-0.487642\pi\) | ||||
0.0388153 | + | 0.999246i | \(0.487642\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −72.7471 | − | 126.002i | −0.421476 | − | 0.730018i | 0.574608 | − | 0.818429i | \(-0.305155\pi\) |
−0.996084 | + | 0.0884105i | \(0.971821\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 236.924 | 1.19506 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.685331 | − | 1.18703i | 0.00304507 | − | 0.00527422i | −0.864499 | − | 0.502635i | \(-0.832364\pi\) |
0.867544 | + | 0.497361i | \(0.165697\pi\) | |||||||
\(38\) | −38.6613 | − | 66.9634i | −0.165045 | − | 0.285866i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.7849 | − | 23.8761i | 0.0544896 | − | 0.0943787i | ||||
\(41\) | 168.000 | 0.639932 | 0.319966 | − | 0.947429i | \(-0.396329\pi\) | ||||
0.319966 | + | 0.947429i | \(0.396329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 299.371 | 1.06171 | 0.530856 | − | 0.847462i | \(-0.321871\pi\) | ||||
0.530856 | + | 0.847462i | \(0.321871\pi\) | |||||||
\(44\) | 72.2471 | − | 125.136i | 0.247538 | − | 0.428748i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −36.2471 | − | 62.7818i | −0.116181 | − | 0.201232i | ||||
\(47\) | −251.355 | + | 435.359i | −0.780082 | + | 1.35114i | 0.151812 | + | 0.988409i | \(0.451489\pi\) |
−0.931894 | + | 0.362732i | \(0.881844\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −226.247 | −0.639923 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.4622 | + | 35.4416i | 0.0545692 | + | 0.0945167i | ||||
\(53\) | −312.556 | − | 541.363i | −0.810054 | − | 1.40305i | −0.912825 | − | 0.408350i | \(-0.866104\pi\) |
0.102771 | − | 0.994705i | \(-0.467229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 124.490 | 0.305204 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.1236 | + | 20.9986i | −0.0274466 | + | 0.0475388i | ||||
\(59\) | 21.1098 | + | 36.5632i | 0.0465806 | + | 0.0806800i | 0.888376 | − | 0.459117i | \(-0.151834\pi\) |
−0.841795 | + | 0.539797i | \(0.818501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −219.586 | + | 380.334i | −0.460903 | + | 0.798307i | −0.999006 | − | 0.0445717i | \(-0.985808\pi\) |
0.538103 | + | 0.842879i | \(0.319141\pi\) | |||||||
\(62\) | 290.988 | 0.596058 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −17.6293 | + | 30.5349i | −0.0336408 | + | 0.0582675i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 381.809 | + | 661.312i | 0.696200 | + | 1.20585i | 0.969775 | + | 0.244003i | \(0.0784605\pi\) |
−0.273575 | + | 0.961851i | \(0.588206\pi\) | |||||||
\(68\) | −236.924 | + | 410.365i | −0.422519 | + | 0.731825i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1020.49 | −1.70578 | −0.852890 | − | 0.522091i | \(-0.825152\pi\) | ||||
−0.852890 | + | 0.522091i | \(0.825152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 289.642 | + | 501.674i | 0.464384 | + | 0.804336i | 0.999173 | − | 0.0406491i | \(-0.0129426\pi\) |
−0.534790 | + | 0.844985i | \(0.679609\pi\) | |||||||
\(74\) | 1.37066 | + | 2.37406i | 0.00215319 | + | 0.00372944i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 154.645 | 0.233408 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −471.365 | + | 816.428i | −0.671300 | + | 1.16273i | 0.306236 | + | 0.951956i | \(0.400930\pi\) |
−0.977536 | + | 0.210770i | \(0.932403\pi\) | |||||||
\(80\) | 27.5698 | + | 47.7523i | 0.0385299 | + | 0.0667358i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −168.000 | + | 290.985i | −0.226250 | + | 0.391876i | ||||
\(83\) | −474.714 | −0.627790 | −0.313895 | − | 0.949458i | \(-0.601634\pi\) | ||||
−0.313895 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −408.247 | −0.520948 | ||||||||
\(86\) | −299.371 | + | 518.525i | −0.375372 | + | 0.650163i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 144.494 | + | 250.271i | 0.175036 | + | 0.303171i | ||||
\(89\) | −410.952 | + | 711.790i | −0.489447 | + | 0.847748i | −0.999926 | − | 0.0121424i | \(-0.996135\pi\) |
0.510479 | + | 0.859890i | \(0.329468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 144.988 | 0.164305 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −502.709 | − | 870.718i | −0.551601 | − | 0.955401i | ||||
\(95\) | 66.6178 | + | 115.385i | 0.0719457 | + | 0.124614i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1108.16 | 1.15997 | 0.579985 | − | 0.814627i | \(-0.303058\pi\) | ||||
0.579985 | + | 0.814627i | \(0.303058\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 226.247 | − | 391.871i | 0.226247 | − | 0.391871i | ||||
\(101\) | −942.961 | − | 1633.26i | −0.928991 | − | 1.60906i | −0.785013 | − | 0.619479i | \(-0.787344\pi\) |
−0.143978 | − | 0.989581i | \(-0.545989\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 241.072 | − | 417.549i | 0.230617 | − | 0.399440i | −0.727373 | − | 0.686242i | \(-0.759259\pi\) |
0.957990 | + | 0.286802i | \(0.0925923\pi\) | |||||||
\(104\) | −81.8489 | −0.0771725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1250.22 | 1.14559 | ||||||||
\(107\) | −865.297 | + | 1498.74i | −0.781789 | + | 1.35410i | 0.149109 | + | 0.988821i | \(0.452359\pi\) |
−0.930898 | + | 0.365278i | \(0.880974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −574.415 | − | 994.916i | −0.504761 | − | 0.874272i | −0.999985 | − | 0.00550668i | \(-0.998247\pi\) |
0.495223 | − | 0.868766i | \(-0.335086\pi\) | |||||||
\(110\) | −124.490 | + | 215.623i | −0.107906 | + | 0.186898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1331.51 | −1.10847 | −0.554237 | − | 0.832359i | \(-0.686990\pi\) | ||||
−0.554237 | + | 0.832359i | \(0.686990\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 62.4578 | + | 108.180i | 0.0506454 | + | 0.0877204i | ||||
\(116\) | −24.2471 | − | 41.9972i | −0.0194077 | − | 0.0336150i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −84.4391 | −0.0658750 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0444 | − | 22.5936i | 0.00980047 | − | 0.0169749i | ||||
\(122\) | −439.172 | − | 760.667i | −0.325908 | − | 0.564488i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −290.988 | + | 504.007i | −0.210738 | + | 0.365009i | ||||
\(125\) | 820.627 | 0.587193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −830.236 | −0.580090 | −0.290045 | − | 0.957013i | \(-0.593670\pi\) | ||||
−0.290045 | + | 0.957013i | \(0.593670\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −35.2587 | − | 61.0698i | −0.0237876 | − | 0.0412014i | ||||
\(131\) | −986.245 | + | 1708.23i | −0.657776 | + | 1.13930i | 0.323414 | + | 0.946257i | \(0.395169\pi\) |
−0.981190 | + | 0.193044i | \(0.938164\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1527.24 | −0.984575 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −473.849 | − | 820.730i | −0.298766 | − | 0.517478i | ||||
\(137\) | −34.3938 | − | 59.5718i | −0.0214486 | − | 0.0371501i | 0.855102 | − | 0.518460i | \(-0.173494\pi\) |
−0.876550 | + | 0.481310i | \(0.840161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1864.48 | −1.13772 | −0.568860 | − | 0.822435i | \(-0.692615\pi\) | ||||
−0.568860 | + | 0.822435i | \(0.692615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1020.49 | − | 1767.55i | 0.603084 | − | 1.04457i | ||||
\(143\) | −184.792 | − | 320.069i | −0.108064 | − | 0.187172i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.8902 | − | 36.1829i | 0.0119644 | − | 0.0207230i | ||||
\(146\) | −1158.57 | −0.656738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.48265 | −0.00304507 | ||||||||
\(149\) | −10.1467 | + | 17.5746i | −0.00557885 | + | 0.00966286i | −0.868801 | − | 0.495161i | \(-0.835109\pi\) |
0.863222 | + | 0.504824i | \(0.168442\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 790.162 | + | 1368.60i | 0.425844 | + | 0.737584i | 0.996499 | − | 0.0836063i | \(-0.0266438\pi\) |
−0.570655 | + | 0.821190i | \(0.693310\pi\) | |||||||
\(152\) | −154.645 | + | 267.854i | −0.0825223 | + | 0.142933i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −501.405 | −0.259831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1692.18 | + | 2930.93i | 0.860193 | + | 1.48990i | 0.871742 | + | 0.489965i | \(0.162991\pi\) |
−0.0115487 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(158\) | −942.730 | − | 1632.86i | −0.474681 | − | 0.822171i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −110.279 | −0.0544896 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −785.853 | + | 1361.14i | −0.377624 | + | 0.654065i | −0.990716 | − | 0.135947i | \(-0.956592\pi\) |
0.613092 | + | 0.790012i | \(0.289926\pi\) | |||||||
\(164\) | −336.000 | − | 581.969i | −0.159983 | − | 0.277098i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 474.714 | − | 822.228i | 0.221957 | − | 0.384442i | ||||
\(167\) | 2473.92 | 1.14633 | 0.573167 | − | 0.819439i | \(-0.305715\pi\) | ||||
0.573167 | + | 0.819439i | \(0.305715\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2092.32 | −0.952355 | ||||||||
\(170\) | 408.247 | − | 707.105i | 0.184183 | − | 0.319014i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −598.741 | − | 1037.05i | −0.265428 | − | 0.459735i | ||||
\(173\) | −2075.67 | + | 3595.17i | −0.912198 | + | 1.57997i | −0.101246 | + | 0.994861i | \(0.532283\pi\) |
−0.810952 | + | 0.585112i | \(0.801050\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −577.977 | −0.247538 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −821.904 | − | 1423.58i | −0.346092 | − | 0.599448i | ||||
\(179\) | −2108.97 | − | 3652.84i | −0.880623 | − | 1.52528i | −0.850650 | − | 0.525733i | \(-0.823791\pi\) |
−0.0299728 | − | 0.999551i | \(-0.509542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3504.65 | −1.43922 | −0.719609 | − | 0.694380i | \(-0.755679\pi\) | ||||
−0.719609 | + | 0.694380i | \(0.755679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −144.988 | + | 251.127i | −0.0580907 | + | 0.100616i | ||||
\(185\) | −2.36180 | − | 4.09076i | −0.000938612 | − | 0.00162572i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2139.64 | − | 3705.96i | 0.836716 | − | 1.44923i | ||||
\(188\) | 2010.84 | 0.780082 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −266.471 | −0.101747 | ||||||||
\(191\) | 991.483 | − | 1717.30i | 0.375608 | − | 0.650572i | −0.614810 | − | 0.788676i | \(-0.710767\pi\) |
0.990418 | + | 0.138103i | \(0.0441005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1055.87 | − | 1828.82i | −0.393799 | − | 0.682080i | 0.599148 | − | 0.800638i | \(-0.295506\pi\) |
−0.992947 | + | 0.118558i | \(0.962173\pi\) | |||||||
\(194\) | −1108.16 | + | 1919.40i | −0.410111 | + | 0.710333i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3932.65 | −1.42228 | −0.711141 | − | 0.703049i | \(-0.751821\pi\) | ||||
−0.711141 | + | 0.703049i | \(0.751821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −276.352 | − | 478.656i | −0.0984426 | − | 0.170508i | 0.812598 | − | 0.582825i | \(-0.198053\pi\) |
−0.911040 | + | 0.412318i | \(0.864719\pi\) | |||||||
\(200\) | 452.494 | + | 783.743i | 0.159981 | + | 0.277095i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3771.84 | 1.31379 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 289.483 | − | 501.399i | 0.0986261 | − | 0.170825i | ||||
\(206\) | 482.144 | + | 835.098i | 0.163071 | + | 0.282447i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 81.8489 | − | 141.766i | 0.0272846 | − | 0.0472583i | ||||
\(209\) | −1396.58 | −0.462219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1720.90 | 0.561476 | 0.280738 | − | 0.959784i | \(-0.409421\pi\) | ||||
0.280738 | + | 0.959784i | \(0.409421\pi\) | |||||||
\(212\) | −1250.22 | + | 2165.45i | −0.405027 | + | 0.701527i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1730.59 | − | 2997.48i | −0.552808 | − | 0.957492i | ||||
\(215\) | 515.849 | − | 893.476i | 0.163631 | − | 0.283417i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2297.66 | 0.713840 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −248.980 | − | 431.245i | −0.0763009 | − | 0.132157i | ||||
\(221\) | 606.000 | + | 1049.62i | 0.184452 | + | 0.319481i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4788.43 | −1.43793 | −0.718963 | − | 0.695049i | \(-0.755383\pi\) | ||||
−0.718963 | + | 0.695049i | \(0.755383\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1331.51 | − | 2306.24i | 0.391905 | − | 0.678799i | ||||
\(227\) | −2043.80 | − | 3539.96i | −0.597584 | − | 1.03505i | −0.993177 | − | 0.116619i | \(-0.962794\pi\) |
0.395593 | − | 0.918426i | \(-0.370539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2033.30 | + | 3521.79i | −0.586745 | + | 1.01627i | 0.407911 | + | 0.913022i | \(0.366257\pi\) |
−0.994655 | + | 0.103250i | \(0.967076\pi\) | |||||||
\(230\) | −249.831 | −0.0716234 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.9884 | 0.0274466 | ||||||||
\(233\) | 89.1351 | − | 154.387i | 0.0250620 | − | 0.0434086i | −0.853222 | − | 0.521547i | \(-0.825355\pi\) |
0.878284 | + | 0.478139i | \(0.158688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 866.224 | + | 1500.34i | 0.240452 | + | 0.416475i | ||||
\(236\) | 84.4391 | − | 146.253i | 0.0232903 | − | 0.0403400i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2118.67 | 0.573412 | 0.286706 | − | 0.958019i | \(-0.407440\pi\) | ||||
0.286706 | + | 0.958019i | \(0.407440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1199.15 | + | 2076.99i | 0.320516 | + | 0.555149i | 0.980595 | − | 0.196047i | \(-0.0628105\pi\) |
−0.660079 | + | 0.751196i | \(0.729477\pi\) | |||||||
\(242\) | 26.0888 | + | 45.1872i | 0.00692998 | + | 0.0120031i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1756.69 | 0.460903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 197.774 | − | 342.555i | 0.0509477 | − | 0.0882439i | ||||
\(248\) | −581.977 | − | 1008.01i | −0.149014 | − | 0.258100i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −820.627 | + | 1421.37i | −0.207604 | + | 0.359581i | ||||
\(251\) | −1550.76 | −0.389973 | −0.194986 | − | 0.980806i | \(-0.562466\pi\) | ||||
−0.194986 | + | 0.980806i | \(0.562466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1309.37 | −0.325374 | ||||||||
\(254\) | 830.236 | − | 1438.01i | 0.205093 | − | 0.355231i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2697.72 | − | 4672.59i | 0.654783 | − | 1.13412i | −0.327166 | − | 0.944967i | \(-0.606093\pi\) |
0.981948 | − | 0.189150i | \(-0.0605732\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 141.035 | 0.0336408 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1972.49 | − | 3416.45i | −0.465118 | − | 0.805607i | ||||
\(263\) | 1790.97 | + | 3102.04i | 0.419907 | + | 0.727301i | 0.995930 | − | 0.0901330i | \(-0.0287292\pi\) |
−0.576022 | + | 0.817434i | \(0.695396\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2154.27 | −0.499381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1527.24 | − | 2645.25i | 0.348100 | − | 0.602927i | ||||
\(269\) | 587.774 | + | 1018.05i | 0.133224 | + | 0.230750i | 0.924918 | − | 0.380168i | \(-0.124134\pi\) |
−0.791694 | + | 0.610918i | \(0.790800\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 129.664 | − | 224.584i | 0.0290646 | − | 0.0503413i | −0.851127 | − | 0.524959i | \(-0.824080\pi\) |
0.880192 | + | 0.474618i | \(0.157414\pi\) | |||||||
\(272\) | 1895.40 | 0.422519 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 137.575 | 0.0303329 | ||||||||
\(275\) | −2043.21 | + | 3538.95i | −0.448038 | + | 0.776024i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 649.461 | + | 1124.90i | 0.140875 | + | 0.244003i | 0.927826 | − | 0.373012i | \(-0.121675\pi\) |
−0.786951 | + | 0.617015i | \(0.788342\pi\) | |||||||
\(278\) | 1864.48 | − | 3229.37i | 0.402245 | − | 0.696708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4524.25 | 0.960477 | 0.480238 | − | 0.877138i | \(-0.340550\pi\) | ||||
0.480238 | + | 0.877138i | \(0.340550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3239.03 | + | 5610.16i | 0.680354 | + | 1.17841i | 0.974873 | + | 0.222762i | \(0.0715072\pi\) |
−0.294519 | + | 0.955646i | \(0.595160\pi\) | |||||||
\(284\) | 2040.99 | + | 3535.10i | 0.426445 | + | 0.738624i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 739.168 | 0.152825 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4560.15 | + | 7898.41i | −0.928180 | + | 1.60766i | ||||
\(290\) | 41.7805 | + | 72.3659i | 0.00846011 | + | 0.0146533i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1158.57 | − | 2006.70i | 0.232192 | − | 0.402168i | ||||
\(293\) | −2890.91 | −0.576413 | −0.288207 | − | 0.957568i | \(-0.593059\pi\) | ||||
−0.288207 | + | 0.957568i | \(0.593059\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 145.498 | 0.0287160 | ||||||||
\(296\) | 5.48265 | − | 9.49622i | 0.00107660 | − | 0.00186472i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.2934 | − | 35.1492i | −0.00394485 | − | 0.00683267i | ||||
\(299\) | 185.424 | − | 321.164i | 0.0358641 | − | 0.0621184i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3160.65 | −0.602235 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −309.291 | − | 535.707i | −0.0583521 | − | 0.101069i | ||||
\(305\) | 756.741 | + | 1310.71i | 0.142068 | + | 0.246070i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3137.42 | 0.583264 | 0.291632 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291632 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 501.405 | − | 868.460i | 0.0918642 | − | 0.159114i | ||||
\(311\) | 3957.47 | + | 6854.55i | 0.721568 | + | 1.24979i | 0.960371 | + | 0.278725i | \(0.0899118\pi\) |
−0.238803 | + | 0.971068i | \(0.576755\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3808.30 | − | 6596.18i | 0.687726 | − | 1.19118i | −0.284846 | − | 0.958573i | \(-0.591943\pi\) |
0.972572 | − | 0.232602i | \(-0.0747241\pi\) | |||||||
\(314\) | −6768.70 | −1.21650 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3770.92 | 0.671300 | ||||||||
\(317\) | −995.745 | + | 1724.68i | −0.176425 | + | 0.305577i | −0.940653 | − | 0.339369i | \(-0.889787\pi\) |
0.764229 | + | 0.644945i | \(0.223120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 218.973 | + | 379.272i | 0.0384330 | + | 0.0665679i | ||||
\(320\) | 110.279 | − | 191.009i | 0.0192650 | − | 0.0333679i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4579.91 | 0.788956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −578.690 | − | 1002.32i | −0.0987690 | − | 0.171073i | ||||
\(326\) | −1571.71 | − | 2722.28i | −0.267021 | − | 0.462494i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1344.00 | 0.226250 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1424.31 | + | 2466.99i | −0.236518 | + | 0.409661i | −0.959713 | − | 0.280983i | \(-0.909340\pi\) |
0.723195 | + | 0.690644i | \(0.242673\pi\) | |||||||
\(332\) | 949.428 | + | 1644.46i | 0.156948 | + | 0.271841i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2473.92 | + | 4284.96i | −0.405290 | + | 0.701983i | ||||
\(335\) | 2631.60 | 0.429192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5813.87 | −0.939768 | −0.469884 | − | 0.882728i | \(-0.655704\pi\) | ||||
−0.469884 | + | 0.882728i | \(0.655704\pi\) | |||||||
\(338\) | 2092.32 | − | 3624.01i | 0.336708 | − | 0.583196i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 816.494 | + | 1414.21i | 0.130237 | + | 0.225577i | ||||
\(341\) | 2627.88 | − | 4551.63i | 0.417325 | − | 0.722828i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2394.97 | 0.375372 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4151.34 | − | 7190.33i | −0.645022 | − | 1.11721i | ||||
\(347\) | 1717.55 | + | 2974.89i | 0.265715 | + | 0.460231i | 0.967751 | − | 0.251910i | \(-0.0810587\pi\) |
−0.702036 | + | 0.712142i | \(0.747725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3034.99 | 0.465499 | 0.232750 | − | 0.972537i | \(-0.425228\pi\) | ||||
0.232750 | + | 0.972537i | \(0.425228\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 577.977 | − | 1001.09i | 0.0875178 | − | 0.151585i | ||||
\(353\) | 4110.22 | + | 7119.11i | 0.619730 | + | 1.07340i | 0.989535 | + | 0.144295i | \(0.0460914\pi\) |
−0.369804 | + | 0.929110i | \(0.620575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1758.42 | + | 3045.68i | −0.262894 | + | 0.455346i | ||||
\(356\) | 3287.62 | 0.489447 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8435.86 | 1.24539 | ||||||||
\(359\) | 4950.80 | − | 8575.03i | 0.727836 | − | 1.26065i | −0.229961 | − | 0.973200i | \(-0.573860\pi\) |
0.957796 | − | 0.287448i | \(-0.0928070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2682.15 | + | 4645.62i | 0.391041 | + | 0.677303i | ||||
\(362\) | 3504.65 | − | 6070.23i | 0.508840 | − | 0.881337i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1996.34 | 0.286283 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5514.01 | + | 9550.55i | 0.784276 | + | 1.35841i | 0.929431 | + | 0.368997i | \(0.120299\pi\) |
−0.145155 | + | 0.989409i | \(0.546368\pi\) | |||||||
\(368\) | −289.977 | − | 502.255i | −0.0410763 | − | 0.0711463i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.44721 | 0.00132740 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1373.19 | − | 2378.43i | 0.190619 | − | 0.330162i | −0.754836 | − | 0.655913i | \(-0.772284\pi\) |
0.945456 | + | 0.325751i | \(0.105617\pi\) | |||||||
\(374\) | 4279.28 | + | 7411.92i | 0.591647 | + | 1.02476i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2010.84 | + | 3482.87i | −0.275801 | + | 0.477701i | ||||
\(377\) | −124.037 | −0.0169450 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4184.22 | −0.567095 | −0.283547 | − | 0.958958i | \(-0.591511\pi\) | ||||
−0.283547 | + | 0.958958i | \(0.591511\pi\) | |||||||
\(380\) | 266.471 | − | 461.541i | 0.0359728 | − | 0.0623068i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1982.97 | + | 3434.60i | 0.265595 | + | 0.460024i | ||||
\(383\) | 1530.29 | − | 2650.54i | 0.204162 | − | 0.353619i | −0.745703 | − | 0.666278i | \(-0.767886\pi\) |
0.949865 | + | 0.312659i | \(0.101220\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4223.48 | 0.556916 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2216.33 | − | 3838.79i | −0.289992 | − | 0.502282i | ||||
\(389\) | −2459.81 | − | 4260.51i | −0.320610 | − | 0.555312i | 0.660004 | − | 0.751262i | \(-0.270554\pi\) |
−0.980614 | + | 0.195950i | \(0.937221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4293.91 | 0.555377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3932.65 | − | 6811.55i | 0.502853 | − | 0.870967i | ||||
\(395\) | 1624.43 | + | 2813.59i | 0.206921 | + | 0.358398i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6586.63 | + | 11408.4i | −0.832678 | + | 1.44224i | 0.0632286 | + | 0.997999i | \(0.479860\pi\) |
−0.895907 | + | 0.444242i | \(0.853473\pi\) | |||||||
\(398\) | 1105.41 | 0.139219 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1809.98 | −0.226247 | ||||||||
\(401\) | 1331.19 | − | 2305.69i | 0.165777 | − | 0.287134i | −0.771154 | − | 0.636648i | \(-0.780320\pi\) |
0.936931 | + | 0.349515i | \(0.113654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 744.284 | + | 1289.14i | 0.0919985 | + | 0.159346i | ||||
\(404\) | −3771.84 | + | 6533.02i | −0.464496 | + | 0.804530i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.5132 | 0.00603016 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6496.09 | − | 11251.6i | −0.785357 | − | 1.36028i | −0.928786 | − | 0.370617i | \(-0.879146\pi\) |
0.143429 | − | 0.989661i | \(-0.454187\pi\) | |||||||
\(410\) | 578.965 | + | 1002.80i | 0.0697392 | + | 0.120792i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1928.58 | −0.230617 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −817.984 | + | 1416.79i | −0.0967549 | + | 0.167584i | ||||
\(416\) | 163.698 | + | 283.533i | 0.0192931 | + | 0.0334167i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1396.58 | − | 2418.96i | 0.163419 | − | 0.283050i | ||||
\(419\) | −7236.96 | −0.843791 | −0.421896 | − | 0.906644i | \(-0.638635\pi\) | ||||
−0.421896 | + | 0.906644i | \(0.638635\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3706.07 | 0.429032 | 0.214516 | − | 0.976720i | \(-0.431183\pi\) | ||||
0.214516 | + | 0.976720i | \(0.431183\pi\) | |||||||
\(422\) | −1720.90 | + | 2980.68i | −0.198512 | + | 0.343832i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2500.45 | − | 4330.90i | −0.286397 | − | 0.496055i | ||||
\(425\) | 6700.43 | − | 11605.5i | 0.764750 | − | 1.32459i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6922.38 | 0.781789 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1031.70 | + | 1786.95i | 0.115704 | + | 0.200406i | ||||
\(431\) | 3191.19 | + | 5527.30i | 0.356645 | + | 0.617728i | 0.987398 | − | 0.158256i | \(-0.0505871\pi\) |
−0.630753 | + | 0.775984i | \(0.717254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7275.62 | 0.807492 | 0.403746 | − | 0.914871i | \(-0.367708\pi\) | ||||
0.403746 | + | 0.914871i | \(0.367708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2297.66 | + | 3979.66i | −0.252381 | + | 0.437136i | ||||
\(437\) | −700.681 | − | 1213.61i | −0.0767005 | − | 0.132849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4880.18 | − | 8452.72i | 0.530566 | − | 0.918967i | −0.468798 | − | 0.883305i | \(-0.655313\pi\) |
0.999364 | − | 0.0356614i | \(-0.0113538\pi\) | |||||||
\(440\) | 995.918 | 0.107906 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2424.00 | −0.260855 | ||||||||
\(443\) | 2866.58 | − | 4965.06i | 0.307439 | − | 0.532499i | −0.670363 | − | 0.742034i | \(-0.733861\pi\) |
0.977801 | + | 0.209534i | \(0.0671948\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1416.23 | + | 2452.99i | 0.150867 | + | 0.261309i | ||||
\(446\) | 4788.43 | − | 8293.81i | 0.508383 | − | 0.880546i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16628.4 | 1.74775 | 0.873877 | − | 0.486147i | \(-0.161598\pi\) | ||||
0.873877 | + | 0.486147i | \(0.161598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3034.38 | + | 5255.70i | 0.316814 | + | 0.548739i | ||||
\(452\) | 2663.01 | + | 4612.47i | 0.277118 | + | 0.479983i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8175.18 | 0.845111 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8559.65 | + | 14825.8i | −0.876157 | + | 1.51755i | −0.0206311 | + | 0.999787i | \(0.506568\pi\) |
−0.855526 | + | 0.517761i | \(0.826766\pi\) | |||||||
\(458\) | −4066.61 | − | 7043.57i | −0.414891 | − | 0.718613i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 249.831 | − | 432.720i | 0.0253227 | − | 0.0438602i | ||||
\(461\) | 6956.95 | 0.702858 | 0.351429 | − | 0.936215i | \(-0.385696\pi\) | ||||
0.351429 | + | 0.936215i | \(0.385696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6594.47 | 0.661924 | 0.330962 | − | 0.943644i | \(-0.392627\pi\) | ||||
0.330962 | + | 0.943644i | \(0.392627\pi\) | |||||||
\(464\) | −96.9884 | + | 167.989i | −0.00970383 | + | 0.0168075i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 178.270 | + | 308.773i | 0.0177215 | + | 0.0306945i | ||||
\(467\) | 7232.91 | − | 12527.8i | 0.716700 | − | 1.24136i | −0.245600 | − | 0.969371i | \(-0.578985\pi\) |
0.962300 | − | 0.271990i | \(-0.0876818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3464.90 | −0.340050 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 168.878 | + | 292.506i | 0.0164687 | + | 0.0285247i | ||||
\(473\) | 5407.17 | + | 9365.49i | 0.525627 | + | 0.910413i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4373.51 | −0.422464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2118.67 | + | 3669.65i | −0.202732 | + | 0.351142i | ||||
\(479\) | −2037.74 | − | 3529.46i | −0.194377 | − | 0.336671i | 0.752319 | − | 0.658799i | \(-0.228935\pi\) |
−0.946696 | + | 0.322128i | \(0.895602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.01170 | + | 12.1446i | −0.000664669 | + | 0.00115124i | ||||
\(482\) | −4796.61 | −0.453277 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −104.355 | −0.00980047 | ||||||||
\(485\) | 1909.49 | − | 3307.33i | 0.178774 | − | 0.309646i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2189.40 | − | 3792.14i | −0.203719 | − | 0.352851i | 0.746005 | − | 0.665940i | \(-0.231969\pi\) |
−0.949724 | + | 0.313089i | \(0.898636\pi\) | |||||||
\(488\) | −1756.69 | + | 3042.67i | −0.162954 | + | 0.282244i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6612.37 | 0.607764 | 0.303882 | − | 0.952710i | \(-0.401717\pi\) | ||||
0.303882 | + | 0.952710i | \(0.401717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −718.092 | − | 1243.77i | −0.0656008 | − | 0.113624i | ||||
\(494\) | 395.548 | + | 685.110i | 0.0360254 | + | 0.0623979i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2327.91 | 0.210738 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5728.21 | − | 9921.56i | 0.513888 | − | 0.890080i | −0.485982 | − | 0.873969i | \(-0.661538\pi\) |
0.999870 | − | 0.0161114i | \(-0.00512863\pi\) | |||||||
\(500\) | −1641.25 | − | 2842.73i | −0.146798 | − | 0.254262i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1550.76 | − | 2686.00i | 0.137876 | − | 0.238808i | ||||
\(503\) | −7697.10 | −0.682300 | −0.341150 | − | 0.940009i | \(-0.610816\pi\) | ||||
−0.341150 | + | 0.940009i | \(0.610816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6499.30 | −0.572704 | ||||||||
\(506\) | 1309.37 | − | 2267.90i | 0.115037 | − | 0.199250i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1660.47 | + | 2876.02i | 0.145023 | + | 0.251187i | ||||
\(509\) | −2311.98 | + | 4004.47i | −0.201330 | + | 0.348713i | −0.948957 | − | 0.315405i | \(-0.897860\pi\) |
0.747627 | + | 0.664118i | \(0.231193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5395.44 | + | 9345.18i | 0.463001 | + | 0.801942i | ||||
\(515\) | −830.788 | − | 1438.97i | −0.0710852 | − | 0.123123i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18159.6 | −1.54480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −141.035 | + | 244.279i | −0.0118938 | + | 0.0206007i | ||||
\(521\) | −1743.35 | − | 3019.57i | −0.146598 | − | 0.253915i | 0.783370 | − | 0.621556i | \(-0.213499\pi\) |
−0.929968 | + | 0.367641i | \(0.880166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2207.57 | + | 3823.62i | −0.184570 | + | 0.319685i | −0.943432 | − | 0.331567i | \(-0.892423\pi\) |
0.758862 | + | 0.651252i | \(0.225756\pi\) | |||||||
\(524\) | 7889.96 | 0.657776 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7163.86 | −0.593839 | ||||||||
\(527\) | −8617.78 | + | 14926.4i | −0.712327 | + | 1.23379i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5426.57 | + | 9399.10i | 0.446008 | + | 0.772508i | ||||
\(530\) | 2154.27 | − | 3731.31i | 0.176558 | − | 0.305807i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1718.83 | −0.139682 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2982.01 | + | 5164.99i | 0.240978 | + | 0.417387i | ||||
\(536\) | 3054.47 | + | 5290.50i | 0.246144 | + | 0.426334i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2351.10 | −0.188407 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5402.24 | − | 9356.96i | 0.429317 | − | 0.743599i | −0.567496 | − | 0.823376i | \(-0.692088\pi\) |
0.996813 | + | 0.0797775i | \(0.0254210\pi\) | |||||||
\(542\) | 259.327 | + | 449.168i | 0.0205518 | + | 0.0355967i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1895.40 | + | 3282.92i | −0.149383 | + | 0.258739i | ||||
\(545\) | −3959.12 | −0.311175 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18783.4 | 1.46823 | 0.734113 | − | 0.679027i | \(-0.237598\pi\) | ||||
0.734113 | + | 0.679027i | \(0.237598\pi\) | |||||||
\(548\) | −137.575 | + | 238.287i | −0.0107243 | + | 0.0185750i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4086.42 | − | 7077.90i | −0.316810 | − | 0.548732i | ||||
\(551\) | −234.356 | + | 405.917i | −0.0181196 | + | 0.0313841i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2597.85 | −0.199227 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3728.96 | + | 6458.74i | 0.284430 | + | 0.492647i | ||||
\(557\) | 725.568 | + | 1256.72i | 0.0551944 | + | 0.0955995i | 0.892302 | − | 0.451438i | \(-0.149089\pi\) |
−0.837108 | + | 0.547038i | \(0.815755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3062.89 | −0.231747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4524.25 | + | 7836.23i | −0.339580 | + | 0.588169i | ||||
\(563\) | 8390.55 | + | 14532.9i | 0.628098 | + | 1.08790i | 0.987933 | + | 0.154882i | \(0.0494998\pi\) |
−0.359835 | + | 0.933016i | \(0.617167\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2294.33 | + | 3973.90i | −0.170838 | + | 0.295900i | ||||
\(566\) | −12956.1 | −0.962165 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8163.95 | −0.603084 | ||||||||
\(569\) | 7361.42 | − | 12750.4i | 0.542367 | − | 0.939407i | −0.456401 | − | 0.889774i | \(-0.650862\pi\) |
0.998768 | − | 0.0496328i | \(-0.0158051\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4858.56 | − | 8415.27i | −0.356085 | − | 0.616757i | 0.631218 | − | 0.775605i | \(-0.282555\pi\) |
−0.987303 | + | 0.158849i | \(0.949222\pi\) | |||||||
\(572\) | −739.168 | + | 1280.28i | −0.0540318 | + | 0.0935858i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4100.40 | −0.297389 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10094.4 | − | 17484.1i | −0.728313 | − | 1.26148i | −0.957596 | − | 0.288116i | \(-0.906971\pi\) |
0.229282 | − | 0.973360i | \(-0.426362\pi\) | |||||||
\(578\) | −9120.30 | − | 15796.8i | −0.656322 | − | 1.13678i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −167.122 | −0.0119644 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11290.6 | − | 19556.0i | 0.802076 | − | 1.38924i | ||||
\(584\) | 2317.13 | + | 4013.39i | 0.164184 | + | 0.284376i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2890.91 | − | 5007.21i | 0.203793 | − | 0.352979i | ||||
\(587\) | 21720.8 | 1.52728 | 0.763641 | − | 0.645641i | \(-0.223410\pi\) | ||||
0.763641 | + | 0.645641i | \(0.223410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5625.00 | 0.393504 | ||||||||
\(590\) | −145.498 | + | 252.010i | −0.0101526 | + | 0.0175849i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.9653 | + | 18.9924i | 0.000761268 | + | 0.00131856i | ||||
\(593\) | −9762.14 | + | 16908.5i | −0.676025 | + | 1.17091i | 0.300143 | + | 0.953894i | \(0.402966\pi\) |
−0.976168 | + | 0.217016i | \(0.930368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 81.1735 | 0.00557885 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 370.848 | + | 642.328i | 0.0253597 | + | 0.0439243i | ||||
\(599\) | −5799.34 | − | 10044.7i | −0.395583 | − | 0.685171i | 0.597592 | − | 0.801800i | \(-0.296124\pi\) |
−0.993175 | + | 0.116630i | \(0.962791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9335.68 | 0.633628 | 0.316814 | − | 0.948488i | \(-0.397387\pi\) | ||||
0.316814 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3160.65 | − | 5474.40i | 0.212922 | − | 0.368792i | ||||
\(605\) | −44.9540 | − | 77.8626i | −0.00302089 | − | 0.00523234i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7575.45 | − | 13121.1i | 0.506553 | − | 0.877376i | −0.493418 | − | 0.869792i | \(-0.664253\pi\) |
0.999971 | − | 0.00758385i | \(-0.00241404\pi\) | |||||||
\(608\) | 1237.16 | 0.0825223 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3026.97 | −0.200915 | ||||||||
\(611\) | 2571.64 | − | 4454.21i | 0.170274 | − | 0.294923i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12396.7 | − | 21471.7i | −0.816798 | − | 1.41474i | −0.908029 | − | 0.418906i | \(-0.862414\pi\) |
0.0912312 | − | 0.995830i | \(-0.470920\pi\) | |||||||
\(614\) | −3137.42 | + | 5434.17i | −0.206215 | + | 0.357175i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25194.6 | −1.64391 | −0.821957 | − | 0.569550i | \(-0.807118\pi\) | ||||
−0.821957 | + | 0.569550i | \(0.807118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3023.24 | − | 5236.40i | −0.196307 | − | 0.340014i | 0.751021 | − | 0.660278i | \(-0.229562\pi\) |
−0.947328 | + | 0.320264i | \(0.896228\pi\) | |||||||
\(620\) | 1002.81 | + | 1736.92i | 0.0649578 | + | 0.112510i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15829.9 | −1.02045 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5656.19 | + | 9796.81i | −0.361996 | + | 0.626996i | ||||
\(626\) | 7616.61 | + | 13192.4i | 0.486295 | + | 0.842288i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6768.70 | − | 11723.7i | 0.430097 | − | 0.744949i | ||||
\(629\) | −162.372 | −0.0102928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6537.14 | −0.412424 | −0.206212 | − | 0.978507i | \(-0.566114\pi\) | ||||
−0.206212 | + | 0.978507i | \(0.566114\pi\) | |||||||
\(632\) | −3770.92 | + | 6531.42i | −0.237340 | + | 0.411086i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1991.49 | − | 3449.36i | −0.124751 | − | 0.216075i | ||||
\(635\) | −1430.59 | + | 2477.85i | −0.0894034 | + | 0.154851i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −875.892 | −0.0543525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 220.558 | + | 382.018i | 0.0136224 | + | 0.0235947i | ||||
\(641\) | −4623.39 | − | 8007.95i | −0.284888 | − | 0.493440i | 0.687694 | − | 0.726000i | \(-0.258623\pi\) |
−0.972582 | + | 0.232561i | \(0.925290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 157.563 | 0.00966355 | 0.00483178 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483178 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4579.91 | + | 7932.63i | −0.278938 | + | 0.483135i | ||||
\(647\) | −6353.00 | − | 11003.7i | −0.386031 | − | 0.668625i | 0.605881 | − | 0.795556i | \(-0.292821\pi\) |
−0.991912 | + | 0.126930i | \(0.959488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −762.560 | + | 1320.79i | −0.0461219 | + | 0.0798854i | ||||
\(650\) | 2314.76 | 0.139680 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6286.83 | 0.377624 | ||||||||
\(653\) | −8552.41 | + | 14813.2i | −0.512529 | + | 0.887727i | 0.487365 | + | 0.873198i | \(0.337958\pi\) |
−0.999894 | + | 0.0145285i | \(0.995375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3398.82 | + | 5886.93i | 0.202752 | + | 0.351178i | ||||
\(656\) | −1344.00 | + | 2327.88i | −0.0799914 | + | 0.138549i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12518.0 | −0.739956 | −0.369978 | − | 0.929040i | \(-0.620635\pi\) | ||||
−0.369978 | + | 0.929040i | \(0.620635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2390.24 | − | 4140.01i | −0.140650 | − | 0.243613i | 0.787092 | − | 0.616836i | \(-0.211586\pi\) |
−0.927741 | + | 0.373223i | \(0.878252\pi\) | |||||||
\(662\) | −2848.63 | − | 4933.97i | −0.167243 | − | 0.289674i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3797.71 | −0.221957 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −219.722 | + | 380.569i | −0.0127551 | + | 0.0220925i | ||||
\(668\) | −4947.84 | − | 8569.92i | −0.286584 | − | 0.496377i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2631.60 | + | 4558.06i | −0.151742 | + | 0.262826i | ||||
\(671\) | −15864.4 | −0.912727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28447.0 | −1.62935 | −0.814673 | − | 0.579920i | \(-0.803084\pi\) | ||||
−0.814673 | + | 0.579920i | \(0.803084\pi\) | |||||||
\(674\) | 5813.87 | − | 10069.9i | 0.332258 | − | 0.575488i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4184.65 | + | 7248.02i | 0.238089 | + | 0.412382i | ||||
\(677\) | −7939.27 | + | 13751.2i | −0.450710 | + | 0.780653i | −0.998430 | − | 0.0560084i | \(-0.982163\pi\) |
0.547720 | + | 0.836662i | \(0.315496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3265.98 | −0.184183 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5255.77 | + | 9103.26i | 0.295093 | + | 0.511117i | ||||
\(683\) | −1219.23 | − | 2111.76i | −0.0683052 | − | 0.118308i | 0.829850 | − | 0.557986i | \(-0.188426\pi\) |
−0.898155 | + | 0.439678i | \(0.855092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −237.057 | −0.0132226 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2394.97 | + | 4148.20i | −0.132714 | + | 0.229867i | ||||
\(689\) | 3197.79 | + | 5538.74i | 0.176816 | + | 0.306254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11243.5 | − | 19474.3i | 0.618990 | − | 1.07212i | −0.370681 | − | 0.928760i | \(-0.620876\pi\) |
0.989670 | − | 0.143361i | \(-0.0457910\pi\) | |||||||
\(692\) | 16605.4 | 0.912198 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6870.21 | −0.375777 | ||||||||
\(695\) | −3212.70 | + | 5564.56i | −0.175345 | + | 0.303706i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9950.83 | − | 17235.3i | −0.540767 | − | 0.936635i | ||||
\(698\) | −3034.99 | + | 5256.75i | −0.164579 | + | 0.285059i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3916.29 | 0.211008 | 0.105504 | − | 0.994419i | \(-0.466354\pi\) | ||||
0.105504 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.4958 | + | 45.8921i | 0.00142149 | + | 0.00246210i | ||||
\(704\) | 1155.95 | + | 2002.17i | 0.0618844 | + | 0.107187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16440.9 | −0.876431 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11455.2 | − | 19840.9i | 0.606780 | − | 1.05097i | −0.384987 | − | 0.922922i | \(-0.625794\pi\) |
0.991767 | − | 0.128053i | \(-0.0408726\pi\) | |||||||
\(710\) | −3516.85 | − | 6091.36i | −0.185894 | − | 0.321979i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3287.62 | + | 5694.32i | −0.173046 | + | 0.299724i | ||||
\(713\) | 5273.74 | 0.277003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1273.67 | −0.0666189 | ||||||||
\(716\) | −8435.86 | + | 14611.3i | −0.440311 | + | 0.762642i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9901.59 | + | 17150.1i | 0.514658 | + | 0.891413i | ||||
\(719\) | −10236.4 | + | 17729.9i | −0.530949 | + | 0.919630i | 0.468399 | + | 0.883517i | \(0.344831\pi\) |
−0.999348 | + | 0.0361132i | \(0.988502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10728.6 | −0.553016 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7009.29 | + | 12140.5i | 0.359804 | + | 0.623199i | ||||
\(725\) | 685.730 | + | 1187.72i | 0.0351274 | + | 0.0608424i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11208.5 | −0.571802 | −0.285901 | − | 0.958259i | \(-0.592293\pi\) | ||||
−0.285901 | + | 0.958259i | \(0.592293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1996.34 | + | 3457.76i | −0.101216 | + | 0.175312i | ||||
\(731\) | −17732.1 | − | 30712.8i | −0.897187 | − | 1.55397i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17719.0 | + | 30690.2i | −0.892860 | + | 1.54648i | −0.0564289 | + | 0.998407i | \(0.517971\pi\) |
−0.836431 | + | 0.548072i | \(0.815362\pi\) | |||||||
\(734\) | −22056.1 | −1.10913 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1159.91 | 0.0580907 | ||||||||
\(737\) | −13792.3 | + | 23889.0i | −0.689343 | + | 1.19398i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8967.69 | + | 15532.5i | 0.446389 | + | 0.773169i | 0.998148 | − | 0.0608348i | \(-0.0193763\pi\) |
−0.551758 | + | 0.834004i | \(0.686043\pi\) | |||||||
\(740\) | −9.44721 | + | 16.3630i | −0.000469306 | + | 0.000812862i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19031.0 | −0.939676 | −0.469838 | − | 0.882753i | \(-0.655688\pi\) | ||||
−0.469838 | + | 0.882753i | \(0.655688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.9677 | + | 60.5659i | 0.00171962 | + | 0.00297847i | ||||
\(746\) | 2746.37 | + | 4756.86i | 0.134788 | + | 0.233460i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17117.1 | −0.836716 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1364.07 | − | 2362.63i | 0.0662790 | − | 0.114799i | −0.830982 | − | 0.556300i | \(-0.812221\pi\) |
0.897261 | + | 0.441501i | \(0.145554\pi\) | |||||||
\(752\) | −4021.67 | − | 6965.74i | −0.195020 | − | 0.337785i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 124.037 | − | 214.839i | 0.00599095 | − | 0.0103766i | ||||
\(755\) | 5446.15 | 0.262524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6617.58 | −0.317728 | −0.158864 | − | 0.987300i | \(-0.550783\pi\) | ||||
−0.158864 | + | 0.987300i | \(0.550783\pi\) | |||||||
\(758\) | 4184.22 | − | 7247.28i | 0.200498 | − | 0.347273i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 532.942 | + | 923.083i | 0.0254366 | + | 0.0440575i | ||||
\(761\) | 300.054 | − | 519.709i | 0.0142930 | − | 0.0247562i | −0.858790 | − | 0.512327i | \(-0.828784\pi\) |
0.873083 | + | 0.487571i | \(0.162117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7931.86 | −0.375608 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3060.58 | + | 5301.08i | 0.144364 | + | 0.250047i | ||||
\(767\) | −215.976 | − | 374.082i | −0.0101675 | − | 0.0176106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28329.2 | 1.32845 | 0.664223 | − | 0.747534i | \(-0.268762\pi\) | ||||
0.664223 | + | 0.747534i | \(0.268762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4223.48 | + | 7315.29i | −0.196900 | + | 0.341040i | ||||
\(773\) | −11918.5 | − | 20643.5i | −0.554565 | − | 0.960536i | −0.997937 | − | 0.0641977i | \(-0.979551\pi\) |
0.443372 | − | 0.896338i | \(-0.353782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8229.41 | − | 14253.8i | 0.381431 | − | 0.660658i | ||||
\(776\) | 8865.32 | 0.410111 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9839.23 | 0.453411 | ||||||||
\(779\) | −3247.55 | + | 5624.93i | −0.149365 | + | 0.258708i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18431.9 | − | 31925.1i | −0.844490 | − | 1.46270i | ||||
\(782\) | −4293.91 | + | 7437.28i | −0.196356 | + | 0.340098i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11663.2 | 0.530291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −268.455 | − | 464.977i | −0.0121593 | − | 0.0210606i | 0.859882 | − | 0.510493i | \(-0.170537\pi\) |
−0.872041 | + | 0.489433i | \(0.837204\pi\) | |||||||
\(788\) | 7865.30 | + | 13623.1i | 0.355571 | + | 0.615866i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6497.71 | −0.292631 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2246.61 | − | 3891.24i | 0.100604 | − | 0.174252i | ||||
\(794\) | −13173.3 | − | 22816.7i | −0.588792 | − | 1.01982i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1105.41 | + | 1914.62i | −0.0492213 | + | 0.0852538i | ||||
\(797\) | −8857.47 | −0.393661 | −0.196830 | − | 0.980438i | \(-0.563065\pi\) | ||||
−0.196830 | + | 0.980438i | \(0.563065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59552.1 | 2.63680 | ||||||||
\(800\) | 1809.98 | − | 3134.97i | 0.0799904 | − | 0.138547i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2662.38 | + | 4611.37i | 0.117222 | + | 0.203034i | ||||
\(803\) | −10462.9 | + | 18122.3i | −0.459810 | + | 0.796414i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2977.13 | −0.130106 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7543.69 | − | 13066.0i | −0.328448 | − | 0.568889i | ||||
\(809\) | −10916.5 | − | 18907.9i | −0.474416 | − | 0.821713i | 0.525155 | − | 0.851007i | \(-0.324007\pi\) |
−0.999571 | + | 0.0292939i | \(0.990674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37942.3 | 1.64283 | 0.821415 | − | 0.570330i | \(-0.193185\pi\) | ||||
0.821415 | + | 0.570330i | \(0.193185\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −49.5132 | + | 85.7593i | −0.00213199 | + | 0.00369271i | ||||
\(815\) | 2708.22 | + | 4690.78i | 0.116399 | + | 0.201609i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5787.03 | + | 10023.4i | −0.247812 | + | 0.429224i | ||||
\(818\) | 25984.4 | 1.11066 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2315.86 | −0.0986261 | ||||||||
\(821\) | 9038.66 | − | 15655.4i | 0.384228 | − | 0.665503i | −0.607434 | − | 0.794370i | \(-0.707801\pi\) |
0.991662 | + | 0.128868i | \(0.0411343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2451.37 | + | 4245.90i | 0.103827 | + | 0.179833i | 0.913258 | − | 0.407381i | \(-0.133558\pi\) |
−0.809431 | + | 0.587214i | \(0.800225\pi\) | |||||||
\(824\) | 1928.58 | − | 3340.39i | 0.0815353 | − | 0.141223i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19578.9 | −0.823247 | −0.411623 | − | 0.911354i | \(-0.635038\pi\) | ||||
−0.411623 | + | 0.911354i | \(0.635038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18965.1 | − | 32848.5i | −0.794554 | − | 1.37621i | −0.923122 | − | 0.384507i | \(-0.874371\pi\) |
0.128568 | − | 0.991701i | \(-0.458962\pi\) | |||||||
\(830\) | −1635.97 | − | 2833.58i | −0.0684160 | − | 0.118500i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −654.791 | −0.0272846 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4262.84 | − | 7383.46i | 0.176673 | − | 0.306006i | ||||
\(836\) | 2793.17 | + | 4837.91i | 0.115555 | + | 0.200147i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7236.96 | − | 12534.8i | 0.298325 | − | 0.516715i | ||||
\(839\) | −5954.22 | −0.245009 | −0.122504 | − | 0.992468i | \(-0.539093\pi\) | ||||
−0.122504 | + | 0.992468i | \(0.539093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24242.0 | −0.993973 | ||||||||
\(842\) | −3706.07 | + | 6419.09i | −0.151686 | + | 0.262728i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3441.79 | − | 5961.36i | −0.140369 | − | 0.243126i | ||||
\(845\) | −3605.31 | + | 6244.58i | −0.146777 | + | 0.254225i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10001.8 | 0.405027 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13400.9 | + | 23211.0i | 0.540760 | + | 0.936624i | ||||
\(851\) | 24.8413 | + | 43.0263i | 0.00100064 | + | 0.00173317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26196.2 | 1.05151 | 0.525757 | − | 0.850635i | \(-0.323782\pi\) | ||||
0.525757 | + | 0.850635i | \(0.323782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6922.38 | + | 11989.9i | −0.276404 | + | 0.478746i | ||||
\(857\) | −18438.6 | − | 31936.6i | −0.734949 | − | 1.27297i | −0.954746 | − | 0.297423i | \(-0.903873\pi\) |
0.219797 | − | 0.975546i | \(-0.429461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17239.1 | − | 29859.0i | 0.684740 | − | 1.18600i | −0.288779 | − | 0.957396i | \(-0.593249\pi\) |
0.973519 | − | 0.228608i | \(-0.0734174\pi\) | |||||||
\(860\) | −4126.79 | −0.163631 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12764.8 | −0.504373 | ||||||||
\(863\) | 839.846 | − | 1454.66i | 0.0331271 | − | 0.0573778i | −0.848987 | − | 0.528414i | \(-0.822787\pi\) |
0.882114 | + | 0.471037i | \(0.156120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7153.22 | + | 12389.7i | 0.281175 | + | 0.487010i | ||||
\(866\) | −7275.62 | + | 12601.7i | −0.285492 | + | 0.494486i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34054.7 | −1.32938 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3906.33 | − | 6765.96i | −0.151964 | − | 0.263210i | ||||
\(872\) | −4595.32 | − | 7959.33i | −0.178460 | − | 0.309102i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2802.72 | 0.108471 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1251.91 | + | 2168.37i | −0.0482030 | + | 0.0834901i | −0.889120 | − | 0.457674i | \(-0.848683\pi\) |
0.840917 | + | 0.541164i | \(0.182016\pi\) | |||||||
\(878\) | 9760.36 | + | 16905.4i | 0.375167 | + | 0.649808i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −995.918 | + | 1724.98i | −0.0381505 | + | 0.0660785i | ||||
\(881\) | 34886.0 | 1.33410 | 0.667048 | − | 0.745014i | \(-0.267557\pi\) | ||||
0.667048 | + | 0.745014i | \(0.267557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35334.0 | 1.34664 | 0.673320 | − | 0.739351i | \(-0.264868\pi\) | ||||
0.673320 | + | 0.739351i | \(0.264868\pi\) | |||||||
\(884\) | 2424.00 | − | 4198.49i | 0.0922262 | − | 0.159740i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5733.16 | + | 9930.12i | 0.217392 | + | 0.376534i | ||||
\(887\) | −13326.4 | + | 23082.0i | −0.504460 | + | 0.873750i | 0.495527 | + | 0.868593i | \(0.334975\pi\) |
−0.999987 | + | 0.00515772i | \(0.998358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5664.93 | −0.213358 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9576.87 | + | 16587.6i | 0.359481 | + | 0.622640i | ||||
\(893\) | −9717.71 | − | 16831.6i | −0.364155 | − | 0.630735i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14535.9 | −0.542885 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16628.4 | + | 28801.2i | −0.617924 | + | 1.07028i | ||||
\(899\) | −881.953 | − | 1527.59i | −0.0327195 | − | 0.0566718i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37026.1 | + | 64131.0i | −1.36905 | + | 2.37127i | ||||
\(902\) | −12137.5 | −0.448043 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10652.0 | −0.391905 | ||||||||
\(905\) | −6038.90 | + | 10459.7i | −0.221812 | + | 0.384189i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23027.5 | + | 39884.8i | 0.843016 | + | 1.46015i | 0.887333 | + | 0.461130i | \(0.152556\pi\) |
−0.0443164 | + | 0.999018i | \(0.514111\pi\) | |||||||
\(908\) | −8175.18 | + | 14159.8i | −0.298792 | + | 0.517523i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14227.1 | 0.517416 | 0.258708 | − | 0.965956i | \(-0.416703\pi\) | ||||
0.258708 | + | 0.965956i | \(0.416703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8574.17 | − | 14850.9i | −0.310804 | − | 0.538328i | ||||
\(914\) | −17119.3 | − | 29651.5i | −0.619536 | − | 1.07307i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16266.4 | 0.586745 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3343.47 | + | 5791.07i | −0.120012 | + | 0.207867i | −0.919772 | − | 0.392453i | \(-0.871627\pi\) |
0.799760 | + | 0.600320i | \(0.204960\pi\) | |||||||
\(920\) | 499.662 | + | 865.441i | 0.0179058 | + | 0.0310138i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6956.95 | + | 12049.8i | −0.248498 | + | 0.430411i | ||||
\(923\) | 10440.8 | 0.372332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 155.054 | 0.00551151 | ||||||||
\(926\) | −6594.47 | + | 11422.0i | −0.234026 | + | 0.405344i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −193.977 | − | 335.978i | −0.00686164 | − | 0.0118847i | ||||
\(929\) | −6769.82 | + | 11725.7i | −0.239086 | + | 0.414109i | −0.960452 | − | 0.278445i | \(-0.910181\pi\) |
0.721366 | + | 0.692554i | \(0.243514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −713.081 | −0.0250620 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14465.8 | + | 25055.5i | 0.506784 | + | 0.877775i | ||||
\(935\) | −7373.67 | − | 12771.6i | −0.257909 | − | 0.446711i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12017.0 | 0.418974 | 0.209487 | − | 0.977811i | \(-0.432821\pi\) | ||||
0.209487 | + | 0.977811i | \(0.432821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3464.90 | − | 6001.38i | 0.120226 | − | 0.208238i | ||||
\(941\) | 27619.7 | + | 47838.8i | 0.956831 | + | 1.65728i | 0.730122 | + | 0.683316i | \(0.239463\pi\) |
0.226708 | + | 0.973963i | \(0.427204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3044.76 | + | 5273.67i | −0.105144 | + | 0.182115i | ||||
\(944\) | −675.513 | −0.0232903 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21628.7 | −0.743349 | ||||||||
\(947\) | 23994.9 | − | 41560.4i | 0.823368 | − | 1.42611i | −0.0797929 | − | 0.996811i | \(-0.525426\pi\) |
0.903161 | − | 0.429303i | \(-0.141241\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2963.36 | − | 5132.68i | −0.101364 | − | 0.175568i | ||||
\(950\) | 4373.51 | − | 7575.14i | 0.149363 | − | 0.258705i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19900.0 | −0.676415 | −0.338207 | − | 0.941072i | \(-0.609821\pi\) | ||||
−0.338207 | + | 0.941072i | \(0.609821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3416.87 | − | 5918.19i | −0.115777 | − | 0.200532i | ||||
\(956\) | −4237.34 | − | 7339.29i | −0.143353 | − | 0.248295i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8150.94 | 0.274890 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4311.22 | − | 7467.25i | 0.144715 | − | 0.250654i | ||||
\(962\) | −14.0234 | − | 24.2892i | −0.000469992 | − | 0.000814050i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4796.61 | − | 8307.98i | 0.160258 | − | 0.277575i | ||||
\(965\) | −7277.53 | −0.242769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −423.293 | −0.0140767 | −0.00703836 | − | 0.999975i | \(-0.502240\pi\) | ||||
−0.00703836 | + | 0.999975i | \(0.502240\pi\) | |||||||
\(968\) | 104.355 | − | 180.749i | 0.00346499 | − | 0.00600154i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3818.98 | + | 6614.67i | 0.126412 | + | 0.218953i | ||||
\(971\) | 872.300 | − | 1510.87i | 0.0288295 | − | 0.0499342i | −0.851251 | − | 0.524759i | \(-0.824155\pi\) |
0.880080 | + | 0.474825i | \(0.157489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8757.58 | 0.288102 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3513.37 | − | 6085.34i | −0.115226 | − | 0.199577i | ||||
\(977\) | 1830.67 | + | 3170.82i | 0.0599472 | + | 0.103832i | 0.894441 | − | 0.447185i | \(-0.147573\pi\) |
−0.834494 | + | 0.551017i | \(0.814240\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29690.1 | −0.969254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6612.37 | + | 11453.0i | −0.214877 | + | 0.372178i | ||||
\(983\) | −13597.1 | − | 23550.8i | −0.441179 | − | 0.764144i | 0.556598 | − | 0.830782i | \(-0.312106\pi\) |
−0.997777 | + | 0.0666376i | \(0.978773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6776.39 | + | 11737.1i | −0.219202 | + | 0.379669i | ||||
\(986\) | 2872.37 | 0.0927736 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1582.19 | −0.0509477 | ||||||||
\(989\) | −5425.66 | + | 9397.52i | −0.174445 | + | 0.302147i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6769.84 | + | 11725.7i | 0.217004 | + | 0.375862i | 0.953891 | − | 0.300154i | \(-0.0970381\pi\) |
−0.736886 | + | 0.676016i | \(0.763705\pi\) | |||||||
\(992\) | −2327.91 | + | 4032.05i | −0.0745072 | + | 0.129050i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1904.74 | −0.0606878 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11431.9 | + | 19800.6i | 0.363142 | + | 0.628980i | 0.988476 | − | 0.151377i | \(-0.0483708\pi\) |
−0.625335 | + | 0.780357i | \(0.715037\pi\) | |||||||
\(998\) | 11456.4 | + | 19843.1i | 0.363374 | + | 0.629382i | ||||
\(999\) | 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.z.667.2 | 4 | ||
3.2 | odd | 2 | 882.4.g.bj.667.1 | 4 | |||
7.2 | even | 3 | 882.4.a.bh.1.1 | 2 | |||
7.3 | odd | 6 | 126.4.g.e.109.1 | yes | 4 | ||
7.4 | even | 3 | inner | 882.4.g.z.361.2 | 4 | ||
7.5 | odd | 6 | 882.4.a.bd.1.2 | 2 | |||
7.6 | odd | 2 | 126.4.g.e.37.1 | ✓ | 4 | ||
21.2 | odd | 6 | 882.4.a.u.1.2 | 2 | |||
21.5 | even | 6 | 882.4.a.ba.1.1 | 2 | |||
21.11 | odd | 6 | 882.4.g.bj.361.1 | 4 | |||
21.17 | even | 6 | 126.4.g.f.109.2 | yes | 4 | ||
21.20 | even | 2 | 126.4.g.f.37.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.g.e.37.1 | ✓ | 4 | 7.6 | odd | 2 | ||
126.4.g.e.109.1 | yes | 4 | 7.3 | odd | 6 | ||
126.4.g.f.37.2 | yes | 4 | 21.20 | even | 2 | ||
126.4.g.f.109.2 | yes | 4 | 21.17 | even | 6 | ||
882.4.a.u.1.2 | 2 | 21.2 | odd | 6 | |||
882.4.a.ba.1.1 | 2 | 21.5 | even | 6 | |||
882.4.a.bd.1.2 | 2 | 7.5 | odd | 6 | |||
882.4.a.bh.1.1 | 2 | 7.2 | even | 3 | |||
882.4.g.z.361.2 | 4 | 7.4 | even | 3 | inner | ||
882.4.g.z.667.2 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bj.361.1 | 4 | 21.11 | odd | 6 | |||
882.4.g.bj.667.1 | 4 | 3.2 | odd | 2 |