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 | 361.1 | ||
Root | \(3.72311 + 6.44862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.bj.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 | ||||
\(5\) | −1.72311 | − | 2.98452i | −0.154120 | − | 0.266943i | 0.778618 | − | 0.627498i | \(-0.215921\pi\) |
−0.932738 | + | 0.360554i | \(0.882587\pi\) | |||||||
\(6\) | 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 | \(-0.998193\pi\) |
0.504908 | + | 0.863173i | \(0.331526\pi\) | |||||||
\(12\) | 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 | −0.0405493 | − | 0.999178i | \(-0.512911\pi\) |
0.885588 | − | 0.464472i | \(-0.153756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.3307 | − | 33.4817i | −0.233408 | − | 0.404275i | 0.725401 | − | 0.688327i | \(-0.241655\pi\) |
−0.958809 | + | 0.284052i | \(0.908321\pi\) | |||||||
\(20\) | 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 | \(-0.114128\pi\) |
−0.772103 | + | 0.635497i | \(0.780795\pi\) | |||||||
\(24\) | 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 | \(-0.512358\pi\) | ||||
−0.0388153 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −72.7471 | + | 126.002i | −0.421476 | + | 0.730018i | −0.996084 | − | 0.0884105i | \(-0.971821\pi\) |
0.574608 | + | 0.818429i | \(0.305155\pi\) | |||||||
\(32\) | 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 | 0.867544 | − | 0.497361i | \(-0.165697\pi\) |
−0.864499 | + | 0.502635i | \(0.832364\pi\) | |||||||
\(38\) | 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 | \(-0.603671\pi\) | ||||
−0.319966 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(42\) | 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 | 0.931894 | + | 0.362732i | \(0.118156\pi\) |
−0.151812 | + | 0.988409i | \(0.548511\pi\) | |||||||
\(48\) | 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 | −0.102771 | − | 0.994705i | \(-0.532771\pi\) |
0.912825 | − | 0.408350i | \(-0.133896\pi\) | |||||||
\(54\) | 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 | \(-0.848166\pi\) |
0.841795 | + | 0.539797i | \(0.181499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −219.586 | − | 380.334i | −0.460903 | − | 0.798307i | 0.538103 | − | 0.842879i | \(-0.319141\pi\) |
−0.999006 | + | 0.0445717i | \(0.985808\pi\) | |||||||
\(62\) | −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 | −0.273575 | − | 0.961851i | \(-0.588206\pi\) |
0.969775 | − | 0.244003i | \(-0.0784605\pi\) | |||||||
\(68\) | 236.924 | + | 410.365i | 0.422519 | + | 0.731825i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1020.49 | 1.70578 | 0.852890 | − | 0.522091i | \(-0.174848\pi\) | ||||
0.852890 | + | 0.522091i | \(0.174848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 289.642 | − | 501.674i | 0.464384 | − | 0.804336i | −0.534790 | − | 0.844985i | \(-0.679609\pi\) |
0.999173 | + | 0.0406491i | \(0.0129426\pi\) | |||||||
\(74\) | −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 | −0.977536 | − | 0.210770i | \(-0.932403\pi\) |
0.306236 | − | 0.951956i | \(-0.400930\pi\) | |||||||
\(80\) | −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 | \(-0.398366\pi\) | ||||
0.313895 | + | 0.949458i | \(0.398366\pi\) | |||||||
\(84\) | 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 | \(-0.00386515\pi\) |
−0.510479 | + | 0.859890i | \(0.670532\pi\) | |||||||
\(90\) | 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 | 0.143978 | − | 0.989581i | \(-0.454011\pi\) |
0.785013 | − | 0.619479i | \(-0.212656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 241.072 | + | 417.549i | 0.230617 | + | 0.399440i | 0.957990 | − | 0.286802i | \(-0.0925923\pi\) |
−0.727373 | + | 0.686242i | \(0.759259\pi\) | |||||||
\(104\) | 81.8489 | 0.0771725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1250.22 | 1.14559 | ||||||||
\(107\) | 865.297 | + | 1498.74i | 0.781789 | + | 1.35410i | 0.930898 | + | 0.365278i | \(0.119026\pi\) |
−0.149109 | + | 0.988821i | \(0.547641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −574.415 | + | 994.916i | −0.504761 | + | 0.874272i | 0.495223 | + | 0.868766i | \(0.335086\pi\) |
−0.999985 | + | 0.00550668i | \(0.998247\pi\) | |||||||
\(110\) | 124.490 | + | 215.623i | 0.107906 | + | 0.186898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1331.51 | 1.10847 | 0.554237 | − | 0.832359i | \(-0.313010\pi\) | ||||
0.554237 | + | 0.832359i | \(0.313010\pi\) | |||||||
\(114\) | 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 | 0.981190 | + | 0.193044i | \(0.0618359\pi\) |
−0.323414 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(132\) | 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 | \(-0.826506\pi\) |
0.876550 | + | 0.481310i | \(0.159839\pi\) | |||||||
\(138\) | 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 | \(-0.164891\pi\) |
−0.863222 | + | 0.504824i | \(0.831558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 790.162 | − | 1368.60i | 0.425844 | − | 0.737584i | −0.570655 | − | 0.821190i | \(-0.693310\pi\) |
0.996499 | + | 0.0836063i | \(0.0266438\pi\) | |||||||
\(152\) | 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 | −0.0115487 | − | 0.999933i | \(-0.503676\pi\) |
0.871742 | − | 0.489965i | \(-0.162991\pi\) | |||||||
\(158\) | 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 | 0.613092 | − | 0.790012i | \(-0.289926\pi\) |
−0.990716 | + | 0.135947i | \(0.956592\pi\) | |||||||
\(164\) | 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 | \(-0.694285\pi\) | ||||
−0.573167 | + | 0.819439i | \(0.694285\pi\) | |||||||
\(168\) | 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 | 0.810952 | + | 0.585112i | \(0.198950\pi\) |
0.101246 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(174\) | 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 | 0.0299728 | − | 0.999551i | \(-0.490458\pi\) |
0.850650 | − | 0.525733i | \(-0.176209\pi\) | |||||||
\(180\) | 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 | \(-0.289233\pi\) |
−0.990418 | + | 0.138103i | \(0.955899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1055.87 | + | 1828.82i | −0.393799 | + | 0.682080i | −0.992947 | − | 0.118558i | \(-0.962173\pi\) |
0.599148 | + | 0.800638i | \(0.295506\pi\) | |||||||
\(194\) | 1108.16 | + | 1919.40i | 0.410111 | + | 0.710333i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3932.65 | 1.42228 | 0.711141 | − | 0.703049i | \(-0.248179\pi\) | ||||
0.711141 | + | 0.703049i | \(0.248179\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −276.352 | + | 478.656i | −0.0984426 | + | 0.170508i | −0.911040 | − | 0.412318i | \(-0.864719\pi\) |
0.812598 | + | 0.582825i | \(0.198053\pi\) | |||||||
\(200\) | −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 | −0.395593 | − | 0.918426i | \(-0.629461\pi\) |
0.993177 | − | 0.116619i | \(-0.0372058\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2033.30 | − | 3521.79i | −0.586745 | − | 1.01627i | −0.994655 | − | 0.103250i | \(-0.967076\pi\) |
0.407911 | − | 0.913022i | \(-0.366257\pi\) | |||||||
\(230\) | 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 | \(-0.174645\pi\) |
−0.878284 | + | 0.478139i | \(0.841312\pi\) | |||||||
\(234\) | 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 | \(-0.592560\pi\) | ||||
−0.286706 | + | 0.958019i | \(0.592560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1199.15 | − | 2076.99i | 0.320516 | − | 0.555149i | −0.660079 | − | 0.751196i | \(-0.729477\pi\) |
0.980595 | + | 0.196047i | \(0.0628105\pi\) | |||||||
\(242\) | −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 | \(-0.437534\pi\) | ||||
0.194986 | + | 0.980806i | \(0.437534\pi\) | |||||||
\(252\) | 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 | −0.981948 | − | 0.189150i | \(-0.939427\pi\) |
0.327166 | − | 0.944967i | \(-0.393907\pi\) | |||||||
\(258\) | 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 | \(-0.971271\pi\) |
0.576022 | + | 0.817434i | \(0.304604\pi\) | |||||||
\(264\) | 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 | \(-0.875866\pi\) |
0.791694 | + | 0.610918i | \(0.209200\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 129.664 | + | 224.584i | 0.0290646 | + | 0.0503413i | 0.880192 | − | 0.474618i | \(-0.157414\pi\) |
−0.851127 | + | 0.524959i | \(0.824080\pi\) | |||||||
\(272\) | −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 | −0.786951 | − | 0.617015i | \(-0.788342\pi\) |
0.927826 | + | 0.373012i | \(0.121675\pi\) | |||||||
\(278\) | −1864.48 | − | 3229.37i | −0.402245 | − | 0.696708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4524.25 | −0.960477 | −0.480238 | − | 0.877138i | \(-0.659450\pi\) | ||||
−0.480238 | + | 0.877138i | \(0.659450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3239.03 | − | 5610.16i | 0.680354 | − | 1.17841i | −0.294519 | − | 0.955646i | \(-0.595160\pi\) |
0.974873 | − | 0.222762i | \(-0.0715072\pi\) | |||||||
\(284\) | −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 | \(-0.406941\pi\) | ||||
0.288207 | + | 0.957568i | \(0.406941\pi\) | |||||||
\(294\) | 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 | 0.238803 | + | 0.971068i | \(0.423245\pi\) |
−0.960371 | + | 0.278725i | \(0.910088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3808.30 | + | 6596.18i | 0.687726 | + | 1.19118i | 0.972572 | + | 0.232602i | \(0.0747241\pi\) |
−0.284846 | + | 0.958573i | \(0.591943\pi\) | |||||||
\(314\) | 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 | \(-0.110213\pi\) |
−0.764229 | + | 0.644945i | \(0.776880\pi\) | |||||||
\(318\) | 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 | 0.723195 | − | 0.690644i | \(-0.242673\pi\) |
−0.959713 | + | 0.280983i | \(0.909340\pi\) | |||||||
\(332\) | −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 | \(-0.918941\pi\) |
0.702036 | + | 0.712142i | \(0.252275\pi\) | |||||||
\(348\) | 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 | 0.369804 | + | 0.929110i | \(0.379425\pi\) |
−0.989535 | + | 0.144295i | \(0.953909\pi\) | |||||||
\(354\) | 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 | −0.957796 | − | 0.287448i | \(-0.907193\pi\) |
0.229961 | − | 0.973200i | \(-0.426140\pi\) | |||||||
\(360\) | 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 | −0.145155 | − | 0.989409i | \(-0.546368\pi\) |
0.929431 | − | 0.368997i | \(-0.120299\pi\) | |||||||
\(368\) | 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 | 0.945456 | − | 0.325751i | \(-0.105617\pi\) |
−0.754836 | + | 0.655913i | \(0.772284\pi\) | |||||||
\(374\) | −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 | \(-0.232114\pi\) |
−0.949865 | + | 0.312659i | \(0.898780\pi\) | |||||||
\(384\) | 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 | \(-0.729446\pi\) |
0.980614 | + | 0.195950i | \(0.0627789\pi\) | |||||||
\(390\) | 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 | −0.895907 | − | 0.444242i | \(-0.853473\pi\) |
0.0632286 | − | 0.997999i | \(-0.479860\pi\) | |||||||
\(398\) | −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 | \(-0.219680\pi\) |
−0.936931 | + | 0.349515i | \(0.886346\pi\) | |||||||
\(402\) | 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 | 0.143429 | + | 0.989661i | \(0.454187\pi\) |
−0.928786 | + | 0.370617i | \(0.879146\pi\) | |||||||
\(410\) | −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 | \(-0.361365\pi\) | ||||
0.421896 | + | 0.906644i | \(0.361365\pi\) | |||||||
\(420\) | 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 | \(-0.949413\pi\) |
0.630753 | + | 0.775984i | \(0.282746\pi\) | |||||||
\(432\) | 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 | 0.999364 | + | 0.0356614i | \(0.0113538\pi\) |
−0.468798 | + | 0.883305i | \(0.655313\pi\) | |||||||
\(440\) | −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 | \(-0.266139\pi\) |
−0.977801 | + | 0.209534i | \(0.932805\pi\) | |||||||
\(444\) | 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 | \(-0.838402\pi\) | ||||
−0.873877 | + | 0.486147i | \(0.838402\pi\) | |||||||
\(450\) | 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 | −0.855526 | − | 0.517761i | \(-0.826766\pi\) |
−0.0206311 | − | 0.999787i | \(-0.506568\pi\) | |||||||
\(458\) | 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 | \(-0.614304\pi\) | ||||
−0.351429 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(462\) | 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 | −0.962300 | − | 0.271990i | \(-0.912318\pi\) |
0.245600 | − | 0.969371i | \(-0.421015\pi\) | |||||||
\(468\) | 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 | \(-0.771065\pi\) |
0.946696 | + | 0.322128i | \(0.104398\pi\) | |||||||
\(480\) | 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 | −0.949724 | − | 0.313089i | \(-0.898636\pi\) |
0.746005 | + | 0.665940i | \(0.231969\pi\) | |||||||
\(488\) | 1756.69 | + | 3042.67i | 0.162954 | + | 0.282244i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6612.37 | −0.607764 | −0.303882 | − | 0.952710i | \(-0.598283\pi\) | ||||
−0.303882 | + | 0.952710i | \(0.598283\pi\) | |||||||
\(492\) | 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 | 0.999870 | + | 0.0161114i | \(0.00512863\pi\) |
−0.485982 | + | 0.873969i | \(0.661538\pi\) | |||||||
\(500\) | 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 | \(-0.389184\pi\) | ||||
0.341150 | + | 0.940009i | \(0.389184\pi\) | |||||||
\(504\) | 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 | \(-0.102140\pi\) |
−0.747627 | + | 0.664118i | \(0.768807\pi\) | |||||||
\(510\) | 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 | \(-0.786501\pi\) |
0.929968 | + | 0.367641i | \(0.119834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2207.57 | − | 3823.62i | −0.184570 | − | 0.319685i | 0.758862 | − | 0.651252i | \(-0.225756\pi\) |
−0.943432 | + | 0.331567i | \(0.892423\pi\) | |||||||
\(524\) | −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 | 0.996813 | − | 0.0797775i | \(-0.0254210\pi\) |
−0.567496 | + | 0.823376i | \(0.692088\pi\) | |||||||
\(542\) | −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 | \(-0.850911\pi\) |
0.837108 | + | 0.547038i | \(0.184245\pi\) | |||||||
\(558\) | 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 | 0.359835 | + | 0.933016i | \(0.382833\pi\) |
−0.987933 | + | 0.154882i | \(0.950500\pi\) | |||||||
\(564\) | 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 | −0.998768 | − | 0.0496328i | \(-0.984195\pi\) |
0.456401 | − | 0.889774i | \(-0.349138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4858.56 | + | 8415.27i | −0.356085 | + | 0.616757i | −0.987303 | − | 0.158849i | \(-0.949222\pi\) |
0.631218 | + | 0.775605i | \(0.282555\pi\) | |||||||
\(572\) | 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 | 0.229282 | + | 0.973360i | \(0.426362\pi\) |
−0.957596 | + | 0.288116i | \(0.906971\pi\) | |||||||
\(578\) | 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 | \(-0.776590\pi\) | ||||
−0.763641 | + | 0.645641i | \(0.776590\pi\) | |||||||
\(588\) | 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 | 0.976168 | + | 0.217016i | \(0.0696322\pi\) |
−0.300143 | + | 0.953894i | \(0.597034\pi\) | |||||||
\(594\) | 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 | \(-0.703876\pi\) |
0.993175 | + | 0.116630i | \(0.0372091\pi\) | |||||||
\(600\) | 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 | 0.999971 | + | 0.00758385i | \(0.00241404\pi\) |
−0.493418 | + | 0.869792i | \(0.664253\pi\) | |||||||
\(608\) | −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 | 0.0912312 | + | 0.995830i | \(0.470920\pi\) |
−0.908029 | + | 0.418906i | \(0.862414\pi\) | |||||||
\(614\) | 3137.42 | + | 5434.17i | 0.206215 | + | 0.357175i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25194.6 | 1.64391 | 0.821957 | − | 0.569550i | \(-0.192882\pi\) | ||||
0.821957 | + | 0.569550i | \(0.192882\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3023.24 | + | 5236.40i | −0.196307 | + | 0.340014i | −0.947328 | − | 0.320264i | \(-0.896228\pi\) |
0.751021 | + | 0.660278i | \(0.229562\pi\) | |||||||
\(620\) | −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 | \(-0.741377\pi\) |
0.972582 | + | 0.232561i | \(0.0747104\pi\) | |||||||
\(642\) | 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 | \(-0.707179\pi\) |
0.991912 | + | 0.126930i | \(0.0405124\pi\) | |||||||
\(648\) | 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 | 0.999894 | + | 0.0145285i | \(0.00462474\pi\) |
−0.487365 | + | 0.873198i | \(0.662042\pi\) | |||||||
\(654\) | 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 | \(-0.379365\pi\) | ||||
0.369978 | + | 0.929040i | \(0.379365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2390.24 | + | 4140.01i | −0.140650 | + | 0.243613i | −0.927741 | − | 0.373223i | \(-0.878252\pi\) |
0.787092 | + | 0.616836i | \(0.211586\pi\) | |||||||
\(662\) | 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 | \(-0.0178374\pi\) |
−0.547720 | + | 0.836662i | \(0.684504\pi\) | |||||||
\(678\) | 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 | \(-0.811574\pi\) |
0.898155 | + | 0.439678i | \(0.144908\pi\) | |||||||
\(684\) | 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 | 0.989670 | + | 0.143361i | \(0.0457910\pi\) |
−0.370681 | + | 0.928760i | \(0.620876\pi\) | |||||||
\(692\) | −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 | \(-0.533646\pi\) | ||||
−0.105504 | + | 0.994419i | \(0.533646\pi\) | |||||||
\(702\) | 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 | 0.991767 | + | 0.128053i | \(0.0408726\pi\) |
−0.384987 | + | 0.922922i | \(0.625794\pi\) | |||||||
\(710\) | 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 | 0.999348 | + | 0.0361132i | \(0.0114977\pi\) |
−0.468399 | + | 0.883517i | \(0.655169\pi\) | |||||||
\(720\) | 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 | −0.836431 | − | 0.548072i | \(-0.815362\pi\) |
−0.0564289 | − | 0.998407i | \(-0.517971\pi\) | |||||||
\(734\) | 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 | −0.551758 | − | 0.834004i | \(-0.686043\pi\) |
0.998148 | + | 0.0608348i | \(0.0193763\pi\) | |||||||
\(740\) | 9.44721 | + | 16.3630i | 0.000469306 | + | 0.000812862i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19031.0 | 0.939676 | 0.469838 | − | 0.882753i | \(-0.344312\pi\) | ||||
0.469838 | + | 0.882753i | \(0.344312\pi\) | |||||||
\(744\) | 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 | 0.897261 | − | 0.441501i | \(-0.145554\pi\) |
−0.830982 | + | 0.556300i | \(0.812221\pi\) | |||||||
\(752\) | 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 | \(-0.171216\pi\) |
−0.873083 | + | 0.487571i | \(0.837883\pi\) | |||||||
\(762\) | 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 | −0.443372 | − | 0.896338i | \(-0.646218\pi\) |
0.997937 | − | 0.0641977i | \(-0.0204488\pi\) | |||||||
\(774\) | 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 | −0.872041 | − | 0.489433i | \(-0.837204\pi\) |
0.859882 | + | 0.510493i | \(0.170537\pi\) | |||||||
\(788\) | −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 | \(-0.436935\pi\) | ||||
0.196830 | + | 0.980438i | \(0.436935\pi\) | |||||||
\(798\) | 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 | \(-0.675993\pi\) |
0.999571 | + | 0.0292939i | \(0.00932587\pi\) | |||||||
\(810\) | 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 | \(-0.292199\pi\) |
−0.991662 | + | 0.128868i | \(0.958866\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2451.37 | − | 4245.90i | 0.103827 | − | 0.179833i | −0.809431 | − | 0.587214i | \(-0.800225\pi\) |
0.913258 | + | 0.407381i | \(0.133558\pi\) | |||||||
\(824\) | −1928.58 | − | 3340.39i | −0.0815353 | − | 0.141223i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19578.9 | 0.823247 | 0.411623 | − | 0.911354i | \(-0.364962\pi\) | ||||
0.411623 | + | 0.911354i | \(0.364962\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18965.1 | + | 32848.5i | −0.794554 | + | 1.37621i | 0.128568 | + | 0.991701i | \(0.458962\pi\) |
−0.923122 | + | 0.384507i | \(0.874371\pi\) | |||||||
\(830\) | 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 | \(-0.460907\pi\) | ||||
0.122504 | + | 0.992468i | \(0.460907\pi\) | |||||||
\(840\) | 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 | −0.219797 | − | 0.975546i | \(-0.570539\pi\) |
0.954746 | − | 0.297423i | \(-0.0961272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17239.1 | + | 29859.0i | 0.684740 | + | 1.18600i | 0.973519 | + | 0.228608i | \(0.0734174\pi\) |
−0.288779 | + | 0.957396i | \(0.593249\pi\) | |||||||
\(860\) | 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 | \(-0.177213\pi\) |
−0.882114 | + | 0.471037i | \(0.843880\pi\) | |||||||
\(864\) | 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 | 0.840917 | − | 0.541164i | \(-0.182016\pi\) |
−0.889120 | + | 0.457674i | \(0.848683\pi\) | |||||||
\(878\) | −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 | \(-0.732443\pi\) | ||||
−0.667048 | + | 0.745014i | \(0.732443\pi\) | |||||||
\(882\) | 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 | 0.999987 | + | 0.00515772i | \(0.00164176\pi\) |
−0.495527 | + | 0.868593i | \(0.665025\pi\) | |||||||
\(888\) | 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 | −0.0443164 | − | 0.999018i | \(-0.514111\pi\) |
0.887333 | − | 0.461130i | \(-0.152556\pi\) | |||||||
\(908\) | 8175.18 | + | 14159.8i | 0.298792 | + | 0.517523i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14227.1 | −0.517416 | −0.258708 | − | 0.965956i | \(-0.583297\pi\) | ||||
−0.258708 | + | 0.965956i | \(0.583297\pi\) | |||||||
\(912\) | 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 | 0.799760 | − | 0.600320i | \(-0.204960\pi\) |
−0.919772 | + | 0.392453i | \(0.871627\pi\) | |||||||
\(920\) | −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 | \(-0.0898189\pi\) |
−0.721366 | + | 0.692554i | \(0.756486\pi\) | |||||||
\(930\) | 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 | −0.226708 | + | 0.973963i | \(0.572796\pi\) |
−0.730122 | + | 0.683316i | \(0.760537\pi\) | |||||||
\(942\) | 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 | −0.903161 | − | 0.429303i | \(-0.858759\pi\) |
0.0797929 | − | 0.996811i | \(-0.474574\pi\) | |||||||
\(948\) | 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 | \(-0.390179\pi\) | ||||
0.338207 | + | 0.941072i | \(0.390179\pi\) | |||||||
\(954\) | 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 | \(-0.175845\pi\) |
−0.880080 | + | 0.474825i | \(0.842511\pi\) | |||||||
\(972\) | 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 | \(-0.852427\pi\) |
0.834494 | + | 0.551017i | \(0.185760\pi\) | |||||||
\(978\) | 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 | \(-0.687894\pi\) |
0.997777 | + | 0.0666376i | \(0.0212271\pi\) | |||||||
\(984\) | 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 | −0.736886 | − | 0.676016i | \(-0.763705\pi\) |
0.953891 | + | 0.300154i | \(0.0970381\pi\) | |||||||
\(992\) | 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 | −0.625335 | − | 0.780357i | \(-0.715037\pi\) |
0.988476 | + | 0.151377i | \(0.0483708\pi\) | |||||||
\(998\) | −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.bj.361.1 | 4 | ||
3.2 | odd | 2 | 882.4.g.z.361.2 | 4 | |||
7.2 | even | 3 | inner | 882.4.g.bj.667.1 | 4 | ||
7.3 | odd | 6 | 882.4.a.ba.1.1 | 2 | |||
7.4 | even | 3 | 882.4.a.u.1.2 | 2 | |||
7.5 | odd | 6 | 126.4.g.f.37.2 | yes | 4 | ||
7.6 | odd | 2 | 126.4.g.f.109.2 | yes | 4 | ||
21.2 | odd | 6 | 882.4.g.z.667.2 | 4 | |||
21.5 | even | 6 | 126.4.g.e.37.1 | ✓ | 4 | ||
21.11 | odd | 6 | 882.4.a.bh.1.1 | 2 | |||
21.17 | even | 6 | 882.4.a.bd.1.2 | 2 | |||
21.20 | even | 2 | 126.4.g.e.109.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.g.e.37.1 | ✓ | 4 | 21.5 | even | 6 | ||
126.4.g.e.109.1 | yes | 4 | 21.20 | even | 2 | ||
126.4.g.f.37.2 | yes | 4 | 7.5 | odd | 6 | ||
126.4.g.f.109.2 | yes | 4 | 7.6 | odd | 2 | ||
882.4.a.u.1.2 | 2 | 7.4 | even | 3 | |||
882.4.a.ba.1.1 | 2 | 7.3 | odd | 6 | |||
882.4.a.bd.1.2 | 2 | 21.17 | even | 6 | |||
882.4.a.bh.1.1 | 2 | 21.11 | odd | 6 | |||
882.4.g.z.361.2 | 4 | 3.2 | odd | 2 | |||
882.4.g.z.667.2 | 4 | 21.2 | odd | 6 | |||
882.4.g.bj.361.1 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bj.667.1 | 4 | 7.2 | even | 3 | inner |