Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(2.85284 + 0.928053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.4.bc.d.257.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.47555 | − | 3.86271i | 0.668870 | − | 0.743380i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.623706 | + | 1.08029i | 0.0557859 | + | 0.0966240i | 0.892570 | − | 0.450909i | \(-0.148900\pi\) |
−0.836784 | + | 0.547533i | \(0.815567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0808 | − | 15.5363i | −0.544314 | − | 0.838881i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.84113 | − | 26.8501i | −0.105227 | − | 0.994448i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −35.2392 | − | 20.3453i | −0.965910 | − | 0.557668i | −0.0679230 | − | 0.997691i | \(-0.521637\pi\) |
−0.897987 | + | 0.440022i | \(0.854971\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.5973i | 0.418101i | 0.977905 | + | 0.209050i | \(0.0670373\pi\) | ||||
−0.977905 | + | 0.209050i | \(0.932963\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.34057 | + | 1.34540i | 0.109142 | + | 0.0231588i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −52.3592 | + | 90.6889i | −0.746999 | + | 1.29384i | 0.202256 | + | 0.979333i | \(0.435173\pi\) |
−0.949255 | + | 0.314507i | \(0.898161\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.0345 | + | 20.2272i | −0.423025 | + | 0.244234i | −0.696371 | − | 0.717682i | \(-0.745203\pi\) |
0.273346 | + | 0.961916i | \(0.411870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −95.0487 | − | 15.0578i | −0.987683 | − | 0.156470i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −69.6324 | + | 40.2023i | −0.631276 | + | 0.364467i | −0.781246 | − | 0.624223i | \(-0.785416\pi\) |
0.149970 | + | 0.988691i | \(0.452082\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.7220 | − | 106.906i | 0.493776 | − | 0.855245i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −113.589 | − | 82.3444i | −0.809636 | − | 0.586933i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 211.712i | − | 1.35565i | −0.735222 | − | 0.677827i | \(-0.762922\pi\) | ||
0.735222 | − | 0.677827i | \(-0.237078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 86.6242 | + | 50.0125i | 0.501876 | + | 0.289758i | 0.729488 | − | 0.683994i | \(-0.239758\pi\) |
−0.227612 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −201.064 | + | 65.4076i | −1.06063 | + | 0.345030i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.4962 | − | 20.5803i | 0.0506910 | − | 0.0993916i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 94.9875 | + | 164.523i | 0.422050 | + | 0.731012i | 0.996140 | − | 0.0877801i | \(-0.0279773\pi\) |
−0.574090 | + | 0.818792i | \(0.694644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 75.6987 | + | 68.1113i | 0.310808 | + | 0.279655i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −186.753 | −0.711362 | −0.355681 | − | 0.934607i | \(-0.615751\pi\) | ||||
−0.355681 | + | 0.934607i | \(0.615751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −158.618 | −0.562536 | −0.281268 | − | 0.959629i | \(-0.590755\pi\) | ||||
−0.281268 | + | 0.959629i | \(0.590755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.2339 | − | 19.8158i | 0.0902174 | − | 0.0656437i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −179.034 | − | 310.097i | −0.555635 | − | 0.962388i | −0.997854 | − | 0.0654808i | \(-0.979142\pi\) |
0.442219 | − | 0.896907i | \(-0.354191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −139.753 | + | 313.238i | −0.407444 | + | 0.913230i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 168.328 | + | 517.442i | 0.462170 | + | 1.42071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −366.460 | − | 211.576i | −0.949758 | − | 0.548343i | −0.0567521 | − | 0.998388i | \(-0.518074\pi\) |
−0.893006 | + | 0.450045i | \(0.851408\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 50.7580i | − | 0.124440i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.6323 | + | 205.629i | −0.101390 | + | 0.477829i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −312.781 | + | 541.753i | −0.690180 | + | 1.19543i | 0.281599 | + | 0.959532i | \(0.409135\pi\) |
−0.971779 | + | 0.235895i | \(0.924198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 699.575 | − | 403.900i | 1.46838 | − | 0.847772i | 0.469011 | − | 0.883192i | \(-0.344611\pi\) |
0.999372 | + | 0.0354209i | \(0.0112772\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −388.510 | + | 314.812i | −0.776948 | + | 0.629565i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.1708 | + | 12.2229i | −0.0403986 | + | 0.0233241i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 149.272 | − | 258.547i | 0.272187 | − | 0.471441i | −0.697235 | − | 0.716843i | \(-0.745587\pi\) |
0.969421 | + | 0.245402i | \(0.0789199\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −86.7208 | + | 408.695i | −0.151304 | + | 0.713059i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 455.386i | − | 0.761189i | −0.924742 | − | 0.380594i | \(-0.875719\pi\) | ||
0.924742 | − | 0.380594i | \(-0.124281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −434.467 | − | 250.840i | −0.696582 | − | 0.402172i | 0.109491 | − | 0.993988i | \(-0.465078\pi\) |
−0.806073 | + | 0.591816i | \(0.798411\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −198.428 | − | 609.970i | −0.305500 | − | 0.939110i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 39.1491 | + | 752.584i | 0.0579410 | + | 1.11383i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −30.9561 | − | 53.6176i | −0.0440865 | − | 0.0763601i | 0.843140 | − | 0.537694i | \(-0.180704\pi\) |
−0.887227 | + | 0.461334i | \(0.847371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −712.856 | + | 152.569i | −0.977855 | + | 0.209285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73.1180 | 0.0966957 | 0.0483478 | − | 0.998831i | \(-0.484604\pi\) | ||||
0.0483478 | + | 0.998831i | \(0.484604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.627 | −0.166688 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −817.783 | − | 735.816i | −1.00777 | − | 0.906755i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 57.3723 | + | 99.3717i | 0.0683309 | + | 0.118353i | 0.898167 | − | 0.439655i | \(-0.144899\pi\) |
−0.829836 | + | 0.558008i | \(0.811566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 304.469 | − | 197.557i | 0.350737 | − | 0.227578i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 494.251 | − | 160.784i | 0.551090 | − | 0.179274i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −43.7025 | − | 25.2316i | −0.0471977 | − | 0.0272496i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1416.51i | − | 1.48273i | −0.671101 | − | 0.741366i | \(-0.734178\pi\) | ||
0.671101 | − | 0.741366i | \(-0.265822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −446.156 | + | 1003.98i | −0.452933 | + | 1.01923i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 120.406 | − | 208.549i | 0.118622 | − | 0.205459i | −0.800600 | − | 0.599199i | \(-0.795486\pi\) |
0.919222 | + | 0.393740i | \(0.128819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 960.453 | − | 554.518i | 0.918799 | − | 0.530469i | 0.0355471 | − | 0.999368i | \(-0.488683\pi\) |
0.883252 | + | 0.468899i | \(0.155349\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −43.0157 | − | 112.072i | −0.0399800 | − | 0.104163i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −924.644 | + | 533.843i | −0.835408 | + | 0.482323i | −0.855701 | − | 0.517471i | \(-0.826874\pi\) |
0.0202926 | + | 0.999794i | \(0.493540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.04376 | + | 8.73604i | −0.00443215 | + | 0.00767671i | −0.868233 | − | 0.496157i | \(-0.834744\pi\) |
0.863801 | + | 0.503833i | \(0.168077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 965.640 | + | 204.899i | 0.825716 | + | 0.175208i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 884.294i | − | 0.736171i | −0.929792 | − | 0.368086i | \(-0.880013\pi\) | ||
0.929792 | − | 0.368086i | \(-0.119987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −86.8602 | − | 50.1487i | −0.0704326 | − | 0.0406643i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 526.189 | − | 55.6784i | 0.415780 | − | 0.0439954i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1936.79 | − | 100.751i | 1.49198 | − | 0.0776122i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 162.366 | + | 281.226i | 0.121988 | + | 0.211289i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −649.067 | + | 721.372i | −0.475808 | + | 0.528812i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 309.912 | 0.221755 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 840.132 | 0.587005 | 0.293503 | − | 0.955958i | \(-0.405179\pi\) | ||||
0.293503 | + | 0.955958i | \(0.405179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −551.285 | + | 612.697i | −0.376263 | + | 0.418178i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 258.951 | + | 448.517i | 0.172707 | + | 0.299138i | 0.939366 | − | 0.342918i | \(-0.111415\pi\) |
−0.766658 | + | 0.642056i | \(0.778082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 667.434 | + | 340.400i | 0.435142 | + | 0.221928i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.1098 | − | 174.067i | 0.0115455 | − | 0.110973i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 950.957 | + | 549.035i | 0.593034 | + | 0.342389i | 0.766296 | − | 0.642487i | \(-0.222097\pi\) |
−0.173262 | + | 0.984876i | \(0.555431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 828.268i | − | 0.505416i | −0.967543 | − | 0.252708i | \(-0.918679\pi\) | ||
0.967543 | − | 0.252708i | \(-0.0813212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1820.06 | − | 386.197i | −1.08707 | − | 0.230664i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 398.714 | − | 690.592i | 0.233162 | − | 0.403848i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 228.710 | − | 132.046i | 0.130989 | − | 0.0756264i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 724.230 | + | 1628.50i | 0.406350 | + | 0.913717i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 773.007 | − | 446.296i | 0.425015 | − | 0.245382i | −0.272206 | − | 0.962239i | \(-0.587753\pi\) |
0.697221 | + | 0.716857i | \(0.254420\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 712.518 | − | 1234.12i | 0.383999 | − | 0.665106i | −0.607630 | − | 0.794220i | \(-0.707880\pi\) |
0.991630 | + | 0.129113i | \(0.0412131\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2583.76 | + | 1148.19i | 1.36526 | + | 0.606705i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 124.772i | 0.0646577i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −244.872 | − | 141.377i | −0.124477 | − | 0.0718670i | 0.436468 | − | 0.899720i | \(-0.356229\pi\) |
−0.560946 | + | 0.827853i | \(0.689562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2090.91 | + | 680.189i | −1.04289 | + | 0.339261i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1326.55 | + | 676.557i | 0.649358 | + | 0.331181i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1158.07 | + | 2005.83i | 0.556484 | + | 0.963858i | 0.997786 | + | 0.0664997i | \(0.0211832\pi\) |
−0.441303 | + | 0.897358i | \(0.645484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −196.064 | − | 176.412i | −0.0925063 | − | 0.0832342i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2344.70 | 1.08646 | 0.543229 | − | 0.839585i | \(-0.317202\pi\) | ||||
0.543229 | + | 0.839585i | \(0.317202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1812.95 | 0.825192 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 642.640 | + | 883.213i | 0.287391 | + | 0.394977i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 516.901 | + | 895.298i | 0.227163 | + | 0.393458i | 0.956966 | − | 0.290199i | \(-0.0937216\pi\) |
−0.729803 | + | 0.683657i | \(0.760388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2283.13 | + | 118.767i | −0.986218 | + | 0.0513026i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1005.55 | + | 3091.07i | 0.427016 | + | 1.31265i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 125.472 | + | 72.4412i | 0.0523922 | + | 0.0302486i | 0.525967 | − | 0.850505i | \(-0.323703\pi\) |
−0.473575 | + | 0.880753i | \(0.657037\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2057.17i | − | 0.844797i | −0.906410 | − | 0.422398i | \(-0.861188\pi\) | ||
0.906410 | − | 0.422398i | \(-0.138812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 871.257 | − | 4106.03i | 0.351941 | − | 1.65862i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −118.489 | + | 205.228i | −0.0470889 | + | 0.0815604i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3690.19 | − | 2130.53i | 1.44307 | − | 0.833155i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −134.257 | + | 2594.85i | −0.0516706 | + | 0.998664i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2553.66 | − | 1474.36i | 0.967417 | − | 0.558538i | 0.0689690 | − | 0.997619i | \(-0.478029\pi\) |
0.898448 | + | 0.439080i | \(0.144696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1135.40 | − | 1966.57i | 0.423460 | − | 0.733455i | −0.572815 | − | 0.819685i | \(-0.694149\pi\) |
0.996275 | + | 0.0862300i | \(0.0274820\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.3662 | + | 124.258i | −0.00968270 | + | 0.0456323i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 495.849i | − | 0.179329i | −0.995972 | − | 0.0896645i | \(-0.971421\pi\) | ||
0.995972 | − | 0.0896645i | \(-0.0285795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −727.207 | − | 419.853i | −0.259047 | − | 0.149561i | 0.364853 | − | 0.931065i | \(-0.381119\pi\) |
−0.623900 | + | 0.781504i | \(0.714453\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −479.890 | − | 1475.19i | −0.168402 | − | 0.517670i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3289.22 | + | 2134.24i | −1.13723 | + | 0.737902i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −116.479 | − | 201.747i | −0.0396840 | − | 0.0687347i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1277.27 | + | 1755.42i | 0.428871 | + | 0.589420i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1646.12 | 0.544805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4001.71 | −1.30564 | −0.652818 | − | 0.757514i | \(-0.726414\pi\) | ||||
−0.652818 | + | 0.757514i | \(0.726414\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1759.03 | − | 1582.72i | −0.565852 | − | 0.509136i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −98.9311 | − | 171.354i | −0.0313816 | − | 0.0543545i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −96.2355 | − | 1849.99i | −0.0301055 | − | 0.578734i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2478.93 | + | 806.416i | −0.764889 | + | 0.248825i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1777.26 | − | 1026.10i | −0.540955 | − | 0.312321i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3040.54i | − | 0.913047i | −0.889711 | − | 0.456523i | \(-0.849095\pi\) | ||
0.889711 | − | 0.456523i | \(-0.150905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3045.79 | − | 1353.51i | −0.902455 | − | 0.401040i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2198.24 | + | 3807.46i | −0.642741 | + | 1.11326i | 0.342078 | + | 0.939672i | \(0.388869\pi\) |
−0.984818 | + | 0.173588i | \(0.944464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1717.81 | + | 991.778i | −0.495703 | + | 0.286194i | −0.726937 | − | 0.686704i | \(-0.759057\pi\) |
0.231234 | + | 0.972898i | \(0.425724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3043.08 | + | 2464.42i | 0.866754 | + | 0.701935i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3787.78 | + | 2186.87i | −1.06500 | + | 0.614879i | −0.926812 | − | 0.375526i | \(-0.877462\pi\) |
−0.138191 | + | 0.990406i | \(0.544129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 223.329 | − | 386.818i | 0.0619932 | − | 0.107375i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −314.699 | − | 66.7758i | −0.0862527 | − | 0.0183019i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3826.41i | − | 1.03561i | −0.855500 | − | 0.517803i | \(-0.826750\pi\) | ||
0.855500 | − | 0.517803i | \(-0.173250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2979.03 | + | 1719.94i | 0.796250 | + | 0.459715i | 0.842158 | − | 0.539231i | \(-0.181285\pi\) |
−0.0459083 | + | 0.998946i | \(0.514618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1888.24 | + | 3283.82i | −0.498479 | + | 0.866902i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −425.553 | + | 44.3943i | −0.110970 | + | 0.0115765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −396.398 | − | 686.582i | −0.102114 | − | 0.176867i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 254.125 | − | 282.434i | 0.0646768 | − | 0.0718816i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2046.61 | 0.514664 | 0.257332 | − | 0.966323i | \(-0.417157\pi\) | ||||
0.257332 | + | 0.966323i | \(0.417157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3271.72 | 0.813008 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −454.000 | + | 504.575i | −0.111493 | + | 0.123913i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3025.57 | − | 5240.44i | −0.734357 | − | 1.27194i | −0.955005 | − | 0.296590i | \(-0.904150\pi\) |
0.220648 | − | 0.975354i | \(-0.429183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1598.53 | − | 3134.29i | 0.383505 | − | 0.751950i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5684.49 | + | 601.501i | −1.34813 | + | 0.142651i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5433.69 | − | 3137.14i | −1.27398 | − | 0.735530i | −0.298242 | − | 0.954490i | \(-0.596400\pi\) |
−0.975734 | + | 0.218960i | \(0.929733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 527.844i | − | 0.122359i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 583.245 | + | 123.758i | 0.133685 | + | 0.0283666i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1668.18 | + | 2889.37i | −0.378106 | + | 0.654899i | −0.990787 | − | 0.135432i | \(-0.956758\pi\) |
0.612681 | + | 0.790331i | \(0.290091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2462.26 | + | 1421.59i | −0.551925 | + | 0.318654i | −0.749898 | − | 0.661553i | \(-0.769897\pi\) |
0.197973 | + | 0.980207i | \(0.436564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 295.091 | − | 1862.70i | 0.0654202 | − | 0.412951i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4350.06 | + | 2511.51i | −0.953886 | + | 0.550726i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3174.17 | + | 5497.82i | −0.688510 | + | 1.19253i | 0.283809 | + | 0.958881i | \(0.408402\pi\) |
−0.972320 | + | 0.233654i | \(0.924932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1096.73 | − | 2467.96i | 0.235339 | − | 0.529580i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3735.88i | − | 0.793110i | −0.918011 | − | 0.396555i | \(-0.870206\pi\) | ||
0.918011 | − | 0.396555i | \(-0.129794\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4777.96 | + | 2758.56i | 1.00361 | + | 0.579432i | 0.909313 | − | 0.416112i | \(-0.136608\pi\) |
0.0942927 | + | 0.995545i | \(0.469941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −249.353 | + | 81.1164i | −0.0518259 | + | 0.0168594i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1882.62 | + | 2901.44i | 0.387205 | + | 0.596748i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3026.48 | − | 5242.01i | −0.616014 | − | 1.06697i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5471.58 | − | 4923.16i | −1.10223 | − | 0.991755i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7574.50 | 1.51026 | 0.755131 | − | 0.655574i | \(-0.227573\pi\) | ||||
0.755131 | + | 0.655574i | \(0.227573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −780.333 | −0.154009 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2327.45 | + | 5212.75i | 0.454721 | + | 1.01843i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −787.855 | − | 1364.61i | −0.152384 | − | 0.263937i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1599.01 | + | 2464.34i | 0.306196 | + | 0.471901i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −387.088 | − | 1189.91i | −0.0733915 | − | 0.225606i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 872.657 | + | 503.829i | 0.163830 | + | 0.0945874i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10635.6i | 1.97723i | 0.150480 | + | 0.988613i | \(0.451918\pi\) | ||||
−0.150480 | + | 0.988613i | \(0.548082\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1196.16 | − | 5637.21i | 0.220217 | − | 1.03783i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2885.59 | − | 4997.99i | 0.526132 | − | 0.911287i | −0.473405 | − | 0.880845i | \(-0.656975\pi\) |
0.999537 | − | 0.0304419i | \(-0.00969146\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2030.41 | + | 1172.26i | −0.366664 | + | 0.211694i | −0.672000 | − | 0.740551i | \(-0.734565\pi\) |
0.305336 | + | 0.952245i | \(0.401231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −582.404 | − | 223.354i | −0.104174 | − | 0.0399509i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6852.10 | + | 3956.06i | −1.21405 | + | 0.700929i | −0.963638 | − | 0.267211i | \(-0.913898\pi\) |
−0.250407 | + | 0.968141i | \(0.580565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4307.36 | + | 7460.56i | −0.756005 | + | 1.30944i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1151.56 | + | 5427.03i | −0.200230 | + | 0.943637i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4236.32i | − | 0.729769i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2095.06 | + | 1209.58i | 0.357579 | + | 0.206448i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.2150 | + | 49.8451i | 0.00274218 | + | 0.00842949i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3012.94 | + | 5907.57i | −0.504889 | + | 0.989953i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2440.02 | − | 4226.23i | −0.405182 | − | 0.701797i | 0.589160 | − | 0.808016i | \(-0.299459\pi\) |
−0.994343 | + | 0.106220i | \(0.966125\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4147.59 | − | 3017.86i | 0.682543 | − | 0.496629i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 372.407 | 0.0607367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4136.39 | −0.668616 | −0.334308 | − | 0.942464i | \(-0.608503\pi\) | ||||
−0.334308 | + | 0.942464i | \(0.608503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3415.77 | − | 3073.41i | −0.547255 | − | 0.492403i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2035.04 | − | 3524.80i | −0.323178 | − | 0.559761i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6275.39 | − | 986.454i | 0.987869 | − | 0.155287i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −495.597 | + | 161.222i | −0.0773393 | + | 0.0251591i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2009.83 | − | 1160.38i | −0.310933 | − | 0.179517i | 0.336411 | − | 0.941715i | \(-0.390787\pi\) |
−0.647344 | + | 0.762198i | \(0.724120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 226.795i | − | 0.0347853i | −0.999849 | − | 0.0173926i | \(-0.994463\pi\) | ||
0.999849 | − | 0.0173926i | \(-0.00553653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1613.73 | − | 2226.03i | 0.245397 | − | 0.338509i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 742.854 | − | 1286.66i | 0.112006 | − | 0.194000i | −0.804573 | − | 0.593854i | \(-0.797606\pi\) |
0.916579 | + | 0.399854i | \(0.130939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 491.949 | − | 284.027i | 0.0735491 | − | 0.0424636i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6342.25 | − | 7831.45i | 0.940245 | − | 1.16102i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9419.94 | + | 5438.60i | −1.38486 | + | 0.799550i | −0.992730 | − | 0.120359i | \(-0.961595\pi\) |
−0.392131 | + | 0.919909i | \(0.628262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2611.22 | + | 4522.77i | −0.380700 | + | 0.659392i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1650.61 | + | 350.241i | 0.238662 | + | 0.0506416i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 625.800i | − | 0.0897421i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3299.69 | + | 1905.08i | 0.469325 | + | 0.270965i | 0.715957 | − | 0.698144i | \(-0.245991\pi\) |
−0.246632 | + | 0.969109i | \(0.579324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 530.587 | + | 5014.32i | 0.0748544 | + | 0.707413i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 407.121 | + | 7826.30i | 0.0569721 | + | 1.09521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4869.55 | + | 8434.30i | 0.675967 | + | 1.17081i | 0.976185 | + | 0.216938i | \(0.0696070\pi\) |
−0.300219 | + | 0.953870i | \(0.597060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1077.11 | − | 1197.10i | 0.148325 | − | 0.164848i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4148.98 | 0.566800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −320.171 | −0.0433933 | −0.0216967 | − | 0.999765i | \(-0.506907\pi\) | ||||
−0.0216967 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2919.92 | − | 3245.19i | 0.392630 | − | 0.436368i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2185.13 | + | 3784.75i | 0.291527 | + | 0.504939i | 0.974171 | − | 0.225812i | \(-0.0725034\pi\) |
−0.682644 | + | 0.730751i | \(0.739170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −788.592 | + | 511.683i | −0.104391 | + | 0.0677346i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 450.654 | + | 4258.92i | 0.0591939 | + | 0.559413i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11877.4 | − | 6857.42i | −1.54809 | − | 0.893791i | −0.998288 | − | 0.0584981i | \(-0.981369\pi\) |
−0.549805 | − | 0.835293i | \(-0.685298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8419.84i | − | 1.08903i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2632.49 | + | 558.587i | 0.337892 | + | 0.0716971i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.6150 | − | 66.8832i | 0.00491882 | − | 0.00851964i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2181.61 | + | 1259.55i | −0.275798 | + | 0.159232i | −0.631520 | − | 0.775360i | \(-0.717568\pi\) |
0.355722 | + | 0.934592i | \(0.384235\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3634.57 | − | 1395.03i | 0.456030 | − | 0.175035i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2268.96 | + | 1309.98i | −0.282560 | + | 0.163136i | −0.634582 | − | 0.772856i | \(-0.718828\pi\) |
0.352022 | + | 0.935992i | \(0.385494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −980.109 | + | 1697.60i | −0.121148 | + | 0.209835i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −609.431 | − | 674.933i | −0.0747725 | − | 0.0828091i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7730.22i | − | 0.941456i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12058.7 | − | 6962.09i | −1.45786 | − | 0.841694i | −0.458952 | − | 0.888461i | \(-0.651775\pi\) |
−0.998906 | + | 0.0467669i | \(0.985108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5425.86 | − | 1765.08i | 0.651187 | − | 0.211836i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11569.9 | − | 601.863i | 1.37850 | − | 0.0717088i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.6041 | + | 78.9886i | 0.00539426 | + | 0.00934313i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3199.36 | − | 2878.69i | −0.375716 | − | 0.338057i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15171.1 | 1.76887 | 0.884433 | − | 0.466666i | \(-0.154545\pi\) | ||||
0.884433 | + | 0.466666i | \(0.154545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1052.53 | −0.121846 | −0.0609228 | − | 0.998142i | \(-0.519404\pi\) | ||||
−0.0609228 | + | 0.998142i | \(0.519404\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7817.47 | + | 5688.11i | −0.898577 | + | 0.653819i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6463.43 | + | 11195.0i | 0.737700 | + | 1.27773i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13327.4 | − | 6797.16i | −1.51044 | − | 0.770345i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1281.81 | − | 3940.30i | −0.144258 | − | 0.443449i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6923.58 | + | 3997.33i | 0.773776 | + | 0.446740i | 0.834220 | − | 0.551432i | \(-0.185918\pi\) |
−0.0604442 | + | 0.998172i | \(0.519252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12889.4i | − | 1.43055i | −0.698845 | − | 0.715273i | \(-0.746303\pi\) | ||
0.698845 | − | 0.715273i | \(-0.253697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 284.838 | − | 1342.38i | 0.0313953 | − | 0.147959i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1626.36 | − | 2816.94i | 0.178030 | − | 0.308358i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12456.7 | + | 7191.89i | −1.35427 | + | 0.781891i | −0.988845 | − | 0.148948i | \(-0.952411\pi\) |
−0.365430 | + | 0.930839i | \(0.619078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8807.53 | + | 2862.44i | 0.951034 | + | 0.309085i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3432.16 | − | 1981.56i | 0.368097 | − | 0.212521i | −0.304530 | − | 0.952503i | \(-0.598499\pi\) |
0.672627 | + | 0.739982i | \(0.265166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −71.5668 | + | 123.957i | −0.00762380 | + | 0.0132048i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 962.710 | − | 4537.03i | 0.101867 | − | 0.480076i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13479.1i | − | 1.41675i | −0.705838 | − | 0.708373i | \(-0.749430\pi\) | ||
0.705838 | − | 0.708373i | \(-0.250570\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6581.00 | + | 3799.54i | 0.687112 | + | 0.396704i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2290.65 | − | 7041.49i | −0.237581 | − | 0.730327i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 403.318 | + | 205.698i | 0.0415557 | + | 0.0211940i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1989.79 | − | 3446.42i | −0.203673 | − | 0.352772i | 0.746036 | − | 0.665905i | \(-0.231955\pi\) |
−0.949709 | + | 0.313134i | \(0.898621\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13415.1 | − | 5989.74i | 1.36419 | − | 0.609101i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9053.72 | 0.914694 | 0.457347 | − | 0.889288i | \(-0.348800\pi\) | ||||
0.457347 | + | 0.889288i | \(0.348800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5736.10 | 0.575764 | 0.287882 | − | 0.957666i | \(-0.407049\pi\) | ||||
0.287882 | + | 0.957666i | \(0.407049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 481.960 | + | 433.652i | 0.0480653 | + | 0.0432476i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6196.30 | − | 10732.3i | −0.613984 | − | 1.06345i | −0.990562 | − | 0.137067i | \(-0.956232\pi\) |
0.376578 | − | 0.926385i | \(-0.377101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5521.65 | + | 287.234i | −0.543638 | + | 0.0282798i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1397.17 | + | 454.509i | −0.136684 | + | 0.0444643i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5589.57 | + | 3227.14i | 0.543359 | + | 0.313709i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4993.85i | 0.482387i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4639.67 | + | 10440.6i | −0.445359 | + | 1.00219i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4133.87 | + | 7160.07i | −0.394324 | + | 0.682989i | −0.993015 | − | 0.117991i | \(-0.962355\pi\) |
0.598691 | + | 0.800980i | \(0.295688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3224.21 | + | 1861.50i | −0.305637 | + | 0.176460i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7223.82 | − | 2772.67i | 0.680529 | − | 0.261202i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1530.24 | − | 883.487i | 0.143268 | − | 0.0827156i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 470.075 | − | 814.194i | 0.0437395 | − | 0.0757590i | −0.843327 | − | 0.537401i | \(-0.819406\pi\) |
0.887066 | + | 0.461642i | \(0.152740\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11772.9 | + | 2498.08i | 1.08873 | + | 0.231017i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1057.30i | − | 0.0971801i | −0.998819 | − | 0.0485900i | \(-0.984527\pi\) | ||
0.998819 | − | 0.0485900i | \(-0.0154728\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19199.9 | + | 11085.1i | 1.75400 | + | 1.01267i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1362.86 | + | 144.210i | −0.123749 | + | 0.0130944i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7075.02 | + | 4590.68i | −0.638547 | + | 0.414326i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3086.65 | − | 5346.23i | −0.276909 | − | 0.479620i | 0.693706 | − | 0.720258i | \(-0.255977\pi\) |
−0.970615 | + | 0.240638i | \(0.922643\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8149.12 | − | 9056.91i | 0.726699 | − | 0.807651i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4284.28 | 0.379775 | 0.189887 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189887 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 300.390 | 0.0264697 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6300.98 | − | 7002.89i | 0.551946 | − | 0.613431i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7550.52 | + | 13077.9i | 0.657507 | + | 1.13884i | 0.981259 | + | 0.192693i | \(0.0617223\pi\) |
−0.323752 | + | 0.946142i | \(0.604944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 482.673 | + | 9278.68i | 0.0417851 | + | 0.803258i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5645.13 | + | 587.315i | 0.485845 | + | 0.0505470i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1198.08 | + | 691.712i | 0.102512 | + | 0.0591854i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14570.1i | 1.23944i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5254.79 | + | 1115.01i | 0.444431 | + | 0.0943037i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6894.00 | + | 11940.8i | −0.579715 | + | 1.00410i | 0.415796 | + | 0.909458i | \(0.363503\pi\) |
−0.995512 | + | 0.0946385i | \(0.969830\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 832.513 | − | 480.652i | 0.0696047 | − | 0.0401863i | −0.464794 | − | 0.885419i | \(-0.653872\pi\) |
0.534398 | + | 0.845233i | \(0.320538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7476.36 | + | 9231.85i | −0.621514 | + | 0.767449i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9071.15 | + | 5237.23i | −0.749802 | + | 0.432898i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2851.06 | + | 4938.17i | −0.234327 | + | 0.405866i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15434.8 | + | 6859.02i | 1.26142 | + | 0.560557i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3659.84i | − | 0.297421i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1153.41 | − | 665.922i | −0.0932080 | − | 0.0538137i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 715.903 | − | 232.889i | 0.0575298 | − | 0.0187149i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11297.7 | − | 8194.92i | 0.902834 | − | 0.654880i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 597.846 | + | 1035.50i | 0.0475109 | + | 0.0822913i | 0.888803 | − | 0.458290i | \(-0.151538\pi\) |
−0.841292 | + | 0.540581i | \(0.818204\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7946.26 | − | 7149.79i | −0.628005 | − | 0.565059i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.5833 | −0.000989006 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18601.8 | −1.45403 | −0.727014 | − | 0.686622i | \(-0.759093\pi\) | ||||
−0.727014 | + | 0.686622i | \(0.759093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12832.3 | − | 17636.1i | −0.997578 | − | 1.37102i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4282.34 | + | 7417.24i | 0.331096 | + | 0.573475i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −520.955 | + | 1021.45i | −0.0400601 | + | 0.0785473i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 380.925 | + | 1170.97i | 0.0291340 | + | 0.0895582i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5908.09 | + | 3411.04i | 0.449432 | + | 0.259480i | 0.707590 | − | 0.706623i | \(-0.249782\pi\) |
−0.258158 | + | 0.966103i | \(0.583116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3108.49i | − | 0.235197i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4595.80 | − | 21658.9i | 0.345873 | − | 1.63002i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5679.80 | − | 9837.71i | 0.425178 | − | 0.736430i | −0.571259 | − | 0.820770i | \(-0.693545\pi\) |
0.996437 | + | 0.0843399i | \(0.0268782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 955.293 | − | 551.539i | 0.0711318 | − | 0.0410680i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9556.55 | + | 9537.12i | 0.707826 | + | 0.706387i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18467.2 | − | 10662.1i | 1.36061 | − | 0.785549i | 0.370905 | − | 0.928671i | \(-0.379047\pi\) |
0.989705 | + | 0.143122i | \(0.0457141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7384.00 | + | 12789.5i | −0.541175 | + | 0.937343i | 0.457662 | + | 0.889126i | \(0.348687\pi\) |
−0.998837 | + | 0.0482163i | \(0.984646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3180.36 | − | 14988.3i | 0.231870 | − | 1.09275i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9925.45i | 0.719861i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16718.5 | + | 9652.44i | 1.20624 | + | 0.696424i | 0.961936 | − | 0.273275i | \(-0.0881068\pi\) |
0.244305 | + | 0.969698i | \(0.421440\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3650.16 | − | 11220.6i | −0.261996 | − | 0.805377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −737.091 | − | 1135.98i | −0.0526328 | − | 0.0811162i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8609.17 | + | 14911.5i | 0.611587 | + | 1.05930i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 388.336 | + | 533.710i | 0.0274457 | + | 0.0377200i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4397.46 | −0.309204 | −0.154602 | − | 0.987977i | \(-0.549410\pi\) | ||||
−0.154602 | + | 0.987977i | \(0.549410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4046.45 | −0.283075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1915.32 | − | 1723.35i | −0.133310 | − | 0.119948i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10970.1 | − | 19000.8i | −0.759677 | − | 1.31580i | −0.943015 | − | 0.332749i | \(-0.892024\pi\) |
0.183339 | − | 0.983050i | \(-0.441309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1316.83 | + | 2029.46i | 0.0907307 | + | 0.139832i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4149.21 | + | 1349.77i | −0.284449 | + | 0.0925335i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4765.07 | + | 2751.12i | 0.325034 | + | 0.187659i | 0.653634 | − | 0.756810i | \(-0.273243\pi\) |
−0.328600 | + | 0.944469i | \(0.606577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5814.58i | − | 0.394645i | −0.980339 | − | 0.197322i | \(-0.936775\pi\) | ||
0.980339 | − | 0.197322i | \(-0.0632246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7366.11 | − | 3273.41i | −0.497465 | − | 0.221067i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −202.537 | + | 350.804i | −0.0136104 | + | 0.0235739i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11510.7 | − | 6645.69i | 0.769693 | − | 0.444382i | −0.0630721 | − | 0.998009i | \(-0.520090\pi\) |
0.832765 | + | 0.553627i | \(0.186756\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3187.91 | + | 20123.0i | −0.212119 | + | 1.33896i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6077.05 | − | 3508.59i | 0.402375 | − | 0.232311i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9797.17 | + | 16969.2i | −0.645520 | + | 1.11807i | 0.338661 | + | 0.940909i | \(0.390026\pi\) |
−0.984181 | + | 0.177166i | \(0.943307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1184.12 | − | 251.257i | −0.0776394 | − | 0.0164743i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 348.388i | 0.0227319i | 0.999935 | + | 0.0113660i | \(0.00361797\pi\) | ||||
−0.999935 | + | 0.0113660i | \(0.996382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5867.68 | − | 3387.71i | −0.381005 | − | 0.219973i | 0.297251 | − | 0.954799i | \(-0.403930\pi\) |
−0.678255 | + | 0.734826i | \(0.737264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11219.9 | + | 1167.31i | 0.725022 | + | 0.0754307i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 965.508 | − | 1893.10i | 0.0620903 | − | 0.121742i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7521.95 | − | 13028.4i | −0.481405 | − | 0.833818i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5721.16 | − | 6358.48i | 0.364404 | − | 0.404997i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19893.9 | −1.26108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7326.82 | 0.462244 | 0.231122 | − | 0.972925i | \(-0.425760\pi\) | ||||
0.231122 | + | 0.972925i | \(0.425760\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13908.2 | + | 15457.5i | −0.873301 | + | 0.970584i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 523.995 | + | 907.586i | 0.0327466 | + | 0.0567188i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6138.62 | − | 2738.79i | −0.381822 | − | 0.170353i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12227.2 | + | 1293.81i | −0.756963 | + | 0.0800975i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2433.38 | − | 1404.91i | −0.149942 | − | 0.0865689i | 0.423152 | − | 0.906059i | \(-0.360924\pi\) |
−0.573094 | + | 0.819490i | \(0.694257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27485.5i | − | 1.68573i | −0.538128 | − | 0.842863i | \(-0.680868\pi\) | ||
0.538128 | − | 0.842863i | \(-0.319132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1005.73 | − | 213.405i | −0.0613962 | − | 0.0130276i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14659.9 | + | 25391.7i | −0.890790 | + | 1.54289i | −0.0518595 | + | 0.998654i | \(0.516515\pi\) |
−0.838930 | + | 0.544239i | \(0.816819\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22044.3 | − | 12727.3i | 1.33330 | − | 0.769783i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7480.44 | − | 6057.99i | −0.450356 | − | 0.364718i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14500.6 | + | 8371.91i | −0.868992 | + | 0.501713i | −0.867013 | − | 0.498285i | \(-0.833963\pi\) |
−0.00197863 | + | 0.999998i | \(0.500630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −323.019 | + | 559.485i | −0.0192693 | + | 0.0333754i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5500.69 | + | 12378.1i | −0.326640 | + | 0.735034i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9520.47i | − | 0.562769i | −0.959595 | − | 0.281385i | \(-0.909206\pi\) | ||
0.959595 | − | 0.281385i | \(-0.0907937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20217.5 | − | 11672.6i | −1.18966 | − | 0.686853i | −0.231434 | − | 0.972851i | \(-0.574342\pi\) |
−0.958230 | + | 0.285998i | \(0.907675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10140.5 | + | 3298.77i | −0.594002 | + | 0.193233i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 48.5515 | + | 933.331i | 0.00283120 | + | 0.0544256i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8511.31 | + | 14742.0i | 0.494092 | + | 0.855792i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11744.7 | − | 10567.5i | −0.678740 | − | 0.610709i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32869.9 | −1.89110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12283.5 | −0.703559 | −0.351780 | − | 0.936083i | \(-0.614423\pi\) | ||||
−0.351780 | + | 0.936083i | \(0.614423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15814.0 | + | 7060.82i | −0.901750 | + | 0.402624i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6495.88 | − | 11251.2i | −0.368769 | − | 0.638727i | 0.620604 | − | 0.784124i | \(-0.286887\pi\) |
−0.989373 | + | 0.145397i | \(0.953554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22007.4 | + | 14279.6i | −1.24384 | + | 0.807072i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7067.05 | + | 21724.2i | 0.397665 | + | 1.22243i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7366.62 | − | 4253.12i | −0.412703 | − | 0.238274i | 0.279248 | − | 0.960219i | \(-0.409915\pi\) |
−0.691950 | + | 0.721945i | \(0.743248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1369.74i | 0.0764018i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2139.38 | + | 10082.4i | −0.118810 | + | 0.559923i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4146.31 | − | 7181.62i | 0.229263 | − | 0.397095i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22372.0 | − | 12916.5i | 1.23165 | − | 0.711093i | 0.264276 | − | 0.964447i | \(-0.414867\pi\) |
0.967374 | + | 0.253354i | \(0.0815336\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20095.7 | − | 3189.34i | 1.10155 | − | 0.174824i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 894.770 | − | 516.595i | 0.0488353 | − | 0.0281951i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9778.22 | − | 16936.4i | 0.531387 | − | 0.920389i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4717.33 | + | 22231.7i | −0.255259 | + | 1.20298i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22607.8i | 1.21810i | 0.793134 | + | 0.609048i | \(0.208448\pi\) | ||||
−0.793134 | + | 0.609048i | \(0.791552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6655.69 | − | 3842.67i | −0.357076 | − | 0.206158i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −717.975 | − | 2207.06i | −0.0383553 | − | 0.117905i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4453.86 | + | 231.688i | −0.236923 | + | 0.0123246i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5472.41 | + | 9478.50i | 0.289874 | + | 0.502077i | 0.973779 | − | 0.227494i | \(-0.0730532\pi\) |
−0.683905 | + | 0.729571i | \(0.739720\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1351.69 | + | 983.509i | −0.0712971 | + | 0.0518769i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8042.46 | −0.422430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 994.720 | 0.0520285 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14780.3 | − | 13298.9i | −0.769849 | − | 0.692685i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12885.3 | − | 22317.9i | −0.668344 | − | 1.15761i | −0.978367 | − | 0.206877i | \(-0.933670\pi\) |
0.310023 | − | 0.950729i | \(-0.399663\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18297.3 | − | 9331.88i | −0.945116 | − | 0.482021i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16997.4 | − | 5529.40i | 0.874330 | − | 0.284427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22633.2 | − | 13067.3i | −1.15942 | − | 0.669389i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15593.1i | − | 0.795485i | −0.917497 | − | 0.397742i | \(-0.869794\pi\) | ||
0.917497 | − | 0.397742i | \(-0.130206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6121.81 | + | 18706.8i | 0.311020 | + | 0.950403i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8305.13 | − | 14384.9i | 0.420214 | − | 0.727832i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 692.858 | − | 400.022i | 0.0349131 | − | 0.0201571i | −0.482442 | − | 0.875928i | \(-0.660250\pi\) |
0.517355 | + | 0.855771i | \(0.326917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1307.55 | + | 1798.08i | −0.0656185 | + | 0.0902358i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10520.5 | + | 6073.99i | −0.525815 | + | 0.303580i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −454.445 | + | 787.122i | −0.0226211 | + | 0.0391810i | −0.877114 | − | 0.480282i | \(-0.840534\pi\) |
0.854493 | + | 0.519463i | \(0.173868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4029.77 | − | 855.076i | −0.199781 | − | 0.0423914i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8109.00i | − | 0.400391i | −0.979756 | − | 0.200195i | \(-0.935842\pi\) | ||
0.979756 | − | 0.200195i | \(-0.0641577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 964.258 | + | 556.715i | 0.0474197 | + | 0.0273778i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −207.737 | − | 1963.22i | −0.0101750 | − | 0.0961588i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17615.1 | + | 8983.95i | 0.859337 | + | 0.438273i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10382.2 | − | 17982.5i | −0.504463 | − | 0.873756i | −0.999987 | − | 0.00516122i | \(-0.998357\pi\) |
0.495524 | − | 0.868594i | \(-0.334976\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7113.09 | − | 7905.46i | 0.344243 | − | 0.382591i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1777.61 | 0.0856870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23295.6 | 1.11848 | 0.559242 | − | 0.829005i | \(-0.311092\pi\) | ||||
0.559242 | + | 0.829005i | \(0.311092\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11371.0 | − | 12637.7i | 0.543796 | − | 0.604374i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5014.38 | + | 8685.16i | 0.238858 | + | 0.413715i | 0.960387 | − | 0.278670i | \(-0.0898935\pi\) |
−0.721529 | + | 0.692385i | \(0.756560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 186.571 | − | 9.70535i | 0.00885233 | − | 0.000460494i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 371.128 | + | 3507.35i | 0.0175401 | + | 0.165763i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10616.9 | − | 6129.66i | −0.499809 | − | 0.288565i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13500.3i | − | 0.633074i | −0.948580 | − | 0.316537i | \(-0.897480\pi\) | ||
0.948580 | − | 0.316537i | \(-0.102520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30757.8 | − | 6526.49i | −1.43673 | − | 0.304858i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11644.9 | − | 20169.5i | 0.541833 | − | 0.938482i | −0.456966 | − | 0.889484i | \(-0.651064\pi\) |
0.998799 | − | 0.0489979i | \(-0.0156028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10693.2 | − | 6173.74i | 0.495629 | − | 0.286151i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6551.10 | − | 17068.0i | −0.302470 | − | 0.788046i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6542.79 | − | 3777.48i | 0.300924 | − | 0.173739i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9264.99 | + | 16047.4i | −0.424491 | + | 0.735240i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17433.3 | + | 24048.1i | −0.795677 | + | 1.09759i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 352.711i | − | 0.0160367i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20635.4 | + | 11913.8i | 0.934653 | + | 0.539622i | 0.888280 | − | 0.459302i | \(-0.151901\pi\) |
0.0463726 | + | 0.998924i | \(0.485234\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31002.9 | + | 10085.5i | −1.39890 | + | 0.455074i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13738.7 | + | 8914.42i | −0.617560 | + | 0.400709i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7915.34 | + | 13709.8i | 0.354454 | + | 0.613932i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2038.91 | − | 1834.55i | −0.0909594 | − | 0.0818424i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12609.3 | −0.560406 | −0.280203 | − | 0.959941i | \(-0.590402\pi\) | ||||
−0.280203 | + | 0.959941i | \(0.590402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37496.4 | 1.66023 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2505.14 | − | 1822.78i | 0.110505 | − | 0.0804054i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10206.8 | + | 17678.8i | 0.448557 | + | 0.776924i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 96.4977 | + | 1855.03i | 0.00422497 | + | 0.0812188i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5362.97 | + | 16485.8i | 0.233935 | + | 0.719118i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30281.4 | + | 17483.0i | 1.31599 | + | 0.759789i | 0.983082 | − | 0.183169i | \(-0.0586354\pi\) |
0.332912 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5691.42i | − | 0.246428i | −0.992380 | − | 0.123214i | \(-0.960680\pi\) | ||
0.992380 | − | 0.123214i | \(-0.0393201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3066.52 | + | 14451.8i | −0.132285 | + | 0.623428i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1444.59 | + | 2502.10i | −0.0620879 | + | 0.107539i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5557.12 | − | 3208.40i | 0.237967 | − | 0.137390i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6169.47 | − | 7613.75i | −0.263222 | − | 0.324842i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10487.0 | − | 6054.70i | 0.445798 | − | 0.257382i | −0.260256 | − | 0.965540i | \(-0.583807\pi\) |
0.706054 | + | 0.708158i | \(0.250474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15861.0 | + | 27472.0i | −0.671784 | + | 1.16356i | 0.305614 | + | 0.952155i | \(0.401138\pi\) |
−0.977398 | + | 0.211408i | \(0.932195\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5417.61 | + | 25531.9i | −0.228627 | + | 1.07746i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36401.9i | 1.53061i | 0.643666 | + | 0.765307i | \(0.277413\pi\) | ||||
−0.643666 | + | 0.765307i | \(0.722587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27287.8 | + | 15754.6i | 1.14324 | + | 0.660049i | 0.947230 | − | 0.320554i | \(-0.103869\pi\) |
0.196007 | + | 0.980602i | \(0.437202\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10204.5 | + | 31368.9i | 0.425983 | + | 1.30948i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21089.8 | − | 29075.0i | −0.877214 | − | 1.20935i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1462.40 | + | 2532.96i | 0.0606090 | + | 0.104978i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5721.28 | − | 12813.9i | −0.236268 | − | 0.529166i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13781.4 | 0.567090 | 0.283545 | − | 0.958959i | \(-0.408490\pi\) | ||||
0.283545 | + | 0.958959i | \(0.408490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20433.0 | −0.837796 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14430.6 | − | 12984.2i | −0.589582 | − | 0.530487i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1130.74 | + | 1958.51i | 0.0460341 | + | 0.0797334i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2732.43 | − | 5357.56i | 0.110847 | − | 0.217341i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27261.6 | − | 8868.40i | 1.10202 | − | 0.358496i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13228.4 | − | 7637.43i | −0.532860 | − | 0.307647i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 11376.3i | − | 0.456645i | −0.973586 | − | 0.228322i | \(-0.926676\pi\) | ||
0.973586 | − | 0.228322i | \(-0.0733240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −553.308 | + | 1245.10i | −0.0221318 | + | 0.0498030i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21559.6 | + | 37342.3i | −0.859349 | + | 1.48844i | 0.0132022 | + | 0.999913i | \(0.495797\pi\) |
−0.872551 | + | 0.488523i | \(0.837536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32325.9 | + | 18663.4i | −1.28399 | + | 0.741311i | −0.977575 | − | 0.210588i | \(-0.932462\pi\) |
−0.306413 | + | 0.951899i | \(0.599129\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17750.6 | + | 2812.07i | 0.702600 | + | 0.111307i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30262.7 | − | 17472.2i | 1.19369 | − | 0.689176i | 0.234547 | − | 0.972105i | \(-0.424639\pi\) |
0.959141 | + | 0.282929i | \(0.0913060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −644.788 | + | 1116.80i | −0.0253450 | + | 0.0438988i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30767.1 | − | 6528.45i | −1.20520 | − | 0.255730i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2519.25i | 0.0983426i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5066.82 | + | 2925.33i | 0.197110 | + | 0.113801i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38033.5 | + | 4024.49i | −1.47450 | + | 0.156023i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3124.17 | − | 4814.88i | −0.120704 | − | 0.186026i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2054.59 | − | 3558.66i | −0.0791092 | − | 0.137021i | 0.823757 | − | 0.566944i | \(-0.191874\pi\) |
−0.902866 | + | 0.429922i | \(0.858541\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26325.5 | − | 29258.1i | 1.01017 | − | 1.12270i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15697.6 | 0.600301 | 0.300151 | − | 0.953892i | \(-0.402963\pi\) | ||||
0.300151 | + | 0.953892i | \(0.402963\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44102.6 | 1.68083 | 0.840413 | − | 0.541946i | \(-0.182312\pi\) | ||||
0.840413 | + | 0.541946i | \(0.182312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2712.09 | + | 3014.20i | −0.103012 | + | 0.114487i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14164.5 | + | 24533.5i | 0.536185 | + | 0.928699i | 0.999105 | + | 0.0422991i | \(0.0134682\pi\) |
−0.462920 | + | 0.886400i | \(0.653198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8469.24 | − | 13052.5i | −0.319515 | − | 0.492428i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28224.5 | + | 9126.89i | 1.06123 | + | 0.343168i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12544.8 | + | 7242.73i | 0.470095 | + | 0.271409i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 180.728i | 0.00674979i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8009.31 | − | 1699.49i | −0.298131 | − | 0.0632602i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10588.3 | − | 18339.4i | 0.392812 | − | 0.680370i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38375.1 | − | 22155.9i | 1.41894 | − | 0.819223i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15076.5 | + | 2388.43i | 0.555607 | + | 0.0880201i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2222.34 | − | 1283.07i | 0.0816277 | − | 0.0471278i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7102.79 | − | 12302.4i | 0.260027 | − | 0.450380i | −0.706222 | − | 0.707991i | \(-0.749602\pi\) |
0.966249 | + | 0.257611i | \(0.0829353\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5941.64 | − | 2640.39i | −0.216800 | − | 0.0963434i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17955.9i | 0.653025i | 0.945193 | + | 0.326512i | \(0.105873\pi\) | ||||
−0.945193 | + | 0.326512i | \(0.894127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2576.62 | − | 1487.61i | −0.0933993 | − | 0.0539241i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4979.11 | − | 1619.74i | 0.179895 | − | 0.0585214i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4357.84 | − | 8544.57i | 0.156934 | − | 0.307706i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21121.3 | − | 36583.1i | −0.758135 | − | 1.31313i | −0.943800 | − | 0.330516i | \(-0.892777\pi\) |
0.185665 | − | 0.982613i | \(-0.440556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41082.5 | + | 36964.7i | 1.46983 | + | 1.32251i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8924.34 | 0.318254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23451.3 | 0.833593 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17617.6 | − | 24212.8i | −0.624206 | − | 0.857878i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22338.1 | − | 38690.6i | −0.788900 | − | 1.36641i | −0.926642 | − | 0.375946i | \(-0.877318\pi\) |
0.137742 | − | 0.990468i | \(-0.456016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1439.74 | − | 13801.0i | −0.0506826 | − | 0.485831i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9276.80 | − | 28517.0i | −0.325519 | − | 1.00065i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4603.19 | + | 2657.65i | 0.161006 | + | 0.0929566i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15309.3i | − | 0.533761i | −0.963730 | − | 0.266880i | \(-0.914007\pi\) | ||
0.963730 | − | 0.266880i | \(-0.0859929\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2528.70 | + | 11917.2i | −0.0878817 | + | 0.414166i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21192.2 | − | 36706.0i | 0.734162 | − | 1.27161i | −0.220928 | − | 0.975290i | \(-0.570909\pi\) |
0.955090 | − | 0.296316i | \(-0.0957582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13004.0 | − | 7507.87i | 0.449066 | − | 0.259268i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2886.93 | + | 1473.39i | −0.0993775 | + | 0.0507188i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10648.1 | + | 6147.69i | −0.365383 | + | 0.210954i | −0.671439 | − | 0.741060i | \(-0.734324\pi\) |
0.306057 | + | 0.952013i | \(0.400990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4915.78 | − | 8514.37i | 0.168148 | − | 0.291242i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8533.67 | + | 40217.2i | −0.290981 | + | 1.37133i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1322.78i | 0.0449621i | 0.999747 | + | 0.0224811i | \(0.00715655\pi\) | ||||
−0.999747 | + | 0.0224811i | \(0.992843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3185.47 | + | 1839.13i | 0.107936 | + | 0.0623171i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13847.6 | + | 42567.6i | 0.467742 | + | 1.43784i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1056.47 | − | 20309.1i | −0.0355737 | − | 0.683852i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9893.00 | − | 17135.2i | −0.332080 | − | 0.575180i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16960.8 | + | 23310.1i | 0.567553 | + | 0.780017i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2832.62 | 0.0944925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36887.2 | −1.22669 | −0.613346 | − | 0.789814i | \(-0.710177\pi\) | ||||
−0.613346 | + | 0.789814i | \(0.710177\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16363.7 | − | 14723.5i | −0.542495 | − | 0.488120i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3409.79 | − | 5905.93i | −0.112693 | − | 0.195191i | 0.804162 | − | 0.594410i | \(-0.202614\pi\) |
−0.916855 | + | 0.399220i | \(0.869281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12868.2 | + | 8349.64i | −0.423984 | + | 0.275105i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11953.8 | − | 3888.65i | 0.392643 | − | 0.127730i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42700.8 | + | 24653.3i | 1.39828 | + | 0.807298i | 0.994213 | − | 0.107431i | \(-0.0342624\pi\) |
0.404068 | + | 0.914729i | \(0.367596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4669.03i | − | 0.152424i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 248.894 | + | 110.605i | 0.00810047 | + | 0.00359975i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9765.55 | − | 16914.4i | 0.316859 | − | 0.548816i | −0.662972 | − | 0.748644i | \(-0.730705\pi\) |
0.979831 | + | 0.199828i | \(0.0640384\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 535.661 | − | 309.264i | 0.0173275 | − | 0.0100040i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12347.6 | + | 32170.1i | 0.398206 | + | 1.03747i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11045.0 | − | 6376.81i | 0.355116 | − | 0.205026i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9285.39 | − | 16082.8i | 0.297639 | − | 0.515526i | −0.677956 | − | 0.735102i | \(-0.737134\pi\) |
0.975595 | + | 0.219576i | \(0.0704675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24805.1 | − | 5263.39i | −0.792716 | − | 0.168206i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1047.46i | − | 0.0333735i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19389.3 | + | 11194.4i | 0.615913 | + | 0.355598i | 0.775276 | − | 0.631622i | \(-0.217611\pi\) |
−0.159363 | + | 0.987220i | \(0.550944\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2758.05 | − | 26509.7i | 0.0873481 | − | 0.839569i |
(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 | 336.4.bc.d.17.5 | 12 | ||
3.2 | odd | 2 | inner | 336.4.bc.d.17.3 | 12 | ||
4.3 | odd | 2 | 21.4.g.a.17.3 | yes | 12 | ||
7.5 | odd | 6 | inner | 336.4.bc.d.257.3 | 12 | ||
12.11 | even | 2 | 21.4.g.a.17.4 | yes | 12 | ||
21.5 | even | 6 | inner | 336.4.bc.d.257.5 | 12 | ||
28.3 | even | 6 | 147.4.c.a.146.5 | 12 | |||
28.11 | odd | 6 | 147.4.c.a.146.6 | 12 | |||
28.19 | even | 6 | 21.4.g.a.5.4 | yes | 12 | ||
28.23 | odd | 6 | 147.4.g.d.68.4 | 12 | |||
28.27 | even | 2 | 147.4.g.d.80.3 | 12 | |||
84.11 | even | 6 | 147.4.c.a.146.7 | 12 | |||
84.23 | even | 6 | 147.4.g.d.68.3 | 12 | |||
84.47 | odd | 6 | 21.4.g.a.5.3 | ✓ | 12 | ||
84.59 | odd | 6 | 147.4.c.a.146.8 | 12 | |||
84.83 | odd | 2 | 147.4.g.d.80.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.g.a.5.3 | ✓ | 12 | 84.47 | odd | 6 | ||
21.4.g.a.5.4 | yes | 12 | 28.19 | even | 6 | ||
21.4.g.a.17.3 | yes | 12 | 4.3 | odd | 2 | ||
21.4.g.a.17.4 | yes | 12 | 12.11 | even | 2 | ||
147.4.c.a.146.5 | 12 | 28.3 | even | 6 | |||
147.4.c.a.146.6 | 12 | 28.11 | odd | 6 | |||
147.4.c.a.146.7 | 12 | 84.11 | even | 6 | |||
147.4.c.a.146.8 | 12 | 84.59 | odd | 6 | |||
147.4.g.d.68.3 | 12 | 84.23 | even | 6 | |||
147.4.g.d.68.4 | 12 | 28.23 | odd | 6 | |||
147.4.g.d.80.3 | 12 | 28.27 | even | 2 | |||
147.4.g.d.80.4 | 12 | 84.83 | odd | 2 | |||
336.4.bc.d.17.3 | 12 | 3.2 | odd | 2 | inner | ||
336.4.bc.d.17.5 | 12 | 1.1 | even | 1 | trivial | ||
336.4.bc.d.257.3 | 12 | 7.5 | odd | 6 | inner | ||
336.4.bc.d.257.5 | 12 | 21.5 | even | 6 | inner |