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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{11} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(2.99617 - 0.151487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.e.17.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −5.18952 | + | 0.262384i | −0.998724 | + | 0.0504958i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.24534 | + | 3.88904i | −0.200829 | + | 0.347846i | −0.948796 | − | 0.315890i | \(-0.897697\pi\) |
0.747967 | + | 0.663736i | \(0.231030\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.71288 | + | 15.7690i | 0.524446 | + | 0.851443i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.8623 | − | 2.72329i | 0.994900 | − | 0.100863i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.2835 | − | 11.7107i | 0.555974 | − | 0.320992i | −0.195554 | − | 0.980693i | \(-0.562650\pi\) |
0.751528 | + | 0.659701i | \(0.229317\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.91384i | 0.126170i | 0.998008 | + | 0.0630848i | \(0.0200939\pi\) | ||||
−0.998008 | + | 0.0630848i | \(0.979906\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.6318 | − | 20.7714i | 0.183008 | − | 0.357544i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −58.0418 | − | 100.531i | −0.828071 | − | 1.43426i | −0.899549 | − | 0.436819i | \(-0.856105\pi\) |
0.0714778 | − | 0.997442i | \(-0.477228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.02533 | − | 4.63343i | −0.0969019 | − | 0.0559464i | 0.450766 | − | 0.892642i | \(-0.351151\pi\) |
−0.547668 | + | 0.836696i | \(0.684484\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −54.5428 | − | 79.2849i | −0.566772 | − | 0.823875i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 107.721 | + | 62.1928i | 0.976583 | + | 0.563830i | 0.901237 | − | 0.433327i | \(-0.142661\pi\) |
0.0753461 | + | 0.997157i | \(0.475994\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.4169 | + | 90.7888i | 0.419335 | + | 0.726310i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −138.688 | + | 21.1808i | −0.988538 | + | 0.150972i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 207.807i | 1.33065i | 0.746555 | + | 0.665324i | \(0.231707\pi\) | ||||
−0.746555 | + | 0.665324i | \(0.768293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −122.764 | + | 70.8780i | −0.711262 | + | 0.410647i | −0.811528 | − | 0.584314i | \(-0.801364\pi\) |
0.100266 | + | 0.994961i | \(0.468030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −102.189 | + | 66.0951i | −0.539056 | + | 0.348657i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −83.1348 | + | 2.36716i | −0.401496 | + | 0.0114321i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −149.838 | + | 259.526i | −0.665761 | + | 1.15313i | 0.313317 | + | 0.949648i | \(0.398560\pi\) |
−0.979078 | + | 0.203483i | \(0.934774\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.55170 | − | 30.6900i | −0.00637103 | − | 0.126009i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 508.379 | 1.93647 | 0.968237 | − | 0.250032i | \(-0.0804412\pi\) | ||||
0.968237 | + | 0.250032i | \(0.0804412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −391.127 | −1.38712 | −0.693562 | − | 0.720397i | \(-0.743959\pi\) | ||||
−0.693562 | + | 0.720397i | \(0.743959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −49.7240 | + | 110.583i | −0.164720 | + | 0.366329i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −40.2575 | + | 69.7281i | −0.124940 | + | 0.216402i | −0.921709 | − | 0.387881i | \(-0.873207\pi\) |
0.796770 | + | 0.604283i | \(0.206540\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −154.320 | + | 306.324i | −0.449912 | + | 0.893073i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 327.587 | + | 506.481i | 0.899439 | + | 1.39062i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −258.697 | + | 149.359i | −0.670467 | + | 0.387094i | −0.796254 | − | 0.604963i | \(-0.793188\pi\) |
0.125786 | + | 0.992057i | \(0.459855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 105.178i | 0.257858i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 42.8634 | + | 21.9396i | 0.0996034 | + | 0.0509818i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 102.276 | + | 177.147i | 0.225682 | + | 0.390892i | 0.956524 | − | 0.291655i | \(-0.0942058\pi\) |
−0.730842 | + | 0.682547i | \(0.760872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −543.757 | − | 313.939i | −1.14133 | − | 0.658946i | −0.194569 | − | 0.980889i | \(-0.562331\pi\) |
−0.946759 | + | 0.321943i | \(0.895664\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 303.854 | + | 397.139i | 0.607651 | + | 0.794204i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.9992 | − | 13.2786i | −0.0438876 | − | 0.0253385i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −51.3894 | − | 89.0091i | −0.0937048 | − | 0.162301i | 0.815363 | − | 0.578951i | \(-0.196538\pi\) |
−0.909067 | + | 0.416649i | \(0.863204\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −575.340 | − | 294.487i | −1.00381 | − | 0.513798i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 46.9785i | − | 0.0785256i | −0.999229 | − | 0.0392628i | \(-0.987499\pi\) | ||
0.999229 | − | 0.0392628i | \(-0.0125010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −228.182 | + | 131.741i | −0.365845 | + | 0.211221i | −0.671642 | − | 0.740876i | \(-0.734411\pi\) |
0.305797 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −295.840 | − | 457.397i | −0.455476 | − | 0.704209i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 381.677 | + | 206.105i | 0.564885 | + | 0.305038i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −533.634 | + | 924.281i | −0.759981 | + | 1.31633i | 0.182878 | + | 0.983136i | \(0.441459\pi\) |
−0.942860 | + | 0.333190i | \(0.891875\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 714.167 | − | 146.308i | 0.979653 | − | 0.200697i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −270.436 | −0.357642 | −0.178821 | − | 0.983882i | \(-0.557228\pi\) | ||||
−0.178821 | + | 0.983882i | \(0.557228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 521.294 | 0.665203 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.5252 | − | 1078.42i | −0.0671921 | − | 1.32895i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −443.765 | + | 768.624i | −0.528528 | + | 0.915438i | 0.470918 | + | 0.882177i | \(0.343923\pi\) |
−0.999447 | + | 0.0332610i | \(0.989411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −93.2551 | + | 57.4405i | −0.107426 | + | 0.0661692i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 618.491 | − | 400.034i | 0.689618 | − | 0.446039i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 36.0392 | − | 20.8072i | 0.0389215 | − | 0.0224713i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 219.564i | 0.229828i | 0.993375 | + | 0.114914i | \(0.0366593\pi\) | ||||
−0.993375 | + | 0.114914i | \(0.963341\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 512.971 | − | 369.815i | 0.520763 | − | 0.375432i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −492.533 | − | 853.093i | −0.485237 | − | 0.840455i | 0.514619 | − | 0.857419i | \(-0.327933\pi\) |
−0.999856 | + | 0.0169642i | \(0.994600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1112.87 | + | 642.516i | 1.06461 | + | 0.614650i | 0.926703 | − | 0.375796i | \(-0.122631\pi\) |
0.137903 | + | 0.990446i | \(0.455964\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 430.809 | − | 34.0976i | 0.400406 | − | 0.0316913i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 158.409 | + | 91.4575i | 0.143121 | + | 0.0826311i | 0.569851 | − | 0.821748i | \(-0.307001\pi\) |
−0.426729 | + | 0.904379i | \(0.640334\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 291.471 | + | 504.843i | 0.256127 | + | 0.443625i | 0.965201 | − | 0.261509i | \(-0.0842201\pi\) |
−0.709074 | + | 0.705134i | \(0.750887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 709.490 | − | 1386.13i | 0.606683 | − | 1.18528i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2283.94i | − | 1.90137i | −0.310152 | − | 0.950687i | \(-0.600380\pi\) | ||
0.310152 | − | 0.950687i | \(-0.399620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −483.741 | + | 279.288i | −0.392253 | + | 0.226467i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.1051 | + | 158.859i | 0.0127258 | + | 0.125526i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1021.52 | − | 1891.71i | 0.786914 | − | 1.45725i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −391.219 | + | 677.611i | −0.293928 | + | 0.509099i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2638.25 | + | 133.390i | −1.93400 | + | 0.0977838i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1032.11 | −0.738517 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1554.48 | 1.08613 | 0.543064 | − | 0.839692i | \(-0.317264\pi\) | ||||
0.543064 | + | 0.839692i | \(0.317264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2029.76 | − | 102.625i | 1.38535 | − | 0.0700439i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1047.46 | + | 1814.26i | −0.698605 | + | 1.21002i | 0.270345 | + | 0.962763i | \(0.412862\pi\) |
−0.968950 | + | 0.247256i | \(0.920471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.88481 | − | 171.555i | −0.00318471 | − | 0.111847i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 229.028 | − | 586.921i | 0.146012 | − | 0.374179i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −529.002 | + | 305.420i | −0.329896 | + | 0.190465i | −0.655795 | − | 0.754939i | \(-0.727666\pi\) |
0.325899 | + | 0.945405i | \(0.394333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1806.61i | − | 1.10241i | −0.834370 | − | 0.551204i | \(-0.814169\pi\) | ||
0.834370 | − | 0.551204i | \(-0.185831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 190.622 | − | 372.419i | 0.113853 | − | 0.222435i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 69.2553 | + | 119.954i | 0.0404994 | + | 0.0701470i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −808.170 | − | 466.597i | −0.462861 | − | 0.267233i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 720.472 | − | 1630.17i | 0.404242 | − | 0.914652i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2341.75 | + | 1352.01i | 1.28754 | + | 0.743363i | 0.978215 | − | 0.207592i | \(-0.0665627\pi\) |
0.309328 | + | 0.950956i | \(0.399896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 770.352 | + | 1334.29i | 0.415168 | + | 0.719092i | 0.995446 | − | 0.0953266i | \(-0.0303895\pi\) |
−0.580278 | + | 0.814418i | \(0.697056\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1832.91 | − | 2542.44i | −0.968512 | − | 1.34343i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 636.580i | − | 0.329880i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 477.498 | − | 275.684i | 0.242729 | − | 0.140140i | −0.373701 | − | 0.927549i | \(-0.621911\pi\) |
0.616430 | + | 0.787409i | \(0.288578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1303.32 | − | 842.979i | 0.650065 | − | 0.420456i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 65.5670 | + | 2302.72i | 0.0320957 | + | 1.12720i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1155.82 | + | 2001.94i | −0.555403 | + | 0.961986i | 0.442469 | + | 0.896784i | \(0.354103\pi\) |
−0.997872 | + | 0.0652023i | \(0.979231\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.5970 | − | 545.824i | −0.0130207 | − | 0.257529i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2580.87 | −1.19589 | −0.597944 | − | 0.801538i | \(-0.704016\pi\) | ||||
−0.597944 | + | 0.801538i | \(0.704016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2162.03 | 0.984081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −228.197 | − | 102.609i | −0.102051 | − | 0.0458873i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 501.050 | − | 867.845i | 0.220197 | − | 0.381393i | −0.734670 | − | 0.678424i | \(-0.762663\pi\) |
0.954868 | + | 0.297031i | \(0.0959965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −922.524 | + | 1708.38i | −0.398493 | + | 0.737951i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −577.245 | − | 892.475i | −0.245132 | − | 0.378997i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2598.36 | − | 1500.17i | 1.08498 | − | 0.626411i | 0.152742 | − | 0.988266i | \(-0.451190\pi\) |
0.932234 | + | 0.361855i | \(0.117856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 967.850i | 0.397457i | 0.980055 | + | 0.198729i | \(0.0636812\pi\) | ||||
−0.980055 | + | 0.198729i | \(0.936319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2904.21 | + | 1486.52i | 1.17315 | + | 0.600473i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −672.872 | − | 1165.45i | −0.267408 | − | 0.463165i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2354.59 | − | 1359.42i | −0.920773 | − | 0.531608i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1681.06 | − | 1981.24i | −0.646980 | − | 0.762507i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 356.214 | + | 205.660i | 0.134946 | + | 0.0779113i | 0.565953 | − | 0.824437i | \(-0.308508\pi\) |
−0.431007 | + | 0.902349i | \(0.641842\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −408.212 | − | 707.043i | −0.152247 | − | 0.263700i | 0.779806 | − | 0.626021i | \(-0.215318\pi\) |
−0.932053 | + | 0.362321i | \(0.881984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 122.839 | + | 62.8749i | 0.0451111 | + | 0.0230901i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 633.331i | − | 0.229051i | −0.993420 | − | 0.114525i | \(-0.963465\pi\) | ||
0.993420 | − | 0.114525i | \(-0.0365347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2964.48 | − | 1711.54i | 1.05601 | − | 0.609688i | 0.131685 | − | 0.991292i | \(-0.457961\pi\) |
0.924326 | + | 0.381603i | \(0.124628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 290.041 | + | 448.431i | 0.101781 | + | 0.157363i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3276.90 | + | 2018.41i | −1.13297 | + | 0.697854i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1141.48 | + | 1977.11i | −0.388901 | + | 0.673596i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3063.01 | + | 1377.29i | 1.02847 | + | 0.462454i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −217.043 | −0.0718333 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1023.65 | −0.333986 | −0.166993 | − | 0.985958i | \(-0.553406\pi\) | ||||
−0.166993 | + | 0.985958i | \(0.553406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3264 | + | 243.796i | 0.00396521 | + | 0.0784254i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 878.212 | − | 1521.11i | 0.278575 | − | 0.482506i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2310.07 | − | 1247.43i | −0.722661 | − | 0.390237i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1149.59 | − | 743.545i | 0.354713 | − | 0.229425i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 594.527 | − | 343.250i | 0.180960 | − | 0.104477i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1521.32i | − | 0.456840i | −0.973563 | − | 0.228420i | \(-0.926644\pi\) | ||
0.973563 | − | 0.228420i | \(-0.0733559\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1655.28 | + | 2296.05i | 0.490454 | + | 0.680311i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 729.575 | + | 1263.66i | 0.213320 | + | 0.369481i | 0.952752 | − | 0.303751i | \(-0.0982390\pi\) |
−0.739432 | + | 0.673232i | \(0.764906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4152.17 | + | 2397.26i | 1.19818 | + | 0.691770i | 0.960149 | − | 0.279488i | \(-0.0901646\pi\) |
0.238031 | + | 0.971257i | \(0.423498\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2034.80 | − | 969.443i | −0.579568 | − | 0.276124i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1445.76 | − | 834.708i | −0.406501 | − | 0.234693i | 0.282784 | − | 0.959183i | \(-0.408742\pi\) |
−0.689285 | + | 0.724490i | \(0.742075\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −180.784 | − | 313.126i | −0.0501831 | − | 0.0869196i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2526.79 | − | 4936.60i | 0.692543 | − | 1.35302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3529.25i | − | 0.955181i | −0.878583 | − | 0.477590i | \(-0.841510\pi\) | ||
0.878583 | − | 0.477590i | \(-0.158490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4269.15 | + | 2464.80i | −1.14108 | + | 0.658803i | −0.946698 | − | 0.322123i | \(-0.895603\pi\) |
−0.194382 | + | 0.980926i | \(0.562270\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3667.80 | + | 946.654i | −0.968269 | + | 0.249909i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −844.806 | − | 1287.96i | −0.220297 | − | 0.335855i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.4014 | − | 47.4605i | 0.00705873 | − | 0.0122261i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1403.44 | − | 70.9581i | 0.357185 | − | 0.0180594i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1294.99 | −0.325652 | −0.162826 | − | 0.986655i | \(-0.552061\pi\) | ||||
−0.162826 | + | 0.986655i | \(0.552061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2913.29 | 0.723940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2705.27 | + | 136.779i | −0.664355 | + | 0.0335900i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 728.040 | − | 1261.00i | 0.176708 | − | 0.306067i | −0.764043 | − | 0.645165i | \(-0.776789\pi\) |
0.940751 | + | 0.339098i | \(0.110122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5547.82 | + | 157.967i | −1.33098 | + | 0.0378980i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 565.920 | + | 5582.18i | 0.134213 | + | 1.32386i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1850.30 | − | 1068.27i | 0.433820 | − | 0.250466i | −0.267153 | − | 0.963654i | \(-0.586083\pi\) |
0.700973 | + | 0.713188i | \(0.252749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1341.44i | − | 0.310959i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2101.26 | − | 4105.23i | 0.481628 | − | 0.940958i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1443.73 | + | 2500.61i | 0.327233 | + | 0.566784i | 0.981962 | − | 0.189080i | \(-0.0605506\pi\) |
−0.654729 | + | 0.755864i | \(0.727217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5072.92 | + | 2928.85i | 1.13711 | + | 0.656513i | 0.945714 | − | 0.324999i | \(-0.105364\pi\) |
0.191400 | + | 0.981512i | \(0.438697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 468.878 | − | 322.557i | 0.103948 | − | 0.0715094i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2126.40 | + | 1227.68i | 0.466279 | + | 0.269206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1401.52 | + | 2427.50i | 0.304003 | + | 0.526549i | 0.977039 | − | 0.213061i | \(-0.0683433\pi\) |
−0.673036 | + | 0.739610i | \(0.735010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3104.71 | + | 2238.27i | −0.666215 | + | 0.480293i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4665.53i | 0.990469i | 0.868759 | + | 0.495235i | \(0.164918\pi\) | ||||
−0.868759 | + | 0.495235i | \(0.835082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4654.53 | + | 2687.29i | −0.977679 | + | 0.564463i | −0.901569 | − | 0.432636i | \(-0.857583\pi\) |
−0.0761103 | + | 0.997099i | \(0.524250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −181.567 | + | 117.436i | −0.0377371 | + | 0.0244080i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4937.83 | + | 8016.61i | 1.01558 | + | 1.64880i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4281.21 | + | 7415.27i | −0.871404 | + | 1.50932i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −57.6101 | − | 1139.43i | −0.0116054 | − | 0.229535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1302.13 | −0.259630 | −0.129815 | − | 0.991538i | \(-0.541438\pi\) | ||||
−0.129815 | + | 0.991538i | \(0.541438\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −918.578 | −0.181294 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2565.04 | + | 2053.76i | −0.501141 | + | 0.401249i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −367.799 | + | 637.046i | −0.0711383 | + | 0.123215i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3798.97 | − | 6167.66i | −0.727472 | − | 1.18106i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2779.85 | + | 4297.91i | 0.527057 | + | 0.814880i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2441.84 | − | 1409.80i | 0.458424 | − | 0.264671i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 644.894i | 0.119889i | 0.998202 | + | 0.0599447i | \(0.0190924\pi\) | ||||
−0.998202 | + | 0.0599447i | \(0.980908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5943.85 | − | 3042.35i | −1.09428 | − | 0.560108i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 668.420 | + | 1157.74i | 0.121873 | + | 0.211091i | 0.920506 | − | 0.390727i | \(-0.127776\pi\) |
−0.798633 | + | 0.601818i | \(0.794443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1459.67 | − | 842.739i | −0.263595 | − | 0.152187i | 0.362378 | − | 0.932031i | \(-0.381965\pi\) |
−0.625973 | + | 0.779844i | \(0.715298\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2226.75 | + | 289.988i | −0.398295 | + | 0.0518697i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2609.95 | − | 1506.85i | −0.462427 | − | 0.266982i | 0.250637 | − | 0.968081i | \(-0.419360\pi\) |
−0.713064 | + | 0.701099i | \(0.752693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2433.57 | + | 4215.06i | 0.427127 | + | 0.739806i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −846.064 | − | 433.057i | −0.147111 | − | 0.0752987i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1075.73i | 0.185310i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −536.910 | + | 309.985i | −0.0916382 | + | 0.0529074i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1645.06 | − | 2543.42i | −0.278202 | − | 0.430126i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1490.56 | + | 42.4417i | −0.249778 | + | 0.00711211i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −394.460 | + | 683.225i | −0.0655030 | + | 0.113454i | −0.896917 | − | 0.442199i | \(-0.854199\pi\) |
0.831414 | + | 0.555653i | \(0.187532\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3318.22 | + | 7379.53i | −0.546058 | + | 1.21440i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 461.547 | 0.0752746 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1906.16 | 0.308116 | 0.154058 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154058 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 599.269 | + | 11852.6i | 0.0960113 | + | 1.89895i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1660.06 | + | 2875.31i | −0.263629 | + | 0.456618i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6329.30 | + | 541.828i | −0.996356 | + | 0.0852944i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2437.10 | − | 1576.30i | 0.380317 | − | 0.245985i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4538.98 | + | 2620.58i | −0.702205 | + | 0.405418i | −0.808168 | − | 0.588952i | \(-0.799541\pi\) |
0.105963 | + | 0.994370i | \(0.466207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4502.54i | − | 0.690588i | −0.938495 | − | 0.345294i | \(-0.887779\pi\) | ||
0.938495 | − | 0.345294i | \(-0.112221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −125.260 | − | 820.179i | −0.0190481 | − | 0.124723i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4799.70 | + | 8313.33i | 0.723689 | + | 1.25347i | 0.959511 | + | 0.281671i | \(0.0908885\pi\) |
−0.235822 | + | 0.971796i | \(0.575778\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 182.701 | + | 105.483i | 0.0273148 | + | 0.0157702i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4804.86 | + | 10085.1i | −0.712325 | + | 1.49513i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8803.94 | − | 5082.96i | −1.29430 | − | 0.747265i | −0.314888 | − | 0.949129i | \(-0.601967\pi\) |
−0.979414 | + | 0.201863i | \(0.935300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3386.56 | − | 5865.70i | −0.493740 | − | 0.855183i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1852.44 | − | 3619.13i | 0.267846 | − | 0.523292i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1183.21i | − | 0.169677i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −332.544 | + | 191.995i | −0.0472988 | + | 0.0273080i | −0.523463 | − | 0.852048i | \(-0.675360\pi\) |
0.476164 | + | 0.879356i | \(0.342027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13656.2 | − | 1384.47i | 1.92660 | − | 0.195318i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4867.92 | − | 2628.68i | −0.681213 | − | 0.367855i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1481.79 | − | 2566.54i | 0.205695 | − | 0.356275i | −0.744659 | − | 0.667445i | \(-0.767388\pi\) |
0.950354 | + | 0.311171i | \(0.100721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5356.16 | − | 270.809i | 0.737575 | − | 0.0372920i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1228.94 | −0.167887 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13195.4 | 1.78839 | 0.894195 | − | 0.447677i | \(-0.147749\pi\) | ||||
0.894195 | + | 0.447677i | \(0.147749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8067.03 | + | 407.871i | −1.08474 | + | 0.0548448i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4475.95 | − | 7752.57i | 0.597155 | − | 1.03430i | −0.396084 | − | 0.918214i | \(-0.629631\pi\) |
0.993239 | − | 0.116088i | \(-0.0370356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1658.55 | + | 1021.58i | −0.219552 | + | 0.135233i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10506.6 | + | 1065.15i | −1.38005 | + | 0.139909i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7594.74 | − | 4384.82i | 0.989893 | − | 0.571515i | 0.0846507 | − | 0.996411i | \(-0.473023\pi\) |
0.905242 | + | 0.424896i | \(0.139689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14439.1i | − | 1.86757i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4959.80 | − | 9689.97i | 0.636613 | − | 1.24375i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2396.38 | − | 4150.65i | −0.305253 | − | 0.528713i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1187.30 | − | 685.490i | −0.150098 | − | 0.0866594i | 0.423070 | − | 0.906097i | \(-0.360953\pi\) |
−0.573168 | + | 0.819438i | \(0.694286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 70.3631 | + | 889.007i | 0.00882847 | + | 0.111544i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2392.14 | + | 1381.10i | 0.297899 | + | 0.171992i | 0.641499 | − | 0.767124i | \(-0.278313\pi\) |
−0.343599 | + | 0.939116i | \(0.611646\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −419.161 | − | 726.008i | −0.0518112 | − | 0.0897396i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1034.55 | + | 3105.94i | −0.126931 | + | 0.381075i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7018.82i | 0.854815i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2310.01 | − | 1333.69i | 0.279273 | − | 0.161239i | −0.353821 | − | 0.935313i | \(-0.615118\pi\) |
0.633094 | + | 0.774075i | \(0.281784\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2665.13 | − | 1723.78i | 0.319857 | − | 0.206881i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1800.03 | + | 3333.40i | −0.214465 | + | 0.397157i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 607.221 | − | 1051.74i | 0.0718249 | − | 0.124404i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 474.025 | + | 9375.45i | 0.0556670 | + | 1.10100i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14480.6 | 1.68836 | 0.844179 | − | 0.536061i | \(-0.180088\pi\) | ||||
0.844179 | + | 0.536061i | \(0.180088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14248.8 | 1.64951 | 0.824753 | − | 0.565494i | \(-0.191314\pi\) | ||||
0.824753 | + | 0.565494i | \(0.191314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −891.520 | + | 1982.69i | −0.102476 | + | 0.227900i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6084.75 | − | 10539.1i | 0.694479 | − | 1.20287i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −330.971 | − | 11623.7i | −0.0375101 | − | 1.31736i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −390.876 | − | 604.331i | −0.0439899 | − | 0.0680125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4826.49 | + | 2786.57i | −0.539405 | + | 0.311426i | −0.744838 | − | 0.667246i | \(-0.767473\pi\) |
0.205433 | + | 0.978671i | \(0.434140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2939.93i | − | 0.326291i | −0.986602 | − | 0.163146i | \(-0.947836\pi\) | ||
0.986602 | − | 0.163146i | \(-0.0521640\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4316.44 | + | 2209.37i | 0.475765 | + | 0.243520i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −576.332 | − | 998.236i | −0.0630885 | − | 0.109273i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8290.73 | + | 4786.66i | 0.901355 | + | 0.520398i | 0.877640 | − | 0.479321i | \(-0.159117\pi\) |
0.0237157 | + | 0.999719i | \(0.492450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3311.18 | + | 8648.83i | −0.357540 | + | 0.933898i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6197.42 | + | 3578.08i | 0.664669 | + | 0.383747i | 0.794054 | − | 0.607848i | \(-0.207967\pi\) |
−0.129385 | + | 0.991594i | \(0.541300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1992.81 | − | 3451.64i | −0.212288 | − | 0.367693i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12507.3 | − | 6401.86i | −1.32344 | − | 0.677400i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14839.2i | − | 1.55970i | −0.625964 | − | 0.779852i | \(-0.715294\pi\) | ||
0.625964 | − | 0.779852i | \(-0.284706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10311.7 | − | 5953.48i | 1.07663 | − | 0.621593i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4347.85 | − | 6722.19i | −0.450949 | − | 0.697210i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.9990 | − | 491.646i | −0.00144238 | − | 0.0506565i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3787.42 | − | 6560.00i | 0.387676 | − | 0.671474i | −0.604461 | − | 0.796635i | \(-0.706611\pi\) |
0.992136 | + | 0.125161i | \(0.0399447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10179.0 | + | 12713.1i | 1.03511 | + | 1.29281i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14850.5 | −1.50034 | −0.750170 | − | 0.661245i | \(-0.770029\pi\) | ||||
−0.750170 | + | 0.661245i | \(0.770029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3361.43 | −0.337406 | −0.168703 | − | 0.985667i | \(-0.553958\pi\) | ||||
−0.168703 | + | 0.985667i | \(0.553958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 167.028 | + | 3303.55i | 0.0166575 | + | 0.329459i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −115.422 | + | 199.917i | −0.0114371 | + | 0.0198096i | −0.871687 | − | 0.490063i | \(-0.836974\pi\) |
0.860250 | + | 0.509872i | \(0.170307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 904.441 | − | 1674.89i | 0.0890473 | − | 0.164903i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2405.65 | + | 1555.95i | −0.235343 | + | 0.152218i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7933.44 | + | 4580.37i | −0.771205 | + | 0.445255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 971.480i | − | 0.0938411i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6542.45 | + | 4716.63i | −0.628005 | + | 0.452745i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2200.43 | − | 3811.26i | −0.209896 | − | 0.363551i | 0.741786 | − | 0.670637i | \(-0.233979\pi\) |
−0.951682 | + | 0.307087i | \(0.900646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1534.80 | − | 886.116i | −0.145490 | − | 0.0839988i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −944.458 | − | 11932.8i | −0.0889738 | − | 1.12415i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −853.894 | − | 492.996i | −0.0799450 | − | 0.0461563i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5972.31 | − | 10344.3i | −0.555711 | − | 0.962520i | −0.997848 | − | 0.0655721i | \(-0.979113\pi\) |
0.442137 | − | 0.896948i | \(-0.354221\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5472.87 | − | 10692.4i | 0.506118 | − | 0.988804i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19916.7i | − | 1.83060i | −0.402768 | − | 0.915302i | \(-0.631952\pi\) | ||
0.402768 | − | 0.915302i | \(-0.368048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20891.1 | − | 12061.5i | 1.90850 | − | 1.10187i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 286.430 | + | 2825.32i | 0.0260083 | + | 0.256543i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 740.801 | − | 456.296i | 0.0668601 | − | 0.0411825i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 665.569 | − | 1152.80i | 0.0597093 | − | 0.103420i | −0.834626 | − | 0.550818i | \(-0.814316\pi\) |
0.894335 | + | 0.447398i | \(0.147649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13393.5 | − | 677.177i | 1.19436 | − | 0.0603873i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10393.2 | −0.921288 | −0.460644 | − | 0.887585i | \(-0.652382\pi\) | ||||
−0.460644 | + | 0.887585i | \(0.652382\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4423.62 | 0.389799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11219.9 | + | 567.281i | −0.982826 | + | 0.0496919i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5132.02 | + | 8888.91i | −0.446901 | + | 0.774055i | −0.998182 | − | 0.0602640i | \(-0.980806\pi\) |
0.551281 | + | 0.834319i | \(0.314139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4293.73 | − | 2318.61i | −0.371709 | − | 0.200723i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1211.16 | + | 472.618i | 0.104238 | + | 0.0406756i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4997.54 | + | 2885.33i | −0.427608 | + | 0.246879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1885.78i | 0.160418i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2372.50 | + | 4635.17i | −0.200658 | + | 0.392026i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1549.97 | − | 2684.63i | −0.130337 | − | 0.225750i | 0.793470 | − | 0.608610i | \(-0.208273\pi\) |
−0.923806 | + | 0.382860i | \(0.874939\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8265.94 | + | 4772.34i | 0.691098 | + | 0.399005i | 0.804023 | − | 0.594598i | \(-0.202689\pi\) |
−0.112925 | + | 0.993603i | \(0.536022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4339.21 | − | 9107.74i | 0.360721 | − | 0.757132i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14250.9 | + | 8227.77i | 1.17795 | + | 0.680090i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1652.39 | + | 2862.03i | 0.135809 | + | 0.235229i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3229.80 | + | 4480.06i | 0.263957 | + | 0.366136i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3006.47i | 0.244324i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −711.364 | + | 410.706i | −0.0574859 | + | 0.0331895i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13090.6 | + | 8466.91i | −1.05196 | + | 0.680399i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 457.119 | + | 8020.53i | 0.0365297 | + | 0.640944i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3403.83 | − | 5895.60i | 0.270503 | − | 0.468524i | −0.698488 | − | 0.715622i | \(-0.746143\pi\) |
0.968991 | + | 0.247098i | \(0.0794768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −253.948 | − | 5022.68i | −0.0200699 | − | 0.396950i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2617.80 | −0.205751 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14906.9 | 1.16521 | 0.582606 | − | 0.812754i | \(-0.302033\pi\) | ||||
0.582606 | + | 0.812754i | \(0.302033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15461.5 | − | 6952.30i | −1.20197 | − | 0.540468i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 962.859 | − | 1667.72i | 0.0744449 | − | 0.128942i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19758.1 | + | 562.586i | −1.51935 | + | 0.0432615i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3797.68 | + | 5871.57i | 0.290455 | + | 0.449071i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10661.9 | − | 6155.67i | 0.811061 | − | 0.468266i | −0.0362634 | − | 0.999342i | \(-0.511546\pi\) |
0.847324 | + | 0.531076i | \(0.178212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2313.06i | − | 0.175013i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12575.9 | + | 6436.95i | 0.946442 | + | 0.484435i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −417.925 | − | 723.867i | −0.0312850 | − | 0.0541872i | 0.849959 | − | 0.526849i | \(-0.176627\pi\) |
−0.881244 | + | 0.472662i | \(0.843293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8882.34 | + | 5128.22i | 0.661386 | + | 0.381851i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9243.75 | + | 9840.60i | 0.684658 | + | 0.728865i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5291.04 | + | 3054.78i | 0.389828 | + | 0.225067i | 0.682086 | − | 0.731272i | \(-0.261073\pi\) |
−0.292258 | + | 0.956340i | \(0.594407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6319.69 | − | 10946.0i | −0.463171 | − | 0.802236i | 0.535946 | − | 0.844252i | \(-0.319955\pi\) |
−0.999117 | + | 0.0420166i | \(0.986622\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1902.54 | − | 973.814i | −0.138708 | − | 0.0709977i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13039.8i | 0.945736i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15334.7 | + | 8853.51i | −1.10640 | + | 0.638781i | −0.937895 | − | 0.346920i | \(-0.887228\pi\) |
−0.168506 | + | 0.985701i | \(0.553894\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2303.94 | + | 3562.11i | 0.165369 | + | 0.255676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2626.72 | − | 4264.50i | −0.187564 | − | 0.304512i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3498.19 | + | 6059.05i | −0.248508 | + | 0.430429i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −653.972 | − | 294.060i | −0.0462195 | − | 0.0207827i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11725.2 | −0.824446 | −0.412223 | − | 0.911083i | \(-0.635248\pi\) | ||||
−0.412223 | + | 0.911083i | \(0.635248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1313.63 | 0.0918968 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 166.176 | + | 3286.69i | 0.0115661 | + | 0.228758i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7523.76 | + | 13031.5i | −0.521018 | + | 0.902430i | 0.478683 | + | 0.877988i | \(0.341114\pi\) |
−0.999701 | + | 0.0244425i | \(0.992219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5063.27 | + | 8220.26i | 0.348864 | + | 0.566383i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14935.1 | + | 9659.91i | −1.02388 | + | 0.662234i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5292.70 | − | 3055.74i | 0.361025 | − | 0.208438i | −0.308505 | − | 0.951223i | \(-0.599829\pi\) |
0.669530 | + | 0.742785i | \(0.266495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7494.08i | − | 0.508636i | −0.967121 | − | 0.254318i | \(-0.918149\pi\) | ||
0.967121 | − | 0.254318i | \(-0.0818509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1622.84 | − | 2251.04i | −0.109597 | − | 0.152022i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1756.84 | − | 3042.93i | −0.118059 | − | 0.204484i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17917.1 | − | 10344.5i | −1.19808 | − | 0.691711i | −0.237953 | − | 0.971277i | \(-0.576476\pi\) |
−0.960127 | + | 0.279565i | \(0.909810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16476.0 | − | 11334.4i | 1.09629 | − | 0.754174i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −412.361 | − | 238.077i | −0.0273033 | − | 0.0157636i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11645.5 | + | 20170.6i | 0.767305 | + | 1.32901i | 0.939019 | + | 0.343865i | \(0.111736\pi\) |
−0.171714 | + | 0.985147i | \(0.554931\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5404.99 | − | 10559.7i | 0.354391 | − | 0.692374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11640.9i | 0.759554i | 0.925078 | + | 0.379777i | \(0.123999\pi\) | ||||
−0.925078 | + | 0.379777i | \(0.876001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13978.4 | − | 8070.44i | 0.907657 | − | 0.524036i | 0.0279803 | − | 0.999608i | \(-0.491092\pi\) |
0.879676 | + | 0.475573i | \(0.157759\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16256.9 | − | 6343.78i | −1.05051 | − | 0.409931i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16430.6 | + | 467.841i | −1.05663 | + | 0.0300861i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4234.68 | + | 7334.68i | −0.271019 | + | 0.469420i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1126.35 | − | 56.9485i | 0.0717417 | − | 0.00362728i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34787.4 | 2.20519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9424.67 | −0.594596 | −0.297298 | − | 0.954785i | \(-0.596086\pi\) | ||||
−0.297298 | + | 0.954785i | \(0.596086\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5312.26 | − | 268.589i | 0.333560 | − | 0.0168649i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3490.34 | + | 6045.45i | −0.218126 | + | 0.377805i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1811.55 | − | 912.623i | −0.112679 | − | 0.0567652i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −127.936 | − | 1261.95i | −0.00792031 | − | 0.0781252i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1459.54 | + | 842.666i | −0.0899351 | + | 0.0519241i | −0.544293 | − | 0.838895i | \(-0.683202\pi\) |
0.454358 | + | 0.890819i | \(0.349869\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10186.5i | 0.624752i | 0.949958 | + | 0.312376i | \(0.101125\pi\) | ||||
−0.949958 | + | 0.312376i | \(0.898875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4158.39 | + | 8124.26i | −0.253855 | + | 0.495957i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −163.793 | − | 283.698i | −0.00995266 | − | 0.0172385i | 0.861006 | − | 0.508594i | \(-0.169835\pi\) |
−0.870959 | + | 0.491356i | \(0.836501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4149.04 | + | 2395.45i | 0.250946 | + | 0.144884i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12315.4 | + | 5867.46i | 0.741445 | + | 0.353247i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1769.92 | + | 1021.87i | 0.106068 | + | 0.0612384i | 0.552096 | − | 0.833781i | \(-0.313828\pi\) |
−0.446028 | + | 0.895019i | \(0.647162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4703.82 | − | 8147.25i | −0.280600 | − | 0.486014i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5770.73 | + | 4160.28i | −0.342675 | + | 0.247044i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27567.4i | − | 1.62955i | −0.579778 | − | 0.814774i | \(-0.696861\pi\) | ||
0.579778 | − | 0.814774i | \(-0.303139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18417.0 | − | 10633.0i | 1.08372 | − | 0.625684i | 0.151820 | − | 0.988408i | \(-0.451487\pi\) |
0.931897 | + | 0.362724i | \(0.118153\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2995.25 | + | 1937.30i | −0.175454 | + | 0.113482i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 678.152 | + | 366.202i | 0.0395453 | + | 0.0213544i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12924.1 | + | 22385.2i | −0.750260 | + | 1.29949i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 399.170 | + | 7894.94i | 0.0230685 | + | 0.456257i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14705.8 | −0.846065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9377.40 | −0.537106 | −0.268553 | − | 0.963265i | \(-0.586545\pi\) | ||||
−0.268553 | + | 0.963265i | \(0.586545\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9192.58 | − | 11481.1i | −0.524182 | − | 0.654677i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5342.31 | − | 9253.15i | 0.303282 | − | 0.525299i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.976877 | + | 0.213801i | \(0.0685844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3462.30 | + | 2132.60i | −0.195686 | + | 0.120533i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4117.71 | − | 6366.37i | −0.231705 | − | 0.358238i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24985.9 | − | 14425.6i | 1.39979 | − | 0.808172i | 0.405424 | − | 0.914129i | \(-0.367124\pi\) |
0.994371 | + | 0.105957i | \(0.0337906\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2743.08i | − | 0.153004i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22176.8 | − | 11351.2i | −1.23158 | − | 0.630384i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −883.284 | − | 1529.89i | −0.0488395 | − | 0.0845926i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1139.99 | + | 658.171i | 0.0627599 | + | 0.0362344i | 0.531052 | − | 0.847339i | \(-0.321797\pi\) |
−0.468292 | + | 0.883574i | \(0.655130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10814.0 | + | 4497.05i | 0.592771 | + | 0.246506i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7025.98 | + | 4056.45i | 0.383469 | + | 0.221396i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29507.3 | − | 51108.1i | −1.60354 | − | 2.77741i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7721.80 | + | 3952.39i | 0.417833 | + | 0.213867i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12811.2i | − | 0.690259i | −0.938555 | − | 0.345129i | \(-0.887835\pi\) | ||
0.938555 | − | 0.345129i | \(-0.112165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2404.99 | − | 1388.52i | 0.129027 | − | 0.0744938i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1020.34 | + | 1577.54i | 0.0545081 | + | 0.0842747i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8668.46 | − | 16052.7i | 0.461119 | − | 0.853925i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16482.9 | + | 28549.2i | −0.873101 | + | 1.51226i | −0.0143290 | + | 0.999897i | \(0.504561\pi\) |
−0.858772 | + | 0.512358i | \(0.828772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11817.6 | + | 26281.6i | −0.623337 | + | 1.38627i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17632.4 | −0.926141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −622.006 | −0.0325339 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 926.018 | + | 18315.1i | 0.0482326 | + | 0.953962i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4307.48 | + | 7460.77i | −0.223424 | + | 0.386982i | −0.955845 | − | 0.293870i | \(-0.905057\pi\) |
0.732421 | + | 0.680851i | \(0.238390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 677.375 | + | 23789.5i | 0.0349886 | + | 1.22880i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21508.1 | − | 13911.3i | 1.10636 | − | 0.715582i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18866.5 | + | 10892.6i | −0.966463 | + | 0.557988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26635.3i | 1.35880i | 0.733768 | + | 0.679400i | \(0.237760\pi\) | ||||
−0.733768 | + | 0.679400i | \(0.762240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18785.7 | − | 5875.05i | 0.954415 | − | 0.298484i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22701.7 | + | 39320.5i | 1.14864 | + | 1.98950i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5328.35 | − | 3076.33i | −0.268496 | − | 0.155016i | 0.359708 | − | 0.933065i | \(-0.382876\pi\) |
−0.628204 | + | 0.778049i | \(0.716210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4722.08 | + | 6462.22i | 0.236975 | + | 0.324303i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2084.72 | − | 1203.61i | −0.104195 | − | 0.0601569i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7364.30 | + | 12755.3i | 0.366577 | + | 0.634929i | 0.989028 | − | 0.147729i | \(-0.0471965\pi\) |
−0.622451 | + | 0.782659i | \(0.713863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −129.747 | + | 253.487i | −0.00643236 | + | 0.0125669i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27255.1i | 1.34575i | 0.739755 | + | 0.672876i | \(0.234941\pi\) | ||||
−0.739755 | + | 0.672876i | \(0.765059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10516.1 | + | 6071.45i | −0.517152 | + | 0.298578i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7264.55 | + | 736.478i | −0.355818 | + | 0.0360727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 96.4195 | + | 3386.26i | 0.00470373 | + | 0.165195i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3075.69 | + | 5327.25i | −0.149445 | + | 0.258847i | −0.931023 | − | 0.364961i | \(-0.881082\pi\) |
0.781577 | + | 0.623809i | \(0.214415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6720.36 | − | 339.783i | 0.325237 | − | 0.0164441i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6918.80 | −0.333511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21107.3 | −1.01342 | −0.506710 | − | 0.862117i | \(-0.669139\pi\) | ||||
−0.506710 | + | 0.862117i | \(0.669139\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15118.6 | + | 764.399i | −0.723016 | + | 0.0365559i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7530.97 | − | 13044.0i | 0.358735 | − | 0.621348i | −0.629015 | − | 0.777393i | \(-0.716541\pi\) |
0.987750 | + | 0.156046i | \(0.0498748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5129.82 | + | 9499.67i | −0.243397 | + | 0.450736i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14003.2 | − | 1419.64i | 0.661811 | − | 0.0670942i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1047.62 | + | 604.845i | −0.0493187 | + | 0.0284742i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26099.2i | 1.22387i | 0.790906 | + | 0.611937i | \(0.209610\pi\) | ||||
−0.790906 | + | 0.611937i | \(0.790390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3447.31 | + | 6735.03i | −0.161027 | + | 0.314599i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.84542 | − | 15.3207i | −0.000411575 | − | 0.000712869i | 0.865820 | − | 0.500356i | \(-0.166798\pi\) |
−0.866231 | + | 0.499644i | \(0.833464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12869.8 | − | 7430.41i | −0.596514 | − | 0.344398i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28749.1 | − | 2275.43i | 1.32737 | − | 0.105059i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4079.91 | − | 2355.54i | −0.187648 | − | 0.108339i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −550.151 | − | 952.889i | −0.0252061 | − | 0.0436582i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4401.53 | − | 28820.4i | −0.200891 | − | 1.31540i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2476.01i | 0.112577i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2066.21 | + | 1192.93i | −0.0935865 | + | 0.0540322i | −0.546063 | − | 0.837744i | \(-0.683874\pi\) |
0.452476 | + | 0.891776i | \(0.350541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9321.90 | + | 6029.32i | −0.420619 | + | 0.272053i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36015.4 | − | 22183.7i | 1.61891 | − | 0.997169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1856.58 | − | 3215.70i | 0.0831390 | − | 0.144001i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 351.973 | + | 6961.45i | 0.0157021 | + | 0.310563i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13183.5 | −0.585927 | −0.292964 | − | 0.956124i | \(-0.594641\pi\) | ||||
−0.292964 | + | 0.956124i | \(0.594641\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9346.49 | 0.413836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9827.37 | + | 21855.5i | −0.433499 | + | 0.964078i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3085.56 | + | 5344.35i | −0.135600 | + | 0.234867i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9102.59 | − | 4915.39i | −0.398539 | − | 0.215211i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8148.37 | − | 12598.2i | −0.355435 | − | 0.549537i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26645.9 | + | 15384.0i | −1.15800 | + | 0.668570i | −0.950823 | − | 0.309734i | \(-0.899760\pi\) |
−0.207174 | + | 0.978304i | \(0.566426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42776.4i | 1.85214i | 0.377357 | + | 0.926068i | \(0.376833\pi\) | ||||
−0.377357 | + | 0.926068i | \(0.623167\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27094.5 | − | 13868.3i | −1.16881 | − | 0.598256i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5190.41 | − | 8990.05i | −0.223082 | − | 0.386390i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3138.92 | + | 1812.26i | 0.134415 | + | 0.0776045i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2348.62 | + | 1796.94i | −0.100204 | + | 0.0766671i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36141.5 | + | 20866.3i | 1.53635 | + | 0.887014i | 0.999048 | + | 0.0436263i | \(0.0138911\pi\) |
0.537305 | + | 0.843388i | \(0.319442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7822.35 | − | 13548.7i | −0.331312 | − | 0.573850i | 0.651457 | − | 0.758685i | \(-0.274158\pi\) |
−0.982769 | + | 0.184836i | \(0.940825\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11357.1 | − | 5813.13i | −0.479278 | − | 0.245318i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24395.1i | 1.02576i | 0.858461 | + | 0.512879i | \(0.171421\pi\) | ||||
−0.858461 | + | 0.512879i | \(0.828579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32786.9 | − | 18929.5i | 1.37362 | − | 0.793062i | 0.382242 | − | 0.924062i | \(-0.375152\pi\) |
0.991382 | + | 0.131000i | \(0.0418188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7910.13 | − | 12229.8i | −0.330204 | − | 0.510526i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39752.2 | − | 2265.62i | 1.65346 | − | 0.0942367i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5794.92 | − | 10037.1i | 0.240169 | − | 0.415986i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15524.7 | − | 12430.2i | 0.641113 | − | 0.513321i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40533.9 | 1.66792 | 0.833960 | − | 0.551826i | \(-0.186069\pi\) | ||||
0.833960 | + | 0.551826i | \(0.186069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18794.8 | −0.770625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1224.16 | − | 24211.9i | −0.0500145 | − | 0.989206i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4854.48 | + | 8408.21i | −0.197632 | + | 0.342309i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14485.1 | + | 412.444i | −0.587619 | + | 0.0167317i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23449.7 | − | 15167.1i | 0.947929 | − | 0.613112i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32281.4 | + | 18637.6i | −1.30034 | + | 0.750752i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38466.5i | 1.54404i | 0.635598 | + | 0.772021i | \(0.280754\pi\) | ||||
−0.635598 | + | 0.772021i | \(0.719246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 911.431 | − | 657.075i | 0.0364565 | − | 0.0262824i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13054.1 | − | 22610.3i | −0.520326 | − | 0.901230i | −0.999721 | − | 0.0236312i | \(-0.992477\pi\) |
0.479395 | − | 0.877599i | \(-0.340856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21033.3 | − | 12143.6i | −0.835445 | − | 0.482345i | 0.0202681 | − | 0.999795i | \(-0.493548\pi\) |
−0.855713 | + | 0.517450i | \(0.826881\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27728.4 | − | 40306.8i | −1.09754 | − | 1.59541i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32475.9 | − | 18750.0i | −1.28099 | − | 0.739579i | −0.303960 | − | 0.952685i | \(-0.598309\pi\) |
−0.977029 | + | 0.213106i | \(0.931642\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2250.06 | + | 3897.21i | 0.0884441 | + | 0.153190i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20271.8 | − | 39605.1i | 0.794079 | − | 1.55139i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24996.9i | 0.975791i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 526.386 | − | 303.909i | 0.0204775 | − | 0.0118227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 597.938 | + | 5898.00i | 0.0231811 | + | 0.228656i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10024.8 | − | 16275.3i | −0.387313 | − | 0.628806i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7420.70 | − | 12853.0i | 0.285723 | − | 0.494887i | −0.687061 | − | 0.726600i | \(-0.741100\pi\) |
0.972784 | + | 0.231713i | \(0.0744329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6757.45 | − | 341.659i | 0.259298 | − | 0.0131102i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30469.3 | 1.16520 | 0.582598 | − | 0.812760i | \(-0.302036\pi\) | ||||
0.582598 | + | 0.812760i | \(0.302036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6758.53 | 0.257580 | 0.128790 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128790 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4766.98 | − | 241.020i | 0.181062 | − | 0.00915457i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17666.5 | + | 30599.4i | −0.668754 | + | 1.15832i | 0.309499 | + | 0.950900i | \(0.399839\pi\) |
−0.978253 | + | 0.207416i | \(0.933495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15098.5 | + | 24512.6i | 0.569616 | + | 0.924776i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12772.5 | − | 11331.0i | 0.480240 | − | 0.426043i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 646.160 | − | 373.061i | 0.0242138 | − | 0.0139798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13473.5i | 0.503207i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1741.55 | − | 3402.47i | 0.0648257 | − | 0.126650i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14728.9 | − | 25511.3i | −0.546427 | − | 0.946439i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30030.5 | + | 17338.1i | 1.11039 | + | 0.641084i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21333.1 | + | 31010.4i | 0.786182 | + | 1.14282i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3764.01 | − | 2173.15i | −0.138254 | − | 0.0798210i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10481.2 | − | 18153.9i | −0.383706 | − | 0.664598i | 0.607883 | − | 0.794027i | \(-0.292019\pi\) |
−0.991589 | + | 0.129429i | \(0.958686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15553.8 | − | 21574.7i | −0.567533 | − | 0.787226i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5419.65i | − | 0.197103i | −0.995132 | − | 0.0985516i | \(-0.968579\pi\) | ||
0.995132 | − | 0.0985516i | \(-0.0314209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5485.41 | + | 3167.00i | −0.198840 | + | 0.114800i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12302.1 | + | 7956.87i | −0.444474 | + | 0.287482i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38782.8 | + | 1104.29i | −1.39664 | + | 0.0397677i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12706.3 | − | 22007.9i | 0.456084 | − | 0.789961i | −0.542666 | − | 0.839949i | \(-0.682585\pi\) |
0.998750 | + | 0.0499878i | \(0.0159183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −169.210 | − | 3346.69i | −0.00605390 | − | 0.119736i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 277.823 | 0.00990754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31416.1 | −1.11671 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31644.0 | + | 14228.8i | 1.12117 | + | 0.504137i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −276.744 | + | 479.335i | −0.00977360 | + | 0.0169284i | −0.870871 | − | 0.491512i | \(-0.836444\pi\) |
0.861097 | + | 0.508440i | \(0.169778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2657.80 | − | 1743.32i | 0.0935615 | − | 0.0613696i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3772.55 | − | 5832.73i | −0.132377 | − | 0.204668i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10573.7 | − | 6104.72i | 0.369836 | − | 0.213525i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18956.6i | 0.660923i | 0.943819 | + | 0.330462i | \(0.107204\pi\) | ||||
−0.943819 | + | 0.330462i | \(0.892796\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7796.09 | + | 3990.42i | 0.270943 | + | 0.138682i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16542.7 | − | 28652.8i | −0.573089 | − | 0.992619i | −0.996246 | − | 0.0865632i | \(-0.972412\pi\) |
0.423157 | − | 0.906056i | \(-0.360922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54763.2 | + | 31617.5i | 1.89113 | + | 1.09184i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11479.7 | − | 2089.16i | 0.395168 | − | 0.0719158i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11619.3 | − | 6708.40i | −0.398708 | − | 0.230194i | 0.287219 | − | 0.957865i | \(-0.407269\pi\) |
−0.685926 | + | 0.727671i | \(0.740603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −779.096 | − | 1349.43i | −0.0266497 | − | 0.0461586i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13939.8 | + | 7135.05i | 0.475319 | + | 0.243291i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36353.5i | − | 1.23568i | −0.786303 | − | 0.617841i | \(-0.788007\pi\) | ||
0.786303 | − | 0.617841i | \(-0.211993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1599.64 | + | 923.554i | −0.0542023 | + | 0.0312937i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13735.0 | − | 21235.6i | −0.463939 | − | 0.717294i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9954.29 | − | 5375.31i | −0.335183 | − | 0.180999i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4848.13 | + | 8397.21i | −0.162738 | + | 0.281871i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4504.30 | + | 2025.37i | 0.150726 | + | 0.0677741i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3666.29 | 0.122303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3453.28 | −0.114840 | −0.0574198 | − | 0.998350i | \(-0.518287\pi\) | ||||
−0.0574198 | + | 0.998350i | \(0.518287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −282.254 | − | 5582.53i | −0.00935739 | − | 0.185074i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25320.0 | − | 43855.6i | 0.836826 | − | 1.44943i | −0.0557091 | − | 0.998447i | \(-0.517742\pi\) |
0.892535 | − | 0.450978i | \(-0.148925\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28488.4 | − | 17547.4i | 0.938638 | − | 0.578154i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2704.97 | − | 1749.55i | 0.0888497 | − | 0.0574672i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26914.6 | − | 15539.1i | 0.881344 | − | 0.508844i | 0.0102426 | − | 0.999948i | \(-0.496740\pi\) |
0.871101 | + | 0.491103i | \(0.163406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20787.2i | 0.678613i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9204.42 | + | 12767.5i | 0.299566 | + | 0.415529i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20154.8 | − | 34909.1i | −0.653956 | − | 1.13268i | −0.982155 | − | 0.188076i | \(-0.939775\pi\) |
0.328199 | − | 0.944609i | \(-0.393558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2463.05 | + | 1422.04i | 0.0796744 | + | 0.0460001i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7724.14 | − | 611.350i | 0.249100 | − | 0.0197158i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42132.6 | − | 24325.3i | −1.35464 | − | 0.782102i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2007.28 | + | 3476.71i | 0.0643425 | + | 0.111444i | 0.896402 | − | 0.443242i | \(-0.146172\pi\) |
−0.832060 | + | 0.554686i | \(0.812838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1867.79 | − | 3649.11i | 0.0596904 | − | 0.116617i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15372.0i | 0.489773i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36113.8 | − | 20850.3i | 1.14718 | − | 0.662323i | 0.198980 | − | 0.980004i | \(-0.436237\pi\) |
0.948198 | + | 0.317680i | \(0.102904\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15283.7 | − | 39166.9i | 0.484039 | − | 1.24043i |
(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.e.257.1 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.257.3 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.5.8 | yes | 16 | ||
7.3 | odd | 6 | inner | 336.4.bc.e.17.3 | 16 | ||
12.11 | even | 2 | 42.4.f.a.5.3 | ✓ | 16 | ||
21.17 | even | 6 | inner | 336.4.bc.e.17.1 | 16 | ||
28.3 | even | 6 | 42.4.f.a.17.3 | yes | 16 | ||
28.11 | odd | 6 | 294.4.f.a.227.2 | 16 | |||
28.19 | even | 6 | 294.4.d.a.293.6 | 16 | |||
28.23 | odd | 6 | 294.4.d.a.293.3 | 16 | |||
28.27 | even | 2 | 294.4.f.a.215.5 | 16 | |||
84.11 | even | 6 | 294.4.f.a.227.5 | 16 | |||
84.23 | even | 6 | 294.4.d.a.293.14 | 16 | |||
84.47 | odd | 6 | 294.4.d.a.293.11 | 16 | |||
84.59 | odd | 6 | 42.4.f.a.17.8 | yes | 16 | ||
84.83 | odd | 2 | 294.4.f.a.215.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.3 | ✓ | 16 | 12.11 | even | 2 | ||
42.4.f.a.5.8 | yes | 16 | 4.3 | odd | 2 | ||
42.4.f.a.17.3 | yes | 16 | 28.3 | even | 6 | ||
42.4.f.a.17.8 | yes | 16 | 84.59 | odd | 6 | ||
294.4.d.a.293.3 | 16 | 28.23 | odd | 6 | |||
294.4.d.a.293.6 | 16 | 28.19 | even | 6 | |||
294.4.d.a.293.11 | 16 | 84.47 | odd | 6 | |||
294.4.d.a.293.14 | 16 | 84.23 | even | 6 | |||
294.4.f.a.215.2 | 16 | 84.83 | odd | 2 | |||
294.4.f.a.215.5 | 16 | 28.27 | even | 2 | |||
294.4.f.a.227.2 | 16 | 28.11 | odd | 6 | |||
294.4.f.a.227.5 | 16 | 84.11 | even | 6 | |||
336.4.bc.e.17.1 | 16 | 21.17 | even | 6 | inner | ||
336.4.bc.e.17.3 | 16 | 7.3 | odd | 6 | inner | ||
336.4.bc.e.257.1 | 16 | 1.1 | even | 1 | trivial | ||
336.4.bc.e.257.3 | 16 | 3.2 | odd | 2 | inner |