Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(95,336)]
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([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bj (of order \(6\), degree \(2\), 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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.8275904784.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 4x^{4} - 18x^{3} + 45x^{2} - 81x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.1 | ||
Root | \(0.906034 - 1.47618i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.95 |
Dual form | 336.2.bj.e.191.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.73142 | − | 0.0465589i | −0.999639 | − | 0.0268808i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41502 | + | 1.97166i | −1.52724 | + | 0.881755i | −0.527768 | + | 0.849388i | \(0.676971\pi\) |
−0.999476 | + | 0.0323665i | \(0.989696\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.13746 | − | 2.38876i | 0.429919 | − | 0.902867i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.99566 | + | 0.161227i | 0.998555 | + | 0.0537422i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.76424 | − | 3.05575i | 0.531938 | − | 0.921344i | −0.467367 | − | 0.884064i | \(-0.654797\pi\) |
0.999305 | − | 0.0372805i | \(-0.0118695\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00465 | − | 3.25479i | 1.55039 | − | 0.840383i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.35387 | + | 2.51371i | 1.05597 | + | 0.609664i | 0.924314 | − | 0.381632i | \(-0.124638\pi\) |
0.131654 | + | 0.991296i | \(0.457971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.63746 | − | 1.52274i | 0.605075 | − | 0.349340i | −0.165961 | − | 0.986132i | \(-0.553073\pi\) |
0.771035 | + | 0.636792i | \(0.219739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08064 | + | 4.08300i | −0.454033 | + | 0.890985i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.825391 | + | 1.42962i | 0.172106 | + | 0.298096i | 0.939156 | − | 0.343491i | \(-0.111610\pi\) |
−0.767050 | + | 0.641587i | \(0.778276\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.27492 | − | 9.13642i | 1.05498 | − | 1.82728i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.17926 | − | 0.418627i | −0.996749 | − | 0.0805648i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.80257i | − | 1.26320i | −0.775292 | − | 0.631602i | \(-0.782397\pi\) | ||
0.775292 | − | 0.631602i | \(-0.217603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.19692 | + | 5.20867i | −0.556513 | + | 0.906712i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.825391 | + | 10.4004i | 0.139517 | + | 1.75798i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.637459 | − | 1.10411i | −0.104798 | − | 0.181515i | 0.808858 | − | 0.588004i | \(-0.200086\pi\) |
−0.913655 | + | 0.406489i | \(0.866753\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.46285 | − | 0.0931179i | −0.554500 | − | 0.0149108i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.16818i | − | 0.338612i | −0.985563 | − | 0.169306i | \(-0.945847\pi\) | ||
0.985563 | − | 0.169306i | \(-0.0541527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.837253i | 0.127680i | 0.997960 | + | 0.0638400i | \(0.0203347\pi\) | ||||
−0.997960 | + | 0.0638400i | \(0.979665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.5481 | + | 5.35585i | −1.57242 | + | 0.798403i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47617 | − | 4.28886i | −0.361187 | − | 0.625594i | 0.626969 | − | 0.779044i | \(-0.284295\pi\) |
−0.988156 | + | 0.153450i | \(0.950962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.41238 | − | 5.43424i | −0.630339 | − | 0.776320i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.42136 | − | 4.55501i | −1.03920 | − | 0.637829i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.36737 | + | 4.83090i | 1.14935 | + | 0.663576i | 0.948728 | − | 0.316094i | \(-0.102371\pi\) |
0.200619 | + | 0.979669i | \(0.435705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.9140i | 1.87616i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.63746 | + | 2.51371i | −0.614246 | + | 0.332949i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.06580 | − | 8.77423i | 0.659512 | − | 1.14231i | −0.321231 | − | 0.947001i | \(-0.604096\pi\) |
0.980742 | − | 0.195307i | \(-0.0625702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.63746 | + | 9.76436i | 0.721803 | + | 1.25020i | 0.960277 | + | 0.279050i | \(0.0900195\pi\) |
−0.238474 | + | 0.971149i | \(0.576647\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.79258 | − | 6.97254i | 0.477820 | − | 0.878458i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.83004 | + | 3.94333i | −0.847163 | + | 0.489110i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9124 | + | 8.03231i | 1.69967 | + | 0.981303i | 0.946067 | + | 0.323970i | \(0.105018\pi\) |
0.753600 | + | 0.657333i | \(0.228316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.36254 | − | 2.51371i | −0.164031 | − | 0.302615i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3585 | −1.22933 | −0.614665 | − | 0.788788i | \(-0.710709\pi\) | ||||
−0.614665 | + | 0.788788i | \(0.710709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.63746 | − | 6.30026i | 0.425732 | − | 0.737390i | −0.570756 | − | 0.821120i | \(-0.693350\pi\) |
0.996489 | + | 0.0837296i | \(0.0266832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.55851 | + | 15.5734i | −1.10372 | + | 1.79827i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.29272 | − | 7.69014i | −0.603161 | − | 0.876373i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.50000 | + | 2.59808i | −0.506290 | + | 0.292306i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94801 | + | 0.965962i | 0.994224 | + | 0.107329i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.17926 | −0.568498 | −0.284249 | − | 0.958751i | \(-0.591744\pi\) | ||||
−0.284249 | + | 0.958751i | \(0.591744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.8248 | −2.15030 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.316720 | + | 11.7781i | −0.0339560 | + | 1.26275i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.23157 | − | 3.59780i | 0.660545 | − | 0.381366i | −0.131940 | − | 0.991258i | \(-0.542121\pi\) |
0.792485 | + | 0.609892i | \(0.208787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.27492 | − | 4.77753i | 0.238476 | − | 0.500821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.55682 | + | 1.56930i | 0.265129 | + | 0.162728i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00465 | + | 10.4004i | −0.616064 | + | 1.06705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.27492 | 0.434052 | 0.217026 | − | 0.976166i | \(-0.430364\pi\) | ||||
0.217026 | + | 0.976166i | \(0.430364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.77774 | − | 8.86957i | 0.580685 | − | 0.891425i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1839 | − | 6.45704i | −1.11284 | − | 0.642499i | −0.173277 | − | 0.984873i | \(-0.555436\pi\) |
−0.939564 | + | 0.342374i | \(0.888769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.18729 | + | 2.41753i | −0.412586 | + | 0.238207i | −0.691900 | − | 0.721993i | \(-0.743226\pi\) |
0.279314 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.944873 | − | 18.0459i | −0.0922102 | − | 1.76110i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.113457 | + | 0.196514i | 0.0109683 | + | 0.0189977i | 0.871457 | − | 0.490471i | \(-0.163175\pi\) |
−0.860489 | + | 0.509469i | \(0.829842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.91238 | − | 6.77643i | 0.374738 | − | 0.649065i | −0.615550 | − | 0.788098i | \(-0.711066\pi\) |
0.990288 | + | 0.139033i | \(0.0443995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.05231 | + | 1.94136i | 0.0998804 | + | 0.184266i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.16818i | 0.203965i | 0.994786 | + | 0.101982i | \(0.0325186\pi\) | ||||
−0.994786 | + | 0.101982i | \(0.967481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.63746 | − | 3.25479i | −0.525696 | − | 0.303511i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.99133 | + | 0.322453i | 0.553899 | + | 0.0298108i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.9570 | − | 7.54112i | 1.00443 | − | 0.691294i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.725083 | − | 1.25588i | −0.0659166 | − | 0.114171i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.100948 | + | 3.75404i | −0.00910218 | + | 0.338490i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 21.8848i | 1.95744i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.77753i | 0.423937i | 0.977277 | + | 0.211968i | \(0.0679874\pi\) | ||||
−0.977277 | + | 0.211968i | \(0.932013\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0389816 | − | 1.44964i | 0.00343214 | − | 0.127634i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.76424 | − | 3.05575i | −0.154142 | − | 0.266982i | 0.778604 | − | 0.627516i | \(-0.215928\pi\) |
−0.932746 | + | 0.360533i | \(0.882595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.637459 | − | 8.03231i | −0.0552747 | − | 0.696490i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.5127 | − | 8.78214i | 1.59332 | − | 0.755847i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.598477 | + | 0.345531i | 0.0511313 | + | 0.0295207i | 0.525348 | − | 0.850888i | \(-0.323935\pi\) |
−0.474216 | + | 0.880408i | \(0.657269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.8997i | − | 1.77269i | −0.463026 | − | 0.886345i | \(-0.653236\pi\) | ||
0.463026 | − | 0.886345i | \(-0.346764\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08762 | + | 7.54112i | 0.344240 | + | 0.635077i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.52848 | − | 6.11151i | 0.295066 | − | 0.511070i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.4124 | + | 23.2309i | 1.11384 | + | 1.92922i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.38669 | + | 9.61441i | 0.609244 | + | 0.792983i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.23157 | − | 3.59780i | 0.510510 | − | 0.294743i | −0.222533 | − | 0.974925i | \(-0.571433\pi\) |
0.733043 | + | 0.680182i | \(0.238099\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.774917 | + | 0.447399i | 0.0630619 | + | 0.0364088i | 0.531199 | − | 0.847247i | \(-0.321741\pi\) |
−0.468138 | + | 0.883656i | \(0.655075\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.6375 | + | 8.23219i | 1.02168 | + | 0.665533i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.83004 | 0.548602 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.18729 | + | 12.4488i | −0.573608 | + | 0.993519i | 0.422583 | + | 0.906324i | \(0.361124\pi\) |
−0.996191 | + | 0.0871947i | \(0.972210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.2626 | − | 8.75392i | −1.13109 | − | 0.694231i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.35387 | − | 0.345531i | 0.343133 | − | 0.0272316i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.63746 | + | 3.25479i | −0.441560 | + | 0.254935i | −0.704259 | − | 0.709943i | \(-0.748721\pi\) |
0.262699 | + | 0.964878i | \(0.415387\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.647819 | − | 24.0910i | 0.0504326 | − | 1.87548i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1139 | 1.09217 | 0.546084 | − | 0.837731i | \(-0.316118\pi\) | ||||
0.546084 | + | 0.837731i | \(0.316118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.14645 | − | 4.13638i | 0.622974 | − | 0.316317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.42852 | + | 4.28886i | −0.564780 | + | 0.326076i | −0.755062 | − | 0.655654i | \(-0.772393\pi\) |
0.190282 | + | 0.981730i | \(0.439060\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.8248 | − | 22.9928i | −1.19624 | − | 1.73809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.17958 | + | 14.9561i | −0.689979 | + | 1.12417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.12696 | + | 7.14810i | −0.308463 | + | 0.534274i | −0.978026 | − | 0.208481i | \(-0.933148\pi\) |
0.669563 | + | 0.742755i | \(0.266481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0997 | 1.12235 | 0.561175 | − | 0.827697i | \(-0.310350\pi\) | ||||
0.561175 | + | 0.827697i | \(0.310350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.30622 | − | 17.1687i | −0.687935 | − | 1.26915i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.35387 | + | 2.51371i | 0.320103 | + | 0.184812i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.3625 | − | 8.86957i | 1.12342 | − | 0.648607i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.89120 | + | 11.8959i | −0.501261 | + | 0.865296i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.30622 | + | 16.1188i | 0.673374 | + | 1.16632i | 0.976941 | + | 0.213508i | \(0.0684891\pi\) |
−0.303567 | + | 0.952810i | \(0.598178\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.04983 | + | 10.4786i | −0.435477 | + | 0.754268i | −0.997334 | − | 0.0729662i | \(-0.976753\pi\) |
0.561858 | + | 0.827234i | \(0.310087\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0093 | − | 6.50958i | 0.860004 | − | 0.466160i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.9415i | − | 1.27828i | −0.769091 | − | 0.639139i | \(-0.779291\pi\) | ||
0.769091 | − | 0.639139i | \(-0.220709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3625 | − | 10.6016i | −1.30169 | − | 0.751529i | −0.320993 | − | 0.947082i | \(-0.604017\pi\) |
−0.980693 | + | 0.195553i | \(0.937350\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.7143 | − | 14.5551i | −1.67267 | − | 1.02664i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.2497 | − | 7.73764i | −1.14051 | − | 0.543076i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.27492 | + | 7.40437i | 0.298573 | + | 0.517144i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.24210 | + | 4.41574i | 0.155837 | + | 0.306915i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.7459i | − | 0.743309i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.78959i | − | 0.123201i | −0.998101 | − | 0.0616004i | \(-0.980380\pi\) | ||
0.998101 | − | 0.0616004i | \(-0.0196204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.9350 | + | 0.482282i | 1.22889 | + | 0.0330454i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65078 | − | 2.85924i | −0.112582 | − | 0.194998i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.77492 | + | 2.59808i | −0.256258 | + | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.59132 | + | 10.7391i | −0.445400 | + | 0.725680i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.70774 | + | 5.02742i | 0.585746 | + | 0.338181i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0312i | 0.671740i | 0.941908 | + | 0.335870i | \(0.109030\pi\) | ||||
−0.941908 | + | 0.335870i | \(0.890970\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.2749 | − | 26.5192i | 1.15166 | − | 1.76795i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7735 | + | 23.8565i | −0.914182 | + | 1.58341i | −0.106088 | + | 0.994357i | \(0.533833\pi\) |
−0.808094 | + | 0.589054i | \(0.799501\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.36254 | − | 7.55614i | −0.288285 | − | 0.499324i | 0.685116 | − | 0.728434i | \(-0.259752\pi\) |
−0.973400 | + | 0.229110i | \(0.926418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.80590 | + | 13.5613i | 0.579386 | + | 0.892270i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.598477 | − | 0.345531i | 0.0392075 | − | 0.0226365i | −0.480268 | − | 0.877122i | \(-0.659461\pi\) |
0.519476 | + | 0.854485i | \(0.326127\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9124 | + | 9.76436i | 1.10324 | + | 0.636957i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.91238 | − | 4.28886i | 0.513964 | − | 0.278591i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9617 | 1.09716 | 0.548579 | − | 0.836099i | \(-0.315169\pi\) | ||||
0.548579 | + | 0.836099i | \(0.315169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | + | 6.06218i | −0.225455 | + | 0.390499i | −0.956456 | − | 0.291877i | \(-0.905720\pi\) |
0.731001 | + | 0.682376i | \(0.239053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4478 | − | 2.08910i | −0.990979 | − | 0.134016i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.7829 | + | 9.85832i | 1.64721 | + | 0.629825i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.27492 | − | 3.04547i | 0.335635 | − | 0.193779i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.96750 | + | 0.241141i | 0.568292 | + | 0.0152817i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.7824 | 0.743698 | 0.371849 | − | 0.928293i | \(-0.378724\pi\) | ||||
0.371849 | + | 0.928293i | \(0.378724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.82475 | 0.366199 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 34.3251 | + | 0.923019i | 2.14952 | + | 0.0578017i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9393 | + | 8.62521i | −0.931888 | + | 0.538026i | −0.887408 | − | 0.460984i | \(-0.847496\pi\) |
−0.0444801 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.36254 | + | 0.266857i | −0.208938 | + | 0.0165817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.09675 | − | 20.3782i | 0.0678874 | − | 1.26138i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9570 | − | 18.9781i | 0.675638 | − | 1.17024i | −0.300645 | − | 0.953736i | \(-0.597202\pi\) |
0.976282 | − | 0.216502i | \(-0.0694649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.0997 | −2.34044 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9570 | + | 5.93918i | −0.670558 | + | 0.363472i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.41502 | − | 1.97166i | −0.208218 | − | 0.120214i | 0.392265 | − | 0.919852i | \(-0.371692\pi\) |
−0.600483 | + | 0.799638i | \(0.705025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.95017 | − | 1.70328i | 0.179210 | − | 0.103467i | −0.407712 | − | 0.913111i | \(-0.633673\pi\) |
0.586921 | + | 0.809644i | \(0.300340\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.16128 | + | 8.16601i | −0.251852 | + | 0.494229i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.6124 | − | 32.2377i | −1.12237 | − | 1.94401i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.63746 | + | 11.4964i | −0.398806 | + | 0.690753i | −0.993579 | − | 0.113141i | \(-0.963909\pi\) |
0.594773 | + | 0.803894i | \(0.297242\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.35387 | − | 2.83616i | −0.260659 | − | 0.169797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7733i | 0.940957i | 0.882411 | + | 0.470478i | \(0.155919\pi\) | ||||
−0.882411 | + | 0.470478i | \(0.844081\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.7371 | − | 10.2405i | −1.05436 | − | 0.608737i | −0.130495 | − | 0.991449i | \(-0.541657\pi\) |
−0.923868 | + | 0.382712i | \(0.874990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.8808 | − | 17.7279i | 0.644525 | − | 1.05011i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.17926 | − | 2.46621i | −0.305722 | − | 0.145576i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.13746 | + | 7.16629i | 0.243380 | + | 0.421546i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.40170 | − | 0.199036i | −0.433895 | − | 0.0116677i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 13.3071i | − | 0.777409i | −0.921362 | − | 0.388705i | \(-0.872923\pi\) | ||
0.921362 | − | 0.388705i | \(-0.127077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.9523i | 2.32611i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.4167 | + | 15.0880i | −0.604437 | + | 0.875494i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.65078 | + | 2.85924i | 0.0954672 | + | 0.165354i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 0.952341i | 0.115278 | + | 0.0548920i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.0635 | + | 11.7006i | 1.09517 | + | 0.672181i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −38.5041 | − | 22.2303i | −2.20474 | − | 1.27291i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.36254 | − | 3.99082i | 0.418840 | − | 0.227030i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1839 | + | 19.3711i | −0.634182 | + | 1.09843i | 0.352506 | + | 0.935809i | \(0.385330\pi\) |
−0.986688 | + | 0.162625i | \(0.948004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.22508 | + | 3.85396i | 0.125769 | + | 0.217838i | 0.922033 | − | 0.387111i | \(-0.126527\pi\) |
−0.796264 | + | 0.604949i | \(0.793193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.795780 | + | 31.2891i | 0.0448371 | + | 1.76294i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.29272 | + | 3.05575i | −0.297269 | + | 0.171628i | −0.641215 | − | 0.767361i | \(-0.721569\pi\) |
0.343947 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.7870 | − | 12.0014i | −1.16385 | − | 0.671947i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.187293 | − | 0.345531i | −0.0104537 | − | 0.0192857i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.3109 | 0.851920 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5498 | − | 18.2728i | 0.585200 | − | 1.01360i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.08949 | + | 11.5507i | −0.392050 | + | 0.638757i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.0616 | + | 1.03659i | −0.720110 | + | 0.0571492i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4622 | + | 14.1233i | −1.34456 | + | 0.776285i | −0.987474 | − | 0.157785i | \(-0.949565\pi\) |
−0.357091 | + | 0.934070i | \(0.616231\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.73160 | − | 3.41032i | −0.0948911 | − | 0.186884i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −63.3481 | −3.46108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.8248 | −1.13440 | −0.567198 | − | 0.823581i | \(-0.691973\pi\) | ||||
−0.567198 | + | 0.823581i | \(0.691973\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.100948 | − | 3.75404i | 0.00548274 | − | 0.203891i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.29272 | + | 3.05575i | −0.286617 | + | 0.165478i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0000 | + | 4.35890i | −0.971909 | + | 0.235358i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.60930 | + | 5.89790i | 0.517347 | + | 0.317532i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.1839 | + | 19.3711i | −0.600384 | + | 1.03990i | 0.392379 | + | 0.919804i | \(0.371652\pi\) |
−0.992763 | + | 0.120092i | \(0.961681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.45017 | 0.291741 | 0.145870 | − | 0.989304i | \(-0.453402\pi\) | ||||
0.145870 | + | 0.989304i | \(0.453402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.3585 | − | 0.837253i | −0.552897 | − | 0.0446893i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.35387 | + | 2.51371i | 0.231733 | + | 0.133791i | 0.611371 | − | 0.791344i | \(-0.290618\pi\) |
−0.379638 | + | 0.925135i | \(0.623952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35.3746 | − | 20.4235i | 1.87749 | − | 1.08397i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.3223 | + | 12.5467i | −1.02265 | + | 0.664044i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.4108 | − | 19.7641i | −0.602241 | − | 1.04311i | −0.992481 | − | 0.122398i | \(-0.960941\pi\) |
0.390241 | − | 0.920713i | \(-0.372392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.86254 | + | 8.42217i | −0.255923 | + | 0.443272i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.19695 | + | 2.20822i | 0.0628238 | + | 0.115902i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.6874i | 1.50157i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5997 | + | 14.7800i | 1.33629 | + | 0.771508i | 0.986255 | − | 0.165228i | \(-0.0528359\pi\) |
0.350036 | + | 0.936736i | \(0.386169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.349568 | − | 6.49513i | 0.0181978 | − | 0.338123i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.0574 | − | 14.4927i | 1.09325 | − | 0.752424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9124 | − | 25.8290i | −0.772134 | − | 1.33737i | −0.936392 | − | 0.350957i | \(-0.885856\pi\) |
0.164258 | − | 0.986417i | \(-0.447477\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.01893 | − | 37.8919i | 0.0526175 | − | 1.95673i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13.6051i | − | 0.700700i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.222437 | − | 8.27193i | 0.0113958 | − | 0.423784i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.4855 | + | 25.0896i | 0.740173 | + | 1.28202i | 0.952416 | + | 0.304801i | \(0.0985900\pi\) |
−0.212243 | + | 0.977217i | \(0.568077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.2371 | + | 15.8265i | 1.69392 | + | 0.806595i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.134988 | + | 2.50813i | −0.00686180 | + | 0.127495i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.8917 | + | 11.4845i | 1.00855 | + | 0.582285i | 0.910766 | − | 0.412923i | \(-0.135492\pi\) |
0.0977811 | + | 0.995208i | \(0.468826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.29917i | 0.419707i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.91238 | + | 5.37295i | 0.146910 | + | 0.271029i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.2451 | − | 17.7450i | 0.515485 | − | 0.892847i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.18729 | − | 5.52055i | −0.159966 | − | 0.277069i | 0.774890 | − | 0.632096i | \(-0.217805\pi\) |
−0.934856 | + | 0.355027i | \(0.884472\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.729736 | + | 13.9370i | 0.0365325 | + | 0.697724i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.6740 | − | 18.2870i | 1.58173 | − | 0.913210i | 0.587119 | − | 0.809501i | \(-0.300262\pi\) |
0.994608 | − | 0.103709i | \(-0.0330712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | − | 1.73205i | −0.149441 | − | 0.0862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.4622 | + | 14.3437i | −1.61306 | + | 0.712744i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.49852 | −0.222983 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.22508 | − | 14.2463i | 0.406704 | − | 0.704432i | −0.587814 | − | 0.808996i | \(-0.700011\pi\) |
0.994518 | + | 0.104564i | \(0.0333446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.02013 | − | 0.626125i | −0.0503193 | − | 0.0308845i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.1974 | − | 22.0813i | −0.747816 | − | 1.08655i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6873 | − | 10.2118i | 0.868235 | − | 0.501276i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.973068 | + | 36.1863i | −0.0476513 | + | 1.77205i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.1679 | 1.47380 | 0.736899 | − | 0.676002i | \(-0.236289\pi\) | ||||
0.736899 | + | 0.676002i | \(0.236289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0997 | 0.540965 | 0.270482 | − | 0.962725i | \(-0.412817\pi\) | ||||
0.270482 | + | 0.962725i | \(0.412817\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.72631 | − | 13.2472i | −0.327044 | − | 0.644101i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 45.9326 | − | 26.5192i | 2.22806 | − | 1.28637i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.7371 | − | 2.35999i | 1.43908 | − | 0.114208i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.39384 | + | 10.4173i | −0.308698 | + | 0.502953i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8347 | − | 22.2303i | 0.618226 | − | 1.07080i | −0.371584 | − | 0.928399i | \(-0.621185\pi\) |
0.989809 | − | 0.142399i | \(-0.0454815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.1409 | − | 40.8471i | −1.06158 | − | 1.95847i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.35387 | + | 2.51371i | 0.208274 | + | 0.120247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.32475 | − | 4.80630i | 0.397319 | − | 0.229392i | −0.288008 | − | 0.957628i | \(-0.592993\pi\) |
0.685326 | + | 0.728236i | \(0.259660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3419 | − | 16.9905i | −0.587707 | − | 0.809074i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.0751 | + | 29.5750i | 0.811263 | + | 1.40515i | 0.911980 | + | 0.410234i | \(0.134553\pi\) |
−0.100717 | + | 0.994915i | \(0.532114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1873 | + | 24.5731i | −0.672542 | + | 1.16488i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9570 | + | 5.93918i | −0.518248 | + | 0.280914i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.3784i | 1.38645i | 0.720719 | + | 0.693227i | \(0.243812\pi\) | ||||
−0.720719 | + | 0.693227i | \(0.756188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.62541 | − | 3.82518i | −0.311979 | − | 0.180121i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.32088 | − | 0.810717i | −0.0620604 | − | 0.0380908i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.65078 | + | 20.8007i | 0.0773899 | + | 0.975153i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3248 | − | 24.8112i | −0.670084 | − | 1.16062i | −0.977880 | − | 0.209167i | \(-0.932925\pi\) |
0.307796 | − | 0.951452i | \(-0.400408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.4975 | − | 14.8418i | −1.00342 | − | 0.692756i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.6051i | − | 0.633654i | −0.948483 | − | 0.316827i | \(-0.897382\pi\) | ||
0.948483 | − | 0.316827i | \(-0.102618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.9715i | − | 0.649310i | −0.945832 | − | 0.324655i | \(-0.894752\pi\) | ||
0.945832 | − | 0.324655i | \(-0.105248\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.8257 | − | 0.318000i | −0.548404 | − | 0.0147469i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4855 | + | 25.0896i | 0.670308 | + | 1.16101i | 0.977817 | + | 0.209462i | \(0.0671714\pi\) |
−0.307509 | + | 0.951545i | \(0.599495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.0120 | − | 24.0969i | 1.61671 | − | 1.11269i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.0239 | − | 21.2195i | 0.600108 | − | 0.977741i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.55844 | + | 1.47712i | 0.117637 | + | 0.0679179i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 32.1293i | − | 1.47419i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.2870 | + | 15.8208i | 1.11202 | + | 0.724385i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.24926 | + | 3.89583i | −0.102771 | + | 0.178005i | −0.912825 | − | 0.408350i | \(-0.866104\pi\) |
0.810054 | + | 0.586355i | \(0.199438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27492 | − | 2.20822i | −0.0581312 | − | 0.100686i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.55449 | + | 0.395549i | −0.343741 | + | 0.0179981i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.5989 | + | 8.42870i | −0.662904 | + | 0.382728i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.22508 | + | 1.28465i | 0.100828 | + | 0.0582131i | 0.549566 | − | 0.835450i | \(-0.314793\pi\) |
−0.448738 | + | 0.893663i | \(0.648126\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.91238 | − | 5.37295i | 0.448253 | − | 0.242973i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1409 | −0.999206 | −0.499603 | − | 0.866255i | \(-0.666521\pi\) | ||||
−0.499603 | + | 0.866255i | \(0.666521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0997 | − | 29.6175i | 0.770130 | − | 1.33390i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.24330 | + | 41.6815i | −0.100829 | + | 1.87345i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.7824 | + | 24.7441i | −0.528512 | + | 1.10992i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.1873 | + | 12.8098i | −0.993240 | + | 0.573447i | −0.906241 | − | 0.422761i | \(-0.861061\pi\) |
−0.0869986 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.4372 | − | 0.657129i | −1.09177 | − | 0.0293584i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.9244 | 2.26611 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.5828 | + | 0.419030i | 0.692058 | + | 0.0186098i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.36737 | − | 4.83090i | 0.370877 | − | 0.214126i | −0.302964 | − | 0.953002i | \(-0.597976\pi\) |
0.673842 | + | 0.738876i | \(0.264643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.9124 | − | 15.8553i | −0.482735 | − | 0.701398i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.2975 | + | 6.78254i | −0.631252 | + | 0.299457i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.53313 | − | 16.5119i | 0.420080 | − | 0.727600i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4743 | −0.768517 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0616 | − | 7.07997i | 0.573341 | − | 0.310776i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.8170 | − | 9.70930i | −0.736766 | − | 0.425372i | 0.0841261 | − | 0.996455i | \(-0.473190\pi\) |
−0.820892 | + | 0.571083i | \(0.806523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.4622 | − | 12.3912i | 0.938477 | − | 0.541830i | 0.0489944 | − | 0.998799i | \(-0.484398\pi\) |
0.889483 | + | 0.456969i | \(0.151065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.3288 | + | 40.5471i | 1.14909 | + | 1.76962i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.35387 | − | 7.54112i | −0.189658 | − | 0.328497i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1375 | − | 17.5586i | 0.440759 | − | 0.763417i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.5901 | − | 25.4679i | 0.719949 | − | 1.10521i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.33635i | − | 0.187828i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.774917 | − | 0.447399i | −0.0335026 | − | 0.0193427i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.47832 | − | 12.1842i | 0.322713 | − | 0.525789i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.3902 | + | 3.89583i | −1.05056 | + | 0.167805i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3625 | + | 23.1446i | 0.574501 | + | 0.995064i | 0.996096 | + | 0.0882799i | \(0.0281370\pi\) |
−0.421595 | + | 0.906784i | \(0.638530\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1439 | − | 0.703025i | −1.12194 | − | 0.0301697i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.8556i | 1.32171i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0192i | 0.556659i | 0.960486 | + | 0.278329i | \(0.0897807\pi\) | ||||
−0.960486 | + | 0.278329i | \(0.910219\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3137 | + | 30.1597i | 0.653571 | + | 1.28718i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3585 | − | 17.9415i | −0.441288 | − | 0.764333i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.08762 | + | 13.7046i | 0.0462505 | + | 0.582780i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.42136 | − | 4.55501i | −0.315019 | − | 0.193349i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3197 | − | 7.69014i | −0.564375 | − | 0.325842i | 0.190525 | − | 0.981682i | \(-0.438981\pi\) |
−0.754899 | + | 0.655841i | \(0.772314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.67451i | 0.0708241i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.0120 | + | 14.6417i | −1.14045 | + | 0.618174i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.0005 | − | 24.2495i | 0.590049 | − | 1.02199i | −0.404176 | − | 0.914681i | \(-0.632442\pi\) |
0.994225 | − | 0.107314i | \(-0.0342249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.27492 | − | 7.40437i | −0.179847 | − | 0.311504i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.4854 | − | 20.2759i | 0.524339 | − | 0.851509i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.8710 | + | 18.9781i | −1.37802 | + | 0.795603i | −0.991921 | − | 0.126853i | \(-0.959512\pi\) |
−0.386103 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.4622 | − | 8.92711i | −0.647073 | − | 0.373588i | 0.140261 | − | 0.990115i | \(-0.455206\pi\) |
−0.787334 | + | 0.616527i | \(0.788539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.3625 | − | 28.3419i | −0.641779 | − | 1.18400i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.4155 | 0.726276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0498 | − | 29.5312i | 0.709794 | − | 1.22940i | −0.255140 | − | 0.966904i | \(-0.582121\pi\) |
0.964933 | − | 0.262495i | \(-0.0845453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.9627 | − | 17.8613i | 0.455595 | − | 0.742289i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.89120 | + | 12.3720i | −0.244408 | + | 0.513278i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.5241 | − | 17.0457i | 1.22276 | − | 0.705962i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.0963 | + | 10.7117i | −0.872224 | + | 0.442874i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.17926 | 0.213771 | 0.106886 | − | 0.994271i | \(-0.465912\pi\) | ||||
0.106886 | + | 0.994271i | \(0.465912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.27492 | −0.217349 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.835337 | + | 31.0643i | −0.0343612 | + | 1.27782i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.1839 | + | 6.45704i | −0.459268 | + | 0.265159i | −0.711737 | − | 0.702446i | \(-0.752091\pi\) |
0.252468 | + | 0.967605i | \(0.418758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.5498 | + | 47.3566i | −0.924453 | + | 1.94143i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.2998 | + | 19.2108i | 1.28101 | + | 0.786248i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.598477 | − | 1.03659i | 0.0244531 | − | 0.0423540i | −0.853540 | − | 0.521028i | \(-0.825549\pi\) |
0.877993 | + | 0.478673i | \(0.158882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9244 | 0.731152 | 0.365576 | − | 0.930781i | \(-0.380872\pi\) | ||||
0.365576 | + | 0.930781i | \(0.380872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.3818 | + | 26.3052i | 1.64447 | + | 1.07123i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.95235 | + | 2.85924i | 0.201342 | + | 0.116245i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.0498 | − | 17.3493i | 1.21969 | − | 0.704186i | 0.254835 | − | 0.966985i | \(-0.417979\pi\) |
0.964851 | + | 0.262799i | \(0.0846456\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.7749 | + | 14.1537i | 1.12550 | + | 0.573537i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.95235 | − | 8.57772i | −0.200351 | − | 0.347017i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.9124 | + | 32.7572i | −0.763864 | + | 1.32305i | 0.176982 | + | 0.984214i | \(0.443367\pi\) |
−0.940845 | + | 0.338837i | \(0.889967\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.05696 | − | 13.0192i | −0.284564 | − | 0.524983i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 38.0512i | − | 1.53188i | −0.642911 | − | 0.765941i | \(-0.722273\pi\) | ||
0.642911 | − | 0.765941i | \(-0.277727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.46221 | − | 5.46301i | −0.380318 | − | 0.219577i | 0.297638 | − | 0.954679i | \(-0.403801\pi\) |
−0.677957 | + | 0.735102i | \(0.737134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.67644 | − | 7.74990i | −0.147530 | − | 0.310993i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.50613 | − | 18.9781i | −0.0603420 | − | 0.760341i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.7749 | − | 29.0550i | −0.670997 | − | 1.16220i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.500317 | + | 18.6057i | −0.0199808 | + | 0.743040i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.40954i | − | 0.255565i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.0219i | 1.47382i | 0.675992 | + | 0.736909i | \(0.263715\pi\) | ||||
−0.675992 | + | 0.736909i | \(0.736285\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.0833216 | + | 3.09855i | −0.00331174 | + | 0.123156i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.41968 | − | 16.3154i | −0.373808 | − | 0.647455i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.82475 | − | 10.8685i | −0.349649 | − | 0.430625i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.0307 | − | 1.67007i | −1.22755 | − | 0.0660669i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.23157 | + | 3.59780i | 0.246132 | + | 0.142104i | 0.617992 | − | 0.786184i | \(-0.287946\pi\) |
−0.371860 | + | 0.928289i | \(0.621280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.09095i | 0.240204i | 0.992762 | + | 0.120102i | \(0.0383221\pi\) | ||||
−0.992762 | + | 0.120102i | \(0.961678\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.72508 | + | 5.02742i | 0.107300 | + | 0.197954i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.58078 | + | 7.93415i | −0.180089 | + | 0.311924i | −0.941911 | − | 0.335863i | \(-0.890972\pi\) |
0.761822 | + | 0.647787i | \(0.224305\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.8746 | − | 30.9597i | −0.701639 | − | 1.21527i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.65695 | − | 4.32262i | 0.260906 | − | 0.169417i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2721 | − | 10.5494i | 0.715041 | − | 0.412829i | −0.0978837 | − | 0.995198i | \(-0.531207\pi\) |
0.812925 | + | 0.582369i | \(0.197874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0498 | + | 6.95698i | 0.470826 | + | 0.271832i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9124 | − | 18.2870i | 0.464746 | − | 0.713445i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.1895 | −1.76033 | −0.880166 | − | 0.474666i | \(-0.842569\pi\) | ||||
−0.880166 | + | 0.474666i | \(0.842569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6375 | + | 25.3528i | −0.569331 | + | 0.986110i | 0.427301 | + | 0.904109i | \(0.359464\pi\) |
−0.996632 | + | 0.0820011i | \(0.973869\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.8427 | − | 9.11002i | −0.576444 | − | 0.353804i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.0140 | + | 26.1737i | 0.698551 | + | 1.01497i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.72508 | − | 5.61478i | 0.376557 | − | 0.217405i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.467043 | − | 17.3683i | 0.0180569 | − | 0.671498i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7833 | 1.53582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2749 | 0.473163 | 0.236582 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236582 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.1449 | + | 45.1117i | −1.19877 | + | 1.73635i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.9258 | + | 6.30802i | −0.419913 | + | 0.242437i | −0.695040 | − | 0.718971i | \(-0.744613\pi\) |
0.275127 | + | 0.961408i | \(0.411280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.86254 | − | 10.2118i | 0.186607 | − | 0.391892i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.9586 | − | 40.6644i | 0.956415 | − | 1.55826i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.3497 | + | 21.3903i | −0.472547 | + | 0.818476i | −0.999506 | − | 0.0314147i | \(-0.989999\pi\) |
0.526959 | + | 0.849891i | \(0.323332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.72508 | −0.104120 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.20161 | + | 13.2860i | 0.274758 | + | 0.506893i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.7347 | + | 9.66181i | 0.637543 | + | 0.368085i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.7371 | + | 15.4367i | −1.01713 | + | 0.587239i | −0.913271 | − | 0.407353i | \(-0.866452\pi\) |
−0.103857 | + | 0.994592i | \(0.533119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.6154 | − | 23.8904i | −0.555191 | − | 0.907522i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.2072 | + | 71.3729i | 1.56308 | + | 2.70733i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.45017 | − | 9.43996i | 0.206440 | − | 0.357564i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.05231 | + | 0.570396i | −0.0398018 | + | 0.0215744i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.5759i | − | 0.852679i | −0.904563 | − | 0.426340i | \(-0.859803\pi\) | ||
0.904563 | − | 0.426340i | \(-0.140197\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.36254 | − | 1.94136i | −0.126821 | − | 0.0732199i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.8279 | − | 17.6937i | −1.08572 | − | 0.666383i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.1456 | + | 19.3711i | −1.05852 | + | 0.728526i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1873 | + | 17.6449i | 0.382592 | + | 0.662668i | 0.991432 | − | 0.130625i | \(-0.0416982\pi\) |
−0.608840 | + | 0.793293i | \(0.708365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8994 | + | 7.05744i | −0.521267 | + | 0.264675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.85924i | − | 0.107079i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.8279i | 1.04070i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.3678 | − | 0.789717i | −1.09676 | − | 0.0294925i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.53313 | − | 16.5119i | −0.355526 | − | 0.615789i | 0.631682 | − | 0.775228i | \(-0.282365\pi\) |
−0.987208 | + | 0.159439i | \(0.949032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.01204 | + | 12.7523i | 0.0376905 | + | 0.474920i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.34224 | − | 10.3332i | 0.235870 | − | 0.384298i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −62.1511 | − | 35.8830i | −2.30824 | − | 1.33266i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7534i | 0.398821i | 0.979916 | + | 0.199411i | \(0.0639027\pi\) | ||||
−0.979916 | + | 0.199411i | \(0.936097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.6495 | + | 4.33635i | 0.987019 | + | 0.160606i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.10461 | + | 3.64529i | −0.0778418 | + | 0.134826i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.6375 | − | 28.8169i | −0.614519 | − | 1.06438i | −0.990469 | − | 0.137737i | \(-0.956017\pi\) |
0.375950 | − | 0.926640i | \(-0.377316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −44.1821 | − | 18.2694i | −1.62968 | − | 0.673876i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.0895 | − | 28.3419i | 1.80824 | − | 1.04399i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8368 | + | 20.6904i | 1.31828 | + | 0.761108i | 0.983451 | − | 0.181172i | \(-0.0579890\pi\) |
0.334826 | + | 0.942280i | \(0.391322\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.27492 | + | 5.02742i | −0.340723 | + | 0.184687i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9233 | −1.24453 | −0.622263 | − | 0.782808i | \(-0.713786\pi\) | ||||
−0.622263 | + | 0.782808i | \(0.713786\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1873 | + | 24.5731i | −0.519782 | + | 0.900289i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.5153 | − | 0.835035i | −0.567676 | − | 0.0305523i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.598477 | − | 0.0474962i | 0.0218679 | − | 0.00173547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.59967 | + | 4.38767i | −0.277316 | + | 0.160108i | −0.632208 | − | 0.774799i | \(-0.717851\pi\) |
0.354892 | + | 0.934907i | \(0.384518\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.4003 | − | 0.548576i | −0.743429 | − | 0.0199912i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.52848 | −0.128415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0997 | −0.548807 | −0.274403 | − | 0.961615i | \(-0.588480\pi\) | ||||
−0.274403 | + | 0.961615i | \(0.588480\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.0851 | − | 0.271194i | −0.366067 | − | 0.00984373i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.67313 | + | 2.12068i | −0.133151 | + | 0.0768746i | −0.565096 | − | 0.825025i | \(-0.691161\pi\) |
0.431945 | + | 0.901900i | \(0.357827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.7371 | − | 17.0537i | −0.424913 | − | 0.617384i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −59.3883 | − | 3.19628i | −2.14719 | − | 0.115562i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.1316 | − | 17.5485i | 0.365831 | − | 0.633638i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.8248 | −1.03945 | −0.519724 | − | 0.854334i | \(-0.673965\pi\) | ||||
−0.519724 | + | 0.854334i | \(0.673965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.2679 | − | 14.2384i | 0.946014 | − | 0.512782i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.2118 | + | 27.2578i | 1.69809 | + | 0.980394i | 0.947570 | + | 0.319547i | \(0.103531\pi\) |
0.750521 | + | 0.660846i | \(0.229802\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.8248 | + | 9.13642i | −0.568442 | + | 0.328190i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.83441 | − | 0.305487i | 0.209308 | − | 0.0109593i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.30156 | − | 5.71848i | −0.118291 | − | 0.204886i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2749 | + | 31.6531i | −0.653928 | + | 1.13264i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.84774 | + | 35.2323i | −0.101770 | + | 1.25910i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 56.6837i | − | 2.02313i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.7371 | + | 18.9008i | 1.16695 | + | 0.673740i | 0.952960 | − | 0.303095i | \(-0.0980199\pi\) |
0.213992 | + | 0.976835i | \(0.431353\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.8548 | + | 32.3490i | −0.706850 | + | 1.15165i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.17926 | + | 2.46621i | 0.184153 | + | 0.0876884i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2749 | + | 19.5287i | 0.400384 | + | 0.693486i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 65.9667 | + | 1.77388i | 2.33960 | + | 0.0629130i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.7441i | 0.876479i | 0.898858 | + | 0.438240i | \(0.144398\pi\) | ||||
−0.898858 | + | 0.438240i | \(0.855602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.8975i | − | 0.880811i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.2477 | − | 9.77310i | 0.680086 | − | 0.345315i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.8347 | − | 22.2303i | −0.452927 | − | 0.784492i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.1873 | + | 9.76436i | −0.500036 | + | 0.344149i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.82106 | + | 3.57279i | 0.204911 | + | 0.125768i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.5787 | + | 24.0055i | 1.46183 | + | 0.843988i | 0.999096 | − | 0.0425085i | \(-0.0135350\pi\) |
0.462735 | + | 0.886497i | \(0.346868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.41644i | − | 0.155082i | −0.996989 | − | 0.0775411i | \(-0.975293\pi\) | ||
0.996989 | − | 0.0775411i | \(-0.0247069\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.18729 | + | 2.81174i | −0.181926 | + | 0.0986121i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.8347 | − | 22.2303i | 0.449580 | − | 0.778695i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.27492 | + | 2.20822i | 0.0446037 | + | 0.0772559i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.58515 | − | 13.9451i | 0.265047 | − | 0.487281i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.4906 | + | 19.9132i | −1.20373 | + | 0.694974i | −0.961383 | − | 0.275216i | \(-0.911251\pi\) |
−0.242347 | + | 0.970190i | \(0.577917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9124 | − | 9.76436i | −0.589528 | − | 0.340364i | 0.175383 | − | 0.984500i | \(-0.443884\pi\) |
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.7251 | + | 56.6837i | 1.06971 | + | 1.97347i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.02700 | −0.279126 | −0.139563 | − | 0.990213i | \(-0.544570\pi\) | ||||
−0.139563 | + | 0.990213i | \(0.544570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.18729 | + | 8.98466i | −0.180162 | + | 0.312050i | −0.941936 | − | 0.335793i | \(-0.890996\pi\) |
0.761774 | + | 0.647843i | \(0.224329\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0275 | − | 19.5961i | 0.417230 | − | 0.679783i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.55082 | − | 34.7514i | −0.192325 | − | 1.20406i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.1993 | + | 27.8279i | −1.66801 | + | 0.963024i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.40635 | + | 5.11331i | 0.256001 | + | 0.176742i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.7170 | 0.715232 | 0.357616 | − | 0.933869i | \(-0.383590\pi\) | ||||
0.357616 | + | 0.933869i | \(0.383590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.2749 | −0.595687 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.734389 | − | 27.3103i | 0.0252937 | − | 0.940617i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.7352 | − | 17.7450i | 1.05732 | − | 0.610446i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.82475 | + | 0.303539i | −0.131420 | + | 0.0104297i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.2337 | + | 18.5565i | 1.03762 | + | 0.636859i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05231 | − | 1.82265i | 0.0360726 | − | 0.0624795i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.5498 | 1.31992 | 0.659961 | − | 0.751300i | \(-0.270573\pi\) | ||||
0.659961 | + | 0.751300i | \(0.270573\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.6647 | + | 30.1879i | −0.672520 | + | 1.03240i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0886 | − | 12.1755i | −0.720373 | − | 0.415908i | 0.0945168 | − | 0.995523i | \(-0.469869\pi\) |
−0.814890 | + | 0.579616i | \(0.803203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0120 | + | 20.2142i | −1.19460 | + | 0.689700i | −0.959345 | − | 0.282235i | \(-0.908924\pi\) |
−0.235250 | + | 0.971935i | \(0.575591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.85268 | + | 4.51120i | 0.301698 | + | 0.153741i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.825391 | + | 1.42962i | 0.0280966 | + | 0.0486648i | 0.879732 | − | 0.475470i | \(-0.157722\pi\) |
−0.851635 | + | 0.524135i | \(0.824389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.9124 | − | 29.2931i | 0.575038 | − | 0.995995i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.83004 | − | 12.6005i | −0.231960 | − | 0.427936i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.3345i | 0.621956i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.8248 | + | 16.0646i | 0.942806 | + | 0.544329i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.8062 | + | 0.689230i | 0.433425 | + | 0.0233269i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 52.2776 | + | 24.8931i | 1.76731 | + | 0.841539i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.91238 | + | 10.2405i | 0.199647 | + | 0.345798i | 0.948414 | − | 0.317035i | \(-0.102687\pi\) |
−0.748767 | + | 0.662833i | \(0.769354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.619564 | + | 23.0402i | −0.0208974 | + | 0.777128i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.8739i | 0.770642i | 0.922783 | + | 0.385321i | \(0.125909\pi\) | ||||
−0.922783 | + | 0.385321i | \(0.874091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.1051i | − | 1.28234i | −0.767399 | − | 0.641170i | \(-0.778449\pi\) | ||
0.767399 | − | 0.641170i | \(-0.221551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.86013 | − | 69.1743i | 0.0625277 | − | 2.32527i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.8347 | − | 22.2303i | −0.430947 | − | 0.746422i | 0.566008 | − | 0.824400i | \(-0.308487\pi\) |
−0.996955 | + | 0.0779776i | \(0.975154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4124 | + | 5.43424i | 0.382759 | + | 0.182258i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.7382 | − | 25.6387i | 0.627753 | − | 0.858930i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0616 | − | 7.54112i | −0.437090 | − | 0.252354i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.5479i | − | 1.08796i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.72508 | − | 5.02742i | −0.0909879 | − | 0.167861i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.89120 | + | 10.2039i | −0.196482 | + | 0.340317i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.2870 | + | 42.0663i | 0.809116 | + | 1.40143i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.41851 | − | 1.74203i | −0.113761 | − | 0.0579710i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −51.5657 | + | 29.7715i | −1.71410 | + | 0.989637i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.0120 | − | 21.9463i | −1.26217 | − | 0.728714i | −0.288675 | − | 0.957427i | \(-0.593215\pi\) |
−0.973494 | + | 0.228713i | \(0.926548\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.4622 | − | 21.1463i | −1.07670 | − | 0.701377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8693 | −0.592037 | −0.296018 | − | 0.955182i | \(-0.595659\pi\) | ||||
−0.296018 | + | 0.955182i | \(0.595659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.13746 | + | 15.8265i | −0.302406 | + | 0.523782i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 65.6319 | + | 40.2829i | 2.16972 | + | 1.33171i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.30622 | + | 0.738558i | −0.307318 | + | 0.0243893i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.3625 | − | 17.5298i | 1.00157 | − | 0.578255i | 0.0928560 | − | 0.995680i | \(-0.470400\pi\) |
0.908712 | + | 0.417424i | \(0.137067\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.806424 | − | 29.9892i | 0.0265726 | − | 0.988176i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.7170 | −0.681910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4502 | −0.442239 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.9335 | + | 6.56702i | −0.424792 | + | 0.215689i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.55082 | + | 3.20477i | −0.182117 | + | 0.105145i | −0.588287 | − | 0.808652i | \(-0.700197\pi\) |
0.406170 | + | 0.913797i | \(0.366864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.9124 | − | 7.61369i | −0.652602 | − | 0.249529i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.2660 | − | 33.0189i | 0.663479 | − | 1.08099i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −34.9756 | + | 60.5795i | −1.14382 | + | 1.98116i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.1752 | −0.887777 | −0.443888 | − | 0.896082i | \(-0.646401\pi\) | ||||
−0.443888 | + | 0.896082i | \(0.646401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.67313 | − | 6.77643i | −0.119868 | − | 0.221141i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.340371 | + | 0.196514i | 0.0110958 | + | 0.00640616i | 0.505538 | − | 0.862805i | \(-0.331294\pi\) |
−0.494442 | + | 0.869211i | \(0.664628\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.09967 | − | 1.78959i | 0.100939 | − | 0.0582772i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0789532 | − | 54.2117i | 0.00256835 | − | 1.76351i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.23157 | − | 10.7934i | −0.202499 | − | 0.350738i | 0.746834 | − | 0.665010i | \(-0.231573\pi\) |
−0.949333 | + | 0.314272i | \(0.898240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.27492 | − | 12.6005i | 0.236154 | − | 0.409030i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.30622 | − | 5.04438i | 0.301775 | − | 0.163575i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.3290i | 1.95425i | 0.212670 | + | 0.977124i | \(0.431784\pi\) | ||||
−0.212670 | + | 0.977124i | \(0.568216\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.5619 | − | 36.6975i | −2.05681 | − | 1.18750i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.4323 | + | 21.7473i | 1.14536 | + | 0.702989i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.50613 | − | 1.03659i | 0.0486356 | − | 0.0334733i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.308196 | + | 0.606981i | 0.00993149 | + | 0.0195597i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 47.7130i | − | 1.53593i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30.8158i | − | 0.990970i | −0.868616 | − | 0.495485i | \(-0.834990\pi\) | ||
0.868616 | − | 0.495485i | \(-0.165010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.5096 | − | 0.712858i | −0.851612 | − | 0.0229003i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.7735 | + | 23.8565i | 0.442014 | + | 0.765591i | 0.997839 | − | 0.0657086i | \(-0.0209308\pi\) |
−0.555825 | + | 0.831299i | \(0.687597\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.9244 | − | 23.7725i | −1.60050 | − | 0.762113i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.1170 | + | 31.1469i | −0.612234 | + | 0.997498i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.1633 | + | 13.9507i | 0.773051 | + | 0.446321i | 0.833962 | − | 0.551822i | \(-0.186067\pi\) |
−0.0609108 | + | 0.998143i | \(0.519401\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 25.3895i | − | 0.811452i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8127 | − | 19.6691i | 0.409078 | − | 0.627987i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.5901 | − | 28.7349i | 0.529142 | − | 0.916500i | −0.470281 | − | 0.882517i | \(-0.655847\pi\) |
0.999422 | − | 0.0339834i | \(-0.0108193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.3746 | + | 61.2706i | 1.12713 | + | 1.95224i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.6635 | − | 1.18665i | 0.721386 | − | 0.0377714i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.19695 | + | 0.691062i | −0.0380609 | + | 0.0219745i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.5997 | − | 9.58382i | −0.527306 | − | 0.304440i | 0.212613 | − | 0.977137i | \(-0.431803\pi\) |
−0.739919 | + | 0.672696i | \(0.765136\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.0120 | − | 23.3144i | 1.36495 | − | 0.739861i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 83.6113 | 2.65066 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.6375 | + | 18.4246i | −0.336892 | + | 0.583514i | −0.983846 | − | 0.179015i | \(-0.942709\pi\) |
0.646955 | + | 0.762528i | \(0.276042\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.83935 | + | 5.98534i | 0.0898332 | + | 0.189368i |
(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 | 336.2.bj.e.95.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 336.2.bj.e.95.2 | yes | 8 | |
4.3 | odd | 2 | 336.2.bj.g.95.4 | yes | 8 | ||
7.2 | even | 3 | 336.2.bj.g.191.3 | yes | 8 | ||
7.3 | odd | 6 | 2352.2.h.m.2255.3 | 8 | |||
7.4 | even | 3 | 2352.2.h.n.2255.6 | 8 | |||
12.11 | even | 2 | 336.2.bj.g.95.3 | yes | 8 | ||
21.2 | odd | 6 | 336.2.bj.g.191.4 | yes | 8 | ||
21.11 | odd | 6 | 2352.2.h.n.2255.4 | 8 | |||
21.17 | even | 6 | 2352.2.h.m.2255.5 | 8 | |||
28.3 | even | 6 | 2352.2.h.m.2255.6 | 8 | |||
28.11 | odd | 6 | 2352.2.h.n.2255.3 | 8 | |||
28.23 | odd | 6 | inner | 336.2.bj.e.191.2 | yes | 8 | |
84.11 | even | 6 | 2352.2.h.n.2255.5 | 8 | |||
84.23 | even | 6 | inner | 336.2.bj.e.191.1 | yes | 8 | |
84.59 | odd | 6 | 2352.2.h.m.2255.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bj.e.95.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
336.2.bj.e.95.2 | yes | 8 | 3.2 | odd | 2 | inner | |
336.2.bj.e.191.1 | yes | 8 | 84.23 | even | 6 | inner | |
336.2.bj.e.191.2 | yes | 8 | 28.23 | odd | 6 | inner | |
336.2.bj.g.95.3 | yes | 8 | 12.11 | even | 2 | ||
336.2.bj.g.95.4 | yes | 8 | 4.3 | odd | 2 | ||
336.2.bj.g.191.3 | yes | 8 | 7.2 | even | 3 | ||
336.2.bj.g.191.4 | yes | 8 | 21.2 | odd | 6 | ||
2352.2.h.m.2255.3 | 8 | 7.3 | odd | 6 | |||
2352.2.h.m.2255.4 | 8 | 84.59 | odd | 6 | |||
2352.2.h.m.2255.5 | 8 | 21.17 | even | 6 | |||
2352.2.h.m.2255.6 | 8 | 28.3 | even | 6 | |||
2352.2.h.n.2255.3 | 8 | 28.11 | odd | 6 | |||
2352.2.h.n.2255.4 | 8 | 21.11 | odd | 6 | |||
2352.2.h.n.2255.5 | 8 | 84.11 | even | 6 | |||
2352.2.h.n.2255.6 | 8 | 7.4 | even | 3 |