Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
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, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(0.895402 + 1.55088i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.j.193.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 52.0958 | − | 90.2327i | 0.931919 | − | 1.61413i | 0.151881 | − | 0.988399i | \(-0.451467\pi\) |
0.780038 | − | 0.625732i | \(-0.215200\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.12980 | + | 129.446i | 0.0549961 | + | 0.998487i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −248.830 | − | 430.986i | −0.620041 | − | 1.07394i | −0.989477 | − | 0.144687i | \(-0.953782\pi\) |
0.369436 | − | 0.929256i | \(-0.379551\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −206.551 | −0.338977 | −0.169488 | − | 0.985532i | \(-0.554211\pi\) | ||||
−0.169488 | + | 0.985532i | \(0.554211\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 937.725 | 1.07609 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.5793 | − | 54.6969i | −0.0265021 | − | 0.0459030i | 0.852470 | − | 0.522776i | \(-0.175104\pi\) |
−0.878972 | + | 0.476873i | \(0.841770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 661.977 | − | 1146.58i | 0.420687 | − | 0.728651i | −0.575320 | − | 0.817929i | \(-0.695122\pi\) |
0.996007 | + | 0.0892772i | \(0.0284557\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −976.845 | + | 638.077i | −0.483367 | + | 0.315736i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −97.2187 | + | 168.388i | −0.0383204 | + | 0.0663729i | −0.884550 | − | 0.466446i | \(-0.845534\pi\) |
0.846229 | + | 0.532819i | \(0.178867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3865.45 | − | 6695.16i | −1.23695 | − | 2.14245i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4323.14 | 0.954562 | 0.477281 | − | 0.878751i | \(-0.341622\pi\) | ||||
0.477281 | + | 0.878751i | \(0.341622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3762.66 | − | 6517.11i | −0.703219 | − | 1.21801i | −0.967331 | − | 0.253518i | \(-0.918412\pi\) |
0.264112 | − | 0.964492i | \(-0.414921\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2239.47 | − | 3878.87i | 0.357981 | − | 0.620041i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12051.7 | + | 6100.24i | 1.66294 | + | 0.841738i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5177.82 | + | 8968.25i | −0.621789 | + | 1.07697i | 0.367364 | + | 0.930077i | \(0.380260\pi\) |
−0.989152 | + | 0.146892i | \(0.953073\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −929.481 | − | 1609.91i | −0.0978541 | − | 0.169488i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4180.92 | −0.388429 | −0.194215 | − | 0.980959i | \(-0.562216\pi\) | ||||
−0.194215 | + | 0.980959i | \(0.562216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5960.87 | −0.491630 | −0.245815 | − | 0.969317i | \(-0.579056\pi\) | ||||
−0.245815 | + | 0.969317i | \(0.579056\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4219.76 | + | 7308.85i | 0.310640 | + | 0.538044i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2194.87 | + | 3801.62i | −0.144932 | + | 0.251029i | −0.929348 | − | 0.369206i | \(-0.879630\pi\) |
0.784416 | + | 0.620236i | \(0.212963\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16705.3 | + | 1845.84i | −0.993951 | + | 0.109826i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 284.214 | − | 492.273i | 0.0153010 | − | 0.0265021i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8892.39 | − | 15402.1i | −0.434839 | − | 0.753164i | 0.562443 | − | 0.826836i | \(-0.309862\pi\) |
−0.997283 | + | 0.0736720i | \(0.976528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −51852.0 | −2.31131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11915.6 | 0.485768 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1750.23 | + | 3031.49i | 0.0654585 | + | 0.113377i | 0.896897 | − | 0.442239i | \(-0.145816\pi\) |
−0.831439 | + | 0.555616i | \(0.812482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5316.23 | − | 9207.98i | 0.182928 | − | 0.316840i | −0.759949 | − | 0.649983i | \(-0.774776\pi\) |
0.942876 | + | 0.333143i | \(0.108109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9369.11 | − | 4742.41i | −0.297404 | − | 0.150538i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10760.5 | + | 18637.7i | −0.315899 | + | 0.547153i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6637.37 | − | 11496.3i | −0.180638 | − | 0.312874i | 0.761460 | − | 0.648212i | \(-0.224483\pi\) |
−0.942098 | + | 0.335338i | \(0.891150\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1749.94 | −0.0442486 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38811.1 | −0.913713 | −0.456857 | − | 0.889540i | \(-0.651025\pi\) | ||||
−0.456857 | + | 0.889540i | \(0.651025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15687.8 | − | 27172.1i | −0.344552 | − | 0.596782i | 0.640720 | − | 0.767775i | \(-0.278636\pi\) |
−0.985272 | + | 0.170992i | \(0.945303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 34789.1 | − | 60256.5i | 0.714151 | − | 1.23695i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 54015.1 | − | 35282.8i | 1.03822 | − | 0.678166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19745.7 | − | 34200.6i | 0.355964 | − | 0.616547i | −0.631319 | − | 0.775523i | \(-0.717486\pi\) |
0.987282 | + | 0.158976i | \(0.0508194\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 102372. | 1.63112 | 0.815559 | − | 0.578675i | \(-0.196430\pi\) | ||||
0.815559 | + | 0.578675i | \(0.196430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6580.60 | −0.0987912 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19454.1 | + | 33695.5i | 0.275558 | + | 0.477281i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 56410.5 | − | 97705.8i | 0.754892 | − | 1.30751i | −0.190536 | − | 0.981680i | \(-0.561023\pi\) |
0.945428 | − | 0.325831i | \(-0.105644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1472.67 | − | 26737.2i | −0.0186424 | − | 0.338464i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 33863.9 | − | 58654.0i | 0.406004 | − | 0.703219i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −68972.6 | − | 119464.i | −0.784092 | − | 1.35809i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 30334.3 | 0.327345 | 0.163672 | − | 0.986515i | \(-0.447666\pi\) | ||||
0.163672 | + | 0.986515i | \(0.447666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40310.4 | 0.413361 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −53398.2 | − | 92488.4i | −0.520862 | − | 0.902160i | −0.999706 | − | 0.0242599i | \(-0.992277\pi\) |
0.478843 | − | 0.877900i | \(-0.341056\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 78767.8 | − | 136430.i | 0.731570 | − | 1.26712i | −0.224643 | − | 0.974441i | \(-0.572121\pi\) |
0.956212 | − | 0.292674i | \(-0.0945452\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6685.79 | + | 121384.i | 0.0591806 | + | 1.07446i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −44662.2 | + | 77357.1i | −0.377121 | + | 0.653192i | −0.990642 | − | 0.136486i | \(-0.956419\pi\) |
0.613521 | + | 0.789678i | \(0.289752\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −83802.3 | − | 145150.i | −0.675600 | − | 1.17017i | −0.976293 | − | 0.216452i | \(-0.930551\pi\) |
0.300693 | − | 0.953721i | \(-0.402782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −93200.8 | −0.717980 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −115794. | −0.853079 | −0.426539 | − | 0.904469i | \(-0.640267\pi\) | ||||
−0.426539 | + | 0.904469i | \(0.640267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10129.4 | + | 17544.6i | 0.0714230 | + | 0.123708i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8365.33 | − | 14489.2i | 0.0564961 | − | 0.0978541i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6855.13 | − | 4477.78i | 0.0443760 | − | 0.0289865i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −43307.1 | + | 75010.0i | −0.268903 | + | 0.465753i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18814.1 | − | 32587.0i | −0.112130 | − | 0.194215i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −479898. | −2.74709 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −201513. | −1.10865 | −0.554325 | − | 0.832300i | \(-0.687023\pi\) | ||||
−0.554325 | + | 0.832300i | \(0.687023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26823.9 | − | 46460.4i | −0.141921 | − | 0.245815i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19234.8 | − | 33315.6i | 0.0979285 | − | 0.169617i | −0.812899 | − | 0.582405i | \(-0.802112\pi\) |
0.910827 | + | 0.412788i | \(0.135445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 153139. | + | 77515.2i | 0.750685 | + | 0.379977i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −37977.9 | + | 65779.6i | −0.179348 | + | 0.310640i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 120861. | + | 209337.i | 0.550155 | + | 0.952896i | 0.998263 | + | 0.0589167i | \(0.0187646\pi\) |
−0.448108 | + | 0.893979i | \(0.647902\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 53112.2 | 0.233162 | 0.116581 | − | 0.993181i | \(-0.462807\pi\) | ||||
0.116581 | + | 0.993181i | \(0.462807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −39507.6 | −0.167353 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 51396.1 | + | 89020.7i | 0.210180 | + | 0.364042i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 225218. | − | 390088.i | 0.889574 | − | 1.54079i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −89560.9 | − | 121899.i | −0.341842 | − | 0.465271i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −64531.0 | + | 111771.i | −0.238124 | + | 0.412443i | −0.960176 | − | 0.279396i | \(-0.909866\pi\) |
0.722052 | + | 0.691839i | \(0.243199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76603.2 | + | 132681.i | 0.273404 | + | 0.473549i | 0.969731 | − | 0.244175i | \(-0.0785172\pi\) |
−0.696327 | + | 0.717724i | \(0.745184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5115.85 | 0.0176681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −784075. | −2.62137 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 75593.9 | + | 130932.i | 0.244758 | + | 0.423934i | 0.962064 | − | 0.272825i | \(-0.0879581\pi\) |
−0.717305 | + | 0.696759i | \(0.754625\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 80031.5 | − | 138619.i | 0.251055 | − | 0.434839i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22490.2 | − | 11384.0i | −0.0683799 | − | 0.0346122i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16458.3 | + | 28506.7i | −0.0485196 | + | 0.0840384i | −0.889265 | − | 0.457392i | \(-0.848784\pi\) |
0.840746 | + | 0.541430i | \(0.182117\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −233334. | − | 404146.i | −0.667219 | − | 1.15566i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −217586. | −0.603725 | −0.301862 | − | 0.953352i | \(-0.597608\pi\) | ||||
−0.301862 | + | 0.953352i | \(0.597608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328630. | −0.885095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 53620.2 | + | 92872.9i | 0.140229 | + | 0.242884i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 210621. | − | 364807.i | 0.535041 | − | 0.926718i | −0.464121 | − | 0.885772i | \(-0.653630\pi\) |
0.999161 | − | 0.0409458i | \(-0.0130371\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 839100. | − | 548101.i | 2.07118 | − | 1.35290i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15752.1 | + | 27283.4i | −0.0377925 | + | 0.0654585i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1747.03 | + | 3025.94i | 0.00407538 | + | 0.00705876i | 0.868056 | − | 0.496466i | \(-0.165369\pi\) |
−0.863981 | + | 0.503525i | \(0.832036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 594611. | 1.34908 | 0.674538 | − | 0.738240i | \(-0.264343\pi\) | ||||
0.674538 | + | 0.738240i | \(0.264343\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 95692.2 | 0.211227 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 539486. | + | 934418.i | 1.15891 | + | 2.00730i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15715.7 | + | 27220.5i | −0.0328648 | + | 0.0569235i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5197.62 | − | 94365.8i | −0.0105840 | − | 0.192159i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 414322. | − | 717627.i | 0.821778 | − | 1.42336i | −0.0825782 | − | 0.996585i | \(-0.526315\pi\) |
0.904357 | − | 0.426777i | \(-0.140351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −109869. | − | 190299.i | −0.212316 | − | 0.367743i | 0.740123 | − | 0.672472i | \(-0.234767\pi\) |
−0.952439 | + | 0.304729i | \(0.901434\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −193688. | −0.364768 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 475612. | 0.873146 | 0.436573 | − | 0.899669i | \(-0.356192\pi\) | ||||
0.436573 | + | 0.899669i | \(0.356192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 313778. | + | 543479.i | 0.561681 | + | 0.972859i | 0.997350 | + | 0.0727525i | \(0.0231783\pi\) |
−0.435669 | + | 0.900107i | \(0.643488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 59736.4 | − | 103466.i | 0.104291 | − | 0.180638i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30823.1 | + | 559611.i | 0.0524972 | + | 0.953117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −217808. | + | 377255.i | −0.361984 | + | 0.626975i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7874.71 | − | 13639.4i | −0.0127735 | − | 0.0221243i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −658879. | −1.04337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −570989. | −0.882920 | −0.441460 | − | 0.897281i | \(-0.645539\pi\) | ||||
−0.441460 | + | 0.897281i | \(0.645539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −174650. | − | 302502.i | −0.263766 | − | 0.456857i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −310536. | + | 537865.i | −0.458159 | + | 0.793555i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 816785. | − | 533525.i | 1.17749 | − | 0.769140i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 141190. | − | 244549.i | 0.198927 | − | 0.344552i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6522.75 | + | 11297.7i | 0.00898359 | + | 0.0155600i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4233.11 | −0.00570029 | −0.00285015 | − | 0.999996i | \(-0.500907\pi\) | ||||
−0.00285015 | + | 0.999996i | \(0.500907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 626204. | 0.824630 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 564931. | + | 978490.i | 0.727664 | + | 1.26035i | 0.957868 | + | 0.287209i | \(0.0927274\pi\) |
−0.230204 | + | 0.973142i | \(0.573939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −402322. | + | 696842.i | −0.506973 | + | 0.878103i | 0.492994 | + | 0.870032i | \(0.335902\pi\) |
−0.999967 | + | 0.00807048i | \(0.997431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 518070. | + | 262234.i | 0.638791 | + | 0.323339i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −584636. | + | 1.01262e6i | −0.705498 | + | 1.22196i | 0.261013 | + | 0.965335i | \(0.415943\pi\) |
−0.966511 | + | 0.256624i | \(0.917390\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 228687. | + | 396098.i | 0.270130 | + | 0.467878i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 355423. | 0.411031 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.70554e6 | 1.93138 | 0.965689 | − | 0.259700i | \(-0.0836238\pi\) | ||||
0.965689 | + | 0.259700i | \(0.0836238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −475598. | − | 823760.i | −0.527470 | − | 0.913604i | −0.999487 | − | 0.0320153i | \(-0.989807\pi\) |
0.472018 | − | 0.881589i | \(-0.343526\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −703723. | + | 1.60353e6i | −0.749008 | + | 1.70672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −136732. | + | 236827.i | −0.142603 | + | 0.246996i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 460673. | + | 797909.i | 0.470863 | + | 0.815559i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.14498e6 | −1.14713 | −0.573566 | − | 0.819159i | \(-0.694440\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 96763.6 | 0.0950409 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −29612.7 | − | 51290.7i | −0.0285186 | − | 0.0493956i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −591869. | + | 1.02515e6i | −0.558976 | + | 0.968175i | 0.438606 | + | 0.898679i | \(0.355472\pi\) |
−0.997582 | + | 0.0694955i | \(0.977861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.19782e6 | − | 606305.i | −1.10954 | − | 0.561619i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −175087. | + | 303260.i | −0.159094 | + | 0.275558i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 224158. | + | 388253.i | 0.199832 | + | 0.346119i | 0.948474 | − | 0.316856i | \(-0.102627\pi\) |
−0.748642 | + | 0.662975i | \(0.769294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.85303e6 | −1.62094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.01539e6 | 0.871674 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −373737. | − | 647332.i | −0.314909 | − | 0.545439i | 0.664509 | − | 0.747280i | \(-0.268641\pi\) |
−0.979418 | + | 0.201841i | \(0.935307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −116319. | + | 201470.i | −0.0962114 | + | 0.166643i | −0.910114 | − | 0.414359i | \(-0.864006\pi\) |
0.813902 | + | 0.581002i | \(0.197339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 201769. | − | 131796.i | 0.163850 | − | 0.107027i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.92368e6 | + | 3.33191e6i | −1.53391 | + | 2.65682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21462e6 | + | 2.10379e6i | 0.951134 | + | 1.64741i | 0.742977 | + | 0.669317i | \(0.233413\pi\) |
0.208157 | + | 0.978095i | \(0.433253\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 609550. | 0.468812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.51704e6 | 1.90163 | 0.950813 | − | 0.309766i | \(-0.100251\pi\) | ||||
0.950813 | + | 0.309766i | \(0.100251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 130497. | + | 226028.i | 0.0968579 | + | 0.167763i | 0.910382 | − | 0.413768i | \(-0.135787\pi\) |
−0.813525 | + | 0.581530i | \(0.802454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 620753. | − | 1.07518e6i | 0.452696 | − | 0.784092i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29809.1 | − | 541201.i | −0.0213621 | − | 0.387841i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 707934. | − | 1.22618e6i | 0.498595 | − | 0.863592i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 136505. | + | 236433.i | 0.0944963 | + | 0.163672i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 65011.7 | 0.0442408 | 0.0221204 | − | 0.999755i | \(-0.492958\pi\) | ||||
0.0221204 | + | 0.999755i | \(0.492958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 364720. | 0.244008 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 181397. | + | 314189.i | 0.119327 | + | 0.206680i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20080.6 | − | 34780.7i | 0.0129897 | − | 0.0224989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42499.8 | − | 771608.i | −0.0270377 | − | 0.490886i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 480584. | − | 832395.i | 0.300720 | − | 0.520862i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −553907. | − | 959395.i | −0.340947 | − | 0.590538i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.35599e6 | 1.42668 | 0.713342 | − | 0.700816i | \(-0.247181\pi\) | ||||
0.713342 | + | 0.700816i | \(0.247181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.41782e6 | 0.844744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.05903e6 | − | 1.83429e6i | −0.620878 | − | 1.07539i | −0.989323 | − | 0.145742i | \(-0.953443\pi\) |
0.368445 | − | 0.929650i | \(-0.379890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 93756.8 | − | 162392.i | 0.0540931 | − | 0.0936920i | −0.837711 | − | 0.546114i | \(-0.816107\pi\) |
0.891804 | + | 0.452422i | \(0.149440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −916012. | + | 598340.i | −0.520145 | + | 0.339760i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 502705. | − | 870711.i | 0.280974 | − | 0.486661i | −0.690651 | − | 0.723188i | \(-0.742676\pi\) |
0.971625 | + | 0.236527i | \(0.0760093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07573e6 | − | 1.86321e6i | −0.591868 | − | 1.02515i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −803919. | −0.435461 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −83619.1 | −0.0445964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 798415. | + | 1.38290e6i | 0.419296 | + | 0.726241i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 754220. | − | 1.30635e6i | 0.390058 | − | 0.675600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −507753. | − | 257011.i | −0.258620 | − | 0.130907i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 839920. | − | 1.45478e6i | 0.421374 | − | 0.729841i | −0.574700 | − | 0.818364i | \(-0.694881\pi\) |
0.996074 | + | 0.0885229i | \(0.0282146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −419404. | − | 726429.i | −0.207263 | − | 0.358990i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.38312e6 | −0.673360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −995036. | −0.477270 | −0.238635 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238635 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −521072. | − | 902523.i | −0.246263 | − | 0.426539i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.87252e6 | + | 3.24330e6i | −0.872049 | + | 1.51043i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −358042. | − | 2.14927e6i | −0.164323 | − | 0.986407i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −91164.4 | + | 157901.i | −0.0412361 | + | 0.0714230i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.02833e6 | + | 3.51317e6i | 0.904304 | + | 1.56630i | 0.821849 | + | 0.569705i | \(0.192943\pi\) |
0.0824546 | + | 0.996595i | \(0.473724\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.86202e6 | 1.25779 | 0.628897 | − | 0.777488i | \(-0.283507\pi\) | ||||
0.628897 | + | 0.777488i | \(0.283507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 150576. | 0.0652361 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −416343. | − | 721126.i | −0.177834 | − | 0.308017i | 0.763305 | − | 0.646039i | \(-0.223576\pi\) |
−0.941138 | + | 0.338022i | \(0.890242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.02190e6 | + | 3.50203e6i | −0.851507 | + | 1.47485i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 65748.9 | + | 33280.4i | 0.0273035 | + | 0.0138203i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.34875e6 | + | 2.33611e6i | −0.552327 | + | 0.956659i | 0.445779 | + | 0.895143i | \(0.352927\pi\) |
−0.998106 | + | 0.0615157i | \(0.980407\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361621. | + | 626346.i | 0.146045 | + | 0.252957i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −779527. | −0.310502 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.26908e6 | −1.28438 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 727411. | + | 1.25991e6i | 0.281913 | + | 0.488287i | 0.971856 | − | 0.235576i | \(-0.0756978\pi\) |
−0.689943 | + | 0.723864i | \(0.742364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 169327. | − | 293283.i | 0.0647382 | − | 0.112130i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.93033e6 | − | 1.26089e6i | 0.728110 | − | 0.475602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.02344e6 | − | 1.77265e6i | 0.380883 | − | 0.659708i | −0.610306 | − | 0.792166i | \(-0.708953\pi\) |
0.991189 | + | 0.132457i | \(0.0422868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.15954e6 | − | 3.74043e6i | −0.793018 | − | 1.37355i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −892950. | −0.323574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 416898. | 0.149084 | 0.0745421 | − | 0.997218i | \(-0.476250\pi\) | ||||
0.0745421 | + | 0.997218i | \(0.476250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −906810. | − | 1.57064e6i | −0.320040 | − | 0.554325i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.93813e6 | + | 3.35694e6i | −0.675127 | + | 1.16935i | 0.301305 | + | 0.953528i | \(0.402578\pi\) |
−0.976432 | + | 0.215827i | \(0.930755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −369694. | − | 6.71201e6i | −0.127113 | − | 2.30782i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 241415. | − | 418143.i | 0.0819383 | − | 0.141921i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.41901e6 | − | 2.45780e6i | −0.475458 | − | 0.823517i | 0.524147 | − | 0.851628i | \(-0.324384\pi\) |
−0.999605 | + | 0.0281111i | \(0.991051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12280.4 | 0.00406228 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 346226. | 0.113078 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.05734e6 | − | 3.56342e6i | −0.663458 | − | 1.14914i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.17133e6 | + | 3.76085e6i | −0.691432 | + | 1.19760i | 0.279937 | + | 0.960018i | \(0.409686\pi\) |
−0.971369 | + | 0.237577i | \(0.923647\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 84955.8 | + | 1.54242e6i | 0.0267153 | + | 0.485032i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.70152e6 | + | 2.94712e6i | −0.528417 | + | 0.915244i | 0.471034 | + | 0.882115i | \(0.343881\pi\) |
−0.999451 | + | 0.0331296i | \(0.989453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 777182. | + | 1.34612e6i | 0.238375 | + | 0.412877i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −683602. | −0.207093 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.15359e6 | 1.54214 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.64716e6 | + | 4.58501e6i | 0.782477 | + | 1.35529i | 0.930495 | + | 0.366305i | \(0.119377\pi\) |
−0.148018 | + | 0.988985i | \(0.547289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.08775e6 | + | 1.88404e6i | −0.317632 | + | 0.550155i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −379935. | + | 248174.i | −0.109606 | + | 0.0715947i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.33315e6 | − | 9.23728e6i | 1.52007 | − | 2.63284i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 239005. | + | 413969.i | 0.0673080 | + | 0.116581i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.87267e6 | −0.799376 | −0.399688 | − | 0.916651i | \(-0.630881\pi\) | ||||
−0.399688 | + | 0.916651i | \(0.630881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.08688e6 | 0.573843 | 0.286921 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286921 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −177784. | − | 307932.i | −0.0483106 | − | 0.0836765i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −244137. | + | 422857.i | −0.0655633 | + | 0.113559i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.22984e6 | + | 622512.i | 0.326421 | + | 0.165226i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −462565. | + | 801187.i | −0.121347 | + | 0.210180i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.21432e6 | − | 2.10326e6i | −0.314876 | − | 0.545380i | 0.664535 | − | 0.747257i | \(-0.268629\pi\) |
−0.979411 | + | 0.201876i | \(0.935296\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 956219. | 0.245097 | 0.122548 | − | 0.992463i | \(-0.460893\pi\) | ||||
0.122548 | + | 0.992463i | \(0.460893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.05392e6 | 1.02719 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 128713. | + | 222938.i | 0.0322418 | + | 0.0558444i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.32102e6 | − | 2.28808e6i | 0.327152 | − | 0.566644i | −0.654794 | − | 0.755808i | \(-0.727244\pi\) |
0.981946 | + | 0.189164i | \(0.0605778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 547084. | − | 1.24660e6i | 0.133955 | − | 0.305233i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.71983e6 | + | 2.97883e6i | −0.416366 | + | 0.721168i | −0.995571 | − | 0.0940147i | \(-0.970030\pi\) |
0.579205 | + | 0.815182i | \(0.303363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.87750e6 | − | 1.01801e7i | −1.40700 | − | 2.43699i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.16156e6 | −0.274962 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.39903e6 | 1.02977 | 0.514886 | − | 0.857259i | \(-0.327834\pi\) | ||||
0.514886 | + | 0.857259i | \(0.327834\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04034e6 | + | 1.80192e6i | 0.240842 | + | 0.417151i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −689429. | + | 1.19413e6i | −0.157850 | + | 0.273404i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.48929e6 | − | 1.26001e6i | −0.563698 | − | 0.285329i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.12555e6 | − | 1.94951e6i | 0.252101 | − | 0.436652i | −0.712003 | − | 0.702176i | \(-0.752212\pi\) |
0.964104 | + | 0.265524i | \(0.0855451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23021.3 | + | 39874.1i | 0.00510033 | + | 0.00883403i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.85307e6 | 0.406107 | 0.203053 | − | 0.979168i | \(-0.434913\pi\) | ||||
0.203053 | + | 0.979168i | \(0.434913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.01089e6 | 0.652744 | 0.326372 | − | 0.945241i | \(-0.394174\pi\) | ||||
0.326372 | + | 0.945241i | \(0.394174\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.52834e6 | − | 6.11126e6i | −0.756725 | − | 1.31069i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −533627. | + | 924270.i | −0.113226 | + | 0.196113i | −0.917069 | − | 0.398728i | \(-0.869452\pi\) |
0.803843 | + | 0.594841i | \(0.202785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.44082e6 | − | 941145.i | 0.302466 | − | 0.197572i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −680345. | + | 1.17839e6i | −0.141311 | + | 0.244758i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.48324e6 | + | 2.56905e6i | 0.304831 | + | 0.527983i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.02354e7 | −2.08147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.44057e6 | 0.289893 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.84394e6 | − | 4.92585e6i | −0.566346 | − | 0.980939i | −0.996923 | − | 0.0783858i | \(-0.975023\pi\) |
0.430577 | − | 0.902554i | \(-0.358310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06949e6 | − | 1.85240e6i | 0.210772 | − | 0.365068i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12476.7 | − | 226522.i | −0.00243350 | − | 0.0441816i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.58029e6 | − | 2.73715e6i | 0.305059 | − | 0.528377i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.42239e6 | − | 5.92775e6i | −0.653893 | − | 1.13258i | −0.982170 | − | 0.187995i | \(-0.939801\pi\) |
0.328277 | − | 0.944582i | \(-0.393532\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −296250. | −0.0560256 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.60132e6 | −1.04854 | −0.524272 | − | 0.851551i | \(-0.675662\pi\) | ||||
−0.524272 | + | 0.851551i | \(0.675662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −136522. | − | 236462.i | −0.0252979 | − | 0.0438172i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.10001e6 | − | 3.63732e6i | 0.385219 | − | 0.667219i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −276715. | − | 5.02392e6i | −0.0502507 | − | 0.912330i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.16764e6 | + | 2.02242e6i | −0.209923 | + | 0.363596i | −0.951690 | − | 0.307061i | \(-0.900655\pi\) |
0.741767 | + | 0.670657i | \(0.233988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −979135. | − | 1.69591e6i | −0.174280 | − | 0.301862i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.08278e7 | 1.90819 | 0.954093 | − | 0.299510i | \(-0.0968233\pi\) | ||||
0.954093 | + | 0.299510i | \(0.0968233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11273e7 | −1.94161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.47883e6 | − | 2.56141e6i | −0.255505 | − | 0.442547i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.58924e6 | + | 2.75264e6i | −0.271890 | + | 0.470928i | −0.969346 | − | 0.245700i | \(-0.920982\pi\) |
0.697455 | + | 0.716628i | \(0.254316\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.40546e6 | − | 2.22445e6i | 0.576930 | − | 0.376852i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −482582. | + | 835856.i | −0.0809613 | + | 0.140229i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.20695e6 | − | 1.42149e7i | −1.36353 | − | 2.36170i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18460e6 | 0.359455 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79118e6 | 0.617812 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.17918e6 | + | 5.50651e6i | 0.513123 | + | 0.888755i | 0.999884 | + | 0.0152197i | \(0.00484477\pi\) |
−0.486761 | + | 0.873535i | \(0.661822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.61094e6 | + | 6.25433e6i | −0.577252 | + | 0.999830i | 0.418541 | + | 0.908198i | \(0.362542\pi\) |
−0.995793 | + | 0.0916321i | \(0.970792\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.04798e6 | + | 4.07368e6i | 1.27435 | + | 0.645043i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −237644. | + | 411612.i | −0.0372735 | + | 0.0645597i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.19927e6 | + | 5.54130e6i | 0.497063 | + | 0.860939i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −283538. | −0.0436390 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 863574. | 0.131668 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.65343e6 | + | 8.05997e6i | 0.702892 | + | 1.21744i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15723.3 | + | 27233.5i | −0.00235292 | + | 0.00407538i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.95232e6 | + | 6.74046e6i | 0.734237 | + | 0.999350i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.71583e6 | − | 8.16805e6i | 0.692731 | − | 1.19985i | −0.278209 | − | 0.960521i | \(-0.589741\pi\) |
0.970940 | − | 0.239325i | \(-0.0769260\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.67575e6 | + | 4.63453e6i | 0.389444 | + | 0.674538i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.74630e7 | −2.51842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.91568e6 | −1.41695 | −0.708474 | − | 0.705737i | \(-0.750616\pi\) | ||||
−0.708474 | + | 0.705737i | \(0.750616\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 430615. | + | 745847.i | 0.0609759 | + | 0.105613i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.86182e6 | − | 4.95682e6i | 0.401572 | − | 0.695543i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.56790e6 | + | 2.31216e6i | 0.635191 | + | 0.321517i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.85538e6 | + | 8.40976e6i | −0.669099 | + | 1.15891i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.82306e6 | − | 8.35379e6i | −0.658696 | − | 1.14089i | −0.980953 | − | 0.194243i | \(-0.937775\pi\) |
0.322258 | − | 0.946652i | \(-0.395558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.23123e6 | 0.166651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −282883. | −0.0379490 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.54752e6 | + | 2.68038e6i | 0.205762 | + | 0.356390i | 0.950375 | − | 0.311106i | \(-0.100699\pi\) |
−0.744613 | + | 0.667496i | \(0.767366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.03238e6 | + | 1.04484e7i | −0.795000 | + | 1.37698i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 712120. | − | 465158.i | 0.0930241 | − | 0.0607635i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.15927e6 | − | 1.06682e7i | 0.797533 | − | 1.38137i | −0.123685 | − | 0.992322i | \(-0.539471\pi\) |
0.921218 | − | 0.389046i | \(-0.127195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.61755e6 | − | 2.80168e6i | −0.207619 | − | 0.359607i | 0.743345 | − | 0.668908i | \(-0.233238\pi\) |
−0.950964 | + | 0.309302i | \(0.899905\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.45780e6 | 0.948908 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.50318e6 | 0.189601 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.52525e6 | + | 7.83796e6i | 0.565852 | + | 0.980084i | 0.996970 | + | 0.0777887i | \(0.0247859\pi\) |
−0.431118 | + | 0.902296i | \(0.641881\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 988825. | − | 1.71269e6i | 0.122581 | − | 0.212316i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 729890. | + | 1.32516e7i | 0.0897051 | + | 1.62865i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.42538e6 | + | 7.66499e6i | −0.539237 | + | 0.933986i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −871598. | − | 1.50965e6i | −0.105300 | − | 0.182384i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.13170e6 | 0.255347 | 0.127673 | − | 0.991816i | \(-0.459249\pi\) | ||||
0.127673 | + | 0.991816i | \(0.459249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.96318e6 | −1.18334 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.14025e6 | + | 3.70703e6i | 0.252056 | + | 0.436573i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.63467e6 | − | 6.29543e6i | 0.424451 | − | 0.735171i | −0.571918 | − | 0.820311i | \(-0.693800\pi\) |
0.996369 | + | 0.0851397i | \(0.0271337\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −46918.4 | − | 851830.i | −0.00543313 | − | 0.0986417i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.82400e6 | + | 4.89131e6i | −0.324286 | + | 0.561681i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.10282e6 | − | 1.91015e6i | −0.125585 | − | 0.217520i | 0.796376 | − | 0.604802i | \(-0.206748\pi\) |
−0.921962 | + | 0.387281i | \(0.873414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00121e7 | −1.13067 | −0.565336 | − | 0.824860i | \(-0.691254\pi\) | ||||
−0.565336 | + | 0.824860i | \(0.691254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.07525e6 | 0.120425 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.51224e6 | + | 7.81542e6i | 0.501191 | + | 0.868088i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.16069e6 | − | 5.47448e6i | 0.348185 | − | 0.603075i | −0.637742 | − | 0.770250i | \(-0.720131\pi\) |
0.985927 | + | 0.167175i | \(0.0534646\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.22303e6 | + | 2.75849e6i | −0.461404 | + | 0.301390i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 453353. | − | 785231.i | 0.0491285 | − | 0.0850931i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.15392e6 | − | 1.23910e7i | −0.768941 | − | 1.33185i | −0.938138 | − | 0.346263i | \(-0.887451\pi\) |
0.169196 | − | 0.985582i | \(-0.445883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.92055e6 | −0.417984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.73991e7 | 1.83999 | 0.919993 | − | 0.391936i | \(-0.128194\pi\) | ||||
0.919993 | + | 0.391936i | \(0.128194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.13368e6 | + | 7.15975e6i | 0.433621 | + | 0.751054i | 0.997182 | − | 0.0750208i | \(-0.0239023\pi\) |
−0.563561 | + | 0.826074i | \(0.690569\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 70872.4 | − | 122755.i | 0.00737476 | − | 0.0127735i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.30498e7 | + | 6.60547e6i | 1.34705 | + | 0.681841i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.29211e7 | + | 2.23800e7i | −1.32312 | + | 2.29172i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.96495e6 | − | 5.13545e6i | −0.301196 | − | 0.521687i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 654048. | 0.0659148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.83238e6 | −0.283190 | −0.141595 | − | 0.989925i | \(-0.545223\pi\) | ||||
−0.141595 | + | 0.989925i | \(0.545223\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.56945e6 | − | 4.45041e6i | −0.254877 | − | 0.441460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.04980e7 | + | 1.81831e7i | −1.03317 | + | 1.78951i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.45051e6 | − | 381261.i | 0.336926 | − | 0.0372284i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.57185e6 | − | 2.72252e6i | 0.152286 | − | 0.263766i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.78588e6 | + | 3.09324e6i | 0.171675 | + | 0.297350i | 0.939006 | − | 0.343902i | \(-0.111749\pi\) |
−0.767330 | + | 0.641252i | \(0.778415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.96911e6 | 0.569354 | 0.284677 | − | 0.958624i | \(-0.408114\pi\) | ||||
0.284677 | + | 0.958624i | \(0.408114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.58966e6 | −0.529037 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −841379. | − | 1.45731e6i | −0.0790189 | − | 0.136865i | 0.823808 | − | 0.566869i | \(-0.191845\pi\) |
−0.902827 | + | 0.430004i | \(0.858512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 871021. | − | 1.50865e6i | 0.0811739 | − | 0.140597i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.83395e6 | + | 3.96534e6i | 0.724483 | + | 0.366715i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.51526e6 | + | 1.47489e7i | −0.781475 | + | 1.35355i | 0.149608 | + | 0.988745i | \(0.452199\pi\) |
−0.931082 | + | 0.364809i | \(0.881134\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00411e6 | − | 3.47121e6i | −0.182523 | − | 0.316139i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.54143e6 | 0.229702 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.99303e7 | 1.78772 | 0.893862 | − | 0.448342i | \(-0.147985\pi\) | ||||
0.893862 | + | 0.448342i | \(0.147985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.77867e6 | − | 8.27691e6i | −0.425406 | − | 0.736825i | 0.571052 | − | 0.820914i | \(-0.306535\pi\) |
−0.996458 | + | 0.0840888i | \(0.973202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −58704.7 | + | 101680.i | −0.00518668 | + | 0.00898359i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.49723e7 | − | 9.77995e6i | 1.31291 | − | 0.857595i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −420290. | + | 727963.i | −0.0365792 | + | 0.0633570i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19049.0 | − | 32993.8i | −0.00164553 | − | 0.00285015i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.29135e6 | −0.453691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80397e7 | 1.53530 | 0.767648 | − | 0.640872i | \(-0.221427\pi\) | ||||
0.767648 | + | 0.640872i | \(0.221427\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.81792e6 | + | 4.88077e6i | 0.238050 | + | 0.412315i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.23704e6 | − | 1.25349e7i | 0.606861 | − | 1.05111i | −0.384894 | − | 0.922961i | \(-0.625762\pi\) |
0.991754 | − | 0.128153i | \(-0.0409048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 216278. | + | 3.92665e6i | 0.0180027 | + | 0.326849i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.08438e6 | + | 8.80641e6i | −0.420117 | + | 0.727664i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.34392e6 | + | 2.32774e6i | 0.110236 | + | 0.190934i | 0.915865 | − | 0.401486i | \(-0.131506\pi\) |
−0.805629 | + | 0.592420i | \(0.798173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.51854e7 | 2.05080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.24179e6 | −0.585402 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.83674e6 | + | 3.18132e6i | 0.147400 | + | 0.255305i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.33814e6 | − | 4.04977e6i | 0.186284 | − | 0.322653i | −0.757725 | − | 0.652574i | \(-0.773689\pi\) |
0.944008 | + | 0.329922i | \(0.107022\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 287405. | + | 5.21801e6i | 0.0227333 | + | 0.412735i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.76693e6 | − | 4.79246e6i | 0.217288 | − | 0.376354i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 132030. | + | 228683.i | 0.0102942 | + | 0.0178301i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.05235e7 | −0.814639 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.34801e6 | 0.487913 | 0.243957 | − | 0.969786i | \(-0.421555\pi\) | ||||
0.243957 | + | 0.969786i | \(0.421555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.85520e6 | + | 1.18736e7i | 0.523157 | + | 0.906135i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.05818e6 | + | 3.56488e6i | −0.155959 | + | 0.270130i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.15915e7 | − | 7.57158e6i | 0.872150 | − | 0.569690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.20526e6 | − | 5.55168e6i | 0.239468 | − | 0.414771i | −0.721094 | − | 0.692838i | \(-0.756360\pi\) |
0.960562 | + | 0.278067i | \(0.0896936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.59940e6 | + | 2.77025e6i | 0.118655 | + | 0.205516i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.46320e6 | 0.107790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.07101e7 | 0.783481 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.67493e6 | + | 1.32934e7i | 0.557541 | + | 0.965689i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.67253e6 | − | 6.36100e6i | 0.264937 | − | 0.458885i | −0.702610 | − | 0.711575i | \(-0.747982\pi\) |
0.967547 | + | 0.252691i | \(0.0813155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82218e7 | + | 9.22343e6i | 1.30543 | + | 0.660776i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.28038e6 | − | 7.41384e6i | 0.304535 | − | 0.527470i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.67109e7 | − | 2.89441e7i | −1.18074 | − | 2.04510i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.57839e7 | −1.10759 | −0.553793 | − | 0.832655i | \(-0.686820\pi\) | ||||
−0.553793 | + | 0.832655i | \(0.686820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 188240. | + | 326041.i | 0.0130292 | + | 0.0225673i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.76835e6 | + | 1.17231e7i | −0.465289 | + | 0.805905i | −0.999215 | − | 0.0396269i | \(-0.987383\pi\) |
0.533925 | + | 0.845532i | \(0.320716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.56650e7 | + | 1.73089e6i | −1.06958 | + | 0.118182i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.30315e6 | + | 5.72123e6i | −0.224006 | + | 0.387990i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.66851e6 | − | 6.35405e6i | −0.247103 | − | 0.427996i | 0.715617 | − | 0.698492i | \(-0.246145\pi\) |
−0.962721 | + | 0.270497i | \(0.912812\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.46118e6 | −0.164664 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.20844e7 | −0.803068 | −0.401534 | − | 0.915844i | \(-0.631523\pi\) | ||||
−0.401534 | + | 0.915844i | \(0.631523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.72360e6 | + | 1.16456e7i | 0.443824 | + | 0.768726i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.14606e6 | + | 7.18118e6i | −0.271853 | + | 0.470863i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.03320e7 | − | 5.22978e6i | −0.672944 | − | 0.340627i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.39088e6 | − | 7.60523e6i | 0.284087 | − | 0.492054i | −0.688300 | − | 0.725426i | \(-0.741643\pi\) |
0.972387 | + | 0.233372i | \(0.0749761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.15241e6 | − | 8.92423e6i | −0.331148 | − | 0.573566i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.59628e7 | 1.01916 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 465874. | 0.0295480 | 0.0147740 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147740 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 435436. | + | 754198.i | 0.0274360 | + | 0.0475205i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.49891e6 | + | 1.29885e7i | −0.469393 | + | 0.813013i | −0.999388 | − | 0.0349882i | \(-0.988861\pi\) |
0.529995 | + | 0.848001i | \(0.322194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.81915e7 | − | 1.18827e7i | 1.13125 | − | 0.738932i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 266514. | − | 461616.i | 0.0164652 | − | 0.0285186i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −361513. | − | 626159.i | −0.0221889 | − | 0.0384323i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.85606e7 | −1.13181 | −0.565907 | − | 0.824469i | \(-0.691474\pi\) | ||||
−0.565907 | + | 0.824469i | \(0.691474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.06537e7 | −0.645450 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.13802e6 | − | 1.06314e7i | −0.369470 | − | 0.639941i | 0.620013 | − | 0.784592i | \(-0.287128\pi\) |
−0.989483 | + | 0.144651i | \(0.953794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.90888e7 | + | 5.03832e7i | −1.73969 | + | 3.01323i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −664503. | − | 1.20644e7i | −0.0394861 | − | 0.716893i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.76767e6 | + | 4.79375e6i | −0.163407 | + | 0.283029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.65736e6 | + | 1.67270e7i | 0.566540 | + | 0.981276i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.15157e6 | −0.183706 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.57525e7 | 0.912380 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.63496e6 | + | 4.56388e6i | 0.151648 | + | 0.262662i | 0.931833 | − | 0.362886i | \(-0.118209\pi\) |
−0.780185 | + | 0.625548i | \(0.784875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.01742e6 | + | 3.49428e6i | −0.115373 | + | 0.199832i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −825586. | − | 1.49890e7i | −0.0469160 | − | 0.851788i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.09807e6 | + | 1.90192e6i | −0.0620082 | + | 0.107401i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.33862e6 | − | 1.44429e7i | −0.467925 | − | 0.810470i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.11889e7 | 0.623940 | 0.311970 | − | 0.950092i | \(-0.399011\pi\) | ||||
0.311970 | + | 0.950092i | \(0.399011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 277250. | 0.0153640 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.56925e6 | + | 7.91417e6i | 0.251631 | + | 0.435837i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.80719e6 | + | 1.35225e7i | −0.427274 | + | 0.740059i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.19885e6 | + | 1.43629e6i | −0.119593 | + | 0.0781184i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.36363e6 | − | 5.82599e6i | 0.181813 | − | 0.314909i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.52526e6 | − | 6.10592e6i | −0.189374 | − | 0.328005i | 0.755668 | − | 0.654955i | \(-0.227312\pi\) |
−0.945042 | + | 0.326950i | \(0.893979\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.54873e7 | 1.36073 | 0.680364 | − | 0.732875i | \(-0.261822\pi\) | ||||
0.680364 | + | 0.732875i | \(0.261822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.09374e6 | −0.111095 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.71482e6 | + | 2.97016e6i | 0.0904326 | + | 0.156634i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.94596e6 | + | 6.83460e6i | −0.206822 | + | 0.358227i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.93520e6 | + | 979550.i | 0.100813 | + | 0.0510290i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.17439e7 | − | 2.03411e7i | 0.608073 | − | 1.05321i | −0.383485 | − | 0.923547i | \(-0.625276\pi\) |
0.991558 | − | 0.129666i | \(-0.0413904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.04517e6 | − | 1.04705e7i | −0.311107 | − | 0.538852i | 0.667496 | − | 0.744614i | \(-0.267366\pi\) |
−0.978602 | + | 0.205761i | \(0.934033\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.46263e7 | −1.77121 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.33335e6 | −0.169480 | −0.0847398 | − | 0.996403i | \(-0.527006\pi\) | ||||
−0.0847398 | + | 0.996403i | \(0.527006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.85267e6 | + | 6.67302e6i | 0.194704 | + | 0.337238i | 0.946804 | − | 0.321812i | \(-0.104292\pi\) |
−0.752099 | + | 0.659050i | \(0.770959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.09316e7 | + | 1.89341e7i | −0.549138 | + | 0.951134i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 628505. | + | 855440.i | 0.0313831 | + | 0.0427147i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.13353e7 | + | 1.96333e7i | −0.562622 | + | 0.974490i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.74298e6 | + | 4.75098e6i | 0.135335 | + | 0.234406i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.40843e7 | −1.18121 | −0.590607 | − | 0.806959i | \(-0.701112\pi\) | ||||
−0.590607 | + | 0.806959i | \(0.701112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.82163e6 | −0.0888116 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.13267e7 | + | 1.96184e7i | 0.548952 | + | 0.950813i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.71202e7 | + | 2.96531e7i | −0.824837 | + | 1.42866i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00185e7 | − | 5.07110e6i | −0.479837 | − | 0.242881i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.17447e6 | + | 2.03425e6i | −0.0559209 | + | 0.0968579i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.00676e6 | − | 1.74376e6i | −0.0476544 | − | 0.0825398i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.82938e7 | −1.33143 | −0.665716 | − | 0.746206i | \(-0.731874\pi\) | ||||
−0.665716 | + | 0.746206i | \(0.731874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.11736e7 | 0.522728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.08088e7 | − | 1.87214e7i | −0.502719 | − | 0.870734i | −0.999995 | − | 0.00314220i | \(-0.999000\pi\) |
0.497276 | − | 0.867592i | \(-0.334334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.62691e7 | − | 2.81789e7i | 0.752282 | − | 1.30299i | −0.194432 | − | 0.980916i | \(-0.562286\pi\) |
0.946714 | − | 0.322075i | \(-0.104380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.08411e6 | − | 2.66774e6i | 0.187754 | − | 0.122641i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.03192e6 | − | 6.98349e6i | 0.184283 | − | 0.319187i | −0.759052 | − | 0.651030i | \(-0.774337\pi\) |
0.943335 | + | 0.331843i | \(0.107670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.19450e7 | − | 3.80098e7i | −0.997229 | − | 1.72725i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.27428e7 | 0.575728 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.96533e7 | −0.882849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.37096e6 | + | 2.37457e6i | 0.0612321 | + | 0.106057i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.22854e6 | + | 2.12790e6i | −0.0545574 | + | 0.0944963i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.42157e6 | − | 6.21206e7i | −0.151080 | − | 2.74294i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.51559e6 | + | 1.47494e7i | −0.373866 | + | 0.647555i | −0.990157 | − | 0.139964i | \(-0.955301\pi\) |
0.616291 | + | 0.787519i | \(0.288635\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 292553. | + | 506716.i | 0.0127712 | + | 0.0221204i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.24740e7 | 0.541459 | 0.270729 | − | 0.962655i | \(-0.412735\pi\) | ||||
0.270729 | + | 0.962655i | \(0.412735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.28955e6 | −0.314629 | −0.157315 | − | 0.987549i | \(-0.550284\pi\) | ||||
−0.157315 | + | 0.987549i | \(0.550284\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.64124e6 | + | 2.84271e6i | 0.0704390 | + | 0.122004i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.38377e6 | − | 1.62532e7i | 0.400469 | − | 0.693632i | −0.593314 | − | 0.804971i | \(-0.702181\pi\) |
0.993782 | + | 0.111339i | \(0.0355140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.43675e6 | − | 2.60850e7i | −0.0609714 | − | 1.10697i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.63257e6 | + | 2.82770e6i | −0.0688935 | + | 0.119327i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.90591e6 | + | 5.03318e6i | 0.121942 | + | 0.211210i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 364052. | 0.0151917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 361452. | 0.0149992 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.62665e7 | − | 2.81744e7i | −0.671266 | − | 1.16267i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −561631. | + | 972773.i | −0.0230483 | + | 0.0399208i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.82284e6 | − | 3.80349e6i | 0.237638 | − | 0.155225i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.09767e7 | − | 5.36533e7i | 1.25723 | − | 2.17758i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 631833. | + | 1.09437e6i | 0.0255026 | + | 0.0441718i | 0.878495 | − | 0.477751i | \(-0.158548\pi\) |
−0.852992 | + | 0.521923i | \(0.825215\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.65051e6 | 0.347242 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.47718e7 | 0.988921 | 0.494461 | − | 0.869200i | \(-0.335366\pi\) | ||||
0.494461 | + | 0.869200i | \(0.335366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.54732e7 | − | 4.41208e7i | −1.01136 | − | 1.75173i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.98516e6 | − | 8.63456e6i | 0.196846 | − | 0.340947i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.44970e6 | + | 2.25233e6i | 0.174746 | + | 0.0884520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.68338e6 | + | 8.11185e6i | −0.182924 | + | 0.316834i | −0.942875 | − | 0.333147i | \(-0.891890\pi\) |
0.759951 | + | 0.649980i | \(0.225223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.06020e7 | + | 1.83631e7i | 0.411848 | + | 0.713342i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.01648e6 | 0.309727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00586e7 | 3.07648 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.38019e6 | + | 1.10508e7i | 0.243857 | + | 0.422372i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.43675e6 | − | 5.95263e6i | 0.130650 | − | 0.226292i | −0.793277 | − | 0.608860i | \(-0.791627\pi\) |
0.923927 | + | 0.382568i | \(0.124960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.94215e6 | + | 2.03759e7i | −0.338118 | + | 0.770446i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.53125e6 | − | 1.65086e7i | 0.358464 | − | 0.620878i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.63745e6 | + | 2.83615e6i | 0.0612546 | + | 0.106096i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.26197e7 | −1.58585 | −0.792923 | − | 0.609322i | \(-0.791442\pi\) | ||||
−0.792923 | + | 0.609322i | \(0.791442\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.68762e6 | 0.0624614 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.25113e6 | − | 3.89907e6i | −0.0828755 | − | 0.143545i | 0.821608 | − | 0.570052i | \(-0.193077\pi\) |
−0.904484 | + | 0.426508i | \(0.859744\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 406463. | − | 704015.i | 0.0148848 | − | 0.0257812i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.78566e6 | − | 4.44707e6i | −0.320033 | − | 0.161992i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.68863e7 | − | 2.92479e7i | 0.611870 | − | 1.05979i | −0.379055 | − | 0.925374i | \(-0.623751\pi\) |
0.990925 | − | 0.134415i | \(-0.0429156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.24034e6 | + | 5.61243e6i | 0.116795 | + | 0.202295i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.04870e6 | 0.324440 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.81813e7 | 1.71849 | 0.859244 | − | 0.511566i | \(-0.170934\pi\) | ||||
0.859244 | + | 0.511566i | \(0.170934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.31689e7 | − | 7.47708e7i | −1.53166 | − | 2.65292i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.68153e6 | − | 1.67689e7i | 0.341715 | − | 0.591868i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.62361e7 | + | 1.71375e7i | −0.921198 | + | 0.601728i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40006e7 | + | 2.42498e7i | −0.489033 | + | 0.847030i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.61763e6 | − | 6.26593e6i | −0.125707 | − | 0.217731i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.28950e7 | −0.791446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.54640e7 | 1.21961 | 0.609805 | − | 0.792551i | \(-0.291248\pi\) | ||||
0.609805 | + | 0.792551i | \(0.291248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −376286. | − | 651747.i | −0.0128739 | − | 0.0222982i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.92148e6 | + | 6.79221e6i | −0.133476 | + | 0.231187i | −0.925014 | − | 0.379933i | \(-0.875947\pi\) |
0.791538 | + | 0.611119i | \(0.209280\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 378679. | + | 6.87514e6i | 0.0128230 | + | 0.232809i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.18573e6 | + | 1.24461e7i | −0.242080 | + | 0.419296i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.23767e7 | + | 2.14371e7i | 0.414829 | + | 0.718505i | 0.995410 | − | 0.0956975i | \(-0.0305081\pi\) |
−0.580582 | + | 0.814202i | \(0.697175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.61464e7 | −1.87226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.35760e7 | 0.450400 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.26564e7 | + | 3.92421e7i | 0.747838 | + | 1.29529i | 0.948857 | + | 0.315707i | \(0.102242\pi\) |
−0.201018 | + | 0.979587i | \(0.564425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.47774e7 | − | 4.29157e7i | 0.813701 | − | 1.40937i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −281681. | − | 5.11409e6i | −0.00920376 | − | 0.167100i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 579508. | − | 1.00374e6i | 0.0188395 | − | 0.0326309i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.87071e7 | − | 3.24017e7i | −0.605095 | − | 1.04805i | −0.992037 | − | 0.125951i | \(-0.959802\pi\) |
0.386942 | − | 0.922104i | \(-0.373531\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.51186e7 | 0.486561 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.53861e7 | 2.09376 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.32639e7 | − | 4.02943e7i | −0.741216 | − | 1.28382i | −0.951942 | − | 0.306279i | \(-0.900916\pi\) |
0.210726 | − | 0.977545i | \(-0.432417\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.77463e6 | − | 6.53786e6i | 0.119663 | − | 0.207263i |
(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 | 336.6.q.j.289.4 | 8 | ||
4.3 | odd | 2 | 21.6.e.c.16.3 | yes | 8 | ||
7.4 | even | 3 | inner | 336.6.q.j.193.4 | 8 | ||
12.11 | even | 2 | 63.6.e.e.37.2 | 8 | |||
28.3 | even | 6 | 147.6.e.o.67.3 | 8 | |||
28.11 | odd | 6 | 21.6.e.c.4.3 | ✓ | 8 | ||
28.19 | even | 6 | 147.6.a.l.1.2 | 4 | |||
28.23 | odd | 6 | 147.6.a.m.1.2 | 4 | |||
28.27 | even | 2 | 147.6.e.o.79.3 | 8 | |||
84.11 | even | 6 | 63.6.e.e.46.2 | 8 | |||
84.23 | even | 6 | 441.6.a.w.1.3 | 4 | |||
84.47 | odd | 6 | 441.6.a.v.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.c.4.3 | ✓ | 8 | 28.11 | odd | 6 | ||
21.6.e.c.16.3 | yes | 8 | 4.3 | odd | 2 | ||
63.6.e.e.37.2 | 8 | 12.11 | even | 2 | |||
63.6.e.e.46.2 | 8 | 84.11 | even | 6 | |||
147.6.a.l.1.2 | 4 | 28.19 | even | 6 | |||
147.6.a.m.1.2 | 4 | 28.23 | odd | 6 | |||
147.6.e.o.67.3 | 8 | 28.3 | even | 6 | |||
147.6.e.o.79.3 | 8 | 28.27 | even | 2 | |||
336.6.q.j.193.4 | 8 | 7.4 | even | 3 | inner | ||
336.6.q.j.289.4 | 8 | 1.1 | even | 1 | trivial | ||
441.6.a.v.1.3 | 4 | 84.47 | odd | 6 | |||
441.6.a.w.1.3 | 4 | 84.23 | even | 6 |