Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(719,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bq (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 719.1 | ||
Character | \(\chi\) | \(=\) | 1120.719 |
Dual form | 1120.2.bq.b.1039.1 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.60233 | − | 2.77531i | −0.925105 | − | 1.60233i | −0.791392 | − | 0.611308i | \(-0.790644\pi\) |
−0.133712 | − | 0.991020i | \(-0.542690\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.12896 | + | 0.683763i | 0.952100 | + | 0.305788i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23600 | + | 1.41432i | −0.845129 | + | 0.534562i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.63491 | + | 6.29586i | −1.21164 | + | 2.09862i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23701 | + | 2.14257i | 0.372973 | + | 0.646008i | 0.990021 | − | 0.140917i | \(-0.0450052\pi\) |
−0.617049 | + | 0.786925i | \(0.711672\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.90697i | − | 0.806248i | −0.915145 | − | 0.403124i | \(-0.867924\pi\) | ||
0.915145 | − | 0.403124i | \(-0.132076\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.51364 | − | 7.00414i | −0.390819 | − | 1.80846i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.21515 | + | 2.10471i | 0.294718 | + | 0.510467i | 0.974919 | − | 0.222559i | \(-0.0714409\pi\) |
−0.680201 | + | 0.733026i | \(0.738108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.38329 | + | 1.95334i | 0.776179 | + | 0.448127i | 0.835075 | − | 0.550137i | \(-0.185424\pi\) |
−0.0588952 | + | 0.998264i | \(0.518758\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.50799 | + | 3.93940i | 1.63838 | + | 0.859648i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.86568 | − | 4.96350i | 0.597535 | − | 1.03496i | −0.395649 | − | 0.918402i | \(-0.629480\pi\) |
0.993184 | − | 0.116559i | \(-0.0371864\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.06494 | + | 2.91141i | 0.812987 | + | 0.582281i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.6833 | 2.63336 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.71148i | − | 0.874900i | −0.899243 | − | 0.437450i | \(-0.855882\pi\) | ||
0.899243 | − | 0.437450i | \(-0.144118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.92617 | + | 6.80032i | 0.705161 | + | 1.22137i | 0.966634 | + | 0.256163i | \(0.0824584\pi\) |
−0.261473 | + | 0.965211i | \(0.584208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.96419 | − | 6.86619i | 0.690078 | − | 1.19525i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.72741 | + | 1.48213i | −0.968110 | + | 0.250526i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.67865 | − | 2.90751i | 0.275969 | − | 0.477991i | −0.694411 | − | 0.719579i | \(-0.744335\pi\) |
0.970379 | + | 0.241588i | \(0.0776681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.06775 | + | 4.65792i | −1.29187 | + | 0.745864i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.75850i | 0.899327i | 0.893198 | + | 0.449664i | \(0.148456\pi\) | ||||
−0.893198 | + | 0.449664i | \(0.851544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.763818i | − | 0.116481i | −0.998303 | − | 0.0582406i | \(-0.981451\pi\) | ||
0.998303 | − | 0.0582406i | \(-0.0185491\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.0435 | + | 10.9182i | −1.79533 | + | 1.62759i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.86896 | + | 1.65640i | 0.418481 | + | 0.241610i | 0.694427 | − | 0.719563i | \(-0.255658\pi\) |
−0.275946 | + | 0.961173i | \(0.588991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.99940 | − | 6.32484i | 0.428486 | − | 0.903548i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.89415 | − | 6.74487i | 0.545290 | − | 0.944471i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.474139 | − | 0.821232i | −0.0651280 | − | 0.112805i | 0.831623 | − | 0.555341i | \(-0.187412\pi\) |
−0.896751 | + | 0.442536i | \(0.854079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16854 | + | 5.40726i | 0.157566 | + | 0.729114i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.5196i | − | 1.65826i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.41474 | − | 3.70355i | 0.835128 | − | 0.482161i | −0.0204773 | − | 0.999790i | \(-0.506519\pi\) |
0.855605 | + | 0.517629i | \(0.173185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.145254 | + | 0.251587i | −0.0185978 | + | 0.0322124i | −0.875175 | − | 0.483807i | \(-0.839254\pi\) |
0.856577 | + | 0.516020i | \(0.172587\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.776680 | − | 19.2185i | −0.0978524 | − | 2.42130i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.98768 | − | 6.18882i | 0.246541 | − | 0.767628i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.12005 | + | 2.37871i | −0.503344 | + | 0.290606i | −0.730094 | − | 0.683347i | \(-0.760524\pi\) |
0.226749 | + | 0.973953i | \(0.427190\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.3670 | −2.21113 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.87114i | − | 0.934132i | −0.884222 | − | 0.467066i | \(-0.845311\pi\) | ||
0.884222 | − | 0.467066i | \(-0.154689\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.915891 | + | 1.58637i | 0.107197 | + | 0.185671i | 0.914634 | − | 0.404284i | \(-0.132479\pi\) |
−0.807437 | + | 0.589954i | \(0.799146\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.56671 | − | 15.9465i | 0.180908 | − | 1.84134i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.79623 | − | 3.04125i | −0.660541 | − | 0.346583i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.69463 | + | 0.978393i | 0.190660 | + | 0.110078i | 0.592292 | − | 0.805724i | \(-0.298223\pi\) |
−0.401631 | + | 0.915801i | \(0.631557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0205 | − | 19.0880i | −1.22449 | − | 2.12089i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.61627 | −0.726230 | −0.363115 | − | 0.931744i | \(-0.618287\pi\) | ||||
−0.363115 | + | 0.931744i | \(0.618287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.14789 | + | 5.31172i | 0.124506 | + | 0.576137i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.0758 | + | 7.54934i | −1.40188 | + | 0.809374i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.72584 | + | 2.15111i | 0.394938 | + | 0.228018i | 0.684298 | − | 0.729203i | \(-0.260109\pi\) |
−0.289359 | + | 0.957221i | \(0.593442\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.11138 | + | 6.49998i | 0.430990 | + | 0.681383i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.5820 | − | 21.7927i | 1.30469 | − | 2.25980i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.86726 | + | 6.47195i | 0.601968 | + | 0.664008i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.9453 | 1.61900 | 0.809498 | − | 0.587123i | \(-0.199739\pi\) | ||||
0.809498 | + | 0.587123i | \(0.199739\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.9857 | −1.80763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.08259 | − | 10.5354i | −0.605240 | − | 1.04831i | −0.992013 | − | 0.126132i | \(-0.959744\pi\) |
0.386773 | − | 0.922175i | \(-0.373590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9386 | + | 6.31541i | 1.07781 | + | 0.622276i | 0.930306 | − | 0.366785i | \(-0.119542\pi\) |
0.147507 | + | 0.989061i | \(0.452875\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.2906 | + | 13.5205i | 1.29703 | + | 1.31947i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.49616 | + | 4.90526i | 0.821355 | + | 0.474209i | 0.850883 | − | 0.525355i | \(-0.176067\pi\) |
−0.0295287 | + | 0.999564i | \(0.509401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.87979 | − | 1.66265i | 0.275834 | − | 0.159253i | −0.355702 | − | 0.934599i | \(-0.615758\pi\) |
0.631536 | + | 0.775347i | \(0.282425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.7590 | −1.02120 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.24090i | 0.587095i | 0.955945 | + | 0.293547i | \(0.0948358\pi\) | ||||
−0.955945 | + | 0.293547i | \(0.905164\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.49476 | − | 8.60764i | 0.885391 | − | 0.802667i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.3018 | + | 10.5666i | 1.69201 | + | 0.976880i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.69382 | − | 2.98751i | −0.521951 | − | 0.273865i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.43961 | − | 4.22553i | 0.221783 | − | 0.384139i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.9817 | − | 9.22701i | 1.44102 | − | 0.831972i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.66337 | + | 8.97772i | 0.595990 | + | 0.802992i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.2612 | −1.53169 | −0.765843 | − | 0.643027i | \(-0.777678\pi\) | ||||
−0.765843 | + | 0.643027i | \(0.777678\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.11984 | + | 1.22389i | −0.186641 | + | 0.107757i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.77736 | − | 1.02616i | −0.155289 | − | 0.0896562i | 0.420342 | − | 0.907366i | \(-0.361910\pi\) |
−0.575631 | + | 0.817710i | \(0.695243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3277 | + | 0.417375i | −0.895524 | + | 0.0361910i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 29.1313 | + | 9.35616i | 2.50722 | + | 0.805250i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.40950 | + | 4.27788i | −0.633036 | + | 0.365484i | −0.781927 | − | 0.623370i | \(-0.785763\pi\) |
0.148891 | + | 0.988854i | \(0.452430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3454i | 1.13194i | 0.824426 | + | 0.565970i | \(0.191498\pi\) | ||||
−0.824426 | + | 0.565970i | \(0.808502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 10.6164i | − | 0.894059i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.22837 | − | 3.59595i | 0.520842 | − | 0.300708i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.22154 | − | 10.0306i | 0.267534 | − | 0.832992i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −22.3594 | + | 1.81019i | −1.84418 | + | 0.149302i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0494 | + | 5.80204i | 0.823281 | + | 0.475321i | 0.851547 | − | 0.524279i | \(-0.175665\pi\) |
−0.0282658 | + | 0.999600i | \(0.508998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.4070 | − | 7.74053i | 1.09104 | − | 0.629915i | 0.157190 | − | 0.987568i | \(-0.449756\pi\) |
0.933854 | + | 0.357653i | \(0.116423\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.6679 | −1.42837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.70884 | + | 17.1622i | 0.297902 | + | 1.37850i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.73719 | + | 1.00296i | −0.138643 | + | 0.0800453i | −0.567717 | − | 0.823224i | \(-0.692173\pi\) |
0.429074 | + | 0.903269i | \(0.358840\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.51945 | + | 2.63177i | −0.120500 | + | 0.208713i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.612315 | + | 15.1514i | 0.0482572 | + | 1.19409i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.2898 | − | 8.25020i | −1.11926 | − | 0.646205i | −0.178048 | − | 0.984022i | \(-0.556978\pi\) |
−0.941212 | + | 0.337816i | \(0.890312\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.1345 | − | 11.9073i | 1.02252 | − | 0.926979i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.67196i | − | 0.361527i | −0.983527 | − | 0.180763i | \(-0.942143\pi\) | ||
0.983527 | − | 0.180763i | \(-0.0578568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.54954 | 0.349965 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.5959 | + | 14.2005i | −1.88090 | + | 1.08594i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.44746 | + | 3.72244i | 0.490191 | + | 0.283012i | 0.724654 | − | 0.689113i | \(-0.242000\pi\) |
−0.234463 | + | 0.972125i | \(0.575333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2069 | − | 0.760790i | −0.998345 | − | 0.0575103i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.5570 | − | 11.8686i | −1.54516 | − | 0.892099i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.86291 | + | 8.42281i | 0.363471 | + | 0.629550i | 0.988530 | − | 0.151028i | \(-0.0482583\pi\) |
−0.625059 | + | 0.780578i | \(0.714925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.72502 | −0.425537 | −0.212769 | − | 0.977103i | \(-0.568248\pi\) | ||||
−0.212769 | + | 0.977103i | \(0.568248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.930977 | 0.0688198 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.56183 | − | 5.04217i | 0.408914 | − | 0.370708i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00632 | + | 5.20709i | −0.219844 | + | 0.380780i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −30.5959 | + | 19.3526i | −2.22553 | + | 1.40769i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.66537 | + | 1.53885i | 0.192860 | + | 0.111347i | 0.593321 | − | 0.804966i | \(-0.297817\pi\) |
−0.400461 | + | 0.916314i | \(0.631150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.3501 | + | 9.43976i | −1.17691 | + | 0.679488i | −0.955297 | − | 0.295647i | \(-0.904465\pi\) |
−0.221611 | + | 0.975135i | \(0.571132\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.3608 | + | 4.40009i | −1.45807 | + | 0.315097i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.81372 | 0.342964 | 0.171482 | − | 0.985187i | \(-0.445145\pi\) | ||||
0.171482 | + | 0.985187i | \(0.445145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0922 | − | 20.9442i | −0.857190 | − | 1.48470i | −0.874598 | − | 0.484848i | \(-0.838875\pi\) |
0.0174086 | − | 0.999848i | \(-0.494458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.2034 | + | 7.62296i | 0.931293 | + | 0.537682i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.66354 | + | 10.5349i | 0.467689 | + | 0.739404i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.93745 | + | 12.2596i | −0.275004 | + | 0.856249i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.8330 | + | 36.0838i | 1.44799 | + | 2.50800i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.66522i | 0.668557i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8628 | 1.71163 | 0.855814 | − | 0.517284i | \(-0.173057\pi\) | ||||
0.855814 | + | 0.517284i | \(0.173057\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.8449 | + | 12.6121i | −1.49679 | + | 0.864170i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.522271 | − | 1.62614i | 0.0356186 | − | 0.110902i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.3967 | − | 9.65267i | −1.24885 | − | 0.655266i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.93512 | − | 5.08377i | 0.198337 | − | 0.343529i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.11832 | − | 3.53241i | 0.411563 | − | 0.237616i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.76281i | 0.452871i | 0.974026 | + | 0.226436i | \(0.0727073\pi\) | ||||
−0.974026 | + | 0.226436i | \(0.927293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −33.1055 | + | 15.0095i | −2.20703 | + | 1.00064i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.30970 | + | 7.46462i | 0.286045 | + | 0.495444i | 0.972862 | − | 0.231386i | \(-0.0743260\pi\) |
−0.686817 | + | 0.726830i | \(0.740993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3387 | + | 17.9071i | −0.683200 | + | 1.18334i | 0.290799 | + | 0.956784i | \(0.406079\pi\) |
−0.973999 | + | 0.226552i | \(0.927255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.847038 | + | 20.9594i | 0.0557310 | + | 1.37903i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1261 | + | 11.0424i | 1.25299 | + | 0.723414i | 0.971702 | − | 0.236210i | \(-0.0759053\pi\) |
0.281287 | + | 0.959624i | \(0.409239\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.97532 | + | 5.48809i | 0.324554 | + | 0.358003i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.27083i | − | 0.407334i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7855i | 0.697656i | 0.937187 | + | 0.348828i | \(0.113420\pi\) | ||||
−0.937187 | + | 0.348828i | \(0.886580\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4652 | + | 8.92882i | −0.996200 | + | 0.575156i | −0.907122 | − | 0.420868i | \(-0.861725\pi\) |
−0.0890780 | + | 0.996025i | \(0.528392\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7918 | + | 25.6201i | −0.948893 | + | 1.64353i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.7103 | − | 11.4144i | 0.684256 | − | 0.729242i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.67830 | − | 9.83511i | 0.361302 | − | 0.625793i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.6014 | + | 18.3622i | 0.671839 | + | 1.16366i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.0237i | − | 0.695810i | −0.937530 | − | 0.347905i | \(-0.886893\pi\) | ||
0.937530 | − | 0.347905i | \(-0.113107\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1795 | 0.891457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9024 | − | 11.6969i | 0.807979 | − | 0.732487i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5353 | + | 26.9079i | −0.969065 | + | 1.67847i | −0.270793 | + | 0.962638i | \(0.587286\pi\) |
−0.698272 | + | 0.715832i | \(0.746048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.358681 | + | 8.87534i | 0.0222873 | + | 0.551487i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.6628 | + | 17.1258i | 1.83608 | + | 1.06006i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.32868 | − | 16.1577i | −0.575231 | − | 0.996329i | −0.996017 | − | 0.0891689i | \(-0.971579\pi\) |
0.420786 | − | 0.907160i | \(-0.361754\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.447894 | − | 2.07257i | −0.0275139 | − | 0.127317i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 13.7872i | − | 0.843761i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.41984 | + | 2.45923i | 0.0865689 | + | 0.149942i | 0.906059 | − | 0.423152i | \(-0.139076\pi\) |
−0.819490 | + | 0.573094i | \(0.805743\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.37179 | − | 16.2324i | 0.569296 | − | 0.986049i | −0.427340 | − | 0.904091i | \(-0.640549\pi\) |
0.996636 | − | 0.0819580i | \(-0.0261173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.4517 | − | 21.8255i | 0.693089 | − | 1.32094i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.20951 | + | 12.3108i | −0.0729362 | + | 0.742371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9110 | − | 20.6304i | −0.715661 | − | 1.23956i | −0.962704 | − | 0.270557i | \(-0.912792\pi\) |
0.247043 | − | 0.969004i | \(-0.420541\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −57.0851 | −3.41760 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3608 | 0.618073 | 0.309037 | − | 0.951050i | \(-0.399993\pi\) | ||||
0.309037 | + | 0.951050i | \(0.399993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.67454 | − | 8.09653i | −0.277872 | − | 0.481289i | 0.692983 | − | 0.720953i | \(-0.256296\pi\) |
−0.970856 | + | 0.239665i | \(0.922963\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.56043 | − | 26.6537i | 0.507076 | − | 1.57883i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.14436 | − | 12.8760i | −0.480747 | − | 0.760047i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.54680 | − | 9.60734i | 0.326282 | − | 0.565138i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.5495 | − | 44.2531i | −1.49774 | − | 2.59416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0747i | 0.939094i | 0.882907 | + | 0.469547i | \(0.155583\pi\) | ||||
−0.882907 | + | 0.469547i | \(0.844417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1891 | − | 3.49855i | 0.942564 | − | 0.203693i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9264 | + | 29.3174i | 0.982171 | + | 1.70117i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.4287 | − | 8.33043i | −0.834435 | − | 0.481761i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.08028 | + | 1.70790i | 0.0622665 | + | 0.0984417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.4926 | + | 33.7622i | −1.11982 | + | 1.93959i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.481265 | + | 0.436299i | −0.0275572 | + | 0.0249824i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.9824 | 0.855091 | 0.427545 | − | 0.903994i | \(-0.359378\pi\) | ||||
0.427545 | + | 0.903994i | \(0.359378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 40.4774i | − | 2.30268i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4750 | + | 26.8036i | 0.877509 | + | 1.51989i | 0.854066 | + | 0.520165i | \(0.174130\pi\) |
0.0234437 | + | 0.999725i | \(0.492537\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.57151 | − | 2.72194i | 0.0888271 | − | 0.153853i | −0.818189 | − | 0.574950i | \(-0.805021\pi\) |
0.907016 | + | 0.421097i | \(0.138355\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.4874 | − | 41.4464i | 0.647239 | − | 2.33524i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.89262 | − | 3.27812i | 0.106300 | − | 0.184118i | −0.807968 | − | 0.589226i | \(-0.799433\pi\) |
0.914269 | + | 0.405108i | \(0.132766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0947 | − | 5.82815i | 0.565192 | − | 0.326314i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 31.4393i | − | 1.75477i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.49444i | 0.528285i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.46336 | − | 11.8166i | 0.469463 | − | 0.655469i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.22873 | − | 5.32821i | −0.510350 | − | 0.294651i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.75767 | + | 0.353925i | −0.482826 | + | 0.0195125i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.83340 | − | 6.63965i | 0.210703 | − | 0.364948i | −0.741232 | − | 0.671249i | \(-0.765758\pi\) |
0.951935 | + | 0.306301i | \(0.0990914\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.2035 | + | 21.1371i | 0.668748 | + | 1.15831i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3979 | + | 2.24704i | −0.568098 | + | 0.122769i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.8688i | − | 1.35469i | −0.735667 | − | 0.677344i | \(-0.763131\pi\) | ||
0.735667 | − | 0.677344i | \(-0.236869\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3205 | − | 9.99998i | 0.940719 | − | 0.543124i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.71342 | + | 16.8241i | −0.526011 | + | 0.911078i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23868 | + | 18.3845i | 0.120877 | + | 0.992667i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −39.1026 | − | 12.5587i | −2.10522 | − | 0.676137i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.3450 | + | 11.1689i | −1.03850 | + | 0.599576i | −0.919407 | − | 0.393308i | \(-0.871331\pi\) |
−0.119089 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.23220 | −0.333602 | −0.166801 | − | 0.985991i | \(-0.553344\pi\) | ||||
−0.166801 | + | 0.985991i | \(0.553344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 39.7770i | − | 2.12314i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.05250 | + | 8.75119i | 0.268918 | + | 0.465779i | 0.968583 | − | 0.248692i | \(-0.0800008\pi\) |
−0.699665 | + | 0.714471i | \(0.746667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.38199 | − | 16.7573i | 0.285646 | − | 0.889387i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.832072 | + | 20.5891i | 0.0440379 | + | 1.08969i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4425 | − | 10.6478i | −0.973359 | − | 0.561969i | −0.0731003 | − | 0.997325i | \(-0.523289\pi\) |
−0.900259 | + | 0.435356i | \(0.856623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.86891 | − | 3.23705i | −0.0983638 | − | 0.170371i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.6362 | −0.820689 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.865194 | + | 4.00357i | 0.0452863 | + | 0.209556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.2490 | − | 15.1549i | 1.37019 | − | 0.791077i | 0.379234 | − | 0.925301i | \(-0.376187\pi\) |
0.990951 | + | 0.134224i | \(0.0428541\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.2547 | − | 20.9317i | −1.88734 | − | 1.08966i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.22166 | + | 1.16569i | 0.115343 | + | 0.0605198i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.6702 | + | 20.2134i | −0.604260 | + | 1.04661i | 0.387908 | + | 0.921698i | \(0.373198\pi\) |
−0.992168 | + | 0.124911i | \(0.960136\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.2391 | − | 32.8782i | 0.735303 | − | 1.69782i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.6961 | −0.705386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.55433 | −0.490773 | −0.245387 | − | 0.969425i | \(-0.578915\pi\) | ||||
−0.245387 | + | 0.969425i | \(0.578915\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.6582 | + | 47.9053i | 1.41697 | + | 2.45427i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2249 | + | 9.36744i | 0.829052 | + | 0.478654i | 0.853528 | − | 0.521047i | \(-0.174458\pi\) |
−0.0244757 | + | 0.999700i | \(0.507792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2604 | − | 10.4379i | −0.522920 | − | 0.531967i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.80889 | + | 2.77641i | 0.244450 | + | 0.141133i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.5104 | + | 10.6870i | −0.938515 | + | 0.541852i | −0.889494 | − | 0.456946i | \(-0.848943\pi\) |
−0.0490204 | + | 0.998798i | \(0.515610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9290 | 0.704417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.57699i | 0.331765i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.93880 | + | 3.24168i | 0.147867 | + | 0.163107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.251200 | − | 0.145030i | −0.0126073 | − | 0.00727885i | 0.493683 | − | 0.869642i | \(-0.335650\pi\) |
−0.506290 | + | 0.862363i | \(0.668984\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.7067 | + | 27.9938i | 0.886443 | + | 1.40144i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4012 | − | 23.2115i | 0.669223 | − | 1.15913i | −0.308899 | − | 0.951095i | \(-0.599960\pi\) |
0.978122 | − | 0.208033i | \(-0.0667063\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7683 | − | 11.4132i | 0.984730 | − | 0.568534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.4104 | − | 48.1729i | −0.517299 | − | 2.39373i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.30603 | 0.411715 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0759 | − | 6.39466i | 0.547667 | − | 0.316195i | −0.200514 | − | 0.979691i | \(-0.564261\pi\) |
0.748180 | + | 0.663495i | \(0.230928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.7449 | + | 13.7091i | 1.17125 | + | 0.676221i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.10536 | + | 17.3536i | −0.448045 | + | 0.853916i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0858 | − | 4.52396i | −0.691444 | − | 0.222073i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.0376 | − | 21.3837i | 1.81374 | − | 1.04716i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.3606i | − | 0.555002i | −0.960725 | − | 0.277501i | \(-0.910494\pi\) | ||
0.960725 | − | 0.277501i | \(-0.0895062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 36.1939i | − | 1.76398i | −0.471266 | − | 0.881991i | \(-0.656203\pi\) | ||
0.471266 | − | 0.881991i | \(-0.343797\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.8569 | + | 12.0417i | −1.01409 | + | 0.585488i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.18814 | + | 12.0933i | −0.0576332 | + | 0.586612i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0310367 | − | 0.767984i | −0.00150197 | − | 0.0371654i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.9598 | − | 11.5238i | −0.963667 | − | 0.556374i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.0484 | + | 15.0391i | −1.25471 | + | 0.724406i | −0.972041 | − | 0.234812i | \(-0.924552\pi\) |
−0.282667 | + | 0.959218i | \(0.591219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9510 | −0.670442 | −0.335221 | − | 0.942139i | \(-0.608811\pi\) | ||||
−0.335221 | + | 0.942139i | \(0.608811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −32.9999 | + | 7.13147i | −1.58222 | + | 0.341928i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.3908 | − | 11.1953i | 0.927588 | − | 0.535543i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.58413 | + | 9.67200i | −0.266516 | + | 0.461619i | −0.967960 | − | 0.251106i | \(-0.919206\pi\) |
0.701444 | + | 0.712725i | \(0.252539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 28.9177 | + | 41.8740i | 1.37703 | + | 1.99400i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0785 | + | 9.28292i | 0.763912 | + | 0.441045i | 0.830699 | − | 0.556722i | \(-0.187941\pi\) |
−0.0667865 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.46131 | + | 7.12722i | 0.306295 | + | 0.337863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 37.1871i | − | 1.75889i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.39895 | −0.396371 | −0.198186 | − | 0.980165i | \(-0.563505\pi\) | ||||
−0.198186 | + | 0.980165i | \(0.563505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.3380 | + | 7.12333i | −0.580972 | + | 0.335424i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.9648 | − | 24.8057i | −2.01866 | − | 1.16547i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.30852 | + | 16.6494i | 0.201986 | + | 0.780536i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.5026 | + | 14.1466i | 1.14618 | + | 0.661749i | 0.947954 | − | 0.318406i | \(-0.103148\pi\) |
0.198229 | + | 0.980156i | \(0.436481\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.6274 | + | 28.7994i | 0.776099 | + | 1.34424i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.5889 | −1.47124 | −0.735621 | − | 0.677393i | \(-0.763110\pi\) | ||||
−0.735621 | + | 0.677393i | \(0.763110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6027 | −0.957487 | −0.478744 | − | 0.877955i | \(-0.658908\pi\) | ||||
−0.478744 | + | 0.877955i | \(0.658908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 41.6877 | − | 37.7927i | 1.93322 | − | 1.75259i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.18604 | − | 14.1786i | 0.378805 | − | 0.656109i | −0.612084 | − | 0.790793i | \(-0.709669\pi\) |
0.990889 | + | 0.134684i | \(0.0430019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.84818 | − | 11.1459i | 0.270044 | − | 0.514669i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.56708 | + | 3.21416i | 0.256518 | + | 0.148101i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.63653 | − | 0.944851i | 0.0752478 | − | 0.0434443i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.06588 | + | 17.7903i | 0.370088 | + | 0.816277i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.89381 | 0.315646 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7679 | + | 32.5069i | 0.857526 | + | 1.48528i | 0.874282 | + | 0.485419i | \(0.161333\pi\) |
−0.0167554 | + | 0.999860i | \(0.505334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.45203 | − | 4.87978i | −0.385379 | − | 0.222499i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 41.0687 | − | 25.9768i | 1.86869 | − | 1.18199i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.9468 | + | 10.9028i | 1.54145 | + | 0.495070i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.1439 | − | 21.0339i | −0.550294 | − | 0.953138i | −0.998253 | − | 0.0590835i | \(-0.981182\pi\) |
0.447959 | − | 0.894054i | \(-0.352151\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.8781i | 2.39123i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.9769 | −0.721025 | −0.360513 | − | 0.932754i | \(-0.617398\pi\) | ||||
−0.360513 | + | 0.932754i | \(0.617398\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.91630 | − | 5.72518i | 0.446608 | − | 0.257849i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −38.2908 | − | 12.2980i | −1.72105 | − | 0.552752i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.1323 | + | 17.5999i | 0.499352 | + | 0.789462i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.03517 | + | 12.1853i | −0.314937 | + | 0.545487i | −0.979424 | − | 0.201813i | \(-0.935317\pi\) |
0.664487 | + | 0.747300i | \(0.268650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9661 | + | 7.48601i | −0.579285 | + | 0.334450i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.77499i | 0.391258i | 0.980678 | + | 0.195629i | \(0.0626748\pi\) | ||||
−0.980678 | + | 0.195629i | \(0.937325\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.74590 | − | 26.5884i | −0.255689 | − | 1.18317i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.28986 | − | 12.6264i | −0.323754 | − | 0.560758i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.8686 | − | 30.9493i | 0.792011 | − | 1.37180i | −0.132709 | − | 0.991155i | \(-0.542367\pi\) |
0.924720 | − | 0.380649i | \(-0.124299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.29157 | − | 2.25176i | −0.189848 | − | 0.0996121i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 46.2946 | + | 26.7282i | 2.04396 | + | 1.18008i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.9696 | + | 20.9247i | 0.835901 | + | 0.922051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.19591i | 0.360456i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 23.8583i | − | 1.04726i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.6318 | + | 19.9947i | −1.51724 | + | 0.875982i | −0.517450 | + | 0.855713i | \(0.673119\pi\) |
−0.999795 | + | 0.0202683i | \(0.993548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3266 | + | 30.0106i | −0.757641 | + | 1.31227i | 0.186409 | + | 0.982472i | \(0.440315\pi\) |
−0.944050 | + | 0.329801i | \(0.893018\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.0503 | + | 37.8722i | 0.831423 | + | 1.65288i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.54180 | + | 16.5269i | −0.415647 | + | 0.719922i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.92420 | − | 8.52897i | −0.214096 | − | 0.370825i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 53.8484i | 2.33682i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.7398 | 0.725080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7339 | + | 16.2525i | 0.637004 | + | 0.702655i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.5840 | − | 26.9922i | 0.672497 | − | 1.16480i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.2617 | − | 1.39748i | 0.743513 | − | 0.0601938i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.2321 | − | 13.9904i | −1.04182 | − | 0.601495i | −0.121472 | − | 0.992595i | \(-0.538761\pi\) |
−0.920348 | + | 0.391100i | \(0.872095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.17336 | + | 15.8887i | 0.393667 | + | 0.681851i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.26781 | − | 1.57061i | 0.311319 | − | 0.0672777i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.5628i | − | 0.494391i | −0.968966 | − | 0.247196i | \(-0.920491\pi\) | ||
0.968966 | − | 0.247196i | \(-0.0795090\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.05597 | − | 1.82899i | −0.0450677 | − | 0.0780596i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.20314 | − | 15.9403i | 0.392067 | − | 0.679080i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.17295 | + | 0.209055i | −0.219976 | + | 0.00888993i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.9055 | − | 7.35661i | −0.972283 | − | 0.312271i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.6698 | − | 39.2653i | −0.960552 | − | 1.66372i | −0.721118 | − | 0.692812i | \(-0.756371\pi\) |
−0.239434 | − | 0.970913i | \(-0.576962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.22040 | −0.0939127 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.2684 | 0.813514 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.15902 | − | 8.93569i | −0.217427 | − | 0.376594i | 0.736594 | − | 0.676335i | \(-0.236433\pi\) |
−0.954021 | + | 0.299741i | \(0.903100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.26730 | + | 13.2866i | −0.179527 | + | 0.558973i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 51.6383 | + | 27.0943i | 2.16860 | + | 1.13785i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.72049 | + | 8.17613i | −0.197893 | + | 0.342761i | −0.947845 | − | 0.318731i | \(-0.896743\pi\) |
0.749952 | + | 0.661492i | \(0.230077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8128 | − | 25.6565i | −0.619895 | − | 1.07369i | −0.989504 | − | 0.144503i | \(-0.953842\pi\) |
0.369609 | − | 0.929187i | \(-0.379492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.86299i | − | 0.412032i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.0996 | − | 11.8332i | 1.08843 | − | 0.493477i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.61237 | − | 13.1850i | −0.316907 | − | 0.548899i | 0.662934 | − | 0.748678i | \(-0.269311\pi\) |
−0.979841 | + | 0.199779i | \(0.935978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 52.3966 | + | 30.2512i | 2.17753 | + | 1.25720i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.7940 | − | 9.35752i | 0.613758 | − | 0.388216i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17303 | − | 2.03175i | 0.0485819 | − | 0.0841463i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.7389 | + | 35.0099i | 1.31224 | + | 1.44748i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.3201 | −1.00380 | −0.501899 | − | 0.864926i | \(-0.667365\pi\) | ||||
−0.501899 | + | 0.864926i | \(0.667365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.6766i | 1.26401i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.71317 | − | 13.3596i | −0.317277 | − | 0.549540i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.82898 | − | 8.36403i | 0.198302 | − | 0.343470i | −0.749676 | − | 0.661805i | \(-0.769791\pi\) |
0.947978 | + | 0.318336i | \(0.103124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0792 | − | 10.2535i | −0.413205 | − | 0.420353i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.7512 | + | 67.1190i | −1.58598 | + | 2.74700i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.10218 | − | 5.25515i | 0.371905 | − | 0.214719i | −0.302385 | − | 0.953186i | \(-0.597783\pi\) |
0.674290 | + | 0.738466i | \(0.264450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.14888i | 0.373191i | 0.982437 | + | 0.186595i | \(0.0597453\pi\) | ||||
−0.982437 | + | 0.186595i | \(0.940255\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 34.5857i | − | 1.40844i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.08309 | − | 7.32786i | 0.328624 | − | 0.297920i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.1138 | − | 24.3144i | −1.70935 | − | 0.986892i | −0.935366 | − | 0.353682i | \(-0.884929\pi\) |
−0.773981 | − | 0.633209i | \(-0.781737\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.5604 | − | 35.3738i | 0.752106 | − | 1.43342i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.81509 | − | 8.33998i | 0.194798 | − | 0.337399i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.92021 | + | 5.05795i | 0.117946 | + | 0.204289i | 0.918954 | − | 0.394366i | \(-0.129036\pi\) |
−0.801008 | + | 0.598654i | \(0.795702\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 40.3334 | − | 8.71627i | 1.62640 | − | 0.351474i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 49.5048i | 1.99299i | 0.0836564 | + | 0.996495i | \(0.473340\pi\) | ||||
−0.0836564 | + | 0.996495i | \(0.526660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.25280 | + | 4.76475i | −0.331708 | + | 0.191512i | −0.656599 | − | 0.754240i | \(-0.728006\pi\) |
0.324891 | + | 0.945751i | \(0.394672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.2120 | − | 67.9172i | 1.57352 | − | 2.72542i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.3733 | + | 0.459633i | −0.455663 | + | 0.0184148i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.04742 | + | 23.6694i | 0.321897 | + | 0.946775i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.8240 | − | 15.4869i | 1.07125 | − | 0.618485i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.15928 | 0.325332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.60958i | − | 0.302933i | −0.988462 | − | 0.151466i | \(-0.951601\pi\) | ||
0.988462 | − | 0.151466i | \(-0.0483995\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.8384 | − | 69.0021i | −1.58343 | − | 2.74259i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36.7485 | − | 11.8026i | −1.45832 | − | 0.468371i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.3861 | − | 8.71916i | −0.728484 | − | 0.345466i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 49.5555 | + | 28.6109i | 1.96039 | + | 1.13183i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.7911 | − | 18.6907i | −0.426222 | − | 0.738238i | 0.570312 | − | 0.821428i | \(-0.306822\pi\) |
−0.996534 | + | 0.0831906i | \(0.973489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.1575 | 1.38648 | 0.693239 | − | 0.720708i | \(-0.256183\pi\) | ||||
0.693239 | + | 0.720708i | \(0.256183\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.34990 | + | 1.15614i | −0.210652 | + | 0.0455231i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0712919 | − | 0.0411604i | 0.00280277 | − | 0.00161818i | −0.498598 | − | 0.866833i | \(-0.666152\pi\) |
0.501401 | + | 0.865215i | \(0.332818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.8702 | + | 9.16266i | 0.622960 | + | 0.359666i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.68843 | + | 66.5235i | 0.105368 | + | 2.60726i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.0368 | + | 20.8484i | −0.471037 | + | 0.815859i | −0.999451 | − | 0.0331271i | \(-0.989453\pi\) |
0.528415 | + | 0.848987i | \(0.322787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.08229 | − | 3.39995i | −0.120435 | − | 0.132847i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.3167 | −0.519536 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.3082 | −1.60914 | −0.804569 | − | 0.593859i | \(-0.797604\pi\) | ||||
−0.804569 | + | 0.593859i | \(0.797604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.80101 | − | 16.9759i | −0.381215 | − | 0.660284i | 0.610021 | − | 0.792385i | \(-0.291161\pi\) |
−0.991236 | + | 0.132101i | \(0.957828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.6071 | − | 11.3202i | −0.761477 | − | 0.439639i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.2726 | − | 6.17311i | −0.863695 | − | 0.239383i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.3854 | − | 13.5016i | −0.905487 | − | 0.522783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.7689 | − | 10.8362i | 0.725648 | − | 0.418953i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.718722 | −0.0277460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 38.8213i | − | 1.49645i | −0.663444 | − | 0.748226i | \(-0.730906\pi\) | ||
0.663444 | − | 0.748226i | \(-0.269094\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 55.6219 | + | 39.8377i | 2.14089 | + | 1.53336i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5675 | − | 19.3802i | −1.29010 | − | 0.744842i | −0.311431 | − | 0.950269i | \(-0.600808\pi\) |
−0.978672 | + | 0.205427i | \(0.934142\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.6536 | + | 22.5517i | −1.36826 | + | 0.865454i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.8111 | − | 23.9216i | 0.529243 | − | 0.916676i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.8093 | + | 18.3651i | −1.21715 | + | 0.702721i | −0.964307 | − | 0.264786i | \(-0.914699\pi\) |
−0.252842 | + | 0.967508i | \(0.581365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.6996 | + | 4.04108i | −0.714474 | + | 0.154402i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 66.2639 | 2.52812 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.38730 | + | 1.37831i | −0.0909487 | + | 0.0525093i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.1244 | − | 13.3509i | −0.879693 | − | 0.507891i | −0.00913605 | − | 0.999958i | \(-0.502908\pi\) |
−0.870557 | + | 0.492067i | \(0.836241\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.2161 | − | 25.4375i | 1.52768 | − | 0.966292i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.12507 | + | 28.4118i | −0.346134 | + | 1.07772i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.1200 | + | 6.99747i | −0.459077 | + | 0.265048i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 70.7744i | − | 2.67693i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7252i | 1.08494i | 0.840076 | + | 0.542468i | \(0.182510\pi\) | ||||
−0.840076 | + | 0.542468i | \(0.817490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3587 | − | 6.55796i | 0.428402 | − | 0.247338i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.25907 | − | 22.6018i | 0.273392 | − | 0.851233i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.5010 | + | 14.9543i | 1.07189 | + | 0.562416i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.2847 | + | 15.1755i | 0.987142 | + | 0.569927i | 0.904419 | − | 0.426646i | \(-0.140305\pi\) |
0.0827230 | + | 0.996573i | \(0.473638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.3196 | + | 7.11275i | −0.462023 | + | 0.266749i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.0045 | 1.68543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.7187 | − | 3.39690i | 0.587847 | − | 0.127037i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.9332 | − | 17.2819i | 1.11787 | − | 0.645405i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6997 | − | 41.0491i | 0.883849 | − | 1.53087i | 0.0368218 | − | 0.999322i | \(-0.488277\pi\) |
0.847027 | − | 0.531549i | \(-0.178390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.3907 | + | 1.34943i | −1.24354 | + | 0.0502553i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.5606 | + | 28.6138i | 1.84318 | + | 1.06416i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.7170 | − | 19.1519i | 0.509438 | − | 0.711283i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3064i | 0.530595i | 0.964167 | + | 0.265297i | \(0.0854701\pi\) | ||||
−0.964167 | + | 0.265297i | \(0.914530\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.6824 | 1.06231 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.60762 | − | 0.928157i | 0.0594598 | − | 0.0343291i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.48221 | + | 3.74251i | 0.239426 | + | 0.138233i | 0.614913 | − | 0.788595i | \(-0.289191\pi\) |
−0.375487 | + | 0.926828i | \(0.622524\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −48.8401 | − | 11.4347i | −1.80149 | − | 0.421777i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.1931 | − | 5.88498i | −0.375467 | − | 0.216776i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.8579 | − | 20.5385i | −0.436199 | − | 0.755519i | 0.561193 | − | 0.827685i | \(-0.310342\pi\) |
−0.997393 | + | 0.0721655i | \(0.977009\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.3940 | −1.33697 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.32810 | 0.158783 | 0.0793914 | − | 0.996844i | \(-0.474702\pi\) | ||||
0.0793914 | + | 0.996844i | \(0.474702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.4276 | + | 19.2237i | 0.638498 | + | 0.704303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.0496 | − | 41.6551i | 0.879928 | − | 1.52408i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.9350 | + | 1.04812i | −0.947645 | + | 0.0382974i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.87523 | − | 1.08267i | −0.0684282 | − | 0.0395071i | 0.465396 | − | 0.885103i | \(-0.345912\pi\) |
−0.533824 | + | 0.845596i | \(0.679245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.5942 | + | 17.6636i | −1.11492 | + | 0.643697i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.8356 | − | 7.31207i | 1.23140 | − | 0.266113i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.9602 | −0.798158 | −0.399079 | − | 0.916917i | \(-0.630670\pi\) | ||||
−0.399079 | + | 0.916917i | \(0.630670\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.7202 | − | 39.3525i | −0.824691 | − | 1.42841i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.54542 | − | 3.20165i | −0.201021 | − | 0.116060i | 0.396110 | − | 0.918203i | \(-0.370360\pi\) |
−0.597132 | + | 0.802143i | \(0.703693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.08769 | + | 7.79062i | −0.147984 | + | 0.282039i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −37.6143 | − | 12.0807i | −1.35995 | − | 0.436777i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.7661 | − | 18.6474i | −0.388741 | − | 0.673320i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.2214i | 0.440714i | 0.975419 | + | 0.220357i | \(0.0707222\pi\) | ||||
−0.975419 | + | 0.220357i | \(0.929278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 99.5706 | 3.58595 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.6408 | − | 24.0413i | 1.49772 | − | 0.864706i | 0.497719 | − | 0.867338i | \(-0.334171\pi\) |
0.999997 | + | 0.00263190i | \(0.000837761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.83888 | + | 39.0736i | −0.137897 | + | 1.40356i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0571 | − | 15.2167i | 0.863045 | − | 0.545895i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2483 | + | 19.4827i | −0.403013 | + | 0.698039i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.8644 | − | 9.73668i | 0.603456 | − | 0.348406i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 64.4688i | − | 2.30393i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.38419 | + | 0.947448i | −0.156478 | + | 0.0338159i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4764 | − | 23.3419i | −0.480384 | − | 0.832049i | 0.519363 | − | 0.854554i | \(-0.326169\pi\) |
−0.999747 | + | 0.0225049i | \(0.992836\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.8952 | + | 51.7800i | −1.06430 | + | 1.84342i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.82663 | − | 13.9547i | −0.313839 | − | 0.496171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.731355 | + | 0.422248i | 0.0259712 | + | 0.0149945i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.03436 | + | 4.56398i | −0.178550 | + | 0.161868i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.04481i | 0.0370090i | 0.999829 | + | 0.0185045i | \(0.00589050\pi\) | ||||
−0.999829 | + | 0.0185045i | \(0.994109\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.05110i | 0.284828i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.0862 | + | 15.6382i | −0.957044 | + | 0.552550i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.26593 | + | 3.92471i | −0.0799631 | + | 0.138500i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.05635 | + | 32.6753i | −0.319194 | + | 1.15165i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.55009 | − | 7.88098i | 0.160171 | − | 0.277424i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.5368 | − | 35.5707i | −0.722034 | − | 1.25060i | −0.960183 | − | 0.279371i | \(-0.909874\pi\) |
0.238150 | − | 0.971229i | \(-0.423459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 52.7552i | − | 1.85249i | −0.376926 | − | 0.926244i | \(-0.623019\pi\) | ||
0.376926 | − | 0.926244i | \(-0.376981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −60.0667 | −2.10663 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.7811 | − | 27.3351i | −0.868046 | − | 0.957508i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.49200 | − | 2.58422i | 0.0521984 | − | 0.0904103i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −55.8675 | + | 2.25778i | −1.95217 | + | 0.0788933i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0058 | + | 14.4371i | 0.872710 | + | 0.503859i | 0.868248 | − | 0.496131i | \(-0.165246\pi\) |
0.00446216 | + | 0.999990i | \(0.498580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.70757 | − | 11.6178i | −0.233811 | − | 0.404973i | 0.725115 | − | 0.688627i | \(-0.241786\pi\) |
−0.958926 | + | 0.283655i | \(0.908453\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.1045 | − | 16.3692i | 1.25700 | − | 0.569903i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.8083i | 1.07131i | 0.844437 | + | 0.535655i | \(0.179935\pi\) | ||||
−0.844437 | + | 0.535655i | \(0.820065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.18705 | + | 14.1804i | 0.284348 | + | 0.492505i | 0.972451 | − | 0.233108i | \(-0.0748896\pi\) |
−0.688103 | + | 0.725613i | \(0.741556\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.1706 | + | 66.1134i | −1.32412 | + | 2.29345i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.9567 | − | 1.37279i | 0.587514 | − | 0.0475643i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.19451 | − | 9.94640i | 0.110551 | − | 0.344210i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.7231 | + | 93.0511i | 1.85694 | + | 3.21632i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.6109 | −0.815137 | −0.407569 | − | 0.913175i | \(-0.633623\pi\) | ||||
−0.407569 | + | 0.913175i | \(0.633623\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.80193 | 0.234549 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.6014 | − | 28.7545i | −0.571783 | − | 0.990356i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.68579 | + | 3.11081i | 0.333201 | + | 0.107015i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.521277 | + | 12.8987i | 0.0179113 | + | 0.443204i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9803 | + | 25.9466i | −0.514122 | + | 0.890485i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.62094 | − | 16.6640i | −0.329802 | − | 0.571233i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.4550i | − | 1.31667i | −0.752724 | − | 0.658336i | \(-0.771260\pi\) | ||
0.752724 | − | 0.658336i | \(-0.228740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −62.0734 | + | 13.4144i | −2.12287 | + | 0.458764i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.83986 | − | 15.3111i | −0.301964 | − | 0.523017i | 0.674617 | − | 0.738168i | \(-0.264309\pi\) |
−0.976581 | + | 0.215151i | \(0.930976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4581 | − | 6.03798i | −0.356825 | − | 0.206013i | 0.310862 | − | 0.950455i | \(-0.399382\pi\) |
−0.667687 | + | 0.744442i | \(0.732716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.6851 | + | 43.2348i | −0.773105 | + | 1.47344i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.86108 | − | 6.68759i | 0.131433 | − | 0.227648i | −0.792796 | − | 0.609487i | \(-0.791376\pi\) |
0.924229 | + | 0.381838i | \(0.124709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.1811 | + | 12.3335i | 0.380169 | + | 0.419350i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.5512 | −1.20738 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.84113i | 0.164224i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.91484 | + | 11.9769i | 0.234300 | + | 0.405820i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57.9596 | + | 100.389i | −1.96164 | + | 3.39765i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.5967 | − | 10.6501i | −0.932938 | − | 0.360038i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.57193 | − | 7.91882i | 0.154383 | − | 0.267399i | −0.778451 | − | 0.627705i | \(-0.783994\pi\) |
0.932834 | + | 0.360306i | \(0.117328\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.6123 | − | 25.7570i | 1.50474 | − | 0.868760i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.52233i | − | 0.152361i | −0.997094 | − | 0.0761805i | \(-0.975727\pi\) | ||
0.997094 | − | 0.0761805i | \(-0.0242725\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 37.8342i | − | 1.27322i | −0.771185 | − | 0.636611i | \(-0.780336\pi\) | ||
0.771185 | − | 0.636611i | \(-0.219664\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.6498 | − | 39.3239i | −1.19835 | − | 1.32186i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0412 | + | 7.52933i | 0.437880 | + | 0.252810i | 0.702698 | − | 0.711488i | \(-0.251979\pi\) |
−0.264818 | + | 0.964298i | \(0.585312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.5961 | − | 24.4129i | 1.29447 | − | 0.818782i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.2648 | − | 47.2241i | 0.913406 | − | 1.58207i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.47101 | + | 11.2081i | 0.216544 | + | 0.375066i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.59373 | + | 21.2569i | 0.153552 | + | 0.710539i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 53.3923i | 1.78272i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.0396 | − | 18.4981i | 1.06858 | − | 0.616945i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.15230 | − | 1.99585i | 0.0383888 | − | 0.0664913i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.00899 | − | 5.73474i | 0.100133 | − | 0.190840i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1883 | − | 3.91456i | −0.405154 | − | 0.130124i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.3608 | + | 22.1476i | −1.27375 | + | 0.735400i | −0.975692 | − | 0.219148i | \(-0.929672\pi\) |
−0.298058 | + | 0.954548i | \(0.596339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 88.4388 | 2.93333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.0968i | 1.36160i | 0.732470 | + | 0.680799i | \(0.238367\pi\) | ||||
−0.732470 | + | 0.680799i | \(0.761633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.18440 | − | 14.1758i | −0.270864 | − | 0.469150i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.98201 | + | 0.636568i | 0.0655233 | + | 0.0210443i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.42551 | − | 0.219262i | 0.179166 | − | 0.00724068i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.1904 | − | 7.61549i | −0.435112 | − | 0.251212i | 0.266410 | − | 0.963860i | \(-0.414162\pi\) |
−0.701522 | + | 0.712648i | \(0.747496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.0067 | − | 41.5809i | −0.791049 | − | 1.37014i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.8811 | −0.753142 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2886 | − | 6.93160i | 0.502684 | − | 0.227910i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −79.5218 | + | 45.9119i | −2.61184 | + | 1.50795i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.33630 | − | 3.65826i | −0.207887 | − | 0.120024i | 0.392442 | − | 0.919777i | \(-0.371630\pi\) |
−0.600329 | + | 0.799753i | \(0.704964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5024 | − | 15.5399i | 0.737487 | − | 0.509299i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 49.5922 | − | 85.8962i | 1.62358 | − | 2.81212i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.96074 | + | 9.03008i | −0.325751 | + | 0.295315i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5605 | −0.606347 | −0.303173 | − | 0.952935i | \(-0.598046\pi\) | ||||
−0.303173 | + | 0.952935i | \(0.598046\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0723 | −0.328698 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.91298 | + | 13.7057i | 0.257956 | + | 0.446792i | 0.965694 | − | 0.259682i | \(-0.0836178\pi\) |
−0.707738 | + | 0.706475i | \(0.750284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.5823 | + | 16.5020i | 0.930768 | + | 0.537379i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −78.3701 | + | 20.2805i | −2.54938 | + | 0.659726i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.2327 | − | 7.63993i | −0.430006 | − | 0.248264i | 0.269343 | − | 0.963044i | \(-0.413193\pi\) |
−0.699349 | + | 0.714780i | \(0.746527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.61153 | − | 2.66247i | 0.149696 | − | 0.0864273i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.1304 | −0.393356 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.4292i | 0.435014i | 0.976059 | + | 0.217507i | \(0.0697924\pi\) | ||||
−0.976059 | + | 0.217507i | \(0.930208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.62226 | + | 5.09864i | 0.149573 | + | 0.164988i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −32.3499 | − | 18.6772i | −1.04572 | − | 0.603749i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5174 | − | 20.0447i | 0.339623 | − | 0.647278i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3296 | + | 26.5516i | −0.494503 | + | 0.856504i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −61.7656 | + | 35.6604i | −1.99037 | + | 1.14914i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41.2633 | + | 8.91724i | −1.32831 | + | 0.287056i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1963 | −0.649468 | −0.324734 | − | 0.945805i | \(-0.605275\pi\) | ||||
−0.324734 | + | 0.945805i | \(0.605275\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.3501 | − | 15.2132i | 0.846486 | − | 0.488719i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0745 | + | 13.8994i | 0.772587 | + | 0.446053i | 0.833797 | − | 0.552071i | \(-0.186162\pi\) |
−0.0612095 | + | 0.998125i | \(0.519496\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.8746 | − | 29.8403i | −0.605092 | − | 0.956635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −46.3560 | − | 4.55436i | −1.48458 | − | 0.145856i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.2559 | − | 20.3550i | 1.12794 | − | 0.651214i | 0.184521 | − | 0.982829i | \(-0.440927\pi\) |
0.943415 | + | 0.331615i | \(0.107593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6438i | 0.340177i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.1743i | 0.771826i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.7777 | − | 20.0789i | 1.10924 | − | 0.640418i | 0.170605 | − | 0.985339i | \(-0.445428\pi\) |
0.938632 | + | 0.344921i | \(0.112094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2482 | + | 3.29145i | 0.326536 | + | 0.104874i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.0149 | + | 23.7382i | 0.477930 | + | 0.755595i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.79121 | − | 2.18886i | −0.120553 | − | 0.0696016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.03398 | − | 3.48372i | 0.191676 | − | 0.110664i | −0.401091 | − | 0.916038i | \(-0.631369\pi\) |
0.592767 | + | 0.805374i | \(0.298036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.5695 | −0.779689 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.4228 | − | 52.8576i | −0.362128 | − | 1.67570i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7596 | + | 7.94408i | −0.435770 | + | 0.251592i | −0.701802 | − | 0.712373i | \(-0.747621\pi\) |
0.266032 | + | 0.963964i | \(0.414287\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.9695 | − | 39.7844i | 0.726724 | − | 1.25872i |
(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 | 1120.2.bq.b.719.1 | 80 | ||
4.3 | odd | 2 | 280.2.ba.b.19.12 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.2.bq.b.719.39 | 80 | ||
7.3 | odd | 6 | inner | 1120.2.bq.b.1039.40 | 80 | ||
8.3 | odd | 2 | inner | 1120.2.bq.b.719.2 | 80 | ||
8.5 | even | 2 | 280.2.ba.b.19.3 | ✓ | 80 | ||
20.19 | odd | 2 | 280.2.ba.b.19.29 | yes | 80 | ||
28.3 | even | 6 | 280.2.ba.b.59.38 | yes | 80 | ||
35.24 | odd | 6 | inner | 1120.2.bq.b.1039.2 | 80 | ||
40.19 | odd | 2 | inner | 1120.2.bq.b.719.40 | 80 | ||
40.29 | even | 2 | 280.2.ba.b.19.38 | yes | 80 | ||
56.3 | even | 6 | inner | 1120.2.bq.b.1039.39 | 80 | ||
56.45 | odd | 6 | 280.2.ba.b.59.29 | yes | 80 | ||
140.59 | even | 6 | 280.2.ba.b.59.3 | yes | 80 | ||
280.59 | even | 6 | inner | 1120.2.bq.b.1039.1 | 80 | ||
280.269 | odd | 6 | 280.2.ba.b.59.12 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.ba.b.19.3 | ✓ | 80 | 8.5 | even | 2 | ||
280.2.ba.b.19.12 | yes | 80 | 4.3 | odd | 2 | ||
280.2.ba.b.19.29 | yes | 80 | 20.19 | odd | 2 | ||
280.2.ba.b.19.38 | yes | 80 | 40.29 | even | 2 | ||
280.2.ba.b.59.3 | yes | 80 | 140.59 | even | 6 | ||
280.2.ba.b.59.12 | yes | 80 | 280.269 | odd | 6 | ||
280.2.ba.b.59.29 | yes | 80 | 56.45 | odd | 6 | ||
280.2.ba.b.59.38 | yes | 80 | 28.3 | even | 6 | ||
1120.2.bq.b.719.1 | 80 | 1.1 | even | 1 | trivial | ||
1120.2.bq.b.719.2 | 80 | 8.3 | odd | 2 | inner | ||
1120.2.bq.b.719.39 | 80 | 5.4 | even | 2 | inner | ||
1120.2.bq.b.719.40 | 80 | 40.19 | odd | 2 | inner | ||
1120.2.bq.b.1039.1 | 80 | 280.59 | even | 6 | inner | ||
1120.2.bq.b.1039.2 | 80 | 35.24 | odd | 6 | inner | ||
1120.2.bq.b.1039.39 | 80 | 56.3 | even | 6 | inner | ||
1120.2.bq.b.1039.40 | 80 | 7.3 | odd | 6 | inner |