Properties

Label 720.2.q.f.241.1
Level $720$
Weight $2$
Character 720.241
Analytic conductor $5.749$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,2,Mod(241,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.241");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.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: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 241.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 720.241
Dual form 720.2.q.f.481.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.18614 + 2.05446i) q^{7} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.18614 + 2.05446i) q^{7} +(-2.50000 + 1.65831i) q^{9} +(0.686141 - 1.18843i) q^{11} +(-2.37228 - 4.10891i) q^{13} +(1.18614 - 1.26217i) q^{15} -7.37228 q^{17} -3.37228 q^{19} +(4.00000 + 0.939764i) q^{21} +(-2.18614 - 3.78651i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.00000 + 3.31662i) q^{27} +(2.18614 - 3.78651i) q^{29} +(-3.37228 - 5.84096i) q^{31} +(-2.31386 - 0.543620i) q^{33} -2.37228 q^{35} -4.00000 q^{37} +(-5.62772 + 5.98844i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.68614 + 9.84868i) q^{43} +(-2.68614 - 1.33591i) q^{45} +(-0.813859 + 1.40965i) q^{47} +(0.686141 + 1.18843i) q^{49} +(3.68614 + 12.2255i) q^{51} +11.4891 q^{53} +1.37228 q^{55} +(1.68614 + 5.59230i) q^{57} +(-0.686141 - 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} +(-0.441578 - 7.10313i) q^{63} +(2.37228 - 4.10891i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-5.18614 + 5.51856i) q^{69} +6.00000 q^{71} -14.1168 q^{73} +(1.68614 + 0.396143i) q^{75} +(1.62772 + 2.81929i) q^{77} +(1.00000 - 1.73205i) q^{79} +(3.50000 - 8.29156i) q^{81} +(0.813859 - 1.40965i) q^{83} +(-3.68614 - 6.38458i) q^{85} +(-7.37228 - 1.73205i) q^{87} -1.11684 q^{89} +11.2554 q^{91} +(-8.00000 + 8.51278i) q^{93} +(-1.68614 - 2.92048i) q^{95} +(1.31386 - 2.27567i) q^{97} +(0.255437 + 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9} - 3 q^{11} + 2 q^{13} - q^{15} - 18 q^{17} - 2 q^{19} + 16 q^{21} - 3 q^{23} - 2 q^{25} + 16 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 2 q^{35} - 16 q^{37} - 34 q^{39} + 6 q^{41} - 17 q^{43} - 5 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 6 q^{55} + q^{57} + 3 q^{59} - q^{61} - 19 q^{63} - 2 q^{65} - 14 q^{67} - 15 q^{69} + 24 q^{71} - 22 q^{73} + q^{75} + 18 q^{77} + 4 q^{79} + 14 q^{81} + 9 q^{83} - 9 q^{85} - 18 q^{87} + 30 q^{89} + 68 q^{91} - 32 q^{93} - q^{95} + 11 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 1.65831i −0.288675 0.957427i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.18614 + 2.05446i −0.448319 + 0.776511i −0.998277 0.0586811i \(-0.981310\pi\)
0.549958 + 0.835192i \(0.314644\pi\)
\(8\) 0 0
\(9\) −2.50000 + 1.65831i −0.833333 + 0.552771i
\(10\) 0 0
\(11\) 0.686141 1.18843i 0.206879 0.358325i −0.743851 0.668346i \(-0.767003\pi\)
0.950730 + 0.310021i \(0.100336\pi\)
\(12\) 0 0
\(13\) −2.37228 4.10891i −0.657952 1.13961i −0.981145 0.193274i \(-0.938089\pi\)
0.323192 0.946333i \(-0.395244\pi\)
\(14\) 0 0
\(15\) 1.18614 1.26217i 0.306260 0.325891i
\(16\) 0 0
\(17\) −7.37228 −1.78804 −0.894020 0.448026i \(-0.852127\pi\)
−0.894020 + 0.448026i \(0.852127\pi\)
\(18\) 0 0
\(19\) −3.37228 −0.773654 −0.386827 0.922152i \(-0.626429\pi\)
−0.386827 + 0.922152i \(0.626429\pi\)
\(20\) 0 0
\(21\) 4.00000 + 0.939764i 0.872872 + 0.205073i
\(22\) 0 0
\(23\) −2.18614 3.78651i −0.455842 0.789541i 0.542894 0.839801i \(-0.317328\pi\)
−0.998736 + 0.0502598i \(0.983995\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) 2.18614 3.78651i 0.405956 0.703137i −0.588476 0.808515i \(-0.700272\pi\)
0.994432 + 0.105378i \(0.0336052\pi\)
\(30\) 0 0
\(31\) −3.37228 5.84096i −0.605680 1.04907i −0.991944 0.126680i \(-0.959568\pi\)
0.386264 0.922388i \(-0.373765\pi\)
\(32\) 0 0
\(33\) −2.31386 0.543620i −0.402791 0.0946322i
\(34\) 0 0
\(35\) −2.37228 −0.400989
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) −5.62772 + 5.98844i −0.901156 + 0.958918i
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) −5.68614 + 9.84868i −0.867128 + 1.50191i −0.00221007 + 0.999998i \(0.500703\pi\)
−0.864918 + 0.501913i \(0.832630\pi\)
\(44\) 0 0
\(45\) −2.68614 1.33591i −0.400426 0.199145i
\(46\) 0 0
\(47\) −0.813859 + 1.40965i −0.118714 + 0.205618i −0.919258 0.393655i \(-0.871210\pi\)
0.800545 + 0.599273i \(0.204544\pi\)
\(48\) 0 0
\(49\) 0.686141 + 1.18843i 0.0980201 + 0.169776i
\(50\) 0 0
\(51\) 3.68614 + 12.2255i 0.516163 + 1.71192i
\(52\) 0 0
\(53\) 11.4891 1.57815 0.789076 0.614295i \(-0.210560\pi\)
0.789076 + 0.614295i \(0.210560\pi\)
\(54\) 0 0
\(55\) 1.37228 0.185038
\(56\) 0 0
\(57\) 1.68614 + 5.59230i 0.223335 + 0.740718i
\(58\) 0 0
\(59\) −0.686141 1.18843i −0.0893279 0.154720i 0.817899 0.575361i \(-0.195139\pi\)
−0.907227 + 0.420641i \(0.861805\pi\)
\(60\) 0 0
\(61\) −4.55842 + 7.89542i −0.583646 + 1.01090i 0.411397 + 0.911456i \(0.365041\pi\)
−0.995043 + 0.0994483i \(0.968292\pi\)
\(62\) 0 0
\(63\) −0.441578 7.10313i −0.0556336 0.894910i
\(64\) 0 0
\(65\) 2.37228 4.10891i 0.294245 0.509648i
\(66\) 0 0
\(67\) −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i \(-0.307305\pi\)
−0.996659 + 0.0816792i \(0.973972\pi\)
\(68\) 0 0
\(69\) −5.18614 + 5.51856i −0.624338 + 0.664356i
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −14.1168 −1.65225 −0.826126 0.563486i \(-0.809460\pi\)
−0.826126 + 0.563486i \(0.809460\pi\)
\(74\) 0 0
\(75\) 1.68614 + 0.396143i 0.194699 + 0.0457427i
\(76\) 0 0
\(77\) 1.62772 + 2.81929i 0.185496 + 0.321288i
\(78\) 0 0
\(79\) 1.00000 1.73205i 0.112509 0.194871i −0.804272 0.594261i \(-0.797445\pi\)
0.916781 + 0.399390i \(0.130778\pi\)
\(80\) 0 0
\(81\) 3.50000 8.29156i 0.388889 0.921285i
\(82\) 0 0
\(83\) 0.813859 1.40965i 0.0893327 0.154729i −0.817897 0.575365i \(-0.804860\pi\)
0.907229 + 0.420637i \(0.138193\pi\)
\(84\) 0 0
\(85\) −3.68614 6.38458i −0.399818 0.692505i
\(86\) 0 0
\(87\) −7.37228 1.73205i −0.790392 0.185695i
\(88\) 0 0
\(89\) −1.11684 −0.118385 −0.0591926 0.998247i \(-0.518853\pi\)
−0.0591926 + 0.998247i \(0.518853\pi\)
\(90\) 0 0
\(91\) 11.2554 1.17989
\(92\) 0 0
\(93\) −8.00000 + 8.51278i −0.829561 + 0.882734i
\(94\) 0 0
\(95\) −1.68614 2.92048i −0.172994 0.299635i
\(96\) 0 0
\(97\) 1.31386 2.27567i 0.133402 0.231059i −0.791584 0.611061i \(-0.790743\pi\)
0.924986 + 0.380001i \(0.124076\pi\)
\(98\) 0 0
\(99\) 0.255437 + 4.10891i 0.0256724 + 0.412961i
\(100\) 0 0
\(101\) 4.37228 7.57301i 0.435058 0.753543i −0.562242 0.826973i \(-0.690061\pi\)
0.997300 + 0.0734297i \(0.0233944\pi\)
\(102\) 0 0
\(103\) −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i \(-0.877647\pi\)
0.138767 0.990325i \(-0.455686\pi\)
\(104\) 0 0
\(105\) 1.18614 + 3.93398i 0.115755 + 0.383917i
\(106\) 0 0
\(107\) 14.4891 1.40072 0.700358 0.713791i \(-0.253024\pi\)
0.700358 + 0.713791i \(0.253024\pi\)
\(108\) 0 0
\(109\) 9.62772 0.922168 0.461084 0.887356i \(-0.347461\pi\)
0.461084 + 0.887356i \(0.347461\pi\)
\(110\) 0 0
\(111\) 2.00000 + 6.63325i 0.189832 + 0.629600i
\(112\) 0 0
\(113\) −7.37228 12.7692i −0.693526 1.20122i −0.970675 0.240395i \(-0.922723\pi\)
0.277149 0.960827i \(-0.410610\pi\)
\(114\) 0 0
\(115\) 2.18614 3.78651i 0.203859 0.353094i
\(116\) 0 0
\(117\) 12.7446 + 6.33830i 1.17824 + 0.585976i
\(118\) 0 0
\(119\) 8.74456 15.1460i 0.801613 1.38843i
\(120\) 0 0
\(121\) 4.55842 + 7.89542i 0.414402 + 0.717765i
\(122\) 0 0
\(123\) 3.55842 3.78651i 0.320852 0.341418i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.11684 −0.808989 −0.404495 0.914540i \(-0.632553\pi\)
−0.404495 + 0.914540i \(0.632553\pi\)
\(128\) 0 0
\(129\) 19.1753 + 4.50506i 1.68829 + 0.396648i
\(130\) 0 0
\(131\) 4.37228 + 7.57301i 0.382008 + 0.661657i 0.991349 0.131251i \(-0.0418993\pi\)
−0.609341 + 0.792908i \(0.708566\pi\)
\(132\) 0 0
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) 0 0
\(135\) −0.872281 + 5.12241i −0.0750740 + 0.440867i
\(136\) 0 0
\(137\) 0.941578 1.63086i 0.0804444 0.139334i −0.822996 0.568046i \(-0.807699\pi\)
0.903441 + 0.428713i \(0.141033\pi\)
\(138\) 0 0
\(139\) 9.05842 + 15.6896i 0.768325 + 1.33078i 0.938470 + 0.345359i \(0.112243\pi\)
−0.170145 + 0.985419i \(0.554424\pi\)
\(140\) 0 0
\(141\) 2.74456 + 0.644810i 0.231134 + 0.0543028i
\(142\) 0 0
\(143\) −6.51087 −0.544467
\(144\) 0 0
\(145\) 4.37228 0.363098
\(146\) 0 0
\(147\) 1.62772 1.73205i 0.134252 0.142857i
\(148\) 0 0
\(149\) −9.55842 16.5557i −0.783056 1.35629i −0.930153 0.367171i \(-0.880326\pi\)
0.147097 0.989122i \(-0.453007\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) 0 0
\(153\) 18.4307 12.2255i 1.49003 0.988377i
\(154\) 0 0
\(155\) 3.37228 5.84096i 0.270868 0.469157i
\(156\) 0 0
\(157\) −2.37228 4.10891i −0.189329 0.327927i 0.755698 0.654920i \(-0.227298\pi\)
−0.945027 + 0.326993i \(0.893964\pi\)
\(158\) 0 0
\(159\) −5.74456 19.0526i −0.455573 1.51097i
\(160\) 0 0
\(161\) 10.3723 0.817450
\(162\) 0 0
\(163\) −1.48913 −0.116637 −0.0583186 0.998298i \(-0.518574\pi\)
−0.0583186 + 0.998298i \(0.518574\pi\)
\(164\) 0 0
\(165\) −0.686141 2.27567i −0.0534160 0.177161i
\(166\) 0 0
\(167\) 3.81386 + 6.60580i 0.295125 + 0.511172i 0.975014 0.222143i \(-0.0713053\pi\)
−0.679889 + 0.733315i \(0.737972\pi\)
\(168\) 0 0
\(169\) −4.75544 + 8.23666i −0.365803 + 0.633589i
\(170\) 0 0
\(171\) 8.43070 5.59230i 0.644712 0.427654i
\(172\) 0 0
\(173\) −4.62772 + 8.01544i −0.351839 + 0.609403i −0.986572 0.163329i \(-0.947777\pi\)
0.634733 + 0.772732i \(0.281110\pi\)
\(174\) 0 0
\(175\) −1.18614 2.05446i −0.0896638 0.155302i
\(176\) 0 0
\(177\) −1.62772 + 1.73205i −0.122347 + 0.130189i
\(178\) 0 0
\(179\) 3.25544 0.243323 0.121661 0.992572i \(-0.461178\pi\)
0.121661 + 0.992572i \(0.461178\pi\)
\(180\) 0 0
\(181\) −7.86141 −0.584334 −0.292167 0.956367i \(-0.594376\pi\)
−0.292167 + 0.956367i \(0.594376\pi\)
\(182\) 0 0
\(183\) 15.3723 + 3.61158i 1.13635 + 0.266976i
\(184\) 0 0
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 0 0
\(187\) −5.05842 + 8.76144i −0.369908 + 0.640700i
\(188\) 0 0
\(189\) −11.5584 + 4.28384i −0.840751 + 0.311604i
\(190\) 0 0
\(191\) −2.74456 + 4.75372i −0.198590 + 0.343967i −0.948071 0.318058i \(-0.896969\pi\)
0.749482 + 0.662025i \(0.230303\pi\)
\(192\) 0 0
\(193\) −1.94158 3.36291i −0.139758 0.242068i 0.787647 0.616127i \(-0.211299\pi\)
−0.927405 + 0.374059i \(0.877966\pi\)
\(194\) 0 0
\(195\) −8.00000 1.87953i −0.572892 0.134596i
\(196\) 0 0
\(197\) 17.4891 1.24605 0.623024 0.782202i \(-0.285904\pi\)
0.623024 + 0.782202i \(0.285904\pi\)
\(198\) 0 0
\(199\) 9.48913 0.672666 0.336333 0.941743i \(-0.390813\pi\)
0.336333 + 0.941743i \(0.390813\pi\)
\(200\) 0 0
\(201\) −8.30298 + 8.83518i −0.585647 + 0.623186i
\(202\) 0 0
\(203\) 5.18614 + 8.98266i 0.363996 + 0.630459i
\(204\) 0 0
\(205\) −1.50000 + 2.59808i −0.104765 + 0.181458i
\(206\) 0 0
\(207\) 11.7446 + 5.84096i 0.816304 + 0.405975i
\(208\) 0 0
\(209\) −2.31386 + 4.00772i −0.160053 + 0.277220i
\(210\) 0 0
\(211\) −3.62772 6.28339i −0.249742 0.432567i 0.713712 0.700439i \(-0.247013\pi\)
−0.963454 + 0.267873i \(0.913679\pi\)
\(212\) 0 0
\(213\) −3.00000 9.94987i −0.205557 0.681754i
\(214\) 0 0
\(215\) −11.3723 −0.775583
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) 7.05842 + 23.4101i 0.476964 + 1.58191i
\(220\) 0 0
\(221\) 17.4891 + 30.2921i 1.17645 + 2.03766i
\(222\) 0 0
\(223\) 6.18614 10.7147i 0.414255 0.717510i −0.581095 0.813836i \(-0.697376\pi\)
0.995350 + 0.0963255i \(0.0307090\pi\)
\(224\) 0 0
\(225\) −0.186141 2.99422i −0.0124094 0.199615i
\(226\) 0 0
\(227\) 0.941578 1.63086i 0.0624947 0.108244i −0.833085 0.553145i \(-0.813428\pi\)
0.895580 + 0.444901i \(0.146761\pi\)
\(228\) 0 0
\(229\) −9.18614 15.9109i −0.607037 1.05142i −0.991726 0.128373i \(-0.959025\pi\)
0.384689 0.923046i \(-0.374309\pi\)
\(230\) 0 0
\(231\) 3.86141 4.10891i 0.254062 0.270347i
\(232\) 0 0
\(233\) −10.1168 −0.662776 −0.331388 0.943494i \(-0.607517\pi\)
−0.331388 + 0.943494i \(0.607517\pi\)
\(234\) 0 0
\(235\) −1.62772 −0.106181
\(236\) 0 0
\(237\) −3.37228 0.792287i −0.219053 0.0514646i
\(238\) 0 0
\(239\) −7.37228 12.7692i −0.476873 0.825969i 0.522776 0.852470i \(-0.324897\pi\)
−0.999649 + 0.0265017i \(0.991563\pi\)
\(240\) 0 0
\(241\) −5.24456 + 9.08385i −0.337832 + 0.585142i −0.984025 0.178032i \(-0.943027\pi\)
0.646193 + 0.763174i \(0.276360\pi\)
\(242\) 0 0
\(243\) −15.5000 1.65831i −0.994325 0.106381i
\(244\) 0 0
\(245\) −0.686141 + 1.18843i −0.0438359 + 0.0759260i
\(246\) 0 0
\(247\) 8.00000 + 13.8564i 0.509028 + 0.881662i
\(248\) 0 0
\(249\) −2.74456 0.644810i −0.173930 0.0408632i
\(250\) 0 0
\(251\) −15.6060 −0.985040 −0.492520 0.870301i \(-0.663924\pi\)
−0.492520 + 0.870301i \(0.663924\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) −8.74456 + 9.30506i −0.547606 + 0.582706i
\(256\) 0 0
\(257\) 0.686141 + 1.18843i 0.0428003 + 0.0741323i 0.886632 0.462476i \(-0.153039\pi\)
−0.843832 + 0.536608i \(0.819705\pi\)
\(258\) 0 0
\(259\) 4.74456 8.21782i 0.294813 0.510631i
\(260\) 0 0
\(261\) 0.813859 + 13.0916i 0.0503766 + 0.810348i
\(262\) 0 0
\(263\) 2.74456 4.75372i 0.169237 0.293127i −0.768915 0.639351i \(-0.779203\pi\)
0.938152 + 0.346224i \(0.112536\pi\)
\(264\) 0 0
\(265\) 5.74456 + 9.94987i 0.352886 + 0.611216i
\(266\) 0 0
\(267\) 0.558422 + 1.85208i 0.0341749 + 0.113345i
\(268\) 0 0
\(269\) 4.37228 0.266583 0.133291 0.991077i \(-0.457445\pi\)
0.133291 + 0.991077i \(0.457445\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) −5.62772 18.6650i −0.340605 1.12966i
\(274\) 0 0
\(275\) 0.686141 + 1.18843i 0.0413758 + 0.0716651i
\(276\) 0 0
\(277\) −2.62772 + 4.55134i −0.157884 + 0.273464i −0.934106 0.356997i \(-0.883801\pi\)
0.776221 + 0.630461i \(0.217134\pi\)
\(278\) 0 0
\(279\) 18.1168 + 9.01011i 1.08463 + 0.539421i
\(280\) 0 0
\(281\) −2.18614 + 3.78651i −0.130414 + 0.225884i −0.923836 0.382788i \(-0.874964\pi\)
0.793422 + 0.608672i \(0.208297\pi\)
\(282\) 0 0
\(283\) −15.9307 27.5928i −0.946982 1.64022i −0.751733 0.659467i \(-0.770782\pi\)
−0.195249 0.980754i \(-0.562551\pi\)
\(284\) 0 0
\(285\) −4.00000 + 4.25639i −0.236940 + 0.252127i
\(286\) 0 0
\(287\) −7.11684 −0.420094
\(288\) 0 0
\(289\) 37.3505 2.19709
\(290\) 0 0
\(291\) −4.43070 1.04095i −0.259732 0.0610218i
\(292\) 0 0
\(293\) 4.11684 + 7.13058i 0.240509 + 0.416573i 0.960859 0.277037i \(-0.0893524\pi\)
−0.720351 + 0.693610i \(0.756019\pi\)
\(294\) 0 0
\(295\) 0.686141 1.18843i 0.0399487 0.0691931i
\(296\) 0 0
\(297\) 6.68614 2.47805i 0.387969 0.143791i
\(298\) 0 0
\(299\) −10.3723 + 17.9653i −0.599845 + 1.03896i
\(300\) 0 0
\(301\) −13.4891 23.3639i −0.777500 1.34667i
\(302\) 0 0
\(303\) −14.7446 3.46410i −0.847053 0.199007i
\(304\) 0 0
\(305\) −9.11684 −0.522029
\(306\) 0 0
\(307\) 33.2337 1.89675 0.948373 0.317156i \(-0.102728\pi\)
0.948373 + 0.317156i \(0.102728\pi\)
\(308\) 0 0
\(309\) −18.9783 + 20.1947i −1.07963 + 1.14884i
\(310\) 0 0
\(311\) −4.62772 8.01544i −0.262414 0.454514i 0.704469 0.709735i \(-0.251185\pi\)
−0.966883 + 0.255221i \(0.917852\pi\)
\(312\) 0 0
\(313\) −4.68614 + 8.11663i −0.264876 + 0.458779i −0.967531 0.252752i \(-0.918664\pi\)
0.702655 + 0.711531i \(0.251998\pi\)
\(314\) 0 0
\(315\) 5.93070 3.93398i 0.334157 0.221655i
\(316\) 0 0
\(317\) 4.37228 7.57301i 0.245572 0.425343i −0.716720 0.697361i \(-0.754358\pi\)
0.962292 + 0.272018i \(0.0876910\pi\)
\(318\) 0 0
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) 0 0
\(321\) −7.24456 24.0275i −0.404352 1.34108i
\(322\) 0 0
\(323\) 24.8614 1.38333
\(324\) 0 0
\(325\) 4.74456 0.263181
\(326\) 0 0
\(327\) −4.81386 15.9658i −0.266207 0.882909i
\(328\) 0 0
\(329\) −1.93070 3.34408i −0.106443 0.184365i
\(330\) 0 0
\(331\) −9.11684 + 15.7908i −0.501107 + 0.867943i 0.498892 + 0.866664i \(0.333740\pi\)
−0.999999 + 0.00127880i \(0.999593\pi\)
\(332\) 0 0
\(333\) 10.0000 6.63325i 0.547997 0.363500i
\(334\) 0 0
\(335\) 3.50000 6.06218i 0.191225 0.331212i
\(336\) 0 0
\(337\) −1.68614 2.92048i −0.0918499 0.159089i 0.816440 0.577431i \(-0.195945\pi\)
−0.908290 + 0.418342i \(0.862611\pi\)
\(338\) 0 0
\(339\) −17.4891 + 18.6101i −0.949879 + 1.01076i
\(340\) 0 0
\(341\) −9.25544 −0.501210
\(342\) 0 0
\(343\) −19.8614 −1.07242
\(344\) 0 0
\(345\) −7.37228 1.73205i −0.396910 0.0932505i
\(346\) 0 0
\(347\) −11.0584 19.1537i −0.593647 1.02823i −0.993736 0.111751i \(-0.964354\pi\)
0.400089 0.916476i \(-0.368979\pi\)
\(348\) 0 0
\(349\) −0.441578 + 0.764836i −0.0236371 + 0.0409407i −0.877602 0.479390i \(-0.840858\pi\)
0.853965 + 0.520331i \(0.174191\pi\)
\(350\) 0 0
\(351\) 4.13859 24.3036i 0.220902 1.29723i
\(352\) 0 0
\(353\) −15.1753 + 26.2843i −0.807698 + 1.39897i 0.106757 + 0.994285i \(0.465953\pi\)
−0.914455 + 0.404689i \(0.867380\pi\)
\(354\) 0 0
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) 0 0
\(357\) −29.4891 6.92820i −1.56073 0.366679i
\(358\) 0 0
\(359\) −5.48913 −0.289705 −0.144852 0.989453i \(-0.546271\pi\)
−0.144852 + 0.989453i \(0.546271\pi\)
\(360\) 0 0
\(361\) −7.62772 −0.401459
\(362\) 0 0
\(363\) 10.8139 11.5070i 0.567580 0.603961i
\(364\) 0 0
\(365\) −7.05842 12.2255i −0.369455 0.639914i
\(366\) 0 0
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) 0 0
\(369\) −8.05842 4.00772i −0.419505 0.208634i
\(370\) 0 0
\(371\) −13.6277 + 23.6039i −0.707516 + 1.22545i
\(372\) 0 0
\(373\) −3.74456 6.48577i −0.193886 0.335821i 0.752649 0.658422i \(-0.228776\pi\)
−0.946535 + 0.322602i \(0.895443\pi\)
\(374\) 0 0
\(375\) 0.500000 + 1.65831i 0.0258199 + 0.0856349i
\(376\) 0 0
\(377\) −20.7446 −1.06840
\(378\) 0 0
\(379\) 10.8614 0.557913 0.278956 0.960304i \(-0.410011\pi\)
0.278956 + 0.960304i \(0.410011\pi\)
\(380\) 0 0
\(381\) 4.55842 + 15.1186i 0.233535 + 0.774548i
\(382\) 0 0
\(383\) 11.4891 + 19.8997i 0.587067 + 1.01683i 0.994614 + 0.103646i \(0.0330508\pi\)
−0.407547 + 0.913184i \(0.633616\pi\)
\(384\) 0 0
\(385\) −1.62772 + 2.81929i −0.0829562 + 0.143684i
\(386\) 0 0
\(387\) −2.11684 34.0511i −0.107605 1.73092i
\(388\) 0 0
\(389\) 5.18614 8.98266i 0.262948 0.455439i −0.704076 0.710124i \(-0.748639\pi\)
0.967024 + 0.254686i \(0.0819720\pi\)
\(390\) 0 0
\(391\) 16.1168 + 27.9152i 0.815064 + 1.41173i
\(392\) 0 0
\(393\) 10.3723 11.0371i 0.523212 0.556749i
\(394\) 0 0
\(395\) 2.00000 0.100631
\(396\) 0 0
\(397\) 11.2554 0.564894 0.282447 0.959283i \(-0.408854\pi\)
0.282447 + 0.959283i \(0.408854\pi\)
\(398\) 0 0
\(399\) −13.4891 3.16915i −0.675301 0.158656i
\(400\) 0 0
\(401\) −8.05842 13.9576i −0.402418 0.697009i 0.591599 0.806232i \(-0.298497\pi\)
−0.994017 + 0.109223i \(0.965164\pi\)
\(402\) 0 0
\(403\) −16.0000 + 27.7128i −0.797017 + 1.38047i
\(404\) 0 0
\(405\) 8.93070 1.11469i 0.443770 0.0553895i
\(406\) 0 0
\(407\) −2.74456 + 4.75372i −0.136043 + 0.235633i
\(408\) 0 0
\(409\) 5.43070 + 9.40625i 0.268531 + 0.465109i 0.968483 0.249081i \(-0.0801285\pi\)
−0.699952 + 0.714190i \(0.746795\pi\)
\(410\) 0 0
\(411\) −3.17527 0.746000i −0.156624 0.0367975i
\(412\) 0 0
\(413\) 3.25544 0.160190
\(414\) 0 0
\(415\) 1.62772 0.0799016
\(416\) 0 0
\(417\) 21.4891 22.8665i 1.05233 1.11978i
\(418\) 0 0
\(419\) −15.8614 27.4728i −0.774880 1.34213i −0.934862 0.355012i \(-0.884477\pi\)
0.159981 0.987120i \(-0.448857\pi\)
\(420\) 0 0
\(421\) 19.2337 33.3137i 0.937393 1.62361i 0.167082 0.985943i \(-0.446566\pi\)
0.770311 0.637669i \(-0.220101\pi\)
\(422\) 0 0
\(423\) −0.302985 4.87375i −0.0147316 0.236970i
\(424\) 0 0
\(425\) 3.68614 6.38458i 0.178804 0.309698i
\(426\) 0 0
\(427\) −10.8139 18.7302i −0.523319 0.906416i
\(428\) 0 0
\(429\) 3.25544 + 10.7971i 0.157174 + 0.521287i
\(430\) 0 0
\(431\) 26.2337 1.26363 0.631816 0.775118i \(-0.282310\pi\)
0.631816 + 0.775118i \(0.282310\pi\)
\(432\) 0 0
\(433\) 0.627719 0.0301662 0.0150831 0.999886i \(-0.495199\pi\)
0.0150831 + 0.999886i \(0.495199\pi\)
\(434\) 0 0
\(435\) −2.18614 7.25061i −0.104817 0.347640i
\(436\) 0 0
\(437\) 7.37228 + 12.7692i 0.352664 + 0.610832i
\(438\) 0 0
\(439\) 8.11684 14.0588i 0.387396 0.670989i −0.604703 0.796451i \(-0.706708\pi\)
0.992098 + 0.125462i \(0.0400414\pi\)
\(440\) 0 0
\(441\) −3.68614 1.83324i −0.175531 0.0872972i
\(442\) 0 0
\(443\) −13.2446 + 22.9403i −0.629268 + 1.08992i 0.358431 + 0.933556i \(0.383312\pi\)
−0.987699 + 0.156368i \(0.950021\pi\)
\(444\) 0 0
\(445\) −0.558422 0.967215i −0.0264717 0.0458504i
\(446\) 0 0
\(447\) −22.6753 + 24.1287i −1.07250 + 1.14125i
\(448\) 0 0
\(449\) −18.8614 −0.890125 −0.445062 0.895500i \(-0.646819\pi\)
−0.445062 + 0.895500i \(0.646819\pi\)
\(450\) 0 0
\(451\) 4.11684 0.193855
\(452\) 0 0
\(453\) 16.8614 + 3.96143i 0.792218 + 0.186124i
\(454\) 0 0
\(455\) 5.62772 + 9.74749i 0.263832 + 0.456970i
\(456\) 0 0
\(457\) −15.0584 + 26.0820i −0.704403 + 1.22006i 0.262503 + 0.964931i \(0.415452\pi\)
−0.966906 + 0.255131i \(0.917881\pi\)
\(458\) 0 0
\(459\) −29.4891 24.4511i −1.37643 1.14128i
\(460\) 0 0
\(461\) −9.55842 + 16.5557i −0.445180 + 0.771075i −0.998065 0.0621833i \(-0.980194\pi\)
0.552885 + 0.833258i \(0.313527\pi\)
\(462\) 0 0
\(463\) 10.0000 + 17.3205i 0.464739 + 0.804952i 0.999190 0.0402476i \(-0.0128147\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 0 0
\(465\) −11.3723 2.67181i −0.527377 0.123902i
\(466\) 0 0
\(467\) −25.8832 −1.19773 −0.598865 0.800850i \(-0.704381\pi\)
−0.598865 + 0.800850i \(0.704381\pi\)
\(468\) 0 0
\(469\) 16.6060 0.766792
\(470\) 0 0
\(471\) −5.62772 + 5.98844i −0.259312 + 0.275933i
\(472\) 0 0
\(473\) 7.80298 + 13.5152i 0.358782 + 0.621428i
\(474\) 0 0
\(475\) 1.68614 2.92048i 0.0773654 0.134001i
\(476\) 0 0
\(477\) −28.7228 + 19.0526i −1.31513 + 0.872357i
\(478\) 0 0
\(479\) −11.7446 + 20.3422i −0.536623 + 0.929458i 0.462460 + 0.886640i \(0.346967\pi\)
−0.999083 + 0.0428178i \(0.986366\pi\)
\(480\) 0 0
\(481\) 9.48913 + 16.4356i 0.432667 + 0.749401i
\(482\) 0 0
\(483\) −5.18614 17.2005i −0.235978 0.782649i
\(484\) 0 0
\(485\) 2.62772 0.119319
\(486\) 0 0
\(487\) 1.25544 0.0568893 0.0284446 0.999595i \(-0.490945\pi\)
0.0284446 + 0.999595i \(0.490945\pi\)
\(488\) 0 0
\(489\) 0.744563 + 2.46943i 0.0336703 + 0.111672i
\(490\) 0 0
\(491\) 1.80298 + 3.12286i 0.0813676 + 0.140933i 0.903838 0.427876i \(-0.140738\pi\)
−0.822470 + 0.568808i \(0.807405\pi\)
\(492\) 0 0
\(493\) −16.1168 + 27.9152i −0.725866 + 1.25724i
\(494\) 0 0
\(495\) −3.43070 + 2.27567i −0.154199 + 0.102284i
\(496\) 0 0
\(497\) −7.11684 + 12.3267i −0.319234 + 0.552930i
\(498\) 0 0
\(499\) −1.05842 1.83324i −0.0473815 0.0820671i 0.841362 0.540472i \(-0.181754\pi\)
−0.888743 + 0.458405i \(0.848421\pi\)
\(500\) 0 0
\(501\) 9.04755 9.62747i 0.404215 0.430124i
\(502\) 0 0
\(503\) −21.8614 −0.974752 −0.487376 0.873192i \(-0.662046\pi\)
−0.487376 + 0.873192i \(0.662046\pi\)
\(504\) 0 0
\(505\) 8.74456 0.389128
\(506\) 0 0
\(507\) 16.0367 + 3.76767i 0.712214 + 0.167328i
\(508\) 0 0
\(509\) −4.67527 8.09780i −0.207228 0.358929i 0.743613 0.668611i \(-0.233111\pi\)
−0.950840 + 0.309682i \(0.899777\pi\)
\(510\) 0 0
\(511\) 16.7446 29.0024i 0.740736 1.28299i
\(512\) 0 0
\(513\) −13.4891 11.1846i −0.595559 0.493812i
\(514\) 0 0
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) 1.11684 + 1.93443i 0.0491187 + 0.0850762i
\(518\) 0 0
\(519\) 15.6060 + 3.66648i 0.685026 + 0.160941i
\(520\) 0 0
\(521\) −41.2337 −1.80648 −0.903240 0.429135i \(-0.858818\pi\)
−0.903240 + 0.429135i \(0.858818\pi\)
\(522\) 0 0
\(523\) 11.1168 0.486106 0.243053 0.970013i \(-0.421851\pi\)
0.243053 + 0.970013i \(0.421851\pi\)
\(524\) 0 0
\(525\) −2.81386 + 2.99422i −0.122807 + 0.130678i
\(526\) 0 0
\(527\) 24.8614 + 43.0612i 1.08298 + 1.87578i
\(528\) 0 0
\(529\) 1.94158 3.36291i 0.0844164 0.146214i
\(530\) 0 0
\(531\) 3.68614 + 1.83324i 0.159965 + 0.0795559i
\(532\) 0 0
\(533\) 7.11684 12.3267i 0.308265 0.533930i
\(534\) 0 0
\(535\) 7.24456 + 12.5480i 0.313210 + 0.542495i
\(536\) 0 0
\(537\) −1.62772 5.39853i −0.0702412 0.232964i
\(538\) 0 0
\(539\) 1.88316 0.0811133
\(540\) 0 0
\(541\) 21.6277 0.929848 0.464924 0.885351i \(-0.346082\pi\)
0.464924 + 0.885351i \(0.346082\pi\)
\(542\) 0 0
\(543\) 3.93070 + 13.0367i 0.168683 + 0.559457i
\(544\) 0 0
\(545\) 4.81386 + 8.33785i 0.206203 + 0.357154i
\(546\) 0 0
\(547\) 19.7337 34.1798i 0.843752 1.46142i −0.0429494 0.999077i \(-0.513675\pi\)
0.886701 0.462343i \(-0.152991\pi\)
\(548\) 0 0
\(549\) −1.69702 27.2978i −0.0724269 1.16504i
\(550\) 0 0
\(551\) −7.37228 + 12.7692i −0.314070 + 0.543985i
\(552\) 0 0
\(553\) 2.37228 + 4.10891i 0.100880 + 0.174729i
\(554\) 0 0
\(555\) −4.74456 + 5.04868i −0.201395 + 0.214304i
\(556\) 0 0
\(557\) −9.76631 −0.413812 −0.206906 0.978361i \(-0.566339\pi\)
−0.206906 + 0.978361i \(0.566339\pi\)
\(558\) 0 0
\(559\) 53.9565 2.28212
\(560\) 0 0
\(561\) 17.0584 + 4.00772i 0.720207 + 0.169206i
\(562\) 0 0
\(563\) 8.36141 + 14.4824i 0.352391 + 0.610360i 0.986668 0.162747i \(-0.0520353\pi\)
−0.634277 + 0.773106i \(0.718702\pi\)
\(564\) 0 0
\(565\) 7.37228 12.7692i 0.310154 0.537203i
\(566\) 0 0
\(567\) 12.8832 + 17.0256i 0.541042 + 0.715006i
\(568\) 0 0
\(569\) −4.80298 + 8.31901i −0.201352 + 0.348751i −0.948964 0.315384i \(-0.897867\pi\)
0.747613 + 0.664135i \(0.231200\pi\)
\(570\) 0 0
\(571\) −15.8030 27.3716i −0.661334 1.14546i −0.980265 0.197687i \(-0.936657\pi\)
0.318931 0.947778i \(-0.396676\pi\)
\(572\) 0 0
\(573\) 9.25544 + 2.17448i 0.386651 + 0.0908403i
\(574\) 0 0
\(575\) 4.37228 0.182337
\(576\) 0 0
\(577\) −23.8832 −0.994269 −0.497134 0.867674i \(-0.665614\pi\)
−0.497134 + 0.867674i \(0.665614\pi\)
\(578\) 0 0
\(579\) −4.60597 + 4.90120i −0.191418 + 0.203687i
\(580\) 0 0
\(581\) 1.93070 + 3.34408i 0.0800991 + 0.138736i
\(582\) 0 0
\(583\) 7.88316 13.6540i 0.326487 0.565492i
\(584\) 0 0
\(585\) 0.883156 + 14.2063i 0.0365140 + 0.587357i
\(586\) 0 0
\(587\) 13.5000 23.3827i 0.557205 0.965107i −0.440524 0.897741i \(-0.645207\pi\)
0.997728 0.0673658i \(-0.0214594\pi\)
\(588\) 0 0
\(589\) 11.3723 + 19.6974i 0.468587 + 0.811616i
\(590\) 0 0
\(591\) −8.74456 29.0024i −0.359703 1.19300i
\(592\) 0 0
\(593\) 37.7228 1.54909 0.774545 0.632519i \(-0.217979\pi\)
0.774545 + 0.632519i \(0.217979\pi\)
\(594\) 0 0
\(595\) 17.4891 0.716984
\(596\) 0 0
\(597\) −4.74456 15.7359i −0.194182 0.644029i
\(598\) 0 0
\(599\) −19.1168 33.1113i −0.781093 1.35289i −0.931305 0.364239i \(-0.881329\pi\)
0.150212 0.988654i \(-0.452004\pi\)
\(600\) 0 0
\(601\) −13.4307 + 23.2627i −0.547850 + 0.948904i 0.450572 + 0.892740i \(0.351220\pi\)
−0.998422 + 0.0561635i \(0.982113\pi\)
\(602\) 0 0
\(603\) 18.8030 + 9.35135i 0.765717 + 0.380816i
\(604\) 0 0
\(605\) −4.55842 + 7.89542i −0.185326 + 0.320994i
\(606\) 0 0
\(607\) 0.441578 + 0.764836i 0.0179231 + 0.0310437i 0.874848 0.484398i \(-0.160961\pi\)
−0.856925 + 0.515442i \(0.827628\pi\)
\(608\) 0 0
\(609\) 12.3030 13.0916i 0.498542 0.530497i
\(610\) 0 0
\(611\) 7.72281 0.312432
\(612\) 0 0
\(613\) −0.233688 −0.00943857 −0.00471928 0.999989i \(-0.501502\pi\)
−0.00471928 + 0.999989i \(0.501502\pi\)
\(614\) 0 0
\(615\) 5.05842 + 1.18843i 0.203975 + 0.0479221i
\(616\) 0 0
\(617\) 11.0584 + 19.1537i 0.445195 + 0.771101i 0.998066 0.0621663i \(-0.0198009\pi\)
−0.552870 + 0.833267i \(0.686468\pi\)
\(618\) 0 0
\(619\) −19.0584 + 33.0102i −0.766023 + 1.32679i 0.173682 + 0.984802i \(0.444434\pi\)
−0.939704 + 0.341988i \(0.888900\pi\)
\(620\) 0 0
\(621\) 3.81386 22.3966i 0.153045 0.898746i
\(622\) 0 0
\(623\) 1.32473 2.29451i 0.0530743 0.0919275i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 7.80298 + 1.83324i 0.311621 + 0.0732126i
\(628\) 0 0
\(629\) 29.4891 1.17581
\(630\) 0 0
\(631\) −33.7228 −1.34248 −0.671242 0.741238i \(-0.734239\pi\)
−0.671242 + 0.741238i \(0.734239\pi\)
\(632\) 0 0
\(633\) −8.60597 + 9.15759i −0.342057 + 0.363981i
\(634\) 0 0
\(635\) −4.55842 7.89542i −0.180895 0.313320i
\(636\) 0 0
\(637\) 3.25544 5.63858i 0.128985 0.223409i
\(638\) 0 0
\(639\) −15.0000 + 9.94987i −0.593391 + 0.393611i
\(640\) 0 0
\(641\) 19.5000 33.7750i 0.770204 1.33403i −0.167247 0.985915i \(-0.553488\pi\)
0.937451 0.348117i \(-0.113179\pi\)
\(642\) 0 0
\(643\) 5.50000 + 9.52628i 0.216899 + 0.375680i 0.953858 0.300257i \(-0.0970725\pi\)
−0.736959 + 0.675937i \(0.763739\pi\)
\(644\) 0 0
\(645\) 5.68614 + 18.8588i 0.223892 + 0.742564i
\(646\) 0 0
\(647\) −24.0951 −0.947276 −0.473638 0.880720i \(-0.657059\pi\)
−0.473638 + 0.880720i \(0.657059\pi\)
\(648\) 0 0
\(649\) −1.88316 −0.0739203
\(650\) 0 0
\(651\) −8.00000 26.5330i −0.313545 1.03991i
\(652\) 0 0
\(653\) 18.8614 + 32.6689i 0.738104 + 1.27843i 0.953348 + 0.301873i \(0.0976119\pi\)
−0.215244 + 0.976560i \(0.569055\pi\)
\(654\) 0 0
\(655\) −4.37228 + 7.57301i −0.170839 + 0.295902i
\(656\) 0 0
\(657\) 35.2921 23.4101i 1.37688 0.913316i
\(658\) 0 0
\(659\) −2.74456 + 4.75372i −0.106913 + 0.185179i −0.914518 0.404545i \(-0.867430\pi\)
0.807605 + 0.589724i \(0.200763\pi\)
\(660\) 0 0
\(661\) −11.1168 19.2549i −0.432395 0.748930i 0.564684 0.825307i \(-0.308998\pi\)
−0.997079 + 0.0763770i \(0.975665\pi\)
\(662\) 0 0
\(663\) 41.4891 44.1485i 1.61130 1.71458i
\(664\) 0 0
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) −19.1168 −0.740207
\(668\) 0 0
\(669\) −20.8614 4.90120i −0.806549 0.189491i
\(670\) 0 0
\(671\) 6.25544 + 10.8347i 0.241488 + 0.418270i
\(672\) 0 0
\(673\) 5.00000 8.66025i 0.192736 0.333828i −0.753420 0.657539i \(-0.771597\pi\)
0.946156 + 0.323711i \(0.104931\pi\)
\(674\) 0 0
\(675\) −4.87228 + 1.80579i −0.187534 + 0.0695049i
\(676\) 0 0
\(677\) 21.8614 37.8651i 0.840202 1.45527i −0.0495215 0.998773i \(-0.515770\pi\)
0.889724 0.456500i \(-0.150897\pi\)
\(678\) 0 0
\(679\) 3.11684 + 5.39853i 0.119613 + 0.207177i
\(680\) 0 0
\(681\) −3.17527 0.746000i −0.121676 0.0285868i
\(682\) 0 0
\(683\) −33.0951 −1.26635 −0.633174 0.774009i \(-0.718248\pi\)
−0.633174 + 0.774009i \(0.718248\pi\)
\(684\) 0 0
\(685\) 1.88316 0.0719517
\(686\) 0 0
\(687\) −21.7921 + 23.1889i −0.831421 + 0.884713i
\(688\) 0 0
\(689\) −27.2554 47.2078i −1.03835 1.79847i
\(690\) 0 0
\(691\) −0.883156 + 1.52967i −0.0335968 + 0.0581914i −0.882335 0.470622i \(-0.844030\pi\)
0.848738 + 0.528813i \(0.177363\pi\)
\(692\) 0 0
\(693\) −8.74456 4.34896i −0.332178 0.165203i
\(694\) 0 0
\(695\) −9.05842 + 15.6896i −0.343606 + 0.595142i
\(696\) 0 0
\(697\) −11.0584 19.1537i −0.418868 0.725500i
\(698\) 0 0
\(699\) 5.05842 + 16.7769i 0.191327 + 0.634560i
\(700\) 0 0
\(701\) 14.1386 0.534007 0.267004 0.963696i \(-0.413966\pi\)
0.267004 + 0.963696i \(0.413966\pi\)
\(702\) 0 0
\(703\) 13.4891 0.508752
\(704\) 0 0
\(705\) 0.813859 + 2.69927i 0.0306517 + 0.101660i
\(706\) 0 0
\(707\) 10.3723 + 17.9653i 0.390090 + 0.675655i
\(708\) 0 0
\(709\) 12.9307 22.3966i 0.485623 0.841123i −0.514241 0.857646i \(-0.671926\pi\)
0.999863 + 0.0165226i \(0.00525955\pi\)
\(710\) 0 0
\(711\) 0.372281 + 5.98844i 0.0139616 + 0.224584i
\(712\) 0 0
\(713\) −14.7446 + 25.5383i −0.552188 + 0.956418i
\(714\) 0 0
\(715\) −3.25544 5.63858i −0.121746 0.210871i
\(716\) 0 0
\(717\) −17.4891 + 18.6101i −0.653143 + 0.695008i
\(718\) 0 0
\(719\) 38.2337 1.42588 0.712938 0.701227i \(-0.247364\pi\)
0.712938 + 0.701227i \(0.247364\pi\)
\(720\) 0 0
\(721\) 37.9565 1.41357
\(722\) 0 0
\(723\) 17.6861 + 4.15520i 0.657755 + 0.154534i
\(724\) 0 0
\(725\) 2.18614 + 3.78651i 0.0811912 + 0.140627i
\(726\) 0 0
\(727\) 0.441578 0.764836i 0.0163772 0.0283662i −0.857721 0.514116i \(-0.828120\pi\)
0.874098 + 0.485750i \(0.161453\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) 41.9198 72.6073i 1.55046 2.68548i
\(732\) 0 0
\(733\) −17.1168 29.6472i −0.632225 1.09505i −0.987096 0.160131i \(-0.948808\pi\)
0.354871 0.934915i \(-0.384525\pi\)
\(734\) 0 0
\(735\) 2.31386 + 0.543620i 0.0853480 + 0.0200517i
\(736\) 0 0
\(737\) −9.60597 −0.353840
\(738\) 0 0
\(739\) 23.8832 0.878556 0.439278 0.898351i \(-0.355234\pi\)
0.439278 + 0.898351i \(0.355234\pi\)
\(740\) 0 0
\(741\) 18.9783 20.1947i 0.697183 0.741871i
\(742\) 0 0
\(743\) 12.5584 + 21.7518i 0.460724 + 0.797997i 0.998997 0.0447732i \(-0.0142565\pi\)
−0.538273 + 0.842770i \(0.680923\pi\)
\(744\) 0 0
\(745\) 9.55842 16.5557i 0.350193 0.606553i
\(746\) 0 0
\(747\) 0.302985 + 4.87375i 0.0110856 + 0.178321i
\(748\) 0 0
\(749\) −17.1861 + 29.7673i −0.627968 + 1.08767i
\(750\) 0 0
\(751\) −9.11684 15.7908i −0.332678 0.576216i 0.650358 0.759628i \(-0.274619\pi\)
−0.983036 + 0.183412i \(0.941286\pi\)
\(752\) 0 0
\(753\) 7.80298 + 25.8796i 0.284357 + 0.943104i
\(754\) 0 0
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) 3.00000 + 9.94987i 0.108893 + 0.361158i
\(760\) 0 0
\(761\) −6.04755 10.4747i −0.219223 0.379706i 0.735347 0.677690i \(-0.237019\pi\)
−0.954571 + 0.297984i \(0.903686\pi\)
\(762\) 0 0
\(763\) −11.4198 + 19.7797i −0.413426 + 0.716074i
\(764\) 0 0
\(765\) 19.8030 + 9.84868i 0.715978 + 0.356080i
\(766\) 0 0
\(767\) −3.25544 + 5.63858i −0.117547 + 0.203597i
\(768\) 0 0
\(769\) 9.06930 + 15.7085i 0.327047 + 0.566462i 0.981925 0.189273i \(-0.0606131\pi\)
−0.654877 + 0.755735i \(0.727280\pi\)
\(770\) 0 0
\(771\) 1.62772 1.73205i 0.0586209 0.0623783i
\(772\) 0 0
\(773\) 14.7446 0.530325 0.265163 0.964204i \(-0.414574\pi\)
0.265163 + 0.964204i \(0.414574\pi\)
\(774\) 0 0
\(775\) 6.74456 0.242272
\(776\) 0 0
\(777\) −16.0000 3.75906i −0.573997 0.134855i
\(778\) 0 0
\(779\) −5.05842 8.76144i −0.181237 0.313911i
\(780\) 0 0
\(781\) 4.11684 7.13058i 0.147312 0.255152i
\(782\) 0 0
\(783\) 21.3030 7.89542i 0.761307 0.282159i
\(784\) 0 0
\(785\) 2.37228 4.10891i 0.0846704 0.146653i
\(786\) 0 0
\(787\) −14.0000 24.2487i −0.499046 0.864373i 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) 0 0
\(789\) −9.25544 2.17448i −0.329502 0.0774136i
\(790\) 0 0
\(791\) 34.9783 1.24368
\(792\) 0 0
\(793\) 43.2554 1.53605
\(794\) 0 0
\(795\) 13.6277 14.5012i 0.483325 0.514305i
\(796\) 0 0
\(797\) −1.62772 2.81929i −0.0576568 0.0998644i 0.835756 0.549100i \(-0.185030\pi\)
−0.893413 + 0.449236i \(0.851696\pi\)
\(798\) 0 0
\(799\) 6.00000 10.3923i 0.212265 0.367653i
\(800\) 0 0
\(801\) 2.79211 1.85208i 0.0986544 0.0654399i
\(802\) 0 0
\(803\) −9.68614 + 16.7769i −0.341816 + 0.592044i
\(804\) 0 0
\(805\) 5.18614 + 8.98266i 0.182787 + 0.316597i
\(806\) 0 0
\(807\) −2.18614 7.25061i −0.0769558 0.255234i
\(808\) 0 0
\(809\) −12.3505 −0.434222 −0.217111 0.976147i \(-0.569663\pi\)
−0.217111 + 0.976147i \(0.569663\pi\)
\(810\) 0 0
\(811\) −9.37228 −0.329105 −0.164553 0.986368i \(-0.552618\pi\)
−0.164553 + 0.986368i \(0.552618\pi\)
\(812\) 0 0
\(813\) 4.00000 + 13.2665i 0.140286 + 0.465276i
\(814\) 0 0
\(815\) −0.744563 1.28962i −0.0260809 0.0451734i
\(816\) 0 0
\(817\) 19.1753 33.2125i 0.670858 1.16196i
\(818\) 0 0
\(819\) −28.1386 + 18.6650i −0.983242 + 0.652209i
\(820\) 0 0
\(821\) −25.4198 + 44.0284i −0.887158 + 1.53660i −0.0439382 + 0.999034i \(0.513990\pi\)
−0.843220 + 0.537569i \(0.819343\pi\)
\(822\) 0 0
\(823\) 19.0475 + 32.9913i 0.663956 + 1.15001i 0.979567 + 0.201117i \(0.0644570\pi\)
−0.315612 + 0.948888i \(0.602210\pi\)
\(824\) 0 0
\(825\) 1.62772 1.73205i 0.0566699 0.0603023i
\(826\) 0 0
\(827\) −8.13859 −0.283007 −0.141503 0.989938i \(-0.545194\pi\)
−0.141503 + 0.989938i \(0.545194\pi\)
\(828\) 0 0
\(829\) −32.8832 −1.14208 −0.571040 0.820923i \(-0.693460\pi\)
−0.571040 + 0.820923i \(0.693460\pi\)
\(830\) 0 0
\(831\) 8.86141 + 2.08191i 0.307399 + 0.0722206i
\(832\) 0 0
\(833\) −5.05842 8.76144i −0.175264 0.303566i
\(834\) 0 0
\(835\) −3.81386 + 6.60580i −0.131984 + 0.228603i
\(836\) 0 0
\(837\) 5.88316 34.5484i 0.203352 1.19417i
\(838\) 0 0
\(839\) 22.1168 38.3075i 0.763558 1.32252i −0.177447 0.984130i \(-0.556784\pi\)
0.941005 0.338391i \(-0.109883\pi\)
\(840\) 0 0
\(841\) 4.94158 + 8.55906i 0.170399 + 0.295140i
\(842\) 0 0
\(843\) 7.37228 + 1.73205i 0.253915 + 0.0596550i
\(844\) 0 0
\(845\) −9.51087 −0.327184
\(846\) 0 0
\(847\) −21.6277 −0.743137
\(848\) 0 0
\(849\) −37.7921 + 40.2145i −1.29702 + 1.38016i
\(850\) 0 0
\(851\) 8.74456 + 15.1460i 0.299760 + 0.519199i
\(852\) 0 0
\(853\) 0.883156 1.52967i 0.0302387 0.0523749i −0.850510 0.525959i \(-0.823707\pi\)
0.880749 + 0.473584i \(0.157040\pi\)
\(854\) 0 0
\(855\) 9.05842 + 4.50506i 0.309791 + 0.154070i
\(856\) 0 0
\(857\) −11.7446 + 20.3422i −0.401187 + 0.694876i −0.993869 0.110560i \(-0.964735\pi\)
0.592683 + 0.805436i \(0.298069\pi\)
\(858\) 0 0
\(859\) 0.0584220 + 0.101190i 0.00199333 + 0.00345255i 0.867020 0.498273i \(-0.166032\pi\)
−0.865027 + 0.501725i \(0.832699\pi\)
\(860\) 0 0
\(861\) 3.55842 + 11.8020i 0.121271 + 0.402209i
\(862\) 0 0
\(863\) 42.6060 1.45032 0.725162 0.688578i \(-0.241765\pi\)
0.725162 + 0.688578i \(0.241765\pi\)
\(864\) 0 0
\(865\) −9.25544 −0.314694
\(866\) 0 0
\(867\) −18.6753 61.9389i −0.634245 2.10355i
\(868\) 0 0
\(869\) −1.37228 2.37686i −0.0465515 0.0806295i
\(870\) 0 0
\(871\) −16.6060 + 28.7624i −0.562672 + 0.974576i
\(872\) 0 0
\(873\) 0.489125 + 7.86797i 0.0165544 + 0.266290i
\(874\) 0 0
\(875\) 1.18614 2.05446i 0.0400989 0.0694533i
\(876\) 0 0
\(877\) 27.9783 + 48.4598i 0.944758 + 1.63637i 0.756234 + 0.654301i \(0.227037\pi\)
0.188524 + 0.982069i \(0.439630\pi\)
\(878\) 0 0
\(879\) 9.76631 10.3923i 0.329410 0.350524i
\(880\) 0 0
\(881\) 27.3505 0.921463 0.460731 0.887540i \(-0.347587\pi\)
0.460731 + 0.887540i \(0.347587\pi\)
\(882\) 0 0
\(883\) −12.7228 −0.428157 −0.214078 0.976816i \(-0.568675\pi\)
−0.214078 + 0.976816i \(0.568675\pi\)
\(884\) 0 0
\(885\) −2.31386 0.543620i −0.0777795 0.0182736i
\(886\) 0 0
\(887\) −18.8614 32.6689i −0.633304 1.09691i −0.986872 0.161506i \(-0.948365\pi\)
0.353568 0.935409i \(-0.384968\pi\)
\(888\) 0 0
\(889\) 10.8139 18.7302i 0.362685 0.628189i
\(890\) 0 0
\(891\) −7.45245 9.84868i −0.249667 0.329943i
\(892\) 0 0
\(893\) 2.74456 4.75372i 0.0918433 0.159077i
\(894\) 0 0
\(895\) 1.62772 + 2.81929i 0.0544086 + 0.0942385i
\(896\) 0 0
\(897\) 34.9783 + 8.21782i 1.16789 + 0.274385i
\(898\) 0 0
\(899\) −29.4891 −0.983517
\(900\) 0 0
\(901\) −84.7011 −2.82180
\(902\) 0 0
\(903\) −32.0000 + 34.0511i −1.06489 + 1.13315i
\(904\) 0 0
\(905\) −3.93070 6.80818i −0.130661 0.226311i
\(906\) 0 0
\(907\) −3.50000 + 6.06218i −0.116216 + 0.201291i −0.918265 0.395966i \(-0.870410\pi\)
0.802049 + 0.597258i \(0.203743\pi\)
\(908\) 0 0
\(909\) 1.62772 + 26.1831i 0.0539880 + 0.868440i
\(910\) 0 0
\(911\) −21.0000 + 36.3731i −0.695761 + 1.20509i 0.274162 + 0.961683i \(0.411599\pi\)
−0.969923 + 0.243410i \(0.921734\pi\)
\(912\) 0 0
\(913\) −1.11684 1.93443i −0.0369621 0.0640203i
\(914\) 0 0
\(915\) 4.55842 + 15.1186i 0.150697 + 0.499805i
\(916\) 0 0
\(917\) −20.7446 −0.685046
\(918\) 0 0
\(919\) −42.4674 −1.40087 −0.700435 0.713716i \(-0.747011\pi\)
−0.700435 + 0.713716i \(0.747011\pi\)
\(920\) 0 0
\(921\) −16.6168 55.1118i −0.547544 1.81600i
\(922\) 0 0
\(923\) −14.2337 24.6535i −0.468508 0.811479i
\(924\) 0 0
\(925\) 2.00000 3.46410i 0.0657596 0.113899i
\(926\) 0 0
\(927\) 42.9783 + 21.3745i 1.41159 + 0.702031i
\(928\) 0 0
\(929\) 19.9783 34.6033i 0.655465 1.13530i −0.326312 0.945262i \(-0.605806\pi\)
0.981777 0.190037i \(-0.0608607\pi\)
\(930\) 0 0
\(931\) −2.31386 4.00772i −0.0758337 0.131348i
\(932\) 0 0
\(933\) −10.9783 + 11.6819i −0.359412 + 0.382449i
\(934\) 0 0
\(935\) −10.1168 −0.330856
\(936\) 0 0
\(937\) −17.7228 −0.578979 −0.289490 0.957181i \(-0.593486\pi\)
−0.289490 + 0.957181i \(0.593486\pi\)
\(938\) 0 0
\(939\) 15.8030 + 3.71277i 0.515711 + 0.121162i
\(940\) 0 0
\(941\) −18.8139 32.5866i −0.613314 1.06229i −0.990678 0.136226i \(-0.956503\pi\)
0.377363 0.926065i \(-0.376831\pi\)
\(942\) 0 0
\(943\) 6.55842 11.3595i 0.213572 0.369917i
\(944\) 0 0
\(945\) −9.48913 7.86797i −0.308681 0.255945i
\(946\) 0 0
\(947\) 11.3614 19.6785i 0.369196 0.639466i −0.620244 0.784409i \(-0.712966\pi\)
0.989440 + 0.144943i \(0.0462997\pi\)
\(948\) 0 0
\(949\) 33.4891 + 58.0049i 1.08710 + 1.88292i
\(950\) 0 0
\(951\) −14.7446 3.46410i −0.478125 0.112331i
\(952\) 0 0
\(953\) 30.8614 0.999699 0.499850 0.866112i \(-0.333389\pi\)
0.499850 + 0.866112i \(0.333389\pi\)
\(954\) 0 0
\(955\) −5.48913 −0.177624
\(956\) 0 0
\(957\) −7.11684 + 7.57301i −0.230055 + 0.244801i
\(958\) 0 0
\(959\) 2.23369 + 3.86886i 0.0721295 + 0.124932i
\(960\) 0 0
\(961\) −7.24456 + 12.5480i −0.233696 + 0.404773i
\(962\) 0 0
\(963\) −36.2228 + 24.0275i −1.16726 + 0.774275i
\(964\) 0 0
\(965\) 1.94158 3.36291i 0.0625016 0.108256i
\(966\) 0 0
\(967\) 9.44158 + 16.3533i 0.303621 + 0.525886i 0.976953 0.213453i \(-0.0684711\pi\)
−0.673333 + 0.739340i \(0.735138\pi\)
\(968\) 0 0
\(969\) −12.4307 41.2280i −0.399332 1.32443i
\(970\) 0 0
\(971\) −22.9783 −0.737407 −0.368704 0.929547i \(-0.620198\pi\)
−0.368704 + 0.929547i \(0.620198\pi\)
\(972\) 0 0
\(973\) −42.9783 −1.37782
\(974\) 0 0
\(975\) −2.37228 7.86797i −0.0759738 0.251977i
\(976\) 0 0
\(977\) 20.0584 + 34.7422i 0.641726 + 1.11150i 0.985047 + 0.172284i \(0.0551146\pi\)
−0.343322 + 0.939218i \(0.611552\pi\)
\(978\) 0 0
\(979\) −0.766312 + 1.32729i −0.0244914 + 0.0424204i
\(980\) 0 0
\(981\) −24.0693 + 15.9658i −0.768474 + 0.509748i
\(982\) 0 0
\(983\) 7.93070 13.7364i 0.252950 0.438123i −0.711387 0.702801i \(-0.751932\pi\)
0.964337 + 0.264678i \(0.0852658\pi\)
\(984\) 0 0
\(985\) 8.74456 + 15.1460i 0.278625 + 0.482593i
\(986\) 0 0
\(987\) −4.58017 + 4.87375i −0.145788 + 0.155133i
\(988\) 0 0
\(989\) 49.7228 1.58109
\(990\) 0 0
\(991\) 18.2337 0.579212 0.289606 0.957146i \(-0.406476\pi\)
0.289606 + 0.957146i \(0.406476\pi\)
\(992\) 0 0
\(993\) 30.7446 + 7.22316i 0.975649 + 0.229220i
\(994\) 0 0
\(995\) 4.74456 + 8.21782i 0.150413 + 0.260523i
\(996\) 0 0
\(997\) −7.00000 + 12.1244i −0.221692 + 0.383982i −0.955322 0.295567i \(-0.904491\pi\)
0.733630 + 0.679549i \(0.237825\pi\)
\(998\) 0 0
\(999\) −16.0000 13.2665i −0.506218 0.419733i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 720.2.q.f.241.1 4
3.2 odd 2 2160.2.q.f.721.1 4
4.3 odd 2 90.2.e.c.61.2 yes 4
9.2 odd 6 6480.2.a.bn.1.2 2
9.4 even 3 inner 720.2.q.f.481.2 4
9.5 odd 6 2160.2.q.f.1441.1 4
9.7 even 3 6480.2.a.be.1.2 2
12.11 even 2 270.2.e.c.181.2 4
20.3 even 4 450.2.j.g.349.1 8
20.7 even 4 450.2.j.g.349.4 8
20.19 odd 2 450.2.e.j.151.1 4
36.7 odd 6 810.2.a.i.1.1 2
36.11 even 6 810.2.a.k.1.1 2
36.23 even 6 270.2.e.c.91.2 4
36.31 odd 6 90.2.e.c.31.1 4
60.23 odd 4 1350.2.j.f.1099.3 8
60.47 odd 4 1350.2.j.f.1099.2 8
60.59 even 2 1350.2.e.l.451.1 4
180.7 even 12 4050.2.c.v.649.1 4
180.23 odd 12 1350.2.j.f.199.2 8
180.43 even 12 4050.2.c.v.649.4 4
180.47 odd 12 4050.2.c.ba.649.3 4
180.59 even 6 1350.2.e.l.901.1 4
180.67 even 12 450.2.j.g.49.1 8
180.79 odd 6 4050.2.a.bw.1.2 2
180.83 odd 12 4050.2.c.ba.649.2 4
180.103 even 12 450.2.j.g.49.4 8
180.119 even 6 4050.2.a.bo.1.2 2
180.139 odd 6 450.2.e.j.301.2 4
180.167 odd 12 1350.2.j.f.199.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.e.c.31.1 4 36.31 odd 6
90.2.e.c.61.2 yes 4 4.3 odd 2
270.2.e.c.91.2 4 36.23 even 6
270.2.e.c.181.2 4 12.11 even 2
450.2.e.j.151.1 4 20.19 odd 2
450.2.e.j.301.2 4 180.139 odd 6
450.2.j.g.49.1 8 180.67 even 12
450.2.j.g.49.4 8 180.103 even 12
450.2.j.g.349.1 8 20.3 even 4
450.2.j.g.349.4 8 20.7 even 4
720.2.q.f.241.1 4 1.1 even 1 trivial
720.2.q.f.481.2 4 9.4 even 3 inner
810.2.a.i.1.1 2 36.7 odd 6
810.2.a.k.1.1 2 36.11 even 6
1350.2.e.l.451.1 4 60.59 even 2
1350.2.e.l.901.1 4 180.59 even 6
1350.2.j.f.199.2 8 180.23 odd 12
1350.2.j.f.199.3 8 180.167 odd 12
1350.2.j.f.1099.2 8 60.47 odd 4
1350.2.j.f.1099.3 8 60.23 odd 4
2160.2.q.f.721.1 4 3.2 odd 2
2160.2.q.f.1441.1 4 9.5 odd 6
4050.2.a.bo.1.2 2 180.119 even 6
4050.2.a.bw.1.2 2 180.79 odd 6
4050.2.c.v.649.1 4 180.7 even 12
4050.2.c.v.649.4 4 180.43 even 12
4050.2.c.ba.649.2 4 180.83 odd 12
4050.2.c.ba.649.3 4 180.47 odd 12
6480.2.a.be.1.2 2 9.7 even 3
6480.2.a.bn.1.2 2 9.2 odd 6