Properties

Label 252.2.bm.a.173.4
Level $252$
Weight $2$
Character 252.173
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
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] = [252,2,Mod(173,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.173");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 173.4
Root \(-1.61108 - 0.635951i\) of defining polynomial
Character \(\chi\) \(=\) 252.173
Dual form 252.2.bm.a.185.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.127742 + 1.72733i) q^{3} +2.18300 q^{5} +(2.64473 - 0.0736382i) q^{7} +(-2.96736 + 0.441307i) q^{9} +O(q^{10})\) \(q+(0.127742 + 1.72733i) q^{3} +2.18300 q^{5} +(2.64473 - 0.0736382i) q^{7} +(-2.96736 + 0.441307i) q^{9} -1.46518i q^{11} +(-2.92752 + 1.69021i) q^{13} +(0.278862 + 3.77077i) q^{15} +(-1.32136 - 2.28866i) q^{17} +(6.87816 + 3.97111i) q^{19} +(0.465041 + 4.55892i) q^{21} +4.00964i q^{23} -0.234498 q^{25} +(-1.14134 - 5.06925i) q^{27} +(-6.71261 - 3.87553i) q^{29} +(0.612252 + 0.353484i) q^{31} +(2.53086 - 0.187166i) q^{33} +(5.77345 - 0.160752i) q^{35} +(1.41738 - 2.45498i) q^{37} +(-3.29352 - 4.84090i) q^{39} +(-3.74173 - 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} +(-6.47776 + 0.963374i) q^{45} +(-6.27538 - 10.8693i) q^{47} +(6.98915 - 0.389506i) q^{49} +(3.78448 - 2.57478i) q^{51} +(2.41675 - 1.39531i) q^{53} -3.19850i q^{55} +(-5.98079 + 12.3881i) q^{57} +(6.71650 - 11.6333i) q^{59} +(6.75061 - 3.89747i) q^{61} +(-7.81537 + 1.38565i) q^{63} +(-6.39079 + 3.68972i) q^{65} +(-2.92029 + 5.05809i) q^{67} +(-6.92598 + 0.512200i) q^{69} +11.6854i q^{71} +(-3.95924 + 2.28587i) q^{73} +(-0.0299553 - 0.405056i) q^{75} +(-0.107894 - 3.87501i) q^{77} +(-4.69189 - 8.12659i) q^{79} +(8.61050 - 2.61904i) q^{81} +(-1.70847 + 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} +(5.83685 - 12.0900i) q^{87} +(-4.61937 + 8.00099i) q^{89} +(-7.61803 + 4.68571i) q^{91} +(-0.532375 + 1.10272i) q^{93} +(15.0150 + 8.66894i) q^{95} +(-6.38394 - 3.68577i) q^{97} +(0.646596 + 4.34773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



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
\(3\) 0.127742 + 1.72733i 0.0737520 + 0.997277i
\(4\) 0 0
\(5\) 2.18300 0.976269 0.488134 0.872769i \(-0.337678\pi\)
0.488134 + 0.872769i \(0.337678\pi\)
\(6\) 0 0
\(7\) 2.64473 0.0736382i 0.999613 0.0278326i
\(8\) 0 0
\(9\) −2.96736 + 0.441307i −0.989121 + 0.147102i
\(10\) 0 0
\(11\) 1.46518i 0.441770i −0.975300 0.220885i \(-0.929106\pi\)
0.975300 0.220885i \(-0.0708945\pi\)
\(12\) 0 0
\(13\) −2.92752 + 1.69021i −0.811948 + 0.468779i −0.847632 0.530585i \(-0.821972\pi\)
0.0356837 + 0.999363i \(0.488639\pi\)
\(14\) 0 0
\(15\) 0.278862 + 3.77077i 0.0720017 + 0.973610i
\(16\) 0 0
\(17\) −1.32136 2.28866i −0.320476 0.555081i 0.660110 0.751169i \(-0.270509\pi\)
−0.980586 + 0.196088i \(0.937176\pi\)
\(18\) 0 0
\(19\) 6.87816 + 3.97111i 1.57796 + 0.911034i 0.995144 + 0.0984279i \(0.0313814\pi\)
0.582813 + 0.812606i \(0.301952\pi\)
\(20\) 0 0
\(21\) 0.465041 + 4.55892i 0.101480 + 0.994838i
\(22\) 0 0
\(23\) 4.00964i 0.836068i 0.908431 + 0.418034i \(0.137281\pi\)
−0.908431 + 0.418034i \(0.862719\pi\)
\(24\) 0 0
\(25\) −0.234498 −0.0468996
\(26\) 0 0
\(27\) −1.14134 5.06925i −0.219651 0.975578i
\(28\) 0 0
\(29\) −6.71261 3.87553i −1.24650 0.719667i −0.276091 0.961132i \(-0.589039\pi\)
−0.970410 + 0.241464i \(0.922372\pi\)
\(30\) 0 0
\(31\) 0.612252 + 0.353484i 0.109964 + 0.0634876i 0.553973 0.832534i \(-0.313111\pi\)
−0.444009 + 0.896022i \(0.646444\pi\)
\(32\) 0 0
\(33\) 2.53086 0.187166i 0.440567 0.0325814i
\(34\) 0 0
\(35\) 5.77345 0.160752i 0.975890 0.0271721i
\(36\) 0 0
\(37\) 1.41738 2.45498i 0.233016 0.403596i −0.725678 0.688034i \(-0.758474\pi\)
0.958694 + 0.284438i \(0.0918071\pi\)
\(38\) 0 0
\(39\) −3.29352 4.84090i −0.527385 0.775164i
\(40\) 0 0
\(41\) −3.74173 6.48086i −0.584360 1.01214i −0.994955 0.100323i \(-0.968012\pi\)
0.410595 0.911818i \(-0.365321\pi\)
\(42\) 0 0
\(43\) −1.27112 + 2.20164i −0.193844 + 0.335748i −0.946521 0.322642i \(-0.895429\pi\)
0.752677 + 0.658390i \(0.228762\pi\)
\(44\) 0 0
\(45\) −6.47776 + 0.963374i −0.965648 + 0.143611i
\(46\) 0 0
\(47\) −6.27538 10.8693i −0.915358 1.58545i −0.806376 0.591403i \(-0.798574\pi\)
−0.108983 0.994044i \(-0.534759\pi\)
\(48\) 0 0
\(49\) 6.98915 0.389506i 0.998451 0.0556437i
\(50\) 0 0
\(51\) 3.78448 2.57478i 0.529933 0.360541i
\(52\) 0 0
\(53\) 2.41675 1.39531i 0.331966 0.191661i −0.324748 0.945801i \(-0.605279\pi\)
0.656714 + 0.754140i \(0.271946\pi\)
\(54\) 0 0
\(55\) 3.19850i 0.431286i
\(56\) 0 0
\(57\) −5.98079 + 12.3881i −0.792176 + 1.64085i
\(58\) 0 0
\(59\) 6.71650 11.6333i 0.874414 1.51453i 0.0170287 0.999855i \(-0.494579\pi\)
0.857385 0.514675i \(-0.172087\pi\)
\(60\) 0 0
\(61\) 6.75061 3.89747i 0.864327 0.499020i −0.00113176 0.999999i \(-0.500360\pi\)
0.865459 + 0.500980i \(0.167027\pi\)
\(62\) 0 0
\(63\) −7.81537 + 1.38565i −0.984644 + 0.174575i
\(64\) 0 0
\(65\) −6.39079 + 3.68972i −0.792680 + 0.457654i
\(66\) 0 0
\(67\) −2.92029 + 5.05809i −0.356770 + 0.617945i −0.987419 0.158124i \(-0.949455\pi\)
0.630649 + 0.776068i \(0.282789\pi\)
\(68\) 0 0
\(69\) −6.92598 + 0.512200i −0.833791 + 0.0616616i
\(70\) 0 0
\(71\) 11.6854i 1.38680i 0.720554 + 0.693398i \(0.243887\pi\)
−0.720554 + 0.693398i \(0.756113\pi\)
\(72\) 0 0
\(73\) −3.95924 + 2.28587i −0.463394 + 0.267541i −0.713470 0.700685i \(-0.752878\pi\)
0.250076 + 0.968226i \(0.419544\pi\)
\(74\) 0 0
\(75\) −0.0299553 0.405056i −0.00345894 0.0467719i
\(76\) 0 0
\(77\) −0.107894 3.87501i −0.0122956 0.441599i
\(78\) 0 0
\(79\) −4.69189 8.12659i −0.527879 0.914312i −0.999472 0.0324963i \(-0.989654\pi\)
0.471593 0.881816i \(-0.343679\pi\)
\(80\) 0 0
\(81\) 8.61050 2.61904i 0.956722 0.291004i
\(82\) 0 0
\(83\) −1.70847 + 2.95917i −0.187529 + 0.324811i −0.944426 0.328724i \(-0.893381\pi\)
0.756896 + 0.653535i \(0.226715\pi\)
\(84\) 0 0
\(85\) −2.88452 4.99614i −0.312871 0.541908i
\(86\) 0 0
\(87\) 5.83685 12.0900i 0.625776 1.29618i
\(88\) 0 0
\(89\) −4.61937 + 8.00099i −0.489653 + 0.848103i −0.999929 0.0119070i \(-0.996210\pi\)
0.510276 + 0.860010i \(0.329543\pi\)
\(90\) 0 0
\(91\) −7.61803 + 4.68571i −0.798586 + 0.491196i
\(92\) 0 0
\(93\) −0.532375 + 1.10272i −0.0552047 + 0.114347i
\(94\) 0 0
\(95\) 15.0150 + 8.66894i 1.54051 + 0.889414i
\(96\) 0 0
\(97\) −6.38394 3.68577i −0.648191 0.374233i 0.139572 0.990212i \(-0.455427\pi\)
−0.787763 + 0.615979i \(0.788761\pi\)
\(98\) 0 0
\(99\) 0.646596 + 4.34773i 0.0649853 + 0.436964i
\(100\) 0 0
\(101\) 7.92714 0.788780 0.394390 0.918943i \(-0.370956\pi\)
0.394390 + 0.918943i \(0.370956\pi\)
\(102\) 0 0
\(103\) 3.77385i 0.371849i −0.982564 0.185924i \(-0.940472\pi\)
0.982564 0.185924i \(-0.0595280\pi\)
\(104\) 0 0
\(105\) 1.01519 + 9.95213i 0.0990720 + 0.971229i
\(106\) 0 0
\(107\) 6.88241 + 3.97356i 0.665347 + 0.384138i 0.794311 0.607511i \(-0.207832\pi\)
−0.128964 + 0.991649i \(0.541165\pi\)
\(108\) 0 0
\(109\) 0.505142 + 0.874932i 0.0483838 + 0.0838033i 0.889203 0.457513i \(-0.151260\pi\)
−0.840819 + 0.541316i \(0.817926\pi\)
\(110\) 0 0
\(111\) 4.42163 + 2.13469i 0.419682 + 0.202616i
\(112\) 0 0
\(113\) −10.5557 + 6.09431i −0.992992 + 0.573304i −0.906167 0.422919i \(-0.861005\pi\)
−0.0868250 + 0.996224i \(0.527672\pi\)
\(114\) 0 0
\(115\) 8.75305i 0.816226i
\(116\) 0 0
\(117\) 7.94112 6.30739i 0.734157 0.583118i
\(118\) 0 0
\(119\) −3.66316 5.95557i −0.335801 0.545946i
\(120\) 0 0
\(121\) 8.85324 0.804840
\(122\) 0 0
\(123\) 10.7166 7.29109i 0.966286 0.657416i
\(124\) 0 0
\(125\) −11.4269 −1.02206
\(126\) 0 0
\(127\) 6.79350 0.602826 0.301413 0.953494i \(-0.402542\pi\)
0.301413 + 0.953494i \(0.402542\pi\)
\(128\) 0 0
\(129\) −3.96535 1.91441i −0.349130 0.168554i
\(130\) 0 0
\(131\) 13.7358 1.20010 0.600051 0.799961i \(-0.295147\pi\)
0.600051 + 0.799961i \(0.295147\pi\)
\(132\) 0 0
\(133\) 18.4833 + 9.99599i 1.60270 + 0.866762i
\(134\) 0 0
\(135\) −2.49155 11.0662i −0.214439 0.952427i
\(136\) 0 0
\(137\) 20.0950i 1.71683i 0.512954 + 0.858416i \(0.328551\pi\)
−0.512954 + 0.858416i \(0.671449\pi\)
\(138\) 0 0
\(139\) −8.51403 + 4.91558i −0.722151 + 0.416934i −0.815544 0.578695i \(-0.803562\pi\)
0.0933930 + 0.995629i \(0.470229\pi\)
\(140\) 0 0
\(141\) 17.9732 12.2281i 1.51362 1.02980i
\(142\) 0 0
\(143\) 2.47646 + 4.28936i 0.207092 + 0.358694i
\(144\) 0 0
\(145\) −14.6536 8.46029i −1.21692 0.702589i
\(146\) 0 0
\(147\) 1.56562 + 12.0228i 0.129130 + 0.991628i
\(148\) 0 0
\(149\) 20.0354i 1.64136i −0.571386 0.820682i \(-0.693594\pi\)
0.571386 0.820682i \(-0.306406\pi\)
\(150\) 0 0
\(151\) −22.2337 −1.80935 −0.904675 0.426103i \(-0.859886\pi\)
−0.904675 + 0.426103i \(0.859886\pi\)
\(152\) 0 0
\(153\) 4.93094 + 6.20815i 0.398643 + 0.501899i
\(154\) 0 0
\(155\) 1.33655 + 0.771657i 0.107354 + 0.0619810i
\(156\) 0 0
\(157\) 6.95305 + 4.01435i 0.554914 + 0.320380i 0.751102 0.660187i \(-0.229523\pi\)
−0.196188 + 0.980566i \(0.562856\pi\)
\(158\) 0 0
\(159\) 2.71889 + 3.99629i 0.215622 + 0.316927i
\(160\) 0 0
\(161\) 0.295263 + 10.6044i 0.0232700 + 0.835744i
\(162\) 0 0
\(163\) −6.22604 + 10.7838i −0.487661 + 0.844654i −0.999899 0.0141893i \(-0.995483\pi\)
0.512238 + 0.858844i \(0.328817\pi\)
\(164\) 0 0
\(165\) 5.52488 0.408584i 0.430111 0.0318082i
\(166\) 0 0
\(167\) 9.85984 + 17.0777i 0.762978 + 1.32152i 0.941309 + 0.337546i \(0.109597\pi\)
−0.178332 + 0.983970i \(0.557070\pi\)
\(168\) 0 0
\(169\) −0.786412 + 1.36211i −0.0604933 + 0.104777i
\(170\) 0 0
\(171\) −22.1625 8.74834i −1.69481 0.669002i
\(172\) 0 0
\(173\) 0.913733 + 1.58263i 0.0694699 + 0.120325i 0.898668 0.438629i \(-0.144536\pi\)
−0.829198 + 0.558955i \(0.811203\pi\)
\(174\) 0 0
\(175\) −0.620183 + 0.0172680i −0.0468814 + 0.00130534i
\(176\) 0 0
\(177\) 20.9526 + 10.1156i 1.57489 + 0.760333i
\(178\) 0 0
\(179\) −12.1182 + 6.99645i −0.905757 + 0.522939i −0.879064 0.476705i \(-0.841831\pi\)
−0.0266934 + 0.999644i \(0.508498\pi\)
\(180\) 0 0
\(181\) 16.3594i 1.21599i −0.793942 0.607994i \(-0.791975\pi\)
0.793942 0.607994i \(-0.208025\pi\)
\(182\) 0 0
\(183\) 7.59456 + 11.1627i 0.561406 + 0.825170i
\(184\) 0 0
\(185\) 3.09415 5.35923i 0.227486 0.394018i
\(186\) 0 0
\(187\) −3.35330 + 1.93603i −0.245218 + 0.141577i
\(188\) 0 0
\(189\) −3.39183 13.3227i −0.246719 0.969087i
\(190\) 0 0
\(191\) −11.8326 + 6.83153i −0.856173 + 0.494312i −0.862729 0.505667i \(-0.831247\pi\)
0.00655557 + 0.999979i \(0.497913\pi\)
\(192\) 0 0
\(193\) 2.18885 3.79119i 0.157557 0.272896i −0.776430 0.630203i \(-0.782972\pi\)
0.933987 + 0.357307i \(0.116305\pi\)
\(194\) 0 0
\(195\) −7.18976 10.5677i −0.514869 0.756768i
\(196\) 0 0
\(197\) 1.00603i 0.0716767i −0.999358 0.0358384i \(-0.988590\pi\)
0.999358 0.0358384i \(-0.0114101\pi\)
\(198\) 0 0
\(199\) −5.67639 + 3.27726i −0.402388 + 0.232319i −0.687514 0.726171i \(-0.741298\pi\)
0.285126 + 0.958490i \(0.407965\pi\)
\(200\) 0 0
\(201\) −9.11006 4.39819i −0.642574 0.310224i
\(202\) 0 0
\(203\) −18.0384 9.75540i −1.26605 0.684695i
\(204\) 0 0
\(205\) −8.16820 14.1477i −0.570492 0.988121i
\(206\) 0 0
\(207\) −1.76948 11.8981i −0.122987 0.826972i
\(208\) 0 0
\(209\) 5.81840 10.0778i 0.402467 0.697094i
\(210\) 0 0
\(211\) −9.11202 15.7825i −0.627297 1.08651i −0.988092 0.153866i \(-0.950828\pi\)
0.360794 0.932645i \(-0.382506\pi\)
\(212\) 0 0
\(213\) −20.1845 + 1.49271i −1.38302 + 0.102279i
\(214\) 0 0
\(215\) −2.77486 + 4.80620i −0.189244 + 0.327780i
\(216\) 0 0
\(217\) 1.64527 + 0.889784i 0.111688 + 0.0604024i
\(218\) 0 0
\(219\) −4.45422 6.54693i −0.300989 0.442401i
\(220\) 0 0
\(221\) 7.73660 + 4.46673i 0.520420 + 0.300464i
\(222\) 0 0
\(223\) 8.71705 + 5.03279i 0.583737 + 0.337021i 0.762617 0.646850i \(-0.223914\pi\)
−0.178880 + 0.983871i \(0.557247\pi\)
\(224\) 0 0
\(225\) 0.695841 0.103486i 0.0463894 0.00689904i
\(226\) 0 0
\(227\) 19.8874 1.31998 0.659988 0.751276i \(-0.270561\pi\)
0.659988 + 0.751276i \(0.270561\pi\)
\(228\) 0 0
\(229\) 17.7655i 1.17398i −0.809595 0.586988i \(-0.800313\pi\)
0.809595 0.586988i \(-0.199687\pi\)
\(230\) 0 0
\(231\) 6.67966 0.681371i 0.439489 0.0448309i
\(232\) 0 0
\(233\) 13.9077 + 8.02962i 0.911124 + 0.526038i 0.880793 0.473502i \(-0.157010\pi\)
0.0303317 + 0.999540i \(0.490344\pi\)
\(234\) 0 0
\(235\) −13.6992 23.7277i −0.893636 1.54782i
\(236\) 0 0
\(237\) 13.4380 9.14256i 0.872890 0.593873i
\(238\) 0 0
\(239\) −7.11117 + 4.10564i −0.459983 + 0.265572i −0.712037 0.702142i \(-0.752227\pi\)
0.252054 + 0.967713i \(0.418894\pi\)
\(240\) 0 0
\(241\) 28.4765i 1.83433i 0.398505 + 0.917166i \(0.369529\pi\)
−0.398505 + 0.917166i \(0.630471\pi\)
\(242\) 0 0
\(243\) 5.62387 + 14.5386i 0.360772 + 0.932654i
\(244\) 0 0
\(245\) 15.2573 0.850293i 0.974756 0.0543232i
\(246\) 0 0
\(247\) −26.8479 −1.70829
\(248\) 0 0
\(249\) −5.32971 2.57310i −0.337757 0.163063i
\(250\) 0 0
\(251\) −0.656343 −0.0414280 −0.0207140 0.999785i \(-0.506594\pi\)
−0.0207140 + 0.999785i \(0.506594\pi\)
\(252\) 0 0
\(253\) 5.87486 0.369349
\(254\) 0 0
\(255\) 8.26153 5.62075i 0.517357 0.351985i
\(256\) 0 0
\(257\) −7.64084 −0.476623 −0.238311 0.971189i \(-0.576594\pi\)
−0.238311 + 0.971189i \(0.576594\pi\)
\(258\) 0 0
\(259\) 3.56781 6.59712i 0.221693 0.409925i
\(260\) 0 0
\(261\) 21.6291 + 8.53778i 1.33880 + 0.528475i
\(262\) 0 0
\(263\) 6.62669i 0.408619i −0.978906 0.204310i \(-0.934505\pi\)
0.978906 0.204310i \(-0.0654949\pi\)
\(264\) 0 0
\(265\) 5.27577 3.04597i 0.324088 0.187112i
\(266\) 0 0
\(267\) −14.4105 6.95714i −0.881907 0.425770i
\(268\) 0 0
\(269\) −4.38347 7.59239i −0.267265 0.462916i 0.700890 0.713270i \(-0.252786\pi\)
−0.968154 + 0.250354i \(0.919453\pi\)
\(270\) 0 0
\(271\) 14.2608 + 8.23346i 0.866280 + 0.500147i 0.866110 0.499853i \(-0.166613\pi\)
0.000169619 1.00000i \(0.499946\pi\)
\(272\) 0 0
\(273\) −9.06693 12.5603i −0.548755 0.760185i
\(274\) 0 0
\(275\) 0.343583i 0.0207188i
\(276\) 0 0
\(277\) −17.7746 −1.06797 −0.533987 0.845493i \(-0.679307\pi\)
−0.533987 + 0.845493i \(0.679307\pi\)
\(278\) 0 0
\(279\) −1.97277 0.778725i −0.118107 0.0466210i
\(280\) 0 0
\(281\) −14.0252 8.09748i −0.836676 0.483055i 0.0194568 0.999811i \(-0.493806\pi\)
−0.856133 + 0.516755i \(0.827140\pi\)
\(282\) 0 0
\(283\) 24.5717 + 14.1865i 1.46063 + 0.843298i 0.999041 0.0437937i \(-0.0139444\pi\)
0.461594 + 0.887091i \(0.347278\pi\)
\(284\) 0 0
\(285\) −13.0561 + 27.0434i −0.773376 + 1.60191i
\(286\) 0 0
\(287\) −10.3731 16.8646i −0.612304 0.995484i
\(288\) 0 0
\(289\) 5.00804 8.67417i 0.294590 0.510246i
\(290\) 0 0
\(291\) 5.55106 11.4980i 0.325409 0.674027i
\(292\) 0 0
\(293\) 4.38260 + 7.59088i 0.256034 + 0.443464i 0.965176 0.261602i \(-0.0842507\pi\)
−0.709142 + 0.705066i \(0.750917\pi\)
\(294\) 0 0
\(295\) 14.6621 25.3956i 0.853663 1.47859i
\(296\) 0 0
\(297\) −7.42739 + 1.67228i −0.430981 + 0.0970353i
\(298\) 0 0
\(299\) −6.77711 11.7383i −0.391931 0.678844i
\(300\) 0 0
\(301\) −3.19964 + 5.91635i −0.184424 + 0.341013i
\(302\) 0 0
\(303\) 1.01263 + 13.6928i 0.0581741 + 0.786632i
\(304\) 0 0
\(305\) 14.7366 8.50818i 0.843816 0.487177i
\(306\) 0 0
\(307\) 12.8497i 0.733372i 0.930345 + 0.366686i \(0.119508\pi\)
−0.930345 + 0.366686i \(0.880492\pi\)
\(308\) 0 0
\(309\) 6.51871 0.482080i 0.370836 0.0274246i
\(310\) 0 0
\(311\) −3.29671 + 5.71007i −0.186939 + 0.323789i −0.944228 0.329291i \(-0.893190\pi\)
0.757289 + 0.653080i \(0.226523\pi\)
\(312\) 0 0
\(313\) −2.95711 + 1.70729i −0.167146 + 0.0965018i −0.581239 0.813733i \(-0.697432\pi\)
0.414093 + 0.910234i \(0.364099\pi\)
\(314\) 0 0
\(315\) −17.0610 + 3.02487i −0.961277 + 0.170432i
\(316\) 0 0
\(317\) −27.8003 + 16.0505i −1.56142 + 0.901485i −0.564304 + 0.825567i \(0.690855\pi\)
−0.997114 + 0.0759182i \(0.975811\pi\)
\(318\) 0 0
\(319\) −5.67836 + 9.83521i −0.317927 + 0.550666i
\(320\) 0 0
\(321\) −5.98449 + 12.3958i −0.334022 + 0.691866i
\(322\) 0 0
\(323\) 20.9890i 1.16786i
\(324\) 0 0
\(325\) 0.686498 0.396350i 0.0380801 0.0219855i
\(326\) 0 0
\(327\) −1.44677 + 0.984315i −0.0800066 + 0.0544327i
\(328\) 0 0
\(329\) −17.3971 28.2842i −0.959131 1.55936i
\(330\) 0 0
\(331\) 14.4416 + 25.0137i 0.793784 + 1.37487i 0.923608 + 0.383338i \(0.125225\pi\)
−0.129824 + 0.991537i \(0.541441\pi\)
\(332\) 0 0
\(333\) −3.12249 + 7.91032i −0.171111 + 0.433483i
\(334\) 0 0
\(335\) −6.37501 + 11.0418i −0.348304 + 0.603280i
\(336\) 0 0
\(337\) 4.82568 + 8.35833i 0.262872 + 0.455307i 0.967004 0.254762i \(-0.0819971\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(338\) 0 0
\(339\) −11.8753 17.4546i −0.644978 0.948006i
\(340\) 0 0
\(341\) 0.517919 0.897063i 0.0280469 0.0485787i
\(342\) 0 0
\(343\) 18.4557 1.54481i 0.996515 0.0834117i
\(344\) 0 0
\(345\) −15.1194 + 1.11813i −0.814004 + 0.0601983i
\(346\) 0 0
\(347\) 10.6758 + 6.16367i 0.573106 + 0.330883i 0.758389 0.651802i \(-0.225987\pi\)
−0.185283 + 0.982685i \(0.559320\pi\)
\(348\) 0 0
\(349\) 10.2211 + 5.90115i 0.547123 + 0.315881i 0.747961 0.663743i \(-0.231033\pi\)
−0.200838 + 0.979624i \(0.564366\pi\)
\(350\) 0 0
\(351\) 11.9094 + 12.9112i 0.635676 + 0.689151i
\(352\) 0 0
\(353\) 13.1971 0.702411 0.351205 0.936298i \(-0.385772\pi\)
0.351205 + 0.936298i \(0.385772\pi\)
\(354\) 0 0
\(355\) 25.5092i 1.35389i
\(356\) 0 0
\(357\) 9.81931 7.08827i 0.519693 0.375151i
\(358\) 0 0
\(359\) 5.22483 + 3.01656i 0.275756 + 0.159208i 0.631501 0.775375i \(-0.282439\pi\)
−0.355745 + 0.934583i \(0.615773\pi\)
\(360\) 0 0
\(361\) 22.0394 + 38.1733i 1.15997 + 2.00912i
\(362\) 0 0
\(363\) 1.13093 + 15.2925i 0.0593585 + 0.802648i
\(364\) 0 0
\(365\) −8.64304 + 4.99006i −0.452397 + 0.261192i
\(366\) 0 0
\(367\) 17.1767i 0.896618i −0.893879 0.448309i \(-0.852026\pi\)
0.893879 0.448309i \(-0.147974\pi\)
\(368\) 0 0
\(369\) 13.9631 + 17.5798i 0.726891 + 0.915169i
\(370\) 0 0
\(371\) 6.28889 3.86818i 0.326503 0.200826i
\(372\) 0 0
\(373\) 4.71804 0.244291 0.122146 0.992512i \(-0.461023\pi\)
0.122146 + 0.992512i \(0.461023\pi\)
\(374\) 0 0
\(375\) −1.45970 19.7381i −0.0753786 1.01927i
\(376\) 0 0
\(377\) 26.2017 1.34946
\(378\) 0 0
\(379\) 9.34015 0.479771 0.239886 0.970801i \(-0.422890\pi\)
0.239886 + 0.970801i \(0.422890\pi\)
\(380\) 0 0
\(381\) 0.867816 + 11.7346i 0.0444596 + 0.601184i
\(382\) 0 0
\(383\) 5.70071 0.291293 0.145646 0.989337i \(-0.453474\pi\)
0.145646 + 0.989337i \(0.453474\pi\)
\(384\) 0 0
\(385\) −0.235532 8.45916i −0.0120038 0.431119i
\(386\) 0 0
\(387\) 2.80027 7.09403i 0.142346 0.360610i
\(388\) 0 0
\(389\) 7.66342i 0.388551i 0.980947 + 0.194275i \(0.0622355\pi\)
−0.980947 + 0.194275i \(0.937764\pi\)
\(390\) 0 0
\(391\) 9.17668 5.29816i 0.464085 0.267939i
\(392\) 0 0
\(393\) 1.75464 + 23.7263i 0.0885100 + 1.19683i
\(394\) 0 0
\(395\) −10.2424 17.7404i −0.515351 0.892615i
\(396\) 0 0
\(397\) −1.12810 0.651310i −0.0566178 0.0326883i 0.471424 0.881907i \(-0.343740\pi\)
−0.528042 + 0.849218i \(0.677074\pi\)
\(398\) 0 0
\(399\) −14.9053 + 33.2037i −0.746199 + 1.66226i
\(400\) 0 0
\(401\) 9.45443i 0.472132i 0.971737 + 0.236066i \(0.0758581\pi\)
−0.971737 + 0.236066i \(0.924142\pi\)
\(402\) 0 0
\(403\) −2.38984 −0.119047
\(404\) 0 0
\(405\) 18.7967 5.71736i 0.934018 0.284098i
\(406\) 0 0
\(407\) −3.59700 2.07673i −0.178296 0.102940i
\(408\) 0 0
\(409\) −16.5182 9.53678i −0.816771 0.471563i 0.0325304 0.999471i \(-0.489643\pi\)
−0.849302 + 0.527908i \(0.822977\pi\)
\(410\) 0 0
\(411\) −34.7108 + 2.56698i −1.71216 + 0.126620i
\(412\) 0 0
\(413\) 16.9067 31.2615i 0.831922 1.53828i
\(414\) 0 0
\(415\) −3.72961 + 6.45987i −0.183079 + 0.317102i
\(416\) 0 0
\(417\) −9.57845 14.0786i −0.469059 0.689434i
\(418\) 0 0
\(419\) 4.20003 + 7.27466i 0.205185 + 0.355390i 0.950192 0.311666i \(-0.100887\pi\)
−0.745007 + 0.667057i \(0.767554\pi\)
\(420\) 0 0
\(421\) 19.7178 34.1522i 0.960985 1.66448i 0.240951 0.970537i \(-0.422541\pi\)
0.720035 0.693938i \(-0.244126\pi\)
\(422\) 0 0
\(423\) 23.4180 + 29.4837i 1.13862 + 1.43355i
\(424\) 0 0
\(425\) 0.309855 + 0.536685i 0.0150302 + 0.0260331i
\(426\) 0 0
\(427\) 17.5665 10.8048i 0.850103 0.522883i
\(428\) 0 0
\(429\) −7.09280 + 4.82561i −0.342444 + 0.232983i
\(430\) 0 0
\(431\) −10.3340 + 5.96634i −0.497772 + 0.287389i −0.727793 0.685797i \(-0.759454\pi\)
0.230021 + 0.973186i \(0.426120\pi\)
\(432\) 0 0
\(433\) 12.2121i 0.586875i 0.955978 + 0.293437i \(0.0947992\pi\)
−0.955978 + 0.293437i \(0.905201\pi\)
\(434\) 0 0
\(435\) 12.7419 26.3925i 0.610925 1.26542i
\(436\) 0 0
\(437\) −15.9227 + 27.5789i −0.761686 + 1.31928i
\(438\) 0 0
\(439\) 14.4639 8.35076i 0.690326 0.398560i −0.113408 0.993548i \(-0.536177\pi\)
0.803734 + 0.594989i \(0.202843\pi\)
\(440\) 0 0
\(441\) −20.5675 + 4.24017i −0.979404 + 0.201913i
\(442\) 0 0
\(443\) 26.2403 15.1499i 1.24672 0.719791i 0.276262 0.961082i \(-0.410904\pi\)
0.970453 + 0.241291i \(0.0775708\pi\)
\(444\) 0 0
\(445\) −10.0841 + 17.4662i −0.478033 + 0.827977i
\(446\) 0 0
\(447\) 34.6078 2.55936i 1.63689 0.121054i
\(448\) 0 0
\(449\) 30.1253i 1.42170i −0.703343 0.710851i \(-0.748310\pi\)
0.703343 0.710851i \(-0.251690\pi\)
\(450\) 0 0
\(451\) −9.49566 + 5.48232i −0.447133 + 0.258152i
\(452\) 0 0
\(453\) −2.84018 38.4050i −0.133443 1.80442i
\(454\) 0 0
\(455\) −16.6302 + 10.2289i −0.779635 + 0.479539i
\(456\) 0 0
\(457\) −12.6159 21.8513i −0.590146 1.02216i −0.994212 0.107433i \(-0.965737\pi\)
0.404067 0.914730i \(-0.367596\pi\)
\(458\) 0 0
\(459\) −10.0937 + 9.31043i −0.471132 + 0.434574i
\(460\) 0 0
\(461\) 12.3174 21.3344i 0.573680 0.993643i −0.422503 0.906361i \(-0.638849\pi\)
0.996184 0.0872820i \(-0.0278181\pi\)
\(462\) 0 0
\(463\) −6.33215 10.9676i −0.294280 0.509708i 0.680537 0.732713i \(-0.261746\pi\)
−0.974817 + 0.223006i \(0.928413\pi\)
\(464\) 0 0
\(465\) −1.16218 + 2.40724i −0.0538946 + 0.111633i
\(466\) 0 0
\(467\) −10.4723 + 18.1385i −0.484599 + 0.839350i −0.999843 0.0176932i \(-0.994368\pi\)
0.515245 + 0.857043i \(0.327701\pi\)
\(468\) 0 0
\(469\) −7.35090 + 13.5923i −0.339433 + 0.627635i
\(470\) 0 0
\(471\) −6.04592 + 12.5230i −0.278581 + 0.577031i
\(472\) 0 0
\(473\) 3.22581 + 1.86242i 0.148323 + 0.0856344i
\(474\) 0 0
\(475\) −1.61291 0.931217i −0.0740056 0.0427271i
\(476\) 0 0
\(477\) −6.55562 + 5.20692i −0.300161 + 0.238409i
\(478\) 0 0
\(479\) 31.7705 1.45163 0.725816 0.687889i \(-0.241463\pi\)
0.725816 + 0.687889i \(0.241463\pi\)
\(480\) 0 0
\(481\) 9.58267i 0.436932i
\(482\) 0 0
\(483\) −18.2796 + 1.86465i −0.831751 + 0.0848443i
\(484\) 0 0
\(485\) −13.9362 8.04605i −0.632809 0.365352i
\(486\) 0 0
\(487\) −17.7821 30.7995i −0.805784 1.39566i −0.915761 0.401724i \(-0.868411\pi\)
0.109977 0.993934i \(-0.464922\pi\)
\(488\) 0 0
\(489\) −19.4226 9.37691i −0.878320 0.424038i
\(490\) 0 0
\(491\) 2.75734 1.59195i 0.124437 0.0718437i −0.436490 0.899709i \(-0.643778\pi\)
0.560926 + 0.827866i \(0.310445\pi\)
\(492\) 0 0
\(493\) 20.4838i 0.922544i
\(494\) 0 0
\(495\) 1.41152 + 9.49112i 0.0634431 + 0.426594i
\(496\) 0 0
\(497\) 0.860489 + 30.9046i 0.0385982 + 1.38626i
\(498\) 0 0
\(499\) 32.0427 1.43443 0.717215 0.696852i \(-0.245417\pi\)
0.717215 + 0.696852i \(0.245417\pi\)
\(500\) 0 0
\(501\) −28.2395 + 19.2128i −1.26165 + 0.858364i
\(502\) 0 0
\(503\) −11.6608 −0.519930 −0.259965 0.965618i \(-0.583711\pi\)
−0.259965 + 0.965618i \(0.583711\pi\)
\(504\) 0 0
\(505\) 17.3050 0.770061
\(506\) 0 0
\(507\) −2.45327 1.18440i −0.108954 0.0526010i
\(508\) 0 0
\(509\) −26.8854 −1.19167 −0.595836 0.803106i \(-0.703179\pi\)
−0.595836 + 0.803106i \(0.703179\pi\)
\(510\) 0 0
\(511\) −10.3028 + 6.33705i −0.455769 + 0.280335i
\(512\) 0 0
\(513\) 12.2802 39.3995i 0.542185 1.73953i
\(514\) 0 0
\(515\) 8.23834i 0.363024i
\(516\) 0 0
\(517\) −15.9255 + 9.19459i −0.700402 + 0.404378i
\(518\) 0 0
\(519\) −2.61701 + 1.78049i −0.114874 + 0.0781549i
\(520\) 0 0
\(521\) −17.0385 29.5116i −0.746471 1.29293i −0.949504 0.313754i \(-0.898413\pi\)
0.203033 0.979172i \(-0.434920\pi\)
\(522\) 0 0
\(523\) 4.71003 + 2.71933i 0.205955 + 0.118908i 0.599430 0.800427i \(-0.295394\pi\)
−0.393475 + 0.919335i \(0.628727\pi\)
\(524\) 0 0
\(525\) −0.109051 1.06906i −0.00475938 0.0466575i
\(526\) 0 0
\(527\) 1.86831i 0.0813850i
\(528\) 0 0
\(529\) 6.92280 0.300991
\(530\) 0 0
\(531\) −14.7964 + 37.4843i −0.642111 + 1.62668i
\(532\) 0 0
\(533\) 21.9080 + 12.6486i 0.948940 + 0.547871i
\(534\) 0 0
\(535\) 15.0243 + 8.67429i 0.649558 + 0.375022i
\(536\) 0 0
\(537\) −13.6332 20.0384i −0.588316 0.864722i
\(538\) 0 0
\(539\) −0.570698 10.2404i −0.0245817 0.441085i
\(540\) 0 0
\(541\) 11.8329 20.4952i 0.508737 0.881158i −0.491212 0.871040i \(-0.663446\pi\)
0.999949 0.0101183i \(-0.00322080\pi\)
\(542\) 0 0
\(543\) 28.2582 2.08979i 1.21268 0.0896815i
\(544\) 0 0
\(545\) 1.10273 + 1.90998i 0.0472356 + 0.0818145i
\(546\) 0 0
\(547\) −12.0824 + 20.9273i −0.516606 + 0.894788i 0.483208 + 0.875505i \(0.339471\pi\)
−0.999814 + 0.0192822i \(0.993862\pi\)
\(548\) 0 0
\(549\) −18.3115 + 14.5443i −0.781518 + 0.620735i
\(550\) 0 0
\(551\) −30.7803 53.3130i −1.31128 2.27121i
\(552\) 0 0
\(553\) −13.0072 21.1471i −0.553122 0.899266i
\(554\) 0 0
\(555\) 9.65243 + 4.66003i 0.409723 + 0.197807i
\(556\) 0 0
\(557\) 7.36315 4.25111i 0.311987 0.180126i −0.335829 0.941923i \(-0.609016\pi\)
0.647815 + 0.761798i \(0.275683\pi\)
\(558\) 0 0
\(559\) 8.59381i 0.363480i
\(560\) 0 0
\(561\) −3.77253 5.54496i −0.159276 0.234108i
\(562\) 0 0
\(563\) 0.473776 0.820605i 0.0199673 0.0345844i −0.855869 0.517192i \(-0.826977\pi\)
0.875836 + 0.482608i \(0.160310\pi\)
\(564\) 0 0
\(565\) −23.0430 + 13.3039i −0.969427 + 0.559699i
\(566\) 0 0
\(567\) 22.5795 7.56069i 0.948252 0.317519i
\(568\) 0 0
\(569\) −15.7859 + 9.11401i −0.661781 + 0.382079i −0.792955 0.609280i \(-0.791458\pi\)
0.131175 + 0.991359i \(0.458125\pi\)
\(570\) 0 0
\(571\) 6.12121 10.6023i 0.256165 0.443691i −0.709046 0.705162i \(-0.750874\pi\)
0.965211 + 0.261471i \(0.0842077\pi\)
\(572\) 0 0
\(573\) −13.3118 19.5661i −0.556110 0.817385i
\(574\) 0 0
\(575\) 0.940253i 0.0392112i
\(576\) 0 0
\(577\) −10.2500 + 5.91784i −0.426713 + 0.246363i −0.697945 0.716151i \(-0.745902\pi\)
0.271232 + 0.962514i \(0.412569\pi\)
\(578\) 0 0
\(579\) 6.82827 + 3.29657i 0.283773 + 0.137001i
\(580\) 0 0
\(581\) −4.30054 + 7.95199i −0.178416 + 0.329904i
\(582\) 0 0
\(583\) −2.04439 3.54098i −0.0846699 0.146653i
\(584\) 0 0
\(585\) 17.3355 13.7690i 0.716734 0.569280i
\(586\) 0 0
\(587\) −3.57681 + 6.19521i −0.147631 + 0.255704i −0.930351 0.366669i \(-0.880498\pi\)
0.782721 + 0.622373i \(0.213831\pi\)
\(588\) 0 0
\(589\) 2.80745 + 4.86264i 0.115679 + 0.200362i
\(590\) 0 0
\(591\) 1.73775 0.128513i 0.0714815 0.00528630i
\(592\) 0 0
\(593\) −13.4811 + 23.3500i −0.553603 + 0.958869i 0.444408 + 0.895825i \(0.353414\pi\)
−0.998011 + 0.0630442i \(0.979919\pi\)
\(594\) 0 0
\(595\) −7.99668 13.0010i −0.327832 0.532990i
\(596\) 0 0
\(597\) −6.38604 9.38637i −0.261363 0.384158i
\(598\) 0 0
\(599\) −30.5223 17.6221i −1.24711 0.720018i −0.276576 0.960992i \(-0.589200\pi\)
−0.970532 + 0.240974i \(0.922533\pi\)
\(600\) 0 0
\(601\) −3.39266 1.95875i −0.138389 0.0798991i 0.429207 0.903206i \(-0.358793\pi\)
−0.567596 + 0.823307i \(0.692126\pi\)
\(602\) 0 0
\(603\) 6.43340 16.2979i 0.261988 0.663704i
\(604\) 0 0
\(605\) 19.3266 0.785740
\(606\) 0 0
\(607\) 14.4772i 0.587613i −0.955865 0.293807i \(-0.905078\pi\)
0.955865 0.293807i \(-0.0949222\pi\)
\(608\) 0 0
\(609\) 14.5466 32.4045i 0.589457 1.31310i
\(610\) 0 0
\(611\) 36.7426 + 21.2134i 1.48645 + 0.858201i
\(612\) 0 0
\(613\) −6.51761 11.2888i −0.263244 0.455952i 0.703858 0.710341i \(-0.251459\pi\)
−0.967102 + 0.254389i \(0.918126\pi\)
\(614\) 0 0
\(615\) 23.3944 15.9165i 0.943355 0.641814i
\(616\) 0 0
\(617\) −3.14491 + 1.81571i −0.126609 + 0.0730979i −0.561967 0.827160i \(-0.689955\pi\)
0.435358 + 0.900258i \(0.356622\pi\)
\(618\) 0 0
\(619\) 16.4818i 0.662460i 0.943550 + 0.331230i \(0.107464\pi\)
−0.943550 + 0.331230i \(0.892536\pi\)
\(620\) 0 0
\(621\) 20.3259 4.57637i 0.815649 0.183643i
\(622\) 0 0
\(623\) −11.6278 + 21.5006i −0.465858 + 0.861403i
\(624\) 0 0
\(625\) −23.7725 −0.950901
\(626\) 0 0
\(627\) 18.1509 + 8.76296i 0.724878 + 0.349959i
\(628\) 0 0
\(629\) −7.49147 −0.298704
\(630\) 0 0
\(631\) −34.8383 −1.38689 −0.693446 0.720508i \(-0.743909\pi\)
−0.693446 + 0.720508i \(0.743909\pi\)
\(632\) 0 0
\(633\) 26.0976 17.7556i 1.03729 0.705721i
\(634\) 0 0
\(635\) 14.8302 0.588520
\(636\) 0 0
\(637\) −19.8026 + 12.9534i −0.784606 + 0.513232i
\(638\) 0 0
\(639\) −5.15683 34.6747i −0.204001 1.37171i
\(640\) 0 0
\(641\) 8.37779i 0.330903i 0.986218 + 0.165451i \(0.0529081\pi\)
−0.986218 + 0.165451i \(0.947092\pi\)
\(642\) 0 0
\(643\) 18.0021 10.3935i 0.709934 0.409881i −0.101103 0.994876i \(-0.532237\pi\)
0.811037 + 0.584995i \(0.198904\pi\)
\(644\) 0 0
\(645\) −8.65637 4.17915i −0.340844 0.164554i
\(646\) 0 0
\(647\) −4.74770 8.22325i −0.186651 0.323289i 0.757480 0.652858i \(-0.226430\pi\)
−0.944132 + 0.329568i \(0.893097\pi\)
\(648\) 0 0
\(649\) −17.0450 9.84091i −0.669073 0.386290i
\(650\) 0 0
\(651\) −1.32678 + 2.95559i −0.0520007 + 0.115839i
\(652\) 0 0
\(653\) 7.67583i 0.300379i 0.988657 + 0.150189i \(0.0479883\pi\)
−0.988657 + 0.150189i \(0.952012\pi\)
\(654\) 0 0
\(655\) 29.9853 1.17162
\(656\) 0 0
\(657\) 10.7397 8.53025i 0.418997 0.332797i
\(658\) 0 0
\(659\) 38.0493 + 21.9678i 1.48219 + 0.855743i 0.999796 0.0202102i \(-0.00643354\pi\)
0.482395 + 0.875954i \(0.339767\pi\)
\(660\) 0 0
\(661\) −22.1649 12.7969i −0.862115 0.497742i 0.00260513 0.999997i \(-0.499171\pi\)
−0.864720 + 0.502254i \(0.832504\pi\)
\(662\) 0 0
\(663\) −6.72724 + 13.9343i −0.261264 + 0.541162i
\(664\) 0 0
\(665\) 40.3490 + 21.8213i 1.56467 + 0.846193i
\(666\) 0 0
\(667\) 15.5395 26.9151i 0.601691 1.04216i
\(668\) 0 0
\(669\) −7.57977 + 15.7002i −0.293051 + 0.607003i
\(670\) 0 0
\(671\) −5.71051 9.89089i −0.220452 0.381834i
\(672\) 0 0
\(673\) −7.64671 + 13.2445i −0.294759 + 0.510538i −0.974929 0.222517i \(-0.928573\pi\)
0.680170 + 0.733055i \(0.261906\pi\)
\(674\) 0 0
\(675\) 0.267642 + 1.18873i 0.0103016 + 0.0457543i
\(676\) 0 0
\(677\) 22.6459 + 39.2238i 0.870352 + 1.50749i 0.861633 + 0.507532i \(0.169442\pi\)
0.00871898 + 0.999962i \(0.497225\pi\)
\(678\) 0 0
\(679\) −17.1552 9.27776i −0.658356 0.356048i
\(680\) 0 0
\(681\) 2.54047 + 34.3523i 0.0973509 + 1.31638i
\(682\) 0 0
\(683\) −24.0891 + 13.9079i −0.921744 + 0.532169i −0.884191 0.467126i \(-0.845290\pi\)
−0.0375529 + 0.999295i \(0.511956\pi\)
\(684\) 0 0
\(685\) 43.8674i 1.67609i
\(686\) 0 0
\(687\) 30.6869 2.26940i 1.17078 0.0865831i
\(688\) 0 0
\(689\) −4.71672 + 8.16961i −0.179693 + 0.311237i
\(690\) 0 0
\(691\) 14.1115 8.14729i 0.536828 0.309938i −0.206965 0.978348i \(-0.566359\pi\)
0.743792 + 0.668411i \(0.233025\pi\)
\(692\) 0 0
\(693\) 2.03023 + 11.4510i 0.0771220 + 0.434986i
\(694\) 0 0
\(695\) −18.5862 + 10.7307i −0.705013 + 0.407040i
\(696\) 0 0
\(697\) −9.88831 + 17.1271i −0.374546 + 0.648733i
\(698\) 0 0
\(699\) −12.0932 + 25.0490i −0.457408 + 0.947439i
\(700\) 0 0
\(701\) 0.393403i 0.0148586i 0.999972 + 0.00742932i \(0.00236485\pi\)
−0.999972 + 0.00742932i \(0.997635\pi\)
\(702\) 0 0
\(703\) 19.4980 11.2572i 0.735379 0.424572i
\(704\) 0 0
\(705\) 39.2356 26.6941i 1.47770 1.00536i
\(706\) 0 0
\(707\) 20.9651 0.583740i 0.788474 0.0219538i
\(708\) 0 0
\(709\) 16.3183 + 28.2641i 0.612846 + 1.06148i 0.990758 + 0.135639i \(0.0433087\pi\)
−0.377912 + 0.925841i \(0.623358\pi\)
\(710\) 0 0
\(711\) 17.5089 + 22.0440i 0.656633 + 0.826714i
\(712\) 0 0
\(713\) −1.41734 + 2.45491i −0.0530799 + 0.0919372i
\(714\) 0 0
\(715\) 5.40612 + 9.36368i 0.202178 + 0.350182i
\(716\) 0 0
\(717\) −8.00020 11.7589i −0.298773 0.439144i
\(718\) 0 0
\(719\) −0.106604 + 0.184643i −0.00397565 + 0.00688602i −0.868006 0.496553i \(-0.834599\pi\)
0.864031 + 0.503439i \(0.167932\pi\)
\(720\) 0 0
\(721\) −0.277900 9.98081i −0.0103495 0.371705i
\(722\) 0 0
\(723\) −49.1884 + 3.63765i −1.82934 + 0.135286i
\(724\) 0 0
\(725\) 1.57409 + 0.908804i 0.0584604 + 0.0337521i
\(726\) 0 0
\(727\) −31.8208 18.3717i −1.18017 0.681370i −0.224114 0.974563i \(-0.571949\pi\)
−0.956053 + 0.293193i \(0.905282\pi\)
\(728\) 0 0
\(729\) −24.3947 + 11.5715i −0.903507 + 0.428574i
\(730\) 0 0
\(731\) 6.71841 0.248489
\(732\) 0 0
\(733\) 10.8753i 0.401689i 0.979623 + 0.200844i \(0.0643685\pi\)
−0.979623 + 0.200844i \(0.935631\pi\)
\(734\) 0 0
\(735\) 3.41775 + 26.2459i 0.126065 + 0.968095i
\(736\) 0 0
\(737\) 7.41104 + 4.27877i 0.272989 + 0.157610i
\(738\) 0 0
\(739\) 6.91282 + 11.9734i 0.254292 + 0.440447i 0.964703 0.263340i \(-0.0848242\pi\)
−0.710411 + 0.703787i \(0.751491\pi\)
\(740\) 0 0
\(741\) −3.42961 46.3753i −0.125990 1.70364i
\(742\) 0 0
\(743\) −15.8751 + 9.16552i −0.582403 + 0.336250i −0.762088 0.647474i \(-0.775825\pi\)
0.179685 + 0.983724i \(0.442492\pi\)
\(744\) 0 0
\(745\) 43.7373i 1.60241i
\(746\) 0 0
\(747\) 3.76377 9.53488i 0.137709 0.348863i
\(748\) 0 0
\(749\) 18.4947 + 10.0022i 0.675781 + 0.365471i
\(750\) 0 0
\(751\) −19.9417 −0.727682 −0.363841 0.931461i \(-0.618535\pi\)
−0.363841 + 0.931461i \(0.618535\pi\)
\(752\) 0 0
\(753\) −0.0838426 1.13372i −0.00305540 0.0413152i
\(754\) 0 0
\(755\) −48.5362 −1.76641
\(756\) 0 0
\(757\) −46.9292 −1.70567 −0.852836 0.522178i \(-0.825119\pi\)
−0.852836 + 0.522178i \(0.825119\pi\)
\(758\) 0 0
\(759\) 0.750467 + 10.1478i 0.0272402 + 0.368343i
\(760\) 0 0
\(761\) 53.5538 1.94132 0.970661 0.240452i \(-0.0772956\pi\)
0.970661 + 0.240452i \(0.0772956\pi\)
\(762\) 0 0
\(763\) 1.40039 + 2.27676i 0.0506976 + 0.0824242i
\(764\) 0 0
\(765\) 10.7643 + 13.5524i 0.389183 + 0.489988i
\(766\) 0 0
\(767\) 45.4091i 1.63963i
\(768\) 0 0
\(769\) 34.7306 20.0517i 1.25242 0.723085i 0.280830 0.959758i \(-0.409390\pi\)
0.971589 + 0.236673i \(0.0760570\pi\)
\(770\) 0 0
\(771\) −0.976058 13.1983i −0.0351519 0.475325i
\(772\) 0 0
\(773\) 7.82375 + 13.5511i 0.281401 + 0.487400i 0.971730 0.236095i \(-0.0758677\pi\)
−0.690329 + 0.723495i \(0.742534\pi\)
\(774\) 0 0
\(775\) −0.143572 0.0828913i −0.00515726 0.00297755i
\(776\) 0 0
\(777\) 11.8512 + 5.32007i 0.425159 + 0.190856i
\(778\) 0 0
\(779\) 59.4352i 2.12949i
\(780\) 0 0
\(781\) 17.1212 0.612645
\(782\) 0 0
\(783\) −11.9847 + 38.4512i −0.428297 + 1.37413i
\(784\) 0 0
\(785\) 15.1785 + 8.76333i 0.541745 + 0.312777i
\(786\) 0 0
\(787\) −39.9920 23.0894i −1.42556 0.823048i −0.428795 0.903402i \(-0.641062\pi\)
−0.996766 + 0.0803536i \(0.974395\pi\)
\(788\) 0 0
\(789\) 11.4465 0.846508i 0.407506 0.0301365i
\(790\) 0 0
\(791\) −27.4680 + 16.8951i −0.976651 + 0.600720i
\(792\) 0 0
\(793\) −13.1750 + 22.8198i −0.467859 + 0.810356i
\(794\) 0 0
\(795\) 5.93534 + 8.72392i 0.210505 + 0.309406i
\(796\) 0 0
\(797\) 16.9388 + 29.3388i 0.600002 + 1.03923i 0.992820 + 0.119618i \(0.0381669\pi\)
−0.392818 + 0.919616i \(0.628500\pi\)
\(798\) 0 0
\(799\) −16.5840 + 28.7244i −0.586701 + 1.01620i
\(800\) 0 0
\(801\) 10.1765 25.7804i 0.359568 0.910906i
\(802\) 0 0
\(803\) 3.34922 + 5.80102i 0.118191 + 0.204714i
\(804\) 0 0
\(805\) 0.644559 + 23.1494i 0.0227177 + 0.815910i
\(806\) 0 0
\(807\) 12.5546 8.54158i 0.441944 0.300678i
\(808\) 0 0
\(809\) 33.7873 19.5071i 1.18790 0.685834i 0.230070 0.973174i \(-0.426104\pi\)
0.957829 + 0.287340i \(0.0927711\pi\)
\(810\) 0 0
\(811\) 7.73397i 0.271577i −0.990738 0.135788i \(-0.956643\pi\)
0.990738 0.135788i \(-0.0433567\pi\)
\(812\) 0 0
\(813\) −12.4002 + 25.6849i −0.434895 + 0.900807i
\(814\) 0 0
\(815\) −13.5915 + 23.5411i −0.476088 + 0.824609i
\(816\) 0 0
\(817\) −17.4859 + 10.0955i −0.611755 + 0.353197i
\(818\) 0 0
\(819\) 20.5376 17.2661i 0.717643 0.603326i
\(820\) 0 0
\(821\) −0.443638 + 0.256134i −0.0154831 + 0.00893915i −0.507722 0.861521i \(-0.669512\pi\)
0.492238 + 0.870460i \(0.336179\pi\)
\(822\) 0 0
\(823\) 24.1753 41.8728i 0.842698 1.45960i −0.0449080 0.998991i \(-0.514299\pi\)
0.887606 0.460604i \(-0.152367\pi\)
\(824\) 0 0
\(825\) −0.593482 + 0.0438900i −0.0206624 + 0.00152805i
\(826\) 0 0
\(827\) 17.3086i 0.601879i 0.953643 + 0.300940i \(0.0973003\pi\)
−0.953643 + 0.300940i \(0.902700\pi\)
\(828\) 0 0
\(829\) 33.0205 19.0644i 1.14685 0.662134i 0.198733 0.980054i \(-0.436317\pi\)
0.948118 + 0.317919i \(0.102984\pi\)
\(830\) 0 0
\(831\) −2.27057 30.7027i −0.0787652 1.06507i
\(832\) 0 0
\(833\) −10.1266 15.4811i −0.350866 0.536388i
\(834\) 0 0
\(835\) 21.5241 + 37.2808i 0.744871 + 1.29015i
\(836\) 0 0
\(837\) 1.09311 3.50711i 0.0377835 0.121223i
\(838\) 0 0
\(839\) 15.2026 26.3317i 0.524852 0.909071i −0.474729 0.880132i \(-0.657454\pi\)
0.999581 0.0289389i \(-0.00921281\pi\)
\(840\) 0 0
\(841\) 15.5394 + 26.9151i 0.535842 + 0.928106i
\(842\) 0 0
\(843\) 12.1954 25.2607i 0.420033 0.870024i
\(844\) 0 0
\(845\) −1.71674 + 2.97348i −0.0590577 + 0.102291i
\(846\) 0 0
\(847\) 23.4144 0.651937i 0.804528 0.0224008i
\(848\) 0 0
\(849\) −21.3659 + 44.2557i −0.733276 + 1.51885i
\(850\) 0 0
\(851\) 9.84358 + 5.68319i 0.337434 + 0.194817i
\(852\) 0 0
\(853\) −27.7143 16.0008i −0.948919 0.547858i −0.0561738 0.998421i \(-0.517890\pi\)
−0.892745 + 0.450563i \(0.851223\pi\)
\(854\) 0 0
\(855\) −48.3807 19.0976i −1.65459 0.653126i
\(856\) 0 0
\(857\) −45.1549 −1.54246 −0.771230 0.636556i \(-0.780358\pi\)
−0.771230 + 0.636556i \(0.780358\pi\)
\(858\) 0 0
\(859\) 18.2340i 0.622137i −0.950388 0.311068i \(-0.899313\pi\)
0.950388 0.311068i \(-0.100687\pi\)
\(860\) 0 0
\(861\) 27.8057 20.0721i 0.947614 0.684055i
\(862\) 0 0
\(863\) 6.61966 + 3.82186i 0.225336 + 0.130098i 0.608419 0.793616i \(-0.291804\pi\)
−0.383083 + 0.923714i \(0.625138\pi\)
\(864\) 0 0
\(865\) 1.99468 + 3.45489i 0.0678213 + 0.117470i
\(866\) 0 0
\(867\) 15.6229 + 7.54249i 0.530583 + 0.256157i
\(868\) 0 0
\(869\) −11.9069 + 6.87448i −0.403915 + 0.233201i
\(870\) 0 0
\(871\) 19.7436i 0.668985i
\(872\) 0 0
\(873\) 20.5700 + 8.11975i 0.696190 + 0.274812i
\(874\) 0 0
\(875\) −30.2211 + 0.841458i −1.02166 + 0.0284465i
\(876\) 0 0
\(877\) 16.0316 0.541350 0.270675 0.962671i \(-0.412753\pi\)
0.270675 + 0.962671i \(0.412753\pi\)
\(878\) 0 0
\(879\) −12.5521 + 8.53988i −0.423373 + 0.288043i
\(880\) 0 0
\(881\) −24.7532 −0.833958 −0.416979 0.908916i \(-0.636911\pi\)
−0.416979 + 0.908916i \(0.636911\pi\)
\(882\) 0 0
\(883\) −11.6958 −0.393595 −0.196798 0.980444i \(-0.563054\pi\)
−0.196798 + 0.980444i \(0.563054\pi\)
\(884\) 0 0
\(885\) 45.7396 + 22.0823i 1.53752 + 0.742289i
\(886\) 0 0
\(887\) 55.0859 1.84960 0.924801 0.380451i \(-0.124231\pi\)
0.924801 + 0.380451i \(0.124231\pi\)
\(888\) 0 0
\(889\) 17.9669 0.500261i 0.602592 0.0167782i
\(890\) 0 0
\(891\) −3.83737 12.6160i −0.128557 0.422651i
\(892\) 0 0
\(893\) 99.6808i 3.33569i
\(894\) 0 0
\(895\) −26.4541 + 15.2733i −0.884262 + 0.510529i
\(896\) 0 0
\(897\) 19.4102 13.2058i 0.648089 0.440929i
\(898\) 0 0
\(899\) −2.73987 4.74560i −0.0913799 0.158275i
\(900\) 0 0
\(901\) −6.38677 3.68741i −0.212774 0.122845i
\(902\) 0 0
\(903\) −10.6282 4.77108i −0.353686 0.158771i
\(904\) 0 0
\(905\) 35.7127i 1.18713i
\(906\) 0 0
\(907\) −25.8767 −0.859220 −0.429610 0.903014i \(-0.641349\pi\)
−0.429610 + 0.903014i \(0.641349\pi\)
\(908\) 0 0
\(909\) −23.5227 + 3.49830i −0.780199 + 0.116031i
\(910\) 0 0
\(911\) −3.86306 2.23034i −0.127989 0.0738944i 0.434639 0.900605i \(-0.356876\pi\)
−0.562627 + 0.826711i \(0.690209\pi\)
\(912\) 0 0
\(913\) 4.33572 + 2.50323i 0.143491 + 0.0828448i
\(914\) 0 0
\(915\) 16.5790 + 24.3682i 0.548083 + 0.805587i
\(916\) 0 0
\(917\) 36.3274 1.01148i 1.19964 0.0334020i
\(918\) 0 0
\(919\) −21.2352 + 36.7805i −0.700485 + 1.21328i 0.267811 + 0.963471i \(0.413700\pi\)
−0.968296 + 0.249804i \(0.919634\pi\)
\(920\) 0 0
\(921\) −22.1958 + 1.64145i −0.731375 + 0.0540877i
\(922\) 0 0
\(923\) −19.7507 34.2091i −0.650101 1.12601i
\(924\) 0 0
\(925\) −0.332373 + 0.575688i −0.0109284 + 0.0189285i
\(926\) 0 0
\(927\) 1.66543 + 11.1984i 0.0546998 + 0.367804i
\(928\) 0 0
\(929\) −7.72508 13.3802i −0.253452 0.438991i 0.711022 0.703170i \(-0.248233\pi\)
−0.964474 + 0.264178i \(0.914899\pi\)
\(930\) 0 0
\(931\) 49.6193 + 25.0756i 1.62621 + 0.821819i
\(932\) 0 0
\(933\) −10.2843 4.96511i −0.336694 0.162550i
\(934\) 0 0
\(935\) −7.32027 + 4.22636i −0.239398 + 0.138217i
\(936\) 0 0
\(937\) 46.1410i 1.50736i −0.657241 0.753680i \(-0.728277\pi\)
0.657241 0.753680i \(-0.271723\pi\)
\(938\) 0 0
\(939\) −3.32681 4.88983i −0.108566 0.159574i
\(940\) 0 0
\(941\) −20.5052 + 35.5161i −0.668451 + 1.15779i 0.309886 + 0.950774i \(0.399709\pi\)
−0.978337 + 0.207017i \(0.933624\pi\)
\(942\) 0 0
\(943\) 25.9859 15.0030i 0.846218 0.488564i
\(944\) 0 0
\(945\) −7.40437 29.0836i −0.240864 0.946089i
\(946\) 0 0
\(947\) −8.50657 + 4.91127i −0.276426 + 0.159595i −0.631804 0.775128i \(-0.717685\pi\)
0.355378 + 0.934723i \(0.384352\pi\)
\(948\) 0 0
\(949\) 7.72718 13.3839i 0.250835 0.434459i
\(950\) 0 0
\(951\) −31.2758 45.9700i −1.01419 1.49068i
\(952\) 0 0
\(953\) 17.0826i 0.553359i 0.960962 + 0.276679i \(0.0892340\pi\)
−0.960962 + 0.276679i \(0.910766\pi\)
\(954\) 0 0
\(955\) −25.8305 + 14.9132i −0.835855 + 0.482581i
\(956\) 0 0
\(957\) −17.7141 8.55205i −0.572614 0.276449i
\(958\) 0 0
\(959\) 1.47976 + 53.1458i 0.0477840 + 1.71617i
\(960\) 0 0
\(961\) −15.2501 26.4139i −0.491939 0.852063i
\(962\) 0 0
\(963\) −22.1762 8.75374i −0.714617 0.282085i
\(964\) 0 0
\(965\) 4.77826 8.27619i 0.153818 0.266420i
\(966\) 0 0
\(967\) 21.3240 + 36.9343i 0.685735 + 1.18773i 0.973205 + 0.229938i \(0.0738523\pi\)
−0.287471 + 0.957789i \(0.592814\pi\)
\(968\) 0 0
\(969\) 36.2550 2.68118i 1.16468 0.0861318i
\(970\) 0 0
\(971\) −11.7562 + 20.3623i −0.377275 + 0.653459i −0.990665 0.136321i \(-0.956472\pi\)
0.613390 + 0.789780i \(0.289805\pi\)
\(972\) 0 0
\(973\) −22.1553 + 13.6273i −0.710267 + 0.436872i
\(974\) 0 0
\(975\) 0.772323 + 1.13518i 0.0247341 + 0.0363549i
\(976\) 0 0
\(977\) −30.1944 17.4327i −0.966003 0.557722i −0.0679878 0.997686i \(-0.521658\pi\)
−0.898015 + 0.439964i \(0.854991\pi\)
\(978\) 0 0
\(979\) 11.7229 + 6.76824i 0.374666 + 0.216314i
\(980\) 0 0
\(981\) −1.88505 2.37332i −0.0601851 0.0757742i
\(982\) 0 0
\(983\) −26.3608 −0.840780 −0.420390 0.907343i \(-0.638107\pi\)
−0.420390 + 0.907343i \(0.638107\pi\)
\(984\) 0 0
\(985\) 2.19617i 0.0699757i
\(986\) 0 0
\(987\) 46.6338 33.6636i 1.48437 1.07152i
\(988\) 0 0
\(989\) −8.82780 5.09673i −0.280708 0.162067i
\(990\) 0 0
\(991\) 0.0805213 + 0.139467i 0.00255784 + 0.00443031i 0.867301 0.497783i \(-0.165852\pi\)
−0.864744 + 0.502214i \(0.832519\pi\)
\(992\) 0 0
\(993\) −41.3621 + 28.1408i −1.31259 + 0.893022i
\(994\) 0 0
\(995\) −12.3916 + 7.15427i −0.392839 + 0.226806i
\(996\) 0 0
\(997\) 16.8378i 0.533259i −0.963799 0.266629i \(-0.914090\pi\)
0.963799 0.266629i \(-0.0859100\pi\)
\(998\) 0 0
\(999\) −14.0626 4.38310i −0.444922 0.138675i
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 252.2.bm.a.173.4 yes 16
3.2 odd 2 756.2.bm.a.89.3 16
4.3 odd 2 1008.2.df.d.929.5 16
7.2 even 3 1764.2.x.b.1469.2 16
7.3 odd 6 252.2.w.a.101.2 yes 16
7.4 even 3 1764.2.w.b.1109.7 16
7.5 odd 6 1764.2.x.a.1469.7 16
7.6 odd 2 1764.2.bm.a.1685.5 16
9.2 odd 6 2268.2.t.b.2105.6 16
9.4 even 3 756.2.w.a.341.3 16
9.5 odd 6 252.2.w.a.5.2 16
9.7 even 3 2268.2.t.a.2105.3 16
12.11 even 2 3024.2.df.d.1601.3 16
21.2 odd 6 5292.2.x.b.4409.6 16
21.5 even 6 5292.2.x.a.4409.3 16
21.11 odd 6 5292.2.w.b.521.6 16
21.17 even 6 756.2.w.a.521.3 16
21.20 even 2 5292.2.bm.a.4625.6 16
28.3 even 6 1008.2.ca.d.353.7 16
36.23 even 6 1008.2.ca.d.257.7 16
36.31 odd 6 3024.2.ca.d.2609.3 16
63.4 even 3 5292.2.bm.a.2285.6 16
63.5 even 6 1764.2.x.b.293.2 16
63.13 odd 6 5292.2.w.b.1097.6 16
63.23 odd 6 1764.2.x.a.293.7 16
63.31 odd 6 756.2.bm.a.17.3 16
63.32 odd 6 1764.2.bm.a.1697.5 16
63.38 even 6 2268.2.t.a.1781.3 16
63.40 odd 6 5292.2.x.b.881.6 16
63.41 even 6 1764.2.w.b.509.7 16
63.52 odd 6 2268.2.t.b.1781.6 16
63.58 even 3 5292.2.x.a.881.3 16
63.59 even 6 inner 252.2.bm.a.185.4 yes 16
84.59 odd 6 3024.2.ca.d.2033.3 16
252.31 even 6 3024.2.df.d.17.3 16
252.59 odd 6 1008.2.df.d.689.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.w.a.5.2 16 9.5 odd 6
252.2.w.a.101.2 yes 16 7.3 odd 6
252.2.bm.a.173.4 yes 16 1.1 even 1 trivial
252.2.bm.a.185.4 yes 16 63.59 even 6 inner
756.2.w.a.341.3 16 9.4 even 3
756.2.w.a.521.3 16 21.17 even 6
756.2.bm.a.17.3 16 63.31 odd 6
756.2.bm.a.89.3 16 3.2 odd 2
1008.2.ca.d.257.7 16 36.23 even 6
1008.2.ca.d.353.7 16 28.3 even 6
1008.2.df.d.689.5 16 252.59 odd 6
1008.2.df.d.929.5 16 4.3 odd 2
1764.2.w.b.509.7 16 63.41 even 6
1764.2.w.b.1109.7 16 7.4 even 3
1764.2.x.a.293.7 16 63.23 odd 6
1764.2.x.a.1469.7 16 7.5 odd 6
1764.2.x.b.293.2 16 63.5 even 6
1764.2.x.b.1469.2 16 7.2 even 3
1764.2.bm.a.1685.5 16 7.6 odd 2
1764.2.bm.a.1697.5 16 63.32 odd 6
2268.2.t.a.1781.3 16 63.38 even 6
2268.2.t.a.2105.3 16 9.7 even 3
2268.2.t.b.1781.6 16 63.52 odd 6
2268.2.t.b.2105.6 16 9.2 odd 6
3024.2.ca.d.2033.3 16 84.59 odd 6
3024.2.ca.d.2609.3 16 36.31 odd 6
3024.2.df.d.17.3 16 252.31 even 6
3024.2.df.d.1601.3 16 12.11 even 2
5292.2.w.b.521.6 16 21.11 odd 6
5292.2.w.b.1097.6 16 63.13 odd 6
5292.2.x.a.881.3 16 63.58 even 3
5292.2.x.a.4409.3 16 21.5 even 6
5292.2.x.b.881.6 16 63.40 odd 6
5292.2.x.b.4409.6 16 21.2 odd 6
5292.2.bm.a.2285.6 16 63.4 even 3
5292.2.bm.a.4625.6 16 21.20 even 2