Properties

Label 432.2.u.e.49.4
Level $432$
Weight $2$
Character 432.49
Analytic conductor $3.450$
Analytic rank $0$
Dimension $24$
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] = [432,2,Mod(49,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.u (of order \(9\), degree \(6\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 49.4
Character \(\chi\) \(=\) 432.49
Dual form 432.2.u.e.97.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.57237 - 0.726388i) q^{3} +(-1.78916 + 0.651202i) q^{5} +(0.623407 + 3.53552i) q^{7} +(1.94472 - 2.28431i) q^{9} +O(q^{10})\) \(q+(1.57237 - 0.726388i) q^{3} +(-1.78916 + 0.651202i) q^{5} +(0.623407 + 3.53552i) q^{7} +(1.94472 - 2.28431i) q^{9} +(4.04987 + 1.47403i) q^{11} +(-0.0714443 - 0.0599489i) q^{13} +(-2.34021 + 2.32356i) q^{15} +(1.83982 - 3.18667i) q^{17} +(3.88233 + 6.72439i) q^{19} +(3.54838 + 5.10632i) q^{21} +(1.14509 - 6.49415i) q^{23} +(-1.05319 + 0.883728i) q^{25} +(1.39854 - 5.00441i) q^{27} +(-3.61880 + 3.03653i) q^{29} +(0.0708700 - 0.401924i) q^{31} +(7.43863 - 0.624046i) q^{33} +(-3.41771 - 5.91964i) q^{35} +(2.11523 - 3.66369i) q^{37} +(-0.155883 - 0.0423658i) q^{39} +(-5.23989 - 4.39679i) q^{41} +(-10.2909 - 3.74557i) q^{43} +(-1.99188 + 5.35340i) q^{45} +(0.472016 + 2.67694i) q^{47} +(-5.53338 + 2.01399i) q^{49} +(0.578134 - 6.34706i) q^{51} +1.12782 q^{53} -8.20576 q^{55} +(10.9890 + 7.75318i) q^{57} +(-1.48162 + 0.539264i) q^{59} +(1.39919 + 7.93519i) q^{61} +(9.28855 + 5.45154i) q^{63} +(0.166864 + 0.0607336i) q^{65} +(7.15926 + 6.00733i) q^{67} +(-2.91676 - 11.0430i) q^{69} +(2.22008 - 3.84530i) q^{71} +(-4.95978 - 8.59058i) q^{73} +(-1.01407 + 2.15457i) q^{75} +(-2.68675 + 15.2373i) q^{77} +(-4.33935 + 3.64114i) q^{79} +(-1.43612 - 8.88468i) q^{81} +(-5.85999 + 4.91711i) q^{83} +(-1.21658 + 6.89956i) q^{85} +(-3.48440 + 7.40321i) q^{87} +(-5.55242 - 9.61708i) q^{89} +(0.167411 - 0.289965i) q^{91} +(-0.180518 - 0.683453i) q^{93} +(-11.3250 - 9.50284i) q^{95} +(13.0206 + 4.73910i) q^{97} +(11.2430 - 6.38456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{7} + 6 q^{9} - 6 q^{11} + 12 q^{13} + 3 q^{15} + 6 q^{17} - 9 q^{19} - 18 q^{21} - 24 q^{23} - 24 q^{25} - 9 q^{29} + 27 q^{31} + 21 q^{33} + 18 q^{35} + 15 q^{37} + 15 q^{39} - 6 q^{41} - 39 q^{43} - 69 q^{45} + 36 q^{47} + 3 q^{49} + 36 q^{51} - 18 q^{53} + 54 q^{55} + 27 q^{57} + 30 q^{59} + 12 q^{61} - 18 q^{63} - 18 q^{65} - 54 q^{67} - 57 q^{69} + 36 q^{73} + 51 q^{75} - 24 q^{77} + 45 q^{79} + 18 q^{81} - 33 q^{83} - 57 q^{85} - 90 q^{87} + 9 q^{89} - 39 q^{91} + 42 q^{93} - 87 q^{95} + 57 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\)

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
\(3\) 1.57237 0.726388i 0.907811 0.419380i
\(4\) 0 0
\(5\) −1.78916 + 0.651202i −0.800137 + 0.291226i −0.709543 0.704662i \(-0.751099\pi\)
−0.0905940 + 0.995888i \(0.528877\pi\)
\(6\) 0 0
\(7\) 0.623407 + 3.53552i 0.235626 + 1.33630i 0.841292 + 0.540581i \(0.181795\pi\)
−0.605667 + 0.795718i \(0.707093\pi\)
\(8\) 0 0
\(9\) 1.94472 2.28431i 0.648240 0.761436i
\(10\) 0 0
\(11\) 4.04987 + 1.47403i 1.22108 + 0.444437i 0.870534 0.492108i \(-0.163773\pi\)
0.350547 + 0.936545i \(0.385996\pi\)
\(12\) 0 0
\(13\) −0.0714443 0.0599489i −0.0198151 0.0166268i 0.632826 0.774294i \(-0.281895\pi\)
−0.652641 + 0.757667i \(0.726339\pi\)
\(14\) 0 0
\(15\) −2.34021 + 2.32356i −0.604239 + 0.599940i
\(16\) 0 0
\(17\) 1.83982 3.18667i 0.446223 0.772881i −0.551914 0.833901i \(-0.686102\pi\)
0.998137 + 0.0610206i \(0.0194355\pi\)
\(18\) 0 0
\(19\) 3.88233 + 6.72439i 0.890667 + 1.54268i 0.839077 + 0.544013i \(0.183096\pi\)
0.0515903 + 0.998668i \(0.483571\pi\)
\(20\) 0 0
\(21\) 3.54838 + 5.10632i 0.774321 + 1.11429i
\(22\) 0 0
\(23\) 1.14509 6.49415i 0.238769 1.35412i −0.595761 0.803162i \(-0.703149\pi\)
0.834530 0.550963i \(-0.185739\pi\)
\(24\) 0 0
\(25\) −1.05319 + 0.883728i −0.210637 + 0.176746i
\(26\) 0 0
\(27\) 1.39854 5.00441i 0.269149 0.963099i
\(28\) 0 0
\(29\) −3.61880 + 3.03653i −0.671993 + 0.563869i −0.913655 0.406491i \(-0.866752\pi\)
0.241661 + 0.970361i \(0.422308\pi\)
\(30\) 0 0
\(31\) 0.0708700 0.401924i 0.0127286 0.0721876i −0.977782 0.209625i \(-0.932776\pi\)
0.990510 + 0.137438i \(0.0438867\pi\)
\(32\) 0 0
\(33\) 7.43863 0.624046i 1.29490 0.108632i
\(34\) 0 0
\(35\) −3.41771 5.91964i −0.577698 1.00060i
\(36\) 0 0
\(37\) 2.11523 3.66369i 0.347742 0.602307i −0.638106 0.769949i \(-0.720282\pi\)
0.985848 + 0.167641i \(0.0536151\pi\)
\(38\) 0 0
\(39\) −0.155883 0.0423658i −0.0249613 0.00678396i
\(40\) 0 0
\(41\) −5.23989 4.39679i −0.818333 0.686663i 0.134248 0.990948i \(-0.457138\pi\)
−0.952581 + 0.304285i \(0.901583\pi\)
\(42\) 0 0
\(43\) −10.2909 3.74557i −1.56934 0.571195i −0.596492 0.802619i \(-0.703439\pi\)
−0.972853 + 0.231424i \(0.925661\pi\)
\(44\) 0 0
\(45\) −1.99188 + 5.35340i −0.296931 + 0.798038i
\(46\) 0 0
\(47\) 0.472016 + 2.67694i 0.0688506 + 0.390471i 0.999687 + 0.0250341i \(0.00796943\pi\)
−0.930836 + 0.365437i \(0.880919\pi\)
\(48\) 0 0
\(49\) −5.53338 + 2.01399i −0.790483 + 0.287712i
\(50\) 0 0
\(51\) 0.578134 6.34706i 0.0809550 0.888766i
\(52\) 0 0
\(53\) 1.12782 0.154918 0.0774590 0.996996i \(-0.475319\pi\)
0.0774590 + 0.996996i \(0.475319\pi\)
\(54\) 0 0
\(55\) −8.20576 −1.10646
\(56\) 0 0
\(57\) 10.9890 + 7.75318i 1.45553 + 1.02693i
\(58\) 0 0
\(59\) −1.48162 + 0.539264i −0.192890 + 0.0702062i −0.436659 0.899627i \(-0.643838\pi\)
0.243769 + 0.969833i \(0.421616\pi\)
\(60\) 0 0
\(61\) 1.39919 + 7.93519i 0.179148 + 1.01600i 0.933247 + 0.359236i \(0.116963\pi\)
−0.754099 + 0.656761i \(0.771926\pi\)
\(62\) 0 0
\(63\) 9.28855 + 5.45154i 1.17025 + 0.686829i
\(64\) 0 0
\(65\) 0.166864 + 0.0607336i 0.0206970 + 0.00753308i
\(66\) 0 0
\(67\) 7.15926 + 6.00733i 0.874642 + 0.733912i 0.965070 0.261991i \(-0.0843790\pi\)
−0.0904279 + 0.995903i \(0.528823\pi\)
\(68\) 0 0
\(69\) −2.91676 11.0430i −0.351136 1.32942i
\(70\) 0 0
\(71\) 2.22008 3.84530i 0.263475 0.456353i −0.703688 0.710509i \(-0.748465\pi\)
0.967163 + 0.254157i \(0.0817979\pi\)
\(72\) 0 0
\(73\) −4.95978 8.59058i −0.580498 1.00545i −0.995420 0.0955950i \(-0.969525\pi\)
0.414922 0.909857i \(-0.363809\pi\)
\(74\) 0 0
\(75\) −1.01407 + 2.15457i −0.117095 + 0.248789i
\(76\) 0 0
\(77\) −2.68675 + 15.2373i −0.306183 + 1.73645i
\(78\) 0 0
\(79\) −4.33935 + 3.64114i −0.488215 + 0.409661i −0.853386 0.521280i \(-0.825455\pi\)
0.365171 + 0.930940i \(0.381010\pi\)
\(80\) 0 0
\(81\) −1.43612 8.88468i −0.159569 0.987187i
\(82\) 0 0
\(83\) −5.85999 + 4.91711i −0.643217 + 0.539723i −0.905004 0.425402i \(-0.860133\pi\)
0.261787 + 0.965126i \(0.415688\pi\)
\(84\) 0 0
\(85\) −1.21658 + 6.89956i −0.131957 + 0.748363i
\(86\) 0 0
\(87\) −3.48440 + 7.40321i −0.373567 + 0.793707i
\(88\) 0 0
\(89\) −5.55242 9.61708i −0.588556 1.01941i −0.994422 0.105476i \(-0.966363\pi\)
0.405866 0.913933i \(-0.366970\pi\)
\(90\) 0 0
\(91\) 0.167411 0.289965i 0.0175495 0.0303966i
\(92\) 0 0
\(93\) −0.180518 0.683453i −0.0187189 0.0708708i
\(94\) 0 0
\(95\) −11.3250 9.50284i −1.16193 0.974971i
\(96\) 0 0
\(97\) 13.0206 + 4.73910i 1.32204 + 0.481182i 0.904111 0.427298i \(-0.140535\pi\)
0.417927 + 0.908481i \(0.362757\pi\)
\(98\) 0 0
\(99\) 11.2430 6.38456i 1.12996 0.641673i
\(100\) 0 0
\(101\) −3.08856 17.5161i −0.307324 1.74292i −0.612361 0.790578i \(-0.709780\pi\)
0.305038 0.952340i \(-0.401331\pi\)
\(102\) 0 0
\(103\) 14.5354 5.29045i 1.43222 0.521284i 0.494650 0.869092i \(-0.335296\pi\)
0.937566 + 0.347808i \(0.113074\pi\)
\(104\) 0 0
\(105\) −9.67387 6.82531i −0.944074 0.666083i
\(106\) 0 0
\(107\) −15.7763 −1.52515 −0.762576 0.646899i \(-0.776065\pi\)
−0.762576 + 0.646899i \(0.776065\pi\)
\(108\) 0 0
\(109\) −15.1398 −1.45013 −0.725063 0.688683i \(-0.758189\pi\)
−0.725063 + 0.688683i \(0.758189\pi\)
\(110\) 0 0
\(111\) 0.664677 7.29718i 0.0630884 0.692617i
\(112\) 0 0
\(113\) −0.168455 + 0.0613127i −0.0158469 + 0.00576782i −0.349931 0.936775i \(-0.613795\pi\)
0.334085 + 0.942543i \(0.391573\pi\)
\(114\) 0 0
\(115\) 2.18024 + 12.3648i 0.203309 + 1.15302i
\(116\) 0 0
\(117\) −0.275881 + 0.0466169i −0.0255052 + 0.00430973i
\(118\) 0 0
\(119\) 12.4135 + 4.51813i 1.13794 + 0.414177i
\(120\) 0 0
\(121\) 5.80218 + 4.86861i 0.527471 + 0.442601i
\(122\) 0 0
\(123\) −11.4328 3.10721i −1.03086 0.280167i
\(124\) 0 0
\(125\) 6.06880 10.5115i 0.542810 0.940175i
\(126\) 0 0
\(127\) −7.32560 12.6883i −0.650042 1.12591i −0.983112 0.183004i \(-0.941418\pi\)
0.333070 0.942902i \(-0.391916\pi\)
\(128\) 0 0
\(129\) −18.9019 + 1.58573i −1.66422 + 0.139615i
\(130\) 0 0
\(131\) −2.24848 + 12.7518i −0.196451 + 1.11413i 0.713887 + 0.700261i \(0.246933\pi\)
−0.910338 + 0.413867i \(0.864178\pi\)
\(132\) 0 0
\(133\) −21.3539 + 17.9181i −1.85162 + 1.55369i
\(134\) 0 0
\(135\) 0.756670 + 9.86442i 0.0651238 + 0.848994i
\(136\) 0 0
\(137\) 3.10358 2.60421i 0.265157 0.222493i −0.500509 0.865731i \(-0.666854\pi\)
0.765666 + 0.643238i \(0.222410\pi\)
\(138\) 0 0
\(139\) 0.853818 4.84224i 0.0724199 0.410714i −0.926949 0.375188i \(-0.877578\pi\)
0.999369 0.0355260i \(-0.0113106\pi\)
\(140\) 0 0
\(141\) 2.68668 + 3.86628i 0.226259 + 0.325599i
\(142\) 0 0
\(143\) −0.200974 0.348096i −0.0168063 0.0291093i
\(144\) 0 0
\(145\) 4.49722 7.78941i 0.373474 0.646875i
\(146\) 0 0
\(147\) −7.23761 + 7.18612i −0.596948 + 0.592701i
\(148\) 0 0
\(149\) −4.61113 3.86920i −0.377759 0.316977i 0.434063 0.900883i \(-0.357080\pi\)
−0.811822 + 0.583905i \(0.801524\pi\)
\(150\) 0 0
\(151\) −18.3155 6.66631i −1.49050 0.542497i −0.536917 0.843635i \(-0.680411\pi\)
−0.953581 + 0.301138i \(0.902633\pi\)
\(152\) 0 0
\(153\) −3.70138 10.3999i −0.299239 0.840783i
\(154\) 0 0
\(155\) 0.134935 + 0.765257i 0.0108383 + 0.0614669i
\(156\) 0 0
\(157\) 15.0274 5.46952i 1.19932 0.436516i 0.336331 0.941744i \(-0.390814\pi\)
0.862986 + 0.505228i \(0.168592\pi\)
\(158\) 0 0
\(159\) 1.77336 0.819235i 0.140636 0.0649696i
\(160\) 0 0
\(161\) 23.6740 1.86578
\(162\) 0 0
\(163\) 4.65600 0.364686 0.182343 0.983235i \(-0.441632\pi\)
0.182343 + 0.983235i \(0.441632\pi\)
\(164\) 0 0
\(165\) −12.9025 + 5.96057i −1.00446 + 0.464029i
\(166\) 0 0
\(167\) 7.66800 2.79092i 0.593368 0.215968i −0.0278422 0.999612i \(-0.508864\pi\)
0.621210 + 0.783644i \(0.286641\pi\)
\(168\) 0 0
\(169\) −2.25592 12.7939i −0.173532 0.984149i
\(170\) 0 0
\(171\) 22.9106 + 4.20864i 1.75202 + 0.321842i
\(172\) 0 0
\(173\) 8.14124 + 2.96317i 0.618967 + 0.225286i 0.632422 0.774624i \(-0.282061\pi\)
−0.0134552 + 0.999909i \(0.504283\pi\)
\(174\) 0 0
\(175\) −3.78100 3.17263i −0.285817 0.239829i
\(176\) 0 0
\(177\) −1.93794 + 1.92415i −0.145665 + 0.144628i
\(178\) 0 0
\(179\) −3.46176 + 5.99595i −0.258744 + 0.448158i −0.965906 0.258894i \(-0.916642\pi\)
0.707162 + 0.707052i \(0.249975\pi\)
\(180\) 0 0
\(181\) 1.68344 + 2.91581i 0.125129 + 0.216730i 0.921783 0.387705i \(-0.126732\pi\)
−0.796654 + 0.604435i \(0.793399\pi\)
\(182\) 0 0
\(183\) 7.96407 + 11.4607i 0.588721 + 0.847202i
\(184\) 0 0
\(185\) −1.39869 + 7.93238i −0.102834 + 0.583200i
\(186\) 0 0
\(187\) 12.1483 10.1936i 0.888371 0.745432i
\(188\) 0 0
\(189\) 18.5650 + 1.82477i 1.35041 + 0.132732i
\(190\) 0 0
\(191\) 8.01432 6.72482i 0.579896 0.486591i −0.305017 0.952347i \(-0.598662\pi\)
0.884913 + 0.465756i \(0.154218\pi\)
\(192\) 0 0
\(193\) −1.68702 + 9.56759i −0.121435 + 0.688690i 0.861927 + 0.507032i \(0.169258\pi\)
−0.983362 + 0.181658i \(0.941854\pi\)
\(194\) 0 0
\(195\) 0.306489 0.0257122i 0.0219482 0.00184129i
\(196\) 0 0
\(197\) 9.11902 + 15.7946i 0.649703 + 1.12532i 0.983194 + 0.182565i \(0.0584401\pi\)
−0.333491 + 0.942753i \(0.608227\pi\)
\(198\) 0 0
\(199\) 1.84955 3.20351i 0.131111 0.227091i −0.792994 0.609229i \(-0.791479\pi\)
0.924105 + 0.382138i \(0.124812\pi\)
\(200\) 0 0
\(201\) 15.6207 + 4.24537i 1.10180 + 0.299446i
\(202\) 0 0
\(203\) −12.9917 10.9013i −0.911837 0.765122i
\(204\) 0 0
\(205\) 12.2382 + 4.45434i 0.854754 + 0.311105i
\(206\) 0 0
\(207\) −12.6077 15.2451i −0.876299 1.05961i
\(208\) 0 0
\(209\) 5.81096 + 32.9556i 0.401952 + 2.27958i
\(210\) 0 0
\(211\) 10.4191 3.79222i 0.717277 0.261068i 0.0425077 0.999096i \(-0.486465\pi\)
0.674769 + 0.738029i \(0.264243\pi\)
\(212\) 0 0
\(213\) 0.697625 7.65889i 0.0478005 0.524778i
\(214\) 0 0
\(215\) 20.8512 1.42204
\(216\) 0 0
\(217\) 1.46519 0.0994634
\(218\) 0 0
\(219\) −14.0387 9.90489i −0.948649 0.669311i
\(220\) 0 0
\(221\) −0.322482 + 0.117374i −0.0216925 + 0.00789543i
\(222\) 0 0
\(223\) −0.303478 1.72111i −0.0203224 0.115254i 0.972959 0.230978i \(-0.0741924\pi\)
−0.993281 + 0.115724i \(0.963081\pi\)
\(224\) 0 0
\(225\) −0.0294473 + 4.12441i −0.00196315 + 0.274960i
\(226\) 0 0
\(227\) 3.20256 + 1.16564i 0.212562 + 0.0773661i 0.446106 0.894980i \(-0.352810\pi\)
−0.233545 + 0.972346i \(0.575033\pi\)
\(228\) 0 0
\(229\) 7.13172 + 5.98422i 0.471277 + 0.395449i 0.847260 0.531178i \(-0.178250\pi\)
−0.375983 + 0.926627i \(0.622695\pi\)
\(230\) 0 0
\(231\) 6.84362 + 25.9103i 0.450277 + 1.70478i
\(232\) 0 0
\(233\) 0.129911 0.225012i 0.00851074 0.0147410i −0.861739 0.507352i \(-0.830624\pi\)
0.870249 + 0.492611i \(0.163958\pi\)
\(234\) 0 0
\(235\) −2.58774 4.48210i −0.168805 0.292380i
\(236\) 0 0
\(237\) −4.17819 + 8.87729i −0.271403 + 0.576642i
\(238\) 0 0
\(239\) −4.20753 + 23.8621i −0.272163 + 1.54351i 0.475670 + 0.879624i \(0.342206\pi\)
−0.747833 + 0.663887i \(0.768906\pi\)
\(240\) 0 0
\(241\) 0.0881066 0.0739302i 0.00567545 0.00476226i −0.639945 0.768420i \(-0.721043\pi\)
0.645621 + 0.763658i \(0.276599\pi\)
\(242\) 0 0
\(243\) −8.71184 12.9269i −0.558865 0.829259i
\(244\) 0 0
\(245\) 8.58861 7.20670i 0.548706 0.460419i
\(246\) 0 0
\(247\) 0.125750 0.713161i 0.00800125 0.0453773i
\(248\) 0 0
\(249\) −5.64236 + 11.9882i −0.357570 + 0.759719i
\(250\) 0 0
\(251\) 1.67852 + 2.90728i 0.105947 + 0.183506i 0.914125 0.405433i \(-0.132879\pi\)
−0.808178 + 0.588939i \(0.799546\pi\)
\(252\) 0 0
\(253\) 14.2101 24.6126i 0.893379 1.54738i
\(254\) 0 0
\(255\) 3.09884 + 11.7324i 0.194057 + 0.734711i
\(256\) 0 0
\(257\) −11.3304 9.50736i −0.706773 0.593053i 0.216919 0.976190i \(-0.430399\pi\)
−0.923692 + 0.383137i \(0.874844\pi\)
\(258\) 0 0
\(259\) 14.2717 + 5.19447i 0.886800 + 0.322769i
\(260\) 0 0
\(261\) −0.101182 + 14.1716i −0.00626302 + 0.877203i
\(262\) 0 0
\(263\) 4.24341 + 24.0656i 0.261660 + 1.48395i 0.778380 + 0.627793i \(0.216042\pi\)
−0.516720 + 0.856154i \(0.672847\pi\)
\(264\) 0 0
\(265\) −2.01785 + 0.734439i −0.123956 + 0.0451162i
\(266\) 0 0
\(267\) −15.7162 11.0884i −0.961817 0.678601i
\(268\) 0 0
\(269\) −26.8785 −1.63881 −0.819405 0.573216i \(-0.805696\pi\)
−0.819405 + 0.573216i \(0.805696\pi\)
\(270\) 0 0
\(271\) −6.72696 −0.408634 −0.204317 0.978905i \(-0.565497\pi\)
−0.204317 + 0.978905i \(0.565497\pi\)
\(272\) 0 0
\(273\) 0.0526063 0.577539i 0.00318388 0.0349543i
\(274\) 0 0
\(275\) −5.56791 + 2.02655i −0.335758 + 0.122206i
\(276\) 0 0
\(277\) −3.84460 21.8038i −0.231000 1.31007i −0.850876 0.525366i \(-0.823928\pi\)
0.619877 0.784699i \(-0.287183\pi\)
\(278\) 0 0
\(279\) −0.780294 0.943518i −0.0467150 0.0564870i
\(280\) 0 0
\(281\) 12.1745 + 4.43114i 0.726267 + 0.264340i 0.678584 0.734523i \(-0.262594\pi\)
0.0476833 + 0.998863i \(0.484816\pi\)
\(282\) 0 0
\(283\) 16.1963 + 13.5903i 0.962772 + 0.807862i 0.981402 0.191965i \(-0.0614858\pi\)
−0.0186295 + 0.999826i \(0.505930\pi\)
\(284\) 0 0
\(285\) −24.7100 6.71565i −1.46369 0.397801i
\(286\) 0 0
\(287\) 12.2783 21.2667i 0.724767 1.25533i
\(288\) 0 0
\(289\) 1.73010 + 2.99661i 0.101770 + 0.176271i
\(290\) 0 0
\(291\) 23.9156 2.00634i 1.40196 0.117614i
\(292\) 0 0
\(293\) 0.165668 0.939551i 0.00967844 0.0548891i −0.979586 0.201025i \(-0.935573\pi\)
0.989264 + 0.146136i \(0.0466838\pi\)
\(294\) 0 0
\(295\) 2.29968 1.92966i 0.133893 0.112349i
\(296\) 0 0
\(297\) 13.0405 18.2057i 0.756689 1.05640i
\(298\) 0 0
\(299\) −0.471128 + 0.395323i −0.0272460 + 0.0228621i
\(300\) 0 0
\(301\) 6.82713 38.7186i 0.393509 2.23170i
\(302\) 0 0
\(303\) −17.5799 25.2984i −1.00994 1.45335i
\(304\) 0 0
\(305\) −7.67078 13.2862i −0.439228 0.760765i
\(306\) 0 0
\(307\) 7.13734 12.3622i 0.407350 0.705550i −0.587242 0.809411i \(-0.699786\pi\)
0.994592 + 0.103861i \(0.0331197\pi\)
\(308\) 0 0
\(309\) 19.0122 18.8769i 1.08156 1.07387i
\(310\) 0 0
\(311\) 10.7918 + 9.05541i 0.611948 + 0.513485i 0.895261 0.445542i \(-0.146989\pi\)
−0.283313 + 0.959028i \(0.591434\pi\)
\(312\) 0 0
\(313\) −1.84547 0.671697i −0.104312 0.0379666i 0.289337 0.957227i \(-0.406565\pi\)
−0.393649 + 0.919261i \(0.628787\pi\)
\(314\) 0 0
\(315\) −20.1688 3.70496i −1.13638 0.208751i
\(316\) 0 0
\(317\) 3.19130 + 18.0988i 0.179241 + 1.01653i 0.933134 + 0.359530i \(0.117063\pi\)
−0.753892 + 0.656998i \(0.771826\pi\)
\(318\) 0 0
\(319\) −19.1316 + 6.96333i −1.07116 + 0.389872i
\(320\) 0 0
\(321\) −24.8062 + 11.4597i −1.38455 + 0.639618i
\(322\) 0 0
\(323\) 28.5712 1.58974
\(324\) 0 0
\(325\) 0.128223 0.00711252
\(326\) 0 0
\(327\) −23.8054 + 10.9973i −1.31644 + 0.608154i
\(328\) 0 0
\(329\) −9.17009 + 3.33764i −0.505564 + 0.184010i
\(330\) 0 0
\(331\) 3.34429 + 18.9664i 0.183819 + 1.04249i 0.927464 + 0.373913i \(0.121984\pi\)
−0.743645 + 0.668574i \(0.766905\pi\)
\(332\) 0 0
\(333\) −4.25546 11.9567i −0.233198 0.655223i
\(334\) 0 0
\(335\) −16.7211 6.08597i −0.913569 0.332512i
\(336\) 0 0
\(337\) −13.2011 11.0771i −0.719111 0.603406i 0.208028 0.978123i \(-0.433295\pi\)
−0.927139 + 0.374717i \(0.877740\pi\)
\(338\) 0 0
\(339\) −0.220338 + 0.218770i −0.0119671 + 0.0118820i
\(340\) 0 0
\(341\) 0.879462 1.52327i 0.0476255 0.0824899i
\(342\) 0 0
\(343\) 1.99517 + 3.45573i 0.107729 + 0.186592i
\(344\) 0 0
\(345\) 12.4098 + 17.8584i 0.668120 + 0.961461i
\(346\) 0 0
\(347\) −2.53577 + 14.3811i −0.136127 + 0.772015i 0.837941 + 0.545761i \(0.183759\pi\)
−0.974068 + 0.226255i \(0.927352\pi\)
\(348\) 0 0
\(349\) −8.80655 + 7.38958i −0.471404 + 0.395555i −0.847306 0.531104i \(-0.821777\pi\)
0.375902 + 0.926659i \(0.377333\pi\)
\(350\) 0 0
\(351\) −0.399926 + 0.273696i −0.0213465 + 0.0146088i
\(352\) 0 0
\(353\) −21.1652 + 17.7597i −1.12651 + 0.945252i −0.998915 0.0465747i \(-0.985169\pi\)
−0.127593 + 0.991827i \(0.540725\pi\)
\(354\) 0 0
\(355\) −1.46802 + 8.32558i −0.0779147 + 0.441876i
\(356\) 0 0
\(357\) 22.8005 1.91280i 1.20673 0.101236i
\(358\) 0 0
\(359\) −4.62882 8.01735i −0.244300 0.423140i 0.717635 0.696420i \(-0.245225\pi\)
−0.961935 + 0.273280i \(0.911891\pi\)
\(360\) 0 0
\(361\) −20.6450 + 35.7581i −1.08658 + 1.88201i
\(362\) 0 0
\(363\) 12.6597 + 3.44064i 0.664462 + 0.180587i
\(364\) 0 0
\(365\) 14.4680 + 12.1401i 0.757292 + 0.635443i
\(366\) 0 0
\(367\) −8.88697 3.23459i −0.463896 0.168844i 0.0994892 0.995039i \(-0.468279\pi\)
−0.563385 + 0.826194i \(0.690501\pi\)
\(368\) 0 0
\(369\) −20.2337 + 3.41899i −1.05333 + 0.177985i
\(370\) 0 0
\(371\) 0.703091 + 3.98743i 0.0365027 + 0.207017i
\(372\) 0 0
\(373\) 18.6244 6.77871i 0.964333 0.350989i 0.188603 0.982053i \(-0.439604\pi\)
0.775730 + 0.631065i \(0.217382\pi\)
\(374\) 0 0
\(375\) 1.90702 20.9363i 0.0984781 1.08114i
\(376\) 0 0
\(377\) 0.440579 0.0226910
\(378\) 0 0
\(379\) 10.9928 0.564661 0.282331 0.959317i \(-0.408893\pi\)
0.282331 + 0.959317i \(0.408893\pi\)
\(380\) 0 0
\(381\) −20.7352 14.6296i −1.06230 0.749495i
\(382\) 0 0
\(383\) 27.8315 10.1298i 1.42212 0.517610i 0.487459 0.873146i \(-0.337924\pi\)
0.934663 + 0.355536i \(0.115702\pi\)
\(384\) 0 0
\(385\) −5.11553 29.0116i −0.260711 1.47857i
\(386\) 0 0
\(387\) −28.5689 + 16.2234i −1.45224 + 0.824683i
\(388\) 0 0
\(389\) −16.6995 6.07813i −0.846700 0.308174i −0.118006 0.993013i \(-0.537650\pi\)
−0.728694 + 0.684839i \(0.759872\pi\)
\(390\) 0 0
\(391\) −18.5879 15.5971i −0.940033 0.788781i
\(392\) 0 0
\(393\) 5.72728 + 21.6838i 0.288903 + 1.09380i
\(394\) 0 0
\(395\) 5.39267 9.34038i 0.271335 0.469966i
\(396\) 0 0
\(397\) −16.0935 27.8748i −0.807711 1.39900i −0.914446 0.404708i \(-0.867373\pi\)
0.106735 0.994287i \(-0.465960\pi\)
\(398\) 0 0
\(399\) −20.5609 + 43.6851i −1.02933 + 2.18699i
\(400\) 0 0
\(401\) 0.432589 2.45333i 0.0216024 0.122514i −0.972100 0.234569i \(-0.924632\pi\)
0.993702 + 0.112055i \(0.0357433\pi\)
\(402\) 0 0
\(403\) −0.0291581 + 0.0244666i −0.00145247 + 0.00121877i
\(404\) 0 0
\(405\) 8.35517 + 14.9609i 0.415171 + 0.743415i
\(406\) 0 0
\(407\) 13.9668 11.7196i 0.692310 0.580917i
\(408\) 0 0
\(409\) 0.905806 5.13708i 0.0447892 0.254012i −0.954189 0.299204i \(-0.903279\pi\)
0.998978 + 0.0451919i \(0.0143899\pi\)
\(410\) 0 0
\(411\) 2.98832 6.34920i 0.147403 0.313183i
\(412\) 0 0
\(413\) −2.83023 4.90210i −0.139266 0.241216i
\(414\) 0 0
\(415\) 7.28244 12.6135i 0.357481 0.619175i
\(416\) 0 0
\(417\) −2.17483 8.23402i −0.106502 0.403222i
\(418\) 0 0
\(419\) −20.1987 16.9487i −0.986770 0.827999i −0.00167338 0.999999i \(-0.500533\pi\)
−0.985097 + 0.172000i \(0.944977\pi\)
\(420\) 0 0
\(421\) −3.90486 1.42125i −0.190311 0.0692677i 0.245106 0.969496i \(-0.421177\pi\)
−0.435418 + 0.900228i \(0.643399\pi\)
\(422\) 0 0
\(423\) 7.03289 + 4.12767i 0.341951 + 0.200694i
\(424\) 0 0
\(425\) 0.878472 + 4.98206i 0.0426121 + 0.241665i
\(426\) 0 0
\(427\) −27.1827 + 9.89370i −1.31546 + 0.478790i
\(428\) 0 0
\(429\) −0.568859 0.401353i −0.0274648 0.0193775i
\(430\) 0 0
\(431\) −14.9050 −0.717950 −0.358975 0.933347i \(-0.616874\pi\)
−0.358975 + 0.933347i \(0.616874\pi\)
\(432\) 0 0
\(433\) 38.2825 1.83974 0.919870 0.392223i \(-0.128294\pi\)
0.919870 + 0.392223i \(0.128294\pi\)
\(434\) 0 0
\(435\) 1.41318 15.5146i 0.0677566 0.743868i
\(436\) 0 0
\(437\) 48.1149 17.5124i 2.30165 0.837730i
\(438\) 0 0
\(439\) 4.20756 + 23.8623i 0.200816 + 1.13888i 0.903889 + 0.427767i \(0.140700\pi\)
−0.703073 + 0.711118i \(0.748189\pi\)
\(440\) 0 0
\(441\) −6.16032 + 16.5566i −0.293349 + 0.788409i
\(442\) 0 0
\(443\) −0.0820238 0.0298542i −0.00389707 0.00141842i 0.340071 0.940400i \(-0.389549\pi\)
−0.343968 + 0.938981i \(0.611771\pi\)
\(444\) 0 0
\(445\) 16.1968 + 13.5908i 0.767804 + 0.644264i
\(446\) 0 0
\(447\) −10.0610 2.73436i −0.475868 0.129331i
\(448\) 0 0
\(449\) −11.8525 + 20.5291i −0.559352 + 0.968826i 0.438198 + 0.898878i \(0.355617\pi\)
−0.997551 + 0.0699482i \(0.977717\pi\)
\(450\) 0 0
\(451\) −14.7399 25.5302i −0.694073 1.20217i
\(452\) 0 0
\(453\) −33.6412 + 2.82225i −1.58060 + 0.132601i
\(454\) 0 0
\(455\) −0.110700 + 0.627813i −0.00518971 + 0.0294323i
\(456\) 0 0
\(457\) −14.0590 + 11.7969i −0.657651 + 0.551835i −0.909382 0.415962i \(-0.863445\pi\)
0.251731 + 0.967797i \(0.419000\pi\)
\(458\) 0 0
\(459\) −13.3743 13.6639i −0.624260 0.637776i
\(460\) 0 0
\(461\) 27.1996 22.8232i 1.26681 1.06298i 0.271889 0.962329i \(-0.412352\pi\)
0.994922 0.100652i \(-0.0320928\pi\)
\(462\) 0 0
\(463\) −2.05421 + 11.6500i −0.0954674 + 0.541422i 0.899136 + 0.437670i \(0.144196\pi\)
−0.994603 + 0.103753i \(0.966915\pi\)
\(464\) 0 0
\(465\) 0.768042 + 1.10525i 0.0356171 + 0.0512550i
\(466\) 0 0
\(467\) 8.97741 + 15.5493i 0.415425 + 0.719537i 0.995473 0.0950451i \(-0.0302995\pi\)
−0.580048 + 0.814582i \(0.696966\pi\)
\(468\) 0 0
\(469\) −16.7759 + 29.0567i −0.774638 + 1.34171i
\(470\) 0 0
\(471\) 19.6557 19.5159i 0.905687 0.899243i
\(472\) 0 0
\(473\) −36.1556 30.3382i −1.66244 1.39495i
\(474\) 0 0
\(475\) −10.0313 3.65111i −0.460270 0.167525i
\(476\) 0 0
\(477\) 2.19330 2.57629i 0.100424 0.117960i
\(478\) 0 0
\(479\) −5.00978 28.4119i −0.228903 1.29817i −0.855082 0.518493i \(-0.826493\pi\)
0.626179 0.779679i \(-0.284618\pi\)
\(480\) 0 0
\(481\) −0.370756 + 0.134944i −0.0169050 + 0.00615292i
\(482\) 0 0
\(483\) 37.2244 17.1965i 1.69377 0.782469i
\(484\) 0 0
\(485\) −26.3820 −1.19794
\(486\) 0 0
\(487\) 9.64498 0.437056 0.218528 0.975831i \(-0.429875\pi\)
0.218528 + 0.975831i \(0.429875\pi\)
\(488\) 0 0
\(489\) 7.32098 3.38207i 0.331066 0.152942i
\(490\) 0 0
\(491\) −0.847092 + 0.308316i −0.0382287 + 0.0139141i −0.361064 0.932541i \(-0.617586\pi\)
0.322835 + 0.946455i \(0.395364\pi\)
\(492\) 0 0
\(493\) 3.01847 + 17.1186i 0.135945 + 0.770982i
\(494\) 0 0
\(495\) −15.9579 + 18.7445i −0.717255 + 0.842502i
\(496\) 0 0
\(497\) 14.9791 + 5.45195i 0.671905 + 0.244554i
\(498\) 0 0
\(499\) −0.913635 0.766631i −0.0408999 0.0343191i 0.622109 0.782931i \(-0.286276\pi\)
−0.663008 + 0.748612i \(0.730721\pi\)
\(500\) 0 0
\(501\) 10.0297 9.95832i 0.448093 0.444905i
\(502\) 0 0
\(503\) −12.7334 + 22.0550i −0.567756 + 0.983383i 0.429031 + 0.903290i \(0.358855\pi\)
−0.996787 + 0.0800931i \(0.974478\pi\)
\(504\) 0 0
\(505\) 16.9325 + 29.3279i 0.753485 + 1.30507i
\(506\) 0 0
\(507\) −12.8405 18.4782i −0.570267 0.820645i
\(508\) 0 0
\(509\) −2.40094 + 13.6164i −0.106420 + 0.603536i 0.884224 + 0.467063i \(0.154688\pi\)
−0.990644 + 0.136473i \(0.956423\pi\)
\(510\) 0 0
\(511\) 27.2802 22.8908i 1.20680 1.01263i
\(512\) 0 0
\(513\) 39.0812 10.0244i 1.72548 0.442590i
\(514\) 0 0
\(515\) −22.5610 + 18.9310i −0.994158 + 0.834197i
\(516\) 0 0
\(517\) −2.03429 + 11.5370i −0.0894678 + 0.507397i
\(518\) 0 0
\(519\) 14.9535 1.25449i 0.656385 0.0550659i
\(520\) 0 0
\(521\) 1.12013 + 1.94012i 0.0490737 + 0.0849982i 0.889519 0.456898i \(-0.151040\pi\)
−0.840445 + 0.541897i \(0.817706\pi\)
\(522\) 0 0
\(523\) −7.58187 + 13.1322i −0.331532 + 0.574230i −0.982812 0.184607i \(-0.940899\pi\)
0.651280 + 0.758837i \(0.274232\pi\)
\(524\) 0 0
\(525\) −8.24971 2.24210i −0.360047 0.0978531i
\(526\) 0 0
\(527\) −1.15041 0.965308i −0.0501126 0.0420495i
\(528\) 0 0
\(529\) −19.2499 7.00637i −0.836950 0.304625i
\(530\) 0 0
\(531\) −1.64949 + 4.43319i −0.0715816 + 0.192384i
\(532\) 0 0
\(533\) 0.110778 + 0.628252i 0.00479831 + 0.0272126i
\(534\) 0 0
\(535\) 28.2263 10.2735i 1.22033 0.444164i
\(536\) 0 0
\(537\) −1.08780 + 11.9425i −0.0469421 + 0.515355i
\(538\) 0 0
\(539\) −25.3782 −1.09311
\(540\) 0 0
\(541\) −1.43395 −0.0616501 −0.0308251 0.999525i \(-0.509813\pi\)
−0.0308251 + 0.999525i \(0.509813\pi\)
\(542\) 0 0
\(543\) 4.76501 + 3.36191i 0.204486 + 0.144273i
\(544\) 0 0
\(545\) 27.0875 9.85903i 1.16030 0.422315i
\(546\) 0 0
\(547\) 3.17185 + 17.9885i 0.135619 + 0.769132i 0.974427 + 0.224705i \(0.0721417\pi\)
−0.838808 + 0.544427i \(0.816747\pi\)
\(548\) 0 0
\(549\) 20.8474 + 12.2356i 0.889747 + 0.522201i
\(550\) 0 0
\(551\) −34.4682 12.5454i −1.46839 0.534451i
\(552\) 0 0
\(553\) −15.5785 13.0719i −0.662465 0.555874i
\(554\) 0 0
\(555\) 3.56272 + 13.4887i 0.151229 + 0.572562i
\(556\) 0 0
\(557\) −20.3587 + 35.2623i −0.862626 + 1.49411i 0.00675958 + 0.999977i \(0.497848\pi\)
−0.869385 + 0.494135i \(0.835485\pi\)
\(558\) 0 0
\(559\) 0.510682 + 0.884527i 0.0215995 + 0.0374115i
\(560\) 0 0
\(561\) 11.6971 24.8526i 0.493854 1.04928i
\(562\) 0 0
\(563\) −3.81761 + 21.6507i −0.160893 + 0.912469i 0.792306 + 0.610124i \(0.208880\pi\)
−0.953199 + 0.302345i \(0.902231\pi\)
\(564\) 0 0
\(565\) 0.261467 0.219397i 0.0110000 0.00923009i
\(566\) 0 0
\(567\) 30.5166 10.6162i 1.28158 0.445838i
\(568\) 0 0
\(569\) 3.66760 3.07748i 0.153754 0.129015i −0.562666 0.826685i \(-0.690224\pi\)
0.716420 + 0.697670i \(0.245780\pi\)
\(570\) 0 0
\(571\) 5.85551 33.2082i 0.245045 1.38972i −0.575342 0.817913i \(-0.695131\pi\)
0.820387 0.571808i \(-0.193758\pi\)
\(572\) 0 0
\(573\) 7.71669 16.3954i 0.322369 0.684929i
\(574\) 0 0
\(575\) 4.53307 + 7.85150i 0.189042 + 0.327430i
\(576\) 0 0
\(577\) 1.49507 2.58954i 0.0622407 0.107804i −0.833226 0.552933i \(-0.813509\pi\)
0.895467 + 0.445129i \(0.146842\pi\)
\(578\) 0 0
\(579\) 4.29715 + 16.2693i 0.178583 + 0.676128i
\(580\) 0 0
\(581\) −21.0377 17.6527i −0.872790 0.732358i
\(582\) 0 0
\(583\) 4.56753 + 1.66244i 0.189168 + 0.0688514i
\(584\) 0 0
\(585\) 0.463239 0.263059i 0.0191526 0.0108762i
\(586\) 0 0
\(587\) −4.81406 27.3019i −0.198698 1.12687i −0.907054 0.421015i \(-0.861674\pi\)
0.708356 0.705856i \(-0.249437\pi\)
\(588\) 0 0
\(589\) 2.97783 1.08384i 0.122699 0.0446589i
\(590\) 0 0
\(591\) 25.8115 + 18.2111i 1.06174 + 0.749104i
\(592\) 0 0
\(593\) 17.5131 0.719175 0.359588 0.933111i \(-0.382917\pi\)
0.359588 + 0.933111i \(0.382917\pi\)
\(594\) 0 0
\(595\) −25.1519 −1.03113
\(596\) 0 0
\(597\) 0.581190 6.38061i 0.0237865 0.261141i
\(598\) 0 0
\(599\) −15.5166 + 5.64757i −0.633990 + 0.230754i −0.638967 0.769234i \(-0.720638\pi\)
0.00497679 + 0.999988i \(0.498416\pi\)
\(600\) 0 0
\(601\) 4.45317 + 25.2552i 0.181649 + 1.03018i 0.930186 + 0.367088i \(0.119645\pi\)
−0.748538 + 0.663092i \(0.769244\pi\)
\(602\) 0 0
\(603\) 27.6453 4.67136i 1.12581 0.190232i
\(604\) 0 0
\(605\) −13.5515 4.93234i −0.550946 0.200528i
\(606\) 0 0
\(607\) −11.3733 9.54334i −0.461628 0.387352i 0.382101 0.924120i \(-0.375200\pi\)
−0.843730 + 0.536768i \(0.819645\pi\)
\(608\) 0 0
\(609\) −28.3464 7.70395i −1.14865 0.312180i
\(610\) 0 0
\(611\) 0.126757 0.219549i 0.00512802 0.00888200i
\(612\) 0 0
\(613\) −6.85101 11.8663i −0.276709 0.479275i 0.693856 0.720114i \(-0.255911\pi\)
−0.970565 + 0.240839i \(0.922577\pi\)
\(614\) 0 0
\(615\) 22.4786 1.88579i 0.906426 0.0760424i
\(616\) 0 0
\(617\) −2.55504 + 14.4903i −0.102862 + 0.583359i 0.889191 + 0.457536i \(0.151268\pi\)
−0.992053 + 0.125822i \(0.959843\pi\)
\(618\) 0 0
\(619\) −7.04409 + 5.91070i −0.283126 + 0.237571i −0.773280 0.634065i \(-0.781385\pi\)
0.490154 + 0.871636i \(0.336941\pi\)
\(620\) 0 0
\(621\) −30.8979 14.8128i −1.23989 0.594418i
\(622\) 0 0
\(623\) 30.5399 25.6260i 1.22356 1.02669i
\(624\) 0 0
\(625\) −2.81929 + 15.9890i −0.112772 + 0.639559i
\(626\) 0 0
\(627\) 33.0755 + 47.5975i 1.32091 + 1.90086i
\(628\) 0 0
\(629\) −7.78332 13.4811i −0.310341 0.537527i
\(630\) 0 0
\(631\) −11.0133 + 19.0757i −0.438434 + 0.759390i −0.997569 0.0696865i \(-0.977800\pi\)
0.559135 + 0.829077i \(0.311133\pi\)
\(632\) 0 0
\(633\) 13.6280 13.5311i 0.541665 0.537812i
\(634\) 0 0
\(635\) 21.3693 + 17.9310i 0.848017 + 0.711570i
\(636\) 0 0
\(637\) 0.516065 + 0.187832i 0.0204472 + 0.00744219i
\(638\) 0 0
\(639\) −4.46640 12.5494i −0.176688 0.496446i
\(640\) 0 0
\(641\) −4.36992 24.7830i −0.172601 0.978871i −0.940876 0.338751i \(-0.889996\pi\)
0.768275 0.640120i \(-0.221115\pi\)
\(642\) 0 0
\(643\) −3.95532 + 1.43962i −0.155982 + 0.0567730i −0.418831 0.908064i \(-0.637560\pi\)
0.262849 + 0.964837i \(0.415338\pi\)
\(644\) 0 0
\(645\) 32.7858 15.1460i 1.29094 0.596375i
\(646\) 0 0
\(647\) −4.11266 −0.161685 −0.0808427 0.996727i \(-0.525761\pi\)
−0.0808427 + 0.996727i \(0.525761\pi\)
\(648\) 0 0
\(649\) −6.79524 −0.266737
\(650\) 0 0
\(651\) 2.30382 1.06429i 0.0902940 0.0417130i
\(652\) 0 0
\(653\) 41.8307 15.2251i 1.63696 0.595806i 0.650459 0.759541i \(-0.274577\pi\)
0.986504 + 0.163736i \(0.0523544\pi\)
\(654\) 0 0
\(655\) −4.28108 24.2792i −0.167276 0.948667i
\(656\) 0 0
\(657\) −29.2689 5.37664i −1.14189 0.209763i
\(658\) 0 0
\(659\) −6.48613 2.36076i −0.252664 0.0919621i 0.212583 0.977143i \(-0.431812\pi\)
−0.465247 + 0.885181i \(0.654035\pi\)
\(660\) 0 0
\(661\) 8.46406 + 7.10219i 0.329214 + 0.276243i 0.792379 0.610029i \(-0.208842\pi\)
−0.463166 + 0.886272i \(0.653287\pi\)
\(662\) 0 0
\(663\) −0.421804 + 0.418803i −0.0163815 + 0.0162650i
\(664\) 0 0
\(665\) 26.5373 45.9640i 1.02907 1.78241i
\(666\) 0 0
\(667\) 15.5758 + 26.9781i 0.603098 + 1.04460i
\(668\) 0 0
\(669\) −1.72737 2.48578i −0.0667841 0.0961059i
\(670\) 0 0
\(671\) −6.03019 + 34.1989i −0.232793 + 1.32023i
\(672\) 0 0
\(673\) 29.9308 25.1149i 1.15375 0.968108i 0.153945 0.988079i \(-0.450802\pi\)
0.999801 + 0.0199715i \(0.00635755\pi\)
\(674\) 0 0
\(675\) 2.94962 + 6.50650i 0.113531 + 0.250435i
\(676\) 0 0
\(677\) −2.70666 + 2.27115i −0.104025 + 0.0872875i −0.693317 0.720633i \(-0.743851\pi\)
0.589292 + 0.807920i \(0.299407\pi\)
\(678\) 0 0
\(679\) −8.63804 + 48.9888i −0.331498 + 1.88002i
\(680\) 0 0
\(681\) 5.88234 0.493485i 0.225412 0.0189104i
\(682\) 0 0
\(683\) −7.32049 12.6795i −0.280111 0.485166i 0.691301 0.722567i \(-0.257038\pi\)
−0.971412 + 0.237401i \(0.923704\pi\)
\(684\) 0 0
\(685\) −3.85694 + 6.68041i −0.147366 + 0.255245i
\(686\) 0 0
\(687\) 15.5606 + 4.22904i 0.593674 + 0.161348i
\(688\) 0 0
\(689\) −0.0805764 0.0676116i −0.00306972 0.00257580i
\(690\) 0 0
\(691\) 20.6717 + 7.52387i 0.786387 + 0.286221i 0.703833 0.710365i \(-0.251470\pi\)
0.0825536 + 0.996587i \(0.473692\pi\)
\(692\) 0 0
\(693\) 29.5817 + 35.7696i 1.12372 + 1.35878i
\(694\) 0 0
\(695\) 1.62566 + 9.21956i 0.0616647 + 0.349718i
\(696\) 0 0
\(697\) −23.6516 + 8.60848i −0.895868 + 0.326069i
\(698\) 0 0
\(699\) 0.0408223 0.448169i 0.00154404 0.0169513i
\(700\) 0 0
\(701\) −3.32994 −0.125770 −0.0628850 0.998021i \(-0.520030\pi\)
−0.0628850 + 0.998021i \(0.520030\pi\)
\(702\) 0 0
\(703\) 32.8481 1.23889
\(704\) 0 0
\(705\) −7.32463 5.16783i −0.275862 0.194632i
\(706\) 0 0
\(707\) 60.0031 21.8393i 2.25665 0.821352i
\(708\) 0 0
\(709\) 6.92601 + 39.2793i 0.260112 + 1.47517i 0.782603 + 0.622522i \(0.213892\pi\)
−0.522491 + 0.852645i \(0.674997\pi\)
\(710\) 0 0
\(711\) −0.121329 + 16.9934i −0.00455019 + 0.637303i
\(712\) 0 0
\(713\) −2.52900 0.920481i −0.0947118 0.0344723i
\(714\) 0 0
\(715\) 0.586255 + 0.491927i 0.0219247 + 0.0183970i
\(716\) 0 0
\(717\) 10.7173 + 40.5764i 0.400246 + 1.51536i
\(718\) 0 0
\(719\) −3.91776 + 6.78576i −0.146108 + 0.253066i −0.929786 0.368101i \(-0.880008\pi\)
0.783678 + 0.621167i \(0.213341\pi\)
\(720\) 0 0
\(721\) 27.7659 + 48.0920i 1.03406 + 1.79104i
\(722\) 0 0
\(723\) 0.0848346 0.180246i 0.00315503 0.00670340i
\(724\) 0 0
\(725\) 1.12780 6.39606i 0.0418854 0.237544i
\(726\) 0 0
\(727\) 14.7514 12.3779i 0.547100 0.459072i −0.326857 0.945074i \(-0.605990\pi\)
0.873958 + 0.486002i \(0.161545\pi\)
\(728\) 0 0
\(729\) −23.0882 13.9977i −0.855118 0.518433i
\(730\) 0 0
\(731\) −30.8693 + 25.9024i −1.14174 + 0.958036i
\(732\) 0 0
\(733\) −4.67878 + 26.5347i −0.172815 + 0.980081i 0.767821 + 0.640664i \(0.221341\pi\)
−0.940636 + 0.339417i \(0.889770\pi\)
\(734\) 0 0
\(735\) 8.26965 17.5703i 0.305030 0.648090i
\(736\) 0 0
\(737\) 20.1391 + 34.8819i 0.741832 + 1.28489i
\(738\) 0 0
\(739\) −8.49490 + 14.7136i −0.312490 + 0.541249i −0.978901 0.204336i \(-0.934496\pi\)
0.666411 + 0.745585i \(0.267830\pi\)
\(740\) 0 0
\(741\) −0.320306 1.21270i −0.0117667 0.0445496i
\(742\) 0 0
\(743\) −36.7413 30.8296i −1.34791 1.13103i −0.979518 0.201356i \(-0.935465\pi\)
−0.368389 0.929672i \(-0.620090\pi\)
\(744\) 0 0
\(745\) 10.7697 + 3.91985i 0.394571 + 0.143612i
\(746\) 0 0
\(747\) −0.163846 + 22.9484i −0.00599482 + 0.839639i
\(748\) 0 0
\(749\) −9.83504 55.7773i −0.359365 2.03806i
\(750\) 0 0
\(751\) −43.6185 + 15.8758i −1.59166 + 0.579317i −0.977698 0.210018i \(-0.932648\pi\)
−0.613963 + 0.789335i \(0.710426\pi\)
\(752\) 0 0
\(753\) 4.75107 + 3.35207i 0.173139 + 0.122156i
\(754\) 0 0
\(755\) 37.1106 1.35059
\(756\) 0 0
\(757\) −25.3033 −0.919663 −0.459831 0.888006i \(-0.652090\pi\)
−0.459831 + 0.888006i \(0.652090\pi\)
\(758\) 0 0
\(759\) 4.46528 49.0222i 0.162079 1.77939i
\(760\) 0 0
\(761\) −11.2576 + 4.09745i −0.408089 + 0.148532i −0.537904 0.843006i \(-0.680784\pi\)
0.129815 + 0.991538i \(0.458562\pi\)
\(762\) 0 0
\(763\) −9.43823 53.5268i −0.341687 1.93780i
\(764\) 0 0
\(765\) 13.3948 + 16.1968i 0.484290 + 0.585595i
\(766\) 0 0
\(767\) 0.138181 + 0.0502939i 0.00498944 + 0.00181601i
\(768\) 0 0
\(769\) −2.38352 2.00001i −0.0859521 0.0721224i 0.598799 0.800899i \(-0.295645\pi\)
−0.684751 + 0.728777i \(0.740089\pi\)
\(770\) 0 0
\(771\) −24.7217 6.71884i −0.890331 0.241973i
\(772\) 0 0
\(773\) 2.22463 3.85318i 0.0800144 0.138589i −0.823241 0.567691i \(-0.807837\pi\)
0.903256 + 0.429102i \(0.141170\pi\)
\(774\) 0 0
\(775\) 0.280552 + 0.485930i 0.0100777 + 0.0174551i
\(776\) 0 0
\(777\) 26.2136 2.19913i 0.940409 0.0788934i
\(778\) 0 0
\(779\) 9.22276 52.3049i 0.330440 1.87402i
\(780\) 0 0
\(781\) 14.6591 12.3005i 0.524545 0.440146i
\(782\) 0 0
\(783\) 10.1350 + 22.3566i 0.362196 + 0.798961i
\(784\) 0 0
\(785\) −23.3247 + 19.5717i −0.832493 + 0.698545i
\(786\) 0 0
\(787\) −0.0870600 + 0.493742i −0.00310335 + 0.0176000i −0.986320 0.164841i \(-0.947289\pi\)
0.983217 + 0.182441i \(0.0583999\pi\)
\(788\) 0 0
\(789\) 24.1532 + 34.7577i 0.859876 + 1.23741i
\(790\) 0 0
\(791\) −0.321788 0.557354i −0.0114415 0.0198172i
\(792\) 0 0
\(793\) 0.375742 0.650804i 0.0133430 0.0231107i
\(794\) 0 0
\(795\) −2.63933 + 2.62056i −0.0936075 + 0.0929416i
\(796\) 0 0
\(797\) 14.8816 + 12.4871i 0.527132 + 0.442316i 0.867110 0.498117i \(-0.165975\pi\)
−0.339978 + 0.940434i \(0.610419\pi\)
\(798\) 0 0
\(799\) 9.39894 + 3.42093i 0.332510 + 0.121024i
\(800\) 0 0
\(801\) −32.7663 6.01910i −1.15774 0.212674i
\(802\) 0 0
\(803\) −7.42365 42.1016i −0.261975 1.48573i
\(804\) 0 0
\(805\) −42.3567 + 15.4166i −1.49288 + 0.543363i
\(806\) 0 0
\(807\) −42.2630 + 19.5242i −1.48773 + 0.687284i
\(808\) 0 0
\(809\) 29.1598 1.02520 0.512602 0.858626i \(-0.328682\pi\)
0.512602 + 0.858626i \(0.328682\pi\)
\(810\) 0 0
\(811\) 11.5541 0.405718 0.202859 0.979208i \(-0.434977\pi\)
0.202859 + 0.979208i \(0.434977\pi\)
\(812\) 0 0
\(813\) −10.5773 + 4.88639i −0.370962 + 0.171373i
\(814\) 0 0
\(815\) −8.33035 + 3.03200i −0.291799 + 0.106206i
\(816\) 0 0
\(817\) −14.7659 83.7415i −0.516593 2.92974i
\(818\) 0 0
\(819\) −0.336801 0.946320i −0.0117688 0.0330671i
\(820\) 0 0
\(821\) −16.3219 5.94070i −0.569640 0.207332i 0.0411112 0.999155i \(-0.486910\pi\)
−0.610751 + 0.791823i \(0.709132\pi\)
\(822\) 0 0
\(823\) 16.4607 + 13.8122i 0.573785 + 0.481463i 0.882899 0.469562i \(-0.155588\pi\)
−0.309114 + 0.951025i \(0.600033\pi\)
\(824\) 0 0
\(825\) −7.28277 + 7.23096i −0.253554 + 0.251750i
\(826\) 0 0
\(827\) −9.01618 + 15.6165i −0.313523 + 0.543039i −0.979123 0.203271i \(-0.934843\pi\)
0.665599 + 0.746309i \(0.268176\pi\)
\(828\) 0 0
\(829\) 4.72545 + 8.18473i 0.164122 + 0.284267i 0.936343 0.351086i \(-0.114188\pi\)
−0.772221 + 0.635354i \(0.780854\pi\)
\(830\) 0 0
\(831\) −21.8832 31.4911i −0.759120 1.09241i
\(832\) 0 0
\(833\) −3.76254 + 21.3384i −0.130364 + 0.739333i
\(834\) 0 0
\(835\) −11.9018 + 9.98683i −0.411880 + 0.345609i
\(836\) 0 0
\(837\) −1.91228 0.916767i −0.0660979 0.0316881i
\(838\) 0 0
\(839\) −16.4071 + 13.7672i −0.566437 + 0.475297i −0.880462 0.474118i \(-0.842767\pi\)
0.314024 + 0.949415i \(0.398323\pi\)
\(840\) 0 0
\(841\) −1.16063 + 6.58227i −0.0400218 + 0.226975i
\(842\) 0 0
\(843\) 22.3615 1.87597i 0.770172 0.0646118i
\(844\) 0 0
\(845\) 12.3676 + 21.4214i 0.425459 + 0.736917i
\(846\) 0 0
\(847\) −13.5959 + 23.5488i −0.467161 + 0.809147i
\(848\) 0 0
\(849\) 35.3386 + 9.60428i 1.21282 + 0.329618i
\(850\) 0 0
\(851\) −21.3704 17.9319i −0.732569 0.614698i
\(852\) 0 0
\(853\) 13.5008 + 4.91390i 0.462260 + 0.168249i 0.562643 0.826700i \(-0.309785\pi\)
−0.100383 + 0.994949i \(0.532007\pi\)
\(854\) 0 0
\(855\) −43.7315 + 7.38950i −1.49558 + 0.252716i
\(856\) 0 0
\(857\) −3.16456 17.9471i −0.108099 0.613062i −0.989937 0.141509i \(-0.954805\pi\)
0.881838 0.471553i \(-0.156307\pi\)
\(858\) 0 0
\(859\) −2.36124 + 0.859419i −0.0805643 + 0.0293230i −0.381988 0.924167i \(-0.624760\pi\)
0.301424 + 0.953490i \(0.402538\pi\)
\(860\) 0 0
\(861\) 3.85827 42.3580i 0.131489 1.44356i
\(862\) 0 0
\(863\) −20.8427 −0.709494 −0.354747 0.934962i \(-0.615433\pi\)
−0.354747 + 0.934962i \(0.615433\pi\)
\(864\) 0 0
\(865\) −16.4956 −0.560868
\(866\) 0 0
\(867\) 4.89706 + 3.45508i 0.166313 + 0.117341i
\(868\) 0 0
\(869\) −22.9409 + 8.34982i −0.778218 + 0.283248i
\(870\) 0 0
\(871\) −0.151355 0.858379i −0.00512848 0.0290851i
\(872\) 0 0
\(873\) 36.1469 20.5267i 1.22339 0.694725i
\(874\) 0 0
\(875\) 40.9468 + 14.9034i 1.38425 + 0.503827i
\(876\) 0 0
\(877\) −19.3397 16.2279i −0.653055 0.547978i 0.254941 0.966957i \(-0.417944\pi\)
−0.907996 + 0.418978i \(0.862388\pi\)
\(878\) 0 0
\(879\) −0.421986 1.59766i −0.0142332 0.0538879i
\(880\) 0 0
\(881\) 1.53902 2.66567i 0.0518510 0.0898087i −0.838935 0.544232i \(-0.816821\pi\)
0.890786 + 0.454423i \(0.150155\pi\)
\(882\) 0 0
\(883\) 2.97051 + 5.14507i 0.0999655 + 0.173145i 0.911670 0.410923i \(-0.134793\pi\)
−0.811705 + 0.584068i \(0.801460\pi\)
\(884\) 0 0
\(885\) 2.21428 4.70461i 0.0744321 0.158144i
\(886\) 0 0
\(887\) 8.28140 46.9662i 0.278062 1.57697i −0.451001 0.892523i \(-0.648933\pi\)
0.729064 0.684446i \(-0.239956\pi\)
\(888\) 0 0
\(889\) 40.2929 33.8098i 1.35138 1.13394i
\(890\) 0 0
\(891\) 7.28021 38.0987i 0.243896 1.27635i
\(892\) 0 0
\(893\) −16.1682 + 13.5668i −0.541050 + 0.453995i
\(894\) 0 0
\(895\) 2.28908 12.9820i 0.0765155 0.433941i
\(896\) 0 0
\(897\) −0.453631 + 0.963818i −0.0151463 + 0.0321809i
\(898\) 0 0
\(899\) 0.963989 + 1.66968i 0.0321508 + 0.0556869i
\(900\) 0 0
\(901\) 2.07499 3.59399i 0.0691280 0.119733i
\(902\) 0 0
\(903\) −17.3899 65.8392i −0.578700 2.19099i
\(904\) 0 0
\(905\) −4.91073 4.12059i −0.163238 0.136973i
\(906\) 0 0
\(907\) −18.3493 6.67861i −0.609280 0.221760i 0.0189083 0.999821i \(-0.493981\pi\)
−0.628188 + 0.778062i \(0.716203\pi\)
\(908\) 0 0
\(909\) −46.0186 27.0087i −1.52634 0.895823i
\(910\) 0 0
\(911\) 7.17655 + 40.7002i 0.237770 + 1.34846i 0.836702 + 0.547659i \(0.184481\pi\)
−0.598932 + 0.800800i \(0.704408\pi\)
\(912\) 0 0
\(913\) −30.9802 + 11.2759i −1.02529 + 0.373177i
\(914\) 0 0
\(915\) −21.7123 15.3189i −0.717785 0.506427i
\(916\) 0 0
\(917\) −46.4858 −1.53510
\(918\) 0 0
\(919\) −10.8664 −0.358451 −0.179225 0.983808i \(-0.557359\pi\)
−0.179225 + 0.983808i \(0.557359\pi\)
\(920\) 0 0
\(921\) 2.24279 24.6225i 0.0739025 0.811341i
\(922\) 0 0
\(923\) −0.389134 + 0.141633i −0.0128085 + 0.00466191i
\(924\) 0 0
\(925\) 1.00997 + 5.72784i 0.0332077 + 0.188330i
\(926\) 0 0
\(927\) 16.1823 43.4918i 0.531496 1.42846i
\(928\) 0 0
\(929\) −38.8774 14.1502i −1.27552 0.464253i −0.386575 0.922258i \(-0.626342\pi\)
−0.888950 + 0.458005i \(0.848564\pi\)
\(930\) 0 0
\(931\) −35.0252 29.3897i −1.14791 0.963208i
\(932\) 0 0
\(933\) 23.5465 + 6.39945i 0.770878 + 0.209509i
\(934\) 0 0
\(935\) −15.0972 + 26.1490i −0.493730 + 0.855165i
\(936\) 0 0
\(937\) 1.37182 + 2.37606i 0.0448154 + 0.0776226i 0.887563 0.460686i \(-0.152397\pi\)
−0.842748 + 0.538309i \(0.819063\pi\)
\(938\) 0 0
\(939\) −3.38969 + 0.284370i −0.110618 + 0.00928005i
\(940\) 0 0
\(941\) −6.52803 + 37.0223i −0.212808 + 1.20689i 0.671863 + 0.740675i \(0.265494\pi\)
−0.884671 + 0.466216i \(0.845617\pi\)
\(942\) 0 0
\(943\) −34.5536 + 28.9939i −1.12522 + 0.944172i
\(944\) 0 0
\(945\) −34.4041 + 8.82476i −1.11917 + 0.287070i
\(946\) 0 0
\(947\) 12.2257 10.2586i 0.397283 0.333360i −0.422159 0.906522i \(-0.638728\pi\)
0.819442 + 0.573161i \(0.194283\pi\)
\(948\) 0 0
\(949\) −0.160648 + 0.911082i −0.00521486 + 0.0295750i
\(950\) 0 0
\(951\) 18.1646 + 26.1399i 0.589029 + 0.847644i
\(952\) 0 0
\(953\) −16.2253 28.1031i −0.525589 0.910347i −0.999556 0.0298045i \(-0.990512\pi\)
0.473966 0.880543i \(-0.342822\pi\)
\(954\) 0 0
\(955\) −9.95971 + 17.2507i −0.322289 + 0.558220i
\(956\) 0 0
\(957\) −25.0239 + 24.8459i −0.808909 + 0.803154i
\(958\) 0 0
\(959\) 11.1420 + 9.34927i 0.359795 + 0.301904i
\(960\) 0 0
\(961\) 28.9740 + 10.5457i 0.934644 + 0.340182i
\(962\) 0 0
\(963\) −30.6805 + 36.0379i −0.988665 + 1.16130i
\(964\) 0 0
\(965\) −3.21207 18.2166i −0.103400 0.586412i
\(966\) 0 0
\(967\) 17.1492 6.24181i 0.551482 0.200723i −0.0512227 0.998687i \(-0.516312\pi\)
0.602705 + 0.797964i \(0.294090\pi\)
\(968\) 0 0
\(969\) 44.9246 20.7538i 1.44319 0.666707i
\(970\) 0 0
\(971\) −33.9067 −1.08812 −0.544058 0.839047i \(-0.683113\pi\)
−0.544058 + 0.839047i \(0.683113\pi\)
\(972\) 0 0
\(973\) 17.6521 0.565900
\(974\) 0 0
\(975\) 0.201614 0.0931394i 0.00645682 0.00298285i
\(976\) 0 0
\(977\) −28.5514 + 10.3919i −0.913441 + 0.332465i −0.755626 0.655003i \(-0.772667\pi\)
−0.157815 + 0.987469i \(0.550445\pi\)
\(978\) 0 0
\(979\) −8.31071 47.1324i −0.265611 1.50636i
\(980\) 0 0
\(981\) −29.4426 + 34.5839i −0.940030 + 1.10418i
\(982\) 0 0
\(983\) −2.45754 0.894473i −0.0783835 0.0285292i 0.302531 0.953140i \(-0.402168\pi\)
−0.380914 + 0.924610i \(0.624391\pi\)
\(984\) 0 0
\(985\) −26.6009 22.3208i −0.847574 0.711199i
\(986\) 0 0
\(987\) −11.9944 + 11.9091i −0.381786 + 0.379070i
\(988\) 0 0
\(989\) −36.1084 + 62.5415i −1.14818 + 1.98870i
\(990\) 0 0
\(991\) 27.0413 + 46.8370i 0.858996 + 1.48783i 0.872888 + 0.487922i \(0.162245\pi\)
−0.0138913 + 0.999904i \(0.504422\pi\)
\(992\) 0 0
\(993\) 19.0354 + 27.3930i 0.604071 + 0.869291i
\(994\) 0 0
\(995\) −1.22301 + 6.93603i −0.0387720 + 0.219887i
\(996\) 0 0
\(997\) −13.1904 + 11.0680i −0.417743 + 0.350528i −0.827304 0.561755i \(-0.810126\pi\)
0.409561 + 0.912283i \(0.365682\pi\)
\(998\) 0 0
\(999\) −15.3764 15.7093i −0.486487 0.497020i
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 432.2.u.e.49.4 24
4.3 odd 2 216.2.q.a.49.1 24
12.11 even 2 648.2.q.a.361.4 24
27.16 even 9 inner 432.2.u.e.97.4 24
108.11 even 18 648.2.q.a.289.4 24
108.23 even 18 5832.2.a.i.1.3 12
108.31 odd 18 5832.2.a.h.1.10 12
108.43 odd 18 216.2.q.a.97.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.q.a.49.1 24 4.3 odd 2
216.2.q.a.97.1 yes 24 108.43 odd 18
432.2.u.e.49.4 24 1.1 even 1 trivial
432.2.u.e.97.4 24 27.16 even 9 inner
648.2.q.a.289.4 24 108.11 even 18
648.2.q.a.361.4 24 12.11 even 2
5832.2.a.h.1.10 12 108.31 odd 18
5832.2.a.i.1.3 12 108.23 even 18