Properties

Label 1815.2.c.j.364.5
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
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] = [1815,2,Mod(364,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1815.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (of order \(2\), degree \(1\), 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: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.5
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.j.364.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.10651i q^{2} -1.00000i q^{3} -2.43738 q^{4} +(-0.823234 + 2.07901i) q^{5} -2.10651 q^{6} +3.31633i q^{7} +0.921348i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.10651i q^{2} -1.00000i q^{3} -2.43738 q^{4} +(-0.823234 + 2.07901i) q^{5} -2.10651 q^{6} +3.31633i q^{7} +0.921348i q^{8} -1.00000 q^{9} +(4.37946 + 1.73415i) q^{10} +2.43738i q^{12} +2.49889i q^{13} +6.98587 q^{14} +(2.07901 + 0.823234i) q^{15} -2.93393 q^{16} -6.81019i q^{17} +2.10651i q^{18} +1.14769 q^{19} +(2.00654 - 5.06734i) q^{20} +3.31633 q^{21} -5.89026i q^{23} +0.921348 q^{24} +(-3.64457 - 3.42303i) q^{25} +5.26393 q^{26} +1.00000i q^{27} -8.08315i q^{28} +1.12257 q^{29} +(1.73415 - 4.37946i) q^{30} -1.09673 q^{31} +8.02306i q^{32} -14.3457 q^{34} +(-6.89468 - 2.73011i) q^{35} +2.43738 q^{36} -11.5389i q^{37} -2.41763i q^{38} +2.49889 q^{39} +(-1.91549 - 0.758486i) q^{40} -0.932568 q^{41} -6.98587i q^{42} -0.552188i q^{43} +(0.823234 - 2.07901i) q^{45} -12.4079 q^{46} -2.13427i q^{47} +2.93393i q^{48} -3.99802 q^{49} +(-7.21064 + 7.67732i) q^{50} -6.81019 q^{51} -6.09074i q^{52} -11.6356i q^{53} +2.10651 q^{54} -3.05549 q^{56} -1.14769i q^{57} -2.36469i q^{58} -8.39837 q^{59} +(-5.06734 - 2.00654i) q^{60} -8.21313 q^{61} +2.31027i q^{62} -3.31633i q^{63} +11.0328 q^{64} +(-5.19521 - 2.05717i) q^{65} -4.15419i q^{67} +16.5990i q^{68} -5.89026 q^{69} +(-5.75101 + 14.5237i) q^{70} +12.5340 q^{71} -0.921348i q^{72} +5.73761i q^{73} -24.3067 q^{74} +(-3.42303 + 3.64457i) q^{75} -2.79736 q^{76} -5.26393i q^{78} +3.86754 q^{79} +(2.41532 - 6.09968i) q^{80} +1.00000 q^{81} +1.96446i q^{82} +6.08055i q^{83} -8.08315 q^{84} +(14.1585 + 5.60638i) q^{85} -1.16319 q^{86} -1.12257i q^{87} -12.5950 q^{89} +(-4.37946 - 1.73415i) q^{90} -8.28712 q^{91} +14.3568i q^{92} +1.09673i q^{93} -4.49586 q^{94} +(-0.944820 + 2.38607i) q^{95} +8.02306 q^{96} -2.86873i q^{97} +8.42187i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9} - 6 q^{10} - 12 q^{14} + 48 q^{16} + 32 q^{19} - 2 q^{20} - 16 q^{21} + 24 q^{24} + 2 q^{25} + 32 q^{26} - 8 q^{30} - 12 q^{34} + 10 q^{35} + 24 q^{36} + 36 q^{39} + 34 q^{40} + 2 q^{45} - 56 q^{46} - 24 q^{49} + 46 q^{50} - 36 q^{51} + 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} - 40 q^{61} + 12 q^{64} + 10 q^{65} - 2 q^{70} + 64 q^{71} - 136 q^{74} + 20 q^{75} - 68 q^{76} + 64 q^{79} + 76 q^{80} + 24 q^{81} + 60 q^{84} - 72 q^{86} + 20 q^{89} + 6 q^{90} - 4 q^{94} + 64 q^{95} - 56 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.10651i 1.48953i −0.667328 0.744764i \(-0.732562\pi\)
0.667328 0.744764i \(-0.267438\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −2.43738 −1.21869
\(5\) −0.823234 + 2.07901i −0.368162 + 0.929762i
\(6\) −2.10651 −0.859979
\(7\) 3.31633i 1.25345i 0.779239 + 0.626727i \(0.215606\pi\)
−0.779239 + 0.626727i \(0.784394\pi\)
\(8\) 0.921348i 0.325746i
\(9\) −1.00000 −0.333333
\(10\) 4.37946 + 1.73415i 1.38491 + 0.548387i
\(11\) 0 0
\(12\) 2.43738i 0.703611i
\(13\) 2.49889i 0.693066i 0.938038 + 0.346533i \(0.112641\pi\)
−0.938038 + 0.346533i \(0.887359\pi\)
\(14\) 6.98587 1.86705
\(15\) 2.07901 + 0.823234i 0.536798 + 0.212558i
\(16\) −2.93393 −0.733484
\(17\) 6.81019i 1.65171i −0.563880 0.825857i \(-0.690692\pi\)
0.563880 0.825857i \(-0.309308\pi\)
\(18\) 2.10651i 0.496509i
\(19\) 1.14769 0.263299 0.131649 0.991296i \(-0.457973\pi\)
0.131649 + 0.991296i \(0.457973\pi\)
\(20\) 2.00654 5.06734i 0.448675 1.13309i
\(21\) 3.31633 0.723682
\(22\) 0 0
\(23\) 5.89026i 1.22820i −0.789226 0.614102i \(-0.789518\pi\)
0.789226 0.614102i \(-0.210482\pi\)
\(24\) 0.921348 0.188069
\(25\) −3.64457 3.42303i −0.728914 0.684605i
\(26\) 5.26393 1.03234
\(27\) 1.00000i 0.192450i
\(28\) 8.08315i 1.52757i
\(29\) 1.12257 0.208455 0.104228 0.994553i \(-0.466763\pi\)
0.104228 + 0.994553i \(0.466763\pi\)
\(30\) 1.73415 4.37946i 0.316611 0.799575i
\(31\) −1.09673 −0.196978 −0.0984892 0.995138i \(-0.531401\pi\)
−0.0984892 + 0.995138i \(0.531401\pi\)
\(32\) 8.02306i 1.41829i
\(33\) 0 0
\(34\) −14.3457 −2.46027
\(35\) −6.89468 2.73011i −1.16541 0.461473i
\(36\) 2.43738 0.406230
\(37\) 11.5389i 1.89698i −0.316810 0.948489i \(-0.602612\pi\)
0.316810 0.948489i \(-0.397388\pi\)
\(38\) 2.41763i 0.392191i
\(39\) 2.49889 0.400142
\(40\) −1.91549 0.758486i −0.302866 0.119927i
\(41\) −0.932568 −0.145643 −0.0728213 0.997345i \(-0.523200\pi\)
−0.0728213 + 0.997345i \(0.523200\pi\)
\(42\) 6.98587i 1.07794i
\(43\) 0.552188i 0.0842079i −0.999113 0.0421040i \(-0.986594\pi\)
0.999113 0.0421040i \(-0.0134061\pi\)
\(44\) 0 0
\(45\) 0.823234 2.07901i 0.122721 0.309921i
\(46\) −12.4079 −1.82944
\(47\) 2.13427i 0.311316i −0.987811 0.155658i \(-0.950250\pi\)
0.987811 0.155658i \(-0.0497497\pi\)
\(48\) 2.93393i 0.423477i
\(49\) −3.99802 −0.571146
\(50\) −7.21064 + 7.67732i −1.01974 + 1.08574i
\(51\) −6.81019 −0.953617
\(52\) 6.09074i 0.844633i
\(53\) 11.6356i 1.59827i −0.601150 0.799136i \(-0.705291\pi\)
0.601150 0.799136i \(-0.294709\pi\)
\(54\) 2.10651 0.286660
\(55\) 0 0
\(56\) −3.05549 −0.408307
\(57\) 1.14769i 0.152016i
\(58\) 2.36469i 0.310500i
\(59\) −8.39837 −1.09337 −0.546687 0.837337i \(-0.684111\pi\)
−0.546687 + 0.837337i \(0.684111\pi\)
\(60\) −5.06734 2.00654i −0.654191 0.259043i
\(61\) −8.21313 −1.05158 −0.525792 0.850613i \(-0.676231\pi\)
−0.525792 + 0.850613i \(0.676231\pi\)
\(62\) 2.31027i 0.293405i
\(63\) 3.31633i 0.417818i
\(64\) 11.0328 1.37910
\(65\) −5.19521 2.05717i −0.644386 0.255160i
\(66\) 0 0
\(67\) 4.15419i 0.507515i −0.967268 0.253757i \(-0.918334\pi\)
0.967268 0.253757i \(-0.0816665\pi\)
\(68\) 16.5990i 2.01293i
\(69\) −5.89026 −0.709104
\(70\) −5.75101 + 14.5237i −0.687377 + 1.73591i
\(71\) 12.5340 1.48752 0.743759 0.668448i \(-0.233041\pi\)
0.743759 + 0.668448i \(0.233041\pi\)
\(72\) 0.921348i 0.108582i
\(73\) 5.73761i 0.671537i 0.941945 + 0.335768i \(0.108996\pi\)
−0.941945 + 0.335768i \(0.891004\pi\)
\(74\) −24.3067 −2.82560
\(75\) −3.42303 + 3.64457i −0.395257 + 0.420839i
\(76\) −2.79736 −0.320880
\(77\) 0 0
\(78\) 5.26393i 0.596022i
\(79\) 3.86754 0.435132 0.217566 0.976046i \(-0.430188\pi\)
0.217566 + 0.976046i \(0.430188\pi\)
\(80\) 2.41532 6.09968i 0.270040 0.681965i
\(81\) 1.00000 0.111111
\(82\) 1.96446i 0.216939i
\(83\) 6.08055i 0.667427i 0.942675 + 0.333714i \(0.108302\pi\)
−0.942675 + 0.333714i \(0.891698\pi\)
\(84\) −8.08315 −0.881944
\(85\) 14.1585 + 5.60638i 1.53570 + 0.608097i
\(86\) −1.16319 −0.125430
\(87\) 1.12257i 0.120352i
\(88\) 0 0
\(89\) −12.5950 −1.33506 −0.667531 0.744582i \(-0.732649\pi\)
−0.667531 + 0.744582i \(0.732649\pi\)
\(90\) −4.37946 1.73415i −0.461635 0.182796i
\(91\) −8.28712 −0.868726
\(92\) 14.3568i 1.49680i
\(93\) 1.09673i 0.113726i
\(94\) −4.49586 −0.463713
\(95\) −0.944820 + 2.38607i −0.0969365 + 0.244805i
\(96\) 8.02306 0.818850
\(97\) 2.86873i 0.291275i −0.989338 0.145638i \(-0.953477\pi\)
0.989338 0.145638i \(-0.0465234\pi\)
\(98\) 8.42187i 0.850737i
\(99\) 0 0
\(100\) 8.88321 + 8.34322i 0.888321 + 0.834322i
\(101\) 9.87001 0.982103 0.491052 0.871131i \(-0.336613\pi\)
0.491052 + 0.871131i \(0.336613\pi\)
\(102\) 14.3457i 1.42044i
\(103\) 7.71953i 0.760628i −0.924857 0.380314i \(-0.875816\pi\)
0.924857 0.380314i \(-0.124184\pi\)
\(104\) −2.30234 −0.225763
\(105\) −2.73011 + 6.89468i −0.266432 + 0.672852i
\(106\) −24.5105 −2.38067
\(107\) 15.5114i 1.49954i −0.661697 0.749771i \(-0.730163\pi\)
0.661697 0.749771i \(-0.269837\pi\)
\(108\) 2.43738i 0.234537i
\(109\) −6.79834 −0.651163 −0.325581 0.945514i \(-0.605560\pi\)
−0.325581 + 0.945514i \(0.605560\pi\)
\(110\) 0 0
\(111\) −11.5389 −1.09522
\(112\) 9.72988i 0.919388i
\(113\) 0.301489i 0.0283617i 0.999899 + 0.0141808i \(0.00451405\pi\)
−0.999899 + 0.0141808i \(0.995486\pi\)
\(114\) −2.41763 −0.226431
\(115\) 12.2459 + 4.84907i 1.14194 + 0.452178i
\(116\) −2.73612 −0.254042
\(117\) 2.49889i 0.231022i
\(118\) 17.6912i 1.62861i
\(119\) 22.5848 2.07035
\(120\) −0.758486 + 1.91549i −0.0692399 + 0.174860i
\(121\) 0 0
\(122\) 17.3010i 1.56636i
\(123\) 0.932568i 0.0840868i
\(124\) 2.67315 0.240056
\(125\) 10.1168 4.75915i 0.904878 0.425671i
\(126\) −6.98587 −0.622351
\(127\) 6.70539i 0.595007i −0.954721 0.297504i \(-0.903846\pi\)
0.954721 0.297504i \(-0.0961540\pi\)
\(128\) 7.19453i 0.635913i
\(129\) −0.552188 −0.0486175
\(130\) −4.33344 + 10.9438i −0.380068 + 0.959831i
\(131\) −8.07729 −0.705716 −0.352858 0.935677i \(-0.614790\pi\)
−0.352858 + 0.935677i \(0.614790\pi\)
\(132\) 0 0
\(133\) 3.80612i 0.330033i
\(134\) −8.75084 −0.755957
\(135\) −2.07901 0.823234i −0.178933 0.0708527i
\(136\) 6.27456 0.538039
\(137\) 6.43781i 0.550020i −0.961441 0.275010i \(-0.911319\pi\)
0.961441 0.275010i \(-0.0886811\pi\)
\(138\) 12.4079i 1.05623i
\(139\) −6.97567 −0.591669 −0.295834 0.955239i \(-0.595598\pi\)
−0.295834 + 0.955239i \(0.595598\pi\)
\(140\) 16.8050 + 6.65433i 1.42028 + 0.562393i
\(141\) −2.13427 −0.179738
\(142\) 26.4031i 2.21570i
\(143\) 0 0
\(144\) 2.93393 0.244495
\(145\) −0.924135 + 2.33383i −0.0767452 + 0.193814i
\(146\) 12.0863 1.00027
\(147\) 3.99802i 0.329751i
\(148\) 28.1246i 2.31183i
\(149\) 19.0205 1.55822 0.779110 0.626887i \(-0.215671\pi\)
0.779110 + 0.626887i \(0.215671\pi\)
\(150\) 7.67732 + 7.21064i 0.626851 + 0.588746i
\(151\) 3.90081 0.317444 0.158722 0.987323i \(-0.449263\pi\)
0.158722 + 0.987323i \(0.449263\pi\)
\(152\) 1.05742i 0.0857685i
\(153\) 6.81019i 0.550571i
\(154\) 0 0
\(155\) 0.902865 2.28011i 0.0725199 0.183143i
\(156\) −6.09074 −0.487649
\(157\) 18.3843i 1.46723i −0.679568 0.733613i \(-0.737833\pi\)
0.679568 0.733613i \(-0.262167\pi\)
\(158\) 8.14701i 0.648141i
\(159\) −11.6356 −0.922763
\(160\) −16.6800 6.60486i −1.31867 0.522160i
\(161\) 19.5340 1.53950
\(162\) 2.10651i 0.165503i
\(163\) 17.5720i 1.37635i 0.725547 + 0.688173i \(0.241587\pi\)
−0.725547 + 0.688173i \(0.758413\pi\)
\(164\) 2.27302 0.177493
\(165\) 0 0
\(166\) 12.8087 0.994151
\(167\) 12.0777i 0.934598i −0.884099 0.467299i \(-0.845227\pi\)
0.884099 0.467299i \(-0.154773\pi\)
\(168\) 3.05549i 0.235736i
\(169\) 6.75557 0.519659
\(170\) 11.8099 29.8249i 0.905778 2.28747i
\(171\) −1.14769 −0.0877662
\(172\) 1.34589i 0.102623i
\(173\) 24.2436i 1.84321i 0.388133 + 0.921603i \(0.373120\pi\)
−0.388133 + 0.921603i \(0.626880\pi\)
\(174\) −2.36469 −0.179267
\(175\) 11.3519 12.0866i 0.858121 0.913660i
\(176\) 0 0
\(177\) 8.39837i 0.631260i
\(178\) 26.5314i 1.98861i
\(179\) 19.9390 1.49031 0.745155 0.666891i \(-0.232375\pi\)
0.745155 + 0.666891i \(0.232375\pi\)
\(180\) −2.00654 + 5.06734i −0.149558 + 0.377697i
\(181\) −5.13290 −0.381525 −0.190763 0.981636i \(-0.561096\pi\)
−0.190763 + 0.981636i \(0.561096\pi\)
\(182\) 17.4569i 1.29399i
\(183\) 8.21313i 0.607132i
\(184\) 5.42698 0.400082
\(185\) 23.9894 + 9.49919i 1.76374 + 0.698395i
\(186\) 2.31027 0.169397
\(187\) 0 0
\(188\) 5.20204i 0.379397i
\(189\) −3.31633 −0.241227
\(190\) 5.02627 + 1.99027i 0.364644 + 0.144390i
\(191\) −2.81336 −0.203568 −0.101784 0.994807i \(-0.532455\pi\)
−0.101784 + 0.994807i \(0.532455\pi\)
\(192\) 11.0328i 0.796222i
\(193\) 19.3032i 1.38948i 0.719263 + 0.694738i \(0.244480\pi\)
−0.719263 + 0.694738i \(0.755520\pi\)
\(194\) −6.04300 −0.433862
\(195\) −2.05717 + 5.19521i −0.147317 + 0.372037i
\(196\) 9.74470 0.696050
\(197\) 3.57956i 0.255033i 0.991836 + 0.127516i \(0.0407006\pi\)
−0.991836 + 0.127516i \(0.959299\pi\)
\(198\) 0 0
\(199\) −12.7087 −0.900893 −0.450447 0.892803i \(-0.648735\pi\)
−0.450447 + 0.892803i \(0.648735\pi\)
\(200\) 3.15380 3.35792i 0.223007 0.237441i
\(201\) −4.15419 −0.293014
\(202\) 20.7913i 1.46287i
\(203\) 3.72279i 0.261289i
\(204\) 16.5990 1.16216
\(205\) 0.767722 1.93882i 0.0536200 0.135413i
\(206\) −16.2613 −1.13298
\(207\) 5.89026i 0.409401i
\(208\) 7.33157i 0.508353i
\(209\) 0 0
\(210\) 14.5237 + 5.75101i 1.00223 + 0.396857i
\(211\) −3.49518 −0.240618 −0.120309 0.992736i \(-0.538389\pi\)
−0.120309 + 0.992736i \(0.538389\pi\)
\(212\) 28.3604i 1.94780i
\(213\) 12.5340i 0.858819i
\(214\) −32.6749 −2.23361
\(215\) 1.14801 + 0.454581i 0.0782933 + 0.0310021i
\(216\) −0.921348 −0.0626898
\(217\) 3.63711i 0.246903i
\(218\) 14.3208i 0.969925i
\(219\) 5.73761 0.387712
\(220\) 0 0
\(221\) 17.0179 1.14475
\(222\) 24.3067i 1.63136i
\(223\) 5.20558i 0.348591i 0.984693 + 0.174296i \(0.0557648\pi\)
−0.984693 + 0.174296i \(0.944235\pi\)
\(224\) −26.6071 −1.77776
\(225\) 3.64457 + 3.42303i 0.242971 + 0.228202i
\(226\) 0.635089 0.0422455
\(227\) 9.70244i 0.643973i −0.946744 0.321987i \(-0.895649\pi\)
0.946744 0.321987i \(-0.104351\pi\)
\(228\) 2.79736i 0.185260i
\(229\) −18.5011 −1.22259 −0.611293 0.791404i \(-0.709350\pi\)
−0.611293 + 0.791404i \(0.709350\pi\)
\(230\) 10.2146 25.7961i 0.673531 1.70095i
\(231\) 0 0
\(232\) 1.03427i 0.0679034i
\(233\) 14.9543i 0.979692i −0.871809 0.489846i \(-0.837053\pi\)
0.871809 0.489846i \(-0.162947\pi\)
\(234\) −5.26393 −0.344114
\(235\) 4.43717 + 1.75701i 0.289449 + 0.114614i
\(236\) 20.4700 1.33249
\(237\) 3.86754i 0.251224i
\(238\) 47.5751i 3.08384i
\(239\) 1.50716 0.0974901 0.0487451 0.998811i \(-0.484478\pi\)
0.0487451 + 0.998811i \(0.484478\pi\)
\(240\) −6.09968 2.41532i −0.393733 0.155908i
\(241\) −7.09571 −0.457075 −0.228537 0.973535i \(-0.573394\pi\)
−0.228537 + 0.973535i \(0.573394\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 20.0185 1.28156
\(245\) 3.29131 8.31193i 0.210274 0.531029i
\(246\) 1.96446 0.125250
\(247\) 2.86795i 0.182483i
\(248\) 1.01047i 0.0641649i
\(249\) 6.08055 0.385339
\(250\) −10.0252 21.3112i −0.634049 1.34784i
\(251\) −13.6786 −0.863386 −0.431693 0.902021i \(-0.642084\pi\)
−0.431693 + 0.902021i \(0.642084\pi\)
\(252\) 8.08315i 0.509191i
\(253\) 0 0
\(254\) −14.1250 −0.886279
\(255\) 5.60638 14.1585i 0.351085 0.886637i
\(256\) 6.91021 0.431888
\(257\) 8.30411i 0.517996i 0.965878 + 0.258998i \(0.0833924\pi\)
−0.965878 + 0.258998i \(0.916608\pi\)
\(258\) 1.16319i 0.0724171i
\(259\) 38.2667 2.37777
\(260\) 12.6627 + 5.01410i 0.785308 + 0.310962i
\(261\) −1.12257 −0.0694851
\(262\) 17.0149i 1.05118i
\(263\) 11.1345i 0.686582i 0.939229 + 0.343291i \(0.111542\pi\)
−0.939229 + 0.343291i \(0.888458\pi\)
\(264\) 0 0
\(265\) 24.1905 + 9.57882i 1.48601 + 0.588422i
\(266\) 8.01763 0.491593
\(267\) 12.5950i 0.770799i
\(268\) 10.1253i 0.618504i
\(269\) −22.7563 −1.38748 −0.693739 0.720227i \(-0.744038\pi\)
−0.693739 + 0.720227i \(0.744038\pi\)
\(270\) −1.73415 + 4.37946i −0.105537 + 0.266525i
\(271\) 7.79448 0.473481 0.236740 0.971573i \(-0.423921\pi\)
0.236740 + 0.971573i \(0.423921\pi\)
\(272\) 19.9806i 1.21150i
\(273\) 8.28712i 0.501559i
\(274\) −13.5613 −0.819269
\(275\) 0 0
\(276\) 14.3568 0.864179
\(277\) 9.46719i 0.568828i −0.958702 0.284414i \(-0.908201\pi\)
0.958702 0.284414i \(-0.0917991\pi\)
\(278\) 14.6943i 0.881307i
\(279\) 1.09673 0.0656595
\(280\) 2.51539 6.35240i 0.150323 0.379628i
\(281\) 31.3016 1.86729 0.933647 0.358194i \(-0.116607\pi\)
0.933647 + 0.358194i \(0.116607\pi\)
\(282\) 4.49586i 0.267725i
\(283\) 24.4123i 1.45116i −0.688136 0.725581i \(-0.741571\pi\)
0.688136 0.725581i \(-0.258429\pi\)
\(284\) −30.5503 −1.81282
\(285\) 2.38607 + 0.944820i 0.141338 + 0.0559663i
\(286\) 0 0
\(287\) 3.09270i 0.182556i
\(288\) 8.02306i 0.472763i
\(289\) −29.3787 −1.72816
\(290\) 4.91623 + 1.94670i 0.288691 + 0.114314i
\(291\) −2.86873 −0.168168
\(292\) 13.9847i 0.818395i
\(293\) 11.8197i 0.690512i 0.938509 + 0.345256i \(0.112208\pi\)
−0.938509 + 0.345256i \(0.887792\pi\)
\(294\) 8.42187 0.491173
\(295\) 6.91383 17.4603i 0.402539 1.01658i
\(296\) 10.6313 0.617933
\(297\) 0 0
\(298\) 40.0669i 2.32101i
\(299\) 14.7191 0.851227
\(300\) 8.34322 8.88321i 0.481696 0.512872i
\(301\) 1.83124 0.105551
\(302\) 8.21710i 0.472841i
\(303\) 9.87001i 0.567018i
\(304\) −3.36725 −0.193125
\(305\) 6.76133 17.0752i 0.387153 0.977723i
\(306\) 14.3457 0.820091
\(307\) 22.3217i 1.27396i −0.770878 0.636982i \(-0.780182\pi\)
0.770878 0.636982i \(-0.219818\pi\)
\(308\) 0 0
\(309\) −7.71953 −0.439149
\(310\) −4.80308 1.90189i −0.272796 0.108020i
\(311\) −19.4834 −1.10480 −0.552401 0.833578i \(-0.686288\pi\)
−0.552401 + 0.833578i \(0.686288\pi\)
\(312\) 2.30234i 0.130345i
\(313\) 17.3527i 0.980833i 0.871488 + 0.490416i \(0.163155\pi\)
−0.871488 + 0.490416i \(0.836845\pi\)
\(314\) −38.7267 −2.18547
\(315\) 6.89468 + 2.73011i 0.388471 + 0.153824i
\(316\) −9.42667 −0.530292
\(317\) 0.830717i 0.0466577i −0.999728 0.0233289i \(-0.992574\pi\)
0.999728 0.0233289i \(-0.00742648\pi\)
\(318\) 24.5105i 1.37448i
\(319\) 0 0
\(320\) −9.08256 + 22.9373i −0.507731 + 1.28223i
\(321\) −15.5114 −0.865762
\(322\) 41.1486i 2.29312i
\(323\) 7.81600i 0.434894i
\(324\) −2.43738 −0.135410
\(325\) 8.55375 9.10736i 0.474477 0.505186i
\(326\) 37.0156 2.05010
\(327\) 6.79834i 0.375949i
\(328\) 0.859219i 0.0474425i
\(329\) 7.07794 0.390220
\(330\) 0 0
\(331\) −31.5311 −1.73311 −0.866554 0.499084i \(-0.833670\pi\)
−0.866554 + 0.499084i \(0.833670\pi\)
\(332\) 14.8206i 0.813387i
\(333\) 11.5389i 0.632326i
\(334\) −25.4417 −1.39211
\(335\) 8.63660 + 3.41987i 0.471868 + 0.186847i
\(336\) −9.72988 −0.530809
\(337\) 16.2339i 0.884319i 0.896936 + 0.442160i \(0.145788\pi\)
−0.896936 + 0.442160i \(0.854212\pi\)
\(338\) 14.2307i 0.774047i
\(339\) 0.301489 0.0163746
\(340\) −34.5096 13.6649i −1.87154 0.741083i
\(341\) 0 0
\(342\) 2.41763i 0.130730i
\(343\) 9.95555i 0.537549i
\(344\) 0.508758 0.0274304
\(345\) 4.84907 12.2459i 0.261065 0.659298i
\(346\) 51.0694 2.74551
\(347\) 12.4500i 0.668350i 0.942511 + 0.334175i \(0.108458\pi\)
−0.942511 + 0.334175i \(0.891542\pi\)
\(348\) 2.73612i 0.146671i
\(349\) −32.6297 −1.74663 −0.873314 0.487157i \(-0.838034\pi\)
−0.873314 + 0.487157i \(0.838034\pi\)
\(350\) −25.4605 23.9128i −1.36092 1.27819i
\(351\) −2.49889 −0.133381
\(352\) 0 0
\(353\) 15.7921i 0.840530i −0.907402 0.420265i \(-0.861937\pi\)
0.907402 0.420265i \(-0.138063\pi\)
\(354\) 17.6912 0.940279
\(355\) −10.3185 + 26.0584i −0.547647 + 1.38304i
\(356\) 30.6987 1.62703
\(357\) 22.5848i 1.19531i
\(358\) 42.0017i 2.21986i
\(359\) −18.1622 −0.958563 −0.479282 0.877661i \(-0.659103\pi\)
−0.479282 + 0.877661i \(0.659103\pi\)
\(360\) 1.91549 + 0.758486i 0.100955 + 0.0399757i
\(361\) −17.6828 −0.930674
\(362\) 10.8125i 0.568292i
\(363\) 0 0
\(364\) 20.1989 1.05871
\(365\) −11.9286 4.72340i −0.624369 0.247234i
\(366\) 17.3010 0.904340
\(367\) 0.472046i 0.0246406i 0.999924 + 0.0123203i \(0.00392177\pi\)
−0.999924 + 0.0123203i \(0.996078\pi\)
\(368\) 17.2816i 0.900868i
\(369\) 0.932568 0.0485475
\(370\) 20.0101 50.5340i 1.04028 2.62714i
\(371\) 38.5874 2.00336
\(372\) 2.67315i 0.138596i
\(373\) 15.4102i 0.797910i 0.916970 + 0.398955i \(0.130627\pi\)
−0.916970 + 0.398955i \(0.869373\pi\)
\(374\) 0 0
\(375\) −4.75915 10.1168i −0.245761 0.522432i
\(376\) 1.96641 0.101410
\(377\) 2.80516i 0.144473i
\(378\) 6.98587i 0.359314i
\(379\) 19.2746 0.990068 0.495034 0.868874i \(-0.335156\pi\)
0.495034 + 0.868874i \(0.335156\pi\)
\(380\) 2.30289 5.81575i 0.118136 0.298342i
\(381\) −6.70539 −0.343527
\(382\) 5.92637i 0.303220i
\(383\) 7.44824i 0.380587i −0.981727 0.190294i \(-0.939056\pi\)
0.981727 0.190294i \(-0.0609440\pi\)
\(384\) −7.19453 −0.367144
\(385\) 0 0
\(386\) 40.6624 2.06966
\(387\) 0.552188i 0.0280693i
\(388\) 6.99218i 0.354974i
\(389\) 0.713819 0.0361921 0.0180960 0.999836i \(-0.494240\pi\)
0.0180960 + 0.999836i \(0.494240\pi\)
\(390\) 10.9438 + 4.33344i 0.554159 + 0.219432i
\(391\) −40.1138 −2.02864
\(392\) 3.68357i 0.186048i
\(393\) 8.07729i 0.407446i
\(394\) 7.54037 0.379878
\(395\) −3.18389 + 8.04066i −0.160199 + 0.404569i
\(396\) 0 0
\(397\) 0.764171i 0.0383526i 0.999816 + 0.0191763i \(0.00610438\pi\)
−0.999816 + 0.0191763i \(0.993896\pi\)
\(398\) 26.7709i 1.34191i
\(399\) 3.80612 0.190544
\(400\) 10.6929 + 10.0429i 0.534646 + 0.502147i
\(401\) −15.7544 −0.786740 −0.393370 0.919380i \(-0.628691\pi\)
−0.393370 + 0.919380i \(0.628691\pi\)
\(402\) 8.75084i 0.436452i
\(403\) 2.74060i 0.136519i
\(404\) −24.0570 −1.19688
\(405\) −0.823234 + 2.07901i −0.0409068 + 0.103307i
\(406\) 7.84210 0.389197
\(407\) 0 0
\(408\) 6.27456i 0.310637i
\(409\) 2.62100 0.129600 0.0648001 0.997898i \(-0.479359\pi\)
0.0648001 + 0.997898i \(0.479359\pi\)
\(410\) −4.08414 1.61721i −0.201701 0.0798684i
\(411\) −6.43781 −0.317554
\(412\) 18.8154i 0.926970i
\(413\) 27.8517i 1.37049i
\(414\) 12.4079 0.609815
\(415\) −12.6415 5.00572i −0.620548 0.245721i
\(416\) −20.0487 −0.982968
\(417\) 6.97567i 0.341600i
\(418\) 0 0
\(419\) 18.0078 0.879737 0.439868 0.898062i \(-0.355025\pi\)
0.439868 + 0.898062i \(0.355025\pi\)
\(420\) 6.65433 16.8050i 0.324698 0.819998i
\(421\) 1.17117 0.0570792 0.0285396 0.999593i \(-0.490914\pi\)
0.0285396 + 0.999593i \(0.490914\pi\)
\(422\) 7.36264i 0.358408i
\(423\) 2.13427i 0.103772i
\(424\) 10.7204 0.520630
\(425\) −23.3115 + 24.8202i −1.13077 + 1.20396i
\(426\) −26.4031 −1.27923
\(427\) 27.2374i 1.31811i
\(428\) 37.8072i 1.82748i
\(429\) 0 0
\(430\) 0.957578 2.41828i 0.0461785 0.116620i
\(431\) 35.0921 1.69033 0.845163 0.534508i \(-0.179503\pi\)
0.845163 + 0.534508i \(0.179503\pi\)
\(432\) 2.93393i 0.141159i
\(433\) 18.2260i 0.875888i 0.899002 + 0.437944i \(0.144293\pi\)
−0.899002 + 0.437944i \(0.855707\pi\)
\(434\) −7.66161 −0.367769
\(435\) 2.33383 + 0.924135i 0.111898 + 0.0443089i
\(436\) 16.5701 0.793566
\(437\) 6.76021i 0.323385i
\(438\) 12.0863i 0.577507i
\(439\) 19.8155 0.945743 0.472871 0.881131i \(-0.343218\pi\)
0.472871 + 0.881131i \(0.343218\pi\)
\(440\) 0 0
\(441\) 3.99802 0.190382
\(442\) 35.8483i 1.70513i
\(443\) 16.6884i 0.792892i −0.918058 0.396446i \(-0.870243\pi\)
0.918058 0.396446i \(-0.129757\pi\)
\(444\) 28.1246 1.33474
\(445\) 10.3686 26.1850i 0.491519 1.24129i
\(446\) 10.9656 0.519236
\(447\) 19.0205i 0.899639i
\(448\) 36.5883i 1.72863i
\(449\) 13.1971 0.622808 0.311404 0.950278i \(-0.399201\pi\)
0.311404 + 0.950278i \(0.399201\pi\)
\(450\) 7.21064 7.67732i 0.339913 0.361912i
\(451\) 0 0
\(452\) 0.734843i 0.0345641i
\(453\) 3.90081i 0.183276i
\(454\) −20.4383 −0.959216
\(455\) 6.82224 17.2290i 0.319832 0.807708i
\(456\) 1.05742 0.0495184
\(457\) 21.2673i 0.994840i 0.867510 + 0.497420i \(0.165719\pi\)
−0.867510 + 0.497420i \(0.834281\pi\)
\(458\) 38.9727i 1.82107i
\(459\) 6.81019 0.317872
\(460\) −29.8480 11.8190i −1.39167 0.551065i
\(461\) −20.0772 −0.935086 −0.467543 0.883970i \(-0.654861\pi\)
−0.467543 + 0.883970i \(0.654861\pi\)
\(462\) 0 0
\(463\) 0.962526i 0.0447324i 0.999750 + 0.0223662i \(0.00711997\pi\)
−0.999750 + 0.0223662i \(0.992880\pi\)
\(464\) −3.29353 −0.152898
\(465\) −2.28011 0.902865i −0.105738 0.0418694i
\(466\) −31.5015 −1.45928
\(467\) 14.9130i 0.690092i −0.938586 0.345046i \(-0.887863\pi\)
0.938586 0.345046i \(-0.112137\pi\)
\(468\) 6.09074i 0.281544i
\(469\) 13.7766 0.636146
\(470\) 3.70115 9.34695i 0.170721 0.431143i
\(471\) −18.3843 −0.847103
\(472\) 7.73783i 0.356162i
\(473\) 0 0
\(474\) −8.14701 −0.374204
\(475\) −4.18285 3.92858i −0.191922 0.180256i
\(476\) −55.0478 −2.52311
\(477\) 11.6356i 0.532757i
\(478\) 3.17485i 0.145214i
\(479\) 0.475527 0.0217274 0.0108637 0.999941i \(-0.496542\pi\)
0.0108637 + 0.999941i \(0.496542\pi\)
\(480\) −6.60486 + 16.6800i −0.301469 + 0.761335i
\(481\) 28.8343 1.31473
\(482\) 14.9472i 0.680825i
\(483\) 19.5340i 0.888829i
\(484\) 0 0
\(485\) 5.96412 + 2.36164i 0.270817 + 0.107236i
\(486\) −2.10651 −0.0955532
\(487\) 35.3529i 1.60199i −0.598668 0.800997i \(-0.704303\pi\)
0.598668 0.800997i \(-0.295697\pi\)
\(488\) 7.56716i 0.342549i
\(489\) 17.5720 0.794634
\(490\) −17.5091 6.93317i −0.790983 0.313209i
\(491\) −30.1328 −1.35987 −0.679937 0.733271i \(-0.737993\pi\)
−0.679937 + 0.733271i \(0.737993\pi\)
\(492\) 2.27302i 0.102476i
\(493\) 7.64488i 0.344308i
\(494\) 6.04137 0.271814
\(495\) 0 0
\(496\) 3.21773 0.144480
\(497\) 41.5670i 1.86453i
\(498\) 12.8087i 0.573973i
\(499\) 36.4797 1.63306 0.816528 0.577305i \(-0.195896\pi\)
0.816528 + 0.577305i \(0.195896\pi\)
\(500\) −24.6586 + 11.5999i −1.10277 + 0.518761i
\(501\) −12.0777 −0.539590
\(502\) 28.8141i 1.28604i
\(503\) 15.4251i 0.687772i −0.939011 0.343886i \(-0.888257\pi\)
0.939011 0.343886i \(-0.111743\pi\)
\(504\) 3.05549 0.136102
\(505\) −8.12534 + 20.5199i −0.361573 + 0.913122i
\(506\) 0 0
\(507\) 6.75557i 0.300025i
\(508\) 16.3436i 0.725130i
\(509\) −12.6374 −0.560142 −0.280071 0.959979i \(-0.590358\pi\)
−0.280071 + 0.959979i \(0.590358\pi\)
\(510\) −29.8249 11.8099i −1.32067 0.522951i
\(511\) −19.0278 −0.841740
\(512\) 28.9455i 1.27922i
\(513\) 1.14769i 0.0506719i
\(514\) 17.4927 0.771570
\(515\) 16.0490 + 6.35498i 0.707203 + 0.280034i
\(516\) 1.34589 0.0592497
\(517\) 0 0
\(518\) 80.6091i 3.54176i
\(519\) 24.2436 1.06418
\(520\) 1.89537 4.78660i 0.0831174 0.209906i
\(521\) −9.18439 −0.402376 −0.201188 0.979553i \(-0.564480\pi\)
−0.201188 + 0.979553i \(0.564480\pi\)
\(522\) 2.36469i 0.103500i
\(523\) 33.5841i 1.46853i −0.678863 0.734265i \(-0.737527\pi\)
0.678863 0.734265i \(-0.262473\pi\)
\(524\) 19.6874 0.860050
\(525\) −12.0866 11.3519i −0.527502 0.495436i
\(526\) 23.4549 1.02268
\(527\) 7.46893i 0.325352i
\(528\) 0 0
\(529\) −11.6952 −0.508486
\(530\) 20.1779 50.9576i 0.876471 2.21346i
\(531\) 8.39837 0.364458
\(532\) 9.27697i 0.402208i
\(533\) 2.33038i 0.100940i
\(534\) 26.5314 1.14813
\(535\) 32.2484 + 12.7695i 1.39422 + 0.552074i
\(536\) 3.82745 0.165321
\(537\) 19.9390i 0.860431i
\(538\) 47.9364i 2.06669i
\(539\) 0 0
\(540\) 5.06734 + 2.00654i 0.218064 + 0.0863476i
\(541\) 44.6024 1.91761 0.958803 0.284072i \(-0.0916855\pi\)
0.958803 + 0.284072i \(0.0916855\pi\)
\(542\) 16.4191i 0.705262i
\(543\) 5.13290i 0.220274i
\(544\) 54.6385 2.34261
\(545\) 5.59663 14.1338i 0.239733 0.605426i
\(546\) 17.4569 0.747086
\(547\) 19.2310i 0.822256i 0.911578 + 0.411128i \(0.134865\pi\)
−0.911578 + 0.411128i \(0.865135\pi\)
\(548\) 15.6914i 0.670304i
\(549\) 8.21313 0.350528
\(550\) 0 0
\(551\) 1.28836 0.0548860
\(552\) 5.42698i 0.230988i
\(553\) 12.8260i 0.545418i
\(554\) −19.9427 −0.847285
\(555\) 9.49919 23.9894i 0.403218 1.01829i
\(556\) 17.0024 0.721061
\(557\) 33.3669i 1.41380i −0.707314 0.706900i \(-0.750093\pi\)
0.707314 0.706900i \(-0.249907\pi\)
\(558\) 2.31027i 0.0978016i
\(559\) 1.37986 0.0583617
\(560\) 20.2285 + 8.00997i 0.854811 + 0.338483i
\(561\) 0 0
\(562\) 65.9370i 2.78139i
\(563\) 2.09215i 0.0881735i 0.999028 + 0.0440868i \(0.0140378\pi\)
−0.999028 + 0.0440868i \(0.985962\pi\)
\(564\) 5.20204 0.219045
\(565\) −0.626798 0.248196i −0.0263696 0.0104417i
\(566\) −51.4248 −2.16155
\(567\) 3.31633i 0.139273i
\(568\) 11.5482i 0.484553i
\(569\) 9.31615 0.390553 0.195277 0.980748i \(-0.437439\pi\)
0.195277 + 0.980748i \(0.437439\pi\)
\(570\) 1.99027 5.02627i 0.0833633 0.210527i
\(571\) 2.32989 0.0975029 0.0487514 0.998811i \(-0.484476\pi\)
0.0487514 + 0.998811i \(0.484476\pi\)
\(572\) 0 0
\(573\) 2.81336i 0.117530i
\(574\) −6.51480 −0.271922
\(575\) −20.1625 + 21.4675i −0.840835 + 0.895255i
\(576\) −11.0328 −0.459699
\(577\) 29.4627i 1.22655i 0.789869 + 0.613275i \(0.210148\pi\)
−0.789869 + 0.613275i \(0.789852\pi\)
\(578\) 61.8864i 2.57414i
\(579\) 19.3032 0.802214
\(580\) 2.25247 5.68842i 0.0935287 0.236199i
\(581\) −20.1651 −0.836589
\(582\) 6.04300i 0.250491i
\(583\) 0 0
\(584\) −5.28634 −0.218750
\(585\) 5.19521 + 2.05717i 0.214795 + 0.0850534i
\(586\) 24.8982 1.02854
\(587\) 41.5167i 1.71358i 0.515667 + 0.856789i \(0.327544\pi\)
−0.515667 + 0.856789i \(0.672456\pi\)
\(588\) 9.74470i 0.401865i
\(589\) −1.25871 −0.0518642
\(590\) −36.7803 14.5640i −1.51422 0.599592i
\(591\) 3.57956 0.147243
\(592\) 33.8543i 1.39140i
\(593\) 9.36964i 0.384765i −0.981320 0.192383i \(-0.938379\pi\)
0.981320 0.192383i \(-0.0616214\pi\)
\(594\) 0 0
\(595\) −18.5926 + 46.9541i −0.762222 + 1.92493i
\(596\) −46.3602 −1.89899
\(597\) 12.7087i 0.520131i
\(598\) 31.0059i 1.26793i
\(599\) −1.31702 −0.0538122 −0.0269061 0.999638i \(-0.508566\pi\)
−0.0269061 + 0.999638i \(0.508566\pi\)
\(600\) −3.35792 3.15380i −0.137086 0.128753i
\(601\) 15.6267 0.637425 0.318713 0.947851i \(-0.396750\pi\)
0.318713 + 0.947851i \(0.396750\pi\)
\(602\) 3.85752i 0.157221i
\(603\) 4.15419i 0.169172i
\(604\) −9.50777 −0.386866
\(605\) 0 0
\(606\) −20.7913 −0.844588
\(607\) 24.2123i 0.982746i −0.870949 0.491373i \(-0.836495\pi\)
0.870949 0.491373i \(-0.163505\pi\)
\(608\) 9.20800i 0.373434i
\(609\) 3.72279 0.150855
\(610\) −35.9691 14.2428i −1.45634 0.576675i
\(611\) 5.33330 0.215762
\(612\) 16.5990i 0.670976i
\(613\) 4.08630i 0.165044i 0.996589 + 0.0825221i \(0.0262975\pi\)
−0.996589 + 0.0825221i \(0.973702\pi\)
\(614\) −47.0208 −1.89760
\(615\) −1.93882 0.767722i −0.0781807 0.0309575i
\(616\) 0 0
\(617\) 16.9835i 0.683731i −0.939749 0.341866i \(-0.888941\pi\)
0.939749 0.341866i \(-0.111059\pi\)
\(618\) 16.2613i 0.654124i
\(619\) 32.1306 1.29144 0.645720 0.763575i \(-0.276558\pi\)
0.645720 + 0.763575i \(0.276558\pi\)
\(620\) −2.20063 + 5.55750i −0.0883793 + 0.223195i
\(621\) 5.89026 0.236368
\(622\) 41.0420i 1.64563i
\(623\) 41.7690i 1.67344i
\(624\) −7.33157 −0.293498
\(625\) 1.56579 + 24.9509i 0.0626314 + 0.998037i
\(626\) 36.5536 1.46098
\(627\) 0 0
\(628\) 44.8095i 1.78809i
\(629\) −78.5819 −3.13326
\(630\) 5.75101 14.5237i 0.229126 0.578638i
\(631\) −6.31566 −0.251422 −0.125711 0.992067i \(-0.540121\pi\)
−0.125711 + 0.992067i \(0.540121\pi\)
\(632\) 3.56335i 0.141742i
\(633\) 3.49518i 0.138921i
\(634\) −1.74991 −0.0694980
\(635\) 13.9406 + 5.52011i 0.553215 + 0.219059i
\(636\) 28.3604 1.12456
\(637\) 9.99059i 0.395842i
\(638\) 0 0
\(639\) −12.5340 −0.495839
\(640\) 14.9575 + 5.92278i 0.591247 + 0.234119i
\(641\) 14.6862 0.580072 0.290036 0.957016i \(-0.406333\pi\)
0.290036 + 0.957016i \(0.406333\pi\)
\(642\) 32.6749i 1.28958i
\(643\) 16.1510i 0.636933i −0.947934 0.318467i \(-0.896832\pi\)
0.947934 0.318467i \(-0.103168\pi\)
\(644\) −47.6119 −1.87617
\(645\) 0.454581 1.14801i 0.0178991 0.0452027i
\(646\) −16.4645 −0.647786
\(647\) 27.7874i 1.09243i −0.837644 0.546217i \(-0.816067\pi\)
0.837644 0.546217i \(-0.183933\pi\)
\(648\) 0.921348i 0.0361940i
\(649\) 0 0
\(650\) −19.1847 18.0186i −0.752488 0.706746i
\(651\) −3.63711 −0.142550
\(652\) 42.8297i 1.67734i
\(653\) 34.0655i 1.33309i −0.745467 0.666543i \(-0.767773\pi\)
0.745467 0.666543i \(-0.232227\pi\)
\(654\) 14.3208 0.559986
\(655\) 6.64951 16.7928i 0.259818 0.656148i
\(656\) 2.73609 0.106826
\(657\) 5.73761i 0.223846i
\(658\) 14.9098i 0.581243i
\(659\) −14.4196 −0.561709 −0.280855 0.959750i \(-0.590618\pi\)
−0.280855 + 0.959750i \(0.590618\pi\)
\(660\) 0 0
\(661\) 26.4275 1.02791 0.513956 0.857817i \(-0.328179\pi\)
0.513956 + 0.857817i \(0.328179\pi\)
\(662\) 66.4206i 2.58151i
\(663\) 17.0179i 0.660920i
\(664\) −5.60231 −0.217412
\(665\) −7.91297 3.13333i −0.306852 0.121505i
\(666\) 24.3067 0.941867
\(667\) 6.61220i 0.256026i
\(668\) 29.4379i 1.13899i
\(669\) 5.20558 0.201259
\(670\) 7.20399 18.1931i 0.278314 0.702860i
\(671\) 0 0
\(672\) 26.6071i 1.02639i
\(673\) 36.3130i 1.39976i 0.714260 + 0.699881i \(0.246764\pi\)
−0.714260 + 0.699881i \(0.753236\pi\)
\(674\) 34.1970 1.31722
\(675\) 3.42303 3.64457i 0.131752 0.140280i
\(676\) −16.4659 −0.633304
\(677\) 11.3442i 0.435994i −0.975949 0.217997i \(-0.930048\pi\)
0.975949 0.217997i \(-0.0699523\pi\)
\(678\) 0.635089i 0.0243904i
\(679\) 9.51364 0.365100
\(680\) −5.16543 + 13.0449i −0.198085 + 0.500248i
\(681\) −9.70244 −0.371798
\(682\) 0 0
\(683\) 39.4269i 1.50863i 0.656514 + 0.754314i \(0.272030\pi\)
−0.656514 + 0.754314i \(0.727970\pi\)
\(684\) 2.79736 0.106960
\(685\) 13.3843 + 5.29983i 0.511387 + 0.202496i
\(686\) 20.9715 0.800694
\(687\) 18.5011i 0.705860i
\(688\) 1.62008i 0.0617651i
\(689\) 29.0760 1.10771
\(690\) −25.7961 10.2146i −0.982042 0.388863i
\(691\) 14.7763 0.562118 0.281059 0.959691i \(-0.409314\pi\)
0.281059 + 0.959691i \(0.409314\pi\)
\(692\) 59.0909i 2.24630i
\(693\) 0 0
\(694\) 26.2260 0.995526
\(695\) 5.74261 14.5025i 0.217830 0.550111i
\(696\) 1.03427 0.0392040
\(697\) 6.35096i 0.240560i
\(698\) 68.7348i 2.60165i
\(699\) −14.9543 −0.565625
\(700\) −27.6688 + 29.4596i −1.04578 + 1.11347i
\(701\) −7.12932 −0.269271 −0.134635 0.990895i \(-0.542986\pi\)
−0.134635 + 0.990895i \(0.542986\pi\)
\(702\) 5.26393i 0.198674i
\(703\) 13.2431i 0.499472i
\(704\) 0 0
\(705\) 1.75701 4.43717i 0.0661727 0.167114i
\(706\) −33.2662 −1.25199
\(707\) 32.7322i 1.23102i
\(708\) 20.4700i 0.769311i
\(709\) 5.35482 0.201104 0.100552 0.994932i \(-0.467939\pi\)
0.100552 + 0.994932i \(0.467939\pi\)
\(710\) 54.8923 + 21.7359i 2.06007 + 0.815735i
\(711\) −3.86754 −0.145044
\(712\) 11.6043i 0.434891i
\(713\) 6.46002i 0.241930i
\(714\) −47.5751 −1.78045
\(715\) 0 0
\(716\) −48.5989 −1.81623
\(717\) 1.50716i 0.0562860i
\(718\) 38.2588i 1.42781i
\(719\) 40.7829 1.52095 0.760473 0.649370i \(-0.224967\pi\)
0.760473 + 0.649370i \(0.224967\pi\)
\(720\) −2.41532 + 6.09968i −0.0900135 + 0.227322i
\(721\) 25.6005 0.953412
\(722\) 37.2490i 1.38626i
\(723\) 7.09571i 0.263892i
\(724\) 12.5108 0.464961
\(725\) −4.09127 3.84257i −0.151946 0.142710i
\(726\) 0 0
\(727\) 28.6101i 1.06109i 0.847656 + 0.530546i \(0.178013\pi\)
−0.847656 + 0.530546i \(0.821987\pi\)
\(728\) 7.63532i 0.282984i
\(729\) −1.00000 −0.0370370
\(730\) −9.94988 + 25.1276i −0.368262 + 0.930015i
\(731\) −3.76051 −0.139087
\(732\) 20.0185i 0.739907i
\(733\) 4.39612i 0.162374i 0.996699 + 0.0811871i \(0.0258711\pi\)
−0.996699 + 0.0811871i \(0.974129\pi\)
\(734\) 0.994370 0.0367029
\(735\) −8.31193 3.29131i −0.306590 0.121402i
\(736\) 47.2579 1.74195
\(737\) 0 0
\(738\) 1.96446i 0.0723129i
\(739\) 10.5172 0.386882 0.193441 0.981112i \(-0.438035\pi\)
0.193441 + 0.981112i \(0.438035\pi\)
\(740\) −58.4714 23.1532i −2.14945 0.851127i
\(741\) 2.86795 0.105357
\(742\) 81.2848i 2.98406i
\(743\) 34.4901i 1.26532i −0.774431 0.632659i \(-0.781964\pi\)
0.774431 0.632659i \(-0.218036\pi\)
\(744\) −1.01047 −0.0370456
\(745\) −15.6583 + 39.5438i −0.573677 + 1.44877i
\(746\) 32.4617 1.18851
\(747\) 6.08055i 0.222476i
\(748\) 0 0
\(749\) 51.4408 1.87961
\(750\) −21.3112 + 10.0252i −0.778176 + 0.366068i
\(751\) −2.38104 −0.0868854 −0.0434427 0.999056i \(-0.513833\pi\)
−0.0434427 + 0.999056i \(0.513833\pi\)
\(752\) 6.26181i 0.228345i
\(753\) 13.6786i 0.498476i
\(754\) 5.90910 0.215197
\(755\) −3.21128 + 8.10983i −0.116871 + 0.295147i
\(756\) 8.08315 0.293981
\(757\) 8.39549i 0.305139i 0.988293 + 0.152570i \(0.0487548\pi\)
−0.988293 + 0.152570i \(0.951245\pi\)
\(758\) 40.6021i 1.47473i
\(759\) 0 0
\(760\) −2.19840 0.870508i −0.0797442 0.0315767i
\(761\) 10.4681 0.379467 0.189734 0.981836i \(-0.439238\pi\)
0.189734 + 0.981836i \(0.439238\pi\)
\(762\) 14.1250i 0.511693i
\(763\) 22.5455i 0.816202i
\(764\) 6.85724 0.248086
\(765\) −14.1585 5.60638i −0.511900 0.202699i
\(766\) −15.6898 −0.566895
\(767\) 20.9866i 0.757781i
\(768\) 6.91021i 0.249351i
\(769\) 9.70799 0.350079 0.175040 0.984561i \(-0.443995\pi\)
0.175040 + 0.984561i \(0.443995\pi\)
\(770\) 0 0
\(771\) 8.30411 0.299065
\(772\) 47.0493i 1.69334i
\(773\) 31.9598i 1.14952i 0.818324 + 0.574758i \(0.194904\pi\)
−0.818324 + 0.574758i \(0.805096\pi\)
\(774\) 1.16319 0.0418100
\(775\) 3.99711 + 3.75413i 0.143580 + 0.134852i
\(776\) 2.64310 0.0948817
\(777\) 38.2667i 1.37281i
\(778\) 1.50367i 0.0539090i
\(779\) −1.07030 −0.0383475
\(780\) 5.01410 12.6627i 0.179534 0.453398i
\(781\) 0 0
\(782\) 84.5001i 3.02172i
\(783\) 1.12257i 0.0401172i
\(784\) 11.7299 0.418926
\(785\) 38.2211 + 15.1346i 1.36417 + 0.540176i
\(786\) 17.0149 0.606901
\(787\) 46.4715i 1.65653i 0.560336 + 0.828266i \(0.310672\pi\)
−0.560336 + 0.828266i \(0.689328\pi\)
\(788\) 8.72475i 0.310806i
\(789\) 11.1345 0.396398
\(790\) 16.9377 + 6.70690i 0.602617 + 0.238621i
\(791\) −0.999835 −0.0355500
\(792\) 0 0
\(793\) 20.5237i 0.728817i
\(794\) 1.60973 0.0571273
\(795\) 9.57882 24.1905i 0.339726 0.857950i
\(796\) 30.9759 1.09791
\(797\) 32.2353i 1.14183i 0.821008 + 0.570917i \(0.193412\pi\)
−0.821008 + 0.570917i \(0.806588\pi\)
\(798\) 8.01763i 0.283821i
\(799\) −14.5348 −0.514204
\(800\) 27.4631 29.2406i 0.970968 1.03381i
\(801\) 12.5950 0.445021
\(802\) 33.1869i 1.17187i
\(803\) 0 0
\(804\) 10.1253 0.357093
\(805\) −16.0811 + 40.6115i −0.566784 + 1.43137i
\(806\) −5.77310 −0.203349
\(807\) 22.7563i 0.801061i
\(808\) 9.09372i 0.319916i
\(809\) −21.1977 −0.745273 −0.372637 0.927977i \(-0.621546\pi\)
−0.372637 + 0.927977i \(0.621546\pi\)
\(810\) 4.37946 + 1.73415i 0.153878 + 0.0609319i
\(811\) −23.6049 −0.828879 −0.414440 0.910077i \(-0.636022\pi\)
−0.414440 + 0.910077i \(0.636022\pi\)
\(812\) 9.07387i 0.318430i
\(813\) 7.79448i 0.273364i
\(814\) 0 0
\(815\) −36.5324 14.4659i −1.27967 0.506718i
\(816\) 19.9806 0.699463
\(817\) 0.633743i 0.0221718i
\(818\) 5.52117i 0.193043i
\(819\) 8.28712 0.289575
\(820\) −1.87123 + 4.72564i −0.0653462 + 0.165026i
\(821\) −44.5174 −1.55367 −0.776834 0.629706i \(-0.783175\pi\)
−0.776834 + 0.629706i \(0.783175\pi\)
\(822\) 13.5613i 0.473005i
\(823\) 0.136429i 0.00475560i −0.999997 0.00237780i \(-0.999243\pi\)
0.999997 0.00237780i \(-0.000756879\pi\)
\(824\) 7.11238 0.247771
\(825\) 0 0
\(826\) −58.6700 −2.04139
\(827\) 11.7712i 0.409325i −0.978833 0.204662i \(-0.934390\pi\)
0.978833 0.204662i \(-0.0656096\pi\)
\(828\) 14.3568i 0.498934i
\(829\) −11.0290 −0.383052 −0.191526 0.981488i \(-0.561344\pi\)
−0.191526 + 0.981488i \(0.561344\pi\)
\(830\) −10.5446 + 26.6295i −0.366008 + 0.924324i
\(831\) −9.46719 −0.328413
\(832\) 27.5696i 0.955805i
\(833\) 27.2273i 0.943369i
\(834\) 14.6943 0.508823
\(835\) 25.1096 + 9.94275i 0.868953 + 0.344083i
\(836\) 0 0
\(837\) 1.09673i 0.0379085i
\(838\) 37.9335i 1.31039i
\(839\) 10.5903 0.365616 0.182808 0.983149i \(-0.441481\pi\)
0.182808 + 0.983149i \(0.441481\pi\)
\(840\) −6.35240 2.51539i −0.219179 0.0867891i
\(841\) −27.7398 −0.956546
\(842\) 2.46708i 0.0850211i
\(843\) 31.3016i 1.07808i
\(844\) 8.51910 0.293239
\(845\) −5.56142 + 14.0449i −0.191319 + 0.483159i
\(846\) 4.49586 0.154571
\(847\) 0 0
\(848\) 34.1381i 1.17231i
\(849\) −24.4123 −0.837829
\(850\) 52.2840 + 49.1058i 1.79333 + 1.68431i
\(851\) −67.9670 −2.32988
\(852\) 30.5503i 1.04663i
\(853\) 44.5811i 1.52643i 0.646145 + 0.763215i \(0.276380\pi\)
−0.646145 + 0.763215i \(0.723620\pi\)
\(854\) −57.3759 −1.96336
\(855\) 0.944820 2.38607i 0.0323122 0.0816017i
\(856\) 14.2914 0.488470
\(857\) 24.3105i 0.830430i −0.909723 0.415215i \(-0.863706\pi\)
0.909723 0.415215i \(-0.136294\pi\)
\(858\) 0 0
\(859\) 35.5045 1.21140 0.605699 0.795694i \(-0.292893\pi\)
0.605699 + 0.795694i \(0.292893\pi\)
\(860\) −2.79813 1.10799i −0.0954154 0.0377820i
\(861\) −3.09270 −0.105399
\(862\) 73.9218i 2.51779i
\(863\) 11.6720i 0.397319i −0.980069 0.198659i \(-0.936341\pi\)
0.980069 0.198659i \(-0.0636588\pi\)
\(864\) −8.02306 −0.272950
\(865\) −50.4027 19.9582i −1.71374 0.678598i
\(866\) 38.3933 1.30466
\(867\) 29.3787i 0.997752i
\(868\) 8.86503i 0.300899i
\(869\) 0 0
\(870\) 1.94670 4.91623i 0.0659992 0.166676i
\(871\) 10.3808 0.351741
\(872\) 6.26364i 0.212114i
\(873\) 2.86873i 0.0970917i
\(874\) −14.2404 −0.481690
\(875\) 15.7829 + 33.5508i 0.533559 + 1.13422i
\(876\) −13.9847 −0.472501
\(877\) 26.4819i 0.894230i −0.894476 0.447115i \(-0.852451\pi\)
0.894476 0.447115i \(-0.147549\pi\)
\(878\) 41.7416i 1.40871i
\(879\) 11.8197 0.398667
\(880\) 0 0
\(881\) 10.3488 0.348658 0.174329 0.984687i \(-0.444224\pi\)
0.174329 + 0.984687i \(0.444224\pi\)
\(882\) 8.42187i 0.283579i
\(883\) 2.71148i 0.0912487i 0.998959 + 0.0456243i \(0.0145277\pi\)
−0.998959 + 0.0456243i \(0.985472\pi\)
\(884\) −41.4791 −1.39509
\(885\) −17.4603 6.91383i −0.586922 0.232406i
\(886\) −35.1543 −1.18103
\(887\) 0.122673i 0.00411896i 0.999998 + 0.00205948i \(0.000655553\pi\)
−0.999998 + 0.00205948i \(0.999344\pi\)
\(888\) 10.6313i 0.356764i
\(889\) 22.2373 0.745814
\(890\) −55.1590 21.8416i −1.84894 0.732131i
\(891\) 0 0
\(892\) 12.6880i 0.424825i
\(893\) 2.44949i 0.0819690i
\(894\) −40.0669 −1.34004
\(895\) −16.4145 + 41.4534i −0.548675 + 1.38563i
\(896\) 23.8594 0.797087
\(897\) 14.7191i 0.491456i
\(898\) 27.7997i 0.927689i
\(899\) −1.23115 −0.0410612
\(900\) −8.88321 8.34322i −0.296107 0.278107i
\(901\) −79.2406 −2.63989
\(902\) 0 0
\(903\) 1.83124i 0.0609398i
\(904\) −0.277776 −0.00923870
\(905\) 4.22558 10.6713i 0.140463 0.354728i
\(906\) −8.21710 −0.272995
\(907\) 13.8188i 0.458844i −0.973327 0.229422i \(-0.926316\pi\)
0.973327 0.229422i \(-0.0736836\pi\)
\(908\) 23.6485i 0.784804i
\(909\) −9.87001 −0.327368
\(910\) −36.2931 14.3711i −1.20310 0.476398i
\(911\) 23.2558 0.770501 0.385250 0.922812i \(-0.374115\pi\)
0.385250 + 0.922812i \(0.374115\pi\)
\(912\) 3.36725i 0.111501i
\(913\) 0 0
\(914\) 44.7997 1.48184
\(915\) −17.0752 6.76133i −0.564488 0.223523i
\(916\) 45.0942 1.48995
\(917\) 26.7869i 0.884583i
\(918\) 14.3457i 0.473480i
\(919\) −26.4278 −0.871772 −0.435886 0.900002i \(-0.643565\pi\)
−0.435886 + 0.900002i \(0.643565\pi\)
\(920\) −4.46768 + 11.2828i −0.147295 + 0.371981i
\(921\) −22.3217 −0.735524
\(922\) 42.2927i 1.39284i
\(923\) 31.3212i 1.03095i
\(924\) 0 0
\(925\) −39.4978 + 42.0542i −1.29868 + 1.38273i
\(926\) 2.02757 0.0666301
\(927\) 7.71953i 0.253543i
\(928\) 9.00641i 0.295650i
\(929\) 8.03463 0.263608 0.131804 0.991276i \(-0.457923\pi\)
0.131804 + 0.991276i \(0.457923\pi\)
\(930\) −1.90189 + 4.80308i −0.0623656 + 0.157499i
\(931\) −4.58850 −0.150382
\(932\) 36.4494i 1.19394i
\(933\) 19.4834i 0.637858i
\(934\) −31.4144 −1.02791
\(935\) 0 0
\(936\) 2.30234 0.0752545
\(937\) 13.4913i 0.440740i 0.975416 + 0.220370i \(0.0707265\pi\)
−0.975416 + 0.220370i \(0.929274\pi\)
\(938\) 29.0206i 0.947557i
\(939\) 17.3527 0.566284
\(940\) −10.8151 4.28249i −0.352749 0.139680i
\(941\) −31.9040 −1.04004 −0.520021 0.854154i \(-0.674076\pi\)
−0.520021 + 0.854154i \(0.674076\pi\)
\(942\) 38.7267i 1.26178i
\(943\) 5.49307i 0.178879i
\(944\) 24.6403 0.801973
\(945\) 2.73011 6.89468i 0.0888106 0.224284i
\(946\) 0 0
\(947\) 10.2719i 0.333793i −0.985974 0.166896i \(-0.946625\pi\)
0.985974 0.166896i \(-0.0533745\pi\)
\(948\) 9.42667i 0.306164i
\(949\) −14.3376 −0.465419
\(950\) −8.27559 + 8.81120i −0.268496 + 0.285873i
\(951\) −0.830717 −0.0269379
\(952\) 20.8085i 0.674407i
\(953\) 9.83426i 0.318563i 0.987233 + 0.159281i \(0.0509177\pi\)
−0.987233 + 0.159281i \(0.949082\pi\)
\(954\) 24.5105 0.793557
\(955\) 2.31606 5.84901i 0.0749458 0.189270i
\(956\) −3.67353 −0.118810
\(957\) 0 0
\(958\) 1.00170i 0.0323635i
\(959\) 21.3499 0.689424
\(960\) 22.9373 + 9.08256i 0.740297 + 0.293138i
\(961\) −29.7972 −0.961199
\(962\) 60.7397i 1.95833i
\(963\) 15.5114i 0.499848i
\(964\) 17.2949 0.557033
\(965\) −40.1316 15.8911i −1.29188 0.511551i
\(966\) −41.1486 −1.32393
\(967\) 3.85001i 0.123808i 0.998082 + 0.0619041i \(0.0197173\pi\)
−0.998082 + 0.0619041i \(0.980283\pi\)
\(968\) 0 0
\(969\) −7.81600 −0.251086
\(970\) 4.97481 12.5635i 0.159731 0.403389i
\(971\) 21.3920 0.686502 0.343251 0.939244i \(-0.388472\pi\)
0.343251 + 0.939244i \(0.388472\pi\)
\(972\) 2.43738i 0.0781790i
\(973\) 23.1336i 0.741630i
\(974\) −74.4713 −2.38621
\(975\) −9.10736 8.55375i −0.291669 0.273939i
\(976\) 24.0968 0.771320
\(977\) 16.6681i 0.533258i 0.963799 + 0.266629i \(0.0859099\pi\)
−0.963799 + 0.266629i \(0.914090\pi\)
\(978\) 37.0156i 1.18363i
\(979\) 0 0
\(980\) −8.02217 + 20.2593i −0.256259 + 0.647161i
\(981\) 6.79834 0.217054
\(982\) 63.4750i 2.02557i
\(983\) 51.8570i 1.65398i 0.562216 + 0.826991i \(0.309949\pi\)
−0.562216 + 0.826991i \(0.690051\pi\)
\(984\) −0.859219 −0.0273909
\(985\) −7.44194 2.94682i −0.237120 0.0938933i
\(986\) −16.1040 −0.512856
\(987\) 7.07794i 0.225293i
\(988\) 6.99029i 0.222391i
\(989\) −3.25253 −0.103425
\(990\) 0 0
\(991\) 19.8195 0.629588 0.314794 0.949160i \(-0.398065\pi\)
0.314794 + 0.949160i \(0.398065\pi\)
\(992\) 8.79912i 0.279372i
\(993\) 31.5311i 1.00061i
\(994\) 87.5613 2.77727
\(995\) 10.4622 26.4215i 0.331674 0.837616i
\(996\) −14.8206 −0.469609
\(997\) 51.6594i 1.63607i 0.575168 + 0.818036i \(0.304937\pi\)
−0.575168 + 0.818036i \(0.695063\pi\)
\(998\) 76.8449i 2.43248i
\(999\) 11.5389 0.365074
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 1815.2.c.j.364.5 24
5.2 odd 4 9075.2.a.dz.1.10 12
5.3 odd 4 9075.2.a.dy.1.3 12
5.4 even 2 inner 1815.2.c.j.364.20 24
11.3 even 5 165.2.s.a.64.3 yes 48
11.4 even 5 165.2.s.a.49.10 yes 48
11.10 odd 2 1815.2.c.k.364.20 24
33.14 odd 10 495.2.ba.c.64.10 48
33.26 odd 10 495.2.ba.c.379.3 48
55.3 odd 20 825.2.n.p.526.2 24
55.4 even 10 165.2.s.a.49.3 48
55.14 even 10 165.2.s.a.64.10 yes 48
55.32 even 4 9075.2.a.dx.1.3 12
55.37 odd 20 825.2.n.o.676.5 24
55.43 even 4 9075.2.a.ea.1.10 12
55.47 odd 20 825.2.n.o.526.5 24
55.48 odd 20 825.2.n.p.676.2 24
55.54 odd 2 1815.2.c.k.364.5 24
165.14 odd 10 495.2.ba.c.64.3 48
165.59 odd 10 495.2.ba.c.379.10 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.s.a.49.3 48 55.4 even 10
165.2.s.a.49.10 yes 48 11.4 even 5
165.2.s.a.64.3 yes 48 11.3 even 5
165.2.s.a.64.10 yes 48 55.14 even 10
495.2.ba.c.64.3 48 165.14 odd 10
495.2.ba.c.64.10 48 33.14 odd 10
495.2.ba.c.379.3 48 33.26 odd 10
495.2.ba.c.379.10 48 165.59 odd 10
825.2.n.o.526.5 24 55.47 odd 20
825.2.n.o.676.5 24 55.37 odd 20
825.2.n.p.526.2 24 55.3 odd 20
825.2.n.p.676.2 24 55.48 odd 20
1815.2.c.j.364.5 24 1.1 even 1 trivial
1815.2.c.j.364.20 24 5.4 even 2 inner
1815.2.c.k.364.5 24 55.54 odd 2
1815.2.c.k.364.20 24 11.10 odd 2
9075.2.a.dx.1.3 12 55.32 even 4
9075.2.a.dy.1.3 12 5.3 odd 4
9075.2.a.dz.1.10 12 5.2 odd 4
9075.2.a.ea.1.10 12 55.43 even 4