Properties

Label 576.2.y.a.335.18
Level $576$
Weight $2$
Character 576.335
Analytic conductor $4.599$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,2,Mod(47,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.y (of order \(12\), degree \(4\), 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: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 335.18
Character \(\chi\) \(=\) 576.335
Dual form 576.2.y.a.239.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36987 - 1.05993i) q^{3} +(-2.78704 - 0.746784i) q^{5} +(-1.16672 + 2.02082i) q^{7} +(0.753089 - 2.90394i) q^{9} +O(q^{10})\) \(q+(1.36987 - 1.05993i) q^{3} +(-2.78704 - 0.746784i) q^{5} +(-1.16672 + 2.02082i) q^{7} +(0.753089 - 2.90394i) q^{9} +(-5.53982 + 1.48439i) q^{11} +(-3.90572 - 1.04654i) q^{13} +(-4.60942 + 1.93107i) q^{15} -6.45489i q^{17} +(1.50499 + 1.50499i) q^{19} +(0.543676 + 4.00491i) q^{21} +(0.0418190 - 0.0241442i) q^{23} +(2.87976 + 1.66263i) q^{25} +(-2.04634 - 4.77624i) q^{27} +(-5.08507 + 1.36254i) q^{29} +(1.65029 - 0.952797i) q^{31} +(-6.01548 + 7.90525i) q^{33} +(4.76082 - 4.76082i) q^{35} +(0.489763 + 0.489763i) q^{37} +(-6.45959 + 2.70618i) q^{39} +(0.0155357 + 0.0269087i) q^{41} +(1.01892 + 3.80267i) q^{43} +(-4.26750 + 7.53099i) q^{45} +(-0.0913288 + 0.158186i) q^{47} +(0.777520 + 1.34670i) q^{49} +(-6.84175 - 8.84237i) q^{51} +(6.62061 - 6.62061i) q^{53} +16.5482 q^{55} +(3.65682 + 0.466453i) q^{57} +(-1.11363 + 4.15614i) q^{59} +(-1.71427 - 6.39775i) q^{61} +(4.98970 + 4.90995i) q^{63} +(10.1039 + 5.83347i) q^{65} +(-0.216578 + 0.808279i) q^{67} +(0.0316954 - 0.0773998i) q^{69} +1.04372i q^{71} +4.74654i q^{73} +(5.70717 - 0.774762i) q^{75} +(3.46374 - 12.9269i) q^{77} +(-7.29908 - 4.21413i) q^{79} +(-7.86571 - 4.37385i) q^{81} +(-3.20973 - 11.9789i) q^{83} +(-4.82041 + 17.9900i) q^{85} +(-5.52169 + 7.25633i) q^{87} +2.85193 q^{89} +(6.67175 - 6.67175i) q^{91} +(1.25079 - 3.05441i) q^{93} +(-3.07055 - 5.31835i) q^{95} +(3.29818 - 5.71262i) q^{97} +(0.138600 + 17.2052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 1.36987 1.05993i 0.790895 0.611952i
\(4\) 0 0
\(5\) −2.78704 0.746784i −1.24640 0.333972i −0.425456 0.904979i \(-0.639886\pi\)
−0.820945 + 0.571007i \(0.806553\pi\)
\(6\) 0 0
\(7\) −1.16672 + 2.02082i −0.440979 + 0.763799i −0.997762 0.0668592i \(-0.978702\pi\)
0.556783 + 0.830658i \(0.312036\pi\)
\(8\) 0 0
\(9\) 0.753089 2.90394i 0.251030 0.967979i
\(10\) 0 0
\(11\) −5.53982 + 1.48439i −1.67032 + 0.447560i −0.965196 0.261527i \(-0.915774\pi\)
−0.705121 + 0.709087i \(0.749107\pi\)
\(12\) 0 0
\(13\) −3.90572 1.04654i −1.08325 0.290257i −0.327325 0.944912i \(-0.606147\pi\)
−0.755928 + 0.654655i \(0.772814\pi\)
\(14\) 0 0
\(15\) −4.60942 + 1.93107i −1.19015 + 0.498601i
\(16\) 0 0
\(17\) 6.45489i 1.56554i −0.622310 0.782771i \(-0.713806\pi\)
0.622310 0.782771i \(-0.286194\pi\)
\(18\) 0 0
\(19\) 1.50499 + 1.50499i 0.345267 + 0.345267i 0.858343 0.513076i \(-0.171494\pi\)
−0.513076 + 0.858343i \(0.671494\pi\)
\(20\) 0 0
\(21\) 0.543676 + 4.00491i 0.118640 + 0.873943i
\(22\) 0 0
\(23\) 0.0418190 0.0241442i 0.00871987 0.00503442i −0.495634 0.868532i \(-0.665064\pi\)
0.504354 + 0.863497i \(0.331731\pi\)
\(24\) 0 0
\(25\) 2.87976 + 1.66263i 0.575952 + 0.332526i
\(26\) 0 0
\(27\) −2.04634 4.77624i −0.393819 0.919188i
\(28\) 0 0
\(29\) −5.08507 + 1.36254i −0.944274 + 0.253018i −0.697931 0.716165i \(-0.745896\pi\)
−0.246343 + 0.969183i \(0.579229\pi\)
\(30\) 0 0
\(31\) 1.65029 0.952797i 0.296401 0.171127i −0.344424 0.938814i \(-0.611926\pi\)
0.640825 + 0.767687i \(0.278592\pi\)
\(32\) 0 0
\(33\) −6.01548 + 7.90525i −1.04716 + 1.37613i
\(34\) 0 0
\(35\) 4.76082 4.76082i 0.804725 0.804725i
\(36\) 0 0
\(37\) 0.489763 + 0.489763i 0.0805165 + 0.0805165i 0.746218 0.665702i \(-0.231868\pi\)
−0.665702 + 0.746218i \(0.731868\pi\)
\(38\) 0 0
\(39\) −6.45959 + 2.70618i −1.03436 + 0.433336i
\(40\) 0 0
\(41\) 0.0155357 + 0.0269087i 0.00242628 + 0.00420243i 0.867236 0.497897i \(-0.165894\pi\)
−0.864810 + 0.502100i \(0.832561\pi\)
\(42\) 0 0
\(43\) 1.01892 + 3.80267i 0.155384 + 0.579901i 0.999072 + 0.0430675i \(0.0137130\pi\)
−0.843688 + 0.536834i \(0.819620\pi\)
\(44\) 0 0
\(45\) −4.26750 + 7.53099i −0.636162 + 1.12265i
\(46\) 0 0
\(47\) −0.0913288 + 0.158186i −0.0133217 + 0.0230738i −0.872609 0.488419i \(-0.837574\pi\)
0.859288 + 0.511493i \(0.170907\pi\)
\(48\) 0 0
\(49\) 0.777520 + 1.34670i 0.111074 + 0.192386i
\(50\) 0 0
\(51\) −6.84175 8.84237i −0.958036 1.23818i
\(52\) 0 0
\(53\) 6.62061 6.62061i 0.909411 0.909411i −0.0868136 0.996225i \(-0.527668\pi\)
0.996225 + 0.0868136i \(0.0276684\pi\)
\(54\) 0 0
\(55\) 16.5482 2.23136
\(56\) 0 0
\(57\) 3.65682 + 0.466453i 0.484357 + 0.0617832i
\(58\) 0 0
\(59\) −1.11363 + 4.15614i −0.144983 + 0.541083i 0.854773 + 0.519001i \(0.173696\pi\)
−0.999756 + 0.0220815i \(0.992971\pi\)
\(60\) 0 0
\(61\) −1.71427 6.39775i −0.219490 0.819148i −0.984537 0.175174i \(-0.943951\pi\)
0.765047 0.643974i \(-0.222716\pi\)
\(62\) 0 0
\(63\) 4.98970 + 4.90995i 0.628643 + 0.618595i
\(64\) 0 0
\(65\) 10.1039 + 5.83347i 1.25323 + 0.723552i
\(66\) 0 0
\(67\) −0.216578 + 0.808279i −0.0264592 + 0.0987470i −0.977893 0.209107i \(-0.932944\pi\)
0.951434 + 0.307854i \(0.0996109\pi\)
\(68\) 0 0
\(69\) 0.0316954 0.0773998i 0.00381568 0.00931784i
\(70\) 0 0
\(71\) 1.04372i 0.123867i 0.998080 + 0.0619333i \(0.0197266\pi\)
−0.998080 + 0.0619333i \(0.980273\pi\)
\(72\) 0 0
\(73\) 4.74654i 0.555540i 0.960648 + 0.277770i \(0.0895953\pi\)
−0.960648 + 0.277770i \(0.910405\pi\)
\(74\) 0 0
\(75\) 5.70717 0.774762i 0.659008 0.0894618i
\(76\) 0 0
\(77\) 3.46374 12.9269i 0.394730 1.47315i
\(78\) 0 0
\(79\) −7.29908 4.21413i −0.821211 0.474126i 0.0296228 0.999561i \(-0.490569\pi\)
−0.850834 + 0.525435i \(0.823903\pi\)
\(80\) 0 0
\(81\) −7.86571 4.37385i −0.873968 0.485983i
\(82\) 0 0
\(83\) −3.20973 11.9789i −0.352313 1.31485i −0.883832 0.467805i \(-0.845045\pi\)
0.531519 0.847047i \(-0.321622\pi\)
\(84\) 0 0
\(85\) −4.82041 + 17.9900i −0.522847 + 1.95129i
\(86\) 0 0
\(87\) −5.52169 + 7.25633i −0.591987 + 0.777961i
\(88\) 0 0
\(89\) 2.85193 0.302304 0.151152 0.988511i \(-0.451702\pi\)
0.151152 + 0.988511i \(0.451702\pi\)
\(90\) 0 0
\(91\) 6.67175 6.67175i 0.699390 0.699390i
\(92\) 0 0
\(93\) 1.25079 3.05441i 0.129701 0.316727i
\(94\) 0 0
\(95\) −3.07055 5.31835i −0.315032 0.545651i
\(96\) 0 0
\(97\) 3.29818 5.71262i 0.334880 0.580028i −0.648582 0.761145i \(-0.724638\pi\)
0.983462 + 0.181116i \(0.0579710\pi\)
\(98\) 0 0
\(99\) 0.138600 + 17.2052i 0.0139299 + 1.72918i
\(100\) 0 0
\(101\) −2.15095 8.02745i −0.214027 0.798761i −0.986507 0.163721i \(-0.947650\pi\)
0.772479 0.635040i \(-0.219016\pi\)
\(102\) 0 0
\(103\) −3.39607 5.88217i −0.334625 0.579588i 0.648788 0.760970i \(-0.275276\pi\)
−0.983413 + 0.181382i \(0.941943\pi\)
\(104\) 0 0
\(105\) 1.47556 11.5678i 0.144000 1.12891i
\(106\) 0 0
\(107\) −11.9162 11.9162i −1.15198 1.15198i −0.986155 0.165828i \(-0.946970\pi\)
−0.165828 0.986155i \(-0.553030\pi\)
\(108\) 0 0
\(109\) −0.518803 + 0.518803i −0.0496923 + 0.0496923i −0.731516 0.681824i \(-0.761187\pi\)
0.681824 + 0.731516i \(0.261187\pi\)
\(110\) 0 0
\(111\) 1.19003 + 0.151796i 0.112952 + 0.0144079i
\(112\) 0 0
\(113\) −9.60012 + 5.54263i −0.903103 + 0.521407i −0.878206 0.478283i \(-0.841259\pi\)
−0.0248974 + 0.999690i \(0.507926\pi\)
\(114\) 0 0
\(115\) −0.134582 + 0.0360611i −0.0125498 + 0.00336271i
\(116\) 0 0
\(117\) −5.98043 + 10.5538i −0.552891 + 0.975703i
\(118\) 0 0
\(119\) 13.0442 + 7.53107i 1.19576 + 0.690372i
\(120\) 0 0
\(121\) 18.9599 10.9465i 1.72362 0.995135i
\(122\) 0 0
\(123\) 0.0498033 + 0.0203946i 0.00449062 + 0.00183892i
\(124\) 0 0
\(125\) 3.41689 + 3.41689i 0.305616 + 0.305616i
\(126\) 0 0
\(127\) 12.0823i 1.07213i 0.844176 + 0.536067i \(0.180090\pi\)
−0.844176 + 0.536067i \(0.819910\pi\)
\(128\) 0 0
\(129\) 5.42636 + 4.12917i 0.477764 + 0.363553i
\(130\) 0 0
\(131\) 2.61991 + 0.702002i 0.228902 + 0.0613342i 0.371447 0.928454i \(-0.378862\pi\)
−0.142545 + 0.989788i \(0.545528\pi\)
\(132\) 0 0
\(133\) −4.79721 + 1.28541i −0.415971 + 0.111459i
\(134\) 0 0
\(135\) 2.13641 + 14.8397i 0.183873 + 1.27720i
\(136\) 0 0
\(137\) −7.51859 + 13.0226i −0.642356 + 1.11259i 0.342549 + 0.939500i \(0.388710\pi\)
−0.984905 + 0.173094i \(0.944624\pi\)
\(138\) 0 0
\(139\) 8.28951 + 2.22117i 0.703107 + 0.188397i 0.592622 0.805481i \(-0.298093\pi\)
0.110485 + 0.993878i \(0.464760\pi\)
\(140\) 0 0
\(141\) 0.0425579 + 0.313497i 0.00358402 + 0.0264012i
\(142\) 0 0
\(143\) 23.1905 1.93928
\(144\) 0 0
\(145\) 15.1898 1.26144
\(146\) 0 0
\(147\) 2.49251 + 1.02069i 0.205579 + 0.0841852i
\(148\) 0 0
\(149\) −0.977298 0.261866i −0.0800634 0.0214529i 0.218565 0.975822i \(-0.429862\pi\)
−0.298628 + 0.954369i \(0.596529\pi\)
\(150\) 0 0
\(151\) 8.29411 14.3658i 0.674965 1.16907i −0.301514 0.953462i \(-0.597492\pi\)
0.976479 0.215612i \(-0.0691747\pi\)
\(152\) 0 0
\(153\) −18.7446 4.86111i −1.51541 0.392997i
\(154\) 0 0
\(155\) −5.31096 + 1.42307i −0.426587 + 0.114304i
\(156\) 0 0
\(157\) 21.2306 + 5.68871i 1.69438 + 0.454009i 0.971515 0.236977i \(-0.0761566\pi\)
0.722868 + 0.690986i \(0.242823\pi\)
\(158\) 0 0
\(159\) 2.05198 16.0868i 0.162733 1.27576i
\(160\) 0 0
\(161\) 0.112678i 0.00888030i
\(162\) 0 0
\(163\) −0.153221 0.153221i −0.0120012 0.0120012i 0.701081 0.713082i \(-0.252701\pi\)
−0.713082 + 0.701081i \(0.752701\pi\)
\(164\) 0 0
\(165\) 22.6689 17.5400i 1.76477 1.36548i
\(166\) 0 0
\(167\) −1.83025 + 1.05669i −0.141629 + 0.0817694i −0.569140 0.822241i \(-0.692724\pi\)
0.427511 + 0.904010i \(0.359390\pi\)
\(168\) 0 0
\(169\) 2.90111 + 1.67495i 0.223162 + 0.128843i
\(170\) 0 0
\(171\) 5.50377 3.23700i 0.420884 0.247539i
\(172\) 0 0
\(173\) 2.17246 0.582108i 0.165169 0.0442568i −0.175287 0.984517i \(-0.556085\pi\)
0.340456 + 0.940261i \(0.389419\pi\)
\(174\) 0 0
\(175\) −6.71976 + 3.87966i −0.507966 + 0.293274i
\(176\) 0 0
\(177\) 2.87969 + 6.87374i 0.216451 + 0.516662i
\(178\) 0 0
\(179\) −4.33235 + 4.33235i −0.323815 + 0.323815i −0.850229 0.526413i \(-0.823536\pi\)
0.526413 + 0.850229i \(0.323536\pi\)
\(180\) 0 0
\(181\) −13.9507 13.9507i −1.03695 1.03695i −0.999291 0.0376558i \(-0.988011\pi\)
−0.0376558 0.999291i \(-0.511989\pi\)
\(182\) 0 0
\(183\) −9.12951 6.94708i −0.674873 0.513543i
\(184\) 0 0
\(185\) −0.999240 1.73073i −0.0734656 0.127246i
\(186\) 0 0
\(187\) 9.58157 + 35.7589i 0.700674 + 2.61495i
\(188\) 0 0
\(189\) 12.0394 + 1.43725i 0.875741 + 0.104545i
\(190\) 0 0
\(191\) −3.83161 + 6.63654i −0.277246 + 0.480203i −0.970699 0.240298i \(-0.922755\pi\)
0.693454 + 0.720501i \(0.256088\pi\)
\(192\) 0 0
\(193\) −3.79037 6.56511i −0.272836 0.472567i 0.696751 0.717314i \(-0.254628\pi\)
−0.969587 + 0.244747i \(0.921295\pi\)
\(194\) 0 0
\(195\) 20.0240 2.71831i 1.43395 0.194662i
\(196\) 0 0
\(197\) 12.6000 12.6000i 0.897715 0.897715i −0.0975188 0.995234i \(-0.531091\pi\)
0.995234 + 0.0975188i \(0.0310906\pi\)
\(198\) 0 0
\(199\) −23.1095 −1.63819 −0.819096 0.573656i \(-0.805524\pi\)
−0.819096 + 0.573656i \(0.805524\pi\)
\(200\) 0 0
\(201\) 0.560037 + 1.33679i 0.0395020 + 0.0942902i
\(202\) 0 0
\(203\) 3.17941 11.8657i 0.223151 0.832811i
\(204\) 0 0
\(205\) −0.0232037 0.0865974i −0.00162062 0.00604822i
\(206\) 0 0
\(207\) −0.0386199 0.139623i −0.00268427 0.00970444i
\(208\) 0 0
\(209\) −10.5713 6.10336i −0.731234 0.422178i
\(210\) 0 0
\(211\) −3.42605 + 12.7862i −0.235859 + 0.880238i 0.741901 + 0.670510i \(0.233925\pi\)
−0.977760 + 0.209728i \(0.932742\pi\)
\(212\) 0 0
\(213\) 1.10627 + 1.42976i 0.0758004 + 0.0979654i
\(214\) 0 0
\(215\) 11.3591i 0.774683i
\(216\) 0 0
\(217\) 4.44660i 0.301855i
\(218\) 0 0
\(219\) 5.03100 + 6.50214i 0.339964 + 0.439374i
\(220\) 0 0
\(221\) −6.75527 + 25.2110i −0.454409 + 1.69588i
\(222\) 0 0
\(223\) −14.1219 8.15328i −0.945672 0.545984i −0.0539380 0.998544i \(-0.517177\pi\)
−0.891734 + 0.452561i \(0.850511\pi\)
\(224\) 0 0
\(225\) 6.99689 7.11054i 0.466460 0.474036i
\(226\) 0 0
\(227\) 5.96068 + 22.2456i 0.395624 + 1.47649i 0.820714 + 0.571339i \(0.193576\pi\)
−0.425090 + 0.905151i \(0.639758\pi\)
\(228\) 0 0
\(229\) −5.05838 + 18.8781i −0.334267 + 1.24750i 0.570394 + 0.821371i \(0.306791\pi\)
−0.904661 + 0.426131i \(0.859876\pi\)
\(230\) 0 0
\(231\) −8.95671 21.3794i −0.589308 1.40666i
\(232\) 0 0
\(233\) −18.4018 −1.20554 −0.602771 0.797914i \(-0.705937\pi\)
−0.602771 + 0.797914i \(0.705937\pi\)
\(234\) 0 0
\(235\) 0.372668 0.372668i 0.0243102 0.0243102i
\(236\) 0 0
\(237\) −14.4655 + 1.96372i −0.939634 + 0.127558i
\(238\) 0 0
\(239\) −12.4328 21.5343i −0.804212 1.39294i −0.916821 0.399298i \(-0.869254\pi\)
0.112609 0.993639i \(-0.464079\pi\)
\(240\) 0 0
\(241\) 0.256221 0.443788i 0.0165047 0.0285869i −0.857655 0.514225i \(-0.828079\pi\)
0.874160 + 0.485638i \(0.161413\pi\)
\(242\) 0 0
\(243\) −15.4110 + 2.34552i −0.988615 + 0.150465i
\(244\) 0 0
\(245\) −1.16128 4.33395i −0.0741914 0.276886i
\(246\) 0 0
\(247\) −4.30304 7.45308i −0.273796 0.474228i
\(248\) 0 0
\(249\) −17.0937 13.0074i −1.08327 0.824310i
\(250\) 0 0
\(251\) 7.88443 + 7.88443i 0.497661 + 0.497661i 0.910709 0.413048i \(-0.135536\pi\)
−0.413048 + 0.910709i \(0.635536\pi\)
\(252\) 0 0
\(253\) −0.195830 + 0.195830i −0.0123117 + 0.0123117i
\(254\) 0 0
\(255\) 12.4649 + 29.7533i 0.780580 + 1.86322i
\(256\) 0 0
\(257\) 10.6490 6.14820i 0.664266 0.383514i −0.129635 0.991562i \(-0.541380\pi\)
0.793900 + 0.608048i \(0.208047\pi\)
\(258\) 0 0
\(259\) −1.56114 + 0.418306i −0.0970046 + 0.0259923i
\(260\) 0 0
\(261\) 0.127223 + 15.7928i 0.00787492 + 0.977553i
\(262\) 0 0
\(263\) 8.46535 + 4.88747i 0.521996 + 0.301375i 0.737751 0.675073i \(-0.235888\pi\)
−0.215755 + 0.976448i \(0.569221\pi\)
\(264\) 0 0
\(265\) −23.3961 + 13.5077i −1.43721 + 0.829773i
\(266\) 0 0
\(267\) 3.90677 3.02285i 0.239091 0.184995i
\(268\) 0 0
\(269\) 5.64229 + 5.64229i 0.344016 + 0.344016i 0.857875 0.513859i \(-0.171784\pi\)
−0.513859 + 0.857875i \(0.671784\pi\)
\(270\) 0 0
\(271\) 11.0524i 0.671386i −0.941971 0.335693i \(-0.891029\pi\)
0.941971 0.335693i \(-0.108971\pi\)
\(272\) 0 0
\(273\) 2.06783 16.2110i 0.125151 0.981137i
\(274\) 0 0
\(275\) −18.4213 4.93598i −1.11085 0.297651i
\(276\) 0 0
\(277\) 25.2727 6.77180i 1.51849 0.406878i 0.599246 0.800565i \(-0.295467\pi\)
0.919245 + 0.393687i \(0.128801\pi\)
\(278\) 0 0
\(279\) −1.52405 5.50989i −0.0912423 0.329869i
\(280\) 0 0
\(281\) −12.8442 + 22.2468i −0.766219 + 1.32713i 0.173381 + 0.984855i \(0.444531\pi\)
−0.939600 + 0.342275i \(0.888802\pi\)
\(282\) 0 0
\(283\) −31.3627 8.40360i −1.86432 0.499542i −0.864323 0.502937i \(-0.832253\pi\)
−0.999994 + 0.00339463i \(0.998919\pi\)
\(284\) 0 0
\(285\) −9.84335 4.03088i −0.583070 0.238768i
\(286\) 0 0
\(287\) −0.0725036 −0.00427975
\(288\) 0 0
\(289\) −24.6657 −1.45092
\(290\) 0 0
\(291\) −1.53690 11.3214i −0.0900950 0.663672i
\(292\) 0 0
\(293\) −22.0583 5.91051i −1.28866 0.345296i −0.451510 0.892266i \(-0.649114\pi\)
−0.837152 + 0.546971i \(0.815781\pi\)
\(294\) 0 0
\(295\) 6.20747 10.7517i 0.361413 0.625986i
\(296\) 0 0
\(297\) 18.4262 + 23.4219i 1.06919 + 1.35908i
\(298\) 0 0
\(299\) −0.188601 + 0.0505356i −0.0109071 + 0.00292255i
\(300\) 0 0
\(301\) −8.87331 2.37760i −0.511449 0.137042i
\(302\) 0 0
\(303\) −11.4551 8.71670i −0.658076 0.500761i
\(304\) 0 0
\(305\) 19.1110i 1.09429i
\(306\) 0 0
\(307\) −10.3124 10.3124i −0.588560 0.588560i 0.348681 0.937241i \(-0.386630\pi\)
−0.937241 + 0.348681i \(0.886630\pi\)
\(308\) 0 0
\(309\) −10.8869 4.45821i −0.619333 0.253619i
\(310\) 0 0
\(311\) 0.887812 0.512578i 0.0503432 0.0290656i −0.474617 0.880192i \(-0.657413\pi\)
0.524960 + 0.851127i \(0.324080\pi\)
\(312\) 0 0
\(313\) 9.53399 + 5.50445i 0.538893 + 0.311130i 0.744630 0.667477i \(-0.232626\pi\)
−0.205737 + 0.978607i \(0.565959\pi\)
\(314\) 0 0
\(315\) −10.2398 17.4104i −0.576947 0.980967i
\(316\) 0 0
\(317\) 18.3465 4.91593i 1.03044 0.276106i 0.296295 0.955096i \(-0.404249\pi\)
0.734147 + 0.678990i \(0.237582\pi\)
\(318\) 0 0
\(319\) 26.1478 15.0965i 1.46400 0.845239i
\(320\) 0 0
\(321\) −28.9540 3.69329i −1.61605 0.206139i
\(322\) 0 0
\(323\) 9.71452 9.71452i 0.540531 0.540531i
\(324\) 0 0
\(325\) −9.50755 9.50755i −0.527384 0.527384i
\(326\) 0 0
\(327\) −0.160797 + 1.26059i −0.00889210 + 0.0697107i
\(328\) 0 0
\(329\) −0.213111 0.369119i −0.0117492 0.0203502i
\(330\) 0 0
\(331\) −4.94329 18.4486i −0.271708 1.01403i −0.958015 0.286716i \(-0.907436\pi\)
0.686307 0.727312i \(-0.259230\pi\)
\(332\) 0 0
\(333\) 1.79108 1.05341i 0.0981504 0.0577263i
\(334\) 0 0
\(335\) 1.20722 2.09097i 0.0659575 0.114242i
\(336\) 0 0
\(337\) −14.6805 25.4274i −0.799699 1.38512i −0.919812 0.392359i \(-0.871659\pi\)
0.120113 0.992760i \(-0.461674\pi\)
\(338\) 0 0
\(339\) −7.27610 + 17.7682i −0.395184 + 0.965034i
\(340\) 0 0
\(341\) −7.72800 + 7.72800i −0.418495 + 0.418495i
\(342\) 0 0
\(343\) −19.9627 −1.07788
\(344\) 0 0
\(345\) −0.146137 + 0.192046i −0.00786776 + 0.0103394i
\(346\) 0 0
\(347\) −5.49514 + 20.5081i −0.294995 + 1.10093i 0.646227 + 0.763145i \(0.276346\pi\)
−0.941222 + 0.337789i \(0.890321\pi\)
\(348\) 0 0
\(349\) −6.64137 24.7859i −0.355504 1.32676i −0.879849 0.475254i \(-0.842356\pi\)
0.524345 0.851506i \(-0.324310\pi\)
\(350\) 0 0
\(351\) 2.99394 + 20.7962i 0.159805 + 1.11002i
\(352\) 0 0
\(353\) 19.1119 + 11.0343i 1.01723 + 0.587296i 0.913299 0.407289i \(-0.133526\pi\)
0.103927 + 0.994585i \(0.466859\pi\)
\(354\) 0 0
\(355\) 0.779432 2.90888i 0.0413680 0.154387i
\(356\) 0 0
\(357\) 25.8513 3.50937i 1.36819 0.185735i
\(358\) 0 0
\(359\) 13.1522i 0.694145i 0.937838 + 0.347073i \(0.112824\pi\)
−0.937838 + 0.347073i \(0.887176\pi\)
\(360\) 0 0
\(361\) 14.4700i 0.761581i
\(362\) 0 0
\(363\) 14.3700 35.0914i 0.754231 1.84182i
\(364\) 0 0
\(365\) 3.54464 13.2288i 0.185535 0.692425i
\(366\) 0 0
\(367\) 5.13483 + 2.96459i 0.268036 + 0.154751i 0.627995 0.778218i \(-0.283876\pi\)
−0.359959 + 0.932968i \(0.617209\pi\)
\(368\) 0 0
\(369\) 0.0898410 0.0248502i 0.00467694 0.00129365i
\(370\) 0 0
\(371\) 5.65466 + 21.1035i 0.293575 + 1.09564i
\(372\) 0 0
\(373\) 9.31148 34.7509i 0.482130 1.79933i −0.110520 0.993874i \(-0.535252\pi\)
0.592650 0.805460i \(-0.298082\pi\)
\(374\) 0 0
\(375\) 8.30237 + 1.05903i 0.428732 + 0.0546878i
\(376\) 0 0
\(377\) 21.2868 1.09633
\(378\) 0 0
\(379\) −4.54655 + 4.54655i −0.233540 + 0.233540i −0.814169 0.580628i \(-0.802807\pi\)
0.580628 + 0.814169i \(0.302807\pi\)
\(380\) 0 0
\(381\) 12.8064 + 16.5512i 0.656094 + 0.847945i
\(382\) 0 0
\(383\) 16.4216 + 28.4430i 0.839104 + 1.45337i 0.890645 + 0.454700i \(0.150253\pi\)
−0.0515410 + 0.998671i \(0.516413\pi\)
\(384\) 0 0
\(385\) −19.3071 + 33.4409i −0.983983 + 1.70431i
\(386\) 0 0
\(387\) 11.8100 0.0951387i 0.600338 0.00483617i
\(388\) 0 0
\(389\) 8.46615 + 31.5961i 0.429251 + 1.60199i 0.754462 + 0.656344i \(0.227898\pi\)
−0.325211 + 0.945641i \(0.605435\pi\)
\(390\) 0 0
\(391\) −0.155848 0.269937i −0.00788159 0.0136513i
\(392\) 0 0
\(393\) 4.33301 1.81527i 0.218571 0.0915683i
\(394\) 0 0
\(395\) 17.1958 + 17.1958i 0.865213 + 0.865213i
\(396\) 0 0
\(397\) −26.7370 + 26.7370i −1.34189 + 1.34189i −0.447720 + 0.894174i \(0.647764\pi\)
−0.894174 + 0.447720i \(0.852236\pi\)
\(398\) 0 0
\(399\) −5.20911 + 6.84556i −0.260782 + 0.342706i
\(400\) 0 0
\(401\) 2.15088 1.24181i 0.107410 0.0620130i −0.445333 0.895365i \(-0.646915\pi\)
0.552743 + 0.833352i \(0.313581\pi\)
\(402\) 0 0
\(403\) −7.44272 + 1.99427i −0.370748 + 0.0993418i
\(404\) 0 0
\(405\) 18.6557 + 18.0641i 0.927010 + 0.897611i
\(406\) 0 0
\(407\) −3.44020 1.98620i −0.170524 0.0984522i
\(408\) 0 0
\(409\) 6.04923 3.49252i 0.299115 0.172694i −0.342930 0.939361i \(-0.611419\pi\)
0.642045 + 0.766667i \(0.278086\pi\)
\(410\) 0 0
\(411\) 3.50355 + 25.8084i 0.172818 + 1.27304i
\(412\) 0 0
\(413\) −7.09951 7.09951i −0.349344 0.349344i
\(414\) 0 0
\(415\) 35.7825i 1.75649i
\(416\) 0 0
\(417\) 13.7098 5.74361i 0.671374 0.281266i
\(418\) 0 0
\(419\) −29.1858 7.82032i −1.42582 0.382048i −0.538276 0.842768i \(-0.680924\pi\)
−0.887545 + 0.460721i \(0.847591\pi\)
\(420\) 0 0
\(421\) −31.2445 + 8.37195i −1.52277 + 0.408024i −0.920651 0.390386i \(-0.872341\pi\)
−0.602114 + 0.798410i \(0.705675\pi\)
\(422\) 0 0
\(423\) 0.390584 + 0.384342i 0.0189909 + 0.0186873i
\(424\) 0 0
\(425\) 10.7321 18.5885i 0.520584 0.901677i
\(426\) 0 0
\(427\) 14.9288 + 4.00016i 0.722455 + 0.193581i
\(428\) 0 0
\(429\) 31.7679 24.5803i 1.53377 1.18675i
\(430\) 0 0
\(431\) −30.2342 −1.45633 −0.728164 0.685403i \(-0.759626\pi\)
−0.728164 + 0.685403i \(0.759626\pi\)
\(432\) 0 0
\(433\) 34.5522 1.66047 0.830237 0.557410i \(-0.188205\pi\)
0.830237 + 0.557410i \(0.188205\pi\)
\(434\) 0 0
\(435\) 20.8081 16.1002i 0.997670 0.771944i
\(436\) 0 0
\(437\) 0.0992738 + 0.0266003i 0.00474891 + 0.00127247i
\(438\) 0 0
\(439\) −1.65747 + 2.87082i −0.0791066 + 0.137017i −0.902865 0.429925i \(-0.858540\pi\)
0.823758 + 0.566941i \(0.191873\pi\)
\(440\) 0 0
\(441\) 4.49629 1.24368i 0.214109 0.0592229i
\(442\) 0 0
\(443\) −15.4752 + 4.14656i −0.735248 + 0.197009i −0.606965 0.794729i \(-0.707613\pi\)
−0.128283 + 0.991738i \(0.540947\pi\)
\(444\) 0 0
\(445\) −7.94843 2.12977i −0.376792 0.100961i
\(446\) 0 0
\(447\) −1.61633 + 0.677147i −0.0764499 + 0.0320279i
\(448\) 0 0
\(449\) 11.1511i 0.526253i −0.964761 0.263126i \(-0.915246\pi\)
0.964761 0.263126i \(-0.0847536\pi\)
\(450\) 0 0
\(451\) −0.126008 0.126008i −0.00593349 0.00593349i
\(452\) 0 0
\(453\) −3.86494 28.4705i −0.181591 1.33766i
\(454\) 0 0
\(455\) −23.5768 + 13.6121i −1.10530 + 0.638143i
\(456\) 0 0
\(457\) −20.6193 11.9046i −0.964530 0.556872i −0.0669658 0.997755i \(-0.521332\pi\)
−0.897564 + 0.440884i \(0.854665\pi\)
\(458\) 0 0
\(459\) −30.8301 + 13.2089i −1.43903 + 0.616540i
\(460\) 0 0
\(461\) 11.5986 3.10783i 0.540199 0.144746i 0.0216051 0.999767i \(-0.493122\pi\)
0.518594 + 0.855021i \(0.326456\pi\)
\(462\) 0 0
\(463\) 11.7247 6.76924i 0.544892 0.314593i −0.202168 0.979351i \(-0.564799\pi\)
0.747059 + 0.664758i \(0.231465\pi\)
\(464\) 0 0
\(465\) −5.76697 + 7.57868i −0.267437 + 0.351453i
\(466\) 0 0
\(467\) 11.6000 11.6000i 0.536784 0.536784i −0.385799 0.922583i \(-0.626074\pi\)
0.922583 + 0.385799i \(0.126074\pi\)
\(468\) 0 0
\(469\) −1.38070 1.38070i −0.0637549 0.0637549i
\(470\) 0 0
\(471\) 35.1128 14.7102i 1.61791 0.677808i
\(472\) 0 0
\(473\) −11.2893 19.5536i −0.519081 0.899075i
\(474\) 0 0
\(475\) 1.83176 + 6.83624i 0.0840471 + 0.313668i
\(476\) 0 0
\(477\) −14.2399 24.2118i −0.652002 1.10858i
\(478\) 0 0
\(479\) 2.09571 3.62988i 0.0957555 0.165853i −0.814168 0.580629i \(-0.802807\pi\)
0.909924 + 0.414776i \(0.136140\pi\)
\(480\) 0 0
\(481\) −1.40032 2.42543i −0.0638493 0.110590i
\(482\) 0 0
\(483\) 0.119431 + 0.154355i 0.00543432 + 0.00702338i
\(484\) 0 0
\(485\) −13.4582 + 13.4582i −0.611107 + 0.611107i
\(486\) 0 0
\(487\) 26.7152 1.21058 0.605291 0.796004i \(-0.293057\pi\)
0.605291 + 0.796004i \(0.293057\pi\)
\(488\) 0 0
\(489\) −0.372296 0.0474890i −0.0168358 0.00214753i
\(490\) 0 0
\(491\) 0.681269 2.54253i 0.0307452 0.114743i −0.948848 0.315733i \(-0.897749\pi\)
0.979593 + 0.200991i \(0.0644161\pi\)
\(492\) 0 0
\(493\) 8.79506 + 32.8236i 0.396109 + 1.47830i
\(494\) 0 0
\(495\) 12.4623 48.0549i 0.560137 2.15991i
\(496\) 0 0
\(497\) −2.10917 1.21773i −0.0946091 0.0546226i
\(498\) 0 0
\(499\) 2.46533 9.20074i 0.110363 0.411882i −0.888535 0.458809i \(-0.848276\pi\)
0.998898 + 0.0469272i \(0.0149429\pi\)
\(500\) 0 0
\(501\) −1.38718 + 3.38747i −0.0619745 + 0.151341i
\(502\) 0 0
\(503\) 11.5953i 0.517010i 0.966010 + 0.258505i \(0.0832299\pi\)
−0.966010 + 0.258505i \(0.916770\pi\)
\(504\) 0 0
\(505\) 23.9791i 1.06706i
\(506\) 0 0
\(507\) 5.74948 0.780505i 0.255343 0.0346634i
\(508\) 0 0
\(509\) 2.97882 11.1171i 0.132034 0.492757i −0.867959 0.496637i \(-0.834568\pi\)
0.999992 + 0.00387934i \(0.00123484\pi\)
\(510\) 0 0
\(511\) −9.59190 5.53789i −0.424321 0.244982i
\(512\) 0 0
\(513\) 4.10846 10.2679i 0.181393 0.453339i
\(514\) 0 0
\(515\) 5.07227 + 18.9300i 0.223511 + 0.834154i
\(516\) 0 0
\(517\) 0.271135 1.01189i 0.0119245 0.0445029i
\(518\) 0 0
\(519\) 2.35899 3.10007i 0.103548 0.136078i
\(520\) 0 0
\(521\) 12.7808 0.559939 0.279969 0.960009i \(-0.409676\pi\)
0.279969 + 0.960009i \(0.409676\pi\)
\(522\) 0 0
\(523\) 22.1010 22.1010i 0.966409 0.966409i −0.0330445 0.999454i \(-0.510520\pi\)
0.999454 + 0.0330445i \(0.0105203\pi\)
\(524\) 0 0
\(525\) −5.09303 + 12.4371i −0.222278 + 0.542800i
\(526\) 0 0
\(527\) −6.15020 10.6525i −0.267907 0.464029i
\(528\) 0 0
\(529\) −11.4988 + 19.9166i −0.499949 + 0.865938i
\(530\) 0 0
\(531\) 11.2305 + 6.36386i 0.487362 + 0.276168i
\(532\) 0 0
\(533\) −0.0325174 0.121357i −0.00140849 0.00525654i
\(534\) 0 0
\(535\) 24.3121 + 42.1097i 1.05110 + 1.82056i
\(536\) 0 0
\(537\) −1.34276 + 10.5268i −0.0579445 + 0.454263i
\(538\) 0 0
\(539\) −6.30635 6.30635i −0.271634 0.271634i
\(540\) 0 0
\(541\) 4.90029 4.90029i 0.210680 0.210680i −0.593876 0.804556i \(-0.702403\pi\)
0.804556 + 0.593876i \(0.202403\pi\)
\(542\) 0 0
\(543\) −33.8974 4.32385i −1.45468 0.185554i
\(544\) 0 0
\(545\) 1.83336 1.05849i 0.0785324 0.0453407i
\(546\) 0 0
\(547\) 29.1873 7.82071i 1.24796 0.334390i 0.426411 0.904529i \(-0.359778\pi\)
0.821548 + 0.570140i \(0.193111\pi\)
\(548\) 0 0
\(549\) −19.8697 + 0.160065i −0.848017 + 0.00683141i
\(550\) 0 0
\(551\) −9.70357 5.60236i −0.413386 0.238668i
\(552\) 0 0
\(553\) 17.0320 9.83343i 0.724275 0.418160i
\(554\) 0 0
\(555\) −3.20329 1.31176i −0.135972 0.0556809i
\(556\) 0 0
\(557\) 5.23259 + 5.23259i 0.221712 + 0.221712i 0.809219 0.587507i \(-0.199891\pi\)
−0.587507 + 0.809219i \(0.699891\pi\)
\(558\) 0 0
\(559\) 15.9185i 0.673281i
\(560\) 0 0
\(561\) 51.0275 + 38.8293i 2.15438 + 1.63937i
\(562\) 0 0
\(563\) 25.0312 + 6.70709i 1.05494 + 0.282670i 0.744291 0.667855i \(-0.232787\pi\)
0.310648 + 0.950525i \(0.399454\pi\)
\(564\) 0 0
\(565\) 30.8950 8.27830i 1.29976 0.348271i
\(566\) 0 0
\(567\) 18.0159 10.7921i 0.756595 0.453227i
\(568\) 0 0
\(569\) 12.2193 21.1644i 0.512259 0.887259i −0.487640 0.873045i \(-0.662142\pi\)
0.999899 0.0142138i \(-0.00452456\pi\)
\(570\) 0 0
\(571\) −5.29056 1.41760i −0.221403 0.0593248i 0.146412 0.989224i \(-0.453227\pi\)
−0.367815 + 0.929899i \(0.619894\pi\)
\(572\) 0 0
\(573\) 1.78548 + 13.1525i 0.0745893 + 0.549452i
\(574\) 0 0
\(575\) 0.160572 0.00669630
\(576\) 0 0
\(577\) 18.8956 0.786634 0.393317 0.919403i \(-0.371327\pi\)
0.393317 + 0.919403i \(0.371327\pi\)
\(578\) 0 0
\(579\) −12.1509 4.97581i −0.504973 0.206788i
\(580\) 0 0
\(581\) 27.9520 + 7.48972i 1.15964 + 0.310726i
\(582\) 0 0
\(583\) −26.8494 + 46.5045i −1.11199 + 1.92602i
\(584\) 0 0
\(585\) 24.5491 24.9479i 1.01498 1.03147i
\(586\) 0 0
\(587\) 40.3694 10.8169i 1.66622 0.446463i 0.702133 0.712045i \(-0.252231\pi\)
0.964088 + 0.265583i \(0.0855643\pi\)
\(588\) 0 0
\(589\) 3.91761 + 1.04972i 0.161422 + 0.0432530i
\(590\) 0 0
\(591\) 3.90523 30.6156i 0.160640 1.25936i
\(592\) 0 0
\(593\) 8.51816i 0.349799i 0.984586 + 0.174899i \(0.0559600\pi\)
−0.984586 + 0.174899i \(0.944040\pi\)
\(594\) 0 0
\(595\) −30.7306 30.7306i −1.25983 1.25983i
\(596\) 0 0
\(597\) −31.6571 + 24.4945i −1.29564 + 1.00249i
\(598\) 0 0
\(599\) 30.1886 17.4294i 1.23347 0.712145i 0.265719 0.964051i \(-0.414391\pi\)
0.967752 + 0.251906i \(0.0810573\pi\)
\(600\) 0 0
\(601\) −17.4933 10.0997i −0.713565 0.411977i 0.0988146 0.995106i \(-0.468495\pi\)
−0.812380 + 0.583129i \(0.801828\pi\)
\(602\) 0 0
\(603\) 2.18409 + 1.23763i 0.0889430 + 0.0504004i
\(604\) 0 0
\(605\) −61.0165 + 16.3493i −2.48067 + 0.664695i
\(606\) 0 0
\(607\) −0.0948018 + 0.0547339i −0.00384789 + 0.00222158i −0.501923 0.864912i \(-0.667374\pi\)
0.498075 + 0.867134i \(0.334040\pi\)
\(608\) 0 0
\(609\) −8.22148 19.6245i −0.333151 0.795224i
\(610\) 0 0
\(611\) 0.522253 0.522253i 0.0211281 0.0211281i
\(612\) 0 0
\(613\) 13.4094 + 13.4094i 0.541603 + 0.541603i 0.923999 0.382396i \(-0.124901\pi\)
−0.382396 + 0.923999i \(0.624901\pi\)
\(614\) 0 0
\(615\) −0.123573 0.0940328i −0.00498296 0.00379177i
\(616\) 0 0
\(617\) 1.92944 + 3.34190i 0.0776765 + 0.134540i 0.902247 0.431219i \(-0.141917\pi\)
−0.824571 + 0.565759i \(0.808583\pi\)
\(618\) 0 0
\(619\) −1.30529 4.87142i −0.0524642 0.195799i 0.934720 0.355386i \(-0.115650\pi\)
−0.987184 + 0.159587i \(0.948984\pi\)
\(620\) 0 0
\(621\) −0.200895 0.150330i −0.00806163 0.00603255i
\(622\) 0 0
\(623\) −3.32741 + 5.76324i −0.133310 + 0.230899i
\(624\) 0 0
\(625\) −15.2845 26.4735i −0.611379 1.05894i
\(626\) 0 0
\(627\) −20.9505 + 2.84408i −0.836682 + 0.113582i
\(628\) 0 0
\(629\) 3.16137 3.16137i 0.126052 0.126052i
\(630\) 0 0
\(631\) −33.0513 −1.31575 −0.657876 0.753127i \(-0.728545\pi\)
−0.657876 + 0.753127i \(0.728545\pi\)
\(632\) 0 0
\(633\) 8.85925 + 21.1468i 0.352123 + 0.840510i
\(634\) 0 0
\(635\) 9.02289 33.6739i 0.358063 1.33631i
\(636\) 0 0
\(637\) −1.62740 6.07355i −0.0644801 0.240643i
\(638\) 0 0
\(639\) 3.03089 + 0.786012i 0.119900 + 0.0310942i
\(640\) 0 0
\(641\) 3.03668 + 1.75323i 0.119942 + 0.0692483i 0.558770 0.829322i \(-0.311273\pi\)
−0.438829 + 0.898571i \(0.644607\pi\)
\(642\) 0 0
\(643\) −0.373234 + 1.39293i −0.0147189 + 0.0549318i −0.972895 0.231248i \(-0.925719\pi\)
0.958176 + 0.286180i \(0.0923856\pi\)
\(644\) 0 0
\(645\) −12.0399 15.5605i −0.474069 0.612693i
\(646\) 0 0
\(647\) 17.3282i 0.681241i 0.940201 + 0.340621i \(0.110637\pi\)
−0.940201 + 0.340621i \(0.889363\pi\)
\(648\) 0 0
\(649\) 24.6773i 0.968668i
\(650\) 0 0
\(651\) 4.71309 + 6.09126i 0.184721 + 0.238735i
\(652\) 0 0
\(653\) −1.08794 + 4.06026i −0.0425745 + 0.158890i −0.983940 0.178497i \(-0.942877\pi\)
0.941366 + 0.337387i \(0.109543\pi\)
\(654\) 0 0
\(655\) −6.77753 3.91301i −0.264820 0.152894i
\(656\) 0 0
\(657\) 13.7836 + 3.57456i 0.537751 + 0.139457i
\(658\) 0 0
\(659\) −12.1404 45.3085i −0.472922 1.76497i −0.629187 0.777254i \(-0.716612\pi\)
0.156265 0.987715i \(-0.450055\pi\)
\(660\) 0 0
\(661\) −8.48771 + 31.6766i −0.330134 + 1.23208i 0.578915 + 0.815388i \(0.303476\pi\)
−0.909049 + 0.416689i \(0.863191\pi\)
\(662\) 0 0
\(663\) 17.4681 + 41.6960i 0.678406 + 1.61934i
\(664\) 0 0
\(665\) 14.3299 0.555690
\(666\) 0 0
\(667\) −0.179755 + 0.179755i −0.00696015 + 0.00696015i
\(668\) 0 0
\(669\) −27.9871 + 3.79931i −1.08204 + 0.146890i
\(670\) 0 0
\(671\) 18.9935 + 32.8977i 0.733236 + 1.27000i
\(672\) 0 0
\(673\) −1.37128 + 2.37512i −0.0528588 + 0.0915541i −0.891244 0.453524i \(-0.850167\pi\)
0.838385 + 0.545078i \(0.183500\pi\)
\(674\) 0 0
\(675\) 2.04815 17.1567i 0.0788333 0.660363i
\(676\) 0 0
\(677\) 9.17117 + 34.2273i 0.352477 + 1.31546i 0.883630 + 0.468185i \(0.155092\pi\)
−0.531154 + 0.847276i \(0.678241\pi\)
\(678\) 0 0
\(679\) 7.69612 + 13.3301i 0.295350 + 0.511561i
\(680\) 0 0
\(681\) 31.7441 + 24.1556i 1.21644 + 0.925645i
\(682\) 0 0
\(683\) 0.646566 + 0.646566i 0.0247402 + 0.0247402i 0.719369 0.694628i \(-0.244431\pi\)
−0.694628 + 0.719369i \(0.744431\pi\)
\(684\) 0 0
\(685\) 30.6796 30.6796i 1.17221 1.17221i
\(686\) 0 0
\(687\) 13.0802 + 31.2221i 0.499041 + 1.19120i
\(688\) 0 0
\(689\) −32.7870 + 18.9296i −1.24908 + 0.721159i
\(690\) 0 0
\(691\) 34.5305 9.25241i 1.31360 0.351978i 0.467024 0.884245i \(-0.345326\pi\)
0.846577 + 0.532266i \(0.178659\pi\)
\(692\) 0 0
\(693\) −34.9303 19.7936i −1.32689 0.751895i
\(694\) 0 0
\(695\) −21.4444 12.3810i −0.813434 0.469636i
\(696\) 0 0
\(697\) 0.173693 0.100282i 0.00657908 0.00379844i
\(698\) 0 0
\(699\) −25.2081 + 19.5047i −0.953458 + 0.737734i
\(700\) 0 0
\(701\) −25.7079 25.7079i −0.970975 0.970975i 0.0286153 0.999590i \(-0.490890\pi\)
−0.999590 + 0.0286153i \(0.990890\pi\)
\(702\) 0 0
\(703\) 1.47417i 0.0555995i
\(704\) 0 0
\(705\) 0.115504 0.905509i 0.00435013 0.0341034i
\(706\) 0 0
\(707\) 18.7316 + 5.01912i 0.704474 + 0.188763i
\(708\) 0 0
\(709\) 24.0199 6.43610i 0.902085 0.241713i 0.222173 0.975007i \(-0.428685\pi\)
0.679911 + 0.733294i \(0.262018\pi\)
\(710\) 0 0
\(711\) −17.7344 + 18.0225i −0.665093 + 0.675896i
\(712\) 0 0
\(713\) 0.0460091 0.0796901i 0.00172305 0.00298442i
\(714\) 0 0
\(715\) −64.6326 17.3183i −2.41712 0.647666i
\(716\) 0 0
\(717\) −39.8562 16.3212i −1.48846 0.609527i
\(718\) 0 0
\(719\) −3.00765 −0.112167 −0.0560833 0.998426i \(-0.517861\pi\)
−0.0560833 + 0.998426i \(0.517861\pi\)
\(720\) 0 0
\(721\) 15.8491 0.590251
\(722\) 0 0
\(723\) −0.119395 0.879510i −0.00444036 0.0327093i
\(724\) 0 0
\(725\) −16.9092 4.53080i −0.627992 0.168270i
\(726\) 0 0
\(727\) 19.1265 33.1281i 0.709363 1.22865i −0.255730 0.966748i \(-0.582316\pi\)
0.965094 0.261905i \(-0.0843507\pi\)
\(728\) 0 0
\(729\) −18.6250 + 19.5477i −0.689814 + 0.723987i
\(730\) 0 0
\(731\) 24.5458 6.57703i 0.907859 0.243260i
\(732\) 0 0
\(733\) −11.4887 3.07838i −0.424343 0.113702i 0.0403263 0.999187i \(-0.487160\pi\)
−0.464670 + 0.885484i \(0.653827\pi\)
\(734\) 0 0
\(735\) −6.18449 4.70608i −0.228119 0.173586i
\(736\) 0 0
\(737\) 4.79920i 0.176781i
\(738\) 0 0
\(739\) 30.0692 + 30.0692i 1.10611 + 1.10611i 0.993657 + 0.112457i \(0.0358720\pi\)
0.112457 + 0.993657i \(0.464128\pi\)
\(740\) 0 0
\(741\) −13.7944 5.64883i −0.506748 0.207515i
\(742\) 0 0
\(743\) 4.00273 2.31098i 0.146846 0.0847815i −0.424777 0.905298i \(-0.639647\pi\)
0.571623 + 0.820517i \(0.306314\pi\)
\(744\) 0 0
\(745\) 2.52821 + 1.45966i 0.0926264 + 0.0534779i
\(746\) 0 0
\(747\) −37.2031 + 0.299699i −1.36119 + 0.0109654i
\(748\) 0 0
\(749\) 37.9834 10.1776i 1.38788 0.371882i
\(750\) 0 0
\(751\) −10.7097 + 6.18323i −0.390801 + 0.225629i −0.682507 0.730879i \(-0.739110\pi\)
0.291706 + 0.956508i \(0.405777\pi\)
\(752\) 0 0
\(753\) 19.1576 + 2.44369i 0.698142 + 0.0890529i
\(754\) 0 0
\(755\) −33.8442 + 33.8442i −1.23172 + 1.23172i
\(756\) 0 0
\(757\) 15.8033 + 15.8033i 0.574380 + 0.574380i 0.933349 0.358969i \(-0.116872\pi\)
−0.358969 + 0.933349i \(0.616872\pi\)
\(758\) 0 0
\(759\) −0.0606953 + 0.475829i −0.00220310 + 0.0172715i
\(760\) 0 0
\(761\) −3.67823 6.37089i −0.133336 0.230944i 0.791625 0.611008i \(-0.209236\pi\)
−0.924961 + 0.380063i \(0.875902\pi\)
\(762\) 0 0
\(763\) −0.443110 1.65371i −0.0160416 0.0598682i
\(764\) 0 0
\(765\) 48.6117 + 27.5463i 1.75756 + 0.995938i
\(766\) 0 0
\(767\) 8.69908 15.0673i 0.314106 0.544047i
\(768\) 0 0
\(769\) 0.792301 + 1.37231i 0.0285711 + 0.0494866i 0.879957 0.475053i \(-0.157571\pi\)
−0.851386 + 0.524539i \(0.824238\pi\)
\(770\) 0 0
\(771\) 8.07107 19.7094i 0.290672 0.709818i
\(772\) 0 0
\(773\) −6.11545 + 6.11545i −0.219958 + 0.219958i −0.808481 0.588523i \(-0.799710\pi\)
0.588523 + 0.808481i \(0.299710\pi\)
\(774\) 0 0
\(775\) 6.33660 0.227617
\(776\) 0 0
\(777\) −1.69518 + 2.22773i −0.0608144 + 0.0799193i
\(778\) 0 0
\(779\) −0.0171161 + 0.0638783i −0.000613249 + 0.00228868i
\(780\) 0 0
\(781\) −1.54928 5.78201i −0.0554377 0.206896i
\(782\) 0 0
\(783\) 16.9136 + 21.4993i 0.604444 + 0.768323i
\(784\) 0 0
\(785\) −54.9221 31.7093i −1.96025 1.13175i
\(786\) 0 0
\(787\) −7.49992 + 27.9901i −0.267343 + 0.997739i 0.693457 + 0.720498i \(0.256087\pi\)
−0.960800 + 0.277241i \(0.910580\pi\)
\(788\) 0 0
\(789\) 16.7768 2.27749i 0.597271 0.0810809i
\(790\) 0 0
\(791\) 25.8668i 0.919719i
\(792\) 0 0
\(793\) 26.7819i 0.951053i
\(794\) 0 0
\(795\) −17.7323 + 43.3021i −0.628900 + 1.53577i
\(796\) 0 0
\(797\) −11.6075 + 43.3197i −0.411158 + 1.53446i 0.381250 + 0.924472i \(0.375494\pi\)
−0.792408 + 0.609991i \(0.791173\pi\)
\(798\) 0 0
\(799\) 1.02107 + 0.589518i 0.0361230 + 0.0208556i
\(800\) 0 0
\(801\) 2.14776 8.28182i 0.0758872 0.292624i
\(802\) 0 0
\(803\) −7.04571 26.2949i −0.248638 0.927928i
\(804\) 0 0
\(805\) 0.0841464 0.314039i 0.00296577 0.0110684i
\(806\) 0 0
\(807\) 13.7096 + 1.74876i 0.482602 + 0.0615593i
\(808\) 0 0
\(809\) 17.6588 0.620851 0.310426 0.950598i \(-0.399528\pi\)
0.310426 + 0.950598i \(0.399528\pi\)
\(810\) 0 0
\(811\) 0.326636 0.326636i 0.0114697 0.0114697i −0.701349 0.712818i \(-0.747418\pi\)
0.712818 + 0.701349i \(0.247418\pi\)
\(812\) 0 0
\(813\) −11.7148 15.1404i −0.410856 0.530996i
\(814\) 0 0
\(815\) 0.312609 + 0.541455i 0.0109502 + 0.0189663i
\(816\) 0 0
\(817\) −4.18950 + 7.25642i −0.146572 + 0.253870i
\(818\) 0 0
\(819\) −14.3499 24.3988i −0.501427 0.852563i
\(820\) 0 0
\(821\) −10.5662 39.4337i −0.368764 1.37625i −0.862246 0.506490i \(-0.830943\pi\)
0.493482 0.869756i \(-0.335724\pi\)
\(822\) 0 0
\(823\) −3.27150 5.66640i −0.114037 0.197518i 0.803357 0.595497i \(-0.203045\pi\)
−0.917394 + 0.397979i \(0.869712\pi\)
\(824\) 0 0
\(825\) −30.4666 + 12.7637i −1.06071 + 0.444375i
\(826\) 0 0
\(827\) 0.510932 + 0.510932i 0.0177668 + 0.0177668i 0.715934 0.698168i \(-0.246001\pi\)
−0.698168 + 0.715934i \(0.746001\pi\)
\(828\) 0 0
\(829\) 0.210205 0.210205i 0.00730073 0.00730073i −0.703447 0.710748i \(-0.748357\pi\)
0.710748 + 0.703447i \(0.248357\pi\)
\(830\) 0 0
\(831\) 27.4427 36.0639i 0.951976 1.25104i
\(832\) 0 0
\(833\) 8.69283 5.01881i 0.301189 0.173891i
\(834\) 0 0
\(835\) 5.89009 1.57824i 0.203835 0.0546174i
\(836\) 0 0
\(837\) −7.92785 5.93245i −0.274027 0.205055i
\(838\) 0 0
\(839\) −25.1098 14.4971i −0.866885 0.500496i −0.000573152 1.00000i \(-0.500182\pi\)
−0.866312 + 0.499504i \(0.833516\pi\)
\(840\) 0 0
\(841\) −1.11330 + 0.642762i −0.0383895 + 0.0221642i
\(842\) 0 0
\(843\) 5.98520 + 44.0891i 0.206141 + 1.51851i
\(844\) 0 0
\(845\) −6.83466 6.83466i −0.235119 0.235119i
\(846\) 0 0
\(847\) 51.0860i 1.75534i
\(848\) 0 0
\(849\) −51.8700 + 21.7304i −1.78018 + 0.745787i
\(850\) 0 0
\(851\) 0.0323063 + 0.00865646i 0.00110745 + 0.000296740i
\(852\) 0 0
\(853\) 27.1702 7.28025i 0.930292 0.249271i 0.238313 0.971189i \(-0.423406\pi\)
0.691979 + 0.721918i \(0.256739\pi\)
\(854\) 0 0
\(855\) −17.7566 + 4.91150i −0.607262 + 0.167970i
\(856\) 0 0
\(857\) 28.3745 49.1461i 0.969256 1.67880i 0.271537 0.962428i \(-0.412468\pi\)
0.697719 0.716372i \(-0.254198\pi\)
\(858\) 0 0
\(859\) 6.27967 + 1.68263i 0.214259 + 0.0574106i 0.364352 0.931261i \(-0.381291\pi\)
−0.150093 + 0.988672i \(0.547957\pi\)
\(860\) 0 0
\(861\) −0.0993205 + 0.0768489i −0.00338483 + 0.00261900i
\(862\) 0 0
\(863\) −12.7093 −0.432629 −0.216314 0.976324i \(-0.569404\pi\)
−0.216314 + 0.976324i \(0.569404\pi\)
\(864\) 0 0
\(865\) −6.48942 −0.220647
\(866\) 0 0
\(867\) −33.7887 + 26.1439i −1.14753 + 0.887894i
\(868\) 0 0
\(869\) 46.6910 + 12.5108i 1.58388 + 0.424400i
\(870\) 0 0
\(871\) 1.69178 2.93026i 0.0573239 0.0992880i
\(872\) 0 0
\(873\) −14.1053 13.8798i −0.477391 0.469761i
\(874\) 0 0
\(875\) −10.8915 + 2.91836i −0.368199 + 0.0986587i
\(876\) 0 0
\(877\) 35.3558 + 9.47357i 1.19388 + 0.319900i 0.800419 0.599441i \(-0.204610\pi\)
0.393463 + 0.919341i \(0.371277\pi\)
\(878\) 0 0
\(879\) −36.4818 + 15.2837i −1.23050 + 0.515506i
\(880\) 0 0
\(881\) 39.6546i 1.33600i −0.744163 0.667998i \(-0.767151\pi\)
0.744163 0.667998i \(-0.232849\pi\)
\(882\) 0 0
\(883\) −16.6423 16.6423i −0.560060 0.560060i 0.369265 0.929324i \(-0.379610\pi\)
−0.929324 + 0.369265i \(0.879610\pi\)
\(884\) 0 0
\(885\) −2.89259 21.3079i −0.0972334 0.716256i
\(886\) 0 0
\(887\) −0.0199051 + 0.0114922i −0.000668349 + 0.000385871i −0.500334 0.865832i \(-0.666789\pi\)
0.499666 + 0.866218i \(0.333456\pi\)
\(888\) 0 0
\(889\) −24.4162 14.0967i −0.818894 0.472789i
\(890\) 0 0
\(891\) 50.0671 + 12.5545i 1.67731 + 0.420593i
\(892\) 0 0
\(893\) −0.375517 + 0.100619i −0.0125662 + 0.00336710i
\(894\) 0 0
\(895\) 15.3098 8.83910i 0.511749 0.295458i
\(896\) 0 0
\(897\) −0.204795 + 0.269132i −0.00683791 + 0.00898605i
\(898\) 0 0
\(899\) −7.09363 + 7.09363i −0.236586 + 0.236586i
\(900\) 0 0
\(901\) −42.7353 42.7353i −1.42372 1.42372i
\(902\) 0 0
\(903\) −14.6754 + 6.14810i −0.488366 + 0.204596i
\(904\) 0 0
\(905\) 28.4629 + 49.2992i 0.946140 + 1.63876i
\(906\) 0 0
\(907\) −10.2175 38.1323i −0.339267 1.26616i −0.899169 0.437602i \(-0.855828\pi\)
0.559902 0.828559i \(-0.310839\pi\)
\(908\) 0 0
\(909\) −24.9311 + 0.200838i −0.826911 + 0.00666139i
\(910\) 0 0
\(911\) −22.7704 + 39.4395i −0.754417 + 1.30669i 0.191246 + 0.981542i \(0.438747\pi\)
−0.945664 + 0.325147i \(0.894586\pi\)
\(912\) 0 0
\(913\) 35.5626 + 61.5962i 1.17695 + 2.03854i
\(914\) 0 0
\(915\) 20.2563 + 26.1795i 0.669653 + 0.865469i
\(916\) 0 0
\(917\) −4.47532 + 4.47532i −0.147788 + 0.147788i
\(918\) 0 0
\(919\) 11.2611 0.371468 0.185734 0.982600i \(-0.440534\pi\)
0.185734 + 0.982600i \(0.440534\pi\)
\(920\) 0 0
\(921\) −25.0571 3.19621i −0.825659 0.105319i
\(922\) 0 0
\(923\) 1.09229 4.07647i 0.0359531 0.134179i
\(924\) 0 0
\(925\) 0.596105 + 2.22469i 0.0195998 + 0.0731475i
\(926\) 0 0
\(927\) −19.6390 + 5.43219i −0.645030 + 0.178417i
\(928\) 0 0
\(929\) −16.8724 9.74127i −0.553564 0.319601i 0.196994 0.980405i \(-0.436882\pi\)
−0.750558 + 0.660804i \(0.770215\pi\)
\(930\) 0 0
\(931\) −0.856614 + 3.19693i −0.0280744 + 0.104775i
\(932\) 0 0
\(933\) 0.672889 1.64319i 0.0220294 0.0537955i
\(934\) 0 0
\(935\) 106.817i 3.49328i
\(936\) 0 0
\(937\) 5.47240i 0.178775i −0.995997 0.0893877i \(-0.971509\pi\)
0.995997 0.0893877i \(-0.0284910\pi\)
\(938\) 0 0
\(939\) 18.8947 2.56499i 0.616604 0.0837054i
\(940\) 0 0
\(941\) 3.21380 11.9941i 0.104767 0.390995i −0.893552 0.448960i \(-0.851795\pi\)
0.998319 + 0.0579650i \(0.0184612\pi\)
\(942\) 0 0
\(943\) 0.00129938 0.000750197i 4.23136e−5 2.44298e-5i
\(944\) 0 0
\(945\) −32.4811 12.9965i −1.05661 0.422778i
\(946\) 0 0
\(947\) −0.00640230 0.0238937i −0.000208047 0.000776441i 0.965822 0.259207i \(-0.0834613\pi\)
−0.966030 + 0.258431i \(0.916795\pi\)
\(948\) 0 0
\(949\) 4.96742 18.5387i 0.161249 0.601790i
\(950\) 0 0
\(951\) 19.9218 26.1802i 0.646008 0.848952i
\(952\) 0 0
\(953\) −47.9215 −1.55233 −0.776164 0.630531i \(-0.782837\pi\)
−0.776164 + 0.630531i \(0.782837\pi\)
\(954\) 0 0
\(955\) 15.6349 15.6349i 0.505934 0.505934i
\(956\) 0 0
\(957\) 19.8179 48.3951i 0.640622 1.56439i
\(958\) 0 0
\(959\) −17.5442 30.3875i −0.566532 0.981262i
\(960\) 0 0
\(961\) −13.6844 + 23.7020i −0.441431 + 0.764581i
\(962\) 0 0
\(963\) −43.5779 + 25.6299i −1.40428 + 0.825913i
\(964\) 0 0
\(965\) 5.66117 + 21.1278i 0.182240 + 0.680127i
\(966\) 0 0
\(967\) −6.27580 10.8700i −0.201816 0.349556i 0.747297 0.664490i \(-0.231351\pi\)
−0.949114 + 0.314934i \(0.898018\pi\)
\(968\) 0 0
\(969\) 3.01090 23.6044i 0.0967242 0.758282i
\(970\) 0 0
\(971\) −16.0701 16.0701i −0.515715 0.515715i 0.400557 0.916272i \(-0.368817\pi\)
−0.916272 + 0.400557i \(0.868817\pi\)
\(972\) 0 0
\(973\) −14.1601 + 14.1601i −0.453953 + 0.453953i
\(974\) 0 0
\(975\) −23.1015 2.94675i −0.739839 0.0943716i
\(976\) 0 0
\(977\) 47.1397 27.2161i 1.50813 0.870721i 0.508178 0.861252i \(-0.330319\pi\)
0.999955 0.00946892i \(-0.00301410\pi\)
\(978\) 0 0
\(979\) −15.7992 + 4.23337i −0.504943 + 0.135299i
\(980\) 0 0
\(981\) 1.11587 + 1.89728i 0.0356269 + 0.0605754i
\(982\) 0 0
\(983\) −16.9623 9.79319i −0.541014 0.312354i 0.204476 0.978872i \(-0.434451\pi\)
−0.745490 + 0.666517i \(0.767784\pi\)
\(984\) 0 0
\(985\) −44.5262 + 25.7072i −1.41872 + 0.819101i
\(986\) 0 0
\(987\) −0.683175 0.279762i −0.0217457 0.00890491i
\(988\) 0 0
\(989\) 0.134423 + 0.134423i 0.00427439 + 0.00427439i
\(990\) 0 0
\(991\) 29.8539i 0.948341i 0.880433 + 0.474171i \(0.157252\pi\)
−0.880433 + 0.474171i \(0.842748\pi\)
\(992\) 0 0
\(993\) −26.3260 20.0327i −0.835429 0.635717i
\(994\) 0 0
\(995\) 64.4071 + 17.2578i 2.04184 + 0.547110i
\(996\) 0 0
\(997\) 27.6880 7.41898i 0.876888 0.234961i 0.207824 0.978166i \(-0.433362\pi\)
0.669064 + 0.743205i \(0.266695\pi\)
\(998\) 0 0
\(999\) 1.33700 3.34145i 0.0423009 0.105719i
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 576.2.y.a.335.18 88
3.2 odd 2 1728.2.z.a.143.19 88
4.3 odd 2 144.2.u.a.11.2 88
9.4 even 3 1728.2.z.a.719.19 88
9.5 odd 6 inner 576.2.y.a.527.7 88
12.11 even 2 432.2.v.a.251.21 88
16.3 odd 4 inner 576.2.y.a.47.7 88
16.13 even 4 144.2.u.a.83.10 yes 88
36.23 even 6 144.2.u.a.59.10 yes 88
36.31 odd 6 432.2.v.a.395.13 88
48.29 odd 4 432.2.v.a.35.13 88
48.35 even 4 1728.2.z.a.1007.19 88
144.13 even 12 432.2.v.a.179.21 88
144.67 odd 12 1728.2.z.a.1583.19 88
144.77 odd 12 144.2.u.a.131.2 yes 88
144.131 even 12 inner 576.2.y.a.239.18 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.2 88 4.3 odd 2
144.2.u.a.59.10 yes 88 36.23 even 6
144.2.u.a.83.10 yes 88 16.13 even 4
144.2.u.a.131.2 yes 88 144.77 odd 12
432.2.v.a.35.13 88 48.29 odd 4
432.2.v.a.179.21 88 144.13 even 12
432.2.v.a.251.21 88 12.11 even 2
432.2.v.a.395.13 88 36.31 odd 6
576.2.y.a.47.7 88 16.3 odd 4 inner
576.2.y.a.239.18 88 144.131 even 12 inner
576.2.y.a.335.18 88 1.1 even 1 trivial
576.2.y.a.527.7 88 9.5 odd 6 inner
1728.2.z.a.143.19 88 3.2 odd 2
1728.2.z.a.719.19 88 9.4 even 3
1728.2.z.a.1007.19 88 48.35 even 4
1728.2.z.a.1583.19 88 144.67 odd 12