Properties

Label 912.2.bo.a.289.1
Level $912$
Weight $2$
Character 912.289
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
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] = [912,2,Mod(289,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("912.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 289.1
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 912.289
Dual form 912.2.bo.a.385.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.173648 - 0.984808i) q^{3} +(-0.907604 + 0.761570i) q^{5} +(-0.733956 + 1.27125i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\) \(q+(-0.173648 - 0.984808i) q^{3} +(-0.907604 + 0.761570i) q^{5} +(-0.733956 + 1.27125i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.592396 + 1.02606i) q^{11} +(0.446967 - 2.53487i) q^{13} +(0.907604 + 0.761570i) q^{15} +(-2.09240 - 0.761570i) q^{17} +(-0.819078 + 4.28125i) q^{19} +(1.37939 + 0.502055i) q^{21} +(-0.907604 - 0.761570i) q^{23} +(-0.624485 + 3.54163i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-8.84389 + 3.21891i) q^{29} +(-3.96451 + 6.86673i) q^{31} +(0.907604 - 0.761570i) q^{33} +(-0.302004 - 1.71275i) q^{35} -0.0641778 q^{37} -2.57398 q^{39} +(1.68092 + 9.53298i) q^{41} +(5.55303 - 4.65955i) q^{43} +(0.592396 - 1.02606i) q^{45} +(-4.57145 + 1.66387i) q^{47} +(2.42262 + 4.19610i) q^{49} +(-0.386659 + 2.19285i) q^{51} +(-1.11334 - 0.934204i) q^{53} +(-1.31908 - 0.480105i) q^{55} +(4.35844 + 0.0632028i) q^{57} +(1.31908 + 0.480105i) q^{59} +(5.97565 + 5.01417i) q^{61} +(0.254900 - 1.44561i) q^{63} +(1.52481 + 2.64106i) q^{65} +(8.19119 - 2.98135i) q^{67} +(-0.592396 + 1.02606i) q^{69} +(-11.2135 + 9.40923i) q^{71} +(1.13563 + 6.44047i) q^{73} +3.59627 q^{75} -1.73917 q^{77} +(-2.24035 - 12.7057i) q^{79} +(0.766044 - 0.642788i) q^{81} +(1.94949 - 3.37662i) q^{83} +(2.47906 - 0.902302i) q^{85} +(4.70574 + 8.15058i) q^{87} +(2.15523 - 12.2229i) q^{89} +(2.89440 + 2.42869i) q^{91} +(7.45084 + 2.71188i) q^{93} +(-2.51707 - 4.50946i) q^{95} +(-12.1356 - 4.41701i) q^{97} +(-0.907604 - 0.761570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 9 q^{5} - 9 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 9 q^{5} - 9 q^{7} + 15 q^{13} + 9 q^{15} - 9 q^{17} + 12 q^{19} - 3 q^{21} - 9 q^{23} + 9 q^{25} + 3 q^{27} - 9 q^{29} + 9 q^{31} + 9 q^{33} + 36 q^{35} + 18 q^{37} + 27 q^{41} + 21 q^{43} - 27 q^{47} - 12 q^{49} - 9 q^{51} + 9 q^{55} + 18 q^{57} - 9 q^{59} - 3 q^{61} + 3 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{71} - 12 q^{73} - 6 q^{75} + 18 q^{77} + 21 q^{79} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 24 q^{91} + 33 q^{93} - 36 q^{95} - 54 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.173648 0.984808i −0.100256 0.568579i
\(4\) 0 0
\(5\) −0.907604 + 0.761570i −0.405893 + 0.340584i −0.822766 0.568380i \(-0.807570\pi\)
0.416873 + 0.908965i \(0.363126\pi\)
\(6\) 0 0
\(7\) −0.733956 + 1.27125i −0.277409 + 0.480487i −0.970740 0.240133i \(-0.922809\pi\)
0.693331 + 0.720619i \(0.256142\pi\)
\(8\) 0 0
\(9\) −0.939693 + 0.342020i −0.313231 + 0.114007i
\(10\) 0 0
\(11\) 0.592396 + 1.02606i 0.178614 + 0.309369i 0.941406 0.337275i \(-0.109505\pi\)
−0.762792 + 0.646644i \(0.776172\pi\)
\(12\) 0 0
\(13\) 0.446967 2.53487i 0.123966 0.703047i −0.857950 0.513733i \(-0.828262\pi\)
0.981916 0.189315i \(-0.0606266\pi\)
\(14\) 0 0
\(15\) 0.907604 + 0.761570i 0.234342 + 0.196637i
\(16\) 0 0
\(17\) −2.09240 0.761570i −0.507481 0.184708i 0.0755749 0.997140i \(-0.475921\pi\)
−0.583056 + 0.812432i \(0.698143\pi\)
\(18\) 0 0
\(19\) −0.819078 + 4.28125i −0.187909 + 0.982186i
\(20\) 0 0
\(21\) 1.37939 + 0.502055i 0.301007 + 0.109557i
\(22\) 0 0
\(23\) −0.907604 0.761570i −0.189248 0.158798i 0.543241 0.839577i \(-0.317197\pi\)
−0.732489 + 0.680779i \(0.761642\pi\)
\(24\) 0 0
\(25\) −0.624485 + 3.54163i −0.124897 + 0.708326i
\(26\) 0 0
\(27\) 0.500000 + 0.866025i 0.0962250 + 0.166667i
\(28\) 0 0
\(29\) −8.84389 + 3.21891i −1.64227 + 0.597737i −0.987434 0.158034i \(-0.949485\pi\)
−0.654836 + 0.755771i \(0.727262\pi\)
\(30\) 0 0
\(31\) −3.96451 + 6.86673i −0.712047 + 1.23330i 0.252041 + 0.967717i \(0.418898\pi\)
−0.964088 + 0.265584i \(0.914435\pi\)
\(32\) 0 0
\(33\) 0.907604 0.761570i 0.157994 0.132572i
\(34\) 0 0
\(35\) −0.302004 1.71275i −0.0510479 0.289507i
\(36\) 0 0
\(37\) −0.0641778 −0.0105508 −0.00527538 0.999986i \(-0.501679\pi\)
−0.00527538 + 0.999986i \(0.501679\pi\)
\(38\) 0 0
\(39\) −2.57398 −0.412166
\(40\) 0 0
\(41\) 1.68092 + 9.53298i 0.262516 + 1.48880i 0.776017 + 0.630713i \(0.217237\pi\)
−0.513501 + 0.858089i \(0.671652\pi\)
\(42\) 0 0
\(43\) 5.55303 4.65955i 0.846830 0.710574i −0.112259 0.993679i \(-0.535809\pi\)
0.959089 + 0.283104i \(0.0913643\pi\)
\(44\) 0 0
\(45\) 0.592396 1.02606i 0.0883092 0.152956i
\(46\) 0 0
\(47\) −4.57145 + 1.66387i −0.666815 + 0.242701i −0.653176 0.757206i \(-0.726564\pi\)
−0.0136389 + 0.999907i \(0.504342\pi\)
\(48\) 0 0
\(49\) 2.42262 + 4.19610i 0.346088 + 0.599443i
\(50\) 0 0
\(51\) −0.386659 + 2.19285i −0.0541431 + 0.307061i
\(52\) 0 0
\(53\) −1.11334 0.934204i −0.152929 0.128323i 0.563113 0.826380i \(-0.309604\pi\)
−0.716042 + 0.698057i \(0.754048\pi\)
\(54\) 0 0
\(55\) −1.31908 0.480105i −0.177864 0.0647374i
\(56\) 0 0
\(57\) 4.35844 + 0.0632028i 0.577290 + 0.00837141i
\(58\) 0 0
\(59\) 1.31908 + 0.480105i 0.171729 + 0.0625044i 0.426454 0.904509i \(-0.359763\pi\)
−0.254725 + 0.967014i \(0.581985\pi\)
\(60\) 0 0
\(61\) 5.97565 + 5.01417i 0.765104 + 0.641998i 0.939450 0.342686i \(-0.111337\pi\)
−0.174346 + 0.984684i \(0.555781\pi\)
\(62\) 0 0
\(63\) 0.254900 1.44561i 0.0321144 0.182130i
\(64\) 0 0
\(65\) 1.52481 + 2.64106i 0.189130 + 0.327583i
\(66\) 0 0
\(67\) 8.19119 2.98135i 1.00071 0.364230i 0.210854 0.977518i \(-0.432376\pi\)
0.789859 + 0.613288i \(0.210153\pi\)
\(68\) 0 0
\(69\) −0.592396 + 1.02606i −0.0713161 + 0.123523i
\(70\) 0 0
\(71\) −11.2135 + 9.40923i −1.33079 + 1.11667i −0.346904 + 0.937901i \(0.612767\pi\)
−0.983891 + 0.178769i \(0.942789\pi\)
\(72\) 0 0
\(73\) 1.13563 + 6.44047i 0.132915 + 0.753801i 0.976289 + 0.216473i \(0.0694552\pi\)
−0.843373 + 0.537328i \(0.819434\pi\)
\(74\) 0 0
\(75\) 3.59627 0.415261
\(76\) 0 0
\(77\) −1.73917 −0.198197
\(78\) 0 0
\(79\) −2.24035 12.7057i −0.252059 1.42950i −0.803510 0.595292i \(-0.797037\pi\)
0.551450 0.834208i \(-0.314075\pi\)
\(80\) 0 0
\(81\) 0.766044 0.642788i 0.0851160 0.0714208i
\(82\) 0 0
\(83\) 1.94949 3.37662i 0.213985 0.370632i −0.738973 0.673735i \(-0.764689\pi\)
0.952958 + 0.303102i \(0.0980224\pi\)
\(84\) 0 0
\(85\) 2.47906 0.902302i 0.268891 0.0978684i
\(86\) 0 0
\(87\) 4.70574 + 8.15058i 0.504508 + 0.873833i
\(88\) 0 0
\(89\) 2.15523 12.2229i 0.228454 1.29563i −0.627517 0.778603i \(-0.715929\pi\)
0.855971 0.517024i \(-0.172960\pi\)
\(90\) 0 0
\(91\) 2.89440 + 2.42869i 0.303416 + 0.254596i
\(92\) 0 0
\(93\) 7.45084 + 2.71188i 0.772616 + 0.281209i
\(94\) 0 0
\(95\) −2.51707 4.50946i −0.258246 0.462661i
\(96\) 0 0
\(97\) −12.1356 4.41701i −1.23219 0.448479i −0.357841 0.933783i \(-0.616487\pi\)
−0.874346 + 0.485303i \(0.838709\pi\)
\(98\) 0 0
\(99\) −0.907604 0.761570i −0.0912176 0.0765407i
\(100\) 0 0
\(101\) 2.38578 13.5304i 0.237394 1.34633i −0.600118 0.799911i \(-0.704880\pi\)
0.837513 0.546418i \(-0.184009\pi\)
\(102\) 0 0
\(103\) 8.56805 + 14.8403i 0.844235 + 1.46226i 0.886284 + 0.463142i \(0.153278\pi\)
−0.0420491 + 0.999116i \(0.513389\pi\)
\(104\) 0 0
\(105\) −1.63429 + 0.594831i −0.159490 + 0.0580496i
\(106\) 0 0
\(107\) −5.25150 + 9.09586i −0.507681 + 0.879330i 0.492279 + 0.870437i \(0.336164\pi\)
−0.999960 + 0.00889246i \(0.997169\pi\)
\(108\) 0 0
\(109\) −6.16044 + 5.16923i −0.590064 + 0.495122i −0.888234 0.459390i \(-0.848068\pi\)
0.298171 + 0.954512i \(0.403623\pi\)
\(110\) 0 0
\(111\) 0.0111444 + 0.0632028i 0.00105778 + 0.00599894i
\(112\) 0 0
\(113\) −19.1411 −1.80065 −0.900324 0.435220i \(-0.856670\pi\)
−0.900324 + 0.435220i \(0.856670\pi\)
\(114\) 0 0
\(115\) 1.40373 0.130899
\(116\) 0 0
\(117\) 0.446967 + 2.53487i 0.0413221 + 0.234349i
\(118\) 0 0
\(119\) 2.50387 2.10100i 0.229529 0.192598i
\(120\) 0 0
\(121\) 4.79813 8.31061i 0.436194 0.755510i
\(122\) 0 0
\(123\) 9.09627 3.31077i 0.820183 0.298522i
\(124\) 0 0
\(125\) −5.09240 8.82029i −0.455478 0.788911i
\(126\) 0 0
\(127\) −1.26352 + 7.16577i −0.112119 + 0.635859i 0.876017 + 0.482280i \(0.160191\pi\)
−0.988136 + 0.153579i \(0.950920\pi\)
\(128\) 0 0
\(129\) −5.55303 4.65955i −0.488917 0.410250i
\(130\) 0 0
\(131\) −6.48293 2.35959i −0.566416 0.206159i 0.0429093 0.999079i \(-0.486337\pi\)
−0.609325 + 0.792920i \(0.708560\pi\)
\(132\) 0 0
\(133\) −4.84137 4.18350i −0.419800 0.362755i
\(134\) 0 0
\(135\) −1.11334 0.405223i −0.0958211 0.0348760i
\(136\) 0 0
\(137\) 12.1211 + 10.1708i 1.03557 + 0.868950i 0.991504 0.130079i \(-0.0415230\pi\)
0.0440702 + 0.999028i \(0.485967\pi\)
\(138\) 0 0
\(139\) 2.68732 15.2405i 0.227935 1.29269i −0.629058 0.777358i \(-0.716559\pi\)
0.856993 0.515327i \(-0.172330\pi\)
\(140\) 0 0
\(141\) 2.43242 + 4.21307i 0.204847 + 0.354805i
\(142\) 0 0
\(143\) 2.86571 1.04303i 0.239643 0.0872230i
\(144\) 0 0
\(145\) 5.57532 9.65674i 0.463005 0.801949i
\(146\) 0 0
\(147\) 3.71167 3.11446i 0.306133 0.256876i
\(148\) 0 0
\(149\) 0.386659 + 2.19285i 0.0316764 + 0.179646i 0.996541 0.0831016i \(-0.0264826\pi\)
−0.964865 + 0.262747i \(0.915371\pi\)
\(150\) 0 0
\(151\) −6.59627 −0.536797 −0.268398 0.963308i \(-0.586494\pi\)
−0.268398 + 0.963308i \(0.586494\pi\)
\(152\) 0 0
\(153\) 2.22668 0.180017
\(154\) 0 0
\(155\) −1.63129 9.25152i −0.131029 0.743100i
\(156\) 0 0
\(157\) 7.08899 5.94837i 0.565763 0.474732i −0.314474 0.949266i \(-0.601828\pi\)
0.880237 + 0.474534i \(0.157384\pi\)
\(158\) 0 0
\(159\) −0.726682 + 1.25865i −0.0576296 + 0.0998174i
\(160\) 0 0
\(161\) 1.63429 0.594831i 0.128800 0.0468793i
\(162\) 0 0
\(163\) −1.57011 2.71951i −0.122980 0.213008i 0.797961 0.602709i \(-0.205912\pi\)
−0.920942 + 0.389700i \(0.872579\pi\)
\(164\) 0 0
\(165\) −0.243756 + 1.38241i −0.0189764 + 0.107620i
\(166\) 0 0
\(167\) −12.1591 10.2027i −0.940899 0.789508i 0.0368422 0.999321i \(-0.488270\pi\)
−0.977742 + 0.209813i \(0.932715\pi\)
\(168\) 0 0
\(169\) 5.99020 + 2.18025i 0.460785 + 0.167712i
\(170\) 0 0
\(171\) −0.694593 4.30320i −0.0531168 0.329074i
\(172\) 0 0
\(173\) −3.25237 1.18377i −0.247273 0.0900002i 0.215410 0.976524i \(-0.430891\pi\)
−0.462684 + 0.886524i \(0.653113\pi\)
\(174\) 0 0
\(175\) −4.04395 3.39328i −0.305694 0.256508i
\(176\) 0 0
\(177\) 0.243756 1.38241i 0.0183218 0.103908i
\(178\) 0 0
\(179\) −0.315207 0.545955i −0.0235597 0.0408066i 0.854005 0.520265i \(-0.174167\pi\)
−0.877565 + 0.479458i \(0.840833\pi\)
\(180\) 0 0
\(181\) 11.0778 4.03201i 0.823410 0.299697i 0.104259 0.994550i \(-0.466753\pi\)
0.719151 + 0.694853i \(0.244531\pi\)
\(182\) 0 0
\(183\) 3.90033 6.75557i 0.288321 0.499386i
\(184\) 0 0
\(185\) 0.0582480 0.0488759i 0.00428248 0.00359342i
\(186\) 0 0
\(187\) −0.458111 2.59808i −0.0335004 0.189990i
\(188\) 0 0
\(189\) −1.46791 −0.106775
\(190\) 0 0
\(191\) −11.4192 −0.826265 −0.413133 0.910671i \(-0.635565\pi\)
−0.413133 + 0.910671i \(0.635565\pi\)
\(192\) 0 0
\(193\) 1.64796 + 9.34602i 0.118622 + 0.672741i 0.984893 + 0.173166i \(0.0553996\pi\)
−0.866270 + 0.499576i \(0.833489\pi\)
\(194\) 0 0
\(195\) 2.33615 1.96026i 0.167295 0.140377i
\(196\) 0 0
\(197\) −3.56758 + 6.17923i −0.254180 + 0.440252i −0.964672 0.263452i \(-0.915139\pi\)
0.710493 + 0.703705i \(0.248472\pi\)
\(198\) 0 0
\(199\) −16.6814 + 6.07153i −1.18251 + 0.430399i −0.857089 0.515169i \(-0.827729\pi\)
−0.325424 + 0.945568i \(0.605507\pi\)
\(200\) 0 0
\(201\) −4.35844 7.54904i −0.307421 0.532468i
\(202\) 0 0
\(203\) 2.39899 13.6053i 0.168376 0.954907i
\(204\) 0 0
\(205\) −8.78564 7.37203i −0.613616 0.514885i
\(206\) 0 0
\(207\) 1.11334 + 0.405223i 0.0773825 + 0.0281649i
\(208\) 0 0
\(209\) −4.87804 + 1.69577i −0.337421 + 0.117299i
\(210\) 0 0
\(211\) 2.03209 + 0.739620i 0.139895 + 0.0509175i 0.411019 0.911627i \(-0.365173\pi\)
−0.271124 + 0.962544i \(0.587395\pi\)
\(212\) 0 0
\(213\) 11.2135 + 9.40923i 0.768335 + 0.644709i
\(214\) 0 0
\(215\) −1.49138 + 8.45805i −0.101711 + 0.576834i
\(216\) 0 0
\(217\) −5.81954 10.0797i −0.395056 0.684258i
\(218\) 0 0
\(219\) 6.14543 2.23675i 0.415270 0.151146i
\(220\) 0 0
\(221\) −2.86571 + 4.96356i −0.192769 + 0.333885i
\(222\) 0 0
\(223\) 21.6446 18.1619i 1.44943 1.21621i 0.516429 0.856330i \(-0.327261\pi\)
0.932997 0.359883i \(-0.117183\pi\)
\(224\) 0 0
\(225\) −0.624485 3.54163i −0.0416323 0.236109i
\(226\) 0 0
\(227\) 21.0232 1.39536 0.697680 0.716409i \(-0.254216\pi\)
0.697680 + 0.716409i \(0.254216\pi\)
\(228\) 0 0
\(229\) 7.96080 0.526064 0.263032 0.964787i \(-0.415277\pi\)
0.263032 + 0.964787i \(0.415277\pi\)
\(230\) 0 0
\(231\) 0.302004 + 1.71275i 0.0198704 + 0.112691i
\(232\) 0 0
\(233\) 11.2515 9.44113i 0.737110 0.618509i −0.194950 0.980813i \(-0.562454\pi\)
0.932060 + 0.362304i \(0.118010\pi\)
\(234\) 0 0
\(235\) 2.88191 4.99162i 0.187995 0.325617i
\(236\) 0 0
\(237\) −12.1236 + 4.41263i −0.787513 + 0.286631i
\(238\) 0 0
\(239\) 7.86484 + 13.6223i 0.508734 + 0.881153i 0.999949 + 0.0101147i \(0.00321967\pi\)
−0.491215 + 0.871038i \(0.663447\pi\)
\(240\) 0 0
\(241\) 1.71079 9.70237i 0.110202 0.624985i −0.878813 0.477166i \(-0.841664\pi\)
0.989015 0.147818i \(-0.0472250\pi\)
\(242\) 0 0
\(243\) −0.766044 0.642788i −0.0491418 0.0412348i
\(244\) 0 0
\(245\) −5.39440 1.96340i −0.344636 0.125437i
\(246\) 0 0
\(247\) 10.4863 + 3.98983i 0.667229 + 0.253867i
\(248\) 0 0
\(249\) −3.66385 1.33353i −0.232187 0.0845091i
\(250\) 0 0
\(251\) −3.54117 2.97140i −0.223517 0.187553i 0.524152 0.851625i \(-0.324382\pi\)
−0.747669 + 0.664072i \(0.768827\pi\)
\(252\) 0 0
\(253\) 0.243756 1.38241i 0.0153248 0.0869112i
\(254\) 0 0
\(255\) −1.31908 2.28471i −0.0826039 0.143074i
\(256\) 0 0
\(257\) 2.83527 1.03196i 0.176860 0.0643716i −0.252073 0.967708i \(-0.581112\pi\)
0.428932 + 0.903337i \(0.358890\pi\)
\(258\) 0 0
\(259\) 0.0471036 0.0815859i 0.00292688 0.00506950i
\(260\) 0 0
\(261\) 7.20961 6.04958i 0.446263 0.374460i
\(262\) 0 0
\(263\) 0.869585 + 4.93166i 0.0536209 + 0.304099i 0.999810 0.0195163i \(-0.00621264\pi\)
−0.946189 + 0.323616i \(0.895102\pi\)
\(264\) 0 0
\(265\) 1.72193 0.105778
\(266\) 0 0
\(267\) −12.4115 −0.759570
\(268\) 0 0
\(269\) −4.26945 24.2132i −0.260313 1.47631i −0.782058 0.623206i \(-0.785830\pi\)
0.521745 0.853102i \(-0.325281\pi\)
\(270\) 0 0
\(271\) 1.28699 1.07991i 0.0781790 0.0656000i −0.602861 0.797846i \(-0.705973\pi\)
0.681040 + 0.732246i \(0.261528\pi\)
\(272\) 0 0
\(273\) 1.88919 3.27217i 0.114339 0.198040i
\(274\) 0 0
\(275\) −4.00387 + 1.45729i −0.241442 + 0.0878779i
\(276\) 0 0
\(277\) 14.9907 + 25.9646i 0.900702 + 1.56006i 0.826585 + 0.562812i \(0.190280\pi\)
0.0741168 + 0.997250i \(0.476386\pi\)
\(278\) 0 0
\(279\) 1.37686 7.80856i 0.0824304 0.467486i
\(280\) 0 0
\(281\) 13.4914 + 11.3206i 0.804828 + 0.675331i 0.949367 0.314168i \(-0.101725\pi\)
−0.144539 + 0.989499i \(0.546170\pi\)
\(282\) 0 0
\(283\) 14.9547 + 5.44307i 0.888965 + 0.323557i 0.745822 0.666145i \(-0.232057\pi\)
0.143143 + 0.989702i \(0.454279\pi\)
\(284\) 0 0
\(285\) −4.00387 + 3.26189i −0.237169 + 0.193218i
\(286\) 0 0
\(287\) −13.3525 4.85992i −0.788174 0.286872i
\(288\) 0 0
\(289\) −9.22462 7.74038i −0.542625 0.455316i
\(290\) 0 0
\(291\) −2.24257 + 12.7183i −0.131462 + 0.745558i
\(292\) 0 0
\(293\) −0.134285 0.232589i −0.00784503 0.0135880i 0.862076 0.506779i \(-0.169164\pi\)
−0.869921 + 0.493191i \(0.835831\pi\)
\(294\) 0 0
\(295\) −1.56283 + 0.568825i −0.0909917 + 0.0331183i
\(296\) 0 0
\(297\) −0.592396 + 1.02606i −0.0343743 + 0.0595381i
\(298\) 0 0
\(299\) −2.33615 + 1.96026i −0.135103 + 0.113365i
\(300\) 0 0
\(301\) 1.84776 + 10.4792i 0.106503 + 0.604010i
\(302\) 0 0
\(303\) −13.7392 −0.789295
\(304\) 0 0
\(305\) −9.24216 −0.529205
\(306\) 0 0
\(307\) 0.0992034 + 0.562610i 0.00566184 + 0.0321099i 0.987508 0.157570i \(-0.0503660\pi\)
−0.981846 + 0.189680i \(0.939255\pi\)
\(308\) 0 0
\(309\) 13.1270 11.0149i 0.746770 0.626614i
\(310\) 0 0
\(311\) 7.17617 12.4295i 0.406924 0.704812i −0.587620 0.809137i \(-0.699935\pi\)
0.994543 + 0.104325i \(0.0332682\pi\)
\(312\) 0 0
\(313\) 2.25877 0.822125i 0.127673 0.0464693i −0.277393 0.960756i \(-0.589471\pi\)
0.405067 + 0.914287i \(0.367248\pi\)
\(314\) 0 0
\(315\) 0.869585 + 1.50617i 0.0489956 + 0.0848628i
\(316\) 0 0
\(317\) 2.44104 13.8438i 0.137102 0.777546i −0.836270 0.548317i \(-0.815269\pi\)
0.973373 0.229228i \(-0.0736203\pi\)
\(318\) 0 0
\(319\) −8.54189 7.16750i −0.478254 0.401303i
\(320\) 0 0
\(321\) 9.86959 + 3.59224i 0.550867 + 0.200499i
\(322\) 0 0
\(323\) 4.97431 8.33429i 0.276778 0.463732i
\(324\) 0 0
\(325\) 8.69846 + 3.16598i 0.482504 + 0.175617i
\(326\) 0 0
\(327\) 6.16044 + 5.16923i 0.340673 + 0.285859i
\(328\) 0 0
\(329\) 1.24005 7.03266i 0.0683660 0.387723i
\(330\) 0 0
\(331\) 13.4213 + 23.2463i 0.737700 + 1.27773i 0.953529 + 0.301303i \(0.0974214\pi\)
−0.215829 + 0.976431i \(0.569245\pi\)
\(332\) 0 0
\(333\) 0.0603074 0.0219501i 0.00330482 0.00120286i
\(334\) 0 0
\(335\) −5.16385 + 8.94405i −0.282131 + 0.488665i
\(336\) 0 0
\(337\) −16.0266 + 13.4479i −0.873026 + 0.732556i −0.964733 0.263230i \(-0.915212\pi\)
0.0917071 + 0.995786i \(0.470768\pi\)
\(338\) 0 0
\(339\) 3.32383 + 18.8504i 0.180525 + 1.02381i
\(340\) 0 0
\(341\) −9.39424 −0.508727
\(342\) 0 0
\(343\) −17.3878 −0.938851
\(344\) 0 0
\(345\) −0.243756 1.38241i −0.0131234 0.0744263i
\(346\) 0 0
\(347\) 25.7670 21.6211i 1.38324 1.16068i 0.415249 0.909708i \(-0.363694\pi\)
0.967994 0.250972i \(-0.0807502\pi\)
\(348\) 0 0
\(349\) −13.5758 + 23.5140i −0.726695 + 1.25867i 0.231577 + 0.972817i \(0.425611\pi\)
−0.958272 + 0.285857i \(0.907722\pi\)
\(350\) 0 0
\(351\) 2.41875 0.880352i 0.129103 0.0469897i
\(352\) 0 0
\(353\) 8.37258 + 14.5017i 0.445627 + 0.771849i 0.998096 0.0616847i \(-0.0196473\pi\)
−0.552468 + 0.833534i \(0.686314\pi\)
\(354\) 0 0
\(355\) 3.01161 17.0797i 0.159840 0.906496i
\(356\) 0 0
\(357\) −2.50387 2.10100i −0.132519 0.111197i
\(358\) 0 0
\(359\) −4.45336 1.62089i −0.235040 0.0855474i 0.221815 0.975089i \(-0.428802\pi\)
−0.456855 + 0.889541i \(0.651024\pi\)
\(360\) 0 0
\(361\) −17.6582 7.01336i −0.929380 0.369124i
\(362\) 0 0
\(363\) −9.01754 3.28212i −0.473298 0.172266i
\(364\) 0 0
\(365\) −5.93557 4.98054i −0.310682 0.260693i
\(366\) 0 0
\(367\) −1.52687 + 8.65933i −0.0797022 + 0.452014i 0.918672 + 0.395020i \(0.129262\pi\)
−0.998375 + 0.0569932i \(0.981849\pi\)
\(368\) 0 0
\(369\) −4.84002 8.38316i −0.251962 0.436410i
\(370\) 0 0
\(371\) 2.00475 0.729669i 0.104081 0.0378825i
\(372\) 0 0
\(373\) 4.72281 8.18015i 0.244538 0.423552i −0.717464 0.696596i \(-0.754697\pi\)
0.962002 + 0.273044i \(0.0880304\pi\)
\(374\) 0 0
\(375\) −7.80200 + 6.54666i −0.402894 + 0.338068i
\(376\) 0 0
\(377\) 4.20661 + 23.8569i 0.216652 + 1.22869i
\(378\) 0 0
\(379\) −36.9077 −1.89582 −0.947910 0.318540i \(-0.896808\pi\)
−0.947910 + 0.318540i \(0.896808\pi\)
\(380\) 0 0
\(381\) 7.27631 0.372777
\(382\) 0 0
\(383\) 5.11721 + 29.0211i 0.261477 + 1.48291i 0.778882 + 0.627171i \(0.215787\pi\)
−0.517405 + 0.855741i \(0.673102\pi\)
\(384\) 0 0
\(385\) 1.57848 1.32450i 0.0804467 0.0675028i
\(386\) 0 0
\(387\) −3.62449 + 6.27779i −0.184243 + 0.319118i
\(388\) 0 0
\(389\) −16.6211 + 6.04958i −0.842722 + 0.306726i −0.727069 0.686564i \(-0.759118\pi\)
−0.115653 + 0.993290i \(0.536896\pi\)
\(390\) 0 0
\(391\) 1.31908 + 2.28471i 0.0667086 + 0.115543i
\(392\) 0 0
\(393\) −1.19800 + 6.79417i −0.0604309 + 0.342721i
\(394\) 0 0
\(395\) 11.7096 + 9.82553i 0.589174 + 0.494376i
\(396\) 0 0
\(397\) −11.8302 4.30585i −0.593742 0.216104i 0.0276326 0.999618i \(-0.491203\pi\)
−0.621374 + 0.783514i \(0.713425\pi\)
\(398\) 0 0
\(399\) −3.27925 + 5.49427i −0.164168 + 0.275058i
\(400\) 0 0
\(401\) 22.6211 + 8.23340i 1.12964 + 0.411156i 0.838163 0.545420i \(-0.183630\pi\)
0.291480 + 0.956577i \(0.405852\pi\)
\(402\) 0 0
\(403\) 15.6343 + 13.1187i 0.778799 + 0.653490i
\(404\) 0 0
\(405\) −0.205737 + 1.16679i −0.0102232 + 0.0579784i
\(406\) 0 0
\(407\) −0.0380187 0.0658503i −0.00188452 0.00326408i
\(408\) 0 0
\(409\) 33.2276 12.0939i 1.64300 0.598003i 0.655440 0.755247i \(-0.272483\pi\)
0.987560 + 0.157244i \(0.0502610\pi\)
\(410\) 0 0
\(411\) 7.91147 13.7031i 0.390244 0.675923i
\(412\) 0 0
\(413\) −1.57848 + 1.32450i −0.0776718 + 0.0651744i
\(414\) 0 0
\(415\) 0.802166 + 4.54931i 0.0393768 + 0.223317i
\(416\) 0 0
\(417\) −15.4757 −0.757846
\(418\) 0 0
\(419\) −4.57903 −0.223700 −0.111850 0.993725i \(-0.535678\pi\)
−0.111850 + 0.993725i \(0.535678\pi\)
\(420\) 0 0
\(421\) 0.0482857 + 0.273842i 0.00235330 + 0.0133462i 0.985962 0.166971i \(-0.0533987\pi\)
−0.983608 + 0.180317i \(0.942288\pi\)
\(422\) 0 0
\(423\) 3.72668 3.12706i 0.181197 0.152043i
\(424\) 0 0
\(425\) 4.00387 6.93491i 0.194216 0.336392i
\(426\) 0 0
\(427\) −10.7601 + 3.91636i −0.520718 + 0.189526i
\(428\) 0 0
\(429\) −1.52481 2.64106i −0.0736188 0.127511i
\(430\) 0 0
\(431\) 2.08079 11.8007i 0.100228 0.568421i −0.892792 0.450470i \(-0.851256\pi\)
0.993019 0.117951i \(-0.0376325\pi\)
\(432\) 0 0
\(433\) −22.3286 18.7359i −1.07305 0.900392i −0.0777205 0.996975i \(-0.524764\pi\)
−0.995325 + 0.0965831i \(0.969209\pi\)
\(434\) 0 0
\(435\) −10.4782 3.81374i −0.502390 0.182855i
\(436\) 0 0
\(437\) 4.00387 3.26189i 0.191531 0.156038i
\(438\) 0 0
\(439\) 5.91787 + 2.15393i 0.282445 + 0.102801i 0.479358 0.877619i \(-0.340870\pi\)
−0.196913 + 0.980421i \(0.563092\pi\)
\(440\) 0 0
\(441\) −3.71167 3.11446i −0.176746 0.148308i
\(442\) 0 0
\(443\) −3.62583 + 20.5631i −0.172268 + 0.976982i 0.768981 + 0.639271i \(0.220764\pi\)
−0.941250 + 0.337711i \(0.890347\pi\)
\(444\) 0 0
\(445\) 7.35251 + 12.7349i 0.348542 + 0.603693i
\(446\) 0 0
\(447\) 2.09240 0.761570i 0.0989669 0.0360210i
\(448\) 0 0
\(449\) −20.6878 + 35.8323i −0.976317 + 1.69103i −0.300798 + 0.953688i \(0.597253\pi\)
−0.675519 + 0.737343i \(0.736080\pi\)
\(450\) 0 0
\(451\) −8.78564 + 7.37203i −0.413700 + 0.347135i
\(452\) 0 0
\(453\) 1.14543 + 6.49605i 0.0538170 + 0.305211i
\(454\) 0 0
\(455\) −4.47659 −0.209866
\(456\) 0 0
\(457\) −27.6245 −1.29222 −0.646111 0.763244i \(-0.723606\pi\)
−0.646111 + 0.763244i \(0.723606\pi\)
\(458\) 0 0
\(459\) −0.386659 2.19285i −0.0180477 0.102354i
\(460\) 0 0
\(461\) −14.1800 + 11.8985i −0.660431 + 0.554167i −0.910216 0.414134i \(-0.864084\pi\)
0.249785 + 0.968301i \(0.419640\pi\)
\(462\) 0 0
\(463\) −1.80928 + 3.13376i −0.0840843 + 0.145638i −0.905001 0.425410i \(-0.860130\pi\)
0.820916 + 0.571048i \(0.193463\pi\)
\(464\) 0 0
\(465\) −8.82770 + 3.21302i −0.409375 + 0.149000i
\(466\) 0 0
\(467\) −7.20099 12.4725i −0.333222 0.577158i 0.649920 0.760003i \(-0.274803\pi\)
−0.983142 + 0.182845i \(0.941469\pi\)
\(468\) 0 0
\(469\) −2.22193 + 12.6012i −0.102599 + 0.581870i
\(470\) 0 0
\(471\) −7.08899 5.94837i −0.326644 0.274086i
\(472\) 0 0
\(473\) 8.07057 + 2.93745i 0.371085 + 0.135064i
\(474\) 0 0
\(475\) −14.6511 5.57445i −0.672239 0.255773i
\(476\) 0 0
\(477\) 1.36571 + 0.497079i 0.0625318 + 0.0227597i
\(478\) 0 0
\(479\) 24.4029 + 20.4764i 1.11499 + 0.935592i 0.998341 0.0575808i \(-0.0183387\pi\)
0.116654 + 0.993173i \(0.462783\pi\)
\(480\) 0 0
\(481\) −0.0286853 + 0.162683i −0.00130794 + 0.00741768i
\(482\) 0 0
\(483\) −0.869585 1.50617i −0.0395675 0.0685329i
\(484\) 0 0
\(485\) 14.3782 5.23324i 0.652881 0.237629i
\(486\) 0 0
\(487\) −9.87346 + 17.1013i −0.447409 + 0.774935i −0.998217 0.0596972i \(-0.980986\pi\)
0.550808 + 0.834632i \(0.314320\pi\)
\(488\) 0 0
\(489\) −2.40554 + 2.01849i −0.108782 + 0.0912793i
\(490\) 0 0
\(491\) 5.06758 + 28.7397i 0.228697 + 1.29700i 0.855491 + 0.517818i \(0.173256\pi\)
−0.626794 + 0.779185i \(0.715633\pi\)
\(492\) 0 0
\(493\) 20.9564 0.943827
\(494\) 0 0
\(495\) 1.40373 0.0630931
\(496\) 0 0
\(497\) −3.73127 21.1611i −0.167370 0.949204i
\(498\) 0 0
\(499\) 4.12449 3.46085i 0.184637 0.154929i −0.545784 0.837926i \(-0.683768\pi\)
0.730421 + 0.682997i \(0.239324\pi\)
\(500\) 0 0
\(501\) −7.93629 + 13.7461i −0.354567 + 0.614128i
\(502\) 0 0
\(503\) 23.1040 8.40917i 1.03016 0.374946i 0.229016 0.973423i \(-0.426449\pi\)
0.801141 + 0.598476i \(0.204227\pi\)
\(504\) 0 0
\(505\) 8.13903 + 14.0972i 0.362182 + 0.627318i
\(506\) 0 0
\(507\) 1.10694 6.27779i 0.0491611 0.278807i
\(508\) 0 0
\(509\) −3.64362 3.05736i −0.161501 0.135515i 0.558456 0.829534i \(-0.311394\pi\)
−0.719957 + 0.694019i \(0.755838\pi\)
\(510\) 0 0
\(511\) −9.02094 3.28336i −0.399063 0.145247i
\(512\) 0 0
\(513\) −4.11721 + 1.43128i −0.181779 + 0.0631927i
\(514\) 0 0
\(515\) −19.0783 6.94394i −0.840691 0.305987i
\(516\) 0 0
\(517\) −4.41534 3.70491i −0.194187 0.162942i
\(518\) 0 0
\(519\) −0.601014 + 3.40852i −0.0263816 + 0.149618i
\(520\) 0 0
\(521\) 14.8145 + 25.6595i 0.649035 + 1.12416i 0.983354 + 0.181701i \(0.0581603\pi\)
−0.334319 + 0.942460i \(0.608506\pi\)
\(522\) 0 0
\(523\) −10.0890 + 3.67209i −0.441161 + 0.160569i −0.553044 0.833152i \(-0.686534\pi\)
0.111883 + 0.993721i \(0.464312\pi\)
\(524\) 0 0
\(525\) −2.63950 + 4.57175i −0.115197 + 0.199527i
\(526\) 0 0
\(527\) 13.5248 11.3487i 0.589150 0.494356i
\(528\) 0 0
\(529\) −3.75015 21.2682i −0.163050 0.924703i
\(530\) 0 0
\(531\) −1.40373 −0.0609168
\(532\) 0 0
\(533\) 24.9162 1.07924
\(534\) 0 0
\(535\) −2.16085 12.2548i −0.0934219 0.529822i
\(536\) 0 0
\(537\) −0.482926 + 0.405223i −0.0208398 + 0.0174867i
\(538\) 0 0
\(539\) −2.87030 + 4.97151i −0.123633 + 0.214138i
\(540\) 0 0
\(541\) −27.8209 + 10.1260i −1.19611 + 0.435350i −0.861866 0.507136i \(-0.830704\pi\)
−0.334247 + 0.942485i \(0.608482\pi\)
\(542\) 0 0
\(543\) −5.89440 10.2094i −0.252953 0.438127i
\(544\) 0 0
\(545\) 1.65451 9.38322i 0.0708716 0.401933i
\(546\) 0 0
\(547\) −10.2365 8.58943i −0.437680 0.367257i 0.397160 0.917749i \(-0.369996\pi\)
−0.834841 + 0.550492i \(0.814440\pi\)
\(548\) 0 0
\(549\) −7.33022 2.66798i −0.312846 0.113867i
\(550\) 0 0
\(551\) −6.53714 40.4995i −0.278492 1.72534i
\(552\) 0 0
\(553\) 17.7964 + 6.47735i 0.756779 + 0.275445i
\(554\) 0 0
\(555\) −0.0582480 0.0488759i −0.00247249 0.00207466i
\(556\) 0 0
\(557\) −0.589403 + 3.34267i −0.0249738 + 0.141634i −0.994745 0.102382i \(-0.967354\pi\)
0.969771 + 0.244015i \(0.0784647\pi\)
\(558\) 0 0
\(559\) −9.32934 16.1589i −0.394589 0.683449i
\(560\) 0 0
\(561\) −2.47906 + 0.902302i −0.104666 + 0.0380952i
\(562\) 0 0
\(563\) −20.7724 + 35.9789i −0.875454 + 1.51633i −0.0191757 + 0.999816i \(0.506104\pi\)
−0.856278 + 0.516515i \(0.827229\pi\)
\(564\) 0 0
\(565\) 17.3726 14.5773i 0.730870 0.613273i
\(566\) 0 0
\(567\) 0.254900 + 1.44561i 0.0107048 + 0.0607099i
\(568\) 0 0
\(569\) 2.17705 0.0912668 0.0456334 0.998958i \(-0.485469\pi\)
0.0456334 + 0.998958i \(0.485469\pi\)
\(570\) 0 0
\(571\) 2.50980 0.105032 0.0525159 0.998620i \(-0.483276\pi\)
0.0525159 + 0.998620i \(0.483276\pi\)
\(572\) 0 0
\(573\) 1.98293 + 11.2457i 0.0828379 + 0.469797i
\(574\) 0 0
\(575\) 3.26399 2.73881i 0.136118 0.114216i
\(576\) 0 0
\(577\) −5.75537 + 9.96859i −0.239599 + 0.414998i −0.960599 0.277937i \(-0.910349\pi\)
0.721000 + 0.692935i \(0.243683\pi\)
\(578\) 0 0
\(579\) 8.91787 3.24584i 0.370614 0.134892i
\(580\) 0 0
\(581\) 2.86168 + 4.95658i 0.118723 + 0.205634i
\(582\) 0 0
\(583\) 0.299011 1.69577i 0.0123838 0.0702318i
\(584\) 0 0
\(585\) −2.33615 1.96026i −0.0965880 0.0810470i
\(586\) 0 0
\(587\) 15.6887 + 5.71021i 0.647540 + 0.235685i 0.644848 0.764311i \(-0.276921\pi\)
0.00269254 + 0.999996i \(0.499143\pi\)
\(588\) 0 0
\(589\) −26.1509 22.5974i −1.07753 0.931111i
\(590\) 0 0
\(591\) 6.70486 + 2.44037i 0.275801 + 0.100383i
\(592\) 0 0
\(593\) 34.1544 + 28.6589i 1.40255 + 1.17688i 0.959953 + 0.280160i \(0.0903875\pi\)
0.442598 + 0.896720i \(0.354057\pi\)
\(594\) 0 0
\(595\) −0.672466 + 3.81374i −0.0275684 + 0.156348i
\(596\) 0 0
\(597\) 8.87598 + 15.3737i 0.363270 + 0.629202i
\(598\) 0 0
\(599\) −7.99912 + 2.91144i −0.326835 + 0.118958i −0.500226 0.865895i \(-0.666750\pi\)
0.173391 + 0.984853i \(0.444528\pi\)
\(600\) 0 0
\(601\) −16.7613 + 29.0314i −0.683708 + 1.18422i 0.290134 + 0.956986i \(0.406300\pi\)
−0.973841 + 0.227230i \(0.927033\pi\)
\(602\) 0 0
\(603\) −6.67752 + 5.60310i −0.271930 + 0.228176i
\(604\) 0 0
\(605\) 1.97431 + 11.1969i 0.0802670 + 0.455217i
\(606\) 0 0
\(607\) −1.89393 −0.0768724 −0.0384362 0.999261i \(-0.512238\pi\)
−0.0384362 + 0.999261i \(0.512238\pi\)
\(608\) 0 0
\(609\) −13.8152 −0.559820
\(610\) 0 0
\(611\) 2.17442 + 12.3317i 0.0879676 + 0.498889i
\(612\) 0 0
\(613\) 6.50799 5.46085i 0.262855 0.220562i −0.501829 0.864967i \(-0.667339\pi\)
0.764684 + 0.644405i \(0.222895\pi\)
\(614\) 0 0
\(615\) −5.73442 + 9.93231i −0.231234 + 0.400509i
\(616\) 0 0
\(617\) 26.4688 9.63387i 1.06560 0.387845i 0.251068 0.967970i \(-0.419218\pi\)
0.814528 + 0.580124i \(0.196996\pi\)
\(618\) 0 0
\(619\) −11.4483 19.8291i −0.460146 0.796997i 0.538821 0.842420i \(-0.318870\pi\)
−0.998968 + 0.0454230i \(0.985536\pi\)
\(620\) 0 0
\(621\) 0.205737 1.16679i 0.00825594 0.0468218i
\(622\) 0 0
\(623\) 13.9565 + 11.7109i 0.559156 + 0.469188i
\(624\) 0 0
\(625\) −5.55778 2.02287i −0.222311 0.0809147i
\(626\) 0 0
\(627\) 2.51707 + 4.50946i 0.100522 + 0.180091i
\(628\) 0 0
\(629\) 0.134285 + 0.0488759i 0.00535431 + 0.00194881i
\(630\) 0 0
\(631\) 24.8883 + 20.8838i 0.990788 + 0.831370i 0.985682 0.168617i \(-0.0539302\pi\)
0.00510629 + 0.999987i \(0.498375\pi\)
\(632\) 0 0
\(633\) 0.375515 2.12965i 0.0149254 0.0846460i
\(634\) 0 0
\(635\) −4.31046 7.46594i −0.171055 0.296277i
\(636\) 0 0
\(637\) 11.7194 4.26552i 0.464340 0.169006i
\(638\) 0 0
\(639\) 7.31908 12.6770i 0.289538 0.501495i
\(640\) 0 0
\(641\) 5.67159 4.75903i 0.224014 0.187970i −0.523872 0.851797i \(-0.675513\pi\)
0.747887 + 0.663826i \(0.231069\pi\)
\(642\) 0 0
\(643\) 7.38847 + 41.9021i 0.291373 + 1.65246i 0.681590 + 0.731734i \(0.261289\pi\)
−0.390217 + 0.920723i \(0.627600\pi\)
\(644\) 0 0
\(645\) 8.58853 0.338173
\(646\) 0 0
\(647\) 41.2063 1.61999 0.809993 0.586440i \(-0.199471\pi\)
0.809993 + 0.586440i \(0.199471\pi\)
\(648\) 0 0
\(649\) 0.288800 + 1.63787i 0.0113364 + 0.0642919i
\(650\) 0 0
\(651\) −8.91606 + 7.48146i −0.349448 + 0.293222i
\(652\) 0 0
\(653\) 13.3353 23.0974i 0.521850 0.903870i −0.477827 0.878454i \(-0.658576\pi\)
0.999677 0.0254163i \(-0.00809113\pi\)
\(654\) 0 0
\(655\) 7.68092 2.79563i 0.300118 0.109234i
\(656\) 0 0
\(657\) −3.26991 5.66366i −0.127572 0.220960i
\(658\) 0 0
\(659\) 2.18567 12.3955i 0.0851416 0.482862i −0.912184 0.409780i \(-0.865605\pi\)
0.997326 0.0730819i \(-0.0232835\pi\)
\(660\) 0 0
\(661\) 6.35432 + 5.33191i 0.247154 + 0.207387i 0.757946 0.652317i \(-0.226203\pi\)
−0.510791 + 0.859705i \(0.670648\pi\)
\(662\) 0 0
\(663\) 5.38578 + 1.96026i 0.209166 + 0.0761304i
\(664\) 0 0
\(665\) 7.58007 + 0.109920i 0.293943 + 0.00426253i
\(666\) 0 0
\(667\) 10.4782 + 3.81374i 0.405717 + 0.147669i
\(668\) 0 0
\(669\) −21.6446 18.1619i −0.836827 0.702181i
\(670\) 0 0
\(671\) −1.60488 + 9.10175i −0.0619559 + 0.351369i
\(672\) 0 0
\(673\) −0.812681 1.40761i −0.0313266 0.0542592i 0.849937 0.526884i \(-0.176640\pi\)
−0.881264 + 0.472625i \(0.843307\pi\)
\(674\) 0 0
\(675\) −3.37939 + 1.23000i −0.130073 + 0.0473426i
\(676\) 0 0
\(677\) 6.64203 11.5043i 0.255274 0.442147i −0.709696 0.704508i \(-0.751168\pi\)
0.964970 + 0.262361i \(0.0845011\pi\)
\(678\) 0 0
\(679\) 14.5221 12.1855i 0.557308 0.467637i
\(680\) 0 0
\(681\) −3.65064 20.7038i −0.139893 0.793373i
\(682\) 0 0
\(683\) −2.90673 −0.111223 −0.0556114 0.998452i \(-0.517711\pi\)
−0.0556114 + 0.998452i \(0.517711\pi\)
\(684\) 0 0
\(685\) −18.7469 −0.716283
\(686\) 0 0
\(687\) −1.38238 7.83986i −0.0527410 0.299109i
\(688\) 0 0
\(689\) −2.86571 + 2.40462i −0.109175 + 0.0916087i
\(690\) 0 0
\(691\) −7.18004 + 12.4362i −0.273142 + 0.473095i −0.969665 0.244439i \(-0.921396\pi\)
0.696523 + 0.717535i \(0.254729\pi\)
\(692\) 0 0
\(693\) 1.63429 0.594831i 0.0620814 0.0225958i
\(694\) 0 0
\(695\) 9.16772 + 15.8790i 0.347751 + 0.602323i
\(696\) 0 0
\(697\) 3.74288 21.2269i 0.141772 0.804027i
\(698\) 0 0
\(699\) −11.2515 9.44113i −0.425571 0.357096i
\(700\) 0 0
\(701\) −45.7195 16.6405i −1.72680 0.628504i −0.728406 0.685146i \(-0.759738\pi\)
−0.998395 + 0.0566421i \(0.981961\pi\)
\(702\) 0 0
\(703\) 0.0525666 0.274761i 0.00198259 0.0103628i
\(704\) 0 0
\(705\) −5.41622 1.97134i −0.203987 0.0742451i
\(706\) 0 0
\(707\) 15.4495 + 12.9637i 0.581038 + 0.487549i
\(708\) 0 0
\(709\) −1.69207 + 9.59619i −0.0635469 + 0.360392i 0.936408 + 0.350913i \(0.114129\pi\)
−0.999955 + 0.00947962i \(0.996982\pi\)
\(710\) 0 0
\(711\) 6.45084 + 11.1732i 0.241925 + 0.419027i
\(712\) 0 0
\(713\) 8.82770 3.21302i 0.330600 0.120328i
\(714\) 0 0
\(715\) −1.80659 + 3.12910i −0.0675626 + 0.117022i
\(716\) 0 0
\(717\) 12.0496 10.1108i 0.450002 0.377596i
\(718\) 0 0
\(719\) −0.841777 4.77396i −0.0313930 0.178038i 0.965080 0.261957i \(-0.0843677\pi\)
−0.996473 + 0.0839181i \(0.973257\pi\)
\(720\) 0 0
\(721\) −25.1543 −0.936794
\(722\) 0 0
\(723\) −9.85204 −0.366401
\(724\) 0 0
\(725\) −5.87733 33.3320i −0.218278 1.23792i
\(726\) 0 0
\(727\) 10.8714 9.12218i 0.403198 0.338323i −0.418530 0.908203i \(-0.637455\pi\)
0.821728 + 0.569880i \(0.193010\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) −15.1677 + 5.52060i −0.560998 + 0.204187i
\(732\) 0 0
\(733\) −5.31908 9.21291i −0.196465 0.340287i 0.750915 0.660399i \(-0.229613\pi\)
−0.947380 + 0.320112i \(0.896279\pi\)
\(734\) 0 0
\(735\) −0.996845 + 5.65339i −0.0367692 + 0.208528i
\(736\) 0 0
\(737\) 7.91147 + 6.63852i 0.291423 + 0.244533i
\(738\) 0 0
\(739\) −25.9368 9.44021i −0.954099 0.347264i −0.182381 0.983228i \(-0.558380\pi\)
−0.771718 + 0.635964i \(0.780603\pi\)
\(740\) 0 0
\(741\) 2.10829 11.0198i 0.0774499 0.404824i
\(742\) 0 0
\(743\) 1.13816 + 0.414255i 0.0417549 + 0.0151975i 0.362813 0.931862i \(-0.381816\pi\)
−0.321058 + 0.947059i \(0.604039\pi\)
\(744\) 0 0
\(745\) −2.02094 1.69577i −0.0740417 0.0621283i
\(746\) 0 0
\(747\) −0.677052 + 3.83975i −0.0247720 + 0.140489i
\(748\) 0 0
\(749\) −7.70873 13.3519i −0.281671 0.487868i
\(750\) 0 0
\(751\) 46.0925 16.7763i 1.68194 0.612175i 0.688364 0.725365i \(-0.258329\pi\)
0.993573 + 0.113190i \(0.0361069\pi\)
\(752\) 0 0
\(753\) −2.31134 + 4.00335i −0.0842298 + 0.145890i
\(754\) 0 0
\(755\) 5.98680 5.02352i 0.217882 0.182825i
\(756\) 0 0
\(757\) 6.26445 + 35.5275i 0.227685 + 1.29127i 0.857484 + 0.514510i \(0.172026\pi\)
−0.629799 + 0.776758i \(0.716863\pi\)
\(758\) 0 0
\(759\) −1.40373 −0.0509523
\(760\) 0 0
\(761\) 4.72193 0.171170 0.0855850 0.996331i \(-0.472724\pi\)
0.0855850 + 0.996331i \(0.472724\pi\)
\(762\) 0 0
\(763\) −2.04988 11.6254i −0.0742106 0.420869i
\(764\) 0 0
\(765\) −2.02094 + 1.69577i −0.0730674 + 0.0613108i
\(766\) 0 0
\(767\) 1.80659 3.12910i 0.0652322 0.112985i
\(768\) 0 0
\(769\) −20.3893 + 7.42112i −0.735259 + 0.267612i −0.682389 0.730989i \(-0.739059\pi\)
−0.0528696 + 0.998601i \(0.516837\pi\)
\(770\) 0 0
\(771\) −1.50862 2.61300i −0.0543316 0.0941050i
\(772\) 0 0
\(773\) 7.65611 43.4199i 0.275371 1.56171i −0.462410 0.886666i \(-0.653015\pi\)
0.737781 0.675040i \(-0.235874\pi\)
\(774\) 0 0
\(775\) −21.8436 18.3290i −0.784647 0.658397i
\(776\) 0 0
\(777\) −0.0885259 0.0322208i −0.00317585 0.00115591i
\(778\) 0 0
\(779\) −42.1899 0.611806i −1.51161 0.0219202i
\(780\) 0 0
\(781\) −16.2973 5.93172i −0.583162 0.212253i
\(782\) 0 0
\(783\) −7.20961 6.04958i −0.257650 0.216194i
\(784\) 0 0
\(785\) −1.90390 + 10.7975i −0.0679529 + 0.385380i
\(786\) 0 0
\(787\) −10.0694 17.4407i −0.358935 0.621694i 0.628848 0.777528i \(-0.283527\pi\)
−0.987783 + 0.155834i \(0.950193\pi\)
\(788\) 0 0
\(789\) 4.70574 1.71275i 0.167529 0.0609755i
\(790\) 0 0
\(791\) 14.0488 24.3332i 0.499516 0.865187i
\(792\) 0 0
\(793\) 15.3812 12.9064i 0.546202 0.458318i
\(794\) 0 0
\(795\) −0.299011 1.69577i −0.0106048 0.0601429i
\(796\) 0 0
\(797\) 12.0729 0.427642 0.213821 0.976873i \(-0.431409\pi\)
0.213821 + 0.976873i \(0.431409\pi\)
\(798\) 0 0
\(799\) 10.8324 0.383224
\(800\) 0 0
\(801\) 2.15523 + 12.2229i 0.0761513 + 0.431875i
\(802\) 0 0
\(803\) −5.93557 + 4.98054i −0.209462 + 0.175759i
\(804\) 0 0
\(805\) −1.03028 + 1.78449i −0.0363125 + 0.0628951i
\(806\) 0 0
\(807\) −23.1040 + 8.40917i −0.813300 + 0.296017i
\(808\) 0 0
\(809\) 19.4868 + 33.7521i 0.685119 + 1.18666i 0.973399 + 0.229115i \(0.0735833\pi\)
−0.288280 + 0.957546i \(0.593083\pi\)
\(810\) 0 0
\(811\) 3.71641 21.0768i 0.130501 0.740108i −0.847387 0.530976i \(-0.821825\pi\)
0.977888 0.209131i \(-0.0670636\pi\)
\(812\) 0 0
\(813\) −1.28699 1.07991i −0.0451367 0.0378742i
\(814\) 0 0
\(815\) 3.49613 + 1.27249i 0.122464 + 0.0445733i
\(816\) 0 0
\(817\) 15.4003 + 27.5905i 0.538789 + 0.965268i
\(818\) 0 0
\(819\) −3.55051 1.29228i −0.124065 0.0451559i
\(820\) 0 0
\(821\) 37.4564 + 31.4296i 1.30724 + 1.09690i 0.988846 + 0.148941i \(0.0475865\pi\)
0.318390 + 0.947960i \(0.396858\pi\)
\(822\) 0 0
\(823\) 5.20217 29.5030i 0.181336 1.02841i −0.749237 0.662302i \(-0.769579\pi\)
0.930573 0.366107i \(-0.119310\pi\)
\(824\) 0 0
\(825\) 2.13041 + 3.68999i 0.0741715 + 0.128469i
\(826\) 0 0
\(827\) −21.7601 + 7.92003i −0.756673 + 0.275407i −0.691411 0.722462i \(-0.743011\pi\)
−0.0652623 + 0.997868i \(0.520788\pi\)
\(828\) 0 0
\(829\) −15.4290 + 26.7238i −0.535872 + 0.928157i 0.463249 + 0.886228i \(0.346684\pi\)
−0.999121 + 0.0419290i \(0.986650\pi\)
\(830\) 0 0
\(831\) 22.9670 19.2716i 0.796718 0.668525i
\(832\) 0 0
\(833\) −1.87346 10.6249i −0.0649114 0.368131i
\(834\) 0 0
\(835\) 18.8057 0.650798
\(836\) 0 0
\(837\) −7.92902 −0.274067
\(838\) 0 0
\(839\) −1.95707 11.0991i −0.0675656 0.383184i −0.999774 0.0212615i \(-0.993232\pi\)
0.932208 0.361922i \(-0.117879\pi\)
\(840\) 0 0
\(841\) 45.6377 38.2946i 1.57372 1.32050i
\(842\) 0 0
\(843\) 8.80587 15.2522i 0.303290 0.525314i
\(844\) 0 0
\(845\) −7.09714 + 2.58315i −0.244149 + 0.0888630i
\(846\) 0 0
\(847\) 7.04323 + 12.1992i 0.242008 + 0.419171i
\(848\) 0 0
\(849\) 2.76352 15.6727i 0.0948437 0.537885i
\(850\) 0 0
\(851\) 0.0582480 + 0.0488759i 0.00199672 + 0.00167544i
\(852\) 0 0
\(853\) 18.4338 + 6.70934i 0.631160 + 0.229723i 0.637736 0.770255i \(-0.279871\pi\)
−0.00657610 + 0.999978i \(0.502093\pi\)
\(854\) 0 0
\(855\) 3.90760 + 3.37662i 0.133637 + 0.115478i
\(856\) 0 0
\(857\) −21.7707 7.92388i −0.743672 0.270675i −0.0577318 0.998332i \(-0.518387\pi\)
−0.685941 + 0.727657i \(0.740609\pi\)
\(858\) 0 0
\(859\) −1.85529 1.55677i −0.0633015 0.0531163i 0.610588 0.791948i \(-0.290933\pi\)
−0.673889 + 0.738832i \(0.735378\pi\)
\(860\) 0 0
\(861\) −2.46744 + 13.9936i −0.0840903 + 0.476900i
\(862\) 0 0
\(863\) −8.33615 14.4386i −0.283766 0.491497i 0.688543 0.725195i \(-0.258251\pi\)
−0.972309 + 0.233698i \(0.924917\pi\)
\(864\) 0 0
\(865\) 3.85339 1.40252i 0.131019 0.0476871i
\(866\) 0 0
\(867\) −6.02094 + 10.4286i −0.204482 + 0.354173i
\(868\) 0 0
\(869\) 11.7096 9.82553i 0.397221 0.333308i
\(870\) 0 0
\(871\) −3.89615 22.0962i −0.132016 0.748701i
\(872\) 0 0
\(873\) 12.9145 0.437088
\(874\) 0 0
\(875\) 14.9504 0.505415
\(876\) 0 0
\(877\) −6.63294 37.6173i −0.223979 1.27025i −0.864628 0.502412i \(-0.832446\pi\)
0.640650 0.767833i \(-0.278665\pi\)
\(878\) 0 0
\(879\) −0.205737 + 0.172634i −0.00693934 + 0.00582280i
\(880\) 0 0
\(881\) 11.7592 20.3676i 0.396179 0.686202i −0.597072 0.802188i \(-0.703669\pi\)
0.993251 + 0.115986i \(0.0370027\pi\)
\(882\) 0 0
\(883\) −17.3042 + 6.29822i −0.582334 + 0.211952i −0.616354 0.787469i \(-0.711391\pi\)
0.0340206 + 0.999421i \(0.489169\pi\)
\(884\) 0 0
\(885\) 0.831566 + 1.44032i 0.0279528 + 0.0484157i
\(886\) 0 0
\(887\) 4.78317 27.1267i 0.160603 0.910827i −0.792879 0.609379i \(-0.791419\pi\)
0.953483 0.301448i \(-0.0974699\pi\)
\(888\) 0 0
\(889\) −8.18210 6.86560i −0.274419 0.230265i
\(890\) 0 0
\(891\) 1.11334 + 0.405223i 0.0372983 + 0.0135755i
\(892\) 0 0
\(893\) −3.37908 20.9344i −0.113077 0.700542i
\(894\) 0 0
\(895\) 0.701867 + 0.255459i 0.0234608 + 0.00853904i
\(896\) 0 0
\(897\) 2.33615 + 1.96026i 0.0780018 + 0.0654513i
\(898\) 0 0
\(899\) 12.9583 73.4900i 0.432183 2.45103i
\(900\) 0 0
\(901\) 1.61809 + 2.80261i 0.0539063 + 0.0933685i
\(902\) 0 0
\(903\) 9.99912 3.63938i 0.332750 0.121111i
\(904\) 0 0
\(905\) −6.98364 + 12.0960i −0.232144 + 0.402085i
\(906\) 0 0
\(907\) −15.9559 + 13.3886i −0.529807 + 0.444561i −0.868035 0.496504i \(-0.834617\pi\)
0.338228 + 0.941064i \(0.390172\pi\)
\(908\) 0 0
\(909\) 2.38578 + 13.5304i 0.0791314 + 0.448776i
\(910\) 0 0
\(911\) −13.7300 −0.454895 −0.227448 0.973790i \(-0.573038\pi\)
−0.227448 + 0.973790i \(0.573038\pi\)
\(912\) 0 0
\(913\) 4.61949 0.152883
\(914\) 0 0
\(915\) 1.60488 + 9.10175i 0.0530559 + 0.300895i
\(916\) 0 0
\(917\) 7.75781 6.50957i 0.256185 0.214965i
\(918\) 0 0
\(919\) −22.2245 + 38.4939i −0.733117 + 1.26980i 0.222427 + 0.974949i \(0.428602\pi\)
−0.955544 + 0.294847i \(0.904731\pi\)
\(920\) 0 0
\(921\) 0.536837 0.195393i 0.0176894 0.00643840i
\(922\) 0 0
\(923\) 18.8391 + 32.6304i 0.620098 + 1.07404i
\(924\) 0 0
\(925\) 0.0400781 0.227294i 0.00131776 0.00747338i
\(926\) 0 0
\(927\) −13.1270 11.0149i −0.431148 0.361776i
\(928\) 0 0
\(929\) −9.12866 3.32256i −0.299502 0.109010i 0.187898 0.982188i \(-0.439832\pi\)
−0.487400 + 0.873179i \(0.662055\pi\)
\(930\) 0 0
\(931\) −19.9489 + 6.93491i −0.653798 + 0.227282i
\(932\) 0 0
\(933\) −13.4868 4.90879i −0.441538 0.160707i
\(934\) 0 0
\(935\) 2.39440 + 2.00914i 0.0783053 + 0.0657059i
\(936\) 0 0
\(937\) −1.98808 + 11.2750i −0.0649479 + 0.368338i 0.934960 + 0.354754i \(0.115435\pi\)
−0.999908 + 0.0135842i \(0.995676\pi\)
\(938\) 0 0
\(939\) −1.20187 2.08169i −0.0392214 0.0679335i
\(940\) 0 0
\(941\) −42.3546 + 15.4158i −1.38072 + 0.502541i −0.922397 0.386243i \(-0.873772\pi\)
−0.458324 + 0.888785i \(0.651550\pi\)
\(942\) 0 0
\(943\) 5.73442 9.93231i 0.186738 0.323441i
\(944\) 0 0
\(945\) 1.33228 1.11792i 0.0433391 0.0363658i
\(946\) 0 0
\(947\) −7.66014 43.4428i −0.248921 1.41170i −0.811207 0.584759i \(-0.801189\pi\)
0.562286 0.826943i \(-0.309922\pi\)
\(948\) 0 0
\(949\) 16.8334 0.546435
\(950\) 0 0
\(951\) −14.0574 −0.455841
\(952\) 0 0
\(953\) 0.318201 + 1.80460i 0.0103075 + 0.0584569i 0.989528 0.144343i \(-0.0461069\pi\)
−0.979220 + 0.202800i \(0.934996\pi\)
\(954\) 0 0
\(955\) 10.3641 8.69653i 0.335375 0.281413i
\(956\) 0 0
\(957\) −5.57532 + 9.65674i −0.180225 + 0.312158i
\(958\) 0 0
\(959\) −21.8259 + 7.94399i −0.704796 + 0.256525i
\(960\) 0 0
\(961\) −15.9346 27.5996i −0.514021 0.890310i
\(962\) 0 0
\(963\) 1.82383 10.3434i 0.0587720 0.333312i
\(964\) 0 0
\(965\) −8.61334 7.22745i −0.277273 0.232660i
\(966\) 0 0
\(967\) 15.4941 + 5.63938i 0.498256 + 0.181350i 0.578909 0.815392i \(-0.303479\pi\)
−0.0806536 + 0.996742i \(0.525701\pi\)
\(968\) 0 0
\(969\) −9.07145 3.45150i −0.291417 0.110878i
\(970\) 0 0
\(971\) 41.8803 + 15.2432i 1.34400 + 0.489177i 0.911071 0.412249i \(-0.135257\pi\)
0.432932 + 0.901426i \(0.357479\pi\)
\(972\) 0 0
\(973\) 17.4021 + 14.6021i 0.557887 + 0.468123i
\(974\) 0 0
\(975\) 1.60741 9.11608i 0.0514784 0.291948i
\(976\) 0 0
\(977\) −15.7049 27.2016i −0.502443 0.870257i −0.999996 0.00282321i \(-0.999101\pi\)
0.497553 0.867434i \(-0.334232\pi\)
\(978\) 0 0
\(979\) 13.8182 5.02941i 0.441632 0.160741i
\(980\) 0 0
\(981\) 4.02094 6.96448i 0.128379 0.222359i
\(982\) 0 0
\(983\) 22.2592 18.6777i 0.709959 0.595727i −0.214628 0.976696i \(-0.568854\pi\)
0.924588 + 0.380969i \(0.124410\pi\)
\(984\) 0 0
\(985\) −1.46797 8.32526i −0.0467733 0.265265i
\(986\) 0 0
\(987\) −7.14115 −0.227305
\(988\) 0 0
\(989\) −8.58853 −0.273099
\(990\) 0 0
\(991\) −0.686137 3.89127i −0.0217959 0.123610i 0.971969 0.235111i \(-0.0755454\pi\)
−0.993764 + 0.111501i \(0.964434\pi\)
\(992\) 0 0
\(993\) 20.5626 17.2541i 0.652534 0.547541i
\(994\) 0 0
\(995\) 10.5162 18.2146i 0.333386 0.577441i
\(996\) 0 0
\(997\) 44.2139 16.0926i 1.40027 0.509656i 0.472011 0.881592i \(-0.343528\pi\)
0.928258 + 0.371936i \(0.121306\pi\)
\(998\) 0 0
\(999\) −0.0320889 0.0555796i −0.00101525 0.00175846i
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 912.2.bo.a.289.1 6
4.3 odd 2 114.2.i.a.61.1 yes 6
12.11 even 2 342.2.u.e.289.1 6
19.5 even 9 inner 912.2.bo.a.385.1 6
76.43 odd 18 114.2.i.a.43.1 6
76.47 odd 18 2166.2.a.q.1.2 3
76.67 even 18 2166.2.a.s.1.2 3
228.47 even 18 6498.2.a.br.1.2 3
228.119 even 18 342.2.u.e.271.1 6
228.143 odd 18 6498.2.a.bm.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.i.a.43.1 6 76.43 odd 18
114.2.i.a.61.1 yes 6 4.3 odd 2
342.2.u.e.271.1 6 228.119 even 18
342.2.u.e.289.1 6 12.11 even 2
912.2.bo.a.289.1 6 1.1 even 1 trivial
912.2.bo.a.385.1 6 19.5 even 9 inner
2166.2.a.q.1.2 3 76.47 odd 18
2166.2.a.s.1.2 3 76.67 even 18
6498.2.a.bm.1.2 3 228.143 odd 18
6498.2.a.br.1.2 3 228.47 even 18