Properties

Label 304.2.u.b.225.1
Level $304$
Weight $2$
Character 304.225
Analytic conductor $2.427$
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] = [304,2,Mod(17,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.u (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.42745222145\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 225.1
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 304.225
Dual form 304.2.u.b.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.613341 + 0.223238i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(0.766044 + 1.32683i) q^{7} +(-1.97178 + 1.65452i) q^{9} +O(q^{10})\) \(q+(-0.613341 + 0.223238i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(0.766044 + 1.32683i) q^{7} +(-1.97178 + 1.65452i) q^{9} +(-0.592396 + 1.02606i) q^{11} +(-2.55303 - 0.929228i) q^{13} +(-0.152704 - 0.866025i) q^{15} +(2.97178 + 2.49362i) q^{17} +(-0.819078 + 4.28125i) q^{19} +(-0.766044 - 0.642788i) q^{21} +(0.879385 + 4.98724i) q^{23} +(2.99273 + 1.08926i) q^{25} +(1.81908 - 3.15074i) q^{27} +(-3.56418 + 2.99070i) q^{29} +(-1.91875 - 3.32337i) q^{31} +(0.134285 - 0.761570i) q^{33} +(-1.93969 + 0.705990i) q^{35} -4.10607 q^{37} +1.77332 q^{39} +(9.38326 - 3.41523i) q^{41} +(1.51114 - 8.57013i) q^{43} +(-1.73396 - 3.00330i) q^{45} +(-0.439693 + 0.368946i) q^{47} +(2.32635 - 4.02936i) q^{49} +(-2.37939 - 0.866025i) q^{51} +(0.511144 + 2.89884i) q^{53} +(-1.22281 - 1.02606i) q^{55} +(-0.453363 - 2.80872i) q^{57} +(3.01501 + 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(-3.70574 - 1.34878i) q^{63} +(1.83022 - 3.17004i) q^{65} +(2.97771 - 2.49860i) q^{67} +(-1.65270 - 2.86257i) q^{69} +(1.20439 - 6.83045i) q^{71} +(-5.75877 + 2.09602i) q^{73} -2.07873 q^{75} -1.81521 q^{77} +(9.21688 - 3.35467i) q^{79} +(0.928548 - 5.26606i) q^{81} +(6.15910 + 10.6679i) q^{83} +(-4.00387 + 3.35965i) q^{85} +(1.51842 - 2.62998i) q^{87} +(2.27972 + 0.829748i) q^{89} +(-0.722811 - 4.09927i) q^{91} +(1.91875 + 1.61002i) q^{93} +(-5.48886 - 2.08840i) q^{95} +(5.64543 + 4.73708i) q^{97} +(-0.529563 - 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{19} - 6 q^{23} - 6 q^{27} - 3 q^{29} - 9 q^{31} - 9 q^{33} - 6 q^{35} + 24 q^{39} + 21 q^{41} + 3 q^{43} - 15 q^{45} + 3 q^{47} + 15 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} + 24 q^{57} - 12 q^{59} - 12 q^{61} - 12 q^{63} - 12 q^{65} + 30 q^{67} - 12 q^{69} + 6 q^{71} - 12 q^{73} - 30 q^{75} - 18 q^{77} + 39 q^{79} + 6 q^{81} + 21 q^{87} - 12 q^{89} - 15 q^{91} + 9 q^{93} - 39 q^{95} + 18 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)

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
\(3\) −0.613341 + 0.223238i −0.354112 + 0.128886i −0.512950 0.858418i \(-0.671448\pi\)
0.158838 + 0.987305i \(0.449225\pi\)
\(4\) 0 0
\(5\) −0.233956 + 1.32683i −0.104628 + 0.593375i 0.886740 + 0.462268i \(0.152964\pi\)
−0.991368 + 0.131107i \(0.958147\pi\)
\(6\) 0 0
\(7\) 0.766044 + 1.32683i 0.289538 + 0.501494i 0.973699 0.227836i \(-0.0731651\pi\)
−0.684162 + 0.729330i \(0.739832\pi\)
\(8\) 0 0
\(9\) −1.97178 + 1.65452i −0.657261 + 0.551507i
\(10\) 0 0
\(11\) −0.592396 + 1.02606i −0.178614 + 0.309369i −0.941406 0.337275i \(-0.890495\pi\)
0.762792 + 0.646644i \(0.223828\pi\)
\(12\) 0 0
\(13\) −2.55303 0.929228i −0.708084 0.257722i −0.0372256 0.999307i \(-0.511852\pi\)
−0.670859 + 0.741585i \(0.734074\pi\)
\(14\) 0 0
\(15\) −0.152704 0.866025i −0.0394279 0.223607i
\(16\) 0 0
\(17\) 2.97178 + 2.49362i 0.720763 + 0.604792i 0.927596 0.373584i \(-0.121871\pi\)
−0.206833 + 0.978376i \(0.566316\pi\)
\(18\) 0 0
\(19\) −0.819078 + 4.28125i −0.187909 + 0.982186i
\(20\) 0 0
\(21\) −0.766044 0.642788i −0.167165 0.140268i
\(22\) 0 0
\(23\) 0.879385 + 4.98724i 0.183364 + 1.03991i 0.928039 + 0.372484i \(0.121494\pi\)
−0.744674 + 0.667428i \(0.767395\pi\)
\(24\) 0 0
\(25\) 2.99273 + 1.08926i 0.598545 + 0.217853i
\(26\) 0 0
\(27\) 1.81908 3.15074i 0.350082 0.606359i
\(28\) 0 0
\(29\) −3.56418 + 2.99070i −0.661851 + 0.555359i −0.910641 0.413198i \(-0.864412\pi\)
0.248790 + 0.968557i \(0.419967\pi\)
\(30\) 0 0
\(31\) −1.91875 3.32337i −0.344617 0.596895i 0.640667 0.767819i \(-0.278658\pi\)
−0.985284 + 0.170924i \(0.945325\pi\)
\(32\) 0 0
\(33\) 0.134285 0.761570i 0.0233761 0.132572i
\(34\) 0 0
\(35\) −1.93969 + 0.705990i −0.327868 + 0.119334i
\(36\) 0 0
\(37\) −4.10607 −0.675033 −0.337517 0.941320i \(-0.609587\pi\)
−0.337517 + 0.941320i \(0.609587\pi\)
\(38\) 0 0
\(39\) 1.77332 0.283958
\(40\) 0 0
\(41\) 9.38326 3.41523i 1.46542 0.533369i 0.518566 0.855038i \(-0.326466\pi\)
0.946852 + 0.321669i \(0.104244\pi\)
\(42\) 0 0
\(43\) 1.51114 8.57013i 0.230447 1.30693i −0.621545 0.783378i \(-0.713495\pi\)
0.851993 0.523554i \(-0.175394\pi\)
\(44\) 0 0
\(45\) −1.73396 3.00330i −0.258483 0.447705i
\(46\) 0 0
\(47\) −0.439693 + 0.368946i −0.0641358 + 0.0538163i −0.674292 0.738465i \(-0.735551\pi\)
0.610156 + 0.792281i \(0.291107\pi\)
\(48\) 0 0
\(49\) 2.32635 4.02936i 0.332336 0.575623i
\(50\) 0 0
\(51\) −2.37939 0.866025i −0.333181 0.121268i
\(52\) 0 0
\(53\) 0.511144 + 2.89884i 0.0702111 + 0.398187i 0.999579 + 0.0290308i \(0.00924209\pi\)
−0.929367 + 0.369156i \(0.879647\pi\)
\(54\) 0 0
\(55\) −1.22281 1.02606i −0.164884 0.138354i
\(56\) 0 0
\(57\) −0.453363 2.80872i −0.0600494 0.372023i
\(58\) 0 0
\(59\) 3.01501 + 2.52990i 0.392521 + 0.329365i 0.817595 0.575794i \(-0.195307\pi\)
−0.425073 + 0.905159i \(0.639752\pi\)
\(60\) 0 0
\(61\) −0.784463 4.44891i −0.100440 0.569624i −0.992944 0.118585i \(-0.962164\pi\)
0.892504 0.451040i \(-0.148947\pi\)
\(62\) 0 0
\(63\) −3.70574 1.34878i −0.466879 0.169930i
\(64\) 0 0
\(65\) 1.83022 3.17004i 0.227011 0.393195i
\(66\) 0 0
\(67\) 2.97771 2.49860i 0.363785 0.305252i −0.442512 0.896763i \(-0.645913\pi\)
0.806297 + 0.591510i \(0.201468\pi\)
\(68\) 0 0
\(69\) −1.65270 2.86257i −0.198962 0.344613i
\(70\) 0 0
\(71\) 1.20439 6.83045i 0.142935 0.810625i −0.826067 0.563572i \(-0.809427\pi\)
0.969002 0.247053i \(-0.0794622\pi\)
\(72\) 0 0
\(73\) −5.75877 + 2.09602i −0.674013 + 0.245321i −0.656275 0.754522i \(-0.727869\pi\)
−0.0177383 + 0.999843i \(0.505647\pi\)
\(74\) 0 0
\(75\) −2.07873 −0.240031
\(76\) 0 0
\(77\) −1.81521 −0.206862
\(78\) 0 0
\(79\) 9.21688 3.35467i 1.03698 0.377430i 0.233246 0.972418i \(-0.425065\pi\)
0.803735 + 0.594988i \(0.202843\pi\)
\(80\) 0 0
\(81\) 0.928548 5.26606i 0.103172 0.585118i
\(82\) 0 0
\(83\) 6.15910 + 10.6679i 0.676049 + 1.17095i 0.976161 + 0.217047i \(0.0696426\pi\)
−0.300112 + 0.953904i \(0.597024\pi\)
\(84\) 0 0
\(85\) −4.00387 + 3.35965i −0.434281 + 0.364405i
\(86\) 0 0
\(87\) 1.51842 2.62998i 0.162792 0.281963i
\(88\) 0 0
\(89\) 2.27972 + 0.829748i 0.241649 + 0.0879532i 0.460006 0.887916i \(-0.347847\pi\)
−0.218356 + 0.975869i \(0.570070\pi\)
\(90\) 0 0
\(91\) −0.722811 4.09927i −0.0757712 0.429720i
\(92\) 0 0
\(93\) 1.91875 + 1.61002i 0.198965 + 0.166951i
\(94\) 0 0
\(95\) −5.48886 2.08840i −0.563145 0.214265i
\(96\) 0 0
\(97\) 5.64543 + 4.73708i 0.573207 + 0.480977i 0.882708 0.469922i \(-0.155718\pi\)
−0.309502 + 0.950899i \(0.600162\pi\)
\(98\) 0 0
\(99\) −0.529563 3.00330i −0.0532231 0.301843i
\(100\) 0 0
\(101\) −2.03936 0.742267i −0.202924 0.0738584i 0.238559 0.971128i \(-0.423325\pi\)
−0.441483 + 0.897270i \(0.645547\pi\)
\(102\) 0 0
\(103\) −6.23783 + 10.8042i −0.614631 + 1.06457i 0.375818 + 0.926694i \(0.377362\pi\)
−0.990449 + 0.137879i \(0.955971\pi\)
\(104\) 0 0
\(105\) 1.03209 0.866025i 0.100722 0.0845154i
\(106\) 0 0
\(107\) −3.34002 5.78509i −0.322892 0.559266i 0.658191 0.752851i \(-0.271322\pi\)
−0.981083 + 0.193585i \(0.937988\pi\)
\(108\) 0 0
\(109\) 1.64156 9.30975i 0.157233 0.891712i −0.799483 0.600689i \(-0.794893\pi\)
0.956716 0.291023i \(-0.0939957\pi\)
\(110\) 0 0
\(111\) 2.51842 0.916629i 0.239038 0.0870026i
\(112\) 0 0
\(113\) 1.31046 0.123278 0.0616388 0.998099i \(-0.480367\pi\)
0.0616388 + 0.998099i \(0.480367\pi\)
\(114\) 0 0
\(115\) −6.82295 −0.636243
\(116\) 0 0
\(117\) 6.57145 2.39181i 0.607531 0.221123i
\(118\) 0 0
\(119\) −1.03209 + 5.85327i −0.0946114 + 0.536568i
\(120\) 0 0
\(121\) 4.79813 + 8.31061i 0.436194 + 0.755510i
\(122\) 0 0
\(123\) −4.99273 + 4.18939i −0.450179 + 0.377745i
\(124\) 0 0
\(125\) −5.51367 + 9.54996i −0.493158 + 0.854174i
\(126\) 0 0
\(127\) −13.6284 4.96032i −1.20932 0.440157i −0.342853 0.939389i \(-0.611393\pi\)
−0.866468 + 0.499232i \(0.833615\pi\)
\(128\) 0 0
\(129\) 0.986329 + 5.59375i 0.0868415 + 0.492502i
\(130\) 0 0
\(131\) 15.1741 + 12.7326i 1.32577 + 1.11245i 0.985047 + 0.172288i \(0.0551159\pi\)
0.340722 + 0.940164i \(0.389329\pi\)
\(132\) 0 0
\(133\) −6.30793 + 2.19285i −0.546967 + 0.190144i
\(134\) 0 0
\(135\) 3.75490 + 3.15074i 0.323170 + 0.271172i
\(136\) 0 0
\(137\) 1.77197 + 10.0494i 0.151390 + 0.858575i 0.962012 + 0.273006i \(0.0880179\pi\)
−0.810622 + 0.585569i \(0.800871\pi\)
\(138\) 0 0
\(139\) −1.56031 0.567905i −0.132344 0.0481691i 0.274999 0.961444i \(-0.411322\pi\)
−0.407343 + 0.913275i \(0.633545\pi\)
\(140\) 0 0
\(141\) 0.187319 0.324446i 0.0157751 0.0273232i
\(142\) 0 0
\(143\) 2.46585 2.06910i 0.206205 0.173026i
\(144\) 0 0
\(145\) −3.13429 5.42874i −0.260288 0.450832i
\(146\) 0 0
\(147\) −0.527341 + 2.99070i −0.0434944 + 0.246669i
\(148\) 0 0
\(149\) −10.5312 + 3.83305i −0.862750 + 0.314015i −0.735228 0.677820i \(-0.762925\pi\)
−0.127523 + 0.991836i \(0.540703\pi\)
\(150\) 0 0
\(151\) 11.0419 0.898576 0.449288 0.893387i \(-0.351678\pi\)
0.449288 + 0.893387i \(0.351678\pi\)
\(152\) 0 0
\(153\) −9.98545 −0.807276
\(154\) 0 0
\(155\) 4.85844 1.76833i 0.390239 0.142036i
\(156\) 0 0
\(157\) 1.90895 10.8262i 0.152351 0.864023i −0.808817 0.588060i \(-0.799892\pi\)
0.961168 0.275964i \(-0.0889969\pi\)
\(158\) 0 0
\(159\) −0.960637 1.66387i −0.0761835 0.131954i
\(160\) 0 0
\(161\) −5.94356 + 4.98724i −0.468418 + 0.393050i
\(162\) 0 0
\(163\) −3.16637 + 5.48432i −0.248010 + 0.429565i −0.962973 0.269596i \(-0.913110\pi\)
0.714964 + 0.699161i \(0.246443\pi\)
\(164\) 0 0
\(165\) 0.979055 + 0.356347i 0.0762194 + 0.0277416i
\(166\) 0 0
\(167\) 2.39259 + 13.5690i 0.185144 + 1.05000i 0.925770 + 0.378087i \(0.123418\pi\)
−0.740626 + 0.671917i \(0.765471\pi\)
\(168\) 0 0
\(169\) −4.30406 3.61154i −0.331082 0.277811i
\(170\) 0 0
\(171\) −5.46838 9.79687i −0.418177 0.749186i
\(172\) 0 0
\(173\) 19.3405 + 16.2286i 1.47043 + 1.23384i 0.915734 + 0.401784i \(0.131610\pi\)
0.554696 + 0.832053i \(0.312835\pi\)
\(174\) 0 0
\(175\) 0.847296 + 4.80526i 0.0640496 + 0.363243i
\(176\) 0 0
\(177\) −2.41400 0.878624i −0.181447 0.0660414i
\(178\) 0 0
\(179\) 2.91534 5.04952i 0.217903 0.377419i −0.736264 0.676695i \(-0.763412\pi\)
0.954167 + 0.299276i \(0.0967450\pi\)
\(180\) 0 0
\(181\) 10.3892 8.71756i 0.772222 0.647971i −0.169055 0.985607i \(-0.554072\pi\)
0.941277 + 0.337635i \(0.109627\pi\)
\(182\) 0 0
\(183\) 1.47431 + 2.55358i 0.108984 + 0.188766i
\(184\) 0 0
\(185\) 0.960637 5.44804i 0.0706274 0.400548i
\(186\) 0 0
\(187\) −4.31908 + 1.57202i −0.315842 + 0.114957i
\(188\) 0 0
\(189\) 5.57398 0.405447
\(190\) 0 0
\(191\) 10.2841 0.744128 0.372064 0.928207i \(-0.378650\pi\)
0.372064 + 0.928207i \(0.378650\pi\)
\(192\) 0 0
\(193\) −12.9684 + 4.72010i −0.933484 + 0.339760i −0.763590 0.645702i \(-0.776565\pi\)
−0.169895 + 0.985462i \(0.554343\pi\)
\(194\) 0 0
\(195\) −0.414878 + 2.35289i −0.0297100 + 0.168494i
\(196\) 0 0
\(197\) 3.97044 + 6.87700i 0.282882 + 0.489966i 0.972093 0.234594i \(-0.0753762\pi\)
−0.689211 + 0.724560i \(0.742043\pi\)
\(198\) 0 0
\(199\) −20.7101 + 17.3778i −1.46810 + 1.23188i −0.550219 + 0.835020i \(0.685456\pi\)
−0.917879 + 0.396861i \(0.870100\pi\)
\(200\) 0 0
\(201\) −1.26857 + 2.19723i −0.0894781 + 0.154981i
\(202\) 0 0
\(203\) −6.69846 2.43804i −0.470140 0.171117i
\(204\) 0 0
\(205\) 2.33615 + 13.2490i 0.163164 + 0.925349i
\(206\) 0 0
\(207\) −9.98545 8.37879i −0.694037 0.582366i
\(208\) 0 0
\(209\) −3.90760 3.37662i −0.270295 0.233566i
\(210\) 0 0
\(211\) 6.18345 + 5.18853i 0.425686 + 0.357193i 0.830321 0.557285i \(-0.188157\pi\)
−0.404635 + 0.914478i \(0.632601\pi\)
\(212\) 0 0
\(213\) 0.786112 + 4.45826i 0.0538635 + 0.305475i
\(214\) 0 0
\(215\) 11.0175 + 4.01006i 0.751390 + 0.273484i
\(216\) 0 0
\(217\) 2.93969 5.09170i 0.199559 0.345647i
\(218\) 0 0
\(219\) 3.06418 2.57115i 0.207058 0.173742i
\(220\) 0 0
\(221\) −5.26991 9.12776i −0.354493 0.614000i
\(222\) 0 0
\(223\) 2.68732 15.2405i 0.179956 1.02058i −0.752310 0.658809i \(-0.771060\pi\)
0.932266 0.361773i \(-0.117828\pi\)
\(224\) 0 0
\(225\) −7.70321 + 2.80374i −0.513547 + 0.186916i
\(226\) 0 0
\(227\) −9.87258 −0.655266 −0.327633 0.944805i \(-0.606251\pi\)
−0.327633 + 0.944805i \(0.606251\pi\)
\(228\) 0 0
\(229\) 20.1189 1.32949 0.664746 0.747070i \(-0.268540\pi\)
0.664746 + 0.747070i \(0.268540\pi\)
\(230\) 0 0
\(231\) 1.11334 0.405223i 0.0732524 0.0266617i
\(232\) 0 0
\(233\) 0.613808 3.48108i 0.0402119 0.228053i −0.958078 0.286507i \(-0.907506\pi\)
0.998290 + 0.0584538i \(0.0186170\pi\)
\(234\) 0 0
\(235\) −0.386659 0.669713i −0.0252229 0.0436873i
\(236\) 0 0
\(237\) −4.90420 + 4.11511i −0.318562 + 0.267305i
\(238\) 0 0
\(239\) 5.98680 10.3694i 0.387254 0.670743i −0.604825 0.796358i \(-0.706757\pi\)
0.992079 + 0.125615i \(0.0400904\pi\)
\(240\) 0 0
\(241\) −12.1236 4.41263i −0.780950 0.284243i −0.0793814 0.996844i \(-0.525294\pi\)
−0.701569 + 0.712602i \(0.747517\pi\)
\(242\) 0 0
\(243\) 2.50134 + 14.1858i 0.160461 + 0.910021i
\(244\) 0 0
\(245\) 4.80200 + 4.02936i 0.306789 + 0.257426i
\(246\) 0 0
\(247\) 6.06939 10.1691i 0.386186 0.647042i
\(248\) 0 0
\(249\) −6.15910 5.16810i −0.390317 0.327515i
\(250\) 0 0
\(251\) −2.49407 14.1446i −0.157424 0.892798i −0.956536 0.291615i \(-0.905807\pi\)
0.799112 0.601183i \(-0.205304\pi\)
\(252\) 0 0
\(253\) −5.63816 2.05212i −0.354468 0.129016i
\(254\) 0 0
\(255\) 1.70574 2.95442i 0.106817 0.185013i
\(256\) 0 0
\(257\) 3.81315 3.19961i 0.237858 0.199586i −0.516065 0.856549i \(-0.672604\pi\)
0.753923 + 0.656963i \(0.228159\pi\)
\(258\) 0 0
\(259\) −3.14543 5.44804i −0.195447 0.338525i
\(260\) 0 0
\(261\) 2.07960 11.7940i 0.128724 0.730031i
\(262\) 0 0
\(263\) −22.5929 + 8.22313i −1.39314 + 0.507060i −0.926133 0.377196i \(-0.876888\pi\)
−0.467002 + 0.884256i \(0.654666\pi\)
\(264\) 0 0
\(265\) −3.96585 −0.243620
\(266\) 0 0
\(267\) −1.58347 −0.0969070
\(268\) 0 0
\(269\) 12.3204 4.48427i 0.751189 0.273411i 0.0620832 0.998071i \(-0.480226\pi\)
0.689106 + 0.724660i \(0.258003\pi\)
\(270\) 0 0
\(271\) 4.61381 26.1662i 0.280269 1.58948i −0.441443 0.897290i \(-0.645533\pi\)
0.721711 0.692194i \(-0.243356\pi\)
\(272\) 0 0
\(273\) 1.35844 + 2.35289i 0.0822166 + 0.142403i
\(274\) 0 0
\(275\) −2.89053 + 2.42544i −0.174305 + 0.146260i
\(276\) 0 0
\(277\) 8.25537 14.2987i 0.496017 0.859127i −0.503973 0.863720i \(-0.668129\pi\)
0.999989 + 0.00459317i \(0.00146206\pi\)
\(278\) 0 0
\(279\) 9.28194 + 3.37835i 0.555695 + 0.202256i
\(280\) 0 0
\(281\) −3.36706 19.0955i −0.200862 1.13914i −0.903820 0.427913i \(-0.859249\pi\)
0.702958 0.711231i \(-0.251862\pi\)
\(282\) 0 0
\(283\) 8.66431 + 7.27022i 0.515040 + 0.432170i 0.862899 0.505377i \(-0.168647\pi\)
−0.347859 + 0.937547i \(0.613091\pi\)
\(284\) 0 0
\(285\) 3.83275 + 0.0555796i 0.227032 + 0.00329225i
\(286\) 0 0
\(287\) 11.7194 + 9.83375i 0.691775 + 0.580468i
\(288\) 0 0
\(289\) −0.338678 1.92074i −0.0199222 0.112985i
\(290\) 0 0
\(291\) −4.52007 1.64517i −0.264971 0.0964416i
\(292\) 0 0
\(293\) −1.94949 + 3.37662i −0.113891 + 0.197264i −0.917336 0.398115i \(-0.869665\pi\)
0.803445 + 0.595379i \(0.202998\pi\)
\(294\) 0 0
\(295\) −4.06212 + 3.40852i −0.236506 + 0.198452i
\(296\) 0 0
\(297\) 2.15523 + 3.73297i 0.125059 + 0.216609i
\(298\) 0 0
\(299\) 2.38919 13.5497i 0.138170 0.783602i
\(300\) 0 0
\(301\) 12.5287 4.56007i 0.722141 0.262838i
\(302\) 0 0
\(303\) 1.41653 0.0813773
\(304\) 0 0
\(305\) 6.08647 0.348510
\(306\) 0 0
\(307\) 21.7777 7.92642i 1.24292 0.452385i 0.364914 0.931041i \(-0.381098\pi\)
0.878002 + 0.478657i \(0.158876\pi\)
\(308\) 0 0
\(309\) 1.41400 8.01919i 0.0804397 0.456196i
\(310\) 0 0
\(311\) −1.73055 2.99740i −0.0981306 0.169967i 0.812780 0.582570i \(-0.197953\pi\)
−0.910911 + 0.412603i \(0.864620\pi\)
\(312\) 0 0
\(313\) −17.5346 + 14.7133i −0.991115 + 0.831644i −0.985729 0.168341i \(-0.946159\pi\)
−0.00538626 + 0.999985i \(0.501715\pi\)
\(314\) 0 0
\(315\) 2.65657 4.60132i 0.149681 0.259255i
\(316\) 0 0
\(317\) −24.5453 8.93378i −1.37860 0.501771i −0.456849 0.889544i \(-0.651022\pi\)
−0.921755 + 0.387773i \(0.873244\pi\)
\(318\) 0 0
\(319\) −0.957234 5.42874i −0.0535948 0.303951i
\(320\) 0 0
\(321\) 3.34002 + 2.80261i 0.186422 + 0.156427i
\(322\) 0 0
\(323\) −13.1099 + 10.6805i −0.729456 + 0.594277i
\(324\) 0 0
\(325\) −6.62836 5.56185i −0.367675 0.308516i
\(326\) 0 0
\(327\) 1.07145 + 6.07650i 0.0592514 + 0.336031i
\(328\) 0 0
\(329\) −0.826352 0.300767i −0.0455583 0.0165818i
\(330\) 0 0
\(331\) 9.52229 16.4931i 0.523392 0.906542i −0.476237 0.879317i \(-0.658000\pi\)
0.999629 0.0272251i \(-0.00866710\pi\)
\(332\) 0 0
\(333\) 8.09627 6.79357i 0.443673 0.372286i
\(334\) 0 0
\(335\) 2.61856 + 4.53547i 0.143067 + 0.247799i
\(336\) 0 0
\(337\) 0.295445 1.67555i 0.0160939 0.0912731i −0.975703 0.219098i \(-0.929688\pi\)
0.991797 + 0.127825i \(0.0407996\pi\)
\(338\) 0 0
\(339\) −0.803758 + 0.292544i −0.0436542 + 0.0158888i
\(340\) 0 0
\(341\) 4.54664 0.246214
\(342\) 0 0
\(343\) 17.8530 0.963970
\(344\) 0 0
\(345\) 4.18479 1.52314i 0.225302 0.0820031i
\(346\) 0 0
\(347\) 0.851167 4.82721i 0.0456930 0.259138i −0.953400 0.301708i \(-0.902443\pi\)
0.999094 + 0.0425697i \(0.0135544\pi\)
\(348\) 0 0
\(349\) 14.0646 + 24.3607i 0.752863 + 1.30400i 0.946430 + 0.322910i \(0.104661\pi\)
−0.193566 + 0.981087i \(0.562006\pi\)
\(350\) 0 0
\(351\) −7.57192 + 6.35359i −0.404159 + 0.339130i
\(352\) 0 0
\(353\) 4.15998 7.20529i 0.221413 0.383499i −0.733824 0.679340i \(-0.762266\pi\)
0.955237 + 0.295841i \(0.0955997\pi\)
\(354\) 0 0
\(355\) 8.78106 + 3.19604i 0.466050 + 0.169628i
\(356\) 0 0
\(357\) −0.673648 3.82045i −0.0356532 0.202200i
\(358\) 0 0
\(359\) −19.0967 16.0241i −1.00789 0.845718i −0.0198296 0.999803i \(-0.506312\pi\)
−0.988057 + 0.154086i \(0.950757\pi\)
\(360\) 0 0
\(361\) −17.6582 7.01336i −0.929380 0.369124i
\(362\) 0 0
\(363\) −4.79813 4.02611i −0.251837 0.211316i
\(364\) 0 0
\(365\) −1.43376 8.13127i −0.0750466 0.425610i
\(366\) 0 0
\(367\) −2.42989 0.884409i −0.126839 0.0461657i 0.277821 0.960633i \(-0.410388\pi\)
−0.404660 + 0.914467i \(0.632610\pi\)
\(368\) 0 0
\(369\) −12.8512 + 22.2589i −0.669005 + 1.15875i
\(370\) 0 0
\(371\) −3.45471 + 2.89884i −0.179359 + 0.150500i
\(372\) 0 0
\(373\) 11.6917 + 20.2505i 0.605371 + 1.04853i 0.991993 + 0.126295i \(0.0403086\pi\)
−0.386622 + 0.922238i \(0.626358\pi\)
\(374\) 0 0
\(375\) 1.24985 7.08824i 0.0645419 0.366035i
\(376\) 0 0
\(377\) 11.8785 4.32342i 0.611774 0.222668i
\(378\) 0 0
\(379\) −25.4388 −1.30670 −0.653352 0.757054i \(-0.726638\pi\)
−0.653352 + 0.757054i \(0.726638\pi\)
\(380\) 0 0
\(381\) 9.46616 0.484966
\(382\) 0 0
\(383\) −25.8234 + 9.39895i −1.31951 + 0.480264i −0.903303 0.429003i \(-0.858865\pi\)
−0.416212 + 0.909268i \(0.636643\pi\)
\(384\) 0 0
\(385\) 0.424678 2.40847i 0.0216436 0.122747i
\(386\) 0 0
\(387\) 11.1998 + 19.3986i 0.569318 + 0.986088i
\(388\) 0 0
\(389\) −2.56031 + 2.14835i −0.129813 + 0.108926i −0.705383 0.708827i \(-0.749225\pi\)
0.575570 + 0.817753i \(0.304780\pi\)
\(390\) 0 0
\(391\) −9.82295 + 17.0138i −0.496768 + 0.860427i
\(392\) 0 0
\(393\) −12.1493 4.42198i −0.612851 0.223060i
\(394\) 0 0
\(395\) 2.29473 + 13.0141i 0.115460 + 0.654808i
\(396\) 0 0
\(397\) −10.0530 8.43550i −0.504547 0.423365i 0.354658 0.934996i \(-0.384597\pi\)
−0.859206 + 0.511631i \(0.829042\pi\)
\(398\) 0 0
\(399\) 3.37939 2.75314i 0.169181 0.137829i
\(400\) 0 0
\(401\) 13.1099 + 11.0005i 0.654679 + 0.549341i 0.908487 0.417914i \(-0.137239\pi\)
−0.253808 + 0.967255i \(0.581683\pi\)
\(402\) 0 0
\(403\) 1.81046 + 10.2676i 0.0901854 + 0.511467i
\(404\) 0 0
\(405\) 6.76991 + 2.46405i 0.336400 + 0.122440i
\(406\) 0 0
\(407\) 2.43242 4.21307i 0.120571 0.208834i
\(408\) 0 0
\(409\) −6.73964 + 5.65523i −0.333254 + 0.279633i −0.794024 0.607886i \(-0.792018\pi\)
0.460770 + 0.887519i \(0.347573\pi\)
\(410\) 0 0
\(411\) −3.33022 5.76811i −0.164268 0.284520i
\(412\) 0 0
\(413\) −1.04710 + 5.93842i −0.0515246 + 0.292211i
\(414\) 0 0
\(415\) −15.5954 + 5.67626i −0.765548 + 0.278637i
\(416\) 0 0
\(417\) 1.08378 0.0530728
\(418\) 0 0
\(419\) −6.84018 −0.334165 −0.167082 0.985943i \(-0.553435\pi\)
−0.167082 + 0.985943i \(0.553435\pi\)
\(420\) 0 0
\(421\) 4.53209 1.64955i 0.220880 0.0803939i −0.229210 0.973377i \(-0.573614\pi\)
0.450090 + 0.892983i \(0.351392\pi\)
\(422\) 0 0
\(423\) 0.256549 1.45496i 0.0124738 0.0707426i
\(424\) 0 0
\(425\) 6.17752 + 10.6998i 0.299654 + 0.519015i
\(426\) 0 0
\(427\) 5.30200 4.44891i 0.256582 0.215298i
\(428\) 0 0
\(429\) −1.05051 + 1.81953i −0.0507190 + 0.0878478i
\(430\) 0 0
\(431\) 1.22503 + 0.445875i 0.0590077 + 0.0214771i 0.371355 0.928491i \(-0.378893\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(432\) 0 0
\(433\) 3.44238 + 19.5227i 0.165430 + 0.938202i 0.948620 + 0.316419i \(0.102480\pi\)
−0.783189 + 0.621783i \(0.786409\pi\)
\(434\) 0 0
\(435\) 3.13429 + 2.62998i 0.150277 + 0.126098i
\(436\) 0 0
\(437\) −22.0719 0.320070i −1.05584 0.0153110i
\(438\) 0 0
\(439\) 26.4800 + 22.2193i 1.26382 + 1.06047i 0.995264 + 0.0972078i \(0.0309912\pi\)
0.268557 + 0.963264i \(0.413453\pi\)
\(440\) 0 0
\(441\) 2.07960 + 11.7940i 0.0990287 + 0.561620i
\(442\) 0 0
\(443\) 15.9843 + 5.81780i 0.759436 + 0.276412i 0.692571 0.721350i \(-0.256478\pi\)
0.0668650 + 0.997762i \(0.478700\pi\)
\(444\) 0 0
\(445\) −1.63429 + 2.83067i −0.0774726 + 0.134186i
\(446\) 0 0
\(447\) 5.60354 4.70193i 0.265038 0.222394i
\(448\) 0 0
\(449\) −18.7049 32.3978i −0.882737 1.52895i −0.848286 0.529539i \(-0.822365\pi\)
−0.0344512 0.999406i \(-0.510968\pi\)
\(450\) 0 0
\(451\) −2.05438 + 11.6510i −0.0967369 + 0.548622i
\(452\) 0 0
\(453\) −6.77244 + 2.46497i −0.318197 + 0.115814i
\(454\) 0 0
\(455\) 5.60813 0.262913
\(456\) 0 0
\(457\) 9.11112 0.426200 0.213100 0.977030i \(-0.431644\pi\)
0.213100 + 0.977030i \(0.431644\pi\)
\(458\) 0 0
\(459\) 13.2626 4.82721i 0.619047 0.225315i
\(460\) 0 0
\(461\) −4.24540 + 24.0769i −0.197728 + 1.12137i 0.710751 + 0.703443i \(0.248355\pi\)
−0.908480 + 0.417929i \(0.862756\pi\)
\(462\) 0 0
\(463\) −0.125362 0.217134i −0.00582609 0.0100911i 0.863098 0.505037i \(-0.168521\pi\)
−0.868924 + 0.494946i \(0.835188\pi\)
\(464\) 0 0
\(465\) −2.58512 + 2.16918i −0.119882 + 0.100593i
\(466\) 0 0
\(467\) 7.68092 13.3037i 0.355431 0.615624i −0.631761 0.775163i \(-0.717668\pi\)
0.987192 + 0.159539i \(0.0510009\pi\)
\(468\) 0 0
\(469\) 5.59627 + 2.03687i 0.258412 + 0.0940541i
\(470\) 0 0
\(471\) 1.24598 + 7.06629i 0.0574116 + 0.325597i
\(472\) 0 0
\(473\) 7.89827 + 6.62744i 0.363163 + 0.304730i
\(474\) 0 0
\(475\) −7.11468 + 11.9204i −0.326444 + 0.546946i
\(476\) 0 0
\(477\) −5.80406 4.87019i −0.265750 0.222991i
\(478\) 0 0
\(479\) 0.124896 + 0.708319i 0.00570663 + 0.0323639i 0.987528 0.157443i \(-0.0503250\pi\)
−0.981821 + 0.189807i \(0.939214\pi\)
\(480\) 0 0
\(481\) 10.4829 + 3.81547i 0.477980 + 0.173971i
\(482\) 0 0
\(483\) 2.53209 4.38571i 0.115214 0.199557i
\(484\) 0 0
\(485\) −7.60607 + 6.38225i −0.345374 + 0.289803i
\(486\) 0 0
\(487\) 5.87346 + 10.1731i 0.266152 + 0.460988i 0.967865 0.251471i \(-0.0809145\pi\)
−0.701713 + 0.712460i \(0.747581\pi\)
\(488\) 0 0
\(489\) 0.717759 4.07061i 0.0324582 0.184079i
\(490\) 0 0
\(491\) 0.0834734 0.0303818i 0.00376710 0.00137111i −0.340136 0.940376i \(-0.610473\pi\)
0.343903 + 0.939005i \(0.388251\pi\)
\(492\) 0 0
\(493\) −18.0496 −0.812914
\(494\) 0 0
\(495\) 4.10876 0.184675
\(496\) 0 0
\(497\) 9.98545 3.63441i 0.447909 0.163025i
\(498\) 0 0
\(499\) −2.55097 + 14.4673i −0.114197 + 0.647645i 0.872947 + 0.487815i \(0.162206\pi\)
−0.987145 + 0.159830i \(0.948905\pi\)
\(500\) 0 0
\(501\) −4.49660 7.78833i −0.200893 0.347957i
\(502\) 0 0
\(503\) 3.75671 3.15225i 0.167503 0.140552i −0.555183 0.831728i \(-0.687352\pi\)
0.722686 + 0.691176i \(0.242907\pi\)
\(504\) 0 0
\(505\) 1.46198 2.53223i 0.0650573 0.112683i
\(506\) 0 0
\(507\) 3.44609 + 1.25427i 0.153046 + 0.0557043i
\(508\) 0 0
\(509\) 1.11375 + 6.31640i 0.0493662 + 0.279969i 0.999491 0.0319002i \(-0.0101559\pi\)
−0.950125 + 0.311870i \(0.899045\pi\)
\(510\) 0 0
\(511\) −7.19253 6.03525i −0.318179 0.266984i
\(512\) 0 0
\(513\) 11.9991 + 10.3686i 0.529774 + 0.457786i
\(514\) 0 0
\(515\) −12.8760 10.8042i −0.567384 0.476091i
\(516\) 0 0
\(517\) −0.118089 0.669713i −0.00519353 0.0294540i
\(518\) 0 0
\(519\) −15.4851 5.63613i −0.679723 0.247399i
\(520\) 0 0
\(521\) 17.9067 31.0154i 0.784508 1.35881i −0.144785 0.989463i \(-0.546249\pi\)
0.929293 0.369344i \(-0.120418\pi\)
\(522\) 0 0
\(523\) −29.7015 + 24.9225i −1.29875 + 1.08978i −0.308395 + 0.951258i \(0.599792\pi\)
−0.990359 + 0.138526i \(0.955764\pi\)
\(524\) 0 0
\(525\) −1.59240 2.75811i −0.0694979 0.120374i
\(526\) 0 0
\(527\) 2.58512 14.6610i 0.112610 0.638641i
\(528\) 0 0
\(529\) −2.48633 + 0.904950i −0.108101 + 0.0393456i
\(530\) 0 0
\(531\) −10.1307 −0.439636
\(532\) 0 0
\(533\) −27.1293 −1.17510
\(534\) 0 0
\(535\) 8.45723 3.07818i 0.365638 0.133081i
\(536\) 0 0
\(537\) −0.660855 + 3.74789i −0.0285180 + 0.161734i
\(538\) 0 0
\(539\) 2.75624 + 4.77396i 0.118720 + 0.205629i
\(540\) 0 0
\(541\) 7.26991 6.10018i 0.312558 0.262267i −0.472990 0.881068i \(-0.656825\pi\)
0.785548 + 0.618800i \(0.212381\pi\)
\(542\) 0 0
\(543\) −4.42602 + 7.66610i −0.189939 + 0.328984i
\(544\) 0 0
\(545\) 11.9684 + 4.35613i 0.512669 + 0.186596i
\(546\) 0 0
\(547\) −2.46791 13.9962i −0.105520 0.598435i −0.991011 0.133779i \(-0.957289\pi\)
0.885491 0.464657i \(-0.153822\pi\)
\(548\) 0 0
\(549\) 8.90760 + 7.47437i 0.380167 + 0.318998i
\(550\) 0 0
\(551\) −9.88460 17.7088i −0.421098 0.754418i
\(552\) 0 0
\(553\) 11.5116 + 9.65939i 0.489524 + 0.410759i
\(554\) 0 0
\(555\) 0.627011 + 3.55596i 0.0266152 + 0.150942i
\(556\) 0 0
\(557\) −21.1805 7.70908i −0.897447 0.326644i −0.148218 0.988955i \(-0.547354\pi\)
−0.749229 + 0.662311i \(0.769576\pi\)
\(558\) 0 0
\(559\) −11.8216 + 20.4756i −0.500001 + 0.866026i
\(560\) 0 0
\(561\) 2.29813 1.92836i 0.0970273 0.0814155i
\(562\) 0 0
\(563\) −21.4859 37.2147i −0.905524 1.56841i −0.820213 0.572058i \(-0.806145\pi\)
−0.0853106 0.996354i \(-0.527188\pi\)
\(564\) 0 0
\(565\) −0.306589 + 1.73875i −0.0128983 + 0.0731500i
\(566\) 0 0
\(567\) 7.69846 2.80201i 0.323305 0.117673i
\(568\) 0 0
\(569\) 7.42696 0.311354 0.155677 0.987808i \(-0.450244\pi\)
0.155677 + 0.987808i \(0.450244\pi\)
\(570\) 0 0
\(571\) −4.04458 −0.169260 −0.0846301 0.996412i \(-0.526971\pi\)
−0.0846301 + 0.996412i \(0.526971\pi\)
\(572\) 0 0
\(573\) −6.30763 + 2.29579i −0.263505 + 0.0959080i
\(574\) 0 0
\(575\) −2.80066 + 15.8833i −0.116796 + 0.662381i
\(576\) 0 0
\(577\) −1.61721 2.80109i −0.0673254 0.116611i 0.830398 0.557171i \(-0.188113\pi\)
−0.897723 + 0.440560i \(0.854780\pi\)
\(578\) 0 0
\(579\) 6.90033 5.79006i 0.286768 0.240627i
\(580\) 0 0
\(581\) −9.43629 + 16.3441i −0.391483 + 0.678069i
\(582\) 0 0
\(583\) −3.27719 1.19280i −0.135727 0.0494007i
\(584\) 0 0
\(585\) 1.63610 + 9.27876i 0.0676443 + 0.383630i
\(586\) 0 0
\(587\) 31.2610 + 26.2311i 1.29028 + 1.08267i 0.991738 + 0.128279i \(0.0409452\pi\)
0.298543 + 0.954396i \(0.403499\pi\)
\(588\) 0 0
\(589\) 15.7998 5.49254i 0.651019 0.226316i
\(590\) 0 0
\(591\) −3.97044 3.33159i −0.163322 0.137043i
\(592\) 0 0
\(593\) −1.92127 10.8961i −0.0788973 0.447449i −0.998507 0.0546164i \(-0.982606\pi\)
0.919610 0.392832i \(-0.128505\pi\)
\(594\) 0 0
\(595\) −7.52481 2.73881i −0.308487 0.112280i
\(596\) 0 0
\(597\) 8.82295 15.2818i 0.361099 0.625442i
\(598\) 0 0
\(599\) 34.1332 28.6411i 1.39464 1.17024i 0.431224 0.902245i \(-0.358082\pi\)
0.963419 0.268000i \(-0.0863626\pi\)
\(600\) 0 0
\(601\) 2.49953 + 4.32932i 0.101958 + 0.176597i 0.912491 0.409096i \(-0.134156\pi\)
−0.810533 + 0.585693i \(0.800823\pi\)
\(602\) 0 0
\(603\) −1.73742 + 9.85337i −0.0707530 + 0.401260i
\(604\) 0 0
\(605\) −12.1493 + 4.42198i −0.493939 + 0.179779i
\(606\) 0 0
\(607\) 31.1881 1.26589 0.632943 0.774199i \(-0.281847\pi\)
0.632943 + 0.774199i \(0.281847\pi\)
\(608\) 0 0
\(609\) 4.65270 0.188537
\(610\) 0 0
\(611\) 1.46538 0.533356i 0.0592831 0.0215773i
\(612\) 0 0
\(613\) 2.84255 16.1209i 0.114809 0.651117i −0.872035 0.489444i \(-0.837200\pi\)
0.986844 0.161673i \(-0.0516890\pi\)
\(614\) 0 0
\(615\) −4.39053 7.60462i −0.177043 0.306648i
\(616\) 0 0
\(617\) 12.3014 10.3221i 0.495235 0.415551i −0.360663 0.932696i \(-0.617450\pi\)
0.855898 + 0.517145i \(0.173005\pi\)
\(618\) 0 0
\(619\) 11.9213 20.6483i 0.479156 0.829923i −0.520558 0.853826i \(-0.674276\pi\)
0.999714 + 0.0239031i \(0.00760931\pi\)
\(620\) 0 0
\(621\) 17.3131 + 6.30147i 0.694753 + 0.252869i
\(622\) 0 0
\(623\) 0.645430 + 3.66041i 0.0258586 + 0.146651i
\(624\) 0 0
\(625\) 0.817267 + 0.685768i 0.0326907 + 0.0274307i
\(626\) 0 0
\(627\) 3.15048 + 1.19869i 0.125818 + 0.0478712i
\(628\) 0 0
\(629\) −12.2023 10.2390i −0.486539 0.408255i
\(630\) 0 0
\(631\) −3.72874 21.1467i −0.148439 0.841838i −0.964541 0.263931i \(-0.914981\pi\)
0.816103 0.577907i \(-0.196130\pi\)
\(632\) 0 0
\(633\) −4.95084 1.80196i −0.196778 0.0716214i
\(634\) 0 0
\(635\) 9.76991 16.9220i 0.387707 0.671529i
\(636\) 0 0
\(637\) −9.68345 + 8.12538i −0.383672 + 0.321939i
\(638\) 0 0
\(639\) 8.92633 + 15.4609i 0.353120 + 0.611622i
\(640\) 0 0
\(641\) 2.21466 12.5600i 0.0874738 0.496089i −0.909322 0.416094i \(-0.863399\pi\)
0.996795 0.0799944i \(-0.0254902\pi\)
\(642\) 0 0
\(643\) 26.8828 9.78456i 1.06016 0.385865i 0.247669 0.968845i \(-0.420335\pi\)
0.812487 + 0.582979i \(0.198113\pi\)
\(644\) 0 0
\(645\) −7.65270 −0.301325
\(646\) 0 0
\(647\) −16.7128 −0.657046 −0.328523 0.944496i \(-0.606551\pi\)
−0.328523 + 0.944496i \(0.606551\pi\)
\(648\) 0 0
\(649\) −4.38191 + 1.59489i −0.172005 + 0.0626047i
\(650\) 0 0
\(651\) −0.666374 + 3.77920i −0.0261173 + 0.148118i
\(652\) 0 0
\(653\) −13.5000 23.3827i −0.528296 0.915035i −0.999456 0.0329874i \(-0.989498\pi\)
0.471160 0.882048i \(-0.343835\pi\)
\(654\) 0 0
\(655\) −20.4440 + 17.1546i −0.798814 + 0.670285i
\(656\) 0 0
\(657\) 7.88713 13.6609i 0.307706 0.532963i
\(658\) 0 0
\(659\) −41.2533 15.0150i −1.60700 0.584900i −0.626157 0.779697i \(-0.715373\pi\)
−0.980844 + 0.194797i \(0.937595\pi\)
\(660\) 0 0
\(661\) −1.86777 10.5927i −0.0726480 0.412007i −0.999345 0.0361971i \(-0.988476\pi\)
0.926697 0.375810i \(-0.122636\pi\)
\(662\) 0 0
\(663\) 5.26991 + 4.42198i 0.204667 + 0.171736i
\(664\) 0 0
\(665\) −1.43376 8.88257i −0.0555989 0.344451i
\(666\) 0 0
\(667\) −18.0496 15.1454i −0.698884 0.586434i
\(668\) 0 0
\(669\) 1.75402 + 9.94756i 0.0678144 + 0.384595i
\(670\) 0 0
\(671\) 5.02956 + 1.83061i 0.194164 + 0.0706700i
\(672\) 0 0
\(673\) −2.32888 + 4.03374i −0.0897717 + 0.155489i −0.907415 0.420237i \(-0.861947\pi\)
0.817643 + 0.575726i \(0.195280\pi\)
\(674\) 0 0
\(675\) 8.87598 7.44783i 0.341637 0.286667i
\(676\) 0 0
\(677\) −1.63429 2.83067i −0.0628107 0.108791i 0.832910 0.553408i \(-0.186673\pi\)
−0.895721 + 0.444617i \(0.853340\pi\)
\(678\) 0 0
\(679\) −1.96064 + 11.1193i −0.0752423 + 0.426721i
\(680\) 0 0
\(681\) 6.05525 2.20393i 0.232038 0.0844549i
\(682\) 0 0
\(683\) −6.21894 −0.237961 −0.118981 0.992897i \(-0.537963\pi\)
−0.118981 + 0.992897i \(0.537963\pi\)
\(684\) 0 0
\(685\) −13.7483 −0.525297
\(686\) 0 0
\(687\) −12.3397 + 4.49129i −0.470790 + 0.171353i
\(688\) 0 0
\(689\) 1.38872 7.87581i 0.0529060 0.300045i
\(690\) 0 0
\(691\) 11.1088 + 19.2409i 0.422597 + 0.731959i 0.996193 0.0871792i \(-0.0277853\pi\)
−0.573596 + 0.819139i \(0.694452\pi\)
\(692\) 0 0
\(693\) 3.57919 3.00330i 0.135962 0.114086i
\(694\) 0 0
\(695\) 1.11856 1.93739i 0.0424292 0.0734896i
\(696\) 0 0
\(697\) 36.4013 + 13.2490i 1.37880 + 0.501841i
\(698\) 0 0
\(699\) 0.400634 + 2.27211i 0.0151534 + 0.0859391i
\(700\) 0 0
\(701\) −21.2750 17.8518i −0.803544 0.674254i 0.145513 0.989356i \(-0.453517\pi\)
−0.949058 + 0.315102i \(0.897961\pi\)
\(702\) 0 0
\(703\) 3.36319 17.5791i 0.126845 0.663008i
\(704\) 0 0
\(705\) 0.386659 + 0.324446i 0.0145624 + 0.0122193i
\(706\) 0 0
\(707\) −0.577382 3.27449i −0.0217147 0.123150i
\(708\) 0 0
\(709\) 5.73947 + 2.08900i 0.215551 + 0.0784540i 0.447538 0.894265i \(-0.352301\pi\)
−0.231988 + 0.972719i \(0.574523\pi\)
\(710\) 0 0
\(711\) −12.6233 + 21.8642i −0.473411 + 0.819972i
\(712\) 0 0
\(713\) 14.8871 12.4918i 0.557527 0.467821i
\(714\) 0 0
\(715\) 2.16843 + 3.75584i 0.0810948 + 0.140460i
\(716\) 0 0
\(717\) −1.35710 + 7.69648i −0.0506817 + 0.287430i
\(718\) 0 0
\(719\) 36.3885 13.2443i 1.35706 0.493930i 0.441917 0.897056i \(-0.354299\pi\)
0.915144 + 0.403126i \(0.132076\pi\)
\(720\) 0 0
\(721\) −19.1138 −0.711835
\(722\) 0 0
\(723\) 8.42097 0.313179
\(724\) 0 0
\(725\) −13.9243 + 5.06802i −0.517134 + 0.188221i
\(726\) 0 0
\(727\) 1.92366 10.9096i 0.0713445 0.404615i −0.928132 0.372252i \(-0.878586\pi\)
0.999476 0.0323628i \(-0.0103032\pi\)
\(728\) 0 0
\(729\) 3.31996 + 5.75033i 0.122961 + 0.212975i
\(730\) 0 0
\(731\) 25.8614 21.7003i 0.956520 0.802615i
\(732\) 0 0
\(733\) 7.90373 13.6897i 0.291931 0.505639i −0.682335 0.731039i \(-0.739036\pi\)
0.974266 + 0.225400i \(0.0723689\pi\)
\(734\) 0 0
\(735\) −3.84477 1.39938i −0.141816 0.0516170i
\(736\) 0 0
\(737\) 0.799726 + 4.53547i 0.0294583 + 0.167066i
\(738\) 0 0
\(739\) −1.18685 0.995887i −0.0436591 0.0366343i 0.620697 0.784050i \(-0.286850\pi\)
−0.664356 + 0.747416i \(0.731294\pi\)
\(740\) 0 0
\(741\) −1.45249 + 7.59202i −0.0533584 + 0.278900i
\(742\) 0 0
\(743\) −29.2349 24.5310i −1.07252 0.899955i −0.0772453 0.997012i \(-0.524612\pi\)
−0.995279 + 0.0970576i \(0.969057\pi\)
\(744\) 0 0
\(745\) −2.62196 14.8699i −0.0960611 0.544790i
\(746\) 0 0
\(747\) −29.7946 10.8444i −1.09013 0.396774i
\(748\) 0 0
\(749\) 5.11721 8.86327i 0.186979 0.323857i
\(750\) 0 0
\(751\) 19.4179 16.2935i 0.708568 0.594559i −0.215629 0.976475i \(-0.569180\pi\)
0.924197 + 0.381916i \(0.124736\pi\)
\(752\) 0 0
\(753\) 4.68732 + 8.11867i 0.170815 + 0.295861i
\(754\) 0 0
\(755\) −2.58331 + 14.6507i −0.0940163 + 0.533193i
\(756\) 0 0
\(757\) −39.8153 + 14.4916i −1.44711 + 0.526705i −0.941783 0.336222i \(-0.890851\pi\)
−0.505328 + 0.862927i \(0.668628\pi\)
\(758\) 0 0
\(759\) 3.91622 0.142150
\(760\) 0 0
\(761\) −2.85710 −0.103570 −0.0517848 0.998658i \(-0.516491\pi\)
−0.0517848 + 0.998658i \(0.516491\pi\)
\(762\) 0 0
\(763\) 13.6099 4.95361i 0.492713 0.179333i
\(764\) 0 0
\(765\) 2.33615 13.2490i 0.0844638 0.479018i
\(766\) 0 0
\(767\) −5.34658 9.26055i −0.193054 0.334379i
\(768\) 0 0
\(769\) 14.6472 12.2905i 0.528193 0.443207i −0.339284 0.940684i \(-0.610185\pi\)
0.867477 + 0.497477i \(0.165740\pi\)
\(770\) 0 0
\(771\) −1.62449 + 2.81369i −0.0585044 + 0.101333i
\(772\) 0 0
\(773\) −2.36319 0.860130i −0.0849980 0.0309367i 0.299171 0.954199i \(-0.403290\pi\)
−0.384169 + 0.923263i \(0.625512\pi\)
\(774\) 0 0
\(775\) −2.12226 12.0360i −0.0762340 0.432344i
\(776\) 0 0
\(777\) 3.14543 + 2.63933i 0.112842 + 0.0946854i
\(778\) 0 0
\(779\) 6.93582 + 42.9694i 0.248502 + 1.53954i
\(780\) 0 0
\(781\) 6.29498 + 5.28211i 0.225252 + 0.189009i
\(782\) 0 0
\(783\) 2.93939 + 16.6701i 0.105045 + 0.595741i
\(784\) 0 0
\(785\) 13.9179 + 5.06569i 0.496750 + 0.180802i
\(786\) 0 0
\(787\) 1.36303 2.36083i 0.0485866 0.0841545i −0.840709 0.541487i \(-0.817862\pi\)
0.889296 + 0.457332i \(0.151195\pi\)
\(788\) 0 0
\(789\) 12.0214 10.0872i 0.427974 0.359112i
\(790\) 0 0
\(791\) 1.00387 + 1.73875i 0.0356935 + 0.0618230i
\(792\) 0 0
\(793\) −2.13129 + 12.0872i −0.0756844 + 0.429228i
\(794\) 0 0
\(795\) 2.43242 0.885328i 0.0862690 0.0313993i
\(796\) 0 0
\(797\) 22.0327 0.780439 0.390219 0.920722i \(-0.372399\pi\)
0.390219 + 0.920722i \(0.372399\pi\)
\(798\) 0 0
\(799\) −2.22668 −0.0787743
\(800\) 0 0
\(801\) −5.86794 + 2.13575i −0.207333 + 0.0754632i
\(802\) 0 0
\(803\) 1.26083 7.15052i 0.0444937 0.252336i
\(804\) 0 0
\(805\) −5.22668 9.05288i −0.184216 0.319072i
\(806\) 0 0
\(807\) −6.55556 + 5.50077i −0.230767 + 0.193636i
\(808\) 0 0
\(809\) −27.3603 + 47.3893i −0.961935 + 1.66612i −0.244302 + 0.969699i \(0.578559\pi\)
−0.717633 + 0.696422i \(0.754774\pi\)
\(810\) 0 0
\(811\) −2.17112 0.790224i −0.0762384 0.0277485i 0.303619 0.952793i \(-0.401805\pi\)
−0.379858 + 0.925045i \(0.624027\pi\)
\(812\) 0 0
\(813\) 3.01145 + 17.0788i 0.105616 + 0.598979i
\(814\) 0 0
\(815\) −6.53596 5.48432i −0.228945 0.192107i
\(816\) 0 0
\(817\) 35.4531 + 13.4892i 1.24035 + 0.471927i
\(818\) 0 0
\(819\) 8.20755 + 6.88695i 0.286795 + 0.240650i
\(820\) 0 0
\(821\) 0.192944 + 1.09424i 0.00673379 + 0.0381892i 0.987990 0.154521i \(-0.0493834\pi\)
−0.981256 + 0.192710i \(0.938272\pi\)
\(822\) 0 0
\(823\) 19.4024 + 7.06191i 0.676327 + 0.246163i 0.657270 0.753656i \(-0.271711\pi\)
0.0190572 + 0.999818i \(0.493934\pi\)
\(824\) 0 0
\(825\) 1.23143 2.13290i 0.0428729 0.0742580i
\(826\) 0 0
\(827\) −27.8116 + 23.3367i −0.967103 + 0.811495i −0.982094 0.188392i \(-0.939672\pi\)
0.0149913 + 0.999888i \(0.495228\pi\)
\(828\) 0 0
\(829\) 3.57486 + 6.19183i 0.124160 + 0.215051i 0.921404 0.388606i \(-0.127043\pi\)
−0.797244 + 0.603657i \(0.793710\pi\)
\(830\) 0 0
\(831\) −1.87134 + 10.6129i −0.0649161 + 0.368157i
\(832\) 0 0
\(833\) 16.9611 6.17334i 0.587667 0.213893i
\(834\) 0 0
\(835\) −18.5635 −0.642418
\(836\) 0 0
\(837\) −13.9614 −0.482577
\(838\) 0 0
\(839\) −32.5197 + 11.8362i −1.12270 + 0.408631i −0.835638 0.549280i \(-0.814902\pi\)
−0.287065 + 0.957911i \(0.592680\pi\)
\(840\) 0 0
\(841\) −1.27672 + 7.24065i −0.0440249 + 0.249678i
\(842\) 0 0
\(843\) 6.32800 + 10.9604i 0.217948 + 0.377497i
\(844\) 0 0
\(845\) 5.79885 4.86581i 0.199486 0.167389i
\(846\) 0 0
\(847\) −7.35117 + 12.7326i −0.252589 + 0.437497i
\(848\) 0 0
\(849\) −6.93717 2.52492i −0.238083 0.0866551i
\(850\) 0 0
\(851\) −3.61081 20.4779i −0.123777 0.701975i
\(852\) 0 0
\(853\) 25.4716 + 21.3732i 0.872132 + 0.731805i 0.964546 0.263915i \(-0.0850139\pi\)
−0.0924142 + 0.995721i \(0.529458\pi\)
\(854\) 0 0
\(855\) 14.2781 4.96356i 0.488301 0.169750i
\(856\) 0 0
\(857\) −2.97700 2.49800i −0.101692 0.0853299i 0.590524 0.807020i \(-0.298921\pi\)
−0.692216 + 0.721690i \(0.743366\pi\)
\(858\) 0 0
\(859\) −0.287866 1.63257i −0.00982187 0.0557026i 0.979503 0.201430i \(-0.0645589\pi\)
−0.989325 + 0.145727i \(0.953448\pi\)
\(860\) 0 0
\(861\) −9.38326 3.41523i −0.319780 0.116391i
\(862\) 0 0
\(863\) −26.3594 + 45.6558i −0.897284 + 1.55414i −0.0663308 + 0.997798i \(0.521129\pi\)
−0.830953 + 0.556343i \(0.812204\pi\)
\(864\) 0 0
\(865\) −26.0574 + 21.8647i −0.885977 + 0.743423i
\(866\) 0 0
\(867\) 0.636507 + 1.10246i 0.0216169 + 0.0374416i
\(868\) 0 0
\(869\) −2.01795 + 11.4444i −0.0684543 + 0.388224i
\(870\) 0 0
\(871\) −9.92396 + 3.61203i −0.336261 + 0.122389i
\(872\) 0 0
\(873\) −18.9691 −0.642008
\(874\) 0 0
\(875\) −16.8949 −0.571151
\(876\) 0 0
\(877\) 19.9119 7.24735i 0.672378 0.244726i 0.0168069 0.999859i \(-0.494650\pi\)
0.655572 + 0.755133i \(0.272428\pi\)
\(878\) 0 0
\(879\) 0.441914 2.50622i 0.0149054 0.0845327i
\(880\) 0 0
\(881\) −16.0505 27.8003i −0.540755 0.936616i −0.998861 0.0477179i \(-0.984805\pi\)
0.458106 0.888898i \(-0.348528\pi\)
\(882\) 0 0
\(883\) 36.2315 30.4018i 1.21929 1.02310i 0.220425 0.975404i \(-0.429256\pi\)
0.998862 0.0476989i \(-0.0151888\pi\)
\(884\) 0 0
\(885\) 1.73055 2.99740i 0.0581719 0.100757i
\(886\) 0 0
\(887\) 9.92602 + 3.61278i 0.333283 + 0.121305i 0.503241 0.864146i \(-0.332141\pi\)
−0.169958 + 0.985451i \(0.554363\pi\)
\(888\) 0 0
\(889\) −3.85844 21.8823i −0.129408 0.733909i
\(890\) 0 0
\(891\) 4.85323 + 4.07234i 0.162589 + 0.136429i
\(892\) 0 0
\(893\) −1.21941 2.18463i −0.0408059 0.0731059i
\(894\) 0 0
\(895\) 6.01779 + 5.04952i 0.201153 + 0.168787i
\(896\) 0 0
\(897\) 1.55943 + 8.84397i 0.0520679 + 0.295291i
\(898\) 0 0
\(899\) 16.7780 + 6.10668i 0.559576 + 0.203669i
\(900\) 0 0
\(901\) −5.70961 + 9.88933i −0.190215 + 0.329461i
\(902\) 0 0
\(903\) −6.66637 + 5.59375i −0.221843 + 0.186148i
\(904\) 0 0
\(905\) 9.13610 + 15.8242i 0.303694 + 0.526014i
\(906\) 0 0
\(907\) −7.45306 + 42.2684i −0.247475 + 1.40350i 0.567200 + 0.823580i \(0.308027\pi\)
−0.814674 + 0.579919i \(0.803084\pi\)
\(908\) 0 0
\(909\) 5.24928 1.91058i 0.174107 0.0633699i
\(910\) 0 0
\(911\) 55.1411 1.82691 0.913454 0.406942i \(-0.133405\pi\)
0.913454 + 0.406942i \(0.133405\pi\)
\(912\) 0 0
\(913\) −14.5945 −0.483008
\(914\) 0 0
\(915\) −3.73308 + 1.35873i −0.123412 + 0.0449182i
\(916\) 0 0
\(917\) −5.26991 + 29.8872i −0.174028 + 0.986961i
\(918\) 0 0
\(919\) −12.2788 21.2676i −0.405041 0.701552i 0.589285 0.807925i \(-0.299410\pi\)
−0.994326 + 0.106373i \(0.966076\pi\)
\(920\) 0 0
\(921\) −11.5876 + 9.72319i −0.381826 + 0.320390i
\(922\) 0 0
\(923\) −9.42190 + 16.3192i −0.310126 + 0.537154i
\(924\) 0 0
\(925\) −12.2883 4.47259i −0.404038 0.147058i
\(926\) 0 0
\(927\) −5.57620 31.6242i −0.183146 1.03867i
\(928\) 0 0
\(929\) −17.0654 14.3195i −0.559896 0.469809i 0.318379 0.947963i \(-0.396861\pi\)
−0.878276 + 0.478155i \(0.841306\pi\)
\(930\) 0 0
\(931\) 15.3452 + 13.2601i 0.502920 + 0.434581i
\(932\) 0 0
\(933\) 1.73055 + 1.45211i 0.0566557 + 0.0475398i
\(934\) 0 0
\(935\) −1.07532 6.09845i −0.0351668 0.199441i
\(936\) 0 0
\(937\) 8.97565 + 3.26687i 0.293222 + 0.106724i 0.484443 0.874823i \(-0.339022\pi\)
−0.191221 + 0.981547i \(0.561245\pi\)
\(938\) 0 0
\(939\) 7.47013 12.9386i 0.243779 0.422237i
\(940\) 0 0
\(941\) −42.6883 + 35.8197i −1.39160 + 1.16769i −0.426909 + 0.904295i \(0.640398\pi\)
−0.964688 + 0.263394i \(0.915158\pi\)
\(942\) 0 0
\(943\) 25.2841 + 43.7933i 0.823362 + 1.42610i
\(944\) 0 0
\(945\) −1.30406 + 7.39571i −0.0424212 + 0.240582i
\(946\) 0 0
\(947\) −25.4119 + 9.24919i −0.825777 + 0.300558i −0.720125 0.693845i \(-0.755915\pi\)
−0.105653 + 0.994403i \(0.533693\pi\)
\(948\) 0 0
\(949\) 16.6500 0.540482
\(950\) 0 0
\(951\) 17.0490 0.552852
\(952\) 0 0
\(953\) −21.7361 + 7.91128i −0.704100 + 0.256272i −0.669161 0.743118i \(-0.733346\pi\)
−0.0349398 + 0.999389i \(0.511124\pi\)
\(954\) 0 0
\(955\) −2.40601 + 13.6452i −0.0778567 + 0.441547i
\(956\) 0 0
\(957\) 1.79901 + 3.11598i 0.0581538 + 0.100725i
\(958\) 0 0
\(959\) −11.9764 + 10.0494i −0.386737 + 0.324511i
\(960\) 0 0
\(961\) 8.13681 14.0934i 0.262478 0.454625i
\(962\) 0 0
\(963\) 16.1573 + 5.88079i 0.520663 + 0.189506i
\(964\) 0 0
\(965\) −3.22874 18.3111i −0.103937 0.589455i
\(966\) 0 0
\(967\) −29.9026 25.0913i −0.961603 0.806881i 0.0196101 0.999808i \(-0.493758\pi\)
−0.981213 + 0.192927i \(0.938202\pi\)
\(968\) 0 0
\(969\) 5.65657 9.47740i 0.181715 0.304458i
\(970\) 0 0
\(971\) 31.5631 + 26.4845i 1.01291 + 0.849930i 0.988720 0.149778i \(-0.0478559\pi\)
0.0241869 + 0.999707i \(0.492300\pi\)
\(972\) 0 0
\(973\) −0.441752 2.50530i −0.0141619 0.0803162i
\(974\) 0 0
\(975\) 5.30706 + 1.93161i 0.169962 + 0.0618610i
\(976\) 0 0
\(977\) −11.2469 + 19.4802i −0.359821 + 0.623227i −0.987931 0.154897i \(-0.950495\pi\)
0.628110 + 0.778125i \(0.283829\pi\)
\(978\) 0 0
\(979\) −2.20187 + 1.84759i −0.0703720 + 0.0590491i
\(980\) 0 0
\(981\) 12.1664 + 21.0728i 0.388442 + 0.672802i
\(982\) 0 0
\(983\) 7.73536 43.8694i 0.246720 1.39922i −0.569746 0.821821i \(-0.692958\pi\)
0.816465 0.577395i \(-0.195931\pi\)
\(984\) 0 0
\(985\) −10.0535 + 3.65917i −0.320331 + 0.116591i
\(986\) 0 0
\(987\) 0.573978 0.0182699
\(988\) 0 0
\(989\) 44.0702 1.40135
\(990\) 0 0
\(991\) −42.5959 + 15.5036i −1.35310 + 0.492489i −0.913915 0.405907i \(-0.866956\pi\)
−0.439187 + 0.898395i \(0.644734\pi\)
\(992\) 0 0
\(993\) −2.15853 + 12.2416i −0.0684988 + 0.388476i
\(994\) 0 0
\(995\) −18.2121 31.5443i −0.577363 1.00002i
\(996\) 0 0
\(997\) −8.03667 + 6.74357i −0.254524 + 0.213571i −0.761117 0.648614i \(-0.775349\pi\)
0.506593 + 0.862185i \(0.330905\pi\)
\(998\) 0 0
\(999\) −7.46926 + 12.9371i −0.236317 + 0.409313i
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 304.2.u.b.225.1 6
4.3 odd 2 19.2.e.a.16.1 yes 6
12.11 even 2 171.2.u.c.73.1 6
19.5 even 9 5776.2.a.br.1.2 3
19.6 even 9 inner 304.2.u.b.177.1 6
19.14 odd 18 5776.2.a.bi.1.2 3
20.3 even 4 475.2.u.a.149.1 12
20.7 even 4 475.2.u.a.149.2 12
20.19 odd 2 475.2.l.a.301.1 6
28.3 even 6 931.2.x.b.814.1 6
28.11 odd 6 931.2.x.a.814.1 6
28.19 even 6 931.2.v.a.263.1 6
28.23 odd 6 931.2.v.b.263.1 6
28.27 even 2 931.2.w.a.491.1 6
76.3 even 18 361.2.c.h.68.1 6
76.7 odd 6 361.2.e.g.62.1 6
76.11 odd 6 361.2.e.f.245.1 6
76.15 even 18 361.2.e.b.28.1 6
76.23 odd 18 361.2.e.f.28.1 6
76.27 even 6 361.2.e.b.245.1 6
76.31 even 6 361.2.e.a.62.1 6
76.35 odd 18 361.2.c.i.68.3 6
76.43 odd 18 361.2.a.g.1.1 3
76.47 odd 18 361.2.e.g.99.1 6
76.51 even 18 361.2.e.h.234.1 6
76.55 odd 18 361.2.c.i.292.3 6
76.59 even 18 361.2.c.h.292.1 6
76.63 odd 18 19.2.e.a.6.1 6
76.67 even 18 361.2.e.a.99.1 6
76.71 even 18 361.2.a.h.1.3 3
76.75 even 2 361.2.e.h.54.1 6
228.71 odd 18 3249.2.a.s.1.1 3
228.119 even 18 3249.2.a.z.1.3 3
228.215 even 18 171.2.u.c.82.1 6
380.63 even 36 475.2.u.a.424.2 12
380.119 odd 18 9025.2.a.bd.1.3 3
380.139 odd 18 475.2.l.a.101.1 6
380.299 even 18 9025.2.a.x.1.1 3
380.367 even 36 475.2.u.a.424.1 12
532.139 even 18 931.2.w.a.785.1 6
532.215 even 18 931.2.x.b.557.1 6
532.291 odd 18 931.2.v.b.177.1 6
532.367 even 18 931.2.v.a.177.1 6
532.443 odd 18 931.2.x.a.557.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.e.a.6.1 6 76.63 odd 18
19.2.e.a.16.1 yes 6 4.3 odd 2
171.2.u.c.73.1 6 12.11 even 2
171.2.u.c.82.1 6 228.215 even 18
304.2.u.b.177.1 6 19.6 even 9 inner
304.2.u.b.225.1 6 1.1 even 1 trivial
361.2.a.g.1.1 3 76.43 odd 18
361.2.a.h.1.3 3 76.71 even 18
361.2.c.h.68.1 6 76.3 even 18
361.2.c.h.292.1 6 76.59 even 18
361.2.c.i.68.3 6 76.35 odd 18
361.2.c.i.292.3 6 76.55 odd 18
361.2.e.a.62.1 6 76.31 even 6
361.2.e.a.99.1 6 76.67 even 18
361.2.e.b.28.1 6 76.15 even 18
361.2.e.b.245.1 6 76.27 even 6
361.2.e.f.28.1 6 76.23 odd 18
361.2.e.f.245.1 6 76.11 odd 6
361.2.e.g.62.1 6 76.7 odd 6
361.2.e.g.99.1 6 76.47 odd 18
361.2.e.h.54.1 6 76.75 even 2
361.2.e.h.234.1 6 76.51 even 18
475.2.l.a.101.1 6 380.139 odd 18
475.2.l.a.301.1 6 20.19 odd 2
475.2.u.a.149.1 12 20.3 even 4
475.2.u.a.149.2 12 20.7 even 4
475.2.u.a.424.1 12 380.367 even 36
475.2.u.a.424.2 12 380.63 even 36
931.2.v.a.177.1 6 532.367 even 18
931.2.v.a.263.1 6 28.19 even 6
931.2.v.b.177.1 6 532.291 odd 18
931.2.v.b.263.1 6 28.23 odd 6
931.2.w.a.491.1 6 28.27 even 2
931.2.w.a.785.1 6 532.139 even 18
931.2.x.a.557.1 6 532.443 odd 18
931.2.x.a.814.1 6 28.11 odd 6
931.2.x.b.557.1 6 532.215 even 18
931.2.x.b.814.1 6 28.3 even 6
3249.2.a.s.1.1 3 228.71 odd 18
3249.2.a.z.1.3 3 228.119 even 18
5776.2.a.bi.1.2 3 19.14 odd 18
5776.2.a.br.1.2 3 19.5 even 9
9025.2.a.x.1.1 3 380.299 even 18
9025.2.a.bd.1.3 3 380.119 odd 18