Properties

Label 378.2.g.a.109.1
Level $378$
Weight $2$
Character 378.109
Analytic conductor $3.018$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(109,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.2.g.a.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} -4.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +3.00000 q^{20} +(-3.00000 - 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(2.00000 + 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} -3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(7.50000 + 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.50000 - 2.59808i) q^{40} -6.00000 q^{41} +8.00000 q^{43} +(-3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(1.00000 - 6.92820i) q^{49} +4.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-2.00000 + 1.73205i) q^{56} +(1.50000 + 2.59808i) q^{58} +(1.50000 - 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 - 7.79423i) q^{70} +6.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-8.50000 - 14.7224i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{83} +18.0000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{89} +(8.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} -10.0000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 3 q^{5} - 4 q^{7} + 2 q^{8} - 3 q^{10} - 8 q^{13} + 5 q^{14} - q^{16} - 6 q^{17} + 4 q^{19} + 6 q^{20} - 6 q^{23} - 4 q^{25} + 4 q^{26} - q^{28} - 6 q^{29} - 8 q^{31} - q^{32}+ \cdots - 13 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 0 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 0 0
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 7.50000 + 2.59808i 1.26773 + 0.439155i
\(36\) 0 0
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 0 0
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 + 10.3923i 0.744208 + 1.28901i
\(66\) 0 0
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) −1.50000 7.79423i −0.179284 0.931589i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 3.50000 6.06218i 0.409644 0.709524i −0.585206 0.810885i \(-0.698986\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) −8.50000 14.7224i −0.956325 1.65640i −0.731307 0.682048i \(-0.761089\pi\)
−0.225018 0.974355i \(-0.572244\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 18.0000 1.95237
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) 8.00000 6.92820i 0.838628 0.726273i
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 6.00000 10.3923i 0.615587 1.06623i
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −9.00000 + 15.5885i −0.839254 + 1.45363i
\(116\) 1.50000 2.59808i 0.139272 0.241225i
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) −3.00000 15.5885i −0.275010 1.42899i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 0 0
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 6.00000 10.3923i 0.526235 0.911465i
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) −10.0000 3.46410i −0.867110 0.300376i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) −6.00000 + 5.19615i −0.507093 + 0.439155i
\(141\) 0 0
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) 0 0
\(144\) 0 0
\(145\) 4.50000 + 7.79423i 0.373705 + 0.647275i
\(146\) −7.00000 −0.579324
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i \(0.162991\pi\)
−0.0115483 + 0.999933i \(0.503676\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) 0 0
\(154\) 0 0
\(155\) 24.0000 1.92773
\(156\) 0 0
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −8.50000 + 14.7224i −0.676224 + 1.17125i
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) 15.0000 + 5.19615i 1.18217 + 0.409514i
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) −9.00000 15.5885i −0.690268 1.19558i
\(171\) 0 0
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0 0
\(175\) −2.00000 10.3923i −0.151186 0.785584i
\(176\) 0 0
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 7.50000 12.9904i 0.560576 0.970947i −0.436870 0.899525i \(-0.643913\pi\)
0.997446 0.0714220i \(-0.0227537\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −10.0000 3.46410i −0.741249 0.256776i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) 0 0
\(187\) 0 0
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0 0
\(193\) −13.0000 + 22.5167i −0.935760 + 1.62078i −0.162488 + 0.986710i \(0.551952\pi\)
−0.773272 + 0.634074i \(0.781381\pi\)
\(194\) 5.00000 + 8.66025i 0.358979 + 0.621770i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 0 0
\(199\) −5.50000 + 9.52628i −0.389885 + 0.675300i −0.992434 0.122782i \(-0.960818\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) −15.0000 −1.05540
\(203\) 6.00000 5.19615i 0.421117 0.364698i
\(204\) 0 0
\(205\) 9.00000 + 15.5885i 0.628587 + 1.08875i
\(206\) −4.00000 + 6.92820i −0.278693 + 0.482711i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 0 0
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) −12.0000 20.7846i −0.818393 1.41750i
\(216\) 0 0
\(217\) −4.00000 20.7846i −0.271538 1.41095i
\(218\) −4.00000 −0.270914
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 20.7846i 0.807207 1.39812i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 18.0000 1.18688
\(231\) 0 0
\(232\) −3.00000 −0.196960
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 0 0
\(235\) −9.00000 + 15.5885i −0.587095 + 1.01688i
\(236\) 1.50000 + 2.59808i 0.0976417 + 0.169120i
\(237\) 0 0
\(238\) −12.0000 + 10.3923i −0.777844 + 0.673633i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 5.50000 9.52628i 0.353553 0.612372i
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) −19.5000 + 7.79423i −1.24581 + 0.497955i
\(246\) 0 0
\(247\) −8.00000 13.8564i −0.509028 0.881662i
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.50000 4.33013i −0.156864 0.271696i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) 20.0000 + 6.92820i 1.24274 + 0.430498i
\(260\) −12.0000 −0.744208
\(261\) 0 0
\(262\) 6.00000 10.3923i 0.370681 0.642039i
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) 27.0000 1.65860
\(266\) 2.00000 + 10.3923i 0.122628 + 0.637193i
\(267\) 0 0
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i \(0.387814\pi\)
−0.985389 + 0.170321i \(0.945520\pi\)
\(270\) 0 0
\(271\) 12.5000 + 21.6506i 0.759321 + 1.31518i 0.943197 + 0.332233i \(0.107802\pi\)
−0.183876 + 0.982949i \(0.558865\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 0 0
\(277\) 14.0000 24.2487i 0.841178 1.45696i −0.0477206 0.998861i \(-0.515196\pi\)
0.888899 0.458103i \(-0.151471\pi\)
\(278\) −1.00000 1.73205i −0.0599760 0.103882i
\(279\) 0 0
\(280\) 7.50000 + 2.59808i 0.448211 + 0.155265i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 10.3923i 0.708338 0.613438i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 0 0
\(292\) 3.50000 + 6.06218i 0.204822 + 0.354762i
\(293\) −3.00000 −0.175262 −0.0876309 0.996153i \(-0.527930\pi\)
−0.0876309 + 0.996153i \(0.527930\pi\)
\(294\) 0 0
\(295\) −9.00000 −0.524000
\(296\) −4.00000 6.92820i −0.232495 0.402694i
\(297\) 0 0
\(298\) 10.5000 18.1865i 0.608249 1.05352i
\(299\) 12.0000 + 20.7846i 0.693978 + 1.20201i
\(300\) 0 0
\(301\) −16.0000 + 13.8564i −0.922225 + 0.798670i
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 15.0000 25.9808i 0.858898 1.48765i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −12.0000 20.7846i −0.681554 1.18049i
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0 0
\(313\) −2.50000 4.33013i −0.141308 0.244753i 0.786681 0.617359i \(-0.211798\pi\)
−0.927990 + 0.372606i \(0.878464\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 17.0000 0.956325
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) −3.00000 15.5885i −0.167183 0.868711i
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 8.00000 13.8564i 0.443760 0.768615i
\(326\) −1.00000 + 1.73205i −0.0553849 + 0.0959294i
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 0 0
\(331\) −1.00000 1.73205i −0.0549650 0.0952021i 0.837234 0.546845i \(-0.184171\pi\)
−0.892199 + 0.451643i \(0.850838\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) 0 0
\(334\) −3.00000 5.19615i −0.164153 0.284321i
\(335\) −30.0000 −1.63908
\(336\) 0 0
\(337\) −7.00000 −0.381314 −0.190657 0.981657i \(-0.561062\pi\)
−0.190657 + 0.981657i \(0.561062\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) 0 0
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) 0 0
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 4.50000 7.79423i 0.241921 0.419020i
\(347\) −16.5000 + 28.5788i −0.885766 + 1.53419i −0.0409337 + 0.999162i \(0.513033\pi\)
−0.844833 + 0.535031i \(0.820300\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −8.00000 + 6.92820i −0.427618 + 0.370328i
\(351\) 0 0
\(352\) 0 0
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 0 0
\(355\) −9.00000 15.5885i −0.477670 0.827349i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) −18.0000 31.1769i −0.950004 1.64545i −0.745409 0.666608i \(-0.767746\pi\)
−0.204595 0.978847i \(-0.565588\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) 2.00000 + 10.3923i 0.104828 + 0.544705i
\(365\) −21.0000 −1.09919
\(366\) 0 0
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 0 0
\(370\) 24.0000 1.24770
\(371\) −4.50000 23.3827i −0.233628 1.21397i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 6.00000 + 10.3923i 0.307794 + 0.533114i
\(381\) 0 0
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) 0 0
\(388\) 5.00000 8.66025i 0.253837 0.439658i
\(389\) 4.50000 7.79423i 0.228159 0.395183i −0.729103 0.684403i \(-0.760063\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) 0 0
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) −25.5000 + 44.1673i −1.28304 + 2.22230i
\(396\) 0 0
\(397\) −16.0000 27.7128i −0.803017 1.39087i −0.917622 0.397455i \(-0.869893\pi\)
0.114605 0.993411i \(-0.463440\pi\)
\(398\) 11.0000 0.551380
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) 16.0000 27.7128i 0.797017 1.38047i
\(404\) 7.50000 + 12.9904i 0.373139 + 0.646296i
\(405\) 0 0
\(406\) −7.50000 2.59808i −0.372219 0.128940i
\(407\) 0 0
\(408\) 0 0
\(409\) 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) 9.00000 15.5885i 0.444478 0.769859i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 1.50000 + 7.79423i 0.0738102 + 0.383529i
\(414\) 0 0
\(415\) 18.0000 + 31.1769i 0.883585 + 1.53041i
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 0 0
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 2.00000 + 3.46410i 0.0973585 + 0.168630i
\(423\) 0 0
\(424\) −4.50000 + 7.79423i −0.218539 + 0.378521i
\(425\) −12.0000 20.7846i −0.582086 1.00820i
\(426\) 0 0
\(427\) −25.0000 8.66025i −1.20983 0.419099i
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) −12.0000 + 20.7846i −0.578691 + 1.00232i
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0 0
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) −16.0000 + 13.8564i −0.768025 + 0.665129i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 12.0000 20.7846i 0.574038 0.994263i
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) 19.5000 + 33.7750i 0.926473 + 1.60470i 0.789175 + 0.614168i \(0.210508\pi\)
0.137298 + 0.990530i \(0.456158\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 0.500000 + 0.866025i 0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 0 0
\(454\) 3.00000 0.140797
\(455\) −30.0000 10.3923i −1.40642 0.487199i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) 0 0
\(460\) −9.00000 15.5885i −0.419627 0.726816i
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 0 0
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 0 0
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) 16.5000 + 28.5788i 0.763529 + 1.32247i 0.941021 + 0.338349i \(0.109868\pi\)
−0.177492 + 0.984122i \(0.556798\pi\)
\(468\) 0 0
\(469\) 5.00000 + 25.9808i 0.230879 + 1.19968i
\(470\) 18.0000 0.830278
\(471\) 0 0
\(472\) 1.50000 2.59808i 0.0690431 0.119586i
\(473\) 0 0
\(474\) 0 0
\(475\) −16.0000 −0.734130
\(476\) 15.0000 + 5.19615i 0.687524 + 0.238165i
\(477\) 0 0
\(478\) 0 0
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) −1.00000 −0.0455488
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) 0 0
\(487\) 6.50000 11.2583i 0.294543 0.510164i −0.680335 0.732901i \(-0.738166\pi\)
0.974879 + 0.222737i \(0.0714992\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 0 0
\(490\) 16.5000 + 12.9904i 0.745394 + 0.586846i
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −8.00000 + 13.8564i −0.359937 + 0.623429i
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) −12.0000 + 10.3923i −0.538274 + 0.466159i
\(498\) 0 0
\(499\) −1.00000 1.73205i −0.0447661 0.0775372i 0.842774 0.538267i \(-0.180921\pi\)
−0.887540 + 0.460730i \(0.847588\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) −45.0000 −2.00247
\(506\) 0 0
\(507\) 0 0
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) 3.50000 + 18.1865i 0.154831 + 0.804525i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0 0
\(515\) −12.0000 + 20.7846i −0.528783 + 0.915879i
\(516\) 0 0
\(517\) 0 0
\(518\) −4.00000 20.7846i −0.175750 0.913223i
\(519\) 0 0
\(520\) 6.00000 + 10.3923i 0.263117 + 0.455733i
\(521\) 15.0000 25.9808i 0.657162 1.13824i −0.324185 0.945994i \(-0.605090\pi\)
0.981347 0.192244i \(-0.0615766\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −18.0000 −0.784837
\(527\) −24.0000 41.5692i −1.04546 1.81078i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −13.5000 23.3827i −0.586403 1.01568i
\(531\) 0 0
\(532\) 8.00000 6.92820i 0.346844 0.300376i
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 5.00000 8.66025i 0.215967 0.374066i
\(537\) 0 0
\(538\) 21.0000 0.905374
\(539\) 0 0
\(540\) 0 0
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) 12.5000 21.6506i 0.536921 0.929974i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) −12.0000 −0.514024
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) 0 0
\(550\) 0 0
\(551\) −6.00000 10.3923i −0.255609 0.442727i
\(552\) 0 0
\(553\) 42.5000 + 14.7224i 1.80728 + 0.626061i
\(554\) −28.0000 −1.18961
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 3.00000 5.19615i 0.127114 0.220168i −0.795443 0.606028i \(-0.792762\pi\)
0.922557 + 0.385860i \(0.126095\pi\)
\(558\) 0 0
\(559\) −32.0000 −1.35346
\(560\) −1.50000 7.79423i −0.0633866 0.329366i
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −7.50000 + 12.9904i −0.316087 + 0.547479i −0.979668 0.200625i \(-0.935703\pi\)
0.663581 + 0.748105i \(0.269036\pi\)
\(564\) 0 0
\(565\) 9.00000 + 15.5885i 0.378633 + 0.655811i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −15.0000 5.19615i −0.626088 0.216883i
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) −11.5000 + 19.9186i −0.478751 + 0.829222i −0.999703 0.0243645i \(-0.992244\pi\)
0.520952 + 0.853586i \(0.325577\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) 0 0
\(580\) −9.00000 −0.373705
\(581\) 24.0000 20.7846i 0.995688 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) 3.50000 6.06218i 0.144831 0.250855i
\(585\) 0 0
\(586\) 1.50000 + 2.59808i 0.0619644 + 0.107326i
\(587\) −15.0000 −0.619116 −0.309558 0.950881i \(-0.600181\pi\)
−0.309558 + 0.950881i \(0.600181\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 4.50000 + 7.79423i 0.185262 + 0.320883i
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 0 0
\(595\) −36.0000 + 31.1769i −1.47586 + 1.27813i
\(596\) −21.0000 −0.860194
\(597\) 0 0
\(598\) 12.0000 20.7846i 0.490716 0.849946i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −25.0000 −1.01977 −0.509886 0.860242i \(-0.670312\pi\)
−0.509886 + 0.860242i \(0.670312\pi\)
\(602\) 20.0000 + 6.92820i 0.815139 + 0.282372i
\(603\) 0 0
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 16.5000 28.5788i 0.670820 1.16190i
\(606\) 0 0
\(607\) −5.50000 9.52628i −0.223238 0.386660i 0.732551 0.680712i \(-0.238329\pi\)
−0.955789 + 0.294052i \(0.904996\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −30.0000 −1.21466
\(611\) 12.0000 + 20.7846i 0.485468 + 0.840855i
\(612\) 0 0
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) 8.00000 13.8564i 0.321547 0.556936i −0.659260 0.751915i \(-0.729130\pi\)
0.980807 + 0.194979i \(0.0624638\pi\)
\(620\) −12.0000 + 20.7846i −0.481932 + 0.834730i
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 15.0000 + 5.19615i 0.600962 + 0.208179i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −2.50000 + 4.33013i −0.0999201 + 0.173067i
\(627\) 0 0
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −8.50000 14.7224i −0.338112 0.585627i
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −7.50000 12.9904i −0.297628 0.515508i
\(636\) 0 0
\(637\) −4.00000 + 27.7128i −0.158486 + 1.09802i
\(638\) 0 0
\(639\) 0 0
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 0 0
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) −12.0000 + 10.3923i −0.472866 + 0.409514i
\(645\) 0 0
\(646\) 12.0000 + 20.7846i 0.472134 + 0.817760i
\(647\) −21.0000 + 36.3731i −0.825595 + 1.42997i 0.0758684 + 0.997118i \(0.475827\pi\)
−0.901464 + 0.432855i \(0.857506\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −16.0000 −0.627572
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) 0 0
\(655\) 18.0000 31.1769i 0.703318 1.21818i
\(656\) 3.00000 + 5.19615i 0.117130 + 0.202876i
\(657\) 0 0
\(658\) −3.00000 15.5885i −0.116952 0.607701i
\(659\) 21.0000 0.818044 0.409022 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) −1.00000 + 1.73205i −0.0388661 + 0.0673181i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 6.00000 + 31.1769i 0.232670 + 1.20899i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) −3.00000 + 5.19615i −0.116073 + 0.201045i
\(669\) 0 0
\(670\) 15.0000 + 25.9808i 0.579501 + 1.00372i
\(671\) 0 0
\(672\) 0 0
\(673\) −43.0000 −1.65753 −0.828764 0.559598i \(-0.810955\pi\)
−0.828764 + 0.559598i \(0.810955\pi\)
\(674\) 3.50000 + 6.06218i 0.134815 + 0.233506i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 10.5000 + 18.1865i 0.403548 + 0.698965i 0.994151 0.107997i \(-0.0344436\pi\)
−0.590603 + 0.806962i \(0.701110\pi\)
\(678\) 0 0
\(679\) 20.0000 17.3205i 0.767530 0.664700i
\(680\) 18.0000 0.690268
\(681\) 0 0
\(682\) 0 0
\(683\) 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i \(-0.778250\pi\)
0.939184 + 0.343413i \(0.111583\pi\)
\(684\) 0 0
\(685\) 36.0000 1.37549
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 18.0000 31.1769i 0.685745 1.18775i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −9.00000 −0.342129
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) −3.00000 5.19615i −0.113796 0.197101i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 5.00000 + 8.66025i 0.189253 + 0.327795i
\(699\) 0 0
\(700\) 10.0000 + 3.46410i 0.377964 + 0.130931i
\(701\) −39.0000 −1.47301 −0.736505 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) 0 0
\(703\) 16.0000 27.7128i 0.603451 1.04521i
\(704\) 0 0
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) 7.50000 + 38.9711i 0.282067 + 1.46566i
\(708\) 0 0
\(709\) −4.00000 6.92820i −0.150223 0.260194i 0.781086 0.624423i \(-0.214666\pi\)
−0.931309 + 0.364229i \(0.881333\pi\)
\(710\) −9.00000 + 15.5885i −0.337764 + 0.585024i
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 48.0000 1.79761
\(714\) 0 0
\(715\) 0 0
\(716\) 7.50000 + 12.9904i 0.280288 + 0.485473i
\(717\) 0 0
\(718\) −18.0000 + 31.1769i −0.671754 + 1.16351i
\(719\) 12.0000 + 20.7846i 0.447524 + 0.775135i 0.998224 0.0595683i \(-0.0189724\pi\)
−0.550700 + 0.834703i \(0.685639\pi\)
\(720\) 0 0
\(721\) 20.0000 + 6.92820i 0.744839 + 0.258020i
\(722\) −3.00000 −0.111648
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 6.00000 10.3923i 0.222834 0.385961i
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 8.00000 6.92820i 0.296500 0.256776i
\(729\) 0 0
\(730\) 10.5000 + 18.1865i 0.388622 + 0.673114i
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) 0 0
\(733\) −22.0000 38.1051i −0.812589 1.40744i −0.911047 0.412303i \(-0.864724\pi\)
0.0984580 0.995141i \(-0.468609\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 0 0
\(739\) −7.00000 + 12.1244i −0.257499 + 0.446002i −0.965571 0.260138i \(-0.916232\pi\)
0.708072 + 0.706140i \(0.249565\pi\)
\(740\) −12.0000 20.7846i −0.441129 0.764057i
\(741\) 0 0
\(742\) −18.0000 + 15.5885i −0.660801 + 0.572270i
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 31.5000 54.5596i 1.15407 1.99891i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 0 0
\(748\) 0 0
\(749\) −7.50000 2.59808i −0.274044 0.0949316i
\(750\) 0 0
\(751\) 21.5000 + 37.2391i 0.784546 + 1.35887i 0.929270 + 0.369402i \(0.120437\pi\)
−0.144724 + 0.989472i \(0.546229\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) 0 0
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) 24.0000 0.873449
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 5.00000 + 8.66025i 0.181608 + 0.314555i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) −24.0000 41.5692i −0.869999 1.50688i −0.861996 0.506915i \(-0.830786\pi\)
−0.00800331 0.999968i \(-0.502548\pi\)
\(762\) 0 0
\(763\) 2.00000 + 10.3923i 0.0724049 + 0.376227i
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) −3.00000 + 5.19615i −0.108394 + 0.187745i
\(767\) −6.00000 + 10.3923i −0.216647 + 0.375244i
\(768\) 0 0
\(769\) 26.0000 0.937584 0.468792 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −13.0000 22.5167i −0.467880 0.810392i
\(773\) 9.00000 15.5885i 0.323708 0.560678i −0.657542 0.753418i \(-0.728404\pi\)
0.981250 + 0.192740i \(0.0617373\pi\)
\(774\) 0 0
\(775\) −16.0000 27.7128i −0.574737 0.995474i
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) −9.00000 −0.322666
\(779\) −12.0000 20.7846i −0.429945 0.744686i
\(780\) 0 0
\(781\) 0 0
\(782\) −18.0000 31.1769i −0.643679 1.11488i
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 42.0000 1.49904
\(786\) 0 0
\(787\) 11.0000 19.0526i 0.392108 0.679150i −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) 7.50000 12.9904i 0.267176 0.462763i
\(789\) 0 0
\(790\) 51.0000 1.81450
\(791\) 12.0000 10.3923i 0.426671 0.369508i
\(792\) 0 0
\(793\) −20.0000 34.6410i −0.710221 1.23014i
\(794\) −16.0000 + 27.7128i −0.567819 + 0.983491i
\(795\) 0 0
\(796\) −5.50000 9.52628i −0.194942 0.337650i
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 36.0000 1.27359
\(800\) −2.00000 3.46410i −0.0707107 0.122474i
\(801\) 0 0
\(802\) 9.00000 15.5885i 0.317801 0.550448i
\(803\) 0 0
\(804\) 0 0
\(805\) −9.00000 46.7654i −0.317208 1.64826i
\(806\) −32.0000 −1.12715
\(807\) 0 0
\(808\) 7.50000 12.9904i 0.263849 0.457000i
\(809\) −12.0000 + 20.7846i −0.421898 + 0.730748i −0.996125 0.0879478i \(-0.971969\pi\)
0.574228 + 0.818696i \(0.305302\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 1.50000 + 7.79423i 0.0526397 + 0.273524i
\(813\) 0 0
\(814\) 0 0
\(815\) −3.00000 + 5.19615i −0.105085 + 0.182013i
\(816\) 0 0
\(817\) 16.0000 + 27.7128i 0.559769 + 0.969549i
\(818\) −25.0000 −0.874105
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) −10.5000 18.1865i −0.366453 0.634714i 0.622556 0.782576i \(-0.286094\pi\)
−0.989008 + 0.147861i \(0.952761\pi\)
\(822\) 0 0
\(823\) −11.5000 + 19.9186i −0.400865 + 0.694318i −0.993831 0.110910i \(-0.964624\pi\)
0.592966 + 0.805228i \(0.297957\pi\)
\(824\) −4.00000 6.92820i −0.139347 0.241355i
\(825\) 0 0
\(826\) 6.00000 5.19615i 0.208767 0.180797i
\(827\) 21.0000 0.730242 0.365121 0.930960i \(-0.381028\pi\)
0.365121 + 0.930960i \(0.381028\pi\)
\(828\) 0 0
\(829\) −16.0000 + 27.7128i −0.555703 + 0.962506i 0.442145 + 0.896943i \(0.354217\pi\)
−0.997848 + 0.0655624i \(0.979116\pi\)
\(830\) 18.0000 31.1769i 0.624789 1.08217i
\(831\) 0 0
\(832\) −4.00000 −0.138675
\(833\) 33.0000 + 25.9808i 1.14338 + 0.900180i
\(834\) 0 0
\(835\) −9.00000 15.5885i −0.311458 0.539461i
\(836\) 0 0
\(837\) 0 0
\(838\) −6.00000 10.3923i −0.207267 0.358996i
\(839\) −24.0000 −0.828572 −0.414286 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) −16.0000 27.7128i −0.551396 0.955047i
\(843\) 0 0
\(844\) 2.00000 3.46410i 0.0688428 0.119239i
\(845\) −4.50000 7.79423i −0.154805 0.268130i
\(846\) 0 0
\(847\) −27.5000 9.52628i −0.944911 0.327327i
\(848\) 9.00000 0.309061
\(849\) 0 0
\(850\) −12.0000 + 20.7846i −0.411597 + 0.712906i
\(851\) −24.0000 + 41.5692i −0.822709 + 1.42497i
\(852\) 0 0
\(853\) 44.0000 1.50653 0.753266 0.657716i \(-0.228477\pi\)
0.753266 + 0.657716i \(0.228477\pi\)
\(854\) 5.00000 + 25.9808i 0.171096 + 0.889043i
\(855\) 0 0
\(856\) 1.50000 + 2.59808i 0.0512689 + 0.0888004i
\(857\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(858\) 0 0
\(859\) −7.00000 12.1244i −0.238837 0.413678i 0.721544 0.692369i \(-0.243433\pi\)
−0.960381 + 0.278691i \(0.910099\pi\)
\(860\) 24.0000 0.818393
\(861\) 0 0
\(862\) 12.0000 0.408722
\(863\) −21.0000 36.3731i −0.714848 1.23815i −0.963018 0.269437i \(-0.913162\pi\)
0.248170 0.968717i \(-0.420171\pi\)
\(864\) 0 0
\(865\) 13.5000 23.3827i 0.459014 0.795035i
\(866\) 3.50000 + 6.06218i 0.118935 + 0.206001i
\(867\) 0 0
\(868\) 20.0000 + 6.92820i 0.678844 + 0.235159i
\(869\) 0 0
\(870\) 0 0
\(871\) −20.0000 + 34.6410i −0.677674 + 1.17377i
\(872\) 2.00000 3.46410i 0.0677285 0.117309i
\(873\) 0 0
\(874\) −24.0000 −0.811812
\(875\) 6.00000 5.19615i 0.202837 0.175662i
\(876\) 0 0
\(877\) −7.00000 12.1244i −0.236373 0.409410i 0.723298 0.690536i \(-0.242625\pi\)
−0.959671 + 0.281126i \(0.909292\pi\)
\(878\) −4.00000 + 6.92820i −0.134993 + 0.233816i
\(879\) 0 0
\(880\) 0 0
\(881\) 6.00000 0.202145 0.101073 0.994879i \(-0.467773\pi\)
0.101073 + 0.994879i \(0.467773\pi\)
\(882\) 0 0
\(883\) 32.0000 1.07689 0.538443 0.842662i \(-0.319013\pi\)
0.538443 + 0.842662i \(0.319013\pi\)
\(884\) 12.0000 + 20.7846i 0.403604 + 0.699062i
\(885\) 0 0
\(886\) 19.5000 33.7750i 0.655115 1.13469i
\(887\) 21.0000 + 36.3731i 0.705111 + 1.22129i 0.966651 + 0.256096i \(0.0824362\pi\)
−0.261540 + 0.965193i \(0.584230\pi\)
\(888\) 0 0
\(889\) −10.0000 + 8.66025i −0.335389 + 0.290456i
\(890\) 18.0000 0.603361
\(891\) 0 0
\(892\) 0.500000 0.866025i 0.0167412 0.0289967i
\(893\) 12.0000 20.7846i 0.401565 0.695530i
\(894\) 0 0
\(895\) −45.0000 −1.50418
\(896\) 2.50000 + 0.866025i 0.0835191 + 0.0289319i
\(897\) 0 0
\(898\) −3.00000 5.19615i −0.100111 0.173398i
\(899\) 12.0000 20.7846i 0.400222 0.693206i
\(900\) 0 0
\(901\) −27.0000 46.7654i −0.899500 1.55798i
\(902\) 0 0
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) 15.0000 + 25.9808i 0.498617 + 0.863630i
\(906\) 0 0
\(907\) −4.00000 + 6.92820i −0.132818 + 0.230047i −0.924762 0.380547i \(-0.875736\pi\)
0.791944 + 0.610594i \(0.209069\pi\)
\(908\) −1.50000 2.59808i −0.0497792 0.0862202i
\(909\) 0 0
\(910\) 6.00000 + 31.1769i 0.198898 + 1.03350i
\(911\) −54.0000 −1.78910 −0.894550 0.446968i \(-0.852504\pi\)
−0.894550 + 0.446968i \(0.852504\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.500000 0.866025i 0.0165385 0.0286456i
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) −30.0000 10.3923i −0.990687 0.343184i
\(918\) 0 0
\(919\) 18.5000 + 32.0429i 0.610259 + 1.05700i 0.991197 + 0.132398i \(0.0422678\pi\)
−0.380938 + 0.924601i \(0.624399\pi\)
\(920\) −9.00000 + 15.5885i −0.296721 + 0.513936i
\(921\) 0 0
\(922\) 16.5000 + 28.5788i 0.543399 + 0.941194i
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) 32.0000 1.05215
\(926\) 9.50000 + 16.4545i 0.312189 + 0.540728i
\(927\) 0 0
\(928\) 1.50000 2.59808i 0.0492399 0.0852860i
\(929\) −3.00000 5.19615i −0.0984268 0.170480i 0.812607 0.582812i \(-0.198048\pi\)
−0.911034 + 0.412332i \(0.864714\pi\)
\(930\) 0 0
\(931\) 26.0000 10.3923i 0.852116 0.340594i
\(932\) 18.0000 0.589610
\(933\) 0 0
\(934\) 16.5000 28.5788i 0.539896 0.935128i
\(935\) 0 0
\(936\) 0 0
\(937\) −1.00000 −0.0326686 −0.0163343 0.999867i \(-0.505200\pi\)
−0.0163343 + 0.999867i \(0.505200\pi\)
\(938\) 20.0000 17.3205i 0.653023 0.565535i
\(939\) 0 0
\(940\) −9.00000 15.5885i −0.293548 0.508439i
\(941\) −9.00000 + 15.5885i −0.293392 + 0.508169i −0.974609 0.223912i \(-0.928117\pi\)
0.681218 + 0.732081i \(0.261451\pi\)
\(942\) 0 0
\(943\) 18.0000 + 31.1769i 0.586161 + 1.01526i
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 0 0
\(947\) −22.5000 38.9711i −0.731152 1.26639i −0.956391 0.292089i \(-0.905650\pi\)
0.225240 0.974303i \(-0.427684\pi\)
\(948\) 0 0
\(949\) −14.0000 + 24.2487i −0.454459 + 0.787146i
\(950\) 8.00000 + 13.8564i 0.259554 + 0.449561i
\(951\) 0 0
\(952\) −3.00000 15.5885i −0.0972306 0.505225i
\(953\) −48.0000 −1.55487 −0.777436 0.628962i \(-0.783480\pi\)
−0.777436 + 0.628962i \(0.783480\pi\)
\(954\) 0 0
\(955\) 27.0000 46.7654i 0.873699 1.51329i
\(956\) 0 0
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) −6.00000 31.1769i −0.193750 1.00676i
\(960\) 0 0
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) 16.0000 27.7128i 0.515861 0.893497i
\(963\) 0 0
\(964\) 0.500000 + 0.866025i 0.0161039 + 0.0278928i
\(965\) 78.0000 2.51091
\(966\) 0 0
\(967\) −37.0000 −1.18984 −0.594920 0.803785i \(-0.702816\pi\)
−0.594920 + 0.803785i \(0.702816\pi\)
\(968\) 5.50000 + 9.52628i 0.176777 + 0.306186i
\(969\) 0 0
\(970\) 15.0000 25.9808i 0.481621 0.834192i
\(971\) 1.50000 + 2.59808i 0.0481373 + 0.0833762i 0.889090 0.457732i \(-0.151338\pi\)
−0.840953 + 0.541108i \(0.818005\pi\)
\(972\) 0 0
\(973\) −4.00000 + 3.46410i −0.128234 + 0.111054i
\(974\) −13.0000 −0.416547
\(975\) 0 0
\(976\) 5.00000 8.66025i 0.160046 0.277208i
\(977\) −6.00000 + 10.3923i −0.191957 + 0.332479i −0.945899 0.324462i \(-0.894817\pi\)
0.753942 + 0.656941i \(0.228150\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 3.00000 20.7846i 0.0958315 0.663940i
\(981\) 0 0
\(982\) −13.5000 23.3827i −0.430802 0.746171i
\(983\) 12.0000 20.7846i 0.382741 0.662926i −0.608712 0.793391i \(-0.708314\pi\)
0.991453 + 0.130465i \(0.0416470\pi\)
\(984\) 0 0
\(985\) 22.5000 + 38.9711i 0.716910 + 1.24172i
\(986\) −18.0000 −0.573237
\(987\) 0 0
\(988\) 16.0000 0.509028
\(989\) −24.0000 41.5692i −0.763156 1.32182i
\(990\) 0 0
\(991\) −11.5000 + 19.9186i −0.365310 + 0.632735i −0.988826 0.149076i \(-0.952370\pi\)
0.623516 + 0.781810i \(0.285704\pi\)
\(992\) −4.00000 6.92820i −0.127000 0.219971i
\(993\) 0 0
\(994\) 15.0000 + 5.19615i 0.475771 + 0.164812i
\(995\) 33.0000 1.04617
\(996\) 0 0
\(997\) −16.0000 + 27.7128i −0.506725 + 0.877674i 0.493245 + 0.869891i \(0.335811\pi\)
−0.999970 + 0.00778294i \(0.997523\pi\)
\(998\) −1.00000 + 1.73205i −0.0316544 + 0.0548271i
\(999\) 0 0
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 378.2.g.a.109.1 2
3.2 odd 2 378.2.g.f.109.1 yes 2
7.2 even 3 inner 378.2.g.a.163.1 yes 2
7.3 odd 6 2646.2.a.r.1.1 1
7.4 even 3 2646.2.a.bc.1.1 1
9.2 odd 6 1134.2.h.k.109.1 2
9.4 even 3 1134.2.e.j.865.1 2
9.5 odd 6 1134.2.e.f.865.1 2
9.7 even 3 1134.2.h.g.109.1 2
21.2 odd 6 378.2.g.f.163.1 yes 2
21.11 odd 6 2646.2.a.b.1.1 1
21.17 even 6 2646.2.a.m.1.1 1
63.2 odd 6 1134.2.e.f.919.1 2
63.16 even 3 1134.2.e.j.919.1 2
63.23 odd 6 1134.2.h.k.541.1 2
63.58 even 3 1134.2.h.g.541.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.g.a.109.1 2 1.1 even 1 trivial
378.2.g.a.163.1 yes 2 7.2 even 3 inner
378.2.g.f.109.1 yes 2 3.2 odd 2
378.2.g.f.163.1 yes 2 21.2 odd 6
1134.2.e.f.865.1 2 9.5 odd 6
1134.2.e.f.919.1 2 63.2 odd 6
1134.2.e.j.865.1 2 9.4 even 3
1134.2.e.j.919.1 2 63.16 even 3
1134.2.h.g.109.1 2 9.7 even 3
1134.2.h.g.541.1 2 63.58 even 3
1134.2.h.k.109.1 2 9.2 odd 6
1134.2.h.k.541.1 2 63.23 odd 6
2646.2.a.b.1.1 1 21.11 odd 6
2646.2.a.m.1.1 1 21.17 even 6
2646.2.a.r.1.1 1 7.3 odd 6
2646.2.a.bc.1.1 1 7.4 even 3