Properties

Label 126.2.g.b.37.1
Level $126$
Weight $2$
Character 126.37
Analytic conductor $1.006$
Analytic rank $0$
Dimension $2$
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] = [126,2,Mod(37,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.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: \(1.00611506547\)
Analytic rank: \(0\)
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: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.37
Dual form 126.2.g.b.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} -4.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{19} -3.00000 q^{20} -3.00000 q^{22} +(-2.00000 - 3.46410i) q^{25} +(2.00000 - 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.00000 - 5.19615i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.50000 - 2.59808i) q^{40} -10.0000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +4.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(4.50000 - 7.79423i) q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(5.00000 + 8.66025i) q^{67} +(1.50000 + 7.79423i) q^{70} +6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +(0.500000 - 0.866025i) q^{79} +(1.50000 + 2.59808i) q^{80} +9.00000 q^{83} +(5.00000 - 8.66025i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 - 3.46410i) q^{91} +(-3.00000 - 5.19615i) q^{94} +(-6.00000 - 10.3923i) q^{95} -1.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} + 3 q^{10} + 3 q^{11} - 8 q^{13} - 4 q^{14} - q^{16} + 4 q^{19} - 6 q^{20} - 6 q^{22} - 4 q^{25} + 4 q^{26} - q^{28} - 18 q^{29} + q^{31} - q^{32} + 12 q^{35} - 8 q^{37} + 4 q^{38} + 3 q^{40} - 20 q^{43} + 3 q^{44} - 6 q^{47} + 11 q^{49} + 8 q^{50} + 4 q^{52} - 3 q^{53} + 18 q^{55} + 5 q^{56} + 9 q^{58} + 3 q^{59} + 10 q^{61} - 2 q^{62} + 2 q^{64} - 12 q^{65} + 10 q^{67} + 3 q^{70} + 12 q^{71} - 2 q^{73} - 8 q^{74} - 8 q^{76} + 3 q^{77} + q^{79} + 3 q^{80} + 18 q^{83} + 10 q^{86} + 3 q^{88} + 6 q^{89} - 20 q^{91} - 6 q^{94} - 12 q^{95} - 2 q^{97} - 13 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 6.00000 5.19615i 1.01419 0.878310i
\(36\) 0 0
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 0 0
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) −1.00000 −0.127000
\(63\) 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 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 0 0
\(69\) 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
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) 0 0
\(82\) 0 0
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 0 0
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) −6.00000 10.3923i −0.615587 1.06623i
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −4.50000 + 7.79423i −0.429058 + 0.743151i
\(111\) 0 0
\(112\) −2.00000 + 1.73205i −0.188982 + 0.163663i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 5.00000 + 8.66025i 0.452679 + 0.784063i
\(123\) 0 0
\(124\) 0.500000 0.866025i 0.0449013 0.0777714i
\(125\) 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
\(131\) −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 0 0
\(133\) 8.00000 6.92820i 0.693688 0.600751i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) −7.50000 2.59808i −0.633866 0.219578i
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −6.00000 10.3923i −0.501745 0.869048i
\(144\) 0 0
\(145\) −13.5000 + 23.3827i −1.12111 + 1.94183i
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i \(-0.153711\pi\)
−0.844963 + 0.534824i \(0.820378\pi\)
\(152\) 2.00000 3.46410i 0.162221 0.280976i
\(153\) 0 0
\(154\) −7.50000 2.59808i −0.604367 0.209359i
\(155\) 3.00000 0.240966
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) 0.500000 + 0.866025i 0.0397779 + 0.0688973i
\(159\) 0 0
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 0 0
\(175\) −2.00000 10.3923i −0.151186 0.785584i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 8.00000 6.92820i 0.592999 0.513553i
\(183\) 0 0
\(184\) 0 0
\(185\) 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
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) 0.500000 0.866025i 0.0358979 0.0621770i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) 0 0
\(202\) 18.0000 1.26648
\(203\) −22.5000 7.79423i −1.57919 0.547048i
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 0 0
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) −15.0000 + 25.9808i −1.02299 + 1.77187i
\(216\) 0 0
\(217\) 0.500000 + 2.59808i 0.0339422 + 0.176369i
\(218\) 14.0000 0.948200
\(219\) 0 0
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) 0 0
\(222\) 0 0
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −13.5000 23.3827i −0.896026 1.55196i −0.832529 0.553981i \(-0.813108\pi\)
−0.0634974 0.997982i \(-0.520225\pi\)
\(228\) 0 0
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −12.0000 + 20.7846i −0.786146 + 1.36165i 0.142166 + 0.989843i \(0.454593\pi\)
−0.928312 + 0.371802i \(0.878740\pi\)
\(234\) 0 0
\(235\) 9.00000 + 15.5885i 0.587095 + 1.01688i
\(236\) 1.50000 2.59808i 0.0976417 0.169120i
\(237\) 0 0
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 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
\(248\) 0.500000 + 0.866025i 0.0317500 + 0.0549927i
\(249\) 0 0
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) −27.0000 −1.70422 −0.852112 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 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
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) 0 0
\(259\) −16.0000 + 13.8564i −0.994192 + 0.860995i
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −4.50000 7.79423i −0.278011 0.481529i
\(263\) −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 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 0.985389 + 0.170321i \(0.0544803\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 0 0
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −1.00000 + 1.73205i −0.0599760 + 0.103882i
\(279\) 0 0
\(280\) 6.00000 5.19615i 0.358569 0.310530i
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −13.5000 23.3827i −0.792747 1.37308i
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) −33.0000 −1.92788 −0.963940 0.266119i \(-0.914259\pi\)
−0.963940 + 0.266119i \(0.914259\pi\)
\(294\) 0 0
\(295\) 9.00000 0.524000
\(296\) −4.00000 + 6.92820i −0.232495 + 0.402694i
\(297\) 0 0
\(298\) 9.00000 + 15.5885i 0.521356 + 0.903015i
\(299\) 0 0
\(300\) 0 0
\(301\) −25.0000 8.66025i −1.44098 0.499169i
\(302\) −1.00000 −0.0575435
\(303\) 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 \(0.426686\pi\)
\(308\) 6.00000 5.19615i 0.341882 0.296078i
\(309\) 0 0
\(310\) −1.50000 + 2.59808i −0.0851943 + 0.147561i
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i \(-0.493462\pi\)
0.855574 0.517681i \(-0.173205\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 0 0
\(319\) −13.5000 23.3827i −0.755855 1.30918i
\(320\) 1.50000 2.59808i 0.0838525 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) 8.00000 + 13.8564i 0.443079 + 0.767435i
\(327\) 0 0
\(328\) 0 0
\(329\) −12.0000 + 10.3923i −0.661581 + 0.572946i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) −4.50000 7.79423i −0.246970 0.427764i
\(333\) 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
\(340\) 0 0
\(341\) −1.50000 + 2.59808i −0.0812296 + 0.140694i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 9.00000 + 15.5885i 0.483843 + 0.838041i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 10.0000 + 3.46410i 0.534522 + 0.185164i
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) 9.00000 15.5885i 0.477670 0.827349i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 15.0000 25.9808i 0.791670 1.37121i −0.133263 0.991081i \(-0.542545\pi\)
0.924932 0.380131i \(-0.124121\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) −4.00000 + 6.92820i −0.210235 + 0.364138i
\(363\) 0 0
\(364\) 2.00000 + 10.3923i 0.104828 + 0.544705i
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) −1.50000 7.79423i −0.0778761 0.404656i
\(372\) 0 0
\(373\) −4.00000 + 6.92820i −0.207112 + 0.358729i −0.950804 0.309794i \(-0.899740\pi\)
0.743691 + 0.668523i \(0.233073\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) −6.00000 + 10.3923i −0.307794 + 0.533114i
\(381\) 0 0
\(382\) 0 0
\(383\) 9.00000 15.5885i 0.459879 0.796533i −0.539076 0.842257i \(-0.681226\pi\)
0.998954 + 0.0457244i \(0.0145596\pi\)
\(384\) 0 0
\(385\) 22.5000 + 7.79423i 1.14671 + 0.397231i
\(386\) −19.0000 −0.967075
\(387\) 0 0
\(388\) 0.500000 + 0.866025i 0.0253837 + 0.0439658i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) 0 0
\(397\) 2.00000 3.46410i 0.100377 0.173858i −0.811463 0.584404i \(-0.801328\pi\)
0.911840 + 0.410546i \(0.134662\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 12.0000 20.7846i 0.599251 1.03793i −0.393680 0.919247i \(-0.628798\pi\)
0.992932 0.118686i \(-0.0378683\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) −9.00000 + 15.5885i −0.447767 + 0.775555i
\(405\) 0 0
\(406\) 18.0000 15.5885i 0.893325 0.773642i
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 1.50000 + 7.79423i 0.0738102 + 0.383529i
\(414\) 0 0
\(415\) 13.5000 23.3827i 0.662689 1.14781i
\(416\) 2.00000 + 3.46410i 0.0980581 + 0.169842i
\(417\) 0 0
\(418\) −6.00000 + 10.3923i −0.293470 + 0.508304i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) −7.00000 + 12.1244i −0.340755 + 0.590204i
\(423\) 0 0
\(424\) −1.50000 2.59808i −0.0728464 0.126174i
\(425\) 0 0
\(426\) 0 0
\(427\) 20.0000 17.3205i 0.967868 0.838198i
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) −15.0000 25.9808i −0.723364 1.25290i
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −2.50000 0.866025i −0.120004 0.0415705i
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 0 0
\(438\) 0 0
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 0 0
\(443\) −16.5000 + 28.5788i −0.783939 + 1.35782i 0.145692 + 0.989330i \(0.453459\pi\)
−0.929631 + 0.368492i \(0.879874\pi\)
\(444\) 0 0
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) 9.50000 16.4545i 0.449838 0.779142i
\(447\) 0 0
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 27.0000 1.26717
\(455\) −24.0000 + 20.7846i −1.12514 + 0.974398i
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 2.00000 + 3.46410i 0.0934539 + 0.161867i
\(459\) 0 0
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) 18.0000 31.1769i 0.832941 1.44270i −0.0627555 0.998029i \(-0.519989\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(468\) 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
\(473\) −15.0000 25.9808i −0.689701 1.19460i
\(474\) 0 0
\(475\) −16.0000 −0.734130
\(476\) 0 0
\(477\) 0 0
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0 0
\(481\) 16.0000 27.7128i 0.729537 1.26360i
\(482\) −1.00000 −0.0455488
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −1.50000 + 2.59808i −0.0681115 + 0.117973i
\(486\) 0 0
\(487\) −20.5000 35.5070i −0.928944 1.60898i −0.785093 0.619378i \(-0.787385\pi\)
−0.143851 0.989599i \(-0.545949\pi\)
\(488\) 5.00000 8.66025i 0.226339 0.392031i
\(489\) 0 0
\(490\) −3.00000 + 20.7846i −0.135526 + 0.938953i
\(491\) 33.0000 1.48927 0.744635 0.667472i \(-0.232624\pi\)
0.744635 + 0.667472i \(0.232624\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 13.8564i −0.359937 0.623429i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 15.0000 + 5.19615i 0.672842 + 0.233079i
\(498\) 0 0
\(499\) −1.00000 + 1.73205i −0.0447661 + 0.0775372i −0.887540 0.460730i \(-0.847588\pi\)
0.842774 + 0.538267i \(0.180921\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 13.5000 23.3827i 0.602534 1.04362i
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) −54.0000 −2.40297
\(506\) 0 0
\(507\) 0 0
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) −1.50000 + 2.59808i −0.0664863 + 0.115158i −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) −1.00000 5.19615i −0.0442374 0.229864i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) 12.0000 + 20.7846i 0.528783 + 0.915879i
\(516\) 0 0
\(517\) −18.0000 −0.791639
\(518\) −4.00000 20.7846i −0.175750 0.913223i
\(519\) 0 0
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) 0 0
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 6.00000 0.261612
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) −10.0000 3.46410i −0.433555 0.150188i
\(533\) 0 0
\(534\) 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
\(539\) −3.00000 + 20.7846i −0.129219 + 0.895257i
\(540\) 0 0
\(541\) −13.0000 + 22.5167i −0.558914 + 0.968067i 0.438674 + 0.898646i \(0.355448\pi\)
−0.997587 + 0.0694205i \(0.977885\pi\)
\(542\) −5.50000 9.52628i −0.236245 0.409189i
\(543\) 0 0
\(544\) 0 0
\(545\) −42.0000 −1.79908
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 9.00000 15.5885i 0.384461 0.665906i
\(549\) 0 0
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) −18.0000 + 31.1769i −0.766826 + 1.32818i
\(552\) 0 0
\(553\) 2.00000 1.73205i 0.0850487 0.0736543i
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) 1.50000 + 2.59808i 0.0635570 + 0.110084i 0.896053 0.443947i \(-0.146422\pi\)
−0.832496 + 0.554031i \(0.813089\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 1.50000 + 7.79423i 0.0633866 + 0.329366i
\(561\) 0 0
\(562\) 3.00000 5.19615i 0.126547 0.219186i
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −18.0000 + 31.1769i −0.754599 + 1.30700i 0.190974 + 0.981595i \(0.438835\pi\)
−0.945573 + 0.325409i \(0.894498\pi\)
\(570\) 0 0
\(571\) 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i \(0.0852845\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(572\) −6.00000 + 10.3923i −0.250873 + 0.434524i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.5000 19.9186i −0.478751 0.829222i 0.520952 0.853586i \(-0.325577\pi\)
−0.999703 + 0.0243645i \(0.992244\pi\)
\(578\) 8.50000 + 14.7224i 0.353553 + 0.612372i
\(579\) 0 0
\(580\) 27.0000 1.12111
\(581\) 22.5000 + 7.79423i 0.933457 + 0.323359i
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) 16.5000 28.5788i 0.681609 1.18058i
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) −4.50000 + 7.79423i −0.185262 + 0.320883i
\(591\) 0 0
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i \(-0.669314\pi\)
0.999965 + 0.00831589i \(0.00264706\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 0 0
\(599\) −9.00000 15.5885i −0.367730 0.636927i 0.621480 0.783430i \(-0.286532\pi\)
−0.989210 + 0.146503i \(0.953198\pi\)
\(600\) 0 0
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) 20.0000 17.3205i 0.815139 0.705931i
\(603\) 0 0
\(604\) 0.500000 0.866025i 0.0203447 0.0352381i
\(605\) −3.00000 5.19615i −0.121967 0.211254i
\(606\) 0 0
\(607\) 3.50000 6.06218i 0.142061 0.246056i −0.786212 0.617957i \(-0.787961\pi\)
0.928272 + 0.371901i \(0.121294\pi\)
\(608\) −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 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 0 0
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 17.0000 + 29.4449i 0.683288 + 1.18349i 0.973972 + 0.226670i \(0.0727838\pi\)
−0.290684 + 0.956819i \(0.593883\pi\)
\(620\) −1.50000 2.59808i −0.0602414 0.104341i
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 12.0000 10.3923i 0.480770 0.416359i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 15.5000 + 26.8468i 0.619505 + 1.07301i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 0 0
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) 0.500000 0.866025i 0.0198889 0.0344486i
\(633\) 0 0
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) 7.50000 12.9904i 0.297628 0.515508i
\(636\) 0 0
\(637\) −22.0000 17.3205i −0.871672 0.686264i
\(638\) 27.0000 1.06894
\(639\) 0 0
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 0 0
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 0 0
\(649\) −4.50000 + 7.79423i −0.176640 + 0.305950i
\(650\) −16.0000 −0.627572
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) 1.50000 2.59808i 0.0586995 0.101671i −0.835182 0.549973i \(-0.814638\pi\)
0.893882 + 0.448303i \(0.147971\pi\)
\(654\) 0 0
\(655\) 13.5000 + 23.3827i 0.527489 + 0.913637i
\(656\) 0 0
\(657\) 0 0
\(658\) −3.00000 15.5885i −0.116952 0.607701i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −10.0000 17.3205i −0.388661 0.673181i
\(663\) 0 0
\(664\) 9.00000 0.349268
\(665\) −6.00000 31.1769i −0.232670 1.20899i
\(666\) 0 0
\(667\) 0 0
\(668\) 3.00000 + 5.19615i 0.116073 + 0.201045i
\(669\) 0 0
\(670\) −15.0000 + 25.9808i −0.579501 + 1.00372i
\(671\) 30.0000 1.15814
\(672\) 0 0
\(673\) 29.0000 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(674\) 3.50000 6.06218i 0.134815 0.233506i
\(675\) 0 0
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) −16.5000 + 28.5788i −0.634147 + 1.09837i 0.352549 + 0.935793i \(0.385315\pi\)
−0.986695 + 0.162581i \(0.948018\pi\)
\(678\) 0 0
\(679\) −2.50000 0.866025i −0.0959412 0.0332350i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.50000 2.59808i −0.0574380 0.0994855i
\(683\) 16.5000 + 28.5788i 0.631355 + 1.09354i 0.987275 + 0.159022i \(0.0508342\pi\)
−0.355920 + 0.934516i \(0.615832\pi\)
\(684\) 0 0
\(685\) 54.0000 2.06323
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 0 0
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 3.00000 5.19615i 0.113796 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) 0 0
\(700\) −8.00000 + 6.92820i −0.302372 + 0.261861i
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) 0 0
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) −9.00000 46.7654i −0.338480 1.75879i
\(708\) 0 0
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) 9.00000 + 15.5885i 0.337764 + 0.585024i
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) 15.0000 + 25.9808i 0.559795 + 0.969593i
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 0 0
\(721\) −16.0000 + 13.8564i −0.595871 + 0.516040i
\(722\) −3.00000 −0.111648
\(723\) 0 0
\(724\) −4.00000 6.92820i −0.148659 0.257485i
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 0 0
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) −10.0000 3.46410i −0.370625 0.128388i
\(729\) 0 0
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) 0 0
\(733\) 5.00000 8.66025i 0.184679 0.319874i −0.758789 0.651336i \(-0.774209\pi\)
0.943468 + 0.331463i \(0.107542\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 0 0
\(737\) −15.0000 + 25.9808i −0.552532 + 0.957014i
\(738\) 0 0
\(739\) −25.0000 43.3013i −0.919640 1.59286i −0.799962 0.600050i \(-0.795147\pi\)
−0.119677 0.992813i \(-0.538186\pi\)
\(740\) 12.0000 20.7846i 0.441129 0.764057i
\(741\) 0 0
\(742\) 7.50000 + 2.59808i 0.275334 + 0.0953784i
\(743\) −42.0000 −1.54083 −0.770415 0.637542i \(-0.779951\pi\)
−0.770415 + 0.637542i \(0.779951\pi\)
\(744\) 0 0
\(745\) −27.0000 46.7654i −0.989203 1.71335i
\(746\) −4.00000 6.92820i −0.146450 0.253660i
\(747\) 0 0
\(748\) 0 0
\(749\) −6.00000 + 5.19615i −0.219235 + 0.189863i
\(750\) 0 0
\(751\) 3.50000 6.06218i 0.127717 0.221212i −0.795075 0.606511i \(-0.792568\pi\)
0.922792 + 0.385299i \(0.125902\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 0 0
\(754\) −18.0000 + 31.1769i −0.655521 + 1.13540i
\(755\) 3.00000 0.109181
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −4.00000 + 6.92820i −0.145287 + 0.251644i
\(759\) 0 0
\(760\) −6.00000 10.3923i −0.217643 0.376969i
\(761\) 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) 0 0
\(763\) −7.00000 36.3731i −0.253417 1.31679i
\(764\) 0 0
\(765\) 0 0
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) −6.00000 10.3923i −0.216647 0.375244i
\(768\) 0 0
\(769\) −19.0000 −0.685158 −0.342579 0.939489i \(-0.611300\pi\)
−0.342579 + 0.939489i \(0.611300\pi\)
\(770\) −18.0000 + 15.5885i −0.648675 + 0.561769i
\(771\) 0 0
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) 3.00000 + 5.19615i 0.107903 + 0.186893i 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) 0 0
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) −1.00000 −0.0358979
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 0 0
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) −25.0000 43.3013i −0.891154 1.54352i −0.838494 0.544911i \(-0.816563\pi\)
−0.0526599 0.998613i \(-0.516770\pi\)
\(788\) 3.00000 + 5.19615i 0.106871 + 0.185105i
\(789\) 0 0
\(790\) 3.00000 0.106735
\(791\) 0 0
\(792\) 0 0
\(793\) −20.0000 + 34.6410i −0.710221 + 1.23014i
\(794\) 2.00000 + 3.46410i 0.0709773 + 0.122936i
\(795\) 0 0
\(796\) −10.0000 + 17.3205i −0.354441 + 0.613909i
\(797\) 33.0000 1.16892 0.584460 0.811423i \(-0.301306\pi\)
0.584460 + 0.811423i \(0.301306\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −2.00000 + 3.46410i −0.0707107 + 0.122474i
\(801\) 0 0
\(802\) 12.0000 + 20.7846i 0.423735 + 0.733930i
\(803\) 3.00000 5.19615i 0.105868 0.183368i
\(804\) 0 0
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 0 0
\(808\) −9.00000 15.5885i −0.316619 0.548400i
\(809\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) 4.50000 + 23.3827i 0.157919 + 0.820571i
\(813\) 0 0
\(814\) 12.0000 20.7846i 0.420600 0.728500i
\(815\) −24.0000 41.5692i −0.840683 1.45611i
\(816\) 0 0
\(817\) −20.0000 + 34.6410i −0.699711 + 1.21194i
\(818\) −25.0000 −0.874105
\(819\) 0 0
\(820\) 0 0
\(821\) −1.50000 + 2.59808i −0.0523504 + 0.0906735i −0.891013 0.453978i \(-0.850005\pi\)
0.838663 + 0.544651i \(0.183338\pi\)
\(822\) 0 0
\(823\) 20.0000 + 34.6410i 0.697156 + 1.20751i 0.969448 + 0.245295i \(0.0788849\pi\)
−0.272292 + 0.962215i \(0.587782\pi\)
\(824\) −4.00000 + 6.92820i −0.139347 + 0.241355i
\(825\) 0 0
\(826\) −7.50000 2.59808i −0.260958 0.0903986i
\(827\) −15.0000 −0.521601 −0.260801 0.965393i \(-0.583986\pi\)
−0.260801 + 0.965393i \(0.583986\pi\)
\(828\) 0 0
\(829\) 2.00000 + 3.46410i 0.0694629 + 0.120313i 0.898665 0.438636i \(-0.144538\pi\)
−0.829202 + 0.558949i \(0.811205\pi\)
\(830\) 13.5000 + 23.3827i 0.468592 + 0.811625i
\(831\) 0 0
\(832\) −4.00000 −0.138675
\(833\) 0 0
\(834\) 0 0
\(835\) −9.00000 + 15.5885i −0.311458 + 0.539461i
\(836\) −6.00000 10.3923i −0.207514 0.359425i
\(837\) 0 0
\(838\) 0 0
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 11.0000 19.0526i 0.379085 0.656595i
\(843\) 0 0
\(844\) −7.00000 12.1244i −0.240950 0.417338i
\(845\) 4.50000 7.79423i 0.154805 0.268130i
\(846\) 0 0
\(847\) 4.00000 3.46410i 0.137442 0.119028i
\(848\) 3.00000 0.103020
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −10.0000 −0.342393 −0.171197 0.985237i \(-0.554763\pi\)
−0.171197 + 0.985237i \(0.554763\pi\)
\(854\) 5.00000 + 25.9808i 0.171096 + 0.889043i
\(855\) 0 0
\(856\) −1.50000 + 2.59808i −0.0512689 + 0.0888004i
\(857\) −21.0000 36.3731i −0.717346 1.24248i −0.962048 0.272882i \(-0.912023\pi\)
0.244701 0.969599i \(-0.421310\pi\)
\(858\) 0 0
\(859\) −25.0000 + 43.3013i −0.852989 + 1.47742i 0.0255092 + 0.999675i \(0.491879\pi\)
−0.878498 + 0.477746i \(0.841454\pi\)
\(860\) 30.0000 1.02299
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) 3.00000 5.19615i 0.102121 0.176879i −0.810437 0.585826i \(-0.800770\pi\)
0.912558 + 0.408946i \(0.134104\pi\)
\(864\) 0 0
\(865\) −27.0000 46.7654i −0.918028 1.59007i
\(866\) 17.0000 29.4449i 0.577684 1.00058i
\(867\) 0 0
\(868\) 2.00000 1.73205i 0.0678844 0.0587896i
\(869\) 3.00000 0.101768
\(870\) 0 0
\(871\) −20.0000 34.6410i −0.677674 1.17377i
\(872\) −7.00000 12.1244i −0.237050 0.410582i
\(873\) 0 0
\(874\) 0 0
\(875\) 7.50000 + 2.59808i 0.253546 + 0.0878310i
\(876\) 0 0
\(877\) −16.0000 + 27.7128i −0.540282 + 0.935795i 0.458606 + 0.888640i \(0.348349\pi\)
−0.998888 + 0.0471555i \(0.984984\pi\)
\(878\) −17.5000 30.3109i −0.590596 1.02294i
\(879\) 0 0
\(880\) −4.50000 + 7.79423i −0.151695 + 0.262743i
\(881\) 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 \(0.319013\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −16.5000 28.5788i −0.554328 0.960125i
\(887\) −12.0000 + 20.7846i −0.402921 + 0.697879i −0.994077 0.108678i \(-0.965338\pi\)
0.591156 + 0.806557i \(0.298672\pi\)
\(888\) 0 0
\(889\) 12.5000 + 4.33013i 0.419237 + 0.145228i
\(890\) 18.0000 0.603361
\(891\) 0 0
\(892\) 9.50000 + 16.4545i 0.318084 + 0.550937i
\(893\) 12.0000 + 20.7846i 0.401565 + 0.695530i
\(894\) 0 0
\(895\) 36.0000 1.20335
\(896\) −2.00000 + 1.73205i −0.0668153 + 0.0578638i
\(897\) 0 0
\(898\) 6.00000 10.3923i 0.200223 0.346796i
\(899\) −4.50000 7.79423i −0.150083 0.259952i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 12.0000 20.7846i 0.398893 0.690904i
\(906\) 0 0
\(907\) −4.00000 6.92820i −0.132818 0.230047i 0.791944 0.610594i \(-0.209069\pi\)
−0.924762 + 0.380547i \(0.875736\pi\)
\(908\) −13.5000 + 23.3827i −0.448013 + 0.775982i
\(909\) 0 0
\(910\) −6.00000 31.1769i −0.198898 1.03350i
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) 0 0
\(913\) 13.5000 + 23.3827i 0.446785 + 0.773854i
\(914\) 0.500000 + 0.866025i 0.0165385 + 0.0286456i
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) −18.0000 + 15.5885i −0.594412 + 0.514776i
\(918\) 0 0
\(919\) −4.00000 + 6.92820i −0.131948 + 0.228540i −0.924427 0.381358i \(-0.875456\pi\)
0.792480 + 0.609898i \(0.208790\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 15.0000 25.9808i 0.493999 0.855631i
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) 32.0000 1.05215
\(926\) −4.00000 + 6.92820i −0.131448 + 0.227675i
\(927\) 0 0
\(928\) 4.50000 + 7.79423i 0.147720 + 0.255858i
\(929\) −3.00000 + 5.19615i −0.0984268 + 0.170480i −0.911034 0.412332i \(-0.864714\pi\)
0.812607 + 0.582812i \(0.198048\pi\)
\(930\) 0 0
\(931\) 26.0000 10.3923i 0.852116 0.340594i
\(932\) 24.0000 0.786146
\(933\) 0 0
\(934\) 18.0000 + 31.1769i 0.588978 + 1.02014i
\(935\) 0 0
\(936\) 0 0
\(937\) 35.0000 1.14340 0.571700 0.820463i \(-0.306284\pi\)
0.571700 + 0.820463i \(0.306284\pi\)
\(938\) −25.0000 8.66025i −0.816279 0.282767i
\(939\) 0 0
\(940\) 9.00000 15.5885i 0.293548 0.508439i
\(941\) −4.50000 7.79423i −0.146696 0.254085i 0.783309 0.621633i \(-0.213531\pi\)
−0.930004 + 0.367549i \(0.880197\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 30.0000 0.975384
\(947\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(948\) 0 0
\(949\) 4.00000 + 6.92820i 0.129845 + 0.224899i
\(950\) 8.00000 13.8564i 0.259554 0.449561i
\(951\) 0 0
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −12.0000 20.7846i −0.388108 0.672222i
\(957\) 0 0
\(958\) 18.0000 0.581554
\(959\) 9.00000 + 46.7654i 0.290625 + 1.51013i
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) 16.0000 + 27.7128i 0.515861 + 0.893497i
\(963\) 0 0
\(964\) 0.500000 0.866025i 0.0161039 0.0278928i
\(965\) 57.0000 1.83489
\(966\) 0 0
\(967\) −1.00000 −0.0321578 −0.0160789 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(968\) 1.00000 1.73205i 0.0321412 0.0556702i
\(969\) 0 0
\(970\) −1.50000 2.59808i −0.0481621 0.0834192i
\(971\) −19.5000 + 33.7750i −0.625785 + 1.08389i 0.362604 + 0.931943i \(0.381888\pi\)
−0.988389 + 0.151948i \(0.951445\pi\)
\(972\) 0 0
\(973\) 5.00000 + 1.73205i 0.160293 + 0.0555270i
\(974\) 41.0000 1.31372
\(975\) 0 0
\(976\) 5.00000 + 8.66025i 0.160046 + 0.277208i
\(977\) 21.0000 + 36.3731i 0.671850 + 1.16368i 0.977379 + 0.211495i \(0.0678332\pi\)
−0.305530 + 0.952183i \(0.598833\pi\)
\(978\) 0 0
\(979\) 18.0000 0.575282
\(980\) −16.5000 12.9904i −0.527073 0.414963i
\(981\) 0 0
\(982\) −16.5000 + 28.5788i −0.526536 + 0.911987i
\(983\) 18.0000 + 31.1769i 0.574111 + 0.994389i 0.996138 + 0.0878058i \(0.0279855\pi\)
−0.422027 + 0.906583i \(0.638681\pi\)
\(984\) 0 0
\(985\) −9.00000 + 15.5885i −0.286764 + 0.496690i
\(986\) 0 0
\(987\) 0 0
\(988\) 16.0000 0.509028
\(989\) 0 0
\(990\) 0 0
\(991\) 6.50000 + 11.2583i 0.206479 + 0.357633i 0.950603 0.310409i \(-0.100466\pi\)
−0.744124 + 0.668042i \(0.767133\pi\)
\(992\) 0.500000 0.866025i 0.0158750 0.0274963i
\(993\) 0 0
\(994\) −12.0000 + 10.3923i −0.380617 + 0.329624i
\(995\) −60.0000 −1.90213
\(996\) 0 0
\(997\) −7.00000 12.1244i −0.221692 0.383982i 0.733630 0.679549i \(-0.237825\pi\)
−0.955322 + 0.295567i \(0.904491\pi\)
\(998\) −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 126.2.g.b.37.1 2
3.2 odd 2 42.2.e.b.37.1 yes 2
4.3 odd 2 1008.2.s.n.289.1 2
7.2 even 3 882.2.a.g.1.1 1
7.3 odd 6 882.2.g.b.361.1 2
7.4 even 3 inner 126.2.g.b.109.1 2
7.5 odd 6 882.2.a.k.1.1 1
7.6 odd 2 882.2.g.b.667.1 2
9.2 odd 6 1134.2.e.a.919.1 2
9.4 even 3 1134.2.h.a.541.1 2
9.5 odd 6 1134.2.h.p.541.1 2
9.7 even 3 1134.2.e.p.919.1 2
12.11 even 2 336.2.q.d.289.1 2
15.2 even 4 1050.2.o.b.499.2 4
15.8 even 4 1050.2.o.b.499.1 4
15.14 odd 2 1050.2.i.e.751.1 2
21.2 odd 6 294.2.a.d.1.1 1
21.5 even 6 294.2.a.a.1.1 1
21.11 odd 6 42.2.e.b.25.1 2
21.17 even 6 294.2.e.f.67.1 2
21.20 even 2 294.2.e.f.79.1 2
24.5 odd 2 1344.2.q.v.961.1 2
24.11 even 2 1344.2.q.j.961.1 2
28.11 odd 6 1008.2.s.n.865.1 2
28.19 even 6 7056.2.a.bz.1.1 1
28.23 odd 6 7056.2.a.g.1.1 1
63.4 even 3 1134.2.e.p.865.1 2
63.11 odd 6 1134.2.h.p.109.1 2
63.25 even 3 1134.2.h.a.109.1 2
63.32 odd 6 1134.2.e.a.865.1 2
84.11 even 6 336.2.q.d.193.1 2
84.23 even 6 2352.2.a.m.1.1 1
84.47 odd 6 2352.2.a.n.1.1 1
84.59 odd 6 2352.2.q.m.1537.1 2
84.83 odd 2 2352.2.q.m.961.1 2
105.32 even 12 1050.2.o.b.949.1 4
105.44 odd 6 7350.2.a.ce.1.1 1
105.53 even 12 1050.2.o.b.949.2 4
105.74 odd 6 1050.2.i.e.151.1 2
105.89 even 6 7350.2.a.cw.1.1 1
168.5 even 6 9408.2.a.db.1.1 1
168.11 even 6 1344.2.q.j.193.1 2
168.53 odd 6 1344.2.q.v.193.1 2
168.107 even 6 9408.2.a.bu.1.1 1
168.131 odd 6 9408.2.a.bm.1.1 1
168.149 odd 6 9408.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.e.b.25.1 2 21.11 odd 6
42.2.e.b.37.1 yes 2 3.2 odd 2
126.2.g.b.37.1 2 1.1 even 1 trivial
126.2.g.b.109.1 2 7.4 even 3 inner
294.2.a.a.1.1 1 21.5 even 6
294.2.a.d.1.1 1 21.2 odd 6
294.2.e.f.67.1 2 21.17 even 6
294.2.e.f.79.1 2 21.20 even 2
336.2.q.d.193.1 2 84.11 even 6
336.2.q.d.289.1 2 12.11 even 2
882.2.a.g.1.1 1 7.2 even 3
882.2.a.k.1.1 1 7.5 odd 6
882.2.g.b.361.1 2 7.3 odd 6
882.2.g.b.667.1 2 7.6 odd 2
1008.2.s.n.289.1 2 4.3 odd 2
1008.2.s.n.865.1 2 28.11 odd 6
1050.2.i.e.151.1 2 105.74 odd 6
1050.2.i.e.751.1 2 15.14 odd 2
1050.2.o.b.499.1 4 15.8 even 4
1050.2.o.b.499.2 4 15.2 even 4
1050.2.o.b.949.1 4 105.32 even 12
1050.2.o.b.949.2 4 105.53 even 12
1134.2.e.a.865.1 2 63.32 odd 6
1134.2.e.a.919.1 2 9.2 odd 6
1134.2.e.p.865.1 2 63.4 even 3
1134.2.e.p.919.1 2 9.7 even 3
1134.2.h.a.109.1 2 63.25 even 3
1134.2.h.a.541.1 2 9.4 even 3
1134.2.h.p.109.1 2 63.11 odd 6
1134.2.h.p.541.1 2 9.5 odd 6
1344.2.q.j.193.1 2 168.11 even 6
1344.2.q.j.961.1 2 24.11 even 2
1344.2.q.v.193.1 2 168.53 odd 6
1344.2.q.v.961.1 2 24.5 odd 2
2352.2.a.m.1.1 1 84.23 even 6
2352.2.a.n.1.1 1 84.47 odd 6
2352.2.q.m.961.1 2 84.83 odd 2
2352.2.q.m.1537.1 2 84.59 odd 6
7056.2.a.g.1.1 1 28.23 odd 6
7056.2.a.bz.1.1 1 28.19 even 6
7350.2.a.ce.1.1 1 105.44 odd 6
7350.2.a.cw.1.1 1 105.89 even 6
9408.2.a.d.1.1 1 168.149 odd 6
9408.2.a.bm.1.1 1 168.131 odd 6
9408.2.a.bu.1.1 1 168.107 even 6
9408.2.a.db.1.1 1 168.5 even 6