Properties

Label 189.2.p.b.26.1
Level $189$
Weight $2$
Character 189.26
Analytic conductor $1.509$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(26,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.p (of order \(6\), 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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 189.26
Dual form 189.2.p.b.80.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(-1.22474 + 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(-1.22474 + 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} +2.82843i q^{8} +(3.00000 - 1.73205i) q^{10} +(4.89898 - 2.82843i) q^{11} +3.46410i q^{13} +(-2.44949 - 2.82843i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-1.22474 - 2.12132i) q^{17} +(1.50000 + 0.866025i) q^{19} -8.00000 q^{22} +(6.12372 + 3.53553i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.44949 - 4.24264i) q^{26} +1.41421i q^{29} +(-4.50000 + 2.59808i) q^{31} +3.46410i q^{34} +(-4.89898 + 4.24264i) q^{35} +(2.00000 - 3.46410i) q^{37} +(-1.22474 - 2.12132i) q^{38} +(-6.00000 - 3.46410i) q^{40} -2.44949 q^{41} -7.00000 q^{43} +(-5.00000 - 8.66025i) q^{46} +(-3.67423 + 6.36396i) q^{47} +(5.50000 + 4.33013i) q^{49} +1.41421i q^{50} +(1.22474 - 0.707107i) q^{53} +13.8564i q^{55} +(-2.44949 + 7.07107i) q^{56} +(1.00000 - 1.73205i) q^{58} +(-7.34847 - 12.7279i) q^{59} +(-4.50000 - 2.59808i) q^{61} +7.34847 q^{62} -8.00000 q^{64} +(-7.34847 - 4.24264i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(9.00000 - 1.73205i) q^{70} -2.82843i q^{71} +(10.5000 - 6.06218i) q^{73} +(-4.89898 + 2.82843i) q^{74} +(14.6969 - 2.82843i) q^{77} +(2.00000 - 3.46410i) q^{79} +(4.89898 + 8.48528i) q^{80} +(3.00000 + 1.73205i) q^{82} +9.79796 q^{83} +6.00000 q^{85} +(8.57321 + 4.94975i) q^{86} +(8.00000 + 13.8564i) q^{88} +(1.22474 - 2.12132i) q^{89} +(-3.00000 + 8.66025i) q^{91} +(9.00000 - 5.19615i) q^{94} +(-3.67423 + 2.12132i) q^{95} -8.66025i q^{97} +(-3.67423 - 9.19239i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 10 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 10 q^{7} + 12 q^{10} + 8 q^{16} + 6 q^{19} - 32 q^{22} - 2 q^{25} - 18 q^{31} + 8 q^{37} - 24 q^{40} - 28 q^{43} - 20 q^{46} + 22 q^{49} + 4 q^{58} - 18 q^{61} - 32 q^{64} - 4 q^{67} + 36 q^{70} + 42 q^{73} + 8 q^{79} + 12 q^{82} + 24 q^{85} + 32 q^{88} - 12 q^{91} + 36 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) −1.22474 + 2.12132i −0.547723 + 0.948683i 0.450708 + 0.892672i \(0.351172\pi\)
−0.998430 + 0.0560116i \(0.982162\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 3.00000 1.73205i 0.948683 0.547723i
\(11\) 4.89898 2.82843i 1.47710 0.852803i 0.477432 0.878668i \(-0.341568\pi\)
0.999665 + 0.0258656i \(0.00823419\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) −2.44949 2.82843i −0.654654 0.755929i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.22474 2.12132i −0.297044 0.514496i 0.678414 0.734680i \(-0.262668\pi\)
−0.975458 + 0.220184i \(0.929334\pi\)
\(18\) 0 0
\(19\) 1.50000 + 0.866025i 0.344124 + 0.198680i 0.662094 0.749421i \(-0.269668\pi\)
−0.317970 + 0.948101i \(0.603001\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −8.00000 −1.70561
\(23\) 6.12372 + 3.53553i 1.27688 + 0.737210i 0.976274 0.216537i \(-0.0694763\pi\)
0.300610 + 0.953747i \(0.402810\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 2.44949 4.24264i 0.480384 0.832050i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.41421i 0.262613i 0.991342 + 0.131306i \(0.0419172\pi\)
−0.991342 + 0.131306i \(0.958083\pi\)
\(30\) 0 0
\(31\) −4.50000 + 2.59808i −0.808224 + 0.466628i −0.846339 0.532645i \(-0.821198\pi\)
0.0381148 + 0.999273i \(0.487865\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 3.46410i 0.594089i
\(35\) −4.89898 + 4.24264i −0.828079 + 0.717137i
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −1.22474 2.12132i −0.198680 0.344124i
\(39\) 0 0
\(40\) −6.00000 3.46410i −0.948683 0.547723i
\(41\) −2.44949 −0.382546 −0.191273 0.981537i \(-0.561262\pi\)
−0.191273 + 0.981537i \(0.561262\pi\)
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −5.00000 8.66025i −0.737210 1.27688i
\(47\) −3.67423 + 6.36396i −0.535942 + 0.928279i 0.463175 + 0.886267i \(0.346710\pi\)
−0.999117 + 0.0420122i \(0.986623\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 1.41421i 0.200000i
\(51\) 0 0
\(52\) 0 0
\(53\) 1.22474 0.707107i 0.168232 0.0971286i −0.413520 0.910495i \(-0.635701\pi\)
0.581752 + 0.813366i \(0.302368\pi\)
\(54\) 0 0
\(55\) 13.8564i 1.86840i
\(56\) −2.44949 + 7.07107i −0.327327 + 0.944911i
\(57\) 0 0
\(58\) 1.00000 1.73205i 0.131306 0.227429i
\(59\) −7.34847 12.7279i −0.956689 1.65703i −0.730454 0.682962i \(-0.760692\pi\)
−0.226235 0.974073i \(-0.572642\pi\)
\(60\) 0 0
\(61\) −4.50000 2.59808i −0.576166 0.332650i 0.183442 0.983030i \(-0.441276\pi\)
−0.759608 + 0.650381i \(0.774609\pi\)
\(62\) 7.34847 0.933257
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −7.34847 4.24264i −0.911465 0.526235i
\(66\) 0 0
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 9.00000 1.73205i 1.07571 0.207020i
\(71\) 2.82843i 0.335673i −0.985815 0.167836i \(-0.946322\pi\)
0.985815 0.167836i \(-0.0536780\pi\)
\(72\) 0 0
\(73\) 10.5000 6.06218i 1.22893 0.709524i 0.262126 0.965034i \(-0.415577\pi\)
0.966807 + 0.255510i \(0.0822432\pi\)
\(74\) −4.89898 + 2.82843i −0.569495 + 0.328798i
\(75\) 0 0
\(76\) 0 0
\(77\) 14.6969 2.82843i 1.67487 0.322329i
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 4.89898 + 8.48528i 0.547723 + 0.948683i
\(81\) 0 0
\(82\) 3.00000 + 1.73205i 0.331295 + 0.191273i
\(83\) 9.79796 1.07547 0.537733 0.843115i \(-0.319281\pi\)
0.537733 + 0.843115i \(0.319281\pi\)
\(84\) 0 0
\(85\) 6.00000 0.650791
\(86\) 8.57321 + 4.94975i 0.924473 + 0.533745i
\(87\) 0 0
\(88\) 8.00000 + 13.8564i 0.852803 + 1.47710i
\(89\) 1.22474 2.12132i 0.129823 0.224860i −0.793785 0.608198i \(-0.791893\pi\)
0.923608 + 0.383339i \(0.125226\pi\)
\(90\) 0 0
\(91\) −3.00000 + 8.66025i −0.314485 + 0.907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 9.00000 5.19615i 0.928279 0.535942i
\(95\) −3.67423 + 2.12132i −0.376969 + 0.217643i
\(96\) 0 0
\(97\) 8.66025i 0.879316i −0.898165 0.439658i \(-0.855100\pi\)
0.898165 0.439658i \(-0.144900\pi\)
\(98\) −3.67423 9.19239i −0.371154 0.928571i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.89898 + 8.48528i 0.487467 + 0.844317i 0.999896 0.0144123i \(-0.00458773\pi\)
−0.512429 + 0.858729i \(0.671254\pi\)
\(102\) 0 0
\(103\) 12.0000 + 6.92820i 1.18240 + 0.682656i 0.956567 0.291511i \(-0.0941580\pi\)
0.225828 + 0.974167i \(0.427491\pi\)
\(104\) −9.79796 −0.960769
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −12.2474 7.07107i −1.18401 0.683586i −0.227068 0.973879i \(-0.572914\pi\)
−0.956938 + 0.290293i \(0.906247\pi\)
\(108\) 0 0
\(109\) −8.50000 14.7224i −0.814152 1.41015i −0.909935 0.414751i \(-0.863869\pi\)
0.0957826 0.995402i \(-0.469465\pi\)
\(110\) 9.79796 16.9706i 0.934199 1.61808i
\(111\) 0 0
\(112\) 8.00000 6.92820i 0.755929 0.654654i
\(113\) 2.82843i 0.266076i −0.991111 0.133038i \(-0.957527\pi\)
0.991111 0.133038i \(-0.0424732\pi\)
\(114\) 0 0
\(115\) −15.0000 + 8.66025i −1.39876 + 0.807573i
\(116\) 0 0
\(117\) 0 0
\(118\) 20.7846i 1.91338i
\(119\) −1.22474 6.36396i −0.112272 0.583383i
\(120\) 0 0
\(121\) 10.5000 18.1865i 0.954545 1.65332i
\(122\) 3.67423 + 6.36396i 0.332650 + 0.576166i
\(123\) 0 0
\(124\) 0 0
\(125\) −9.79796 −0.876356
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 9.79796 + 5.65685i 0.866025 + 0.500000i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) −8.57321 + 14.8492i −0.749045 + 1.29738i 0.199236 + 0.979952i \(0.436154\pi\)
−0.948281 + 0.317433i \(0.897179\pi\)
\(132\) 0 0
\(133\) 3.00000 + 3.46410i 0.260133 + 0.300376i
\(134\) 2.82843i 0.244339i
\(135\) 0 0
\(136\) 6.00000 3.46410i 0.514496 0.297044i
\(137\) −6.12372 + 3.53553i −0.523185 + 0.302061i −0.738237 0.674542i \(-0.764341\pi\)
0.215052 + 0.976603i \(0.431008\pi\)
\(138\) 0 0
\(139\) 6.92820i 0.587643i −0.955860 0.293821i \(-0.905073\pi\)
0.955860 0.293821i \(-0.0949270\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.00000 + 3.46410i −0.167836 + 0.290701i
\(143\) 9.79796 + 16.9706i 0.819346 + 1.41915i
\(144\) 0 0
\(145\) −3.00000 1.73205i −0.249136 0.143839i
\(146\) −17.1464 −1.41905
\(147\) 0 0
\(148\) 0 0
\(149\) −8.57321 4.94975i −0.702345 0.405499i 0.105875 0.994379i \(-0.466236\pi\)
−0.808220 + 0.588880i \(0.799569\pi\)
\(150\) 0 0
\(151\) −5.50000 9.52628i −0.447584 0.775238i 0.550645 0.834740i \(-0.314382\pi\)
−0.998228 + 0.0595022i \(0.981049\pi\)
\(152\) −2.44949 + 4.24264i −0.198680 + 0.344124i
\(153\) 0 0
\(154\) −20.0000 6.92820i −1.61165 0.558291i
\(155\) 12.7279i 1.02233i
\(156\) 0 0
\(157\) −9.00000 + 5.19615i −0.718278 + 0.414698i −0.814119 0.580699i \(-0.802779\pi\)
0.0958404 + 0.995397i \(0.469446\pi\)
\(158\) −4.89898 + 2.82843i −0.389742 + 0.225018i
\(159\) 0 0
\(160\) 0 0
\(161\) 12.2474 + 14.1421i 0.965234 + 1.11456i
\(162\) 0 0
\(163\) −11.5000 + 19.9186i −0.900750 + 1.56014i −0.0742262 + 0.997241i \(0.523649\pi\)
−0.826523 + 0.562902i \(0.809685\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −12.0000 6.92820i −0.931381 0.537733i
\(167\) 4.89898 0.379094 0.189547 0.981872i \(-0.439298\pi\)
0.189547 + 0.981872i \(0.439298\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −7.34847 4.24264i −0.563602 0.325396i
\(171\) 0 0
\(172\) 0 0
\(173\) 3.67423 6.36396i 0.279347 0.483843i −0.691876 0.722017i \(-0.743215\pi\)
0.971223 + 0.238174i \(0.0765487\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) 22.6274i 1.70561i
\(177\) 0 0
\(178\) −3.00000 + 1.73205i −0.224860 + 0.129823i
\(179\) 8.57321 4.94975i 0.640792 0.369961i −0.144127 0.989559i \(-0.546038\pi\)
0.784920 + 0.619598i \(0.212704\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i −0.815086 0.579340i \(-0.803310\pi\)
0.815086 0.579340i \(-0.196690\pi\)
\(182\) 9.79796 8.48528i 0.726273 0.628971i
\(183\) 0 0
\(184\) −10.0000 + 17.3205i −0.737210 + 1.27688i
\(185\) 4.89898 + 8.48528i 0.360180 + 0.623850i
\(186\) 0 0
\(187\) −12.0000 6.92820i −0.877527 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) −1.22474 0.707107i −0.0886194 0.0511645i 0.455035 0.890473i \(-0.349627\pi\)
−0.543655 + 0.839309i \(0.682960\pi\)
\(192\) 0 0
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) −6.12372 + 10.6066i −0.439658 + 0.761510i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.82843i 0.201517i −0.994911 0.100759i \(-0.967873\pi\)
0.994911 0.100759i \(-0.0321270\pi\)
\(198\) 0 0
\(199\) 1.50000 0.866025i 0.106332 0.0613909i −0.445891 0.895087i \(-0.647113\pi\)
0.552223 + 0.833696i \(0.313780\pi\)
\(200\) 2.44949 1.41421i 0.173205 0.100000i
\(201\) 0 0
\(202\) 13.8564i 0.974933i
\(203\) −1.22474 + 3.53553i −0.0859602 + 0.248146i
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) −9.79796 16.9706i −0.682656 1.18240i
\(207\) 0 0
\(208\) 12.0000 + 6.92820i 0.832050 + 0.480384i
\(209\) 9.79796 0.677739
\(210\) 0 0
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 10.0000 + 17.3205i 0.683586 + 1.18401i
\(215\) 8.57321 14.8492i 0.584688 1.01271i
\(216\) 0 0
\(217\) −13.5000 + 2.59808i −0.916440 + 0.176369i
\(218\) 24.0416i 1.62830i
\(219\) 0 0
\(220\) 0 0
\(221\) 7.34847 4.24264i 0.494312 0.285391i
\(222\) 0 0
\(223\) 13.8564i 0.927894i −0.885863 0.463947i \(-0.846433\pi\)
0.885863 0.463947i \(-0.153567\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.00000 + 3.46410i −0.133038 + 0.230429i
\(227\) 1.22474 + 2.12132i 0.0812892 + 0.140797i 0.903804 0.427947i \(-0.140763\pi\)
−0.822515 + 0.568744i \(0.807430\pi\)
\(228\) 0 0
\(229\) −1.50000 0.866025i −0.0991228 0.0572286i 0.449619 0.893220i \(-0.351560\pi\)
−0.548742 + 0.835992i \(0.684893\pi\)
\(230\) 24.4949 1.61515
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) 13.4722 + 7.77817i 0.882593 + 0.509565i 0.871512 0.490373i \(-0.163140\pi\)
0.0110803 + 0.999939i \(0.496473\pi\)
\(234\) 0 0
\(235\) −9.00000 15.5885i −0.587095 1.01688i
\(236\) 0 0
\(237\) 0 0
\(238\) −3.00000 + 8.66025i −0.194461 + 0.561361i
\(239\) 9.89949i 0.640345i 0.947359 + 0.320173i \(0.103741\pi\)
−0.947359 + 0.320173i \(0.896259\pi\)
\(240\) 0 0
\(241\) −10.5000 + 6.06218i −0.676364 + 0.390499i −0.798484 0.602016i \(-0.794364\pi\)
0.122119 + 0.992515i \(0.461031\pi\)
\(242\) −25.7196 + 14.8492i −1.65332 + 0.954545i
\(243\) 0 0
\(244\) 0 0
\(245\) −15.9217 + 6.36396i −1.01720 + 0.406579i
\(246\) 0 0
\(247\) −3.00000 + 5.19615i −0.190885 + 0.330623i
\(248\) −7.34847 12.7279i −0.466628 0.808224i
\(249\) 0 0
\(250\) 12.0000 + 6.92820i 0.758947 + 0.438178i
\(251\) 7.34847 0.463831 0.231916 0.972736i \(-0.425501\pi\)
0.231916 + 0.972736i \(0.425501\pi\)
\(252\) 0 0
\(253\) 40.0000 2.51478
\(254\) 1.22474 + 0.707107i 0.0768473 + 0.0443678i
\(255\) 0 0
\(256\) 0 0
\(257\) 9.79796 16.9706i 0.611180 1.05859i −0.379862 0.925043i \(-0.624029\pi\)
0.991042 0.133551i \(-0.0426381\pi\)
\(258\) 0 0
\(259\) 8.00000 6.92820i 0.497096 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 21.0000 12.1244i 1.29738 0.749045i
\(263\) −17.1464 + 9.89949i −1.05729 + 0.610429i −0.924683 0.380739i \(-0.875670\pi\)
−0.132612 + 0.991168i \(0.542336\pi\)
\(264\) 0 0
\(265\) 3.46410i 0.212798i
\(266\) −1.22474 6.36396i −0.0750939 0.390199i
\(267\) 0 0
\(268\) 0 0
\(269\) −12.2474 21.2132i −0.746740 1.29339i −0.949377 0.314138i \(-0.898285\pi\)
0.202637 0.979254i \(-0.435049\pi\)
\(270\) 0 0
\(271\) 19.5000 + 11.2583i 1.18454 + 0.683895i 0.957061 0.289888i \(-0.0936180\pi\)
0.227480 + 0.973783i \(0.426951\pi\)
\(272\) −9.79796 −0.594089
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) −4.89898 2.82843i −0.295420 0.170561i
\(276\) 0 0
\(277\) 12.5000 + 21.6506i 0.751052 + 1.30086i 0.947313 + 0.320309i \(0.103787\pi\)
−0.196261 + 0.980552i \(0.562880\pi\)
\(278\) −4.89898 + 8.48528i −0.293821 + 0.508913i
\(279\) 0 0
\(280\) −12.0000 13.8564i −0.717137 0.828079i
\(281\) 5.65685i 0.337460i 0.985662 + 0.168730i \(0.0539665\pi\)
−0.985662 + 0.168730i \(0.946033\pi\)
\(282\) 0 0
\(283\) −22.5000 + 12.9904i −1.33749 + 0.772198i −0.986434 0.164158i \(-0.947509\pi\)
−0.351052 + 0.936356i \(0.614176\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 27.7128i 1.63869i
\(287\) −6.12372 2.12132i −0.361472 0.125218i
\(288\) 0 0
\(289\) 5.50000 9.52628i 0.323529 0.560369i
\(290\) 2.44949 + 4.24264i 0.143839 + 0.249136i
\(291\) 0 0
\(292\) 0 0
\(293\) −24.4949 −1.43101 −0.715504 0.698609i \(-0.753803\pi\)
−0.715504 + 0.698609i \(0.753803\pi\)
\(294\) 0 0
\(295\) 36.0000 2.09600
\(296\) 9.79796 + 5.65685i 0.569495 + 0.328798i
\(297\) 0 0
\(298\) 7.00000 + 12.1244i 0.405499 + 0.702345i
\(299\) −12.2474 + 21.2132i −0.708288 + 1.22679i
\(300\) 0 0
\(301\) −17.5000 6.06218i −1.00868 0.349418i
\(302\) 15.5563i 0.895167i
\(303\) 0 0
\(304\) 6.00000 3.46410i 0.344124 0.198680i
\(305\) 11.0227 6.36396i 0.631158 0.364399i
\(306\) 0 0
\(307\) 5.19615i 0.296560i 0.988945 + 0.148280i \(0.0473737\pi\)
−0.988945 + 0.148280i \(0.952626\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −9.00000 + 15.5885i −0.511166 + 0.885365i
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 4.50000 + 2.59808i 0.254355 + 0.146852i 0.621757 0.783210i \(-0.286419\pi\)
−0.367402 + 0.930062i \(0.619753\pi\)
\(314\) 14.6969 0.829396
\(315\) 0 0
\(316\) 0 0
\(317\) 2.44949 + 1.41421i 0.137577 + 0.0794301i 0.567209 0.823574i \(-0.308023\pi\)
−0.429632 + 0.903004i \(0.641357\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 9.79796 16.9706i 0.547723 0.948683i
\(321\) 0 0
\(322\) −5.00000 25.9808i −0.278639 1.44785i
\(323\) 4.24264i 0.236067i
\(324\) 0 0
\(325\) 3.00000 1.73205i 0.166410 0.0960769i
\(326\) 28.1691 16.2635i 1.56014 0.900750i
\(327\) 0 0
\(328\) 6.92820i 0.382546i
\(329\) −14.6969 + 12.7279i −0.810268 + 0.701713i
\(330\) 0 0
\(331\) −8.50000 + 14.7224i −0.467202 + 0.809218i −0.999298 0.0374662i \(-0.988071\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −6.00000 3.46410i −0.328305 0.189547i
\(335\) 4.89898 0.267660
\(336\) 0 0
\(337\) −1.00000 −0.0544735 −0.0272367 0.999629i \(-0.508671\pi\)
−0.0272367 + 0.999629i \(0.508671\pi\)
\(338\) −1.22474 0.707107i −0.0666173 0.0384615i
\(339\) 0 0
\(340\) 0 0
\(341\) −14.6969 + 25.4558i −0.795884 + 1.37851i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 19.7990i 1.06749i
\(345\) 0 0
\(346\) −9.00000 + 5.19615i −0.483843 + 0.279347i
\(347\) 26.9444 15.5563i 1.44645 0.835109i 0.448183 0.893942i \(-0.352071\pi\)
0.998268 + 0.0588334i \(0.0187381\pi\)
\(348\) 0 0
\(349\) 1.73205i 0.0927146i 0.998925 + 0.0463573i \(0.0147613\pi\)
−0.998925 + 0.0463573i \(0.985239\pi\)
\(350\) −1.22474 + 3.53553i −0.0654654 + 0.188982i
\(351\) 0 0
\(352\) 0 0
\(353\) −17.1464 29.6985i −0.912612 1.58069i −0.810360 0.585932i \(-0.800728\pi\)
−0.102252 0.994758i \(-0.532605\pi\)
\(354\) 0 0
\(355\) 6.00000 + 3.46410i 0.318447 + 0.183855i
\(356\) 0 0
\(357\) 0 0
\(358\) −14.0000 −0.739923
\(359\) 9.79796 + 5.65685i 0.517116 + 0.298557i 0.735754 0.677249i \(-0.236828\pi\)
−0.218638 + 0.975806i \(0.570161\pi\)
\(360\) 0 0
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) −11.0227 + 19.0919i −0.579340 + 1.00345i
\(363\) 0 0
\(364\) 0 0
\(365\) 29.6985i 1.55449i
\(366\) 0 0
\(367\) 7.50000 4.33013i 0.391497 0.226031i −0.291312 0.956628i \(-0.594092\pi\)
0.682808 + 0.730597i \(0.260758\pi\)
\(368\) 24.4949 14.1421i 1.27688 0.737210i
\(369\) 0 0
\(370\) 13.8564i 0.720360i
\(371\) 3.67423 0.707107i 0.190757 0.0367112i
\(372\) 0 0
\(373\) 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) 9.79796 + 16.9706i 0.506640 + 0.877527i
\(375\) 0 0
\(376\) −18.0000 10.3923i −0.928279 0.535942i
\(377\) −4.89898 −0.252310
\(378\) 0 0
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.00000 + 1.73205i 0.0511645 + 0.0886194i
\(383\) 17.1464 29.6985i 0.876142 1.51752i 0.0205998 0.999788i \(-0.493442\pi\)
0.855542 0.517734i \(-0.173224\pi\)
\(384\) 0 0
\(385\) −12.0000 + 34.6410i −0.611577 + 1.76547i
\(386\) 5.65685i 0.287926i
\(387\) 0 0
\(388\) 0 0
\(389\) 23.2702 13.4350i 1.17984 0.681183i 0.223865 0.974620i \(-0.428132\pi\)
0.955978 + 0.293437i \(0.0947991\pi\)
\(390\) 0 0
\(391\) 17.3205i 0.875936i
\(392\) −12.2474 + 15.5563i −0.618590 + 0.785714i
\(393\) 0 0
\(394\) −2.00000 + 3.46410i −0.100759 + 0.174519i
\(395\) 4.89898 + 8.48528i 0.246494 + 0.426941i
\(396\) 0 0
\(397\) −16.5000 9.52628i −0.828111 0.478110i 0.0250943 0.999685i \(-0.492011\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −2.44949 −0.122782
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −19.5959 11.3137i −0.978573 0.564980i −0.0767343 0.997052i \(-0.524449\pi\)
−0.901839 + 0.432072i \(0.857783\pi\)
\(402\) 0 0
\(403\) −9.00000 15.5885i −0.448322 0.776516i
\(404\) 0 0
\(405\) 0 0
\(406\) 4.00000 3.46410i 0.198517 0.171920i
\(407\) 22.6274i 1.12160i
\(408\) 0 0
\(409\) −9.00000 + 5.19615i −0.445021 + 0.256933i −0.705725 0.708486i \(-0.749379\pi\)
0.260704 + 0.965419i \(0.416045\pi\)
\(410\) −7.34847 + 4.24264i −0.362915 + 0.209529i
\(411\) 0 0
\(412\) 0 0
\(413\) −7.34847 38.1838i −0.361595 1.87890i
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 0 0
\(417\) 0 0
\(418\) −12.0000 6.92820i −0.586939 0.338869i
\(419\) −2.44949 −0.119665 −0.0598327 0.998208i \(-0.519057\pi\)
−0.0598327 + 0.998208i \(0.519057\pi\)
\(420\) 0 0
\(421\) 11.0000 0.536107 0.268054 0.963404i \(-0.413620\pi\)
0.268054 + 0.963404i \(0.413620\pi\)
\(422\) 1.22474 + 0.707107i 0.0596196 + 0.0344214i
\(423\) 0 0
\(424\) 2.00000 + 3.46410i 0.0971286 + 0.168232i
\(425\) −1.22474 + 2.12132i −0.0594089 + 0.102899i
\(426\) 0 0
\(427\) −9.00000 10.3923i −0.435541 0.502919i
\(428\) 0 0
\(429\) 0 0
\(430\) −21.0000 + 12.1244i −1.01271 + 0.584688i
\(431\) −24.4949 + 14.1421i −1.17988 + 0.681203i −0.955986 0.293411i \(-0.905209\pi\)
−0.223891 + 0.974614i \(0.571876\pi\)
\(432\) 0 0
\(433\) 5.19615i 0.249711i 0.992175 + 0.124856i \(0.0398468\pi\)
−0.992175 + 0.124856i \(0.960153\pi\)
\(434\) 18.3712 + 6.36396i 0.881845 + 0.305480i
\(435\) 0 0
\(436\) 0 0
\(437\) 6.12372 + 10.6066i 0.292937 + 0.507383i
\(438\) 0 0
\(439\) 18.0000 + 10.3923i 0.859093 + 0.495998i 0.863708 0.503992i \(-0.168136\pi\)
−0.00461537 + 0.999989i \(0.501469\pi\)
\(440\) −39.1918 −1.86840
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) 13.4722 + 7.77817i 0.640083 + 0.369552i 0.784647 0.619943i \(-0.212844\pi\)
−0.144563 + 0.989496i \(0.546178\pi\)
\(444\) 0 0
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −9.79796 + 16.9706i −0.463947 + 0.803579i
\(447\) 0 0
\(448\) −20.0000 6.92820i −0.944911 0.327327i
\(449\) 35.3553i 1.66852i 0.551370 + 0.834261i \(0.314105\pi\)
−0.551370 + 0.834261i \(0.685895\pi\)
\(450\) 0 0
\(451\) −12.0000 + 6.92820i −0.565058 + 0.326236i
\(452\) 0 0
\(453\) 0 0
\(454\) 3.46410i 0.162578i
\(455\) −14.6969 16.9706i −0.689003 0.795592i
\(456\) 0 0
\(457\) −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i \(-0.870643\pi\)
0.801611 + 0.597847i \(0.203977\pi\)
\(458\) 1.22474 + 2.12132i 0.0572286 + 0.0991228i
\(459\) 0 0
\(460\) 0 0
\(461\) 24.4949 1.14084 0.570421 0.821353i \(-0.306780\pi\)
0.570421 + 0.821353i \(0.306780\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 4.89898 + 2.82843i 0.227429 + 0.131306i
\(465\) 0 0
\(466\) −11.0000 19.0526i −0.509565 0.882593i
\(467\) −2.44949 + 4.24264i −0.113349 + 0.196326i −0.917119 0.398615i \(-0.869491\pi\)
0.803770 + 0.594941i \(0.202824\pi\)
\(468\) 0 0
\(469\) −1.00000 5.19615i −0.0461757 0.239936i
\(470\) 25.4558i 1.17419i
\(471\) 0 0
\(472\) 36.0000 20.7846i 1.65703 0.956689i
\(473\) −34.2929 + 19.7990i −1.57679 + 0.910359i
\(474\) 0 0
\(475\) 1.73205i 0.0794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.00000 12.1244i 0.320173 0.554555i
\(479\) 1.22474 + 2.12132i 0.0559600 + 0.0969256i 0.892648 0.450754i \(-0.148845\pi\)
−0.836688 + 0.547679i \(0.815511\pi\)
\(480\) 0 0
\(481\) 12.0000 + 6.92820i 0.547153 + 0.315899i
\(482\) 17.1464 0.780998
\(483\) 0 0
\(484\) 0 0
\(485\) 18.3712 + 10.6066i 0.834192 + 0.481621i
\(486\) 0 0
\(487\) 6.50000 + 11.2583i 0.294543 + 0.510164i 0.974879 0.222737i \(-0.0714992\pi\)
−0.680335 + 0.732901i \(0.738166\pi\)
\(488\) 7.34847 12.7279i 0.332650 0.576166i
\(489\) 0 0
\(490\) 24.0000 + 3.46410i 1.08421 + 0.156492i
\(491\) 5.65685i 0.255290i 0.991820 + 0.127645i \(0.0407419\pi\)
−0.991820 + 0.127645i \(0.959258\pi\)
\(492\) 0 0
\(493\) 3.00000 1.73205i 0.135113 0.0780076i
\(494\) 7.34847 4.24264i 0.330623 0.190885i
\(495\) 0 0
\(496\) 20.7846i 0.933257i
\(497\) 2.44949 7.07107i 0.109875 0.317181i
\(498\) 0 0
\(499\) 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −9.00000 5.19615i −0.401690 0.231916i
\(503\) −22.0454 −0.982956 −0.491478 0.870890i \(-0.663543\pi\)
−0.491478 + 0.870890i \(0.663543\pi\)
\(504\) 0 0
\(505\) −24.0000 −1.06799
\(506\) −48.9898 28.2843i −2.17786 1.25739i
\(507\) 0 0
\(508\) 0 0
\(509\) 9.79796 16.9706i 0.434287 0.752207i −0.562950 0.826491i \(-0.690334\pi\)
0.997237 + 0.0742838i \(0.0236671\pi\)
\(510\) 0 0
\(511\) 31.5000 6.06218i 1.39348 0.268175i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) −24.0000 + 13.8564i −1.05859 + 0.611180i
\(515\) −29.3939 + 16.9706i −1.29525 + 0.747812i
\(516\) 0 0
\(517\) 41.5692i 1.82821i
\(518\) −14.6969 + 2.82843i −0.645746 + 0.124274i
\(519\) 0 0
\(520\) 12.0000 20.7846i 0.526235 0.911465i
\(521\) −12.2474 21.2132i −0.536570 0.929367i −0.999086 0.0427559i \(-0.986386\pi\)
0.462515 0.886611i \(-0.346947\pi\)
\(522\) 0 0
\(523\) −3.00000 1.73205i −0.131181 0.0757373i 0.432973 0.901407i \(-0.357464\pi\)
−0.564154 + 0.825669i \(0.690798\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 28.0000 1.22086
\(527\) 11.0227 + 6.36396i 0.480157 + 0.277218i
\(528\) 0 0
\(529\) 13.5000 + 23.3827i 0.586957 + 1.01664i
\(530\) 2.44949 4.24264i 0.106399 0.184289i
\(531\) 0 0
\(532\) 0 0
\(533\) 8.48528i 0.367538i
\(534\) 0 0
\(535\) 30.0000 17.3205i 1.29701 0.748831i
\(536\) 4.89898 2.82843i 0.211604 0.122169i
\(537\) 0 0
\(538\) 34.6410i 1.49348i
\(539\) 39.1918 + 5.65685i 1.68811 + 0.243658i
\(540\) 0 0
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) −15.9217 27.5772i −0.683895 1.18454i
\(543\) 0 0
\(544\) 0 0
\(545\) 41.6413 1.78372
\(546\) 0 0
\(547\) −25.0000 −1.06892 −0.534461 0.845193i \(-0.679486\pi\)
−0.534461 + 0.845193i \(0.679486\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 4.00000 + 6.92820i 0.170561 + 0.295420i
\(551\) −1.22474 + 2.12132i −0.0521759 + 0.0903713i
\(552\) 0 0
\(553\) 8.00000 6.92820i 0.340195 0.294617i
\(554\) 35.3553i 1.50210i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.22474 0.707107i 0.0518941 0.0299611i −0.473828 0.880617i \(-0.657128\pi\)
0.525723 + 0.850656i \(0.323795\pi\)
\(558\) 0 0
\(559\) 24.2487i 1.02561i
\(560\) 4.89898 + 25.4558i 0.207020 + 1.07571i
\(561\) 0 0
\(562\) 4.00000 6.92820i 0.168730 0.292249i
\(563\) 11.0227 + 19.0919i 0.464552 + 0.804627i 0.999181 0.0404596i \(-0.0128822\pi\)
−0.534630 + 0.845087i \(0.679549\pi\)
\(564\) 0 0
\(565\) 6.00000 + 3.46410i 0.252422 + 0.145736i
\(566\) 36.7423 1.54440
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) 31.8434 + 18.3848i 1.33494 + 0.770730i 0.986053 0.166434i \(-0.0532251\pi\)
0.348891 + 0.937163i \(0.386558\pi\)
\(570\) 0 0
\(571\) −20.5000 35.5070i −0.857898 1.48592i −0.873930 0.486052i \(-0.838437\pi\)
0.0160316 0.999871i \(-0.494897\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 6.00000 + 6.92820i 0.250435 + 0.289178i
\(575\) 7.07107i 0.294884i
\(576\) 0 0
\(577\) −3.00000 + 1.73205i −0.124892 + 0.0721062i −0.561144 0.827718i \(-0.689639\pi\)
0.436253 + 0.899824i \(0.356305\pi\)
\(578\) −13.4722 + 7.77817i −0.560369 + 0.323529i
\(579\) 0 0
\(580\) 0 0
\(581\) 24.4949 + 8.48528i 1.01622 + 0.352029i
\(582\) 0 0
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) 17.1464 + 29.6985i 0.709524 + 1.22893i
\(585\) 0 0
\(586\) 30.0000 + 17.3205i 1.23929 + 0.715504i
\(587\) −26.9444 −1.11211 −0.556057 0.831144i \(-0.687686\pi\)
−0.556057 + 0.831144i \(0.687686\pi\)
\(588\) 0 0
\(589\) −9.00000 −0.370839
\(590\) −44.0908 25.4558i −1.81519 1.04800i
\(591\) 0 0
\(592\) −8.00000 13.8564i −0.328798 0.569495i
\(593\) 4.89898 8.48528i 0.201177 0.348449i −0.747731 0.664002i \(-0.768857\pi\)
0.948908 + 0.315553i \(0.102190\pi\)
\(594\) 0 0
\(595\) 15.0000 + 5.19615i 0.614940 + 0.213021i
\(596\) 0 0
\(597\) 0 0
\(598\) 30.0000 17.3205i 1.22679 0.708288i
\(599\) −6.12372 + 3.53553i −0.250209 + 0.144458i −0.619860 0.784713i \(-0.712811\pi\)
0.369651 + 0.929171i \(0.379477\pi\)
\(600\) 0 0
\(601\) 22.5167i 0.918474i 0.888314 + 0.459237i \(0.151877\pi\)
−0.888314 + 0.459237i \(0.848123\pi\)
\(602\) 17.1464 + 19.7990i 0.698836 + 0.806947i
\(603\) 0 0
\(604\) 0 0
\(605\) 25.7196 + 44.5477i 1.04565 + 1.81112i
\(606\) 0 0
\(607\) 25.5000 + 14.7224i 1.03501 + 0.597565i 0.918417 0.395614i \(-0.129468\pi\)
0.116596 + 0.993179i \(0.462802\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −18.0000 −0.728799
\(611\) −22.0454 12.7279i −0.891862 0.514917i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 3.67423 6.36396i 0.148280 0.256829i
\(615\) 0 0
\(616\) 8.00000 + 41.5692i 0.322329 + 1.67487i
\(617\) 45.2548i 1.82189i −0.412527 0.910946i \(-0.635354\pi\)
0.412527 0.910946i \(-0.364646\pi\)
\(618\) 0 0
\(619\) 30.0000 17.3205i 1.20580 0.696170i 0.243962 0.969785i \(-0.421553\pi\)
0.961839 + 0.273615i \(0.0882193\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.89898 4.24264i 0.196273 0.169978i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −3.67423 6.36396i −0.146852 0.254355i
\(627\) 0 0
\(628\) 0 0
\(629\) −9.79796 −0.390670
\(630\) 0 0
\(631\) 11.0000 0.437903 0.218952 0.975736i \(-0.429736\pi\)
0.218952 + 0.975736i \(0.429736\pi\)
\(632\) 9.79796 + 5.65685i 0.389742 + 0.225018i
\(633\) 0 0
\(634\) −2.00000 3.46410i −0.0794301 0.137577i
\(635\) 1.22474 2.12132i 0.0486025 0.0841820i
\(636\) 0 0
\(637\) −15.0000 + 19.0526i −0.594322 + 0.754890i
\(638\) 11.3137i 0.447914i
\(639\) 0 0
\(640\) −24.0000 + 13.8564i −0.948683 + 0.547723i
\(641\) −6.12372 + 3.53553i −0.241873 + 0.139645i −0.616037 0.787717i \(-0.711263\pi\)
0.374165 + 0.927362i \(0.377930\pi\)
\(642\) 0 0
\(643\) 22.5167i 0.887970i −0.896034 0.443985i \(-0.853564\pi\)
0.896034 0.443985i \(-0.146436\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) −12.2474 21.2132i −0.481497 0.833977i 0.518278 0.855212i \(-0.326573\pi\)
−0.999775 + 0.0212354i \(0.993240\pi\)
\(648\) 0 0
\(649\) −72.0000 41.5692i −2.82625 1.63173i
\(650\) −4.89898 −0.192154
\(651\) 0 0
\(652\) 0 0
\(653\) 13.4722 + 7.77817i 0.527208 + 0.304383i 0.739879 0.672740i \(-0.234883\pi\)
−0.212671 + 0.977124i \(0.568216\pi\)
\(654\) 0 0
\(655\) −21.0000 36.3731i −0.820538 1.42121i
\(656\) −4.89898 + 8.48528i −0.191273 + 0.331295i
\(657\) 0 0
\(658\) 27.0000 5.19615i 1.05257 0.202567i
\(659\) 7.07107i 0.275450i −0.990471 0.137725i \(-0.956021\pi\)
0.990471 0.137725i \(-0.0439790\pi\)
\(660\) 0 0
\(661\) −40.5000 + 23.3827i −1.57527 + 0.909481i −0.579761 + 0.814787i \(0.696854\pi\)
−0.995506 + 0.0946945i \(0.969813\pi\)
\(662\) 20.8207 12.0208i 0.809218 0.467202i
\(663\) 0 0
\(664\) 27.7128i 1.07547i
\(665\) −11.0227 + 2.12132i −0.427442 + 0.0822613i
\(666\) 0 0
\(667\) −5.00000 + 8.66025i −0.193601 + 0.335326i
\(668\) 0 0
\(669\) 0 0
\(670\) −6.00000 3.46410i −0.231800 0.133830i
\(671\) −29.3939 −1.13474
\(672\) 0 0
\(673\) −25.0000 −0.963679 −0.481840 0.876259i \(-0.660031\pi\)
−0.481840 + 0.876259i \(0.660031\pi\)
\(674\) 1.22474 + 0.707107i 0.0471754 + 0.0272367i
\(675\) 0 0
\(676\) 0 0
\(677\) −7.34847 + 12.7279i −0.282425 + 0.489174i −0.971981 0.235058i \(-0.924472\pi\)
0.689557 + 0.724232i \(0.257805\pi\)
\(678\) 0 0
\(679\) 7.50000 21.6506i 0.287824 0.830875i
\(680\) 16.9706i 0.650791i
\(681\) 0 0
\(682\) 36.0000 20.7846i 1.37851 0.795884i
\(683\) −31.8434 + 18.3848i −1.21845 + 0.703474i −0.964587 0.263766i \(-0.915035\pi\)
−0.253866 + 0.967239i \(0.581702\pi\)
\(684\) 0 0
\(685\) 17.3205i 0.661783i
\(686\) −1.22474 26.1630i −0.0467610 0.998906i
\(687\) 0 0
\(688\) −14.0000 + 24.2487i −0.533745 + 0.924473i
\(689\) 2.44949 + 4.24264i 0.0933181 + 0.161632i
\(690\) 0 0
\(691\) −4.50000 2.59808i −0.171188 0.0988355i 0.411958 0.911203i \(-0.364845\pi\)
−0.583146 + 0.812367i \(0.698178\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −44.0000 −1.67022
\(695\) 14.6969 + 8.48528i 0.557487 + 0.321865i
\(696\) 0 0
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 1.22474 2.12132i 0.0463573 0.0802932i
\(699\) 0 0
\(700\) 0 0
\(701\) 15.5563i 0.587555i −0.955874 0.293778i \(-0.905087\pi\)
0.955874 0.293778i \(-0.0949125\pi\)
\(702\) 0 0
\(703\) 6.00000 3.46410i 0.226294 0.130651i
\(704\) −39.1918 + 22.6274i −1.47710 + 0.852803i
\(705\) 0 0
\(706\) 48.4974i 1.82522i
\(707\) 4.89898 + 25.4558i 0.184245 + 0.957366i
\(708\) 0 0
\(709\) −2.50000 + 4.33013i −0.0938895 + 0.162621i −0.909145 0.416481i \(-0.863263\pi\)
0.815255 + 0.579102i \(0.196597\pi\)
\(710\) −4.89898 8.48528i −0.183855 0.318447i
\(711\) 0 0
\(712\) 6.00000 + 3.46410i 0.224860 + 0.129823i
\(713\) −36.7423 −1.37601
\(714\) 0 0
\(715\) −48.0000 −1.79510
\(716\) 0 0
\(717\) 0 0
\(718\) −8.00000 13.8564i −0.298557 0.517116i
\(719\) 12.2474 21.2132i 0.456753 0.791119i −0.542034 0.840356i \(-0.682346\pi\)
0.998787 + 0.0492373i \(0.0156791\pi\)
\(720\) 0 0
\(721\) 24.0000 + 27.7128i 0.893807 + 1.03208i
\(722\) 22.6274i 0.842105i
\(723\) 0 0
\(724\) 0 0
\(725\) 1.22474 0.707107i 0.0454859 0.0262613i
\(726\) 0 0
\(727\) 32.9090i 1.22053i 0.792199 + 0.610263i \(0.208936\pi\)
−0.792199 + 0.610263i \(0.791064\pi\)
\(728\) −24.4949 8.48528i −0.907841 0.314485i
\(729\) 0 0
\(730\) 21.0000 36.3731i 0.777245 1.34623i
\(731\) 8.57321 + 14.8492i 0.317092 + 0.549219i
\(732\) 0 0
\(733\) −37.5000 21.6506i −1.38509 0.799684i −0.392337 0.919822i \(-0.628333\pi\)
−0.992757 + 0.120137i \(0.961667\pi\)
\(734\) −12.2474 −0.452062
\(735\) 0 0
\(736\) 0 0
\(737\) −9.79796 5.65685i −0.360912 0.208373i
\(738\) 0 0
\(739\) −2.50000 4.33013i −0.0919640 0.159286i 0.816373 0.577524i \(-0.195981\pi\)
−0.908337 + 0.418238i \(0.862648\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −5.00000 1.73205i −0.183556 0.0635856i
\(743\) 35.3553i 1.29706i 0.761188 + 0.648531i \(0.224616\pi\)
−0.761188 + 0.648531i \(0.775384\pi\)
\(744\) 0 0
\(745\) 21.0000 12.1244i 0.769380 0.444202i
\(746\) −1.22474 + 0.707107i −0.0448411 + 0.0258890i
\(747\) 0 0
\(748\) 0 0
\(749\) −24.4949 28.2843i −0.895024 1.03348i
\(750\) 0 0
\(751\) 18.5000 32.0429i 0.675075 1.16926i −0.301373 0.953506i \(-0.597445\pi\)
0.976447 0.215757i \(-0.0692219\pi\)
\(752\) 14.6969 + 25.4558i 0.535942 + 0.928279i
\(753\) 0 0
\(754\) 6.00000 + 3.46410i 0.218507 + 0.126155i
\(755\) 26.9444 0.980607
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 12.2474 + 7.07107i 0.444847 + 0.256833i
\(759\) 0 0
\(760\) −6.00000 10.3923i −0.217643 0.376969i
\(761\) −4.89898 + 8.48528i −0.177588 + 0.307591i −0.941054 0.338257i \(-0.890163\pi\)
0.763466 + 0.645848i \(0.223496\pi\)
\(762\) 0 0
\(763\) −8.50000 44.1673i −0.307721 1.59896i
\(764\) 0 0
\(765\) 0 0
\(766\) −42.0000 + 24.2487i −1.51752 + 0.876142i
\(767\) 44.0908 25.4558i 1.59203 0.919157i
\(768\) 0 0
\(769\) 50.2295i 1.81132i 0.424003 + 0.905661i \(0.360624\pi\)
−0.424003 + 0.905661i \(0.639376\pi\)
\(770\) 39.1918 33.9411i 1.41238 1.22315i
\(771\) 0 0
\(772\) 0 0
\(773\) 20.8207 + 36.0624i 0.748867 + 1.29708i 0.948366 + 0.317178i \(0.102735\pi\)
−0.199499 + 0.979898i \(0.563931\pi\)
\(774\) 0 0
\(775\) 4.50000 + 2.59808i 0.161645 + 0.0933257i
\(776\) 24.4949 0.879316
\(777\) 0 0
\(778\) −38.0000 −1.36237
\(779\) −3.67423 2.12132i −0.131643 0.0760042i
\(780\) 0 0
\(781\) −8.00000 13.8564i −0.286263 0.495821i
\(782\) −12.2474 + 21.2132i −0.437968 + 0.758583i
\(783\) 0 0
\(784\) 26.0000 10.3923i 0.928571 0.371154i
\(785\) 25.4558i 0.908558i
\(786\) 0 0
\(787\) −22.5000 + 12.9904i −0.802038 + 0.463057i −0.844183 0.536054i \(-0.819914\pi\)
0.0421450 + 0.999112i \(0.486581\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 13.8564i 0.492989i
\(791\) 2.44949 7.07107i 0.0870938 0.251418i
\(792\) 0 0
\(793\) 9.00000 15.5885i 0.319599 0.553562i
\(794\) 13.4722 + 23.3345i 0.478110 + 0.828111i
\(795\) 0 0
\(796\) 0 0
\(797\) −39.1918 −1.38825 −0.694123 0.719856i \(-0.744208\pi\)
−0.694123 + 0.719856i \(0.744208\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794
\(800\) 0 0
\(801\) 0 0
\(802\) 16.0000 + 27.7128i 0.564980 + 0.978573i
\(803\) 34.2929 59.3970i 1.21017 2.09607i
\(804\) 0 0
\(805\) −45.0000 + 8.66025i −1.58604 + 0.305234i
\(806\) 25.4558i 0.896644i
\(807\) 0 0
\(808\) −24.0000 + 13.8564i −0.844317 + 0.487467i
\(809\) −9.79796 + 5.65685i −0.344478 + 0.198884i −0.662250 0.749283i \(-0.730398\pi\)
0.317773 + 0.948167i \(0.397065\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −16.0000 + 27.7128i −0.560800 + 0.971334i
\(815\) −28.1691 48.7904i −0.986722 1.70905i
\(816\) 0 0
\(817\) −10.5000 6.06218i −0.367348 0.212089i
\(818\) 14.6969 0.513866
\(819\) 0 0
\(820\) 0 0
\(821\) −34.2929 19.7990i −1.19683 0.690990i −0.236982 0.971514i \(-0.576158\pi\)
−0.959847 + 0.280525i \(0.909492\pi\)
\(822\) 0 0
\(823\) −11.5000 19.9186i −0.400865 0.694318i 0.592966 0.805228i \(-0.297957\pi\)
−0.993831 + 0.110910i \(0.964624\pi\)
\(824\) −19.5959 + 33.9411i −0.682656 + 1.18240i
\(825\) 0 0
\(826\) −18.0000 + 51.9615i −0.626300 + 1.80797i
\(827\) 22.6274i 0.786832i 0.919360 + 0.393416i \(0.128707\pi\)
−0.919360 + 0.393416i \(0.871293\pi\)
\(828\) 0 0
\(829\) 28.5000 16.4545i 0.989846 0.571488i 0.0846177 0.996413i \(-0.473033\pi\)
0.905228 + 0.424926i \(0.139700\pi\)
\(830\) 29.3939 16.9706i 1.02028 0.589057i
\(831\) 0 0
\(832\) 27.7128i 0.960769i
\(833\) 2.44949 16.9706i 0.0848698 0.587995i
\(834\) 0 0
\(835\) −6.00000 + 10.3923i −0.207639 + 0.359641i
\(836\) 0 0
\(837\) 0 0
\(838\) 3.00000 + 1.73205i 0.103633 + 0.0598327i
\(839\) 24.4949 0.845658 0.422829 0.906210i \(-0.361037\pi\)
0.422829 + 0.906210i \(0.361037\pi\)
\(840\) 0 0
\(841\) 27.0000 0.931034
\(842\) −13.4722 7.77817i −0.464282 0.268054i
\(843\) 0 0
\(844\) 0 0
\(845\) −1.22474 + 2.12132i −0.0421325 + 0.0729756i
\(846\) 0 0
\(847\) 42.0000 36.3731i 1.44314 1.24979i
\(848\) 5.65685i 0.194257i
\(849\) 0 0
\(850\) 3.00000 1.73205i 0.102899 0.0594089i
\(851\) 24.4949 14.1421i 0.839674 0.484786i
\(852\) 0 0
\(853\) 8.66025i 0.296521i −0.988948 0.148261i \(-0.952633\pi\)
0.988948 0.148261i \(-0.0473675\pi\)
\(854\) 3.67423 + 19.0919i 0.125730 + 0.653311i
\(855\) 0 0
\(856\) 20.0000 34.6410i 0.683586 1.18401i
\(857\) −2.44949 4.24264i −0.0836730 0.144926i 0.821152 0.570710i \(-0.193332\pi\)
−0.904825 + 0.425784i \(0.859998\pi\)
\(858\) 0 0
\(859\) 43.5000 + 25.1147i 1.48420 + 0.856904i 0.999839 0.0179638i \(-0.00571836\pi\)
0.484362 + 0.874868i \(0.339052\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 40.0000 1.36241
\(863\) −1.22474 0.707107i −0.0416908 0.0240702i 0.479010 0.877810i \(-0.340996\pi\)
−0.520701 + 0.853739i \(0.674329\pi\)
\(864\) 0 0
\(865\) 9.00000 + 15.5885i 0.306009 + 0.530023i
\(866\) 3.67423 6.36396i 0.124856 0.216256i
\(867\) 0 0
\(868\) 0 0
\(869\) 22.6274i 0.767583i
\(870\) 0 0
\(871\) 6.00000 3.46410i 0.203302 0.117377i
\(872\) 41.6413 24.0416i 1.41015 0.814152i
\(873\) 0 0
\(874\) 17.3205i 0.585875i
\(875\) −24.4949 8.48528i −0.828079 0.286855i
\(876\) 0 0
\(877\) −17.5000 + 30.3109i −0.590933 + 1.02353i 0.403174 + 0.915123i \(0.367907\pi\)
−0.994107 + 0.108403i \(0.965426\pi\)
\(878\) −14.6969 25.4558i −0.495998 0.859093i
\(879\) 0 0
\(880\) 48.0000 + 27.7128i 1.61808 + 0.934199i
\(881\) 36.7423 1.23788 0.618941 0.785438i \(-0.287562\pi\)
0.618941 + 0.785438i \(0.287562\pi\)
\(882\) 0 0
\(883\) −37.0000 −1.24515 −0.622575 0.782560i \(-0.713913\pi\)
−0.622575 + 0.782560i \(0.713913\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −11.0000 19.0526i −0.369552 0.640083i
\(887\) −26.9444 + 46.6690i −0.904704 + 1.56699i −0.0833899 + 0.996517i \(0.526575\pi\)
−0.821314 + 0.570476i \(0.806759\pi\)
\(888\) 0 0
\(889\) −2.50000 0.866025i −0.0838473 0.0290456i
\(890\) 8.48528i 0.284427i
\(891\) 0 0
\(892\) 0 0
\(893\) −11.0227 + 6.36396i −0.368861 + 0.212962i
\(894\) 0 0
\(895\) 24.2487i 0.810545i
\(896\) 19.5959 + 22.6274i 0.654654 + 0.755929i
\(897\) 0 0
\(898\) 25.0000 43.3013i 0.834261 1.44498i
\(899\) −3.67423 6.36396i −0.122543 0.212250i
\(900\) 0 0
\(901\) −3.00000 1.73205i −0.0999445 0.0577030i
\(902\) 19.5959 0.652473
\(903\) 0 0
\(904\) 8.00000 0.266076
\(905\) 33.0681 + 19.0919i 1.09922 + 0.634636i
\(906\) 0 0
\(907\) 8.00000 + 13.8564i 0.265636 + 0.460094i 0.967730 0.251990i \(-0.0810849\pi\)
−0.702094 + 0.712084i \(0.747752\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 6.00000 + 31.1769i 0.198898 + 1.03350i
\(911\) 52.3259i 1.73363i 0.498626 + 0.866817i \(0.333838\pi\)
−0.498626 + 0.866817i \(0.666162\pi\)
\(912\) 0 0
\(913\) 48.0000 27.7128i 1.58857 0.917160i
\(914\) 6.12372 3.53553i 0.202555 0.116945i
\(915\) 0 0
\(916\) 0 0
\(917\) −34.2929 + 29.6985i −1.13245 + 0.980730i
\(918\) 0 0
\(919\) −2.50000 + 4.33013i −0.0824674 + 0.142838i −0.904309 0.426878i \(-0.859613\pi\)
0.821842 + 0.569716i \(0.192947\pi\)
\(920\) −24.4949 42.4264i −0.807573 1.39876i
\(921\) 0 0
\(922\) −30.0000 17.3205i −0.987997 0.570421i
\(923\) 9.79796 0.322504
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 1.22474 + 0.707107i 0.0402476 + 0.0232370i
\(927\) 0 0
\(928\) 0 0
\(929\) −11.0227 + 19.0919i −0.361643 + 0.626384i −0.988231 0.152966i \(-0.951117\pi\)
0.626588 + 0.779350i \(0.284451\pi\)
\(930\) 0 0
\(931\) 4.50000 + 11.2583i 0.147482 + 0.368977i
\(932\) 0 0
\(933\) 0 0
\(934\) 6.00000 3.46410i 0.196326 0.113349i
\(935\) 29.3939 16.9706i 0.961283 0.554997i
\(936\) 0 0
\(937\) 10.3923i 0.339502i 0.985487 + 0.169751i \(0.0542963\pi\)
−0.985487 + 0.169751i \(0.945704\pi\)
\(938\) −2.44949 + 7.07107i −0.0799787 + 0.230879i
\(939\) 0 0
\(940\) 0 0
\(941\) −7.34847 12.7279i −0.239553 0.414918i 0.721033 0.692901i \(-0.243668\pi\)
−0.960586 + 0.277982i \(0.910334\pi\)
\(942\) 0 0
\(943\) −15.0000 8.66025i −0.488467 0.282017i
\(944\) −58.7878 −1.91338
\(945\) 0 0
\(946\) 56.0000 1.82072
\(947\) −8.57321 4.94975i −0.278592 0.160845i 0.354194 0.935172i \(-0.384755\pi\)
−0.632786 + 0.774327i \(0.718089\pi\)
\(948\) 0 0
\(949\) 21.0000 + 36.3731i 0.681689 + 1.18072i
\(950\) −1.22474 + 2.12132i −0.0397360 + 0.0688247i
\(951\) 0 0
\(952\) 18.0000 3.46410i 0.583383 0.112272i
\(953\) 18.3848i 0.595541i 0.954637 + 0.297771i \(0.0962431\pi\)
−0.954637 + 0.297771i \(0.903757\pi\)
\(954\) 0 0
\(955\) 3.00000 1.73205i 0.0970777 0.0560478i
\(956\) 0 0
\(957\) 0 0
\(958\) 3.46410i 0.111920i
\(959\) −18.3712 + 3.53553i −0.593236 + 0.114168i
\(960\) 0 0
\(961\) −2.00000 + 3.46410i −0.0645161 + 0.111745i
\(962\) −9.79796 16.9706i −0.315899 0.547153i
\(963\) 0 0
\(964\) 0 0
\(965\) −9.79796 −0.315407
\(966\) 0 0
\(967\) −34.0000 −1.09337 −0.546683 0.837340i \(-0.684110\pi\)
−0.546683 + 0.837340i \(0.684110\pi\)
\(968\) 51.4393 + 29.6985i 1.65332 + 0.954545i
\(969\) 0 0
\(970\) −15.0000 25.9808i −0.481621 0.834192i
\(971\) −6.12372 + 10.6066i −0.196520 + 0.340382i −0.947398 0.320059i \(-0.896297\pi\)
0.750878 + 0.660441i \(0.229631\pi\)
\(972\) 0 0
\(973\) 6.00000 17.3205i 0.192351 0.555270i
\(974\) 18.3848i 0.589086i
\(975\) 0 0
\(976\) −18.0000 + 10.3923i −0.576166 + 0.332650i
\(977\) −31.8434 + 18.3848i −1.01876 + 0.588181i −0.913744 0.406290i \(-0.866822\pi\)
−0.105015 + 0.994471i \(0.533489\pi\)
\(978\) 0 0
\(979\) 13.8564i 0.442853i
\(980\) 0 0
\(981\) 0 0
\(982\) 4.00000 6.92820i 0.127645 0.221088i
\(983\) −2.44949 4.24264i −0.0781266 0.135319i 0.824315 0.566131i \(-0.191561\pi\)
−0.902442 + 0.430812i \(0.858227\pi\)
\(984\) 0 0
\(985\) 6.00000 + 3.46410i 0.191176 + 0.110375i
\(986\) −4.89898 −0.156015
\(987\) 0 0
\(988\) 0 0
\(989\) −42.8661 24.7487i −1.36306 0.786964i
\(990\) 0 0
\(991\) 29.0000 + 50.2295i 0.921215 + 1.59559i 0.797537 + 0.603269i \(0.206136\pi\)
0.123678 + 0.992322i \(0.460531\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −8.00000 + 6.92820i −0.253745 + 0.219749i
\(995\) 4.24264i 0.134501i
\(996\) 0 0
\(997\) 34.5000 19.9186i 1.09263 0.630828i 0.158352 0.987383i \(-0.449382\pi\)
0.934274 + 0.356555i \(0.116049\pi\)
\(998\) −30.6186 + 17.6777i −0.969216 + 0.559577i
\(999\) 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 189.2.p.b.26.1 4
3.2 odd 2 inner 189.2.p.b.26.2 yes 4
7.2 even 3 1323.2.c.c.1322.4 4
7.3 odd 6 inner 189.2.p.b.80.2 yes 4
7.5 odd 6 1323.2.c.c.1322.3 4
9.2 odd 6 567.2.i.e.215.1 4
9.4 even 3 567.2.s.c.26.2 4
9.5 odd 6 567.2.s.c.26.1 4
9.7 even 3 567.2.i.e.215.2 4
21.2 odd 6 1323.2.c.c.1322.1 4
21.5 even 6 1323.2.c.c.1322.2 4
21.17 even 6 inner 189.2.p.b.80.1 yes 4
63.31 odd 6 567.2.i.e.269.2 4
63.38 even 6 567.2.s.c.458.2 4
63.52 odd 6 567.2.s.c.458.1 4
63.59 even 6 567.2.i.e.269.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.b.26.1 4 1.1 even 1 trivial
189.2.p.b.26.2 yes 4 3.2 odd 2 inner
189.2.p.b.80.1 yes 4 21.17 even 6 inner
189.2.p.b.80.2 yes 4 7.3 odd 6 inner
567.2.i.e.215.1 4 9.2 odd 6
567.2.i.e.215.2 4 9.7 even 3
567.2.i.e.269.1 4 63.59 even 6
567.2.i.e.269.2 4 63.31 odd 6
567.2.s.c.26.1 4 9.5 odd 6
567.2.s.c.26.2 4 9.4 even 3
567.2.s.c.458.1 4 63.52 odd 6
567.2.s.c.458.2 4 63.38 even 6
1323.2.c.c.1322.1 4 21.2 odd 6
1323.2.c.c.1322.2 4 21.5 even 6
1323.2.c.c.1322.3 4 7.5 odd 6
1323.2.c.c.1322.4 4 7.2 even 3