Properties

Label 1008.2.t.h.193.2
Level $1008$
Weight $2$
Character 1008.193
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.2
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1008.193
Dual form 1008.2.t.h.961.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.796790 + 1.53790i) q^{3} +0.593579 q^{5} +(0.0665372 - 2.64491i) q^{7} +(-1.73025 - 2.45076i) q^{9} +O(q^{10})\) \(q+(-0.796790 + 1.53790i) q^{3} +0.593579 q^{5} +(0.0665372 - 2.64491i) q^{7} +(-1.73025 - 2.45076i) q^{9} +0.593579 q^{11} +(-1.25729 + 2.17770i) q^{13} +(-0.472958 + 0.912864i) q^{15} +(1.46050 - 2.52967i) q^{17} +(-2.69076 - 4.66053i) q^{19} +(4.01459 + 2.20977i) q^{21} -4.46050 q^{23} -4.64766 q^{25} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +(-3.93346 - 6.81296i) q^{31} +(-0.472958 + 0.912864i) q^{33} +(0.0394951 - 1.56997i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-2.34728 - 3.66876i) q^{39} +(-0.136673 + 0.236725i) q^{41} +(5.58113 + 9.66679i) q^{43} +(-1.02704 - 1.45472i) q^{45} +(6.08113 - 10.5328i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(2.72665 + 4.26172i) q^{51} +(4.02704 - 6.97504i) q^{53} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} +(4.32383 + 7.48910i) q^{59} +(3.32383 - 5.75705i) q^{61} +(-6.59718 + 4.41330i) q^{63} +(-0.746304 + 1.29264i) q^{65} +(-0.956906 - 1.65741i) q^{67} +(3.55408 - 6.85980i) q^{69} +14.4107 q^{71} +(3.95691 - 6.85356i) q^{73} +(3.70321 - 7.14763i) q^{75} +(0.0394951 - 1.56997i) q^{77} +(-4.62422 + 8.00938i) q^{79} +(-3.01245 + 8.48087i) q^{81} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(10.7178 - 0.488786i) q^{87} +(-6.21780 - 10.7695i) q^{89} +(5.67617 + 3.47033i) q^{91} +(13.6118 - 0.620765i) q^{93} +(-1.59718 - 2.76639i) q^{95} +(5.86693 + 10.1618i) q^{97} +(-1.02704 - 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9} - 2 q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} - 4 q^{25} + 7 q^{27} - 5 q^{29} - 20 q^{31} - 12 q^{33} + 13 q^{35} + 3 q^{37} - q^{39} + 6 q^{43} + 3 q^{45} + 9 q^{47} - 12 q^{49} + 18 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} + 14 q^{59} + 8 q^{61} - 26 q^{63} - 12 q^{65} - q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} + 25 q^{75} + 13 q^{77} - 5 q^{79} - 40 q^{81} - 2 q^{83} - 2 q^{85} + 36 q^{87} - 9 q^{89} + 46 q^{91} + 37 q^{93} + 4 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −0.796790 + 1.53790i −0.460027 + 0.887905i
\(4\) 0 0
\(5\) 0.593579 0.265457 0.132728 0.991152i \(-0.457626\pi\)
0.132728 + 0.991152i \(0.457626\pi\)
\(6\) 0 0
\(7\) 0.0665372 2.64491i 0.0251487 0.999684i
\(8\) 0 0
\(9\) −1.73025 2.45076i −0.576751 0.816920i
\(10\) 0 0
\(11\) 0.593579 0.178971 0.0894855 0.995988i \(-0.471478\pi\)
0.0894855 + 0.995988i \(0.471478\pi\)
\(12\) 0 0
\(13\) −1.25729 + 2.17770i −0.348711 + 0.603985i −0.986021 0.166623i \(-0.946714\pi\)
0.637310 + 0.770608i \(0.280047\pi\)
\(14\) 0 0
\(15\) −0.472958 + 0.912864i −0.122117 + 0.235700i
\(16\) 0 0
\(17\) 1.46050 2.52967i 0.354224 0.613535i −0.632760 0.774348i \(-0.718078\pi\)
0.986985 + 0.160813i \(0.0514116\pi\)
\(18\) 0 0
\(19\) −2.69076 4.66053i −0.617302 1.06920i −0.989976 0.141236i \(-0.954892\pi\)
0.372674 0.927962i \(-0.378441\pi\)
\(20\) 0 0
\(21\) 4.01459 + 2.20977i 0.876055 + 0.482211i
\(22\) 0 0
\(23\) −4.46050 −0.930080 −0.465040 0.885290i \(-0.653960\pi\)
−0.465040 + 0.885290i \(0.653960\pi\)
\(24\) 0 0
\(25\) −4.64766 −0.929533
\(26\) 0 0
\(27\) 5.14766 0.708209i 0.990668 0.136295i
\(28\) 0 0
\(29\) −3.09718 5.36447i −0.575132 0.996157i −0.996027 0.0890480i \(-0.971618\pi\)
0.420896 0.907109i \(-0.361716\pi\)
\(30\) 0 0
\(31\) −3.93346 6.81296i −0.706471 1.22364i −0.966158 0.257951i \(-0.916953\pi\)
0.259687 0.965693i \(-0.416380\pi\)
\(32\) 0 0
\(33\) −0.472958 + 0.912864i −0.0823314 + 0.158909i
\(34\) 0 0
\(35\) 0.0394951 1.56997i 0.00667590 0.265373i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −2.34728 3.66876i −0.375865 0.587471i
\(40\) 0 0
\(41\) −0.136673 + 0.236725i −0.0213448 + 0.0369702i −0.876500 0.481401i \(-0.840128\pi\)
0.855156 + 0.518371i \(0.173461\pi\)
\(42\) 0 0
\(43\) 5.58113 + 9.66679i 0.851114 + 1.47417i 0.880204 + 0.474596i \(0.157406\pi\)
−0.0290902 + 0.999577i \(0.509261\pi\)
\(44\) 0 0
\(45\) −1.02704 1.45472i −0.153102 0.216857i
\(46\) 0 0
\(47\) 6.08113 10.5328i 0.887023 1.53637i 0.0436467 0.999047i \(-0.486102\pi\)
0.843377 0.537323i \(-0.180564\pi\)
\(48\) 0 0
\(49\) −6.99115 0.351971i −0.998735 0.0502815i
\(50\) 0 0
\(51\) 2.72665 + 4.26172i 0.381808 + 0.596760i
\(52\) 0 0
\(53\) 4.02704 6.97504i 0.553157 0.958096i −0.444888 0.895586i \(-0.646756\pi\)
0.998044 0.0625092i \(-0.0199103\pi\)
\(54\) 0 0
\(55\) 0.352336 0.0475090
\(56\) 0 0
\(57\) 9.31138 0.424646i 1.23332 0.0562457i
\(58\) 0 0
\(59\) 4.32383 + 7.48910i 0.562915 + 0.974997i 0.997240 + 0.0742412i \(0.0236535\pi\)
−0.434325 + 0.900756i \(0.643013\pi\)
\(60\) 0 0
\(61\) 3.32383 5.75705i 0.425573 0.737114i −0.570901 0.821019i \(-0.693406\pi\)
0.996474 + 0.0839050i \(0.0267392\pi\)
\(62\) 0 0
\(63\) −6.59718 + 4.41330i −0.831166 + 0.556024i
\(64\) 0 0
\(65\) −0.746304 + 1.29264i −0.0925676 + 0.160332i
\(66\) 0 0
\(67\) −0.956906 1.65741i −0.116905 0.202485i 0.801635 0.597814i \(-0.203964\pi\)
−0.918540 + 0.395329i \(0.870631\pi\)
\(68\) 0 0
\(69\) 3.55408 6.85980i 0.427861 0.825822i
\(70\) 0 0
\(71\) 14.4107 1.71023 0.855117 0.518435i \(-0.173485\pi\)
0.855117 + 0.518435i \(0.173485\pi\)
\(72\) 0 0
\(73\) 3.95691 6.85356i 0.463121 0.802149i −0.535994 0.844222i \(-0.680063\pi\)
0.999115 + 0.0420732i \(0.0133963\pi\)
\(74\) 0 0
\(75\) 3.70321 7.14763i 0.427610 0.825337i
\(76\) 0 0
\(77\) 0.0394951 1.56997i 0.00450089 0.178914i
\(78\) 0 0
\(79\) −4.62422 + 8.00938i −0.520265 + 0.901126i 0.479457 + 0.877565i \(0.340834\pi\)
−0.999722 + 0.0235607i \(0.992500\pi\)
\(80\) 0 0
\(81\) −3.01245 + 8.48087i −0.334717 + 0.942319i
\(82\) 0 0
\(83\) −3.85087 6.66991i −0.422688 0.732118i 0.573513 0.819196i \(-0.305580\pi\)
−0.996201 + 0.0870787i \(0.972247\pi\)
\(84\) 0 0
\(85\) 0.866926 1.50156i 0.0940313 0.162867i
\(86\) 0 0
\(87\) 10.7178 0.488786i 1.14907 0.0524033i
\(88\) 0 0
\(89\) −6.21780 10.7695i −0.659085 1.14157i −0.980853 0.194751i \(-0.937610\pi\)
0.321767 0.946819i \(-0.395723\pi\)
\(90\) 0 0
\(91\) 5.67617 + 3.47033i 0.595024 + 0.363790i
\(92\) 0 0
\(93\) 13.6118 0.620765i 1.41147 0.0643704i
\(94\) 0 0
\(95\) −1.59718 2.76639i −0.163867 0.283826i
\(96\) 0 0
\(97\) 5.86693 + 10.1618i 0.595696 + 1.03178i 0.993448 + 0.114283i \(0.0364570\pi\)
−0.397752 + 0.917493i \(0.630210\pi\)
\(98\) 0 0
\(99\) −1.02704 1.45472i −0.103222 0.146205i
\(100\) 0 0
\(101\) −1.62276 −0.161470 −0.0807352 0.996736i \(-0.525727\pi\)
−0.0807352 + 0.996736i \(0.525727\pi\)
\(102\) 0 0
\(103\) −6.38151 −0.628789 −0.314395 0.949292i \(-0.601802\pi\)
−0.314395 + 0.949292i \(0.601802\pi\)
\(104\) 0 0
\(105\) 2.38298 + 1.31167i 0.232555 + 0.128006i
\(106\) 0 0
\(107\) −9.35447 16.2024i −0.904331 1.56635i −0.821813 0.569758i \(-0.807037\pi\)
−0.0825182 0.996590i \(-0.526296\pi\)
\(108\) 0 0
\(109\) −1.43346 + 2.48283i −0.137301 + 0.237812i −0.926474 0.376359i \(-0.877176\pi\)
0.789173 + 0.614171i \(0.210509\pi\)
\(110\) 0 0
\(111\) −1.73025 + 0.0789082i −0.164228 + 0.00748964i
\(112\) 0 0
\(113\) −6.16012 + 10.6696i −0.579495 + 1.00371i 0.416042 + 0.909345i \(0.363417\pi\)
−0.995537 + 0.0943695i \(0.969916\pi\)
\(114\) 0 0
\(115\) −2.64766 −0.246896
\(116\) 0 0
\(117\) 7.51245 0.686640i 0.694527 0.0634799i
\(118\) 0 0
\(119\) −6.59358 4.03123i −0.604432 0.369542i
\(120\) 0 0
\(121\) −10.6477 −0.967969
\(122\) 0 0
\(123\) −0.255158 0.398809i −0.0230069 0.0359594i
\(124\) 0 0
\(125\) −5.72665 −0.512207
\(126\) 0 0
\(127\) −12.3346 −1.09452 −0.547261 0.836962i \(-0.684329\pi\)
−0.547261 + 0.836962i \(0.684329\pi\)
\(128\) 0 0
\(129\) −19.3135 + 0.880794i −1.70046 + 0.0775496i
\(130\) 0 0
\(131\) 1.18716 0.103723 0.0518613 0.998654i \(-0.483485\pi\)
0.0518613 + 0.998654i \(0.483485\pi\)
\(132\) 0 0
\(133\) −12.5057 + 6.80672i −1.08438 + 0.590218i
\(134\) 0 0
\(135\) 3.05555 0.420378i 0.262980 0.0361804i
\(136\) 0 0
\(137\) 2.52179 0.215451 0.107725 0.994181i \(-0.465643\pi\)
0.107725 + 0.994181i \(0.465643\pi\)
\(138\) 0 0
\(139\) −2.45691 + 4.25549i −0.208392 + 0.360946i −0.951208 0.308550i \(-0.900156\pi\)
0.742816 + 0.669496i \(0.233490\pi\)
\(140\) 0 0
\(141\) 11.3530 + 17.7446i 0.956096 + 1.49436i
\(142\) 0 0
\(143\) −0.746304 + 1.29264i −0.0624091 + 0.108096i
\(144\) 0 0
\(145\) −1.83842 3.18424i −0.152673 0.264437i
\(146\) 0 0
\(147\) 6.11177 10.4712i 0.504090 0.863651i
\(148\) 0 0
\(149\) 18.0512 1.47881 0.739404 0.673262i \(-0.235107\pi\)
0.739404 + 0.673262i \(0.235107\pi\)
\(150\) 0 0
\(151\) −1.64766 −0.134085 −0.0670425 0.997750i \(-0.521356\pi\)
−0.0670425 + 0.997750i \(0.521356\pi\)
\(152\) 0 0
\(153\) −8.72665 + 0.797618i −0.705508 + 0.0644836i
\(154\) 0 0
\(155\) −2.33482 4.04403i −0.187537 0.324824i
\(156\) 0 0
\(157\) 3.30039 + 5.71644i 0.263400 + 0.456222i 0.967143 0.254233i \(-0.0818229\pi\)
−0.703743 + 0.710454i \(0.748490\pi\)
\(158\) 0 0
\(159\) 7.51819 + 11.7508i 0.596231 + 0.931900i
\(160\) 0 0
\(161\) −0.296790 + 11.7977i −0.0233903 + 0.929785i
\(162\) 0 0
\(163\) 2.99115 + 5.18082i 0.234285 + 0.405793i 0.959065 0.283188i \(-0.0913919\pi\)
−0.724780 + 0.688980i \(0.758059\pi\)
\(164\) 0 0
\(165\) −0.280738 + 0.541857i −0.0218554 + 0.0421835i
\(166\) 0 0
\(167\) −3.73025 + 6.46099i −0.288656 + 0.499966i −0.973489 0.228733i \(-0.926542\pi\)
0.684833 + 0.728700i \(0.259875\pi\)
\(168\) 0 0
\(169\) 3.33842 + 5.78231i 0.256802 + 0.444793i
\(170\) 0 0
\(171\) −6.76615 + 14.6583i −0.517420 + 1.12095i
\(172\) 0 0
\(173\) 12.8296 22.2215i 0.975414 1.68947i 0.296851 0.954924i \(-0.404063\pi\)
0.678562 0.734543i \(-0.262603\pi\)
\(174\) 0 0
\(175\) −0.309243 + 12.2927i −0.0233766 + 0.929239i
\(176\) 0 0
\(177\) −14.9626 + 0.682372i −1.12466 + 0.0512902i
\(178\) 0 0
\(179\) −7.51819 + 13.0219i −0.561936 + 0.973301i 0.435392 + 0.900241i \(0.356610\pi\)
−0.997328 + 0.0730602i \(0.976723\pi\)
\(180\) 0 0
\(181\) −0.0861875 −0.00640627 −0.00320313 0.999995i \(-0.501020\pi\)
−0.00320313 + 0.999995i \(0.501020\pi\)
\(182\) 0 0
\(183\) 6.20535 + 9.69886i 0.458712 + 0.716961i
\(184\) 0 0
\(185\) 0.296790 + 0.514055i 0.0218204 + 0.0377941i
\(186\) 0 0
\(187\) 0.866926 1.50156i 0.0633959 0.109805i
\(188\) 0 0
\(189\) −1.53064 13.6623i −0.111338 0.993783i
\(190\) 0 0
\(191\) 1.99115 3.44877i 0.144074 0.249544i −0.784953 0.619555i \(-0.787313\pi\)
0.929027 + 0.370011i \(0.120646\pi\)
\(192\) 0 0
\(193\) −3.39037 5.87229i −0.244044 0.422697i 0.717818 0.696230i \(-0.245141\pi\)
−0.961862 + 0.273534i \(0.911808\pi\)
\(194\) 0 0
\(195\) −1.39329 2.17770i −0.0997759 0.155948i
\(196\) 0 0
\(197\) 11.0584 0.787875 0.393938 0.919137i \(-0.371113\pi\)
0.393938 + 0.919137i \(0.371113\pi\)
\(198\) 0 0
\(199\) −2.80924 + 4.86575i −0.199142 + 0.344924i −0.948250 0.317523i \(-0.897149\pi\)
0.749109 + 0.662447i \(0.230482\pi\)
\(200\) 0 0
\(201\) 3.31138 0.151016i 0.233567 0.0106518i
\(202\) 0 0
\(203\) −14.3946 + 7.83483i −1.01031 + 0.549898i
\(204\) 0 0
\(205\) −0.0811263 + 0.140515i −0.00566611 + 0.00981399i
\(206\) 0 0
\(207\) 7.71780 + 10.9316i 0.536424 + 0.759801i
\(208\) 0 0
\(209\) −1.59718 2.76639i −0.110479 0.191355i
\(210\) 0 0
\(211\) −9.66225 + 16.7355i −0.665177 + 1.15212i 0.314060 + 0.949403i \(0.398311\pi\)
−0.979237 + 0.202717i \(0.935023\pi\)
\(212\) 0 0
\(213\) −11.4823 + 22.1622i −0.786754 + 1.51853i
\(214\) 0 0
\(215\) 3.31284 + 5.73801i 0.225934 + 0.391329i
\(216\) 0 0
\(217\) −18.2814 + 9.95036i −1.24102 + 0.675474i
\(218\) 0 0
\(219\) 7.38725 + 11.5462i 0.499184 + 0.780217i
\(220\) 0 0
\(221\) 3.67257 + 6.36108i 0.247044 + 0.427892i
\(222\) 0 0
\(223\) −12.6623 21.9317i −0.847927 1.46865i −0.883055 0.469270i \(-0.844517\pi\)
0.0351275 0.999383i \(-0.488816\pi\)
\(224\) 0 0
\(225\) 8.04163 + 11.3903i 0.536109 + 0.759354i
\(226\) 0 0
\(227\) −4.81711 −0.319723 −0.159862 0.987139i \(-0.551105\pi\)
−0.159862 + 0.987139i \(0.551105\pi\)
\(228\) 0 0
\(229\) −9.29533 −0.614253 −0.307126 0.951669i \(-0.599367\pi\)
−0.307126 + 0.951669i \(0.599367\pi\)
\(230\) 0 0
\(231\) 2.38298 + 1.31167i 0.156788 + 0.0863017i
\(232\) 0 0
\(233\) 0.0971780 + 0.168317i 0.00636634 + 0.0110268i 0.869191 0.494476i \(-0.164640\pi\)
−0.862825 + 0.505503i \(0.831307\pi\)
\(234\) 0 0
\(235\) 3.60963 6.25206i 0.235466 0.407840i
\(236\) 0 0
\(237\) −8.63307 13.4934i −0.560778 0.876488i
\(238\) 0 0
\(239\) 6.82743 11.8255i 0.441630 0.764925i −0.556181 0.831061i \(-0.687734\pi\)
0.997811 + 0.0661361i \(0.0210672\pi\)
\(240\) 0 0
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) 0 0
\(243\) −10.6424 11.3903i −0.682711 0.730689i
\(244\) 0 0
\(245\) −4.14980 0.208922i −0.265121 0.0133476i
\(246\) 0 0
\(247\) 13.5323 0.861039
\(248\) 0 0
\(249\) 13.3260 0.607731i 0.844499 0.0385134i
\(250\) 0 0
\(251\) 19.5438 1.23359 0.616796 0.787123i \(-0.288430\pi\)
0.616796 + 0.787123i \(0.288430\pi\)
\(252\) 0 0
\(253\) −2.64766 −0.166457
\(254\) 0 0
\(255\) 1.61849 + 2.52967i 0.101353 + 0.158414i
\(256\) 0 0
\(257\) 8.32743 0.519451 0.259725 0.965683i \(-0.416368\pi\)
0.259725 + 0.965683i \(0.416368\pi\)
\(258\) 0 0
\(259\) 2.32383 1.26483i 0.144396 0.0785930i
\(260\) 0 0
\(261\) −7.78813 + 16.8723i −0.482073 + 1.04437i
\(262\) 0 0
\(263\) 17.0905 1.05384 0.526921 0.849914i \(-0.323346\pi\)
0.526921 + 0.849914i \(0.323346\pi\)
\(264\) 0 0
\(265\) 2.39037 4.14024i 0.146839 0.254333i
\(266\) 0 0
\(267\) 21.5167 0.981271i 1.31680 0.0600528i
\(268\) 0 0
\(269\) −5.00720 + 8.67272i −0.305294 + 0.528785i −0.977327 0.211737i \(-0.932088\pi\)
0.672033 + 0.740522i \(0.265421\pi\)
\(270\) 0 0
\(271\) −5.10457 8.84137i −0.310081 0.537075i 0.668299 0.743893i \(-0.267023\pi\)
−0.978380 + 0.206818i \(0.933689\pi\)
\(272\) 0 0
\(273\) −9.85973 + 5.96423i −0.596738 + 0.360972i
\(274\) 0 0
\(275\) −2.75876 −0.166359
\(276\) 0 0
\(277\) 19.3422 1.16216 0.581081 0.813846i \(-0.302630\pi\)
0.581081 + 0.813846i \(0.302630\pi\)
\(278\) 0 0
\(279\) −9.89104 + 21.4281i −0.592161 + 1.28287i
\(280\) 0 0
\(281\) −6.40136 11.0875i −0.381873 0.661424i 0.609457 0.792819i \(-0.291388\pi\)
−0.991330 + 0.131396i \(0.958054\pi\)
\(282\) 0 0
\(283\) −8.17617 14.1615i −0.486023 0.841816i 0.513848 0.857881i \(-0.328219\pi\)
−0.999871 + 0.0160650i \(0.994886\pi\)
\(284\) 0 0
\(285\) 5.52704 0.252061i 0.327394 0.0149308i
\(286\) 0 0
\(287\) 0.617023 + 0.377240i 0.0364217 + 0.0222678i
\(288\) 0 0
\(289\) 4.23385 + 7.33325i 0.249050 + 0.431367i
\(290\) 0 0
\(291\) −20.3025 + 0.925898i −1.19016 + 0.0542771i
\(292\) 0 0
\(293\) −10.3889 + 17.9941i −0.606926 + 1.05123i 0.384817 + 0.922993i \(0.374264\pi\)
−0.991744 + 0.128235i \(0.959069\pi\)
\(294\) 0 0
\(295\) 2.56654 + 4.44537i 0.149430 + 0.258820i
\(296\) 0 0
\(297\) 3.05555 0.420378i 0.177301 0.0243928i
\(298\) 0 0
\(299\) 5.60817 9.71363i 0.324329 0.561754i
\(300\) 0 0
\(301\) 25.9392 14.1184i 1.49511 0.813771i
\(302\) 0 0
\(303\) 1.29300 2.49563i 0.0742807 0.143370i
\(304\) 0 0
\(305\) 1.97296 3.41726i 0.112971 0.195672i
\(306\) 0 0
\(307\) 22.6768 1.29424 0.647118 0.762390i \(-0.275974\pi\)
0.647118 + 0.762390i \(0.275974\pi\)
\(308\) 0 0
\(309\) 5.08472 9.81411i 0.289260 0.558305i
\(310\) 0 0
\(311\) −3.25729 5.64180i −0.184704 0.319917i 0.758773 0.651356i \(-0.225799\pi\)
−0.943477 + 0.331439i \(0.892466\pi\)
\(312\) 0 0
\(313\) −0.133074 + 0.230492i −0.00752181 + 0.0130282i −0.869762 0.493472i \(-0.835728\pi\)
0.862240 + 0.506500i \(0.169061\pi\)
\(314\) 0 0
\(315\) −3.91595 + 2.61965i −0.220639 + 0.147600i
\(316\) 0 0
\(317\) −7.86186 + 13.6171i −0.441566 + 0.764815i −0.997806 0.0662067i \(-0.978910\pi\)
0.556240 + 0.831022i \(0.312244\pi\)
\(318\) 0 0
\(319\) −1.83842 3.18424i −0.102932 0.178283i
\(320\) 0 0
\(321\) 32.3712 1.47629i 1.80678 0.0823985i
\(322\) 0 0
\(323\) −15.7195 −0.874654
\(324\) 0 0
\(325\) 5.84348 10.1212i 0.324138 0.561424i
\(326\) 0 0
\(327\) −2.67617 4.18281i −0.147992 0.231310i
\(328\) 0 0
\(329\) −27.4538 16.7849i −1.51358 0.925381i
\(330\) 0 0
\(331\) −12.5811 + 21.7912i −0.691521 + 1.19775i 0.279818 + 0.960053i \(0.409726\pi\)
−0.971339 + 0.237697i \(0.923608\pi\)
\(332\) 0 0
\(333\) 1.25729 2.72382i 0.0688993 0.149265i
\(334\) 0 0
\(335\) −0.568000 0.983804i −0.0310331 0.0537510i
\(336\) 0 0
\(337\) −9.36693 + 16.2240i −0.510249 + 0.883777i 0.489681 + 0.871902i \(0.337113\pi\)
−0.999929 + 0.0118752i \(0.996220\pi\)
\(338\) 0 0
\(339\) −11.5005 17.9751i −0.624620 0.976272i
\(340\) 0 0
\(341\) −2.33482 4.04403i −0.126438 0.218997i
\(342\) 0 0
\(343\) −1.39610 + 18.4676i −0.0753825 + 0.997155i
\(344\) 0 0
\(345\) 2.10963 4.07183i 0.113579 0.219220i
\(346\) 0 0
\(347\) 11.2719 + 19.5235i 0.605106 + 1.04808i 0.992035 + 0.125965i \(0.0402028\pi\)
−0.386928 + 0.922110i \(0.626464\pi\)
\(348\) 0 0
\(349\) 1.89543 + 3.28298i 0.101460 + 0.175734i 0.912286 0.409553i \(-0.134315\pi\)
−0.810826 + 0.585287i \(0.800982\pi\)
\(350\) 0 0
\(351\) −4.92986 + 12.1005i −0.263137 + 0.645876i
\(352\) 0 0
\(353\) 6.83482 0.363781 0.181890 0.983319i \(-0.441778\pi\)
0.181890 + 0.983319i \(0.441778\pi\)
\(354\) 0 0
\(355\) 8.55389 0.453993
\(356\) 0 0
\(357\) 11.4533 6.92820i 0.606173 0.366679i
\(358\) 0 0
\(359\) 6.32237 + 10.9507i 0.333682 + 0.577954i 0.983231 0.182366i \(-0.0583755\pi\)
−0.649549 + 0.760320i \(0.725042\pi\)
\(360\) 0 0
\(361\) −4.98035 + 8.62622i −0.262124 + 0.454012i
\(362\) 0 0
\(363\) 8.48395 16.3750i 0.445292 0.859465i
\(364\) 0 0
\(365\) 2.34874 4.06813i 0.122939 0.212936i
\(366\) 0 0
\(367\) −6.54377 −0.341582 −0.170791 0.985307i \(-0.554632\pi\)
−0.170791 + 0.985307i \(0.554632\pi\)
\(368\) 0 0
\(369\) 0.816635 0.0746406i 0.0425123 0.00388563i
\(370\) 0 0
\(371\) −18.1804 11.1153i −0.943881 0.577077i
\(372\) 0 0
\(373\) 9.42840 0.488184 0.244092 0.969752i \(-0.421510\pi\)
0.244092 + 0.969752i \(0.421510\pi\)
\(374\) 0 0
\(375\) 4.56294 8.80700i 0.235629 0.454792i
\(376\) 0 0
\(377\) 15.5763 0.802218
\(378\) 0 0
\(379\) 7.27762 0.373826 0.186913 0.982376i \(-0.440152\pi\)
0.186913 + 0.982376i \(0.440152\pi\)
\(380\) 0 0
\(381\) 9.82810 18.9694i 0.503509 0.971831i
\(382\) 0 0
\(383\) 24.0833 1.23060 0.615299 0.788294i \(-0.289035\pi\)
0.615299 + 0.788294i \(0.289035\pi\)
\(384\) 0 0
\(385\) 0.0234435 0.931900i 0.00119479 0.0474940i
\(386\) 0 0
\(387\) 14.0342 30.4040i 0.713400 1.54552i
\(388\) 0 0
\(389\) −16.2983 −0.826354 −0.413177 0.910651i \(-0.635581\pi\)
−0.413177 + 0.910651i \(0.635581\pi\)
\(390\) 0 0
\(391\) −6.51459 + 11.2836i −0.329457 + 0.570636i
\(392\) 0 0
\(393\) −0.945916 + 1.82573i −0.0477151 + 0.0920958i
\(394\) 0 0
\(395\) −2.74484 + 4.75420i −0.138108 + 0.239210i
\(396\) 0 0
\(397\) −6.08619 10.5416i −0.305457 0.529067i 0.671906 0.740636i \(-0.265476\pi\)
−0.977363 + 0.211569i \(0.932143\pi\)
\(398\) 0 0
\(399\) −0.503599 24.6561i −0.0252115 1.23435i
\(400\) 0 0
\(401\) −33.3609 −1.66596 −0.832981 0.553301i \(-0.813368\pi\)
−0.832981 + 0.553301i \(0.813368\pi\)
\(402\) 0 0
\(403\) 19.7821 0.985416
\(404\) 0 0
\(405\) −1.78813 + 5.03407i −0.0888529 + 0.250145i
\(406\) 0 0
\(407\) 0.296790 + 0.514055i 0.0147113 + 0.0254808i
\(408\) 0 0
\(409\) 2.89037 + 5.00627i 0.142920 + 0.247544i 0.928595 0.371095i \(-0.121018\pi\)
−0.785675 + 0.618639i \(0.787684\pi\)
\(410\) 0 0
\(411\) −2.00933 + 3.87825i −0.0991131 + 0.191300i
\(412\) 0 0
\(413\) 20.0957 10.9379i 0.988846 0.538217i
\(414\) 0 0
\(415\) −2.28580 3.95912i −0.112205 0.194346i
\(416\) 0 0
\(417\) −4.58686 7.16920i −0.224620 0.351077i
\(418\) 0 0
\(419\) −15.4356 + 26.7352i −0.754078 + 1.30610i 0.191753 + 0.981443i \(0.438583\pi\)
−0.945831 + 0.324659i \(0.894751\pi\)
\(420\) 0 0
\(421\) −1.86693 3.23361i −0.0909884 0.157597i 0.816939 0.576724i \(-0.195669\pi\)
−0.907927 + 0.419128i \(0.862336\pi\)
\(422\) 0 0
\(423\) −36.3353 + 3.32105i −1.76668 + 0.161475i
\(424\) 0 0
\(425\) −6.78794 + 11.7570i −0.329263 + 0.570301i
\(426\) 0 0
\(427\) −15.0057 9.17431i −0.726178 0.443976i
\(428\) 0 0
\(429\) −1.39329 2.17770i −0.0672689 0.105140i
\(430\) 0 0
\(431\) 14.0979 24.4182i 0.679070 1.17618i −0.296192 0.955128i \(-0.595717\pi\)
0.975261 0.221055i \(-0.0709499\pi\)
\(432\) 0 0
\(433\) 12.5438 0.602815 0.301407 0.953495i \(-0.402544\pi\)
0.301407 + 0.953495i \(0.402544\pi\)
\(434\) 0 0
\(435\) 6.36186 0.290133i 0.305028 0.0139108i
\(436\) 0 0
\(437\) 12.0021 + 20.7883i 0.574140 + 0.994440i
\(438\) 0 0
\(439\) 13.0203 22.5519i 0.621426 1.07634i −0.367794 0.929907i \(-0.619887\pi\)
0.989220 0.146434i \(-0.0467797\pi\)
\(440\) 0 0
\(441\) 11.2339 + 17.7426i 0.534945 + 0.844887i
\(442\) 0 0
\(443\) −11.7865 + 20.4148i −0.559992 + 0.969935i 0.437504 + 0.899216i \(0.355863\pi\)
−0.997496 + 0.0707186i \(0.977471\pi\)
\(444\) 0 0
\(445\) −3.69076 6.39258i −0.174959 0.303037i
\(446\) 0 0
\(447\) −14.3830 + 27.7608i −0.680291 + 1.31304i
\(448\) 0 0
\(449\) 13.6870 0.645928 0.322964 0.946411i \(-0.395321\pi\)
0.322964 + 0.946411i \(0.395321\pi\)
\(450\) 0 0
\(451\) −0.0811263 + 0.140515i −0.00382009 + 0.00661659i
\(452\) 0 0
\(453\) 1.31284 2.53394i 0.0616827 0.119055i
\(454\) 0 0
\(455\) 3.36926 + 2.05992i 0.157953 + 0.0965705i
\(456\) 0 0
\(457\) 11.1762 19.3577i 0.522799 0.905515i −0.476849 0.878985i \(-0.658221\pi\)
0.999648 0.0265293i \(-0.00844554\pi\)
\(458\) 0 0
\(459\) 5.72665 14.0562i 0.267297 0.656088i
\(460\) 0 0
\(461\) −3.98755 6.90663i −0.185719 0.321674i 0.758100 0.652138i \(-0.226128\pi\)
−0.943818 + 0.330464i \(0.892795\pi\)
\(462\) 0 0
\(463\) 14.3676 24.8854i 0.667719 1.15652i −0.310821 0.950468i \(-0.600604\pi\)
0.978540 0.206055i \(-0.0660625\pi\)
\(464\) 0 0
\(465\) 8.07966 0.368473i 0.374685 0.0170875i
\(466\) 0 0
\(467\) −16.7829 29.0688i −0.776619 1.34514i −0.933880 0.357586i \(-0.883600\pi\)
0.157261 0.987557i \(-0.449733\pi\)
\(468\) 0 0
\(469\) −4.44738 + 2.42066i −0.205361 + 0.111775i
\(470\) 0 0
\(471\) −11.4210 + 0.520856i −0.526252 + 0.0239998i
\(472\) 0 0
\(473\) 3.31284 + 5.73801i 0.152325 + 0.263834i
\(474\) 0 0
\(475\) 12.5057 + 21.6606i 0.573802 + 0.993855i
\(476\) 0 0
\(477\) −24.0620 + 2.19927i −1.10172 + 0.100698i
\(478\) 0 0
\(479\) −0.367120 −0.0167741 −0.00838707 0.999965i \(-0.502670\pi\)
−0.00838707 + 0.999965i \(0.502670\pi\)
\(480\) 0 0
\(481\) −2.51459 −0.114655
\(482\) 0 0
\(483\) −17.9071 9.85668i −0.814801 0.448495i
\(484\) 0 0
\(485\) 3.48249 + 6.03184i 0.158132 + 0.273892i
\(486\) 0 0
\(487\) 14.9538 25.9007i 0.677621 1.17367i −0.298075 0.954543i \(-0.596344\pi\)
0.975695 0.219131i \(-0.0703222\pi\)
\(488\) 0 0
\(489\) −10.3509 + 0.472052i −0.468083 + 0.0213469i
\(490\) 0 0
\(491\) 0.255158 0.441947i 0.0115151 0.0199448i −0.860210 0.509939i \(-0.829668\pi\)
0.871726 + 0.489994i \(0.163001\pi\)
\(492\) 0 0
\(493\) −18.0938 −0.814903
\(494\) 0 0
\(495\) −0.609631 0.863492i −0.0274009 0.0388111i
\(496\) 0 0
\(497\) 0.958848 38.1151i 0.0430102 1.70969i
\(498\) 0 0
\(499\) 19.0191 0.851410 0.425705 0.904862i \(-0.360026\pi\)
0.425705 + 0.904862i \(0.360026\pi\)
\(500\) 0 0
\(501\) −6.96410 10.8848i −0.311133 0.486297i
\(502\) 0 0
\(503\) 37.7807 1.68456 0.842280 0.539040i \(-0.181213\pi\)
0.842280 + 0.539040i \(0.181213\pi\)
\(504\) 0 0
\(505\) −0.963235 −0.0428634
\(506\) 0 0
\(507\) −11.5526 + 0.526858i −0.513070 + 0.0233986i
\(508\) 0 0
\(509\) −11.2163 −0.497155 −0.248578 0.968612i \(-0.579963\pi\)
−0.248578 + 0.968612i \(0.579963\pi\)
\(510\) 0 0
\(511\) −17.8638 10.9217i −0.790248 0.483147i
\(512\) 0 0
\(513\) −17.1517 22.0852i −0.757268 0.975086i
\(514\) 0 0
\(515\) −3.78794 −0.166916
\(516\) 0 0
\(517\) 3.60963 6.25206i 0.158751 0.274965i
\(518\) 0 0
\(519\) 23.9518 + 37.4364i 1.05137 + 1.64327i
\(520\) 0 0
\(521\) −13.7360 + 23.7914i −0.601785 + 1.04232i 0.390766 + 0.920490i \(0.372210\pi\)
−0.992551 + 0.121831i \(0.961123\pi\)
\(522\) 0 0
\(523\) −11.0919 19.2118i −0.485016 0.840072i 0.514836 0.857289i \(-0.327853\pi\)
−0.999852 + 0.0172166i \(0.994520\pi\)
\(524\) 0 0
\(525\) −18.6585 10.2703i −0.814322 0.448231i
\(526\) 0 0
\(527\) −22.9794 −1.00100
\(528\) 0 0
\(529\) −3.10390 −0.134952
\(530\) 0 0
\(531\) 10.8727 23.5547i 0.471833 1.02219i
\(532\) 0 0
\(533\) −0.343677 0.595265i −0.0148863 0.0257838i
\(534\) 0 0
\(535\) −5.55262 9.61742i −0.240061 0.415797i
\(536\) 0 0
\(537\) −14.0359 21.9379i −0.605694 0.946690i
\(538\) 0 0
\(539\) −4.14980 0.208922i −0.178745 0.00899893i
\(540\) 0 0
\(541\) 14.9246 + 25.8502i 0.641659 + 1.11139i 0.985062 + 0.172198i \(0.0550869\pi\)
−0.343403 + 0.939188i \(0.611580\pi\)
\(542\) 0 0
\(543\) 0.0686733 0.132547i 0.00294705 0.00568816i
\(544\) 0 0
\(545\) −0.850874 + 1.47376i −0.0364474 + 0.0631288i
\(546\) 0 0
\(547\) −8.84348 15.3174i −0.378120 0.654923i 0.612669 0.790340i \(-0.290096\pi\)
−0.990789 + 0.135417i \(0.956763\pi\)
\(548\) 0 0
\(549\) −19.8602 + 1.81523i −0.847613 + 0.0774720i
\(550\) 0 0
\(551\) −16.6675 + 28.8690i −0.710060 + 1.22986i
\(552\) 0 0
\(553\) 20.8765 + 12.7636i 0.887757 + 0.542763i
\(554\) 0 0
\(555\) −1.02704 + 0.0468383i −0.0435955 + 0.00198818i
\(556\) 0 0
\(557\) 15.0651 26.0935i 0.638328 1.10562i −0.347472 0.937690i \(-0.612960\pi\)
0.985800 0.167926i \(-0.0537069\pi\)
\(558\) 0 0
\(559\) −28.0685 −1.18717
\(560\) 0 0
\(561\) 1.61849 + 2.52967i 0.0683325 + 0.106803i
\(562\) 0 0
\(563\) 2.04883 + 3.54867i 0.0863478 + 0.149559i 0.905965 0.423353i \(-0.139147\pi\)
−0.819617 + 0.572912i \(0.805814\pi\)
\(564\) 0 0
\(565\) −3.65652 + 6.33327i −0.153831 + 0.266443i
\(566\) 0 0
\(567\) 22.2307 + 8.53197i 0.933603 + 0.358309i
\(568\) 0 0
\(569\) −3.11849 + 5.40138i −0.130734 + 0.226437i −0.923960 0.382490i \(-0.875067\pi\)
0.793226 + 0.608927i \(0.208400\pi\)
\(570\) 0 0
\(571\) 17.8011 + 30.8323i 0.744951 + 1.29029i 0.950218 + 0.311587i \(0.100861\pi\)
−0.205266 + 0.978706i \(0.565806\pi\)
\(572\) 0 0
\(573\) 3.71732 + 5.81012i 0.155293 + 0.242721i
\(574\) 0 0
\(575\) 20.7309 0.864539
\(576\) 0 0
\(577\) 23.1388 40.0776i 0.963281 1.66845i 0.249118 0.968473i \(-0.419859\pi\)
0.714164 0.699979i \(-0.246807\pi\)
\(578\) 0 0
\(579\) 11.7324 0.535056i 0.487581 0.0222362i
\(580\) 0 0
\(581\) −17.8976 + 9.74143i −0.742516 + 0.404143i
\(582\) 0 0
\(583\) 2.39037 4.14024i 0.0989990 0.171471i
\(584\) 0 0
\(585\) 4.45924 0.407575i 0.184367 0.0168512i
\(586\) 0 0
\(587\) −1.13161 1.96001i −0.0467066 0.0808982i 0.841727 0.539903i \(-0.181539\pi\)
−0.888434 + 0.459005i \(0.848206\pi\)
\(588\) 0 0
\(589\) −21.1680 + 36.6640i −0.872212 + 1.51072i
\(590\) 0 0
\(591\) −8.81118 + 17.0066i −0.362444 + 0.699558i
\(592\) 0 0
\(593\) 23.0979 + 40.0067i 0.948515 + 1.64288i 0.748555 + 0.663072i \(0.230748\pi\)
0.199960 + 0.979804i \(0.435919\pi\)
\(594\) 0 0
\(595\) −3.91381 2.39285i −0.160451 0.0980974i
\(596\) 0 0
\(597\) −5.24465 8.19731i −0.214649 0.335493i
\(598\) 0 0
\(599\) −8.39037 14.5325i −0.342821 0.593784i 0.642134 0.766592i \(-0.278049\pi\)
−0.984955 + 0.172808i \(0.944716\pi\)
\(600\) 0 0
\(601\) −5.69961 9.87202i −0.232492 0.402688i 0.726049 0.687643i \(-0.241355\pi\)
−0.958541 + 0.284955i \(0.908021\pi\)
\(602\) 0 0
\(603\) −2.40623 + 5.21289i −0.0979891 + 0.212285i
\(604\) 0 0
\(605\) −6.32023 −0.256954
\(606\) 0 0
\(607\) 14.4284 0.585631 0.292815 0.956169i \(-0.405408\pi\)
0.292815 + 0.956169i \(0.405408\pi\)
\(608\) 0 0
\(609\) −0.579664 28.3802i −0.0234892 1.15002i
\(610\) 0 0
\(611\) 15.2915 + 26.4857i 0.618629 + 1.07150i
\(612\) 0 0
\(613\) 12.2053 21.1403i 0.492969 0.853848i −0.506998 0.861947i \(-0.669245\pi\)
0.999967 + 0.00809942i \(0.00257815\pi\)
\(614\) 0 0
\(615\) −0.151457 0.236725i −0.00610733 0.00954566i
\(616\) 0 0
\(617\) 24.4698 42.3830i 0.985119 1.70628i 0.343710 0.939076i \(-0.388316\pi\)
0.641408 0.767200i \(-0.278350\pi\)
\(618\) 0 0
\(619\) 44.6591 1.79500 0.897501 0.441012i \(-0.145380\pi\)
0.897501 + 0.441012i \(0.145380\pi\)
\(620\) 0 0
\(621\) −22.9612 + 3.15897i −0.921400 + 0.126765i
\(622\) 0 0
\(623\) −28.8982 + 15.7290i −1.15778 + 0.630168i
\(624\) 0 0
\(625\) 19.8391 0.793564
\(626\) 0 0
\(627\) 5.52704 0.252061i 0.220729 0.0100663i
\(628\) 0 0
\(629\) 2.92101 0.116468
\(630\) 0 0
\(631\) −33.2852 −1.32506 −0.662532 0.749034i \(-0.730518\pi\)
−0.662532 + 0.749034i \(0.730518\pi\)
\(632\) 0 0
\(633\) −18.0387 28.1942i −0.716974 1.12062i
\(634\) 0 0
\(635\) −7.32158 −0.290548
\(636\) 0 0
\(637\) 9.55641 14.7821i 0.378639 0.585687i
\(638\) 0 0
\(639\) −24.9341 35.3172i −0.986379 1.39713i
\(640\) 0 0
\(641\) 30.7879 1.21605 0.608025 0.793918i \(-0.291962\pi\)
0.608025 + 0.793918i \(0.291962\pi\)
\(642\) 0 0
\(643\) 13.7345 23.7889i 0.541637 0.938142i −0.457174 0.889378i \(-0.651138\pi\)
0.998810 0.0487649i \(-0.0155285\pi\)
\(644\) 0 0
\(645\) −11.4641 + 0.522821i −0.451399 + 0.0205861i
\(646\) 0 0
\(647\) 6.63521 11.4925i 0.260857 0.451818i −0.705613 0.708598i \(-0.749328\pi\)
0.966470 + 0.256780i \(0.0826615\pi\)
\(648\) 0 0
\(649\) 2.56654 + 4.44537i 0.100745 + 0.174496i
\(650\) 0 0
\(651\) −0.736182 36.0433i −0.0288532 1.41265i
\(652\) 0 0
\(653\) −17.1416 −0.670803 −0.335402 0.942075i \(-0.608872\pi\)
−0.335402 + 0.942075i \(0.608872\pi\)
\(654\) 0 0
\(655\) 0.704673 0.0275338
\(656\) 0 0
\(657\) −23.6429 + 2.16096i −0.922397 + 0.0843072i
\(658\) 0 0
\(659\) −4.26089 7.38008i −0.165981 0.287487i 0.771022 0.636808i \(-0.219746\pi\)
−0.937003 + 0.349321i \(0.886412\pi\)
\(660\) 0 0
\(661\) −17.1680 29.7358i −0.667757 1.15659i −0.978530 0.206105i \(-0.933921\pi\)
0.310773 0.950484i \(-0.399412\pi\)
\(662\) 0 0
\(663\) −12.7089 + 0.579592i −0.493575 + 0.0225095i
\(664\) 0 0
\(665\) −7.42315 + 4.04033i −0.287857 + 0.156677i
\(666\) 0 0
\(667\) 13.8150 + 23.9282i 0.534918 + 0.926505i
\(668\) 0 0
\(669\) 43.8178 1.99831i 1.69409 0.0772592i
\(670\) 0 0
\(671\) 1.97296 3.41726i 0.0761652 0.131922i
\(672\) 0 0
\(673\) −7.70155 13.3395i −0.296873 0.514199i 0.678546 0.734558i \(-0.262610\pi\)
−0.975419 + 0.220359i \(0.929277\pi\)
\(674\) 0 0
\(675\) −23.9246 + 3.29152i −0.920859 + 0.126691i
\(676\) 0 0
\(677\) 3.69076 6.39258i 0.141847 0.245687i −0.786345 0.617788i \(-0.788029\pi\)
0.928192 + 0.372101i \(0.121362\pi\)
\(678\) 0 0
\(679\) 27.2675 14.8414i 1.04643 0.569560i
\(680\) 0 0
\(681\) 3.83823 7.40822i 0.147081 0.283884i
\(682\) 0 0
\(683\) −4.79893 + 8.31198i −0.183626 + 0.318049i −0.943113 0.332474i \(-0.892117\pi\)
0.759487 + 0.650523i \(0.225450\pi\)
\(684\) 0 0
\(685\) 1.49688 0.0571929
\(686\) 0 0
\(687\) 7.40642 14.2953i 0.282573 0.545398i
\(688\) 0 0
\(689\) 10.1264 + 17.5394i 0.385783 + 0.668197i
\(690\) 0 0
\(691\) −7.07227 + 12.2495i −0.269042 + 0.465994i −0.968615 0.248567i \(-0.920040\pi\)
0.699573 + 0.714561i \(0.253374\pi\)
\(692\) 0 0
\(693\) −3.91595 + 2.61965i −0.148755 + 0.0995121i
\(694\) 0 0
\(695\) −1.45837 + 2.52597i −0.0553191 + 0.0958155i
\(696\) 0 0
\(697\) 0.399223 + 0.691475i 0.0151217 + 0.0261915i
\(698\) 0 0
\(699\) −0.336285 + 0.0153363i −0.0127195 + 0.000580072i
\(700\) 0 0
\(701\) 37.3753 1.41164 0.705822 0.708389i \(-0.250578\pi\)
0.705822 + 0.708389i \(0.250578\pi\)
\(702\) 0 0
\(703\) 2.69076 4.66053i 0.101484 0.175775i
\(704\) 0 0
\(705\) 6.73891 + 10.5328i 0.253802 + 0.396689i
\(706\) 0 0
\(707\) −0.107974 + 4.29205i −0.00406077 + 0.161419i
\(708\) 0 0
\(709\) 5.24338 9.08180i 0.196919 0.341074i −0.750609 0.660747i \(-0.770240\pi\)
0.947528 + 0.319673i \(0.103573\pi\)
\(710\) 0 0
\(711\) 27.6301 2.52540i 1.03621 0.0947099i
\(712\) 0 0
\(713\) 17.5452 + 30.3892i 0.657074 + 1.13809i
\(714\) 0 0
\(715\) −0.442991 + 0.767282i −0.0165669 + 0.0286947i
\(716\) 0 0
\(717\) 12.7463 + 19.9223i 0.476019 + 0.744011i
\(718\) 0 0
\(719\) −1.11995 1.93981i −0.0417670 0.0723426i 0.844386 0.535735i \(-0.179965\pi\)
−0.886153 + 0.463392i \(0.846632\pi\)
\(720\) 0 0
\(721\) −0.424608 + 16.8786i −0.0158132 + 0.628590i
\(722\) 0 0
\(723\) 10.3583 19.9927i 0.385228 0.743535i
\(724\) 0 0
\(725\) 14.3946 + 24.9322i 0.534604 + 0.925961i
\(726\) 0 0
\(727\) −0.185023 0.320469i −0.00686211 0.0118855i 0.862574 0.505931i \(-0.168851\pi\)
−0.869436 + 0.494045i \(0.835518\pi\)
\(728\) 0 0
\(729\) 25.9969 7.29124i 0.962847 0.270046i
\(730\) 0 0
\(731\) 32.6050 1.20594
\(732\) 0 0
\(733\) 14.0191 0.517806 0.258903 0.965903i \(-0.416639\pi\)
0.258903 + 0.965903i \(0.416639\pi\)
\(734\) 0 0
\(735\) 3.62782 6.21550i 0.133814 0.229262i
\(736\) 0 0
\(737\) −0.568000 0.983804i −0.0209225 0.0362389i
\(738\) 0 0
\(739\) −13.3872 + 23.1874i −0.492458 + 0.852962i −0.999962 0.00868705i \(-0.997235\pi\)
0.507504 + 0.861649i \(0.330568\pi\)
\(740\) 0 0
\(741\) −10.7824 + 20.8113i −0.396101 + 0.764521i
\(742\) 0 0
\(743\) 5.04669 8.74113i 0.185145 0.320681i −0.758480 0.651696i \(-0.774058\pi\)
0.943625 + 0.331015i \(0.107391\pi\)
\(744\) 0 0
\(745\) 10.7148 0.392560
\(746\) 0 0
\(747\) −9.68337 + 20.9782i −0.354296 + 0.767552i
\(748\) 0 0
\(749\) −43.4764 + 23.6637i −1.58859 + 0.864653i
\(750\) 0 0
\(751\) −11.5146 −0.420173 −0.210087 0.977683i \(-0.567375\pi\)
−0.210087 + 0.977683i \(0.567375\pi\)
\(752\) 0 0
\(753\) −15.5723 + 30.0563i −0.567485 + 1.09531i
\(754\) 0 0
\(755\) −0.978019 −0.0355938
\(756\) 0 0
\(757\) −15.2484 −0.554214 −0.277107 0.960839i \(-0.589376\pi\)
−0.277107 + 0.960839i \(0.589376\pi\)
\(758\) 0 0
\(759\) 2.10963 4.07183i 0.0765748 0.147798i
\(760\) 0 0
\(761\) −1.70175 −0.0616883 −0.0308442 0.999524i \(-0.509820\pi\)
−0.0308442 + 0.999524i \(0.509820\pi\)
\(762\) 0 0
\(763\) 6.47150 + 3.95659i 0.234284 + 0.143238i
\(764\) 0 0
\(765\) −5.17996 + 0.473449i −0.187282 + 0.0171176i
\(766\) 0 0
\(767\) −21.7453 −0.785178
\(768\) 0 0
\(769\) 24.1211 41.7790i 0.869829 1.50659i 0.00765823 0.999971i \(-0.497562\pi\)
0.862171 0.506618i \(-0.169104\pi\)
\(770\) 0 0
\(771\) −6.63521 + 12.8067i −0.238961 + 0.461223i
\(772\) 0 0
\(773\) 3.10243 5.37357i 0.111587 0.193274i −0.804823 0.593514i \(-0.797740\pi\)
0.916410 + 0.400240i \(0.131073\pi\)
\(774\) 0 0
\(775\) 18.2814 + 31.6643i 0.656688 + 1.13742i
\(776\) 0 0
\(777\) 0.0935793 + 4.58162i 0.00335714 + 0.164365i
\(778\) 0 0
\(779\) 1.47102 0.0527046
\(780\) 0 0
\(781\) 8.55389 0.306082
\(782\) 0 0
\(783\) −19.7424 25.4210i −0.705536 0.908474i
\(784\) 0 0
\(785\) 1.95904 + 3.39316i 0.0699212 + 0.121107i
\(786\) 0 0
\(787\) 3.04883 + 5.28073i 0.108679 + 0.188238i 0.915235 0.402920i \(-0.132005\pi\)
−0.806556 + 0.591157i \(0.798671\pi\)
\(788\) 0 0
\(789\) −13.6175 + 26.2834i −0.484796 + 0.935712i
\(790\) 0 0
\(791\) 27.8104 + 17.0029i 0.988824 + 0.604554i
\(792\) 0 0
\(793\) 8.35807 + 14.4766i 0.296804 + 0.514079i
\(794\) 0 0
\(795\) 4.46264 + 6.97504i 0.158274 + 0.247379i
\(796\) 0 0
\(797\) −6.22860 + 10.7882i −0.220628 + 0.382139i −0.954999 0.296609i \(-0.904144\pi\)
0.734371 + 0.678749i \(0.237477\pi\)
\(798\) 0 0
\(799\) −17.7630 30.7665i −0.628411 1.08844i
\(800\) 0 0
\(801\) −15.6352 + 33.8724i −0.552443 + 1.19682i
\(802\) 0 0
\(803\) 2.34874 4.06813i 0.0828852 0.143561i
\(804\) 0 0
\(805\) −0.176168 + 7.00284i −0.00620911 + 0.246818i
\(806\) 0 0
\(807\) −9.34806 14.6109i −0.329067 0.514328i
\(808\) 0 0
\(809\) −2.81644 + 4.87822i −0.0990208 + 0.171509i −0.911280 0.411788i \(-0.864904\pi\)
0.812259 + 0.583297i \(0.198238\pi\)
\(810\) 0 0
\(811\) 45.6414 1.60269 0.801344 0.598204i \(-0.204119\pi\)
0.801344 + 0.598204i \(0.204119\pi\)
\(812\) 0 0
\(813\) 17.6644 0.805585i 0.619517 0.0282531i
\(814\) 0 0
\(815\) 1.77548 + 3.07523i 0.0621924 + 0.107720i
\(816\) 0 0
\(817\) 30.0349 52.0220i 1.05079 1.82002i
\(818\) 0 0
\(819\) −1.31625 19.9155i −0.0459933 0.695903i
\(820\) 0 0
\(821\) −16.3473 + 28.3143i −0.570524 + 0.988176i 0.425988 + 0.904729i \(0.359926\pi\)
−0.996512 + 0.0834476i \(0.973407\pi\)
\(822\) 0 0
\(823\) −5.21994 9.04119i −0.181956 0.315156i 0.760591 0.649231i \(-0.224909\pi\)
−0.942546 + 0.334075i \(0.891576\pi\)
\(824\) 0 0
\(825\) 2.19815 4.24268i 0.0765297 0.147711i
\(826\) 0 0
\(827\) −16.7060 −0.580925 −0.290463 0.956886i \(-0.593809\pi\)
−0.290463 + 0.956886i \(0.593809\pi\)
\(828\) 0 0
\(829\) −13.1046 + 22.6978i −0.455141 + 0.788327i −0.998696 0.0510466i \(-0.983744\pi\)
0.543556 + 0.839373i \(0.317078\pi\)
\(830\) 0 0
\(831\) −15.4117 + 29.7463i −0.534625 + 1.03189i
\(832\) 0 0
\(833\) −11.1010 + 17.1712i −0.384626 + 0.594948i
\(834\) 0 0
\(835\) −2.21420 + 3.83511i −0.0766256 + 0.132719i
\(836\) 0 0
\(837\) −25.0731 32.2851i −0.866655 1.11594i
\(838\) 0 0
\(839\) −11.1886 19.3793i −0.386274 0.669046i 0.605671 0.795715i \(-0.292905\pi\)
−0.991945 + 0.126669i \(0.959571\pi\)
\(840\) 0 0
\(841\) −4.68502 + 8.11470i −0.161553 + 0.279817i
\(842\) 0 0
\(843\) 22.1519 1.01024i 0.762953 0.0347945i
\(844\) 0 0
\(845\) 1.98162 + 3.43226i 0.0681697 + 0.118073i
\(846\) 0 0
\(847\) −0.708466 + 28.1622i −0.0243432 + 0.967663i
\(848\) 0 0
\(849\) 28.2937 1.29033i 0.971036 0.0442842i
\(850\) 0 0
\(851\) −2.23025 3.86291i −0.0764521 0.132419i
\(852\) 0 0
\(853\) 4.96264 + 8.59555i 0.169918 + 0.294306i 0.938391 0.345576i \(-0.112317\pi\)
−0.768473 + 0.639882i \(0.778983\pi\)
\(854\) 0 0
\(855\) −4.01625 + 8.70086i −0.137353 + 0.297563i
\(856\) 0 0
\(857\) 7.79552 0.266290 0.133145 0.991097i \(-0.457492\pi\)
0.133145 + 0.991097i \(0.457492\pi\)
\(858\) 0 0
\(859\) −16.3422 −0.557589 −0.278795 0.960351i \(-0.589935\pi\)
−0.278795 + 0.960351i \(0.589935\pi\)
\(860\) 0 0
\(861\) −1.07179 + 0.648337i −0.0365266 + 0.0220953i
\(862\) 0 0
\(863\) −0.730252 1.26483i −0.0248581 0.0430555i 0.853329 0.521373i \(-0.174580\pi\)
−0.878187 + 0.478318i \(0.841247\pi\)
\(864\) 0 0
\(865\) 7.61537 13.1902i 0.258930 0.448480i
\(866\) 0 0
\(867\) −14.6513 + 0.668172i −0.497583 + 0.0226923i
\(868\) 0 0
\(869\) −2.74484 + 4.75420i −0.0931124 + 0.161275i
\(870\) 0 0
\(871\) 4.81245 0.163064
\(872\) 0 0
\(873\) 14.7529 31.9609i 0.499310 1.08171i
\(874\) 0 0
\(875\) −0.381036 + 15.1465i −0.0128814 + 0.512045i
\(876\) 0 0
\(877\) −2.40935 −0.0813578 −0.0406789 0.999172i \(-0.512952\pi\)
−0.0406789 + 0.999172i \(0.512952\pi\)
\(878\) 0 0
\(879\) −19.3953 30.3146i −0.654188 1.02249i
\(880\) 0 0
\(881\) −18.9607 −0.638802 −0.319401 0.947620i \(-0.603482\pi\)
−0.319401 + 0.947620i \(0.603482\pi\)
\(882\) 0 0
\(883\) −3.64008 −0.122498 −0.0612492 0.998123i \(-0.519508\pi\)
−0.0612492 + 0.998123i \(0.519508\pi\)
\(884\) 0 0
\(885\) −8.88151 + 0.405042i −0.298549 + 0.0136153i
\(886\) 0 0
\(887\) 24.4572 0.821192 0.410596 0.911817i \(-0.365321\pi\)
0.410596 + 0.911817i \(0.365321\pi\)
\(888\) 0 0
\(889\) −0.820712 + 32.6240i −0.0275258 + 1.09418i
\(890\) 0 0
\(891\) −1.78813 + 5.03407i −0.0599046 + 0.168648i
\(892\) 0 0
\(893\) −65.4513 −2.19025
\(894\) 0 0
\(895\) −4.46264 + 7.72952i −0.149170 + 0.258369i
\(896\) 0 0
\(897\) 10.4700 + 16.3645i 0.349584 + 0.546395i
\(898\) 0 0
\(899\) −24.3653 + 42.2019i −0.812627 + 1.40751i
\(900\) 0 0
\(901\) −11.7630 20.3742i −0.391883 0.678762i
\(902\) 0 0
\(903\) 1.04456 + 51.1412i 0.0347607 + 1.70187i
\(904\) 0 0
\(905\) −0.0511591 −0.00170059
\(906\) 0 0
\(907\) −10.0368 −0.333265 −0.166633 0.986019i \(-0.553289\pi\)
−0.166633 + 0.986019i \(0.553289\pi\)
\(908\) 0 0
\(909\) 2.80778 + 3.97699i 0.0931282 + 0.131908i
\(910\) 0 0
\(911\) −11.4459 19.8249i −0.379220 0.656828i 0.611729 0.791067i \(-0.290474\pi\)
−0.990949 + 0.134239i \(0.957141\pi\)
\(912\) 0 0
\(913\) −2.28580 3.95912i −0.0756489 0.131028i
\(914\) 0 0
\(915\) 3.68337 + 5.75705i 0.121768 + 0.190322i
\(916\) 0 0
\(917\) 0.0789903 3.13993i 0.00260849 0.103690i
\(918\) 0 0
\(919\) −10.8910 18.8638i −0.359262 0.622261i 0.628575 0.777749i \(-0.283638\pi\)
−0.987838 + 0.155488i \(0.950305\pi\)
\(920\) 0 0
\(921\) −18.0687 + 34.8746i −0.595383 + 1.14916i
\(922\) 0 0
\(923\) −18.1185 + 31.3821i −0.596377 + 1.03296i
\(924\) 0 0
\(925\) −2.32383 4.02499i −0.0764071 0.132341i
\(926\) 0 0
\(927\) 11.0416 + 15.6396i 0.362655 + 0.513671i
\(928\) 0 0
\(929\) 16.4189 28.4383i 0.538686 0.933031i −0.460289 0.887769i \(-0.652254\pi\)
0.998975 0.0452622i \(-0.0144123\pi\)
\(930\) 0 0
\(931\) 17.1711 + 33.5295i 0.562760 + 1.09888i
\(932\) 0 0
\(933\) 11.2719 0.514055i 0.369025 0.0168294i
\(934\) 0 0
\(935\) 0.514589 0.891294i 0.0168289 0.0291484i
\(936\) 0 0
\(937\) −8.78074 −0.286854 −0.143427 0.989661i \(-0.545812\pi\)
−0.143427 + 0.989661i \(0.545812\pi\)
\(938\) 0 0
\(939\) −0.248440 0.388308i −0.00810754 0.0126720i
\(940\) 0 0
\(941\) −2.13307 3.69459i −0.0695362 0.120440i 0.829161 0.559010i \(-0.188819\pi\)
−0.898697 + 0.438570i \(0.855485\pi\)
\(942\) 0 0
\(943\) 0.609631 1.05591i 0.0198523 0.0343852i
\(944\) 0 0
\(945\) −0.908557 8.10963i −0.0295554 0.263806i
\(946\) 0 0
\(947\) −11.5292 + 19.9691i −0.374648 + 0.648909i −0.990274 0.139129i \(-0.955570\pi\)
0.615626 + 0.788038i \(0.288903\pi\)
\(948\) 0 0
\(949\) 9.94999 + 17.2339i 0.322990 + 0.559436i
\(950\) 0 0
\(951\) −14.6775 22.9407i −0.475951 0.743904i
\(952\) 0 0
\(953\) −36.5552 −1.18414 −0.592070 0.805886i \(-0.701689\pi\)
−0.592070 + 0.805886i \(0.701689\pi\)
\(954\) 0 0
\(955\) 1.18190 2.04712i 0.0382455 0.0662431i
\(956\) 0 0
\(957\) 6.36186 0.290133i 0.205650 0.00937867i
\(958\) 0 0
\(959\) 0.167793 6.66991i 0.00541831 0.215383i
\(960\) 0 0
\(961\) −15.4443 + 26.7502i −0.498202 + 0.862911i
\(962\) 0 0
\(963\) −23.5227 + 50.9599i −0.758007 + 1.64216i
\(964\) 0 0
\(965\) −2.01245 3.48567i −0.0647832 0.112208i
\(966\) 0 0
\(967\) −26.7719 + 46.3703i −0.860926 + 1.49117i 0.0101108 + 0.999949i \(0.496782\pi\)
−0.871037 + 0.491218i \(0.836552\pi\)
\(968\) 0 0
\(969\) 12.5251 24.1749i 0.402364 0.776610i
\(970\) 0 0
\(971\) 15.9897 + 27.6949i 0.513133 + 0.888773i 0.999884 + 0.0152321i \(0.00484870\pi\)
−0.486751 + 0.873541i \(0.661818\pi\)
\(972\) 0 0
\(973\) 11.0919 + 6.78146i 0.355591 + 0.217403i
\(974\) 0 0
\(975\) 10.9093 + 17.0511i 0.349379 + 0.546074i
\(976\) 0 0
\(977\) 13.7104 + 23.7471i 0.438635 + 0.759738i 0.997584 0.0694638i \(-0.0221288\pi\)
−0.558950 + 0.829202i \(0.688796\pi\)
\(978\) 0 0
\(979\) −3.69076 6.39258i −0.117957 0.204308i
\(980\) 0 0
\(981\) 8.56507 0.782849i 0.273462 0.0249945i
\(982\) 0 0
\(983\) 59.1564 1.88680 0.943398 0.331662i \(-0.107610\pi\)
0.943398 + 0.331662i \(0.107610\pi\)
\(984\) 0 0
\(985\) 6.56401 0.209147
\(986\) 0 0
\(987\) 47.6883 28.8471i 1.51794 0.918212i
\(988\) 0 0
\(989\) −24.8946 43.1188i −0.791604 1.37110i
\(990\) 0 0
\(991\) −6.41887 + 11.1178i −0.203902 + 0.353169i −0.949782 0.312911i \(-0.898696\pi\)
0.745880 + 0.666080i \(0.232029\pi\)
\(992\) 0 0
\(993\) −23.4880 36.7114i −0.745370 1.16500i
\(994\) 0 0
\(995\) −1.66751 + 2.88821i −0.0528636 + 0.0915624i
\(996\) 0 0
\(997\) −5.78074 −0.183078 −0.0915389 0.995802i \(-0.529179\pi\)
−0.0915389 + 0.995802i \(0.529179\pi\)
\(998\) 0 0
\(999\) 3.18716 + 4.10390i 0.100837 + 0.129842i
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 1008.2.t.h.193.2 6
3.2 odd 2 3024.2.t.h.1873.2 6
4.3 odd 2 126.2.h.d.67.2 yes 6
7.2 even 3 1008.2.q.g.625.2 6
9.2 odd 6 3024.2.q.g.2881.2 6
9.7 even 3 1008.2.q.g.529.2 6
12.11 even 2 378.2.h.c.361.2 6
21.2 odd 6 3024.2.q.g.2305.2 6
28.3 even 6 882.2.f.o.589.3 6
28.11 odd 6 882.2.f.n.589.1 6
28.19 even 6 882.2.e.o.373.2 6
28.23 odd 6 126.2.e.c.121.2 yes 6
28.27 even 2 882.2.h.p.67.2 6
36.7 odd 6 126.2.e.c.25.2 6
36.11 even 6 378.2.e.d.235.2 6
36.23 even 6 1134.2.g.l.487.2 6
36.31 odd 6 1134.2.g.m.487.2 6
63.2 odd 6 3024.2.t.h.289.2 6
63.16 even 3 inner 1008.2.t.h.961.2 6
84.11 even 6 2646.2.f.l.1765.2 6
84.23 even 6 378.2.e.d.37.2 6
84.47 odd 6 2646.2.e.p.1549.2 6
84.59 odd 6 2646.2.f.m.1765.2 6
84.83 odd 2 2646.2.h.o.361.2 6
252.11 even 6 2646.2.f.l.883.2 6
252.23 even 6 1134.2.g.l.163.2 6
252.31 even 6 7938.2.a.bw.1.2 3
252.47 odd 6 2646.2.h.o.667.2 6
252.59 odd 6 7938.2.a.bz.1.2 3
252.67 odd 6 7938.2.a.bv.1.2 3
252.79 odd 6 126.2.h.d.79.2 yes 6
252.83 odd 6 2646.2.e.p.2125.2 6
252.95 even 6 7938.2.a.ca.1.2 3
252.115 even 6 882.2.f.o.295.3 6
252.151 odd 6 882.2.f.n.295.1 6
252.187 even 6 882.2.h.p.79.2 6
252.191 even 6 378.2.h.c.289.2 6
252.223 even 6 882.2.e.o.655.2 6
252.227 odd 6 2646.2.f.m.883.2 6
252.247 odd 6 1134.2.g.m.163.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.2 6 36.7 odd 6
126.2.e.c.121.2 yes 6 28.23 odd 6
126.2.h.d.67.2 yes 6 4.3 odd 2
126.2.h.d.79.2 yes 6 252.79 odd 6
378.2.e.d.37.2 6 84.23 even 6
378.2.e.d.235.2 6 36.11 even 6
378.2.h.c.289.2 6 252.191 even 6
378.2.h.c.361.2 6 12.11 even 2
882.2.e.o.373.2 6 28.19 even 6
882.2.e.o.655.2 6 252.223 even 6
882.2.f.n.295.1 6 252.151 odd 6
882.2.f.n.589.1 6 28.11 odd 6
882.2.f.o.295.3 6 252.115 even 6
882.2.f.o.589.3 6 28.3 even 6
882.2.h.p.67.2 6 28.27 even 2
882.2.h.p.79.2 6 252.187 even 6
1008.2.q.g.529.2 6 9.7 even 3
1008.2.q.g.625.2 6 7.2 even 3
1008.2.t.h.193.2 6 1.1 even 1 trivial
1008.2.t.h.961.2 6 63.16 even 3 inner
1134.2.g.l.163.2 6 252.23 even 6
1134.2.g.l.487.2 6 36.23 even 6
1134.2.g.m.163.2 6 252.247 odd 6
1134.2.g.m.487.2 6 36.31 odd 6
2646.2.e.p.1549.2 6 84.47 odd 6
2646.2.e.p.2125.2 6 252.83 odd 6
2646.2.f.l.883.2 6 252.11 even 6
2646.2.f.l.1765.2 6 84.11 even 6
2646.2.f.m.883.2 6 252.227 odd 6
2646.2.f.m.1765.2 6 84.59 odd 6
2646.2.h.o.361.2 6 84.83 odd 2
2646.2.h.o.667.2 6 252.47 odd 6
3024.2.q.g.2305.2 6 21.2 odd 6
3024.2.q.g.2881.2 6 9.2 odd 6
3024.2.t.h.289.2 6 63.2 odd 6
3024.2.t.h.1873.2 6 3.2 odd 2
7938.2.a.bv.1.2 3 252.67 odd 6
7938.2.a.bw.1.2 3 252.31 even 6
7938.2.a.bz.1.2 3 252.59 odd 6
7938.2.a.ca.1.2 3 252.95 even 6