Properties

Label 504.2.c.f.253.7
Level $504$
Weight $2$
Character 504.253
Analytic conductor $4.024$
Analytic rank $0$
Dimension $8$
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] = [504,2,Mod(253,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.253");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.c (of order \(2\), degree \(1\), 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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.386672896.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 253.7
Root \(1.40961 + 0.114062i\) of defining polynomial
Character \(\chi\) \(=\) 504.253
Dual form 504.2.c.f.253.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40961 - 0.114062i) q^{2} +(1.97398 - 0.321565i) q^{4} +1.12875i q^{5} +1.00000 q^{7} +(2.74586 - 0.678435i) q^{8} +O(q^{10})\) \(q+(1.40961 - 0.114062i) q^{2} +(1.97398 - 0.321565i) q^{4} +1.12875i q^{5} +1.00000 q^{7} +(2.74586 - 0.678435i) q^{8} +(0.128747 + 1.59109i) q^{10} +4.76717i q^{11} +0.456247i q^{13} +(1.40961 - 0.114062i) q^{14} +(3.79319 - 1.26952i) q^{16} -0.415006 q^{17} -7.63843i q^{19} +(0.362965 + 2.22812i) q^{20} +(0.543753 + 6.71984i) q^{22} -1.58499 q^{23} +3.72593 q^{25} +(0.0520404 + 0.643129i) q^{26} +(1.97398 - 0.321565i) q^{28} -6.72593i q^{29} -5.89592 q^{31} +(5.20210 - 2.22219i) q^{32} +(-0.584994 + 0.0473363i) q^{34} +1.12875i q^{35} +5.89592i q^{37} +(-0.871253 - 10.7672i) q^{38} +(0.765782 + 3.09938i) q^{40} +0.415006 q^{41} +9.43967i q^{43} +(1.53295 + 9.41030i) q^{44} +(-2.23422 + 0.180787i) q^{46} -11.2769 q^{47} +1.00000 q^{49} +(5.25209 - 0.424987i) q^{50} +(0.146713 + 0.900623i) q^{52} -7.63843i q^{53} -5.38093 q^{55} +(2.74586 - 0.678435i) q^{56} +(-0.767172 - 9.48091i) q^{58} -4.00000i q^{59} -1.80125i q^{61} +(-8.31092 + 0.672500i) q^{62} +(7.07945 - 3.72577i) q^{64} -0.514988 q^{65} -8.09467i q^{67} +(-0.819213 + 0.133451i) q^{68} +(0.128747 + 1.59109i) q^{70} -10.2068 q^{71} -3.34500 q^{73} +(0.672500 + 8.31092i) q^{74} +(-2.45625 - 15.0781i) q^{76} +4.76717i q^{77} -4.83001 q^{79} +(1.43297 + 4.28155i) q^{80} +(0.584994 - 0.0473363i) q^{82} -5.53434i q^{83} -0.468436i q^{85} +(1.07671 + 13.3062i) q^{86} +(3.23422 + 13.0900i) q^{88} -4.92999 q^{89} +0.456247i q^{91} +(-3.12875 + 0.509678i) q^{92} +(-15.8959 + 1.28626i) q^{94} +8.62185 q^{95} +16.4468 q^{97} +(1.40961 - 0.114062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8} - 4 q^{10} - 6 q^{16} - 4 q^{17} - 24 q^{20} - 12 q^{23} - 24 q^{25} + 28 q^{26} + 2 q^{28} + 8 q^{31} + 30 q^{32} - 4 q^{34} - 12 q^{38} + 28 q^{40} + 4 q^{41} - 16 q^{44} + 4 q^{46} + 8 q^{49} + 20 q^{50} - 12 q^{52} - 8 q^{55} + 6 q^{56} + 44 q^{58} - 12 q^{62} + 26 q^{64} + 16 q^{65} + 16 q^{68} - 4 q^{70} + 28 q^{71} - 8 q^{73} - 4 q^{74} - 24 q^{76} - 40 q^{79} + 4 q^{80} + 4 q^{82} - 24 q^{86} + 4 q^{88} - 20 q^{89} - 20 q^{92} - 72 q^{94} - 40 q^{95} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40961 0.114062i 0.996742 0.0806539i
\(3\) 0 0
\(4\) 1.97398 0.321565i 0.986990 0.160782i
\(5\) 1.12875i 0.504791i 0.967624 + 0.252395i \(0.0812184\pi\)
−0.967624 + 0.252395i \(0.918782\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.74586 0.678435i 0.970807 0.239863i
\(9\) 0 0
\(10\) 0.128747 + 1.59109i 0.0407134 + 0.503146i
\(11\) 4.76717i 1.43736i 0.695343 + 0.718678i \(0.255253\pi\)
−0.695343 + 0.718678i \(0.744747\pi\)
\(12\) 0 0
\(13\) 0.456247i 0.126540i 0.997996 + 0.0632701i \(0.0201530\pi\)
−0.997996 + 0.0632701i \(0.979847\pi\)
\(14\) 1.40961 0.114062i 0.376733 0.0304843i
\(15\) 0 0
\(16\) 3.79319 1.26952i 0.948298 0.317381i
\(17\) −0.415006 −0.100654 −0.0503268 0.998733i \(-0.516026\pi\)
−0.0503268 + 0.998733i \(0.516026\pi\)
\(18\) 0 0
\(19\) 7.63843i 1.75237i −0.481970 0.876187i \(-0.660079\pi\)
0.481970 0.876187i \(-0.339921\pi\)
\(20\) 0.362965 + 2.22812i 0.0811615 + 0.498224i
\(21\) 0 0
\(22\) 0.543753 + 6.71984i 0.115928 + 1.43267i
\(23\) −1.58499 −0.330494 −0.165247 0.986252i \(-0.552842\pi\)
−0.165247 + 0.986252i \(0.552842\pi\)
\(24\) 0 0
\(25\) 3.72593 0.745186
\(26\) 0.0520404 + 0.643129i 0.0102060 + 0.126128i
\(27\) 0 0
\(28\) 1.97398 0.321565i 0.373047 0.0607700i
\(29\) 6.72593i 1.24897i −0.781035 0.624487i \(-0.785308\pi\)
0.781035 0.624487i \(-0.214692\pi\)
\(30\) 0 0
\(31\) −5.89592 −1.05894 −0.529469 0.848329i \(-0.677609\pi\)
−0.529469 + 0.848329i \(0.677609\pi\)
\(32\) 5.20210 2.22219i 0.919611 0.392831i
\(33\) 0 0
\(34\) −0.584994 + 0.0473363i −0.100326 + 0.00811811i
\(35\) 1.12875i 0.190793i
\(36\) 0 0
\(37\) 5.89592i 0.969283i 0.874713 + 0.484642i \(0.161050\pi\)
−0.874713 + 0.484642i \(0.838950\pi\)
\(38\) −0.871253 10.7672i −0.141336 1.74667i
\(39\) 0 0
\(40\) 0.765782 + 3.09938i 0.121081 + 0.490054i
\(41\) 0.415006 0.0648130 0.0324065 0.999475i \(-0.489683\pi\)
0.0324065 + 0.999475i \(0.489683\pi\)
\(42\) 0 0
\(43\) 9.43967i 1.43954i 0.694214 + 0.719768i \(0.255752\pi\)
−0.694214 + 0.719768i \(0.744248\pi\)
\(44\) 1.53295 + 9.41030i 0.231102 + 1.41866i
\(45\) 0 0
\(46\) −2.23422 + 0.180787i −0.329417 + 0.0266557i
\(47\) −11.2769 −1.64490 −0.822449 0.568839i \(-0.807393\pi\)
−0.822449 + 0.568839i \(0.807393\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 5.25209 0.424987i 0.742758 0.0601022i
\(51\) 0 0
\(52\) 0.146713 + 0.900623i 0.0203454 + 0.124894i
\(53\) 7.63843i 1.04922i −0.851343 0.524609i \(-0.824211\pi\)
0.851343 0.524609i \(-0.175789\pi\)
\(54\) 0 0
\(55\) −5.38093 −0.725565
\(56\) 2.74586 0.678435i 0.366930 0.0906597i
\(57\) 0 0
\(58\) −0.767172 9.48091i −0.100735 1.24490i
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) 0 0
\(61\) 1.80125i 0.230626i −0.993329 0.115313i \(-0.963213\pi\)
0.993329 0.115313i \(-0.0367871\pi\)
\(62\) −8.31092 + 0.672500i −1.05549 + 0.0854075i
\(63\) 0 0
\(64\) 7.07945 3.72577i 0.884931 0.465721i
\(65\) −0.514988 −0.0638764
\(66\) 0 0
\(67\) 8.09467i 0.988922i −0.869200 0.494461i \(-0.835366\pi\)
0.869200 0.494461i \(-0.164634\pi\)
\(68\) −0.819213 + 0.133451i −0.0993441 + 0.0161833i
\(69\) 0 0
\(70\) 0.128747 + 1.59109i 0.0153882 + 0.190171i
\(71\) −10.2068 −1.21133 −0.605665 0.795720i \(-0.707093\pi\)
−0.605665 + 0.795720i \(0.707093\pi\)
\(72\) 0 0
\(73\) −3.34500 −0.391503 −0.195751 0.980654i \(-0.562715\pi\)
−0.195751 + 0.980654i \(0.562715\pi\)
\(74\) 0.672500 + 8.31092i 0.0781765 + 0.966125i
\(75\) 0 0
\(76\) −2.45625 15.0781i −0.281751 1.72958i
\(77\) 4.76717i 0.543270i
\(78\) 0 0
\(79\) −4.83001 −0.543419 −0.271709 0.962379i \(-0.587589\pi\)
−0.271709 + 0.962379i \(0.587589\pi\)
\(80\) 1.43297 + 4.28155i 0.160211 + 0.478692i
\(81\) 0 0
\(82\) 0.584994 0.0473363i 0.0646018 0.00522742i
\(83\) 5.53434i 0.607473i −0.952756 0.303737i \(-0.901766\pi\)
0.952756 0.303737i \(-0.0982343\pi\)
\(84\) 0 0
\(85\) 0.468436i 0.0508090i
\(86\) 1.07671 + 13.3062i 0.116104 + 1.43485i
\(87\) 0 0
\(88\) 3.23422 + 13.0900i 0.344769 + 1.39540i
\(89\) −4.92999 −0.522578 −0.261289 0.965261i \(-0.584148\pi\)
−0.261289 + 0.965261i \(0.584148\pi\)
\(90\) 0 0
\(91\) 0.456247i 0.0478277i
\(92\) −3.12875 + 0.509678i −0.326194 + 0.0531376i
\(93\) 0 0
\(94\) −15.8959 + 1.28626i −1.63954 + 0.132667i
\(95\) 8.62185 0.884583
\(96\) 0 0
\(97\) 16.4468 1.66992 0.834962 0.550308i \(-0.185490\pi\)
0.834962 + 0.550308i \(0.185490\pi\)
\(98\) 1.40961 0.114062i 0.142392 0.0115220i
\(99\) 0 0
\(100\) 7.35491 1.19813i 0.735491 0.119813i
\(101\) 16.4056i 1.63242i 0.577757 + 0.816209i \(0.303928\pi\)
−0.577757 + 0.816209i \(0.696072\pi\)
\(102\) 0 0
\(103\) −17.1728 −1.69208 −0.846042 0.533117i \(-0.821021\pi\)
−0.846042 + 0.533117i \(0.821021\pi\)
\(104\) 0.309534 + 1.25279i 0.0303523 + 0.122846i
\(105\) 0 0
\(106\) −0.871253 10.7672i −0.0846236 1.04580i
\(107\) 12.7672i 1.23425i −0.786865 0.617125i \(-0.788297\pi\)
0.786865 0.617125i \(-0.211703\pi\)
\(108\) 0 0
\(109\) 7.27685i 0.696996i 0.937310 + 0.348498i \(0.113308\pi\)
−0.937310 + 0.348498i \(0.886692\pi\)
\(110\) −7.58499 + 0.613759i −0.723201 + 0.0585196i
\(111\) 0 0
\(112\) 3.79319 1.26952i 0.358423 0.119959i
\(113\) 3.34500 0.314671 0.157336 0.987545i \(-0.449710\pi\)
0.157336 + 0.987545i \(0.449710\pi\)
\(114\) 0 0
\(115\) 1.78906i 0.166830i
\(116\) −2.16282 13.2769i −0.200813 1.23272i
\(117\) 0 0
\(118\) −0.456247 5.63843i −0.0420010 0.519059i
\(119\) −0.415006 −0.0380435
\(120\) 0 0
\(121\) −11.7259 −1.06599
\(122\) −0.205454 2.53905i −0.0186009 0.229875i
\(123\) 0 0
\(124\) −11.6384 + 1.89592i −1.04516 + 0.170259i
\(125\) 9.84937i 0.880954i
\(126\) 0 0
\(127\) −10.4468 −0.927007 −0.463504 0.886095i \(-0.653408\pi\)
−0.463504 + 0.886095i \(0.653408\pi\)
\(128\) 9.55427 6.05937i 0.844486 0.535577i
\(129\) 0 0
\(130\) −0.725930 + 0.0587405i −0.0636683 + 0.00515188i
\(131\) 6.25749i 0.546720i 0.961912 + 0.273360i \(0.0881350\pi\)
−0.961912 + 0.273360i \(0.911865\pi\)
\(132\) 0 0
\(133\) 7.63843i 0.662335i
\(134\) −0.923293 11.4103i −0.0797604 0.985700i
\(135\) 0 0
\(136\) −1.13955 + 0.281554i −0.0977152 + 0.0241431i
\(137\) 12.9618 1.10740 0.553702 0.832715i \(-0.313215\pi\)
0.553702 + 0.832715i \(0.313215\pi\)
\(138\) 0 0
\(139\) 18.3644i 1.55764i 0.627245 + 0.778822i \(0.284183\pi\)
−0.627245 + 0.778822i \(0.715817\pi\)
\(140\) 0.362965 + 2.22812i 0.0306762 + 0.188311i
\(141\) 0 0
\(142\) −14.3876 + 1.16421i −1.20738 + 0.0976985i
\(143\) −2.17501 −0.181883
\(144\) 0 0
\(145\) 7.59187 0.630471
\(146\) −4.71513 + 0.381537i −0.390227 + 0.0315762i
\(147\) 0 0
\(148\) 1.89592 + 11.6384i 0.155844 + 0.956673i
\(149\) 15.6384i 1.28115i −0.767896 0.640575i \(-0.778696\pi\)
0.767896 0.640575i \(-0.221304\pi\)
\(150\) 0 0
\(151\) 15.2769 1.24321 0.621606 0.783330i \(-0.286480\pi\)
0.621606 + 0.783330i \(0.286480\pi\)
\(152\) −5.18218 20.9740i −0.420330 1.70122i
\(153\) 0 0
\(154\) 0.543753 + 6.71984i 0.0438168 + 0.541500i
\(155\) 6.65500i 0.534543i
\(156\) 0 0
\(157\) 21.7824i 1.73843i −0.494437 0.869214i \(-0.664626\pi\)
0.494437 0.869214i \(-0.335374\pi\)
\(158\) −6.80841 + 0.550920i −0.541648 + 0.0438288i
\(159\) 0 0
\(160\) 2.50829 + 5.87186i 0.198298 + 0.464211i
\(161\) −1.58499 −0.124915
\(162\) 0 0
\(163\) 4.60966i 0.361056i 0.983570 + 0.180528i \(0.0577807\pi\)
−0.983570 + 0.180528i \(0.942219\pi\)
\(164\) 0.819213 0.133451i 0.0639698 0.0104208i
\(165\) 0 0
\(166\) −0.631258 7.80125i −0.0489951 0.605494i
\(167\) 22.9618 1.77684 0.888420 0.459032i \(-0.151804\pi\)
0.888420 + 0.459032i \(0.151804\pi\)
\(168\) 0 0
\(169\) 12.7918 0.983988
\(170\) −0.0534307 0.660311i −0.00409795 0.0506435i
\(171\) 0 0
\(172\) 3.03546 + 18.6337i 0.231452 + 1.42081i
\(173\) 0.216252i 0.0164413i −0.999966 0.00822067i \(-0.997383\pi\)
0.999966 0.00822067i \(-0.00261675\pi\)
\(174\) 0 0
\(175\) 3.72593 0.281654
\(176\) 6.05204 + 18.0828i 0.456190 + 1.36304i
\(177\) 0 0
\(178\) −6.94935 + 0.562324i −0.520876 + 0.0421480i
\(179\) 22.6165i 1.69044i 0.534419 + 0.845220i \(0.320530\pi\)
−0.534419 + 0.845220i \(0.679470\pi\)
\(180\) 0 0
\(181\) 7.73310i 0.574797i −0.957811 0.287398i \(-0.907210\pi\)
0.957811 0.287398i \(-0.0927903\pi\)
\(182\) 0.0520404 + 0.643129i 0.00385749 + 0.0476719i
\(183\) 0 0
\(184\) −4.35217 + 1.07532i −0.320846 + 0.0792734i
\(185\) −6.65500 −0.489285
\(186\) 0 0
\(187\) 1.97840i 0.144675i
\(188\) −22.2603 + 3.62624i −1.62350 + 0.264470i
\(189\) 0 0
\(190\) 12.1534 0.983424i 0.881701 0.0713451i
\(191\) −10.2068 −0.738541 −0.369271 0.929322i \(-0.620392\pi\)
−0.369271 + 0.929322i \(0.620392\pi\)
\(192\) 0 0
\(193\) 5.96407 0.429303 0.214651 0.976691i \(-0.431138\pi\)
0.214651 + 0.976691i \(0.431138\pi\)
\(194\) 23.1836 1.87596i 1.66448 0.134686i
\(195\) 0 0
\(196\) 1.97398 0.321565i 0.140999 0.0229689i
\(197\) 18.8084i 1.34004i 0.742341 + 0.670022i \(0.233715\pi\)
−0.742341 + 0.670022i \(0.766285\pi\)
\(198\) 0 0
\(199\) 3.27685 0.232290 0.116145 0.993232i \(-0.462946\pi\)
0.116145 + 0.993232i \(0.462946\pi\)
\(200\) 10.2309 2.52780i 0.723432 0.178743i
\(201\) 0 0
\(202\) 1.87125 + 23.1254i 0.131661 + 1.62710i
\(203\) 6.72593i 0.472068i
\(204\) 0 0
\(205\) 0.468436i 0.0327170i
\(206\) −24.2068 + 1.95876i −1.68657 + 0.136473i
\(207\) 0 0
\(208\) 0.579217 + 1.73063i 0.0401615 + 0.119998i
\(209\) 36.4137 2.51879
\(210\) 0 0
\(211\) 10.1628i 0.699637i −0.936817 0.349819i \(-0.886243\pi\)
0.936817 0.349819i \(-0.113757\pi\)
\(212\) −2.45625 15.0781i −0.168696 1.03557i
\(213\) 0 0
\(214\) −1.45625 17.9967i −0.0995470 1.23023i
\(215\) −10.6550 −0.726665
\(216\) 0 0
\(217\) −5.89592 −0.400241
\(218\) 0.830011 + 10.2575i 0.0562154 + 0.694725i
\(219\) 0 0
\(220\) −10.6218 + 1.73032i −0.716125 + 0.116658i
\(221\) 0.189345i 0.0127367i
\(222\) 0 0
\(223\) 21.9668 1.47101 0.735504 0.677520i \(-0.236945\pi\)
0.735504 + 0.677520i \(0.236945\pi\)
\(224\) 5.20210 2.22219i 0.347580 0.148476i
\(225\) 0 0
\(226\) 4.71513 0.381537i 0.313646 0.0253795i
\(227\) 7.91752i 0.525504i 0.964863 + 0.262752i \(0.0846301\pi\)
−0.964863 + 0.262752i \(0.915370\pi\)
\(228\) 0 0
\(229\) 13.1606i 0.869676i 0.900509 + 0.434838i \(0.143194\pi\)
−0.900509 + 0.434838i \(0.856806\pi\)
\(230\) −0.204063 2.52187i −0.0134555 0.166287i
\(231\) 0 0
\(232\) −4.56311 18.4684i −0.299583 1.21251i
\(233\) −17.2769 −1.13184 −0.565922 0.824459i \(-0.691480\pi\)
−0.565922 + 0.824459i \(0.691480\pi\)
\(234\) 0 0
\(235\) 12.7287i 0.830330i
\(236\) −1.28626 7.89592i −0.0837283 0.513981i
\(237\) 0 0
\(238\) −0.584994 + 0.0473363i −0.0379196 + 0.00306836i
\(239\) 10.5219 0.680603 0.340301 0.940316i \(-0.389471\pi\)
0.340301 + 0.940316i \(0.389471\pi\)
\(240\) 0 0
\(241\) −6.10686 −0.393378 −0.196689 0.980466i \(-0.563019\pi\)
−0.196689 + 0.980466i \(0.563019\pi\)
\(242\) −16.5289 + 1.33748i −1.06252 + 0.0859766i
\(243\) 0 0
\(244\) −0.579217 3.55562i −0.0370806 0.227626i
\(245\) 1.12875i 0.0721130i
\(246\) 0 0
\(247\) 3.48501 0.221746
\(248\) −16.1893 + 4.00000i −1.02802 + 0.254000i
\(249\) 0 0
\(250\) 1.12344 + 13.8837i 0.0710524 + 0.878084i
\(251\) 19.8743i 1.25446i −0.778836 0.627228i \(-0.784189\pi\)
0.778836 0.627228i \(-0.215811\pi\)
\(252\) 0 0
\(253\) 7.55594i 0.475038i
\(254\) −14.7259 + 1.19159i −0.923987 + 0.0747668i
\(255\) 0 0
\(256\) 12.7766 9.63110i 0.798539 0.601944i
\(257\) 14.7550 0.920391 0.460195 0.887818i \(-0.347779\pi\)
0.460195 + 0.887818i \(0.347779\pi\)
\(258\) 0 0
\(259\) 5.89592i 0.366355i
\(260\) −1.01658 + 0.165602i −0.0630454 + 0.0102702i
\(261\) 0 0
\(262\) 0.713741 + 8.82060i 0.0440951 + 0.544939i
\(263\) 15.7600 0.971804 0.485902 0.874013i \(-0.338491\pi\)
0.485902 + 0.874013i \(0.338491\pi\)
\(264\) 0 0
\(265\) 8.62185 0.529636
\(266\) −0.871253 10.7672i −0.0534199 0.660178i
\(267\) 0 0
\(268\) −2.60296 15.9787i −0.159001 0.976056i
\(269\) 21.8331i 1.33119i −0.746315 0.665593i \(-0.768179\pi\)
0.746315 0.665593i \(-0.231821\pi\)
\(270\) 0 0
\(271\) −18.8328 −1.14401 −0.572005 0.820250i \(-0.693834\pi\)
−0.572005 + 0.820250i \(0.693834\pi\)
\(272\) −1.57420 + 0.526860i −0.0954496 + 0.0319456i
\(273\) 0 0
\(274\) 18.2711 1.47845i 1.10380 0.0893164i
\(275\) 17.7622i 1.07110i
\(276\) 0 0
\(277\) 24.4684i 1.47017i 0.677977 + 0.735083i \(0.262857\pi\)
−0.677977 + 0.735083i \(0.737143\pi\)
\(278\) 2.09467 + 25.8865i 0.125630 + 1.55257i
\(279\) 0 0
\(280\) 0.765782 + 3.09938i 0.0457642 + 0.185223i
\(281\) −14.5150 −0.865892 −0.432946 0.901420i \(-0.642526\pi\)
−0.432946 + 0.901420i \(0.642526\pi\)
\(282\) 0 0
\(283\) 16.5509i 0.983850i 0.870638 + 0.491925i \(0.163707\pi\)
−0.870638 + 0.491925i \(0.836293\pi\)
\(284\) −20.1481 + 3.28216i −1.19557 + 0.194760i
\(285\) 0 0
\(286\) −3.06591 + 0.248086i −0.181291 + 0.0146696i
\(287\) 0.415006 0.0244970
\(288\) 0 0
\(289\) −16.8278 −0.989869
\(290\) 10.7016 0.865943i 0.628417 0.0508499i
\(291\) 0 0
\(292\) −6.60296 + 1.07563i −0.386409 + 0.0629467i
\(293\) 9.44377i 0.551711i 0.961199 + 0.275855i \(0.0889611\pi\)
−0.961199 + 0.275855i \(0.911039\pi\)
\(294\) 0 0
\(295\) 4.51499 0.262873
\(296\) 4.00000 + 16.1893i 0.232495 + 0.940987i
\(297\) 0 0
\(298\) −1.78375 22.0440i −0.103330 1.27698i
\(299\) 0.723150i 0.0418208i
\(300\) 0 0
\(301\) 9.43967i 0.544094i
\(302\) 21.5343 1.74251i 1.23916 0.100270i
\(303\) 0 0
\(304\) −9.69717 28.9740i −0.556171 1.66177i
\(305\) 2.03315 0.116418
\(306\) 0 0
\(307\) 0.361575i 0.0206362i −0.999947 0.0103181i \(-0.996716\pi\)
0.999947 0.0103181i \(-0.00328441\pi\)
\(308\) 1.53295 + 9.41030i 0.0873482 + 0.536202i
\(309\) 0 0
\(310\) −0.759082 9.38093i −0.0431130 0.532801i
\(311\) 11.2769 0.639452 0.319726 0.947510i \(-0.396409\pi\)
0.319726 + 0.947510i \(0.396409\pi\)
\(312\) 0 0
\(313\) 25.5837 1.44607 0.723037 0.690809i \(-0.242745\pi\)
0.723037 + 0.690809i \(0.242745\pi\)
\(314\) −2.48454 30.7047i −0.140211 1.73276i
\(315\) 0 0
\(316\) −9.53434 + 1.55316i −0.536349 + 0.0873721i
\(317\) 0.361575i 0.0203081i 0.999948 + 0.0101540i \(0.00323218\pi\)
−0.999948 + 0.0101540i \(0.996768\pi\)
\(318\) 0 0
\(319\) 32.0637 1.79522
\(320\) 4.20545 + 7.99091i 0.235092 + 0.446705i
\(321\) 0 0
\(322\) −2.23422 + 0.180787i −0.124508 + 0.0100749i
\(323\) 3.16999i 0.176383i
\(324\) 0 0
\(325\) 1.69995i 0.0942960i
\(326\) 0.525786 + 6.49781i 0.0291206 + 0.359880i
\(327\) 0 0
\(328\) 1.13955 0.281554i 0.0629209 0.0155462i
\(329\) −11.2769 −0.621713
\(330\) 0 0
\(331\) 7.80403i 0.428948i −0.976730 0.214474i \(-0.931196\pi\)
0.976730 0.214474i \(-0.0688037\pi\)
\(332\) −1.77965 10.9247i −0.0976710 0.599570i
\(333\) 0 0
\(334\) 32.3671 2.61907i 1.77105 0.143309i
\(335\) 9.13684 0.499199
\(336\) 0 0
\(337\) 8.76186 0.477289 0.238645 0.971107i \(-0.423297\pi\)
0.238645 + 0.971107i \(0.423297\pi\)
\(338\) 18.0315 1.45906i 0.980782 0.0793625i
\(339\) 0 0
\(340\) −0.150633 0.924684i −0.00816920 0.0501480i
\(341\) 28.1069i 1.52207i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 6.40421 + 25.9200i 0.345292 + 1.39751i
\(345\) 0 0
\(346\) −0.0246661 0.304830i −0.00132606 0.0163878i
\(347\) 2.07717i 0.111509i 0.998445 + 0.0557543i \(0.0177563\pi\)
−0.998445 + 0.0557543i \(0.982244\pi\)
\(348\) 0 0
\(349\) 18.7381i 1.00303i 0.865149 + 0.501514i \(0.167224\pi\)
−0.865149 + 0.501514i \(0.832776\pi\)
\(350\) 5.25209 0.424987i 0.280736 0.0227165i
\(351\) 0 0
\(352\) 10.5936 + 24.7993i 0.564638 + 1.32181i
\(353\) 13.2450 0.704961 0.352481 0.935819i \(-0.385338\pi\)
0.352481 + 0.935819i \(0.385338\pi\)
\(354\) 0 0
\(355\) 11.5209i 0.611468i
\(356\) −9.73171 + 1.58531i −0.515779 + 0.0840213i
\(357\) 0 0
\(358\) 2.57968 + 31.8804i 0.136341 + 1.68493i
\(359\) 5.69186 0.300405 0.150202 0.988655i \(-0.452007\pi\)
0.150202 + 0.988655i \(0.452007\pi\)
\(360\) 0 0
\(361\) −39.3455 −2.07082
\(362\) −0.882052 10.9006i −0.0463596 0.572924i
\(363\) 0 0
\(364\) 0.146713 + 0.900623i 0.00768985 + 0.0472055i
\(365\) 3.77566i 0.197627i
\(366\) 0 0
\(367\) 11.2769 0.588647 0.294323 0.955706i \(-0.404906\pi\)
0.294323 + 0.955706i \(0.404906\pi\)
\(368\) −6.01219 + 2.01219i −0.313407 + 0.104893i
\(369\) 0 0
\(370\) −9.38093 + 0.759082i −0.487691 + 0.0394628i
\(371\) 7.63843i 0.396567i
\(372\) 0 0
\(373\) 7.08751i 0.366977i 0.983022 + 0.183489i \(0.0587390\pi\)
−0.983022 + 0.183489i \(0.941261\pi\)
\(374\) −0.225660 2.78877i −0.0116686 0.144204i
\(375\) 0 0
\(376\) −30.9646 + 7.65061i −1.59688 + 0.394550i
\(377\) 3.06869 0.158046
\(378\) 0 0
\(379\) 6.67781i 0.343016i 0.985183 + 0.171508i \(0.0548639\pi\)
−0.985183 + 0.171508i \(0.945136\pi\)
\(380\) 17.0194 2.77248i 0.873075 0.142225i
\(381\) 0 0
\(382\) −14.3876 + 1.16421i −0.736135 + 0.0595662i
\(383\) 18.6550 0.953226 0.476613 0.879113i \(-0.341864\pi\)
0.476613 + 0.879113i \(0.341864\pi\)
\(384\) 0 0
\(385\) −5.38093 −0.274238
\(386\) 8.40699 0.680273i 0.427904 0.0346250i
\(387\) 0 0
\(388\) 32.4657 5.28872i 1.64820 0.268494i
\(389\) 20.3428i 1.03142i −0.856764 0.515709i \(-0.827528\pi\)
0.856764 0.515709i \(-0.172472\pi\)
\(390\) 0 0
\(391\) 0.657782 0.0332654
\(392\) 2.74586 0.678435i 0.138687 0.0342662i
\(393\) 0 0
\(394\) 2.14532 + 26.5125i 0.108080 + 1.33568i
\(395\) 5.45186i 0.274313i
\(396\) 0 0
\(397\) 10.9031i 0.547210i 0.961842 + 0.273605i \(0.0882161\pi\)
−0.961842 + 0.273605i \(0.911784\pi\)
\(398\) 4.61907 0.373764i 0.231533 0.0187351i
\(399\) 0 0
\(400\) 14.1332 4.73016i 0.706659 0.236508i
\(401\) −29.1756 −1.45696 −0.728479 0.685068i \(-0.759772\pi\)
−0.728479 + 0.685068i \(0.759772\pi\)
\(402\) 0 0
\(403\) 2.69000i 0.133998i
\(404\) 5.27546 + 32.3843i 0.262464 + 1.61118i
\(405\) 0 0
\(406\) −0.767172 9.48091i −0.0380741 0.470530i
\(407\) −28.1069 −1.39321
\(408\) 0 0
\(409\) −31.7237 −1.56864 −0.784318 0.620359i \(-0.786987\pi\)
−0.784318 + 0.620359i \(0.786987\pi\)
\(410\) 0.0534307 + 0.660311i 0.00263875 + 0.0326104i
\(411\) 0 0
\(412\) −33.8987 + 5.52216i −1.67007 + 0.272057i
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) 6.24687 0.306647
\(416\) 1.01387 + 2.37345i 0.0497089 + 0.116368i
\(417\) 0 0
\(418\) 51.3290 4.15341i 2.51058 0.203150i
\(419\) 19.2769i 0.941736i 0.882204 + 0.470868i \(0.156059\pi\)
−0.882204 + 0.470868i \(0.843941\pi\)
\(420\) 0 0
\(421\) 19.3234i 0.941765i −0.882196 0.470882i \(-0.843936\pi\)
0.882196 0.470882i \(-0.156064\pi\)
\(422\) −1.15919 14.3256i −0.0564285 0.697358i
\(423\) 0 0
\(424\) −5.18218 20.9740i −0.251669 1.01859i
\(425\) −1.54628 −0.0750057
\(426\) 0 0
\(427\) 1.80125i 0.0871684i
\(428\) −4.10547 25.2021i −0.198445 1.21819i
\(429\) 0 0
\(430\) −15.0194 + 1.21533i −0.724298 + 0.0586084i
\(431\) −14.4150 −0.694346 −0.347173 0.937801i \(-0.612858\pi\)
−0.347173 + 0.937801i \(0.612858\pi\)
\(432\) 0 0
\(433\) −9.27685 −0.445817 −0.222908 0.974839i \(-0.571555\pi\)
−0.222908 + 0.974839i \(0.571555\pi\)
\(434\) −8.31092 + 0.672500i −0.398937 + 0.0322810i
\(435\) 0 0
\(436\) 2.33998 + 14.3644i 0.112065 + 0.687928i
\(437\) 12.1069i 0.579150i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −14.7753 + 3.65061i −0.704383 + 0.174036i
\(441\) 0 0
\(442\) −0.0215971 0.266902i −0.00102727 0.0126952i
\(443\) 15.6465i 0.743388i 0.928355 + 0.371694i \(0.121223\pi\)
−0.928355 + 0.371694i \(0.878777\pi\)
\(444\) 0 0
\(445\) 5.56472i 0.263793i
\(446\) 30.9646 2.50558i 1.46622 0.118643i
\(447\) 0 0
\(448\) 7.07945 3.72577i 0.334473 0.176026i
\(449\) 12.6550 0.597226 0.298613 0.954374i \(-0.403476\pi\)
0.298613 + 0.954374i \(0.403476\pi\)
\(450\) 0 0
\(451\) 1.97840i 0.0931594i
\(452\) 6.60296 1.07563i 0.310577 0.0505935i
\(453\) 0 0
\(454\) 0.903087 + 11.1606i 0.0423840 + 0.523792i
\(455\) −0.514988 −0.0241430
\(456\) 0 0
\(457\) −23.9237 −1.11910 −0.559551 0.828796i \(-0.689026\pi\)
−0.559551 + 0.828796i \(0.689026\pi\)
\(458\) 1.50112 + 18.5512i 0.0701427 + 0.866842i
\(459\) 0 0
\(460\) −0.575298 3.53156i −0.0268234 0.164660i
\(461\) 6.74558i 0.314173i 0.987585 + 0.157086i \(0.0502101\pi\)
−0.987585 + 0.157086i \(0.949790\pi\)
\(462\) 0 0
\(463\) −11.1700 −0.519113 −0.259557 0.965728i \(-0.583576\pi\)
−0.259557 + 0.965728i \(0.583576\pi\)
\(464\) −8.53873 25.5127i −0.396401 1.18440i
\(465\) 0 0
\(466\) −24.3536 + 1.97063i −1.12816 + 0.0912877i
\(467\) 3.70935i 0.171648i 0.996310 + 0.0858242i \(0.0273523\pi\)
−0.996310 + 0.0858242i \(0.972648\pi\)
\(468\) 0 0
\(469\) 8.09467i 0.373777i
\(470\) −1.45186 17.9425i −0.0669693 0.827624i
\(471\) 0 0
\(472\) −2.71374 10.9834i −0.124910 0.505553i
\(473\) −45.0005 −2.06913
\(474\) 0 0
\(475\) 28.4602i 1.30585i
\(476\) −0.819213 + 0.133451i −0.0375485 + 0.00611672i
\(477\) 0 0
\(478\) 14.8317 1.20014i 0.678386 0.0548933i
\(479\) 2.17501 0.0993788 0.0496894 0.998765i \(-0.484177\pi\)
0.0496894 + 0.998765i \(0.484177\pi\)
\(480\) 0 0
\(481\) −2.69000 −0.122653
\(482\) −8.60827 + 0.696560i −0.392096 + 0.0317274i
\(483\) 0 0
\(484\) −23.1467 + 3.77064i −1.05212 + 0.171393i
\(485\) 18.5643i 0.842962i
\(486\) 0 0
\(487\) −4.51499 −0.204594 −0.102297 0.994754i \(-0.532619\pi\)
−0.102297 + 0.994754i \(0.532619\pi\)
\(488\) −1.22203 4.94596i −0.0553187 0.223893i
\(489\) 0 0
\(490\) 0.128747 + 1.59109i 0.00581620 + 0.0718781i
\(491\) 1.91221i 0.0862967i −0.999069 0.0431483i \(-0.986261\pi\)
0.999069 0.0431483i \(-0.0137388\pi\)
\(492\) 0 0
\(493\) 2.79130i 0.125714i
\(494\) 4.91249 0.397507i 0.221024 0.0178847i
\(495\) 0 0
\(496\) −22.3644 + 7.48501i −1.00419 + 0.336087i
\(497\) −10.2068 −0.457840
\(498\) 0 0
\(499\) 27.4065i 1.22688i −0.789740 0.613442i \(-0.789784\pi\)
0.789740 0.613442i \(-0.210216\pi\)
\(500\) 3.16721 + 19.4425i 0.141642 + 0.869493i
\(501\) 0 0
\(502\) −2.26690 28.0150i −0.101177 1.25037i
\(503\) −17.1368 −0.764094 −0.382047 0.924143i \(-0.624781\pi\)
−0.382047 + 0.924143i \(0.624781\pi\)
\(504\) 0 0
\(505\) −18.5178 −0.824030
\(506\) −0.861845 10.6509i −0.0383137 0.473490i
\(507\) 0 0
\(508\) −20.6218 + 3.35933i −0.914947 + 0.149046i
\(509\) 21.6437i 0.959342i 0.877449 + 0.479671i \(0.159244\pi\)
−0.877449 + 0.479671i \(0.840756\pi\)
\(510\) 0 0
\(511\) −3.34500 −0.147974
\(512\) 16.9115 15.0334i 0.747388 0.664388i
\(513\) 0 0
\(514\) 20.7987 1.68298i 0.917392 0.0742331i
\(515\) 19.3837i 0.854148i
\(516\) 0 0
\(517\) 53.7587i 2.36430i
\(518\) 0.672500 + 8.31092i 0.0295479 + 0.365161i
\(519\) 0 0
\(520\) −1.41408 + 0.349386i −0.0620116 + 0.0153216i
\(521\) −28.3137 −1.24045 −0.620223 0.784426i \(-0.712958\pi\)
−0.620223 + 0.784426i \(0.712958\pi\)
\(522\) 0 0
\(523\) 15.0687i 0.658908i 0.944172 + 0.329454i \(0.106865\pi\)
−0.944172 + 0.329454i \(0.893135\pi\)
\(524\) 2.01219 + 12.3522i 0.0879029 + 0.539607i
\(525\) 0 0
\(526\) 22.2154 1.79762i 0.968638 0.0783798i
\(527\) 2.44684 0.106586
\(528\) 0 0
\(529\) −20.4878 −0.890774
\(530\) 12.1534 0.983424i 0.527911 0.0427172i
\(531\) 0 0
\(532\) −2.45625 15.0781i −0.106492 0.653718i
\(533\) 0.189345i 0.00820145i
\(534\) 0 0
\(535\) 14.4109 0.623038
\(536\) −5.49171 22.2268i −0.237206 0.960052i
\(537\) 0 0
\(538\) −2.49032 30.7760i −0.107365 1.32685i
\(539\) 4.76717i 0.205337i
\(540\) 0 0
\(541\) 46.2990i 1.99055i −0.0971017 0.995274i \(-0.530957\pi\)
0.0971017 0.995274i \(-0.469043\pi\)
\(542\) −26.5468 + 2.14810i −1.14028 + 0.0922689i
\(543\) 0 0
\(544\) −2.15890 + 0.922220i −0.0925622 + 0.0395399i
\(545\) −8.21372 −0.351837
\(546\) 0 0
\(547\) 2.03714i 0.0871020i −0.999051 0.0435510i \(-0.986133\pi\)
0.999051 0.0435510i \(-0.0138671\pi\)
\(548\) 25.5864 4.16807i 1.09300 0.178051i
\(549\) 0 0
\(550\) 2.02598 + 25.0376i 0.0863882 + 1.06761i
\(551\) −51.3755 −2.18867
\(552\) 0 0
\(553\) −4.83001 −0.205393
\(554\) 2.79092 + 34.4909i 0.118575 + 1.46538i
\(555\) 0 0
\(556\) 5.90533 + 36.2509i 0.250442 + 1.53738i
\(557\) 11.1234i 0.471315i 0.971836 + 0.235658i \(0.0757244\pi\)
−0.971836 + 0.235658i \(0.924276\pi\)
\(558\) 0 0
\(559\) −4.30683 −0.182159
\(560\) 1.43297 + 4.28155i 0.0605541 + 0.180929i
\(561\) 0 0
\(562\) −20.4604 + 1.65561i −0.863071 + 0.0698375i
\(563\) 37.2437i 1.56963i −0.619727 0.784817i \(-0.712757\pi\)
0.619727 0.784817i \(-0.287243\pi\)
\(564\) 0 0
\(565\) 3.77566i 0.158843i
\(566\) 1.88783 + 23.3303i 0.0793514 + 0.980645i
\(567\) 0 0
\(568\) −28.0265 + 6.92468i −1.17597 + 0.290553i
\(569\) −22.9369 −0.961564 −0.480782 0.876840i \(-0.659647\pi\)
−0.480782 + 0.876840i \(0.659647\pi\)
\(570\) 0 0
\(571\) 35.1634i 1.47154i 0.677231 + 0.735770i \(0.263180\pi\)
−0.677231 + 0.735770i \(0.736820\pi\)
\(572\) −4.29343 + 0.699406i −0.179517 + 0.0292436i
\(573\) 0 0
\(574\) 0.584994 0.0473363i 0.0244172 0.00197578i
\(575\) −5.90558 −0.246280
\(576\) 0 0
\(577\) 13.7918 0.574162 0.287081 0.957906i \(-0.407315\pi\)
0.287081 + 0.957906i \(0.407315\pi\)
\(578\) −23.7205 + 1.91941i −0.986644 + 0.0798368i
\(579\) 0 0
\(580\) 14.9862 2.44128i 0.622268 0.101369i
\(581\) 5.53434i 0.229603i
\(582\) 0 0
\(583\) 36.4137 1.50810
\(584\) −9.18489 + 2.26937i −0.380073 + 0.0939070i
\(585\) 0 0
\(586\) 1.07717 + 13.3120i 0.0444976 + 0.549914i
\(587\) 26.9862i 1.11384i 0.830566 + 0.556920i \(0.188017\pi\)
−0.830566 + 0.556920i \(0.811983\pi\)
\(588\) 0 0
\(589\) 45.0355i 1.85566i
\(590\) 6.36436 0.514988i 0.262016 0.0212017i
\(591\) 0 0
\(592\) 7.48501 + 22.3644i 0.307632 + 0.919169i
\(593\) 31.8337 1.30725 0.653627 0.756817i \(-0.273247\pi\)
0.653627 + 0.756817i \(0.273247\pi\)
\(594\) 0 0
\(595\) 0.468436i 0.0192040i
\(596\) −5.02876 30.8699i −0.205986 1.26448i
\(597\) 0 0
\(598\) −0.0824838 1.01936i −0.00337301 0.0416846i
\(599\) 34.9006 1.42600 0.712999 0.701165i \(-0.247336\pi\)
0.712999 + 0.701165i \(0.247336\pi\)
\(600\) 0 0
\(601\) −0.175010 −0.00713881 −0.00356941 0.999994i \(-0.501136\pi\)
−0.00356941 + 0.999994i \(0.501136\pi\)
\(602\) 1.07671 + 13.3062i 0.0438833 + 0.542321i
\(603\) 0 0
\(604\) 30.1562 4.91249i 1.22704 0.199887i
\(605\) 13.2356i 0.538104i
\(606\) 0 0
\(607\) −32.1705 −1.30576 −0.652881 0.757461i \(-0.726440\pi\)
−0.652881 + 0.757461i \(0.726440\pi\)
\(608\) −16.9740 39.7359i −0.688387 1.61150i
\(609\) 0 0
\(610\) 2.86594 0.231905i 0.116039 0.00938956i
\(611\) 5.14503i 0.208146i
\(612\) 0 0
\(613\) 8.37869i 0.338412i −0.985581 0.169206i \(-0.945880\pi\)
0.985581 0.169206i \(-0.0541203\pi\)
\(614\) −0.0412419 0.509678i −0.00166439 0.0205689i
\(615\) 0 0
\(616\) 3.23422 + 13.0900i 0.130310 + 0.527410i
\(617\) −28.9618 −1.16596 −0.582980 0.812487i \(-0.698113\pi\)
−0.582980 + 0.812487i \(0.698113\pi\)
\(618\) 0 0
\(619\) 6.85497i 0.275524i 0.990465 + 0.137762i \(0.0439910\pi\)
−0.990465 + 0.137762i \(0.956009\pi\)
\(620\) −2.14001 13.1368i −0.0859450 0.527588i
\(621\) 0 0
\(622\) 15.8959 1.28626i 0.637368 0.0515743i
\(623\) −4.92999 −0.197516
\(624\) 0 0
\(625\) 7.51221 0.300488
\(626\) 36.0629 2.91812i 1.44136 0.116632i
\(627\) 0 0
\(628\) −7.00446 42.9981i −0.279508 1.71581i
\(629\) 2.44684i 0.0975619i
\(630\) 0 0
\(631\) −40.2055 −1.60056 −0.800278 0.599629i \(-0.795315\pi\)
−0.800278 + 0.599629i \(0.795315\pi\)
\(632\) −13.2625 + 3.27685i −0.527555 + 0.130346i
\(633\) 0 0
\(634\) 0.0412419 + 0.509678i 0.00163793 + 0.0202419i
\(635\) 11.7918i 0.467945i
\(636\) 0 0
\(637\) 0.456247i 0.0180772i
\(638\) 45.1971 3.65724i 1.78937 0.144792i
\(639\) 0 0
\(640\) 6.83949 + 10.7844i 0.270355 + 0.426289i
\(641\) 24.0737 0.950854 0.475427 0.879755i \(-0.342294\pi\)
0.475427 + 0.879755i \(0.342294\pi\)
\(642\) 0 0
\(643\) 23.7559i 0.936841i 0.883506 + 0.468421i \(0.155177\pi\)
−0.883506 + 0.468421i \(0.844823\pi\)
\(644\) −3.12875 + 0.509678i −0.123290 + 0.0200841i
\(645\) 0 0
\(646\) 0.361575 + 4.46844i 0.0142260 + 0.175808i
\(647\) 32.6218 1.28250 0.641249 0.767333i \(-0.278417\pi\)
0.641249 + 0.767333i \(0.278417\pi\)
\(648\) 0 0
\(649\) 19.0687 0.748512
\(650\) 0.193899 + 2.39625i 0.00760535 + 0.0939888i
\(651\) 0 0
\(652\) 1.48230 + 9.09938i 0.0580515 + 0.356359i
\(653\) 14.4109i 0.563942i 0.959423 + 0.281971i \(0.0909883\pi\)
−0.959423 + 0.281971i \(0.909012\pi\)
\(654\) 0 0
\(655\) −7.06313 −0.275979
\(656\) 1.57420 0.526860i 0.0614620 0.0205704i
\(657\) 0 0
\(658\) −15.8959 + 1.28626i −0.619687 + 0.0501436i
\(659\) 23.3315i 0.908866i −0.890781 0.454433i \(-0.849842\pi\)
0.890781 0.454433i \(-0.150158\pi\)
\(660\) 0 0
\(661\) 44.1468i 1.71711i 0.512721 + 0.858555i \(0.328638\pi\)
−0.512721 + 0.858555i \(0.671362\pi\)
\(662\) −0.890142 11.0006i −0.0345963 0.427551i
\(663\) 0 0
\(664\) −3.75469 15.1965i −0.145710 0.589739i
\(665\) 8.62185 0.334341
\(666\) 0 0
\(667\) 10.6606i 0.412779i
\(668\) 45.3262 7.38371i 1.75372 0.285684i
\(669\) 0 0
\(670\) 12.8793 1.04216i 0.497572 0.0402623i
\(671\) 8.58685 0.331492
\(672\) 0 0
\(673\) 11.6960 0.450846 0.225423 0.974261i \(-0.427624\pi\)
0.225423 + 0.974261i \(0.427624\pi\)
\(674\) 12.3508 0.999394i 0.475734 0.0384952i
\(675\) 0 0
\(676\) 25.2508 4.11340i 0.971186 0.158208i
\(677\) 0.648756i 0.0249337i −0.999922 0.0124669i \(-0.996032\pi\)
0.999922 0.0124669i \(-0.00396843\pi\)
\(678\) 0 0
\(679\) 16.4468 0.631172
\(680\) −0.317804 1.28626i −0.0121872 0.0493258i
\(681\) 0 0
\(682\) −3.20592 39.6196i −0.122761 1.51711i
\(683\) 22.4909i 0.860589i −0.902689 0.430294i \(-0.858410\pi\)
0.902689 0.430294i \(-0.141590\pi\)
\(684\) 0 0
\(685\) 14.6306i 0.559007i
\(686\) 1.40961 0.114062i 0.0538190 0.00435490i
\(687\) 0 0
\(688\) 11.9839 + 35.8065i 0.456882 + 1.36511i
\(689\) 3.48501 0.132768
\(690\) 0 0
\(691\) 45.2681i 1.72208i 0.508538 + 0.861039i \(0.330186\pi\)
−0.508538 + 0.861039i \(0.669814\pi\)
\(692\) −0.0695390 0.426877i −0.00264348 0.0162274i
\(693\) 0 0
\(694\) 0.236926 + 2.92800i 0.00899360 + 0.111145i
\(695\) −20.7287 −0.786285
\(696\) 0 0
\(697\) −0.172230 −0.00652366
\(698\) 2.13730 + 26.4134i 0.0808982 + 0.999761i
\(699\) 0 0
\(700\) 7.35491 1.19813i 0.277990 0.0452850i
\(701\) 1.03091i 0.0389370i 0.999810 + 0.0194685i \(0.00619740\pi\)
−0.999810 + 0.0194685i \(0.993803\pi\)
\(702\) 0 0
\(703\) 45.0355 1.69855
\(704\) 17.7614 + 33.7490i 0.669408 + 1.27196i
\(705\) 0 0
\(706\) 18.6703 1.51075i 0.702664 0.0568579i
\(707\) 16.4056i 0.616996i
\(708\) 0 0
\(709\) 10.5481i 0.396144i −0.980188 0.198072i \(-0.936532\pi\)
0.980188 0.198072i \(-0.0634679\pi\)
\(710\) −1.31410 16.2400i −0.0493173 0.609476i
\(711\) 0 0
\(712\) −13.5371 + 3.34468i −0.507322 + 0.125347i
\(713\) 9.34500 0.349973
\(714\) 0 0
\(715\) 2.45504i 0.0918131i
\(716\) 7.27268 + 44.6446i 0.271793 + 1.66845i
\(717\) 0 0
\(718\) 8.02328 0.649224i 0.299426 0.0242288i
\(719\) 7.00502 0.261243 0.130622 0.991432i \(-0.458303\pi\)
0.130622 + 0.991432i \(0.458303\pi\)
\(720\) 0 0
\(721\) −17.1728 −0.639547
\(722\) −55.4617 + 4.48783i −2.06407 + 0.167020i
\(723\) 0 0
\(724\) −2.48669 15.2650i −0.0924171 0.567318i
\(725\) 25.0603i 0.930718i
\(726\) 0 0
\(727\) −17.8028 −0.660270 −0.330135 0.943934i \(-0.607094\pi\)
−0.330135 + 0.943934i \(0.607094\pi\)
\(728\) 0.309534 + 1.25279i 0.0114721 + 0.0464315i
\(729\) 0 0
\(730\) −0.430659 5.32219i −0.0159394 0.196983i
\(731\) 3.91752i 0.144895i
\(732\) 0 0
\(733\) 34.3300i 1.26801i −0.773330 0.634004i \(-0.781410\pi\)
0.773330 0.634004i \(-0.218590\pi\)
\(734\) 15.8959 1.28626i 0.586729 0.0474767i
\(735\) 0 0
\(736\) −8.24531 + 3.52216i −0.303926 + 0.129828i
\(737\) 38.5887 1.42143
\(738\) 0 0
\(739\) 0.0946726i 0.00348259i 0.999998 + 0.00174129i \(0.000554271\pi\)
−0.999998 + 0.00174129i \(0.999446\pi\)
\(740\) −13.1368 + 2.14001i −0.482920 + 0.0786684i
\(741\) 0 0
\(742\) −0.871253 10.7672i −0.0319847 0.395275i
\(743\) 13.2755 0.487032 0.243516 0.969897i \(-0.421699\pi\)
0.243516 + 0.969897i \(0.421699\pi\)
\(744\) 0 0
\(745\) 17.6518 0.646713
\(746\) 0.808414 + 9.99059i 0.0295981 + 0.365782i
\(747\) 0 0
\(748\) −0.636184 3.90533i −0.0232612 0.142793i
\(749\) 12.7672i 0.466502i
\(750\) 0 0
\(751\) 15.4187 0.562637 0.281318 0.959615i \(-0.409228\pi\)
0.281318 + 0.959615i \(0.409228\pi\)
\(752\) −42.7753 + 14.3162i −1.55985 + 0.522059i
\(753\) 0 0
\(754\) 4.32564 0.350020i 0.157531 0.0127470i
\(755\) 17.2437i 0.627562i
\(756\) 0 0
\(757\) 9.96685i 0.362251i −0.983460 0.181126i \(-0.942026\pi\)
0.983460 0.181126i \(-0.0579741\pi\)
\(758\) 0.761683 + 9.41308i 0.0276656 + 0.341899i
\(759\) 0 0
\(760\) 23.6744 5.84937i 0.858759 0.212179i
\(761\) −23.4837 −0.851283 −0.425642 0.904892i \(-0.639952\pi\)
−0.425642 + 0.904892i \(0.639952\pi\)
\(762\) 0 0
\(763\) 7.27685i 0.263440i
\(764\) −20.1481 + 3.28216i −0.728933 + 0.118744i
\(765\) 0 0
\(766\) 26.2962 2.12782i 0.950121 0.0768814i
\(767\) 1.82499 0.0658966
\(768\) 0 0
\(769\) 22.9369 0.827125 0.413562 0.910476i \(-0.364284\pi\)
0.413562 + 0.910476i \(0.364284\pi\)
\(770\) −7.58499 + 0.613759i −0.273344 + 0.0221183i
\(771\) 0 0
\(772\) 11.7729 1.91783i 0.423718 0.0690243i
\(773\) 35.0956i 1.26230i 0.775660 + 0.631150i \(0.217417\pi\)
−0.775660 + 0.631150i \(0.782583\pi\)
\(774\) 0 0
\(775\) −21.9678 −0.789106
\(776\) 45.1607 11.1581i 1.62117 0.400553i
\(777\) 0 0
\(778\) −2.32033 28.6753i −0.0831880 1.02806i
\(779\) 3.16999i 0.113577i
\(780\) 0 0
\(781\) 48.6578i 1.74111i
\(782\) 0.927213 0.0750278i 0.0331571 0.00268299i
\(783\) 0 0
\(784\) 3.79319 1.26952i 0.135471 0.0453402i
\(785\) 24.5869 0.877542
\(786\) 0 0
\(787\) 17.9480i 0.639778i −0.947455 0.319889i \(-0.896354\pi\)
0.947455 0.319889i \(-0.103646\pi\)
\(788\) 6.04812 + 37.1274i 0.215455 + 1.32261i
\(789\) 0 0
\(790\) −0.621849 7.68498i −0.0221244 0.273419i
\(791\) 3.34500 0.118934
\(792\) 0 0
\(793\) 0.821814 0.0291835
\(794\) 1.24363 + 15.3691i 0.0441346 + 0.545428i
\(795\) 0 0
\(796\) 6.46844 1.05372i 0.229268 0.0373481i
\(797\) 34.4199i 1.21922i −0.792703 0.609608i \(-0.791327\pi\)
0.792703 0.609608i \(-0.208673\pi\)
\(798\) 0 0
\(799\) 4.67996 0.165565
\(800\) 19.3827 8.27972i 0.685281 0.292732i
\(801\) 0 0
\(802\) −41.1260 + 3.32782i −1.45221 + 0.117509i
\(803\) 15.9462i 0.562729i
\(804\) 0 0
\(805\) 1.78906i 0.0630560i
\(806\) −0.306826 3.79184i −0.0108075 0.133562i
\(807\) 0 0
\(808\) 11.1301 + 45.0474i 0.391557 + 1.58476i
\(809\) −1.89314 −0.0665592 −0.0332796 0.999446i \(-0.510595\pi\)
−0.0332796 + 0.999446i \(0.510595\pi\)
\(810\) 0 0
\(811\) 10.3400i 0.363086i −0.983383 0.181543i \(-0.941891\pi\)
0.983383 0.181543i \(-0.0581091\pi\)
\(812\) −2.16282 13.2769i −0.0759002 0.465926i
\(813\) 0 0
\(814\) −39.6196 + 3.20592i −1.38867 + 0.112367i
\(815\) −5.20314 −0.182258
\(816\) 0 0
\(817\) 72.1042 2.52261
\(818\) −44.7179 + 3.61846i −1.56353 + 0.126517i
\(819\) 0 0
\(820\) 0.150633 + 0.924684i 0.00526032 + 0.0322914i
\(821\) 2.40029i 0.0837706i 0.999122 + 0.0418853i \(0.0133364\pi\)
−0.999122 + 0.0418853i \(0.986664\pi\)
\(822\) 0 0
\(823\) 25.8655 0.901616 0.450808 0.892621i \(-0.351136\pi\)
0.450808 + 0.892621i \(0.351136\pi\)
\(824\) −47.1540 + 11.6506i −1.64269 + 0.405868i
\(825\) 0 0
\(826\) −0.456247 5.63843i −0.0158749 0.196186i
\(827\) 17.0928i 0.594375i 0.954819 + 0.297188i \(0.0960487\pi\)
−0.954819 + 0.297188i \(0.903951\pi\)
\(828\) 0 0
\(829\) 41.8893i 1.45488i 0.686174 + 0.727438i \(0.259289\pi\)
−0.686174 + 0.727438i \(0.740711\pi\)
\(830\) 8.80563 0.712530i 0.305648 0.0247323i
\(831\) 0 0
\(832\) 1.69987 + 3.22998i 0.0589325 + 0.111979i
\(833\) −0.415006 −0.0143791
\(834\) 0 0
\(835\) 25.9181i 0.896933i
\(836\) 71.8799 11.7094i 2.48602 0.404976i
\(837\) 0 0
\(838\) 2.19875 + 27.1728i 0.0759547 + 0.938668i
\(839\) 24.5500 0.847560 0.423780 0.905765i \(-0.360703\pi\)
0.423780 + 0.905765i \(0.360703\pi\)
\(840\) 0 0
\(841\) −16.2381 −0.559936
\(842\) −2.20406 27.2384i −0.0759570 0.938697i
\(843\) 0 0
\(844\) −3.26800 20.0612i −0.112489 0.690535i
\(845\) 14.4387i 0.496708i
\(846\) 0 0
\(847\) −11.7259 −0.402908
\(848\) −9.69717 28.9740i −0.333002 0.994972i
\(849\) 0 0
\(850\) −2.17965 + 0.176372i −0.0747613 + 0.00604950i
\(851\) 9.34500i 0.320342i
\(852\) 0 0
\(853\) 38.7193i 1.32572i 0.748742 + 0.662862i \(0.230658\pi\)
−0.748742 + 0.662862i \(0.769342\pi\)
\(854\) −0.205454 2.53905i −0.00703048 0.0868844i
\(855\) 0 0
\(856\) −8.66170 35.0568i −0.296051 1.19822i
\(857\) 45.2074 1.54425 0.772127 0.635468i \(-0.219193\pi\)
0.772127 + 0.635468i \(0.219193\pi\)
\(858\) 0 0
\(859\) 57.1890i 1.95126i −0.219418 0.975631i \(-0.570416\pi\)
0.219418 0.975631i \(-0.429584\pi\)
\(860\) −21.0328 + 3.42627i −0.717211 + 0.116835i
\(861\) 0 0
\(862\) −20.3195 + 1.64420i −0.692084 + 0.0560018i
\(863\) 45.1106 1.53558 0.767791 0.640701i \(-0.221356\pi\)
0.767791 + 0.640701i \(0.221356\pi\)
\(864\) 0 0
\(865\) 0.244094 0.00829944
\(866\) −13.0767 + 1.05813i −0.444365 + 0.0359569i
\(867\) 0 0
\(868\) −11.6384 + 1.89592i −0.395034 + 0.0643517i
\(869\) 23.0255i 0.781086i
\(870\) 0 0
\(871\) 3.69317 0.125138
\(872\) 4.93687 + 19.9812i 0.167184 + 0.676648i
\(873\) 0 0
\(874\) 1.38093 + 17.0659i 0.0467107 + 0.577263i
\(875\) 9.84937i 0.332969i
\(876\) 0 0
\(877\) 17.6600i 0.596337i 0.954513 + 0.298168i \(0.0963757\pi\)
−0.954513 + 0.298168i \(0.903624\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −20.4109 + 6.83122i −0.688052 + 0.230280i
\(881\) −6.78998 −0.228760 −0.114380 0.993437i \(-0.536488\pi\)
−0.114380 + 0.993437i \(0.536488\pi\)
\(882\) 0 0
\(883\) 28.6015i 0.962516i −0.876579 0.481258i \(-0.840180\pi\)
0.876579 0.481258i \(-0.159820\pi\)
\(884\) −0.0608867 0.373764i −0.00204784 0.0125710i
\(885\) 0 0
\(886\) 1.78467 + 22.0554i 0.0599572 + 0.740967i
\(887\) −23.5919 −0.792138 −0.396069 0.918221i \(-0.629626\pi\)
−0.396069 + 0.918221i \(0.629626\pi\)
\(888\) 0 0
\(889\) −10.4468 −0.350376
\(890\) −0.634722 7.84406i −0.0212759 0.262933i
\(891\) 0 0
\(892\) 43.3621 7.06376i 1.45187 0.236512i
\(893\) 86.1374i 2.88248i
\(894\) 0 0
\(895\) −25.5284 −0.853319
\(896\) 9.55427 6.05937i 0.319186 0.202429i
\(897\) 0 0
\(898\) 17.8386 1.44345i 0.595281 0.0481687i
\(899\) 39.6555i 1.32259i
\(900\) 0 0
\(901\) 3.16999i 0.105608i
\(902\) 0.225660 + 2.78877i 0.00751367 + 0.0928559i
\(903\) 0 0
\(904\) 9.18489 2.26937i 0.305485 0.0754780i
\(905\) 8.72871 0.290152
\(906\) 0 0
\(907\) 2.02096i 0.0671050i −0.999437 0.0335525i \(-0.989318\pi\)
0.999437 0.0335525i \(-0.0106821\pi\)
\(908\) 2.54599 + 15.6290i 0.0844918 + 0.518667i
\(909\) 0 0
\(910\) −0.725930 + 0.0587405i −0.0240644 + 0.00194723i
\(911\) −52.5524 −1.74114 −0.870569 0.492046i \(-0.836249\pi\)
−0.870569 + 0.492046i \(0.836249\pi\)
\(912\) 0 0
\(913\) 26.3832 0.873156
\(914\) −33.7229 + 2.72878i −1.11546 + 0.0902599i
\(915\) 0 0
\(916\) 4.23198 + 25.9787i 0.139828 + 0.858361i
\(917\) 6.25749i 0.206641i
\(918\) 0 0
\(919\) 21.5237 0.710002 0.355001 0.934866i \(-0.384480\pi\)
0.355001 + 0.934866i \(0.384480\pi\)
\(920\) −1.21376 4.91249i −0.0400165 0.161960i
\(921\) 0 0
\(922\) 0.769413 + 9.50861i 0.0253393 + 0.313149i
\(923\) 4.65685i 0.153282i
\(924\) 0 0
\(925\) 21.9678i 0.722296i
\(926\) −15.7453 + 1.27407i −0.517422 + 0.0418685i
\(927\) 0 0
\(928\) −14.9463 34.9890i −0.490636 1.14857i
\(929\) 15.7500 0.516739 0.258370 0.966046i \(-0.416815\pi\)
0.258370 + 0.966046i \(0.416815\pi\)
\(930\) 0 0
\(931\) 7.63843i 0.250339i
\(932\) −34.1042 + 5.55562i −1.11712 + 0.181981i
\(933\) 0 0
\(934\) 0.423096 + 5.22873i 0.0138441 + 0.171089i
\(935\) 2.23312 0.0730307
\(936\) 0 0
\(937\) 17.0687 0.557610 0.278805 0.960348i \(-0.410062\pi\)
0.278805 + 0.960348i \(0.410062\pi\)
\(938\) −0.923293 11.4103i −0.0301466 0.372560i
\(939\) 0 0
\(940\) −4.09310 25.1262i −0.133502 0.819527i
\(941\) 26.5456i 0.865362i −0.901547 0.432681i \(-0.857568\pi\)
0.901547 0.432681i \(-0.142432\pi\)
\(942\) 0 0
\(943\) −0.657782 −0.0214203
\(944\) −5.07810 15.1728i −0.165278 0.493832i
\(945\) 0 0
\(946\) −63.4330 + 5.13285i −2.06239 + 0.166883i
\(947\) 20.3265i 0.660522i −0.943890 0.330261i \(-0.892863\pi\)
0.943890 0.330261i \(-0.107137\pi\)
\(948\) 0 0
\(949\) 1.52615i 0.0495408i
\(950\) −3.24623 40.1177i −0.105322 1.30159i
\(951\) 0 0
\(952\) −1.13955 + 0.281554i −0.0369329 + 0.00912523i
\(953\) 38.6855 1.25315 0.626573 0.779362i \(-0.284457\pi\)
0.626573 + 0.779362i \(0.284457\pi\)
\(954\) 0 0
\(955\) 11.5209i 0.372809i
\(956\) 20.7700 3.38346i 0.671748 0.109429i
\(957\) 0 0
\(958\) 3.06591 0.248086i 0.0990550 0.00801529i
\(959\) 12.9618 0.418559
\(960\) 0 0
\(961\) 3.76186 0.121350
\(962\) −3.79184 + 0.306826i −0.122254 + 0.00989247i
\(963\) 0 0
\(964\) −12.0548 + 1.96375i −0.388260 + 0.0632482i
\(965\) 6.73192i 0.216708i
\(966\) 0 0
\(967\) −26.6606 −0.857346 −0.428673 0.903460i \(-0.641019\pi\)
−0.428673 + 0.903460i \(0.641019\pi\)
\(968\) −32.1977 + 7.95529i −1.03487 + 0.255693i
\(969\) 0 0
\(970\) 2.11748 + 26.1684i 0.0679882 + 0.840216i
\(971\) 3.27685i 0.105159i −0.998617 0.0525796i \(-0.983256\pi\)
0.998617 0.0525796i \(-0.0167443\pi\)
\(972\) 0 0
\(973\) 18.3644i 0.588734i
\(974\) −6.36436 + 0.514988i −0.203927 + 0.0165013i
\(975\) 0 0
\(976\) −2.28673 6.83247i −0.0731963 0.218702i
\(977\) −12.0387 −0.385153 −0.192576 0.981282i \(-0.561684\pi\)
−0.192576 + 0.981282i \(0.561684\pi\)
\(978\) 0 0
\(979\) 23.5021i 0.751131i
\(980\) 0.362965 + 2.22812i 0.0115945 + 0.0711748i
\(981\) 0 0
\(982\) −0.218110 2.69546i −0.00696016 0.0860155i
\(983\) −4.42188 −0.141036 −0.0705181 0.997510i \(-0.522465\pi\)
−0.0705181 + 0.997510i \(0.522465\pi\)
\(984\) 0 0
\(985\) −21.2299 −0.676442
\(986\) 0.318381 + 3.93463i 0.0101393 + 0.125304i
\(987\) 0 0
\(988\) 6.87934 1.12066i 0.218861 0.0356528i
\(989\) 14.9618i 0.475758i
\(990\) 0 0
\(991\) −9.10184 −0.289129 −0.144565 0.989495i \(-0.546178\pi\)
−0.144565 + 0.989495i \(0.546178\pi\)
\(992\) −30.6712 + 13.1018i −0.973811 + 0.415984i
\(993\) 0 0
\(994\) −14.3876 + 1.16421i −0.456348 + 0.0369266i
\(995\) 3.69873i 0.117258i
\(996\) 0 0
\(997\) 42.8556i 1.35725i −0.734485 0.678625i \(-0.762576\pi\)
0.734485 0.678625i \(-0.237424\pi\)
\(998\) −3.12604 38.6324i −0.0989530 1.22289i
\(999\) 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 504.2.c.f.253.7 8
3.2 odd 2 168.2.c.b.85.2 yes 8
4.3 odd 2 2016.2.c.e.1009.6 8
8.3 odd 2 2016.2.c.e.1009.3 8
8.5 even 2 inner 504.2.c.f.253.8 8
12.11 even 2 672.2.c.b.337.6 8
21.20 even 2 1176.2.c.c.589.2 8
24.5 odd 2 168.2.c.b.85.1 8
24.11 even 2 672.2.c.b.337.3 8
48.5 odd 4 5376.2.a.bm.1.3 4
48.11 even 4 5376.2.a.bq.1.3 4
48.29 odd 4 5376.2.a.bp.1.2 4
48.35 even 4 5376.2.a.bl.1.2 4
84.83 odd 2 4704.2.c.c.2353.3 8
168.83 odd 2 4704.2.c.c.2353.6 8
168.125 even 2 1176.2.c.c.589.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.c.b.85.1 8 24.5 odd 2
168.2.c.b.85.2 yes 8 3.2 odd 2
504.2.c.f.253.7 8 1.1 even 1 trivial
504.2.c.f.253.8 8 8.5 even 2 inner
672.2.c.b.337.3 8 24.11 even 2
672.2.c.b.337.6 8 12.11 even 2
1176.2.c.c.589.1 8 168.125 even 2
1176.2.c.c.589.2 8 21.20 even 2
2016.2.c.e.1009.3 8 8.3 odd 2
2016.2.c.e.1009.6 8 4.3 odd 2
4704.2.c.c.2353.3 8 84.83 odd 2
4704.2.c.c.2353.6 8 168.83 odd 2
5376.2.a.bl.1.2 4 48.35 even 4
5376.2.a.bm.1.3 4 48.5 odd 4
5376.2.a.bp.1.2 4 48.29 odd 4
5376.2.a.bq.1.3 4 48.11 even 4