Properties

Label 1368.2.e.g.379.5
Level $1368$
Weight $2$
Character 1368.379
Analytic conductor $10.924$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1368,2,Mod(379,1368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1368.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.e (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: \(10.9235349965\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.5
Character \(\chi\) \(=\) 1368.379
Dual form 1368.2.e.g.379.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33983 - 0.452615i) q^{2} +(1.59028 + 1.21285i) q^{4} -0.393257i q^{5} +1.35370i q^{7} +(-1.58175 - 2.34480i) q^{8} +O(q^{10})\) \(q+(-1.33983 - 0.452615i) q^{2} +(1.59028 + 1.21285i) q^{4} -0.393257i q^{5} +1.35370i q^{7} +(-1.58175 - 2.34480i) q^{8} +(-0.177994 + 0.526897i) q^{10} -1.21598 q^{11} -3.30636 q^{13} +(0.612703 - 1.81372i) q^{14} +(1.05798 + 3.85755i) q^{16} +0.00555711 q^{17} +(2.48659 - 3.58007i) q^{19} +(0.476963 - 0.625388i) q^{20} +(1.62920 + 0.550370i) q^{22} +0.677182i q^{23} +4.84535 q^{25} +(4.42996 + 1.49651i) q^{26} +(-1.64183 + 2.15275i) q^{28} +5.04174 q^{29} +4.84195 q^{31} +(0.328479 - 5.64731i) q^{32} +(-0.00744557 - 0.00251523i) q^{34} +0.532350 q^{35} -4.23826 q^{37} +(-4.95199 + 3.67121i) q^{38} +(-0.922108 + 0.622032i) q^{40} -1.96739i q^{41} +4.59845 q^{43} +(-1.93374 - 1.47480i) q^{44} +(0.306503 - 0.907308i) q^{46} +10.9421i q^{47} +5.16751 q^{49} +(-6.49194 - 2.19308i) q^{50} +(-5.25804 - 4.01013i) q^{52} +4.67945 q^{53} +0.478192i q^{55} +(3.17414 - 2.14120i) q^{56} +(-6.75507 - 2.28197i) q^{58} +9.88941i q^{59} -4.99390i q^{61} +(-6.48738 - 2.19154i) q^{62} +(-2.99616 + 7.41775i) q^{64} +1.30025i q^{65} +2.46296i q^{67} +(0.00883735 + 0.00673995i) q^{68} +(-0.713258 - 0.240950i) q^{70} -0.424001 q^{71} -1.23201 q^{73} +(5.67855 + 1.91830i) q^{74} +(8.29646 - 2.67744i) q^{76} -1.64606i q^{77} +11.1012 q^{79} +(1.51701 - 0.416056i) q^{80} +(-0.890470 + 2.63596i) q^{82} +7.42465 q^{83} -0.00218537i q^{85} +(-6.16114 - 2.08133i) q^{86} +(1.92337 + 2.85122i) q^{88} +11.9802i q^{89} -4.47581i q^{91} +(-0.821323 + 1.07691i) q^{92} +(4.95256 - 14.6605i) q^{94} +(-1.40789 - 0.977868i) q^{95} +2.05436i q^{97} +(-6.92357 - 2.33889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).

\(n\) \(343\) \(685\) \(1009\) \(1217\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33983 0.452615i −0.947402 0.320047i
\(3\) 0 0
\(4\) 1.59028 + 1.21285i 0.795140 + 0.606426i
\(5\) 0.393257i 0.175870i −0.996126 0.0879349i \(-0.971973\pi\)
0.996126 0.0879349i \(-0.0280268\pi\)
\(6\) 0 0
\(7\) 1.35370i 0.511649i 0.966723 + 0.255824i \(0.0823469\pi\)
−0.966723 + 0.255824i \(0.917653\pi\)
\(8\) −1.58175 2.34480i −0.559231 0.829012i
\(9\) 0 0
\(10\) −0.177994 + 0.526897i −0.0562866 + 0.166619i
\(11\) −1.21598 −0.366631 −0.183316 0.983054i \(-0.558683\pi\)
−0.183316 + 0.983054i \(0.558683\pi\)
\(12\) 0 0
\(13\) −3.30636 −0.917020 −0.458510 0.888689i \(-0.651617\pi\)
−0.458510 + 0.888689i \(0.651617\pi\)
\(14\) 0.612703 1.81372i 0.163752 0.484737i
\(15\) 0 0
\(16\) 1.05798 + 3.85755i 0.264494 + 0.964387i
\(17\) 0.00555711 0.00134780 0.000673898 1.00000i \(-0.499785\pi\)
0.000673898 1.00000i \(0.499785\pi\)
\(18\) 0 0
\(19\) 2.48659 3.58007i 0.570462 0.821324i
\(20\) 0.476963 0.625388i 0.106652 0.139841i
\(21\) 0 0
\(22\) 1.62920 + 0.550370i 0.347347 + 0.117339i
\(23\) 0.677182i 0.141202i 0.997505 + 0.0706011i \(0.0224918\pi\)
−0.997505 + 0.0706011i \(0.977508\pi\)
\(24\) 0 0
\(25\) 4.84535 0.969070
\(26\) 4.42996 + 1.49651i 0.868786 + 0.293490i
\(27\) 0 0
\(28\) −1.64183 + 2.15275i −0.310277 + 0.406832i
\(29\) 5.04174 0.936228 0.468114 0.883668i \(-0.344934\pi\)
0.468114 + 0.883668i \(0.344934\pi\)
\(30\) 0 0
\(31\) 4.84195 0.869639 0.434820 0.900518i \(-0.356812\pi\)
0.434820 + 0.900518i \(0.356812\pi\)
\(32\) 0.328479 5.64731i 0.0580674 0.998313i
\(33\) 0 0
\(34\) −0.00744557 0.00251523i −0.00127690 0.000431358i
\(35\) 0.532350 0.0899836
\(36\) 0 0
\(37\) −4.23826 −0.696766 −0.348383 0.937352i \(-0.613269\pi\)
−0.348383 + 0.937352i \(0.613269\pi\)
\(38\) −4.95199 + 3.67121i −0.803319 + 0.595549i
\(39\) 0 0
\(40\) −0.922108 + 0.622032i −0.145798 + 0.0983519i
\(41\) 1.96739i 0.307254i −0.988129 0.153627i \(-0.950905\pi\)
0.988129 0.153627i \(-0.0490955\pi\)
\(42\) 0 0
\(43\) 4.59845 0.701257 0.350629 0.936515i \(-0.385968\pi\)
0.350629 + 0.936515i \(0.385968\pi\)
\(44\) −1.93374 1.47480i −0.291523 0.222335i
\(45\) 0 0
\(46\) 0.306503 0.907308i 0.0451914 0.133775i
\(47\) 10.9421i 1.59607i 0.602612 + 0.798034i \(0.294127\pi\)
−0.602612 + 0.798034i \(0.705873\pi\)
\(48\) 0 0
\(49\) 5.16751 0.738215
\(50\) −6.49194 2.19308i −0.918098 0.310148i
\(51\) 0 0
\(52\) −5.25804 4.01013i −0.729159 0.556105i
\(53\) 4.67945 0.642772 0.321386 0.946948i \(-0.395851\pi\)
0.321386 + 0.946948i \(0.395851\pi\)
\(54\) 0 0
\(55\) 0.478192i 0.0644793i
\(56\) 3.17414 2.14120i 0.424163 0.286130i
\(57\) 0 0
\(58\) −6.75507 2.28197i −0.886984 0.299637i
\(59\) 9.88941i 1.28749i 0.765240 + 0.643745i \(0.222620\pi\)
−0.765240 + 0.643745i \(0.777380\pi\)
\(60\) 0 0
\(61\) 4.99390i 0.639403i −0.947518 0.319701i \(-0.896417\pi\)
0.947518 0.319701i \(-0.103583\pi\)
\(62\) −6.48738 2.19154i −0.823897 0.278326i
\(63\) 0 0
\(64\) −2.99616 + 7.41775i −0.374520 + 0.927219i
\(65\) 1.30025i 0.161276i
\(66\) 0 0
\(67\) 2.46296i 0.300899i 0.988618 + 0.150450i \(0.0480721\pi\)
−0.988618 + 0.150450i \(0.951928\pi\)
\(68\) 0.00883735 + 0.00673995i 0.00107169 + 0.000817339i
\(69\) 0 0
\(70\) −0.713258 0.240950i −0.0852506 0.0287990i
\(71\) −0.424001 −0.0503197 −0.0251598 0.999683i \(-0.508009\pi\)
−0.0251598 + 0.999683i \(0.508009\pi\)
\(72\) 0 0
\(73\) −1.23201 −0.144196 −0.0720978 0.997398i \(-0.522969\pi\)
−0.0720978 + 0.997398i \(0.522969\pi\)
\(74\) 5.67855 + 1.91830i 0.660118 + 0.222998i
\(75\) 0 0
\(76\) 8.29646 2.67744i 0.951670 0.307124i
\(77\) 1.64606i 0.187586i
\(78\) 0 0
\(79\) 11.1012 1.24899 0.624494 0.781030i \(-0.285305\pi\)
0.624494 + 0.781030i \(0.285305\pi\)
\(80\) 1.51701 0.416056i 0.169607 0.0465165i
\(81\) 0 0
\(82\) −0.890470 + 2.63596i −0.0983359 + 0.291093i
\(83\) 7.42465 0.814961 0.407481 0.913214i \(-0.366407\pi\)
0.407481 + 0.913214i \(0.366407\pi\)
\(84\) 0 0
\(85\) 0.00218537i 0.000237037i
\(86\) −6.16114 2.08133i −0.664372 0.224435i
\(87\) 0 0
\(88\) 1.92337 + 2.85122i 0.205032 + 0.303941i
\(89\) 11.9802i 1.26990i 0.772552 + 0.634952i \(0.218980\pi\)
−0.772552 + 0.634952i \(0.781020\pi\)
\(90\) 0 0
\(91\) 4.47581i 0.469192i
\(92\) −0.821323 + 1.07691i −0.0856288 + 0.112276i
\(93\) 0 0
\(94\) 4.95256 14.6605i 0.510817 1.51212i
\(95\) −1.40789 0.977868i −0.144446 0.100327i
\(96\) 0 0
\(97\) 2.05436i 0.208589i 0.994546 + 0.104295i \(0.0332585\pi\)
−0.994546 + 0.104295i \(0.966742\pi\)
\(98\) −6.92357 2.33889i −0.699386 0.236264i
\(99\) 0 0
\(100\) 7.70546 + 5.87670i 0.770546 + 0.587670i
\(101\) 8.75636i 0.871291i −0.900118 0.435645i \(-0.856520\pi\)
0.900118 0.435645i \(-0.143480\pi\)
\(102\) 0 0
\(103\) 9.60437 0.946346 0.473173 0.880969i \(-0.343108\pi\)
0.473173 + 0.880969i \(0.343108\pi\)
\(104\) 5.22982 + 7.75275i 0.512826 + 0.760220i
\(105\) 0 0
\(106\) −6.26966 2.11799i −0.608964 0.205718i
\(107\) 7.32145i 0.707791i 0.935285 + 0.353896i \(0.115143\pi\)
−0.935285 + 0.353896i \(0.884857\pi\)
\(108\) 0 0
\(109\) −6.70281 −0.642013 −0.321006 0.947077i \(-0.604021\pi\)
−0.321006 + 0.947077i \(0.604021\pi\)
\(110\) 0.216437 0.640695i 0.0206364 0.0610878i
\(111\) 0 0
\(112\) −5.22195 + 1.43218i −0.493428 + 0.135328i
\(113\) 2.04224i 0.192118i −0.995376 0.0960588i \(-0.969376\pi\)
0.995376 0.0960588i \(-0.0306237\pi\)
\(114\) 0 0
\(115\) 0.266307 0.0248332
\(116\) 8.01778 + 6.11489i 0.744432 + 0.567753i
\(117\) 0 0
\(118\) 4.47609 13.2501i 0.412058 1.21977i
\(119\) 0.00752263i 0.000689598i
\(120\) 0 0
\(121\) −9.52140 −0.865582
\(122\) −2.26031 + 6.69096i −0.204639 + 0.605771i
\(123\) 0 0
\(124\) 7.70005 + 5.87257i 0.691484 + 0.527372i
\(125\) 3.87175i 0.346300i
\(126\) 0 0
\(127\) −5.00649 −0.444254 −0.222127 0.975018i \(-0.571300\pi\)
−0.222127 + 0.975018i \(0.571300\pi\)
\(128\) 7.37173 8.58240i 0.651575 0.758584i
\(129\) 0 0
\(130\) 0.588513 1.74211i 0.0516160 0.152793i
\(131\) 16.6424 1.45406 0.727028 0.686608i \(-0.240901\pi\)
0.727028 + 0.686608i \(0.240901\pi\)
\(132\) 0 0
\(133\) 4.84632 + 3.36608i 0.420229 + 0.291876i
\(134\) 1.11477 3.29995i 0.0963019 0.285072i
\(135\) 0 0
\(136\) −0.00878993 0.0130303i −0.000753730 0.00111734i
\(137\) 13.3028 1.13653 0.568267 0.822844i \(-0.307614\pi\)
0.568267 + 0.822844i \(0.307614\pi\)
\(138\) 0 0
\(139\) 14.9252 1.26594 0.632968 0.774178i \(-0.281836\pi\)
0.632968 + 0.774178i \(0.281836\pi\)
\(140\) 0.846585 + 0.645662i 0.0715495 + 0.0545684i
\(141\) 0 0
\(142\) 0.568089 + 0.191909i 0.0476729 + 0.0161047i
\(143\) 4.02046 0.336208
\(144\) 0 0
\(145\) 1.98270i 0.164654i
\(146\) 1.65068 + 0.557625i 0.136611 + 0.0461494i
\(147\) 0 0
\(148\) −6.74002 5.14039i −0.554027 0.422538i
\(149\) 19.2617i 1.57798i −0.614408 0.788989i \(-0.710605\pi\)
0.614408 0.788989i \(-0.289395\pi\)
\(150\) 0 0
\(151\) 19.3294 1.57300 0.786501 0.617589i \(-0.211890\pi\)
0.786501 + 0.617589i \(0.211890\pi\)
\(152\) −12.3277 0.167793i −0.999907 0.0136098i
\(153\) 0 0
\(154\) −0.745033 + 2.20544i −0.0600365 + 0.177720i
\(155\) 1.90413i 0.152943i
\(156\) 0 0
\(157\) 2.56382i 0.204615i −0.994753 0.102307i \(-0.967377\pi\)
0.994753 0.102307i \(-0.0326226\pi\)
\(158\) −14.8738 5.02459i −1.18329 0.399735i
\(159\) 0 0
\(160\) −2.22084 0.129177i −0.175573 0.0102123i
\(161\) −0.916699 −0.0722460
\(162\) 0 0
\(163\) −16.0963 −1.26076 −0.630378 0.776288i \(-0.717100\pi\)
−0.630378 + 0.776288i \(0.717100\pi\)
\(164\) 2.38615 3.12870i 0.186327 0.244310i
\(165\) 0 0
\(166\) −9.94775 3.36051i −0.772096 0.260826i
\(167\) 16.5107 1.27764 0.638818 0.769358i \(-0.279424\pi\)
0.638818 + 0.769358i \(0.279424\pi\)
\(168\) 0 0
\(169\) −2.06797 −0.159075
\(170\) −0.000989132 0.00292802i −7.58629e−5 0.000224569i
\(171\) 0 0
\(172\) 7.31282 + 5.57725i 0.557598 + 0.425261i
\(173\) 13.8251 1.05110 0.525550 0.850763i \(-0.323860\pi\)
0.525550 + 0.850763i \(0.323860\pi\)
\(174\) 0 0
\(175\) 6.55913i 0.495823i
\(176\) −1.28648 4.69069i −0.0969717 0.353574i
\(177\) 0 0
\(178\) 5.42244 16.0515i 0.406429 1.20311i
\(179\) 9.07865i 0.678570i −0.940684 0.339285i \(-0.889815\pi\)
0.940684 0.339285i \(-0.110185\pi\)
\(180\) 0 0
\(181\) −4.43828 −0.329895 −0.164947 0.986302i \(-0.552745\pi\)
−0.164947 + 0.986302i \(0.552745\pi\)
\(182\) −2.02582 + 5.99681i −0.150164 + 0.444513i
\(183\) 0 0
\(184\) 1.58786 1.07113i 0.117058 0.0789648i
\(185\) 1.66673i 0.122540i
\(186\) 0 0
\(187\) −0.00675732 −0.000494144
\(188\) −13.2712 + 17.4010i −0.967898 + 1.26910i
\(189\) 0 0
\(190\) 1.44373 + 1.94741i 0.104739 + 0.141280i
\(191\) 10.7380i 0.776976i −0.921454 0.388488i \(-0.872997\pi\)
0.921454 0.388488i \(-0.127003\pi\)
\(192\) 0 0
\(193\) 24.4529i 1.76016i 0.474826 + 0.880080i \(0.342511\pi\)
−0.474826 + 0.880080i \(0.657489\pi\)
\(194\) 0.929836 2.75250i 0.0667584 0.197618i
\(195\) 0 0
\(196\) 8.21778 + 6.26743i 0.586984 + 0.447673i
\(197\) 0.602544i 0.0429295i −0.999770 0.0214647i \(-0.993167\pi\)
0.999770 0.0214647i \(-0.00683297\pi\)
\(198\) 0 0
\(199\) 1.82192i 0.129152i −0.997913 0.0645761i \(-0.979430\pi\)
0.997913 0.0645761i \(-0.0205695\pi\)
\(200\) −7.66411 11.3614i −0.541934 0.803370i
\(201\) 0 0
\(202\) −3.96326 + 11.7320i −0.278854 + 0.825462i
\(203\) 6.82498i 0.479020i
\(204\) 0 0
\(205\) −0.773689 −0.0540368
\(206\) −12.8682 4.34708i −0.896570 0.302875i
\(207\) 0 0
\(208\) −3.49805 12.7545i −0.242546 0.884362i
\(209\) −3.02364 + 4.35328i −0.209149 + 0.301123i
\(210\) 0 0
\(211\) 5.00976i 0.344886i 0.985020 + 0.172443i \(0.0551660\pi\)
−0.985020 + 0.172443i \(0.944834\pi\)
\(212\) 7.44164 + 5.67549i 0.511094 + 0.389794i
\(213\) 0 0
\(214\) 3.31380 9.80948i 0.226527 0.670563i
\(215\) 1.80837i 0.123330i
\(216\) 0 0
\(217\) 6.55452i 0.444950i
\(218\) 8.98061 + 3.03379i 0.608244 + 0.205474i
\(219\) 0 0
\(220\) −0.579976 + 0.760458i −0.0391020 + 0.0512701i
\(221\) −0.0183738 −0.00123596
\(222\) 0 0
\(223\) −6.38809 −0.427778 −0.213889 0.976858i \(-0.568613\pi\)
−0.213889 + 0.976858i \(0.568613\pi\)
\(224\) 7.64474 + 0.444661i 0.510786 + 0.0297101i
\(225\) 0 0
\(226\) −0.924347 + 2.73625i −0.0614867 + 0.182012i
\(227\) 12.2227i 0.811248i −0.914040 0.405624i \(-0.867054\pi\)
0.914040 0.405624i \(-0.132946\pi\)
\(228\) 0 0
\(229\) 22.2874i 1.47280i −0.676549 0.736398i \(-0.736525\pi\)
0.676549 0.736398i \(-0.263475\pi\)
\(230\) −0.356805 0.120534i −0.0235270 0.00794780i
\(231\) 0 0
\(232\) −7.97475 11.8219i −0.523568 0.776144i
\(233\) −6.96654 −0.456393 −0.228197 0.973615i \(-0.573283\pi\)
−0.228197 + 0.973615i \(0.573283\pi\)
\(234\) 0 0
\(235\) 4.30306 0.280700
\(236\) −11.9944 + 15.7269i −0.780769 + 1.02374i
\(237\) 0 0
\(238\) 0.00340486 0.0100790i 0.000220704 0.000653327i
\(239\) 9.25488i 0.598648i 0.954151 + 0.299324i \(0.0967612\pi\)
−0.954151 + 0.299324i \(0.903239\pi\)
\(240\) 0 0
\(241\) 7.83870i 0.504935i 0.967605 + 0.252468i \(0.0812421\pi\)
−0.967605 + 0.252468i \(0.918758\pi\)
\(242\) 12.7570 + 4.30953i 0.820053 + 0.277027i
\(243\) 0 0
\(244\) 6.05686 7.94169i 0.387751 0.508414i
\(245\) 2.03216i 0.129830i
\(246\) 0 0
\(247\) −8.22156 + 11.8370i −0.523125 + 0.753170i
\(248\) −7.65873 11.3534i −0.486330 0.720941i
\(249\) 0 0
\(250\) −1.75241 + 5.18748i −0.110832 + 0.328085i
\(251\) 8.09717 0.511089 0.255544 0.966797i \(-0.417745\pi\)
0.255544 + 0.966797i \(0.417745\pi\)
\(252\) 0 0
\(253\) 0.823439i 0.0517691i
\(254\) 6.70784 + 2.26601i 0.420887 + 0.142182i
\(255\) 0 0
\(256\) −13.7614 + 8.16239i −0.860086 + 0.510149i
\(257\) 4.42157i 0.275810i 0.990445 + 0.137905i \(0.0440369\pi\)
−0.990445 + 0.137905i \(0.955963\pi\)
\(258\) 0 0
\(259\) 5.73732i 0.356500i
\(260\) −1.57701 + 2.06776i −0.0978021 + 0.128237i
\(261\) 0 0
\(262\) −22.2980 7.53262i −1.37758 0.465367i
\(263\) 0.798438i 0.0492338i 0.999697 + 0.0246169i \(0.00783660\pi\)
−0.999697 + 0.0246169i \(0.992163\pi\)
\(264\) 0 0
\(265\) 1.84023i 0.113044i
\(266\) −4.96970 6.70349i −0.304712 0.411017i
\(267\) 0 0
\(268\) −2.98721 + 3.91680i −0.182473 + 0.239257i
\(269\) −14.3823 −0.876903 −0.438451 0.898755i \(-0.644473\pi\)
−0.438451 + 0.898755i \(0.644473\pi\)
\(270\) 0 0
\(271\) 29.7531i 1.80737i 0.428197 + 0.903686i \(0.359149\pi\)
−0.428197 + 0.903686i \(0.640851\pi\)
\(272\) 0.00587928 + 0.0214368i 0.000356484 + 0.00129980i
\(273\) 0 0
\(274\) −17.8235 6.02105i −1.07675 0.363745i
\(275\) −5.89184 −0.355291
\(276\) 0 0
\(277\) 26.7252i 1.60576i −0.596138 0.802882i \(-0.703299\pi\)
0.596138 0.802882i \(-0.296701\pi\)
\(278\) −19.9972 6.75536i −1.19935 0.405159i
\(279\) 0 0
\(280\) −0.842042 1.24825i −0.0503217 0.0745974i
\(281\) 9.71220i 0.579381i −0.957120 0.289690i \(-0.906448\pi\)
0.957120 0.289690i \(-0.0935524\pi\)
\(282\) 0 0
\(283\) −0.279927 −0.0166399 −0.00831995 0.999965i \(-0.502648\pi\)
−0.00831995 + 0.999965i \(0.502648\pi\)
\(284\) −0.674280 0.514251i −0.0400112 0.0305152i
\(285\) 0 0
\(286\) −5.38673 1.81972i −0.318524 0.107602i
\(287\) 2.66325 0.157206
\(288\) 0 0
\(289\) −17.0000 −0.999998
\(290\) −0.897400 + 2.65648i −0.0526971 + 0.155994i
\(291\) 0 0
\(292\) −1.95923 1.49424i −0.114656 0.0874440i
\(293\) −26.6739 −1.55831 −0.779154 0.626833i \(-0.784351\pi\)
−0.779154 + 0.626833i \(0.784351\pi\)
\(294\) 0 0
\(295\) 3.88908 0.226431
\(296\) 6.70386 + 9.93788i 0.389654 + 0.577627i
\(297\) 0 0
\(298\) −8.71812 + 25.8073i −0.505027 + 1.49498i
\(299\) 2.23901i 0.129485i
\(300\) 0 0
\(301\) 6.22491i 0.358798i
\(302\) −25.8980 8.74877i −1.49026 0.503435i
\(303\) 0 0
\(304\) 16.4410 + 5.80451i 0.942958 + 0.332911i
\(305\) −1.96388 −0.112452
\(306\) 0 0
\(307\) 18.0033i 1.02750i 0.857939 + 0.513751i \(0.171744\pi\)
−0.857939 + 0.513751i \(0.828256\pi\)
\(308\) 1.99643 2.61770i 0.113757 0.149157i
\(309\) 0 0
\(310\) −0.861837 + 2.55121i −0.0489491 + 0.144899i
\(311\) 19.2359i 1.09077i −0.838186 0.545385i \(-0.816384\pi\)
0.838186 0.545385i \(-0.183616\pi\)
\(312\) 0 0
\(313\) −20.0287 −1.13209 −0.566044 0.824375i \(-0.691527\pi\)
−0.566044 + 0.824375i \(0.691527\pi\)
\(314\) −1.16042 + 3.43507i −0.0654864 + 0.193852i
\(315\) 0 0
\(316\) 17.6541 + 13.4642i 0.993119 + 0.757419i
\(317\) −11.0972 −0.623283 −0.311642 0.950200i \(-0.600879\pi\)
−0.311642 + 0.950200i \(0.600879\pi\)
\(318\) 0 0
\(319\) −6.13065 −0.343250
\(320\) 2.91708 + 1.17826i 0.163070 + 0.0658668i
\(321\) 0 0
\(322\) 1.22822 + 0.414912i 0.0684460 + 0.0231221i
\(323\) 0.0138182 0.0198948i 0.000768867 0.00110698i
\(324\) 0 0
\(325\) −16.0205 −0.888656
\(326\) 21.5662 + 7.28541i 1.19444 + 0.403502i
\(327\) 0 0
\(328\) −4.61313 + 3.11191i −0.254718 + 0.171826i
\(329\) −14.8123 −0.816627
\(330\) 0 0
\(331\) 23.0048i 1.26446i 0.774781 + 0.632230i \(0.217860\pi\)
−0.774781 + 0.632230i \(0.782140\pi\)
\(332\) 11.8073 + 9.00501i 0.648008 + 0.494214i
\(333\) 0 0
\(334\) −22.1215 7.47299i −1.21044 0.408904i
\(335\) 0.968578 0.0529191
\(336\) 0 0
\(337\) 14.7725i 0.804710i 0.915484 + 0.402355i \(0.131808\pi\)
−0.915484 + 0.402355i \(0.868192\pi\)
\(338\) 2.77073 + 0.935995i 0.150708 + 0.0509114i
\(339\) 0 0
\(340\) 0.00265053 0.00347535i 0.000143745 0.000188477i
\(341\) −5.88770 −0.318837
\(342\) 0 0
\(343\) 16.4711i 0.889356i
\(344\) −7.27358 10.7824i −0.392165 0.581351i
\(345\) 0 0
\(346\) −18.5232 6.25743i −0.995813 0.336401i
\(347\) −32.3507 −1.73668 −0.868338 0.495973i \(-0.834811\pi\)
−0.868338 + 0.495973i \(0.834811\pi\)
\(348\) 0 0
\(349\) 28.8848i 1.54617i −0.634303 0.773084i \(-0.718713\pi\)
0.634303 0.773084i \(-0.281287\pi\)
\(350\) 2.96876 8.78810i 0.158687 0.469744i
\(351\) 0 0
\(352\) −0.399423 + 6.86700i −0.0212893 + 0.366012i
\(353\) 22.1629 1.17961 0.589806 0.807545i \(-0.299204\pi\)
0.589806 + 0.807545i \(0.299204\pi\)
\(354\) 0 0
\(355\) 0.166741i 0.00884971i
\(356\) −14.5303 + 19.0519i −0.770103 + 1.00975i
\(357\) 0 0
\(358\) −4.10913 + 12.1638i −0.217174 + 0.642878i
\(359\) 21.0084i 1.10878i 0.832256 + 0.554391i \(0.187049\pi\)
−0.832256 + 0.554391i \(0.812951\pi\)
\(360\) 0 0
\(361\) −6.63376 17.8043i −0.349145 0.937069i
\(362\) 5.94653 + 2.00883i 0.312543 + 0.105582i
\(363\) 0 0
\(364\) 5.42850 7.11778i 0.284531 0.373073i
\(365\) 0.484495i 0.0253596i
\(366\) 0 0
\(367\) 4.90961i 0.256280i −0.991756 0.128140i \(-0.959099\pi\)
0.991756 0.128140i \(-0.0409007\pi\)
\(368\) −2.61226 + 0.716443i −0.136174 + 0.0373472i
\(369\) 0 0
\(370\) 0.754386 2.23313i 0.0392186 0.116095i
\(371\) 6.33456i 0.328874i
\(372\) 0 0
\(373\) −16.5859 −0.858784 −0.429392 0.903118i \(-0.641272\pi\)
−0.429392 + 0.903118i \(0.641272\pi\)
\(374\) 0.00905365 + 0.00305846i 0.000468153 + 0.000158149i
\(375\) 0 0
\(376\) 25.6570 17.3076i 1.32316 0.892572i
\(377\) −16.6698 −0.858540
\(378\) 0 0
\(379\) 25.6241i 1.31622i −0.752920 0.658112i \(-0.771356\pi\)
0.752920 0.658112i \(-0.228644\pi\)
\(380\) −1.05292 3.26264i −0.0540138 0.167370i
\(381\) 0 0
\(382\) −4.86019 + 14.3871i −0.248669 + 0.736108i
\(383\) −24.1194 −1.23245 −0.616223 0.787572i \(-0.711338\pi\)
−0.616223 + 0.787572i \(0.711338\pi\)
\(384\) 0 0
\(385\) −0.647326 −0.0329908
\(386\) 11.0678 32.7627i 0.563334 1.66758i
\(387\) 0 0
\(388\) −2.49164 + 3.26701i −0.126494 + 0.165857i
\(389\) 26.1872i 1.32774i 0.747847 + 0.663871i \(0.231087\pi\)
−0.747847 + 0.663871i \(0.768913\pi\)
\(390\) 0 0
\(391\) 0.00376317i 0.000190312i
\(392\) −8.17368 12.1168i −0.412833 0.611989i
\(393\) 0 0
\(394\) −0.272721 + 0.807306i −0.0137395 + 0.0406715i
\(395\) 4.36564i 0.219659i
\(396\) 0 0
\(397\) 5.83861i 0.293032i 0.989208 + 0.146516i \(0.0468059\pi\)
−0.989208 + 0.146516i \(0.953194\pi\)
\(398\) −0.824627 + 2.44106i −0.0413348 + 0.122359i
\(399\) 0 0
\(400\) 5.12626 + 18.6912i 0.256313 + 0.934559i
\(401\) 10.8439i 0.541519i 0.962647 + 0.270759i \(0.0872748\pi\)
−0.962647 + 0.270759i \(0.912725\pi\)
\(402\) 0 0
\(403\) −16.0092 −0.797476
\(404\) 10.6202 13.9251i 0.528374 0.692798i
\(405\) 0 0
\(406\) 3.08909 9.14431i 0.153309 0.453824i
\(407\) 5.15364 0.255456
\(408\) 0 0
\(409\) 23.8663i 1.18011i −0.807363 0.590055i \(-0.799106\pi\)
0.807363 0.590055i \(-0.200894\pi\)
\(410\) 1.03661 + 0.350183i 0.0511945 + 0.0172943i
\(411\) 0 0
\(412\) 15.2736 + 11.6487i 0.752477 + 0.573889i
\(413\) −13.3872 −0.658743
\(414\) 0 0
\(415\) 2.91979i 0.143327i
\(416\) −1.08607 + 18.6720i −0.0532490 + 0.915472i
\(417\) 0 0
\(418\) 6.02151 4.46411i 0.294522 0.218347i
\(419\) −10.0928 −0.493064 −0.246532 0.969135i \(-0.579291\pi\)
−0.246532 + 0.969135i \(0.579291\pi\)
\(420\) 0 0
\(421\) 21.2013 1.03329 0.516645 0.856200i \(-0.327181\pi\)
0.516645 + 0.856200i \(0.327181\pi\)
\(422\) 2.26749 6.71221i 0.110380 0.326745i
\(423\) 0 0
\(424\) −7.40171 10.9724i −0.359459 0.532866i
\(425\) 0.0269261 0.00130611
\(426\) 0 0
\(427\) 6.76021 0.327150
\(428\) −8.87984 + 11.6431i −0.429223 + 0.562793i
\(429\) 0 0
\(430\) −0.818497 + 2.42291i −0.0394714 + 0.116843i
\(431\) 29.6252 1.42700 0.713498 0.700657i \(-0.247110\pi\)
0.713498 + 0.700657i \(0.247110\pi\)
\(432\) 0 0
\(433\) 37.6370i 1.80872i −0.426770 0.904360i \(-0.640349\pi\)
0.426770 0.904360i \(-0.359651\pi\)
\(434\) 2.96667 8.78193i 0.142405 0.421546i
\(435\) 0 0
\(436\) −10.6593 8.12952i −0.510490 0.389333i
\(437\) 2.42436 + 1.68387i 0.115973 + 0.0805506i
\(438\) 0 0
\(439\) −4.58779 −0.218963 −0.109482 0.993989i \(-0.534919\pi\)
−0.109482 + 0.993989i \(0.534919\pi\)
\(440\) 1.12126 0.756377i 0.0534541 0.0360589i
\(441\) 0 0
\(442\) 0.0246177 + 0.00831626i 0.00117095 + 0.000395564i
\(443\) 2.78642 0.132387 0.0661935 0.997807i \(-0.478915\pi\)
0.0661935 + 0.997807i \(0.478915\pi\)
\(444\) 0 0
\(445\) 4.71131 0.223338
\(446\) 8.55894 + 2.89135i 0.405278 + 0.136909i
\(447\) 0 0
\(448\) −10.0414 4.05589i −0.474410 0.191623i
\(449\) 25.9258i 1.22352i 0.791045 + 0.611758i \(0.209537\pi\)
−0.791045 + 0.611758i \(0.790463\pi\)
\(450\) 0 0
\(451\) 2.39230i 0.112649i
\(452\) 2.47693 3.24773i 0.116505 0.152760i
\(453\) 0 0
\(454\) −5.53217 + 16.3763i −0.259638 + 0.768577i
\(455\) −1.76014 −0.0825167
\(456\) 0 0
\(457\) 11.1120 0.519798 0.259899 0.965636i \(-0.416311\pi\)
0.259899 + 0.965636i \(0.416311\pi\)
\(458\) −10.0876 + 29.8613i −0.471364 + 1.39533i
\(459\) 0 0
\(460\) 0.423502 + 0.322991i 0.0197459 + 0.0150595i
\(461\) 40.3495i 1.87927i 0.342185 + 0.939633i \(0.388833\pi\)
−0.342185 + 0.939633i \(0.611167\pi\)
\(462\) 0 0
\(463\) 3.44187i 0.159957i −0.996797 0.0799787i \(-0.974515\pi\)
0.996797 0.0799787i \(-0.0254852\pi\)
\(464\) 5.33404 + 19.4488i 0.247627 + 0.902886i
\(465\) 0 0
\(466\) 9.33397 + 3.15316i 0.432388 + 0.146067i
\(467\) 31.1938 1.44348 0.721738 0.692166i \(-0.243344\pi\)
0.721738 + 0.692166i \(0.243344\pi\)
\(468\) 0 0
\(469\) −3.33410 −0.153955
\(470\) −5.76535 1.94763i −0.265936 0.0898374i
\(471\) 0 0
\(472\) 23.1887 15.6425i 1.06734 0.720005i
\(473\) −5.59162 −0.257103
\(474\) 0 0
\(475\) 12.0484 17.3467i 0.552818 0.795920i
\(476\) −0.00912384 + 0.0119631i −0.000418191 + 0.000548327i
\(477\) 0 0
\(478\) 4.18890 12.3999i 0.191596 0.567160i
\(479\) 0.844102i 0.0385680i −0.999814 0.0192840i \(-0.993861\pi\)
0.999814 0.0192840i \(-0.00613867\pi\)
\(480\) 0 0
\(481\) 14.0132 0.638949
\(482\) 3.54791 10.5025i 0.161603 0.478376i
\(483\) 0 0
\(484\) −15.1417 11.5481i −0.688258 0.524912i
\(485\) 0.807893 0.0366845
\(486\) 0 0
\(487\) −31.4332 −1.42437 −0.712186 0.701990i \(-0.752295\pi\)
−0.712186 + 0.701990i \(0.752295\pi\)
\(488\) −11.7097 + 7.89907i −0.530072 + 0.357574i
\(489\) 0 0
\(490\) −0.919785 + 2.72274i −0.0415517 + 0.123001i
\(491\) −33.2319 −1.49974 −0.749868 0.661588i \(-0.769883\pi\)
−0.749868 + 0.661588i \(0.769883\pi\)
\(492\) 0 0
\(493\) 0.0280175 0.00126184
\(494\) 16.3731 12.1383i 0.736660 0.546130i
\(495\) 0 0
\(496\) 5.12266 + 18.6780i 0.230014 + 0.838669i
\(497\) 0.573969i 0.0257460i
\(498\) 0 0
\(499\) −1.07956 −0.0483275 −0.0241638 0.999708i \(-0.507692\pi\)
−0.0241638 + 0.999708i \(0.507692\pi\)
\(500\) 4.69586 6.15717i 0.210005 0.275357i
\(501\) 0 0
\(502\) −10.8488 3.66490i −0.484206 0.163573i
\(503\) 34.2767i 1.52832i 0.645025 + 0.764162i \(0.276847\pi\)
−0.645025 + 0.764162i \(0.723153\pi\)
\(504\) 0 0
\(505\) −3.44350 −0.153234
\(506\) −0.372701 + 1.10327i −0.0165686 + 0.0490462i
\(507\) 0 0
\(508\) −7.96172 6.07214i −0.353244 0.269407i
\(509\) −15.7347 −0.697429 −0.348715 0.937229i \(-0.613382\pi\)
−0.348715 + 0.937229i \(0.613382\pi\)
\(510\) 0 0
\(511\) 1.66776i 0.0737775i
\(512\) 22.1323 4.70759i 0.978119 0.208048i
\(513\) 0 0
\(514\) 2.00127 5.92415i 0.0882722 0.261303i
\(515\) 3.77698i 0.166434i
\(516\) 0 0
\(517\) 13.3053i 0.585169i
\(518\) −2.59680 + 7.68702i −0.114097 + 0.337748i
\(519\) 0 0
\(520\) 3.04882 2.05666i 0.133700 0.0901907i
\(521\) 31.7648i 1.39164i −0.718215 0.695822i \(-0.755040\pi\)
0.718215 0.695822i \(-0.244960\pi\)
\(522\) 0 0
\(523\) 36.2049i 1.58313i −0.611086 0.791564i \(-0.709267\pi\)
0.611086 0.791564i \(-0.290733\pi\)
\(524\) 26.4661 + 20.1848i 1.15618 + 0.881778i
\(525\) 0 0
\(526\) 0.361385 1.06977i 0.0157571 0.0466442i
\(527\) 0.0269072 0.00117210
\(528\) 0 0
\(529\) 22.5414 0.980062
\(530\) −0.832915 + 2.46559i −0.0361795 + 0.107098i
\(531\) 0 0
\(532\) 3.62444 + 11.2309i 0.157139 + 0.486921i
\(533\) 6.50490i 0.281758i
\(534\) 0 0
\(535\) 2.87921 0.124479
\(536\) 5.77516 3.89578i 0.249449 0.168272i
\(537\) 0 0
\(538\) 19.2698 + 6.50964i 0.830779 + 0.280650i
\(539\) −6.28358 −0.270653
\(540\) 0 0
\(541\) 13.8419i 0.595108i 0.954705 + 0.297554i \(0.0961708\pi\)
−0.954705 + 0.297554i \(0.903829\pi\)
\(542\) 13.4667 39.8640i 0.578444 1.71231i
\(543\) 0 0
\(544\) 0.00182539 0.0313827i 7.82631e−5 0.00134552i
\(545\) 2.63593i 0.112911i
\(546\) 0 0
\(547\) 12.2681i 0.524545i 0.964994 + 0.262272i \(0.0844719\pi\)
−0.964994 + 0.262272i \(0.915528\pi\)
\(548\) 21.1552 + 16.1343i 0.903704 + 0.689225i
\(549\) 0 0
\(550\) 7.89405 + 2.66673i 0.336603 + 0.113710i
\(551\) 12.5367 18.0498i 0.534083 0.768946i
\(552\) 0 0
\(553\) 15.0277i 0.639043i
\(554\) −12.0962 + 35.8072i −0.513920 + 1.52130i
\(555\) 0 0
\(556\) 23.7352 + 18.1020i 1.00660 + 0.767697i
\(557\) 41.7859i 1.77053i −0.465090 0.885263i \(-0.653978\pi\)
0.465090 0.885263i \(-0.346022\pi\)
\(558\) 0 0
\(559\) −15.2041 −0.643067
\(560\) 0.563214 + 2.05357i 0.0238001 + 0.0867790i
\(561\) 0 0
\(562\) −4.39589 + 13.0127i −0.185429 + 0.548906i
\(563\) 5.24786i 0.221171i 0.993867 + 0.110585i \(0.0352726\pi\)
−0.993867 + 0.110585i \(0.964727\pi\)
\(564\) 0 0
\(565\) −0.803124 −0.0337877
\(566\) 0.375054 + 0.126699i 0.0157647 + 0.00532556i
\(567\) 0 0
\(568\) 0.670662 + 0.994197i 0.0281403 + 0.0417156i
\(569\) 32.6133i 1.36722i −0.729846 0.683611i \(-0.760408\pi\)
0.729846 0.683611i \(-0.239592\pi\)
\(570\) 0 0
\(571\) 27.2472 1.14026 0.570129 0.821555i \(-0.306893\pi\)
0.570129 + 0.821555i \(0.306893\pi\)
\(572\) 6.39366 + 4.87623i 0.267332 + 0.203885i
\(573\) 0 0
\(574\) −3.56829 1.20542i −0.148938 0.0503135i
\(575\) 3.28118i 0.136835i
\(576\) 0 0
\(577\) −13.9778 −0.581902 −0.290951 0.956738i \(-0.593972\pi\)
−0.290951 + 0.956738i \(0.593972\pi\)
\(578\) 22.7770 + 7.69444i 0.947400 + 0.320047i
\(579\) 0 0
\(580\) 2.40472 3.15305i 0.0998507 0.130923i
\(581\) 10.0507i 0.416974i
\(582\) 0 0
\(583\) −5.69011 −0.235660
\(584\) 1.94872 + 2.88881i 0.0806387 + 0.119540i
\(585\) 0 0
\(586\) 35.7385 + 12.0730i 1.47634 + 0.498732i
\(587\) −7.74807 −0.319797 −0.159899 0.987133i \(-0.551117\pi\)
−0.159899 + 0.987133i \(0.551117\pi\)
\(588\) 0 0
\(589\) 12.0399 17.3345i 0.496096 0.714255i
\(590\) −5.21070 1.76025i −0.214521 0.0724685i
\(591\) 0 0
\(592\) −4.48398 16.3493i −0.184291 0.671953i
\(593\) 10.7668 0.442140 0.221070 0.975258i \(-0.429045\pi\)
0.221070 + 0.975258i \(0.429045\pi\)
\(594\) 0 0
\(595\) 0.00295833 0.000121280
\(596\) 23.3616 30.6314i 0.956927 1.25471i
\(597\) 0 0
\(598\) −1.01341 + 2.99989i −0.0414414 + 0.122675i
\(599\) 17.5934 0.718845 0.359422 0.933175i \(-0.382974\pi\)
0.359422 + 0.933175i \(0.382974\pi\)
\(600\) 0 0
\(601\) 12.6891i 0.517599i −0.965931 0.258799i \(-0.916673\pi\)
0.965931 0.258799i \(-0.0833269\pi\)
\(602\) 2.81749 8.34030i 0.114832 0.339925i
\(603\) 0 0
\(604\) 30.7391 + 23.4437i 1.25076 + 0.953910i
\(605\) 3.74436i 0.152230i
\(606\) 0 0
\(607\) 28.0538 1.13867 0.569334 0.822106i \(-0.307201\pi\)
0.569334 + 0.822106i \(0.307201\pi\)
\(608\) −19.4010 15.2185i −0.786813 0.617192i
\(609\) 0 0
\(610\) 2.63127 + 0.888883i 0.106537 + 0.0359898i
\(611\) 36.1785i 1.46363i
\(612\) 0 0
\(613\) 0.510517i 0.0206196i −0.999947 0.0103098i \(-0.996718\pi\)
0.999947 0.0103098i \(-0.00328177\pi\)
\(614\) 8.14856 24.1213i 0.328849 0.973457i
\(615\) 0 0
\(616\) −3.85969 + 2.60365i −0.155511 + 0.104904i
\(617\) −31.9714 −1.28712 −0.643560 0.765396i \(-0.722543\pi\)
−0.643560 + 0.765396i \(0.722543\pi\)
\(618\) 0 0
\(619\) 8.53505 0.343053 0.171526 0.985180i \(-0.445130\pi\)
0.171526 + 0.985180i \(0.445130\pi\)
\(620\) 2.30943 3.02810i 0.0927488 0.121611i
\(621\) 0 0
\(622\) −8.70647 + 25.7728i −0.349098 + 1.03340i
\(623\) −16.2176 −0.649745
\(624\) 0 0
\(625\) 22.7042 0.908166
\(626\) 26.8350 + 9.06529i 1.07254 + 0.362322i
\(627\) 0 0
\(628\) 3.10953 4.07719i 0.124084 0.162697i
\(629\) −0.0235525 −0.000939099
\(630\) 0 0
\(631\) 4.94467i 0.196844i −0.995145 0.0984221i \(-0.968620\pi\)
0.995145 0.0984221i \(-0.0313795\pi\)
\(632\) −17.5593 26.0302i −0.698473 1.03543i
\(633\) 0 0
\(634\) 14.8684 + 5.02278i 0.590499 + 0.199480i
\(635\) 1.96884i 0.0781309i
\(636\) 0 0
\(637\) −17.0857 −0.676958
\(638\) 8.21401 + 2.77482i 0.325196 + 0.109856i
\(639\) 0 0
\(640\) −3.37509 2.89898i −0.133412 0.114592i
\(641\) 9.73828i 0.384639i −0.981332 0.192320i \(-0.938399\pi\)
0.981332 0.192320i \(-0.0616010\pi\)
\(642\) 0 0
\(643\) −34.7059 −1.36867 −0.684334 0.729168i \(-0.739907\pi\)
−0.684334 + 0.729168i \(0.739907\pi\)
\(644\) −1.45781 1.11182i −0.0574456 0.0438119i
\(645\) 0 0
\(646\) −0.0275188 + 0.0204013i −0.00108271 + 0.000802678i
\(647\) 15.7832i 0.620502i −0.950655 0.310251i \(-0.899587\pi\)
0.950655 0.310251i \(-0.100413\pi\)
\(648\) 0 0
\(649\) 12.0253i 0.472034i
\(650\) 21.4647 + 7.25111i 0.841914 + 0.284412i
\(651\) 0 0
\(652\) −25.5975 19.5224i −1.00248 0.764556i
\(653\) 18.6709i 0.730650i −0.930880 0.365325i \(-0.880958\pi\)
0.930880 0.365325i \(-0.119042\pi\)
\(654\) 0 0
\(655\) 6.54475i 0.255725i
\(656\) 7.58930 2.08145i 0.296312 0.0812670i
\(657\) 0 0
\(658\) 19.8459 + 6.70426i 0.773674 + 0.261359i
\(659\) 5.70895i 0.222389i −0.993799 0.111195i \(-0.964532\pi\)
0.993799 0.111195i \(-0.0354677\pi\)
\(660\) 0 0
\(661\) 37.3664 1.45338 0.726692 0.686963i \(-0.241057\pi\)
0.726692 + 0.686963i \(0.241057\pi\)
\(662\) 10.4123 30.8225i 0.404687 1.19795i
\(663\) 0 0
\(664\) −11.7439 17.4093i −0.455752 0.675612i
\(665\) 1.32374 1.90585i 0.0513323 0.0739057i
\(666\) 0 0
\(667\) 3.41418i 0.132198i
\(668\) 26.2566 + 20.0251i 1.01590 + 0.774793i
\(669\) 0 0
\(670\) −1.29773 0.438393i −0.0501356 0.0169366i
\(671\) 6.07247i 0.234425i
\(672\) 0 0
\(673\) 23.1675i 0.893040i 0.894774 + 0.446520i \(0.147337\pi\)
−0.894774 + 0.446520i \(0.852663\pi\)
\(674\) 6.68626 19.7926i 0.257545 0.762384i
\(675\) 0 0
\(676\) −3.28865 2.50814i −0.126487 0.0964671i
\(677\) 28.2705 1.08652 0.543262 0.839564i \(-0.317189\pi\)
0.543262 + 0.839564i \(0.317189\pi\)
\(678\) 0 0
\(679\) −2.78098 −0.106724
\(680\) −0.00512425 + 0.00345670i −0.000196506 + 0.000132558i
\(681\) 0 0
\(682\) 7.88850 + 2.66486i 0.302066 + 0.102043i
\(683\) 26.5216i 1.01482i −0.861704 0.507411i \(-0.830603\pi\)
0.861704 0.507411i \(-0.169397\pi\)
\(684\) 0 0
\(685\) 5.23142i 0.199882i
\(686\) 7.45507 22.0684i 0.284636 0.842577i
\(687\) 0 0
\(688\) 4.86505 + 17.7388i 0.185478 + 0.676284i
\(689\) −15.4720 −0.589435
\(690\) 0 0
\(691\) 8.53640 0.324740 0.162370 0.986730i \(-0.448086\pi\)
0.162370 + 0.986730i \(0.448086\pi\)
\(692\) 21.9857 + 16.7678i 0.835771 + 0.637414i
\(693\) 0 0
\(694\) 43.3444 + 14.6424i 1.64533 + 0.555818i
\(695\) 5.86942i 0.222640i
\(696\) 0 0
\(697\) 0.0109330i 0.000414116i
\(698\) −13.0737 + 38.7007i −0.494847 + 1.46484i
\(699\) 0 0
\(700\) −7.95526 + 10.4308i −0.300680 + 0.394249i
\(701\) 14.2487i 0.538166i −0.963117 0.269083i \(-0.913279\pi\)
0.963117 0.269083i \(-0.0867207\pi\)
\(702\) 0 0
\(703\) −10.5388 + 15.1733i −0.397479 + 0.572271i
\(704\) 3.64327 9.01982i 0.137311 0.339947i
\(705\) 0 0
\(706\) −29.6945 10.0313i −1.11757 0.377531i
\(707\) 11.8535 0.445795
\(708\) 0 0
\(709\) 51.2166i 1.92348i 0.273963 + 0.961740i \(0.411665\pi\)
−0.273963 + 0.961740i \(0.588335\pi\)
\(710\) 0.0754697 0.223405i 0.00283233 0.00838423i
\(711\) 0 0
\(712\) 28.0913 18.9497i 1.05276 0.710170i
\(713\) 3.27888i 0.122795i
\(714\) 0 0
\(715\) 1.58107i 0.0591288i
\(716\) 11.0111 14.4376i 0.411503 0.539558i
\(717\) 0 0
\(718\) 9.50872 28.1477i 0.354862 1.05046i
\(719\) 39.4189i 1.47008i 0.678026 + 0.735038i \(0.262836\pi\)
−0.678026 + 0.735038i \(0.737164\pi\)
\(720\) 0 0
\(721\) 13.0014i 0.484197i
\(722\) 0.829608 + 26.8572i 0.0308748 + 0.999523i
\(723\) 0 0
\(724\) −7.05810 5.38298i −0.262312 0.200057i
\(725\) 24.4290 0.907270
\(726\) 0 0
\(727\) 32.9620i 1.22249i 0.791440 + 0.611246i \(0.209332\pi\)
−0.791440 + 0.611246i \(0.790668\pi\)
\(728\) −10.4949 + 7.07959i −0.388966 + 0.262387i
\(729\) 0 0
\(730\) 0.219290 0.649140i 0.00811628 0.0240258i
\(731\) 0.0255541 0.000945152
\(732\) 0 0
\(733\) 39.5261i 1.45993i 0.683485 + 0.729965i \(0.260464\pi\)
−0.683485 + 0.729965i \(0.739536\pi\)
\(734\) −2.22217 + 6.57804i −0.0820216 + 0.242800i
\(735\) 0 0
\(736\) 3.82426 + 0.222440i 0.140964 + 0.00819925i
\(737\) 2.99491i 0.110319i
\(738\) 0 0
\(739\) −2.89967 −0.106666 −0.0533330 0.998577i \(-0.516984\pi\)
−0.0533330 + 0.998577i \(0.516984\pi\)
\(740\) −2.02149 + 2.65056i −0.0743116 + 0.0974366i
\(741\) 0 0
\(742\) 2.86712 8.48722i 0.105255 0.311576i
\(743\) −44.8357 −1.64486 −0.822431 0.568865i \(-0.807383\pi\)
−0.822431 + 0.568865i \(0.807383\pi\)
\(744\) 0 0
\(745\) −7.57478 −0.277519
\(746\) 22.2222 + 7.50702i 0.813614 + 0.274851i
\(747\) 0 0
\(748\) −0.0107460 0.00819563i −0.000392914 0.000299662i
\(749\) −9.91101 −0.362141
\(750\) 0 0
\(751\) 19.9481 0.727918 0.363959 0.931415i \(-0.381425\pi\)
0.363959 + 0.931415i \(0.381425\pi\)
\(752\) −42.2097 + 11.5765i −1.53923 + 0.422151i
\(753\) 0 0
\(754\) 22.3347 + 7.54501i 0.813382 + 0.274773i
\(755\) 7.60141i 0.276644i
\(756\) 0 0
\(757\) 24.8537i 0.903322i 0.892190 + 0.451661i \(0.149168\pi\)
−0.892190 + 0.451661i \(0.850832\pi\)
\(758\) −11.5979 + 34.3319i −0.421253 + 1.24699i
\(759\) 0 0
\(760\) −0.0659856 + 4.84795i −0.00239355 + 0.175854i
\(761\) 29.7493 1.07841 0.539206 0.842174i \(-0.318725\pi\)
0.539206 + 0.842174i \(0.318725\pi\)
\(762\) 0 0
\(763\) 9.07356i 0.328485i
\(764\) 13.0236 17.0765i 0.471179 0.617804i
\(765\) 0 0
\(766\) 32.3159 + 10.9168i 1.16762 + 0.394441i
\(767\) 32.6980i 1.18065i
\(768\) 0 0
\(769\) −17.7979 −0.641809 −0.320905 0.947112i \(-0.603987\pi\)
−0.320905 + 0.947112i \(0.603987\pi\)
\(770\) 0.867306 + 0.292989i 0.0312555 + 0.0105586i
\(771\) 0 0
\(772\) −29.6578 + 38.8870i −1.06741 + 1.39957i
\(773\) −2.50404 −0.0900641 −0.0450320 0.998986i \(-0.514339\pi\)
−0.0450320 + 0.998986i \(0.514339\pi\)
\(774\) 0 0
\(775\) 23.4609 0.842741
\(776\) 4.81707 3.24948i 0.172923 0.116650i
\(777\) 0 0
\(778\) 11.8527 35.0863i 0.424940 1.25790i
\(779\) −7.04338 4.89208i −0.252355 0.175277i
\(780\) 0 0
\(781\) 0.515576 0.0184488
\(782\) 0.00170327 0.00504201i 6.09088e−5 0.000180302i
\(783\) 0 0
\(784\) 5.46710 + 19.9339i 0.195254 + 0.711926i
\(785\) −1.00824 −0.0359856
\(786\) 0 0
\(787\) 48.3385i 1.72308i 0.507689 + 0.861540i \(0.330500\pi\)
−0.507689 + 0.861540i \(0.669500\pi\)
\(788\) 0.730797 0.958213i 0.0260336 0.0341349i
\(789\) 0 0
\(790\) −1.97595 + 5.84921i −0.0703013 + 0.208105i
\(791\) 2.76457 0.0982967
\(792\) 0 0
\(793\) 16.5116i 0.586345i
\(794\) 2.64264 7.82274i 0.0937839 0.277619i
\(795\) 0 0
\(796\) 2.20972 2.89736i 0.0783214 0.102694i
\(797\) −4.38865 −0.155454 −0.0777271 0.996975i \(-0.524766\pi\)
−0.0777271 + 0.996975i \(0.524766\pi\)
\(798\) 0 0
\(799\) 0.0608064i 0.00215118i
\(800\) 1.59160 27.3632i 0.0562714 0.967435i
\(801\) 0 0
\(802\) 4.90811 14.5290i 0.173312 0.513036i
\(803\) 1.49809 0.0528666
\(804\) 0 0
\(805\) 0.360498i 0.0127059i
\(806\) 21.4496 + 7.24602i 0.755530 + 0.255230i
\(807\) 0 0
\(808\) −20.5319 + 13.8503i −0.722310 + 0.487253i
\(809\) 1.71674 0.0603574 0.0301787 0.999545i \(-0.490392\pi\)
0.0301787 + 0.999545i \(0.490392\pi\)
\(810\) 0 0
\(811\) 39.8836i 1.40050i −0.713897 0.700251i \(-0.753072\pi\)
0.713897 0.700251i \(-0.246928\pi\)
\(812\) −8.27770 + 10.8536i −0.290490 + 0.380888i
\(813\) 0 0
\(814\) −6.90499 2.33261i −0.242020 0.0817580i
\(815\) 6.32997i 0.221729i
\(816\) 0 0
\(817\) 11.4345 16.4628i 0.400041 0.575959i
\(818\) −10.8022 + 31.9767i −0.377691 + 1.11804i
\(819\) 0 0
\(820\) −1.23038 0.938371i −0.0429668 0.0327693i
\(821\) 21.5429i 0.751853i 0.926650 + 0.375926i \(0.122675\pi\)
−0.926650 + 0.375926i \(0.877325\pi\)
\(822\) 0 0
\(823\) 51.4146i 1.79220i −0.443852 0.896100i \(-0.646388\pi\)
0.443852 0.896100i \(-0.353612\pi\)
\(824\) −15.1917 22.5203i −0.529227 0.784532i
\(825\) 0 0
\(826\) 17.9366 + 6.05927i 0.624094 + 0.210829i
\(827\) 28.1995i 0.980592i 0.871556 + 0.490296i \(0.163111\pi\)
−0.871556 + 0.490296i \(0.836889\pi\)
\(828\) 0 0
\(829\) −56.6258 −1.96670 −0.983348 0.181734i \(-0.941829\pi\)
−0.983348 + 0.181734i \(0.941829\pi\)
\(830\) −1.32154 + 3.91202i −0.0458714 + 0.135788i
\(831\) 0 0
\(832\) 9.90640 24.5258i 0.343443 0.850278i
\(833\) 0.0287164 0.000994964
\(834\) 0 0
\(835\) 6.49295i 0.224698i
\(836\) −10.0883 + 3.25571i −0.348912 + 0.112601i
\(837\) 0 0
\(838\) 13.5226 + 4.56814i 0.467130 + 0.157804i
\(839\) −12.4990 −0.431513 −0.215756 0.976447i \(-0.569222\pi\)
−0.215756 + 0.976447i \(0.569222\pi\)
\(840\) 0 0
\(841\) −3.58083 −0.123477
\(842\) −28.4061 9.59604i −0.978940 0.330701i
\(843\) 0 0
\(844\) −6.07610 + 7.96691i −0.209148 + 0.274232i
\(845\) 0.813244i 0.0279764i
\(846\) 0 0
\(847\) 12.8891i 0.442874i
\(848\) 4.95075 + 18.0512i 0.170009 + 0.619882i
\(849\) 0 0
\(850\) −0.0360764 0.0121872i −0.00123741 0.000418016i
\(851\) 2.87008i 0.0983850i
\(852\) 0 0
\(853\) 32.9738i 1.12900i 0.825433 + 0.564500i \(0.190931\pi\)
−0.825433 + 0.564500i \(0.809069\pi\)
\(854\) −9.05753 3.05977i −0.309942 0.104703i
\(855\) 0 0
\(856\) 17.1673 11.5807i 0.586767 0.395819i
\(857\) 32.4358i 1.10799i −0.832521 0.553993i \(-0.813103\pi\)
0.832521 0.553993i \(-0.186897\pi\)
\(858\) 0 0
\(859\) 18.7433 0.639514 0.319757 0.947500i \(-0.396399\pi\)
0.319757 + 0.947500i \(0.396399\pi\)
\(860\) 2.19329 2.87582i 0.0747906 0.0980646i
\(861\) 0 0
\(862\) −39.6927 13.4088i −1.35194 0.456706i
\(863\) −29.2455 −0.995529 −0.497765 0.867312i \(-0.665846\pi\)
−0.497765 + 0.867312i \(0.665846\pi\)
\(864\) 0 0
\(865\) 5.43680i 0.184857i
\(866\) −17.0351 + 50.4271i −0.578876 + 1.71358i
\(867\) 0 0
\(868\) −7.94967 + 10.4235i −0.269829 + 0.353797i
\(869\) −13.4989 −0.457918
\(870\) 0 0
\(871\) 8.14345i 0.275930i
\(872\) 10.6021 + 15.7167i 0.359034 + 0.532236i
\(873\) 0 0
\(874\) −2.48608 3.35340i −0.0840928 0.113431i
\(875\) 5.24117 0.177184
\(876\) 0 0
\(877\) 29.1471 0.984229 0.492114 0.870531i \(-0.336224\pi\)
0.492114 + 0.870531i \(0.336224\pi\)
\(878\) 6.14685 + 2.07650i 0.207446 + 0.0700786i
\(879\) 0 0
\(880\) −1.84465 + 0.505915i −0.0621831 + 0.0170544i
\(881\) 9.86763 0.332449 0.166224 0.986088i \(-0.446842\pi\)
0.166224 + 0.986088i \(0.446842\pi\)
\(882\) 0 0
\(883\) −45.5997 −1.53455 −0.767276 0.641317i \(-0.778388\pi\)
−0.767276 + 0.641317i \(0.778388\pi\)
\(884\) −0.0292195 0.0222847i −0.000982758 0.000749516i
\(885\) 0 0
\(886\) −3.73333 1.26118i −0.125424 0.0423701i
\(887\) 5.88747 0.197682 0.0988410 0.995103i \(-0.468486\pi\)
0.0988410 + 0.995103i \(0.468486\pi\)
\(888\) 0 0
\(889\) 6.77726i 0.227302i
\(890\) −6.31235 2.13241i −0.211591 0.0714786i
\(891\) 0 0
\(892\) −10.1588 7.74781i −0.340143 0.259416i
\(893\) 39.1734 + 27.2085i 1.31089 + 0.910497i
\(894\) 0 0
\(895\) −3.57024 −0.119340
\(896\) 11.6180 + 9.97908i 0.388129 + 0.333378i
\(897\) 0 0
\(898\) 11.7344 34.7362i 0.391583 1.15916i
\(899\) 24.4118 0.814181
\(900\) 0 0
\(901\) 0.0260042 0.000866326
\(902\) 1.08279 3.20527i 0.0360530 0.106724i
\(903\) 0 0
\(904\) −4.78864 + 3.23030i −0.159268 + 0.107438i
\(905\) 1.74538i 0.0580185i
\(906\) 0 0
\(907\) 32.4697i 1.07814i 0.842261 + 0.539069i \(0.181224\pi\)
−0.842261 + 0.539069i \(0.818776\pi\)
\(908\) 14.8243 19.4375i 0.491962 0.645055i
\(909\) 0 0
\(910\) 2.35829 + 0.796667i 0.0781765 + 0.0264092i
\(911\) −22.2375 −0.736760 −0.368380 0.929675i \(-0.620087\pi\)
−0.368380 + 0.929675i \(0.620087\pi\)
\(912\) 0 0
\(913\) −9.02821 −0.298790
\(914\) −14.8882 5.02947i −0.492458 0.166360i
\(915\) 0 0
\(916\) 27.0314 35.4433i 0.893142 1.17108i
\(917\) 22.5288i 0.743966i
\(918\) 0 0
\(919\) 1.82361i 0.0601553i 0.999548 + 0.0300776i \(0.00957546\pi\)
−0.999548 + 0.0300776i \(0.990425\pi\)
\(920\) −0.421229 0.624435i −0.0138875 0.0205870i
\(921\) 0 0
\(922\) 18.2628 54.0614i 0.601453 1.78042i
\(923\) 1.40190 0.0461441
\(924\) 0 0
\(925\) −20.5359 −0.675215
\(926\) −1.55784 + 4.61152i −0.0511939 + 0.151544i
\(927\) 0 0
\(928\) 1.65611 28.4723i 0.0543644 0.934648i
\(929\) 48.0824 1.57753 0.788767 0.614693i \(-0.210720\pi\)
0.788767 + 0.614693i \(0.210720\pi\)
\(930\) 0 0
\(931\) 12.8495 18.5000i 0.421124 0.606314i
\(932\) −11.0787 8.44939i −0.362896 0.276769i
\(933\) 0 0
\(934\) −41.7943 14.1188i −1.36755 0.461980i
\(935\) 0.00265736i 8.69050e-5i
\(936\) 0 0
\(937\) 12.8423 0.419540 0.209770 0.977751i \(-0.432728\pi\)
0.209770 + 0.977751i \(0.432728\pi\)
\(938\) 4.46713 + 1.50907i 0.145857 + 0.0492727i
\(939\) 0 0
\(940\) 6.84306 + 5.21897i 0.223196 + 0.170224i
\(941\) 4.78698 0.156051 0.0780256 0.996951i \(-0.475138\pi\)
0.0780256 + 0.996951i \(0.475138\pi\)
\(942\) 0 0
\(943\) 1.33228 0.0433850
\(944\) −38.1489 + 10.4628i −1.24164 + 0.340534i
\(945\) 0 0
\(946\) 7.49181 + 2.53085i 0.243580 + 0.0822850i
\(947\) 26.3364 0.855817 0.427908 0.903822i \(-0.359251\pi\)
0.427908 + 0.903822i \(0.359251\pi\)
\(948\) 0 0
\(949\) 4.07346 0.132230
\(950\) −23.9941 + 17.7883i −0.778472 + 0.577128i
\(951\) 0 0
\(952\) 0.0176391 0.0118989i 0.000571685 0.000385645i
\(953\) 50.7687i 1.64456i −0.569084 0.822279i \(-0.692702\pi\)
0.569084 0.822279i \(-0.307298\pi\)
\(954\) 0 0
\(955\) −4.22280 −0.136647
\(956\) −11.2248 + 14.7178i −0.363036 + 0.476009i
\(957\) 0 0
\(958\) −0.382053 + 1.13095i −0.0123436 + 0.0365394i
\(959\) 18.0079i 0.581507i
\(960\) 0 0
\(961\) −7.55556 −0.243728
\(962\) −18.7753 6.34260i −0.605341 0.204494i
\(963\) 0 0
\(964\) −9.50719 + 12.4657i −0.306206 + 0.401494i
\(965\) 9.61628 0.309559
\(966\) 0 0
\(967\) 49.0390i 1.57699i −0.615042 0.788494i \(-0.710861\pi\)
0.615042 0.788494i \(-0.289139\pi\)
\(968\) 15.0604 + 22.3258i 0.484060 + 0.717577i
\(969\) 0 0
\(970\) −1.08244 0.365665i −0.0347550 0.0117408i
\(971\) 22.1251i 0.710027i 0.934861 + 0.355013i \(0.115524\pi\)
−0.934861 + 0.355013i \(0.884476\pi\)
\(972\) 0 0
\(973\) 20.2041i 0.647715i
\(974\) 42.1150 + 14.2271i 1.34945 + 0.455866i
\(975\) 0 0
\(976\) 19.2642 5.28342i 0.616632 0.169118i
\(977\) 45.0576i 1.44152i 0.693184 + 0.720761i \(0.256207\pi\)
−0.693184 + 0.720761i \(0.743793\pi\)
\(978\) 0 0
\(979\) 14.5677i 0.465586i
\(980\) 2.46471 3.23170i 0.0787322 0.103233i
\(981\) 0 0
\(982\) 44.5251 + 15.0413i 1.42085 + 0.479986i
\(983\) −58.9765 −1.88106 −0.940529 0.339713i \(-0.889670\pi\)
−0.940529 + 0.339713i \(0.889670\pi\)
\(984\) 0 0
\(985\) −0.236955 −0.00755000
\(986\) −0.0375386 0.0126811i −0.00119547 0.000403850i
\(987\) 0 0
\(988\) −27.4311 + 8.85259i −0.872700 + 0.281638i
\(989\) 3.11399i 0.0990192i
\(990\) 0 0
\(991\) −36.9320 −1.17318 −0.586592 0.809882i \(-0.699531\pi\)
−0.586592 + 0.809882i \(0.699531\pi\)
\(992\) 1.59048 27.3440i 0.0504977 0.868172i
\(993\) 0 0
\(994\) −0.259787 + 0.769019i −0.00823994 + 0.0243918i
\(995\) −0.716481 −0.0227140
\(996\) 0 0
\(997\) 34.0903i 1.07965i 0.841777 + 0.539825i \(0.181510\pi\)
−0.841777 + 0.539825i \(0.818490\pi\)
\(998\) 1.44642 + 0.488623i 0.0457856 + 0.0154671i
\(999\) 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 1368.2.e.g.379.5 40
3.2 odd 2 456.2.e.a.379.36 yes 40
4.3 odd 2 5472.2.e.g.5167.31 40
8.3 odd 2 inner 1368.2.e.g.379.35 40
8.5 even 2 5472.2.e.g.5167.16 40
12.11 even 2 1824.2.e.a.1519.25 40
19.18 odd 2 inner 1368.2.e.g.379.36 40
24.5 odd 2 1824.2.e.a.1519.9 40
24.11 even 2 456.2.e.a.379.6 yes 40
57.56 even 2 456.2.e.a.379.5 40
76.75 even 2 5472.2.e.g.5167.15 40
152.37 odd 2 5472.2.e.g.5167.32 40
152.75 even 2 inner 1368.2.e.g.379.6 40
228.227 odd 2 1824.2.e.a.1519.10 40
456.227 odd 2 456.2.e.a.379.35 yes 40
456.341 even 2 1824.2.e.a.1519.26 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.e.a.379.5 40 57.56 even 2
456.2.e.a.379.6 yes 40 24.11 even 2
456.2.e.a.379.35 yes 40 456.227 odd 2
456.2.e.a.379.36 yes 40 3.2 odd 2
1368.2.e.g.379.5 40 1.1 even 1 trivial
1368.2.e.g.379.6 40 152.75 even 2 inner
1368.2.e.g.379.35 40 8.3 odd 2 inner
1368.2.e.g.379.36 40 19.18 odd 2 inner
1824.2.e.a.1519.9 40 24.5 odd 2
1824.2.e.a.1519.10 40 228.227 odd 2
1824.2.e.a.1519.25 40 12.11 even 2
1824.2.e.a.1519.26 40 456.341 even 2
5472.2.e.g.5167.15 40 76.75 even 2
5472.2.e.g.5167.16 40 8.5 even 2
5472.2.e.g.5167.31 40 4.3 odd 2
5472.2.e.g.5167.32 40 152.37 odd 2