Properties

Label 1368.2.g.b.685.13
Level $1368$
Weight $2$
Character 1368.685
Analytic conductor $10.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1368,2,Mod(685,1368)]
 
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([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("1368.685");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.g (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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + 48 x^{7} - 40 x^{6} + 32 x^{5} + 64 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 685.13
Root \(0.340606 - 1.37258i\) of defining polynomial
Character \(\chi\) \(=\) 1368.685
Dual form 1368.2.g.b.685.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37258 - 0.340606i) q^{2} +(1.76798 - 0.935021i) q^{4} -2.13486i q^{5} +3.29464 q^{7} +(2.10822 - 1.88558i) q^{8} +O(q^{10})\) \(q+(1.37258 - 0.340606i) q^{2} +(1.76798 - 0.935021i) q^{4} -2.13486i q^{5} +3.29464 q^{7} +(2.10822 - 1.88558i) q^{8} +(-0.727145 - 2.93027i) q^{10} +3.71210i q^{11} +2.32843i q^{13} +(4.52218 - 1.12218i) q^{14} +(2.25147 - 3.30619i) q^{16} +6.48822 q^{17} -1.00000i q^{19} +(-1.99614 - 3.77437i) q^{20} +(1.26436 + 5.09517i) q^{22} -7.32651 q^{23} +0.442384 q^{25} +(0.793079 + 3.19597i) q^{26} +(5.82485 - 3.08056i) q^{28} +2.59857i q^{29} -1.34204 q^{31} +(1.96423 - 5.30489i) q^{32} +(8.90563 - 2.20993i) q^{34} -7.03360i q^{35} -3.72986i q^{37} +(-0.340606 - 1.37258i) q^{38} +(-4.02544 - 4.50075i) q^{40} -6.52385 q^{41} -1.97202i q^{43} +(3.47089 + 6.56290i) q^{44} +(-10.0563 + 2.49545i) q^{46} -5.45991 q^{47} +3.85468 q^{49} +(0.607210 - 0.150679i) q^{50} +(2.17714 + 4.11661i) q^{52} -4.98640i q^{53} +7.92480 q^{55} +(6.94584 - 6.21231i) q^{56} +(0.885089 + 3.56676i) q^{58} -9.67136i q^{59} +8.15570i q^{61} +(-1.84206 + 0.457105i) q^{62} +(0.889191 - 7.95043i) q^{64} +4.97088 q^{65} -0.524986i q^{67} +(11.4710 - 6.06662i) q^{68} +(-2.39569 - 9.65420i) q^{70} -7.17489 q^{71} -6.33130 q^{73} +(-1.27041 - 5.11955i) q^{74} +(-0.935021 - 1.76798i) q^{76} +12.2300i q^{77} -8.75644 q^{79} +(-7.05824 - 4.80657i) q^{80} +(-8.95453 + 2.22206i) q^{82} +7.74008i q^{83} -13.8514i q^{85} +(-0.671680 - 2.70676i) q^{86} +(6.99945 + 7.82592i) q^{88} +1.04368 q^{89} +7.67136i q^{91} +(-12.9531 + 6.85044i) q^{92} +(-7.49419 + 1.85968i) q^{94} -2.13486 q^{95} -0.117594 q^{97} +(5.29088 - 1.31293i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8} - 8 q^{10} - 4 q^{14} + 2 q^{16} + 8 q^{17} - 8 q^{20} + 20 q^{22} - 24 q^{25} + 10 q^{26} - 14 q^{28} + 16 q^{31} + 20 q^{32} - 2 q^{38} + 28 q^{40} - 16 q^{41} + 28 q^{44} - 48 q^{46} - 24 q^{47} + 24 q^{49} - 12 q^{50} + 8 q^{52} + 16 q^{55} + 48 q^{56} + 38 q^{58} + 16 q^{62} + 14 q^{64} - 16 q^{65} + 26 q^{68} - 32 q^{70} - 48 q^{71} + 20 q^{74} - 4 q^{76} - 48 q^{79} - 4 q^{80} - 12 q^{82} - 48 q^{86} + 40 q^{88} + 16 q^{89} - 62 q^{92} - 36 q^{94} - 16 q^{95} + 32 q^{97} + 48 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37258 0.340606i 0.970564 0.240845i
\(3\) 0 0
\(4\) 1.76798 0.935021i 0.883988 0.467510i
\(5\) 2.13486i 0.954737i −0.878703 0.477369i \(-0.841591\pi\)
0.878703 0.477369i \(-0.158409\pi\)
\(6\) 0 0
\(7\) 3.29464 1.24526 0.622629 0.782517i \(-0.286064\pi\)
0.622629 + 0.782517i \(0.286064\pi\)
\(8\) 2.10822 1.88558i 0.745369 0.666653i
\(9\) 0 0
\(10\) −0.727145 2.93027i −0.229944 0.926633i
\(11\) 3.71210i 1.11924i 0.828749 + 0.559620i \(0.189053\pi\)
−0.828749 + 0.559620i \(0.810947\pi\)
\(12\) 0 0
\(13\) 2.32843i 0.645792i 0.946435 + 0.322896i \(0.104656\pi\)
−0.946435 + 0.322896i \(0.895344\pi\)
\(14\) 4.52218 1.12218i 1.20860 0.299914i
\(15\) 0 0
\(16\) 2.25147 3.30619i 0.562868 0.826547i
\(17\) 6.48822 1.57362 0.786812 0.617192i \(-0.211730\pi\)
0.786812 + 0.617192i \(0.211730\pi\)
\(18\) 0 0
\(19\) 1.00000i 0.229416i
\(20\) −1.99614 3.77437i −0.446350 0.843976i
\(21\) 0 0
\(22\) 1.26436 + 5.09517i 0.269563 + 1.08629i
\(23\) −7.32651 −1.52768 −0.763842 0.645404i \(-0.776689\pi\)
−0.763842 + 0.645404i \(0.776689\pi\)
\(24\) 0 0
\(25\) 0.442384 0.0884769
\(26\) 0.793079 + 3.19597i 0.155536 + 0.626782i
\(27\) 0 0
\(28\) 5.82485 3.08056i 1.10079 0.582171i
\(29\) 2.59857i 0.482542i 0.970458 + 0.241271i \(0.0775643\pi\)
−0.970458 + 0.241271i \(0.922436\pi\)
\(30\) 0 0
\(31\) −1.34204 −0.241037 −0.120518 0.992711i \(-0.538456\pi\)
−0.120518 + 0.992711i \(0.538456\pi\)
\(32\) 1.96423 5.30489i 0.347230 0.937780i
\(33\) 0 0
\(34\) 8.90563 2.20993i 1.52730 0.378999i
\(35\) 7.03360i 1.18889i
\(36\) 0 0
\(37\) 3.72986i 0.613186i −0.951841 0.306593i \(-0.900811\pi\)
0.951841 0.306593i \(-0.0991890\pi\)
\(38\) −0.340606 1.37258i −0.0552536 0.222663i
\(39\) 0 0
\(40\) −4.02544 4.50075i −0.636478 0.711631i
\(41\) −6.52385 −1.01885 −0.509427 0.860514i \(-0.670143\pi\)
−0.509427 + 0.860514i \(0.670143\pi\)
\(42\) 0 0
\(43\) 1.97202i 0.300729i −0.988631 0.150365i \(-0.951955\pi\)
0.988631 0.150365i \(-0.0480448\pi\)
\(44\) 3.47089 + 6.56290i 0.523256 + 0.989394i
\(45\) 0 0
\(46\) −10.0563 + 2.49545i −1.48271 + 0.367935i
\(47\) −5.45991 −0.796410 −0.398205 0.917297i \(-0.630367\pi\)
−0.398205 + 0.917297i \(0.630367\pi\)
\(48\) 0 0
\(49\) 3.85468 0.550669
\(50\) 0.607210 0.150679i 0.0858724 0.0213092i
\(51\) 0 0
\(52\) 2.17714 + 4.11661i 0.301914 + 0.570872i
\(53\) 4.98640i 0.684935i −0.939530 0.342467i \(-0.888737\pi\)
0.939530 0.342467i \(-0.111263\pi\)
\(54\) 0 0
\(55\) 7.92480 1.06858
\(56\) 6.94584 6.21231i 0.928177 0.830155i
\(57\) 0 0
\(58\) 0.885089 + 3.56676i 0.116218 + 0.468338i
\(59\) 9.67136i 1.25910i −0.776958 0.629552i \(-0.783238\pi\)
0.776958 0.629552i \(-0.216762\pi\)
\(60\) 0 0
\(61\) 8.15570i 1.04423i 0.852875 + 0.522115i \(0.174857\pi\)
−0.852875 + 0.522115i \(0.825143\pi\)
\(62\) −1.84206 + 0.457105i −0.233941 + 0.0580525i
\(63\) 0 0
\(64\) 0.889191 7.95043i 0.111149 0.993804i
\(65\) 4.97088 0.616561
\(66\) 0 0
\(67\) 0.524986i 0.0641372i −0.999486 0.0320686i \(-0.989790\pi\)
0.999486 0.0320686i \(-0.0102095\pi\)
\(68\) 11.4710 6.06662i 1.39106 0.735686i
\(69\) 0 0
\(70\) −2.39569 9.65420i −0.286339 1.15390i
\(71\) −7.17489 −0.851503 −0.425751 0.904840i \(-0.639990\pi\)
−0.425751 + 0.904840i \(0.639990\pi\)
\(72\) 0 0
\(73\) −6.33130 −0.741022 −0.370511 0.928828i \(-0.620817\pi\)
−0.370511 + 0.928828i \(0.620817\pi\)
\(74\) −1.27041 5.11955i −0.147683 0.595136i
\(75\) 0 0
\(76\) −0.935021 1.76798i −0.107254 0.202801i
\(77\) 12.2300i 1.39374i
\(78\) 0 0
\(79\) −8.75644 −0.985176 −0.492588 0.870263i \(-0.663949\pi\)
−0.492588 + 0.870263i \(0.663949\pi\)
\(80\) −7.05824 4.80657i −0.789135 0.537391i
\(81\) 0 0
\(82\) −8.95453 + 2.22206i −0.988862 + 0.245386i
\(83\) 7.74008i 0.849585i 0.905291 + 0.424792i \(0.139653\pi\)
−0.905291 + 0.424792i \(0.860347\pi\)
\(84\) 0 0
\(85\) 13.8514i 1.50240i
\(86\) −0.671680 2.70676i −0.0724291 0.291877i
\(87\) 0 0
\(88\) 6.99945 + 7.82592i 0.746144 + 0.834246i
\(89\) 1.04368 0.110630 0.0553148 0.998469i \(-0.482384\pi\)
0.0553148 + 0.998469i \(0.482384\pi\)
\(90\) 0 0
\(91\) 7.67136i 0.804178i
\(92\) −12.9531 + 6.85044i −1.35045 + 0.714208i
\(93\) 0 0
\(94\) −7.49419 + 1.85968i −0.772966 + 0.191811i
\(95\) −2.13486 −0.219032
\(96\) 0 0
\(97\) −0.117594 −0.0119398 −0.00596992 0.999982i \(-0.501900\pi\)
−0.00596992 + 0.999982i \(0.501900\pi\)
\(98\) 5.29088 1.31293i 0.534459 0.132626i
\(99\) 0 0
\(100\) 0.782125 0.413639i 0.0782125 0.0413639i
\(101\) 10.6142i 1.05615i 0.849197 + 0.528077i \(0.177087\pi\)
−0.849197 + 0.528077i \(0.822913\pi\)
\(102\) 0 0
\(103\) 12.4190 1.22368 0.611840 0.790982i \(-0.290430\pi\)
0.611840 + 0.790982i \(0.290430\pi\)
\(104\) 4.39045 + 4.90885i 0.430519 + 0.481353i
\(105\) 0 0
\(106\) −1.69840 6.84425i −0.164963 0.664773i
\(107\) 16.5439i 1.59936i 0.600430 + 0.799678i \(0.294996\pi\)
−0.600430 + 0.799678i \(0.705004\pi\)
\(108\) 0 0
\(109\) 17.4437i 1.67080i −0.549641 0.835401i \(-0.685235\pi\)
0.549641 0.835401i \(-0.314765\pi\)
\(110\) 10.8775 2.69924i 1.03712 0.257362i
\(111\) 0 0
\(112\) 7.41780 10.8927i 0.700916 1.02926i
\(113\) 14.3193 1.34705 0.673523 0.739166i \(-0.264780\pi\)
0.673523 + 0.739166i \(0.264780\pi\)
\(114\) 0 0
\(115\) 15.6411i 1.45854i
\(116\) 2.42972 + 4.59421i 0.225594 + 0.426561i
\(117\) 0 0
\(118\) −3.29413 13.2748i −0.303249 1.22204i
\(119\) 21.3764 1.95957
\(120\) 0 0
\(121\) −2.77968 −0.252698
\(122\) 2.77788 + 11.1944i 0.251498 + 1.01349i
\(123\) 0 0
\(124\) −2.37269 + 1.25483i −0.213073 + 0.112687i
\(125\) 11.6187i 1.03921i
\(126\) 0 0
\(127\) 2.63985 0.234248 0.117124 0.993117i \(-0.462632\pi\)
0.117124 + 0.993117i \(0.462632\pi\)
\(128\) −1.48748 11.2155i −0.131475 0.991319i
\(129\) 0 0
\(130\) 6.82295 1.69311i 0.598412 0.148496i
\(131\) 15.3670i 1.34263i 0.741174 + 0.671313i \(0.234269\pi\)
−0.741174 + 0.671313i \(0.765731\pi\)
\(132\) 0 0
\(133\) 3.29464i 0.285682i
\(134\) −0.178813 0.720587i −0.0154471 0.0622492i
\(135\) 0 0
\(136\) 13.6786 12.2340i 1.17293 1.04906i
\(137\) 4.91853 0.420218 0.210109 0.977678i \(-0.432618\pi\)
0.210109 + 0.977678i \(0.432618\pi\)
\(138\) 0 0
\(139\) 9.80377i 0.831545i 0.909469 + 0.415773i \(0.136489\pi\)
−0.909469 + 0.415773i \(0.863511\pi\)
\(140\) −6.57656 12.4352i −0.555821 1.05097i
\(141\) 0 0
\(142\) −9.84814 + 2.44381i −0.826438 + 0.205080i
\(143\) −8.64338 −0.722796
\(144\) 0 0
\(145\) 5.54758 0.460701
\(146\) −8.69024 + 2.15648i −0.719209 + 0.178471i
\(147\) 0 0
\(148\) −3.48750 6.59431i −0.286671 0.542049i
\(149\) 0.724147i 0.0593244i 0.999560 + 0.0296622i \(0.00944316\pi\)
−0.999560 + 0.0296622i \(0.990557\pi\)
\(150\) 0 0
\(151\) −15.7252 −1.27970 −0.639850 0.768500i \(-0.721003\pi\)
−0.639850 + 0.768500i \(0.721003\pi\)
\(152\) −1.88558 2.10822i −0.152941 0.170999i
\(153\) 0 0
\(154\) 4.16563 + 16.7868i 0.335676 + 1.35272i
\(155\) 2.86505i 0.230127i
\(156\) 0 0
\(157\) 0.141127i 0.0112632i 0.999984 + 0.00563160i \(0.00179260\pi\)
−0.999984 + 0.00563160i \(0.998207\pi\)
\(158\) −12.0189 + 2.98249i −0.956176 + 0.237275i
\(159\) 0 0
\(160\) −11.3252 4.19334i −0.895334 0.331513i
\(161\) −24.1383 −1.90236
\(162\) 0 0
\(163\) 8.41859i 0.659395i 0.944087 + 0.329697i \(0.106947\pi\)
−0.944087 + 0.329697i \(0.893053\pi\)
\(164\) −11.5340 + 6.09993i −0.900654 + 0.476325i
\(165\) 0 0
\(166\) 2.63632 + 10.6239i 0.204618 + 0.824576i
\(167\) −5.16538 −0.399709 −0.199854 0.979826i \(-0.564047\pi\)
−0.199854 + 0.979826i \(0.564047\pi\)
\(168\) 0 0
\(169\) 7.57839 0.582953
\(170\) −4.71788 19.0123i −0.361845 1.45817i
\(171\) 0 0
\(172\) −1.84388 3.48647i −0.140594 0.265841i
\(173\) 3.13988i 0.238721i 0.992851 + 0.119360i \(0.0380844\pi\)
−0.992851 + 0.119360i \(0.961916\pi\)
\(174\) 0 0
\(175\) 1.45750 0.110177
\(176\) 12.2729 + 8.35769i 0.925104 + 0.629984i
\(177\) 0 0
\(178\) 1.43254 0.355483i 0.107373 0.0266446i
\(179\) 18.1898i 1.35957i 0.733410 + 0.679786i \(0.237927\pi\)
−0.733410 + 0.679786i \(0.762073\pi\)
\(180\) 0 0
\(181\) 14.0798i 1.04654i −0.852166 0.523271i \(-0.824712\pi\)
0.852166 0.523271i \(-0.175288\pi\)
\(182\) 2.61291 + 10.5296i 0.193682 + 0.780505i
\(183\) 0 0
\(184\) −15.4459 + 13.8147i −1.13869 + 1.01843i
\(185\) −7.96273 −0.585431
\(186\) 0 0
\(187\) 24.0849i 1.76126i
\(188\) −9.65299 + 5.10513i −0.704016 + 0.372330i
\(189\) 0 0
\(190\) −2.93027 + 0.727145i −0.212584 + 0.0527527i
\(191\) −4.87409 −0.352677 −0.176338 0.984330i \(-0.556425\pi\)
−0.176338 + 0.984330i \(0.556425\pi\)
\(192\) 0 0
\(193\) −9.99845 −0.719704 −0.359852 0.933009i \(-0.617173\pi\)
−0.359852 + 0.933009i \(0.617173\pi\)
\(194\) −0.161407 + 0.0400531i −0.0115884 + 0.00287565i
\(195\) 0 0
\(196\) 6.81498 3.60421i 0.486785 0.257444i
\(197\) 19.2209i 1.36943i −0.728810 0.684716i \(-0.759926\pi\)
0.728810 0.684716i \(-0.240074\pi\)
\(198\) 0 0
\(199\) −11.7323 −0.831683 −0.415842 0.909437i \(-0.636513\pi\)
−0.415842 + 0.909437i \(0.636513\pi\)
\(200\) 0.932644 0.834150i 0.0659479 0.0589833i
\(201\) 0 0
\(202\) 3.61526 + 14.5689i 0.254369 + 1.02506i
\(203\) 8.56137i 0.600890i
\(204\) 0 0
\(205\) 13.9275i 0.972737i
\(206\) 17.0461 4.22998i 1.18766 0.294717i
\(207\) 0 0
\(208\) 7.69824 + 5.24240i 0.533777 + 0.363495i
\(209\) 3.71210 0.256771
\(210\) 0 0
\(211\) 0.399383i 0.0274947i 0.999906 + 0.0137473i \(0.00437605\pi\)
−0.999906 + 0.0137473i \(0.995624\pi\)
\(212\) −4.66239 8.81583i −0.320214 0.605474i
\(213\) 0 0
\(214\) 5.63494 + 22.7078i 0.385196 + 1.55228i
\(215\) −4.20997 −0.287118
\(216\) 0 0
\(217\) −4.42153 −0.300153
\(218\) −5.94142 23.9429i −0.402404 1.62162i
\(219\) 0 0
\(220\) 14.0109 7.40986i 0.944611 0.499572i
\(221\) 15.1074i 1.01623i
\(222\) 0 0
\(223\) −19.2548 −1.28939 −0.644697 0.764438i \(-0.723017\pi\)
−0.644697 + 0.764438i \(0.723017\pi\)
\(224\) 6.47143 17.4777i 0.432391 1.16778i
\(225\) 0 0
\(226\) 19.6545 4.87724i 1.30739 0.324429i
\(227\) 20.0414i 1.33019i −0.746758 0.665096i \(-0.768391\pi\)
0.746758 0.665096i \(-0.231609\pi\)
\(228\) 0 0
\(229\) 18.2013i 1.20277i 0.798958 + 0.601387i \(0.205385\pi\)
−0.798958 + 0.601387i \(0.794615\pi\)
\(230\) 5.32744 + 21.4687i 0.351281 + 1.41560i
\(231\) 0 0
\(232\) 4.89981 + 5.47836i 0.321688 + 0.359672i
\(233\) −14.2376 −0.932739 −0.466369 0.884590i \(-0.654438\pi\)
−0.466369 + 0.884590i \(0.654438\pi\)
\(234\) 0 0
\(235\) 11.6561i 0.760362i
\(236\) −9.04293 17.0987i −0.588645 1.11303i
\(237\) 0 0
\(238\) 29.3409 7.28093i 1.90189 0.471952i
\(239\) −8.31368 −0.537767 −0.268884 0.963173i \(-0.586655\pi\)
−0.268884 + 0.963173i \(0.586655\pi\)
\(240\) 0 0
\(241\) −26.1776 −1.68625 −0.843125 0.537718i \(-0.819287\pi\)
−0.843125 + 0.537718i \(0.819287\pi\)
\(242\) −3.81534 + 0.946775i −0.245260 + 0.0608610i
\(243\) 0 0
\(244\) 7.62575 + 14.4191i 0.488189 + 0.923087i
\(245\) 8.22920i 0.525744i
\(246\) 0 0
\(247\) 2.32843 0.148155
\(248\) −2.82931 + 2.53051i −0.179661 + 0.160688i
\(249\) 0 0
\(250\) −3.95740 15.9477i −0.250288 1.00862i
\(251\) 29.4740i 1.86038i 0.367075 + 0.930191i \(0.380359\pi\)
−0.367075 + 0.930191i \(0.619641\pi\)
\(252\) 0 0
\(253\) 27.1967i 1.70984i
\(254\) 3.62341 0.899147i 0.227353 0.0564175i
\(255\) 0 0
\(256\) −5.86175 14.8876i −0.366360 0.930473i
\(257\) −1.28195 −0.0799657 −0.0399828 0.999200i \(-0.512730\pi\)
−0.0399828 + 0.999200i \(0.512730\pi\)
\(258\) 0 0
\(259\) 12.2886i 0.763575i
\(260\) 8.78838 4.64787i 0.545032 0.288249i
\(261\) 0 0
\(262\) 5.23411 + 21.0926i 0.323364 + 1.30310i
\(263\) 29.2736 1.80509 0.902544 0.430597i \(-0.141697\pi\)
0.902544 + 0.430597i \(0.141697\pi\)
\(264\) 0 0
\(265\) −10.6453 −0.653933
\(266\) −1.12218 4.52218i −0.0688050 0.277272i
\(267\) 0 0
\(268\) −0.490873 0.928161i −0.0299848 0.0566965i
\(269\) 14.1850i 0.864875i 0.901664 + 0.432437i \(0.142346\pi\)
−0.901664 + 0.432437i \(0.857654\pi\)
\(270\) 0 0
\(271\) 26.3185 1.59874 0.799369 0.600840i \(-0.205167\pi\)
0.799369 + 0.600840i \(0.205167\pi\)
\(272\) 14.6080 21.4513i 0.885743 1.30067i
\(273\) 0 0
\(274\) 6.75110 1.67528i 0.407849 0.101207i
\(275\) 1.64217i 0.0990269i
\(276\) 0 0
\(277\) 3.58863i 0.215620i 0.994172 + 0.107810i \(0.0343838\pi\)
−0.994172 + 0.107810i \(0.965616\pi\)
\(278\) 3.33922 + 13.4565i 0.200273 + 0.807068i
\(279\) 0 0
\(280\) −13.2624 14.8284i −0.792580 0.886165i
\(281\) 4.42597 0.264031 0.132016 0.991248i \(-0.457855\pi\)
0.132016 + 0.991248i \(0.457855\pi\)
\(282\) 0 0
\(283\) 0.493151i 0.0293148i 0.999893 + 0.0146574i \(0.00466576\pi\)
−0.999893 + 0.0146574i \(0.995334\pi\)
\(284\) −12.6850 + 6.70867i −0.752718 + 0.398086i
\(285\) 0 0
\(286\) −11.8638 + 2.94399i −0.701519 + 0.174082i
\(287\) −21.4938 −1.26874
\(288\) 0 0
\(289\) 25.0970 1.47630
\(290\) 7.61452 1.88954i 0.447140 0.110957i
\(291\) 0 0
\(292\) −11.1936 + 5.91989i −0.655054 + 0.346436i
\(293\) 12.7228i 0.743275i −0.928378 0.371637i \(-0.878796\pi\)
0.928378 0.371637i \(-0.121204\pi\)
\(294\) 0 0
\(295\) −20.6470 −1.20211
\(296\) −7.03295 7.86338i −0.408782 0.457050i
\(297\) 0 0
\(298\) 0.246649 + 0.993952i 0.0142880 + 0.0575781i
\(299\) 17.0593i 0.986565i
\(300\) 0 0
\(301\) 6.49709i 0.374486i
\(302\) −21.5842 + 5.35610i −1.24203 + 0.308209i
\(303\) 0 0
\(304\) −3.30619 2.25147i −0.189623 0.129131i
\(305\) 17.4113 0.996966
\(306\) 0 0
\(307\) 10.2166i 0.583092i −0.956557 0.291546i \(-0.905830\pi\)
0.956557 0.291546i \(-0.0941697\pi\)
\(308\) 11.4354 + 21.6224i 0.651590 + 1.23205i
\(309\) 0 0
\(310\) 0.975855 + 3.93253i 0.0554248 + 0.223353i
\(311\) −0.184934 −0.0104867 −0.00524333 0.999986i \(-0.501669\pi\)
−0.00524333 + 0.999986i \(0.501669\pi\)
\(312\) 0 0
\(313\) −19.0733 −1.07809 −0.539044 0.842278i \(-0.681214\pi\)
−0.539044 + 0.842278i \(0.681214\pi\)
\(314\) 0.0480689 + 0.193709i 0.00271268 + 0.0109317i
\(315\) 0 0
\(316\) −15.4812 + 8.18745i −0.870883 + 0.460580i
\(317\) 0.911635i 0.0512025i −0.999672 0.0256013i \(-0.991850\pi\)
0.999672 0.0256013i \(-0.00815002\pi\)
\(318\) 0 0
\(319\) −9.64615 −0.540081
\(320\) −16.9730 1.89830i −0.948821 0.106118i
\(321\) 0 0
\(322\) −33.1318 + 8.22164i −1.84636 + 0.458174i
\(323\) 6.48822i 0.361014i
\(324\) 0 0
\(325\) 1.03006i 0.0571376i
\(326\) 2.86742 + 11.5552i 0.158812 + 0.639984i
\(327\) 0 0
\(328\) −13.7537 + 12.3012i −0.759422 + 0.679221i
\(329\) −17.9885 −0.991736
\(330\) 0 0
\(331\) 2.45230i 0.134791i 0.997726 + 0.0673953i \(0.0214689\pi\)
−0.997726 + 0.0673953i \(0.978531\pi\)
\(332\) 7.23714 + 13.6843i 0.397190 + 0.751022i
\(333\) 0 0
\(334\) −7.08992 + 1.75936i −0.387943 + 0.0962678i
\(335\) −1.12077 −0.0612342
\(336\) 0 0
\(337\) 35.1467 1.91456 0.957282 0.289156i \(-0.0933746\pi\)
0.957282 + 0.289156i \(0.0933746\pi\)
\(338\) 10.4020 2.58125i 0.565793 0.140401i
\(339\) 0 0
\(340\) −12.9514 24.4890i −0.702387 1.32810i
\(341\) 4.98177i 0.269778i
\(342\) 0 0
\(343\) −10.3627 −0.559533
\(344\) −3.71839 4.15744i −0.200482 0.224154i
\(345\) 0 0
\(346\) 1.06946 + 4.30975i 0.0574946 + 0.231694i
\(347\) 5.30643i 0.284864i −0.989805 0.142432i \(-0.954508\pi\)
0.989805 0.142432i \(-0.0454922\pi\)
\(348\) 0 0
\(349\) 26.8913i 1.43946i −0.694255 0.719729i \(-0.744266\pi\)
0.694255 0.719729i \(-0.255734\pi\)
\(350\) 2.00054 0.496433i 0.106933 0.0265355i
\(351\) 0 0
\(352\) 19.6923 + 7.29140i 1.04960 + 0.388633i
\(353\) 3.21383 0.171055 0.0855275 0.996336i \(-0.472742\pi\)
0.0855275 + 0.996336i \(0.472742\pi\)
\(354\) 0 0
\(355\) 15.3174i 0.812961i
\(356\) 1.84520 0.975861i 0.0977952 0.0517205i
\(357\) 0 0
\(358\) 6.19557 + 24.9671i 0.327446 + 1.31955i
\(359\) 15.6827 0.827699 0.413850 0.910345i \(-0.364184\pi\)
0.413850 + 0.910345i \(0.364184\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) −4.79566 19.3257i −0.252054 1.01574i
\(363\) 0 0
\(364\) 7.17289 + 13.5628i 0.375961 + 0.710883i
\(365\) 13.5164i 0.707481i
\(366\) 0 0
\(367\) 14.3509 0.749111 0.374555 0.927205i \(-0.377795\pi\)
0.374555 + 0.927205i \(0.377795\pi\)
\(368\) −16.4954 + 24.2228i −0.859884 + 1.26270i
\(369\) 0 0
\(370\) −10.9295 + 2.71215i −0.568198 + 0.140998i
\(371\) 16.4284i 0.852921i
\(372\) 0 0
\(373\) 9.08701i 0.470508i −0.971934 0.235254i \(-0.924408\pi\)
0.971934 0.235254i \(-0.0755921\pi\)
\(374\) 8.20347 + 33.0586i 0.424191 + 1.70942i
\(375\) 0 0
\(376\) −11.5107 + 10.2951i −0.593619 + 0.530929i
\(377\) −6.05060 −0.311622
\(378\) 0 0
\(379\) 18.2006i 0.934900i −0.884020 0.467450i \(-0.845173\pi\)
0.884020 0.467450i \(-0.154827\pi\)
\(380\) −3.77437 + 1.99614i −0.193621 + 0.102400i
\(381\) 0 0
\(382\) −6.69010 + 1.66015i −0.342295 + 0.0849404i
\(383\) 22.4154 1.14537 0.572686 0.819775i \(-0.305901\pi\)
0.572686 + 0.819775i \(0.305901\pi\)
\(384\) 0 0
\(385\) 26.1094 1.33066
\(386\) −13.7237 + 3.40553i −0.698518 + 0.173337i
\(387\) 0 0
\(388\) −0.207903 + 0.109953i −0.0105547 + 0.00558200i
\(389\) 34.9213i 1.77058i −0.465038 0.885291i \(-0.653959\pi\)
0.465038 0.885291i \(-0.346041\pi\)
\(390\) 0 0
\(391\) −47.5360 −2.40400
\(392\) 8.12652 7.26831i 0.410451 0.367105i
\(393\) 0 0
\(394\) −6.54676 26.3823i −0.329821 1.32912i
\(395\) 18.6937i 0.940584i
\(396\) 0 0
\(397\) 31.3443i 1.57313i 0.617510 + 0.786563i \(0.288142\pi\)
−0.617510 + 0.786563i \(0.711858\pi\)
\(398\) −16.1036 + 3.99610i −0.807201 + 0.200307i
\(399\) 0 0
\(400\) 0.996016 1.46261i 0.0498008 0.0731303i
\(401\) −1.64321 −0.0820579 −0.0410290 0.999158i \(-0.513064\pi\)
−0.0410290 + 0.999158i \(0.513064\pi\)
\(402\) 0 0
\(403\) 3.12484i 0.155659i
\(404\) 9.92451 + 18.7657i 0.493763 + 0.933627i
\(405\) 0 0
\(406\) 2.91605 + 11.7512i 0.144721 + 0.583202i
\(407\) 13.8456 0.686302
\(408\) 0 0
\(409\) −2.46645 −0.121958 −0.0609791 0.998139i \(-0.519422\pi\)
−0.0609791 + 0.998139i \(0.519422\pi\)
\(410\) 4.74378 + 19.1166i 0.234279 + 0.944104i
\(411\) 0 0
\(412\) 21.9565 11.6120i 1.08172 0.572083i
\(413\) 31.8637i 1.56791i
\(414\) 0 0
\(415\) 16.5240 0.811130
\(416\) 12.3521 + 4.57357i 0.605611 + 0.224238i
\(417\) 0 0
\(418\) 5.09517 1.26436i 0.249213 0.0618420i
\(419\) 4.25063i 0.207657i −0.994595 0.103828i \(-0.966891\pi\)
0.994595 0.103828i \(-0.0331093\pi\)
\(420\) 0 0
\(421\) 31.4900i 1.53473i 0.641212 + 0.767364i \(0.278432\pi\)
−0.641212 + 0.767364i \(0.721568\pi\)
\(422\) 0.136032 + 0.548187i 0.00662195 + 0.0266853i
\(423\) 0 0
\(424\) −9.40224 10.5124i −0.456613 0.510529i
\(425\) 2.87029 0.139229
\(426\) 0 0
\(427\) 26.8701i 1.30034i
\(428\) 15.4689 + 29.2491i 0.747715 + 1.41381i
\(429\) 0 0
\(430\) −5.77854 + 1.43394i −0.278666 + 0.0691508i
\(431\) 21.0564 1.01425 0.507125 0.861872i \(-0.330708\pi\)
0.507125 + 0.861872i \(0.330708\pi\)
\(432\) 0 0
\(433\) −7.53125 −0.361929 −0.180964 0.983490i \(-0.557922\pi\)
−0.180964 + 0.983490i \(0.557922\pi\)
\(434\) −6.06892 + 1.50600i −0.291318 + 0.0722903i
\(435\) 0 0
\(436\) −16.3102 30.8400i −0.781117 1.47697i
\(437\) 7.32651i 0.350475i
\(438\) 0 0
\(439\) 0.823995 0.0393271 0.0196636 0.999807i \(-0.493740\pi\)
0.0196636 + 0.999807i \(0.493740\pi\)
\(440\) 16.7072 14.9428i 0.796486 0.712372i
\(441\) 0 0
\(442\) 5.14567 + 20.7362i 0.244755 + 0.986319i
\(443\) 8.58526i 0.407898i 0.978982 + 0.203949i \(0.0653777\pi\)
−0.978982 + 0.203949i \(0.934622\pi\)
\(444\) 0 0
\(445\) 2.22810i 0.105622i
\(446\) −26.4288 + 6.55829i −1.25144 + 0.310544i
\(447\) 0 0
\(448\) 2.92957 26.1938i 0.138409 1.23754i
\(449\) −2.49451 −0.117723 −0.0588615 0.998266i \(-0.518747\pi\)
−0.0588615 + 0.998266i \(0.518747\pi\)
\(450\) 0 0
\(451\) 24.2172i 1.14034i
\(452\) 25.3162 13.3888i 1.19077 0.629759i
\(453\) 0 0
\(454\) −6.82621 27.5085i −0.320370 1.29104i
\(455\) 16.3773 0.767778
\(456\) 0 0
\(457\) 14.5004 0.678301 0.339150 0.940732i \(-0.389860\pi\)
0.339150 + 0.940732i \(0.389860\pi\)
\(458\) 6.19947 + 24.9828i 0.289682 + 1.16737i
\(459\) 0 0
\(460\) 14.6247 + 27.6530i 0.681881 + 1.28933i
\(461\) 23.1930i 1.08020i 0.841600 + 0.540102i \(0.181614\pi\)
−0.841600 + 0.540102i \(0.818386\pi\)
\(462\) 0 0
\(463\) 26.0637 1.21128 0.605642 0.795737i \(-0.292916\pi\)
0.605642 + 0.795737i \(0.292916\pi\)
\(464\) 8.59136 + 5.85061i 0.398844 + 0.271608i
\(465\) 0 0
\(466\) −19.5424 + 4.84943i −0.905282 + 0.224645i
\(467\) 12.1953i 0.564332i −0.959366 0.282166i \(-0.908947\pi\)
0.959366 0.282166i \(-0.0910529\pi\)
\(468\) 0 0
\(469\) 1.72964i 0.0798674i
\(470\) 3.97015 + 15.9990i 0.183129 + 0.737980i
\(471\) 0 0
\(472\) −18.2361 20.3894i −0.839385 0.938497i
\(473\) 7.32031 0.336588
\(474\) 0 0
\(475\) 0.442384i 0.0202980i
\(476\) 37.7929 19.9874i 1.73224 0.916120i
\(477\) 0 0
\(478\) −11.4112 + 2.83169i −0.521937 + 0.129518i
\(479\) −18.1883 −0.831045 −0.415523 0.909583i \(-0.636401\pi\)
−0.415523 + 0.909583i \(0.636401\pi\)
\(480\) 0 0
\(481\) 8.68475 0.395990
\(482\) −35.9310 + 8.91626i −1.63661 + 0.406125i
\(483\) 0 0
\(484\) −4.91440 + 2.59906i −0.223382 + 0.118139i
\(485\) 0.251046i 0.0113994i
\(486\) 0 0
\(487\) −2.13693 −0.0968334 −0.0484167 0.998827i \(-0.515418\pi\)
−0.0484167 + 0.998827i \(0.515418\pi\)
\(488\) 15.3782 + 17.1940i 0.696139 + 0.778337i
\(489\) 0 0
\(490\) −2.80291 11.2953i −0.126623 0.510268i
\(491\) 2.32773i 0.105049i 0.998620 + 0.0525244i \(0.0167267\pi\)
−0.998620 + 0.0525244i \(0.983273\pi\)
\(492\) 0 0
\(493\) 16.8601i 0.759341i
\(494\) 3.19597 0.793079i 0.143794 0.0356823i
\(495\) 0 0
\(496\) −3.02156 + 4.43702i −0.135672 + 0.199228i
\(497\) −23.6387 −1.06034
\(498\) 0 0
\(499\) 16.9382i 0.758260i 0.925343 + 0.379130i \(0.123777\pi\)
−0.925343 + 0.379130i \(0.876223\pi\)
\(500\) −10.8637 20.5416i −0.485841 0.918648i
\(501\) 0 0
\(502\) 10.0390 + 40.4555i 0.448063 + 1.80562i
\(503\) −8.22413 −0.366696 −0.183348 0.983048i \(-0.558693\pi\)
−0.183348 + 0.983048i \(0.558693\pi\)
\(504\) 0 0
\(505\) 22.6598 1.00835
\(506\) −9.26337 37.3298i −0.411807 1.65951i
\(507\) 0 0
\(508\) 4.66718 2.46831i 0.207073 0.109514i
\(509\) 19.8145i 0.878261i −0.898423 0.439131i \(-0.855287\pi\)
0.898423 0.439131i \(-0.144713\pi\)
\(510\) 0 0
\(511\) −20.8594 −0.922764
\(512\) −13.1165 18.4379i −0.579675 0.814848i
\(513\) 0 0
\(514\) −1.75958 + 0.436639i −0.0776118 + 0.0192593i
\(515\) 26.5128i 1.16829i
\(516\) 0 0
\(517\) 20.2677i 0.891374i
\(518\) −4.18556 16.8671i −0.183903 0.741098i
\(519\) 0 0
\(520\) 10.4797 9.37297i 0.459565 0.411032i
\(521\) 36.0978 1.58147 0.790737 0.612156i \(-0.209698\pi\)
0.790737 + 0.612156i \(0.209698\pi\)
\(522\) 0 0
\(523\) 4.19475i 0.183424i 0.995786 + 0.0917119i \(0.0292339\pi\)
−0.995786 + 0.0917119i \(0.970766\pi\)
\(524\) 14.3685 + 27.1686i 0.627691 + 1.18686i
\(525\) 0 0
\(526\) 40.1805 9.97077i 1.75195 0.434746i
\(527\) −8.70743 −0.379301
\(528\) 0 0
\(529\) 30.6778 1.33382
\(530\) −14.6115 + 3.62584i −0.634683 + 0.157496i
\(531\) 0 0
\(532\) −3.08056 5.82485i −0.133559 0.252539i
\(533\) 15.1903i 0.657967i
\(534\) 0 0
\(535\) 35.3188 1.52696
\(536\) −0.989901 1.10679i −0.0427572 0.0478059i
\(537\) 0 0
\(538\) 4.83150 + 19.4701i 0.208301 + 0.839416i
\(539\) 14.3090i 0.616331i
\(540\) 0 0
\(541\) 6.12211i 0.263210i −0.991302 0.131605i \(-0.957987\pi\)
0.991302 0.131605i \(-0.0420131\pi\)
\(542\) 36.1244 8.96426i 1.55168 0.385048i
\(543\) 0 0
\(544\) 12.7443 34.4193i 0.546409 1.47571i
\(545\) −37.2398 −1.59518
\(546\) 0 0
\(547\) 4.88879i 0.209029i −0.994523 0.104515i \(-0.966671\pi\)
0.994523 0.104515i \(-0.0333289\pi\)
\(548\) 8.69584 4.59893i 0.371468 0.196457i
\(549\) 0 0
\(550\) 0.559335 + 2.25402i 0.0238501 + 0.0961119i
\(551\) 2.59857 0.110703
\(552\) 0 0
\(553\) −28.8493 −1.22680
\(554\) 1.22231 + 4.92570i 0.0519310 + 0.209273i
\(555\) 0 0
\(556\) 9.16673 + 17.3328i 0.388756 + 0.735076i
\(557\) 28.5987i 1.21176i −0.795554 0.605882i \(-0.792820\pi\)
0.795554 0.605882i \(-0.207180\pi\)
\(558\) 0 0
\(559\) 4.59171 0.194209
\(560\) −23.2544 15.8359i −0.982677 0.669191i
\(561\) 0 0
\(562\) 6.07501 1.50751i 0.256259 0.0635905i
\(563\) 9.83345i 0.414431i −0.978295 0.207215i \(-0.933560\pi\)
0.978295 0.207215i \(-0.0664401\pi\)
\(564\) 0 0
\(565\) 30.5697i 1.28608i
\(566\) 0.167970 + 0.676891i 0.00706032 + 0.0284519i
\(567\) 0 0
\(568\) −15.1263 + 13.5288i −0.634683 + 0.567656i
\(569\) 10.3543 0.434075 0.217037 0.976163i \(-0.430361\pi\)
0.217037 + 0.976163i \(0.430361\pi\)
\(570\) 0 0
\(571\) 36.7988i 1.53998i −0.638055 0.769991i \(-0.720261\pi\)
0.638055 0.769991i \(-0.279739\pi\)
\(572\) −15.2813 + 8.08174i −0.638942 + 0.337915i
\(573\) 0 0
\(574\) −29.5020 + 7.32090i −1.23139 + 0.305569i
\(575\) −3.24113 −0.135165
\(576\) 0 0
\(577\) −8.22871 −0.342566 −0.171283 0.985222i \(-0.554791\pi\)
−0.171283 + 0.985222i \(0.554791\pi\)
\(578\) 34.4478 8.54820i 1.43284 0.355558i
\(579\) 0 0
\(580\) 9.80798 5.18710i 0.407254 0.215383i
\(581\) 25.5008i 1.05795i
\(582\) 0 0
\(583\) 18.5100 0.766606
\(584\) −13.3478 + 11.9382i −0.552335 + 0.494004i
\(585\) 0 0
\(586\) −4.33347 17.4631i −0.179014 0.721395i
\(587\) 7.18047i 0.296370i 0.988960 + 0.148185i \(0.0473431\pi\)
−0.988960 + 0.148185i \(0.952657\pi\)
\(588\) 0 0
\(589\) 1.34204i 0.0552976i
\(590\) −28.3397 + 7.03249i −1.16673 + 0.289523i
\(591\) 0 0
\(592\) −12.3316 8.39768i −0.506827 0.345143i
\(593\) 24.7687 1.01713 0.508564 0.861024i \(-0.330177\pi\)
0.508564 + 0.861024i \(0.330177\pi\)
\(594\) 0 0
\(595\) 45.6355i 1.87087i
\(596\) 0.677092 + 1.28027i 0.0277348 + 0.0524420i
\(597\) 0 0
\(598\) −5.81050 23.4153i −0.237609 0.957524i
\(599\) −41.9307 −1.71324 −0.856621 0.515946i \(-0.827440\pi\)
−0.856621 + 0.515946i \(0.827440\pi\)
\(600\) 0 0
\(601\) 2.10027 0.0856718 0.0428359 0.999082i \(-0.486361\pi\)
0.0428359 + 0.999082i \(0.486361\pi\)
\(602\) −2.21295 8.91780i −0.0901930 0.363462i
\(603\) 0 0
\(604\) −27.8018 + 14.7034i −1.13124 + 0.598273i
\(605\) 5.93422i 0.241260i
\(606\) 0 0
\(607\) −11.2877 −0.458152 −0.229076 0.973409i \(-0.573570\pi\)
−0.229076 + 0.973409i \(0.573570\pi\)
\(608\) −5.30489 1.96423i −0.215142 0.0796599i
\(609\) 0 0
\(610\) 23.8984 5.93038i 0.967619 0.240114i
\(611\) 12.7130i 0.514315i
\(612\) 0 0
\(613\) 31.4983i 1.27220i −0.771605 0.636102i \(-0.780546\pi\)
0.771605 0.636102i \(-0.219454\pi\)
\(614\) −3.47984 14.0231i −0.140435 0.565928i
\(615\) 0 0
\(616\) 23.0607 + 25.7836i 0.929142 + 1.03885i
\(617\) 11.4563 0.461214 0.230607 0.973047i \(-0.425929\pi\)
0.230607 + 0.973047i \(0.425929\pi\)
\(618\) 0 0
\(619\) 37.6816i 1.51455i 0.653095 + 0.757276i \(0.273470\pi\)
−0.653095 + 0.757276i \(0.726530\pi\)
\(620\) 2.67889 + 5.06534i 0.107587 + 0.203429i
\(621\) 0 0
\(622\) −0.253838 + 0.0629898i −0.0101780 + 0.00252566i
\(623\) 3.43855 0.137763
\(624\) 0 0
\(625\) −22.5924 −0.903695
\(626\) −26.1797 + 6.49649i −1.04635 + 0.259652i
\(627\) 0 0
\(628\) 0.131957 + 0.249510i 0.00526566 + 0.00995653i
\(629\) 24.2002i 0.964925i
\(630\) 0 0
\(631\) 6.99670 0.278534 0.139267 0.990255i \(-0.455525\pi\)
0.139267 + 0.990255i \(0.455525\pi\)
\(632\) −18.4605 + 16.5109i −0.734319 + 0.656770i
\(633\) 0 0
\(634\) −0.310508 1.25130i −0.0123319 0.0496953i
\(635\) 5.63569i 0.223646i
\(636\) 0 0
\(637\) 8.97538i 0.355617i
\(638\) −13.2402 + 3.28554i −0.524183 + 0.130076i
\(639\) 0 0
\(640\) −23.9435 + 3.17555i −0.946450 + 0.125525i
\(641\) 6.20749 0.245181 0.122591 0.992457i \(-0.460880\pi\)
0.122591 + 0.992457i \(0.460880\pi\)
\(642\) 0 0
\(643\) 29.4008i 1.15945i 0.814811 + 0.579726i \(0.196841\pi\)
−0.814811 + 0.579726i \(0.803159\pi\)
\(644\) −42.6758 + 22.5698i −1.68166 + 0.889374i
\(645\) 0 0
\(646\) −2.20993 8.90563i −0.0869484 0.350387i
\(647\) −5.62285 −0.221057 −0.110529 0.993873i \(-0.535254\pi\)
−0.110529 + 0.993873i \(0.535254\pi\)
\(648\) 0 0
\(649\) 35.9011 1.40924
\(650\) 0.350846 + 1.41385i 0.0137613 + 0.0554557i
\(651\) 0 0
\(652\) 7.87156 + 14.8839i 0.308274 + 0.582897i
\(653\) 34.9447i 1.36749i 0.729721 + 0.683745i \(0.239650\pi\)
−0.729721 + 0.683745i \(0.760350\pi\)
\(654\) 0 0
\(655\) 32.8064 1.28185
\(656\) −14.6883 + 21.5691i −0.573480 + 0.842130i
\(657\) 0 0
\(658\) −24.6907 + 6.12698i −0.962543 + 0.238855i
\(659\) 37.8768i 1.47547i −0.675090 0.737736i \(-0.735895\pi\)
0.675090 0.737736i \(-0.264105\pi\)
\(660\) 0 0
\(661\) 6.77264i 0.263425i −0.991288 0.131713i \(-0.957952\pi\)
0.991288 0.131713i \(-0.0420476\pi\)
\(662\) 0.835268 + 3.36599i 0.0324636 + 0.130823i
\(663\) 0 0
\(664\) 14.5945 + 16.3178i 0.566378 + 0.633254i
\(665\) −7.03360 −0.272751
\(666\) 0 0
\(667\) 19.0385i 0.737172i
\(668\) −9.13226 + 4.82974i −0.353338 + 0.186868i
\(669\) 0 0
\(670\) −1.53835 + 0.381741i −0.0594317 + 0.0147479i
\(671\) −30.2748 −1.16874
\(672\) 0 0
\(673\) 24.6355 0.949630 0.474815 0.880086i \(-0.342515\pi\)
0.474815 + 0.880086i \(0.342515\pi\)
\(674\) 48.2418 11.9712i 1.85821 0.461113i
\(675\) 0 0
\(676\) 13.3984 7.08596i 0.515323 0.272537i
\(677\) 28.2956i 1.08749i 0.839251 + 0.543744i \(0.182994\pi\)
−0.839251 + 0.543744i \(0.817006\pi\)
\(678\) 0 0
\(679\) −0.387430 −0.0148682
\(680\) −26.1179 29.2019i −1.00158 1.11984i
\(681\) 0 0
\(682\) −1.69682 6.83790i −0.0649746 0.261837i
\(683\) 34.4333i 1.31755i −0.752339 0.658777i \(-0.771074\pi\)
0.752339 0.658777i \(-0.228926\pi\)
\(684\) 0 0
\(685\) 10.5004i 0.401198i
\(686\) −14.2237 + 3.52960i −0.543063 + 0.134761i
\(687\) 0 0
\(688\) −6.51985 4.43994i −0.248567 0.169271i
\(689\) 11.6105 0.442325
\(690\) 0 0
\(691\) 2.19928i 0.0836646i 0.999125 + 0.0418323i \(0.0133195\pi\)
−0.999125 + 0.0418323i \(0.986680\pi\)
\(692\) 2.93585 + 5.55123i 0.111604 + 0.211026i
\(693\) 0 0
\(694\) −1.80740 7.28352i −0.0686080 0.276479i
\(695\) 20.9297 0.793907
\(696\) 0 0
\(697\) −42.3282 −1.60329
\(698\) −9.15934 36.9106i −0.346686 1.39709i
\(699\) 0 0
\(700\) 2.57682 1.36279i 0.0973947 0.0515087i
\(701\) 36.0608i 1.36200i −0.732285 0.680999i \(-0.761546\pi\)
0.732285 0.680999i \(-0.238454\pi\)
\(702\) 0 0
\(703\) −3.72986 −0.140675
\(704\) 29.5128 + 3.30076i 1.11230 + 0.124402i
\(705\) 0 0
\(706\) 4.41126 1.09465i 0.166020 0.0411977i
\(707\) 34.9701i 1.31518i
\(708\) 0 0
\(709\) 10.7299i 0.402970i −0.979492 0.201485i \(-0.935423\pi\)
0.979492 0.201485i \(-0.0645768\pi\)
\(710\) 5.21719 + 21.0244i 0.195798 + 0.789031i
\(711\) 0 0
\(712\) 2.20030 1.96794i 0.0824599 0.0737515i
\(713\) 9.83244 0.368228
\(714\) 0 0
\(715\) 18.4524i 0.690080i
\(716\) 17.0079 + 32.1592i 0.635614 + 1.20185i
\(717\) 0 0
\(718\) 21.5258 5.34161i 0.803335 0.199347i
\(719\) −29.1037 −1.08539 −0.542693 0.839931i \(-0.682595\pi\)
−0.542693 + 0.839931i \(0.682595\pi\)
\(720\) 0 0
\(721\) 40.9162 1.52380
\(722\) −1.37258 + 0.340606i −0.0510823 + 0.0126760i
\(723\) 0 0
\(724\) −13.1649 24.8927i −0.489269 0.925130i
\(725\) 1.14957i 0.0426938i
\(726\) 0 0
\(727\) −40.5850 −1.50521 −0.752607 0.658470i \(-0.771204\pi\)
−0.752607 + 0.658470i \(0.771204\pi\)
\(728\) 14.4650 + 16.1729i 0.536107 + 0.599409i
\(729\) 0 0
\(730\) 4.60377 + 18.5524i 0.170393 + 0.686656i
\(731\) 12.7949i 0.473235i
\(732\) 0 0
\(733\) 18.6206i 0.687766i 0.939012 + 0.343883i \(0.111742\pi\)
−0.939012 + 0.343883i \(0.888258\pi\)
\(734\) 19.6978 4.88800i 0.727059 0.180419i
\(735\) 0 0
\(736\) −14.3909 + 38.8663i −0.530457 + 1.43263i
\(737\) 1.94880 0.0717849
\(738\) 0 0
\(739\) 7.89939i 0.290584i 0.989389 + 0.145292i \(0.0464121\pi\)
−0.989389 + 0.145292i \(0.953588\pi\)
\(740\) −14.0779 + 7.44532i −0.517514 + 0.273695i
\(741\) 0 0
\(742\) −5.59562 22.5494i −0.205422 0.827814i
\(743\) 14.4064 0.528521 0.264261 0.964451i \(-0.414872\pi\)
0.264261 + 0.964451i \(0.414872\pi\)
\(744\) 0 0
\(745\) 1.54595 0.0566392
\(746\) −3.09509 12.4727i −0.113319 0.456658i
\(747\) 0 0
\(748\) 22.5199 + 42.5815i 0.823409 + 1.55694i
\(749\) 54.5061i 1.99161i
\(750\) 0 0
\(751\) 14.0914 0.514204 0.257102 0.966384i \(-0.417232\pi\)
0.257102 + 0.966384i \(0.417232\pi\)
\(752\) −12.2928 + 18.0515i −0.448273 + 0.658270i
\(753\) 0 0
\(754\) −8.30496 + 2.06087i −0.302449 + 0.0750525i
\(755\) 33.5711i 1.22178i
\(756\) 0 0
\(757\) 50.2311i 1.82568i 0.408318 + 0.912840i \(0.366116\pi\)
−0.408318 + 0.912840i \(0.633884\pi\)
\(758\) −6.19922 24.9818i −0.225166 0.907380i
\(759\) 0 0
\(760\) −4.50075 + 4.02544i −0.163259 + 0.146018i
\(761\) −23.7483 −0.860875 −0.430437 0.902620i \(-0.641641\pi\)
−0.430437 + 0.902620i \(0.641641\pi\)
\(762\) 0 0
\(763\) 57.4707i 2.08058i
\(764\) −8.61727 + 4.55738i −0.311762 + 0.164880i
\(765\) 0 0
\(766\) 30.7670 7.63481i 1.11166 0.275857i
\(767\) 22.5191 0.813119
\(768\) 0 0
\(769\) −47.4035 −1.70942 −0.854708 0.519109i \(-0.826264\pi\)
−0.854708 + 0.519109i \(0.826264\pi\)
\(770\) 35.8374 8.89302i 1.29149 0.320482i
\(771\) 0 0
\(772\) −17.6770 + 9.34876i −0.636209 + 0.336469i
\(773\) 11.8508i 0.426242i −0.977026 0.213121i \(-0.931637\pi\)
0.977026 0.213121i \(-0.0683628\pi\)
\(774\) 0 0
\(775\) −0.593696 −0.0213262
\(776\) −0.247914 + 0.221732i −0.00889958 + 0.00795972i
\(777\) 0 0
\(778\) −11.8944 47.9325i −0.426435 1.71846i
\(779\) 6.52385i 0.233741i
\(780\) 0 0
\(781\) 26.6339i 0.953036i
\(782\) −65.2472 + 16.1911i −2.33324 + 0.578991i
\(783\) 0 0
\(784\) 8.67871 12.7443i 0.309954 0.455154i
\(785\) 0.301287 0.0107534
\(786\) 0 0
\(787\) 26.3903i 0.940713i 0.882477 + 0.470356i \(0.155875\pi\)
−0.882477 + 0.470356i \(0.844125\pi\)
\(788\) −17.9719 33.9821i −0.640224 1.21056i
\(789\) 0 0
\(790\) 6.36720 + 25.6587i 0.226535 + 0.912897i
\(791\) 47.1770 1.67742
\(792\) 0 0
\(793\) −18.9900 −0.674356
\(794\) 10.6761 + 43.0227i 0.378879 + 1.52682i
\(795\) 0 0
\(796\) −20.7425 + 10.9700i −0.735197 + 0.388821i
\(797\) 14.1893i 0.502610i −0.967908 0.251305i \(-0.919140\pi\)
0.967908 0.251305i \(-0.0808597\pi\)
\(798\) 0 0
\(799\) −35.4251 −1.25325
\(800\) 0.868943 2.34680i 0.0307218 0.0829719i
\(801\) 0 0
\(802\) −2.25544 + 0.559687i −0.0796424 + 0.0197632i
\(803\) 23.5024i 0.829382i
\(804\) 0 0
\(805\) 51.5317i 1.81625i
\(806\) −1.06434 4.28911i −0.0374898 0.151077i
\(807\) 0 0
\(808\) 20.0139 + 22.3771i 0.704087 + 0.787224i
\(809\) 29.9998 1.05474 0.527368 0.849637i \(-0.323179\pi\)
0.527368 + 0.849637i \(0.323179\pi\)
\(810\) 0 0
\(811\) 39.8833i 1.40049i −0.713901 0.700246i \(-0.753073\pi\)
0.713901 0.700246i \(-0.246927\pi\)
\(812\) 8.00506 + 15.1363i 0.280922 + 0.531179i
\(813\) 0 0
\(814\) 19.0043 4.71590i 0.666100 0.165292i
\(815\) 17.9725 0.629549
\(816\) 0 0
\(817\) −1.97202 −0.0689921
\(818\) −3.38541 + 0.840089i −0.118368 + 0.0293730i
\(819\) 0 0
\(820\) 13.0225 + 24.6234i 0.454765 + 0.859888i
\(821\) 56.4395i 1.96975i −0.173256 0.984877i \(-0.555429\pi\)
0.173256 0.984877i \(-0.444571\pi\)
\(822\) 0 0
\(823\) −41.7360 −1.45482 −0.727412 0.686201i \(-0.759277\pi\)
−0.727412 + 0.686201i \(0.759277\pi\)
\(824\) 26.1820 23.4170i 0.912093 0.815769i
\(825\) 0 0
\(826\) −10.8530 43.7356i −0.377623 1.52176i
\(827\) 17.4248i 0.605921i −0.953003 0.302960i \(-0.902025\pi\)
0.953003 0.302960i \(-0.0979750\pi\)
\(828\) 0 0
\(829\) 52.2723i 1.81549i −0.419519 0.907747i \(-0.637801\pi\)
0.419519 0.907747i \(-0.362199\pi\)
\(830\) 22.6805 5.62817i 0.787253 0.195356i
\(831\) 0 0
\(832\) 18.5121 + 2.07042i 0.641790 + 0.0717790i
\(833\) 25.0100 0.866547
\(834\) 0 0
\(835\) 11.0273i 0.381617i
\(836\) 6.56290 3.47089i 0.226983 0.120043i
\(837\) 0 0
\(838\) −1.44779 5.83434i −0.0500130 0.201544i
\(839\) −40.8429 −1.41005 −0.705027 0.709180i \(-0.749065\pi\)
−0.705027 + 0.709180i \(0.749065\pi\)
\(840\) 0 0
\(841\) 22.2474 0.767153
\(842\) 10.7257 + 43.2226i 0.369631 + 1.48955i
\(843\) 0 0
\(844\) 0.373432 + 0.706100i 0.0128541 + 0.0243050i
\(845\) 16.1788i 0.556567i
\(846\) 0 0
\(847\) −9.15805 −0.314674
\(848\) −16.4860 11.2267i −0.566131 0.385528i
\(849\) 0 0
\(850\) 3.93971 0.977638i 0.135131 0.0335327i
\(851\) 27.3269i 0.936754i
\(852\) 0 0
\(853\) 42.8153i 1.46597i −0.680245 0.732984i \(-0.738127\pi\)
0.680245 0.732984i \(-0.261873\pi\)
\(854\) 9.15213 + 36.8815i 0.313180 + 1.26206i
\(855\) 0 0
\(856\) 31.1947 + 34.8781i 1.06621 + 1.19211i
\(857\) −23.2947 −0.795732 −0.397866 0.917444i \(-0.630249\pi\)
−0.397866 + 0.917444i \(0.630249\pi\)
\(858\) 0 0
\(859\) 17.5879i 0.600091i 0.953925 + 0.300045i \(0.0970018\pi\)
−0.953925 + 0.300045i \(0.902998\pi\)
\(860\) −7.44312 + 3.93641i −0.253808 + 0.134230i
\(861\) 0 0
\(862\) 28.9017 7.17193i 0.984394 0.244277i
\(863\) 11.8886 0.404692 0.202346 0.979314i \(-0.435143\pi\)
0.202346 + 0.979314i \(0.435143\pi\)
\(864\) 0 0
\(865\) 6.70319 0.227915
\(866\) −10.3373 + 2.56519i −0.351275 + 0.0871687i
\(867\) 0 0
\(868\) −7.81716 + 4.13422i −0.265332 + 0.140325i
\(869\) 32.5048i 1.10265i
\(870\) 0 0
\(871\) 1.22239 0.0414193
\(872\) −32.8914 36.7751i −1.11384 1.24536i
\(873\) 0 0
\(874\) 2.49545 + 10.0563i 0.0844100 + 0.340158i
\(875\) 38.2795i 1.29408i
\(876\) 0 0
\(877\) 28.6698i 0.968111i 0.875037 + 0.484056i \(0.160837\pi\)
−0.875037 + 0.484056i \(0.839163\pi\)
\(878\) 1.13100 0.280658i 0.0381695 0.00947173i
\(879\) 0 0
\(880\) 17.8425 26.2009i 0.601469 0.883231i
\(881\) 44.2297 1.49014 0.745069 0.666988i \(-0.232417\pi\)
0.745069 + 0.666988i \(0.232417\pi\)
\(882\) 0 0
\(883\) 26.5869i 0.894719i −0.894354 0.447359i \(-0.852364\pi\)
0.894354 0.447359i \(-0.147636\pi\)
\(884\) 14.1257 + 26.7095i 0.475100 + 0.898338i
\(885\) 0 0
\(886\) 2.92419 + 11.7840i 0.0982401 + 0.395891i
\(887\) −16.4124 −0.551074 −0.275537 0.961290i \(-0.588856\pi\)
−0.275537 + 0.961290i \(0.588856\pi\)
\(888\) 0 0
\(889\) 8.69735 0.291700
\(890\) −0.758906 3.05826i −0.0254386 0.102513i
\(891\) 0 0
\(892\) −34.0420 + 18.0036i −1.13981 + 0.602806i
\(893\) 5.45991i 0.182709i
\(894\) 0 0
\(895\) 38.8327 1.29803
\(896\) −4.90070 36.9511i −0.163721 1.23445i
\(897\) 0 0
\(898\) −3.42392 + 0.849644i −0.114258 + 0.0283530i
\(899\) 3.48737i 0.116310i
\(900\) 0 0
\(901\) 32.3529i 1.07783i
\(902\) −8.24851 33.2401i −0.274645 1.10677i
\(903\) 0 0
\(904\) 30.1883 27.0002i 1.00405 0.898012i
\(905\) −30.0583 −0.999172
\(906\) 0 0
\(907\) 47.3380i 1.57183i −0.618333 0.785916i \(-0.712192\pi\)
0.618333 0.785916i \(-0.287808\pi\)
\(908\) −18.7391 35.4326i −0.621879 1.17587i
\(909\) 0 0
\(910\) 22.4792 5.57820i 0.745178 0.184915i
\(911\) −5.30896 −0.175894 −0.0879469 0.996125i \(-0.528031\pi\)
−0.0879469 + 0.996125i \(0.528031\pi\)
\(912\) 0 0
\(913\) −28.7320 −0.950889
\(914\) 19.9030 4.93893i 0.658334 0.163365i
\(915\) 0 0
\(916\) 17.0186 + 32.1794i 0.562310 + 1.06324i
\(917\) 50.6290i 1.67192i
\(918\) 0 0
\(919\) 49.2513 1.62465 0.812326 0.583204i \(-0.198201\pi\)
0.812326 + 0.583204i \(0.198201\pi\)
\(920\) 29.4924 + 32.9748i 0.972337 + 1.08715i
\(921\) 0 0
\(922\) 7.89966 + 31.8343i 0.260162 + 1.04841i
\(923\) 16.7063i 0.549893i
\(924\) 0 0
\(925\) 1.65003i 0.0542528i
\(926\) 35.7747 8.87746i 1.17563 0.291732i
\(927\) 0 0
\(928\) 13.7851 + 5.10418i 0.452519 + 0.167553i
\(929\) 29.2990 0.961270 0.480635 0.876921i \(-0.340406\pi\)
0.480635 + 0.876921i \(0.340406\pi\)
\(930\) 0 0
\(931\) 3.85468i 0.126332i
\(932\) −25.1718 + 13.3125i −0.824529 + 0.436065i
\(933\) 0 0
\(934\) −4.15380 16.7391i −0.135916 0.547720i
\(935\) 51.4179 1.68154
\(936\) 0 0
\(937\) −6.35345 −0.207558 −0.103779 0.994600i \(-0.533093\pi\)
−0.103779 + 0.994600i \(0.533093\pi\)
\(938\) −0.589126 2.37408i −0.0192357 0.0775164i
\(939\) 0 0
\(940\) 10.8987 + 20.6077i 0.355477 + 0.672151i
\(941\) 2.07523i 0.0676505i −0.999428 0.0338253i \(-0.989231\pi\)
0.999428 0.0338253i \(-0.0107690\pi\)
\(942\) 0 0
\(943\) 47.7970 1.55649
\(944\) −31.9753 21.7748i −1.04071 0.708709i
\(945\) 0 0
\(946\) 10.0477 2.49334i 0.326680 0.0810656i
\(947\) 13.3618i 0.434201i −0.976149 0.217101i \(-0.930340\pi\)
0.976149 0.217101i \(-0.0696600\pi\)
\(948\) 0 0
\(949\) 14.7420i 0.478546i
\(950\) −0.150679 0.607210i −0.00488867 0.0197005i
\(951\) 0 0
\(952\) 45.0661 40.3068i 1.46060 1.30635i
\(953\) 52.6796 1.70646 0.853231 0.521534i \(-0.174640\pi\)
0.853231 + 0.521534i \(0.174640\pi\)
\(954\) 0 0
\(955\) 10.4055i 0.336714i
\(956\) −14.6984 + 7.77347i −0.475380 + 0.251412i
\(957\) 0 0
\(958\) −24.9650 + 6.19505i −0.806582 + 0.200153i
\(959\) 16.2048 0.523281
\(960\) 0 0
\(961\) −29.1989 −0.941901
\(962\) 11.9205 2.95808i 0.384334 0.0953722i
\(963\) 0 0
\(964\) −46.2814 + 24.4766i −1.49062 + 0.788339i
\(965\) 21.3453i 0.687128i
\(966\) 0 0
\(967\) −7.17519 −0.230739 −0.115369 0.993323i \(-0.536805\pi\)
−0.115369 + 0.993323i \(0.536805\pi\)
\(968\) −5.86018 + 5.24130i −0.188353 + 0.168462i
\(969\) 0 0
\(970\) 0.0855077 + 0.344582i 0.00274549 + 0.0110638i
\(971\) 14.6991i 0.471718i −0.971787 0.235859i \(-0.924210\pi\)
0.971787 0.235859i \(-0.0757903\pi\)
\(972\) 0 0
\(973\) 32.3000i 1.03549i
\(974\) −2.93311 + 0.727851i −0.0939830 + 0.0233218i
\(975\) 0 0
\(976\) 26.9643 + 18.3623i 0.863106 + 0.587764i
\(977\) −19.5470 −0.625365 −0.312682 0.949858i \(-0.601228\pi\)
−0.312682 + 0.949858i \(0.601228\pi\)
\(978\) 0 0
\(979\) 3.87424i 0.123821i
\(980\) −7.69447 14.5490i −0.245791 0.464751i
\(981\) 0 0
\(982\) 0.792838 + 3.19500i 0.0253005 + 0.101957i
\(983\) −24.0339 −0.766562 −0.383281 0.923632i \(-0.625206\pi\)
−0.383281 + 0.923632i \(0.625206\pi\)
\(984\) 0 0
\(985\) −41.0339 −1.30745
\(986\) 5.74265 + 23.1419i 0.182883 + 0.736988i
\(987\) 0 0
\(988\) 4.11661 2.17714i 0.130967 0.0692639i
\(989\) 14.4480i 0.459419i
\(990\) 0 0
\(991\) 50.5419 1.60552 0.802758 0.596305i \(-0.203365\pi\)
0.802758 + 0.596305i \(0.203365\pi\)
\(992\) −2.63606 + 7.11935i −0.0836951 + 0.226039i
\(993\) 0 0
\(994\) −32.4461 + 8.05149i −1.02913 + 0.255378i
\(995\) 25.0469i 0.794039i
\(996\) 0 0
\(997\) 21.9225i 0.694293i −0.937811 0.347147i \(-0.887151\pi\)
0.937811 0.347147i \(-0.112849\pi\)
\(998\) 5.76927 + 23.2492i 0.182623 + 0.735939i
\(999\) 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.g.b.685.13 16
3.2 odd 2 152.2.c.b.77.4 yes 16
4.3 odd 2 5472.2.g.b.2737.4 16
8.3 odd 2 5472.2.g.b.2737.13 16
8.5 even 2 inner 1368.2.g.b.685.14 16
12.11 even 2 608.2.c.b.305.2 16
24.5 odd 2 152.2.c.b.77.3 16
24.11 even 2 608.2.c.b.305.15 16
48.5 odd 4 4864.2.a.bo.1.8 8
48.11 even 4 4864.2.a.bn.1.1 8
48.29 odd 4 4864.2.a.bq.1.1 8
48.35 even 4 4864.2.a.bp.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.c.b.77.3 16 24.5 odd 2
152.2.c.b.77.4 yes 16 3.2 odd 2
608.2.c.b.305.2 16 12.11 even 2
608.2.c.b.305.15 16 24.11 even 2
1368.2.g.b.685.13 16 1.1 even 1 trivial
1368.2.g.b.685.14 16 8.5 even 2 inner
4864.2.a.bn.1.1 8 48.11 even 4
4864.2.a.bo.1.8 8 48.5 odd 4
4864.2.a.bp.1.8 8 48.35 even 4
4864.2.a.bq.1.1 8 48.29 odd 4
5472.2.g.b.2737.4 16 4.3 odd 2
5472.2.g.b.2737.13 16 8.3 odd 2