LMFDB - Embedded newform 380.2.bb.a.59.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.13
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04981 - 0.947574i) q^{2} +(0.664457 - 0.791869i) q^{3} +(0.204208 + 1.98955i) q^{4} +(-0.681915 - 2.12955i) q^{5} +(-1.44791 + 0.201691i) q^{6} +(1.98367 + 3.43582i) q^{7} +(1.67086 - 2.28215i) q^{8} +(0.335391 + 1.90210i) q^{9} +O(q^{10})$	\(q+(-1.04981 - 0.947574i) q^{2} +(0.664457 - 0.791869i) q^{3} +(0.204208 + 1.98955i) q^{4} +(-0.681915 - 2.12955i) q^{5} +(-1.44791 + 0.201691i) q^{6} +(1.98367 + 3.43582i) q^{7} +(1.67086 - 2.28215i) q^{8} +(0.335391 + 1.90210i) q^{9} +(-1.30203 + 2.88179i) q^{10} +(3.95947 + 2.28600i) q^{11} +(1.71115 + 1.16026i) q^{12} +(1.59714 - 1.34016i) q^{13} +(1.17321 - 5.48664i) q^{14} +(-2.13943 - 0.875008i) q^{15} +(-3.91660 + 0.812561i) q^{16} +(3.02148 + 0.532768i) q^{17} +(1.45028 - 2.31465i) q^{18} +(-2.31915 - 3.69074i) q^{19} +(4.09759 - 1.79157i) q^{20} +(4.03878 + 0.712147i) q^{21} +(-1.99054 - 6.15176i) q^{22} +(-4.89694 - 1.78234i) q^{23} +(-0.696948 - 2.83950i) q^{24} +(-4.06998 + 2.90435i) q^{25} +(-2.94660 - 0.106493i) q^{26} +(4.41473 + 2.54884i) q^{27} +(-6.43065 + 4.64823i) q^{28} +(8.07431 - 1.42372i) q^{29} +(1.41686 + 2.94586i) q^{30} +(-0.128751 - 0.223003i) q^{31} +(4.88165 + 2.85823i) q^{32} +(4.44111 - 1.61643i) q^{33} +(-2.66715 - 3.42238i) q^{34} +(5.96406 - 6.56727i) q^{35} +(-3.71582 + 1.05570i) q^{36} -4.87597 q^{37} +(-1.06258 + 6.07214i) q^{38} -2.15520i q^{39} +(-5.99935 - 2.00196i) q^{40} +(3.49860 - 4.16946i) q^{41} +(-3.56515 - 4.57467i) q^{42} +(-3.50528 + 1.27582i) q^{43} +(-3.73955 + 8.34437i) q^{44} +(3.82191 - 2.01130i) q^{45} +(3.45196 + 6.51133i) q^{46} +(-1.32983 - 7.54185i) q^{47} +(-1.95897 + 3.64135i) q^{48} +(-4.36990 + 7.56889i) q^{49} +(7.02480 + 0.807591i) q^{50} +(2.42953 - 2.03861i) q^{51} +(2.99246 + 2.90391i) q^{52} +(-5.94655 - 2.16437i) q^{53} +(-2.21941 - 6.85908i) q^{54} +(2.16813 - 9.99075i) q^{55} +(11.1555 + 1.21375i) q^{56} +(-4.46356 - 0.615877i) q^{57} +(-9.82559 - 6.15637i) q^{58} +(-0.0505433 + 0.286645i) q^{59} +(1.30398 - 4.43518i) q^{60} +(12.9746 + 4.72236i) q^{61} +(-0.0761478 + 0.356113i) q^{62} +(-5.86996 + 4.92548i) q^{63} +(-2.41643 - 7.62633i) q^{64} +(-3.94305 - 2.48732i) q^{65} +(-6.19402 - 2.51133i) q^{66} +(6.61416 - 1.16625i) q^{67} +(-0.442959 + 6.12017i) q^{68} +(-4.66519 + 2.69345i) q^{69} +(-12.4841 + 1.24301i) q^{70} +(-4.32369 + 1.57370i) q^{71} +(4.90127 + 2.41273i) q^{72} +(-4.91224 + 5.85418i) q^{73} +(5.11885 + 4.62035i) q^{74} +(-0.404465 + 5.15271i) q^{75} +(6.86931 - 5.36773i) q^{76} +18.1387i q^{77} +(-2.04221 + 2.26256i) q^{78} +(-1.37594 - 1.15455i) q^{79} +(4.40118 + 7.78650i) q^{80} +(-0.493133 + 0.179486i) q^{81} +(-7.62374 + 1.06197i) q^{82} +(3.10221 + 5.37319i) q^{83} +(-0.592099 + 8.18078i) q^{84} +(-0.925836 - 6.79770i) q^{85} +(4.88882 + 1.98214i) q^{86} +(4.23764 - 7.33980i) q^{87} +(11.8327 - 5.21651i) q^{88} +(0.410842 + 0.489623i) q^{89} +(-5.91814 - 1.51005i) q^{90} +(7.77274 + 2.82905i) q^{91} +(2.54606 - 10.1067i) q^{92} +(-0.262139 - 0.0462222i) q^{93} +(-5.75039 + 9.17763i) q^{94} +(-6.27816 + 7.45552i) q^{95} +(5.50699 - 1.96646i) q^{96} +(-3.18700 + 18.0744i) q^{97} +(11.7597 - 3.80510i) q^{98} +(-3.02022 + 8.29800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.04981	−	0.947574i	−0.742329	−	0.670036i
$2$	−1.04981	−	0.947574i	−0.742329	−	0.670036i
$3$	0.664457	−	0.791869i	0.383624	−	0.457186i	−0.539330	−	0.842094i	$-0.681323\pi$
$3$	0.664457	−	0.791869i	0.383624	−	0.457186i	0.922955	+	0.384908i	$0.125767\pi$
$4$	0.204208	+	1.98955i	0.102104	+	0.994774i
$5$	−0.681915	−	2.12955i	−0.304962	−	0.952365i
$5$	−0.681915	−	2.12955i	−0.304962	−	0.952365i
$6$	−1.44791	+	0.201691i	−0.591106	+	0.0823400i
$7$	1.98367	+	3.43582i	0.749757	+	1.29862i	0.947939	+	0.318452i	$0.103163\pi$
$7$	1.98367	+	3.43582i	0.749757	+	1.29862i	−0.198182	+	0.980165i	$0.563504\pi$
$8$	1.67086	−	2.28215i	0.590740	−	0.806862i
$9$	0.335391	+	1.90210i	0.111797	+	0.634032i
$10$	−1.30203	+	2.88179i	−0.411736	+	0.911303i
$11$	3.95947	+	2.28600i	1.19382	+	0.689255i	0.959172	−	0.282824i	$-0.0912712\pi$
$11$	3.95947	+	2.28600i	1.19382	+	0.689255i	0.234653	+	0.972079i	$0.424605\pi$
$12$	1.71115	+	1.16026i	0.493966	+	0.334939i
$13$	1.59714	−	1.34016i	0.442967	−	0.371693i	−0.393851	−	0.919174i	$-0.628858\pi$
$13$	1.59714	−	1.34016i	0.442967	−	0.371693i	0.836818	+	0.547481i	$0.184413\pi$
$14$	1.17321	−	5.48664i	0.313554	−	1.46637i
$15$	−2.13943	−	0.875008i	−0.552398	−	0.225926i
$16$	−3.91660	+	0.812561i	−0.979150	+	0.203140i
$17$	3.02148	+	0.532768i	0.732817	+	0.129215i	0.527590	−	0.849499i	$-0.323096\pi$
$17$	3.02148	+	0.532768i	0.732817	+	0.129215i	0.205227	+	0.978714i	$0.434207\pi$
$18$	1.45028	−	2.31465i	0.341834	−	0.545568i
$19$	−2.31915	−	3.69074i	−0.532049	−	0.846714i
$19$	−2.31915	−	3.69074i	−0.532049	−	0.846714i
$20$	4.09759	−	1.79157i	0.916250	−	0.400608i
$21$	4.03878	+	0.712147i	0.881335	+	0.155403i
$22$	−1.99054	−	6.15176i	−0.424385	−	1.31156i
$23$	−4.89694	−	1.78234i	−1.02108	−	0.371644i	−0.223404	−	0.974726i	$-0.571717\pi$
$23$	−4.89694	−	1.78234i	−1.02108	−	0.371644i	−0.797679	+	0.603082i	$0.793939\pi$
$24$	−0.696948	−	2.83950i	−0.142264	−	0.579610i
$25$	−4.06998	+	2.90435i	−0.813997	+	0.580870i
$26$	−2.94660	−	0.106493i	−0.577875	−	0.0208851i
$27$	4.41473	+	2.54884i	0.849615	+	0.490525i
$28$	−6.43065	+	4.64823i	−1.21528	+	0.878433i
$29$	8.07431	−	1.42372i	1.49936	−	0.264378i	0.637077	−	0.770800i	$-0.280143\pi$
$29$	8.07431	−	1.42372i	1.49936	−	0.264378i	0.862286	+	0.506422i	$0.169032\pi$
$30$	1.41686	+	2.94586i	0.258683	+	0.537838i
$31$	−0.128751	−	0.223003i	−0.0231244	−	0.0400526i	0.854232	−	0.519893i	$-0.174028\pi$
$31$	−0.128751	−	0.223003i	−0.0231244	−	0.0400526i	−0.877356	+	0.479840i	$0.840695\pi$
$32$	4.88165	+	2.85823i	0.862962	+	0.505269i
$33$	4.44111	−	1.61643i	0.773098	−	0.281385i
$34$	−2.66715	−	3.42238i	−0.457412	−	0.586934i
$35$	5.96406	−	6.56727i	1.00811	−	1.11007i
$36$	−3.71582	+	1.05570i	−0.619304	+	0.175950i
$37$	−4.87597			−0.801605			−0.400803	−	0.916164i	$-0.631269\pi$
$37$	−4.87597			−0.801605			−0.400803	+	0.916164i	$0.631269\pi$
$38$	−1.06258	+	6.07214i	−0.172373	+	0.985032i
$39$		−	2.15520i		−	0.345109i
$40$	−5.99935	−	2.00196i	−0.948580	−	0.316537i
$41$	3.49860	−	4.16946i	0.546389	−	0.651161i	−0.420218	−	0.907423i	$-0.638047\pi$
$41$	3.49860	−	4.16946i	0.546389	−	0.651161i	0.966607	+	0.256262i	$0.0824910\pi$
$42$	−3.56515	−	4.57467i	−0.550114	−	0.705886i
$43$	−3.50528	+	1.27582i	−0.534550	+	0.194560i	−0.595169	−	0.803601i	$-0.702915\pi$
$43$	−3.50528	+	1.27582i	−0.534550	+	0.194560i	0.0606186	+	0.998161i	$0.480693\pi$
$44$	−3.73955	+	8.34437i	−0.563759	+	1.25796i
$45$	3.82191	−	2.01130i	0.569736	−	0.299827i
$46$	3.45196	+	6.51133i	0.508964	+	0.960044i
$47$	−1.32983	−	7.54185i	−0.193976	−	1.10009i	−0.913870	−	0.406007i	$-0.866921\pi$
$47$	−1.32983	−	7.54185i	−0.193976	−	1.10009i	0.719894	−	0.694084i	$-0.244190\pi$
$48$	−1.95897	+	3.64135i	−0.282753	+	0.525583i
$49$	−4.36990	+	7.56889i	−0.624272	+	1.08127i
$50$	7.02480	+	0.807591i	0.993457	+	0.114211i
$51$	2.42953	−	2.03861i	0.340202	−	0.285463i
$52$	2.99246	+	2.90391i	0.414979	+	0.402700i
$53$	−5.94655	−	2.16437i	−0.816822	−	0.297299i	−0.100383	−	0.994949i	$-0.532007\pi$
$53$	−5.94655	−	2.16437i	−0.816822	−	0.297299i	−0.716439	+	0.697650i	$0.754229\pi$
$54$	−2.21941	−	6.85908i	−0.302024	−	0.933403i
$55$	2.16813	−	9.99075i	0.292351	−	1.34715i
$56$	11.1555	+	1.21375i	1.49072	+	0.162194i
$57$	−4.46356	−	0.615877i	−0.591212	−	0.0815748i
$58$	−9.82559	−	6.15637i	−1.29016	−	0.808371i
$59$	−0.0505433	+	0.286645i	−0.00658017	+	0.0373180i	−0.987921	−	0.154958i	$-0.950476\pi$
$59$	−0.0505433	+	0.286645i	−0.00658017	+	0.0373180i	0.981341	+	0.192276i	$0.0615869\pi$
$60$	1.30398	−	4.43518i	0.168343	−	0.572579i
$61$	12.9746	+	4.72236i	1.66122	+	0.604636i	0.990555	−	0.137119i	$-0.0437844\pi$
$61$	12.9746	+	4.72236i	1.66122	+	0.604636i	0.670670	+	0.741756i	$0.266007\pi$
$62$	−0.0761478	+	0.356113i	−0.00967078	+	0.0452263i
$63$	−5.86996	+	4.92548i	−0.739545	+	0.620552i
$64$	−2.41643	−	7.62633i	−0.302053	−	0.953291i
$65$	−3.94305	−	2.48732i	−0.489076	−	0.308514i
$66$	−6.19402	−	2.51133i	−0.762431	−	0.309124i
$67$	6.61416	−	1.16625i	0.808048	−	0.142481i	0.245662	−	0.969356i	$-0.420995\pi$
$67$	6.61416	−	1.16625i	0.808048	−	0.142481i	0.562386	+	0.826875i	$0.309884\pi$
$68$	−0.442959	+	6.12017i	−0.0537167	+	0.742180i
$69$	−4.66519	+	2.69345i	−0.561623	+	0.324253i
$70$	−12.4841	+	1.24301i	−1.49214	+	0.148568i
$71$	−4.32369	+	1.57370i	−0.513128	+	0.186763i	−0.585589	−	0.810608i	$-0.699137\pi$
$71$	−4.32369	+	1.57370i	−0.513128	+	0.186763i	0.0724613	+	0.997371i	$0.476915\pi$
$72$	4.90127	+	2.41273i	0.577620	+	0.284343i
$73$	−4.91224	+	5.85418i	−0.574934	+	0.685180i	−0.972636	−	0.232335i	$-0.925364\pi$
$73$	−4.91224	+	5.85418i	−0.574934	+	0.685180i	0.397701	+	0.917515i	$0.369808\pi$
$74$	5.11885	+	4.62035i	0.595055	+	0.537104i
$75$	−0.404465	+	5.15271i	−0.0467035	+	0.594984i
$76$	6.86931	−	5.36773i	0.787964	−	0.615721i
$77$			18.1387i			2.06710i
$78$	−2.04221	+	2.26256i	−0.231235	+	0.256184i
$79$	−1.37594	−	1.15455i	−0.154805	−	0.129897i	0.562095	−	0.827073i	$-0.309995\pi$
$79$	−1.37594	−	1.15455i	−0.154805	−	0.129897i	−0.716901	+	0.697175i	$0.754440\pi$
$80$	4.40118	+	7.78650i	0.492067	+	0.870557i
$81$	−0.493133	+	0.179486i	−0.0547925	+	0.0199429i
$82$	−7.62374	+	1.06197i	−0.841901	+	0.117275i
$83$	3.10221	+	5.37319i	0.340512	+	0.589784i	0.984528	−	0.175228i	$-0.0560664\pi$
$83$	3.10221	+	5.37319i	0.340512	+	0.589784i	−0.644016	+	0.765012i	$0.722733\pi$
$84$	−0.592099	+	8.18078i	−0.0646033	+	0.892596i
$85$	−0.925836	−	6.79770i	−0.100421	−	0.737314i
$86$	4.88882	+	1.98214i	0.527174	+	0.213740i
$87$	4.23764	−	7.33980i	0.454322	−	0.786909i
$88$	11.8327	−	5.21651i	1.26137	−	0.556082i
$89$	0.410842	+	0.489623i	0.0435492	+	0.0518999i	0.787379	−	0.616469i	$-0.211437\pi$
$89$	0.410842	+	0.489623i	0.0435492	+	0.0518999i	−0.743830	+	0.668369i	$0.766993\pi$
$90$	−5.91814	−	1.51005i	−0.623826	−	0.159173i
$91$	7.77274	+	2.82905i	0.814805	+	0.296565i
$92$	2.54606	−	10.1067i	0.265445	−	1.05369i
$93$	−0.262139	−	0.0462222i	−0.0271825	−	0.00479302i
$94$	−5.75039	+	9.17763i	−0.593107	+	0.946600i
$95$	−6.27816	+	7.45552i	−0.644125	+	0.764920i
$96$	5.50699	−	1.96646i	0.562055	−	0.200701i
$97$	−3.18700	+	18.0744i	−0.323591	+	1.83517i	0.195807	+	0.980642i	$0.437267\pi$
$97$	−3.18700	+	18.0744i	−0.323591	+	1.83517i	−0.519398	+	0.854532i	$0.673844\pi$
$98$	11.7597	−	3.80510i	1.18791	−	0.384374i
$99$	−3.02022	+	8.29800i	−0.303544	+	0.833980i
$100$	−6.60946	−	7.50433i	−0.660946	−	0.750433i
$101$	−3.59331	+	3.01515i	−0.357548	+	0.300018i	−0.803812	−	0.594883i	$-0.797198\pi$
$101$	−3.59331	+	3.01515i	−0.357548	+	0.300018i	0.446265	+	0.894901i	$0.352754\pi$
$102$	−4.48228	−	0.161995i	−0.443812	−	0.0160399i
$103$	−7.45958	−	4.30679i	−0.735014	−	0.424361i	0.0852396	−	0.996360i	$-0.472834\pi$
$103$	−7.45958	−	4.30679i	−0.735014	−	0.424361i	−0.820254	+	0.572000i	$0.806168\pi$
$104$	−0.389843	−	5.88414i	−0.0382273	−	0.576987i
$105$	−1.23756	−	9.08642i	−0.120773	−	0.886744i
$106$	4.19186	+	7.90698i	0.407150	+	0.767994i
$107$	−10.1060	+	5.83472i	−0.976986	+	0.564063i	−0.901359	−	0.433073i	$-0.857429\pi$
$107$	−10.1060	+	5.83472i	−0.976986	+	0.564063i	−0.0756275	+	0.997136i	$0.524096\pi$
$108$	−4.16953	+	9.30380i	−0.401213	+	0.895259i
$109$	−6.34238	−	17.4255i	−0.607490	−	1.66906i	−0.735692	−	0.677316i	$-0.763143\pi$
$109$	−6.34238	−	17.4255i	−0.607490	−	1.66906i	0.128203	−	0.991748i	$-0.459079\pi$
$110$	−11.7431	+	8.43394i	−1.11966	+	0.804145i
$111$	−3.23988	+	3.86113i	−0.307515	+	0.366483i
$112$	−10.5611	−	11.8449i	−0.997926	−	1.11924i
$113$	−0.0574513			−0.00540456			−0.00270228	−	0.999996i	$-0.500860\pi$
$113$	−0.0574513			−0.00540456			−0.00270228	+	0.999996i	$0.500860\pi$
$114$	4.10230	+	4.87610i	0.384216	+	0.456689i
$115$	−0.456287	+	11.6437i	−0.0425490	+	1.08578i
$116$	4.48139	+	15.7735i	0.416087	+	1.46453i
$117$	3.08478	+	2.58844i	0.285188	+	0.239301i
$118$	0.324678	−	0.253030i	0.0298891	−	0.0232933i
$119$	4.16313	+	11.4381i	0.381633	+	1.04853i
$120$	−5.57160	+	3.42048i	−0.508615	+	0.312246i
$121$	4.95160	+	8.57642i	0.450145	+	0.779675i
$122$	−9.14607	−	17.2520i	−0.828047	−	1.56192i
$123$	−0.977003	−	5.54086i	−0.0880934	−	0.499603i
$124$	0.417384	−	0.301695i	0.0374822	−	0.0270930i
$125$	8.96035	+	6.68672i	0.801438	+	0.598078i
$126$	10.8296	+	0.391395i	0.964778	+	0.0348682i
$127$	4.64726	+	5.53839i	0.412378	+	0.491453i	0.931753	−	0.363094i	$-0.118279\pi$
$127$	4.64726	+	5.53839i	0.412378	+	0.491453i	−0.519375	+	0.854547i	$0.673835\pi$
$128$	−4.68972	+	10.2959i	−0.414516	+	0.910042i
$129$	−1.31883	+	3.62345i	−0.116116	+	0.319027i
$130$	1.78255	+	6.34755i	0.156340	+	0.556717i
$131$	−20.4129	−	3.59935i	−1.78349	−	0.314477i	−0.818056	−	0.575139i	$-0.804948\pi$
$131$	−20.4129	−	3.59935i	−1.78349	−	0.314477i	−0.965430	+	0.260662i	$0.916059\pi$
$132$	4.12288	+	8.50571i	0.358850	+	0.740327i
$133$	8.08029	−	15.2894i	0.700650	−	1.32576i
$134$	−8.04873	−	5.04305i	−0.695304	−	0.435654i
$135$	2.41742	−	11.1395i	0.208059	−	0.958734i
$136$	6.26434	−	6.00529i	0.537163	−	0.514949i
$137$	6.83556	−	18.7805i	0.584001	−	1.60453i	−0.197278	−	0.980348i	$-0.563210\pi$
$137$	6.83556	−	18.7805i	0.584001	−	1.60453i	0.781279	−	0.624182i	$-0.214568\pi$
$138$	7.44981	+	1.59300i	0.634170	+	0.135605i
$139$	0.375344	+	0.447318i	0.0318363	+	0.0379410i	0.781728	−	0.623620i	$-0.214339\pi$
$139$	0.375344	+	0.447318i	0.0318363	+	0.0379410i	−0.749891	+	0.661561i	$0.769894\pi$
$140$	14.2838	+	10.5247i	1.20720	+	0.889499i
$141$	−6.85577	−	3.95818i	−0.577360	−	0.333339i
$142$	6.03026	+	2.44494i	0.506048	+	0.205174i
$143$	9.38743	−	1.65526i	0.785016	−	0.138420i
$144$	−2.85916	−	7.17723i	−0.238264	−	0.598102i
$145$	−8.53789	−	16.2238i	−0.709033	−	1.34731i
$146$	10.7042	−	1.49107i	0.885886	−	0.123402i
$147$	3.08996	+	8.48960i	0.254856	+	0.700210i
$148$	−0.995711	−	9.70098i	−0.0818469	−	0.797416i
$149$	−11.6884	−	9.80770i	−0.957548	−	0.803478i	0.0230042	−	0.999735i	$-0.492677\pi$
$149$	−11.6884	−	9.80770i	−0.957548	−	0.803478i	−0.980553	+	0.196257i	$0.937121\pi$
$150$	5.30718	−	5.02611i	0.433330	−	0.410380i
$151$	−5.24500			−0.426832			−0.213416	−	0.976961i	$-0.568459\pi$
$151$	−5.24500			−0.426832			−0.213416	+	0.976961i	$0.568459\pi$
$152$	−12.2978	−	0.874078i	−0.997484	−	0.0708971i
$153$			5.92583i			0.479075i
$154$	17.1878	−	19.0422i	1.38503	−	1.53446i
$155$	−0.387100	+	0.426251i	−0.0310926	+	0.0342373i
$156$	4.28788	−	0.440109i	0.343305	−	0.0352369i
$157$	3.05158	+	8.38416i	0.243543	+	0.669129i	0.999888	+	0.0149560i	$0.00476082\pi$
$157$	3.05158	+	8.38416i	0.243543	+	0.669129i	−0.756345	+	0.654173i	$0.773017\pi$
$158$	0.350456	+	2.51587i	0.0278807	+	0.200152i
$159$	−5.66513	+	3.27076i	−0.449274	+	0.259388i
$160$	2.75788	−	12.3448i	0.218029	−	0.975942i
$161$	−3.59012	−	20.3606i	−0.282941	−	1.60464i
$162$	0.687772	+	0.278854i	0.0540365	+	0.0219088i
$163$	4.03953	−	6.99668i	0.316401	−	0.548022i	−0.663333	−	0.748324i	$-0.730859\pi$
$163$	4.03953	−	6.99668i	0.316401	−	0.548022i	0.979734	+	0.200302i	$0.0641922\pi$
$164$	9.00979	+	6.10919i	0.703546	+	0.477047i
$165$	−6.47074	−	8.35531i	−0.503746	−	0.650460i
$166$	1.83475	−	8.58040i	0.142405	−	0.665968i
$167$	2.06631	−	5.67714i	0.159896	−	0.439310i	−0.833712	−	0.552200i	$-0.813789\pi$
$167$	2.06631	−	5.67714i	0.159896	−	0.439310i	0.993608	+	0.112890i	$0.0360107\pi$
$168$	8.37348	−	8.02721i	0.646028	−	0.619313i
$169$	−1.50260	+	8.52166i	−0.115584	+	0.655512i
$170$	−5.46937	+	8.01360i	−0.419482	+	0.614615i
$171$	6.24232	−	5.64908i	0.477362	−	0.431996i
$172$	−3.25410	−	6.71339i	−0.248123	−	0.511891i
$173$	2.77551	−	15.7407i	0.211018	−	1.19674i	−0.676666	−	0.736290i	$-0.736576\pi$
$173$	2.77551	−	15.7407i	0.211018	−	1.19674i	0.887684	−	0.460453i	$-0.152313\pi$
$174$	−11.4037	+	3.68993i	−0.864514	+	0.279733i
$175$	−18.0523	−	8.22245i	−1.36463	−	0.621559i
$176$	−17.3652	−	5.73604i	−1.30895	−	0.432370i
$177$	0.193402	+	0.230487i	0.0145370	+	0.0173245i
$178$	0.0326469	−	0.903315i	0.00244699	−	0.0677063i
$179$	7.75350	−	13.4294i	0.579523	−	1.00376i	−0.416010	−	0.909360i	$-0.636572\pi$
$179$	7.75350	−	13.4294i	0.579523	−	1.00376i	0.995534	−	0.0944043i	$-0.0300946\pi$
$180$	4.78204	+	7.19314i	0.356432	+	0.536145i
$181$	−18.9443	+	3.34039i	−1.40812	+	0.248289i	−0.825475	−	0.564439i	$-0.809092\pi$
$181$	−18.9443	+	3.34039i	−1.40812	+	0.248289i	−0.582643	+	0.812728i	$0.697981\pi$
$182$	−5.47918	−	10.3352i	−0.406144	−	0.766097i
$183$	12.3605	−	7.13636i	0.913718	−	0.527535i
$184$	−12.2497	+	8.19751i	−0.903059	+	0.604328i
$185$	3.32500	+	10.3836i	0.244459	+	0.763420i
$186$	0.231398	+	0.296921i	0.0169669	+	0.0217713i
$187$	10.7455	+	9.01659i	0.785792	+	0.659358i
$188$	14.7333	−	4.18586i	1.07454	−	0.305286i
$189$			20.2243i			1.47110i
$190$	13.6555	−	1.87787i	0.990677	−	0.136235i
$191$			0.422809i			0.0305934i	0.999883	+	0.0152967i	$0.00486928\pi$
$191$			0.422809i			0.0305934i	−0.999883	+	0.0152967i	$0.995131\pi$
$192$	−7.64467	−	3.15387i	−0.551706	−	0.227611i
$193$	4.65164	+	3.90319i	0.334832	+	0.280957i	0.794665	−	0.607048i	$-0.207646\pi$
$193$	4.65164	+	3.90319i	0.334832	+	0.280957i	−0.459833	+	0.888005i	$0.652091\pi$
$194$	20.4726	−	15.9548i	1.46984	−	1.14549i
$195$	−4.58962	+	1.46967i	−0.328669	+	0.105245i
$196$	−15.9510	−	7.14850i	−1.13936	−	0.510607i
$197$	−8.04555	+	4.64510i	−0.573222	+	0.330950i	−0.758435	−	0.651748i	$-0.774036\pi$
$197$	−8.04555	+	4.64510i	−0.573222	+	0.330950i	0.185213	+	0.982698i	$0.440702\pi$
$198$	11.0336	−	5.84945i	0.784126	−	0.415702i
$199$	13.8858	−	2.44844i	0.984336	−	0.173565i	0.341760	−	0.939787i	$-0.388977\pi$
$199$	13.8858	−	2.44844i	0.984336	−	0.173565i	0.642576	+	0.766222i	$0.277866\pi$
$200$	−0.172224	+	14.1411i	−0.0121780	+	0.999926i
$201$	3.47130	−	6.01247i	0.244847	−	0.424087i
$202$	6.62937	+	0.239593i	0.466441	+	0.0168577i
$203$	20.9084	+	24.9177i	1.46748	+	1.74888i
$204$	4.55205	+	4.41736i	0.318707	+	0.309277i
$205$	−11.2648	−	4.60722i	−0.786770	−	0.321782i
$206$	3.75015	+	11.5898i	0.261285	+	0.807501i
$207$	1.74780	−	9.91224i	0.121480	−	0.688948i
$208$	−5.16639	+	6.54664i	−0.358225	+	0.453928i
$209$	−0.745561	−	19.9149i	−0.0515715	−	1.37755i
$210$	−7.31086	+	10.7117i	−0.504497	+	0.739178i
$211$	−2.65099	+	15.0345i	−0.182501	+	1.03502i	0.746622	+	0.665248i	$0.231674\pi$
$211$	−2.65099	+	15.0345i	−0.182501	+	1.03502i	−0.929124	+	0.369769i	$0.879437\pi$
$212$	3.09178	−	12.2729i	0.212345	−	0.842909i
$213$	−1.62675	+	4.46945i	−0.111463	+	0.306242i
$214$	16.1382	+	3.45085i	1.10319	+	0.235896i
$215$	5.10723	+	6.59468i	0.348310	+	0.449753i
$216$	13.1933	−	5.81630i	0.897687	−	0.395749i
$217$	0.510799	−	0.884731i	0.0346753	−	0.0600594i
$218$	−9.85369	+	24.3034i	−0.667376	+	1.64603i
$219$	1.37177	+	7.77970i	0.0926958	+	0.525704i
$220$	20.3198	+	2.27342i	1.36996	+	0.153274i
$221$	5.53972	−	3.19836i	0.372642	−	0.215145i
$222$	7.05997	−	0.983440i	0.473834	−	0.0660042i
$223$	−6.03784	−	16.5888i	−0.404324	−	1.11087i	−0.960129	−	0.279558i	$-0.909812\pi$
$223$	−6.03784	−	16.5888i	−0.404324	−	1.11087i	0.555805	−	0.831313i	$-0.312410\pi$
$224$	−0.136773	+	22.4423i	−0.00913855	+	1.49949i
$225$	−6.88939	−	6.76741i	−0.459293	−	0.451161i
$226$	0.0603130	+	0.0544393i	0.00401196	+	0.00362125i
$227$			11.4524i			0.760124i	0.924961	+	0.380062i	$0.124097\pi$
$227$			11.4524i			0.760124i	−0.924961	+	0.380062i	$0.875903\pi$
$228$	0.313824	−	9.00622i	0.0207835	−	0.596452i
$229$	−1.48570			−0.0981780			−0.0490890	−	0.998794i	$-0.515632\pi$
$229$	−1.48570			−0.0981780			−0.0490890	+	0.998794i	$0.515632\pi$
$230$	11.5123	−	11.7913i	0.759097	−	0.777496i
$231$	14.3635	+	12.0524i	0.945047	+	0.792989i
$232$	10.2419	−	20.8056i	0.672416	−	1.36596i
$233$	1.91800	+	5.26965i	0.125652	+	0.345227i	0.986529	−	0.163587i	$-0.0523065\pi$
$233$	1.91800	+	5.26965i	0.125652	+	0.345227i	−0.860877	+	0.508814i	$0.830084\pi$
$234$	−0.785701	−	5.64043i	−0.0513629	−	0.368726i
$235$	−15.1539	+	7.97485i	−0.988533	+	0.520222i
$236$	−0.580615	−	0.0420232i	−0.0377948	−	0.00273547i
$237$	−1.82851	+	0.322415i	−0.118774	+	0.0209431i
$238$	6.46794	−	15.9527i	0.419255	−	1.03406i
$239$	−21.7366	−	12.5496i	−1.40603	−	0.811769i	−0.411023	−	0.911625i	$-0.634828\pi$
$239$	−21.7366	−	12.5496i	−1.40603	−	0.811769i	−0.995002	+	0.0998560i	$0.968162\pi$
$240$	9.09029	+	1.68864i	0.586775	+	0.109001i
$241$	2.71066	+	3.23043i	0.174609	+	0.208090i	0.846250	−	0.532786i	$-0.178855\pi$
$241$	2.71066	+	3.23043i	0.174609	+	0.208090i	−0.671641	+	0.740876i	$0.734410\pi$
$242$	2.92855	−	13.6956i	0.188254	−	0.880388i
$243$	−5.41607	+	14.8805i	−0.347441	+	0.954587i
$244$	−6.74585	+	26.7779i	−0.431859	+	1.71428i
$245$	19.0983	+	4.14459i	1.22014	+	0.264788i
$246$	−4.22471	+	6.74264i	−0.269357	+	0.429895i
$247$	−8.65018	−	2.78660i	−0.550398	−	0.177307i
$248$	−0.724053	−	0.0787789i	−0.0459774	−	0.00500246i
$249$	6.31614	+	1.11371i	0.400269	+	0.0705783i
$250$	−3.07051	−	15.5104i	−0.194196	−	0.980963i
$251$	2.14945	−	5.90557i	0.135672	−	0.372756i	−0.853188	−	0.521603i	$-0.825334\pi$
$251$	2.14945	−	5.90557i	0.135672	−	0.372756i	0.988860	+	0.148847i	$0.0475563\pi$
$252$	−10.9982	−	10.6727i	−0.692819	−	0.672319i
$253$	−15.3149	−	18.2515i	−0.962837	−	1.14746i
$254$	0.369287	−	10.2179i	0.0231711	−	0.641128i
$255$	−5.99807	−	3.78364i	−0.375614	−	0.236941i
$256$	14.6795	−	6.36495i	0.917468	−	0.397809i
$257$	3.78461	+	21.4636i	0.236077	+	1.33886i	0.840333	+	0.542070i	$0.182359\pi$
$257$	3.78461	+	21.4636i	0.236077	+	1.33886i	−0.604256	+	0.796790i	$0.706530\pi$
$258$	4.81801	−	2.55425i	0.299956	−	0.159021i
$259$	−9.67233	−	16.7530i	−0.601009	−	1.04098i
$260$	4.14343	−	8.35282i	0.256965	−	0.518020i
$261$	5.41611	+	14.8806i	0.335249	+	0.921088i
$262$	18.0191	+	23.1214i	1.11322	+	1.42844i
$263$	−18.5204	−	15.5405i	−1.14202	−	0.958267i	−0.142515	−	0.989793i	$-0.545519\pi$
$263$	−18.5204	−	15.5405i	−1.14202	−	0.958267i	−0.999503	+	0.0315254i	$0.989964\pi$
$264$	3.73155	−	12.8361i	0.229661	−	0.790009i
$265$	−0.554088	+	14.1394i	−0.0340374	+	0.868577i
$266$	−22.9706	+	8.39430i	−1.40842	+	0.514688i
$267$	0.660704			0.0404344
$268$	3.67098	+	12.9210i	0.224241	+	0.789277i
$269$	15.2264	−	18.1461i	0.928370	−	1.10639i	−0.0657210	−	0.997838i	$-0.520935\pi$
$269$	15.2264	−	18.1461i	0.928370	−	1.10639i	0.994091	−	0.108550i	$-0.0346208\pi$
$270$	−13.0933	+	9.40367i	−0.796834	+	0.572289i
$271$	−0.387915	−	1.06579i	−0.0235641	−	0.0647419i	0.927353	−	0.374188i	$-0.122079\pi$
$271$	−0.387915	−	1.06579i	−0.0235641	−	0.0647419i	−0.950917	+	0.309446i	$0.899856\pi$
$272$	−12.2668	+	0.368497i	−0.743786	+	0.0223434i
$273$	7.40489	−	4.27522i	0.448164	−	0.258748i
$274$	−24.9720	+	13.2388i	−1.50861	+	0.799787i
$275$	−22.7543	+	2.19570i	−1.37214	+	0.132406i
$276$	−6.31141	−	8.73159i	−0.379902	−	0.525580i
$277$	−20.3177	−	11.7304i	−1.22077	−	0.704814i	−0.255691	−	0.966759i	$-0.582303\pi$
$277$	−20.3177	−	11.7304i	−1.22077	−	0.704814i	−0.965083	+	0.261944i	$0.915636\pi$
$278$	0.0298261	−	0.825266i	0.00178885	−	0.0494962i
$279$	0.380992	−	0.319690i	0.0228094	−	0.0191394i
$280$	−5.02237	−	24.5839i	−0.300144	−	1.46917i
$281$	0.855721	−	2.35107i	0.0510480	−	0.140253i	−0.911548	−	0.411193i	$-0.865112\pi$
$281$	0.855721	−	2.35107i	0.0510480	−	0.140253i	0.962596	+	0.270940i	$0.0873344\pi$
$282$	3.44660	+	10.6517i	0.205242	+	0.634299i
$283$	−0.826243	+	4.68586i	−0.0491151	+	0.278545i	−0.999467	−	0.0326302i	$-0.989612\pi$
$283$	−0.826243	+	4.68586i	−0.0491151	+	0.278545i	0.950352	+	0.311176i	$0.100723\pi$
$284$	−4.01387	−	8.28083i	−0.238180	−	0.491377i
$285$	1.73223	+	9.92535i	0.102608	+	0.587927i
$286$	−11.4235	−	7.15758i	−0.675486	−	0.423236i
$287$	21.2656	+	3.74970i	1.25527	+	0.221338i
$288$	−3.79937	+	10.2440i	−0.223880	+	0.603633i
$289$	−7.12928	−	2.59484i	−0.419369	−	0.152638i
$290$	−6.41010	+	25.1222i	−0.376414	+	1.47523i
$291$	12.1949	+	14.5333i	0.714879	+	0.851959i
$292$	−12.6503	−	8.57767i	−0.740302	−	0.501970i
$293$	−1.26210	+	2.18602i	−0.0737325	+	0.127708i	−0.900534	−	0.434785i	$-0.856824\pi$
$293$	−1.26210	+	2.18602i	−0.0737325	+	0.127708i	0.826802	+	0.562493i	$0.190158\pi$
$294$	4.80064	−	11.8404i	0.279979	−	0.690549i
$295$	0.644892	−	0.0878332i	0.0375471	−	0.00511385i
$296$	−8.14709	+	11.1277i	−0.473540	+	0.646785i
$297$	11.6533	+	20.1841i	0.676194	+	1.17120i
$298$	2.97706	+	21.3718i	0.172456	+	1.23804i
$299$	−10.2097	+	3.71603i	−0.590443	+	0.214904i
$300$	−10.3342	+	0.247520i	−0.596643	+	0.0142906i
$301$	−11.3368	−	9.51271i	−0.653443	−	0.548303i
$302$	5.50626	+	4.97003i	0.316850	+	0.285993i
$303$			4.84887i			0.278560i
$304$	12.0821	+	12.5707i	0.692957	+	0.720979i
$305$	1.20895	−	30.8503i	0.0692240	−	1.76648i
$306$	5.61517	−	6.22101i	0.320998	−	0.355631i
$307$	12.8740	−	15.3426i	0.734758	−	0.875651i	−0.261217	−	0.965280i	$-0.584124\pi$
$307$	12.8740	−	15.3426i	0.734758	−	0.875651i	0.995975	+	0.0896294i	$0.0285683\pi$
$308$	−36.0878	+	3.70406i	−2.05629	+	0.211058i
$309$	−8.36698	+	3.04533i	−0.475981	+	0.173243i
$310$	0.810286	−	0.0806779i	0.0460212	−	0.00458220i
$311$	−12.0659	+	6.96627i	−0.684196	+	0.395021i	−0.801434	−	0.598083i	$-0.795929\pi$
$311$	−12.0659	+	6.96627i	−0.684196	+	0.395021i	0.117238	+	0.993104i	$0.462596\pi$
$312$	−4.91850	−	3.60105i	−0.278455	−	0.203869i
$313$	2.34444	−	0.413387i	0.132515	−	0.0233660i	−0.106997	−	0.994259i	$-0.534124\pi$
$313$	2.34444	−	0.413387i	0.132515	−	0.0233660i	0.239512	+	0.970893i	$0.423012\pi$
$314$	4.74102	−	11.6934i	0.267551	−	0.659896i
$315$	14.4919	+	9.14162i	0.816525	+	0.515072i
$316$	2.01606	−	2.97327i	0.113412	−	0.167259i
$317$	−8.65458	+	7.26205i	−0.486090	+	0.407878i	−0.852622	−	0.522528i	$-0.824989\pi$
$317$	−8.65458	+	7.26205i	−0.486090	+	0.407878i	0.366533	+	0.930405i	$0.380545\pi$
$318$	9.04660	+	1.93444i	0.507308	+	0.108478i
$319$	35.2246	+	12.8207i	1.97220	+	0.717822i
$320$	−14.5929	+	10.3464i	−0.815766	+	0.578382i
$321$	−2.09469	+	11.8796i	−0.116914	+	0.663053i
$322$	−15.5242	+	24.7767i	−0.865130	+	1.38075i
$323$	−5.04095	−	12.3871i	−0.280486	−	0.689235i
$324$	−0.457797	−	0.944459i	−0.0254332	−	0.0524699i
$325$	−2.60804	+	10.0931i	−0.144668	+	0.559863i
$326$	−10.8706	+	3.51744i	−0.602068	+	0.194813i
$327$	−18.0130	−	6.55619i	−0.996120	−	0.362558i
$328$	−3.66967	−	14.9509i	−0.202624	−	0.825527i
$329$	23.2745	−	19.5296i	1.28316	−	1.07670i
$330$	−1.12422	+	14.9030i	−0.0618860	+	0.820383i
$331$	14.6407	−	25.3585i	0.804727	−	1.39383i	−0.111748	−	0.993737i	$-0.535645\pi$
$331$	14.6407	−	25.3585i	0.804727	−	1.39383i	0.916475	−	0.400092i	$-0.131022\pi$
$332$	−10.0567	+	7.26924i	−0.551934	+	0.398951i
$333$	−1.63536	−	9.27458i	−0.0896171	−	0.508244i
$334$	−7.54874	+	4.00194i	−0.413049	+	0.218977i
$335$	−6.99389	−	13.2899i	−0.382117	−	0.726105i
$336$	−16.3970	+	0.492566i	−0.894527	+	0.0268717i
$337$	−15.5806	+	5.67086i	−0.848727	+	0.308911i	−0.729521	−	0.683958i	$-0.760257\pi$
$337$	−15.5806	+	5.67086i	−0.848727	+	0.308911i	−0.119206	+	0.992870i	$0.538035\pi$
$338$	9.65235	−	7.52231i	0.525018	−	0.409160i
$339$	−0.0381739	+	0.0454939i	−0.00207332	+	0.00247089i
$340$	13.3353	−	3.23014i	0.723207	−	0.175179i
$341$		−	1.17730i		−	0.0637544i
$342$	−11.9062	+	0.0154106i	−0.643813	+	0.000833311i
$343$	−6.90241			−0.372695
$344$	−2.94524	+	10.1313i	−0.158797	+	0.546243i
$345$	8.91710	+	8.09806i	0.480080	+	0.435985i
$346$	−17.8292	+	13.8948i	−0.958506	+	0.746987i
$347$	10.6119	−	3.86241i	0.569675	−	0.207345i	−0.0410915	−	0.999155i	$-0.513084\pi$
$347$	10.6119	−	3.86241i	0.569675	−	0.207345i	0.610767	+	0.791811i	$0.290861\pi$
$348$	15.4682	+	6.93214i	0.829185	+	0.371601i
$349$	13.5944	+	23.5462i	0.727691	+	1.26040i	0.957857	+	0.287247i	$0.0927400\pi$
$349$	13.5944	+	23.5462i	0.727691	+	1.26040i	−0.230165	+	0.973152i	$0.573927\pi$
$350$	11.1602	+	25.7379i	0.596535	+	1.37575i
$351$	10.4668	−	1.84558i	0.558676	−	0.0985097i
$352$	12.7948	+	22.4765i	0.681967	+	1.19800i
$353$	5.58477	+	3.22437i	0.297247	+	0.171616i	0.641206	−	0.767369i	$-0.278435\pi$
$353$	5.58477	+	3.22437i	0.297247	+	0.171616i	−0.343958	+	0.938985i	$0.611768\pi$
$354$	0.0153683	−	0.425230i	0.000816817	−	0.0226007i
$355$	6.29966	+	8.13440i	0.334351	+	0.431729i
$356$	−0.890230	+	0.917374i	−0.0471821	+	0.0486207i
$357$	11.8237	+	4.30347i	0.625776	+	0.227764i
$358$	−20.8651	+	6.75138i	−1.10275	+	0.356821i
$359$	21.8079	+	3.84532i	1.15098	+	0.202948i	0.716402	−	0.697688i	$-0.245788\pi$
$359$	21.8079	+	3.84532i	1.15098	+	0.202948i	0.434574	+	0.900636i	$0.356899\pi$
$360$	1.79579	−	12.0828i	0.0946464	−	0.636818i
$361$	−8.24311	+	17.1187i	−0.433848	+	0.900986i
$362$	23.0532	+	14.4443i	1.21165	+	0.759177i
$363$	10.0815	+	1.77765i	0.529143	+	0.0933022i
$364$	−4.04127	+	16.0420i	−0.211820	+	0.840827i
$365$	15.8165	+	6.46882i	0.827874	+	0.338593i
$366$	−19.7385	−	4.22069i	−1.03175	−	0.220619i
$367$	−16.5138	+	13.8568i	−0.862016	+	0.723317i	−0.962401	−	0.271631i	$-0.912437\pi$
$367$	−16.5138	+	13.8568i	−0.862016	+	0.723317i	0.100386	+	0.994949i	$0.467992\pi$
$368$	20.6276	+	3.00165i	1.07529	+	0.156472i
$369$	9.10412	+	5.25627i	0.473942	+	0.273630i
$370$	6.34864	−	14.0515i	0.330050	−	0.730505i
$371$	−4.35963	−	24.7247i	−0.226341	−	1.28364i
$372$	0.0384305	−	0.530977i	0.00199253	−	0.0275299i
$373$	14.6160	+	25.3156i	0.756787	+	1.31079i	0.944481	+	0.328565i	$0.106565\pi$
$373$	14.6160	+	25.3156i	0.756787	+	1.31079i	−0.187695	+	0.982227i	$0.560102\pi$
$374$	−2.73692	−	19.6479i	−0.141523	−	1.01597i
$375$	11.2488	−	2.65238i	0.580884	−	0.136969i
$376$	−19.4336	−	9.56653i	−1.00221	−	0.493356i
$377$	10.9878	−	13.0947i	0.565900	−	0.674414i
$378$	19.1640	−	21.2317i	0.985689	−	1.09204i
$379$	−7.88618			−0.405086			−0.202543	−	0.979273i	$-0.564921\pi$
$379$	−7.88618			−0.405086			−0.202543	+	0.979273i	$0.564921\pi$
$380$	−16.1152	−	10.9682i	−0.826690	−	0.562658i
$381$	7.47359			0.382884
$382$	0.400643	−	0.443870i	0.0204987	−	0.0227104i
$383$	−3.42713	+	4.08430i	−0.175118	+	0.208698i	−0.846463	−	0.532447i	$-0.821272\pi$
$383$	−3.42713	+	4.08430i	−0.175118	+	0.208698i	0.671345	+	0.741145i	$0.265717\pi$
$384$	5.03693	+	10.5549i	0.257040	+	0.538625i
$385$	38.6273	−	12.3691i	1.96863	−	0.630386i
$386$	−1.18478	−	8.50538i	−0.0603039	−	0.432912i
$387$	−3.60237	−	6.23949i	−0.183119	−	0.317171i
$388$	−36.6106	−	2.64976i	−1.85862	−	0.134521i
$389$	4.33138	+	24.5645i	0.219610	+	1.24547i	0.872726	+	0.488211i	$0.162350\pi$
$389$	4.33138	+	24.5645i	0.219610	+	1.24547i	−0.653116	+	0.757258i	$0.726539\pi$
$390$	6.21085	+	2.80613i	0.314499	+	0.142094i
$391$	−13.8464	−	7.99424i	−0.700244	−	0.404286i
$392$	9.97185	+	22.6194i	0.503654	+	1.14245i
$393$	−16.4137	+	13.7728i	−0.827963	+	0.694744i
$394$	12.8479	+	2.74728i	0.647267	+	0.138406i
$395$	−1.52040	+	3.71744i	−0.0764997	+	0.187045i
$396$	−17.1260	−	4.31437i	−0.860615	−	0.216805i
$397$	−2.57500	−	0.454043i	−0.129236	−	0.0227877i	0.108656	−	0.994079i	$-0.465345\pi$
$397$	−2.57500	−	0.454043i	−0.129236	−	0.0227877i	−0.237892	+	0.971292i	$0.576456\pi$
$398$	−16.8975	−	10.5874i	−0.846996	−	0.530698i
$399$	−6.73819	−	16.5577i	−0.337331	−	0.828920i
$400$	13.5805	−	14.6823i	0.679026	−	0.734114i
$401$	4.45669	+	0.785835i	0.222557	+	0.0392427i	0.283814	−	0.958879i	$-0.408400\pi$
$401$	4.45669	+	0.785835i	0.222557	+	0.0392427i	−0.0612577	+	0.998122i	$0.519511\pi$
$402$	−9.34147	+	3.02265i	−0.465910	+	0.150756i
$403$	−0.504493	−	0.183621i	−0.0251306	−	0.00914679i
$404$	−6.73256	−	6.53335i	−0.334957	−	0.325046i
$405$	0.718499	+	0.927758i	0.0357025	+	0.0461007i
$406$	1.66145	−	45.9712i	0.0824565	−	2.28151i
$407$	−19.3063	−	11.1465i	−0.956976	−	0.552511i
$408$	−0.593019	−	8.95079i	−0.0293588	−	0.443130i
$409$	−17.8969	+	3.15570i	−0.884944	+	0.156040i	−0.597606	−	0.801790i	$-0.703881\pi$
$409$	−17.8969	+	3.15570i	−0.884944	+	0.156040i	−0.287338	+	0.957829i	$0.592770\pi$
$410$	7.46027	+	15.5110i	0.368437	+	0.766032i
$411$	−10.3298	−	17.8917i	−0.509531	−	0.882534i
$412$	7.04526	−	15.7207i	0.347095	−	0.774501i
$413$	−1.08512	+	0.394952i	−0.0533954	+	0.0194343i
$414$	−11.2274	+	8.74981i	−0.551798	+	0.430030i
$415$	9.32703	−	10.2704i	0.457846	−	0.504153i
$416$	11.6272	−	1.97720i	0.570069	−	0.0969400i
$417$	0.603618			0.0295593
$418$	−18.0882	+	21.6134i	−0.884722	+	1.05715i
$419$			1.56858i			0.0766301i	0.999266	+	0.0383151i	$0.0121990\pi$
$419$			1.56858i			0.0766301i	−0.999266	+	0.0383151i	$0.987801\pi$
$420$	17.8252	−	4.31769i	0.869778	−	0.210682i
$421$	8.20836	−	9.78234i	0.400051	−	0.476762i	−0.527985	−	0.849254i	$-0.677052\pi$
$421$	8.20836	−	9.78234i	0.400051	−	0.476762i	0.928035	+	0.372492i	$0.121497\pi$
$422$	17.0293	−	13.2714i	0.828974	−	0.646040i
$423$	13.8993	−	5.05894i	0.675808	−	0.245974i
$424$	−14.8753	+	9.95457i	−0.722408	+	0.483437i
$425$	−13.8447	+	6.60707i	−0.671567	+	0.320490i
$426$	5.94292	−	3.15062i	0.287935	−	0.152648i
$427$	9.51212	+	53.9459i	0.460324	+	2.61063i
$428$	−13.6722	−	18.9149i	−0.660869	−	0.914288i
$429$	4.92680	−	8.53346i	0.237868	−	0.411999i
$430$	0.887321	−	11.7626i	0.0427904	−	0.567245i
$431$	−21.4377	+	17.9884i	−1.03262	+	0.866469i	−0.991160	−	0.132671i	$-0.957645\pi$
$431$	−21.4377	+	17.9884i	−1.03262	+	0.866469i	−0.0414579	+	0.999140i	$0.513200\pi$
$432$	−19.3618	−	6.39556i	−0.931545	−	0.307707i
$433$	−7.43239	−	2.70517i	−0.357178	−	0.130002i	0.157198	−	0.987567i	$-0.449754\pi$
$433$	−7.43239	−	2.70517i	−0.357178	−	0.130002i	−0.514375	+	0.857565i	$0.671976\pi$
$434$	−1.37459	+	0.444780i	−0.0659825	+	0.0213501i
$435$	−18.5202	−	4.01914i	−0.887975	−	0.192703i
$436$	33.3738	−	16.1769i	1.59831	−	0.774732i
$437$	4.77857	+	22.2068i	0.228590	+	1.06230i
$438$	5.93174	−	9.46708i	0.283430	−	0.452354i
$439$	5.70310	−	32.3439i	0.272194	−	1.54369i	−0.475541	−	0.879693i	$-0.657748\pi$
$439$	5.70310	−	32.3439i	0.272194	−	1.54369i	0.747735	−	0.663997i	$-0.231141\pi$
$440$	−19.1778	−	21.6412i	−0.914264	−	1.03170i
$441$	−15.8624	−	5.77344i	−0.755352	−	0.274926i
$442$	−8.84634	−	1.89162i	−0.420778	−	0.0899752i
$443$	−27.1882	+	22.8136i	−1.29175	+	1.08391i	−0.300241	+	0.953864i	$0.597067\pi$
$443$	−27.1882	+	22.8136i	−1.29175	+	1.08391i	−0.991508	+	0.130043i	$0.958489\pi$
$444$	−8.34352	−	5.65741i	−0.395966	−	0.268489i
$445$	0.762517	−	1.20879i	0.0361468	−	0.0573022i
$446$	−9.38055	+	23.1365i	−0.444182	+	1.09554i
$447$	−15.5328	+	2.73886i	−0.734678	+	0.129544i
$448$	21.4093	−	23.4305i	1.01149	−	1.10699i
$449$	−17.0572	+	9.84799i	−0.804980	+	0.464755i	−0.845210	−	0.534435i	$-0.820524\pi$
$449$	−17.0572	+	9.84799i	−0.804980	+	0.464755i	0.0402295	+	0.999190i	$0.487191\pi$
$450$	0.819938	+	13.6327i	0.0386523	+	0.642652i
$451$	23.3840	−	8.51107i	1.10111	−	0.400771i
$452$	−0.0117320	−	0.114302i	−0.000551826	−	0.00537632i
$453$	−3.48508	+	4.15335i	−0.163743	+	0.195142i
$454$	10.8520	−	12.0229i	0.509310	−	0.564262i
$455$	0.724249	−	18.4816i	0.0339533	−	0.866432i
$456$	−8.86352	+	9.15746i	−0.415072	+	0.428838i
$457$		−	7.37551i		−	0.345012i	−0.985008	−	0.172506i	$-0.944814\pi$
$457$		−	7.37551i		−	0.345012i	0.985008	−	0.172506i	$-0.0551864\pi$
$458$	1.55971	+	1.40781i	0.0728803	+	0.0657828i
$459$	11.9811	+	10.0533i	0.559228	+	0.469248i
$460$	−23.2589	+	1.46993i	−1.08445	+	0.0685356i
$461$	−6.47105	+	2.35527i	−0.301387	+	0.109696i	−0.488287	−	0.872683i	$-0.662378\pi$
$461$	−6.47105	+	2.35527i	−0.301387	+	0.109696i	0.186900	+	0.982379i	$0.440156\pi$
$462$	−3.65841	−	26.2632i	−0.170205	−	1.22187i
$463$	2.35608	+	4.08086i	0.109497	+	0.189654i	0.915566	−	0.402167i	$-0.131743\pi$
$463$	2.35608	+	4.08086i	0.109497	+	0.189654i	−0.806070	+	0.591820i	$0.798409\pi$
$464$	−30.4670	+	12.1370i	−1.41439	+	0.563447i
$465$	0.0803241	+	0.589758i	0.00372494	+	0.0273494i
$466$	2.97985	−	7.34959i	0.138039	−	0.340463i
$467$	13.1780	−	22.8250i	0.609807	−	1.05622i	−0.381465	−	0.924383i	$-0.624580\pi$
$467$	13.1780	−	22.8250i	0.609807	−	1.05622i	0.991272	−	0.131833i	$-0.0420862\pi$
$468$	−4.51988	+	6.66589i	−0.208932	+	0.308131i
$469$	17.1274	+	20.4116i	0.790868	+	0.942519i
$470$	23.4655	+	5.98738i	1.08238	+	0.276177i
$471$	8.66680	+	3.15446i	0.399345	+	0.145350i
$472$	0.569717	+	0.594292i	0.0262233	+	0.0273545i
$473$	−16.7956	−	2.96151i	−0.772261	−	0.136170i
$474$	2.22510	+	1.39417i	0.102202	+	0.0640364i
$475$	20.1581	+	8.28563i	0.924916	+	0.380171i
$476$	−21.9065	+	10.6185i	−1.00408	+	0.486697i
$477$	2.12242	−	12.0368i	0.0971789	−	0.551129i
$478$	10.9276	+	33.7718i	0.499818	+	1.54469i
$479$	−6.46310	+	17.7572i	−0.295307	+	0.811348i	0.699961	+	0.714181i	$0.253201\pi$
$479$	−6.46310	+	17.7572i	−0.295307	+	0.811348i	−0.995268	+	0.0971677i	$0.969022\pi$
$480$	−7.94298	−	10.3865i	−0.362546	−	0.474075i
$481$	−7.78761	+	6.53458i	−0.355085	+	0.297951i
$482$	0.215398	−	5.95989i	0.00981109	−	0.271466i
$483$	−18.5084	−	10.6858i	−0.842161	−	0.486222i
$484$	−16.0520	+	11.6028i	−0.729638	+	0.527400i
$485$	40.6636	−	5.53831i	1.84644	−	0.251482i
$486$	19.7863	−	10.4896i	0.897523	−	0.475819i
$487$	29.3650	−	16.9539i	1.33065	−	0.768253i	0.345254	−	0.938509i	$-0.387793\pi$
$487$	29.3650	−	16.9539i	1.33065	−	0.768253i	0.985400	+	0.170256i	$0.0544595\pi$
$488$	32.4559	−	21.7195i	1.46921	−	0.983197i
$489$	−2.85636	−	7.84778i	−0.129169	−	0.354889i
$490$	−16.1223	−	22.4480i	−0.728330	−	1.01410i
$491$	23.7768	−	28.3361i	1.07303	−	1.27879i	0.114618	−	0.993410i	$-0.463436\pi$
$491$	23.7768	−	28.3361i	1.07303	−	1.27879i	0.958414	−	0.285380i	$-0.0921198\pi$
$492$	10.8243	−	3.07528i	0.487997	−	0.138644i
$493$	25.1549			1.13292
$494$	6.44055	+	11.1221i	0.289774	+	0.500406i
$495$	19.7306	+	0.773191i	0.886823	+	0.0347524i
$496$	0.685470	+	0.768796i	0.0307785	+	0.0345200i
$497$	−13.9837	−	11.7337i	−0.627256	−	0.526330i
$498$	−5.57544	−	7.15420i	−0.249841	−	0.320587i
$499$	14.0038	+	38.4750i	0.626894	+	1.72238i	0.689447	+	0.724336i	$0.257854\pi$
$499$	14.0038	+	38.4750i	0.626894	+	1.72238i	−0.0625524	+	0.998042i	$0.519924\pi$
$500$	−11.4738	+	19.1925i	−0.513123	+	0.858315i
$501$	−3.12258	−	5.40846i	−0.139506	−	0.241632i
$502$	−7.85248	+	4.16297i	−0.350473	+	0.185802i
$503$	−1.93511	−	10.9746i	−0.0862825	−	0.489332i	−0.997072	−	0.0764623i	$-0.975638\pi$
$503$	−1.93511	−	10.9746i	−0.0862825	−	0.489332i	0.910790	−	0.412870i	$-0.135474\pi$
$504$	1.43279	+	21.6259i	0.0638214	+	0.963296i
$505$	8.87124	+	5.59607i	0.394765	+	0.249022i
$506$	−1.21697	+	33.6726i	−0.0541008	+	1.49693i
$507$	5.74963	+	6.85214i	0.255350	+	0.304314i
$508$	−10.0699	+	10.3769i	−0.446779	+	0.460402i
$509$	9.13289	−	25.0924i	0.404808	−	1.11220i	−0.555075	−	0.831801i	$-0.687310\pi$
$509$	9.13289	−	25.0924i	0.404808	−	1.11220i	0.959883	−	0.280401i	$-0.0904675\pi$
$510$	2.71156	+	9.65572i	0.120070	+	0.427562i
$511$	−29.8582	−	5.26480i	−1.32085	−	0.232901i
$512$	−21.4420	−	7.22790i	−0.947609	−	0.319431i
$513$	−0.831285	−	22.2047i	−0.0367021	−	0.980364i
$514$	16.3652	−	26.1189i	0.721838	−	1.15205i
$515$	−4.08473	+	18.8224i	−0.179995	+	0.829415i
$516$	−7.47834	−	1.88394i	−0.329216	−	0.0829356i
$517$	11.9752	−	32.9017i	0.526671	−	1.44702i
$518$	−5.72055	+	26.7527i	−0.251347	+	1.17545i
$519$	−10.6204	−	12.6569i	−0.466182	−	0.555574i
$520$	−12.2647	+	4.84268i	−0.537844	+	0.212365i
$521$	−24.2785	−	14.0172i	−1.06366	−	0.614105i	−0.137218	−	0.990541i	$-0.543816\pi$
$521$	−24.2785	−	14.0172i	−1.06366	−	0.614105i	−0.926443	+	0.376436i	$0.877150\pi$
$522$	8.41461	−	20.7540i	0.368297	−	0.908378i
$523$	11.0297	−	1.94483i	0.482294	−	0.0850414i	0.0727853	−	0.997348i	$-0.476811\pi$
$523$	11.0297	−	1.94483i	0.482294	−	0.0850414i	0.409509	+	0.912306i	$0.365700\pi$
$524$	2.99260	−	41.3475i	0.130733	−	1.80627i
$525$	−18.5061	+	8.83161i	−0.807672	+	0.385443i
$526$	4.71720	+	33.8640i	0.205680	+	1.47654i
$527$	−0.270210	−	0.742395i	−0.0117705	−	0.0323392i
$528$	−16.0806	+	9.93959i	−0.699818	+	0.432565i
$529$	3.18427	+	2.67192i	0.138446	+	0.116170i
$530$	13.9798	−	14.3187i	0.607245	−	0.621964i
$531$	−0.562179			−0.0243965
$532$	32.0690	+	12.9539i	1.39037	+	0.561623i
$533$		−	11.3479i		−	0.491532i
$534$	−0.693614	−	0.626066i	−0.0300156	−	0.0270925i
$535$	19.3168	+	17.5425i	0.835138	+	0.758429i
$536$	8.38979	−	17.0432i	0.362384	−	0.736152i
$537$	−5.48250	−	15.0630i	−0.236587	−	0.650018i
$538$	−33.1796	+	4.62186i	−1.43048	+	0.199263i
$539$	−34.6050	+	19.9792i	−1.49054	+	0.860565i
$540$	22.6562	+	2.53481i	0.974967	+	0.109081i
$541$	2.40757	+	13.6540i	0.103509	+	0.587031i	0.991805	+	0.127759i	$0.0407785\pi$
$541$	2.40757	+	13.6540i	0.103509	+	0.587031i	−0.888296	+	0.459272i	$0.848110\pi$
$542$	−0.602674	+	1.48645i	−0.0258871	+	0.0638486i
$543$	−9.94251	+	17.2209i	−0.426674	+	0.739021i
$544$	13.2270	+	11.2369i	0.567104	+	0.481777i
$545$	−32.7836	+	25.3892i	−1.40430	+	1.08755i
$546$	−11.8248	−	2.52851i	−0.506056	−	0.108210i
$547$	−0.202171	+	0.555462i	−0.00864423	+	0.0237498i	−0.943940	−	0.330118i	$-0.892911\pi$
$547$	−0.202171	+	0.555462i	−0.00864423	+	0.0237498i	0.935295	+	0.353868i	$0.115134\pi$
$548$	38.7606	+	9.76454i	1.65577	+	0.417120i
$549$	−4.63083	+	26.2627i	−0.197639	+	1.12087i
$550$	25.9683	+	19.2563i	1.10729	+	0.821092i
$551$	−23.9801	−	26.4984i	−1.02159	−	1.12887i
$552$	−1.64804	+	15.1470i	−0.0701452	+	0.644701i
$553$	1.23742	−	7.01774i	0.0526203	−	0.298425i
$554$	10.2143	+	31.5673i	0.433965	+	1.34117i
$555$	10.4318	+	4.26652i	0.442806	+	0.181104i
$556$	−0.813312	+	0.838111i	−0.0344921	+	0.0355438i
$557$	−9.63929	−	11.4877i	−0.408430	−	0.486748i	0.522141	−	0.852859i	$-0.325133\pi$
$557$	−9.63929	−	11.4877i	−0.408430	−	0.486748i	−0.930571	+	0.366111i	$0.880689\pi$
$558$	−0.702900	−	0.0254036i	−0.0297561	−	0.00107542i
$559$	−3.88862	+	6.73529i	−0.164471	+	0.284873i
$560$	−18.0225	+	30.5675i	−0.761590	+	1.29171i
$561$	14.2799	−	2.51793i	0.602898	−	0.106307i
$562$	−3.12616	+	1.65732i	−0.131869	+	0.0699100i
$563$	10.0719	−	5.81500i	0.424479	−	0.245073i	−0.272513	−	0.962152i	$-0.587855\pi$
$563$	10.0719	−	5.81500i	0.424479	−	0.245073i	0.696992	+	0.717079i	$0.254521\pi$
$564$	6.47499	−	14.4482i	0.272646	−	0.608378i
$565$	0.0391769	+	0.122346i	0.00164819	+	0.00514711i
$566$	5.30760	−	4.13634i	0.223095	−	0.173863i
$567$	−1.59489	−	1.33827i	−0.0669793	−	0.0562023i
$568$	−3.63289	+	12.4968i	−0.152433	+	0.524352i
$569$		−	34.7145i		−	1.45531i	−0.685945	−	0.727654i	$-0.740611\pi$
$569$		−	34.7145i		−	1.45531i	0.685945	−	0.727654i	$-0.259389\pi$
$570$	7.58649	−	12.0612i	0.317763	−	0.505186i
$571$			17.7069i			0.741009i	0.928831	+	0.370505i	$0.120815\pi$
$571$			17.7069i			0.741009i	−0.928831	+	0.370505i	$0.879185\pi$
$572$	5.21020	+	18.3387i	0.217849	+	0.766781i
$573$	0.334810	+	0.280939i	0.0139869	+	0.0117364i
$574$	−18.7717	−	24.0872i	−0.783517	−	1.00538i
$575$	25.1070	−	6.96833i	1.04703	−	0.290599i
$576$	13.6956	−	7.15408i	0.570649	−	0.298087i
$577$	32.1774	−	18.5777i	1.33956	−	0.773398i	0.352822	−	0.935691i	$-0.385222\pi$
$577$	32.1774	−	18.5777i	1.33956	−	0.773398i	0.986743	+	0.162293i	$0.0518890\pi$
$578$	5.02559	+	9.47961i	0.209037	+	0.394300i
$579$	6.18163	−	1.08999i	0.256900	−	0.0452983i
$580$	30.5346	−	20.2996i	1.26788	−	0.842893i
$581$	−12.3075	+	21.3173i	−0.510602	+	0.884389i
$582$	0.969048	−	26.8128i	0.0401683	−	1.11143i
$583$	−18.5975	−	22.1636i	−0.770228	−	0.917922i
$584$	5.15244	+	20.9920i	0.213209	+	0.868656i
$585$	3.40865	−	8.33429i	0.140930	−	0.344581i
$586$	3.39638	−	1.09897i	0.140303	−	0.0453982i
$587$	2.19964	−	12.4748i	0.0907889	−	0.514889i	−0.905168	−	0.425054i	$-0.860255\pi$
$587$	2.19964	−	12.4748i	0.0907889	−	0.514889i	0.995957	−	0.0898349i	$-0.0286339\pi$
$588$	−16.2595	+	7.88126i	−0.670529	+	0.325018i
$589$	−0.524454	+	0.992364i	−0.0216098	+	0.0408896i
$590$	−0.760243	−	0.518874i	−0.0312987	−	0.0213617i
$591$	−1.66761	+	9.45750i	−0.0685964	+	0.389029i
$592$	19.0972	−	3.96203i	0.784892	−	0.162838i
$593$	−1.55303	+	4.26691i	−0.0637752	+	0.175221i	−0.967487	−	0.252920i	$-0.918609\pi$
$593$	−1.55303	+	4.26691i	−0.0637752	+	0.175221i	0.903712	+	0.428141i	$0.140831\pi$
$594$	6.89218	−	32.2319i	0.282789	−	1.32249i
$595$	21.5191	−	16.6654i	0.882198	−	0.683215i
$596$	17.1260	−	25.2574i	0.701510	−	1.03458i
$597$	7.28766	−	12.6226i	0.298264	−	0.516608i
$598$	14.2395	+	5.77333i	0.582296	+	0.236089i
$599$	0.980322	+	5.55968i	0.0400549	+	0.227162i	0.998263	−	0.0589082i	$-0.0187619\pi$
$599$	0.980322	+	5.55968i	0.0400549	+	0.227162i	−0.958209	+	0.286071i	$0.907651\pi$
$600$	11.0835	+	9.53252i	0.452480	+	0.389164i
$601$	−33.5942	+	19.3956i	−1.37034	+	0.791164i	−0.990970	−	0.134083i	$-0.957191\pi$
$601$	−33.5942	+	19.3956i	−1.37034	+	0.791164i	−0.379366	+	0.925247i	$0.623858\pi$
$602$	2.88751	+	20.7290i	0.117686	+	0.844851i
$603$	4.43666	+	12.1896i	0.180675	+	0.496400i
$604$	−1.07107	−	10.4352i	−0.0435812	−	0.424601i
$605$	14.8874	−	16.3931i	0.605257	−	0.666473i
$606$	4.59466	−	5.09039i	0.186645	−	0.206783i
$607$			4.10304i			0.166537i	0.996527	+	0.0832686i	$0.0265359\pi$
$607$			4.10304i			0.166537i	−0.996527	+	0.0832686i	$0.973464\pi$
$608$	−0.772285	−	24.6456i	−0.0313203	−	0.999509i
$609$	33.6243			1.36253
$610$	−30.5021	+	31.2414i	−1.23499	+	1.26493i
$611$	−12.2312	−	10.2632i	−0.494822	−	0.415205i
$612$	−11.7897	+	1.21010i	−0.476572	+	0.0489154i
$613$	10.9979	+	30.2165i	0.444202	+	1.22043i	0.936704	+	0.350123i	$0.113860\pi$
$613$	10.9979	+	30.2165i	0.444202	+	1.22043i	−0.492502	+	0.870312i	$0.663917\pi$
$614$	−28.0536	+	3.90781i	−1.13215	+	0.157706i
$615$	−11.1333	+	5.85898i	−0.448939	+	0.236257i
$616$	41.3952	+	30.3073i	1.66786	+	1.22112i
$617$	24.8937	−	4.38943i	1.00218	−	0.176712i	0.351602	−	0.936150i	$-0.385637\pi$
$617$	24.8937	−	4.38943i	1.00218	−	0.176712i	0.650580	+	0.759438i	$0.274526\pi$
$618$	11.6694	+	4.73131i	0.469413	+	0.190321i
$619$	14.5190	+	8.38253i	0.583567	+	0.336922i	0.762550	−	0.646930i	$-0.223947\pi$
$619$	14.5190	+	8.38253i	0.583567	+	0.336922i	−0.178983	+	0.983852i	$0.557281\pi$
$620$	−0.927096	−	0.683110i	−0.0372331	−	0.0274343i
$621$	−17.0757	−	20.3501i	−0.685226	−	0.816621i
$622$	19.2680	+	4.12009i	0.772576	+	0.165201i
$623$	−0.867279	+	2.38283i	−0.0347468	+	0.0954660i
$624$	1.75123	+	8.44107i	0.0701055	+	0.337913i
$625$	8.12952	−	23.6413i	0.325181	−	0.945652i
$626$	−2.85293	−	1.78755i	−0.114026	−	0.0714448i
$627$	−16.2654	−	12.6422i	−0.649578	−	0.504882i
$628$	−16.0575	+	7.78338i	−0.640765	+	0.310591i
$629$	−14.7327	−	2.59777i	−0.587430	−	0.103580i
$630$	−6.55138	−	23.3291i	−0.261013	−	0.929453i
$631$	−6.84502	+	18.8065i	−0.272496	+	0.748677i	0.725664	+	0.688049i	$0.241533\pi$
$631$	−6.84502	+	18.8065i	−0.272496	+	0.748677i	−0.998160	+	0.0606280i	$0.980690\pi$
$632$	−4.93387	+	1.21101i	−0.196259	+	0.0481713i
$633$	10.1439	+	12.0890i	0.403183	+	0.480495i
$634$	15.9670	+	0.577066i	0.634131	+	0.0229182i
$635$	8.62526	−	13.6733i	0.342283	−	0.542609i
$636$	−7.66420	−	10.6031i	−0.303905	−	0.420441i
$637$	3.16418	+	17.9449i	0.125369	+	0.711005i
$638$	−24.8306	−	46.8373i	−0.983054	−	1.85431i
$639$	−4.44345	−	7.69628i	−0.175780	−	0.304460i
$640$	25.1237	+	2.96603i	0.993103	+	0.117242i
$641$	9.77899	+	26.8676i	0.386247	+	1.06120i	0.968677	+	0.248324i	$0.0798797\pi$
$641$	9.77899	+	26.8676i	0.386247	+	1.06120i	−0.582430	+	0.812881i	$0.697898\pi$
$642$	13.4558	−	10.4864i	0.531058	−	0.413867i
$643$	2.49978	+	2.09757i	0.0985819	+	0.0827200i	0.690747	−	0.723097i	$-0.257282\pi$
$643$	2.49978	+	2.09757i	0.0985819	+	0.0827200i	−0.592165	+	0.805817i	$0.701726\pi$
$644$	39.7752	−	11.3005i	1.56736	−	0.445302i
$645$	8.61565	+	0.337626i	0.339241	+	0.0132940i
$646$	−6.44561	+	17.7807i	−0.253599	+	0.699574i
$647$	−3.62076			−0.142347			−0.0711733	−	0.997464i	$-0.522674\pi$
$647$	−3.62076			−0.142347			−0.0711733	+	0.997464i	$0.522674\pi$
$648$	−0.414344	+	1.42530i	−0.0162770	+	0.0559911i
$649$	−0.855396	+	1.01942i	−0.0335772	+	0.0400158i
$650$	12.3019	−	8.12451i	0.482520	−	0.318670i
$651$	−0.361186	−	0.992352i	−0.0141560	−	0.0388933i
$652$	14.7451	+	6.60807i	0.577464	+	0.258792i
$653$	−28.0083	+	16.1706i	−1.09605	+	0.632805i	−0.935181	−	0.354170i	$-0.884763\pi$
$653$	−28.0083	+	16.1706i	−1.09605	+	0.632805i	−0.160870	+	0.986976i	$0.551430\pi$
$654$	12.6978	+	23.9514i	0.496522	+	0.936574i
$655$	6.25489	+	45.9248i	0.244399	+	1.79443i
$656$	−10.3147	+	19.1729i	−0.402719	+	0.748578i
$657$	−12.7827	−	7.38012i	−0.498702	−	0.287926i
$658$	−42.9396	−	1.55189i	−1.67396	−	0.0604988i
$659$	27.5520	−	23.1188i	1.07327	−	0.900582i	0.0779270	−	0.996959i	$-0.475170\pi$
$659$	27.5520	−	23.1188i	1.07327	−	0.900582i	0.995345	+	0.0963770i	$0.0307254\pi$
$660$	15.3019	−	14.5801i	0.595626	−	0.567528i
$661$	16.7489	−	46.0171i	0.651455	−	1.78986i	0.0391562	−	0.999233i	$-0.487533\pi$
$661$	16.7489	−	46.0171i	0.651455	−	1.78986i	0.612299	−	0.790626i	$-0.290245\pi$
$662$	−39.3990	+	12.7485i	−1.53129	+	0.495483i
$663$	1.14822	−	6.51191i	0.0445933	−	0.252901i
$664$	17.4458	+	1.89815i	0.677028	+	0.0736625i
$665$	−38.0696	−	6.78132i	−1.47628	−	0.262968i
$666$	−7.07153	+	11.2862i	−0.274016	+	0.437331i
$667$	−42.0770	−	7.41931i	−1.62923	−	0.287277i
$668$	11.7169	+	2.95171i	0.453340	+	0.114205i
$669$	−17.1481	−	6.24139i	−0.662983	−	0.241306i
$670$	−5.25089	+	20.5791i	−0.202860	+	0.795041i
$671$	40.5771	+	48.3579i	1.56646	+	1.86684i
$672$	17.6805	+	15.0202i	0.682038	+	0.579418i
$673$	7.23324	−	12.5283i	0.278821	−	0.482932i	−0.692271	−	0.721638i	$-0.743390\pi$
$673$	7.23324	−	12.5283i	0.278821	−	0.482932i	0.971092	+	0.238705i	$0.0767230\pi$
$674$	21.7302	+	8.81040i	0.837016	+	0.339364i
$675$	−25.3706	+	2.44816i	−0.976515	+	0.0942296i
$676$	−17.2611	−	1.24930i	−0.663888	−	0.0480502i
$677$	−18.0848	−	31.3239i	−0.695057	−	1.20387i	−0.970161	−	0.242460i	$-0.922046\pi$
$677$	−18.0848	−	31.3239i	−0.695057	−	1.20387i	0.275104	−	0.961414i	$-0.411288\pi$
$678$	0.0831842	−	0.0115874i	0.00319467	−	0.000445012i
$679$	−68.4222	+	24.9037i	−2.62580	+	0.955715i
$680$	−17.0603	−	9.24514i	−0.654234	−	0.354535i
$681$	9.06882	+	7.60964i	0.347518	+	0.291602i
$682$	−1.11558	+	1.23594i	−0.0427177	+	0.0473267i
$683$			35.2724i			1.34966i	0.737973	+	0.674830i	$0.235783\pi$
$683$			35.2724i			1.34966i	−0.737973	+	0.674830i	$0.764217\pi$
$684$	12.5139	+	11.2658i	0.478479	+	0.430759i
$685$	−44.6554	−	1.74993i	−1.70620	−	0.0668615i
$686$	7.24623	+	6.54054i	0.276662	+	0.249719i
$687$	−0.987186	+	1.17648i	−0.0376635	+	0.0448856i
$688$	12.6921	−	7.84512i	0.483882	−	0.299092i
$689$	−12.3981	+	4.51253i	−0.472329	+	0.171914i
$690$	−1.68777	−	16.9510i	−0.0642522	−	0.645315i
$691$	16.0220	−	9.25033i	0.609507	−	0.351899i	−0.163265	−	0.986582i	$-0.552203\pi$
$691$	16.0220	−	9.25033i	0.609507	−	0.351899i	0.772773	+	0.634683i	$0.218869\pi$
$692$	31.8836	+	2.30764i	1.21203	+	0.0877233i
$693$	−34.5016	+	6.08356i	−1.31061	+	0.231095i
$694$	−14.8004	−	6.00074i	−0.561815	−	0.227785i
$695$	0.696634	−	1.10435i	0.0264248	−	0.0418903i
$696$	−9.67002	−	21.9347i	−0.366541	−	0.831434i
$697$	12.7923	−	10.7340i	0.484543	−	0.406580i
$698$	8.04020	−	37.6007i	0.304326	−	1.42321i
$699$	5.44730	+	1.98266i	0.206036	+	0.0749909i
$700$	12.6725	−	37.5950i	0.478977	−	1.42096i
$701$	1.38515	−	7.85560i	0.0523165	−	0.296702i	−0.947412	−	0.320018i	$-0.896311\pi$
$701$	1.38515	−	7.85560i	0.0523165	−	0.296702i	0.999728	+	0.0233157i	$0.00742230\pi$
$702$	−12.7370	−	7.98055i	−0.480726	−	0.301206i
$703$	11.3081	+	17.9960i	0.426493	+	0.678730i
$704$	7.86602	−	35.7202i	0.296462	−	1.34625i
$705$	−3.75410	+	17.2989i	−0.141387	+	0.651513i
$706$	−2.80763	−	8.67696i	−0.105666	−	0.326562i
$707$	−17.4874	−	6.36491i	−0.657683	−	0.239377i
$708$	−0.419071	+	0.431849i	−0.0157496	+	0.0162299i
$709$	21.0922	−	17.6985i	0.792136	−	0.664681i	−0.154137	−	0.988049i	$-0.549260\pi$
$709$	21.0922	−	17.6985i	0.792136	−	0.664681i	0.946273	+	0.323369i	$0.104815\pi$
$710$	1.09449	−	14.5090i	0.0410756	−	0.544512i
$711$	1.73459	−	3.00440i	0.0650523	−	0.112674i
$712$	1.80385	−	0.119511i	0.0676023	−	0.00447887i
$713$	0.233018	+	1.32151i	0.00872660	+	0.0494910i
$714$	−8.33479	−	15.7217i	−0.311922	−	0.588368i
$715$	−9.92639	−	18.8623i	−0.371226	−	0.705409i
$716$	28.3018	+	12.6836i	1.05769	+	0.474007i
$717$	−24.3807	+	8.87386i	−0.910515	+	0.331400i
$718$	−19.2504	−	24.7014i	−0.718420	−	0.921850i
$719$	26.5671	−	31.6614i	0.990785	−	1.18077i	0.00726446	−	0.999974i	$-0.497688\pi$
$719$	26.5671	−	31.6614i	0.990785	−	1.18077i	0.983520	−	0.180798i	$-0.0578679\pi$
$720$	−13.3346	+	10.9830i	−0.496950	+	0.409312i
$721$		−	34.1730i		−	1.27267i
$722$	24.8750	−	10.1605i	0.925751	−	0.378134i
$723$	4.35919			0.162120
$724$	−10.5144	−	37.0084i	−0.390766	−	1.37541i
$725$	−28.7273	+	29.2451i	−1.06691	+	1.08614i
$726$	−8.89925	−	11.4192i	−0.330282	−	0.423806i
$727$	−20.2269	+	7.36199i	−0.750174	+	0.273041i	−0.688679	−	0.725066i	$-0.741809\pi$
$727$	−20.2269	+	7.36199i	−0.750174	+	0.273041i	−0.0614953	+	0.998107i	$0.519587\pi$
$728$	19.4435	−	13.0116i	0.720625	−	0.482243i
$729$	7.39752	+	12.8129i	0.273982	+	0.474551i
$730$	−10.4747	−	21.7784i	−0.387685	−	0.806053i
$731$	−11.2709	+	1.98736i	−0.416867	+	0.0735050i
$732$	16.7222	+	23.1346i	0.618072	+	0.855079i
$733$	30.6070	+	17.6710i	1.13049	+	0.652692i	0.944059	−	0.329776i	$-0.106973\pi$
$733$	30.6070	+	17.6710i	1.13049	+	0.652692i	0.186436	+	0.982467i	$0.440306\pi$
$734$	30.4667	+	1.10110i	1.12455	+	0.0406425i
$735$	15.9719	−	12.3694i	0.589134	−	0.456253i
$736$	−18.8108	−	22.6974i	−0.693376	−	0.836635i
$737$	28.8546	+	10.5022i	1.06287	+	0.386854i
$738$	−4.57691	−	14.1449i	−0.168478	−	0.520682i
$739$	−30.7103	−	5.41506i	−1.12970	−	0.199196i	−0.422603	−	0.906315i	$-0.638883\pi$
$739$	−30.7103	−	5.41506i	−1.12970	−	0.199196i	−0.707095	+	0.707119i	$0.749994\pi$
$740$	−19.9798	+	8.73567i	−0.734470	+	0.321130i
$741$	−7.95430	+	4.99824i	−0.292208	+	0.183615i
$742$	−18.8517	+	30.0873i	−0.692067	+	1.10454i
$743$	5.87565	+	1.03604i	0.215557	+	0.0380085i	0.280384	−	0.959888i	$-0.409538\pi$
$743$	5.87565	+	1.03604i	0.215557	+	0.0380085i	−0.0648267	+	0.997897i	$0.520649\pi$
$744$	−0.543485	+	0.521010i	−0.0199251	+	0.0191011i
$745$	−12.9155	+	31.5790i	−0.473189	+	1.15697i
$746$	8.64440	−	40.4263i	0.316494	−	1.48011i
$747$	−9.17987	+	7.70282i	−0.335874	+	0.281832i
$748$	−15.7446	+	23.2200i	−0.575680	+	0.849008i
$749$	−40.0941	−	23.1483i	−1.46501	−	0.845821i
$750$	−14.3224	−	7.87454i	−0.522981	−	0.287538i
$751$	3.87069	+	21.9518i	0.141244	+	0.801032i	0.970307	+	0.241877i	$0.0777631\pi$
$751$	3.87069	+	21.9518i	0.141244	+	0.801032i	−0.829063	+	0.559155i	$0.811126\pi$
$752$	11.3366	+	28.4578i	0.413404	+	1.03775i
$753$	−3.24822	−	5.62608i	−0.118372	−	0.205026i
$754$	−23.9434	+	3.33526i	−0.871965	+	0.121463i
$755$	3.57665	+	11.1695i	0.130168	+	0.406500i
$756$	−40.2371	+	4.12995i	−1.46341	+	0.150205i
$757$	−2.83015	+	3.37284i	−0.102863	+	0.122588i	−0.815020	−	0.579433i	$-0.803274\pi$
$757$	−2.83015	+	3.37284i	−0.102863	+	0.122588i	0.712157	+	0.702021i	$0.247719\pi$
$758$	8.27900	+	7.47274i	0.300707	+	0.271422i
$759$	−24.6289			−0.893972
$760$	6.52467	+	26.7849i	0.236675	+	0.971589i
$761$	13.2216			0.479284			0.239642	−	0.970861i	$-0.422970\pi$
$761$	13.2216			0.479284			0.239642	+	0.970861i	$0.422970\pi$
$762$	−7.84586	−	7.08178i	−0.284226	−	0.256546i
$763$	47.2898	−	56.3578i	1.71201	−	2.04029i
$764$	−0.841199	+	0.0863409i	−0.0304335	+	0.00312370i
$765$	12.6194	−	4.04092i	0.456254	−	0.146100i
$766$	7.46801	−	1.04028i	0.269830	−	0.0375868i
$767$	0.303425	+	0.525548i	0.0109561	+	0.0189765i
$768$	4.71368	−	15.8535i	0.170090	−	0.572063i
$769$	3.10420	+	17.6048i	0.111940	+	0.634845i	0.988220	+	0.153042i	$0.0489069\pi$
$769$	3.10420	+	17.6048i	0.111940	+	0.634845i	−0.876279	+	0.481803i	$0.839982\pi$
$770$	−52.2720	−	23.6170i	−1.88375	−	0.851099i
$771$	19.5110	+	11.2647i	0.702673	+	0.405688i
$772$	−6.81568	+	10.0517i	−0.245302	+	0.361769i
$773$	13.6644	−	11.4658i	0.491474	−	0.412395i	−0.363080	−	0.931758i	$-0.618275\pi$
$773$	13.6644	−	11.4658i	0.491474	−	0.412395i	0.854554	+	0.519363i	$0.173831\pi$
$774$	−2.13057	+	9.96379i	−0.0765816	+	0.358141i
$775$	1.17169	+	0.533682i	0.0420885	+	0.0191704i
$776$	35.9234	+	37.4730i	1.28958	+	1.34520i
$777$	−19.6930	−	3.47241i	−0.706483	−	0.124572i
$778$	18.7295	−	29.8924i	0.671486	−	1.07169i
$779$	−23.5022	−	3.24280i	−0.842052	−	0.116185i
$780$	−3.86121	−	8.83115i	−0.138253	−	0.316206i
$781$	−20.7170	−	3.65297i	−0.741313	−	0.130713i
$782$	6.96101	+	21.5130i	0.248925	+	0.769302i
$783$	39.2747	+	14.2948i	1.40356	+	0.510856i
$784$	10.9650	−	33.1951i	0.391606	−	1.18554i
$785$	15.7736	−	12.2158i	0.562983	−	0.436000i
$786$	30.2820	+	1.09443i	1.08012	+	0.0390370i
$787$	−1.48812	−	0.859168i	−0.0530458	−	0.0306260i	0.473243	−	0.880932i	$-0.343083\pi$
$787$	−1.48812	−	0.859168i	−0.0530458	−	0.0306260i	−0.526288	+	0.850306i	$0.676417\pi$
$788$	−10.8846	−	15.0584i	−0.387748	−	0.536435i
$789$	−24.6121	+	4.33977i	−0.876212	+	0.154500i
$790$	5.11869	−	2.46192i	0.182115	−	0.0875913i
$791$	−0.113964	−	0.197392i	−0.00405211	−	0.00701846i
$792$	13.8909	+	20.7574i	0.493592	+	0.737583i
$793$	27.0509	−	9.84573i	0.960607	−	0.349632i
$794$	2.27303	+	2.91666i	0.0806668	+	0.103509i
$795$	10.8284	+	9.83380i	0.384044	+	0.348769i
$796$	7.70686	+	27.1264i	0.273162	+	0.961470i
$797$	−33.0094			−1.16925			−0.584626	−	0.811303i	$-0.698759\pi$
$797$	−33.0094			−1.16925			−0.584626	+	0.811303i	$0.698759\pi$
$798$	−8.61579	+	23.7674i	−0.304996	+	0.841355i
$799$		−	23.4960i		−	0.831230i
$800$	−28.1695	+	2.54507i	−0.995943	+	0.0899818i
$801$	−0.793517	+	0.945677i	−0.0280375	+	0.0334138i
$802$	−3.93405	−	5.04802i	−0.138916	−	0.178252i
$803$	−32.8325	+	11.9501i	−1.15863	+	0.421709i
$804$	12.6710	+	5.67853i	0.446870	+	0.200266i
$805$	−40.9108	+	21.5295i	−1.44191	+	0.758817i
$806$	0.355629	+	0.670812i	0.0125265	+	0.0236283i
$807$	−4.25206	−	24.1146i	−0.149680	−	0.848875i
$808$	0.877085	+	13.2384i	0.0308557	+	0.465724i
$809$	1.44369	−	2.50055i	0.0507575	−	0.0879147i	−0.839530	−	0.543313i	$-0.817170\pi$
$809$	1.44369	−	2.50055i	0.0507575	−	0.0879147i	0.890288	+	0.455398i	$0.150503\pi$
$810$	0.124831	−	1.65480i	0.00438611	−	0.0581438i
$811$	−7.26322	+	6.09456i	−0.255046	+	0.214009i	−0.761342	−	0.648351i	$-0.775459\pi$
$811$	−7.26322	+	6.09456i	−0.255046	+	0.214009i	0.506296	+	0.862360i	$0.331015\pi$
$812$	−45.3053	+	46.6867i	−1.58990	+	1.63838i
$813$	−1.10172	−	0.400992i	−0.0386389	−	0.0140634i
$814$	9.70583	+	29.9958i	0.340189	+	1.05135i
$815$	−17.6544	−	3.83125i	−0.618407	−	0.134203i
$816$	−7.85898	+	9.95858i	−0.275119	+	0.348620i
$817$	12.8380	+	9.97827i	0.449144	+	0.349095i
$818$	21.7786	+	13.6457i	0.761471	+	0.477112i
$819$	−2.77421	+	15.7334i	−0.0969389	+	0.549768i
$820$	6.86592	−	23.3528i	0.239768	−	0.815514i
$821$	23.3853	+	8.51154i	0.816151	+	0.297055i	0.716162	−	0.697934i	$-0.245897\pi$
$821$	23.3853	+	8.51154i	0.816151	+	0.297055i	0.0999888	+	0.994989i	$0.468119\pi$
$822$	−6.10940	+	28.5712i	−0.213090	+	0.996534i
$823$	21.4111	−	17.9661i	0.746345	−	0.626258i	−0.188188	−	0.982133i	$-0.560262\pi$
$823$	21.4111	−	17.9661i	0.746345	−	0.626258i	0.934534	+	0.355875i	$0.115817\pi$
$824$	−22.2927	+	9.82783i	−0.776602	+	0.342369i
$825$	−13.3806	+	19.4774i	−0.465851	+	0.678116i
$826$	1.51342	+	0.613608i	0.0526586	+	0.0213502i
$827$	12.4958	−	2.20336i	0.434523	−	0.0766182i	0.0478919	−	0.998853i	$-0.484750\pi$
$827$	12.4958	−	2.20336i	0.434523	−	0.0766182i	0.386631	+	0.922234i	$0.373639\pi$
$828$	20.0778	+	1.45317i	0.697751	+	0.0505011i
$829$	−4.77407	+	2.75631i	−0.165810	+	0.0957307i	−0.580609	−	0.814183i	$-0.697185\pi$
$829$	−4.77407	+	2.75631i	−0.165810	+	0.0957307i	0.414798	+	0.909913i	$0.363852\pi$
$830$	−19.5236	+	1.94390i	−0.677673	+	0.0674739i
$831$	−22.7892	+	8.29461i	−0.790550	+	0.287737i
$832$	−14.0799	−	8.94191i	−0.488132	−	0.310005i
$833$	−17.2360	+	20.5411i	−0.597193	+	0.711707i
$834$	−0.633685	−	0.571972i	−0.0219427	−	0.0198058i
$835$	−13.4988	−	0.528984i	−0.467145	−	0.0183063i
$836$	39.4695	−	5.55011i	1.36508	−	0.191955i
$837$		−	1.31266i		−	0.0453723i
$838$	1.48635	−	1.64671i	0.0513449	−	0.0568847i
$839$	31.2256	+	26.2014i	1.07803	+	0.904572i	0.995756	−	0.0920378i	$-0.0293381\pi$
$839$	31.2256	+	26.2014i	1.07803	+	0.904572i	0.0822716	+	0.996610i	$0.473783\pi$
$840$	−22.8044	−	12.3579i	−0.786826	−	0.426388i
$841$	35.9165	−	13.0725i	1.23850	−	0.450777i
$842$	−17.8867	+	2.49159i	−0.616417	+	0.0858657i
$843$	−1.29315	−	2.23981i	−0.0445385	−	0.0771430i
$844$	−30.4532	−	2.20411i	−1.04824	−	0.0758685i
$845$	19.1720	−	2.61119i	0.659535	−	0.0898277i
$846$	−19.3854	−	7.85970i	−0.666483	−	0.270222i
$847$	−19.6447	+	34.0256i	−0.674999	+	1.16913i
$848$	25.0489	+	3.64503i	0.860184	+	0.125171i
$849$	3.16158	+	3.76783i	0.108505	+	0.129312i
$850$	20.7950	+	6.18271i	0.713264	+	0.212065i
$851$	23.8774	+	8.69065i	0.818505	+	0.297912i
$852$	−9.22438	−	2.32380i	−0.316022	−	0.0796120i
$853$	30.8608	+	5.44159i	1.05665	+	0.186316i	0.674871	−	0.737936i	$-0.264199\pi$
$853$	30.8608	+	5.44159i	1.05665	+	0.186316i	0.381782	+	0.924252i	$0.375310\pi$
$854$	41.1318	−	65.6465i	1.40750	−	2.24638i
$855$	−16.2868	−	9.44115i	−0.556995	−	0.322881i
$856$	−3.57009	+	32.8125i	−0.122023	+	1.12151i
$857$	1.26979	−	7.20135i	0.0433753	−	0.245993i	−0.955409	−	0.295285i	$-0.904585\pi$
$857$	1.26979	−	7.20135i	0.0433753	−	0.245993i	0.998784	+	0.0492918i	$0.0156964\pi$
$858$	−13.2583	+	4.29002i	−0.452631	+	0.146459i
$859$	2.96692	−	8.15155i	0.101230	−	0.278127i	−0.878731	−	0.477318i	$-0.841609\pi$
$859$	2.96692	−	8.15155i	0.101230	−	0.278127i	0.979961	+	0.199191i	$0.0638313\pi$
$860$	−12.0775	+	11.5078i	−0.411839	+	0.392411i
$861$	17.0993	−	14.3481i	0.582744	−	0.488980i
$862$	39.5509	+	1.42941i	1.34711	+	0.0486861i
$863$	41.1611	+	23.7644i	1.40114	+	0.808949i	0.994510	−	0.104643i	$-0.0333700\pi$
$863$	41.1611	+	23.7644i	1.40114	+	0.808949i	0.406631	+	0.913592i	$0.366703\pi$
$864$	14.2660	+	25.0609i	0.485338	+	0.852588i
$865$	−35.4133	+	4.82323i	−1.20409	+	0.163995i
$866$	5.23926	+	9.88265i	0.178037	+	0.335826i
$867$	−6.79187	+	3.92129i	−0.230664	+	0.133174i
$868$	1.86452	+	0.835591i	0.0632860	+	0.0283618i
$869$	−2.80869	−	7.71681i	−0.0952783	−	0.261775i
$870$	15.6343	+	21.7686i	0.530052	+	0.738025i
$871$	9.00076	−	10.7267i	0.304979	−	0.363460i
$872$	−50.3650	−	14.6414i	−1.70557	−	0.495822i
$873$	−35.4481			−1.19974
$874$	16.0260	−	27.8410i	0.542088	−	0.941737i
$875$	−5.19998	+	44.0504i	−0.175791	+	1.48917i
$876$	−15.1980	+	4.31788i	−0.513492	+	0.145888i
$877$	22.7770	+	19.1122i	0.769124	+	0.645372i	0.940484	−	0.339837i	$-0.110372\pi$
$877$	22.7770	+	19.1122i	0.769124	+	0.645372i	−0.171360	+	0.985208i	$0.554816\pi$
$878$	−36.6354	+	28.5509i	−1.23639	+	0.963546i
$879$	0.892430	+	2.45193i	0.0301009	+	0.0827016i
$880$	−0.373610	+	40.8915i	−0.0125944	+	1.37845i
$881$	16.2922	+	28.2189i	0.548899	+	0.950720i	0.998350	+	0.0574157i	$0.0182861\pi$
$881$	16.2922	+	28.2189i	0.548899	+	0.950720i	−0.449452	+	0.893305i	$0.648381\pi$
$882$	11.1818	+	21.0918i	0.376510	+	0.710198i
$883$	−6.68770	−	37.9278i	−0.225059	−	1.27637i	−0.862573	−	0.505933i	$-0.831148\pi$
$883$	−6.68770	−	37.9278i	−0.225059	−	1.27637i	0.637514	−	0.770439i	$-0.279963\pi$
$884$	7.49454	+	10.3684i	0.252069	+	0.348727i
$885$	0.358951	−	0.569031i	0.0120660	−	0.0191278i
$886$	50.1600	+	1.81284i	1.68516	+	0.0609036i
$887$	−8.24938	−	9.83123i	−0.276987	−	0.330100i	0.609559	−	0.792741i	$-0.291347\pi$
$887$	−8.24938	−	9.83123i	−0.276987	−	0.330100i	−0.886546	+	0.462640i	$0.846902\pi$
$888$	3.39830	+	13.8453i	0.114039	+	0.464618i
$889$	−9.81028	+	26.9535i	−0.329026	+	0.903992i
$890$	−1.94592	+	0.546461i	−0.0652273	+	0.0183174i
$891$	−2.36285	−	0.416634i	−0.0791584	−	0.0139578i
$892$	31.7713	−	15.4001i	1.06378	−	0.515635i
$893$	−24.7509	+	22.3987i	−0.828258	+	0.749544i
$894$	18.9018	+	11.8432i	0.632171	+	0.396097i
$895$	−33.8859	−	7.35372i	−1.13268	−	0.245808i
$896$	−44.6779	+	4.31076i	−1.49258	+	0.144012i
$897$	−3.84131	+	10.5539i	−0.128258	+	0.352385i
$898$	27.2386	+	5.82444i	0.908963	+	0.194364i
$899$	−1.35707	−	1.61729i	−0.0452608	−	0.0539398i
$900$	12.0572	−	15.0887i	0.401907	−	0.502957i
$901$	−16.8143	−	9.70773i	−0.560165	−	0.323412i
$902$	−32.6136	−	13.2230i	−1.08592	−	0.440279i
$903$	−15.0656	+	2.65648i	−0.501353	+	0.0884021i
$904$	−0.0959933	+	0.131113i	−0.00319269	+	0.00436074i
$905$	20.0319	+	38.0650i	0.665884	+	1.26532i
$906$	7.59428	−	1.05787i	0.252303	−	0.0351453i
$907$	−6.59780	−	18.1273i	−0.219076	−	0.601908i	0.780658	−	0.624959i	$-0.214884\pi$
$907$	−6.59780	−	18.1273i	−0.219076	−	0.601908i	−0.999734	+	0.0230511i	$0.992662\pi$
$908$	−22.7851	+	2.33867i	−0.756151	+	0.0776115i
$909$	−6.94026	−	5.82357i	−0.230194	−	0.193156i
$910$	−18.2730	+	18.7160i	−0.605745	+	0.620428i
$911$	−26.7525			−0.886350			−0.443175	−	0.896435i	$-0.646148\pi$
$911$	−26.7525			−0.886350			−0.443175	+	0.896435i	$0.646148\pi$
$912$	17.9824	−	1.21477i	0.595457	−	0.0402251i
$913$			28.3666i			0.938798i
$914$	−6.98884	+	7.74289i	−0.231170	+	0.256112i
$915$	−23.6261	−	21.4560i	−0.781055	−	0.709314i
$916$	−0.303392	−	2.95588i	−0.0100243	−	0.0976649i
$917$	−28.1258	−	77.2751i	−0.928796	−	2.55185i
$918$	−3.05161	−	21.9070i	−0.100718	−	0.723039i
$919$	−28.0921	+	16.2190i	−0.926672	+	0.535014i	−0.885757	−	0.464148i	$-0.846360\pi$
$919$	−28.0921	+	16.2190i	−0.926672	+	0.535014i	−0.0409145	+	0.999163i	$0.513027\pi$
$920$	25.8103	+	20.4963i	0.850940	+	0.675745i
$921$	−3.59514	−	20.3891i	−0.118464	−	0.671842i
$922$	9.02518	+	3.65921i	0.297228	+	0.120510i
$923$	−4.79654	+	8.30785i	−0.157880	+	0.273456i
$924$	−21.0457	+	31.0380i	−0.692351	+	1.02108i
$925$	19.8451	−	14.1615i	0.652504	−	0.465628i
$926$	1.39347	−	6.51670i	0.0457923	−	0.214152i
$927$	5.69006	−	15.6333i	0.186886	−	0.513465i
$928$	43.4853	+	16.1282i	1.42748	+	0.529433i
$929$	−0.0861147	+	0.488381i	−0.00282533	+	0.0160233i	−0.986188	−	0.165631i	$-0.947034\pi$
$929$	−0.0861147	+	0.488381i	−0.00282533	+	0.0160233i	0.983362	+	0.181654i	$0.0581451\pi$
$930$	0.474514	−	0.695248i	0.0155599	−	0.0227981i
$931$	38.0693	−	1.42521i	1.24767	−	0.0467094i
$932$	−10.0926	+	4.89205i	−0.330593	+	0.160244i
$933$	−2.50092	+	14.1834i	−0.0818764	+	0.464344i
$934$	−35.4628	+	11.4748i	−1.16038	+	0.375467i
$935$	11.8737	−	29.0318i	0.388313	−	0.949440i
$936$	11.0615	−	2.71501i	0.361555	−	0.0887428i
$937$	−8.03121	−	9.57122i	−0.262368	−	0.312678i	0.618737	−	0.785598i	$-0.287644\pi$
$937$	−8.03121	−	9.57122i	−0.262368	−	0.312678i	−0.881105	+	0.472920i	$0.843200\pi$
$938$	1.36100	−	37.6577i	0.0444381	−	1.22957i
$939$	1.23043	−	2.13116i	0.0401535	−	0.0695479i
$940$	−18.9609	−	28.5209i	−0.618436	−	0.930250i
$941$	−4.79219	+	0.844993i	−0.156221	+	0.0275460i	−0.251212	−	0.967932i	$-0.580829\pi$
$941$	−4.79219	+	0.844993i	−0.156221	+	0.0275460i	0.0949906	+	0.995478i	$0.469718\pi$
$942$	−6.10943	−	11.5240i	−0.199056	−	0.375473i
$943$	−24.5638	+	14.1819i	−0.799908	+	0.461827i
$944$	−0.0349590	−	1.16374i	−0.00113782	−	0.0378766i
$945$	43.0686	−	13.7912i	1.40102	−	0.448629i
$946$	14.8259	+	19.0241i	0.482033	+	0.618526i
$947$	−3.08425	−	2.58799i	−0.100225	−	0.0840984i	0.591299	−	0.806453i	$-0.298616\pi$
$947$	−3.08425	−	2.58799i	−0.100225	−	0.0840984i	−0.691523	+	0.722354i	$0.743060\pi$
$948$	−1.01486	−	3.57206i	−0.0329610	−	0.116015i
$949$			15.9331i			0.517211i
$950$	−13.3109	−	27.7996i	−0.431864	−	0.901939i
$951$			11.6786i			0.378705i
$952$	33.0595	+	9.61062i	1.07146	+	0.311482i
$953$	−36.8782	−	30.9445i	−1.19460	−	1.00239i	−0.999768	−	0.0215538i	$-0.993139\pi$
$953$	−36.8782	−	30.9445i	−1.19460	−	1.00239i	−0.194834	−	0.980836i	$-0.562417\pi$
$954$	−13.6339	+	10.6253i	−0.441415	+	0.344005i
$955$	0.900395	−	0.288320i	0.0291361	−	0.00932982i
$956$	20.5293	−	45.8088i	0.663966	−	1.48156i
$957$	33.5576	−	19.3745i	1.08476	−	0.626288i
$958$	23.6113	−	12.5175i	0.762847	−	0.404421i
$959$	78.0860	−	13.7687i	2.52153	−	0.444614i
$960$	−1.50332	+	18.4304i	−0.0485194	+	0.594838i
$961$	15.4668	−	26.7894i	0.498931	−	0.864173i
$962$	14.3675	+	0.519259i	0.463228	+	0.0167416i
$963$	−14.4877	−	17.2657i	−0.466859	−	0.556380i
$964$	−5.87356	+	6.05266i	−0.189175	+	0.194943i
$965$	5.14001	−	12.5675i	0.165463	−	0.404564i
$966$	9.30471	+	28.7562i	0.299374	+	0.925215i
$967$	−6.39104	+	36.2454i	−0.205522	+	1.16557i	0.691095	+	0.722764i	$0.257129\pi$
$967$	−6.39104	+	36.2454i	−0.205522	+	1.16557i	−0.896616	+	0.442808i	$0.853982\pi$
$968$	27.8461	+	3.02973i	0.895009	+	0.0973793i
$969$	−13.1584	−	4.23890i	−0.422710	−	0.136173i
$970$	−47.9371	−	32.7176i	−1.53917	−	1.05050i
$971$	−2.89599	+	16.4240i	−0.0929368	+	0.527071i	0.902423	+	0.430851i	$0.141786\pi$
$971$	−2.89599	+	16.4240i	−0.0929368	+	0.527071i	−0.995360	+	0.0962203i	$0.969325\pi$
$972$	−30.7115	−	7.73682i	−0.985073	−	0.248158i
$973$	−0.792344	+	2.17695i	−0.0254014	+	0.0697897i
$974$	−46.8927	−	10.0271i	−1.50254	−	0.321289i
$975$	6.25946	+	8.77164i	0.200463	+	0.280917i
$976$	−54.6534	−	7.95295i	−1.74941	−	0.254568i
$977$	8.18503	−	14.1769i	0.261862	−	0.453559i	−0.704875	−	0.709332i	$-0.748997\pi$
$977$	8.18503	−	14.1769i	0.261862	−	0.453559i	0.966737	+	0.255773i	$0.0823300\pi$
$978$	−4.43771	+	10.9453i	−0.141902	+	0.349992i
$979$	0.507439	+	2.87783i	0.0162178	+	0.0919759i
$980$	−4.34585	+	38.8432i	−0.138823	+	1.24080i
$981$	31.0179	−	17.9082i	0.990325	−	0.571764i
$982$	−51.8117	+	7.21727i	−1.65338	+	0.230312i
$983$	0.762412	+	2.09471i	0.0243172	+	0.0668108i	0.951257	−	0.308399i	$-0.0997930\pi$
$983$	0.762412	+	2.09471i	0.0243172	+	0.0668108i	−0.926940	+	0.375209i	$0.877571\pi$
$984$	−14.2775	−	7.02835i	−0.455151	−	0.224056i
$985$	15.3784	+	13.9659i	0.489996	+	0.444989i
$986$	−26.4079	−	23.8361i	−0.840999	−	0.759097i
$987$		−	31.4069i		−	0.999693i
$988$	3.77764	−	17.7790i	0.120183	−	0.565625i
$989$	19.4391			0.618127
$990$	−19.9807	−	19.5079i	−0.635029	−	0.620001i
$991$	3.80912	+	3.19623i	0.121001	+	0.101532i	0.701280	−	0.712886i	$-0.252612\pi$
$991$	3.80912	+	3.19623i	0.121001	+	0.101532i	−0.580280	+	0.814417i	$0.697057\pi$
$992$	0.00887733	−	1.45662i	0.000281855	−	0.0462479i
$993$	−10.3525	−	28.4432i	−0.328526	−	0.902616i
$994$	3.56169	+	25.5688i	0.112970	+	0.810994i
$995$	−14.6830	−	27.9008i	−0.465482	−	0.884516i
$996$	−0.925968	+	12.7937i	−0.0293404	+	0.405384i
$997$	0.694133	−	0.122394i	0.0219834	−	0.00387627i	−0.162646	−	0.986685i	$-0.552003\pi$
$997$	0.694133	−	0.122394i	0.0219834	−	0.00387627i	0.184629	+	0.982808i	$0.440892\pi$
$998$	21.7566	−	53.6611i	0.688693	−	1.69861i
$999$	−21.5261	−	12.4281i	−0.681056	−	0.393208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.13	yes	336
4.3	odd	2	inner	380.2.bb.a.59.49	yes	336
5.4	even	2	inner	380.2.bb.a.59.44	yes	336
19.10	odd	18	inner	380.2.bb.a.219.8	yes	336
20.19	odd	2	inner	380.2.bb.a.59.8	✓	336
76.67	even	18	inner	380.2.bb.a.219.44	yes	336
95.29	odd	18	inner	380.2.bb.a.219.49	yes	336
380.219	even	18	inner	380.2.bb.a.219.13	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.8	✓	336	20.19	odd	2	inner
380.2.bb.a.59.13	yes	336	1.1	even	1	trivial
380.2.bb.a.59.44	yes	336	5.4	even	2	inner
380.2.bb.a.59.49	yes	336	4.3	odd	2	inner
380.2.bb.a.219.8	yes	336	19.10	odd	18	inner
380.2.bb.a.219.13	yes	336	380.219	even	18	inner
380.2.bb.a.219.44	yes	336	76.67	even	18	inner
380.2.bb.a.219.49	yes	336	95.29	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04981 - 0.947574i) q^{2} +(0.664457 - 0.791869i) q^{3} +(0.204208 + 1.98955i) q^{4} +(-0.681915 - 2.12955i) q^{5} +(-1.44791 + 0.201691i) q^{6} +(1.98367 + 3.43582i) q^{7} +(1.67086 - 2.28215i) q^{8} +(0.335391 + 1.90210i) q^{9} +O(q^{10})\)	\(q+(-1.04981 - 0.947574i) q^{2} +(0.664457 - 0.791869i) q^{3} +(0.204208 + 1.98955i) q^{4} +(-0.681915 - 2.12955i) q^{5} +(-1.44791 + 0.201691i) q^{6} +(1.98367 + 3.43582i) q^{7} +(1.67086 - 2.28215i) q^{8} +(0.335391 + 1.90210i) q^{9} +(-1.30203 + 2.88179i) q^{10} +(3.95947 + 2.28600i) q^{11} +(1.71115 + 1.16026i) q^{12} +(1.59714 - 1.34016i) q^{13} +(1.17321 - 5.48664i) q^{14} +(-2.13943 - 0.875008i) q^{15} +(-3.91660 + 0.812561i) q^{16} +(3.02148 + 0.532768i) q^{17} +(1.45028 - 2.31465i) q^{18} +(-2.31915 - 3.69074i) q^{19} +(4.09759 - 1.79157i) q^{20} +(4.03878 + 0.712147i) q^{21} +(-1.99054 - 6.15176i) q^{22} +(-4.89694 - 1.78234i) q^{23} +(-0.696948 - 2.83950i) q^{24} +(-4.06998 + 2.90435i) q^{25} +(-2.94660 - 0.106493i) q^{26} +(4.41473 + 2.54884i) q^{27} +(-6.43065 + 4.64823i) q^{28} +(8.07431 - 1.42372i) q^{29} +(1.41686 + 2.94586i) q^{30} +(-0.128751 - 0.223003i) q^{31} +(4.88165 + 2.85823i) q^{32} +(4.44111 - 1.61643i) q^{33} +(-2.66715 - 3.42238i) q^{34} +(5.96406 - 6.56727i) q^{35} +(-3.71582 + 1.05570i) q^{36} -4.87597 q^{37} +(-1.06258 + 6.07214i) q^{38} -2.15520i q^{39} +(-5.99935 - 2.00196i) q^{40} +(3.49860 - 4.16946i) q^{41} +(-3.56515 - 4.57467i) q^{42} +(-3.50528 + 1.27582i) q^{43} +(-3.73955 + 8.34437i) q^{44} +(3.82191 - 2.01130i) q^{45} +(3.45196 + 6.51133i) q^{46} +(-1.32983 - 7.54185i) q^{47} +(-1.95897 + 3.64135i) q^{48} +(-4.36990 + 7.56889i) q^{49} +(7.02480 + 0.807591i) q^{50} +(2.42953 - 2.03861i) q^{51} +(2.99246 + 2.90391i) q^{52} +(-5.94655 - 2.16437i) q^{53} +(-2.21941 - 6.85908i) q^{54} +(2.16813 - 9.99075i) q^{55} +(11.1555 + 1.21375i) q^{56} +(-4.46356 - 0.615877i) q^{57} +(-9.82559 - 6.15637i) q^{58} +(-0.0505433 + 0.286645i) q^{59} +(1.30398 - 4.43518i) q^{60} +(12.9746 + 4.72236i) q^{61} +(-0.0761478 + 0.356113i) q^{62} +(-5.86996 + 4.92548i) q^{63} +(-2.41643 - 7.62633i) q^{64} +(-3.94305 - 2.48732i) q^{65} +(-6.19402 - 2.51133i) q^{66} +(6.61416 - 1.16625i) q^{67} +(-0.442959 + 6.12017i) q^{68} +(-4.66519 + 2.69345i) q^{69} +(-12.4841 + 1.24301i) q^{70} +(-4.32369 + 1.57370i) q^{71} +(4.90127 + 2.41273i) q^{72} +(-4.91224 + 5.85418i) q^{73} +(5.11885 + 4.62035i) q^{74} +(-0.404465 + 5.15271i) q^{75} +(6.86931 - 5.36773i) q^{76} +18.1387i q^{77} +(-2.04221 + 2.26256i) q^{78} +(-1.37594 - 1.15455i) q^{79} +(4.40118 + 7.78650i) q^{80} +(-0.493133 + 0.179486i) q^{81} +(-7.62374 + 1.06197i) q^{82} +(3.10221 + 5.37319i) q^{83} +(-0.592099 + 8.18078i) q^{84} +(-0.925836 - 6.79770i) q^{85} +(4.88882 + 1.98214i) q^{86} +(4.23764 - 7.33980i) q^{87} +(11.8327 - 5.21651i) q^{88} +(0.410842 + 0.489623i) q^{89} +(-5.91814 - 1.51005i) q^{90} +(7.77274 + 2.82905i) q^{91} +(2.54606 - 10.1067i) q^{92} +(-0.262139 - 0.0462222i) q^{93} +(-5.75039 + 9.17763i) q^{94} +(-6.27816 + 7.45552i) q^{95} +(5.50699 - 1.96646i) q^{96} +(-3.18700 + 18.0744i) q^{97} +(11.7597 - 3.80510i) q^{98} +(-3.02022 + 8.29800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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