LMFDB - Embedded newform 380.2.bb.a.59.8

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			59.8
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31059 + 0.531372i) q^{2} +(0.664457 - 0.791869i) q^{3} +(1.43529 - 1.39282i) q^{4} +(0.846472 + 2.06966i) q^{5} +(-0.450054 + 1.39089i) q^{6} +(1.98367 + 3.43582i) q^{7} +(-1.14097 + 2.58809i) q^{8} +(0.335391 + 1.90210i) q^{9} +O(q^{10})$	\(q+(-1.31059 + 0.531372i) q^{2} +(0.664457 - 0.791869i) q^{3} +(1.43529 - 1.39282i) q^{4} +(0.846472 + 2.06966i) q^{5} +(-0.450054 + 1.39089i) q^{6} +(1.98367 + 3.43582i) q^{7} +(-1.14097 + 2.58809i) q^{8} +(0.335391 + 1.90210i) q^{9} +(-2.20913 - 2.26268i) q^{10} +(-3.95947 - 2.28600i) q^{11} +(-0.149243 - 2.06203i) q^{12} +(-1.59714 + 1.34016i) q^{13} +(-4.42547 - 3.44888i) q^{14} +(2.20134 + 0.704904i) q^{15} +(0.120106 - 3.99820i) 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} +(6.40395 + 0.892059i) q^{22} +(-4.89694 - 1.78234i) q^{23} +(1.29130 + 2.62317i) q^{24} +(-3.56697 + 3.50382i) q^{25} +(1.38107 - 2.60507i) q^{26} +(4.41473 + 2.54884i) q^{27} +(7.63262 + 2.16850i) q^{28} +(8.07431 - 1.42372i) q^{29} +(-3.25962 + 0.245891i) q^{30} +(0.128751 + 0.223003i) q^{31} +(1.96712 + 5.30381i) q^{32} +(-4.44111 + 1.61643i) q^{33} +(4.24302 - 0.907288i) q^{34} +(-5.43185 + 7.01385i) q^{35} +(3.13066 + 2.26292i) q^{36} +4.87597 q^{37} +(-5.00060 - 3.60471i) q^{38} +2.15520i q^{39} +(-6.32225 - 0.170673i) q^{40} +(3.49860 - 4.16946i) q^{41} +(-5.67160 + 1.21276i) q^{42} +(-3.50528 + 1.27582i) q^{43} +(-8.86697 + 2.23376i) q^{44} +(-3.65279 + 2.30422i) q^{45} +(7.36496 - 0.266178i) q^{46} +(-1.32983 - 7.54185i) q^{47} +(-3.08624 - 2.75174i) q^{48} +(-4.36990 + 7.56889i) q^{49} +(2.81301 - 6.48745i) q^{50} +(-2.42953 + 2.03861i) q^{51} +(-0.425756 + 4.14804i) q^{52} +(5.94655 + 2.16437i) q^{53} +(-7.14028 - 0.994627i) q^{54} +(1.37966 - 10.1298i) 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} +(4.14137 - 2.05433i) q^{60} +(12.9746 + 4.72236i) q^{61} +(-0.287237 - 0.223851i) q^{62} +(-5.86996 + 4.92548i) q^{63} +(-5.39638 - 5.90585i) q^{64} +(-4.12561 - 2.17113i) q^{65} +(4.96155 - 4.47836i) q^{66} +(6.61416 - 1.16625i) q^{67} +(-5.07875 + 3.44370i) q^{68} +(-4.66519 + 2.69345i) q^{69} +(3.39197 - 12.0786i) q^{70} +(4.32369 - 1.57370i) q^{71} +(-5.30546 - 1.30221i) q^{72} +(4.91224 - 5.85418i) q^{73} +(-6.39040 + 2.59095i) q^{74} +(0.404465 + 5.15271i) q^{75} +(8.46918 + 2.06712i) q^{76} -18.1387i q^{77} +(-1.14521 - 2.82459i) q^{78} +(1.37594 + 1.15455i) q^{79} +(8.37657 - 3.13578i) q^{80} +(-0.493133 + 0.179486i) q^{81} +(-2.36969 + 7.32351i) q^{82} +(3.10221 + 5.37319i) q^{83} +(6.78871 - 4.60316i) q^{84} +(-1.45495 - 6.70440i) q^{85} +(3.91605 - 3.53468i) q^{86} +(4.23764 - 7.33980i) q^{87} +(10.4340 - 7.63919i) q^{88} +(0.410842 + 0.489623i) q^{89} +(3.56291 - 4.96087i) q^{90} +(-7.77274 - 2.82905i) q^{91} +(-9.51100 + 4.26238i) q^{92} +(0.262139 + 0.0462222i) q^{93} +(5.75039 + 9.17763i) q^{94} +(-5.67548 + 7.92395i) q^{95} +(5.50699 + 1.96646i) q^{96} +(3.18700 - 18.0744i) q^{97} +(1.70525 - 12.2418i) 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 $

$2$	−1.31059	+	0.531372i	−0.926727	+	0.375736i
$2$	−1.31059	+	0.531372i	−0.926727	+	0.375736i
$3$	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	$0.125767\pi$
$4$	1.43529	−	1.39282i	0.717644	−	0.696410i
$5$	0.846472	+	2.06966i	0.378554	+	0.925579i
$5$	0.846472	+	2.06966i	0.378554	+	0.925579i
$6$	−0.450054	+	1.39089i	−0.183734	+	0.567828i
$7$	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	$0.563504\pi$
$8$	−1.14097	+	2.58809i	−0.403393	+	0.915027i
$9$	0.335391	+	1.90210i	0.111797	+	0.634032i
$10$	−2.20913	−	2.26268i	−0.698590	−	0.715522i
$11$	−3.95947	−	2.28600i	−1.19382	−	0.689255i	−0.234653	−	0.972079i	$-0.575395\pi$
$11$	−3.95947	−	2.28600i	−1.19382	−	0.689255i	−0.959172	+	0.282824i	$0.908729\pi$
$12$	−0.149243	−	2.06203i	−0.0430828	−	0.595257i
$13$	−1.59714	+	1.34016i	−0.442967	+	0.371693i	−0.836818	−	0.547481i	$-0.815587\pi$
$13$	−1.59714	+	1.34016i	−0.442967	+	0.371693i	0.393851	+	0.919174i	$0.371142\pi$
$14$	−4.42547	−	3.44888i	−1.18276	−	0.921752i
$15$	2.20134	+	0.704904i	0.568384	+	0.182005i
$16$	0.120106	−	3.99820i	0.0300266	−	0.999549i
$17$	−3.02148	−	0.532768i	−0.732817	−	0.129215i	−0.205227	−	0.978714i	$-0.565793\pi$
$17$	−3.02148	−	0.532768i	−0.732817	−	0.129215i	−0.527590	+	0.849499i	$0.676904\pi$
$18$	−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
$22$	6.40395	+	0.892059i	1.36533	+	0.190188i
$23$	−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	$0.793939\pi$
$24$	1.29130	+	2.62317i	0.263586	+	0.535452i
$25$	−3.56697	+	3.50382i	−0.713394	+	0.700763i
$26$	1.38107	−	2.60507i	0.270850	−	0.510897i
$27$	4.41473	+	2.54884i	0.849615	+	0.490525i
$28$	7.63262	+	2.16850i	1.44243	+	0.409807i
$29$	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	$0.169032\pi$
$30$	−3.25962	+	0.245891i	−0.595123	+	0.0448934i
$31$	0.128751	+	0.223003i	0.0231244	+	0.0400526i	0.877356	−	0.479840i	$-0.159305\pi$
$31$	0.128751	+	0.223003i	0.0231244	+	0.0400526i	−0.854232	+	0.519893i	$0.825972\pi$
$32$	1.96712	+	5.30381i	0.347741	+	0.937591i
$33$	−4.44111	+	1.61643i	−0.773098	+	0.281385i
$34$	4.24302	−	0.907288i	0.727671	−	0.155599i
$35$	−5.43185	+	7.01385i	−0.918150	+	1.18556i
$36$	3.13066	+	2.26292i	0.521777	+	0.377153i
$37$	4.87597			0.801605			0.400803	−	0.916164i	$-0.368731\pi$
$37$	4.87597			0.801605			0.400803	+	0.916164i	$0.368731\pi$
$38$	−5.00060	−	3.60471i	−0.811205	−	0.584762i
$39$			2.15520i			0.345109i
$40$	−6.32225	−	0.170673i	−0.999636	−	0.0269858i
$41$	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	$0.0824910\pi$
$42$	−5.67160	+	1.21276i	−0.875147	+	0.187133i
$43$	−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	$0.480693\pi$
$44$	−8.86697	+	2.23376i	−1.33675	+	0.336751i
$45$	−3.65279	+	2.30422i	−0.544526	+	0.343492i
$46$	7.36496	−	0.266178i	1.08590	−	0.0392459i
$47$	−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	$-0.244190\pi$
$48$	−3.08624	−	2.75174i	−0.445461	−	0.397179i
$49$	−4.36990	+	7.56889i	−0.624272	+	1.08127i
$50$	2.81301	−	6.48745i	0.397819	−	0.917464i
$51$	−2.42953	+	2.03861i	−0.340202	+	0.285463i
$52$	−0.425756	+	4.14804i	−0.0590417	+	0.575230i
$53$	5.94655	+	2.16437i	0.816822	+	0.297299i	0.716439	−	0.697650i	$-0.245771\pi$
$53$	5.94655	+	2.16437i	0.816822	+	0.297299i	0.100383	+	0.994949i	$0.467993\pi$
$54$	−7.14028	−	0.994627i	−0.971669	−	0.135352i
$55$	1.37966	−	10.1298i	0.186033	−	1.36590i
$56$	−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	−0.981341	−	0.192276i	$-0.938413\pi$
$59$	0.0505433	−	0.286645i	0.00658017	−	0.0373180i	0.987921	+	0.154958i	$0.0495242\pi$
$60$	4.14137	−	2.05433i	0.534648	−	0.265213i
$61$	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	$0.266007\pi$
$62$	−0.287237	−	0.223851i	−0.0364792	−	0.0284291i
$63$	−5.86996	+	4.92548i	−0.739545	+	0.620552i
$64$	−5.39638	−	5.90585i	−0.674547	−	0.738231i
$65$	−4.12561	−	2.17113i	−0.511718	−	0.269295i
$66$	4.96155	−	4.47836i	0.610724	−	0.551248i
$67$	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	$0.309884\pi$
$68$	−5.07875	+	3.44370i	−0.615888	+	0.417610i
$69$	−4.66519	+	2.69345i	−0.561623	+	0.324253i
$70$	3.39197	−	12.0786i	0.405417	−	1.44367i
$71$	4.32369	−	1.57370i	0.513128	−	0.186763i	−0.0724613	−	0.997371i	$-0.523085\pi$
$71$	4.32369	−	1.57370i	0.513128	−	0.186763i	0.585589	+	0.810608i	$0.300863\pi$
$72$	−5.30546	−	1.30221i	−0.625255	−	0.153467i
$73$	4.91224	−	5.85418i	0.574934	−	0.685180i	−0.397701	−	0.917515i	$-0.630192\pi$
$73$	4.91224	−	5.85418i	0.574934	−	0.685180i	0.972636	+	0.232335i	$0.0746365\pi$
$74$	−6.39040	+	2.59095i	−0.742869	+	0.301192i
$75$	0.404465	+	5.15271i	0.0467035	+	0.594984i
$76$	8.46918	+	2.06712i	0.971482	+	0.237115i
$77$		−	18.1387i		−	2.06710i
$78$	−1.14521	−	2.82459i	−0.129670	−	0.319822i
$79$	1.37594	+	1.15455i	0.154805	+	0.129897i	0.716901	−	0.697175i	$-0.245560\pi$
$79$	1.37594	+	1.15455i	0.154805	+	0.129897i	−0.562095	+	0.827073i	$0.690005\pi$
$80$	8.37657	−	3.13578i	0.936529	−	0.350591i
$81$	−0.493133	+	0.179486i	−0.0547925	+	0.0199429i
$82$	−2.36969	+	7.32351i	−0.261688	+	0.808746i
$83$	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	$0.722733\pi$
$84$	6.78871	−	4.60316i	0.740709	−	0.502246i
$85$	−1.45495	−	6.70440i	−0.157811	−	0.727195i
$86$	3.91605	−	3.53468i	0.422279	−	0.381154i
$87$	4.23764	−	7.33980i	0.454322	−	0.786909i
$88$	10.4340	−	7.63919i	1.11227	−	0.814341i
$89$	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	$0.766993\pi$
$90$	3.56291	−	4.96087i	0.375564	−	0.522922i
$91$	−7.77274	−	2.82905i	−0.814805	−	0.296565i
$92$	−9.51100	+	4.26238i	−0.991591	+	0.444384i
$93$	0.262139	+	0.0462222i	0.0271825	+	0.00479302i
$94$	5.75039	+	9.17763i	0.593107	+	0.946600i
$95$	−5.67548	+	7.92395i	−0.582291	+	0.812980i
$96$	5.50699	+	1.96646i	0.562055	+	0.200701i
$97$	3.18700	−	18.0744i	0.323591	−	1.83517i	−0.195807	−	0.980642i	$-0.562733\pi$
$97$	3.18700	−	18.0744i	0.323591	−	1.83517i	0.519398	−	0.854532i	$-0.326156\pi$
$98$	1.70525	−	12.2418i	0.172257	−	1.23660i
$99$	3.02022	−	8.29800i	0.303544	−	0.833980i
$100$	−0.239448	+	9.99713i	−0.0239448	+	0.999713i
$101$	−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	$0.352754\pi$
$102$	2.10085	−	3.96277i	0.208015	−	0.392373i
$103$	−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	$0.806168\pi$
$104$	−1.64616	−	5.66261i	−0.161419	−	0.555265i
$105$	1.94482	+	8.96171i	0.189795	+	0.874574i
$106$	−8.94357	+	0.323231i	−0.868677	+	0.0313950i
$107$	−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	$0.524096\pi$
$108$	9.88649	−	2.49059i	0.951328	−	0.239657i
$109$	−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	$-0.459079\pi$
$110$	3.57451	+	14.0091i	0.340816	+	1.33572i
$111$	3.23988	−	3.86113i	0.307515	−	0.366483i
$112$	13.9753	−	7.51844i	1.32054	−	0.710426i
$113$	0.0574513			0.00540456			0.00270228	−	0.999996i	$-0.499140\pi$
$113$	0.0574513			0.00540456			0.00270228	+	0.999996i	$0.499140\pi$
$114$	−6.17715	+	1.56465i	−0.578543	+	0.146542i
$115$	−0.456287	−	11.6437i	−0.0425490	−	1.08578i
$116$	9.60599	−	13.2895i	0.891893	−	1.23390i
$117$	−3.08478	−	2.58844i	−0.285188	−	0.239301i
$118$	0.0860736	+	0.402531i	0.00792372	+	0.0370560i
$119$	−4.16313	−	11.4381i	−0.381633	−	1.04853i
$120$	−4.33602	+	4.89299i	−0.395822	+	0.446667i
$121$	4.95160	+	8.57642i	0.450145	+	0.779675i
$122$	−19.5137	+	0.705247i	−1.76668	+	0.0638501i
$123$	−0.977003	−	5.54086i	−0.0880934	−	0.499603i
$124$	0.495398	+	0.140747i	0.0444881	+	0.0126395i
$125$	−10.2710	−	4.41653i	−0.918670	−	0.395026i
$126$	5.07584	−	9.57441i	0.452192	−	0.852956i
$127$	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	$0.673835\pi$
$128$	10.2106	+	4.87266i	0.902502	+	0.430687i
$129$	−1.31883	+	3.62345i	−0.116116	+	0.319027i
$130$	6.56065	+	0.653225i	0.575407	+	0.0572916i
$131$	20.4129	+	3.59935i	1.78349	+	0.314477i	0.965430	−	0.260662i	$-0.0839409\pi$
$131$	20.4129	+	3.59935i	1.78349	+	0.314477i	0.818056	+	0.575139i	$0.195052\pi$
$132$	−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
$135$	−1.53829	+	11.2945i	−0.132395	+	0.972076i
$136$	4.82627	−	7.21198i	0.413849	−	0.618422i
$137$	−6.83556	+	18.7805i	−0.584001	+	1.60453i	0.197278	+	0.980348i	$0.436790\pi$
$137$	−6.83556	+	18.7805i	−0.584001	+	1.60453i	−0.781279	+	0.624182i	$0.785432\pi$
$138$	4.68292	−	6.00895i	0.398637	−	0.511516i
$139$	−0.375344	−	0.447318i	−0.0318363	−	0.0379410i	0.749891	−	0.661561i	$-0.230106\pi$
$139$	−0.375344	−	0.447318i	−0.0318363	−	0.0379410i	−0.781728	+	0.623620i	$0.785661\pi$
$140$	1.97275	+	17.6325i	0.166728	+	1.49022i
$141$	−6.85577	−	3.95818i	−0.577360	−	0.333339i
$142$	−4.83037	+	4.35996i	−0.405356	+	0.365879i
$143$	9.38743	−	1.65526i	0.785016	−	0.138420i
$144$	7.64524	−	1.11251i	0.637103	−	0.0927088i
$145$	9.78129	+	15.5059i	0.812292	+	1.28770i
$146$	−3.32719	+	10.2827i	−0.275360	+	0.850998i
$147$	3.08996	+	8.48960i	0.254856	+	0.700210i
$148$	6.99843	−	6.79135i	0.575267	−	0.558246i
$149$	−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	$0.937121\pi$
$150$	−3.26809	−	6.53816i	−0.266838	−	0.533839i
$151$	5.24500			0.426832			0.213416	−	0.976961i	$-0.431541\pi$
$151$	5.24500			0.426832			0.213416	+	0.976961i	$0.431541\pi$
$152$	−12.1980	+	1.79113i	−0.989391	+	0.145280i
$153$		−	5.92583i		−	0.479075i
$154$	9.63839	+	23.7724i	0.776683	+	1.91563i
$155$	−0.352557	+	0.455237i	−0.0283180	+	0.0365655i
$156$	3.00181	+	3.09334i	0.240337	+	0.247665i
$157$	−3.05158	−	8.38416i	−0.243543	−	0.669129i	−0.999888	−	0.0149560i	$-0.995239\pi$
$157$	−3.05158	−	8.38416i	−0.243543	−	0.669129i	0.756345	−	0.654173i	$-0.226983\pi$
$158$	−2.41679	−	0.782007i	−0.192269	−	0.0622131i
$159$	5.66513	−	3.27076i	0.449274	−	0.259388i
$160$	−9.31197	+	8.56079i	−0.736176	+	0.676790i
$161$	−3.59012	−	20.3606i	−0.282941	−	1.60464i
$162$	0.550921	−	0.497269i	0.0432844	−	0.0390691i
$163$	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	$0.0641922\pi$
$164$	−0.785818	−	10.8573i	−0.0613620	−	0.847812i
$165$	−7.10474	−	7.82332i	−0.553103	−	0.609044i
$166$	−6.92088	−	5.39361i	−0.537165	−	0.418626i
$167$	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	$0.0360107\pi$
$168$	−6.45122	+	9.64018i	−0.497723	+	0.743756i
$169$	−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	$0.263424\pi$
$173$	−2.77551	+	15.7407i	−0.211018	+	1.19674i	−0.887684	+	0.460453i	$0.847687\pi$
$174$	−1.65364	+	11.8712i	−0.125362	+	0.899955i
$175$	−19.1142	−	5.30505i	−1.44490	−	0.401024i
$176$	−9.61544	+	15.5562i	−0.724791	+	1.17259i
$177$	−0.193402	−	0.230487i	−0.0145370	−	0.0173245i
$178$	−0.798617	−	0.423384i	−0.0598589	−	0.0317340i
$179$	−7.75350	+	13.4294i	−0.579523	+	1.00376i	0.416010	+	0.909360i	$0.363428\pi$
$179$	−7.75350	+	13.4294i	−0.579523	+	1.00376i	−0.995534	+	0.0944043i	$0.969905\pi$
$180$	−2.03345	+	8.39490i	−0.151565	+	0.625719i
$181$	−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	$0.697981\pi$
$182$	11.6902	−	0.422496i	0.866532	−	0.0313175i
$183$	12.3605	−	7.13636i	0.913718	−	0.527535i
$184$	10.2001	−	10.6401i	0.751962	−	0.784399i
$185$	4.12738	+	10.0916i	0.303451	+	0.741949i
$186$	−0.368118	+	0.0787149i	−0.0269917	+	0.00577166i
$187$	10.7455	+	9.01659i	0.785792	+	0.659358i
$188$	−12.4131	−	8.97251i	−0.905320	−	0.654388i
$189$			20.2243i			1.47110i
$190$	3.22766	−	13.4008i	0.234159	−	0.972198i
$191$		−	0.422809i		−	0.0305934i	−0.999883	−	0.0152967i	$-0.995131\pi$
$191$		−	0.422809i		−	0.0305934i	0.999883	−	0.0152967i	$-0.00486928\pi$
$192$	−8.26232	+	0.349041i	−0.596282	+	0.0251899i
$193$	−4.65164	−	3.90319i	−0.334832	−	0.280957i	0.459833	−	0.888005i	$-0.347909\pi$
$193$	−4.65164	−	3.90319i	−0.334832	−	0.280957i	−0.794665	+	0.607048i	$0.792354\pi$
$194$	5.42736	+	25.3816i	0.389662	+	1.82229i
$195$	−4.46054	+	1.82432i	−0.319426	+	0.130642i
$196$	4.27003	+	16.9500i	0.305002	+	1.21072i
$197$	8.04555	−	4.64510i	0.573222	−	0.330950i	−0.185213	−	0.982698i	$-0.559298\pi$
$197$	8.04555	−	4.64510i	0.573222	−	0.330950i	0.758435	+	0.651748i	$0.225964\pi$
$198$	0.451047	+	12.4801i	0.0320545	+	0.886924i
$199$	−13.8858	+	2.44844i	−0.984336	+	0.173565i	−0.642576	−	0.766222i	$-0.722134\pi$
$199$	−13.8858	+	2.44844i	−0.984336	+	0.173565i	−0.341760	+	0.939787i	$0.611023\pi$
$200$	−4.99837	−	13.2294i	−0.353438	−	0.935458i
$201$	3.47130	−	6.01247i	0.244847	−	0.424087i
$202$	3.10719	−	5.86100i	0.218621	−	0.412379i
$203$	20.9084	+	24.9177i	1.46748	+	1.74888i
$204$	−0.647649	+	6.30989i	−0.0453445	+	0.441781i
$205$	11.5908	+	3.71156i	0.809539	+	0.259227i
$206$	12.0649	+	1.68062i	0.840605	+	0.117095i
$207$	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	$-0.768326\pi$
$211$	2.65099	−	15.0345i	0.182501	−	1.03502i	0.929124	−	0.369769i	$-0.120563\pi$
$212$	11.5496	−	5.17598i	0.793230	−	0.355488i
$213$	1.62675	−	4.46945i	0.111463	−	0.306242i
$214$	10.1444	−	13.0170i	0.693460	−	0.889822i
$215$	−5.60763	−	6.17479i	−0.382437	−	0.421117i
$216$	−11.6337	+	8.51754i	−0.791573	+	0.579545i
$217$	−0.510799	+	0.884731i	−0.0346753	+	0.0600594i
$218$	17.5717	+	19.4676i	1.19010	+	1.31851i
$219$	−1.37177	−	7.77970i	−0.0926958	−	0.525704i
$220$	−12.1288	−	16.4608i	−0.817720	−	1.10979i
$221$	5.53972	−	3.19836i	0.372642	−	0.215145i
$222$	−2.19445	+	6.78194i	−0.147282	+	0.455174i
$223$	−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	$-0.312410\pi$
$224$	−14.3208	+	17.2797i	−0.956851	+	1.15455i
$225$	−7.86093	−	5.60958i	−0.524062	−	0.373972i
$226$	−0.0752950	+	0.0305280i	−0.00500855	+	0.00203069i
$227$			11.4524i			0.760124i	0.924961	+	0.380062i	$0.124097\pi$
$227$			11.4524i			0.760124i	−0.924961	+	0.380062i	$0.875903\pi$
$228$	7.26430	−	5.33297i	0.481090	−	0.353184i
$229$	−1.48570			−0.0981780			−0.0490890	−	0.998794i	$-0.515632\pi$
$229$	−1.48570			−0.0981780			−0.0490890	+	0.998794i	$0.515632\pi$
$230$	6.78513	+	15.0176i	0.447398	+	0.990234i
$231$	−14.3635	−	12.0524i	−0.945047	−	0.792989i
$232$	−5.52783	+	22.5214i	−0.362920	+	1.47861i
$233$	−1.91800	−	5.26965i	−0.125652	−	0.345227i	0.860877	−	0.508814i	$-0.169916\pi$
$233$	−1.91800	−	5.26965i	−0.125652	−	0.345227i	−0.986529	+	0.163587i	$0.947694\pi$
$234$	5.41830	+	1.75321i	0.354205	+	0.114611i
$235$	14.4834	−	9.13626i	0.944792	−	0.595984i
$236$	−0.326701	−	0.481816i	−0.0212664	−	0.0313636i
$237$	1.82851	−	0.322415i	0.118774	−	0.0209431i
$238$	11.5340	+	12.7785i	0.747640	+	0.828306i
$239$	21.7366	+	12.5496i	1.40603	+	0.811769i	0.995002	−	0.0998560i	$-0.0318382\pi$
$239$	21.7366	+	12.5496i	1.40603	+	0.811769i	0.411023	+	0.911625i	$0.365172\pi$
$240$	3.08274	−	8.71674i	0.198990	−	0.562663i
$241$	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	$0.734410\pi$
$242$	−11.0468	−	8.60903i	−0.710114	−	0.553409i
$243$	−5.41607	+	14.8805i	−0.347441	+	0.954587i
$244$	25.1997	−	11.2933i	1.61324	−	0.722979i
$245$	−19.3640	−	2.63735i	−1.23712	−	0.168494i
$246$	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
$250$	15.8079	+	0.330515i	0.999781	+	0.0209036i
$251$	−2.14945	+	5.90557i	−0.135672	+	0.372756i	−0.988860	−	0.148847i	$-0.952444\pi$
$251$	−2.14945	+	5.90557i	−0.135672	+	0.372756i	0.853188	+	0.521603i	$0.174666\pi$
$252$	−1.56478	+	15.2453i	−0.0985717	+	0.960362i
$253$	15.3149	+	18.2515i	0.962837	+	1.14746i
$254$	−9.03360	−	4.78914i	−0.566819	−	0.300497i
$255$	−6.27576	−	3.30266i	−0.393003	−	0.206821i
$256$	−15.9711	−	0.960417i	−0.998197	−	0.0600261i
$257$	−3.78461	−	21.4636i	−0.236077	−	1.33886i	−0.840333	−	0.542070i	$-0.817641\pi$
$257$	−3.78461	−	21.4636i	−0.236077	−	1.33886i	0.604256	−	0.796790i	$-0.293470\pi$
$258$	−0.196957	−	5.44964i	−0.0122620	−	0.339280i
$259$	9.67233	+	16.7530i	0.601009	+	1.04098i
$260$	−8.94542	+	2.63003i	−0.554771	+	0.163108i
$261$	5.41611	+	14.8806i	0.335249	+	0.921088i
$262$	−28.6656	+	6.12958i	−1.77096	+	0.378687i
$263$	−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	$0.989964\pi$
$264$	0.883704	−	13.3383i	0.0543882	−	0.820914i
$265$	0.554088	+	14.1394i	0.0340374	+	0.868577i
$266$	2.46559	−	24.3317i	0.151175	−	1.49187i
$267$	0.660704			0.0404344
$268$	7.86884	−	10.8862i	0.480666	−	0.664983i
$269$	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	$-0.0346208\pi$
$270$	−3.98551	−	15.6199i	−0.242550	−	0.950594i
$271$	0.387915	+	1.06579i	0.0235641	+	0.0647419i	0.950917	−	0.309446i	$-0.100144\pi$
$271$	0.387915	+	1.06579i	0.0235641	+	0.0647419i	−0.927353	+	0.374188i	$0.877921\pi$
$272$	−2.49301	+	12.0165i	−0.151161	+	0.728606i
$273$	−7.40489	+	4.27522i	−0.448164	+	0.258748i
$274$	−1.02084	−	28.2458i	−0.0616710	−	1.70639i
$275$	22.1330	−	5.71915i	1.33467	−	0.344878i
$276$	−2.94440	+	10.3636i	−0.177232	+	0.623818i
$277$	20.3177	+	11.7304i	1.22077	+	0.704814i	0.965083	−	0.261944i	$-0.0843636\pi$
$277$	20.3177	+	11.7304i	1.22077	+	0.704814i	0.255691	+	0.966759i	$0.417697\pi$
$278$	0.729615	+	0.386803i	0.0437594	+	0.0231989i
$279$	−0.380992	+	0.319690i	−0.0228094	+	0.0191394i
$280$	−11.9549	−	22.0607i	−0.714440	−	1.31838i
$281$	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	$0.0873344\pi$
$282$	11.0884	+	1.54459i	0.660303	+	0.0919789i
$283$	−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
$285$	2.50362	+	9.75936i	0.148302	+	0.578094i
$286$	−11.4235	+	7.15758i	−0.675486	+	0.423236i
$287$	21.2656	+	3.74970i	1.25527	+	0.221338i
$288$	−9.42862	+	5.52050i	−0.555587	+	0.325299i
$289$	−7.12928	−	2.59484i	−0.419369	−	0.152638i
$290$	−21.0587	−	15.1244i	−1.23661	−	0.888136i
$291$	−12.1949	−	14.5333i	−0.714879	−	0.851959i
$292$	−1.10334	−	15.2443i	−0.0645678	−	0.892106i
$293$	1.26210	−	2.18602i	0.0737325	−	0.127708i	−0.826802	−	0.562493i	$-0.809842\pi$
$293$	1.26210	−	2.18602i	0.0737325	−	0.127708i	0.900534	+	0.434785i	$0.143176\pi$
$294$	−8.56080	−	9.48446i	−0.499276	−	0.553145i
$295$	0.636041	−	0.138030i	0.0370317	−	0.00803641i
$296$	−5.56334	+	12.6194i	−0.323362	+	0.733490i
$297$	−11.6533	−	20.1841i	−0.676194	−	1.17120i
$298$	20.5302	+	6.64301i	1.18928	+	0.384819i
$299$	10.2097	−	3.71603i	0.590443	−	0.214904i
$300$	7.75732	+	6.83228i	0.447869	+	0.394462i
$301$	−11.3368	−	9.51271i	−0.653443	−	0.548303i
$302$	−6.87404	+	2.78704i	−0.395557	+	0.160376i
$303$			4.84887i			0.278560i
$304$	15.0348	−	8.82913i	0.862307	−	0.506385i
$305$	1.20895	+	30.8503i	0.0692240	+	1.76648i
$306$	3.14882	+	7.76633i	0.180006	+	0.443972i
$307$	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	$0.0285683\pi$
$308$	−25.2639	−	26.0343i	−1.43955	−	1.48344i
$309$	−8.36698	+	3.04533i	−0.475981	+	0.173243i
$310$	0.220157	−	0.783967i	0.0125041	−	0.0445263i
$311$	12.0659	−	6.96627i	0.684196	−	0.395021i	−0.117238	−	0.993104i	$-0.537404\pi$
$311$	12.0659	−	6.96627i	0.684196	−	0.395021i	0.801434	+	0.598083i	$0.204071\pi$
$312$	−5.57785	−	2.45902i	−0.315784	−	0.139215i
$313$	−2.34444	+	0.413387i	−0.132515	+	0.0233660i	−0.239512	−	0.970893i	$-0.576988\pi$
$313$	−2.34444	+	0.413387i	−0.132515	+	0.0233660i	0.106997	+	0.994259i	$0.465876\pi$
$314$	8.45448	+	9.36666i	0.477114	+	0.528591i
$315$	−15.1628	−	7.97952i	−0.854328	−	0.449595i
$316$	3.58296	−	0.259323i	0.201557	−	0.0145881i
$317$	8.65458	−	7.26205i	0.486090	−	0.407878i	−0.366533	−	0.930405i	$-0.619455\pi$
$317$	8.65458	−	7.26205i	0.486090	−	0.407878i	0.852622	+	0.522528i	$0.175011\pi$
$318$	−5.68666	+	7.29691i	−0.318892	+	0.409191i
$319$	−35.2246	−	12.8207i	−1.97220	−	0.717822i
$320$	7.65521	−	16.1678i	0.427939	−	0.903807i
$321$	−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
$325$	1.00128	−	10.3764i	0.0555410	−	0.575579i
$326$	−1.57633	+	11.3163i	−0.0873051	+	0.626750i
$327$	−18.0130	−	6.55619i	−0.996120	−	0.362558i
$328$	6.79914	+	13.8119i	0.375420	+	0.762634i
$329$	23.2745	−	19.5296i	1.28316	−	1.07670i
$330$	13.4685	+	6.47790i	0.741416	+	0.356597i
$331$	−14.6407	+	25.3585i	−0.804727	+	1.39383i	0.111748	+	0.993737i	$0.464355\pi$
$331$	−14.6407	+	25.3585i	−0.804727	+	1.39383i	−0.916475	+	0.400092i	$0.868978\pi$
$332$	11.9364	+	3.39125i	0.655097	+	0.186119i
$333$	1.63536	+	9.27458i	0.0896171	+	0.508244i
$334$	0.308587	+	8.53837i	0.0168851	+	0.467199i
$335$	8.01245	+	12.7018i	0.437767	+	0.693976i
$336$	3.33238	−	16.0623i	0.181797	−	0.876271i
$337$	15.5806	−	5.67086i	0.848727	−	0.308911i	0.119206	−	0.992870i	$-0.461965\pi$
$337$	15.5806	−	5.67086i	0.848727	−	0.308911i	0.729521	+	0.683958i	$0.239743\pi$
$338$	−2.55888	−	11.9668i	−0.139185	−	0.650910i
$339$	0.0381739	−	0.0454939i	0.00207332	−	0.00247089i
$340$	−11.4263	−	7.59627i	−0.619678	−	0.411966i
$341$		−	1.17730i		−	0.0637544i
$342$	5.17936	−	10.7206i	0.280068	−	0.579705i
$343$	−6.90241			−0.372695
$344$	0.697490	−	10.5276i	0.0376061	−	0.567612i
$345$	−9.52347	−	7.37542i	−0.512726	−	0.397079i
$346$	−4.72661	−	22.1044i	−0.254104	−	1.18834i
$347$	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	$0.290861\pi$
$348$	−4.14079	−	16.4370i	−0.221970	−	0.881115i
$349$	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	$0.573927\pi$
$350$	27.8698	−	3.20399i	1.48970	−	0.171260i
$351$	−10.4668	+	1.84558i	−0.558676	+	0.0985097i
$352$	4.33578	−	25.4971i	0.231098	−	1.35900i
$353$	−5.58477	−	3.22437i	−0.297247	−	0.171616i	0.343958	−	0.938985i	$-0.388232\pi$
$353$	−5.58477	−	3.22437i	−0.297247	−	0.171616i	−0.641206	+	0.767369i	$0.721565\pi$
$354$	0.375944	+	0.199306i	0.0199812	+	0.0105930i
$355$	6.91690	+	7.61648i	0.367111	+	0.404241i
$356$	1.27163	+	0.130521i	0.0673964	+	0.00691758i
$357$	−11.8237	−	4.30347i	−0.625776	−	0.227764i
$358$	3.02562	−	21.7205i	0.159909	−	1.14796i
$359$	−21.8079	−	3.84532i	−1.15098	−	0.202948i	−0.434574	−	0.900636i	$-0.643101\pi$
$359$	−21.8079	−	3.84532i	−1.15098	−	0.202948i	−0.716402	+	0.697688i	$0.754212\pi$
$360$	−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
$364$	−15.0965	+	6.76553i	−0.791271	+	0.354610i
$365$	16.2742	+	5.21126i	0.851832	+	0.272770i
$366$	−12.4075	+	15.9209i	−0.648552	+	0.832198i
$367$	−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	$0.467992\pi$
$368$	−7.71430	+	19.3649i	−0.402136	+	1.00946i
$369$	9.10412	+	5.25627i	0.473942	+	0.273630i
$370$	−10.7717	−	11.0328i	−0.559993	−	0.573567i
$371$	4.35963	+	24.7247i	0.226341	+	1.28364i
$372$	0.440624	−	0.298770i	0.0228453	−	0.0154905i
$373$	−14.6160	−	25.3156i	−0.756787	−	1.31079i	−0.944481	−	0.328565i	$-0.893435\pi$
$373$	−14.6160	−	25.3156i	−0.756787	−	1.31079i	0.187695	−	0.982227i	$-0.439898\pi$
$374$	−18.8742	−	6.10716i	−0.975959	−	0.315794i
$375$	−10.3220	+	5.19873i	−0.533025	+	0.268461i
$376$	21.0362	+	5.16330i	1.08486	+	0.266277i
$377$	−10.9878	+	13.0947i	−0.565900	+	0.674414i
$378$	−10.7466	−	26.5057i	−0.552746	−	1.36331i
$379$	7.88618			0.405086			0.202543	−	0.979273i	$-0.435079\pi$
$379$	7.88618			0.405086			0.202543	+	0.979273i	$0.435079\pi$
$380$	2.89069	+	19.2781i	0.148289	+	0.988944i
$381$	7.47359			0.382884
$382$	0.224669	+	0.554129i	0.0114951	+	0.0283517i
$383$	−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	$0.265717\pi$
$384$	10.6430	−	4.84781i	0.543126	−	0.247389i
$385$	37.5409	−	15.3539i	1.91326	−	0.782507i
$386$	8.17043	+	2.64373i	0.415864	+	0.134562i
$387$	−3.60237	−	6.23949i	−0.183119	−	0.317171i
$388$	−20.6001	−	30.3809i	−1.04581	−	1.54235i
$389$	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	$0.726539\pi$
$390$	4.87654	−	4.76114i	0.246933	−	0.241089i
$391$	13.8464	+	7.99424i	0.700244	+	0.404286i
$392$	−14.6030	−	19.9456i	−0.737564	−	1.00740i
$393$	16.4137	−	13.7728i	0.827963	−	0.694744i
$394$	−8.07614	+	10.3630i	−0.406870	+	0.522080i
$395$	−1.22483	+	3.82502i	−0.0616280	+	0.192458i
$396$	−7.22272	−	16.1167i	−0.362956	−	0.809892i
$397$	2.57500	+	0.454043i	0.129236	+	0.0227877i	0.237892	−	0.971292i	$-0.423544\pi$
$397$	2.57500	+	0.454043i	0.129236	+	0.0227877i	−0.108656	+	0.994079i	$0.534655\pi$
$398$	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	$0.519511\pi$
$402$	−1.35459	+	9.72443i	−0.0675611	+	0.485011i
$403$	−0.504493	−	0.183621i	−0.0251306	−	0.00914679i
$404$	−0.957883	+	9.33244i	−0.0476565	+	0.464306i
$405$	−0.788897	−	0.868687i	−0.0392006	−	0.0431654i
$406$	−40.6429	−	21.5467i	−2.01707	−	1.06935i
$407$	−19.3063	−	11.1465i	−0.956976	−	0.552511i
$408$	−2.50410	−	8.61382i	−0.123971	−	0.426448i
$409$	−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	$0.592770\pi$
$410$	−17.1630	+	1.29470i	−0.847622	+	0.0639408i
$411$	10.3298	+	17.8917i	0.509531	+	0.882534i
$412$	−16.7052	+	4.20836i	−0.823007	+	0.207331i
$413$	1.08512	−	0.394952i	0.0533954	−	0.0194343i
$414$	2.97644	+	13.9196i	0.146284	+	0.684111i
$415$	−8.49472	+	10.9688i	−0.416990	+	0.538435i
$416$	−10.2497	−	5.83468i	−0.502534	−	0.286069i
$417$	−0.603618			−0.0295593
$418$	11.5594	+	25.7041i	0.565387	+	1.25723i
$419$		−	1.56858i		−	0.0766301i	−0.999266	−	0.0383151i	$-0.987801\pi$
$419$		−	1.56858i		−	0.0766301i	0.999266	−	0.0383151i	$-0.0121990\pi$
$420$	15.2734	+	10.1539i	0.745267	+	0.495458i
$421$	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	$0.121497\pi$
$422$	4.51454	+	21.1127i	0.219765	+	1.02775i
$423$	13.8993	−	5.05894i	0.675808	−	0.245974i
$424$	−12.3864	+	12.9207i	−0.601537	+	0.627486i
$425$	12.6443	−	8.68634i	0.613336	−	0.421349i
$426$	0.242942	+	6.72202i	0.0117706	+	0.325683i
$427$	9.51212	+	53.9459i	0.460324	+	2.61063i
$428$	−6.37835	+	22.4504i	−0.308309	+	1.08518i
$429$	4.92680	−	8.53346i	0.237868	−	0.411999i
$430$	10.6304	+	5.11288i	0.512644	+	0.246565i
$431$	21.4377	−	17.9884i	1.03262	−	0.866469i	0.0414579	−	0.999140i	$-0.486800\pi$
$431$	21.4377	−	17.9884i	1.03262	−	0.866469i	0.991160	+	0.132671i	$0.0423553\pi$
$432$	10.7210	−	17.3448i	0.515815	−	0.834503i
$433$	7.43239	+	2.70517i	0.357178	+	0.130002i	0.514375	−	0.857565i	$-0.328024\pi$
$433$	7.43239	+	2.70517i	0.357178	+	0.130002i	−0.157198	+	0.987567i	$0.550246\pi$
$434$	0.199328	−	1.43094i	0.00956803	−	0.0686874i
$435$	18.7779	+	2.55752i	0.900332	+	0.122624i
$436$	−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	$0.342252\pi$
$439$	−5.70310	+	32.3439i	−0.272194	+	1.54369i	−0.747735	+	0.663997i	$0.768859\pi$
$440$	24.6426	+	15.1284i	1.17479	+	0.721220i
$441$	−15.8624	−	5.77344i	−0.755352	−	0.274926i
$442$	−5.56078	+	7.13538i	−0.264499	+	0.339396i
$443$	−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	$0.958489\pi$
$444$	−0.727707	−	10.0544i	−0.0345354	−	0.477161i
$445$	−0.665585	+	1.26475i	−0.0315518	+	0.0599551i
$446$	16.7280	+	18.5328i	0.792092	+	0.877554i
$447$	−15.5328	+	2.73886i	−0.734678	+	0.129544i
$448$	9.58680	−	30.2563i	0.452934	−	1.42947i
$449$	−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	$0.487191\pi$
$450$	13.2832	+	3.17478i	0.626177	+	0.149660i
$451$	−23.3840	+	8.51107i	−1.10111	+	0.400771i
$452$	0.0824592	−	0.0800193i	0.00387855	−	0.00376379i
$453$	3.48508	−	4.15335i	0.163743	−	0.195142i
$454$	−6.08549	−	15.0094i	−0.285606	−	0.704427i
$455$	−0.724249	−	18.4816i	−0.0339533	−	0.866432i
$456$	−6.68672	+	10.8494i	−0.313134	+	0.508068i
$457$			7.37551i			0.345012i	0.985008	+	0.172506i	$0.0551864\pi$
$457$			7.37551i			0.345012i	−0.985008	+	0.172506i	$0.944814\pi$
$458$	1.94715	−	0.789460i	0.0909842	−	0.0368891i
$459$	−11.9811	−	10.0533i	−0.559228	−	0.469248i
$460$	−16.8725	−	16.0765i	−0.786683	−	0.749572i
$461$	−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	$0.440156\pi$
$462$	25.2289	+	8.16339i	1.17375	+	0.379795i
$463$	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	$0.798409\pi$
$464$	−4.72253	−	32.4537i	−0.219238	−	1.50662i
$465$	0.126229	+	0.581664i	0.00585374	+	0.0269740i
$466$	5.31385	+	5.88718i	0.246159	+	0.272718i
$467$	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	$-0.0420862\pi$
$468$	−8.03278	+	0.581387i	−0.371315	+	0.0268746i
$469$	17.1274	+	20.4116i	0.790868	+	0.942519i
$470$	−14.1270	+	19.6699i	−0.651631	+	0.907307i
$471$	−8.66680	−	3.15446i	−0.399345	−	0.145350i
$472$	0.684194	+	0.457864i	0.0314926	+	0.0210749i
$473$	16.7956	+	2.96151i	0.772261	+	0.136170i
$474$	−2.22510	+	1.39417i	−0.102202	+	0.0640364i
$475$	−21.2040	−	5.03889i	−0.972906	−	0.231200i
$476$	−21.9065	−	10.6185i	−1.00408	−	0.486697i
$477$	−2.12242	+	12.0368i	−0.0971789	+	0.551129i
$478$	−35.1563	−	4.89721i	−1.60801	−	0.223993i
$479$	6.46310	−	17.7572i	0.295307	−	0.811348i	−0.699961	−	0.714181i	$-0.746799\pi$
$479$	6.46310	−	17.7572i	0.295307	−	0.811348i	0.995268	−	0.0971677i	$-0.0309783\pi$
$480$	0.591620	+	13.0621i	0.0270037	+	0.596203i
$481$	−7.78761	+	6.53458i	−0.355085	+	0.297951i
$482$	−5.26912	−	2.79341i	−0.240002	−	0.127236i
$483$	−18.5084	−	10.6858i	−0.842161	−	0.486222i
$484$	19.0524	+	5.41295i	0.866017	+	0.246043i
$485$	40.1055	−	8.70345i	1.82110	−	0.395203i
$486$	−0.808848	−	22.3802i	−0.0366901	−	1.01519i
$487$	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	$0.0544595\pi$
$488$	−27.0255	+	28.1913i	−1.22339	+	1.27616i
$489$	−2.85636	−	7.84778i	−0.129169	−	0.354889i
$490$	26.7797	−	6.83301i	1.20978	−	0.308684i
$491$	−23.7768	+	28.3361i	−1.07303	+	1.27879i	−0.114618	+	0.993410i	$0.536564\pi$
$491$	−23.7768	+	28.3361i	−1.07303	+	1.27879i	−0.958414	+	0.285380i	$0.907880\pi$
$492$	−9.11970	−	6.59194i	−0.411148	−	0.297188i
$493$	−25.1549			−1.13292
$494$	12.8176	−	0.944374i	0.576689	−	0.0424894i
$495$	19.7306	−	0.773191i	0.886823	−	0.0347524i
$496$	0.907075	−	0.487988i	0.0407289	−	0.0219113i
$497$	13.9837	+	11.7337i	0.627256	+	0.526330i
$498$	−8.86966	+	1.89661i	−0.397459	+	0.0849890i
$499$	−14.0038	−	38.4750i	−0.626894	−	1.72238i	−0.689447	−	0.724336i	$-0.742146\pi$
$499$	−14.0038	−	38.4750i	−0.626894	−	1.72238i	0.0625524	−	0.998042i	$-0.480076\pi$
$500$	−20.8933	+	7.96672i	−0.934378	+	0.356282i
$501$	−3.12258	−	5.40846i	−0.139506	−	0.241632i
$502$	−0.321004	−	8.88193i	−0.0143271	−	0.396420i
$503$	−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	$-0.135474\pi$
$504$	−6.05012	−	20.8118i	−0.269494	−	0.927030i
$505$	−9.28196	−	4.88469i	−0.413042	−	0.217366i
$506$	−29.7698	−	15.7824i	−1.32343	−	0.701613i
$507$	5.74963	+	6.85214i	0.255350	+	0.304314i
$508$	14.3842	+	1.47639i	0.638194	+	0.0655043i
$509$	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	$-0.0904675\pi$
$510$	9.97989	+	0.993668i	0.441917	+	0.0440004i
$511$	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
$515$	2.59926	−	19.0844i	0.114537	−	0.840957i
$516$	3.15391	+	7.03759i	0.138843	+	0.309812i
$517$	−11.9752	+	32.9017i	−0.526671	+	1.44702i
$518$	−21.5785	−	16.8167i	−0.948105	−	0.738882i
$519$	10.6204	+	12.6569i	0.466182	+	0.555574i
$520$	10.3262	−	8.20024i	0.452836	−	0.359604i
$521$	−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	$0.877150\pi$
$522$	−15.0054	−	16.6244i	−0.656770	−	0.727631i
$523$	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	$0.365700\pi$
$524$	34.3117	−	23.2654i	1.49891	−	1.01635i
$525$	−16.9015	+	11.6109i	−0.737640	+	0.506743i
$526$	32.5304	+	10.5260i	1.41839	+	0.458954i
$527$	−0.270210	−	0.742395i	−0.0117705	−	0.0323392i
$528$	5.92941	+	17.9506i	0.258044	+	0.781199i
$529$	3.18427	+	2.67192i	0.138446	+	0.116170i
$530$	−8.23946	−	18.2365i	−0.357899	−	0.792145i
$531$	0.562179			0.0243965
$532$	9.69781	+	33.1991i	0.420454	+	1.43936i
$533$			11.3479i			0.491532i
$534$	−0.865911	+	0.351079i	−0.0374717	+	0.0151927i
$535$	−20.6303	−	15.9771i	−0.891927	−	0.690750i
$536$	−4.52818	+	18.4487i	−0.195588	+	0.796861i
$537$	5.48250	+	15.0630i	0.236587	+	0.650018i
$538$	−10.3132	+	31.8730i	−0.444635	+	1.37414i
$539$	34.6050	−	19.9792i	1.49054	−	0.860565i
$540$	13.5233	+	18.3534i	0.581951	+	0.789806i
$541$	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	$0.848110\pi$
$542$	−1.07473	−	1.19068i	−0.0461634	−	0.0511441i
$543$	−9.94251	+	17.2209i	−0.426674	+	0.739021i
$544$	−3.11790	−	17.0734i	−0.133679	−	0.732015i
$545$	30.6963	−	27.8768i	1.31488	−	1.19411i
$546$	7.43304	−	9.53780i	0.318105	−	0.408180i
$547$	−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	$0.115134\pi$
$548$	16.3469	+	36.4762i	0.698305	+	1.55819i
$549$	−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
$554$	−32.8614	−	4.57753i	−1.39615	−	0.194481i
$555$	10.7337	+	3.43709i	0.455620	+	0.145897i
$556$	−1.16176	−	0.119243i	−0.0492696	−	0.00505705i
$557$	9.63929	+	11.4877i	0.408430	+	0.486748i	0.930571	−	0.366111i	$-0.119311\pi$
$557$	9.63929	+	11.4877i	0.408430	+	0.486748i	−0.522141	+	0.852859i	$0.674867\pi$
$558$	0.329450	−	0.621431i	0.0139467	−	0.0263073i
$559$	3.88862	−	6.73529i	0.164471	−	0.284873i
$560$	27.3903	+	22.5600i	1.15745	+	0.953334i
$561$	14.2799	−	2.51793i	0.602898	−	0.106307i
$562$	0.127795	+	3.53600i	0.00539071	+	0.149157i
$563$	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	$0.254521\pi$
$564$	−15.3530	+	3.86772i	−0.646480	+	0.162860i
$565$	0.0486309	+	0.118905i	0.00204592	+	0.00500235i
$566$	−1.40707	−	6.58028i	−0.0591434	−	0.276590i
$567$	−1.59489	−	1.33827i	−0.0669793	−	0.0562023i
$568$	−0.860340	+	12.9856i	−0.0360991	+	0.544865i
$569$		−	34.7145i		−	1.45531i	−0.685945	−	0.727654i	$-0.740611\pi$
$569$		−	34.7145i		−	1.45531i	0.685945	−	0.727654i	$-0.259389\pi$
$570$	−8.46706	−	11.4602i	−0.354646	−	0.480013i
$571$		−	17.7069i		−	0.741009i	−0.928831	−	0.370505i	$-0.879185\pi$
$571$		−	17.7069i		−	0.741009i	0.928831	−	0.370505i	$-0.120815\pi$
$572$	11.1682	−	15.4508i	0.466966	−	0.646029i
$573$	−0.334810	−	0.280939i	−0.0139869	−	0.0117364i
$574$	−29.8629	+	6.38562i	−1.24645	+	0.266530i
$575$	23.7122	−	10.8004i	0.988869	−	0.450409i
$576$	9.42361	−	12.2452i	0.392650	−	0.510217i
$577$	−32.1774	+	18.5777i	−1.33956	+	0.773398i	−0.986743	−	0.162293i	$-0.948111\pi$
$577$	−32.1774	+	18.5777i	−1.33956	+	0.773398i	−0.352822	+	0.935691i	$0.614778\pi$
$578$	10.7224	−	0.387519i	0.445992	−	0.0161187i
$579$	−6.18163	+	1.08999i	−0.256900	+	0.0452983i
$580$	35.6359	+	8.63191i	1.47970	+	0.358420i
$581$	−12.3075	+	21.3173i	−0.510602	+	0.884389i
$582$	23.7051	+	12.5672i	0.982609	+	0.520927i
$583$	−18.5975	−	22.1636i	−0.770228	−	0.917922i
$584$	9.54641	+	19.3927i	0.395033	+	0.802477i
$585$	2.74600	−	8.57548i	0.113533	−	0.354552i
$586$	−0.492504	+	3.53561i	−0.0203452	+	0.146055i
$587$	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
$592$	0.585635	−	19.4951i	0.0240695	−	0.801244i
$593$	1.55303	−	4.26691i	0.0637752	−	0.175221i	−0.903712	−	0.428141i	$-0.859169\pi$
$593$	1.55303	−	4.26691i	0.0637752	−	0.175221i	0.967487	+	0.252920i	$0.0813909\pi$
$594$	25.9980	+	20.2609i	1.06671	+	0.831314i
$595$	20.1490	−	18.2983i	0.826028	−	0.750156i
$596$	−30.4365	+	2.20290i	−1.24673	+	0.0902344i
$597$	−7.28766	+	12.6226i	−0.298264	+	0.516608i
$598$	−11.4062	+	10.2953i	−0.466432	+	0.421008i
$599$	−0.980322	−	5.55968i	−0.0400549	−	0.227162i	0.958209	−	0.286071i	$-0.0923492\pi$
$599$	−0.980322	−	5.55968i	−0.0400549	−	0.227162i	−0.998263	+	0.0589082i	$0.981238\pi$
$600$	−13.7971	−	4.83229i	−0.563266	−	0.197277i
$601$	−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	$0.623858\pi$
$602$	19.9127	+	6.44320i	0.811580	+	0.262605i
$603$	4.43666	+	12.1896i	0.180675	+	0.496400i
$604$	7.52809	−	7.30534i	0.306314	−	0.297250i
$605$	−13.5589	+	17.5078i	−0.551246	+	0.711794i
$606$	−2.57655	−	6.35487i	−0.104665	−	0.258149i
$607$			4.10304i			0.166537i	0.996527	+	0.0832686i	$0.0265359\pi$
$607$			4.10304i			0.166537i	−0.996527	+	0.0832686i	$0.973464\pi$
$608$	−15.0130	+	19.5604i	−0.608856	+	0.793281i
$609$	33.6243			1.36253
$610$	−17.9774	−	39.7897i	−0.727884	−	1.61104i
$611$	12.2312	+	10.2632i	0.494822	+	0.415205i
$612$	−8.25362	−	8.50528i	−0.333633	−	0.343806i
$613$	−10.9979	−	30.2165i	−0.444202	−	1.22043i	−0.936704	−	0.350123i	$-0.886140\pi$
$613$	−10.9979	−	30.2165i	−0.444202	−	1.22043i	0.492502	−	0.870312i	$-0.336083\pi$
$614$	−8.71989	+	26.9488i	−0.351906	+	1.08756i
$615$	10.6407	−	6.71225i	0.429074	−	0.270664i
$616$	46.9445	+	20.6957i	1.89145	+	0.833853i
$617$	−24.8937	+	4.38943i	−1.00218	+	0.176712i	−0.650580	−	0.759438i	$-0.725474\pi$
$617$	−24.8937	+	4.38943i	−1.00218	+	0.176712i	−0.351602	+	0.936150i	$0.614363\pi$
$618$	9.34747	−	8.43716i	0.376011	−	0.339392i
$619$	−14.5190	−	8.38253i	−0.583567	−	0.336922i	0.178983	−	0.983852i	$-0.442719\pi$
$619$	−14.5190	−	8.38253i	−0.583567	−	0.336922i	−0.762550	+	0.646930i	$0.776053\pi$
$620$	0.128042	+	1.14444i	0.00514230	+	0.0459620i
$621$	−17.0757	−	20.3501i	−0.685226	−	0.816621i
$622$	−12.1118	+	15.5414i	−0.485639	+	0.623154i
$623$	−0.867279	+	2.38283i	−0.0347468	+	0.0954660i
$624$	8.61693	+	0.258854i	0.344953	+	0.0103624i
$625$	0.446555	−	24.9960i	0.0178622	−	0.999840i
$626$	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
$630$	24.1123	+	2.40079i	0.960657	+	0.0956499i
$631$	6.84502	−	18.8065i	0.272496	−	0.748677i	−0.725664	−	0.688049i	$-0.758467\pi$
$631$	6.84502	−	18.8065i	0.272496	−	0.748677i	0.998160	−	0.0606280i	$-0.0193103\pi$
$632$	−4.55799	+	2.24375i	−0.181307	+	0.0892515i
$633$	−10.1439	−	12.0890i	−0.403183	−	0.480495i
$634$	−7.48375	+	14.1164i	−0.297218	+	0.560633i
$635$	−7.52880	+	14.3063i	−0.298771	+	0.567730i
$636$	3.57551	−	12.5850i	0.141778	−	0.499027i
$637$	−3.16418	−	17.9449i	−0.125369	−	0.711005i
$638$	52.9776	−	1.91467i	2.09740	−	0.0758026i
$639$	4.44345	+	7.69628i	0.175780	+	0.304460i
$640$	−1.44173	+	25.2571i	−0.0569893	+	0.998375i
$641$	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	$0.697898\pi$
$642$	−3.56719	−	16.6823i	−0.140786	−	0.658398i
$643$	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	$0.701726\pi$
$644$	−33.5115	−	24.2229i	−1.32054	−	0.954517i
$645$	−8.61565	+	0.337626i	−0.339241	+	0.0132940i
$646$	13.1887	+	13.5557i	0.518904	+	0.533343i
$647$	−3.62076			−0.142347			−0.0711733	−	0.997464i	$-0.522674\pi$
$647$	−3.62076			−0.142347			−0.0711733	+	0.997464i	$0.522674\pi$
$648$	0.0981249	−	1.48106i	0.00385471	−	0.0581815i
$649$	−0.855396	+	1.01942i	−0.0335772	+	0.0400158i
$650$	4.20145	+	14.1312i	0.164795	+	0.554273i
$651$	0.361186	+	0.992352i	0.0141560	+	0.0388933i
$652$	−3.94722	−	15.6686i	−0.154585	−	0.613630i
$653$	28.0083	−	16.1706i	1.09605	−	0.632805i	0.160870	−	0.986976i	$-0.448570\pi$
$653$	28.0083	−	16.1706i	1.09605	−	0.632805i	0.935181	+	0.354170i	$0.115237\pi$
$654$	27.0914	−	0.979115i	1.05936	−	0.0382864i
$655$	9.82955	+	45.2945i	0.384072	+	1.76980i
$656$	−16.2501	−	14.4889i	−0.634461	−	0.565695i
$657$	12.7827	+	7.38012i	0.498702	+	0.287926i
$658$	−20.1258	+	37.9627i	−0.784586	+	1.47994i
$659$	−27.5520	+	23.1188i	−1.07327	+	0.900582i	−0.995345	−	0.0963770i	$-0.969275\pi$
$659$	−27.5520	+	23.1188i	−1.07327	+	0.900582i	−0.0779270	+	0.996959i	$0.524830\pi$
$660$	−21.0938	−	1.33310i	−0.821076	−	0.0518908i
$661$	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	$-0.290245\pi$
$662$	5.71320	−	41.0142i	0.222050	−	1.59406i
$663$	1.14822	−	6.51191i	0.0445933	−	0.252901i
$664$	−17.4458	+	1.89815i	−0.677028	+	0.0736625i
$665$	−38.4835	−	3.78140i	−1.49233	−	0.146636i
$666$	−7.07153	−	11.2862i	−0.274016	−	0.437331i
$667$	−42.0770	−	7.41931i	−1.62923	−	0.287277i
$668$	−4.94148	−	11.0263i	−0.191192	−	0.426621i
$669$	−17.1481	−	6.24139i	−0.662983	−	0.241306i
$670$	−17.2504	−	12.3893i	−0.666442	−	0.478641i
$671$	−40.5771	−	48.3579i	−1.56646	−	1.86684i
$672$	4.16767	+	22.8218i	0.160771	+	0.880371i
$673$	−7.23324	+	12.5283i	−0.278821	+	0.482932i	−0.971092	−	0.238705i	$-0.923277\pi$
$673$	−7.23324	+	12.5283i	−0.278821	+	0.482932i	0.692271	+	0.721638i	$0.256610\pi$
$674$	−17.4064	+	15.7112i	−0.670469	+	0.605174i
$675$	−24.6779	+	6.37674i	−0.949852	+	0.245441i
$676$	9.71247	+	14.3239i	0.373557	+	0.550919i
$677$	18.0848	+	31.3239i	0.695057	+	1.20387i	0.970161	+	0.242460i	$0.0779542\pi$
$677$	18.0848	+	31.3239i	0.695057	+	1.20387i	−0.275104	+	0.961414i	$0.588712\pi$
$678$	−0.0258562	+	0.0799084i	−0.000993000	+	0.00306886i
$679$	68.4222	−	24.9037i	2.62580	−	0.955715i
$680$	19.0116	+	3.88398i	0.729063	+	0.148944i
$681$	9.06882	+	7.60964i	0.347518	+	0.291602i
$682$	0.625584	+	1.54296i	0.0239548	+	0.0590829i
$683$			35.2724i			1.34966i	0.737973	+	0.674830i	$0.235783\pi$
$683$			35.2724i			1.34966i	−0.737973	+	0.674830i	$0.764217\pi$
$684$	−1.09138	+	16.8025i	−0.0417299	+	0.642460i
$685$	−44.6554	+	1.74993i	−1.70620	+	0.0668615i
$686$	9.04622	−	3.66774i	0.345386	−	0.140035i
$687$	−0.987186	+	1.17648i	−0.0376635	+	0.0448856i
$688$	4.67996	+	14.1680i	0.178422	+	0.540151i
$689$	−12.3981	+	4.51253i	−0.472329	+	0.171914i
$690$	16.4004	+	4.60564i	0.624354	+	0.175334i
$691$	−16.0220	+	9.25033i	−0.609507	+	0.351899i	−0.772773	−	0.634683i	$-0.781131\pi$
$691$	−16.0220	+	9.25033i	−0.609507	+	0.351899i	0.163265	+	0.986582i	$0.447797\pi$
$692$	17.9403	+	26.4582i	0.681988	+	1.00579i
$693$	34.5016	−	6.08356i	1.31061	−	0.231095i
$694$	−11.8554	+	10.7009i	−0.450026	+	0.406200i
$695$	0.608077	−	1.15548i	0.0230657	−	0.0438297i
$696$	14.1610	+	19.3419i	0.536772	+	0.733151i
$697$	−12.7923	+	10.7340i	−0.484543	+	0.406580i
$698$	−30.3284	−	23.6357i	−1.14795	−	0.894625i
$699$	−5.44730	−	1.98266i	−0.206036	−	0.0749909i
$700$	−34.8233	+	19.0083i	−1.31620	+	0.718447i
$701$	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
$705$	2.38886	−	17.5396i	0.0899698	−	0.660579i
$706$	9.03267	+	1.25823i	0.339949	+	0.0473543i
$707$	−17.4874	−	6.36491i	−0.657683	−	0.239377i
$708$	−0.598614	−	0.0614419i	−0.0224973	−	0.00230913i
$709$	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	$0.104815\pi$
$710$	−13.1124	−	6.30663i	−0.492099	−	0.236684i
$711$	−1.73459	+	3.00440i	−0.0650523	+	0.112674i
$712$	−1.73594	+	0.504651i	−0.0650572	+	0.0189126i
$713$	−0.233018	−	1.32151i	−0.00872660	−	0.0494910i
$714$	17.7828	−	0.642690i	0.665503	−	0.0240521i
$715$	11.3720	+	18.0276i	0.425289	+	0.674196i
$716$	7.57630	+	30.0744i	0.283140	+	1.12393i
$717$	24.3807	−	8.87386i	0.910515	−	0.331400i
$718$	30.6245	−	6.54846i	1.14290	−	0.244386i
$719$	−26.5671	+	31.6614i	−0.990785	+	1.18077i	−0.00726446	+	0.999974i	$0.502312\pi$
$719$	−26.5671	+	31.6614i	−0.990785	+	1.18077i	−0.983520	+	0.180798i	$0.942132\pi$
$720$	8.77399	+	14.8813i	0.326987	+	0.554594i
$721$		−	34.1730i		−	1.27267i
$722$	1.70692	−	26.8158i	0.0635251	−	0.997980i
$723$	4.35919			0.162120
$724$	−22.5380	+	31.1804i	−0.837616	+	1.15881i
$725$	−23.8124	+	33.3693i	−0.884370	+	1.23930i
$726$	−14.1573	+	3.02727i	−0.525428	+	0.112353i
$727$	−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	$0.519587\pi$
$728$	16.1903	−	16.8887i	0.600052	−	0.625936i
$729$	7.39752	+	12.8129i	0.273982	+	0.474551i
$730$	−24.0979	+	1.81784i	−0.891905	+	0.0672813i
$731$	11.2709	−	1.98736i	0.416867	−	0.0735050i
$732$	7.80128	−	27.4587i	0.288344	−	1.01490i
$733$	−30.6070	−	17.6710i	−1.13049	−	0.652692i	−0.186436	−	0.982467i	$-0.559694\pi$
$733$	−30.6070	−	17.6710i	−1.13049	−	0.652692i	−0.944059	+	0.329776i	$0.893027\pi$
$734$	14.2798	−	26.9355i	0.527076	−	0.994208i
$735$	−14.9550	+	13.5814i	−0.551623	+	0.500956i
$736$	−0.179656	−	29.4785i	−0.00662219	−	1.08659i
$737$	−28.8546	−	10.5022i	−1.06287	−	0.386854i
$738$	−14.7248	−	2.05114i	−0.542027	−	0.0755034i
$739$	30.7103	+	5.41506i	1.12970	+	0.199196i	0.707095	−	0.707119i	$-0.250006\pi$
$739$	30.7103	+	5.41506i	1.12970	+	0.199196i	0.422603	+	0.906315i	$0.361117\pi$
$740$	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	$0.520649\pi$
$744$	−0.418719	+	0.625700i	−0.0153510	+	0.0229393i
$745$	10.4047	−	32.4929i	0.381199	−	1.19045i
$746$	32.6075	+	25.4119i	1.19385	+	0.930394i
$747$	−9.17987	+	7.70282i	−0.335874	+	0.281832i
$748$	27.9814	−	2.02521i	1.02310	−	0.0740490i
$749$	−40.0941	−	23.1483i	−1.46501	−	0.845821i
$750$	10.7654	−	12.2982i	0.393097	−	0.449067i
$751$	−3.87069	−	21.9518i	−0.141244	−	0.801032i	−0.970307	−	0.241877i	$-0.922237\pi$
$751$	−3.87069	−	21.9518i	−0.141244	−	0.801032i	0.829063	−	0.559155i	$-0.188874\pi$
$752$	−30.3135	+	4.41110i	−1.10542	+	0.160856i
$753$	3.24822	+	5.62608i	0.118372	+	0.205026i
$754$	7.44231	−	23.0004i	0.271033	−	0.837627i
$755$	4.43975	+	10.8554i	0.161579	+	0.395067i
$756$	28.1688	+	29.0277i	1.02449	+	1.05573i
$757$	2.83015	−	3.37284i	0.102863	−	0.122588i	−0.712157	−	0.702021i	$-0.752281\pi$
$757$	2.83015	−	3.37284i	0.102863	−	0.122588i	0.815020	+	0.579433i	$0.196726\pi$
$758$	−10.3355	+	4.19049i	−0.375404	+	0.152205i
$759$	24.6289			0.893972
$760$	−14.0323	−	23.7296i	−0.509006	−	0.860763i
$761$	13.2216			0.479284			0.239642	−	0.970861i	$-0.422970\pi$
$761$	13.2216			0.479284			0.239642	+	0.970861i	$0.422970\pi$
$762$	−9.79481	+	3.97125i	−0.354828	+	0.143863i
$763$	47.2898	−	56.3578i	1.71201	−	2.04029i
$764$	−0.588897	−	0.606853i	−0.0213056	−	0.0219552i
$765$	12.2645	−	5.01605i	0.443422	−	0.181356i
$766$	2.32128	−	7.17391i	0.0838714	−	0.259204i
$767$	0.303425	+	0.525548i	0.0109561	+	0.0189765i
$768$	−11.3727	+	12.0089i	−0.410376	+	0.433334i
$769$	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	$0.839982\pi$
$770$	−41.0421	+	40.0708i	−1.47905	+	1.44405i
$771$	−19.5110	−	11.2647i	−0.702673	−	0.405688i
$772$	−12.1129	+	0.876692i	−0.435952	+	0.0315529i
$773$	−13.6644	+	11.4658i	−0.491474	+	0.412395i	−0.854554	−	0.519363i	$-0.826169\pi$
$773$	−13.6644	+	11.4658i	−0.491474	+	0.412395i	0.363080	+	0.931758i	$0.381725\pi$
$774$	8.03671	+	6.26321i	0.288874	+	0.225126i
$775$	−1.24061	−	0.344326i	−0.0445642	−	0.0123686i
$776$	43.1418	+	28.8705i	1.54870	+	1.03639i
$777$	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
$782$	−22.3949	−	3.11957i	−0.800840	−	0.111555i
$783$	39.2747	+	14.2948i	1.40356	+	0.510856i
$784$	29.7371	+	18.3808i	1.06204	+	0.656457i
$785$	14.7693	−	13.4127i	0.527138	−	0.478719i
$786$	−14.1932	+	26.7722i	−0.506255	+	0.954933i
$787$	−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	$0.676417\pi$
$788$	5.07790	−	17.8731i	0.180893	−	0.636702i
$789$	−24.6121	+	4.33977i	−0.876212	+	0.154500i
$790$	−0.427257	−	5.66388i	−0.0152011	−	0.201512i
$791$	0.113964	+	0.197392i	0.00405211	+	0.00701846i
$792$	18.0300	+	17.2844i	0.640667	+	0.614173i
$793$	−27.0509	+	9.84573i	−0.960607	+	0.349632i
$794$	−3.61604	+	0.773220i	−0.128328	+	0.0274406i
$795$	11.5647	+	8.95627i	0.410159	+	0.317646i
$796$	−16.5199	+	22.8546i	−0.585531	+	0.810059i
$797$	33.0094			1.16925			0.584626	−	0.811303i	$-0.301241\pi$
$797$	33.0094			1.16925			0.584626	+	0.811303i	$0.301241\pi$
$798$	−17.6293	−	18.1198i	−0.624069	−	0.641435i
$799$			23.4960i			0.831230i
$800$	−25.6002	−	12.0261i	−0.905105	−	0.425188i
$801$	−0.793517	+	0.945677i	−0.0280375	+	0.0334138i
$802$	−6.25846	+	1.33825i	−0.220994	+	0.0472553i
$803$	−32.8325	+	11.9501i	−1.15863	+	0.421709i
$804$	−3.39197	−	13.4645i	−0.119626	−	0.474857i
$805$	39.1005	−	24.6650i	1.37811	−	0.869326i
$806$	0.758754	−	0.0274223i	0.0267260	−	0.000965909i
$807$	−4.25206	−	24.1146i	−0.149680	−	0.848875i
$808$	−3.70360	−	12.7400i	−0.130292	−	0.448191i
$809$	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	$0.150503\pi$
$810$	1.49552	+	0.719294i	0.0525471	+	0.0252734i
$811$	7.26322	−	6.09456i	0.255046	−	0.214009i	−0.506296	−	0.862360i	$-0.668985\pi$
$811$	7.26322	−	6.09456i	0.255046	−	0.214009i	0.761342	+	0.648351i	$0.224541\pi$
$812$	64.7155	+	6.64241i	2.27107	+	0.233103i
$813$	1.10172	+	0.400992i	0.0386389	+	0.0140634i
$814$	31.2255	+	4.34965i	1.09445	+	0.152455i
$815$	17.9001	+	2.43796i	0.627013	+	0.0853981i
$816$	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
$820$	21.8057	−	10.8168i	0.761489	−	0.377738i
$821$	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	$0.468119\pi$
$822$	−23.0453	−	17.9597i	−0.803796	−	0.626418i
$823$	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	$0.115817\pi$
$824$	19.6575	−	14.3921i	0.684801	−	0.501373i
$825$	10.1776	−	21.3266i	0.354340	−	0.742497i
$826$	−1.21228	+	1.09422i	−0.0421807	+	0.0380729i
$827$	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	$0.373639\pi$
$828$	−11.2974	−	16.6613i	−0.392611	−	0.579020i
$829$	−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	$0.363852\pi$
$830$	5.30460	−	18.8894i	0.184125	−	0.655661i
$831$	22.7892	−	8.29461i	0.790550	−	0.287737i
$832$	16.5336	+	2.20046i	0.573198	+	0.0762873i
$833$	17.2360	−	20.5411i	0.597193	−	0.711707i
$834$	0.791095	−	0.320745i	0.0273934	−	0.0111065i
$835$	13.4988	−	0.528984i	0.467145	−	0.0183063i
$836$	−28.8080	−	27.5453i	−0.996346	−	0.952673i
$837$			1.31266i			0.0453723i
$838$	0.833499	+	2.05576i	0.0287927	+	0.0710152i
$839$	−31.2256	−	26.2014i	−1.07803	−	0.904572i	−0.0822716	−	0.996610i	$-0.526217\pi$
$839$	−31.2256	−	26.2014i	−1.07803	−	0.904572i	−0.995756	+	0.0920378i	$0.970662\pi$
$840$	−25.4127	−	5.19168i	−0.876820	−	0.179130i
$841$	35.9165	−	13.0725i	1.23850	−	0.450777i
$842$	−5.55973	+	17.1823i	−0.191601	+	0.592142i
$843$	−1.29315	−	2.23981i	−0.0445385	−	0.0771430i
$844$	−17.1354	−	25.2712i	−0.589825	−	0.869870i
$845$	−18.9088	+	4.10348i	−0.650483	+	0.141164i
$846$	−15.5281	+	14.0159i	−0.533868	+	0.481876i
$847$	−19.6447	+	34.0256i	−0.674999	+	1.16913i
$848$	9.36779	−	23.5155i	0.321691	−	0.807527i
$849$	3.16158	+	3.76783i	0.108505	+	0.129312i
$850$	−11.9557	+	18.1030i	−0.410079	+	0.620928i
$851$	−23.8774	−	8.69065i	−0.818505	−	0.297912i
$852$	−3.89029	−	8.68072i	−0.133279	−	0.297397i
$853$	−30.8608	−	5.44159i	−1.05665	−	0.186316i	−0.381782	−	0.924252i	$-0.624690\pi$
$853$	−30.8608	−	5.44159i	−1.05665	−	0.186316i	−0.674871	+	0.737936i	$0.735801\pi$
$854$	−41.1318	−	65.6465i	−1.40750	−	2.24638i
$855$	−16.9756	−	8.13768i	−0.580554	−	0.278303i
$856$	−3.57009	−	32.8125i	−0.122023	−	1.12151i
$857$	−1.26979	+	7.20135i	−0.0433753	+	0.245993i	−0.998784	−	0.0492918i	$-0.984304\pi$
$857$	−1.26979	+	7.20135i	−0.0433753	+	0.245993i	0.955409	+	0.295285i	$0.0954147\pi$
$858$	−1.92257	+	13.8018i	−0.0656354	+	0.471187i
$859$	−2.96692	+	8.15155i	−0.101230	+	0.278127i	−0.979961	−	0.199191i	$-0.936169\pi$
$859$	−2.96692	+	8.15155i	−0.101230	+	0.278127i	0.878731	+	0.477318i	$0.158391\pi$
$860$	−16.6489	−	1.05219i	−0.567724	−	0.0358793i
$861$	17.0993	−	14.3481i	0.582744	−	0.488980i
$862$	−18.5375	+	34.9668i	−0.631390	+	1.19097i
$863$	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	$0.366703\pi$
$864$	−4.83431	+	28.4288i	−0.164466	+	0.967166i
$865$	−34.9273	+	7.57970i	−1.18756	+	0.257718i
$866$	−11.1783	+	0.403995i	−0.379853	+	0.0137283i
$867$	−6.79187	+	3.92129i	−0.230664	+	0.133174i
$868$	0.499126	+	1.98130i	0.0169414	+	0.0672495i
$869$	−2.80869	−	7.71681i	−0.0952783	−	0.261775i
$870$	−25.9691	+	6.62619i	−0.880436	+	0.224649i
$871$	−9.00076	+	10.7267i	−0.304979	+	0.363460i
$872$	52.3353	+	3.46738i	1.77230	+	0.117420i
$873$	35.4481			1.19974
$874$	18.0628	+	26.5649i	0.610984	+	0.898569i
$875$	−5.19998	−	44.0504i	−0.175791	−	1.48917i
$876$	−12.8046	−	9.25549i	−0.432628	−	0.312714i
$877$	−22.7770	−	19.1122i	−0.769124	−	0.645372i	0.171360	−	0.985208i	$-0.445184\pi$
$877$	−22.7770	−	19.1122i	−0.769124	−	0.645372i	−0.940484	+	0.339837i	$0.889628\pi$
$878$	−9.71220	−	45.4200i	−0.327771	−	1.53285i
$879$	−0.892430	−	2.45193i	−0.0301009	−	0.0827016i
$880$	−40.3352	−	6.73280i	−1.35970	−	0.226963i
$881$	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	$0.648381\pi$
$882$	23.8569	−	0.862218i	0.803305	−	0.0290324i
$883$	−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	$-0.279963\pi$
$884$	3.49636	−	12.3064i	0.117595	−	0.413909i
$885$	0.313320	−	0.595376i	0.0105322	−	0.0200133i
$886$	23.5100	−	44.3463i	0.789835	−	1.48984i
$887$	−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	$0.846902\pi$
$888$	6.29635	+	12.7905i	0.211292	+	0.429221i
$889$	−9.81028	+	26.9535i	−0.329026	+	0.903992i
$890$	0.200254	−	2.01125i	0.00671253	−	0.0674171i
$891$	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
$895$	−34.3575	−	4.67943i	−1.14844	−	0.156416i
$896$	3.51296	+	44.7477i	0.117360	+	1.49491i
$897$	3.84131	−	10.5539i	0.128258	−	0.352385i
$898$	17.1221	−	21.9704i	0.571371	−	0.733162i
$899$	1.35707	+	1.61729i	0.0452608	+	0.0539398i
$900$	−19.0958	+	2.89750i	−0.636528	+	0.0965832i
$901$	−16.8143	−	9.70773i	−0.560165	−	0.323412i
$902$	26.1243	−	23.5801i	0.869842	−	0.785132i
$903$	−15.0656	+	2.65648i	−0.501353	+	0.0884021i
$904$	−0.0655501	+	0.148689i	−0.00218017	+	0.00494532i
$905$	−22.9493	−	36.3806i	−0.762859	−	1.20933i
$906$	−2.36053	+	7.29521i	−0.0784234	+	0.242367i
$907$	−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	$0.992662\pi$
$908$	15.9512	+	16.4375i	0.529358	+	0.545499i
$909$	−6.94026	−	5.82357i	−0.230194	−	0.193156i
$910$	10.7698	+	23.8370i	0.357016	+	0.790188i
$911$	26.7525			0.886350			0.443175	−	0.896435i	$-0.353852\pi$
$911$	26.7525			0.886350			0.443175	+	0.896435i	$0.353852\pi$
$912$	2.99850	−	17.7722i	0.0992901	−	0.588496i
$913$		−	28.3666i		−	0.938798i
$914$	−3.91914	−	9.66626i	−0.129633	−	0.319732i
$915$	25.2327	+	19.5414i	0.834167	+	0.646018i
$916$	−2.13241	+	2.06932i	−0.0704569	+	0.0683721i
$917$	28.1258	+	77.2751i	0.928796	+	2.55185i
$918$	21.0443	+	6.80936i	0.694565	+	0.224742i
$919$	28.0921	−	16.2190i	0.926672	−	0.535014i	0.0409145	−	0.999163i	$-0.486973\pi$
$919$	28.0921	−	16.2190i	0.926672	−	0.535014i	0.885757	+	0.464148i	$0.153640\pi$
$920$	30.6555	+	12.1042i	1.01068	+	0.399063i
$921$	−3.59514	−	20.3891i	−0.118464	−	0.671842i
$922$	7.22937	−	6.52533i	0.238087	−	0.214900i
$923$	−4.79654	+	8.30785i	−0.157880	+	0.273456i
$924$	−37.4025	+	2.70708i	−1.23045	+	0.0890564i
$925$	−17.3925	+	17.0845i	−0.571860	+	0.561735i
$926$	−5.25631	−	4.09637i	−0.172733	−	0.134615i
$927$	5.69006	−	15.6333i	0.186886	−	0.513465i
$928$	23.4343	+	40.0240i	0.769268	+	1.31385i
$929$	−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
$934$	−5.14242	+	36.9167i	−0.168265	+	1.20795i
$935$	−9.56544	+	29.8719i	−0.312823	+	0.976916i
$936$	10.2187	−	5.03035i	0.334010	−	0.164422i
$937$	8.03121	+	9.57122i	0.262368	+	0.312678i	0.881105	−	0.472920i	$-0.156800\pi$
$937$	8.03121	+	9.57122i	0.262368	+	0.312678i	−0.618737	+	0.785598i	$0.712356\pi$
$938$	−33.2931	−	17.6502i	−1.08706	−	0.576300i
$939$	−1.23043	+	2.13116i	−0.0401535	+	0.0695479i
$940$	8.06267	−	33.2859i	0.262975	−	1.08567i
$941$	−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	$0.469718\pi$
$942$	13.0348	−	0.471093i	0.424697	−	0.0153491i
$943$	−24.5638	+	14.1819i	−0.799908	+	0.461827i
$944$	−1.13999	−	0.236510i	−0.0371036	−	0.00769774i
$945$	−41.8573	+	17.1193i	−1.36162	+	0.556890i
$946$	−23.5858	+	5.04336i	−0.766839	+	0.163974i
$947$	−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	$0.743060\pi$
$948$	2.17537	−	3.00954i	0.0706527	−	0.0977453i
$949$			15.9331i			0.517211i
$950$	30.4673	−	4.66328i	0.988488	−	0.151297i
$951$		−	11.6786i		−	0.378705i
$952$	34.3528	+	2.27598i	1.11338	+	0.0737650i
$953$	36.8782	+	30.9445i	1.19460	+	1.00239i	0.999768	+	0.0215538i	$0.00686132\pi$
$953$	36.8782	+	30.9445i	1.19460	+	1.00239i	0.194834	+	0.980836i	$0.437583\pi$
$954$	−3.61441	−	16.9031i	−0.117021	−	0.547259i
$955$	0.875071	−	0.357896i	0.0283166	−	0.0115813i
$956$	48.6777	−	12.2628i	1.57435	−	0.396608i
$957$	−33.5576	+	19.3745i	−1.08476	+	0.626288i
$958$	0.965213	+	26.7067i	0.0311846	+	0.862856i
$959$	−78.0860	+	13.7687i	−2.52153	+	0.444614i
$960$	−7.71622	−	16.8047i	−0.249040	−	0.542370i
$961$	15.4668	−	26.7894i	0.498931	−	0.864173i
$962$	6.73407	−	12.7023i	0.217115	−	0.409538i
$963$	−14.4877	−	17.2657i	−0.466859	−	0.556380i
$964$	8.38998	+	0.861149i	0.270223	+	0.0277358i
$965$	4.14078	−	12.9312i	0.133296	−	0.416271i
$966$	29.9351	+	4.16990i	0.963144	+	0.134164i
$967$	−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	$-0.858214\pi$
$971$	2.89599	−	16.4240i	0.0929368	−	0.527071i	0.995360	−	0.0962203i	$-0.0306753\pi$
$972$	12.9523	+	28.9015i	0.415444	+	0.927015i
$973$	0.792344	−	2.17695i	0.0254014	−	0.0697897i
$974$	−29.4766	+	37.8233i	−0.944491	+	1.21194i
$975$	−7.55144	−	7.68755i	−0.241840	−	0.246199i
$976$	20.4393	−	51.3077i	0.654245	−	1.64232i
$977$	−8.18503	+	14.1769i	−0.261862	+	0.453559i	−0.966737	−	0.255773i	$-0.917670\pi$
$977$	−8.18503	+	14.1769i	−0.261862	+	0.453559i	0.704875	+	0.709332i	$0.251003\pi$
$978$	7.91360	+	8.76742i	0.253049	+	0.280351i
$979$	−0.507439	−	2.87783i	−0.0162178	−	0.0919759i
$980$	−31.4663	+	23.1852i	−1.00515	+	0.740625i
$981$	31.0179	−	17.9082i	0.990325	−	0.571764i
$982$	16.1046	−	49.7713i	0.513919	−	1.58827i
$983$	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	$0.877571\pi$
$984$	15.4550	+	3.79338i	0.492686	+	0.120929i
$985$	16.4241	+	12.7196i	0.523316	+	0.405280i
$986$	32.9677	−	13.3666i	1.04991	−	0.425679i
$987$		−	31.4069i		−	0.999693i
$988$	−16.2967	+	8.04857i	−0.518468	+	0.256059i
$989$	19.4391			0.618127
$990$	−25.4478	+	11.4976i	−0.808784	+	0.365418i
$991$	−3.80912	−	3.19623i	−0.121001	−	0.101532i	0.580280	−	0.814417i	$-0.302943\pi$
$991$	−3.80912	−	3.19623i	−0.121001	−	0.101532i	−0.701280	+	0.712886i	$0.747388\pi$
$992$	−0.929500	+	1.12155i	−0.0295116	+	0.0356091i
$993$	10.3525	+	28.4432i	0.328526	+	0.902616i
$994$	−24.5619	−	7.94756i	−0.779056	−	0.252081i
$995$	−16.8213	−	26.6663i	−0.533272	−	0.845377i
$996$	10.6167	−	7.19876i	0.336402	−	0.228101i
$997$	−0.694133	+	0.122394i	−0.0219834	+	0.00387627i	−0.184629	−	0.982808i	$-0.559108\pi$
$997$	−0.694133	+	0.122394i	−0.0219834	+	0.00387627i	0.162646	+	0.986685i	$0.447997\pi$
$998$	38.7977	+	42.9837i	1.22812	+	1.36063i
$999$	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.59.8	✓	336
4.3	odd	2	inner	380.2.bb.a.59.44	yes	336
5.4	even	2	inner	380.2.bb.a.59.49	yes	336
19.10	odd	18	inner	380.2.bb.a.219.13	yes	336
20.19	odd	2	inner	380.2.bb.a.59.13	yes	336
76.67	even	18	inner	380.2.bb.a.219.49	yes	336
95.29	odd	18	inner	380.2.bb.a.219.44	yes	336
380.219	even	18	inner	380.2.bb.a.219.8	yes	336

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

\(f(q)\)	\(=\)	\(q+(-1.31059 + 0.531372i) q^{2} +(0.664457 - 0.791869i) q^{3} +(1.43529 - 1.39282i) q^{4} +(0.846472 + 2.06966i) q^{5} +(-0.450054 + 1.39089i) q^{6} +(1.98367 + 3.43582i) q^{7} +(-1.14097 + 2.58809i) q^{8} +(0.335391 + 1.90210i) q^{9} +O(q^{10})\)	\(q+(-1.31059 + 0.531372i) q^{2} +(0.664457 - 0.791869i) q^{3} +(1.43529 - 1.39282i) q^{4} +(0.846472 + 2.06966i) q^{5} +(-0.450054 + 1.39089i) q^{6} +(1.98367 + 3.43582i) q^{7} +(-1.14097 + 2.58809i) q^{8} +(0.335391 + 1.90210i) q^{9} +(-2.20913 - 2.26268i) q^{10} +(-3.95947 - 2.28600i) q^{11} +(-0.149243 - 2.06203i) q^{12} +(-1.59714 + 1.34016i) q^{13} +(-4.42547 - 3.44888i) q^{14} +(2.20134 + 0.704904i) q^{15} +(0.120106 - 3.99820i) 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} +(6.40395 + 0.892059i) q^{22} +(-4.89694 - 1.78234i) q^{23} +(1.29130 + 2.62317i) q^{24} +(-3.56697 + 3.50382i) q^{25} +(1.38107 - 2.60507i) q^{26} +(4.41473 + 2.54884i) q^{27} +(7.63262 + 2.16850i) q^{28} +(8.07431 - 1.42372i) q^{29} +(-3.25962 + 0.245891i) q^{30} +(0.128751 + 0.223003i) q^{31} +(1.96712 + 5.30381i) q^{32} +(-4.44111 + 1.61643i) q^{33} +(4.24302 - 0.907288i) q^{34} +(-5.43185 + 7.01385i) q^{35} +(3.13066 + 2.26292i) q^{36} +4.87597 q^{37} +(-5.00060 - 3.60471i) q^{38} +2.15520i q^{39} +(-6.32225 - 0.170673i) q^{40} +(3.49860 - 4.16946i) q^{41} +(-5.67160 + 1.21276i) q^{42} +(-3.50528 + 1.27582i) q^{43} +(-8.86697 + 2.23376i) q^{44} +(-3.65279 + 2.30422i) q^{45} +(7.36496 - 0.266178i) q^{46} +(-1.32983 - 7.54185i) q^{47} +(-3.08624 - 2.75174i) q^{48} +(-4.36990 + 7.56889i) q^{49} +(2.81301 - 6.48745i) q^{50} +(-2.42953 + 2.03861i) q^{51} +(-0.425756 + 4.14804i) q^{52} +(5.94655 + 2.16437i) q^{53} +(-7.14028 - 0.994627i) q^{54} +(1.37966 - 10.1298i) 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} +(4.14137 - 2.05433i) q^{60} +(12.9746 + 4.72236i) q^{61} +(-0.287237 - 0.223851i) q^{62} +(-5.86996 + 4.92548i) q^{63} +(-5.39638 - 5.90585i) q^{64} +(-4.12561 - 2.17113i) q^{65} +(4.96155 - 4.47836i) q^{66} +(6.61416 - 1.16625i) q^{67} +(-5.07875 + 3.44370i) q^{68} +(-4.66519 + 2.69345i) q^{69} +(3.39197 - 12.0786i) q^{70} +(4.32369 - 1.57370i) q^{71} +(-5.30546 - 1.30221i) q^{72} +(4.91224 - 5.85418i) q^{73} +(-6.39040 + 2.59095i) q^{74} +(0.404465 + 5.15271i) q^{75} +(8.46918 + 2.06712i) q^{76} -18.1387i q^{77} +(-1.14521 - 2.82459i) q^{78} +(1.37594 + 1.15455i) q^{79} +(8.37657 - 3.13578i) q^{80} +(-0.493133 + 0.179486i) q^{81} +(-2.36969 + 7.32351i) q^{82} +(3.10221 + 5.37319i) q^{83} +(6.78871 - 4.60316i) q^{84} +(-1.45495 - 6.70440i) q^{85} +(3.91605 - 3.53468i) q^{86} +(4.23764 - 7.33980i) q^{87} +(10.4340 - 7.63919i) q^{88} +(0.410842 + 0.489623i) q^{89} +(3.56291 - 4.96087i) q^{90} +(-7.77274 - 2.82905i) q^{91} +(-9.51100 + 4.26238i) q^{92} +(0.262139 + 0.0462222i) q^{93} +(5.75039 + 9.17763i) q^{94} +(-5.67548 + 7.92395i) q^{95} +(5.50699 + 1.96646i) q^{96} +(3.18700 - 18.0744i) q^{97} +(1.70525 - 12.2418i) 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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