LMFDB - Embedded newform 690.2.n.a.659.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			659.1
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-1.68612 - 0.396228i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.06421 - 0.859668i) q^{5} +(0.632155 - 1.61257i) q^{6} +(0.955977 + 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(2.68601 + 1.33618i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-1.68612 - 0.396228i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.06421 - 0.859668i) q^{5} +(0.632155 - 1.61257i) q^{6} +(0.955977 + 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(2.68601 + 1.33618i) q^{9} +(0.557150 + 2.16554i) q^{10} +(0.130034 + 0.904408i) q^{11} +(1.50619 + 0.855213i) q^{12} +(-2.47130 - 3.84542i) q^{13} +(-0.744166 + 0.858813i) q^{14} +(-3.82114 + 0.631605i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.74601 - 5.94637i) q^{17} +(-1.70483 + 2.46851i) q^{18} +(0.111059 - 0.378232i) q^{19} +(-2.22279 + 0.243289i) q^{20} +(-1.36846 - 1.41469i) q^{21} -0.913708 q^{22} +(1.02121 + 4.68584i) q^{23} +(-1.06086 + 1.36915i) q^{24} +(3.52194 - 3.54907i) q^{25} +(4.15798 - 1.89889i) q^{26} +(-3.99950 - 3.31723i) q^{27} +(-0.744166 - 0.858813i) q^{28} +(2.85664 + 9.72883i) q^{29} +(-0.0813721 - 3.87213i) q^{30} +(3.71757 - 8.14034i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.139098 - 1.57646i) q^{33} +(6.13433 - 0.881983i) q^{34} +(2.50149 + 0.446366i) q^{35} +(-2.20076 - 2.03879i) q^{36} +(4.47941 - 5.16952i) q^{37} +(0.358577 + 0.163757i) q^{38} +(2.64325 + 7.46304i) q^{39} +(0.0755234 - 2.23479i) q^{40} +(7.60595 - 6.59060i) q^{41} +(1.59504 - 1.15320i) q^{42} +(-1.93387 - 4.23459i) q^{43} +(0.130034 - 0.904408i) q^{44} +(6.69316 + 0.449078i) q^{45} +(-4.78348 + 0.343953i) q^{46} +8.91322 q^{47} +(-1.20424 - 1.24491i) q^{48} +(-2.37146 - 5.19278i) q^{49} +(3.01172 + 3.99118i) q^{50} +(0.587869 + 10.7181i) q^{51} +(1.28782 + 4.38590i) q^{52} +(0.827835 - 1.28814i) q^{53} +(3.85265 - 3.48670i) q^{54} +(1.04591 + 1.75510i) q^{55} +(0.955977 - 0.614369i) q^{56} +(-0.337125 + 0.593741i) q^{57} +(-10.0363 + 1.44301i) q^{58} +(2.84841 + 4.43222i) q^{59} +(3.84430 + 0.470518i) q^{60} +(6.70797 + 3.06343i) q^{61} +(7.52841 + 4.83822i) q^{62} +(1.74686 + 2.92755i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-8.40707 - 5.81326i) q^{65} +(1.54062 + 0.362037i) q^{66} +(-0.882061 + 6.13487i) q^{67} +6.19741i q^{68} +(0.134775 - 8.30553i) q^{69} +(-0.797822 + 2.41251i) q^{70} +(-9.58910 - 1.37871i) q^{71} +(2.33124 - 1.88821i) q^{72} +(-1.47294 + 5.01637i) q^{73} +(4.47941 + 5.16952i) q^{74} +(-7.34466 + 4.58867i) q^{75} +(-0.213121 + 0.331622i) q^{76} +(-0.431331 + 0.944482i) q^{77} +(-7.76325 + 1.55424i) q^{78} +(1.62557 + 2.52943i) q^{79} +(2.20130 + 0.392799i) q^{80} +(5.42927 + 7.17796i) q^{81} +(5.44107 + 8.46648i) q^{82} +(7.96766 + 6.90401i) q^{83} +(0.914468 + 1.74292i) q^{84} +(-8.71604 - 10.7736i) q^{85} +(4.46670 - 1.31154i) q^{86} +(-0.961810 - 17.5359i) q^{87} +(0.876696 + 0.257421i) q^{88} +(-6.57963 - 14.4074i) q^{89} +(-1.39704 + 6.56112i) q^{90} -5.19442i q^{91} +(0.340309 - 4.78374i) q^{92} +(-9.49370 + 12.2526i) q^{93} +(-1.26848 + 8.82250i) q^{94} +(-0.0959048 - 0.876226i) q^{95} +(1.40362 - 1.01481i) q^{96} +(-10.6822 - 12.3279i) q^{97} +(5.47742 - 1.60831i) q^{98} +(-0.859176 + 2.60299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−1.68612	−	0.396228i	−0.973482	−	0.228762i
$3$	−1.68612	−	0.396228i	−0.973482	−	0.228762i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	2.06421	−	0.859668i	0.923144	−	0.384455i
$5$	2.06421	−	0.859668i	0.923144	−	0.384455i
$6$	0.632155	−	1.61257i	0.258076	−	0.658329i
$7$	0.955977	+	0.614369i	0.361325	+	0.232210i	0.708689	−	0.705521i	$-0.249287\pi$
$7$	0.955977	+	0.614369i	0.361325	+	0.232210i	−0.347364	+	0.937730i	$0.612923\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	2.68601	+	1.33618i	0.895336	+	0.445392i
$10$	0.557150	+	2.16554i	0.176186	+	0.684805i
$11$	0.130034	+	0.904408i	0.0392068	+	0.272689i	0.999989	−	0.00461363i	$-0.00146857\pi$
$11$	0.130034	+	0.904408i	0.0392068	+	0.272689i	−0.960783	+	0.277303i	$0.910559\pi$
$12$	1.50619	+	0.855213i	0.434800	+	0.246879i
$13$	−2.47130	−	3.84542i	−0.685415	−	1.06653i	−0.993352	−	0.115120i	$-0.963275\pi$
$13$	−2.47130	−	3.84542i	−0.685415	−	1.06653i	0.307936	−	0.951407i	$-0.400362\pi$
$14$	−0.744166	+	0.858813i	−0.198887	+	0.229527i
$15$	−3.82114	+	0.631605i	−0.986613	+	0.163080i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.74601	−	5.94637i	−0.423470	−	1.44221i	−0.844694	−	0.535250i	$-0.820217\pi$
$17$	−1.74601	−	5.94637i	−0.423470	−	1.44221i	0.421224	−	0.906957i	$-0.361601\pi$
$18$	−1.70483	+	2.46851i	−0.401833	+	0.581833i
$19$	0.111059	−	0.378232i	0.0254787	−	0.0867725i	−0.945772	−	0.324831i	$-0.894693\pi$
$19$	0.111059	−	0.378232i	0.0254787	−	0.0867725i	0.971251	+	0.238058i	$0.0765109\pi$
$20$	−2.22279	+	0.243289i	−0.497032	+	0.0544012i
$21$	−1.36846	−	1.41469i	−0.298623	−	0.308710i
$22$	−0.913708			−0.194803
$23$	1.02121	+	4.68584i	0.212937	+	0.977066i
$23$	1.02121	+	4.68584i	0.212937	+	0.977066i
$24$	−1.06086	+	1.36915i	−0.216547	+	0.279477i
$25$	3.52194	−	3.54907i	0.704389	−	0.709815i
$26$	4.15798	−	1.89889i	0.815447	−	0.372402i
$27$	−3.99950	−	3.31723i	−0.769704	−	0.638400i
$28$	−0.744166	−	0.858813i	−0.140634	−	0.162300i
$29$	2.85664	+	9.72883i	0.530465	+	1.80660i	0.588771	+	0.808300i	$0.299612\pi$
$29$	2.85664	+	9.72883i	0.530465	+	1.80660i	−0.0583057	+	0.998299i	$0.518570\pi$
$30$	−0.0813721	−	3.87213i	−0.0148564	−	0.706951i
$31$	3.71757	−	8.14034i	0.667695	−	1.46205i	−0.207479	−	0.978239i	$-0.566526\pi$
$31$	3.71757	−	8.14034i	0.667695	−	1.46205i	0.875174	−	0.483808i	$-0.160747\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	0.139098	−	1.57646i	0.0242139	−	0.274427i
$34$	6.13433	−	0.881983i	1.05203	−	0.151259i
$35$	2.50149	+	0.446366i	0.422830	+	0.0754496i
$36$	−2.20076	−	2.03879i	−0.366793	−	0.339798i
$37$	4.47941	−	5.16952i	0.736411	−	0.849864i	−0.256767	−	0.966473i	$-0.582657\pi$
$37$	4.47941	−	5.16952i	0.736411	−	0.849864i	0.993178	+	0.116610i	$0.0372026\pi$
$38$	0.358577	+	0.163757i	0.0581689	+	0.0265648i
$39$	2.64325	+	7.46304i	0.423259	+	1.19504i
$40$	0.0755234	−	2.23479i	0.0119413	−	0.353352i
$41$	7.60595	−	6.59060i	1.18785	−	1.02928i	0.188969	−	0.981983i	$-0.439485\pi$
$41$	7.60595	−	6.59060i	1.18785	−	1.02928i	0.998881	−	0.0472953i	$-0.0150602\pi$
$42$	1.59504	−	1.15320i	0.246120	−	0.177943i
$43$	−1.93387	−	4.23459i	−0.294913	−	0.645769i	0.702941	−	0.711248i	$-0.251870\pi$
$43$	−1.93387	−	4.23459i	−0.294913	−	0.645769i	−0.997854	+	0.0654792i	$0.979142\pi$
$44$	0.130034	−	0.904408i	0.0196034	−	0.136345i
$45$	6.69316	+	0.449078i	0.997757	+	0.0669446i
$46$	−4.78348	+	0.343953i	−0.705286	+	0.0507130i
$47$	8.91322			1.30013			0.650063	−	0.759880i	$-0.274742\pi$
$47$	8.91322			1.30013			0.650063	+	0.759880i	$0.274742\pi$
$48$	−1.20424	−	1.24491i	−0.173817	−	0.179688i
$49$	−2.37146	−	5.19278i	−0.338780	−	0.741825i
$50$	3.01172	+	3.99118i	0.425922	+	0.564438i
$51$	0.587869	+	10.7181i	0.0823181	+	1.50084i
$52$	1.28782	+	4.38590i	0.178588	+	0.608215i
$53$	0.827835	−	1.28814i	0.113712	−	0.176939i	−0.779733	−	0.626113i	$-0.784645\pi$
$53$	0.827835	−	1.28814i	0.113712	−	0.176939i	0.893445	+	0.449173i	$0.148281\pi$
$54$	3.85265	−	3.48670i	0.524279	−	0.474480i
$55$	1.04591	+	1.75510i	0.141030	+	0.236658i
$56$	0.955977	−	0.614369i	0.127748	−	0.0820986i
$57$	−0.337125	+	0.593741i	−0.0446533	+	0.0786429i
$58$	−10.0363	+	1.44301i	−1.31784	+	0.189476i
$59$	2.84841	+	4.43222i	0.370832	+	0.577025i	0.975649	−	0.219339i	$-0.0703901\pi$
$59$	2.84841	+	4.43222i	0.370832	+	0.577025i	−0.604817	+	0.796365i	$0.706754\pi$
$60$	3.84430	+	0.470518i	0.496297	+	0.0607435i
$61$	6.70797	+	3.06343i	0.858868	+	0.392232i	0.795642	−	0.605768i	$-0.207134\pi$
$61$	6.70797	+	3.06343i	0.858868	+	0.392232i	0.0632259	+	0.997999i	$0.479861\pi$
$62$	7.52841	+	4.83822i	0.956110	+	0.614454i
$63$	1.74686	+	2.92755i	0.220083	+	0.368837i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−8.40707	−	5.81326i	−1.04277	−	0.721046i
$66$	1.54062	+	0.362037i	0.189637	+	0.0445636i
$67$	−0.882061	+	6.13487i	−0.107761	+	0.749493i	0.862259	+	0.506468i	$0.169049\pi$
$67$	−0.882061	+	6.13487i	−0.107761	+	0.749493i	−0.970020	+	0.243026i	$0.921860\pi$
$68$			6.19741i			0.751546i
$69$	0.134775	−	8.30553i	0.0162250	−	0.999868i
$70$	−0.797822	+	2.41251i	−0.0953580	+	0.288350i
$71$	−9.58910	−	1.37871i	−1.13802	−	0.163622i	−0.452559	−	0.891734i	$-0.649489\pi$
$71$	−9.58910	−	1.37871i	−1.13802	−	0.163622i	−0.685458	+	0.728112i	$0.740398\pi$
$72$	2.33124	−	1.88821i	0.274739	−	0.222528i
$73$	−1.47294	+	5.01637i	−0.172395	+	0.587122i	0.827284	+	0.561784i	$0.189885\pi$
$73$	−1.47294	+	5.01637i	−0.172395	+	0.587122i	−0.999679	+	0.0253387i	$0.991934\pi$
$74$	4.47941	+	5.16952i	0.520721	+	0.600945i
$75$	−7.34466	+	4.58867i	−0.848089	+	0.529854i
$76$	−0.213121	+	0.331622i	−0.0244466	+	0.0380397i
$77$	−0.431331	+	0.944482i	−0.0491547	+	0.107634i
$78$	−7.76325	+	1.55424i	−0.879015	+	0.175983i
$79$	1.62557	+	2.52943i	0.182891	+	0.284584i	0.920578	−	0.390559i	$-0.127718\pi$
$79$	1.62557	+	2.52943i	0.182891	+	0.284584i	−0.737687	+	0.675143i	$0.764082\pi$
$80$	2.20130	+	0.392799i	0.246113	+	0.0439162i
$81$	5.42927	+	7.17796i	0.603252	+	0.797551i
$82$	5.44107	+	8.46648i	0.600866	+	0.934966i
$83$	7.96766	+	6.90401i	0.874564	+	0.757814i	0.971391	−	0.237487i	$-0.0763238\pi$
$83$	7.96766	+	6.90401i	0.874564	+	0.757814i	−0.0968267	+	0.995301i	$0.530869\pi$
$84$	0.914468	+	1.74292i	0.0997766	+	0.190168i
$85$	−8.71604	−	10.7736i	−0.945388	−	1.16856i
$86$	4.46670	−	1.31154i	0.481657	−	0.141427i
$87$	−0.961810	−	17.5359i	−0.103117	−	1.88004i
$88$	0.876696	+	0.257421i	0.0934561	+	0.0274412i
$89$	−6.57963	−	14.4074i	−0.697439	−	1.52718i	−0.843049	−	0.537837i	$-0.819242\pi$
$89$	−6.57963	−	14.4074i	−0.697439	−	1.52718i	0.145610	−	0.989342i	$-0.453486\pi$
$90$	−1.39704	+	6.56112i	−0.147261	+	0.691603i
$91$		−	5.19442i		−	0.544524i
$92$	0.340309	−	4.78374i	0.0354796	−	0.498740i
$93$	−9.49370	+	12.2526i	−0.984450	+	1.27053i
$94$	−1.26848	+	8.82250i	−0.130834	+	0.909971i
$95$	−0.0959048	−	0.876226i	−0.00983962	−	0.0898989i
$96$	1.40362	−	1.01481i	0.143257	−	0.103574i
$97$	−10.6822	−	12.3279i	−1.08461	−	1.25171i	−0.965937	−	0.258778i	$-0.916680\pi$
$97$	−10.6822	−	12.3279i	−1.08461	−	1.25171i	−0.118677	−	0.992933i	$-0.537865\pi$
$98$	5.47742	−	1.60831i	0.553303	−	0.162464i
$99$	−0.859176	+	2.60299i	−0.0863504	+	0.261611i
$100$	−4.37917	+	2.41306i	−0.437917	+	0.241306i
$101$	−4.75115	−	4.11690i	−0.472757	−	0.409647i	0.385626	−	0.922655i	$-0.373985\pi$
$101$	−4.75115	−	4.11690i	−0.472757	−	0.409647i	−0.858384	+	0.513008i	$0.828531\pi$
$102$	−10.6927	−	0.943462i	−1.05873	−	0.0934167i
$103$	0.422456	+	2.93825i	0.0416259	+	0.289514i	0.999992	+	0.00397239i	$0.00126445\pi$
$103$	0.422456	+	2.93825i	0.0416259	+	0.289514i	−0.958366	+	0.285542i	$0.907826\pi$
$104$	−4.52453	+	0.650529i	−0.443667	+	0.0637897i
$105$	−4.04096	−	1.74379i	−0.394357	−	0.170176i
$106$	1.15721	+	1.00273i	0.112398	+	0.0973938i
$107$	14.2352	+	6.50102i	1.37617	+	0.628477i	0.959792	−	0.280713i	$-0.0905708\pi$
$107$	14.2352	+	6.50102i	1.37617	+	0.628477i	0.416381	+	0.909190i	$0.363298\pi$
$108$	2.90292	+	4.30964i	0.279334	+	0.414696i
$109$	−1.71763	−	5.84972i	−0.164519	−	0.560301i	−0.999943	−	0.0106947i	$-0.996596\pi$
$109$	−1.71763	−	5.84972i	−0.164519	−	0.560301i	0.835423	−	0.549607i	$-0.185222\pi$
$110$	−1.88609	+	0.785485i	−0.179831	+	0.0748931i
$111$	−9.60114	+	6.94157i	−0.911300	+	0.658864i
$112$	0.472066	+	1.03368i	0.0446061	+	0.0976737i
$113$	−9.64896	−	1.38731i	−0.907698	−	0.130507i	−0.327376	−	0.944894i	$-0.606164\pi$
$113$	−9.64896	−	1.38731i	−0.907698	−	0.130507i	−0.580322	+	0.814387i	$0.697073\pi$
$114$	−0.539719	−	0.418192i	−0.0505494	−	0.0391673i
$115$	6.13627	+	8.79467i	0.572210	+	0.820107i
$116$		−	10.1396i		−	0.941434i
$117$	−1.49977	−	13.6309i	−0.138654	−	1.26018i
$118$	−4.79247	+	2.18865i	−0.441183	+	0.201482i
$119$	1.98412	−	6.75729i	0.181884	−	0.619440i
$120$	−1.01283	+	3.73821i	−0.0924582	+	0.341250i
$121$	9.75338	−	2.86385i	0.886671	−	0.260350i
$122$	−3.98689	+	6.20372i	−0.360956	+	0.561659i
$123$	−15.4359	+	8.09885i	−1.39181	+	0.730249i
$124$	−5.86038	+	6.76324i	−0.526277	+	0.607356i
$125$	4.21901	−	10.3537i	0.377360	−	0.926067i
$126$	−3.14636	+	1.31244i	−0.280300	+	0.116922i
$127$	−14.7504	+	2.12078i	−1.30888	+	0.188189i	−0.761212	−	0.648504i	$-0.775395\pi$
$127$	−14.7504	+	2.12078i	−1.30888	+	0.188189i	−0.547673	+	0.836693i	$0.684486\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	1.58288	+	7.90628i	0.139365	+	0.696109i
$130$	6.95054	−	7.49419i	0.609603	−	0.657284i
$131$	0.345636	−	0.537820i	0.0301983	−	0.0469895i	−0.825826	−	0.563925i	$-0.809291\pi$
$131$	0.345636	−	0.537820i	0.0301983	−	0.0469895i	0.856025	+	0.516935i	$0.172927\pi$
$132$	−0.577605	+	1.47342i	−0.0502741	+	0.128245i
$133$	0.338544	−	0.293350i	0.0293555	−	0.0254367i
$134$	−5.94689	−	1.74617i	−0.513733	−	0.150846i
$135$	−11.1075	−	3.40922i	−0.955984	−	0.293419i
$136$	−6.13433	−	0.881983i	−0.526014	−	0.0756295i
$137$			10.6373i			0.908803i	0.890797	+	0.454402i	$0.150147\pi$
$137$			10.6373i			0.908803i	−0.890797	+	0.454402i	$0.849853\pi$
$138$	8.20181	+	1.31540i	0.698185	+	0.111975i
$139$	−9.73039			−0.825321			−0.412661	−	0.910885i	$-0.635400\pi$
$139$	−9.73039			−0.825321			−0.412661	+	0.910885i	$0.635400\pi$
$140$	−2.27441	−	1.13304i	−0.192223	−	0.0957591i
$141$	−15.0288	−	3.53167i	−1.26565	−	0.297420i
$142$	2.72934	−	9.29529i	0.229041	−	0.780043i
$143$	3.15647	−	2.73510i	0.263958	−	0.228721i
$144$	1.53722	+	2.57623i	0.128102	+	0.214686i
$145$	14.2603	+	17.6266i	1.18425	+	1.46381i
$146$	−4.75569	−	2.17185i	−0.393584	−	0.179744i
$147$	1.94105	+	9.69529i	0.160095	+	0.799654i
$148$	−5.75439	+	3.69812i	−0.473008	+	0.303984i
$149$	1.24372	+	8.65025i	0.101889	+	0.708656i	0.975173	+	0.221444i	$0.0710770\pi$
$149$	1.24372	+	8.65025i	0.101889	+	0.708656i	−0.873284	+	0.487212i	$0.838014\pi$
$150$	−3.49671	−	7.92294i	−0.285505	−	0.646905i
$151$	−1.99413	+	1.28155i	−0.162280	+	0.104291i	−0.619260	−	0.785186i	$-0.712567\pi$
$151$	−1.99413	+	1.28155i	−0.162280	+	0.104291i	0.456980	+	0.889477i	$0.348931\pi$
$152$	−0.297917	−	0.258146i	−0.0241642	−	0.0209384i
$153$	3.25560	−	18.3050i	0.263200	−	1.47987i
$154$	−0.873484	−	0.561354i	−0.0703874	−	0.0452352i
$155$	0.675862	−	19.9993i	0.0542865	−	1.60638i
$156$	−0.433598	−	7.90542i	−0.0347156	−	0.632940i
$157$	17.4466	+	5.12278i	1.39239	+	0.408843i	0.890064	−	0.455836i	$-0.150660\pi$
$157$	17.4466	+	5.12278i	1.39239	+	0.408843i	0.502326	+	0.864678i	$0.332478\pi$
$158$	−2.73503	+	1.24905i	−0.217587	+	0.0993688i
$159$	−1.90623	+	1.84394i	−0.151174	+	0.146234i
$160$	−0.702078	+	2.12299i	−0.0555041	+	0.167837i
$161$	−1.90258	+	5.10696i	−0.149945	+	0.402485i
$162$	−7.87756	+	4.35247i	−0.618920	+	0.341963i
$163$	−15.4066	−	2.21514i	−1.20674	−	0.173503i	−0.490552	−	0.871412i	$-0.663205\pi$
$163$	−15.4066	−	2.21514i	−1.20674	−	0.173503i	−0.716186	+	0.697909i	$0.754114\pi$
$164$	−9.15464	+	4.18079i	−0.714858	+	0.326465i
$165$	−1.06811	−	3.37373i	−0.0831520	−	0.262645i
$166$	−7.96766	+	6.90401i	−0.618410	+	0.535855i
$167$	−6.41448	+	1.88346i	−0.496367	+	0.145747i	−0.520328	−	0.853966i	$-0.674190\pi$
$167$	−6.41448	+	1.88346i	−0.496367	+	0.145747i	0.0239611	+	0.999713i	$0.492372\pi$
$168$	−1.85532	+	0.657116i	−0.143141	+	0.0506976i
$169$	−3.27952	+	7.18116i	−0.252271	+	0.552397i
$170$	11.9043	−	7.09409i	0.913022	−	0.544092i
$171$	0.803691	−	0.867540i	0.0614597	−	0.0663425i
$172$	0.662515	+	4.60789i	0.0505163	+	0.351348i
$173$	2.76882	+	19.2576i	0.210510	+	1.46413i	0.771460	+	0.636278i	$0.219527\pi$
$173$	2.76882	+	19.2576i	0.210510	+	1.46413i	−0.560950	+	0.827850i	$0.689564\pi$
$174$	17.4943	+	1.54359i	1.32624	+	0.117020i
$175$	5.54734	−	1.22906i	0.419339	−	0.0929082i
$176$	−0.379568	+	0.831138i	−0.0286110	+	0.0626494i
$177$	−3.04660	−	8.60187i	−0.228996	−	0.646556i
$178$	15.1971	−	4.46227i	1.13907	−	0.334462i
$179$	3.40016	−	2.94626i	0.254140	−	0.220214i	−0.518468	−	0.855097i	$-0.673497\pi$
$179$	3.40016	−	2.94626i	0.254140	−	0.220214i	0.772608	+	0.634883i	$0.218952\pi$
$180$	−6.29552	−	2.31657i	−0.469240	−	0.172667i
$181$	−13.5975	+	6.20977i	−1.01069	+	0.461569i	−0.850758	−	0.525558i	$-0.823856\pi$
$181$	−13.5975	+	6.20977i	−1.01069	+	0.461569i	−0.159937	+	0.987127i	$0.551129\pi$
$182$	5.14155	+	0.739244i	0.381117	+	0.0547964i
$183$	−10.0966	−	7.82319i	−0.746365	−	0.578307i
$184$	4.68662	+	1.01764i	0.345502	+	0.0750216i
$185$	4.80239	−	14.5218i	0.353079	−	1.06766i
$186$	−10.7768	−	11.1408i	−0.790192	−	0.816882i
$187$	5.15090	−	2.35234i	0.376671	−	0.172020i
$188$	−8.55217	−	2.51114i	−0.623731	−	0.183144i
$189$	−1.78543	−	5.62836i	−0.129871	−	0.409403i
$190$	0.880956	+	0.0297713i	0.0639112	+	0.00215984i
$191$	6.66753	+	4.28496i	0.482445	+	0.310049i	0.759161	−	0.650903i	$-0.225610\pi$
$191$	6.66753	+	4.28496i	0.482445	+	0.310049i	−0.276715	+	0.960952i	$0.589246\pi$
$192$	0.804725	+	1.53376i	0.0580760	+	0.110690i
$193$	5.97374	+	5.17628i	0.429999	+	0.372597i	0.842802	−	0.538224i	$-0.180905\pi$
$193$	5.97374	+	5.17628i	0.429999	+	0.372597i	−0.412802	+	0.910821i	$0.635450\pi$
$194$	13.7227	−	8.81903i	0.985231	−	0.633170i
$195$	11.8720	+	13.1330i	0.850169	+	0.940472i
$196$	0.812427	+	5.65055i	0.0580305	+	0.403611i
$197$	4.26621	−	2.74173i	0.303955	−	0.195340i	−0.379768	−	0.925082i	$-0.623996\pi$
$197$	4.26621	−	2.74173i	0.303955	−	0.195340i	0.683723	+	0.729742i	$0.260360\pi$
$198$	−2.45423	−	1.22088i	−0.174414	−	0.0867638i
$199$	−10.9150	−	4.98472i	−0.773745	−	0.353357i	−0.0109014	−	0.999941i	$-0.503470\pi$
$199$	−10.9150	−	4.98472i	−0.773745	−	0.353357i	−0.762844	+	0.646583i	$0.776197\pi$
$200$	−1.76528	−	4.67801i	−0.124824	−	0.330785i
$201$	3.91807	−	9.99463i	0.276359	−	0.704967i
$202$	4.75115	−	4.11690i	0.334290	−	0.289664i
$203$	−3.24621	+	11.0556i	−0.227839	+	0.775949i
$204$	2.45559	−	10.4496i	0.171925	−	0.731617i
$205$	10.0346	−	20.1430i	0.700845	−	1.40685i
$206$	−2.96846			−0.206823
$207$	−3.51813	+	13.9507i	−0.244527	+	0.969642i
$208$		−	4.57106i		−	0.316946i
$209$	0.356518	+	0.0512595i	0.0246608	+	0.00354569i
$210$	2.30113	−	3.75166i	0.158793	−	0.258889i
$211$	15.8447	+	4.65242i	1.09079	+	0.320286i	0.777188	−	0.629268i	$-0.216645\pi$
$211$	15.8447	+	4.65242i	1.09079	+	0.320286i	0.313605	+	0.949554i	$0.398463\pi$
$212$	−1.15721	+	1.00273i	−0.0794777	+	0.0688678i
$213$	15.6221	+	6.12413i	1.07041	+	0.419619i
$214$	−8.46074	+	13.1652i	−0.578364	+	0.899952i
$215$	−7.63226	−	7.07860i	−0.520516	−	0.482757i
$216$	−4.67891	+	2.26005i	−0.318359	+	0.153777i
$217$	8.55508	−	5.49802i	0.580757	−	0.373230i
$218$	6.03462	−	0.867648i	0.408716	−	0.0587645i
$219$	4.47118	−	7.87459i	0.302135	−	0.532116i
$220$	−0.509072	−	1.97868i	−0.0343216	−	0.133402i
$221$	−18.5514	+	21.4094i	−1.24790	+	1.44015i
$222$	−5.50453	−	10.4913i	−0.369440	−	0.704130i
$223$	−5.77324	+	8.98334i	−0.386605	+	0.601569i	−0.978946	−	0.204118i	$-0.934567\pi$
$223$	−5.77324	+	8.98334i	−0.386605	+	0.601569i	0.592341	+	0.805687i	$0.298204\pi$
$224$	−1.09034	+	0.320153i	−0.0728515	+	0.0213911i
$225$	14.2021	−	4.82690i	0.946810	−	0.321793i
$226$	2.74638	−	9.35332i	0.182687	−	0.622173i
$227$	−6.55117	+	2.99182i	−0.434817	+	0.198574i	−0.620784	−	0.783982i	$-0.713186\pi$
$227$	−6.55117	+	2.99182i	−0.434817	+	0.198574i	0.185967	+	0.982556i	$0.440458\pi$
$228$	0.490745	−	0.474711i	0.0325004	−	0.0314385i
$229$			14.7923i			0.977502i	0.872423	+	0.488751i	$0.162547\pi$
$229$			14.7923i			0.977502i	−0.872423	+	0.488751i	$0.837453\pi$
$230$	−9.57844	+	4.82220i	−0.631583	+	0.317966i
$231$	1.10151	−	1.42161i	0.0724738	−	0.0935348i
$232$	10.0363	+	1.44301i	0.658919	+	0.0947382i
$233$	−3.13206	−	6.85824i	−0.205188	−	0.449299i	0.778861	−	0.627196i	$-0.215798\pi$
$233$	−3.13206	−	6.85824i	−0.205188	−	0.449299i	−0.984049	+	0.177898i	$0.943070\pi$
$234$	13.7056	+	0.455375i	0.895964	+	0.0297688i
$235$	18.3988	−	7.66241i	1.20020	−	0.499840i
$236$	−1.48433	−	5.05517i	−0.0966218	−	0.329064i
$237$	−1.73867	−	4.90903i	−0.112939	−	0.318876i
$238$	6.40614	+	2.92559i	0.415249	+	0.189638i
$239$	−12.4756	−	10.8101i	−0.806976	−	0.699249i	0.150231	−	0.988651i	$-0.451998\pi$
$239$	−12.4756	−	10.8101i	−0.806976	−	0.699249i	−0.957208	+	0.289402i	$0.906544\pi$
$240$	−3.55602	−	1.53452i	−0.229540	−	0.0990529i
$241$	8.53816	−	1.22760i	0.549991	−	0.0790768i	0.138283	−	0.990393i	$-0.455842\pi$
$241$	8.53816	−	1.22760i	0.549991	−	0.0790768i	0.411708	+	0.911316i	$0.364932\pi$
$242$	1.44665	+	10.0617i	0.0929942	+	0.646789i
$243$	−6.31029	−	14.2541i	−0.404805	−	0.914403i
$244$	−5.57318	−	4.82919i	−0.356786	−	0.309157i
$245$	−9.35926	−	8.68032i	−0.597941	−	0.554566i
$246$	−5.81965	−	16.4314i	−0.371048	−	1.04763i
$247$	−1.72892	+	0.507657i	−0.110009	+	0.0323015i
$248$	−5.86038	−	6.76324i	−0.372134	−	0.429466i
$249$	−10.6989	−	14.7980i	−0.678013	−	0.937786i
$250$	9.64793	+	5.64956i	0.610188	+	0.357310i
$251$	−3.58418	+	24.9285i	−0.226231	+	1.57347i	0.487544	+	0.873098i	$0.337893\pi$
$251$	−3.58418	+	24.9285i	−0.226231	+	1.57347i	−0.713776	+	0.700375i	$0.753016\pi$
$252$	−0.851308	−	3.30111i	−0.0536274	−	0.207951i
$253$	−4.10512	+	1.53291i	−0.258087	+	0.0963733i
$254$		−	14.9021i		−	0.935038i
$255$	10.4275	+	21.6191i	0.652996	+	1.35384i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−12.4856	−	3.66611i	−0.778831	−	0.228686i	−0.131930	−	0.991259i	$-0.542117\pi$
$257$	−12.4856	−	3.66611i	−0.778831	−	0.228686i	−0.646902	+	0.762573i	$0.723936\pi$
$258$	−8.05107	+	0.441586i	−0.501238	+	0.0274920i
$259$	7.45821	−	2.18993i	0.463431	−	0.136076i
$260$	6.42874	+	7.94633i	0.398694	+	0.492810i
$261$	−5.32647	+	29.9487i	−0.329700	+	1.85378i
$262$	0.483156	+	0.418657i	0.0298495	+	0.0258647i
$263$	9.83503	+	15.3036i	0.606454	+	0.943661i	0.999706	+	0.0242305i	$0.00771358\pi$
$263$	9.83503	+	15.3036i	0.606454	+	0.943661i	−0.393252	+	0.919431i	$0.628650\pi$
$264$	−1.37622	−	0.781415i	−0.0847004	−	0.0480928i
$265$	0.601458	−	3.37065i	0.0369473	−	0.207057i
$266$	0.242185	+	0.376847i	0.0148493	+	0.0231059i
$267$	5.38544	+	26.8996i	0.329584	+	1.64623i
$268$	2.57472	−	5.63786i	0.157276	−	0.344387i
$269$	−5.64427	+	8.78265i	−0.344137	+	0.535488i	−0.969578	−	0.244784i	$-0.921283\pi$
$269$	−5.64427	+	8.78265i	−0.344137	+	0.535488i	0.625440	+	0.780272i	$0.284919\pi$
$270$	4.95528	−	10.5093i	0.301569	−	0.639575i
$271$	−0.564550	−	0.651525i	−0.0342939	−	0.0395773i	0.738343	−	0.674425i	$-0.235608\pi$
$271$	−0.564550	−	0.651525i	−0.0342939	−	0.0395773i	−0.772637	+	0.634848i	$0.781063\pi$
$272$	1.74601	−	5.94637i	0.105868	−	0.360552i
$273$	−2.05818	+	8.75843i	−0.124566	+	0.530084i
$274$	−10.5290	−	1.51384i	−0.636080	−	0.0914545i
$275$	3.66778	+	2.72377i	0.221176	+	0.164250i
$276$	−2.46925	+	7.93113i	−0.148632	+	0.477398i
$277$			13.4347i			0.807212i	0.914933	+	0.403606i	$0.132243\pi$
$277$			13.4347i			0.807212i	−0.914933	+	0.403606i	$0.867757\pi$
$278$	1.38478	−	9.63135i	0.0830536	−	0.577650i
$279$	20.8623	−	16.8977i	1.24900	−	1.01164i
$280$	1.44519	−	2.09001i	0.0863664	−	0.124902i
$281$	8.66510	+	10.0001i	0.516917	+	0.596554i	0.952856	−	0.303422i	$-0.0981293\pi$
$281$	8.66510	+	10.0001i	0.516917	+	0.596554i	−0.435939	+	0.899976i	$0.643584\pi$
$282$	5.63454	−	14.3732i	0.335532	−	0.855911i
$283$	−25.3685	−	16.3033i	−1.50800	−	0.969132i	−0.993767	−	0.111481i	$-0.964441\pi$
$283$	−25.3685	−	16.3033i	−1.50800	−	0.969132i	−0.514232	−	0.857651i	$-0.671923\pi$
$284$	8.81225	+	4.02442i	0.522911	+	0.238805i
$285$	−0.185478	+	1.51542i	−0.0109868	+	0.0897659i
$286$	2.25805	+	3.51359i	0.133521	+	0.207763i
$287$	11.3202	−	1.62760i	0.668209	−	0.0960740i
$288$	−2.76878	+	1.15494i	−0.163152	+	0.0680554i
$289$	−18.0095	+	11.5740i	−1.05938	+	0.680822i
$290$	−19.4766	+	11.6066i	−1.14371	+	0.681563i
$291$	13.1268	+	25.0190i	0.769508	+	1.46664i
$292$	2.82655	−	4.39820i	0.165411	−	0.257385i
$293$	2.12053	+	7.22185i	0.123882	+	0.421905i	0.997957	−	0.0638867i	$-0.0203496\pi$
$293$	2.12053	+	7.22185i	0.123882	+	0.421905i	−0.874075	+	0.485791i	$0.838531\pi$
$294$	−9.87285	+	0.541507i	−0.575796	+	0.0315813i
$295$	9.68996	+	6.70035i	0.564171	+	0.390109i
$296$	−2.84154	−	6.22212i	−0.165161	−	0.361653i
$297$	2.48005	−	4.04853i	0.143907	−	0.234920i
$298$	−8.73920			−0.506248
$299$	15.4953	−	15.5071i	0.896117	−	0.896800i
$300$	8.33993	−	2.33357i	0.481506	−	0.134729i
$301$	0.752864	−	5.23628i	0.0433943	−	0.301814i
$302$	−0.984710	−	2.15621i	−0.0566637	−	0.124076i
$303$	6.37979	+	8.82413i	0.366509	+	0.506933i
$304$	0.297917	−	0.258146i	0.0170867	−	0.0148057i
$305$	16.4802	+	0.556938i	0.943654	+	0.0318902i
$306$	17.6553	+	5.82753i	1.00929	+	0.333138i
$307$	−20.7597	−	9.48065i	−1.18482	−	0.541090i	−0.277172	−	0.960820i	$-0.589397\pi$
$307$	−20.7597	−	9.48065i	−1.18482	−	0.541090i	−0.907649	+	0.419731i	$0.862124\pi$
$308$	0.679950	−	0.784704i	0.0387438	−	0.0447127i
$309$	0.451904	−	5.12163i	0.0257079	−	0.291359i
$310$	19.6995	+	3.51517i	1.11886	+	0.199648i
$311$	7.18241	−	1.03267i	0.407277	−	0.0585576i	0.0643681	−	0.997926i	$-0.479497\pi$
$311$	7.18241	−	1.03267i	0.407277	−	0.0585576i	0.342909	+	0.939369i	$0.388588\pi$
$312$	7.88666	+	0.695875i	0.446494	+	0.0393961i
$313$	−11.7474	+	13.5572i	−0.664001	+	0.766298i	−0.983425	−	0.181313i	$-0.941965\pi$
$313$	−11.7474	+	13.5572i	−0.664001	+	0.766298i	0.319424	+	0.947612i	$0.396511\pi$
$314$	−7.55355	+	16.5400i	−0.426271	+	0.933404i
$315$	6.12261	+	4.54138i	0.344970	+	0.255878i
$316$	−0.847098	−	2.88495i	−0.0476530	−	0.162291i
$317$	−8.78306	−	10.1362i	−0.493306	−	0.569305i	0.453440	−	0.891287i	$-0.350197\pi$
$317$	−8.78306	−	10.1362i	−0.493306	−	0.569305i	−0.946746	+	0.321982i	$0.895651\pi$
$318$	−1.55389	−	2.14924i	−0.0871378	−	0.120524i
$319$	−8.42737	+	3.84865i	−0.471842	+	0.215483i
$320$	−2.00146	−	0.997065i	−0.111885	−	0.0557376i
$321$	−21.4265	−	16.6019i	−1.19591	−	0.926628i
$322$	−4.78421	−	2.61001i	−0.266614	−	0.145450i
$323$	−2.44302			−0.135933
$324$	−3.18708	−	8.41680i	−0.177060	−	0.467600i
$325$	−22.3515	−	4.77252i	−1.23984	−	0.264732i
$326$	4.38518	−	14.9345i	0.242872	−	0.827148i
$327$	0.578314	+	10.5439i	0.0319808	+	0.583079i
$328$	−2.83539	−	9.65645i	−0.156558	−	0.533188i
$329$	8.52084	+	5.47601i	0.469769	+	0.301902i
$330$	3.49140	−	0.577103i	0.192195	−	0.0317685i
$331$	10.6386	−	12.2776i	0.584748	−	0.674836i	−0.383870	−	0.923387i	$-0.625409\pi$
$331$	10.6386	−	12.2776i	0.584748	−	0.674836i	0.968619	+	0.248551i	$0.0799545\pi$
$332$	−5.69983	−	8.86910i	−0.312819	−	0.486755i
$333$	18.9391	−	7.90008i	1.03786	−	0.432922i
$334$	−0.951414	−	6.61723i	−0.0520591	−	0.362079i
$335$	3.45319	+	13.4219i	0.188668	+	0.733319i
$336$	−0.386387	−	1.92996i	−0.0210792	−	0.105288i
$337$	−0.990198	+	2.16823i	−0.0539395	+	0.118111i	−0.934683	−	0.355483i	$-0.884316\pi$
$337$	−0.990198	+	2.16823i	−0.0539395	+	0.118111i	0.880743	+	0.473594i	$0.157044\pi$
$338$	−6.64134	−	4.26813i	−0.361241	−	0.232156i
$339$	15.7196	+	6.16236i	0.853773	+	0.334694i
$340$	5.32771	+	12.7928i	0.288936	+	0.693785i
$341$	7.84559	+	2.30367i	0.424863	+	0.124751i
$342$	0.744333	+	0.918974i	0.0402489	+	0.0496924i
$343$	2.05528	−	14.2948i	0.110975	−	0.771845i
$344$	−4.65528			−0.250996
$345$	−6.86179	−	17.2602i	−0.369426	−	0.929260i
$346$	−19.4556			−1.04594
$347$	−2.54956	+	17.7326i	−0.136867	+	0.951934i	0.799438	+	0.600748i	$0.205130\pi$
$347$	−2.54956	+	17.7326i	−0.136867	+	0.951934i	−0.936306	+	0.351186i	$0.885779\pi$
$348$	−4.01758	+	17.0965i	−0.215365	+	0.916469i
$349$	4.48842	+	1.31792i	0.240260	+	0.0705466i	0.399646	−	0.916670i	$-0.369133\pi$
$349$	4.48842	+	1.31792i	0.240260	+	0.0705466i	−0.159386	+	0.987216i	$0.550951\pi$
$350$	0.427081	+	5.66579i	0.0228284	+	0.302849i
$351$	−2.87215	+	23.5776i	−0.153304	+	1.25848i
$352$	−0.768660	−	0.493988i	−0.0409697	−	0.0263296i
$353$	−0.0845283	+	0.185091i	−0.00449899	+	0.00985141i	−0.911868	−	0.410483i	$-0.865360\pi$
$353$	−0.0845283	+	0.185091i	−0.00449899	+	0.00985141i	0.907369	+	0.420335i	$0.138087\pi$
$354$	8.94789	−	1.79142i	0.475575	−	0.0952127i
$355$	−20.9792	+	5.39750i	−1.11346	+	0.286470i
$356$	2.25408	+	15.6775i	0.119466	+	0.830904i
$357$	−6.02289	+	10.6074i	−0.318765	+	0.561406i
$358$	2.43238	+	3.78485i	0.128555	+	0.200036i
$359$	17.1471	−	19.7888i	0.904987	−	1.04441i	−0.0938202	−	0.995589i	$-0.529908\pi$
$359$	17.1471	−	19.7888i	0.904987	−	1.04441i	0.998808	−	0.0488218i	$-0.0155466\pi$
$360$	3.18893	−	5.90175i	0.168072	−	0.311050i
$361$	15.8531	+	10.1882i	0.834373	+	0.536219i
$362$	−4.21144	−	14.3428i	−0.221348	−	0.753843i
$363$	−17.5801	+	0.964236i	−0.922717	+	0.0506093i
$364$	−1.46344	+	4.98401i	−0.0767050	+	0.261233i
$365$	1.27195	+	11.6211i	0.0665771	+	0.608276i
$366$	9.18047	−	8.88051i	0.479871	−	0.464192i
$367$	11.5036			0.600485			0.300243	−	0.953863i	$-0.402932\pi$
$367$	11.5036			0.600485			0.300243	+	0.953863i	$0.402932\pi$
$368$	−1.67426	+	4.49409i	−0.0872768	+	0.234271i
$369$	29.2358	−	7.53949i	1.52196	−	0.392490i
$370$	13.6905	+	6.82018i	0.711737	+	0.354564i
$371$	1.58278	−	0.722833i	0.0821740	−	0.0375276i
$372$	12.5611	−	9.08159i	0.651262	−	0.470858i
$373$	1.82996	+	2.11188i	0.0947515	+	0.109349i	0.801145	−	0.598470i	$-0.204225\pi$
$373$	1.82996	+	2.11188i	0.0947515	+	0.109349i	−0.706394	+	0.707819i	$0.749679\pi$
$374$	1.59535	+	5.43325i	0.0824933	+	0.280947i
$375$	−11.2162	+	15.7860i	−0.579202	+	0.815184i
$376$	3.70268	−	8.10775i	0.190951	−	0.418125i
$377$	30.3518	−	35.0279i	1.56320	−	1.80403i
$378$	5.82517	−	0.966258i	0.299614	−	0.0496990i
$379$	0.210121	−	0.0302108i	0.0107932	−	0.00155183i	−0.136916	−	0.990583i	$-0.543719\pi$
$379$	0.210121	−	0.0302108i	0.0107932	−	0.00155183i	0.147709	+	0.989031i	$0.452810\pi$
$380$	−0.154841	+	0.867752i	−0.00794319	+	0.0445147i
$381$	25.7112	+	2.26861i	1.31723	+	0.116225i
$382$	−5.19023	+	5.98985i	−0.265555	+	0.306467i
$383$	−28.5118	−	13.0209i	−1.45689	−	0.665338i	−0.479644	−	0.877463i	$-0.659234\pi$
$383$	−28.5118	−	13.0209i	−1.45689	−	0.665338i	−0.977242	+	0.212125i	$0.931961\pi$
$384$	−1.63267	+	0.578258i	−0.0833169	+	0.0295091i
$385$	−0.0784169	+	2.32041i	−0.00399649	+	0.118259i
$386$	−5.97374	+	5.17628i	−0.304056	+	0.263466i
$387$	0.463764	−	13.9581i	0.0235745	−	0.709531i
$388$	6.77633	+	14.8381i	0.344016	+	0.753290i
$389$	−2.59557	+	18.0526i	−0.131600	+	0.915301i	0.811869	+	0.583840i	$0.198451\pi$
$389$	−2.59557	+	18.0526i	−0.131600	+	0.915301i	−0.943469	+	0.331461i	$0.892459\pi$
$390$	−14.6889	+	9.88210i	−0.743799	+	0.500400i
$391$	26.0807	−	14.2540i	1.31896	−	0.720858i
$392$	−5.70866			−0.288331
$393$	−0.795883	+	0.769879i	−0.0401470	+	0.0388352i
$394$	2.10668	+	4.61298i	0.106133	+	0.232398i
$395$	5.52999	+	3.82384i	0.278244	+	0.192398i
$396$	1.55772	−	2.25550i	0.0782784	−	0.113343i
$397$	5.20139	+	17.7143i	0.261050	+	0.889055i	0.980832	+	0.194855i	$0.0624236\pi$
$397$	5.20139	+	17.7143i	0.261050	+	0.889055i	−0.719782	+	0.694200i	$0.755758\pi$
$398$	6.48735	−	10.0945i	0.325182	−	0.505992i
$399$	−0.687060	+	0.360483i	−0.0343960	+	0.0180467i
$400$	4.88162	−	1.08156i	0.244081	−	0.0540782i
$401$	0.210668	−	0.135388i	0.0105203	−	0.00676096i	−0.535370	−	0.844618i	$-0.679828\pi$
$401$	0.210668	−	0.135388i	0.0105203	−	0.00676096i	0.545890	+	0.837857i	$0.316192\pi$
$402$	9.33530	+	5.30057i	0.465602	+	0.264368i
$403$	−40.4902	+	5.82162i	−2.01696	+	0.289995i
$404$	3.39883	+	5.28869i	0.169098	+	0.263122i
$405$	17.3778	+	10.1495i	0.863510	+	0.504331i
$406$	−10.4811	−	4.78654i	−0.520166	−	0.237552i
$407$	5.25783	+	3.37900i	0.260621	+	0.167491i
$408$	9.99375	+	3.91772i	0.494765	+	0.193956i
$409$	−10.4300	−	12.0368i	−0.515728	−	0.595182i	0.436828	−	0.899545i	$-0.356102\pi$
$409$	−10.4300	−	12.0368i	−0.515728	−	0.595182i	−0.952556	+	0.304363i	$0.901556\pi$
$410$	18.5099	+	12.7991i	0.914138	+	0.632102i
$411$	4.21478	−	17.9357i	0.207900	−	0.884704i
$412$	0.422456	−	2.93825i	0.0208129	−	0.144757i
$413$			5.98708i			0.294605i
$414$	−13.3080	−	5.46772i	−0.654055	−	0.268724i
$415$	22.3821	+	7.40181i	1.09869	+	0.363341i
$416$	4.52453	+	0.650529i	0.221833	+	0.0318948i
$417$	16.4066	+	3.85545i	0.803436	+	0.188802i
$418$	−0.101476	+	0.345594i	−0.00496333	+	0.0169036i
$419$	−10.4325	−	12.0398i	−0.509661	−	0.588180i	0.441351	−	0.897335i	$-0.354500\pi$
$419$	−10.4325	−	12.0398i	−0.509661	−	0.588180i	−0.951012	+	0.309154i	$0.899954\pi$
$420$	3.38599	+	2.81162i	0.165219	+	0.137193i
$421$	10.0357	−	15.6159i	0.489111	−	0.761072i	−0.505711	−	0.862703i	$-0.668770\pi$
$421$	10.0357	−	15.6159i	0.489111	−	0.761072i	0.994822	+	0.101631i	$0.0324062\pi$
$422$	−6.86000	+	15.0213i	−0.333939	+	0.731225i
$423$	23.9410	+	11.9096i	1.16405	+	0.579066i
$424$	−0.827835	−	1.28814i	−0.0402032	−	0.0625575i
$425$	−27.2535	−	14.7461i	−1.32199	−	0.715289i
$426$	−8.28506	+	14.5915i	−0.401412	+	0.706962i
$427$	4.53059	+	7.04974i	0.219251	+	0.341161i
$428$	−11.8271	−	10.2482i	−0.571683	−	0.495366i
$429$	−6.40592	+	3.36103i	−0.309281	+	0.162272i
$430$	8.09273	−	6.54718i	0.390266	−	0.315733i
$431$	6.68325	−	1.96238i	0.321921	−	0.0945244i	−0.116780	−	0.993158i	$-0.537257\pi$
$431$	6.68325	−	1.96238i	0.321921	−	0.0945244i	0.438700	+	0.898633i	$0.355439\pi$
$432$	−1.57117	−	4.95292i	−0.0755928	−	0.238298i
$433$	26.5442	+	7.79408i	1.27563	+	0.374559i	0.848291	−	0.529531i	$-0.177632\pi$
$433$	26.5442	+	7.79408i	1.27563	+	0.374559i	0.427341	+	0.904090i	$0.359450\pi$
$434$	4.22454	+	9.25045i	0.202784	+	0.444036i
$435$	−17.0604	−	35.3709i	−0.817984	−	1.69591i
$436$			6.09668i			0.291978i
$437$	1.88575	+	0.134150i	0.0902078	+	0.00641726i
$438$	7.15813	+	5.54635i	0.342028	+	0.265015i
$439$	1.67590	−	11.6562i	0.0799864	−	0.556318i	−0.909941	−	0.414739i	$-0.863873\pi$
$439$	1.67590	−	11.6562i	0.0799864	−	0.556318i	0.989927	−	0.141579i	$-0.0452179\pi$
$440$	2.03098	−	0.222295i	0.0968234	−	0.0105975i
$441$	0.568704	−	17.1165i	0.0270811	−	0.815073i
$442$	−18.5514	−	21.4094i	−0.882399	−	1.01834i
$443$	25.6971	−	7.54536i	1.22091	−	0.358491i	0.393097	−	0.919497i	$-0.371404\pi$
$443$	25.6971	−	7.54536i	1.22091	−	0.358491i	0.827812	+	0.561006i	$0.189586\pi$
$444$	11.1679	−	3.95543i	0.530005	−	0.187716i
$445$	−25.9673	−	24.0836i	−1.23097	−	1.14167i
$446$	−8.07029	−	6.99294i	−0.382139	−	0.331125i
$447$	1.33041	−	15.0782i	0.0629263	−	0.713173i
$448$	−0.161723	−	1.12481i	−0.00764068	−	0.0531421i
$449$	20.2233	−	2.90767i	0.954398	−	0.137222i	0.352515	−	0.935806i	$-0.385327\pi$
$449$	20.2233	−	2.90767i	0.954398	−	0.137222i	0.601883	+	0.798585i	$0.294417\pi$
$450$	2.75659	+	14.7445i	0.129947	+	0.695064i
$451$	6.94962	+	6.02188i	0.327245	+	0.283559i
$452$	8.86726	+	4.04954i	0.417081	+	0.190474i
$453$	3.87013	−	1.37072i	0.181834	−	0.0644018i
$454$	−2.02904	−	6.91027i	−0.0952275	−	0.324315i
$455$	−4.46548	−	10.7224i	−0.209345	−	0.502674i
$456$	0.400039	+	0.553309i	0.0187335	+	0.0259111i
$457$	−4.15562	−	9.09955i	−0.194392	−	0.425659i	0.787187	−	0.616714i	$-0.211536\pi$
$457$	−4.15562	−	9.09955i	−0.194392	−	0.425659i	−0.981579	+	0.191055i	$0.938809\pi$
$458$	−14.6417	−	2.10516i	−0.684163	−	0.0983678i
$459$	−12.7423	+	29.5744i	−0.594759	+	1.38042i
$460$	−3.40996	−	10.1672i	−0.158990	−	0.474049i
$461$			17.0976i			0.796314i	0.917317	+	0.398157i	$0.130350\pi$
$461$			17.0976i			0.796314i	−0.917317	+	0.398157i	$0.869650\pi$
$462$	1.25038	+	1.29261i	0.0581727	+	0.0601376i
$463$	7.29605	−	3.33199i	0.339076	−	0.154851i	−0.238598	−	0.971118i	$-0.576688\pi$
$463$	7.29605	−	3.33199i	0.339076	−	0.154851i	0.577674	+	0.816268i	$0.303961\pi$
$464$	−2.85664	+	9.72883i	−0.132616	+	0.451650i
$465$	−9.06385	+	33.4534i	−0.420326	+	1.55136i
$466$	7.23417	−	2.12415i	0.335117	−	0.0983991i
$467$	−12.6660	+	19.7087i	−0.586113	+	0.912010i	0.413885	+	0.910329i	$0.364172\pi$
$467$	−12.6660	+	19.7087i	−0.586113	+	0.912010i	−0.999999	+	0.00168120i	$0.999465\pi$
$468$	−2.40125	+	13.5013i	−0.110998	+	0.624098i
$469$	−4.61230	+	5.32288i	−0.212976	+	0.245788i
$470$	4.96600	+	19.3020i	0.229064	+	0.890334i
$471$	−27.3873	−	15.5505i	−1.26194	−	0.716527i
$472$	5.21496	−	0.749798i	0.240038	−	0.0345122i
$473$	3.57832	−	2.29965i	0.164532	−	0.105738i
$474$	5.10650	−	1.02235i	0.234549	−	0.0469580i
$475$	−0.951231	−	1.72627i	−0.0436455	−	0.0792067i
$476$	−3.80750	+	5.92458i	−0.174516	+	0.271553i
$477$	3.94475	−	2.35381i	0.180618	−	0.107774i
$478$	12.4756	−	10.8101i	0.570619	−	0.494444i
$479$	−39.1601	−	11.4984i	−1.78927	−	0.525377i	−0.792811	−	0.609467i	$-0.791383\pi$
$479$	−39.1601	−	11.4984i	−1.78927	−	0.525377i	−0.996458	+	0.0840904i	$0.973202\pi$
$480$	2.02498	−	3.30143i	0.0924271	−	0.150689i
$481$	−30.9490	−	4.44979i	−1.41115	−	0.202893i
$482$			8.62596i			0.392902i
$483$	5.23151	−	7.85710i	0.238042	−	0.357510i
$484$	−10.1651			−0.462052
$485$	−32.6483	−	16.2643i	−1.48248	−	0.738524i
$486$	15.0071	−	4.21749i	0.680736	−	0.191309i
$487$	3.42982	−	11.6809i	0.155420	−	0.529312i	−0.844561	−	0.535459i	$-0.820139\pi$
$487$	3.42982	−	11.6809i	0.155420	−	0.529312i	0.999981	+	0.00614729i	$0.00195675\pi$
$488$	5.57318	−	4.82919i	0.252286	−	0.218607i
$489$	25.0997	+	9.83951i	1.13505	+	0.444958i
$490$	9.92393	−	8.02866i	0.448318	−	0.362698i
$491$	4.58738	+	2.09498i	0.207025	+	0.0945453i	0.516229	−	0.856450i	$-0.327335\pi$
$491$	4.58738	+	2.09498i	0.207025	+	0.0945453i	−0.309204	+	0.950996i	$0.600063\pi$
$492$	17.0924	−	3.42198i	0.770584	−	0.154275i
$493$	52.8635	−	33.9733i	2.38085	−	1.53008i
$494$	−0.256439	−	1.78357i	−0.0115377	−	0.0802467i
$495$	0.464189	+	6.11174i	0.0208638	+	0.274702i
$496$	7.52841	−	4.83822i	0.338036	−	0.217242i
$497$	−8.31993	−	7.20926i	−0.373200	−	0.323380i
$498$	16.1700	−	8.48399i	0.724595	−	0.380177i
$499$	−29.3886	−	18.8869i	−1.31562	−	0.845495i	−0.320796	−	0.947148i	$-0.603950\pi$
$499$	−29.3886	−	18.8869i	−1.31562	−	0.845495i	−0.994820	+	0.101653i	$0.967587\pi$
$500$	−6.96510	+	8.74571i	−0.311489	+	0.391120i
$501$	11.5619	−	0.634147i	0.516546	−	0.0283316i
$502$	−24.1647	−	7.09539i	−1.07852	−	0.316683i
$503$	5.36550	−	2.45034i	0.239236	−	0.109255i	−0.292190	−	0.956360i	$-0.594384\pi$
$503$	5.36550	−	2.45034i	0.239236	−	0.109255i	0.531425	+	0.847105i	$0.321657\pi$
$504$	3.38867	−	0.372846i	0.150943	−	0.0166079i
$505$	−13.3466	−	4.41374i	−0.593914	−	0.196409i
$506$	−0.933090	−	4.28149i	−0.0414809	−	0.190336i
$507$	8.37505	−	10.8089i	0.371949	−	0.480038i
$508$	14.7504	+	2.12078i	0.654442	+	0.0940946i
$509$	−5.65035	+	2.58043i	−0.250447	+	0.114375i	−0.536683	−	0.843784i	$-0.680323\pi$
$509$	−5.65035	+	2.58043i	−0.250447	+	0.114375i	0.286236	+	0.958159i	$0.407596\pi$
$510$	−22.8830	+	7.24465i	−1.01328	+	0.320799i
$511$	−4.49000	+	3.89061i	−0.198626	+	0.172111i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−1.69886	+	1.14433i	−0.0750066	+	0.0505235i
$514$	5.40568	−	11.8368i	0.238434	−	0.522098i
$515$	3.39796	+	5.70200i	0.149732	+	0.251260i
$516$	0.708696	−	8.03197i	0.0311986	−	0.353588i
$517$	1.15902	+	8.06118i	0.0509738	+	0.354530i
$518$	1.10622	+	7.69396i	0.0486047	+	0.338053i
$519$	2.96183	−	33.5677i	0.130010	−	1.47346i
$520$	−8.78035	+	5.23242i	−0.385044	+	0.229457i
$521$	0.259221	−	0.567615i	0.0113567	−	0.0248676i	−0.903869	−	0.427810i	$-0.859285\pi$
$521$	0.259221	−	0.567615i	0.0113567	−	0.0248676i	0.915225	+	0.402942i	$0.132013\pi$
$522$	−28.8858	−	9.53440i	−1.26430	−	0.417309i
$523$	24.8294	−	7.29057i	1.08571	−	0.318794i	0.310551	−	0.950557i	$-0.399486\pi$
$523$	24.8294	−	7.29057i	1.08571	−	0.318794i	0.775162	+	0.631762i	$0.217668\pi$
$524$	−0.483156	+	0.418657i	−0.0211068	+	0.0182891i
$525$	−9.84047	−	0.125668i	−0.429473	−	0.00548458i
$526$	−16.5475	+	7.55700i	−0.721506	+	0.329501i
$527$	−54.8964	−	7.89291i	−2.39132	−	0.343820i
$528$	0.969318	−	1.25100i	0.0421841	−	0.0544429i
$529$	−20.9143	+	9.57048i	−0.909315	+	0.416108i
$530$	3.25075	+	1.07503i	0.141203	+	0.0466963i
$531$	1.72863	+	15.7109i	0.0750163	+	0.681797i
$532$	−0.407477	+	0.186089i	−0.0176664	+	0.00806796i
$533$	−44.1402	−	12.9607i	−1.91192	−	0.561392i
$534$	−27.3922	+	1.50241i	−1.18538	+	0.0650158i
$535$	34.9733	+	1.18190i	1.51203	+	0.0510980i
$536$	5.21405	+	3.35087i	0.225213	+	0.144735i
$537$	−6.90048	+	3.62051i	−0.297778	+	0.156236i
$538$	−7.89000	−	6.83672i	−0.340162	−	0.294752i
$539$	4.38802	−	2.82001i	0.189005	−	0.121466i
$540$	9.69711	+	6.40047i	0.417297	+	0.275432i
$541$	0.424572	+	2.95296i	0.0182538	+	0.126958i	0.996911	−	0.0785430i	$-0.0250268\pi$
$541$	0.424572	+	2.95296i	0.0182538	+	0.126958i	−0.978657	+	0.205501i	$0.934118\pi$
$542$	0.725237	−	0.466082i	0.0311516	−	0.0200199i
$543$	25.3875	−	5.08272i	1.08948	−	0.218120i
$544$	5.63736	+	2.57450i	0.241700	+	0.110381i
$545$	−8.57437	−	10.5985i	−0.367286	−	0.453988i
$546$	−8.37637	−	3.28368i	−0.358476	−	0.140529i
$547$	23.2611	−	20.1559i	0.994575	−	0.861804i	0.00416877	−	0.999991i	$-0.498673\pi$
$547$	23.2611	−	20.1559i	0.994575	−	0.861804i	0.990406	+	0.138187i	$0.0441276\pi$
$548$	2.99686	−	10.2064i	0.128020	−	0.435995i
$549$	13.9244	+	17.1914i	0.594278	+	0.733712i
$550$	−3.21803	+	3.24282i	−0.137217	+	0.138274i
$551$	3.99702			0.170279
$552$	−7.49899	−	3.57284i	−0.319178	−	0.152070i
$553$			3.41678i			0.145296i
$554$	−13.2979	−	1.91196i	−0.564976	−	0.0812312i
$555$	−13.8514	+	22.5827i	−0.587957	+	0.958580i
$556$	9.33625	+	2.74137i	0.395945	+	0.116260i
$557$	8.80579	−	7.63026i	0.373113	−	0.323304i	−0.448039	−	0.894014i	$-0.647877\pi$
$557$	8.80579	−	7.63026i	0.373113	−	0.323304i	0.821152	+	0.570710i	$0.193332\pi$
$558$	13.7567	+	23.0548i	0.582366	+	0.975987i
$559$	−11.5046	+	17.9015i	−0.486592	+	0.757152i
$560$	1.86307	+	1.72792i	0.0787289	+	0.0730178i
$561$	−9.61711	+	1.92540i	−0.406035	+	0.0812903i
$562$	−11.1314	+	7.15375i	−0.469552	+	0.301763i
$563$	−8.52409	+	1.22558i	−0.359248	+	0.0516520i	−0.319576	−	0.947561i	$-0.603540\pi$
$563$	−8.52409	+	1.22558i	−0.359248	+	0.0516520i	−0.0396719	+	0.999213i	$0.512631\pi$
$564$	13.4250	+	7.62270i	0.565295	+	0.320974i
$565$	−21.1101	+	5.43120i	−0.888110	+	0.228492i
$566$	19.7477	−	22.7900i	0.830057	−	0.957937i
$567$	0.780337	+	10.1975i	0.0327711	+	0.428256i
$568$	−5.23757	+	8.14982i	−0.219764	+	0.341959i
$569$	2.26547	−	0.665201i	0.0949733	−	0.0278867i	−0.233901	−	0.972261i	$-0.575149\pi$
$569$	2.26547	−	0.665201i	0.0949733	−	0.0278867i	0.328874	+	0.944374i	$0.393331\pi$
$570$	−1.47360	−	0.399257i	−0.0617224	−	0.0167230i
$571$	−3.60250	+	12.2690i	−0.150760	+	0.513441i	−0.999891	−	0.0147407i	$-0.995308\pi$
$571$	−3.60250	+	12.2690i	−0.150760	+	0.513441i	0.849132	+	0.528181i	$0.177126\pi$
$572$	−3.79918	+	1.73503i	−0.158852	+	0.0725451i
$573$	−9.54444	−	9.86682i	−0.398725	−	0.412192i
$574$			11.4366i			0.477354i
$575$	20.2270	+	12.8789i	0.843526	+	0.537088i
$576$	−0.749146	−	2.90496i	−0.0312144	−	0.121040i
$577$	25.2836	+	3.63524i	1.05257	+	0.151337i	0.646817	−	0.762645i	$-0.276100\pi$
$577$	25.2836	+	3.63524i	1.05257	+	0.151337i	0.405755	+	0.913982i	$0.367009\pi$
$578$	−8.89316	−	19.4733i	−0.369907	−	0.809983i
$579$	−8.02147	−	11.0948i	−0.333361	−	0.461084i
$580$	−8.71665	−	20.9302i	−0.361939	−	0.869079i
$581$	3.37529	+	11.4952i	0.140030	+	0.476900i
$582$	−26.6324	+	9.43264i	−1.10395	+	0.390996i
$583$	1.27265	+	0.581199i	0.0527077	+	0.0240708i
$584$	3.95117	+	3.42371i	0.163501	+	0.141674i
$585$	−14.8139	−	26.8478i	−0.612480	−	1.11002i
$586$	−7.45012	+	1.07117i	−0.307762	+	0.0442494i
$587$	3.99189	+	27.7642i	0.164763	+	1.14595i	0.889503	+	0.456929i	$0.151051\pi$
$587$	3.99189	+	27.7642i	0.164763	+	1.14595i	−0.724740	+	0.689022i	$0.758040\pi$
$588$	0.869057	−	9.84942i	0.0358393	−	0.406183i
$589$	−2.66607	−	2.31016i	−0.109853	−	0.0951886i
$590$	−8.01117	+	8.63777i	−0.329815	+	0.355611i
$591$	−8.27970	+	2.93249i	−0.340581	+	0.120627i
$592$	6.56318	−	1.92712i	0.269745	−	0.0792043i
$593$	13.0277	+	15.0347i	0.534982	+	0.617402i	0.957318	−	0.289037i	$-0.0933351\pi$
$593$	13.0277	+	15.0347i	0.534982	+	0.617402i	−0.422336	+	0.906439i	$0.638790\pi$
$594$	3.65438	+	3.03098i	0.149941	+	0.124362i
$595$	−1.71338	−	15.6542i	−0.0702418	−	0.641758i
$596$	1.24372	−	8.65025i	0.0509447	−	0.354328i
$597$	16.4289	+	12.7297i	0.672392	+	0.520991i
$598$	13.1441	+	17.5445i	0.537501	+	0.717447i
$599$			27.6371i			1.12922i	0.825357	+	0.564611i	$0.190974\pi$
$599$			27.6371i			1.12922i	−0.825357	+	0.564611i	$0.809026\pi$
$600$	1.12292	+	8.58714i	0.0458431	+	0.350569i
$601$	12.5572	+	27.4964i	0.512219	+	1.12160i	0.972302	+	0.233727i	$0.0750922\pi$
$601$	12.5572	+	27.4964i	0.512219	+	1.12160i	−0.460083	+	0.887876i	$0.652180\pi$
$602$	5.07584	+	1.49040i	0.206876	+	0.0607442i
$603$	−10.5665	+	15.2997i	−0.430301	+	0.623052i
$604$	2.27441	−	0.667826i	0.0925442	−	0.0271734i
$605$	17.6711	−	14.2963i	0.718432	−	0.581226i
$606$	−9.64225	+	5.05905i	−0.391690	+	0.205510i
$607$	22.1014	+	19.1510i	0.897069	+	0.777315i	0.975591	−	0.219597i	$-0.0704744\pi$
$607$	22.1014	+	19.1510i	0.897069	+	0.777315i	−0.0785212	+	0.996912i	$0.525020\pi$
$608$	0.213121	+	0.331622i	0.00864319	+	0.0134491i
$609$	9.85403	−	17.3548i	0.399305	−	0.703252i
$610$	−2.89665	+	16.2332i	−0.117282	+	0.657263i
$611$	−22.0272	−	34.2751i	−0.891127	−	1.38662i
$612$	−8.28083	+	16.6463i	−0.334733	+	0.672886i
$613$	0.700560	−	1.53401i	0.0282953	−	0.0619581i	−0.894957	−	0.446153i	$-0.852794\pi$
$613$	0.700560	−	1.53401i	0.0282953	−	0.0619581i	0.923252	+	0.384195i	$0.125521\pi$
$614$	12.3386	−	19.1992i	0.497944	−	0.774816i
$615$	−24.9007	+	29.9875i	−1.00409	+	1.20921i
$616$	0.679950	+	0.784704i	0.0273960	+	0.0316166i
$617$	−8.90832	+	30.3390i	−0.358636	+	1.22140i	0.560731	+	0.827998i	$0.310520\pi$
$617$	−8.90832	+	30.3390i	−0.358636	+	1.22140i	−0.919366	+	0.393402i	$0.871298\pi$
$618$	5.00519	+	1.17619i	0.201338	+	0.0473132i
$619$	−11.5292	−	1.65765i	−0.463399	−	0.0666267i	−0.0933386	−	0.995634i	$-0.529754\pi$
$619$	−11.5292	−	1.65765i	−0.463399	−	0.0666267i	−0.370060	+	0.929008i	$0.620663\pi$
$620$	−6.28293	+	18.9987i	−0.252328	+	0.763007i
$621$	11.4597	−	22.1286i	0.459860	−	0.887991i
$622$			7.25627i			0.290950i
$623$	2.56147	−	17.8154i	0.102623	−	0.713761i
$624$	−1.81118	+	7.70736i	−0.0725053	+	0.308541i
$625$	−0.191839	−	24.9993i	−0.00767355	−	0.999971i
$626$	−11.7474	−	13.5572i	−0.469520	−	0.541855i
$627$	−0.580822	−	0.227692i	−0.0231958	−	0.00909314i
$628$	−15.2966	−	9.83055i	−0.610402	−	0.392282i
$629$	−38.5610	−	17.6102i	−1.53753	−	0.702165i
$630$	−5.36649	+	5.41398i	−0.213806	+	0.215698i
$631$	19.1110	+	29.7372i	0.760795	+	1.18382i	0.978185	+	0.207736i	$0.0666094\pi$
$631$	19.1110	+	29.7372i	0.760795	+	1.18382i	−0.217390	+	0.976085i	$0.569754\pi$
$632$	2.97614	−	0.427904i	0.118384	−	0.0170211i
$633$	−24.8726	−	14.1226i	−0.988598	−	0.561325i
$634$	11.2830	−	7.25113i	0.448104	−	0.287979i
$635$	−28.6247	+	17.0582i	−1.13594	+	0.676933i
$636$	2.34851	−	1.23220i	0.0931244	−	0.0488601i
$637$	−14.1078	+	21.9522i	−0.558972	+	0.869777i
$638$	−2.61014	−	8.88931i	−0.103336	−	0.351931i
$639$	−23.9142	−	16.5159i	−0.946031	−	0.653361i
$640$	1.27175	−	1.83920i	0.0502705	−	0.0727006i
$641$	−8.89291	−	19.4728i	−0.351249	−	0.769128i	−0.999967	−	0.00809917i	$-0.997422\pi$
$641$	−8.89291	−	19.4728i	−0.351249	−	0.769128i	0.648718	−	0.761029i	$-0.275305\pi$
$642$	19.4822	−	18.8457i	0.768902	−	0.743779i
$643$	−0.0334375			−0.00131865			−0.000659323	−	1.00000i	$-0.500210\pi$
$643$	−0.0334375			−0.00131865			−0.000659323		1.00000i	$0.500210\pi$
$644$	3.26431	−	4.36407i	0.128632	−	0.171969i
$645$	10.0642	+	14.9595i	0.396276	+	0.589029i
$646$	0.347678	−	2.41815i	0.0136792	−	0.0951410i
$647$	−7.02734	−	15.3877i	−0.276273	−	0.604954i	0.719732	−	0.694252i	$-0.244265\pi$
$647$	−7.02734	−	15.3877i	−0.276273	−	0.604954i	−0.996005	+	0.0892983i	$0.971538\pi$
$648$	8.78470	−	1.95680i	0.345096	−	0.0768704i
$649$	−3.63814	+	3.15247i	−0.142809	+	0.123745i
$650$	7.90488	−	21.4447i	0.310055	−	0.841132i
$651$	−16.6034	+	5.88056i	−0.650737	+	0.230477i
$652$	14.1585	+	6.46595i	0.554488	+	0.253226i
$653$	5.93377	−	6.84794i	0.232206	−	0.267980i	−0.627674	−	0.778477i	$-0.715993\pi$
$653$	5.93377	−	6.84794i	0.232206	−	0.267980i	0.859880	+	0.510496i	$0.170538\pi$
$654$	−10.5189	−	0.928127i	−0.411321	−	0.0362926i
$655$	0.251119	−	1.40731i	0.00981204	−	0.0549880i
$656$	9.96168	−	1.43227i	0.388938	−	0.0559209i
$657$	−10.6591	+	11.5059i	−0.415851	+	0.448888i
$658$	−6.63291	+	7.65479i	−0.258578	+	0.298415i
$659$	8.20148	−	17.9587i	0.319484	−	0.699573i	−0.679948	−	0.733260i	$-0.737998\pi$
$659$	8.20148	−	17.9587i	0.319484	−	0.699573i	0.999432	+	0.0336871i	$0.0107250\pi$
$660$	0.0743503	+	3.53799i	0.00289408	+	0.137716i
$661$	−6.37940	−	21.7262i	−0.248130	−	0.845053i	−0.985516	−	0.169582i	$-0.945758\pi$
$661$	−6.37940	−	21.7262i	−0.248130	−	0.845053i	0.737386	−	0.675471i	$-0.236060\pi$
$662$	10.6386	+	12.2776i	0.413480	+	0.477181i
$663$	39.7629	−	28.7483i	1.54426	−	1.11649i
$664$	9.59000	−	4.37960i	0.372164	−	0.169962i
$665$	0.446643	−	0.896573i	0.0173201	−	0.0347676i
$666$	5.12435	+	19.8707i	0.198564	+	0.769972i
$667$	−42.6705	+	23.3210i	−1.65221	+	0.902992i
$668$	6.68528			0.258661
$669$	13.2938	−	12.8595i	0.513969	−	0.497176i
$670$	−13.7768	+	1.50790i	−0.532243	+	0.0582551i
$671$	−1.89832	+	6.46509i	−0.0732839	+	0.249582i
$672$	1.96530	−	0.107793i	0.0758131	−	0.00415821i
$673$	11.5868	+	39.4612i	0.446640	+	1.52112i	0.808280	+	0.588798i	$0.200399\pi$
$673$	11.5868	+	39.4612i	0.446640	+	1.52112i	−0.361640	+	0.932318i	$0.617783\pi$
$674$	−2.00524	−	1.28869i	−0.0772390	−	0.0496385i
$675$	−25.8591	+	2.51144i	−0.995317	+	0.0966655i
$676$	5.16985	−	5.96632i	0.198840	−	0.229474i
$677$	3.54764	+	5.52023i	0.136347	+	0.212160i	0.902712	−	0.430245i	$-0.141573\pi$
$677$	3.54764	+	5.52023i	0.136347	+	0.212160i	−0.766365	+	0.642405i	$0.777937\pi$
$678$	−8.33678	+	14.6826i	−0.320172	+	0.563883i
$679$	−2.63805	−	18.3480i	−0.101239	−	0.704133i
$680$	−13.4208	+	3.45288i	−0.514663	+	0.132412i
$681$	12.2315	−	2.44881i	0.468713	−	0.0938387i
$682$	−3.39677	+	7.43789i	−0.130069	+	0.284812i
$683$	−12.3272	−	7.92223i	−0.471688	−	0.303136i	0.283116	−	0.959086i	$-0.408632\pi$
$683$	−12.3272	−	7.92223i	−0.471688	−	0.303136i	−0.754804	+	0.655950i	$0.772268\pi$
$684$	−1.01555	+	0.605973i	−0.0388305	+	0.0231700i
$685$	9.14452	+	21.9576i	0.349394	+	0.838956i
$686$	13.8568	+	4.06872i	0.529054	+	0.155344i
$687$	5.86112	−	24.9416i	0.223616	−	0.951581i
$688$	0.662515	−	4.60789i	0.0252581	−	0.175674i
$689$	−6.99926			−0.266650
$690$	18.0611	−	4.33556i	0.687574	−	0.165052i
$691$	−12.8771			−0.489870			−0.244935	−	0.969540i	$-0.578767\pi$
$691$	−12.8771			−0.489870			−0.244935	+	0.969540i	$0.578767\pi$
$692$	2.76882	−	19.2576i	0.105255	−	0.732064i
$693$	−2.42055	+	1.96055i	−0.0919492	+	0.0744752i
$694$	−17.1892	−	5.04721i	−0.652494	−	0.191590i
$695$	−20.0856	+	8.36491i	−0.761890	+	0.317299i
$696$	−16.3507	−	6.40977i	−0.619773	−	0.242962i
$697$	−52.4702	−	33.7206i	−1.98745	−	1.27726i
$698$	−1.94327	+	4.25518i	−0.0735540	+	0.161061i
$699$	2.56360	+	12.8048i	0.0969641	+	0.484323i
$700$	−5.66890	−	0.383592i	−0.214264	−	0.0144984i
$701$	−5.60529	−	38.9857i	−0.211709	−	1.47247i	−0.767448	−	0.641112i	$-0.778474\pi$
$701$	−5.60529	−	38.9857i	−0.211709	−	1.47247i	0.555739	−	0.831357i	$-0.312436\pi$
$702$	−22.9289	−	6.19836i	−0.865395	−	0.233942i
$703$	−1.45780	−	2.26838i	−0.0549820	−	0.0855536i
$704$	0.598351	−	0.690534i	0.0225512	−	0.0260255i
$705$	−34.0586	+	5.62964i	−1.28272	+	0.212024i
$706$	−0.171178	−	0.110009i	−0.00644235	−	0.00414025i
$707$	−2.01270	−	6.85462i	−0.0756954	−	0.257795i
$708$	0.499763	+	9.11176i	0.0187823	+	0.342441i
$709$	−12.9321	+	44.0427i	−0.485676	+	1.65406i	0.243627	+	0.969869i	$0.421663\pi$
$709$	−12.9321	+	44.0427i	−0.485676	+	1.65406i	−0.729303	+	0.684191i	$0.760155\pi$
$710$	−2.35692	−	21.5338i	−0.0884535	−	0.808148i
$711$	0.986518	+	8.96612i	0.0369973	+	0.336256i
$712$	−15.8387			−0.593580
$713$	41.9408	+	9.10693i	1.57069	+	0.341057i
$714$	−9.64233	−	7.47119i	−0.360855	−	0.279602i
$715$	4.16435	−	8.35934i	0.155738	−	0.312622i
$716$	−4.09249	+	1.86898i	−0.152944	+	0.0698470i
$717$	16.7520	+	23.1703i	0.625615	+	0.865312i
$718$	17.1471	+	19.7888i	0.639923	+	0.738510i
$719$	5.65708	+	19.2663i	0.210974	+	0.718510i	0.995185	+	0.0980161i	$0.0312497\pi$
$719$	5.65708	+	19.2663i	0.210974	+	0.718510i	−0.784211	+	0.620494i	$0.786932\pi$
$720$	5.38785	+	3.99638i	0.200793	+	0.148936i
$721$	−1.40131	+	3.06844i	−0.0521875	+	0.114275i
$722$	−12.3406	+	14.2418i	−0.459269	+	0.530025i
$723$	−14.8828	−	1.31317i	−0.553496	−	0.0488374i
$724$	14.7962	−	2.12737i	0.549897	−	0.0790632i
$725$	44.5893	+	24.1260i	1.65600	+	0.896015i
$726$	1.54749	−	17.5384i	0.0574327	−	0.650911i
$727$	−2.30834	+	2.66397i	−0.0856116	+	0.0988010i	−0.796939	−	0.604060i	$-0.793549\pi$
$727$	−2.30834	+	2.66397i	−0.0856116	+	0.0988010i	0.711327	+	0.702861i	$0.248094\pi$
$728$	−4.72501	−	2.15784i	−0.175121	−	0.0799749i
$729$	4.99203	+	26.5345i	0.184890	+	0.982759i
$730$	−11.6838	−	0.394848i	−0.432438	−	0.0146140i
$731$	−21.8039	+	18.8932i	−0.806445	+	0.698789i
$732$	7.48360	+	10.3508i	0.276602	+	0.382578i
$733$	18.1318	+	39.7032i	0.669715	+	1.46647i	0.873185	+	0.487389i	$0.162051\pi$
$733$	18.1318	+	39.7032i	0.669715	+	1.46647i	−0.203470	+	0.979081i	$0.565222\pi$
$734$	−1.63714	+	11.3866i	−0.0604279	+	0.420285i
$735$	12.3415	+	18.3445i	0.455222	+	0.676646i
$736$	−4.21008	−	2.29679i	−0.155185	−	0.0846610i
$737$	−5.66312			−0.208604
$738$	3.30206	+	30.0112i	0.121550	+	1.10473i
$739$	13.1449	+	28.7834i	0.483544	+	1.05881i	0.981474	+	0.191596i	$0.0613665\pi$
$739$	13.1449	+	28.7834i	0.483544	+	1.05881i	−0.497930	+	0.867217i	$0.665906\pi$
$740$	−8.69912	+	12.5806i	−0.319786	+	0.462471i
$741$	3.11632	−	0.170924i	0.114481	−	0.00627906i
$742$	0.490222	+	1.66954i	0.0179966	+	0.0612908i
$743$	0.127897	−	0.199011i	0.00469208	−	0.00730102i	−0.838900	−	0.544286i	$-0.816801\pi$
$743$	0.127897	−	0.199011i	0.00469208	−	0.00730102i	0.843592	+	0.536985i	$0.180437\pi$
$744$	7.20152	+	13.7257i	0.264021	+	0.503208i
$745$	10.0036	+	16.7868i	0.366505	+	0.615019i
$746$	−2.35082	+	1.51078i	−0.0860695	+	0.0553135i
$747$	12.1762	+	29.1904i	0.445504	+	1.06802i
$748$	−5.60499	+	0.805875i	−0.204939	+	0.0294657i
$749$	9.61455	+	14.9605i	0.351308	+	0.546646i
$750$	−14.0291	−	13.3486i	−0.512269	−	0.487423i
$751$	−12.8333	−	5.86078i	−0.468295	−	0.213863i	0.167269	−	0.985911i	$-0.446505\pi$
$751$	−12.8333	−	5.86078i	−0.468295	−	0.213863i	−0.635564	+	0.772048i	$0.719232\pi$
$752$	7.49828	+	4.81885i	0.273434	+	0.175725i
$753$	15.9207	−	40.6123i	0.580183	−	1.47999i
$754$	30.3518	+	35.0279i	1.10535	+	1.27564i
$755$	−3.01460	+	4.35967i	−0.109712	+	0.158665i
$756$	0.127415	+	5.90339i	0.00463405	+	0.214704i
$757$	6.72746	−	46.7905i	0.244514	−	1.70063i	−0.384410	−	0.923162i	$-0.625595\pi$
$757$	6.72746	−	46.7905i	0.244514	−	1.70063i	0.628924	−	0.777467i	$-0.283496\pi$
$758$			0.212282i			0.00771042i
$759$	7.52911	−	0.958111i	0.273289	−	0.0347772i
$760$	−0.836883	−	0.276759i	−0.0303569	−	0.0100391i
$761$	0.151958	+	0.0218482i	0.00550846	+	0.000791997i	0.145069	−	0.989422i	$-0.453660\pi$
$761$	0.151958	+	0.0218482i	0.00550846	+	0.000791997i	−0.139560	+	0.990214i	$0.544569\pi$
$762$	−5.90461	+	25.1267i	−0.213901	+	0.910243i
$763$	1.95187	−	6.64746i	0.0706625	−	0.240654i
$764$	−5.19023	−	5.98985i	−0.187776	−	0.216705i
$765$	−9.01595	−	40.5841i	−0.325972	−	1.46732i
$766$	16.9460	−	26.3686i	0.612285	−	0.952735i
$767$	10.0044	−	21.9067i	0.361240	−	0.791004i
$768$	−0.340018	−	1.69835i	−0.0122694	−	0.0612839i
$769$	18.3873	+	28.6113i	0.663064	+	1.03175i	0.996048	+	0.0888156i	$0.0283082\pi$
$769$	18.3873	+	28.6113i	0.663064	+	1.03175i	−0.332984	+	0.942933i	$0.608055\pi$
$770$	−2.28563	−	0.407848i	−0.0823686	−	0.0146978i
$771$	19.5996	+	11.1287i	0.705864	+	0.400789i
$772$	−4.27344	−	6.64960i	−0.153804	−	0.239324i
$773$	−7.91290	−	6.85656i	−0.284607	−	0.246613i	0.500843	−	0.865538i	$-0.333023\pi$
$773$	−7.91290	−	6.85656i	−0.284607	−	0.246613i	−0.785451	+	0.618924i	$0.787569\pi$
$774$	13.7501	+	2.44549i	0.494235	+	0.0879014i
$775$	−15.7976	−	41.8637i	−0.567466	−	1.50379i
$776$	−15.6514	+	4.59567i	−0.561853	+	0.164975i
$777$	−13.4432	+	0.737332i	−0.482271	+	0.0264517i
$778$	−17.4994	−	5.13829i	−0.627385	−	0.184217i
$779$	−1.64807	−	3.60876i	−0.0590481	−	0.129297i
$780$	−7.69107	−	15.9457i	−0.275385	−	0.570948i
$781$		−	8.85174i		−	0.316740i
$782$	10.3973	+	27.8438i	0.371806	+	0.995693i
$783$	20.8476	−	48.3866i	0.745032	−	1.72920i
$784$	0.812427	−	5.65055i	0.0290152	−	0.201805i
$785$	40.4174	−	4.42377i	1.44256	−	0.157891i
$786$	−0.648776	−	0.897347i	−0.0231411	−	0.0320073i
$787$	16.1693	+	18.6604i	0.576375	+	0.665172i	0.966821	−	0.255454i	$-0.0822248\pi$
$787$	16.1693	+	18.6604i	0.576375	+	0.665172i	−0.390446	+	0.920626i	$0.627679\pi$
$788$	−4.86583	+	1.42874i	−0.173338	+	0.0508967i
$789$	−10.5193	−	29.7007i	−0.374498	−	1.05737i
$790$	−4.57192	+	4.92951i	−0.162662	+	0.175384i
$791$	−8.37187	−	7.25427i	−0.297669	−	0.257932i
$792$	2.01085	+	1.86286i	0.0714525	+	0.0661937i
$793$	−4.79725	−	33.3656i	−0.170355	−	1.18485i
$794$	−18.2742	+	2.62744i	−0.648528	+	0.0932442i
$795$	−2.34968	+	5.44501i	−0.0833344	+	0.193115i
$796$	9.06852	+	7.85792i	0.321425	+	0.278517i
$797$	−34.0423	−	15.5466i	−1.20584	−	0.550690i	−0.291866	−	0.956459i	$-0.594276\pi$
$797$	−34.0423	−	15.5466i	−1.20584	−	0.550690i	−0.913975	+	0.405770i	$0.867004\pi$
$798$	−0.259035	−	0.731369i	−0.00916975	−	0.0258902i
$799$	−15.5626	−	53.0013i	−0.550565	−	1.87505i
$800$	0.375828	+	4.98586i	0.0132875	+	0.176277i
$801$	1.57787	−	47.4899i	0.0557513	−	1.67797i
$802$	0.104029	+	0.227791i	0.00367339	+	0.00804359i
$803$	−4.72838	−	0.679839i	−0.166861	−	0.0239910i
$804$	−6.57517	+	8.48593i	−0.231888	+	0.299276i
$805$	0.462956	+	12.1774i	0.0163170	+	0.429198i
$806$		−	40.9066i		−	1.44087i
$807$	12.9969	−	12.5722i	0.457511	−	0.442562i
$808$	−5.71856	+	2.61158i	−0.201178	+	0.0918751i
$809$	−14.3704	+	48.9410i	−0.505236	+	1.72067i	0.172172	+	0.985067i	$0.444921\pi$
$809$	−14.3704	+	48.9410i	−0.505236	+	1.72067i	−0.677408	+	0.735608i	$0.736897\pi$
$810$	−12.5193	+	15.7565i	−0.439883	+	0.553627i
$811$	15.6209	−	4.58672i	0.548526	−	0.161062i	0.00428497	−	0.999991i	$-0.498636\pi$
$811$	15.6209	−	4.58672i	0.548526	−	0.161062i	0.544241	+	0.838929i	$0.316818\pi$
$812$	6.22943	−	9.69319i	0.218610	−	0.340164i
$813$	0.693746	+	1.32224i	0.0243307	+	0.0463730i
$814$	−4.09288	+	4.72343i	−0.143455	+	0.165556i
$815$	−33.7068	+	8.67205i	−1.18070	+	0.303769i
$816$	−5.30011	+	9.33448i	−0.185541	+	0.326772i
$817$	−1.81643	+	0.261164i	−0.0635489	+	0.00913696i
$818$	13.3986	−	8.61078i	0.468472	−	0.301069i
$819$	6.94067	−	13.9523i	0.242527	−	0.487531i
$820$	−15.3030	+	16.5000i	−0.534405	+	0.576204i
$821$	17.1371	−	26.6659i	0.598089	−	0.930645i	−0.401799	−	0.915728i	$-0.631615\pi$
$821$	17.1371	−	26.6659i	0.598089	−	0.930645i	0.999889	−	0.0149175i	$-0.00474858\pi$
$822$	17.1533	+	6.72440i	0.598291	+	0.234540i
$823$	31.0843	−	26.9347i	1.08353	−	0.938883i	0.0851826	−	0.996365i	$-0.472853\pi$
$823$	31.0843	−	26.9347i	1.08353	−	0.938883i	0.998347	+	0.0574820i	$0.0183072\pi$
$824$	2.84822	+	0.836313i	0.0992224	+	0.0291343i
$825$	−5.10509	−	6.04589i	−0.177736	−	0.210491i
$826$	−5.92614	−	0.852050i	−0.206197	−	0.0296466i
$827$			2.35399i			0.0818562i	0.999162	+	0.0409281i	$0.0130315\pi$
$827$			2.35399i			0.0818562i	−0.999162	+	0.0409281i	$0.986969\pi$
$828$	7.30600	−	12.3945i	0.253901	−	0.430737i
$829$	6.73659			0.233971			0.116986	−	0.993134i	$-0.462677\pi$
$829$	6.73659			0.233971			0.116986	+	0.993134i	$0.462677\pi$
$830$	−10.5118	+	21.1009i	−0.364869	+	0.732422i
$831$	5.32320	−	22.6525i	0.184660	−	0.785807i
$832$	−1.28782	+	4.38590i	−0.0446470	+	0.152054i
$833$	−26.7376	+	23.1682i	−0.926402	+	0.802732i
$834$	−6.15112	+	15.6909i	−0.212996	+	0.543333i
$835$	−11.6217	+	9.40218i	−0.402185	+	0.325376i
$836$	−0.327635	−	0.149626i	−0.0113315	−	0.00517492i
$837$	−41.8717	+	20.2253i	−1.44730	+	0.699088i
$838$	13.4019	−	8.61288i	0.462961	−	0.297527i
$839$	4.56948	+	31.7814i	0.157756	+	1.09722i	0.902756	+	0.430152i	$0.141540\pi$
$839$	4.56948	+	31.7814i	0.157756	+	1.09722i	−0.745000	+	0.667064i	$0.767551\pi$
$840$	−3.26488	+	2.95139i	−0.112649	+	0.101833i
$841$	−62.0934	+	39.9050i	−2.14115	+	1.37603i
$842$	14.0287	+	12.1559i	0.483461	+	0.418921i
$843$	−10.6481	−	20.2947i	−0.366740	−	0.698986i
$844$	−13.8921	−	8.92793i	−0.478187	−	0.307312i
$845$	−0.596225	+	17.6427i	−0.0205108	+	0.606928i
$846$	−15.1956	+	22.0024i	−0.522434	+	0.756457i
$847$	11.0835	+	3.25440i	0.380833	+	0.111823i
$848$	1.39284	−	0.636088i	0.0478303	−	0.0218434i
$849$	36.3145	+	37.5411i	1.24631	+	1.28841i
$850$	18.4745	−	24.8775i	0.633671	−	0.853290i
$851$	28.7980	+	15.7107i	0.987183	+	0.538554i
$852$	−13.2639	−	10.2773i	−0.454415	−	0.352095i
$853$	13.5062	+	1.94190i	0.462443	+	0.0664893i	0.369599	−	0.929191i	$-0.379495\pi$
$853$	13.5062	+	1.94190i	0.462443	+	0.0664893i	0.0928442	+	0.995681i	$0.470404\pi$
$854$	−7.62275	+	3.48119i	−0.260845	+	0.119124i
$855$	0.913191	−	2.48169i	0.0312305	−	0.0848721i
$856$	11.8271	−	10.2482i	0.404241	−	0.350277i
$857$	53.4127	−	15.6834i	1.82454	−	0.535734i	0.824976	−	0.565168i	$-0.191189\pi$
$857$	53.4127	−	15.6834i	1.82454	−	0.535734i	0.999567	+	0.0294339i	$0.00937045\pi$
$858$	−2.41516	−	6.81904i	−0.0824521	−	0.232798i
$859$	−24.1175	+	52.8099i	−0.822878	+	1.80185i	−0.285890	+	0.958262i	$0.592289\pi$
$859$	−24.1175	+	52.8099i	−0.822878	+	1.80185i	−0.536988	+	0.843590i	$0.680438\pi$
$860$	5.32883	+	8.94212i	0.181712	+	0.304924i
$861$	−19.7321	−	1.74105i	−0.672468	−	0.0593348i
$862$	0.991279	+	6.89450i	0.0337631	+	0.234827i
$863$	−4.34944	−	30.2510i	−0.148057	−	1.02976i	−0.919396	−	0.393333i	$-0.871322\pi$
$863$	−4.34944	−	30.2510i	−0.148057	−	1.02976i	0.771339	−	0.636424i	$-0.219587\pi$
$864$	5.12611	−	0.850301i	0.174394	−	0.0289278i
$865$	22.2706	+	37.3715i	0.757222	+	1.27067i
$866$	−11.4924	+	25.1648i	−0.390527	+	0.855134i
$867$	34.9521	−	12.3793i	1.18703	−	0.420422i
$868$	−9.75751	+	2.86506i	−0.331192	+	0.0972466i
$869$	−2.07626	+	1.79909i	−0.0704323	+	0.0610299i
$870$	37.4388	−	11.8529i	1.26930	−	0.401852i
$871$	25.7710	−	11.7692i	0.873216	−	0.398784i
$872$	−6.03462	−	0.867648i	−0.204358	−	0.0293823i
$873$	−12.2202	−	47.3862i	−0.413591	−	1.60378i
$874$	−0.401155	+	1.84747i	−0.0135693	+	0.0624915i
$875$	10.3943	−	7.30591i	0.351392	−	0.246985i
$876$	−6.50860	+	6.29594i	−0.219905	+	0.212720i
$877$	−30.7409	+	14.0389i	−1.03805	+	0.474060i	−0.860178	−	0.509995i	$-0.829647\pi$
$877$	−30.7409	+	14.0389i	−1.03805	+	0.474060i	−0.177868	+	0.984054i	$0.556920\pi$
$878$	11.2990	+	3.31769i	0.381323	+	0.111967i
$879$	−0.713965	−	13.0171i	−0.0240814	−	0.439056i
$880$	−0.0690063	+	2.04195i	−0.00232620	+	0.0688340i
$881$	0.650801	+	0.418244i	0.0219260	+	0.0140910i	0.551558	−	0.834137i	$-0.314034\pi$
$881$	0.650801	+	0.418244i	0.0219260	+	0.0140910i	−0.529632	+	0.848228i	$0.677670\pi$
$882$	16.8614	+	2.99885i	0.567752	+	0.100977i
$883$	18.4893	+	16.0211i	0.622216	+	0.539153i	0.907909	−	0.419168i	$-0.137678\pi$
$883$	18.4893	+	16.0211i	0.622216	+	0.539153i	−0.285693	+	0.958321i	$0.592224\pi$
$884$	23.8316	−	15.3157i	0.801545	−	0.515122i
$885$	−13.6836	−	15.1370i	−0.459969	−	0.508826i
$886$	3.81148	+	26.5094i	0.128049	+	0.890601i
$887$	11.6648	−	7.49653i	0.391667	−	0.251709i	−0.329955	−	0.943997i	$-0.607034\pi$
$887$	11.6648	−	7.49653i	0.391667	−	0.251709i	0.721621	+	0.692288i	$0.243397\pi$
$888$	2.32581	+	11.6171i	0.0780491	+	0.389846i
$889$	−15.4040	−	7.03476i	−0.516632	−	0.235938i
$890$	27.5340	−	22.2755i	0.922941	−	0.746678i
$891$	−5.78581	+	5.84365i	−0.193832	+	0.195770i
$892$	8.07029	−	6.99294i	0.270213	−	0.234141i
$893$	0.989894	−	3.37127i	0.0331255	−	0.112815i
$894$	14.7353	+	3.46272i	0.492824	+	0.115811i
$895$	4.48586	−	9.00471i	0.149946	−	0.300994i
$896$	1.13637			0.0379635
$897$	−32.2713	+	20.0072i	−1.07751	+	0.668021i
$898$			20.4313i			0.681801i
$899$	89.8157	+	12.9136i	2.99552	+	0.430691i
$900$	−14.9868	+	0.630166i	−0.499559	+	0.0210055i
$901$	−9.10515	−	2.67351i	−0.303337	−	0.0890676i
$902$	−6.94962	+	6.02188i	−0.231397	+	0.200507i
$903$	−3.34418	+	8.53070i	−0.111287	+	0.283884i
$904$	−5.27027	+	8.20070i	−0.175286	+	0.272751i
$905$	−22.7298	+	24.5076i	−0.755564	+	0.814661i
$906$	0.805987	+	4.02581i	0.0267771	+	0.133748i
$907$	−19.1321	+	12.2955i	−0.635272	+	0.408265i	−0.818258	−	0.574851i	$-0.805060\pi$
$907$	−19.1321	+	12.2955i	−0.635272	+	0.408265i	0.182986	+	0.983116i	$0.441424\pi$
$908$	7.12870	−	1.02495i	0.236574	−	0.0340142i
$909$	−7.26073	−	17.4064i	−0.240823	−	0.577334i
$910$	11.2488	−	2.89407i	0.372893	−	0.0959375i
$911$	−10.0730	+	11.6248i	−0.333732	+	0.385147i	−0.897669	−	0.440671i	$-0.854741\pi$
$911$	−10.0730	+	11.6248i	−0.333732	+	0.385147i	0.563937	+	0.825818i	$0.309286\pi$
$912$	−0.604608	+	0.317223i	−0.0200206	+	0.0105043i
$913$	−5.20798	+	8.10377i	−0.172359	+	0.268196i
$914$	9.59833	−	2.81833i	0.317485	−	0.0932219i
$915$	−27.5669	−	7.46898i	−0.911335	−	0.246917i
$916$	4.16747	−	14.1931i	0.137697	−	0.468953i
$917$	0.660840	−	0.301796i	0.0218229	−	0.00996617i
$918$	−27.4600	−	16.8215i	−0.906315	−	0.555191i
$919$		−	59.0770i		−	1.94877i	−0.224883	−	0.974386i	$-0.572200\pi$
$919$		−	59.0770i		−	1.94877i	0.224883	−	0.974386i	$-0.427800\pi$
$920$	10.5490	−	1.92831i	0.347791	−	0.0635744i
$921$	31.2469	+	24.2111i	1.02962	+	0.797783i
$922$	−16.9236	−	2.43324i	−0.557348	−	0.0801345i
$923$	18.3959	+	40.2813i	0.605507	+	1.32588i
$924$	−1.45740	+	1.05369i	−0.0479449	+	0.0346639i
$925$	−2.57076	−	34.1045i	−0.0845262	−	1.12135i
$926$	2.25974	+	7.69597i	0.0742597	+	0.252905i
$927$	−2.79130	+	8.45663i	−0.0916782	+	0.277752i
$928$	−9.22326	−	4.21212i	−0.302768	−	0.138270i
$929$	−26.3421	−	22.8255i	−0.864255	−	0.748881i	0.105122	−	0.994459i	$-0.466477\pi$
$929$	−26.3421	−	22.8255i	−0.864255	−	0.748881i	−0.969377	+	0.245578i	$0.921022\pi$
$930$	−31.8229	−	13.7325i	−1.04352	−	0.450306i
$931$	−2.22745	+	0.320259i	−0.0730017	+	0.0104961i
$932$	1.07299	+	7.46284i	0.0351471	+	0.244453i
$933$	−12.5196	−	1.10466i	−0.409873	−	0.0361649i
$934$	−17.7055	−	15.3419i	−0.579343	−	0.502004i
$935$	8.61033	−	9.28379i	0.281588	−	0.303612i
$936$	−13.0221	−	4.29825i	−0.425642	−	0.140493i
$937$	32.7334	−	9.61140i	1.06935	−	0.313991i	0.300742	−	0.953706i	$-0.402766\pi$
$937$	32.7334	−	9.61140i	1.06935	−	0.313991i	0.768612	+	0.639715i	$0.220948\pi$
$938$	−4.61230	−	5.32288i	−0.150597	−	0.173798i
$939$	25.1793	−	18.2044i	0.821694	−	0.594079i
$940$	−19.8122	+	2.16849i	−0.646204	+	0.0707284i
$941$	1.68379	−	11.7110i	0.0548901	−	0.381769i	−0.943796	−	0.330528i	$-0.892773\pi$
$941$	1.68379	−	11.7110i	0.0548901	−	0.381769i	0.998686	−	0.0512410i	$-0.0163176\pi$
$942$	19.2898	−	24.8955i	0.628495	−	0.811138i
$943$	38.6498	+	28.9099i	1.25861	+	0.941436i
$944$			5.26859i			0.171478i
$945$	−8.52403	−	10.0833i	−0.277287	−	0.328008i
$946$	1.76699	+	3.86918i	0.0574499	+	0.125798i
$947$	−9.93189	−	2.91627i	−0.322743	−	0.0947659i	0.116348	−	0.993209i	$-0.462881\pi$
$947$	−9.93189	−	2.91627i	−0.322743	−	0.0947659i	−0.439091	+	0.898443i	$0.644699\pi$
$948$	0.285211	+	5.20002i	0.00926323	+	0.168889i
$949$	22.9301	−	6.73290i	0.744344	−	0.218559i
$950$	1.84407	−	0.695875i	0.0598296	−	0.0225772i
$951$	10.7931	+	20.5709i	0.349989	+	0.667058i
$952$	−5.32242	−	4.61190i	−0.172501	−	0.149473i
$953$	−6.10662	−	9.50209i	−0.197813	−	0.307803i	0.728150	−	0.685418i	$-0.240381\pi$
$953$	−6.10662	−	9.50209i	−0.197813	−	0.307803i	−0.925963	+	0.377615i	$0.876744\pi$
$954$	1.76846	+	4.23958i	0.0572559	+	0.137261i
$955$	17.4468	+	3.11321i	0.564566	+	0.100741i
$956$	8.92464	+	13.8870i	0.288644	+	0.449138i
$957$	15.7345	−	3.15013i	0.508624	−	0.101829i
$958$	16.9545	−	37.1251i	0.547774	−	1.19946i
$959$	−6.53521	+	10.1690i	−0.211033	+	0.328374i
$960$	2.97965	+	2.47421i	0.0961677	+	0.0798547i
$961$	−32.1441	−	37.0963i	−1.03691	−	1.19665i
$962$	8.80899	−	30.0007i	0.284013	−	0.967260i
$963$	29.5495	+	36.4826i	0.952218	+	1.17563i
$964$	−8.53816	−	1.22760i	−0.274995	−	0.0395384i
$965$	16.7810	+	5.54950i	0.540198	+	0.178645i
$966$	7.03260	+	6.29644i	0.226270	+	0.202585i
$967$		−	10.2820i		−	0.330648i	−0.986239	−	0.165324i	$-0.947133\pi$
$967$		−	10.2820i		−	0.330648i	0.986239	−	0.165324i	$-0.0528670\pi$
$968$	1.44665	−	10.0617i	0.0464971	−	0.323394i
$969$	4.11923	+	0.967993i	0.132329	+	0.0310964i
$970$	20.7451	−	30.0013i	0.666085	−	0.963284i
$971$	−4.37615	−	5.05034i	−0.140437	−	0.162073i	0.681174	−	0.732122i	$-0.261470\pi$
$971$	−4.37615	−	5.05034i	−0.140437	−	0.162073i	−0.821611	+	0.570049i	$0.806924\pi$
$972$	2.03883	+	15.4546i	0.0653954	+	0.495705i
$973$	−9.30204	−	5.97806i	−0.298210	−	0.191648i
$974$	11.0739	+	5.05727i	0.354830	+	0.162046i
$975$	35.7962	+	16.9033i	1.14640	+	0.541339i
$976$	3.98689	+	6.20372i	0.127617	+	0.198576i
$977$	−13.1747	+	1.89423i	−0.421495	+	0.0606018i	−0.349799	−	0.936825i	$-0.613750\pi$
$977$	−13.1747	+	1.89423i	−0.421495	+	0.0606018i	−0.0716956	+	0.997427i	$0.522841\pi$
$978$	−13.3114	+	23.4439i	−0.425652	+	0.749654i
$979$	12.1746	−	7.82412i	0.389101	−	0.250060i
$980$	6.53462	+	10.9655i	0.208741	+	0.350281i
$981$	3.20268	−	18.0074i	0.102254	−	0.574934i
$982$	−2.72651	+	4.24254i	−0.0870065	+	0.135385i
$983$	−10.7746	−	36.6949i	−0.343656	−	1.17039i	−0.932207	−	0.361925i	$-0.882120\pi$
$983$	−10.7746	−	36.6949i	−0.343656	−	1.17039i	0.588551	−	0.808460i	$-0.299699\pi$
$984$	0.954654	+	17.4054i	0.0304333	+	0.554864i
$985$	6.44939	−	9.32703i	0.205495	−	0.297184i
$986$	26.1043	+	57.1603i	0.831329	+	1.82036i
$987$	−12.1974	−	12.6094i	−0.388248	−	0.401362i
$988$	1.80191			0.0573265
$989$	17.8677	−	13.3862i	0.568161	−	0.425657i
$990$	−6.11559	−	0.410326i	−0.194366	−	0.0130410i
$991$	−0.955695	+	6.64700i	−0.0303587	+	0.211149i	−0.999354	−	0.0359285i	$-0.988561\pi$
$991$	−0.955695	+	6.64700i	−0.0303587	+	0.211149i	0.968996	+	0.247078i	$0.0794702\pi$
$992$	3.71757	+	8.14034i	0.118033	+	0.258456i
$993$	−22.8026	+	16.4861i	−0.723619	+	0.523172i
$994$	8.31993	−	7.20926i	0.263892	−	0.228664i
$995$	−26.8161	−	0.906233i	−0.850128	−	0.0287295i
$996$	6.09641	+	17.2128i	0.193172	+	0.545409i
$997$	−3.18421	−	1.45418i	−0.100845	−	0.0460544i	0.364354	−	0.931261i	$-0.381290\pi$
$997$	−3.18421	−	1.45418i	−0.100845	−	0.0460544i	−0.465199	+	0.885206i	$0.654017\pi$
$998$	22.8771	−	26.4016i	0.724163	−	0.835728i
$999$	−35.0639	+	5.81627i	−1.10937	+	0.184019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.659.1	yes	240
3.2	odd	2		690.2.n.b.659.8	yes	240
5.4	even	2		690.2.n.b.659.24	yes	240
15.14	odd	2	inner	690.2.n.a.659.17	yes	240
23.20	odd	22	inner	690.2.n.a.89.17	yes	240
69.20	even	22		690.2.n.b.89.24	yes	240
115.89	odd	22		690.2.n.b.89.8	yes	240
345.89	even	22	inner	690.2.n.a.89.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.1	✓	240	345.89	even	22	inner
690.2.n.a.89.17	yes	240	23.20	odd	22	inner
690.2.n.a.659.1	yes	240	1.1	even	1	trivial
690.2.n.a.659.17	yes	240	15.14	odd	2	inner
690.2.n.b.89.8	yes	240	115.89	odd	22
690.2.n.b.89.24	yes	240	69.20	even	22
690.2.n.b.659.8	yes	240	3.2	odd	2
690.2.n.b.659.24	yes	240	5.4	even	2

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-1.68612 - 0.396228i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.06421 - 0.859668i) q^{5} +(0.632155 - 1.61257i) q^{6} +(0.955977 + 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(2.68601 + 1.33618i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-1.68612 - 0.396228i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.06421 - 0.859668i) q^{5} +(0.632155 - 1.61257i) q^{6} +(0.955977 + 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(2.68601 + 1.33618i) q^{9} +(0.557150 + 2.16554i) q^{10} +(0.130034 + 0.904408i) q^{11} +(1.50619 + 0.855213i) q^{12} +(-2.47130 - 3.84542i) q^{13} +(-0.744166 + 0.858813i) q^{14} +(-3.82114 + 0.631605i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.74601 - 5.94637i) q^{17} +(-1.70483 + 2.46851i) q^{18} +(0.111059 - 0.378232i) q^{19} +(-2.22279 + 0.243289i) q^{20} +(-1.36846 - 1.41469i) q^{21} -0.913708 q^{22} +(1.02121 + 4.68584i) q^{23} +(-1.06086 + 1.36915i) q^{24} +(3.52194 - 3.54907i) q^{25} +(4.15798 - 1.89889i) q^{26} +(-3.99950 - 3.31723i) q^{27} +(-0.744166 - 0.858813i) q^{28} +(2.85664 + 9.72883i) q^{29} +(-0.0813721 - 3.87213i) q^{30} +(3.71757 - 8.14034i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.139098 - 1.57646i) q^{33} +(6.13433 - 0.881983i) q^{34} +(2.50149 + 0.446366i) q^{35} +(-2.20076 - 2.03879i) q^{36} +(4.47941 - 5.16952i) q^{37} +(0.358577 + 0.163757i) q^{38} +(2.64325 + 7.46304i) q^{39} +(0.0755234 - 2.23479i) q^{40} +(7.60595 - 6.59060i) q^{41} +(1.59504 - 1.15320i) q^{42} +(-1.93387 - 4.23459i) q^{43} +(0.130034 - 0.904408i) q^{44} +(6.69316 + 0.449078i) q^{45} +(-4.78348 + 0.343953i) q^{46} +8.91322 q^{47} +(-1.20424 - 1.24491i) q^{48} +(-2.37146 - 5.19278i) q^{49} +(3.01172 + 3.99118i) q^{50} +(0.587869 + 10.7181i) q^{51} +(1.28782 + 4.38590i) q^{52} +(0.827835 - 1.28814i) q^{53} +(3.85265 - 3.48670i) q^{54} +(1.04591 + 1.75510i) q^{55} +(0.955977 - 0.614369i) q^{56} +(-0.337125 + 0.593741i) q^{57} +(-10.0363 + 1.44301i) q^{58} +(2.84841 + 4.43222i) q^{59} +(3.84430 + 0.470518i) q^{60} +(6.70797 + 3.06343i) q^{61} +(7.52841 + 4.83822i) q^{62} +(1.74686 + 2.92755i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-8.40707 - 5.81326i) q^{65} +(1.54062 + 0.362037i) q^{66} +(-0.882061 + 6.13487i) q^{67} +6.19741i q^{68} +(0.134775 - 8.30553i) q^{69} +(-0.797822 + 2.41251i) q^{70} +(-9.58910 - 1.37871i) q^{71} +(2.33124 - 1.88821i) q^{72} +(-1.47294 + 5.01637i) q^{73} +(4.47941 + 5.16952i) q^{74} +(-7.34466 + 4.58867i) q^{75} +(-0.213121 + 0.331622i) q^{76} +(-0.431331 + 0.944482i) q^{77} +(-7.76325 + 1.55424i) q^{78} +(1.62557 + 2.52943i) q^{79} +(2.20130 + 0.392799i) q^{80} +(5.42927 + 7.17796i) q^{81} +(5.44107 + 8.46648i) q^{82} +(7.96766 + 6.90401i) q^{83} +(0.914468 + 1.74292i) q^{84} +(-8.71604 - 10.7736i) q^{85} +(4.46670 - 1.31154i) q^{86} +(-0.961810 - 17.5359i) q^{87} +(0.876696 + 0.257421i) q^{88} +(-6.57963 - 14.4074i) q^{89} +(-1.39704 + 6.56112i) q^{90} -5.19442i q^{91} +(0.340309 - 4.78374i) q^{92} +(-9.49370 + 12.2526i) q^{93} +(-1.26848 + 8.82250i) q^{94} +(-0.0959048 - 0.876226i) q^{95} +(1.40362 - 1.01481i) q^{96} +(-10.6822 - 12.3279i) q^{97} +(5.47742 - 1.60831i) q^{98} +(-0.859176 + 2.60299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

L-functions

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