LMFDB - Embedded newform 690.2.q.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (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:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(-1.10251 - 1.33584i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.527715 + 1.64970i) q^{6} +(-3.34609 + 2.89940i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.568927 + 2.94556i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(-1.10251 - 1.33584i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.527715 + 1.64970i) q^{6} +(-3.34609 + 2.89940i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.568927 + 2.94556i) q^{9} +(0.755750 + 0.654861i) q^{10} +(-4.01839 - 2.58246i) q^{11} +(1.67312 - 0.447955i) q^{12} +(2.41711 - 2.78949i) q^{13} +(4.24816 + 1.24737i) q^{14} +(1.43420 + 0.971113i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.62463 - 3.55744i) q^{17} +(2.78555 - 1.11388i) q^{18} +(7.60893 + 3.47488i) q^{19} +(0.142315 - 0.989821i) q^{20} +(7.56224 + 1.27320i) q^{21} +4.77667i q^{22} +(3.34534 + 3.43638i) q^{23} +(-1.28140 - 1.16534i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-3.65346 - 0.525288i) q^{26} +(4.56204 - 2.48753i) q^{27} +(-1.24737 - 4.24816i) q^{28} +(5.54481 - 2.53223i) q^{29} +(0.0415636 - 1.73155i) q^{30} +(1.22933 + 8.55015i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(0.980579 + 8.21512i) q^{33} +(-2.11437 + 3.29002i) q^{34} +(2.39369 - 3.72466i) q^{35} +(-2.44303 - 1.74114i) q^{36} +(2.66373 - 9.07181i) q^{37} +(-1.19044 - 8.27970i) q^{38} +(-6.39121 - 0.153412i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(1.46755 + 4.99802i) q^{41} +(-3.01737 - 7.05011i) q^{42} +(-3.91106 - 0.562326i) q^{43} +(4.01839 - 2.58246i) q^{44} +(-0.283979 - 2.98653i) q^{45} +(1.08224 - 4.67213i) q^{46} -0.0662848i q^{47} +(-0.287566 + 1.70801i) q^{48} +(1.79357 - 12.4746i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(-2.96099 + 6.09237i) q^{51} +(1.53331 + 3.35748i) q^{52} +(2.25260 + 2.59964i) q^{53} +(-4.55907 - 2.49297i) q^{54} +(4.58318 + 1.34574i) q^{55} +(-2.89940 + 3.34609i) q^{56} +(-3.74707 - 13.9954i) q^{57} +(-5.12799 - 3.29556i) q^{58} +(3.24536 + 2.81212i) q^{59} +(-1.47915 + 0.901182i) q^{60} +(-4.76718 + 0.685417i) q^{61} +(6.52822 - 5.65674i) q^{62} +(-6.63668 - 11.5057i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.53331 + 3.35748i) q^{65} +(6.38086 - 5.26635i) q^{66} +(-1.26011 - 1.96076i) q^{67} +3.91086 q^{68} +(0.902158 - 8.25749i) q^{69} -4.42751 q^{70} +(6.84012 + 10.6434i) q^{71} +(-0.143939 + 2.99654i) q^{72} +(-2.39376 + 5.24160i) q^{73} +(-9.07181 + 2.66373i) q^{74} +(-1.64970 - 0.527715i) q^{75} +(-6.32173 + 5.47781i) q^{76} +(20.9335 - 3.00978i) q^{77} +(3.32629 + 5.45957i) q^{78} +(6.35877 + 5.50990i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-8.35264 - 3.35161i) q^{81} +(3.41119 - 3.93672i) q^{82} +(2.94984 + 0.866151i) q^{83} +(-4.29961 + 6.34995i) q^{84} +(2.56107 + 2.95563i) q^{85} +(1.64142 + 3.59421i) q^{86} +(-9.49587 - 4.61515i) q^{87} +(-4.34501 - 1.98430i) q^{88} +(-0.473277 + 3.29171i) q^{89} +(-2.35890 + 1.85354i) q^{90} +16.3421i q^{91} +(-4.51554 + 1.61551i) q^{92} +(10.0663 - 11.0688i) q^{93} +(-0.0557623 + 0.0358362i) q^{94} +(-8.27970 - 1.19044i) q^{95} +(1.59234 - 0.681505i) q^{96} +(-0.758750 - 2.58406i) q^{97} +(-11.4639 + 5.23541i) q^{98} +(9.89297 - 10.3672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	−1.10251	−	1.33584i	−0.636537	−	0.771246i
$3$	−1.10251	−	1.33584i	−0.636537	−	0.771246i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.527715	+	1.64970i	−0.215439	+	0.673488i
$7$	−3.34609	+	2.89940i	−1.26470	+	1.09587i	−0.273730	+	0.961807i	$0.588257\pi$
$7$	−3.34609	+	2.89940i	−1.26470	+	1.09587i	−0.990973	+	0.134064i	$0.957197\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−0.568927	+	2.94556i	−0.189642	+	0.981853i
$10$	0.755750	+	0.654861i	0.238989	+	0.207085i
$11$	−4.01839	−	2.58246i	−1.21159	−	0.778642i	−0.230667	−	0.973033i	$-0.574091\pi$
$11$	−4.01839	−	2.58246i	−1.21159	−	0.778642i	−0.980924	+	0.194391i	$0.937727\pi$
$12$	1.67312	−	0.447955i	0.482989	−	0.129313i
$13$	2.41711	−	2.78949i	0.670386	−	0.773666i	−0.314051	−	0.949406i	$-0.601686\pi$
$13$	2.41711	−	2.78949i	0.670386	−	0.773666i	0.984437	+	0.175740i	$0.0562317\pi$
$14$	4.24816	+	1.24737i	1.13537	+	0.333375i
$15$	1.43420	+	0.971113i	0.370310	+	0.250740i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.62463	−	3.55744i	−0.394031	−	0.862807i	−0.997841	−	0.0656786i	$-0.979079\pi$
$17$	−1.62463	−	3.55744i	−0.394031	−	0.862807i	0.603810	−	0.797128i	$-0.293648\pi$
$18$	2.78555	−	1.11388i	0.656560	−	0.262544i
$19$	7.60893	+	3.47488i	1.74561	+	0.797193i	0.989811	+	0.142387i	$0.0454777\pi$
$19$	7.60893	+	3.47488i	1.74561	+	0.797193i	0.755797	+	0.654806i	$0.227250\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	7.56224	+	1.27320i	1.65022	+	0.277835i
$22$			4.77667i			1.01839i
$23$	3.34534	+	3.43638i	0.697552	+	0.716534i
$23$	3.34534	+	3.43638i	0.697552	+	0.716534i
$24$	−1.28140	−	1.16534i	−0.261565	−	0.237873i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−3.65346	−	0.525288i	−0.716502	−	0.103017i
$27$	4.56204	−	2.48753i	0.877965	−	0.478725i
$28$	−1.24737	−	4.24816i	−0.235731	−	0.802828i
$29$	5.54481	−	2.53223i	1.02964	−	0.470223i	0.172343	−	0.985037i	$-0.444866\pi$
$29$	5.54481	−	2.53223i	1.02964	−	0.470223i	0.857302	+	0.514814i	$0.172139\pi$
$30$	0.0415636	−	1.73155i	0.00758843	−	0.316137i
$31$	1.22933	+	8.55015i	0.220794	+	1.53565i	0.735048	+	0.678015i	$0.237160\pi$
$31$	1.22933	+	8.55015i	0.220794	+	1.53565i	−0.514254	+	0.857638i	$0.671931\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	0.980579	+	8.21512i	0.170697	+	1.43007i
$34$	−2.11437	+	3.29002i	−0.362612	+	0.564235i
$35$	2.39369	−	3.72466i	0.404608	−	0.629582i
$36$	−2.44303	−	1.74114i	−0.407172	−	0.290191i
$37$	2.66373	−	9.07181i	0.437914	−	1.49140i	−0.384832	−	0.922987i	$-0.625740\pi$
$37$	2.66373	−	9.07181i	0.437914	−	1.49140i	0.822745	−	0.568410i	$-0.192441\pi$
$38$	−1.19044	−	8.27970i	−0.193115	−	1.34315i
$39$	−6.39121	−	0.153412i	−1.02341	−	0.0245656i
$40$	−0.909632	+	0.415415i	−0.143825	+	0.0656829i
$41$	1.46755	+	4.99802i	0.229193	+	0.780560i	0.991128	+	0.132907i	$0.0424312\pi$
$41$	1.46755	+	4.99802i	0.229193	+	0.780560i	−0.761935	+	0.647653i	$0.775751\pi$
$42$	−3.01737	−	7.05011i	−0.465590	−	1.08785i
$43$	−3.91106	−	0.562326i	−0.596432	−	0.0857539i	−0.162514	−	0.986706i	$-0.551960\pi$
$43$	−3.91106	−	0.562326i	−0.596432	−	0.0857539i	−0.433918	+	0.900952i	$0.642869\pi$
$44$	4.01839	−	2.58246i	0.605795	−	0.389321i
$45$	−0.283979	−	2.98653i	−0.0423331	−	0.445205i
$46$	1.08224	−	4.67213i	0.159567	−	0.688867i
$47$		−	0.0662848i		−	0.00966863i	−0.999988	−	0.00483431i	$-0.998461\pi$
$47$		−	0.0662848i		−	0.00966863i	0.999988	−	0.00483431i	$-0.00153882\pi$
$48$	−0.287566	+	1.70801i	−0.0415066	+	0.246530i
$49$	1.79357	−	12.4746i	0.256224	−	1.78208i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	−2.96099	+	6.09237i	−0.414622	+	0.853103i
$52$	1.53331	+	3.35748i	0.212632	+	0.465598i
$53$	2.25260	+	2.59964i	0.309418	+	0.357088i	0.889066	−	0.457780i	$-0.151355\pi$
$53$	2.25260	+	2.59964i	0.309418	+	0.357088i	−0.579647	+	0.814867i	$0.696810\pi$
$54$	−4.55907	−	2.49297i	−0.620410	−	0.339251i
$55$	4.58318	+	1.34574i	0.617996	+	0.181460i
$56$	−2.89940	+	3.34609i	−0.387449	+	0.447140i
$57$	−3.74707	−	13.9954i	−0.496312	−	1.85374i
$58$	−5.12799	−	3.29556i	−0.673339	−	0.432728i
$59$	3.24536	+	2.81212i	0.422511	+	0.366107i	0.840011	−	0.542569i	$-0.182548\pi$
$59$	3.24536	+	2.81212i	0.422511	+	0.366107i	−0.417501	+	0.908677i	$0.637094\pi$
$60$	−1.47915	+	0.901182i	−0.190957	+	0.116342i
$61$	−4.76718	+	0.685417i	−0.610375	+	0.0877587i	−0.440569	−	0.897719i	$-0.645223\pi$
$61$	−4.76718	+	0.685417i	−0.610375	+	0.0877587i	−0.169806	+	0.985477i	$0.554314\pi$
$62$	6.52822	−	5.65674i	0.829085	−	0.718406i
$63$	−6.63668	−	11.5057i	−0.836143	−	1.44958i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−1.53331	+	3.35748i	−0.190184	+	0.416444i
$66$	6.38086	−	5.26635i	0.785429	−	0.648242i
$67$	−1.26011	−	1.96076i	−0.153947	−	0.239545i	0.755710	−	0.654906i	$-0.227292\pi$
$67$	−1.26011	−	1.96076i	−0.153947	−	0.239545i	−0.909657	+	0.415361i	$0.863655\pi$
$68$	3.91086			0.474261
$69$	0.902158	−	8.25749i	0.108607	−	0.994085i
$70$	−4.42751			−0.529189
$71$	6.84012	+	10.6434i	0.811773	+	1.26314i	0.961606	+	0.274432i	$0.0884899\pi$
$71$	6.84012	+	10.6434i	0.811773	+	1.26314i	−0.149833	+	0.988711i	$0.547874\pi$
$72$	−0.143939	+	2.99654i	−0.0169634	+	0.353146i
$73$	−2.39376	+	5.24160i	−0.280168	+	0.613483i	−0.996437	−	0.0843418i	$-0.973121\pi$
$73$	−2.39376	+	5.24160i	−0.280168	+	0.613483i	0.716269	+	0.697825i	$0.245849\pi$
$74$	−9.07181	+	2.66373i	−1.05458	+	0.309652i
$75$	−1.64970	−	0.527715i	−0.190491	−	0.0609352i
$76$	−6.32173	+	5.47781i	−0.725152	+	0.628348i
$77$	20.9335	−	3.00978i	2.38559	−	0.342996i
$78$	3.32629	+	5.45957i	0.376628	+	0.618174i
$79$	6.35877	+	5.50990i	0.715417	+	0.619912i	0.934570	−	0.355778i	$-0.115784\pi$
$79$	6.35877	+	5.50990i	0.715417	+	0.619912i	−0.219153	+	0.975690i	$0.570330\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	−8.35264	−	3.35161i	−0.928072	−	0.372402i
$82$	3.41119	−	3.93672i	0.376703	−	0.434738i
$83$	2.94984	+	0.866151i	0.323787	+	0.0950724i	0.439587	−	0.898200i	$-0.355125\pi$
$83$	2.94984	+	0.866151i	0.323787	+	0.0950724i	−0.115800	+	0.993273i	$0.536943\pi$
$84$	−4.29961	+	6.34995i	−0.469126	+	0.692836i
$85$	2.56107	+	2.95563i	0.277787	+	0.320583i
$86$	1.64142	+	3.59421i	0.176999	+	0.387574i
$87$	−9.49587	−	4.61515i	−1.01806	−	0.494796i
$88$	−4.34501	−	1.98430i	−0.463180	−	0.211527i
$89$	−0.473277	+	3.29171i	−0.0501672	+	0.348921i	0.949242	+	0.314547i	$0.101853\pi$
$89$	−0.473277	+	3.29171i	−0.0501672	+	0.348921i	−0.999409	+	0.0343735i	$0.989056\pi$
$90$	−2.35890	+	1.85354i	−0.248650	+	0.195380i
$91$			16.3421i			1.71311i
$92$	−4.51554	+	1.61551i	−0.470778	+	0.168428i
$93$	10.0663	−	11.0688i	1.04382	−	1.14779i
$94$	−0.0557623	+	0.0358362i	−0.00575144	+	0.00369623i
$95$	−8.27970	−	1.19044i	−0.849480	−	0.122137i
$96$	1.59234	−	0.681505i	0.162518	−	0.0695558i
$97$	−0.758750	−	2.58406i	−0.0770394	−	0.262372i	0.911963	−	0.410273i	$-0.134567\pi$
$97$	−0.758750	−	2.58406i	−0.0770394	−	0.262372i	−0.989002	+	0.147901i	$0.952748\pi$
$98$	−11.4639	+	5.23541i	−1.15803	+	0.528856i
$99$	9.89297	−	10.3672i	0.994281	−	1.04194i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	3.24407	−	11.0483i	0.322797	−	1.09934i	−0.625041	−	0.780592i	$-0.714918\pi$
$101$	3.24407	−	11.0483i	0.322797	−	1.09934i	0.947838	−	0.318753i	$-0.103264\pi$
$102$	6.72606	−	0.802841i	0.665979	−	0.0794931i
$103$	6.17251	−	9.60462i	0.608196	−	0.946371i	−0.391462	−	0.920194i	$-0.628030\pi$
$103$	6.17251	−	9.60462i	0.608196	−	0.946371i	0.999657	−	0.0261765i	$-0.00833318\pi$
$104$	1.99552	−	3.10509i	0.195677	−	0.304479i
$105$	−7.61462	+	0.908901i	−0.743111	+	0.0886997i
$106$	0.969108	−	3.30048i	0.0941281	−	0.320571i
$107$	0.955526	+	6.64583i	0.0923742	+	0.642476i	0.982431	+	0.186627i	$0.0597555\pi$
$107$	0.955526	+	6.64583i	0.0923742	+	0.642476i	−0.890057	+	0.455850i	$0.849335\pi$
$108$	0.367594	+	5.18313i	0.0353717	+	0.498747i
$109$	−12.7270	+	5.81223i	−1.21903	+	0.556711i	−0.917876	−	0.396866i	$-0.870098\pi$
$109$	−12.7270	+	5.81223i	−1.21903	+	0.556711i	−0.301150	+	0.953577i	$0.597370\pi$
$110$	−1.34574	−	4.58318i	−0.128312	−	0.436989i
$111$	−15.0553	+	6.44350i	−1.42898	+	0.611590i
$112$	4.38244	+	0.630100i	0.414102	+	0.0595389i
$113$	1.91170	−	1.22857i	0.179838	−	0.115575i	−0.447625	−	0.894221i	$-0.647730\pi$
$113$	1.91170	−	1.22857i	0.179838	−	0.115575i	0.627462	+	0.778647i	$0.284094\pi$
$114$	−9.74786	+	10.7187i	−0.912971	+	1.00390i
$115$	−4.17797	−	2.35469i	−0.389598	−	0.219576i
$116$			6.09566i			0.565968i
$117$	6.84146	+	8.70676i	0.632493	+	0.804940i
$118$	0.611133	−	4.25052i	0.0562594	−	0.391292i
$119$	15.7506	+	7.19306i	1.44386	+	0.659387i
$120$	1.55781	+	0.757120i	0.142208	+	0.0691153i
$121$	4.90879	+	10.7487i	0.446254	+	0.977159i
$122$	3.15394	+	3.63984i	0.285545	+	0.329536i
$123$	5.05855	−	7.47080i	0.456114	−	0.673620i
$124$	−8.28817	−	2.43363i	−0.744300	−	0.218546i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−6.09111	+	11.8036i	−0.542639	+	1.05154i
$127$	2.79724	+	1.79768i	0.248215	+	0.159518i	0.658833	−	0.752290i	$-0.271051\pi$
$127$	2.79724	+	1.79768i	0.248215	+	0.159518i	−0.410618	+	0.911808i	$0.634687\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	3.56082	+	5.84452i	0.313513	+	0.514581i
$130$	3.65346	−	0.525288i	0.320430	−	0.0460708i
$131$	2.42372	−	2.10017i	0.211762	−	0.183492i	−0.542521	−	0.840042i	$-0.682530\pi$
$131$	2.42372	−	2.10017i	0.211762	−	0.183492i	0.754283	+	0.656550i	$0.227985\pi$
$132$	−7.88009	−	2.52072i	−0.685873	−	0.219400i
$133$	−35.5352	+	10.4341i	−3.08130	+	0.904750i
$134$	−0.968235	+	2.12014i	−0.0836427	+	0.183152i
$135$	−3.67643	+	3.67204i	−0.316417	+	0.316039i
$136$	−2.11437	−	3.29002i	−0.181306	−	0.282117i
$137$	−1.16936			−0.0999053			−0.0499527	−	0.998752i	$-0.515907\pi$
$137$	−1.16936			−0.0999053			−0.0499527	+	0.998752i	$0.515907\pi$
$138$	−7.43438	+	3.70539i	−0.632857	+	0.315424i
$139$	6.27243			0.532020			0.266010	−	0.963970i	$-0.414295\pi$
$139$	6.27243			0.532020			0.266010	+	0.963970i	$0.414295\pi$
$140$	2.39369	+	3.72466i	0.202304	+	0.314791i
$141$	−0.0885457	+	0.0730799i	−0.00745689	+	0.00615443i
$142$	5.25578	−	11.5086i	0.441055	−	0.965776i
$143$	−16.9167	+	4.96718i	−1.41464	+	0.415376i
$144$	2.59867	−	1.49897i	0.216556	−	0.124914i
$145$	−4.60679	+	3.99181i	−0.382573	+	0.331502i
$146$	5.70368	−	0.820065i	0.472040	−	0.0678691i
$147$	−18.6414	+	11.3575i	−1.53752	+	0.936747i
$148$	7.14546	+	6.19158i	0.587353	+	0.508945i
$149$	17.2923	+	11.1131i	1.41664	+	0.910418i	0.999999	+	0.00134529i	$0.000428220\pi$
$149$	17.2923	+	11.1131i	1.41664	+	0.910418i	0.416638	+	0.909072i	$0.363208\pi$
$150$	0.447955	+	1.67312i	0.0365753	+	0.136610i
$151$	12.8715	−	14.8545i	1.04746	−	1.20884i	0.0700425	−	0.997544i	$-0.477687\pi$
$151$	12.8715	−	14.8545i	1.04746	−	1.20884i	0.977422	−	0.211295i	$-0.0677680\pi$
$152$	8.02601	+	2.35665i	0.650995	+	0.191149i
$153$	11.4030	−	2.76152i	0.921874	−	0.223256i
$154$	−13.8495	−	15.9832i	−1.11602	−	1.28796i
$155$	−3.58839	−	7.85747i	−0.288226	−	0.631127i
$156$	2.79455	−	5.74992i	0.223743	−	0.460362i
$157$	2.90424	+	1.32632i	0.231784	+	0.105852i	0.527922	−	0.849293i	$-0.322971\pi$
$157$	2.90424	+	1.32632i	0.231784	+	0.105852i	−0.296138	+	0.955145i	$0.595699\pi$
$158$	1.19742	−	8.32821i	0.0952613	−	0.662557i
$159$	0.989174	−	5.87525i	0.0784466	−	0.465937i
$160$		−	1.00000i		−	0.0790569i
$161$	−21.1572	−	1.79893i	−1.66742	−	0.141776i
$162$	1.69622	+	8.83871i	0.133268	+	0.694435i
$163$	−4.31521	+	2.77322i	−0.337993	+	0.217215i	−0.698616	−	0.715497i	$-0.746200\pi$
$163$	−4.31521	+	2.77322i	−0.337993	+	0.217215i	0.360623	+	0.932712i	$0.382564\pi$
$164$	−5.15601	−	0.741322i	−0.402616	−	0.0578875i
$165$	−3.25533	−	7.60609i	−0.253427	−	0.592133i
$166$	−0.866151	−	2.94984i	−0.0672263	−	0.228952i
$167$	−9.87937	+	4.51176i	−0.764489	+	0.349130i	−0.759202	−	0.650856i	$-0.774410\pi$
$167$	−9.87937	+	4.51176i	−0.764489	+	0.349130i	−0.00528739	+	0.999986i	$0.501683\pi$
$168$	7.66646	+	0.184023i	0.591480	+	0.0141977i
$169$	−0.0887613	−	0.617349i	−0.00682779	−	0.0474884i
$170$	1.10182	−	3.75244i	0.0845055	−	0.287799i
$171$	−14.5644	+	20.4356i	−1.11377	+	1.56275i
$172$	2.13622	−	3.32403i	0.162886	−	0.253455i
$173$	−5.49413	+	8.54904i	−0.417711	+	0.649971i	−0.984801	−	0.173684i	$-0.944433\pi$
$173$	−5.49413	+	8.54904i	−0.417711	+	0.649971i	0.567090	+	0.823656i	$0.308069\pi$
$174$	1.25135	+	10.4836i	0.0948644	+	0.794758i
$175$	−1.24737	+	4.24816i	−0.0942926	+	0.321131i
$176$	0.679791	+	4.72805i	0.0512412	+	0.356390i
$177$	0.178484	−	7.43569i	0.0134157	−	0.558901i
$178$	3.02504	−	1.38149i	0.226736	−	0.103547i
$179$	−3.57011	−	12.1587i	−0.266842	−	0.908781i	−0.978499	−	0.206253i	$-0.933873\pi$
$179$	−3.57011	−	12.1587i	−0.266842	−	0.908781i	0.711656	−	0.702528i	$-0.247945\pi$
$180$	2.83461	+	0.982333i	0.211279	+	0.0732188i
$181$	19.1956	+	2.75991i	1.42680	+	0.205142i	0.812053	−	0.583584i	$-0.198350\pi$
$181$	19.1956	+	2.75991i	1.42680	+	0.205142i	0.614745	+	0.788726i	$0.289259\pi$
$182$	13.7478	−	8.83519i	1.01906	−	0.654908i
$183$	6.17149	+	5.61250i	0.456210	+	0.414888i
$184$	3.80034	+	2.92531i	0.280165	+	0.215657i
$185$			9.45480i			0.695131i
$186$	−14.7539	−	2.48402i	−1.08181	−	0.182137i
$187$	−2.65857	+	18.4907i	−0.194414	+	1.35218i
$188$	0.0602947	+	0.0275357i	0.00439745	+	0.00200825i
$189$	−8.05265	+	21.5507i	−0.585744	+	1.56758i
$190$	3.47488	+	7.60893i	0.252094	+	0.552010i
$191$	−3.96040	−	4.57055i	−0.286565	−	0.330713i	0.594155	−	0.804350i	$-0.297486\pi$
$191$	−3.96040	−	4.57055i	−0.286565	−	0.330713i	−0.880720	+	0.473637i	$0.842941\pi$
$192$	−1.43420	−	0.971113i	−0.103505	−	0.0700841i
$193$	21.3756	+	6.27643i	1.53865	+	0.451787i	0.937684	−	0.347490i	$-0.112966\pi$
$193$	21.3756	+	6.27643i	1.53865	+	0.451787i	0.600962	+	0.799277i	$0.294784\pi$
$194$	−1.76364	+	2.03535i	−0.126622	+	0.146130i
$195$	6.17554	−	1.65341i	0.442240	−	0.118403i
$196$	10.6022	+	6.81361i	0.757299	+	0.486686i
$197$	19.7536	+	17.1166i	1.40738	+	1.21951i	0.942531	+	0.334118i	$0.108438\pi$
$197$	19.7536	+	17.1166i	1.40738	+	1.21951i	0.464853	+	0.885388i	$0.346107\pi$
$198$	−14.0700	−	2.71758i	−0.999909	−	0.193130i
$199$	−0.654715	+	0.0941338i	−0.0464115	+	0.00667297i	−0.165481	−	0.986213i	$-0.552918\pi$
$199$	−0.654715	+	0.0941338i	−0.0464115	+	0.00667297i	0.119070	+	0.992886i	$0.462009\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	−1.22998	+	3.84507i	−0.0867560	+	0.271210i
$202$	−11.0483	+	3.24407i	−0.777354	+	0.228252i
$203$	−11.2115	+	24.5497i	−0.786890	+	1.72305i
$204$	−4.31178	−	5.22428i	−0.301885	−	0.365772i
$205$	−2.81621	−	4.38211i	−0.196693	−	0.306060i
$206$	−11.4170			−0.795462
$207$	−12.0253	+	7.89886i	−0.835817	+	0.549009i
$208$	−3.69103			−0.255927
$209$	−21.6019	−	33.6132i	−1.49424	−	2.32508i
$210$	4.88139	+	5.91444i	0.336848	+	0.408135i
$211$	−1.12037	+	2.45327i	−0.0771295	+	0.168890i	−0.944269	−	0.329176i	$-0.893229\pi$
$211$	−1.12037	+	2.45327i	−0.0771295	+	0.168890i	0.867139	+	0.498066i	$0.165956\pi$
$212$	−3.30048	+	0.969108i	−0.226678	+	0.0665586i
$213$	6.67658	−	20.8718i	0.457472	−	1.43011i
$214$	5.07423	−	4.39685i	0.346867	−	0.300562i
$215$	3.91106	−	0.562326i	0.266732	−	0.0383503i
$216$	4.16159	−	3.11145i	0.283161	−	0.211708i
$217$	−28.9038	−	25.0453i	−1.96212	−	1.70018i
$218$	11.7703	+	7.56431i	0.797185	+	0.512320i
$219$	9.64108	−	2.58126i	0.651484	−	0.174426i
$220$	−3.12805	+	3.60997i	−0.210893	+	0.243384i
$221$	−13.8504	−	4.06684i	−0.931677	−	0.273565i
$222$	13.5601	+	9.18168i	0.910095	+	0.616234i
$223$	−6.02928	−	6.95815i	−0.403750	−	0.465953i	0.517068	−	0.855944i	$-0.327023\pi$
$223$	−6.02928	−	6.95815i	−0.403750	−	0.465953i	−0.920818	+	0.389992i	$0.872478\pi$
$224$	−1.83925	−	4.02740i	−0.122890	−	0.269092i
$225$	1.11388	+	2.78555i	0.0742586	+	0.185703i
$226$	−2.06709	−	0.944007i	−0.137501	−	0.0627944i
$227$	−0.818290	+	5.69133i	−0.0543118	+	0.377747i	0.944478	+	0.328573i	$0.106568\pi$
$227$	−0.818290	+	5.69133i	−0.0543118	+	0.377747i	−0.998790	+	0.0491736i	$0.984341\pi$
$228$	14.2873	+	2.40545i	0.946197	+	0.159305i
$229$		−	25.4796i		−	1.68374i	−0.539679	−	0.841871i	$-0.681454\pi$
$229$		−	25.4796i		−	1.68374i	0.539679	−	0.841871i	$-0.318546\pi$
$230$	0.277892	+	4.78777i	0.0183236	+	0.315696i
$231$	−27.1000	−	24.6454i	−1.78305	−	1.62155i
$232$	5.12799	−	3.29556i	0.336669	−	0.216364i
$233$	20.1986	+	2.90411i	1.32325	+	0.190255i	0.767476	−	0.641078i	$-0.221512\pi$
$233$	20.1986	+	2.90411i	1.32325	+	0.190255i	0.555776	+	0.831332i	$0.312421\pi$
$234$	3.62582	−	10.4626i	0.237027	−	0.683964i
$235$	0.0186746	+	0.0635998i	0.00121819	+	0.00414879i
$236$	−3.90617	+	1.78389i	−0.254270	+	0.116121i
$237$	0.349710	−	14.5690i	0.0227161	−	0.946360i
$238$	−2.46423	−	17.1391i	−0.159733	−	1.11096i
$239$	4.24591	−	14.4602i	0.274645	−	0.935356i	−0.700475	−	0.713677i	$-0.747028\pi$
$239$	4.24591	−	14.4602i	0.274645	−	0.935356i	0.975120	−	0.221678i	$-0.0711535\pi$
$240$	−0.205285	−	1.71984i	−0.0132511	−	0.111015i
$241$	−1.96783	+	3.06200i	−0.126759	+	0.197241i	−0.898832	−	0.438293i	$-0.855583\pi$
$241$	−1.96783	+	3.06200i	−0.126759	+	0.197241i	0.772074	+	0.635533i	$0.219220\pi$
$242$	6.38853	−	9.94075i	0.410670	−	0.639015i
$243$	4.73169	+	14.8530i	0.303538	+	0.952819i
$244$	1.35688	−	4.62111i	0.0868654	−	0.295836i
$245$	1.79357	+	12.4746i	0.114587	+	0.796970i
$246$	−9.01970	−	0.216506i	−0.575075	−	0.0138039i
$247$	28.0848	−	12.8259i	1.78699	−	0.816092i
$248$	2.43363	+	8.28817i	0.154536	+	0.526300i
$249$	−2.09520	−	4.89545i	−0.132778	−	0.310237i
$250$	0.989821	+	0.142315i	0.0626018	+	0.00900078i
$251$	−8.81730	+	5.66654i	−0.556543	+	0.357669i	−0.788478	−	0.615063i	$-0.789131\pi$
$251$	−8.81730	+	5.66654i	−0.556543	+	0.357669i	0.231935	+	0.972731i	$0.425494\pi$
$252$	13.2229	−	1.25732i	0.832963	−	0.0792037i
$253$	−4.56857	−	22.4479i	−0.287224	−	1.41129i
$254$		−	3.32509i		−	0.208635i
$255$	1.12463	−	6.67980i	0.0704271	−	0.418305i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	9.43172	+	4.30732i	0.588335	+	0.268683i	0.687260	−	0.726411i	$-0.258813\pi$
$257$	9.43172	+	4.30732i	0.588335	+	0.268683i	−0.0989255	+	0.995095i	$0.531541\pi$
$258$	2.99160	−	6.15534i	0.186249	−	0.383215i
$259$	17.3898	+	38.0783i	1.08055	+	2.36607i
$260$	−2.41711	−	2.78949i	−0.149903	−	0.172997i
$261$	4.30424	+	17.7732i	0.266426	+	1.10013i
$262$	−3.07714	−	0.903529i	−0.190106	−	0.0558202i
$263$	10.6059	−	12.2399i	0.653988	−	0.754742i	−0.327795	−	0.944749i	$-0.606306\pi$
$263$	10.6059	−	12.2399i	0.653988	−	0.754742i	0.981783	+	0.190007i	$0.0608510\pi$
$264$	2.13973	+	7.99195i	0.131691	+	0.491871i
$265$	−2.89376	−	1.85970i	−0.177762	−	0.114241i
$266$	27.9895	+	24.2530i	1.71615	+	1.48705i
$267$	4.91899	−	2.99694i	0.301037	−	0.183410i
$268$	2.30704	−	0.331702i	0.140925	−	0.0202620i
$269$	18.8725	−	16.3531i	1.15068	−	0.997068i	0.150714	−	0.988577i	$-0.451843\pi$
$269$	18.8725	−	16.3531i	1.15068	−	0.997068i	0.999964	−	0.00849034i	$-0.00270259\pi$
$270$	5.07674	+	1.10755i	0.308961	+	0.0674036i
$271$	−15.9704	+	4.68934i	−0.970135	+	0.284857i	−0.728146	−	0.685422i	$-0.759618\pi$
$271$	−15.9704	+	4.68934i	−0.970135	+	0.284857i	−0.241989	+	0.970279i	$0.577800\pi$
$272$	−1.62463	+	3.55744i	−0.0985077	+	0.215702i
$273$	21.8304	−	18.0174i	1.32123	−	1.09046i
$274$	0.632205	+	0.983730i	0.0381929	+	0.0594293i
$275$	−4.77667			−0.288044
$276$	7.13651	+	4.25092i	0.429567	+	0.255875i
$277$	−6.60732			−0.396996			−0.198498	−	0.980101i	$-0.563606\pi$
$277$	−6.60732			−0.396996			−0.198498	+	0.980101i	$0.563606\pi$
$278$	−3.39113	−	5.27670i	−0.203386	−	0.316475i
$279$	−25.8844	−	1.24336i	−1.54966	−	0.0744378i
$280$	1.83925	−	4.02740i	0.109916	−	0.240683i
$281$	−23.7216	+	6.96529i	−1.41511	+	0.415514i	−0.897845	−	0.440311i	$-0.854868\pi$
$281$	−23.7216	+	6.96529i	−1.41511	+	0.415514i	−0.517266	+	0.855825i	$0.673050\pi$
$282$	0.109350	+	0.0349794i	0.00651170	+	0.00208299i
$283$	−4.91723	+	4.26080i	−0.292299	+	0.253278i	−0.788649	−	0.614844i	$-0.789219\pi$
$283$	−4.91723	+	4.26080i	−0.292299	+	0.253278i	0.496350	+	0.868123i	$0.334673\pi$
$284$	−12.5231	+	1.80055i	−0.743109	+	0.106843i
$285$	7.53825	+	12.3728i	0.446527	+	0.732903i
$286$	13.3245	+	11.5457i	0.787894	+	0.682714i
$287$	−19.4018	−	12.4688i	−1.14525	−	0.736010i
$288$	−2.66596	−	1.37574i	−0.157093	−	0.0810663i
$289$	1.11665	−	1.28869i	0.0656855	−	0.0758051i
$290$	5.84874	+	1.71735i	0.343450	+	0.100846i
$291$	−2.61536	+	3.86253i	−0.153315	+	0.226426i
$292$	−3.77352	−	4.35488i	−0.220829	−	0.254850i
$293$	−5.06014	−	11.0802i	−0.295616	−	0.647309i	0.702297	−	0.711885i	$-0.252158\pi$
$293$	−5.06014	−	11.0802i	−0.295616	−	0.647309i	−0.997913	+	0.0645751i	$0.979431\pi$
$294$	19.6328	+	9.54186i	1.14501	+	0.556493i
$295$	−3.90617	−	1.78389i	−0.227426	−	0.103862i
$296$	1.34556	−	9.35856i	0.0782090	−	0.543955i
$297$	−24.7560	−	1.78545i	−1.43649	−	0.103602i
$298$		−	20.5554i		−	1.19074i
$299$	17.6718	−	1.02571i	1.02199	−	0.0593182i
$300$	1.16534	−	1.28140i	0.0672808	−	0.0739817i
$301$	14.7172	−	9.45815i	0.848284	−	0.545159i
$302$	−19.4552	−	2.79724i	−1.11952	−	0.160963i
$303$	−18.3353	+	7.84733i	−1.05334	+	0.450817i
$304$	−2.35665	−	8.02601i	−0.135163	−	0.460323i
$305$	4.38097	−	2.00072i	0.250854	−	0.114561i
$306$	−8.48804	−	8.09979i	−0.485229	−	0.463034i
$307$	0.661874	+	4.60343i	0.0377751	+	0.262732i	0.999953	−	0.00969003i	$-0.00308448\pi$
$307$	0.661874	+	4.60343i	0.0377751	+	0.262732i	−0.962178	+	0.272422i	$0.912175\pi$
$308$	−5.95829	+	20.2921i	−0.339505	+	1.15625i
$309$	−19.6355	+	2.34375i	−1.11702	+	0.133331i
$310$	−4.67010	+	7.26681i	−0.265244	+	0.412727i
$311$	−2.40384	+	3.74044i	−0.136309	+	0.212101i	−0.902697	−	0.430277i	$-0.858416\pi$
$311$	−2.40384	+	3.74044i	−0.136309	+	0.212101i	0.766388	+	0.642378i	$0.222052\pi$
$312$	−6.34799	+	0.757713i	−0.359384	+	0.0428971i
$313$	−4.21347	+	14.3498i	−0.238159	+	0.811097i	0.750493	+	0.660878i	$0.229816\pi$
$313$	−4.21347	+	14.3498i	−0.238159	+	0.811097i	−0.988653	+	0.150219i	$0.952002\pi$
$314$	−0.454378	−	3.16027i	−0.0256421	−	0.178344i
$315$	9.60937	+	9.16982i	0.541426	+	0.516661i
$316$	−7.65351	+	3.49524i	−0.430544	+	0.196623i
$317$	3.36704	+	11.4671i	0.189112	+	0.644057i	0.998395	+	0.0566373i	$0.0180379\pi$
$317$	3.36704	+	11.4671i	0.189112	+	0.644057i	−0.809283	+	0.587419i	$0.800144\pi$
$318$	−5.47736	+	2.34425i	−0.307155	+	0.131459i
$319$	−28.8206	−	4.14377i	−1.61364	−	0.232007i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	7.82427	−	8.60354i	0.436708	−	0.480203i
$322$	9.92511	+	18.7712i	0.553105	+	1.04608i
$323$		−	32.7137i		−	1.82024i
$324$	6.51855	−	6.20552i	0.362142	−	0.344751i
$325$	0.525288	−	3.65346i	0.0291377	−	0.202657i
$326$	4.66595	+	2.13087i	0.258423	+	0.118018i
$327$	21.7959	+	10.5932i	1.20532	+	0.585803i
$328$	2.16391	+	4.73830i	0.119482	+	0.261629i
$329$	0.192186	+	0.221795i	0.0105956	+	0.0122279i
$330$	−4.63869	+	6.85072i	−0.255351	+	0.377120i
$331$	9.07319	+	2.66413i	0.498708	+	0.146434i	0.521406	−	0.853309i	$-0.325408\pi$
$331$	9.07319	+	2.66413i	0.498708	+	0.146434i	−0.0226985	+	0.999742i	$0.507226\pi$
$332$	−2.01329	+	2.32346i	−0.110493	+	0.127516i
$333$	25.2061	+	13.0074i	1.38129	+	0.712799i
$334$	9.13673	+	5.87182i	0.499939	+	0.321292i
$335$	1.76147	+	1.52633i	0.0962396	+	0.0833921i
$336$	−3.98999	−	6.54893i	−0.217672	−	0.357273i
$337$	−0.117599	+	0.0169082i	−0.00640603	+	0.000921048i	−0.145517	−	0.989356i	$-0.546485\pi$
$337$	−0.117599	+	0.0169082i	−0.00640603	+	0.000921048i	0.139111	+	0.990277i	$0.455575\pi$
$338$	−0.471359	+	0.408435i	−0.0256385	+	0.0222159i
$339$	−3.74885	−	1.19920i	−0.203610	−	0.0651316i
$340$	−3.75244	+	1.10182i	−0.203505	+	0.0597544i
$341$	17.1405	−	37.5326i	0.928213	−	2.03250i
$342$	25.0656	+	1.20403i	1.35539	+	0.0651063i
$343$	13.4115	+	20.8687i	0.724151	+	1.12680i
$344$	−3.95128			−0.213039
$345$	1.46079	+	8.17717i	0.0786462	+	0.440244i
$346$	10.1623			0.546327
$347$	−0.981373	−	1.52705i	−0.0526829	−	0.0819761i	0.813913	−	0.580987i	$-0.197333\pi$
$347$	−0.981373	−	1.52705i	−0.0526829	−	0.0819761i	−0.866596	+	0.499011i	$0.833697\pi$
$348$	8.14281	−	6.72055i	0.436501	−	0.360259i
$349$	9.22421	−	20.1982i	0.493761	−	1.08118i	−0.484687	−	0.874688i	$-0.661066\pi$
$349$	9.22421	−	20.1982i	0.493761	−	1.08118i	0.978447	−	0.206497i	$-0.0662063\pi$
$350$	4.24816	−	1.24737i	0.227074	−	0.0666749i
$351$	4.08801	−	18.7384i	0.218202	−	1.00018i
$352$	3.60997	−	3.12805i	0.192412	−	0.166726i
$353$	4.69383	−	0.674871i	0.249827	−	0.0359198i	−0.0162633	−	0.999868i	$-0.505177\pi$
$353$	4.69383	−	0.674871i	0.249827	−	0.0359198i	0.266091	+	0.963948i	$0.414268\pi$
$354$	−6.35179	+	3.86989i	−0.337594	+	0.205682i
$355$	−9.56165	−	8.28522i	−0.507480	−	0.439734i
$356$	−2.79764	−	1.79793i	−0.148275	−	0.0952903i
$357$	−7.75650	−	28.9707i	−0.410517	−	1.53329i
$358$	−8.29837	+	9.57683i	−0.438583	+	0.506151i
$359$	−28.3666	−	8.32920i	−1.49713	−	0.439598i	−0.572324	−	0.820027i	$-0.693958\pi$
$359$	−28.3666	−	8.32920i	−1.49713	−	0.439598i	−0.924810	+	0.380429i	$0.875776\pi$
$360$	−0.706116	−	2.91572i	−0.0372156	−	0.153672i
$361$	33.3787	+	38.5210i	1.75677	+	2.02742i
$362$	−8.05614	−	17.6405i	−0.423421	−	0.927163i
$363$	8.94658	−	18.4080i	0.469574	−	0.966169i
$364$	−14.8653	−	6.78874i	−0.779152	−	0.355827i
$365$	0.820065	−	5.70368i	0.0429242	−	0.298544i
$366$	1.38498	−	8.22613i	0.0723939	−	0.429987i
$367$		−	10.3230i		−	0.538857i	−0.963020	−	0.269429i	$-0.913165\pi$
$367$		−	10.3230i		−	0.538857i	0.963020	−	0.269429i	$-0.0868348\pi$
$368$	0.406308	−	4.77859i	0.0211803	−	0.249101i
$369$	−15.5569	+	1.47925i	−0.809860	+	0.0770069i
$370$	7.95388	−	5.11165i	0.413503	−	0.265742i
$371$	−15.0748	−	2.16743i	−0.782644	−	0.112527i
$372$	5.88689	+	13.7548i	0.305221	+	0.713151i
$373$	8.52431	+	29.0311i	0.441372	+	1.50318i	0.817128	+	0.576457i	$0.195565\pi$
$373$	8.52431	+	29.0311i	0.441372	+	1.50318i	−0.375755	+	0.926719i	$0.622617\pi$
$374$	16.9927	−	7.76032i	0.878673	−	0.401277i
$375$	1.73155	+	0.0415636i	0.0894170	+	0.00214633i
$376$	−0.00943331	−	0.0656101i	−0.000486486	−	0.00338358i
$377$	6.33877	−	21.5879i	0.326463	−	1.11183i
$378$	22.4832	−	4.87685i	1.15641	−	0.250838i
$379$	−8.90953	+	13.8635i	−0.457652	+	0.712120i	−0.991013	−	0.133768i	$-0.957292\pi$
$379$	−8.90953	+	13.8635i	−0.457652	+	0.712120i	0.533361	+	0.845888i	$0.320929\pi$
$380$	4.52238	−	7.03695i	0.231993	−	0.360988i
$381$	−0.682591	−	5.71863i	−0.0349702	−	0.292974i
$382$	−1.70384	+	5.80273i	−0.0871758	+	0.296894i
$383$	0.0385631	+	0.268212i	0.00197048	+	0.0137050i	0.990783	−	0.135459i	$-0.0432509\pi$
$383$	0.0385631	+	0.268212i	0.00197048	+	0.0137050i	−0.988812	+	0.149164i	$0.952342\pi$
$384$	−0.0415636	+	1.73155i	−0.00212103	+	0.0883629i
$385$	−19.2376	+	8.78551i	−0.980438	+	0.447751i
$386$	−6.27643	−	21.3756i	−0.319462	−	1.08799i
$387$	3.88147	−	11.2003i	0.197306	−	0.569346i
$388$	2.66574	+	0.383276i	0.135333	+	0.0194579i
$389$	2.22974	−	1.43297i	0.113052	−	0.0726543i	−0.482893	−	0.875679i	$-0.660414\pi$
$389$	2.22974	−	1.43297i	0.113052	−	0.0726543i	0.595945	+	0.803025i	$0.296778\pi$
$390$	−4.72969	−	4.30129i	−0.239497	−	0.217804i
$391$	6.78977	−	17.4837i	0.343374	−	0.884189i
$392$		−	12.6028i		−	0.636539i
$393$	−5.47767	−	0.922237i	−0.276312	−	0.0465207i
$394$	3.71979	−	25.8717i	0.187400	−	1.30340i
$395$	−7.65351	−	3.49524i	−0.385090	−	0.175865i
$396$	5.32063	+	13.3056i	0.267372	+	0.668634i
$397$	2.33125	+	5.10473i	0.117002	+	0.256199i	0.959068	−	0.283176i	$-0.0913879\pi$
$397$	2.33125	+	5.10473i	0.117002	+	0.256199i	−0.842066	+	0.539375i	$0.818661\pi$
$398$	0.433156	+	0.499889i	0.0217121	+	0.0250571i
$399$	53.1163	+	35.9656i	2.65914	+	1.80053i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	14.2984	−	16.5012i	0.714026	−	0.824030i	−0.276549	−	0.961000i	$-0.589191\pi$
$401$	14.2984	−	16.5012i	0.714026	−	0.824030i	0.990575	+	0.136970i	$0.0437364\pi$
$402$	3.89965	−	1.04408i	0.194497	−	0.0520738i
$403$	26.8220	+	17.2375i	1.33610	+	0.858659i
$404$	8.70223	+	7.54053i	0.432952	+	0.375155i
$405$	8.95856	+	0.862639i	0.445155	+	0.0428649i
$406$	26.7139	−	3.84088i	1.32579	−	0.190619i
$407$	−34.1315	+	29.5751i	−1.69184	+	1.46598i
$408$	−2.06382	+	6.45175i	−0.102174	+	0.319409i
$409$	15.9245	−	4.67584i	0.787414	−	0.231206i	0.136784	−	0.990601i	$-0.456323\pi$
$409$	15.9245	−	4.67584i	0.787414	−	0.231206i	0.650630	+	0.759395i	$0.274505\pi$
$410$	−2.16391	+	4.73830i	−0.106868	+	0.234008i
$411$	1.28924	+	1.56208i	0.0635934	+	0.0770516i
$412$	6.17251	+	9.60462i	0.304098	+	0.473185i
$413$	−19.0128			−0.935557
$414$	13.1463	+	5.84589i	0.646106	+	0.287310i
$415$	−3.07437			−0.150915
$416$	1.99552	+	3.10509i	0.0978385	+	0.152240i
$417$	−6.91544	−	8.37894i	−0.338650	−	0.410319i
$418$	−16.5984	+	36.3454i	−0.811853	+	1.77771i
$419$	0.0533779	−	0.0156732i	0.00260768	−	0.000765685i	−0.280428	−	0.959875i	$-0.590477\pi$
$419$	0.0533779	−	0.0156732i	0.00260768	−	0.000765685i	0.283036	+	0.959109i	$0.408658\pi$
$420$	2.33646	−	7.30407i	0.114008	−	0.356402i
$421$	−2.82063	+	2.44409i	−0.137469	+	0.119118i	−0.720881	−	0.693058i	$-0.756263\pi$
$421$	−2.82063	+	2.44409i	−0.137469	+	0.119118i	0.583412	+	0.812176i	$0.301717\pi$
$422$	2.66954	−	0.383822i	0.129951	−	0.0186842i
$423$	0.195246	+	0.0377112i	0.00949317	+	0.00183358i
$424$	2.59964	+	2.25260i	0.126250	+	0.109396i
$425$	−3.29002	−	2.11437i	−0.159590	−	0.102562i
$426$	−21.1681	+	5.66747i	−1.02560	+	0.274590i
$427$	13.9641	−	16.1154i	0.675771	−	0.779881i
$428$	−6.44220	−	1.89160i	−0.311395	−	0.0914339i
$429$	25.2862	+	17.1215i	1.22083	+	0.826636i
$430$	−2.58754	−	2.98618i	−0.124782	−	0.144006i
$431$	−5.29696	−	11.5987i	−0.255146	−	0.558691i	0.738104	−	0.674687i	$-0.235721\pi$
$431$	−5.29696	−	11.5987i	−0.255146	−	0.558691i	−0.993250	+	0.115996i	$0.962994\pi$
$432$	−4.86745	−	1.81878i	−0.234185	−	0.0875059i
$433$	−33.4453	−	15.2739i	−1.60728	−	0.734019i	−0.609027	−	0.793150i	$-0.708440\pi$
$433$	−33.4453	−	15.2739i	−1.60728	−	0.734019i	−0.998250	+	0.0591308i	$0.981167\pi$
$434$	−5.44286	+	37.8559i	−0.261265	+	1.81714i
$435$	10.4115	+	1.75290i	0.499191	+	0.0840453i
$436$		−	13.9914i		−	0.670066i
$437$	13.5135	+	37.7718i	0.646437	+	1.80687i
$438$	−7.38386	−	6.71506i	−0.352814	−	0.320858i
$439$	5.73323	−	3.68452i	0.273632	−	0.175853i	−0.396627	−	0.917980i	$-0.629819\pi$
$439$	5.73323	−	3.68452i	0.273632	−	0.175853i	0.670259	+	0.742127i	$0.266183\pi$
$440$	4.72805	+	0.679791i	0.225401	+	0.0324078i
$441$	35.7242	+	12.3802i	1.70115	+	0.589532i
$442$	4.06684	+	13.8504i	0.193440	+	0.658795i
$443$	−6.21590	+	2.83871i	−0.295326	+	0.134871i	−0.557568	−	0.830131i	$-0.688265\pi$
$443$	−6.21590	+	2.83871i	−0.295326	+	0.134871i	0.262242	+	0.965002i	$0.415538\pi$
$444$	0.392975	−	16.3715i	0.0186498	−	0.776956i
$445$	−0.473277	−	3.29171i	−0.0224355	−	0.156042i
$446$	−2.59390	+	8.83401i	−0.122825	+	0.418303i
$447$	−4.21971	−	35.3520i	−0.199585	−	1.67209i
$448$	−2.39369	+	3.72466i	−0.113091	+	0.175974i
$449$	−13.2326	+	20.5903i	−0.624486	+	0.971719i	0.374524	+	0.927217i	$0.377806\pi$
$449$	−13.2326	+	20.5903i	−0.624486	+	0.971719i	−0.999009	+	0.0445013i	$0.985830\pi$
$450$	1.74114	−	2.44303i	0.0820783	−	0.115166i
$451$	7.01002	−	23.8739i	0.330089	−	1.12418i
$452$	0.323402	+	2.24931i	0.0152116	+	0.105799i
$453$	−34.0341	−	0.816943i	−1.59906	−	0.0383833i
$454$	5.23026	−	2.38858i	0.245468	−	0.112102i
$455$	−4.60409	−	15.6801i	−0.215843	−	0.735094i
$456$	−5.70068	−	13.3197i	−0.266959	−	0.623751i
$457$	38.6935	+	5.56329i	1.81001	+	0.260240i	0.962643	−	0.270773i	$-0.0872792\pi$
$457$	38.6935	+	5.56329i	1.81001	+	0.260240i	0.847364	+	0.531012i	$0.178188\pi$
$458$	−21.4348	+	13.7753i	−1.00158	+	0.643679i
$459$	−16.2609	−	12.1879i	−0.758992	−	0.568882i
$460$	3.87749	−	2.82224i	0.180789	−	0.131588i
$461$			0.0121818i			0.000567362i	1.00000		0.000283681i	$9.02985e-5\pi$
$461$			0.0121818i			0.000567362i	−1.00000		0.000283681i	$0.999910\pi$
$462$	−6.08166	+	36.1223i	−0.282945	+	1.68056i
$463$	−4.19564	+	29.1813i	−0.194988	+	1.35617i	0.623579	+	0.781760i	$0.285678\pi$
$463$	−4.19564	+	29.1813i	−0.194988	+	1.35617i	−0.818567	+	0.574411i	$0.805231\pi$
$464$	−5.54481	−	2.53223i	−0.257411	−	0.117556i
$465$	−6.54006	+	13.4565i	−0.303288	+	0.624029i
$466$	−8.47707	−	18.5622i	−0.392693	−	0.859877i
$467$	−17.1520	−	19.7945i	−0.793701	−	0.915980i	0.204317	−	0.978905i	$-0.434503\pi$
$467$	−17.1520	−	19.7945i	−0.793701	−	0.915980i	−0.998018	+	0.0629249i	$0.979957\pi$
$468$	−10.7620	+	2.60629i	−0.497473	+	0.120476i
$469$	9.90147	+	2.90733i	0.457207	+	0.134248i
$470$	0.0434073	−	0.0500947i	0.00200223	−	0.00231070i
$471$	−1.43022	−	5.34189i	−0.0659009	−	0.246141i
$472$	3.61254	+	2.32164i	0.166281	+	0.106862i
$473$	14.2640	+	12.3598i	0.655859	+	0.568305i
$474$	−12.4453	+	7.58241i	−0.571632	+	0.348272i
$475$	8.27970	−	1.19044i	0.379899	−	0.0546212i
$476$	−13.0861	+	11.3392i	−0.599800	+	0.519729i
$477$	−8.93896	+	5.15616i	−0.409287	+	0.236085i
$478$	−14.4602	+	4.24591i	−0.661396	+	0.194203i
$479$	17.7430	−	38.8517i	0.810698	−	1.77518i	0.206318	−	0.978485i	$-0.433852\pi$
$479$	17.7430	−	38.8517i	0.810698	−	1.77518i	0.604380	−	0.796696i	$-0.293421\pi$
$480$	−1.33584	+	1.10251i	−0.0609724	+	0.0503226i
$481$	−18.8673	−	29.3580i	−0.860273	−	1.33861i
$482$	3.63980			0.165788
$483$	20.9231	+	30.2460i	0.952033	+	1.37624i
$484$	−11.8166			−0.537118
$485$	1.45603	+	2.26563i	0.0661149	+	0.102877i
$486$	9.93698	−	12.0107i	0.450751	−	0.544816i
$487$	−1.01829	+	2.22973i	−0.0461429	+	0.101039i	−0.931299	−	0.364254i	$-0.881324\pi$
$487$	−1.01829	+	2.22973i	−0.0461429	+	0.101039i	0.885157	+	0.465293i	$0.154051\pi$
$488$	−4.62111	+	1.35688i	−0.209188	+	0.0614231i
$489$	8.46214	+	2.70691i	0.382671	+	0.122411i
$490$	9.52459	−	8.25310i	0.430277	−	0.372837i
$491$	−16.2269	+	2.33308i	−0.732309	+	0.105290i	−0.498374	−	0.866962i	$-0.666069\pi$
$491$	−16.2269	+	2.33308i	−0.732309	+	0.105290i	−0.233935	+	0.972252i	$0.575160\pi$
$492$	4.69428	+	7.70491i	0.211635	+	0.347364i
$493$	−18.0165	−	15.6114i	−0.811423	−	0.703102i
$494$	−25.9736	−	16.6922i	−1.16861	−	0.751019i
$495$	−6.57146	+	12.7344i	−0.295365	+	0.572369i
$496$	5.65674	−	6.52822i	0.253995	−	0.293126i
$497$	−53.7472	−	15.7816i	−2.41089	−	0.707902i
$498$	−2.98556	+	4.40928i	−0.133786	+	0.197584i
$499$	−3.56343	−	4.11242i	−0.159521	−	0.184097i	0.670362	−	0.742034i	$-0.266139\pi$
$499$	−3.56343	−	4.11242i	−0.159521	−	0.184097i	−0.829884	+	0.557937i	$0.811593\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	16.9191	+	8.22297i	0.755891	+	0.367375i
$502$	9.53399	+	4.35403i	0.425523	+	0.194330i
$503$	2.03798	−	14.1744i	0.0908689	−	0.632007i	−0.892589	−	0.450871i	$-0.851113\pi$
$503$	2.03798	−	14.1744i	0.0908689	−	0.632007i	0.983458	−	0.181136i	$-0.0579775\pi$
$504$	−8.20656	−	10.4440i	−0.365549	−	0.465215i
$505$			11.5147i			0.512398i
$506$	−16.4144	+	15.9796i	−0.729711	+	0.710380i
$507$	−0.726817	+	0.799206i	−0.0322791	+	0.0354940i
$508$	−2.79724	+	1.79768i	−0.124108	+	0.0797591i
$509$	34.7226	+	4.99236i	1.53905	+	0.221282i	0.859036	−	0.511915i	$-0.171064\pi$
$509$	34.7226	+	4.99236i	1.53905	+	0.221282i	0.680016	+	0.733197i	$0.261973\pi$
$510$	−6.22742	+	2.66527i	−0.275755	+	0.118020i
$511$	−7.18778	−	24.4793i	−0.317969	−	1.08290i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	43.3561	−	3.07486i	1.91422	−	0.135759i
$514$	−1.47562	−	10.2632i	−0.0650869	−	0.452690i
$515$	−3.21655	+	10.9546i	−0.141738	+	0.482716i
$516$	−6.79558	+	0.811139i	−0.299159	+	0.0357084i
$517$	−0.171178	+	0.266358i	−0.00752840	+	0.0117144i
$518$	22.6319	−	35.2159i	0.994388	−	1.54730i
$519$	17.4775	−	2.08616i	0.767177	−	0.0915723i
$520$	−1.03988	+	3.54152i	−0.0456019	+	0.155306i
$521$	4.40391	+	30.6298i	0.192939	+	1.34192i	0.824178	+	0.566330i	$0.191637\pi$
$521$	4.40391	+	30.6298i	0.192939	+	1.34192i	−0.631240	+	0.775588i	$0.717454\pi$
$522$	12.6247	−	13.2299i	0.552569	−	0.579056i
$523$	0.0374930	−	0.0171225i	0.00163946	−	0.000748715i	−0.414595	−	0.910006i	$-0.636077\pi$
$523$	0.0374930	−	0.0171225i	0.00163946	−	0.000748715i	0.416235	+	0.909257i	$0.363350\pi$
$524$	0.903529	+	3.07714i	0.0394708	+	0.134425i
$525$	7.05011	−	3.01737i	0.307692	−	0.131689i
$526$	−16.0308	−	2.30488i	−0.698976	−	0.100498i
$527$	28.4195	−	18.2641i	1.23797	−	0.795596i
$528$	5.56643	−	6.12083i	0.242248	−	0.266375i
$529$	−0.617379	+	22.9917i	−0.0268426	+	0.999640i
$530$			3.43982i			0.149416i
$531$	−10.1297	+	7.95952i	−0.439590	+	0.345414i
$532$	5.27069	−	36.6585i	0.228513	−	1.58935i
$533$	17.4892	+	7.98705i	0.757541	+	0.345957i
$534$	−5.18059	−	2.51785i	−0.224186	−	0.108958i
$535$	−2.78917	−	6.10742i	−0.120586	−	0.264047i
$536$	−1.52633	−	1.76147i	−0.0659273	−	0.0760841i
$537$	−12.3059	+	18.1742i	−0.531039	+	0.784273i
$538$	−23.9604	−	7.03540i	−1.03301	−	0.303318i
$539$	−39.4224	+	45.4958i	−1.69804	+	1.95964i
$540$	−1.81296	−	4.86962i	−0.0780174	−	0.209555i
$541$	3.75537	+	2.41343i	0.161456	+	0.103762i	0.618874	−	0.785490i	$-0.287589\pi$
$541$	3.75537	+	2.41343i	0.161456	+	0.103762i	−0.457418	+	0.889252i	$0.651226\pi$
$542$	12.5792	+	10.8999i	0.540323	+	0.468192i
$543$	−17.4766	−	28.6850i	−0.749993	−	1.23099i
$544$	3.87105	−	0.556573i	0.165970	−	0.0238629i
$545$	10.5740	−	9.16241i	0.452940	−	0.392474i
$546$	−26.9595	−	8.62395i	−1.15376	−	0.369071i
$547$	−39.4402	+	11.5807i	−1.68634	+	0.495154i	−0.977628	−	0.210343i	$-0.932542\pi$
$547$	−39.4402	+	11.5807i	−1.68634	+	0.495154i	−0.708712	+	0.705497i	$0.750724\pi$
$548$	0.485771	−	1.06369i	0.0207511	−	0.0454386i
$549$	0.693239	−	14.4320i	0.0295867	−	0.615941i
$550$	2.58246	+	4.01839i	0.110117	+	0.171345i
$551$	50.9892			2.17221
$552$	−0.282187	−	8.30183i	−0.0120107	−	0.353349i
$553$	−37.2524			−1.58413
$554$	3.57219	+	5.55844i	0.151768	+	0.236155i
$555$	12.6301	−	10.4240i	0.536117	−	0.442476i
$556$	−2.60566	+	5.70560i	−0.110505	+	0.241971i
$557$	−37.0014	+	10.8646i	−1.56780	+	0.460348i	−0.946360	−	0.323113i	$-0.895271\pi$
$557$	−37.0014	+	10.8646i	−1.56780	+	0.460348i	−0.621441	+	0.783461i	$0.713452\pi$
$558$	12.9482	+	22.4475i	0.548140	+	0.950280i
$559$	−11.0221	+	9.55068i	−0.466184	+	0.403951i
$560$	−4.38244	+	0.630100i	−0.185192	+	0.0266266i
$561$	27.6318	−	16.8349i	1.16661	−	0.710769i
$562$	18.6844	+	16.1901i	0.788155	+	0.682940i
$563$	−6.04857	−	3.88718i	−0.254917	−	0.163825i	0.406941	−	0.913454i	$-0.366595\pi$
$563$	−6.04857	−	3.88718i	−0.254917	−	0.163825i	−0.661858	+	0.749629i	$0.730232\pi$
$564$	−0.0296926	−	0.110902i	−0.00125028	−	0.00466984i
$565$	−1.48813	+	1.71740i	−0.0626062	+	0.0722514i
$566$	6.24287	+	1.83307i	0.262407	+	0.0770498i
$567$	37.6664	−	13.0029i	1.58184	−	0.546069i
$568$	8.28522	+	9.56165i	0.347640	+	0.401198i
$569$	6.54702	+	14.3360i	0.274465	+	0.600995i	0.995796	−	0.0915953i	$-0.0291966\pi$
$569$	6.54702	+	14.3360i	0.274465	+	0.600995i	−0.721331	+	0.692590i	$0.756469\pi$
$570$	6.33319	−	13.0308i	0.265268	−	0.545801i
$571$	−31.8419	−	14.5417i	−1.33254	−	0.608552i	−0.383454	−	0.923560i	$-0.625265\pi$
$571$	−31.8419	−	14.5417i	−1.33254	−	0.608552i	−0.949089	+	0.315008i	$0.897993\pi$
$572$	2.50913	−	17.4514i	0.104912	−	0.729679i
$573$	−1.73911	+	10.3296i	−0.0726526	+	0.431523i
$574$			23.0630i			0.962632i
$575$	4.67213	+	1.08224i	0.194841	+	0.0451324i
$576$	0.283979	+	2.98653i	0.0118325	+	0.124439i
$577$	−5.72621	+	3.68001i	−0.238385	+	0.153201i	−0.654379	−	0.756166i	$-0.727070\pi$
$577$	−5.72621	+	3.68001i	−0.238385	+	0.153201i	0.415994	+	0.909367i	$0.363434\pi$
$578$	−1.68782	−	0.242672i	−0.0702041	−	0.0100938i
$579$	−15.1826	−	35.4741i	−0.630965	−	1.47425i
$580$	−1.71735	−	5.84874i	−0.0713089	−	0.242856i
$581$	−12.3817	+	5.65455i	−0.513681	+	0.234590i
$582$	4.66334	+	0.111937i	0.193302	+	0.00463995i
$583$	−2.33836	−	16.2636i	−0.0968448	−	0.673571i
$584$	−1.62344	+	5.52892i	−0.0671783	+	0.228788i
$585$	−9.01731	−	6.42661i	−0.372820	−	0.265708i
$586$	−6.58550	+	10.2472i	−0.272045	+	0.423310i
$587$	−7.45676	+	11.6030i	−0.307774	+	0.478905i	−0.960342	−	0.278825i	$-0.910055\pi$
$587$	−7.45676	+	11.6030i	−0.307774	+	0.478905i	0.652568	+	0.757730i	$0.273692\pi$
$588$	−2.58717	−	21.6749i	−0.106693	−	0.893858i
$589$	−20.3569	+	69.3293i	−0.838792	+	2.85666i
$590$	0.611133	+	4.25052i	0.0251600	+	0.174991i
$591$	1.08638	−	45.2589i	0.0446876	−	1.86170i
$592$	−8.60039	+	3.92767i	−0.353474	+	0.161426i
$593$	3.30287	+	11.2485i	0.135633	+	0.461922i	0.999097	−	0.0424876i	$-0.0135283\pi$
$593$	3.30287	+	11.2485i	0.135633	+	0.461922i	−0.863464	+	0.504410i	$0.831710\pi$
$594$	11.8821	+	21.7914i	0.487528	+	0.894111i
$595$	−17.1391	−	2.46423i	−0.702635	−	0.101024i
$596$	−17.2923	+	11.1131i	−0.708319	+	0.455209i
$597$	0.847580	+	0.770809i	0.0346891	+	0.0315471i
$598$	−10.4170	−	14.3119i	−0.425982	−	0.585259i
$599$			33.1417i			1.35413i	0.735921	+	0.677067i	$0.236749\pi$
$599$			33.1417i			1.35413i	−0.735921	+	0.677067i	$0.763251\pi$
$600$	−1.70801	−	0.287566i	−0.0697293	−	0.0117398i
$601$	2.61992	−	18.2219i	0.106869	−	0.743288i	−0.863968	−	0.503547i	$-0.832028\pi$
$601$	2.61992	−	18.2219i	0.106869	−	0.743288i	0.970837	−	0.239741i	$-0.0770627\pi$
$602$	−15.9134	−	7.26741i	−0.648582	−	0.296198i
$603$	6.49246	−	2.59619i	0.264393	−	0.105725i
$604$	8.16509	+	17.8791i	0.332233	+	0.727489i
$605$	−7.73822	−	8.93038i	−0.314603	−	0.363072i
$606$	16.5144	+	11.1821i	0.670853	+	0.454241i
$607$	5.71059	+	1.67678i	0.231786	+	0.0680584i	0.395563	−	0.918439i	$-0.370550\pi$
$607$	5.71059	+	1.67678i	0.231786	+	0.0680584i	−0.163777	+	0.986497i	$0.552368\pi$
$608$	−5.47781	+	6.32173i	−0.222154	+	0.256380i
$609$	45.1552	−	12.0897i	1.82978	−	0.489898i
$610$	−4.05165	−	2.60384i	−0.164046	−	0.105426i
$611$	−0.184901	−	0.160218i	−0.00748029	−	0.00648171i
$612$	−2.22499	+	11.5197i	−0.0899400	+	0.465655i
$613$	−34.1414	+	4.90879i	−1.37896	+	0.198264i	−0.791588	−	0.611055i	$-0.790746\pi$
$613$	−34.1414	+	4.90879i	−1.37896	+	0.198264i	−0.587370	+	0.809319i	$0.699836\pi$
$614$	3.51482	−	3.04561i	0.141847	−	0.122911i
$615$	−2.74888	+	8.59334i	−0.110845	+	0.346517i
$616$	20.2921	−	5.95829i	0.817591	−	0.240066i
$617$	4.93863	−	10.8141i	0.198822	−	0.435359i	−0.783791	−	0.621024i	$-0.786717\pi$
$617$	4.93863	−	10.8141i	0.198822	−	0.435359i	0.982613	+	0.185666i	$0.0594441\pi$
$618$	12.5874	+	15.2513i	0.506341	+	0.613497i
$619$	21.3625	+	33.2407i	0.858631	+	1.33606i	0.940633	+	0.339424i	$0.110232\pi$
$619$	21.3625	+	33.2407i	0.858631	+	1.33606i	−0.0820023	+	0.996632i	$0.526131\pi$
$620$	8.63808			0.346914
$621$	23.8097	+	7.35527i	0.955449	+	0.295157i
$622$	4.44627			0.178279
$623$	−7.96037	−	12.3866i	−0.318925	−	0.496258i
$624$	4.06941	+	4.93062i	0.162907	+	0.197383i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	14.3498	−	4.21347i	0.573532	−	0.168404i
$627$	−21.0854	+	65.9157i	−0.842071	+	2.63242i
$628$	−2.41293	+	2.09082i	−0.0962865	+	0.0834328i
$629$	−36.6000	+	5.26229i	−1.45934	+	0.209821i
$630$	2.51893	−	13.0415i	0.100356	−	0.519586i
$631$	34.9946	+	30.3230i	1.39311	+	1.20714i	0.950616	+	0.310368i	$0.100452\pi$
$631$	34.9946	+	30.3230i	1.39311	+	1.20714i	0.442496	+	0.896770i	$0.354093\pi$
$632$	7.07818	+	4.54887i	0.281555	+	0.180944i
$633$	4.51240	−	1.20813i	0.179352	−	0.0480189i
$634$	7.82638	−	9.03212i	0.310825	−	0.358711i
$635$	−3.19040	−	0.936785i	−0.126607	−	0.0371752i
$636$	4.93339	+	3.34045i	0.195622	+	0.132457i
$637$	−30.4624	−	35.1555i	−1.20697	−	1.39291i
$638$	12.0956	+	26.4857i	0.478870	+	1.04858i
$639$	−35.2424	+	14.0927i	−1.39417	+	0.557497i
$640$	0.909632	+	0.415415i	0.0359564	+	0.0164207i
$641$	−1.08397	+	7.53918i	−0.0428142	+	0.297780i	0.957152	+	0.289585i	$0.0935174\pi$
$641$	−1.08397	+	7.53918i	−0.0428142	+	0.297780i	−0.999966	+	0.00819424i	$0.997392\pi$
$642$	−11.4679	−	1.93077i	−0.452601	−	0.0762013i
$643$		−	0.303528i		−	0.0119700i	−0.999982	−	0.00598498i	$-0.998095\pi$
$643$		−	0.303528i		−	0.0119700i	0.999982	−	0.00598498i	$-0.00190509\pi$
$644$	10.4254	−	18.4980i	0.410818	−	0.728924i
$645$	−5.06318	−	4.60458i	−0.199362	−	0.181305i
$646$	−27.5205	+	17.6864i	−1.08278	+	0.695861i
$647$	−6.55693	−	0.942744i	−0.257780	−	0.0370631i	0.0122134	−	0.999925i	$-0.496112\pi$
$647$	−6.55693	−	0.942744i	−0.257780	−	0.0370631i	−0.269993	+	0.962862i	$0.587021\pi$
$648$	−8.74461	−	2.12880i	−0.343521	−	0.0836270i
$649$	−5.77894	−	19.6813i	−0.226843	−	0.772557i
$650$	−3.35748	+	1.53331i	−0.131691	+	0.0601413i
$651$	−1.58961	+	66.2235i	−0.0623016	+	2.59550i
$652$	−0.730003	−	5.07729i	−0.0285891	−	0.198842i
$653$	−0.685145	+	2.33339i	−0.0268118	+	0.0913126i	−0.971812	−	0.235757i	$-0.924243\pi$
$653$	−0.685145	+	2.33339i	−0.0268118	+	0.0913126i	0.945000	+	0.327070i	$0.106061\pi$
$654$	−2.87222	−	24.0630i	−0.112313	−	0.940937i
$655$	−1.73386	+	2.69794i	−0.0677475	+	0.105417i
$656$	2.81621	−	4.38211i	0.109955	−	0.171093i
$657$	−14.0776	−	10.0330i	−0.549218	−	0.391426i
$658$	0.0826819	−	0.281589i	0.00322327	−	0.0109775i
$659$	1.26870	+	8.82397i	0.0494214	+	0.343733i	0.999497	+	0.0317135i	$0.0100964\pi$
$659$	1.26870	+	8.82397i	0.0494214	+	0.343733i	−0.950076	+	0.312020i	$0.898995\pi$
$660$	8.27106	+	0.198535i	0.321950	+	0.00772798i
$661$	5.07453	−	2.31746i	0.197376	−	0.0901387i	−0.314275	−	0.949332i	$-0.601761\pi$
$661$	5.07453	−	2.31746i	0.197376	−	0.0901387i	0.511651	+	0.859193i	$0.329034\pi$
$662$	−2.66413	−	9.07319i	−0.103544	−	0.352640i
$663$	9.83759	+	22.9856i	0.382060	+	0.892687i
$664$	3.04308	+	0.437529i	0.118094	+	0.0169794i
$665$	31.1562	−	20.0229i	1.20818	−	0.776453i
$666$	−2.68496	−	28.2370i	−0.104040	−	1.09416i
$667$	27.2510	+	10.5829i	1.05516	+	0.409771i
$668$		−	10.8608i		−	0.420219i
$669$	−2.64761	+	15.7256i	−0.102362	+	0.607987i
$670$	0.331702	−	2.30704i	0.0128148	−	0.0891288i
$671$	20.9265	+	9.55680i	0.807857	+	0.368936i
$672$	−3.35216	+	6.89721i	−0.129312	+	0.266066i
$673$	−13.1018	−	28.6890i	−0.505038	−	1.10588i	−0.974799	−	0.223085i	$-0.928387\pi$
$673$	−13.1018	−	28.6890i	−0.505038	−	1.10588i	0.469761	−	0.882794i	$-0.344340\pi$
$674$	0.0778030	+	0.0897894i	0.00299686	+	0.00345856i
$675$	2.49297	−	4.55907i	0.0959546	−	0.175479i
$676$	0.598433	+	0.175716i	0.0230166	+	0.00675830i
$677$	−10.7948	+	12.4579i	−0.414880	+	0.478797i	−0.924270	−	0.381739i	$-0.875325\pi$
$677$	−10.7948	+	12.4579i	−0.414880	+	0.478797i	0.509391	+	0.860535i	$0.329871\pi$
$678$	1.01795	+	3.80207i	0.0390942	+	0.146018i
$679$	10.0311	+	6.44659i	0.384958	+	0.247397i
$680$	2.95563	+	2.56107i	0.113343	+	0.0982125i
$681$	8.50488	−	5.18167i	0.325908	−	0.198562i
$682$	−40.8413	+	5.87209i	−1.56389	+	0.224854i
$683$	19.5543	−	16.9439i	0.748226	−	0.648342i	−0.194882	−	0.980827i	$-0.562432\pi$
$683$	19.5543	−	16.9439i	0.748226	−	0.648342i	0.943109	+	0.332485i	$0.107887\pi$
$684$	−12.5386	−	21.7375i	−0.479426	−	0.831154i
$685$	1.12199	−	0.329447i	0.0428692	−	0.0125875i
$686$	10.3050	−	22.5649i	0.393448	−	0.861532i
$687$	−34.0367	+	28.0917i	−1.29858	+	1.07176i
$688$	2.13622	+	3.32403i	0.0814428	+	0.126727i
$689$	12.6965			0.483697
$690$	6.08931	−	5.64981i	0.231816	−	0.215084i
$691$	−43.0325			−1.63703			−0.818517	−	0.574482i	$-0.805203\pi$
$691$	−43.0325			−1.63703			−0.818517	+	0.574482i	$0.805203\pi$
$692$	−5.49413	−	8.54904i	−0.208856	−	0.324986i
$693$	−3.04413	+	63.3732i	−0.115637	+	2.40735i
$694$	−0.754063	+	1.65117i	−0.0286238	+	0.0626774i
$695$	−6.01835	+	1.76715i	−0.228289	+	0.0670317i
$696$	−10.0560	−	3.21677i	−0.381172	−	0.121931i
$697$	15.3960	−	13.3407i	0.583163	−	0.505314i
$698$	−21.9788	+	3.16007i	−0.831909	+	0.119611i
$699$	−18.3898	−	30.1838i	−0.695565	−	1.14166i
$700$	−3.34609	−	2.89940i	−0.126470	−	0.109587i
$701$	−25.0258	−	16.0831i	−0.945211	−	0.607450i	−0.0253434	−	0.999679i	$-0.508068\pi$
$701$	−25.0258	−	16.0831i	−0.945211	−	0.607450i	−0.919868	+	0.392228i	$0.871704\pi$
$702$	−17.9739	+	6.69169i	−0.678381	+	0.252562i
$703$	51.7916	−	59.7707i	1.95336	−	2.25429i
$704$	−4.58318	−	1.34574i	−0.172735	−	0.0507196i
$705$	0.0643700	−	0.0950658i	0.00242431	−	0.00358039i
$706$	−3.10541	−	3.58384i	−0.116874	−	0.134880i
$707$	21.1785	+	46.3744i	0.796498	+	1.74409i
$708$	6.68960	+	3.25125i	0.251410	+	0.122189i
$709$	29.5085	+	13.4761i	1.10822	+	0.506105i	0.883553	−	0.468331i	$-0.155145\pi$
$709$	29.5085	+	13.4761i	1.10822	+	0.506105i	0.224663	+	0.974436i	$0.427872\pi$
$710$	−1.80055	+	12.5231i	−0.0675734	+	0.469984i
$711$	−19.8474	+	15.5954i	−0.744336	+	0.584873i
$712$			3.32556i			0.124631i
$713$	−25.2690	+	32.8276i	−0.946333	+	1.22940i
$714$	−20.1782	+	22.1879i	−0.755152	+	0.830363i
$715$	14.8320	−	9.53195i	0.554685	−	0.356475i
$716$	12.5430	+	1.80341i	0.468753	+	0.0673965i
$717$	−23.9977	+	10.2708i	−0.896211	+	0.383569i
$718$	8.32920	+	28.3666i	0.310843	+	1.05863i
$719$	2.49705	−	1.14037i	0.0931244	−	0.0425285i	−0.368308	−	0.929704i	$-0.620063\pi$
$719$	2.49705	−	1.14037i	0.0931244	−	0.0425285i	0.461433	+	0.887175i	$0.347336\pi$
$720$	−2.07110	+	2.17038i	−0.0771854	+	0.0808852i
$721$	7.19387	+	50.0345i	0.267914	+	1.86338i
$722$	14.3601	−	48.9060i	0.534427	−	1.82009i
$723$	6.25989	−	0.747197i	0.232808	−	0.0277886i
$724$	−10.4846	+	16.3144i	−0.389659	+	0.606321i
$725$	3.29556	−	5.12799i	0.122394	−	0.190449i
$726$	−20.3227	+	2.42577i	−0.754245	+	0.0900287i
$727$	−6.50772	+	22.1633i	−0.241358	+	0.821990i	0.746333	+	0.665573i	$0.231813\pi$
$727$	−6.50772	+	22.1633i	−0.241358	+	0.821990i	−0.987691	+	0.156417i	$0.950005\pi$
$728$	2.32572	+	16.1757i	0.0861969	+	0.599512i
$729$	14.6244	−	22.6964i	0.541645	−	0.840607i
$730$	−5.24160	+	2.39376i	−0.194000	+	0.0885970i
$731$	4.35359	+	14.8270i	0.161023	+	0.548395i
$732$	−7.66904	+	3.28227i	−0.283456	+	0.121316i
$733$	6.48711	+	0.932706i	0.239607	+	0.0344503i	0.261072	−	0.965319i	$-0.415924\pi$
$733$	6.48711	+	0.932706i	0.239607	+	0.0344503i	−0.0214651	+	0.999770i	$0.506833\pi$
$734$	−8.68428	+	5.58105i	−0.320542	+	0.206000i
$735$	14.6866	−	16.1493i	0.541722	−	0.595676i
$736$	−4.23967	+	2.24169i	−0.156276	+	0.0826299i
$737$			11.1333i			0.410100i
$738$	9.65513	+	12.2876i	0.355410	+	0.452311i
$739$	7.58290	−	52.7402i	0.278941	−	1.94008i	−0.0574286	−	0.998350i	$-0.518290\pi$
$739$	7.58290	−	52.7402i	0.278941	−	1.94008i	0.336370	−	0.941730i	$-0.390801\pi$
$740$	−8.60039	−	3.92767i	−0.316157	−	0.144384i
$741$	−48.0972	−	23.3760i	−1.76689	−	0.858739i
$742$	6.32669	+	13.8535i	0.232260	+	0.508579i
$743$	16.2809	+	18.7892i	0.597290	+	0.689309i	0.971230	−	0.238144i	$-0.0765390\pi$
$743$	16.2809	+	18.7892i	0.597290	+	0.689309i	−0.373940	+	0.927453i	$0.621994\pi$
$744$	8.38855	−	12.3888i	0.307539	−	0.454194i
$745$	−19.7227	−	5.79111i	−0.722584	−	0.212170i
$746$	19.8140	−	22.8665i	0.725441	−	0.837203i
$747$	−4.22954	+	8.19615i	−0.154751	+	0.299881i
$748$	−15.7154	−	10.0997i	−0.574611	−	0.369280i
$749$	−22.4662	−	19.4671i	−0.820897	−	0.711311i
$750$	−0.901182	−	1.47915i	−0.0329065	−	0.0540107i
$751$	16.3776	−	2.35475i	0.597628	−	0.0859260i	0.163139	−	0.986603i	$-0.447838\pi$
$751$	16.3776	−	2.35475i	0.597628	−	0.0859260i	0.434489	+	0.900677i	$0.356929\pi$
$752$	−0.0500947	+	0.0434073i	−0.00182677	+	0.00158290i
$753$	17.2908	+	5.53105i	0.630111	+	0.201563i
$754$	−21.5879	+	6.33877i	−0.786184	+	0.230844i
$755$	−8.16509	+	17.8791i	−0.297158	+	0.650686i
$756$	−16.2580	−	16.2774i	−0.591297	−	0.592004i
$757$	17.6980	+	27.5387i	0.643246	+	1.00091i	0.997827	+	0.0658849i	$0.0209870\pi$
$757$	17.6980	+	27.5387i	0.643246	+	1.00091i	−0.354581	+	0.935025i	$0.615377\pi$
$758$	16.4796			0.598565
$759$	−24.9499	+	30.8520i	−0.905624	+	1.11986i
$760$	−8.36484			−0.303425
$761$	13.0560	+	20.3156i	0.473280	+	0.736438i	0.993028	−	0.117882i	$-0.0376103\pi$
$761$	13.0560	+	20.3156i	0.473280	+	0.736438i	−0.519747	+	0.854320i	$0.673974\pi$
$762$	−4.44178	+	3.66595i	−0.160909	+	0.132804i
$763$	25.7337	−	56.3489i	0.931622	−	2.03997i
$764$	5.80273	−	1.70384i	0.209935	−	0.0616426i
$765$	−10.1630	+	5.86224i	−0.367446	+	0.211950i
$766$	0.204786	−	0.177448i	0.00739921	−	0.00641145i
$767$	15.6888	−	2.25571i	0.566490	−	0.0814490i
$768$	1.47915	−	0.901182i	0.0533741	−	0.0325186i
$769$	−28.3350	−	24.5524i	−1.02179	−	0.885382i	−0.0283293	−	0.999599i	$-0.509019\pi$
$769$	−28.3350	−	24.5524i	−1.02179	−	0.885382i	−0.993456	+	0.114217i	$0.963564\pi$
$770$	17.7915	+	11.4339i	0.641160	+	0.412048i
$771$	−4.64472	−	17.3481i	−0.167275	−	0.624778i
$772$	−14.5890	+	16.8366i	−0.525068	+	0.605961i
$773$	6.23058	+	1.82946i	0.224098	+	0.0658012i	0.391854	−	0.920027i	$-0.371834\pi$
$773$	6.23058	+	1.82946i	0.224098	+	0.0658012i	−0.167756	+	0.985829i	$0.553652\pi$
$774$	−11.5208	+	2.79006i	−0.414107	+	0.100287i
$775$	5.65674	+	6.52822i	0.203196	+	0.234501i
$776$	−1.11878	−	2.44978i	−0.0401618	−	0.0879420i
$777$	31.6940	−	65.2118i	1.13702	−	2.33946i
$778$	−2.41098	−	1.10106i	−0.0864377	−	0.0394748i
$779$	−6.20104	+	43.1292i	−0.222175	+	1.54526i
$780$	−1.06141	+	6.30432i	−0.0380047	+	0.225731i
$781$		−	60.4339i		−	2.16249i
$782$	−18.3791	+	3.74048i	−0.657234	+	0.133759i
$783$	18.9966	−	25.3450i	0.678885	−	0.905756i
$784$	−10.6022	+	6.81361i	−0.378649	+	0.243343i
$785$	−3.16027	−	0.454378i	−0.112795	−	0.0162175i
$786$	2.18562	+	5.10671i	0.0779584	+	0.182150i
$787$	5.97998	+	20.3659i	0.213163	+	0.725967i	0.994765	+	0.102189i	$0.0325847\pi$
$787$	5.97998	+	20.3659i	0.213163	+	0.725967i	−0.781602	+	0.623778i	$0.785597\pi$
$788$	−23.7757	+	10.8580i	−0.846975	+	0.386801i
$789$	−28.0436	−	0.673149i	−0.998379	−	0.0239647i
$790$	1.19742	+	8.32821i	0.0426022	+	0.296304i
$791$	−2.83458	+	9.65371i	−0.100786	+	0.343246i
$792$	8.31687	−	11.6696i	0.295527	−	0.414660i
$793$	−9.61084	+	14.9548i	−0.341291	+	0.531059i
$794$	3.03400	−	4.72100i	0.107673	−	0.167542i
$795$	0.706143	+	5.91594i	0.0250443	+	0.209817i
$796$	0.186351	−	0.634654i	0.00660505	−	0.0224947i
$797$	−4.65600	−	32.3832i	−0.164924	−	1.14707i	−0.889185	−	0.457547i	$-0.848728\pi$
$797$	−4.65600	−	32.3832i	−0.164924	−	1.14707i	0.724261	−	0.689526i	$-0.242181\pi$
$798$	1.53932	−	64.1288i	0.0544915	−	2.27013i
$799$	−0.235804	+	0.107688i	−0.00834216	+	0.00380973i
$800$	0.281733	+	0.959493i	0.00996075	+	0.0339232i
$801$	−9.42667	−	3.26681i	−0.333075	−	0.115427i
$802$	−21.6120	−	3.10733i	−0.763145	−	0.109724i
$803$	23.1553	−	14.8810i	0.817133	−	0.525139i
$804$	−2.98665	−	2.71613i	−0.105331	−	0.0957904i
$805$	20.8070	−	4.23462i	0.733352	−	0.149251i
$806$		−	31.8834i		−	1.12304i
$807$	−42.6523	−	7.18108i	−1.50143	−	0.252786i
$808$	1.63871	−	11.3975i	0.0576497	−	0.400963i
$809$	−14.1882	−	6.47955i	−0.498832	−	0.227809i	0.150078	−	0.988674i	$-0.452048\pi$
$809$	−14.1882	−	6.47955i	−0.498832	−	0.227809i	−0.648910	+	0.760865i	$0.724775\pi$
$810$	−4.11767	−	8.00280i	−0.144680	−	0.281190i
$811$	10.8537	+	23.7664i	0.381126	+	0.834550i	0.998840	+	0.0481474i	$0.0153317\pi$
$811$	10.8537	+	23.7664i	0.381126	+	0.834550i	−0.617714	+	0.786403i	$0.711941\pi$
$812$	−17.6738	−	20.3966i	−0.620228	−	0.715781i
$813$	23.8718	+	16.1639i	0.837222	+	0.566891i
$814$	43.3331	+	12.7237i	1.51882	+	0.445967i
$815$	3.35911	−	3.87661i	0.117664	−	0.135792i
$816$	6.54334	−	1.75189i	0.229063	−	0.0613283i
$817$	−27.8050	−	17.8692i	−0.972774	−	0.625164i
$818$	−12.5430	−	10.8686i	−0.438555	−	0.380010i
$819$	−48.1365	−	9.29744i	−1.68203	−	0.324879i
$820$	5.15601	−	0.741322i	0.180056	−	0.0258881i
$821$	5.72467	−	4.96046i	0.199792	−	0.173121i	−0.549218	−	0.835679i	$-0.685075\pi$
$821$	5.72467	−	4.96046i	0.199792	−	0.173121i	0.749011	+	0.662558i	$0.230529\pi$
$822$	0.617089	−	1.92910i	0.0215235	−	0.0672851i
$823$	−30.2262	+	8.87522i	−1.05362	+	0.309371i	−0.762279	−	0.647249i	$-0.775920\pi$
$823$	−30.2262	+	8.87522i	−1.05362	+	0.309371i	−0.291341	+	0.956619i	$0.594101\pi$
$824$	4.74280	−	10.3853i	0.165223	−	0.361789i
$825$	5.26635	+	6.38086i	0.183351	+	0.222153i
$826$	10.2791	+	15.9945i	0.357655	+	0.556522i
$827$	42.0729			1.46302			0.731509	−	0.681831i	$-0.238816\pi$
$827$	42.0729			1.46302			0.731509	+	0.681831i	$0.238816\pi$
$828$	−2.18956	−	14.2199i	−0.0760924	−	0.494176i
$829$	12.2172			0.424321			0.212160	−	0.977235i	$-0.431950\pi$
$829$	12.2172			0.424321			0.212160	+	0.977235i	$0.431950\pi$
$830$	1.66213	+	2.58633i	0.0576934	+	0.0897727i
$831$	7.28467	+	8.82632i	0.252702	+	0.306182i
$832$	1.53331	−	3.35748i	0.0531579	−	0.116400i
$833$	−47.2914	+	13.8860i	−1.63855	+	0.481122i
$834$	−3.31005	+	10.3476i	−0.114618	+	0.358309i
$835$	8.20808	−	7.11234i	0.284052	−	0.246133i
$836$	39.5494	−	5.68635i	1.36785	−	0.196666i
$837$	26.8770	+	35.9482i	0.929004	+	1.24255i
$838$	−0.0420434	−	0.0364308i	−0.00145237	−	0.00125848i
$839$	0.644138	+	0.413962i	0.0222381	+	0.0142916i	0.551713	−	0.834034i	$-0.313975\pi$
$839$	0.644138	+	0.413962i	0.0222381	+	0.0142916i	−0.529475	+	0.848326i	$0.677611\pi$
$840$	−7.40776	+	1.98332i	−0.255592	+	0.0684312i
$841$	5.34173	−	6.16469i	0.184198	−	0.212575i
$842$	3.58105	+	1.05149i	0.123411	+	0.0362368i
$843$	35.4579	+	24.0089i	1.22123	+	0.826910i
$844$	−1.76615	−	2.03825i	−0.0607935	−	0.0701595i
$845$	0.259093	+	0.567335i	0.00891307	+	0.0195169i
$846$	−0.0738332	−	0.184639i	−0.00253844	−	0.00634803i
$847$	−47.5902	−	21.7337i	−1.63522	−	0.746779i
$848$	0.489537	−	3.40480i	0.0168108	−	0.116921i
$849$	11.1131	+	1.87103i	0.381399	+	0.0642135i
$850$			3.91086i			0.134141i
$851$	40.0852	−	21.1948i	1.37410	−	0.726547i
$852$	16.2121	+	14.7437i	0.555419	+	0.505111i
$853$	14.1307	−	9.08122i	0.483825	−	0.310935i	−0.275893	−	0.961188i	$-0.588974\pi$
$853$	14.1307	−	9.08122i	0.483825	−	0.310935i	0.759718	+	0.650253i	$0.225337\pi$
$854$	−21.1067	−	3.03469i	−0.722258	−	0.103845i
$855$	8.21706	−	23.7111i	0.281018	−	0.810902i
$856$	1.89160	+	6.44220i	0.0646535	+	0.220190i
$857$	22.2269	−	10.1507i	0.759258	−	0.346741i	0.00212097	−	0.999998i	$-0.499325\pi$
$857$	22.2269	−	10.1507i	0.759258	−	0.346741i	0.757137	+	0.653256i	$0.226598\pi$
$858$	0.732800	−	30.5287i	0.0250174	−	1.04223i
$859$	−5.88354	−	40.9209i	−0.200744	−	1.39620i	−0.802084	−	0.597211i	$-0.796275\pi$
$859$	−5.88354	−	40.9209i	−0.200744	−	1.39620i	0.601340	−	0.798993i	$-0.294634\pi$
$860$	−1.11320	+	3.79123i	−0.0379600	+	0.129280i
$861$	4.73449	+	39.6647i	0.161351	+	1.35177i
$862$	−6.89371	+	10.7268i	−0.234801	+	0.365357i
$863$	24.8547	−	38.6747i	0.846064	−	1.31650i	−0.100812	−	0.994905i	$-0.532144\pi$
$863$	24.8547	−	38.6747i	0.846064	−	1.31650i	0.946877	−	0.321597i	$-0.104219\pi$
$864$	1.10149	+	5.07806i	0.0374734	+	0.172759i
$865$	2.86304	−	9.75062i	0.0973463	−	0.331531i
$866$	5.23262	+	36.3937i	0.177812	+	1.23671i
$867$	−2.95260	−	0.0708732i	−0.100276	−	0.00240698i
$868$	34.7890	−	15.8876i	1.18082	−	0.539261i
$869$	−11.3229	−	38.5622i	−0.384103	−	1.30813i
$870$	−4.15422	−	9.70637i	−0.140841	−	0.329077i
$871$	−8.51536	−	1.22432i	−0.288532	−	0.0414846i
$872$	−11.7703	+	7.56431i	−0.398593	+	0.256160i
$873$	8.04319	−	0.764800i	0.272221	−	0.0258846i
$874$	24.4697	−	31.7892i	0.827702	−	1.07529i
$875$		−	4.42751i		−	0.149677i
$876$	−1.65705	+	9.84213i	−0.0559866	+	0.332535i
$877$	−1.27842	+	8.89160i	−0.0431691	+	0.300248i	0.956786	+	0.290792i	$0.0939189\pi$
$877$	−1.27842	+	8.89160i	−0.0431691	+	0.300248i	−0.999955	+	0.00945547i	$0.996990\pi$
$878$	−6.19924	−	2.83110i	−0.209214	−	0.0955449i
$879$	−9.22242	+	18.9755i	−0.311065	+	0.640029i
$880$	−1.98430	−	4.34501i	−0.0668908	−	0.146470i
$881$	−32.5531	−	37.5682i	−1.09674	−	1.26571i	−0.961474	−	0.274897i	$-0.911356\pi$
$881$	−32.5531	−	37.5682i	−1.09674	−	1.26571i	−0.135267	−	0.990809i	$-0.543189\pi$
$882$	−8.89906	−	36.7463i	−0.299647	−	1.23731i
$883$	−1.58698	−	0.465979i	−0.0534061	−	0.0156814i	0.254920	−	0.966962i	$-0.417951\pi$
$883$	−1.58698	−	0.465979i	−0.0534061	−	0.0156814i	−0.308326	+	0.951281i	$0.599769\pi$
$884$	9.45298	−	10.9093i	0.317938	−	0.366920i
$885$	1.92362	+	7.18478i	0.0646618	+	0.241514i
$886$	5.74864	+	3.69443i	0.193129	+	0.124117i
$887$	−11.6131	−	10.0628i	−0.389931	−	0.337877i	0.437729	−	0.899107i	$-0.355783\pi$
$887$	−11.6131	−	10.0628i	−0.389931	−	0.337877i	−0.827660	+	0.561230i	$0.810328\pi$
$888$	−13.9850	+	8.52050i	−0.469307	+	0.285929i
$889$	−14.5720	+	2.09514i	−0.488729	+	0.0702687i
$890$	−2.51329	+	2.17778i	−0.0842457	+	0.0729993i
$891$	24.9088	+	35.0385i	0.834475	+	1.17383i
$892$	8.83401	−	2.59390i	0.295785	−	0.0868502i
$893$	0.230332	−	0.504356i	0.00770776	−	0.0168776i
$894$	−27.4586	+	22.6626i	−0.918354	+	0.757949i
$895$	6.85098	+	10.6603i	0.229003	+	0.356336i
$896$	4.42751			0.147913
$897$	−20.8536	−	22.4758i	−0.696281	−	0.750446i
$898$	24.4758			0.816768
$899$	28.4673	+	44.2960i	0.949438	+	1.47735i
$900$	−2.99654	−	0.143939i	−0.0998848	−	0.00479796i
$901$	5.58843	−	12.2369i	0.186177	−	0.407672i
$902$	−23.8739	+	7.01002i	−0.794915	+	0.233408i
$903$	−28.8604	−	9.23202i	−0.960416	−	0.307222i
$904$	1.71740	−	1.48813i	0.0571198	−	0.0494946i
$905$	−19.1956	+	2.75991i	−0.638083	+	0.0917425i
$906$	17.7130	+	29.0730i	0.588474	+	0.965886i
$907$	23.2240	+	20.1237i	0.771139	+	0.668196i	0.948793	−	0.315897i	$-0.102306\pi$
$907$	23.2240	+	20.1237i	0.771139	+	0.668196i	−0.177655	+	0.984093i	$0.556851\pi$
$908$	−4.83709	−	3.10861i	−0.160524	−	0.103163i
$909$	30.6977	+	15.8413i	1.01818	+	0.525421i
$910$	−10.7018	+	12.3505i	−0.354760	+	0.409415i
$911$	−5.64892	−	1.65867i	−0.187157	−	0.0549542i	0.186811	−	0.982396i	$-0.440185\pi$
$911$	−5.64892	−	1.65867i	−0.187157	−	0.0549542i	−0.373968	+	0.927442i	$0.622003\pi$
$912$	−8.12321	+	11.9969i	−0.268986	+	0.397257i
$913$	−9.61681	−	11.0984i	−0.318270	−	0.367303i
$914$	−16.2392	−	35.5588i	−0.537144	−	1.17618i
$915$	−7.50272	−	3.64645i	−0.248032	−	0.120548i
$916$	23.1771	+	10.5846i	0.765793	+	0.349726i
$917$	−2.02076	+	14.0547i	−0.0667314	+	0.464127i
$918$	−1.46182	+	20.2688i	−0.0482473	+	0.668969i
$919$			31.2580i			1.03111i	0.856858	+	0.515553i	$0.172414\pi$
$919$			31.2580i			1.03111i	−0.856858	+	0.515553i	$0.827586\pi$
$920$	−4.47055	−	1.73613i	−0.147390	−	0.0572386i
$921$	5.41972	−	5.95950i	0.178586	−	0.196372i
$922$	0.0102480	−	0.00658597i	0.000337499	−	0.000216897i
$923$	46.2231	+	6.64588i	1.52145	+	0.218752i
$924$	33.6760	−	14.4130i	1.10786	−	0.474152i
$925$	−2.66373	−	9.07181i	−0.0875827	−	0.298279i
$926$	26.8172	−	12.2470i	0.881269	−	0.402462i
$927$	24.7793	+	23.6458i	0.813858	+	0.776631i
$928$	0.867503	+	6.03361i	0.0284772	+	0.198063i
$929$	−6.47561	+	22.0539i	−0.212458	+	0.723566i	0.782444	+	0.622721i	$0.213973\pi$
$929$	−6.47561	+	22.0539i	−0.212458	+	0.723566i	−0.994902	+	0.100845i	$0.967845\pi$
$930$	14.8561	−	1.77327i	0.487152	−	0.0581478i
$931$	56.9948	−	88.6856i	1.86793	−	2.90655i
$932$	−11.0325	+	17.1668i	−0.361380	+	0.562319i
$933$	7.64689	−	0.912753i	0.250348	−	0.0298822i
$934$	−7.37910	+	25.1309i	−0.241452	+	0.822309i
$935$	−2.65857	−	18.4907i	−0.0869445	−	0.604712i
$936$	8.01093	+	7.64450i	0.261845	+	0.249868i
$937$	13.9195	−	6.35683i	0.454731	−	0.207669i	−0.174863	−	0.984593i	$-0.555948\pi$
$937$	13.9195	−	6.35683i	0.454731	−	0.207669i	0.629594	+	0.776924i	$0.283221\pi$
$938$	−2.90733	−	9.90147i	−0.0949278	−	0.323295i
$939$	23.8144	−	10.1923i	0.777153	−	0.332613i
$940$	−0.0656101	−	0.00943331i	−0.00213996	−	0.000307680i
$941$	8.25622	−	5.30595i	0.269145	−	0.172969i	−0.399106	−	0.916905i	$-0.630680\pi$
$941$	8.25622	−	5.30595i	0.269145	−	0.172969i	0.668251	+	0.743936i	$0.267043\pi$
$942$	−3.72065	+	4.09122i	−0.121225	+	0.133299i
$943$	−12.2656	+	21.7632i	−0.399424	+	0.708706i
$944$		−	4.29423i		−	0.139765i
$945$	1.65494	−	22.9464i	0.0538351	−	0.746447i
$946$	2.68605	−	18.6819i	0.0873309	−	0.607400i
$947$	40.4268	+	18.4623i	1.31369	+	0.599944i	0.944226	−	0.329299i	$-0.106812\pi$
$947$	40.4268	+	18.4623i	1.31369	+	0.599944i	0.369469	+	0.929243i	$0.379540\pi$
$948$	13.1072	+	6.37030i	0.425701	+	0.206898i
$949$	8.83543	+	19.3469i	0.286810	+	0.628027i
$950$	−5.47781	−	6.32173i	−0.177724	−	0.205104i
$951$	11.6060	−	17.1405i	0.376350	−	0.555818i
$952$	16.6140	+	4.87830i	0.538462	+	0.158107i
$953$	−13.2579	+	15.3005i	−0.429466	+	0.495631i	−0.928697	−	0.370838i	$-0.879070\pi$
$953$	−13.2579	+	15.3005i	−0.429466	+	0.495631i	0.499231	+	0.866469i	$0.333616\pi$
$954$	9.17041	+	4.73230i	0.296903	+	0.153214i
$955$	5.08765	+	3.26964i	0.164633	+	0.105803i
$956$	11.3897	+	9.86922i	0.368369	+	0.319193i
$957$	26.2397	+	43.0682i	0.848208	+	1.39220i
$958$	−42.2767	+	6.07848i	−1.36590	+	0.196387i
$959$	3.91279	−	3.39045i	0.126351	−	0.109483i
$960$	1.64970	+	0.527715i	0.0532439	+	0.0170319i
$961$	−41.8496	+	12.2882i	−1.34999	+	0.396392i
$962$	−14.4971	+	31.7443i	−0.467406	+	1.02348i
$963$	−20.1193	−	0.966430i	−0.648336	−	0.0311428i
$964$	−1.96783	−	3.06200i	−0.0633794	−	0.0986203i
$965$	−22.2780			−0.717153
$966$	14.1327	−	33.9538i	0.454712	−	1.09245i
$967$	−1.27169			−0.0408947			−0.0204473	−	0.999791i	$-0.506509\pi$
$967$	−1.27169			−0.0408947			−0.0204473	+	0.999791i	$0.506509\pi$
$968$	6.38853	+	9.94075i	0.205335	+	0.319508i
$969$	−43.7002	+	36.0673i	−1.40385	+	1.15865i
$970$	1.11878	−	2.44978i	0.0359218	−	0.0786577i
$971$	39.3220	−	11.5460i	1.26190	−	0.370528i	0.418701	−	0.908124i	$-0.362486\pi$
$971$	39.3220	−	11.5460i	1.26190	−	0.370528i	0.843203	+	0.537596i	$0.180667\pi$
$972$	−15.4764	−	1.86605i	−0.496405	−	0.0598537i
$973$	−20.9881	+	18.1863i	−0.672847	+	0.583025i
$974$	2.42630	−	0.348849i	0.0777436	−	0.0111778i
$975$	−5.45957	+	3.32629i	−0.174846	+	0.106527i
$976$	3.63984	+	3.15394i	0.116509	+	0.100955i
$977$	8.10332	+	5.20769i	0.259248	+	0.166609i	0.663808	−	0.747903i	$-0.268939\pi$
$977$	8.10332	+	5.20769i	0.259248	+	0.166609i	−0.404560	+	0.914511i	$0.632575\pi$
$978$	−2.29778	−	8.58227i	−0.0734750	−	0.274431i
$979$	10.4025	−	12.0052i	0.332466	−	0.383687i
$980$	−12.0923	−	3.55063i	−0.386275	−	0.113421i
$981$	−9.87954	−	40.7949i	−0.315429	−	1.30248i
$982$	10.7356	+	12.3896i	0.342588	+	0.395367i
$983$	−23.3246	−	51.0737i	−0.743939	−	1.62900i	−0.776964	−	0.629545i	$-0.783241\pi$
$983$	−23.3246	−	51.0737i	−0.743939	−	1.62900i	0.0330251	−	0.999455i	$-0.489486\pi$
$984$	3.94386	−	8.11467i	0.125726	−	0.258686i
$985$	−23.7757	−	10.8580i	−0.757558	−	0.345965i
$986$	−3.39268	+	23.5966i	−0.108045	+	0.751469i
$987$	0.0843939	−	0.501261i	0.00268629	−	0.0159553i
$988$			30.8749i			0.982261i
$989$	−11.1515	−	15.3211i	−0.354596	−	0.487181i
$990$	14.2657	−	1.35647i	0.453393	−	0.0431116i
$991$	33.6441	−	21.6218i	1.06874	−	0.686838i	0.116811	−	0.993154i	$-0.462733\pi$
$991$	33.6441	−	21.6218i	1.06874	−	0.686838i	0.951930	+	0.306316i	$0.0990964\pi$
$992$	−8.55015	−	1.22933i	−0.271468	−	0.0390312i
$993$	−6.44448	−	15.0576i	−0.204509	−	0.477837i
$994$	15.7816	+	53.7472i	0.500562	+	1.70476i
$995$	0.601674	−	0.274775i	0.0190743	−	0.00871096i
$996$	5.32344	+	0.127782i	0.168680	+	0.00404892i
$997$	−4.58598	−	31.8962i	−0.145239	−	1.01016i	−0.923877	−	0.382689i	$-0.874998\pi$
$997$	−4.58598	−	31.8962i	−0.145239	−	1.01016i	0.778638	−	0.627474i	$-0.215911\pi$
$998$	−1.53305	+	5.22109i	−0.0485279	+	0.165271i
$999$	−10.4144	−	48.0121i	−0.329496	−	1.51903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.11.3	✓	160
3.2	odd	2		690.2.q.b.11.15	yes	160
23.21	odd	22		690.2.q.b.251.15	yes	160
69.44	even	22	inner	690.2.q.a.251.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.3	✓	160	1.1	even	1	trivial
690.2.q.a.251.3	yes	160	69.44	even	22	inner
690.2.q.b.11.15	yes	160	3.2	odd	2
690.2.q.b.251.15	yes	160	23.21	odd	22

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.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(-1.10251 - 1.33584i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.527715 + 1.64970i) q^{6} +(-3.34609 + 2.89940i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.568927 + 2.94556i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(-1.10251 - 1.33584i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.527715 + 1.64970i) q^{6} +(-3.34609 + 2.89940i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.568927 + 2.94556i) q^{9} +(0.755750 + 0.654861i) q^{10} +(-4.01839 - 2.58246i) q^{11} +(1.67312 - 0.447955i) q^{12} +(2.41711 - 2.78949i) q^{13} +(4.24816 + 1.24737i) q^{14} +(1.43420 + 0.971113i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.62463 - 3.55744i) q^{17} +(2.78555 - 1.11388i) q^{18} +(7.60893 + 3.47488i) q^{19} +(0.142315 - 0.989821i) q^{20} +(7.56224 + 1.27320i) q^{21} +4.77667i q^{22} +(3.34534 + 3.43638i) q^{23} +(-1.28140 - 1.16534i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-3.65346 - 0.525288i) q^{26} +(4.56204 - 2.48753i) q^{27} +(-1.24737 - 4.24816i) q^{28} +(5.54481 - 2.53223i) q^{29} +(0.0415636 - 1.73155i) q^{30} +(1.22933 + 8.55015i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(0.980579 + 8.21512i) q^{33} +(-2.11437 + 3.29002i) q^{34} +(2.39369 - 3.72466i) q^{35} +(-2.44303 - 1.74114i) q^{36} +(2.66373 - 9.07181i) q^{37} +(-1.19044 - 8.27970i) q^{38} +(-6.39121 - 0.153412i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(1.46755 + 4.99802i) q^{41} +(-3.01737 - 7.05011i) q^{42} +(-3.91106 - 0.562326i) q^{43} +(4.01839 - 2.58246i) q^{44} +(-0.283979 - 2.98653i) q^{45} +(1.08224 - 4.67213i) q^{46} -0.0662848i q^{47} +(-0.287566 + 1.70801i) q^{48} +(1.79357 - 12.4746i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(-2.96099 + 6.09237i) q^{51} +(1.53331 + 3.35748i) q^{52} +(2.25260 + 2.59964i) q^{53} +(-4.55907 - 2.49297i) q^{54} +(4.58318 + 1.34574i) q^{55} +(-2.89940 + 3.34609i) q^{56} +(-3.74707 - 13.9954i) q^{57} +(-5.12799 - 3.29556i) q^{58} +(3.24536 + 2.81212i) q^{59} +(-1.47915 + 0.901182i) q^{60} +(-4.76718 + 0.685417i) q^{61} +(6.52822 - 5.65674i) q^{62} +(-6.63668 - 11.5057i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.53331 + 3.35748i) q^{65} +(6.38086 - 5.26635i) q^{66} +(-1.26011 - 1.96076i) q^{67} +3.91086 q^{68} +(0.902158 - 8.25749i) q^{69} -4.42751 q^{70} +(6.84012 + 10.6434i) q^{71} +(-0.143939 + 2.99654i) q^{72} +(-2.39376 + 5.24160i) q^{73} +(-9.07181 + 2.66373i) q^{74} +(-1.64970 - 0.527715i) q^{75} +(-6.32173 + 5.47781i) q^{76} +(20.9335 - 3.00978i) q^{77} +(3.32629 + 5.45957i) q^{78} +(6.35877 + 5.50990i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-8.35264 - 3.35161i) q^{81} +(3.41119 - 3.93672i) q^{82} +(2.94984 + 0.866151i) q^{83} +(-4.29961 + 6.34995i) q^{84} +(2.56107 + 2.95563i) q^{85} +(1.64142 + 3.59421i) q^{86} +(-9.49587 - 4.61515i) q^{87} +(-4.34501 - 1.98430i) q^{88} +(-0.473277 + 3.29171i) q^{89} +(-2.35890 + 1.85354i) q^{90} +16.3421i q^{91} +(-4.51554 + 1.61551i) q^{92} +(10.0663 - 11.0688i) q^{93} +(-0.0557623 + 0.0358362i) q^{94} +(-8.27970 - 1.19044i) q^{95} +(1.59234 - 0.681505i) q^{96} +(-0.758750 - 2.58406i) q^{97} +(-11.4639 + 5.23541i) q^{98} +(9.89297 - 10.3672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more