LMFDB - Embedded newform 552.2.bb.a.85.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.36
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.940019 - 1.05658i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.232727 - 1.98641i) q^{4} +(-2.80703 + 1.28193i) q^{5} +(-1.39707 - 0.219564i) q^{6} +(-0.413734 + 0.121483i) q^{7} +(-2.31758 - 1.62137i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.940019 - 1.05658i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.232727 - 1.98641i) q^{4} +(-2.80703 + 1.28193i) q^{5} +(-1.39707 - 0.219564i) q^{6} +(-0.413734 + 0.121483i) q^{7} +(-2.31758 - 1.62137i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.28420 + 4.17089i) q^{10} +(-2.98204 + 2.58395i) q^{11} +(-1.54526 + 1.26972i) q^{12} +(0.0814265 - 0.277313i) q^{13} +(-0.260561 + 0.551341i) q^{14} +(2.59602 + 1.66836i) q^{15} +(-3.89168 + 0.924586i) q^{16} +(-0.737711 + 5.13089i) q^{17} +(0.570602 + 1.29399i) q^{18} +(2.87505 - 0.413370i) q^{19} +(3.19971 + 5.27758i) q^{20} +(0.325880 + 0.282377i) q^{21} +(-0.0730198 + 5.57973i) q^{22} +(-1.29334 - 4.61815i) q^{23} +(-0.111009 + 2.82625i) q^{24} +(2.96177 - 3.41806i) q^{25} +(-0.216461 - 0.346713i) q^{26} +(0.989821 - 0.142315i) q^{27} +(0.337604 + 0.793575i) q^{28} +(-5.51836 - 0.793421i) q^{29} +(4.20307 - 1.17461i) q^{30} +(-3.14536 - 2.02140i) q^{31} +(-2.68135 + 4.98100i) q^{32} +(3.78597 + 1.11166i) q^{33} +(4.72774 + 5.60259i) q^{34} +(1.00563 - 0.871385i) q^{35} +(1.90358 + 0.613490i) q^{36} +(-8.93908 - 4.08234i) q^{37} +(2.26584 - 3.42630i) q^{38} +(-0.277313 + 0.0814265i) q^{39} +(8.58398 + 1.58027i) q^{40} +(0.861891 + 1.88728i) q^{41} +(0.604687 - 0.0788792i) q^{42} +(2.21248 + 3.44268i) q^{43} +(5.82680 + 5.32221i) q^{44} -3.08589i q^{45} +(-6.09521 - 2.97463i) q^{46} -1.86659 q^{47} +(2.88181 + 2.77402i) q^{48} +(-5.73236 + 3.68396i) q^{49} +(-0.827342 - 6.34240i) q^{50} +(4.71522 - 2.15337i) q^{51} +(-0.569809 - 0.0972083i) q^{52} +(0.329804 + 1.12321i) q^{53} +(0.780084 - 1.17961i) q^{54} +(5.05823 - 11.0760i) q^{55} +(1.15583 + 0.389270i) q^{56} +(-1.90212 - 2.19516i) q^{57} +(-6.02568 + 5.08477i) q^{58} +(2.87791 - 9.80125i) q^{59} +(2.70989 - 5.54504i) q^{60} +(1.41018 - 2.19428i) q^{61} +(-5.09248 + 1.42317i) q^{62} +(0.0613663 - 0.426812i) q^{63} +(2.74231 + 7.51530i) q^{64} +(0.126929 + 0.882809i) q^{65} +(4.73345 - 2.95520i) q^{66} +(-3.91390 - 3.39141i) q^{67} +(10.3638 + 0.271299i) q^{68} +(-3.18580 + 3.58479i) q^{69} +(0.0246244 - 1.88165i) q^{70} +(-6.35385 + 7.33274i) q^{71} +(2.43761 - 1.43460i) q^{72} +(-1.86525 - 12.9731i) q^{73} +(-12.7162 + 5.60738i) q^{74} +(-4.47671 - 0.643654i) q^{75} +(-1.49023 - 5.61483i) q^{76} +(0.919865 - 1.43134i) q^{77} +(-0.174646 + 0.369546i) q^{78} +(13.5471 + 3.97780i) q^{79} +(9.73879 - 7.58418i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(2.80426 + 0.863420i) q^{82} +(9.95434 + 4.54600i) q^{83} +(0.485076 - 0.713049i) q^{84} +(-4.50665 - 15.3483i) q^{85} +(5.71724 + 0.898525i) q^{86} +(2.31598 + 5.07130i) q^{87} +(11.1006 - 1.15351i) q^{88} +(-7.56875 + 4.86414i) q^{89} +(-3.26050 - 2.90080i) q^{90} +0.124626i q^{91} +(-8.87255 + 3.64388i) q^{92} +3.73890i q^{93} +(-1.75463 + 1.97220i) q^{94} +(-7.54043 + 4.84594i) q^{95} +(5.63993 - 0.437236i) q^{96} +(-3.88948 - 8.51677i) q^{97} +(-1.49612 + 9.51970i) q^{98} +(-1.11166 - 3.78597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.940019	−	1.05658i	0.664694	−	0.747116i
$2$	0.940019	−	1.05658i	0.664694	−	0.747116i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$4$	−0.232727	−	1.98641i	−0.116364	−	0.993207i
$5$	−2.80703	+	1.28193i	−1.25534	+	0.573295i	−0.928341	−	0.371729i	$-0.878765\pi$
$5$	−2.80703	+	1.28193i	−1.25534	+	0.573295i	−0.327000	+	0.945024i	$0.606038\pi$
$6$	−1.39707	−	0.219564i	−0.570350	−	0.0896365i
$7$	−0.413734	+	0.121483i	−0.156377	+	0.0459164i	−0.358984	−	0.933344i	$-0.616877\pi$
$7$	−0.413734	+	0.121483i	−0.156377	+	0.0459164i	0.202607	+	0.979260i	$0.435059\pi$
$8$	−2.31758	−	1.62137i	−0.819387	−	0.573241i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	−1.28420	+	4.17089i	−0.406100	+	1.31895i
$11$	−2.98204	+	2.58395i	−0.899119	+	0.779091i	−0.975959	−	0.217953i	$-0.930062\pi$
$11$	−2.98204	+	2.58395i	−0.899119	+	0.779091i	0.0768407	+	0.997043i	$0.475517\pi$
$12$	−1.54526	+	1.26972i	−0.446077	+	0.366536i
$13$	0.0814265	−	0.277313i	0.0225836	−	0.0769128i	−0.947430	−	0.319963i	$-0.896330\pi$
$13$	0.0814265	−	0.277313i	0.0225836	−	0.0769128i	0.970014	+	0.243050i	$0.0781478\pi$
$14$	−0.260561	+	0.551341i	−0.0696379	+	0.147352i
$15$	2.59602	+	1.66836i	0.670289	+	0.430769i
$16$	−3.89168	+	0.924586i	−0.972919	+	0.231146i
$17$	−0.737711	+	5.13089i	−0.178921	+	1.24442i	0.680344	+	0.732893i	$0.261831\pi$
$17$	−0.737711	+	5.13089i	−0.178921	+	1.24442i	−0.859265	+	0.511531i	$0.829079\pi$
$18$	0.570602	+	1.29399i	0.134492	+	0.304997i
$19$	2.87505	−	0.413370i	0.659581	−	0.0948335i	0.195607	−	0.980682i	$-0.437332\pi$
$19$	2.87505	−	0.413370i	0.659581	−	0.0948335i	0.463974	+	0.885849i	$0.346423\pi$
$20$	3.19971	+	5.27758i	0.715477	+	1.18010i
$21$	0.325880	+	0.282377i	0.0711129	+	0.0616196i
$22$	−0.0730198	+	5.57973i	−0.0155679	+	1.18960i
$23$	−1.29334	−	4.61815i	−0.269680	−	0.962950i
$23$	−1.29334	−	4.61815i	−0.269680	−	0.962950i
$24$	−0.111009	+	2.82625i	−0.0226596	+	0.576905i
$25$	2.96177	−	3.41806i	0.592354	−	0.683613i
$26$	−0.216461	−	0.346713i	−0.0424516	−	0.0679961i
$27$	0.989821	−	0.142315i	0.190491	−	0.0273885i
$28$	0.337604	+	0.793575i	0.0638011	+	0.149972i
$29$	−5.51836	−	0.793421i	−1.02473	−	0.147335i	−0.390603	−	0.920559i	$-0.627733\pi$
$29$	−5.51836	−	0.793421i	−1.02473	−	0.147335i	−0.634132	+	0.773225i	$0.718642\pi$
$30$	4.20307	−	1.17461i	0.767372	−	0.214454i
$31$	−3.14536	−	2.02140i	−0.564924	−	0.363054i	0.226793	−	0.973943i	$-0.427176\pi$
$31$	−3.14536	−	2.02140i	−0.564924	−	0.363054i	−0.791717	+	0.610889i	$0.790812\pi$
$32$	−2.68135	+	4.98100i	−0.474000	+	0.880525i
$33$	3.78597	+	1.11166i	0.659053	+	0.193515i
$34$	4.72774	+	5.60259i	0.810801	+	0.960836i
$35$	1.00563	−	0.871385i	0.169983	−	0.147291i
$36$	1.90358	+	0.613490i	0.317264	+	0.102248i
$37$	−8.93908	−	4.08234i	−1.46958	−	0.671133i	−0.489911	−	0.871773i	$-0.662971\pi$
$37$	−8.93908	−	4.08234i	−1.46958	−	0.671133i	−0.979665	+	0.200640i	$0.935698\pi$
$38$	2.26584	−	3.42630i	0.367568	−	0.555819i
$39$	−0.277313	+	0.0814265i	−0.0444056	+	0.0130387i
$40$	8.58398	+	1.58027i	1.35725	+	0.249863i
$41$	0.861891	+	1.88728i	0.134605	+	0.294743i	0.964917	−	0.262555i	$-0.0845652\pi$
$41$	0.861891	+	1.88728i	0.134605	+	0.294743i	−0.830312	+	0.557299i	$0.811838\pi$
$42$	0.604687	−	0.0788792i	0.0933053	−	0.0121713i
$43$	2.21248	+	3.44268i	0.337399	+	0.525004i	0.967950	−	0.251145i	$-0.0808070\pi$
$43$	2.21248	+	3.44268i	0.337399	+	0.525004i	−0.630550	+	0.776149i	$0.717171\pi$
$44$	5.82680	+	5.32221i	0.878423	+	0.802353i
$45$		−	3.08589i		−	0.460018i
$46$	−6.09521	−	2.97463i	−0.898690	−	0.438585i
$47$	−1.86659			−0.272270			−0.136135	−	0.990690i	$-0.543468\pi$
$47$	−1.86659			−0.272270			−0.136135	+	0.990690i	$0.543468\pi$
$48$	2.88181	+	2.77402i	0.415953	+	0.400395i
$49$	−5.73236	+	3.68396i	−0.818908	+	0.526280i
$50$	−0.827342	−	6.34240i	−0.117004	−	0.896950i
$51$	4.71522	−	2.15337i	0.660263	−	0.301532i
$52$	−0.569809	−	0.0972083i	−0.0790182	−	0.0134804i
$53$	0.329804	+	1.12321i	0.0453021	+	0.154285i	0.979038	−	0.203678i	$-0.0652896\pi$
$53$	0.329804	+	1.12321i	0.0453021	+	0.154285i	−0.933736	+	0.357963i	$0.883471\pi$
$54$	0.780084	−	1.17961i	0.106156	−	0.160524i
$55$	5.05823	−	11.0760i	0.682052	−	1.49349i
$56$	1.15583	+	0.389270i	0.154454	+	0.0520184i
$57$	−1.90212	−	2.19516i	−0.251942	−	0.290756i
$58$	−6.02568	+	5.08477i	−0.791211	+	0.667663i
$59$	2.87791	−	9.80125i	0.374672	−	1.27601i	−0.529305	−	0.848432i	$-0.677547\pi$
$59$	2.87791	−	9.80125i	0.374672	−	1.27601i	0.903976	−	0.427583i	$-0.140635\pi$
$60$	2.70989	−	5.54504i	0.349845	−	0.715862i
$61$	1.41018	−	2.19428i	0.180555	−	0.280949i	−0.739165	−	0.673525i	$-0.764780\pi$
$61$	1.41018	−	2.19428i	0.180555	−	0.280949i	0.919720	+	0.392576i	$0.128416\pi$
$62$	−5.09248	+	1.42317i	−0.646745	+	0.180743i
$63$	0.0613663	−	0.426812i	0.00773143	−	0.0537733i
$64$	2.74231	+	7.51530i	0.342789	+	0.939413i
$65$	0.126929	+	0.882809i	0.0157436	+	0.109499i
$66$	4.73345	−	2.95520i	0.582647	−	0.363760i
$67$	−3.91390	−	3.39141i	−0.478159	−	0.414327i	0.382150	−	0.924100i	$-0.375184\pi$
$67$	−3.91390	−	3.39141i	−0.478159	−	0.414327i	−0.860309	+	0.509773i	$0.829729\pi$
$68$	10.3638	+	0.271299i	1.25679	+	0.0328999i
$69$	−3.18580	+	3.58479i	−0.383525	+	0.431557i
$70$	0.0246244	−	1.88165i	0.00294318	−	0.224900i
$71$	−6.35385	+	7.33274i	−0.754064	+	0.870236i	−0.994956	−	0.100316i	$-0.968015\pi$
$71$	−6.35385	+	7.33274i	−0.754064	+	0.870236i	0.240892	+	0.970552i	$0.422560\pi$
$72$	2.43761	−	1.43460i	0.287275	−	0.169069i
$73$	−1.86525	−	12.9731i	−0.218311	−	1.51839i	−0.744272	−	0.667877i	$-0.767203\pi$
$73$	−1.86525	−	12.9731i	−0.218311	−	1.51839i	0.525961	−	0.850509i	$-0.323706\pi$
$74$	−12.7162	+	5.60738i	−1.47823	+	0.651845i
$75$	−4.47671	−	0.643654i	−0.516926	−	0.0743228i
$76$	−1.49023	−	5.61483i	−0.170941	−	0.644066i
$77$	0.919865	−	1.43134i	0.104828	−	0.163116i
$78$	−0.174646	+	0.369546i	−0.0197748	+	0.0418429i
$79$	13.5471	+	3.97780i	1.52417	+	0.447538i	0.933261	−	0.359198i	$-0.116950\pi$
$79$	13.5471	+	3.97780i	1.52417	+	0.447538i	0.590912	+	0.806736i	$0.298768\pi$
$80$	9.73879	−	7.58418i	1.08883	−	0.847937i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	2.80426	+	0.863420i	0.309678	+	0.0953488i
$83$	9.95434	+	4.54600i	1.09263	+	0.498988i	0.878464	−	0.477809i	$-0.158569\pi$
$83$	9.95434	+	4.54600i	1.09263	+	0.498988i	0.214167	+	0.976797i	$0.431296\pi$
$84$	0.485076	−	0.713049i	0.0529261	−	0.0778001i
$85$	−4.50665	−	15.3483i	−0.488815	−	1.66475i
$86$	5.71724	+	0.898525i	0.616506	+	0.0968905i
$87$	2.31598	+	5.07130i	0.248300	+	0.543700i
$88$	11.1006	−	1.15351i	1.18333	−	0.122964i
$89$	−7.56875	+	4.86414i	−0.802286	+	0.515598i	−0.876361	−	0.481655i	$-0.840036\pi$
$89$	−7.56875	+	4.86414i	−0.802286	+	0.515598i	0.0740751	+	0.997253i	$0.476400\pi$
$90$	−3.26050	−	2.90080i	−0.343687	−	0.305771i
$91$			0.124626i			0.0130644i
$92$	−8.87255	+	3.64388i	−0.925027	+	0.379901i
$93$			3.73890i			0.387706i
$94$	−1.75463	+	1.97220i	−0.180976	+	0.203417i
$95$	−7.54043	+	4.84594i	−0.773632	+	0.497183i
$96$	5.63993	−	0.437236i	0.575623	−	0.0446252i
$97$	−3.88948	−	8.51677i	−0.394917	−	0.864747i	−0.997761	−	0.0668875i	$-0.978693\pi$
$97$	−3.88948	−	8.51677i	−0.394917	−	0.864747i	0.602844	−	0.797859i	$-0.294034\pi$
$98$	−1.49612	+	9.51970i	−0.151131	+	0.961634i
$99$	−1.11166	−	3.78597i	−0.111726	−	0.380504i
$100$	−7.47897	−	5.08782i	−0.747897	−	0.508782i
$101$	−6.98062	−	3.18794i	−0.694598	−	0.317212i	0.0366459	−	0.999328i	$-0.488333\pi$
$101$	−6.98062	−	3.18794i	−0.694598	−	0.317212i	−0.731244	+	0.682116i	$0.761060\pi$
$102$	2.15719	−	7.00622i	0.213593	−	0.693719i
$103$	−2.77792	−	3.20589i	−0.273717	−	0.315886i	0.602203	−	0.798343i	$-0.294290\pi$
$103$	−2.77792	−	3.20589i	−0.273717	−	0.315886i	−0.875920	+	0.482457i	$0.839744\pi$
$104$	−0.638340	+	0.510671i	−0.0625943	+	0.0500755i
$105$	−1.27674	−	0.374885i	−0.124597	−	0.0365850i
$106$	1.49679	+	0.707375i	0.145381	+	0.0687063i
$107$	5.19437	−	8.08260i	0.502159	−	0.781374i	−0.493952	−	0.869489i	$-0.664448\pi$
$107$	5.19437	−	8.08260i	0.502159	−	0.781374i	0.996110	+	0.0881152i	$0.0280844\pi$
$108$	−0.513055	−	1.93307i	−0.0493687	−	0.186010i
$109$	−10.1340	−	1.45705i	−0.970661	−	0.139560i	−0.361297	−	0.932451i	$-0.617666\pi$
$109$	−10.1340	−	1.45705i	−0.970661	−	0.139560i	−0.609364	+	0.792891i	$0.708575\pi$
$110$	−6.94784	−	15.7561i	−0.662450	−	1.50228i
$111$	1.39855	+	9.72711i	0.132744	+	0.923257i
$112$	1.49780	−	0.855307i	0.141529	−	0.0808189i
$113$	−12.7593	+	14.7251i	−1.20030	+	1.38522i	−0.297741	+	0.954647i	$0.596233\pi$
$113$	−12.7593	+	14.7251i	−1.20030	+	1.38522i	−0.902557	+	0.430571i	$0.858312\pi$
$114$	−4.10739	−	0.0537519i	−0.384693	−	0.00503432i
$115$	9.55057	+	11.3053i	0.890595	+	1.05422i
$116$	−0.291787	+	11.1464i	−0.0270918	+	1.03492i
$117$	0.218427	+	0.189268i	0.0201936	+	0.0174978i
$118$	−7.65053	−	12.2541i	−0.704289	−	1.12808i
$119$	−0.318102	−	2.21245i	−0.0291603	−	0.202815i
$120$	−3.31144	−	8.07566i	−0.302292	−	0.737204i
$121$	0.650288	−	4.52285i	0.0591171	−	0.411169i
$122$	−0.992841	−	3.55264i	−0.0898876	−	0.321641i
$123$	1.12171	−	1.74541i	0.101141	−	0.157378i
$124$	−3.28333	+	6.71842i	−0.294851	+	0.603332i
$125$	0.414922	−	1.41310i	0.0371118	−	0.126391i
$126$	−0.393276	−	0.466050i	−0.0350358	−	0.0415190i
$127$	10.3278	+	11.9190i	0.916447	+	1.05764i	0.998139	+	0.0609783i	$0.0194220\pi$
$127$	10.3278	+	11.9190i	0.916447	+	1.05764i	−0.0816924	+	0.996658i	$0.526033\pi$
$128$	10.5183	+	4.16706i	0.929699	+	0.368319i
$129$	1.70001	−	3.72251i	0.149678	−	0.327748i
$130$	1.05207	+	0.695747i	0.0922730	+	0.0610210i
$131$	−2.17670	−	7.41316i	−0.190179	−	0.647691i	−0.998279	−	0.0586452i	$-0.981322\pi$
$131$	−2.17670	−	7.41316i	−0.190179	−	0.647691i	0.808100	−	0.589046i	$-0.200496\pi$
$132$	1.32712	−	7.77922i	0.115511	−	0.677094i
$133$	−1.13929	+	0.520296i	−0.0987889	+	0.0451154i
$134$	−7.26244	+	0.947358i	−0.627379	+	0.0818393i
$135$	−2.59602	+	1.66836i	−0.223430	+	0.143590i
$136$	10.0288	−	10.6951i	0.859961	−	0.917100i
$137$	6.18493			0.528415			0.264207	−	0.964466i	$-0.414890\pi$
$137$	6.18493			0.528415			0.264207	+	0.964466i	$0.414890\pi$
$138$	0.792905	+	6.73582i	0.0674965	+	0.573391i
$139$		−	1.79176i		−	0.151975i	−0.997109	−	0.0759876i	$-0.975789\pi$
$139$		−	1.79176i		−	0.151975i	0.997109	−	0.0759876i	$-0.0242110\pi$
$140$	−1.96497	−	1.79480i	−0.166070	−	0.151689i
$141$	1.00915	+	1.57027i	0.0849861	+	0.132241i
$142$	1.77489	+	13.6063i	0.148945	+	1.14181i
$143$	0.473747	+	1.03736i	0.0396167	+	0.0867485i
$144$	0.775628	−	3.92408i	0.0646357	−	0.327007i
$145$	16.5073	−	4.84699i	1.37086	−	0.402520i
$146$	−15.4605	−	10.2242i	−1.27952	−	0.846158i
$147$	6.19829	+	2.83067i	0.511227	+	0.233469i
$148$	−6.02885	+	18.7068i	−0.495568	+	1.53769i
$149$	5.15559	−	4.46734i	0.422362	−	0.365979i	−0.417593	−	0.908634i	$-0.637126\pi$
$149$	5.15559	−	4.46734i	0.422362	−	0.365979i	0.839956	+	0.542655i	$0.182581\pi$
$150$	−4.88827	+	4.12496i	−0.399125	+	0.336802i
$151$	1.04245	+	0.306091i	0.0848334	+	0.0249093i	0.323874	−	0.946100i	$-0.395015\pi$
$151$	1.04245	+	0.306091i	0.0848334	+	0.0249093i	−0.239040	+	0.971010i	$0.576833\pi$
$152$	−7.33337	−	3.70351i	−0.594815	−	0.300394i
$153$	−4.36077	−	2.80250i	−0.352547	−	0.226568i
$154$	−0.647634	−	2.31740i	−0.0521878	−	0.186741i
$155$	11.4204	+	1.64201i	0.917309	+	0.131889i
$156$	0.226285	+	0.531908i	0.0181173	+	0.0425868i
$157$	1.49488	−	0.214931i	0.119304	−	0.0171533i	−0.0824041	−	0.996599i	$-0.526260\pi$
$157$	1.49488	−	0.214931i	0.119304	−	0.0171533i	0.201708	+	0.979446i	$0.435351\pi$
$158$	16.9375	−	10.5745i	1.34747	−	0.841258i
$159$	0.766599	−	0.884703i	0.0607953	−	0.0701615i
$160$	1.14135	−	17.4191i	0.0902316	−	1.37710i
$161$	1.09613	+	1.75357i	0.0863870	+	0.138200i
$162$	−1.41409	−	0.0185057i	−0.111102	−	0.00145394i
$163$	15.6477	+	13.5588i	1.22562	+	1.06201i	0.996057	+	0.0887126i	$0.0282753\pi$
$163$	15.6477	+	13.5588i	1.22562	+	1.06201i	0.229563	+	0.973294i	$0.426270\pi$
$164$	3.54833	−	2.15129i	0.277078	−	0.167988i
$165$	−12.0524	+	1.73287i	−0.938278	+	0.134904i
$166$	14.1605	−	6.24425i	1.09907	−	0.484648i
$167$	3.07724	−	21.4027i	0.238124	−	1.65619i	−0.423161	−	0.906055i	$-0.639079\pi$
$167$	3.07724	−	21.4027i	0.238124	−	1.65619i	0.661285	−	0.750135i	$-0.270012\pi$
$168$	−0.297414	−	1.18280i	−0.0229460	−	0.0912551i
$169$	10.8660	+	6.98317i	0.835848	+	0.537167i
$170$	−20.4530	−	9.66601i	−1.56867	−	0.741349i
$171$	−0.818324	+	2.78696i	−0.0625788	+	0.213124i
$172$	6.32368	−	5.19610i	0.482176	−	0.396199i
$173$	−12.3705	+	10.7191i	−0.940512	+	0.814958i	−0.982899	−	0.184143i	$-0.941049\pi$
$173$	−12.3705	+	10.7191i	−0.940512	+	0.814958i	0.0423875	+	0.999101i	$0.486504\pi$
$174$	7.53531	+	2.32009i	0.571250	+	0.175886i
$175$	−0.810148	+	1.77398i	−0.0612414	+	0.134100i
$176$	9.21604	−	12.8131i	0.694686	−	0.965820i
$177$	−9.80125	+	2.87791i	−0.736707	+	0.216317i
$178$	−1.97541	+	12.5694i	−0.148063	+	0.942115i
$179$	−15.6684	+	7.15552i	−1.17111	+	0.534829i	−0.903454	−	0.428685i	$-0.858977\pi$
$179$	−15.6684	+	7.15552i	−1.17111	+	0.534829i	−0.267658	+	0.963514i	$0.586250\pi$
$180$	−6.12986	+	0.718172i	−0.456893	+	0.0535294i
$181$	12.0778	+	18.7934i	0.897736	+	1.39690i	0.917773	+	0.397105i	$0.129985\pi$
$181$	12.0778	+	18.7934i	0.897736	+	1.39690i	−0.0200379	+	0.999799i	$0.506379\pi$
$182$	0.131677	+	0.117151i	0.00976058	+	0.00868380i
$183$	−2.60835			−0.192815
$184$	−4.49031	+	12.7999i	−0.331030	+	0.943620i
$185$	30.3255			2.22958
$186$	3.95045	+	3.51464i	0.289661	+	0.257706i
$187$	−11.0581	−	17.2067i	−0.808648	−	1.25828i
$188$	0.434407	+	3.70782i	0.0316824	+	0.270420i
$189$	−0.392234	+	0.179127i	−0.0285308	+	0.0130296i
$190$	−1.96802	+	12.5224i	−0.142775	+	0.908468i
$191$	−14.5873	+	4.28323i	−1.05550	+	0.309924i	−0.763039	−	0.646353i	$-0.776293\pi$
$191$	−14.5873	+	4.28323i	−1.05550	+	0.309924i	−0.292464	+	0.956276i	$0.594475\pi$
$192$	4.83967	−	6.37006i	0.349273	−	0.459719i
$193$	6.44000	−	14.1016i	0.463562	−	1.01506i	−0.523100	−	0.852271i	$-0.675224\pi$
$193$	6.44000	−	14.1016i	0.463562	−	1.01506i	0.986661	−	0.162787i	$-0.0520482\pi$
$194$	−12.6548	−	3.89638i	−0.908564	−	0.279744i
$195$	0.674043	−	0.584062i	0.0482692	−	0.0418255i
$196$	8.65195	+	10.5295i	0.617996	+	0.752105i
$197$	0.647479	−	2.20511i	0.0461310	−	0.157108i	−0.933206	−	0.359341i	$-0.883002\pi$
$197$	0.647479	−	2.20511i	0.0461310	−	0.157108i	0.979337	+	0.202233i	$0.0648198\pi$
$198$	−5.04517	−	2.38433i	−0.358544	−	0.169447i
$199$	−15.8993	−	10.2179i	−1.12707	−	0.724324i	−0.162124	−	0.986770i	$-0.551834\pi$
$199$	−15.8993	−	10.2179i	−1.12707	−	0.724324i	−0.964947	+	0.262446i	$0.915471\pi$
$200$	−12.4061	+	3.11949i	−0.877242	+	0.220581i
$201$	−0.737024	+	5.12611i	−0.0519857	+	0.361568i
$202$	−9.93024	+	4.37887i	−0.698690	+	0.308096i
$203$	2.37953	−	0.342124i	0.167010	−	0.0240124i
$204$	−5.37484	−	8.86523i	−0.376314	−	0.620690i
$205$	−4.83871	−	4.19276i	−0.337950	−	0.292835i
$206$	−5.99859	−	0.0785012i	−0.417941	−	0.00546944i
$207$	4.73809	+	0.741983i	0.329320	+	0.0515714i
$208$	−0.0604857	+	1.15450i	−0.00419393	+	0.0800501i
$209$	−7.50538	+	8.66167i	−0.519158	+	0.599140i
$210$	−1.59626	+	0.996581i	−0.110152	+	0.0687706i
$211$	−0.721379	+	0.103719i	−0.0496618	+	0.00714028i	−0.167101	−	0.985940i	$-0.553441\pi$
$211$	−0.721379	+	0.103719i	−0.0496618	+	0.00714028i	0.117439	+	0.993080i	$0.462531\pi$
$212$	2.15441	−	0.916530i	0.147965	−	0.0629475i
$213$	9.60385	+	1.38082i	0.658045	+	0.0946125i
$214$	−3.65711	−	13.0861i	−0.249995	−	0.894545i
$215$	−10.6238	−	6.82747i	−0.724534	−	0.465630i
$216$	−2.52473	−	1.27504i	−0.171786	−	0.0867557i
$217$	1.54691	+	0.454214i	0.105011	+	0.0308341i
$218$	−11.0656	+	9.33774i	−0.749460	+	0.632432i
$219$	−9.90523	+	8.58293i	−0.669333	+	0.579981i
$220$	−23.1787	−	7.47005i	−1.56271	−	0.503631i
$221$	1.36279	+	0.622368i	0.0916715	+	0.0418650i
$222$	11.5921	+	7.66599i	0.778014	+	0.514508i
$223$	5.52041	−	1.62094i	0.369674	−	0.108546i	−0.0916186	−	0.995794i	$-0.529204\pi$
$223$	5.52041	−	1.62094i	0.369674	−	0.108546i	0.461292	+	0.887248i	$0.347386\pi$
$224$	0.504258	−	2.38655i	0.0336922	−	0.159458i
$225$	1.87882	+	4.11404i	0.125254	+	0.274269i
$226$	3.56420	+	27.3231i	0.237087	+	1.81751i
$227$	13.9213	+	21.6620i	0.923992	+	1.43776i	0.898939	+	0.438073i	$0.144339\pi$
$227$	13.9213	+	21.6620i	0.923992	+	1.43776i	0.0250521	+	0.999686i	$0.492025\pi$
$228$	−3.91782	+	4.28927i	−0.259464	+	0.284064i
$229$			14.7488i			0.974626i	0.873227	+	0.487313i	$0.162023\pi$
$229$			14.7488i			0.974626i	−0.873227	+	0.487313i	$0.837977\pi$
$230$	20.9227	+	0.536246i	1.37960	+	0.0353590i
$231$	−1.70143			−0.111946
$232$	11.5028	+	10.7861i	0.755195	+	0.708144i
$233$	1.15139	−	0.739951i	0.0754298	−	0.0484758i	−0.502382	−	0.864646i	$-0.667543\pi$
$233$	1.15139	−	0.739951i	0.0754298	−	0.0484758i	0.577812	+	0.816170i	$0.303907\pi$
$234$	0.405303	−	0.0528702i	0.0264955	−	0.00345624i
$235$	5.23957	−	2.39283i	0.341792	−	0.156091i
$236$	−20.1391	−	3.43569i	−1.31094	−	0.223645i
$237$	−3.97780	−	13.5471i	−0.258386	−	0.879982i
$238$	−2.63665	−	1.74364i	−0.170909	−	0.113024i
$239$	7.14375	−	15.6426i	0.462091	−	1.01184i	−0.524915	−	0.851154i	$-0.675903\pi$
$239$	7.14375	−	15.6426i	0.462091	−	1.01184i	0.987006	−	0.160683i	$-0.0513697\pi$
$240$	−11.6454	−	4.09248i	−0.751708	−	0.264168i
$241$	−0.732093	−	0.844880i	−0.0471582	−	0.0544235i	0.731680	−	0.681648i	$-0.238736\pi$
$241$	−0.732093	−	0.844880i	−0.0471582	−	0.0544235i	−0.778839	+	0.627224i	$0.784191\pi$
$242$	−4.16748	−	4.93865i	−0.267896	−	0.317469i
$243$	−0.281733	+	0.959493i	−0.0180732	+	0.0615515i
$244$	−4.68694	−	2.29053i	−0.300051	−	0.146636i
$245$	11.3683	−	17.6895i	0.726295	−	1.13014i
$246$	−0.789741	−	2.82589i	−0.0503520	−	0.180172i
$247$	0.119472	−	0.830948i	0.00760184	−	0.0528720i
$248$	4.01217	+	9.78455i	0.254773	+	0.621320i
$249$	−1.55739	−	10.8319i	−0.0986955	−	0.686442i
$250$	−1.10302	−	1.76674i	−0.0697608	−	0.111738i
$251$	6.76203	+	5.85933i	0.426815	+	0.369838i	0.841618	−	0.540074i	$-0.181604\pi$
$251$	6.76203	+	5.85933i	0.426815	+	0.369838i	−0.414802	+	0.909912i	$0.636149\pi$
$252$	−0.862107	−	0.0225680i	−0.0543076	−	0.00142165i
$253$	15.7899	+	10.4296i	0.992700	+	0.655701i
$254$	22.3017	+	0.291854i	1.39933	+	0.0183125i
$255$	−10.4753	+	12.0891i	−0.655988	+	0.757051i
$256$	14.2903	−	7.19638i	0.893143	−	0.449774i
$257$	−1.75150	−	12.1820i	−0.109256	−	0.759891i	−0.968623	−	0.248533i	$-0.920052\pi$
$257$	−1.75150	−	12.1820i	−0.109256	−	0.759891i	0.859368	−	0.511358i	$-0.170857\pi$
$258$	−2.33509	−	5.29543i	−0.145376	−	0.329679i
$259$	4.19434	+	0.603055i	0.260624	+	0.0374720i
$260$	1.72408	−	0.457587i	0.106923	−	0.0283783i
$261$	3.01413	−	4.69008i	0.186570	−	0.290309i
$262$	−9.87875	−	4.66865i	−0.610311	−	0.288430i
$263$	5.84297	+	1.71565i	0.360293	+	0.105792i	0.456869	−	0.889534i	$-0.348971\pi$
$263$	5.84297	+	1.71565i	0.360293	+	0.105792i	−0.0965758	+	0.995326i	$0.530789\pi$
$264$	−6.97186	−	8.71482i	−0.429088	−	0.536360i
$265$	−2.36564	−	2.73010i	−0.145320	−	0.167709i
$266$	−0.521219	+	1.69284i	−0.0319580	+	0.103795i
$267$	8.18395	+	3.73749i	0.500850	+	0.228730i
$268$	−5.82587	+	8.56389i	−0.355872	+	0.523123i
$269$	4.24520	+	14.4578i	0.258834	+	0.881508i	0.981686	+	0.190505i	$0.0610126\pi$
$269$	4.24520	+	14.4578i	0.258834	+	0.881508i	−0.722852	+	0.691003i	$0.757169\pi$
$270$	−0.677550	+	4.31120i	−0.0412344	+	0.262371i
$271$	−0.850180	−	1.86163i	−0.0516447	−	0.113086i	0.882051	−	0.471155i	$-0.156163\pi$
$271$	−0.850180	−	1.86163i	−0.0516447	−	0.113086i	−0.933695	+	0.358069i	$0.883435\pi$
$272$	−1.87302	−	20.6498i	−0.113568	−	1.25208i
$273$	0.104842	−	0.0673779i	0.00634533	−	0.00407790i
$274$	5.81396	−	6.53488i	0.351234	−	0.394787i
$275$			17.8459i			1.07615i
$276$	7.86229	+	5.49403i	0.473254	+	0.330702i
$277$			23.7790i			1.42874i	0.699767	+	0.714371i	$0.253287\pi$
$277$			23.7790i			1.42874i	−0.699767	+	0.714371i	$0.746713\pi$
$278$	−1.89314	−	1.68429i	−0.113543	−	0.101017i
$279$	3.14536	−	2.02140i	0.188308	−	0.121018i
$280$	−3.74347	+	0.388997i	−0.223715	+	0.0232470i
$281$	9.10992	+	19.9479i	0.543452	+	1.18999i	0.959773	+	0.280777i	$0.0905921\pi$
$281$	9.10992	+	19.9479i	0.543452	+	1.18999i	−0.416321	+	0.909218i	$0.636681\pi$
$282$	2.60775	+	0.409835i	0.155289	+	0.0244053i
$283$	−1.03043	−	3.50934i	−0.0612530	−	0.208609i	0.923180	−	0.384367i	$-0.125580\pi$
$283$	−1.03043	−	3.50934i	−0.0612530	−	0.208609i	−0.984433	+	0.175759i	$0.943762\pi$
$284$	16.0446	+	10.9149i	0.952070	+	0.647677i
$285$	8.15333	+	3.72350i	0.482962	+	0.220561i
$286$	1.54139	+	0.474587i	0.0911441	+	0.0280629i
$287$	−0.585867	−	0.676127i	−0.0345826	−	0.0399105i
$288$	−3.41700	−	4.50822i	−0.201349	−	0.265650i
$289$	−9.47046	−	2.78078i	−0.557086	−	0.163575i
$290$	10.3960	−	21.9976i	0.610472	−	1.29174i
$291$	−5.06195	+	7.87655i	−0.296737	+	0.461731i
$292$	−25.3358	+	6.72435i	−1.48267	+	0.393513i
$293$	21.0214	+	3.02243i	1.22809	+	0.176572i	0.725663	−	0.688050i	$-0.241533\pi$
$293$	21.0214	+	3.02243i	1.22809	+	0.176572i	0.502423	+	0.864622i	$0.332442\pi$
$294$	8.81734	−	3.88812i	0.514238	−	0.226760i
$295$	4.48612	+	31.2017i	0.261192	+	1.81663i
$296$	14.0980	+	23.9547i	0.819429	+	1.39234i
$297$	−2.58395	+	2.98204i	−0.149936	+	0.173035i
$298$	0.126242	−	9.64669i	0.00731303	−	0.558818i
$299$	−1.38598	−	0.0173789i	−0.0801536	−	0.00100505i
$300$	−0.236709	+	9.04240i	−0.0136664	+	0.522063i
$301$	−1.33361	−	1.15558i	−0.0768678	−	0.0666063i
$302$	1.30333	−	0.813702i	0.0749984	−	0.0468233i
$303$	1.09214	+	7.59601i	0.0627419	+	0.436379i
$304$	−10.8066	+	4.26693i	−0.619799	+	0.244725i
$305$	−1.14550	+	7.96716i	−0.0655914	+	0.456198i
$306$	−7.06027	+	1.97311i	−0.403609	+	0.112795i
$307$	−2.04582	+	3.18335i	−0.116761	+	0.181683i	−0.894715	−	0.446638i	$-0.852621\pi$
$307$	−2.04582	+	3.18335i	−0.116761	+	0.181683i	0.777954	+	0.628321i	$0.216258\pi$
$308$	−3.05731	−	1.49412i	−0.174206	−	0.0851354i
$309$	−1.19511	+	4.07017i	−0.0679875	+	0.231544i
$310$	12.4703	−	10.5231i	0.708267	−	0.597670i
$311$	−19.1655	−	22.1182i	−1.08678	−	1.25421i	−0.965169	−	0.261628i	$-0.915741\pi$
$311$	−19.1655	−	22.1182i	−1.08678	−	1.25421i	−0.121607	−	0.992578i	$-0.538805\pi$
$312$	0.774717	+	0.260916i	0.0438597	+	0.0147714i
$313$	−6.62409	+	14.5047i	−0.374416	+	0.819856i	0.624820	+	0.780769i	$0.285172\pi$
$313$	−6.62409	+	14.5047i	−0.374416	+	0.819856i	−0.999236	+	0.0390871i	$0.987555\pi$
$314$	1.17812	−	1.78150i	0.0664852	−	0.100536i
$315$	0.374885	+	1.27674i	0.0211224	+	0.0719362i
$316$	4.74877	−	27.8360i	0.267139	−	1.56590i
$317$	−22.5086	+	10.2794i	−1.26421	+	0.577346i	−0.930832	−	0.365447i	$-0.880916\pi$
$317$	−22.5086	+	10.2794i	−1.26421	+	0.577346i	−0.333379	+	0.942793i	$0.608189\pi$
$318$	−0.214142	−	1.64161i	−0.0120085	−	0.0920570i
$319$	18.5061	−	11.8932i	1.03614	−	0.665890i
$320$	−17.3318	−	17.5802i	−0.968877	−	0.982764i
$321$	−9.60780			−0.536255
$322$	2.88317	+	0.490238i	0.160673	+	0.0273199i
$323$			15.0565i			0.837767i
$324$	−1.34883	+	1.47671i	−0.0749348	+	0.0820393i
$325$	−0.706708	−	1.09966i	−0.0392011	−	0.0609981i
$326$	29.0351	−	3.78752i	1.60810	−	0.209771i
$327$	4.25311	+	9.31300i	0.235197	+	0.515010i
$328$	1.06248	−	5.77135i	0.0586657	−	0.318670i
$329$	0.772272	−	0.226760i	0.0425767	−	0.0125017i
$330$	−9.49856	+	14.3633i	−0.522879	+	0.790672i
$331$	−18.2472	−	8.33322i	−1.00296	−	0.458035i	−0.154894	−	0.987931i	$-0.549504\pi$
$331$	−18.2472	−	8.33322i	−1.00296	−	0.458035i	−0.848063	+	0.529896i	$0.822231\pi$
$332$	6.71358	−	20.8314i	0.368456	−	1.14327i
$333$	7.42686	−	6.43541i	0.406989	−	0.352658i
$334$	−19.7210	−	23.3703i	−1.07909	−	1.27877i
$335$	15.3340	+	4.50246i	0.837784	+	0.245996i
$336$	−1.52930	−	0.797614i	−0.0834302	−	0.0435134i
$337$	−27.9645	−	17.9717i	−1.52332	−	0.978981i	−0.991208	−	0.132310i	$-0.957761\pi$
$337$	−27.9645	−	17.9717i	−1.52332	−	0.978981i	−0.532116	−	0.846671i	$-0.678603\pi$
$338$	17.5926	−	4.91652i	0.956909	−	0.267424i
$339$	19.2857	+	2.77287i	1.04746	+	0.150602i
$340$	−29.4392	+	12.5240i	−1.59656	+	0.679211i
$341$	14.6028	−	2.09957i	0.790786	−	0.113698i
$342$	2.17540	+	3.48442i	0.117632	+	0.188416i
$343$	3.90077	−	4.50173i	0.210622	−	0.243070i
$344$	0.454284	−	11.5659i	0.0244933	−	0.623592i
$345$	4.34719	−	14.1466i	0.234045	−	0.761625i
$346$	−0.302911	+	23.1466i	−0.0162846	+	1.24437i
$347$	−26.3813	−	22.8595i	−1.41622	−	1.22716i	−0.936935	−	0.349504i	$-0.886350\pi$
$347$	−26.3813	−	22.8595i	−1.41622	−	1.22716i	−0.479286	−	0.877659i	$-0.659104\pi$
$348$	9.53470	−	5.78073i	0.511114	−	0.309880i
$349$	−10.9584	+	1.57558i	−0.586589	+	0.0843388i	−0.429218	−	0.903201i	$-0.641211\pi$
$349$	−10.9584	+	1.57558i	−0.586589	+	0.0843388i	−0.157371	+	0.987540i	$0.550302\pi$
$350$	1.11280	+	2.52356i	0.0594814	+	0.134890i
$351$	0.0411319	−	0.286079i	0.00219546	−	0.0152698i
$352$	−4.87477	−	21.7820i	−0.259826	−	1.16099i
$353$	30.0302	+	19.2992i	1.59835	+	1.02719i	0.968023	+	0.250860i	$0.0807133\pi$
$353$	30.0302	+	19.2992i	1.59835	+	1.02719i	0.630322	+	0.776334i	$0.282923\pi$
$354$	−6.17262	+	13.0611i	−0.328071	+	0.694190i
$355$	8.43542	−	28.7284i	0.447705	−	1.52474i
$356$	11.4236	+	13.9026i	0.605452	+	0.736839i
$357$	−1.68925	+	1.46374i	−0.0894046	+	0.0774695i
$358$	−7.16822	+	23.2813i	−0.378852	+	1.23045i
$359$	−7.45138	+	16.3162i	−0.393269	+	0.861138i	0.604640	+	0.796499i	$0.293317\pi$
$359$	−7.45138	+	16.3162i	−0.393269	+	0.861138i	−0.997909	+	0.0646394i	$0.979410\pi$
$360$	−5.00338	+	7.15179i	−0.263701	+	0.376933i
$361$	−10.1353	+	2.97600i	−0.533439	+	0.156632i
$362$	31.2101	+	4.90500i	1.64037	+	0.257801i
$363$	−4.15644	+	1.89818i	−0.218156	+	0.0996287i
$364$	0.247559	−	0.0290039i	0.0129756	−	0.00152022i
$365$	21.8664	+	34.0247i	1.14454	+	1.78094i
$366$	−2.45190	+	2.75593i	−0.128163	+	0.144055i
$367$	−19.4380			−1.01466			−0.507328	−	0.861753i	$-0.669367\pi$
$367$	−19.4380			−1.01466			−0.507328	+	0.861753i	$0.669367\pi$
$368$	9.30314	+	16.7765i	0.484959	+	0.874537i
$369$	−2.07477			−0.108008
$370$	28.5066	−	32.0414i	1.48199	−	1.66575i
$371$	−0.272903	−	0.424645i	−0.0141684	−	0.0220465i
$372$	7.42700	−	0.870144i	0.385072	−	0.0451149i
$373$	−4.46810	+	2.04051i	−0.231350	+	0.105654i	−0.527717	−	0.849420i	$-0.676952\pi$
$373$	−4.46810	+	2.04051i	−0.231350	+	0.105654i	0.296368	+	0.955074i	$0.404225\pi$
$374$	−28.5751	−	4.49089i	−1.47758	−	0.232218i
$375$	−1.41310	+	0.414922i	−0.0729719	+	0.0214265i
$376$	4.32596	+	3.02643i	0.223094	+	0.156076i
$377$	−0.669367	+	1.46571i	−0.0344742	+	0.0754879i
$378$	−0.179445	+	0.582811i	−0.00922966	+	0.0299765i
$379$	−18.2231	+	15.7904i	−0.936060	+	0.811101i	−0.982201	−	0.187834i	$-0.939853\pi$
$379$	−18.2231	+	15.7904i	−0.936060	+	0.811101i	0.0461407	+	0.998935i	$0.485308\pi$
$380$	11.3809	+	13.8506i	0.583828	+	0.710523i
$381$	4.44321	−	15.1322i	0.227633	−	0.775246i
$382$	−9.18680	+	19.4390i	−0.470038	+	0.994587i
$383$	11.0615	+	7.10881i	0.565218	+	0.363243i	0.791830	−	0.610742i	$-0.209129\pi$
$383$	11.0615	+	7.10881i	0.565218	+	0.363243i	−0.226612	+	0.973985i	$0.572765\pi$
$384$	−2.18110	−	11.1015i	−0.111304	−	0.566520i
$385$	−0.747217	+	5.19701i	−0.0380817	+	0.264864i
$386$	−8.84580	−	20.0602i	−0.450239	−	1.02104i
$387$	−4.05067	+	0.582398i	−0.205907	+	0.0296050i
$388$	−16.0126	+	9.70819i	−0.812918	+	0.492859i
$389$	−27.4192	−	23.7589i	−1.39021	−	1.20462i	−0.952132	−	0.305687i	$-0.901114\pi$
$389$	−27.4192	−	23.7589i	−1.39021	−	1.20462i	−0.438078	−	0.898937i	$-0.644341\pi$
$390$	0.0165050	−	1.26121i	0.000835762	−	0.0638639i
$391$	24.6493	−	3.22914i	1.24657	−	0.163304i
$392$	19.2582	+	0.756421i	0.972688	+	0.0382050i
$393$	−5.05954	+	5.83901i	−0.255220	+	0.294539i
$394$	−1.72124	−	2.75696i	−0.0867147	−	0.138894i
$395$	−43.1265	+	6.20065i	−2.16993	+	0.311989i
$396$	−7.26179	+	3.08932i	−0.364919	+	0.155244i
$397$	20.3018	+	2.91896i	1.01892	+	0.146498i	0.631476	−	0.775396i	$-0.282450\pi$
$397$	20.3018	+	2.91896i	1.01892	+	0.146498i	0.387442	+	0.921894i	$0.373359\pi$
$398$	−25.7416	+	7.19391i	−1.29031	+	0.360598i
$399$	1.05365	+	0.677138i	0.0527483	+	0.0338993i
$400$	−8.36595	+	16.0404i	−0.418298	+	0.802020i
$401$	−14.9289	−	4.38351i	−0.745512	−	0.218902i	−0.113153	−	0.993578i	$-0.536095\pi$
$401$	−14.9289	−	4.38351i	−0.745512	−	0.218902i	−0.632359	+	0.774675i	$0.717913\pi$
$402$	4.72334	+	5.59737i	0.235579	+	0.279172i
$403$	−0.816677	+	0.707655i	−0.0406816	+	0.0352508i
$404$	−4.70799	+	14.6083i	−0.234231	+	0.726792i
$405$	2.80703	+	1.28193i	0.139482	+	0.0636995i
$406$	1.87532	−	2.83576i	0.0930705	−	0.140737i
$407$	37.2053	−	10.9244i	1.84420	−	0.541505i
$408$	−14.4193	−	2.65453i	−0.713861	−	0.131419i
$409$	−0.208267	−	0.456042i	−0.0102982	−	0.0225498i	0.904413	−	0.426658i	$-0.140309\pi$
$409$	−0.208267	−	0.456042i	−0.0102982	−	0.0225498i	−0.914711	+	0.404108i	$0.867582\pi$
$410$	−8.97847	+	1.17121i	−0.443415	+	0.0578418i
$411$	−3.34383	−	5.20310i	−0.164939	−	0.256650i
$412$	−5.72173	+	6.26420i	−0.281889	+	0.308615i
$413$			4.40473i			0.216743i
$414$	5.23786	−	4.30869i	0.257427	−	0.211761i
$415$	−33.7698			−1.65769
$416$	1.16296	+	1.14916i	0.0570190	+	0.0563422i
$417$	−1.50733	+	0.968700i	−0.0738141	+	0.0474374i
$418$	2.09656	+	16.0722i	0.102546	+	0.786116i
$419$	−0.0614186	+	0.0280489i	−0.00300050	+	0.00137028i	−0.416915	−	0.908946i	$-0.636889\pi$
$419$	−0.0614186	+	0.0280489i	−0.00300050	+	0.00137028i	0.413914	+	0.910316i	$0.364161\pi$
$420$	−0.447544	+	2.62338i	−0.0218379	+	0.128008i
$421$	6.24432	+	21.2662i	0.304330	+	1.03645i	0.959673	+	0.281120i	$0.0907060\pi$
$421$	6.24432	+	21.2662i	0.304330	+	1.03645i	−0.655343	+	0.755332i	$0.727476\pi$
$422$	−0.568523	+	0.859692i	−0.0276753	+	0.0418492i
$423$	0.775409	−	1.69791i	0.0377017	−	0.0825552i
$424$	1.05680	−	3.13786i	0.0513225	−	0.152388i
$425$	15.3528	+	17.7181i	0.744720	+	0.859452i
$426$	10.4868	−	8.84924i	0.508085	−	0.428747i
$427$	−0.316871	+	1.07916i	−0.0153345	+	0.0522244i
$428$	−17.2643	−	8.43712i	−0.834499	−	0.407824i
$429$	0.616557	−	0.959381i	0.0297676	−	0.0463193i
$430$	−17.2003	+	4.80690i	−0.829472	+	0.231809i
$431$	2.42382	−	16.8580i	0.116751	−	0.812023i	−0.844343	−	0.535803i	$-0.820009\pi$
$431$	2.42382	−	16.8580i	0.116751	−	0.812023i	0.961094	−	0.276220i	$-0.0890818\pi$
$432$	−3.72048	+	1.46902i	−0.179002	+	0.0706782i
$433$	−4.00543	−	27.8584i	−0.192489	−	1.33879i	−0.825394	−	0.564558i	$-0.809047\pi$
$433$	−4.00543	−	27.8584i	−0.192489	−	1.33879i	0.632905	−	0.774229i	$-0.281862\pi$
$434$	1.93404	−	1.20747i	0.0928369	−	0.0579603i
$435$	−13.0021	−	11.2664i	−0.623402	−	0.540181i
$436$	−0.535842	+	20.4694i	−0.0256622	+	0.980307i
$437$	−5.62742	−	12.7428i	−0.269196	−	0.609569i
$438$	−0.242545	+	18.5338i	−0.0115892	+	0.885579i
$439$	−5.55064	+	6.40578i	−0.264918	+	0.305731i	−0.872587	−	0.488459i	$-0.837559\pi$
$439$	−5.55064	+	6.40578i	−0.264918	+	0.305731i	0.607669	+	0.794190i	$0.292105\pi$
$440$	−29.6811	+	17.4681i	−1.41499	+	0.832761i
$441$	−0.969743	−	6.74471i	−0.0461782	−	0.321177i
$442$	1.93864	−	0.854866i	0.0922115	−	0.0406618i
$443$	0.767245	+	0.110313i	0.0364529	+	0.00524114i	0.160517	−	0.987033i	$-0.448684\pi$
$443$	0.767245	+	0.110313i	0.0364529	+	0.00524114i	−0.124064	+	0.992274i	$0.539593\pi$
$444$	18.9966	−	5.04186i	0.901538	−	0.239276i
$445$	15.0102	−	23.3564i	0.711553	−	1.10720i
$446$	3.47664	−	7.35647i	0.164624	−	0.348339i
$447$	−6.54549	−	1.92193i	−0.309591	−	0.0909041i
$448$	−2.04757	−	2.77619i	−0.0967387	−	0.131163i
$449$	3.32305	+	3.83500i	0.156824	+	0.180985i	0.828724	−	0.559657i	$-0.189067\pi$
$449$	3.32305	+	3.83500i	0.156824	+	0.180985i	−0.671900	+	0.740642i	$0.734522\pi$
$450$	6.11294	+	1.88215i	0.288167	+	0.0887254i
$451$	−7.44683	−	3.40085i	−0.350657	−	0.160140i
$452$	32.2195	+	21.9184i	1.51548	+	1.03095i
$453$	−0.306091	−	1.04245i	−0.0143814	−	0.0489786i
$454$	35.9740	+	5.65370i	1.68834	+	0.265341i
$455$	−0.159761	−	0.349829i	−0.00748973	−	0.0164002i
$456$	0.849129	+	8.17149i	0.0397641	+	0.382665i
$457$	−28.7814	+	18.4967i	−1.34634	+	0.865240i	−0.997411	−	0.0719097i	$-0.977091\pi$
$457$	−28.7814	+	18.4967i	−1.34634	+	0.865240i	−0.348928	+	0.937149i	$0.613454\pi$
$458$	15.5833	+	13.8641i	0.728159	+	0.647828i
$459$			5.18366i			0.241952i
$460$	20.2343	−	21.6024i	0.943430	−	1.00722i
$461$		−	28.6367i		−	1.33374i	−0.745172	−	0.666872i	$-0.767633\pi$
$461$		−	28.6367i		−	1.33374i	0.745172	−	0.666872i	$-0.232367\pi$
$462$	−1.59938	+	1.79770i	−0.0744100	+	0.0836368i
$463$	−5.41653	+	3.48099i	−0.251727	+	0.161775i	−0.660419	−	0.750897i	$-0.729621\pi$
$463$	−5.41653	+	3.48099i	−0.251727	+	0.161775i	0.408692	+	0.912672i	$0.365985\pi$
$464$	22.2093	−	2.01446i	1.03104	−	0.0935191i
$465$	−4.79300	−	10.4952i	−0.222270	−	0.486703i
$466$	0.300507	−	1.91210i	0.0139207	−	0.0885763i
$467$	−10.2054	−	34.7564i	−0.472249	−	1.60833i	−0.759520	−	0.650484i	$-0.774566\pi$
$467$	−10.2054	−	34.7564i	−0.472249	−	1.60833i	0.287271	−	0.957849i	$-0.407252\pi$
$468$	0.325131	−	0.477934i	0.0150292	−	0.0220925i
$469$	2.03131	+	0.927670i	0.0937974	+	0.0428358i
$470$	2.39708	−	7.78534i	0.110569	−	0.359111i
$471$	−0.989002	−	1.14137i	−0.0455708	−	0.0525915i
$472$	−22.5612	+	18.0490i	−1.03847	+	0.830772i
$473$	−15.4934	−	4.54928i	−0.712388	−	0.209176i
$474$	−18.0529	−	8.53171i	−0.829196	−	0.391874i
$475$	7.10231	−	11.0514i	0.325876	−	0.507073i
$476$	−4.32080	+	1.14678i	−0.198044	+	0.0525625i
$477$	−1.15871	−	0.166598i	−0.0530539	−	0.00762800i
$478$	−9.81245	−	22.2523i	−0.448811	−	1.01780i
$479$	−1.71989	−	11.9621i	−0.0785838	−	0.546562i	−0.990640	−	0.136498i	$-0.956415\pi$
$479$	−1.71989	−	11.9621i	−0.0785838	−	0.546562i	0.912057	−	0.410064i	$-0.134494\pi$
$480$	−15.2709	+	8.45731i	−0.697020	+	0.386022i
$481$	−1.85996	+	2.14651i	−0.0848071	+	0.0978726i
$482$	−1.58087	−	0.0206882i	−0.0720065	−	0.000942321i
$483$	0.882583	−	1.87017i	0.0401589	−	0.0850957i
$484$	−9.13560	−	0.239149i	−0.415254	−	0.0108704i
$485$	21.8357	+	18.9208i	0.991510	+	0.859148i
$486$	0.748948	+	1.19962i	0.0339730	+	0.0544157i
$487$	−0.240826	−	1.67498i	−0.0109129	−	0.0759007i	0.983637	−	0.180161i	$-0.0576617\pi$
$487$	−0.240826	−	1.67498i	−0.0109129	−	0.0759007i	−0.994550	+	0.104260i	$0.966753\pi$
$488$	−6.82594	+	2.79899i	−0.308996	+	0.126704i
$489$	2.94661	−	20.4941i	0.133250	−	0.926775i
$490$	−8.00390	−	28.6400i	−0.361579	−	1.29382i
$491$	−16.0442	+	24.9653i	−0.724067	+	1.12667i	0.262756	+	0.964862i	$0.415369\pi$
$491$	−16.0442	+	24.9653i	−0.724067	+	1.12667i	−0.986822	+	0.161807i	$0.948268\pi$
$492$	−3.72815	−	1.82197i	−0.168078	−	0.0821406i
$493$	8.14192	−	27.7288i	0.366694	−	1.24884i
$494$	−0.765658	−	0.907339i	−0.0344486	−	0.0408231i
$495$	7.97380	+	9.20226i	0.358396	+	0.413611i
$496$	14.1097	+	4.95848i	0.633544	+	0.222642i
$497$	1.73800	−	3.80569i	0.0779601	−	0.170709i
$498$	−12.9087	−	8.53667i	−0.578454	−	0.382537i
$499$	−1.12587	−	3.83436i	−0.0504008	−	0.171649i	0.930446	−	0.366428i	$-0.119419\pi$
$499$	−1.12587	−	3.83436i	−0.0504008	−	0.171649i	−0.980847	+	0.194779i	$0.937601\pi$
$500$	−2.90356	−	0.495341i	−0.129851	−	0.0221523i
$501$	−19.6688	+	8.98243i	−0.878736	+	0.401305i
$502$	12.5473	−	1.63675i	0.560013	−	0.0730516i
$503$	15.1481	−	9.73510i	0.675421	−	0.434067i	−0.157455	−	0.987526i	$-0.550329\pi$
$503$	15.1481	−	9.73510i	0.675421	−	0.434067i	0.832876	+	0.553460i	$0.186693\pi$
$504$	−0.834242	+	0.889672i	−0.0371601	+	0.0396291i
$505$	23.6815			1.05381
$506$	25.8624	−	6.87928i	1.14973	−	0.305821i
$507$		−	12.9165i		−	0.573640i
$508$	21.2724	−	23.2892i	0.943810	−	1.03329i
$509$	−12.0776	−	18.7931i	−0.535330	−	0.832989i	0.463252	−	0.886227i	$-0.346682\pi$
$509$	−12.0776	−	18.7931i	−0.535330	−	0.832989i	−0.998582	+	0.0532372i	$0.983046\pi$
$510$	2.92617	+	22.4320i	0.129573	+	0.993306i
$511$	2.34773	+	5.14082i	0.103858	+	0.227416i
$512$	5.82959	−	21.8636i	0.257634	−	0.966243i
$513$	2.78696	−	0.818324i	0.123047	−	0.0361299i
$514$	−14.5177	−	9.60069i	−0.640348	−	0.423468i
$515$	11.9074	+	5.43794i	0.524704	+	0.239624i
$516$	−7.79008	−	2.51060i	−0.342939	−	0.110523i
$517$	5.56624	−	4.82318i	0.244803	−	0.212123i
$518$	4.57994	−	3.86478i	0.201231	−	0.169809i
$519$	15.7055	+	4.61155i	0.689394	+	0.202424i
$520$	1.13719	−	2.25177i	0.0498693	−	0.0987468i
$521$	−7.24179	−	4.65402i	−0.317269	−	0.203896i	0.372307	−	0.928110i	$-0.378567\pi$
$521$	−7.24179	−	4.65402i	−0.317269	−	0.203896i	−0.689576	+	0.724213i	$0.742203\pi$
$522$	−2.12211	−	7.59344i	−0.0928822	−	0.332356i
$523$	−13.6995	−	1.96969i	−0.599037	−	0.0861286i	−0.163876	−	0.986481i	$-0.552400\pi$
$523$	−13.6995	−	1.96969i	−0.599037	−	0.0861286i	−0.435162	+	0.900352i	$0.643309\pi$
$524$	−14.2190	+	6.04907i	−0.621161	+	0.264255i
$525$	1.93036	−	0.277544i	0.0842480	−	0.0121130i
$526$	7.30523	−	4.56083i	0.318523	−	0.198862i
$527$	12.6920	−	14.6473i	0.552871	−	0.638047i
$528$	−15.7616	−	0.825771i	−0.685935	−	0.0359371i
$529$	−19.6545	+	11.9457i	−0.854545	+	0.519377i
$530$	−5.10832	−	0.0668506i	−0.221891	−	0.00290381i
$531$	7.72001	+	6.68943i	0.335020	+	0.290296i
$532$	1.29867	+	2.14201i	0.0563043	+	0.0928680i
$533$	0.593548	−	0.0853393i	0.0257094	−	0.00369646i
$534$	11.6420	−	5.13370i	0.503800	−	0.222157i
$535$	−4.21945	+	29.3469i	−0.182423	+	1.26878i
$536$	3.57201	+	14.2057i	0.154287	+	0.613594i
$537$	14.4906	+	9.31254i	0.625315	+	0.401866i
$538$	19.2664	+	9.10523i	0.830634	+	0.392554i
$539$	7.57493	−	25.7979i	0.326275	−	1.11119i
$540$	3.91822	+	4.76850i	0.168613	+	0.205203i
$541$	9.30335	−	8.06140i	0.399982	−	0.346587i	−0.431524	−	0.902101i	$-0.642024\pi$
$541$	9.30335	−	8.06140i	0.399982	−	0.346587i	0.831507	+	0.555515i	$0.187479\pi$
$542$	−2.76615	−	0.851688i	−0.118816	−	0.0365831i
$543$	9.28028	−	20.3210i	0.398255	−	0.872057i
$544$	−23.5789	−	17.4323i	−1.01094	−	0.747402i
$545$	30.3143	−	8.90107i	1.29852	−	0.381280i
$546$	0.0273633	−	0.174111i	0.00117104	−	0.00745125i
$547$	2.58245	−	1.17936i	0.110417	−	0.0504260i	−0.359440	−	0.933168i	$-0.617032\pi$
$547$	2.58245	−	1.17936i	0.110417	−	0.0504260i	0.469858	+	0.882742i	$0.344305\pi$
$548$	−1.43940	−	12.2858i	−0.0614883	−	0.524825i
$549$	1.41018	+	2.19428i	0.0601850	+	0.0936497i
$550$	18.8556	+	16.7755i	0.804006	+	0.715308i
$551$	−16.1935			−0.689868
$552$	13.1956	−	3.14265i	0.561642	−	0.133760i
$553$	−6.08816			−0.258895
$554$	25.1245	+	22.3527i	1.06744	+	0.949677i
$555$	−16.3952	−	25.5114i	−0.695938	−	1.08290i
$556$	−3.55918	+	0.416992i	−0.150943	+	0.0176844i
$557$	8.69208	−	3.96954i	0.368295	−	0.168195i	−0.222666	−	0.974895i	$-0.571476\pi$
$557$	8.69208	−	3.96954i	0.368295	−	0.168195i	0.590961	+	0.806700i	$0.298749\pi$
$558$	0.820926	−	5.22349i	0.0347526	−	0.221128i
$559$	1.13485	−	0.333223i	0.0479992	−	0.0140938i
$560$	−3.10792	+	4.32094i	−0.131334	+	0.182593i
$561$	−8.49677	+	18.6053i	−0.358734	+	0.785517i
$562$	29.6401	+	9.12608i	1.25029	+	0.384961i
$563$	9.63622	−	8.34983i	0.406118	−	0.351904i	−0.427721	−	0.903911i	$-0.640683\pi$
$563$	9.63622	−	8.34983i	0.406118	−	0.351904i	0.833839	+	0.552007i	$0.186138\pi$
$564$	2.88436	−	2.37004i	0.121453	−	0.0997968i
$565$	16.9394	−	57.6902i	0.712645	−	2.42705i
$566$	−4.67653	−	2.21011i	−0.196569	−	0.0928978i
$567$	0.362749	+	0.233125i	0.0152340	+	0.00979033i
$568$	26.6146	−	6.69222i	1.11673	−	0.280799i
$569$	3.95397	−	27.5005i	0.165759	−	1.15288i	−0.721772	−	0.692131i	$-0.756672\pi$
$569$	3.95397	−	27.5005i	0.165759	−	1.15288i	0.887531	−	0.460748i	$-0.152419\pi$
$570$	11.5985	−	5.11449i	0.485807	−	0.214223i
$571$	−29.1959	+	4.19773i	−1.22181	+	0.175670i	−0.722880	−	0.690974i	$-0.757182\pi$
$571$	−29.1959	+	4.19773i	−1.22181	+	0.175670i	−0.498929	+	0.866643i	$0.666273\pi$
$572$	1.95037	−	1.18248i	0.0815492	−	0.0494419i
$573$	11.4898	+	9.95596i	0.479993	+	0.415916i
$574$	−1.26511	−	0.0165560i	−0.0528046	−	0.000691034i
$575$	−19.6157	−	9.25716i	−0.818031	−	0.386050i
$576$	−7.97535	−	0.627476i	−0.332306	−	0.0261449i
$577$	28.7125	−	33.1360i	1.19532	−	1.37947i	0.288749	−	0.957405i	$-0.406761\pi$
$577$	28.7125	−	33.1360i	1.19532	−	1.37947i	0.906567	−	0.422063i	$-0.138694\pi$
$578$	−11.8405	+	7.39233i	−0.492501	+	0.307480i
$579$	−15.3448	+	2.20625i	−0.637707	+	0.0916885i
$580$	−13.4698	−	31.6623i	−0.559304	−	1.31471i
$581$	−4.67072	−	0.671548i	−0.193774	−	0.0278605i
$582$	3.56388	+	12.7525i	0.147728	+	0.528607i
$583$	−3.88581	−	2.49726i	−0.160934	−	0.103426i
$584$	−16.7113	+	33.0904i	−0.691520	+	1.36929i
$585$	−0.855759	−	0.251274i	−0.0353813	−	0.0103889i
$586$	22.9540	−	19.3697i	0.948221	−	0.800156i
$587$	32.2662	−	27.9588i	1.33177	−	1.15398i	0.356168	−	0.934422i	$-0.384083\pi$
$587$	32.2662	−	27.9588i	1.33177	−	1.15398i	0.975599	−	0.219561i	$-0.0704624\pi$
$588$	4.18036	−	12.9711i	0.172395	−	0.534921i
$589$	−9.87866	−	4.51143i	−0.407043	−	0.185890i
$590$	37.1841	+	24.5902i	1.53085	+	1.01236i
$591$	−2.20511	+	0.647479i	−0.0907062	+	0.0266337i
$592$	38.5625	+	7.62220i	1.58491	+	0.313271i
$593$	12.2007	+	26.7157i	0.501021	+	1.09708i	0.976136	+	0.217159i	$0.0696792\pi$
$593$	12.2007	+	26.7157i	0.501021	+	1.09708i	−0.475115	+	0.879924i	$0.657594\pi$
$594$	0.721802	+	5.53333i	0.0296159	+	0.227035i
$595$	3.72912	+	5.80262i	0.152879	+	0.237884i
$596$	−10.0738	−	9.20146i	−0.412640	−	0.376906i
$597$			18.8995i			0.773506i
$598$	−1.32121	+	1.44807i	−0.0540285	+	0.0592159i
$599$	−33.8034			−1.38117			−0.690585	−	0.723251i	$-0.742647\pi$
$599$	−33.8034			−1.38117			−0.690585	+	0.723251i	$0.742647\pi$
$600$	9.33151	+	8.75013i	0.380957	+	0.357223i
$601$	13.0828	−	8.40779i	0.533657	−	0.342961i	−0.245896	−	0.969296i	$-0.579082\pi$
$601$	13.0828	−	8.40779i	0.533657	−	0.342961i	0.779554	+	0.626335i	$0.215446\pi$
$602$	−2.47458	+	0.322799i	−0.100856	+	0.0131563i
$603$	4.71083	−	2.15136i	0.191840	−	0.0876103i
$604$	0.365416	−	2.14197i	0.0148686	−	0.0871556i
$605$	3.97259	+	13.5294i	0.161509	+	0.550048i
$606$	9.05243	+	5.98646i	0.367730	+	0.243183i
$607$	−4.87871	+	10.6829i	−0.198021	+	0.433605i	−0.982428	−	0.186641i	$-0.940240\pi$
$607$	−4.87871	+	10.6829i	−0.198021	+	0.433605i	0.784407	+	0.620246i	$0.212967\pi$
$608$	−5.65002	+	15.4290i	−0.229139	+	0.625729i
$609$	−1.57428	−	1.81682i	−0.0637931	−	0.0736212i
$610$	7.34115	+	8.69960i	0.297235	+	0.352237i
$611$	−0.151990	+	0.517630i	−0.00614885	+	0.0209411i
$612$	−4.55204	+	9.31451i	−0.184005	+	0.376517i
$613$	−5.34873	+	8.32278i	−0.216033	+	0.336154i	−0.932309	−	0.361663i	$-0.882209\pi$
$613$	−5.34873	+	8.32278i	−0.216033	+	0.336154i	0.716276	+	0.697817i	$0.245845\pi$
$614$	1.44036	+	5.15398i	0.0581283	+	0.207998i
$615$	−0.911174	+	6.33736i	−0.0367421	+	0.255547i
$616$	−4.45259	+	1.82579i	−0.179400	+	0.0735632i
$617$	−5.01611	−	34.8878i	−0.201941	−	1.40453i	−0.798516	−	0.601973i	$-0.794381\pi$
$617$	−5.01611	−	34.8878i	−0.201941	−	1.40453i	0.596575	−	0.802557i	$-0.296528\pi$
$618$	3.17704	+	5.08877i	0.127799	+	0.204700i
$619$	−15.2726	−	13.2338i	−0.613859	−	0.531912i	0.291493	−	0.956573i	$-0.405848\pi$
$619$	−15.2726	−	13.2338i	−0.613859	−	0.531912i	−0.905353	+	0.424661i	$0.860393\pi$
$620$	0.603862	−	23.0678i	0.0242517	−	0.926425i
$621$	−1.93741	−	4.38708i	−0.0777455	−	0.176047i
$622$	−41.3856	−	0.541597i	−1.65941	−	0.0217161i
$623$	2.54054	−	2.93194i	0.101785	−	0.117466i
$624$	1.00393	−	0.573285i	0.0401892	−	0.0229498i
$625$	3.86506	+	26.8821i	0.154602	+	1.07528i
$626$	9.09865	+	20.6336i	0.363655	+	0.824685i
$627$	11.3444	+	1.63108i	0.453051	+	0.0651389i
$628$	−0.774840	−	2.91942i	−0.0309195	−	0.116498i
$629$	27.5405	−	42.8539i	1.09811	−	1.70870i
$630$	1.70138	+	0.804065i	0.0677846	+	0.0320347i
$631$	16.5514	+	4.85993i	0.658901	+	0.193471i	0.594055	−	0.804425i	$-0.297526\pi$
$631$	16.5514	+	4.85993i	0.658901	+	0.193471i	0.0648458	+	0.997895i	$0.479344\pi$
$632$	−24.9470	−	31.1838i	−0.992340	−	1.24043i
$633$	0.477260	+	0.550788i	0.0189694	+	0.0218918i
$634$	−10.2976	+	33.4450i	−0.408969	+	1.32827i
$635$	−44.2697	−	20.2173i	−1.75679	−	0.802300i
$636$	−1.93579	−	1.31689i	−0.0767592	−	0.0522180i
$637$	0.554845	+	1.88963i	0.0219838	+	0.0748699i
$638$	4.83003	−	30.7331i	0.191223	−	1.21673i
$639$	−4.03061	−	8.82580i	−0.159448	−	0.349143i
$640$	−34.8672	+	1.78671i	−1.37825	+	0.0706260i
$641$	−22.4721	+	14.4420i	−0.887596	+	0.570424i	−0.903088	−	0.429456i	$-0.858705\pi$
$641$	−22.4721	+	14.4420i	−0.887596	+	0.570424i	0.0154912	+	0.999880i	$0.495069\pi$
$642$	−9.03152	+	10.1514i	−0.356446	+	0.400645i
$643$			33.8914i			1.33655i	0.743916	+	0.668273i	$0.232966\pi$
$643$			33.8914i			1.33655i	−0.743916	+	0.668273i	$0.767034\pi$
$644$	3.22821	−	2.58547i	0.127209	−	0.101882i
$645$			12.6285i			0.497246i
$646$	15.9084	+	14.1534i	0.625909	+	0.556859i
$647$	−26.9127	+	17.2958i	−1.05805	+	0.679966i	−0.949386	−	0.314112i	$-0.898293\pi$
$647$	−26.9127	+	17.2958i	−1.05805	+	0.679966i	−0.108662	+	0.994079i	$0.534657\pi$
$648$	0.292338	+	2.81328i	0.0114841	+	0.110516i
$649$	16.7439	+	36.6641i	0.657257	+	1.43919i
$650$	−1.82620	−	0.287006i	−0.0716294	−	0.0112573i
$651$	−0.454214	−	1.54691i	−0.0178021	−	0.0606282i
$652$	23.2917	−	34.2383i	0.912174	−	1.34087i
$653$	38.4206	+	17.5461i	1.50351	+	0.686632i	0.985646	−	0.168828i	$-0.0539982\pi$
$653$	38.4206	+	17.5461i	1.50351	+	0.686632i	0.517869	+	0.855460i	$0.326726\pi$
$654$	13.8379	+	4.26065i	0.541107	+	0.166605i
$655$	15.6132	+	18.0186i	0.610058	+	0.704044i
$656$	−5.09915	−	6.54778i	−0.199088	−	0.255648i
$657$	12.5756	+	3.69253i	0.490620	+	0.144059i
$658$	0.486361	−	1.02913i	0.0189603	−	0.0401195i
$659$	15.2418	−	23.7166i	0.593735	−	0.923869i	−0.406214	−	0.913778i	$-0.633151\pi$
$659$	15.2418	−	23.7166i	0.593735	−	0.923869i	0.999949	−	0.0100914i	$-0.00321225\pi$
$660$	6.24713	+	23.5378i	0.243169	+	0.916206i
$661$	−32.4644	−	4.66768i	−1.26272	−	0.181552i	−0.521755	−	0.853095i	$-0.674723\pi$
$661$	−32.4644	−	4.66768i	−1.26272	−	0.181552i	−0.740965	+	0.671544i	$0.765632\pi$
$662$	−25.9574	+	11.4463i	−1.00886	+	0.444872i
$663$	−0.213214	−	1.48293i	−0.00828053	−	0.0575924i
$664$	−15.6992	−	26.6754i	−0.609247	−	1.03521i
$665$	2.53104	−	2.92097i	0.0981494	−	0.113270i
$666$	0.181858	−	13.8965i	0.00704685	−	0.538478i
$667$	3.47299	+	26.5108i	0.134475	+	1.02650i
$668$	−43.2307	−	1.13168i	−1.67265	−	0.0437861i
$669$	−4.34818	−	3.76772i	−0.168110	−	0.145668i
$670$	19.1714	−	11.9692i	0.740657	−	0.462410i
$671$	1.46471	+	10.1873i	0.0565444	+	0.393275i
$672$	−2.28032	+	0.866058i	−0.0879651	+	0.0334089i
$673$	−3.58761	+	24.9524i	−0.138292	+	0.961844i	0.795990	+	0.605310i	$0.206951\pi$
$673$	−3.58761	+	24.9524i	−0.138292	+	0.961844i	−0.934282	+	0.356534i	$0.883958\pi$
$674$	−45.2758	+	12.6530i	−1.74396	+	0.487377i
$675$	2.44518	−	3.80478i	0.0941151	−	0.146446i
$676$	11.3426	−	23.2096i	0.436255	−	0.892677i
$677$	6.48890	−	22.0992i	0.249389	−	0.849340i	−0.735702	−	0.677305i	$-0.763148\pi$
$677$	6.48890	−	22.0992i	0.249389	−	0.849340i	0.985091	−	0.172035i	$-0.0550342\pi$
$678$	21.0587	−	17.7704i	0.808755	−	0.682468i
$679$	2.64386	+	3.05117i	0.101462	+	0.117093i
$680$	−14.4407	+	42.8777i	−0.553776	+	1.64428i
$681$	10.6968	−	23.4227i	0.409903	−	0.897562i
$682$	11.5085	−	17.4027i	0.440685	−	0.666383i
$683$	−10.6256	−	36.1874i	−0.406577	−	1.38467i	−0.867590	−	0.497280i	$-0.834332\pi$
$683$	−10.6256	−	36.1874i	−0.406577	−	1.38467i	0.461014	−	0.887393i	$-0.347486\pi$
$684$	5.72649	+	0.976929i	0.218958	+	0.0373538i
$685$	−17.3613	+	7.92863i	−0.663341	+	0.302938i
$686$	−1.08964	−	8.35319i	−0.0416027	−	0.318926i
$687$	12.4075	−	7.97379i	0.473374	−	0.304219i
$688$	−11.7933	−	11.3522i	−0.449615	−	0.432798i
$689$	0.338336			0.0128896
$690$	−10.8605	−	17.8912i	−0.413454	−	0.681106i
$691$			31.3424i			1.19232i	0.802865	+	0.596161i	$0.203308\pi$
$691$			31.3424i			1.19232i	−0.802865	+	0.596161i	$0.796692\pi$
$692$	24.1715	+	22.0783i	0.918863	+	0.839291i
$693$	0.919865	+	1.43134i	0.0349428	+	0.0543720i
$694$	−48.9518	+	6.38558i	−1.85819	+	0.242393i
$695$	2.29691	+	5.02953i	0.0871267	+	0.190781i
$696$	2.85499	−	15.5082i	0.108218	−	0.587836i
$697$	−10.3192	+	3.03001i	−0.390869	+	0.114770i
$698$	−8.63637	+	13.0595i	−0.326891	+	0.494309i
$699$	−1.24497	−	0.568560i	−0.0470892	−	0.0215049i
$700$	3.71239	+	1.19644i	0.140315	+	0.0452210i
$701$	−27.6114	+	23.9254i	−1.04287	+	0.903651i	−0.995456	−	0.0952248i	$-0.969643\pi$
$701$	−27.6114	+	23.9254i	−1.04287	+	0.903651i	−0.0474126	+	0.998875i	$0.515098\pi$
$702$	−0.263601	−	0.312379i	−0.00994896	−	0.0117900i
$703$	−27.3878	−	8.04179i	−1.03295	−	0.303302i
$704$	−27.5968	−	15.3249i	−1.04010	−	0.577580i
$705$	−4.84570	−	3.11414i	−0.182500	−	0.117285i
$706$	48.6201	−	13.5877i	1.82984	−	0.511379i
$707$	3.27541	+	0.470932i	0.123184	+	0.0177112i
$708$	7.99774	+	18.7996i	0.300573	+	0.706531i
$709$	1.26819	−	0.182339i	0.0476280	−	0.00684787i	−0.118460	−	0.992959i	$-0.537796\pi$
$709$	1.26819	−	0.182339i	0.0476280	−	0.00684787i	0.166088	+	0.986111i	$0.446887\pi$
$710$	−22.4244	−	35.9179i	−0.841573	−	1.34798i
$711$	−9.24602	+	10.6705i	−0.346753	+	0.400174i
$712$	25.4277	+	0.998745i	0.952944	+	0.0374295i
$713$	−5.26710	+	17.1401i	−0.197254	+	0.641902i
$714$	−0.0413639	+	3.16078i	−0.00154800	+	0.118289i
$715$	−2.65964	−	2.30459i	−0.0994650	−	0.0861869i
$716$	17.8603	+	29.4587i	0.667471	+	1.10092i
$717$	−17.0216	+	2.44734i	−0.635684	+	0.0913976i
$718$	10.2350	+	23.2106i	0.381967	+	0.866211i
$719$	0.884886	−	6.15451i	0.0330007	−	0.229525i	−0.966646	−	0.256117i	$-0.917557\pi$
$719$	0.884886	−	6.15451i	0.0330007	−	0.229525i	0.999646	+	0.0265927i	$0.00846572\pi$
$720$	2.85317	+	12.0093i	0.106332	+	0.447560i
$721$	1.53878	+	0.988917i	0.0573073	+	0.0368292i
$722$	−6.38302	+	13.5063i	−0.237551	+	0.502653i
$723$	−0.314959	+	1.07265i	−0.0117135	+	0.0398924i
$724$	34.5207	−	28.3652i	1.28295	−	1.05419i
$725$	−19.0561	+	16.5122i	−0.707725	+	0.613248i
$726$	−1.90155	+	6.17594i	−0.0705731	+	0.229211i
$727$	−15.6711	+	34.3149i	−0.581209	+	1.27267i	0.359401	+	0.933183i	$0.382981\pi$
$727$	−15.6711	+	34.3149i	−0.581209	+	1.27267i	−0.940611	+	0.339488i	$0.889746\pi$
$728$	0.202065	−	0.288830i	0.00748903	−	0.0107048i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	56.5047	+	8.88031i	2.09133	+	0.328675i
$731$	−19.2962	+	8.81228i	−0.713695	+	0.325934i
$732$	0.607034	+	5.18126i	0.0224366	+	0.191505i
$733$	14.1527	+	22.0221i	0.522743	+	0.813403i	0.997782	−	0.0665610i	$-0.0212027\pi$
$733$	14.1527	+	22.0221i	0.522743	+	0.813403i	−0.475040	+	0.879964i	$0.657566\pi$
$734$	−18.2721	+	20.5378i	−0.674435	+	0.758065i
$735$	−21.0275			−0.775611
$736$	26.4709	+	5.94074i	0.975730	+	0.218978i
$737$	20.4346			0.752719
$738$	−1.95033	+	2.19216i	−0.0717925	+	0.0806947i
$739$	−19.7783	−	30.7757i	−0.727557	−	1.13210i	−0.986108	−	0.166103i	$-0.946881\pi$
$739$	−19.7783	−	30.7757i	−0.727557	−	1.13210i	0.258551	−	0.965998i	$-0.416755\pi$
$740$	−7.05758	−	60.2390i	−0.259442	−	2.21443i
$741$	−0.763630	+	0.348738i	−0.0280526	+	0.0128112i
$742$	−0.705206	−	0.110831i	−0.0258889	−	0.00406872i
$743$	30.3704	−	8.91756i	1.11418	−	0.327153i	0.327710	−	0.944778i	$-0.393723\pi$
$743$	30.3704	−	8.91756i	1.11418	−	0.327153i	0.786473	+	0.617625i	$0.211905\pi$
$744$	6.06214	−	8.66518i	0.222249	−	0.317681i
$745$	−8.74508	+	19.1490i	−0.320395	+	0.701567i
$746$	−2.04413	+	6.63904i	−0.0748411	+	0.243072i
$747$	−8.27037	+	7.16631i	−0.302597	+	0.262202i
$748$	−31.6062	+	25.9704i	−1.15564	+	0.949573i
$749$	−1.16719	+	3.97508i	−0.0426481	+	0.145246i
$750$	−0.889938	+	1.88308i	−0.0324959	+	0.0687605i
$751$	3.92397	+	2.52178i	0.143188	+	0.0920211i	0.610273	−	0.792191i	$-0.291060\pi$
$751$	3.92397	+	2.52178i	0.143188	+	0.0920211i	−0.467086	+	0.884212i	$0.654696\pi$
$752$	7.26416	−	1.72582i	0.264897	−	0.0629342i
$753$	1.27335	−	8.85637i	0.0464036	−	0.322744i
$754$	0.919423	+	2.08504i	0.0334834	+	0.0759325i
$755$	−3.31857	+	0.477139i	−0.120775	+	0.0173649i
$756$	0.447105	+	0.737452i	0.0162610	+	0.0268209i
$757$	−25.7588	−	22.3201i	−0.936220	−	0.811239i	0.0460062	−	0.998941i	$-0.485351\pi$
$757$	−25.7588	−	22.3201i	−0.936220	−	0.811239i	−0.982226	+	0.187702i	$0.939896\pi$
$758$	−0.446221	+	34.0976i	−0.0162075	+	1.23848i
$759$	0.237263	−	18.9219i	0.00861210	−	0.686822i
$760$	25.3326	+	0.995008i	0.918910	+	0.0360927i
$761$	−0.355064	+	0.409765i	−0.0128710	+	0.0148540i	−0.762149	−	0.647402i	$-0.775855\pi$
$761$	−0.355064	+	0.409765i	−0.0128710	+	0.0148540i	0.749278	+	0.662256i	$0.230401\pi$
$762$	−11.8117	−	18.9192i	−0.427892	−	0.685369i
$763$	4.36979	−	0.628281i	0.158197	−	0.0227453i
$764$	11.9031	+	27.9797i	0.430641	+	1.01227i
$765$	15.8334	+	2.27650i	0.572458	+	0.0823070i
$766$	17.9091	−	5.00498i	0.647082	−	0.180837i
$767$	−2.48368	−	1.59616i	−0.0896804	−	0.0576341i
$768$	−13.7799	−	8.13110i	−0.497239	−	0.293406i
$769$	20.1700	+	5.92244i	0.727349	+	0.213569i	0.624385	−	0.781116i	$-0.285349\pi$
$769$	20.1700	+	5.92244i	0.727349	+	0.213569i	0.102963	+	0.994685i	$0.467168\pi$
$770$	4.78866	+	5.67478i	0.172571	+	0.204505i
$771$	−9.30120	+	8.05953i	−0.334974	+	0.290257i
$772$	−29.5104	−	9.51067i	−1.06210	−	0.342296i
$773$	42.8743	+	19.5800i	1.54208	+	0.704245i	0.991448	−	0.130503i	$-0.0416592\pi$
$773$	42.8743	+	19.5800i	1.54208	+	0.704245i	0.550633	+	0.834748i	$0.314387\pi$
$774$	−3.19236	+	4.82733i	−0.114747	+	0.173515i
$775$	−16.2251	+	4.76412i	−0.582823	+	0.171132i
$776$	−4.79469	+	26.0445i	−0.172119	+	0.934944i
$777$	−1.76031	−	3.85454i	−0.0631508	−	0.138281i
$778$	−50.8778	+	6.63682i	−1.82406	+	0.237941i
$779$	3.25812	+	5.06974i	0.116734	+	0.181642i
$780$	−1.31706	−	1.20300i	−0.0471582	−	0.0430743i
$781$		−	38.2846i		−	1.36993i
$782$	19.7590	−	29.0795i	0.706580	−	1.03988i
$783$	−5.57511			−0.199238
$784$	18.9023	−	19.6368i	0.675083	−	0.701316i
$785$	−3.92063	+	2.51964i	−0.139933	+	0.0899297i
$786$	1.41333	+	10.8346i	0.0504119	+	0.386457i
$787$	18.8797	−	8.62206i	0.672988	−	0.307343i	−0.0494527	−	0.998776i	$-0.515748\pi$
$787$	18.8797	−	8.62206i	0.672988	−	0.307343i	0.722440	+	0.691433i	$0.243020\pi$
$788$	−4.53095	−	0.772972i	−0.161408	−	0.0275360i
$789$	−1.71565	−	5.84297i	−0.0610788	−	0.208015i
$790$	−33.9882	+	51.3954i	−1.20925	+	1.82857i
$791$	3.49013	−	7.64231i	0.124095	−	0.271729i
$792$	−3.56211	+	10.5767i	−0.126574	+	0.375826i
$793$	−0.493677	−	0.569734i	−0.0175310	−	0.0202318i
$794$	22.1682	−	18.7066i	0.786720	−	0.663873i
$795$	−1.01774	+	3.46611i	−0.0360956	+	0.122930i
$796$	−16.5967	+	33.9605i	−0.588254	+	1.20370i
$797$	−9.88792	+	15.3859i	−0.350248	+	0.544996i	−0.971021	−	0.238994i	$-0.923182\pi$
$797$	−9.88792	+	15.3859i	−0.350248	+	0.544996i	0.620773	+	0.783990i	$0.286819\pi$
$798$	1.70590	−	0.476741i	0.0603882	−	0.0168764i
$799$	1.37700	−	9.57727i	0.0487149	−	0.338819i
$800$	9.08383	+	23.9176i	0.321162	+	0.845615i
$801$	−1.28041	−	8.90541i	−0.0452409	−	0.314657i
$802$	−18.6650	+	11.6530i	−0.659083	+	0.411481i
$803$	39.0841	+	33.8665i	1.37925	+	1.19512i
$804$	10.3541	+	0.271047i	0.365161	+	0.00955908i
$805$	−5.32481	−	3.51716i	−0.187675	−	0.123963i
$806$	−0.0199976	+	1.52809i	−0.000704385	+	0.0538248i
$807$	9.86756	−	11.3878i	0.347354	−	0.400868i
$808$	11.0093	+	18.7065i	0.387305	+	0.658092i
$809$	1.22993	+	8.55437i	0.0432421	+	0.300755i	0.999953	+	0.00971486i	$0.00309239\pi$
$809$	1.22993	+	8.55437i	0.0432421	+	0.300755i	−0.956711	+	0.291041i	$0.905999\pi$
$810$	3.99312	−	1.76082i	0.140304	−	0.0618688i
$811$	−37.6801	−	5.41758i	−1.32313	−	0.190237i	−0.555706	−	0.831379i	$-0.687552\pi$
$811$	−37.6801	−	5.41758i	−1.32313	−	0.190237i	−0.767422	+	0.641142i	$0.778461\pi$
$812$	−1.23338	−	4.64710i	−0.0432832	−	0.163081i
$813$	−1.10646	+	1.72169i	−0.0388054	+	0.0603824i
$814$	23.4311	−	49.5796i	0.821259	−	1.73776i
$815$	−61.3049	−	18.0007i	−2.14742	−	0.630538i
$816$	−16.3591	+	12.7398i	−0.572684	+	0.445983i
$817$	7.78408	+	8.98330i	0.272330	+	0.314286i
$818$	−0.677621	−	0.208637i	−0.0236924	−	0.00729482i
$819$	−0.113364	−	0.0517715i	−0.00396125	−	0.00180904i
$820$	−7.20246	+	10.5874i	−0.251521	+	0.369729i
$821$	3.25846	+	11.0973i	0.113721	+	0.387298i	0.996609	−	0.0822858i	$-0.0262220\pi$
$821$	3.25846	+	11.0973i	0.113721	+	0.387298i	−0.882888	+	0.469584i	$0.844404\pi$
$822$	−8.64076	−	1.35799i	−0.301381	−	0.0473652i
$823$	0.932818	+	2.04259i	0.0325160	+	0.0712001i	0.925193	−	0.379497i	$-0.123903\pi$
$823$	0.932818	+	2.04259i	0.0325160	+	0.0712001i	−0.892677	+	0.450697i	$0.851176\pi$
$824$	1.24010	+	11.9339i	0.0432009	+	0.415739i
$825$	15.0129	−	9.64821i	0.522682	−	0.335907i
$826$	4.65396	+	4.14054i	0.161932	+	0.144068i
$827$			35.0959i			1.22041i	0.792245	+	0.610203i	$0.208912\pi$
$827$			35.0959i			1.22041i	−0.792245	+	0.610203i	$0.791088\pi$
$828$	0.371202	−	9.58448i	0.0129002	−	0.333084i
$829$			17.1608i			0.596020i	0.954563	+	0.298010i	$0.0963230\pi$
$829$			17.1608i			0.596020i	−0.954563	+	0.298010i	$0.903677\pi$
$830$	−31.7442	+	35.6805i	−1.10186	+	1.23849i
$831$	20.0042	−	12.8559i	0.693938	−	0.445967i
$832$	2.30739	−	0.148534i	0.0799943	−	0.00514949i
$833$	−14.6732	−	32.1298i	−0.508396	−	1.11323i
$834$	−0.393406	+	2.50321i	−0.0136225	+	0.0866790i
$835$	18.7988	+	64.0228i	0.650559	+	2.21560i
$836$	18.9524	+	12.8930i	0.655481	+	0.445913i
$837$	−3.40102	−	1.55319i	−0.117557	−	0.0536863i
$838$	−0.0280987	+	0.0912603i	−0.000970653	+	0.00315253i
$839$	12.9039	+	14.8919i	0.445491	+	0.514124i	0.933433	−	0.358752i	$-0.116798\pi$
$839$	12.9039	+	14.8919i	0.445491	+	0.514124i	−0.487942	+	0.872876i	$0.662252\pi$
$840$	2.35112	+	2.93890i	0.0811212	+	0.101402i
$841$	1.99754	+	0.586530i	0.0688806	+	0.0202252i
$842$	28.3393	+	13.3930i	0.976636	+	0.461554i
$843$	11.8561	−	18.4484i	0.408345	−	0.635398i
$844$	0.373913	+	1.40882i	0.0128706	+	0.0484935i
$845$	−39.4532	−	5.67251i	−1.35723	−	0.195140i
$846$	−1.06508	−	2.41535i	−0.0366182	−	0.0830415i
$847$	0.280405	+	1.95026i	0.00963483	+	0.0670117i
$848$	−2.32200	−	4.06624i	−0.0797377	−	0.139635i
$849$	−2.39515	+	2.76415i	−0.0822013	+	0.0948653i
$850$	33.1525	+	0.433854i	1.13712	+	0.0148811i
$851$	−7.29157	+	46.5618i	−0.249952	+	1.59612i
$852$	0.507810	−	19.3986i	0.0173973	−	0.664584i
$853$	43.2657	+	37.4900i	1.48139	+	1.28363i	0.870751	+	0.491724i	$0.163633\pi$
$853$	43.2657	+	37.4900i	1.48139	+	1.28363i	0.610640	+	0.791909i	$0.290912\pi$
$854$	0.842359	+	1.34923i	0.0288249	+	0.0461699i
$855$	−1.27562	−	8.87210i	−0.0436251	−	0.303419i
$856$	−25.1432	+	10.3100i	−0.859378	+	0.352389i
$857$	4.44668	−	30.9273i	0.151896	−	1.05646i	−0.761143	−	0.648584i	$-0.775361\pi$
$857$	4.44668	−	30.9273i	0.151896	−	1.05646i	0.913039	−	0.407873i	$-0.133729\pi$
$858$	−0.434089	−	1.55328i	−0.0148195	−	0.0530280i
$859$	−3.37050	+	5.24461i	−0.115000	+	0.178944i	−0.893982	−	0.448103i	$-0.852100\pi$
$859$	−3.37050	+	5.24461i	−0.115000	+	0.178944i	0.778982	+	0.627046i	$0.215736\pi$
$860$	−11.0897	+	22.6921i	−0.378157	+	0.773794i
$861$	−0.252050	+	0.858404i	−0.00858985	+	0.0292543i
$862$	−15.5334	−	18.4078i	−0.529071	−	0.626973i
$863$	1.19139	+	1.37494i	0.0405554	+	0.0468034i	0.775665	−	0.631145i	$-0.217415\pi$
$863$	1.19139	+	1.37494i	0.0405554	+	0.0468034i	−0.735109	+	0.677948i	$0.762869\pi$
$864$	−1.94519	+	5.31190i	−0.0661766	+	0.180714i
$865$	20.9833	−	45.9469i	0.713452	−	1.56224i
$866$	−33.1998	−	21.9553i	−1.12817	−	0.746073i
$867$	2.78078	+	9.47046i	0.0944402	+	0.321634i
$868$	0.542248	−	3.17851i	0.0184051	−	0.107886i
$869$	−50.6766	+	23.1432i	−1.71909	+	0.785080i
$870$	−24.1260	+	3.14715i	−0.817949	+	0.106698i
$871$	−1.25918	+	0.809224i	−0.0426656	+	0.0274195i
$872$	21.1239	+	19.8078i	0.715345	+	0.670777i
$873$	9.36287			0.316885
$874$	−18.7536	−	6.03262i	−0.634352	−	0.204056i
$875$			0.635052i			0.0214687i
$876$	19.3545	+	17.6784i	0.653927	+	0.597298i
$877$	11.9286	+	18.5612i	0.402799	+	0.626768i	0.982103	−	0.188344i	$-0.0603119\pi$
$877$	11.9286	+	18.5612i	0.402799	+	0.626768i	−0.579304	+	0.815112i	$0.696676\pi$
$878$	1.55052	+	11.8863i	0.0523275	+	0.401142i
$879$	−8.82242	−	19.3184i	−0.297573	−	0.651594i
$880$	−9.44430	+	47.7809i	−0.318367	+	1.61069i
$881$	−21.3168	+	6.25919i	−0.718182	+	0.210877i	−0.620349	−	0.784326i	$-0.713009\pi$
$881$	−21.3168	+	6.25919i	−0.718182	+	0.210877i	−0.0978328	+	0.995203i	$0.531191\pi$
$882$	−8.03791	−	5.31554i	−0.270650	−	0.178984i
$883$	49.3483	+	22.5366i	1.66070	+	0.758418i	0.999970	+	0.00779663i	$0.00248177\pi$
$883$	49.3483	+	22.5366i	1.66070	+	0.758418i	0.660733	+	0.750621i	$0.270246\pi$
$884$	0.919119	−	2.85192i	0.0309133	−	0.0959203i
$885$	23.8231	−	20.6429i	0.800806	−	0.693902i
$886$	0.837780	−	0.706960i	0.0281458	−	0.0237508i
$887$	−9.49001	−	2.78652i	−0.318643	−	0.0935622i	0.118500	−	0.992954i	$-0.462192\pi$
$887$	−9.49001	−	2.78652i	−0.318643	−	0.0935622i	−0.437143	+	0.899392i	$0.644010\pi$
$888$	12.5300	−	24.8109i	0.420480	−	0.832599i
$889$	−5.72093	−	3.67662i	−0.191874	−	0.123310i
$890$	−10.5680	−	37.8150i	−0.354240	−	1.26756i
$891$	3.90564	+	0.561546i	0.130844	+	0.0188125i
$892$	−4.50460	−	10.5886i	−0.150825	−	0.354532i
$893$	−5.36654	+	0.771591i	−0.179584	+	0.0258203i
$894$	−8.18356	+	5.10919i	−0.273699	+	0.170877i
$895$	34.8088	−	40.1715i	1.16353	−	1.34279i
$896$	−4.85803	−	0.446250i	−0.162295	−	0.0149082i
$897$	0.734700	+	1.17536i	0.0245309	+	0.0392441i
$898$	7.17572	+	0.0939058i	0.239457	+	0.00313368i
$899$	15.7534	+	13.6504i	0.525406	+	0.455267i
$900$	7.73492	−	4.68956i	0.257831	−	0.156319i
$901$	−6.00637	+	0.863586i	−0.200101	+	0.0287702i
$902$	−10.5934	+	4.67131i	−0.352723	+	0.155538i
$903$	−0.251131	+	1.74665i	−0.00835711	+	0.0581250i
$904$	53.4455	−	13.4388i	1.77757	−	0.446968i
$905$	−57.9945	−	37.2708i	−1.92780	−	1.23892i
$906$	−1.38916	−	0.656513i	−0.0461519	−	0.0218112i
$907$	16.6884	−	56.8354i	0.554129	−	1.88719i	0.103123	−	0.994669i	$-0.467116\pi$
$907$	16.6884	−	56.8354i	0.554129	−	1.88719i	0.451006	−	0.892521i	$-0.351065\pi$
$908$	39.7899	−	32.6949i	1.32047	−	1.08502i
$909$	5.79971	−	5.02548i	0.192364	−	0.166685i
$910$	−0.519801	−	0.160045i	−0.0172312	−	0.00530543i
$911$	−9.43167	+	20.6525i	−0.312485	+	0.684247i	−0.999084	−	0.0427894i	$-0.986376\pi$
$911$	−9.43167	+	20.6525i	−0.312485	+	0.684247i	0.686599	+	0.727036i	$0.259103\pi$
$912$	9.43204	+	6.78418i	0.312326	+	0.224647i
$913$	−41.4309	+	12.1652i	−1.37116	+	0.402609i
$914$	−7.51184	+	47.7972i	−0.248470	+	1.58099i
$915$	7.32171	−	3.34371i	0.242048	−	0.110540i
$916$	29.2972	−	3.43244i	0.968005	−	0.113411i
$917$	1.80115	+	2.80265i	0.0594793	+	0.0925516i
$918$	5.47695	+	4.87274i	0.180766	+	0.160824i
$919$	−14.6822			−0.484322			−0.242161	−	0.970236i	$-0.577856\pi$
$919$	−14.6822			−0.484322			−0.242161	+	0.970236i	$0.577856\pi$
$920$	−3.80408	−	41.6859i	−0.125417	−	1.37434i
$921$	3.78406			0.124689
$922$	−30.2570	−	26.9191i	−0.996461	−	0.886532i
$923$	1.51609	+	2.35909i	0.0499028	+	0.0776503i
$924$	0.395971	+	3.37975i	0.0130265	+	0.111186i
$925$	−40.4292	+	18.4634i	−1.32930	+	0.607073i
$926$	−1.41369	+	8.99520i	−0.0464568	+	0.295601i
$927$	4.07017	−	1.19511i	0.133682	−	0.0392526i
$928$	18.7487	−	25.3595i	0.615456	−	0.832467i
$929$	1.57762	−	3.45451i	0.0517601	−	0.113339i	−0.881985	−	0.471278i	$-0.843793\pi$
$929$	1.57762	−	3.45451i	0.0517601	−	0.113339i	0.933745	+	0.357939i	$0.116520\pi$
$930$	−15.5945	−	4.80150i	−0.511365	−	0.157447i
$931$	−14.9580	+	12.9612i	−0.490228	+	0.424785i
$932$	−1.73781	−	2.11492i	−0.0569238	−	0.0692765i
$933$	−8.24533	+	28.0810i	−0.269940	+	0.919331i
$934$	−46.3162	−	21.8888i	−1.51551	−	0.716225i
$935$	53.0982	+	34.1241i	1.73650	+	1.11598i
$936$	−0.199347	−	0.792795i	−0.00651587	−	0.0259133i
$937$	−6.98856	+	48.6065i	−0.228306	+	1.58791i	0.476935	+	0.878938i	$0.341748\pi$
$937$	−6.98856	+	48.6065i	−0.228306	+	1.58791i	−0.705242	+	0.708967i	$0.749162\pi$
$938$	2.88963	−	1.27422i	0.0943499	−	0.0416048i
$939$	15.7834	−	2.26931i	0.515072	−	0.0740562i
$940$	−5.97254	−	9.85107i	−0.194803	−	0.321307i
$941$	−36.6802	−	31.7836i	−1.19574	−	1.03612i	−0.998444	−	0.0557720i	$-0.982238\pi$
$941$	−36.6802	−	31.7836i	−1.19574	−	1.03612i	−0.197298	−	0.980344i	$-0.563217\pi$
$942$	−2.13563	−	0.0279482i	−0.0695826	−	0.000910600i
$943$	7.60101	−	6.42123i	0.247523	−	0.209104i
$944$	−2.13778	+	40.8042i	−0.0695790	+	1.32806i
$945$	0.871385	−	1.00563i	0.0283461	−	0.0327132i
$946$	−19.3708	+	12.0936i	−0.629799	+	0.393198i
$947$	−47.2052	+	6.78708i	−1.53396	+	0.220550i	−0.856941	−	0.515414i	$-0.827638\pi$
$947$	−47.2052	+	6.78708i	−1.53396	+	0.220550i	−0.677020	+	0.735964i	$0.736729\pi$
$948$	−25.9845	+	11.0544i	−0.843937	+	0.359029i
$949$	−3.74949	−	0.539095i	−0.121714	−	0.0174998i
$950$	−5.00040	−	17.8927i	−0.162234	−	0.580516i
$951$	20.8166	+	13.3780i	0.675025	+	0.433813i
$952$	−2.84997	+	5.64327i	−0.0923682	+	0.182900i
$953$	−46.2546	−	13.5816i	−1.49833	−	0.439950i	−0.573143	−	0.819455i	$-0.694276\pi$
$953$	−46.2546	−	13.5816i	−1.49833	−	0.439950i	−0.925190	+	0.379505i	$0.876094\pi$
$954$	−1.26524	+	1.06767i	−0.0409636	+	0.0345671i
$955$	35.4563	−	30.7231i	1.14734	−	0.994175i
$956$	−32.7353	−	10.5500i	−1.05873	−	0.341210i
$957$	−20.0104	−	9.13842i	−0.646843	−	0.295403i
$958$	−14.2557	−	9.42740i	−0.460579	−	0.304586i
$959$	−2.55892	+	0.751367i	−0.0826318	+	0.0242629i
$960$	−5.41914	+	24.0850i	−0.174902	+	0.777341i
$961$	−7.07063	−	15.4825i	−0.228085	−	0.499436i
$962$	0.519563	+	3.98297i	0.0167514	+	0.128416i
$963$	5.19437	+	8.08260i	0.167386	+	0.260458i
$964$	−1.50790	+	1.65087i	−0.0485663	+	0.0531708i
$965$			47.8393i			1.54000i
$966$	−1.14634	−	2.69052i	−0.0368830	−	0.0865660i
$967$	48.6864			1.56565			0.782825	−	0.622243i	$-0.213778\pi$
$967$	48.6864			1.56565			0.782825	+	0.622243i	$0.213778\pi$
$968$	−8.84032	+	9.42769i	−0.284139	+	0.303018i
$969$	12.6663	−	8.14017i	0.406902	−	0.261500i
$970$	40.5174	−	5.28534i	1.30093	−	0.169702i
$971$	−8.36563	+	3.82046i	−0.268466	+	0.122604i	−0.545100	−	0.838371i	$-0.683508\pi$
$971$	−8.36563	+	3.82046i	−0.268466	+	0.122604i	0.276634	+	0.960975i	$0.410781\pi$
$972$	1.97152	+	0.336337i	0.0632364	+	0.0107880i
$973$	0.217669	+	0.741314i	0.00697816	+	0.0237654i
$974$	−1.99614	−	1.32006i	−0.0639603	−	0.0422975i
$975$	−0.543017	+	1.18904i	−0.0173905	+	0.0380798i
$976$	−3.45916	+	9.84327i	−0.110725	+	0.315075i
$977$	−8.40372	−	9.69842i	−0.268859	−	0.310280i	0.605225	−	0.796054i	$-0.293083\pi$
$977$	−8.40372	−	9.69842i	−0.268859	−	0.310280i	−0.874084	+	0.485775i	$0.838538\pi$
$978$	−18.8838	−	22.3782i	−0.603838	−	0.715575i
$979$	10.0016	−	34.0623i	0.319653	−	1.08864i
$980$	−37.7843	−	18.4654i	−1.20697	−	0.589854i
$981$	5.53520	−	8.61293i	0.176725	−	0.274990i
$982$	11.2960	+	40.4199i	0.360470	+	1.28985i
$983$	−4.56965	+	31.7826i	−0.145749	+	1.01371i	0.777328	+	0.629095i	$0.216574\pi$
$983$	−4.56965	+	31.7826i	−0.145749	+	1.01371i	−0.923078	+	0.384614i	$0.874335\pi$
$984$	−5.42959	+	2.22641i	−0.173089	+	0.0709755i
$985$	1.00930	+	7.01984i	0.0321590	+	0.223671i
$986$	−21.6442	−	34.6682i	−0.689292	−	1.10406i
$987$	−0.608284	−	0.527081i	−0.0193619	−	0.0167772i
$988$	−1.67841	−	0.0439369i	−0.0533974	−	0.00139782i
$989$	13.0373	−	14.6701i	0.414562	−	0.466482i
$990$	17.2185	+	0.225331i	0.547239	+	0.00716150i
$991$	14.0601	−	16.2262i	0.446633	−	0.515442i	−0.487132	−	0.873328i	$-0.661957\pi$
$991$	14.0601	−	16.2262i	0.446633	−	0.515442i	0.933765	+	0.357886i	$0.116503\pi$
$992$	18.5024	−	10.2470i	0.587452	−	0.325341i
$993$	2.85483	+	19.8558i	0.0905954	+	0.630105i
$994$	−2.38727	−	5.41377i	−0.0757196	−	0.171714i
$995$	57.7283	+	8.30008i	1.83011	+	0.263130i
$996$	−21.1541	+	5.61449i	−0.670295	+	0.177902i
$997$	−30.8391	+	47.9866i	−0.976684	+	1.51975i	−0.127375	+	0.991855i	$0.540655\pi$
$997$	−30.8391	+	47.9866i	−0.976684	+	1.51975i	−0.849309	+	0.527895i	$0.822981\pi$
$998$	−5.10965	−	2.41480i	−0.161743	−	0.0764391i
$999$	−9.42907	−	2.76862i	−0.298323	−	0.0875954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.36	yes	480
8.5	even	2	inner	552.2.bb.a.85.35	yes	480
23.13	even	11	inner	552.2.bb.a.13.35	✓	480
184.13	even	22	inner	552.2.bb.a.13.36	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.35	✓	480	23.13	even	11	inner
552.2.bb.a.13.36	yes	480	184.13	even	22	inner
552.2.bb.a.85.35	yes	480	8.5	even	2	inner
552.2.bb.a.85.36	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.940019 - 1.05658i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.232727 - 1.98641i) q^{4} +(-2.80703 + 1.28193i) q^{5} +(-1.39707 - 0.219564i) q^{6} +(-0.413734 + 0.121483i) q^{7} +(-2.31758 - 1.62137i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.940019 - 1.05658i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.232727 - 1.98641i) q^{4} +(-2.80703 + 1.28193i) q^{5} +(-1.39707 - 0.219564i) q^{6} +(-0.413734 + 0.121483i) q^{7} +(-2.31758 - 1.62137i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.28420 + 4.17089i) q^{10} +(-2.98204 + 2.58395i) q^{11} +(-1.54526 + 1.26972i) q^{12} +(0.0814265 - 0.277313i) q^{13} +(-0.260561 + 0.551341i) q^{14} +(2.59602 + 1.66836i) q^{15} +(-3.89168 + 0.924586i) q^{16} +(-0.737711 + 5.13089i) q^{17} +(0.570602 + 1.29399i) q^{18} +(2.87505 - 0.413370i) q^{19} +(3.19971 + 5.27758i) q^{20} +(0.325880 + 0.282377i) q^{21} +(-0.0730198 + 5.57973i) q^{22} +(-1.29334 - 4.61815i) q^{23} +(-0.111009 + 2.82625i) q^{24} +(2.96177 - 3.41806i) q^{25} +(-0.216461 - 0.346713i) q^{26} +(0.989821 - 0.142315i) q^{27} +(0.337604 + 0.793575i) q^{28} +(-5.51836 - 0.793421i) q^{29} +(4.20307 - 1.17461i) q^{30} +(-3.14536 - 2.02140i) q^{31} +(-2.68135 + 4.98100i) q^{32} +(3.78597 + 1.11166i) q^{33} +(4.72774 + 5.60259i) q^{34} +(1.00563 - 0.871385i) q^{35} +(1.90358 + 0.613490i) q^{36} +(-8.93908 - 4.08234i) q^{37} +(2.26584 - 3.42630i) q^{38} +(-0.277313 + 0.0814265i) q^{39} +(8.58398 + 1.58027i) q^{40} +(0.861891 + 1.88728i) q^{41} +(0.604687 - 0.0788792i) q^{42} +(2.21248 + 3.44268i) q^{43} +(5.82680 + 5.32221i) q^{44} -3.08589i q^{45} +(-6.09521 - 2.97463i) q^{46} -1.86659 q^{47} +(2.88181 + 2.77402i) q^{48} +(-5.73236 + 3.68396i) q^{49} +(-0.827342 - 6.34240i) q^{50} +(4.71522 - 2.15337i) q^{51} +(-0.569809 - 0.0972083i) q^{52} +(0.329804 + 1.12321i) q^{53} +(0.780084 - 1.17961i) q^{54} +(5.05823 - 11.0760i) q^{55} +(1.15583 + 0.389270i) q^{56} +(-1.90212 - 2.19516i) q^{57} +(-6.02568 + 5.08477i) q^{58} +(2.87791 - 9.80125i) q^{59} +(2.70989 - 5.54504i) q^{60} +(1.41018 - 2.19428i) q^{61} +(-5.09248 + 1.42317i) q^{62} +(0.0613663 - 0.426812i) q^{63} +(2.74231 + 7.51530i) q^{64} +(0.126929 + 0.882809i) q^{65} +(4.73345 - 2.95520i) q^{66} +(-3.91390 - 3.39141i) q^{67} +(10.3638 + 0.271299i) q^{68} +(-3.18580 + 3.58479i) q^{69} +(0.0246244 - 1.88165i) q^{70} +(-6.35385 + 7.33274i) q^{71} +(2.43761 - 1.43460i) q^{72} +(-1.86525 - 12.9731i) q^{73} +(-12.7162 + 5.60738i) q^{74} +(-4.47671 - 0.643654i) q^{75} +(-1.49023 - 5.61483i) q^{76} +(0.919865 - 1.43134i) q^{77} +(-0.174646 + 0.369546i) q^{78} +(13.5471 + 3.97780i) q^{79} +(9.73879 - 7.58418i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(2.80426 + 0.863420i) q^{82} +(9.95434 + 4.54600i) q^{83} +(0.485076 - 0.713049i) q^{84} +(-4.50665 - 15.3483i) q^{85} +(5.71724 + 0.898525i) q^{86} +(2.31598 + 5.07130i) q^{87} +(11.1006 - 1.15351i) q^{88} +(-7.56875 + 4.86414i) q^{89} +(-3.26050 - 2.90080i) q^{90} +0.124626i q^{91} +(-8.87255 + 3.64388i) q^{92} +3.73890i q^{93} +(-1.75463 + 1.97220i) q^{94} +(-7.54043 + 4.84594i) q^{95} +(5.63993 - 0.437236i) q^{96} +(-3.88948 - 8.51677i) q^{97} +(-1.49612 + 9.51970i) q^{98} +(-1.11166 - 3.78597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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