LMFDB - Embedded newform 990.2.n.j.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(91,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,0,-2,2,0,-1,-2,0,-8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$2.51217 - 1.82520i$ of defining polynomial
Character	$\chi$	$=$	990.91
Dual form			990.2.n.j.631.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.675538 + 2.07909i) q^{7} +(0.309017 + 0.951057i) q^{8} -1.00000 q^{10} +(-1.92705 - 2.69935i) q^{11} +(5.11739 - 3.71800i) q^{13} +(-0.675538 - 2.07909i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.34945 + 0.980434i) q^{17} +(1.82119 + 5.60505i) q^{19} +(0.809017 - 0.587785i) q^{20} +(3.14565 + 1.05113i) q^{22} +3.26042 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.95467 + 6.01586i) q^{26} +(1.76858 + 1.28495i) q^{28} +(1.95002 - 6.00154i) q^{29} +(-3.74888 + 2.72372i) q^{31} +1.00000 q^{32} -1.66801 q^{34} +(-1.76858 + 1.28495i) q^{35} +(-0.849452 + 2.61434i) q^{37} +(-4.76794 - 3.46411i) q^{38} +(-0.309017 + 0.951057i) q^{40} +(2.89414 + 8.90725i) q^{41} +1.29259 q^{43} +(-3.16272 + 0.998590i) q^{44} +(-2.63773 + 1.91643i) q^{46} +(-0.582494 - 1.79273i) q^{47} +(1.79684 + 1.30548i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.95467 - 6.01586i) q^{52} +(6.36099 - 4.62153i) q^{53} +(0.0276194 - 3.31651i) q^{55} -2.18609 q^{56} +(1.95002 + 6.00154i) q^{58} +(-2.47991 + 7.63236i) q^{59} +(3.51153 + 2.55128i) q^{61} +(1.43195 - 4.40708i) q^{62} +(-0.809017 + 0.587785i) q^{64} +6.32545 q^{65} +5.61675 q^{67} +(1.34945 - 0.980434i) q^{68} +(0.675538 - 2.07909i) q^{70} +(11.1539 + 8.10380i) q^{71} +(4.32382 - 13.3074i) q^{73} +(-0.849452 - 2.61434i) q^{74} +5.89350 q^{76} +(6.91399 - 2.18301i) q^{77} +(-1.40632 + 1.02175i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-7.57696 - 5.50498i) q^{82} +(7.25616 + 5.27191i) q^{83} +(0.515445 + 1.58638i) q^{85} +(-1.04573 + 0.759764i) q^{86} +(1.97174 - 2.66688i) q^{88} -13.3656 q^{89} +(4.27308 + 13.1512i) q^{91} +(1.00752 - 3.10084i) q^{92} +(1.52499 + 1.10797i) q^{94} +(-1.82119 + 5.60505i) q^{95} +(-9.72751 + 7.06745i) q^{97} -2.22102 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8} - 8 q^{10} - 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} - 26 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 22 q^{29}+ \cdots + 22 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8 - 8 * q^10 - 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 - 26 * q^23 - 2 * q^25 + 6 * q^26 + 4 * q^28 + 22 * q^29 - 26 * q^31 + 8 * q^32 + 2 * q^34 - 4 * q^35 - 8 * q^37 + 3 * q^38 + 2 * q^40 + 15 * q^41 + 38 * q^43 - 7 * q^44 - 6 * q^46 - 6 * q^47 + 27 * q^49 - 2 * q^50 + 6 * q^52 + 4 * q^53 - 8 * q^55 - 6 * q^56 + 22 * q^58 - 39 * q^59 - 20 * q^61 + 14 * q^62 - 2 * q^64 + 14 * q^65 - 26 * q^67 + 12 * q^68 + q^70 - 2 * q^71 + 8 * q^73 - 8 * q^74 + 8 * q^76 - 16 * q^77 + 14 * q^79 + 2 * q^80 - 15 * q^82 + 21 * q^83 + 13 * q^85 - 17 * q^86 - 7 * q^88 - 32 * q^89 + 53 * q^91 + 19 * q^92 + 9 * q^94 + 7 * q^95 - 31 * q^97 + 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−0.675538	+	2.07909i	−0.255329	+	0.785823i	0.738435	+	0.674325i	$0.235565\pi$
$7$	−0.675538	+	2.07909i	−0.255329	+	0.785823i	−0.993765	+	0.111499i	$0.964435\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−1.92705	−	2.69935i	−0.581028	−	0.813884i
$11$	−1.92705	−	2.69935i	−0.581028	−	0.813884i
$12$		0			0
$13$	5.11739	−	3.71800i	1.41931	−	1.03119i	0.427425	−	0.904051i	$-0.359421\pi$
$13$	5.11739	−	3.71800i	1.41931	−	1.03119i	0.991885	−	0.127138i	$-0.0405790\pi$
$14$	−0.675538	−	2.07909i	−0.180545	−	0.555661i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.34945	+	0.980434i	0.327290	+	0.237790i	0.739280	−	0.673398i	$-0.235166\pi$
$17$	1.34945	+	0.980434i	0.327290	+	0.237790i	−0.411990	+	0.911188i	$0.635166\pi$
$18$		0			0
$19$	1.82119	+	5.60505i	0.417810	+	1.28589i	0.909713	+	0.415237i	$0.136301\pi$
$19$	1.82119	+	5.60505i	0.417810	+	1.28589i	−0.491903	+	0.870650i	$0.663699\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$		0			0
$22$	3.14565	+	1.05113i	0.670656	+	0.224101i
$23$	3.26042			0.679844			0.339922	−	0.940454i	$-0.389599\pi$
$23$	3.26042			0.679844			0.339922	+	0.940454i	$0.389599\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.95467	+	6.01586i	−0.383342	+	1.17981i
$27$		0			0
$28$	1.76858	+	1.28495i	0.334231	+	0.242833i
$29$	1.95002	−	6.00154i	0.362110	−	1.11446i	−0.589662	−	0.807650i	$-0.700739\pi$
$29$	1.95002	−	6.00154i	0.362110	−	1.11446i	0.951771	−	0.306808i	$-0.0992611\pi$
$30$		0			0
$31$	−3.74888	+	2.72372i	−0.673319	+	0.489195i	−0.871135	−	0.491044i	$-0.836615\pi$
$31$	−3.74888	+	2.72372i	−0.673319	+	0.489195i	0.197815	+	0.980239i	$0.436615\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.66801			−0.286062
$35$	−1.76858	+	1.28495i	−0.298945	+	0.217196i
$36$		0			0
$37$	−0.849452	+	2.61434i	−0.139649	+	0.429795i	−0.996284	−	0.0861273i	$-0.972551\pi$
$37$	−0.849452	+	2.61434i	−0.139649	+	0.429795i	0.856635	+	0.515923i	$0.172551\pi$
$38$	−4.76794	−	3.46411i	−0.773462	−	0.561953i
$39$		0			0
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	2.89414	+	8.90725i	0.451989	+	1.39108i	0.874634	+	0.484783i	$0.161102\pi$
$41$	2.89414	+	8.90725i	0.451989	+	1.39108i	−0.422645	+	0.906295i	$0.638898\pi$
$42$		0			0
$43$	1.29259			0.197118			0.0985589	−	0.995131i	$-0.468577\pi$
$43$	1.29259			0.197118			0.0985589	+	0.995131i	$0.468577\pi$
$44$	−3.16272	+	0.998590i	−0.476798	+	0.150543i
$45$		0			0
$46$	−2.63773	+	1.91643i	−0.388913	+	0.282561i
$47$	−0.582494	−	1.79273i	−0.0849655	−	0.261497i	0.899543	−	0.436831i	$-0.143899\pi$
$47$	−0.582494	−	1.79273i	−0.0849655	−	0.261497i	−0.984509	+	0.175334i	$0.943899\pi$
$48$		0			0
$49$	1.79684	+	1.30548i	0.256692	+	0.186497i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$		0			0
$52$	−1.95467	−	6.01586i	−0.271064	−	0.834249i
$53$	6.36099	−	4.62153i	0.873749	−	0.634816i	−0.0578416	−	0.998326i	$-0.518422\pi$
$53$	6.36099	−	4.62153i	0.873749	−	0.634816i	0.931590	+	0.363510i	$0.118422\pi$
$54$		0			0
$55$	0.0276194	−	3.31651i	0.00372420	−	0.447198i
$56$	−2.18609			−0.292128
$57$		0			0
$58$	1.95002	+	6.00154i	0.256050	+	0.788041i
$59$	−2.47991	+	7.63236i	−0.322856	+	0.993649i	0.649543	+	0.760325i	$0.274960\pi$
$59$	−2.47991	+	7.63236i	−0.322856	+	0.993649i	−0.972399	+	0.233324i	$0.925040\pi$
$60$		0			0
$61$	3.51153	+	2.55128i	0.449606	+	0.326658i	0.789440	−	0.613828i	$-0.210371\pi$
$61$	3.51153	+	2.55128i	0.449606	+	0.326658i	−0.339834	+	0.940485i	$0.610371\pi$
$62$	1.43195	−	4.40708i	0.181857	−	0.559699i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.32545			0.784575
$66$		0			0
$67$	5.61675			0.686196			0.343098	−	0.939300i	$-0.388524\pi$
$67$	5.61675			0.686196			0.343098	+	0.939300i	$0.388524\pi$
$68$	1.34945	−	0.980434i	0.163645	−	0.118895i
$69$		0			0
$70$	0.675538	−	2.07909i	0.0807423	−	0.248499i
$71$	11.1539	+	8.10380i	1.32373	+	0.961744i	0.999878	+	0.0156347i	$0.00497689\pi$
$71$	11.1539	+	8.10380i	1.32373	+	0.961744i	0.323849	+	0.946109i	$0.395023\pi$
$72$		0			0
$73$	4.32382	−	13.3074i	0.506065	−	1.55751i	−0.292908	−	0.956141i	$-0.594623\pi$
$73$	4.32382	−	13.3074i	0.506065	−	1.55751i	0.798973	−	0.601367i	$-0.205377\pi$
$74$	−0.849452	−	2.61434i	−0.0987467	−	0.303911i
$75$		0			0
$76$	5.89350			0.676031
$77$	6.91399	−	2.18301i	0.787922	−	0.248777i
$78$		0			0
$79$	−1.40632	+	1.02175i	−0.158223	+	0.114956i	−0.664080	−	0.747662i	$-0.731176\pi$
$79$	−1.40632	+	1.02175i	−0.158223	+	0.114956i	0.505857	+	0.862617i	$0.331176\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$		0			0
$82$	−7.57696	−	5.50498i	−0.836735	−	0.607924i
$83$	7.25616	+	5.27191i	0.796467	+	0.578667i	0.909876	−	0.414881i	$-0.136177\pi$
$83$	7.25616	+	5.27191i	0.796467	+	0.578667i	−0.113408	+	0.993548i	$0.536177\pi$
$84$		0			0
$85$	0.515445	+	1.58638i	0.0559078	+	0.172067i
$86$	−1.04573	+	0.759764i	−0.112763	+	0.0819275i
$87$		0			0
$88$	1.97174	−	2.66688i	0.210188	−	0.284290i
$89$	−13.3656			−1.41675			−0.708377	−	0.705834i	$-0.750572\pi$
$89$	−13.3656			−1.41675			−0.708377	+	0.705834i	$0.750572\pi$
$90$		0			0
$91$	4.27308	+	13.1512i	0.447941	+	1.37862i
$92$	1.00752	−	3.10084i	0.105042	−	0.323285i
$93$		0			0
$94$	1.52499	+	1.10797i	0.157291	+	0.114278i
$95$	−1.82119	+	5.60505i	−0.186850	+	0.575066i
$96$		0			0
$97$	−9.72751	+	7.06745i	−0.987679	+	0.717591i	−0.959412	−	0.282010i	$-0.908999\pi$
$97$	−9.72751	+	7.06745i	−0.987679	+	0.717591i	−0.0282672	+	0.999600i	$0.508999\pi$
$98$	−2.22102			−0.224357
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.00000	+	0.726543i	−0.0995037	+	0.0722937i	−0.636425	−	0.771339i	$-0.719587\pi$
$101$	−1.00000	+	0.726543i	−0.0995037	+	0.0722937i	0.536921	+	0.843633i	$0.319587\pi$
$102$		0			0
$103$	−5.75879	+	17.7237i	−0.567431	+	1.74637i	0.0931861	+	0.995649i	$0.470295\pi$
$103$	−5.75879	+	17.7237i	−0.567431	+	1.74637i	−0.660617	+	0.750723i	$0.729705\pi$
$104$	5.11739	+	3.71800i	0.501802	+	0.364580i
$105$		0			0
$106$	−2.42968	+	7.47779i	−0.235991	+	0.726307i
$107$	−3.07270	−	9.45681i	−0.297050	−	0.914224i	−0.982525	−	0.186129i	$-0.940406\pi$
$107$	−3.07270	−	9.45681i	−0.297050	−	0.914224i	0.685476	−	0.728095i	$-0.259594\pi$
$108$		0			0
$109$	4.81263			0.460966			0.230483	−	0.973076i	$-0.425969\pi$
$109$	4.81263			0.460966			0.230483	+	0.973076i	$0.425969\pi$
$110$	1.92705	+	2.69935i	0.183737	+	0.257373i
$111$		0			0
$112$	1.76858	−	1.28495i	0.167115	−	0.121416i
$113$	0.329357	+	1.01366i	0.0309833	+	0.0953567i	0.965352	−	0.260950i	$-0.0840358\pi$
$113$	0.329357	+	1.01366i	0.0309833	+	0.0953567i	−0.934369	+	0.356307i	$0.884036\pi$
$114$		0			0
$115$	2.63773	+	1.91643i	0.245970	+	0.178708i
$116$	−5.10522	−	3.70916i	−0.474008	−	0.344387i
$117$		0			0
$118$	−2.47991	−	7.63236i	−0.228294	−	0.702616i
$119$	−2.95002	+	2.14332i	−0.270428	+	0.196477i
$120$		0			0
$121$	−3.57295	+	10.4036i	−0.324814	+	0.945778i
$122$	−4.34050			−0.392970
$123$		0			0
$124$	1.43195	+	4.40708i	0.128593	+	0.395767i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	5.02802	+	3.65307i	0.446164	+	0.324157i	0.788079	−	0.615574i	$-0.211076\pi$
$127$	5.02802	+	3.65307i	0.446164	+	0.324157i	−0.341915	+	0.939731i	$0.611076\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	−5.11739	+	3.71800i	−0.448825	+	0.326091i
$131$	−3.22756			−0.281993			−0.140997	−	0.990010i	$-0.545031\pi$
$131$	−3.22756			−0.281993			−0.140997	+	0.990010i	$0.545031\pi$
$132$		0			0
$133$	−12.8837			−1.11716
$134$	−4.54405	+	3.30144i	−0.392546	+	0.285201i
$135$		0			0
$136$	−0.515445	+	1.58638i	−0.0441990	+	0.136031i
$137$	12.9242	+	9.38996i	1.10419	+	0.802239i	0.981738	−	0.190236i	$-0.0609253\pi$
$137$	12.9242	+	9.38996i	1.10419	+	0.802239i	0.122449	+	0.992475i	$0.460925\pi$
$138$		0			0
$139$	6.87093	−	21.1465i	0.582784	−	1.79363i	−0.0252068	−	0.999682i	$-0.508024\pi$
$139$	6.87093	−	21.1465i	0.582784	−	1.79363i	0.607991	−	0.793944i	$-0.291976\pi$
$140$	0.675538	+	2.07909i	0.0570934	+	0.175715i
$141$		0			0
$142$	−13.7870			−1.15698
$143$	−19.8977	−	6.64884i	−1.66393	−	0.556004i
$144$		0			0
$145$	5.10522	−	3.70916i	0.423965	−	0.308029i
$146$	4.32382	+	13.3074i	0.357842	+	1.10132i
$147$		0			0
$148$	2.22389	+	1.61575i	0.182803	+	0.132814i
$149$	5.17104	+	3.75698i	0.423628	+	0.307784i	0.779096	−	0.626905i	$-0.215678\pi$
$149$	5.17104	+	3.75698i	0.423628	+	0.307784i	−0.355468	+	0.934688i	$0.615678\pi$
$150$		0			0
$151$	−4.21698	−	12.9785i	−0.343173	−	1.05618i	−0.962555	−	0.271087i	$-0.912617\pi$
$151$	−4.21698	−	12.9785i	−0.343173	−	1.05618i	0.619382	−	0.785090i	$-0.287383\pi$
$152$	−4.76794	+	3.46411i	−0.386731	+	0.280977i
$153$		0			0
$154$	−4.31040	+	5.83003i	−0.347342	+	0.469797i
$155$	−4.63387			−0.372202
$156$		0			0
$157$	−6.79985	−	20.9278i	−0.542687	−	1.67022i	−0.726427	−	0.687244i	$-0.758820\pi$
$157$	−6.79985	−	20.9278i	−0.542687	−	1.67022i	0.183740	−	0.982975i	$-0.441180\pi$
$158$	0.537165	−	1.65322i	0.0427345	−	0.131523i
$159$		0			0
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	−2.20254	+	6.77871i	−0.173584	+	0.534237i
$162$		0			0
$163$	6.80575	−	4.94466i	0.533067	−	0.387296i	−0.288437	−	0.957499i	$-0.593135\pi$
$163$	6.80575	−	4.94466i	0.533067	−	0.387296i	0.821504	+	0.570203i	$0.193135\pi$
$164$	9.36564			0.731333
$165$		0			0
$166$	−8.96911			−0.696138
$167$	9.57369	−	6.95569i	0.740834	−	0.538248i	−0.152138	−	0.988359i	$-0.548616\pi$
$167$	9.57369	−	6.95569i	0.740834	−	0.538248i	0.892972	+	0.450112i	$0.148616\pi$
$168$		0			0
$169$	8.34694	−	25.6892i	0.642072	−	1.97610i
$170$	−1.34945	−	0.980434i	−0.103498	−	0.0751959i
$171$		0			0
$172$	0.399432	−	1.22932i	0.0304564	−	0.0937351i
$173$	−4.43293	−	13.6432i	−0.337029	−	1.03727i	−0.965714	−	0.259609i	$-0.916406\pi$
$173$	−4.43293	−	13.6432i	−0.337029	−	1.03727i	0.628684	−	0.777661i	$-0.283594\pi$
$174$		0			0
$175$	−2.18609			−0.165253
$176$	−0.0276194	+	3.31651i	−0.00208189	+	0.249991i
$177$		0			0
$178$	10.8130	−	7.85612i	0.810471	−	0.588841i
$179$	−3.75329	−	11.5514i	−0.280534	−	0.863395i	−0.987702	−	0.156349i	$-0.950027\pi$
$179$	−3.75329	−	11.5514i	−0.280534	−	0.863395i	0.707168	−	0.707046i	$-0.249973\pi$
$180$		0			0
$181$	5.18083	+	3.76409i	0.385088	+	0.279783i	0.763440	−	0.645879i	$-0.223509\pi$
$181$	5.18083	+	3.76409i	0.385088	+	0.279783i	−0.378352	+	0.925662i	$0.623509\pi$
$182$	−11.1871	−	8.12788i	−0.829241	−	0.602479i
$183$		0			0
$184$	1.00752	+	3.10084i	0.0742757	+	0.228597i
$185$	−2.22389	+	1.61575i	−0.163504	+	0.118793i
$186$		0			0
$187$	0.0460695	−	5.53198i	0.00336894	−	0.404539i
$188$	−1.88499			−0.137477
$189$		0			0
$190$	−1.82119	−	5.60505i	−0.132123	−	0.406633i
$191$	−4.25112	+	13.0836i	−0.307600	+	0.946696i	0.671094	+	0.741372i	$0.265825\pi$
$191$	−4.25112	+	13.0836i	−0.307600	+	0.946696i	−0.978694	+	0.205323i	$0.934175\pi$
$192$		0			0
$193$	8.85410	+	6.43288i	0.637332	+	0.463049i	0.858933	−	0.512089i	$-0.171128\pi$
$193$	8.85410	+	6.43288i	0.637332	+	0.463049i	−0.221600	+	0.975138i	$0.571128\pi$
$194$	3.71558	−	11.4354i	0.266763	−	0.821012i
$195$		0			0
$196$	1.79684	−	1.30548i	0.128346	−	0.0932487i
$197$	−11.9113			−0.848646			−0.424323	−	0.905511i	$-0.639488\pi$
$197$	−11.9113			−0.848646			−0.424323	+	0.905511i	$0.639488\pi$
$198$		0			0
$199$	−15.2636			−1.08201			−0.541004	−	0.841020i	$-0.681956\pi$
$199$	−15.2636			−1.08201			−0.541004	+	0.841020i	$0.681956\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$		0			0
$202$	0.381966	−	1.17557i	0.0268750	−	0.0827129i
$203$	11.1605	+	8.10855i	0.783311	+	0.569108i
$204$		0			0
$205$	−2.89414	+	8.90725i	−0.202136	+	0.622109i
$206$	−5.75879	−	17.7237i	−0.401234	−	1.23487i
$207$		0			0
$208$	−6.32545			−0.438591
$209$	11.6205	−	15.7172i	0.803803	−	1.08718i
$210$		0			0
$211$	−3.02009	+	2.19423i	−0.207912	+	0.151057i	−0.686868	−	0.726782i	$-0.741015\pi$
$211$	−3.02009	+	2.19423i	−0.207912	+	0.151057i	0.478957	+	0.877839i	$0.341015\pi$
$212$	−2.42968	−	7.47779i	−0.166871	−	0.513577i
$213$		0			0
$214$	8.04444	+	5.84463i	0.549907	+	0.399531i
$215$	1.04573	+	0.759764i	0.0713179	+	0.0518155i
$216$		0			0
$217$	−3.13036	−	9.63426i	−0.212503	−	0.654016i
$218$	−3.89350	+	2.82879i	−0.263701	+	0.191590i
$219$		0			0
$220$	−3.14565	−	1.05113i	−0.212080	−	0.0708669i
$221$	10.5509			0.709733
$222$		0			0
$223$	−5.99199	−	18.4414i	−0.401253	−	1.23493i	−0.923984	−	0.382432i	$-0.875087\pi$
$223$	−5.99199	−	18.4414i	−0.401253	−	1.23493i	0.522731	−	0.852498i	$-0.324913\pi$
$224$	−0.675538	+	2.07909i	−0.0451363	+	0.138915i
$225$		0			0
$226$	−0.862267	−	0.626474i	−0.0573571	−	0.0416724i
$227$	−1.85068	+	5.69581i	−0.122834	+	0.378044i	−0.993500	−	0.113830i	$-0.963688\pi$
$227$	−1.85068	+	5.69581i	−0.122834	+	0.378044i	0.870666	+	0.491874i	$0.163688\pi$
$228$		0			0
$229$	−13.4709	+	9.78715i	−0.890179	+	0.646753i	−0.935925	−	0.352200i	$-0.885434\pi$
$229$	−13.4709	+	9.78715i	−0.890179	+	0.646753i	0.0457456	+	0.998953i	$0.485434\pi$
$230$	−3.26042			−0.214986
$231$		0			0
$232$	6.31040			0.414298
$233$	7.79461	−	5.66311i	0.510642	−	0.371003i	−0.302425	−	0.953173i	$-0.597796\pi$
$233$	7.79461	−	5.66311i	0.510642	−	0.371003i	0.813067	+	0.582170i	$0.197796\pi$
$234$		0			0
$235$	0.582494	−	1.79273i	0.0379977	−	0.116945i
$236$	6.49248	+	4.71706i	0.422624	+	0.307054i
$237$		0			0
$238$	1.12681	−	3.46796i	0.0730401	−	0.224794i
$239$	−3.69811	−	11.3816i	−0.239211	−	0.736216i	−0.996535	−	0.0831762i	$-0.973494\pi$
$239$	−3.69811	−	11.3816i	−0.239211	−	0.736216i	0.757324	−	0.653039i	$-0.226506\pi$
$240$		0			0
$241$	−9.67120			−0.622977			−0.311488	−	0.950250i	$-0.600828\pi$
$241$	−9.67120			−0.622977			−0.311488	+	0.950250i	$0.600828\pi$
$242$	−3.22448	−	10.5168i	−0.207278	−	0.676044i
$243$		0			0
$244$	3.51153	−	2.55128i	0.224803	−	0.163329i
$245$	0.686333	+	2.11231i	0.0438482	+	0.134951i
$246$		0			0
$247$	30.1594	+	21.9121i	1.91899	+	1.39423i
$248$	−3.74888	−	2.72372i	−0.238054	−	0.172957i
$249$		0			0
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−19.0533	+	13.8431i	−1.20264	+	0.873767i	−0.994541	−	0.104342i	$-0.966726\pi$
$251$	−19.0533	+	13.8431i	−1.20264	+	0.873767i	−0.208095	+	0.978109i	$0.566726\pi$
$252$		0			0
$253$	−6.28299	−	8.80100i	−0.395008	−	0.553314i
$254$	−6.21497			−0.389962
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.09380	−	15.6771i	0.317743	−	0.977912i	−0.656868	−	0.754006i	$-0.728119\pi$
$257$	5.09380	−	15.6771i	0.317743	−	0.977912i	0.974611	−	0.223906i	$-0.0718809\pi$
$258$		0			0
$259$	−4.86163	−	3.53218i	−0.302087	−	0.219479i
$260$	1.95467	−	6.01586i	0.121224	−	0.373088i
$261$		0			0
$262$	2.61115	−	1.89711i	0.161317	−	0.117204i
$263$	−8.61724			−0.531362			−0.265681	−	0.964061i	$-0.585597\pi$
$263$	−8.61724			−0.531362			−0.265681	+	0.964061i	$0.585597\pi$
$264$		0			0
$265$	7.86261			0.482996
$266$	10.4231	−	7.57285i	0.639084	−	0.464322i
$267$		0			0
$268$	1.73567	−	5.34185i	0.106023	−	0.326305i
$269$	−12.4603	−	9.05292i	−0.759716	−	0.551966i	0.139107	−	0.990277i	$-0.455577\pi$
$269$	−12.4603	−	9.05292i	−0.759716	−	0.551966i	−0.898823	+	0.438311i	$0.855577\pi$
$270$		0			0
$271$	1.65217	−	5.08487i	0.100362	−	0.308884i	−0.888252	−	0.459357i	$-0.848080\pi$
$271$	1.65217	−	5.08487i	0.100362	−	0.308884i	0.988614	+	0.150473i	$0.0480798\pi$
$272$	−0.515445	−	1.58638i	−0.0312534	−	0.0961881i
$273$		0			0
$274$	−15.9752			−0.965095
$275$	1.97174	−	2.66688i	0.118900	−	0.160819i
$276$		0			0
$277$	−3.72711	+	2.70790i	−0.223940	+	0.162702i	−0.694099	−	0.719880i	$-0.744197\pi$
$277$	−3.72711	+	2.70790i	−0.223940	+	0.162702i	0.470158	+	0.882582i	$0.344197\pi$
$278$	6.87093	+	21.1465i	0.412091	+	1.26829i
$279$		0			0
$280$	−1.76858	−	1.28495i	−0.105693	−	0.0767905i
$281$	−16.5731	−	12.0411i	−0.988668	−	0.718310i	−0.0290392	−	0.999578i	$-0.509245\pi$
$281$	−16.5731	−	12.0411i	−0.988668	−	0.718310i	−0.959629	+	0.281269i	$0.909245\pi$
$282$		0			0
$283$	−1.28000	−	3.93943i	−0.0760879	−	0.234175i	0.905778	−	0.423754i	$-0.139288\pi$
$283$	−1.28000	−	3.93943i	−0.0760879	−	0.234175i	−0.981865	+	0.189579i	$0.939288\pi$
$284$	11.1539	−	8.10380i	0.661863	−	0.480872i
$285$		0			0
$286$	20.0056	−	6.31653i	1.18296	−	0.373504i
$287$	−20.4741			−1.20855
$288$		0			0
$289$	−4.39352	−	13.5219i	−0.258442	−	0.795404i
$290$	−1.95002	+	6.00154i	−0.114509	+	0.352423i
$291$		0			0
$292$	−11.3199	−	8.22440i	−0.662448	−	0.481296i
$293$	6.03267	−	18.5666i	0.352432	−	1.08467i	−0.605051	−	0.796186i	$-0.706847\pi$
$293$	6.03267	−	18.5666i	0.352432	−	1.08467i	0.957484	−	0.288488i	$-0.0931525\pi$
$294$		0			0
$295$	−6.49248	+	4.71706i	−0.378007	+	0.274638i
$296$	−2.74888			−0.159776
$297$		0			0
$298$	−6.39176			−0.370264
$299$	16.6848	−	12.1222i	0.964909	−	0.701048i
$300$		0			0
$301$	−0.873193	+	2.68741i	−0.0503300	+	0.154900i
$302$	11.0402	+	8.02117i	0.635292	+	0.461566i
$303$		0			0
$304$	1.82119	−	5.60505i	0.104453	−	0.321472i
$305$	1.34129	+	4.12806i	0.0768019	+	0.236372i
$306$		0			0
$307$	3.01131			0.171865			0.0859323	−	0.996301i	$-0.472613\pi$
$307$	3.01131			0.171865			0.0859323	+	0.996301i	$0.472613\pi$
$308$	0.0603784	−	7.25018i	0.00344038	−	0.413117i
$309$		0			0
$310$	3.74888	−	2.72372i	0.212922	−	0.154697i
$311$	4.43520	+	13.6501i	0.251497	+	0.774028i	0.994500	+	0.104740i	$0.0334009\pi$
$311$	4.43520	+	13.6501i	0.251497	+	0.774028i	−0.743003	+	0.669288i	$0.766599\pi$
$312$		0			0
$313$	−18.2502	−	13.2595i	−1.03156	−	0.749473i	−0.0629406	−	0.998017i	$-0.520048\pi$
$313$	−18.2502	−	13.2595i	−1.03156	−	0.749473i	−0.968621	+	0.248544i	$0.920048\pi$
$314$	17.8022	+	12.9341i	1.00464	+	0.729912i
$315$		0			0
$316$	0.537165	+	1.65322i	0.0302179	+	0.0930011i
$317$	7.33634	−	5.33016i	0.412050	−	0.299372i	−0.362381	−	0.932030i	$-0.618036\pi$
$317$	7.33634	−	5.33016i	0.412050	−	0.299372i	0.774431	+	0.632658i	$0.218036\pi$
$318$		0			0
$319$	−19.9580	+	6.30150i	−1.11744	+	0.352816i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−2.20254	−	6.77871i	−0.122743	−	0.377763i
$323$	−3.03777	+	9.34930i	−0.169026	+	0.520209i
$324$		0			0
$325$	5.11739	+	3.71800i	0.283862	+	0.206238i
$326$	−2.59956	+	8.00064i	−0.143977	+	0.443114i
$327$		0			0
$328$	−7.57696	+	5.50498i	−0.418368	+	0.303962i
$329$	4.12076			0.227185
$330$		0			0
$331$	−24.4809			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$331$	−24.4809			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$332$	7.25616	−	5.27191i	0.398234	−	0.289334i
$333$		0			0
$334$	−3.65682	+	11.2545i	−0.200092	+	0.615821i
$335$	4.54405	+	3.30144i	0.248268	+	0.180377i
$336$		0			0
$337$	2.63571	−	8.11189i	0.143576	−	0.441883i	−0.853249	−	0.521504i	$-0.825371\pi$
$337$	2.63571	−	8.11189i	0.143576	−	0.441883i	0.996825	+	0.0796214i	$0.0253711\pi$
$338$	8.34694	+	25.6892i	0.454014	+	1.39731i
$339$		0			0
$340$	1.66801			0.0904608
$341$	14.5766	+	4.87078i	0.789365	+	0.263768i
$342$		0			0
$343$	−16.3081	+	11.8486i	−0.880556	+	0.639762i
$344$	0.399432	+	1.22932i	0.0215359	+	0.0662807i
$345$		0			0
$346$	11.6056	+	8.43193i	0.623919	+	0.453304i
$347$	−7.73014	−	5.61627i	−0.414975	−	0.301497i	0.360638	−	0.932706i	$-0.382559\pi$
$347$	−7.73014	−	5.61627i	−0.414975	−	0.301497i	−0.775613	+	0.631209i	$0.782559\pi$
$348$		0			0
$349$	6.47788	+	19.9369i	0.346753	+	1.06720i	0.960639	+	0.277801i	$0.0896057\pi$
$349$	6.47788	+	19.9369i	0.346753	+	1.06720i	−0.613885	+	0.789395i	$0.710394\pi$
$350$	1.76858	−	1.28495i	0.0945347	−	0.0686835i
$351$		0			0
$352$	−1.92705	−	2.69935i	−0.102712	−	0.143876i
$353$	−7.85985			−0.418338			−0.209169	−	0.977880i	$-0.567076\pi$
$353$	−7.85985			−0.418338			−0.209169	+	0.977880i	$0.567076\pi$
$354$		0			0
$355$	4.26042	+	13.1122i	0.226119	+	0.695924i
$356$	−4.13021	+	12.7115i	−0.218901	+	0.673707i
$357$		0			0
$358$	9.82624	+	7.13918i	0.519333	+	0.377317i
$359$	−1.94348	+	5.98142i	−0.102573	+	0.315687i	−0.989153	−	0.146888i	$-0.953074\pi$
$359$	−1.94348	+	5.98142i	−0.102573	+	0.315687i	0.886580	+	0.462575i	$0.153074\pi$
$360$		0			0
$361$	−12.7285	+	9.24783i	−0.669923	+	0.486728i
$362$	−6.40386			−0.336579
$363$		0			0
$364$	13.8280			0.724783
$365$	11.3199	−	8.22440i	0.592511	−	0.430485i
$366$		0			0
$367$	1.38246	−	4.25476i	0.0721636	−	0.222097i	−0.908469	−	0.417952i	$-0.862748\pi$
$367$	1.38246	−	4.25476i	0.0721636	−	0.222097i	0.980633	+	0.195855i	$0.0627482\pi$
$368$	−2.63773	−	1.91643i	−0.137501	−	0.0999006i
$369$		0			0
$370$	0.849452	−	2.61434i	0.0441609	−	0.135913i
$371$	5.31150	+	16.3471i	0.275759	+	0.848699i
$372$		0			0
$373$	29.4655			1.52567			0.762833	−	0.646596i	$-0.223808\pi$
$373$	29.4655			1.52567			0.762833	+	0.646596i	$0.223808\pi$
$374$	3.21435	+	4.50255i	0.166210	+	0.232821i
$375$		0			0
$376$	1.52499	−	1.10797i	0.0786454	−	0.0571392i
$377$	−12.3347	−	37.9624i	−0.635272	−	1.95517i
$378$		0			0
$379$	−7.33961	−	5.33254i	−0.377010	−	0.273914i	0.383102	−	0.923706i	$-0.374856\pi$
$379$	−7.33961	−	5.33254i	−0.377010	−	0.273914i	−0.760112	+	0.649792i	$0.774856\pi$
$380$	4.76794	+	3.46411i	0.244590	+	0.177705i
$381$		0			0
$382$	−4.25112	−	13.0836i	−0.217506	−	0.669415i
$383$	−6.29724	+	4.57521i	−0.321774	+	0.233782i	−0.736932	−	0.675967i	$-0.763726\pi$
$383$	−6.29724	+	4.57521i	−0.321774	+	0.233782i	0.415158	+	0.909749i	$0.363726\pi$
$384$		0			0
$385$	6.87668	+	2.29785i	0.350468	+	0.117109i
$386$	−10.9443			−0.557049
$387$		0			0
$388$	3.71558	+	11.4354i	0.188630	+	0.580543i
$389$	−6.21448	+	19.1262i	−0.315087	+	0.969737i	0.660632	+	0.750710i	$0.270288\pi$
$389$	−6.21448	+	19.1262i	−0.315087	+	0.969737i	−0.975719	+	0.219027i	$0.929712\pi$
$390$		0			0
$391$	4.39978	+	3.19662i	0.222506	+	0.161660i
$392$	−0.686333	+	2.11231i	−0.0346650	+	0.106688i
$393$		0			0
$394$	9.63645	−	7.00129i	0.485477	−	0.352720i
$395$	−1.73830			−0.0874634
$396$		0			0
$397$	18.0218			0.904488			0.452244	−	0.891894i	$-0.350624\pi$
$397$	18.0218			0.904488			0.452244	+	0.891894i	$0.350624\pi$
$398$	12.3485	−	8.97172i	0.618975	−	0.449712i
$399$		0			0
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	6.96852	+	5.06293i	0.347991	+	0.252831i	0.748026	−	0.663670i	$-0.231002\pi$
$401$	6.96852	+	5.06293i	0.347991	+	0.252831i	−0.400035	+	0.916500i	$0.631002\pi$
$402$		0			0
$403$	−9.05770	+	27.8767i	−0.451196	+	1.38864i
$404$	0.381966	+	1.17557i	0.0190035	+	0.0584868i
$405$		0			0
$406$	−13.7951			−0.684639
$407$	8.69396	−	2.74501i	0.430943	−	0.136065i
$408$		0			0
$409$	20.4587	−	14.8641i	1.01162	−	0.734983i	0.0470691	−	0.998892i	$-0.485012\pi$
$409$	20.4587	−	14.8641i	1.01162	−	0.734983i	0.964548	+	0.263909i	$0.0850119\pi$
$410$	−2.89414	−	8.90725i	−0.142931	−	0.439898i
$411$		0			0
$412$	15.0767	+	10.9539i	0.742776	+	0.539659i
$413$	−14.1931	−	10.3119i	−0.698398	−	0.507416i
$414$		0			0
$415$	2.77161	+	8.53013i	0.136053	+	0.418728i
$416$	5.11739	−	3.71800i	0.250901	−	0.182290i
$417$		0			0
$418$	−0.162775	+	19.5459i	−0.00796158	+	0.956019i
$419$	3.97713			0.194296			0.0971478	−	0.995270i	$-0.469028\pi$
$419$	3.97713			0.194296			0.0971478	+	0.995270i	$0.469028\pi$
$420$		0			0
$421$	−2.67126	−	8.22131i	−0.130189	−	0.400682i	0.864621	−	0.502424i	$-0.167558\pi$
$421$	−2.67126	−	8.22131i	−0.130189	−	0.400682i	−0.994811	+	0.101742i	$0.967558\pi$
$422$	1.15357	−	3.55033i	0.0561551	−	0.172828i
$423$		0			0
$424$	6.36099	+	4.62153i	0.308917	+	0.224441i
$425$	−0.515445	+	1.58638i	−0.0250027	+	0.0769505i
$426$		0			0
$427$	−7.67652	+	5.57732i	−0.371493	+	0.269905i
$428$	−9.94348			−0.480636
$429$		0			0
$430$	−1.29259			−0.0623341
$431$	−10.6253	+	7.71970i	−0.511801	+	0.371845i	−0.813506	−	0.581556i	$-0.802444\pi$
$431$	−10.6253	+	7.71970i	−0.511801	+	0.371845i	0.301705	+	0.953401i	$0.402444\pi$
$432$		0			0
$433$	−2.19526	+	6.75631i	−0.105497	+	0.324687i	−0.989847	−	0.142138i	$-0.954602\pi$
$433$	−2.19526	+	6.75631i	−0.105497	+	0.324687i	0.884350	+	0.466825i	$0.154602\pi$
$434$	8.19539	+	5.95430i	0.393391	+	0.285815i
$435$		0			0
$436$	1.48718	−	4.57708i	0.0712232	−	0.219203i
$437$	5.93785	+	18.2748i	0.284046	+	0.874203i
$438$		0			0
$439$	−8.09996			−0.386590			−0.193295	−	0.981141i	$-0.561917\pi$
$439$	−8.09996			−0.386590			−0.193295	+	0.981141i	$0.561917\pi$
$440$	3.16272	−	0.998590i	0.150777	−	0.0476059i
$441$		0			0
$442$	−8.53588	+	6.20168i	−0.406011	+	0.294984i
$443$	−1.52979	−	4.70821i	−0.0726826	−	0.223694i	0.908116	−	0.418720i	$-0.137521\pi$
$443$	−1.52979	−	4.70821i	−0.0726826	−	0.223694i	−0.980798	+	0.195026i	$0.937521\pi$
$444$		0			0
$445$	−10.8130	−	7.85612i	−0.512587	−	0.372416i
$446$	15.6872	+	11.3974i	0.742812	+	0.539684i
$447$		0			0
$448$	−0.675538	−	2.07909i	−0.0319162	−	0.0982279i
$449$	−6.77645	+	4.92338i	−0.319800	+	0.232349i	−0.736090	−	0.676883i	$-0.763330\pi$
$449$	−6.77645	+	4.92338i	−0.319800	+	0.232349i	0.416290	+	0.909232i	$0.363330\pi$
$450$		0			0
$451$	18.4666	−	24.9770i	0.869558	−	1.17612i
$452$	1.06582			0.0501320
$453$		0			0
$454$	−1.85068	−	5.69581i	−0.0868568	−	0.267318i
$455$	−4.27308	+	13.1512i	−0.200325	+	0.616537i
$456$		0			0
$457$	13.4199	+	9.75011i	0.627755	+	0.456091i	0.855622	−	0.517602i	$-0.173175\pi$
$457$	13.4199	+	9.75011i	0.627755	+	0.456091i	−0.227867	+	0.973692i	$0.573175\pi$
$458$	5.14541	−	15.8359i	0.240429	−	0.739965i
$459$		0			0
$460$	2.63773	−	1.91643i	0.122985	−	0.0893538i
$461$	−20.8011			−0.968805			−0.484403	−	0.874845i	$-0.660963\pi$
$461$	−20.8011			−0.968805			−0.484403	+	0.874845i	$0.660963\pi$
$462$		0			0
$463$	−5.79409			−0.269274			−0.134637	−	0.990895i	$-0.542987\pi$
$463$	−5.79409			−0.269274			−0.134637	+	0.990895i	$0.542987\pi$
$464$	−5.10522	+	3.70916i	−0.237004	+	0.172193i
$465$		0			0
$466$	−2.97728	+	9.16311i	−0.137920	+	0.424473i
$467$	2.72453	+	1.97949i	0.126076	+	0.0915999i	0.649036	−	0.760757i	$-0.275172\pi$
$467$	2.72453	+	1.97949i	0.126076	+	0.0915999i	−0.522960	+	0.852357i	$0.675172\pi$
$468$		0			0
$469$	−3.79433	+	11.6778i	−0.175206	+	0.539229i
$470$	0.582494	+	1.79273i	0.0268685	+	0.0826926i
$471$		0			0
$472$	−8.02514			−0.369387
$473$	−2.49088	−	3.48914i	−0.114531	−	0.160431i
$474$		0			0
$475$	−4.76794	+	3.46411i	−0.218768	+	0.158944i
$476$	1.12681	+	3.46796i	0.0516471	+	0.158954i
$477$		0			0
$478$	9.68178	+	7.03423i	0.442834	+	0.321738i
$479$	−12.2763	−	8.91922i	−0.560917	−	0.407530i	0.270878	−	0.962614i	$-0.412686\pi$
$479$	−12.2763	−	8.91922i	−0.560917	−	0.407530i	−0.831794	+	0.555084i	$0.812686\pi$
$480$		0			0
$481$	5.37316	+	16.5369i	0.244995	+	0.754017i
$482$	7.82417	−	5.68459i	0.356381	−	0.258926i
$483$		0			0
$484$	8.79027	+	6.61295i	0.399558	+	0.300589i
$485$	−12.0239			−0.545975
$486$		0			0
$487$	3.96507	+	12.2032i	0.179674	+	0.552981i	0.999816	−	0.0191795i	$-0.00610541\pi$
$487$	3.96507	+	12.2032i	0.179674	+	0.552981i	−0.820142	+	0.572161i	$0.806105\pi$
$488$	−1.34129	+	4.12806i	−0.0607172	+	0.186868i
$489$		0			0
$490$	−1.79684	−	1.30548i	−0.0811731	−	0.0589757i
$491$	4.34756	−	13.3804i	0.196203	−	0.603850i	−0.803758	−	0.594957i	$-0.797169\pi$
$491$	4.34756	−	13.3804i	0.196203	−	0.603850i	0.999960	−	0.00889318i	$-0.00283082\pi$
$492$		0			0
$493$	8.51558	−	6.18693i	0.383522	−	0.278645i
$494$	−37.2790			−1.67726
$495$		0			0
$496$	4.63387			0.208067
$497$	−24.3834	+	17.7156i	−1.09375	+	0.794654i
$498$		0			0
$499$	4.46624	−	13.7457i	0.199936	−	0.615340i	−0.799947	−	0.600070i	$-0.795139\pi$
$499$	4.46624	−	13.7457i	0.199936	−	0.615340i	0.999883	−	0.0152700i	$-0.00486078\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$		0			0
$502$	7.27773	−	22.3986i	0.324821	−	0.999696i
$503$	8.65278	+	26.6305i	0.385808	+	1.18740i	0.935892	+	0.352287i	$0.114596\pi$
$503$	8.65278	+	26.6305i	0.385808	+	1.18740i	−0.550084	+	0.835110i	$0.685404\pi$
$504$		0			0
$505$	−1.23607			−0.0550043
$506$	10.2561	+	3.42711i	0.455941	+	0.152354i
$507$		0			0
$508$	5.02802	−	3.65307i	0.223082	−	0.162079i
$509$	7.81214	+	24.0433i	0.346267	+	1.06570i	0.960902	+	0.276889i	$0.0893034\pi$
$509$	7.81214	+	24.0433i	0.346267	+	1.06570i	−0.614635	+	0.788812i	$0.710697\pi$
$510$		0			0
$511$	24.7463	+	17.9793i	1.09471	+	0.795355i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	5.09380	+	15.6771i	0.224678	+	0.691488i
$515$	−15.0767	+	10.9539i	−0.664359	+	0.482685i
$516$		0			0
$517$	−3.71671	+	5.02704i	−0.163461	+	0.221089i
$518$	6.00930			0.264034
$519$		0			0
$520$	1.95467	+	6.01586i	0.0857180	+	0.263813i
$521$	11.6676	−	35.9091i	0.511166	−	1.57321i	−0.278985	−	0.960296i	$-0.589998\pi$
$521$	11.6676	−	35.9091i	0.511166	−	1.57321i	0.790151	−	0.612912i	$-0.210002\pi$
$522$		0			0
$523$	−12.0268	−	8.73796i	−0.525894	−	0.382084i	0.292926	−	0.956135i	$-0.405371\pi$
$523$	−12.0268	−	8.73796i	−0.525894	−	0.382084i	−0.818820	+	0.574051i	$0.805371\pi$
$524$	−0.997371	+	3.06959i	−0.0435703	+	0.134096i
$525$		0			0
$526$	6.97150	−	5.06509i	0.303972	−	0.220848i
$527$	−7.72937			−0.336697
$528$		0			0
$529$	−12.3697			−0.537812
$530$	−6.36099	+	4.62153i	−0.276304	+	0.200746i
$531$		0			0
$532$	−3.98129	+	12.2531i	−0.172611	+	0.531241i
$533$	47.9276	+	34.8215i	2.07598	+	1.50829i
$534$		0			0
$535$	3.07270	−	9.45681i	0.132845	−	0.408854i
$536$	1.73567	+	5.34185i	0.0749696	+	0.230733i
$537$		0			0
$538$	15.4017			0.664016
$539$	0.0613432	−	7.36603i	0.00264224	−	0.317277i
$540$		0			0
$541$	18.4473	−	13.4027i	0.793111	−	0.576229i	−0.115774	−	0.993276i	$-0.536935\pi$
$541$	18.4473	−	13.4027i	0.793111	−	0.576229i	0.908885	+	0.417047i	$0.136935\pi$
$542$	1.65217	+	5.08487i	0.0709669	+	0.218414i
$543$		0			0
$544$	1.34945	+	0.980434i	0.0578573	+	0.0420358i
$545$	3.89350	+	2.82879i	0.166779	+	0.121172i
$546$		0			0
$547$	5.20860	+	16.0304i	0.222704	+	0.685411i	0.998517	+	0.0544484i	$0.0173400\pi$
$547$	5.20860	+	16.0304i	0.222704	+	0.685411i	−0.775813	+	0.630963i	$0.782660\pi$
$548$	12.9242	−	9.38996i	0.552093	−	0.401119i
$549$		0			0
$550$	−0.0276194	+	3.31651i	−0.00117769	+	0.141416i
$551$	37.1903			1.58436
$552$		0			0
$553$	−1.17429	−	3.61409i	−0.0499359	−	0.153687i
$554$	1.42363	−	4.38148i	0.0604842	−	0.186151i
$555$		0			0
$556$	−17.9883	−	13.0693i	−0.762875	−	0.554261i
$557$	−2.97951	+	9.16999i	−0.126246	+	0.388545i	−0.994126	−	0.108229i	$-0.965482\pi$
$557$	−2.97951	+	9.16999i	−0.126246	+	0.388545i	0.867880	+	0.496774i	$0.165482\pi$
$558$		0			0
$559$	6.61468	−	4.80585i	0.279771	−	0.203266i
$560$	2.18609			0.0923791
$561$		0			0
$562$	20.4855			0.864128
$563$	−8.26339	+	6.00370i	−0.348260	+	0.253026i	−0.748139	−	0.663542i	$-0.769052\pi$
$563$	−8.26339	+	6.00370i	−0.348260	+	0.253026i	0.399878	+	0.916568i	$0.369052\pi$
$564$		0			0
$565$	−0.329357	+	1.01366i	−0.0138561	+	0.0426448i
$566$	3.35108	+	2.43470i	0.140856	+	0.102338i
$567$		0			0
$568$	−4.26042	+	13.1122i	−0.178763	+	0.550176i
$569$	−6.78339	−	20.8771i	−0.284374	−	0.875214i	−0.986585	−	0.163245i	$-0.947804\pi$
$569$	−6.78339	−	20.8771i	−0.284374	−	0.875214i	0.702211	−	0.711969i	$-0.252196\pi$
$570$		0			0
$571$	37.5878			1.57300			0.786501	−	0.617589i	$-0.211891\pi$
$571$	37.5878			1.57300			0.786501	+	0.617589i	$0.211891\pi$
$572$	−12.4721	+	16.8692i	−0.521486	+	0.705337i
$573$		0			0
$574$	16.5639	−	12.0344i	0.691364	−	0.502305i
$575$	1.00752	+	3.10084i	0.0420167	+	0.129314i
$576$		0			0
$577$	15.4225	+	11.2051i	0.642047	+	0.466475i	0.860553	−	0.509361i	$-0.170118\pi$
$577$	15.4225	+	11.2051i	0.642047	+	0.466475i	−0.218506	+	0.975836i	$0.570118\pi$
$578$	11.5024	+	8.35697i	0.478436	+	0.347604i
$579$		0			0
$580$	−1.95002	−	6.00154i	−0.0809702	−	0.249201i
$581$	−15.8626	+	11.5249i	−0.658092	+	0.478132i
$582$		0			0
$583$	−24.7330	−	8.26459i	−1.02434	−	0.342284i
$584$	13.9922			0.579000
$585$		0			0
$586$	6.03267	+	18.5666i	0.249207	+	0.766981i
$587$	−8.13953	+	25.0509i	−0.335954	+	1.03396i	0.630296	+	0.776355i	$0.282934\pi$
$587$	−8.13953	+	25.0509i	−0.335954	+	1.03396i	−0.966250	+	0.257606i	$0.917066\pi$
$588$		0			0
$589$	−22.0940	−	16.0523i	−0.910369	−	0.661422i
$590$	2.47991	−	7.63236i	0.102096	−	0.314219i
$591$		0			0
$592$	2.22389	−	1.61575i	0.0914014	−	0.0664070i
$593$	−21.9693			−0.902173			−0.451087	−	0.892480i	$-0.648963\pi$
$593$	−21.9693			−0.902173			−0.451087	+	0.892480i	$0.648963\pi$
$594$		0			0
$595$	−3.64643			−0.149489
$596$	5.17104	−	3.75698i	0.211814	−	0.153892i
$597$		0			0
$598$	−6.37304	+	19.6142i	−0.260613	+	0.802084i
$599$	22.7727	+	16.5454i	0.930469	+	0.676025i	0.946108	−	0.323852i	$-0.104978\pi$
$599$	22.7727	+	16.5454i	0.930469	+	0.676025i	−0.0156386	+	0.999878i	$0.504978\pi$
$600$		0			0
$601$	−8.86288	+	27.2771i	−0.361524	+	1.11266i	0.590605	+	0.806961i	$0.298889\pi$
$601$	−8.86288	+	27.2771i	−0.361524	+	1.11266i	−0.952129	+	0.305696i	$0.901111\pi$
$602$	−0.873193	−	2.68741i	−0.0355887	−	0.109531i
$603$		0			0
$604$	−13.6464			−0.555265
$605$	−9.00563	+	6.31653i	−0.366131	+	0.256803i
$606$		0			0
$607$	−18.5387	+	13.4692i	−0.752465	+	0.546698i	−0.896590	−	0.442862i	$-0.853963\pi$
$607$	−18.5387	+	13.4692i	−0.752465	+	0.546698i	0.144125	+	0.989559i	$0.453963\pi$
$608$	1.82119	+	5.60505i	0.0738591	+	0.227315i
$609$		0			0
$610$	−3.51153	−	2.55128i	−0.142178	−	0.103298i
$611$	−9.64624	−	7.00841i	−0.390245	−	0.283530i
$612$		0			0
$613$	12.7915	+	39.3683i	0.516645	+	1.59007i	0.780269	+	0.625444i	$0.215082\pi$
$613$	12.7915	+	39.3683i	0.516645	+	1.59007i	−0.263624	+	0.964626i	$0.584918\pi$
$614$	−2.43620	+	1.77000i	−0.0983170	+	0.0714315i
$615$		0			0
$616$	4.21270	+	5.90101i	0.169735	+	0.237758i
$617$	13.7801			0.554765			0.277382	−	0.960760i	$-0.410533\pi$
$617$	13.7801			0.554765			0.277382	+	0.960760i	$0.410533\pi$
$618$		0			0
$619$	6.93772	+	21.3521i	0.278851	+	0.858214i	0.988175	+	0.153331i	$0.0490002\pi$
$619$	6.93772	+	21.3521i	0.278851	+	0.858214i	−0.709324	+	0.704882i	$0.751000\pi$
$620$	−1.43195	+	4.40708i	−0.0575083	+	0.176992i
$621$		0			0
$622$	−11.6115	−	8.43624i	−0.465578	−	0.338263i
$623$	9.02900	−	27.7884i	0.361739	−	1.11332i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	22.5585			0.901618
$627$		0			0
$628$	−22.0048			−0.878086
$629$	−3.70948	+	2.69510i	−0.147907	+	0.107461i
$630$		0			0
$631$	13.5301	−	41.6415i	0.538626	−	1.65772i	−0.197055	−	0.980393i	$-0.563138\pi$
$631$	13.5301	−	41.6415i	0.538626	−	1.65772i	0.735681	−	0.677328i	$-0.236862\pi$
$632$	−1.40632	−	1.02175i	−0.0559402	−	0.0406430i
$633$		0			0
$634$	−2.80223	+	8.62438i	−0.111291	+	0.342518i
$635$	1.92053	+	5.91079i	0.0762139	+	0.234562i
$636$		0			0
$637$	14.0489			0.556639
$638$	12.4425	−	16.8291i	0.492602	−	0.666269i
$639$		0			0
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	−11.3033	−	34.7881i	−0.446455	−	1.37405i	−0.880881	−	0.473339i	$-0.843049\pi$
$641$	−11.3033	−	34.7881i	−0.446455	−	1.37405i	0.434426	−	0.900708i	$-0.356951\pi$
$642$		0			0
$643$	9.35931	+	6.79994i	0.369095	+	0.268163i	0.756836	−	0.653605i	$-0.226744\pi$
$643$	9.35931	+	6.79994i	0.369095	+	0.268163i	−0.387740	+	0.921769i	$0.626744\pi$
$644$	5.76632	+	4.18947i	0.227225	+	0.165088i
$645$		0			0
$646$	−3.03777	−	9.34930i	−0.119520	−	0.367843i
$647$	20.1803	−	14.6619i	0.793371	−	0.576418i	−0.115591	−	0.993297i	$-0.536876\pi$
$647$	20.1803	−	14.6619i	0.793371	−	0.576418i	0.908962	+	0.416879i	$0.136876\pi$
$648$		0			0
$649$	25.3813	−	8.01383i	0.996303	−	0.314570i
$650$	−6.32545			−0.248104
$651$		0			0
$652$	−2.59956	−	8.00064i	−0.101807	−	0.313329i
$653$	−0.614175	+	1.89024i	−0.0240345	+	0.0739707i	−0.962354	−	0.271798i	$-0.912382\pi$
$653$	−0.614175	+	1.89024i	−0.0240345	+	0.0739707i	0.938320	+	0.345769i	$0.112382\pi$
$654$		0			0
$655$	−2.61115	−	1.89711i	−0.102026	−	0.0741263i
$656$	2.89414	−	8.90725i	0.112997	−	0.347770i
$657$		0			0
$658$	−3.33376	+	2.42212i	−0.129964	+	0.0944241i
$659$	−20.4602			−0.797018			−0.398509	−	0.917165i	$-0.630472\pi$
$659$	−20.4602			−0.797018			−0.398509	+	0.917165i	$0.630472\pi$
$660$		0			0
$661$	−24.5565			−0.955135			−0.477568	−	0.878595i	$-0.658481\pi$
$661$	−24.5565			−0.955135			−0.477568	+	0.878595i	$0.658481\pi$
$662$	19.8055	−	14.3895i	0.769763	−	0.559265i
$663$		0			0
$664$	−2.77161	+	8.53013i	−0.107559	+	0.331033i
$665$	−10.4231	−	7.57285i	−0.404192	−	0.293663i
$666$		0			0
$667$	6.35788	−	19.5675i	0.246178	−	0.757658i
$668$	−3.65682	−	11.2545i	−0.141487	−	0.435451i
$669$		0			0
$670$	−5.61675			−0.216994
$671$	0.119882	−	14.3953i	0.00462799	−	0.555724i
$672$		0			0
$673$	28.1064	−	20.4205i	1.08342	−	0.787151i	0.105144	−	0.994457i	$-0.466470\pi$
$673$	28.1064	−	20.4205i	1.08342	−	0.787151i	0.978276	+	0.207306i	$0.0664696\pi$
$674$	2.63571	+	8.11189i	0.101524	+	0.312458i
$675$		0			0
$676$	−21.8526	−	15.8768i	−0.840484	−	0.610647i
$677$	32.0961	+	23.3192i	1.23355	+	0.896229i	0.997151	−	0.0754258i	$-0.0240316\pi$
$677$	32.0961	+	23.3192i	1.23355	+	0.896229i	0.236403	+	0.971655i	$0.424032\pi$
$678$		0			0
$679$	−8.12258	−	24.9987i	−0.311716	−	0.959363i
$680$	−1.34945	+	0.980434i	−0.0517491	+	0.0375979i
$681$		0			0
$682$	−14.6557	+	4.62734i	−0.561194	+	0.177190i
$683$	−39.6464			−1.51703			−0.758514	−	0.651657i	$-0.774074\pi$
$683$	−39.6464			−1.51703			−0.758514	+	0.651657i	$0.774074\pi$
$684$		0			0
$685$	4.93660	+	15.1933i	0.188618	+	0.580505i
$686$	6.22915	−	19.1714i	0.237830	−	0.731966i
$687$		0			0
$688$	−1.04573	−	0.759764i	−0.0398679	−	0.0289657i
$689$	15.3688	−	47.3003i	0.585505	−	1.80200i
$690$		0			0
$691$	−15.4284	+	11.2094i	−0.586925	+	0.426426i	−0.841214	−	0.540702i	$-0.818159\pi$
$691$	−15.4284	+	11.2094i	−0.586925	+	0.426426i	0.254289	+	0.967128i	$0.418159\pi$
$692$	−14.3453			−0.545325
$693$		0			0
$694$	9.55497			0.362702
$695$	17.9883	−	13.0693i	0.682336	−	0.495746i
$696$		0			0
$697$	−4.82747	+	14.8574i	−0.182853	+	0.562765i
$698$	−16.9593	−	12.3217i	−0.641920	−	0.466382i
$699$		0			0
$700$	−0.675538	+	2.07909i	−0.0255329	+	0.0785823i
$701$	−3.42136	−	10.5299i	−0.129223	−	0.397708i	0.865424	−	0.501041i	$-0.167049\pi$
$701$	−3.42136	−	10.5299i	−0.129223	−	0.397708i	−0.994647	+	0.103333i	$0.967049\pi$
$702$		0			0
$703$	−16.2005			−0.611015
$704$	3.14565	+	1.05113i	0.118556	+	0.0396158i
$705$		0			0
$706$	6.35875	−	4.61990i	0.239315	−	0.173872i
$707$	−0.835011	−	2.56990i	−0.0314038	−	0.0966511i
$708$		0			0
$709$	21.3229	+	15.4920i	0.800798	+	0.581814i	0.911148	−	0.412079i	$-0.135197\pi$
$709$	21.3229	+	15.4920i	0.800798	+	0.581814i	−0.110350	+	0.993893i	$0.535197\pi$
$710$	−11.1539	−	8.10380i	−0.418599	−	0.304130i
$711$		0			0
$712$	−4.13021	−	12.7115i	−0.154786	−	0.476383i
$713$	−12.2229	+	8.88047i	−0.457752	+	0.332576i
$714$		0			0
$715$	−12.1895	−	17.0746i	−0.455860	−	0.638553i
$716$	−12.1459			−0.453914
$717$		0			0
$718$	−1.94348	−	5.98142i	−0.0725300	−	0.223225i
$719$	−2.01657	+	6.20636i	−0.0752053	+	0.231458i	−0.981592	−	0.190992i	$-0.938830\pi$
$719$	−2.01657	+	6.20636i	−0.0752053	+	0.231458i	0.906386	+	0.422450i	$0.138830\pi$
$720$		0			0
$721$	−32.9590	−	23.9461i	−1.22746	−	0.891801i
$722$	4.86187	−	14.9633i	0.180940	−	0.556876i
$723$		0			0
$724$	5.18083	−	3.76409i	0.192544	−	0.139891i
$725$	6.31040			0.234362
$726$		0			0
$727$	−38.4232			−1.42504			−0.712519	−	0.701653i	$-0.752446\pi$
$727$	−38.4232			−1.42504			−0.712519	+	0.701653i	$0.752446\pi$
$728$	−11.1871	+	8.12788i	−0.414620	+	0.301239i
$729$		0			0
$730$	−4.32382	+	13.3074i	−0.160032	+	0.492527i
$731$	1.74428	+	1.26730i	0.0645147	+	0.0468727i
$732$		0			0
$733$	1.19539	−	3.67903i	0.0441527	−	0.135888i	−0.926550	−	0.376171i	$-0.877240\pi$
$733$	1.19539	−	3.67903i	0.0441527	−	0.135888i	0.970703	+	0.240283i	$0.0772404\pi$
$734$	1.38246	+	4.25476i	0.0510274	+	0.157046i
$735$		0			0
$736$	3.26042			0.120181
$737$	−10.8238	−	15.1616i	−0.398699	−	0.558483i
$738$		0			0
$739$	−3.67758	+	2.67192i	−0.135282	+	0.0982881i	−0.653368	−	0.757040i	$-0.726645\pi$
$739$	−3.67758	+	2.67192i	−0.135282	+	0.0982881i	0.518086	+	0.855328i	$0.326645\pi$
$740$	0.849452	+	2.61434i	0.0312265	+	0.0961052i
$741$		0			0
$742$	−13.9057	−	10.1031i	−0.510493	−	0.370895i
$743$	5.04931	+	3.66854i	0.185241	+	0.134586i	0.676541	−	0.736405i	$-0.263478\pi$
$743$	5.04931	+	3.66854i	0.185241	+	0.134586i	−0.491300	+	0.870990i	$0.663478\pi$
$744$		0			0
$745$	1.97516	+	6.07892i	0.0723643	+	0.222714i
$746$	−23.8381	+	17.3194i	−0.872774	+	0.634108i
$747$		0			0
$748$	−5.24699	−	1.75329i	−0.191849	−	0.0641067i
$749$	21.7373			0.794264
$750$		0			0
$751$	6.65297	+	20.4757i	0.242770	+	0.747170i	0.995995	+	0.0894068i	$0.0284971\pi$
$751$	6.65297	+	20.4757i	0.242770	+	0.747170i	−0.753225	+	0.657763i	$0.771503\pi$
$752$	−0.582494	+	1.79273i	−0.0212414	+	0.0653743i
$753$		0			0
$754$	32.2928	+	23.4621i	1.17603	+	0.854439i
$755$	4.21698	−	12.9785i	0.153472	−	0.472337i
$756$		0			0
$757$	22.6882	−	16.4839i	0.824617	−	0.599119i	−0.0934143	−	0.995627i	$-0.529778\pi$
$757$	22.6882	−	16.4839i	0.824617	−	0.599119i	0.918031	+	0.396508i	$0.129778\pi$
$758$	9.07226			0.329519
$759$		0			0
$760$	−5.89350			−0.213780
$761$	37.7869	−	27.4538i	1.36977	−	0.995198i	0.372018	−	0.928226i	$-0.378666\pi$
$761$	37.7869	−	27.4538i	1.36977	−	0.995198i	0.997755	−	0.0669722i	$-0.0213339\pi$
$762$		0			0
$763$	−3.25112	+	10.0059i	−0.117698	+	0.362238i
$764$	11.1296	+	8.08610i	0.402654	+	0.292545i
$765$		0			0
$766$	2.40533	−	7.40285i	0.0869081	−	0.267476i
$767$	15.6865	+	48.2781i	0.566407	+	1.74322i
$768$		0			0
$769$	−43.7091			−1.57619			−0.788095	−	0.615554i	$-0.788932\pi$
$769$	−43.7091			−1.57619			−0.788095	+	0.615554i	$0.788932\pi$
$770$	−6.91399	+	2.18301i	−0.249163	+	0.0786701i
$771$		0			0
$772$	8.85410	−	6.43288i	0.318666	−	0.231524i
$773$	4.68783	+	14.4276i	0.168609	+	0.518926i	0.999284	−	0.0378317i	$-0.0120451\pi$
$773$	4.68783	+	14.4276i	0.168609	+	0.518926i	−0.830675	+	0.556758i	$0.812045\pi$
$774$		0			0
$775$	−3.74888	−	2.72372i	−0.134664	−	0.0978390i
$776$	−9.72751	−	7.06745i	−0.349197	−	0.253707i
$777$		0			0
$778$	−6.21448	−	19.1262i	−0.222800	−	0.685708i
$779$	−44.6548	+	32.4436i	−1.59992	+	1.16241i
$780$		0			0
$781$	0.380789	−	45.7247i	0.0136257	−	1.63616i
$782$	−5.43842			−0.194478
$783$		0			0
$784$	−0.686333	−	2.11231i	−0.0245119	−	0.0754398i
$785$	6.79985	−	20.9278i	0.242697	−	0.746944i
$786$		0			0
$787$	20.5684	+	14.9438i	0.733184	+	0.532690i	0.890569	−	0.454848i	$-0.150306\pi$
$787$	20.5684	+	14.9438i	0.733184	+	0.532690i	−0.157385	+	0.987537i	$0.550306\pi$
$788$	−3.68080	+	11.3283i	−0.131123	+	0.403555i
$789$		0			0
$790$	1.40632	−	1.02175i	0.0500345	−	0.0363522i
$791$	−2.32998			−0.0828445
$792$		0			0
$793$	27.4556			0.974976
$794$	−14.5799	+	10.5929i	−0.517422	+	0.375929i
$795$		0			0
$796$	−4.71671	+	14.5165i	−0.167179	+	0.514525i
$797$	20.1437	+	14.6353i	0.713527	+	0.518408i	0.884310	−	0.466901i	$-0.154630\pi$
$797$	20.1437	+	14.6353i	0.713527	+	0.518408i	−0.170783	+	0.985309i	$0.554630\pi$
$798$		0			0
$799$	0.971609	−	2.99030i	0.0343730	−	0.105789i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$		0			0
$802$	−8.61357			−0.304156
$803$	−44.2534	+	13.9725i	−1.56167	+	0.493077i
$804$		0			0
$805$	−5.76632	+	4.18947i	−0.203236	+	0.147660i
$806$	−9.05770	−	27.8767i	−0.319044	−	0.981916i
$807$		0			0
$808$	−1.00000	−	0.726543i	−0.0351799	−	0.0255597i
$809$	7.24534	+	5.26405i	0.254732	+	0.185074i	0.707822	−	0.706391i	$-0.249678\pi$
$809$	7.24534	+	5.26405i	0.254732	+	0.185074i	−0.453089	+	0.891465i	$0.649678\pi$
$810$		0			0
$811$	−5.94284	−	18.2902i	−0.208681	−	0.642255i	−0.999542	−	0.0302590i	$-0.990367\pi$
$811$	−5.94284	−	18.2902i	−0.208681	−	0.642255i	0.790861	−	0.611996i	$-0.209633\pi$
$812$	11.1605	−	8.10855i	0.391655	−	0.284554i
$813$		0			0
$814$	−5.42008	+	7.33094i	−0.189974	+	0.256949i
$815$	8.41237			0.294672
$816$		0			0
$817$	2.35405	+	7.24502i	0.0823578	+	0.253471i
$818$	−7.81452	+	24.0506i	−0.273228	+	0.840910i
$819$		0			0
$820$	7.57696	+	5.50498i	0.264599	+	0.192242i
$821$	−4.18658	+	12.8850i	−0.146113	+	0.449688i	−0.997152	−	0.0754129i	$-0.975973\pi$
$821$	−4.18658	+	12.8850i	−0.146113	+	0.449688i	0.851040	+	0.525101i	$0.175973\pi$
$822$		0			0
$823$	7.64605	−	5.55518i	0.266525	−	0.193641i	−0.446494	−	0.894787i	$-0.647328\pi$
$823$	7.64605	−	5.55518i	0.266525	−	0.193641i	0.713018	+	0.701145i	$0.247328\pi$
$824$	−18.6358			−0.649210
$825$		0			0
$826$	17.5437			0.610422
$827$	30.8750	−	22.4320i	1.07363	−	0.780036i	0.0970666	−	0.995278i	$-0.469054\pi$
$827$	30.8750	−	22.4320i	1.07363	−	0.780036i	0.976561	+	0.215242i	$0.0690540\pi$
$828$		0			0
$829$	−15.2096	+	46.8105i	−0.528253	+	1.62580i	0.229540	+	0.973299i	$0.426278\pi$
$829$	−15.2096	+	46.8105i	−0.528253	+	1.62580i	−0.757792	+	0.652496i	$0.773722\pi$
$830$	−7.25616	−	5.27191i	−0.251865	−	0.182991i
$831$		0			0
$832$	−1.95467	+	6.01586i	−0.0677660	+	0.208562i
$833$	1.14481	+	3.52337i	0.0396654	+	0.122078i
$834$		0			0
$835$	11.8337			0.409523
$836$	−11.3571	−	15.9086i	−0.392793	−	0.550211i
$837$		0			0
$838$	−3.21757	+	2.33770i	−0.111149	+	0.0807545i
$839$	−13.4241	−	41.3152i	−0.463452	−	1.42636i	−0.860919	−	0.508743i	$-0.830110\pi$
$839$	−13.4241	−	41.3152i	−0.463452	−	1.42636i	0.397466	−	0.917617i	$-0.369890\pi$
$840$		0			0
$841$	−8.75447	−	6.36049i	−0.301878	−	0.219327i
$842$	6.99346	+	5.08105i	0.241011	+	0.175104i
$843$		0			0
$844$	1.15357	+	3.55033i	0.0397076	+	0.122208i
$845$	21.8526	−	15.8768i	0.751751	−	0.546179i
$846$		0			0
$847$	−19.2163	−	14.4565i	−0.660280	−	0.496731i
$848$	−7.86261			−0.270003
$849$		0			0
$850$	−0.515445	−	1.58638i	−0.0176796	−	0.0544122i
$851$	−2.76957	+	8.52385i	−0.0949395	+	0.292194i
$852$		0			0
$853$	−31.6722	−	23.0112i	−1.08443	−	0.787888i	−0.105984	−	0.994368i	$-0.533799\pi$
$853$	−31.6722	−	23.0112i	−1.08443	−	0.787888i	−0.978451	+	0.206480i	$0.933799\pi$
$854$	2.93217	−	9.02429i	0.100337	−	0.308805i
$855$		0			0
$856$	8.04444	−	5.84463i	0.274953	−	0.199765i
$857$	7.40798			0.253052			0.126526	−	0.991963i	$-0.459617\pi$
$857$	7.40798			0.253052			0.126526	+	0.991963i	$0.459617\pi$
$858$		0			0
$859$	−12.2156			−0.416792			−0.208396	−	0.978045i	$-0.566824\pi$
$859$	−12.2156			−0.416792			−0.208396	+	0.978045i	$0.566824\pi$
$860$	1.04573	−	0.759764i	0.0356589	−	0.0259077i
$861$		0			0
$862$	4.05849	−	12.4907i	0.138233	−	0.425436i
$863$	−41.7007	−	30.2973i	−1.41951	−	1.03133i	−0.991853	−	0.127391i	$-0.959340\pi$
$863$	−41.7007	−	30.2973i	−1.41951	−	1.03133i	−0.427656	−	0.903942i	$-0.640660\pi$
$864$		0			0
$865$	4.43293	−	13.6432i	0.150724	−	0.463881i
$866$	−2.19526	−	6.75631i	−0.0745979	−	0.229589i
$867$		0			0
$868$	−10.1301			−0.343837
$869$	5.46809	+	1.82717i	0.185492	+	0.0619826i
$870$		0			0
$871$	28.7431	−	20.8831i	0.973924	−	0.707597i
$872$	1.48718	+	4.57708i	0.0503624	+	0.155000i
$873$		0			0
$874$	−15.5455	−	11.2945i	−0.525834	−	0.382041i
$875$	−1.76858	−	1.28495i	−0.0597890	−	0.0434392i
$876$		0			0
$877$	−4.34545	−	13.3739i	−0.146735	−	0.451605i	0.850495	−	0.525984i	$-0.176303\pi$
$877$	−4.34545	−	13.3739i	−0.146735	−	0.451605i	−0.997230	+	0.0743786i	$0.976303\pi$
$878$	6.55301	−	4.76104i	0.221153	−	0.160677i
$879$		0			0
$880$	−1.97174	+	2.66688i	−0.0664673	+	0.0899005i
$881$	−53.6578			−1.80778			−0.903889	−	0.427767i	$-0.859300\pi$
$881$	−53.6578			−1.80778			−0.903889	+	0.427767i	$0.859300\pi$
$882$		0			0
$883$	−4.51566	−	13.8978i	−0.151964	−	0.467697i	0.845877	−	0.533379i	$-0.179078\pi$
$883$	−4.51566	−	13.8978i	−0.151964	−	0.467697i	−0.997841	+	0.0656815i	$0.979078\pi$
$884$	3.26042	−	10.0345i	0.109660	−	0.337498i
$885$		0			0
$886$	4.00505	+	2.90984i	0.134552	+	0.0977579i
$887$	0.153422	−	0.472186i	0.00515142	−	0.0158544i	−0.948448	−	0.316933i	$-0.897347\pi$
$887$	0.153422	−	0.472186i	0.00515142	−	0.0158544i	0.953599	+	0.301079i	$0.0973468\pi$
$888$		0			0
$889$	−10.9917	+	7.98593i	−0.368649	+	0.267839i
$890$	13.3656			0.448017
$891$		0			0
$892$	−19.3905			−0.649241
$893$	8.98753	−	6.52982i	0.300756	−	0.218512i
$894$		0			0
$895$	3.75329	−	11.5514i	0.125459	−	0.386122i
$896$	1.76858	+	1.28495i	0.0590842	+	0.0429272i
$897$		0			0
$898$	2.58837	−	7.96620i	0.0863752	−	0.265835i
$899$	9.03615	+	27.8104i	0.301372	+	0.927529i
$900$		0			0
$901$	13.1149			0.436922
$902$	−0.258673	+	31.0612i	−0.00861288	+	1.03423i
$903$		0			0
$904$	−0.862267	+	0.626474i	−0.0286786	+	0.0208362i
$905$	1.97890	+	6.09043i	0.0657809	+	0.202453i
$906$		0			0
$907$	−19.8576	−	14.4274i	−0.659362	−	0.479054i	0.207086	−	0.978323i	$-0.433602\pi$
$907$	−19.8576	−	14.4274i	−0.659362	−	0.479054i	−0.866447	+	0.499268i	$0.833602\pi$
$908$	4.84515	+	3.52020i	0.160792	+	0.116822i
$909$		0			0
$910$	−4.27308	−	13.1512i	−0.141651	−	0.435958i
$911$	26.6748	−	19.3803i	0.883774	−	0.642099i	−0.0504732	−	0.998725i	$-0.516073\pi$
$911$	26.6748	−	19.3803i	0.883774	−	0.642099i	0.934247	+	0.356626i	$0.116073\pi$
$912$		0			0
$913$	0.247721	−	29.7461i	0.00819838	−	0.984454i
$914$	−16.5879			−0.548678
$915$		0			0
$916$	5.14541	+	15.8359i	0.170009	+	0.523234i
$917$	2.18034	−	6.71040i	0.0720012	−	0.221597i
$918$		0			0
$919$	21.5867	+	15.6836i	0.712078	+	0.517355i	0.883843	−	0.467783i	$-0.154947\pi$
$919$	21.5867	+	15.6836i	0.712078	+	0.517355i	−0.171765	+	0.985138i	$0.554947\pi$
$920$	−1.00752	+	3.10084i	−0.0332171	+	0.102232i
$921$		0			0
$922$	16.8285	−	12.2266i	0.554216	−	0.402662i
$923$	87.2089			2.87052
$924$		0			0
$925$	−2.74888			−0.0903827
$926$	4.68752	−	3.40568i	0.154041	−	0.111918i
$927$		0			0
$928$	1.95002	−	6.00154i	0.0640125	−	0.197010i
$929$	−10.2252	−	7.42906i	−0.335479	−	0.243740i	0.407273	−	0.913306i	$-0.366480\pi$
$929$	−10.2252	−	7.42906i	−0.335479	−	0.243740i	−0.742752	+	0.669567i	$0.766480\pi$
$930$		0			0
$931$	−4.04490	+	12.4489i	−0.132566	+	0.407997i
$932$	−2.97728	−	9.16311i	−0.0975239	−	0.300148i
$933$		0			0
$934$	−3.36771			−0.110195
$935$	3.28889	−	4.44839i	0.107558	−	0.145478i
$936$		0			0
$937$	−47.4472	+	34.4724i	−1.55003	+	1.12616i	−0.606402	+	0.795158i	$0.707388\pi$
$937$	−47.4472	+	34.4724i	−1.55003	+	1.12616i	−0.943629	+	0.331005i	$0.892612\pi$
$938$	−3.79433	−	11.6778i	−0.123889	−	0.381292i
$939$		0			0
$940$	−1.52499	−	1.10797i	−0.0497397	−	0.0361380i
$941$	−30.2547	−	21.9813i	−0.986274	−	0.716570i	−0.0271720	−	0.999631i	$-0.508650\pi$
$941$	−30.2547	−	21.9813i	−0.986274	−	0.716570i	−0.959102	+	0.283061i	$0.908650\pi$
$942$		0			0
$943$	9.43611	+	29.0414i	0.307282	+	0.945717i
$944$	6.49248	−	4.71706i	0.211312	−	0.153527i
$945$		0			0
$946$	4.06603	+	1.35867i	0.132198	+	0.0441742i
$947$	−57.0728			−1.85462			−0.927308	−	0.374298i	$-0.877884\pi$
$947$	−57.0728			−1.85462			−0.927308	+	0.374298i	$0.877884\pi$
$948$		0			0
$949$	−27.3501	−	84.1749i	−0.887822	−	2.73243i
$950$	1.82119	−	5.60505i	0.0590873	−	0.181852i
$951$		0			0
$952$	−2.95002	−	2.14332i	−0.0956107	−	0.0694652i
$953$	−0.804955	+	2.47740i	−0.0260751	+	0.0802508i	−0.963247	−	0.268616i	$-0.913434\pi$
$953$	−0.804955	+	2.47740i	−0.0260751	+	0.0802508i	0.937172	+	0.348867i	$0.113434\pi$
$954$		0			0
$955$	−11.1296	+	8.08610i	−0.360144	+	0.261660i
$956$	−11.9673			−0.387051
$957$		0			0
$958$	15.1743			0.490259
$959$	−28.2534	+	20.5273i	−0.912349	+	0.662861i
$960$		0			0
$961$	−2.94407	+	9.06091i	−0.0949700	+	0.292287i
$962$	−14.0671	−	10.2204i	−0.453542	−	0.329518i
$963$		0			0
$964$	−2.98857	+	9.19786i	−0.0962552	+	0.296243i
$965$	3.38197	+	10.4086i	0.108869	+	0.335065i
$966$		0			0
$967$	5.55100			0.178508			0.0892540	−	0.996009i	$-0.471552\pi$
$967$	5.55100			0.178508			0.0892540	+	0.996009i	$0.471552\pi$
$968$	−10.9985	−	0.183200i	−0.353504	−	0.00588827i
$969$		0			0
$970$	9.72751	−	7.06745i	0.312331	−	0.226922i
$971$	10.8588	+	33.4200i	0.348476	+	1.07250i	0.959696	+	0.281039i	$0.0906791\pi$
$971$	10.8588	+	33.4200i	0.348476	+	1.07250i	−0.611220	+	0.791461i	$0.709321\pi$
$972$		0			0
$973$	39.3241	+	28.5706i	1.26067	+	0.915931i
$974$	−10.3807	−	7.54201i	−0.332619	−	0.241662i
$975$		0			0
$976$	−1.34129	−	4.12806i	−0.0429335	−	0.132136i
$977$	−28.1587	+	20.4585i	−0.900876	+	0.654525i	−0.938691	−	0.344760i	$-0.887960\pi$
$977$	−28.1587	+	20.4585i	−0.900876	+	0.654525i	0.0378147	+	0.999285i	$0.487960\pi$
$978$		0			0
$979$	25.7563	+	36.0785i	0.823174	+	1.15307i
$980$	2.22102			0.0709479
$981$		0			0
$982$	4.34756	+	13.3804i	0.138736	+	0.426986i
$983$	7.03664	−	21.6566i	0.224434	−	0.690737i	−0.773914	−	0.633290i	$-0.781704\pi$
$983$	7.03664	−	21.6566i	0.224434	−	0.690737i	0.998349	−	0.0574469i	$-0.0182960\pi$
$984$		0			0
$985$	−9.63645	−	7.00129i	−0.307043	−	0.223080i
$986$	−3.25266	+	10.0107i	−0.103586	+	0.318804i
$987$		0			0
$988$	30.1594	−	21.9121i	0.959497	−	0.697115i
$989$	4.21438			0.134009
$990$		0			0
$991$	55.0090			1.74742			0.873709	−	0.486448i	$-0.161708\pi$
$991$	55.0090			1.74742			0.873709	+	0.486448i	$0.161708\pi$
$992$	−3.74888	+	2.72372i	−0.119027	+	0.0864783i
$993$		0			0
$994$	9.31365	−	28.6645i	0.295411	−	0.909181i
$995$	−12.3485	−	8.97172i	−0.391474	−	0.284423i
$996$		0			0
$997$	5.49445	−	16.9102i	0.174011	−	0.535551i	−0.825576	−	0.564291i	$-0.809150\pi$
$997$	5.49445	−	16.9102i	0.174011	−	0.535551i	0.999587	+	0.0287402i	$0.00914955\pi$
$998$	4.46624	+	13.7457i	0.141376	+	0.435111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.j.91.1		8
3.2	odd	2		110.2.g.c.91.1	yes	8
11.4	even	5	inner	990.2.n.j.631.1		8
12.11	even	2		880.2.bo.g.641.2		8
15.2	even	4		550.2.ba.f.399.3		16
15.8	even	4		550.2.ba.f.399.2		16
15.14	odd	2		550.2.h.l.201.2		8
33.2	even	10		1210.2.a.v.1.1		4
33.20	odd	10		1210.2.a.u.1.1		4
33.26	odd	10		110.2.g.c.81.1	✓	8
132.35	odd	10		9680.2.a.ci.1.4		4
132.59	even	10		880.2.bo.g.81.2		8
132.119	even	10		9680.2.a.cj.1.4		4
165.59	odd	10		550.2.h.l.301.2		8
165.92	even	20		550.2.ba.f.499.2		16
165.119	odd	10		6050.2.a.dh.1.4		4
165.134	even	10		6050.2.a.cy.1.4		4
165.158	even	20		550.2.ba.f.499.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.81.1	✓	8	33.26	odd	10
110.2.g.c.91.1	yes	8	3.2	odd	2
550.2.h.l.201.2		8	15.14	odd	2
550.2.h.l.301.2		8	165.59	odd	10
550.2.ba.f.399.2		16	15.8	even	4
550.2.ba.f.399.3		16	15.2	even	4
550.2.ba.f.499.2		16	165.92	even	20
550.2.ba.f.499.3		16	165.158	even	20
880.2.bo.g.81.2		8	132.59	even	10
880.2.bo.g.641.2		8	12.11	even	2
990.2.n.j.91.1		8	1.1	even	1	trivial
990.2.n.j.631.1		8	11.4	even	5	inner
1210.2.a.u.1.1		4	33.20	odd	10
1210.2.a.v.1.1		4	33.2	even	10
6050.2.a.cy.1.4		4	165.134	even	10
6050.2.a.dh.1.4		4	165.119	odd	10
9680.2.a.ci.1.4		4	132.35	odd	10
9680.2.a.cj.1.4		4	132.119	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.675538 + 2.07909i) q^{7} +(0.309017 + 0.951057i) q^{8} -1.00000 q^{10} +(-1.92705 - 2.69935i) q^{11} +(5.11739 - 3.71800i) q^{13} +(-0.675538 - 2.07909i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.34945 + 0.980434i) q^{17} +(1.82119 + 5.60505i) q^{19} +(0.809017 - 0.587785i) q^{20} +(3.14565 + 1.05113i) q^{22} +3.26042 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.95467 + 6.01586i) q^{26} +(1.76858 + 1.28495i) q^{28} +(1.95002 - 6.00154i) q^{29} +(-3.74888 + 2.72372i) q^{31} +1.00000 q^{32} -1.66801 q^{34} +(-1.76858 + 1.28495i) q^{35} +(-0.849452 + 2.61434i) q^{37} +(-4.76794 - 3.46411i) q^{38} +(-0.309017 + 0.951057i) q^{40} +(2.89414 + 8.90725i) q^{41} +1.29259 q^{43} +(-3.16272 + 0.998590i) q^{44} +(-2.63773 + 1.91643i) q^{46} +(-0.582494 - 1.79273i) q^{47} +(1.79684 + 1.30548i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.95467 - 6.01586i) q^{52} +(6.36099 - 4.62153i) q^{53} +(0.0276194 - 3.31651i) q^{55} -2.18609 q^{56} +(1.95002 + 6.00154i) q^{58} +(-2.47991 + 7.63236i) q^{59} +(3.51153 + 2.55128i) q^{61} +(1.43195 - 4.40708i) q^{62} +(-0.809017 + 0.587785i) q^{64} +6.32545 q^{65} +5.61675 q^{67} +(1.34945 - 0.980434i) q^{68} +(0.675538 - 2.07909i) q^{70} +(11.1539 + 8.10380i) q^{71} +(4.32382 - 13.3074i) q^{73} +(-0.849452 - 2.61434i) q^{74} +5.89350 q^{76} +(6.91399 - 2.18301i) q^{77} +(-1.40632 + 1.02175i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-7.57696 - 5.50498i) q^{82} +(7.25616 + 5.27191i) q^{83} +(0.515445 + 1.58638i) q^{85} +(-1.04573 + 0.759764i) q^{86} +(1.97174 - 2.66688i) q^{88} -13.3656 q^{89} +(4.27308 + 13.1512i) q^{91} +(1.00752 - 3.10084i) q^{92} +(1.52499 + 1.10797i) q^{94} +(-1.82119 + 5.60505i) q^{95} +(-9.72751 + 7.06745i) q^{97} -2.22102 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8} - 8 q^{10} - 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} - 26 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 22 q^{29}+ \cdots + 22 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8 - 8 * q^10 - 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 - 26 * q^23 - 2 * q^25 + 6 * q^26 + 4 * q^28 + 22 * q^29 - 26 * q^31 + 8 * q^32 + 2 * q^34 - 4 * q^35 - 8 * q^37 + 3 * q^38 + 2 * q^40 + 15 * q^41 + 38 * q^43 - 7 * q^44 - 6 * q^46 - 6 * q^47 + 27 * q^49 - 2 * q^50 + 6 * q^52 + 4 * q^53 - 8 * q^55 - 6 * q^56 + 22 * q^58 - 39 * q^59 - 20 * q^61 + 14 * q^62 - 2 * q^64 + 14 * q^65 - 26 * q^67 + 12 * q^68 + q^70 - 2 * q^71 + 8 * q^73 - 8 * q^74 + 8 * q^76 - 16 * q^77 + 14 * q^79 + 2 * q^80 - 15 * q^82 + 21 * q^83 + 13 * q^85 - 17 * q^86 - 7 * q^88 - 32 * q^89 + 53 * q^91 + 19 * q^92 + 9 * q^94 + 7 * q^95 - 31 * q^97 + 22 * q^98

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