LMFDB - Embedded newform 650.2.l.a.391.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			391.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	650.391
Dual form			650.2.l.a.261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.690983 + 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.309017 + 0.951057i) q^{8} +(-1.61803 + 1.17557i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.690983 + 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.309017 + 0.951057i) q^{8} +(-1.61803 + 1.17557i) q^{9} +(-0.690983 + 2.12663i) q^{10} +(1.11803 + 0.812299i) q^{11} +(-1.80902 + 1.31433i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-4.04508 + 2.93893i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.927051 - 2.85317i) q^{17} -2.00000 q^{18} +(0.881966 - 2.71441i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(0.427051 + 1.31433i) q^{22} +(-2.80902 - 2.04087i) q^{23} -2.23607 q^{24} +(-4.04508 + 2.93893i) q^{25} +1.00000 q^{26} +(1.80902 + 1.31433i) q^{27} +(-1.30902 - 4.02874i) q^{29} -5.00000 q^{30} +(-0.545085 + 1.67760i) q^{31} -1.00000 q^{32} +(-0.954915 + 2.93893i) q^{33} +(2.42705 - 1.76336i) q^{34} +(-1.61803 - 1.17557i) q^{36} +(7.35410 - 5.34307i) q^{37} +(2.30902 - 1.67760i) q^{38} +(1.80902 + 1.31433i) q^{39} -2.23607 q^{40} +(-1.80902 + 1.31433i) q^{41} +0.527864 q^{43} +(-0.427051 + 1.31433i) q^{44} +(-3.61803 - 2.62866i) q^{45} +(-1.07295 - 3.30220i) q^{46} +(-1.02786 - 3.16344i) q^{47} +(-1.80902 - 1.31433i) q^{48} -7.00000 q^{49} -5.00000 q^{50} +6.70820 q^{51} +(0.809017 + 0.587785i) q^{52} +(-1.16312 - 3.57971i) q^{53} +(0.690983 + 2.12663i) q^{54} +(-0.954915 + 2.93893i) q^{55} +6.38197 q^{57} +(1.30902 - 4.02874i) q^{58} +(-6.04508 + 4.39201i) q^{59} +(-4.04508 - 2.93893i) q^{60} +(7.73607 + 5.62058i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.80902 + 1.31433i) q^{65} +(-2.50000 + 1.81636i) q^{66} +(3.07295 - 9.45756i) q^{67} +3.00000 q^{68} +(2.39919 - 7.38394i) q^{69} +(-1.14590 - 3.52671i) q^{71} +(-0.618034 - 1.90211i) q^{72} +(4.04508 + 2.93893i) q^{73} +9.09017 q^{74} +(-9.04508 - 6.57164i) q^{75} +2.85410 q^{76} +(0.690983 + 2.12663i) q^{78} +(4.92705 + 15.1639i) q^{79} +(-1.80902 - 1.31433i) q^{80} +(-3.39919 + 10.4616i) q^{81} -2.23607 q^{82} +(-3.80902 + 11.7229i) q^{83} +6.70820 q^{85} +(0.427051 + 0.310271i) q^{86} +(7.66312 - 5.56758i) q^{87} +(-1.11803 + 0.812299i) q^{88} +(3.61803 + 2.62866i) q^{89} +(-1.38197 - 4.25325i) q^{90} +(1.07295 - 3.30220i) q^{92} -3.94427 q^{93} +(1.02786 - 3.16344i) q^{94} +6.38197 q^{95} +(-0.690983 - 2.12663i) q^{96} +(-2.90983 - 8.95554i) q^{97} +(-5.66312 - 4.11450i) q^{98} -2.76393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 5 q^{3} - q^{4} + 5 q^{5} - 5 q^{6} + q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + q^2 + 5 * q^3 - q^4 + 5 * q^5 - 5 * q^6 + q^8 - 2 * q^9	$ 4 q + q^{2} + 5 q^{3} - q^{4} + 5 q^{5} - 5 q^{6} + q^{8} - 2 q^{9} - 5 q^{10} - 5 q^{12} + q^{13} - 5 q^{15} - q^{16} - 3 q^{17} - 8 q^{18} + 8 q^{19} - 5 q^{20} - 5 q^{22} - 9 q^{23} - 5 q^{25} + 4 q^{26} + 5 q^{27} - 3 q^{29} - 20 q^{30} + 9 q^{31} - 4 q^{32} - 15 q^{33} + 3 q^{34} - 2 q^{36} + 16 q^{37} + 7 q^{38} + 5 q^{39} - 5 q^{41} + 20 q^{43} + 5 q^{44} - 10 q^{45} - 11 q^{46} - 22 q^{47} - 5 q^{48} - 28 q^{49} - 20 q^{50} + q^{52} + 11 q^{53} + 5 q^{54} - 15 q^{55} + 30 q^{57} + 3 q^{58} - 13 q^{59} - 5 q^{60} + 22 q^{61} + q^{62} - q^{64} + 5 q^{65} - 10 q^{66} + 19 q^{67} + 12 q^{68} - 15 q^{69} - 18 q^{71} + 2 q^{72} + 5 q^{73} + 14 q^{74} - 25 q^{75} - 2 q^{76} + 5 q^{78} + 13 q^{79} - 5 q^{80} + 11 q^{81} - 13 q^{83} - 5 q^{86} + 15 q^{87} + 10 q^{89} - 10 q^{90} + 11 q^{92} + 20 q^{93} + 22 q^{94} + 30 q^{95} - 5 q^{96} - 34 q^{97} - 7 q^{98} - 20 q^{99}+O(q^{100}) $ 4 * q + q^2 + 5 * q^3 - q^4 + 5 * q^5 - 5 * q^6 + q^8 - 2 * q^9 - 5 * q^10 - 5 * q^12 + q^13 - 5 * q^15 - q^16 - 3 * q^17 - 8 * q^18 + 8 * q^19 - 5 * q^20 - 5 * q^22 - 9 * q^23 - 5 * q^25 + 4 * q^26 + 5 * q^27 - 3 * q^29 - 20 * q^30 + 9 * q^31 - 4 * q^32 - 15 * q^33 + 3 * q^34 - 2 * q^36 + 16 * q^37 + 7 * q^38 + 5 * q^39 - 5 * q^41 + 20 * q^43 + 5 * q^44 - 10 * q^45 - 11 * q^46 - 22 * q^47 - 5 * q^48 - 28 * q^49 - 20 * q^50 + q^52 + 11 * q^53 + 5 * q^54 - 15 * q^55 + 30 * q^57 + 3 * q^58 - 13 * q^59 - 5 * q^60 + 22 * q^61 + q^62 - q^64 + 5 * q^65 - 10 * q^66 + 19 * q^67 + 12 * q^68 - 15 * q^69 - 18 * q^71 + 2 * q^72 + 5 * q^73 + 14 * q^74 - 25 * q^75 - 2 * q^76 + 5 * q^78 + 13 * q^79 - 5 * q^80 + 11 * q^81 - 13 * q^83 - 5 * q^86 + 15 * q^87 + 10 * q^89 - 10 * q^90 + 11 * q^92 + 20 * q^93 + 22 * q^94 + 30 * q^95 - 5 * q^96 - 34 * q^97 - 7 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	0.690983	+	2.12663i	0.398939	+	1.22781i	0.925851	+	0.377889i	$0.123350\pi$
$3$	0.690983	+	2.12663i	0.398939	+	1.22781i	−0.526912	+	0.849920i	$0.676650\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$6$	−0.690983	+	2.12663i	−0.282093	+	0.868192i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−1.61803	+	1.17557i	−0.539345	+	0.391857i
$10$	−0.690983	+	2.12663i	−0.218508	+	0.672499i
$11$	1.11803	+	0.812299i	0.337100	+	0.244917i	0.743437	−	0.668806i	$-0.233194\pi$
$11$	1.11803	+	0.812299i	0.337100	+	0.244917i	−0.406337	+	0.913723i	$0.633194\pi$
$12$	−1.80902	+	1.31433i	−0.522218	+	0.379414i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$		0			0
$15$	−4.04508	+	2.93893i	−1.04444	+	0.758827i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.927051	−	2.85317i	0.224843	−	0.691995i	−0.773465	−	0.633839i	$-0.781478\pi$
$17$	0.927051	−	2.85317i	0.224843	−	0.691995i	0.998308	−	0.0581558i	$-0.0185220\pi$
$18$	−2.00000			−0.471405
$19$	0.881966	−	2.71441i	0.202337	−	0.622729i	−0.797475	−	0.603352i	$-0.793832\pi$
$19$	0.881966	−	2.71441i	0.202337	−	0.622729i	0.999812	−	0.0193774i	$-0.00616839\pi$
$20$	−1.80902	+	1.31433i	−0.404508	+	0.293893i
$21$		0			0
$22$	0.427051	+	1.31433i	0.0910476	+	0.280216i
$23$	−2.80902	−	2.04087i	−0.585721	−	0.425551i	0.255061	−	0.966925i	$-0.417904\pi$
$23$	−2.80902	−	2.04087i	−0.585721	−	0.425551i	−0.840782	+	0.541374i	$0.817904\pi$
$24$	−2.23607			−0.456435
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	1.00000			0.196116
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$		0			0
$29$	−1.30902	−	4.02874i	−0.243078	−	0.748118i	−0.995947	−	0.0899469i	$-0.971330\pi$
$29$	−1.30902	−	4.02874i	−0.243078	−	0.748118i	0.752868	−	0.658171i	$-0.228670\pi$
$30$	−5.00000			−0.912871
$31$	−0.545085	+	1.67760i	−0.0979002	+	0.301306i	−0.987999	−	0.154463i	$-0.950635\pi$
$31$	−0.545085	+	1.67760i	−0.0979002	+	0.301306i	0.890098	+	0.455768i	$0.150635\pi$
$32$	−1.00000			−0.176777
$33$	−0.954915	+	2.93893i	−0.166229	+	0.511601i
$34$	2.42705	−	1.76336i	0.416236	−	0.302413i
$35$		0			0
$36$	−1.61803	−	1.17557i	−0.269672	−	0.195928i
$37$	7.35410	−	5.34307i	1.20901	−	0.878395i	0.213867	−	0.976863i	$-0.431394\pi$
$37$	7.35410	−	5.34307i	1.20901	−	0.878395i	0.995140	+	0.0984679i	$0.0313942\pi$
$38$	2.30902	−	1.67760i	0.374572	−	0.272143i
$39$	1.80902	+	1.31433i	0.289675	+	0.210461i
$40$	−2.23607			−0.353553
$41$	−1.80902	+	1.31433i	−0.282521	+	0.205264i	−0.720016	−	0.693957i	$-0.755866\pi$
$41$	−1.80902	+	1.31433i	−0.282521	+	0.205264i	0.437495	+	0.899221i	$0.355866\pi$
$42$		0			0
$43$	0.527864			0.0804985			0.0402493	−	0.999190i	$-0.487185\pi$
$43$	0.527864			0.0804985			0.0402493	+	0.999190i	$0.487185\pi$
$44$	−0.427051	+	1.31433i	−0.0643804	+	0.198142i
$45$	−3.61803	−	2.62866i	−0.539345	−	0.391857i
$46$	−1.07295	−	3.30220i	−0.158198	−	0.486882i
$47$	−1.02786	−	3.16344i	−0.149929	−	0.461435i	0.847683	−	0.530504i	$-0.177997\pi$
$47$	−1.02786	−	3.16344i	−0.149929	−	0.461435i	−0.997612	+	0.0690687i	$0.977997\pi$
$48$	−1.80902	−	1.31433i	−0.261109	−	0.189707i
$49$	−7.00000			−1.00000
$50$	−5.00000			−0.707107
$51$	6.70820			0.939336
$52$	0.809017	+	0.587785i	0.112190	+	0.0815111i
$53$	−1.16312	−	3.57971i	−0.159767	−	0.491711i	0.838846	−	0.544369i	$-0.183231\pi$
$53$	−1.16312	−	3.57971i	−0.159767	−	0.491711i	−0.998613	+	0.0526576i	$0.983231\pi$
$54$	0.690983	+	2.12663i	0.0940309	+	0.289397i
$55$	−0.954915	+	2.93893i	−0.128761	+	0.396285i
$56$		0			0
$57$	6.38197			0.845312
$58$	1.30902	−	4.02874i	0.171882	−	0.528999i
$59$	−6.04508	+	4.39201i	−0.787003	+	0.571791i	−0.907073	−	0.420974i	$-0.861688\pi$
$59$	−6.04508	+	4.39201i	−0.787003	+	0.571791i	0.120070	+	0.992765i	$0.461688\pi$
$60$	−4.04508	−	2.93893i	−0.522218	−	0.379414i
$61$	7.73607	+	5.62058i	0.990502	+	0.719642i	0.960031	−	0.279894i	$-0.0902993\pi$
$61$	7.73607	+	5.62058i	0.990502	+	0.719642i	0.0304710	+	0.999536i	$0.490299\pi$
$62$	−1.42705	+	1.03681i	−0.181236	+	0.131675i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.80902	+	1.31433i	0.224381	+	0.163022i
$66$	−2.50000	+	1.81636i	−0.307729	+	0.223578i
$67$	3.07295	−	9.45756i	0.375420	−	1.15543i	−0.567774	−	0.823184i	$-0.692195\pi$
$67$	3.07295	−	9.45756i	0.375420	−	1.15543i	0.943195	−	0.332241i	$-0.107805\pi$
$68$	3.00000			0.363803
$69$	2.39919	−	7.38394i	0.288828	−	0.888922i
$70$		0			0
$71$	−1.14590	−	3.52671i	−0.135993	−	0.418544i	0.859750	−	0.510715i	$-0.170619\pi$
$71$	−1.14590	−	3.52671i	−0.135993	−	0.418544i	−0.995743	+	0.0921713i	$0.970619\pi$
$72$	−0.618034	−	1.90211i	−0.0728360	−	0.224166i
$73$	4.04508	+	2.93893i	0.473441	+	0.343975i	0.798781	−	0.601622i	$-0.205479\pi$
$73$	4.04508	+	2.93893i	0.473441	+	0.343975i	−0.325340	+	0.945597i	$0.605479\pi$
$74$	9.09017			1.05671
$75$	−9.04508	−	6.57164i	−1.04444	−	0.758827i
$76$	2.85410			0.327388
$77$		0			0
$78$	0.690983	+	2.12663i	0.0782384	+	0.240793i
$79$	4.92705	+	15.1639i	0.554337	+	1.70607i	0.697689	+	0.716401i	$0.254212\pi$
$79$	4.92705	+	15.1639i	0.554337	+	1.70607i	−0.143352	+	0.989672i	$0.545788\pi$
$80$	−1.80902	−	1.31433i	−0.202254	−	0.146946i
$81$	−3.39919	+	10.4616i	−0.377687	+	1.16240i
$82$	−2.23607			−0.246932
$83$	−3.80902	+	11.7229i	−0.418094	+	1.28676i	0.491360	+	0.870956i	$0.336500\pi$
$83$	−3.80902	+	11.7229i	−0.418094	+	1.28676i	−0.909454	+	0.415804i	$0.863500\pi$
$84$		0			0
$85$	6.70820			0.727607
$86$	0.427051	+	0.310271i	0.0460501	+	0.0334574i
$87$	7.66312	−	5.56758i	0.821573	−	0.596907i
$88$	−1.11803	+	0.812299i	−0.119183	+	0.0865914i
$89$	3.61803	+	2.62866i	0.383511	+	0.278637i	0.762791	−	0.646645i	$-0.223828\pi$
$89$	3.61803	+	2.62866i	0.383511	+	0.278637i	−0.379280	+	0.925282i	$0.623828\pi$
$90$	−1.38197	−	4.25325i	−0.145672	−	0.448332i
$91$		0			0
$92$	1.07295	−	3.30220i	0.111863	−	0.344278i
$93$	−3.94427			−0.409002
$94$	1.02786	−	3.16344i	0.106016	−	0.326284i
$95$	6.38197			0.654776
$96$	−0.690983	−	2.12663i	−0.0705232	−	0.217048i
$97$	−2.90983	−	8.95554i	−0.295448	−	0.909297i	−0.983070	−	0.183228i	$-0.941345\pi$
$97$	−2.90983	−	8.95554i	−0.295448	−	0.909297i	0.687622	−	0.726069i	$-0.258655\pi$
$98$	−5.66312	−	4.11450i	−0.572061	−	0.415627i
$99$	−2.76393			−0.277786
$100$	−4.04508	−	2.93893i	−0.404508	−	0.293893i
$101$	−7.61803			−0.758023			−0.379011	−	0.925392i	$-0.623736\pi$
$101$	−7.61803			−0.758023			−0.379011	+	0.925392i	$0.623736\pi$
$102$	5.42705	+	3.94298i	0.537358	+	0.390414i
$103$	1.50000	+	4.61653i	0.147799	+	0.454880i	0.997360	−	0.0726107i	$-0.0231331\pi$
$103$	1.50000	+	4.61653i	0.147799	+	0.454880i	−0.849561	+	0.527490i	$0.823133\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$		0			0
$106$	1.16312	−	3.57971i	0.112972	−	0.347692i
$107$	6.38197			0.616968			0.308484	−	0.951230i	$-0.400178\pi$
$107$	6.38197			0.616968			0.308484	+	0.951230i	$0.400178\pi$
$108$	−0.690983	+	2.12663i	−0.0664899	+	0.204635i
$109$	6.35410	−	4.61653i	0.608613	−	0.442183i	−0.240313	−	0.970695i	$-0.577250\pi$
$109$	6.35410	−	4.61653i	0.608613	−	0.442183i	0.848925	+	0.528513i	$0.177250\pi$
$110$	−2.50000	+	1.81636i	−0.238366	+	0.173183i
$111$	16.4443	+	11.9475i	1.56082	+	1.13400i
$112$		0			0
$113$	10.5451	−	7.66145i	0.991998	−	0.720729i	0.0316404	−	0.999499i	$-0.489927\pi$
$113$	10.5451	−	7.66145i	0.991998	−	0.720729i	0.960358	+	0.278770i	$0.0899269\pi$
$114$	5.16312	+	3.75123i	0.483570	+	0.351334i
$115$	2.39919	−	7.38394i	0.223725	−	0.688556i
$116$	3.42705	−	2.48990i	0.318194	−	0.231181i
$117$	−0.618034	+	1.90211i	−0.0571373	+	0.175850i
$118$	−7.47214			−0.687866
$119$		0			0
$120$	−1.54508	−	4.75528i	−0.141046	−	0.434096i
$121$	−2.80902	−	8.64527i	−0.255365	−	0.785933i
$122$	2.95492	+	9.09429i	0.267525	+	0.823359i
$123$	−4.04508	−	2.93893i	−0.364733	−	0.264994i
$124$	−1.76393			−0.158406
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$		0			0
$127$	−4.47214	−	3.24920i	−0.396838	−	0.288320i	0.371414	−	0.928467i	$-0.378873\pi$
$127$	−4.47214	−	3.24920i	−0.396838	−	0.288320i	−0.768252	+	0.640148i	$0.778873\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.364745	+	1.12257i	0.0321140	+	0.0988368i
$130$	0.690983	+	2.12663i	0.0606032	+	0.186518i
$131$	−5.20820	+	16.0292i	−0.455043	+	1.40048i	0.416042	+	0.909345i	$0.363417\pi$
$131$	−5.20820	+	16.0292i	−0.455043	+	1.40048i	−0.871085	+	0.491133i	$0.836583\pi$
$132$	−3.09017			−0.268965
$133$		0			0
$134$	8.04508	−	5.84510i	0.694989	−	0.504939i
$135$	−1.54508	+	4.75528i	−0.132980	+	0.409270i
$136$	2.42705	+	1.76336i	0.208118	+	0.151207i
$137$	6.42705	−	4.66953i	0.549100	−	0.398945i	−0.278354	−	0.960479i	$-0.589789\pi$
$137$	6.42705	−	4.66953i	0.549100	−	0.398945i	0.827454	+	0.561534i	$0.189789\pi$
$138$	6.28115	−	4.56352i	0.534687	−	0.388473i
$139$	7.35410	+	5.34307i	0.623767	+	0.453193i	0.854235	−	0.519887i	$-0.174026\pi$
$139$	7.35410	+	5.34307i	0.623767	+	0.453193i	−0.230468	+	0.973080i	$0.574026\pi$
$140$		0			0
$141$	6.01722	−	4.37177i	0.506741	−	0.368169i
$142$	1.14590	−	3.52671i	0.0961616	−	0.295955i
$143$	1.38197			0.115566
$144$	0.618034	−	1.90211i	0.0515028	−	0.158509i
$145$	7.66312	−	5.56758i	0.636387	−	0.462363i
$146$	1.54508	+	4.75528i	0.127872	+	0.393550i
$147$	−4.83688	−	14.8864i	−0.398939	−	1.22781i
$148$	7.35410	+	5.34307i	0.604503	+	0.439197i
$149$	−0.381966			−0.0312919			−0.0156459	−	0.999878i	$-0.504980\pi$
$149$	−0.381966			−0.0312919			−0.0156459	+	0.999878i	$0.504980\pi$
$150$	−3.45492	−	10.6331i	−0.282093	−	0.868192i
$151$	−6.70820			−0.545906			−0.272953	−	0.962027i	$-0.588000\pi$
$151$	−6.70820			−0.545906			−0.272953	+	0.962027i	$0.588000\pi$
$152$	2.30902	+	1.67760i	0.187286	+	0.136071i
$153$	1.85410	+	5.70634i	0.149895	+	0.461330i
$154$		0			0
$155$	−3.94427			−0.316812
$156$	−0.690983	+	2.12663i	−0.0553229	+	0.170266i
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	−4.92705	+	15.1639i	−0.391975	+	1.20638i
$159$	6.80902	−	4.94704i	0.539990	−	0.392326i
$160$	−0.690983	−	2.12663i	−0.0546270	−	0.168125i
$161$		0			0
$162$	−8.89919	+	6.46564i	−0.699186	+	0.507988i
$163$	−5.42705	+	3.94298i	−0.425079	+	0.308838i	−0.779678	−	0.626180i	$-0.784617\pi$
$163$	−5.42705	+	3.94298i	−0.425079	+	0.308838i	0.354599	+	0.935019i	$0.384617\pi$
$164$	−1.80902	−	1.31433i	−0.141260	−	0.102632i
$165$	−6.90983			−0.537930
$166$	−9.97214	+	7.24518i	−0.773988	+	0.562335i
$167$	5.48278	−	16.8743i	0.424270	−	1.30577i	−0.479421	−	0.877585i	$-0.659153\pi$
$167$	5.48278	−	16.8743i	0.424270	−	1.30577i	0.903691	−	0.428184i	$-0.140847\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	5.42705	+	3.94298i	0.416236	+	0.302413i
$171$	1.76393	+	5.42882i	0.134891	+	0.415153i
$172$	0.163119	+	0.502029i	0.0124377	+	0.0382793i
$173$	−6.89919	−	5.01255i	−0.524535	−	0.381097i	0.293774	−	0.955875i	$-0.405089\pi$
$173$	−6.89919	−	5.01255i	−0.524535	−	0.381097i	−0.818310	+	0.574777i	$0.805089\pi$
$174$	9.47214			0.718081
$175$		0			0
$176$	−1.38197			−0.104170
$177$	−13.5172	−	9.82084i	−1.01602	−	0.738179i
$178$	1.38197	+	4.25325i	0.103583	+	0.318795i
$179$	2.19098	+	6.74315i	0.163762	+	0.504007i	0.998943	−	0.0459681i	$-0.0146373\pi$
$179$	2.19098	+	6.74315i	0.163762	+	0.504007i	−0.835181	+	0.549975i	$0.814637\pi$
$180$	1.38197	−	4.25325i	0.103006	−	0.317019i
$181$	6.30902	−	19.4172i	0.468946	−	1.44327i	−0.385006	−	0.922914i	$-0.625801\pi$
$181$	6.30902	−	19.4172i	0.468946	−	1.44327i	0.853952	−	0.520352i	$-0.174199\pi$
$182$		0			0
$183$	−6.60739	+	20.3355i	−0.488432	+	1.50324i
$184$	2.80902	−	2.04087i	0.207083	−	0.150455i
$185$	16.4443	+	11.9475i	1.20901	+	0.878395i
$186$	−3.19098	−	2.31838i	−0.233974	−	0.169992i
$187$	3.35410	−	2.43690i	0.245276	−	0.178204i
$188$	2.69098	−	1.95511i	0.196260	−	0.142591i
$189$		0			0
$190$	5.16312	+	3.75123i	0.374572	+	0.272143i
$191$	−20.0623	+	14.5761i	−1.45166	+	1.05469i	−0.466217	+	0.884670i	$0.654383\pi$
$191$	−20.0623	+	14.5761i	−1.45166	+	1.05469i	−0.985441	+	0.170021i	$0.945617\pi$
$192$	0.690983	−	2.12663i	0.0498674	−	0.153476i
$193$	−12.4721			−0.897764			−0.448882	−	0.893591i	$-0.648178\pi$
$193$	−12.4721			−0.897764			−0.448882	+	0.893591i	$0.648178\pi$
$194$	2.90983	−	8.95554i	0.208914	−	0.642970i
$195$	−1.54508	+	4.75528i	−0.110646	+	0.340533i
$196$	−2.16312	−	6.65740i	−0.154508	−	0.475528i
$197$	−4.06231	−	12.5025i	−0.289427	−	0.890766i	−0.985037	−	0.172345i	$-0.944865\pi$
$197$	−4.06231	−	12.5025i	−0.289427	−	0.890766i	0.695609	−	0.718420i	$-0.255135\pi$
$198$	−2.23607	−	1.62460i	−0.158910	−	0.115455i
$199$	18.2705			1.29516			0.647581	−	0.761997i	$-0.275781\pi$
$199$	18.2705			1.29516			0.647581	+	0.761997i	$0.275781\pi$
$200$	−1.54508	−	4.75528i	−0.109254	−	0.336249i
$201$	22.2361			1.56841
$202$	−6.16312	−	4.47777i	−0.433636	−	0.315055i
$203$		0			0
$204$	2.07295	+	6.37988i	0.145135	+	0.446681i
$205$	−4.04508	−	2.93893i	−0.282521	−	0.205264i
$206$	−1.50000	+	4.61653i	−0.104510	+	0.321649i
$207$	6.94427			0.482660
$208$	−0.309017	+	0.951057i	−0.0214265	+	0.0659439i
$209$	3.19098	−	2.31838i	0.220725	−	0.160366i
$210$		0			0
$211$	−4.61803	−	3.35520i	−0.317919	−	0.230981i	0.417368	−	0.908737i	$-0.362953\pi$
$211$	−4.61803	−	3.35520i	−0.317919	−	0.230981i	−0.735287	+	0.677756i	$0.762953\pi$
$212$	3.04508	−	2.21238i	0.209137	−	0.151947i
$213$	6.70820	−	4.87380i	0.459639	−	0.333947i
$214$	5.16312	+	3.75123i	0.352944	+	0.256428i
$215$	0.364745	+	1.12257i	0.0248754	+	0.0765586i
$216$	−1.80902	+	1.31433i	−0.123088	+	0.0894287i
$217$		0			0
$218$	7.85410			0.531947
$219$	−3.45492	+	10.6331i	−0.233462	+	0.718521i
$220$	−3.09017			−0.208339
$221$	−0.927051	−	2.85317i	−0.0623602	−	0.191925i
$222$	6.28115	+	19.3314i	0.421563	+	1.29744i
$223$	−4.50000	−	3.26944i	−0.301342	−	0.218938i	0.426830	−	0.904332i	$-0.359630\pi$
$223$	−4.50000	−	3.26944i	−0.301342	−	0.218938i	−0.728173	+	0.685394i	$0.759630\pi$
$224$		0			0
$225$	3.09017	−	9.51057i	0.206011	−	0.634038i
$226$	13.0344			0.867038
$227$	−13.7812	−	10.0126i	−0.914687	−	0.664559i	0.0275087	−	0.999622i	$-0.491243\pi$
$227$	−13.7812	−	10.0126i	−0.914687	−	0.664559i	−0.942196	+	0.335062i	$0.891243\pi$
$228$	1.97214	+	6.06961i	0.130608	+	0.401970i
$229$	−8.29180	−	25.5195i	−0.547937	−	1.68638i	−0.713902	−	0.700246i	$-0.753074\pi$
$229$	−8.29180	−	25.5195i	−0.547937	−	1.68638i	0.165964	−	0.986132i	$-0.446926\pi$
$230$	6.28115	−	4.56352i	0.414167	−	0.300910i
$231$		0			0
$232$	4.23607			0.278111
$233$	−5.64590	+	17.3763i	−0.369875	+	1.13836i	0.576997	+	0.816747i	$0.304225\pi$
$233$	−5.64590	+	17.3763i	−0.369875	+	1.13836i	−0.946872	+	0.321612i	$0.895775\pi$
$234$	−1.61803	+	1.17557i	−0.105774	+	0.0768494i
$235$	6.01722	−	4.37177i	0.392520	−	0.285183i
$236$	−6.04508	−	4.39201i	−0.393502	−	0.285896i
$237$	−28.8435	+	20.9560i	−1.87358	+	1.36124i
$238$		0			0
$239$	4.57295	+	3.32244i	0.295799	+	0.214911i	0.725779	−	0.687928i	$-0.241479\pi$
$239$	4.57295	+	3.32244i	0.295799	+	0.214911i	−0.429980	+	0.902838i	$0.641479\pi$
$240$	1.54508	−	4.75528i	0.0997348	−	0.306952i
$241$	1.30902	−	0.951057i	0.0843212	−	0.0612629i	−0.544826	−	0.838549i	$-0.683404\pi$
$241$	1.30902	−	0.951057i	0.0843212	−	0.0612629i	0.629147	+	0.777286i	$0.283404\pi$
$242$	2.80902	−	8.64527i	0.180570	−	0.555739i
$243$	−17.8885			−1.14755
$244$	−2.95492	+	9.09429i	−0.189169	+	0.582202i
$245$	−4.83688	−	14.8864i	−0.309017	−	0.951057i
$246$	−1.54508	−	4.75528i	−0.0985110	−	0.303186i
$247$	−0.881966	−	2.71441i	−0.0561182	−	0.172714i
$248$	−1.42705	−	1.03681i	−0.0906178	−	0.0658377i
$249$	−27.5623			−1.74669
$250$	−3.45492	−	10.6331i	−0.218508	−	0.672499i
$251$	4.03444			0.254652			0.127326	−	0.991861i	$-0.459361\pi$
$251$	4.03444			0.254652			0.127326	+	0.991861i	$0.459361\pi$
$252$		0			0
$253$	−1.48278	−	4.56352i	−0.0932215	−	0.286906i
$254$	−1.70820	−	5.25731i	−0.107182	−	0.329873i
$255$	4.63525	+	14.2658i	0.290271	+	0.893362i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.47214			−0.0918293			−0.0459147	−	0.998945i	$-0.514620\pi$
$257$	−1.47214			−0.0918293			−0.0459147	+	0.998945i	$0.514620\pi$
$258$	−0.364745	+	1.12257i	−0.0227080	+	0.0698882i
$259$		0			0
$260$	−0.690983	+	2.12663i	−0.0428529	+	0.131888i
$261$	6.85410	+	4.97980i	0.424258	+	0.308242i
$262$	−13.6353	+	9.90659i	−0.842389	+	0.612031i
$263$	−4.92705	+	3.57971i	−0.303815	+	0.220735i	−0.729238	−	0.684260i	$-0.760125\pi$
$263$	−4.92705	+	3.57971i	−0.303815	+	0.220735i	0.425423	+	0.904995i	$0.360125\pi$
$264$	−2.50000	−	1.81636i	−0.153864	−	0.111789i
$265$	6.80902	−	4.94704i	0.418275	−	0.303894i
$266$		0			0
$267$	−3.09017	+	9.51057i	−0.189115	+	0.582037i
$268$	9.94427			0.607443
$269$	−2.30902	+	7.10642i	−0.140783	+	0.433286i	−0.996445	−	0.0842497i	$-0.973151\pi$
$269$	−2.30902	+	7.10642i	−0.140783	+	0.433286i	0.855661	+	0.517536i	$0.173151\pi$
$270$	−4.04508	+	2.93893i	−0.246176	+	0.178857i
$271$	−6.29180	−	19.3642i	−0.382199	−	1.17629i	−0.938492	−	0.345302i	$-0.887776\pi$
$271$	−6.29180	−	19.3642i	−0.382199	−	1.17629i	0.556292	−	0.830987i	$-0.312224\pi$
$272$	0.927051	+	2.85317i	0.0562107	+	0.172999i
$273$		0			0
$274$	7.94427			0.479931
$275$	−6.90983			−0.416678
$276$	7.76393			0.467334
$277$	−14.6631	−	10.6534i	−0.881021	−	0.640100i	0.0525001	−	0.998621i	$-0.483281\pi$
$277$	−14.6631	−	10.6534i	−0.881021	−	0.640100i	−0.933522	+	0.358521i	$0.883281\pi$
$278$	2.80902	+	8.64527i	0.168474	+	0.518509i
$279$	−1.09017	−	3.35520i	−0.0652668	−	0.200870i
$280$		0			0
$281$	0.562306	−	1.73060i	0.0335444	−	0.103239i	−0.932882	−	0.360181i	$-0.882715\pi$
$281$	0.562306	−	1.73060i	0.0335444	−	0.103239i	0.966427	+	0.256942i	$0.0827149\pi$
$282$	7.43769			0.442908
$283$	−6.22542	+	19.1599i	−0.370063	+	1.13894i	0.576686	+	0.816966i	$0.304345\pi$
$283$	−6.22542	+	19.1599i	−0.370063	+	1.13894i	−0.946749	+	0.321971i	$0.895655\pi$
$284$	3.00000	−	2.17963i	0.178017	−	0.129337i
$285$	4.40983	+	13.5721i	0.261216	+	0.803940i
$286$	1.11803	+	0.812299i	0.0661107	+	0.0480323i
$287$		0			0
$288$	1.61803	−	1.17557i	0.0953436	−	0.0692712i
$289$	6.47214	+	4.70228i	0.380714	+	0.276605i
$290$	9.47214			0.556223
$291$	17.0344	−	12.3762i	0.998577	−	0.725508i
$292$	−1.54508	+	4.75528i	−0.0904193	+	0.278282i
$293$	−8.56231			−0.500215			−0.250108	−	0.968218i	$-0.580466\pi$
$293$	−8.56231			−0.500215			−0.250108	+	0.968218i	$0.580466\pi$
$294$	4.83688	−	14.8864i	0.282093	−	0.868192i
$295$	−13.5172	−	9.82084i	−0.787003	−	0.571791i
$296$	2.80902	+	8.64527i	0.163271	+	0.502496i
$297$	0.954915	+	2.93893i	0.0554098	+	0.170534i
$298$	−0.309017	−	0.224514i	−0.0179009	−	0.0130057i
$299$	−3.47214			−0.200799
$300$	3.45492	−	10.6331i	0.199470	−	0.613904i
$301$		0			0
$302$	−5.42705	−	3.94298i	−0.312292	−	0.226893i
$303$	−5.26393	−	16.2007i	−0.302405	−	0.930707i
$304$	0.881966	+	2.71441i	0.0505842	+	0.155682i
$305$	−6.60739	+	20.3355i	−0.378338	+	1.16440i
$306$	−1.85410	+	5.70634i	−0.105992	+	0.326210i
$307$	−0.437694			−0.0249805			−0.0124903	−	0.999922i	$-0.503976\pi$
$307$	−0.437694			−0.0249805			−0.0124903	+	0.999922i	$0.503976\pi$
$308$		0			0
$309$	−8.78115	+	6.37988i	−0.499542	+	0.362939i
$310$	−3.19098	−	2.31838i	−0.181236	−	0.131675i
$311$	12.5623	+	9.12705i	0.712343	+	0.517547i	0.883929	−	0.467622i	$-0.154889\pi$
$311$	12.5623	+	9.12705i	0.712343	+	0.517547i	−0.171586	+	0.985169i	$0.554889\pi$
$312$	−1.80902	+	1.31433i	−0.102415	+	0.0744092i
$313$	12.1180	−	8.80427i	0.684952	−	0.497647i	−0.190045	−	0.981775i	$-0.560863\pi$
$313$	12.1180	−	8.80427i	0.684952	−	0.497647i	0.874997	+	0.484129i	$0.160863\pi$
$314$	6.47214	+	4.70228i	0.365244	+	0.265365i
$315$		0			0
$316$	−12.8992	+	9.37181i	−0.725636	+	0.527205i
$317$	−2.93769	+	9.04129i	−0.164997	+	0.507810i	−0.999036	−	0.0438963i	$-0.986023\pi$
$317$	−2.93769	+	9.04129i	−0.164997	+	0.507810i	0.834039	+	0.551706i	$0.186023\pi$
$318$	8.41641			0.471969
$319$	1.80902	−	5.56758i	0.101286	−	0.311725i
$320$	0.690983	−	2.12663i	0.0386271	−	0.118882i
$321$	4.40983	+	13.5721i	0.246133	+	0.757519i
$322$		0			0
$323$	−6.92705	−	5.03280i	−0.385431	−	0.280032i
$324$	−11.0000			−0.611111
$325$	−1.54508	+	4.75528i	−0.0857059	+	0.263776i
$326$	−6.70820			−0.371533
$327$	14.2082	+	10.3229i	0.785715	+	0.570856i
$328$	−0.690983	−	2.12663i	−0.0381532	−	0.117423i
$329$		0			0
$330$	−5.59017	−	4.06150i	−0.307729	−	0.223578i
$331$	−1.45492	+	4.47777i	−0.0799694	+	0.246120i	−0.983046	−	0.183359i	$-0.941303\pi$
$331$	−1.45492	+	4.47777i	−0.0799694	+	0.246120i	0.903077	+	0.429479i	$0.141303\pi$
$332$	−12.3262			−0.676490
$333$	−5.61803	+	17.2905i	−0.307866	+	0.947515i
$334$	14.3541	−	10.4289i	0.785422	−	0.570642i
$335$	22.2361			1.21489
$336$		0			0
$337$	−27.2705	+	19.8132i	−1.48552	+	1.07929i	−0.509794	+	0.860297i	$0.670278\pi$
$337$	−27.2705	+	19.8132i	−1.48552	+	1.07929i	−0.975726	+	0.218996i	$0.929722\pi$
$338$	0.809017	−	0.587785i	0.0440047	−	0.0319713i
$339$	23.5795	+	17.1315i	1.28066	+	0.930457i
$340$	2.07295	+	6.37988i	0.112421	+	0.345998i
$341$	−1.97214	+	1.43284i	−0.106797	+	0.0775927i
$342$	−1.76393	+	5.42882i	−0.0953825	+	0.293557i
$343$		0			0
$344$	−0.163119	+	0.502029i	−0.00879478	+	0.0270676i
$345$	17.3607			0.934668
$346$	−2.63525	−	8.11048i	−0.141672	−	0.436022i
$347$	1.84346	+	5.67358i	0.0989621	+	0.304574i	0.988266	−	0.152743i	$-0.0488106\pi$
$347$	1.84346	+	5.67358i	0.0989621	+	0.304574i	−0.889304	+	0.457317i	$0.848811\pi$
$348$	7.66312	+	5.56758i	0.410786	+	0.298454i
$349$	−13.2361			−0.708510			−0.354255	−	0.935149i	$-0.615266\pi$
$349$	−13.2361			−0.708510			−0.354255	+	0.935149i	$0.615266\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$	−1.11803	−	0.812299i	−0.0595914	−	0.0432957i
$353$	2.23607	+	6.88191i	0.119014	+	0.366287i	0.992763	−	0.120090i	$-0.0383182\pi$
$353$	2.23607	+	6.88191i	0.119014	+	0.366287i	−0.873749	+	0.486377i	$0.838318\pi$
$354$	−5.16312	−	15.8904i	−0.274417	−	0.844568i
$355$	6.70820	−	4.87380i	0.356034	−	0.258674i
$356$	−1.38197	+	4.25325i	−0.0732441	+	0.225422i
$357$		0			0
$358$	−2.19098	+	6.74315i	−0.115797	+	0.356387i
$359$	−9.78115	+	7.10642i	−0.516230	+	0.375063i	−0.815182	−	0.579205i	$-0.803363\pi$
$359$	−9.78115	+	7.10642i	−0.516230	+	0.375063i	0.298952	+	0.954268i	$0.403363\pi$
$360$	3.61803	−	2.62866i	0.190687	−	0.138542i
$361$	8.78115	+	6.37988i	0.462166	+	0.335783i
$362$	16.5172	−	12.0005i	0.868126	−	0.630730i
$363$	16.4443	−	11.9475i	0.863100	−	0.627079i
$364$		0			0
$365$	−3.45492	+	10.6331i	−0.180839	+	0.556564i
$366$	−17.2984	+	12.5680i	−0.904200	+	0.656940i
$367$	−2.24671	+	6.91467i	−0.117277	+	0.360943i	−0.992415	−	0.122931i	$-0.960771\pi$
$367$	−2.24671	+	6.91467i	−0.117277	+	0.360943i	0.875138	+	0.483874i	$0.160771\pi$
$368$	3.47214			0.180998
$369$	1.38197	−	4.25325i	0.0719423	−	0.221416i
$370$	6.28115	+	19.3314i	0.326542	+	1.00499i
$371$		0			0
$372$	−1.21885	−	3.75123i	−0.0631943	−	0.194492i
$373$	−28.5623	−	20.7517i	−1.47890	−	1.07448i	−0.977909	−	0.209031i	$-0.932969\pi$
$373$	−28.5623	−	20.7517i	−1.47890	−	1.07448i	−0.500991	−	0.865452i	$-0.667031\pi$
$374$	4.14590			0.214379
$375$	7.72542	−	23.7764i	0.398939	−	1.22781i
$376$	3.32624			0.171538
$377$	−3.42705	−	2.48990i	−0.176502	−	0.128236i
$378$		0			0
$379$	4.30902	+	13.2618i	0.221339	+	0.681212i	0.998643	+	0.0520863i	$0.0165871\pi$
$379$	4.30902	+	13.2618i	0.221339	+	0.681212i	−0.777303	+	0.629126i	$0.783413\pi$
$380$	1.97214	+	6.06961i	0.101168	+	0.311364i
$381$	3.81966	−	11.7557i	0.195687	−	0.602263i
$382$	−24.7984			−1.26880
$383$	2.10081	−	6.46564i	0.107347	−	0.330379i	−0.882927	−	0.469509i	$-0.844431\pi$
$383$	2.10081	−	6.46564i	0.107347	−	0.330379i	0.990274	+	0.139131i	$0.0444308\pi$
$384$	1.80902	−	1.31433i	0.0923160	−	0.0670715i
$385$		0			0
$386$	−10.0902	−	7.33094i	−0.513576	−	0.373135i
$387$	−0.854102	+	0.620541i	−0.0434164	+	0.0315439i
$388$	7.61803	−	5.53483i	0.386747	−	0.280988i
$389$	−9.75329	−	7.08618i	−0.494511	−	0.359284i	0.312405	−	0.949949i	$-0.398865\pi$
$389$	−9.75329	−	7.08618i	−0.494511	−	0.359284i	−0.806917	+	0.590665i	$0.798865\pi$
$390$	−4.04508	+	2.93893i	−0.204831	+	0.148818i
$391$	−8.42705	+	6.12261i	−0.426174	+	0.309634i
$392$	2.16312	−	6.65740i	0.109254	−	0.336249i
$393$	−37.6869			−1.90105
$394$	4.06231	−	12.5025i	0.204656	−	0.629866i
$395$	−28.8435	+	20.9560i	−1.45127	+	1.05441i
$396$	−0.854102	−	2.62866i	−0.0429202	−	0.132095i
$397$	2.63525	+	8.11048i	0.132260	+	0.407053i	0.995154	−	0.0983315i	$-0.0313505\pi$
$397$	2.63525	+	8.11048i	0.132260	+	0.407053i	−0.862894	+	0.505385i	$0.831351\pi$
$398$	14.7812	+	10.7391i	0.740912	+	0.538304i
$399$		0			0
$400$	1.54508	−	4.75528i	0.0772542	−	0.237764i
$401$	−28.0902			−1.40276			−0.701378	−	0.712789i	$-0.747432\pi$
$401$	−28.0902			−1.40276			−0.701378	+	0.712789i	$0.747432\pi$
$402$	17.9894	+	13.0700i	0.897228	+	0.651874i
$403$	0.545085	+	1.67760i	0.0271526	+	0.0835672i
$404$	−2.35410	−	7.24518i	−0.117121	−	0.360461i
$405$	−24.5967			−1.22222
$406$		0			0
$407$	12.5623			0.622690
$408$	−2.07295	+	6.37988i	−0.102626	+	0.315851i
$409$	21.4894	−	15.6129i	1.06258	−	0.772010i	0.0880163	−	0.996119i	$-0.471947\pi$
$409$	21.4894	−	15.6129i	1.06258	−	0.772010i	0.974564	+	0.224109i	$0.0719472\pi$
$410$	−1.54508	−	4.75528i	−0.0763063	−	0.234847i
$411$	14.3713	+	10.4414i	0.708885	+	0.515035i
$412$	−3.92705	+	2.85317i	−0.193472	+	0.140566i
$413$		0			0
$414$	5.61803	+	4.08174i	0.276111	+	0.200607i
$415$	−27.5623			−1.35298
$416$	−0.809017	+	0.587785i	−0.0396653	+	0.0288185i
$417$	−6.28115	+	19.3314i	−0.307589	+	0.946663i
$418$	3.94427			0.192921
$419$	−0.937694	+	2.88593i	−0.0458094	+	0.140987i	−0.971345	−	0.237674i	$-0.923615\pi$
$419$	−0.937694	+	2.88593i	−0.0458094	+	0.140987i	0.925536	+	0.378660i	$0.123615\pi$
$420$		0			0
$421$	−9.35410	−	28.7890i	−0.455891	−	1.40309i	−0.870086	−	0.492900i	$-0.835937\pi$
$421$	−9.35410	−	28.7890i	−0.455891	−	1.40309i	0.414195	−	0.910188i	$-0.364063\pi$
$422$	−1.76393	−	5.42882i	−0.0858669	−	0.264271i
$423$	5.38197	+	3.91023i	0.261680	+	0.190122i
$424$	3.76393			0.182793
$425$	4.63525	+	14.2658i	0.224843	+	0.691995i
$426$	8.29180			0.401739
$427$		0			0
$428$	1.97214	+	6.06961i	0.0953268	+	0.293386i
$429$	0.954915	+	2.93893i	0.0461037	+	0.141893i
$430$	−0.364745	+	1.12257i	−0.0175896	+	0.0541351i
$431$	−2.10739	+	6.48588i	−0.101509	+	0.312414i	−0.988895	−	0.148613i	$-0.952519\pi$
$431$	−2.10739	+	6.48588i	−0.101509	+	0.312414i	0.887386	+	0.461027i	$0.152519\pi$
$432$	−2.23607			−0.107583
$433$	7.70820	−	23.7234i	0.370433	−	1.14007i	−0.576076	−	0.817396i	$-0.695417\pi$
$433$	7.70820	−	23.7234i	0.370433	−	1.14007i	0.946509	−	0.322678i	$-0.104583\pi$
$434$		0			0
$435$	17.1353	+	12.4495i	0.821573	+	0.596907i
$436$	6.35410	+	4.61653i	0.304306	+	0.221091i
$437$	−8.01722	+	5.82485i	−0.383516	+	0.278640i
$438$	−9.04508	+	6.57164i	−0.432191	+	0.314005i
$439$	22.7082	+	16.4985i	1.08380	+	0.787429i	0.978342	−	0.206994i	$-0.0663681\pi$
$439$	22.7082	+	16.4985i	1.08380	+	0.787429i	0.105461	+	0.994423i	$0.466368\pi$
$440$	−2.50000	−	1.81636i	−0.119183	−	0.0865914i
$441$	11.3262	−	8.22899i	0.539345	−	0.391857i
$442$	0.927051	−	2.85317i	0.0440953	−	0.135711i
$443$	−35.8328			−1.70247			−0.851234	−	0.524786i	$-0.824145\pi$
$443$	−35.8328			−1.70247			−0.851234	+	0.524786i	$0.824145\pi$
$444$	−6.28115	+	19.3314i	−0.298090	+	0.917428i
$445$	−3.09017	+	9.51057i	−0.146488	+	0.450844i
$446$	−1.71885	−	5.29007i	−0.0813898	−	0.250492i
$447$	−0.263932	−	0.812299i	−0.0124836	−	0.0384204i
$448$		0			0
$449$	−35.7426			−1.68680			−0.843400	−	0.537286i	$-0.819449\pi$
$449$	−35.7426			−1.68680			−0.843400	+	0.537286i	$0.819449\pi$
$450$	8.09017	−	5.87785i	0.381374	−	0.277085i
$451$	−3.09017			−0.145510
$452$	10.5451	+	7.66145i	0.495999	+	0.360364i
$453$	−4.63525	−	14.2658i	−0.217783	−	0.670268i
$454$	−5.26393	−	16.2007i	−0.247049	−	0.760337i
$455$		0			0
$456$	−1.97214	+	6.06961i	−0.0923537	+	0.284236i
$457$	9.18034			0.429438			0.214719	−	0.976676i	$-0.431116\pi$
$457$	9.18034			0.429438			0.214719	+	0.976676i	$0.431116\pi$
$458$	8.29180	−	25.5195i	0.387450	−	1.19245i
$459$	5.42705	−	3.94298i	0.253313	−	0.184043i
$460$	7.76393			0.361995
$461$	0.545085	+	0.396027i	0.0253871	+	0.0184448i	0.600406	−	0.799695i	$-0.295005\pi$
$461$	0.545085	+	0.396027i	0.0253871	+	0.0184448i	−0.575019	+	0.818140i	$0.695005\pi$
$462$		0			0
$463$	32.9336	−	23.9277i	1.53056	−	1.11201i	0.574627	−	0.818416i	$-0.305147\pi$
$463$	32.9336	−	23.9277i	1.53056	−	1.11201i	0.955929	−	0.293598i	$-0.0948527\pi$
$464$	3.42705	+	2.48990i	0.159097	+	0.115591i
$465$	−2.72542	−	8.38800i	−0.126389	−	0.388984i
$466$	−14.7812	+	10.7391i	−0.684724	+	0.497481i
$467$	0.107391	−	0.330515i	0.00496946	−	0.0152944i	−0.948541	−	0.316654i	$-0.897441\pi$
$467$	0.107391	−	0.330515i	0.00496946	−	0.0152944i	0.953510	+	0.301360i	$0.0974405\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$	7.43769			0.343075
$471$	5.52786	+	17.0130i	0.254711	+	0.783918i
$472$	−2.30902	−	7.10642i	−0.106281	−	0.327100i
$473$	0.590170	+	0.428784i	0.0271360	+	0.0197155i
$474$	−35.6525			−1.63757
$475$	4.40983	+	13.5721i	0.202337	+	0.622729i
$476$		0			0
$477$	6.09017	+	4.42477i	0.278850	+	0.202596i
$478$	1.74671	+	5.37582i	0.0798927	+	0.245884i
$479$	5.53444	+	17.0333i	0.252875	+	0.778270i	0.994241	+	0.107168i	$0.0341784\pi$
$479$	5.53444	+	17.0333i	0.252875	+	0.778270i	−0.741366	+	0.671101i	$0.765822\pi$
$480$	4.04508	−	2.93893i	0.184632	−	0.134143i
$481$	2.80902	−	8.64527i	0.128080	−	0.394190i
$482$	1.61803			0.0736994
$483$		0			0
$484$	7.35410	−	5.34307i	0.334277	−	0.242867i
$485$	17.0344	−	12.3762i	0.773494	−	0.561976i
$486$	−14.4721	−	10.5146i	−0.656469	−	0.476953i
$487$	15.7254	−	11.4252i	0.712587	−	0.517725i	−0.171420	−	0.985198i	$-0.554836\pi$
$487$	15.7254	−	11.4252i	0.712587	−	0.517725i	0.884007	+	0.467473i	$0.154836\pi$
$488$	−7.73607	+	5.62058i	−0.350195	+	0.254432i
$489$	−12.1353	−	8.81678i	−0.548775	−	0.398709i
$490$	4.83688	−	14.8864i	0.218508	−	0.672499i
$491$	−27.2984	+	19.8334i	−1.23196	+	0.895070i	−0.997035	−	0.0769439i	$-0.975484\pi$
$491$	−27.2984	+	19.8334i	−1.23196	+	0.895070i	−0.234923	+	0.972014i	$0.575484\pi$
$492$	1.54508	−	4.75528i	0.0696578	−	0.214385i
$493$	−12.7082			−0.572349
$494$	0.881966	−	2.71441i	0.0396815	−	0.122127i
$495$	−1.90983	−	5.87785i	−0.0858405	−	0.264190i
$496$	−0.545085	−	1.67760i	−0.0244750	−	0.0753264i
$497$		0			0
$498$	−22.2984	−	16.2007i	−0.999214	−	0.725971i
$499$	−18.7082			−0.837494			−0.418747	−	0.908103i	$-0.637531\pi$
$499$	−18.7082			−0.837494			−0.418747	+	0.908103i	$0.637531\pi$
$500$	3.45492	−	10.6331i	0.154508	−	0.475528i
$501$	39.6738			1.77249
$502$	3.26393	+	2.37139i	0.145676	+	0.105840i
$503$	−9.10739	−	28.0297i	−0.406078	−	1.24978i	−0.919991	−	0.391939i	$-0.871805\pi$
$503$	−9.10739	−	28.0297i	−0.406078	−	1.24978i	0.513913	−	0.857842i	$-0.328195\pi$
$504$		0			0
$505$	−5.26393	−	16.2007i	−0.234242	−	0.720922i
$506$	1.48278	−	4.56352i	0.0659176	−	0.202873i
$507$	2.23607			0.0993073
$508$	1.70820	−	5.25731i	0.0757893	−	0.233255i
$509$	5.51722	−	4.00850i	0.244547	−	0.177673i	−0.458760	−	0.888560i	$-0.651706\pi$
$509$	5.51722	−	4.00850i	0.244547	−	0.177673i	0.703306	+	0.710887i	$0.251706\pi$
$510$	−4.63525	+	14.2658i	−0.205253	+	0.631702i
$511$		0			0
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	5.16312	−	3.75123i	0.227957	−	0.165621i
$514$	−1.19098	−	0.865300i	−0.0525320	−	0.0381667i
$515$	−8.78115	+	6.37988i	−0.386944	+	0.281131i
$516$	−0.954915	+	0.693786i	−0.0420378	+	0.0305422i
$517$	1.42047	−	4.37177i	0.0624723	−	0.192270i
$518$		0			0
$519$	5.89261	−	18.1356i	0.258657	−	0.796064i
$520$	−1.80902	+	1.31433i	−0.0793306	+	0.0576371i
$521$	12.5066	+	38.4913i	0.547923	+	1.68633i	0.713936	+	0.700210i	$0.246911\pi$
$521$	12.5066	+	38.4913i	0.547923	+	1.68633i	−0.166013	+	0.986124i	$0.553089\pi$
$522$	2.61803	+	8.05748i	0.114588	+	0.352666i
$523$	5.92705	+	4.30625i	0.259172	+	0.188299i	0.709782	−	0.704422i	$-0.248793\pi$
$523$	5.92705	+	4.30625i	0.259172	+	0.188299i	−0.450610	+	0.892721i	$0.648793\pi$
$524$	−16.8541			−0.736275
$525$		0			0
$526$	−6.09017			−0.265544
$527$	4.28115	+	3.11044i	0.186490	+	0.135493i
$528$	−0.954915	−	2.93893i	−0.0415573	−	0.127900i
$529$	−3.38197	−	10.4086i	−0.147042	−	0.452549i
$530$	8.41641			0.365585
$531$	4.61803	−	14.2128i	0.200406	−	0.616785i
$532$		0			0
$533$	−0.690983	+	2.12663i	−0.0299298	+	0.0921144i
$534$	−8.09017	+	5.87785i	−0.350096	+	0.254360i
$535$	4.40983	+	13.5721i	0.190654	+	0.586771i
$536$	8.04508	+	5.84510i	0.347495	+	0.252470i
$537$	−12.8262	+	9.31881i	−0.553493	+	0.402136i
$538$	−6.04508	+	4.39201i	−0.260622	+	0.189353i
$539$	−7.82624	−	5.68609i	−0.337100	−	0.244917i
$540$	−5.00000			−0.215166
$541$	33.3885	−	24.2582i	1.43549	−	1.04294i	0.446524	−	0.894772i	$-0.352662\pi$
$541$	33.3885	−	24.2582i	1.43549	−	1.04294i	0.988962	−	0.148170i	$-0.0473381\pi$
$542$	6.29180	−	19.3642i	0.270256	−	0.831762i
$543$	45.6525			1.95914
$544$	−0.927051	+	2.85317i	−0.0397470	+	0.122329i
$545$	14.2082	+	10.3229i	0.608613	+	0.442183i
$546$		0			0
$547$	0.854102	+	2.62866i	0.0365188	+	0.112393i	0.967654	−	0.252280i	$-0.0811806\pi$
$547$	0.854102	+	2.62866i	0.0365188	+	0.112393i	−0.931135	+	0.364674i	$0.881181\pi$
$548$	6.42705	+	4.66953i	0.274550	+	0.199472i
$549$	−19.1246			−0.816219
$550$	−5.59017	−	4.06150i	−0.238366	−	0.173183i
$551$	−12.0902			−0.515059
$552$	6.28115	+	4.56352i	0.267344	+	0.194237i
$553$		0			0
$554$	−5.60081	−	17.2375i	−0.237956	−	0.732352i
$555$	−14.0451	+	43.2263i	−0.596181	+	1.83486i
$556$	−2.80902	+	8.64527i	−0.119129	+	0.366641i
$557$	37.3820			1.58392			0.791962	−	0.610570i	$-0.209060\pi$
$557$	37.3820			1.58392			0.791962	+	0.610570i	$0.209060\pi$
$558$	1.09017	−	3.35520i	0.0461506	−	0.142037i
$559$	0.427051	−	0.310271i	0.0180623	−	0.0131231i
$560$		0			0
$561$	7.50000	+	5.44907i	0.316650	+	0.230060i
$562$	1.47214	−	1.06957i	0.0620983	−	0.0451171i
$563$	28.9894	−	21.0620i	1.22176	−	0.887657i	0.225511	−	0.974241i	$-0.427595\pi$
$563$	28.9894	−	21.0620i	1.22176	−	0.887657i	0.996245	+	0.0865831i	$0.0275948\pi$
$564$	6.01722	+	4.37177i	0.253371	+	0.184085i
$565$	23.5795	+	17.1315i	0.991998	+	0.720729i
$566$	−16.2984	+	11.8415i	−0.685072	+	0.497734i
$567$		0			0
$568$	3.70820			0.155593
$569$	−9.89919	+	30.4666i	−0.414996	+	1.27722i	0.497259	+	0.867602i	$0.334340\pi$
$569$	−9.89919	+	30.4666i	−0.414996	+	1.27722i	−0.912255	+	0.409623i	$0.865660\pi$
$570$	−4.40983	+	13.5721i	−0.184707	+	0.568471i
$571$	−12.1074	−	37.2627i	−0.506679	−	1.55940i	−0.797930	−	0.602750i	$-0.794072\pi$
$571$	−12.1074	−	37.2627i	−0.506679	−	1.55940i	0.291252	−	0.956646i	$-0.405928\pi$
$572$	0.427051	+	1.31433i	0.0178559	+	0.0549548i
$573$	−44.8607	−	32.5932i	−1.87408	−	1.36160i
$574$		0			0
$575$	17.3607			0.723990
$576$	2.00000			0.0833333
$577$	1.51722	+	1.10233i	0.0631627	+	0.0458904i	0.618919	−	0.785455i	$-0.287571\pi$
$577$	1.51722	+	1.10233i	0.0631627	+	0.0458904i	−0.555756	+	0.831346i	$0.687571\pi$
$578$	2.47214	+	7.60845i	0.102827	+	0.316470i
$579$	−8.61803	−	26.5236i	−0.358153	−	1.10228i
$580$	7.66312	+	5.56758i	0.318194	+	0.231181i
$581$		0			0
$582$	21.0557			0.872788
$583$	1.60739	−	4.94704i	0.0665713	−	0.204885i
$584$	−4.04508	+	2.93893i	−0.167387	+	0.121614i
$585$	−4.47214			−0.184900
$586$	−6.92705	−	5.03280i	−0.286154	−	0.207903i
$587$	17.9894	−	13.0700i	0.742500	−	0.539458i	−0.150993	−	0.988535i	$-0.548247\pi$
$587$	17.9894	−	13.0700i	0.742500	−	0.539458i	0.893493	+	0.449077i	$0.148247\pi$
$588$	12.6631	−	9.20029i	0.522218	−	0.379414i
$589$	4.07295	+	2.95917i	0.167823	+	0.121931i
$590$	−5.16312	−	15.8904i	−0.212562	−	0.654199i
$591$	23.7812	−	17.2780i	0.978226	−	0.710723i
$592$	−2.80902	+	8.64527i	−0.115450	+	0.355318i
$593$	25.3607			1.04144			0.520719	−	0.853728i	$-0.325664\pi$
$593$	25.3607			1.04144			0.520719	+	0.853728i	$0.325664\pi$
$594$	−0.954915	+	2.93893i	−0.0391806	+	0.120586i
$595$		0			0
$596$	−0.118034	−	0.363271i	−0.00483486	−	0.0148802i
$597$	12.6246	+	38.8546i	0.516691	+	1.59021i
$598$	−2.80902	−	2.04087i	−0.114869	−	0.0834574i
$599$	20.6180			0.842430			0.421215	−	0.906961i	$-0.361604\pi$
$599$	20.6180			0.842430			0.421215	+	0.906961i	$0.361604\pi$
$600$	9.04508	−	6.57164i	0.369264	−	0.268286i
$601$	−14.1246			−0.576155			−0.288077	−	0.957607i	$-0.593016\pi$
$601$	−14.1246			−0.576155			−0.288077	+	0.957607i	$0.593016\pi$
$602$		0			0
$603$	6.14590	+	18.9151i	0.250280	+	0.770284i
$604$	−2.07295	−	6.37988i	−0.0843471	−	0.259594i
$605$	16.4443	−	11.9475i	0.668555	−	0.485733i
$606$	5.26393	−	16.2007i	0.213833	−	0.658109i
$607$	39.1246			1.58802			0.794010	−	0.607905i	$-0.207990\pi$
$607$	39.1246			1.58802			0.794010	+	0.607905i	$0.207990\pi$
$608$	−0.881966	+	2.71441i	−0.0357684	+	0.110084i
$609$		0			0
$610$	−17.2984	+	12.5680i	−0.700391	+	0.508864i
$611$	−2.69098	−	1.95511i	−0.108866	−	0.0790954i
$612$	−4.85410	+	3.52671i	−0.196215	+	0.142559i
$613$	12.0000	−	8.71851i	0.484675	−	0.352137i	−0.318458	−	0.947937i	$-0.603165\pi$
$613$	12.0000	−	8.71851i	0.484675	−	0.352137i	0.803133	+	0.595800i	$0.203165\pi$
$614$	−0.354102	−	0.257270i	−0.0142904	−	0.0103826i
$615$	3.45492	−	10.6331i	0.139316	−	0.428769i
$616$		0			0
$617$	2.61803	−	8.05748i	0.105398	−	0.324382i	−0.884426	−	0.466681i	$-0.845450\pi$
$617$	2.61803	−	8.05748i	0.105398	−	0.324382i	0.989824	+	0.142299i	$0.0454495\pi$
$618$	−10.8541			−0.436616
$619$	−9.48936	+	29.2052i	−0.381409	+	1.17386i	0.557642	+	0.830081i	$0.311706\pi$
$619$	−9.48936	+	29.2052i	−0.381409	+	1.17386i	−0.939052	+	0.343776i	$0.888294\pi$
$620$	−1.21885	−	3.75123i	−0.0489501	−	0.150653i
$621$	−2.39919	−	7.38394i	−0.0962761	−	0.296307i
$622$	4.79837	+	14.7679i	0.192397	+	0.592138i
$623$		0			0
$624$	−2.23607			−0.0895144
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	14.9787			0.598670
$627$	7.13525	+	5.18407i	0.284955	+	0.207032i
$628$	2.47214	+	7.60845i	0.0986490	+	0.303610i
$629$	−8.42705	−	25.9358i	−0.336009	−	1.03413i
$630$		0			0
$631$	−6.05166	+	18.6251i	−0.240913	+	0.741454i	0.755369	+	0.655300i	$0.227458\pi$
$631$	−6.05166	+	18.6251i	−0.240913	+	0.741454i	−0.996282	+	0.0861539i	$0.972542\pi$
$632$	−15.9443			−0.634229
$633$	3.94427	−	12.1392i	0.156771	−	0.482491i
$634$	−7.69098	+	5.58783i	−0.305448	+	0.221921i
$635$	3.81966	−	11.7557i	0.151579	−	0.466511i
$636$	6.80902	+	4.94704i	0.269995	+	0.196163i
$637$	−5.66312	+	4.11450i	−0.224381	+	0.163022i
$638$	4.73607	−	3.44095i	0.187503	−	0.136229i
$639$	6.00000	+	4.35926i	0.237356	+	0.172449i
$640$	1.80902	−	1.31433i	0.0715077	−	0.0519534i
$641$	4.30902	−	3.13068i	0.170196	−	0.123655i	−0.499427	−	0.866356i	$-0.666456\pi$
$641$	4.30902	−	3.13068i	0.170196	−	0.123655i	0.669622	+	0.742702i	$0.266456\pi$
$642$	−4.40983	+	13.5721i	−0.174042	+	0.535647i
$643$	−0.236068			−0.00930961			−0.00465481	−	0.999989i	$-0.501482\pi$
$643$	−0.236068			−0.00930961			−0.00465481	+	0.999989i	$0.501482\pi$
$644$		0			0
$645$	−2.13525	+	1.55135i	−0.0840756	+	0.0610845i
$646$	−2.64590	−	8.14324i	−0.104101	−	0.320391i
$647$	−5.05166	−	15.5474i	−0.198601	−	0.611232i	−0.999916	−	0.0129885i	$-0.995866\pi$
$647$	−5.05166	−	15.5474i	−0.198601	−	0.611232i	0.801314	−	0.598244i	$-0.204134\pi$
$648$	−8.89919	−	6.46564i	−0.349593	−	0.253994i
$649$	−10.3262			−0.405340
$650$	−4.04508	+	2.93893i	−0.158661	+	0.115274i
$651$		0			0
$652$	−5.42705	−	3.94298i	−0.212540	−	0.154419i
$653$	6.46149	+	19.8864i	0.252858	+	0.778216i	0.994244	+	0.107138i	$0.0341686\pi$
$653$	6.46149	+	19.8864i	0.252858	+	0.778216i	−0.741386	+	0.671078i	$0.765831\pi$
$654$	5.42705	+	16.7027i	0.212214	+	0.653129i
$655$	−37.6869			−1.47255
$656$	0.690983	−	2.12663i	0.0269784	−	0.0830308i
$657$	−10.0000			−0.390137
$658$		0			0
$659$	−29.4164	+	21.3723i	−1.14590	+	0.832545i	−0.987930	−	0.154898i	$-0.950495\pi$
$659$	−29.4164	+	21.3723i	−1.14590	+	0.832545i	−0.157970	+	0.987444i	$0.550495\pi$
$660$	−2.13525	−	6.57164i	−0.0831147	−	0.255801i
$661$	−13.0623	−	9.49032i	−0.508065	−	0.369131i	0.304024	−	0.952664i	$-0.401670\pi$
$661$	−13.0623	−	9.49032i	−0.508065	−	0.369131i	−0.812089	+	0.583534i	$0.801670\pi$
$662$	−3.80902	+	2.76741i	−0.148042	+	0.107559i
$663$	5.42705	−	3.94298i	0.210769	−	0.153133i
$664$	−9.97214	−	7.24518i	−0.386994	−	0.281168i
$665$		0			0
$666$	−14.7082	+	10.6861i	−0.569931	+	0.414079i
$667$	−4.54508	+	13.9883i	−0.175986	+	0.541630i
$668$	17.7426			0.686484
$669$	3.84346	−	11.8290i	0.148597	−	0.457334i
$670$	17.9894	+	13.0700i	0.694989	+	0.504939i
$671$	4.08359	+	12.5680i	0.157645	+	0.485182i
$672$		0			0
$673$	26.9894	+	19.6089i	1.04036	+	0.755868i	0.970356	−	0.241678i	$-0.0776979\pi$
$673$	26.9894	+	19.6089i	1.04036	+	0.755868i	0.0700068	+	0.997547i	$0.477698\pi$
$674$	−33.7082			−1.29839
$675$	−11.1803			−0.430331
$676$	1.00000			0.0384615
$677$	12.1074	+	8.79653i	0.465325	+	0.338078i	0.795616	−	0.605801i	$-0.207147\pi$
$677$	12.1074	+	8.79653i	0.465325	+	0.338078i	−0.330292	+	0.943879i	$0.607147\pi$
$678$	9.00658	+	27.7194i	0.345896	+	1.06456i
$679$		0			0
$680$	−2.07295	+	6.37988i	−0.0794940	+	0.244657i
$681$	11.7705	−	36.2259i	0.451047	−	1.38818i
$682$	−2.43769			−0.0933441
$683$	10.8820	−	33.4912i	0.416387	−	1.28151i	−0.494618	−	0.869111i	$-0.664692\pi$
$683$	10.8820	−	33.4912i	0.416387	−	1.28151i	0.911005	−	0.412396i	$-0.135308\pi$
$684$	−4.61803	+	3.35520i	−0.176575	+	0.128289i
$685$	14.3713	+	10.4414i	0.549100	+	0.398945i
$686$		0			0
$687$	48.5410	−	35.2671i	1.85196	−	1.34552i
$688$	−0.427051	+	0.310271i	−0.0162812	+	0.0118290i
$689$	−3.04508	−	2.21238i	−0.116008	−	0.0842851i
$690$	14.0451	+	10.2044i	0.534687	+	0.388473i
$691$	28.1803	−	20.4742i	1.07203	−	0.778876i	0.0957545	−	0.995405i	$-0.469474\pi$
$691$	28.1803	−	20.4742i	1.07203	−	0.778876i	0.976276	+	0.216529i	$0.0694736\pi$
$692$	2.63525	−	8.11048i	0.100177	−	0.308314i
$693$		0			0
$694$	−1.84346	+	5.67358i	−0.0699767	+	0.215366i
$695$	−6.28115	+	19.3314i	−0.238258	+	0.733282i
$696$	2.92705	+	9.00854i	0.110950	+	0.341468i
$697$	2.07295	+	6.37988i	0.0785185	+	0.241655i
$698$	−10.7082	−	7.77997i	−0.405311	−	0.294476i
$699$	−40.8541			−1.54524
$700$		0			0
$701$	−33.4721			−1.26423			−0.632113	−	0.774877i	$-0.717812\pi$
$701$	−33.4721			−1.26423			−0.632113	+	0.774877i	$0.717812\pi$
$702$	1.80902	+	1.31433i	0.0682769	+	0.0496061i
$703$	−8.01722	−	24.6745i	−0.302375	−	0.930615i
$704$	−0.427051	−	1.31433i	−0.0160951	−	0.0495356i
$705$	13.4549	+	9.77557i	0.506741	+	0.368169i
$706$	−2.23607	+	6.88191i	−0.0841555	+	0.259004i
$707$		0			0
$708$	5.16312	−	15.8904i	0.194042	−	0.597200i
$709$	28.8435	−	20.9560i	1.08324	−	0.787019i	0.104994	−	0.994473i	$-0.466518\pi$
$709$	28.8435	−	20.9560i	1.08324	−	0.787019i	0.978245	+	0.207454i	$0.0665177\pi$
$710$	8.29180			0.311186
$711$	−25.7984	−	18.7436i	−0.967515	−	0.702941i
$712$	−3.61803	+	2.62866i	−0.135592	+	0.0985130i
$713$	4.95492	−	3.59996i	0.185563	−	0.134819i
$714$		0			0
$715$	0.954915	+	2.93893i	0.0357118	+	0.109910i
$716$	−5.73607	+	4.16750i	−0.214367	+	0.155747i
$717$	−3.90576	+	12.0207i	−0.145863	+	0.448922i
$718$	−12.0902			−0.451201
$719$	8.36068	−	25.7315i	0.311801	−	0.959624i	−0.665251	−	0.746620i	$-0.731675\pi$
$719$	8.36068	−	25.7315i	0.311801	−	0.959624i	0.977051	−	0.213004i	$-0.0683247\pi$
$720$	4.47214			0.166667
$721$		0			0
$722$	3.35410	+	10.3229i	0.124827	+	0.384177i
$723$	2.92705	+	2.12663i	0.108858	+	0.0790901i
$724$	20.4164			0.758770
$725$	17.1353	+	12.4495i	0.636387	+	0.462363i
$726$	20.3262			0.754377
$727$	−33.8713	−	24.6090i	−1.25622	−	0.912696i	−0.257652	−	0.966238i	$-0.582949\pi$
$727$	−33.8713	−	24.6090i	−1.25622	−	0.912696i	−0.998566	+	0.0535420i	$0.982949\pi$
$728$		0			0
$729$	−2.16312	−	6.65740i	−0.0801155	−	0.246570i
$730$	−9.04508	+	6.57164i	−0.334774	+	0.243227i
$731$	0.489357	−	1.50609i	0.0180995	−	0.0557046i
$732$	−21.3820			−0.790300
$733$	15.2812	−	47.0306i	0.564422	−	1.73711i	−0.105240	−	0.994447i	$-0.533561\pi$
$733$	15.2812	−	47.0306i	0.564422	−	1.73711i	0.669662	−	0.742666i	$-0.266439\pi$
$734$	−5.88197	+	4.27350i	−0.217107	+	0.157738i
$735$	28.3156	−	20.5725i	1.04444	−	0.758827i
$736$	2.80902	+	2.04087i	0.103542	+	0.0752275i
$737$	11.1180	−	8.07772i	0.409538	−	0.297547i
$738$	3.61803	−	2.62866i	0.133182	−	0.0967621i
$739$	38.4787	+	27.9564i	1.41546	+	1.02839i	0.992500	+	0.122246i	$0.0390098\pi$
$739$	38.4787	+	27.9564i	1.41546	+	1.02839i	0.422963	+	0.906147i	$0.360990\pi$
$740$	−6.28115	+	19.3314i	−0.230900	+	0.710636i
$741$	5.16312	−	3.75123i	0.189672	−	0.137805i
$742$		0			0
$743$	30.7082			1.12657			0.563287	−	0.826261i	$-0.309536\pi$
$743$	30.7082			1.12657			0.563287	+	0.826261i	$0.309536\pi$
$744$	1.21885	−	3.75123i	0.0446851	−	0.137527i
$745$	−0.263932	−	0.812299i	−0.00966972	−	0.0297603i
$746$	−10.9098	−	33.5770i	−0.399437	−	1.22934i
$747$	−7.61803	−	23.4459i	−0.278729	−	0.857841i
$748$	3.35410	+	2.43690i	0.122638	+	0.0891018i
$749$		0			0
$750$	20.2254	−	14.6946i	0.738528	−	0.536572i
$751$	−13.4164			−0.489572			−0.244786	−	0.969577i	$-0.578718\pi$
$751$	−13.4164			−0.489572			−0.244786	+	0.969577i	$0.578718\pi$
$752$	2.69098	+	1.95511i	0.0981301	+	0.0712957i
$753$	2.78773	+	8.57975i	0.101591	+	0.312664i
$754$	−1.30902	−	4.02874i	−0.0476716	−	0.146718i
$755$	−4.63525	−	14.2658i	−0.168694	−	0.519187i
$756$		0			0
$757$	−32.1246			−1.16759			−0.583794	−	0.811902i	$-0.698433\pi$
$757$	−32.1246			−1.16759			−0.583794	+	0.811902i	$0.698433\pi$
$758$	−4.30902	+	13.2618i	−0.156511	+	0.481690i
$759$	8.68034	−	6.30664i	0.315076	−	0.228916i
$760$	−1.97214	+	6.06961i	−0.0715369	+	0.220168i
$761$	3.89919	+	2.83293i	0.141345	+	0.102693i	0.656211	−	0.754578i	$-0.272158\pi$
$761$	3.89919	+	2.83293i	0.141345	+	0.102693i	−0.514866	+	0.857271i	$0.672158\pi$
$762$	10.0000	−	7.26543i	0.362262	−	0.263199i
$763$		0			0
$764$	−20.0623	−	14.5761i	−0.725829	−	0.527345i
$765$	−10.8541	+	7.88597i	−0.392431	+	0.285118i
$766$	5.50000	−	3.99598i	0.198723	−	0.144381i
$767$	−2.30902	+	7.10642i	−0.0833738	+	0.256598i
$768$	2.23607			0.0806872
$769$	−9.71478	+	29.8990i	−0.350324	+	1.07819i	0.608347	+	0.793671i	$0.291833\pi$
$769$	−9.71478	+	29.8990i	−0.350324	+	1.07819i	−0.958671	+	0.284516i	$0.908167\pi$
$770$		0			0
$771$	−1.01722	−	3.13068i	−0.0366343	−	0.112749i
$772$	−3.85410	−	11.8617i	−0.138712	−	0.426912i
$773$	38.8885	+	28.2542i	1.39872	+	1.01623i	0.994844	+	0.101420i	$0.0323387\pi$
$773$	38.8885	+	28.2542i	1.39872	+	1.01623i	0.403880	+	0.914812i	$0.367661\pi$
$774$	−1.05573			−0.0379474
$775$	−2.72542	−	8.38800i	−0.0979002	−	0.301306i
$776$	9.41641			0.338029
$777$		0			0
$778$	−3.72542	−	11.4657i	−0.133563	−	0.411064i
$779$	1.97214	+	6.06961i	0.0706591	+	0.217466i
$780$	−5.00000			−0.179029
$781$	1.58359	−	4.87380i	0.0566654	−	0.174398i
$782$	−10.4164			−0.372490
$783$	2.92705	−	9.00854i	0.104604	−	0.321939i
$784$	5.66312	−	4.11450i	0.202254	−	0.146946i
$785$	5.52786	+	17.0130i	0.197298	+	0.607221i
$786$	−30.4894	−	22.1518i	−1.08752	−	0.790129i
$787$	−13.3992	+	9.73508i	−0.477629	+	0.347018i	−0.800407	−	0.599457i	$-0.795383\pi$
$787$	−13.3992	+	9.73508i	−0.477629	+	0.347018i	0.322778	+	0.946475i	$0.395383\pi$
$788$	10.6353	−	7.72696i	0.378865	−	0.275262i
$789$	−11.0172	−	8.00448i	−0.392223	−	0.284967i
$790$	−35.6525			−1.26846
$791$		0			0
$792$	0.854102	−	2.62866i	0.0303492	−	0.0934052i
$793$	9.56231			0.339567
$794$	−2.63525	+	8.11048i	−0.0935217	+	0.287830i
$795$	15.2254	+	11.0619i	0.539990	+	0.392326i
$796$	5.64590	+	17.3763i	0.200114	+	0.615886i
$797$	14.8156	+	45.5977i	0.524795	+	1.61515i	0.764720	+	0.644362i	$0.222877\pi$
$797$	14.8156	+	45.5977i	0.524795	+	1.61515i	−0.239925	+	0.970791i	$0.577123\pi$
$798$		0			0
$799$	−9.97871			−0.353022
$800$	4.04508	−	2.93893i	0.143015	−	0.103907i
$801$	−8.94427			−0.316030
$802$	−22.7254	−	16.5110i	−0.802463	−	0.583023i
$803$	2.13525	+	6.57164i	0.0753515	+	0.231908i
$804$	6.87132	+	21.1478i	0.242333	+	0.745824i
$805$		0			0
$806$	−0.545085	+	1.67760i	−0.0191998	+	0.0590909i
$807$	−16.7082			−0.588157
$808$	2.35410	−	7.24518i	0.0828170	−	0.254885i
$809$	21.7533	−	15.8047i	0.764805	−	0.555663i	−0.135575	−	0.990767i	$-0.543288\pi$
$809$	21.7533	−	15.8047i	0.764805	−	0.555663i	0.900380	+	0.435104i	$0.143288\pi$
$810$	−19.8992	−	14.4576i	−0.699186	−	0.507988i
$811$	−10.3090	−	7.48994i	−0.361999	−	0.263007i	0.391887	−	0.920014i	$-0.371823\pi$
$811$	−10.3090	−	7.48994i	−0.361999	−	0.263007i	−0.753885	+	0.657006i	$0.771823\pi$
$812$		0			0
$813$	36.8328	−	26.7606i	1.29178	−	0.938535i
$814$	10.1631	+	7.38394i	0.356217	+	0.258807i
$815$	−12.1353	−	8.81678i	−0.425079	−	0.308838i
$816$	−5.42705	+	3.94298i	−0.189985	+	0.138032i
$817$	0.465558	−	1.43284i	0.0162878	−	0.0501287i
$818$	26.5623			0.928729
$819$		0			0
$820$	1.54508	−	4.75528i	0.0539567	−	0.166062i
$821$	10.3992	+	32.0054i	0.362934	+	1.11700i	0.951265	+	0.308376i	$0.0997854\pi$
$821$	10.3992	+	32.0054i	0.362934	+	1.11700i	−0.588330	+	0.808621i	$0.700215\pi$
$822$	5.48936	+	16.8945i	0.191463	+	0.589263i
$823$	−19.4164	−	14.1068i	−0.676813	−	0.491734i	0.195486	−	0.980707i	$-0.437372\pi$
$823$	−19.4164	−	14.1068i	−0.676813	−	0.491734i	−0.872299	+	0.488973i	$0.837372\pi$
$824$	−4.85410			−0.169101
$825$	−4.77458	−	14.6946i	−0.166229	−	0.511601i
$826$		0			0
$827$	−44.1525	−	32.0787i	−1.53533	−	1.11548i	−0.953180	−	0.302404i	$-0.902211\pi$
$827$	−44.1525	−	32.0787i	−1.53533	−	1.11548i	−0.582152	−	0.813080i	$-0.697789\pi$
$828$	2.14590	+	6.60440i	0.0745751	+	0.229519i
$829$	11.6525	+	35.8626i	0.404707	+	1.24556i	0.921139	+	0.389233i	$0.127260\pi$
$829$	11.6525	+	35.8626i	0.404707	+	1.24556i	−0.516432	+	0.856328i	$0.672740\pi$
$830$	−22.2984	−	16.2007i	−0.773988	−	0.562335i
$831$	12.5238	−	38.5443i	0.434446	−	1.33709i
$832$	−1.00000			−0.0346688
$833$	−6.48936	+	19.9722i	−0.224843	+	0.691995i
$834$	−16.4443	+	11.9475i	−0.569419	+	0.413707i
$835$	39.6738			1.37297
$836$	3.19098	+	2.31838i	0.110362	+	0.0801830i
$837$	−3.19098	+	2.31838i	−0.110297	+	0.0801351i
$838$	−2.45492	+	1.78360i	−0.0848036	+	0.0616134i
$839$	−31.5517	−	22.9236i	−1.08928	−	0.791411i	−0.110006	−	0.993931i	$-0.535087\pi$
$839$	−31.5517	−	22.9236i	−1.08928	−	0.791411i	−0.979278	+	0.202519i	$0.935087\pi$
$840$		0			0
$841$	8.94427	−	6.49839i	0.308423	−	0.224083i
$842$	9.35410	−	28.7890i	0.322364	−	0.992133i
$843$	4.06888			0.140140
$844$	1.76393	−	5.42882i	0.0607170	−	0.186868i
$845$	2.23607			0.0769231
$846$	2.05573	+	6.32688i	0.0706774	+	0.217523i
$847$		0			0
$848$	3.04508	+	2.21238i	0.104569	+	0.0759736i
$849$	−45.0476			−1.54603
$850$	−4.63525	+	14.2658i	−0.158988	+	0.489315i
$851$	−31.5623			−1.08194
$852$	6.70820	+	4.87380i	0.229819	+	0.166973i
$853$	9.93363	+	30.5726i	0.340121	+	1.04678i	0.964144	+	0.265379i	$0.0854971\pi$
$853$	9.93363	+	30.5726i	0.340121	+	1.04678i	−0.624023	+	0.781406i	$0.714503\pi$
$854$		0			0
$855$	−10.3262	+	7.50245i	−0.353150	+	0.256578i
$856$	−1.97214	+	6.06961i	−0.0674062	+	0.207455i
$857$	−37.7426			−1.28926			−0.644632	−	0.764493i	$-0.722989\pi$
$857$	−37.7426			−1.28926			−0.644632	+	0.764493i	$0.722989\pi$
$858$	−0.954915	+	2.93893i	−0.0326003	+	0.100333i
$859$	−13.7533	+	9.99235i	−0.469256	+	0.340935i	−0.797151	−	0.603780i	$-0.793661\pi$
$859$	−13.7533	+	9.99235i	−0.469256	+	0.340935i	0.327895	+	0.944714i	$0.393661\pi$
$860$	−0.954915	+	0.693786i	−0.0325623	+	0.0236579i
$861$		0			0
$862$	−5.51722	+	4.00850i	−0.187917	+	0.136530i
$863$	5.69098	−	4.13474i	0.193723	−	0.140748i	−0.486696	−	0.873572i	$-0.661798\pi$
$863$	5.69098	−	4.13474i	0.193723	−	0.140748i	0.680419	+	0.732823i	$0.261798\pi$
$864$	−1.80902	−	1.31433i	−0.0615440	−	0.0447143i
$865$	5.89261	−	18.1356i	0.200355	−	0.616628i
$866$	20.1803	−	14.6619i	0.685756	−	0.498231i
$867$	−5.52786	+	17.0130i	−0.187736	+	0.577792i
$868$		0			0
$869$	−6.80902	+	20.9560i	−0.230980	+	0.710884i
$870$	6.54508	+	20.1437i	0.221899	+	0.682935i
$871$	−3.07295	−	9.45756i	−0.104123	−	0.320457i
$872$	2.42705	+	7.46969i	0.0821903	+	0.252956i
$873$	15.2361	+	11.0697i	0.515663	+	0.374651i
$874$	−9.90983			−0.335205
$875$		0			0
$876$	−11.1803			−0.377749
$877$	16.7533	+	12.1720i	0.565718	+	0.411018i	0.833547	−	0.552448i	$-0.186306\pi$
$877$	16.7533	+	12.1720i	0.565718	+	0.411018i	−0.267829	+	0.963466i	$0.586306\pi$
$878$	8.67376	+	26.6951i	0.292725	+	0.900916i
$879$	−5.91641	−	18.2088i	−0.199555	−	0.614169i
$880$	−0.954915	−	2.93893i	−0.0321902	−	0.0990712i
$881$	2.32624	−	7.15942i	0.0783729	−	0.241207i	−0.904192	−	0.427126i	$-0.859526\pi$
$881$	2.32624	−	7.15942i	0.0783729	−	0.241207i	0.982565	+	0.185919i	$0.0595261\pi$
$882$	14.0000			0.471405
$883$	−14.6008	+	44.9367i	−0.491356	+	1.51224i	0.331202	+	0.943560i	$0.392546\pi$
$883$	−14.6008	+	44.9367i	−0.491356	+	1.51224i	−0.822559	+	0.568680i	$0.807454\pi$
$884$	2.42705	−	1.76336i	0.0816306	−	0.0593081i
$885$	11.5451	−	35.5321i	0.388084	−	1.19440i
$886$	−28.9894	−	21.0620i	−0.973916	−	0.707592i
$887$	−35.1803	+	25.5600i	−1.18124	+	0.858221i	−0.992311	−	0.123769i	$-0.960502\pi$
$887$	−35.1803	+	25.5600i	−1.18124	+	0.858221i	−0.188929	+	0.981991i	$0.560502\pi$
$888$	−16.4443	+	11.9475i	−0.551834	+	0.400931i
$889$		0			0
$890$	−8.09017	+	5.87785i	−0.271183	+	0.197026i
$891$	−12.2984	+	8.93529i	−0.412011	+	0.299344i
$892$	1.71885	−	5.29007i	0.0575513	−	0.177125i
$893$	−9.49342			−0.317685
$894$	0.263932	−	0.812299i	0.00882721	−	0.0271674i
$895$	−12.8262	+	9.31881i	−0.428734	+	0.311493i
$896$		0			0
$897$	−2.39919	−	7.38394i	−0.0801065	−	0.246543i
$898$	−28.9164	−	21.0090i	−0.964953	−	0.701079i
$899$	7.47214			0.249210
$900$	10.0000			0.333333
$901$	−11.2918			−0.376184
$902$	−2.50000	−	1.81636i	−0.0832409	−	0.0604781i
$903$		0			0
$904$	4.02786	+	12.3965i	0.133965	+	0.412301i
$905$	45.6525			1.51754
$906$	4.63525	−	14.2658i	0.153996	−	0.473951i
$907$	8.38197			0.278319			0.139159	−	0.990270i	$-0.455560\pi$
$907$	8.38197			0.278319			0.139159	+	0.990270i	$0.455560\pi$
$908$	5.26393	−	16.2007i	0.174690	−	0.537640i
$909$	12.3262	−	8.95554i	0.408836	−	0.297036i
$910$		0			0
$911$	−36.2705	−	26.3521i	−1.20170	−	0.873083i	−0.207245	−	0.978289i	$-0.566450\pi$
$911$	−36.2705	−	26.3521i	−1.20170	−	0.873083i	−0.994450	+	0.105206i	$0.966450\pi$
$912$	−5.16312	+	3.75123i	−0.170968	+	0.124215i
$913$	−13.7812	+	10.0126i	−0.456090	+	0.331368i
$914$	7.42705	+	5.39607i	0.245665	+	0.178486i
$915$	−47.8115			−1.58060
$916$	21.7082	−	15.7719i	0.717259	−	0.521119i
$917$		0			0
$918$	6.70820			0.221404
$919$	−18.3647	+	56.5209i	−0.605797	+	1.86445i	−0.114581	+	0.993414i	$0.536552\pi$
$919$	−18.3647	+	56.5209i	−0.605797	+	1.86445i	−0.491216	+	0.871038i	$0.663448\pi$
$920$	6.28115	+	4.56352i	0.207083	+	0.150455i
$921$	−0.302439	−	0.930812i	−0.00996571	−	0.0306713i
$922$	0.208204	+	0.640786i	0.00685683	+	0.0211032i
$923$	−3.00000	−	2.17963i	−0.0987462	−	0.0717433i
$924$		0			0
$925$	−14.0451	+	43.2263i	−0.461800	+	1.42127i
$926$	40.7082			1.33775
$927$	−7.85410	−	5.70634i	−0.257963	−	0.187421i
$928$	1.30902	+	4.02874i	0.0429706	+	0.132250i
$929$	−10.7467	−	33.0750i	−0.352588	−	1.08515i	−0.957395	−	0.288782i	$-0.906750\pi$
$929$	−10.7467	−	33.0750i	−0.352588	−	1.08515i	0.604807	−	0.796372i	$-0.293250\pi$
$930$	2.72542	−	8.38800i	0.0893702	−	0.275053i
$931$	−6.17376	+	19.0009i	−0.202337	+	0.622729i
$932$	−18.2705			−0.598470
$933$	−10.7295	+	33.0220i	−0.351268	+	1.08109i
$934$	0.281153	−	0.204270i	0.00919961	−	0.00668390i
$935$	7.50000	+	5.44907i	0.245276	+	0.178204i
$936$	−1.61803	−	1.17557i	−0.0528871	−	0.0384247i
$937$	4.69098	−	3.40820i	0.153248	−	0.111341i	−0.508519	−	0.861051i	$-0.669807\pi$
$937$	4.69098	−	3.40820i	0.153248	−	0.111341i	0.661767	+	0.749710i	$0.269807\pi$
$938$		0			0
$939$	27.0967	+	19.6869i	0.884269	+	0.642459i
$940$	6.01722	+	4.37177i	0.196260	+	0.142591i
$941$	2.33688	−	1.69784i	0.0761801	−	0.0553481i	−0.549043	−	0.835794i	$-0.685008\pi$
$941$	2.33688	−	1.69784i	0.0761801	−	0.0553481i	0.625223	+	0.780446i	$0.285008\pi$
$942$	−5.52786	+	17.0130i	−0.180108	+	0.554314i
$943$	7.76393			0.252828
$944$	2.30902	−	7.10642i	0.0751521	−	0.231294i
$945$		0			0
$946$	0.225425	+	0.693786i	0.00732919	+	0.0225569i
$947$	4.56637	+	14.0538i	0.148387	+	0.456689i	0.997431	−	0.0716337i	$-0.0228213\pi$
$947$	4.56637	+	14.0538i	0.148387	+	0.456689i	−0.849044	+	0.528322i	$0.822821\pi$
$948$	−28.8435	−	20.9560i	−0.936792	−	0.680619i
$949$	5.00000			0.162307
$950$	−4.40983	+	13.5721i	−0.143074	+	0.440336i
$951$	−21.2574			−0.689317
$952$		0			0
$953$	17.6803	+	54.4145i	0.572722	+	1.76266i	0.643807	+	0.765188i	$0.277354\pi$
$953$	17.6803	+	54.4145i	0.572722	+	1.76266i	−0.0710846	+	0.997470i	$0.522646\pi$
$954$	2.32624	+	7.15942i	0.0753147	+	0.231795i
$955$	−44.8607	−	32.5932i	−1.45166	−	1.05469i
$956$	−1.74671	+	5.37582i	−0.0564927	+	0.173867i
$957$	13.0902			0.423145
$958$	−5.53444	+	17.0333i	−0.178810	+	0.550320i
$959$		0			0
$960$	5.00000			0.161374
$961$	22.5623	+	16.3925i	0.727816	+	0.528790i
$962$	7.35410	−	5.34307i	0.237106	−	0.172267i
$963$	−10.3262	+	7.50245i	−0.332758	+	0.241763i
$964$	1.30902	+	0.951057i	0.0421606	+	0.0306315i
$965$	−8.61803	−	26.5236i	−0.277424	−	0.853824i
$966$		0			0
$967$	0.309017	−	0.951057i	0.00993732	−	0.0305839i	−0.945965	−	0.324269i	$-0.894882\pi$
$967$	0.309017	−	0.951057i	0.00993732	−	0.0305839i	0.955902	+	0.293685i	$0.0948817\pi$
$968$	9.09017			0.292169
$969$	5.91641	−	18.2088i	0.190062	−	0.584952i
$970$	21.0557			0.676059
$971$	5.83688	+	17.9641i	0.187314	+	0.576495i	0.999981	−	0.00623504i	$-0.00198469\pi$
$971$	5.83688	+	17.9641i	0.187314	+	0.576495i	−0.812666	+	0.582730i	$0.801985\pi$
$972$	−5.52786	−	17.0130i	−0.177306	−	0.545693i
$973$		0			0
$974$	19.4377			0.622824
$975$	−11.1803			−0.358057
$976$	−9.56231			−0.306082
$977$	11.4721	+	8.33499i	0.367026	+	0.266660i	0.755977	−	0.654599i	$-0.227162\pi$
$977$	11.4721	+	8.33499i	0.367026	+	0.266660i	−0.388951	+	0.921259i	$0.627162\pi$
$978$	−4.63525	−	14.2658i	−0.148219	−	0.456172i
$979$	1.90983	+	5.87785i	0.0610384	+	0.187857i
$980$	12.6631	−	9.20029i	0.404508	−	0.293893i
$981$	−4.85410	+	14.9394i	−0.154980	+	0.476978i
$982$	−33.7426			−1.07677
$983$	−12.3435	+	37.9893i	−0.393695	+	1.21167i	0.536278	+	0.844042i	$0.319830\pi$
$983$	−12.3435	+	37.9893i	−0.393695	+	1.21167i	−0.929973	+	0.367628i	$0.880170\pi$
$984$	4.04508	−	2.93893i	0.128953	−	0.0936895i
$985$	23.7812	−	17.2780i	0.757731	−	0.550523i
$986$	−10.2812	−	7.46969i	−0.327419	−	0.237884i
$987$		0			0
$988$	2.30902	−	1.67760i	0.0734596	−	0.0533715i
$989$	−1.48278	−	1.07730i	−0.0471496	−	0.0342562i
$990$	1.90983	−	5.87785i	0.0606984	−	0.186810i
$991$	26.5344	−	19.2784i	0.842894	−	0.612399i	−0.0802833	−	0.996772i	$-0.525583\pi$
$991$	26.5344	−	19.2784i	0.842894	−	0.612399i	0.923178	+	0.384374i	$0.125583\pi$
$992$	0.545085	−	1.67760i	0.0173065	−	0.0532638i
$993$	−10.5279			−0.334092
$994$		0			0
$995$	12.6246	+	38.8546i	0.400227	+	1.23177i
$996$	−8.51722	−	26.2133i	−0.269878	−	0.830601i
$997$	12.0451	+	37.0710i	0.381472	+	1.17405i	0.939008	+	0.343896i	$0.111747\pi$
$997$	12.0451	+	37.0710i	0.381472	+	1.17405i	−0.557536	+	0.830153i	$0.688253\pi$
$998$	−15.1353	−	10.9964i	−0.479098	−	0.348085i
$999$	20.3262			0.643094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.a.391.1	yes	4
25.11	even	5	inner	650.2.l.a.261.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.a.261.1	✓	4	25.11	even	5	inner
650.2.l.a.391.1	yes	4	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.690983 + 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.309017 + 0.951057i) q^{8} +(-1.61803 + 1.17557i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.690983 + 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.309017 + 0.951057i) q^{8} +(-1.61803 + 1.17557i) q^{9} +(-0.690983 + 2.12663i) q^{10} +(1.11803 + 0.812299i) q^{11} +(-1.80902 + 1.31433i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-4.04508 + 2.93893i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.927051 - 2.85317i) q^{17} -2.00000 q^{18} +(0.881966 - 2.71441i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(0.427051 + 1.31433i) q^{22} +(-2.80902 - 2.04087i) q^{23} -2.23607 q^{24} +(-4.04508 + 2.93893i) q^{25} +1.00000 q^{26} +(1.80902 + 1.31433i) q^{27} +(-1.30902 - 4.02874i) q^{29} -5.00000 q^{30} +(-0.545085 + 1.67760i) q^{31} -1.00000 q^{32} +(-0.954915 + 2.93893i) q^{33} +(2.42705 - 1.76336i) q^{34} +(-1.61803 - 1.17557i) q^{36} +(7.35410 - 5.34307i) q^{37} +(2.30902 - 1.67760i) q^{38} +(1.80902 + 1.31433i) q^{39} -2.23607 q^{40} +(-1.80902 + 1.31433i) q^{41} +0.527864 q^{43} +(-0.427051 + 1.31433i) q^{44} +(-3.61803 - 2.62866i) q^{45} +(-1.07295 - 3.30220i) q^{46} +(-1.02786 - 3.16344i) q^{47} +(-1.80902 - 1.31433i) q^{48} -7.00000 q^{49} -5.00000 q^{50} +6.70820 q^{51} +(0.809017 + 0.587785i) q^{52} +(-1.16312 - 3.57971i) q^{53} +(0.690983 + 2.12663i) q^{54} +(-0.954915 + 2.93893i) q^{55} +6.38197 q^{57} +(1.30902 - 4.02874i) q^{58} +(-6.04508 + 4.39201i) q^{59} +(-4.04508 - 2.93893i) q^{60} +(7.73607 + 5.62058i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.80902 + 1.31433i) q^{65} +(-2.50000 + 1.81636i) q^{66} +(3.07295 - 9.45756i) q^{67} +3.00000 q^{68} +(2.39919 - 7.38394i) q^{69} +(-1.14590 - 3.52671i) q^{71} +(-0.618034 - 1.90211i) q^{72} +(4.04508 + 2.93893i) q^{73} +9.09017 q^{74} +(-9.04508 - 6.57164i) q^{75} +2.85410 q^{76} +(0.690983 + 2.12663i) q^{78} +(4.92705 + 15.1639i) q^{79} +(-1.80902 - 1.31433i) q^{80} +(-3.39919 + 10.4616i) q^{81} -2.23607 q^{82} +(-3.80902 + 11.7229i) q^{83} +6.70820 q^{85} +(0.427051 + 0.310271i) q^{86} +(7.66312 - 5.56758i) q^{87} +(-1.11803 + 0.812299i) q^{88} +(3.61803 + 2.62866i) q^{89} +(-1.38197 - 4.25325i) q^{90} +(1.07295 - 3.30220i) q^{92} -3.94427 q^{93} +(1.02786 - 3.16344i) q^{94} +6.38197 q^{95} +(-0.690983 - 2.12663i) q^{96} +(-2.90983 - 8.95554i) q^{97} +(-5.66312 - 4.11450i) q^{98} -2.76393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 5 q^{3} - q^{4} + 5 q^{5} - 5 q^{6} + q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + q^2 + 5 * q^3 - q^4 + 5 * q^5 - 5 * q^6 + q^8 - 2 * q^9	\( 4 q + q^{2} + 5 q^{3} - q^{4} + 5 q^{5} - 5 q^{6} + q^{8} - 2 q^{9} - 5 q^{10} - 5 q^{12} + q^{13} - 5 q^{15} - q^{16} - 3 q^{17} - 8 q^{18} + 8 q^{19} - 5 q^{20} - 5 q^{22} - 9 q^{23} - 5 q^{25} + 4 q^{26} + 5 q^{27} - 3 q^{29} - 20 q^{30} + 9 q^{31} - 4 q^{32} - 15 q^{33} + 3 q^{34} - 2 q^{36} + 16 q^{37} + 7 q^{38} + 5 q^{39} - 5 q^{41} + 20 q^{43} + 5 q^{44} - 10 q^{45} - 11 q^{46} - 22 q^{47} - 5 q^{48} - 28 q^{49} - 20 q^{50} + q^{52} + 11 q^{53} + 5 q^{54} - 15 q^{55} + 30 q^{57} + 3 q^{58} - 13 q^{59} - 5 q^{60} + 22 q^{61} + q^{62} - q^{64} + 5 q^{65} - 10 q^{66} + 19 q^{67} + 12 q^{68} - 15 q^{69} - 18 q^{71} + 2 q^{72} + 5 q^{73} + 14 q^{74} - 25 q^{75} - 2 q^{76} + 5 q^{78} + 13 q^{79} - 5 q^{80} + 11 q^{81} - 13 q^{83} - 5 q^{86} + 15 q^{87} + 10 q^{89} - 10 q^{90} + 11 q^{92} + 20 q^{93} + 22 q^{94} + 30 q^{95} - 5 q^{96} - 34 q^{97} - 7 q^{98} - 20 q^{99}+O(q^{100}) \) 4 * q + q^2 + 5 * q^3 - q^4 + 5 * q^5 - 5 * q^6 + q^8 - 2 * q^9 - 5 * q^10 - 5 * q^12 + q^13 - 5 * q^15 - q^16 - 3 * q^17 - 8 * q^18 + 8 * q^19 - 5 * q^20 - 5 * q^22 - 9 * q^23 - 5 * q^25 + 4 * q^26 + 5 * q^27 - 3 * q^29 - 20 * q^30 + 9 * q^31 - 4 * q^32 - 15 * q^33 + 3 * q^34 - 2 * q^36 + 16 * q^37 + 7 * q^38 + 5 * q^39 - 5 * q^41 + 20 * q^43 + 5 * q^44 - 10 * q^45 - 11 * q^46 - 22 * q^47 - 5 * q^48 - 28 * q^49 - 20 * q^50 + q^52 + 11 * q^53 + 5 * q^54 - 15 * q^55 + 30 * q^57 + 3 * q^58 - 13 * q^59 - 5 * q^60 + 22 * q^61 + q^62 - q^64 + 5 * q^65 - 10 * q^66 + 19 * q^67 + 12 * q^68 - 15 * q^69 - 18 * q^71 + 2 * q^72 + 5 * q^73 + 14 * q^74 - 25 * q^75 - 2 * q^76 + 5 * q^78 + 13 * q^79 - 5 * q^80 + 11 * q^81 - 13 * q^83 - 5 * q^86 + 15 * q^87 + 10 * q^89 - 10 * q^90 + 11 * q^92 + 20 * q^93 + 22 * q^94 + 30 * q^95 - 5 * q^96 - 34 * q^97 - 7 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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