LMFDB - Embedded newform 1110.2.l.a.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.16157 + 1.91070i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.90687 - 2.90687i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.16157 + 1.91070i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.90687 - 2.90687i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.91070 - 1.16157i) q^{10} -2.74715i q^{11} +(0.707107 - 0.707107i) q^{12} +5.21529i q^{13} +(2.90687 + 2.90687i) q^{14} +(-0.529716 - 2.17242i) q^{15} +1.00000 q^{16} +4.16103 q^{17} +1.00000 q^{18} +(1.87829 - 1.87829i) q^{19} +(1.16157 - 1.91070i) q^{20} +4.11094i q^{21} +2.74715 q^{22} -0.941868i q^{23} +(0.707107 + 0.707107i) q^{24} +(-2.30153 - 4.43880i) q^{25} -5.21529 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.90687 + 2.90687i) q^{28} +(4.28806 + 4.28806i) q^{29} +(2.17242 - 0.529716i) q^{30} +(5.51242 - 5.51242i) q^{31} +1.00000i q^{32} +(1.94253 + 1.94253i) q^{33} +4.16103i q^{34} +(2.17763 + 8.93067i) q^{35} +1.00000i q^{36} +(5.41489 + 2.77109i) q^{37} +(1.87829 + 1.87829i) q^{38} +(-3.68777 - 3.68777i) q^{39} +(1.91070 + 1.16157i) q^{40} +7.59421i q^{41} -4.11094 q^{42} -6.23482i q^{43} +2.74715i q^{44} +(1.91070 + 1.16157i) q^{45} +0.941868 q^{46} +(-6.04950 + 6.04950i) q^{47} +(-0.707107 + 0.707107i) q^{48} -9.89979i q^{49} +(4.43880 - 2.30153i) q^{50} +(-2.94229 + 2.94229i) q^{51} -5.21529i q^{52} +(8.31822 + 8.31822i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(5.24898 + 3.19100i) q^{55} +(-2.90687 - 2.90687i) q^{56} +2.65630i q^{57} +(-4.28806 + 4.28806i) q^{58} +(-1.92935 + 1.92935i) q^{59} +(0.529716 + 2.17242i) q^{60} +(-8.68618 + 8.68618i) q^{61} +(5.51242 + 5.51242i) q^{62} +(-2.90687 - 2.90687i) q^{63} -1.00000 q^{64} +(-9.96485 - 6.05791i) q^{65} +(-1.94253 + 1.94253i) q^{66} +(-5.51165 - 5.51165i) q^{67} -4.16103 q^{68} +(0.666001 + 0.666001i) q^{69} +(-8.93067 + 2.17763i) q^{70} -8.51973 q^{71} -1.00000 q^{72} +(2.98121 - 2.98121i) q^{73} +(-2.77109 + 5.41489i) q^{74} +(4.76613 + 1.51128i) q^{75} +(-1.87829 + 1.87829i) q^{76} +(-7.98561 - 7.98561i) q^{77} +(3.68777 - 3.68777i) q^{78} +(-1.46581 + 1.46581i) q^{79} +(-1.16157 + 1.91070i) q^{80} -1.00000 q^{81} -7.59421 q^{82} +(7.26193 + 7.26193i) q^{83} -4.11094i q^{84} +(-4.83331 + 7.95047i) q^{85} +6.23482 q^{86} -6.06423 q^{87} -2.74715 q^{88} +(1.62770 + 1.62770i) q^{89} +(-1.16157 + 1.91070i) q^{90} +(15.1602 + 15.1602i) q^{91} +0.941868i q^{92} +7.79574i q^{93} +(-6.04950 - 6.04950i) q^{94} +(1.40708 + 5.77059i) q^{95} +(-0.707107 - 0.707107i) q^{96} +10.0910 q^{97} +9.89979 q^{98} -2.74715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.16157	+	1.91070i	−0.519468	+	0.854490i
$5$	−1.16157	+	1.91070i	−0.519468	+	0.854490i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	2.90687	−	2.90687i	1.09869	−	1.09869i	0.104130	−	0.994564i	$-0.466794\pi$
$7$	2.90687	−	2.90687i	1.09869	−	1.09869i	0.994564	−	0.104130i	$-0.0332058\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.91070	−	1.16157i	−0.604216	−	0.367319i
$11$		−	2.74715i		−	0.828297i	−0.910209	−	0.414149i	$-0.864079\pi$
$11$		−	2.74715i		−	0.828297i	0.910209	−	0.414149i	$-0.135921\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$			5.21529i			1.44646i	0.690606	+	0.723231i	$0.257344\pi$
$13$			5.21529i			1.44646i	−0.690606	+	0.723231i	$0.742656\pi$
$14$	2.90687	+	2.90687i	0.776894	+	0.776894i
$15$	−0.529716	−	2.17242i	−0.136772	−	0.560916i
$16$	1.00000			0.250000
$17$	4.16103			1.00920			0.504599	−	0.863354i	$-0.331640\pi$
$17$	4.16103			1.00920			0.504599	+	0.863354i	$0.331640\pi$
$18$	1.00000			0.235702
$19$	1.87829	−	1.87829i	0.430909	−	0.430909i	−0.458029	−	0.888937i	$-0.651444\pi$
$19$	1.87829	−	1.87829i	0.430909	−	0.430909i	0.888937	+	0.458029i	$0.151444\pi$
$20$	1.16157	−	1.91070i	0.259734	−	0.427245i
$21$			4.11094i			0.897080i
$22$	2.74715			0.585695
$23$		−	0.941868i		−	0.196393i	−0.995167	−	0.0981965i	$-0.968693\pi$
$23$		−	0.941868i		−	0.196393i	0.995167	−	0.0981965i	$-0.0313074\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−2.30153	−	4.43880i	−0.460306	−	0.887760i
$26$	−5.21529			−1.02280
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.90687	+	2.90687i	−0.549347	+	0.549347i
$29$	4.28806	+	4.28806i	0.796273	+	0.796273i	0.982506	−	0.186233i	$-0.0596279\pi$
$29$	4.28806	+	4.28806i	0.796273	+	0.796273i	−0.186233	+	0.982506i	$0.559628\pi$
$30$	2.17242	−	0.529716i	0.396627	−	0.0967125i
$31$	5.51242	−	5.51242i	0.990060	−	0.990060i	−0.00989083	−	0.999951i	$-0.503148\pi$
$31$	5.51242	−	5.51242i	0.990060	−	0.990060i	0.999951	+	0.00989083i	$0.00314840\pi$
$32$			1.00000i			0.176777i
$33$	1.94253	+	1.94253i	0.338151	+	0.338151i
$34$			4.16103i			0.713611i
$35$	2.17763	+	8.93067i	0.368086	+	1.50956i
$36$			1.00000i			0.166667i
$37$	5.41489	+	2.77109i	0.890202	+	0.455565i
$37$	5.41489	+	2.77109i	0.890202	+	0.455565i
$38$	1.87829	+	1.87829i	0.304699	+	0.304699i
$39$	−3.68777	−	3.68777i	−0.590516	−	0.590516i
$40$	1.91070	+	1.16157i	0.302108	+	0.183660i
$41$			7.59421i			1.18602i	0.805196	+	0.593008i	$0.202060\pi$
$41$			7.59421i			1.18602i	−0.805196	+	0.593008i	$0.797940\pi$
$42$	−4.11094			−0.634331
$43$		−	6.23482i		−	0.950802i	−0.879769	−	0.475401i	$-0.842303\pi$
$43$		−	6.23482i		−	0.950802i	0.879769	−	0.475401i	$-0.157697\pi$
$44$			2.74715i			0.414149i
$45$	1.91070	+	1.16157i	0.284830	+	0.173156i
$46$	0.941868			0.138871
$47$	−6.04950	+	6.04950i	−0.882410	+	0.882410i	−0.993779	−	0.111369i	$-0.964477\pi$
$47$	−6.04950	+	6.04950i	−0.882410	+	0.882410i	0.111369	+	0.993779i	$0.464477\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	9.89979i		−	1.41426i
$50$	4.43880	−	2.30153i	0.627741	−	0.325485i
$51$	−2.94229	+	2.94229i	−0.412004	+	0.412004i
$52$		−	5.21529i		−	0.723231i
$53$	8.31822	+	8.31822i	1.14259	+	1.14259i	0.987974	+	0.154621i	$0.0494156\pi$
$53$	8.31822	+	8.31822i	1.14259	+	1.14259i	0.154621	+	0.987974i	$0.450584\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	5.24898	+	3.19100i	0.707772	+	0.430274i
$56$	−2.90687	−	2.90687i	−0.388447	−	0.388447i
$57$			2.65630i			0.351836i
$58$	−4.28806	+	4.28806i	−0.563050	+	0.563050i
$59$	−1.92935	+	1.92935i	−0.251180	+	0.251180i	−0.821454	−	0.570274i	$-0.806837\pi$
$59$	−1.92935	+	1.92935i	−0.251180	+	0.251180i	0.570274	+	0.821454i	$0.306837\pi$
$60$	0.529716	+	2.17242i	0.0683860	+	0.280458i
$61$	−8.68618	+	8.68618i	−1.11215	+	1.11215i	−0.119292	+	0.992859i	$0.538063\pi$
$61$	−8.68618	+	8.68618i	−1.11215	+	1.11215i	−0.992859	+	0.119292i	$0.961937\pi$
$62$	5.51242	+	5.51242i	0.700078	+	0.700078i
$63$	−2.90687	−	2.90687i	−0.366231	−	0.366231i
$64$	−1.00000			−0.125000
$65$	−9.96485	−	6.05791i	−1.23599	−	0.751391i
$66$	−1.94253	+	1.94253i	−0.239109	+	0.239109i
$67$	−5.51165	−	5.51165i	−0.673355	−	0.673355i	0.285133	−	0.958488i	$-0.407962\pi$
$67$	−5.51165	−	5.51165i	−0.673355	−	0.673355i	−0.958488	+	0.285133i	$0.907962\pi$
$68$	−4.16103			−0.504599
$69$	0.666001	+	0.666001i	0.0801771	+	0.0801771i
$70$	−8.93067	+	2.17763i	−1.06742	+	0.260276i
$71$	−8.51973			−1.01111			−0.505553	−	0.862796i	$-0.668711\pi$
$71$	−8.51973			−1.01111			−0.505553	+	0.862796i	$0.668711\pi$
$72$	−1.00000			−0.117851
$73$	2.98121	−	2.98121i	0.348924	−	0.348924i	−0.510785	−	0.859709i	$-0.670645\pi$
$73$	2.98121	−	2.98121i	0.348924	−	0.348924i	0.859709	+	0.510785i	$0.170645\pi$
$74$	−2.77109	+	5.41489i	−0.322133	+	0.629468i
$75$	4.76613	+	1.51128i	0.550346	+	0.174508i
$76$	−1.87829	+	1.87829i	−0.215454	+	0.215454i
$77$	−7.98561	−	7.98561i	−0.910045	−	0.910045i
$78$	3.68777	−	3.68777i	0.417558	−	0.417558i
$79$	−1.46581	+	1.46581i	−0.164916	+	0.164916i	−0.784741	−	0.619824i	$-0.787204\pi$
$79$	−1.46581	+	1.46581i	−0.164916	+	0.164916i	0.619824	+	0.784741i	$0.287204\pi$
$80$	−1.16157	+	1.91070i	−0.129867	+	0.213622i
$81$	−1.00000			−0.111111
$82$	−7.59421			−0.838640
$83$	7.26193	+	7.26193i	0.797101	+	0.797101i	0.982637	−	0.185536i	$-0.0594023\pi$
$83$	7.26193	+	7.26193i	0.797101	+	0.797101i	−0.185536	+	0.982637i	$0.559402\pi$
$84$		−	4.11094i		−	0.448540i
$85$	−4.83331	+	7.95047i	−0.524246	+	0.862350i
$86$	6.23482			0.672318
$87$	−6.06423			−0.650154
$88$	−2.74715			−0.292847
$89$	1.62770	+	1.62770i	0.172535	+	0.172535i	0.788092	−	0.615557i	$-0.211069\pi$
$89$	1.62770	+	1.62770i	0.172535	+	0.172535i	−0.615557	+	0.788092i	$0.711069\pi$
$90$	−1.16157	+	1.91070i	−0.122440	+	0.201405i
$91$	15.1602	+	15.1602i	1.58922	+	1.58922i
$92$			0.941868i			0.0981965i
$93$			7.79574i			0.808381i
$94$	−6.04950	−	6.04950i	−0.623958	−	0.623958i
$95$	1.40708	+	5.77059i	0.144364	+	0.592051i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	10.0910			1.02459			0.512294	−	0.858810i	$-0.328796\pi$
$97$	10.0910			1.02459			0.512294	+	0.858810i	$0.328796\pi$
$98$	9.89979			1.00003
$99$	−2.74715			−0.276099
$100$	2.30153	+	4.43880i	0.230153	+	0.443880i
$101$			9.40183i			0.935517i	0.883856	+	0.467759i	$0.154938\pi$
$101$			9.40183i			0.935517i	−0.883856	+	0.467759i	$0.845062\pi$
$102$	−2.94229	−	2.94229i	−0.291330	−	0.291330i
$103$	7.77490			0.766084			0.383042	−	0.923731i	$-0.374877\pi$
$103$	7.77490			0.766084			0.383042	+	0.923731i	$0.374877\pi$
$104$	5.21529			0.511402
$105$	−7.85475	−	4.77512i	−0.766546	−	0.466004i
$106$	−8.31822	+	8.31822i	−0.807937	+	0.807937i
$107$	5.67037	−	5.67037i	0.548176	−	0.548176i	−0.377737	−	0.925913i	$-0.623298\pi$
$107$	5.67037	−	5.67037i	0.548176	−	0.548176i	0.925913	+	0.377737i	$0.123298\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	5.58777	−	5.58777i	0.535211	−	0.535211i	−0.386908	−	0.922118i	$-0.626457\pi$
$109$	5.58777	−	5.58777i	0.535211	−	0.535211i	0.922118	+	0.386908i	$0.126457\pi$
$110$	−3.19100	+	5.24898i	−0.304250	+	0.500470i
$111$	−5.78837	+	1.86945i	−0.549407	+	0.177440i
$112$	2.90687	−	2.90687i	0.274673	−	0.274673i
$113$	−14.2804			−1.34339			−0.671694	−	0.740829i	$-0.734433\pi$
$113$	−14.2804			−1.34339			−0.671694	+	0.740829i	$0.734433\pi$
$114$	−2.65630			−0.248785
$115$	1.79963	+	1.09404i	0.167816	+	0.102020i
$116$	−4.28806	−	4.28806i	−0.398136	−	0.398136i
$117$	5.21529			0.482154
$118$	−1.92935	−	1.92935i	−0.177611	−	0.177611i
$119$	12.0956	−	12.0956i	1.10880	−	1.10880i
$120$	−2.17242	+	0.529716i	−0.198314	+	0.0483562i
$121$	3.45316			0.313923
$122$	−8.68618	−	8.68618i	−0.786410	−	0.786410i
$123$	−5.36992	−	5.36992i	−0.484189	−	0.484189i
$124$	−5.51242	+	5.51242i	−0.495030	+	0.495030i
$125$	11.1546	+	0.758434i	0.997696	+	0.0678364i
$126$	2.90687	−	2.90687i	0.258965	−	0.258965i
$127$	8.01885	−	8.01885i	0.711558	−	0.711558i	−0.255303	−	0.966861i	$-0.582175\pi$
$127$	8.01885	−	8.01885i	0.711558	−	0.711558i	0.966861	+	0.255303i	$0.0821752\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.40869	+	4.40869i	0.388163	+	0.388163i
$130$	6.05791	−	9.96485i	0.531314	−	0.873975i
$131$	6.63665	−	6.63665i	0.579847	−	0.579847i	−0.355014	−	0.934861i	$-0.615524\pi$
$131$	6.63665	−	6.63665i	0.579847	−	0.579847i	0.934861	+	0.355014i	$0.115524\pi$
$132$	−1.94253	−	1.94253i	−0.169075	−	0.169075i
$133$		−	10.9199i		−	0.946874i
$134$	5.51165	−	5.51165i	0.476134	−	0.476134i
$135$	−2.17242	+	0.529716i	−0.186972	+	0.0455907i
$136$		−	4.16103i		−	0.356806i
$137$	7.91811	−	7.91811i	0.676490	−	0.676490i	−0.282714	−	0.959204i	$-0.591235\pi$
$137$	7.91811	−	7.91811i	0.676490	−	0.676490i	0.959204	+	0.282714i	$0.0912348\pi$
$138$	−0.666001	+	0.666001i	−0.0566938	+	0.0566938i
$139$	−13.0683			−1.10844			−0.554221	−	0.832369i	$-0.686984\pi$
$139$	−13.0683			−1.10844			−0.554221	+	0.832369i	$0.686984\pi$
$140$	−2.17763	−	8.93067i	−0.184043	−	0.754779i
$141$		−	8.55529i		−	0.720485i
$142$		−	8.51973i		−	0.714960i
$143$	14.3272			1.19810
$144$		−	1.00000i		−	0.0833333i
$145$	−13.1741	+	3.21232i	−1.09405	+	0.266769i
$146$	2.98121	+	2.98121i	0.246727	+	0.246727i
$147$	7.00021	+	7.00021i	0.577368	+	0.577368i
$148$	−5.41489	−	2.77109i	−0.445101	−	0.227783i
$149$		−	6.80855i		−	0.557778i	−0.960323	−	0.278889i	$-0.910034\pi$
$149$		−	6.80855i		−	0.557778i	0.960323	−	0.278889i	$-0.0899661\pi$
$150$	−1.51128	+	4.76613i	−0.123395	+	0.389153i
$151$			17.8917i			1.45600i	0.685575	+	0.728002i	$0.259551\pi$
$151$			17.8917i			1.45600i	−0.685575	+	0.728002i	$0.740449\pi$
$152$	−1.87829	−	1.87829i	−0.152349	−	0.152349i
$153$		−	4.16103i		−	0.336399i
$154$	7.98561	−	7.98561i	0.643499	−	0.643499i
$155$	4.12953	+	16.9356i	0.331692	+	1.36030i
$156$	3.68777	+	3.68777i	0.295258	+	0.295258i
$157$	3.05662	−	3.05662i	0.243945	−	0.243945i	−0.574535	−	0.818480i	$-0.694817\pi$
$157$	3.05662	−	3.05662i	0.243945	−	0.243945i	0.818480	+	0.574535i	$0.194817\pi$
$158$	−1.46581	−	1.46581i	−0.116613	−	0.116613i
$159$	−11.7637			−0.932925
$160$	−1.91070	−	1.16157i	−0.151054	−	0.0918298i
$161$	−2.73789	−	2.73789i	−0.215776	−	0.215776i
$162$		−	1.00000i		−	0.0785674i
$163$	19.5350			1.53010			0.765050	−	0.643971i	$-0.222714\pi$
$163$	19.5350			1.53010			0.765050	+	0.643971i	$0.222714\pi$
$164$		−	7.59421i		−	0.593008i
$165$	−5.96796	+	1.45521i	−0.464605	+	0.113288i
$166$	−7.26193	+	7.26193i	−0.563635	+	0.563635i
$167$	−7.60664			−0.588620			−0.294310	−	0.955710i	$-0.595090\pi$
$167$	−7.60664			−0.588620			−0.294310	+	0.955710i	$0.595090\pi$
$168$	4.11094			0.317166
$169$	−14.1993			−1.09225
$170$	−7.95047	−	4.83331i	−0.609773	−	0.370698i
$171$	−1.87829	−	1.87829i	−0.143636	−	0.143636i
$172$			6.23482i			0.475401i
$173$	17.6561	−	17.6561i	1.34237	−	1.34237i	0.448675	−	0.893695i	$-0.351896\pi$
$173$	17.6561	−	17.6561i	1.34237	−	1.34237i	0.893695	−	0.448675i	$-0.148104\pi$
$174$		−	6.06423i		−	0.459728i
$175$	−19.5933	−	6.21277i	−1.48111	−	0.469642i
$176$		−	2.74715i		−	0.207074i
$177$		−	2.72851i		−	0.205087i
$178$	−1.62770	+	1.62770i	−0.122001	+	0.122001i
$179$	5.23093	+	5.23093i	0.390978	+	0.390978i	0.875036	−	0.484058i	$-0.160838\pi$
$179$	5.23093	+	5.23093i	0.390978	+	0.390978i	−0.484058	+	0.875036i	$0.660838\pi$
$180$	−1.91070	−	1.16157i	−0.142415	−	0.0865780i
$181$	6.81886			0.506842			0.253421	−	0.967356i	$-0.418444\pi$
$181$	6.81886			0.506842			0.253421	+	0.967356i	$0.418444\pi$
$182$	−15.1602	+	15.1602i	−1.12375	+	1.12375i
$183$		−	12.2841i		−	0.908068i
$184$	−0.941868			−0.0694354
$185$	−11.5845	+	7.12741i	−0.851707	+	0.524018i
$186$	−7.79574			−0.571612
$187$		−	11.4310i		−	0.835916i
$188$	6.04950	−	6.04950i	0.441205	−	0.441205i
$189$	4.11094			0.299027
$190$	−5.77059	+	1.40708i	−0.418643	+	0.102081i
$191$	−7.19163	−	7.19163i	−0.520368	−	0.520368i	0.397315	−	0.917683i	$-0.369942\pi$
$191$	−7.19163	−	7.19163i	−0.520368	−	0.520368i	−0.917683	+	0.397315i	$0.869942\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	16.3418i		−	1.17631i	−0.808749	−	0.588154i	$-0.799855\pi$
$193$		−	16.3418i		−	1.17631i	0.808749	−	0.588154i	$-0.200145\pi$
$194$			10.0910i			0.724493i
$195$	11.3298	−	2.76262i	0.811344	−	0.197836i
$196$			9.89979i			0.707128i
$197$	−11.4834	+	11.4834i	−0.818161	+	0.818161i	−0.985841	−	0.167680i	$-0.946372\pi$
$197$	−11.4834	+	11.4834i	−0.818161	+	0.818161i	0.167680	+	0.985841i	$0.446372\pi$
$198$		−	2.74715i		−	0.195232i
$199$	12.9349	+	12.9349i	0.916929	+	0.916929i	0.996805	−	0.0798762i	$-0.0254525\pi$
$199$	12.9349	+	12.9349i	0.916929	+	0.916929i	−0.0798762	+	0.996805i	$0.525452\pi$
$200$	−4.43880	+	2.30153i	−0.313871	+	0.162743i
$201$	7.79465			0.549792
$202$	−9.40183			−0.661511
$203$	24.9297			1.74972
$204$	2.94229	−	2.94229i	0.206002	−	0.206002i
$205$	−14.5102	−	8.82118i	−1.01344	−	0.616098i
$206$			7.77490i			0.541703i
$207$	−0.941868			−0.0654644
$208$			5.21529i			0.361616i
$209$	−5.15994	−	5.15994i	−0.356921	−	0.356921i
$210$	4.77512	−	7.85475i	0.329515	−	0.542030i
$211$	−23.4609			−1.61512			−0.807558	−	0.589788i	$-0.799211\pi$
$211$	−23.4609			−1.61512			−0.807558	+	0.589788i	$0.799211\pi$
$212$	−8.31822	−	8.31822i	−0.571297	−	0.571297i
$213$	6.02436	−	6.02436i	0.412782	−	0.412782i
$214$	5.67037	+	5.67037i	0.387619	+	0.387619i
$215$	11.9129	+	7.24216i	0.812450	+	0.493911i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$		−	32.0478i		−	2.17555i
$218$	5.58777	+	5.58777i	0.378451	+	0.378451i
$219$			4.21607i			0.284895i
$220$	−5.24898	−	3.19100i	−0.353886	−	0.215137i
$221$			21.7010i			1.45977i
$222$	−1.86945	−	5.78837i	−0.125469	−	0.388490i
$223$	−2.83314	−	2.83314i	−0.189721	−	0.189721i	0.605854	−	0.795576i	$-0.292831\pi$
$223$	−2.83314	−	2.83314i	−0.189721	−	0.189721i	−0.795576	+	0.605854i	$0.792831\pi$
$224$	2.90687	+	2.90687i	0.194223	+	0.194223i
$225$	−4.43880	+	2.30153i	−0.295920	+	0.153435i
$226$		−	14.2804i		−	0.949919i
$227$	7.49379			0.497380			0.248690	−	0.968583i	$-0.420000\pi$
$227$	7.49379			0.497380			0.248690	+	0.968583i	$0.420000\pi$
$228$		−	2.65630i		−	0.175918i
$229$			24.0930i			1.59211i	0.605224	+	0.796055i	$0.293083\pi$
$229$			24.0930i			1.59211i	−0.605224	+	0.796055i	$0.706917\pi$
$230$	−1.09404	+	1.79963i	−0.0721390	+	0.118664i
$231$	11.2934			0.743049
$232$	4.28806	−	4.28806i	0.281525	−	0.281525i
$233$	−7.78522	+	7.78522i	−0.510027	+	0.510027i	−0.914535	−	0.404508i	$-0.867443\pi$
$233$	−7.78522	+	7.78522i	−0.510027	+	0.510027i	0.404508	+	0.914535i	$0.367443\pi$
$234$			5.21529i			0.340934i
$235$	−4.53187	−	18.5857i	−0.295627	−	1.21239i
$236$	1.92935	−	1.92935i	0.125590	−	0.125590i
$237$		−	2.07297i		−	0.134654i
$238$	12.0956	+	12.0956i	0.784040	+	0.784040i
$239$	1.88427	−	1.88427i	0.121884	−	0.121884i	−0.643534	−	0.765418i	$-0.722532\pi$
$239$	1.88427	−	1.88427i	0.121884	−	0.121884i	0.765418	+	0.643534i	$0.222532\pi$
$240$	−0.529716	−	2.17242i	−0.0341930	−	0.140229i
$241$	−18.1268	−	18.1268i	−1.16765	−	1.16765i	−0.982760	−	0.184888i	$-0.940808\pi$
$241$	−18.1268	−	18.1268i	−1.16765	−	1.16765i	−0.184888	−	0.982760i	$-0.559192\pi$
$242$			3.45316i			0.221977i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	8.68618	−	8.68618i	0.556076	−	0.556076i
$245$	18.9155	+	11.4993i	1.20847	+	0.734661i
$246$	5.36992	−	5.36992i	0.342373	−	0.342373i
$247$	9.79582	+	9.79582i	0.623293	+	0.623293i
$248$	−5.51242	−	5.51242i	−0.350039	−	0.350039i
$249$	−10.2699			−0.650830
$250$	−0.758434	+	11.1546i	−0.0479676	+	0.705478i
$251$	−10.2960	+	10.2960i	−0.649879	+	0.649879i	−0.952964	−	0.303085i	$-0.901983\pi$
$251$	−10.2960	+	10.2960i	−0.649879	+	0.649879i	0.303085	+	0.952964i	$0.401983\pi$
$252$	2.90687	+	2.90687i	0.183116	+	0.183116i
$253$	−2.58745			−0.162672
$254$	8.01885	+	8.01885i	0.503148	+	0.503148i
$255$	−2.20417	−	9.03950i	−0.138030	−	0.566076i
$256$	1.00000			0.0625000
$257$	2.69763			0.168274			0.0841369	−	0.996454i	$-0.473187\pi$
$257$	2.69763			0.168274			0.0841369	+	0.996454i	$0.473187\pi$
$258$	−4.40869	+	4.40869i	−0.274473	+	0.274473i
$259$	23.7956	−	7.68517i	1.47859	−	0.477533i
$260$	9.96485	+	6.05791i	0.617994	+	0.375695i
$261$	4.28806	−	4.28806i	0.265424	−	0.265424i
$262$	6.63665	+	6.63665i	0.410014	+	0.410014i
$263$	15.0006	−	15.0006i	0.924974	−	0.924974i	−0.0724014	−	0.997376i	$-0.523066\pi$
$263$	15.0006	−	15.0006i	0.924974	−	0.924974i	0.997376	+	0.0724014i	$0.0230663\pi$
$264$	1.94253	−	1.94253i	0.119554	−	0.119554i
$265$	−25.5557	+	6.23144i	−1.56988	+	0.382794i
$266$	10.9199			0.669541
$267$	−2.30191			−0.140875
$268$	5.51165	+	5.51165i	0.336678	+	0.336678i
$269$			3.86256i			0.235505i	0.993043	+	0.117752i	$0.0375689\pi$
$269$			3.86256i			0.235505i	−0.993043	+	0.117752i	$0.962431\pi$
$270$	−0.529716	−	2.17242i	−0.0322375	−	0.132209i
$271$	−11.2551			−0.683697			−0.341848	−	0.939755i	$-0.611053\pi$
$271$	−11.2551			−0.683697			−0.341848	+	0.939755i	$0.611053\pi$
$272$	4.16103			0.252300
$273$	−21.4397			−1.29759
$274$	7.91811	+	7.91811i	0.478351	+	0.478351i
$275$	−12.1941	+	6.32265i	−0.735330	+	0.381270i
$276$	−0.666001	−	0.666001i	−0.0400886	−	0.0400886i
$277$		−	16.2009i		−	0.973420i	−0.873564	−	0.486710i	$-0.838197\pi$
$277$		−	16.2009i		−	0.973420i	0.873564	−	0.486710i	$-0.161803\pi$
$278$		−	13.0683i		−	0.783787i
$279$	−5.51242	−	5.51242i	−0.330020	−	0.330020i
$280$	8.93067	−	2.17763i	0.533710	−	0.130138i
$281$	−7.78699	−	7.78699i	−0.464533	−	0.464533i	0.435605	−	0.900138i	$-0.356534\pi$
$281$	−7.78699	−	7.78699i	−0.464533	−	0.464533i	−0.900138	+	0.435605i	$0.856534\pi$
$282$	8.55529			0.509460
$283$	21.1035			1.25447			0.627237	−	0.778829i	$-0.284186\pi$
$283$	21.1035			1.25447			0.627237	+	0.778829i	$0.284186\pi$
$284$	8.51973			0.505553
$285$	−5.07539	−	3.08547i	−0.300640	−	0.182767i
$286$			14.3272i			0.847185i
$287$	22.0754	+	22.0754i	1.30307	+	1.30307i
$288$	1.00000			0.0589256
$289$	0.314185			0.0184815
$290$	−3.21232	−	13.1741i	−0.188634	−	0.773607i
$291$	−7.13543	+	7.13543i	−0.418286	+	0.418286i
$292$	−2.98121	+	2.98121i	−0.174462	+	0.174462i
$293$	−2.76877	−	2.76877i	−0.161753	−	0.161753i	0.621590	−	0.783343i	$-0.286487\pi$
$293$	−2.76877	−	2.76877i	−0.161753	−	0.161753i	−0.783343	+	0.621590i	$0.786487\pi$
$294$	−7.00021	+	7.00021i	−0.408261	+	0.408261i
$295$	−1.44534	−	5.92747i	−0.0841507	−	0.345110i
$296$	2.77109	−	5.41489i	0.161067	−	0.314734i
$297$	1.94253	−	1.94253i	0.112717	−	0.112717i
$298$	6.80855			0.394408
$299$	4.91212			0.284075
$300$	−4.76613	−	1.51128i	−0.275173	−	0.0872538i
$301$	−18.1238	−	18.1238i	−1.04464	−	1.04464i
$302$	−17.8917			−1.02955
$303$	−6.64810	−	6.64810i	−0.381923	−	0.381923i
$304$	1.87829	−	1.87829i	0.107727	−	0.107727i
$305$	−6.50709	−	26.6862i	−0.372595	−	1.52805i
$306$	4.16103			0.237870
$307$	−6.12720	−	6.12720i	−0.349698	−	0.349698i	0.510299	−	0.859997i	$-0.329535\pi$
$307$	−6.12720	−	6.12720i	−0.349698	−	0.349698i	−0.859997	+	0.510299i	$0.829535\pi$
$308$	7.98561	+	7.98561i	0.455023	+	0.455023i
$309$	−5.49768	+	5.49768i	−0.312752	+	0.312752i
$310$	−16.9356	+	4.12953i	−0.961878	+	0.234542i
$311$	−1.06423	+	1.06423i	−0.0603471	+	0.0603471i	−0.736636	−	0.676289i	$-0.763587\pi$
$311$	−1.06423	+	1.06423i	−0.0603471	+	0.0603471i	0.676289	+	0.736636i	$0.263587\pi$
$312$	−3.68777	+	3.68777i	−0.208779	+	0.208779i
$313$		−	7.63668i		−	0.431650i	−0.976432	−	0.215825i	$-0.930756\pi$
$313$		−	7.63668i		−	0.431650i	0.976432	−	0.215825i	$-0.0692441\pi$
$314$	3.05662	+	3.05662i	0.172495	+	0.172495i
$315$	8.93067	−	2.17763i	0.503186	−	0.122695i
$316$	1.46581	−	1.46581i	0.0824581	−	0.0824581i
$317$	−19.5287	−	19.5287i	−1.09684	−	1.09684i	−0.994778	−	0.102064i	$-0.967455\pi$
$317$	−19.5287	−	19.5287i	−1.09684	−	1.09684i	−0.102064	−	0.994778i	$-0.532545\pi$
$318$		−	11.7637i		−	0.659677i
$319$	11.7800	−	11.7800i	0.659551	−	0.659551i
$320$	1.16157	−	1.91070i	0.0649335	−	0.106811i
$321$			8.01912i			0.447584i
$322$	2.73789	−	2.73789i	0.152577	−	0.152577i
$323$	7.81562	−	7.81562i	0.434872	−	0.434872i
$324$	1.00000			0.0555556
$325$	23.1497	−	12.0032i	1.28411	−	0.665815i
$326$			19.5350i			1.08194i
$327$			7.90229i			0.436998i
$328$	7.59421			0.419320
$329$			35.1702i			1.93900i
$330$	−1.45521	−	5.96796i	−0.0801067	−	0.328526i
$331$	−10.6002	−	10.6002i	−0.582640	−	0.582640i	0.352988	−	0.935628i	$-0.385166\pi$
$331$	−10.6002	−	10.6002i	−0.582640	−	0.582640i	−0.935628	+	0.352988i	$0.885166\pi$
$332$	−7.26193	−	7.26193i	−0.398550	−	0.398550i
$333$	2.77109	−	5.41489i	0.151855	−	0.296734i
$334$		−	7.60664i		−	0.416217i
$335$	16.9332	−	4.12895i	0.925162	−	0.225589i
$336$			4.11094i			0.224270i
$337$	14.7087	+	14.7087i	0.801235	+	0.801235i	0.983289	−	0.182054i	$-0.0582746\pi$
$337$	14.7087	+	14.7087i	0.801235	+	0.801235i	−0.182054	+	0.983289i	$0.558275\pi$
$338$		−	14.1993i		−	0.772340i
$339$	10.0978	−	10.0978i	0.548436	−	0.548436i
$340$	4.83331	−	7.95047i	0.262123	−	0.431175i
$341$	−15.1435	−	15.1435i	−0.820064	−	0.820064i
$342$	1.87829	−	1.87829i	0.101566	−	0.101566i
$343$	−8.42932	−	8.42932i	−0.455140	−	0.455140i
$344$	−6.23482			−0.336159
$345$	−2.04613	+	0.498923i	−0.110160	+	0.0268611i
$346$	17.6561	+	17.6561i	0.949199	+	0.949199i
$347$			5.20503i			0.279421i	0.990192	+	0.139710i	$0.0446172\pi$
$347$			5.20503i			0.279421i	−0.990192	+	0.139710i	$0.955383\pi$
$348$	6.06423			0.325077
$349$		−	8.31963i		−	0.445339i	−0.974894	−	0.222670i	$-0.928523\pi$
$349$		−	8.31963i		−	0.445339i	0.974894	−	0.222670i	$-0.0714771\pi$
$350$	6.21277	−	19.5933i	0.332087	−	1.04730i
$351$	−3.68777	+	3.68777i	−0.196839	+	0.196839i
$352$	2.74715			0.146424
$353$	−32.6034			−1.73530			−0.867651	−	0.497173i	$-0.834371\pi$
$353$	−32.6034			−1.73530			−0.867651	+	0.497173i	$0.834371\pi$
$354$	2.72851			0.145019
$355$	9.89623	−	16.2786i	0.525237	−	0.863980i
$356$	−1.62770	−	1.62770i	−0.0862677	−	0.0862677i
$357$			17.1057i			0.905331i
$358$	−5.23093	+	5.23093i	−0.276463	+	0.276463i
$359$		−	17.3163i		−	0.913921i	−0.889487	−	0.456960i	$-0.848938\pi$
$359$		−	17.3163i		−	0.913921i	0.889487	−	0.456960i	$-0.151062\pi$
$360$	1.16157	−	1.91070i	0.0612199	−	0.100703i
$361$			11.9441i			0.628635i
$362$			6.81886i			0.358391i
$363$	−2.44175	+	2.44175i	−0.128159	+	0.128159i
$364$	−15.1602	−	15.1602i	−0.794610	−	0.794610i
$365$	2.23332	+	9.15906i	0.116897	+	0.479407i
$366$	12.2841			0.642101
$367$	−19.8485	+	19.8485i	−1.03608	+	1.03608i	−0.0367606	+	0.999324i	$0.511704\pi$
$367$	−19.8485	+	19.8485i	−1.03608	+	1.03608i	−0.999324	+	0.0367606i	$0.988296\pi$
$368$		−	0.941868i		−	0.0490983i
$369$	7.59421			0.395339
$370$	−7.12741	−	11.5845i	−0.370536	−	0.602248i
$371$	48.3600			2.51072
$372$		−	7.79574i		−	0.404190i
$373$	−19.3419	+	19.3419i	−1.00149	+	1.00149i	−0.00148728	+	0.999999i	$0.500473\pi$
$373$	−19.3419	+	19.3419i	−1.00149	+	1.00149i	−0.999999	+	0.00148728i	$0.999527\pi$
$374$	11.4310			0.591082
$375$	−8.42378	+	7.35119i	−0.435002	+	0.379614i
$376$	6.04950	+	6.04950i	0.311979	+	0.311979i
$377$	−22.3635	+	22.3635i	−1.15178	+	1.15178i
$378$			4.11094i			0.211444i
$379$			3.56273i			0.183005i	0.995805	+	0.0915027i	$0.0291670\pi$
$379$			3.56273i			0.183005i	−0.995805	+	0.0915027i	$0.970833\pi$
$380$	−1.40708	−	5.77059i	−0.0721819	−	0.296025i
$381$			11.3404i			0.580985i
$382$	7.19163	−	7.19163i	0.367956	−	0.367956i
$383$		−	17.5102i		−	0.894730i	−0.894351	−	0.447365i	$-0.852362\pi$
$383$		−	17.5102i		−	0.894730i	0.894351	−	0.447365i	$-0.147638\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	24.5339	−	5.98228i	1.25036	−	0.304885i
$386$	16.3418			0.831776
$387$	−6.23482			−0.316934
$388$	−10.0910			−0.512294
$389$	−5.52680	+	5.52680i	−0.280220	+	0.280220i	−0.833197	−	0.552977i	$-0.813492\pi$
$389$	−5.52680	+	5.52680i	−0.280220	+	0.280220i	0.552977	+	0.833197i	$0.313492\pi$
$390$	2.76262	+	11.3298i	0.139891	+	0.573707i
$391$		−	3.91914i		−	0.198200i
$392$	−9.89979			−0.500015
$393$			9.38564i			0.473443i
$394$	−11.4834	−	11.4834i	−0.578527	−	0.578527i
$395$	−1.09808	−	4.50335i	−0.0552505	−	0.226588i
$396$	2.74715			0.138050
$397$	−7.17123	−	7.17123i	−0.359913	−	0.359913i	0.503867	−	0.863781i	$-0.331910\pi$
$397$	−7.17123	−	7.17123i	−0.359913	−	0.359913i	−0.863781	+	0.503867i	$0.831910\pi$
$398$	−12.9349	+	12.9349i	−0.648366	+	0.648366i
$399$	7.72152	+	7.72152i	0.386560	+	0.386560i
$400$	−2.30153	−	4.43880i	−0.115076	−	0.221940i
$401$	12.3057	−	12.3057i	0.614518	−	0.614518i	−0.329602	−	0.944120i	$-0.606914\pi$
$401$	12.3057	−	12.3057i	0.614518	−	0.614518i	0.944120	+	0.329602i	$0.106914\pi$
$402$			7.79465i			0.388762i
$403$	28.7489	+	28.7489i	1.43208	+	1.43208i
$404$		−	9.40183i		−	0.467759i
$405$	1.16157	−	1.91070i	0.0577187	−	0.0949433i
$406$			24.9297i			1.23724i
$407$	7.61262	−	14.8755i	0.377343	−	0.737352i
$408$	2.94229	+	2.94229i	0.145665	+	0.145665i
$409$	20.8384	+	20.8384i	1.03039	+	1.03039i	0.999523	+	0.0308695i	$0.00982762\pi$
$409$	20.8384	+	20.8384i	1.03039	+	1.03039i	0.0308695	+	0.999523i	$0.490172\pi$
$410$	8.82118	−	14.5102i	0.435647	−	0.716610i
$411$			11.1979i			0.552352i
$412$	−7.77490			−0.383042
$413$			11.2167i			0.551939i
$414$		−	0.941868i		−	0.0462903i
$415$	−22.3106	+	5.44014i	−1.09518	+	0.267046i
$416$	−5.21529			−0.255701
$417$	9.24072	−	9.24072i	0.452520	−	0.452520i
$418$	5.15994	−	5.15994i	0.252381	−	0.252381i
$419$		−	36.4587i		−	1.78113i	−0.454860	−	0.890563i	$-0.650311\pi$
$419$		−	36.4587i		−	1.78113i	0.454860	−	0.890563i	$-0.349689\pi$
$420$	7.85475	+	4.77512i	0.383273	+	0.233002i
$421$	15.1883	−	15.1883i	0.740231	−	0.740231i	−0.232392	−	0.972622i	$-0.574655\pi$
$421$	15.1883	−	15.1883i	0.740231	−	0.740231i	0.972622	+	0.232392i	$0.0746551\pi$
$422$		−	23.4609i		−	1.14206i
$423$	6.04950	+	6.04950i	0.294137	+	0.294137i
$424$	8.31822	−	8.31822i	0.403968	−	0.403968i
$425$	−9.57674	−	18.4700i	−0.464540	−	0.895926i
$426$	6.02436	+	6.02436i	0.291881	+	0.291881i
$427$			50.4992i			2.44383i
$428$	−5.67037	+	5.67037i	−0.274088	+	0.274088i
$429$	−10.1309	+	10.1309i	−0.489123	+	0.489123i
$430$	−7.24216	+	11.9129i	−0.349248	+	0.574489i
$431$	−6.39166	+	6.39166i	−0.307875	+	0.307875i	−0.844085	−	0.536210i	$-0.819856\pi$
$431$	−6.39166	+	6.39166i	−0.307875	+	0.307875i	0.536210	+	0.844085i	$0.319856\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	15.4619	+	15.4619i	0.743053	+	0.743053i	0.973164	−	0.230111i	$-0.0739089\pi$
$433$	15.4619	+	15.4619i	0.743053	+	0.743053i	−0.230111	+	0.973164i	$0.573909\pi$
$434$	32.0478			1.53834
$435$	7.04401	−	11.5869i	0.337734	−	0.555550i
$436$	−5.58777	+	5.58777i	−0.267605	+	0.267605i
$437$	−1.76910	−	1.76910i	−0.0846275	−	0.0846275i
$438$	−4.21607			−0.201451
$439$	−15.6685	−	15.6685i	−0.747816	−	0.747816i	0.226253	−	0.974069i	$-0.427352\pi$
$439$	−15.6685	−	15.6685i	−0.747816	−	0.747816i	−0.974069	+	0.226253i	$0.927352\pi$
$440$	3.19100	−	5.24898i	0.152125	−	0.250235i
$441$	−9.89979			−0.471419
$442$	−21.7010			−1.03221
$443$	−27.2120	+	27.2120i	−1.29288	+	1.29288i	−0.359887	+	0.932996i	$0.617185\pi$
$443$	−27.2120	+	27.2120i	−1.29288	+	1.29288i	−0.932996	+	0.359887i	$0.882815\pi$
$444$	5.78837	−	1.86945i	0.274704	−	0.0887200i
$445$	−5.00071	+	1.21936i	−0.237056	+	0.0578031i
$446$	2.83314	−	2.83314i	0.134153	−	0.134153i
$447$	4.81437	+	4.81437i	0.227712	+	0.227712i
$448$	−2.90687	+	2.90687i	−0.137337	+	0.137337i
$449$	18.9735	−	18.9735i	0.895416	−	0.895416i	−0.0996105	−	0.995027i	$-0.531760\pi$
$449$	18.9735	−	18.9735i	0.895416	−	0.895416i	0.995027	+	0.0996105i	$0.0317597\pi$
$450$	−2.30153	−	4.43880i	−0.108495	−	0.209247i
$451$	20.8624			0.982374
$452$	14.2804			0.671694
$453$	−12.6513	−	12.6513i	−0.594411	−	0.594411i
$454$			7.49379i			0.351701i
$455$	−46.5761	+	11.3570i	−2.18352	+	0.532423i
$456$	2.65630			0.124393
$457$	−9.71477			−0.454438			−0.227219	−	0.973844i	$-0.572963\pi$
$457$	−9.71477			−0.454438			−0.227219	+	0.973844i	$0.572963\pi$
$458$	−24.0930			−1.12579
$459$	2.94229	+	2.94229i	0.137335	+	0.137335i
$460$	−1.79963	−	1.09404i	−0.0839080	−	0.0510100i
$461$	17.2735	+	17.2735i	0.804507	+	0.804507i	0.983796	−	0.179290i	$-0.0573799\pi$
$461$	17.2735	+	17.2735i	0.804507	+	0.804507i	−0.179290	+	0.983796i	$0.557380\pi$
$462$			11.2934i			0.525415i
$463$			16.3891i			0.761664i	0.924644	+	0.380832i	$0.124362\pi$
$463$			16.3891i			0.761664i	−0.924644	+	0.380832i	$0.875638\pi$
$464$	4.28806	+	4.28806i	0.199068	+	0.199068i
$465$	−14.8953	−	9.05527i	−0.690753	−	0.419928i
$466$	−7.78522	−	7.78522i	−0.360643	−	0.360643i
$467$	1.29508			0.0599293			0.0299647	−	0.999551i	$-0.490461\pi$
$467$	1.29508			0.0599293			0.0299647	+	0.999551i	$0.490461\pi$
$468$	−5.21529			−0.241077
$469$	−32.0433			−1.47962
$470$	18.5857	−	4.53187i	0.857293	−	0.209040i
$471$			4.32271i			0.199180i
$472$	1.92935	+	1.92935i	0.0888054	+	0.0888054i
$473$	−17.1280			−0.787547
$474$	2.07297			0.0952144
$475$	−12.6603	−	4.01441i	−0.580894	−	0.184194i
$476$	−12.0956	+	12.0956i	−0.554400	+	0.554400i
$477$	8.31822	−	8.31822i	0.380865	−	0.380865i
$478$	1.88427	+	1.88427i	0.0861847	+	0.0861847i
$479$	−27.0885	+	27.0885i	−1.23770	+	1.23770i	−0.276766	+	0.960937i	$0.589263\pi$
$479$	−27.0885	+	27.0885i	−1.23770	+	1.23770i	−0.960937	+	0.276766i	$0.910737\pi$
$480$	2.17242	−	0.529716i	0.0991569	−	0.0241781i
$481$	−14.4521	+	28.2402i	−0.658958	+	1.28764i
$482$	18.1268	−	18.1268i	0.825652	−	0.825652i
$483$	3.87196			0.176180
$484$	−3.45316			−0.156962
$485$	−11.7214	+	19.2809i	−0.532241	+	0.875500i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−27.5508			−1.24844			−0.624222	−	0.781247i	$-0.714584\pi$
$487$	−27.5508			−1.24844			−0.624222	+	0.781247i	$0.714584\pi$
$488$	8.68618	+	8.68618i	0.393205	+	0.393205i
$489$	−13.8133	+	13.8133i	−0.624661	+	0.624661i
$490$	−11.4993	+	18.9155i	−0.519484	+	0.854515i
$491$	−24.9010			−1.12376			−0.561882	−	0.827217i	$-0.689923\pi$
$491$	−24.9010			−1.12376			−0.561882	+	0.827217i	$0.689923\pi$
$492$	5.36992	+	5.36992i	0.242095	+	0.242095i
$493$	17.8428	+	17.8428i	0.803597	+	0.803597i
$494$	−9.79582	+	9.79582i	−0.440735	+	0.440735i
$495$	3.19100	−	5.24898i	0.143425	−	0.235924i
$496$	5.51242	−	5.51242i	0.247515	−	0.247515i
$497$	−24.7657	+	24.7657i	−1.11090	+	1.11090i
$498$		−	10.2699i		−	0.460206i
$499$	9.41283	+	9.41283i	0.421376	+	0.421376i	0.885677	−	0.464301i	$-0.153695\pi$
$499$	9.41283	+	9.41283i	0.421376	+	0.421376i	−0.464301	+	0.885677i	$0.653695\pi$
$500$	−11.1546	−	0.758434i	−0.498848	−	0.0339182i
$501$	5.37871	−	5.37871i	0.240303	−	0.240303i
$502$	−10.2960	−	10.2960i	−0.459534	−	0.459534i
$503$		−	32.7145i		−	1.45867i	−0.684158	−	0.729334i	$-0.739830\pi$
$503$		−	32.7145i		−	1.45867i	0.684158	−	0.729334i	$-0.260170\pi$
$504$	−2.90687	+	2.90687i	−0.129482	+	0.129482i
$505$	−17.9641	−	10.9208i	−0.799390	−	0.485971i
$506$		−	2.58745i		−	0.115026i
$507$	10.0404	−	10.0404i	0.445910	−	0.445910i
$508$	−8.01885	+	8.01885i	−0.355779	+	0.355779i
$509$	−13.1690			−0.583707			−0.291854	−	0.956463i	$-0.594272\pi$
$509$	−13.1690			−0.583707			−0.291854	+	0.956463i	$0.594272\pi$
$510$	9.03950	−	2.20417i	0.400276	−	0.0976021i
$511$		−	17.3320i		−	0.766722i
$512$			1.00000i			0.0441942i
$513$	2.65630			0.117279
$514$			2.69763i			0.118988i
$515$	−9.03106	+	14.8555i	−0.397956	+	0.654611i
$516$	−4.40869	−	4.40869i	−0.194082	−	0.194082i
$517$	16.6189	+	16.6189i	0.730898	+	0.730898i
$518$	7.68517	+	23.7956i	0.337667	+	1.04552i
$519$			24.9695i			1.09604i
$520$	−6.05791	+	9.96485i	−0.265657	+	0.436988i
$521$		−	30.7232i		−	1.34601i	−0.739639	−	0.673004i	$-0.765004\pi$
$521$		−	30.7232i		−	1.34601i	0.739639	−	0.673004i	$-0.234996\pi$
$522$	4.28806	+	4.28806i	0.187683	+	0.187683i
$523$			17.6544i			0.771972i	0.922505	+	0.385986i	$0.126139\pi$
$523$			17.6544i			0.771972i	−0.922505	+	0.385986i	$0.873861\pi$
$524$	−6.63665	+	6.63665i	−0.289924	+	0.289924i
$525$	18.2476	−	9.46144i	0.796392	−	0.412931i
$526$	15.0006	+	15.0006i	0.654055	+	0.654055i
$527$	22.9374	−	22.9374i	0.999167	−	0.999167i
$528$	1.94253	+	1.94253i	0.0845377	+	0.0845377i
$529$	22.1129			0.961430
$530$	−6.23144	−	25.5557i	−0.270676	−	1.11007i
$531$	1.92935	+	1.92935i	0.0837266	+	0.0837266i
$532$			10.9199i			0.473437i
$533$	−39.6060			−1.71553
$534$		−	2.30191i		−	0.0996134i
$535$	4.24786	+	17.4209i	0.183651	+	0.753170i
$536$	−5.51165	+	5.51165i	−0.238067	+	0.238067i
$537$	−7.39765			−0.319232
$538$	−3.86256			−0.166527
$539$	−27.1962			−1.17142
$540$	2.17242	−	0.529716i	0.0934860	−	0.0227953i
$541$	−24.2940	−	24.2940i	−1.04448	−	1.04448i	−0.998964	−	0.0455156i	$-0.985507\pi$
$541$	−24.2940	−	24.2940i	−1.04448	−	1.04448i	−0.0455156	−	0.998964i	$-0.514493\pi$
$542$		−	11.2551i		−	0.483447i
$543$	−4.82166	+	4.82166i	−0.206917	+	0.206917i
$544$			4.16103i			0.178403i
$545$	4.18597	+	17.1671i	0.179307	+	0.735357i
$546$		−	21.4397i		−	0.917536i
$547$			22.8223i			0.975811i	0.872896	+	0.487906i	$0.162239\pi$
$547$			22.8223i			0.975811i	−0.872896	+	0.487906i	$0.837761\pi$
$548$	−7.91811	+	7.91811i	−0.338245	+	0.338245i
$549$	8.68618	+	8.68618i	0.370717	+	0.370717i
$550$	−6.32265	−	12.1941i	−0.269599	−	0.519957i
$551$	16.1084			0.686242
$552$	0.666001	−	0.666001i	0.0283469	−	0.0283469i
$553$			8.52183i			0.362385i
$554$	16.2009			0.688312
$555$	3.15162	−	13.2313i	0.133779	−	0.561637i
$556$	13.0683			0.554221
$557$		−	22.2337i		−	0.942073i	−0.882114	−	0.471036i	$-0.843880\pi$
$557$		−	22.2337i		−	0.942073i	0.882114	−	0.471036i	$-0.156120\pi$
$558$	5.51242	−	5.51242i	0.233359	−	0.233359i
$559$	32.5164			1.37530
$560$	2.17763	+	8.93067i	0.0920216	+	0.377390i
$561$	8.08293	+	8.08293i	0.341261	+	0.341261i
$562$	7.78699	−	7.78699i	0.328474	−	0.328474i
$563$		−	25.9596i		−	1.09407i	−0.837110	−	0.547034i	$-0.815757\pi$
$563$		−	25.9596i		−	1.09407i	0.837110	−	0.547034i	$-0.184243\pi$
$564$			8.55529i			0.360243i
$565$	16.5876	−	27.2855i	0.697847	−	1.14791i
$566$			21.1035i			0.887046i
$567$	−2.90687	+	2.90687i	−0.122077	+	0.122077i
$568$			8.51973i			0.357480i
$569$	−4.18660	−	4.18660i	−0.175512	−	0.175512i	0.613884	−	0.789396i	$-0.289606\pi$
$569$	−4.18660	−	4.18660i	−0.175512	−	0.175512i	−0.789396	+	0.613884i	$0.789606\pi$
$570$	3.08547	−	5.07539i	0.129236	−	0.212585i
$571$	−24.7600			−1.03617			−0.518087	−	0.855328i	$-0.673356\pi$
$571$	−24.7600			−1.03617			−0.518087	+	0.855328i	$0.673356\pi$
$572$	−14.3272			−0.599050
$573$	10.1705			0.424879
$574$	−22.0754	+	22.0754i	−0.921409	+	0.921409i
$575$	−4.18077	+	2.16774i	−0.174350	+	0.0904009i
$576$			1.00000i			0.0416667i
$577$	34.1071			1.41990			0.709948	−	0.704254i	$-0.248718\pi$
$577$	34.1071			1.41990			0.709948	+	0.704254i	$0.248718\pi$
$578$			0.314185i			0.0130684i
$579$	11.5554	+	11.5554i	0.480226	+	0.480226i
$580$	13.1741	−	3.21232i	0.547023	−	0.133384i
$581$	42.2190			1.75154
$582$	−7.13543	−	7.13543i	−0.295773	−	0.295773i
$583$	22.8514	−	22.8514i	0.946408	−	0.946408i
$584$	−2.98121	−	2.98121i	−0.123363	−	0.123363i
$585$	−6.05791	+	9.96485i	−0.250464	+	0.411996i
$586$	2.76877	−	2.76877i	0.114377	−	0.114377i
$587$			46.3514i			1.91313i	0.291522	+	0.956564i	$0.405838\pi$
$587$			46.3514i			1.91313i	−0.291522	+	0.956564i	$0.594162\pi$
$588$	−7.00021	−	7.00021i	−0.288684	−	0.288684i
$589$		−	20.7078i		−	0.853251i
$590$	5.92747	−	1.44534i	0.244030	−	0.0595035i
$591$		−	16.2400i		−	0.668026i
$592$	5.41489	+	2.77109i	0.222551	+	0.113891i
$593$	−16.9988	−	16.9988i	−0.698058	−	0.698058i	0.265934	−	0.963991i	$-0.414320\pi$
$593$	−16.9988	−	16.9988i	−0.698058	−	0.698058i	−0.963991	+	0.265934i	$0.914320\pi$
$594$	1.94253	+	1.94253i	0.0797030	+	0.0797030i
$595$	9.06118	+	37.1608i	0.371472	+	1.52344i
$596$			6.80855i			0.278889i
$597$	−18.2927			−0.748669
$598$			4.91212i			0.200871i
$599$		−	12.7894i		−	0.522561i	−0.965263	−	0.261281i	$-0.915855\pi$
$599$		−	12.7894i		−	0.522561i	0.965263	−	0.261281i	$-0.0841448\pi$
$600$	1.51128	−	4.76613i	0.0616977	−	0.194577i
$601$	17.7183			0.722744			0.361372	−	0.932422i	$-0.382308\pi$
$601$	17.7183			0.722744			0.361372	+	0.932422i	$0.382308\pi$
$602$	18.1238	−	18.1238i	0.738672	−	0.738672i
$603$	−5.51165	+	5.51165i	−0.224452	+	0.224452i
$604$		−	17.8917i		−	0.728002i
$605$	−4.01107	+	6.59794i	−0.163073	+	0.268244i
$606$	6.64810	−	6.64810i	0.270061	−	0.270061i
$607$		−	33.5114i		−	1.36018i	−0.733127	−	0.680092i	$-0.761940\pi$
$607$		−	33.5114i		−	1.36018i	0.733127	−	0.680092i	$-0.238060\pi$
$608$	1.87829	+	1.87829i	0.0761746	+	0.0761746i
$609$	−17.6279	+	17.6279i	−0.714320	+	0.714320i
$610$	26.6862	−	6.50709i	1.08049	−	0.263464i
$611$	−31.5499	−	31.5499i	−1.27637	−	1.27637i
$612$			4.16103i			0.168200i
$613$	1.15839	−	1.15839i	0.0467871	−	0.0467871i	−0.683326	−	0.730113i	$-0.739467\pi$
$613$	1.15839	−	1.15839i	0.0467871	−	0.0467871i	0.730113	+	0.683326i	$0.239467\pi$
$614$	6.12720	−	6.12720i	0.247274	−	0.247274i
$615$	16.4978	−	4.02278i	0.665256	−	0.162214i
$616$	−7.98561	+	7.98561i	−0.321750	+	0.321750i
$617$	−15.5057	−	15.5057i	−0.624237	−	0.624237i	0.322375	−	0.946612i	$-0.395519\pi$
$617$	−15.5057	−	15.5057i	−0.624237	−	0.624237i	−0.946612	+	0.322375i	$0.895519\pi$
$618$	−5.49768	−	5.49768i	−0.221149	−	0.221149i
$619$	−23.4133			−0.941060			−0.470530	−	0.882384i	$-0.655937\pi$
$619$	−23.4133			−0.941060			−0.470530	+	0.882384i	$0.655937\pi$
$620$	−4.12953	−	16.9356i	−0.165846	−	0.680151i
$621$	0.666001	−	0.666001i	0.0267257	−	0.0267257i
$622$	−1.06423	−	1.06423i	−0.0426719	−	0.0426719i
$623$	9.46300			0.379127
$624$	−3.68777	−	3.68777i	−0.147629	−	0.147629i
$625$	−14.4059	+	20.4321i	−0.576237	+	0.817283i
$626$	7.63668			0.305223
$627$	7.29726			0.291424
$628$	−3.05662	+	3.05662i	−0.121972	+	0.121972i
$629$	22.5315	+	11.5306i	0.898391	+	0.459756i
$630$	2.17763	+	8.93067i	0.0867588	+	0.355806i
$631$	−29.2036	+	29.2036i	−1.16258	+	1.16258i	−0.178667	+	0.983910i	$0.557179\pi$
$631$	−29.2036	+	29.2036i	−1.16258	+	1.16258i	−0.983910	+	0.178667i	$0.942821\pi$
$632$	1.46581	+	1.46581i	0.0583067	+	0.0583067i
$633$	16.5894	−	16.5894i	0.659368	−	0.659368i
$634$	19.5287	−	19.5287i	0.775584	−	0.775584i
$635$	6.00718	+	24.6360i	0.238388	+	0.977651i
$636$	11.7637			0.466462
$637$	51.6303			2.04567
$638$	11.7800	+	11.7800i	0.466373	+	0.466373i
$639$			8.51973i			0.337035i
$640$	1.91070	+	1.16157i	0.0755269	+	0.0459149i
$641$	−27.5707			−1.08898			−0.544488	−	0.838769i	$-0.683276\pi$
$641$	−27.5707			−1.08898			−0.544488	+	0.838769i	$0.683276\pi$
$642$	−8.01912			−0.316489
$643$	−18.0002			−0.709858			−0.354929	−	0.934893i	$-0.615495\pi$
$643$	−18.0002			−0.709858			−0.354929	+	0.934893i	$0.615495\pi$
$644$	2.73789	+	2.73789i	0.107888	+	0.107888i
$645$	−13.5446	+	3.30269i	−0.533320	+	0.130043i
$646$	7.81562	+	7.81562i	0.307501	+	0.307501i
$647$		−	26.1609i		−	1.02849i	−0.857643	−	0.514245i	$-0.828072\pi$
$647$		−	26.1609i		−	1.02849i	0.857643	−	0.514245i	$-0.171928\pi$
$648$			1.00000i			0.0392837i
$649$	5.30021	+	5.30021i	0.208052	+	0.208052i
$650$	12.0032	+	23.1497i	0.470802	+	0.908004i
$651$	22.6612	+	22.6612i	0.888163	+	0.888163i
$652$	−19.5350			−0.765050
$653$	−27.1758			−1.06347			−0.531735	−	0.846911i	$-0.678460\pi$
$653$	−27.1758			−1.06347			−0.531735	+	0.846911i	$0.678460\pi$
$654$	−7.90229			−0.309004
$655$	4.97173	+	20.3895i	0.194261	+	0.796685i
$656$			7.59421i			0.296504i
$657$	−2.98121	−	2.98121i	−0.116308	−	0.116308i
$658$	−35.1702			−1.37108
$659$	−11.2236			−0.437210			−0.218605	−	0.975813i	$-0.570151\pi$
$659$	−11.2236			−0.437210			−0.218605	+	0.975813i	$0.570151\pi$
$660$	5.96796	−	1.45521i	0.232303	−	0.0566440i
$661$	−1.74533	+	1.74533i	−0.0678853	+	0.0678853i	−0.740234	−	0.672349i	$-0.765285\pi$
$661$	−1.74533	+	1.74533i	−0.0678853	+	0.0678853i	0.672349	+	0.740234i	$0.265285\pi$
$662$	10.6002	−	10.6002i	0.411988	−	0.411988i
$663$	−15.3449	−	15.3449i	−0.595948	−	0.595948i
$664$	7.26193	−	7.26193i	0.281818	−	0.281818i
$665$	20.8646	+	12.6842i	0.809094	+	0.491871i
$666$	5.41489	+	2.77109i	0.209823	+	0.107378i
$667$	4.03879	−	4.03879i	0.156382	−	0.156382i
$668$	7.60664			0.294310
$669$	4.00667			0.154907
$670$	4.12895	+	16.9332i	0.159515	+	0.654188i
$671$	23.8623	+	23.8623i	0.921192	+	0.921192i
$672$	−4.11094			−0.158583
$673$	21.3478	+	21.3478i	0.822898	+	0.822898i	0.986523	−	0.163624i	$-0.0523185\pi$
$673$	21.3478	+	21.3478i	0.822898	+	0.822898i	−0.163624	+	0.986523i	$0.552318\pi$
$674$	−14.7087	+	14.7087i	−0.566558	+	0.566558i
$675$	1.51128	−	4.76613i	0.0581692	−	0.183449i
$676$	14.1993			0.546127
$677$	29.6755	+	29.6755i	1.14052	+	1.14052i	0.988355	+	0.152168i	$0.0486254\pi$
$677$	29.6755	+	29.6755i	1.14052	+	1.14052i	0.152168	+	0.988355i	$0.451375\pi$
$678$	10.0978	+	10.0978i	0.387803	+	0.387803i
$679$	29.3333	−	29.3333i	1.12571	−	1.12571i
$680$	7.95047	+	4.83331i	0.304887	+	0.185349i
$681$	−5.29891	+	5.29891i	−0.203055	+	0.203055i
$682$	15.1435	−	15.1435i	0.579873	−	0.579873i
$683$		−	3.99926i		−	0.153027i	−0.997069	−	0.0765137i	$-0.975621\pi$
$683$		−	3.99926i		−	0.153027i	0.997069	−	0.0765137i	$-0.0243789\pi$
$684$	1.87829	+	1.87829i	0.0718181	+	0.0718181i
$685$	5.93171	+	24.3265i	0.226639	+	0.929469i
$686$	8.42932	−	8.42932i	0.321833	−	0.321833i
$687$	−17.0363	−	17.0363i	−0.649976	−	0.649976i
$688$		−	6.23482i		−	0.237700i
$689$	−43.3819	+	43.3819i	−1.65272	+	1.65272i
$690$	−0.498923	−	2.04613i	−0.0189937	−	0.0778949i
$691$		−	20.3772i		−	0.775184i	−0.921831	−	0.387592i	$-0.873307\pi$
$691$		−	20.3772i		−	0.775184i	0.921831	−	0.387592i	$-0.126693\pi$
$692$	−17.6561	+	17.6561i	−0.671185	+	0.671185i
$693$	−7.98561	+	7.98561i	−0.303348	+	0.303348i
$694$	−5.20503			−0.197580
$695$	15.1797	−	24.9697i	0.575801	−	0.947153i
$696$			6.06423i			0.229864i
$697$			31.5998i			1.19693i
$698$	8.31963			0.314902
$699$		−	11.0100i		−	0.416435i
$700$	19.5933	+	6.21277i	0.740556	+	0.234821i
$701$	−5.28962	−	5.28962i	−0.199786	−	0.199786i	0.600122	−	0.799908i	$-0.295119\pi$
$701$	−5.28962	−	5.28962i	−0.199786	−	0.199786i	−0.799908	+	0.600122i	$0.795119\pi$
$702$	−3.68777	−	3.68777i	−0.139186	−	0.139186i
$703$	15.3756	−	4.96581i	0.579903	−	0.187289i
$704$			2.74715i			0.103537i
$705$	16.3466	+	9.93753i	0.615647	+	0.374269i
$706$		−	32.6034i		−	1.22704i
$707$	27.3299	+	27.3299i	1.02785	+	1.02785i
$708$			2.72851i			0.102544i
$709$	17.3563	−	17.3563i	0.651828	−	0.651828i	−0.301605	−	0.953433i	$-0.597522\pi$
$709$	17.3563	−	17.3563i	0.651828	−	0.651828i	0.953433	+	0.301605i	$0.0975224\pi$
$710$	16.2786	+	9.89623i	0.610926	+	0.371399i
$711$	1.46581	+	1.46581i	0.0549721	+	0.0549721i
$712$	1.62770	−	1.62770i	0.0610005	−	0.0610005i
$713$	−5.19197	−	5.19197i	−0.194441	−	0.194441i
$714$	−17.1057			−0.640166
$715$	−16.6420	+	27.3750i	−0.622375	+	1.02377i
$716$	−5.23093	−	5.23093i	−0.195489	−	0.195489i
$717$			2.66477i			0.0995175i
$718$	17.3163			0.646240
$719$			10.6066i			0.395558i	0.980247	+	0.197779i	$0.0633729\pi$
$719$			10.6066i			0.395558i	−0.980247	+	0.197779i	$0.936627\pi$
$720$	1.91070	+	1.16157i	0.0712075	+	0.0432890i
$721$	22.6006	−	22.6006i	0.841691	−	0.841691i
$722$	−11.9441			−0.444512
$723$	25.6351			0.953381
$724$	−6.81886			−0.253421
$725$	9.16475	−	28.9029i	0.340370	−	1.07343i
$726$	−2.44175	−	2.44175i	−0.0906219	−	0.0906219i
$727$		−	41.4047i		−	1.53561i	−0.640681	−	0.767807i	$-0.721348\pi$
$727$		−	41.4047i		−	1.53561i	0.640681	−	0.767807i	$-0.278652\pi$
$728$	15.1602	−	15.1602i	0.561874	−	0.561874i
$729$			1.00000i			0.0370370i
$730$	−9.15906	+	2.23332i	−0.338992	+	0.0826588i
$731$		−	25.9433i		−	0.959548i
$732$			12.2841i			0.454034i
$733$	−33.6863	+	33.6863i	−1.24423	+	1.24423i	−0.286005	+	0.958228i	$0.592327\pi$
$733$	−33.6863	+	33.6863i	−1.24423	+	1.24423i	−0.958228	+	0.286005i	$0.907673\pi$
$734$	−19.8485	−	19.8485i	−0.732622	−	0.732622i
$735$	−21.5065	+	5.24408i	−0.793279	+	0.193431i
$736$	0.941868			0.0347177
$737$	−15.1413	+	15.1413i	−0.557738	+	0.557738i
$738$			7.59421i			0.279547i
$739$	−30.7911			−1.13267			−0.566335	−	0.824175i	$-0.691639\pi$
$739$	−30.7911			−1.13267			−0.566335	+	0.824175i	$0.691639\pi$
$740$	11.5845	−	7.12741i	0.425854	−	0.262009i
$741$	−13.8534			−0.508917
$742$			48.3600i			1.77535i
$743$	−21.8367	+	21.8367i	−0.801110	+	0.801110i	−0.983269	−	0.182159i	$-0.941691\pi$
$743$	−21.8367	+	21.8367i	−0.801110	+	0.801110i	0.182159	+	0.983269i	$0.441691\pi$
$744$	7.79574			0.285806
$745$	13.0091	+	7.90857i	0.476615	+	0.289748i
$746$	−19.3419	−	19.3419i	−0.708158	−	0.708158i
$747$	7.26193	−	7.26193i	0.265700	−	0.265700i
$748$			11.4310i			0.417958i
$749$		−	32.9661i		−	1.20455i
$750$	−7.35119	−	8.42378i	−0.268427	−	0.307593i
$751$			4.98993i			0.182085i	0.995847	+	0.0910426i	$0.0290199\pi$
$751$			4.98993i			0.182085i	−0.995847	+	0.0910426i	$0.970980\pi$
$752$	−6.04950	+	6.04950i	−0.220603	+	0.220603i
$753$		−	14.5608i		−	0.530624i
$754$	−22.3635	−	22.3635i	−0.814430	−	0.814430i
$755$	−34.1856	−	20.7824i	−1.24414	−	0.756348i
$756$	−4.11094			−0.149513
$757$	−5.34349			−0.194213			−0.0971063	−	0.995274i	$-0.530959\pi$
$757$	−5.34349			−0.194213			−0.0971063	+	0.995274i	$0.530959\pi$
$758$	−3.56273			−0.129404
$759$	1.82961	−	1.82961i	0.0664105	−	0.0664105i
$760$	5.77059	−	1.40708i	0.209321	−	0.0510403i
$761$		−	29.9342i		−	1.08511i	−0.840019	−	0.542557i	$-0.817456\pi$
$761$		−	29.9342i		−	1.08511i	0.840019	−	0.542557i	$-0.182544\pi$
$762$	−11.3404			−0.410818
$763$		−	32.4858i		−	1.17607i
$764$	7.19163	+	7.19163i	0.260184	+	0.260184i
$765$	7.95047	+	4.83331i	0.287450	+	0.174749i
$766$	17.5102			0.632670
$767$	−10.0621	−	10.0621i	−0.363322	−	0.363322i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−17.9570	−	17.9570i	−0.647546	−	0.647546i	0.304853	−	0.952399i	$-0.401393\pi$
$769$	−17.9570	−	17.9570i	−0.647546	−	0.647546i	−0.952399	+	0.304853i	$0.901393\pi$
$770$	5.98228	+	24.5339i	0.215586	+	0.884141i
$771$	−1.90752	+	1.90752i	−0.0686975	+	0.0686975i
$772$			16.3418i			0.588154i
$773$	20.5041	+	20.5041i	0.737483	+	0.737483i	0.972090	−	0.234607i	$-0.0753804\pi$
$773$	20.5041	+	20.5041i	0.737483	+	0.737483i	−0.234607	+	0.972090i	$0.575380\pi$
$774$		−	6.23482i		−	0.224106i
$775$	−37.1556	−	11.7815i	−1.33467	−	0.423206i
$776$		−	10.0910i		−	0.362247i
$777$	−11.3918	+	22.2603i	−0.408678	+	0.798583i
$778$	−5.52680	−	5.52680i	−0.198145	−	0.198145i
$779$	14.2641	+	14.2641i	0.511065	+	0.511065i
$780$	−11.3298	+	2.76262i	−0.405672	+	0.0989178i
$781$			23.4050i			0.837496i
$782$	3.91914			0.140148
$783$			6.06423i			0.216718i
$784$		−	9.89979i		−	0.353564i
$785$	2.28981	+	9.39073i	0.0817268	+	0.335170i
$786$	−9.38564			−0.334775
$787$	0.00644958	−	0.00644958i	0.000229903	−	0.000229903i	−0.706992	−	0.707222i	$-0.749948\pi$
$787$	0.00644958	−	0.00644958i	0.000229903	−	0.000229903i	0.707222	+	0.706992i	$0.249948\pi$
$788$	11.4834	−	11.4834i	0.409080	−	0.409080i
$789$			21.2140i			0.755238i
$790$	4.50335	−	1.09808i	0.160222	−	0.0390680i
$791$	−41.5113	+	41.5113i	−1.47597	+	1.47597i
$792$			2.74715i			0.0976158i
$793$	−45.3010	−	45.3010i	−1.60869	−	1.60869i
$794$	7.17123	−	7.17123i	0.254497	−	0.254497i
$795$	13.6644	−	22.4769i	0.484625	−	0.797175i
$796$	−12.9349	−	12.9349i	−0.458464	−	0.458464i
$797$			16.8684i			0.597510i	0.954330	+	0.298755i	$0.0965713\pi$
$797$			16.8684i			0.597510i	−0.954330	+	0.298755i	$0.903429\pi$
$798$	−7.72152	+	7.72152i	−0.273339	+	0.273339i
$799$	−25.1722	+	25.1722i	−0.890527	+	0.890527i
$800$	4.43880	−	2.30153i	0.156935	−	0.0813714i
$801$	1.62770	−	1.62770i	0.0575118	−	0.0575118i
$802$	12.3057	+	12.3057i	0.434530	+	0.434530i
$803$	−8.18983	−	8.18983i	−0.289013	−	0.289013i
$804$	−7.79465			−0.274896
$805$	8.41151	−	2.05104i	0.296467	−	0.0722896i
$806$	−28.7489	+	28.7489i	−1.01264	+	1.01264i
$807$	−2.73124	−	2.73124i	−0.0961444	−	0.0961444i
$808$	9.40183			0.330755
$809$	32.7152	+	32.7152i	1.15020	+	1.15020i	0.986511	+	0.163692i	$0.0523404\pi$
$809$	32.7152	+	32.7152i	1.15020	+	1.15020i	0.163692	+	0.986511i	$0.447660\pi$
$810$	1.91070	+	1.16157i	0.0671351	+	0.0408133i
$811$	−32.0761			−1.12634			−0.563172	−	0.826339i	$-0.690419\pi$
$811$	−32.0761			−1.12634			−0.563172	+	0.826339i	$0.690419\pi$
$812$	−24.9297			−0.874860
$813$	7.95854	−	7.95854i	0.279118	−	0.279118i
$814$	14.8755	+	7.61262i	0.521387	+	0.266822i
$815$	−22.6912	+	37.3255i	−0.794838	+	1.30745i
$816$	−2.94229	+	2.94229i	−0.103001	+	0.103001i
$817$	−11.7108	−	11.7108i	−0.409709	−	0.409709i
$818$	−20.8384	+	20.8384i	−0.728598	+	0.728598i
$819$	15.1602	−	15.1602i	0.529740	−	0.529740i
$820$	14.5102	+	8.82118i	0.506720	+	0.308049i
$821$	46.5821			1.62573			0.812863	−	0.582455i	$-0.197908\pi$
$821$	46.5821			1.62573			0.812863	+	0.582455i	$0.197908\pi$
$822$	−11.1979			−0.390572
$823$	14.9085	+	14.9085i	0.519678	+	0.519678i	0.917474	−	0.397796i	$-0.130225\pi$
$823$	14.9085	+	14.9085i	0.519678	+	0.519678i	−0.397796	+	0.917474i	$0.630225\pi$
$824$		−	7.77490i		−	0.270851i
$825$	4.15171	−	13.0933i	0.144544	−	0.455850i
$826$	−11.2167			−0.390280
$827$	32.9874			1.14708			0.573542	−	0.819176i	$-0.305569\pi$
$827$	32.9874			1.14708			0.573542	+	0.819176i	$0.305569\pi$
$828$	0.941868			0.0327322
$829$	−26.5468	−	26.5468i	−0.922009	−	0.922009i	0.0751625	−	0.997171i	$-0.476052\pi$
$829$	−26.5468	−	26.5468i	−0.922009	−	0.922009i	−0.997171	+	0.0751625i	$0.976052\pi$
$830$	−5.44014	−	22.3106i	−0.188830	−	0.774411i
$831$	11.4558	+	11.4558i	0.397397	+	0.397397i
$832$		−	5.21529i		−	0.180808i
$833$		−	41.1933i		−	1.42726i
$834$	9.24072	+	9.24072i	0.319980	+	0.319980i
$835$	8.83562	−	14.5340i	0.305769	−	0.502970i
$836$	5.15994	+	5.15994i	0.178460	+	0.178460i
$837$	7.79574			0.269460
$838$	36.4587			1.25945
$839$	28.9665			1.00004			0.500018	−	0.866015i	$-0.333327\pi$
$839$	28.9665			1.00004			0.500018	+	0.866015i	$0.333327\pi$
$840$	−4.77512	+	7.85475i	−0.164757	+	0.271015i
$841$			7.77493i			0.268101i
$842$	15.1883	+	15.1883i	0.523422	+	0.523422i
$843$	11.0125			0.379289
$844$	23.4609			0.807558
$845$	16.4934	−	27.1305i	0.567391	−	0.933319i
$846$	−6.04950	+	6.04950i	−0.207986	+	0.207986i
$847$	10.0379	−	10.0379i	0.344906	−	0.344906i
$848$	8.31822	+	8.31822i	0.285649	+	0.285649i
$849$	−14.9224	+	14.9224i	−0.512136	+	0.512136i
$850$	18.4700	−	9.57674i	0.633516	−	0.328479i
$851$	2.61001	−	5.10011i	0.0894698	−	0.174830i
$852$	−6.02436	+	6.02436i	−0.206391	+	0.206391i
$853$	46.9335			1.60697			0.803487	−	0.595323i	$-0.202976\pi$
$853$	46.9335			1.60697			0.803487	+	0.595323i	$0.202976\pi$
$854$	−50.4992			−1.72805
$855$	5.77059	−	1.40708i	0.197350	−	0.0481213i
$856$	−5.67037	−	5.67037i	−0.193809	−	0.193809i
$857$	−20.5633			−0.702429			−0.351214	−	0.936295i	$-0.614231\pi$
$857$	−20.5633			−0.702429			−0.351214	+	0.936295i	$0.614231\pi$
$858$	−10.1309	−	10.1309i	−0.345862	−	0.345862i
$859$	−35.4390	+	35.4390i	−1.20916	+	1.20916i	−0.237863	+	0.971299i	$0.576447\pi$
$859$	−35.4390	+	35.4390i	−1.20916	+	1.20916i	−0.971299	+	0.237863i	$0.923553\pi$
$860$	−11.9129	−	7.24216i	−0.406225	−	0.246956i
$861$	−31.2193			−1.06395
$862$	−6.39166	−	6.39166i	−0.217701	−	0.217701i
$863$	−36.0727	−	36.0727i	−1.22793	−	1.22793i	−0.964746	−	0.263181i	$-0.915228\pi$
$863$	−36.0727	−	36.0727i	−1.22793	−	1.22793i	−0.263181	−	0.964746i	$-0.584772\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	13.2268	+	54.2443i	0.449723	+	1.84436i
$866$	−15.4619	+	15.4619i	−0.525418	+	0.525418i
$867$	−0.222162	+	0.222162i	−0.00754503	+	0.00754503i
$868$			32.0478i			1.08777i
$869$	4.02680	+	4.02680i	0.136600	+	0.136600i
$870$	11.5869	+	7.04401i	0.392833	+	0.238814i
$871$	28.7449	−	28.7449i	0.973983	−	0.973983i
$872$	−5.58777	−	5.58777i	−0.189226	−	0.189226i
$873$		−	10.0910i		−	0.341529i
$874$	1.76910	−	1.76910i	0.0598407	−	0.0598407i
$875$	34.6296	−	30.2203i	1.17069	−	1.02163i
$876$		−	4.21607i		−	0.142448i
$877$	11.9117	−	11.9117i	0.402229	−	0.402229i	−0.476789	−	0.879018i	$-0.658199\pi$
$877$	11.9117	−	11.9117i	0.402229	−	0.402229i	0.879018	+	0.476789i	$0.158199\pi$
$878$	15.6685	−	15.6685i	0.528785	−	0.528785i
$879$	3.91564			0.132071
$880$	5.24898	+	3.19100i	0.176943	+	0.107569i
$881$		−	0.418792i		−	0.0141095i	−0.999975	−	0.00705473i	$-0.997754\pi$
$881$		−	0.418792i		−	0.0141095i	0.999975	−	0.00705473i	$-0.00224561\pi$
$882$		−	9.89979i		−	0.333343i
$883$	26.3766			0.887643			0.443821	−	0.896115i	$-0.353622\pi$
$883$	26.3766			0.887643			0.443821	+	0.896115i	$0.353622\pi$
$884$		−	21.7010i		−	0.729884i
$885$	5.21336	+	3.16934i	0.175245	+	0.106536i
$886$	−27.2120	−	27.2120i	−0.914206	−	0.914206i
$887$	−22.4081	−	22.4081i	−0.752390	−	0.752390i	0.222535	−	0.974925i	$-0.428567\pi$
$887$	−22.4081	−	22.4081i	−0.752390	−	0.752390i	−0.974925	+	0.222535i	$0.928567\pi$
$888$	1.86945	+	5.78837i	0.0627345	+	0.194245i
$889$		−	46.6195i		−	1.56357i
$890$	−1.21936	−	5.00071i	−0.0408730	−	0.167624i
$891$			2.74715i			0.0920330i
$892$	2.83314	+	2.83314i	0.0948606	+	0.0948606i
$893$			22.7254i			0.760477i
$894$	−4.81437	+	4.81437i	−0.161017	+	0.161017i
$895$	−16.0708	+	3.91865i	−0.537187	+	0.130986i
$896$	−2.90687	−	2.90687i	−0.0971117	−	0.0971117i
$897$	−3.47339	+	3.47339i	−0.115973	+	0.115973i
$898$	18.9735	+	18.9735i	0.633155	+	0.633155i
$899$	47.2752			1.57672
$900$	4.43880	−	2.30153i	0.147960	−	0.0767176i
$901$	34.6124	+	34.6124i	1.15310	+	1.15310i
$902$			20.8624i			0.694644i
$903$	25.6310			0.852945
$904$			14.2804i			0.474959i
$905$	−7.92055	+	13.0288i	−0.263288	+	0.433091i
$906$	12.6513	−	12.6513i	0.420312	−	0.420312i
$907$	23.3935			0.776769			0.388384	−	0.921497i	$-0.373033\pi$
$907$	23.3935			0.776769			0.388384	+	0.921497i	$0.373033\pi$
$908$	−7.49379			−0.248690
$909$	9.40183			0.311839
$910$	−11.3570	−	46.5761i	−0.376480	−	1.54398i
$911$	26.3920	+	26.3920i	0.874406	+	0.874406i	0.992949	−	0.118543i	$-0.0378223\pi$
$911$	26.3920	+	26.3920i	0.874406	+	0.874406i	−0.118543	+	0.992949i	$0.537822\pi$
$912$			2.65630i			0.0879589i
$913$	19.9496	−	19.9496i	0.660237	−	0.660237i
$914$		−	9.71477i		−	0.321336i
$915$	23.4712	+	14.2688i	0.775935	+	0.471712i
$916$		−	24.0930i		−	0.796055i
$917$		−	38.5838i		−	1.27415i
$918$	−2.94229	+	2.94229i	−0.0971102	+	0.0971102i
$919$	28.2985	+	28.2985i	0.933482	+	0.933482i	0.997922	−	0.0644393i	$-0.0205259\pi$
$919$	28.2985	+	28.2985i	0.933482	+	0.933482i	−0.0644393	+	0.997922i	$0.520526\pi$
$920$	1.09404	−	1.79963i	0.0360695	−	0.0593319i
$921$	8.66517			0.285527
$922$	−17.2735	+	17.2735i	−0.568872	+	0.568872i
$923$		−	44.4329i		−	1.46253i
$924$	−11.2934			−0.371524
$925$	−0.162193	−	30.4134i	−0.00533286	−	0.999986i
$926$	−16.3891			−0.538578
$927$		−	7.77490i		−	0.255361i
$928$	−4.28806	+	4.28806i	−0.140762	+	0.140762i
$929$	−31.6997			−1.04003			−0.520016	−	0.854156i	$-0.674074\pi$
$929$	−31.6997			−1.04003			−0.520016	+	0.854156i	$0.674074\pi$
$930$	9.05527	−	14.8953i	0.296934	−	0.488436i
$931$	−18.5947	−	18.5947i	−0.609415	−	0.609415i
$932$	7.78522	−	7.78522i	0.255013	−	0.255013i
$933$		−	1.50505i		−	0.0492732i
$934$			1.29508i			0.0423764i
$935$	21.8412	+	13.2778i	0.714282	+	0.434232i
$936$		−	5.21529i		−	0.170467i
$937$	30.6502	−	30.6502i	1.00130	−	1.00130i	0.00129830	−	0.999999i	$-0.499587\pi$
$937$	30.6502	−	30.6502i	1.00130	−	1.00130i	0.999999	−	0.00129830i	$-0.000413263\pi$
$938$		−	32.0433i		−	1.04625i
$939$	5.39995	+	5.39995i	0.176221	+	0.176221i
$940$	4.53187	+	18.5857i	0.147813	+	0.606197i
$941$	−7.87515			−0.256722			−0.128361	−	0.991727i	$-0.540972\pi$
$941$	−7.87515			−0.256722			−0.128361	+	0.991727i	$0.540972\pi$
$942$	−4.32271			−0.140841
$943$	7.15275			0.232925
$944$	−1.92935	+	1.92935i	−0.0627949	+	0.0627949i
$945$	−4.77512	+	7.85475i	−0.155335	+	0.255515i
$946$		−	17.1280i		−	0.556880i
$947$	−7.99597			−0.259834			−0.129917	−	0.991525i	$-0.541471\pi$
$947$	−7.99597			−0.259834			−0.129917	+	0.991525i	$0.541471\pi$
$948$			2.07297i			0.0673268i
$949$	15.5479	+	15.5479i	0.504706	+	0.504706i
$950$	4.01441	−	12.6603i	0.130245	−	0.410754i
$951$	27.6178			0.895567
$952$	−12.0956	−	12.0956i	−0.392020	−	0.392020i
$953$	−40.8082	+	40.8082i	−1.32191	+	1.32191i	−0.409677	+	0.912231i	$0.634359\pi$
$953$	−40.8082	+	40.8082i	−1.32191	+	1.32191i	−0.912231	+	0.409677i	$0.865641\pi$
$954$	8.31822	+	8.31822i	0.269312	+	0.269312i
$955$	22.0946	−	5.38748i	0.714964	−	0.174335i
$956$	−1.88427	+	1.88427i	−0.0609418	+	0.0609418i
$957$			16.6594i			0.538521i
$958$	−27.0885	−	27.0885i	−0.875189	−	0.875189i
$959$		−	46.0338i		−	1.48651i
$960$	0.529716	+	2.17242i	0.0170965	+	0.0701145i
$961$		−	29.7736i		−	0.960439i
$962$	−28.2402	−	14.4521i	−0.910502	−	0.465953i
$963$	−5.67037	−	5.67037i	−0.182725	−	0.182725i
$964$	18.1268	+	18.1268i	0.583824	+	0.583824i
$965$	31.2242	+	18.9821i	1.00514	+	0.611055i
$966$			3.87196i			0.124578i
$967$	−35.2833			−1.13463			−0.567317	−	0.823500i	$-0.692018\pi$
$967$	−35.2833			−1.13463			−0.567317	+	0.823500i	$0.692018\pi$
$968$		−	3.45316i		−	0.110989i
$969$			11.0529i			0.355072i
$970$	−19.2809	−	11.7214i	−0.619072	−	0.376351i
$971$	−29.9340			−0.960629			−0.480314	−	0.877096i	$-0.659477\pi$
$971$	−29.9340			−0.960629			−0.480314	+	0.877096i	$0.659477\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−37.9880	+	37.9880i	−1.21784	+	1.21784i
$974$		−	27.5508i		−	0.882783i
$975$	−7.88177	+	24.8568i	−0.252419	+	0.796054i
$976$	−8.68618	+	8.68618i	−0.278038	+	0.278038i
$977$			55.5148i			1.77608i	0.459770	+	0.888038i	$0.347932\pi$
$977$			55.5148i			1.77608i	−0.459770	+	0.888038i	$0.652068\pi$
$978$	−13.8133	−	13.8133i	−0.441702	−	0.441702i
$979$	4.47153	−	4.47153i	0.142911	−	0.142911i
$980$	−18.9155	−	11.4993i	−0.604234	−	0.367330i
$981$	−5.58777	−	5.58777i	−0.178404	−	0.178404i
$982$		−	24.9010i		−	0.794622i
$983$	−3.83723	+	3.83723i	−0.122388	+	0.122388i	−0.765648	−	0.643260i	$-0.777582\pi$
$983$	−3.83723	+	3.83723i	−0.122388	+	0.122388i	0.643260	+	0.765648i	$0.277582\pi$
$984$	−5.36992	+	5.36992i	−0.171187	+	0.171187i
$985$	−8.60261	−	35.2801i	−0.274102	−	1.12412i
$986$	−17.8428	+	17.8428i	−0.568229	+	0.568229i
$987$	−24.8691	−	24.8691i	−0.791593	−	0.791593i
$988$	−9.79582	−	9.79582i	−0.311647	−	0.311647i
$989$	−5.87238			−0.186731
$990$	5.24898	+	3.19100i	0.166823	+	0.101417i
$991$	0.156434	−	0.156434i	0.00496928	−	0.00496928i	−0.704618	−	0.709587i	$-0.748882\pi$
$991$	0.156434	−	0.156434i	0.00496928	−	0.00496928i	0.709587	+	0.704618i	$0.248882\pi$
$992$	5.51242	+	5.51242i	0.175020	+	0.175020i
$993$	14.9909			0.475723
$994$	−24.7657	−	24.7657i	−0.785522	−	0.785522i
$995$	−39.7393	+	9.68992i	−1.25982	+	0.307191i
$996$	10.2699			0.325415
$997$	3.25867			0.103203			0.0516016	−	0.998668i	$-0.483567\pi$
$997$	3.25867			0.103203			0.0516016	+	0.998668i	$0.483567\pi$
$998$	−9.41283	+	9.41283i	−0.297958	+	0.297958i
$999$	1.86945	+	5.78837i	0.0591467	+	0.183136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.43.9	✓	36
5.2	odd	4		1110.2.o.a.487.10	yes	36
37.31	odd	4		1110.2.o.a.253.10	yes	36
185.142	even	4	inner	1110.2.l.a.697.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.9	✓	36	1.1	even	1	trivial
1110.2.l.a.697.9	yes	36	185.142	even	4	inner
1110.2.o.a.253.10	yes	36	37.31	odd	4
1110.2.o.a.487.10	yes	36	5.2	odd	4

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.16157 + 1.91070i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.90687 - 2.90687i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.16157 + 1.91070i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.90687 - 2.90687i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.91070 - 1.16157i) q^{10} -2.74715i q^{11} +(0.707107 - 0.707107i) q^{12} +5.21529i q^{13} +(2.90687 + 2.90687i) q^{14} +(-0.529716 - 2.17242i) q^{15} +1.00000 q^{16} +4.16103 q^{17} +1.00000 q^{18} +(1.87829 - 1.87829i) q^{19} +(1.16157 - 1.91070i) q^{20} +4.11094i q^{21} +2.74715 q^{22} -0.941868i q^{23} +(0.707107 + 0.707107i) q^{24} +(-2.30153 - 4.43880i) q^{25} -5.21529 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.90687 + 2.90687i) q^{28} +(4.28806 + 4.28806i) q^{29} +(2.17242 - 0.529716i) q^{30} +(5.51242 - 5.51242i) q^{31} +1.00000i q^{32} +(1.94253 + 1.94253i) q^{33} +4.16103i q^{34} +(2.17763 + 8.93067i) q^{35} +1.00000i q^{36} +(5.41489 + 2.77109i) q^{37} +(1.87829 + 1.87829i) q^{38} +(-3.68777 - 3.68777i) q^{39} +(1.91070 + 1.16157i) q^{40} +7.59421i q^{41} -4.11094 q^{42} -6.23482i q^{43} +2.74715i q^{44} +(1.91070 + 1.16157i) q^{45} +0.941868 q^{46} +(-6.04950 + 6.04950i) q^{47} +(-0.707107 + 0.707107i) q^{48} -9.89979i q^{49} +(4.43880 - 2.30153i) q^{50} +(-2.94229 + 2.94229i) q^{51} -5.21529i q^{52} +(8.31822 + 8.31822i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(5.24898 + 3.19100i) q^{55} +(-2.90687 - 2.90687i) q^{56} +2.65630i q^{57} +(-4.28806 + 4.28806i) q^{58} +(-1.92935 + 1.92935i) q^{59} +(0.529716 + 2.17242i) q^{60} +(-8.68618 + 8.68618i) q^{61} +(5.51242 + 5.51242i) q^{62} +(-2.90687 - 2.90687i) q^{63} -1.00000 q^{64} +(-9.96485 - 6.05791i) q^{65} +(-1.94253 + 1.94253i) q^{66} +(-5.51165 - 5.51165i) q^{67} -4.16103 q^{68} +(0.666001 + 0.666001i) q^{69} +(-8.93067 + 2.17763i) q^{70} -8.51973 q^{71} -1.00000 q^{72} +(2.98121 - 2.98121i) q^{73} +(-2.77109 + 5.41489i) q^{74} +(4.76613 + 1.51128i) q^{75} +(-1.87829 + 1.87829i) q^{76} +(-7.98561 - 7.98561i) q^{77} +(3.68777 - 3.68777i) q^{78} +(-1.46581 + 1.46581i) q^{79} +(-1.16157 + 1.91070i) q^{80} -1.00000 q^{81} -7.59421 q^{82} +(7.26193 + 7.26193i) q^{83} -4.11094i q^{84} +(-4.83331 + 7.95047i) q^{85} +6.23482 q^{86} -6.06423 q^{87} -2.74715 q^{88} +(1.62770 + 1.62770i) q^{89} +(-1.16157 + 1.91070i) q^{90} +(15.1602 + 15.1602i) q^{91} +0.941868i q^{92} +7.79574i q^{93} +(-6.04950 - 6.04950i) q^{94} +(1.40708 + 5.77059i) q^{95} +(-0.707107 - 0.707107i) q^{96} +10.0910 q^{97} +9.89979 q^{98} -2.74715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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