LMFDB - Embedded newform 1110.2.o.a.487.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			487.10
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	1.91070	−	1.16157i	0.854490	−	0.519468i
$5$	1.91070	−	1.16157i	0.854490	−	0.519468i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	2.90687	+	2.90687i	1.09869	+	1.09869i	0.994564	+	0.104130i	$0.0332058\pi$
$7$	2.90687	+	2.90687i	1.09869	+	1.09869i	0.104130	+	0.994564i	$0.466794\pi$
$8$	−1.00000			−0.353553
$9$			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
$13$	5.21529			1.44646			0.723231	−	0.690606i	$-0.242656\pi$
$13$	5.21529			1.44646			0.723231	+	0.690606i	$0.242656\pi$
$14$	−2.90687	−	2.90687i	−0.776894	−	0.776894i
$15$	2.17242	+	0.529716i	0.560916	+	0.136772i
$16$	1.00000			0.250000
$17$			4.16103i			1.00920i	0.863354	+	0.504599i	$0.168360\pi$
$17$			4.16103i			1.00920i	−0.863354	+	0.504599i	$0.831640\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.87829	+	1.87829i	−0.430909	+	0.430909i	−0.888937	−	0.458029i	$-0.848556\pi$
$19$	−1.87829	+	1.87829i	−0.430909	+	0.430909i	0.458029	+	0.888937i	$0.348556\pi$
$20$	1.91070	−	1.16157i	0.427245	−	0.259734i
$21$			4.11094i			0.897080i
$22$			2.74715i			0.585695i
$23$	−0.941868			−0.196393			−0.0981965	−	0.995167i	$-0.531307\pi$
$23$	−0.941868			−0.196393			−0.0981965	+	0.995167i	$0.531307\pi$
$24$	−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	0.186233	−	0.982506i	$-0.440372\pi$
$29$	−4.28806	−	4.28806i	−0.796273	−	0.796273i	−0.982506	+	0.186233i	$0.940372\pi$
$30$	−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	$0.00314840\pi$
$32$	−1.00000			−0.176777
$33$	1.94253	−	1.94253i	0.338151	−	0.338151i
$34$		−	4.16103i		−	0.713611i
$35$	8.93067	+	2.17763i	1.50956	+	0.368086i
$36$			1.00000i			0.166667i
$37$	−2.77109	+	5.41489i	−0.455565	+	0.890202i
$37$	−2.77109	+	5.41489i	−0.455565	+	0.890202i
$38$	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	$0.797940\pi$
$42$		−	4.11094i		−	0.634331i
$43$	−6.23482			−0.950802			−0.475401	−	0.879769i	$-0.657697\pi$
$43$	−6.23482			−0.950802			−0.475401	+	0.879769i	$0.657697\pi$
$44$		−	2.74715i		−	0.414149i
$45$	1.16157	+	1.91070i	0.173156	+	0.284830i
$46$	0.941868			0.138871
$47$	−6.04950	−	6.04950i	−0.882410	−	0.882410i	0.111369	−	0.993779i	$-0.464477\pi$
$47$	−6.04950	−	6.04950i	−0.882410	−	0.882410i	−0.993779	+	0.111369i	$0.964477\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			9.89979i			1.41426i
$50$	−2.30153	+	4.43880i	−0.325485	+	0.627741i
$51$	−2.94229	+	2.94229i	−0.412004	+	0.412004i
$52$	5.21529			0.723231
$53$	8.31822	−	8.31822i	1.14259	−	1.14259i	0.154621	−	0.987974i	$-0.450584\pi$
$53$	8.31822	−	8.31822i	1.14259	−	1.14259i	0.987974	−	0.154621i	$-0.0494156\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−3.19100	−	5.24898i	−0.430274	−	0.707772i
$56$	−2.90687	−	2.90687i	−0.388447	−	0.388447i
$57$	−2.65630			−0.351836
$58$	4.28806	+	4.28806i	0.563050	+	0.563050i
$59$	1.92935	−	1.92935i	0.251180	−	0.251180i	−0.570274	−	0.821454i	$-0.693163\pi$
$59$	1.92935	−	1.92935i	0.251180	−	0.251180i	0.821454	+	0.570274i	$0.193163\pi$
$60$	2.17242	+	0.529716i	0.280458	+	0.0683860i
$61$	−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	$-0.592038\pi$
$67$	5.51165	−	5.51165i	0.673355	−	0.673355i	0.958488	+	0.285133i	$0.0920377\pi$
$68$			4.16103i			0.504599i
$69$	−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	$0.668711\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−2.98121	−	2.98121i	−0.348924	−	0.348924i	0.510785	−	0.859709i	$-0.329355\pi$
$73$	−2.98121	−	2.98121i	−0.348924	−	0.348924i	−0.859709	+	0.510785i	$0.829355\pi$
$74$	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	−0.619824	−	0.784741i	$-0.712796\pi$
$79$	1.46581	−	1.46581i	0.164916	−	0.164916i	0.784741	+	0.619824i	$0.212796\pi$
$80$	1.91070	−	1.16157i	0.213622	−	0.129867i
$81$	−1.00000			−0.111111
$82$		−	7.59421i		−	0.838640i
$83$	7.26193	−	7.26193i	0.797101	−	0.797101i	−0.185536	−	0.982637i	$-0.559402\pi$
$83$	7.26193	−	7.26193i	0.797101	−	0.797101i	0.982637	+	0.185536i	$0.0594023\pi$
$84$			4.11094i			0.448540i
$85$	4.83331	+	7.95047i	0.524246	+	0.862350i
$86$	6.23482			0.672318
$87$		−	6.06423i		−	0.650154i
$88$			2.74715i			0.292847i
$89$	−1.62770	−	1.62770i	−0.172535	−	0.172535i	0.615557	−	0.788092i	$-0.288931\pi$
$89$	−1.62770	−	1.62770i	−0.172535	−	0.172535i	−0.788092	+	0.615557i	$0.788931\pi$
$90$	−1.16157	−	1.91070i	−0.122440	−	0.201405i
$91$	15.1602	+	15.1602i	1.58922	+	1.58922i
$92$	−0.941868			−0.0981965
$93$	7.79574			0.808381
$94$	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
$97$			10.0910i			1.02459i	0.858810	+	0.512294i	$0.171204\pi$
$97$			10.0910i			1.02459i	−0.858810	+	0.512294i	$0.828796\pi$
$98$		−	9.89979i		−	1.00003i
$99$	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
$103$		−	7.77490i		−	0.766084i	−0.923731	−	0.383042i	$-0.874877\pi$
$103$		−	7.77490i		−	0.766084i	0.923731	−	0.383042i	$-0.125123\pi$
$104$	−5.21529			−0.511402
$105$	4.77512	+	7.85475i	0.466004	+	0.766546i
$106$	−8.31822	+	8.31822i	−0.807937	+	0.807937i
$107$	5.67037	+	5.67037i	0.548176	+	0.548176i	0.925913	−	0.377737i	$-0.123298\pi$
$107$	5.67037	+	5.67037i	0.548176	+	0.548176i	−0.377737	+	0.925913i	$0.623298\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−5.58777	+	5.58777i	−0.535211	+	0.535211i	−0.922118	−	0.386908i	$-0.873543\pi$
$109$	−5.58777	+	5.58777i	−0.535211	+	0.535211i	0.386908	+	0.922118i	$0.373543\pi$
$110$	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
$113$			14.2804i			1.34339i	0.740829	+	0.671694i	$0.234433\pi$
$113$			14.2804i			1.34339i	−0.740829	+	0.671694i	$0.765567\pi$
$114$	2.65630			0.248785
$115$	−1.79963	+	1.09404i	−0.167816	+	0.102020i
$116$	−4.28806	−	4.28806i	−0.398136	−	0.398136i
$117$			5.21529i			0.482154i
$118$	−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
$125$	−0.758434	−	11.1546i	−0.0678364	−	0.997696i
$126$	2.90687	−	2.90687i	0.258965	−	0.258965i
$127$	8.01885	+	8.01885i	0.711558	+	0.711558i	0.966861	−	0.255303i	$-0.0821752\pi$
$127$	8.01885	+	8.01885i	0.711558	+	0.711558i	−0.255303	+	0.966861i	$0.582175\pi$
$128$	−1.00000			−0.0883883
$129$	−4.40869	−	4.40869i	−0.388163	−	0.388163i
$130$	−9.96485	+	6.05791i	−0.873975	+	0.531314i
$131$	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
$133$	−10.9199			−0.946874
$134$	−5.51165	+	5.51165i	−0.476134	+	0.476134i
$135$	−0.529716	+	2.17242i	−0.0455907	+	0.186972i
$136$		−	4.16103i		−	0.356806i
$137$	7.91811	+	7.91811i	0.676490	+	0.676490i	0.959204	−	0.282714i	$-0.0912348\pi$
$137$	7.91811	+	7.91811i	0.676490	+	0.676490i	−0.282714	+	0.959204i	$0.591235\pi$
$138$	0.666001	+	0.666001i	0.0566938	+	0.0566938i
$139$	13.0683			1.10844			0.554221	−	0.832369i	$-0.313016\pi$
$139$	13.0683			1.10844			0.554221	+	0.832369i	$0.313016\pi$
$140$	8.93067	+	2.17763i	0.754779	+	0.184043i
$141$		−	8.55529i		−	0.720485i
$142$	8.51973			0.714960
$143$		−	14.3272i		−	1.19810i
$144$			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
$148$	−2.77109	+	5.41489i	−0.227783	+	0.445101i
$149$			6.80855i			0.557778i	0.960323	+	0.278889i	$0.0899661\pi$
$149$			6.80855i			0.557778i	−0.960323	+	0.278889i	$0.910034\pi$
$150$	−4.76613	+	1.51128i	−0.389153	+	0.123395i
$151$			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
$153$	−4.16103			−0.336399
$154$	−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	0.818480	−	0.574535i	$-0.194817\pi$
$157$	3.05662	+	3.05662i	0.243945	+	0.243945i	−0.574535	+	0.818480i	$0.694817\pi$
$158$	−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
$162$	1.00000			0.0785674
$163$		−	19.5350i		−	1.53010i	−0.643971	−	0.765050i	$-0.722714\pi$
$163$		−	19.5350i		−	1.53010i	0.643971	−	0.765050i	$-0.277286\pi$
$164$			7.59421i			0.593008i
$165$	1.45521	−	5.96796i	0.113288	−	0.464605i
$166$	−7.26193	+	7.26193i	−0.563635	+	0.563635i
$167$		−	7.60664i		−	0.588620i	−0.955710	−	0.294310i	$-0.904910\pi$
$167$		−	7.60664i		−	0.588620i	0.955710	−	0.294310i	$-0.0950898\pi$
$168$		−	4.11094i		−	0.317166i
$169$	14.1993			1.09225
$170$	−4.83331	−	7.95047i	−0.370698	−	0.609773i
$171$	−1.87829	−	1.87829i	−0.143636	−	0.143636i
$172$	−6.23482			−0.475401
$173$	−17.6561	−	17.6561i	−1.34237	−	1.34237i	−0.893695	−	0.448675i	$-0.851896\pi$
$173$	−17.6561	−	17.6561i	−1.34237	−	1.34237i	−0.448675	−	0.893695i	$-0.648104\pi$
$174$			6.06423i			0.459728i
$175$	19.5933	−	6.21277i	1.48111	−	0.469642i
$176$		−	2.74715i		−	0.207074i
$177$	2.72851			0.205087
$178$	1.62770	+	1.62770i	0.122001	+	0.122001i
$179$	−5.23093	−	5.23093i	−0.390978	−	0.390978i	0.484058	−	0.875036i	$-0.339162\pi$
$179$	−5.23093	−	5.23093i	−0.390978	−	0.390978i	−0.875036	+	0.484058i	$0.839162\pi$
$180$	1.16157	+	1.91070i	0.0865780	+	0.142415i
$181$	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
$183$	−12.2841			−0.908068
$184$	0.941868			0.0694354
$185$	0.995030	+	13.5650i	0.0731560	+	0.997321i
$186$	−7.79574			−0.571612
$187$	11.4310			0.835916
$188$	−6.04950	−	6.04950i	−0.441205	−	0.441205i
$189$	−4.11094			−0.299027
$190$	1.40708	−	5.77059i	0.102081	−	0.418643i
$191$	−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
$193$	−16.3418			−1.17631			−0.588154	−	0.808749i	$-0.700145\pi$
$193$	−16.3418			−1.17631			−0.588154	+	0.808749i	$0.700145\pi$
$194$		−	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	0.167680	−	0.985841i	$-0.446372\pi$
$197$	−11.4834	−	11.4834i	−0.818161	−	0.818161i	−0.985841	+	0.167680i	$0.946372\pi$
$198$	−2.74715			−0.195232
$199$	−12.9349	−	12.9349i	−0.916929	−	0.916929i	0.0798762	−	0.996805i	$-0.474548\pi$
$199$	−12.9349	−	12.9349i	−0.916929	−	0.916929i	−0.996805	+	0.0798762i	$0.974548\pi$
$200$	−2.30153	+	4.43880i	−0.162743	+	0.313871i
$201$	7.79465			0.549792
$202$		−	9.40183i		−	0.661511i
$203$		−	24.9297i		−	1.74972i
$204$	−2.94229	+	2.94229i	−0.206002	+	0.206002i
$205$	8.82118	+	14.5102i	0.616098	+	1.01344i
$206$			7.77490i			0.541703i
$207$		−	0.941868i		−	0.0654644i
$208$	5.21529			0.361616
$209$	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
$217$	32.0478			2.17555
$218$	5.58777	−	5.58777i	0.378451	−	0.378451i
$219$		−	4.21607i		−	0.284895i
$220$	−3.19100	−	5.24898i	−0.215137	−	0.353886i
$221$			21.7010i			1.45977i
$222$	5.78837	−	1.86945i	0.388490	−	0.125469i
$223$	−2.83314	+	2.83314i	−0.189721	+	0.189721i	−0.795576	−	0.605854i	$-0.792831\pi$
$223$	−2.83314	+	2.83314i	−0.189721	+	0.189721i	0.605854	+	0.795576i	$0.292831\pi$
$224$	−2.90687	−	2.90687i	−0.194223	−	0.194223i
$225$	4.43880	+	2.30153i	0.295920	+	0.153435i
$226$		−	14.2804i		−	0.949919i
$227$			7.49379i			0.497380i	0.968583	+	0.248690i	$0.0800001\pi$
$227$			7.49379i			0.497380i	−0.968583	+	0.248690i	$0.920000\pi$
$228$	−2.65630			−0.175918
$229$		−	24.0930i		−	1.59211i	−0.605224	−	0.796055i	$-0.706917\pi$
$229$		−	24.0930i		−	1.59211i	0.605224	−	0.796055i	$-0.293083\pi$
$230$	1.79963	−	1.09404i	0.118664	−	0.0721390i
$231$	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	$-0.132557\pi$
$233$	7.78522	+	7.78522i	0.510027	+	0.510027i	−0.404508	+	0.914535i	$0.632557\pi$
$234$		−	5.21529i		−	0.340934i
$235$	−18.5857	−	4.53187i	−1.21239	−	0.295627i
$236$	1.92935	−	1.92935i	0.125590	−	0.125590i
$237$	2.07297			0.134654
$238$	12.0956	−	12.0956i	0.784040	−	0.784040i
$239$	−1.88427	+	1.88427i	−0.121884	+	0.121884i	−0.765418	−	0.643534i	$-0.777468\pi$
$239$	−1.88427	+	1.88427i	−0.121884	+	0.121884i	0.643534	+	0.765418i	$0.277468\pi$
$240$	2.17242	+	0.529716i	0.140229	+	0.0341930i
$241$	−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	$-0.559192\pi$
$242$	−3.45316			−0.221977
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−8.68618	+	8.68618i	−0.556076	+	0.556076i
$245$	11.4993	+	18.9155i	0.734661	+	1.20847i
$246$	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
$253$			2.58745i			0.162672i
$254$	−8.01885	−	8.01885i	−0.503148	−	0.503148i
$255$	−2.20417	+	9.03950i	−0.138030	+	0.566076i
$256$	1.00000			0.0625000
$257$			2.69763i			0.168274i	0.996454	+	0.0841369i	$0.0268133\pi$
$257$			2.69763i			0.168274i	−0.996454	+	0.0841369i	$0.973187\pi$
$258$	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	$-0.476934\pi$
$263$	−15.0006	−	15.0006i	−0.924974	−	0.924974i	−0.997376	+	0.0724014i	$0.976934\pi$
$264$	−1.94253	+	1.94253i	−0.119554	+	0.119554i
$265$	6.23144	−	25.5557i	0.382794	−	1.56988i
$266$	10.9199			0.669541
$267$		−	2.30191i		−	0.140875i
$268$	5.51165	−	5.51165i	0.336678	−	0.336678i
$269$		−	3.86256i		−	0.235505i	−0.993043	−	0.117752i	$-0.962431\pi$
$269$		−	3.86256i		−	0.235505i	0.993043	−	0.117752i	$-0.0375689\pi$
$270$	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	$0.611053\pi$
$272$			4.16103i			0.252300i
$273$			21.4397i			1.29759i
$274$	−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
$277$	16.2009			0.973420			0.486710	−	0.873564i	$-0.338197\pi$
$277$	16.2009			0.973420			0.486710	+	0.873564i	$0.338197\pi$
$278$	−13.0683			−0.783787
$279$	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	$0.856534\pi$
$282$			8.55529i			0.509460i
$283$		−	21.1035i		−	1.25447i	−0.778829	−	0.627237i	$-0.784186\pi$
$283$		−	21.1035i		−	1.25447i	0.778829	−	0.627237i	$-0.215814\pi$
$284$	−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
$288$		−	1.00000i		−	0.0589256i
$289$	−0.314185			−0.0184815
$290$	13.1741	+	3.21232i	0.773607	+	0.188634i
$291$	−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	−0.783343	−	0.621590i	$-0.786487\pi$
$293$	−2.76877	+	2.76877i	−0.161753	+	0.161753i	0.621590	+	0.783343i	$0.286487\pi$
$294$	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
$298$		−	6.80855i		−	0.394408i
$299$	−4.91212			−0.284075
$300$	4.76613	−	1.51128i	0.275173	−	0.0872538i
$301$	−18.1238	−	18.1238i	−1.04464	−	1.04464i
$302$		−	17.8917i		−	1.02955i
$303$	−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	$-0.670465\pi$
$307$	6.12720	−	6.12720i	0.349698	−	0.349698i	0.859997	+	0.510299i	$0.170465\pi$
$308$	7.98561	−	7.98561i	0.455023	−	0.455023i
$309$	5.49768	−	5.49768i	0.312752	−	0.312752i
$310$	−4.12953	+	16.9356i	−0.234542	+	0.961878i
$311$	−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
$313$	−7.63668			−0.431650			−0.215825	−	0.976432i	$-0.569244\pi$
$313$	−7.63668			−0.431650			−0.215825	+	0.976432i	$0.569244\pi$
$314$	−3.05662	−	3.05662i	−0.172495	−	0.172495i
$315$	−2.17763	+	8.93067i	−0.122695	+	0.503186i
$316$	1.46581	−	1.46581i	0.0824581	−	0.0824581i
$317$	19.5287	−	19.5287i	1.09684	−	1.09684i	0.102064	−	0.994778i	$-0.467455\pi$
$317$	19.5287	−	19.5287i	1.09684	−	1.09684i	0.994778	−	0.102064i	$-0.0325445\pi$
$318$	−11.7637			−0.659677
$319$	−11.7800	+	11.7800i	−0.659551	+	0.659551i
$320$	1.91070	−	1.16157i	0.106811	−	0.0649335i
$321$			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
$325$	12.0032	−	23.1497i	0.665815	−	1.28411i
$326$			19.5350i			1.08194i
$327$	−7.90229			−0.436998
$328$		−	7.59421i		−	0.419320i
$329$		−	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
$333$	−5.41489	−	2.77109i	−0.296734	−	0.151855i
$334$			7.60664i			0.416217i
$335$	4.12895	−	16.9332i	0.225589	−	0.925162i
$336$			4.11094i			0.224270i
$337$	−14.7087	+	14.7087i	−0.801235	+	0.801235i	−0.983289	−	0.182054i	$-0.941725\pi$
$337$	−14.7087	+	14.7087i	−0.801235	+	0.801235i	0.182054	+	0.983289i	$0.441725\pi$
$338$	−14.1993			−0.772340
$339$	−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
$347$	−5.20503			−0.279421			−0.139710	−	0.990192i	$-0.544617\pi$
$347$	−5.20503			−0.279421			−0.139710	+	0.990192i	$0.544617\pi$
$348$		−	6.06423i		−	0.325077i
$349$			8.31963i			0.445339i	0.974894	+	0.222670i	$0.0714771\pi$
$349$			8.31963i			0.445339i	−0.974894	+	0.222670i	$0.928523\pi$
$350$	−19.5933	+	6.21277i	−1.04730	+	0.332087i
$351$	−3.68777	+	3.68777i	−0.196839	+	0.196839i
$352$			2.74715i			0.146424i
$353$			32.6034i			1.73530i	0.497173	+	0.867651i	$0.334371\pi$
$353$			32.6034i			1.73530i	−0.497173	+	0.867651i	$0.665629\pi$
$354$	−2.72851			−0.145019
$355$	−16.2786	+	9.89623i	−0.863980	+	0.525237i
$356$	−1.62770	−	1.62770i	−0.0862677	−	0.0862677i
$357$	−17.1057			−0.905331
$358$	5.23093	+	5.23093i	0.276463	+	0.276463i
$359$			17.3163i			0.913921i	0.889487	+	0.456960i	$0.151062\pi$
$359$			17.3163i			0.913921i	−0.889487	+	0.456960i	$0.848938\pi$
$360$	−1.16157	−	1.91070i	−0.0612199	−	0.100703i
$361$			11.9441i			0.628635i
$362$	−6.81886			−0.358391
$363$	2.44175	+	2.44175i	0.128159	+	0.128159i
$364$	15.1602	+	15.1602i	0.794610	+	0.794610i
$365$	−9.15906	−	2.23332i	−0.479407	−	0.116897i
$366$	12.2841			0.642101
$367$	−19.8485	−	19.8485i	−1.03608	−	1.03608i	−0.999324	−	0.0367606i	$-0.988296\pi$
$367$	−19.8485	−	19.8485i	−1.03608	−	1.03608i	−0.0367606	−	0.999324i	$-0.511704\pi$
$368$	−0.941868			−0.0490983
$369$	−7.59421			−0.395339
$370$	−0.995030	−	13.5650i	−0.0517291	−	0.705212i
$371$	48.3600			2.51072
$372$	7.79574			0.404190
$373$	19.3419	+	19.3419i	1.00149	+	1.00149i	0.999999	+	0.00148728i	$0.000473415\pi$
$373$	19.3419	+	19.3419i	1.00149	+	1.00149i	0.00148728	+	0.999999i	$0.499527\pi$
$374$	−11.4310			−0.591082
$375$	7.35119	−	8.42378i	0.379614	−	0.435002i
$376$	6.04950	+	6.04950i	0.311979	+	0.311979i
$377$	−22.3635	−	22.3635i	−1.15178	−	1.15178i
$378$	4.11094			0.211444
$379$		−	3.56273i		−	0.183005i	−0.995805	−	0.0915027i	$-0.970833\pi$
$379$		−	3.56273i		−	0.183005i	0.995805	−	0.0915027i	$-0.0291670\pi$
$380$	−1.40708	+	5.77059i	−0.0721819	+	0.296025i
$381$			11.3404i			0.580985i
$382$	7.19163	+	7.19163i	0.367956	+	0.367956i
$383$	−17.5102			−0.894730			−0.447365	−	0.894351i	$-0.647638\pi$
$383$	−17.5102			−0.894730			−0.447365	+	0.894351i	$0.647638\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	5.98228	−	24.5339i	0.304885	−	1.25036i
$386$	16.3418			0.831776
$387$		−	6.23482i		−	0.316934i
$388$			10.0910i			0.512294i
$389$	5.52680	−	5.52680i	0.280220	−	0.280220i	−0.552977	−	0.833197i	$-0.686508\pi$
$389$	5.52680	−	5.52680i	0.280220	−	0.280220i	0.833197	+	0.552977i	$0.186508\pi$
$390$	−11.3298	−	2.76262i	−0.573707	−	0.139891i
$391$		−	3.91914i		−	0.198200i
$392$		−	9.89979i		−	0.500015i
$393$	9.38564			0.473443
$394$	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	$-0.668090\pi$
$397$	7.17123	−	7.17123i	0.359913	−	0.359913i	0.863781	+	0.503867i	$0.168090\pi$
$398$	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	$0.106914\pi$
$402$	−7.79465			−0.388762
$403$	28.7489	−	28.7489i	1.43208	−	1.43208i
$404$			9.40183i			0.467759i
$405$	−1.91070	+	1.16157i	−0.0949433	+	0.0577187i
$406$			24.9297i			1.23724i
$407$	14.8755	+	7.61262i	0.737352	+	0.377343i
$408$	2.94229	−	2.94229i	0.145665	−	0.145665i
$409$	−20.8384	−	20.8384i	−1.03039	−	1.03039i	−0.999523	−	0.0308695i	$-0.990172\pi$
$409$	−20.8384	−	20.8384i	−1.03039	−	1.03039i	−0.0308695	−	0.999523i	$-0.509828\pi$
$410$	−8.82118	−	14.5102i	−0.435647	−	0.716610i
$411$			11.1979i			0.552352i
$412$		−	7.77490i		−	0.383042i
$413$	11.2167			0.551939
$414$			0.941868i			0.0462903i
$415$	5.44014	−	22.3106i	0.267046	−	1.09518i
$416$	−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	$0.349689\pi$
$419$			36.4587i			1.78113i	−0.454860	+	0.890563i	$0.650311\pi$
$420$	4.77512	+	7.85475i	0.233002	+	0.383273i
$421$	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	$0.0746551\pi$
$422$	23.4609			1.14206
$423$	6.04950	−	6.04950i	0.294137	−	0.294137i
$424$	−8.31822	+	8.31822i	−0.403968	+	0.403968i
$425$	18.4700	+	9.57674i	0.895926	+	0.464540i
$426$	6.02436	+	6.02436i	0.291881	+	0.291881i
$427$	−50.4992			−2.44383
$428$	5.67037	+	5.67037i	0.274088	+	0.274088i
$429$	10.1309	−	10.1309i	0.489123	−	0.489123i
$430$	11.9129	−	7.24216i	0.574489	−	0.349248i
$431$	−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	−0.230111	−	0.973164i	$-0.573909\pi$
$433$	15.4619	−	15.4619i	0.743053	−	0.743053i	0.973164	+	0.230111i	$0.0739089\pi$
$434$	−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
$438$			4.21607i			0.201451i
$439$	15.6685	+	15.6685i	0.747816	+	0.747816i	0.974069	−	0.226253i	$-0.0726476\pi$
$439$	15.6685	+	15.6685i	0.747816	+	0.747816i	−0.226253	+	0.974069i	$0.572648\pi$
$440$	3.19100	+	5.24898i	0.152125	+	0.250235i
$441$	−9.89979			−0.471419
$442$		−	21.7010i		−	1.03221i
$443$	27.2120	+	27.2120i	1.29288	+	1.29288i	0.932996	+	0.359887i	$0.117185\pi$
$443$	27.2120	+	27.2120i	1.29288	+	1.29288i	0.359887	+	0.932996i	$0.382815\pi$
$444$	−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	−0.995027	−	0.0996105i	$-0.968240\pi$
$449$	−18.9735	+	18.9735i	−0.895416	+	0.895416i	0.0996105	+	0.995027i	$0.468240\pi$
$450$	−4.43880	−	2.30153i	−0.209247	−	0.108495i
$451$	20.8624			0.982374
$452$			14.2804i			0.671694i
$453$	−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
$457$		−	9.71477i		−	0.454438i	−0.973844	−	0.227219i	$-0.927037\pi$
$457$		−	9.71477i		−	0.454438i	0.973844	−	0.227219i	$-0.0729632\pi$
$458$			24.0930i			1.12579i
$459$	−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	$0.557380\pi$
$462$	−11.2934			−0.525415
$463$	16.3891			0.761664			0.380832	−	0.924644i	$-0.375638\pi$
$463$	16.3891			0.761664			0.380832	+	0.924644i	$0.375638\pi$
$464$	−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
$467$			1.29508i			0.0599293i	0.999551	+	0.0299647i	$0.00953947\pi$
$467$			1.29508i			0.0599293i	−0.999551	+	0.0299647i	$0.990461\pi$
$468$			5.21529i			0.241077i
$469$	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
$473$			17.1280i			0.787547i
$474$	−2.07297			−0.0952144
$475$	4.01441	+	12.6603i	0.184194	+	0.580894i
$476$	−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	$-0.410737\pi$
$479$	27.0885	−	27.0885i	1.23770	−	1.23770i	0.960937	−	0.276766i	$-0.0892628\pi$
$480$	−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
$483$		−	3.87196i		−	0.176180i
$484$	3.45316			0.156962
$485$	11.7214	+	19.2809i	0.532241	+	0.875500i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$		−	27.5508i		−	1.24844i	−0.781247	−	0.624222i	$-0.785416\pi$
$487$		−	27.5508i		−	1.24844i	0.781247	−	0.624222i	$-0.214584\pi$
$488$	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
$495$	5.24898	−	3.19100i	0.235924	−	0.143425i
$496$	5.51242	−	5.51242i	0.247515	−	0.247515i
$497$	−24.7657	−	24.7657i	−1.11090	−	1.11090i
$498$	−10.2699			−0.460206
$499$	−9.41283	−	9.41283i	−0.421376	−	0.421376i	0.464301	−	0.885677i	$-0.346305\pi$
$499$	−9.41283	−	9.41283i	−0.421376	−	0.421376i	−0.885677	+	0.464301i	$0.846305\pi$
$500$	−0.758434	−	11.1546i	−0.0339182	−	0.498848i
$501$	5.37871	−	5.37871i	0.240303	−	0.240303i
$502$	10.2960	−	10.2960i	0.459534	−	0.459534i
$503$	−32.7145			−1.45867			−0.729334	−	0.684158i	$-0.760170\pi$
$503$	−32.7145			−1.45867			−0.729334	+	0.684158i	$0.760170\pi$
$504$	2.90687	−	2.90687i	0.129482	−	0.129482i
$505$	10.9208	+	17.9641i	0.485971	+	0.799390i
$506$		−	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	$-0.405728\pi$
$509$	13.1690			0.583707			0.291854	+	0.956463i	$0.405728\pi$
$510$	2.20417	−	9.03950i	0.0976021	−	0.400276i
$511$		−	17.3320i		−	0.766722i
$512$	−1.00000			−0.0441942
$513$		−	2.65630i		−	0.117279i
$514$		−	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
$518$	23.7956	−	7.68517i	1.04552	−	0.337667i
$519$		−	24.9695i		−	1.09604i
$520$	−9.96485	+	6.05791i	−0.436988	+	0.265657i
$521$		−	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
$523$	17.6544			0.771972			0.385986	−	0.922505i	$-0.373861\pi$
$523$	17.6544			0.771972			0.385986	+	0.922505i	$0.373861\pi$
$524$	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
$532$	−10.9199			−0.473437
$533$			39.6060i			1.71553i
$534$			2.30191i			0.0996134i
$535$	17.4209	+	4.24786i	0.753170	+	0.183651i
$536$	−5.51165	+	5.51165i	−0.238067	+	0.238067i
$537$		−	7.39765i		−	0.319232i
$538$			3.86256i			0.166527i
$539$	27.1962			1.17142
$540$	−0.529716	+	2.17242i	−0.0227953	+	0.0934860i
$541$	−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	$-0.514493\pi$
$542$	11.2551			0.483447
$543$	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
$547$	−22.8223			−0.975811			−0.487906	−	0.872896i	$-0.662239\pi$
$547$	−22.8223			−0.975811			−0.487906	+	0.872896i	$0.662239\pi$
$548$	7.91811	+	7.91811i	0.338245	+	0.338245i
$549$	−8.68618	−	8.68618i	−0.370717	−	0.370717i
$550$	12.1941	+	6.32265i	0.519957	+	0.269599i
$551$	16.1084			0.686242
$552$	0.666001	+	0.666001i	0.0283469	+	0.0283469i
$553$	8.52183			0.362385
$554$	−16.2009			−0.688312
$555$	−8.88833	+	10.2955i	−0.377289	+	0.437020i
$556$	13.0683			0.554221
$557$	22.2337			0.942073			0.471036	−	0.882114i	$-0.343880\pi$
$557$	22.2337			0.942073			0.471036	+	0.882114i	$0.343880\pi$
$558$	−5.51242	−	5.51242i	−0.233359	−	0.233359i
$559$	−32.5164			−1.37530
$560$	8.93067	+	2.17763i	0.377390	+	0.0920216i
$561$	8.08293	+	8.08293i	0.341261	+	0.341261i
$562$	7.78699	+	7.78699i	0.328474	+	0.328474i
$563$	−25.9596			−1.09407			−0.547034	−	0.837110i	$-0.684243\pi$
$563$	−25.9596			−1.09407			−0.547034	+	0.837110i	$0.684243\pi$
$564$		−	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
$568$	8.51973			0.357480
$569$	4.18660	+	4.18660i	0.175512	+	0.175512i	0.789396	−	0.613884i	$-0.210394\pi$
$569$	4.18660	+	4.18660i	0.175512	+	0.175512i	−0.613884	+	0.789396i	$0.710394\pi$
$570$	5.07539	−	3.08547i	0.212585	−	0.129236i
$571$	−24.7600			−1.03617			−0.518087	−	0.855328i	$-0.673356\pi$
$571$	−24.7600			−1.03617			−0.518087	+	0.855328i	$0.673356\pi$
$572$		−	14.3272i		−	0.599050i
$573$		−	10.1705i		−	0.424879i
$574$	22.0754	−	22.0754i	0.921409	−	0.921409i
$575$	−2.16774	+	4.18077i	−0.0904009	+	0.174350i
$576$			1.00000i			0.0416667i
$577$			34.1071i			1.41990i	0.704254	+	0.709948i	$0.251282\pi$
$577$			34.1071i			1.41990i	−0.704254	+	0.709948i	$0.748718\pi$
$578$	0.314185			0.0130684
$579$	−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
$587$	−46.3514			−1.91313			−0.956564	−	0.291522i	$-0.905838\pi$
$587$	−46.3514			−1.91313			−0.956564	+	0.291522i	$0.905838\pi$
$588$	−7.00021	+	7.00021i	−0.288684	+	0.288684i
$589$			20.7078i			0.853251i
$590$	−1.44534	+	5.92747i	−0.0595035	+	0.244030i
$591$		−	16.2400i		−	0.668026i
$592$	−2.77109	+	5.41489i	−0.113891	+	0.222551i
$593$	−16.9988	+	16.9988i	−0.698058	+	0.698058i	−0.963991	−	0.265934i	$-0.914320\pi$
$593$	−16.9988	+	16.9988i	−0.698058	+	0.698058i	0.265934	+	0.963991i	$0.414320\pi$
$594$	−1.94253	−	1.94253i	−0.0797030	−	0.0797030i
$595$	−9.06118	+	37.1608i	−0.371472	+	1.52344i
$596$			6.80855i			0.278889i
$597$		−	18.2927i		−	0.748669i
$598$	4.91212			0.200871
$599$			12.7894i			0.522561i	0.965263	+	0.261281i	$0.0841448\pi$
$599$			12.7894i			0.522561i	−0.965263	+	0.261281i	$0.915855\pi$
$600$	−4.76613	+	1.51128i	−0.194577	+	0.0616977i
$601$	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
$605$	6.59794	−	4.01107i	0.268244	−	0.163073i
$606$	6.64810	−	6.64810i	0.270061	−	0.270061i
$607$	33.5114			1.36018			0.680092	−	0.733127i	$-0.261940\pi$
$607$	33.5114			1.36018			0.680092	+	0.733127i	$0.261940\pi$
$608$	1.87829	−	1.87829i	0.0761746	−	0.0761746i
$609$	17.6279	−	17.6279i	0.714320	−	0.714320i
$610$	6.50709	−	26.6862i	0.263464	−	1.08049i
$611$	−31.5499	−	31.5499i	−1.27637	−	1.27637i
$612$	−4.16103			−0.168200
$613$	−1.15839	−	1.15839i	−0.0467871	−	0.0467871i	0.683326	−	0.730113i	$-0.260533\pi$
$613$	−1.15839	−	1.15839i	−0.0467871	−	0.0467871i	−0.730113	+	0.683326i	$0.760533\pi$
$614$	−6.12720	+	6.12720i	−0.247274	+	0.247274i
$615$	−4.02278	+	16.4978i	−0.162214	+	0.665256i
$616$	−7.98561	+	7.98561i	−0.321750	+	0.321750i
$617$	15.5057	−	15.5057i	0.624237	−	0.624237i	−0.322375	−	0.946612i	$-0.604481\pi$
$617$	15.5057	−	15.5057i	0.624237	−	0.624237i	0.946612	+	0.322375i	$0.104481\pi$
$618$	−5.49768	+	5.49768i	−0.221149	+	0.221149i
$619$	23.4133			0.941060			0.470530	−	0.882384i	$-0.344063\pi$
$619$	23.4133			0.941060			0.470530	+	0.882384i	$0.344063\pi$
$620$	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
$623$		−	9.46300i		−	0.379127i
$624$	3.68777	+	3.68777i	0.147629	+	0.147629i
$625$	−14.4059	−	20.4321i	−0.576237	−	0.817283i
$626$	7.63668			0.305223
$627$			7.29726i			0.291424i
$628$	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
$635$	24.6360	+	6.00718i	0.977651	+	0.238388i
$636$	11.7637			0.466462
$637$			51.6303i			2.04567i
$638$	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	$0.683276\pi$
$642$		−	8.01912i		−	0.316489i
$643$			18.0002i			0.709858i	0.934893	+	0.354929i	$0.115495\pi$
$643$			18.0002i			0.709858i	−0.934893	+	0.354929i	$0.884505\pi$
$644$	−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
$647$	26.1609			1.02849			0.514245	−	0.857643i	$-0.328072\pi$
$647$	26.1609			1.02849			0.514245	+	0.857643i	$0.328072\pi$
$648$	1.00000			0.0392837
$649$	−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
$652$		−	19.5350i		−	0.765050i
$653$			27.1758i			1.06347i	0.846911	+	0.531735i	$0.178460\pi$
$653$			27.1758i			1.06347i	−0.846911	+	0.531735i	$0.821540\pi$
$654$	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
$658$			35.1702i			1.37108i
$659$	11.2236			0.437210			0.218605	−	0.975813i	$-0.429849\pi$
$659$	11.2236			0.437210			0.218605	+	0.975813i	$0.429849\pi$
$660$	1.45521	−	5.96796i	0.0566440	−	0.232303i
$661$	−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
$668$		−	7.60664i		−	0.294310i
$669$	−4.00667			−0.154907
$670$	−4.12895	+	16.9332i	−0.159515	+	0.654188i
$671$	23.8623	+	23.8623i	0.921192	+	0.921192i
$672$		−	4.11094i		−	0.158583i
$673$	21.3478	−	21.3478i	0.822898	−	0.822898i	−0.163624	−	0.986523i	$-0.552318\pi$
$673$	21.3478	−	21.3478i	0.822898	−	0.822898i	0.986523	+	0.163624i	$0.0523185\pi$
$674$	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	−0.152168	+	0.988355i	$0.548625\pi$
$677$	−29.6755	+	29.6755i	−1.14052	+	1.14052i	−0.988355	+	0.152168i	$0.951375\pi$
$678$	10.0978	−	10.0978i	0.387803	−	0.387803i
$679$	−29.3333	+	29.3333i	−1.12571	+	1.12571i
$680$	−4.83331	−	7.95047i	−0.185349	−	0.304887i
$681$	−5.29891	+	5.29891i	−0.203055	+	0.203055i
$682$	15.1435	+	15.1435i	0.579873	+	0.579873i
$683$	−3.99926			−0.153027			−0.0765137	−	0.997069i	$-0.524379\pi$
$683$	−3.99926			−0.153027			−0.0765137	+	0.997069i	$0.524379\pi$
$684$	−1.87829	−	1.87829i	−0.0718181	−	0.0718181i
$685$	24.3265	+	5.93171i	0.929469	+	0.226639i
$686$	8.42932	−	8.42932i	0.321833	−	0.321833i
$687$	17.0363	−	17.0363i	0.649976	−	0.649976i
$688$	−6.23482			−0.237700
$689$	43.3819	−	43.3819i	1.65272	−	1.65272i
$690$	2.04613	+	0.498923i	0.0778949	+	0.0189937i
$691$		−	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
$695$	24.9697	−	15.1797i	0.947153	−	0.575801i
$696$			6.06423i			0.229864i
$697$	−31.5998			−1.19693
$698$		−	8.31963i		−	0.314902i
$699$			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
$703$	−4.96581	−	15.3756i	−0.187289	−	0.579903i
$704$		−	2.74715i		−	0.103537i
$705$	−9.93753	−	16.3466i	−0.374269	−	0.615647i
$706$		−	32.6034i		−	1.22704i
$707$	−27.3299	+	27.3299i	−1.02785	+	1.02785i
$708$	2.72851			0.102544
$709$	−17.3563	+	17.3563i	−0.651828	+	0.651828i	−0.953433	−	0.301605i	$-0.902478\pi$
$709$	−17.3563	+	17.3563i	−0.651828	+	0.651828i	0.301605	+	0.953433i	$0.402478\pi$
$710$	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
$717$	−2.66477			−0.0995175
$718$		−	17.3163i		−	0.646240i
$719$		−	10.6066i		−	0.395558i	−0.980247	−	0.197779i	$-0.936627\pi$
$719$		−	10.6066i		−	0.395558i	0.980247	−	0.197779i	$-0.0633729\pi$
$720$	1.16157	+	1.91070i	0.0432890	+	0.0712075i
$721$	22.6006	−	22.6006i	0.841691	−	0.841691i
$722$		−	11.9441i		−	0.444512i
$723$		−	25.6351i		−	0.953381i
$724$	6.81886			0.253421
$725$	−28.9029	+	9.16475i	−1.07343	+	0.340370i
$726$	−2.44175	−	2.44175i	−0.0906219	−	0.0906219i
$727$	41.4047			1.53561			0.767807	−	0.640681i	$-0.221348\pi$
$727$	41.4047			1.53561			0.767807	+	0.640681i	$0.221348\pi$
$728$	−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
$732$	−12.2841			−0.454034
$733$	33.6863	+	33.6863i	1.24423	+	1.24423i	0.958228	+	0.286005i	$0.0923272\pi$
$733$	33.6863	+	33.6863i	1.24423	+	1.24423i	0.286005	+	0.958228i	$0.407673\pi$
$734$	19.8485	+	19.8485i	0.732622	+	0.732622i
$735$	−5.24408	+	21.5065i	−0.193431	+	0.793279i
$736$	0.941868			0.0347177
$737$	−15.1413	−	15.1413i	−0.557738	−	0.557738i
$738$	7.59421			0.279547
$739$	30.7911			1.13267			0.566335	−	0.824175i	$-0.308361\pi$
$739$	30.7911			1.13267			0.566335	+	0.824175i	$0.308361\pi$
$740$	0.995030	+	13.5650i	0.0365780	+	0.498660i
$741$	−13.8534			−0.508917
$742$	−48.3600			−1.77535
$743$	21.8367	+	21.8367i	0.801110	+	0.801110i	0.983269	−	0.182159i	$-0.0583086\pi$
$743$	21.8367	+	21.8367i	0.801110	+	0.801110i	−0.182159	+	0.983269i	$0.558309\pi$
$744$	−7.79574			−0.285806
$745$	7.90857	+	13.0091i	0.289748	+	0.476615i
$746$	−19.3419	−	19.3419i	−0.708158	−	0.708158i
$747$	7.26193	+	7.26193i	0.265700	+	0.265700i
$748$	11.4310			0.417958
$749$			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
$753$	−14.5608			−0.530624
$754$	22.3635	+	22.3635i	0.814430	+	0.814430i
$755$	20.7824	+	34.1856i	0.756348	+	1.24414i
$756$	−4.11094			−0.149513
$757$		−	5.34349i		−	0.194213i	−0.995274	−	0.0971063i	$-0.969041\pi$
$757$		−	5.34349i		−	0.194213i	0.995274	−	0.0971063i	$-0.0309587\pi$
$758$			3.56273i			0.129404i
$759$	−1.82961	+	1.82961i	−0.0664105	+	0.0664105i
$760$	1.40708	−	5.77059i	0.0510403	−	0.209321i
$761$		−	29.9342i		−	1.08511i	−0.840019	−	0.542557i	$-0.817456\pi$
$761$		−	29.9342i		−	1.08511i	0.840019	−	0.542557i	$-0.182544\pi$
$762$		−	11.3404i		−	0.410818i
$763$	−32.4858			−1.17607
$764$	−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	0.952399	−	0.304853i	$-0.0986074\pi$
$769$	17.9570	+	17.9570i	0.647546	+	0.647546i	−0.304853	+	0.952399i	$0.598607\pi$
$770$	−5.98228	+	24.5339i	−0.215586	+	0.884141i
$771$	−1.90752	+	1.90752i	−0.0686975	+	0.0686975i
$772$	−16.3418			−0.588154
$773$	20.5041	−	20.5041i	0.737483	−	0.737483i	−0.234607	−	0.972090i	$-0.575380\pi$
$773$	20.5041	−	20.5041i	0.737483	−	0.737483i	0.972090	+	0.234607i	$0.0753804\pi$
$774$			6.23482i			0.224106i
$775$	−11.7815	−	37.1556i	−0.423206	−	1.33467i
$776$		−	10.0910i		−	0.362247i
$777$	−22.2603	−	11.3918i	−0.798583	−	0.408678i
$778$	−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
$782$			3.91914i			0.140148i
$783$	6.06423			0.216718
$784$			9.89979i			0.353564i
$785$	9.39073	+	2.28981i	0.335170	+	0.0817268i
$786$	−9.38564			−0.334775
$787$	0.00644958	+	0.00644958i	0.000229903	+	0.000229903i	0.707222	−	0.706992i	$-0.249948\pi$
$787$	0.00644958	+	0.00644958i	0.000229903	+	0.000229903i	−0.706992	+	0.707222i	$0.749948\pi$
$788$	−11.4834	−	11.4834i	−0.409080	−	0.409080i
$789$		−	21.2140i		−	0.755238i
$790$	−1.09808	+	4.50335i	−0.0390680	+	0.160222i
$791$	−41.5113	+	41.5113i	−1.47597	+	1.47597i
$792$	−2.74715			−0.0976158
$793$	−45.3010	+	45.3010i	−1.60869	+	1.60869i
$794$	−7.17123	+	7.17123i	−0.254497	+	0.254497i
$795$	22.4769	−	13.6644i	0.797175	−	0.484625i
$796$	−12.9349	−	12.9349i	−0.458464	−	0.458464i
$797$	−16.8684			−0.597510			−0.298755	−	0.954330i	$-0.596571\pi$
$797$	−16.8684			−0.597510			−0.298755	+	0.954330i	$0.596571\pi$
$798$	7.72152	+	7.72152i	0.273339	+	0.273339i
$799$	25.1722	−	25.1722i	0.890527	−	0.890527i
$800$	−2.30153	+	4.43880i	−0.0813714	+	0.156935i
$801$	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
$808$		−	9.40183i		−	0.330755i
$809$	−32.7152	−	32.7152i	−1.15020	−	1.15020i	−0.986511	−	0.163692i	$-0.947660\pi$
$809$	−32.7152	−	32.7152i	−1.15020	−	1.15020i	−0.163692	−	0.986511i	$-0.552340\pi$
$810$	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	$0.690419\pi$
$812$		−	24.9297i		−	0.874860i
$813$	−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
$820$	8.82118	+	14.5102i	0.308049	+	0.506720i
$821$	46.5821			1.62573			0.812863	−	0.582455i	$-0.197908\pi$
$821$	46.5821			1.62573			0.812863	+	0.582455i	$0.197908\pi$
$822$		−	11.1979i		−	0.390572i
$823$	14.9085	−	14.9085i	0.519678	−	0.519678i	−0.397796	−	0.917474i	$-0.630225\pi$
$823$	14.9085	−	14.9085i	0.519678	−	0.519678i	0.917474	+	0.397796i	$0.130225\pi$
$824$			7.77490i			0.270851i
$825$	−4.15171	−	13.0933i	−0.144544	−	0.455850i
$826$	−11.2167			−0.390280
$827$			32.9874i			1.14708i	0.819176	+	0.573542i	$0.194431\pi$
$827$			32.9874i			1.14708i	−0.819176	+	0.573542i	$0.805569\pi$
$828$		−	0.941868i		−	0.0327322i
$829$	26.5468	+	26.5468i	0.922009	+	0.922009i	0.997171	−	0.0751625i	$-0.0239475\pi$
$829$	26.5468	+	26.5468i	0.922009	+	0.922009i	−0.0751625	+	0.997171i	$0.523948\pi$
$830$	−5.44014	+	22.3106i	−0.188830	+	0.774411i
$831$	11.4558	+	11.4558i	0.397397	+	0.397397i
$832$	5.21529			0.180808
$833$	−41.1933			−1.42726
$834$	−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
$837$			7.79574i			0.269460i
$838$		−	36.4587i		−	1.25945i
$839$	−28.9665			−1.00004			−0.500018	−	0.866015i	$-0.666673\pi$
$839$	−28.9665			−1.00004			−0.500018	+	0.866015i	$0.666673\pi$
$840$	−4.77512	−	7.85475i	−0.164757	−	0.271015i
$841$			7.77493i			0.268101i
$842$	−15.1883	+	15.1883i	−0.523422	+	0.523422i
$843$		−	11.0125i		−	0.379289i
$844$	−23.4609			−0.807558
$845$	27.1305	−	16.4934i	0.933319	−	0.567391i
$846$	−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
$853$		−	46.9335i		−	1.60697i	−0.595323	−	0.803487i	$-0.702976\pi$
$853$		−	46.9335i		−	1.60697i	0.595323	−	0.803487i	$-0.297024\pi$
$854$	50.4992			1.72805
$855$	−5.77059	−	1.40708i	−0.197350	−	0.0481213i
$856$	−5.67037	−	5.67037i	−0.193809	−	0.193809i
$857$		−	20.5633i		−	0.702429i	−0.936295	−	0.351214i	$-0.885769\pi$
$857$		−	20.5633i		−	0.702429i	0.936295	−	0.351214i	$-0.114231\pi$
$858$	−10.1309	+	10.1309i	−0.345862	+	0.345862i
$859$	35.4390	−	35.4390i	1.20916	−	1.20916i	0.237863	−	0.971299i	$-0.423553\pi$
$859$	35.4390	−	35.4390i	1.20916	−	1.20916i	0.971299	−	0.237863i	$-0.0764469\pi$
$860$	−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	−0.263181	+	0.964746i	$0.584772\pi$
$863$	−36.0727	+	36.0727i	−1.22793	+	1.22793i	−0.964746	+	0.263181i	$0.915228\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−54.2443	−	13.2268i	−1.84436	−	0.449723i
$866$	−15.4619	+	15.4619i	−0.525418	+	0.525418i
$867$	−0.222162	−	0.222162i	−0.00754503	−	0.00754503i
$868$	32.0478			1.08777
$869$	−4.02680	−	4.02680i	−0.136600	−	0.136600i
$870$	7.04401	+	11.5869i	0.238814	+	0.392833i
$871$	28.7449	−	28.7449i	0.973983	−	0.973983i
$872$	5.58777	−	5.58777i	0.189226	−	0.189226i
$873$	−10.0910			−0.341529
$874$	−1.76910	+	1.76910i	−0.0598407	+	0.0598407i
$875$	30.2203	−	34.6296i	1.02163	−	1.17069i
$876$		−	4.21607i		−	0.142448i
$877$	11.9117	+	11.9117i	0.402229	+	0.402229i	0.879018	−	0.476789i	$-0.158199\pi$
$877$	11.9117	+	11.9117i	0.402229	+	0.402229i	−0.476789	+	0.879018i	$0.658199\pi$
$878$	−15.6685	−	15.6685i	−0.528785	−	0.528785i
$879$	−3.91564			−0.132071
$880$	−3.19100	−	5.24898i	−0.107569	−	0.176943i
$881$		−	0.418792i		−	0.0141095i	−0.999975	−	0.00705473i	$-0.997754\pi$
$881$		−	0.418792i		−	0.0141095i	0.999975	−	0.00705473i	$-0.00224561\pi$
$882$	9.89979			0.333343
$883$		−	26.3766i		−	0.887643i	−0.896115	−	0.443821i	$-0.853622\pi$
$883$		−	26.3766i		−	0.887643i	0.896115	−	0.443821i	$-0.146378\pi$
$884$			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	$-0.571433\pi$
$887$	22.4081	−	22.4081i	0.752390	−	0.752390i	0.974925	+	0.222535i	$0.0714332\pi$
$888$	5.78837	−	1.86945i	0.194245	−	0.0627345i
$889$			46.6195i			1.56357i
$890$	5.00071	+	1.21936i	0.167624	+	0.0408730i
$891$			2.74715i			0.0920330i
$892$	−2.83314	+	2.83314i	−0.0948606	+	0.0948606i
$893$	22.7254			0.760477
$894$	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
$902$	−20.8624			−0.694644
$903$		−	25.6310i		−	0.852945i
$904$		−	14.2804i		−	0.474959i
$905$	13.0288	−	7.92055i	0.433091	−	0.263288i
$906$	12.6513	−	12.6513i	0.420312	−	0.420312i
$907$			23.3935i			0.776769i	0.921497	+	0.388384i	$0.126967\pi$
$907$			23.3935i			0.776769i	−0.921497	+	0.388384i	$0.873033\pi$
$908$			7.49379i			0.248690i
$909$	−9.40183			−0.311839
$910$	−46.5761	−	11.3570i	−1.54398	−	0.376480i
$911$	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	$0.537822\pi$
$912$	−2.65630			−0.0879589
$913$	−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
$917$	38.5838			1.27415
$918$	2.94229	+	2.94229i	0.0971102	+	0.0971102i
$919$	−28.2985	−	28.2985i	−0.933482	−	0.933482i	0.0644393	−	0.997922i	$-0.479474\pi$
$919$	−28.2985	−	28.2985i	−0.933482	−	0.933482i	−0.997922	+	0.0644393i	$0.979474\pi$
$920$	1.79963	−	1.09404i	0.0593319	−	0.0360695i
$921$	8.66517			0.285527
$922$	−17.2735	−	17.2735i	−0.568872	−	0.568872i
$923$	−44.4329			−1.46253
$924$	11.2934			0.371524
$925$	17.6579	+	24.7629i	0.580587	+	0.814198i
$926$	−16.3891			−0.538578
$927$	7.77490			0.255361
$928$	4.28806	+	4.28806i	0.140762	+	0.140762i
$929$	31.6997			1.04003			0.520016	−	0.854156i	$-0.325926\pi$
$929$	31.6997			1.04003			0.520016	+	0.854156i	$0.325926\pi$
$930$	−14.8953	+	9.05527i	−0.488436	+	0.296934i
$931$	−18.5947	−	18.5947i	−0.609415	−	0.609415i
$932$	7.78522	+	7.78522i	0.255013	+	0.255013i
$933$	−1.50505			−0.0492732
$934$		−	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	0.999999	+	0.00129830i	$0.000413263\pi$
$937$	30.6502	+	30.6502i	1.00130	+	1.00130i	0.00129830	+	0.999999i	$0.499587\pi$
$938$	−32.0433			−1.04625
$939$	−5.39995	−	5.39995i	−0.176221	−	0.176221i
$940$	−18.5857	−	4.53187i	−0.606197	−	0.147813i
$941$	−7.87515			−0.256722			−0.128361	−	0.991727i	$-0.540972\pi$
$941$	−7.87515			−0.256722			−0.128361	+	0.991727i	$0.540972\pi$
$942$		−	4.32271i		−	0.140841i
$943$		−	7.15275i		−	0.232925i
$944$	1.92935	−	1.92935i	0.0627949	−	0.0627949i
$945$	−7.85475	+	4.77512i	−0.255515	+	0.155335i
$946$		−	17.1280i		−	0.556880i
$947$		−	7.99597i		−	0.259834i	−0.991525	−	0.129917i	$-0.958529\pi$
$947$		−	7.99597i		−	0.259834i	0.991525	−	0.129917i	$-0.0414711\pi$
$948$	2.07297			0.0673268
$949$	−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	0.912231	+	0.409677i	$0.134359\pi$
$953$	40.8082	+	40.8082i	1.32191	+	1.32191i	0.409677	+	0.912231i	$0.365641\pi$
$954$	−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
$957$	−16.6594			−0.538521
$958$	−27.0885	+	27.0885i	−0.875189	+	0.875189i
$959$			46.0338i			1.48651i
$960$	2.17242	+	0.529716i	0.0701145	+	0.0170965i
$961$		−	29.7736i		−	0.960439i
$962$	14.4521	−	28.2402i	0.465953	−	0.910502i
$963$	−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
$967$		−	35.2833i		−	1.13463i	−0.823500	−	0.567317i	$-0.807982\pi$
$967$		−	35.2833i		−	1.13463i	0.823500	−	0.567317i	$-0.192018\pi$
$968$	−3.45316			−0.110989
$969$		−	11.0529i		−	0.355072i
$970$	−11.7214	−	19.2809i	−0.376351	−	0.619072i
$971$	−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
$975$	24.8568	−	7.88177i	0.796054	−	0.252419i
$976$	−8.68618	+	8.68618i	−0.278038	+	0.278038i
$977$	−55.5148			−1.77608			−0.888038	−	0.459770i	$-0.847932\pi$
$977$	−55.5148			−1.77608			−0.888038	+	0.459770i	$0.847932\pi$
$978$	−13.8133	+	13.8133i	−0.441702	+	0.441702i
$979$	−4.47153	+	4.47153i	−0.142911	+	0.142911i
$980$	11.4993	+	18.9155i	0.367330	+	0.604234i
$981$	−5.58777	−	5.58777i	−0.178404	−	0.178404i
$982$	24.9010			0.794622
$983$	3.83723	+	3.83723i	0.122388	+	0.122388i	0.765648	−	0.643260i	$-0.222418\pi$
$983$	3.83723	+	3.83723i	0.122388	+	0.122388i	−0.643260	+	0.765648i	$0.722418\pi$
$984$	5.36992	−	5.36992i	0.171187	−	0.171187i
$985$	−35.2801	−	8.60261i	−1.12412	−	0.274102i
$986$	−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
$993$		−	14.9909i		−	0.475723i
$994$	24.7657	+	24.7657i	0.785522	+	0.785522i
$995$	−39.7393	−	9.68992i	−1.25982	−	0.307191i
$996$	10.2699			0.325415
$997$			3.25867i			0.103203i	0.998668	+	0.0516016i	$0.0164326\pi$
$997$			3.25867i			0.103203i	−0.998668	+	0.0516016i	$0.983567\pi$
$998$	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.o.a.487.10	yes	36
5.3	odd	4		1110.2.l.a.43.9	✓	36
37.31	odd	4		1110.2.l.a.697.9	yes	36
185.68	even	4	inner	1110.2.o.a.253.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.9	✓	36	5.3	odd	4
1110.2.l.a.697.9	yes	36	37.31	odd	4
1110.2.o.a.253.10	yes	36	185.68	even	4	inner
1110.2.o.a.487.10	yes	36	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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