LMFDB - Embedded newform 1110.2.o.a.253.14

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			253.14
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.02734 + 0.943349i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.02734 + 0.943349i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(2.02734 - 0.943349i) q^{10} -0.497352i q^{11} +(0.707107 - 0.707107i) q^{12} -1.53056 q^{13} +(0.516238 - 0.516238i) q^{14} +(-0.766495 + 2.10059i) q^{15} +1.00000 q^{16} -2.55573i q^{17} +1.00000i q^{18} +(2.36425 + 2.36425i) q^{19} +(-2.02734 + 0.943349i) q^{20} +0.730071i q^{21} +0.497352i q^{22} +5.13868 q^{23} +(-0.707107 + 0.707107i) q^{24} +(3.22019 - 3.82497i) q^{25} +1.53056 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.516238 + 0.516238i) q^{28} +(-7.56116 + 7.56116i) q^{29} +(0.766495 - 2.10059i) q^{30} +(5.92380 + 5.92380i) q^{31} -1.00000 q^{32} +(-0.351681 - 0.351681i) q^{33} +2.55573i q^{34} +(0.559596 - 1.53358i) q^{35} -1.00000i q^{36} +(4.64120 + 3.93182i) q^{37} +(-2.36425 - 2.36425i) q^{38} +(-1.08227 + 1.08227i) q^{39} +(2.02734 - 0.943349i) q^{40} -2.70364i q^{41} -0.730071i q^{42} +9.05230 q^{43} -0.497352i q^{44} +(0.943349 + 2.02734i) q^{45} -5.13868 q^{46} +(-9.26908 + 9.26908i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.46700i q^{49} +(-3.22019 + 3.82497i) q^{50} +(-1.80718 - 1.80718i) q^{51} -1.53056 q^{52} +(-0.413793 - 0.413793i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.469177 + 1.00830i) q^{55} +(0.516238 - 0.516238i) q^{56} +3.34355 q^{57} +(7.56116 - 7.56116i) q^{58} +(5.91307 + 5.91307i) q^{59} +(-0.766495 + 2.10059i) q^{60} +(10.7956 + 10.7956i) q^{61} +(-5.92380 - 5.92380i) q^{62} +(0.516238 + 0.516238i) q^{63} +1.00000 q^{64} +(3.10295 - 1.44385i) q^{65} +(0.351681 + 0.351681i) q^{66} +(-9.29726 - 9.29726i) q^{67} -2.55573i q^{68} +(3.63359 - 3.63359i) q^{69} +(-0.559596 + 1.53358i) q^{70} -4.10631 q^{71} +1.00000i q^{72} +(-2.63103 + 2.63103i) q^{73} +(-4.64120 - 3.93182i) q^{74} +(-0.427648 - 4.98168i) q^{75} +(2.36425 + 2.36425i) q^{76} +(0.256752 + 0.256752i) q^{77} +(1.08227 - 1.08227i) q^{78} +(-0.827925 - 0.827925i) q^{79} +(-2.02734 + 0.943349i) q^{80} -1.00000 q^{81} +2.70364i q^{82} +(11.2038 + 11.2038i) q^{83} +0.730071i q^{84} +(2.41095 + 5.18133i) q^{85} -9.05230 q^{86} +10.6931i q^{87} +0.497352i q^{88} +(6.24255 - 6.24255i) q^{89} +(-0.943349 - 2.02734i) q^{90} +(0.790132 - 0.790132i) q^{91} +5.13868 q^{92} +8.37752 q^{93} +(9.26908 - 9.26908i) q^{94} +(-7.02344 - 2.56282i) q^{95} +(-0.707107 + 0.707107i) q^{96} -3.13965i q^{97} -6.46700i q^{98} -0.497352 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−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
$5$	−2.02734	+	0.943349i	−0.906652	+	0.421878i
$5$	−2.02734	+	0.943349i	−0.906652	+	0.421878i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−0.516238	+	0.516238i	−0.195120	+	0.195120i	−0.797904	−	0.602784i	$-0.794058\pi$
$7$	−0.516238	+	0.516238i	−0.195120	+	0.195120i	0.602784	+	0.797904i	$0.294058\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	2.02734	−	0.943349i	0.641100	−	0.298313i
$11$		−	0.497352i		−	0.149957i	−0.997185	−	0.0749787i	$-0.976111\pi$
$11$		−	0.497352i		−	0.149957i	0.997185	−	0.0749787i	$-0.0238889\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−1.53056			−0.424500			−0.212250	−	0.977215i	$-0.568079\pi$
$13$	−1.53056			−0.424500			−0.212250	+	0.977215i	$0.568079\pi$
$14$	0.516238	−	0.516238i	0.137970	−	0.137970i
$15$	−0.766495	+	2.10059i	−0.197908	+	0.542370i
$16$	1.00000			0.250000
$17$		−	2.55573i		−	0.619856i	−0.950760	−	0.309928i	$-0.899695\pi$
$17$		−	2.55573i		−	0.619856i	0.950760	−	0.309928i	$-0.100305\pi$
$18$			1.00000i			0.235702i
$19$	2.36425	+	2.36425i	0.542396	+	0.542396i	0.924231	−	0.381835i	$-0.124708\pi$
$19$	2.36425	+	2.36425i	0.542396	+	0.542396i	−0.381835	+	0.924231i	$0.624708\pi$
$20$	−2.02734	+	0.943349i	−0.453326	+	0.210939i
$21$			0.730071i			0.159315i
$22$			0.497352i			0.106036i
$23$	5.13868			1.07149			0.535744	−	0.844380i	$-0.320031\pi$
$23$	5.13868			1.07149			0.535744	+	0.844380i	$0.320031\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	3.22019	−	3.82497i	0.644037	−	0.764994i
$26$	1.53056			0.300167
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.516238	+	0.516238i	−0.0975599	+	0.0975599i
$29$	−7.56116	+	7.56116i	−1.40407	+	1.40407i	−0.617504	+	0.786568i	$0.711856\pi$
$29$	−7.56116	+	7.56116i	−1.40407	+	1.40407i	−0.786568	+	0.617504i	$0.788144\pi$
$30$	0.766495	−	2.10059i	0.139942	−	0.383514i
$31$	5.92380	+	5.92380i	1.06395	+	1.06395i	0.997811	+	0.0661351i	$0.0210668\pi$
$31$	5.92380	+	5.92380i	1.06395	+	1.06395i	0.0661351	+	0.997811i	$0.478933\pi$
$32$	−1.00000			−0.176777
$33$	−0.351681	−	0.351681i	−0.0612198	−	0.0612198i
$34$			2.55573i			0.438305i
$35$	0.559596	−	1.53358i	0.0945890	−	0.259223i
$36$		−	1.00000i		−	0.166667i
$37$	4.64120	+	3.93182i	0.763009	+	0.646388i
$37$	4.64120	+	3.93182i	0.763009	+	0.646388i
$38$	−2.36425	−	2.36425i	−0.383532	−	0.383532i
$39$	−1.08227	+	1.08227i	−0.173301	+	0.173301i
$40$	2.02734	−	0.943349i	0.320550	−	0.149157i
$41$		−	2.70364i		−	0.422238i	−0.977460	−	0.211119i	$-0.932289\pi$
$41$		−	2.70364i		−	0.422238i	0.977460	−	0.211119i	$-0.0677108\pi$
$42$		−	0.730071i		−	0.112652i
$43$	9.05230			1.38046			0.690232	−	0.723588i	$-0.257509\pi$
$43$	9.05230			1.38046			0.690232	+	0.723588i	$0.257509\pi$
$44$		−	0.497352i		−	0.0749787i
$45$	0.943349	+	2.02734i	0.140626	+	0.302217i
$46$	−5.13868			−0.757656
$47$	−9.26908	+	9.26908i	−1.35203	+	1.35203i	−0.468650	+	0.883384i	$0.655260\pi$
$47$	−9.26908	+	9.26908i	−1.35203	+	1.35203i	−0.883384	+	0.468650i	$0.844740\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			6.46700i			0.923857i
$50$	−3.22019	+	3.82497i	−0.455403	+	0.540933i
$51$	−1.80718	−	1.80718i	−0.253055	−	0.253055i
$52$	−1.53056			−0.212250
$53$	−0.413793	−	0.413793i	−0.0568388	−	0.0568388i	0.678116	−	0.734955i	$-0.262797\pi$
$53$	−0.413793	−	0.413793i	−0.0568388	−	0.0568388i	−0.734955	+	0.678116i	$0.762797\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	0.469177	+	1.00830i	0.0632638	+	0.135959i
$56$	0.516238	−	0.516238i	0.0689852	−	0.0689852i
$57$	3.34355			0.442865
$58$	7.56116	−	7.56116i	0.992829	−	0.992829i
$59$	5.91307	+	5.91307i	0.769817	+	0.769817i	0.978074	−	0.208257i	$-0.0667792\pi$
$59$	5.91307	+	5.91307i	0.769817	+	0.769817i	−0.208257	+	0.978074i	$0.566779\pi$
$60$	−0.766495	+	2.10059i	−0.0989541	+	0.271185i
$61$	10.7956	+	10.7956i	1.38223	+	1.38223i	0.840645	+	0.541586i	$0.182176\pi$
$61$	10.7956	+	10.7956i	1.38223	+	1.38223i	0.541586	+	0.840645i	$0.317824\pi$
$62$	−5.92380	−	5.92380i	−0.752323	−	0.752323i
$63$	0.516238	+	0.516238i	0.0650399	+	0.0650399i
$64$	1.00000			0.125000
$65$	3.10295	−	1.44385i	0.384874	−	0.179087i
$66$	0.351681	+	0.351681i	0.0432889	+	0.0432889i
$67$	−9.29726	−	9.29726i	−1.13584	−	1.13584i	−0.989188	−	0.146653i	$-0.953150\pi$
$67$	−9.29726	−	9.29726i	−1.13584	−	1.13584i	−0.146653	−	0.989188i	$-0.546850\pi$
$68$		−	2.55573i		−	0.309928i
$69$	3.63359	−	3.63359i	0.437433	−	0.437433i
$70$	−0.559596	+	1.53358i	−0.0668845	+	0.183298i
$71$	−4.10631			−0.487329			−0.243664	−	0.969860i	$-0.578350\pi$
$71$	−4.10631			−0.487329			−0.243664	+	0.969860i	$0.578350\pi$
$72$			1.00000i			0.117851i
$73$	−2.63103	+	2.63103i	−0.307938	+	0.307938i	−0.844109	−	0.536171i	$-0.819870\pi$
$73$	−2.63103	+	2.63103i	−0.307938	+	0.307938i	0.536171	+	0.844109i	$0.319870\pi$
$74$	−4.64120	−	3.93182i	−0.539529	−	0.457065i
$75$	−0.427648	−	4.98168i	−0.0493805	−	0.575235i
$76$	2.36425	+	2.36425i	0.271198	+	0.271198i
$77$	0.256752	+	0.256752i	0.0292596	+	0.0292596i
$78$	1.08227	−	1.08227i	0.122543	−	0.122543i
$79$	−0.827925	−	0.827925i	−0.0931489	−	0.0931489i	0.658997	−	0.752146i	$-0.270981\pi$
$79$	−0.827925	−	0.827925i	−0.0931489	−	0.0931489i	−0.752146	+	0.658997i	$0.770981\pi$
$80$	−2.02734	+	0.943349i	−0.226663	+	0.105470i
$81$	−1.00000			−0.111111
$82$			2.70364i			0.298567i
$83$	11.2038	+	11.2038i	1.22978	+	1.22978i	0.964048	+	0.265729i	$0.0856126\pi$
$83$	11.2038	+	11.2038i	1.22978	+	1.22978i	0.265729	+	0.964048i	$0.414387\pi$
$84$			0.730071i			0.0796573i
$85$	2.41095	+	5.18133i	0.261504	+	0.561994i
$86$	−9.05230			−0.976135
$87$			10.6931i			1.14642i
$88$			0.497352i			0.0530179i
$89$	6.24255	−	6.24255i	0.661709	−	0.661709i	−0.294074	−	0.955783i	$-0.595011\pi$
$89$	6.24255	−	6.24255i	0.661709	−	0.661709i	0.955783	+	0.294074i	$0.0950112\pi$
$90$	−0.943349	−	2.02734i	−0.0994377	−	0.213700i
$91$	0.790132	−	0.790132i	0.0828284	−	0.0828284i
$92$	5.13868			0.535744
$93$	8.37752			0.868708
$94$	9.26908	−	9.26908i	0.956032	−	0.956032i
$95$	−7.02344	−	2.56282i	−0.720590	−	0.262940i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$		−	3.13965i		−	0.318783i	−0.987215	−	0.159391i	$-0.949047\pi$
$97$		−	3.13965i		−	0.318783i	0.987215	−	0.159391i	$-0.0509532\pi$
$98$		−	6.46700i		−	0.653265i
$99$	−0.497352			−0.0499858
$100$	3.22019	−	3.82497i	0.322019	−	0.382497i
$101$		−	4.17592i		−	0.415519i	−0.978180	−	0.207760i	$-0.933383\pi$
$101$		−	4.17592i		−	0.415519i	0.978180	−	0.207760i	$-0.0666172\pi$
$102$	1.80718	+	1.80718i	0.178937	+	0.178937i
$103$		−	15.6656i		−	1.54357i	−0.635881	−	0.771787i	$-0.719363\pi$
$103$		−	15.6656i		−	1.54357i	0.635881	−	0.771787i	$-0.280637\pi$
$104$	1.53056			0.150083
$105$	−0.688712	−	1.48010i	−0.0672114	−	0.144443i
$106$	0.413793	+	0.413793i	0.0401911	+	0.0401911i
$107$	−0.609066	+	0.609066i	−0.0588806	+	0.0588806i	−0.735934	−	0.677053i	$-0.763257\pi$
$107$	−0.609066	+	0.609066i	−0.0588806	+	0.0588806i	0.677053	+	0.735934i	$0.263257\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−0.255676	−	0.255676i	−0.0244894	−	0.0244894i	0.694756	−	0.719245i	$-0.255512\pi$
$109$	−0.255676	−	0.255676i	−0.0244894	−	0.0244894i	−0.719245	+	0.694756i	$0.755512\pi$
$110$	−0.469177	−	1.00830i	−0.0447342	−	0.0961376i
$111$	6.06205	−	0.501607i	0.575384	−	0.0476104i
$112$	−0.516238	+	0.516238i	−0.0487799	+	0.0487799i
$113$		−	12.8460i		−	1.20845i	−0.796813	−	0.604226i	$-0.793482\pi$
$113$		−	12.8460i		−	1.20845i	0.796813	−	0.604226i	$-0.206518\pi$
$114$	−3.34355			−0.313153
$115$	−10.4178	+	4.84756i	−0.971467	+	0.452038i
$116$	−7.56116	+	7.56116i	−0.702036	+	0.702036i
$117$			1.53056i			0.141500i
$118$	−5.91307	−	5.91307i	−0.544343	−	0.544343i
$119$	1.31937	+	1.31937i	0.120946	+	0.120946i
$120$	0.766495	−	2.10059i	0.0699711	−	0.191757i
$121$	10.7526			0.977513
$122$	−10.7956	−	10.7956i	−0.977385	−	0.977385i
$123$	−1.91176	−	1.91176i	−0.172378	−	0.172378i
$124$	5.92380	+	5.92380i	0.531973	+	0.531973i
$125$	−2.92012	+	10.7923i	−0.261183	+	0.965289i
$126$	−0.516238	−	0.516238i	−0.0459902	−	0.0459902i
$127$	−0.504136	+	0.504136i	−0.0447349	+	0.0447349i	−0.729120	−	0.684385i	$-0.760071\pi$
$127$	−0.504136	+	0.504136i	−0.0447349	+	0.0447349i	0.684385	+	0.729120i	$0.260071\pi$
$128$	−1.00000			−0.0883883
$129$	6.40095	−	6.40095i	0.563572	−	0.563572i
$130$	−3.10295	+	1.44385i	−0.272147	+	0.126634i
$131$	15.2212	+	15.2212i	1.32988	+	1.32988i	0.905472	+	0.424407i	$0.139517\pi$
$131$	15.2212	+	15.2212i	1.32988	+	1.32988i	0.424407	+	0.905472i	$0.360483\pi$
$132$	−0.351681	−	0.351681i	−0.0306099	−	0.0306099i
$133$	−2.44103			−0.211664
$134$	9.29726	+	9.29726i	0.803161	+	0.803161i
$135$	2.10059	+	0.766495i	0.180790	+	0.0659694i
$136$			2.55573i			0.219152i
$137$	−10.5042	+	10.5042i	−0.897430	+	0.897430i	−0.995208	−	0.0977781i	$-0.968826\pi$
$137$	−10.5042	+	10.5042i	−0.897430	+	0.897430i	0.0977781	+	0.995208i	$0.468826\pi$
$138$	−3.63359	+	3.63359i	−0.309312	+	0.309312i
$139$	0.111253			0.00943637			0.00471819	−	0.999989i	$-0.498498\pi$
$139$	0.111253			0.00943637			0.00471819	+	0.999989i	$0.498498\pi$
$140$	0.559596	−	1.53358i	0.0472945	−	0.129611i
$141$			13.1085i			1.10393i
$142$	4.10631			0.344594
$143$			0.761226i			0.0636569i
$144$		−	1.00000i		−	0.0833333i
$145$	8.19620	−	22.4618i	0.680657	−	1.86535i
$146$	2.63103	−	2.63103i	0.217745	−	0.217745i
$147$	4.57286	+	4.57286i	0.377163	+	0.377163i
$148$	4.64120	+	3.93182i	0.381505	+	0.323194i
$149$			16.2537i			1.33155i	0.746150	+	0.665777i	$0.231900\pi$
$149$			16.2537i			1.33155i	−0.746150	+	0.665777i	$0.768100\pi$
$150$	0.427648	+	4.98168i	0.0349173	+	0.406752i
$151$			15.7270i			1.27985i	0.768438	+	0.639924i	$0.221034\pi$
$151$			15.7270i			1.27985i	−0.768438	+	0.639924i	$0.778966\pi$
$152$	−2.36425	−	2.36425i	−0.191766	−	0.191766i
$153$	−2.55573			−0.206619
$154$	−0.256752	−	0.256752i	−0.0206897	−	0.0206897i
$155$	−17.5977	−	6.42132i	−1.41348	−	0.515773i
$156$	−1.08227	+	1.08227i	−0.0866507	+	0.0866507i
$157$	−3.60469	+	3.60469i	−0.287685	+	0.287685i	−0.836164	−	0.548479i	$-0.815207\pi$
$157$	−3.60469	+	3.60469i	−0.287685	+	0.287685i	0.548479	+	0.836164i	$0.315207\pi$
$158$	0.827925	+	0.827925i	0.0658662	+	0.0658662i
$159$	−0.585191			−0.0464087
$160$	2.02734	−	0.943349i	0.160275	−	0.0745783i
$161$	−2.65278	+	2.65278i	−0.209068	+	0.209068i
$162$	1.00000			0.0785674
$163$			12.0896i			0.946929i	0.880813	+	0.473465i	$0.156997\pi$
$163$			12.0896i			0.946929i	−0.880813	+	0.473465i	$0.843003\pi$
$164$		−	2.70364i		−	0.211119i
$165$	1.04473	+	0.381218i	0.0813324	+	0.0296778i
$166$	−11.2038	−	11.2038i	−0.869583	−	0.869583i
$167$		−	11.3927i		−	0.881596i	−0.897606	−	0.440798i	$-0.854695\pi$
$167$		−	11.3927i		−	0.881596i	0.897606	−	0.440798i	$-0.145305\pi$
$168$		−	0.730071i		−	0.0563262i
$169$	−10.6574			−0.819800
$170$	−2.41095	−	5.18133i	−0.184911	−	0.397390i
$171$	2.36425	−	2.36425i	0.180799	−	0.180799i
$172$	9.05230			0.690232
$173$	13.4370	−	13.4370i	1.02160	−	1.02160i	0.0218360	−	0.999762i	$-0.493049\pi$
$173$	13.4370	−	13.4370i	1.02160	−	1.02160i	0.999762	−	0.0218360i	$-0.00695117\pi$
$174$		−	10.6931i		−	0.810641i
$175$	0.312213	+	3.63698i	0.0236011	+	0.274930i
$176$		−	0.497352i		−	0.0374893i
$177$	8.36235			0.628553
$178$	−6.24255	+	6.24255i	−0.467899	+	0.467899i
$179$	−7.63199	+	7.63199i	−0.570442	+	0.570442i	−0.932252	−	0.361810i	$-0.882159\pi$
$179$	−7.63199	+	7.63199i	−0.570442	+	0.570442i	0.361810	+	0.932252i	$0.382159\pi$
$180$	0.943349	+	2.02734i	0.0703131	+	0.151109i
$181$	9.48047			0.704677			0.352339	−	0.935873i	$-0.385387\pi$
$181$	9.48047			0.704677			0.352339	+	0.935873i	$0.385387\pi$
$182$	−0.790132	+	0.790132i	−0.0585685	+	0.0585685i
$183$	15.2672			1.12859
$184$	−5.13868			−0.378828
$185$	−13.1184	−	3.59286i	−0.964481	−	0.264152i
$186$	−8.37752			−0.614269
$187$	−1.27110			−0.0929520
$188$	−9.26908	+	9.26908i	−0.676017	+	0.676017i
$189$	0.730071			0.0531049
$190$	7.02344	+	2.56282i	0.509534	+	0.185926i
$191$	13.3339	−	13.3339i	0.964808	−	0.964808i	−0.0345933	−	0.999401i	$-0.511014\pi$
$191$	13.3339	−	13.3339i	0.964808	−	0.964808i	0.999401	+	0.0345933i	$0.0110136\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	8.67065			0.624127			0.312064	−	0.950061i	$-0.398980\pi$
$193$	8.67065			0.624127			0.312064	+	0.950061i	$0.398980\pi$
$194$			3.13965i			0.225413i
$195$	1.17316	−	3.21508i	0.0840120	−	0.230236i
$196$			6.46700i			0.461928i
$197$	5.35975	−	5.35975i	0.381867	−	0.381867i	−0.489908	−	0.871774i	$-0.662970\pi$
$197$	5.35975	−	5.35975i	0.381867	−	0.381867i	0.871774	+	0.489908i	$0.162970\pi$
$198$	0.497352			0.0353453
$199$	−13.1621	+	13.1621i	−0.933037	+	0.933037i	−0.997895	−	0.0648573i	$-0.979341\pi$
$199$	−13.1621	+	13.1621i	−0.933037	+	0.933037i	0.0648573	+	0.997895i	$0.479341\pi$
$200$	−3.22019	+	3.82497i	−0.227702	+	0.270466i
$201$	−13.1483			−0.927410
$202$			4.17592i			0.293816i
$203$		−	7.80672i		−	0.547924i
$204$	−1.80718	−	1.80718i	−0.126528	−	0.126528i
$205$	2.55048	+	5.48119i	0.178133	+	0.382823i
$206$			15.6656i			1.09147i
$207$		−	5.13868i		−	0.357163i
$208$	−1.53056			−0.106125
$209$	1.17586	−	1.17586i	0.0813363	−	0.0813363i
$210$	0.688712	+	1.48010i	0.0475256	+	0.102137i
$211$	−24.6681			−1.69822			−0.849112	−	0.528213i	$-0.822862\pi$
$211$	−24.6681			−1.69822			−0.849112	+	0.528213i	$0.822862\pi$
$212$	−0.413793	−	0.413793i	−0.0284194	−	0.0284194i
$213$	−2.90360	+	2.90360i	−0.198951	+	0.198951i
$214$	0.609066	−	0.609066i	0.0416349	−	0.0416349i
$215$	−18.3521	+	8.53948i	−1.25160	+	0.582388i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−6.11618			−0.415194
$218$	0.255676	+	0.255676i	0.0173166	+	0.0173166i
$219$			3.72083i			0.251431i
$220$	0.469177	+	1.00830i	0.0316319	+	0.0679796i
$221$			3.91170i			0.263129i
$222$	−6.06205	+	0.501607i	−0.406858	+	0.0336657i
$223$	−11.0405	−	11.0405i	−0.739328	−	0.739328i	0.233120	−	0.972448i	$-0.425106\pi$
$223$	−11.0405	−	11.0405i	−0.739328	−	0.739328i	−0.972448	+	0.233120i	$0.925106\pi$
$224$	0.516238	−	0.516238i	0.0344926	−	0.0344926i
$225$	−3.82497	−	3.22019i	−0.254998	−	0.214679i
$226$			12.8460i			0.854505i
$227$		−	28.9019i		−	1.91829i	−0.282922	−	0.959143i	$-0.591304\pi$
$227$		−	28.9019i		−	1.91829i	0.282922	−	0.959143i	$-0.408696\pi$
$228$	3.34355			0.221432
$229$		−	27.5614i		−	1.82131i	−0.413171	−	0.910654i	$-0.635579\pi$
$229$		−	27.5614i		−	1.82131i	0.413171	−	0.910654i	$-0.364421\pi$
$230$	10.4178	−	4.84756i	0.686931	−	0.319639i
$231$	0.363102			0.0238904
$232$	7.56116	−	7.56116i	0.496414	−	0.496414i
$233$	−7.51093	+	7.51093i	−0.492057	+	0.492057i	−0.908954	−	0.416897i	$-0.863118\pi$
$233$	−7.51093	+	7.51093i	−0.492057	+	0.492057i	0.416897	+	0.908954i	$0.363118\pi$
$234$		−	1.53056i		−	0.100056i
$235$	10.0476	−	27.5355i	0.655431	−	1.79622i
$236$	5.91307	+	5.91307i	0.384908	+	0.384908i
$237$	−1.17086			−0.0760557
$238$	−1.31937	−	1.31937i	−0.0855219	−	0.0855219i
$239$	−6.73852	−	6.73852i	−0.435879	−	0.435879i	0.454744	−	0.890622i	$-0.349731\pi$
$239$	−6.73852	−	6.73852i	−0.435879	−	0.435879i	−0.890622	+	0.454744i	$0.849731\pi$
$240$	−0.766495	+	2.10059i	−0.0494770	+	0.135593i
$241$	−8.91683	+	8.91683i	−0.574384	+	0.574384i	−0.933350	−	0.358967i	$-0.883129\pi$
$241$	−8.91683	+	8.91683i	−0.574384	+	0.574384i	0.358967	+	0.933350i	$0.383129\pi$
$242$	−10.7526			−0.691206
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	10.7956	+	10.7956i	0.691116	+	0.691116i
$245$	−6.10063	−	13.1108i	−0.389755	−	0.837617i
$246$	1.91176	+	1.91176i	0.121890	+	0.121890i
$247$	−3.61862	−	3.61862i	−0.230247	−	0.230247i
$248$	−5.92380	−	5.92380i	−0.376162	−	0.376162i
$249$	15.8446			1.00411
$250$	2.92012	−	10.7923i	0.184684	−	0.682563i
$251$	−8.72803	−	8.72803i	−0.550908	−	0.550908i	0.375795	−	0.926703i	$-0.377370\pi$
$251$	−8.72803	−	8.72803i	−0.550908	−	0.550908i	−0.926703	+	0.375795i	$0.877370\pi$
$252$	0.516238	+	0.516238i	0.0325200	+	0.0325200i
$253$		−	2.55573i		−	0.160677i
$254$	0.504136	−	0.504136i	0.0316323	−	0.0316323i
$255$	5.36855	+	1.95896i	0.336192	+	0.122675i
$256$	1.00000			0.0625000
$257$			6.57411i			0.410082i	0.978753	+	0.205041i	$0.0657327\pi$
$257$			6.57411i			0.410082i	−0.978753	+	0.205041i	$0.934267\pi$
$258$	−6.40095	+	6.40095i	−0.398505	+	0.398505i
$259$	−4.42572	+	0.366209i	−0.275001	+	0.0227551i
$260$	3.10295	−	1.44385i	0.192437	−	0.0895437i
$261$	7.56116	+	7.56116i	0.468024	+	0.468024i
$262$	−15.2212	−	15.2212i	−0.940366	−	0.940366i
$263$	0.841547	−	0.841547i	0.0518920	−	0.0518920i	−0.680685	−	0.732577i	$-0.738318\pi$
$263$	0.841547	−	0.841547i	0.0518920	−	0.0518920i	0.732577	+	0.680685i	$0.238318\pi$
$264$	0.351681	+	0.351681i	0.0216445	+	0.0216445i
$265$	1.22925	+	0.448546i	0.0755121	+	0.0275540i
$266$	2.44103			0.149669
$267$		−	8.82830i		−	0.540283i
$268$	−9.29726	−	9.29726i	−0.567920	−	0.567920i
$269$		−	16.4147i		−	1.00082i	−0.865788	−	0.500412i	$-0.833182\pi$
$269$		−	16.4147i		−	1.00082i	0.865788	−	0.500412i	$-0.166818\pi$
$270$	−2.10059	−	0.766495i	−0.127838	−	0.0466474i
$271$	3.57932			0.217428			0.108714	−	0.994073i	$-0.465327\pi$
$271$	3.57932			0.217428			0.108714	+	0.994073i	$0.465327\pi$
$272$		−	2.55573i		−	0.154964i
$273$		−	1.11742i		−	0.0676291i
$274$	10.5042	−	10.5042i	0.634579	−	0.634579i
$275$	−1.90236	−	1.60157i	−0.114716	−	0.0965781i
$276$	3.63359	−	3.63359i	0.218717	−	0.218717i
$277$	−11.1501			−0.669946			−0.334973	−	0.942228i	$-0.608727\pi$
$277$	−11.1501			−0.669946			−0.334973	+	0.942228i	$0.608727\pi$
$278$	−0.111253			−0.00667252
$279$	5.92380	−	5.92380i	0.354649	−	0.354649i
$280$	−0.559596	+	1.53358i	−0.0334422	+	0.0916490i
$281$	−12.0088	+	12.0088i	−0.716383	+	0.716383i	−0.967863	−	0.251480i	$-0.919083\pi$
$281$	−12.0088	+	12.0088i	−0.716383	+	0.716383i	0.251480	+	0.967863i	$0.419083\pi$
$282$		−	13.1085i		−	0.780597i
$283$		−	23.9142i		−	1.42155i	−0.703419	−	0.710776i	$-0.748344\pi$
$283$		−	23.9142i		−	1.42155i	0.703419	−	0.710776i	$-0.251656\pi$
$284$	−4.10631			−0.243664
$285$	−6.77851	+	3.15414i	−0.401524	+	0.186835i
$286$		−	0.761226i		−	0.0450122i
$287$	1.39572	+	1.39572i	0.0823870	+	0.0823870i
$288$			1.00000i			0.0589256i
$289$	10.4682			0.615778
$290$	−8.19620	+	22.4618i	−0.481297	+	1.31900i
$291$	−2.22007	−	2.22007i	−0.130143	−	0.130143i
$292$	−2.63103	+	2.63103i	−0.153969	+	0.153969i
$293$	17.4755	+	17.4755i	1.02093	+	1.02093i	0.999776	+	0.0211515i	$0.00673323\pi$
$293$	17.4755	+	17.4755i	1.02093	+	1.02093i	0.0211515	+	0.999776i	$0.493267\pi$
$294$	−4.57286	−	4.57286i	−0.266694	−	0.266694i
$295$	−17.5659	−	6.40970i	−1.02273	−	0.373187i
$296$	−4.64120	−	3.93182i	−0.269764	−	0.228533i
$297$	−0.351681	+	0.351681i	−0.0204066	+	0.0204066i
$298$		−	16.2537i		−	0.941552i
$299$	−7.86504			−0.454847
$300$	−0.427648	−	4.98168i	−0.0246902	−	0.287617i
$301$	−4.67315	+	4.67315i	−0.269356	+	0.269356i
$302$		−	15.7270i		−	0.904989i
$303$	−2.95282	−	2.95282i	−0.169635	−	0.169635i
$304$	2.36425	+	2.36425i	0.135599	+	0.135599i
$305$	−32.0702	−	11.7023i	−1.83634	−	0.670070i
$306$	2.55573			0.146102
$307$	−6.16080	−	6.16080i	−0.351615	−	0.351615i	0.509095	−	0.860710i	$-0.329980\pi$
$307$	−6.16080	−	6.16080i	−0.351615	−	0.351615i	−0.860710	+	0.509095i	$0.829980\pi$
$308$	0.256752	+	0.256752i	0.0146298	+	0.0146298i
$309$	−11.0772	−	11.0772i	−0.630161	−	0.630161i
$310$	17.5977	+	6.42132i	0.999485	+	0.364707i
$311$	−12.1752	−	12.1752i	−0.690392	−	0.690392i	0.271926	−	0.962318i	$-0.412339\pi$
$311$	−12.1752	−	12.1752i	−0.690392	−	0.690392i	−0.962318	+	0.271926i	$0.912339\pi$
$312$	1.08227	−	1.08227i	0.0612713	−	0.0612713i
$313$	3.47014			0.196144			0.0980720	−	0.995179i	$-0.468732\pi$
$313$	3.47014			0.196144			0.0980720	+	0.995179i	$0.468732\pi$
$314$	3.60469	−	3.60469i	0.203424	−	0.203424i
$315$	−1.53358	−	0.559596i	−0.0864075	−	0.0315297i
$316$	−0.827925	−	0.827925i	−0.0465744	−	0.0465744i
$317$	6.39255	+	6.39255i	0.359041	+	0.359041i	0.863460	−	0.504418i	$-0.168293\pi$
$317$	6.39255	+	6.39255i	0.359041	+	0.359041i	−0.504418	+	0.863460i	$0.668293\pi$
$318$	0.585191			0.0328159
$319$	3.76056	+	3.76056i	0.210551	+	0.210551i
$320$	−2.02734	+	0.943349i	−0.113332	+	0.0527348i
$321$			0.861349i			0.0480758i
$322$	2.65278	−	2.65278i	0.147834	−	0.147834i
$323$	6.04239	−	6.04239i	0.336208	−	0.336208i
$324$	−1.00000			−0.0555556
$325$	−4.92868	+	5.85434i	−0.273394	+	0.324740i
$326$		−	12.0896i		−	0.669580i
$327$	−0.361581			−0.0199955
$328$			2.70364i			0.149284i
$329$		−	9.57011i		−	0.527617i
$330$	−1.04473	−	0.381218i	−0.0575107	−	0.0209854i
$331$	−12.6298	+	12.6298i	−0.694194	+	0.694194i	−0.963152	−	0.268958i	$-0.913321\pi$
$331$	−12.6298	+	12.6298i	−0.694194	+	0.694194i	0.268958	+	0.963152i	$0.413321\pi$
$332$	11.2038	+	11.2038i	0.614888	+	0.614888i
$333$	3.93182	−	4.64120i	0.215463	−	0.254336i
$334$			11.3927i			0.623383i
$335$	27.6192	+	10.0781i	1.50900	+	0.550626i
$336$			0.730071i			0.0398286i
$337$	11.4706	+	11.4706i	0.624845	+	0.624845i	0.946766	−	0.321921i	$-0.104329\pi$
$337$	11.4706	+	11.4706i	0.624845	+	0.624845i	−0.321921	+	0.946766i	$0.604329\pi$
$338$	10.6574			0.579686
$339$	−9.08351	−	9.08351i	−0.493349	−	0.493349i
$340$	2.41095	+	5.18133i	0.130752	+	0.280997i
$341$	2.94621	−	2.94621i	0.159546	−	0.159546i
$342$	−2.36425	+	2.36425i	−0.127844	+	0.127844i
$343$	−6.95218	−	6.95218i	−0.375382	−	0.375382i
$344$	−9.05230			−0.488068
$345$	−3.93877	+	10.7943i	−0.212056	+	0.581143i
$346$	−13.4370	+	13.4370i	−0.722379	+	0.722379i
$347$	−2.52563			−0.135583			−0.0677914	−	0.997700i	$-0.521595\pi$
$347$	−2.52563			−0.135583			−0.0677914	+	0.997700i	$0.521595\pi$
$348$			10.6931i			0.573210i
$349$			5.42724i			0.290514i	0.989394	+	0.145257i	$0.0464008\pi$
$349$			5.42724i			0.290514i	−0.989394	+	0.145257i	$0.953599\pi$
$350$	−0.312213	−	3.63698i	−0.0166885	−	0.194405i
$351$	1.08227	+	1.08227i	0.0577672	+	0.0577672i
$352$			0.497352i			0.0265090i
$353$			16.8913i			0.899034i	0.893272	+	0.449517i	$0.148404\pi$
$353$			16.8913i			0.899034i	−0.893272	+	0.449517i	$0.851596\pi$
$354$	−8.36235			−0.444454
$355$	8.32486	−	3.87368i	0.441838	−	0.205594i
$356$	6.24255	−	6.24255i	0.330854	−	0.330854i
$357$	1.86587			0.0987522
$358$	7.63199	−	7.63199i	0.403363	−	0.403363i
$359$		−	10.2084i		−	0.538781i	−0.963031	−	0.269391i	$-0.913178\pi$
$359$		−	10.2084i		−	0.538781i	0.963031	−	0.269391i	$-0.0868223\pi$
$360$	−0.943349	−	2.02734i	−0.0497189	−	0.106850i
$361$		−	7.82065i		−	0.411613i
$362$	−9.48047			−0.498282
$363$	7.60327	−	7.60327i	0.399068	−	0.399068i
$364$	0.790132	−	0.790132i	0.0414142	−	0.0414142i
$365$	2.85200	−	7.81595i	0.149280	−	0.409105i
$366$	−15.2672			−0.798032
$367$	−13.8736	+	13.8736i	−0.724195	+	0.724195i	−0.969457	−	0.245262i	$-0.921126\pi$
$367$	−13.8736	+	13.8736i	−0.724195	+	0.724195i	0.245262	+	0.969457i	$0.421126\pi$
$368$	5.13868			0.267872
$369$	−2.70364			−0.140746
$370$	13.1184	+	3.59286i	0.681991	+	0.186784i
$371$	0.427231			0.0221807
$372$	8.37752			0.434354
$373$	−6.36168	+	6.36168i	−0.329395	+	0.329395i	−0.852356	−	0.522961i	$-0.824827\pi$
$373$	−6.36168	+	6.36168i	−0.329395	+	0.329395i	0.522961	+	0.852356i	$0.324827\pi$
$374$	1.27110			0.0657270
$375$	5.56645	+	9.69612i	0.287450	+	0.500705i
$376$	9.26908	−	9.26908i	0.478016	−	0.478016i
$377$	11.5728	−	11.5728i	0.596029	−	0.596029i
$378$	−0.730071			−0.0375508
$379$		−	10.4081i		−	0.534627i	−0.963610	−	0.267313i	$-0.913864\pi$
$379$		−	10.4081i		−	0.534627i	0.963610	−	0.267313i	$-0.0861359\pi$
$380$	−7.02344	−	2.56282i	−0.360295	−	0.131470i
$381$			0.712957i			0.0365259i
$382$	−13.3339	+	13.3339i	−0.682222	+	0.682222i
$383$	−20.7631			−1.06094			−0.530472	−	0.847703i	$-0.677985\pi$
$383$	−20.7631			−1.06094			−0.530472	+	0.847703i	$0.677985\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−0.762730	−	0.278316i	−0.0388723	−	0.0141843i
$386$	−8.67065			−0.441325
$387$		−	9.05230i		−	0.460154i
$388$		−	3.13965i		−	0.159391i
$389$	20.8063	+	20.8063i	1.05492	+	1.05492i	0.998401	+	0.0565210i	$0.0180008\pi$
$389$	20.8063	+	20.8063i	1.05492	+	1.05492i	0.0565210	+	0.998401i	$0.481999\pi$
$390$	−1.17316	+	3.21508i	−0.0594055	+	0.162802i
$391$		−	13.1331i		−	0.664169i
$392$		−	6.46700i		−	0.326633i
$393$	21.5260			1.08584
$394$	−5.35975	+	5.35975i	−0.270020	+	0.270020i
$395$	2.45951	+	0.897461i	0.123751	+	0.0451561i
$396$	−0.497352			−0.0249929
$397$	5.88311	+	5.88311i	0.295265	+	0.295265i	0.839156	−	0.543891i	$-0.183050\pi$
$397$	5.88311	+	5.88311i	0.295265	+	0.295265i	−0.543891	+	0.839156i	$0.683050\pi$
$398$	13.1621	−	13.1621i	0.659757	−	0.659757i
$399$	−1.72607	+	1.72607i	−0.0864116	+	0.0864116i
$400$	3.22019	−	3.82497i	0.161009	−	0.191249i
$401$	−14.5564	−	14.5564i	−0.726914	−	0.726914i	0.243090	−	0.970004i	$-0.421839\pi$
$401$	−14.5564	−	14.5564i	−0.726914	−	0.726914i	−0.970004	+	0.243090i	$0.921839\pi$
$402$	13.1483			0.655778
$403$	−9.06671	−	9.06671i	−0.451645	−	0.451645i
$404$		−	4.17592i		−	0.207760i
$405$	2.02734	−	0.943349i	0.100739	−	0.0468754i
$406$			7.80672i			0.387441i
$407$	1.95550	−	2.30831i	0.0969306	−	0.114419i
$408$	1.80718	+	1.80718i	0.0894686	+	0.0894686i
$409$	11.0869	−	11.0869i	0.548211	−	0.548211i	−0.377712	−	0.925923i	$-0.623289\pi$
$409$	11.0869	−	11.0869i	0.548211	−	0.548211i	0.925923	+	0.377712i	$0.123289\pi$
$410$	−2.55048	−	5.48119i	−0.125959	−	0.270697i
$411$			14.8551i			0.732749i
$412$		−	15.6656i		−	0.771787i
$413$	−6.10511			−0.300413
$414$			5.13868i			0.252552i
$415$	−33.2830	−	12.1448i	−1.63380	−	0.596164i
$416$	1.53056			0.0750417
$417$	0.0786679	−	0.0786679i	0.00385238	−	0.00385238i
$418$	−1.17586	+	1.17586i	−0.0575134	+	0.0575134i
$419$		−	22.0253i		−	1.07601i	−0.842942	−	0.538004i	$-0.819178\pi$
$419$		−	22.0253i		−	1.07601i	0.842942	−	0.538004i	$-0.180822\pi$
$420$	−0.688712	−	1.48010i	−0.0336057	−	0.0722215i
$421$	22.6650	+	22.6650i	1.10463	+	1.10463i	0.993845	+	0.110782i	$0.0353356\pi$
$421$	22.6650	+	22.6650i	1.10463	+	1.10463i	0.110782	+	0.993845i	$0.464664\pi$
$422$	24.6681			1.20083
$423$	9.26908	+	9.26908i	0.450678	+	0.450678i
$424$	0.413793	+	0.413793i	0.0200956	+	0.0200956i
$425$	−9.77561	−	8.22994i	−0.474187	−	0.399211i
$426$	2.90360	−	2.90360i	0.140680	−	0.140680i
$427$	−11.1462			−0.539401
$428$	−0.609066	+	0.609066i	−0.0294403	+	0.0294403i
$429$	0.538268	+	0.538268i	0.0259878	+	0.0259878i
$430$	18.3521	−	8.53948i	0.885015	−	0.411810i
$431$	17.9692	+	17.9692i	0.865547	+	0.865547i	0.991976	−	0.126428i	$-0.0403514\pi$
$431$	17.9692	+	17.9692i	0.865547	+	0.865547i	−0.126428	+	0.991976i	$0.540351\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−18.0984	−	18.0984i	−0.869755	−	0.869755i	0.122690	−	0.992445i	$-0.460848\pi$
$433$	−18.0984	−	18.0984i	−0.869755	−	0.869755i	−0.992445	+	0.122690i	$0.960848\pi$
$434$	6.11618			0.293586
$435$	−10.0873	−	21.6785i	−0.483650	−	1.03940i
$436$	−0.255676	−	0.255676i	−0.0122447	−	0.0122447i
$437$	12.1491	+	12.1491i	0.581171	+	0.581171i
$438$		−	3.72083i		−	0.177788i
$439$	−24.7771	+	24.7771i	−1.18255	+	1.18255i	−0.203463	+	0.979083i	$0.565220\pi$
$439$	−24.7771	+	24.7771i	−1.18255	+	1.18255i	−0.979083	+	0.203463i	$0.934780\pi$
$440$	−0.469177	−	1.00830i	−0.0223671	−	0.0480688i
$441$	6.46700			0.307952
$442$		−	3.91170i		−	0.186060i
$443$	−11.6985	+	11.6985i	−0.555811	+	0.555811i	−0.928112	−	0.372301i	$-0.878569\pi$
$443$	−11.6985	+	11.6985i	−0.555811	+	0.555811i	0.372301	+	0.928112i	$0.378569\pi$
$444$	6.06205	−	0.501607i	0.287692	−	0.0238052i
$445$	−6.76685	+	18.5446i	−0.320779	+	0.879101i
$446$	11.0405	+	11.0405i	0.522784	+	0.522784i
$447$	11.4931	+	11.4931i	0.543605	+	0.543605i
$448$	−0.516238	+	0.516238i	−0.0243900	+	0.0243900i
$449$	16.3835	+	16.3835i	0.773187	+	0.773187i	0.978662	−	0.205475i	$-0.0658740\pi$
$449$	16.3835	+	16.3835i	0.773187	+	0.773187i	−0.205475	+	0.978662i	$0.565874\pi$
$450$	3.82497	+	3.22019i	0.180311	+	0.151801i
$451$	−1.34466			−0.0633177
$452$		−	12.8460i		−	0.604226i
$453$	11.1207	+	11.1207i	0.522496	+	0.522496i
$454$			28.9019i			1.35643i
$455$	−0.856493	+	2.34723i	−0.0401530	+	0.110040i
$456$	−3.34355			−0.156576
$457$			36.6470i			1.71427i	0.515089	+	0.857137i	$0.327759\pi$
$457$			36.6470i			1.71427i	−0.515089	+	0.857137i	$0.672241\pi$
$458$			27.5614i			1.28786i
$459$	−1.80718	+	1.80718i	−0.0843518	+	0.0843518i
$460$	−10.4178	+	4.84756i	−0.485734	+	0.226019i
$461$	−4.87965	+	4.87965i	−0.227268	+	0.227268i	−0.811550	−	0.584283i	$-0.801376\pi$
$461$	−4.87965	+	4.87965i	−0.227268	+	0.227268i	0.584283	+	0.811550i	$0.301376\pi$
$462$	−0.363102			−0.0168931
$463$	3.03199			0.140908			0.0704542	−	0.997515i	$-0.477555\pi$
$463$	3.03199			0.140908			0.0704542	+	0.997515i	$0.477555\pi$
$464$	−7.56116	+	7.56116i	−0.351018	+	0.351018i
$465$	−16.9840	+	7.90292i	−0.787616	+	0.366489i
$466$	7.51093	−	7.51093i	0.347937	−	0.347937i
$467$			7.88298i			0.364781i	0.983226	+	0.182390i	$0.0583835\pi$
$467$			7.88298i			0.364781i	−0.983226	+	0.182390i	$0.941616\pi$
$468$			1.53056i			0.0707500i
$469$	9.59920			0.443250
$470$	−10.0476	+	27.5355i	−0.463460	+	1.27012i
$471$			5.09780i			0.234894i
$472$	−5.91307	−	5.91307i	−0.272171	−	0.272171i
$473$		−	4.50218i		−	0.207011i
$474$	1.17086			0.0537795
$475$	16.6565	−	1.42986i	0.764253	−	0.0656066i
$476$	1.31937	+	1.31937i	0.0604731	+	0.0604731i
$477$	−0.413793	+	0.413793i	−0.0189463	+	0.0189463i
$478$	6.73852	+	6.73852i	0.308213	+	0.308213i
$479$	22.2999	+	22.2999i	1.01891	+	1.01891i	0.999818	+	0.0190898i	$0.00607685\pi$
$479$	22.2999	+	22.2999i	1.01891	+	1.01891i	0.0190898	+	0.999818i	$0.493923\pi$
$480$	0.766495	−	2.10059i	0.0349855	−	0.0958785i
$481$	−7.10363	−	6.01788i	−0.323897	−	0.274392i
$482$	8.91683	−	8.91683i	0.406151	−	0.406151i
$483$			3.75160i			0.170704i
$484$	10.7526			0.488756
$485$	2.96178	+	6.36512i	0.134488	+	0.289025i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$		−	12.8810i		−	0.583695i	−0.956465	−	0.291847i	$-0.905730\pi$
$487$		−	12.8810i		−	0.583695i	0.956465	−	0.291847i	$-0.0942699\pi$
$488$	−10.7956	−	10.7956i	−0.488693	−	0.488693i
$489$	8.54863	+	8.54863i	0.386582	+	0.386582i
$490$	6.10063	+	13.1108i	0.275599	+	0.592285i
$491$	0.897235			0.0404916			0.0202458	−	0.999795i	$-0.493555\pi$
$491$	0.897235			0.0404916			0.0202458	+	0.999795i	$0.493555\pi$
$492$	−1.91176	−	1.91176i	−0.0861890	−	0.0861890i
$493$	19.3243	+	19.3243i	0.870323	+	0.870323i
$494$	3.61862	+	3.61862i	0.162809	+	0.162809i
$495$	1.00830	−	0.469177i	0.0453197	−	0.0210879i
$496$	5.92380	+	5.92380i	0.265986	+	0.265986i
$497$	2.11983	−	2.11983i	0.0950875	−	0.0950875i
$498$	−15.8446			−0.710012
$499$	17.8190	−	17.8190i	0.797689	−	0.797689i	−0.185042	−	0.982731i	$-0.559242\pi$
$499$	17.8190	−	17.8190i	0.797689	−	0.797689i	0.982731	+	0.185042i	$0.0592421\pi$
$500$	−2.92012	+	10.7923i	−0.130592	+	0.482645i
$501$	−8.05588	−	8.05588i	−0.359910	−	0.359910i
$502$	8.72803	+	8.72803i	0.389551	+	0.389551i
$503$	17.9635			0.800955			0.400477	−	0.916307i	$-0.368844\pi$
$503$	17.9635			0.800955			0.400477	+	0.916307i	$0.368844\pi$
$504$	−0.516238	−	0.516238i	−0.0229951	−	0.0229951i
$505$	3.93935	+	8.46599i	0.175299	+	0.376731i
$506$			2.55573i			0.113616i
$507$	−7.53592	+	7.53592i	−0.334682	+	0.334682i
$508$	−0.504136	+	0.504136i	−0.0223674	+	0.0223674i
$509$	8.36462			0.370755			0.185378	−	0.982667i	$-0.440649\pi$
$509$	8.36462			0.370755			0.185378	+	0.982667i	$0.440649\pi$
$510$	−5.36855	−	1.95896i	−0.237723	−	0.0867441i
$511$		−	2.71647i		−	0.120170i
$512$	−1.00000			−0.0441942
$513$		−	3.34355i		−	0.147622i
$514$		−	6.57411i		−	0.289972i
$515$	14.7781	+	31.7594i	0.651200	+	1.39948i
$516$	6.40095	−	6.40095i	0.281786	−	0.281786i
$517$	4.61000	+	4.61000i	0.202747	+	0.202747i
$518$	4.42572	−	0.366209i	0.194455	−	0.0160903i
$519$		−	19.0028i		−	0.834131i
$520$	−3.10295	+	1.44385i	−0.136074	+	0.0633170i
$521$		−	16.5234i		−	0.723904i	−0.932197	−	0.361952i	$-0.882110\pi$
$521$		−	16.5234i		−	0.723904i	0.932197	−	0.361952i	$-0.117890\pi$
$522$	−7.56116	−	7.56116i	−0.330943	−	0.330943i
$523$	14.2767			0.624278			0.312139	−	0.950036i	$-0.398954\pi$
$523$	14.2767			0.624278			0.312139	+	0.950036i	$0.398954\pi$
$524$	15.2212	+	15.2212i	0.664939	+	0.664939i
$525$	2.79250	+	2.35096i	0.121875	+	0.102605i
$526$	−0.841547	+	0.841547i	−0.0366932	+	0.0366932i
$527$	15.1397	−	15.1397i	0.659494	−	0.659494i
$528$	−0.351681	−	0.351681i	−0.0153050	−	0.0153050i
$529$	3.40599			0.148087
$530$	−1.22925	−	0.448546i	−0.0533951	−	0.0194836i
$531$	5.91307	−	5.91307i	0.256606	−	0.256606i
$532$	−2.44103			−0.105832
$533$			4.13808i			0.179240i
$534$			8.82830i			0.382038i
$535$	0.660220	−	1.80934i	0.0285438	−	0.0782247i
$536$	9.29726	+	9.29726i	0.401580	+	0.401580i
$537$			10.7933i			0.465764i
$538$			16.4147i			0.707689i
$539$	3.21637			0.138539
$540$	2.10059	+	0.766495i	0.0903951	+	0.0329847i
$541$	−2.99943	+	2.99943i	−0.128955	+	0.128955i	−0.768639	−	0.639683i	$-0.779066\pi$
$541$	−2.99943	+	2.99943i	−0.128955	+	0.128955i	0.639683	+	0.768639i	$0.279066\pi$
$542$	−3.57932			−0.153745
$543$	6.70370	−	6.70370i	0.287683	−	0.287683i
$544$			2.55573i			0.109576i
$545$	0.759534	+	0.277150i	0.0325349	+	0.0118718i
$546$			1.11742i			0.0478210i
$547$	−20.8842			−0.892944			−0.446472	−	0.894798i	$-0.647320\pi$
$547$	−20.8842			−0.892944			−0.446472	+	0.894798i	$0.647320\pi$
$548$	−10.5042	+	10.5042i	−0.448715	+	0.448715i
$549$	10.7956	−	10.7956i	0.460744	−	0.460744i
$550$	1.90236	+	1.60157i	0.0811168	+	0.0682910i
$551$	−35.7529			−1.52313
$552$	−3.63359	+	3.63359i	−0.154656	+	0.154656i
$553$	0.854813			0.0363504
$554$	11.1501			0.473723
$555$	−11.8166	+	6.73555i	−0.501587	+	0.285908i
$556$	0.111253			0.00471819
$557$	−10.1584			−0.430426			−0.215213	−	0.976567i	$-0.569045\pi$
$557$	−10.1584			−0.430426			−0.215213	+	0.976567i	$0.569045\pi$
$558$	−5.92380	+	5.92380i	−0.250774	+	0.250774i
$559$	−13.8551			−0.586007
$560$	0.559596	−	1.53358i	0.0236472	−	0.0648056i
$561$	−0.898803	+	0.898803i	−0.0379475	+	0.0379475i
$562$	12.0088	−	12.0088i	0.506559	−	0.506559i
$563$	13.4772			0.567996			0.283998	−	0.958825i	$-0.408339\pi$
$563$	13.4772			0.567996			0.283998	+	0.958825i	$0.408339\pi$
$564$			13.1085i			0.551966i
$565$	12.1183	+	26.0432i	0.509820	+	1.09565i
$566$			23.9142i			1.00519i
$567$	0.516238	−	0.516238i	0.0216800	−	0.0216800i
$568$	4.10631			0.172297
$569$	0.956429	−	0.956429i	0.0400956	−	0.0400956i	−0.686775	−	0.726870i	$-0.740974\pi$
$569$	0.956429	−	0.956429i	0.0400956	−	0.0400956i	0.726870	+	0.686775i	$0.240974\pi$
$570$	6.77851	−	3.15414i	0.283920	−	0.132112i
$571$	−1.80272			−0.0754415			−0.0377208	−	0.999288i	$-0.512010\pi$
$571$	−1.80272			−0.0754415			−0.0377208	+	0.999288i	$0.512010\pi$
$572$			0.761226i			0.0318285i
$573$		−	18.8570i		−	0.787763i
$574$	−1.39572	−	1.39572i	−0.0582564	−	0.0582564i
$575$	16.5475	−	19.6553i	0.690078	−	0.819682i
$576$		−	1.00000i		−	0.0416667i
$577$			21.8641i			0.910216i	0.890436	+	0.455108i	$0.150399\pi$
$577$			21.8641i			0.910216i	−0.890436	+	0.455108i	$0.849601\pi$
$578$	−10.4682			−0.435421
$579$	6.13108	−	6.13108i	0.254799	−	0.254799i
$580$	8.19620	−	22.4618i	0.340329	−	0.932676i
$581$	−11.5677			−0.479907
$582$	2.22007	+	2.22007i	0.0920247	+	0.0920247i
$583$	−0.205801	+	0.205801i	−0.00852340	+	0.00852340i
$584$	2.63103	−	2.63103i	0.108873	−	0.108873i
$585$	−1.44385	−	3.10295i	−0.0596958	−	0.128291i
$586$	−17.4755	−	17.4755i	−0.721905	−	0.721905i
$587$	13.4925			0.556896			0.278448	−	0.960451i	$-0.410180\pi$
$587$	13.4925			0.556896			0.278448	+	0.960451i	$0.410180\pi$
$588$	4.57286	+	4.57286i	0.188581	+	0.188581i
$589$			28.0107i			1.15416i
$590$	17.5659	+	6.40970i	0.723176	+	0.263883i
$591$		−	7.57983i		−	0.311793i
$592$	4.64120	+	3.93182i	0.190752	+	0.161597i
$593$	−21.6151	−	21.6151i	−0.887628	−	0.887628i	0.106667	−	0.994295i	$-0.465982\pi$
$593$	−21.6151	−	21.6151i	−0.887628	−	0.887628i	−0.994295	+	0.106667i	$0.965982\pi$
$594$	0.351681	−	0.351681i	0.0144296	−	0.0144296i
$595$	−3.91942	−	1.43018i	−0.160681	−	0.0586316i
$596$			16.2537i			0.665777i
$597$			18.6140i			0.761822i
$598$	7.86504			0.321625
$599$			1.58656i			0.0648249i	0.999475	+	0.0324125i	$0.0103190\pi$
$599$			1.58656i			0.0648249i	−0.999475	+	0.0324125i	$0.989681\pi$
$600$	0.427648	+	4.98168i	0.0174586	+	0.203376i
$601$	39.5787			1.61445			0.807224	−	0.590245i	$-0.200969\pi$
$601$	39.5787			1.61445			0.807224	+	0.590245i	$0.200969\pi$
$602$	4.67315	−	4.67315i	0.190463	−	0.190463i
$603$	−9.29726	+	9.29726i	−0.378614	+	0.378614i
$604$			15.7270i			0.639924i
$605$	−21.7992	+	10.1435i	−0.886264	+	0.412392i
$606$	2.95282	+	2.95282i	0.119950	+	0.119950i
$607$	−29.3879			−1.19282			−0.596409	−	0.802680i	$-0.703407\pi$
$607$	−29.3879			−1.19282			−0.596409	+	0.802680i	$0.703407\pi$
$608$	−2.36425	−	2.36425i	−0.0958830	−	0.0958830i
$609$	−5.52018	−	5.52018i	−0.223689	−	0.223689i
$610$	32.0702	+	11.7023i	1.29849	+	0.473811i
$611$	14.1869	−	14.1869i	0.573939	−	0.573939i
$612$	−2.55573			−0.103309
$613$	11.9588	−	11.9588i	0.483011	−	0.483011i	−0.423081	−	0.906092i	$-0.639051\pi$
$613$	11.9588	−	11.9588i	0.483011	−	0.483011i	0.906092	+	0.423081i	$0.139051\pi$
$614$	6.16080	+	6.16080i	0.248630	+	0.248630i
$615$	5.67925	+	2.07233i	0.229009	+	0.0835644i
$616$	−0.256752	−	0.256752i	−0.0103448	−	0.0103448i
$617$	19.8923	+	19.8923i	0.800835	+	0.800835i	0.983226	−	0.182391i	$-0.0583836\pi$
$617$	19.8923	+	19.8923i	0.800835	+	0.800835i	−0.182391	+	0.983226i	$0.558384\pi$
$618$	11.0772	+	11.0772i	0.445591	+	0.445591i
$619$	−25.0352			−1.00625			−0.503125	−	0.864213i	$-0.667817\pi$
$619$	−25.0352			−1.00625			−0.503125	+	0.864213i	$0.667817\pi$
$620$	−17.5977	−	6.42132i	−0.706742	−	0.257887i
$621$	−3.63359	−	3.63359i	−0.145811	−	0.145811i
$622$	12.1752	+	12.1752i	0.488181	+	0.488181i
$623$			6.44528i			0.258225i
$624$	−1.08227	+	1.08227i	−0.0433254	+	0.0433254i
$625$	−4.26081	−	24.6342i	−0.170432	−	0.985369i
$626$	−3.47014			−0.138695
$627$		−	1.66292i		−	0.0664108i
$628$	−3.60469	+	3.60469i	−0.143843	+	0.143843i
$629$	10.0487	−	11.8617i	0.400668	−	0.472956i
$630$	1.53358	+	0.559596i	0.0610993	+	0.0222948i
$631$	−14.6446	−	14.6446i	−0.582990	−	0.582990i	0.352733	−	0.935724i	$-0.385252\pi$
$631$	−14.6446	−	14.6446i	−0.582990	−	0.582990i	−0.935724	+	0.352733i	$0.885252\pi$
$632$	0.827925	+	0.827925i	0.0329331	+	0.0329331i
$633$	−17.4430	+	17.4430i	−0.693297	+	0.693297i
$634$	−6.39255	−	6.39255i	−0.253881	−	0.253881i
$635$	0.546478	−	1.49763i	0.0216863	−	0.0594317i
$636$	−0.585191			−0.0232043
$637$		−	9.89811i		−	0.392177i
$638$	−3.76056	−	3.76056i	−0.148882	−	0.148882i
$639$			4.10631i			0.162443i
$640$	2.02734	−	0.943349i	0.0801375	−	0.0372891i
$641$	18.7683			0.741305			0.370652	−	0.928772i	$-0.379134\pi$
$641$	18.7683			0.741305			0.370652	+	0.928772i	$0.379134\pi$
$642$		−	0.861349i		−	0.0339947i
$643$		−	33.3318i		−	1.31448i	−0.753683	−	0.657238i	$-0.771725\pi$
$643$		−	33.3318i		−	1.31448i	0.753683	−	0.657238i	$-0.228275\pi$
$644$	−2.65278	+	2.65278i	−0.104534	+	0.104534i
$645$	−6.93855	+	19.0152i	−0.273205	+	0.748723i
$646$	−6.04239	+	6.04239i	−0.237735	+	0.237735i
$647$	20.5310			0.807156			0.403578	−	0.914945i	$-0.367766\pi$
$647$	20.5310			0.807156			0.403578	+	0.914945i	$0.367766\pi$
$648$	1.00000			0.0392837
$649$	2.94088	−	2.94088i	0.115440	−	0.115440i
$650$	4.92868	−	5.85434i	0.193319	−	0.229626i
$651$	−4.32479	+	4.32479i	−0.169502	+	0.169502i
$652$			12.0896i			0.473465i
$653$			26.4235i			1.03403i	0.855976	+	0.517016i	$0.172957\pi$
$653$			26.4235i			1.03403i	−0.855976	+	0.517016i	$0.827043\pi$
$654$	0.361581			0.0141389
$655$	−45.2173	−	16.4995i	−1.76678	−	0.644690i
$656$		−	2.70364i		−	0.105560i
$657$	2.63103	+	2.63103i	0.102646	+	0.102646i
$658$			9.57011i			0.373082i
$659$	39.4006			1.53483			0.767414	−	0.641152i	$-0.221543\pi$
$659$	39.4006			1.53483			0.767414	+	0.641152i	$0.221543\pi$
$660$	1.04473	+	0.381218i	0.0406662	+	0.0148389i
$661$	7.90042	+	7.90042i	0.307291	+	0.307291i	0.843858	−	0.536567i	$-0.180279\pi$
$661$	7.90042	+	7.90042i	0.307291	+	0.307291i	−0.536567	+	0.843858i	$0.680279\pi$
$662$	12.6298	−	12.6298i	0.490870	−	0.490870i
$663$	2.76599	+	2.76599i	0.107422	+	0.107422i
$664$	−11.2038	−	11.2038i	−0.434792	−	0.434792i
$665$	4.94879	−	2.30274i	0.191906	−	0.0892966i
$666$	−3.93182	+	4.64120i	−0.152355	+	0.179843i
$667$	−38.8543	+	38.8543i	−1.50445	+	1.50445i
$668$		−	11.3927i		−	0.440798i
$669$	−15.6137			−0.603659
$670$	−27.6192	−	10.0781i	−1.06702	−	0.389351i
$671$	5.36920	−	5.36920i	0.207276	−	0.207276i
$672$		−	0.730071i		−	0.0281631i
$673$	−31.7666	−	31.7666i	−1.22451	−	1.22451i	−0.966011	−	0.258503i	$-0.916771\pi$
$673$	−31.7666	−	31.7666i	−1.22451	−	1.22451i	−0.258503	−	0.966011i	$-0.583229\pi$
$674$	−11.4706	−	11.4706i	−0.441832	−	0.441832i
$675$	−4.98168	+	0.427648i	−0.191745	+	0.0164602i
$676$	−10.6574			−0.409900
$677$	21.1045	+	21.1045i	0.811110	+	0.811110i	0.984800	−	0.173690i	$-0.0555691\pi$
$677$	21.1045	+	21.1045i	0.811110	+	0.811110i	−0.173690	+	0.984800i	$0.555569\pi$
$678$	9.08351	+	9.08351i	0.348850	+	0.348850i
$679$	1.62081	+	1.62081i	0.0622008	+	0.0622008i
$680$	−2.41095	−	5.18133i	−0.0924556	−	0.198695i
$681$	−20.4367	−	20.4367i	−0.783137	−	0.783137i
$682$	−2.94621	+	2.94621i	−0.112816	+	0.112816i
$683$	35.4086			1.35487			0.677437	−	0.735581i	$-0.263091\pi$
$683$	35.4086			1.35487			0.677437	+	0.735581i	$0.263091\pi$
$684$	2.36425	−	2.36425i	0.0903993	−	0.0903993i
$685$	11.3864	−	31.2045i	0.435051	−	1.19226i
$686$	6.95218	+	6.95218i	0.265435	+	0.265435i
$687$	−19.4888	−	19.4888i	−0.743546	−	0.743546i
$688$	9.05230			0.345116
$689$	0.633334	+	0.633334i	0.0241281	+	0.0241281i
$690$	3.93877	−	10.7943i	0.149946	−	0.410930i
$691$		−	22.4704i		−	0.854814i	−0.904059	−	0.427407i	$-0.859427\pi$
$691$		−	22.4704i		−	0.854814i	0.904059	−	0.427407i	$-0.140573\pi$
$692$	13.4370	−	13.4370i	0.510799	−	0.510799i
$693$	0.256752	−	0.256752i	0.00975321	−	0.00975321i
$694$	2.52563			0.0958715
$695$	−0.225548	+	0.104951i	−0.00855551	+	0.00398100i
$696$		−	10.6931i		−	0.405321i
$697$	−6.90979			−0.261727
$698$		−	5.42724i		−	0.205424i
$699$			10.6221i			0.401763i
$700$	0.312213	+	3.63698i	0.0118005	+	0.137465i
$701$	15.2902	−	15.2902i	0.577504	−	0.577504i	−0.356711	−	0.934215i	$-0.616102\pi$
$701$	15.2902	−	15.2902i	0.577504	−	0.577504i	0.934215	+	0.356711i	$0.116102\pi$
$702$	−1.08227	−	1.08227i	−0.0408475	−	0.0408475i
$703$	1.67715	+	20.2688i	0.0632549	+	0.764451i
$704$		−	0.497352i		−	0.0187447i
$705$	−12.3658	−	26.5753i	−0.465725	−	1.00088i
$706$		−	16.8913i		−	0.635713i
$707$	2.15577	+	2.15577i	0.0810760	+	0.0810760i
$708$	8.36235			0.314276
$709$	11.5740	+	11.5740i	0.434672	+	0.434672i	0.890214	−	0.455542i	$-0.150555\pi$
$709$	11.5740	+	11.5740i	0.434672	+	0.434672i	−0.455542	+	0.890214i	$0.650555\pi$
$710$	−8.32486	+	3.87368i	−0.312427	+	0.145377i
$711$	−0.827925	+	0.827925i	−0.0310496	+	0.0310496i
$712$	−6.24255	+	6.24255i	−0.233949	+	0.233949i
$713$	30.4405	+	30.4405i	1.14001	+	1.14001i
$714$	−1.86587			−0.0698283
$715$	−0.718102	−	1.54326i	−0.0268555	−	0.0577147i
$716$	−7.63199	+	7.63199i	−0.285221	+	0.285221i
$717$	−9.52971			−0.355893
$718$			10.2084i			0.380976i
$719$		−	33.1940i		−	1.23793i	−0.785420	−	0.618963i	$-0.787553\pi$
$719$		−	33.1940i		−	1.23793i	0.785420	−	0.618963i	$-0.212447\pi$
$720$	0.943349	+	2.02734i	0.0351565	+	0.0755544i
$721$	8.08716	+	8.08716i	0.301182	+	0.301182i
$722$			7.82065i			0.291054i
$723$			12.6103i			0.468982i
$724$	9.48047			0.352339
$725$	4.57288	+	53.2695i	0.169832	+	1.97838i
$726$	−7.60327	+	7.60327i	−0.282184	+	0.282184i
$727$	25.8130			0.957352			0.478676	−	0.877992i	$-0.341117\pi$
$727$	25.8130			0.957352			0.478676	+	0.877992i	$0.341117\pi$
$728$	−0.790132	+	0.790132i	−0.0292842	+	0.0292842i
$729$			1.00000i			0.0370370i
$730$	−2.85200	+	7.81595i	−0.105557	+	0.289281i
$731$		−	23.1353i		−	0.855689i
$732$	15.2672			0.564294
$733$	−29.0185	+	29.0185i	−1.07182	+	1.07182i	−0.0746110	+	0.997213i	$0.523772\pi$
$733$	−29.0185	+	29.0185i	−1.07182	+	1.07182i	−0.997213	+	0.0746110i	$0.976228\pi$
$734$	13.8736	−	13.8736i	0.512083	−	0.512083i
$735$	−13.5845	−	4.95692i	−0.501073	−	0.182839i
$736$	−5.13868			−0.189414
$737$	−4.62401	+	4.62401i	−0.170328	+	0.170328i
$738$	2.70364			0.0995225
$739$	−33.6130			−1.23647			−0.618236	−	0.785992i	$-0.712153\pi$
$739$	−33.6130			−1.23647			−0.618236	+	0.785992i	$0.712153\pi$
$740$	−13.1184	−	3.59286i	−0.482241	−	0.132076i
$741$	−5.11750			−0.187996
$742$	−0.427231			−0.0156842
$743$	−15.7302	+	15.7302i	−0.577084	+	0.577084i	−0.934099	−	0.357015i	$-0.883795\pi$
$743$	−15.7302	+	15.7302i	−0.577084	+	0.577084i	0.357015	+	0.934099i	$0.383795\pi$
$744$	−8.37752			−0.307135
$745$	−15.3329	−	32.9517i	−0.561754	−	1.20726i
$746$	6.36168	−	6.36168i	0.232918	−	0.232918i
$747$	11.2038	−	11.2038i	0.409926	−	0.409926i
$748$	−1.27110			−0.0464760
$749$		−	0.628846i		−	0.0229775i
$750$	−5.56645	−	9.69612i	−0.203258	−	0.354052i
$751$		−	12.7266i		−	0.464401i	−0.972668	−	0.232201i	$-0.925407\pi$
$751$		−	12.7266i		−	0.464401i	0.972668	−	0.232201i	$-0.0745926\pi$
$752$	−9.26908	+	9.26908i	−0.338009	+	0.338009i
$753$	−12.3433			−0.449815
$754$	−11.5728	+	11.5728i	−0.421456	+	0.421456i
$755$	−14.8361	−	31.8840i	−0.539940	−	1.16038i
$756$	0.730071			0.0265524
$757$		−	49.4794i		−	1.79836i	−0.437578	−	0.899181i	$-0.644164\pi$
$757$		−	49.4794i		−	1.79836i	0.437578	−	0.899181i	$-0.355836\pi$
$758$			10.4081i			0.378038i
$759$	−1.80718	−	1.80718i	−0.0655963	−	0.0655963i
$760$	7.02344	+	2.56282i	0.254767	+	0.0929632i
$761$		−	10.2526i		−	0.371657i	−0.982582	−	0.185828i	$-0.940503\pi$
$761$		−	10.2526i		−	0.371657i	0.982582	−	0.185828i	$-0.0594968\pi$
$762$		−	0.712957i		−	0.0258277i
$763$	0.263980			0.00955671
$764$	13.3339	−	13.3339i	0.482404	−	0.482404i
$765$	5.18133	−	2.41095i	0.187331	−	0.0871680i
$766$	20.7631			0.750200
$767$	−9.05030	−	9.05030i	−0.326787	−	0.326787i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−18.0896	+	18.0896i	−0.652327	+	0.652327i	−0.953553	−	0.301226i	$-0.902604\pi$
$769$	−18.0896	+	18.0896i	−0.652327	+	0.652327i	0.301226	+	0.953553i	$0.402604\pi$
$770$	0.762730	+	0.278316i	0.0274869	+	0.0100298i
$771$	4.64860	+	4.64860i	0.167415	+	0.167415i
$772$	8.67065			0.312064
$773$	21.4323	+	21.4323i	0.770866	+	0.770866i	0.978258	−	0.207392i	$-0.0664976\pi$
$773$	21.4323	+	21.4323i	0.770866	+	0.770866i	−0.207392	+	0.978258i	$0.566498\pi$
$774$			9.05230i			0.325378i
$775$	41.7341	−	3.58263i	1.49913	−	0.128692i
$776$			3.13965i			0.112707i
$777$	−2.87051	+	3.38841i	−0.102979	+	0.121558i
$778$	−20.8063	−	20.8063i	−0.745943	−	0.745943i
$779$	6.39209	−	6.39209i	0.229020	−	0.229020i
$780$	1.17316	−	3.21508i	0.0420060	−	0.115118i
$781$			2.04228i			0.0730785i
$782$			13.1331i			0.469638i
$783$	10.6931			0.382140
$784$			6.46700i			0.230964i
$785$	3.90744	−	10.7084i	0.139462	−	0.382199i
$786$	−21.5260			−0.767806
$787$	16.7084	−	16.7084i	0.595590	−	0.595590i	−0.343546	−	0.939136i	$-0.611628\pi$
$787$	16.7084	−	16.7084i	0.595590	−	0.595590i	0.939136	+	0.343546i	$0.111628\pi$
$788$	5.35975	−	5.35975i	0.190933	−	0.190933i
$789$		−	1.19013i		−	0.0423696i
$790$	−2.45951	−	0.897461i	−0.0875053	−	0.0319302i
$791$	6.63161	+	6.63161i	0.235793	+	0.235793i
$792$	0.497352			0.0176726
$793$	−16.5232	−	16.5232i	−0.586757	−	0.586757i
$794$	−5.88311	−	5.88311i	−0.208784	−	0.208784i
$795$	1.18638	−	0.552040i	0.0420766	−	0.0195788i
$796$	−13.1621	+	13.1621i	−0.466519	+	0.466519i
$797$	13.0313			0.461591			0.230796	−	0.973002i	$-0.425867\pi$
$797$	13.0313			0.461591			0.230796	+	0.973002i	$0.425867\pi$
$798$	1.72607	−	1.72607i	0.0611022	−	0.0611022i
$799$	23.6893	+	23.6893i	0.838067	+	0.838067i
$800$	−3.22019	+	3.82497i	−0.113851	+	0.135233i
$801$	−6.24255	−	6.24255i	−0.220570	−	0.220570i
$802$	14.5564	+	14.5564i	0.514006	+	0.514006i
$803$	1.30855	+	1.30855i	0.0461776	+	0.0461776i
$804$	−13.1483			−0.463705
$805$	2.87558	−	7.88058i	0.101351	−	0.277754i
$806$	9.06671	+	9.06671i	0.319361	+	0.319361i
$807$	−11.6070	−	11.6070i	−0.408584	−	0.408584i
$808$			4.17592i			0.146908i
$809$	4.63922	−	4.63922i	0.163106	−	0.163106i	−0.620835	−	0.783941i	$-0.713206\pi$
$809$	4.63922	−	4.63922i	0.163106	−	0.163106i	0.783941	+	0.620835i	$0.213206\pi$
$810$	−2.02734	+	0.943349i	−0.0712333	+	0.0331459i
$811$	55.6848			1.95536			0.977679	−	0.210105i	$-0.0673805\pi$
$811$	55.6848			1.95536			0.977679	+	0.210105i	$0.0673805\pi$
$812$		−	7.80672i		−	0.273962i
$813$	2.53096	−	2.53096i	0.0887647	−	0.0887647i
$814$	−1.95550	+	2.30831i	−0.0685403	+	0.0809063i
$815$	−11.4047	−	24.5096i	−0.399489	−	0.858536i
$816$	−1.80718	−	1.80718i	−0.0632638	−	0.0632638i
$817$	21.4019	+	21.4019i	0.748758	+	0.748758i
$818$	−11.0869	+	11.0869i	−0.387644	+	0.387644i
$819$	−0.790132	−	0.790132i	−0.0276095	−	0.0276095i
$820$	2.55048	+	5.48119i	0.0890666	+	0.191412i
$821$	−17.4399			−0.608658			−0.304329	−	0.952567i	$-0.598432\pi$
$821$	−17.4399			−0.608658			−0.304329	+	0.952567i	$0.598432\pi$
$822$		−	14.8551i		−	0.518132i
$823$	−18.0594	−	18.0594i	−0.629511	−	0.629511i	0.318434	−	0.947945i	$-0.396843\pi$
$823$	−18.0594	−	18.0594i	−0.629511	−	0.629511i	−0.947945	+	0.318434i	$0.896843\pi$
$824$			15.6656i			0.545736i
$825$	−2.47765	+	0.212691i	−0.0862606	+	0.00740497i
$826$	6.10511			0.212424
$827$			18.6866i			0.649797i	0.945749	+	0.324899i	$0.105330\pi$
$827$			18.6866i			0.649797i	−0.945749	+	0.324899i	$0.894670\pi$
$828$		−	5.13868i		−	0.178581i
$829$	−0.406665	+	0.406665i	−0.0141241	+	0.0141241i	−0.714134	−	0.700009i	$-0.753179\pi$
$829$	−0.406665	+	0.406665i	−0.0141241	+	0.0141241i	0.700009	+	0.714134i	$0.253179\pi$
$830$	33.2830	+	12.1448i	1.15527	+	0.421551i
$831$	−7.88433	+	7.88433i	−0.273504	+	0.273504i
$832$	−1.53056			−0.0530625
$833$	16.5279			0.572658
$834$	−0.0786679	+	0.0786679i	−0.00272405	+	0.00272405i
$835$	10.7473	+	23.0969i	0.371926	+	0.799301i
$836$	1.17586	−	1.17586i	0.0406681	−	0.0406681i
$837$		−	8.37752i		−	0.289569i
$838$			22.0253i			0.760853i
$839$	−33.2804			−1.14897			−0.574483	−	0.818516i	$-0.694797\pi$
$839$	−33.2804			−1.14897			−0.574483	+	0.818516i	$0.694797\pi$
$840$	0.688712	+	1.48010i	0.0237628	+	0.0510683i
$841$		−	85.3422i		−	2.94283i
$842$	−22.6650	−	22.6650i	−0.781089	−	0.781089i
$843$			16.9830i			0.584924i
$844$	−24.6681			−0.849112
$845$	21.6061	−	10.0536i	0.743273	−	0.345856i
$846$	−9.26908	−	9.26908i	−0.318677	−	0.318677i
$847$	−5.55092	+	5.55092i	−0.190732	+	0.190732i
$848$	−0.413793	−	0.413793i	−0.0142097	−	0.0142097i
$849$	−16.9099	−	16.9099i	−0.580346	−	0.580346i
$850$	9.77561	+	8.22994i	0.335300	+	0.282284i
$851$	23.8496	+	20.2044i	0.817555	+	0.692597i
$852$	−2.90360	+	2.90360i	−0.0994756	+	0.0994756i
$853$			13.7096i			0.469409i	0.972067	+	0.234705i	$0.0754123\pi$
$853$			13.7096i			0.469409i	−0.972067	+	0.234705i	$0.924588\pi$
$854$	11.1462			0.381414
$855$	−2.56282	+	7.02344i	−0.0876465	+	0.240197i
$856$	0.609066	−	0.609066i	0.0208174	−	0.0208174i
$857$		−	11.0849i		−	0.378651i	−0.981914	−	0.189326i	$-0.939370\pi$
$857$		−	11.0849i		−	0.378651i	0.981914	−	0.189326i	$-0.0606302\pi$
$858$	−0.538268	−	0.538268i	−0.0183762	−	0.0183762i
$859$	15.5947	+	15.5947i	0.532084	+	0.532084i	0.921192	−	0.389108i	$-0.127217\pi$
$859$	15.5947	+	15.5947i	0.532084	+	0.532084i	−0.389108	+	0.921192i	$0.627217\pi$
$860$	−18.3521	+	8.53948i	−0.625800	+	0.291194i
$861$	1.97385			0.0672687
$862$	−17.9692	−	17.9692i	−0.612034	−	0.612034i
$863$	−0.801311	−	0.801311i	−0.0272770	−	0.0272770i	0.693337	−	0.720614i	$-0.256140\pi$
$863$	−0.801311	−	0.801311i	−0.0272770	−	0.0272770i	−0.720614	+	0.693337i	$0.756140\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−14.5656	+	39.9172i	−0.495244	+	1.35722i
$866$	18.0984	+	18.0984i	0.615010	+	0.615010i
$867$	7.40215	−	7.40215i	0.251390	−	0.251390i
$868$	−6.11618			−0.207597
$869$	−0.411770	+	0.411770i	−0.0139684	+	0.0139684i
$870$	10.0873	+	21.6785i	0.341992	+	0.734970i
$871$	14.2300	+	14.2300i	0.482165	+	0.482165i
$872$	0.255676	+	0.255676i	0.00865830	+	0.00865830i
$873$	−3.13965			−0.106261
$874$	−12.1491	−	12.1491i	−0.410950	−	0.410950i
$875$	−4.06390	−	7.07885i	−0.137385	−	0.239309i
$876$			3.72083i			0.125715i
$877$	−7.57864	+	7.57864i	−0.255912	+	0.255912i	−0.823389	−	0.567477i	$-0.807920\pi$
$877$	−7.57864	+	7.57864i	−0.255912	+	0.255912i	0.567477	+	0.823389i	$0.307920\pi$
$878$	24.7771	−	24.7771i	0.836186	−	0.836186i
$879$	24.7140			0.833584
$880$	0.469177	+	1.00830i	0.0158159	+	0.0339898i
$881$		−	23.3650i		−	0.787188i	−0.919284	−	0.393594i	$-0.871232\pi$
$881$		−	23.3650i		−	0.787188i	0.919284	−	0.393594i	$-0.128768\pi$
$882$	−6.46700			−0.217755
$883$			12.2410i			0.411943i	0.978558	+	0.205972i	$0.0660355\pi$
$883$			12.2410i			0.411943i	−0.978558	+	0.205972i	$0.933965\pi$
$884$			3.91170i			0.131565i
$885$	−16.9533	+	7.88861i	−0.569879	+	0.265173i
$886$	11.6985	−	11.6985i	0.393018	−	0.393018i
$887$	9.25112	+	9.25112i	0.310622	+	0.310622i	0.845151	−	0.534528i	$-0.179511\pi$
$887$	9.25112	+	9.25112i	0.310622	+	0.310622i	−0.534528	+	0.845151i	$0.679511\pi$
$888$	−6.06205	+	0.501607i	−0.203429	+	0.0168328i
$889$		−	0.520509i		−	0.0174573i
$890$	6.76685	−	18.5446i	0.226825	−	0.621618i
$891$			0.497352i			0.0166619i
$892$	−11.0405	−	11.0405i	−0.369664	−	0.369664i
$893$	−43.8288			−1.46668
$894$	−11.4931	−	11.4931i	−0.384387	−	0.384387i
$895$	8.27299	−	22.6722i	0.276535	−	0.757850i
$896$	0.516238	−	0.516238i	0.0172463	−	0.0172463i
$897$	−5.56142	+	5.56142i	−0.185690	+	0.185690i
$898$	−16.3835	−	16.3835i	−0.546726	−	0.546726i
$899$	−89.5816			−2.98771
$900$	−3.82497	−	3.22019i	−0.127499	−	0.107340i
$901$	−1.05754	+	1.05754i	−0.0352319	+	0.0352319i
$902$	1.34466			0.0447724
$903$			6.60883i			0.219928i
$904$			12.8460i			0.427253i
$905$	−19.2201	+	8.94339i	−0.638898	+	0.297288i
$906$	−11.1207	−	11.1207i	−0.369460	−	0.369460i
$907$			28.2255i			0.937213i	0.883407	+	0.468606i	$0.155244\pi$
$907$			28.2255i			0.937213i	−0.883407	+	0.468606i	$0.844756\pi$
$908$		−	28.9019i		−	0.959143i
$909$	−4.17592			−0.138506
$910$	0.856493	−	2.34723i	0.0283925	−	0.0778100i
$911$	−11.7600	+	11.7600i	−0.389626	+	0.389626i	−0.874554	−	0.484928i	$-0.838846\pi$
$911$	−11.7600	+	11.7600i	−0.389626	+	0.389626i	0.484928	+	0.874554i	$0.338846\pi$
$912$	3.34355			0.110716
$913$	5.57223	−	5.57223i	0.184414	−	0.184414i
$914$		−	36.6470i		−	1.21217i
$915$	−30.9518	+	14.4023i	−1.02324	+	0.476127i
$916$		−	27.5614i		−	0.910654i
$917$	−15.7155			−0.518971
$918$	1.80718	−	1.80718i	0.0596457	−	0.0596457i
$919$	16.8392	−	16.8392i	0.555476	−	0.555476i	−0.372540	−	0.928016i	$-0.621513\pi$
$919$	16.8392	−	16.8392i	0.555476	−	0.555476i	0.928016	+	0.372540i	$0.121513\pi$
$920$	10.4178	−	4.84756i	0.343466	−	0.159819i
$921$	−8.71269			−0.287093
$922$	4.87965	−	4.87965i	0.160703	−	0.160703i
$923$	6.28494			0.206871
$924$	0.363102			0.0119452
$925$	29.9846	−	5.09126i	0.985889	−	0.167400i
$926$	−3.03199			−0.0996373
$927$	−15.6656			−0.514524
$928$	7.56116	−	7.56116i	0.248207	−	0.248207i
$929$	24.9345			0.818075			0.409038	−	0.912518i	$-0.365865\pi$
$929$	24.9345			0.818075			0.409038	+	0.912518i	$0.365865\pi$
$930$	16.9840	−	7.90292i	0.556929	−	0.259147i
$931$	−15.2896	+	15.2896i	−0.501096	+	0.501096i
$932$	−7.51093	+	7.51093i	−0.246029	+	0.246029i
$933$	−17.2183			−0.563703
$934$		−	7.88298i		−	0.257939i
$935$	2.57695	−	1.19909i	0.0842751	−	0.0392144i
$936$		−	1.53056i		−	0.0500278i
$937$	−3.73610	+	3.73610i	−0.122053	+	0.122053i	−0.765495	−	0.643442i	$-0.777506\pi$
$937$	−3.73610	+	3.73610i	−0.122053	+	0.122053i	0.643442	+	0.765495i	$0.277506\pi$
$938$	−9.59920			−0.313425
$939$	2.45376	−	2.45376i	0.0800755	−	0.0800755i
$940$	10.0476	−	27.5355i	0.327715	−	0.898110i
$941$	21.1387			0.689100			0.344550	−	0.938768i	$-0.388031\pi$
$941$	21.1387			0.689100			0.344550	+	0.938768i	$0.388031\pi$
$942$		−	5.09780i		−	0.166095i
$943$		−	13.8931i		−	0.452423i
$944$	5.91307	+	5.91307i	0.192454	+	0.192454i
$945$	−1.48010	+	0.688712i	−0.0481476	+	0.0224038i
$946$			4.50218i			0.146379i
$947$			1.08920i			0.0353942i	0.999843	+	0.0176971i	$0.00563346\pi$
$947$			1.08920i			0.0353942i	−0.999843	+	0.0176971i	$0.994367\pi$
$948$	−1.17086			−0.0380279
$949$	4.02694	−	4.02694i	0.130720	−	0.130720i
$950$	−16.6565	+	1.42986i	−0.540409	+	0.0463909i
$951$	9.04043			0.293156
$952$	−1.31937	−	1.31937i	−0.0427609	−	0.0427609i
$953$	−6.11358	+	6.11358i	−0.198038	+	0.198038i	−0.799159	−	0.601120i	$-0.794721\pi$
$953$	−6.11358	+	6.11358i	−0.198038	+	0.198038i	0.601120	+	0.799159i	$0.294721\pi$
$954$	0.413793	−	0.413793i	0.0133970	−	0.0133970i
$955$	−14.4538	+	39.6109i	−0.467714	+	1.28178i
$956$	−6.73852	−	6.73852i	−0.217939	−	0.217939i
$957$	5.31823			0.171914
$958$	−22.2999	−	22.2999i	−0.720476	−	0.720476i
$959$		−	10.8453i		−	0.350213i
$960$	−0.766495	+	2.10059i	−0.0247385	+	0.0677963i
$961$			39.1828i			1.26396i
$962$	7.10363	+	6.01788i	0.229030	+	0.194024i
$963$	0.609066	+	0.609066i	0.0196269	+	0.0196269i
$964$	−8.91683	+	8.91683i	−0.287192	+	0.287192i
$965$	−17.5783	+	8.17945i	−0.565867	+	0.263306i
$966$		−	3.75160i		−	0.120706i
$967$			20.1527i			0.648066i	0.946046	+	0.324033i	$0.105039\pi$
$967$			20.1527i			0.648066i	−0.946046	+	0.324033i	$0.894961\pi$
$968$	−10.7526			−0.345603
$969$		−	8.54523i		−	0.274512i
$970$	−2.96178	−	6.36512i	−0.0950971	−	0.204372i
$971$	−16.1896			−0.519550			−0.259775	−	0.965669i	$-0.583648\pi$
$971$	−16.1896			−0.519550			−0.259775	+	0.965669i	$0.583648\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−0.0574331	+	0.0574331i	−0.00184122	+	0.00184122i
$974$			12.8810i			0.412734i
$975$	0.654539	+	7.62474i	0.0209620	+	0.244187i
$976$	10.7956	+	10.7956i	0.345558	+	0.345558i
$977$	−6.24061			−0.199655			−0.0998273	−	0.995005i	$-0.531829\pi$
$977$	−6.24061			−0.199655			−0.0998273	+	0.995005i	$0.531829\pi$
$978$	−8.54863	−	8.54863i	−0.273355	−	0.273355i
$979$	−3.10474	−	3.10474i	−0.0992281	−	0.0992281i
$980$	−6.10063	−	13.1108i	−0.194878	−	0.418808i
$981$	−0.255676	+	0.255676i	−0.00816312	+	0.00816312i
$982$	−0.897235			−0.0286319
$983$	−3.22372	+	3.22372i	−0.102821	+	0.102821i	−0.756646	−	0.653825i	$-0.773163\pi$
$983$	−3.22372	+	3.22372i	−0.102821	+	0.102821i	0.653825	+	0.756646i	$0.273163\pi$
$984$	1.91176	+	1.91176i	0.0609448	+	0.0609448i
$985$	−5.80991	+	15.9221i	−0.185119	+	0.507322i
$986$	−19.3243	−	19.3243i	−0.615411	−	0.615411i
$987$	−6.76709	−	6.76709i	−0.215399	−	0.215399i
$988$	−3.61862	−	3.61862i	−0.115124	−	0.115124i
$989$	46.5169			1.47915
$990$	−1.00830	+	0.469177i	−0.0320459	+	0.0149114i
$991$	4.95581	+	4.95581i	0.157427	+	0.157427i	0.781425	−	0.623999i	$-0.214493\pi$
$991$	4.95581	+	4.95581i	0.157427	+	0.157427i	−0.623999	+	0.781425i	$0.714493\pi$
$992$	−5.92380	−	5.92380i	−0.188081	−	0.188081i
$993$			17.8612i			0.566807i
$994$	−2.11983	+	2.11983i	−0.0672370	+	0.0672370i
$995$	14.2676	−	39.1005i	0.452312	−	1.23957i
$996$	15.8446			0.502054
$997$		−	28.8366i		−	0.913265i	−0.889655	−	0.456633i	$-0.849055\pi$
$997$		−	28.8366i		−	0.913265i	0.889655	−	0.456633i	$-0.150945\pi$
$998$	−17.8190	+	17.8190i	−0.564051	+	0.564051i
$999$	−0.501607	−	6.06205i	−0.0158701	−	0.191795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.14	yes	36
5.2	odd	4		1110.2.l.a.697.5	yes	36
37.6	odd	4		1110.2.l.a.43.5	✓	36
185.117	even	4	inner	1110.2.o.a.487.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.5	✓	36	37.6	odd	4
1110.2.l.a.697.5	yes	36	5.2	odd	4
1110.2.o.a.253.14	yes	36	1.1	even	1	trivial
1110.2.o.a.487.14	yes	36	185.117	even	4	inner

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.02734 + 0.943349i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.02734 + 0.943349i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(2.02734 - 0.943349i) q^{10} -0.497352i q^{11} +(0.707107 - 0.707107i) q^{12} -1.53056 q^{13} +(0.516238 - 0.516238i) q^{14} +(-0.766495 + 2.10059i) q^{15} +1.00000 q^{16} -2.55573i q^{17} +1.00000i q^{18} +(2.36425 + 2.36425i) q^{19} +(-2.02734 + 0.943349i) q^{20} +0.730071i q^{21} +0.497352i q^{22} +5.13868 q^{23} +(-0.707107 + 0.707107i) q^{24} +(3.22019 - 3.82497i) q^{25} +1.53056 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.516238 + 0.516238i) q^{28} +(-7.56116 + 7.56116i) q^{29} +(0.766495 - 2.10059i) q^{30} +(5.92380 + 5.92380i) q^{31} -1.00000 q^{32} +(-0.351681 - 0.351681i) q^{33} +2.55573i q^{34} +(0.559596 - 1.53358i) q^{35} -1.00000i q^{36} +(4.64120 + 3.93182i) q^{37} +(-2.36425 - 2.36425i) q^{38} +(-1.08227 + 1.08227i) q^{39} +(2.02734 - 0.943349i) q^{40} -2.70364i q^{41} -0.730071i q^{42} +9.05230 q^{43} -0.497352i q^{44} +(0.943349 + 2.02734i) q^{45} -5.13868 q^{46} +(-9.26908 + 9.26908i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.46700i q^{49} +(-3.22019 + 3.82497i) q^{50} +(-1.80718 - 1.80718i) q^{51} -1.53056 q^{52} +(-0.413793 - 0.413793i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.469177 + 1.00830i) q^{55} +(0.516238 - 0.516238i) q^{56} +3.34355 q^{57} +(7.56116 - 7.56116i) q^{58} +(5.91307 + 5.91307i) q^{59} +(-0.766495 + 2.10059i) q^{60} +(10.7956 + 10.7956i) q^{61} +(-5.92380 - 5.92380i) q^{62} +(0.516238 + 0.516238i) q^{63} +1.00000 q^{64} +(3.10295 - 1.44385i) q^{65} +(0.351681 + 0.351681i) q^{66} +(-9.29726 - 9.29726i) q^{67} -2.55573i q^{68} +(3.63359 - 3.63359i) q^{69} +(-0.559596 + 1.53358i) q^{70} -4.10631 q^{71} +1.00000i q^{72} +(-2.63103 + 2.63103i) q^{73} +(-4.64120 - 3.93182i) q^{74} +(-0.427648 - 4.98168i) q^{75} +(2.36425 + 2.36425i) q^{76} +(0.256752 + 0.256752i) q^{77} +(1.08227 - 1.08227i) q^{78} +(-0.827925 - 0.827925i) q^{79} +(-2.02734 + 0.943349i) q^{80} -1.00000 q^{81} +2.70364i q^{82} +(11.2038 + 11.2038i) q^{83} +0.730071i q^{84} +(2.41095 + 5.18133i) q^{85} -9.05230 q^{86} +10.6931i q^{87} +0.497352i q^{88} +(6.24255 - 6.24255i) q^{89} +(-0.943349 - 2.02734i) q^{90} +(0.790132 - 0.790132i) q^{91} +5.13868 q^{92} +8.37752 q^{93} +(9.26908 - 9.26908i) q^{94} +(-7.02344 - 2.56282i) q^{95} +(-0.707107 + 0.707107i) q^{96} -3.13965i q^{97} -6.46700i q^{98} -0.497352 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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