LMFDB - Embedded newform 1110.2.l.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.943349 - 2.02734i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.943349 - 2.02734i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.02734 - 0.943349i) q^{10} +0.497352i q^{11} +(0.707107 - 0.707107i) q^{12} -1.53056i q^{13} +(-0.516238 - 0.516238i) q^{14} +(2.10059 + 0.766495i) q^{15} +1.00000 q^{16} +2.55573 q^{17} +1.00000 q^{18} +(-2.36425 + 2.36425i) q^{19} +(0.943349 + 2.02734i) q^{20} -0.730071i q^{21} -0.497352 q^{22} +5.13868i 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} +1.00000i q^{32} +(-0.351681 - 0.351681i) q^{33} +2.55573i q^{34} +(1.53358 + 0.559596i) q^{35} +1.00000i q^{36} +(-3.93182 - 4.64120i) q^{37} +(-2.36425 - 2.36425i) q^{38} +(1.08227 + 1.08227i) q^{39} +(-2.02734 + 0.943349i) q^{40} +2.70364i q^{41} +0.730071 q^{42} +9.05230i q^{43} -0.497352i q^{44} +(-2.02734 + 0.943349i) q^{45} -5.13868 q^{46} +(-9.26908 + 9.26908i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.46700i q^{49} +(-3.82497 - 3.22019i) q^{50} +(-1.80718 + 1.80718i) q^{51} +1.53056i q^{52} +(-0.413793 - 0.413793i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(1.00830 - 0.469177i) q^{55} +(0.516238 + 0.516238i) q^{56} -3.34355i q^{57} +(-7.56116 + 7.56116i) q^{58} +(-5.91307 + 5.91307i) q^{59} +(-2.10059 - 0.766495i) 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} -2.55573 q^{68} +(-3.63359 - 3.63359i) q^{69} +(-0.559596 + 1.53358i) q^{70} -4.10631 q^{71} -1.00000 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} +(-0.943349 - 2.02734i) q^{80} -1.00000 q^{81} -2.70364 q^{82} +(11.2038 + 11.2038i) q^{83} +0.730071i q^{84} +(-2.41095 - 5.18133i) q^{85} -9.05230 q^{86} -10.6931 q^{87} +0.497352 q^{88} +(-6.24255 - 6.24255i) q^{89} +(-0.943349 - 2.02734i) q^{90} +(0.790132 + 0.790132i) q^{91} -5.13868i q^{92} +8.37752i q^{93} +(-9.26908 - 9.26908i) q^{94} +(7.02344 + 2.56282i) q^{95} +(-0.707107 - 0.707107i) q^{96} +3.13965 q^{97} -6.46700 q^{98} +0.497352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.943349	−	2.02734i	−0.421878	−	0.906652i
$5$	−0.943349	−	2.02734i	−0.421878	−	0.906652i
$6$	−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	$0.294058\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	2.02734	−	0.943349i	0.641100	−	0.298313i
$11$			0.497352i			0.149957i	0.997185	+	0.0749787i	$0.0238889\pi$
$11$			0.497352i			0.149957i	−0.997185	+	0.0749787i	$0.976111\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$		−	1.53056i		−	0.424500i	−0.977215	−	0.212250i	$-0.931921\pi$
$13$		−	1.53056i		−	0.424500i	0.977215	−	0.212250i	$-0.0680791\pi$
$14$	−0.516238	−	0.516238i	−0.137970	−	0.137970i
$15$	2.10059	+	0.766495i	0.542370	+	0.197908i
$16$	1.00000			0.250000
$17$	2.55573			0.619856			0.309928	−	0.950760i	$-0.399695\pi$
$17$	2.55573			0.619856			0.309928	+	0.950760i	$0.399695\pi$
$18$	1.00000			0.235702
$19$	−2.36425	+	2.36425i	−0.542396	+	0.542396i	−0.924231	−	0.381835i	$-0.875292\pi$
$19$	−2.36425	+	2.36425i	−0.542396	+	0.542396i	0.381835	+	0.924231i	$0.375292\pi$
$20$	0.943349	+	2.02734i	0.210939	+	0.453326i
$21$		−	0.730071i		−	0.159315i
$22$	−0.497352			−0.106036
$23$			5.13868i			1.07149i	0.844380	+	0.535744i	$0.179969\pi$
$23$			5.13868i			1.07149i	−0.844380	+	0.535744i	$0.820031\pi$
$24$	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	0.786568	+	0.617504i	$0.211856\pi$
$29$	7.56116	+	7.56116i	1.40407	+	1.40407i	0.617504	+	0.786568i	$0.288144\pi$
$30$	−0.766495	+	2.10059i	−0.139942	+	0.383514i
$31$	5.92380	−	5.92380i	1.06395	−	1.06395i	0.0661351	−	0.997811i	$-0.478933\pi$
$31$	5.92380	−	5.92380i	1.06395	−	1.06395i	0.997811	−	0.0661351i	$-0.0210668\pi$
$32$			1.00000i			0.176777i
$33$	−0.351681	−	0.351681i	−0.0612198	−	0.0612198i
$34$			2.55573i			0.438305i
$35$	1.53358	+	0.559596i	0.259223	+	0.0945890i
$36$			1.00000i			0.166667i
$37$	−3.93182	−	4.64120i	−0.646388	−	0.763009i
$37$	−3.93182	−	4.64120i	−0.646388	−	0.763009i
$38$	−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	$0.0677108\pi$
$41$			2.70364i			0.422238i	−0.977460	+	0.211119i	$0.932289\pi$
$42$	0.730071			0.112652
$43$			9.05230i			1.38046i	0.723588	+	0.690232i	$0.242491\pi$
$43$			9.05230i			1.38046i	−0.723588	+	0.690232i	$0.757509\pi$
$44$		−	0.497352i		−	0.0749787i
$45$	−2.02734	+	0.943349i	−0.302217	+	0.140626i
$46$	−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
$50$	−3.82497	−	3.22019i	−0.540933	−	0.455403i
$51$	−1.80718	+	1.80718i	−0.253055	+	0.253055i
$52$			1.53056i			0.212250i
$53$	−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
$55$	1.00830	−	0.469177i	0.135959	−	0.0632638i
$56$	0.516238	+	0.516238i	0.0689852	+	0.0689852i
$57$		−	3.34355i		−	0.442865i
$58$	−7.56116	+	7.56116i	−0.992829	+	0.992829i
$59$	−5.91307	+	5.91307i	−0.769817	+	0.769817i	−0.978074	−	0.208257i	$-0.933221\pi$
$59$	−5.91307	+	5.91307i	−0.769817	+	0.769817i	0.208257	+	0.978074i	$0.433221\pi$
$60$	−2.10059	−	0.766495i	−0.271185	−	0.0989541i
$61$	10.7956	−	10.7956i	1.38223	−	1.38223i	0.541586	−	0.840645i	$-0.317824\pi$
$61$	10.7956	−	10.7956i	1.38223	−	1.38223i	0.840645	−	0.541586i	$-0.182176\pi$
$62$	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	$0.0468500\pi$
$67$	9.29726	+	9.29726i	1.13584	+	1.13584i	0.146653	+	0.989188i	$0.453150\pi$
$68$	−2.55573			−0.309928
$69$	−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	$0.578350\pi$
$72$	−1.00000			−0.117851
$73$	2.63103	−	2.63103i	0.307938	−	0.307938i	−0.536171	−	0.844109i	$-0.680130\pi$
$73$	2.63103	−	2.63103i	0.307938	−	0.307938i	0.844109	+	0.536171i	$0.180130\pi$
$74$	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	$-0.729019\pi$
$79$	0.827925	−	0.827925i	0.0931489	−	0.0931489i	0.752146	+	0.658997i	$0.229019\pi$
$80$	−0.943349	−	2.02734i	−0.105470	−	0.226663i
$81$	−1.00000			−0.111111
$82$	−2.70364			−0.298567
$83$	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
$87$	−10.6931			−1.14642
$88$	0.497352			0.0530179
$89$	−6.24255	−	6.24255i	−0.661709	−	0.661709i	0.294074	−	0.955783i	$-0.404989\pi$
$89$	−6.24255	−	6.24255i	−0.661709	−	0.661709i	−0.955783	+	0.294074i	$0.904989\pi$
$90$	−0.943349	−	2.02734i	−0.0994377	−	0.213700i
$91$	0.790132	+	0.790132i	0.0828284	+	0.0828284i
$92$		−	5.13868i		−	0.535744i
$93$			8.37752i			0.868708i
$94$	−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
$97$	3.13965			0.318783			0.159391	−	0.987215i	$-0.449047\pi$
$97$	3.13965			0.318783			0.159391	+	0.987215i	$0.449047\pi$
$98$	−6.46700			−0.653265
$99$	0.497352			0.0499858
$100$	3.22019	−	3.82497i	0.322019	−	0.382497i
$101$			4.17592i			0.415519i	0.978180	+	0.207760i	$0.0666172\pi$
$101$			4.17592i			0.415519i	−0.978180	+	0.207760i	$0.933383\pi$
$102$	−1.80718	−	1.80718i	−0.178937	−	0.178937i
$103$	−15.6656			−1.54357			−0.771787	−	0.635881i	$-0.780637\pi$
$103$	−15.6656			−1.54357			−0.771787	+	0.635881i	$0.780637\pi$
$104$	−1.53056			−0.150083
$105$	−1.48010	+	0.688712i	−0.144443	+	0.0672114i
$106$	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	$-0.744488\pi$
$109$	0.255676	−	0.255676i	0.0244894	−	0.0244894i	0.719245	+	0.694756i	$0.244488\pi$
$110$	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
$113$	−12.8460			−1.20845			−0.604226	−	0.796813i	$-0.706518\pi$
$113$	−12.8460			−1.20845			−0.604226	+	0.796813i	$0.706518\pi$
$114$	3.34355			0.313153
$115$	10.4178	−	4.84756i	0.971467	−	0.452038i
$116$	−7.56116	−	7.56116i	−0.702036	−	0.702036i
$117$	−1.53056			−0.141500
$118$	−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
$125$	10.7923	+	2.92012i	0.965289	+	0.261183i
$126$	−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	$0.260071\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.40095	−	6.40095i	−0.563572	−	0.563572i
$130$	−1.44385	−	3.10295i	−0.126634	−	0.272147i
$131$	15.2212	−	15.2212i	1.32988	−	1.32988i	0.424407	−	0.905472i	$-0.360483\pi$
$131$	15.2212	−	15.2212i	1.32988	−	1.32988i	0.905472	−	0.424407i	$-0.139517\pi$
$132$	0.351681	+	0.351681i	0.0306099	+	0.0306099i
$133$		−	2.44103i		−	0.211664i
$134$	−9.29726	+	9.29726i	−0.803161	+	0.803161i
$135$	0.766495	−	2.10059i	0.0659694	−	0.180790i
$136$		−	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	$-0.501502\pi$
$139$	−0.111253			−0.00943637			−0.00471819	+	0.999989i	$0.501502\pi$
$140$	−1.53358	−	0.559596i	−0.129611	−	0.0472945i
$141$		−	13.1085i		−	1.10393i
$142$		−	4.10631i		−	0.344594i
$143$	0.761226			0.0636569
$144$		−	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
$148$	3.93182	+	4.64120i	0.323194	+	0.381505i
$149$			16.2537i			1.33155i	0.746150	+	0.665777i	$0.231900\pi$
$149$			16.2537i			1.33155i	−0.746150	+	0.665777i	$0.768100\pi$
$150$	4.98168	−	0.427648i	0.406752	−	0.0349173i
$151$		−	15.7270i		−	1.27985i	−0.768438	−	0.639924i	$-0.778966\pi$
$151$		−	15.7270i		−	1.27985i	0.768438	−	0.639924i	$-0.221034\pi$
$152$	2.36425	+	2.36425i	0.191766	+	0.191766i
$153$		−	2.55573i		−	0.206619i
$154$	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
$162$		−	1.00000i		−	0.0785674i
$163$	12.0896			0.946929			0.473465	−	0.880813i	$-0.343003\pi$
$163$	12.0896			0.946929			0.473465	+	0.880813i	$0.343003\pi$
$164$		−	2.70364i		−	0.211119i
$165$	−0.381218	+	1.04473i	−0.0296778	+	0.0813324i
$166$	−11.2038	+	11.2038i	−0.869583	+	0.869583i
$167$	11.3927			0.881596			0.440798	−	0.897606i	$-0.354695\pi$
$167$	11.3927			0.881596			0.440798	+	0.897606i	$0.354695\pi$
$168$	−0.730071			−0.0563262
$169$	10.6574			0.819800
$170$	5.18133	−	2.41095i	0.397390	−	0.184911i
$171$	2.36425	+	2.36425i	0.180799	+	0.180799i
$172$		−	9.05230i		−	0.690232i
$173$	−13.4370	+	13.4370i	−1.02160	+	1.02160i	−0.0218360	+	0.999762i	$0.506951\pi$
$173$	−13.4370	+	13.4370i	−1.02160	+	1.02160i	−0.999762	+	0.0218360i	$0.993049\pi$
$174$		−	10.6931i		−	0.810641i
$175$	−0.312213	−	3.63698i	−0.0236011	−	0.274930i
$176$			0.497352i			0.0374893i
$177$		−	8.36235i		−	0.628553i
$178$	6.24255	−	6.24255i	0.467899	−	0.467899i
$179$	7.63199	+	7.63199i	0.570442	+	0.570442i	0.932252	−	0.361810i	$-0.117841\pi$
$179$	7.63199	+	7.63199i	0.570442	+	0.570442i	−0.361810	+	0.932252i	$0.617841\pi$
$180$	2.02734	−	0.943349i	0.151109	−	0.0703131i
$181$	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
$183$			15.2672i			1.12859i
$184$	5.13868			0.378828
$185$	−5.70020	+	12.3494i	−0.419087	+	0.907946i
$186$	−8.37752			−0.614269
$187$			1.27110i			0.0929520i
$188$	9.26908	−	9.26908i	0.676017	−	0.676017i
$189$	−0.730071			−0.0531049
$190$	−2.56282	+	7.02344i	−0.185926	+	0.509534i
$191$	13.3339	+	13.3339i	0.964808	+	0.964808i	0.999401	−	0.0345933i	$-0.0110136\pi$
$191$	13.3339	+	13.3339i	0.964808	+	0.964808i	−0.0345933	+	0.999401i	$0.511014\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$			8.67065i			0.624127i	0.950061	+	0.312064i	$0.101020\pi$
$193$			8.67065i			0.624127i	−0.950061	+	0.312064i	$0.898980\pi$
$194$			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	$0.162970\pi$
$198$			0.497352i			0.0353453i
$199$	13.1621	+	13.1621i	0.933037	+	0.933037i	0.997895	−	0.0648573i	$-0.0206592\pi$
$199$	13.1621	+	13.1621i	0.933037	+	0.933037i	−0.0648573	+	0.997895i	$0.520659\pi$
$200$	3.82497	+	3.22019i	0.270466	+	0.227702i
$201$	−13.1483			−0.927410
$202$	−4.17592			−0.293816
$203$	−7.80672			−0.547924
$204$	1.80718	−	1.80718i	0.126528	−	0.126528i
$205$	5.48119	−	2.55048i	0.382823	−	0.178133i
$206$		−	15.6656i		−	1.09147i
$207$	5.13868			0.357163
$208$		−	1.53056i		−	0.106125i
$209$	−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
$217$			6.11618i			0.415194i
$218$	0.255676	+	0.255676i	0.0173166	+	0.0173166i
$219$			3.72083i			0.251431i
$220$	−1.00830	+	0.469177i	−0.0679796	+	0.0316319i
$221$		−	3.91170i		−	0.263129i
$222$	−0.501607	+	6.06205i	−0.0336657	+	0.406858i
$223$	−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
$227$	28.9019			1.91829			0.959143	−	0.282922i	$-0.0913038\pi$
$227$	28.9019			1.91829			0.959143	+	0.282922i	$0.0913038\pi$
$228$			3.34355i			0.221432i
$229$		−	27.5614i		−	1.82131i	−0.413171	−	0.910654i	$-0.635579\pi$
$229$		−	27.5614i		−	1.82131i	0.413171	−	0.910654i	$-0.364421\pi$
$230$	4.84756	+	10.4178i	0.319639	+	0.686931i
$231$	0.363102			0.0238904
$232$	7.56116	−	7.56116i	0.496414	−	0.496414i
$233$	7.51093	−	7.51093i	0.492057	−	0.492057i	−0.416897	−	0.908954i	$-0.636882\pi$
$233$	7.51093	−	7.51093i	0.492057	−	0.492057i	0.908954	+	0.416897i	$0.136882\pi$
$234$		−	1.53056i		−	0.100056i
$235$	27.5355	+	10.0476i	1.79622	+	0.655431i
$236$	5.91307	−	5.91307i	0.384908	−	0.384908i
$237$			1.17086i			0.0760557i
$238$	−1.31937	−	1.31937i	−0.0855219	−	0.0855219i
$239$	6.73852	−	6.73852i	0.435879	−	0.435879i	−0.454744	−	0.890622i	$-0.650269\pi$
$239$	6.73852	−	6.73852i	0.435879	−	0.435879i	0.890622	+	0.454744i	$0.150269\pi$
$240$	2.10059	+	0.766495i	0.135593	+	0.0494770i
$241$	−8.91683	−	8.91683i	−0.574384	−	0.574384i	0.358967	−	0.933350i	$-0.383129\pi$
$241$	−8.91683	−	8.91683i	−0.574384	−	0.574384i	−0.933350	+	0.358967i	$0.883129\pi$
$242$			10.7526i			0.691206i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−10.7956	+	10.7956i	−0.691116	+	0.691116i
$245$	13.1108	−	6.10063i	0.837617	−	0.389755i
$246$	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	−0.926703	−	0.375795i	$-0.877370\pi$
$251$	−8.72803	+	8.72803i	−0.550908	+	0.550908i	0.375795	+	0.926703i	$0.377370\pi$
$252$	−0.516238	−	0.516238i	−0.0325200	−	0.0325200i
$253$	−2.55573			−0.160677
$254$	−0.504136	−	0.504136i	−0.0316323	−	0.0316323i
$255$	5.36855	+	1.95896i	0.336192	+	0.122675i
$256$	1.00000			0.0625000
$257$	−6.57411			−0.410082			−0.205041	−	0.978753i	$-0.565733\pi$
$257$	−6.57411			−0.410082			−0.205041	+	0.978753i	$0.565733\pi$
$258$	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	−0.732577	−	0.680685i	$-0.761682\pi$
$263$	−0.841547	+	0.841547i	−0.0518920	+	0.0518920i	0.680685	+	0.732577i	$0.261682\pi$
$264$	−0.351681	+	0.351681i	−0.0216445	+	0.0216445i
$265$	−0.448546	+	1.22925i	−0.0275540	+	0.0755121i
$266$	2.44103			0.149669
$267$	8.82830			0.540283
$268$	−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	$0.465327\pi$
$272$	2.55573			0.154964
$273$	−1.11742			−0.0676291
$274$	−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
$277$			11.1501i			0.669946i	0.942228	+	0.334973i	$0.108727\pi$
$277$			11.1501i			0.669946i	−0.942228	+	0.334973i	$0.891273\pi$
$278$		−	0.111253i		−	0.00667252i
$279$	−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	0.251480	−	0.967863i	$-0.419083\pi$
$281$	−12.0088	−	12.0088i	−0.716383	−	0.716383i	−0.967863	+	0.251480i	$0.919083\pi$
$282$	13.1085			0.780597
$283$	−23.9142			−1.42155			−0.710776	−	0.703419i	$-0.751656\pi$
$283$	−23.9142			−1.42155			−0.710776	+	0.703419i	$0.751656\pi$
$284$	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
$288$	1.00000			0.0589256
$289$	−10.4682			−0.615778
$290$	22.4618	+	8.19620i	1.31900	+	0.481297i
$291$	−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
$298$	−16.2537			−0.941552
$299$	7.86504			0.454847
$300$	0.427648	+	4.98168i	0.0246902	+	0.287617i
$301$	−4.67315	−	4.67315i	−0.269356	−	0.269356i
$302$	15.7270			0.904989
$303$	−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	0.860710	−	0.509095i	$-0.170020\pi$
$307$	6.16080	+	6.16080i	0.351615	+	0.351615i	−0.509095	+	0.860710i	$0.670020\pi$
$308$	0.256752	+	0.256752i	0.0146298	+	0.0146298i
$309$	11.0772	−	11.0772i	0.630161	−	0.630161i
$310$	6.42132	−	17.5977i	0.364707	−	0.999485i
$311$	−12.1752	+	12.1752i	−0.690392	+	0.690392i	−0.962318	−	0.271926i	$-0.912339\pi$
$311$	−12.1752	+	12.1752i	−0.690392	+	0.690392i	0.271926	+	0.962318i	$0.412339\pi$
$312$	1.08227	−	1.08227i	0.0612713	−	0.0612713i
$313$			3.47014i			0.196144i	0.995179	+	0.0980720i	$0.0312675\pi$
$313$			3.47014i			0.196144i	−0.995179	+	0.0980720i	$0.968732\pi$
$314$	−3.60469	−	3.60469i	−0.203424	−	0.203424i
$315$	0.559596	−	1.53358i	0.0315297	−	0.0864075i
$316$	−0.827925	+	0.827925i	−0.0465744	+	0.0465744i
$317$	−6.39255	−	6.39255i	−0.359041	−	0.359041i	0.504418	−	0.863460i	$-0.331707\pi$
$317$	−6.39255	−	6.39255i	−0.359041	−	0.359041i	−0.863460	+	0.504418i	$0.831707\pi$
$318$			0.585191i			0.0328159i
$319$	−3.76056	+	3.76056i	−0.210551	+	0.210551i
$320$	0.943349	+	2.02734i	0.0527348	+	0.113332i
$321$		−	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
$325$	5.85434	+	4.92868i	0.324740	+	0.273394i
$326$			12.0896i			0.669580i
$327$			0.361581i			0.0199955i
$328$	2.70364			0.149284
$329$		−	9.57011i		−	0.527617i
$330$	−1.04473	−	0.381218i	−0.0575107	−	0.0209854i
$331$	−12.6298	−	12.6298i	−0.694194	−	0.694194i	0.268958	−	0.963152i	$-0.413321\pi$
$331$	−12.6298	−	12.6298i	−0.694194	−	0.694194i	−0.963152	+	0.268958i	$0.913321\pi$
$332$	−11.2038	−	11.2038i	−0.614888	−	0.614888i
$333$	−4.64120	+	3.93182i	−0.254336	+	0.215463i
$334$			11.3927i			0.623383i
$335$	10.0781	−	27.6192i	0.550626	−	1.50900i
$336$		−	0.730071i		−	0.0398286i
$337$	−11.4706	−	11.4706i	−0.624845	−	0.624845i	0.321921	−	0.946766i	$-0.395671\pi$
$337$	−11.4706	−	11.4706i	−0.624845	−	0.624845i	−0.946766	+	0.321921i	$0.895671\pi$
$338$			10.6574i			0.579686i
$339$	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
$347$			2.52563i			0.135583i	0.997700	+	0.0677914i	$0.0215952\pi$
$347$			2.52563i			0.135583i	−0.997700	+	0.0677914i	$0.978405\pi$
$348$	10.6931			0.573210
$349$			5.42724i			0.290514i	0.989394	+	0.145257i	$0.0464008\pi$
$349$			5.42724i			0.290514i	−0.989394	+	0.145257i	$0.953599\pi$
$350$	3.63698	−	0.312213i	0.194405	−	0.0166885i
$351$	1.08227	−	1.08227i	0.0577672	−	0.0577672i
$352$	−0.497352			−0.0265090
$353$	16.8913			0.899034			0.449517	−	0.893272i	$-0.351596\pi$
$353$	16.8913			0.899034			0.449517	+	0.893272i	$0.351596\pi$
$354$	8.36235			0.444454
$355$	3.87368	+	8.32486i	0.205594	+	0.441838i
$356$	6.24255	+	6.24255i	0.330854	+	0.330854i
$357$		−	1.86587i		−	0.0987522i
$358$	−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
$362$			9.48047i			0.498282i
$363$	−7.60327	+	7.60327i	−0.399068	+	0.399068i
$364$	−0.790132	−	0.790132i	−0.0414142	−	0.0414142i
$365$	−7.81595	−	2.85200i	−0.409105	−	0.149280i
$366$	−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	$0.421126\pi$
$368$			5.13868i			0.267872i
$369$	2.70364			0.140746
$370$	−12.3494	−	5.70020i	−0.642015	−	0.296339i
$371$	0.427231			0.0221807
$372$		−	8.37752i		−	0.434354i
$373$	6.36168	−	6.36168i	0.329395	−	0.329395i	−0.522961	−	0.852356i	$-0.675173\pi$
$373$	6.36168	−	6.36168i	0.329395	−	0.329395i	0.852356	+	0.522961i	$0.175173\pi$
$374$	−1.27110			−0.0657270
$375$	−9.69612	+	5.56645i	−0.500705	+	0.287450i
$376$	9.26908	+	9.26908i	0.478016	+	0.478016i
$377$	11.5728	−	11.5728i	0.596029	−	0.596029i
$378$		−	0.730071i		−	0.0375508i
$379$		−	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
$383$		−	20.7631i		−	1.06094i	−0.847703	−	0.530472i	$-0.822015\pi$
$383$		−	20.7631i		−	1.06094i	0.847703	−	0.530472i	$-0.177985\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−0.278316	+	0.762730i	−0.0141843	+	0.0388723i
$386$	−8.67065			−0.441325
$387$	9.05230			0.460154
$388$	−3.13965			−0.159391
$389$	−20.8063	+	20.8063i	−1.05492	+	1.05492i	−0.0565210	+	0.998401i	$0.518001\pi$
$389$	−20.8063	+	20.8063i	−1.05492	+	1.05492i	−0.998401	+	0.0565210i	$0.981999\pi$
$390$	3.21508	+	1.17316i	0.162802	+	0.0594055i
$391$			13.1331i			0.664169i
$392$	6.46700			0.326633
$393$			21.5260i			1.08584i
$394$	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	0.543891	−	0.839156i	$-0.316950\pi$
$397$	−5.88311	−	5.88311i	−0.295265	−	0.295265i	−0.839156	+	0.543891i	$0.816950\pi$
$398$	−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	−0.970004	−	0.243090i	$-0.921839\pi$
$401$	−14.5564	+	14.5564i	−0.726914	+	0.726914i	0.243090	+	0.970004i	$0.421839\pi$
$402$		−	13.1483i		−	0.655778i
$403$	−9.06671	−	9.06671i	−0.451645	−	0.451645i
$404$		−	4.17592i		−	0.207760i
$405$	0.943349	+	2.02734i	0.0468754	+	0.100739i
$406$		−	7.80672i		−	0.387441i
$407$	2.30831	−	1.95550i	0.114419	−	0.0969306i
$408$	1.80718	+	1.80718i	0.0894686	+	0.0894686i
$409$	−11.0869	−	11.0869i	−0.548211	−	0.548211i	0.377712	−	0.925923i	$-0.376711\pi$
$409$	−11.0869	−	11.0869i	−0.548211	−	0.548211i	−0.925923	+	0.377712i	$0.876711\pi$
$410$	2.55048	+	5.48119i	0.125959	+	0.270697i
$411$		−	14.8551i		−	0.732749i
$412$	15.6656			0.771787
$413$		−	6.10511i		−	0.300413i
$414$			5.13868i			0.252552i
$415$	12.1448	−	33.2830i	0.596164	−	1.63380i
$416$	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	$-0.180822\pi$
$420$	1.48010	−	0.688712i	0.0722215	−	0.0336057i
$421$	22.6650	−	22.6650i	1.10463	−	1.10463i	0.110782	−	0.993845i	$-0.464664\pi$
$421$	22.6650	−	22.6650i	1.10463	−	1.10463i	0.993845	−	0.110782i	$-0.0353356\pi$
$422$		−	24.6681i		−	1.20083i
$423$	9.26908	+	9.26908i	0.450678	+	0.450678i
$424$	−0.413793	+	0.413793i	−0.0200956	+	0.0200956i
$425$	−8.22994	+	9.77561i	−0.399211	+	0.474187i
$426$	2.90360	+	2.90360i	0.140680	+	0.140680i
$427$			11.1462i			0.539401i
$428$	0.609066	−	0.609066i	0.0294403	−	0.0294403i
$429$	−0.538268	+	0.538268i	−0.0259878	+	0.0259878i
$430$	8.53948	+	18.3521i	0.411810	+	0.885015i
$431$	17.9692	−	17.9692i	0.865547	−	0.865547i	−0.126428	−	0.991976i	$-0.540351\pi$
$431$	17.9692	−	17.9692i	0.865547	−	0.865547i	0.991976	+	0.126428i	$0.0403514\pi$
$432$	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
$438$	−3.72083			−0.177788
$439$	24.7771	+	24.7771i	1.18255	+	1.18255i	0.979083	+	0.203463i	$0.0652198\pi$
$439$	24.7771	+	24.7771i	1.18255	+	1.18255i	0.203463	+	0.979083i	$0.434780\pi$
$440$	−0.469177	−	1.00830i	−0.0223671	−	0.0480688i
$441$	6.46700			0.307952
$442$	3.91170			0.186060
$443$	11.6985	−	11.6985i	0.555811	−	0.555811i	−0.372301	−	0.928112i	$-0.621431\pi$
$443$	11.6985	−	11.6985i	0.555811	−	0.555811i	0.928112	+	0.372301i	$0.121431\pi$
$444$	−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	$-0.934126\pi$
$449$	−16.3835	+	16.3835i	−0.773187	+	0.773187i	0.205475	+	0.978662i	$0.434126\pi$
$450$	−3.22019	+	3.82497i	−0.151801	+	0.180311i
$451$	−1.34466			−0.0633177
$452$	12.8460			0.604226
$453$	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
$457$	−36.6470			−1.71427			−0.857137	−	0.515089i	$-0.827759\pi$
$457$	−36.6470			−1.71427			−0.857137	+	0.515089i	$0.827759\pi$
$458$	27.5614			1.28786
$459$	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	0.584283	−	0.811550i	$-0.301376\pi$
$461$	−4.87965	−	4.87965i	−0.227268	−	0.227268i	−0.811550	+	0.584283i	$0.801376\pi$
$462$			0.363102i			0.0168931i
$463$			3.03199i			0.140908i	0.997515	+	0.0704542i	$0.0224449\pi$
$463$			3.03199i			0.140908i	−0.997515	+	0.0704542i	$0.977555\pi$
$464$	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
$467$	−7.88298			−0.364781			−0.182390	−	0.983226i	$-0.558384\pi$
$467$	−7.88298			−0.364781			−0.182390	+	0.983226i	$0.558384\pi$
$468$	1.53056			0.0707500
$469$	−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
$473$	−4.50218			−0.207011
$474$	−1.17086			−0.0537795
$475$	−1.42986	−	16.6565i	−0.0656066	−	0.764253i
$476$	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	−0.0190898	+	0.999818i	$0.506077\pi$
$479$	−22.2999	+	22.2999i	−1.01891	+	1.01891i	−0.999818	+	0.0190898i	$0.993923\pi$
$480$	−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
$483$	3.75160			0.170704
$484$	−10.7526			−0.488756
$485$	−2.96178	−	6.36512i	−0.134488	−	0.289025i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	12.8810			0.583695			0.291847	−	0.956465i	$-0.405730\pi$
$487$	12.8810			0.583695			0.291847	+	0.956465i	$0.405730\pi$
$488$	−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
$495$	−0.469177	−	1.00830i	−0.0210879	−	0.0453197i
$496$	5.92380	−	5.92380i	0.265986	−	0.265986i
$497$	2.11983	−	2.11983i	0.0950875	−	0.0950875i
$498$		−	15.8446i		−	0.710012i
$499$	−17.8190	−	17.8190i	−0.797689	−	0.797689i	0.185042	−	0.982731i	$-0.440758\pi$
$499$	−17.8190	−	17.8190i	−0.797689	−	0.797689i	−0.982731	+	0.185042i	$0.940758\pi$
$500$	−10.7923	−	2.92012i	−0.482645	−	0.130592i
$501$	−8.05588	+	8.05588i	−0.359910	+	0.359910i
$502$	−8.72803	−	8.72803i	−0.389551	−	0.389551i
$503$			17.9635i			0.800955i	0.916307	+	0.400477i	$0.131156\pi$
$503$			17.9635i			0.800955i	−0.916307	+	0.400477i	$0.868844\pi$
$504$	0.516238	−	0.516238i	0.0229951	−	0.0229951i
$505$	8.46599	−	3.93935i	0.376731	−	0.175299i
$506$		−	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	$-0.559351\pi$
$509$	−8.36462			−0.370755			−0.185378	+	0.982667i	$0.559351\pi$
$510$	−1.95896	+	5.36855i	−0.0867441	+	0.237723i
$511$			2.71647i			0.120170i
$512$			1.00000i			0.0441942i
$513$	−3.34355			−0.147622
$514$		−	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
$518$	−0.366209	+	4.42572i	−0.0160903	+	0.194455i
$519$		−	19.0028i		−	0.834131i
$520$	1.44385	+	3.10295i	0.0633170	+	0.136074i
$521$			16.5234i			0.723904i	0.932197	+	0.361952i	$0.117890\pi$
$521$			16.5234i			0.723904i	−0.932197	+	0.361952i	$0.882110\pi$
$522$	7.56116	+	7.56116i	0.330943	+	0.330943i
$523$			14.2767i			0.624278i	0.950036	+	0.312139i	$0.101046\pi$
$523$			14.2767i			0.624278i	−0.950036	+	0.312139i	$0.898954\pi$
$524$	−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
$532$			2.44103i			0.105832i
$533$	4.13808			0.179240
$534$			8.82830i			0.382038i
$535$	1.80934	+	0.660220i	0.0782247	+	0.0285438i
$536$	9.29726	−	9.29726i	0.401580	−	0.401580i
$537$	−10.7933			−0.465764
$538$	16.4147			0.707689
$539$	−3.21637			−0.138539
$540$	−0.766495	+	2.10059i	−0.0329847	+	0.0903951i
$541$	−2.99943	−	2.99943i	−0.128955	−	0.128955i	0.639683	−	0.768639i	$-0.279066\pi$
$541$	−2.99943	−	2.99943i	−0.128955	−	0.128955i	−0.768639	+	0.639683i	$0.779066\pi$
$542$			3.57932i			0.153745i
$543$	−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
$547$			20.8842i			0.892944i	0.894798	+	0.446472i	$0.147320\pi$
$547$			20.8842i			0.892944i	−0.894798	+	0.446472i	$0.852680\pi$
$548$	10.5042	−	10.5042i	0.448715	−	0.448715i
$549$	−10.7956	−	10.7956i	−0.460744	−	0.460744i
$550$	1.60157	−	1.90236i	0.0682910	−	0.0811168i
$551$	−35.7529			−1.52313
$552$	−3.63359	+	3.63359i	−0.154656	+	0.154656i
$553$			0.854813i			0.0363504i
$554$	−11.1501			−0.473723
$555$	−4.70170	−	12.7630i	−0.199576	−	0.541759i
$556$	0.111253			0.00471819
$557$			10.1584i			0.430426i	0.976567	+	0.215213i	$0.0690446\pi$
$557$			10.1584i			0.430426i	−0.976567	+	0.215213i	$0.930955\pi$
$558$	5.92380	−	5.92380i	0.250774	−	0.250774i
$559$	13.8551			0.586007
$560$	1.53358	+	0.559596i	0.0648056	+	0.0236472i
$561$	−0.898803	−	0.898803i	−0.0379475	−	0.0379475i
$562$	12.0088	−	12.0088i	0.506559	−	0.506559i
$563$			13.4772i			0.567996i	0.958825	+	0.283998i	$0.0916610\pi$
$563$			13.4772i			0.567996i	−0.958825	+	0.283998i	$0.908339\pi$
$564$			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
$568$			4.10631i			0.172297i
$569$	−0.956429	−	0.956429i	−0.0400956	−	0.0400956i	0.686775	−	0.726870i	$-0.259026\pi$
$569$	−0.956429	−	0.956429i	−0.0400956	−	0.0400956i	−0.726870	+	0.686775i	$0.759026\pi$
$570$	−3.15414	−	6.77851i	−0.132112	−	0.283920i
$571$	−1.80272			−0.0754415			−0.0377208	−	0.999288i	$-0.512010\pi$
$571$	−1.80272			−0.0754415			−0.0377208	+	0.999288i	$0.512010\pi$
$572$	−0.761226			−0.0318285
$573$	−18.8570			−0.787763
$574$	1.39572	−	1.39572i	0.0582564	−	0.0582564i
$575$	−19.6553	−	16.5475i	−0.819682	−	0.690078i
$576$			1.00000i			0.0416667i
$577$	−21.8641			−0.910216			−0.455108	−	0.890436i	$-0.650399\pi$
$577$	−21.8641			−0.910216			−0.455108	+	0.890436i	$0.650399\pi$
$578$		−	10.4682i		−	0.435421i
$579$	−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
$587$		−	13.4925i		−	0.556896i	−0.960451	−	0.278448i	$-0.910180\pi$
$587$		−	13.4925i		−	0.556896i	0.960451	−	0.278448i	$-0.0898200\pi$
$588$	4.57286	+	4.57286i	0.188581	+	0.188581i
$589$			28.0107i			1.15416i
$590$	−6.40970	+	17.5659i	−0.263883	+	0.723176i
$591$			7.57983i			0.311793i
$592$	−3.93182	−	4.64120i	−0.161597	−	0.190752i
$593$	−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
$597$	−18.6140			−0.761822
$598$			7.86504i			0.321625i
$599$			1.58656i			0.0648249i	0.999475	+	0.0324125i	$0.0103190\pi$
$599$			1.58656i			0.0648249i	−0.999475	+	0.0324125i	$0.989681\pi$
$600$	−4.98168	+	0.427648i	−0.203376	+	0.0174586i
$601$	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
$605$	−10.1435	−	21.7992i	−0.412392	−	0.886264i
$606$	2.95282	−	2.95282i	0.119950	−	0.119950i
$607$			29.3879i			1.19282i	0.802680	+	0.596409i	$0.203407\pi$
$607$			29.3879i			1.19282i	−0.802680	+	0.596409i	$0.796593\pi$
$608$	−2.36425	−	2.36425i	−0.0958830	−	0.0958830i
$609$	5.52018	−	5.52018i	0.223689	−	0.223689i
$610$	11.7023	−	32.0702i	0.473811	−	1.29849i
$611$	14.1869	+	14.1869i	0.573939	+	0.573939i
$612$			2.55573i			0.103309i
$613$	−11.9588	+	11.9588i	−0.483011	+	0.483011i	−0.906092	−	0.423081i	$-0.860949\pi$
$613$	−11.9588	+	11.9588i	−0.483011	+	0.483011i	0.423081	+	0.906092i	$0.360949\pi$
$614$	−6.16080	+	6.16080i	−0.248630	+	0.248630i
$615$	−2.07233	+	5.67925i	−0.0835644	+	0.229009i
$616$	−0.256752	+	0.256752i	−0.0103448	+	0.0103448i
$617$	−19.8923	−	19.8923i	−0.800835	−	0.800835i	0.182391	−	0.983226i	$-0.441616\pi$
$617$	−19.8923	−	19.8923i	−0.800835	−	0.800835i	−0.983226	+	0.182391i	$0.941616\pi$
$618$	11.0772	+	11.0772i	0.445591	+	0.445591i
$619$	25.0352			1.00625			0.503125	−	0.864213i	$-0.332183\pi$
$619$	25.0352			1.00625			0.503125	+	0.864213i	$0.332183\pi$
$620$	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
$623$	6.44528			0.258225
$624$	1.08227	+	1.08227i	0.0433254	+	0.0433254i
$625$	−4.26081	−	24.6342i	−0.170432	−	0.985369i
$626$	−3.47014			−0.138695
$627$	1.66292			0.0664108
$628$	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	−0.935724	−	0.352733i	$-0.885252\pi$
$631$	−14.6446	+	14.6446i	−0.582990	+	0.582990i	0.352733	+	0.935724i	$0.385252\pi$
$632$	−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
$635$	1.49763	+	0.546478i	0.0594317	+	0.0216863i
$636$	−0.585191			−0.0232043
$637$	9.89811			0.392177
$638$	−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	$0.379134\pi$
$642$	0.861349			0.0339947
$643$	−33.3318			−1.31448			−0.657238	−	0.753683i	$-0.728275\pi$
$643$	−33.3318			−1.31448			−0.657238	+	0.753683i	$0.728275\pi$
$644$	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
$647$		−	20.5310i		−	0.807156i	−0.914945	−	0.403578i	$-0.867766\pi$
$647$		−	20.5310i		−	0.807156i	0.914945	−	0.403578i	$-0.132234\pi$
$648$			1.00000i			0.0392837i
$649$	−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
$652$	−12.0896			−0.473465
$653$	26.4235			1.03403			0.517016	−	0.855976i	$-0.327043\pi$
$653$	26.4235			1.03403			0.517016	+	0.855976i	$0.327043\pi$
$654$	−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
$658$	9.57011			0.373082
$659$	−39.4006			−1.53483			−0.767414	−	0.641152i	$-0.778457\pi$
$659$	−39.4006			−1.53483			−0.767414	+	0.641152i	$0.778457\pi$
$660$	0.381218	−	1.04473i	0.0148389	−	0.0406662i
$661$	7.90042	−	7.90042i	0.307291	−	0.307291i	−0.536567	−	0.843858i	$-0.680279\pi$
$661$	7.90042	−	7.90042i	0.307291	−	0.307291i	0.843858	+	0.536567i	$0.180279\pi$
$662$	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
$668$	−11.3927			−0.440798
$669$	15.6137			0.603659
$670$	27.6192	+	10.0781i	1.06702	+	0.389351i
$671$	5.36920	+	5.36920i	0.207276	+	0.207276i
$672$	0.730071			0.0281631
$673$	−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	0.173690	−	0.984800i	$-0.444431\pi$
$677$	−21.1045	−	21.1045i	−0.811110	−	0.811110i	−0.984800	+	0.173690i	$0.944431\pi$
$678$	9.08351	+	9.08351i	0.348850	+	0.348850i
$679$	−1.62081	+	1.62081i	−0.0622008	+	0.0622008i
$680$	−5.18133	+	2.41095i	−0.198695	+	0.0924556i
$681$	−20.4367	+	20.4367i	−0.783137	+	0.783137i
$682$	−2.94621	+	2.94621i	−0.112816	+	0.112816i
$683$			35.4086i			1.35487i	0.735581	+	0.677437i	$0.236909\pi$
$683$			35.4086i			1.35487i	−0.735581	+	0.677437i	$0.763091\pi$
$684$	−2.36425	−	2.36425i	−0.0903993	−	0.0903993i
$685$	31.2045	+	11.3864i	1.19226	+	0.435051i
$686$	6.95218	−	6.95218i	0.265435	−	0.265435i
$687$	19.4888	+	19.4888i	0.743546	+	0.743546i
$688$			9.05230i			0.345116i
$689$	−0.633334	+	0.633334i	−0.0241281	+	0.0241281i
$690$	−10.7943	−	3.93877i	−0.410930	−	0.149946i
$691$			22.4704i			0.854814i	0.904059	+	0.427407i	$0.140573\pi$
$691$			22.4704i			0.854814i	−0.904059	+	0.427407i	$0.859427\pi$
$692$	13.4370	−	13.4370i	0.510799	−	0.510799i
$693$	−0.256752	+	0.256752i	−0.00975321	+	0.00975321i
$694$	−2.52563			−0.0958715
$695$	0.104951	+	0.225548i	0.00398100	+	0.00855551i
$696$			10.6931i			0.405321i
$697$			6.90979i			0.261727i
$698$	−5.42724			−0.205424
$699$			10.6221i			0.401763i
$700$	0.312213	+	3.63698i	0.0118005	+	0.137465i
$701$	15.2902	+	15.2902i	0.577504	+	0.577504i	0.934215	−	0.356711i	$-0.116102\pi$
$701$	15.2902	+	15.2902i	0.577504	+	0.577504i	−0.356711	+	0.934215i	$0.616102\pi$
$702$	1.08227	+	1.08227i	0.0408475	+	0.0408475i
$703$	20.2688	+	1.67715i	0.764451	+	0.0632549i
$704$		−	0.497352i		−	0.0187447i
$705$	−26.5753	+	12.3658i	−1.00088	+	0.465725i
$706$			16.8913i			0.635713i
$707$	−2.15577	−	2.15577i	−0.0810760	−	0.0810760i
$708$			8.36235i			0.314276i
$709$	−11.5740	+	11.5740i	−0.434672	+	0.434672i	−0.890214	−	0.455542i	$-0.849445\pi$
$709$	−11.5740	+	11.5740i	−0.434672	+	0.434672i	0.455542	+	0.890214i	$0.349445\pi$
$710$	−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
$717$			9.52971i			0.355893i
$718$	10.2084			0.380976
$719$		−	33.1940i		−	1.23793i	−0.785420	−	0.618963i	$-0.787553\pi$
$719$		−	33.1940i		−	1.23793i	0.785420	−	0.618963i	$-0.212447\pi$
$720$	−2.02734	+	0.943349i	−0.0755544	+	0.0351565i
$721$	8.08716	−	8.08716i	0.301182	−	0.301182i
$722$	−7.82065			−0.291054
$723$	12.6103			0.468982
$724$	−9.48047			−0.352339
$725$	−53.2695	+	4.57288i	−1.97838	+	0.169832i
$726$	−7.60327	−	7.60327i	−0.282184	−	0.282184i
$727$		−	25.8130i		−	0.957352i	−0.877992	−	0.478676i	$-0.841117\pi$
$727$		−	25.8130i		−	0.957352i	0.877992	−	0.478676i	$-0.158883\pi$
$728$	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
$732$		−	15.2672i		−	0.564294i
$733$	29.0185	−	29.0185i	1.07182	−	1.07182i	0.0746110	−	0.997213i	$-0.476228\pi$
$733$	29.0185	−	29.0185i	1.07182	−	1.07182i	0.997213	−	0.0746110i	$-0.0237715\pi$
$734$	−13.8736	−	13.8736i	−0.512083	−	0.512083i
$735$	−4.95692	+	13.5845i	−0.182839	+	0.501073i
$736$	−5.13868			−0.189414
$737$	−4.62401	+	4.62401i	−0.170328	+	0.170328i
$738$			2.70364i			0.0995225i
$739$	33.6130			1.23647			0.618236	−	0.785992i	$-0.287847\pi$
$739$	33.6130			1.23647			0.618236	+	0.785992i	$0.287847\pi$
$740$	5.70020	−	12.3494i	0.209543	−	0.453973i
$741$	−5.11750			−0.187996
$742$			0.427231i			0.0156842i
$743$	15.7302	−	15.7302i	0.577084	−	0.577084i	−0.357015	−	0.934099i	$-0.616205\pi$
$743$	15.7302	−	15.7302i	0.577084	−	0.577084i	0.934099	+	0.357015i	$0.116205\pi$
$744$	8.37752			0.307135
$745$	32.9517	−	15.3329i	1.20726	−	0.561754i
$746$	6.36168	+	6.36168i	0.232918	+	0.232918i
$747$	11.2038	−	11.2038i	0.409926	−	0.409926i
$748$		−	1.27110i		−	0.0464760i
$749$		−	0.628846i		−	0.0229775i
$750$	−5.56645	−	9.69612i	−0.203258	−	0.354052i
$751$			12.7266i			0.464401i	0.972668	+	0.232201i	$0.0745926\pi$
$751$			12.7266i			0.464401i	−0.972668	+	0.232201i	$0.925407\pi$
$752$	−9.26908	+	9.26908i	−0.338009	+	0.338009i
$753$		−	12.3433i		−	0.449815i
$754$	11.5728	+	11.5728i	0.421456	+	0.421456i
$755$	−31.8840	+	14.8361i	−1.16038	+	0.539940i
$756$	0.730071			0.0265524
$757$	49.4794			1.79836			0.899181	−	0.437578i	$-0.144164\pi$
$757$	49.4794			1.79836			0.899181	+	0.437578i	$0.144164\pi$
$758$	10.4081			0.378038
$759$	1.80718	−	1.80718i	0.0655963	−	0.0655963i
$760$	2.56282	−	7.02344i	0.0929632	−	0.254767i
$761$			10.2526i			0.371657i	0.982582	+	0.185828i	$0.0594968\pi$
$761$			10.2526i			0.371657i	−0.982582	+	0.185828i	$0.940503\pi$
$762$	0.712957			0.0258277
$763$			0.263980i			0.00955671i
$764$	−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	$-0.0973959\pi$
$769$	18.0896	+	18.0896i	0.652327	+	0.652327i	−0.301226	+	0.953553i	$0.597396\pi$
$770$	−0.762730	−	0.278316i	−0.0274869	−	0.0100298i
$771$	4.64860	−	4.64860i	0.167415	−	0.167415i
$772$		−	8.67065i		−	0.312064i
$773$	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
$775$	3.58263	+	41.7341i	0.128692	+	1.49913i
$776$		−	3.13965i		−	0.112707i
$777$	−3.38841	+	2.87051i	−0.121558	+	0.102979i
$778$	−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
$782$	−13.1331			−0.469638
$783$			10.6931i			0.382140i
$784$			6.46700i			0.230964i
$785$	10.7084	+	3.90744i	0.382199	+	0.139462i
$786$	−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
$790$	0.897461	−	2.45951i	0.0319302	−	0.0875053i
$791$	6.63161	−	6.63161i	0.235793	−	0.235793i
$792$		−	0.497352i		−	0.0176726i
$793$	−16.5232	−	16.5232i	−0.586757	−	0.586757i
$794$	5.88311	−	5.88311i	0.208784	−	0.208784i
$795$	−0.552040	−	1.18638i	−0.0195788	−	0.0420766i
$796$	−13.1621	−	13.1621i	−0.466519	−	0.466519i
$797$		−	13.0313i		−	0.461591i	−0.973002	−	0.230796i	$-0.925867\pi$
$797$		−	13.0313i		−	0.461591i	0.973002	−	0.230796i	$-0.0741329\pi$
$798$	−1.72607	+	1.72607i	−0.0611022	+	0.0611022i
$799$	−23.6893	+	23.6893i	−0.838067	+	0.838067i
$800$	−3.82497	−	3.22019i	−0.135233	−	0.113851i
$801$	−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
$808$	4.17592			0.146908
$809$	−4.63922	−	4.63922i	−0.163106	−	0.163106i	0.620835	−	0.783941i	$-0.286794\pi$
$809$	−4.63922	−	4.63922i	−0.163106	−	0.163106i	−0.783941	+	0.620835i	$0.786794\pi$
$810$	−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	$0.0673805\pi$
$812$	7.80672			0.273962
$813$	−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
$820$	−5.48119	+	2.55048i	−0.191412	+	0.0890666i
$821$	−17.4399			−0.608658			−0.304329	−	0.952567i	$-0.598432\pi$
$821$	−17.4399			−0.608658			−0.304329	+	0.952567i	$0.598432\pi$
$822$	14.8551			0.518132
$823$	−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
$827$	−18.6866			−0.649797			−0.324899	−	0.945749i	$-0.605330\pi$
$827$	−18.6866			−0.649797			−0.324899	+	0.945749i	$0.605330\pi$
$828$	−5.13868			−0.178581
$829$	0.406665	+	0.406665i	0.0141241	+	0.0141241i	0.714134	−	0.700009i	$-0.246821\pi$
$829$	0.406665	+	0.406665i	0.0141241	+	0.0141241i	−0.700009	+	0.714134i	$0.746821\pi$
$830$	33.2830	+	12.1448i	1.15527	+	0.421551i
$831$	−7.88433	−	7.88433i	−0.273504	−	0.273504i
$832$			1.53056i			0.0530625i
$833$			16.5279i			0.572658i
$834$	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
$837$	8.37752			0.289569
$838$	22.0253			0.760853
$839$	33.2804			1.14897			0.574483	−	0.818516i	$-0.305203\pi$
$839$	33.2804			1.14897			0.574483	+	0.818516i	$0.305203\pi$
$840$	0.688712	+	1.48010i	0.0237628	+	0.0510683i
$841$			85.3422i			2.94283i
$842$	22.6650	+	22.6650i	0.781089	+	0.781089i
$843$	16.9830			0.584924
$844$	24.6681			0.849112
$845$	−10.0536	−	21.6061i	−0.345856	−	0.743273i
$846$	−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
$853$	13.7096			0.469409			0.234705	−	0.972067i	$-0.424588\pi$
$853$	13.7096			0.469409			0.234705	+	0.972067i	$0.424588\pi$
$854$	−11.1462			−0.381414
$855$	2.56282	−	7.02344i	0.0876465	−	0.240197i
$856$	0.609066	+	0.609066i	0.0208174	+	0.0208174i
$857$	11.0849			0.378651			0.189326	−	0.981914i	$-0.439370\pi$
$857$	11.0849			0.378651			0.189326	+	0.981914i	$0.439370\pi$
$858$	−0.538268	−	0.538268i	−0.0183762	−	0.0183762i
$859$	−15.5947	+	15.5947i	−0.532084	+	0.532084i	−0.921192	−	0.389108i	$-0.872783\pi$
$859$	−15.5947	+	15.5947i	−0.532084	+	0.532084i	0.389108	+	0.921192i	$0.372783\pi$
$860$	−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
$865$	39.9172	+	14.5656i	1.35722	+	0.495244i
$866$	18.0984	−	18.0984i	0.615010	−	0.615010i
$867$	7.40215	−	7.40215i	0.251390	−	0.251390i
$868$		−	6.11618i		−	0.207597i
$869$	0.411770	+	0.411770i	0.0139684	+	0.0139684i
$870$	−21.6785	+	10.0873i	−0.734970	+	0.341992i
$871$	14.2300	−	14.2300i	0.482165	−	0.482165i
$872$	−0.255676	−	0.255676i	−0.00865830	−	0.00865830i
$873$		−	3.13965i		−	0.106261i
$874$	12.1491	−	12.1491i	0.410950	−	0.410950i
$875$	−7.07885	+	4.06390i	−0.239309	+	0.137385i
$876$		−	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
$880$	1.00830	−	0.469177i	0.0339898	−	0.0158159i
$881$			23.3650i			0.787188i	0.919284	+	0.393594i	$0.128768\pi$
$881$			23.3650i			0.787188i	−0.919284	+	0.393594i	$0.871232\pi$
$882$			6.46700i			0.217755i
$883$	12.2410			0.411943			0.205972	−	0.978558i	$-0.433965\pi$
$883$	12.2410			0.411943			0.205972	+	0.978558i	$0.433965\pi$
$884$			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	0.534528	−	0.845151i	$-0.320489\pi$
$887$	−9.25112	−	9.25112i	−0.310622	−	0.310622i	−0.845151	+	0.534528i	$0.820489\pi$
$888$	0.501607	−	6.06205i	0.0168328	−	0.203429i
$889$		−	0.520509i		−	0.0174573i
$890$	−18.5446	−	6.76685i	−0.621618	−	0.226825i
$891$		−	0.497352i		−	0.0166619i
$892$	11.0405	+	11.0405i	0.369664	+	0.369664i
$893$		−	43.8288i		−	1.46668i
$894$	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
$902$		−	1.34466i		−	0.0447724i
$903$	6.60883			0.219928
$904$			12.8460i			0.427253i
$905$	−8.94339	−	19.2201i	−0.297288	−	0.638898i
$906$	−11.1207	+	11.1207i	−0.369460	+	0.369460i
$907$	−28.2255			−0.937213			−0.468606	−	0.883407i	$-0.655244\pi$
$907$	−28.2255			−0.937213			−0.468606	+	0.883407i	$0.655244\pi$
$908$	−28.9019			−0.959143
$909$	4.17592			0.138506
$910$	2.34723	+	0.856493i	0.0778100	+	0.0283925i
$911$	−11.7600	−	11.7600i	−0.389626	−	0.389626i	0.484928	−	0.874554i	$-0.338846\pi$
$911$	−11.7600	−	11.7600i	−0.389626	−	0.389626i	−0.874554	+	0.484928i	$0.838846\pi$
$912$		−	3.34355i		−	0.110716i
$913$	−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
$917$			15.7155i			0.518971i
$918$	−1.80718	+	1.80718i	−0.0596457	+	0.0596457i
$919$	−16.8392	−	16.8392i	−0.555476	−	0.555476i	0.372540	−	0.928016i	$-0.378487\pi$
$919$	−16.8392	−	16.8392i	−0.555476	−	0.555476i	−0.928016	+	0.372540i	$0.878487\pi$
$920$	−4.84756	−	10.4178i	−0.159819	−	0.343466i
$921$	−8.71269			−0.287093
$922$	4.87965	−	4.87965i	0.160703	−	0.160703i
$923$			6.28494i			0.206871i
$924$	−0.363102			−0.0119452
$925$	30.4137	−	0.0935743i	0.999995	−	0.00307671i
$926$	−3.03199			−0.0996373
$927$			15.6656i			0.514524i
$928$	−7.56116	+	7.56116i	−0.248207	+	0.248207i
$929$	−24.9345			−0.818075			−0.409038	−	0.912518i	$-0.634135\pi$
$929$	−24.9345			−0.818075			−0.409038	+	0.912518i	$0.634135\pi$
$930$	7.90292	+	16.9840i	0.259147	+	0.556929i
$931$	−15.2896	−	15.2896i	−0.501096	−	0.501096i
$932$	−7.51093	+	7.51093i	−0.246029	+	0.246029i
$933$		−	17.2183i		−	0.563703i
$934$		−	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	$0.277506\pi$
$938$		−	9.59920i		−	0.313425i
$939$	−2.45376	−	2.45376i	−0.0800755	−	0.0800755i
$940$	−27.5355	−	10.0476i	−0.898110	−	0.327715i
$941$	21.1387			0.689100			0.344550	−	0.938768i	$-0.388031\pi$
$941$	21.1387			0.689100			0.344550	+	0.938768i	$0.388031\pi$
$942$	5.09780			0.166095
$943$	−13.8931			−0.452423
$944$	−5.91307	+	5.91307i	−0.192454	+	0.192454i
$945$	0.688712	+	1.48010i	0.0224038	+	0.0481476i
$946$		−	4.50218i		−	0.146379i
$947$	−1.08920			−0.0353942			−0.0176971	−	0.999843i	$-0.505633\pi$
$947$	−1.08920			−0.0353942			−0.0176971	+	0.999843i	$0.505633\pi$
$948$		−	1.17086i		−	0.0380279i
$949$	−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	−0.601120	−	0.799159i	$-0.705279\pi$
$953$	6.11358	−	6.11358i	0.198038	−	0.198038i	0.799159	+	0.601120i	$0.205279\pi$
$954$	−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
$957$		−	5.31823i		−	0.171914i
$958$	−22.2999	−	22.2999i	−0.720476	−	0.720476i
$959$		−	10.8453i		−	0.350213i
$960$	−2.10059	−	0.766495i	−0.0677963	−	0.0247385i
$961$		−	39.1828i		−	1.26396i
$962$	−6.01788	−	7.10363i	−0.194024	−	0.229030i
$963$	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
$967$	−20.1527			−0.648066			−0.324033	−	0.946046i	$-0.605039\pi$
$967$	−20.1527			−0.648066			−0.324033	+	0.946046i	$0.605039\pi$
$968$		−	10.7526i		−	0.345603i
$969$		−	8.54523i		−	0.274512i
$970$	6.36512	−	2.96178i	0.204372	−	0.0950971i
$971$	−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
$975$	−7.62474	+	0.654539i	−0.244187	+	0.0209620i
$976$	10.7956	−	10.7956i	0.345558	−	0.345558i
$977$			6.24061i			0.199655i	0.995005	+	0.0998273i	$0.0318290\pi$
$977$			6.24061i			0.199655i	−0.995005	+	0.0998273i	$0.968171\pi$
$978$	−8.54863	−	8.54863i	−0.273355	−	0.273355i
$979$	3.10474	−	3.10474i	0.0992281	−	0.0992281i
$980$	−13.1108	+	6.10063i	−0.418808	+	0.194878i
$981$	−0.255676	−	0.255676i	−0.00816312	−	0.00816312i
$982$			0.897235i			0.0286319i
$983$	3.22372	−	3.22372i	0.102821	−	0.102821i	−0.653825	−	0.756646i	$-0.726837\pi$
$983$	3.22372	−	3.22372i	0.102821	−	0.102821i	0.756646	+	0.653825i	$0.226837\pi$
$984$	−1.91176	+	1.91176i	−0.0609448	+	0.0609448i
$985$	−15.9221	−	5.80991i	−0.507322	−	0.185119i
$986$	−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	−0.623999	−	0.781425i	$-0.714493\pi$
$991$	4.95581	−	4.95581i	0.157427	−	0.157427i	0.781425	+	0.623999i	$0.214493\pi$
$992$	5.92380	+	5.92380i	0.188081	+	0.188081i
$993$	17.8612			0.566807
$994$	2.11983	+	2.11983i	0.0672370	+	0.0672370i
$995$	14.2676	−	39.1005i	0.452312	−	1.23957i
$996$	15.8446			0.502054
$997$	28.8366			0.913265			0.456633	−	0.889655i	$-0.349055\pi$
$997$	28.8366			0.913265			0.456633	+	0.889655i	$0.349055\pi$
$998$	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.l.a.43.5	✓	36
5.2	odd	4		1110.2.o.a.487.14	yes	36
37.31	odd	4		1110.2.o.a.253.14	yes	36
185.142	even	4	inner	1110.2.l.a.697.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.5	✓	36	1.1	even	1	trivial
1110.2.l.a.697.5	yes	36	185.142	even	4	inner
1110.2.o.a.253.14	yes	36	37.31	odd	4
1110.2.o.a.487.14	yes	36	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.943349 - 2.02734i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.943349 - 2.02734i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.02734 - 0.943349i) q^{10} +0.497352i q^{11} +(0.707107 - 0.707107i) q^{12} -1.53056i q^{13} +(-0.516238 - 0.516238i) q^{14} +(2.10059 + 0.766495i) q^{15} +1.00000 q^{16} +2.55573 q^{17} +1.00000 q^{18} +(-2.36425 + 2.36425i) q^{19} +(0.943349 + 2.02734i) q^{20} -0.730071i q^{21} -0.497352 q^{22} +5.13868i 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} +1.00000i q^{32} +(-0.351681 - 0.351681i) q^{33} +2.55573i q^{34} +(1.53358 + 0.559596i) q^{35} +1.00000i q^{36} +(-3.93182 - 4.64120i) q^{37} +(-2.36425 - 2.36425i) q^{38} +(1.08227 + 1.08227i) q^{39} +(-2.02734 + 0.943349i) q^{40} +2.70364i q^{41} +0.730071 q^{42} +9.05230i q^{43} -0.497352i q^{44} +(-2.02734 + 0.943349i) q^{45} -5.13868 q^{46} +(-9.26908 + 9.26908i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.46700i q^{49} +(-3.82497 - 3.22019i) q^{50} +(-1.80718 + 1.80718i) q^{51} +1.53056i q^{52} +(-0.413793 - 0.413793i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(1.00830 - 0.469177i) q^{55} +(0.516238 + 0.516238i) q^{56} -3.34355i q^{57} +(-7.56116 + 7.56116i) q^{58} +(-5.91307 + 5.91307i) q^{59} +(-2.10059 - 0.766495i) 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} -2.55573 q^{68} +(-3.63359 - 3.63359i) q^{69} +(-0.559596 + 1.53358i) q^{70} -4.10631 q^{71} -1.00000 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} +(-0.943349 - 2.02734i) q^{80} -1.00000 q^{81} -2.70364 q^{82} +(11.2038 + 11.2038i) q^{83} +0.730071i q^{84} +(-2.41095 - 5.18133i) q^{85} -9.05230 q^{86} -10.6931 q^{87} +0.497352 q^{88} +(-6.24255 - 6.24255i) q^{89} +(-0.943349 - 2.02734i) q^{90} +(0.790132 + 0.790132i) q^{91} -5.13868i q^{92} +8.37752i q^{93} +(-9.26908 - 9.26908i) q^{94} +(7.02344 + 2.56282i) q^{95} +(-0.707107 - 0.707107i) q^{96} +3.13965 q^{97} -6.46700 q^{98} +0.497352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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