LMFDB - Embedded newform 690.2.i.f.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.838057 + 1.51580i) q^{3} -1.00000i q^{4} +(2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.59532 - 2.54066i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.838057 + 1.51580i) q^{3} -1.00000i q^{4} +(2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.59532 - 2.54066i) q^{9} +(1.62719 - 1.53370i) q^{10} -3.77229i q^{11} +(1.51580 + 0.838057i) q^{12} +(3.87255 - 3.87255i) q^{13} +3.38810 q^{14} +(-1.97334 + 3.33256i) q^{15} -1.00000 q^{16} +(-2.58226 + 2.58226i) q^{17} +(-2.92458 - 0.668456i) q^{18} +6.80541i q^{19} +(0.0661068 - 2.23509i) q^{20} +(-5.63926 + 1.62371i) q^{21} +(-2.66741 - 2.66741i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.66443 - 0.479239i) q^{24} +(4.99126 + 0.295509i) q^{25} -5.47661i q^{26} +(5.18811 - 0.288974i) q^{27} +(2.39575 - 2.39575i) q^{28} +6.48520 q^{29} +(0.961112 + 3.75183i) q^{30} -7.09492 q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.71805 + 3.16139i) q^{33} +3.65187i q^{34} +(5.19634 + 5.51309i) q^{35} +(-2.54066 + 1.59532i) q^{36} +(4.68887 + 4.68887i) q^{37} +(4.81215 + 4.81215i) q^{38} +(2.62461 + 9.11544i) q^{39} +(-1.53370 - 1.62719i) q^{40} -8.03681i q^{41} +(-2.83942 + 5.13569i) q^{42} +(-2.86760 + 2.86760i) q^{43} -3.77229 q^{44} +(-3.39773 - 5.78407i) q^{45} +1.00000 q^{46} +(3.40424 - 3.40424i) q^{47} +(0.838057 - 1.51580i) q^{48} +4.47922i q^{49} +(3.73831 - 3.32040i) q^{50} +(-1.75012 - 6.07829i) q^{51} +(-3.87255 - 3.87255i) q^{52} +(-1.15188 - 1.15188i) q^{53} +(3.46421 - 3.87288i) q^{54} +(0.249374 - 8.43140i) q^{55} -3.38810i q^{56} +(-10.3157 - 5.70332i) q^{57} +(4.58573 - 4.58573i) q^{58} +0.993207 q^{59} +(3.33256 + 1.97334i) q^{60} -11.6640 q^{61} +(-5.01686 + 5.01686i) q^{62} +(2.26480 - 9.90877i) q^{63} +1.00000i q^{64} +(8.91150 - 8.39950i) q^{65} +(6.27871 - 1.80783i) q^{66} +(1.09345 + 1.09345i) q^{67} +(2.58226 + 2.58226i) q^{68} +(-1.66443 + 0.479239i) q^{69} +(7.57271 + 0.223976i) q^{70} +9.26157i q^{71} +(-0.668456 + 2.92458i) q^{72} +(2.14788 - 2.14788i) q^{73} +6.63106 q^{74} +(-4.63090 + 7.31812i) q^{75} +6.80541 q^{76} +(9.03745 - 9.03745i) q^{77} +(8.30147 + 4.58971i) q^{78} +4.59709i q^{79} +(-2.23509 - 0.0661068i) q^{80} +(-3.90991 + 8.10633i) q^{81} +(-5.68288 - 5.68288i) q^{82} +(-5.20343 - 5.20343i) q^{83} +(1.62371 + 5.63926i) q^{84} +(-5.94230 + 5.60089i) q^{85} +4.05539i q^{86} +(-5.43497 + 9.83029i) q^{87} +(-2.66741 + 2.66741i) q^{88} -9.56617 q^{89} +(-6.49251 - 1.68739i) q^{90} +18.5553 q^{91} +(0.707107 - 0.707107i) q^{92} +(5.94594 - 10.7545i) q^{93} -4.81432i q^{94} +(-0.449884 + 15.2107i) q^{95} +(-0.479239 - 1.66443i) q^{96} +(-10.5684 - 10.5684i) q^{97} +(3.16729 + 3.16729i) q^{98} +(-9.58410 + 6.01801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.838057	+	1.51580i	−0.483853	+	0.875150i
$3$	−0.838057	+	1.51580i	−0.483853	+	0.875150i
$4$		−	1.00000i		−	0.500000i
$5$	2.23509	+	0.0661068i	0.999563	+	0.0295639i
$5$	2.23509	+	0.0661068i	0.999563	+	0.0295639i
$6$	0.479239	+	1.66443i	0.195649	+	0.679501i
$7$	2.39575	+	2.39575i	0.905508	+	0.905508i	0.995906	−	0.0903979i	$-0.0288139\pi$
$7$	2.39575	+	2.39575i	0.905508	+	0.905508i	−0.0903979	+	0.995906i	$0.528814\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.59532	−	2.54066i	−0.531773	−	0.846887i
$10$	1.62719	−	1.53370i	0.514563	−	0.485000i
$11$		−	3.77229i		−	1.13739i	−0.822549	−	0.568694i	$-0.807449\pi$
$11$		−	3.77229i		−	1.13739i	0.822549	−	0.568694i	$-0.192551\pi$
$12$	1.51580	+	0.838057i	0.437575	+	0.241926i
$13$	3.87255	−	3.87255i	1.07405	−	1.07405i	0.0770227	−	0.997029i	$-0.475459\pi$
$13$	3.87255	−	3.87255i	1.07405	−	1.07405i	0.997029	−	0.0770227i	$-0.0245414\pi$
$14$	3.38810			0.905508
$15$	−1.97334	+	3.33256i	−0.509514	+	0.860462i
$16$	−1.00000			−0.250000
$17$	−2.58226	+	2.58226i	−0.626291	+	0.626291i	−0.947133	−	0.320842i	$-0.896034\pi$
$17$	−2.58226	+	2.58226i	−0.626291	+	0.626291i	0.320842	+	0.947133i	$0.396034\pi$
$18$	−2.92458	−	0.668456i	−0.689330	−	0.157557i
$19$			6.80541i			1.56127i	0.624988	+	0.780634i	$0.285104\pi$
$19$			6.80541i			1.56127i	−0.624988	+	0.780634i	$0.714896\pi$
$20$	0.0661068	−	2.23509i	0.0147819	−	0.499781i
$21$	−5.63926	+	1.62371i	−1.23059	+	0.354323i
$22$	−2.66741	−	2.66741i	−0.568694	−	0.568694i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	1.66443	−	0.479239i	0.339751	−	0.0978243i
$25$	4.99126	+	0.295509i	0.998252	+	0.0591019i
$26$		−	5.47661i		−	1.07405i
$27$	5.18811	−	0.288974i	0.998452	−	0.0556131i
$28$	2.39575	−	2.39575i	0.452754	−	0.452754i
$29$	6.48520			1.20427			0.602136	−	0.798394i	$-0.294317\pi$
$29$	6.48520			1.20427			0.602136	+	0.798394i	$0.294317\pi$
$30$	0.961112	+	3.75183i	0.175474	+	0.684988i
$31$	−7.09492			−1.27428			−0.637142	−	0.770746i	$-0.719884\pi$
$31$	−7.09492			−1.27428			−0.637142	+	0.770746i	$0.719884\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.71805	+	3.16139i	0.995384	+	0.550328i
$34$			3.65187i			0.626291i
$35$	5.19634	+	5.51309i	0.878342	+	0.931882i
$36$	−2.54066	+	1.59532i	−0.423443	+	0.265887i
$37$	4.68887	+	4.68887i	0.770846	+	0.770846i	0.978254	−	0.207409i	$-0.0665030\pi$
$37$	4.68887	+	4.68887i	0.770846	+	0.770846i	−0.207409	+	0.978254i	$0.566503\pi$
$38$	4.81215	+	4.81215i	0.780634	+	0.780634i
$39$	2.62461	+	9.11544i	0.420273	+	1.45964i
$40$	−1.53370	−	1.62719i	−0.242500	−	0.257282i
$41$		−	8.03681i		−	1.25514i	−0.778561	−	0.627569i	$-0.784050\pi$
$41$		−	8.03681i		−	1.25514i	0.778561	−	0.627569i	$-0.215950\pi$
$42$	−2.83942	+	5.13569i	−0.438132	+	0.792455i
$43$	−2.86760	+	2.86760i	−0.437304	+	0.437304i	−0.891104	−	0.453799i	$-0.850068\pi$
$43$	−2.86760	+	2.86760i	−0.437304	+	0.437304i	0.453799	+	0.891104i	$0.350068\pi$
$44$	−3.77229			−0.568694
$45$	−3.39773	−	5.78407i	−0.506504	−	0.862238i
$46$	1.00000			0.147442
$47$	3.40424	−	3.40424i	0.496559	−	0.496559i	−0.413806	−	0.910365i	$-0.635801\pi$
$47$	3.40424	−	3.40424i	0.496559	−	0.496559i	0.910365	+	0.413806i	$0.135801\pi$
$48$	0.838057	−	1.51580i	0.120963	−	0.218787i
$49$			4.47922i			0.639889i
$50$	3.73831	−	3.32040i	0.528677	−	0.469575i
$51$	−1.75012	−	6.07829i	−0.245066	−	0.851131i
$52$	−3.87255	−	3.87255i	−0.537026	−	0.537026i
$53$	−1.15188	−	1.15188i	−0.158223	−	0.158223i	0.623556	−	0.781779i	$-0.285687\pi$
$53$	−1.15188	−	1.15188i	−0.158223	−	0.158223i	−0.781779	+	0.623556i	$0.785687\pi$
$54$	3.46421	−	3.87288i	0.471420	−	0.527033i
$55$	0.249374	−	8.43140i	0.0336256	−	1.13689i
$56$		−	3.38810i		−	0.452754i
$57$	−10.3157	−	5.70332i	−1.36634	−	0.755424i
$58$	4.58573	−	4.58573i	0.602136	−	0.602136i
$59$	0.993207			0.129304			0.0646522	−	0.997908i	$-0.479406\pi$
$59$	0.993207			0.129304			0.0646522	+	0.997908i	$0.479406\pi$
$60$	3.33256	+	1.97334i	0.430231	+	0.254757i
$61$	−11.6640			−1.49343			−0.746713	−	0.665146i	$-0.768369\pi$
$61$	−11.6640			−1.49343			−0.746713	+	0.665146i	$0.768369\pi$
$62$	−5.01686	+	5.01686i	−0.637142	+	0.637142i
$63$	2.26480	−	9.90877i	0.285337	−	1.24839i
$64$			1.00000i			0.125000i
$65$	8.91150	−	8.39950i	1.10534	−	1.04183i
$66$	6.27871	−	1.80783i	0.772856	−	0.222528i
$67$	1.09345	+	1.09345i	0.133587	+	0.133587i	0.770738	−	0.637152i	$-0.219888\pi$
$67$	1.09345	+	1.09345i	0.133587	+	0.133587i	−0.637152	+	0.770738i	$0.719888\pi$
$68$	2.58226	+	2.58226i	0.313145	+	0.313145i
$69$	−1.66443	+	0.479239i	−0.200374	+	0.0576936i
$70$	7.57271	+	0.223976i	0.905112	+	0.0267703i
$71$			9.26157i			1.09915i	0.835446	+	0.549573i	$0.185210\pi$
$71$			9.26157i			1.09915i	−0.835446	+	0.549573i	$0.814790\pi$
$72$	−0.668456	+	2.92458i	−0.0787783	+	0.344665i
$73$	2.14788	−	2.14788i	0.251390	−	0.251390i	−0.570150	−	0.821540i	$-0.693115\pi$
$73$	2.14788	−	2.14788i	0.251390	−	0.251390i	0.821540	+	0.570150i	$0.193115\pi$
$74$	6.63106			0.770846
$75$	−4.63090	+	7.31812i	−0.534730	+	0.845023i
$76$	6.80541			0.780634
$77$	9.03745	−	9.03745i	1.02991	−	1.02991i
$78$	8.30147	+	4.58971i	0.939956	+	0.519683i
$79$			4.59709i			0.517213i	0.965983	+	0.258607i	$0.0832633\pi$
$79$			4.59709i			0.517213i	−0.965983	+	0.258607i	$0.916737\pi$
$80$	−2.23509	−	0.0661068i	−0.249891	−	0.00739096i
$81$	−3.90991	+	8.10633i	−0.434434	+	0.900704i
$82$	−5.68288	−	5.68288i	−0.627569	−	0.627569i
$83$	−5.20343	−	5.20343i	−0.571151	−	0.571151i	0.361299	−	0.932450i	$-0.382333\pi$
$83$	−5.20343	−	5.20343i	−0.571151	−	0.571151i	−0.932450	+	0.361299i	$0.882333\pi$
$84$	1.62371	+	5.63926i	0.177161	+	0.615293i
$85$	−5.94230	+	5.60089i	−0.644533	+	0.607502i
$86$			4.05539i			0.437304i
$87$	−5.43497	+	9.83029i	−0.582690	+	1.05392i
$88$	−2.66741	+	2.66741i	−0.284347	+	0.284347i
$89$	−9.56617			−1.01401			−0.507006	−	0.861943i	$-0.669248\pi$
$89$	−9.56617			−1.01401			−0.507006	+	0.861943i	$0.669248\pi$
$90$	−6.49251	−	1.68739i	−0.684371	−	0.177867i
$91$	18.5553			1.94512
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	5.94594	−	10.7545i	0.616566	−	1.11519i
$94$		−	4.81432i		−	0.496559i
$95$	−0.449884	+	15.2107i	−0.0461571	+	1.56059i
$96$	−0.479239	−	1.66443i	−0.0489121	−	0.169875i
$97$	−10.5684	−	10.5684i	−1.07306	−	1.07306i	−0.997111	−	0.0759519i	$-0.975800\pi$
$97$	−10.5684	−	10.5684i	−1.07306	−	1.07306i	−0.0759519	−	0.997111i	$-0.524200\pi$
$98$	3.16729	+	3.16729i	0.319944	+	0.319944i
$99$	−9.58410	+	6.01801i	−0.963238	+	0.604833i
$100$	0.295509	−	4.99126i	0.0295509	−	0.499126i
$101$			3.09956i			0.308418i	0.988038	+	0.154209i	$0.0492829\pi$
$101$			3.09956i			0.308418i	−0.988038	+	0.154209i	$0.950717\pi$
$102$	−5.53552	−	3.06048i	−0.548098	−	0.303032i
$103$	−4.89445	+	4.89445i	−0.482264	+	0.482264i	−0.905854	−	0.423590i	$-0.860770\pi$
$103$	−4.89445	+	4.89445i	−0.482264	+	0.482264i	0.423590	+	0.905854i	$0.360770\pi$
$104$	−5.47661			−0.537026
$105$	−12.7116	+	3.25635i	−1.24052	+	0.317787i
$106$	−1.62900			−0.158223
$107$	7.11744	−	7.11744i	0.688069	−	0.688069i	−0.273736	−	0.961805i	$-0.588259\pi$
$107$	7.11744	−	7.11744i	0.688069	−	0.688069i	0.961805	+	0.273736i	$0.0882594\pi$
$108$	−0.288974	−	5.18811i	−0.0278065	−	0.499226i
$109$			18.1228i			1.73584i	0.496700	+	0.867922i	$0.334545\pi$
$109$			18.1228i			1.73584i	−0.496700	+	0.867922i	$0.665455\pi$
$110$	−5.78557	−	6.13824i	−0.551632	−	0.585258i
$111$	−11.0369	+	3.17786i	−1.04758	+	0.301630i
$112$	−2.39575	−	2.39575i	−0.226377	−	0.226377i
$113$	−14.5951	−	14.5951i	−1.37299	−	1.37299i	−0.855978	−	0.517012i	$-0.827044\pi$
$113$	−14.5951	−	14.5951i	−1.37299	−	1.37299i	−0.517012	−	0.855978i	$-0.672956\pi$
$114$	−11.3271	+	3.26142i	−1.06088	+	0.305460i
$115$	1.53370	+	1.62719i	0.143019	+	0.151736i
$116$		−	6.48520i		−	0.602136i
$117$	−16.0168	−	3.66087i	−1.48075	−	0.338448i
$118$	0.702303	−	0.702303i	0.0646522	−	0.0646522i
$119$	−12.3729			−1.13422
$120$	3.75183	−	0.961112i	0.342494	−	0.0877372i
$121$	−3.23015			−0.293650
$122$	−8.24772	+	8.24772i	−0.746713	+	0.746713i
$123$	12.1822	+	6.73531i	1.09843	+	0.607302i
$124$			7.09492i			0.637142i
$125$	11.1364	+	0.990446i	0.996068	+	0.0885882i
$126$	−5.40511	−	8.60801i	−0.481525	−	0.766862i
$127$	4.72572	+	4.72572i	0.419339	+	0.419339i	0.884976	−	0.465637i	$-0.154175\pi$
$127$	4.72572	+	4.72572i	0.419339	+	0.419339i	−0.465637	+	0.884976i	$0.654175\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−1.94350	−	6.74992i	−0.171116	−	0.594298i
$130$	0.362041	−	12.2407i	0.0317531	−	1.07358i
$131$		−	9.59773i		−	0.838558i	−0.907858	−	0.419279i	$-0.862283\pi$
$131$		−	9.59773i		−	0.838558i	0.907858	−	0.419279i	$-0.137717\pi$
$132$	3.16139	−	5.71805i	0.275164	−	0.497692i
$133$	−16.3041	+	16.3041i	−1.41374	+	1.41374i
$134$	1.54638			0.133587
$135$	11.6150	−	0.302914i	0.999660	−	0.0260707i
$136$	3.65187			0.313145
$137$	5.29519	−	5.29519i	0.452399	−	0.452399i	−0.443751	−	0.896150i	$-0.646353\pi$
$137$	5.29519	−	5.29519i	0.452399	−	0.452399i	0.896150	+	0.443751i	$0.146353\pi$
$138$	−0.838057	+	1.51580i	−0.0713402	+	0.129034i
$139$		−	12.6513i		−	1.07307i	−0.843879	−	0.536533i	$-0.819734\pi$
$139$		−	12.6513i		−	1.07307i	0.843879	−	0.536533i	$-0.180266\pi$
$140$	5.51309	−	5.19634i	0.465941	−	0.439171i
$141$	2.30721	+	8.01310i	0.194302	+	0.674825i
$142$	6.54892	+	6.54892i	0.549573	+	0.549573i
$143$	−14.6084	−	14.6084i	−1.22161	−	1.22161i
$144$	1.59532	+	2.54066i	0.132943	+	0.211722i
$145$	14.4950	+	0.428716i	1.20375	+	0.0356029i
$146$		−	3.03756i		−	0.251390i
$147$	−6.78962	−	3.75384i	−0.559998	−	0.309612i
$148$	4.68887	−	4.68887i	0.385423	−	0.385423i
$149$	−13.7580			−1.12710			−0.563551	−	0.826081i	$-0.690565\pi$
$149$	−13.7580			−1.12710			−0.563551	+	0.826081i	$0.690565\pi$
$150$	1.90015	+	8.44923i	0.155147	+	0.689876i
$151$	−1.62442			−0.132194			−0.0660969	−	0.997813i	$-0.521055\pi$
$151$	−1.62442			−0.132194			−0.0660969	+	0.997813i	$0.521055\pi$
$152$	4.81215	−	4.81215i	0.390317	−	0.390317i
$153$	10.6802	+	2.44112i	0.863442	+	0.197353i
$154$		−	12.7809i		−	1.02991i
$155$	−15.8578	−	0.469022i	−1.27373	−	0.0376728i
$156$	9.11544	−	2.62461i	0.729819	−	0.210137i
$157$	−12.9821	−	12.9821i	−1.03608	−	1.03608i	−0.999324	−	0.0367599i	$-0.988296\pi$
$157$	−12.9821	−	12.9821i	−1.03608	−	1.03608i	−0.0367599	−	0.999324i	$-0.511704\pi$
$158$	3.25064	+	3.25064i	0.258607	+	0.258607i
$159$	2.71137	−	0.780682i	0.215025	−	0.0619121i
$160$	−1.62719	+	1.53370i	−0.128641	+	0.121250i
$161$			3.38810i			0.267020i
$162$	2.96732	+	8.49676i	0.233135	+	0.667569i
$163$	−5.71990	+	5.71990i	−0.448017	+	0.448017i	−0.894695	−	0.446678i	$-0.852607\pi$
$163$	−5.71990	+	5.71990i	−0.448017	+	0.448017i	0.446678	+	0.894695i	$0.352607\pi$
$164$	−8.03681			−0.627569
$165$	12.5714	+	7.44400i	0.978679	+	0.579515i
$166$	−7.35876			−0.571151
$167$	−9.01194	+	9.01194i	−0.697365	+	0.697365i	−0.963841	−	0.266476i	$-0.914141\pi$
$167$	−9.01194	+	9.01194i	−0.697365	+	0.697365i	0.266476	+	0.963841i	$0.414141\pi$
$168$	5.13569	+	2.83942i	0.396227	+	0.219066i
$169$		−	16.9933i		−	1.30718i
$170$	−0.241414	+	8.16227i	−0.0185156	+	0.626017i
$171$	17.2902	−	10.8568i	1.32222	−	0.830241i
$172$	2.86760	+	2.86760i	0.218652	+	0.218652i
$173$	−14.7185	−	14.7185i	−1.11903	−	1.11903i	−0.991884	−	0.127145i	$-0.959419\pi$
$173$	−14.7185	−	14.7185i	−1.11903	−	1.11903i	−0.127145	−	0.991884i	$-0.540581\pi$
$174$	3.10796	+	10.7942i	0.235614	+	0.818304i
$175$	11.2498	+	12.6658i	0.850408	+	0.957442i
$176$			3.77229i			0.284347i
$177$	−0.832364	+	1.50551i	−0.0625643	+	0.113161i
$178$	−6.76430	+	6.76430i	−0.507006	+	0.507006i
$179$	−6.08838			−0.455067			−0.227533	−	0.973770i	$-0.573066\pi$
$179$	−6.08838			−0.455067			−0.227533	+	0.973770i	$0.573066\pi$
$180$	−5.78407	+	3.39773i	−0.431119	+	0.253252i
$181$	−11.1245			−0.826878			−0.413439	−	0.910532i	$-0.635673\pi$
$181$	−11.1245			−0.826878			−0.413439	+	0.910532i	$0.635673\pi$
$182$	13.1206	−	13.1206i	0.972562	−	0.972562i
$183$	9.77513	−	17.6804i	0.722598	−	1.30697i
$184$		−	1.00000i		−	0.0737210i
$185$	10.1701	+	10.7900i	0.747719	+	0.793298i
$186$	−3.40016	−	11.8090i	−0.249312	−	0.865878i
$187$	9.74104	+	9.74104i	0.712335	+	0.712335i
$188$	−3.40424	−	3.40424i	−0.248280	−	0.248280i
$189$	13.1217	+	11.7371i	0.954465	+	0.853748i
$190$	10.4375	+	11.0737i	0.757214	+	0.803371i
$191$		−	5.61428i		−	0.406235i	−0.979154	−	0.203118i	$-0.934893\pi$
$191$		−	5.61428i		−	0.406235i	0.979154	−	0.203118i	$-0.0651074\pi$
$192$	−1.51580	−	0.838057i	−0.109394	−	0.0604816i
$193$	9.77402	−	9.77402i	0.703549	−	0.703549i	−0.261621	−	0.965171i	$-0.584257\pi$
$193$	9.77402	−	9.77402i	0.703549	−	0.703549i	0.965171	+	0.261621i	$0.0842572\pi$
$194$	−14.9460			−1.07306
$195$	5.26364	+	20.5473i	0.376937	+	1.47143i
$196$	4.47922			0.319944
$197$	−1.13050	+	1.13050i	−0.0805446	+	0.0805446i	−0.746231	−	0.665687i	$-0.768139\pi$
$197$	−1.13050	+	1.13050i	−0.0805446	+	0.0805446i	0.665687	+	0.746231i	$0.268139\pi$
$198$	−2.52161	+	11.0324i	−0.179203	+	0.784035i
$199$			4.63646i			0.328670i	0.986405	+	0.164335i	$0.0525478\pi$
$199$			4.63646i			0.328670i	−0.986405	+	0.164335i	$0.947452\pi$
$200$	−3.32040	−	3.73831i	−0.234788	−	0.264338i
$201$	−2.57384	+	0.741085i	−0.181545	+	0.0522721i
$202$	2.19172	+	2.19172i	0.154209	+	0.154209i
$203$	15.5369	+	15.5369i	1.09048	+	1.09048i
$204$	−6.07829	+	1.75012i	−0.425565	+	0.122533i
$205$	0.531288	−	17.9630i	0.0371068	−	1.25459i
$206$			6.92180i			0.482264i
$207$	0.668456	−	2.92458i	0.0464609	−	0.203272i
$208$	−3.87255	+	3.87255i	−0.268513	+	0.268513i
$209$	25.6720			1.77577
$210$	−6.68587	+	11.2910i	−0.461369	+	0.779155i
$211$	−8.96557			−0.617215			−0.308608	−	0.951189i	$-0.599863\pi$
$211$	−8.96557			−0.617215			−0.308608	+	0.951189i	$0.599863\pi$
$212$	−1.15188	+	1.15188i	−0.0791114	+	0.0791114i
$213$	−14.0387	−	7.76173i	−0.961918	−	0.531825i
$214$		−	10.0656i		−	0.688069i
$215$	−6.59891	+	6.21977i	−0.450042	+	0.424185i
$216$	−3.87288	−	3.46421i	−0.263516	−	0.235710i
$217$	−16.9976	−	16.9976i	−1.15387	−	1.15387i
$218$	12.8147	+	12.8147i	0.867922	+	0.867922i
$219$	1.45572	+	5.05580i	0.0983681	+	0.341639i
$220$	−8.43140	−	0.249374i	−0.568445	−	0.0168128i
$221$			19.9999i			1.34534i
$222$	−5.55721	+	10.0514i	−0.372976	+	0.674605i
$223$	15.5814	−	15.5814i	1.04341	−	1.04341i	0.0443938	−	0.999014i	$-0.485864\pi$
$223$	15.5814	−	15.5814i	1.04341	−	1.04341i	0.999014	−	0.0443938i	$-0.0141356\pi$
$224$	−3.38810			−0.226377
$225$	−7.21187	−	13.1525i	−0.480791	−	0.876835i
$226$	−20.6406			−1.37299
$227$	−17.4824	+	17.4824i	−1.16035	+	1.16035i	−0.175945	+	0.984400i	$0.556298\pi$
$227$	−17.4824	+	17.4824i	−1.16035	+	1.16035i	−0.984400	+	0.175945i	$0.943702\pi$
$228$	−5.70332	+	10.3157i	−0.377712	+	0.683172i
$229$			9.74724i			0.644116i	0.946720	+	0.322058i	$0.104375\pi$
$229$			9.74724i			0.644116i	−0.946720	+	0.322058i	$0.895625\pi$
$230$	2.23509	+	0.0661068i	0.147378	+	0.00435895i
$231$	6.12510	+	21.2729i	0.403002	+	1.39965i
$232$	−4.58573	−	4.58573i	−0.301068	−	0.301068i
$233$	6.27349	+	6.27349i	0.410990	+	0.410990i	0.882083	−	0.471093i	$-0.156140\pi$
$233$	6.27349	+	6.27349i	0.410990	+	0.410990i	−0.471093	+	0.882083i	$0.656140\pi$
$234$	−13.9142	+	8.73695i	−0.909600	+	0.571152i
$235$	7.83382	−	7.38374i	0.511022	−	0.481662i
$236$		−	0.993207i		−	0.0646522i
$237$	−6.96829	−	3.85263i	−0.452639	−	0.250255i
$238$	−8.74897	+	8.74897i	−0.567111	+	0.567111i
$239$	23.7283			1.53486			0.767428	−	0.641135i	$-0.221536\pi$
$239$	23.7283			1.53486			0.767428	+	0.641135i	$0.221536\pi$
$240$	1.97334	−	3.33256i	0.127378	−	0.215116i
$241$	6.12180			0.394340			0.197170	−	0.980369i	$-0.436825\pi$
$241$	6.12180			0.394340			0.197170	+	0.980369i	$0.436825\pi$
$242$	−2.28406	+	2.28406i	−0.146825	+	0.146825i
$243$	−9.01088	−	12.7202i	−0.578048	−	0.816002i
$244$			11.6640i			0.746713i
$245$	−0.296107	+	10.0115i	−0.0189176	+	0.639609i
$246$	13.3767	−	3.85155i	0.852868	−	0.245566i
$247$	26.3543	+	26.3543i	1.67688	+	1.67688i
$248$	5.01686	+	5.01686i	0.318571	+	0.318571i
$249$	12.2481	−	3.52661i	0.776195	−	0.223490i
$250$	8.57496	−	7.17426i	0.542328	−	0.453740i
$251$		−	14.4578i		−	0.912566i	−0.889835	−	0.456283i	$-0.849180\pi$
$251$		−	14.4578i		−	0.912566i	0.889835	−	0.456283i	$-0.150820\pi$
$252$	−9.90877	−	2.26480i	−0.624194	−	0.142669i
$253$	2.66741	−	2.66741i	0.167699	−	0.167699i
$254$	6.68317			0.419339
$255$	−3.50986	−	13.7012i	−0.219796	−	0.858004i
$256$	1.00000			0.0625000
$257$	18.8018	−	18.8018i	1.17282	−	1.17282i	0.191288	−	0.981534i	$-0.438733\pi$
$257$	18.8018	−	18.8018i	1.17282	−	1.17282i	0.981534	−	0.191288i	$-0.0612665\pi$
$258$	−6.14718	−	3.39865i	−0.382707	−	0.211591i
$259$			22.4667i			1.39601i
$260$	−8.39950	−	8.91150i	−0.520915	−	0.552668i
$261$	−10.3460	−	16.4767i	−0.640400	−	1.01988i
$262$	−6.78662	−	6.78662i	−0.419279	−	0.419279i
$263$	9.69602	+	9.69602i	0.597882	+	0.597882i	0.939749	−	0.341866i	$-0.111059\pi$
$263$	9.69602	+	9.69602i	0.597882	+	0.597882i	−0.341866	+	0.939749i	$0.611059\pi$
$264$	−1.80783	−	6.27871i	−0.111264	−	0.386428i
$265$	−2.49841	−	2.65070i	−0.153476	−	0.162831i
$266$			23.0574i			1.41374i
$267$	8.01700	−	14.5004i	0.490632	−	0.887412i
$268$	1.09345	−	1.09345i	0.0667934	−	0.0667934i
$269$	4.30558			0.262516			0.131258	−	0.991348i	$-0.458098\pi$
$269$	4.30558			0.262516			0.131258	+	0.991348i	$0.458098\pi$
$270$	7.99885	−	8.42724i	0.486795	−	0.512865i
$271$	−8.66444			−0.526327			−0.263164	−	0.964751i	$-0.584766\pi$
$271$	−8.66444			−0.526327			−0.263164	+	0.964751i	$0.584766\pi$
$272$	2.58226	−	2.58226i	0.156573	−	0.156573i
$273$	−15.5504	+	28.1262i	−0.941154	+	1.70228i
$274$		−	7.48853i		−	0.452399i
$275$	1.11475	−	18.8285i	0.0672217	−	1.13540i
$276$	0.479239	+	1.66443i	0.0288468	+	0.100187i
$277$	20.8795	+	20.8795i	1.25453	+	1.25453i	0.953668	+	0.300862i	$0.0972743\pi$
$277$	20.8795	+	20.8795i	1.25453	+	1.25453i	0.300862	+	0.953668i	$0.402726\pi$
$278$	−8.94580	−	8.94580i	−0.536533	−	0.536533i
$279$	11.3187	+	18.0258i	0.677631	+	1.07917i
$280$	0.223976	−	7.57271i	0.0133852	−	0.452556i
$281$			21.9320i			1.30835i	0.756341	+	0.654177i	$0.226985\pi$
$281$			21.9320i			1.30835i	−0.756341	+	0.654177i	$0.773015\pi$
$282$	7.29756	+	4.03467i	0.434564	+	0.240261i
$283$	−1.56401	+	1.56401i	−0.0929709	+	0.0929709i	−0.752063	−	0.659092i	$-0.770941\pi$
$283$	−1.56401	+	1.56401i	−0.0929709	+	0.0929709i	0.659092	+	0.752063i	$0.270941\pi$
$284$	9.26157			0.549573
$285$	−22.6794	−	13.4294i	−1.34341	−	0.795488i
$286$	−20.6594			−1.22161
$287$	19.2542	−	19.2542i	1.13654	−	1.13654i
$288$	2.92458	+	0.668456i	0.172333	+	0.0393891i
$289$			3.66383i			0.215519i
$290$	10.5527	−	9.94637i	0.619674	−	0.584071i
$291$	24.8767	−	7.16273i	1.45830	−	0.419887i
$292$	−2.14788	−	2.14788i	−0.125695	−	0.125695i
$293$	6.39663	+	6.39663i	0.373695	+	0.373695i	0.868821	−	0.495126i	$-0.164878\pi$
$293$	6.39663	+	6.39663i	0.373695	+	0.373695i	−0.495126	+	0.868821i	$0.664878\pi$
$294$	−7.45535	+	2.14662i	−0.434805	+	0.125193i
$295$	2.21991	+	0.0656577i	0.129248	+	0.00382274i
$296$		−	6.63106i		−	0.385423i
$297$	−1.09009	−	19.5710i	−0.0632536	−	1.13563i
$298$	−9.72840	+	9.72840i	−0.563551	+	0.563551i
$299$	5.47661			0.316721
$300$	7.31812	+	4.63090i	0.422512	+	0.267365i
$301$	−13.7401			−0.791965
$302$	−1.14864	+	1.14864i	−0.0660969	+	0.0660969i
$303$	−4.69832	−	2.59761i	−0.269912	−	0.149229i
$304$		−	6.80541i		−	0.390317i
$305$	−26.0702	−	0.771072i	−1.49277	−	0.0441514i
$306$	9.27817	−	5.82591i	0.530397	−	0.333045i
$307$	−17.5324	−	17.5324i	−1.00063	−	1.00063i	−1.00000		0.000625972i	$-0.999801\pi$
$307$	−17.5324	−	17.5324i	−1.00063	−	1.00063i	−0.000625972	−	1.00000i	$-0.500199\pi$
$308$	−9.03745	−	9.03745i	−0.514957	−	0.514957i
$309$	−3.31719	−	11.5208i	−0.188709	−	0.655398i
$310$	−11.5448	+	10.8815i	−0.655700	+	0.618027i
$311$			1.02922i			0.0583619i	0.999574	+	0.0291810i	$0.00928991\pi$
$311$			1.02922i			0.0583619i	−0.999574	+	0.0291810i	$0.990710\pi$
$312$	4.58971	−	8.30147i	0.259841	−	0.469978i
$313$	−5.15305	+	5.15305i	−0.291268	+	0.291268i	−0.837581	−	0.546313i	$-0.816031\pi$
$313$	−5.15305	+	5.15305i	−0.291268	+	0.291268i	0.546313	+	0.837581i	$0.316031\pi$
$314$	−18.3595			−1.03608
$315$	5.71706	−	21.9973i	0.322120	−	1.23941i
$316$	4.59709			0.258607
$317$	2.15191	−	2.15191i	0.120863	−	0.120863i	−0.644088	−	0.764951i	$-0.722763\pi$
$317$	2.15191	−	2.15191i	0.120863	−	0.120863i	0.764951	+	0.644088i	$0.222763\pi$
$318$	1.36520	−	2.46925i	0.0765565	−	0.138469i
$319$		−	24.4640i		−	1.36972i
$320$	−0.0661068	+	2.23509i	−0.00369548	+	0.124945i
$321$	4.82382	+	16.7535i	0.269239	+	0.935087i
$322$	2.39575	+	2.39575i	0.133510	+	0.133510i
$323$	−17.5734	−	17.5734i	−0.977808	−	0.977808i
$324$	8.10633	+	3.90991i	0.450352	+	0.217217i
$325$	20.4733	−	18.1845i	1.13565	−	1.00870i
$326$			8.08915i			0.448017i
$327$	−27.4705	−	15.1879i	−1.51912	−	0.839893i
$328$	−5.68288	+	5.68288i	−0.313785	+	0.313785i
$329$	16.3114			0.899276
$330$	14.1530	−	3.62559i	0.779097	−	0.199582i
$331$	−10.0289			−0.551239			−0.275619	−	0.961267i	$-0.588883\pi$
$331$	−10.0289			−0.551239			−0.275619	+	0.961267i	$0.588883\pi$
$332$	−5.20343	+	5.20343i	−0.285575	+	0.285575i
$333$	4.43257	−	19.3931i	0.242904	−	1.06273i
$334$			12.7448i			0.697365i
$335$	2.37169	+	2.51626i	0.129579	+	0.137478i
$336$	5.63926	−	1.62371i	0.307647	−	0.0885806i
$337$	17.9924	+	17.9924i	0.980107	+	0.980107i	0.999806	−	0.0196990i	$-0.00627080\pi$
$337$	17.9924	+	17.9924i	0.980107	+	0.980107i	−0.0196990	+	0.999806i	$0.506271\pi$
$338$	−12.0161	−	12.0161i	−0.653588	−	0.653588i
$339$	34.3548	−	9.89176i	1.86590	−	0.537247i
$340$	5.60089	+	5.94230i	0.303751	+	0.322266i
$341$			26.7641i			1.44936i
$342$	4.54912	−	19.9030i	0.245988	−	1.07623i
$343$	6.03915	−	6.03915i	0.326084	−	0.326084i
$344$	4.05539			0.218652
$345$	−3.75183	+	0.961112i	−0.201992	+	0.0517446i
$346$	−20.8151			−1.11903
$347$	−16.7568	+	16.7568i	−0.899551	+	0.899551i	−0.995396	−	0.0958454i	$-0.969445\pi$
$347$	−16.7568	+	16.7568i	−0.899551	+	0.899551i	0.0958454	+	0.995396i	$0.469445\pi$
$348$	9.83029	+	5.43497i	0.526959	+	0.291345i
$349$		−	13.6323i		−	0.729723i	−0.931062	−	0.364861i	$-0.881116\pi$
$349$		−	13.6323i		−	0.729723i	0.931062	−	0.364861i	$-0.118884\pi$
$350$	16.9109	+	1.00122i	0.903925	+	0.0535172i
$351$	18.9722	−	21.2103i	1.01266	−	1.13212i
$352$	2.66741	+	2.66741i	0.142173	+	0.142173i
$353$	4.64603	+	4.64603i	0.247283	+	0.247283i	0.819855	−	0.572571i	$-0.194054\pi$
$353$	4.64603	+	4.64603i	0.247283	+	0.247283i	−0.572571	+	0.819855i	$0.694054\pi$
$354$	0.475983	+	1.65312i	0.0252982	+	0.0878625i
$355$	−0.612253	+	20.7005i	−0.0324950	+	1.09867i
$356$			9.56617i			0.507006i
$357$	10.3692	−	18.7549i	0.548796	−	0.992614i
$358$	−4.30513	+	4.30513i	−0.227533	+	0.227533i
$359$	−34.5145			−1.82160			−0.910802	−	0.412845i	$-0.864535\pi$
$359$	−34.5145			−1.82160			−0.910802	+	0.412845i	$0.864535\pi$
$360$	−1.68739	+	6.49251i	−0.0889335	+	0.342185i
$361$	−27.3136			−1.43756
$362$	−7.86622	+	7.86622i	−0.413439	+	0.413439i
$363$	2.70705	−	4.89628i	0.142083	−	0.256988i
$364$		−	18.5553i		−	0.972562i
$365$	4.94269	−	4.65871i	0.258712	−	0.243848i
$366$	−5.58986	−	19.4140i	−0.292187	−	1.01478i
$367$	8.38016	+	8.38016i	0.437441	+	0.437441i	0.891150	−	0.453709i	$-0.149899\pi$
$367$	8.38016	+	8.38016i	0.437441	+	0.437441i	−0.453709	+	0.891150i	$0.649899\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−20.4188	+	12.8213i	−1.06296	+	0.667450i
$370$	14.8210	+	0.438358i	0.770509	+	0.0227892i
$371$		−	5.51923i		−	0.286544i
$372$	−10.7545	−	5.94594i	−0.557595	−	0.308283i
$373$	7.63967	−	7.63967i	0.395567	−	0.395567i	−0.481099	−	0.876666i	$-0.659762\pi$
$373$	7.63967	−	7.63967i	0.395567	−	0.395567i	0.876666	+	0.481099i	$0.159762\pi$
$374$	13.7759			0.712335
$375$	−10.8342	+	16.0505i	−0.559478	+	0.828845i
$376$	−4.81432			−0.248280
$377$	25.1143	−	25.1143i	1.29345	−	1.29345i
$378$	17.5778	−	0.979073i	0.904106	−	0.0503581i
$379$			1.05138i			0.0540060i	0.999635	+	0.0270030i	$0.00859636\pi$
$379$			1.05138i			0.0540060i	−0.999635	+	0.0270030i	$0.991404\pi$
$380$	15.2107	+	0.449884i	0.780293	+	0.0230786i
$381$	−11.1237	+	3.20284i	−0.569883	+	0.164086i
$382$	−3.96990	−	3.96990i	−0.203118	−	0.203118i
$383$	16.4304	+	16.4304i	0.839554	+	0.839554i	0.988800	−	0.149246i	$-0.0476845\pi$
$383$	16.4304	+	16.4304i	0.839554	+	0.839554i	−0.149246	+	0.988800i	$0.547685\pi$
$384$	−1.66443	+	0.479239i	−0.0849376	+	0.0244561i
$385$	20.7970	−	19.6021i	1.05991	−	0.999015i
$386$		−	13.8225i		−	0.703549i
$387$	11.8603	+	2.71085i	0.602894	+	0.137800i
$388$	−10.5684	+	10.5684i	−0.536532	+	0.536532i
$389$	−4.44285			−0.225261			−0.112631	−	0.993637i	$-0.535928\pi$
$389$	−4.44285			−0.225261			−0.112631	+	0.993637i	$0.535928\pi$
$390$	18.2511	+	10.8072i	0.924181	+	0.547244i
$391$	−3.65187			−0.184683
$392$	3.16729	−	3.16729i	0.159972	−	0.159972i
$393$	14.5483	+	8.04345i	0.733863	+	0.405738i
$394$			1.59876i			0.0805446i
$395$	−0.303899	+	10.2749i	−0.0152908	+	0.516987i
$396$	6.01801	+	9.58410i	0.302416	+	0.481619i
$397$	2.78289	+	2.78289i	0.139669	+	0.139669i	0.773485	−	0.633815i	$-0.218512\pi$
$397$	2.78289	+	2.78289i	0.139669	+	0.139669i	−0.633815	+	0.773485i	$0.718512\pi$
$398$	3.27847	+	3.27847i	0.164335	+	0.164335i
$399$	−11.0500	−	38.3775i	−0.553192	−	1.92128i
$400$	−4.99126	−	0.295509i	−0.249563	−	0.0147755i
$401$		−	1.11565i		−	0.0557131i	−0.999612	−	0.0278565i	$-0.991132\pi$
$401$		−	1.11565i		−	0.0557131i	0.999612	−	0.0278565i	$-0.00886816\pi$
$402$	−1.29595	+	2.34401i	−0.0646363	+	0.116908i
$403$	−27.4754	+	27.4754i	−1.36865	+	1.36865i
$404$	3.09956			0.154209
$405$	−9.27488	+	17.8599i	−0.460872	+	0.887466i
$406$	21.9725			1.09048
$407$	17.6878	−	17.6878i	0.876750	−	0.876750i
$408$	−3.06048	+	5.53552i	−0.151516	+	0.274049i
$409$			15.3832i			0.760653i	0.924852	+	0.380326i	$0.124188\pi$
$409$			15.3832i			0.760653i	−0.924852	+	0.380326i	$0.875812\pi$
$410$	−12.3261	−	13.0774i	−0.608742	−	0.645849i
$411$	3.58880	+	12.4641i	0.177022	+	0.614811i
$412$	4.89445	+	4.89445i	0.241132	+	0.241132i
$413$	2.37947	+	2.37947i	0.117086	+	0.117086i
$414$	−1.59532	−	2.54066i	−0.0784057	−	0.124867i
$415$	−11.2862	−	11.9741i	−0.554016	−	0.587786i
$416$			5.47661i			0.268513i
$417$	19.1768	+	10.6025i	0.939094	+	0.519206i
$418$	18.1528	−	18.1528i	0.887883	−	0.887883i
$419$	3.29476			0.160960			0.0804798	−	0.996756i	$-0.474355\pi$
$419$	3.29476			0.160960			0.0804798	+	0.996756i	$0.474355\pi$
$420$	3.25635	+	12.7116i	0.158893	+	0.620262i
$421$	26.2854			1.28107			0.640537	−	0.767927i	$-0.278712\pi$
$421$	26.2854			1.28107			0.640537	+	0.767927i	$0.278712\pi$
$422$	−6.33962	+	6.33962i	−0.308608	+	0.308608i
$423$	−14.0799	−	3.21816i	−0.684586	−	0.156472i
$424$			1.62900i			0.0791114i
$425$	−13.6518	+	12.1257i	−0.662211	+	0.588181i
$426$	−15.4152	+	4.43851i	−0.746871	+	0.215046i
$427$	−27.9441	−	27.9441i	−1.35231	−	1.35231i
$428$	−7.11744	−	7.11744i	−0.344035	−	0.344035i
$429$	34.3861	−	9.90077i	1.66018	−	0.478014i
$430$	−0.268089	+	9.06417i	−0.0129284	+	0.437113i
$431$			12.3440i			0.594591i	0.954786	+	0.297296i	$0.0960847\pi$
$431$			12.3440i			0.594591i	−0.954786	+	0.297296i	$0.903915\pi$
$432$	−5.18811	+	0.288974i	−0.249613	+	0.0139033i
$433$	4.20594	−	4.20594i	0.202124	−	0.202124i	−0.598785	−	0.800910i	$-0.704350\pi$
$433$	4.20594	−	4.20594i	0.202124	−	0.202124i	0.800910	+	0.598785i	$0.204350\pi$
$434$	−24.0383			−1.15387
$435$	−12.7975	+	21.6123i	−0.613593	+	1.03623i
$436$	18.1228			0.867922
$437$	−4.81215	+	4.81215i	−0.230196	+	0.230196i
$438$	4.60434	+	2.54565i	0.220004	+	0.121636i
$439$		−	23.3960i		−	1.11663i	−0.829629	−	0.558315i	$-0.811448\pi$
$439$		−	23.3960i		−	1.11663i	0.829629	−	0.558315i	$-0.188552\pi$
$440$	−6.13824	+	5.78557i	−0.292629	+	0.275816i
$441$	11.3802	−	7.14579i	0.541913	−	0.340276i
$442$	14.1421	+	14.1421i	0.672669	+	0.672669i
$443$	1.58931	+	1.58931i	0.0755103	+	0.0755103i	0.743853	−	0.668343i	$-0.232996\pi$
$443$	1.58931	+	1.58931i	0.0755103	+	0.0755103i	−0.668343	+	0.743853i	$0.732996\pi$
$444$	3.17786	+	11.0369i	0.150815	+	0.523790i
$445$	−21.3813	−	0.632389i	−1.01357	−	0.0299781i
$446$		−	22.0354i		−	1.04341i
$447$	11.5300	−	20.8545i	0.545351	−	0.986383i
$448$	−2.39575	+	2.39575i	−0.113188	+	0.113188i
$449$	−22.0511			−1.04066			−0.520328	−	0.853966i	$-0.674190\pi$
$449$	−22.0511			−1.04066			−0.520328	+	0.853966i	$0.674190\pi$
$450$	−14.3998	−	4.20068i	−0.678813	−	0.198022i
$451$	−30.3172			−1.42758
$452$	−14.5951	+	14.5951i	−0.686495	+	0.686495i
$453$	1.36136	−	2.46231i	0.0639623	−	0.115689i
$454$			24.7238i			1.16035i
$455$	41.4728	+	1.22663i	1.94427	+	0.0575054i
$456$	3.26142	+	11.3271i	0.152730	+	0.530442i
$457$	26.3823	+	26.3823i	1.23411	+	1.23411i	0.962370	+	0.271741i	$0.0875993\pi$
$457$	26.3823	+	26.3823i	1.23411	+	1.23411i	0.271741	+	0.962370i	$0.412401\pi$
$458$	6.89234	+	6.89234i	0.322058	+	0.322058i
$459$	−12.6509	+	14.1433i	−0.590492	+	0.660152i
$460$	1.62719	−	1.53370i	0.0758682	−	0.0715093i
$461$		−	12.2104i		−	0.568695i	−0.958721	−	0.284348i	$-0.908223\pi$
$461$		−	12.2104i		−	0.568695i	0.958721	−	0.284348i	$-0.0917770\pi$
$462$	19.3733	+	10.7111i	0.901328	+	0.498326i
$463$	12.7159	−	12.7159i	0.590959	−	0.590959i	−0.346931	−	0.937891i	$-0.612776\pi$
$463$	12.7159	−	12.7159i	0.590959	−	0.590959i	0.937891	+	0.346931i	$0.112776\pi$
$464$	−6.48520			−0.301068
$465$	14.0007	−	23.6442i	0.649266	−	1.09647i
$466$	8.87206			0.410990
$467$	−13.8067	+	13.8067i	−0.638896	+	0.638896i	−0.950283	−	0.311387i	$-0.899207\pi$
$467$	−13.8067	+	13.8067i	−0.638896	+	0.638896i	0.311387	+	0.950283i	$0.399207\pi$
$468$	−3.66087	+	16.0168i	−0.169224	+	0.740376i
$469$			5.23929i			0.241928i
$470$	0.318259	−	10.7604i	0.0146802	−	0.496342i
$471$	30.5580	−	8.79857i	1.40804	−	0.405417i
$472$	−0.702303	−	0.702303i	−0.0323261	−	0.0323261i
$473$	10.8174	+	10.8174i	0.497385	+	0.497385i
$474$	−7.65154	+	2.20311i	−0.351447	+	0.101192i
$475$	−2.01106	+	33.9676i	−0.0922739	+	1.55854i
$476$			12.3729i			0.567111i
$477$	−1.08892	+	4.76415i	−0.0498581	+	0.218136i
$478$	16.7784	−	16.7784i	0.767428	−	0.767428i
$479$	−12.4597			−0.569300			−0.284650	−	0.958632i	$-0.591877\pi$
$479$	−12.4597			−0.569300			−0.284650	+	0.958632i	$0.591877\pi$
$480$	−0.961112	−	3.75183i	−0.0438686	−	0.171247i
$481$	36.3158			1.65586
$482$	4.32877	−	4.32877i	0.197170	−	0.197170i
$483$	−5.13569	−	2.83942i	−0.233682	−	0.129198i
$484$			3.23015i			0.146825i
$485$	−22.9228	−	24.3201i	−1.04087	−	1.10432i
$486$	−15.3662	−	2.62290i	−0.697025	−	0.118977i
$487$	−1.80667	−	1.80667i	−0.0818682	−	0.0818682i	0.664987	−	0.746855i	$-0.268437\pi$
$487$	−1.80667	−	1.80667i	−0.0818682	−	0.0818682i	−0.746855	+	0.664987i	$0.768437\pi$
$488$	8.24772	+	8.24772i	0.373357	+	0.373357i
$489$	−3.87664	−	13.4638i	−0.175308	−	0.608856i
$490$	6.86980	+	7.28855i	0.310346	+	0.329263i
$491$		−	28.0135i		−	1.26423i	−0.774874	−	0.632116i	$-0.782187\pi$
$491$		−	28.0135i		−	1.26423i	0.774874	−	0.632116i	$-0.217813\pi$
$492$	6.73531	−	12.1822i	0.303651	−	0.549217i
$493$	−16.7465	+	16.7465i	−0.754224	+	0.754224i
$494$	37.2706			1.67688
$495$	−21.8192	+	12.8172i	−0.980698	+	0.576091i
$496$	7.09492			0.318571
$497$	−22.1884	+	22.1884i	−0.995286	+	0.995286i
$498$	6.16706	−	11.1544i	0.276353	−	0.499842i
$499$			26.7176i			1.19605i	0.801479	+	0.598023i	$0.204047\pi$
$499$			26.7176i			1.19605i	−0.801479	+	0.598023i	$0.795953\pi$
$500$	0.990446	−	11.1364i	0.0442941	−	0.498034i
$501$	−6.10781	−	21.2129i	−0.272877	−	0.947720i
$502$	−10.2232	−	10.2232i	−0.456283	−	0.456283i
$503$	26.3520	+	26.3520i	1.17498	+	1.17498i	0.981007	+	0.193973i	$0.0621374\pi$
$503$	26.3520	+	26.3520i	1.17498	+	1.17498i	0.193973	+	0.981007i	$0.437863\pi$
$504$	−8.60801	+	5.40511i	−0.383431	+	0.240763i
$505$	−0.204902	+	6.92780i	−0.00911802	+	0.308283i
$506$		−	3.77229i		−	0.167699i
$507$	25.7585	+	14.2413i	1.14397	+	0.632480i
$508$	4.72572	−	4.72572i	0.209670	−	0.209670i
$509$	−9.42990			−0.417973			−0.208986	−	0.977919i	$-0.567016\pi$
$509$	−9.42990			−0.417973			−0.208986	+	0.977919i	$0.567016\pi$
$510$	−12.1701	−	7.20638i	−0.538900	−	0.319104i
$511$	10.2915			0.455271
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.96659	+	35.3072i	0.0868270	+	1.55885i
$514$		−	26.5897i		−	1.17282i
$515$	−11.2631	+	10.6160i	−0.496311	+	0.467796i
$516$	−6.74992	+	1.94350i	−0.297149	+	0.0855580i
$517$	−12.8418	−	12.8418i	−0.564780	−	0.564780i
$518$	15.8864	+	15.8864i	0.698007	+	0.698007i
$519$	34.6454	−	9.97543i	1.52076	−	0.437873i
$520$	−12.2407	−	0.362041i	−0.536791	−	0.0158766i
$521$			13.8604i			0.607237i	0.952794	+	0.303618i	$0.0981948\pi$
$521$			13.8604i			0.607237i	−0.952794	+	0.303618i	$0.901805\pi$
$522$	−18.9665	−	4.33507i	−0.830141	−	0.189741i
$523$	14.8570	−	14.8570i	0.649650	−	0.649650i	−0.303259	−	0.952908i	$-0.598075\pi$
$523$	14.8570	−	14.8570i	0.649650	−	0.649650i	0.952908	+	0.303259i	$0.0980746\pi$
$524$	−9.59773			−0.419279
$525$	−28.6268	+	6.43790i	−1.24938	+	0.280973i
$526$	13.7122			0.597882
$527$	18.3209	−	18.3209i	0.798073	−	0.798073i
$528$	−5.71805	−	3.16139i	−0.248846	−	0.137582i
$529$			1.00000i			0.0434783i
$530$	−3.64097	−	0.107688i	−0.158154	−	0.00467768i
$531$	−1.58448	−	2.52340i	−0.0687607	−	0.109506i
$532$	16.3041	+	16.3041i	0.706870	+	0.706870i
$533$	−31.1229	−	31.1229i	−1.34808	−	1.34808i
$534$	−4.58448	−	15.9222i	−0.198390	−	0.689022i
$535$	16.3786	−	15.4376i	0.708110	−	0.667426i
$536$		−	1.54638i		−	0.0667934i
$537$	5.10241	−	9.22879i	0.220185	−	0.398251i
$538$	3.04451	−	3.04451i	0.131258	−	0.131258i
$539$	16.8969			0.727801
$540$	−0.302914	−	11.6150i	−0.0130353	−	0.499830i
$541$	−19.6739			−0.845846			−0.422923	−	0.906166i	$-0.638996\pi$
$541$	−19.6739			−0.845846			−0.422923	+	0.906166i	$0.638996\pi$
$542$	−6.12669	+	6.12669i	−0.263164	+	0.263164i
$543$	9.32297	−	16.8626i	0.400087	−	0.723642i
$544$		−	3.65187i		−	0.156573i
$545$	−1.19804	+	40.5060i	−0.0513183	+	1.73509i
$546$	8.89243	+	30.8840i	0.380561	+	1.32171i
$547$	20.3990	+	20.3990i	0.872198	+	0.872198i	0.992712	−	0.120514i	$-0.0384543\pi$
$547$	20.3990	+	20.3990i	0.872198	+	0.872198i	−0.120514	+	0.992712i	$0.538454\pi$
$548$	−5.29519	−	5.29519i	−0.226199	−	0.226199i
$549$	18.6079	+	29.6343i	0.794165	+	1.26476i
$550$	−12.5255	−	14.1020i	−0.534089	−	0.601311i
$551$			44.1345i			1.88019i
$552$	1.51580	+	0.838057i	0.0645169	+	0.0356701i
$553$	−11.0135	+	11.0135i	−0.468341	+	0.468341i
$554$	29.5281			1.25453
$555$	−24.8787	+	6.37320i	−1.05604	+	0.270527i
$556$	−12.6513			−0.536533
$557$	−3.65261	+	3.65261i	−0.154766	+	0.154766i	−0.780243	−	0.625477i	$-0.784904\pi$
$557$	−3.65261	+	3.65261i	−0.154766	+	0.154766i	0.625477	+	0.780243i	$0.284904\pi$
$558$	20.7496	+	4.74264i	0.878403	+	0.200772i
$559$			22.2098i			0.939375i
$560$	−5.19634	−	5.51309i	−0.219585	−	0.232971i
$561$	−22.9291	+	6.60195i	−0.968065	+	0.278735i
$562$	15.5083	+	15.5083i	0.654177	+	0.654177i
$563$	26.8125	+	26.8125i	1.13001	+	1.13001i	0.990175	+	0.139836i	$0.0446576\pi$
$563$	26.8125	+	26.8125i	1.13001	+	1.13001i	0.139836	+	0.990175i	$0.455342\pi$
$564$	8.01310	−	2.30721i	0.337412	−	0.0971511i
$565$	−31.6565	−	33.5862i	−1.33180	−	1.41298i
$566$			2.21185i			0.0929709i
$567$	−28.7879	+	10.0536i	−1.20898	+	0.422211i
$568$	6.54892	−	6.54892i	0.274787	−	0.274787i
$569$	−35.3739			−1.48295			−0.741475	−	0.670980i	$-0.765874\pi$
$569$	−35.3739			−1.48295			−0.741475	+	0.670980i	$0.765874\pi$
$570$	−25.5328	+	6.54076i	−1.06945	+	0.273962i
$571$	−33.8705			−1.41744			−0.708718	−	0.705492i	$-0.750726\pi$
$571$	−33.8705			−1.41744			−0.708718	+	0.705492i	$0.750726\pi$
$572$	−14.6084	+	14.6084i	−0.610807	+	0.610807i
$573$	8.51015	+	4.70509i	0.355516	+	0.196558i
$574$		−	27.2295i		−	1.13654i
$575$	3.32040	+	3.73831i	0.138470	+	0.155898i
$576$	2.54066	−	1.59532i	0.105861	−	0.0664717i
$577$	25.3921	+	25.3921i	1.05709	+	1.05709i	0.998269	+	0.0588185i	$0.0187333\pi$
$577$	25.3921	+	25.3921i	1.05709	+	1.05709i	0.0588185	+	0.998269i	$0.481267\pi$
$578$	2.59072	+	2.59072i	0.107760	+	0.107760i
$579$	6.62430	+	23.0067i	0.275297	+	0.956125i
$580$	0.428716	−	14.4950i	0.0178015	−	0.601873i
$581$		−	24.9322i		−	1.03436i
$582$	12.5256	−	22.6553i	0.519204	−	0.939091i
$583$	−4.34522	+	4.34522i	−0.179961	+	0.179961i
$584$	−3.03756			−0.125695
$585$	−35.5570	−	9.24120i	−1.47010	−	0.382077i
$586$	9.04621			0.373695
$587$	−31.7362	+	31.7362i	−1.30989	+	1.30989i	−0.388402	+	0.921490i	$0.626973\pi$
$587$	−31.7362	+	31.7362i	−1.30989	+	1.30989i	−0.921490	+	0.388402i	$0.873027\pi$
$588$	−3.75384	+	6.78962i	−0.154806	+	0.279999i
$589$		−	48.2838i		−	1.98950i
$590$	1.61614	−	1.52328i	0.0665354	−	0.0627126i
$591$	−0.766190	−	2.66103i	−0.0315169	−	0.109460i
$592$	−4.68887	−	4.68887i	−0.192711	−	0.192711i
$593$	−21.4857	−	21.4857i	−0.882314	−	0.882314i	0.111456	−	0.993769i	$-0.464449\pi$
$593$	−21.4857	−	21.4857i	−0.882314	−	0.882314i	−0.993769	+	0.111456i	$0.964449\pi$
$594$	−14.6096	−	13.0680i	−0.599440	−	0.536187i
$595$	−27.6546	−	0.817933i	−1.13373	−	0.0335320i
$596$			13.7580i			0.563551i
$597$	−7.02796	−	3.88562i	−0.287635	−	0.159028i
$598$	3.87255	−	3.87255i	0.158360	−	0.158360i
$599$	−28.3661			−1.15901			−0.579504	−	0.814969i	$-0.696754\pi$
$599$	−28.3661			−1.15901			−0.579504	+	0.814969i	$0.696754\pi$
$600$	8.44923	−	1.90015i	0.344938	−	0.0775734i
$601$	40.0727			1.63460			0.817300	−	0.576213i	$-0.195470\pi$
$601$	40.0727			1.63460			0.817300	+	0.576213i	$0.195470\pi$
$602$	−9.71571	+	9.71571i	−0.395983	+	0.395983i
$603$	1.03369	−	4.52251i	0.0420950	−	0.184171i
$604$			1.62442i			0.0660969i
$605$	−7.21969	−	0.213535i	−0.293522	−	0.00868144i
$606$	−5.15900	+	1.48543i	−0.209570	+	0.0603415i
$607$	−1.59716	−	1.59716i	−0.0648268	−	0.0648268i	0.673950	−	0.738777i	$-0.264596\pi$
$607$	−1.59716	−	1.59716i	−0.0648268	−	0.0648268i	−0.738777	+	0.673950i	$0.764596\pi$
$608$	−4.81215	−	4.81215i	−0.195159	−	0.195159i
$609$	−36.5717	+	10.5301i	−1.48196	+	0.426701i
$610$	−18.9796	+	17.8892i	−0.768463	+	0.724311i
$611$		−	26.3662i		−	1.06666i
$612$	2.44112	−	10.6802i	0.0986763	−	0.431721i
$613$	12.0113	−	12.0113i	0.485130	−	0.485130i	−0.421636	−	0.906765i	$-0.638544\pi$
$613$	12.0113	−	12.0113i	0.485130	−	0.485130i	0.906765	+	0.421636i	$0.138544\pi$
$614$	−24.7945			−1.00063
$615$	26.7831	+	15.8593i	1.08000	+	0.639511i
$616$	−12.7809			−0.514957
$617$	20.3489	−	20.3489i	0.819214	−	0.819214i	−0.166780	−	0.985994i	$-0.553337\pi$
$617$	20.3489	−	20.3489i	0.819214	−	0.819214i	0.985994	+	0.166780i	$0.0533370\pi$
$618$	−10.4921	−	5.80086i	−0.422053	−	0.233345i
$619$		−	11.4711i		−	0.461063i	−0.973065	−	0.230531i	$-0.925954\pi$
$619$		−	11.4711i		−	0.461063i	0.973065	−	0.230531i	$-0.0740464\pi$
$620$	−0.469022	+	15.8578i	−0.0188364	+	0.636864i
$621$	3.87288	+	3.46421i	0.155413	+	0.139014i
$622$	0.727771	+	0.727771i	0.0291810	+	0.0291810i
$623$	−22.9181	−	22.9181i	−0.918196	−	0.918196i
$624$	−2.62461	−	9.11544i	−0.105068	−	0.364910i
$625$	24.8253	+	2.94993i	0.993014	+	0.117997i
$626$			7.28751i			0.291268i
$627$	−21.5146	+	38.9137i	−0.859209	+	1.55406i
$628$	−12.9821	+	12.9821i	−0.518042	+	0.518042i
$629$	−24.2158			−0.965547
$630$	−11.5119	−	19.5970i	−0.458643	−	0.780763i
$631$	1.12832			0.0449177			0.0224588	−	0.999748i	$-0.492851\pi$
$631$	1.12832			0.0449177			0.0224588	+	0.999748i	$0.492851\pi$
$632$	3.25064	−	3.25064i	0.129303	−	0.129303i
$633$	7.51366	−	13.5900i	0.298641	−	0.540156i
$634$		−	3.04326i		−	0.120863i
$635$	10.2500	+	10.8748i	0.406759	+	0.431553i
$636$	−0.780682	−	2.71137i	−0.0309561	−	0.107513i
$637$	17.3460	+	17.3460i	0.687274	+	0.687274i
$638$	−17.2987	−	17.2987i	−0.684862	−	0.684862i
$639$	23.5305	−	14.7752i	0.930852	−	0.584497i
$640$	1.53370	+	1.62719i	0.0606249	+	0.0643204i
$641$		−	31.3115i		−	1.23673i	−0.785892	−	0.618364i	$-0.787796\pi$
$641$		−	31.3115i		−	1.23673i	0.785892	−	0.618364i	$-0.212204\pi$
$642$	15.2574	+	8.43553i	0.602163	+	0.332924i
$643$	5.97111	−	5.97111i	0.235478	−	0.235478i	−0.579497	−	0.814974i	$-0.696751\pi$
$643$	5.97111	−	5.97111i	0.235478	−	0.235478i	0.814974	+	0.579497i	$0.196751\pi$
$644$	3.38810			0.133510
$645$	−3.89769	−	15.2152i	−0.153471	−	0.599097i
$646$	−24.8525			−0.977808
$647$	10.0814	−	10.0814i	0.396340	−	0.396340i	−0.480600	−	0.876940i	$-0.659581\pi$
$647$	10.0814	−	10.0814i	0.396340	−	0.396340i	0.876940	+	0.480600i	$0.159581\pi$
$648$	8.49676	−	2.96732i	0.333784	−	0.116567i
$649$		−	3.74666i		−	0.147069i
$650$	1.61839	−	27.3352i	0.0634785	−	1.07217i
$651$	40.0101	−	11.5201i	1.56812	−	0.451508i
$652$	5.71990	+	5.71990i	0.224008	+	0.224008i
$653$	14.5180	+	14.5180i	0.568134	+	0.568134i	0.931605	−	0.363472i	$-0.118409\pi$
$653$	14.5180	+	14.5180i	0.568134	+	0.568134i	−0.363472	+	0.931605i	$0.618409\pi$
$654$	−30.1641	+	8.68513i	−1.17951	+	0.339615i
$655$	0.634475	−	21.4518i	0.0247910	−	0.838191i
$656$			8.03681i			0.313785i
$657$	−8.88357	−	2.03047i	−0.346581	−	0.0792163i
$658$	11.5339	−	11.5339i	0.449638	−	0.449638i
$659$	−20.3327			−0.792048			−0.396024	−	0.918240i	$-0.629610\pi$
$659$	−20.3327			−0.792048			−0.396024	+	0.918240i	$0.629610\pi$
$660$	7.44400	−	12.5714i	0.289757	−	0.489340i
$661$	−31.1622			−1.21207			−0.606035	−	0.795438i	$-0.707241\pi$
$661$	−31.1622			−1.21207			−0.606035	+	0.795438i	$0.707241\pi$
$662$	−7.09151	+	7.09151i	−0.275619	+	0.275619i
$663$	−30.3159	−	16.7610i	−1.17737	−	0.650945i
$664$			7.35876i			0.285575i
$665$	−37.5188	+	35.3632i	−1.45492	+	1.37133i
$666$	−10.5787	−	16.8473i	−0.409915	−	0.652819i
$667$	4.58573	+	4.58573i	0.177560	+	0.177560i
$668$	9.01194	+	9.01194i	0.348682	+	0.348682i
$669$	10.5602	+	36.6764i	0.408282	+	1.41799i
$670$	3.45630	+	0.102226i	0.133528	+	0.00394934i
$671$			44.0001i			1.69860i
$672$	2.83942	−	5.13569i	0.109533	−	0.198114i
$673$	32.7647	−	32.7647i	1.26299	−	1.26299i	0.313348	−	0.949638i	$-0.398549\pi$
$673$	32.7647	−	32.7647i	1.26299	−	1.26299i	0.949638	−	0.313348i	$-0.101451\pi$
$674$	25.4451			0.980107
$675$	25.9806	+	0.0907905i	0.999994	+	0.00349453i
$676$	−16.9933			−0.653588
$677$	−10.4956	+	10.4956i	−0.403380	+	0.403380i	−0.879422	−	0.476043i	$-0.842071\pi$
$677$	−10.4956	+	10.4956i	−0.403380	+	0.403380i	0.476043	+	0.879422i	$0.342071\pi$
$678$	17.2980	−	31.2870i	0.664325	−	1.20157i
$679$		−	50.6387i		−	1.94333i
$680$	8.16227	+	0.241414i	0.313009	+	0.00925779i
$681$	−11.8486	−	41.1510i	−0.454040	−	1.57691i
$682$	18.9250	+	18.9250i	0.724678	+	0.724678i
$683$	2.34519	+	2.34519i	0.0897362	+	0.0897362i	0.750550	−	0.660814i	$-0.229789\pi$
$683$	2.34519	+	2.34519i	0.0897362	+	0.0897362i	−0.660814	+	0.750550i	$0.729789\pi$
$684$	−10.8568	−	17.2902i	−0.415121	−	0.661109i
$685$	12.1853	−	11.4852i	0.465575	−	0.438826i
$686$		−	8.54065i		−	0.326084i
$687$	−14.7749	−	8.16874i	−0.563698	−	0.311657i
$688$	2.86760	−	2.86760i	0.109326	−	0.109326i
$689$	−8.92143			−0.339879
$690$	−1.97334	+	3.33256i	−0.0751237	+	0.126868i
$691$	49.5125			1.88355			0.941773	−	0.336250i	$-0.109159\pi$
$691$	49.5125			1.88355			0.941773	+	0.336250i	$0.109159\pi$
$692$	−14.7185	+	14.7185i	−0.559515	+	0.559515i
$693$	−37.3787	−	8.54346i	−1.41990	−	0.324539i
$694$			23.6977i			0.899551i
$695$	0.836335	−	28.2767i	0.0317240	−	1.07260i
$696$	10.7942	−	3.10796i	0.409152	−	0.117807i
$697$	20.7532	+	20.7532i	0.786082	+	0.786082i
$698$	−9.63952	−	9.63952i	−0.364861	−	0.364861i
$699$	−14.7669	+	4.25184i	−0.558536	+	0.160819i
$700$	12.6658	−	11.2498i	0.478721	−	0.425204i
$701$			43.6716i			1.64945i	0.565532	+	0.824726i	$0.308671\pi$
$701$			43.6716i			1.64945i	−0.565532	+	0.824726i	$0.691329\pi$
$702$	−1.58260	−	28.4133i	−0.0597314	−	1.07239i
$703$	−31.9097	+	31.9097i	−1.20350	+	1.20350i
$704$	3.77229			0.142173
$705$	4.62710	+	18.0625i	0.174267	+	0.680274i
$706$	6.57049			0.247283
$707$	−7.42577	+	7.42577i	−0.279275	+	0.279275i
$708$	1.50551	+	0.832364i	0.0565804	+	0.0312822i
$709$		−	17.3686i		−	0.652292i	−0.945319	−	0.326146i	$-0.894250\pi$
$709$		−	17.3686i		−	0.652292i	0.945319	−	0.326146i	$-0.105750\pi$
$710$	14.2045	+	15.0704i	0.533085	+	0.565581i
$711$	11.6796	−	7.33384i	0.438021	−	0.275040i
$712$	6.76430	+	6.76430i	0.253503	+	0.253503i
$713$	−5.01686	−	5.01686i	−0.187883	−	0.187883i
$714$	−5.92958	−	20.5938i	−0.221909	−	0.770705i
$715$	−31.6853	−	33.6167i	−1.18496	−	1.25719i
$716$			6.08838i			0.227533i
$717$	−19.8857	+	35.9674i	−0.742644	+	1.34323i
$718$	−24.4054	+	24.4054i	−0.910802	+	0.910802i
$719$	13.0073			0.485089			0.242545	−	0.970140i	$-0.422018\pi$
$719$	13.0073			0.485089			0.242545	+	0.970140i	$0.422018\pi$
$720$	3.39773	+	5.78407i	0.126626	+	0.215559i
$721$	−23.4517			−0.873388
$722$	−19.3136	+	19.3136i	−0.718779	+	0.718779i
$723$	−5.13042	+	9.27945i	−0.190802	+	0.345106i
$724$			11.1245i			0.413439i
$725$	32.3693	+	1.91644i	1.20217	+	0.0711747i
$726$	−1.54802	−	5.37637i	−0.0574523	−	0.199536i
$727$	3.34014	+	3.34014i	0.123879	+	0.123879i	0.766328	−	0.642449i	$-0.222082\pi$
$727$	3.34014	+	3.34014i	0.123879	+	0.123879i	−0.642449	+	0.766328i	$0.722082\pi$
$728$	−13.1206	−	13.1206i	−0.486281	−	0.486281i
$729$	26.8330	−	2.99846i	0.993814	−	0.111054i
$730$	0.200803	−	6.78921i	0.00743206	−	0.251280i
$731$		−	14.8098i		−	0.547760i
$732$	−17.6804	−	9.77513i	−0.653486	−	0.361299i
$733$	21.3827	−	21.3827i	0.789788	−	0.789788i	−0.191671	−	0.981459i	$-0.561391\pi$
$733$	21.3827	−	21.3827i	0.789788	−	0.789788i	0.981459	+	0.191671i	$0.0613906\pi$
$734$	11.8513			0.437441
$735$	−14.9273	−	8.83902i	−0.550600	−	0.326032i
$736$	−1.00000			−0.0368605
$737$	4.12483	−	4.12483i	0.151940	−	0.151940i
$738$	−5.37225	+	23.5043i	−0.197755	+	0.865205i
$739$		−	27.3440i		−	1.00587i	−0.864326	−	0.502933i	$-0.832254\pi$
$739$		−	27.3440i		−	1.00587i	0.864326	−	0.502933i	$-0.167746\pi$
$740$	10.7900	−	10.1701i	0.396649	−	0.373860i
$741$	−62.0343	+	17.8615i	−2.27889	+	0.656159i
$742$	−3.90268	−	3.90268i	−0.143272	−	0.143272i
$743$	−24.1777	−	24.1777i	−0.886995	−	0.886995i	0.107238	−	0.994233i	$-0.465799\pi$
$743$	−24.1777	−	24.1777i	−0.886995	−	0.886995i	−0.994233	+	0.107238i	$0.965799\pi$
$744$	−11.8090	+	3.40016i	−0.432939	+	0.124656i
$745$	−30.7505	−	0.909500i	−1.12661	−	0.0333215i
$746$		−	10.8041i		−	0.395567i
$747$	−4.91901	+	21.5213i	−0.179977	+	0.787423i
$748$	9.74104	−	9.74104i	0.356168	−	0.356168i
$749$	34.1032			1.24610
$750$	3.68846	+	19.0104i	0.134684	+	0.694162i
$751$	34.8097			1.27022			0.635112	−	0.772420i	$-0.280954\pi$
$751$	34.8097			1.27022			0.635112	+	0.772420i	$0.280954\pi$
$752$	−3.40424	+	3.40424i	−0.124140	+	0.124140i
$753$	21.9151	+	12.1164i	0.798632	+	0.441548i
$754$		−	35.5169i		−	1.29345i
$755$	−3.63074	−	0.107385i	−0.132136	−	0.00390816i
$756$	11.7371	−	13.1217i	0.426874	−	0.477232i
$757$	−18.4573	−	18.4573i	−0.670841	−	0.670841i	0.287069	−	0.957910i	$-0.407319\pi$
$757$	−18.4573	−	18.4573i	−0.670841	−	0.670841i	−0.957910	+	0.287069i	$0.907319\pi$
$758$	0.743441	+	0.743441i	0.0270030	+	0.0270030i
$759$	1.80783	+	6.27871i	0.0656200	+	0.227903i
$760$	11.0737	−	10.4375i	0.401686	−	0.378607i
$761$			4.20612i			0.152472i	0.997090	+	0.0762358i	$0.0242902\pi$
$761$			4.20612i			0.152472i	−0.997090	+	0.0762358i	$0.975710\pi$
$762$	−5.60088	+	10.1304i	−0.202898	+	0.366985i
$763$	−43.4176	+	43.4176i	−1.57182	+	1.57182i
$764$	−5.61428			−0.203118
$765$	23.7098	+	6.16215i	0.857230	+	0.222793i
$766$	23.2361			0.839554
$767$	3.84624	−	3.84624i	0.138880	−	0.138880i
$768$	−0.838057	+	1.51580i	−0.0302408	+	0.0546968i
$769$		−	32.2378i		−	1.16253i	−0.813716	−	0.581263i	$-0.802559\pi$
$769$		−	32.2378i		−	1.16253i	0.813716	−	0.581263i	$-0.197441\pi$
$770$	0.844904	−	28.5664i	0.0304482	−	1.02946i
$771$	12.7428	+	44.2567i	0.458922	+	1.59387i
$772$	−9.77402	−	9.77402i	−0.351775	−	0.351775i
$773$	−0.232058	−	0.232058i	−0.00834653	−	0.00834653i	0.702921	−	0.711268i	$-0.251879\pi$
$773$	−0.232058	−	0.232058i	−0.00834653	−	0.00834653i	−0.711268	+	0.702921i	$0.751879\pi$
$774$	10.3034	−	6.46965i	0.370347	−	0.232547i
$775$	−35.4126	−	2.09661i	−1.27206	−	0.0753126i
$776$			14.9460i			0.536532i
$777$	−34.0551	−	18.8284i	−1.22172	−	0.675465i
$778$	−3.14157	+	3.14157i	−0.112631	+	0.112631i
$779$	54.6938			1.95961
$780$	20.5473	−	5.26364i	0.735713	−	0.188469i
$781$	34.9373			1.25016
$782$	−2.58226	+	2.58226i	−0.0923416	+	0.0923416i
$783$	33.6459	−	1.87406i	1.20241	−	0.0669733i
$784$		−	4.47922i		−	0.159972i
$785$	−28.1580	−	29.8744i	−1.00500	−	1.06626i
$786$	15.9748	−	4.59961i	0.569801	−	0.164063i
$787$	0.613938	+	0.613938i	0.0218845	+	0.0218845i	0.717964	−	0.696080i	$-0.245074\pi$
$787$	0.613938	+	0.613938i	0.0218845	+	0.0218845i	−0.696080	+	0.717964i	$0.745074\pi$
$788$	1.13050	+	1.13050i	0.0402723	+	0.0402723i
$789$	−22.8231	+	6.57144i	−0.812523	+	0.233949i
$790$	7.05058	+	7.48035i	0.250848	+	0.266139i
$791$		−	69.9323i		−	2.48651i
$792$	11.0324	+	2.52161i	0.392018	+	0.0896014i
$793$	−45.1695	+	45.1695i	−1.60402	+	1.60402i
$794$	3.93560			0.139669
$795$	6.11175	−	1.56566i	0.216762	−	0.0555281i
$796$	4.63646			0.164335
$797$	2.57948	−	2.57948i	0.0913700	−	0.0913700i	−0.659944	−	0.751314i	$-0.729420\pi$
$797$	2.57948	−	2.57948i	0.0913700	−	0.0913700i	0.751314	+	0.659944i	$0.229420\pi$
$798$	−34.9505	−	19.3234i	−1.23723	−	0.684042i
$799$			17.5813i			0.621981i
$800$	−3.73831	+	3.32040i	−0.132169	+	0.117394i
$801$	15.2611	+	24.3044i	0.539225	+	0.858753i
$802$	−0.788886	−	0.788886i	−0.0278565	−	0.0278565i
$803$	−8.10241	−	8.10241i	−0.285928	−	0.285928i
$804$	0.741085	+	2.57384i	0.0261361	+	0.0907724i
$805$	−0.223976	+	7.57271i	−0.00789413	+	0.266903i
$806$			38.8561i			1.36865i
$807$	−3.60833	+	6.52642i	−0.127019	+	0.229741i
$808$	2.19172	−	2.19172i	0.0771044	−	0.0771044i
$809$	54.2052			1.90575			0.952876	−	0.303359i	$-0.0981083\pi$
$809$	54.2052			1.90575			0.952876	+	0.303359i	$0.0981083\pi$
$810$	6.07054	+	19.1872i	0.213297	+	0.674169i
$811$	−24.4217			−0.857561			−0.428781	−	0.903409i	$-0.641057\pi$
$811$	−24.4217			−0.857561			−0.428781	+	0.903409i	$0.641057\pi$
$812$	15.5369	−	15.5369i	0.545239	−	0.545239i
$813$	7.26130	−	13.1336i	0.254665	−	0.460615i
$814$		−	25.0143i		−	0.876750i
$815$	−13.1626	+	12.4064i	−0.461066	+	0.434576i
$816$	1.75012	+	6.07829i	0.0612664	+	0.212783i
$817$	−19.5152	−	19.5152i	−0.682750	−	0.682750i
$818$	10.8776	+	10.8776i	0.380326	+	0.380326i
$819$	−29.6017	−	47.1427i	−1.03437	−	1.64730i
$820$	−17.9630	−	0.531288i	−0.627295	−	0.0185534i
$821$		−	23.6788i		−	0.826396i	−0.910641	−	0.413198i	$-0.864412\pi$
$821$		−	23.6788i		−	0.826396i	0.910641	−	0.413198i	$-0.135588\pi$
$822$	11.3511	+	6.27581i	0.395916	+	0.218894i
$823$	−21.7706	+	21.7706i	−0.758875	+	0.758875i	−0.976118	−	0.217243i	$-0.930294\pi$
$823$	−21.7706	+	21.7706i	−0.758875	+	0.758875i	0.217243	+	0.976118i	$0.430294\pi$
$824$	6.92180			0.241132
$825$	27.6060	+	17.4691i	0.961119	+	0.608195i
$826$	3.36508			0.117086
$827$	10.4409	−	10.4409i	0.363065	−	0.363065i	−0.501875	−	0.864940i	$-0.667356\pi$
$827$	10.4409	−	10.4409i	0.363065	−	0.363065i	0.864940	+	0.501875i	$0.167356\pi$
$828$	−2.92458	−	0.668456i	−0.101636	−	0.0232304i
$829$			17.3634i			0.603056i	0.953457	+	0.301528i	$0.0974967\pi$
$829$			17.3634i			0.603056i	−0.953457	+	0.301528i	$0.902503\pi$
$830$	−16.4475	−	0.486464i	−0.570901	−	0.0168854i
$831$	−49.1475	+	14.1510i	−1.70491	+	0.490894i
$832$	3.87255	+	3.87255i	0.134257	+	0.134257i
$833$	−11.5665	−	11.5665i	−0.400756	−	0.400756i
$834$	21.0572	−	6.06298i	0.729150	−	0.209944i
$835$	−20.7383	+	19.5468i	−0.717677	+	0.676443i
$836$		−	25.6720i		−	0.887883i
$837$	−36.8092	+	2.05025i	−1.27231	+	0.0708669i
$838$	2.32975	−	2.32975i	0.0804798	−	0.0804798i
$839$	−7.86161			−0.271413			−0.135706	−	0.990749i	$-0.543330\pi$
$839$	−7.86161			−0.271413			−0.135706	+	0.990749i	$0.543330\pi$
$840$	11.2910	+	6.68587i	0.389578	+	0.230684i
$841$	13.0578			0.450270
$842$	18.5866	−	18.5866i	0.640537	−	0.640537i
$843$	−33.2446	−	18.3803i	−1.14501	−	0.633051i
$844$			8.96557i			0.308608i
$845$	1.12337	−	37.9815i	0.0386451	−	1.30660i
$846$	−12.2315	+	7.68038i	−0.420529	+	0.264057i
$847$	−7.73864	−	7.73864i	−0.265903	−	0.265903i
$848$	1.15188	+	1.15188i	0.0395557	+	0.0395557i
$849$	−1.06000	−	3.68147i	−0.0363792	−	0.126348i
$850$	−1.07916	+	18.2274i	−0.0370150	+	0.625196i
$851$			6.63106i			0.227310i
$852$	−7.76173	+	14.0387i	−0.265912	+	0.480959i
$853$	−22.8283	+	22.8283i	−0.781627	+	0.781627i	−0.980105	−	0.198478i	$-0.936400\pi$
$853$	−22.8283	+	22.8283i	−0.781627	+	0.781627i	0.198478	+	0.980105i	$0.436400\pi$
$854$	−39.5189			−1.35231
$855$	39.3629	−	23.1230i	1.34618	−	0.790788i
$856$	−10.0656			−0.344035
$857$	−32.4516	+	32.4516i	−1.10852	+	1.10852i	−0.115180	+	0.993345i	$0.536744\pi$
$857$	−32.4516	+	32.4516i	−1.10852	+	1.10852i	−0.993345	+	0.115180i	$0.963256\pi$
$858$	17.3137	−	31.3155i	0.591081	−	1.06909i
$859$			35.0172i			1.19477i	0.801954	+	0.597386i	$0.203794\pi$
$859$			35.0172i			1.19477i	−0.801954	+	0.597386i	$0.796206\pi$
$860$	6.21977	+	6.59891i	0.212092	+	0.225021i
$861$	13.0494	+	45.3216i	0.444724	+	1.54456i
$862$	8.72855	+	8.72855i	0.297296	+	0.297296i
$863$	−10.3748	−	10.3748i	−0.353162	−	0.353162i	0.508123	−	0.861285i	$-0.330340\pi$
$863$	−10.3748	−	10.3748i	−0.353162	−	0.353162i	−0.861285	+	0.508123i	$0.830340\pi$
$864$	−3.46421	+	3.87288i	−0.117855	+	0.131758i
$865$	−31.9243	−	33.8702i	−1.08546	−	1.15162i
$866$		−	5.94809i		−	0.202124i
$867$	−5.55365	−	3.07050i	−0.188612	−	0.104280i
$868$	−16.9976	+	16.9976i	−0.576937	+	0.576937i
$869$	17.3416			0.588272
$870$	6.23301	+	24.3314i	0.211319	+	0.824912i
$871$	8.46892			0.286958
$872$	12.8147	−	12.8147i	0.433961	−	0.433961i
$873$	−9.99077	+	43.7109i	−0.338136	+	1.47939i
$874$			6.80541i			0.230196i
$875$	24.3071	+	29.0528i	0.821730	+	0.982165i
$876$	5.05580	−	1.45572i	0.170820	−	0.0491841i
$877$	39.1429	+	39.1429i	1.32176	+	1.32176i	0.912349	+	0.409413i	$0.134267\pi$
$877$	39.1429	+	39.1429i	1.32176	+	1.32176i	0.409413	+	0.912349i	$0.365733\pi$
$878$	−16.5435	−	16.5435i	−0.558315	−	0.558315i
$879$	−15.0568	+	4.33529i	−0.507853	+	0.146226i
$880$	−0.249374	+	8.43140i	−0.00840639	+	0.284223i
$881$			16.8954i			0.569221i	0.958643	+	0.284611i	$0.0918643\pi$
$881$			16.8954i			0.569221i	−0.958643	+	0.284611i	$0.908136\pi$
$882$	2.99416	−	13.0998i	0.100819	−	0.441095i
$883$	3.79807	−	3.79807i	0.127815	−	0.127815i	−0.640305	−	0.768121i	$-0.721192\pi$
$883$	3.79807	−	3.79807i	0.127815	−	0.127815i	0.768121	+	0.640305i	$0.221192\pi$
$884$	19.9999			0.672669
$885$	−1.95993	+	3.30992i	−0.0658824	+	0.111262i
$886$	2.24762			0.0755103
$887$	−1.76712	+	1.76712i	−0.0593341	+	0.0593341i	−0.736151	−	0.676817i	$-0.763359\pi$
$887$	−1.76712	+	1.76712i	−0.0593341	+	0.0593341i	0.676817	+	0.736151i	$0.263359\pi$
$888$	10.0514	+	5.55721i	0.337303	+	0.186488i
$889$			22.6432i			0.759430i
$890$	−15.5660	+	14.6717i	−0.521773	+	0.491795i
$891$	30.5794	+	14.7493i	1.02445	+	0.494120i
$892$	−15.5814	−	15.5814i	−0.521704	−	0.521704i
$893$	23.1672	+	23.1672i	0.775262	+	0.775262i
$894$	−6.59339	−	22.8993i	−0.220516	−	0.765867i
$895$	−13.6081	−	0.402483i	−0.454868	−	0.0134535i
$896$			3.38810i			0.113188i
$897$	−4.58971	+	8.30147i	−0.153246	+	0.277178i
$898$	−15.5925	+	15.5925i	−0.520328	+	0.520328i
$899$	−46.0119			−1.53458
$900$	−13.1525	+	7.21187i	−0.438418	+	0.240396i
$901$	5.94892			0.198187
$902$	−21.4375	+	21.4375i	−0.713790	+	0.713790i
$903$	11.5150	−	20.8273i	0.383194	−	0.693088i
$904$			20.6406i			0.686495i
$905$	−24.8643	−	0.735406i	−0.826517	−	0.0244457i
$906$	−0.778487	−	2.70374i	−0.0258635	−	0.0898258i
$907$	1.92387	+	1.92387i	0.0638810	+	0.0638810i	0.738326	−	0.674445i	$-0.235617\pi$
$907$	1.92387	+	1.92387i	0.0638810	+	0.0638810i	−0.674445	+	0.738326i	$0.735617\pi$
$908$	17.4824	+	17.4824i	0.580173	+	0.580173i
$909$	7.87493	−	4.94479i	0.261195	−	0.164008i
$910$	30.1931	−	28.4583i	1.00089	−	0.943385i
$911$		−	15.9216i		−	0.527508i	−0.964590	−	0.263754i	$-0.915039\pi$
$911$		−	15.9216i		−	0.527508i	0.964590	−	0.263754i	$-0.0849607\pi$
$912$	10.3157	+	5.70332i	0.341586	+	0.188856i
$913$	−19.6288	+	19.6288i	−0.649620	+	0.649620i
$914$	37.3102			1.23411
$915$	23.0171	−	38.8711i	0.760921	−	1.28504i
$916$	9.74724			0.322058
$917$	22.9938	−	22.9938i	0.759321	−	0.759321i
$918$	1.05530	+	18.9463i	0.0348300	+	0.625322i
$919$			16.0962i			0.530965i	0.964116	+	0.265483i	$0.0855313\pi$
$919$			16.0962i			0.530965i	−0.964116	+	0.265483i	$0.914469\pi$
$920$	0.0661068	−	2.23509i	0.00217948	−	0.0736888i
$921$	41.2688	−	11.8825i	1.35985	−	0.391542i
$922$	−8.63406	−	8.63406i	−0.284348	−	0.284348i
$923$	35.8659	+	35.8659i	1.18054	+	1.18054i
$924$	21.2729	−	6.12510i	0.699827	−	0.201501i
$925$	22.0178	+	24.7890i	0.723940	+	0.815056i
$926$		−	17.9830i		−	0.590959i
$927$	20.2433	+	4.62692i	0.664879	+	0.151968i
$928$	−4.58573	+	4.58573i	−0.150534	+	0.150534i
$929$	30.0036			0.984388			0.492194	−	0.870486i	$-0.336195\pi$
$929$	30.0036			0.984388			0.492194	+	0.870486i	$0.336195\pi$
$930$	−6.81901	−	26.6189i	−0.223604	−	0.872870i
$931$	−30.4829			−0.999038
$932$	6.27349	−	6.27349i	0.205495	−	0.205495i
$933$	−1.56010	−	0.862548i	−0.0510754	−	0.0282386i
$934$			19.5256i			0.638896i
$935$	21.1282	+	22.4161i	0.690965	+	0.733083i
$936$	8.73695	+	13.9142i	0.285576	+	0.454800i
$937$	6.00639	+	6.00639i	0.196220	+	0.196220i	0.798378	−	0.602157i	$-0.205692\pi$
$937$	6.00639	+	6.00639i	0.196220	+	0.196220i	−0.602157	+	0.798378i	$0.705692\pi$
$938$	3.70473	+	3.70473i	0.120964	+	0.120964i
$939$	−3.49246	−	12.1296i	−0.113972	−	0.395833i
$940$	−7.38374	−	7.83382i	−0.240831	−	0.255511i
$941$			53.2449i			1.73573i	0.496796	+	0.867867i	$0.334510\pi$
$941$			53.2449i			1.73573i	−0.496796	+	0.867867i	$0.665490\pi$
$942$	15.3863	−	27.8293i	0.501312	−	0.906728i
$943$	5.68288	−	5.68288i	0.185060	−	0.185060i
$944$	−0.993207			−0.0323261
$945$	28.5523	+	27.1009i	0.928807	+	0.881593i
$946$	15.2981			0.497385
$947$	13.3329	−	13.3329i	0.433261	−	0.433261i	−0.456475	−	0.889736i	$-0.650888\pi$
$947$	13.3329	−	13.3329i	0.433261	−	0.433261i	0.889736	+	0.456475i	$0.150888\pi$
$948$	−3.85263	+	6.96829i	−0.125127	+	0.226320i
$949$		−	16.6355i		−	0.540012i
$950$	22.5967	+	25.4407i	0.733133	+	0.825406i
$951$	1.45845	+	5.06530i	0.0472935	+	0.164254i
$952$	8.74897	+	8.74897i	0.283556	+	0.283556i
$953$	−7.38618	−	7.38618i	−0.239262	−	0.239262i	0.577283	−	0.816544i	$-0.304113\pi$
$953$	−7.38618	−	7.38618i	−0.239262	−	0.239262i	−0.816544	+	0.577283i	$0.804113\pi$
$954$	2.59878	+	4.13875i	0.0841387	+	0.133997i
$955$	0.371142	−	12.5484i	0.0120099	−	0.406057i
$956$		−	23.7283i		−	0.767428i
$957$	37.0827	+	20.5023i	1.19871	+	0.662744i
$958$	−8.81037	+	8.81037i	−0.284650	+	0.284650i
$959$	25.3719			0.819301
$960$	−3.33256	−	1.97334i	−0.107558	−	0.0636892i
$961$	19.3378			0.623801
$962$	25.6791	−	25.6791i	0.827928	−	0.827928i
$963$	−29.4376	−	6.72840i	−0.948614	−	0.216820i
$964$		−	6.12180i		−	0.197170i
$965$	22.4919	−	21.1997i	0.724041	−	0.682442i
$966$	−5.63926	+	1.62371i	−0.181440	+	0.0522420i
$967$	1.76939	+	1.76939i	0.0568999	+	0.0568999i	0.734984	−	0.678084i	$-0.237190\pi$
$967$	1.76939	+	1.76939i	0.0568999	+	0.0568999i	−0.678084	+	0.734984i	$0.737190\pi$
$968$	2.28406	+	2.28406i	0.0734126	+	0.0734126i
$969$	41.3652	−	11.9103i	1.32884	−	0.382613i
$970$	−33.4058	−	0.988035i	−1.07259	−	0.0317239i
$971$		−	53.9969i		−	1.73284i	−0.499314	−	0.866421i	$-0.666414\pi$
$971$		−	53.9969i		−	1.73284i	0.499314	−	0.866421i	$-0.333586\pi$
$972$	−12.7202	+	9.01088i	−0.408001	+	0.289024i
$973$	30.3093	−	30.3093i	0.971670	−	0.971670i
$974$	−2.55502			−0.0818682
$975$	10.4064	+	46.2731i	0.333271	+	1.48193i
$976$	11.6640			0.373357
$977$	6.00002	−	6.00002i	0.191958	−	0.191958i	−0.604584	−	0.796541i	$-0.706661\pi$
$977$	6.00002	−	6.00002i	0.191958	−	0.191958i	0.796541	+	0.604584i	$0.206661\pi$
$978$	−12.2616	−	6.77917i	−0.392082	−	0.216774i
$979$			36.0863i			1.15332i
$980$	10.0115	+	0.296107i	0.319805	+	0.00945879i
$981$	46.0437	−	28.9116i	1.47006	−	0.923076i
$982$	−19.8085	−	19.8085i	−0.632116	−	0.632116i
$983$	−11.3165	−	11.3165i	−0.360940	−	0.360940i	0.503219	−	0.864159i	$-0.332149\pi$
$983$	−11.3165	−	11.3165i	−0.360940	−	0.360940i	−0.864159	+	0.503219i	$0.832149\pi$
$984$	−3.85155	−	13.3767i	−0.122783	−	0.426434i
$985$	−2.60150	+	2.45203i	−0.0828906	+	0.0781282i
$986$			23.6831i			0.754224i
$987$	−13.6699	+	24.7249i	−0.435117	+	0.787001i
$988$	26.3543	−	26.3543i	0.838442	−	0.838442i
$989$	−4.05539			−0.128954
$990$	−6.36534	+	24.4916i	−0.202304	+	0.778395i
$991$	−28.3161			−0.899490			−0.449745	−	0.893157i	$-0.648485\pi$
$991$	−28.3161			−0.899490			−0.449745	+	0.893157i	$0.648485\pi$
$992$	5.01686	−	5.01686i	0.159286	−	0.159286i
$993$	8.40480	−	15.2019i	0.266718	−	0.482416i
$994$			31.3791i			0.995286i
$995$	−0.306501	+	10.3629i	−0.00971675	+	0.328526i
$996$	−3.52661	−	12.2481i	−0.111745	−	0.388097i
$997$	−25.6038	−	25.6038i	−0.810882	−	0.810882i	0.173884	−	0.984766i	$-0.444368\pi$
$997$	−25.6038	−	25.6038i	−0.810882	−	0.810882i	−0.984766	+	0.173884i	$0.944368\pi$
$998$	18.8922	+	18.8922i	0.598023	+	0.598023i
$999$	25.6813	+	22.9714i	0.812522	+	0.726783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.11	yes	32
3.2	odd	2	inner	690.2.i.f.47.2	✓	32
5.3	odd	4	inner	690.2.i.f.323.2	yes	32
15.8	even	4	inner	690.2.i.f.323.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.2	✓	32	3.2	odd	2	inner
690.2.i.f.47.11	yes	32	1.1	even	1	trivial
690.2.i.f.323.2	yes	32	5.3	odd	4	inner
690.2.i.f.323.11	yes	32	15.8	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.838057 + 1.51580i) q^{3} -1.00000i q^{4} +(2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.59532 - 2.54066i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.838057 + 1.51580i) q^{3} -1.00000i q^{4} +(2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.59532 - 2.54066i) q^{9} +(1.62719 - 1.53370i) q^{10} -3.77229i q^{11} +(1.51580 + 0.838057i) q^{12} +(3.87255 - 3.87255i) q^{13} +3.38810 q^{14} +(-1.97334 + 3.33256i) q^{15} -1.00000 q^{16} +(-2.58226 + 2.58226i) q^{17} +(-2.92458 - 0.668456i) q^{18} +6.80541i q^{19} +(0.0661068 - 2.23509i) q^{20} +(-5.63926 + 1.62371i) q^{21} +(-2.66741 - 2.66741i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.66443 - 0.479239i) q^{24} +(4.99126 + 0.295509i) q^{25} -5.47661i q^{26} +(5.18811 - 0.288974i) q^{27} +(2.39575 - 2.39575i) q^{28} +6.48520 q^{29} +(0.961112 + 3.75183i) q^{30} -7.09492 q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.71805 + 3.16139i) q^{33} +3.65187i q^{34} +(5.19634 + 5.51309i) q^{35} +(-2.54066 + 1.59532i) q^{36} +(4.68887 + 4.68887i) q^{37} +(4.81215 + 4.81215i) q^{38} +(2.62461 + 9.11544i) q^{39} +(-1.53370 - 1.62719i) q^{40} -8.03681i q^{41} +(-2.83942 + 5.13569i) q^{42} +(-2.86760 + 2.86760i) q^{43} -3.77229 q^{44} +(-3.39773 - 5.78407i) q^{45} +1.00000 q^{46} +(3.40424 - 3.40424i) q^{47} +(0.838057 - 1.51580i) q^{48} +4.47922i q^{49} +(3.73831 - 3.32040i) q^{50} +(-1.75012 - 6.07829i) q^{51} +(-3.87255 - 3.87255i) q^{52} +(-1.15188 - 1.15188i) q^{53} +(3.46421 - 3.87288i) q^{54} +(0.249374 - 8.43140i) q^{55} -3.38810i q^{56} +(-10.3157 - 5.70332i) q^{57} +(4.58573 - 4.58573i) q^{58} +0.993207 q^{59} +(3.33256 + 1.97334i) q^{60} -11.6640 q^{61} +(-5.01686 + 5.01686i) q^{62} +(2.26480 - 9.90877i) q^{63} +1.00000i q^{64} +(8.91150 - 8.39950i) q^{65} +(6.27871 - 1.80783i) q^{66} +(1.09345 + 1.09345i) q^{67} +(2.58226 + 2.58226i) q^{68} +(-1.66443 + 0.479239i) q^{69} +(7.57271 + 0.223976i) q^{70} +9.26157i q^{71} +(-0.668456 + 2.92458i) q^{72} +(2.14788 - 2.14788i) q^{73} +6.63106 q^{74} +(-4.63090 + 7.31812i) q^{75} +6.80541 q^{76} +(9.03745 - 9.03745i) q^{77} +(8.30147 + 4.58971i) q^{78} +4.59709i q^{79} +(-2.23509 - 0.0661068i) q^{80} +(-3.90991 + 8.10633i) q^{81} +(-5.68288 - 5.68288i) q^{82} +(-5.20343 - 5.20343i) q^{83} +(1.62371 + 5.63926i) q^{84} +(-5.94230 + 5.60089i) q^{85} +4.05539i q^{86} +(-5.43497 + 9.83029i) q^{87} +(-2.66741 + 2.66741i) q^{88} -9.56617 q^{89} +(-6.49251 - 1.68739i) q^{90} +18.5553 q^{91} +(0.707107 - 0.707107i) q^{92} +(5.94594 - 10.7545i) q^{93} -4.81432i q^{94} +(-0.449884 + 15.2107i) q^{95} +(-0.479239 - 1.66443i) q^{96} +(-10.5684 - 10.5684i) q^{97} +(3.16729 + 3.16729i) q^{98} +(-9.58410 + 6.01801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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