LMFDB - Embedded newform 690.2.i.f.323.2

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			323.2
Character	$\chi$	$=$	690.323
Dual form			690.2.i.f.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.51580 - 0.838057i) q^{3} +1.00000i q^{4} +(-2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 - 2.39575i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.59532 + 2.54066i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.51580 - 0.838057i) 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} +(0.838057 - 1.51580i) q^{12} +(3.87255 + 3.87255i) q^{13} -3.38810 q^{14} +(3.44336 + 1.77293i) q^{15} -1.00000 q^{16} +(2.58226 + 2.58226i) q^{17} +(0.668456 - 2.92458i) 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} +(-0.288974 - 5.18811i) q^{27} +(2.39575 + 2.39575i) q^{28} -6.48520 q^{29} +(-1.18117 - 3.68847i) q^{30} -7.09492 q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.16139 + 5.71805i) 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} +(5.13569 + 2.83942i) q^{42} +(-2.86760 - 2.86760i) q^{43} +3.77229 q^{44} +(-3.73364 - 5.57314i) q^{45} +1.00000 q^{46} +(-3.40424 - 3.40424i) q^{47} +(1.51580 + 0.838057i) 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} +(-5.70332 + 10.3157i) q^{57} +(4.58573 + 4.58573i) q^{58} -0.993207 q^{59} +(-1.77293 + 3.44336i) q^{60} -11.6640 q^{61} +(5.01686 + 5.01686i) q^{62} +(9.90877 + 2.26480i) 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} +(2.92458 + 0.668456i) q^{72} +(2.14788 + 2.14788i) q^{73} -6.63106 q^{74} +(-7.81342 - 3.73503i) q^{75} +6.80541 q^{76} +(-9.03745 - 9.03745i) q^{77} +(-4.58971 + 8.30147i) 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} +(9.83029 + 5.43497i) q^{87} +(-2.66741 - 2.66741i) q^{88} +9.56617 q^{89} +(-1.30072 + 6.58089i) q^{90} +18.5553 q^{91} +(-0.707107 - 0.707107i) q^{92} +(10.7545 + 5.94594i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	−1.51580	−	0.838057i	−0.875150	−	0.483853i
$3$	−1.51580	−	0.838057i	−0.875150	−	0.483853i
$4$			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	−0.0903979	−	0.995906i	$-0.528814\pi$
$7$	2.39575	−	2.39575i	0.905508	−	0.905508i	0.995906	+	0.0903979i	$0.0288139\pi$
$8$	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	$-0.192551\pi$
$12$	0.838057	−	1.51580i	0.241926	−	0.437575i
$13$	3.87255	+	3.87255i	1.07405	+	1.07405i	0.997029	+	0.0770227i	$0.0245414\pi$
$13$	3.87255	+	3.87255i	1.07405	+	1.07405i	0.0770227	+	0.997029i	$0.475459\pi$
$14$	−3.38810			−0.905508
$15$	3.44336	+	1.77293i	0.889072	+	0.457768i
$16$	−1.00000			−0.250000
$17$	2.58226	+	2.58226i	0.626291	+	0.626291i	0.947133	−	0.320842i	$-0.103966\pi$
$17$	2.58226	+	2.58226i	0.626291	+	0.626291i	−0.320842	+	0.947133i	$0.603966\pi$
$18$	0.668456	−	2.92458i	0.157557	−	0.689330i
$19$		−	6.80541i		−	1.56127i	−0.624988	−	0.780634i	$-0.714896\pi$
$19$		−	6.80541i		−	1.56127i	0.624988	−	0.780634i	$-0.285104\pi$
$20$	−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
$27$	−0.288974	−	5.18811i	−0.0556131	−	0.998452i
$28$	2.39575	+	2.39575i	0.452754	+	0.452754i
$29$	−6.48520			−1.20427			−0.602136	−	0.798394i	$-0.705683\pi$
$29$	−6.48520			−1.20427			−0.602136	+	0.798394i	$0.705683\pi$
$30$	−1.18117	−	3.68847i	−0.215652	−	0.673420i
$31$	−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
$33$	−3.16139	+	5.71805i	−0.550328	+	0.995384i
$34$		−	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	−0.207409	−	0.978254i	$-0.566503\pi$
$37$	4.68887	−	4.68887i	0.770846	−	0.770846i	0.978254	+	0.207409i	$0.0665030\pi$
$38$	−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	$-0.215950\pi$
$42$	5.13569	+	2.83942i	0.792455	+	0.438132i
$43$	−2.86760	−	2.86760i	−0.437304	−	0.437304i	0.453799	−	0.891104i	$-0.350068\pi$
$43$	−2.86760	−	2.86760i	−0.437304	−	0.437304i	−0.891104	+	0.453799i	$0.850068\pi$
$44$	3.77229			0.568694
$45$	−3.73364	−	5.57314i	−0.556578	−	0.830795i
$46$	1.00000			0.147442
$47$	−3.40424	−	3.40424i	−0.496559	−	0.496559i	0.413806	−	0.910365i	$-0.364199\pi$
$47$	−3.40424	−	3.40424i	−0.496559	−	0.496559i	−0.910365	+	0.413806i	$0.864199\pi$
$48$	1.51580	+	0.838057i	0.218787	+	0.120963i
$49$		−	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	$-0.714313\pi$
$53$	1.15188	−	1.15188i	0.158223	−	0.158223i	0.781779	+	0.623556i	$0.214313\pi$
$54$	−3.46421	+	3.87288i	−0.471420	+	0.527033i
$55$	0.249374	+	8.43140i	0.0336256	+	1.13689i
$56$		−	3.38810i		−	0.452754i
$57$	−5.70332	+	10.3157i	−0.755424	+	1.36634i
$58$	4.58573	+	4.58573i	0.602136	+	0.602136i
$59$	−0.993207			−0.129304			−0.0646522	−	0.997908i	$-0.520594\pi$
$59$	−0.993207			−0.129304			−0.0646522	+	0.997908i	$0.520594\pi$
$60$	−1.77293	+	3.44336i	−0.228884	+	0.444536i
$61$	−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
$63$	9.90877	+	2.26480i	1.24839	+	0.285337i
$64$		−	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	−0.637152	−	0.770738i	$-0.719888\pi$
$67$	1.09345	−	1.09345i	0.133587	−	0.133587i	0.770738	+	0.637152i	$0.219888\pi$
$68$	−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	$0.814790\pi$
$72$	2.92458	+	0.668456i	0.344665	+	0.0787783i
$73$	2.14788	+	2.14788i	0.251390	+	0.251390i	0.821540	−	0.570150i	$-0.193115\pi$
$73$	2.14788	+	2.14788i	0.251390	+	0.251390i	−0.570150	+	0.821540i	$0.693115\pi$
$74$	−6.63106			−0.770846
$75$	−7.81342	−	3.73503i	−0.902216	−	0.431284i
$76$	6.80541			0.780634
$77$	−9.03745	−	9.03745i	−1.02991	−	1.02991i
$78$	−4.58971	+	8.30147i	−0.519683	+	0.939956i
$79$		−	4.59709i		−	0.517213i	−0.965983	−	0.258607i	$-0.916737\pi$
$79$		−	4.59709i		−	0.517213i	0.965983	−	0.258607i	$-0.0832633\pi$
$80$	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	$-0.617667\pi$
$83$	5.20343	−	5.20343i	0.571151	−	0.571151i	0.932450	+	0.361299i	$0.117667\pi$
$84$	−1.62371	−	5.63926i	−0.177161	−	0.615293i
$85$	−5.94230	−	5.60089i	−0.644533	−	0.607502i
$86$			4.05539i			0.437304i
$87$	9.83029	+	5.43497i	1.05392	+	0.582690i
$88$	−2.66741	−	2.66741i	−0.284347	−	0.284347i
$89$	9.56617			1.01401			0.507006	−	0.861943i	$-0.330752\pi$
$89$	9.56617			1.01401			0.507006	+	0.861943i	$0.330752\pi$
$90$	−1.30072	+	6.58089i	−0.137108	+	0.693687i
$91$	18.5553			1.94512
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$	10.7545	+	5.94594i	1.11519	+	0.616566i
$94$			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	−0.0759519	+	0.997111i	$0.524200\pi$
$97$	−10.5684	+	10.5684i	−1.07306	+	1.07306i	−0.997111	+	0.0759519i	$0.975800\pi$
$98$	−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	$0.950717\pi$
$102$	−3.06048	+	5.53552i	−0.303032	+	0.548098i
$103$	−4.89445	−	4.89445i	−0.482264	−	0.482264i	0.423590	−	0.905854i	$-0.360770\pi$
$103$	−4.89445	−	4.89445i	−0.482264	−	0.482264i	−0.905854	+	0.423590i	$0.860770\pi$
$104$	5.47661			0.537026
$105$	12.4969	−	4.00193i	1.21957	−	0.390549i
$106$	−1.62900			−0.158223
$107$	−7.11744	−	7.11744i	−0.688069	−	0.688069i	0.273736	−	0.961805i	$-0.411741\pi$
$107$	−7.11744	−	7.11744i	−0.688069	−	0.688069i	−0.961805	+	0.273736i	$0.911741\pi$
$108$	5.18811	−	0.288974i	0.499226	−	0.0278065i
$109$		−	18.1228i		−	1.73584i	−0.496700	−	0.867922i	$-0.665455\pi$
$109$		−	18.1228i		−	1.73584i	0.496700	−	0.867922i	$-0.334545\pi$
$110$	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	0.517012	−	0.855978i	$-0.327044\pi$
$113$	14.5951	−	14.5951i	1.37299	−	1.37299i	0.855978	−	0.517012i	$-0.172956\pi$
$114$	11.3271	−	3.26142i	1.06088	−	0.305460i
$115$	1.53370	−	1.62719i	0.143019	−	0.151736i
$116$		−	6.48520i		−	0.602136i
$117$	−3.66087	+	16.0168i	−0.338448	+	1.48075i
$118$	0.702303	+	0.702303i	0.0646522	+	0.0646522i
$119$	12.3729			1.13422
$120$	3.68847	−	1.18117i	0.336710	−	0.107826i
$121$	−3.23015			−0.293650
$122$	8.24772	+	8.24772i	0.746713	+	0.746713i
$123$	−6.73531	+	12.1822i	−0.607302	+	1.09843i
$124$		−	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	−0.465637	−	0.884976i	$-0.654175\pi$
$127$	4.72572	−	4.72572i	0.419339	−	0.419339i	0.884976	+	0.465637i	$0.154175\pi$
$128$	−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	$-0.137717\pi$
$132$	−5.71805	−	3.16139i	−0.497692	−	0.275164i
$133$	−16.3041	−	16.3041i	−1.41374	−	1.41374i
$134$	−1.54638			−0.133587
$135$	0.988853	+	11.5768i	0.0851069	+	0.996372i
$136$	3.65187			0.313145
$137$	−5.29519	−	5.29519i	−0.452399	−	0.452399i	0.443751	−	0.896150i	$-0.353647\pi$
$137$	−5.29519	−	5.29519i	−0.452399	−	0.452399i	−0.896150	+	0.443751i	$0.853647\pi$
$138$	−1.51580	−	0.838057i	−0.129034	−	0.0713402i
$139$			12.6513i			1.07307i	0.843879	+	0.536533i	$0.180266\pi$
$139$			12.6513i			1.07307i	−0.843879	+	0.536533i	$0.819734\pi$
$140$	−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
$147$	−3.75384	+	6.78962i	−0.309612	+	0.559998i
$148$	4.68887	+	4.68887i	0.385423	+	0.385423i
$149$	13.7580			1.12710			0.563551	−	0.826081i	$-0.309435\pi$
$149$	13.7580			1.12710			0.563551	+	0.826081i	$0.309435\pi$
$150$	2.88386	+	8.16599i	0.235466	+	0.666750i
$151$	−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
$153$	−2.44112	+	10.6802i	−0.197353	+	0.863442i
$154$			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	−0.0367599	+	0.999324i	$0.511704\pi$
$157$	−12.9821	+	12.9821i	−1.03608	+	1.03608i	−0.999324	+	0.0367599i	$0.988296\pi$
$158$	−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
$162$	8.49676	−	2.96732i	0.667569	−	0.233135i
$163$	−5.71990	−	5.71990i	−0.448017	−	0.448017i	0.446678	−	0.894695i	$-0.352607\pi$
$163$	−5.71990	−	5.71990i	−0.448017	−	0.448017i	−0.894695	+	0.446678i	$0.852607\pi$
$164$	8.03681			0.627569
$165$	6.68800	−	12.9893i	0.520660	−	1.01122i
$166$	−7.35876			−0.571151
$167$	9.01194	+	9.01194i	0.697365	+	0.697365i	0.963841	−	0.266476i	$-0.0858595\pi$
$167$	9.01194	+	9.01194i	0.697365	+	0.697365i	−0.266476	+	0.963841i	$0.585859\pi$
$168$	−2.83942	+	5.13569i	−0.219066	+	0.396227i
$169$			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	0.127145	−	0.991884i	$-0.459419\pi$
$173$	14.7185	−	14.7185i	1.11903	−	1.11903i	0.991884	−	0.127145i	$-0.0405814\pi$
$174$	−3.10796	−	10.7942i	−0.235614	−	0.818304i
$175$	11.2498	−	12.6658i	0.850408	−	0.957442i
$176$			3.77229i			0.284347i
$177$	1.50551	+	0.832364i	0.113161	+	0.0625643i
$178$	−6.76430	−	6.76430i	−0.507006	−	0.507006i
$179$	6.08838			0.455067			0.227533	−	0.973770i	$-0.426934\pi$
$179$	6.08838			0.455067			0.227533	+	0.973770i	$0.426934\pi$
$180$	5.57314	−	3.73364i	0.415398	−	0.278289i
$181$	−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
$183$	17.6804	+	9.77513i	1.30697	+	0.722598i
$184$			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	$-0.0651074\pi$
$192$	−0.838057	+	1.51580i	−0.0604816	+	0.109394i
$193$	9.77402	+	9.77402i	0.703549	+	0.703549i	0.965171	−	0.261621i	$-0.0842572\pi$
$193$	9.77402	+	9.77402i	0.703549	+	0.703549i	−0.261621	+	0.965171i	$0.584257\pi$
$194$	14.9460			1.07306
$195$	6.46883	+	20.2003i	0.463242	+	1.44658i
$196$	4.47922			0.319944
$197$	1.13050	+	1.13050i	0.0805446	+	0.0805446i	0.746231	−	0.665687i	$-0.231861\pi$
$197$	1.13050	+	1.13050i	0.0805446	+	0.0805446i	−0.665687	+	0.746231i	$0.731861\pi$
$198$	−11.0324	−	2.52161i	−0.784035	−	0.179203i
$199$		−	4.63646i		−	0.328670i	−0.986405	−	0.164335i	$-0.947452\pi$
$199$		−	4.63646i		−	0.328670i	0.986405	−	0.164335i	$-0.0525478\pi$
$200$	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
$207$	−2.92458	−	0.668456i	−0.203272	−	0.0464609i
$208$	−3.87255	−	3.87255i	−0.268513	−	0.268513i
$209$	−25.6720			−1.77577
$210$	−11.6664	−	6.00686i	−0.805061	−	0.414513i
$211$	−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
$213$	7.76173	−	14.0387i	0.531825	−	0.961918i
$214$			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
$222$	10.0514	+	5.55721i	0.674605	+	0.372976i
$223$	15.5814	+	15.5814i	1.04341	+	1.04341i	0.999014	+	0.0443938i	$0.0141356\pi$
$223$	15.5814	+	15.5814i	1.04341	+	1.04341i	0.0443938	+	0.999014i	$0.485864\pi$
$224$	3.38810			0.226377
$225$	8.71345	+	12.2097i	0.580896	+	0.813977i
$226$	−20.6406			−1.37299
$227$	17.4824	+	17.4824i	1.16035	+	1.16035i	0.984400	+	0.175945i	$0.0562982\pi$
$227$	17.4824	+	17.4824i	1.16035	+	1.16035i	0.175945	+	0.984400i	$0.443702\pi$
$228$	−10.3157	−	5.70332i	−0.683172	−	0.377712i
$229$		−	9.74724i		−	0.644116i	−0.946720	−	0.322058i	$-0.895625\pi$
$229$		−	9.74724i		−	0.644116i	0.946720	−	0.322058i	$-0.104375\pi$
$230$	−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	$-0.843860\pi$
$233$	−6.27349	+	6.27349i	−0.410990	+	0.410990i	0.471093	+	0.882083i	$0.343860\pi$
$234$	13.9142	−	8.73695i	0.909600	−	0.571152i
$235$	7.83382	+	7.38374i	0.511022	+	0.481662i
$236$		−	0.993207i		−	0.0646522i
$237$	−3.85263	+	6.96829i	−0.250255	+	0.452639i
$238$	−8.74897	−	8.74897i	−0.567111	−	0.567111i
$239$	−23.7283			−1.53486			−0.767428	−	0.641135i	$-0.778464\pi$
$239$	−23.7283			−1.53486			−0.767428	+	0.641135i	$0.778464\pi$
$240$	−3.44336	−	1.77293i	−0.222268	−	0.114442i
$241$	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
$243$	12.7202	−	9.01088i	0.816002	−	0.578048i
$244$		−	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	$-0.150820\pi$
$252$	−2.26480	+	9.90877i	−0.142669	+	0.624194i
$253$	2.66741	+	2.66741i	0.167699	+	0.167699i
$254$	−6.68317			−0.419339
$255$	4.31349	+	13.4698i	0.270121	+	0.843514i
$256$	1.00000			0.0625000
$257$	−18.8018	−	18.8018i	−1.17282	−	1.17282i	−0.981534	−	0.191288i	$-0.938733\pi$
$257$	−18.8018	−	18.8018i	−1.17282	−	1.17282i	−0.191288	−	0.981534i	$-0.561267\pi$
$258$	3.39865	−	6.14718i	0.211591	−	0.382707i
$259$		−	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	$-0.888941\pi$
$263$	−9.69602	+	9.69602i	−0.597882	+	0.597882i	0.341866	+	0.939749i	$0.388941\pi$
$264$	1.80783	+	6.27871i	0.111264	+	0.386428i
$265$	−2.49841	+	2.65070i	−0.153476	+	0.162831i
$266$			23.0574i			1.41374i
$267$	−14.5004	−	8.01700i	−0.887412	−	0.490632i
$268$	1.09345	+	1.09345i	0.0667934	+	0.0667934i
$269$	−4.30558			−0.262516			−0.131258	−	0.991348i	$-0.541902\pi$
$269$	−4.30558			−0.262516			−0.131258	+	0.991348i	$0.541902\pi$
$270$	7.48681	−	8.88525i	0.455632	−	0.540739i
$271$	−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
$273$	−28.1262	−	15.5504i	−1.70228	−	0.941154i
$274$			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	0.300862	−	0.953668i	$-0.402726\pi$
$277$	20.8795	−	20.8795i	1.25453	−	1.25453i	0.953668	−	0.300862i	$-0.0972743\pi$
$278$	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	$0.773015\pi$
$282$	4.03467	−	7.29756i	0.240261	−	0.434564i
$283$	−1.56401	−	1.56401i	−0.0929709	−	0.0929709i	0.659092	−	0.752063i	$-0.270941\pi$
$283$	−1.56401	−	1.56401i	−0.0929709	−	0.0929709i	−0.752063	+	0.659092i	$0.770941\pi$
$284$	−9.26157			−0.549573
$285$	12.0655	−	23.4335i	0.714699	−	1.38808i
$286$	−20.6594			−1.22161
$287$	−19.2542	−	19.2542i	−1.13654	−	1.13654i
$288$	−0.668456	+	2.92458i	−0.0393891	+	0.172333i
$289$		−	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	$-0.835122\pi$
$293$	−6.39663	+	6.39663i	−0.373695	+	0.373695i	0.495126	+	0.868821i	$0.335122\pi$
$294$	7.45535	−	2.14662i	0.434805	−	0.125193i
$295$	2.21991	−	0.0656577i	0.129248	−	0.00382274i
$296$		−	6.63106i		−	0.385423i
$297$	−19.5710	+	1.09009i	−1.13563	+	0.0632536i
$298$	−9.72840	−	9.72840i	−0.563551	−	0.563551i
$299$	−5.47661			−0.316721
$300$	3.73503	−	7.81342i	0.215642	−	0.451108i
$301$	−13.7401			−0.791965
$302$	1.14864	+	1.14864i	0.0660969	+	0.0660969i
$303$	2.59761	−	4.69832i	0.149229	−	0.269912i
$304$			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	−0.000625972		1.00000i	$0.500199\pi$
$307$	−17.5324	+	17.5324i	−1.00063	+	1.00063i	−1.00000		0.000625972i	$0.999801\pi$
$308$	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	$0.990710\pi$
$312$	−8.30147	−	4.58971i	−0.469978	−	0.259841i
$313$	−5.15305	−	5.15305i	−0.291268	−	0.291268i	0.546313	−	0.837581i	$-0.316031\pi$
$313$	−5.15305	−	5.15305i	−0.291268	−	0.291268i	−0.837581	+	0.546313i	$0.816031\pi$
$314$	18.3595			1.03608
$315$	−22.2967	−	4.40699i	−1.25628	−	0.248306i
$316$	4.59709			0.258607
$317$	−2.15191	−	2.15191i	−0.120863	−	0.120863i	0.644088	−	0.764951i	$-0.277237\pi$
$317$	−2.15191	−	2.15191i	−0.120863	−	0.120863i	−0.764951	+	0.644088i	$0.777237\pi$
$318$	2.46925	+	1.36520i	0.138469	+	0.0765565i
$319$			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
$327$	−15.1879	+	27.4705i	−0.839893	+	1.51912i
$328$	−5.68288	−	5.68288i	−0.313785	−	0.313785i
$329$	−16.3114			−0.899276
$330$	−13.9140	+	4.45572i	−0.765939	+	0.245280i
$331$	−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
$333$	19.3931	+	4.43257i	1.06273	+	0.242904i
$334$		−	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	−0.0196990	−	0.999806i	$-0.506271\pi$
$337$	17.9924	−	17.9924i	0.980107	−	0.980107i	0.999806	+	0.0196990i	$0.00627080\pi$
$338$	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
$342$	−19.9030	−	4.54912i	−1.07623	−	0.245988i
$343$	6.03915	+	6.03915i	0.326084	+	0.326084i
$344$	−4.05539			−0.218652
$345$	−3.68847	+	1.18117i	−0.198581	+	0.0635922i
$346$	−20.8151			−1.11903
$347$	16.7568	+	16.7568i	0.899551	+	0.899551i	0.995396	−	0.0958454i	$-0.0305554\pi$
$347$	16.7568	+	16.7568i	0.899551	+	0.899551i	−0.0958454	+	0.995396i	$0.530555\pi$
$348$	−5.43497	+	9.83029i	−0.291345	+	0.526959i
$349$			13.6323i			0.729723i	0.931062	+	0.364861i	$0.118884\pi$
$349$			13.6323i			0.729723i	−0.931062	+	0.364861i	$0.881116\pi$
$350$	−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	$-0.805946\pi$
$353$	−4.64603	+	4.64603i	−0.247283	+	0.247283i	0.572571	+	0.819855i	$0.305946\pi$
$354$	−0.475983	−	1.65312i	−0.0252982	−	0.0878625i
$355$	−0.612253	−	20.7005i	−0.0324950	−	1.09867i
$356$			9.56617i			0.507006i
$357$	−18.7549	−	10.3692i	−0.992614	−	0.548796i
$358$	−4.30513	−	4.30513i	−0.227533	−	0.227533i
$359$	34.5145			1.82160			0.910802	−	0.412845i	$-0.135465\pi$
$359$	34.5145			1.82160			0.910802	+	0.412845i	$0.135465\pi$
$360$	−6.58089	−	1.30072i	−0.346843	−	0.0685542i
$361$	−27.3136			−1.43756
$362$	7.86622	+	7.86622i	0.413439	+	0.413439i
$363$	4.89628	+	2.70705i	0.256988	+	0.142083i
$364$			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	−0.453709	−	0.891150i	$-0.649899\pi$
$367$	8.38016	−	8.38016i	0.437441	−	0.437441i	0.891150	+	0.453709i	$0.149899\pi$
$368$	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
$372$	−5.94594	+	10.7545i	−0.308283	+	0.557595i
$373$	7.63967	+	7.63967i	0.395567	+	0.395567i	0.876666	−	0.481099i	$-0.159762\pi$
$373$	7.63967	+	7.63967i	0.395567	+	0.395567i	−0.481099	+	0.876666i	$0.659762\pi$
$374$	−13.7759			−0.712335
$375$	17.7106	+	7.83160i	0.914572	+	0.404422i
$376$	−4.81432			−0.248280
$377$	−25.1143	−	25.1143i	−1.29345	−	1.29345i
$378$	0.979073	+	17.5778i	0.0503581	+	0.904106i
$379$		−	1.05138i		−	0.0540060i	−0.999635	−	0.0270030i	$-0.991404\pi$
$379$		−	1.05138i		−	0.0540060i	0.999635	−	0.0270030i	$-0.00859636\pi$
$380$	−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	$-0.952315\pi$
$383$	−16.4304	+	16.4304i	−0.839554	+	0.839554i	0.149246	+	0.988800i	$0.452315\pi$
$384$	1.66443	−	0.479239i	0.0849376	−	0.0244561i
$385$	20.7970	+	19.6021i	1.05991	+	0.999015i
$386$		−	13.8225i		−	0.703549i
$387$	2.71085	−	11.8603i	0.137800	−	0.602894i
$388$	−10.5684	−	10.5684i	−0.536532	−	0.536532i
$389$	4.44285			0.225261			0.112631	−	0.993637i	$-0.464072\pi$
$389$	4.44285			0.225261			0.112631	+	0.993637i	$0.464072\pi$
$390$	9.70964	−	18.8579i	0.491667	−	0.954909i
$391$	−3.65187			−0.184683
$392$	−3.16729	−	3.16729i	−0.159972	−	0.159972i
$393$	−8.04345	+	14.5483i	−0.405738	+	0.733863i
$394$		−	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	−0.633815	−	0.773485i	$-0.718512\pi$
$397$	2.78289	−	2.78289i	0.139669	−	0.139669i	0.773485	+	0.633815i	$0.218512\pi$
$398$	−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	$-0.00886816\pi$
$402$	2.34401	+	1.29595i	0.116908	+	0.0646363i
$403$	−27.4754	−	27.4754i	−1.36865	−	1.36865i
$404$	−3.09956			−0.154209
$405$	8.20311	−	18.3769i	0.407616	−	0.913154i
$406$	21.9725			1.09048
$407$	−17.6878	−	17.6878i	−0.876750	−	0.876750i
$408$	−5.53552	−	3.06048i	−0.274049	−	0.151516i
$409$		−	15.3832i		−	0.760653i	−0.924852	−	0.380326i	$-0.875812\pi$
$409$		−	15.3832i		−	0.760653i	0.924852	−	0.380326i	$-0.124188\pi$
$410$	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
$417$	10.6025	−	19.1768i	0.519206	−	0.939094i
$418$	18.1528	+	18.1528i	0.887883	+	0.887883i
$419$	−3.29476			−0.160960			−0.0804798	−	0.996756i	$-0.525645\pi$
$419$	−3.29476			−0.160960			−0.0804798	+	0.996756i	$0.525645\pi$
$420$	4.00193	+	12.4969i	0.195274	+	0.609787i
$421$	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
$423$	3.21816	−	14.0799i	0.156472	−	0.684586i
$424$		−	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	$0.903915\pi$
$432$	0.288974	+	5.18811i	0.0139033	+	0.249613i
$433$	4.20594	+	4.20594i	0.202124	+	0.202124i	0.800910	−	0.598785i	$-0.204350\pi$
$433$	4.20594	+	4.20594i	0.202124	+	0.202124i	−0.598785	+	0.800910i	$0.704350\pi$
$434$	24.0383			1.15387
$435$	−22.3309	−	11.4978i	−1.07068	−	0.551277i
$436$	18.1228			0.867922
$437$	4.81215	+	4.81215i	0.230196	+	0.230196i
$438$	−2.54565	+	4.60434i	−0.121636	+	0.220004i
$439$			23.3960i			1.11663i	0.829629	+	0.558315i	$0.188552\pi$
$439$			23.3960i			1.11663i	−0.829629	+	0.558315i	$0.811448\pi$
$440$	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	$-0.767004\pi$
$443$	−1.58931	+	1.58931i	−0.0755103	+	0.0755103i	0.668343	+	0.743853i	$0.267004\pi$
$444$	−3.17786	−	11.0369i	−0.150815	−	0.523790i
$445$	−21.3813	+	0.632389i	−1.01357	+	0.0299781i
$446$		−	22.0354i		−	1.04341i
$447$	−20.8545	−	11.5300i	−0.986383	−	0.545351i
$448$	−2.39575	−	2.39575i	−0.113188	−	0.113188i
$449$	22.0511			1.04066			0.520328	−	0.853966i	$-0.325810\pi$
$449$	22.0511			1.04066			0.520328	+	0.853966i	$0.325810\pi$
$450$	2.47220	−	14.7949i	0.116540	−	0.697437i
$451$	−30.3172			−1.42758
$452$	14.5951	+	14.5951i	0.686495	+	0.686495i
$453$	2.46231	+	1.36136i	0.115689	+	0.0639623i
$454$		−	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	0.271741	−	0.962370i	$-0.412401\pi$
$457$	26.3823	−	26.3823i	1.23411	−	1.23411i	0.962370	−	0.271741i	$-0.0875993\pi$
$458$	−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	$-0.0917770\pi$
$462$	10.7111	−	19.3733i	0.498326	−	0.901328i
$463$	12.7159	+	12.7159i	0.590959	+	0.590959i	0.937891	−	0.346931i	$-0.112776\pi$
$463$	12.7159	+	12.7159i	0.590959	+	0.590959i	−0.346931	+	0.937891i	$0.612776\pi$
$464$	6.48520			0.301068
$465$	−24.4303	−	12.5788i	−1.13293	−	0.583327i
$466$	8.87206			0.410990
$467$	13.8067	+	13.8067i	0.638896	+	0.638896i	0.950283	−	0.311387i	$-0.100793\pi$
$467$	13.8067	+	13.8067i	0.638896	+	0.638896i	−0.311387	+	0.950283i	$0.600793\pi$
$468$	−16.0168	−	3.66087i	−0.740376	−	0.169224i
$469$		−	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
$477$	4.76415	+	1.08892i	0.218136	+	0.0498581i
$478$	16.7784	+	16.7784i	0.767428	+	0.767428i
$479$	12.4597			0.569300			0.284650	−	0.958632i	$-0.408123\pi$
$479$	12.4597			0.569300			0.284650	+	0.958632i	$0.408123\pi$
$480$	1.18117	+	3.68847i	0.0539129	+	0.168355i
$481$	36.3158			1.65586
$482$	−4.32877	−	4.32877i	−0.197170	−	0.197170i
$483$	2.83942	−	5.13569i	0.129198	−	0.233682i
$484$		−	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	−0.746855	−	0.664987i	$-0.768437\pi$
$487$	−1.80667	+	1.80667i	−0.0818682	+	0.0818682i	0.664987	+	0.746855i	$0.268437\pi$
$488$	−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	$-0.217813\pi$
$492$	−12.1822	−	6.73531i	−0.549217	−	0.303651i
$493$	−16.7465	−	16.7465i	−0.754224	−	0.754224i
$494$	−37.2706			−1.67688
$495$	−21.0235	+	14.0844i	−0.944936	+	0.633045i
$496$	7.09492			0.318571
$497$	22.1884	+	22.1884i	0.995286	+	0.995286i
$498$	11.1544	+	6.16706i	0.499842	+	0.276353i
$499$		−	26.7176i		−	1.19605i	−0.801479	−	0.598023i	$-0.795953\pi$
$499$		−	26.7176i		−	1.19605i	0.801479	−	0.598023i	$-0.204047\pi$
$500$	−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	−0.193973	+	0.981007i	$0.562137\pi$
$503$	−26.3520	+	26.3520i	−1.17498	+	1.17498i	−0.981007	+	0.193973i	$0.937863\pi$
$504$	8.60801	−	5.40511i	0.383431	−	0.240763i
$505$	−0.204902	−	6.92780i	−0.00911802	−	0.308283i
$506$		−	3.77229i		−	0.167699i
$507$	14.2413	−	25.7585i	0.632480	−	1.14397i
$508$	4.72572	+	4.72572i	0.209670	+	0.209670i
$509$	9.42990			0.417973			0.208986	−	0.977919i	$-0.432984\pi$
$509$	9.42990			0.417973			0.208986	+	0.977919i	$0.432984\pi$
$510$	6.47451	−	12.5747i	0.286696	−	0.556817i
$511$	10.2915			0.455271
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−35.3072	+	1.96659i	−1.55885	+	0.0868270i
$514$			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	$0.901805\pi$
$522$	−4.33507	+	18.9665i	−0.189741	+	0.830141i
$523$	14.8570	+	14.8570i	0.649650	+	0.649650i	0.952908	−	0.303259i	$-0.0980746\pi$
$523$	14.8570	+	14.8570i	0.649650	+	0.649650i	−0.303259	+	0.952908i	$0.598075\pi$
$524$	9.59773			0.419279
$525$	−27.6672	+	9.77081i	−1.20749	+	0.426433i
$526$	13.7122			0.597882
$527$	−18.3209	−	18.3209i	−0.798073	−	0.798073i
$528$	3.16139	−	5.71805i	0.137582	−	0.248846i
$529$		−	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
$537$	−9.22879	−	5.10241i	−0.398251	−	0.220185i
$538$	3.04451	+	3.04451i	0.131258	+	0.131258i
$539$	−16.8969			−0.727801
$540$	−11.5768	+	0.988853i	−0.498186	+	0.0425534i
$541$	−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
$543$	16.8626	+	9.32297i	0.723642	+	0.400087i
$544$			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	−0.120514	−	0.992712i	$-0.538454\pi$
$547$	20.3990	−	20.3990i	0.872198	−	0.872198i	0.992712	+	0.120514i	$0.0384543\pi$
$548$	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
$552$	0.838057	−	1.51580i	0.0356701	−	0.0645169i
$553$	−11.0135	−	11.0135i	−0.468341	−	0.468341i
$554$	−29.5281			−1.25453
$555$	24.4585	−	7.83243i	1.03821	−	0.332468i
$556$	−12.6513			−0.536533
$557$	3.65261	+	3.65261i	0.154766	+	0.154766i	0.780243	−	0.625477i	$-0.215096\pi$
$557$	3.65261	+	3.65261i	0.154766	+	0.154766i	−0.625477	+	0.780243i	$0.715096\pi$
$558$	−4.74264	+	20.7496i	−0.200772	+	0.878403i
$559$		−	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	−0.139836	+	0.990175i	$0.544658\pi$
$563$	−26.8125	+	26.8125i	−1.13001	+	1.13001i	−0.990175	+	0.139836i	$0.955342\pi$
$564$	−8.01310	+	2.30721i	−0.337412	+	0.0971511i
$565$	−31.6565	+	33.5862i	−1.33180	+	1.41298i
$566$			2.21185i			0.0929709i
$567$	10.0536	+	28.7879i	0.422211	+	1.20898i
$568$	6.54892	+	6.54892i	0.274787	+	0.274787i
$569$	35.3739			1.48295			0.741475	−	0.670980i	$-0.234126\pi$
$569$	35.3739			1.48295			0.741475	+	0.670980i	$0.234126\pi$
$570$	−25.1016	+	8.03837i	−1.05139	+	0.336690i
$571$	−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
$573$	−4.70509	+	8.51015i	−0.196558	+	0.355516i
$574$			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	0.0588185	−	0.998269i	$-0.481267\pi$
$577$	25.3921	−	25.3921i	1.05709	−	1.05709i	0.998269	−	0.0588185i	$-0.0187333\pi$
$578$	−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
$582$	−22.6553	−	12.5256i	−0.939091	−	0.519204i
$583$	−4.34522	−	4.34522i	−0.179961	−	0.179961i
$584$	3.03756			0.125695
$585$	7.12357	−	36.0410i	0.294523	−	1.49011i
$586$	9.04621			0.373695
$587$	31.7362	+	31.7362i	1.30989	+	1.30989i	0.921490	+	0.388402i	$0.126973\pi$
$587$	31.7362	+	31.7362i	1.30989	+	1.30989i	0.388402	+	0.921490i	$0.373027\pi$
$588$	−6.78962	−	3.75384i	−0.279999	−	0.154806i
$589$			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	$-0.535551\pi$
$593$	21.4857	−	21.4857i	0.882314	−	0.882314i	0.993769	+	0.111456i	$0.0355513\pi$
$594$	14.6096	+	13.0680i	0.599440	+	0.536187i
$595$	−27.6546	+	0.817933i	−1.13373	+	0.0335320i
$596$			13.7580i			0.563551i
$597$	−3.88562	+	7.02796i	−0.159028	+	0.287635i
$598$	3.87255	+	3.87255i	0.158360	+	0.158360i
$599$	28.3661			1.15901			0.579504	−	0.814969i	$-0.303246\pi$
$599$	28.3661			1.15901			0.579504	+	0.814969i	$0.303246\pi$
$600$	−8.16599	+	2.88386i	−0.333375	+	0.117733i
$601$	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
$603$	4.52251	+	1.03369i	0.184171	+	0.0420950i
$604$		−	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	−0.738777	−	0.673950i	$-0.764596\pi$
$607$	−1.59716	+	1.59716i	−0.0648268	+	0.0648268i	0.673950	+	0.738777i	$0.264596\pi$
$608$	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
$612$	−10.6802	−	2.44112i	−0.431721	−	0.0986763i
$613$	12.0113	+	12.0113i	0.485130	+	0.485130i	0.906765	−	0.421636i	$-0.138544\pi$
$613$	12.0113	+	12.0113i	0.485130	+	0.485130i	−0.421636	+	0.906765i	$0.638544\pi$
$614$	24.7945			1.00063
$615$	14.2487	−	27.6736i	0.574563	−	1.11591i
$616$	−12.7809			−0.514957
$617$	−20.3489	−	20.3489i	−0.819214	−	0.819214i	0.166780	−	0.985994i	$-0.446663\pi$
$617$	−20.3489	−	20.3489i	−0.819214	−	0.819214i	−0.985994	+	0.166780i	$0.946663\pi$
$618$	5.80086	−	10.4921i	0.233345	−	0.422053i
$619$			11.4711i			0.461063i	0.973065	+	0.230531i	$0.0740464\pi$
$619$			11.4711i			0.461063i	−0.973065	+	0.230531i	$0.925954\pi$
$620$	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
$627$	38.9137	+	21.5146i	1.55406	+	0.859209i
$628$	−12.9821	−	12.9821i	−0.518042	−	0.518042i
$629$	24.2158			0.965547
$630$	12.6499	+	18.8824i	0.503986	+	0.752292i
$631$	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
$633$	13.5900	+	7.51366i	0.540156	+	0.298641i
$634$			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	$-0.212204\pi$
$642$	8.43553	−	15.2574i	0.332924	−	0.602163i
$643$	5.97111	+	5.97111i	0.235478	+	0.235478i	0.814974	−	0.579497i	$-0.196751\pi$
$643$	5.97111	+	5.97111i	0.235478	+	0.235478i	−0.579497	+	0.814974i	$0.696751\pi$
$644$	−3.38810			−0.133510
$645$	−4.79012	−	14.9582i	−0.188611	−	0.588979i
$646$	−24.8525			−0.977808
$647$	−10.0814	−	10.0814i	−0.396340	−	0.396340i	0.480600	−	0.876940i	$-0.340419\pi$
$647$	−10.0814	−	10.0814i	−0.396340	−	0.396340i	−0.876940	+	0.480600i	$0.840419\pi$
$648$	2.96732	+	8.49676i	0.116567	+	0.333784i
$649$			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	$-0.881591\pi$
$653$	−14.5180	+	14.5180i	−0.568134	+	0.568134i	0.363472	+	0.931605i	$0.381591\pi$
$654$	30.1641	−	8.68513i	1.17951	−	0.339615i
$655$	0.634475	+	21.4518i	0.0247910	+	0.838191i
$656$			8.03681i			0.313785i
$657$	−2.03047	+	8.88357i	−0.0792163	+	0.346581i
$658$	11.5339	+	11.5339i	0.449638	+	0.449638i
$659$	20.3327			0.792048			0.396024	−	0.918240i	$-0.370390\pi$
$659$	20.3327			0.792048			0.396024	+	0.918240i	$0.370390\pi$
$660$	12.9893	+	6.68800i	0.505609	+	0.260330i
$661$	−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
$663$	16.7610	−	30.3159i	0.650945	−	1.17737i
$664$		−	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
$672$	−5.13569	−	2.83942i	−0.198114	−	0.109533i
$673$	32.7647	+	32.7647i	1.26299	+	1.26299i	0.949638	+	0.313348i	$0.101451\pi$
$673$	32.7647	+	32.7647i	1.26299	+	1.26299i	0.313348	+	0.949638i	$0.398549\pi$
$674$	−25.4451			−0.980107
$675$	−2.97548	−	25.8098i	−0.114526	−	0.993420i
$676$	−16.9933			−0.653588
$677$	10.4956	+	10.4956i	0.403380	+	0.403380i	0.879422	−	0.476043i	$-0.157929\pi$
$677$	10.4956	+	10.4956i	0.403380	+	0.403380i	−0.476043	+	0.879422i	$0.657929\pi$
$678$	31.2870	+	17.2980i	1.20157	+	0.664325i
$679$			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	$-0.770211\pi$
$683$	−2.34519	+	2.34519i	−0.0897362	+	0.0897362i	0.660814	+	0.750550i	$0.270211\pi$
$684$	10.8568	+	17.2902i	0.415121	+	0.661109i
$685$	12.1853	+	11.4852i	0.465575	+	0.438826i
$686$		−	8.54065i		−	0.326084i
$687$	−8.16874	+	14.7749i	−0.311657	+	0.563698i
$688$	2.86760	+	2.86760i	0.109326	+	0.109326i
$689$	8.92143			0.339879
$690$	3.44336	+	1.77293i	0.131086	+	0.0674942i
$691$	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
$693$	8.54346	−	37.3787i	0.324539	−	1.41990i
$694$		−	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	$0.691329\pi$
$702$	−28.4133	+	1.58260i	−1.07239	+	0.0597314i
$703$	−31.9097	−	31.9097i	−1.20350	−	1.20350i
$704$	−3.77229			−0.142173
$705$	−5.68654	−	17.7575i	−0.214168	−	0.668786i
$706$	6.57049			0.247283
$707$	7.42577	+	7.42577i	0.279275	+	0.279275i
$708$	−0.832364	+	1.50551i	−0.0312822	+	0.0565804i
$709$			17.3686i			0.652292i	0.945319	+	0.326146i	$0.105750\pi$
$709$			17.3686i			0.652292i	−0.945319	+	0.326146i	$0.894250\pi$
$710$	−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
$717$	35.9674	+	19.8857i	1.34323	+	0.742644i
$718$	−24.4054	−	24.4054i	−0.910802	−	0.910802i
$719$	−13.0073			−0.485089			−0.242545	−	0.970140i	$-0.577982\pi$
$719$	−13.0073			−0.485089			−0.242545	+	0.970140i	$0.577982\pi$
$720$	3.73364	+	5.57314i	0.139145	+	0.207699i
$721$	−23.4517			−0.873388
$722$	19.3136	+	19.3136i	0.718779	+	0.718779i
$723$	−9.27945	−	5.13042i	−0.345106	−	0.190802i
$724$		−	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	−0.642449	−	0.766328i	$-0.722082\pi$
$727$	3.34014	−	3.34014i	0.123879	−	0.123879i	0.766328	+	0.642449i	$0.222082\pi$
$728$	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
$732$	−9.77513	+	17.6804i	−0.361299	+	0.653486i
$733$	21.3827	+	21.3827i	0.789788	+	0.789788i	0.981459	−	0.191671i	$-0.0613906\pi$
$733$	21.3827	+	21.3827i	0.789788	+	0.789788i	−0.191671	+	0.981459i	$0.561391\pi$
$734$	−11.8513			−0.437441
$735$	7.94134	−	15.4236i	0.292921	−	0.568907i
$736$	−1.00000			−0.0368605
$737$	−4.12483	−	4.12483i	−0.151940	−	0.151940i
$738$	−23.5043	−	5.37225i	−0.865205	−	0.197755i
$739$			27.3440i			1.00587i	0.864326	+	0.502933i	$0.167746\pi$
$739$			27.3440i			1.00587i	−0.864326	+	0.502933i	$0.832254\pi$
$740$	−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	$-0.534201\pi$
$743$	24.1777	−	24.1777i	0.886995	−	0.886995i	0.994233	+	0.107238i	$0.0342007\pi$
$744$	11.8090	−	3.40016i	0.432939	−	0.124656i
$745$	−30.7505	+	0.909500i	−1.12661	+	0.0333215i
$746$		−	10.8041i		−	0.395567i
$747$	21.5213	+	4.91901i	0.787423	+	0.179977i
$748$	9.74104	+	9.74104i	0.356168	+	0.356168i
$749$	−34.1032			−1.24610
$750$	−6.98552	−	18.0611i	−0.255075	−	0.659497i
$751$	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
$753$	−12.1164	+	21.9151i	−0.441548	+	0.798632i
$754$			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	−0.957910	−	0.287069i	$-0.907319\pi$
$757$	−18.4573	+	18.4573i	−0.670841	+	0.670841i	0.287069	+	0.957910i	$0.407319\pi$
$758$	−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	$0.975710\pi$
$762$	10.1304	+	5.60088i	0.366985	+	0.202898i
$763$	−43.4176	−	43.4176i	−1.57182	−	1.57182i
$764$	5.61428			0.203118
$765$	4.75008	−	24.0326i	0.171740	−	0.868899i
$766$	23.2361			0.839554
$767$	−3.84624	−	3.84624i	−0.138880	−	0.138880i
$768$	−1.51580	−	0.838057i	−0.0546968	−	0.0302408i
$769$			32.2378i			1.16253i	0.813716	+	0.581263i	$0.197441\pi$
$769$			32.2378i			1.16253i	−0.813716	+	0.581263i	$0.802559\pi$
$770$	−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	$-0.748121\pi$
$773$	0.232058	−	0.232058i	0.00834653	−	0.00834653i	0.711268	+	0.702921i	$0.248121\pi$
$774$	−10.3034	+	6.46965i	−0.370347	+	0.232547i
$775$	−35.4126	+	2.09661i	−1.27206	+	0.0753126i
$776$			14.9460i			0.536532i
$777$	−18.8284	+	34.0551i	−0.675465	+	1.22172i
$778$	−3.14157	−	3.14157i	−0.112631	−	0.112631i
$779$	−54.6938			−1.95961
$780$	−20.2003	+	6.46883i	−0.723288	+	0.231621i
$781$	34.9373			1.25016
$782$	2.58226	+	2.58226i	0.0923416	+	0.0923416i
$783$	1.87406	+	33.6459i	0.0669733	+	1.20241i
$784$			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	−0.696080	−	0.717964i	$-0.745074\pi$
$787$	0.613938	−	0.613938i	0.0218845	−	0.0218845i	0.717964	+	0.696080i	$0.245074\pi$
$788$	−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
$792$	2.52161	−	11.0324i	0.0896014	−	0.392018i
$793$	−45.1695	−	45.1695i	−1.60402	−	1.60402i
$794$	−3.93560			−0.139669
$795$	6.00854	−	1.92414i	0.213101	−	0.0682421i
$796$	4.63646			0.164335
$797$	−2.57948	−	2.57948i	−0.0913700	−	0.0913700i	0.659944	−	0.751314i	$-0.270580\pi$
$797$	−2.57948	−	2.57948i	−0.0913700	−	0.0913700i	−0.751314	+	0.659944i	$0.770580\pi$
$798$	19.3234	−	34.9505i	0.684042	−	1.23723i
$799$		−	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
$807$	6.52642	+	3.60833i	0.229741	+	0.127019i
$808$	2.19172	+	2.19172i	0.0771044	+	0.0771044i
$809$	−54.2052			−1.90575			−0.952876	−	0.303359i	$-0.901892\pi$
$809$	−54.2052			−1.90575			−0.952876	+	0.303359i	$0.901892\pi$
$810$	−18.7949	+	7.19393i	−0.660385	+	0.252769i
$811$	−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
$813$	13.1336	+	7.26130i	0.460615	+	0.254665i
$814$			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	$-0.135588\pi$
$822$	6.27581	−	11.3511i	0.218894	−	0.395916i
$823$	−21.7706	−	21.7706i	−0.758875	−	0.758875i	0.217243	−	0.976118i	$-0.430294\pi$
$823$	−21.7706	−	21.7706i	−0.758875	−	0.758875i	−0.976118	+	0.217243i	$0.930294\pi$
$824$	−6.92180			−0.241132
$825$	−14.0896	+	29.4745i	−0.490537	+	1.02617i
$826$	3.36508			0.117086
$827$	−10.4409	−	10.4409i	−0.363065	−	0.363065i	0.501875	−	0.864940i	$-0.332644\pi$
$827$	−10.4409	−	10.4409i	−0.363065	−	0.363065i	−0.864940	+	0.501875i	$0.832644\pi$
$828$	0.668456	−	2.92458i	0.0232304	−	0.101636i
$829$		−	17.3634i		−	0.603056i	−0.953457	−	0.301528i	$-0.902503\pi$
$829$		−	17.3634i		−	0.603056i	0.953457	−	0.301528i	$-0.0974967\pi$
$830$	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
$837$	2.05025	+	36.8092i	0.0708669	+	1.27231i
$838$	2.32975	+	2.32975i	0.0804798	+	0.0804798i
$839$	7.86161			0.271413			0.135706	−	0.990749i	$-0.456670\pi$
$839$	7.86161			0.271413			0.135706	+	0.990749i	$0.456670\pi$
$840$	6.00686	−	11.6664i	0.207256	−	0.402531i
$841$	13.0578			0.450270
$842$	−18.5866	−	18.5866i	−0.640537	−	0.640537i
$843$	18.3803	−	33.2446i	0.633051	−	1.14501i
$844$		−	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
$852$	14.0387	+	7.76173i	0.480959	+	0.265912i
$853$	−22.8283	−	22.8283i	−0.781627	−	0.781627i	0.198478	−	0.980105i	$-0.436400\pi$
$853$	−22.8283	−	22.8283i	−0.781627	−	0.781627i	−0.980105	+	0.198478i	$0.936400\pi$
$854$	39.5189			1.35231
$855$	−37.9275	+	25.4090i	−1.29709	+	0.868968i
$856$	−10.0656			−0.344035
$857$	32.4516	+	32.4516i	1.10852	+	1.10852i	0.993345	+	0.115180i	$0.0367444\pi$
$857$	32.4516	+	32.4516i	1.10852	+	1.10852i	0.115180	+	0.993345i	$0.463256\pi$
$858$	31.3155	+	17.3137i	1.06909	+	0.591081i
$859$		−	35.0172i		−	1.19477i	−0.801954	−	0.597386i	$-0.796206\pi$
$859$		−	35.0172i		−	1.19477i	0.801954	−	0.597386i	$-0.203794\pi$
$860$	−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	$-0.669660\pi$
$863$	10.3748	−	10.3748i	0.353162	−	0.353162i	0.861285	+	0.508123i	$0.169660\pi$
$864$	3.46421	−	3.87288i	0.117855	−	0.131758i
$865$	−31.9243	+	33.8702i	−1.08546	+	1.15162i
$866$		−	5.94809i		−	0.202124i
$867$	−3.07050	+	5.55365i	−0.104280	+	0.188612i
$868$	−16.9976	−	16.9976i	−0.576937	−	0.576937i
$869$	−17.3416			−0.588272
$870$	7.66014	+	23.9205i	0.259703	+	0.810980i
$871$	8.46892			0.286958
$872$	−12.8147	−	12.8147i	−0.433961	−	0.433961i
$873$	−43.7109	−	9.99077i	−1.47939	−	0.338136i
$874$		−	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	0.409413	−	0.912349i	$-0.365733\pi$
$877$	39.1429	−	39.1429i	1.32176	−	1.32176i	0.912349	−	0.409413i	$-0.134267\pi$
$878$	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	$0.908136\pi$
$882$	−13.0998	−	2.99416i	−0.441095	−	0.100819i
$883$	3.79807	+	3.79807i	0.127815	+	0.127815i	0.768121	−	0.640305i	$-0.221192\pi$
$883$	3.79807	+	3.79807i	0.127815	+	0.127815i	−0.640305	+	0.768121i	$0.721192\pi$
$884$	−19.9999			−0.672669
$885$	−3.41997	−	1.76088i	−0.114961	−	0.0591915i
$886$	2.24762			0.0755103
$887$	1.76712	+	1.76712i	0.0593341	+	0.0593341i	0.736151	−	0.676817i	$-0.236641\pi$
$887$	1.76712	+	1.76712i	0.0593341	+	0.0593341i	−0.676817	+	0.736151i	$0.736641\pi$
$888$	−5.55721	+	10.0514i	−0.186488	+	0.337303i
$889$		−	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
$897$	8.30147	+	4.58971i	0.277178	+	0.153246i
$898$	−15.5925	−	15.5925i	−0.520328	−	0.520328i
$899$	46.0119			1.53458
$900$	−12.2097	+	8.71345i	−0.406989	+	0.290448i
$901$	5.94892			0.198187
$902$	21.4375	+	21.4375i	0.713790	+	0.713790i
$903$	20.8273	+	11.5150i	0.693088	+	0.383194i
$904$		−	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	−0.674445	−	0.738326i	$-0.735617\pi$
$907$	1.92387	−	1.92387i	0.0638810	−	0.0638810i	0.738326	+	0.674445i	$0.235617\pi$
$908$	−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	$-0.0849607\pi$
$912$	5.70332	−	10.3157i	0.188856	−	0.341586i
$913$	−19.6288	−	19.6288i	−0.649620	−	0.649620i
$914$	−37.3102			−1.23411
$915$	−40.1635	−	20.6795i	−1.32776	−	0.683643i
$916$	9.74724			0.322058
$917$	−22.9938	−	22.9938i	−0.759321	−	0.759321i
$918$	−18.9463	+	1.05530i	−0.625322	+	0.0348300i
$919$		−	16.0962i		−	0.530965i	−0.964116	−	0.265483i	$-0.914469\pi$
$919$		−	16.0962i		−	0.530965i	0.964116	−	0.265483i	$-0.0855313\pi$
$920$	−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
$927$	4.62692	−	20.2433i	0.151968	−	0.664879i
$928$	−4.58573	−	4.58573i	−0.150534	−	0.150534i
$929$	−30.0036			−0.984388			−0.492194	−	0.870486i	$-0.663805\pi$
$929$	−30.0036			−0.984388			−0.492194	+	0.870486i	$0.663805\pi$
$930$	8.38032	+	26.1694i	0.274802	+	0.858128i
$931$	−30.4829			−0.999038
$932$	−6.27349	−	6.27349i	−0.205495	−	0.205495i
$933$	0.862548	−	1.56010i	0.0282386	−	0.0510754i
$934$		−	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	−0.602157	−	0.798378i	$-0.705692\pi$
$937$	6.00639	−	6.00639i	0.196220	−	0.196220i	0.798378	+	0.602157i	$0.205692\pi$
$938$	−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	$0.665490\pi$
$942$	−27.8293	−	15.3863i	−0.906728	−	0.501312i
$943$	5.68288	+	5.68288i	0.185060	+	0.185060i
$944$	0.993207			0.0323261
$945$	30.1041	+	25.3660i	0.979287	+	0.825158i
$946$	15.2981			0.497385
$947$	−13.3329	−	13.3329i	−0.433261	−	0.433261i	0.456475	−	0.889736i	$-0.349112\pi$
$947$	−13.3329	−	13.3329i	−0.433261	−	0.433261i	−0.889736	+	0.456475i	$0.849112\pi$
$948$	−6.96829	−	3.85263i	−0.226320	−	0.125127i
$949$			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	$-0.695887\pi$
$953$	7.38618	−	7.38618i	0.239262	−	0.239262i	0.816544	+	0.577283i	$0.195887\pi$
$954$	−2.59878	−	4.13875i	−0.0841387	−	0.133997i
$955$	0.371142	+	12.5484i	0.0120099	+	0.406057i
$956$		−	23.7283i		−	0.767428i
$957$	20.5023	−	37.0827i	0.662744	−	1.19871i
$958$	−8.81037	−	8.81037i	−0.284650	−	0.284650i
$959$	−25.3719			−0.819301
$960$	1.77293	−	3.44336i	0.0572210	−	0.111134i
$961$	19.3378			0.623801
$962$	−25.6791	−	25.6791i	−0.827928	−	0.827928i
$963$	6.72840	−	29.4376i	0.216820	−	0.948614i
$964$			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	−0.678084	−	0.734984i	$-0.737190\pi$
$967$	1.76939	−	1.76939i	0.0568999	−	0.0568999i	0.734984	+	0.678084i	$0.237190\pi$
$968$	−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	$-0.333586\pi$
$972$	9.01088	+	12.7202i	0.289024	+	0.408001i
$973$	30.3093	+	30.3093i	0.971670	+	0.971670i
$974$	2.55502			0.0818682
$975$	−15.7938	−	44.7219i	−0.505806	−	1.43225i
$976$	11.6640			0.373357
$977$	−6.00002	−	6.00002i	−0.191958	−	0.191958i	0.604584	−	0.796541i	$-0.293339\pi$
$977$	−6.00002	−	6.00002i	−0.191958	−	0.191958i	−0.796541	+	0.604584i	$0.793339\pi$
$978$	6.77917	−	12.2616i	0.216774	−	0.392082i
$979$		−	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	$-0.667851\pi$
$983$	11.3165	−	11.3165i	0.360940	−	0.360940i	0.864159	+	0.503219i	$0.167851\pi$
$984$	3.85155	+	13.3767i	0.122783	+	0.426434i
$985$	−2.60150	−	2.45203i	−0.0828906	−	0.0781282i
$986$			23.6831i			0.754224i
$987$	24.7249	+	13.6699i	0.787001	+	0.435117i
$988$	26.3543	+	26.3543i	0.838442	+	0.838442i
$989$	4.05539			0.128954
$990$	24.8250	+	4.90671i	0.788991	+	0.155945i
$991$	−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
$993$	15.2019	+	8.40480i	0.482416	+	0.266718i
$994$		−	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	−0.984766	−	0.173884i	$-0.944368\pi$
$997$	−25.6038	+	25.6038i	−0.810882	+	0.810882i	0.173884	+	0.984766i	$0.444368\pi$
$998$	−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.323.2	yes	32
3.2	odd	2	inner	690.2.i.f.323.11	yes	32
5.2	odd	4	inner	690.2.i.f.47.11	yes	32
15.2	even	4	inner	690.2.i.f.47.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.2	✓	32	15.2	even	4	inner
690.2.i.f.47.11	yes	32	5.2	odd	4	inner
690.2.i.f.323.2	yes	32	1.1	even	1	trivial
690.2.i.f.323.11	yes	32	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.51580 - 0.838057i) q^{3} +1.00000i q^{4} +(-2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 - 2.39575i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.59532 + 2.54066i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.51580 - 0.838057i) 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} +(0.838057 - 1.51580i) q^{12} +(3.87255 + 3.87255i) q^{13} -3.38810 q^{14} +(3.44336 + 1.77293i) q^{15} -1.00000 q^{16} +(2.58226 + 2.58226i) q^{17} +(0.668456 - 2.92458i) 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} +(-0.288974 - 5.18811i) q^{27} +(2.39575 + 2.39575i) q^{28} -6.48520 q^{29} +(-1.18117 - 3.68847i) q^{30} -7.09492 q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.16139 + 5.71805i) 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} +(5.13569 + 2.83942i) q^{42} +(-2.86760 - 2.86760i) q^{43} +3.77229 q^{44} +(-3.73364 - 5.57314i) q^{45} +1.00000 q^{46} +(-3.40424 - 3.40424i) q^{47} +(1.51580 + 0.838057i) 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} +(-5.70332 + 10.3157i) q^{57} +(4.58573 + 4.58573i) q^{58} -0.993207 q^{59} +(-1.77293 + 3.44336i) q^{60} -11.6640 q^{61} +(5.01686 + 5.01686i) q^{62} +(9.90877 + 2.26480i) 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} +(2.92458 + 0.668456i) q^{72} +(2.14788 + 2.14788i) q^{73} -6.63106 q^{74} +(-7.81342 - 3.73503i) q^{75} +6.80541 q^{76} +(-9.03745 - 9.03745i) q^{77} +(-4.58971 + 8.30147i) 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} +(9.83029 + 5.43497i) q^{87} +(-2.66741 - 2.66741i) q^{88} +9.56617 q^{89} +(-1.30072 + 6.58089i) q^{90} +18.5553 q^{91} +(-0.707107 - 0.707107i) q^{92} +(10.7545 + 5.94594i) 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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