LMFDB - Embedded newform 663.2.j.a.157.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(157,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("663.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.j (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:	$5.29408165401$
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			157.13
Character	$\chi$	$=$	663.157
Dual form			663.2.j.a.625.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49170i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.225164 q^{4} +(0.731803 - 0.731803i) q^{5} +(-1.05479 - 1.05479i) q^{6} +(-0.0312384 - 0.0312384i) q^{7} +2.64752i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.49170i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.225164 q^{4} +(0.731803 - 0.731803i) q^{5} +(-1.05479 - 1.05479i) q^{6} +(-0.0312384 - 0.0312384i) q^{7} +2.64752i q^{8} -1.00000i q^{9} +(1.09163 + 1.09163i) q^{10} +(2.62783 + 2.62783i) q^{11} +(0.159215 - 0.159215i) q^{12} -1.00000 q^{13} +(0.0465982 - 0.0465982i) q^{14} +1.03493i q^{15} -4.39963 q^{16} +(2.32967 - 3.40186i) q^{17} +1.49170 q^{18} +4.41518i q^{19} +(-0.164776 + 0.164776i) q^{20} +0.0441777 q^{21} +(-3.91993 + 3.91993i) q^{22} +(2.82224 + 2.82224i) q^{23} +(-1.87208 - 1.87208i) q^{24} +3.92893i q^{25} -1.49170i q^{26} +(0.707107 + 0.707107i) q^{27} +(0.00703375 + 0.00703375i) q^{28} +(-1.50003 + 1.50003i) q^{29} -1.54380 q^{30} +(0.427909 - 0.427909i) q^{31} -1.26788i q^{32} -3.71631 q^{33} +(5.07454 + 3.47517i) q^{34} -0.0457207 q^{35} +0.225164i q^{36} +(-7.53120 + 7.53120i) q^{37} -6.58612 q^{38} +(0.707107 - 0.707107i) q^{39} +(1.93746 + 1.93746i) q^{40} +(1.87781 + 1.87781i) q^{41} +0.0658999i q^{42} -3.13962i q^{43} +(-0.591692 - 0.591692i) q^{44} +(-0.731803 - 0.731803i) q^{45} +(-4.20994 + 4.20994i) q^{46} +1.35348 q^{47} +(3.11101 - 3.11101i) q^{48} -6.99805i q^{49} -5.86077 q^{50} +(0.758149 + 4.05280i) q^{51} +0.225164 q^{52} -2.47439i q^{53} +(-1.05479 + 1.05479i) q^{54} +3.84611 q^{55} +(0.0827042 - 0.0827042i) q^{56} +(-3.12201 - 3.12201i) q^{57} +(-2.23759 - 2.23759i) q^{58} -6.41726i q^{59} -0.233028i q^{60} +(-7.89593 - 7.89593i) q^{61} +(0.638312 + 0.638312i) q^{62} +(-0.0312384 + 0.0312384i) q^{63} -6.90797 q^{64} +(-0.731803 + 0.731803i) q^{65} -5.54362i q^{66} -0.572369 q^{67} +(-0.524558 + 0.765975i) q^{68} -3.99125 q^{69} -0.0682015i q^{70} +(5.12317 - 5.12317i) q^{71} +2.64752 q^{72} +(1.11865 - 1.11865i) q^{73} +(-11.2343 - 11.2343i) q^{74} +(-2.77817 - 2.77817i) q^{75} -0.994139i q^{76} -0.164178i q^{77} +(1.05479 + 1.05479i) q^{78} +(11.9512 + 11.9512i) q^{79} +(-3.21966 + 3.21966i) q^{80} -1.00000 q^{81} +(-2.80113 + 2.80113i) q^{82} -5.05886i q^{83} -0.00994722 q^{84} +(-0.784628 - 4.19435i) q^{85} +4.68337 q^{86} -2.12136i q^{87} +(-6.95724 + 6.95724i) q^{88} +17.5049 q^{89} +(1.09163 - 1.09163i) q^{90} +(0.0312384 + 0.0312384i) q^{91} +(-0.635467 - 0.635467i) q^{92} +0.605155i q^{93} +2.01898i q^{94} +(3.23105 + 3.23105i) q^{95} +(0.896525 + 0.896525i) q^{96} +(-8.89382 + 8.89382i) q^{97} +10.4390 q^{98} +(2.62783 - 2.62783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{4} - 4 q^{5} - 4 q^{6}+O(q^{10}) $ 32 * q - 24 * q^4 - 4 * q^5 - 4 * q^6	$ 32 q - 24 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{10} - 4 q^{11} - 32 q^{13} + 24 q^{14} - 12 q^{17} - 28 q^{20} + 16 q^{21} + 20 q^{23} + 4 q^{24} + 16 q^{28} + 52 q^{29} - 16 q^{30} + 20 q^{31} - 16 q^{33} + 32 q^{34} - 8 q^{35} - 20 q^{37} + 16 q^{38} - 80 q^{40} - 20 q^{41} + 44 q^{44} + 4 q^{45} - 32 q^{46} + 24 q^{47} + 16 q^{48} - 16 q^{50} + 4 q^{51} + 24 q^{52} - 4 q^{54} - 8 q^{55} - 68 q^{56} - 8 q^{57} - 64 q^{58} - 12 q^{61} + 16 q^{62} + 40 q^{64} + 4 q^{65} - 80 q^{67} + 20 q^{68} + 16 q^{69} + 4 q^{71} - 36 q^{73} + 48 q^{74} - 16 q^{75} + 4 q^{78} + 8 q^{79} + 76 q^{80} - 32 q^{81} + 4 q^{82} - 8 q^{84} + 52 q^{85} + 48 q^{86} - 60 q^{88} + 8 q^{89} + 4 q^{90} - 124 q^{92} - 48 q^{95} + 16 q^{96} + 40 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 24 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^10 - 4 * q^11 - 32 * q^13 + 24 * q^14 - 12 * q^17 - 28 * q^20 + 16 * q^21 + 20 * q^23 + 4 * q^24 + 16 * q^28 + 52 * q^29 - 16 * q^30 + 20 * q^31 - 16 * q^33 + 32 * q^34 - 8 * q^35 - 20 * q^37 + 16 * q^38 - 80 * q^40 - 20 * q^41 + 44 * q^44 + 4 * q^45 - 32 * q^46 + 24 * q^47 + 16 * q^48 - 16 * q^50 + 4 * q^51 + 24 * q^52 - 4 * q^54 - 8 * q^55 - 68 * q^56 - 8 * q^57 - 64 * q^58 - 12 * q^61 + 16 * q^62 + 40 * q^64 + 4 * q^65 - 80 * q^67 + 20 * q^68 + 16 * q^69 + 4 * q^71 - 36 * q^73 + 48 * q^74 - 16 * q^75 + 4 * q^78 + 8 * q^79 + 76 * q^80 - 32 * q^81 + 4 * q^82 - 8 * q^84 + 52 * q^85 + 48 * q^86 - 60 * q^88 + 8 * q^89 + 4 * q^90 - 124 * q^92 - 48 * q^95 + 16 * q^96 + 40 * q^97 + 48 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$			1.49170i			1.05479i	0.849620	+	0.527395i	$0.176831\pi$
$2$			1.49170i			1.05479i	−0.849620	+	0.527395i	$0.823169\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−0.225164			−0.112582
$5$	0.731803	−	0.731803i	0.327272	−	0.327272i	−0.524276	−	0.851548i	$-0.675664\pi$
$5$	0.731803	−	0.731803i	0.327272	−	0.327272i	0.851548	+	0.524276i	$0.175664\pi$
$6$	−1.05479	−	1.05479i	−0.430616	−	0.430616i
$7$	−0.0312384	−	0.0312384i	−0.0118070	−	0.0118070i	0.701179	−	0.712986i	$-0.252658\pi$
$7$	−0.0312384	−	0.0312384i	−0.0118070	−	0.0118070i	−0.712986	+	0.701179i	$0.752658\pi$
$8$			2.64752i			0.936040i
$9$		−	1.00000i		−	0.333333i
$10$	1.09163	+	1.09163i	0.345204	+	0.345204i
$11$	2.62783	+	2.62783i	0.792321	+	0.792321i	0.981871	−	0.189550i	$-0.0607029\pi$
$11$	2.62783	+	2.62783i	0.792321	+	0.792321i	−0.189550	+	0.981871i	$0.560703\pi$
$12$	0.159215	−	0.159215i	0.0459613	−	0.0459613i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	0.0465982	−	0.0465982i	0.0124539	−	0.0124539i
$15$			1.03493i			0.267217i
$16$	−4.39963			−1.09991
$17$	2.32967	−	3.40186i	0.565028	−	0.825071i
$17$	2.32967	−	3.40186i	0.565028	−	0.825071i
$18$	1.49170			0.351597
$19$			4.41518i			1.01291i	0.862266	+	0.506456i	$0.169045\pi$
$19$			4.41518i			1.01291i	−0.862266	+	0.506456i	$0.830955\pi$
$20$	−0.164776	+	0.164776i	−0.0368449	+	0.0368449i
$21$	0.0441777			0.00964037
$22$	−3.91993	+	3.91993i	−0.835732	+	0.835732i
$23$	2.82224	+	2.82224i	0.588478	+	0.588478i	0.937219	−	0.348741i	$-0.113391\pi$
$23$	2.82224	+	2.82224i	0.588478	+	0.588478i	−0.348741	+	0.937219i	$0.613391\pi$
$24$	−1.87208	−	1.87208i	−0.382137	−	0.382137i
$25$			3.92893i			0.785785i
$26$		−	1.49170i		−	0.292546i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.00703375	+	0.00703375i	0.00132925	+	0.00132925i
$29$	−1.50003	+	1.50003i	−0.278548	+	0.278548i	−0.832529	−	0.553981i	$-0.813108\pi$
$29$	−1.50003	+	1.50003i	−0.278548	+	0.278548i	0.553981	+	0.832529i	$0.313108\pi$
$30$	−1.54380			−0.281858
$31$	0.427909	−	0.427909i	0.0768548	−	0.0768548i	−0.667634	−	0.744489i	$-0.732693\pi$
$31$	0.427909	−	0.427909i	0.0768548	−	0.0768548i	0.744489	+	0.667634i	$0.232693\pi$
$32$		−	1.26788i		−	0.224131i
$33$	−3.71631			−0.646927
$34$	5.07454	+	3.47517i	0.870277	+	0.595986i
$35$	−0.0457207			−0.00772821
$36$			0.225164i			0.0375273i
$37$	−7.53120	+	7.53120i	−1.23812	+	1.23812i	−0.277355	+	0.960768i	$0.589458\pi$
$37$	−7.53120	+	7.53120i	−1.23812	+	1.23812i	−0.960768	+	0.277355i	$0.910542\pi$
$38$	−6.58612			−1.06841
$39$	0.707107	−	0.707107i	0.113228	−	0.113228i
$40$	1.93746	+	1.93746i	0.306340	+	0.306340i
$41$	1.87781	+	1.87781i	0.293265	+	0.293265i	0.838369	−	0.545104i	$-0.183510\pi$
$41$	1.87781	+	1.87781i	0.293265	+	0.293265i	−0.545104	+	0.838369i	$0.683510\pi$
$42$			0.0658999i			0.0101686i
$43$		−	3.13962i		−	0.478788i	−0.970922	−	0.239394i	$-0.923051\pi$
$43$		−	3.13962i		−	0.478788i	0.970922	−	0.239394i	$-0.0769488\pi$
$44$	−0.591692	−	0.591692i	−0.0892010	−	0.0892010i
$45$	−0.731803	−	0.731803i	−0.109091	−	0.109091i
$46$	−4.20994	+	4.20994i	−0.620721	+	0.620721i
$47$	1.35348			0.197425			0.0987126	−	0.995116i	$-0.468528\pi$
$47$	1.35348			0.197425			0.0987126	+	0.995116i	$0.468528\pi$
$48$	3.11101	−	3.11101i	0.449035	−	0.449035i
$49$		−	6.99805i		−	0.999721i
$50$	−5.86077			−0.828839
$51$	0.758149	+	4.05280i	0.106162	+	0.567506i
$52$	0.225164			0.0312246
$53$		−	2.47439i		−	0.339883i	−0.985454	−	0.169942i	$-0.945642\pi$
$53$		−	2.47439i		−	0.339883i	0.985454	−	0.169942i	$-0.0543579\pi$
$54$	−1.05479	+	1.05479i	−0.143539	+	0.143539i
$55$	3.84611			0.518610
$56$	0.0827042	−	0.0827042i	0.0110518	−	0.0110518i
$57$	−3.12201	−	3.12201i	−0.413520	−	0.413520i
$58$	−2.23759	−	2.23759i	−0.293810	−	0.293810i
$59$		−	6.41726i		−	0.835457i	−0.908572	−	0.417728i	$-0.862826\pi$
$59$		−	6.41726i		−	0.835457i	0.908572	−	0.417728i	$-0.137174\pi$
$60$		−	0.233028i		−	0.0300838i
$61$	−7.89593	−	7.89593i	−1.01097	−	1.01097i	−0.999939	−	0.0110312i	$-0.996489\pi$
$61$	−7.89593	−	7.89593i	−1.01097	−	1.01097i	−0.0110312	−	0.999939i	$-0.503511\pi$
$62$	0.638312	+	0.638312i	0.0810656	+	0.0810656i
$63$	−0.0312384	+	0.0312384i	−0.00393567	+	0.00393567i
$64$	−6.90797			−0.863496
$65$	−0.731803	+	0.731803i	−0.0907690	+	0.0907690i
$66$		−	5.54362i		−	0.682372i
$67$	−0.572369			−0.0699259			−0.0349630	−	0.999389i	$-0.511131\pi$
$67$	−0.572369			−0.0699259			−0.0349630	+	0.999389i	$0.511131\pi$
$68$	−0.524558	+	0.765975i	−0.0636119	+	0.0928881i
$69$	−3.99125			−0.480491
$70$		−	0.0682015i		−	0.00815164i
$71$	5.12317	−	5.12317i	0.608008	−	0.608008i	−0.334417	−	0.942425i	$-0.608539\pi$
$71$	5.12317	−	5.12317i	0.608008	−	0.608008i	0.942425	+	0.334417i	$0.108539\pi$
$72$	2.64752			0.312013
$73$	1.11865	−	1.11865i	0.130928	−	0.130928i	−0.638606	−	0.769534i	$-0.720489\pi$
$73$	1.11865	−	1.11865i	0.130928	−	0.130928i	0.769534	+	0.638606i	$0.220489\pi$
$74$	−11.2343	−	11.2343i	−1.30596	−	1.30596i
$75$	−2.77817	−	2.77817i	−0.320796	−	0.320796i
$76$		−	0.994139i		−	0.114036i
$77$		−	0.164178i		−	0.0187099i
$78$	1.05479	+	1.05479i	0.119431	+	0.119431i
$79$	11.9512	+	11.9512i	1.34461	+	1.34461i	0.891406	+	0.453205i	$0.149719\pi$
$79$	11.9512	+	11.9512i	1.34461	+	1.34461i	0.453205	+	0.891406i	$0.350281\pi$
$80$	−3.21966	+	3.21966i	−0.359969	+	0.359969i
$81$	−1.00000			−0.111111
$82$	−2.80113	+	2.80113i	−0.309333	+	0.309333i
$83$		−	5.05886i		−	0.555282i	−0.960685	−	0.277641i	$-0.910447\pi$
$83$		−	5.05886i		−	0.555282i	0.960685	−	0.277641i	$-0.0895525\pi$
$84$	−0.00994722			−0.00108533
$85$	−0.784628	−	4.19435i	−0.0851049	−	0.454941i
$86$	4.68337			0.505021
$87$		−	2.12136i		−	0.227434i
$88$	−6.95724	+	6.95724i	−0.741644	+	0.741644i
$89$	17.5049			1.85552			0.927760	−	0.373177i	$-0.121731\pi$
$89$	17.5049			1.85552			0.927760	+	0.373177i	$0.121731\pi$
$90$	1.09163	−	1.09163i	0.115068	−	0.115068i
$91$	0.0312384	+	0.0312384i	0.00327467	+	0.00327467i
$92$	−0.635467	−	0.635467i	−0.0662520	−	0.0662520i
$93$			0.605155i			0.0627517i
$94$			2.01898i			0.208242i
$95$	3.23105	+	3.23105i	0.331498	+	0.331498i
$96$	0.896525	+	0.896525i	0.0915012	+	0.0915012i
$97$	−8.89382	+	8.89382i	−0.903031	+	0.903031i	−0.995697	−	0.0926661i	$-0.970461\pi$
$97$	−8.89382	+	8.89382i	−0.903031	+	0.903031i	0.0926661	+	0.995697i	$0.470461\pi$
$98$	10.4390			1.05450
$99$	2.62783	−	2.62783i	0.264107	−	0.264107i
$100$		−	0.884652i		−	0.0884652i
$101$	−3.24918			−0.323306			−0.161653	−	0.986848i	$-0.551682\pi$
$101$	−3.24918			−0.323306			−0.161653	+	0.986848i	$0.551682\pi$
$102$	−6.04556	+	1.13093i	−0.598600	+	0.111979i
$103$	−0.538290			−0.0530393			−0.0265197	−	0.999648i	$-0.508442\pi$
$103$	−0.538290			−0.0530393			−0.0265197	+	0.999648i	$0.508442\pi$
$104$		−	2.64752i		−	0.259611i
$105$	0.0323294	−	0.0323294i	0.00315503	−	0.00315503i
$106$	3.69104			0.358506
$107$	2.33783	−	2.33783i	0.226006	−	0.226006i	−0.585016	−	0.811022i	$-0.698912\pi$
$107$	2.33783	−	2.33783i	0.226006	−	0.226006i	0.811022	+	0.585016i	$0.198912\pi$
$108$	−0.159215	−	0.159215i	−0.0153204	−	0.0153204i
$109$	0.434472	+	0.434472i	0.0416148	+	0.0416148i	0.727608	−	0.685993i	$-0.240632\pi$
$109$	0.434472	+	0.434472i	0.0416148	+	0.0416148i	−0.685993	+	0.727608i	$0.740632\pi$
$110$			5.73724i			0.547024i
$111$		−	10.6507i		−	1.01092i
$112$	0.137437	+	0.137437i	0.0129866	+	0.0129866i
$113$	−1.58111	−	1.58111i	−0.148738	−	0.148738i	0.628816	−	0.777554i	$-0.283540\pi$
$113$	−1.58111	−	1.58111i	−0.148738	−	0.148738i	−0.777554	+	0.628816i	$0.783540\pi$
$114$	4.65709	−	4.65709i	0.436177	−	0.436177i
$115$	4.13065			0.385186
$116$	0.337752	−	0.337752i	0.0313595	−	0.0313595i
$117$			1.00000i			0.0924500i
$118$	9.57262			0.881231
$119$	−0.179044	+	0.0334933i	−0.0164129	+	0.00307033i
$120$	−2.73999			−0.250126
$121$			2.81099i			0.255545i
$122$	11.7783	−	11.7783i	1.06636	−	1.06636i
$123$	−2.65562			−0.239450
$124$	−0.0963496	+	0.0963496i	−0.00865245	+	0.00865245i
$125$	6.53422	+	6.53422i	0.584438	+	0.584438i
$126$	−0.0465982	−	0.0465982i	−0.00415130	−	0.00415130i
$127$			10.6044i			0.940990i	0.882403	+	0.470495i	$0.155925\pi$
$127$			10.6044i			0.940990i	−0.882403	+	0.470495i	$0.844075\pi$
$128$		−	12.8404i		−	1.13494i
$129$	2.22005	+	2.22005i	0.195464	+	0.195464i
$130$	−1.09163	−	1.09163i	−0.0957423	−	0.0957423i
$131$	5.05767	−	5.05767i	0.441891	−	0.441891i	−0.450756	−	0.892647i	$-0.648846\pi$
$131$	5.05767	−	5.05767i	0.441891	−	0.441891i	0.892647	+	0.450756i	$0.148846\pi$
$132$	0.836779			0.0728323
$133$	0.137923	−	0.137923i	0.0119595	−	0.0119595i
$134$		−	0.853801i		−	0.0737572i
$135$	1.03493			0.0890723
$136$	9.00648	+	6.16785i	0.772300	+	0.528889i
$137$	6.42718			0.549111			0.274555	−	0.961571i	$-0.411469\pi$
$137$	6.42718			0.549111			0.274555	+	0.961571i	$0.411469\pi$
$138$		−	5.95375i		−	0.506817i
$139$	14.9398	−	14.9398i	1.26718	−	1.26718i	0.319639	−	0.947539i	$-0.396438\pi$
$139$	14.9398	−	14.9398i	1.26718	−	1.26718i	0.947539	−	0.319639i	$-0.103562\pi$
$140$	0.0102946			0.000870056
$141$	−0.957054	+	0.957054i	−0.0805985	+	0.0805985i
$142$	7.64222	+	7.64222i	0.641321	+	0.641321i
$143$	−2.62783	−	2.62783i	−0.219750	−	0.219750i
$144$			4.39963i			0.366636i
$145$			2.19545i			0.182322i
$146$	1.66869	+	1.66869i	0.138102	+	0.138102i
$147$	4.94837	+	4.94837i	0.408134	+	0.408134i
$148$	1.69575	−	1.69575i	0.139390	−	0.139390i
$149$	12.5439			1.02764			0.513819	−	0.857898i	$-0.328230\pi$
$149$	12.5439			1.02764			0.513819	+	0.857898i	$0.328230\pi$
$150$	4.14419	−	4.14419i	0.338372	−	0.338372i
$151$		−	12.1992i		−	0.992760i	−0.868105	−	0.496380i	$-0.834662\pi$
$151$		−	12.1992i		−	0.992760i	0.868105	−	0.496380i	$-0.165338\pi$
$152$	−11.6893			−0.948127
$153$	−3.40186	−	2.32967i	−0.275024	−	0.188343i
$154$	0.244905			0.0197350
$155$		−	0.626291i		−	0.0503049i
$156$	−0.159215	+	0.159215i	−0.0127474	+	0.0127474i
$157$	19.2663			1.53762			0.768809	−	0.639479i	$-0.220850\pi$
$157$	19.2663			1.53762			0.768809	+	0.639479i	$0.220850\pi$
$158$	−17.8275	+	17.8275i	−1.41828	+	1.41828i
$159$	1.74966	+	1.74966i	0.138757	+	0.138757i
$160$	−0.927837	−	0.927837i	−0.0733520	−	0.0733520i
$161$		−	0.176325i		−	0.0138963i
$162$		−	1.49170i		−	0.117199i
$163$	−11.8223	−	11.8223i	−0.925995	−	0.925995i	0.0714496	−	0.997444i	$-0.477237\pi$
$163$	−11.8223	−	11.8223i	−0.925995	−	0.925995i	−0.997444	+	0.0714496i	$0.977237\pi$
$164$	−0.422815	−	0.422815i	−0.0330163	−	0.0330163i
$165$	−2.71961	+	2.71961i	−0.211721	+	0.211721i
$166$	7.54629			0.585706
$167$	−5.04530	+	5.04530i	−0.390417	+	0.390417i	−0.874836	−	0.484419i	$-0.839031\pi$
$167$	−5.04530	+	5.04530i	−0.390417	+	0.390417i	0.484419	+	0.874836i	$0.339031\pi$
$168$			0.116961i			0.00902377i
$169$	1.00000			0.0769231
$170$	6.25671	−	1.17043i	0.479868	−	0.0897678i
$171$	4.41518			0.337638
$172$			0.706929i			0.0539028i
$173$	−6.85842	+	6.85842i	−0.521436	+	0.521436i	−0.918005	−	0.396569i	$-0.870201\pi$
$173$	−6.85842	+	6.85842i	−0.521436	+	0.521436i	0.396569	+	0.918005i	$0.370201\pi$
$174$	3.16443			0.239895
$175$	0.122733	−	0.122733i	0.00927777	−	0.00927777i
$176$	−11.5615	−	11.5615i	−0.871479	−	0.871479i
$177$	4.53769	+	4.53769i	0.341074	+	0.341074i
$178$			26.1121i			1.95718i
$179$		−	18.1790i		−	1.35876i	−0.733785	−	0.679382i	$-0.762248\pi$
$179$		−	18.1790i		−	1.35876i	0.733785	−	0.679382i	$-0.237752\pi$
$180$	0.164776	+	0.164776i	0.0122816	+	0.0122816i
$181$	−0.870528	−	0.870528i	−0.0647058	−	0.0647058i	0.674013	−	0.738719i	$-0.264569\pi$
$181$	−0.870528	−	0.870528i	−0.0647058	−	0.0647058i	−0.738719	+	0.674013i	$0.764569\pi$
$182$	−0.0465982	+	0.0465982i	−0.00345409	+	0.00345409i
$183$	11.1665			0.825454
$184$	−7.47195	+	7.47195i	−0.550839	+	0.550839i
$185$			11.0227i			0.810407i
$186$	−0.902709			−0.0661898
$187$	15.0615	−	2.81752i	1.10141	−	0.206037i
$188$	−0.304754			−0.0222265
$189$		−	0.0441777i		−	0.00321346i
$190$	−4.81975	+	4.81975i	−0.349661	+	0.349661i
$191$	−0.401367			−0.0290419			−0.0145210	−	0.999895i	$-0.504622\pi$
$191$	−0.401367			−0.0290419			−0.0145210	+	0.999895i	$0.504622\pi$
$192$	4.88467	−	4.88467i	0.352521	−	0.352521i
$193$	−6.56340	−	6.56340i	−0.472444	−	0.472444i	0.430261	−	0.902705i	$-0.358422\pi$
$193$	−6.56340	−	6.56340i	−0.472444	−	0.472444i	−0.902705	+	0.430261i	$0.858422\pi$
$194$	−13.2669	−	13.2669i	−0.952508	−	0.952508i
$195$		−	1.03493i		−	0.0741126i
$196$			1.57571i			0.112550i
$197$	−2.10322	−	2.10322i	−0.149848	−	0.149848i	0.628202	−	0.778050i	$-0.283791\pi$
$197$	−2.10322	−	2.10322i	−0.149848	−	0.149848i	−0.778050	+	0.628202i	$0.783791\pi$
$198$	3.91993	+	3.91993i	0.278577	+	0.278577i
$199$	−3.49309	+	3.49309i	−0.247619	+	0.247619i	−0.819993	−	0.572374i	$-0.806023\pi$
$199$	−3.49309	+	3.49309i	−0.247619	+	0.247619i	0.572374	+	0.819993i	$0.306023\pi$
$200$	−10.4019			−0.735526
$201$	0.404726	−	0.404726i	0.0285471	−	0.0285471i
$202$		−	4.84680i		−	0.341020i
$203$	0.0937170			0.00657764
$204$	−0.170708	−	0.912544i	−0.0119519	−	0.0638909i
$205$	2.74838			0.191955
$206$		−	0.802967i		−	0.0559453i
$207$	2.82224	−	2.82224i	0.196159	−	0.196159i
$208$	4.39963			0.305059
$209$	−11.6024	+	11.6024i	−0.802552	+	0.802552i
$210$	0.0482257	+	0.0482257i	0.00332789	+	0.00332789i
$211$	−14.6765	−	14.6765i	−1.01037	−	1.01037i	−0.999946	−	0.0104253i	$-0.996681\pi$
$211$	−14.6765	−	14.6765i	−1.01037	−	1.01037i	−0.0104253	−	0.999946i	$-0.503319\pi$
$212$			0.557142i			0.0382647i
$213$			7.24525i			0.496436i
$214$	3.48733	+	3.48733i	0.238389	+	0.238389i
$215$	−2.29759	−	2.29759i	−0.156694	−	0.156694i
$216$	−1.87208	+	1.87208i	−0.127379	+	0.127379i
$217$	−0.0267344			−0.00181485
$218$	−0.648100	+	0.648100i	−0.0438949	+	0.0438949i
$219$			1.58201i			0.106902i
$220$	−0.866005			−0.0583860
$221$	−2.32967	+	3.40186i	−0.156711	+	0.228834i
$222$	15.8877			1.06631
$223$			3.07914i			0.206194i	0.994671	+	0.103097i	$0.0328753\pi$
$223$			3.07914i			0.206194i	−0.994671	+	0.103097i	$0.967125\pi$
$224$	−0.0396065	+	0.0396065i	−0.00264632	+	0.00264632i
$225$	3.92893			0.261928
$226$	2.35853	−	2.35853i	0.156887	−	0.156887i
$227$	16.8783	+	16.8783i	1.12025	+	1.12025i	0.991703	+	0.128549i	$0.0410318\pi$
$227$	16.8783	+	16.8783i	1.12025	+	1.12025i	0.128549	+	0.991703i	$0.458968\pi$
$228$	0.702963	+	0.702963i	0.0465548	+	0.0465548i
$229$		−	20.5510i		−	1.35805i	−0.734115	−	0.679025i	$-0.762403\pi$
$229$		−	20.5510i		−	1.35805i	0.734115	−	0.679025i	$-0.237597\pi$
$230$			6.16169i			0.406290i
$231$	0.116092	+	0.116092i	0.00763827	+	0.00763827i
$232$	−3.97136	−	3.97136i	−0.260732	−	0.260732i
$233$	−10.9707	+	10.9707i	−0.718714	+	0.718714i	−0.968342	−	0.249628i	$-0.919692\pi$
$233$	−10.9707	+	10.9707i	−0.718714	+	0.718714i	0.249628	+	0.968342i	$0.419692\pi$
$234$	−1.49170			−0.0975154
$235$	0.990480	−	0.990480i	0.0646118	−	0.0646118i
$236$			1.44493i			0.0940573i
$237$	−16.9015			−1.09787
$238$	−0.0499619	−	0.267079i	−0.00323855	−	0.0173122i
$239$	28.1562			1.82127			0.910637	−	0.413208i	$-0.135592\pi$
$239$	28.1562			1.82127			0.910637	+	0.413208i	$0.135592\pi$
$240$		−	4.55329i		−	0.293914i
$241$	16.7552	−	16.7552i	1.07930	−	1.07930i	0.0827224	−	0.996573i	$-0.473639\pi$
$241$	16.7552	−	16.7552i	1.07930	−	1.07930i	0.996573	−	0.0827224i	$-0.0263615\pi$
$242$	−4.19315			−0.269546
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	1.77788	+	1.77788i	0.113817	+	0.113817i
$245$	−5.12120	−	5.12120i	−0.327181	−	0.327181i
$246$		−	3.96139i		−	0.252569i
$247$		−	4.41518i		−	0.280931i
$248$	1.13290	+	1.13290i	0.0719391	+	0.0719391i
$249$	3.57715	+	3.57715i	0.226693	+	0.226693i
$250$	−9.74708	+	9.74708i	−0.616460	+	0.616460i
$251$	−13.7930			−0.870607			−0.435304	−	0.900284i	$-0.643359\pi$
$251$	−13.7930			−0.870607			−0.435304	+	0.900284i	$0.643359\pi$
$252$	0.00703375	−	0.00703375i	0.000443085	−	0.000443085i
$253$			14.8328i			0.932527i
$254$	−15.8186			−0.992546
$255$	3.52067	+	2.41104i	0.220473	+	0.150985i
$256$	5.33801			0.333625
$257$		−	13.5449i		−	0.844908i	−0.906384	−	0.422454i	$-0.861169\pi$
$257$		−	13.5449i		−	0.844908i	0.906384	−	0.422454i	$-0.138831\pi$
$258$	−3.31164	+	3.31164i	−0.206174	+	0.206174i
$259$	0.470525			0.0292370
$260$	0.164776	−	0.164776i	0.0102189	−	0.0102189i
$261$	1.50003	+	1.50003i	0.0928495	+	0.0928495i
$262$	7.54452	+	7.54452i	0.466102	+	0.466102i
$263$		−	17.1171i		−	1.05549i	−0.849403	−	0.527744i	$-0.823038\pi$
$263$		−	17.1171i		−	1.05549i	0.849403	−	0.527744i	$-0.176962\pi$
$264$		−	9.83902i		−	0.605550i
$265$	−1.81077	−	1.81077i	−0.111234	−	0.111234i
$266$	0.205740	+	0.205740i	0.0126147	+	0.0126147i
$267$	−12.3779	+	12.3779i	−0.757513	+	0.757513i
$268$	0.128877			0.00787239
$269$	−12.1535	+	12.1535i	−0.741010	+	0.741010i	−0.972772	−	0.231763i	$-0.925551\pi$
$269$	−12.1535	+	12.1535i	−0.741010	+	0.741010i	0.231763	+	0.972772i	$0.425551\pi$
$270$			1.54380i			0.0939525i
$271$	12.2061			0.741469			0.370734	−	0.928739i	$-0.379106\pi$
$271$	12.2061			0.741469			0.370734	+	0.928739i	$0.379106\pi$
$272$	−10.2497	+	14.9669i	−0.621479	+	0.907502i
$273$	−0.0441777			−0.00267376
$274$			9.58741i			0.579197i
$275$	−10.3246	+	10.3246i	−0.622594	+	0.622594i
$276$	0.898686			0.0540945
$277$	−13.9502	+	13.9502i	−0.838186	+	0.838186i	−0.988620	−	0.150434i	$-0.951933\pi$
$277$	−13.9502	+	13.9502i	−0.838186	+	0.838186i	0.150434	+	0.988620i	$0.451933\pi$
$278$	22.2857	+	22.2857i	1.33661	+	1.33661i
$279$	−0.427909	−	0.427909i	−0.0256183	−	0.0256183i
$280$		−	0.121047i		−	0.00723391i
$281$		−	22.5461i		−	1.34499i	−0.740102	−	0.672494i	$-0.765223\pi$
$281$		−	22.5461i		−	1.34499i	0.740102	−	0.672494i	$-0.234777\pi$
$282$	−1.42764	−	1.42764i	−0.0850145	−	0.0850145i
$283$	−7.85641	−	7.85641i	−0.467015	−	0.467015i	0.433931	−	0.900946i	$-0.357126\pi$
$283$	−7.85641	−	7.85641i	−0.467015	−	0.467015i	−0.900946	+	0.433931i	$0.857126\pi$
$284$	−1.15355	+	1.15355i	−0.0684506	+	0.0684506i
$285$	−4.56939			−0.270667
$286$	3.91993	−	3.91993i	0.231790	−	0.231790i
$287$		−	0.117319i		−	0.00692515i
$288$	−1.26788			−0.0747104
$289$	−6.14526	−	15.8504i	−0.361486	−	0.932378i
$290$	−3.27495			−0.192312
$291$		−	12.5778i		−	0.737322i
$292$	−0.251880	+	0.251880i	−0.0147401	+	0.0147401i
$293$	−13.2033			−0.771343			−0.385671	−	0.922636i	$-0.626030\pi$
$293$	−13.2033			−0.771343			−0.385671	+	0.922636i	$0.626030\pi$
$294$	−7.38147	+	7.38147i	−0.430496	+	0.430496i
$295$	−4.69618	−	4.69618i	−0.273422	−	0.273422i
$296$	−19.9390	−	19.9390i	−1.15893	−	1.15893i
$297$			3.71631i			0.215642i
$298$			18.7118i			1.08394i
$299$	−2.82224	−	2.82224i	−0.163215	−	0.163215i
$300$	0.625543	+	0.625543i	0.0361158	+	0.0361158i
$301$	−0.0980768	+	0.0980768i	−0.00565305	+	0.00565305i
$302$	18.1976			1.04715
$303$	2.29752	−	2.29752i	0.131989	−	0.131989i
$304$		−	19.4252i		−	1.11411i
$305$	−11.5565			−0.661726
$306$	3.47517	−	5.07454i	0.198662	−	0.290092i
$307$	27.9190			1.59342			0.796711	−	0.604360i	$-0.206571\pi$
$307$	27.9190			1.59342			0.796711	+	0.604360i	$0.206571\pi$
$308$			0.0369670i			0.00210639i
$309$	0.380629	−	0.380629i	0.0216532	−	0.0216532i
$310$	0.934237			0.0530611
$311$	7.14652	−	7.14652i	0.405242	−	0.405242i	−0.474834	−	0.880076i	$-0.657492\pi$
$311$	7.14652	−	7.14652i	0.405242	−	0.405242i	0.880076	+	0.474834i	$0.157492\pi$
$312$	1.87208	+	1.87208i	0.105986	+	0.105986i
$313$	−20.6848	−	20.6848i	−1.16918	−	1.16918i	−0.982403	−	0.186773i	$-0.940197\pi$
$313$	−20.6848	−	20.6848i	−1.16918	−	1.16918i	−0.186773	−	0.982403i	$-0.559803\pi$
$314$			28.7395i			1.62186i
$315$			0.0457207i			0.00257607i
$316$	−2.69097	−	2.69097i	−0.151379	−	0.151379i
$317$	5.08267	+	5.08267i	0.285471	+	0.285471i	0.835286	−	0.549815i	$-0.185302\pi$
$317$	5.08267	+	5.08267i	0.285471	+	0.285471i	−0.549815	+	0.835286i	$0.685302\pi$
$318$	−2.60996	+	2.60996i	−0.146359	+	0.146359i
$319$	−7.88365			−0.441400
$320$	−5.05527	+	5.05527i	−0.282598	+	0.282598i
$321$			3.30618i			0.184533i
$322$	0.263023			0.0146577
$323$	15.0198	+	10.2859i	0.835725	+	0.572325i
$324$	0.225164			0.0125091
$325$		−	3.92893i		−	0.217938i
$326$	17.6353	−	17.6353i	0.976730	−	0.976730i
$327$	−0.614436			−0.0339784
$328$	−4.97154	+	4.97154i	−0.274507	+	0.274507i
$329$	−0.0422805	−	0.0422805i	−0.00233100	−	0.00233100i
$330$	−4.05684	−	4.05684i	−0.223322	−	0.223322i
$331$		−	0.111140i		−	0.00610879i	−0.999995	−	0.00305439i	$-0.999028\pi$
$331$		−	0.111140i		−	0.00610879i	0.999995	−	0.00305439i	$-0.000972246\pi$
$332$			1.13907i			0.0625146i
$333$	7.53120	+	7.53120i	0.412707	+	0.412707i
$334$	−7.52606	−	7.52606i	−0.411808	−	0.411808i
$335$	−0.418861	+	0.418861i	−0.0228848	+	0.0228848i
$336$	−0.194366			−0.0106035
$337$	−22.0971	+	22.0971i	−1.20371	+	1.20371i	−0.230675	+	0.973031i	$0.574093\pi$
$337$	−22.0971	+	22.0971i	−1.20371	+	1.20371i	−0.973031	+	0.230675i	$0.925907\pi$
$338$			1.49170i			0.0811377i
$339$	2.23602			0.121444
$340$	0.176670	+	0.944416i	0.00958126	+	0.0512181i
$341$	2.24895			0.121787
$342$			6.58612i			0.356137i
$343$	−0.437276	+	0.437276i	−0.0236107	+	0.0236107i
$344$	8.31222			0.448165
$345$	−2.92081	+	2.92081i	−0.157251	+	0.157251i
$346$	−10.2307	−	10.2307i	−0.550005	−	0.550005i
$347$	−17.7587	−	17.7587i	−0.953340	−	0.953340i	0.0456193	−	0.998959i	$-0.485474\pi$
$347$	−17.7587	−	17.7587i	−0.953340	−	0.953340i	−0.998959	+	0.0456193i	$0.985474\pi$
$348$			0.477654i			0.0256049i
$349$		−	13.8628i		−	0.742059i	−0.928621	−	0.371029i	$-0.879005\pi$
$349$		−	13.8628i		−	0.742059i	0.928621	−	0.371029i	$-0.120995\pi$
$350$	0.183081	+	0.183081i	0.00978610	+	0.00978610i
$351$	−0.707107	−	0.707107i	−0.0377426	−	0.0377426i
$352$	3.33177	−	3.33177i	0.177584	−	0.177584i
$353$	−34.7409			−1.84907			−0.924536	−	0.381094i	$-0.875548\pi$
$353$	−34.7409			−1.84907			−0.924536	+	0.381094i	$0.875548\pi$
$354$	−6.76887	+	6.76887i	−0.359761	+	0.359761i
$355$		−	7.49830i		−	0.397968i
$356$	−3.94148			−0.208898
$357$	0.102920	−	0.150286i	0.00544709	−	0.00795400i
$358$	27.1176			1.43321
$359$			16.8044i			0.886904i	0.896298	+	0.443452i	$0.146246\pi$
$359$			16.8044i			0.886904i	−0.896298	+	0.443452i	$0.853754\pi$
$360$	1.93746	−	1.93746i	0.102113	−	0.102113i
$361$	−0.493853			−0.0259922
$362$	1.29856	−	1.29856i	0.0682511	−	0.0682511i
$363$	−1.98767	−	1.98767i	−0.104326	−	0.104326i
$364$	−0.00703375	−	0.00703375i	−0.000368669	−	0.000368669i
$365$		−	1.63726i		−	0.0856984i
$366$			16.6571i			0.870680i
$367$	−4.47843	−	4.47843i	−0.233772	−	0.233772i	0.580493	−	0.814265i	$-0.302860\pi$
$367$	−4.47843	−	4.47843i	−0.233772	−	0.233772i	−0.814265	+	0.580493i	$0.802860\pi$
$368$	−12.4168	−	12.4168i	−0.647272	−	0.647272i
$369$	1.87781	−	1.87781i	0.0977549	−	0.0977549i
$370$	−16.4426			−0.854809
$371$	−0.0772959	+	0.0772959i	−0.00401300	+	0.00401300i
$372$		−	0.136259i		−	0.00706470i
$373$	−20.9501			−1.08475			−0.542377	−	0.840135i	$-0.682476\pi$
$373$	−20.9501			−1.08475			−0.542377	+	0.840135i	$0.682476\pi$
$374$	4.20289	+	22.4672i	0.217326	+	1.16175i
$375$	−9.24078			−0.477192
$376$			3.58336i			0.184798i
$377$	1.50003	−	1.50003i	0.0772554	−	0.0772554i
$378$	0.0658999			0.00338952
$379$	−14.7352	+	14.7352i	−0.756895	+	0.756895i	−0.975756	−	0.218861i	$-0.929766\pi$
$379$	−14.7352	+	14.7352i	−0.756895	+	0.756895i	0.218861	+	0.975756i	$0.429766\pi$
$380$	−0.727514	−	0.727514i	−0.0373207	−	0.0373207i
$381$	−7.49845	−	7.49845i	−0.384157	−	0.384157i
$382$		−	0.598719i		−	0.0306331i
$383$		−	13.6330i		−	0.696613i	−0.937381	−	0.348307i	$-0.886757\pi$
$383$		−	13.6330i		−	0.696613i	0.937381	−	0.348307i	$-0.113243\pi$
$384$	9.07950	+	9.07950i	0.463336	+	0.463336i
$385$	−0.120146	−	0.120146i	−0.00612322	−	0.00612322i
$386$	9.79061	−	9.79061i	0.498329	−	0.498329i
$387$	−3.13962			−0.159596
$388$	2.00257	−	2.00257i	0.101665	−	0.101665i
$389$			18.1370i			0.919584i	0.888027	+	0.459792i	$0.152076\pi$
$389$			18.1370i			0.919584i	−0.888027	+	0.459792i	$0.847924\pi$
$390$	1.54380			0.0781732
$391$	16.1758	−	3.02596i	0.818044	−	0.153030i
$392$	18.5275			0.935779
$393$			7.15263i			0.360802i
$394$	3.13736	−	3.13736i	0.158058	−	0.158058i
$395$	17.4918			0.880108
$396$	−0.591692	+	0.591692i	−0.0297337	+	0.0297337i
$397$	−0.269705	−	0.269705i	−0.0135361	−	0.0135361i	0.700306	−	0.713842i	$-0.253047\pi$
$397$	−0.269705	−	0.269705i	−0.0135361	−	0.0135361i	−0.713842	+	0.700306i	$0.753047\pi$
$398$	−5.21063	−	5.21063i	−0.261186	−	0.261186i
$399$			0.195053i			0.00976486i
$400$		−	17.2858i		−	0.864291i
$401$	9.96462	+	9.96462i	0.497609	+	0.497609i	0.910693	−	0.413084i	$-0.135548\pi$
$401$	9.96462	+	9.96462i	0.497609	+	0.497609i	−0.413084	+	0.910693i	$0.635548\pi$
$402$	0.603729	+	0.603729i	0.0301112	+	0.0301112i
$403$	−0.427909	+	0.427909i	−0.0213157	+	0.0213157i
$404$	0.731598			0.0363984
$405$	−0.731803	+	0.731803i	−0.0363636	+	0.0363636i
$406$			0.139797i			0.00693803i
$407$	−39.5815			−1.96198
$408$	−10.7299	+	2.00721i	−0.531208	+	0.0993719i
$409$	3.86215			0.190971			0.0954855	−	0.995431i	$-0.469560\pi$
$409$	3.86215			0.190971			0.0954855	+	0.995431i	$0.469560\pi$
$410$			4.09975i			0.202472i
$411$	−4.54470	+	4.54470i	−0.224174	+	0.224174i
$412$	0.121203			0.00597126
$413$	−0.200465	+	0.200465i	−0.00986424	+	0.00986424i
$414$	4.20994	+	4.20994i	0.206907	+	0.206907i
$415$	−3.70209	−	3.70209i	−0.181728	−	0.181728i
$416$			1.26788i			0.0621628i
$417$			21.1281i			1.03465i
$418$	−17.3072	−	17.3072i	−0.846524	−	0.846524i
$419$	26.5023	+	26.5023i	1.29472	+	1.29472i	0.931833	+	0.362888i	$0.118209\pi$
$419$	26.5023	+	26.5023i	1.29472	+	1.29472i	0.362888	+	0.931833i	$0.381791\pi$
$420$	−0.00727941	+	0.00727941i	−0.000355199	+	0.000355199i
$421$	−5.57536			−0.271726			−0.135863	−	0.990728i	$-0.543381\pi$
$421$	−5.57536			−0.271726			−0.135863	+	0.990728i	$0.543381\pi$
$422$	21.8929	−	21.8929i	1.06573	−	1.06573i
$423$		−	1.35348i		−	0.0658084i
$424$	6.55099			0.318144
$425$	13.3656	+	9.15311i	0.648329	+	0.443991i
$426$	−10.8077			−0.523636
$427$			0.493312i			0.0238731i
$428$	−0.526393	+	0.526393i	−0.0254442	+	0.0254442i
$429$	3.71631			0.179425
$430$	3.42731	−	3.42731i	0.165279	−	0.165279i
$431$	12.8497	+	12.8497i	0.618947	+	0.618947i	0.945261	−	0.326314i	$-0.105807\pi$
$431$	12.8497	+	12.8497i	0.618947	+	0.618947i	−0.326314	+	0.945261i	$0.605807\pi$
$432$	−3.11101	−	3.11101i	−0.149678	−	0.149678i
$433$			22.0644i			1.06035i	0.847888	+	0.530175i	$0.177874\pi$
$433$			22.0644i			1.06035i	−0.847888	+	0.530175i	$0.822126\pi$
$434$		−	0.0398796i		−	0.00191428i
$435$	−1.55242	−	1.55242i	−0.0744328	−	0.0744328i
$436$	−0.0978272	−	0.0978272i	−0.00468507	−	0.00468507i
$437$	−12.4607	+	12.4607i	−0.596077	+	0.596077i
$438$	−2.35988			−0.112760
$439$	−1.81405	+	1.81405i	−0.0865801	+	0.0865801i	−0.749070	−	0.662490i	$-0.769500\pi$
$439$	−1.81405	+	1.81405i	−0.0865801	+	0.0865801i	0.662490	+	0.749070i	$0.269500\pi$
$440$			10.1827i			0.485439i
$441$	−6.99805			−0.333240
$442$	−5.07454	−	3.47517i	−0.241371	−	0.165297i
$443$	−39.5785			−1.88043			−0.940216	−	0.340577i	$-0.889377\pi$
$443$	−39.5785			−1.88043			−0.940216	+	0.340577i	$0.889377\pi$
$444$			2.39816i			0.113812i
$445$	12.8102	−	12.8102i	0.607261	−	0.607261i
$446$	−4.59315			−0.217492
$447$	−8.86990	+	8.86990i	−0.419532	+	0.419532i
$448$	0.215794	+	0.215794i	0.0101953	+	0.0101953i
$449$	24.2192	+	24.2192i	1.14298	+	1.14298i	0.987903	+	0.155073i	$0.0495612\pi$
$449$	24.2192	+	24.2192i	1.14298	+	1.14298i	0.155073	+	0.987903i	$0.450439\pi$
$450$			5.86077i			0.276280i
$451$			9.86914i			0.464719i
$452$	0.356008	+	0.356008i	0.0167452	+	0.0167452i
$453$	8.62617	+	8.62617i	0.405293	+	0.405293i
$454$	−25.1773	+	25.1773i	−1.18163	+	1.18163i
$455$	0.0457207			0.00214342
$456$	8.26558	−	8.26558i	0.387071	−	0.387071i
$457$		−	21.6914i		−	1.01468i	−0.861745	−	0.507341i	$-0.830628\pi$
$457$		−	21.6914i		−	1.01468i	0.861745	−	0.507341i	$-0.169372\pi$
$458$	30.6559			1.43246
$459$	4.05280	−	0.758149i	0.189169	−	0.0353874i
$460$	−0.930073			−0.0433649
$461$			6.41574i			0.298811i	0.988776	+	0.149405i	$0.0477360\pi$
$461$			6.41574i			0.298811i	−0.988776	+	0.149405i	$0.952264\pi$
$462$	−0.173174	+	0.173174i	−0.00805677	+	0.00805677i
$463$	20.8944			0.971043			0.485522	−	0.874225i	$-0.338630\pi$
$463$	20.8944			0.971043			0.485522	+	0.874225i	$0.338630\pi$
$464$	6.59957	−	6.59957i	0.306377	−	0.306377i
$465$	0.442855	+	0.442855i	0.0205369	+	0.0205369i
$466$	−16.3650	−	16.3650i	−0.758092	−	0.758092i
$467$		−	20.0571i		−	0.928133i	−0.885800	−	0.464066i	$-0.846390\pi$
$467$		−	20.0571i		−	0.928133i	0.885800	−	0.464066i	$-0.153610\pi$
$468$		−	0.225164i		−	0.0104082i
$469$	0.0178799	+	0.0178799i	0.000825616	+	0.000825616i
$470$	1.47750	+	1.47750i	0.0681519	+	0.0681519i
$471$	−13.6233	+	13.6233i	−0.627730	+	0.627730i
$472$	16.9898			0.782021
$473$	8.25040	−	8.25040i	0.379354	−	0.379354i
$474$		−	25.2119i		−	1.15802i
$475$	−17.3469			−0.795932
$476$	0.0403141	−	0.00754148i	0.00184780	−	0.000345663i
$477$	−2.47439			−0.113294
$478$			42.0006i			1.92106i
$479$	−5.34820	+	5.34820i	−0.244365	+	0.244365i	−0.818653	−	0.574288i	$-0.805279\pi$
$479$	−5.34820	+	5.34820i	−0.244365	+	0.244365i	0.574288	+	0.818653i	$0.305279\pi$
$480$	1.31216			0.0598917
$481$	7.53120	−	7.53120i	0.343393	−	0.343393i
$482$	24.9937	+	24.9937i	1.13843	+	1.13843i
$483$	0.124680	+	0.124680i	0.00567315	+	0.00567315i
$484$		−	0.632934i		−	0.0287697i
$485$			13.0171i			0.591074i
$486$	1.05479	+	1.05479i	0.0478462	+	0.0478462i
$487$	8.54342	+	8.54342i	0.387139	+	0.387139i	0.873666	−	0.486526i	$-0.161736\pi$
$487$	8.54342	+	8.54342i	0.387139	+	0.387139i	−0.486526	+	0.873666i	$0.661736\pi$
$488$	20.9046	−	20.9046i	0.946308	−	0.946308i
$489$	16.7193			0.756071
$490$	7.63928	−	7.63928i	0.345107	−	0.345107i
$491$			6.85324i			0.309283i	0.987971	+	0.154641i	$0.0494222\pi$
$491$			6.85324i			0.309283i	−0.987971	+	0.154641i	$0.950578\pi$
$492$	0.597950			0.0269577
$493$	1.60831	+	8.59746i	0.0724345	+	0.387210i
$494$	6.58612			0.296324
$495$		−	3.84611i		−	0.172870i
$496$	−1.88264	+	1.88264i	−0.0845331	+	0.0845331i
$497$	−0.320079			−0.0143575
$498$	−5.33603	+	5.33603i	−0.239113	+	0.239113i
$499$	−16.0394	−	16.0394i	−0.718022	−	0.718022i	0.250178	−	0.968200i	$-0.419511\pi$
$499$	−16.0394	−	16.0394i	−0.718022	−	0.718022i	−0.968200	+	0.250178i	$0.919511\pi$
$500$	−1.47127	−	1.47127i	−0.0657972	−	0.0657972i
$501$		−	7.13513i		−	0.318774i
$502$		−	20.5750i		−	0.918308i
$503$	17.4204	+	17.4204i	0.776737	+	0.776737i	0.979274	−	0.202538i	$-0.0649189\pi$
$503$	17.4204	+	17.4204i	0.776737	+	0.776737i	−0.202538	+	0.979274i	$0.564919\pi$
$504$	−0.0827042	−	0.0827042i	−0.00368394	−	0.00368394i
$505$	−2.37776	+	2.37776i	−0.105809	+	0.105809i
$506$	−22.1260			−0.983621
$507$	−0.707107	+	0.707107i	−0.0314037	+	0.0314037i
$508$		−	2.38773i		−	0.105938i
$509$	−23.0243			−1.02053			−0.510267	−	0.860016i	$-0.670453\pi$
$509$	−23.0243			−1.02053			−0.510267	+	0.860016i	$0.670453\pi$
$510$	−3.59654	+	5.25178i	−0.159258	+	0.232553i
$511$	−0.0698897			−0.00309174
$512$		−	17.7180i		−	0.783033i
$513$	−3.12201	+	3.12201i	−0.137840	+	0.137840i
$514$	20.2049			0.891200
$515$	−0.393923	+	0.393923i	−0.0173583	+	0.0173583i
$516$	−0.499874	−	0.499874i	−0.0220057	−	0.0220057i
$517$	3.55671	+	3.55671i	0.156424	+	0.156424i
$518$			0.701882i			0.0308389i
$519$		−	9.69927i		−	0.425751i
$520$	−1.93746	−	1.93746i	−0.0849634	−	0.0849634i
$521$	−2.62786	−	2.62786i	−0.115129	−	0.115129i	0.647195	−	0.762324i	$-0.275942\pi$
$521$	−2.62786	−	2.62786i	−0.115129	−	0.115129i	−0.762324	+	0.647195i	$0.775942\pi$
$522$	−2.23759	+	2.23759i	−0.0979367	+	0.0979367i
$523$	−20.8775			−0.912911			−0.456456	−	0.889746i	$-0.650881\pi$
$523$	−20.8775			−0.912911			−0.456456	+	0.889746i	$0.650881\pi$
$524$	−1.13880	+	1.13880i	−0.0497489	+	0.0497489i
$525$			0.173571i			0.00757527i
$526$	25.5336			1.11332
$527$	−0.458798	−	2.45257i	−0.0199855	−	0.106836i
$528$	16.3504			0.711560
$529$		−	7.06989i		−	0.307386i
$530$	2.70112	−	2.70112i	0.117329	−	0.117329i
$531$	−6.41726			−0.278486
$532$	−0.0310553	+	0.0310553i	−0.00134642	+	0.00134642i
$533$	−1.87781	−	1.87781i	−0.0813370	−	0.0813370i
$534$	−18.4640	−	18.4640i	−0.799017	−	0.799017i
$535$		−	3.42166i		−	0.147931i
$536$		−	1.51536i		−	0.0654535i
$537$	12.8545	+	12.8545i	0.554713	+	0.554713i
$538$	−18.1293	−	18.1293i	−0.781610	−	0.781610i
$539$	18.3897	−	18.3897i	0.792100	−	0.792100i
$540$	−0.233028			−0.0100279
$541$	2.46403	−	2.46403i	0.105937	−	0.105937i	−0.652152	−	0.758089i	$-0.726133\pi$
$541$	2.46403	−	2.46403i	0.105937	−	0.105937i	0.758089	+	0.652152i	$0.226133\pi$
$542$			18.2078i			0.782094i
$543$	1.23111			0.0528321
$544$	−4.31314	−	2.95374i	−0.184924	−	0.126641i
$545$	0.635896			0.0272388
$546$		−	0.0658999i		−	0.00282025i
$547$	21.3402	−	21.3402i	0.912442	−	0.912442i	−0.0840223	−	0.996464i	$-0.526777\pi$
$547$	21.3402	−	21.3402i	0.912442	−	0.912442i	0.996464	+	0.0840223i	$0.0267767\pi$
$548$	−1.44717			−0.0618199
$549$	−7.89593	+	7.89593i	−0.336990	+	0.336990i
$550$	−15.4011	−	15.4011i	−0.656706	−	0.656706i
$551$	−6.62291	−	6.62291i	−0.282145	−	0.282145i
$552$		−	10.5669i		−	0.449758i
$553$		−	0.746670i		−	0.0317516i
$554$	−20.8095	−	20.8095i	−0.884110	−	0.884110i
$555$	−7.79424	−	7.79424i	−0.330847	−	0.330847i
$556$	−3.36390	+	3.36390i	−0.142661	+	0.142661i
$557$	43.0975			1.82610			0.913050	−	0.407848i	$-0.133721\pi$
$557$	43.0975			1.82610			0.913050	+	0.407848i	$0.133721\pi$
$558$	0.638312	−	0.638312i	0.0270219	−	0.0270219i
$559$			3.13962i			0.132792i
$560$	0.201154			0.00850031
$561$	−8.65779	+	12.6424i	−0.365532	+	0.533761i
$562$	33.6320			1.41868
$563$			14.0995i			0.594224i	0.954843	+	0.297112i	$0.0960235\pi$
$563$			14.0995i			0.594224i	−0.954843	+	0.297112i	$0.903977\pi$
$564$	0.215494	−	0.215494i	0.00907393	−	0.00907393i
$565$	−2.31412			−0.0973556
$566$	11.7194	−	11.7194i	0.492603	−	0.492603i
$567$	0.0312384	+	0.0312384i	0.00131189	+	0.00131189i
$568$	13.5637	+	13.5637i	0.569120	+	0.569120i
$569$		−	31.8433i		−	1.33494i	−0.744636	−	0.667471i	$-0.767377\pi$
$569$		−	31.8433i		−	1.33494i	0.744636	−	0.667471i	$-0.232623\pi$
$570$		−	6.81615i		−	0.285497i
$571$	5.82297	+	5.82297i	0.243684	+	0.243684i	0.818372	−	0.574688i	$-0.194877\pi$
$571$	5.82297	+	5.82297i	0.243684	+	0.243684i	−0.574688	+	0.818372i	$0.694877\pi$
$572$	0.591692	+	0.591692i	0.0247399	+	0.0247399i
$573$	0.283810	−	0.283810i	0.0118563	−	0.0118563i
$574$	0.175005			0.00730458
$575$	−11.0884	+	11.0884i	−0.462418	+	0.462418i
$576$			6.90797i			0.287832i
$577$	13.4722			0.560857			0.280428	−	0.959875i	$-0.409523\pi$
$577$	13.4722			0.560857			0.280428	+	0.959875i	$0.409523\pi$
$578$	23.6440	−	9.16687i	0.983463	−	0.381291i
$579$	9.28205			0.385749
$580$		−	0.494336i		−	0.0205262i
$581$	−0.158031	+	0.158031i	−0.00655621	+	0.00655621i
$582$	18.7622			0.777720
$583$	6.50227	−	6.50227i	0.269297	−	0.269297i
$584$	2.96165	+	2.96165i	0.122554	+	0.122554i
$585$	0.731803	+	0.731803i	0.0302563	+	0.0302563i
$586$		−	19.6953i		−	0.813605i
$587$			21.2732i			0.878039i	0.898478	+	0.439019i	$0.144674\pi$
$587$			21.2732i			0.878039i	−0.898478	+	0.439019i	$0.855326\pi$
$588$	−1.11419	−	1.11419i	−0.0459485	−	0.0459485i
$589$	1.88930	+	1.88930i	0.0778472	+	0.0778472i
$590$	7.00528	−	7.00528i	0.288403	−	0.288403i
$591$	2.97440			0.122350
$592$	33.1345	−	33.1345i	1.36182	−	1.36182i
$593$		−	8.12552i		−	0.333675i	−0.985984	−	0.166838i	$-0.946644\pi$
$593$		−	8.12552i		−	0.333675i	0.985984	−	0.166838i	$-0.0533555\pi$
$594$	−5.54362			−0.227457
$595$	−0.106514	+	0.155535i	−0.00436666	+	0.00637633i
$596$	−2.82444			−0.115693
$597$		−	4.93997i		−	0.202180i
$598$	4.20994	−	4.20994i	0.172157	−	0.172157i
$599$	−24.2125			−0.989294			−0.494647	−	0.869094i	$-0.664703\pi$
$599$	−24.2125			−0.989294			−0.494647	+	0.869094i	$0.664703\pi$
$600$	7.35526	−	7.35526i	0.300277	−	0.300277i
$601$	−20.7046	−	20.7046i	−0.844559	−	0.844559i	0.144889	−	0.989448i	$-0.453717\pi$
$601$	−20.7046	−	20.7046i	−0.844559	−	0.844559i	−0.989448	+	0.144889i	$0.953717\pi$
$602$	−0.146301	−	0.146301i	−0.00596278	−	0.00596278i
$603$			0.572369i			0.0233086i
$604$			2.74683i			0.111767i
$605$	2.05710	+	2.05710i	0.0836328	+	0.0836328i
$606$	3.42721	+	3.42721i	0.139221	+	0.139221i
$607$	17.9676	−	17.9676i	0.729282	−	0.729282i	−0.241194	−	0.970477i	$-0.577539\pi$
$607$	17.9676	−	17.9676i	0.729282	−	0.729282i	0.970477	+	0.241194i	$0.0775391\pi$
$608$	5.59791			0.227025
$609$	−0.0662679	+	0.0662679i	−0.00268531	+	0.00268531i
$610$		−	17.2389i		−	0.697981i
$611$	−1.35348			−0.0547559
$612$	0.765975	+	0.524558i	0.0309627	+	0.0212040i
$613$	−11.9862			−0.484117			−0.242058	−	0.970262i	$-0.577823\pi$
$613$	−11.9862			−0.484117			−0.242058	+	0.970262i	$0.577823\pi$
$614$			41.6468i			1.68073i
$615$	−1.94340	+	1.94340i	−0.0783653	+	0.0783653i
$616$	0.434666			0.0175132
$617$	−12.6715	+	12.6715i	−0.510137	+	0.510137i	−0.914568	−	0.404432i	$-0.867469\pi$
$617$	−12.6715	+	12.6715i	−0.510137	+	0.510137i	0.404432	+	0.914568i	$0.367469\pi$
$618$	0.567783	+	0.567783i	0.0228396	+	0.0228396i
$619$	26.2615	+	26.2615i	1.05554	+	1.05554i	0.998364	+	0.0571740i	$0.0182090\pi$
$619$	26.2615	+	26.2615i	1.05554	+	1.05554i	0.0571740	+	0.998364i	$0.481791\pi$
$620$			0.141018i			0.00566342i
$621$			3.99125i			0.160164i
$622$	10.6605	+	10.6605i	0.427445	+	0.427445i
$623$	−0.546826	−	0.546826i	−0.0219081	−	0.0219081i
$624$	−3.11101	+	3.11101i	−0.124540	+	0.124540i
$625$	−10.0811			−0.403244
$626$	30.8555	−	30.8555i	1.23324	−	1.23324i
$627$		−	16.4082i		−	0.655281i
$628$	−4.33807			−0.173108
$629$	8.07484	+	43.1653i	0.321965	+	1.72111i
$630$	−0.0682015			−0.00271721
$631$			36.8305i			1.46620i	0.680122	+	0.733099i	$0.261927\pi$
$631$			36.8305i			1.46620i	−0.680122	+	0.733099i	$0.738073\pi$
$632$	−31.6410	+	31.6410i	−1.25861	+	1.25861i
$633$	20.7557			0.824964
$634$	−7.58181	+	7.58181i	−0.301112	+	0.301112i
$635$	7.76035	+	7.76035i	0.307960	+	0.307960i
$636$	−0.393959	−	0.393959i	−0.0156215	−	0.0156215i
$637$			6.99805i			0.277273i
$638$		−	11.7600i		−	0.465584i
$639$	−5.12317	−	5.12317i	−0.202669	−	0.202669i
$640$	−9.39662	−	9.39662i	−0.371434	−	0.371434i
$641$	−25.3480	+	25.3480i	−1.00119	+	1.00119i	−0.00118696	+	0.999999i	$0.500378\pi$
$641$	−25.3480	+	25.3480i	−1.00119	+	1.00119i	−0.999999	+	0.00118696i	$0.999622\pi$
$642$	−4.93183			−0.194644
$643$	−31.7596	+	31.7596i	−1.25248	+	1.25248i	−0.297869	+	0.954607i	$0.596276\pi$
$643$	−31.7596	+	31.7596i	−1.25248	+	1.25248i	−0.954607	+	0.297869i	$0.903724\pi$
$644$			0.0397019i			0.00156447i
$645$	3.24928			0.127940
$646$	−15.3435	+	22.4050i	−0.603682	+	0.881515i
$647$	40.3683			1.58704			0.793521	−	0.608542i	$-0.208245\pi$
$647$	40.3683			1.58704			0.793521	+	0.608542i	$0.208245\pi$
$648$		−	2.64752i		−	0.104004i
$649$	16.8635	−	16.8635i	0.661950	−	0.661950i
$650$	5.86077			0.229878
$651$	0.0189041	−	0.0189041i	0.000740909	−	0.000740909i
$652$	2.66195	+	2.66195i	0.104250	+	0.104250i
$653$	−1.27356	−	1.27356i	−0.0498383	−	0.0498383i	0.681748	−	0.731587i	$-0.261220\pi$
$653$	−1.27356	−	1.27356i	−0.0498383	−	0.0498383i	−0.731587	+	0.681748i	$0.761220\pi$
$654$		−	0.916553i		−	0.0358400i
$655$		−	7.40244i		−	0.289237i
$656$	−8.26167	−	8.26167i	−0.322564	−	0.322564i
$657$	−1.11865	−	1.11865i	−0.0436427	−	0.0436427i
$658$	0.0630697	−	0.0630697i	0.00245871	−	0.00245871i
$659$	29.2852			1.14079			0.570394	−	0.821371i	$-0.306791\pi$
$659$	29.2852			1.14079			0.570394	+	0.821371i	$0.306791\pi$
$660$	0.612358	−	0.612358i	0.0238360	−	0.0238360i
$661$		−	20.8970i		−	0.812799i	−0.913695	−	0.406400i	$-0.866784\pi$
$661$		−	20.8970i		−	0.812799i	0.913695	−	0.406400i	$-0.133216\pi$
$662$	0.165787			0.00644349
$663$	−0.758149	−	4.05280i	−0.0294441	−	0.157398i
$664$	13.3934			0.519766
$665$		−	0.201865i		−	0.00782800i
$666$	−11.2343	+	11.2343i	−0.435320	+	0.435320i
$667$	−8.46689			−0.327839
$668$	1.13602	−	1.13602i	0.0439539	−	0.0439539i
$669$	−2.17728	−	2.17728i	−0.0841785	−	0.0841785i
$670$	−0.624815	−	0.624815i	−0.0241387	−	0.0241387i
$671$		−	41.4983i		−	1.60203i
$672$		−	0.0560120i		−	0.00216071i
$673$	−3.64900	−	3.64900i	−0.140659	−	0.140659i	0.633271	−	0.773930i	$-0.281712\pi$
$673$	−3.64900	−	3.64900i	−0.140659	−	0.140659i	−0.773930	+	0.633271i	$0.781712\pi$
$674$	−32.9622	−	32.9622i	−1.26966	−	1.26966i
$675$	−2.77817	+	2.77817i	−0.106932	+	0.106932i
$676$	−0.225164			−0.00866014
$677$	17.8463	−	17.8463i	0.685888	−	0.685888i	−0.275433	−	0.961320i	$-0.588821\pi$
$677$	17.8463	−	17.8463i	0.685888	−	0.685888i	0.961320	+	0.275433i	$0.0888212\pi$
$678$			3.33547i			0.128098i
$679$	0.555657			0.0213242
$680$	11.1046	−	2.07732i	0.425843	−	0.0796615i
$681$	−23.8695			−0.914682
$682$			3.35475i			0.128460i
$683$	15.6072	−	15.6072i	0.597192	−	0.597192i	−0.342372	−	0.939564i	$-0.611230\pi$
$683$	15.6072	−	15.6072i	0.597192	−	0.597192i	0.939564	+	0.342372i	$0.111230\pi$
$684$	−0.994139			−0.0380119
$685$	4.70343	−	4.70343i	0.179709	−	0.179709i
$686$	−0.652284	−	0.652284i	−0.0249043	−	0.0249043i
$687$	14.5318	+	14.5318i	0.554422	+	0.554422i
$688$			13.8132i			0.526622i
$689$			2.47439i			0.0942667i
$690$	−4.35697	−	4.35697i	−0.165867	−	0.165867i
$691$	−15.8524	−	15.8524i	−0.603055	−	0.603055i	0.338067	−	0.941122i	$-0.390227\pi$
$691$	−15.8524	−	15.8524i	−0.603055	−	0.603055i	−0.941122	+	0.338067i	$0.890227\pi$
$692$	1.54427	−	1.54427i	0.0587042	−	0.0587042i
$693$	−0.164178			−0.00623662
$694$	26.4907	−	26.4907i	1.00557	−	1.00557i
$695$		−	21.8660i		−	0.829425i
$696$	5.61635			0.212887
$697$	10.7627	−	2.01336i	0.407667	−	0.0762614i
$698$	20.6791			0.782716
$699$		−	15.5149i		−	0.586827i
$700$	−0.0276351	+	0.0276351i	−0.00104451	+	0.00104451i
$701$	−27.7680			−1.04878			−0.524392	−	0.851477i	$-0.675707\pi$
$701$	−27.7680			−1.04878			−0.524392	+	0.851477i	$0.675707\pi$
$702$	1.05479	−	1.05479i	0.0398105	−	0.0398105i
$703$	−33.2517	−	33.2517i	−1.25411	−	1.25411i
$704$	−18.1530	−	18.1530i	−0.684166	−	0.684166i
$705$			1.40075i			0.0527553i
$706$		−	51.8230i		−	1.95038i
$707$	0.101499	+	0.101499i	0.00381727	+	0.00381727i
$708$	−1.02172	−	1.02172i	−0.0383987	−	0.0383987i
$709$	−27.5853	+	27.5853i	−1.03599	+	1.03599i	−0.0366607	+	0.999328i	$0.511672\pi$
$709$	−27.5853	+	27.5853i	−1.03599	+	1.03599i	−0.999328	+	0.0366607i	$0.988328\pi$
$710$	11.1852			0.419773
$711$	11.9512	−	11.9512i	0.448204	−	0.448204i
$712$			46.3447i			1.73684i
$713$	2.41533			0.0904547
$714$	0.224182	+	0.153525i	0.00838980	+	0.00574553i
$715$	−3.84611			−0.143836
$716$			4.09325i			0.152972i
$717$	−19.9094	+	19.9094i	−0.743532	+	0.743532i
$718$	−25.0671			−0.935497
$719$	−2.79317	+	2.79317i	−0.104168	+	0.104168i	−0.757270	−	0.653102i	$-0.773467\pi$
$719$	−2.79317	+	2.79317i	−0.104168	+	0.104168i	0.653102	+	0.757270i	$0.273467\pi$
$720$	3.21966	+	3.21966i	0.119990	+	0.119990i
$721$	0.0168153	+	0.0168153i	0.000626235	+	0.000626235i
$722$		−	0.736679i		−	0.0274164i
$723$			23.6954i			0.881241i
$724$	0.196011	+	0.196011i	0.00728470	+	0.00728470i
$725$	−5.89351	−	5.89351i	−0.218879	−	0.218879i
$726$	2.96501	−	2.96501i	0.110042	−	0.110042i
$727$	4.65542			0.172660			0.0863301	−	0.996267i	$-0.472486\pi$
$727$	4.65542			0.172660			0.0863301	+	0.996267i	$0.472486\pi$
$728$	−0.0827042	+	0.0827042i	−0.00306522	+	0.00306522i
$729$			1.00000i			0.0370370i
$730$	2.44231			0.0903938
$731$	−10.6805	−	7.31429i	−0.395034	−	0.270529i
$732$	−2.51430			−0.0929311
$733$		−	15.2426i		−	0.563000i	−0.959561	−	0.281500i	$-0.909168\pi$
$733$		−	15.2426i		−	0.563000i	0.959561	−	0.281500i	$-0.0908320\pi$
$734$	6.68047	−	6.68047i	0.246581	−	0.246581i
$735$	7.24246			0.267142
$736$	3.57826	−	3.57826i	0.131896	−	0.131896i
$737$	−1.50409	−	1.50409i	−0.0554038	−	0.0554038i
$738$	2.80113	+	2.80113i	0.103111	+	0.103111i
$739$		−	20.0393i		−	0.737157i	−0.929597	−	0.368579i	$-0.879845\pi$
$739$		−	20.0393i		−	0.737157i	0.929597	−	0.368579i	$-0.120155\pi$
$740$		−	2.48192i		−	0.0912371i
$741$	3.12201	+	3.12201i	0.114690	+	0.114690i
$742$	−0.115302	−	0.115302i	−0.00423287	−	0.00423287i
$743$	11.3151	−	11.3151i	0.415109	−	0.415109i	−0.468405	−	0.883514i	$-0.655171\pi$
$743$	11.3151	−	11.3151i	0.415109	−	0.415109i	0.883514	+	0.468405i	$0.155171\pi$
$744$	−1.60216			−0.0587381
$745$	9.17969	−	9.17969i	0.336318	−	0.336318i
$746$		−	31.2512i		−	1.14419i
$747$	−5.05886			−0.185094
$748$	−3.39130	+	0.634403i	−0.123998	+	0.0231961i
$749$	−0.146060			−0.00533691
$750$		−	13.7845i		−	0.503337i
$751$	−2.39989	+	2.39989i	−0.0875732	+	0.0875732i	−0.749536	−	0.661963i	$-0.769724\pi$
$751$	−2.39989	+	2.39989i	−0.0875732	+	0.0875732i	0.661963	+	0.749536i	$0.269724\pi$
$752$	−5.95480			−0.217149
$753$	9.75314	−	9.75314i	0.355424	−	0.355424i
$754$	2.23759	+	2.23759i	0.0814883	+	0.0814883i
$755$	−8.92745	−	8.92745i	−0.324903	−	0.324903i
$756$			0.00994722i			0.000361777i
$757$		−	1.17125i		−	0.0425698i	−0.999773	−	0.0212849i	$-0.993224\pi$
$757$		−	1.17125i		−	0.0425698i	0.999773	−	0.0212849i	$-0.00677571\pi$
$758$	−21.9804	−	21.9804i	−0.798366	−	0.798366i
$759$	−10.4883	−	10.4883i	−0.380703	−	0.380703i
$760$	−8.55426	+	8.55426i	−0.310296	+	0.310296i
$761$	−1.76491			−0.0639778			−0.0319889	−	0.999488i	$-0.510184\pi$
$761$	−1.76491			−0.0639778			−0.0319889	+	0.999488i	$0.510184\pi$
$762$	11.1854	−	11.1854i	0.405205	−	0.405205i
$763$		−	0.0271444i		−	0.000982692i
$764$	0.0903734			0.00326959
$765$	−4.19435	+	0.784628i	−0.151647	+	0.0283683i
$766$	20.3363			0.734781
$767$			6.41726i			0.231714i
$768$	−3.77454	+	3.77454i	−0.136202	+	0.136202i
$769$	31.3994			1.13229			0.566146	−	0.824305i	$-0.308434\pi$
$769$	31.3994			1.13229			0.566146	+	0.824305i	$0.308434\pi$
$770$	0.179222	−	0.179222i	0.00645871	−	0.00645871i
$771$	9.57769	+	9.57769i	0.344932	+	0.344932i
$772$	1.47784	+	1.47784i	0.0531886	+	0.0531886i
$773$		−	14.9090i		−	0.536239i	−0.963386	−	0.268119i	$-0.913598\pi$
$773$		−	14.9090i		−	0.536239i	0.963386	−	0.268119i	$-0.0864022\pi$
$774$		−	4.68337i		−	0.168340i
$775$	1.68122	+	1.68122i	0.0603914	+	0.0603914i
$776$	−23.5466	−	23.5466i	−0.845273	−	0.845273i
$777$	−0.332712	+	0.332712i	−0.0119360	+	0.0119360i
$778$	−27.0550			−0.969968
$779$	−8.29088	+	8.29088i	−0.297052	+	0.297052i
$780$			0.233028i			0.00834373i
$781$	26.9256			0.963475
$782$	4.51383	+	24.1294i	0.161414	+	0.862864i
$783$	−2.12136			−0.0758113
$784$			30.7888i			1.09960i
$785$	14.0991	−	14.0991i	0.503220	−	0.503220i
$786$	−10.6696			−0.380571
$787$	−3.34915	+	3.34915i	−0.119384	+	0.119384i	−0.764275	−	0.644891i	$-0.776903\pi$
$787$	−3.34915	+	3.34915i	−0.119384	+	0.119384i	0.644891	+	0.764275i	$0.276903\pi$
$788$	0.473568	+	0.473568i	0.0168702	+	0.0168702i
$789$	12.1037	+	12.1037i	0.430901	+	0.430901i
$790$			26.0925i			0.928329i
$791$			0.0987823i			0.00351230i
$792$	6.95724	+	6.95724i	0.247215	+	0.247215i
$793$	7.89593	+	7.89593i	0.280393	+	0.280393i
$794$	0.402319	−	0.402319i	0.0142778	−	0.0142778i
$795$	2.56081			0.0908226
$796$	0.786517	−	0.786517i	0.0278773	−	0.0278773i
$797$			33.1318i			1.17359i	0.809736	+	0.586795i	$0.199610\pi$
$797$			33.1318i			1.17359i	−0.809736	+	0.586795i	$0.800390\pi$
$798$	−0.290960			−0.0102999
$799$	3.15316	−	4.60434i	0.111551	−	0.162890i
$800$	4.98140			0.176119
$801$		−	17.5049i		−	0.618507i
$802$	−14.8642	+	14.8642i	−0.524873	+	0.524873i
$803$	5.87925			0.207474
$804$	−0.0911295	+	0.0911295i	−0.00321389	+	0.00321389i
$805$	−0.129035	−	0.129035i	−0.00454788	−	0.00454788i
$806$	−0.638312	−	0.638312i	−0.0224836	−	0.0224836i
$807$		−	17.1876i		−	0.605032i
$808$		−	8.60228i		−	0.302627i
$809$	13.2085	+	13.2085i	0.464385	+	0.464385i	0.900090	−	0.435704i	$-0.143501\pi$
$809$	13.2085	+	13.2085i	0.464385	+	0.464385i	−0.435704	+	0.900090i	$0.643501\pi$
$810$	−1.09163	−	1.09163i	−0.0383560	−	0.0383560i
$811$	−16.5467	+	16.5467i	−0.581032	+	0.581032i	−0.935187	−	0.354155i	$-0.884769\pi$
$811$	−16.5467	+	16.5467i	−0.581032	+	0.581032i	0.354155	+	0.935187i	$0.384769\pi$
$812$	−0.0211017			−0.000740523
$813$	−8.63103	+	8.63103i	−0.302703	+	0.302703i
$814$		−	59.0436i		−	2.06948i
$815$	−17.3032			−0.606105
$816$	−3.33557	−	17.8308i	−0.116768	−	0.624204i
$817$	13.8620			0.484971
$818$			5.76116i			0.201434i
$819$	0.0312384	−	0.0312384i	0.00109156	−	0.00109156i
$820$	−0.618834			−0.0216106
$821$	−13.9497	+	13.9497i	−0.486849	+	0.486849i	−0.907310	−	0.420462i	$-0.861868\pi$
$821$	−13.9497	+	13.9497i	−0.486849	+	0.486849i	0.420462	+	0.907310i	$0.361868\pi$
$822$	−6.77932	−	6.77932i	−0.236456	−	0.236456i
$823$	35.5716	+	35.5716i	1.23995	+	1.23995i	0.960022	+	0.279925i	$0.0903097\pi$
$823$	35.5716	+	35.5716i	1.23995	+	1.23995i	0.279925	+	0.960022i	$0.409690\pi$
$824$		−	1.42513i		−	0.0496469i
$825$		−	14.6011i		−	0.508346i
$826$	−0.299033	−	0.299033i	−0.0104047	−	0.0104047i
$827$	−12.3978	−	12.3978i	−0.431112	−	0.431112i	0.457895	−	0.889007i	$-0.348604\pi$
$827$	−12.3978	−	12.3978i	−0.431112	−	0.431112i	−0.889007	+	0.457895i	$0.848604\pi$
$828$	−0.635467	+	0.635467i	−0.0220840	+	0.0220840i
$829$	−11.9849			−0.416254			−0.208127	−	0.978102i	$-0.566737\pi$
$829$	−11.9849			−0.416254			−0.208127	+	0.978102i	$0.566737\pi$
$830$	5.52240	−	5.52240i	0.191685	−	0.191685i
$831$		−	19.7286i		−	0.684376i
$832$	6.90797			0.239491
$833$	−23.8064	−	16.3032i	−0.824841	−	0.564871i
$834$	−31.5167			−1.09133
$835$			7.38433i			0.255545i
$836$	2.61243	−	2.61243i	0.0903528	−	0.0903528i
$837$	0.605155			0.0209172
$838$	−39.5334	+	39.5334i	−1.36566	+	1.36566i
$839$	14.7689	+	14.7689i	0.509879	+	0.509879i	0.914489	−	0.404610i	$-0.132593\pi$
$839$	14.7689	+	14.7689i	0.509879	+	0.509879i	−0.404610	+	0.914489i	$0.632593\pi$
$840$	0.0855928	+	0.0855928i	0.00295323	+	0.00295323i
$841$			24.4998i			0.844822i
$842$		−	8.31675i		−	0.286614i
$843$	15.9425	+	15.9425i	0.549089	+	0.549089i
$844$	3.30461	+	3.30461i	0.113749	+	0.113749i
$845$	0.731803	−	0.731803i	0.0251748	−	0.0251748i
$846$	2.01898			0.0694140
$847$	0.0878109	−	0.0878109i	0.00301722	−	0.00301722i
$848$			10.8864i			0.373840i
$849$	11.1106			0.381316
$850$	−13.6537	+	19.9375i	−0.468317	+	0.683851i
$851$	−42.5098			−1.45722
$852$		−	1.63137i		−	0.0558897i
$853$	1.44566	−	1.44566i	0.0494986	−	0.0494986i	−0.681924	−	0.731423i	$-0.738857\pi$
$853$	1.44566	−	1.44566i	0.0494986	−	0.0494986i	0.731423	+	0.681924i	$0.238857\pi$
$854$	−0.735873			−0.0251811
$855$	3.23105	−	3.23105i	0.110499	−	0.110499i
$856$	6.18944	+	6.18944i	0.211551	+	0.211551i
$857$	−14.5855	−	14.5855i	−0.498231	−	0.498231i	0.412656	−	0.910887i	$-0.364601\pi$
$857$	−14.5855	−	14.5855i	−0.498231	−	0.498231i	−0.910887	+	0.412656i	$0.864601\pi$
$858$			5.54362i			0.189256i
$859$			24.1830i			0.825114i	0.910932	+	0.412557i	$0.135364\pi$
$859$			24.1830i			0.825114i	−0.910932	+	0.412557i	$0.864636\pi$
$860$	0.517333	+	0.517333i	0.0176409	+	0.0176409i
$861$	0.0829574	+	0.0829574i	0.00282718	+	0.00282718i
$862$	−19.1678	+	19.1678i	−0.652859	+	0.652859i
$863$	37.5742			1.27904			0.639521	−	0.768774i	$-0.279133\pi$
$863$	37.5742			1.27904			0.639521	+	0.768774i	$0.279133\pi$
$864$	0.896525	−	0.896525i	0.0305004	−	0.0305004i
$865$			10.0380i			0.341303i
$866$	−32.9135			−1.11845
$867$	15.5533	+	6.86259i	0.528217	+	0.233066i
$868$	0.00601961			0.000204319
$869$			62.8113i			2.13073i
$870$	2.31574	−	2.31574i	0.0785110	−	0.0785110i
$871$	0.572369			0.0193940
$872$	−1.15027	+	1.15027i	−0.0389531	+	0.0389531i
$873$	8.89382	+	8.89382i	0.301010	+	0.301010i
$874$	−18.5876	−	18.5876i	−0.628736	−	0.628736i
$875$		−	0.408237i		−	0.0138009i
$876$		−	0.356211i		−	0.0120353i
$877$	26.3533	+	26.3533i	0.889887	+	0.889887i	0.994512	−	0.104625i	$-0.0333643\pi$
$877$	26.3533	+	26.3533i	0.889887	+	0.889887i	−0.104625	+	0.994512i	$0.533364\pi$
$878$	−2.70602	−	2.70602i	−0.0913238	−	0.0913238i
$879$	9.33612	−	9.33612i	0.314899	−	0.314899i
$880$	−16.9215			−0.570422
$881$	−24.4854	+	24.4854i	−0.824935	+	0.824935i	−0.986811	−	0.161876i	$-0.948245\pi$
$881$	−24.4854	+	24.4854i	−0.824935	+	0.824935i	0.161876	+	0.986811i	$0.448245\pi$
$882$		−	10.4390i		−	0.351499i
$883$	4.12148			0.138699			0.0693494	−	0.997592i	$-0.477908\pi$
$883$	4.12148			0.138699			0.0693494	+	0.997592i	$0.477908\pi$
$884$	0.524558	−	0.765975i	0.0176428	−	0.0257625i
$885$	6.64140			0.223248
$886$		−	59.0392i		−	1.98346i
$887$	20.3337	−	20.3337i	0.682740	−	0.682740i	−0.277877	−	0.960617i	$-0.589631\pi$
$887$	20.3337	−	20.3337i	0.682740	−	0.682740i	0.960617	+	0.277877i	$0.0896307\pi$
$888$	28.1980			0.946264
$889$	0.331265	−	0.331265i	0.0111103	−	0.0111103i
$890$	19.1089	+	19.1089i	0.640533	+	0.640533i
$891$	−2.62783	−	2.62783i	−0.0880357	−	0.0880357i
$892$		−	0.693310i		−	0.0232137i
$893$			5.97586i			0.199974i
$894$	−13.2312	−	13.2312i	−0.442518	−	0.442518i
$895$	−13.3035	−	13.3035i	−0.444686	−	0.444686i
$896$	−0.401112	+	0.401112i	−0.0134002	+	0.0134002i
$897$	3.99125			0.133264
$898$	−36.1278	+	36.1278i	−1.20560	+	1.20560i
$899$			1.28375i			0.0428156i
$900$	−0.884652			−0.0294884
$901$	−8.41751	−	5.76451i	−0.280428	−	0.192044i
$902$	−14.7218			−0.490181
$903$		−	0.138701i		−	0.00461570i
$904$	4.18601	−	4.18601i	0.139225	−	0.139225i
$905$	−1.27411			−0.0423529
$906$	−12.8676	+	12.8676i	−0.427499	+	0.427499i
$907$	4.54629	+	4.54629i	0.150957	+	0.150957i	0.778545	−	0.627588i	$-0.215958\pi$
$907$	4.54629	+	4.54629i	0.150957	+	0.150957i	−0.627588	+	0.778545i	$0.715958\pi$
$908$	−3.80038	−	3.80038i	−0.126120	−	0.126120i
$909$			3.24918i			0.107769i
$910$			0.0682015i			0.00226086i
$911$	−21.9182	−	21.9182i	−0.726183	−	0.726183i	0.243674	−	0.969857i	$-0.421647\pi$
$911$	−21.9182	−	21.9182i	−0.726183	−	0.726183i	−0.969857	+	0.243674i	$0.921647\pi$
$912$	13.7357	+	13.7357i	0.454834	+	0.454834i
$913$	13.2938	−	13.2938i	0.439961	−	0.439961i
$914$	32.3571			1.07028
$915$	8.17171	−	8.17171i	0.270148	−	0.270148i
$916$			4.62734i			0.152892i
$917$	−0.315987			−0.0104348
$918$	1.13093	+	6.04556i	0.0373262	+	0.199533i
$919$	28.4619			0.938870			0.469435	−	0.882967i	$-0.344458\pi$
$919$	28.4619			0.938870			0.469435	+	0.882967i	$0.344458\pi$
$920$			10.9360i			0.360549i
$921$	−19.7417	+	19.7417i	−0.650512	+	0.650512i
$922$	−9.57035			−0.315183
$923$	−5.12317	+	5.12317i	−0.168631	+	0.168631i
$924$	−0.0261396	−	0.0261396i	−0.000859931	−	0.000859931i
$925$	−29.5896	−	29.5896i	−0.972898	−	0.972898i
$926$			31.1681i			1.02425i
$927$			0.538290i			0.0176798i
$928$	1.90185	+	1.90185i	0.0624314	+	0.0624314i
$929$	−19.0094	−	19.0094i	−0.623679	−	0.623679i	0.322792	−	0.946470i	$-0.395379\pi$
$929$	−19.0094	−	19.0094i	−0.623679	−	0.623679i	−0.946470	+	0.322792i	$0.895379\pi$
$930$	−0.660605	+	0.660605i	−0.0216621	+	0.0216621i
$931$	30.8977			1.01263
$932$	2.47020	−	2.47020i	0.0809141	−	0.0809141i
$933$			10.1067i			0.330879i
$934$	29.9192			0.978985
$935$	8.96018	−	13.0839i	0.293029	−	0.427890i
$936$	−2.64752			−0.0865369
$937$			5.99197i			0.195749i	0.995199	+	0.0978746i	$0.0312044\pi$
$937$			5.99197i			0.195749i	−0.995199	+	0.0978746i	$0.968796\pi$
$938$	−0.0266714	+	0.0266714i	−0.000870851	+	0.000870851i
$939$	29.2528			0.954628
$940$	−0.223020	+	0.223020i	−0.00727412	+	0.00727412i
$941$	−4.33133	−	4.33133i	−0.141197	−	0.141197i	0.632975	−	0.774172i	$-0.281834\pi$
$941$	−4.33133	−	4.33133i	−0.141197	−	0.141197i	−0.774172	+	0.632975i	$0.781834\pi$
$942$	−20.3219	−	20.3219i	−0.662123	−	0.662123i
$943$			10.5993i			0.345160i
$944$			28.2336i			0.918925i
$945$	−0.0323294	−	0.0323294i	−0.00105168	−	0.00105168i
$946$	12.3071	+	12.3071i	0.400139	+	0.400139i
$947$	−27.1109	+	27.1109i	−0.880986	+	0.880986i	−0.993635	−	0.112648i	$-0.964067\pi$
$947$	−27.1109	+	27.1109i	−0.880986	+	0.880986i	0.112648	+	0.993635i	$0.464067\pi$
$948$	3.80560			0.123600
$949$	−1.11865	+	1.11865i	−0.0363129	+	0.0363129i
$950$		−	25.8764i		−	0.839541i
$951$	−7.18798			−0.233086
$952$	−0.0886742	−	0.474022i	−0.00287395	−	0.0153631i
$953$	−10.7250			−0.347418			−0.173709	−	0.984797i	$-0.555575\pi$
$953$	−10.7250			−0.347418			−0.173709	+	0.984797i	$0.555575\pi$
$954$		−	3.69104i		−	0.119502i
$955$	−0.293722	+	0.293722i	−0.00950462	+	0.00950462i
$956$	−6.33975			−0.205042
$957$	5.57458	−	5.57458i	0.180201	−	0.180201i
$958$	−7.97790	−	7.97790i	−0.257754	−	0.257754i
$959$	−0.200775	−	0.200775i	−0.00648335	−	0.00648335i
$960$		−	7.14924i		−	0.230741i
$961$			30.6338i			0.988187i
$962$	11.2343	+	11.2343i	0.362208	+	0.362208i
$963$	−2.33783	−	2.33783i	−0.0753354	−	0.0753354i
$964$	−3.77265	+	3.77265i	−0.121509	+	0.121509i
$965$	−9.60624			−0.309236
$966$	−0.185985	+	0.185985i	−0.00598398	+	0.00598398i
$967$			48.5148i			1.56013i	0.625698	+	0.780066i	$0.284814\pi$
$967$			48.5148i			1.56013i	−0.625698	+	0.780066i	$0.715186\pi$
$968$	−7.44216			−0.239200
$969$	−17.8939	+	3.34737i	−0.574834	+	0.107533i
$970$	−19.4175			−0.623459
$971$			12.8931i			0.413758i	0.978367	+	0.206879i	$0.0663307\pi$
$971$			12.8931i			0.413758i	−0.978367	+	0.206879i	$0.933669\pi$
$972$	−0.159215	+	0.159215i	−0.00510682	+	0.00510682i
$973$	−0.933391			−0.0299231
$974$	−12.7442	+	12.7442i	−0.408351	+	0.408351i
$975$	2.77817	+	2.77817i	0.0889727	+	0.0889727i
$976$	34.7392	+	34.7392i	1.11197	+	1.11197i
$977$		−	26.0916i		−	0.834745i	−0.908735	−	0.417373i	$-0.862951\pi$
$977$		−	26.0916i		−	0.834745i	0.908735	−	0.417373i	$-0.137049\pi$
$978$			24.9401i			0.797497i
$979$	46.0000	+	46.0000i	1.47017	+	1.47017i
$980$	1.15311	+	1.15311i	0.0368347	+	0.0368347i
$981$	0.434472	−	0.434472i	0.0138716	−	0.0138716i
$982$	−10.2230			−0.326228
$983$	−17.1625	+	17.1625i	−0.547400	+	0.547400i	−0.925688	−	0.378288i	$-0.876513\pi$
$983$	−17.1625	+	17.1625i	−0.547400	+	0.547400i	0.378288	+	0.925688i	$0.376513\pi$
$984$		−	7.03082i		−	0.224134i
$985$	−3.07828			−0.0980822
$986$	−12.8248	+	2.39911i	−0.408425	+	0.0764032i
$987$	0.0597936			0.00190325
$988$			0.994139i			0.0316278i
$989$	8.86078	−	8.86078i	0.281756	−	0.281756i
$990$	5.73724			0.182341
$991$	−8.24791	+	8.24791i	−0.262003	+	0.262003i	−0.825868	−	0.563864i	$-0.809314\pi$
$991$	−8.24791	+	8.24791i	−0.262003	+	0.262003i	0.563864	+	0.825868i	$0.309314\pi$
$992$	−0.542537	−	0.542537i	−0.0172256	−	0.0172256i
$993$	0.0785876	+	0.0785876i	0.00249390	+	0.00249390i
$994$		−	0.477461i		−	0.0151441i
$995$			5.11251i			0.162077i
$996$	−0.805445	−	0.805445i	−0.0255215	−	0.0255215i
$997$	41.8649	+	41.8649i	1.32587	+	1.32587i	0.908933	+	0.416941i	$0.136898\pi$
$997$	41.8649	+	41.8649i	1.32587	+	1.32587i	0.416941	+	0.908933i	$0.363102\pi$
$998$	23.9259	−	23.9259i	0.757362	−	0.757362i
$999$	−10.6507			−0.336974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.j.a.157.13	✓	32
17.13	even	4	inner	663.2.j.a.625.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.j.a.157.13	✓	32	1.1	even	1	trivial
663.2.j.a.625.4	yes	32	17.13	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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.49170i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.225164 q^{4} +(0.731803 - 0.731803i) q^{5} +(-1.05479 - 1.05479i) q^{6} +(-0.0312384 - 0.0312384i) q^{7} +2.64752i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.49170i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.225164 q^{4} +(0.731803 - 0.731803i) q^{5} +(-1.05479 - 1.05479i) q^{6} +(-0.0312384 - 0.0312384i) q^{7} +2.64752i q^{8} -1.00000i q^{9} +(1.09163 + 1.09163i) q^{10} +(2.62783 + 2.62783i) q^{11} +(0.159215 - 0.159215i) q^{12} -1.00000 q^{13} +(0.0465982 - 0.0465982i) q^{14} +1.03493i q^{15} -4.39963 q^{16} +(2.32967 - 3.40186i) q^{17} +1.49170 q^{18} +4.41518i q^{19} +(-0.164776 + 0.164776i) q^{20} +0.0441777 q^{21} +(-3.91993 + 3.91993i) q^{22} +(2.82224 + 2.82224i) q^{23} +(-1.87208 - 1.87208i) q^{24} +3.92893i q^{25} -1.49170i q^{26} +(0.707107 + 0.707107i) q^{27} +(0.00703375 + 0.00703375i) q^{28} +(-1.50003 + 1.50003i) q^{29} -1.54380 q^{30} +(0.427909 - 0.427909i) q^{31} -1.26788i q^{32} -3.71631 q^{33} +(5.07454 + 3.47517i) q^{34} -0.0457207 q^{35} +0.225164i q^{36} +(-7.53120 + 7.53120i) q^{37} -6.58612 q^{38} +(0.707107 - 0.707107i) q^{39} +(1.93746 + 1.93746i) q^{40} +(1.87781 + 1.87781i) q^{41} +0.0658999i q^{42} -3.13962i q^{43} +(-0.591692 - 0.591692i) q^{44} +(-0.731803 - 0.731803i) q^{45} +(-4.20994 + 4.20994i) q^{46} +1.35348 q^{47} +(3.11101 - 3.11101i) q^{48} -6.99805i q^{49} -5.86077 q^{50} +(0.758149 + 4.05280i) q^{51} +0.225164 q^{52} -2.47439i q^{53} +(-1.05479 + 1.05479i) q^{54} +3.84611 q^{55} +(0.0827042 - 0.0827042i) q^{56} +(-3.12201 - 3.12201i) q^{57} +(-2.23759 - 2.23759i) q^{58} -6.41726i q^{59} -0.233028i q^{60} +(-7.89593 - 7.89593i) q^{61} +(0.638312 + 0.638312i) q^{62} +(-0.0312384 + 0.0312384i) q^{63} -6.90797 q^{64} +(-0.731803 + 0.731803i) q^{65} -5.54362i q^{66} -0.572369 q^{67} +(-0.524558 + 0.765975i) q^{68} -3.99125 q^{69} -0.0682015i q^{70} +(5.12317 - 5.12317i) q^{71} +2.64752 q^{72} +(1.11865 - 1.11865i) q^{73} +(-11.2343 - 11.2343i) q^{74} +(-2.77817 - 2.77817i) q^{75} -0.994139i q^{76} -0.164178i q^{77} +(1.05479 + 1.05479i) q^{78} +(11.9512 + 11.9512i) q^{79} +(-3.21966 + 3.21966i) q^{80} -1.00000 q^{81} +(-2.80113 + 2.80113i) q^{82} -5.05886i q^{83} -0.00994722 q^{84} +(-0.784628 - 4.19435i) q^{85} +4.68337 q^{86} -2.12136i q^{87} +(-6.95724 + 6.95724i) q^{88} +17.5049 q^{89} +(1.09163 - 1.09163i) q^{90} +(0.0312384 + 0.0312384i) q^{91} +(-0.635467 - 0.635467i) q^{92} +0.605155i q^{93} +2.01898i q^{94} +(3.23105 + 3.23105i) q^{95} +(0.896525 + 0.896525i) q^{96} +(-8.89382 + 8.89382i) q^{97} +10.4390 q^{98} +(2.62783 - 2.62783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 4 q^{5} - 4 q^{6}+O(q^{10}) \) 32 * q - 24 * q^4 - 4 * q^5 - 4 * q^6	\( 32 q - 24 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{10} - 4 q^{11} - 32 q^{13} + 24 q^{14} - 12 q^{17} - 28 q^{20} + 16 q^{21} + 20 q^{23} + 4 q^{24} + 16 q^{28} + 52 q^{29} - 16 q^{30} + 20 q^{31} - 16 q^{33} + 32 q^{34} - 8 q^{35} - 20 q^{37} + 16 q^{38} - 80 q^{40} - 20 q^{41} + 44 q^{44} + 4 q^{45} - 32 q^{46} + 24 q^{47} + 16 q^{48} - 16 q^{50} + 4 q^{51} + 24 q^{52} - 4 q^{54} - 8 q^{55} - 68 q^{56} - 8 q^{57} - 64 q^{58} - 12 q^{61} + 16 q^{62} + 40 q^{64} + 4 q^{65} - 80 q^{67} + 20 q^{68} + 16 q^{69} + 4 q^{71} - 36 q^{73} + 48 q^{74} - 16 q^{75} + 4 q^{78} + 8 q^{79} + 76 q^{80} - 32 q^{81} + 4 q^{82} - 8 q^{84} + 52 q^{85} + 48 q^{86} - 60 q^{88} + 8 q^{89} + 4 q^{90} - 124 q^{92} - 48 q^{95} + 16 q^{96} + 40 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 24 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^10 - 4 * q^11 - 32 * q^13 + 24 * q^14 - 12 * q^17 - 28 * q^20 + 16 * q^21 + 20 * q^23 + 4 * q^24 + 16 * q^28 + 52 * q^29 - 16 * q^30 + 20 * q^31 - 16 * q^33 + 32 * q^34 - 8 * q^35 - 20 * q^37 + 16 * q^38 - 80 * q^40 - 20 * q^41 + 44 * q^44 + 4 * q^45 - 32 * q^46 + 24 * q^47 + 16 * q^48 - 16 * q^50 + 4 * q^51 + 24 * q^52 - 4 * q^54 - 8 * q^55 - 68 * q^56 - 8 * q^57 - 64 * q^58 - 12 * q^61 + 16 * q^62 + 40 * q^64 + 4 * q^65 - 80 * q^67 + 20 * q^68 + 16 * q^69 + 4 * q^71 - 36 * q^73 + 48 * q^74 - 16 * q^75 + 4 * q^78 + 8 * q^79 + 76 * q^80 - 32 * q^81 + 4 * q^82 - 8 * q^84 + 52 * q^85 + 48 * q^86 - 60 * q^88 + 8 * q^89 + 4 * q^90 - 124 * q^92 - 48 * q^95 + 16 * q^96 + 40 * q^97 + 48 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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