LMFDB - Embedded newform 630.2.bv.d.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(73,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	630.73
Dual form			630.2.bv.d.397.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-2.10096 - 0.765474i) q^{5} +(-2.01472 + 1.71490i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.83126 + 1.28316i) q^{10} +(2.58598 - 4.47905i) q^{11} +(0.265680 - 0.265680i) q^{13} +(2.38992 - 1.13502i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.26908 + 0.340048i) q^{17} +(3.75044 + 6.49596i) q^{19} +(-1.43675 - 1.71340i) q^{20} +(-3.65713 + 3.65713i) q^{22} +(-2.01403 + 7.51645i) q^{23} +(3.82810 + 3.21647i) q^{25} +(-0.325390 + 0.187864i) q^{26} +(-2.60225 + 0.477786i) q^{28} +8.10291i q^{29} +(-6.65309 - 3.84116i) q^{31} +(-0.258819 - 0.965926i) q^{32} +1.31385 q^{34} +(5.54557 - 2.06073i) q^{35} +(1.90539 + 0.510547i) q^{37} +(-1.94137 - 7.24530i) q^{38} +(0.944334 + 2.02688i) q^{40} +3.37852i q^{41} +(8.71627 + 8.71627i) q^{43} +(4.47905 - 2.58598i) q^{44} +(3.89080 - 6.73906i) q^{46} +(-0.907271 + 3.38598i) q^{47} +(1.11822 - 6.91011i) q^{49} +(-2.86518 - 4.09765i) q^{50} +(0.362926 - 0.0972457i) q^{52} +(-6.37920 + 1.70930i) q^{53} +(-8.86165 + 7.43083i) q^{55} +(2.63724 + 0.212006i) q^{56} +(2.09719 - 7.82681i) q^{58} +(3.36216 - 5.82343i) q^{59} +(-5.17644 + 2.98862i) q^{61} +(5.43223 + 5.43223i) q^{62} +1.00000i q^{64} +(-0.761556 + 0.354813i) q^{65} +(-0.614064 - 2.29172i) q^{67} +(-1.26908 - 0.340048i) q^{68} +(-5.88997 + 0.555210i) q^{70} +4.54008 q^{71} +(1.81526 + 6.77465i) q^{73} +(-1.70832 - 0.986302i) q^{74} +7.50089i q^{76} +(2.47109 + 13.4588i) q^{77} +(10.3622 - 5.98260i) q^{79} +(-0.387562 - 2.20223i) q^{80} +(0.874425 - 3.26340i) q^{82} +(-5.48051 + 5.48051i) q^{83} +(2.92659 + 0.257017i) q^{85} +(-6.16333 - 10.6752i) q^{86} +(-4.99573 + 1.33860i) q^{88} +(6.80532 + 11.7872i) q^{89} +(-0.0796568 + 0.990888i) q^{91} +(-5.50242 + 5.50242i) q^{92} +(1.75271 - 3.03579i) q^{94} +(-2.90706 - 16.5186i) q^{95} +(-8.75027 - 8.75027i) q^{97} +(-2.86859 + 6.38523i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{7} + 12 q^{10} + 16 q^{16} + 8 q^{22} + 20 q^{28} + 48 q^{31} + 32 q^{37} + 80 q^{43} + 8 q^{46} - 28 q^{58} + 48 q^{61} + 16 q^{67} - 60 q^{70} - 24 q^{73} + 48 q^{82} - 144 q^{85} + 4 q^{88}+ \cdots - 32 q^{91}+O(q^{100}) $ 32 * q + 4 * q^7 + 12 * q^10 + 16 * q^16 + 8 * q^22 + 20 * q^28 + 48 * q^31 + 32 * q^37 + 80 * q^43 + 8 * q^46 - 28 * q^58 + 48 * q^61 + 16 * q^67 - 60 * q^70 - 24 * q^73 + 48 * q^82 - 144 * q^85 + 4 * q^88 - 32 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.10096	−	0.765474i	−0.939580	−	0.342330i
$5$	−2.10096	−	0.765474i	−0.939580	−	0.342330i
$6$		0			0
$7$	−2.01472	+	1.71490i	−0.761494	+	0.648172i
$7$	−2.01472	+	1.71490i	−0.761494	+	0.648172i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.83126	+	1.28316i	0.579094	+	0.405771i
$11$	2.58598	−	4.47905i	0.779703	−	1.35049i	−0.152410	−	0.988317i	$-0.548703\pi$
$11$	2.58598	−	4.47905i	0.779703	−	1.35049i	0.932113	−	0.362168i	$-0.117963\pi$
$12$		0			0
$13$	0.265680	−	0.265680i	0.0736864	−	0.0736864i	−0.669303	−	0.742989i	$-0.733407\pi$
$13$	0.265680	−	0.265680i	0.0736864	−	0.0736864i	0.742989	+	0.669303i	$0.233407\pi$
$14$	2.38992	−	1.13502i	0.638734	−	0.303347i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.26908	+	0.340048i	−0.307797	+	0.0824739i	−0.409411	−	0.912350i	$-0.634266\pi$
$17$	−1.26908	+	0.340048i	−0.307797	+	0.0824739i	0.101615	+	0.994824i	$0.467599\pi$
$18$		0			0
$19$	3.75044	+	6.49596i	0.860411	+	1.49028i	0.871533	+	0.490337i	$0.163126\pi$
$19$	3.75044	+	6.49596i	0.860411	+	1.49028i	−0.0111223	+	0.999938i	$0.503540\pi$
$20$	−1.43675	−	1.71340i	−0.321267	−	0.383128i
$21$		0			0
$22$	−3.65713	+	3.65713i	−0.779703	+	0.779703i
$23$	−2.01403	+	7.51645i	−0.419953	+	1.56729i	0.354749	+	0.934962i	$0.384566\pi$
$23$	−2.01403	+	7.51645i	−0.419953	+	1.56729i	−0.774702	+	0.632326i	$0.782100\pi$
$24$		0			0
$25$	3.82810	+	3.21647i	0.765620	+	0.643293i
$26$	−0.325390	+	0.187864i	−0.0638143	+	0.0368432i
$27$		0			0
$28$	−2.60225	+	0.477786i	−0.491780	+	0.0902931i
$29$			8.10291i			1.50467i	0.658779	+	0.752337i	$0.271073\pi$
$29$			8.10291i			1.50467i	−0.658779	+	0.752337i	$0.728927\pi$
$30$		0			0
$31$	−6.65309	−	3.84116i	−1.19493	−	0.689893i	−0.235510	−	0.971872i	$-0.575676\pi$
$31$	−6.65309	−	3.84116i	−1.19493	−	0.689893i	−0.959421	+	0.281979i	$0.909009\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$	1.31385			0.225323
$35$	5.54557	−	2.06073i	0.937373	−	0.348327i
$36$		0			0
$37$	1.90539	+	0.510547i	0.313244	+	0.0839334i	0.412016	−	0.911177i	$-0.364825\pi$
$37$	1.90539	+	0.510547i	0.313244	+	0.0839334i	−0.0987721	+	0.995110i	$0.531491\pi$
$38$	−1.94137	−	7.24530i	−0.314932	−	1.17534i
$39$		0			0
$40$	0.944334	+	2.02688i	0.149312	+	0.320477i
$41$			3.37852i			0.527636i	0.964572	+	0.263818i	$0.0849818\pi$
$41$			3.37852i			0.527636i	−0.964572	+	0.263818i	$0.915018\pi$
$42$		0			0
$43$	8.71627	+	8.71627i	1.32922	+	1.32922i	0.906052	+	0.423166i	$0.139081\pi$
$43$	8.71627	+	8.71627i	1.32922	+	1.32922i	0.423166	+	0.906052i	$0.360919\pi$
$44$	4.47905	−	2.58598i	0.675243	−	0.389852i
$45$		0			0
$46$	3.89080	−	6.73906i	0.573667	−	0.993620i
$47$	−0.907271	+	3.38598i	−0.132339	+	0.493896i	−0.999995	−	0.00326972i	$-0.998959\pi$
$47$	−0.907271	+	3.38598i	−0.132339	+	0.493896i	0.867656	+	0.497166i	$0.165626\pi$
$48$		0			0
$49$	1.11822	−	6.91011i	0.159746	−	0.987158i
$50$	−2.86518	−	4.09765i	−0.405197	−	0.579496i
$51$		0			0
$52$	0.362926	−	0.0972457i	0.0503288	−	0.0134856i
$53$	−6.37920	+	1.70930i	−0.876251	+	0.234791i	−0.668789	−	0.743452i	$-0.733187\pi$
$53$	−6.37920	+	1.70930i	−0.876251	+	0.234791i	−0.207462	+	0.978243i	$0.566520\pi$
$54$		0			0
$55$	−8.86165	+	7.43083i	−1.19491	+	1.00197i
$56$	2.63724	+	0.212006i	0.352416	+	0.0283305i
$57$		0			0
$58$	2.09719	−	7.82681i	0.275374	−	1.02771i
$59$	3.36216	−	5.82343i	0.437716	−	0.758146i	−0.559797	−	0.828630i	$-0.689121\pi$
$59$	3.36216	−	5.82343i	0.437716	−	0.758146i	0.997513	+	0.0704836i	$0.0224542\pi$
$60$		0			0
$61$	−5.17644	+	2.98862i	−0.662775	+	0.382653i	−0.793334	−	0.608787i	$-0.791656\pi$
$61$	−5.17644	+	2.98862i	−0.662775	+	0.382653i	0.130558	+	0.991441i	$0.458323\pi$
$62$	5.43223	+	5.43223i	0.689893	+	0.689893i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.761556	+	0.354813i	−0.0944594	+	0.0440092i
$66$		0			0
$67$	−0.614064	−	2.29172i	−0.0750198	−	0.279978i	0.918218	−	0.396075i	$-0.129628\pi$
$67$	−0.614064	−	2.29172i	−0.0750198	−	0.279978i	−0.993238	+	0.116098i	$0.962961\pi$
$68$	−1.26908	−	0.340048i	−0.153898	−	0.0412369i
$69$		0			0
$70$	−5.88997	+	0.555210i	−0.703986	+	0.0663603i
$71$	4.54008			0.538808			0.269404	−	0.963027i	$-0.413173\pi$
$71$	4.54008			0.538808			0.269404	+	0.963027i	$0.413173\pi$
$72$		0			0
$73$	1.81526	+	6.77465i	0.212460	+	0.792913i	0.987045	+	0.160443i	$0.0512922\pi$
$73$	1.81526	+	6.77465i	0.212460	+	0.792913i	−0.774585	+	0.632470i	$0.782041\pi$
$74$	−1.70832	−	0.986302i	−0.198589	−	0.114655i
$75$		0			0
$76$			7.50089i			0.860411i
$77$	2.47109	+	13.4588i	0.281607	+	1.53377i
$78$		0			0
$79$	10.3622	−	5.98260i	1.16583	−	0.673095i	0.213140	−	0.977022i	$-0.431631\pi$
$79$	10.3622	−	5.98260i	1.16583	−	0.673095i	0.952695	+	0.303927i	$0.0982978\pi$
$80$	−0.387562	−	2.20223i	−0.0433308	−	0.246216i
$81$		0			0
$82$	0.874425	−	3.26340i	0.0965641	−	0.360382i
$83$	−5.48051	+	5.48051i	−0.601564	+	0.601564i	−0.940727	−	0.339163i	$-0.889856\pi$
$83$	−5.48051	+	5.48051i	−0.601564	+	0.601564i	0.339163	+	0.940727i	$0.389856\pi$
$84$		0			0
$85$	2.92659	+	0.257017i	0.317433	+	0.0278774i
$86$	−6.16333	−	10.6752i	−0.664609	−	1.15114i
$87$		0			0
$88$	−4.99573	+	1.33860i	−0.532547	+	0.142696i
$89$	6.80532	+	11.7872i	0.721363	+	1.24944i	0.960454	+	0.278440i	$0.0898173\pi$
$89$	6.80532	+	11.7872i	0.721363	+	1.24944i	−0.239091	+	0.970997i	$0.576849\pi$
$90$		0			0
$91$	−0.0796568	+	0.990888i	−0.00835031	+	0.103873i
$92$	−5.50242	+	5.50242i	−0.573667	+	0.573667i
$93$		0			0
$94$	1.75271	−	3.03579i	0.180778	−	0.313117i
$95$	−2.90706	−	16.5186i	−0.298258	−	1.69478i
$96$		0			0
$97$	−8.75027	−	8.75027i	−0.888456	−	0.888456i	0.105919	−	0.994375i	$-0.466222\pi$
$97$	−8.75027	−	8.75027i	−0.888456	−	0.888456i	−0.994375	+	0.105919i	$0.966222\pi$
$98$	−2.86859	+	6.38523i	−0.289771	+	0.645006i
$99$		0			0
$100$	1.70700	+	4.69959i	0.170700	+	0.469959i
$101$	8.00611	+	4.62233i	0.796638	+	0.459939i	0.842294	−	0.539018i	$-0.181205\pi$
$101$	8.00611	+	4.62233i	0.796638	+	0.459939i	−0.0456565	+	0.998957i	$0.514538\pi$
$102$		0			0
$103$	−3.37847	−	0.905259i	−0.332891	−	0.0891978i	0.0885021	−	0.996076i	$-0.471792\pi$
$103$	−3.37847	−	0.905259i	−0.332891	−	0.0891978i	−0.421393	+	0.906878i	$0.638459\pi$
$104$	−0.375729			−0.0368432
$105$		0			0
$106$	6.60424			0.641460
$107$	5.66154	+	1.51700i	0.547322	+	0.146654i	0.521875	−	0.853022i	$-0.325233\pi$
$107$	5.66154	+	1.51700i	0.547322	+	0.146654i	0.0254463	+	0.999676i	$0.491899\pi$
$108$		0			0
$109$	−0.113156	−	0.0653306i	−0.0108384	−	0.00625754i	0.494571	−	0.869137i	$-0.335325\pi$
$109$	−0.113156	−	0.0653306i	−0.0108384	−	0.00625754i	−0.505409	+	0.862880i	$0.668659\pi$
$110$	10.4829	−	4.88406i	0.999509	−	0.465677i
$111$		0			0
$112$	−2.49251	−	0.887351i	−0.235520	−	0.0838468i
$113$	−3.87916	−	3.87916i	−0.364921	−	0.364921i	0.500700	−	0.865621i	$-0.333076\pi$
$113$	−3.87916	−	3.87916i	−0.364921	−	0.364921i	−0.865621	+	0.500700i	$0.833076\pi$
$114$		0			0
$115$	9.98504	−	14.2501i	0.931110	−	1.32883i
$116$	−4.05146	+	7.01733i	−0.376168	+	0.651543i
$117$		0			0
$118$	−4.75481	+	4.75481i	−0.437716	+	0.437716i
$119$	1.97369	−	2.86145i	0.180928	−	0.262309i
$120$		0			0
$121$	−7.87461	−	13.6392i	−0.715874	−	1.23993i
$122$	5.77357	−	1.54702i	0.522714	−	0.140061i
$123$		0			0
$124$	−3.84116	−	6.65309i	−0.344947	−	0.597465i
$125$	−5.58058	−	9.68799i	−0.499142	−	0.866520i
$126$		0			0
$127$	9.07777	−	9.07777i	0.805522	−	0.805522i	−0.178431	−	0.983952i	$-0.557102\pi$
$127$	9.07777	−	9.07777i	0.805522	−	0.805522i	0.983952	+	0.178431i	$0.0571021\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$		0			0
$130$	0.827439	−	0.145618i	0.0725712	−	0.0127716i
$131$	−0.982572	+	0.567288i	−0.0858477	+	0.0495642i	−0.542309	−	0.840179i	$-0.682450\pi$
$131$	−0.982572	+	0.567288i	−0.0858477	+	0.0495642i	0.456462	+	0.889743i	$0.349117\pi$
$132$		0			0
$133$	−18.6960	−	6.65592i	−1.62115	−	0.577142i
$134$			2.37256i			0.204958i
$135$		0			0
$136$	1.13782	+	0.656923i	0.0975676	+	0.0563307i
$137$	1.38235	+	5.15899i	0.118102	+	0.440762i	0.999500	−	0.0316115i	$-0.0100639\pi$
$137$	1.38235	+	5.15899i	0.118102	+	0.440762i	−0.881398	+	0.472374i	$0.843397\pi$
$138$		0			0
$139$	−18.5198			−1.57083			−0.785414	−	0.618970i	$-0.787550\pi$
$139$	−18.5198			−1.57083			−0.785414	+	0.618970i	$0.787550\pi$
$140$	5.83297	+	0.988145i	0.492976	+	0.0835135i
$141$		0			0
$142$	−4.38538	−	1.17506i	−0.368013	−	0.0986087i
$143$	−0.502951	−	1.87704i	−0.0420589	−	0.156966i
$144$		0			0
$145$	6.20257	−	17.0239i	0.515095	−	1.41376i
$146$		−	7.01363i		−	0.580452i
$147$		0			0
$148$	1.39484	+	1.39484i	0.114655	+	0.114655i
$149$	−8.57321	+	4.94975i	−0.702345	+	0.405499i	−0.808220	−	0.588880i	$-0.799569\pi$
$149$	−8.57321	+	4.94975i	−0.702345	+	0.405499i	0.105875	+	0.994379i	$0.466236\pi$
$150$		0			0
$151$	5.06845	−	8.77882i	0.412465	−	0.714410i	−0.582694	−	0.812692i	$-0.698001\pi$
$151$	5.06845	−	8.77882i	0.412465	−	0.714410i	0.995159	+	0.0982818i	$0.0313347\pi$
$152$	1.94137	−	7.24530i	0.157466	−	0.587671i
$153$		0			0
$154$	1.09649	−	13.6397i	0.0883577	−	1.09912i
$155$	11.0376	+	13.1629i	0.886561	+	1.05727i
$156$		0			0
$157$	−2.48110	+	0.664809i	−0.198013	+	0.0530575i	−0.356463	−	0.934310i	$-0.616017\pi$
$157$	−2.48110	+	0.664809i	−0.198013	+	0.0530575i	0.158449	+	0.987367i	$0.449351\pi$
$158$	−11.5575	+	3.09682i	−0.919465	+	0.246370i
$159$		0			0
$160$	−0.195622	+	2.22749i	−0.0154652	+	0.176099i
$161$	−8.83226	−	18.5974i	−0.696080	−	1.46568i
$162$		0			0
$163$	2.91842	−	10.8917i	0.228589	−	0.853104i	−0.752346	−	0.658768i	$-0.771078\pi$
$163$	2.91842	−	10.8917i	0.228589	−	0.853104i	0.980935	−	0.194337i	$-0.0622554\pi$
$164$	−1.68926	+	2.92588i	−0.131909	+	0.228473i
$165$		0			0
$166$	6.71223	−	3.87531i	0.520970	−	0.300782i
$167$	−10.5786	−	10.5786i	−0.818599	−	0.818599i	0.167306	−	0.985905i	$-0.446493\pi$
$167$	−10.5786	−	10.5786i	−0.818599	−	0.818599i	−0.985905	+	0.167306i	$0.946493\pi$
$168$		0			0
$169$			12.8588i			0.989141i
$170$	−2.76034	−	1.00572i	−0.211709	−	0.0771348i
$171$		0			0
$172$	3.19038	+	11.9066i	0.243264	+	0.907873i
$173$	−16.9580	−	4.54389i	−1.28929	−	0.345465i	−0.451902	−	0.892068i	$-0.649254\pi$
$173$	−16.9580	−	4.54389i	−1.28929	−	0.345465i	−0.837392	+	0.546602i	$0.815921\pi$
$174$		0			0
$175$	−13.2285	+	0.0845226i	−0.999980	+	0.00638931i
$176$	5.17197			0.389852
$177$		0			0
$178$	−3.52269	−	13.1469i	−0.264037	−	0.985400i
$179$	1.69842	+	0.980586i	0.126946	+	0.0732924i	0.562128	−	0.827050i	$-0.309983\pi$
$179$	1.69842	+	0.980586i	0.126946	+	0.0732924i	−0.435182	+	0.900342i	$0.643316\pi$
$180$		0			0
$181$			25.3622i			1.88515i	0.333988	+	0.942577i	$0.391606\pi$
$181$			25.3622i			1.88515i	−0.333988	+	0.942577i	$0.608394\pi$
$182$	0.333403	−	0.936507i	0.0247135	−	0.0694185i
$183$		0			0
$184$	6.73906	−	3.89080i	0.496810	−	0.286834i
$185$	−3.61234	−	2.53117i	−0.265585	−	0.186095i
$186$		0			0
$187$	−1.75872	+	6.56363i	−0.128610	+	0.479980i
$188$	−2.47871	+	2.47871i	−0.180778	+	0.180778i
$189$		0			0
$190$	−1.46733	+	16.7082i	−0.106452	+	1.21214i
$191$	−0.907736	−	1.57224i	−0.0656815	−	0.113764i	0.831315	−	0.555802i	$-0.187589\pi$
$191$	−0.907736	−	1.57224i	−0.0656815	−	0.113764i	−0.896996	+	0.442039i	$0.854255\pi$
$192$		0			0
$193$	6.71159	−	1.79837i	0.483111	−	0.129449i	−0.00903978	−	0.999959i	$-0.502877\pi$
$193$	6.71159	−	1.79837i	0.483111	−	0.129449i	0.492151	+	0.870510i	$0.336211\pi$
$194$	6.18738	+	10.7169i	0.444228	+	0.769425i
$195$		0			0
$196$	4.42346	−	5.42522i	0.315962	−	0.387515i
$197$	0.403956	−	0.403956i	0.0287807	−	0.0287807i	−0.692570	−	0.721351i	$-0.743522\pi$
$197$	0.403956	−	0.403956i	0.0287807	−	0.0287807i	0.721351	+	0.692570i	$0.243522\pi$
$198$		0			0
$199$	−1.43941	+	2.49313i	−0.102037	+	0.176733i	−0.912524	−	0.409024i	$-0.865869\pi$
$199$	−1.43941	+	2.49313i	−0.102037	+	0.176733i	0.810487	+	0.585757i	$0.199203\pi$
$200$	−0.432490	−	4.98126i	−0.0305817	−	0.352228i
$201$		0			0
$202$	−6.53696	−	6.53696i	−0.459939	−	0.459939i
$203$	−13.8957	−	16.3251i	−0.975287	−	1.14580i
$204$		0			0
$205$	2.58617	−	7.09815i	0.180626	−	0.495756i
$206$	3.02906	+	1.74883i	0.211044	+	0.121847i
$207$		0			0
$208$	0.362926	+	0.0972457i	0.0251644	+	0.00674278i
$209$	38.7943			2.68346
$210$		0			0
$211$	−10.7019			−0.736752			−0.368376	−	0.929677i	$-0.620086\pi$
$211$	−10.7019			−0.736752			−0.368376	+	0.929677i	$0.620086\pi$
$212$	−6.37920	−	1.70930i	−0.438126	−	0.117395i
$213$		0			0
$214$	−5.07600	−	2.93063i	−0.346988	−	0.200334i
$215$	−11.6405	−	24.9846i	−0.793875	−	1.70394i
$216$		0			0
$217$	19.9914	−	3.67051i	1.35710	−	0.249171i
$218$	0.0923914	+	0.0923914i	0.00625754	+	0.00625754i
$219$		0			0
$220$	−11.3898	+	2.00446i	−0.767902	+	0.135141i
$221$	−0.246825	+	0.427513i	−0.0166032	+	0.0287576i
$222$		0			0
$223$	−8.44168	+	8.44168i	−0.565296	+	0.565296i	−0.930807	−	0.365511i	$-0.880894\pi$
$223$	−8.44168	+	8.44168i	−0.565296	+	0.565296i	0.365511	+	0.930807i	$0.380894\pi$
$224$	2.17792	+	1.50222i	0.145518	+	0.100372i
$225$		0			0
$226$	2.74298	+	4.75099i	0.182461	+	0.316031i
$227$	17.2960	−	4.63445i	1.14798	−	0.307599i	0.365823	−	0.930685i	$-0.380788\pi$
$227$	17.2960	−	4.63445i	1.14798	−	0.307599i	0.782154	+	0.623085i	$0.214121\pi$
$228$		0			0
$229$	4.32943	+	7.49879i	0.286097	+	0.495534i	0.972875	−	0.231334i	$-0.0743089\pi$
$229$	4.32943	+	7.49879i	0.286097	+	0.495534i	−0.686778	+	0.726867i	$0.740976\pi$
$230$	−13.3330	+	11.1802i	−0.879152	+	0.737202i
$231$		0			0
$232$	5.72963	−	5.72963i	0.376168	−	0.376168i
$233$	−4.95817	+	18.5041i	−0.324820	+	1.21225i	0.589672	+	0.807643i	$0.299257\pi$
$233$	−4.95817	+	18.5041i	−0.324820	+	1.21225i	−0.914492	+	0.404603i	$0.867410\pi$
$234$		0			0
$235$	4.49802	−	6.41933i	0.293419	−	0.418751i
$236$	5.82343	−	3.36216i	0.379073	−	0.218858i
$237$		0			0
$238$	−2.64704	+	2.25312i	−0.171582	+	0.146048i
$239$		−	6.70759i		−	0.433878i	−0.976185	−	0.216939i	$-0.930393\pi$
$239$		−	6.70759i		−	0.433878i	0.976185	−	0.216939i	$-0.0696073\pi$
$240$		0			0
$241$	−0.374613	−	0.216283i	−0.0241309	−	0.0139320i	0.487886	−	0.872907i	$-0.337768\pi$
$241$	−0.374613	−	0.216283i	−0.0241309	−	0.0139320i	−0.512017	+	0.858975i	$0.671102\pi$
$242$	4.07620	+	15.2126i	0.262028	+	0.977902i
$243$		0			0
$244$	−5.97724			−0.382653
$245$	−7.63886	+	13.6619i	−0.488029	+	0.872828i
$246$		0			0
$247$	2.72227	+	0.729429i	0.173214	+	0.0464125i
$248$	1.98833	+	7.42056i	0.126259	+	0.471206i
$249$		0			0
$250$	2.88299	+	10.8022i	0.182336	+	0.683194i
$251$		−	19.4059i		−	1.22489i	−0.790513	−	0.612446i	$-0.790186\pi$
$251$		−	19.4059i		−	1.22489i	0.790513	−	0.612446i	$-0.209814\pi$
$252$		0			0
$253$	28.4583	+	28.4583i	1.78916	+	1.78916i
$254$	−11.1179	+	6.41895i	−0.697602	+	0.402761i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.82963	+	18.0244i	−0.301264	+	1.12433i	0.634849	+	0.772636i	$0.281062\pi$
$257$	−4.82963	+	18.0244i	−0.301264	+	1.12433i	−0.936114	+	0.351698i	$0.885604\pi$
$258$		0			0
$259$	−4.71437	+	2.23894i	−0.292937	+	0.139121i
$260$	−0.836933	−	0.0735006i	−0.0519044	−	0.00455831i
$261$		0			0
$262$	1.09592	−	0.293650i	0.0677060	−	0.0181418i
$263$	6.57217	−	1.76101i	0.405257	−	0.108588i	−0.0504316	−	0.998728i	$-0.516060\pi$
$263$	6.57217	−	1.76101i	0.405257	−	0.108588i	0.455689	+	0.890139i	$0.349393\pi$
$264$		0			0
$265$	14.7109	+	1.29193i	0.903684	+	0.0793627i
$266$	16.3363	+	11.2680i	1.00164	+	0.690886i
$267$		0			0
$268$	0.614064	−	2.29172i	0.0375099	−	0.139989i
$269$	−3.23386	+	5.60121i	−0.197172	+	0.341512i	−0.947610	−	0.319428i	$-0.896509\pi$
$269$	−3.23386	+	5.60121i	−0.197172	+	0.341512i	0.750438	+	0.660940i	$0.229842\pi$
$270$		0			0
$271$	11.5028	−	6.64116i	0.698747	−	0.403422i	−0.108134	−	0.994136i	$-0.534487\pi$
$271$	11.5028	−	6.64116i	0.698747	−	0.403422i	0.806881	+	0.590715i	$0.201154\pi$
$272$	−0.929030	−	0.929030i	−0.0563307	−	0.0563307i
$273$		0			0
$274$		−	5.34098i		−	0.322660i
$275$	24.3061	−	8.82854i	1.46571	−	0.532381i
$276$		0			0
$277$	0.832945	+	3.10859i	0.0500468	+	0.186777i	0.986424	−	0.164218i	$-0.0525100\pi$
$277$	0.832945	+	3.10859i	0.0500468	+	0.186777i	−0.936377	+	0.350995i	$0.885843\pi$
$278$	17.8888	+	4.79328i	1.07290	+	0.287482i
$279$		0			0
$280$	−5.37847	−	2.46416i	−0.321425	−	0.147262i
$281$	−4.88199			−0.291235			−0.145618	−	0.989341i	$-0.546517\pi$
$281$	−4.88199			−0.291235			−0.145618	+	0.989341i	$0.546517\pi$
$282$		0			0
$283$	−3.14962	−	11.7546i	−0.187226	−	0.698736i	−0.994143	−	0.108071i	$-0.965532\pi$
$283$	−3.14962	−	11.7546i	−0.187226	−	0.698736i	0.806917	−	0.590664i	$-0.201134\pi$
$284$	3.93182	+	2.27004i	0.233311	+	0.134702i
$285$		0			0
$286$			1.94325i			0.114907i
$287$	−5.79383	−	6.80678i	−0.341999	−	0.401792i
$288$		0			0
$289$	−13.2275	+	7.63690i	−0.778089	+	0.449230i
$290$	−10.3973	+	14.8385i	−0.610553	+	0.871347i
$291$		0			0
$292$	−1.81526	+	6.77465i	−0.106230	+	0.396456i
$293$	−3.88255	+	3.88255i	−0.226821	+	0.226821i	−0.811363	−	0.584542i	$-0.801274\pi$
$293$	−3.88255	+	3.88255i	−0.226821	+	0.226821i	0.584542	+	0.811363i	$0.301274\pi$
$294$		0			0
$295$	−11.5215	+	9.66117i	−0.670805	+	0.562495i
$296$	−0.986302	−	1.70832i	−0.0573276	−	0.0992943i
$297$		0			0
$298$	9.56218	−	2.56218i	0.553922	−	0.148423i
$299$	1.46188	+	2.53206i	0.0845429	+	0.146433i
$300$		0			0
$301$	−32.5084	−	2.61333i	−1.87375	−	0.150630i
$302$	−7.16787	+	7.16787i	−0.412465	+	0.412465i
$303$		0			0
$304$	−3.75044	+	6.49596i	−0.215103	+	0.372569i
$305$	13.1632	−	2.31655i	0.753724	−	0.132645i
$306$		0			0
$307$	8.99757	+	8.99757i	0.513519	+	0.513519i	0.915603	−	0.402084i	$-0.131714\pi$
$307$	8.99757	+	8.99757i	0.513519	+	0.513519i	−0.402084	+	0.915603i	$0.631714\pi$
$308$	−4.58935	+	12.8912i	−0.261502	+	0.734543i
$309$		0			0
$310$	−7.25468	−	15.5711i	−0.412038	−	0.884381i
$311$	18.6303	+	10.7562i	1.05643	+	0.609929i	0.924442	−	0.381323i	$-0.124531\pi$
$311$	18.6303	+	10.7562i	1.05643	+	0.609929i	0.131985	+	0.991252i	$0.457865\pi$
$312$		0			0
$313$	13.8043	+	3.69885i	0.780265	+	0.209071i	0.626901	−	0.779099i	$-0.284323\pi$
$313$	13.8043	+	3.69885i	0.780265	+	0.209071i	0.153363	+	0.988170i	$0.450990\pi$
$314$	2.56862			0.144956
$315$		0			0
$316$	11.9652			0.673095
$317$	19.5770	+	5.24563i	1.09955	+	0.294624i	0.762582	−	0.646891i	$-0.223931\pi$
$317$	19.5770	+	5.24563i	1.09955	+	0.294624i	0.336970	+	0.941515i	$0.390598\pi$
$318$		0			0
$319$	36.2934	+	20.9540i	2.03204	+	1.17320i
$320$	0.765474	−	2.10096i	0.0427913	−	0.117447i
$321$		0			0
$322$	3.71794	+	20.2497i	0.207193	+	1.12847i
$323$	−6.96855	−	6.96855i	−0.387740	−	0.387740i
$324$		0			0
$325$	1.87160	−	0.162499i	0.103818	−	0.00901381i
$326$	−5.63796	+	9.76524i	−0.312258	+	0.540847i
$327$		0			0
$328$	2.38897	−	2.38897i	0.131909	−	0.131909i
$329$	−3.97872	−	8.37769i	−0.219354	−	0.461877i
$330$		0			0
$331$	−1.02862	−	1.78163i	−0.0565383	−	0.0979271i	0.836371	−	0.548164i	$-0.184673\pi$
$331$	−1.02862	−	1.78163i	−0.0565383	−	0.0979271i	−0.892909	+	0.450237i	$0.851340\pi$
$332$	−7.48652	+	2.00601i	−0.410876	+	0.110094i
$333$		0			0
$334$	7.48023	+	12.9561i	0.409300	+	0.708928i
$335$	−0.464124	+	5.28486i	−0.0253578	+	0.288743i
$336$		0			0
$337$	−13.1092	+	13.1092i	−0.714105	+	0.714105i	−0.967391	−	0.253287i	$-0.918488\pi$
$337$	−13.1092	+	13.1092i	−0.714105	+	0.714105i	0.253287	+	0.967391i	$0.418488\pi$
$338$	3.32811	−	12.4207i	0.181025	−	0.675596i
$339$		0			0
$340$	2.40599	+	1.68588i	0.130483	+	0.0914295i
$341$	−34.4096	+	19.8664i	−1.86338	+	1.07582i
$342$		0			0
$343$	9.59724	+	15.8396i	0.518202	+	0.855258i
$344$		−	12.3267i		−	0.664609i
$345$		0			0
$346$	15.2041	+	8.77812i	0.817380	+	0.471914i
$347$	0.983922	+	3.67205i	0.0528197	+	0.197126i	0.987294	−	0.158905i	$-0.0507964\pi$
$347$	0.983922	+	3.67205i	0.0528197	+	0.197126i	−0.934474	+	0.356031i	$0.884130\pi$
$348$		0			0
$349$	−25.5306			−1.36662			−0.683312	−	0.730126i	$-0.739461\pi$
$349$	−25.5306			−1.36662			−0.683312	+	0.730126i	$0.739461\pi$
$350$	12.7996	+	3.34214i	0.684168	+	0.178645i
$351$		0			0
$352$	−4.99573	−	1.33860i	−0.266274	−	0.0713478i
$353$	−7.63550	−	28.4961i	−0.406396	−	1.51669i	−0.801466	−	0.598041i	$-0.795946\pi$
$353$	−7.63550	−	28.4961i	−0.406396	−	1.51669i	0.395069	−	0.918651i	$-0.370721\pi$
$354$		0			0
$355$	−9.53853	−	3.47531i	−0.506253	−	0.184450i
$356$			13.6106i			0.721363i
$357$		0			0
$358$	−1.38676	−	1.38676i	−0.0732924	−	0.0732924i
$359$	4.59185	−	2.65110i	0.242348	−	0.139920i	−0.373907	−	0.927466i	$-0.621982\pi$
$359$	4.59185	−	2.65110i	0.242348	−	0.139920i	0.616256	+	0.787546i	$0.288649\pi$
$360$		0			0
$361$	−18.6316	+	32.2710i	−0.980613	+	1.69847i
$362$	6.56421	−	24.4980i	0.345007	−	1.28758i
$363$		0			0
$364$	−0.564429	+	0.818305i	−0.0295841	+	0.0428909i
$365$	1.37202	−	15.6228i	0.0718147	−	0.817736i
$366$		0			0
$367$	−10.1998	+	2.73302i	−0.532423	+	0.142662i	−0.515007	−	0.857186i	$-0.672211\pi$
$367$	−10.1998	+	2.73302i	−0.532423	+	0.142662i	−0.0174162	+	0.999848i	$0.505544\pi$
$368$	−7.51645	+	2.01403i	−0.391822	+	0.104988i
$369$		0			0
$370$	2.83414	+	3.37986i	0.147340	+	0.175711i
$371$	9.92105	−	14.3835i	0.515075	−	0.746753i
$372$		0			0
$373$	5.69653	−	21.2597i	0.294955	−	1.10079i	−0.646298	−	0.763085i	$-0.723684\pi$
$373$	5.69653	−	21.2597i	0.294955	−	1.10079i	0.941253	−	0.337702i	$-0.109650\pi$
$374$	3.39758	−	5.88479i	0.175685	−	0.304295i
$375$		0			0
$376$	3.03579	−	1.75271i	0.156559	−	0.0903892i
$377$	2.15278	+	2.15278i	0.110874	+	0.110874i
$378$		0			0
$379$			14.8451i			0.762541i	0.924464	+	0.381270i	$0.124513\pi$
$379$			14.8451i			0.762541i	−0.924464	+	0.381270i	$0.875487\pi$
$380$	5.74173	−	15.7591i	0.294545	−	0.808424i
$381$		0			0
$382$	0.469879	+	1.75361i	0.0240411	+	0.0897225i
$383$	24.7873	+	6.64174i	1.26657	+	0.339377i	0.828717	−	0.559668i	$-0.189071\pi$
$383$	24.7873	+	6.64174i	1.26657	+	0.339377i	0.437856	+	0.899045i	$0.355738\pi$
$384$		0			0
$385$	5.11065	−	30.1679i	0.260463	−	1.53750i
$386$	−6.94835			−0.353662
$387$		0			0
$388$	−3.20282	−	11.9531i	−0.162599	−	0.606827i
$389$	−12.7527	−	7.36279i	−0.646589	−	0.373308i	0.140559	−	0.990072i	$-0.455110\pi$
$389$	−12.7527	−	7.36279i	−0.646589	−	0.373308i	−0.787148	+	0.616764i	$0.788443\pi$
$390$		0			0
$391$		−	10.2238i		−	0.517041i
$392$	−5.67689	+	4.09548i	−0.286726	+	0.206853i
$393$		0			0
$394$	−0.494743	+	0.285640i	−0.0249248	+	0.0143903i
$395$	−26.3501	+	4.63726i	−1.32582	+	0.233326i
$396$		0			0
$397$	−0.348078	+	1.29904i	−0.0174695	+	0.0651971i	−0.974110	−	0.226073i	$-0.927411\pi$
$397$	−0.348078	+	1.29904i	−0.0174695	+	0.0651971i	0.956641	+	0.291270i	$0.0940779\pi$
$398$	2.03563	−	2.03563i	0.102037	−	0.102037i
$399$		0			0
$400$	−0.871492	+	4.92346i	−0.0435746	+	0.246173i
$401$	−10.4528	−	18.1048i	−0.521989	−	0.904111i	−0.999673	−	0.0255795i	$-0.991857\pi$
$401$	−10.4528	−	18.1048i	−0.521989	−	0.904111i	0.477684	−	0.878532i	$-0.341476\pi$
$402$		0			0
$403$	−2.78812	+	0.747073i	−0.138886	+	0.0372144i
$404$	4.62233	+	8.00611i	0.229969	+	0.398319i
$405$		0			0
$406$	9.19696	+	19.3653i	0.456437	+	0.961086i
$407$	7.21407	−	7.21407i	0.357588	−	0.357588i
$408$		0			0
$409$	−2.52732	+	4.37744i	−0.124968	+	0.216451i	−0.921720	−	0.387855i	$-0.873216\pi$
$409$	−2.52732	+	4.37744i	−0.124968	+	0.216451i	0.796753	+	0.604306i	$0.206549\pi$
$410$	−4.33518	+	6.18693i	−0.214099	+	0.305551i
$411$		0			0
$412$	−2.47321	−	2.47321i	−0.121847	−	0.121847i
$413$	3.21279	+	17.4984i	0.158091	+	0.861039i
$414$		0			0
$415$	15.7095	−	7.31917i	0.771151	−	0.359284i
$416$	−0.325390	−	0.187864i	−0.0159536	−	0.00921080i
$417$		0			0
$418$	−37.4724	−	10.0407i	−1.83284	−	0.491107i
$419$	−27.3949			−1.33833			−0.669164	−	0.743115i	$-0.733348\pi$
$419$	−27.3949			−1.33833			−0.669164	+	0.743115i	$0.733348\pi$
$420$		0			0
$421$	9.41821			0.459015			0.229508	−	0.973307i	$-0.426288\pi$
$421$	9.41821			0.459015			0.229508	+	0.973307i	$0.426288\pi$
$422$	10.3373	+	2.76987i	0.503211	+	0.134835i
$423$		0			0
$424$	5.71944	+	3.30212i	0.277760	+	0.160365i
$425$	−5.95191	−	2.78021i	−0.288710	−	0.134860i
$426$		0			0
$427$	5.30391	−	14.8983i	0.256674	−	0.720980i
$428$	4.14453	+	4.14453i	0.200334	+	0.200334i
$429$		0			0
$430$	4.77735	+	27.1461i	0.230384	+	1.30910i
$431$	4.48816	−	7.77373i	0.216187	−	0.374447i	−0.737452	−	0.675400i	$-0.763971\pi$
$431$	4.48816	−	7.77373i	0.216187	−	0.374447i	0.953639	+	0.300952i	$0.0973045\pi$
$432$		0			0
$433$	10.7835	−	10.7835i	0.518224	−	0.518224i	−0.398810	−	0.917034i	$-0.630577\pi$
$433$	10.7835	−	10.7835i	0.518224	−	0.518224i	0.917034	+	0.398810i	$0.130577\pi$
$434$	−20.2602	−	1.62870i	−0.972519	−	0.0781802i
$435$		0			0
$436$	−0.0653306	−	0.113156i	−0.00312877	−	0.00541919i
$437$	−56.3800	+	15.1070i	−2.69702	+	0.722665i
$438$		0			0
$439$	2.89682	+	5.01745i	0.138258	+	0.239470i	0.926837	−	0.375463i	$-0.122516\pi$
$439$	2.89682	+	5.01745i	0.138258	+	0.239470i	−0.788579	+	0.614933i	$0.789183\pi$
$440$	11.5205	+	1.01175i	0.549219	+	0.0482332i
$441$		0			0
$442$	0.349063	−	0.349063i	0.0166032	−	0.0166032i
$443$	−5.48110	+	20.4558i	−0.260415	+	0.971882i	0.704582	+	0.709622i	$0.251134\pi$
$443$	−5.48110	+	20.4558i	−0.260415	+	0.971882i	−0.964997	+	0.262260i	$0.915532\pi$
$444$		0			0
$445$	−5.27497	−	29.9737i	−0.250058	−	1.42089i
$446$	10.3389	−	5.96917i	0.489561	−	0.282648i
$447$		0			0
$448$	−1.71490	−	2.01472i	−0.0810215	−	0.0951868i
$449$		−	14.3195i		−	0.675780i	−0.941186	−	0.337890i	$-0.890287\pi$
$449$		−	14.3195i		−	0.675780i	0.941186	−	0.337890i	$-0.109713\pi$
$450$		0			0
$451$	15.1326	+	8.73679i	0.712565	+	0.411400i
$452$	−1.41987	−	5.29904i	−0.0667852	−	0.249246i
$453$		0			0
$454$	−17.9062			−0.840377
$455$	0.925855	−	2.02084i	0.0434047	−	0.0947386i
$456$		0			0
$457$	31.6291	+	8.47498i	1.47954	+	0.396443i	0.906192	−	0.422866i	$-0.138976\pi$
$457$	31.6291	+	8.47498i	1.47954	+	0.396443i	0.573353	+	0.819309i	$0.305643\pi$
$458$	−2.24108	−	8.36381i	−0.104719	−	0.390815i
$459$		0			0
$460$	15.7723	−	7.34843i	0.735390	−	0.342622i
$461$			35.9488i			1.67430i	0.546972	+	0.837151i	$0.315781\pi$
$461$			35.9488i			1.67430i	−0.546972	+	0.837151i	$0.684219\pi$
$462$		0			0
$463$	7.46017	+	7.46017i	0.346704	+	0.346704i	0.858880	−	0.512177i	$-0.171161\pi$
$463$	7.46017	+	7.46017i	0.346704	+	0.346704i	−0.512177	+	0.858880i	$0.671161\pi$
$464$	−7.01733	+	4.05146i	−0.325771	+	0.188084i
$465$		0			0
$466$	9.57844	−	16.5904i	0.443713	−	0.768533i
$467$	5.33585	−	19.9137i	0.246914	−	0.921494i	−0.725498	−	0.688224i	$-0.758391\pi$
$467$	5.33585	−	19.9137i	0.246914	−	0.921494i	0.972412	−	0.233270i	$-0.0749426\pi$
$468$		0			0
$469$	5.16724	+	3.56412i	0.238601	+	0.164576i
$470$	−6.00620	+	5.03642i	−0.277045	+	0.232313i
$471$		0			0
$472$	−6.49519	+	1.74038i	−0.298966	+	0.0801076i
$473$	61.5807	−	16.5005i	2.83149	−	0.758694i
$474$		0			0
$475$	−6.53696	+	36.9303i	−0.299936	+	1.69448i
$476$	3.13999	−	1.49124i	0.143921	−	0.0683509i
$477$		0			0
$478$	−1.73605	+	6.47904i	−0.0794052	+	0.296344i
$479$	−2.18200	+	3.77934i	−0.0996983	+	0.172682i	−0.911560	−	0.411168i	$-0.865121\pi$
$479$	−2.18200	+	3.77934i	−0.0996983	+	0.172682i	0.811861	+	0.583850i	$0.198454\pi$
$480$		0			0
$481$	0.641866	−	0.370582i	0.0292666	−	0.0168971i
$482$	0.305870	+	0.305870i	0.0139320	+	0.0139320i
$483$		0			0
$484$		−	15.7492i		−	0.715874i
$485$	11.6859	+	25.0821i	0.530630	+	1.13892i
$486$		0			0
$487$	−6.09135	−	22.7332i	−0.276026	−	1.03014i	−0.955151	−	0.296119i	$-0.904307\pi$
$487$	−6.09135	−	22.7332i	−0.276026	−	1.03014i	0.679125	−	0.734022i	$-0.262359\pi$
$488$	5.77357	+	1.54702i	0.261357	+	0.0700304i
$489$		0			0
$490$	10.9145	−	11.2193i	0.493068	−	0.506837i
$491$	37.0535			1.67220			0.836100	−	0.548577i	$-0.184830\pi$
$491$	37.0535			1.67220			0.836100	+	0.548577i	$0.184830\pi$
$492$		0			0
$493$	−2.75538	−	10.2832i	−0.124096	−	0.463133i
$494$	−2.44072	−	1.40915i	−0.109813	−	0.0634006i
$495$		0			0
$496$		−	7.68233i		−	0.344947i
$497$	−9.14700	+	7.78578i	−0.410299	+	0.349240i
$498$		0			0
$499$	−16.6242	+	9.59800i	−0.744202	+	0.429665i	−0.823595	−	0.567178i	$-0.808035\pi$
$499$	−16.6242	+	9.59800i	−0.744202	+	0.429665i	0.0793930	+	0.996843i	$0.474702\pi$
$500$	0.0110724	−	11.1803i	0.000495172	−	0.500000i
$501$		0			0
$502$	−5.02263	+	18.7447i	−0.224171	+	0.836617i
$503$	22.3585	−	22.3585i	0.996914	−	0.996914i	−0.00308078	−	0.999995i	$-0.500981\pi$
$503$	22.3585	−	22.3585i	0.996914	−	0.996914i	0.999995	+	0.00308078i	$0.000980643\pi$
$504$		0			0
$505$	−13.2823	−	15.8398i	−0.591053	−	0.704862i
$506$	−20.1231	−	34.8542i	−0.894580	−	1.54946i
$507$		0			0
$508$	12.4005	−	3.32269i	0.550182	−	0.147421i
$509$	−7.74622	−	13.4168i	−0.343345	−	0.594691i	0.641706	−	0.766950i	$-0.278227\pi$
$509$	−7.74622	−	13.4168i	−0.343345	−	0.594691i	−0.985052	+	0.172259i	$0.944893\pi$
$510$		0			0
$511$	−15.2751	−	10.5361i	−0.675731	−	0.466088i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	9.33014	−	16.1603i	0.411535	−	0.712799i
$515$	6.40510	+	4.48805i	0.282242	+	0.197767i
$516$		0			0
$517$	12.8198	+	12.8198i	0.563814	+	0.563814i
$518$	5.13321	−	0.942483i	0.225540	−	0.0414103i
$519$		0			0
$520$	0.789392	+	0.287610i	0.0346171	+	0.0126125i
$521$	25.9155	+	14.9623i	1.13538	+	0.655511i	0.945282	−	0.326255i	$-0.105787\pi$
$521$	25.9155	+	14.9623i	1.13538	+	0.655511i	0.190096	+	0.981766i	$0.439120\pi$
$522$		0			0
$523$	−23.0502	−	6.17629i	−1.00792	−	0.270070i	−0.283158	−	0.959073i	$-0.591382\pi$
$523$	−23.0502	−	6.17629i	−1.00792	−	0.270070i	−0.724758	+	0.689003i	$0.758049\pi$
$524$	−1.13458			−0.0495642
$525$		0			0
$526$	−6.80401			−0.296669
$527$	9.74947	+	2.61236i	0.424694	+	0.113796i
$528$		0			0
$529$	−32.5221	−	18.7766i	−1.41400	−	0.816375i
$530$	−13.8753	−	5.05537i	−0.602703	−	0.219591i
$531$		0			0
$532$	−12.8633	−	15.1122i	−0.557694	−	0.655198i
$533$	0.897606	+	0.897606i	0.0388796	+	0.0388796i
$534$		0			0
$535$	−10.7335	−	7.52093i	−0.464048	−	0.325158i
$536$	−1.18628	+	2.05470i	−0.0512395	+	0.0887494i
$537$		0			0
$538$	4.57337	−	4.57337i	0.197172	−	0.197172i
$539$	−28.0590	−	22.8780i	−1.20859	−	0.985425i
$540$		0			0
$541$	2.85409	+	4.94343i	0.122707	+	0.212535i	0.920834	−	0.389954i	$-0.127509\pi$
$541$	2.85409	+	4.94343i	0.122707	+	0.212535i	−0.798127	+	0.602489i	$0.794176\pi$
$542$	−12.8297	+	3.43772i	−0.551084	+	0.147663i
$543$		0			0
$544$	0.656923	+	1.13782i	0.0281653	+	0.0487838i
$545$	0.187728	+	0.223875i	0.00804137	+	0.00958976i
$546$		0			0
$547$	24.1755	−	24.1755i	1.03367	−	1.03367i	0.0342575	−	0.999413i	$-0.489093\pi$
$547$	24.1755	−	24.1755i	1.03367	−	1.03367i	0.999413	−	0.0342575i	$-0.0109066\pi$
$548$	−1.38235	+	5.15899i	−0.0590509	+	0.220381i
$549$		0			0
$550$	−25.7629	+	2.23682i	−1.09853	+	0.0953785i
$551$	−52.6362	+	30.3895i	−2.24238	+	1.29464i
$552$		0			0
$553$	−10.6173	+	29.8234i	−0.451495	+	1.26822i
$554$		−	3.21825i		−	0.136730i
$555$		0			0
$556$	−16.0386	−	9.25990i	−0.680189	−	0.392707i
$557$	−8.24631	−	30.7756i	−0.349407	−	1.30401i	−0.887378	−	0.461042i	$-0.847476\pi$
$557$	−8.24631	−	30.7756i	−0.349407	−	1.30401i	0.537971	−	0.842964i	$-0.319191\pi$
$558$		0			0
$559$	4.63148			0.195891
$560$	4.55743	+	3.77224i	0.192587	+	0.159406i
$561$		0			0
$562$	4.71564	+	1.26355i	0.198917	+	0.0532997i
$563$	3.27600	+	12.2262i	0.138067	+	0.515272i	0.999966	+	0.00819336i	$0.00260806\pi$
$563$	3.27600	+	12.2262i	0.138067	+	0.515272i	−0.861900	+	0.507079i	$0.830725\pi$
$564$		0			0
$565$	5.18059	+	11.1194i	0.217949	+	0.467796i
$566$			12.1692i			0.511510i
$567$		0			0
$568$	−3.21032	−	3.21032i	−0.134702	−	0.134702i
$569$	−12.2235	+	7.05724i	−0.512436	+	0.295855i	−0.733834	−	0.679328i	$-0.762271\pi$
$569$	−12.2235	+	7.05724i	−0.512436	+	0.295855i	0.221399	+	0.975183i	$0.428938\pi$
$570$		0			0
$571$	−2.32235	+	4.02242i	−0.0971872	+	0.168333i	−0.910519	−	0.413466i	$-0.864318\pi$
$571$	−2.32235	+	4.02242i	−0.0971872	+	0.168333i	0.813332	+	0.581800i	$0.197651\pi$
$572$	0.502951	−	1.87704i	0.0210295	−	0.0784830i
$573$		0			0
$574$	3.83468	+	8.07440i	0.160057	+	0.337019i
$575$	−31.8863	+	22.2957i	−1.32975	+	0.929793i
$576$		0			0
$577$	1.40289	−	0.375902i	0.0584029	−	0.0156490i	−0.229499	−	0.973309i	$-0.573709\pi$
$577$	1.40289	−	0.375902i	0.0584029	−	0.0156490i	0.287902	+	0.957660i	$0.407042\pi$
$578$	14.7534	−	3.95315i	0.613659	−	0.164429i
$579$		0			0
$580$	13.8835	−	11.6419i	0.576483	−	0.483402i
$581$	1.64318	−	20.4402i	0.0681705	−	0.848004i
$582$		0			0
$583$	−8.84045	+	32.9930i	−0.366134	+	1.36643i
$584$	3.50682	−	6.07399i	0.145113	−	0.251343i
$585$		0			0
$586$	4.75513	−	2.74537i	0.196433	−	0.113410i
$587$	−11.1465	−	11.1465i	−0.460066	−	0.460066i	0.438611	−	0.898677i	$-0.355471\pi$
$587$	−11.1465	−	11.1465i	−0.460066	−	0.460066i	−0.898677	+	0.438611i	$0.855471\pi$
$588$		0			0
$589$		−	57.6243i		−	2.37437i
$590$	13.6294	−	6.35000i	0.561112	−	0.261426i
$591$		0			0
$592$	0.510547	+	1.90539i	0.0209834	+	0.0783110i
$593$	15.0066	+	4.02100i	0.616246	+	0.165123i	0.553420	−	0.832902i	$-0.313322\pi$
$593$	15.0066	+	4.02100i	0.616246	+	0.165123i	0.0628252	+	0.998025i	$0.479989\pi$
$594$		0			0
$595$	−6.33702	+	4.50099i	−0.259793	+	0.184523i
$596$	−9.89949			−0.405499
$597$		0			0
$598$	−0.756727	−	2.82414i	−0.0309449	−	0.115488i
$599$	36.6022	+	21.1323i	1.49552	+	0.863441i	0.999987	−	0.00514553i	$-0.00163788\pi$
$599$	36.6022	+	21.1323i	1.49552	+	0.863441i	0.495537	+	0.868587i	$0.334971\pi$
$600$		0			0
$601$		−	36.4403i		−	1.48643i	−0.669052	−	0.743216i	$-0.733300\pi$
$601$		−	36.4403i		−	1.48643i	0.669052	−	0.743216i	$-0.266700\pi$
$602$	30.7243	+	10.9381i	1.25223	+	0.445803i
$603$		0			0
$604$	8.77882	−	5.06845i	0.357205	−	0.206232i
$605$	6.10380	+	34.6833i	0.248155	+	1.41008i
$606$		0			0
$607$	5.28879	−	19.7380i	0.214665	−	0.801141i	−0.771619	−	0.636085i	$-0.780553\pi$
$607$	5.28879	−	19.7380i	0.214665	−	0.801141i	0.986284	−	0.165056i	$-0.0527806\pi$
$608$	5.30393	−	5.30393i	0.215103	−	0.215103i
$609$		0			0
$610$	−13.3143	−	1.16928i	−0.539079	−	0.0473426i
$611$	0.658544	+	1.14063i	0.0266418	+	0.0461450i
$612$		0			0
$613$	−10.9822	+	2.94267i	−0.443567	+	0.118853i	−0.473688	−	0.880693i	$-0.657078\pi$
$613$	−10.9822	+	2.94267i	−0.443567	+	0.118853i	0.0301206	+	0.999546i	$0.490411\pi$
$614$	−6.36225	−	11.0197i	−0.256759	−	0.444720i
$615$		0			0
$616$	7.76945	−	11.2641i	0.313040	−	0.453844i
$617$	19.5003	−	19.5003i	0.785051	−	0.785051i	−0.195628	−	0.980678i	$-0.562674\pi$
$617$	19.5003	−	19.5003i	0.785051	−	0.785051i	0.980678	+	0.195628i	$0.0626744\pi$
$618$		0			0
$619$	8.77812	−	15.2041i	0.352822	−	0.611106i	−0.633920	−	0.773398i	$-0.718555\pi$
$619$	8.77812	−	15.2041i	0.352822	−	0.611106i	0.986743	+	0.162292i	$0.0518887\pi$
$620$	2.97738	+	16.9182i	0.119574	+	0.679452i
$621$		0			0
$622$	−15.2116	−	15.2116i	−0.609929	−	0.609929i
$623$	−33.9247	−	12.0774i	−1.35916	−	0.483872i
$624$		0			0
$625$	4.30869	+	24.6259i	0.172348	+	0.985036i
$626$	−12.3766	−	7.14563i	−0.494668	−	0.285597i
$627$		0			0
$628$	−2.48110	−	0.664809i	−0.0990066	−	0.0265288i
$629$	−2.59170			−0.103338
$630$		0			0
$631$	−23.1755			−0.922603			−0.461301	−	0.887243i	$-0.652617\pi$
$631$	−23.1755			−0.922603			−0.461301	+	0.887243i	$0.652617\pi$
$632$	−11.5575	−	3.09682i	−0.459733	−	0.123185i
$633$		0			0
$634$	−17.5522	−	10.1338i	−0.697088	−	0.402464i
$635$	−26.0209	+	12.1233i	−1.03261	+	0.481097i
$636$		0			0
$637$	−1.53879	−	2.13297i	−0.0609690	−	0.0845113i
$638$	−29.6334	−	29.6334i	−1.17320	−	1.17320i
$639$		0			0
$640$	−1.28316	+	1.83126i	−0.0507214	+	0.0723868i
$641$	−8.67383	+	15.0235i	−0.342596	+	0.593393i	−0.984914	−	0.173045i	$-0.944639\pi$
$641$	−8.67383	+	15.0235i	−0.342596	+	0.593393i	0.642318	+	0.766438i	$0.277973\pi$
$642$		0			0
$643$	26.2988	−	26.2988i	1.03712	−	1.03712i	0.0378384	−	0.999284i	$-0.487953\pi$
$643$	26.2988	−	26.2988i	1.03712	−	1.03712i	0.999284	−	0.0378384i	$-0.0120472\pi$
$644$	1.64975	−	20.5220i	0.0650092	−	0.808679i
$645$		0			0
$646$	4.92751	+	8.53469i	0.193870	+	0.335793i
$647$	24.1113	−	6.46061i	0.947914	−	0.253993i	0.248437	−	0.968648i	$-0.420083\pi$
$647$	24.1113	−	6.46061i	0.947914	−	0.253993i	0.699477	+	0.714655i	$0.253416\pi$
$648$		0			0
$649$	−17.3890	−	30.1186i	−0.682577	−	1.18226i
$650$	−1.84989	−	0.327444i	−0.0725585	−	0.0128434i
$651$		0			0
$652$	7.97328	−	7.97328i	0.312258	−	0.312258i
$653$	−9.75652	+	36.4118i	−0.381802	+	1.42490i	0.461345	+	0.887221i	$0.347367\pi$
$653$	−9.75652	+	36.4118i	−0.381802	+	1.42490i	−0.843147	+	0.537683i	$0.819300\pi$
$654$		0			0
$655$	2.49859	−	0.439719i	0.0976281	−	0.0171812i
$656$	−2.92588	+	1.68926i	−0.114237	+	0.0659545i
$657$		0			0
$658$	1.67484	+	9.12200i	0.0652922	+	0.355613i
$659$			22.3934i			0.872324i	0.899868	+	0.436162i	$0.143663\pi$
$659$			22.3934i			0.872324i	−0.899868	+	0.436162i	$0.856337\pi$
$660$		0			0
$661$	22.3529	+	12.9054i	0.869426	+	0.501963i	0.867158	−	0.498034i	$-0.165945\pi$
$661$	22.3529	+	12.9054i	0.869426	+	0.501963i	0.00226869	+	0.999997i	$0.499278\pi$
$662$	0.532455	+	1.98715i	0.0206944	+	0.0772327i
$663$		0			0
$664$	7.75061			0.300782
$665$	34.1848	+	28.2952i	1.32563	+	1.09724i
$666$		0			0
$667$	−60.9051	−	16.3195i	−2.35826	−	0.631893i
$668$	−3.87205	−	14.4507i	−0.149814	−	0.559114i
$669$		0			0
$670$	1.81613	−	4.98466i	0.0701633	−	0.192574i
$671$			30.9141i			1.19342i
$672$		0			0
$673$	−20.6481	−	20.6481i	−0.795927	−	0.795927i	0.186524	−	0.982450i	$-0.440278\pi$
$673$	−20.6481	−	20.6481i	−0.795927	−	0.795927i	−0.982450	+	0.186524i	$0.940278\pi$
$674$	16.0554	−	9.26962i	0.618433	−	0.357052i
$675$		0			0
$676$	−6.42941	+	11.1361i	−0.247285	+	0.428310i
$677$	12.2194	−	45.6033i	0.469628	−	1.75268i	−0.171441	−	0.985194i	$-0.554842\pi$
$677$	12.2194	−	45.6033i	0.469628	−	1.75268i	0.641070	−	0.767483i	$-0.278491\pi$
$678$		0			0
$679$	32.6352	+	2.62353i	1.25243	+	0.100682i
$680$	−1.88767	−	2.25115i	−0.0723889	−	0.0863275i
$681$		0			0
$682$	38.3789	−	10.2836i	1.46960	−	0.393779i
$683$	−5.24140	+	1.40443i	−0.200556	+	0.0537389i	−0.357699	−	0.933837i	$-0.616439\pi$
$683$	−5.24140	+	1.40443i	−0.200556	+	0.0537389i	0.157142	+	0.987576i	$0.449772\pi$
$684$		0			0
$685$	1.04481	−	11.8970i	0.0399202	−	0.454561i
$686$	−5.17063	−	17.7838i	−0.197416	−	0.678990i
$687$		0			0
$688$	−3.19038	+	11.9066i	−0.121632	+	0.453937i
$689$	−1.24070	+	2.14896i	−0.0472669	+	0.0818687i
$690$		0			0
$691$	−6.84020	+	3.94919i	−0.260213	+	0.150234i	−0.624432	−	0.781079i	$-0.714669\pi$
$691$	−6.84020	+	3.94919i	−0.260213	+	0.150234i	0.364219	+	0.931314i	$0.381336\pi$
$692$	−12.4141	−	12.4141i	−0.471914	−	0.471914i
$693$		0			0
$694$		−	3.80158i		−	0.144306i
$695$	38.9094	+	14.1764i	1.47592	+	0.537742i
$696$		0			0
$697$	−1.14886	−	4.28761i	−0.0435162	−	0.162405i
$698$	24.6607	+	6.60782i	0.933422	+	0.250110i
$699$		0			0
$700$	−11.4985	−	6.54104i	−0.434601	−	0.247228i
$701$	16.5213			0.624002			0.312001	−	0.950082i	$-0.399001\pi$
$701$	16.5213			0.624002			0.312001	+	0.950082i	$0.399001\pi$
$702$		0			0
$703$	3.82956	+	14.2921i	0.144434	+	0.539037i
$704$	4.47905	+	2.58598i	0.168811	+	0.0974629i
$705$		0			0
$706$			29.5013i			1.11030i
$707$	−24.0569	+	4.41697i	−0.904754	+	0.166117i
$708$		0			0
$709$	17.6039	−	10.1636i	0.661129	−	0.381703i	−0.131578	−	0.991306i	$-0.542004\pi$
$709$	17.6039	−	10.1636i	0.661129	−	0.381703i	0.792707	+	0.609603i	$0.208671\pi$
$710$	8.31404	+	5.82565i	0.312020	+	0.218633i
$711$		0			0
$712$	3.52269	−	13.1469i	0.132019	−	0.492700i
$713$	42.2714	−	42.2714i	1.58308	−	1.58308i
$714$		0			0
$715$	−0.380142	+	4.32859i	−0.0142165	+	0.161880i
$716$	0.980586	+	1.69842i	0.0366462	+	0.0634731i
$717$		0			0
$718$	−5.12154	+	1.37231i	−0.191134	+	0.0512142i
$719$	13.0472	+	22.5984i	0.486578	+	0.842778i	0.999881	−	0.0154296i	$-0.00491158\pi$
$719$	13.0472	+	22.5984i	0.486578	+	0.842778i	−0.513303	+	0.858208i	$0.671578\pi$
$720$		0			0
$721$	8.35912	−	3.96990i	0.311310	−	0.147847i
$722$	26.3491	−	26.3491i	0.980613	−	0.980613i
$723$		0			0
$724$	−12.6811	+	21.9643i	−0.471289	+	0.816296i
$725$	−26.0627	+	31.0188i	−0.967946	+	1.15201i
$726$		0			0
$727$	−11.3764	−	11.3764i	−0.421926	−	0.421926i	0.463940	−	0.885867i	$-0.346435\pi$
$727$	−11.3764	−	11.3764i	−0.421926	−	0.421926i	−0.885867	+	0.463940i	$0.846435\pi$
$728$	0.756989	−	0.644337i	0.0280559	−	0.0238807i
$729$		0			0
$730$	−5.36875	+	14.7354i	−0.198706	+	0.545381i
$731$	−14.0256	−	8.09767i	−0.518755	−	0.299503i
$732$		0			0
$733$	14.9615	+	4.00892i	0.552616	+	0.148073i	0.524312	−	0.851526i	$-0.324323\pi$
$733$	14.9615	+	4.00892i	0.552616	+	0.148073i	0.0283041	+	0.999599i	$0.490989\pi$
$734$	10.5596			0.389761
$735$		0			0
$736$	7.78160			0.286834
$737$	−11.8527	−	3.17592i	−0.436599	−	0.116986i
$738$		0			0
$739$	32.3862	+	18.6982i	1.19135	+	0.687824i	0.958612	−	0.284716i	$-0.0918994\pi$
$739$	32.3862	+	18.6982i	1.19135	+	0.687824i	0.232734	+	0.972540i	$0.425233\pi$
$740$	−1.86280	−	3.99822i	−0.0684778	−	0.146978i
$741$		0			0
$742$	−13.3057	+	11.3256i	−0.488468	+	0.415777i
$743$	33.9689	+	33.9689i	1.24620	+	1.24620i	0.957386	+	0.288811i	$0.0932599\pi$
$743$	33.9689	+	33.9689i	1.24620	+	1.24620i	0.288811	+	0.957386i	$0.406740\pi$
$744$		0			0
$745$	21.8009	−	3.83667i	0.798724	−	0.140565i
$746$	−11.0048	+	19.0609i	−0.402916	+	0.697871i
$747$		0			0
$748$	−4.80491	+	4.80491i	−0.175685	+	0.175685i
$749$	−14.0079	+	6.65264i	−0.511839	+	0.243082i
$750$		0			0
$751$	5.15430	+	8.92752i	0.188083	+	0.325770i	0.944611	−	0.328192i	$-0.106439\pi$
$751$	5.15430	+	8.92752i	0.188083	+	0.325770i	−0.756528	+	0.653961i	$0.773106\pi$
$752$	−3.38598	+	0.907271i	−0.123474	+	0.0330848i
$753$		0			0
$754$	−1.52225	−	2.63661i	−0.0554370	−	0.0960197i
$755$	−17.3686	+	14.5642i	−0.632108	+	0.530046i
$756$		0			0
$757$	−3.50029	+	3.50029i	−0.127220	+	0.127220i	−0.767850	−	0.640630i	$-0.778673\pi$
$757$	−3.50029	+	3.50029i	−0.127220	+	0.127220i	0.640630	+	0.767850i	$0.278673\pi$
$758$	3.84219	−	14.3393i	0.139555	−	0.520825i
$759$		0			0
$760$	−9.62484	+	13.7360i	−0.349130	+	0.498259i
$761$	3.24761	−	1.87501i	0.117726	−	0.0679689i	−0.439981	−	0.898007i	$-0.645015\pi$
$761$	3.24761	−	1.87501i	0.117726	−	0.0679689i	0.557707	+	0.830038i	$0.311681\pi$
$762$		0			0
$763$	0.340014	−	0.0624282i	0.0123093	−	0.00226005i
$764$		−	1.81547i		−	0.0656815i
$765$		0			0
$766$	−22.2237	−	12.8309i	−0.802975	−	0.463598i
$767$	−0.653911	−	2.44043i	−0.0236114	−	0.0881188i
$768$		0			0
$769$	−1.95836			−0.0706204			−0.0353102	−	0.999376i	$-0.511242\pi$
$769$	−1.95836			−0.0706204			−0.0353102	+	0.999376i	$0.511242\pi$
$770$	−12.7445	+	27.8173i	−0.459281	+	1.00246i
$771$		0			0
$772$	6.71159	+	1.79837i	0.241556	+	0.0647246i
$773$	1.99995	+	7.46390i	0.0719331	+	0.268458i	0.992520	−	0.122079i	$-0.0389561\pi$
$773$	1.99995	+	7.46390i	0.0719331	+	0.268458i	−0.920587	+	0.390537i	$0.872289\pi$
$774$		0			0
$775$	−13.1137	−	36.1038i	−0.471059	−	1.29689i
$776$			12.3748i			0.444228i
$777$		0			0
$778$	10.4126	+	10.4126i	0.373308	+	0.373308i
$779$	−21.9467	+	12.6709i	−0.786323	+	0.453984i
$780$		0			0
$781$	11.7406	−	20.3352i	0.420110	−	0.727652i
$782$	−2.64612	+	9.87546i	−0.0946251	+	0.353146i
$783$		0			0
$784$	6.54344	−	2.48664i	0.233694	−	0.0888086i
$785$	5.72159	+	0.502478i	0.204212	+	0.0179342i
$786$		0			0
$787$	−22.5478	+	6.04166i	−0.803741	+	0.215362i	−0.637226	−	0.770677i	$-0.719918\pi$
$787$	−22.5478	+	6.04166i	−0.803741	+	0.215362i	−0.166515	+	0.986039i	$0.553251\pi$
$788$	0.551814	−	0.147858i	0.0196576	−	0.00526723i
$789$		0			0
$790$	26.6524	+	2.34065i	0.948251	+	0.0832766i
$791$	14.4678	+	1.16306i	0.514417	+	0.0413537i
$792$		0			0
$793$	−0.581261	+	2.16929i	−0.0206412	+	0.0770339i
$794$	0.672435	−	1.16469i	0.0238638	−	0.0413333i
$795$		0			0
$796$	−2.49313	+	1.43941i	−0.0883666	+	0.0510185i
$797$	17.3884	+	17.3884i	0.615928	+	0.615928i	0.944484	−	0.328556i	$-0.106562\pi$
$797$	17.3884	+	17.3884i	0.615928	+	0.615928i	−0.328556	+	0.944484i	$0.606562\pi$
$798$		0			0
$799$		−	4.60559i		−	0.162934i
$800$	2.11608	−	4.53014i	0.0748148	−	0.160165i
$801$		0			0
$802$	5.41078	+	20.1933i	0.191061	+	0.713050i
$803$	35.0383	+	9.38847i	1.23647	+	0.331312i
$804$		0			0
$805$	4.32042	+	45.8334i	0.152275	+	1.61541i
$806$	2.88647			0.101672
$807$		0			0
$808$	−2.39269	−	8.92965i	−0.0841747	−	0.314144i
$809$	−35.3260	−	20.3955i	−1.24200	−	0.717067i	−0.272497	−	0.962157i	$-0.587849\pi$
$809$	−35.3260	−	20.3955i	−1.24200	−	0.717067i	−0.969500	+	0.245089i	$0.921183\pi$
$810$		0			0
$811$		−	18.7583i		−	0.658694i	−0.944209	−	0.329347i	$-0.893171\pi$
$811$		−	18.7583i		−	0.658694i	0.944209	−	0.329347i	$-0.106829\pi$
$812$	−3.87146	−	21.0858i	−0.135862	−	0.739968i
$813$		0			0
$814$	−8.83539	+	5.10112i	−0.309680	+	0.178794i
$815$	−14.4688	+	20.6491i	−0.506821	+	0.723307i
$816$		0			0
$817$	−23.9306	+	89.3104i	−0.837227	+	3.12457i
$818$	3.57417	−	3.57417i	0.124968	−	0.124968i
$819$		0			0
$820$	5.78876	−	4.85409i	0.202152	−	0.169512i
$821$	−11.1282	−	19.2747i	−0.388378	−	0.672691i	0.603853	−	0.797095i	$-0.293631\pi$
$821$	−11.1282	−	19.2747i	−0.388378	−	0.672691i	−0.992232	+	0.124405i	$0.960298\pi$
$822$		0			0
$823$	−51.4628	+	13.7894i	−1.79388	+	0.480669i	−0.992996	−	0.118150i	$-0.962304\pi$
$823$	−51.4628	+	13.7894i	−1.79388	+	0.480669i	−0.800885	+	0.598819i	$0.795637\pi$
$824$	1.74883	+	3.02906i	0.0609233	+	0.105522i
$825$		0			0
$826$	1.42560	−	17.7337i	0.0496029	−	0.617033i
$827$	−38.5557	+	38.5557i	−1.34071	+	1.34071i	−0.445362	+	0.895351i	$0.646925\pi$
$827$	−38.5557	+	38.5557i	−1.34071	+	1.34071i	−0.895351	+	0.445362i	$0.853075\pi$
$828$		0			0
$829$	−15.5028	+	26.8517i	−0.538435	+	0.932597i	0.460554	+	0.887632i	$0.347651\pi$
$829$	−15.5028	+	26.8517i	−0.538435	+	0.932597i	−0.998989	+	0.0449649i	$0.985682\pi$
$830$	−17.0686	+	3.00384i	−0.592459	+	0.104265i
$831$		0			0
$832$	0.265680	+	0.265680i	0.00921080	+	0.00921080i
$833$	0.930656	+	9.14972i	0.0322453	+	0.317019i
$834$		0			0
$835$	14.1277	+	30.3230i	0.488908	+	1.04937i
$836$	33.5969	+	19.3972i	1.16197	+	0.670865i
$837$		0			0
$838$	26.4614	+	7.09032i	0.914095	+	0.244931i
$839$	−45.3891			−1.56701			−0.783503	−	0.621389i	$-0.786569\pi$
$839$	−45.3891			−1.56701			−0.783503	+	0.621389i	$0.786569\pi$
$840$		0			0
$841$	−36.6572			−1.26404
$842$	−9.09729	−	2.43761i	−0.313513	−	0.0840057i
$843$		0			0
$844$	−9.26815	−	5.35097i	−0.319023	−	0.184188i
$845$	9.84310	−	27.0159i	0.338613	−	0.929376i
$846$		0			0
$847$	39.2551	+	13.9751i	1.34882	+	0.480190i
$848$	−4.66990	−	4.66990i	−0.160365	−	0.160365i
$849$		0			0
$850$	5.02953	+	4.22594i	0.172512	+	0.144949i
$851$	−7.67500	+	13.2935i	−0.263096	+	0.455695i
$852$		0			0
$853$	37.3879	−	37.3879i	1.28014	−	1.28014i	0.339550	−	0.940588i	$-0.389725\pi$
$853$	37.3879	−	37.3879i	1.28014	−	1.28014i	0.940588	−	0.339550i	$-0.110275\pi$
$854$	−8.97915	+	13.0179i	−0.307260	+	0.445464i
$855$		0			0
$856$	−2.93063	−	5.07600i	−0.100167	−	0.173494i
$857$	32.2444	−	8.63985i	1.10145	−	0.295132i	0.338093	−	0.941113i	$-0.390218\pi$
$857$	32.2444	−	8.63985i	1.10145	−	0.295132i	0.763353	+	0.645981i	$0.223552\pi$
$858$		0			0
$859$	24.5307	+	42.4884i	0.836977	+	1.44969i	0.892411	+	0.451224i	$0.149013\pi$
$859$	24.5307	+	42.4884i	0.836977	+	1.44969i	−0.0554337	+	0.998462i	$0.517654\pi$
$860$	2.41136	−	27.4576i	0.0822267	−	0.936296i
$861$		0			0
$862$	−6.34722	+	6.34722i	−0.216187	+	0.216187i
$863$	9.13954	−	34.1092i	0.311113	−	1.16109i	−0.616440	−	0.787402i	$-0.711426\pi$
$863$	9.13954	−	34.1092i	0.311113	−	1.16109i	0.927554	−	0.373690i	$-0.121907\pi$
$864$		0			0
$865$	32.1500	+	22.5275i	1.09313	+	0.765957i
$866$	−13.2071	+	7.62512i	−0.448795	+	0.259112i
$867$		0			0
$868$	19.1483	+	6.81692i	0.649935	+	0.231381i
$869$		−	61.8836i		−	2.09926i
$870$		0			0
$871$	−0.772008	−	0.445719i	−0.0261585	−	0.0151026i
$872$	0.0338176	+	0.126209i	0.00114521	+	0.00427398i
$873$		0			0
$874$	58.3689			1.97436
$875$	27.8573	+	9.94848i	0.941748	+	0.336320i
$876$		0			0
$877$	−9.64685	−	2.58487i	−0.325751	−	0.0872847i	0.0922375	−	0.995737i	$-0.470598\pi$
$877$	−9.64685	−	2.58487i	−0.325751	−	0.0872847i	−0.417988	+	0.908452i	$0.637265\pi$
$878$	−1.49951	−	5.59624i	−0.0506059	−	0.188864i
$879$		0			0
$880$	−10.8661	−	3.95900i	−0.366297	−	0.133458i
$881$		−	55.0348i		−	1.85417i	−0.374852	−	0.927085i	$-0.622306\pi$
$881$		−	55.0348i		−	1.85417i	0.374852	−	0.927085i	$-0.377694\pi$
$882$		0			0
$883$	−30.2776	−	30.2776i	−1.01892	−	1.01892i	−0.999817	−	0.0191057i	$-0.993918\pi$
$883$	−30.2776	−	30.2776i	−1.01892	−	1.01892i	−0.0191057	−	0.999817i	$-0.506082\pi$
$884$	−0.427513	+	0.246825i	−0.0143788	+	0.00830162i
$885$		0			0
$886$	10.5887	−	18.3401i	0.355734	−	0.616149i
$887$	1.13628	−	4.24066i	0.0381526	−	0.142387i	−0.944222	−	0.329309i	$-0.893184\pi$
$887$	1.13628	−	4.24066i	0.0381526	−	0.142387i	0.982375	+	0.186921i	$0.0598510\pi$
$888$		0			0
$889$	−2.72172	+	33.8567i	−0.0912835	+	1.13552i
$890$	−2.66254	+	30.3176i	−0.0892484	+	1.01625i
$891$		0			0
$892$	−11.5315	+	3.08987i	−0.386105	+	0.103456i
$893$	−25.3979	+	6.80533i	−0.849907	+	0.227732i
$894$		0			0
$895$	−2.81771	−	3.36027i	−0.0941858	−	0.112322i
$896$	1.13502	+	2.38992i	0.0379183	+	0.0798417i
$897$		0			0
$898$	−3.70617	+	13.8316i	−0.123676	+	0.461567i
$899$	31.1246	−	53.9094i	1.03806	−	1.79798i
$900$		0			0
$901$	7.51446	−	4.33848i	0.250343	−	0.144536i
$902$	−12.3557	−	12.3557i	−0.411400	−	0.411400i
$903$		0			0
$904$			5.48597i			0.182461i
$905$	19.4141	−	53.2850i	0.645346	−	1.77125i
$906$		0			0
$907$	−8.01591	−	29.9158i	−0.266164	−	0.993337i	−0.961534	−	0.274685i	$-0.911426\pi$
$907$	−8.01591	−	29.9158i	−0.266164	−	0.993337i	0.695370	−	0.718652i	$-0.255240\pi$
$908$	17.2960	+	4.63445i	0.573988	+	0.153800i
$909$		0			0
$910$	−1.41734	+	1.71236i	−0.0469844	+	0.0567641i
$911$	−40.8011			−1.35180			−0.675901	−	0.736993i	$-0.736245\pi$
$911$	−40.8011			−1.35180			−0.675901	+	0.736993i	$0.736245\pi$
$912$		0			0
$913$	10.3750	+	38.7200i	0.343362	+	1.28144i
$914$	−28.3578	−	16.3724i	−0.937994	−	0.541551i
$915$		0			0
$916$			8.65885i			0.286097i
$917$	1.00677	−	2.82794i	0.0332464	−	0.0933869i
$918$		0			0
$919$	−10.8623	+	6.27134i	−0.358314	+	0.206873i	−0.668341	−	0.743855i	$-0.732995\pi$
$919$	−10.8623	+	6.27134i	−0.358314	+	0.206873i	0.310027	+	0.950728i	$0.399662\pi$
$920$	−17.1368	+	3.01585i	−0.564985	+	0.0994297i
$921$		0			0
$922$	9.30423	−	34.7239i	0.306419	−	1.14357i
$923$	1.20621	−	1.20621i	0.0397028	−	0.0397028i
$924$		0			0
$925$	5.65186	+	8.08304i	0.185832	+	0.265769i
$926$	−5.27514	−	9.13681i	−0.173352	−	0.300254i
$927$		0			0
$928$	7.82681	−	2.09719i	0.256928	−	0.0688436i
$929$	15.2979	+	26.4968i	0.501909	+	0.869331i	0.999998	+	0.00220528i	$0.000701963\pi$
$929$	15.2979	+	26.4968i	0.501909	+	0.869331i	−0.498089	+	0.867126i	$0.665965\pi$
$930$		0			0
$931$	49.0816	−	18.6520i	1.60858	−	0.611295i
$932$	−13.5460	+	13.5460i	−0.443713	+	0.443713i
$933$		0			0
$934$	−10.3081	+	17.8541i	−0.337290	+	0.584204i
$935$	8.71929	−	12.4437i	0.285151	−	0.406952i
$936$		0			0
$937$	2.47704	+	2.47704i	0.0809213	+	0.0809213i	0.746409	−	0.665488i	$-0.231776\pi$
$937$	2.47704	+	2.47704i	0.0809213	+	0.0809213i	−0.665488	+	0.746409i	$0.731776\pi$
$938$	−4.06871	−	4.78005i	−0.132848	−	0.156074i
$939$		0			0
$940$	7.10507	−	3.31029i	0.231742	−	0.107970i
$941$	35.9162	+	20.7362i	1.17083	+	0.675981i	0.953876	−	0.300200i	$-0.0970533\pi$
$941$	35.9162	+	20.7362i	1.17083	+	0.675981i	0.216958	+	0.976181i	$0.430387\pi$
$942$		0			0
$943$	−25.3945	−	6.80443i	−0.826957	−	0.221583i
$944$	6.72432			0.218858
$945$		0			0
$946$	−63.7531			−2.07279
$947$	41.5961	+	11.1457i	1.35169	+	0.362185i	0.860759	−	0.509012i	$-0.169989\pi$
$947$	41.5961	+	11.1457i	1.35169	+	0.362185i	0.490933	+	0.871197i	$0.336656\pi$
$948$		0			0
$949$	2.28217	+	1.31761i	0.0740824	+	0.0427715i
$950$	15.8725	−	33.9801i	0.514972	−	1.10246i
$951$		0			0
$952$	−3.41896	+	0.627738i	−0.110809	+	0.0203451i
$953$	−10.9239	−	10.9239i	−0.353859	−	0.353859i	0.507684	−	0.861543i	$-0.330502\pi$
$953$	−10.9239	−	10.9239i	−0.353859	−	0.353859i	−0.861543	+	0.507684i	$0.830502\pi$
$954$		0			0
$955$	0.703608	+	3.99808i	0.0227682	+	0.129375i
$956$	3.35380	−	5.80894i	0.108470	−	0.187875i
$957$		0			0
$958$	3.08582	−	3.08582i	0.0996983	−	0.0996983i
$959$	−11.6322	−	8.02335i	−0.375624	−	0.259088i
$960$		0			0
$961$	14.0091	+	24.2644i	0.451906	+	0.782723i
$962$	−0.715909	+	0.191827i	−0.0230818	+	0.00618476i
$963$		0			0
$964$	−0.216283	−	0.374613i	−0.00696600	−	0.0120655i
$965$	−15.4774	−	1.35925i	−0.498236	−	0.0437557i
$966$		0			0
$967$	−0.946186	+	0.946186i	−0.0304273	+	0.0304273i	−0.722157	−	0.691729i	$-0.756849\pi$
$967$	−0.946186	+	0.946186i	−0.0304273	+	0.0304273i	0.691729	+	0.722157i	$0.256849\pi$
$968$	−4.07620	+	15.2126i	−0.131014	+	0.488951i
$969$		0			0
$970$	−4.79599	−	27.2520i	−0.153990	−	0.875009i
$971$	−43.9590	+	25.3797i	−1.41071	+	0.814474i	−0.995455	−	0.0952305i	$-0.969641\pi$
$971$	−43.9590	+	25.3797i	−1.41071	+	0.814474i	−0.415256	+	0.909705i	$0.636308\pi$
$972$		0			0
$973$	37.3123	−	31.7596i	1.19618	−	1.01817i
$974$			23.5352i			0.754116i
$975$		0			0
$976$	−5.17644	−	2.98862i	−0.165694	−	0.0956633i
$977$	−9.55940	−	35.6762i	−0.305832	−	1.14138i	−0.932227	−	0.361875i	$-0.882137\pi$
$977$	−9.55940	−	35.6762i	−0.305832	−	1.14138i	0.626394	−	0.779506i	$-0.284530\pi$
$978$		0			0
$979$	70.3938			2.24980
$980$	−13.4464	+	8.01214i	−0.429530	+	0.255938i
$981$		0			0
$982$	−35.7909	−	9.59015i	−1.14213	−	0.306034i
$983$	−4.88466	−	18.2298i	−0.155796	−	0.581440i	−0.999036	−	0.0439021i	$-0.986021\pi$
$983$	−4.88466	−	18.2298i	−0.155796	−	0.581440i	0.843239	−	0.537538i	$-0.180646\pi$
$984$		0			0
$985$	−1.15792	+	0.539479i	−0.0368942	+	0.0171892i
$986$			10.6460i			0.339037i
$987$		0			0
$988$	1.99284	+	1.99284i	0.0634006	+	0.0634006i
$989$	−83.0702	+	47.9606i	−2.64148	+	1.52506i
$990$		0			0
$991$	−11.1490	+	19.3107i	−0.354161	+	0.613424i	−0.986974	−	0.160880i	$-0.948567\pi$
$991$	−11.1490	+	19.3107i	−0.354161	+	0.613424i	0.632813	+	0.774304i	$0.281900\pi$
$992$	−1.98833	+	7.42056i	−0.0631296	+	0.235603i
$993$		0			0
$994$	10.8504	−	5.15307i	0.344155	−	0.163445i
$995$	4.93257	−	4.13615i	0.156373	−	0.131125i
$996$		0			0
$997$	−55.9272	+	14.9857i	−1.77123	+	0.474600i	−0.988941	−	0.148311i	$-0.952616\pi$
$997$	−55.9272	+	14.9857i	−1.77123	+	0.474600i	−0.782292	+	0.622912i	$0.785950\pi$
$998$	18.5419	−	4.96829i	0.586934	−	0.157268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.d.73.1	✓	32
3.2	odd	2	inner	630.2.bv.d.73.8	yes	32
5.2	odd	4	inner	630.2.bv.d.577.6	yes	32
7.5	odd	6	inner	630.2.bv.d.523.6	yes	32
15.2	even	4	inner	630.2.bv.d.577.3	yes	32
21.5	even	6	inner	630.2.bv.d.523.3	yes	32
35.12	even	12	inner	630.2.bv.d.397.1	yes	32
105.47	odd	12	inner	630.2.bv.d.397.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bv.d.73.1	✓	32	1.1	even	1	trivial
630.2.bv.d.73.8	yes	32	3.2	odd	2	inner
630.2.bv.d.397.1	yes	32	35.12	even	12	inner
630.2.bv.d.397.8	yes	32	105.47	odd	12	inner
630.2.bv.d.523.3	yes	32	21.5	even	6	inner
630.2.bv.d.523.6	yes	32	7.5	odd	6	inner
630.2.bv.d.577.3	yes	32	15.2	even	4	inner
630.2.bv.d.577.6	yes	32	5.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-2.10096 - 0.765474i) q^{5} +(-2.01472 + 1.71490i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.83126 + 1.28316i) q^{10} +(2.58598 - 4.47905i) q^{11} +(0.265680 - 0.265680i) q^{13} +(2.38992 - 1.13502i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.26908 + 0.340048i) q^{17} +(3.75044 + 6.49596i) q^{19} +(-1.43675 - 1.71340i) q^{20} +(-3.65713 + 3.65713i) q^{22} +(-2.01403 + 7.51645i) q^{23} +(3.82810 + 3.21647i) q^{25} +(-0.325390 + 0.187864i) q^{26} +(-2.60225 + 0.477786i) q^{28} +8.10291i q^{29} +(-6.65309 - 3.84116i) q^{31} +(-0.258819 - 0.965926i) q^{32} +1.31385 q^{34} +(5.54557 - 2.06073i) q^{35} +(1.90539 + 0.510547i) q^{37} +(-1.94137 - 7.24530i) q^{38} +(0.944334 + 2.02688i) q^{40} +3.37852i q^{41} +(8.71627 + 8.71627i) q^{43} +(4.47905 - 2.58598i) q^{44} +(3.89080 - 6.73906i) q^{46} +(-0.907271 + 3.38598i) q^{47} +(1.11822 - 6.91011i) q^{49} +(-2.86518 - 4.09765i) q^{50} +(0.362926 - 0.0972457i) q^{52} +(-6.37920 + 1.70930i) q^{53} +(-8.86165 + 7.43083i) q^{55} +(2.63724 + 0.212006i) q^{56} +(2.09719 - 7.82681i) q^{58} +(3.36216 - 5.82343i) q^{59} +(-5.17644 + 2.98862i) q^{61} +(5.43223 + 5.43223i) q^{62} +1.00000i q^{64} +(-0.761556 + 0.354813i) q^{65} +(-0.614064 - 2.29172i) q^{67} +(-1.26908 - 0.340048i) q^{68} +(-5.88997 + 0.555210i) q^{70} +4.54008 q^{71} +(1.81526 + 6.77465i) q^{73} +(-1.70832 - 0.986302i) q^{74} +7.50089i q^{76} +(2.47109 + 13.4588i) q^{77} +(10.3622 - 5.98260i) q^{79} +(-0.387562 - 2.20223i) q^{80} +(0.874425 - 3.26340i) q^{82} +(-5.48051 + 5.48051i) q^{83} +(2.92659 + 0.257017i) q^{85} +(-6.16333 - 10.6752i) q^{86} +(-4.99573 + 1.33860i) q^{88} +(6.80532 + 11.7872i) q^{89} +(-0.0796568 + 0.990888i) q^{91} +(-5.50242 + 5.50242i) q^{92} +(1.75271 - 3.03579i) q^{94} +(-2.90706 - 16.5186i) q^{95} +(-8.75027 - 8.75027i) q^{97} +(-2.86859 + 6.38523i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{7} + 12 q^{10} + 16 q^{16} + 8 q^{22} + 20 q^{28} + 48 q^{31} + 32 q^{37} + 80 q^{43} + 8 q^{46} - 28 q^{58} + 48 q^{61} + 16 q^{67} - 60 q^{70} - 24 q^{73} + 48 q^{82} - 144 q^{85} + 4 q^{88}+ \cdots - 32 q^{91}+O(q^{100}) \) 32 * q + 4 * q^7 + 12 * q^10 + 16 * q^16 + 8 * q^22 + 20 * q^28 + 48 * q^31 + 32 * q^37 + 80 * q^43 + 8 * q^46 - 28 * q^58 + 48 * q^61 + 16 * q^67 - 60 * q^70 - 24 * q^73 + 48 * q^82 - 144 * q^85 + 4 * q^88 - 32 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more