LMFDB - Embedded newform 630.2.bv.d.577.3

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			577.3
Character	$\chi$	$=$	630.577
Dual form			630.2.bv.d.523.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.387562 - 2.20223i) q^{5} +(-1.71490 - 2.01472i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.02688 + 0.944334i) q^{10} +(-2.58598 + 4.47905i) q^{11} +(-0.265680 - 0.265680i) q^{13} +(2.38992 - 1.13502i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.340048 + 1.26908i) q^{17} +(-3.75044 - 6.49596i) q^{19} +(-1.43675 + 1.71340i) q^{20} +(-3.65713 - 3.65713i) q^{22} +(-7.51645 - 2.01403i) q^{23} +(-4.69959 - 1.70700i) q^{25} +(0.325390 - 0.187864i) q^{26} +(0.477786 + 2.60225i) q^{28} +8.10291i q^{29} +(-6.65309 - 3.84116i) q^{31} +(-0.965926 + 0.258819i) q^{32} -1.31385 q^{34} +(-5.10151 + 2.99577i) q^{35} +(-0.510547 + 1.90539i) q^{37} +(7.24530 - 1.94137i) q^{38} +(-1.28316 - 1.83126i) q^{40} -3.37852i q^{41} +(8.71627 - 8.71627i) q^{43} +(4.47905 - 2.58598i) q^{44} +(3.89080 - 6.73906i) q^{46} +(3.38598 + 0.907271i) q^{47} +(-1.11822 + 6.91011i) q^{49} +(2.86518 - 4.09765i) q^{50} +(0.0972457 + 0.362926i) q^{52} +(-1.70930 - 6.37920i) q^{53} +(8.86165 + 7.43083i) q^{55} +(-2.63724 - 0.212006i) q^{56} +(-7.82681 - 2.09719i) q^{58} +(3.36216 - 5.82343i) q^{59} +(-5.17644 + 2.98862i) q^{61} +(5.43223 - 5.43223i) q^{62} -1.00000i q^{64} +(-0.688055 + 0.482120i) q^{65} +(2.29172 - 0.614064i) q^{67} +(0.340048 - 1.26908i) q^{68} +(-1.57332 - 5.70304i) q^{70} -4.54008 q^{71} +(6.77465 - 1.81526i) q^{73} +(-1.70832 - 0.986302i) q^{74} +7.50089i q^{76} +(13.4588 - 2.47109i) q^{77} +(-10.3622 + 5.98260i) q^{79} +(2.10096 - 0.765474i) q^{80} +(3.26340 + 0.874425i) q^{82} +(-5.48051 - 5.48051i) q^{83} +(2.92659 - 0.257017i) q^{85} +(6.16333 + 10.6752i) q^{86} +(1.33860 + 4.99573i) q^{88} +(6.80532 + 11.7872i) q^{89} +(-0.0796568 + 0.990888i) q^{91} +(5.50242 + 5.50242i) q^{92} +(-1.75271 + 3.03579i) q^{94} +(-15.7591 + 5.74173i) q^{95} +(8.75027 - 8.75027i) q^{97} +(-6.38523 - 2.86859i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.387562	−	2.20223i	0.173323	−	0.984865i
$5$	0.387562	−	2.20223i	0.173323	−	0.984865i
$6$		0			0
$7$	−1.71490	−	2.01472i	−0.648172	−	0.761494i
$7$	−1.71490	−	2.01472i	−0.648172	−	0.761494i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	2.02688	+	0.944334i	0.640955	+	0.298625i
$11$	−2.58598	+	4.47905i	−0.779703	+	1.35049i	0.152410	+	0.988317i	$0.451297\pi$
$11$	−2.58598	+	4.47905i	−0.779703	+	1.35049i	−0.932113	+	0.362168i	$0.882037\pi$
$12$		0			0
$13$	−0.265680	−	0.265680i	−0.0736864	−	0.0736864i	0.669303	−	0.742989i	$-0.266593\pi$
$13$	−0.265680	−	0.265680i	−0.0736864	−	0.0736864i	−0.742989	+	0.669303i	$0.766593\pi$
$14$	2.38992	−	1.13502i	0.638734	−	0.303347i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.340048	+	1.26908i	0.0824739	+	0.307797i	0.994824	−	0.101615i	$-0.0324008\pi$
$17$	0.340048	+	1.26908i	0.0824739	+	0.307797i	−0.912350	+	0.409411i	$0.865734\pi$
$18$		0			0
$19$	−3.75044	−	6.49596i	−0.860411	−	1.49028i	−0.871533	−	0.490337i	$-0.836874\pi$
$19$	−3.75044	−	6.49596i	−0.860411	−	1.49028i	0.0111223	−	0.999938i	$-0.496460\pi$
$20$	−1.43675	+	1.71340i	−0.321267	+	0.383128i
$21$		0			0
$22$	−3.65713	−	3.65713i	−0.779703	−	0.779703i
$23$	−7.51645	−	2.01403i	−1.56729	−	0.419953i	−0.632326	−	0.774702i	$-0.717900\pi$
$23$	−7.51645	−	2.01403i	−1.56729	−	0.419953i	−0.934962	+	0.354749i	$0.884566\pi$
$24$		0			0
$25$	−4.69959	−	1.70700i	−0.939918	−	0.341400i
$26$	0.325390	−	0.187864i	0.0638143	−	0.0368432i
$27$		0			0
$28$	0.477786	+	2.60225i	0.0902931	+	0.491780i
$29$			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	$0.909009\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−1.31385			−0.225323
$35$	−5.10151	+	2.99577i	−0.862312	+	0.506377i
$36$		0			0
$37$	−0.510547	+	1.90539i	−0.0839334	+	0.313244i	−0.995110	−	0.0987721i	$-0.968509\pi$
$37$	−0.510547	+	1.90539i	−0.0839334	+	0.313244i	0.911177	+	0.412016i	$0.135175\pi$
$38$	7.24530	−	1.94137i	1.17534	−	0.314932i
$39$		0			0
$40$	−1.28316	−	1.83126i	−0.202885	−	0.289547i
$41$		−	3.37852i		−	0.527636i	−0.964572	−	0.263818i	$-0.915018\pi$
$41$		−	3.37852i		−	0.527636i	0.964572	−	0.263818i	$-0.0849818\pi$
$42$		0			0
$43$	8.71627	−	8.71627i	1.32922	−	1.32922i	0.423166	−	0.906052i	$-0.360919\pi$
$43$	8.71627	−	8.71627i	1.32922	−	1.32922i	0.906052	−	0.423166i	$-0.139081\pi$
$44$	4.47905	−	2.58598i	0.675243	−	0.389852i
$45$		0			0
$46$	3.89080	−	6.73906i	0.573667	−	0.993620i
$47$	3.38598	+	0.907271i	0.493896	+	0.132339i	0.497166	−	0.867656i	$-0.334374\pi$
$47$	3.38598	+	0.907271i	0.493896	+	0.132339i	−0.00326972	+	0.999995i	$0.501041\pi$
$48$		0			0
$49$	−1.11822	+	6.91011i	−0.159746	+	0.987158i
$50$	2.86518	−	4.09765i	0.405197	−	0.579496i
$51$		0			0
$52$	0.0972457	+	0.362926i	0.0134856	+	0.0503288i
$53$	−1.70930	−	6.37920i	−0.234791	−	0.876251i	−0.978243	−	0.207462i	$-0.933480\pi$
$53$	−1.70930	−	6.37920i	−0.234791	−	0.876251i	0.743452	−	0.668789i	$-0.233187\pi$
$54$		0			0
$55$	8.86165	+	7.43083i	1.19491	+	1.00197i
$56$	−2.63724	−	0.212006i	−0.352416	−	0.0283305i
$57$		0			0
$58$	−7.82681	−	2.09719i	−1.02771	−	0.275374i
$59$	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
$65$	−0.688055	+	0.482120i	−0.0853427	+	0.0597996i
$66$		0			0
$67$	2.29172	−	0.614064i	0.279978	−	0.0750198i	−0.116098	−	0.993238i	$-0.537039\pi$
$67$	2.29172	−	0.614064i	0.279978	−	0.0750198i	0.396075	+	0.918218i	$0.370372\pi$
$68$	0.340048	−	1.26908i	0.0412369	−	0.153898i
$69$		0			0
$70$	−1.57332	−	5.70304i	−0.188048	−	0.681644i
$71$	−4.54008			−0.538808			−0.269404	−	0.963027i	$-0.586827\pi$
$71$	−4.54008			−0.538808			−0.269404	+	0.963027i	$0.586827\pi$
$72$		0			0
$73$	6.77465	−	1.81526i	0.792913	−	0.212460i	0.160443	−	0.987045i	$-0.448708\pi$
$73$	6.77465	−	1.81526i	0.792913	−	0.212460i	0.632470	+	0.774585i	$0.282041\pi$
$74$	−1.70832	−	0.986302i	−0.198589	−	0.114655i
$75$		0			0
$76$			7.50089i			0.860411i
$77$	13.4588	−	2.47109i	1.53377	−	0.281607i
$78$		0			0
$79$	−10.3622	+	5.98260i	−1.16583	+	0.673095i	−0.952695	−	0.303927i	$-0.901702\pi$
$79$	−10.3622	+	5.98260i	−1.16583	+	0.673095i	−0.213140	+	0.977022i	$0.568369\pi$
$80$	2.10096	−	0.765474i	0.234895	−	0.0855826i
$81$		0			0
$82$	3.26340	+	0.874425i	0.360382	+	0.0965641i
$83$	−5.48051	−	5.48051i	−0.601564	−	0.601564i	0.339163	−	0.940727i	$-0.389856\pi$
$83$	−5.48051	−	5.48051i	−0.601564	−	0.601564i	−0.940727	+	0.339163i	$0.889856\pi$
$84$		0			0
$85$	2.92659	−	0.257017i	0.317433	−	0.0278774i
$86$	6.16333	+	10.6752i	0.664609	+	1.15114i
$87$		0			0
$88$	1.33860	+	4.99573i	0.142696	+	0.532547i
$89$	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
$95$	−15.7591	+	5.74173i	−1.61685	+	0.589089i
$96$		0			0
$97$	8.75027	−	8.75027i	0.888456	−	0.888456i	−0.105919	−	0.994375i	$-0.533778\pi$
$97$	8.75027	−	8.75027i	0.888456	−	0.888456i	0.994375	+	0.105919i	$0.0337785\pi$
$98$	−6.38523	−	2.86859i	−0.645006	−	0.289771i
$99$		0			0
$100$	3.21647	+	3.82810i	0.321647	+	0.382810i
$101$	−8.00611	−	4.62233i	−0.796638	−	0.459939i	0.0456565	−	0.998957i	$-0.485462\pi$
$101$	−8.00611	−	4.62233i	−0.796638	−	0.459939i	−0.842294	+	0.539018i	$0.818795\pi$
$102$		0			0
$103$	−0.905259	+	3.37847i	−0.0891978	+	0.332891i	−0.996076	−	0.0885021i	$-0.971792\pi$
$103$	−0.905259	+	3.37847i	−0.0891978	+	0.332891i	0.906878	+	0.421393i	$0.138459\pi$
$104$	−0.375729			−0.0368432
$105$		0			0
$106$	6.60424			0.641460
$107$	1.51700	−	5.66154i	0.146654	−	0.547322i	−0.853022	−	0.521875i	$-0.825233\pi$
$107$	1.51700	−	5.66154i	0.146654	−	0.547322i	0.999676	−	0.0254463i	$-0.00810068\pi$
$108$		0			0
$109$	0.113156	+	0.0653306i	0.0108384	+	0.00625754i	0.505409	−	0.862880i	$-0.331341\pi$
$109$	0.113156	+	0.0653306i	0.0108384	+	0.00625754i	−0.494571	+	0.869137i	$0.664675\pi$
$110$	−9.47119	+	6.63646i	−0.903043	+	0.632762i
$111$		0			0
$112$	0.887351	−	2.49251i	0.0838468	−	0.235520i
$113$	3.87916	−	3.87916i	0.364921	−	0.364921i	−0.500700	−	0.865621i	$-0.666924\pi$
$113$	3.87916	−	3.87916i	0.364921	−	0.364921i	0.865621	+	0.500700i	$0.166924\pi$
$114$		0			0
$115$	−7.34843	+	15.7723i	−0.685245	+	1.47078i
$116$	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
$122$	−1.54702	−	5.77357i	−0.140061	−	0.522714i
$123$		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	0.983952	−	0.178431i	$-0.0571021\pi$
$127$	9.07777	+	9.07777i	0.805522	+	0.805522i	−0.178431	+	0.983952i	$0.557102\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	−0.287610	−	0.789392i	−0.0252251	−	0.0692343i
$131$	0.982572	−	0.567288i	0.0858477	−	0.0495642i	−0.456462	−	0.889743i	$-0.650883\pi$
$131$	0.982572	−	0.567288i	0.0858477	−	0.0495642i	0.542309	+	0.840179i	$0.317550\pi$
$132$		0			0
$133$	−6.65592	+	18.6960i	−0.577142	+	1.62115i
$134$			2.37256i			0.204958i
$135$		0			0
$136$	1.13782	+	0.656923i	0.0975676	+	0.0563307i
$137$	5.15899	−	1.38235i	0.440762	−	0.118102i	−0.0316115	−	0.999500i	$-0.510064\pi$
$137$	5.15899	−	1.38235i	0.440762	−	0.118102i	0.472374	+	0.881398i	$0.343397\pi$
$138$		0			0
$139$	18.5198			1.57083			0.785414	−	0.618970i	$-0.212450\pi$
$139$	18.5198			1.57083			0.785414	+	0.618970i	$0.212450\pi$
$140$	5.91592	−	0.0436585i	0.499986	−	0.00368982i
$141$		0			0
$142$	1.17506	−	4.38538i	0.0986087	−	0.368013i
$143$	1.87704	−	0.502951i	0.156966	−	0.0420589i
$144$		0			0
$145$	17.8444	+	3.14038i	1.48190	+	0.260795i
$146$			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	$0.0313347\pi$
$152$	−7.24530	−	1.94137i	−0.587671	−	0.157466i
$153$		0			0
$154$	−1.09649	+	13.6397i	−0.0883577	+	1.09912i
$155$	−11.0376	+	13.1629i	−0.886561	+	1.05727i
$156$		0			0
$157$	−0.664809	−	2.48110i	−0.0530575	−	0.198013i	0.934310	−	0.356463i	$-0.116017\pi$
$157$	−0.664809	−	2.48110i	−0.0530575	−	0.198013i	−0.987367	+	0.158449i	$0.949351\pi$
$158$	−3.09682	−	11.5575i	−0.246370	−	0.919465i
$159$		0			0
$160$	0.195622	+	2.22749i	0.0154652	+	0.176099i
$161$	8.83226	+	18.5974i	0.696080	+	1.46568i
$162$		0			0
$163$	−10.8917	−	2.91842i	−0.853104	−	0.228589i	−0.194337	−	0.980935i	$-0.562255\pi$
$163$	−10.8917	−	2.91842i	−0.853104	−	0.228589i	−0.658768	+	0.752346i	$0.728922\pi$
$164$	−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	−0.985905	−	0.167306i	$-0.946493\pi$
$167$	−10.5786	+	10.5786i	−0.818599	+	0.818599i	0.167306	+	0.985905i	$0.446493\pi$
$168$		0			0
$169$		−	12.8588i		−	0.989141i
$170$	−0.509197	+	2.89339i	−0.0390536	+	0.221913i
$171$		0			0
$172$	−11.9066	+	3.19038i	−0.907873	+	0.243264i
$173$	4.54389	−	16.9580i	0.345465	−	1.28929i	−0.546602	−	0.837392i	$-0.684079\pi$
$173$	4.54389	−	16.9580i	0.345465	−	1.28929i	0.892068	−	0.451902i	$-0.149254\pi$
$174$		0			0
$175$	4.62021	+	12.3957i	0.349255	+	0.937028i
$176$	−5.17197			−0.389852
$177$		0			0
$178$	−13.1469	+	3.52269i	−0.985400	+	0.264037i
$179$	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	$0.608394\pi$
$182$	−0.936507	−	0.333403i	−0.0694185	−	0.0247135i
$183$		0			0
$184$	−6.73906	+	3.89080i	−0.496810	+	0.286834i
$185$	3.99822	+	1.86280i	0.293955	+	0.136956i
$186$		0			0
$187$	−6.56363	−	1.75872i	−0.479980	−	0.128610i
$188$	−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	0.896996	−	0.442039i	$-0.145745\pi$
$191$	0.907736	+	1.57224i	0.0656815	+	0.113764i	−0.831315	+	0.555802i	$0.812411\pi$
$192$		0			0
$193$	−1.79837	−	6.71159i	−0.129449	−	0.483111i	0.870510	−	0.492151i	$-0.163789\pi$
$193$	−1.79837	−	6.71159i	−0.129449	−	0.483111i	−0.999959	+	0.00903978i	$0.997123\pi$
$194$	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	$-0.256478\pi$
$197$	−0.403956	−	0.403956i	−0.0287807	−	0.0287807i	−0.721351	+	0.692570i	$0.756478\pi$
$198$		0			0
$199$	1.43941	−	2.49313i	0.102037	−	0.176733i	−0.810487	−	0.585757i	$-0.800797\pi$
$199$	1.43941	−	2.49313i	0.102037	−	0.176733i	0.912524	+	0.409024i	$0.134131\pi$
$200$	−4.53014	+	2.11608i	−0.320329	+	0.149630i
$201$		0			0
$202$	6.53696	−	6.53696i	0.459939	−	0.459939i
$203$	16.3251	−	13.8957i	1.14580	−	0.975287i
$204$		0			0
$205$	−7.44026	−	1.30939i	−0.519650	−	0.0914515i
$206$	−3.02906	−	1.74883i	−0.211044	−	0.121847i
$207$		0			0
$208$	0.0972457	−	0.362926i	0.00674278	−	0.0251644i
$209$	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	$0.620086\pi$
$212$	−1.70930	+	6.37920i	−0.117395	+	0.438126i
$213$		0			0
$214$	5.07600	+	2.93063i	0.346988	+	0.200334i
$215$	−15.8171	−	22.5733i	−1.07872	−	1.53948i
$216$		0			0
$217$	3.67051	+	19.9914i	0.249171	+	1.35710i
$218$	−0.0923914	+	0.0923914i	−0.00625754	+	0.00625754i
$219$		0			0
$220$	−3.95900	−	10.8661i	−0.266916	−	0.732593i
$221$	0.246825	−	0.427513i	0.0166032	−	0.0287576i
$222$		0			0
$223$	8.44168	+	8.44168i	0.565296	+	0.565296i	0.930807	−	0.365511i	$-0.119106\pi$
$223$	8.44168	+	8.44168i	0.565296	+	0.565296i	−0.365511	+	0.930807i	$0.619106\pi$
$224$	2.17792	+	1.50222i	0.145518	+	0.100372i
$225$		0			0
$226$	2.74298	+	4.75099i	0.182461	+	0.316031i
$227$	−4.63445	−	17.2960i	−0.307599	−	1.14798i	−0.930685	−	0.365823i	$-0.880788\pi$
$227$	−4.63445	−	17.2960i	−0.307599	−	1.14798i	0.623085	−	0.782154i	$-0.285879\pi$
$228$		0			0
$229$	−4.32943	−	7.49879i	−0.286097	−	0.495534i	0.686778	−	0.726867i	$-0.259024\pi$
$229$	−4.32943	−	7.49879i	−0.286097	−	0.495534i	−0.972875	+	0.231334i	$0.925691\pi$
$230$	−13.3330	−	11.1802i	−0.879152	−	0.737202i
$231$		0			0
$232$	5.72963	+	5.72963i	0.376168	+	0.376168i
$233$	−18.5041	−	4.95817i	−1.21225	−	0.324820i	−0.404603	−	0.914492i	$-0.632590\pi$
$233$	−18.5041	−	4.95817i	−1.21225	−	0.324820i	−0.807643	+	0.589672i	$0.799257\pi$
$234$		0			0
$235$	3.31029	−	7.10507i	0.215940	−	0.463483i
$236$	−5.82343	+	3.36216i	−0.379073	+	0.218858i
$237$		0			0
$238$	2.25312	+	2.64704i	0.146048	+	0.171582i
$239$		−	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	$0.671102\pi$
$242$	15.2126	−	4.07620i	0.977902	−	0.262028i
$243$		0			0
$244$	5.97724			0.382653
$245$	14.7842	+	5.14068i	0.944530	+	0.328426i
$246$		0			0
$247$	−0.729429	+	2.72227i	−0.0464125	+	0.173214i
$248$	−7.42056	+	1.98833i	−0.471206	+	0.126259i
$249$		0			0
$250$	−7.91352	−	7.89786i	−0.500495	−	0.499505i
$251$			19.4059i			1.22489i	0.790513	+	0.612446i	$0.209814\pi$
$251$			19.4059i			1.22489i	−0.790513	+	0.612446i	$0.790186\pi$
$252$		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
$257$	18.0244	+	4.82963i	1.12433	+	0.301264i	0.772636	−	0.634849i	$-0.218938\pi$
$257$	18.0244	+	4.82963i	1.12433	+	0.301264i	0.351698	+	0.936114i	$0.385604\pi$
$258$		0			0
$259$	4.71437	−	2.23894i	0.292937	−	0.139121i
$260$	0.836933	−	0.0735006i	0.0519044	−	0.00455831i
$261$		0			0
$262$	0.293650	+	1.09592i	0.0181418	+	0.0677060i
$263$	1.76101	+	6.57217i	0.108588	+	0.405257i	0.998728	−	0.0504316i	$-0.0160597\pi$
$263$	1.76101	+	6.57217i	0.108588	+	0.405257i	−0.890139	+	0.455689i	$0.849393\pi$
$264$		0			0
$265$	−14.7109	+	1.29193i	−0.903684	+	0.0793627i
$266$	−16.3363	−	11.2680i	−1.00164	−	0.690886i
$267$		0			0
$268$	−2.29172	−	0.614064i	−0.139989	−	0.0375099i
$269$	−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
$275$	19.7988	−	16.6355i	1.19391	−	1.00316i
$276$		0			0
$277$	−3.10859	+	0.832945i	−0.186777	+	0.0500468i	−0.350995	−	0.936377i	$-0.614157\pi$
$277$	−3.10859	+	0.832945i	−0.186777	+	0.0500468i	0.164218	+	0.986424i	$0.447490\pi$
$278$	−4.79328	+	17.8888i	−0.287482	+	1.07290i
$279$		0			0
$280$	−1.48898	+	5.72564i	−0.0889837	+	0.342172i
$281$	4.88199			0.291235			0.145618	−	0.989341i	$-0.453483\pi$
$281$	4.88199			0.291235			0.145618	+	0.989341i	$0.453483\pi$
$282$		0			0
$283$	−11.7546	+	3.14962i	−0.698736	+	0.187226i	−0.590664	−	0.806917i	$-0.701134\pi$
$283$	−11.7546	+	3.14962i	−0.698736	+	0.187226i	−0.108071	+	0.994143i	$0.534468\pi$
$284$	3.93182	+	2.27004i	0.233311	+	0.134702i
$285$		0			0
$286$			1.94325i			0.114907i
$287$	−6.80678	+	5.79383i	−0.401792	+	0.341999i
$288$		0			0
$289$	13.2275	−	7.63690i	0.778089	−	0.449230i
$290$	−7.65186	+	16.4236i	−0.449333	+	0.964428i
$291$		0			0
$292$	−6.77465	−	1.81526i	−0.396456	−	0.106230i
$293$	−3.88255	−	3.88255i	−0.226821	−	0.226821i	0.584542	−	0.811363i	$-0.301274\pi$
$293$	−3.88255	−	3.88255i	−0.226821	−	0.226821i	−0.811363	+	0.584542i	$0.801274\pi$
$294$		0			0
$295$	−11.5215	−	9.66117i	−0.670805	−	0.562495i
$296$	0.986302	+	1.70832i	0.0573276	+	0.0992943i
$297$		0			0
$298$	−2.56218	−	9.56218i	−0.148423	−	0.553922i
$299$	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
$305$	4.57542	+	12.5580i	0.261988	+	0.719067i
$306$		0			0
$307$	−8.99757	+	8.99757i	−0.513519	+	0.513519i	−0.915603	−	0.402084i	$-0.868286\pi$
$307$	−8.99757	+	8.99757i	−0.513519	+	0.513519i	0.402084	+	0.915603i	$0.368286\pi$
$308$	−12.8912	−	4.58935i	−0.734543	−	0.261502i
$309$		0			0
$310$	−9.85766	−	14.0683i	−0.559877	−	0.799026i
$311$	−18.6303	−	10.7562i	−1.05643	−	0.609929i	−0.131985	−	0.991252i	$-0.542135\pi$
$311$	−18.6303	−	10.7562i	−1.05643	−	0.609929i	−0.924442	+	0.381323i	$0.875469\pi$
$312$		0			0
$313$	3.69885	−	13.8043i	0.209071	−	0.780265i	−0.779099	−	0.626901i	$-0.784323\pi$
$313$	3.69885	−	13.8043i	0.209071	−	0.780265i	0.988170	−	0.153363i	$-0.0490105\pi$
$314$	2.56862			0.144956
$315$		0			0
$316$	11.9652			0.673095
$317$	5.24563	−	19.5770i	0.294624	−	1.09955i	−0.646891	−	0.762582i	$-0.723931\pi$
$317$	5.24563	−	19.5770i	0.294624	−	1.09955i	0.941515	−	0.336970i	$-0.109402\pi$
$318$		0			0
$319$	−36.2934	−	20.9540i	−2.03204	−	1.17320i
$320$	−2.20223	−	0.387562i	−0.123108	−	0.0216654i
$321$		0			0
$322$	−20.2497	+	3.71794i	−1.12847	+	0.207193i
$323$	6.96855	−	6.96855i	0.387740	−	0.387740i
$324$		0			0
$325$	0.795073	+	1.70210i	0.0441027	+	0.0944157i
$326$	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	$0.851340\pi$
$332$	2.00601	+	7.48652i	0.110094	+	0.410876i
$333$		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	0.253287	−	0.967391i	$-0.418488\pi$
$337$	−13.1092	−	13.1092i	−0.714105	−	0.714105i	−0.967391	+	0.253287i	$0.918488\pi$
$338$	12.4207	+	3.32811i	0.675596	+	0.181025i
$339$		0			0
$340$	−2.66301	−	1.24071i	−0.144422	−	0.0672869i
$341$	34.4096	−	19.8664i	1.86338	−	1.07582i
$342$		0			0
$343$	15.8396	−	9.59724i	0.855258	−	0.518202i
$344$		−	12.3267i		−	0.664609i
$345$		0			0
$346$	15.2041	+	8.77812i	0.817380	+	0.471914i
$347$	3.67205	−	0.983922i	0.197126	−	0.0528197i	−0.158905	−	0.987294i	$-0.550796\pi$
$347$	3.67205	−	0.983922i	0.197126	−	0.0528197i	0.356031	+	0.934474i	$0.384130\pi$
$348$		0			0
$349$	25.5306			1.36662			0.683312	−	0.730126i	$-0.260539\pi$
$349$	25.5306			1.36662			0.683312	+	0.730126i	$0.260539\pi$
$350$	−13.1691	+	1.25453i	−0.703920	+	0.0670574i
$351$		0			0
$352$	1.33860	−	4.99573i	0.0713478	−	0.266274i
$353$	28.4961	−	7.63550i	1.51669	−	0.406396i	0.598041	−	0.801466i	$-0.295946\pi$
$353$	28.4961	−	7.63550i	1.51669	−	0.406396i	0.918651	+	0.395069i	$0.129279\pi$
$354$		0			0
$355$	−1.75956	+	9.99827i	−0.0933878	+	0.530653i
$356$		−	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
$362$	−24.4980	−	6.56421i	−1.28758	−	0.345007i
$363$		0			0
$364$	0.564429	−	0.818305i	0.0295841	−	0.0428909i
$365$	−1.37202	−	15.6228i	−0.0718147	−	0.817736i
$366$		0			0
$367$	−2.73302	−	10.1998i	−0.142662	−	0.532423i	−0.999848	−	0.0174162i	$-0.994456\pi$
$367$	−2.73302	−	10.1998i	−0.142662	−	0.532423i	0.857186	−	0.515007i	$-0.172211\pi$
$368$	−2.01403	−	7.51645i	−0.104988	−	0.391822i
$369$		0			0
$370$	−2.83414	+	3.37986i	−0.147340	+	0.175711i
$371$	−9.92105	+	14.3835i	−0.515075	+	0.746753i
$372$		0			0
$373$	−21.2597	−	5.69653i	−1.10079	−	0.294955i	−0.337702	−	0.941253i	$-0.609650\pi$
$373$	−21.2597	−	5.69653i	−1.10079	−	0.294955i	−0.763085	+	0.646298i	$0.776316\pi$
$374$	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	$-0.875487\pi$
$379$		−	14.8451i		−	0.762541i	0.924464	−	0.381270i	$-0.124513\pi$
$380$	16.5186	+	2.90706i	0.847388	+	0.149129i
$381$		0			0
$382$	−1.75361	+	0.469879i	−0.0897225	+	0.0240411i
$383$	−6.64174	+	24.7873i	−0.339377	+	1.26657i	0.559668	+	0.828717i	$0.310929\pi$
$383$	−6.64174	+	24.7873i	−0.339377	+	1.26657i	−0.899045	+	0.437856i	$0.855738\pi$
$384$		0			0
$385$	−0.225800	−	30.5969i	−0.0115078	−	1.55936i
$386$	6.94835			0.353662
$387$		0			0
$388$	−11.9531	+	3.20282i	−0.606827	+	0.162599i
$389$	−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
$392$	4.09548	+	5.67689i	0.206853	+	0.286726i
$393$		0			0
$394$	0.494743	−	0.285640i	0.0249248	−	0.0143903i
$395$	9.15905	+	25.1385i	0.460842	+	1.26485i
$396$		0			0
$397$	−1.29904	−	0.348078i	−0.0651971	−	0.0174695i	0.226073	−	0.974110i	$-0.427411\pi$
$397$	−1.29904	−	0.348078i	−0.0651971	−	0.0174695i	−0.291270	+	0.956641i	$0.594078\pi$
$398$	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	$0.00814309\pi$
$401$	10.4528	+	18.1048i	0.521989	+	0.904111i	−0.477684	+	0.878532i	$0.658524\pi$
$402$		0			0
$403$	0.747073	+	2.78812i	0.0372144	+	0.138886i
$404$	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	−0.796753	−	0.604306i	$-0.793451\pi$
$409$	2.52732	−	4.37744i	0.124968	−	0.216451i	0.921720	+	0.387855i	$0.126784\pi$
$410$	3.19045	−	6.84785i	0.157565	−	0.338191i
$411$		0			0
$412$	2.47321	−	2.47321i	0.121847	−	0.121847i
$413$	−17.4984	+	3.21279i	−0.861039	+	0.158091i
$414$		0			0
$415$	−14.1934	+	9.94528i	−0.696724	+	0.488194i
$416$	0.325390	+	0.187864i	0.0159536	+	0.00921080i
$417$		0			0
$418$	−10.0407	+	37.4724i	−0.491107	+	1.83284i
$419$	−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	$0.426288\pi$
$422$	2.76987	−	10.3373i	0.134835	−	0.503211i
$423$		0			0
$424$	−5.71944	−	3.30212i	−0.277760	−	0.160365i
$425$	0.568225	−	6.54461i	0.0275630	−	0.317460i
$426$		0			0
$427$	14.8983	+	5.30391i	0.720980	+	0.256674i
$428$	−4.14453	+	4.14453i	−0.200334	+	0.200334i
$429$		0			0
$430$	25.8979	−	9.43574i	1.24891	−	0.455032i
$431$	−4.48816	+	7.77373i	−0.216187	+	0.374447i	−0.953639	−	0.300952i	$-0.902695\pi$
$431$	−4.48816	+	7.77373i	−0.216187	+	0.374447i	0.737452	+	0.675400i	$0.236029\pi$
$432$		0			0
$433$	−10.7835	−	10.7835i	−0.518224	−	0.518224i	0.398810	−	0.917034i	$-0.369423\pi$
$433$	−10.7835	−	10.7835i	−0.518224	−	0.518224i	−0.917034	+	0.398810i	$0.869423\pi$
$434$	−20.2602	−	1.62870i	−0.972519	−	0.0781802i
$435$		0			0
$436$	−0.0653306	−	0.113156i	−0.00312877	−	0.00541919i
$437$	15.1070	+	56.3800i	0.722665	+	2.69702i
$438$		0			0
$439$	−2.89682	−	5.01745i	−0.138258	−	0.239470i	0.788579	−	0.614933i	$-0.210817\pi$
$439$	−2.89682	−	5.01745i	−0.138258	−	0.239470i	−0.926837	+	0.375463i	$0.877484\pi$
$440$	11.5205	−	1.01175i	0.549219	−	0.0482332i
$441$		0			0
$442$	0.349063	+	0.349063i	0.0166032	+	0.0166032i
$443$	−20.4558	−	5.48110i	−0.971882	−	0.260415i	−0.262260	−	0.964997i	$-0.584468\pi$
$443$	−20.4558	−	5.48110i	−0.971882	−	0.260415i	−0.709622	+	0.704582i	$0.751134\pi$
$444$		0			0
$445$	28.5955	−	10.4186i	1.35556	−	0.493889i
$446$	−10.3389	+	5.96917i	−0.489561	+	0.282648i
$447$		0			0
$448$	−2.01472	+	1.71490i	−0.0951868	+	0.0810215i
$449$		−	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
$452$	−5.29904	+	1.41987i	−0.249246	+	0.0667852i
$453$		0			0
$454$	17.9062			0.840377
$455$	2.15129	+	0.559453i	0.100854	+	0.0262276i
$456$		0			0
$457$	−8.47498	+	31.6291i	−0.396443	+	1.47954i	0.422866	+	0.906192i	$0.361024\pi$
$457$	−8.47498	+	31.6291i	−0.396443	+	1.47954i	−0.819309	+	0.573353i	$0.805643\pi$
$458$	8.36381	−	2.24108i	0.390815	−	0.104719i
$459$		0			0
$460$	14.2501	−	9.98504i	0.664414	−	0.465555i
$461$		−	35.9488i		−	1.67430i	−0.546972	−	0.837151i	$-0.684219\pi$
$461$		−	35.9488i		−	1.67430i	0.546972	−	0.837151i	$-0.315781\pi$
$462$		0			0
$463$	7.46017	−	7.46017i	0.346704	−	0.346704i	−0.512177	−	0.858880i	$-0.671161\pi$
$463$	7.46017	−	7.46017i	0.346704	−	0.346704i	0.858880	+	0.512177i	$0.171161\pi$
$464$	−7.01733	+	4.05146i	−0.325771	+	0.188084i
$465$		0			0
$466$	9.57844	−	16.5904i	0.443713	−	0.768533i
$467$	−19.9137	−	5.33585i	−0.921494	−	0.246914i	−0.233270	−	0.972412i	$-0.574943\pi$
$467$	−19.9137	−	5.33585i	−0.921494	−	0.246914i	−0.688224	+	0.725498i	$0.741609\pi$
$468$		0			0
$469$	−5.16724	−	3.56412i	−0.238601	−	0.164576i
$470$	6.00620	+	5.03642i	0.277045	+	0.232313i
$471$		0			0
$472$	−1.74038	−	6.49519i	−0.0801076	−	0.298966i
$473$	16.5005	+	61.5807i	0.758694	+	2.83149i
$474$		0			0
$475$	6.53696	+	36.9303i	0.299936	+	1.69448i
$476$	−3.13999	+	1.49124i	−0.143921	+	0.0683509i
$477$		0			0
$478$	6.47904	+	1.73605i	0.296344	+	0.0794052i
$479$	−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
$485$	−15.8788	−	22.6613i	−0.721019	−	1.02900i
$486$		0			0
$487$	22.7332	−	6.09135i	1.03014	−	0.276026i	0.296119	−	0.955151i	$-0.404307\pi$
$487$	22.7332	−	6.09135i	1.03014	−	0.276026i	0.734022	+	0.679125i	$0.237641\pi$
$488$	−1.54702	+	5.77357i	−0.0700304	+	0.261357i
$489$		0			0
$490$	−8.79195	+	12.9500i	−0.397180	+	0.585020i
$491$	−37.0535			−1.67220			−0.836100	−	0.548577i	$-0.815170\pi$
$491$	−37.0535			−1.67220			−0.836100	+	0.548577i	$0.815170\pi$
$492$		0			0
$493$	−10.2832	+	2.75538i	−0.463133	+	0.124096i
$494$	−2.44072	−	1.40915i	−0.109813	−	0.0634006i
$495$		0			0
$496$		−	7.68233i		−	0.344947i
$497$	7.78578	+	9.14700i	0.349240	+	0.410299i
$498$		0			0
$499$	16.6242	−	9.59800i	0.744202	−	0.429665i	−0.0793930	−	0.996843i	$-0.525298\pi$
$499$	16.6242	−	9.59800i	0.744202	−	0.429665i	0.823595	+	0.567178i	$0.191965\pi$
$500$	9.67692	−	5.59976i	0.432765	−	0.250429i
$501$		0			0
$502$	−18.7447	−	5.02263i	−0.836617	−	0.224171i
$503$	22.3585	+	22.3585i	0.996914	+	0.996914i	0.999995	−	0.00308078i	$-0.000980643\pi$
$503$	22.3585	+	22.3585i	0.996914	+	0.996914i	−0.00308078	+	0.999995i	$0.500981\pi$
$504$		0			0
$505$	−13.2823	+	15.8398i	−0.591053	+	0.704862i
$506$	20.1231	+	34.8542i	0.894580	+	1.54946i
$507$		0			0
$508$	−3.32269	−	12.4005i	−0.147421	−	0.550182i
$509$	−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
$515$	7.08931	+	3.30295i	0.312393	+	0.145545i
$516$		0			0
$517$	−12.8198	+	12.8198i	−0.563814	+	0.563814i
$518$	0.942483	+	5.13321i	0.0414103	+	0.225540i
$519$		0			0
$520$	−0.145618	+	0.827439i	−0.00638578	+	0.0362856i
$521$	−25.9155	−	14.9623i	−1.13538	−	0.655511i	−0.190096	−	0.981766i	$-0.560880\pi$
$521$	−25.9155	−	14.9623i	−1.13538	−	0.655511i	−0.945282	+	0.326255i	$0.894213\pi$
$522$		0			0
$523$	−6.17629	+	23.0502i	−0.270070	+	1.00792i	0.689003	+	0.724758i	$0.258049\pi$
$523$	−6.17629	+	23.0502i	−0.270070	+	1.00792i	−0.959073	+	0.283158i	$0.908618\pi$
$524$	−1.13458			−0.0495642
$525$		0			0
$526$	−6.80401			−0.296669
$527$	2.61236	−	9.74947i	0.113796	−	0.424694i
$528$		0			0
$529$	32.5221	+	18.7766i	1.41400	+	0.816375i
$530$	2.55955	−	14.5440i	0.111180	−	0.631752i
$531$		0			0
$532$	15.1122	−	12.8633i	0.655198	−	0.557694i
$533$	−0.897606	+	0.897606i	−0.0388796	+	0.0388796i
$534$		0			0
$535$	−11.8800	−	5.53498i	−0.513619	−	0.239298i
$536$	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	$0.794176\pi$
$542$	3.43772	+	12.8297i	0.147663	+	0.551084i
$543$		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	0.999413	+	0.0342575i	$0.0109066\pi$
$547$	24.1755	+	24.1755i	1.03367	+	1.03367i	0.0342575	+	0.999413i	$0.489093\pi$
$548$	−5.15899	−	1.38235i	−0.220381	−	0.0590509i
$549$		0			0
$550$	10.9443	+	23.4297i	0.466667	+	0.999048i
$551$	52.6362	−	30.3895i	2.24238	−	1.29464i
$552$		0			0
$553$	29.8234	+	10.6173i	1.26822	+	0.451495i
$554$		−	3.21825i		−	0.136730i
$555$		0			0
$556$	−16.0386	−	9.25990i	−0.680189	−	0.392707i
$557$	−30.7756	+	8.24631i	−1.30401	+	0.349407i	−0.842964	−	0.537971i	$-0.819191\pi$
$557$	−30.7756	+	8.24631i	−1.30401	+	0.349407i	−0.461042	+	0.887378i	$0.652524\pi$
$558$		0			0
$559$	−4.63148			−0.195891
$560$	−5.14517	−	2.92015i	−0.217423	−	0.123399i
$561$		0			0
$562$	−1.26355	+	4.71564i	−0.0532997	+	0.198917i
$563$	−12.2262	+	3.27600i	−0.515272	+	0.138067i	−0.507079	−	0.861900i	$-0.669275\pi$
$563$	−12.2262	+	3.27600i	−0.515272	+	0.138067i	−0.00819336	+	0.999966i	$0.502608\pi$
$564$		0			0
$565$	−7.03938	−	10.0462i	−0.296149	−	0.422647i
$566$		−	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	$0.197651\pi$
$572$	−1.87704	−	0.502951i	−0.0784830	−	0.0210295i
$573$		0			0
$574$	−3.83468	−	8.07440i	−0.160057	−	0.337019i
$575$	31.8863	+	22.2957i	1.32975	+	0.929793i
$576$		0			0
$577$	0.375902	+	1.40289i	0.0156490	+	0.0584029i	0.973309	−	0.229499i	$-0.0737089\pi$
$577$	0.375902	+	1.40289i	0.0156490	+	0.0584029i	−0.957660	+	0.287902i	$0.907042\pi$
$578$	3.95315	+	14.7534i	0.164429	+	0.613659i
$579$		0			0
$580$	−13.8835	−	11.6419i	−0.576483	−	0.483402i
$581$	−1.64318	+	20.4402i	−0.0681705	+	0.848004i
$582$		0			0
$583$	32.9930	+	8.84045i	1.36643	+	0.366134i
$584$	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	−0.898677	−	0.438611i	$-0.855471\pi$
$587$	−11.1465	+	11.1465i	−0.460066	+	0.460066i	0.438611	+	0.898677i	$0.355471\pi$
$588$		0			0
$589$			57.6243i			2.37437i
$590$	12.3140	−	8.62838i	0.506957	−	0.355225i
$591$		0			0
$592$	−1.90539	+	0.510547i	−0.0783110	+	0.0209834i
$593$	−4.02100	+	15.0066i	−0.165123	+	0.616246i	0.832902	+	0.553420i	$0.186678\pi$
$593$	−4.02100	+	15.0066i	−0.165123	+	0.616246i	−0.998025	+	0.0628252i	$0.979989\pi$
$594$		0			0
$595$	−5.53662	−	5.45550i	−0.226979	−	0.223654i
$596$	9.89949			0.405499
$597$		0			0
$598$	−2.82414	+	0.756727i	−0.115488	+	0.0309449i
$599$	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	$-0.266700\pi$
$602$	10.9381	−	30.7243i	0.445803	−	1.25223i
$603$		0			0
$604$	−8.77882	+	5.06845i	−0.357205	+	0.206232i
$605$	−33.0886	+	12.0556i	−1.34524	+	0.490131i
$606$		0			0
$607$	19.7380	+	5.28879i	0.801141	+	0.214665i	0.636085	−	0.771619i	$-0.280553\pi$
$607$	19.7380	+	5.28879i	0.801141	+	0.214665i	0.165056	+	0.986284i	$0.447219\pi$
$608$	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
$613$	2.94267	+	10.9822i	0.118853	+	0.443567i	0.999546	−	0.0301206i	$-0.00958915\pi$
$613$	2.94267	+	10.9822i	0.118853	+	0.443567i	−0.880693	+	0.473688i	$0.842922\pi$
$614$	−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	$-0.437326\pi$
$617$	−19.5003	−	19.5003i	−0.785051	−	0.785051i	−0.980678	+	0.195628i	$0.937326\pi$
$618$		0			0
$619$	−8.77812	+	15.2041i	−0.352822	+	0.611106i	−0.986743	−	0.162292i	$-0.948111\pi$
$619$	−8.77812	+	15.2041i	−0.352822	+	0.611106i	0.633920	+	0.773398i	$0.281445\pi$
$620$	16.1403	−	5.88062i	0.648210	−	0.236171i
$621$		0			0
$622$	15.2116	−	15.2116i	0.609929	−	0.609929i
$623$	12.0774	−	33.9247i	0.483872	−	1.35916i
$624$		0			0
$625$	19.1723	+	16.0444i	0.766893	+	0.641776i
$626$	12.3766	+	7.14563i	0.494668	+	0.285597i
$627$		0			0
$628$	−0.664809	+	2.48110i	−0.0265288	+	0.0990066i
$629$	−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	$0.652617\pi$
$632$	−3.09682	+	11.5575i	−0.123185	+	0.459733i
$633$		0			0
$634$	17.5522	+	10.1338i	0.697088	+	0.402464i
$635$	23.5095	−	16.4731i	0.932946	−	0.653715i
$636$		0			0
$637$	2.13297	−	1.53879i	0.0845113	−	0.0609690i
$638$	29.6334	−	29.6334i	1.17320	−	1.17320i
$639$		0			0
$640$	0.944334	−	2.02688i	0.0373281	−	0.0801194i
$641$	8.67383	−	15.0235i	0.342596	−	0.593393i	−0.642318	−	0.766438i	$-0.722027\pi$
$641$	8.67383	−	15.0235i	0.342596	−	0.593393i	0.984914	+	0.173045i	$0.0553606\pi$
$642$		0			0
$643$	−26.2988	−	26.2988i	−1.03712	−	1.03712i	−0.999284	−	0.0378384i	$-0.987953\pi$
$643$	−26.2988	−	26.2988i	−1.03712	−	1.03712i	−0.0378384	−	0.999284i	$-0.512047\pi$
$644$	1.64975	−	20.5220i	0.0650092	−	0.808679i
$645$		0			0
$646$	4.92751	+	8.53469i	0.193870	+	0.335793i
$647$	−6.46061	−	24.1113i	−0.253993	−	0.947914i	−0.968648	−	0.248437i	$-0.920083\pi$
$647$	−6.46061	−	24.1113i	−0.253993	−	0.947914i	0.714655	−	0.699477i	$-0.246584\pi$
$648$		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
$653$	−36.4118	−	9.75652i	−1.42490	−	0.381802i	−0.537683	−	0.843147i	$-0.680700\pi$
$653$	−36.4118	−	9.75652i	−1.42490	−	0.381802i	−0.887221	+	0.461345i	$0.847367\pi$
$654$		0			0
$655$	−0.868489	−	2.38370i	−0.0339347	−	0.0931390i
$656$	2.92588	−	1.68926i	0.114237	−	0.0659545i
$657$		0			0
$658$	9.12200	−	1.67484i	0.355613	−	0.0652922i
$659$			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	$0.499278\pi$
$662$	1.98715	−	0.532455i	0.0772327	−	0.0206944i
$663$		0			0
$664$	−7.75061			−0.300782
$665$	38.5933	+	21.9037i	1.49658	+	0.849390i
$666$		0			0
$667$	16.3195	−	60.9051i	0.631893	−	2.35826i
$668$	14.4507	−	3.87205i	0.559114	−	0.149814i
$669$		0			0
$670$	5.22491	+	0.919514i	0.201856	+	0.0355239i
$671$		−	30.9141i		−	1.19342i
$672$		0			0
$673$	−20.6481	+	20.6481i	−0.795927	+	0.795927i	−0.982450	−	0.186524i	$-0.940278\pi$
$673$	−20.6481	+	20.6481i	−0.795927	+	0.795927i	0.186524	+	0.982450i	$0.440278\pi$
$674$	16.0554	−	9.26962i	0.618433	−	0.357052i
$675$		0			0
$676$	−6.42941	+	11.1361i	−0.247285	+	0.428310i
$677$	−45.6033	−	12.2194i	−1.75268	−	0.469628i	−0.767483	−	0.641070i	$-0.778491\pi$
$677$	−45.6033	−	12.2194i	−1.75268	−	0.469628i	−0.985194	+	0.171441i	$0.945158\pi$
$678$		0			0
$679$	−32.6352	−	2.62353i	−1.25243	−	0.100682i
$680$	1.88767	−	2.25115i	0.0723889	−	0.0863275i
$681$		0			0
$682$	10.2836	+	38.3789i	0.393779	+	1.46960i
$683$	−1.40443	−	5.24140i	−0.0537389	−	0.200556i	0.933837	−	0.357699i	$-0.116439\pi$
$683$	−1.40443	−	5.24140i	−0.0537389	−	0.200556i	−0.987576	+	0.157142i	$0.949772\pi$
$684$		0			0
$685$	−1.04481	−	11.8970i	−0.0399202	−	0.454561i
$686$	5.17063	+	17.7838i	0.197416	+	0.678990i
$687$		0			0
$688$	11.9066	+	3.19038i	0.453937	+	0.121632i
$689$	−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
$695$	7.17757	−	40.7848i	0.272261	−	1.54705i
$696$		0			0
$697$	4.28761	−	1.14886i	0.162405	−	0.0435162i
$698$	−6.60782	+	24.6607i	−0.250110	+	0.933422i
$699$		0			0
$700$	2.19664	−	13.0451i	0.0830252	−	0.493059i
$701$	−16.5213			−0.624002			−0.312001	−	0.950082i	$-0.600999\pi$
$701$	−16.5213			−0.624002			−0.312001	+	0.950082i	$0.600999\pi$
$702$		0			0
$703$	14.2921	−	3.82956i	0.539037	−	0.144434i
$704$	4.47905	+	2.58598i	0.168811	+	0.0974629i
$705$		0			0
$706$			29.5013i			1.11030i
$707$	4.41697	+	24.0569i	0.166117	+	0.904754i
$708$		0			0
$709$	−17.6039	+	10.1636i	−0.661129	+	0.381703i	−0.792707	−	0.609603i	$-0.791329\pi$
$709$	−17.6039	+	10.1636i	−0.661129	+	0.381703i	0.131578	+	0.991306i	$0.457996\pi$
$710$	−9.20218	−	4.28735i	−0.345352	−	0.160901i
$711$		0			0
$712$	13.1469	+	3.52269i	0.492700	+	0.132019i
$713$	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
$718$	1.37231	+	5.12154i	0.0512142	+	0.191134i
$719$	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
$725$	13.8317	−	38.0804i	0.513695	−	1.41427i
$726$		0			0
$727$	11.3764	−	11.3764i	0.421926	−	0.421926i	−0.463940	−	0.885867i	$-0.653565\pi$
$727$	11.3764	−	11.3764i	0.421926	−	0.421926i	0.885867	+	0.463940i	$0.153565\pi$
$728$	0.644337	+	0.756989i	0.0238807	+	0.0280559i
$729$		0			0
$730$	15.4456	+	2.71822i	0.571667	+	0.100606i
$731$	14.0256	+	8.09767i	0.518755	+	0.299503i
$732$		0			0
$733$	4.00892	−	14.9615i	0.148073	−	0.552616i	−0.851526	−	0.524312i	$-0.824323\pi$
$733$	4.00892	−	14.9615i	0.148073	−	0.552616i	0.999599	−	0.0283041i	$-0.00901066\pi$
$734$	10.5596			0.389761
$735$		0			0
$736$	7.78160			0.286834
$737$	−3.17592	+	11.8527i	−0.116986	+	0.436599i
$738$		0			0
$739$	−32.3862	−	18.6982i	−1.19135	−	0.687824i	−0.232734	−	0.972540i	$-0.574767\pi$
$739$	−32.3862	−	18.6982i	−1.19135	−	0.687824i	−0.958612	+	0.284716i	$0.908101\pi$
$740$	−2.53117	−	3.61234i	−0.0930475	−	0.132792i
$741$		0			0
$742$	−11.3256	−	13.3057i	−0.415777	−	0.488468i
$743$	−33.9689	+	33.9689i	−1.24620	+	1.24620i	−0.288811	+	0.957386i	$0.593260\pi$
$743$	−33.9689	+	33.9689i	−1.24620	+	1.24620i	−0.957386	+	0.288811i	$0.906740\pi$
$744$		0			0
$745$	7.57780	+	20.7985i	0.277629	+	0.761997i
$746$	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	$0.773106\pi$
$752$	0.907271	+	3.38598i	0.0330848	+	0.123474i
$753$		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	0.640630	−	0.767850i	$-0.278673\pi$
$757$	−3.50029	−	3.50029i	−0.127220	−	0.127220i	−0.767850	+	0.640630i	$0.778673\pi$
$758$	14.3393	+	3.84219i	0.520825	+	0.139555i
$759$		0			0
$760$	−7.08334	+	15.2034i	−0.256940	+	0.551485i
$761$	−3.24761	+	1.87501i	−0.117726	+	0.0679689i	−0.557707	−	0.830038i	$-0.688319\pi$
$761$	−3.24761	+	1.87501i	−0.117726	+	0.0679689i	0.439981	+	0.898007i	$0.354985\pi$
$762$		0			0
$763$	−0.0624282	−	0.340014i	−0.00226005	−	0.0123093i
$764$		−	1.81547i		−	0.0656815i
$765$		0			0
$766$	−22.2237	−	12.8309i	−0.802975	−	0.463598i
$767$	−2.44043	+	0.653911i	−0.0881188	+	0.0236114i
$768$		0			0
$769$	1.95836			0.0706204			0.0353102	−	0.999376i	$-0.488758\pi$
$769$	1.95836			0.0706204			0.0353102	+	0.999376i	$0.488758\pi$
$770$	29.6128	+	7.70096i	1.06717	+	0.277523i
$771$		0			0
$772$	−1.79837	+	6.71159i	−0.0647246	+	0.241556i
$773$	−7.46390	+	1.99995i	−0.268458	+	0.0719331i	−0.390537	−	0.920587i	$-0.627711\pi$
$773$	−7.46390	+	1.99995i	−0.268458	+	0.0719331i	0.122079	+	0.992520i	$0.461044\pi$
$774$		0			0
$775$	24.7099	+	29.4087i	0.887607	+	1.05639i
$776$		−	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
$782$	9.87546	+	2.64612i	0.353146	+	0.0946251i
$783$		0			0
$784$	−6.54344	+	2.48664i	−0.233694	+	0.0888086i
$785$	−5.72159	+	0.502478i	−0.204212	+	0.0179342i
$786$		0			0
$787$	−6.04166	−	22.5478i	−0.215362	−	0.803741i	−0.986039	−	0.166515i	$-0.946749\pi$
$787$	−6.04166	−	22.5478i	−0.215362	−	0.803741i	0.770677	−	0.637226i	$-0.219918\pi$
$788$	0.147858	+	0.551814i	0.00526723	+	0.0196576i
$789$		0			0
$790$	−26.6524	+	2.34065i	−0.948251	+	0.0832766i
$791$	−14.4678	−	1.16306i	−0.514417	−	0.0413537i
$792$		0			0
$793$	2.16929	+	0.581261i	0.0770339	+	0.0206412i
$794$	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	−0.328556	−	0.944484i	$-0.606562\pi$
$797$	17.3884	−	17.3884i	0.615928	−	0.615928i	0.944484	+	0.328556i	$0.106562\pi$
$798$		0			0
$799$			4.60559i			0.162934i
$800$	4.98126	+	0.432490i	0.176114	+	0.0152908i
$801$		0			0
$802$	−20.1933	+	5.41078i	−0.713050	+	0.191061i
$803$	−9.38847	+	35.0383i	−0.331312	+	1.23647i
$804$		0			0
$805$	44.3788	−	12.2430i	1.56415	−	0.431508i
$806$	−2.88647			−0.101672
$807$		0			0
$808$	−8.92965	+	2.39269i	−0.314144	+	0.0841747i
$809$	−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	$-0.106829\pi$
$812$	−21.0858	+	3.87146i	−0.739968	+	0.135862i
$813$		0			0
$814$	8.83539	−	5.10112i	0.309680	−	0.178794i
$815$	−10.6482	+	22.8549i	−0.372992	+	0.800573i
$816$		0			0
$817$	−89.3104	−	23.9306i	−3.12457	−	0.837227i
$818$	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	0.992232	−	0.124405i	$-0.0397021\pi$
$821$	11.1282	+	19.2747i	0.388378	+	0.672691i	−0.603853	+	0.797095i	$0.706369\pi$
$822$		0			0
$823$	13.7894	+	51.4628i	0.480669	+	1.79388i	0.598819	+	0.800885i	$0.295637\pi$
$823$	13.7894	+	51.4628i	0.480669	+	1.79388i	−0.118150	+	0.992996i	$0.537696\pi$
$824$	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	0.895351	+	0.445362i	$0.146925\pi$
$827$	38.5557	+	38.5557i	1.34071	+	1.34071i	0.445362	+	0.895351i	$0.353075\pi$
$828$		0			0
$829$	15.5028	−	26.8517i	0.538435	−	0.932597i	−0.460554	−	0.887632i	$-0.652349\pi$
$829$	15.5028	−	26.8517i	0.538435	−	0.932597i	0.998989	−	0.0449649i	$-0.0143176\pi$
$830$	−5.93289	−	16.2838i	−0.205934	−	0.565217i
$831$		0			0
$832$	−0.265680	+	0.265680i	−0.00921080	+	0.00921080i
$833$	−9.14972	+	0.930656i	−0.317019	+	0.0322453i
$834$		0			0
$835$	19.1967	+	27.3964i	0.664328	+	0.948092i
$836$	−33.5969	−	19.3972i	−1.16197	−	0.670865i
$837$		0			0
$838$	7.09032	−	26.4614i	0.244931	−	0.914095i
$839$	−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
$842$	−2.43761	+	9.09729i	−0.0840057	+	0.313513i
$843$		0			0
$844$	9.26815	+	5.35097i	0.319023	+	0.184188i
$845$	−28.3180	−	4.98360i	−0.974170	−	0.171441i
$846$		0			0
$847$	−13.9751	+	39.2551i	−0.480190	+	1.34882i
$848$	4.66990	−	4.66990i	0.160365	−	0.160365i
$849$		0			0
$850$	6.17454	+	2.24273i	0.211785	+	0.0769251i
$851$	7.67500	−	13.2935i	0.263096	−	0.455695i
$852$		0			0
$853$	−37.3879	−	37.3879i	−1.28014	−	1.28014i	−0.940588	−	0.339550i	$-0.889725\pi$
$853$	−37.3879	−	37.3879i	−1.28014	−	1.28014i	−0.339550	−	0.940588i	$-0.610275\pi$
$854$	−8.97915	+	13.0179i	−0.307260	+	0.445464i
$855$		0			0
$856$	−2.93063	−	5.07600i	−0.100167	−	0.173494i
$857$	−8.63985	−	32.2444i	−0.295132	−	1.10145i	−0.941113	−	0.338093i	$-0.890218\pi$
$857$	−8.63985	−	32.2444i	−0.295132	−	1.10145i	0.645981	−	0.763353i	$-0.276448\pi$
$858$		0			0
$859$	−24.5307	−	42.4884i	−0.836977	−	1.44969i	−0.892411	−	0.451224i	$-0.850987\pi$
$859$	−24.5307	−	42.4884i	−0.836977	−	1.44969i	0.0554337	−	0.998462i	$-0.482346\pi$
$860$	2.41136	+	27.4576i	0.0822267	+	0.936296i
$861$		0			0
$862$	−6.34722	−	6.34722i	−0.216187	−	0.216187i
$863$	34.1092	+	9.13954i	1.16109	+	0.311113i	0.787402	−	0.616440i	$-0.211426\pi$
$863$	34.1092	+	9.13954i	1.16109	+	0.311113i	0.373690	+	0.927554i	$0.378093\pi$
$864$		0			0
$865$	−35.5843	−	16.5789i	−1.20990	−	0.563701i
$866$	13.2071	−	7.62512i	0.448795	−	0.259112i
$867$		0			0
$868$	6.81692	−	19.1483i	0.231381	−	0.649935i
$869$		−	61.8836i		−	2.09926i
$870$		0			0
$871$	−0.772008	−	0.445719i	−0.0261585	−	0.0151026i
$872$	0.126209	−	0.0338176i	0.00427398	−	0.00114521i
$873$		0			0
$874$	−58.3689			−1.97436
$875$	29.0888	−	5.37062i	0.983380	−	0.181560i
$876$		0			0
$877$	2.58487	−	9.64685i	0.0872847	−	0.325751i	−0.908452	−	0.417988i	$-0.862735\pi$
$877$	2.58487	−	9.64685i	0.0872847	−	0.325751i	0.995737	+	0.0922375i	$0.0294019\pi$
$878$	5.59624	−	1.49951i	0.188864	−	0.0506059i
$879$		0			0
$880$	−2.00446	+	11.3898i	−0.0675703	+	0.383951i
$881$			55.0348i			1.85417i	0.374852	+	0.927085i	$0.377694\pi$
$881$			55.0348i			1.85417i	−0.374852	+	0.927085i	$0.622306\pi$
$882$		0			0
$883$	−30.2776	+	30.2776i	−1.01892	+	1.01892i	−0.0191057	+	0.999817i	$0.506082\pi$
$883$	−30.2776	+	30.2776i	−1.01892	+	1.01892i	−0.999817	+	0.0191057i	$0.993918\pi$
$884$	−0.427513	+	0.246825i	−0.0143788	+	0.00830162i
$885$		0			0
$886$	10.5887	−	18.3401i	0.355734	−	0.616149i
$887$	−4.24066	−	1.13628i	−0.142387	−	0.0381526i	0.186921	−	0.982375i	$-0.440149\pi$
$887$	−4.24066	−	1.13628i	−0.142387	−	0.0381526i	−0.329309	+	0.944222i	$0.606816\pi$
$888$		0			0
$889$	2.72172	−	33.8567i	0.0912835	−	1.13552i
$890$	2.66254	+	30.3176i	0.0892484	+	1.01625i
$891$		0			0
$892$	−3.08987	−	11.5315i	−0.103456	−	0.386105i
$893$	−6.80533	−	25.3979i	−0.227732	−	0.849907i
$894$		0			0
$895$	2.81771	−	3.36027i	0.0941858	−	0.112322i
$896$	−1.13502	−	2.38992i	−0.0379183	−	0.0798417i
$897$		0			0
$898$	13.8316	+	3.70617i	0.461567	+	0.123676i
$899$	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
$905$	55.8532	+	9.82942i	1.85662	+	0.326741i
$906$		0			0
$907$	29.9158	−	8.01591i	0.993337	−	0.266164i	0.274685	−	0.961534i	$-0.411426\pi$
$907$	29.9158	−	8.01591i	0.993337	−	0.266164i	0.718652	+	0.695370i	$0.244760\pi$
$908$	−4.63445	+	17.2960i	−0.153800	+	0.573988i
$909$		0			0
$910$	−1.09718	+	1.93319i	−0.0363713	+	0.0640845i
$911$	40.8011			1.35180			0.675901	−	0.736993i	$-0.263755\pi$
$911$	40.8011			1.35180			0.675901	+	0.736993i	$0.263755\pi$
$912$		0			0
$913$	38.7200	−	10.3750i	1.28144	−	0.343362i
$914$	−28.3578	−	16.3724i	−0.937994	−	0.541551i
$915$		0			0
$916$			8.65885i			0.286097i
$917$	−2.82794	−	1.00677i	−0.0933869	−	0.0332464i
$918$		0			0
$919$	10.8623	−	6.27134i	0.358314	−	0.206873i	−0.310027	−	0.950728i	$-0.600338\pi$
$919$	10.8623	−	6.27134i	0.358314	−	0.206873i	0.668341	+	0.743855i	$0.267005\pi$
$920$	5.95661	+	16.3489i	0.196384	+	0.539006i
$921$		0			0
$922$	34.7239	+	9.30423i	1.14357	+	0.306419i
$923$	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
$928$	−2.09719	−	7.82681i	−0.0688436	−	0.256928i
$929$	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
$935$	−6.41691	+	13.7730i	−0.209855	+	0.450424i
$936$		0			0
$937$	−2.47704	+	2.47704i	−0.0809213	+	0.0809213i	−0.746409	−	0.665488i	$-0.768224\pi$
$937$	−2.47704	+	2.47704i	−0.0809213	+	0.0809213i	0.665488	+	0.746409i	$0.268224\pi$
$938$	4.78005	−	4.06871i	0.156074	−	0.132848i
$939$		0			0
$940$	−6.41933	+	4.49802i	−0.209375	+	0.146709i
$941$	−35.9162	−	20.7362i	−1.17083	−	0.675981i	−0.216958	−	0.976181i	$-0.569613\pi$
$941$	−35.9162	−	20.7362i	−1.17083	−	0.675981i	−0.953876	+	0.300200i	$0.902947\pi$
$942$		0			0
$943$	−6.80443	+	25.3945i	−0.221583	+	0.826957i
$944$	6.72432			0.218858
$945$		0			0
$946$	−63.7531			−2.07279
$947$	11.1457	−	41.5961i	0.362185	−	1.35169i	−0.509012	−	0.860759i	$-0.669989\pi$
$947$	11.1457	−	41.5961i	0.362185	−	1.35169i	0.871197	−	0.490933i	$-0.163344\pi$
$948$		0			0
$949$	−2.28217	−	1.31761i	−0.0740824	−	0.0427715i
$950$	−37.3639	−	3.24406i	−1.21224	−	0.105251i
$951$		0			0
$952$	−0.627738	−	3.41896i	−0.0203451	−	0.110809i
$953$	10.9239	−	10.9239i	0.353859	−	0.353859i	−0.507684	−	0.861543i	$-0.669498\pi$
$953$	10.9239	−	10.9239i	0.353859	−	0.353859i	0.861543	+	0.507684i	$0.169498\pi$
$954$		0			0
$955$	3.81424	−	1.38970i	0.123426	−	0.0449695i
$956$	−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
$962$	0.191827	+	0.715909i	0.00618476	+	0.0230818i
$963$		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	0.691729	−	0.722157i	$-0.256849\pi$
$967$	−0.946186	−	0.946186i	−0.0304273	−	0.0304273i	−0.722157	+	0.691729i	$0.756849\pi$
$968$	−15.2126	−	4.07620i	−0.488951	−	0.131014i
$969$		0			0
$970$	25.9989	−	9.47255i	0.834775	−	0.304145i
$971$	43.9590	−	25.3797i	1.41071	−	0.814474i	0.415256	−	0.909705i	$-0.363692\pi$
$971$	43.9590	−	25.3797i	1.41071	−	0.814474i	0.995455	+	0.0952305i	$0.0303588\pi$
$972$		0			0
$973$	−31.7596	−	37.3123i	−1.01817	−	1.19618i
$974$			23.5352i			0.754116i
$975$		0			0
$976$	−5.17644	−	2.98862i	−0.165694	−	0.0956633i
$977$	−35.6762	+	9.55940i	−1.14138	+	0.305832i	−0.779506	−	0.626394i	$-0.784530\pi$
$977$	−35.6762	+	9.55940i	−1.14138	+	0.305832i	−0.361875	+	0.932227i	$0.617863\pi$
$978$		0			0
$979$	−70.3938			−2.24980
$980$	−10.2332	−	11.8441i	−0.326887	−	0.378345i
$981$		0			0
$982$	9.59015	−	35.7909i	0.306034	−	1.14213i
$983$	18.2298	−	4.88466i	0.581440	−	0.155796i	0.0439021	−	0.999036i	$-0.486021\pi$
$983$	18.2298	−	4.88466i	0.581440	−	0.155796i	0.537538	+	0.843239i	$0.319354\pi$
$984$		0			0
$985$	−1.04616	+	0.733044i	−0.0333334	+	0.0233567i
$986$		−	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	$0.281900\pi$
$992$	7.42056	+	1.98833i	0.235603	+	0.0631296i
$993$		0			0
$994$	−10.8504	+	5.15307i	−0.344155	+	0.163445i
$995$	−4.93257	−	4.13615i	−0.156373	−	0.131125i
$996$		0			0
$997$	−14.9857	−	55.9272i	−0.474600	−	1.77123i	−0.622912	−	0.782292i	$-0.714050\pi$
$997$	−14.9857	−	55.9272i	−0.474600	−	1.77123i	0.148311	−	0.988941i	$-0.452616\pi$
$998$	4.96829	+	18.5419i	0.157268	+	0.586934i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bv.d.73.1	✓	32	15.8	even	4	inner
630.2.bv.d.73.8	yes	32	5.3	odd	4	inner
630.2.bv.d.397.1	yes	32	21.5	even	6	inner
630.2.bv.d.397.8	yes	32	7.5	odd	6	inner
630.2.bv.d.523.3	yes	32	35.33	even	12	inner
630.2.bv.d.523.6	yes	32	105.68	odd	12	inner
630.2.bv.d.577.3	yes	32	1.1	even	1	trivial
630.2.bv.d.577.6	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.387562 - 2.20223i) q^{5} +(-1.71490 - 2.01472i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.02688 + 0.944334i) q^{10} +(-2.58598 + 4.47905i) q^{11} +(-0.265680 - 0.265680i) q^{13} +(2.38992 - 1.13502i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.340048 + 1.26908i) q^{17} +(-3.75044 - 6.49596i) q^{19} +(-1.43675 + 1.71340i) q^{20} +(-3.65713 - 3.65713i) q^{22} +(-7.51645 - 2.01403i) q^{23} +(-4.69959 - 1.70700i) q^{25} +(0.325390 - 0.187864i) q^{26} +(0.477786 + 2.60225i) q^{28} +8.10291i q^{29} +(-6.65309 - 3.84116i) q^{31} +(-0.965926 + 0.258819i) q^{32} -1.31385 q^{34} +(-5.10151 + 2.99577i) q^{35} +(-0.510547 + 1.90539i) q^{37} +(7.24530 - 1.94137i) q^{38} +(-1.28316 - 1.83126i) q^{40} -3.37852i q^{41} +(8.71627 - 8.71627i) q^{43} +(4.47905 - 2.58598i) q^{44} +(3.89080 - 6.73906i) q^{46} +(3.38598 + 0.907271i) q^{47} +(-1.11822 + 6.91011i) q^{49} +(2.86518 - 4.09765i) q^{50} +(0.0972457 + 0.362926i) q^{52} +(-1.70930 - 6.37920i) q^{53} +(8.86165 + 7.43083i) q^{55} +(-2.63724 - 0.212006i) q^{56} +(-7.82681 - 2.09719i) q^{58} +(3.36216 - 5.82343i) q^{59} +(-5.17644 + 2.98862i) q^{61} +(5.43223 - 5.43223i) q^{62} -1.00000i q^{64} +(-0.688055 + 0.482120i) q^{65} +(2.29172 - 0.614064i) q^{67} +(0.340048 - 1.26908i) q^{68} +(-1.57332 - 5.70304i) q^{70} -4.54008 q^{71} +(6.77465 - 1.81526i) q^{73} +(-1.70832 - 0.986302i) q^{74} +7.50089i q^{76} +(13.4588 - 2.47109i) q^{77} +(-10.3622 + 5.98260i) q^{79} +(2.10096 - 0.765474i) q^{80} +(3.26340 + 0.874425i) q^{82} +(-5.48051 - 5.48051i) q^{83} +(2.92659 - 0.257017i) q^{85} +(6.16333 + 10.6752i) q^{86} +(1.33860 + 4.99573i) q^{88} +(6.80532 + 11.7872i) q^{89} +(-0.0796568 + 0.990888i) q^{91} +(5.50242 + 5.50242i) q^{92} +(-1.75271 + 3.03579i) q^{94} +(-15.7591 + 5.74173i) q^{95} +(8.75027 - 8.75027i) q^{97} +(-6.38523 - 2.86859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{7} + 12 q^{10} + 16 q^{16} + 8 q^{22} + 20 q^{28} + 48 q^{31} + 32 q^{37} + 80 q^{43} + 8 q^{46} - 28 q^{58} + 48 q^{61} + 16 q^{67} - 60 q^{70} - 24 q^{73} + 48 q^{82} - 144 q^{85} + 4 q^{88}+ \cdots - 32 q^{91}+O(q^{100}) \) 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

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