LMFDB - Embedded newform 325.2.x.c.93.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(7,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.7
Character	$\chi$	$=$	325.93
Dual form			325.2.x.c.7.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10480 - 0.637857i) q^{2} +(-0.381652 + 1.42434i) q^{3} +(-0.186277 + 0.322641i) q^{4} +(0.486878 + 1.81705i) q^{6} +(0.0287274 - 0.0497573i) q^{7} +3.02670i q^{8} +(0.714982 + 0.412795i) q^{9} +(-0.181334 + 0.676748i) q^{11} +(-0.388459 - 0.388459i) q^{12} +(-2.57529 + 2.52346i) q^{13} -0.0732958i q^{14} +(1.55805 + 2.69862i) q^{16} +(-1.30506 + 0.349689i) q^{17} +1.05322 q^{18} +(3.88248 - 1.04031i) q^{19} +(0.0599076 + 0.0599076i) q^{21} +(0.231330 + 0.863337i) q^{22} +(2.25440 + 0.604066i) q^{23} +(-4.31106 - 1.15514i) q^{24} +(-1.23558 + 4.43059i) q^{26} +(-3.98891 + 3.98891i) q^{27} +(0.0107025 + 0.0185373i) q^{28} +(7.78617 - 4.49535i) q^{29} +(3.85405 - 3.85405i) q^{31} +(-1.79973 - 1.03908i) q^{32} +(-0.894715 - 0.516564i) q^{33} +(-1.21878 + 1.21878i) q^{34} +(-0.266369 + 0.153788i) q^{36} +(-1.96095 - 3.39647i) q^{37} +(3.62580 - 3.62580i) q^{38} +(-2.61141 - 4.63119i) q^{39} +(-8.25736 - 2.21255i) q^{41} +(0.104398 + 0.0279735i) q^{42} +(-1.80016 - 6.71830i) q^{43} +(-0.184569 - 0.184569i) q^{44} +(2.87597 - 0.770615i) q^{46} +6.66428 q^{47} +(-4.43839 + 1.18926i) q^{48} +(3.49835 + 6.05932i) q^{49} -1.99231i q^{51} +(-0.334455 - 1.30096i) q^{52} +(-3.35108 - 3.35108i) q^{53} +(-1.86260 + 6.95130i) q^{54} +(0.150600 + 0.0869492i) q^{56} +5.92701i q^{57} +(5.73478 - 9.93293i) q^{58} +(-0.783616 - 2.92449i) q^{59} +(3.32298 - 5.75557i) q^{61} +(1.79963 - 6.71629i) q^{62} +(0.0410791 - 0.0237170i) q^{63} -8.88332 q^{64} -1.31798 q^{66} +(13.2550 - 7.65276i) q^{67} +(0.130278 - 0.486205i) q^{68} +(-1.72079 + 2.98050i) q^{69} +(-1.68888 - 6.30298i) q^{71} +(-1.24941 + 2.16403i) q^{72} +8.03602i q^{73} +(-4.33293 - 2.50162i) q^{74} +(-0.387571 + 1.44643i) q^{76} +(0.0284639 + 0.0284639i) q^{77} +(-5.83912 - 3.45083i) q^{78} +15.0122i q^{79} +(-2.92082 - 5.05900i) q^{81} +(-10.5340 + 2.82259i) q^{82} +12.7028 q^{83} +(-0.0304881 + 0.00816925i) q^{84} +(-6.27414 - 6.27414i) q^{86} +(3.43131 + 12.8058i) q^{87} +(-2.04831 - 0.548844i) q^{88} +(-12.8161 - 3.43407i) q^{89} +(0.0515791 + 0.200632i) q^{91} +(-0.614840 + 0.614840i) q^{92} +(4.01859 + 6.96040i) q^{93} +(7.36270 - 4.25086i) q^{94} +(2.16687 - 2.16687i) q^{96} +(-1.42718 - 0.823984i) q^{97} +(7.72996 + 4.46289i) q^{98} +(-0.409009 + 0.409009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{4} - 12 q^{6} - 24 q^{9} + 8 q^{11} - 32 q^{16} + 24 q^{19} + 32 q^{21} - 56 q^{24} + 76 q^{26} + 36 q^{29} + 8 q^{31} - 44 q^{34} - 60 q^{36} - 44 q^{39} - 52 q^{41} + 80 q^{44} - 60 q^{46}+ \cdots - 208 q^{99}+O(q^{100}) $ 40 * q + 24 * q^4 - 12 * q^6 - 24 * q^9 + 8 * q^11 - 32 * q^16 + 24 * q^19 + 32 * q^21 - 56 * q^24 + 76 * q^26 + 36 * q^29 + 8 * q^31 - 44 * q^34 - 60 * q^36 - 44 * q^39 - 52 * q^41 + 80 * q^44 - 60 * q^46 - 28 * q^49 + 68 * q^54 + 72 * q^56 + 72 * q^59 - 144 * q^64 + 24 * q^66 + 80 * q^69 - 52 * q^71 - 168 * q^74 + 8 * q^76 - 20 * q^81 + 248 * q^84 - 168 * q^86 - 60 * q^89 - 100 * q^91 + 156 * q^94 - 36 * q^96 - 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	1.10480	−	0.637857i	0.781212	−	0.451033i	−0.0556477	−	0.998450i	$-0.517722\pi$
$2$	1.10480	−	0.637857i	0.781212	−	0.451033i	0.836860	+	0.547418i	$0.184389\pi$
$3$	−0.381652	+	1.42434i	−0.220347	+	0.822345i	0.763869	+	0.645371i	$0.223297\pi$
$3$	−0.381652	+	1.42434i	−0.220347	+	0.822345i	−0.984216	+	0.176973i	$0.943369\pi$
$4$	−0.186277	+	0.322641i	−0.0931385	+	0.161321i
$5$		0			0
$5$		0			0
$6$	0.486878	+	1.81705i	0.198767	+	0.741809i
$7$	0.0287274	−	0.0497573i	0.0108579	−	0.0188065i	−0.860545	−	0.509374i	$-0.829877\pi$
$7$	0.0287274	−	0.0497573i	0.0108579	−	0.0188065i	0.871403	+	0.490567i	$0.163210\pi$
$8$			3.02670i			1.07010i
$9$	0.714982	+	0.412795i	0.238327	+	0.137598i
$10$		0			0
$11$	−0.181334	+	0.676748i	−0.0546743	+	0.204047i	−0.987860	−	0.155348i	$-0.950350\pi$
$11$	−0.181334	+	0.676748i	−0.0546743	+	0.204047i	0.933186	+	0.359395i	$0.117017\pi$
$12$	−0.388459	−	0.388459i	−0.112138	−	0.112138i
$13$	−2.57529	+	2.52346i	−0.714258	+	0.699882i
$13$	−2.57529	+	2.52346i	−0.714258	+	0.699882i
$14$		−	0.0732958i		−	0.0195891i
$15$		0			0
$16$	1.55805	+	2.69862i	0.389512	+	0.674654i
$17$	−1.30506	+	0.349689i	−0.316523	+	0.0848122i	−0.413583	−	0.910466i	$-0.635723\pi$
$17$	−1.30506	+	0.349689i	−0.316523	+	0.0848122i	0.0970598	+	0.995279i	$0.469056\pi$
$18$	1.05322			0.248245
$19$	3.88248	−	1.04031i	0.890702	−	0.238663i	0.215683	−	0.976463i	$-0.430802\pi$
$19$	3.88248	−	1.04031i	0.890702	−	0.238663i	0.675019	+	0.737801i	$0.264136\pi$
$20$		0			0
$21$	0.0599076	+	0.0599076i	0.0130729	+	0.0130729i
$22$	0.231330	+	0.863337i	0.0493198	+	0.184064i
$23$	2.25440	+	0.604066i	0.470076	+	0.125956i	0.486078	−	0.873916i	$-0.338427\pi$
$23$	2.25440	+	0.604066i	0.470076	+	0.125956i	−0.0160022	+	0.999872i	$0.505094\pi$
$24$	−4.31106	−	1.15514i	−0.879991	−	0.235793i
$25$		0			0
$26$	−1.23558	+	4.43059i	−0.242317	+	0.868910i
$27$	−3.98891	+	3.98891i	−0.767666	+	0.767666i
$28$	0.0107025	+	0.0185373i	0.00202258	+	0.00350322i
$29$	7.78617	−	4.49535i	1.44586	−	0.834765i	0.447625	−	0.894221i	$-0.352270\pi$
$29$	7.78617	−	4.49535i	1.44586	−	0.834765i	0.998231	+	0.0594560i	$0.0189366\pi$
$30$		0			0
$31$	3.85405	−	3.85405i	0.692208	−	0.692208i	−0.270509	−	0.962717i	$-0.587192\pi$
$31$	3.85405	−	3.85405i	0.692208	−	0.692208i	0.962717	+	0.270509i	$0.0871921\pi$
$32$	−1.79973	−	1.03908i	−0.318151	−	0.183685i
$33$	−0.894715	−	0.516564i	−0.155750	−	0.0899222i
$34$	−1.21878	+	1.21878i	−0.209019	+	0.209019i
$35$		0			0
$36$	−0.266369	+	0.153788i	−0.0443949	+	0.0256314i
$37$	−1.96095	−	3.39647i	−0.322379	−	0.558377i	0.658600	−	0.752494i	$-0.271149\pi$
$37$	−1.96095	−	3.39647i	−0.322379	−	0.558377i	−0.980978	+	0.194117i	$0.937816\pi$
$38$	3.62580	−	3.62580i	0.588182	−	0.588182i
$39$	−2.61141	−	4.63119i	−0.418160	−	0.741583i
$40$		0			0
$41$	−8.25736	−	2.21255i	−1.28958	−	0.345543i	−0.452081	−	0.891977i	$-0.649318\pi$
$41$	−8.25736	−	2.21255i	−1.28958	−	0.345543i	−0.837502	+	0.546434i	$0.815985\pi$
$42$	0.104398	+	0.0279735i	0.0161090	+	0.00431640i
$43$	−1.80016	−	6.71830i	−0.274522	−	1.02453i	−0.956161	−	0.292842i	$-0.905399\pi$
$43$	−1.80016	−	6.71830i	−0.274522	−	1.02453i	0.681638	−	0.731689i	$-0.261268\pi$
$44$	−0.184569	−	0.184569i	−0.0278247	−	0.0278247i
$45$		0			0
$46$	2.87597	−	0.770615i	0.424039	−	0.113621i
$47$	6.66428			0.972086			0.486043	−	0.873935i	$-0.338440\pi$
$47$	6.66428			0.972086			0.486043	+	0.873935i	$0.338440\pi$
$48$	−4.43839	+	1.18926i	−0.640626	+	0.171655i
$49$	3.49835	+	6.05932i	0.499764	+	0.865617i
$50$		0			0
$51$		−	1.99231i		−	0.278979i
$52$	−0.334455	−	1.30096i	−0.0463805	−	0.180411i
$53$	−3.35108	−	3.35108i	−0.460307	−	0.460307i	0.438449	−	0.898756i	$-0.355528\pi$
$53$	−3.35108	−	3.35108i	−0.460307	−	0.460307i	−0.898756	+	0.438449i	$0.855528\pi$
$54$	−1.86260	+	6.95130i	−0.253467	+	0.945952i
$55$		0			0
$56$	0.150600	+	0.0869492i	0.0201248	+	0.0116191i
$57$			5.92701i			0.785052i
$58$	5.73478	−	9.93293i	0.753013	−	1.30426i
$59$	−0.783616	−	2.92449i	−0.102018	−	0.380737i	0.895972	−	0.444111i	$-0.146480\pi$
$59$	−0.783616	−	2.92449i	−0.102018	−	0.380737i	−0.997990	+	0.0633744i	$0.979814\pi$
$60$		0			0
$61$	3.32298	−	5.75557i	0.425464	−	0.736925i	−0.571000	−	0.820950i	$-0.693444\pi$
$61$	3.32298	−	5.75557i	0.425464	−	0.736925i	0.996464	+	0.0840254i	$0.0267777\pi$
$62$	1.79963	−	6.71629i	0.228553	−	0.852970i
$63$	0.0410791	−	0.0237170i	0.00517548	−	0.00298806i
$64$	−8.88332			−1.11042
$65$		0			0
$66$	−1.31798			−0.162232
$67$	13.2550	−	7.65276i	1.61935	−	0.934933i	0.632265	−	0.774753i	$-0.282126\pi$
$67$	13.2550	−	7.65276i	1.61935	−	0.934933i	0.987088	−	0.160181i	$-0.0512078\pi$
$68$	0.130278	−	0.486205i	0.0157986	−	0.0589610i
$69$	−1.72079	+	2.98050i	−0.207159	+	0.358810i
$70$		0			0
$71$	−1.68888	−	6.30298i	−0.200433	−	0.748026i	−0.990793	−	0.135384i	$-0.956773\pi$
$71$	−1.68888	−	6.30298i	−0.200433	−	0.748026i	0.790360	−	0.612642i	$-0.209893\pi$
$72$	−1.24941	+	2.16403i	−0.147244	+	0.255034i
$73$			8.03602i			0.940546i	0.882521	+	0.470273i	$0.155844\pi$
$73$			8.03602i			0.940546i	−0.882521	+	0.470273i	$0.844156\pi$
$74$	−4.33293	−	2.50162i	−0.503692	−	0.290807i
$75$		0			0
$76$	−0.387571	+	1.44643i	−0.0444574	+	0.165917i
$77$	0.0284639	+	0.0284639i	0.00324376	+	0.00324376i
$78$	−5.83912	−	3.45083i	−0.661150	−	0.390730i
$79$			15.0122i			1.68901i	0.535551	+	0.844503i	$0.320104\pi$
$79$			15.0122i			1.68901i	−0.535551	+	0.844503i	$0.679896\pi$
$80$		0			0
$81$	−2.92082	−	5.05900i	−0.324535	−	0.562111i
$82$	−10.5340	+	2.82259i	−1.16329	+	0.311702i
$83$	12.7028			1.39432			0.697159	−	0.716916i	$-0.254447\pi$
$83$	12.7028			1.39432			0.697159	+	0.716916i	$0.254447\pi$
$84$	−0.0304881	+	0.00816925i	−0.00332652	+	0.000891339i
$85$		0			0
$86$	−6.27414	−	6.27414i	−0.676558	−	0.676558i
$87$	3.43131	+	12.8058i	0.367875	+	1.37293i
$88$	−2.04831	−	0.548844i	−0.218351	−	0.0585069i
$89$	−12.8161	−	3.43407i	−1.35851	−	0.364011i	−0.495240	−	0.868756i	$-0.664920\pi$
$89$	−12.8161	−	3.43407i	−1.35851	−	0.364011i	−0.863268	+	0.504745i	$0.831586\pi$
$90$		0			0
$91$	0.0515791	+	0.200632i	0.00540696	+	0.0210320i
$92$	−0.614840	+	0.614840i	−0.0641015	+	0.0641015i
$93$	4.01859	+	6.96040i	0.416708	+	0.721759i
$94$	7.36270	−	4.25086i	0.759405	−	0.438443i
$95$		0			0
$96$	2.16687	−	2.16687i	0.221156	−	0.221156i
$97$	−1.42718	−	0.823984i	−0.144908	−	0.0836629i	0.425793	−	0.904821i	$-0.359995\pi$
$97$	−1.42718	−	0.823984i	−0.144908	−	0.0836629i	−0.570701	+	0.821158i	$0.693329\pi$
$98$	7.72996	+	4.46289i	0.780844	+	0.450820i
$99$	−0.409009	+	0.409009i	−0.0411069	+	0.0411069i
$100$		0			0
$101$	−14.5474	+	8.39894i	−1.44752	+	0.835725i	−0.998333	−	0.0577129i	$-0.981619\pi$
$101$	−14.5474	+	8.39894i	−1.44752	+	0.835725i	−0.449186	+	0.893438i	$0.648286\pi$
$102$	−1.27081	−	2.20111i	−0.125829	−	0.217942i
$103$	0.243419	−	0.243419i	0.0239848	−	0.0239848i	−0.695013	−	0.718997i	$-0.744601\pi$
$103$	0.243419	−	0.243419i	0.0239848	−	0.0239848i	0.718997	+	0.695013i	$0.244601\pi$
$104$	−7.63776	−	7.79464i	−0.748944	−	0.764328i
$105$		0			0
$106$	−5.83979	−	1.56477i	−0.567211	−	0.151984i
$107$	5.99327	+	1.60589i	0.579392	+	0.155248i	0.536600	−	0.843837i	$-0.319708\pi$
$107$	5.99327	+	1.60589i	0.579392	+	0.155248i	0.0427913	+	0.999084i	$0.486375\pi$
$108$	−0.543945	−	2.03003i	−0.0523411	−	0.195340i
$109$	8.07848	+	8.07848i	0.773778	+	0.773778i	0.978765	−	0.204986i	$-0.0657150\pi$
$109$	8.07848	+	8.07848i	0.773778	+	0.773778i	−0.204986	+	0.978765i	$0.565715\pi$
$110$		0			0
$111$	5.58614	−	1.49680i	0.530213	−	0.142070i
$112$	0.179034			0.0169172
$113$	−15.8437	+	4.24531i	−1.49045	+	0.399365i	−0.909889	−	0.414852i	$-0.863833\pi$
$113$	−15.8437	+	4.24531i	−1.49045	+	0.399365i	−0.580561	+	0.814217i	$0.697167\pi$
$114$	3.78059	+	6.54817i	0.354084	+	0.613292i
$115$		0			0
$116$			3.34952i			0.310995i
$117$	−2.88296	+	0.741161i	−0.266530	+	0.0685203i
$118$	−2.73115	−	2.73115i	−0.251423	−	0.251423i
$119$	−0.0200913	+	0.0749818i	−0.00184177	+	0.00687357i
$120$		0			0
$121$	9.10117	+	5.25457i	0.827379	+	0.477688i
$122$		−	8.47834i		−	0.767593i
$123$	6.30287	−	10.9169i	0.568311	−	0.984343i
$124$	0.525555	+	1.96140i	0.0471962	+	0.176139i
$125$		0			0
$126$	0.0302561	−	0.0524052i	0.00269543	−	0.00466862i
$127$	−1.53945	+	5.74529i	−0.136604	+	0.509812i	0.863382	+	0.504550i	$0.168342\pi$
$127$	−1.53945	+	5.74529i	−0.136604	+	0.509812i	−0.999986	+	0.00526200i	$0.998325\pi$
$128$	−6.21483	+	3.58813i	−0.549318	+	0.317149i
$129$	10.2562			0.903008
$130$		0			0
$131$	6.72010			0.587138			0.293569	−	0.955938i	$-0.405157\pi$
$131$	6.72010			0.587138			0.293569	+	0.955938i	$0.405157\pi$
$132$	0.333330	−	0.192448i	0.0290126	−	0.0167504i
$133$	0.0597706	−	0.223067i	0.00518277	−	0.0193423i
$134$	9.76273	−	16.9095i	0.843372	−	1.46076i
$135$		0			0
$136$	−1.05841	−	3.95002i	−0.0907575	−	0.338712i
$137$	5.35943	−	9.28281i	0.457887	−	0.793084i	−0.540962	−	0.841047i	$-0.681940\pi$
$137$	5.35943	−	9.28281i	0.457887	−	0.793084i	0.998849	+	0.0479633i	$0.0152730\pi$
$138$			4.39048i			0.373742i
$139$	−16.0903	−	9.28976i	−1.36476	−	0.787947i	−0.374511	−	0.927223i	$-0.622189\pi$
$139$	−16.0903	−	9.28976i	−1.36476	−	0.787947i	−0.990254	+	0.139275i	$0.955523\pi$
$140$		0			0
$141$	−2.54343	+	9.49222i	−0.214196	+	0.799389i
$142$	−5.88627	−	5.88627i	−0.493965	−	0.493965i
$143$	−1.24076	−	2.20041i	−0.103757	−	0.184008i
$144$			2.57262i			0.214385i
$145$		0			0
$146$	5.12583	+	8.87820i	0.424217	+	0.734765i
$147$	−9.96570	+	2.67030i	−0.821957	+	0.220243i
$148$	1.46112			0.120104
$149$	15.3810	−	4.12133i	1.26006	−	0.337632i	0.433846	−	0.900987i	$-0.357156\pi$
$149$	15.3810	−	4.12133i	1.26006	−	0.337632i	0.826215	+	0.563355i	$0.190490\pi$
$150$		0			0
$151$	11.5286	+	11.5286i	0.938183	+	0.938183i	0.998198	−	0.0600146i	$-0.0191147\pi$
$151$	11.5286	+	11.5286i	0.938183	+	0.938183i	−0.0600146	+	0.998198i	$0.519115\pi$
$152$	3.14870	+	11.7511i	0.255393	+	0.953140i
$153$	−1.07744	−	0.288700i	−0.0871061	−	0.0233400i
$154$	0.0496028	+	0.0132910i	0.00399711	+	0.00107102i
$155$		0			0
$156$	1.98066	+	0.0201348i	0.158580	+	0.00161208i
$157$	−4.09090	+	4.09090i	−0.326489	+	0.326489i	−0.851250	−	0.524761i	$-0.824155\pi$
$157$	−4.09090	+	4.09090i	−0.326489	+	0.326489i	0.524761	+	0.851250i	$0.324155\pi$
$158$	9.57564	+	16.5855i	0.761797	+	1.31947i
$159$	6.05204	−	3.49415i	0.479958	−	0.277104i
$160$		0			0
$161$	0.0948197	−	0.0948197i	0.00747284	−	0.00747284i
$162$	−6.45384	−	3.72613i	−0.507062	−	0.292752i
$163$	−0.0172791	−	0.00997608i	−0.00135340	−	0.000781387i	0.499323	−	0.866416i	$-0.333582\pi$
$163$	−0.0172791	−	0.00997608i	−0.00135340	−	0.000781387i	−0.500677	+	0.865634i	$0.666915\pi$
$164$	2.25202	−	2.25202i	0.175853	−	0.175853i
$165$		0			0
$166$	14.0341	−	8.10260i	1.08926	−	0.628884i
$167$	−5.20569	−	9.01652i	−0.402828	−	0.697719i	0.591238	−	0.806497i	$-0.298640\pi$
$167$	−5.20569	−	9.01652i	−0.402828	−	0.697719i	−0.994066	+	0.108778i	$0.965306\pi$
$168$	−0.181322	+	0.181322i	−0.0139893	+	0.0139893i
$169$	0.264282	−	12.9973i	0.0203294	−	0.999793i
$170$		0			0
$171$	3.20533	+	0.858867i	0.245118	+	0.0656792i
$172$	2.50293	+	0.670658i	0.190847	+	0.0511372i
$173$	−3.93459	−	14.6841i	−0.299141	−	1.11641i	−0.937873	−	0.346980i	$-0.887207\pi$
$173$	−3.93459	−	14.6841i	−0.299141	−	1.11641i	0.638731	−	0.769430i	$-0.279460\pi$
$174$	11.9592	+	11.9592i	0.906625	+	0.906625i
$175$		0			0
$176$	−2.10881	+	0.565054i	−0.158958	+	0.0425926i
$177$	4.46455			0.335576
$178$	−16.3497	+	4.38090i	−1.22546	+	0.328362i
$179$	−1.81815	−	3.14913i	−0.135895	−	0.235377i	0.790044	−	0.613050i	$-0.210058\pi$
$179$	−1.81815	−	3.14913i	−0.135895	−	0.235377i	−0.925939	+	0.377673i	$0.876724\pi$
$180$		0			0
$181$			12.2156i			0.907977i	0.891008	+	0.453989i	$0.149999\pi$
$181$			12.2156i			0.907977i	−0.891008	+	0.453989i	$0.850001\pi$
$182$	0.184959	+	0.188758i	0.0137101	+	0.0139917i
$183$	6.92968	+	6.92968i	0.512257	+	0.512257i
$184$	−1.82833	+	6.82340i	−0.134786	+	0.503028i
$185$		0			0
$186$	8.87947	+	5.12657i	0.651075	+	0.375898i
$187$		−	0.946607i		−	0.0692227i
$188$	−1.24140	+	2.15017i	−0.0905386	+	0.156818i
$189$	0.0838864	+	0.313068i	0.00610183	+	0.0227724i
$190$		0			0
$191$	1.46354	−	2.53493i	0.105898	−	0.183421i	−0.808207	−	0.588899i	$-0.799562\pi$
$191$	1.46354	−	2.53493i	0.105898	−	0.183421i	0.914105	+	0.405478i	$0.132895\pi$
$192$	3.39033	−	12.6529i	0.244676	−	0.913144i
$193$	−8.83674	+	5.10190i	−0.636083	+	0.367242i	−0.783104	−	0.621891i	$-0.786365\pi$
$193$	−8.83674	+	5.10190i	−0.636083	+	0.367242i	0.147021	+	0.989133i	$0.453031\pi$
$194$	−2.10234			−0.150939
$195$		0			0
$196$	−2.60665			−0.186189
$197$	10.6347	−	6.13993i	0.757689	−	0.437452i	−0.0707763	−	0.997492i	$-0.522548\pi$
$197$	10.6347	−	6.13993i	0.757689	−	0.437452i	0.828465	+	0.560040i	$0.189214\pi$
$198$	−0.190984	+	0.712762i	−0.0135726	+	0.0506538i
$199$	0.0397692	−	0.0688822i	0.00281916	−	0.00488293i	−0.864612	−	0.502439i	$-0.832436\pi$
$199$	0.0397692	−	0.0688822i	0.00281916	−	0.00488293i	0.867432	+	0.497557i	$0.165769\pi$
$200$		0			0
$201$	5.84138	+	21.8003i	0.412019	+	1.53768i
$202$	−10.7146	+	18.5583i	−0.753879	+	1.30576i
$203$		−	0.516558i		−	0.0362553i
$204$	0.642802	+	0.371122i	0.0450051	+	0.0259837i
$205$		0			0
$206$	0.113663	−	0.424196i	0.00791927	−	0.0295551i
$207$	1.36250	+	1.36250i	0.0947004	+	0.0947004i
$208$	−10.8223	−	3.01806i	−0.750391	−	0.209265i
$209$			2.81610i			0.194794i
$210$		0			0
$211$	−7.92558	−	13.7275i	−0.545619	−	0.945041i	−0.998568	−	0.0535038i	$-0.982961\pi$
$211$	−7.92558	−	13.7275i	−0.545619	−	0.945041i	0.452948	−	0.891537i	$-0.350372\pi$
$212$	1.70543	−	0.456968i	0.117129	−	0.0313847i
$213$	9.62217			0.659300
$214$	7.64570	−	2.04866i	0.522649	−	0.140044i
$215$		0			0
$216$	−12.0732	−	12.0732i	−0.821479	−	0.821479i
$217$	−0.0810503	−	0.302484i	−0.00550205	−	0.0205339i
$218$	14.0780	+	3.77220i	0.953485	+	0.255485i
$219$	−11.4461	−	3.06696i	−0.773453	−	0.207246i
$220$		0			0
$221$	2.47848	−	4.19382i	0.166721	−	0.282107i
$222$	5.21683	−	5.21683i	0.350131	−	0.350131i
$223$	9.53099	+	16.5082i	0.638242	+	1.10547i	0.985818	+	0.167816i	$0.0536715\pi$
$223$	9.53099	+	16.5082i	0.638242	+	1.10547i	−0.347576	+	0.937652i	$0.612995\pi$
$224$	−0.103403	+	0.0596999i	−0.00690893	+	0.00398887i
$225$		0			0
$226$	−14.7962	+	14.7962i	−0.984231	+	0.984231i
$227$	−7.13540	−	4.11962i	−0.473593	−	0.273429i	0.244150	−	0.969738i	$-0.421491\pi$
$227$	−7.13540	−	4.11962i	−0.473593	−	0.273429i	−0.717743	+	0.696309i	$0.754825\pi$
$228$	−1.91230	−	1.10407i	−0.126645	−	0.0731186i
$229$	−8.86778	+	8.86778i	−0.586000	+	0.586000i	−0.936546	−	0.350546i	$-0.885996\pi$
$229$	−8.86778	+	8.86778i	−0.586000	+	0.586000i	0.350546	+	0.936546i	$0.385996\pi$
$230$		0			0
$231$	−0.0514056	+	0.0296790i	−0.00338224	+	0.00195274i
$232$	13.6061	+	23.5664i	0.893283	+	1.54721i
$233$	−8.18840	+	8.18840i	−0.536440	+	0.536440i	−0.922481	−	0.386042i	$-0.873842\pi$
$233$	−8.18840	+	8.18840i	−0.536440	+	0.536440i	0.386042	+	0.922481i	$0.373842\pi$
$234$	−2.71234	+	2.65775i	−0.177311	+	0.173743i
$235$		0			0
$236$	1.08953	+	0.291939i	0.0709225	+	0.0190036i
$237$	−21.3825	−	5.72943i	−1.38894	−	0.372167i
$238$	0.0256308	+	0.0956554i	0.00166140	+	0.00620042i
$239$	−7.20287	−	7.20287i	−0.465915	−	0.465915i	0.434673	−	0.900588i	$-0.356864\pi$
$239$	−7.20287	−	7.20287i	−0.465915	−	0.465915i	−0.900588	+	0.434673i	$0.856864\pi$
$240$		0			0
$241$	−19.2690	+	5.16310i	−1.24122	+	0.332585i	−0.818940	−	0.573880i	$-0.805438\pi$
$241$	−19.2690	+	5.16310i	−1.24122	+	0.332585i	−0.422283	+	0.906464i	$0.638771\pi$
$242$	13.4066			0.861812
$243$	−8.02637	+	2.15066i	−0.514892	+	0.137965i
$244$	1.23799	+	2.14426i	0.0792541	+	0.137272i
$245$		0			0
$246$		−	16.0813i		−	1.02531i
$247$	−7.37335	+	12.4764i	−0.469155	+	0.793853i
$248$	11.6651	+	11.6651i	0.740732	+	0.740732i
$249$	−4.84806	+	18.0932i	−0.307233	+	1.14661i
$250$		0			0
$251$	−14.7445	−	8.51274i	−0.930664	−	0.537319i	−0.0436425	−	0.999047i	$-0.513896\pi$
$251$	−14.7445	−	8.51274i	−0.930664	−	0.537319i	−0.887022	+	0.461728i	$0.847230\pi$
$252$			0.0176718i			0.00111322i
$253$	−0.817600	+	1.41613i	−0.0514021	+	0.0890310i
$254$	1.96389	+	7.32935i	0.123226	+	0.459884i
$255$		0			0
$256$	4.30589	−	7.45802i	0.269118	−	0.466126i
$257$	−1.64915	+	6.15471i	−0.102871	+	0.383920i	−0.998095	−	0.0616965i	$-0.980349\pi$
$257$	−1.64915	+	6.15471i	−0.102871	+	0.383920i	0.895224	+	0.445617i	$0.147016\pi$
$258$	11.3311	−	6.54199i	0.705441	−	0.407286i
$259$	−0.225332			−0.0140015
$260$		0			0
$261$	7.42263			0.459449
$262$	7.42438	−	4.28647i	0.458679	−	0.264819i
$263$	6.70958	−	25.0405i	0.413730	−	1.54406i	−0.373635	−	0.927576i	$-0.621889\pi$
$263$	6.70958	−	25.0405i	0.413730	−	1.54406i	0.787366	−	0.616486i	$-0.211444\pi$
$264$	1.56348	−	2.70803i	0.0962258	−	0.166668i
$265$		0			0
$266$	−0.0762502	−	0.284569i	−0.00467520	−	0.0174481i
$267$	9.78260	−	16.9440i	0.598685	−	1.03695i
$268$			5.70214i			0.348313i
$269$	−12.5106	−	7.22300i	−0.762785	−	0.440394i	0.0675100	−	0.997719i	$-0.478495\pi$
$269$	−12.5106	−	7.22300i	−0.762785	−	0.440394i	−0.830295	+	0.557325i	$0.811828\pi$
$270$		0			0
$271$	4.84782	−	18.0923i	0.294484	−	1.09903i	−0.647143	−	0.762369i	$-0.724036\pi$
$271$	4.84782	−	18.0923i	0.294484	−	1.09903i	0.941626	−	0.336660i	$-0.109297\pi$
$272$	−2.97702	−	2.97702i	−0.180508	−	0.180508i
$273$	−0.305454	−	0.00310517i	−0.0184869	−	0.000187933i
$274$		−	13.6742i		−	0.826089i
$275$		0			0
$276$	−0.641089	−	1.11040i	−0.0385890	−	0.0668381i
$277$	1.87974	−	0.503675i	0.112943	−	0.0302629i	−0.201905	−	0.979405i	$-0.564713\pi$
$277$	1.87974	−	0.503675i	0.112943	−	0.0302629i	0.314848	+	0.949142i	$0.398047\pi$
$278$	−23.7022			−1.42156
$279$	4.34651	−	1.16464i	0.260219	−	0.0697254i
$280$		0			0
$281$	2.02512	+	2.02512i	0.120808	+	0.120808i	0.764926	−	0.644118i	$-0.222775\pi$
$281$	2.02512	+	2.02512i	0.120808	+	0.120808i	−0.644118	+	0.764926i	$0.722775\pi$
$282$	3.24469	+	12.1094i	0.193219	+	0.721102i
$283$	31.2190	+	8.36511i	1.85578	+	0.497254i	0.999805	−	0.0197668i	$-0.00629239\pi$
$283$	31.2190	+	8.36511i	1.85578	+	0.497254i	0.855973	+	0.517021i	$0.172959\pi$
$284$	2.34820	+	0.629199i	0.139340	+	0.0373361i
$285$		0			0
$286$	−2.77434	−	1.63959i	−0.164050	−	0.0969512i
$287$	−0.347303	+	0.347303i	−0.0205006	+	0.0205006i
$288$	−0.857852	−	1.48584i	−0.0505494	−	0.0875541i
$289$	−13.1415	+	7.58727i	−0.773032	+	0.446310i
$290$		0			0
$291$	1.71832	−	1.71832i	0.100730	−	0.100730i
$292$	−2.59275	−	1.49693i	−0.151729	−	0.0876010i
$293$	−17.7843	−	10.2678i	−1.03897	−	0.599851i	−0.119430	−	0.992843i	$-0.538107\pi$
$293$	−17.7843	−	10.2678i	−1.03897	−	0.599851i	−0.919542	+	0.392992i	$0.871440\pi$
$294$	−9.30684	+	9.30684i	−0.542786	+	0.542786i
$295$		0			0
$296$	10.2801	−	5.93522i	0.597519	−	0.344978i
$297$	−1.97616	−	3.42281i	−0.114668	−	0.198612i
$298$	14.3641	−	14.3641i	0.832092	−	0.832092i
$299$	−7.33009	+	4.13325i	−0.423910	+	0.239032i
$300$		0			0
$301$	−0.385998	−	0.103428i	−0.0222486	−	0.00596149i
$302$	20.0904	+	5.38320i	1.15607	+	0.309768i
$303$	−6.41093	−	23.9259i	−0.368299	−	1.37451i
$304$	8.85648	+	8.85648i	0.507954	+	0.507954i
$305$		0			0
$306$	−1.37451	+	0.368299i	−0.0785755	+	0.0210542i
$307$	−5.46579			−0.311949			−0.155975	−	0.987761i	$-0.549852\pi$
$307$	−5.46579			−0.311949			−0.155975	+	0.987761i	$0.549852\pi$
$308$	−0.0144858	+	0.00388146i	−0.000825405	+	0.000221167i
$309$	0.253811	+	0.439613i	0.0144388	+	0.0250087i
$310$		0			0
$311$		−	10.1997i		−	0.578372i	−0.957273	−	0.289186i	$-0.906615\pi$
$311$		−	10.1997i		−	0.578372i	0.957273	−	0.289186i	$-0.0933845\pi$
$312$	14.0172	−	7.90395i	0.793568	−	0.447473i
$313$	−14.2117	−	14.2117i	−0.803291	−	0.803291i	0.180318	−	0.983608i	$-0.442287\pi$
$313$	−14.2117	−	14.2117i	−0.803291	−	0.803291i	−0.983608	+	0.180318i	$0.942287\pi$
$314$	−1.91022	+	7.12904i	−0.107800	+	0.402315i
$315$		0			0
$316$	−4.84356	−	2.79643i	−0.272471	−	0.157311i
$317$		−	19.6481i		−	1.10355i	−0.833993	−	0.551775i	$-0.813951\pi$
$317$		−	19.6481i		−	1.10355i	0.833993	−	0.551775i	$-0.186049\pi$
$318$	4.45753	−	7.72067i	0.249966	−	0.432954i
$319$	1.63032	+	6.08444i	0.0912804	+	0.340663i
$320$		0			0
$321$	−4.57468	+	7.92359i	−0.255334	+	0.442251i
$322$	0.0442755	−	0.165238i	0.00246738	−	0.00920837i
$323$	−4.70308	+	2.71532i	−0.261686	+	0.151085i
$324$	2.17632			0.120907
$325$		0			0
$326$	−0.0254532			−0.00140972
$327$	−14.5897	+	8.42336i	−0.806812	+	0.465813i
$328$	6.69674	−	24.9926i	0.369765	−	1.37998i
$329$	0.191447	−	0.331597i	0.0105548	−	0.0182815i
$330$		0			0
$331$	1.15149	+	4.29744i	0.0632919	+	0.236208i	0.990324	−	0.138773i	$-0.0443158\pi$
$331$	1.15149	+	4.29744i	0.0632919	+	0.236208i	−0.927032	+	0.374981i	$0.877649\pi$
$332$	−2.36625	+	4.09846i	−0.129865	+	0.224932i
$333$		−	3.23789i		−	0.177435i
$334$	−11.5025	−	6.64097i	−0.629389	−	0.363378i
$335$		0			0
$336$	−0.0683288	+	0.255006i	−0.00372764	+	0.0139117i
$337$	−1.54472	−	1.54472i	−0.0841463	−	0.0841463i	0.663781	−	0.747927i	$-0.268951\pi$
$337$	−1.54472	−	1.54472i	−0.0841463	−	0.0841463i	−0.747927	+	0.663781i	$0.768951\pi$
$338$	−7.99845	−	14.5280i	−0.435058	−	0.790220i
$339$		−	24.1871i		−	1.31366i
$340$		0			0
$341$	1.90935	+	3.30709i	0.103397	+	0.179089i
$342$	4.08909	−	1.09567i	0.221113	−	0.0592469i
$343$	0.804177			0.0434215
$344$	20.3343	−	5.44856i	1.09635	−	0.293766i
$345$		0			0
$346$	−13.7133	−	13.7133i	−0.737230	−	0.737230i
$347$	−5.35439	−	19.9829i	−0.287439	−	1.07274i	−0.947039	−	0.321119i	$-0.895941\pi$
$347$	−5.35439	−	19.9829i	−0.287439	−	1.07274i	0.659600	−	0.751617i	$-0.270726\pi$
$348$	−4.77087	−	1.27835i	−0.255745	−	0.0685268i
$349$	16.6859	+	4.47097i	0.893175	+	0.239325i	0.676083	−	0.736826i	$-0.263676\pi$
$349$	16.6859	+	4.47097i	0.893175	+	0.239325i	0.217092	+	0.976151i	$0.430343\pi$
$350$		0			0
$351$	0.206756	−	20.3385i	0.0110358	−	1.08559i
$352$	1.02955	−	1.02955i	0.0548750	−	0.0548750i
$353$	0.622765	+	1.07866i	0.0331464	+	0.0574113i	0.882123	−	0.471020i	$-0.156114\pi$
$353$	0.622765	+	1.07866i	0.0331464	+	0.0574113i	−0.848976	+	0.528431i	$0.822781\pi$
$354$	4.93244	−	2.84774i	0.262156	−	0.151356i
$355$		0			0
$356$	3.49533	−	3.49533i	0.185252	−	0.185252i
$357$	−0.0991320	−	0.0572339i	−0.00524662	−	0.00302914i
$358$	−4.01739	−	2.31944i	−0.212326	−	0.122586i
$359$	−21.0186	+	21.0186i	−1.10932	+	1.10932i	−0.116082	+	0.993240i	$0.537033\pi$
$359$	−21.0186	+	21.0186i	−1.10932	+	1.10932i	−0.993240	+	0.116082i	$0.962967\pi$
$360$		0			0
$361$	−2.46308	+	1.42206i	−0.129636	+	0.0748454i
$362$	7.79179	+	13.4958i	0.409528	+	0.709323i
$363$	−10.9578	+	10.9578i	−0.575134	+	0.575134i
$364$	−0.0743402	−	0.0207316i	−0.00389649	−	0.00108663i
$365$		0			0
$366$	12.0761	+	3.23577i	0.631226	+	0.169136i
$367$	−21.5186	−	5.76588i	−1.12326	−	0.300977i	−0.351058	−	0.936354i	$-0.614178\pi$
$367$	−21.5186	−	5.76588i	−1.12326	−	0.300977i	−0.772202	+	0.635377i	$0.780845\pi$
$368$	1.88233	+	7.02493i	0.0981230	+	0.366200i
$369$	−4.99053	−	4.99053i	−0.259797	−	0.259797i
$370$		0			0
$371$	−0.263009	+	0.0704730i	−0.0136547	+	0.00365877i
$372$	−2.99428			−0.155246
$373$	27.0325	−	7.24333i	1.39969	−	0.375045i	0.521455	−	0.853279i	$-0.325389\pi$
$373$	27.0325	−	7.24333i	1.39969	−	0.375045i	0.878233	+	0.478233i	$0.158723\pi$
$374$	−0.603800	−	1.04581i	−0.0312217	−	0.0540776i
$375$		0			0
$376$			20.1708i			1.04023i
$377$	−8.70785	+	31.2250i	−0.448477	+	1.60817i
$378$	0.292370	+	0.292370i	0.0150379	+	0.0150379i
$379$	2.26804	−	8.46443i	0.116501	−	0.434789i	−0.882894	−	0.469573i	$-0.844408\pi$
$379$	2.26804	−	8.46443i	0.116501	−	0.434789i	0.999395	+	0.0347845i	$0.0110745\pi$
$380$		0			0
$381$	−7.59573	−	4.38540i	−0.389141	−	0.224671i
$382$		−	3.73412i		−	0.191054i
$383$	6.56975	−	11.3791i	0.335699	−	0.581447i	−0.647920	−	0.761708i	$-0.724361\pi$
$383$	6.56975	−	11.3791i	0.335699	−	0.581447i	0.983619	+	0.180261i	$0.0576943\pi$
$384$	−2.73883	−	10.2215i	−0.139765	−	0.521612i
$385$		0			0
$386$	−6.50856	+	11.2732i	−0.331277	+	0.573788i
$387$	1.48620	−	5.54656i	0.0755476	−	0.281948i
$388$	0.531703	−	0.306979i	0.0269931	−	0.0155845i
$389$	22.2271			1.12696			0.563479	−	0.826130i	$-0.309463\pi$
$389$	22.2271			1.12696			0.563479	+	0.826130i	$0.309463\pi$
$390$		0			0
$391$	−3.15336			−0.159472
$392$	−18.3397	+	10.5885i	−0.926297	+	0.534798i
$393$	−2.56474	+	9.57173i	−0.129374	+	0.482830i
$394$	7.83280	−	13.5668i	0.394611	−	0.683486i
$395$		0			0
$396$	−0.0557742	−	0.208152i	−0.00280276	−	0.0104600i
$397$	0.584332	−	1.01209i	0.0293268	−	0.0507955i	−0.850990	−	0.525183i	$-0.823997\pi$
$397$	0.584332	−	1.01209i	0.0293268	−	0.0507955i	0.880316	+	0.474387i	$0.157330\pi$
$398$		−	0.101468i		−	0.00508614i
$399$	0.294912	+	0.170268i	0.0147641	+	0.00852404i
$400$		0			0
$401$	4.15809	−	15.5182i	0.207645	−	0.774941i	−0.780982	−	0.624553i	$-0.785281\pi$
$401$	4.15809	−	15.5182i	0.207645	−	0.774941i	0.988627	−	0.150388i	$-0.0480523\pi$
$402$	20.3590	+	20.3590i	1.01542	+	1.01542i
$403$	−0.199766	+	19.6509i	−0.00995103	+	0.978880i
$404$		−	6.25812i		−	0.311353i
$405$		0			0
$406$	−0.329490	−	0.570694i	−0.0163523	−	0.0283231i
$407$	2.65414	−	0.711176i	0.131561	−	0.0352517i
$408$	6.03013			0.298536
$409$	−1.48123	+	0.396894i	−0.0732420	+	0.0196251i	−0.295254	−	0.955419i	$-0.595404\pi$
$409$	−1.48123	+	0.396894i	−0.0732420	+	0.0196251i	0.222012	+	0.975044i	$0.428738\pi$
$410$		0			0
$411$	11.1765	+	11.1765i	0.551294	+	0.551294i
$412$	0.0331937	+	0.123880i	0.00163533	+	0.00610315i
$413$	−0.168026	−	0.0450225i	−0.00826802	−	0.00221541i
$414$	2.37437	+	0.636212i	0.116694	+	0.0312681i
$415$		0			0
$416$	7.25692	−	1.86563i	0.355800	−	0.0914701i
$417$	19.3727	−	19.3727i	0.948685	−	0.948685i
$418$	1.79627	+	3.11123i	0.0878584	+	0.152175i
$419$	−25.4519	+	14.6947i	−1.24341	+	0.717882i	−0.969786	−	0.243955i	$-0.921555\pi$
$419$	−25.4519	+	14.6947i	−1.24341	+	0.717882i	−0.273622	+	0.961837i	$0.588222\pi$
$420$		0			0
$421$	−22.3691	+	22.3691i	−1.09021	+	1.09021i	−0.0946994	+	0.995506i	$0.530189\pi$
$421$	−22.3691	+	22.3691i	−1.09021	+	1.09021i	−0.995506	+	0.0946994i	$0.969811\pi$
$422$	−17.5124	−	10.1108i	−0.852489	−	0.492185i
$423$	4.76484	+	2.75098i	0.231674	+	0.133757i
$424$	10.1427	−	10.1427i	0.492574	−	0.492574i
$425$		0			0
$426$	10.6306	−	6.13757i	0.515053	−	0.297366i
$427$	−0.190921	−	0.330685i	−0.00923931	−	0.0160030i
$428$	−1.63454	+	1.63454i	−0.0790083	+	0.0790083i
$429$	3.60768	−	0.927474i	0.174181	−	0.0447789i
$430$		0			0
$431$	11.6063	+	3.10991i	0.559057	+	0.149799i	0.527273	−	0.849696i	$-0.323214\pi$
$431$	11.6063	+	3.10991i	0.559057	+	0.149799i	0.0317839	+	0.999495i	$0.489881\pi$
$432$	−16.9794	−	4.54963i	−0.816924	−	0.218894i
$433$	6.72363	+	25.0929i	0.323117	+	1.20589i	0.916191	+	0.400742i	$0.131248\pi$
$433$	6.72363	+	25.0929i	0.323117	+	1.20589i	−0.593074	+	0.805148i	$0.702086\pi$
$434$	−0.282486	−	0.282486i	−0.0135598	−	0.0135598i
$435$		0			0
$436$	−4.11129	+	1.10162i	−0.196895	+	0.0527579i
$437$	9.38108			0.448758
$438$	−14.6019	+	3.91256i	−0.697705	+	0.186950i
$439$	1.61924	+	2.80461i	0.0772823	+	0.133857i	0.902077	−	0.431576i	$-0.142042\pi$
$439$	1.61924	+	2.80461i	0.0772823	+	0.133857i	−0.824794	+	0.565433i	$0.808709\pi$
$440$		0			0
$441$			5.77640i			0.275067i
$442$	0.0631725	−	6.21425i	0.00300481	−	0.295582i
$443$	6.02880	+	6.02880i	0.286437	+	0.286437i	0.835669	−	0.549233i	$-0.185080\pi$
$443$	6.02880	+	6.02880i	0.286437	+	0.286437i	−0.549233	+	0.835669i	$0.685080\pi$
$444$	−0.557640	+	2.08114i	−0.0264644	+	0.0987666i
$445$		0			0
$446$	21.0597	+	12.1588i	0.997205	+	0.575737i
$447$			23.4807i			1.11060i
$448$	−0.255195	+	0.442010i	−0.0120568	+	0.0208830i
$449$	−1.09717	−	4.09470i	−0.0517788	−	0.193241i	0.935192	−	0.354141i	$-0.115227\pi$
$449$	−1.09717	−	4.09470i	−0.0517788	−	0.193241i	−0.986971	+	0.160900i	$0.948560\pi$
$450$		0			0
$451$	2.99468	−	5.18694i	0.141014	−	0.244244i
$452$	1.58161	−	5.90264i	0.0743925	−	0.277637i
$453$	−20.8206	+	12.0208i	−0.978235	+	0.564784i
$454$	−10.5109			−0.493302
$455$		0			0
$456$	−17.9393			−0.840085
$457$	5.69781	−	3.28963i	0.266532	−	0.153882i	−0.360779	−	0.932652i	$-0.617489\pi$
$457$	5.69781	−	3.28963i	0.266532	−	0.153882i	0.627311	+	0.778769i	$0.284156\pi$
$458$	−4.14076	+	15.4535i	−0.193485	+	0.722095i
$459$	3.81088	−	6.60064i	0.177877	−	0.308092i
$460$		0			0
$461$	2.16031	+	8.06240i	0.100616	+	0.375503i	0.997811	−	0.0661310i	$-0.0210655\pi$
$461$	2.16031	+	8.06240i	0.100616	+	0.375503i	−0.897195	+	0.441634i	$0.854399\pi$
$462$	−0.0378620	+	0.0655788i	−0.00176150	+	0.00305100i
$463$			25.1969i			1.17100i	0.810673	+	0.585499i	$0.199101\pi$
$463$			25.1969i			1.17100i	−0.810673	+	0.585499i	$0.800899\pi$
$464$	24.2625	+	14.0079i	1.12636	+	0.650302i
$465$		0			0
$466$	−3.82352	+	14.2696i	−0.177121	+	0.661025i
$467$	−8.08282	−	8.08282i	−0.374028	−	0.374028i	0.494914	−	0.868942i	$-0.335200\pi$
$467$	−8.08282	−	8.08282i	−0.374028	−	0.374028i	−0.868942	+	0.494914i	$0.835200\pi$
$468$	0.297900	−	1.06822i	0.0137704	−	0.0493786i
$469$		−	0.879375i		−	0.0406058i
$470$		0			0
$471$	−4.26555	−	7.38814i	−0.196546	−	0.340428i
$472$	8.85157	−	2.37177i	0.407426	−	0.109170i
$473$	4.87303			0.224062
$474$	−27.2780	+	7.30911i	−1.25292	+	0.335719i
$475$		0			0
$476$	−0.0204497	−	0.0204497i	−0.000937310	−	0.000937310i
$477$	−1.01265	−	3.77927i	−0.0463662	−	0.173041i
$478$	−12.5521	−	3.36334i	−0.574122	−	0.153835i
$479$	34.2136	+	9.16752i	1.56326	+	0.418874i	0.933694	−	0.358072i	$-0.116566\pi$
$479$	34.2136	+	9.16752i	1.56326	+	0.418874i	0.629567	+	0.776946i	$0.283232\pi$
$480$		0			0
$481$	13.6209	+	3.79852i	0.621060	+	0.173198i
$482$	−17.9950	+	17.9950i	−0.819651	+	0.819651i
$483$	0.0988677	+	0.171244i	0.00449864	+	0.00779187i
$484$	−3.39068	+	1.95761i	−0.154122	+	0.0889823i
$485$		0			0
$486$	−7.49572	+	7.49572i	−0.340013	+	0.340013i
$487$	18.4466	+	10.6502i	0.835897	+	0.482606i	0.855868	−	0.517195i	$-0.173024\pi$
$487$	18.4466	+	10.6502i	0.835897	+	0.482606i	−0.0199702	+	0.999801i	$0.506357\pi$
$488$	17.4204	+	10.0577i	0.788583	+	0.455289i
$489$	0.0208039	−	0.0208039i	0.000940787	−	0.000940787i
$490$		0			0
$491$	−30.1957	+	17.4335i	−1.36271	+	0.786762i	−0.989984	−	0.141178i	$-0.954911\pi$
$491$	−30.1957	+	17.4335i	−1.36271	+	0.786762i	−0.372728	+	0.927941i	$0.621578\pi$
$492$	2.34816	+	4.06713i	0.105863	+	0.183361i
$493$	−8.58944	+	8.58944i	−0.386849	+	0.386849i
$494$	−0.187935	+	18.4871i	−0.00845558	+	0.831772i
$495$		0			0
$496$	16.4054	+	4.39582i	0.736625	+	0.197378i
$497$	−0.362136	−	0.0970341i	−0.0162440	−	0.00435257i
$498$	6.18474	+	23.0818i	0.277145	+	1.03432i
$499$	−19.4100	−	19.4100i	−0.868911	−	0.868911i	0.123441	−	0.992352i	$-0.460607\pi$
$499$	−19.4100	−	19.4100i	−0.868911	−	0.868911i	−0.992352	+	0.123441i	$0.960607\pi$
$500$		0			0
$501$	14.8294	−	3.97352i	0.662528	−	0.177524i
$502$	−21.7196			−0.969395
$503$	−14.4408	+	3.86939i	−0.643882	+	0.172528i	−0.565961	−	0.824432i	$-0.691495\pi$
$503$	−14.4408	+	3.86939i	−0.643882	+	0.172528i	−0.0779206	+	0.996960i	$0.524828\pi$
$504$	0.0717843	+	0.124334i	0.00319753	+	0.00553828i
$505$		0			0
$506$			2.08605i			0.0927361i
$507$	18.4118	+	5.33687i	0.817695	+	0.237019i
$508$	−1.56691	−	1.56691i	−0.0695202	−	0.0695202i
$509$	−2.30775	+	8.61262i	−0.102289	+	0.381748i	−0.998024	−	0.0628415i	$-0.979984\pi$
$509$	−2.30775	+	8.61262i	−0.102289	+	0.381748i	0.895734	+	0.444589i	$0.146650\pi$
$510$		0			0
$511$	0.399851	+	0.230854i	0.0176884	+	0.0102124i
$512$		−	25.3387i		−	1.11982i
$513$	−11.3372	+	19.6365i	−0.500548	+	0.866975i
$514$	2.10384	+	7.85165i	0.0927965	+	0.346321i
$515$		0			0
$516$	−1.91050	+	3.30907i	−0.0841049	+	0.145674i
$517$	−1.20846	+	4.51004i	−0.0531481	+	0.198351i
$518$	−0.248947	+	0.143730i	−0.0109381	+	0.00631512i
$519$	22.4168			0.983988
$520$		0			0
$521$	0.624957			0.0273798			0.0136899	−	0.999906i	$-0.495642\pi$
$521$	0.624957			0.0273798			0.0136899	+	0.999906i	$0.495642\pi$
$522$	8.20052	−	4.73457i	0.358927	−	0.207227i
$523$	0.562515	−	2.09934i	0.0245971	−	0.0917976i	−0.952536	−	0.304425i	$-0.901536\pi$
$523$	0.562515	−	2.09934i	0.0245971	−	0.0917976i	0.977133	+	0.212628i	$0.0682022\pi$
$524$	−1.25180	+	2.16818i	−0.0546852	+	0.0947176i
$525$		0			0
$526$	−8.55950	−	31.9445i	−0.373212	−	1.39285i
$527$	−3.68204	+	6.37749i	−0.160392	+	0.277808i
$528$		−	3.21932i		−	0.140103i
$529$	−15.2011	−	8.77639i	−0.660919	−	0.381582i
$530$		0			0
$531$	0.646945	−	2.41443i	0.0280750	−	0.104777i
$532$	0.0608367	+	0.0608367i	0.00263761	+	0.00263761i
$533$	26.8484	−	15.1392i	1.16293	−	0.655750i
$534$		−	24.9596i		−	1.08011i
$535$		0			0
$536$	23.1626	+	40.1188i	1.00047	+	1.73287i
$537$	5.17934	−	1.38780i	0.223505	−	0.0598880i
$538$	−18.4290			−0.794529
$539$	−4.73500	+	1.26874i	−0.203951	+	0.0546485i
$540$		0			0
$541$	31.2159	+	31.2159i	1.34208	+	1.34208i	0.893991	+	0.448084i	$0.147894\pi$
$541$	31.2159	+	31.2159i	1.34208	+	1.34208i	0.448084	+	0.893991i	$0.352106\pi$
$542$	−6.18442	−	23.0806i	−0.265644	−	0.991396i
$543$	−17.3992	−	4.66210i	−0.746670	−	0.200070i
$544$	2.71211	+	0.726709i	0.116281	+	0.0311574i
$545$		0			0
$546$	−0.339447	+	0.191405i	−0.0145270	+	0.00819140i
$547$	31.5617	−	31.5617i	1.34948	−	1.34948i	0.463255	−	0.886225i	$-0.346681\pi$
$547$	31.5617	−	31.5617i	1.34948	−	1.34948i	0.886225	−	0.463255i	$-0.153319\pi$
$548$	1.99668	+	3.45835i	0.0852939	+	0.147733i
$549$	4.75174	−	2.74342i	0.202799	−	0.117086i
$550$		0			0
$551$	25.5531	−	25.5531i	1.08860	−	1.08860i
$552$	−9.02108	−	5.20832i	−0.383963	−	0.221681i
$553$	0.746967	+	0.431261i	0.0317642	+	0.0183391i
$554$	1.75547	−	1.75547i	0.0745826	−	0.0745826i
$555$		0			0
$556$	5.99452	−	3.46094i	0.254224	−	0.146777i
$557$	10.2609	+	17.7724i	0.434769	+	0.753042i	0.997277	−	0.0737502i	$-0.0234968\pi$
$557$	10.2609	+	17.7724i	0.434769	+	0.753042i	−0.562508	+	0.826792i	$0.690163\pi$
$558$	4.05915	−	4.05915i	0.171838	−	0.171838i
$559$	21.5893	+	12.7590i	0.913131	+	0.539647i
$560$		0			0
$561$	1.34829	+	0.361274i	0.0569249	+	0.0152530i
$562$	3.52909	+	0.945617i	0.148866	+	0.0398884i
$563$	−1.45298	−	5.42258i	−0.0612356	−	0.228534i	0.928525	−	0.371269i	$-0.121077\pi$
$563$	−1.45298	−	5.42258i	−0.0612356	−	0.228534i	−0.989761	+	0.142734i	$0.954411\pi$
$564$	−2.58880	−	2.58880i	−0.109008	−	0.109008i
$565$		0			0
$566$	39.8265	−	10.6715i	1.67403	−	0.448556i
$567$	−0.335630			−0.0140951
$568$	19.0772	−	5.11173i	0.800463	−	0.214483i
$569$	7.35274	+	12.7353i	0.308243	+	0.533893i	0.977978	−	0.208708i	$-0.0669257\pi$
$569$	7.35274	+	12.7353i	0.308243	+	0.533893i	−0.669735	+	0.742600i	$0.733592\pi$
$570$		0			0
$571$		−	11.3169i		−	0.473598i	−0.971559	−	0.236799i	$-0.923902\pi$
$571$		−	11.3169i		−	0.473598i	0.971559	−	0.236799i	$-0.0760983\pi$
$572$	0.941070	+	0.00956667i	0.0393481	+	0.000400003i
$573$	3.05204	+	3.05204i	0.127501	+	0.127501i
$574$	−0.162171	+	0.605230i	−0.00676888	+	0.0252618i
$575$		0			0
$576$	−6.35141	−	3.66699i	−0.264642	−	0.152791i
$577$			1.11042i			0.0462273i	0.999733	+	0.0231137i	$0.00735796\pi$
$577$			1.11042i			0.0462273i	−0.999733	+	0.0231137i	$0.992642\pi$
$578$	−9.67918	+	16.7648i	−0.402601	+	0.697325i
$579$	−3.89429	−	14.5337i	−0.161841	−	0.604000i
$580$		0			0
$581$	0.364920	−	0.632059i	0.0151394	−	0.0262222i
$582$	0.802360	−	2.99445i	0.0332589	−	0.124124i
$583$	2.87550	−	1.66017i	0.119091	−	0.0687574i
$584$	−24.3226			−1.00648
$585$		0			0
$586$	−26.1975			−1.08221
$587$	−36.2015	+	20.9010i	−1.49420	+	0.862675i	−0.999978	−	0.00666302i	$-0.997879\pi$
$587$	−36.2015	+	20.9010i	−1.49420	+	0.862675i	−0.494219	+	0.869338i	$0.664546\pi$
$588$	0.994832	−	3.71276i	0.0410262	−	0.153112i
$589$	10.9539	−	18.9727i	0.451347	−	0.781755i
$590$		0			0
$591$	4.68663	+	17.4907i	0.192782	+	0.719473i
$592$	6.11052	−	10.5837i	0.251141	−	0.434989i
$593$		−	44.5360i		−	1.82887i	−0.404730	−	0.914436i	$-0.632634\pi$
$593$		−	44.5360i		−	1.82887i	0.404730	−	0.914436i	$-0.367366\pi$
$594$	−4.36653	−	2.52102i	−0.179161	−	0.103439i
$595$		0			0
$596$	−1.53542	+	5.73026i	−0.0628932	+	0.234721i
$597$	0.0829339	+	0.0829339i	0.00339426	+	0.00339426i
$598$	−5.46186	+	9.24197i	−0.223352	+	0.377932i
$599$			18.2350i			0.745060i	0.928020	+	0.372530i	$0.121510\pi$
$599$			18.2350i			0.745060i	−0.928020	+	0.372530i	$0.878490\pi$
$600$		0			0
$601$	−4.87099	−	8.43680i	−0.198692	−	0.344144i	0.749413	−	0.662103i	$-0.230336\pi$
$601$	−4.87099	−	8.43680i	−0.198692	−	0.344144i	−0.948105	+	0.317959i	$0.897003\pi$
$602$	−0.492424	+	0.131944i	−0.0200697	+	0.00537766i
$603$	12.6361			0.514581
$604$	−5.86711	+	1.57209i	−0.238729	+	0.0639673i
$605$		0			0
$606$	−22.3441	−	22.3441i	−0.907668	−	0.907668i
$607$	−0.161882	−	0.604153i	−0.00657060	−	0.0245218i	0.962563	−	0.271059i	$-0.0873739\pi$
$607$	−0.161882	−	0.604153i	−0.00657060	−	0.0245218i	−0.969133	+	0.246537i	$0.920707\pi$
$608$	−8.06839	−	2.16192i	−0.327216	−	0.0876774i
$609$	0.735756	+	0.197145i	0.0298143	+	0.00798873i
$610$		0			0
$611$	−17.1625	+	16.8171i	−0.694320	+	0.680346i
$612$	0.293850	−	0.293850i	0.0118782	−	0.0118782i
$613$	−22.1012	−	38.2803i	−0.892657	−	1.54613i	−0.836678	−	0.547696i	$-0.815505\pi$
$613$	−22.1012	−	38.2803i	−0.892657	−	1.54613i	−0.0559794	−	0.998432i	$-0.517828\pi$
$614$	−6.03861	+	3.48639i	−0.243698	+	0.140699i
$615$		0			0
$616$	−0.0861516	+	0.0861516i	−0.00347115	+	0.00347115i
$617$	32.7814	+	18.9264i	1.31973	+	0.761946i	0.983685	−	0.179900i	$-0.0575773\pi$
$617$	32.7814	+	18.9264i	1.31973	+	0.761946i	0.336045	+	0.941846i	$0.390911\pi$
$618$	0.560821	+	0.323790i	0.0225595	+	0.0130247i
$619$	31.2469	−	31.2469i	1.25592	−	1.25592i	0.302892	−	0.953025i	$-0.402048\pi$
$619$	31.2469	−	31.2469i	1.25592	−	1.25592i	0.953025	−	0.302892i	$-0.0979522\pi$
$620$		0			0
$621$	−11.4022	+	6.58305i	−0.457553	+	0.264169i
$622$	−6.50595	−	11.2686i	−0.260865	−	0.451831i
$623$	−0.539044	+	0.539044i	−0.0215963	+	0.0215963i
$624$	8.42910	−	14.2628i	0.337434	−	0.570969i
$625$		0			0
$626$	−24.7661	−	6.63605i	−0.989851	−	0.265230i
$627$	−4.01109	−	1.07477i	−0.160188	−	0.0429222i
$628$	−0.557853	−	2.08193i	−0.0222607	−	0.0830782i
$629$	3.74687	+	3.74687i	0.149398	+	0.149398i
$630$		0			0
$631$	−13.3999	+	3.59050i	−0.533443	+	0.142936i	−0.515478	−	0.856903i	$-0.672386\pi$
$631$	−13.3999	+	3.59050i	−0.533443	+	0.142936i	−0.0179655	+	0.999839i	$0.505719\pi$
$632$	−45.4374			−1.80740
$633$	22.5775	−	6.04962i	0.897375	−	0.240451i
$634$	−12.5327	−	21.7073i	−0.497737	−	0.862106i
$635$		0			0
$636$			2.60352i			0.103236i
$637$	−24.2997	−	6.77658i	−0.962791	−	0.268498i
$638$	5.68218	+	5.68218i	0.224960	+	0.224960i
$639$	1.39432	−	5.20368i	0.0551585	−	0.205854i
$640$		0			0
$641$	−25.1285	−	14.5079i	−0.992516	−	0.573029i	−0.0864905	−	0.996253i	$-0.527565\pi$
$641$	−25.1285	−	14.5079i	−0.992516	−	0.573029i	−0.906025	+	0.423223i	$0.860899\pi$
$642$			11.6720i			0.460656i
$643$	16.0252	−	27.7565i	0.631974	−	1.09461i	−0.355174	−	0.934800i	$-0.615578\pi$
$643$	16.0252	−	27.7565i	0.631974	−	1.09461i	0.987148	−	0.159811i	$-0.0510883\pi$
$644$	0.0129300	+	0.0482555i	0.000509514	+	0.00190153i
$645$		0			0
$646$	−3.46398	+	5.99978i	−0.136288	+	0.236058i
$647$	−12.3435	+	46.0665i	−0.485272	+	1.81106i	0.0935595	+	0.995614i	$0.470175\pi$
$647$	−12.3435	+	46.0665i	−0.485272	+	1.81106i	−0.578832	+	0.815447i	$0.696491\pi$
$648$	15.3121	−	8.84044i	0.601515	−	0.347285i
$649$	2.12124			0.0832660
$650$		0			0
$651$	0.461774			0.0180983
$652$	0.00643739	−	0.00371663i	0.000252108	−	0.000145554i
$653$	−2.87396	+	10.7258i	−0.112467	+	0.419731i	−0.999085	−	0.0427708i	$-0.986381\pi$
$653$	−2.87396	+	10.7258i	−0.112467	+	0.419731i	0.886618	+	0.462502i	$0.153048\pi$
$654$	−10.7458	+	18.6123i	−0.420194	+	0.727798i
$655$		0			0
$656$	−6.89453	−	25.7307i	−0.269186	−	1.00462i
$657$	−3.31723	+	5.74561i	−0.129417	+	0.224158i
$658$		−	0.488464i		−	0.0190423i
$659$	18.9606	+	10.9469i	0.738601	+	0.426432i	0.821561	−	0.570121i	$-0.193104\pi$
$659$	18.9606	+	10.9469i	0.738601	+	0.426432i	−0.0829592	+	0.996553i	$0.526437\pi$
$660$		0			0
$661$	10.3265	−	38.5390i	0.401654	−	1.49899i	−0.408490	−	0.912763i	$-0.633945\pi$
$661$	10.3265	−	38.5390i	0.401654	−	1.49899i	0.810144	−	0.586230i	$-0.199389\pi$
$662$	4.01332	+	4.01332i	0.155982	+	0.155982i
$663$	5.02752	+	5.13079i	0.195253	+	0.199263i
$664$			38.4477i			1.49206i
$665$		0			0
$666$	−2.06531	−	3.57722i	−0.0800291	−	0.138614i
$667$	20.2687	−	5.43097i	0.784806	−	0.210288i
$668$	3.87880			0.150075
$669$	−27.1508	+	7.27503i	−1.04971	+	0.281269i
$670$		0			0
$671$	3.29250	+	3.29250i	0.127105	+	0.127105i
$672$	−0.0455691	−	0.170066i	−0.00175787	−	0.00656045i
$673$	−23.4947	−	6.29539i	−0.905655	−	0.242670i	−0.224212	−	0.974540i	$-0.571981\pi$
$673$	−23.4947	−	6.29539i	−0.905655	−	0.242670i	−0.681443	+	0.731871i	$0.738647\pi$
$674$	−2.69192	−	0.721298i	−0.103689	−	0.0277834i
$675$		0			0
$676$	4.14424	+	2.50637i	0.159394	+	0.0963988i
$677$	−12.9788	+	12.9788i	−0.498814	+	0.498814i	−0.911069	−	0.412255i	$-0.864741\pi$
$677$	−12.9788	+	12.9788i	−0.498814	+	0.498814i	0.412255	+	0.911069i	$0.364741\pi$
$678$	−15.4279	−	26.7219i	−0.592505	−	1.02625i
$679$	−0.0819984	+	0.0473418i	−0.00314681	+	0.00181681i
$680$		0			0
$681$	8.59099	−	8.59099i	0.329208	−	0.329208i
$682$	4.21890	+	2.43579i	0.161550	+	0.0932710i
$683$	−8.90541	−	5.14154i	−0.340756	−	0.196736i	0.319850	−	0.947468i	$-0.396367\pi$
$683$	−8.90541	−	5.14154i	−0.340756	−	0.196736i	−0.660606	+	0.750733i	$0.729701\pi$
$684$	−0.874186	+	0.874186i	−0.0334253	+	0.0334253i
$685$		0			0
$686$	0.888455	−	0.512950i	0.0339214	−	0.0195845i
$687$	−9.24636	−	16.0152i	−0.352771	−	0.611017i
$688$	15.3254	−	15.3254i	0.584275	−	0.584275i
$689$	17.0864	+	0.173695i	0.650938	+	0.00661727i
$690$		0			0
$691$	−4.71419	−	1.26316i	−0.179336	−	0.0480530i	0.168033	−	0.985781i	$-0.446258\pi$
$691$	−4.71419	−	1.26316i	−0.179336	−	0.0480530i	−0.347370	+	0.937728i	$0.612925\pi$
$692$	5.47061	+	1.46585i	0.207962	+	0.0557231i
$693$	0.00860141	+	0.0321009i	0.000326740	+	0.00121941i
$694$	−18.6617	−	18.6617i	−0.708390	−	0.708390i
$695$		0			0
$696$	−38.7594	+	10.3856i	−1.46917	+	0.393664i
$697$	11.5501			0.437489
$698$	21.2864	−	5.70368i	0.805702	−	0.215887i
$699$	−8.53797	−	14.7882i	−0.322936	−	0.559341i
$700$		0			0
$701$		−	26.9621i		−	1.01834i	−0.860665	−	0.509172i	$-0.829952\pi$
$701$		−	26.9621i		−	1.01834i	0.860665	−	0.509172i	$-0.170048\pi$
$702$	−12.7446	−	22.6018i	−0.481014	−	0.853051i
$703$	−11.1467	−	11.1467i	−0.420407	−	0.420407i
$704$	1.61085	−	6.01177i	0.0607111	−	0.226577i
$705$		0			0
$706$	1.37606	+	0.794470i	0.0517888	+	0.0299003i
$707$			0.965118i			0.0362970i
$708$	−0.831644	+	1.44045i	−0.0312551	+	0.0541354i
$709$	1.93480	+	7.22076i	0.0726629	+	0.271181i	0.992693	−	0.120666i	$-0.0385029\pi$
$709$	1.93480	+	7.22076i	0.0726629	+	0.271181i	−0.920030	+	0.391847i	$0.871836\pi$
$710$		0			0
$711$	−6.19696	+	10.7335i	−0.232404	+	0.402536i
$712$	10.3939	−	38.7906i	0.389528	−	1.45374i
$713$	11.0167	−	6.36049i	0.412578	−	0.238202i
$714$	−0.146028			−0.00546496
$715$		0			0
$716$	1.35472			0.0506283
$717$	13.0084	−	7.51037i	0.485806	−	0.280480i
$718$	−9.81452	+	36.6283i	−0.366275	+	1.36696i
$719$	−17.6129	+	30.5065i	−0.656852	+	1.13770i	0.324574	+	0.945860i	$0.394779\pi$
$719$	−17.6129	+	30.5065i	−0.656852	+	1.13770i	−0.981426	+	0.191841i	$0.938554\pi$
$720$		0			0
$721$	−0.00511908	−	0.0191047i	−0.000190644	−	0.000711494i
$722$	−1.81414	+	3.14219i	−0.0675155	+	0.116940i
$723$		−	29.4161i		−	1.09400i
$724$	−3.94125	−	2.27548i	−0.146475	−	0.0845677i
$725$		0			0
$726$	−5.11667	+	19.0957i	−0.189897	+	0.708706i
$727$	21.6956	+	21.6956i	0.804645	+	0.804645i	0.983818	−	0.179173i	$-0.0573420\pi$
$727$	21.6956	+	21.6956i	0.804645	+	0.804645i	−0.179173	+	0.983818i	$0.557342\pi$
$728$	−0.607253	+	0.156115i	−0.0225063	+	0.00578599i
$729$		−	29.7780i		−	1.10289i
$730$		0			0
$731$	4.69864	+	8.13828i	0.173785	+	0.301005i
$732$	−3.52664	+	0.944961i	−0.130348	+	0.0349268i
$733$	26.5141			0.979322			0.489661	−	0.871913i	$-0.337121\pi$
$733$	26.5141			0.979322			0.489661	+	0.871913i	$0.337121\pi$
$734$	−27.4515	+	7.35562i	−1.01325	+	0.271501i
$735$		0			0
$736$	−3.42966	−	3.42966i	−0.126419	−	0.126419i
$737$	2.77541	+	10.3580i	0.102234	+	0.381541i
$738$	−8.69679	−	2.33030i	−0.320133	−	0.0857794i
$739$	7.93547	+	2.12630i	0.291911	+	0.0782173i	0.401803	−	0.915726i	$-0.368384\pi$
$739$	7.93547	+	2.12630i	0.291911	+	0.0782173i	−0.109892	+	0.993944i	$0.535050\pi$
$740$		0			0
$741$	−14.9566	−	15.2638i	−0.549444	−	0.560730i
$742$	−0.245620	+	0.245620i	−0.00901701	+	0.00901701i
$743$	−9.77400	−	16.9291i	−0.358573	−	0.621067i	0.629149	−	0.777284i	$-0.283403\pi$
$743$	−9.77400	−	16.9291i	−0.358573	−	0.621067i	−0.987723	+	0.156217i	$0.950070\pi$
$744$	−21.0670	+	12.1631i	−0.772355	+	0.445919i
$745$		0			0
$746$	25.2453	−	25.2453i	0.924295	−	0.924295i
$747$	9.08230	+	5.24367i	0.332304	+	0.191856i
$748$	0.305414	+	0.176331i	0.0111671	+	0.00644730i
$749$	0.252076	−	0.252076i	0.00921065	−	0.00921065i
$750$		0			0
$751$	25.1699	−	14.5318i	0.918463	−	0.530275i	0.0353184	−	0.999376i	$-0.488755\pi$
$751$	25.1699	−	14.5318i	0.918463	−	0.530275i	0.883144	+	0.469101i	$0.155422\pi$
$752$	10.3833	+	17.9843i	0.378639	+	0.655822i
$753$	17.7523	−	17.7523i	0.646930	−	0.646930i
$754$	10.2966	+	40.0517i	0.374981	+	1.45860i
$755$		0			0
$756$	−0.116635	−	0.0312522i	−0.00424197	−	0.00113663i
$757$	7.12278	+	1.90854i	0.258882	+	0.0693671i	0.385925	−	0.922530i	$-0.373882\pi$
$757$	7.12278	+	1.90854i	0.258882	+	0.0693671i	−0.127044	+	0.991897i	$0.540549\pi$
$758$	−2.89337	−	10.7982i	−0.105092	−	0.392208i
$759$	−1.70501	−	1.70501i	−0.0618879	−	0.0618879i
$760$		0			0
$761$	18.8118	−	5.04060i	0.681926	−	0.182722i	0.0988050	−	0.995107i	$-0.468498\pi$
$761$	18.8118	−	5.04060i	0.681926	−	0.182722i	0.583121	+	0.812385i	$0.301831\pi$
$762$	−11.1890			−0.405336
$763$	0.634037	−	0.169890i	0.0229537	−	0.00615042i
$764$	0.545249	+	0.944398i	0.0197264	+	0.0341671i
$765$		0			0
$766$		−	16.7622i		−	0.605645i
$767$	9.39789	+	5.55401i	0.339338	+	0.200544i
$768$	8.97943	+	8.97943i	0.324017	+	0.324017i
$769$	0.929962	−	3.47067i	0.0335353	−	0.125155i	−0.947129	−	0.320853i	$-0.896030\pi$
$769$	0.929962	−	3.47067i	0.0335353	−	0.125155i	0.980664	+	0.195698i	$0.0626971\pi$
$770$		0			0
$771$	−8.13702	−	4.69791i	−0.293047	−	0.169191i
$772$		−	3.80147i		−	0.136818i
$773$	−23.5940	+	40.8660i	−0.848616	+	1.46985i	0.0338268	+	0.999428i	$0.489231\pi$
$773$	−23.5940	+	40.8660i	−0.848616	+	1.46985i	−0.882443	+	0.470419i	$0.844103\pi$
$774$	−1.89596	−	7.07582i	−0.0681489	−	0.254335i
$775$		0			0
$776$	2.49395	−	4.31965i	0.0895277	−	0.155067i
$777$	0.0859984	−	0.320950i	0.00308518	−	0.0115140i
$778$	24.5565	−	14.1777i	0.880393	−	0.508295i
$779$	−34.3608			−1.23110
$780$		0			0
$781$	4.57178			0.163591
$782$	−3.48384	+	2.01140i	−0.124582	+	0.0719273i
$783$	−13.1268	+	48.9899i	−0.469113	+	1.75076i
$784$	−10.9012	+	18.8814i	−0.389328	+	0.674336i
$785$		0			0
$786$	3.27187	+	12.2108i	0.116704	+	0.435545i
$787$	9.80272	−	16.9788i	0.349429	−	0.605229i	−0.636719	−	0.771096i	$-0.719709\pi$
$787$	9.80272	−	16.9788i	0.349429	−	0.605229i	0.986148	+	0.165867i	$0.0530422\pi$
$788$			4.57491i			0.162975i
$789$	33.1055	+	19.1135i	1.17859	+	0.680458i
$790$		0			0
$791$	−0.243913	+	0.910296i	−0.00867255	+	0.0323664i
$792$	−1.23795	−	1.23795i	−0.0439885	−	0.0439885i
$793$	5.96631	+	23.2077i	0.211870	+	0.824129i
$794$		−	1.49088i		−	0.0529094i
$795$		0			0
$796$	0.0148162	+	0.0256624i	0.000525145	+	0.000909578i
$797$	1.95111	−	0.522798i	0.0691118	−	0.0185185i	−0.224097	−	0.974567i	$-0.571943\pi$
$797$	1.95111	−	0.522798i	0.0691118	−	0.0185185i	0.293209	+	0.956048i	$0.405277\pi$
$798$	0.434425			0.0153785
$799$	−8.69728	+	2.33043i	−0.307688	+	0.0824447i
$800$		0			0
$801$	−7.74573	−	7.74573i	−0.273682	−	0.273682i
$802$	−5.30453	−	19.7968i	−0.187309	−	0.699048i
$803$	−5.43836	−	1.45720i	−0.191916	−	0.0514236i
$804$	−8.12180	−	2.17623i	−0.286434	−	0.0767497i
$805$		0			0
$806$	12.3137	+	21.8377i	0.433733	+	0.769201i
$807$	15.0627	−	15.0627i	0.530233	−	0.530233i
$808$	−25.4211	−	44.0306i	−0.894310	−	1.54899i
$809$	12.4850	−	7.20824i	0.438950	−	0.253428i	−0.264202	−	0.964467i	$-0.585109\pi$
$809$	12.4850	−	7.20824i	0.438950	−	0.253428i	0.703152	+	0.711039i	$0.251775\pi$
$810$		0			0
$811$	−13.7132	+	13.7132i	−0.481537	+	0.481537i	−0.905622	−	0.424085i	$-0.860596\pi$
$811$	−13.7132	+	13.7132i	−0.481537	+	0.481537i	0.424085	+	0.905622i	$0.360596\pi$
$812$	0.166663	+	0.0962230i	0.00584873	+	0.00337676i
$813$	23.9195	+	13.8099i	0.838892	+	0.484334i
$814$	2.47867	−	2.47867i	0.0868774	−	0.0868774i
$815$		0			0
$816$	5.37648	−	3.10411i	0.188215	−	0.108666i
$817$	−13.9782	−	24.2109i	−0.489035	−	0.847034i
$818$	−1.38330	+	1.38330i	−0.0483659	+	0.0483659i
$819$	−0.0459417	+	0.164740i	−0.00160533	+	0.00575648i
$820$		0			0
$821$	−37.1425	−	9.95230i	−1.29628	−	0.347338i	−0.456239	−	0.889857i	$-0.650804\pi$
$821$	−37.1425	−	9.95230i	−1.29628	−	0.347338i	−0.840043	+	0.542520i	$0.817470\pi$
$822$	19.4768	+	5.21878i	0.679330	+	0.182026i
$823$	1.38319	+	5.16215i	0.0482151	+	0.179941i	0.985834	−	0.167723i	$-0.0536415\pi$
$823$	1.38319	+	5.16215i	0.0482151	+	0.179941i	−0.937619	+	0.347664i	$0.886975\pi$
$824$	0.736756	+	0.736756i	0.0256661	+	0.0256661i
$825$		0			0
$826$	−0.214353	+	0.0574358i	−0.00745830	+	0.00199845i
$827$	31.8700			1.10823			0.554114	−	0.832440i	$-0.313057\pi$
$827$	31.8700			1.10823			0.554114	+	0.832440i	$0.313057\pi$
$828$	−0.693402	+	0.185797i	−0.0240974	+	0.00645688i
$829$	−17.8848	−	30.9773i	−0.621164	−	1.07589i	−0.989269	−	0.146103i	$-0.953327\pi$
$829$	−17.8848	−	30.9773i	−0.621164	−	1.07589i	0.368105	−	0.929784i	$-0.380007\pi$
$830$		0			0
$831$			2.86962i			0.0995461i
$832$	22.8772	−	22.4167i	0.793123	−	0.777160i
$833$	−6.68443	−	6.68443i	−0.231602	−	0.231602i
$834$	9.04596	−	33.7600i	0.313236	−	1.16901i
$835$		0			0
$836$	−0.908591	−	0.524575i	−0.0314243	−	0.0181428i
$837$			30.7469i			1.06277i
$838$	−18.7462	+	32.4694i	−0.647577	+	1.12164i
$839$	11.0135	+	41.1030i	0.380229	+	1.41903i	0.845553	+	0.533892i	$0.179271\pi$
$839$	11.0135	+	41.1030i	0.380229	+	1.41903i	−0.465324	+	0.885140i	$0.654062\pi$
$840$		0			0
$841$	25.9163	−	44.8884i	0.893666	−	1.54788i
$842$	−10.4451	+	38.9818i	−0.359963	+	1.34340i
$843$	−3.65735	+	2.11157i	−0.125966	+	0.0727265i
$844$	5.90542			0.203273
$845$		0			0
$846$	7.01893			0.241316
$847$	0.522906	−	0.301900i	0.0179673	−	0.0103734i
$848$	3.82215	−	14.2644i	0.131253	−	0.489843i
$849$	−23.8296	+	41.2740i	−0.817828	+	1.41652i
$850$		0			0
$851$	−2.36909	−	8.84156i	−0.0812113	−	0.303085i
$852$	−1.79239	+	3.10451i	−0.0614063	+	0.106359i
$853$			9.37861i			0.321117i	0.987026	+	0.160559i	$0.0513296\pi$
$853$			9.37861i			0.321117i	−0.987026	+	0.160559i	$0.948670\pi$
$854$	−0.421859	−	0.243560i	−0.0144357	−	0.00833447i
$855$		0			0
$856$	−4.86056	+	18.1398i	−0.166130	+	0.620007i
$857$	−37.8273	−	37.8273i	−1.29216	−	1.29216i	−0.933451	−	0.358705i	$-0.883218\pi$
$857$	−37.8273	−	37.8273i	−1.29216	−	1.29216i	−0.358705	−	0.933451i	$-0.616782\pi$
$858$	3.39417	−	3.32586i	0.115875	−	0.113543i
$859$			34.3962i			1.17358i	0.809738	+	0.586791i	$0.199609\pi$
$859$			34.3962i			1.17358i	−0.809738	+	0.586791i	$0.800391\pi$
$860$		0			0
$861$	−0.362130	−	0.627227i	−0.0123414	−	0.0213758i
$862$	14.8063	−	3.96735i	0.504306	−	0.135128i
$863$	−25.9429			−0.883106			−0.441553	−	0.897235i	$-0.645572\pi$
$863$	−25.9429			−0.883106			−0.441553	+	0.897235i	$0.645572\pi$
$864$	11.3238	−	3.03419i	0.385242	−	0.103225i
$865$		0			0
$866$	23.4340	+	23.4340i	0.796319	+	0.796319i
$867$	−5.79139	−	21.6137i	−0.196686	−	0.734041i
$868$	0.112692	+	0.0301956i	0.00382500	+	0.00102491i
$869$	−10.1595	−	2.72222i	−0.344637	−	0.0923451i
$870$		0			0
$871$	−14.8240	+	53.1565i	−0.502292	+	1.80114i
$872$	−24.4511	+	24.4511i	−0.828020	+	0.828020i
$873$	−0.680273	−	1.17827i	−0.0230237	−	0.0398783i
$874$	10.3642	−	5.98379i	0.350575	−	0.202405i
$875$		0			0
$876$	3.12167	−	3.12167i	0.105471	−	0.105471i
$877$	16.2245	+	9.36723i	0.547863	+	0.316309i	0.748260	−	0.663406i	$-0.230890\pi$
$877$	16.2245	+	9.36723i	0.547863	+	0.316309i	−0.200397	+	0.979715i	$0.564223\pi$
$878$	3.57789	+	2.06569i	0.120748	+	0.0697138i
$879$	21.4123	−	21.4123i	0.722218	−	0.722218i
$880$		0			0
$881$	−26.3934	+	15.2382i	−0.889216	+	0.513389i	−0.873686	−	0.486490i	$-0.838277\pi$
$881$	−26.3934	+	15.2382i	−0.889216	+	0.513389i	−0.0155302	+	0.999879i	$0.504944\pi$
$882$	3.68452	+	6.38177i	0.124064	+	0.214885i
$883$	−32.3672	+	32.3672i	−1.08924	+	1.08924i	−0.0936348	+	0.995607i	$0.529849\pi$
$883$	−32.3672	+	32.3672i	−1.08924	+	1.08924i	−0.995607	+	0.0936348i	$0.970151\pi$
$884$	0.891415	+	1.58087i	0.0299815	+	0.0531705i
$885$		0			0
$886$	10.5061	+	2.81511i	0.352960	+	0.0945754i
$887$	16.9889	+	4.55216i	0.570432	+	0.152847i	0.532495	−	0.846433i	$-0.321255\pi$
$887$	16.9889	+	4.55216i	0.570432	+	0.152847i	0.0379371	+	0.999280i	$0.487921\pi$
$888$	4.53037	+	16.9076i	0.152029	+	0.567381i
$889$	0.241646	+	0.241646i	0.00810454	+	0.00810454i
$890$		0			0
$891$	3.95331	−	1.05929i	0.132441	−	0.0354874i
$892$	−7.10162			−0.237780
$893$	25.8739	−	6.93290i	0.865838	−	0.232001i
$894$	14.9774	+	25.9415i	0.500918	+	0.867615i
$895$		0			0
$896$			0.412311i			0.0137743i
$897$	−3.08963	−	12.0180i	−0.103160	−	0.401270i
$898$	−3.82399	−	3.82399i	−0.127608	−	0.127608i
$899$	12.6830	−	47.3336i	0.423002	−	1.57866i
$900$		0			0
$901$	5.54520	+	3.20152i	0.184737	+	0.106658i
$902$		−	7.64071i		−	0.254408i
$903$	0.294634	−	0.510321i	0.00980480	−	0.0169824i
$904$	−12.8493	−	47.9541i	−0.427360	−	1.59493i
$905$		0			0
$906$	−15.3350	+	26.5611i	−0.509473	+	0.882433i
$907$	0.355062	−	1.32511i	0.0117896	−	0.0439996i	−0.959780	−	0.280752i	$-0.909416\pi$
$907$	0.355062	−	1.32511i	0.0117896	−	0.0439996i	0.971570	+	0.236752i	$0.0760829\pi$
$908$	2.65832	−	1.53478i	0.0882195	−	0.0509336i
$909$	−13.8682			−0.459978
$910$		0			0
$911$	9.14814			0.303092			0.151546	−	0.988450i	$-0.451575\pi$
$911$	9.14814			0.303092			0.151546	+	0.988450i	$0.451575\pi$
$912$	−15.9947	+	9.23457i	−0.529639	+	0.305787i
$913$	−2.30346	+	8.59663i	−0.0762334	+	0.284507i
$914$	4.19663	−	7.26877i	0.138812	−	0.240430i
$915$		0			0
$916$	−1.20925	−	4.51298i	−0.0399547	−	0.149113i
$917$	0.193051	−	0.334374i	0.00637511	−	0.0110420i
$918$		−	9.72319i		−	0.320913i
$919$	42.0010	+	24.2493i	1.38549	+	0.799911i	0.992803	−	0.119763i	$-0.0382135\pi$
$919$	42.0010	+	24.2493i	1.38549	+	0.799911i	0.392683	+	0.919674i	$0.371547\pi$
$920$		0			0
$921$	2.08603	−	7.78516i	0.0687369	−	0.256530i
$922$	7.52937	+	7.52937i	0.247967	+	0.247967i
$923$	20.2547	+	11.9702i	0.666691	+	0.394004i
$924$		−	0.0221141i		−	0.000727501i
$925$		0			0
$926$	16.0720	+	27.8375i	0.528159	+	0.914798i
$927$	0.274522	−	0.0735580i	0.00901649	−	0.00241596i
$928$	−18.6841			−0.613334
$929$	−4.95450	+	1.32756i	−0.162552	+	0.0435557i	−0.339177	−	0.940723i	$-0.610149\pi$
$929$	−4.95450	+	1.32756i	−0.162552	+	0.0435557i	0.176625	+	0.984278i	$0.443482\pi$
$930$		0			0
$931$	19.8858	+	19.8858i	0.651731	+	0.651731i
$932$	−1.11660	−	4.16723i	−0.0365756	−	0.136502i
$933$	14.5279	+	3.89273i	0.475621	+	0.127442i
$934$	−14.0856	−	3.77422i	−0.460894	−	0.123496i
$935$		0			0
$936$	−2.24327	−	8.72586i	−0.0733236	−	0.285214i
$937$	−34.8938	+	34.8938i	−1.13993	+	1.13993i	−0.151470	+	0.988462i	$0.548401\pi$
$937$	−34.8938	+	34.8938i	−1.13993	+	1.13993i	−0.988462	+	0.151470i	$0.951599\pi$
$938$	−0.560915	−	0.971534i	−0.0183145	−	0.0317217i
$939$	25.6662	−	14.8184i	0.837585	−	0.483580i
$940$		0			0
$941$	19.4771	−	19.4771i	0.634936	−	0.634936i	−0.314366	−	0.949302i	$-0.601792\pi$
$941$	19.4771	−	19.4771i	0.634936	−	0.634936i	0.949302	+	0.314366i	$0.101792\pi$
$942$	−9.42516	−	5.44162i	−0.307088	−	0.177297i
$943$	−17.2789	−	9.97597i	−0.562678	−	0.324862i
$944$	6.67118	−	6.67118i	0.217128	−	0.217128i
$945$		0			0
$946$	5.38372	−	3.10829i	0.175040	−	0.101059i
$947$	−23.0380	−	39.9030i	−0.748636	−	1.29667i	−0.948477	−	0.316846i	$-0.897376\pi$
$947$	−23.0380	−	39.9030i	−0.748636	−	1.29667i	0.199841	−	0.979828i	$-0.435957\pi$
$948$	5.83163	−	5.83163i	0.189402	−	0.189402i
$949$	−20.2786	−	20.6951i	−0.658271	−	0.671792i
$950$		0			0
$951$	27.9857	+	7.49875i	0.907499	+	0.243163i
$952$	−0.226948	−	0.0608104i	−0.00735541	−	0.00197088i
$953$	13.9406	+	52.0270i	0.451580	+	1.68532i	0.697951	+	0.716145i	$0.254095\pi$
$953$	13.9406	+	52.0270i	0.451580	+	1.68532i	−0.246371	+	0.969176i	$0.579238\pi$
$954$	−3.52942	−	3.52942i	−0.114269	−	0.114269i
$955$		0			0
$956$	3.66568	−	0.982215i	0.118556	−	0.0317671i
$957$	−9.28854			−0.300256
$958$	43.6468	−	11.6951i	1.41016	−	0.377852i
$959$	−0.307925	−	0.533341i	−0.00994341	−	0.0172225i
$960$		0			0
$961$			1.29257i			0.0416957i
$962$	17.4713	−	4.49158i	0.563297	−	0.144814i
$963$	3.62218	+	3.62218i	0.116723	+	0.116723i
$964$	1.92353	−	7.17873i	0.0619529	−	0.231211i
$965$		0			0
$966$	0.218458	+	0.126127i	0.00702878	+	0.00405807i
$967$			36.0291i			1.15862i	0.815109	+	0.579308i	$0.196677\pi$
$967$			36.0291i			1.15862i	−0.815109	+	0.579308i	$0.803323\pi$
$968$	−15.9040	+	27.5465i	−0.511174	+	0.885379i
$969$	−2.07261	−	7.73510i	−0.0665820	−	0.248487i
$970$		0			0
$971$	−27.4824	+	47.6009i	−0.881952	+	1.52759i	−0.0327845	+	0.999462i	$0.510438\pi$
$971$	−27.4824	+	47.6009i	−0.881952	+	1.52759i	−0.849168	+	0.528123i	$0.822896\pi$
$972$	0.801237	−	2.99026i	0.0256997	−	0.0959125i
$973$	−0.924466	+	0.533741i	−0.0296370	+	0.0171109i
$974$	27.1732			0.870684
$975$		0			0
$976$	20.7094			0.662893
$977$	−28.0264	+	16.1811i	−0.896644	+	0.517678i	−0.876110	−	0.482111i	$-0.839870\pi$
$977$	−28.0264	+	16.1811i	−0.896644	+	0.517678i	−0.0205344	+	0.999789i	$0.506537\pi$
$978$	0.00971427	−	0.0362541i	0.000310628	−	0.00115928i
$979$	4.64800	−	8.05058i	0.148551	−	0.257298i
$980$		0			0
$981$	2.44121	+	9.11072i	0.0779419	+	0.290883i
$982$	−22.2401	+	38.5211i	−0.709712	+	1.22926i
$983$		−	7.09085i		−	0.226163i	−0.993586	−	0.113082i	$-0.963928\pi$
$983$		−	7.09085i		−	0.226163i	0.993586	−	0.113082i	$-0.0360721\pi$
$984$	33.0422	+	19.0769i	1.05335	+	0.608149i
$985$		0			0
$986$	−4.01078	+	14.9684i	−0.127729	+	0.476693i
$987$	0.399241	+	0.399241i	0.0127080	+	0.0127080i
$988$	−2.65191	−	4.70301i	−0.0843685	−	0.149623i
$989$		−	16.2332i		−	0.516185i
$990$		0			0
$991$	−23.2558	−	40.2802i	−0.738744	−	1.27954i	−0.953061	−	0.302778i	$-0.902086\pi$
$991$	−23.2558	−	40.2802i	−0.738744	−	1.27954i	0.214317	−	0.976764i	$-0.431247\pi$
$992$	−10.9409	+	2.93161i	−0.347375	+	0.0930788i
$993$	−6.56049			−0.208191
$994$	−0.461982	+	0.123788i	−0.0146532	+	0.00392631i
$995$		0			0
$996$	−4.93454	−	4.93454i	−0.156357	−	0.156357i
$997$	−2.75589	−	10.2851i	−0.0872800	−	0.325733i	0.908456	−	0.417980i	$-0.137262\pi$
$997$	−2.75589	−	10.2851i	−0.0872800	−	0.325733i	−0.995736	+	0.0922467i	$0.970595\pi$
$998$	−33.8250	−	9.06338i	−1.07071	−	0.286896i
$999$	21.3703	+	5.72615i	0.676126	+	0.181167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.x.c.93.7	yes	40
5.2	odd	4		325.2.s.c.132.7	yes	40
5.3	odd	4		325.2.s.c.132.4	✓	40
5.4	even	2	inner	325.2.x.c.93.4	yes	40
13.7	odd	12		325.2.s.c.293.7	yes	40
65.7	even	12	inner	325.2.x.c.7.7	yes	40
65.33	even	12	inner	325.2.x.c.7.4	yes	40
65.59	odd	12		325.2.s.c.293.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.132.4	✓	40	5.3	odd	4
325.2.s.c.132.7	yes	40	5.2	odd	4
325.2.s.c.293.4	yes	40	65.59	odd	12
325.2.s.c.293.7	yes	40	13.7	odd	12
325.2.x.c.7.4	yes	40	65.33	even	12	inner
325.2.x.c.7.7	yes	40	65.7	even	12	inner
325.2.x.c.93.4	yes	40	5.4	even	2	inner
325.2.x.c.93.7	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10480 - 0.637857i) q^{2} +(-0.381652 + 1.42434i) q^{3} +(-0.186277 + 0.322641i) q^{4} +(0.486878 + 1.81705i) q^{6} +(0.0287274 - 0.0497573i) q^{7} +3.02670i q^{8} +(0.714982 + 0.412795i) q^{9} +(-0.181334 + 0.676748i) q^{11} +(-0.388459 - 0.388459i) q^{12} +(-2.57529 + 2.52346i) q^{13} -0.0732958i q^{14} +(1.55805 + 2.69862i) q^{16} +(-1.30506 + 0.349689i) q^{17} +1.05322 q^{18} +(3.88248 - 1.04031i) q^{19} +(0.0599076 + 0.0599076i) q^{21} +(0.231330 + 0.863337i) q^{22} +(2.25440 + 0.604066i) q^{23} +(-4.31106 - 1.15514i) q^{24} +(-1.23558 + 4.43059i) q^{26} +(-3.98891 + 3.98891i) q^{27} +(0.0107025 + 0.0185373i) q^{28} +(7.78617 - 4.49535i) q^{29} +(3.85405 - 3.85405i) q^{31} +(-1.79973 - 1.03908i) q^{32} +(-0.894715 - 0.516564i) q^{33} +(-1.21878 + 1.21878i) q^{34} +(-0.266369 + 0.153788i) q^{36} +(-1.96095 - 3.39647i) q^{37} +(3.62580 - 3.62580i) q^{38} +(-2.61141 - 4.63119i) q^{39} +(-8.25736 - 2.21255i) q^{41} +(0.104398 + 0.0279735i) q^{42} +(-1.80016 - 6.71830i) q^{43} +(-0.184569 - 0.184569i) q^{44} +(2.87597 - 0.770615i) q^{46} +6.66428 q^{47} +(-4.43839 + 1.18926i) q^{48} +(3.49835 + 6.05932i) q^{49} -1.99231i q^{51} +(-0.334455 - 1.30096i) q^{52} +(-3.35108 - 3.35108i) q^{53} +(-1.86260 + 6.95130i) q^{54} +(0.150600 + 0.0869492i) q^{56} +5.92701i q^{57} +(5.73478 - 9.93293i) q^{58} +(-0.783616 - 2.92449i) q^{59} +(3.32298 - 5.75557i) q^{61} +(1.79963 - 6.71629i) q^{62} +(0.0410791 - 0.0237170i) q^{63} -8.88332 q^{64} -1.31798 q^{66} +(13.2550 - 7.65276i) q^{67} +(0.130278 - 0.486205i) q^{68} +(-1.72079 + 2.98050i) q^{69} +(-1.68888 - 6.30298i) q^{71} +(-1.24941 + 2.16403i) q^{72} +8.03602i q^{73} +(-4.33293 - 2.50162i) q^{74} +(-0.387571 + 1.44643i) q^{76} +(0.0284639 + 0.0284639i) q^{77} +(-5.83912 - 3.45083i) q^{78} +15.0122i q^{79} +(-2.92082 - 5.05900i) q^{81} +(-10.5340 + 2.82259i) q^{82} +12.7028 q^{83} +(-0.0304881 + 0.00816925i) q^{84} +(-6.27414 - 6.27414i) q^{86} +(3.43131 + 12.8058i) q^{87} +(-2.04831 - 0.548844i) q^{88} +(-12.8161 - 3.43407i) q^{89} +(0.0515791 + 0.200632i) q^{91} +(-0.614840 + 0.614840i) q^{92} +(4.01859 + 6.96040i) q^{93} +(7.36270 - 4.25086i) q^{94} +(2.16687 - 2.16687i) q^{96} +(-1.42718 - 0.823984i) q^{97} +(7.72996 + 4.46289i) q^{98} +(-0.409009 + 0.409009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{4} - 12 q^{6} - 24 q^{9} + 8 q^{11} - 32 q^{16} + 24 q^{19} + 32 q^{21} - 56 q^{24} + 76 q^{26} + 36 q^{29} + 8 q^{31} - 44 q^{34} - 60 q^{36} - 44 q^{39} - 52 q^{41} + 80 q^{44} - 60 q^{46}+ \cdots - 208 q^{99}+O(q^{100}) \) 40 * q + 24 * q^4 - 12 * q^6 - 24 * q^9 + 8 * q^11 - 32 * q^16 + 24 * q^19 + 32 * q^21 - 56 * q^24 + 76 * q^26 + 36 * q^29 + 8 * q^31 - 44 * q^34 - 60 * q^36 - 44 * q^39 - 52 * q^41 + 80 * q^44 - 60 * q^46 - 28 * q^49 + 68 * q^54 + 72 * q^56 + 72 * q^59 - 144 * q^64 + 24 * q^66 + 80 * q^69 - 52 * q^71 - 168 * q^74 + 8 * q^76 - 20 * q^81 + 248 * q^84 - 168 * q^86 - 60 * q^89 - 100 * q^91 + 156 * q^94 - 36 * q^96 - 208 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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