LMFDB - Embedded newform 900.2.z.b.179.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(179,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.179"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [224] 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			179.7
Character	$\chi$	$=$	900.179
Dual form			900.2.z.b.719.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31270 + 0.526124i) q^{2} +(1.44639 - 1.38129i) q^{4} +(-0.701604 + 2.12315i) q^{5} +3.43527 q^{7} +(-1.17195 + 2.57421i) q^{8} +(-0.196039 - 3.15620i) q^{10} +(0.730731 - 2.24896i) q^{11} +(1.45315 - 0.472157i) q^{13} +(-4.50950 + 1.80738i) q^{14} +(0.184073 - 3.99576i) q^{16} +(3.14556 - 2.28538i) q^{17} +(2.03462 + 2.80041i) q^{19} +(1.91789 + 4.04001i) q^{20} +(0.223997 + 3.33668i) q^{22} +(1.42594 + 0.463318i) q^{23} +(-4.01550 - 2.97922i) q^{25} +(-1.65914 + 1.38434i) q^{26} +(4.96874 - 4.74511i) q^{28} +(2.23743 - 3.07956i) q^{29} +(-1.91642 - 2.63773i) q^{31} +(1.86063 + 5.34210i) q^{32} +(-2.92680 + 4.65499i) q^{34} +(-2.41020 + 7.29359i) q^{35} +(-7.74142 + 2.51534i) q^{37} +(-4.14422 - 2.60566i) q^{38} +(-4.64317 - 4.29429i) q^{40} +(-3.94721 + 1.28253i) q^{41} +11.2094 q^{43} +(-2.04955 - 4.26222i) q^{44} +(-2.11561 + 0.142024i) q^{46} +(2.74947 - 3.78433i) q^{47} +4.80111 q^{49} +(6.83861 + 1.79818i) q^{50} +(1.44963 - 2.69015i) q^{52} +(9.57230 + 6.95468i) q^{53} +(4.26219 + 3.12933i) q^{55} +(-4.02597 + 8.84310i) q^{56} +(-1.31685 + 5.21971i) q^{58} +(-0.280171 - 0.862278i) q^{59} +(-3.37411 + 10.3845i) q^{61} +(3.90347 + 2.45429i) q^{62} +(-5.25307 - 6.03368i) q^{64} +(-0.0170778 + 3.41652i) q^{65} +(12.5591 - 9.12471i) q^{67} +(1.39292 - 7.65048i) q^{68} +(-0.673447 - 10.8424i) q^{70} +(-2.60663 - 1.89383i) q^{71} +(3.87104 + 1.25778i) q^{73} +(8.83881 - 7.37484i) q^{74} +(6.81104 + 1.24008i) q^{76} +(2.51026 - 7.72579i) q^{77} +(-4.64276 + 6.39021i) q^{79} +(8.35444 + 3.19426i) q^{80} +(4.50675 - 3.76030i) q^{82} +(5.24031 + 7.21267i) q^{83} +(2.64526 + 8.28192i) q^{85} +(-14.7147 + 5.89755i) q^{86} +(4.93290 + 4.51672i) q^{88} +(1.86308 + 0.605351i) q^{89} +(4.99197 - 1.62199i) q^{91} +(2.70244 - 1.29951i) q^{92} +(-1.61822 + 6.41427i) q^{94} +(-7.37319 + 2.35501i) q^{95} +(-5.43793 + 7.48466i) q^{97} +(-6.30244 + 2.52598i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 8 q^{4} - 12 q^{10} - 8 q^{16} - 8 q^{25} + 92 q^{34} + 40 q^{37} + 36 q^{40} - 40 q^{46} + 368 q^{49} - 100 q^{52} - 120 q^{58} + 48 q^{61} - 16 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{85} - 120 q^{88}+ \cdots + 200 q^{97}+O(q^{100}) $ 224 * q + 8 * q^4 - 12 * q^10 - 8 * q^16 - 8 * q^25 + 92 * q^34 + 40 * q^37 + 36 * q^40 - 40 * q^46 + 368 * q^49 - 100 * q^52 - 120 * q^58 + 48 * q^61 - 16 * q^64 - 40 * q^70 + 24 * q^76 - 120 * q^85 - 120 * q^88 - 4 * q^94 + 200 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.31270	+	0.526124i	−0.928222	+	0.372026i
$2$	−1.31270	+	0.526124i	−0.928222	+	0.372026i
$3$		0			0
$3$		0			0
$4$	1.44639	−	1.38129i	0.723194	−	0.690645i
$5$	−0.701604	+	2.12315i	−0.313767	+	0.949500i
$5$	−0.701604	+	2.12315i	−0.313767	+	0.949500i
$6$		0			0
$7$	3.43527			1.29841			0.649206	−	0.760613i	$-0.275101\pi$
$7$	3.43527			1.29841			0.649206	+	0.760613i	$0.275101\pi$
$8$	−1.17195	+	2.57421i	−0.414347	+	0.910119i
$9$		0			0
$10$	−0.196039	−	3.15620i	−0.0619929	−	0.998077i
$11$	0.730731	−	2.24896i	0.220324	−	0.678087i	−0.778409	−	0.627758i	$-0.783973\pi$
$11$	0.730731	−	2.24896i	0.220324	−	0.678087i	0.998733	−	0.0503293i	$-0.0160271\pi$
$12$		0			0
$13$	1.45315	−	0.472157i	0.403032	−	0.130953i	−0.100485	−	0.994939i	$-0.532039\pi$
$13$	1.45315	−	0.472157i	0.403032	−	0.130953i	0.503516	+	0.863986i	$0.332039\pi$
$14$	−4.50950	+	1.80738i	−1.20521	+	0.483043i
$15$		0			0
$16$	0.184073	−	3.99576i	0.0460182	−	0.998941i
$17$	3.14556	−	2.28538i	0.762910	−	0.554287i	−0.136891	−	0.990586i	$-0.543711\pi$
$17$	3.14556	−	2.28538i	0.762910	−	0.554287i	0.899802	+	0.436299i	$0.143711\pi$
$18$		0			0
$19$	2.03462	+	2.80041i	0.466774	+	0.642459i	0.975896	−	0.218235i	$-0.0700299\pi$
$19$	2.03462	+	2.80041i	0.466774	+	0.642459i	−0.509122	+	0.860694i	$0.670030\pi$
$20$	1.91789	+	4.04001i	0.428853	+	0.903374i
$21$		0			0
$22$	0.223997	+	3.33668i	0.0477563	+	0.711382i
$23$	1.42594	+	0.463318i	0.297330	+	0.0966084i	0.453883	−	0.891061i	$-0.350038\pi$
$23$	1.42594	+	0.463318i	0.297330	+	0.0966084i	−0.156553	+	0.987670i	$0.550038\pi$
$24$		0			0
$25$	−4.01550	−	2.97922i	−0.803101	−	0.595844i
$26$	−1.65914	+	1.38434i	−0.325385	+	0.271492i
$27$		0			0
$28$	4.96874	−	4.74511i	0.939003	−	0.896742i
$29$	2.23743	−	3.07956i	0.415480	−	0.571859i	−0.549064	−	0.835780i	$-0.685016\pi$
$29$	2.23743	−	3.07956i	0.415480	−	0.571859i	0.964544	+	0.263921i	$0.0850158\pi$
$30$		0			0
$31$	−1.91642	−	2.63773i	−0.344200	−	0.473751i	0.601462	−	0.798901i	$-0.294585\pi$
$31$	−1.91642	−	2.63773i	−0.344200	−	0.473751i	−0.945662	+	0.325151i	$0.894585\pi$
$32$	1.86063	+	5.34210i	0.328916	+	0.944359i
$33$		0			0
$34$	−2.92680	+	4.65499i	−0.501941	+	0.798324i
$35$	−2.41020	+	7.29359i	−0.407399	+	1.23284i
$36$		0			0
$37$	−7.74142	+	2.51534i	−1.27268	+	0.413519i	−0.865997	−	0.500050i	$-0.833315\pi$
$37$	−7.74142	+	2.51534i	−1.27268	+	0.413519i	−0.406684	+	0.913569i	$0.633315\pi$
$38$	−4.14422	−	2.60566i	−0.672281	−	0.422693i
$39$		0			0
$40$	−4.64317	−	4.29429i	−0.734150	−	0.678988i
$41$	−3.94721	+	1.28253i	−0.616451	+	0.200297i	−0.600564	−	0.799577i	$-0.705057\pi$
$41$	−3.94721	+	1.28253i	−0.616451	+	0.200297i	−0.0158868	+	0.999874i	$0.505057\pi$
$42$		0			0
$43$	11.2094			1.70942			0.854712	−	0.519103i	$-0.173734\pi$
$43$	11.2094			1.70942			0.854712	+	0.519103i	$0.173734\pi$
$44$	−2.04955	−	4.26222i	−0.308981	−	0.642554i
$45$		0			0
$46$	−2.11561	+	0.142024i	−0.311929	+	0.0209404i
$47$	2.74947	−	3.78433i	0.401052	−	0.552001i	−0.559956	−	0.828523i	$-0.689182\pi$
$47$	2.74947	−	3.78433i	0.401052	−	0.552001i	0.961008	+	0.276522i	$0.0891818\pi$
$48$		0			0
$49$	4.80111			0.685873
$50$	6.83861	+	1.79818i	0.967125	+	0.254301i
$51$		0			0
$52$	1.44963	−	2.69015i	0.201028	−	0.373056i
$53$	9.57230	+	6.95468i	1.31486	+	0.955299i	0.999981	+	0.00616573i	$0.00196262\pi$
$53$	9.57230	+	6.95468i	1.31486	+	0.955299i	0.314875	+	0.949133i	$0.398037\pi$
$54$		0			0
$55$	4.26219	+	3.12933i	0.574713	+	0.421959i
$56$	−4.02597	+	8.84310i	−0.537993	+	1.18171i
$57$		0			0
$58$	−1.31685	+	5.21971i	−0.172912	+	0.685382i
$59$	−0.280171	−	0.862278i	−0.0364752	−	0.112259i	0.931161	−	0.364608i	$-0.118797\pi$
$59$	−0.280171	−	0.862278i	−0.0364752	−	0.112259i	−0.967636	+	0.252349i	$0.918797\pi$
$60$		0			0
$61$	−3.37411	+	10.3845i	−0.432011	+	1.32959i	0.464108	+	0.885779i	$0.346375\pi$
$61$	−3.37411	+	10.3845i	−0.432011	+	1.32959i	−0.896119	+	0.443814i	$0.853625\pi$
$62$	3.90347	+	2.45429i	0.495741	+	0.311695i
$63$		0			0
$64$	−5.25307	−	6.03368i	−0.656633	−	0.754210i
$65$	−0.0170778	+	3.41652i	−0.00211824	+	0.423767i
$66$		0			0
$67$	12.5591	−	9.12471i	1.53434	−	1.11476i	0.580570	−	0.814210i	$-0.302830\pi$
$67$	12.5591	−	9.12471i	1.53434	−	1.11476i	0.953766	−	0.300550i	$-0.0971703\pi$
$68$	1.39292	−	7.65048i	0.168916	−	0.927757i
$69$		0			0
$70$	−0.673447	−	10.8424i	−0.0804923	−	1.29591i
$71$	−2.60663	−	1.89383i	−0.309350	−	0.224756i	0.422268	−	0.906471i	$-0.361234\pi$
$71$	−2.60663	−	1.89383i	−0.309350	−	0.224756i	−0.731617	+	0.681715i	$0.761234\pi$
$72$		0			0
$73$	3.87104	+	1.25778i	0.453071	+	0.147212i	0.526658	−	0.850077i	$-0.323445\pi$
$73$	3.87104	+	1.25778i	0.453071	+	0.147212i	−0.0735872	+	0.997289i	$0.523445\pi$
$74$	8.83881	−	7.37484i	1.02749	−	0.857308i
$75$		0			0
$76$	6.81104	+	1.24008i	0.781279	+	0.142247i
$77$	2.51026	−	7.72579i	0.286071	−	0.880436i
$78$		0			0
$79$	−4.64276	+	6.39021i	−0.522351	+	0.718954i	−0.985941	−	0.167096i	$-0.946561\pi$
$79$	−4.64276	+	6.39021i	−0.522351	+	0.718954i	0.463590	+	0.886050i	$0.346561\pi$
$80$	8.35444	+	3.19426i	0.934055	+	0.357129i
$81$		0			0
$82$	4.50675	−	3.76030i	0.497688	−	0.415256i
$83$	5.24031	+	7.21267i	0.575199	+	0.791694i	0.993159	−	0.116772i	$-0.0372546\pi$
$83$	5.24031	+	7.21267i	0.575199	+	0.791694i	−0.417960	+	0.908466i	$0.637255\pi$
$84$		0			0
$85$	2.64526	+	8.28192i	0.286919	+	0.898300i
$86$	−14.7147	+	5.89755i	−1.58673	+	0.635950i
$87$		0			0
$88$	4.93290	+	4.51672i	0.525849	+	0.481484i
$89$	1.86308	+	0.605351i	0.197486	+	0.0641671i	0.406090	−	0.913833i	$-0.366892\pi$
$89$	1.86308	+	0.605351i	0.197486	+	0.0641671i	−0.208604	+	0.978000i	$0.566892\pi$
$90$		0			0
$91$	4.99197	−	1.62199i	0.523301	−	0.170031i
$92$	2.70244	−	1.29951i	0.281749	−	0.135483i
$93$		0			0
$94$	−1.61822	+	6.41427i	−0.166907	+	0.661581i
$95$	−7.37319	+	2.35501i	−0.756473	+	0.241619i
$96$		0			0
$97$	−5.43793	+	7.48466i	−0.552138	+	0.759953i	−0.990300	−	0.138943i	$-0.955629\pi$
$97$	−5.43793	+	7.48466i	−0.552138	+	0.759953i	0.438163	+	0.898896i	$0.355629\pi$
$98$	−6.30244	+	2.52598i	−0.636642	+	0.255162i
$99$		0			0
$100$	−9.92314	+	1.23747i	−0.992314	+	0.123747i
$101$			18.1021i			1.80123i	0.434622	+	0.900613i	$0.356882\pi$
$101$			18.1021i			1.80123i	−0.434622	+	0.900613i	$0.643118\pi$
$102$		0			0
$103$	6.46907	+	4.70006i	0.637417	+	0.463110i	0.858962	−	0.512040i	$-0.171110\pi$
$103$	6.46907	+	4.70006i	0.637417	+	0.463110i	−0.221545	+	0.975150i	$0.571110\pi$
$104$	−0.487590	+	4.29405i	−0.0478121	+	0.421067i
$105$		0			0
$106$	−16.2246	−	4.09323i	−1.57587	−	0.397569i
$107$		−	4.67085i		−	0.451548i	−0.974180	−	0.225774i	$-0.927509\pi$
$107$		−	4.67085i		−	0.451548i	0.974180	−	0.225774i	$-0.0724911\pi$
$108$		0			0
$109$	0.329375	+	1.01371i	0.0315484	+	0.0970960i	0.965591	−	0.260066i	$-0.0837444\pi$
$109$	0.329375	+	1.01371i	0.0315484	+	0.0970960i	−0.934042	+	0.357162i	$0.883744\pi$
$110$	−7.24141	−	1.86545i	−0.690441	−	0.177863i
$111$		0			0
$112$	0.632341	−	13.7265i	0.0597506	−	1.29704i
$113$	−3.95661	−	12.1772i	−0.372206	−	1.14553i	−0.945344	−	0.326074i	$-0.894274\pi$
$113$	−3.95661	−	12.1772i	−0.372206	−	1.14553i	0.573138	−	0.819459i	$-0.305726\pi$
$114$		0			0
$115$	−1.98414	+	2.70242i	−0.185022	+	0.252002i
$116$	−1.01757	−	7.54477i	−0.0944793	−	0.700514i
$117$		0			0
$118$	0.821447	+	0.984512i	0.0756203	+	0.0906317i
$119$	10.8059	−	7.85092i	0.990572	−	0.719692i
$120$		0			0
$121$	4.37533	+	3.17887i	0.397758	+	0.288988i
$122$	−1.03429	−	15.4069i	−0.0936406	−	1.39488i
$123$		0			0
$124$	−6.41537	−	1.16804i	−0.576117	−	0.104893i
$125$	9.14261	−	6.43527i	0.817740	−	0.575588i
$126$		0			0
$127$	−5.71122	+	17.5773i	−0.506789	+	1.55973i	0.290954	+	0.956737i	$0.406027\pi$
$127$	−5.71122	+	17.5773i	−0.506789	+	1.55973i	−0.797743	+	0.602998i	$0.793973\pi$
$128$	10.0702	+	5.15667i	0.890087	+	0.455790i
$129$		0			0
$130$	−1.77509	−	4.49387i	−0.155686	−	0.394138i
$131$	5.54960	−	4.03202i	0.484871	−	0.352279i	−0.318338	−	0.947977i	$-0.603125\pi$
$131$	5.54960	−	4.03202i	0.484871	−	0.352279i	0.803208	+	0.595698i	$0.203125\pi$
$132$		0			0
$133$	6.98948	+	9.62019i	0.606065	+	0.834176i
$134$	−11.6856	+	18.5857i	−1.00949	+	1.60556i
$135$		0			0
$136$	2.19661	+	10.7757i	0.188358	+	0.924006i
$137$	−5.15016	−	15.8506i	−0.440008	−	1.35420i	−0.887867	−	0.460100i	$-0.847813\pi$
$137$	−5.15016	−	15.8506i	−0.440008	−	1.35420i	0.447859	−	0.894104i	$-0.352187\pi$
$138$		0			0
$139$	−12.0509	−	3.91556i	−1.02214	−	0.332114i	−0.250463	−	0.968126i	$-0.580583\pi$
$139$	−12.0509	−	3.91556i	−1.02214	−	0.332114i	−0.771679	+	0.636012i	$0.780583\pi$
$140$	6.58848	+	13.8785i	0.556828	+	1.17295i
$141$		0			0
$142$	4.41812	+	1.11462i	0.370760	+	0.0935372i
$143$		−	3.61310i		−	0.302142i
$144$		0			0
$145$	4.96856	+	6.91102i	0.412616	+	0.573929i
$146$	−5.74328	+	0.385557i	−0.475317	+	0.0319089i
$147$		0			0
$148$	−7.72267	+	14.3313i	−0.634800	+	1.17803i
$149$			4.27947i			0.350588i	0.984516	+	0.175294i	$0.0560876\pi$
$149$			4.27947i			0.350588i	−0.984516	+	0.175294i	$0.943912\pi$
$150$		0			0
$151$		−	15.7916i		−	1.28510i	−0.766244	−	0.642550i	$-0.777876\pi$
$151$		−	15.7916i		−	1.28510i	0.766244	−	0.642550i	$-0.222124\pi$
$152$	−9.59331	+	1.95559i	−0.778121	+	0.158619i
$153$		0			0
$154$	0.769491	+	11.4624i	0.0620073	+	0.923666i
$155$	6.94486	−	2.21821i	0.557825	−	0.178171i
$156$		0			0
$157$		−	17.3068i		−	1.38124i	−0.723220	−	0.690618i	$-0.757339\pi$
$157$		−	17.3068i		−	1.38124i	0.723220	−	0.690618i	$-0.242661\pi$
$158$	2.73253	−	10.8311i	0.217388	−	0.861678i
$159$		0			0
$160$	−12.6475	+	0.202354i	−0.999872	+	0.0159975i
$161$	4.89851	+	1.59162i	0.386057	+	0.125437i
$162$		0			0
$163$	5.44935	+	16.7714i	0.426826	+	1.31364i	0.901235	+	0.433331i	$0.142662\pi$
$163$	5.44935	+	16.7714i	0.426826	+	1.31364i	−0.474409	+	0.880305i	$0.657338\pi$
$164$	−3.93765	+	7.30727i	−0.307479	+	0.570602i
$165$		0			0
$166$	−10.6737	−	6.71106i	−0.828443	−	0.520879i
$167$	−9.55072	−	13.1454i	−0.739057	−	1.01722i	−0.998672	−	0.0515122i	$-0.983596\pi$
$167$	−9.55072	−	13.1454i	−0.739057	−	1.01722i	0.259616	−	0.965712i	$-0.416404\pi$
$168$		0			0
$169$	−8.62851	+	6.26898i	−0.663731	+	0.482229i
$170$	−7.82977	−	9.47998i	−0.600516	−	0.727081i
$171$		0			0
$172$	16.2132	−	15.4835i	1.23624	−	1.18061i
$173$	−7.18585	+	22.1158i	−0.546330	+	1.68143i	0.171476	+	0.985188i	$0.445147\pi$
$173$	−7.18585	+	22.1158i	−0.546330	+	1.68143i	−0.717806	+	0.696243i	$0.754853\pi$
$174$		0			0
$175$	−13.7944	−	10.2344i	−1.04276	−	0.773650i
$176$	−8.85180	−	3.33380i	−0.667230	−	0.251295i
$177$		0			0
$178$	−2.76416	+	0.185563i	−0.207183	+	0.0139086i
$179$	0.578608	+	0.420384i	0.0432472	+	0.0314209i	0.609199	−	0.793017i	$-0.291491\pi$
$179$	0.578608	+	0.420384i	0.0432472	+	0.0314209i	−0.565952	+	0.824438i	$0.691491\pi$
$180$		0			0
$181$	3.87505	−	2.81539i	0.288030	−	0.209266i	−0.434382	−	0.900729i	$-0.643033\pi$
$181$	3.87505	−	2.81539i	0.288030	−	0.209266i	0.722412	+	0.691463i	$0.243033\pi$
$182$	−5.69962	+	4.75559i	−0.422484	+	0.352508i
$183$		0			0
$184$	−2.86381	+	3.12769i	−0.211123	+	0.230576i
$185$	0.0909790	−	18.2009i	0.00668891	−	1.33816i
$186$		0			0
$187$	−2.84118	−	8.74424i	−0.207767	−	0.639442i
$188$	−1.25045	−	9.27142i	−0.0911984	−	0.676188i
$189$		0			0
$190$	8.43979	−	6.97065i	0.612287	−	0.505704i
$191$	−6.49285	−	19.9829i	−0.469806	−	1.44592i	−0.852836	−	0.522179i	$-0.825119\pi$
$191$	−6.49285	−	19.9829i	−0.469806	−	1.44592i	0.383030	−	0.923736i	$-0.374881\pi$
$192$		0			0
$193$		−	3.79268i		−	0.273003i	−0.990640	−	0.136502i	$-0.956414\pi$
$193$		−	3.79268i		−	0.273003i	0.990640	−	0.136502i	$-0.0435859\pi$
$194$	3.20053	−	12.6862i	0.229785	−	0.910814i
$195$		0			0
$196$	6.94426	−	6.63173i	0.496019	−	0.473695i
$197$	11.7352	+	8.52610i	0.836097	+	0.607460i	0.921278	−	0.388906i	$-0.127147\pi$
$197$	11.7352	+	8.52610i	0.836097	+	0.607460i	−0.0851809	+	0.996366i	$0.527147\pi$
$198$		0			0
$199$			8.72439i			0.618456i	0.950988	+	0.309228i	$0.100071\pi$
$199$			8.72439i			0.618456i	−0.950988	+	0.309228i	$0.899929\pi$
$200$	12.3751	−	6.84524i	0.875051	−	0.484031i
$201$		0			0
$202$	−9.52394	−	23.7627i	−0.670102	−	1.67194i
$203$	7.68618	−	10.5791i	0.539464	−	0.742509i
$204$		0			0
$205$	0.0463886	−	9.28033i	0.00323992	−	0.648166i
$206$	−10.9648	−	2.76625i	−0.763953	−	0.192734i
$207$		0			0
$208$	−1.61914	−	5.89336i	−0.112267	−	0.408631i
$209$	7.78478	−	2.52943i	0.538485	−	0.174964i
$210$		0			0
$211$	−19.6141	−	6.37301i	−1.35029	−	0.438736i	−0.457502	−	0.889209i	$-0.651256\pi$
$211$	−19.6141	−	6.37301i	−1.35029	−	0.438736i	−0.892790	+	0.450472i	$0.851256\pi$
$212$	23.4517	−	3.16296i	1.61067	−	0.217233i
$213$		0			0
$214$	2.45744	+	6.13144i	0.167987	+	0.419137i
$215$	−7.86459	+	23.7993i	−0.536361	+	1.62310i
$216$		0			0
$217$	−6.58344	−	9.06133i	−0.446913	−	0.615123i
$218$	−0.965710	−	1.15741i	−0.0654061	−	0.0783899i
$219$		0			0
$220$	10.4873	−	1.36110i	0.707053	−	0.0917650i
$221$	3.49191	−	4.80621i	0.234891	−	0.323300i
$222$		0			0
$223$	2.77892	−	8.55265i	0.186090	−	0.572728i	−0.813875	−	0.581040i	$-0.802646\pi$
$223$	2.77892	−	8.55265i	0.186090	−	0.572728i	0.999965	+	0.00831243i	$0.00264596\pi$
$224$	6.39178	+	18.3516i	0.427069	+	1.22617i
$225$		0			0
$226$	11.6006	+	13.9034i	0.771658	+	0.924839i
$227$	−23.5240	−	7.64340i	−1.56134	−	0.507310i	−0.604175	−	0.796852i	$-0.706497\pi$
$227$	−23.5240	−	7.64340i	−1.56134	−	0.507310i	−0.957165	+	0.289542i	$0.906497\pi$
$228$		0			0
$229$	−15.1664	−	11.0190i	−1.00222	−	0.728157i	−0.0396586	−	0.999213i	$-0.512627\pi$
$229$	−15.1664	−	11.0190i	−1.00222	−	0.728157i	−0.962563	+	0.271056i	$0.912627\pi$
$230$	1.18278	−	4.59139i	0.0779902	−	0.302747i
$231$		0			0
$232$	5.30526	+	9.36868i	0.348307	+	0.615084i
$233$	−15.9910	+	11.6181i	−1.04760	+	0.761128i	−0.971755	−	0.235992i	$-0.924166\pi$
$233$	−15.9910	+	11.6181i	−1.04760	+	0.761128i	−0.0758471	+	0.997119i	$0.524166\pi$
$234$		0			0
$235$	6.10564	+	8.49263i	0.398288	+	0.553998i
$236$	−1.59629	−	0.860190i	−0.103910	−	0.0559936i
$237$		0			0
$238$	−10.0543	+	15.9912i	−0.651727	+	1.03655i
$239$	9.07932	−	27.9433i	0.587292	−	1.80750i	−0.00257093	−	0.999997i	$-0.500818\pi$
$239$	9.07932	−	27.9433i	0.587292	−	1.80750i	0.589863	−	0.807503i	$-0.299182\pi$
$240$		0			0
$241$	−8.87392	−	27.3111i	−0.571619	−	1.75926i	−0.647413	−	0.762139i	$-0.724149\pi$
$241$	−8.87392	−	27.3111i	−0.571619	−	1.75926i	0.0757936	−	0.997124i	$-0.475851\pi$
$242$	−7.41600	−	1.87095i	−0.476719	−	0.120269i
$243$		0			0
$244$	9.46367	+	19.6806i	0.605850	+	1.25992i
$245$	−3.36848	+	10.1935i	−0.215204	+	0.651236i
$246$		0			0
$247$	4.27885	+	3.10876i	0.272256	+	0.197806i
$248$	9.03602	−	1.84198i	0.573788	−	0.116966i
$249$		0			0
$250$	−8.61580	+	13.2578i	−0.544911	+	0.838494i
$251$	−3.22553			−0.203593			−0.101797	−	0.994805i	$-0.532459\pi$
$251$	−3.22553			−0.203593			−0.101797	+	0.994805i	$0.532459\pi$
$252$		0			0
$253$	2.08397	−	2.86833i	0.131018	−	0.180330i
$254$	−1.75071	−	26.0786i	−0.109849	−	1.63632i
$255$		0			0
$256$	−15.9322	−	1.47102i	−0.995765	−	0.0919390i
$257$	−13.9266			−0.868718			−0.434359	−	0.900740i	$-0.643025\pi$
$257$	−13.9266			−0.868718			−0.434359	+	0.900740i	$0.643025\pi$
$258$		0			0
$259$	−26.5939	+	8.64088i	−1.65246	+	0.536918i
$260$	4.69451	+	4.96520i	0.291141	+	0.307929i
$261$		0			0
$262$	−5.16364	+	8.21263i	−0.319011	+	0.507378i
$263$	11.6451	−	3.78371i	0.718066	−	0.233314i	0.0728816	−	0.997341i	$-0.476780\pi$
$263$	11.6451	−	3.78371i	0.718066	−	0.233314i	0.645185	+	0.764027i	$0.276780\pi$
$264$		0			0
$265$	−21.4818	+	15.4440i	−1.31961	+	0.948715i
$266$	−14.2365	−	8.95114i	−0.872898	−	0.548830i
$267$		0			0
$268$	5.56143	−	30.5456i	0.339718	−	1.86587i
$269$	−6.04324	−	8.31781i	−0.368463	−	0.507146i	0.584019	−	0.811740i	$-0.301479\pi$
$269$	−6.04324	−	8.31781i	−0.368463	−	0.507146i	−0.952482	+	0.304594i	$0.901479\pi$
$270$		0			0
$271$	11.9844	−	16.4951i	0.728000	−	1.00201i	−0.271220	−	0.962517i	$-0.587427\pi$
$271$	11.9844	−	16.4951i	0.728000	−	1.00201i	0.999220	−	0.0394888i	$-0.0125729\pi$
$272$	−8.55283	−	12.9896i	−0.518592	−	0.787609i
$273$		0			0
$274$	15.1000	+	18.0975i	0.912224	+	1.09331i
$275$	−9.63440	+	6.85370i	−0.580976	+	0.413293i
$276$		0			0
$277$	7.18100	+	2.33325i	0.431464	+	0.140191i	0.516694	−	0.856170i	$-0.327162\pi$
$277$	7.18100	+	2.33325i	0.431464	+	0.140191i	−0.0852299	+	0.996361i	$0.527162\pi$
$278$	17.8793	−	1.20027i	1.07233	−	0.0719874i
$279$		0			0
$280$	−15.9506	−	14.7521i	−0.953229	−	0.881605i
$281$	6.47806	+	8.91628i	0.386449	+	0.531901i	0.957279	−	0.289167i	$-0.0933785\pi$
$281$	6.47806	+	8.91628i	0.386449	+	0.531901i	−0.570830	+	0.821068i	$0.693378\pi$
$282$		0			0
$283$	4.15850	−	3.02133i	0.247197	−	0.179599i	−0.457286	−	0.889319i	$-0.651179\pi$
$283$	4.15850	−	3.02133i	0.247197	−	0.179599i	0.704484	+	0.709720i	$0.251179\pi$
$284$	−6.38612	+	0.861304i	−0.378946	+	0.0511090i
$285$		0			0
$286$	1.90094	+	4.74293i	0.112405	+	0.280455i
$287$	−13.5597	+	4.40583i	−0.800406	+	0.260068i
$288$		0			0
$289$	−0.581718	+	1.79034i	−0.0342187	+	0.105314i
$290$	−10.1583	−	6.45805i	−0.596516	−	0.379230i
$291$		0			0
$292$	7.33638	−	3.52780i	0.429329	−	0.206449i
$293$	−24.2603			−1.41730			−0.708651	−	0.705559i	$-0.750696\pi$
$293$	−24.2603			−1.41730			−0.708651	+	0.705559i	$0.750696\pi$
$294$		0			0
$295$	2.02731	+	0.0101337i	0.118035	+	0.000590007i
$296$	2.59755	−	22.8758i	0.150980	−	1.32963i
$297$		0			0
$298$	−2.25153	−	5.61768i	−0.130428	−	0.325423i
$299$	2.29087			0.132485
$300$		0			0
$301$	38.5075			2.21954
$302$	8.30833	+	20.7297i	0.478090	+	1.19286i
$303$		0			0
$304$	11.5643	−	7.61438i	0.663259	−	0.436715i
$305$	−19.6804	−	14.4495i	−1.12690	−	0.827377i
$306$		0			0
$307$	20.0722			1.14558			0.572790	−	0.819702i	$-0.305861\pi$
$307$	20.0722			1.14558			0.572790	+	0.819702i	$0.305861\pi$
$308$	−7.04075	−	14.6419i	−0.401184	−	0.834299i
$309$		0			0
$310$	−7.94950	+	6.56571i	−0.451501	+	0.372907i
$311$	−9.42055	+	28.9935i	−0.534191	+	1.64407i	0.211201	+	0.977443i	$0.432263\pi$
$311$	−9.42055	+	28.9935i	−0.534191	+	1.64407i	−0.745392	+	0.666627i	$0.767737\pi$
$312$		0			0
$313$	0.223170	−	0.0725124i	0.0126143	−	0.00409864i	−0.302703	−	0.953085i	$-0.597889\pi$
$313$	0.223170	−	0.0725124i	0.0126143	−	0.00409864i	0.315317	+	0.948986i	$0.397889\pi$
$314$	9.10554	+	22.7188i	0.513855	+	1.28209i
$315$		0			0
$316$	2.11151	+	15.6557i	0.118782	+	0.880702i
$317$	−3.68113	+	2.67450i	−0.206753	+	0.150215i	−0.686343	−	0.727278i	$-0.740785\pi$
$317$	−3.68113	+	2.67450i	−0.206753	+	0.150215i	0.479591	+	0.877492i	$0.340785\pi$
$318$		0			0
$319$	−5.29084	−	7.28221i	−0.296230	−	0.407726i
$320$	16.4960	−	6.91978i	0.922152	−	0.386827i
$321$		0			0
$322$	−7.26769	+	0.487893i	−0.405013	+	0.0271892i
$323$	12.8000	+	4.15898i	0.712213	+	0.231412i
$324$		0			0
$325$	−7.24179	−	2.43330i	−0.401702	−	0.134975i
$326$	−15.9772	−	19.1488i	−0.884896	−	1.06056i
$327$		0			0
$328$	1.32444	−	11.6640i	0.0731302	−	0.644036i
$329$	9.44520	−	13.0002i	0.520730	−	0.716724i
$330$		0			0
$331$	−16.6371	−	22.8990i	−0.914459	−	1.25864i	−0.965621	−	0.259955i	$-0.916292\pi$
$331$	−16.6371	−	22.8990i	−0.914459	−	1.25864i	0.0511618	−	0.998690i	$-0.483708\pi$
$332$	17.5423	+	3.19392i	0.962760	+	0.175289i
$333$		0			0
$334$	19.4534	+	12.2312i	1.06444	+	0.669262i
$335$	10.5616	+	33.0667i	0.577041	+	1.80663i
$336$		0			0
$337$	9.01053	−	2.92770i	0.490835	−	0.159482i	−0.0531337	−	0.998587i	$-0.516921\pi$
$337$	9.01053	−	2.92770i	0.490835	−	0.159482i	0.543969	+	0.839105i	$0.316921\pi$
$338$	8.02842	−	12.7690i	0.436689	−	0.694541i
$339$		0			0
$340$	15.2658	+	8.32498i	0.827905	+	0.451486i
$341$	−7.33254	+	2.38249i	−0.397080	+	0.129019i
$342$		0			0
$343$	−7.55380			−0.407867
$344$	−13.1369	+	28.8554i	−0.708294	+	1.55578i
$345$		0			0
$346$	−2.20274	−	32.8121i	−0.118420	−	1.76399i
$347$	−6.60242	+	9.08745i	−0.354436	+	0.487840i	−0.948588	−	0.316513i	$-0.897488\pi$
$347$	−6.60242	+	9.08745i	−0.354436	+	0.487840i	0.594152	+	0.804353i	$0.297488\pi$
$348$		0			0
$349$	18.1568			0.971910			0.485955	−	0.873984i	$-0.338472\pi$
$349$	18.1568			0.971910			0.485955	+	0.873984i	$0.338472\pi$
$350$	23.4925	+	6.17725i	1.25573	+	0.330188i
$351$		0			0
$352$	13.3738	−	0.280847i	0.712826	−	0.0149692i
$353$	−4.87451	−	3.54154i	−0.259444	−	0.188497i	0.450458	−	0.892798i	$-0.351261\pi$
$353$	−4.87451	−	3.54154i	−0.259444	−	0.188497i	−0.709902	+	0.704301i	$0.751261\pi$
$354$		0			0
$355$	5.84969	−	4.20554i	0.310469	−	0.223207i
$356$	3.53090	−	1.69788i	0.187137	−	0.0899876i
$357$		0			0
$358$	−0.980716	−	0.247420i	−0.0518324	−	0.0130765i
$359$	1.45304	+	4.47201i	0.0766887	+	0.236024i	0.982051	−	0.188617i	$-0.0604005\pi$
$359$	1.45304	+	4.47201i	0.0766887	+	0.236024i	−0.905362	+	0.424641i	$0.860400\pi$
$360$		0			0
$361$	2.16868	−	6.67451i	0.114141	−	0.351290i
$362$	−3.60555	+	5.73452i	−0.189503	+	0.301400i
$363$		0			0
$364$	4.97989	−	9.24139i	0.261017	−	0.484380i
$365$	−5.38639	+	7.33633i	−0.281936	+	0.384001i
$366$		0			0
$367$	−11.8779	+	8.62978i	−0.620020	+	0.450471i	−0.852928	−	0.522028i	$-0.825176\pi$
$367$	−11.8779	+	8.62978i	−0.620020	+	0.450471i	0.232909	+	0.972499i	$0.425176\pi$
$368$	2.11378	−	5.61245i	0.110189	−	0.292569i
$369$		0			0
$370$	9.45652	+	23.9403i	0.491621	+	1.24460i
$371$	32.8835	+	23.8912i	1.70722	+	1.24037i
$372$		0			0
$373$	−7.61522	−	2.47433i	−0.394301	−	0.128116i	0.105154	−	0.994456i	$-0.466466\pi$
$373$	−7.61522	−	2.47433i	−0.394301	−	0.128116i	−0.499455	+	0.866340i	$0.666466\pi$
$374$	8.33018	+	9.98379i	0.430743	+	0.516250i
$375$		0			0
$376$	6.51939	+	11.5127i	0.336212	+	0.593725i
$377$	1.79729	−	5.53148i	0.0925649	−	0.284886i
$378$		0			0
$379$	−17.0583	+	23.4787i	−0.876224	+	1.20602i	0.101229	+	0.994863i	$0.467723\pi$
$379$	−17.0583	+	23.4787i	−0.876224	+	1.20602i	−0.977453	+	0.211155i	$0.932277\pi$
$380$	−7.41153	+	13.5908i	−0.380203	+	0.697192i
$381$		0			0
$382$	19.0367	+	22.8157i	0.974002	+	1.16735i
$383$	12.8918	+	17.7441i	0.658741	+	0.906679i	0.999439	−	0.0334938i	$-0.0106634\pi$
$383$	12.8918	+	17.7441i	0.658741	+	0.906679i	−0.340698	+	0.940173i	$0.610663\pi$
$384$		0			0
$385$	14.6418	+	10.7501i	0.746214	+	0.547876i
$386$	1.99542	+	4.97868i	0.101564	+	0.253408i
$387$		0			0
$388$	2.47315	+	18.3371i	0.125555	+	0.930924i
$389$	34.7466	+	11.2899i	1.76172	+	0.572418i	0.997377	−	0.0723886i	$-0.0230622\pi$
$389$	34.7466	+	11.2899i	1.76172	+	0.572418i	0.764346	+	0.644807i	$0.223062\pi$
$390$		0			0
$391$	5.54425	−	1.80144i	0.280385	−	0.0911026i
$392$	−5.62666	+	12.3590i	−0.284189	+	0.624226i
$393$		0			0
$394$	−19.8906	−	5.01810i	−1.00207	−	0.252808i
$395$	−10.3100	−	14.3406i	−0.518751	−	0.721556i
$396$		0			0
$397$	−10.7059	+	14.7354i	−0.537313	+	0.739548i	−0.988223	−	0.153021i	$-0.951100\pi$
$397$	−10.7059	+	14.7354i	−0.537313	+	0.739548i	0.450910	+	0.892570i	$0.351100\pi$
$398$	−4.59011	−	11.4525i	−0.230081	−	0.574064i
$399$		0			0
$400$	−12.6434	+	15.4966i	−0.632170	+	0.774830i
$401$		−	12.6832i		−	0.633368i	−0.948531	−	0.316684i	$-0.897431\pi$
$401$		−	12.6832i		−	0.633368i	0.948531	−	0.316684i	$-0.102569\pi$
$402$		0			0
$403$	−4.03028	−	2.92817i	−0.200762	−	0.145862i
$404$	25.0043	+	26.1826i	1.24401	+	1.30264i
$405$		0			0
$406$	−4.52376	+	17.9311i	−0.224510	+	0.889908i
$407$			19.2482i			0.954096i
$408$		0			0
$409$	−4.16491	−	12.8183i	−0.205941	−	0.633822i	−0.999673	−	0.0255548i	$-0.991865\pi$
$409$	−4.16491	−	12.8183i	−0.205941	−	0.633822i	0.793732	−	0.608268i	$-0.208135\pi$
$410$	4.82171	+	12.2067i	0.238127	+	0.602848i
$411$		0			0
$412$	15.8489	−	2.13757i	0.780821	−	0.105310i
$413$	−0.962465	−	2.96216i	−0.0473598	−	0.145758i
$414$		0			0
$415$	−18.9902	+	6.06551i	−0.932192	+	0.297744i
$416$	5.22609	+	6.88437i	0.256230	+	0.337534i
$417$		0			0
$418$	−8.88833	+	7.41615i	−0.434742	+	0.362736i
$419$	−21.5948	+	15.6895i	−1.05497	+	0.766483i	−0.973152	−	0.230164i	$-0.926074\pi$
$419$	−21.5948	+	15.6895i	−1.05497	+	0.766483i	−0.0818214	+	0.996647i	$0.526074\pi$
$420$		0			0
$421$	1.22050	+	0.886744i	0.0594835	+	0.0432173i	0.617130	−	0.786861i	$-0.288295\pi$
$421$	1.22050	+	0.886744i	0.0594835	+	0.0432173i	−0.557646	+	0.830079i	$0.688295\pi$
$422$	29.1005	−	1.95357i	1.41659	−	0.0950984i
$423$		0			0
$424$	−29.1210	+	16.4905i	−1.41424	+	0.800851i
$425$	−19.4397	−	0.194347i	−0.942962	−	0.00942720i
$426$		0			0
$427$	−11.5910	+	35.6734i	−0.560928	+	1.72636i
$428$	−6.45180	−	6.75585i	−0.311859	−	0.326557i
$429$		0			0
$430$	−2.19748	−	35.3792i	−0.105972	−	1.70614i
$431$	15.3284	−	11.1368i	0.738344	−	0.536439i	−0.153848	−	0.988095i	$-0.549167\pi$
$431$	15.3284	−	11.1368i	0.738344	−	0.536439i	0.892192	+	0.451656i	$0.149167\pi$
$432$		0			0
$433$	15.3692	+	21.1538i	0.738595	+	1.01659i	0.998698	+	0.0510075i	$0.0162433\pi$
$433$	15.3692	+	21.1538i	0.738595	+	1.01659i	−0.260104	+	0.965581i	$0.583757\pi$
$434$	13.4095	+	8.43115i	0.643677	+	0.404708i
$435$		0			0
$436$	1.87663	+	1.01126i	0.0898745	+	0.0484305i
$437$	1.60377	+	4.93591i	0.0767190	+	0.236117i
$438$		0			0
$439$	13.8269	+	4.49263i	0.659922	+	0.214422i	0.619784	−	0.784772i	$-0.287220\pi$
$439$	13.8269	+	4.49263i	0.659922	+	0.214422i	0.0401382	+	0.999194i	$0.487220\pi$
$440$	−13.0506	+	7.30433i	−0.622163	+	0.348220i
$441$		0			0
$442$	−2.05519	+	8.14631i	−0.0977555	+	0.387480i
$443$			22.2812i			1.05861i	0.848432	+	0.529305i	$0.177547\pi$
$443$			22.2812i			1.05861i	−0.848432	+	0.529305i	$0.822453\pi$
$444$		0			0
$445$	−2.59239	+	3.53087i	−0.122891	+	0.167380i
$446$	0.851846	+	12.6892i	0.0403361	+	0.600849i
$447$		0			0
$448$	−18.0457	−	20.7273i	−0.852581	−	0.979275i
$449$		−	1.85840i		−	0.0877033i	−0.999038	−	0.0438517i	$-0.986037\pi$
$449$		−	1.85840i		−	0.0877033i	0.999038	−	0.0438517i	$-0.0139629\pi$
$450$		0			0
$451$			9.81430i			0.462137i
$452$	−22.5430	−	12.1477i	−1.06033	−	0.571380i
$453$		0			0
$454$	34.9014	−	2.34299i	1.63800	−	0.109962i
$455$	−0.0586669	+	11.7367i	−0.00275035	+	0.550224i
$456$		0			0
$457$		−	15.3954i		−	0.720166i	−0.932920	−	0.360083i	$-0.882748\pi$
$457$		−	15.3954i		−	0.720166i	0.932920	−	0.360083i	$-0.117252\pi$
$458$	25.7063	+	6.48532i	1.20118	+	0.303039i
$459$		0			0
$460$	0.862998	+	6.64943i	0.0402375	+	0.310031i
$461$	36.5175	+	11.8652i	1.70079	+	0.552620i	0.988757	−	0.149529i	$-0.0477756\pi$
$461$	36.5175	+	11.8652i	1.70079	+	0.552620i	0.712031	+	0.702148i	$0.247776\pi$
$462$		0			0
$463$	−5.23291	−	16.1053i	−0.243194	−	0.748475i	−0.995928	−	0.0901499i	$-0.971265\pi$
$463$	−5.23291	−	16.1053i	−0.243194	−	0.748475i	0.752734	−	0.658325i	$-0.228735\pi$
$464$	−11.8933	−	9.50709i	−0.552134	−	0.441356i
$465$		0			0
$466$	14.8788	−	23.6644i	0.689249	−	1.09623i
$467$	−20.3268	−	27.9774i	−0.940611	−	1.29464i	−0.955574	−	0.294751i	$-0.904763\pi$
$467$	−20.3268	−	27.9774i	−0.940611	−	1.29464i	0.0149634	−	0.999888i	$-0.495237\pi$
$468$		0			0
$469$	43.1439	−	31.3459i	1.99220	−	1.44742i
$470$	−12.4831	−	7.93600i	−0.575801	−	0.366060i
$471$		0			0
$472$	2.54803	+	0.289328i	0.117282	+	0.0133174i
$473$	8.19109	−	25.2096i	0.376627	−	1.15914i
$474$		0			0
$475$	0.173022	−	17.3066i	0.00793879	−	0.794083i
$476$	4.78506	−	26.2815i	0.219323	−	1.20461i
$477$		0			0
$478$	2.78316	+	41.4581i	0.127299	+	1.89625i
$479$	12.6049	+	9.15800i	0.575933	+	0.418440i	0.837255	−	0.546812i	$-0.184159\pi$
$479$	12.6049	+	9.15800i	0.575933	+	0.418440i	−0.261323	+	0.965251i	$0.584159\pi$
$480$		0			0
$481$	−10.0618	+	7.31033i	−0.458779	+	0.333322i
$482$	26.0179	+	31.1826i	1.18508	+	1.42033i
$483$		0			0
$484$	10.7194	−	1.44574i	0.487244	−	0.0657153i
$485$	−12.0758	−	16.7968i	−0.548332	−	0.762703i
$486$		0			0
$487$	−1.84136	−	5.66711i	−0.0834398	−	0.256801i	0.900629	−	0.434588i	$-0.143106\pi$
$487$	−1.84136	−	5.66711i	−0.0834398	−	0.256801i	−0.984069	+	0.177787i	$0.943106\pi$
$488$	−22.7774	−	20.8557i	−1.03109	−	0.944094i
$489$		0			0
$490$	−0.941203	−	15.1532i	−0.0425192	−	0.684553i
$491$	−3.02850	−	9.32076i	−0.136674	−	0.420640i	0.859173	−	0.511686i	$-0.170979\pi$
$491$	−3.02850	−	9.32076i	−0.136674	−	0.420640i	−0.995847	+	0.0910462i	$0.970979\pi$
$492$		0			0
$493$		−	14.8003i		−	0.666572i
$494$	−7.25246	−	1.82969i	−0.326303	−	0.0823215i
$495$		0			0
$496$	−10.8925	+	7.17204i	−0.489088	+	0.322034i
$497$	−8.95448	−	6.50581i	−0.401663	−	0.291825i
$498$		0			0
$499$		−	26.9543i		−	1.20664i	−0.797498	−	0.603321i	$-0.793844\pi$
$499$		−	26.9543i		−	1.20664i	0.797498	−	0.603321i	$-0.206156\pi$
$500$	4.33478	−	21.9365i	0.193857	−	0.981030i
$501$		0			0
$502$	4.23416	−	1.69703i	0.188980	−	0.0757420i
$503$	−19.2943	+	26.5563i	−0.860289	+	1.18409i	0.121212	+	0.992627i	$0.461322\pi$
$503$	−19.2943	+	26.5563i	−0.860289	+	1.18409i	−0.981501	+	0.191459i	$0.938678\pi$
$504$		0			0
$505$	−38.4334	−	12.7005i	−1.71026	−	0.565165i
$506$	−1.22653	+	4.86170i	−0.0545260	+	0.216129i
$507$		0			0
$508$	16.0188	+	33.3125i	0.710717	+	1.47800i
$509$	0.604155	−	0.196302i	0.0267787	−	0.00870093i	−0.295597	−	0.955313i	$-0.595519\pi$
$509$	0.604155	−	0.196302i	0.0267787	−	0.00870093i	0.322376	+	0.946612i	$0.395519\pi$
$510$		0			0
$511$	13.2981	+	4.32081i	0.588273	+	0.191141i
$512$	21.6883	−	6.45131i	0.958495	−	0.285110i
$513$		0			0
$514$	18.2815	−	7.32712i	0.806364	−	0.323185i
$515$	−14.5176	+	10.4372i	−0.639723	+	0.459918i
$516$		0			0
$517$	−6.50167	−	8.94878i	−0.285943	−	0.393567i
$518$	30.3637	−	25.3346i	1.33411	−	1.11314i
$519$		0			0
$520$	−8.77481	−	4.04795i	−0.384801	−	0.177514i
$521$	−0.742307	+	1.02170i	−0.0325210	+	0.0447614i	−0.824968	−	0.565180i	$-0.808807\pi$
$521$	−0.742307	+	1.02170i	−0.0325210	+	0.0447614i	0.792447	+	0.609941i	$0.208807\pi$
$522$		0			0
$523$	2.02653	−	6.23700i	0.0886138	−	0.272725i	−0.896923	−	0.442187i	$-0.854203\pi$
$523$	2.02653	−	6.23700i	0.0886138	−	0.272725i	0.985537	+	0.169462i	$0.0542029\pi$
$524$	2.45748	−	13.4975i	0.107355	−	0.589640i
$525$		0			0
$526$	−13.2958	+	11.0937i	−0.579726	+	0.483706i
$527$	−12.0565	−	3.91738i	−0.525187	−	0.170644i
$528$		0			0
$529$	−16.7887	−	12.1977i	−0.729945	−	0.530336i
$530$	20.0738	−	31.5754i	0.871950	−	1.37155i
$531$		0			0
$532$	23.3978	+	4.26002i	1.01442	+	0.184695i
$533$	−5.13034	+	3.72741i	−0.222220	+	0.161452i
$534$		0			0
$535$	9.91689	+	3.27709i	0.428745	+	0.141681i
$536$	8.77026	+	43.0234i	0.378818	+	1.85833i
$537$		0			0
$538$	12.3092	+	7.73934i	0.530687	+	0.333667i
$539$	3.50832	−	10.7975i	0.151114	−	0.465081i
$540$		0			0
$541$	−7.29634	−	22.4558i	−0.313694	−	0.965451i	−0.976289	−	0.216473i	$-0.930545\pi$
$541$	−7.29634	−	22.4558i	−0.313694	−	0.965451i	0.662595	−	0.748978i	$-0.269455\pi$
$542$	−7.05350	+	27.9585i	−0.302974	+	1.20092i
$543$		0			0
$544$	18.0615	+	12.5516i	0.774379	+	0.538147i
$545$	−2.38335	−	0.0119134i	−0.102091	−	0.000510314i
$546$		0			0
$547$	−22.5885	−	16.4115i	−0.965812	−	0.701704i	−0.0113190	−	0.999936i	$-0.503603\pi$
$547$	−22.5885	−	16.4115i	−0.965812	−	0.701704i	−0.954493	+	0.298232i	$0.903603\pi$
$548$	−29.3433	−	15.8122i	−1.25349	−	0.675463i
$549$		0			0
$550$	9.04122	−	14.0658i	0.385519	−	0.599766i
$551$	13.1763			0.561331
$552$		0			0
$553$	−15.9491	+	21.9521i	−0.678226	+	0.933499i
$554$	−10.6541	+	0.715229i	−0.452649	+	0.0303872i
$555$		0			0
$556$	−22.8388	+	10.9823i	−0.968579	+	0.465754i
$557$	7.81352			0.331069			0.165535	−	0.986204i	$-0.447065\pi$
$557$	7.81352			0.331069			0.165535	+	0.986204i	$0.447065\pi$
$558$		0			0
$559$	16.2890	−	5.29262i	0.688952	−	0.223854i
$560$	28.6998	+	10.9732i	1.21279	+	0.463700i
$561$		0			0
$562$	−13.1948	−	8.29618i	−0.556591	−	0.349953i
$563$	10.3840	−	3.37397i	0.437633	−	0.142196i	−0.0819101	−	0.996640i	$-0.526102\pi$
$563$	10.3840	−	3.37397i	0.437633	−	0.142196i	0.519544	+	0.854444i	$0.326102\pi$
$564$		0			0
$565$	28.6299	+	0.143109i	1.20447	+	0.00602065i
$566$	−3.86929	+	6.15400i	−0.162639	+	0.258672i
$567$		0			0
$568$	7.92993	−	4.49053i	0.332733	−	0.188418i
$569$	7.10001	+	9.77233i	0.297648	+	0.409677i	0.931480	−	0.363794i	$-0.118519\pi$
$569$	7.10001	+	9.77233i	0.297648	+	0.409677i	−0.633831	+	0.773471i	$0.718519\pi$
$570$		0			0
$571$	−9.21182	+	12.6790i	−0.385503	+	0.530599i	−0.957032	−	0.289983i	$-0.906350\pi$
$571$	−9.21182	+	12.6790i	−0.385503	+	0.530599i	0.571529	+	0.820582i	$0.306350\pi$
$572$	−4.99074	−	5.22594i	−0.208673	−	0.218508i
$573$		0			0
$574$	15.4819	−	12.9177i	0.646203	−	0.539173i
$575$	−4.34556	−	6.10865i	−0.181222	−	0.254748i
$576$		0			0
$577$	−9.30409	−	3.02308i	−0.387334	−	0.125853i	0.108875	−	0.994055i	$-0.465275\pi$
$577$	−9.30409	−	3.02308i	−0.387334	−	0.125853i	−0.496209	+	0.868203i	$0.665275\pi$
$578$	−0.178319	−	2.65625i	−0.00741708	−	0.110485i
$579$		0			0
$580$	16.7326	+	3.13299i	0.694783	+	0.130090i
$581$	18.0019	+	24.7775i	0.746845	+	1.02794i
$582$		0			0
$583$	22.6356	−	16.4457i	0.937470	−	0.681112i
$584$	−7.77444	+	8.49080i	−0.321709	+	0.351352i
$585$		0			0
$586$	31.8466	−	12.7639i	1.31557	−	0.527273i
$587$	19.0031	−	6.17449i	0.784342	−	0.254848i	0.110649	−	0.993860i	$-0.464707\pi$
$587$	19.0031	−	6.17449i	0.784342	−	0.254848i	0.673693	+	0.739011i	$0.264707\pi$
$588$		0			0
$589$	3.48755	−	10.7336i	0.143702	−	0.442269i
$590$	−2.66659	+	1.05331i	−0.109782	+	0.0433643i
$591$		0			0
$592$	8.62571	+	31.3959i	0.354514	+	1.29036i
$593$	7.21240			0.296178			0.148089	−	0.988974i	$-0.452688\pi$
$593$	7.21240			0.296178			0.148089	+	0.988974i	$0.452688\pi$
$594$		0			0
$595$	9.08721	+	28.4507i	0.372539	+	1.16636i
$596$	5.91119	+	6.18977i	0.242132	+	0.253543i
$597$		0			0
$598$	−3.00724	+	1.20528i	−0.122975	+	0.0492877i
$599$	−27.6797			−1.13096			−0.565482	−	0.824761i	$-0.691310\pi$
$599$	−27.6797			−1.13096			−0.565482	+	0.824761i	$0.691310\pi$
$600$		0			0
$601$	−37.3547			−1.52373			−0.761866	−	0.647735i	$-0.775716\pi$
$601$	−37.3547			−1.52373			−0.761866	+	0.647735i	$0.775716\pi$
$602$	−50.5490	+	20.2597i	−2.06022	+	0.825724i
$603$		0			0
$604$	−21.8128	−	22.8407i	−0.887549	−	0.929377i
$605$	−9.81895	+	7.05917i	−0.399197	+	0.286996i
$606$		0			0
$607$	13.0458			0.529514			0.264757	−	0.964315i	$-0.414708\pi$
$607$	13.0458			0.529514			0.264757	+	0.964315i	$0.414708\pi$
$608$	−11.1744	+	16.0797i	−0.453182	+	0.652118i
$609$		0			0
$610$	33.4368	+	8.61361i	1.35382	+	0.348755i
$611$	2.20860	−	6.79738i	0.0893505	−	0.274993i
$612$		0			0
$613$	12.6609	−	4.11379i	0.511371	−	0.166154i	−0.0419549	−	0.999120i	$-0.513359\pi$
$613$	12.6609	−	4.11379i	0.511371	−	0.166154i	0.553325	+	0.832965i	$0.313359\pi$
$614$	−26.3488	+	10.5604i	−1.06335	+	0.426185i
$615$		0			0
$616$	16.9459	+	15.5162i	0.682769	+	0.625164i
$617$	20.3883	−	14.8130i	0.820803	−	0.596348i	−0.0961397	−	0.995368i	$-0.530650\pi$
$617$	20.3883	−	14.8130i	0.820803	−	0.596348i	0.916942	+	0.399020i	$0.130650\pi$
$618$		0			0
$619$	−19.0871	−	26.2712i	−0.767176	−	1.05593i	−0.996583	−	0.0825968i	$-0.973679\pi$
$619$	−19.0871	−	26.2712i	−0.767176	−	1.05593i	0.229407	−	0.973331i	$-0.426321\pi$
$620$	6.98098	−	12.8013i	0.280363	−	0.514111i
$621$		0			0
$622$	−2.88776	−	43.0163i	−0.115789	−	1.72479i
$623$	6.40019	+	2.07955i	0.256418	+	0.0833153i
$624$		0			0
$625$	7.24852	+	23.9261i	0.289941	+	0.957045i
$626$	−0.254806	+	0.212603i	−0.0101841	+	0.00849731i
$627$		0			0
$628$	−23.9058	−	25.0324i	−0.953944	−	0.998901i
$629$	−18.6026	+	25.6042i	−0.741733	+	1.02091i
$630$		0			0
$631$	−19.9530	−	27.4630i	−0.794316	−	1.09328i	−0.993557	−	0.113332i	$-0.963848\pi$
$631$	−19.9530	−	27.4630i	−0.794316	−	1.09328i	0.199241	−	0.979951i	$-0.436152\pi$
$632$	−11.0086	−	19.4404i	−0.437900	−	0.773298i
$633$		0			0
$634$	3.42512	−	5.44755i	0.136029	−	0.216350i
$635$	−33.3122	−	24.4581i	−1.32195	−	0.970589i
$636$		0			0
$637$	6.97673	−	2.26688i	0.276428	−	0.0898170i
$638$	10.7767	+	6.77576i	0.426652	+	0.268255i
$639$		0			0
$640$	−18.0137	+	17.7625i	−0.712053	+	0.702126i
$641$	−42.6296	+	13.8512i	−1.68377	+	0.547089i	−0.985636	−	0.168882i	$-0.945984\pi$
$641$	−42.6296	+	13.8512i	−1.68377	+	0.547089i	−0.698130	+	0.715971i	$0.745984\pi$
$642$		0			0
$643$	30.5522			1.20486			0.602431	−	0.798171i	$-0.294199\pi$
$643$	30.5522			1.20486			0.602431	+	0.798171i	$0.294199\pi$
$644$	9.28364	−	4.46416i	0.365827	−	0.175913i
$645$		0			0
$646$	−18.9908	+	1.27489i	−0.747184	+	0.0501597i
$647$	10.1772	−	14.0077i	0.400107	−	0.550700i	−0.560664	−	0.828043i	$-0.689454\pi$
$647$	10.1772	−	14.0077i	0.400107	−	0.550700i	0.960771	+	0.277344i	$0.0894541\pi$
$648$		0			0
$649$	−2.14396			−0.0841577
$650$	10.7866	−	0.615869i	0.423083	−	0.0241564i
$651$		0			0
$652$	31.0480	+	16.7308i	1.21593	+	0.655227i
$653$	1.88511	+	1.36961i	0.0737701	+	0.0535971i	0.624059	−	0.781377i	$-0.285482\pi$
$653$	1.88511	+	1.36961i	0.0737701	+	0.0535971i	−0.550289	+	0.834974i	$0.685482\pi$
$654$		0			0
$655$	4.66695	+	14.6115i	0.182353	+	0.570918i
$656$	4.39809	+	16.0082i	0.171717	+	0.625015i
$657$		0			0
$658$	−5.55904	+	22.0348i	−0.216714	+	0.859004i
$659$	−7.13053	−	21.9455i	−0.277766	−	0.854876i	−0.988474	−	0.151389i	$-0.951625\pi$
$659$	−7.13053	−	21.9455i	−0.277766	−	0.854876i	0.710708	−	0.703487i	$-0.248375\pi$
$660$		0			0
$661$	−2.22509	+	6.84813i	−0.0865460	+	0.266361i	−0.984958	−	0.172792i	$-0.944721\pi$
$661$	−2.22509	+	6.84813i	−0.0865460	+	0.266361i	0.898412	+	0.439153i	$0.144721\pi$
$662$	33.8874	+	21.3065i	1.31707	+	0.828100i
$663$		0			0
$664$	−24.7083	+	5.03676i	−0.958868	+	0.195464i
$665$	−25.3289	+	8.09012i	−0.982214	+	0.313721i
$666$		0			0
$667$	4.61726	−	3.35464i	0.178781	−	0.129892i
$668$	−31.9717	−	5.82108i	−1.23702	−	0.225224i
$669$		0			0
$670$	−31.2614	−	37.8501i	−1.20773	−	1.46228i
$671$	20.8886	+	15.1765i	0.806397	+	0.585882i
$672$		0			0
$673$	−2.01243	−	0.653879i	−0.0775736	−	0.0252052i	0.269973	−	0.962868i	$-0.412985\pi$
$673$	−2.01243	−	0.653879i	−0.0775736	−	0.0252052i	−0.347547	+	0.937663i	$0.612985\pi$
$674$	−10.2878	+	8.58386i	−0.396273	+	0.330638i
$675$		0			0
$676$	−3.82088	+	20.9858i	−0.146957	+	0.807148i
$677$	−3.44979	+	10.6174i	−0.132586	+	0.408058i	−0.995207	−	0.0977933i	$-0.968822\pi$
$677$	−3.44979	+	10.6174i	−0.132586	+	0.408058i	0.862621	+	0.505851i	$0.168822\pi$
$678$		0			0
$679$	−18.6808	+	25.7119i	−0.716902	+	0.986731i
$680$	−24.4195	−	2.89654i	−0.936444	−	0.111077i
$681$		0			0
$682$	8.37198	−	6.98533i	0.320580	−	0.267482i
$683$	8.37096	+	11.5216i	0.320306	+	0.440863i	0.938561	−	0.345115i	$-0.112160\pi$
$683$	8.37096	+	11.5216i	0.320306	+	0.440863i	−0.618255	+	0.785978i	$0.712160\pi$
$684$		0			0
$685$	37.2664	+	0.186280i	1.42388	+	0.00711738i
$686$	9.91590	−	3.97423i	0.378591	−	0.151737i
$687$		0			0
$688$	2.06335	−	44.7903i	0.0786647	−	1.70761i
$689$	17.1937	+	5.58657i	0.655028	+	0.212831i
$690$		0			0
$691$	7.59176	−	2.46671i	0.288804	−	0.0938381i	−0.161032	−	0.986949i	$-0.551482\pi$
$691$	7.59176	−	2.46671i	0.288804	−	0.0938381i	0.449836	+	0.893111i	$0.351482\pi$
$692$	20.1548	+	41.9137i	0.766170	+	1.59332i
$693$		0			0
$694$	3.88590	−	15.4028i	0.147507	−	0.584683i
$695$	16.7683	−	22.8386i	0.636056	−	0.866317i
$696$		0			0
$697$	−9.48512	+	13.0551i	−0.359275	+	0.494499i
$698$	−23.8345	+	9.55271i	−0.902149	+	0.361576i
$699$		0			0
$700$	−34.0887	+	4.25106i	−1.28843	+	0.160675i
$701$		−	31.3681i		−	1.18476i	−0.805660	−	0.592378i	$-0.798189\pi$
$701$		−	31.3681i		−	1.18476i	0.805660	−	0.592378i	$-0.201811\pi$
$702$		0			0
$703$	−22.7948	−	16.5614i	−0.859723	−	0.624626i
$704$	−17.4081	+	7.40494i	−0.656092	+	0.279084i
$705$		0			0
$706$	8.26208	+	2.08440i	0.310948	+	0.0784474i
$707$			62.1857i			2.33873i
$708$		0			0
$709$	−8.63882	−	26.5876i	−0.324438	−	0.998517i	−0.971694	−	0.236244i	$-0.924083\pi$
$709$	−8.63882	−	26.5876i	−0.324438	−	0.998517i	0.647256	−	0.762273i	$-0.275917\pi$
$710$	−5.46628	+	8.59829i	−0.205146	+	0.322688i
$711$		0			0
$712$	−3.74173	+	4.08651i	−0.140227	+	0.153148i
$713$	−1.51061	−	4.64917i	−0.0565727	−	0.174113i
$714$		0			0
$715$	7.67114	+	2.53497i	0.286884	+	0.0948023i
$716$	1.41756	−	0.191189i	0.0529768	−	0.00714506i
$717$		0			0
$718$	−4.26025	−	5.10595i	−0.158991	−	0.190552i
$719$	−0.750131	+	0.545002i	−0.0279752	+	0.0203251i	−0.601685	−	0.798733i	$-0.705504\pi$
$719$	−0.750131	+	0.545002i	−0.0279752	+	0.0203251i	0.573710	+	0.819059i	$0.305504\pi$
$720$		0			0
$721$	22.2230	+	16.1460i	0.827629	+	0.601308i
$722$	0.664783	+	9.90266i	0.0247407	+	0.368539i
$723$		0			0
$724$	1.71595	−	9.42470i	0.0637728	−	0.350266i
$725$	−18.1591	+	5.70018i	−0.674411	+	0.211699i
$726$		0			0
$727$	−14.2075	+	43.7263i	−0.526928	+	1.62172i	0.233542	+	0.972347i	$0.424968\pi$
$727$	−14.2075	+	43.7263i	−0.526928	+	1.62172i	−0.760471	+	0.649372i	$0.775032\pi$
$728$	−1.67500	+	14.7513i	−0.0620798	+	0.546718i
$729$		0			0
$730$	3.21092	−	12.4643i	0.118841	−	0.461326i
$731$	35.2600	−	25.6179i	1.30414	−	0.947511i
$732$		0			0
$733$	4.63393	+	6.37806i	0.171158	+	0.235579i	0.885975	−	0.463732i	$-0.153490\pi$
$733$	4.63393	+	6.37806i	0.171158	+	0.235579i	−0.714817	+	0.699311i	$0.753490\pi$
$734$	11.0518	−	17.5776i	0.407930	−	0.648800i
$735$		0			0
$736$	0.178070	+	8.47961i	0.00656374	+	0.312562i
$737$	−11.3438	−	34.9126i	−0.417854	−	1.28602i
$738$		0			0
$739$	43.1005	+	14.0042i	1.58548	+	0.515153i	0.963460	−	0.267851i	$-0.0863136\pi$
$739$	43.1005	+	14.0042i	1.58548	+	0.515153i	0.622017	+	0.783004i	$0.286314\pi$
$740$	−25.0092	−	26.4513i	−0.919356	−	0.972368i
$741$		0			0
$742$	−55.7360	−	14.0614i	−2.04613	−	0.516209i
$743$		−	22.8323i		−	0.837637i	−0.908070	−	0.418818i	$-0.862444\pi$
$743$		−	22.8323i		−	0.837637i	0.908070	−	0.418818i	$-0.137556\pi$
$744$		0			0
$745$	−9.08594	−	3.00249i	−0.332883	−	0.110003i
$746$	11.2983	−	0.758477i	0.413661	−	0.0277698i
$747$		0			0
$748$	−16.1878	−	8.72307i	−0.591884	−	0.318947i
$749$		−	16.0456i		−	0.586295i
$750$		0			0
$751$			46.6161i			1.70105i	0.525938	+	0.850523i	$0.323715\pi$
$751$			46.6161i			1.70105i	−0.525938	+	0.850523i	$0.676285\pi$
$752$	−14.6152	−	11.6828i	−0.532960	−	0.426029i
$753$		0			0
$754$	0.550936	+	8.20679i	0.0200639	+	0.298874i
$755$	33.5278	+	11.0794i	1.22020	+	0.403222i
$756$		0			0
$757$			21.8576i			0.794429i	0.917726	+	0.397214i	$0.130023\pi$
$757$			21.8576i			0.794429i	−0.917726	+	0.397214i	$0.869977\pi$
$758$	10.0398	−	39.7953i	0.364661	−	1.44543i
$759$		0			0
$760$	2.57872	−	21.7401i	0.0935399	−	0.788595i
$761$	−5.10206	−	1.65776i	−0.184950	−	0.0600938i	0.215078	−	0.976597i	$-0.430999\pi$
$761$	−5.10206	−	1.65776i	−0.184950	−	0.0600938i	−0.400028	+	0.916503i	$0.630999\pi$
$762$		0			0
$763$	1.13149	+	3.48238i	0.0409628	+	0.126071i
$764$	−36.9934	−	19.9346i	−1.33838	−	0.721207i
$765$		0			0
$766$	−26.2587	−	16.5100i	−0.948766	−	0.596531i
$767$	−0.814262	−	1.12074i	−0.0294013	−	0.0404674i
$768$		0			0
$769$	−9.19533	+	6.68080i	−0.331592	+	0.240916i	−0.741106	−	0.671388i	$-0.765698\pi$
$769$	−9.19533	+	6.68080i	−0.331592	+	0.240916i	0.409514	+	0.912304i	$0.365698\pi$
$770$	−24.8762	−	6.40832i	−0.896477	−	0.230940i
$771$		0			0
$772$	−5.23880	−	5.48569i	−0.188549	−	0.197434i
$773$	−8.05831	+	24.8009i	−0.289837	+	0.892027i	0.695070	+	0.718942i	$0.255374\pi$
$773$	−8.05831	+	24.8009i	−0.289837	+	0.892027i	−0.984907	+	0.173085i	$0.944626\pi$
$774$		0			0
$775$	−0.162971	+	16.3013i	−0.00585408	+	0.585559i
$776$	−12.8941	−	22.7700i	−0.462871	−	0.817395i
$777$		0			0
$778$	−51.5519	+	3.46077i	−1.84822	+	0.124075i
$779$	−11.6227	−	8.44437i	−0.416426	−	0.302551i
$780$		0			0
$781$	−6.16388	+	4.47832i	−0.220561	+	0.160247i
$782$	−6.33019	+	5.28172i	−0.226367	+	0.188874i
$783$		0			0
$784$	0.883754	−	19.1841i	0.0315626	−	0.685146i
$785$	36.7449	+	12.1426i	1.31148	+	0.433386i
$786$		0			0
$787$	−8.00452	−	24.6354i	−0.285330	−	0.878156i	−0.986299	−	0.164965i	$-0.947249\pi$
$787$	−8.00452	−	24.6354i	−0.285330	−	0.878156i	0.700969	−	0.713192i	$-0.252751\pi$
$788$	28.7506	−	3.87764i	1.02420	−	0.138135i
$789$		0			0
$790$	21.0789	+	13.4007i	0.749954	+	0.476776i
$791$	−13.5920	−	41.8320i	−0.483277	−	1.48737i
$792$		0			0
$793$			16.6833i			0.592441i
$794$	6.30103	−	24.9759i	0.223615	−	0.886360i
$795$		0			0
$796$	12.0509	+	12.6188i	0.427133	+	0.447263i
$797$	−4.10905	−	2.98540i	−0.145550	−	0.105748i	0.512627	−	0.858611i	$-0.328672\pi$
$797$	−4.10905	−	2.98540i	−0.145550	−	0.105748i	−0.658177	+	0.752863i	$0.728672\pi$
$798$		0			0
$799$		−	18.1874i		−	0.643425i
$800$	8.44391	−	26.9945i	0.298537	−	0.954398i
$801$		0			0
$802$	6.67292	+	16.6493i	0.235629	+	0.587906i
$803$	5.65738	−	7.78672i	0.199645	−	0.274787i
$804$		0			0
$805$	−6.81607	+	9.28357i	−0.240235	+	0.327203i
$806$	6.83114	+	1.72339i	0.240617	+	0.0607040i
$807$		0			0
$808$	−46.5985	−	21.2147i	−1.63933	−	0.746332i
$809$	24.5989	−	7.99267i	0.864851	−	0.281007i	0.157198	−	0.987567i	$-0.449754\pi$
$809$	24.5989	−	7.99267i	0.864851	−	0.281007i	0.707653	+	0.706560i	$0.249754\pi$
$810$		0			0
$811$	1.23648	+	0.401758i	0.0434188	+	0.0141076i	0.330646	−	0.943755i	$-0.392733\pi$
$811$	1.23648	+	0.401758i	0.0434188	+	0.0141076i	−0.287227	+	0.957863i	$0.592733\pi$
$812$	−3.49564	−	25.9183i	−0.122673	−	0.909556i
$813$		0			0
$814$	−10.1269	−	25.2672i	−0.354948	−	0.885614i
$815$	−39.4314	−	0.197101i	−1.38122	−	0.00690416i
$816$		0			0
$817$	22.8070	+	31.3911i	0.797914	+	1.09823i
$818$	12.2113	+	14.6353i	0.426958	+	0.511713i
$819$		0			0
$820$	−12.7517	−	13.4870i	−0.445310	−	0.470987i
$821$	−9.98077	+	13.7374i	−0.348331	+	0.479437i	−0.946852	−	0.321671i	$-0.895756\pi$
$821$	−9.98077	+	13.7374i	−0.348331	+	0.479437i	0.598520	+	0.801108i	$0.295756\pi$
$822$		0			0
$823$	7.19258	−	22.1365i	0.250718	−	0.771629i	−0.743926	−	0.668262i	$-0.767038\pi$
$823$	7.19258	−	22.1365i	0.250718	−	0.771629i	0.994643	−	0.103367i	$-0.0329616\pi$
$824$	−19.6803	+	11.1445i	−0.685597	+	0.388237i
$825$		0			0
$826$	2.82190	+	3.38207i	0.0981863	+	0.117677i
$827$	−37.9703	−	12.3373i	−1.32036	−	0.429009i	−0.437738	−	0.899102i	$-0.644220\pi$
$827$	−37.9703	−	12.3373i	−1.32036	−	0.429009i	−0.882617	+	0.470093i	$0.844220\pi$
$828$		0			0
$829$	0.184828	+	0.134285i	0.00641934	+	0.00466392i	0.590990	−	0.806679i	$-0.298737\pi$
$829$	0.184828	+	0.134285i	0.00641934	+	0.00466392i	−0.584571	+	0.811343i	$0.698737\pi$
$830$	21.7373	−	17.9534i	0.754513	−	0.623172i
$831$		0			0
$832$	−10.4823	−	6.28757i	−0.363410	−	0.217982i
$833$	15.1022	−	10.9724i	0.523259	−	0.380170i
$834$		0			0
$835$	34.6105	−	11.0547i	1.19775	−	0.382563i
$836$	7.76593	−	14.4116i	0.268590	−	0.498435i
$837$		0			0
$838$	20.0929	−	31.9572i	0.694098	−	1.10394i
$839$	1.95272	−	6.00986i	0.0674154	−	0.207483i	−0.911674	−	0.410915i	$-0.865209\pi$
$839$	1.95272	−	6.00986i	0.0674154	−	0.207483i	0.979089	+	0.203431i	$0.0652094\pi$
$840$		0			0
$841$	4.48391	+	13.8001i	0.154618	+	0.475864i
$842$	−2.06869	−	0.521900i	−0.0712918	−	0.0179859i
$843$		0			0
$844$	−37.1726	+	17.8750i	−1.27953	+	0.615281i
$845$	−7.25616	−	22.7179i	−0.249619	−	0.781520i
$846$		0			0
$847$	15.0305	+	10.9203i	0.516453	+	0.375225i
$848$	29.5513	−	36.9685i	1.01479	−	1.26950i
$849$		0			0
$850$	25.6208	−	9.97255i	0.878785	−	0.342056i
$851$	−12.2042			−0.418356
$852$		0			0
$853$	−0.724183	+	0.996752i	−0.0247956	+	0.0341281i	−0.821235	−	0.570590i	$-0.806714\pi$
$853$	−0.724183	+	0.996752i	−0.0247956	+	0.0341281i	0.796439	+	0.604719i	$0.206714\pi$
$854$	−3.55308	−	52.9270i	−0.121584	−	1.81112i
$855$		0			0
$856$	12.0237	+	5.47400i	0.410962	+	0.187097i
$857$	18.6872			0.638343			0.319172	−	0.947697i	$-0.396595\pi$
$857$	18.6872			0.638343			0.319172	+	0.947697i	$0.396595\pi$
$858$		0			0
$859$	14.1118	−	4.58521i	0.481489	−	0.156445i	−0.0582081	−	0.998304i	$-0.518539\pi$
$859$	14.1118	−	4.58521i	0.481489	−	0.156445i	0.539697	+	0.841859i	$0.318539\pi$
$860$	21.4985	+	45.2863i	0.733092	+	1.54425i
$861$		0			0
$862$	−14.2624	+	22.6839i	−0.485779	+	0.772618i
$863$	−20.7376	+	6.73807i	−0.705917	+	0.229366i	−0.639907	−	0.768453i	$-0.721027\pi$
$863$	−20.7376	+	6.73807i	−0.705917	+	0.229366i	−0.0660104	+	0.997819i	$0.521027\pi$
$864$		0			0
$865$	−41.9134	−	30.7731i	−1.42510	−	1.04632i
$866$	−31.3047	−	19.6827i	−1.06378	−	0.668844i
$867$		0			0
$868$	−22.0385	−	4.01255i	−0.748037	−	0.136195i
$869$	10.9787	+	15.1109i	0.372427	+	0.512602i
$870$		0			0
$871$	13.9419	−	19.1894i	0.472405	−	0.650209i
$872$	−2.99551	−	0.340140i	−0.101441	−	0.0115186i
$873$		0			0
$874$	−4.70218	−	5.63561i	−0.159054	−	0.190627i
$875$	31.4074	−	22.1069i	1.06176	−	0.747350i
$876$		0			0
$877$	−23.5689	−	7.65800i	−0.795865	−	0.258592i	−0.117266	−	0.993101i	$-0.537413\pi$
$877$	−23.5689	−	7.65800i	−0.795865	−	0.258592i	−0.678600	+	0.734508i	$0.737413\pi$
$878$	−20.5143	+	1.37716i	−0.692325	+	0.0464770i
$879$		0			0
$880$	13.2886	−	16.4547i	0.447959	−	0.554687i
$881$	−2.29858	−	3.16373i	−0.0774412	−	0.106589i	0.768539	−	0.639803i	$-0.220984\pi$
$881$	−2.29858	−	3.16373i	−0.0774412	−	0.106589i	−0.845980	+	0.533214i	$0.820984\pi$
$882$		0			0
$883$	−28.8876	+	20.9881i	−0.972146	+	0.706305i	−0.955940	−	0.293564i	$-0.905159\pi$
$883$	−28.8876	+	20.9881i	−0.972146	+	0.706305i	−0.0162061	+	0.999869i	$0.505159\pi$
$884$	−1.58811	−	11.7750i	−0.0534138	−	0.396035i
$885$		0			0
$886$	−11.7227	−	29.2486i	−0.393830	−	0.982626i
$887$	29.4154	−	9.55763i	0.987671	−	0.320914i	0.229743	−	0.973251i	$-0.426212\pi$
$887$	29.4154	−	9.55763i	0.987671	−	0.320914i	0.757929	+	0.652338i	$0.226212\pi$
$888$		0			0
$889$	−19.6196	+	60.3829i	−0.658020	+	2.02518i
$890$	1.54537	−	5.99892i	0.0518010	−	0.201084i
$891$		0			0
$892$	−7.79429	−	16.2089i	−0.260972	−	0.542716i
$893$	16.1918			0.541838
$894$		0			0
$895$	−1.29849	+	0.933527i	−0.0434037	+	0.0312044i
$896$	34.5939	+	17.7146i	1.15570	+	0.591803i
$897$		0			0
$898$	0.977748	+	2.43953i	0.0326279	+	0.0814082i
$899$	−12.4109			−0.413927
$900$		0			0
$901$	46.0043			1.53263
$902$	−5.16354	−	12.8833i	−0.171927	−	0.428966i
$903$		0			0
$904$	35.9835	+	4.08593i	1.19679	+	0.135896i
$905$	3.25873	+	10.2026i	0.108324	+	0.339145i
$906$		0			0
$907$	−26.1280			−0.867565			−0.433782	−	0.901018i	$-0.642821\pi$
$907$	−26.1280			−0.867565			−0.433782	+	0.901018i	$0.642821\pi$
$908$	−44.5825	+	21.4381i	−1.47952	+	0.711449i
$909$		0			0
$910$	−6.09794	−	15.4377i	−0.202145	−	0.511754i
$911$	10.5533	−	32.4796i	0.349645	−	1.07610i	−0.609404	−	0.792860i	$-0.708591\pi$
$911$	10.5533	−	32.4796i	0.349645	−	1.07610i	0.959050	−	0.283238i	$-0.0914088\pi$
$912$		0			0
$913$	20.0503	−	6.51473i	0.663567	−	0.215606i
$914$	8.09988	+	20.2096i	0.267920	+	0.668474i
$915$		0			0
$916$	−37.1569	+	5.01140i	−1.22770	+	0.165581i
$917$	19.0644	−	13.8511i	0.629562	−	0.457403i
$918$		0			0
$919$	−14.5929	−	20.0854i	−0.481376	−	0.662557i	0.497393	−	0.867525i	$-0.334291\pi$
$919$	−14.5929	−	20.0854i	−0.481376	−	0.662557i	−0.978769	+	0.204969i	$0.934291\pi$
$920$	−4.63128	−	8.27469i	−0.152689	−	0.272808i
$921$		0			0
$922$	−54.1792	+	3.63715i	−1.78430	+	0.119783i
$923$	−4.68201	−	1.52128i	−0.154110	−	0.0500734i
$924$		0			0
$925$	38.5794	+	12.9630i	1.26848	+	0.426221i
$926$	15.3426	+	18.3883i	0.504190	+	0.604276i
$927$		0			0
$928$	20.6143	+	6.22265i	0.676699	+	0.204268i
$929$	−12.7076	+	17.4905i	−0.416922	+	0.573844i	−0.964890	−	0.262656i	$-0.915402\pi$
$929$	−12.7076	+	17.4905i	−0.416922	+	0.573844i	0.547968	+	0.836500i	$0.315402\pi$
$930$		0			0
$931$	9.76843	+	13.4451i	0.320147	+	0.440645i
$932$	−7.08113	+	38.8924i	−0.231950	+	1.27396i
$933$		0			0
$934$	41.4026	+	26.0317i	1.35474	+	0.851782i
$935$	20.5587	+	0.102764i	0.672341	+	0.00336076i
$936$		0			0
$937$	−24.2415	+	7.87654i	−0.791935	+	0.257315i	−0.676928	−	0.736049i	$-0.736689\pi$
$937$	−24.2415	+	7.87654i	−0.791935	+	0.257315i	−0.115007	+	0.993365i	$0.536689\pi$
$938$	−40.1434	+	63.8469i	−1.31073	+	2.08468i
$939$		0			0
$940$	20.5619	+	3.84998i	0.670656	+	0.125573i
$941$	12.2676	−	3.98597i	0.399911	−	0.129939i	−0.102155	−	0.994769i	$-0.532574\pi$
$941$	12.2676	−	3.98597i	0.399911	−	0.129939i	0.502065	+	0.864830i	$0.332574\pi$
$942$		0			0
$943$	−6.22272			−0.202640
$944$	−3.49703	+	0.960775i	−0.113819	+	0.0312706i
$945$		0			0
$946$	2.51088	+	37.4023i	0.0816358	+	1.21605i
$947$	29.7012	−	40.8801i	0.965158	−	1.32843i	0.0207028	−	0.999786i	$-0.493410\pi$
$947$	29.7012	−	40.8801i	0.965158	−	1.32843i	0.944455	−	0.328640i	$-0.106590\pi$
$948$		0			0
$949$	6.21908			0.201880
$950$	8.87831	+	22.8096i	0.288051	+	0.740040i
$951$		0			0
$952$	7.54595	+	37.0174i	0.244566	+	1.19974i
$953$	−14.5839	−	10.5958i	−0.472420	−	0.343233i	0.325964	−	0.945382i	$-0.394311\pi$
$953$	−14.5839	−	10.5958i	−0.472420	−	0.343233i	−0.798384	+	0.602149i	$0.794311\pi$
$954$		0			0
$955$	46.9821	+	0.234844i	1.52031	+	0.00759939i
$956$	−25.4656	−	52.9580i	−0.823615	−	1.71278i
$957$		0			0
$958$	−21.3648	−	5.39001i	−0.690264	−	0.174143i
$959$	−17.6922	−	54.4510i	−0.571311	−	1.75831i
$960$		0			0
$961$	6.29458	−	19.3727i	0.203051	−	0.624927i
$962$	9.36204	−	14.8901i	0.301844	−	0.480075i
$963$		0			0
$964$	−50.5597	−	27.2450i	−1.62842	−	0.877502i
$965$	8.05243	+	2.66096i	0.259217	+	0.0856595i
$966$		0			0
$967$	−24.1225	+	17.5260i	−0.775728	+	0.563600i	−0.903694	−	0.428179i	$-0.859155\pi$
$967$	−24.1225	+	17.5260i	−0.775728	+	0.563600i	0.127966	+	0.991779i	$0.459155\pi$
$968$	−13.3107	+	7.53754i	−0.427823	+	0.242266i
$969$		0			0
$970$	24.6891	+	15.6959i	0.792719	+	0.503964i
$971$	−6.56646	−	4.77082i	−0.210728	−	0.153103i	0.477415	−	0.878678i	$-0.341574\pi$
$971$	−6.56646	−	4.77082i	−0.210728	−	0.153103i	−0.688143	+	0.725575i	$0.741574\pi$
$972$		0			0
$973$	−41.3980	−	13.4510i	−1.32716	−	0.431220i
$974$	5.39876	+	6.47046i	0.172987	+	0.207327i
$975$		0			0
$976$	40.8727	+	15.3937i	1.30830	+	0.492739i
$977$	0.236606	−	0.728198i	0.00756969	−	0.0232971i	−0.947200	−	0.320642i	$-0.896101\pi$
$977$	0.236606	−	0.728198i	0.00756969	−	0.0232971i	0.954770	+	0.297345i	$0.0961012\pi$
$978$		0			0
$979$	2.72282	−	3.74764i	0.0870218	−	0.119775i
$980$	9.20800	+	19.3965i	0.294139	+	0.619600i
$981$		0			0
$982$	8.87939	+	10.6420i	0.283353	+	0.339601i
$983$	−12.0654	−	16.6066i	−0.384826	−	0.529668i	0.572029	−	0.820234i	$-0.306157\pi$
$983$	−12.0654	−	16.6066i	−0.384826	−	0.529668i	−0.956855	+	0.290565i	$0.906157\pi$
$984$		0			0
$985$	−26.3356	+	18.9335i	−0.839123	+	0.603273i
$986$	7.78679	+	19.4284i	0.247982	+	0.618727i
$987$		0			0
$988$	10.4830	−	1.41385i	0.333508	−	0.0449807i
$989$	15.9840	+	5.19353i	0.508263	+	0.165145i
$990$		0			0
$991$	−38.4894	+	12.5060i	−1.22266	+	0.397265i	−0.848048	−	0.529919i	$-0.822222\pi$
$991$	−38.4894	+	12.5060i	−1.22266	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$992$	10.5253	−	15.1456i	0.334178	−	0.480873i
$993$		0			0
$994$	15.1774	+	3.82904i	0.481399	+	0.121450i
$995$	−18.5232	−	6.12107i	−0.587224	−	0.194051i
$996$		0			0
$997$	−11.7297	+	16.1446i	−0.371484	+	0.511304i	−0.953304	−	0.302014i	$-0.902341\pi$
$997$	−11.7297	+	16.1446i	−0.371484	+	0.511304i	0.581819	+	0.813318i	$0.302341\pi$
$998$	14.1813	+	35.3831i	0.448902	+	1.12003i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.z.b.179.7	✓	224
3.2	odd	2	inner	900.2.z.b.179.50	yes	224
4.3	odd	2	inner	900.2.z.b.179.37	yes	224
12.11	even	2	inner	900.2.z.b.179.20	yes	224
25.19	even	10	inner	900.2.z.b.719.20	yes	224
75.44	odd	10	inner	900.2.z.b.719.37	yes	224
100.19	odd	10	inner	900.2.z.b.719.50	yes	224
300.119	even	10	inner	900.2.z.b.719.7	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.z.b.179.7	✓	224	1.1	even	1	trivial
900.2.z.b.179.20	yes	224	12.11	even	2	inner
900.2.z.b.179.37	yes	224	4.3	odd	2	inner
900.2.z.b.179.50	yes	224	3.2	odd	2	inner
900.2.z.b.719.7	yes	224	300.119	even	10	inner
900.2.z.b.719.20	yes	224	25.19	even	10	inner
900.2.z.b.719.37	yes	224	75.44	odd	10	inner
900.2.z.b.719.50	yes	224	100.19	odd	10	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31270 + 0.526124i) q^{2} +(1.44639 - 1.38129i) q^{4} +(-0.701604 + 2.12315i) q^{5} +3.43527 q^{7} +(-1.17195 + 2.57421i) q^{8} +(-0.196039 - 3.15620i) q^{10} +(0.730731 - 2.24896i) q^{11} +(1.45315 - 0.472157i) q^{13} +(-4.50950 + 1.80738i) q^{14} +(0.184073 - 3.99576i) q^{16} +(3.14556 - 2.28538i) q^{17} +(2.03462 + 2.80041i) q^{19} +(1.91789 + 4.04001i) q^{20} +(0.223997 + 3.33668i) q^{22} +(1.42594 + 0.463318i) q^{23} +(-4.01550 - 2.97922i) q^{25} +(-1.65914 + 1.38434i) q^{26} +(4.96874 - 4.74511i) q^{28} +(2.23743 - 3.07956i) q^{29} +(-1.91642 - 2.63773i) q^{31} +(1.86063 + 5.34210i) q^{32} +(-2.92680 + 4.65499i) q^{34} +(-2.41020 + 7.29359i) q^{35} +(-7.74142 + 2.51534i) q^{37} +(-4.14422 - 2.60566i) q^{38} +(-4.64317 - 4.29429i) q^{40} +(-3.94721 + 1.28253i) q^{41} +11.2094 q^{43} +(-2.04955 - 4.26222i) q^{44} +(-2.11561 + 0.142024i) q^{46} +(2.74947 - 3.78433i) q^{47} +4.80111 q^{49} +(6.83861 + 1.79818i) q^{50} +(1.44963 - 2.69015i) q^{52} +(9.57230 + 6.95468i) q^{53} +(4.26219 + 3.12933i) q^{55} +(-4.02597 + 8.84310i) q^{56} +(-1.31685 + 5.21971i) q^{58} +(-0.280171 - 0.862278i) q^{59} +(-3.37411 + 10.3845i) q^{61} +(3.90347 + 2.45429i) q^{62} +(-5.25307 - 6.03368i) q^{64} +(-0.0170778 + 3.41652i) q^{65} +(12.5591 - 9.12471i) q^{67} +(1.39292 - 7.65048i) q^{68} +(-0.673447 - 10.8424i) q^{70} +(-2.60663 - 1.89383i) q^{71} +(3.87104 + 1.25778i) q^{73} +(8.83881 - 7.37484i) q^{74} +(6.81104 + 1.24008i) q^{76} +(2.51026 - 7.72579i) q^{77} +(-4.64276 + 6.39021i) q^{79} +(8.35444 + 3.19426i) q^{80} +(4.50675 - 3.76030i) q^{82} +(5.24031 + 7.21267i) q^{83} +(2.64526 + 8.28192i) q^{85} +(-14.7147 + 5.89755i) q^{86} +(4.93290 + 4.51672i) q^{88} +(1.86308 + 0.605351i) q^{89} +(4.99197 - 1.62199i) q^{91} +(2.70244 - 1.29951i) q^{92} +(-1.61822 + 6.41427i) q^{94} +(-7.37319 + 2.35501i) q^{95} +(-5.43793 + 7.48466i) q^{97} +(-6.30244 + 2.52598i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 8 q^{4} - 12 q^{10} - 8 q^{16} - 8 q^{25} + 92 q^{34} + 40 q^{37} + 36 q^{40} - 40 q^{46} + 368 q^{49} - 100 q^{52} - 120 q^{58} + 48 q^{61} - 16 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{85} - 120 q^{88}+ \cdots + 200 q^{97}+O(q^{100}) \) 224 * q + 8 * q^4 - 12 * q^10 - 8 * q^16 - 8 * q^25 + 92 * q^34 + 40 * q^37 + 36 * q^40 - 40 * q^46 + 368 * q^49 - 100 * q^52 - 120 * q^58 + 48 * q^61 - 16 * q^64 - 40 * q^70 + 24 * q^76 - 120 * q^85 - 120 * q^88 - 4 * q^94 + 200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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