LMFDB - Embedded newform 225.2.m.c.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	225.109
Dual form			225.2.m.c.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.179595 - 0.247191i) q^{2} +(0.589185 + 1.81332i) q^{4} +(-2.23537 - 0.0558531i) q^{5} +1.87098i q^{7} +(1.13523 + 0.368860i) q^{8} +O(q^{10})$	\(q+(0.179595 - 0.247191i) q^{2} +(0.589185 + 1.81332i) q^{4} +(-2.23537 - 0.0558531i) q^{5} +1.87098i q^{7} +(1.13523 + 0.368860i) q^{8} +(-0.415267 + 0.542533i) q^{10} +(4.48118 + 3.25577i) q^{11} +(1.99014 + 2.73919i) q^{13} +(0.462489 + 0.336018i) q^{14} +(-2.78995 + 2.02702i) q^{16} +(-6.60386 - 2.14572i) q^{17} +(0.959840 - 2.95408i) q^{19} +(-1.21577 - 4.08636i) q^{20} +(1.60959 - 0.522989i) q^{22} +(2.36499 - 3.25514i) q^{23} +(4.99376 + 0.249705i) q^{25} +1.03452 q^{26} +(-3.39269 + 1.10235i) q^{28} +(1.46346 + 4.50408i) q^{29} +(1.17315 - 3.61059i) q^{31} +3.44100i q^{32} +(-1.71642 + 1.24705i) q^{34} +(0.104500 - 4.18232i) q^{35} +(-4.25582 - 5.85763i) q^{37} +(-0.557841 - 0.767802i) q^{38} +(-2.51707 - 0.887944i) q^{40} +(3.89230 - 2.82792i) q^{41} -8.46556i q^{43} +(-3.26352 + 10.0441i) q^{44} +(-0.379900 - 1.16921i) q^{46} +(-5.89161 + 1.91430i) q^{47} +3.49945 q^{49} +(0.958579 - 1.18957i) q^{50} +(-3.79448 + 5.22266i) q^{52} +(10.1998 - 3.31412i) q^{53} +(-9.83525 - 7.52813i) q^{55} +(-0.690128 + 2.12399i) q^{56} +(1.37620 + 0.447154i) q^{58} +(-4.65783 + 3.38411i) q^{59} +(-2.31025 - 1.67850i) q^{61} +(-0.681815 - 0.938437i) q^{62} +(-4.72932 - 3.43605i) q^{64} +(-4.29570 - 6.23426i) q^{65} +(3.38900 + 1.10115i) q^{67} -13.2392i q^{68} +(-1.01507 - 0.776955i) q^{70} +(2.59287 + 7.98002i) q^{71} +(-0.888997 + 1.22360i) q^{73} -2.21228 q^{74} +5.92223 q^{76} +(-6.09146 + 8.38418i) q^{77} +(0.194499 + 0.598606i) q^{79} +(6.34979 - 4.37531i) q^{80} -1.47002i q^{82} +(-0.882409 - 0.286712i) q^{83} +(14.6422 + 5.16533i) q^{85} +(-2.09261 - 1.52037i) q^{86} +(3.88626 + 5.34898i) q^{88} +(0.776044 + 0.563829i) q^{89} +(-5.12496 + 3.72350i) q^{91} +(7.29604 + 2.37063i) q^{92} +(-0.584905 + 1.80015i) q^{94} +(-2.31059 + 6.54986i) q^{95} +(15.0826 - 4.90063i) q^{97} +(0.628483 - 0.865033i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4}+O(q^{10}) $ 24 * q + 8 * q^4	$ 24 q + 8 q^{4} - 10 q^{10} - 24 q^{16} + 14 q^{19} + 70 q^{22} + 30 q^{28} - 18 q^{31} + 10 q^{34} - 20 q^{37} - 80 q^{40} - 72 q^{49} - 140 q^{52} - 10 q^{55} - 130 q^{58} - 12 q^{61} + 2 q^{64} + 80 q^{67} + 30 q^{70} - 20 q^{73} + 88 q^{76} + 36 q^{79} + 90 q^{85} + 180 q^{88} - 30 q^{91} + 50 q^{94} + 100 q^{97}+O(q^{100}) $ 24 * q + 8 * q^4 - 10 * q^10 - 24 * q^16 + 14 * q^19 + 70 * q^22 + 30 * q^28 - 18 * q^31 + 10 * q^34 - 20 * q^37 - 80 * q^40 - 72 * q^49 - 140 * q^52 - 10 * q^55 - 130 * q^58 - 12 * q^61 + 2 * q^64 + 80 * q^67 + 30 * q^70 - 20 * q^73 + 88 * q^76 + 36 * q^79 + 90 * q^85 + 180 * q^88 - 30 * q^91 + 50 * q^94 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.179595	−	0.247191i	0.126993	−	0.174791i	−0.740786	−	0.671741i	$-0.765547\pi$
$2$	0.179595	−	0.247191i	0.126993	−	0.174791i	0.867779	+	0.496950i	$0.165547\pi$
$3$		0			0
$3$		0			0
$4$	0.589185	+	1.81332i	0.294592	+	0.906662i
$5$	−2.23537	−	0.0558531i	−0.999688	−	0.0249782i
$5$	−2.23537	−	0.0558531i	−0.999688	−	0.0249782i
$6$		0			0
$7$			1.87098i			0.707162i	0.935404	+	0.353581i	$0.115036\pi$
$7$			1.87098i			0.707162i	−0.935404	+	0.353581i	$0.884964\pi$
$8$	1.13523	+	0.368860i	0.401366	+	0.130412i
$9$		0			0
$10$	−0.415267	+	0.542533i	−0.131319	+	0.171564i
$11$	4.48118	+	3.25577i	1.35113	+	0.981651i	0.998955	+	0.0457153i	$0.0145567\pi$
$11$	4.48118	+	3.25577i	1.35113	+	0.981651i	0.352172	+	0.935935i	$0.385443\pi$
$12$		0			0
$13$	1.99014	+	2.73919i	0.551965	+	0.759715i	0.990277	−	0.139108i	$-0.0444235\pi$
$13$	1.99014	+	2.73919i	0.551965	+	0.759715i	−0.438312	+	0.898823i	$0.644424\pi$
$14$	0.462489	+	0.336018i	0.123605	+	0.0898045i
$15$		0			0
$16$	−2.78995	+	2.02702i	−0.697488	+	0.506754i
$17$	−6.60386	−	2.14572i	−1.60167	−	0.520414i	−0.634151	−	0.773209i	$-0.718650\pi$
$17$	−6.60386	−	2.14572i	−1.60167	−	0.520414i	−0.967520	+	0.252795i	$0.918650\pi$
$18$		0			0
$19$	0.959840	−	2.95408i	0.220202	−	0.677713i	−0.778541	−	0.627594i	$-0.784040\pi$
$19$	0.959840	−	2.95408i	0.220202	−	0.677713i	0.998743	−	0.0501192i	$-0.0159601\pi$
$20$	−1.21577	−	4.08636i	−0.271854	−	0.913738i
$21$		0			0
$22$	1.60959	−	0.522989i	0.343167	−	0.111502i
$23$	2.36499	−	3.25514i	0.493135	−	0.678743i	−0.487827	−	0.872940i	$-0.662210\pi$
$23$	2.36499	−	3.25514i	0.493135	−	0.678743i	0.980962	+	0.194198i	$0.0622103\pi$
$24$		0			0
$25$	4.99376	+	0.249705i	0.998752	+	0.0499409i
$26$	1.03452			0.202887
$27$		0			0
$28$	−3.39269	+	1.10235i	−0.641157	+	0.208325i
$29$	1.46346	+	4.50408i	0.271758	+	0.836386i	0.990059	+	0.140653i	$0.0449203\pi$
$29$	1.46346	+	4.50408i	0.271758	+	0.836386i	−0.718300	+	0.695733i	$0.755080\pi$
$30$		0			0
$31$	1.17315	−	3.61059i	0.210705	−	0.648482i	−0.788726	−	0.614745i	$-0.789259\pi$
$31$	1.17315	−	3.61059i	0.210705	−	0.648482i	0.999431	−	0.0337373i	$-0.0107409\pi$
$32$			3.44100i			0.608289i
$33$		0			0
$34$	−1.71642	+	1.24705i	−0.294364	+	0.213868i
$35$	0.104500	−	4.18232i	0.0176637	−	0.706942i
$36$		0			0
$37$	−4.25582	−	5.85763i	−0.699652	−	0.962989i	−0.999958	−	0.00914596i	$-0.997089\pi$
$37$	−4.25582	−	5.85763i	−0.699652	−	0.962989i	0.300306	−	0.953843i	$-0.402911\pi$
$38$	−0.557841	−	0.767802i	−0.0904937	−	0.124554i
$39$		0			0
$40$	−2.51707	−	0.887944i	−0.397983	−	0.140396i
$41$	3.89230	−	2.82792i	0.607875	−	0.441647i	−0.240790	−	0.970577i	$-0.577407\pi$
$41$	3.89230	−	2.82792i	0.607875	−	0.441647i	0.848665	+	0.528930i	$0.177407\pi$
$42$		0			0
$43$		−	8.46556i		−	1.29099i	−0.763766	−	0.645493i	$-0.776652\pi$
$43$		−	8.46556i		−	1.29099i	0.763766	−	0.645493i	$-0.223348\pi$
$44$	−3.26352	+	10.0441i	−0.491994	+	1.51420i
$45$		0			0
$46$	−0.379900	−	1.16921i	−0.0560132	−	0.172391i
$47$	−5.89161	+	1.91430i	−0.859380	+	0.279229i	−0.705369	−	0.708840i	$-0.749219\pi$
$47$	−5.89161	+	1.91430i	−0.859380	+	0.279229i	−0.154010	+	0.988069i	$0.549219\pi$
$48$		0			0
$49$	3.49945			0.499921
$50$	0.958579	−	1.18957i	0.135563	−	0.168230i
$51$		0			0
$52$	−3.79448	+	5.22266i	−0.526200	+	0.724252i
$53$	10.1998	−	3.31412i	1.40105	−	0.455230i	0.491521	−	0.870866i	$-0.336441\pi$
$53$	10.1998	−	3.31412i	1.40105	−	0.455230i	0.909531	+	0.415636i	$0.136441\pi$
$54$		0			0
$55$	−9.83525	−	7.52813i	−1.32618	−	1.01509i
$56$	−0.690128	+	2.12399i	−0.0922222	+	0.283831i
$57$		0			0
$58$	1.37620	+	0.447154i	0.180704	+	0.0587142i
$59$	−4.65783	+	3.38411i	−0.606398	+	0.440574i	−0.848144	−	0.529765i	$-0.822280\pi$
$59$	−4.65783	+	3.38411i	−0.606398	+	0.440574i	0.241746	+	0.970340i	$0.422280\pi$
$60$		0			0
$61$	−2.31025	−	1.67850i	−0.295798	−	0.214910i	0.429981	−	0.902838i	$-0.358520\pi$
$61$	−2.31025	−	1.67850i	−0.295798	−	0.214910i	−0.725779	+	0.687928i	$0.758520\pi$
$62$	−0.681815	−	0.938437i	−0.0865906	−	0.119182i
$63$		0			0
$64$	−4.72932	−	3.43605i	−0.591165	−	0.429506i
$65$	−4.29570	−	6.23426i	−0.532817	−	0.773265i
$66$		0			0
$67$	3.38900	+	1.10115i	0.414032	+	0.134527i	0.508624	−	0.860989i	$-0.330155\pi$
$67$	3.38900	+	1.10115i	0.414032	+	0.134527i	−0.0945916	+	0.995516i	$0.530155\pi$
$68$		−	13.2392i		−	1.60548i
$69$		0			0
$70$	−1.01507	−	0.776955i	−0.121324	−	0.0928639i
$71$	2.59287	+	7.98002i	0.307717	+	0.947054i	0.978650	+	0.205536i	$0.0658938\pi$
$71$	2.59287	+	7.98002i	0.307717	+	0.947054i	−0.670933	+	0.741518i	$0.734106\pi$
$72$		0			0
$73$	−0.888997	+	1.22360i	−0.104049	+	0.143212i	−0.857866	−	0.513873i	$-0.828210\pi$
$73$	−0.888997	+	1.22360i	−0.104049	+	0.143212i	0.753817	+	0.657084i	$0.228210\pi$
$74$	−2.21228			−0.257172
$75$		0			0
$76$	5.92223			0.679327
$77$	−6.09146	+	8.38418i	−0.694186	+	0.955466i
$78$		0			0
$79$	0.194499	+	0.598606i	0.0218828	+	0.0673484i	0.961402	−	0.275149i	$-0.0887272\pi$
$79$	0.194499	+	0.598606i	0.0218828	+	0.0673484i	−0.939519	+	0.342497i	$0.888727\pi$
$80$	6.34979	−	4.37531i	0.709928	−	0.489174i
$81$		0			0
$82$		−	1.47002i		−	0.162337i
$83$	−0.882409	−	0.286712i	−0.0968569	−	0.0314707i	0.260188	−	0.965558i	$-0.416216\pi$
$83$	−0.882409	−	0.286712i	−0.0968569	−	0.0314707i	−0.357045	+	0.934087i	$0.616216\pi$
$84$		0			0
$85$	14.6422	+	5.16533i	1.58817	+	0.560259i
$86$	−2.09261	−	1.52037i	−0.225652	−	0.163946i
$87$		0			0
$88$	3.88626	+	5.34898i	0.414277	+	0.570203i
$89$	0.776044	+	0.563829i	0.0822605	+	0.0597657i	0.628155	−	0.778088i	$-0.283810\pi$
$89$	0.776044	+	0.563829i	0.0822605	+	0.0597657i	−0.545895	+	0.837854i	$0.683810\pi$
$90$		0			0
$91$	−5.12496	+	3.72350i	−0.537242	+	0.390329i
$92$	7.29604	+	2.37063i	0.760664	+	0.247155i
$93$		0			0
$94$	−0.584905	+	1.80015i	−0.0603283	+	0.185672i
$95$	−2.31059	+	6.54986i	−0.237062	+	0.672001i
$96$		0			0
$97$	15.0826	−	4.90063i	1.53140	−	0.497584i	0.582415	−	0.812891i	$-0.302108\pi$
$97$	15.0826	−	4.90063i	1.53140	−	0.497584i	0.948989	+	0.315308i	$0.102108\pi$
$98$	0.628483	−	0.865033i	0.0634864	−	0.0873815i
$99$		0			0
$100$	2.48945	+	9.20243i	0.248945	+	0.920243i
$101$	9.33669			0.929035			0.464518	−	0.885564i	$-0.346228\pi$
$101$	9.33669			0.929035			0.464518	+	0.885564i	$0.346228\pi$
$102$		0			0
$103$	−6.54430	+	2.12637i	−0.644829	+	0.209518i	−0.613133	−	0.789980i	$-0.710091\pi$
$103$	−6.54430	+	2.12637i	−0.644829	+	0.209518i	−0.0316963	+	0.999498i	$0.510091\pi$
$104$	1.24889	+	3.84370i	0.122464	+	0.376906i
$105$		0			0
$106$	1.01261	−	3.11650i	0.0983537	−	0.302702i
$107$		−	10.3647i		−	1.00199i	−0.865450	−	0.500995i	$-0.832967\pi$
$107$		−	10.3647i		−	1.00199i	0.865450	−	0.500995i	$-0.167033\pi$
$108$		0			0
$109$	−4.43536	+	3.22248i	−0.424831	+	0.308658i	−0.779579	−	0.626304i	$-0.784567\pi$
$109$	−4.43536	+	3.22248i	−0.424831	+	0.308658i	0.354748	+	0.934962i	$0.384567\pi$
$110$	−3.62725	+	1.07917i	−0.345845	+	0.102895i
$111$		0			0
$112$	−3.79250	−	5.21993i	−0.358358	−	0.493237i
$113$	4.09583	+	5.63743i	0.385304	+	0.530325i	0.956980	−	0.290154i	$-0.0937066\pi$
$113$	4.09583	+	5.63743i	0.385304	+	0.530325i	−0.571676	+	0.820479i	$0.693707\pi$
$114$		0			0
$115$	−5.46845	+	7.14434i	−0.509935	+	0.666213i
$116$	−7.30511	+	5.30747i	−0.678262	+	0.492786i
$117$		0			0
$118$			1.75914i			0.161942i
$119$	4.01460	−	12.3557i	0.368018	−	1.13264i
$120$		0			0
$121$	6.08176	+	18.7177i	0.552887	+	1.70161i
$122$	−0.829819	+	0.269625i	−0.0751283	+	0.0244107i
$123$		0			0
$124$	7.23838			0.650026
$125$	−11.1490	−	0.837099i	−0.997193	−	0.0748724i
$126$		0			0
$127$	−10.6070	+	14.5993i	−0.941221	+	1.29548i	0.0140969	+	0.999901i	$0.495513\pi$
$127$	−10.6070	+	14.5993i	−0.941221	+	1.29548i	−0.955318	+	0.295579i	$0.904487\pi$
$128$	−8.24390	+	2.67861i	−0.728665	+	0.236758i
$129$		0			0
$130$	−2.31254	−	0.0577812i	−0.202823	−	0.00506775i
$131$	4.75921	−	14.6473i	0.415814	−	1.27974i	−0.495707	−	0.868490i	$-0.665091\pi$
$131$	4.75921	−	14.6473i	0.415814	−	1.27974i	0.911521	−	0.411254i	$-0.134909\pi$
$132$		0			0
$133$	5.52702	+	1.79584i	0.479253	+	0.155719i
$134$	0.880842	−	0.639969i	0.0760931	−	0.0552849i
$135$		0			0
$136$	−6.70545	−	4.87180i	−0.574988	−	0.417753i
$137$	−6.35927	−	8.75278i	−0.543309	−	0.747801i	0.445776	−	0.895144i	$-0.352928\pi$
$137$	−6.35927	−	8.75278i	−0.543309	−	0.747801i	−0.989085	+	0.147344i	$0.952928\pi$
$138$		0			0
$139$	1.94746	+	1.41491i	0.165181	+	0.120011i	0.667305	−	0.744785i	$-0.267448\pi$
$139$	1.94746	+	1.41491i	0.165181	+	0.120011i	−0.502124	+	0.864796i	$0.667448\pi$
$140$	7.64548	−	2.27467i	0.646161	−	0.192245i
$141$		0			0
$142$	2.43826	+	0.792237i	0.204614	+	0.0664831i
$143$			18.7542i			1.56831i
$144$		0			0
$145$	−3.01982	−	10.1500i	−0.250782	−	0.842914i
$146$	0.142804	+	0.439505i	0.0118185	+	0.0363737i
$147$		0			0
$148$	8.11433	−	11.1684i	0.666993	−	0.918038i
$149$	4.53337			0.371388			0.185694	−	0.982608i	$-0.440547\pi$
$149$	4.53337			0.371388			0.185694	+	0.982608i	$0.440547\pi$
$150$		0			0
$151$	10.2345			0.832875			0.416438	−	0.909164i	$-0.363278\pi$
$151$	10.2345			0.832875			0.416438	+	0.909164i	$0.363278\pi$
$152$	2.17928	−	2.99953i	0.176763	−	0.243294i
$153$		0			0
$154$	0.978499	+	3.01151i	0.0788497	+	0.242674i
$155$	−2.82409	+	8.00549i	−0.226837	+	0.643017i
$156$		0			0
$157$			16.1453i			1.28853i	0.764801	+	0.644267i	$0.222837\pi$
$157$			16.1453i			1.28853i	−0.764801	+	0.644267i	$0.777163\pi$
$158$	0.182901	+	0.0594282i	0.0145508	+	0.00472785i
$159$		0			0
$160$	0.192191	−	7.69192i	0.0151940	−	0.608099i
$161$	6.09028	+	4.42485i	0.479981	+	0.348727i
$162$		0			0
$163$	−6.64985	−	9.15273i	−0.520856	−	0.716897i	0.464846	−	0.885391i	$-0.346110\pi$
$163$	−6.64985	−	9.15273i	−0.520856	−	0.716897i	−0.985703	+	0.168494i	$0.946110\pi$
$164$	7.42122	+	5.39184i	0.579500	+	0.421032i
$165$		0			0
$166$	−0.229349	+	0.166632i	−0.0178009	+	0.0129331i
$167$	4.85745	+	1.57828i	0.375881	+	0.122131i	0.490864	−	0.871236i	$-0.336681\pi$
$167$	4.85745	+	1.57828i	0.375881	+	0.122131i	−0.114983	+	0.993367i	$0.536681\pi$
$168$		0			0
$169$	0.474707	−	1.46100i	0.0365159	−	0.112385i
$170$	3.90649	−	2.69176i	0.299614	−	0.206449i
$171$		0			0
$172$	15.3508	−	4.98778i	1.17049	−	0.380315i
$173$	−8.97543	+	12.3536i	−0.682389	+	0.939228i	−0.999959	−	0.00900668i	$-0.997133\pi$
$173$	−8.97543	+	12.3536i	−0.682389	+	0.939228i	0.317570	+	0.948235i	$0.397133\pi$
$174$		0			0
$175$	−0.467191	+	9.34321i	−0.0353163	+	0.706280i
$176$	−19.1018			−1.43985
$177$		0			0
$178$	0.278747	−	0.0905704i	0.0208930	−	0.00678854i
$179$	−6.73336	−	20.7232i	−0.503275	−	1.54892i	−0.803651	−	0.595100i	$-0.797112\pi$
$179$	−6.73336	−	20.7232i	−0.503275	−	1.54892i	0.300376	−	0.953821i	$-0.402888\pi$
$180$		0			0
$181$	4.14000	−	12.7416i	0.307724	−	0.947076i	−0.670923	−	0.741527i	$-0.734102\pi$
$181$	4.14000	−	12.7416i	0.307724	−	0.947076i	0.978647	−	0.205549i	$-0.0658981\pi$
$182$			1.93557i			0.143474i
$183$		0			0
$184$	3.88551	−	2.82299i	0.286444	−	0.208113i
$185$	9.18617	+	13.3317i	0.675380	+	0.980165i
$186$		0			0
$187$	−22.6071	−	31.1160i	−1.65319	−	2.27543i
$188$	−6.94249	−	9.55552i	−0.506333	−	0.696908i
$189$		0			0
$190$	1.20410	+	1.74748i	0.0873544	+	0.126775i
$191$	−4.37200	+	3.17644i	−0.316347	+	0.229839i	−0.734615	−	0.678484i	$-0.762637\pi$
$191$	−4.37200	+	3.17644i	−0.316347	+	0.229839i	0.418268	+	0.908324i	$0.362637\pi$
$192$		0			0
$193$			8.72818i			0.628268i	0.949379	+	0.314134i	$0.101714\pi$
$193$			8.72818i			0.628268i	−0.949379	+	0.314134i	$0.898286\pi$
$194$	1.49736	−	4.60841i	0.107504	−	0.330865i
$195$		0			0
$196$	2.06182	+	6.34564i	0.147273	+	0.453260i
$197$	8.79733	−	2.85843i	0.626784	−	0.203654i	0.0216340	−	0.999766i	$-0.493113\pi$
$197$	8.79733	−	2.85843i	0.626784	−	0.203654i	0.605150	+	0.796112i	$0.293113\pi$
$198$		0			0
$199$	−19.1122			−1.35483			−0.677413	−	0.735603i	$-0.736899\pi$
$199$	−19.1122			−1.35483			−0.677413	+	0.735603i	$0.736899\pi$
$200$	5.57698	+	2.12547i	0.394352	+	0.150293i
$201$		0			0
$202$	1.67682	−	2.30795i	0.117981	−	0.162387i
$203$	−8.42702	+	2.73811i	−0.591461	+	0.192177i
$204$		0			0
$205$	−8.85868	+	6.10406i	−0.618717	+	0.426326i
$206$	−0.649703	+	1.99958i	−0.0452669	+	0.139317i
$207$		0			0
$208$	−11.1048	−	3.60816i	−0.769978	−	0.250181i
$209$	13.9190	−	10.1128i	0.962799	−	0.699514i
$210$		0			0
$211$	−22.9867	−	16.7008i	−1.58247	−	1.14973i	−0.913791	−	0.406185i	$-0.866859\pi$
$211$	−22.9867	−	16.7008i	−1.58247	−	1.14973i	−0.668682	−	0.743548i	$-0.733141\pi$
$212$	12.0192	+	16.5429i	0.825479	+	1.13617i
$213$		0			0
$214$	−2.56206	−	1.86144i	−0.175139	−	0.127246i
$215$	−0.472827	+	18.9237i	−0.0322466	+	1.29058i
$216$		0			0
$217$	6.75533	+	2.19494i	0.458582	+	0.149002i
$218$			1.67512i			0.113454i
$219$		0			0
$220$	7.85617	−	22.2700i	0.529663	−	1.50144i
$221$	−7.26505	−	22.3595i	−0.488700	−	1.50406i
$222$		0			0
$223$	−9.12645	+	12.5615i	−0.611152	+	0.841179i	−0.996672	−	0.0815208i	$-0.974022\pi$
$223$	−9.12645	+	12.5615i	−0.611152	+	0.841179i	0.385519	+	0.922700i	$0.374022\pi$
$224$	−6.43803			−0.430159
$225$		0			0
$226$	2.12911			0.141627
$227$	16.1306	−	22.2018i	1.07062	−	1.47359i	0.201178	−	0.979555i	$-0.435523\pi$
$227$	16.1306	−	22.2018i	1.07062	−	1.47359i	0.869444	−	0.494031i	$-0.164477\pi$
$228$		0			0
$229$	−3.84505	−	11.8338i	−0.254088	−	0.782002i	−0.994008	−	0.109307i	$-0.965137\pi$
$229$	−3.84505	−	11.8338i	−0.254088	−	0.782002i	0.739920	−	0.672695i	$-0.234863\pi$
$230$	0.783913	+	2.63484i	0.0516897	+	0.173736i
$231$		0			0
$232$			5.65299i			0.371137i
$233$	−6.69580	−	2.17560i	−0.438656	−	0.142528i	0.0813593	−	0.996685i	$-0.474074\pi$
$233$	−6.69580	−	2.17560i	−0.438656	−	0.142528i	−0.520016	+	0.854157i	$0.674074\pi$
$234$		0			0
$235$	13.2768	−	3.95010i	0.866086	−	0.257676i
$236$	−8.88082	−	6.45230i	−0.578092	−	0.420009i
$237$		0			0
$238$	−2.33321	−	3.21139i	−0.151239	−	0.208163i
$239$	−20.5743	−	14.9481i	−1.33084	−	0.966914i	−0.999728	−	0.0233243i	$-0.992575\pi$
$239$	−20.5743	−	14.9481i	−1.33084	−	0.966914i	−0.331116	−	0.943590i	$-0.607425\pi$
$240$		0			0
$241$	−11.1012	+	8.06547i	−0.715089	+	0.519543i	−0.884811	−	0.465949i	$-0.845713\pi$
$241$	−11.1012	+	8.06547i	−0.715089	+	0.519543i	0.169722	+	0.985492i	$0.445713\pi$
$242$	5.71911	+	1.85825i	0.367638	+	0.119453i
$243$		0			0
$244$	1.68249	−	5.17818i	0.107711	−	0.331499i
$245$	−7.82257	−	0.195455i	−0.499765	−	0.0124872i
$246$		0			0
$247$	10.0020	−	3.24985i	0.636413	−	0.206783i
$248$	2.66361	−	3.66614i	0.169139	−	0.232800i
$249$		0			0
$250$	−2.20922	+	2.60559i	−0.139723	+	0.164792i
$251$	−17.7275			−1.11895			−0.559474	−	0.828848i	$-0.688997\pi$
$251$	−17.7275			−1.11895			−0.559474	+	0.828848i	$0.688997\pi$
$252$		0			0
$253$	21.1959	−	6.88697i	1.33258	−	0.432980i
$254$	1.70385	+	5.24393i	0.106909	+	0.329033i
$255$		0			0
$256$	2.79444	−	8.60041i	0.174653	−	0.537525i
$257$			21.3592i			1.33235i	0.745795	+	0.666176i	$0.232070\pi$
$257$			21.3592i			1.33235i	−0.745795	+	0.666176i	$0.767930\pi$
$258$		0			0
$259$	10.9595	−	7.96254i	0.680990	−	0.494768i
$260$	8.77377	−	11.4626i	0.544126	−	0.710883i
$261$		0			0
$262$	−2.76596	−	3.80702i	−0.170882	−	0.235199i
$263$	9.91764	+	13.6505i	0.611548	+	0.841724i	0.996704	−	0.0811279i	$-0.0258522\pi$
$263$	9.91764	+	13.6505i	0.611548	+	0.841724i	−0.385156	+	0.922852i	$0.625852\pi$
$264$		0			0
$265$	−22.9855	+	6.83860i	−1.41199	+	0.420092i
$266$	1.43654	−	1.04371i	0.0880799	−	0.0639938i
$267$		0			0
$268$			6.79413i			0.415018i
$269$	1.14122	−	3.51231i	0.0695814	−	0.214150i	−0.910219	−	0.414127i	$-0.864087\pi$
$269$	1.14122	−	3.51231i	0.0695814	−	0.214150i	0.979800	+	0.199978i	$0.0640869\pi$
$270$		0			0
$271$	3.02047	+	9.29607i	0.183481	+	0.564696i	0.999919	−	0.0127372i	$-0.00405448\pi$
$271$	3.02047	+	9.29607i	0.183481	+	0.564696i	−0.816438	+	0.577433i	$0.804054\pi$
$272$	22.7739	−	7.39968i	1.38087	−	0.448671i
$273$		0			0
$274$	−3.30570			−0.199705
$275$	21.5650	+	17.3775i	1.30042	+	1.04790i
$276$		0			0
$277$	−16.5063	+	22.7190i	−0.991768	+	1.36505i	−0.0615257	+	0.998105i	$0.519597\pi$
$277$	−16.5063	+	22.7190i	−0.991768	+	1.36505i	−0.930242	+	0.366946i	$0.880403\pi$
$278$	0.699508	−	0.227284i	0.0419537	−	0.0136316i
$279$		0			0
$280$	1.66132	−	4.70937i	0.0992830	−	0.281439i
$281$	−4.91428	+	15.1246i	−0.293161	+	0.902257i	0.690672	+	0.723168i	$0.257315\pi$
$281$	−4.91428	+	15.1246i	−0.293161	+	0.902257i	−0.983833	+	0.179089i	$0.942685\pi$
$282$		0			0
$283$	7.17171	+	2.33023i	0.426314	+	0.138518i	0.514312	−	0.857603i	$-0.328047\pi$
$283$	7.17171	+	2.33023i	0.426314	+	0.138518i	−0.0879988	+	0.996121i	$0.528047\pi$
$284$	−12.9427	+	9.40341i	−0.768007	+	0.557990i
$285$		0			0
$286$	4.63588	+	3.36816i	0.274125	+	0.199164i
$287$	5.29097	+	7.28240i	0.312316	+	0.429867i
$288$		0			0
$289$	25.2535	+	18.3478i	1.48550	+	1.07928i
$290$	−3.05134	−	1.07642i	−0.179181	−	0.0632096i
$291$		0			0
$292$	−2.74257	−	0.891114i	−0.160497	−	0.0521485i
$293$		−	12.3332i		−	0.720515i	−0.932853	−	0.360258i	$-0.882689\pi$
$293$		−	12.3332i		−	0.720515i	0.932853	−	0.360258i	$-0.117311\pi$
$294$		0			0
$295$	10.6010	−	7.30459i	0.617214	−	0.425290i
$296$	−2.67070	−	8.21958i	−0.155232	−	0.477754i
$297$		0			0
$298$	0.814170	−	1.12061i	0.0471636	−	0.0649151i
$299$	13.6231			0.787844
$300$		0			0
$301$	15.8389			0.912937
$302$	1.83807	−	2.52989i	0.105769	−	0.145579i
$303$		0			0
$304$	3.31007	+	10.1874i	0.189846	+	0.584285i
$305$	5.07052	+	3.88110i	0.290337	+	0.222231i
$306$		0			0
$307$			2.01051i			0.114746i	0.998353	+	0.0573730i	$0.0182724\pi$
$307$			2.01051i			0.114746i	−0.998353	+	0.0573730i	$0.981728\pi$
$308$	−18.7922	−	6.10597i	−1.07079	−	0.347920i
$309$		0			0
$310$	1.47169	+	2.13584i	0.0835866	+	0.121307i
$311$	−19.4217	−	14.1107i	−1.10131	−	0.800145i	−0.120033	−	0.992770i	$-0.538300\pi$
$311$	−19.4217	−	14.1107i	−1.10131	−	0.800145i	−0.981272	+	0.192625i	$0.938300\pi$
$312$		0			0
$313$	−12.7673	−	17.5726i	−0.721649	−	0.993265i	−0.999467	−	0.0326310i	$-0.989611\pi$
$313$	−12.7673	−	17.5726i	−0.721649	−	0.993265i	0.277818	−	0.960634i	$-0.410389\pi$
$314$	3.99097	+	2.89961i	0.225223	+	0.163634i
$315$		0			0
$316$	−0.970871	+	0.705379i	−0.0546157	+	0.0396807i
$317$	−14.4867	−	4.70703i	−0.813657	−	0.264373i	−0.127511	−	0.991837i	$-0.540699\pi$
$317$	−14.4867	−	4.70703i	−0.813657	−	0.264373i	−0.686146	+	0.727464i	$0.740699\pi$
$318$		0			0
$319$	−8.10619	+	24.9483i	−0.453859	+	1.39684i
$320$	10.3799	+	7.94499i	0.580252	+	0.444138i
$321$		0			0
$322$	2.18757	−	0.710783i	0.121908	−	0.0396104i
$323$	−12.6773	+	17.4488i	−0.705383	+	0.970877i
$324$		0			0
$325$	9.25429	+	14.1758i	0.513335	+	0.786332i
$326$	−3.45675			−0.191452
$327$		0			0
$328$	5.46178	−	1.77464i	0.301576	−	0.0979880i
$329$	−3.58161	−	11.0231i	−0.197460	−	0.607721i
$330$		0			0
$331$	1.38672	−	4.26788i	0.0762209	−	0.234584i	−0.905686	−	0.423950i	$-0.860643\pi$
$331$	1.38672	−	4.26788i	0.0762209	−	0.234584i	0.981907	+	0.189366i	$0.0606433\pi$
$332$		−	1.76902i		−	0.0970876i
$333$		0			0
$334$	1.26251	−	0.917268i	0.0690815	−	0.0501907i
$335$	−7.51416	−	2.65077i	−0.410542	−	0.144827i
$336$		0			0
$337$	−5.25025	−	7.22635i	−0.285999	−	0.393644i	0.641710	−	0.766947i	$-0.278225\pi$
$337$	−5.25025	−	7.22635i	−0.285999	−	0.393644i	−0.927710	+	0.373303i	$0.878225\pi$
$338$	−0.275891	−	0.379731i	−0.0150065	−	0.0206547i
$339$		0			0
$340$	−0.739448	+	29.5944i	−0.0401022	+	1.60498i
$341$	17.0124	−	12.3602i	0.921271	−	0.669343i
$342$		0			0
$343$			19.6442i			1.06069i
$344$	3.12260	−	9.61039i	0.168360	−	0.518157i
$345$		0			0
$346$	1.44176	+	4.43729i	0.0775097	+	0.238550i
$347$	−5.54001	+	1.80006i	−0.297403	+	0.0966322i	−0.453918	−	0.891043i	$-0.649974\pi$
$347$	−5.54001	+	1.80006i	−0.297403	+	0.0966322i	0.156515	+	0.987676i	$0.449974\pi$
$348$		0			0
$349$	2.21387			0.118506			0.0592529	−	0.998243i	$-0.481128\pi$
$349$	2.21387			0.118506			0.0592529	+	0.998243i	$0.481128\pi$
$350$	2.22565	+	1.79348i	0.118966	+	0.0958654i
$351$		0			0
$352$	−11.2031	+	15.4198i	−0.597128	+	0.821876i
$353$	−10.3964	+	3.37798i	−0.553342	+	0.179792i	−0.572323	−	0.820028i	$-0.693958\pi$
$353$	−10.3964	+	3.37798i	−0.553342	+	0.179792i	0.0189810	+	0.999820i	$0.493958\pi$
$354$		0			0
$355$	−5.35031	−	17.9831i	−0.283965	−	0.954445i
$356$	−0.565171	+	1.73942i	−0.0299540	+	0.0921890i
$357$		0			0
$358$	−6.33186	−	2.05735i	−0.334649	−	0.108734i
$359$	20.6234	−	14.9838i	1.08846	−	0.790814i	0.109323	−	0.994006i	$-0.465132\pi$
$359$	20.6234	−	14.9838i	1.08846	−	0.790814i	0.979139	+	0.203192i	$0.0651316\pi$
$360$		0			0
$361$	7.56601	+	5.49703i	0.398211	+	0.289317i
$362$	−2.40609	−	3.31170i	−0.126461	−	0.174059i
$363$		0			0
$364$	−9.77146	−	7.09938i	−0.512164	−	0.372109i
$365$	2.05558	−	2.68555i	0.107594	−	0.140568i
$366$		0			0
$367$	20.6329	+	6.70405i	1.07703	+	0.349949i	0.793222	−	0.608932i	$-0.208402\pi$
$367$	20.6329	+	6.70405i	1.07703	+	0.349949i	0.283809	+	0.958881i	$0.408402\pi$
$368$			13.8756i			0.723313i
$369$		0			0
$370$	4.94526	+	0.123563i	0.257092	+	0.00642371i
$371$	6.20064	+	19.0836i	0.321921	+	0.990772i
$372$		0			0
$373$	−9.57075	+	13.1730i	−0.495554	+	0.682072i	−0.981400	−	0.191972i	$-0.938512\pi$
$373$	−9.57075	+	13.1730i	−0.495554	+	0.682072i	0.485846	+	0.874044i	$0.338512\pi$
$374$	−11.7517			−0.607667
$375$		0			0
$376$	−7.39446			−0.381340
$377$	−9.42503	+	12.9724i	−0.485414	+	0.668115i
$378$		0			0
$379$	−5.96922	−	18.3714i	−0.306618	−	0.943675i	−0.979068	−	0.203532i	$-0.934758\pi$
$379$	−5.96922	−	18.3714i	−0.306618	−	0.943675i	0.672450	−	0.740143i	$-0.265242\pi$
$380$	−13.2384	−	0.330775i	−0.679115	−	0.0169684i
$381$		0			0
$382$			1.65119i			0.0844824i
$383$	26.9731	+	8.76408i	1.37826	+	0.447823i	0.902097	−	0.431534i	$-0.142028\pi$
$383$	26.9731	+	8.76408i	1.37826	+	0.447823i	0.476162	+	0.879358i	$0.342028\pi$
$384$		0			0
$385$	14.0850	−	18.4015i	0.717836	−	0.937828i
$386$	2.15753	+	1.56754i	0.109815	+	0.0797855i
$387$		0			0
$388$	17.7729	+	24.4622i	0.902281	+	1.24188i
$389$	8.29135	+	6.02402i	0.420388	+	0.305430i	0.777794	−	0.628519i	$-0.216339\pi$
$389$	8.29135	+	6.02402i	0.420388	+	0.305430i	−0.357406	+	0.933949i	$0.616339\pi$
$390$		0			0
$391$	−22.6027	+	16.4218i	−1.14307	+	0.830488i
$392$	3.97269	+	1.29081i	0.200651	+	0.0651956i
$393$		0			0
$394$	0.873378	−	2.68798i	0.0440002	−	0.135419i
$395$	−0.401343	−	1.34897i	−0.0201938	−	0.0678740i
$396$		0			0
$397$	27.9513	−	9.08192i	1.40283	−	0.455808i	0.492728	−	0.870184i	$-0.336000\pi$
$397$	27.9513	−	9.08192i	1.40283	−	0.455808i	0.910106	+	0.414375i	$0.136000\pi$
$398$	−3.43245	+	4.72436i	−0.172053	+	0.236811i
$399$		0			0
$400$	−14.4385	+	9.42578i	−0.721925	+	0.471289i
$401$	22.6657			1.13187			0.565936	−	0.824449i	$-0.308515\pi$
$401$	22.6657			1.13187			0.565936	+	0.824449i	$0.308515\pi$
$402$		0			0
$403$	12.2248	−	3.97209i	0.608963	−	0.197864i
$404$	5.50104	+	16.9304i	0.273687	+	0.842321i
$405$		0			0
$406$	−0.836615	+	2.57484i	−0.0415205	+	0.127787i
$407$		−	40.1051i		−	1.98793i
$408$		0			0
$409$	6.46073	−	4.69400i	0.319463	−	0.232103i	−0.416484	−	0.909143i	$-0.636738\pi$
$409$	6.46073	−	4.69400i	0.319463	−	0.232103i	0.735946	+	0.677040i	$0.236738\pi$
$410$	−0.0821053	+	3.28604i	−0.00405489	+	0.162286i
$411$		0			0
$412$	−7.71161	−	10.6141i	−0.379924	−	0.522920i
$413$	−6.33160	−	8.71469i	−0.311557	−	0.428822i
$414$		0			0
$415$	1.95650	+	0.690193i	0.0960406	+	0.0338802i
$416$	−9.42556	+	6.84807i	−0.462126	+	0.335754i
$417$		0			0
$418$		−	5.25686i		−	0.257121i
$419$	−5.42334	+	16.6913i	−0.264947	+	0.815424i	0.726758	+	0.686893i	$0.241026\pi$
$419$	−5.42334	+	16.6913i	−0.264947	+	0.815424i	−0.991706	+	0.128531i	$0.958974\pi$
$420$		0			0
$421$	−7.19242	−	22.1360i	−0.350537	−	1.07884i	−0.958552	−	0.284917i	$-0.908034\pi$
$421$	−7.19242	−	22.1360i	−0.350537	−	1.07884i	0.608015	−	0.793925i	$-0.291966\pi$
$422$	−8.25660	+	2.68273i	−0.401925	+	0.130593i
$423$		0			0
$424$	12.8016			0.621702
$425$	−32.4423	−	12.3642i	−1.57368	−	0.599754i
$426$		0			0
$427$	3.14043	−	4.32243i	0.151976	−	0.209177i
$428$	18.7945	−	6.10671i	0.908467	−	0.295179i
$429$		0			0
$430$	4.59284	+	3.51547i	0.221487	+	0.169531i
$431$	3.87712	−	11.9325i	0.186754	−	0.574770i	−0.813220	−	0.581956i	$-0.802287\pi$
$431$	3.87712	−	11.9325i	0.186754	−	0.574770i	0.999974	+	0.00718627i	$0.00228748\pi$
$432$		0			0
$433$	−7.81433	−	2.53903i	−0.375533	−	0.122018i	0.115168	−	0.993346i	$-0.463259\pi$
$433$	−7.81433	−	2.53903i	−0.375533	−	0.122018i	−0.490701	+	0.871328i	$0.663259\pi$
$434$	1.75579	−	1.27566i	0.0842808	−	0.0612336i
$435$		0			0
$436$	−8.45665	−	6.14412i	−0.405000	−	0.294250i
$437$	−7.34592	−	10.1108i	−0.351403	−	0.483665i
$438$		0			0
$439$	−10.7446	−	7.80638i	−0.512810	−	0.372578i	0.301079	−	0.953599i	$-0.402653\pi$
$439$	−10.7446	−	7.80638i	−0.512810	−	0.372578i	−0.813888	+	0.581021i	$0.802653\pi$
$440$	−8.38848	−	12.1740i	−0.399905	−	0.580373i
$441$		0			0
$442$	−6.83184	−	2.21980i	−0.324957	−	0.105585i
$443$			7.03665i			0.334322i	0.985930	+	0.167161i	$0.0534599\pi$
$443$			7.03665i			0.334322i	−0.985930	+	0.167161i	$0.946540\pi$
$444$		0			0
$445$	−1.70325	−	1.30371i	−0.0807420	−	0.0618018i
$446$	1.46602	+	4.51196i	0.0694182	+	0.213647i
$447$		0			0
$448$	6.42876	−	8.84844i	0.303731	−	0.418049i
$449$	−1.17018			−0.0552242			−0.0276121	−	0.999619i	$-0.508790\pi$
$449$	−1.17018			−0.0552242			−0.0276121	+	0.999619i	$0.508790\pi$
$450$		0			0
$451$	26.6492			1.25486
$452$	−7.80929	+	10.7486i	−0.367318	+	0.505570i
$453$		0			0
$454$	−2.59112	−	7.97466i	−0.121607	−	0.374269i
$455$	11.6642	−	8.03716i	0.546824	−	0.376788i
$456$		0			0
$457$		−	5.45077i		−	0.254976i	−0.991840	−	0.127488i	$-0.959309\pi$
$457$		−	5.45077i		−	0.254976i	0.991840	−	0.127488i	$-0.0406915\pi$
$458$	−3.61577	−	1.17483i	−0.168954	−	0.0548964i
$459$		0			0
$460$	−16.1769	−	5.70673i	−0.754254	−	0.266078i
$461$	30.0750	+	21.8508i	1.40073	+	1.01769i	0.994590	+	0.103881i	$0.0331261\pi$
$461$	30.0750	+	21.8508i	1.40073	+	1.01769i	0.406142	+	0.913810i	$0.366874\pi$
$462$		0			0
$463$	−9.22912	−	12.7028i	−0.428913	−	0.590349i	0.538790	−	0.842440i	$-0.318882\pi$
$463$	−9.22912	−	12.7028i	−0.428913	−	0.590349i	−0.967703	+	0.252091i	$0.918882\pi$
$464$	−13.2128	−	9.59969i	−0.613391	−	0.445654i
$465$		0			0
$466$	−1.74032	+	1.26442i	−0.0806187	+	0.0585729i
$467$	10.8479	+	3.52470i	0.501982	+	0.163104i	0.549053	−	0.835788i	$-0.314989\pi$
$467$	10.8479	+	3.52470i	0.501982	+	0.163104i	−0.0470710	+	0.998892i	$0.514989\pi$
$468$		0			0
$469$	−2.06023	+	6.34073i	−0.0951325	+	0.292788i
$470$	1.40802	−	3.99134i	0.0649473	−	0.184107i
$471$		0			0
$472$	−6.53599	+	2.12367i	−0.300843	+	0.0977500i
$473$	27.5619	−	37.9357i	1.26730	−	1.74428i
$474$		0			0
$475$	5.53086	−	14.5123i	0.253773	−	0.665870i
$476$	24.7702			1.13534
$477$		0			0
$478$	−7.39009	+	2.40119i	−0.338015	+	0.109828i
$479$	−1.08418	−	3.33677i	−0.0495376	−	0.152461i	0.923228	−	0.384253i	$-0.125541\pi$
$479$	−1.08418	−	3.33677i	−0.0495376	−	0.152461i	−0.972765	+	0.231792i	$0.925541\pi$
$480$		0			0
$481$	7.57550	−	23.3150i	0.345413	−	1.06307i
$482$			4.19263i			0.190969i
$483$		0			0
$484$	−30.3580	+	22.0564i	−1.37991	+	1.00256i
$485$	−33.9889	+	10.1123i	−1.54336	+	0.459177i
$486$		0			0
$487$	−4.62798	−	6.36987i	−0.209714	−	0.288646i	0.691183	−	0.722680i	$-0.257090\pi$
$487$	−4.62798	−	6.36987i	−0.209714	−	0.288646i	−0.900897	+	0.434034i	$0.857090\pi$
$488$	−2.00355	−	2.75765i	−0.0906963	−	0.124833i
$489$		0			0
$490$	−1.45321	+	1.89857i	−0.0656492	+	0.0857685i
$491$	−20.6055	+	14.9708i	−0.929913	+	0.675621i	−0.945971	−	0.324250i	$-0.894888\pi$
$491$	−20.6055	+	14.9708i	−0.929913	+	0.675621i	0.0160588	+	0.999871i	$0.494888\pi$
$492$		0			0
$493$		−	32.8845i		−	1.48104i
$494$	0.992976	−	3.05606i	0.0446761	−	0.137499i
$495$		0			0
$496$	4.04570	+	12.4514i	0.181657	+	0.559084i
$497$	−14.9304	+	4.85119i	−0.669721	+	0.217606i
$498$		0			0
$499$	−5.04661			−0.225917			−0.112959	−	0.993600i	$-0.536033\pi$
$499$	−5.04661			−0.225917			−0.112959	+	0.993600i	$0.536033\pi$
$500$	−5.05087	−	20.7099i	−0.225882	−	0.926174i
$501$		0			0
$502$	−3.18376	+	4.38208i	−0.142098	+	0.195582i
$503$	−11.0192	+	3.58034i	−0.491320	+	0.159640i	−0.544190	−	0.838962i	$-0.683163\pi$
$503$	−11.0192	+	3.58034i	−0.491320	+	0.159640i	0.0528702	+	0.998601i	$0.483163\pi$
$504$		0			0
$505$	−20.8710	−	0.521483i	−0.928745	−	0.0232057i
$506$	2.10428	−	6.47631i	0.0935467	−	0.287907i
$507$		0			0
$508$	−32.7228	−	10.6323i	−1.45184	−	0.471731i
$509$	−29.4177	+	21.3732i	−1.30392	+	0.947352i	−0.999986	−	0.00534184i	$-0.998300\pi$
$509$	−29.4177	+	21.3732i	−1.30392	+	0.947352i	−0.303932	+	0.952694i	$0.598300\pi$
$510$		0			0
$511$	−2.28933	−	1.66329i	−0.101274	−	0.0735797i
$512$	−11.8141	−	16.2607i	−0.522114	−	0.718629i
$513$		0			0
$514$	5.27981	+	3.83601i	0.232882	+	0.169199i
$515$	14.7477	−	4.38771i	0.649861	−	0.193346i
$516$		0			0
$517$	−32.6339	−	10.6034i	−1.43524	−	0.466336i
$518$		−	4.13912i		−	0.181862i
$519$		0			0
$520$	−2.57706	−	8.66185i	−0.113012	−	0.379847i
$521$	4.00022	+	12.3114i	0.175253	+	0.539373i	0.999645	−	0.0266464i	$-0.00848281\pi$
$521$	4.00022	+	12.3114i	0.175253	+	0.539373i	−0.824392	+	0.566019i	$0.808483\pi$
$522$		0			0
$523$	6.34988	−	8.73986i	0.277661	−	0.382168i	−0.647296	−	0.762238i	$-0.724100\pi$
$523$	6.34988	−	8.73986i	0.277661	−	0.382168i	0.924957	+	0.380071i	$0.124100\pi$
$524$	29.3644			1.28279
$525$		0			0
$526$	5.15543			0.224788
$527$	−15.4947	+	21.3266i	−0.674959	+	0.929001i
$528$		0			0
$529$	2.10468	+	6.47754i	0.0915079	+	0.281632i
$530$	−2.43763	+	6.90998i	−0.105884	+	0.300150i
$531$		0			0
$532$			11.0804i			0.480394i
$533$	15.4924	+	5.03380i	0.671052	+	0.218038i
$534$		0			0
$535$	−0.578899	+	23.1689i	−0.0250280	+	1.00168i
$536$	3.44113	+	2.50013i	0.148634	+	0.107989i
$537$		0			0
$538$	−0.663256	−	0.912893i	−0.0285950	−	0.0393576i
$539$	15.6817	+	11.3934i	0.675457	+	0.490748i
$540$		0			0
$541$	4.77599	−	3.46996i	0.205336	−	0.149185i	−0.480365	−	0.877069i	$-0.659496\pi$
$541$	4.77599	−	3.46996i	0.205336	−	0.149185i	0.685701	+	0.727883i	$0.259496\pi$
$542$	2.84037	+	0.922891i	0.122004	+	0.0396416i
$543$		0			0
$544$	7.38344	−	22.7239i	0.316563	−	0.974279i
$545$	10.0947	−	6.95571i	0.432408	−	0.297950i
$546$		0			0
$547$	12.3063	−	3.99855i	0.526178	−	0.170966i	−0.0338694	−	0.999426i	$-0.510783\pi$
$547$	12.3063	−	3.99855i	0.526178	−	0.170966i	0.560047	+	0.828461i	$0.310783\pi$
$548$	12.1249	−	16.6884i	0.517948	−	0.712894i
$549$		0			0
$550$	8.16852	−	2.20976i	0.348307	−	0.0942244i
$551$	14.7101			0.626672
$552$		0			0
$553$	−1.11998	+	0.363903i	−0.0476263	+	0.0154747i
$554$	2.65148	+	8.16043i	0.112651	+	0.346703i
$555$		0			0
$556$	−1.41828	+	4.36502i	−0.0601485	+	0.185118i
$557$			20.9324i			0.886933i	0.896291	+	0.443466i	$0.146251\pi$
$557$			20.9324i			0.886933i	−0.896291	+	0.443466i	$0.853749\pi$
$558$		0			0
$559$	23.1888	−	16.8476i	0.980781	−	0.712579i
$560$	8.18610	+	11.8803i	0.345926	+	0.502034i
$561$		0			0
$562$	2.85608	+	3.93106i	0.120477	+	0.165822i
$563$	−6.30513	−	8.67827i	−0.265730	−	0.365746i	0.655213	−	0.755445i	$-0.272579\pi$
$563$	−6.30513	−	8.67827i	−0.265730	−	0.365746i	−0.920942	+	0.389699i	$0.872579\pi$
$564$		0			0
$565$	−8.84084	−	12.8305i	−0.371937	−	0.539784i
$566$	1.86401	−	1.35429i	0.0783503	−	0.0569249i
$567$		0			0
$568$			10.0156i			0.420245i
$569$	−12.7117	+	39.1225i	−0.532901	+	1.64010i	0.215240	+	0.976561i	$0.430947\pi$
$569$	−12.7117	+	39.1225i	−0.532901	+	1.64010i	−0.748141	+	0.663540i	$0.769053\pi$
$570$		0			0
$571$	4.94949	+	15.2330i	0.207130	+	0.637479i	0.999619	+	0.0275940i	$0.00878456\pi$
$571$	4.94949	+	15.2330i	0.207130	+	0.637479i	−0.792490	+	0.609885i	$0.791215\pi$
$572$	−34.0075	+	11.0497i	−1.42193	+	0.462011i
$573$		0			0
$574$	2.75038			0.114799
$575$	12.6230	−	15.6648i	0.526417	−	0.653268i
$576$		0			0
$577$	9.76316	−	13.4378i	0.406445	−	0.559424i	−0.555902	−	0.831248i	$-0.687627\pi$
$577$	9.76316	−	13.4378i	0.406445	−	0.559424i	0.962347	+	0.271824i	$0.0876268\pi$
$578$	9.07081	−	2.94729i	0.377296	−	0.122591i
$579$		0			0
$580$	16.6261	−	11.4561i	0.690359	−	0.475691i
$581$	0.536431	−	1.65097i	0.0222549	−	0.0684936i
$582$		0			0
$583$	56.4972	+	18.3571i	2.33988	+	0.760271i
$584$	−1.46056	+	1.06116i	−0.0604383	+	0.0439110i
$585$		0			0
$586$	−3.04867	−	2.21499i	−0.125939	−	0.0915002i
$587$	2.33662	+	3.21609i	0.0964428	+	0.132742i	0.854511	−	0.519433i	$-0.173857\pi$
$587$	2.33662	+	3.21609i	0.0964428	+	0.132742i	−0.758068	+	0.652175i	$0.773857\pi$
$588$		0			0
$589$	−9.53996	−	6.93118i	−0.393087	−	0.285594i
$590$	0.0982536	−	3.93234i	0.00404504	−	0.161892i
$591$		0			0
$592$	23.7471	+	7.71589i	0.975998	+	0.317121i
$593$		−	43.3755i		−	1.78122i	−0.454769	−	0.890609i	$-0.650278\pi$
$593$		−	43.3755i		−	1.78122i	0.454769	−	0.890609i	$-0.349722\pi$
$594$		0			0
$595$	−9.66421	+	27.3952i	−0.396194	+	1.12310i
$596$	2.67099	+	8.22047i	0.109408	+	0.336724i
$597$		0			0
$598$	2.44664	−	3.36751i	0.100051	−	0.137708i
$599$	−45.0977			−1.84264			−0.921321	−	0.388802i	$-0.872889\pi$
$599$	−45.0977			−1.84264			−0.921321	+	0.388802i	$0.872889\pi$
$600$		0			0
$601$	−30.6180			−1.24893			−0.624467	−	0.781051i	$-0.714684\pi$
$601$	−30.6180			−1.24893			−0.624467	+	0.781051i	$0.714684\pi$
$602$	2.84458	−	3.91523i	0.115936	−	0.159573i
$603$		0			0
$604$	6.03004	+	18.5585i	0.245359	+	0.755136i
$605$	−12.5495	−	42.1807i	−0.510211	−	1.71489i
$606$		0			0
$607$			7.94687i			0.322553i	0.986909	+	0.161277i	$0.0515612\pi$
$607$			7.94687i			0.322553i	−0.986909	+	0.161277i	$0.948439\pi$
$608$	10.1650	+	3.30281i	0.412246	+	0.133947i
$609$		0			0
$610$	1.87001	−	0.556363i	0.0757146	−	0.0225265i
$611$	−16.9687	−	12.3285i	−0.686482	−	0.498758i
$612$		0			0
$613$	6.45064	+	8.87854i	0.260539	+	0.358601i	0.919167	−	0.393867i	$-0.128863\pi$
$613$	6.45064	+	8.87854i	0.260539	+	0.358601i	−0.658628	+	0.752468i	$0.728863\pi$
$614$	0.496981	+	0.361078i	0.0200565	+	0.0145719i
$615$		0			0
$616$	−10.0078	+	7.27110i	−0.403226	+	0.292961i
$617$	−15.3376	−	4.98347i	−0.617467	−	0.200627i	−0.0164515	−	0.999865i	$-0.505237\pi$
$617$	−15.3376	−	4.98347i	−0.617467	−	0.200627i	−0.601015	+	0.799238i	$0.705237\pi$
$618$		0			0
$619$	3.21672	−	9.90003i	0.129291	−	0.397916i	−0.865368	−	0.501137i	$-0.832915\pi$
$619$	3.21672	−	9.90003i	0.129291	−	0.397916i	0.994658	+	0.103222i	$0.0329151\pi$
$620$	−16.1805	−	0.404286i	−0.649823	−	0.0162365i
$621$		0			0
$622$	−6.97609	+	2.26667i	−0.279716	+	0.0908851i
$623$	−1.05491	+	1.45196i	−0.0422641	+	0.0581715i
$624$		0			0
$625$	24.8753	+	2.49393i	0.995012	+	0.0997572i
$626$	−6.63674			−0.265257
$627$		0			0
$628$	−29.2766	+	9.51255i	−1.16826	+	0.379592i
$629$	15.5360	+	47.8148i	0.619460	+	1.90650i
$630$		0			0
$631$	−4.90235	+	15.0879i	−0.195160	+	0.600640i	0.804815	+	0.593526i	$0.202264\pi$
$631$	−4.90235	+	15.0879i	−0.195160	+	0.600640i	−0.999975	+	0.00711396i	$0.997736\pi$
$632$			0.751300i			0.0298851i
$633$		0			0
$634$	−3.76528	+	2.73564i	−0.149538	+	0.108646i
$635$	24.5260	−	32.0424i	0.973286	−	1.27157i
$636$		0			0
$637$	6.96439	+	9.58566i	0.275939	+	0.379798i
$638$	4.71116	+	6.48436i	0.186517	+	0.256718i
$639$		0			0
$640$	18.5778	−	5.52723i	0.734351	−	0.218483i
$641$	28.1613	−	20.4604i	1.11230	−	0.808136i	0.129278	−	0.991608i	$-0.458734\pi$
$641$	28.1613	−	20.4604i	1.11230	−	0.808136i	0.983025	+	0.183473i	$0.0587339\pi$
$642$		0			0
$643$		−	9.19973i		−	0.362802i	−0.983409	−	0.181401i	$-0.941937\pi$
$643$		−	9.19973i		−	0.362802i	0.983409	−	0.181401i	$-0.0580632\pi$
$644$	−4.43538	+	13.6507i	−0.174779	+	0.537913i
$645$		0			0
$646$	2.03641	+	6.26743i	0.0801215	+	0.246589i
$647$	7.66689	−	2.49112i	0.301417	−	0.0979362i	−0.154404	−	0.988008i	$-0.549346\pi$
$647$	7.66689	−	2.49112i	0.301417	−	0.0979362i	0.455821	+	0.890072i	$0.349346\pi$
$648$		0			0
$649$	−31.8905			−1.25181
$650$	5.16616	+	0.258325i	0.202633	+	0.0101323i
$651$		0			0
$652$	12.6789	−	17.4510i	0.496543	−	0.683433i
$653$	34.9786	−	11.3652i	1.36882	−	0.444756i	0.469840	−	0.882751i	$-0.344311\pi$
$653$	34.9786	−	11.3652i	1.36882	−	0.444756i	0.898977	+	0.437996i	$0.144311\pi$
$654$		0			0
$655$	−11.4567	+	32.4764i	−0.447650	+	1.26896i
$656$	−5.12708	+	15.7795i	−0.200179	+	0.616087i
$657$		0			0
$658$	−3.36804	−	1.09434i	−0.131300	−	0.0426619i
$659$	−19.5342	+	14.1924i	−0.760944	+	0.552858i	−0.899200	−	0.437539i	$-0.855850\pi$
$659$	−19.5342	+	14.1924i	−0.760944	+	0.552858i	0.138256	+	0.990397i	$0.455850\pi$
$660$		0			0
$661$	12.6232	+	9.17129i	0.490985	+	0.356722i	0.805563	−	0.592510i	$-0.201863\pi$
$661$	12.6232	+	9.17129i	0.490985	+	0.356722i	−0.314578	+	0.949232i	$0.601863\pi$
$662$	−0.805935	−	1.10927i	−0.0313235	−	0.0431132i
$663$		0			0
$664$	−0.895984	−	0.650970i	−0.0347709	−	0.0252625i
$665$	−12.2546	−	4.32306i	−0.475214	−	0.167641i
$666$		0			0
$667$	18.1225	+	5.88835i	0.701705	+	0.227998i
$668$			9.73804i			0.376776i
$669$		0			0
$670$	−2.00475	+	1.38137i	−0.0774503	+	0.0533670i
$671$	−4.88786	−	15.0433i	−0.188694	−	0.580740i
$672$		0			0
$673$	−27.1609	+	37.3838i	−1.04698	+	1.44104i	−0.155577	+	0.987824i	$0.549724\pi$
$673$	−27.1609	+	37.3838i	−1.04698	+	1.44104i	−0.891400	+	0.453216i	$0.850276\pi$
$674$	−2.72921			−0.105125
$675$		0			0
$676$	2.92896			0.112652
$677$	−2.77539	+	3.81999i	−0.106667	+	0.146814i	−0.859013	−	0.511953i	$-0.828922\pi$
$677$	−2.77539	+	3.81999i	−0.106667	+	0.146814i	0.752346	+	0.658768i	$0.228922\pi$
$678$		0			0
$679$	9.16896	+	28.2192i	0.351872	+	1.08295i
$680$	14.7171	+	11.2648i	0.564374	+	0.431985i
$681$		0			0
$682$		−	6.42514i		−	0.246031i
$683$	−8.43275	−	2.73997i	−0.322670	−	0.104842i	0.143203	−	0.989693i	$-0.454260\pi$
$683$	−8.43275	−	2.73997i	−0.322670	−	0.104842i	−0.465873	+	0.884851i	$0.654260\pi$
$684$		0			0
$685$	13.7265	+	19.9209i	0.524461	+	0.761138i
$686$	4.85588	+	3.52800i	0.185398	+	0.134700i
$687$		0			0
$688$	17.1598	+	23.6185i	0.654213	+	0.900447i
$689$	29.3771	+	21.3437i	1.11918	+	0.813129i
$690$		0			0
$691$	41.8582	−	30.4118i	1.59236	−	1.15692i	0.691888	−	0.722005i	$-0.256779\pi$
$691$	41.8582	−	30.4118i	1.59236	−	1.15692i	0.900473	−	0.434913i	$-0.143221\pi$
$692$	−27.6893	−	8.99680i	−1.05259	−	0.342007i
$693$		0			0
$694$	−0.549999	+	1.69272i	−0.0208777	+	0.0642549i
$695$	−4.27427	−	3.27162i	−0.162132	−	0.124100i
$696$		0			0
$697$	−31.7721	+	10.3234i	−1.20346	+	0.391026i
$698$	0.397600	−	0.547250i	0.0150494	−	0.0207137i
$699$		0			0
$700$	−17.2175	+	4.65771i	−0.650761	+	0.176045i
$701$	0.824350			0.0311353			0.0155676	−	0.999879i	$-0.495044\pi$
$701$	0.824350			0.0311353			0.0155676	+	0.999879i	$0.495044\pi$
$702$		0			0
$703$	−21.3888	+	6.94965i	−0.806695	+	0.262111i
$704$	−10.0059	−	30.7951i	−0.377113	−	1.16063i
$705$		0			0
$706$	−1.03213	+	3.17656i	−0.0388446	+	0.119551i
$707$			17.4687i			0.656979i
$708$		0			0
$709$	−11.6753	+	8.48261i	−0.438476	+	0.318571i	−0.785029	−	0.619459i	$-0.787352\pi$
$709$	−11.6753	+	8.48261i	−0.438476	+	0.318571i	0.346553	+	0.938030i	$0.387352\pi$
$710$	−5.40616	−	1.90713i	−0.202889	−	0.0715732i
$711$		0			0
$712$	0.673017	+	0.926329i	0.0252224	+	0.0347156i
$713$	−8.97847	−	12.3578i	−0.336246	−	0.462804i
$714$		0			0
$715$	1.04748	−	41.9226i	0.0391736	−	1.56782i
$716$	33.6106	−	24.4195i	1.25609	−	0.912601i
$717$		0			0
$718$		−	7.78894i		−	0.290681i
$719$	11.2133	−	34.5109i	0.418184	−	1.28704i	−0.491188	−	0.871054i	$-0.663437\pi$
$719$	11.2133	−	34.5109i	0.418184	−	1.28704i	0.909372	−	0.415985i	$-0.136563\pi$
$720$		0			0
$721$	−3.97839	−	12.2442i	−0.148163	−	0.455999i
$722$	2.71763	−	0.883013i	0.101140	−	0.0328623i
$723$		0			0
$724$	25.5439			0.949331
$725$	6.18350	+	22.8577i	0.229649	+	0.848915i
$726$		0			0
$727$	−12.5542	+	17.2794i	−0.465611	+	0.640858i	−0.975660	−	0.219287i	$-0.929627\pi$
$727$	−12.5542	+	17.2794i	−0.465611	+	0.640858i	0.510050	+	0.860145i	$0.329627\pi$
$728$	−7.19148	+	2.33665i	−0.266534	+	0.0866021i
$729$		0			0
$730$	−0.294671	−	0.990431i	−0.0109063	−	0.0366575i
$731$	−18.1648	+	55.9054i	−0.671848	+	2.06773i
$732$		0			0
$733$	13.4275	+	4.36286i	0.495956	+	0.161146i	0.546306	−	0.837586i	$-0.316034\pi$
$733$	13.4275	+	4.36286i	0.495956	+	0.161146i	−0.0503496	+	0.998732i	$0.516034\pi$
$734$	5.36275	−	3.89627i	0.197943	−	0.143814i
$735$		0			0
$736$	11.2009	+	8.13796i	0.412872	+	0.299969i
$737$	11.6016	+	15.9682i	0.427351	+	0.588198i
$738$		0			0
$739$	12.6354	+	9.18018i	0.464802	+	0.337699i	0.795412	−	0.606069i	$-0.207254\pi$
$739$	12.6354	+	9.18018i	0.464802	+	0.337699i	−0.330610	+	0.943767i	$0.607254\pi$
$740$	−18.7623	+	24.5123i	−0.689716	+	0.901091i
$741$		0			0
$742$	5.83090	+	1.89458i	0.214059	+	0.0695520i
$743$			9.33091i			0.342318i	0.985243	+	0.171159i	$0.0547512\pi$
$743$			9.33091i			0.342318i	−0.985243	+	0.171159i	$0.945249\pi$
$744$		0			0
$745$	−10.1338	−	0.253203i	−0.371272	−	0.00927662i
$746$	1.53739	+	4.73161i	0.0562879	+	0.173236i
$747$		0			0
$748$	43.1036	−	59.3271i	1.57603	−	2.16921i
$749$	19.3921			0.708570
$750$		0			0
$751$	−4.05895			−0.148113			−0.0740565	−	0.997254i	$-0.523595\pi$
$751$	−4.05895			−0.148113			−0.0740565	+	0.997254i	$0.523595\pi$
$752$	12.5570	−	17.2832i	0.457906	−	0.630253i
$753$		0			0
$754$	1.51399	+	4.65957i	0.0551361	+	0.169692i
$755$	−22.8780	−	0.571630i	−0.832615	−	0.0208038i
$756$		0			0
$757$		−	10.3385i		−	0.375760i	−0.982192	−	0.187880i	$-0.939838\pi$
$757$		−	10.3385i		−	0.375760i	0.982192	−	0.187880i	$-0.0601615\pi$
$758$	−5.61329	−	1.82387i	−0.203884	−	0.0662458i
$759$		0			0
$760$	−5.03904	+	6.58334i	−0.182785	+	0.238803i
$761$	−4.40577	−	3.20098i	−0.159709	−	0.116035i	0.505060	−	0.863084i	$-0.331470\pi$
$761$	−4.40577	−	3.20098i	−0.159709	−	0.116035i	−0.664769	+	0.747049i	$0.731470\pi$
$762$		0			0
$763$	−6.02918	−	8.29846i	−0.218271	−	0.300424i
$764$	−8.33584	−	6.05634i	−0.301580	−	0.219111i
$765$		0			0
$766$	7.01063	−	5.09352i	0.253304	−	0.184036i
$767$	−18.5395	−	6.02384i	−0.669421	−	0.217508i
$768$		0			0
$769$	−3.03670	+	9.34600i	−0.109506	+	0.337025i	−0.990762	−	0.135615i	$-0.956699\pi$
$769$	−3.03670	+	9.34600i	−0.109506	+	0.337025i	0.881255	+	0.472640i	$0.156699\pi$
$770$	−2.01911	−	6.78649i	−0.0727635	−	0.244568i
$771$		0			0
$772$	−15.8270	+	5.14251i	−0.569627	+	0.185083i
$773$	7.67854	−	10.5686i	0.276178	−	0.380126i	−0.648285	−	0.761398i	$-0.724514\pi$
$773$	7.67854	−	10.5686i	0.276178	−	0.380126i	0.924463	+	0.381271i	$0.124514\pi$
$774$		0			0
$775$	6.76003	−	17.7375i	0.242827	−	0.637150i
$776$	18.9299			0.679544
$777$		0			0
$778$	2.97817	−	0.967666i	0.106773	−	0.0346925i
$779$	−4.61793	−	14.2125i	−0.165455	−	0.509217i
$780$		0			0
$781$	−14.3620	+	44.2017i	−0.513912	+	1.58166i
$782$			8.53647i			0.305263i
$783$		0			0
$784$	−9.76329	+	7.09345i	−0.348689	+	0.253337i
$785$	0.901763	−	36.0907i	0.0321853	−	1.28813i
$786$		0			0
$787$	27.4658	+	37.8034i	0.979050	+	1.34755i	0.937340	+	0.348417i	$0.113281\pi$
$787$	27.4658	+	37.8034i	0.979050	+	1.34755i	0.0417105	+	0.999130i	$0.486719\pi$
$788$	10.3665	+	14.2683i	0.369292	+	0.508286i
$789$		0			0
$790$	−0.405532	−	0.143060i	−0.0144282	−	0.00508983i
$791$	−10.5475	+	7.66321i	−0.375026	+	0.272472i
$792$		0			0
$793$		−	9.66867i		−	0.343344i
$794$	2.77493	−	8.54037i	0.0984787	−	0.303086i
$795$		0			0
$796$	−11.2606	−	34.6566i	−0.399121	−	1.22837i
$797$	14.4505	−	4.69524i	0.511861	−	0.166314i	−0.0416872	−	0.999131i	$-0.513273\pi$
$797$	14.4505	−	4.69524i	0.511861	−	0.166314i	0.553549	+	0.832817i	$0.313273\pi$
$798$		0			0
$799$	43.0149			1.52176
$800$	−0.859234	+	17.1836i	−0.0303785	+	0.607530i
$801$		0			0
$802$	4.07064	−	5.60276i	0.143739	−	0.197840i
$803$	−7.96751	+	2.58880i	−0.281167	+	0.0913568i
$804$		0			0
$805$	−13.3669	−	10.2313i	−0.471121	−	0.360607i
$806$	1.21365	−	3.73524i	0.0427491	−	0.131568i
$807$		0			0
$808$	10.5993	+	3.44393i	0.372883	+	0.121157i
$809$	−3.61698	+	2.62789i	−0.127166	+	0.0923916i	−0.649550	−	0.760319i	$-0.725043\pi$
$809$	−3.61698	+	2.62789i	−0.127166	+	0.0923916i	0.522384	+	0.852710i	$0.325043\pi$
$810$		0			0
$811$	−18.1156	−	13.1618i	−0.636125	−	0.462172i	0.222392	−	0.974957i	$-0.428614\pi$
$811$	−18.1156	−	13.1618i	−0.636125	−	0.462172i	−0.858517	+	0.512786i	$0.828614\pi$
$812$	−9.93015	−	13.6677i	−0.348480	−	0.479641i
$813$		0			0
$814$	−9.91362	−	7.20266i	−0.347472	−	0.252453i
$815$	14.3537	+	20.8312i	0.502787	+	0.729684i
$816$		0			0
$817$	−25.0080	−	8.12558i	−0.874918	−	0.284278i
$818$		−	2.44005i		−	0.0853145i
$819$		0			0
$820$	−16.2880	−	12.4672i	−0.568803	−	0.435375i
$821$	2.30703	+	7.10031i	0.0805160	+	0.247803i	0.983209	−	0.182482i	$-0.0584131\pi$
$821$	2.30703	+	7.10031i	0.0805160	+	0.247803i	−0.902693	+	0.430285i	$0.858413\pi$
$822$		0			0
$823$	−7.06536	+	9.72464i	−0.246283	+	0.338980i	−0.914205	−	0.405252i	$-0.867184\pi$
$823$	−7.06536	+	9.72464i	−0.246283	+	0.338980i	0.667922	+	0.744231i	$0.267184\pi$
$824$	−8.21364			−0.286136
$825$		0			0
$826$	−3.29132			−0.114520
$827$	25.3170	−	34.8458i	0.880357	−	1.21171i	−0.0959652	−	0.995385i	$-0.530594\pi$
$827$	25.3170	−	34.8458i	0.880357	−	1.21171i	0.976322	−	0.216322i	$-0.0694062\pi$
$828$		0			0
$829$	−11.2798	−	34.7155i	−0.391762	−	1.20572i	−0.931454	−	0.363858i	$-0.881459\pi$
$829$	−11.2798	−	34.7155i	−0.391762	−	1.20572i	0.539692	−	0.841863i	$-0.318541\pi$
$830$	0.521986	−	0.359674i	0.0181184	−	0.0124845i
$831$		0			0
$832$		−	19.7927i		−	0.686189i
$833$	−23.1099	−	7.50885i	−0.800710	−	0.260166i
$834$		0			0
$835$	−10.7701	−	3.79935i	−0.372713	−	0.131482i
$836$	26.5386	+	19.2814i	0.917856	+	0.666862i
$837$		0			0
$838$	3.15194	+	4.33828i	0.108882	+	0.149863i
$839$	−16.7199	−	12.1477i	−0.577235	−	0.419386i	0.260491	−	0.965476i	$-0.416116\pi$
$839$	−16.7199	−	12.1477i	−0.577235	−	0.419386i	−0.837726	+	0.546090i	$0.816116\pi$
$840$		0			0
$841$	5.31649	−	3.86266i	0.183327	−	0.133195i
$842$	−6.76354	−	2.19761i	−0.233087	−	0.0757346i
$843$		0			0
$844$	16.7406	−	51.5223i	0.576236	−	1.77347i
$845$	−1.14275	+	3.23936i	−0.0393117	+	0.111437i
$846$		0			0
$847$	−35.0204	+	11.3788i	−1.20332	+	0.390981i
$848$	−21.7392	+	29.9214i	−0.746527	+	1.02751i
$849$		0			0
$850$	−8.88280	+	5.79889i	−0.304678	+	0.198900i
$851$	−29.1324			−0.998645
$852$		0			0
$853$	−28.6554	+	9.31070i	−0.981142	+	0.318792i	−0.755306	−	0.655373i	$-0.772512\pi$
$853$	−28.6554	+	9.31070i	−0.981142	+	0.318792i	−0.225837	+	0.974165i	$0.572512\pi$
$854$	−0.504461	−	1.55257i	−0.0172623	−	0.0531279i
$855$		0			0
$856$	3.82311	−	11.7663i	0.130671	−	0.402165i
$857$			2.03243i			0.0694266i	0.999397	+	0.0347133i	$0.0110518\pi$
$857$			2.03243i			0.0694266i	−0.999397	+	0.0347133i	$0.988948\pi$
$858$		0			0
$859$	−11.4529	+	8.32100i	−0.390767	+	0.283909i	−0.765770	−	0.643115i	$-0.777642\pi$
$859$	−11.4529	+	8.32100i	−0.390767	+	0.283909i	0.375003	+	0.927024i	$0.377642\pi$
$860$	−34.5933	+	10.2921i	−1.17962	+	0.350959i
$861$		0			0
$862$	−2.25331	−	3.10141i	−0.0767479	−	0.105634i
$863$	9.06514	+	12.4771i	0.308581	+	0.424725i	0.934938	−	0.354811i	$-0.115455\pi$
$863$	9.06514	+	12.4771i	0.308581	+	0.424725i	−0.626357	+	0.779536i	$0.715455\pi$
$864$		0			0
$865$	20.7534	−	27.1136i	0.705636	−	0.921890i
$866$	−2.03104	+	1.47564i	−0.0690175	+	0.0501442i
$867$		0			0
$868$			13.5428i			0.459674i
$869$	−1.07734	+	3.31570i	−0.0365462	+	0.112477i
$870$		0			0
$871$	3.72831	+	11.4746i	0.126329	+	0.388800i
$872$	−6.22382	+	2.02224i	−0.210765	+	0.0684817i
$873$		0			0
$874$	−3.81859			−0.129166
$875$	1.56619	−	20.8594i	0.0529469	−	0.705177i
$876$		0			0
$877$	30.1206	−	41.4574i	1.01710	−	1.39992i	0.102882	−	0.994694i	$-0.467194\pi$
$877$	30.1206	−	41.4574i	1.01710	−	1.39992i	0.914217	−	0.405224i	$-0.132806\pi$
$878$	−3.85933	+	1.25397i	−0.130246	+	0.0423196i
$879$		0			0
$880$	42.6995	+	1.06689i	1.43940	+	0.0359649i
$881$	4.96737	−	15.2880i	0.167355	−	0.515066i	−0.831847	−	0.555005i	$-0.812716\pi$
$881$	4.96737	−	15.2880i	0.167355	−	0.515066i	0.999202	+	0.0399390i	$0.0127164\pi$
$882$		0			0
$883$	−28.9446	−	9.40468i	−0.974065	−	0.316493i	−0.221609	−	0.975136i	$-0.571131\pi$
$883$	−28.9446	−	9.40468i	−0.974065	−	0.316493i	−0.752456	+	0.658643i	$0.771131\pi$
$884$	36.2646	−	26.3478i	1.21971	−	0.886172i
$885$		0			0
$886$	1.73940	+	1.26375i	0.0584362	+	0.0424564i
$887$	8.80443	+	12.1183i	0.295624	+	0.406891i	0.930831	−	0.365451i	$-0.119085\pi$
$887$	8.80443	+	12.1183i	0.295624	+	0.406891i	−0.635207	+	0.772342i	$0.719085\pi$
$888$		0			0
$889$	−27.3150	−	19.8455i	−0.916115	−	0.665596i
$890$	−0.628161	+	0.186890i	−0.0210560	+	0.00626455i
$891$		0			0
$892$	−28.1552	−	9.14818i	−0.942706	−	0.306304i
$893$			19.2417i			0.643900i
$894$		0			0
$895$	13.8941	+	46.7000i	0.464429	+	1.56101i
$896$	−5.01161	−	15.4241i	−0.167426	−	0.515284i
$897$		0			0
$898$	−0.210158	+	0.289258i	−0.00701307	+	0.00965266i
$899$	17.9793			0.599642
$900$		0			0
$901$	−74.4693			−2.48093
$902$	4.78605	−	6.58743i	0.159358	−	0.219338i
$903$		0			0
$904$	2.57031	+	7.91059i	0.0854871	+	0.263102i
$905$	−9.96609	+	28.2510i	−0.331284	+	0.939094i
$906$		0			0
$907$		−	34.9255i		−	1.15968i	−0.814730	−	0.579841i	$-0.803115\pi$
$907$		−	34.9255i		−	1.15968i	0.814730	−	0.579841i	$-0.196885\pi$
$908$	49.7629	+	16.1690i	1.65144	+	0.536586i
$909$		0			0
$910$	0.108107	−	4.32671i	0.00358372	−	0.143429i
$911$	−12.2601	−	8.90751i	−0.406197	−	0.295119i	0.365864	−	0.930668i	$-0.380774\pi$
$911$	−12.2601	−	8.90751i	−0.406197	−	0.295119i	−0.772060	+	0.635549i	$0.780774\pi$
$912$		0			0
$913$	−3.02076	−	4.15772i	−0.0999727	−	0.137601i
$914$	−1.34738	−	0.978930i	−0.0445674	−	0.0323801i
$915$		0			0
$916$	19.1931	−	13.9446i	0.634159	−	0.460744i
$917$	27.4048	+	8.90437i	0.904987	+	0.294048i
$918$		0			0
$919$	−10.8648	+	33.4383i	−0.358395	+	1.10303i	0.595619	+	0.803267i	$0.296907\pi$
$919$	−10.8648	+	33.4383i	−0.358395	+	1.10303i	−0.954014	+	0.299761i	$0.903093\pi$
$920$	−8.84323	+	6.09341i	−0.291553	+	0.200894i
$921$		0			0
$922$	10.8026	−	3.50999i	0.355766	−	0.115595i
$923$	−16.6986	+	22.9837i	−0.549642	+	0.756518i
$924$		0			0
$925$	−19.7899	−	30.3143i	−0.650687	−	0.996729i
$926$	−4.79752			−0.157656
$927$		0			0
$928$	−15.4986	+	5.03579i	−0.508765	+	0.165308i
$929$	2.39772	+	7.37943i	0.0786667	+	0.242111i	0.982654	−	0.185448i	$-0.0593736\pi$
$929$	2.39772	+	7.37943i	0.0786667	+	0.242111i	−0.903987	+	0.427559i	$0.859374\pi$
$930$		0			0
$931$	3.35891	−	10.3377i	0.110084	−	0.338803i
$932$		−	13.4235i		−	0.439701i
$933$		0			0
$934$	2.81950	−	2.04849i	0.0922570	−	0.0670286i
$935$	48.7973	+	70.8185i	1.59584	+	2.31601i
$936$		0			0
$937$	18.5527	+	25.5356i	0.606090	+	0.834211i	0.996249	−	0.0865367i	$-0.0275800\pi$
$937$	18.5527	+	25.5356i	0.606090	+	0.834211i	−0.390159	+	0.920747i	$0.627580\pi$
$938$	1.19737	+	1.64803i	0.0390954	+	0.0538102i
$939$		0			0
$940$	14.9853	+	21.7479i	0.488768	+	0.709338i
$941$	−26.2059	+	19.0397i	−0.854289	+	0.620677i	−0.926325	−	0.376725i	$-0.877050\pi$
$941$	−26.2059	+	19.0397i	−0.854289	+	0.620677i	0.0720365	+	0.997402i	$0.477050\pi$
$942$		0			0
$943$		−	19.3580i		−	0.630383i
$944$	6.13547	−	18.8830i	0.199692	−	0.614590i
$945$		0			0
$946$	−4.42739	−	13.6261i	−0.143947	−	0.443023i
$947$	38.4644	−	12.4978i	1.24993	−	0.406125i	0.392031	−	0.919952i	$-0.371773\pi$
$947$	38.4644	−	12.4978i	1.24993	−	0.406125i	0.857894	+	0.513827i	$0.171773\pi$
$948$		0			0
$949$	−5.12090			−0.166231
$950$	−2.59400	−	3.97351i	−0.0841605	−	0.128918i
$951$		0			0
$952$	9.11501	−	12.5457i	0.295419	−	0.406610i
$953$	−43.9530	+	14.2812i	−1.42378	+	0.462613i	−0.916800	−	0.399347i	$-0.869237\pi$
$953$	−43.9530	+	14.2812i	−1.42378	+	0.462613i	−0.506976	+	0.861960i	$0.669237\pi$
$954$		0			0
$955$	9.95045	−	6.85634i	0.321989	−	0.221866i
$956$	14.9837	−	46.1152i	0.484608	−	1.49147i
$957$		0			0
$958$	−1.01954	−	0.331267i	−0.0329397	−	0.0107028i
$959$	16.3762	−	11.8980i	0.528817	−	0.384208i
$960$		0			0
$961$	13.4194	+	9.74978i	0.432885	+	0.314509i
$962$	−4.40274	−	6.05985i	−0.141950	−	0.195377i
$963$		0			0
$964$	−21.1660	−	15.3780i	−0.681710	−	0.495291i
$965$	0.487495	−	19.5107i	0.0156930	−	0.628072i
$966$		0			0
$967$	−12.8420	−	4.17263i	−0.412972	−	0.134183i	0.0951598	−	0.995462i	$-0.469664\pi$
$967$	−12.8420	−	4.17263i	−0.412972	−	0.134183i	−0.508132	+	0.861279i	$0.669664\pi$
$968$			23.4923i			0.755071i
$969$		0			0
$970$	−3.60456	+	10.2179i	−0.115735	+	0.328076i
$971$	−13.1867	−	40.5844i	−0.423181	−	1.30242i	−0.904725	−	0.425995i	$-0.859924\pi$
$971$	−13.1867	−	40.5844i	−0.423181	−	1.30242i	0.481545	−	0.876422i	$-0.340076\pi$
$972$		0			0
$973$	−2.64727	+	3.64365i	−0.0848675	+	0.116810i
$974$	−2.40574			−0.0770848
$975$		0			0
$976$	9.84784			0.315222
$977$	−14.8487	+	20.4375i	−0.475053	+	0.653854i	−0.977545	−	0.210728i	$-0.932417\pi$
$977$	−14.8487	+	20.4375i	−0.475053	+	0.653854i	0.502492	+	0.864582i	$0.332417\pi$
$978$		0			0
$979$	1.64190	+	5.05324i	0.0524752	+	0.161502i
$980$	−4.25451	−	14.3000i	−0.135905	−	0.456797i
$981$		0			0
$982$			7.78217i			0.248339i
$983$	−25.4179	−	8.25877i	−0.810704	−	0.263414i	−0.125808	−	0.992055i	$-0.540152\pi$
$983$	−25.4179	−	8.25877i	−0.810704	−	0.263414i	−0.684896	+	0.728641i	$0.740152\pi$
$984$		0			0
$985$	−19.8249	+	5.89828i	−0.631675	+	0.187935i
$986$	−8.12876	−	5.90589i	−0.258872	−	0.188082i
$987$		0			0
$988$	11.7861	+	16.2221i	0.374965	+	0.516095i
$989$	−27.5565	−	20.0210i	−0.876247	−	0.636631i
$990$		0			0
$991$	−6.10514	+	4.43564i	−0.193936	+	0.140903i	−0.680516	−	0.732733i	$-0.738244\pi$
$991$	−6.10514	+	4.43564i	−0.193936	+	0.140903i	0.486580	+	0.873636i	$0.338244\pi$
$992$	12.4241	+	4.03682i	0.394465	+	0.128169i
$993$		0			0
$994$	−1.48226	+	4.56192i	−0.0470143	+	0.144695i
$995$	42.7228	+	1.06747i	1.35440	+	0.0338412i
$996$		0			0
$997$	−19.7252	+	6.40910i	−0.624702	+	0.202978i	−0.604227	−	0.796812i	$-0.706518\pi$
$997$	−19.7252	+	6.40910i	−0.624702	+	0.202978i	−0.0204754	+	0.999790i	$0.506518\pi$
$998$	−0.906345	+	1.24748i	−0.0286899	+	0.0394882i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.c.109.4	yes	24
3.2	odd	2	inner	225.2.m.c.109.3	yes	24
25.8	odd	20		5625.2.a.bf.1.14		24
25.14	even	10	inner	225.2.m.c.64.4	yes	24
25.17	odd	20		5625.2.a.bf.1.11		24
75.8	even	20		5625.2.a.bf.1.12		24
75.14	odd	10	inner	225.2.m.c.64.3	✓	24
75.17	even	20		5625.2.a.bf.1.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.m.c.64.3	✓	24	75.14	odd	10	inner
225.2.m.c.64.4	yes	24	25.14	even	10	inner
225.2.m.c.109.3	yes	24	3.2	odd	2	inner
225.2.m.c.109.4	yes	24	1.1	even	1	trivial
5625.2.a.bf.1.11		24	25.17	odd	20
5625.2.a.bf.1.12		24	75.8	even	20
5625.2.a.bf.1.13		24	75.17	even	20
5625.2.a.bf.1.14		24	25.8	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.179595 - 0.247191i) q^{2} +(0.589185 + 1.81332i) q^{4} +(-2.23537 - 0.0558531i) q^{5} +1.87098i q^{7} +(1.13523 + 0.368860i) q^{8} +O(q^{10})\)	\(q+(0.179595 - 0.247191i) q^{2} +(0.589185 + 1.81332i) q^{4} +(-2.23537 - 0.0558531i) q^{5} +1.87098i q^{7} +(1.13523 + 0.368860i) q^{8} +(-0.415267 + 0.542533i) q^{10} +(4.48118 + 3.25577i) q^{11} +(1.99014 + 2.73919i) q^{13} +(0.462489 + 0.336018i) q^{14} +(-2.78995 + 2.02702i) q^{16} +(-6.60386 - 2.14572i) q^{17} +(0.959840 - 2.95408i) q^{19} +(-1.21577 - 4.08636i) q^{20} +(1.60959 - 0.522989i) q^{22} +(2.36499 - 3.25514i) q^{23} +(4.99376 + 0.249705i) q^{25} +1.03452 q^{26} +(-3.39269 + 1.10235i) q^{28} +(1.46346 + 4.50408i) q^{29} +(1.17315 - 3.61059i) q^{31} +3.44100i q^{32} +(-1.71642 + 1.24705i) q^{34} +(0.104500 - 4.18232i) q^{35} +(-4.25582 - 5.85763i) q^{37} +(-0.557841 - 0.767802i) q^{38} +(-2.51707 - 0.887944i) q^{40} +(3.89230 - 2.82792i) q^{41} -8.46556i q^{43} +(-3.26352 + 10.0441i) q^{44} +(-0.379900 - 1.16921i) q^{46} +(-5.89161 + 1.91430i) q^{47} +3.49945 q^{49} +(0.958579 - 1.18957i) q^{50} +(-3.79448 + 5.22266i) q^{52} +(10.1998 - 3.31412i) q^{53} +(-9.83525 - 7.52813i) q^{55} +(-0.690128 + 2.12399i) q^{56} +(1.37620 + 0.447154i) q^{58} +(-4.65783 + 3.38411i) q^{59} +(-2.31025 - 1.67850i) q^{61} +(-0.681815 - 0.938437i) q^{62} +(-4.72932 - 3.43605i) q^{64} +(-4.29570 - 6.23426i) q^{65} +(3.38900 + 1.10115i) q^{67} -13.2392i q^{68} +(-1.01507 - 0.776955i) q^{70} +(2.59287 + 7.98002i) q^{71} +(-0.888997 + 1.22360i) q^{73} -2.21228 q^{74} +5.92223 q^{76} +(-6.09146 + 8.38418i) q^{77} +(0.194499 + 0.598606i) q^{79} +(6.34979 - 4.37531i) q^{80} -1.47002i q^{82} +(-0.882409 - 0.286712i) q^{83} +(14.6422 + 5.16533i) q^{85} +(-2.09261 - 1.52037i) q^{86} +(3.88626 + 5.34898i) q^{88} +(0.776044 + 0.563829i) q^{89} +(-5.12496 + 3.72350i) q^{91} +(7.29604 + 2.37063i) q^{92} +(-0.584905 + 1.80015i) q^{94} +(-2.31059 + 6.54986i) q^{95} +(15.0826 - 4.90063i) q^{97} +(0.628483 - 0.865033i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4}+O(q^{10}) \) 24 * q + 8 * q^4	\( 24 q + 8 q^{4} - 10 q^{10} - 24 q^{16} + 14 q^{19} + 70 q^{22} + 30 q^{28} - 18 q^{31} + 10 q^{34} - 20 q^{37} - 80 q^{40} - 72 q^{49} - 140 q^{52} - 10 q^{55} - 130 q^{58} - 12 q^{61} + 2 q^{64} + 80 q^{67} + 30 q^{70} - 20 q^{73} + 88 q^{76} + 36 q^{79} + 90 q^{85} + 180 q^{88} - 30 q^{91} + 50 q^{94} + 100 q^{97}+O(q^{100}) \) 24 * q + 8 * q^4 - 10 * q^10 - 24 * q^16 + 14 * q^19 + 70 * q^22 + 30 * q^28 - 18 * q^31 + 10 * q^34 - 20 * q^37 - 80 * q^40 - 72 * q^49 - 140 * q^52 - 10 * q^55 - 130 * q^58 - 12 * q^61 + 2 * q^64 + 80 * q^67 + 30 * q^70 - 20 * q^73 + 88 * q^76 + 36 * q^79 + 90 * q^85 + 180 * q^88 - 30 * q^91 + 50 * q^94 + 100 * q^97

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