LMFDB - Embedded newform 476.2.bh.a.457.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(9,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

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

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

chi := DirichletCharacter("476.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bh (of order $24$, degree $8$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.10
Character	$\chi$	$=$	476.457
Dual form			476.2.bh.a.25.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40728 - 1.83401i) q^{3} +(-0.546335 + 4.14983i) q^{5} +(-1.90193 + 1.83920i) q^{7} +(-0.606678 - 2.26415i) q^{9} +O(q^{10})$	\(q+(1.40728 - 1.83401i) q^{3} +(-0.546335 + 4.14983i) q^{5} +(-1.90193 + 1.83920i) q^{7} +(-0.606678 - 2.26415i) q^{9} +(0.0289816 - 0.00381550i) q^{11} +5.96827i q^{13} +(6.84197 + 6.84197i) q^{15} +(4.11115 + 0.313738i) q^{17} +(1.06568 - 0.285548i) q^{19} +(0.696552 + 6.07643i) q^{21} +(-3.38583 - 4.41250i) q^{23} +(-12.0930 - 3.24030i) q^{25} +(1.40100 + 0.580313i) q^{27} +(-4.06136 + 1.68227i) q^{29} +(4.40166 - 5.73635i) q^{31} +(0.0337877 - 0.0585220i) q^{33} +(-6.59328 - 8.89751i) q^{35} +(9.07169 + 1.19431i) q^{37} +(10.9458 + 8.39904i) q^{39} +(2.07966 + 0.861421i) q^{41} +(3.27064 - 3.27064i) q^{43} +(9.72730 - 1.28062i) q^{45} +(-5.92176 - 3.41893i) q^{47} +(0.234681 - 6.99606i) q^{49} +(6.36095 - 7.09836i) q^{51} +(-1.07061 + 3.99557i) q^{53} +0.122353i q^{55} +(0.976015 - 2.35631i) q^{57} +(0.582222 + 0.156006i) q^{59} +(4.26353 - 3.27152i) q^{61} +(5.31809 + 3.19046i) q^{63} +(-24.7673 - 3.26068i) q^{65} +(2.50972 + 4.34696i) q^{67} -12.8574 q^{69} +(4.09876 + 9.89527i) q^{71} +(-3.75990 - 2.88507i) q^{73} +(-22.9610 + 17.6186i) q^{75} +(-0.0481036 + 0.0605598i) q^{77} +(3.73971 + 4.87368i) q^{79} +(9.12585 - 5.26881i) q^{81} +(-7.00067 - 7.00067i) q^{83} +(-3.54803 + 16.8892i) q^{85} +(-2.63018 + 9.81598i) q^{87} +(10.0102 + 5.77940i) q^{89} +(-10.9768 - 11.3512i) q^{91} +(-4.32613 - 16.1453i) q^{93} +(0.602757 + 4.57839i) q^{95} +(8.13210 - 3.36843i) q^{97} +(-0.0262214 - 0.0633040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{5}+O(q^{10}) $ 96 * q + 4 * q^5	$ 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) $ 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	1.40728	−	1.83401i	0.812495	−	1.05886i	−0.184609	−	0.982812i	$-0.559102\pi$
$3$	1.40728	−	1.83401i	0.812495	−	1.05886i	0.997104	−	0.0760519i	$-0.0242315\pi$
$4$		0			0
$5$	−0.546335	+	4.14983i	−0.244329	+	1.85586i	0.226990	+	0.973897i	$0.427112\pi$
$5$	−0.546335	+	4.14983i	−0.244329	+	1.85586i	−0.471318	+	0.881963i	$0.656222\pi$
$6$		0			0
$7$	−1.90193	+	1.83920i	−0.718862	+	0.695153i
$7$	−1.90193	+	1.83920i	−0.718862	+	0.695153i
$8$		0			0
$9$	−0.606678	−	2.26415i	−0.202226	−	0.754717i
$10$		0			0
$11$	0.0289816	−	0.00381550i	0.00873829	−	0.00115042i	−0.126156	−	0.992010i	$-0.540264\pi$
$11$	0.0289816	−	0.00381550i	0.00873829	−	0.00115042i	0.134894	+	0.990860i	$0.456931\pi$
$12$		0			0
$13$			5.96827i			1.65530i	0.561244	+	0.827650i	$0.310323\pi$
$13$			5.96827i			1.65530i	−0.561244	+	0.827650i	$0.689677\pi$
$14$		0			0
$15$	6.84197	+	6.84197i	1.76659	+	1.76659i
$16$		0			0
$17$	4.11115	+	0.313738i	0.997101	+	0.0760926i
$17$	4.11115	+	0.313738i	0.997101	+	0.0760926i
$18$		0			0
$19$	1.06568	−	0.285548i	0.244484	−	0.0655092i	−0.134496	−	0.990914i	$-0.542942\pi$
$19$	1.06568	−	0.285548i	0.244484	−	0.0655092i	0.378980	+	0.925405i	$0.376275\pi$
$20$		0			0
$21$	0.696552	+	6.07643i	0.152000	+	1.32599i
$22$		0			0
$23$	−3.38583	−	4.41250i	−0.705994	−	0.920070i	0.293360	−	0.956002i	$-0.405227\pi$
$23$	−3.38583	−	4.41250i	−0.705994	−	0.920070i	−0.999354	+	0.0359324i	$0.988560\pi$
$24$		0			0
$25$	−12.0930	−	3.24030i	−2.41860	−	0.648061i
$26$		0			0
$27$	1.40100	+	0.580313i	0.269623	+	0.111681i
$28$		0			0
$29$	−4.06136	+	1.68227i	−0.754175	+	0.312389i	−0.726444	−	0.687226i	$-0.758828\pi$
$29$	−4.06136	+	1.68227i	−0.754175	+	0.312389i	−0.0277312	+	0.999615i	$0.508828\pi$
$30$		0			0
$31$	4.40166	−	5.73635i	0.790561	−	1.03028i	−0.208078	−	0.978112i	$-0.566721\pi$
$31$	4.40166	−	5.73635i	0.790561	−	1.03028i	0.998638	−	0.0521664i	$-0.0166126\pi$
$32$		0			0
$33$	0.0337877	−	0.0585220i	0.00588168	−	0.0101874i
$34$		0			0
$35$	−6.59328	−	8.89751i	−1.11447	−	1.50395i
$36$		0			0
$37$	9.07169	+	1.19431i	1.49138	+	0.196343i	0.831708	−	0.555213i	$-0.187363\pi$
$37$	9.07169	+	1.19431i	1.49138	+	0.196343i	0.659669	+	0.751557i	$0.270697\pi$
$38$		0			0
$39$	10.9458	+	8.39904i	1.75274	+	1.34492i
$40$		0			0
$41$	2.07966	+	0.861421i	0.324788	+	0.134531i	0.539119	−	0.842230i	$-0.318757\pi$
$41$	2.07966	+	0.861421i	0.324788	+	0.134531i	−0.214331	+	0.976761i	$0.568757\pi$
$42$		0			0
$43$	3.27064	−	3.27064i	0.498768	−	0.498768i	−0.412286	−	0.911054i	$-0.635270\pi$
$43$	3.27064	−	3.27064i	0.498768	−	0.498768i	0.911054	+	0.412286i	$0.135270\pi$
$44$		0			0
$45$	9.72730	−	1.28062i	1.45006	−	0.190904i
$46$		0			0
$47$	−5.92176	−	3.41893i	−0.863778	−	0.498702i	0.00149795	−	0.999999i	$-0.499523\pi$
$47$	−5.92176	−	3.41893i	−0.863778	−	0.498702i	−0.865275	+	0.501297i	$0.832857\pi$
$48$		0			0
$49$	0.234681	−	6.99606i	0.0335259	−	0.999438i
$50$		0			0
$51$	6.36095	−	7.09836i	0.890711	−	0.993969i
$52$		0			0
$53$	−1.07061	+	3.99557i	−0.147060	+	0.548834i	0.852596	+	0.522571i	$0.175027\pi$
$53$	−1.07061	+	3.99557i	−0.147060	+	0.548834i	−0.999655	+	0.0262623i	$0.991639\pi$
$54$		0			0
$55$			0.122353i			0.0164981i
$56$		0			0
$57$	0.976015	−	2.35631i	0.129276	−	0.312101i
$58$		0			0
$59$	0.582222	+	0.156006i	0.0757988	+	0.0203102i	0.296519	−	0.955027i	$-0.404174\pi$
$59$	0.582222	+	0.156006i	0.0757988	+	0.0203102i	−0.220720	+	0.975337i	$0.570841\pi$
$60$		0			0
$61$	4.26353	−	3.27152i	0.545890	−	0.418876i	−0.298655	−	0.954361i	$-0.596538\pi$
$61$	4.26353	−	3.27152i	0.545890	−	0.418876i	0.844545	+	0.535485i	$0.179871\pi$
$62$		0			0
$63$	5.31809	+	3.19046i	0.670016	+	0.401960i
$64$		0			0
$65$	−24.7673	−	3.26068i	−3.07201	−	0.404437i
$66$		0			0
$67$	2.50972	+	4.34696i	0.306611	+	0.531066i	0.977619	−	0.210384i	$-0.0674715\pi$
$67$	2.50972	+	4.34696i	0.306611	+	0.531066i	−0.671008	+	0.741451i	$0.734138\pi$
$68$		0			0
$69$	−12.8574			−1.54785
$70$		0			0
$71$	4.09876	+	9.89527i	0.486433	+	1.17435i	0.956503	+	0.291723i	$0.0942287\pi$
$71$	4.09876	+	9.89527i	0.486433	+	1.17435i	−0.470070	+	0.882629i	$0.655771\pi$
$72$		0			0
$73$	−3.75990	−	2.88507i	−0.440063	−	0.337672i	0.364849	−	0.931067i	$-0.381121\pi$
$73$	−3.75990	−	2.88507i	−0.440063	−	0.337672i	−0.804912	+	0.593395i	$0.797787\pi$
$74$		0			0
$75$	−22.9610	+	17.6186i	−2.65130	+	2.03442i
$76$		0			0
$77$	−0.0481036	+	0.0605598i	−0.00548191	+	0.00690144i
$78$		0			0
$79$	3.73971	+	4.87368i	0.420750	+	0.548332i	0.954850	−	0.297089i	$-0.0960160\pi$
$79$	3.73971	+	4.87368i	0.420750	+	0.548332i	−0.534100	+	0.845422i	$0.679349\pi$
$80$		0			0
$81$	9.12585	−	5.26881i	1.01398	−	0.585424i
$82$		0			0
$83$	−7.00067	−	7.00067i	−0.768424	−	0.768424i	0.209405	−	0.977829i	$-0.432847\pi$
$83$	−7.00067	−	7.00067i	−0.768424	−	0.768424i	−0.977829	+	0.209405i	$0.932847\pi$
$84$		0			0
$85$	−3.54803	+	16.8892i	−0.384837	+	1.83189i
$86$		0			0
$87$	−2.63018	+	9.81598i	−0.281985	+	1.05238i
$88$		0			0
$89$	10.0102	+	5.77940i	1.06108	+	0.612616i	0.925731	−	0.378182i	$-0.123451\pi$
$89$	10.0102	+	5.77940i	1.06108	+	0.612616i	0.135350	+	0.990798i	$0.456784\pi$
$90$		0			0
$91$	−10.9768	−	11.3512i	−1.15069	−	1.18993i
$92$		0			0
$93$	−4.32613	−	16.1453i	−0.448598	−	1.67419i
$94$		0			0
$95$	0.602757	+	4.57839i	0.0618415	+	0.469733i
$96$		0			0
$97$	8.13210	−	3.36843i	0.825689	−	0.342012i	0.0704946	−	0.997512i	$-0.477542\pi$
$97$	8.13210	−	3.36843i	0.825689	−	0.342012i	0.755195	+	0.655500i	$0.227542\pi$
$98$		0			0
$99$	−0.0262214	−	0.0633040i	−0.00263535	−	0.00636229i
$100$		0			0
$101$	−8.65127	−	14.9844i	−0.860833	−	1.49101i	−0.871126	−	0.491060i	$-0.836610\pi$
$101$	−8.65127	−	14.9844i	−0.860833	−	1.49101i	0.0102928	−	0.999947i	$-0.496724\pi$
$102$		0			0
$103$	1.68506	−	2.91860i	0.166034	−	0.287579i	−0.770988	−	0.636849i	$-0.780237\pi$
$103$	1.68506	−	2.91860i	0.166034	−	0.287579i	0.937022	+	0.349271i	$0.113571\pi$
$104$		0			0
$105$	−25.5967	−	0.429196i	−2.49798	−	0.0418853i
$106$		0			0
$107$	−2.15803	+	16.3919i	−0.208625	+	1.58466i	0.491654	+	0.870791i	$0.336393\pi$
$107$	−2.15803	+	16.3919i	−0.208625	+	1.58466i	−0.700278	+	0.713870i	$0.746941\pi$
$108$		0			0
$109$	−0.857791	−	6.51557i	−0.0821614	−	0.624078i	−0.982141	−	0.188146i	$-0.939752\pi$
$109$	−0.857791	−	6.51557i	−0.0821614	−	0.624078i	0.899980	−	0.435932i	$-0.143581\pi$
$110$		0			0
$111$	14.9568	−	14.9568i	1.41964	−	1.41964i
$112$		0			0
$113$	0.206377	−	0.498238i	0.0194143	−	0.0468703i	−0.913875	−	0.405995i	$-0.866925\pi$
$113$	0.206377	−	0.498238i	0.0194143	−	0.0468703i	0.933289	+	0.359125i	$0.116925\pi$
$114$		0			0
$115$	20.1609	−	11.6399i	1.88002	−	1.08543i
$116$		0			0
$117$	13.5131	−	3.62082i	1.24928	−	0.334745i
$118$		0			0
$119$	−8.39615	+	6.96453i	−0.769674	+	0.638437i
$120$		0			0
$121$	−10.6244	+	2.84679i	−0.965851	+	0.258799i
$122$		0			0
$123$	4.50651	−	2.60184i	0.406339	−	0.234600i
$124$		0			0
$125$	12.0447	−	29.0784i	1.07731	−	2.60085i
$126$		0			0
$127$	−3.54817	+	3.54817i	−0.314849	+	0.314849i	−0.846785	−	0.531936i	$-0.821465\pi$
$127$	−3.54817	+	3.54817i	−0.314849	+	0.314849i	0.531936	+	0.846785i	$0.321465\pi$
$128$		0			0
$129$	−1.39566	−	10.6011i	−0.122881	−	0.933374i
$130$		0			0
$131$	−0.861412	+	6.54307i	−0.0752619	+	0.571671i	0.911717	+	0.410819i	$0.134757\pi$
$131$	−0.861412	+	6.54307i	−0.0752619	+	0.571671i	−0.986979	+	0.160851i	$0.948576\pi$
$132$		0			0
$133$	−1.50167	+	2.50309i	−0.130211	+	0.217045i
$134$		0			0
$135$	−3.17362	+	5.49687i	−0.273142	+	0.473095i
$136$		0			0
$137$	−1.46142	−	2.53125i	−0.124857	−	0.216259i	0.796820	−	0.604217i	$-0.206514\pi$
$137$	−1.46142	−	2.53125i	−0.124857	−	0.216259i	−0.921677	+	0.387958i	$0.873181\pi$
$138$		0			0
$139$	2.42162	+	5.84630i	0.205399	+	0.495877i	0.992688	−	0.120707i	$-0.0385161\pi$
$139$	2.42162	+	5.84630i	0.205399	+	0.495877i	−0.787289	+	0.616584i	$0.788516\pi$
$140$		0			0
$141$	−14.6039	+	6.04914i	−1.22987	+	0.509430i
$142$		0			0
$143$	0.0227720	+	0.172970i	0.00190429	+	0.0144645i
$144$		0			0
$145$	−4.76227	−	17.7730i	−0.395485	−	1.47597i
$146$		0			0
$147$	−12.5006	−	10.2758i	−1.03103	−	0.847538i
$148$		0			0
$149$	7.19477	+	4.15390i	0.589418	+	0.340301i	0.764868	−	0.644188i	$-0.222804\pi$
$149$	7.19477	+	4.15390i	0.589418	+	0.340301i	−0.175449	+	0.984489i	$0.556138\pi$
$150$		0			0
$151$	4.97694	−	18.5742i	0.405017	−	1.51154i	−0.399007	−	0.916948i	$-0.630645\pi$
$151$	4.97694	−	18.5742i	0.405017	−	1.51154i	0.804024	−	0.594597i	$-0.202688\pi$
$152$		0			0
$153$	−1.78379	−	9.49861i	−0.144211	−	0.767917i
$154$		0			0
$155$	21.4001	+	21.4001i	1.71890	+	1.71890i
$156$		0			0
$157$	−7.78946	+	4.49724i	−0.621666	+	0.358919i	−0.777517	−	0.628861i	$-0.783521\pi$
$157$	−7.78946	+	4.49724i	−0.621666	+	0.358919i	0.155851	+	0.987781i	$0.450188\pi$
$158$		0			0
$159$	5.82125	+	7.58640i	0.461655	+	0.601641i
$160$		0			0
$161$	14.5551	+	2.16505i	1.14710	+	0.170630i
$162$		0			0
$163$	17.0602	−	13.0908i	1.33626	−	1.02535i	0.339867	−	0.940473i	$-0.389618\pi$
$163$	17.0602	−	13.0908i	1.33626	−	1.02535i	0.996392	−	0.0848740i	$-0.0270488\pi$
$164$		0			0
$165$	0.224397	+	0.172186i	0.0174693	+	0.0134046i
$166$		0			0
$167$	4.75417	+	11.4776i	0.367888	+	0.888161i	0.994096	+	0.108505i	$0.0346063\pi$
$167$	4.75417	+	11.4776i	0.367888	+	0.888161i	−0.626208	+	0.779656i	$0.715394\pi$
$168$		0			0
$169$	−22.6203			−1.74002
$170$		0			0
$171$	−1.29305	−	2.23962i	−0.0988818	−	0.171268i
$172$		0			0
$173$	13.6851	+	1.80167i	1.04046	+	0.136979i	0.631342	−	0.775505i	$-0.282505\pi$
$173$	13.6851	+	1.80167i	1.04046	+	0.136979i	0.409114	+	0.912483i	$0.365838\pi$
$174$		0			0
$175$	28.9596	−	16.0786i	2.18914	−	1.21543i
$176$		0			0
$177$	1.10547	−	0.848254i	0.0830919	−	0.0637586i
$178$		0			0
$179$	−13.7939	−	3.69607i	−1.03101	−	0.276257i	−0.296624	−	0.954994i	$-0.595861\pi$
$179$	−13.7939	−	3.69607i	−1.03101	−	0.276257i	−0.734381	+	0.678737i	$0.762528\pi$
$180$		0			0
$181$	5.44253	−	13.1394i	0.404540	−	0.976647i	−0.582009	−	0.813182i	$-0.697733\pi$
$181$	5.44253	−	13.1394i	0.404540	−	0.976647i	0.986549	−	0.163464i	$-0.0522669\pi$
$182$		0			0
$183$		−	12.4233i		−	0.918357i
$184$		0			0
$185$	−9.91237	+	36.9935i	−0.728772	+	2.71981i
$186$		0			0
$187$	0.120345	−	0.00659349i	0.00880049	−	0.000482163i
$188$		0			0
$189$	−3.73192	+	1.47301i	−0.271457	+	0.107145i
$190$		0			0
$191$	−8.23321	−	4.75345i	−0.595734	−	0.343947i	0.171627	−	0.985162i	$-0.445098\pi$
$191$	−8.23321	−	4.75345i	−0.595734	−	0.343947i	−0.767362	+	0.641215i	$0.778431\pi$
$192$		0			0
$193$	14.8716	−	1.95788i	1.07048	−	0.140931i	0.425368	−	0.905021i	$-0.360145\pi$
$193$	14.8716	−	1.95788i	1.07048	−	0.140931i	0.645110	+	0.764090i	$0.276811\pi$
$194$		0			0
$195$	−40.8347	+	40.8347i	−2.92423	+	2.92423i
$196$		0			0
$197$	−16.3615	−	6.77715i	−1.16571	−	0.482852i	−0.285936	−	0.958249i	$-0.592304\pi$
$197$	−16.3615	−	6.77715i	−1.16571	−	0.482852i	−0.879771	+	0.475397i	$0.842304\pi$
$198$		0			0
$199$	−16.2836	−	12.4949i	−1.15432	−	0.885738i	−0.159477	−	0.987202i	$-0.550981\pi$
$199$	−16.2836	−	12.4949i	−1.15432	−	0.885738i	−0.994839	+	0.101464i	$0.967647\pi$
$200$		0			0
$201$	11.5042	+	1.51456i	0.811447	+	0.106829i
$202$		0			0
$203$	4.63039	−	10.6692i	0.324990	−	0.748832i
$204$		0			0
$205$	−4.71094	+	8.15959i	−0.329026	+	0.569891i
$206$		0			0
$207$	−7.93646	+	10.3430i	−0.551622	+	0.718888i
$208$		0			0
$209$	0.0297956	−	0.0123417i	0.00206100	−	0.000853696i
$210$		0			0
$211$	−1.70451	−	0.706029i	−0.117343	−	0.0486051i	0.323239	−	0.946317i	$-0.395228\pi$
$211$	−1.70451	−	0.706029i	−0.117343	−	0.0486051i	−0.440582	+	0.897712i	$0.645228\pi$
$212$		0			0
$213$	23.9161	+	6.40830i	1.63870	+	0.439089i
$214$		0			0
$215$	11.7857	+	15.3595i	0.803780	+	1.04751i
$216$		0			0
$217$	2.17865	+	19.0057i	0.147897	+	1.29019i
$218$		0			0
$219$	−10.5825	+	2.83557i	−0.715098	+	0.191610i
$220$		0			0
$221$	−1.87247	+	24.5365i	−0.125956	+	1.65050i
$222$		0			0
$223$	3.16328	+	3.16328i	0.211829	+	0.211829i	0.805044	−	0.593215i	$-0.202142\pi$
$223$	3.16328	+	3.16328i	0.211829	+	0.211829i	−0.593215	+	0.805044i	$0.702142\pi$
$224$		0			0
$225$			29.3462i			1.95641i
$226$		0			0
$227$	12.8511	−	1.69188i	0.852960	−	0.112294i	0.308647	−	0.951177i	$-0.400124\pi$
$227$	12.8511	−	1.69188i	0.852960	−	0.112294i	0.544313	+	0.838882i	$0.316790\pi$
$228$		0			0
$229$	1.97651	+	7.37643i	0.130611	+	0.487449i	0.999977	−	0.00672026i	$-0.00213914\pi$
$229$	1.97651	+	7.37643i	0.130611	+	0.487449i	−0.869366	+	0.494169i	$0.835472\pi$
$230$		0			0
$231$	0.0433718	+	0.173447i	0.00285366	+	0.0114120i
$232$		0			0
$233$	−0.130504	+	0.991274i	−0.00854958	+	0.0649405i	−0.995188	−	0.0979859i	$-0.968760\pi$
$233$	−0.130504	+	0.991274i	−0.00854958	+	0.0649405i	0.986638	+	0.162926i	$0.0520933\pi$
$234$		0			0
$235$	17.4232	−	22.7064i	1.13657	−	1.48120i
$236$		0			0
$237$	14.2012			0.922466
$238$		0			0
$239$	−14.3332			−0.927135			−0.463568	−	0.886062i	$-0.653431\pi$
$239$	−14.3332			−0.927135			−0.463568	+	0.886062i	$0.653431\pi$
$240$		0			0
$241$	−17.3467	+	22.6066i	−1.11740	+	1.45622i	−0.243634	+	0.969867i	$0.578340\pi$
$241$	−17.3467	+	22.6066i	−1.11740	+	1.45622i	−0.873763	+	0.486352i	$0.838327\pi$
$242$		0			0
$243$	2.58581	−	19.6412i	0.165880	−	1.25998i
$244$		0			0
$245$	28.9043	+	4.79609i	1.84663	+	0.306411i
$246$		0			0
$247$	1.70423	+	6.36026i	0.108437	+	0.404694i
$248$		0			0
$249$	−22.6912	+	2.98735i	−1.43800	+	0.189316i
$250$		0			0
$251$		−	7.22243i		−	0.455876i	−0.973676	−	0.227938i	$-0.926802\pi$
$251$		−	7.22243i		−	0.455876i	0.973676	−	0.227938i	$-0.0731983\pi$
$252$		0			0
$253$	−0.114963	−	0.114963i	−0.00722765	−	0.00722765i
$254$		0			0
$255$	25.9818	+	30.2749i	1.62704	+	1.89589i
$256$		0			0
$257$	8.96567	−	2.40234i	0.559263	−	0.149854i	0.0318953	−	0.999491i	$-0.489846\pi$
$257$	8.96567	−	2.40234i	0.559263	−	0.149854i	0.527368	+	0.849637i	$0.323179\pi$
$258$		0			0
$259$	−19.4503	+	14.4132i	−1.20858	+	0.895590i
$260$		0			0
$261$	6.27285	+	8.17493i	0.388279	+	0.506016i
$262$		0			0
$263$	−9.77877	−	2.62021i	−0.602985	−	0.161569i	−0.0556038	−	0.998453i	$-0.517708\pi$
$263$	−9.77877	−	2.62021i	−0.602985	−	0.161569i	−0.547381	+	0.836884i	$0.684375\pi$
$264$		0			0
$265$	−15.9960	−	6.62577i	−0.982628	−	0.407018i
$266$		0			0
$267$	24.6867	−	10.2256i	1.51080	−	0.625794i
$268$		0			0
$269$	6.61825	−	8.62508i	0.403522	−	0.525880i	−0.546752	−	0.837294i	$-0.684136\pi$
$269$	6.61825	−	8.62508i	0.403522	−	0.525880i	0.950274	+	0.311414i	$0.100803\pi$
$270$		0			0
$271$	2.28009	−	3.94923i	0.138506	−	0.239899i	−0.788426	−	0.615130i	$-0.789103\pi$
$271$	2.28009	−	3.94923i	0.138506	−	0.239899i	0.926931	+	0.375232i	$0.122437\pi$
$272$		0			0
$273$	−36.2658	+	4.15721i	−2.19490	+	0.251606i
$274$		0			0
$275$	−0.362838	−	0.0477685i	−0.0218799	−	0.00288055i
$276$		0			0
$277$	12.9774	+	9.95789i	0.779735	+	0.598312i	0.920053	−	0.391795i	$-0.128146\pi$
$277$	12.9774	+	9.95789i	0.779735	+	0.598312i	−0.140318	+	0.990107i	$0.544812\pi$
$278$		0			0
$279$	−15.6584	−	6.48590i	−0.937441	−	0.388301i
$280$		0			0
$281$	−0.560550	+	0.560550i	−0.0334396	+	0.0334396i	−0.723629	−	0.690189i	$-0.757527\pi$
$281$	−0.560550	+	0.560550i	−0.0334396	+	0.0334396i	0.690189	+	0.723629i	$0.257527\pi$
$282$		0			0
$283$	24.6522	−	3.24552i	1.46542	−	0.192926i	0.644778	−	0.764369i	$-0.276950\pi$
$283$	24.6522	−	3.24552i	1.46542	−	0.192926i	0.820642	+	0.571443i	$0.193616\pi$
$284$		0			0
$285$	9.24505	+	5.33763i	0.547629	+	0.316174i
$286$		0			0
$287$	−5.53969	+	2.18654i	−0.326997	+	0.129067i
$288$		0			0
$289$	16.8031	+	2.57965i	0.988420	+	0.151744i
$290$		0			0
$291$	5.26645	−	19.6546i	0.308725	−	1.15218i
$292$		0			0
$293$		−	7.25524i		−	0.423856i	−0.977285	−	0.211928i	$-0.932026\pi$
$293$		−	7.25524i		−	0.423856i	0.977285	−	0.211928i	$-0.0679742\pi$
$294$		0			0
$295$	−0.965486	+	2.33089i	−0.0562128	+	0.135710i
$296$		0			0
$297$	0.0428175	+	0.0114729i	0.00248452	+	0.000665725i
$298$		0			0
$299$	26.3350	−	20.2075i	1.52299	−	1.16863i
$300$		0			0
$301$	−0.205167	+	12.2359i	−0.0118256	+	0.705265i
$302$		0			0
$303$	−39.6563	−	5.22085i	−2.27820	−	0.299930i
$304$		0			0
$305$	11.2470	+	19.4803i	0.643999	+	1.11544i
$306$		0			0
$307$	23.5210			1.34242			0.671208	−	0.741269i	$-0.265776\pi$
$307$	23.5210			1.34242			0.671208	+	0.741269i	$0.265776\pi$
$308$		0			0
$309$	−2.98139	−	7.19770i	−0.169605	−	0.409463i
$310$		0			0
$311$	−6.30167	−	4.83544i	−0.357335	−	0.274193i	0.414456	−	0.910070i	$-0.363972\pi$
$311$	−6.30167	−	4.83544i	−0.357335	−	0.274193i	−0.771791	+	0.635877i	$0.780639\pi$
$312$		0			0
$313$	18.3486	−	14.0794i	1.03712	−	0.795812i	0.0578435	−	0.998326i	$-0.481578\pi$
$313$	18.3486	−	14.0794i	1.03712	−	0.795812i	0.979280	+	0.202513i	$0.0649109\pi$
$314$		0			0
$315$	−16.1453	+	20.3261i	−0.909686	+	1.14525i
$316$		0			0
$317$	−5.80177	−	7.56102i	−0.325860	−	0.424669i	0.601481	−	0.798887i	$-0.294578\pi$
$317$	−5.80177	−	7.56102i	−0.325860	−	0.424669i	−0.927341	+	0.374218i	$0.877911\pi$
$318$		0			0
$319$	−0.111286	+	0.0642510i	−0.00623082	+	0.00359737i
$320$		0			0
$321$	27.0258	+	27.0258i	1.50843	+	1.50843i
$322$		0			0
$323$	4.47076	−	0.839587i	0.248759	−	0.0467159i
$324$		0			0
$325$	19.3390	−	72.1742i	1.07274	−	4.00350i
$326$		0			0
$327$	−13.1567	−	7.59605i	−0.727570	−	0.420063i
$328$		0			0
$329$	17.5509	−	4.38874i	0.967611	−	0.241959i
$330$		0			0
$331$	−2.16815	−	8.09164i	−0.119172	−	0.444757i	0.880393	−	0.474245i	$-0.157279\pi$
$331$	−2.16815	−	8.09164i	−0.119172	−	0.444757i	−0.999565	+	0.0294882i	$0.990612\pi$
$332$		0			0
$333$	−2.79949	−	21.2642i	−0.153411	−	1.16527i
$334$		0			0
$335$	−19.4103	+	8.04001i	−1.06050	+	0.439273i
$336$		0			0
$337$	4.49062	+	10.8413i	0.244620	+	0.590564i	0.997731	−	0.0673291i	$-0.0214478\pi$
$337$	4.49062	+	10.8413i	0.244620	+	0.590564i	−0.753111	+	0.657893i	$0.771448\pi$
$338$		0			0
$339$	−0.623341	−	1.07966i	−0.0338552	−	0.0586390i
$340$		0			0
$341$	0.105680	−	0.183043i	0.00572290	−	0.00991235i
$342$		0			0
$343$	12.4208	+	13.7377i	0.670661	+	0.741764i
$344$		0			0
$345$	7.02444	−	53.3559i	0.378183	−	2.87259i
$346$		0			0
$347$	2.02374	+	15.3718i	0.108640	+	0.825202i	0.955832	+	0.293915i	$0.0949582\pi$
$347$	2.02374	+	15.3718i	0.108640	+	0.825202i	−0.847192	+	0.531287i	$0.821708\pi$
$348$		0			0
$349$	−2.98309	+	2.98309i	−0.159681	+	0.159681i	−0.782425	−	0.622744i	$-0.786018\pi$
$349$	−2.98309	+	2.98309i	−0.159681	+	0.159681i	0.622744	+	0.782425i	$0.286018\pi$
$350$		0			0
$351$	−3.46347	+	8.36155i	−0.184866	+	0.446307i
$352$		0			0
$353$	−6.04237	+	3.48857i	−0.321603	+	0.185678i	−0.652107	−	0.758127i	$-0.726115\pi$
$353$	−6.04237	+	3.48857i	−0.321603	+	0.185678i	0.330504	+	0.943805i	$0.392781\pi$
$354$		0			0
$355$	−43.3030	+	11.6030i	−2.29828	+	0.615823i
$356$		0			0
$357$	0.957226	+	25.1997i	0.0506618	+	1.33371i
$358$		0			0
$359$	−20.0313	+	5.36737i	−1.05721	+	0.283279i	−0.745229	−	0.666809i	$-0.767660\pi$
$359$	−20.0313	+	5.36737i	−1.05721	+	0.283279i	−0.311983	+	0.950088i	$0.600993\pi$
$360$		0			0
$361$	−15.4003	+	8.89140i	−0.810545	+	0.467968i
$362$		0			0
$363$	−9.73045	+	23.4914i	−0.510716	+	1.23298i
$364$		0			0
$365$	14.0267	−	14.0267i	0.734193	−	0.734193i
$366$		0			0
$367$	−0.501572	−	3.80982i	−0.0261819	−	0.198871i	0.973355	−	0.229304i	$-0.0736448\pi$
$367$	−0.501572	−	3.80982i	−0.0261819	−	0.198871i	−0.999537	+	0.0304326i	$0.990312\pi$
$368$		0			0
$369$	0.688709	−	5.23126i	0.0358527	−	0.272329i
$370$		0			0
$371$	−5.31243	−	9.56836i	−0.275808	−	0.496765i
$372$		0			0
$373$	4.56404	−	7.90515i	0.236317	−	0.409313i	−0.723338	−	0.690495i	$-0.757393\pi$
$373$	4.56404	−	7.90515i	0.236317	−	0.409313i	0.959655	+	0.281181i	$0.0907263\pi$
$374$		0			0
$375$	−36.3797	−	63.0115i	−1.87864	−	3.25390i
$376$		0			0
$377$	−10.0402	−	24.2393i	−0.517098	−	1.24839i
$378$		0			0
$379$	−8.88383	+	3.67980i	−0.456332	+	0.189019i	−0.598995	−	0.800752i	$-0.704433\pi$
$379$	−8.88383	+	3.67980i	−0.456332	+	0.189019i	0.142664	+	0.989771i	$0.454433\pi$
$380$		0			0
$381$	1.51409	+	11.5006i	0.0775691	+	0.589196i
$382$		0			0
$383$	3.73780	+	13.9497i	0.190993	+	0.712795i	0.993268	+	0.115840i	$0.0369560\pi$
$383$	3.73780	+	13.9497i	0.190993	+	0.712795i	−0.802275	+	0.596954i	$0.796377\pi$
$384$		0			0
$385$	−0.225032	−	0.232708i	−0.0114687	−	0.0118599i
$386$		0			0
$387$	−9.38945	−	5.42100i	−0.477292	−	0.275565i
$388$		0			0
$389$	3.76610	−	14.0553i	0.190949	−	0.712630i	−0.802330	−	0.596881i	$-0.796406\pi$
$389$	3.76610	−	14.0553i	0.190949	−	0.712630i	0.993278	−	0.115749i	$-0.0369269\pi$
$390$		0			0
$391$	−12.5353	−	19.2027i	−0.633937	−	0.971123i
$392$		0			0
$393$	10.7878	+	10.7878i	0.544172	+	0.544172i
$394$		0			0
$395$	−22.2681	+	12.8565i	−1.12043	+	0.646880i
$396$		0			0
$397$	4.74600	+	6.18510i	0.238195	+	0.310421i	0.897120	−	0.441787i	$-0.145655\pi$
$397$	4.74600	+	6.18510i	0.238195	+	0.310421i	−0.658925	+	0.752208i	$0.728989\pi$
$398$		0			0
$399$	2.47741	+	6.27662i	0.124026	+	0.314224i
$400$		0			0
$401$	−16.0911	+	12.3471i	−0.803550	+	0.616586i	−0.926700	−	0.375802i	$-0.877367\pi$
$401$	−16.0911	+	12.3471i	−0.803550	+	0.616586i	0.123149	+	0.992388i	$0.460701\pi$
$402$		0			0
$403$	34.2361	+	26.2703i	1.70542	+	1.30862i
$404$		0			0
$405$	16.8789	+	40.7493i	0.838719	+	2.02485i
$406$		0			0
$407$	0.267469			0.0132580
$408$		0			0
$409$	11.8138	+	20.4621i	0.584156	+	1.01179i	0.994980	+	0.100073i	$0.0319077\pi$
$409$	11.8138	+	20.4621i	0.584156	+	1.01179i	−0.410824	+	0.911715i	$0.634759\pi$
$410$		0			0
$411$	−6.69896	−	0.881935i	−0.330435	−	0.0435026i
$412$		0			0
$413$	−1.39427	+	0.774110i	−0.0686076	+	0.0380915i
$414$		0			0
$415$	32.8763	−	25.2269i	1.61383	−	1.23834i
$416$		0			0
$417$	14.1301	+	3.78614i	0.691952	+	0.185408i
$418$		0			0
$419$	13.2509	−	31.9904i	0.647348	−	1.56284i	−0.169216	−	0.985579i	$-0.554123\pi$
$419$	13.2509	−	31.9904i	0.647348	−	1.56284i	0.816563	−	0.577256i	$-0.195877\pi$
$420$		0			0
$421$		−	40.9342i		−	1.99501i	−0.0705790	−	0.997506i	$-0.522485\pi$
$421$		−	40.9342i		−	1.99501i	0.0705790	−	0.997506i	$-0.477515\pi$
$422$		0			0
$423$	−4.14838	+	15.4820i	−0.201701	+	0.752758i
$424$		0			0
$425$	−48.6995	−	17.1154i	−2.36227	−	0.830219i
$426$		0			0
$427$	−2.09196	+	14.0637i	−0.101237	+	0.680591i
$428$		0			0
$429$	0.349275	+	0.201654i	0.0168632	+	0.00973595i
$430$		0			0
$431$	−11.0431	+	1.45385i	−0.531927	+	0.0700295i	−0.391706	−	0.920091i	$-0.628115\pi$
$431$	−11.0431	+	1.45385i	−0.531927	+	0.0700295i	−0.140222	+	0.990120i	$0.544782\pi$
$432$		0			0
$433$	−18.6407	+	18.6407i	−0.895815	+	0.895815i	−0.995063	−	0.0992473i	$-0.968356\pi$
$433$	−18.6407	+	18.6407i	−0.895815	+	0.895815i	0.0992473	+	0.995063i	$0.468356\pi$
$434$		0			0
$435$	−39.2977	−	16.2776i	−1.88418	−	0.780453i
$436$		0			0
$437$	−4.86819	−	3.73549i	−0.232877	−	0.178693i
$438$		0			0
$439$	15.0369	+	1.97965i	0.717673	+	0.0944835i	0.480514	−	0.876987i	$-0.340450\pi$
$439$	15.0369	+	1.97965i	0.717673	+	0.0944835i	0.237159	+	0.971471i	$0.423784\pi$
$440$		0			0
$441$	−15.9825	+	3.71300i	−0.761073	+	0.176810i
$442$		0			0
$443$	−12.0804	+	20.9239i	−0.573959	+	0.994127i	0.422195	+	0.906505i	$0.361260\pi$
$443$	−12.0804	+	20.9239i	−0.573959	+	0.994127i	−0.996154	+	0.0876214i	$0.972073\pi$
$444$		0			0
$445$	−29.4525	+	38.3832i	−1.39618	+	1.81954i
$446$		0			0
$447$	17.7434	−	7.34954i	0.839232	−	0.347621i
$448$		0			0
$449$	−24.7275	−	10.2425i	−1.16696	−	0.483372i	−0.286775	−	0.957998i	$-0.592583\pi$
$449$	−24.7275	−	10.2425i	−1.16696	−	0.483372i	−0.880187	+	0.474627i	$0.842583\pi$
$450$		0			0
$451$	0.0635586	+	0.0170305i	0.00299286	+	0.000801933i
$452$		0			0
$453$	−27.0612	−	35.2668i	−1.27145	−	1.65698i
$454$		0			0
$455$	53.1027	−	39.3505i	2.48950	−	1.84478i
$456$		0			0
$457$	13.1702	−	3.52896i	0.616078	−	0.165078i	0.0627338	−	0.998030i	$-0.480018\pi$
$457$	13.1702	−	3.52896i	0.616078	−	0.165078i	0.553344	+	0.832953i	$0.313351\pi$
$458$		0			0
$459$	5.57766	+	2.82530i	0.260343	+	0.131874i
$460$		0			0
$461$	18.6284	+	18.6284i	0.867611	+	0.867611i	0.992207	−	0.124597i	$-0.0397637\pi$
$461$	18.6284	+	18.6284i	0.867611	+	0.867611i	−0.124597	+	0.992207i	$0.539764\pi$
$462$		0			0
$463$		−	26.1217i		−	1.21398i	−0.794710	−	0.606990i	$-0.792377\pi$
$463$		−	26.1217i		−	1.21398i	0.794710	−	0.606990i	$-0.207623\pi$
$464$		0			0
$465$	69.3639	−	9.13193i	3.21667	−	0.423483i
$466$		0			0
$467$	1.47944	+	5.52136i	0.0684605	+	0.255498i	0.991671	−	0.128796i	$-0.0411114\pi$
$467$	1.47944	+	5.52136i	0.0684605	+	0.255498i	−0.923211	+	0.384295i	$0.874445\pi$
$468$		0			0
$469$	−12.7683	−	3.65174i	−0.589583	−	0.168622i
$470$		0			0
$471$	−2.71399	+	20.6148i	−0.125054	+	0.949880i
$472$		0			0
$473$	0.0823093	−	0.107268i	0.00378459	−	0.00493217i
$474$		0			0
$475$	−13.8125			−0.633761
$476$		0			0
$477$	9.69609			0.443953
$478$		0			0
$479$	20.7579	−	27.0522i	0.948452	−	1.23605i	−0.0232242	−	0.999730i	$-0.507393\pi$
$479$	20.7579	−	27.0522i	0.948452	−	1.23605i	0.971676	−	0.236316i	$-0.0759402\pi$
$480$		0			0
$481$	−7.12797	+	54.1423i	−0.325007	+	2.46868i
$482$		0			0
$483$	24.4538	−	23.6473i	1.11269	−	1.07599i
$484$		0			0
$485$	9.53554	+	35.5871i	0.432987	+	1.61593i
$486$		0			0
$487$	−16.9094	+	2.22616i	−0.766236	+	0.100877i	−0.503505	−	0.863992i	$-0.667957\pi$
$487$	−16.9094	+	2.22616i	−0.766236	+	0.100877i	−0.262731	+	0.964869i	$0.584623\pi$
$488$		0			0
$489$		−	49.7109i		−	2.24801i
$490$		0			0
$491$	−19.6524	−	19.6524i	−0.886900	−	0.886900i	0.107324	−	0.994224i	$-0.465772\pi$
$491$	−19.6524	−	19.6524i	−0.886900	−	0.886900i	−0.994224	+	0.107324i	$0.965772\pi$
$492$		0			0
$493$	−17.2246	+	5.64186i	−0.775759	+	0.254097i
$494$		0			0
$495$	0.277027	−	0.0742291i	0.0124514	−	0.00333635i
$496$		0			0
$497$	−25.9949	−	11.2817i	−1.16603	−	0.506053i
$498$		0			0
$499$	1.53807	+	2.00445i	0.0688534	+	0.0897315i	0.826510	−	0.562921i	$-0.190323\pi$
$499$	1.53807	+	2.00445i	0.0688534	+	0.0897315i	−0.757657	+	0.652653i	$0.773656\pi$
$500$		0			0
$501$	27.7404	+	7.43301i	1.23935	+	0.332083i
$502$		0			0
$503$	−33.9236	−	14.0516i	−1.51258	−	0.626531i	−0.536491	−	0.843906i	$-0.680251\pi$
$503$	−33.9236	−	14.0516i	−1.51258	−	0.626531i	−0.976088	+	0.217375i	$0.930251\pi$
$504$		0			0
$505$	66.9093	−	27.7148i	2.97743	−	1.23329i
$506$		0			0
$507$	−31.8331	+	41.4857i	−1.41376	+	1.84244i
$508$		0			0
$509$	−13.7845	+	23.8755i	−0.610989	+	1.05826i	0.380085	+	0.924951i	$0.375895\pi$
$509$	−13.7845	+	23.8755i	−0.610989	+	1.05826i	−0.991074	+	0.133312i	$0.957439\pi$
$510$		0			0
$511$	12.4573	−	1.42800i	0.551078	−	0.0631711i
$512$		0			0
$513$	1.65872	+	0.218375i	0.0732345	+	0.00964150i
$514$		0			0
$515$	11.1911	+	8.58724i	0.493139	+	0.378399i
$516$		0			0
$517$	−0.184667	−	0.0764916i	−0.00812165	−	0.00336410i
$518$		0			0
$519$	22.5630	−	22.5630i	0.990406	−	0.990406i
$520$		0			0
$521$	−39.5267	+	5.20379i	−1.73170	+	0.227982i	−0.929434	−	0.368988i	$-0.879704\pi$
$521$	−39.5267	+	5.20379i	−1.73170	+	0.227982i	−0.802263	+	0.596970i	$0.796371\pi$
$522$		0			0
$523$	−30.3914	−	17.5465i	−1.32892	−	0.767254i	−0.343790	−	0.939047i	$-0.611711\pi$
$523$	−30.3914	−	17.5465i	−1.32892	−	0.767254i	−0.985133	+	0.171793i	$0.945044\pi$
$524$		0			0
$525$	11.2661	−	75.7391i	0.491692	−	3.30553i
$526$		0			0
$527$	19.8956	−	22.2020i	0.866665	−	0.967136i
$528$		0			0
$529$	−2.05347	+	7.66365i	−0.0892812	+	0.333202i
$530$		0			0
$531$		−	1.41288i		−	0.0613139i
$532$		0			0
$533$	−5.14120	+	12.4119i	−0.222690	+	0.537621i
$534$		0			0
$535$	−66.8444	−	17.9109i	−2.88994	−	0.774356i
$536$		0			0
$537$	−26.1905	+	20.0967i	−1.13021	+	0.867237i
$538$		0			0
$539$	−0.0198921	−	0.203653i	−0.000856812	−	0.00877195i
$540$		0			0
$541$	−2.29211	−	0.301762i	−0.0985454	−	0.0129737i	0.0810922	−	0.996707i	$-0.474159\pi$
$541$	−2.29211	−	0.301762i	−0.0985454	−	0.0129737i	−0.179638	+	0.983733i	$0.557493\pi$
$542$		0			0
$543$	−16.4386	−	28.4725i	−0.705449	−	1.22187i
$544$		0			0
$545$	27.5071			1.17828
$546$		0			0
$547$	11.7431	+	28.3504i	0.502099	+	1.21217i	0.948339	+	0.317260i	$0.102763\pi$
$547$	11.7431	+	28.3504i	0.502099	+	1.21217i	−0.446240	+	0.894913i	$0.647237\pi$
$548$		0			0
$549$	−9.99382	−	7.66853i	−0.426526	−	0.327285i
$550$		0			0
$551$	−3.84773	+	2.95247i	−0.163919	+	0.125779i
$552$		0			0
$553$	−16.0763	−	2.39133i	−0.683636	−	0.101690i
$554$		0			0
$555$	53.8968	+	70.2396i	2.28779	+	2.98151i
$556$		0			0
$557$	−0.685734	+	0.395908i	−0.0290555	+	0.0167752i	−0.514457	−	0.857516i	$-0.672007\pi$
$557$	−0.685734	+	0.395908i	−0.0290555	+	0.0167752i	0.485402	+	0.874291i	$0.338673\pi$
$558$		0			0
$559$	19.5201	+	19.5201i	0.825611	+	0.825611i
$560$		0			0
$561$	0.157267	−	0.229992i	0.00663981	−	0.00971028i
$562$		0			0
$563$	−4.20606	+	15.6972i	−0.177264	+	0.661559i	0.818891	+	0.573950i	$0.194589\pi$
$563$	−4.20606	+	15.6972i	−0.177264	+	0.661559i	−0.996155	+	0.0876096i	$0.972077\pi$
$564$		0			0
$565$	1.95485	+	1.12863i	0.0822412	+	0.0474820i
$566$		0			0
$567$	−7.66633	+	26.8052i	−0.321956	+	1.12571i
$568$		0			0
$569$	−4.31145	−	16.0906i	−0.180746	−	0.674551i	−0.995501	−	0.0947473i	$-0.969796\pi$
$569$	−4.31145	−	16.0906i	−0.180746	−	0.674551i	0.814756	−	0.579804i	$-0.196871\pi$
$570$		0			0
$571$	−0.707968	−	5.37755i	−0.0296275	−	0.225044i	0.970225	−	0.242205i	$-0.0778705\pi$
$571$	−0.707968	−	5.37755i	−0.0296275	−	0.225044i	−0.999853	+	0.0171611i	$0.994537\pi$
$572$		0			0
$573$	−20.3043	+	8.41032i	−0.848225	+	0.351346i
$574$		0			0
$575$	26.6469	+	64.3314i	1.11125	+	2.68280i
$576$		0			0
$577$	−7.22109	−	12.5073i	−0.300618	−	0.520686i	0.675658	−	0.737215i	$-0.263860\pi$
$577$	−7.22109	−	12.5073i	−0.300618	−	0.520686i	−0.976276	+	0.216529i	$0.930526\pi$
$578$		0			0
$579$	17.3377	−	30.0298i	0.720531	−	1.24800i
$580$		0			0
$581$	26.1904	+	0.439152i	1.08656	+	0.0182191i
$582$		0			0
$583$	−0.0157829	+	0.119883i	−0.000653661	+	0.00496505i
$584$		0			0
$585$	7.64310	+	58.0551i	0.316003	+	2.40028i
$586$		0			0
$587$	−15.6313	+	15.6313i	−0.645173	+	0.645173i	−0.951822	−	0.306650i	$-0.900792\pi$
$587$	−15.6313	+	15.6313i	−0.645173	+	0.645173i	0.306650	+	0.951822i	$0.400792\pi$
$588$		0			0
$589$	3.05275	−	7.36999i	0.125786	−	0.303675i
$590$		0			0
$591$	−35.4546	+	20.4697i	−1.45841	+	0.842011i
$592$		0			0
$593$	3.42659	−	0.918151i	0.140713	−	0.0377040i	−0.187775	−	0.982212i	$-0.560128\pi$
$593$	3.42659	−	0.918151i	0.140713	−	0.0377040i	0.328488	+	0.944508i	$0.393461\pi$
$594$		0			0
$595$	−24.3145	−	38.6476i	−0.996797	−	1.58440i
$596$		0			0
$597$	−45.8313	+	12.2805i	−1.87575	+	0.502606i
$598$		0			0
$599$	5.94366	−	3.43157i	0.242851	−	0.140210i	−0.373635	−	0.927576i	$-0.621889\pi$
$599$	5.94366	−	3.43157i	0.242851	−	0.140210i	0.616487	+	0.787365i	$0.288555\pi$
$600$		0			0
$601$	−2.27474	+	5.49170i	−0.0927884	+	0.224011i	−0.963459	−	0.267855i	$-0.913685\pi$
$601$	−2.27474	+	5.49170i	−0.0927884	+	0.224011i	0.870671	+	0.491866i	$0.163685\pi$
$602$		0			0
$603$	8.31960	−	8.31960i	0.338800	−	0.338800i
$604$		0			0
$605$	−6.00922	−	45.6446i	−0.244310	−	1.85572i
$606$		0			0
$607$	−1.47588	+	11.2104i	−0.0599040	+	0.455016i	0.935037	+	0.354551i	$0.115366\pi$
$607$	−1.47588	+	11.2104i	−0.0599040	+	0.455016i	−0.994941	+	0.100465i	$0.967967\pi$
$608$		0			0
$609$	−13.0511	−	23.5067i	−0.528858	−	0.952542i
$610$		0			0
$611$	20.4051	−	35.3427i	0.825502	−	1.42981i
$612$		0			0
$613$	16.3357	+	28.2943i	0.659793	+	1.14280i	0.980669	+	0.195674i	$0.0626895\pi$
$613$	16.3357	+	28.2943i	0.659793	+	1.14280i	−0.320876	+	0.947121i	$0.603977\pi$
$614$		0			0
$615$	8.33511	+	20.1227i	0.336104	+	0.811427i
$616$		0			0
$617$	−11.1357	+	4.61254i	−0.448305	+	0.185694i	−0.595402	−	0.803428i	$-0.703007\pi$
$617$	−11.1357	+	4.61254i	−0.448305	+	0.185694i	0.147097	+	0.989122i	$0.453007\pi$
$618$		0			0
$619$	−2.35451	−	17.8843i	−0.0946358	−	0.718830i	−0.971322	−	0.237768i	$-0.923584\pi$
$619$	−2.35451	−	17.8843i	−0.0946358	−	0.718830i	0.876686	−	0.481063i	$-0.159749\pi$
$620$		0			0
$621$	−2.18292	−	8.14676i	−0.0875974	−	0.326918i
$622$		0			0
$623$	−29.6682	+	7.41878i	−1.18863	+	0.297227i
$624$		0			0
$625$	59.8786	+	34.5709i	2.39514	+	1.38284i
$626$		0			0
$627$	0.0192960	−	0.0720136i	0.000770608	−	0.00287595i
$628$		0			0
$629$	36.9204	+	7.75612i	1.47211	+	0.309257i
$630$		0			0
$631$	−19.5369	−	19.5369i	−0.777751	−	0.777751i	0.201697	−	0.979448i	$-0.435354\pi$
$631$	−19.5369	−	19.5369i	−0.777751	−	0.777751i	−0.979448	+	0.201697i	$0.935354\pi$
$632$		0			0
$633$	−3.69358	+	2.13249i	−0.146807	+	0.0847589i
$634$		0			0
$635$	−12.7858	−	16.6628i	−0.507390	−	0.661243i
$636$		0			0
$637$	41.7544	+	1.40064i	1.65437	+	0.0554954i
$638$		0			0
$639$	19.9178	−	15.2834i	0.787935	−	0.604604i
$640$		0			0
$641$	−27.4906	−	21.0943i	−1.08581	−	0.833175i	−0.0990091	−	0.995087i	$-0.531567\pi$
$641$	−27.4906	−	21.0943i	−1.08581	−	0.833175i	−0.986805	+	0.161912i	$0.948234\pi$
$642$		0			0
$643$	−17.1062	−	41.2981i	−0.674604	−	1.62864i	−0.773693	−	0.633560i	$-0.781593\pi$
$643$	−17.1062	−	41.2981i	−0.674604	−	1.62864i	0.0990892	−	0.995079i	$-0.468407\pi$
$644$		0			0
$645$	44.7552			1.76223
$646$		0			0
$647$	−1.97617	−	3.42283i	−0.0776914	−	0.134565i	0.824562	−	0.565771i	$-0.191422\pi$
$647$	−1.97617	−	3.42283i	−0.0776914	−	0.134565i	−0.902254	+	0.431206i	$0.858088\pi$
$648$		0			0
$649$	0.0174690	+	0.00229983i	0.000685717	+	9.02763e-5i
$650$		0			0
$651$	37.9225	+	22.7507i	1.48630	+	0.891669i
$652$		0			0
$653$	−12.4185	+	9.52907i	−0.485974	+	0.372901i	−0.822493	−	0.568776i	$-0.807417\pi$
$653$	−12.4185	+	9.52907i	−0.485974	+	0.372901i	0.336518	+	0.941677i	$0.390751\pi$
$654$		0			0
$655$	−26.6820	−	7.14943i	−1.04255	−	0.279351i
$656$		0			0
$657$	−4.25120	+	10.2633i	−0.165855	+	0.400409i
$658$		0			0
$659$		−	5.55503i		−	0.216393i	−0.994130	−	0.108197i	$-0.965492\pi$
$659$		−	5.55503i		−	0.216393i	0.994130	−	0.108197i	$-0.0345076\pi$
$660$		0			0
$661$	5.03688	−	18.7979i	0.195912	−	0.731153i	−0.796117	−	0.605143i	$-0.793116\pi$
$661$	5.03688	−	18.7979i	0.195912	−	0.731153i	0.992029	−	0.126010i	$-0.0402173\pi$
$662$		0			0
$663$	42.3649	+	37.9639i	1.64532	+	1.47439i
$664$		0			0
$665$	−9.56698	−	7.59919i	−0.370992	−	0.294684i
$666$		0			0
$667$	21.1741	+	12.2249i	0.819863	+	0.473348i
$668$		0			0
$669$	10.2531	−	1.34985i	0.396408	−	0.0521881i
$670$		0			0
$671$	0.111082	−	0.111082i	0.00428826	−	0.00428826i
$672$		0			0
$673$	−2.19870	−	0.910733i	−0.0847538	−	0.0351062i	0.339904	−	0.940460i	$-0.389606\pi$
$673$	−2.19870	−	0.910733i	−0.0847538	−	0.0351062i	−0.424658	+	0.905354i	$0.639606\pi$
$674$		0			0
$675$	−15.0619	−	11.5574i	−0.579732	−	0.444844i
$676$		0			0
$677$	42.0493	+	5.53590i	1.61609	+	0.212762i	0.883675	−	0.468101i	$-0.155062\pi$
$677$	42.0493	+	5.53590i	1.61609	+	0.212762i	0.732411	+	0.680863i	$0.238395\pi$
$678$		0			0
$679$	−9.27148	+	21.3631i	−0.355807	+	0.819839i
$680$		0			0
$681$	14.9823	−	25.9500i	0.574121	−	0.994407i
$682$		0			0
$683$	13.3575	−	17.4079i	0.511112	−	0.666095i	−0.464506	−	0.885570i	$-0.653768\pi$
$683$	13.3575	−	17.4079i	0.511112	−	0.666095i	0.975618	+	0.219476i	$0.0704346\pi$
$684$		0			0
$685$	11.3027	−	4.68173i	0.431854	−	0.178880i
$686$		0			0
$687$	16.3099	+	6.75580i	0.622263	+	0.257750i
$688$		0			0
$689$	−23.8466	−	6.38969i	−0.908484	−	0.243428i
$690$		0			0
$691$	16.4880	+	21.4876i	0.627232	+	0.817425i	0.993589	−	0.113049i	$-0.0360618\pi$
$691$	16.4880	+	21.4876i	0.627232	+	0.817425i	−0.366357	+	0.930474i	$0.619395\pi$
$692$		0			0
$693$	0.166300	+	0.0721735i	0.00631722	+	0.00274164i
$694$		0			0
$695$	−25.5842	+	6.85526i	−0.970463	+	0.260035i
$696$		0			0
$697$	8.27952	+	4.19390i	0.313609	+	0.158855i
$698$		0			0
$699$	1.63435	+	1.63435i	0.0618167	+	0.0618167i
$700$		0			0
$701$			44.7518i			1.69025i	0.534566	+	0.845127i	$0.320475\pi$
$701$			44.7518i			1.69025i	−0.534566	+	0.845127i	$0.679525\pi$
$702$		0			0
$703$	10.0085	−	1.31765i	0.377479	−	0.0496961i
$704$		0			0
$705$	−17.1243	−	63.9087i	−0.644938	−	2.40694i
$706$		0			0
$707$	44.0135	+	12.5879i	1.65530	+	0.473418i
$708$		0			0
$709$	0.370727	−	2.81595i	0.0139229	−	0.105755i	−0.983072	−	0.183218i	$-0.941349\pi$
$709$	0.370727	−	2.81595i	0.0139229	−	0.105755i	0.996995	+	0.0774628i	$0.0246819\pi$
$710$		0			0
$711$	8.76596	−	11.4240i	0.328749	−	0.428434i
$712$		0			0
$713$	−40.2149			−1.50606
$714$		0			0
$715$	−0.730238			−0.0273094
$716$		0			0
$717$	−20.1708	+	26.2871i	−0.753292	+	0.981710i
$718$		0			0
$719$	−1.99338	+	15.1412i	−0.0743405	+	0.564672i	0.913224	+	0.407458i	$0.133585\pi$
$719$	−1.99338	+	15.1412i	−0.0743405	+	0.564672i	−0.987565	+	0.157214i	$0.949749\pi$
$720$		0			0
$721$	2.16304	+	8.65014i	0.0805557	+	0.322148i
$722$		0			0
$723$	17.0490	+	63.6278i	0.634059	+	2.36634i
$724$		0			0
$725$	54.5649	−	7.18361i	2.02649	−	0.266793i
$726$		0			0
$727$		−	10.9486i		−	0.406061i	−0.979172	−	0.203030i	$-0.934921\pi$
$727$		−	10.9486i		−	0.406061i	0.979172	−	0.203030i	$-0.0650790\pi$
$728$		0			0
$729$	−10.0294	−	10.0294i	−0.371460	−	0.371460i
$730$		0			0
$731$	14.4722	−	12.4200i	0.535274	−	0.459369i
$732$		0			0
$733$	−16.4886	+	4.41811i	−0.609020	+	0.163187i	−0.550132	−	0.835078i	$-0.685422\pi$
$733$	−16.4886	+	4.41811i	−0.609020	+	0.163187i	−0.0588889	+	0.998265i	$0.518756\pi$
$734$		0			0
$735$	49.4725	−	46.2612i	1.82482	−	1.70637i
$736$		0			0
$737$	0.0893216	+	0.116406i	0.00329021	+	0.00428788i
$738$		0			0
$739$	−23.6733	−	6.34324i	−0.870837	−	0.233340i	−0.204387	−	0.978890i	$-0.565520\pi$
$739$	−23.6733	−	6.34324i	−0.870837	−	0.233340i	−0.666449	+	0.745550i	$0.732187\pi$
$740$		0			0
$741$	14.0631	+	5.82512i	0.516620	+	0.213991i
$742$		0			0
$743$	6.46514	−	2.67795i	0.237183	−	0.0982444i	−0.260926	−	0.965359i	$-0.584028\pi$
$743$	6.46514	−	2.67795i	0.237183	−	0.0982444i	0.498109	+	0.867114i	$0.334028\pi$
$744$		0			0
$745$	−21.1687	+	27.5876i	−0.775563	+	1.01073i
$746$		0			0
$747$	−11.6034	+	20.0977i	−0.424547	+	0.735338i
$748$		0			0
$749$	−26.0435	−	35.1452i	−0.951609	−	1.28418i
$750$		0			0
$751$	−20.1807	−	2.65684i	−0.736404	−	0.0969494i	−0.247011	−	0.969013i	$-0.579448\pi$
$751$	−20.1807	−	2.65684i	−0.736404	−	0.0969494i	−0.489393	+	0.872063i	$0.662782\pi$
$752$		0			0
$753$	−13.2460	−	10.1640i	−0.482710	−	0.370397i
$754$		0			0
$755$	74.3606	+	30.8012i	2.70626	+	1.12097i
$756$		0			0
$757$	−26.8006	+	26.8006i	−0.974084	+	0.974084i	−0.999673	−	0.0255887i	$-0.991854\pi$
$757$	−26.8006	+	26.8006i	−0.974084	+	0.974084i	0.0255887	+	0.999673i	$0.491854\pi$
$758$		0			0
$759$	−0.372627	+	0.0490573i	−0.0135255	+	0.00178067i
$760$		0			0
$761$	−11.7246	−	6.76923i	−0.425018	−	0.245384i	0.272204	−	0.962240i	$-0.412247\pi$
$761$	−11.7246	−	6.76923i	−0.425018	−	0.245384i	−0.697222	+	0.716855i	$0.745581\pi$
$762$		0			0
$763$	13.6149	+	10.8145i	0.492892	+	0.391511i
$764$		0			0
$765$	40.3922	−	2.21302i	1.46038	−	0.0800117i
$766$		0			0
$767$	−0.931085	+	3.47486i	−0.0336195	+	0.125470i
$768$		0			0
$769$			12.0204i			0.433465i	0.976231	+	0.216733i	$0.0695400\pi$
$769$			12.0204i			0.433465i	−0.976231	+	0.216733i	$0.930460\pi$
$770$		0			0
$771$	8.21132	−	19.8239i	0.295723	−	0.713939i
$772$		0			0
$773$	−49.3057	−	13.2114i	−1.77340	−	0.475182i	−0.784048	−	0.620700i	$-0.786848\pi$
$773$	−49.3057	−	13.2114i	−1.77340	−	0.475182i	−0.989356	+	0.145518i	$0.953515\pi$
$774$		0			0
$775$	−71.8166	+	55.1068i	−2.57973	+	1.97950i
$776$		0			0
$777$	−0.938240	+	55.9554i	−0.0336592	+	2.00739i
$778$		0			0
$779$	2.46222	+	0.324158i	0.0882183	+	0.0116142i
$780$		0			0
$781$	0.156544	+	0.271142i	0.00560159	+	0.00970223i
$782$		0			0
$783$	−6.66621			−0.238231
$784$		0			0
$785$	−14.4071	−	34.7819i	−0.514213	−	1.24142i
$786$		0			0
$787$	34.2897	+	26.3114i	1.22230	+	0.937902i	0.999318	−	0.0369215i	$-0.0117551\pi$
$787$	34.2897	+	26.3114i	1.22230	+	0.937902i	0.222979	+	0.974823i	$0.428422\pi$
$788$		0			0
$789$	−18.5670	+	14.2469i	−0.661002	+	0.507204i
$790$		0			0
$791$	0.523845	+	1.32718i	0.0186258	+	0.0471892i
$792$		0			0
$793$	19.5253	+	25.4459i	0.693365	+	0.903611i
$794$		0			0
$795$	−34.6626	+	20.0125i	−1.22936	+	0.709769i
$796$		0			0
$797$	33.2115	+	33.2115i	1.17641	+	1.17641i	0.980652	+	0.195761i	$0.0627178\pi$
$797$	33.2115	+	33.2115i	1.17641	+	1.17641i	0.195761	+	0.980652i	$0.437282\pi$
$798$		0			0
$799$	−23.2726	−	15.9136i	−0.823326	−	0.562983i
$800$		0			0
$801$	7.01247	−	26.1709i	0.247773	−	0.924703i
$802$		0			0
$803$	−0.119976	−	0.0692682i	−0.00423386	−	0.00244442i
$804$		0			0
$805$	−16.9365	+	59.2183i	−0.596935	+	2.08717i
$806$		0			0
$807$	−6.50469	−	24.2758i	−0.228976	−	0.854550i
$808$		0			0
$809$	0.860747	+	6.53802i	0.0302623	+	0.229865i	0.999892	−	0.0147138i	$-0.00468373\pi$
$809$	0.860747	+	6.53802i	0.0302623	+	0.229865i	−0.969629	+	0.244579i	$0.921350\pi$
$810$		0			0
$811$	−20.7639	+	8.60071i	−0.729121	+	0.302012i	−0.716191	−	0.697905i	$-0.754116\pi$
$811$	−20.7639	+	8.60071i	−0.729121	+	0.302012i	−0.0129300	+	0.999916i	$0.504116\pi$
$812$		0			0
$813$	−4.03418	−	9.73938i	−0.141485	−	0.341575i
$814$		0			0
$815$	45.0038	+	77.9489i	1.57642	+	2.73043i
$816$		0			0
$817$	2.55153	−	4.41938i	0.0892666	−	0.154614i
$818$		0			0
$819$	−19.0415	+	31.7398i	−0.665364	+	1.10908i
$820$		0			0
$821$	−1.01138	+	7.68223i	−0.0352976	+	0.268112i	0.964691	+	0.263383i	$0.0848384\pi$
$821$	−1.01138	+	7.68223i	−0.0352976	+	0.268112i	−0.999989	+	0.00472834i	$0.998495\pi$
$822$		0			0
$823$	4.92941	+	37.4426i	0.171828	+	1.30517i	0.832304	+	0.554319i	$0.187021\pi$
$823$	4.92941	+	37.4426i	0.171828	+	1.30517i	−0.660476	+	0.750847i	$0.729646\pi$
$824$		0			0
$825$	−0.598223	+	0.598223i	−0.0208274	+	0.0208274i
$826$		0			0
$827$	5.52797	−	13.3457i	0.192226	−	0.464076i	−0.798153	−	0.602455i	$-0.794189\pi$
$827$	5.52797	−	13.3457i	0.192226	−	0.464076i	0.990379	+	0.138379i	$0.0441893\pi$
$828$		0			0
$829$	−40.9401	+	23.6368i	−1.42191	+	0.820939i	−0.996462	−	0.0840445i	$-0.973216\pi$
$829$	−40.9401	+	23.6368i	−1.42191	+	0.820939i	−0.425446	+	0.904984i	$0.639883\pi$
$830$		0			0
$831$	36.5257	−	9.78702i	1.26706	−	0.339508i
$832$		0			0
$833$	3.15974	−	28.6883i	0.109478	−	0.993989i
$834$		0			0
$835$	−50.2273	+	13.4584i	−1.73819	+	0.465746i
$836$		0			0
$837$	9.49560	−	5.48229i	0.328216	−	0.189496i
$838$		0			0
$839$	−8.08477	+	19.5184i	−0.279117	+	0.673849i	−0.999812	−	0.0194040i	$-0.993823\pi$
$839$	−8.08477	+	19.5184i	−0.279117	+	0.673849i	0.720694	+	0.693253i	$0.243823\pi$
$840$		0			0
$841$	−6.84151	+	6.84151i	−0.235914	+	0.235914i
$842$		0			0
$843$	0.239200	+	1.81691i	0.00823849	+	0.0625775i
$844$		0			0
$845$	12.3582	−	93.8702i	0.425137	−	3.22923i
$846$		0			0
$847$	14.9710	−	24.9547i	0.514409	−	0.857454i
$848$		0			0
$849$	28.7403	−	49.7796i	0.986364	−	1.70843i
$850$		0			0
$851$	−25.4453	−	44.0726i	−0.872254	−	1.51079i
$852$		0			0
$853$	−1.72543	−	4.16556i	−0.0590777	−	0.142626i	0.891584	−	0.452855i	$-0.149594\pi$
$853$	−1.72543	−	4.16556i	−0.0590777	−	0.142626i	−0.950662	+	0.310229i	$0.899594\pi$
$854$		0			0
$855$	10.0005	−	4.14234i	0.342010	−	0.141665i
$856$		0			0
$857$	1.61362	+	12.2566i	0.0551201	+	0.418679i	0.996652	+	0.0817559i	$0.0260528\pi$
$857$	1.61362	+	12.2566i	0.0551201	+	0.418679i	−0.941532	+	0.336923i	$0.890614\pi$
$858$		0			0
$859$	−14.4201	−	53.8164i	−0.492006	−	1.83619i	−0.546191	−	0.837661i	$-0.683923\pi$
$859$	−14.4201	−	53.8164i	−0.492006	−	1.83619i	0.0541846	−	0.998531i	$-0.482744\pi$
$860$		0			0
$861$	−3.78578	+	13.2369i	−0.129019	+	0.451112i
$862$		0			0
$863$	47.2037	+	27.2531i	1.60683	+	0.927705i	0.990073	+	0.140554i	$0.0448882\pi$
$863$	47.2037	+	27.2531i	1.60683	+	0.927705i	0.616759	+	0.787152i	$0.288445\pi$
$864$		0			0
$865$	−14.9533	+	55.8063i	−0.508426	+	1.89747i
$866$		0			0
$867$	28.3778	−	27.1868i	0.963762	−	0.923311i
$868$		0			0
$869$	0.126978	+	0.126978i	0.00430745	+	0.00430745i
$870$		0			0
$871$	−25.9439	+	14.9787i	−0.879074	+	0.507534i
$872$		0			0
$873$	−12.5602	−	16.3688i	−0.425098	−	0.553999i
$874$		0			0
$875$	30.5729	+	77.4576i	1.03355	+	2.61855i
$876$		0			0
$877$	−12.7706	+	9.79923i	−0.431233	+	0.330897i	−0.801464	−	0.598043i	$-0.795945\pi$
$877$	−12.7706	+	9.79923i	−0.431233	+	0.330897i	0.370231	+	0.928940i	$0.379278\pi$
$878$		0			0
$879$	−13.3062	−	10.2102i	−0.448805	−	0.344381i
$880$		0			0
$881$	5.65038	+	13.6412i	0.190366	+	0.459584i	0.990029	−	0.140865i	$-0.0449884\pi$
$881$	5.65038	+	13.6412i	0.190366	+	0.459584i	−0.799663	+	0.600449i	$0.794988\pi$
$882$		0			0
$883$	5.95244			0.200316			0.100158	−	0.994972i	$-0.468065\pi$
$883$	5.95244			0.200316			0.100158	+	0.994972i	$0.468065\pi$
$884$		0			0
$885$	2.91615	+	5.05093i	0.0980254	+	0.169785i
$886$		0			0
$887$	−10.9748	−	1.44486i	−0.368497	−	0.0485136i	−0.0559961	−	0.998431i	$-0.517833\pi$
$887$	−10.9748	−	1.44486i	−0.368497	−	0.0485136i	−0.312501	+	0.949917i	$0.601167\pi$
$888$		0			0
$889$	0.222577	−	13.2742i	0.00746499	−	0.445202i
$890$		0			0
$891$	0.244379	−	0.187518i	0.00818700	−	0.00628211i
$892$		0			0
$893$	−7.28696	−	1.95254i	−0.243849	−	0.0653391i
$894$		0			0
$895$	22.8742	−	55.2231i	0.764599	−	1.84590i
$896$		0			0
$897$		−	76.7363i		−	2.56215i
$898$		0			0
$899$	−8.22661	+	30.7021i	−0.274373	+	1.02397i
$900$		0			0
$901$	−5.65500	+	16.0905i	−0.188395	+	0.536052i
$902$		0			0
$903$	22.1520	+	17.5956i	0.737171	+	0.585546i
$904$		0			0
$905$	51.5530	+	29.7641i	1.71368	+	0.989393i
$906$		0			0
$907$	−45.2346	+	5.95525i	−1.50199	+	0.197741i	−0.836211	−	0.548408i	$-0.815234\pi$
$907$	−45.2346	+	5.95525i	−1.50199	+	0.197741i	−0.665780	+	0.746148i	$0.731901\pi$
$908$		0			0
$909$	−28.6785	+	28.6785i	−0.951206	+	0.951206i
$910$		0			0
$911$	−6.57399	−	2.72303i	−0.217806	−	0.0902182i	0.271113	−	0.962548i	$-0.412608\pi$
$911$	−6.57399	−	2.72303i	−0.217806	−	0.0902182i	−0.488918	+	0.872329i	$0.662608\pi$
$912$		0			0
$913$	−0.229602	−	0.176180i	−0.00759872	−	0.00583070i
$914$		0			0
$915$	51.5546	+	6.78729i	1.70434	+	0.224381i
$916$		0			0
$917$	−10.3957	−	14.0288i	−0.343296	−	0.463271i
$918$		0			0
$919$	−8.74681	+	15.1499i	−0.288531	+	0.499750i	−0.973459	−	0.228860i	$-0.926500\pi$
$919$	−8.74681	+	15.1499i	−0.288531	+	0.499750i	0.684928	+	0.728610i	$0.259833\pi$
$920$		0			0
$921$	33.1008	−	43.1377i	1.09071	−	1.42144i
$922$		0			0
$923$	−59.0577	+	24.4625i	−1.94391	+	0.805192i
$924$		0			0
$925$	−105.834	−	43.8378i	−3.47979	−	1.44138i
$926$		0			0
$927$	−7.63045	−	2.04457i	−0.250617	−	0.0671526i
$928$		0			0
$929$	7.57683	+	9.87432i	0.248588	+	0.323966i	0.900935	−	0.433955i	$-0.142882\pi$
$929$	7.57683	+	9.87432i	0.248588	+	0.323966i	−0.652347	+	0.757920i	$0.726216\pi$
$930$		0			0
$931$	−1.74762	−	7.52257i	−0.0572758	−	0.246542i
$932$		0			0
$933$	−17.7365	+	4.75247i	−0.580666	+	0.155589i
$934$		0			0
$935$	−0.0383869	+	0.503013i	−0.00125538	+	0.0164503i
$936$		0			0
$937$	−34.1664	−	34.1664i	−1.11617	−	1.11617i	−0.992299	−	0.123869i	$-0.960470\pi$
$937$	−34.1664	−	34.1664i	−1.11617	−	1.11617i	−0.123869	−	0.992299i	$-0.539530\pi$
$938$		0			0
$939$		−	53.4650i		−	1.74477i
$940$		0			0
$941$	35.8023	−	4.71346i	1.16712	−	0.153654i	0.478040	−	0.878338i	$-0.341348\pi$
$941$	35.8023	−	4.71346i	1.16712	−	0.153654i	0.689081	+	0.724684i	$0.258014\pi$
$942$		0			0
$943$	−3.24034	−	12.0931i	−0.105520	−	0.393806i
$944$		0			0
$945$	−4.07384	−	16.2916i	−0.132522	−	0.529965i
$946$		0			0
$947$	3.03559	−	23.0576i	0.0986434	−	0.749271i	−0.868617	−	0.495484i	$-0.834991\pi$
$947$	3.03559	−	23.0576i	0.0986434	−	0.749271i	0.967260	−	0.253787i	$-0.0816761\pi$
$948$		0			0
$949$	17.2189	−	22.4401i	0.558949	−	0.728437i
$950$		0			0
$951$	−22.0317			−0.714427
$952$		0			0
$953$	18.3074			0.593035			0.296518	−	0.955027i	$-0.404175\pi$
$953$	18.3074			0.593035			0.296518	+	0.955027i	$0.404175\pi$
$954$		0			0
$955$	24.2241	−	31.5695i	0.783873	−	1.02156i
$956$		0			0
$957$	−0.0387741	+	0.294519i	−0.00125339	+	0.00952043i
$958$		0			0
$959$	7.43500	+	2.12642i	0.240089	+	0.0686658i
$960$		0			0
$961$	−5.50774	−	20.5552i	−0.177669	−	0.663070i
$962$		0			0
$963$	38.4229	−	5.05847i	1.23816	−	0.163007i
$964$		0			0
$965$			62.7841i			2.02109i
$966$		0			0
$967$	−3.96600	−	3.96600i	−0.127538	−	0.127538i	0.640457	−	0.767994i	$-0.278745\pi$
$967$	−3.96600	−	3.96600i	−0.127538	−	0.127538i	−0.767994	+	0.640457i	$0.778745\pi$
$968$		0			0
$969$	4.75181	−	9.38093i	0.152650	−	0.301359i
$970$		0			0
$971$	−12.3533	+	3.31006i	−0.396437	+	0.106225i	−0.451529	−	0.892256i	$-0.649121\pi$
$971$	−12.3533	+	3.31006i	−0.396437	+	0.106225i	0.0550924	+	0.998481i	$0.482455\pi$
$972$		0			0
$973$	−15.3583	−	6.66542i	−0.492364	−	0.213684i
$974$		0			0
$975$	−105.152	−	137.037i	−3.36757	−	4.38871i
$976$		0			0
$977$	10.2557	+	2.74800i	0.328109	+	0.0879164i	0.419113	−	0.907934i	$-0.362341\pi$
$977$	10.2557	+	2.74800i	0.328109	+	0.0879164i	−0.0910045	+	0.995850i	$0.529008\pi$
$978$		0			0
$979$	0.312164	+	0.129302i	0.00997680	+	0.00413253i
$980$		0			0
$981$	−14.2318	+	5.89502i	−0.454387	+	0.188213i
$982$		0			0
$983$	22.7755	−	29.6817i	0.726427	−	0.946698i	−0.273458	−	0.961884i	$-0.588167\pi$
$983$	22.7755	−	29.6817i	0.726427	−	0.946698i	0.999885	+	0.0151863i	$0.00483412\pi$
$984$		0			0
$985$	37.0629	−	64.1948i	1.18092	−	2.04542i
$986$		0			0
$987$	16.6501	−	38.3646i	0.529977	−	1.22116i
$988$		0			0
$989$	−25.5055	−	3.35787i	−0.811028	−	0.106774i
$990$		0			0
$991$	29.3829	+	22.5463i	0.933377	+	0.716206i	0.958982	−	0.283467i	$-0.0914845\pi$
$991$	29.3829	+	22.5463i	0.933377	+	0.716206i	−0.0256048	+	0.999672i	$0.508151\pi$
$992$		0			0
$993$	−17.8913	−	7.41083i	−0.567764	−	0.235176i
$994$		0			0
$995$	60.7479	−	60.7479i	1.92584	−	1.92584i
$996$		0			0
$997$	9.13765	−	1.20299i	0.289392	−	0.0380992i	0.0155676	−	0.999879i	$-0.495044\pi$
$997$	9.13765	−	1.20299i	0.289392	−	0.0380992i	0.273825	+	0.961780i	$0.411711\pi$
$998$		0			0
$999$	12.0164	+	6.93765i	0.380181	+	0.219498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bh.a.457.10	yes	96
7.4	even	3	inner	476.2.bh.a.389.3	yes	96
17.8	even	8	inner	476.2.bh.a.93.3	yes	96
119.25	even	24	inner	476.2.bh.a.25.10	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bh.a.25.10	✓	96	119.25	even	24	inner
476.2.bh.a.93.3	yes	96	17.8	even	8	inner
476.2.bh.a.389.3	yes	96	7.4	even	3	inner
476.2.bh.a.457.10	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40728 - 1.83401i) q^{3} +(-0.546335 + 4.14983i) q^{5} +(-1.90193 + 1.83920i) q^{7} +(-0.606678 - 2.26415i) q^{9} +O(q^{10})\)	\(q+(1.40728 - 1.83401i) q^{3} +(-0.546335 + 4.14983i) q^{5} +(-1.90193 + 1.83920i) q^{7} +(-0.606678 - 2.26415i) q^{9} +(0.0289816 - 0.00381550i) q^{11} +5.96827i q^{13} +(6.84197 + 6.84197i) q^{15} +(4.11115 + 0.313738i) q^{17} +(1.06568 - 0.285548i) q^{19} +(0.696552 + 6.07643i) q^{21} +(-3.38583 - 4.41250i) q^{23} +(-12.0930 - 3.24030i) q^{25} +(1.40100 + 0.580313i) q^{27} +(-4.06136 + 1.68227i) q^{29} +(4.40166 - 5.73635i) q^{31} +(0.0337877 - 0.0585220i) q^{33} +(-6.59328 - 8.89751i) q^{35} +(9.07169 + 1.19431i) q^{37} +(10.9458 + 8.39904i) q^{39} +(2.07966 + 0.861421i) q^{41} +(3.27064 - 3.27064i) q^{43} +(9.72730 - 1.28062i) q^{45} +(-5.92176 - 3.41893i) q^{47} +(0.234681 - 6.99606i) q^{49} +(6.36095 - 7.09836i) q^{51} +(-1.07061 + 3.99557i) q^{53} +0.122353i q^{55} +(0.976015 - 2.35631i) q^{57} +(0.582222 + 0.156006i) q^{59} +(4.26353 - 3.27152i) q^{61} +(5.31809 + 3.19046i) q^{63} +(-24.7673 - 3.26068i) q^{65} +(2.50972 + 4.34696i) q^{67} -12.8574 q^{69} +(4.09876 + 9.89527i) q^{71} +(-3.75990 - 2.88507i) q^{73} +(-22.9610 + 17.6186i) q^{75} +(-0.0481036 + 0.0605598i) q^{77} +(3.73971 + 4.87368i) q^{79} +(9.12585 - 5.26881i) q^{81} +(-7.00067 - 7.00067i) q^{83} +(-3.54803 + 16.8892i) q^{85} +(-2.63018 + 9.81598i) q^{87} +(10.0102 + 5.77940i) q^{89} +(-10.9768 - 11.3512i) q^{91} +(-4.32613 - 16.1453i) q^{93} +(0.602757 + 4.57839i) q^{95} +(8.13210 - 3.36843i) q^{97} +(-0.0262214 - 0.0633040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{5}+O(q^{10}) \) 96 * q + 4 * q^5	\( 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) \) 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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