LMFDB - Embedded newform 432.2.k.d.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, degree $2$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.524142 + 1.31350i) q^{2} +(-1.45055 - 1.37692i) q^{4} +(1.14284 - 1.14284i) q^{5} +4.40079i q^{7} +(2.56887 - 1.18359i) q^{8} +O(q^{10})$	\(q+(-0.524142 + 1.31350i) q^{2} +(-1.45055 - 1.37692i) q^{4} +(1.14284 - 1.14284i) q^{5} +4.40079i q^{7} +(2.56887 - 1.18359i) q^{8} +(0.902107 + 2.10013i) q^{10} +(4.02070 - 4.02070i) q^{11} +(-1.98322 - 1.98322i) q^{13} +(-5.78043 - 2.30664i) q^{14} +(0.208190 + 3.99458i) q^{16} +3.27591 q^{17} +(1.53770 + 1.53770i) q^{19} +(-3.23134 + 0.0841487i) q^{20} +(3.17376 + 7.38860i) q^{22} +8.02513i q^{23} +2.38783i q^{25} +(3.64444 - 1.56546i) q^{26} +(6.05953 - 6.38357i) q^{28} +(0.520201 + 0.520201i) q^{29} +9.97091 q^{31} +(-5.35599 - 1.82027i) q^{32} +(-1.71704 + 4.30290i) q^{34} +(5.02940 + 5.02940i) q^{35} +(-1.92995 + 1.92995i) q^{37} +(-2.82574 + 1.21379i) q^{38} +(1.58315 - 4.28847i) q^{40} -1.02135i q^{41} +(-1.20053 + 1.20053i) q^{43} +(-11.3684 + 0.296049i) q^{44} +(-10.5410 - 4.20631i) q^{46} -4.16250 q^{47} -12.3670 q^{49} +(-3.13641 - 1.25156i) q^{50} +(0.146027 + 5.60749i) q^{52} +(1.08787 - 1.08787i) q^{53} -9.19003i q^{55} +(5.20874 + 11.3051i) q^{56} +(-0.955942 + 0.410623i) q^{58} +(7.31146 - 7.31146i) q^{59} +(-5.59986 - 5.59986i) q^{61} +(-5.22617 + 13.0968i) q^{62} +(5.19822 - 6.08100i) q^{64} -4.53301 q^{65} +(4.24116 + 4.24116i) q^{67} +(-4.75187 - 4.51066i) q^{68} +(-9.24222 + 3.96998i) q^{70} -9.01840i q^{71} -2.45814i q^{73} +(-1.52341 - 3.54655i) q^{74} +(-0.113223 - 4.34780i) q^{76} +(17.6943 + 17.6943i) q^{77} -0.0383076 q^{79} +(4.80309 + 4.32724i) q^{80} +(1.34154 + 0.535333i) q^{82} +(-8.61127 - 8.61127i) q^{83} +(3.74384 - 3.74384i) q^{85} +(-0.947647 - 2.20615i) q^{86} +(5.56980 - 15.0875i) q^{88} -10.6312i q^{89} +(8.72773 - 8.72773i) q^{91} +(11.0500 - 11.6409i) q^{92} +(2.18174 - 5.46744i) q^{94} +3.51469 q^{95} -5.18703 q^{97} +(6.48204 - 16.2440i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.524142	+	1.31350i	−0.370625	+	0.928783i
$2$	−0.524142	+	1.31350i	−0.370625	+	0.928783i
$3$		0			0
$3$		0			0
$4$	−1.45055	−	1.37692i	−0.725275	−	0.688459i
$5$	1.14284	−	1.14284i	0.511094	−	0.511094i	−0.403768	−	0.914861i	$-0.632300\pi$
$5$	1.14284	−	1.14284i	0.511094	−	0.511094i	0.914861	+	0.403768i	$0.132300\pi$
$6$		0			0
$7$			4.40079i			1.66334i	0.555269	+	0.831671i	$0.312615\pi$
$7$			4.40079i			1.66334i	−0.555269	+	0.831671i	$0.687385\pi$
$8$	2.56887	−	1.18359i	0.908234	−	0.418463i
$9$		0			0
$10$	0.902107	+	2.10013i	0.285271	+	0.664119i
$11$	4.02070	−	4.02070i	1.21229	−	1.21229i	0.242014	−	0.970273i	$-0.422192\pi$
$11$	4.02070	−	4.02070i	1.21229	−	1.21229i	0.970273	−	0.242014i	$-0.0778079\pi$
$12$		0			0
$13$	−1.98322	−	1.98322i	−0.550046	−	0.550046i	0.376408	−	0.926454i	$-0.377159\pi$
$13$	−1.98322	−	1.98322i	−0.550046	−	0.550046i	−0.926454	+	0.376408i	$0.877159\pi$
$14$	−5.78043	−	2.30664i	−1.54488	−	0.616475i
$15$		0			0
$16$	0.208190	+	3.99458i	0.0520475	+	0.998645i
$17$	3.27591			0.794524			0.397262	−	0.917705i	$-0.369960\pi$
$17$	3.27591			0.794524			0.397262	+	0.917705i	$0.369960\pi$
$18$		0			0
$19$	1.53770	+	1.53770i	0.352773	+	0.352773i	0.861140	−	0.508368i	$-0.169751\pi$
$19$	1.53770	+	1.53770i	0.352773	+	0.352773i	−0.508368	+	0.861140i	$0.669751\pi$
$20$	−3.23134	+	0.0841487i	−0.722551	+	0.0188162i
$21$		0			0
$22$	3.17376	+	7.38860i	0.676648	+	1.57525i
$23$			8.02513i			1.67336i	0.547695	+	0.836678i	$0.315505\pi$
$23$			8.02513i			1.67336i	−0.547695	+	0.836678i	$0.684495\pi$
$24$		0			0
$25$			2.38783i			0.477567i
$26$	3.64444	−	1.56546i	0.714734	−	0.307013i
$27$		0			0
$28$	6.05953	−	6.38357i	1.14514	−	1.20638i
$29$	0.520201	+	0.520201i	0.0965989	+	0.0965989i	0.753755	−	0.657156i	$-0.228241\pi$
$29$	0.520201	+	0.520201i	0.0965989	+	0.0965989i	−0.657156	+	0.753755i	$0.728241\pi$
$30$		0			0
$31$	9.97091			1.79083			0.895414	−	0.445235i	$-0.146880\pi$
$31$	9.97091			1.79083			0.895414	+	0.445235i	$0.146880\pi$
$32$	−5.35599	−	1.82027i	−0.946814	−	0.321781i
$33$		0			0
$34$	−1.71704	+	4.30290i	−0.294470	+	0.737941i
$35$	5.02940	+	5.02940i	0.850124	+	0.850124i
$36$		0			0
$37$	−1.92995	+	1.92995i	−0.317282	+	0.317282i	−0.847722	−	0.530441i	$-0.822027\pi$
$37$	−1.92995	+	1.92995i	−0.317282	+	0.317282i	0.530441	+	0.847722i	$0.322027\pi$
$38$	−2.82574	+	1.21379i	−0.458395	+	0.196903i
$39$		0			0
$40$	1.58315	−	4.28847i	0.250319	−	0.678066i
$41$		−	1.02135i		−	0.159508i	−0.996815	−	0.0797541i	$-0.974587\pi$
$41$		−	1.02135i		−	0.159508i	0.996815	−	0.0797541i	$-0.0254135\pi$
$42$		0			0
$43$	−1.20053	+	1.20053i	−0.183080	+	0.183080i	−0.792696	−	0.609617i	$-0.791323\pi$
$43$	−1.20053	+	1.20053i	−0.183080	+	0.183080i	0.609617	+	0.792696i	$0.291323\pi$
$44$	−11.3684	+	0.296049i	−1.71385	+	0.0446311i
$45$		0			0
$46$	−10.5410	−	4.20631i	−1.55418	−	0.620187i
$47$	−4.16250			−0.607164			−0.303582	−	0.952805i	$-0.598183\pi$
$47$	−4.16250			−0.607164			−0.303582	+	0.952805i	$0.598183\pi$
$48$		0			0
$49$	−12.3670			−1.76671
$50$	−3.13641	−	1.25156i	−0.443556	−	0.176998i
$51$		0			0
$52$	0.146027	+	5.60749i	0.0202503	+	0.777619i
$53$	1.08787	−	1.08787i	0.149430	−	0.149430i	−0.628433	−	0.777864i	$-0.716303\pi$
$53$	1.08787	−	1.08787i	0.149430	−	0.149430i	0.777864	+	0.628433i	$0.216303\pi$
$54$		0			0
$55$		−	9.19003i		−	1.23918i
$56$	5.20874	+	11.3051i	0.696047	+	1.51070i
$57$		0			0
$58$	−0.955942	+	0.410623i	−0.125521	+	0.0539175i
$59$	7.31146	−	7.31146i	0.951871	−	0.951871i	−0.0470224	−	0.998894i	$-0.514973\pi$
$59$	7.31146	−	7.31146i	0.951871	−	0.951871i	0.998894	+	0.0470224i	$0.0149732\pi$
$60$		0			0
$61$	−5.59986	−	5.59986i	−0.716988	−	0.716988i	0.250999	−	0.967987i	$-0.419241\pi$
$61$	−5.59986	−	5.59986i	−0.716988	−	0.716988i	−0.967987	+	0.250999i	$0.919241\pi$
$62$	−5.22617	+	13.0968i	−0.663725	+	1.66329i
$63$		0			0
$64$	5.19822	−	6.08100i	0.649777	−	0.760124i
$65$	−4.53301			−0.562250
$66$		0			0
$67$	4.24116	+	4.24116i	0.518140	+	0.518140i	0.917008	−	0.398868i	$-0.130597\pi$
$67$	4.24116	+	4.24116i	0.518140	+	0.518140i	−0.398868	+	0.917008i	$0.630597\pi$
$68$	−4.75187	−	4.51066i	−0.576249	−	0.546998i
$69$		0			0
$70$	−9.24222	+	3.96998i	−1.10466	+	0.474504i
$71$		−	9.01840i		−	1.07029i	−0.844761	−	0.535143i	$-0.820258\pi$
$71$		−	9.01840i		−	1.07029i	0.844761	−	0.535143i	$-0.179742\pi$
$72$		0			0
$73$		−	2.45814i		−	0.287704i	−0.989599	−	0.143852i	$-0.954051\pi$
$73$		−	2.45814i		−	0.287704i	0.989599	−	0.143852i	$-0.0459489\pi$
$74$	−1.52341	−	3.54655i	−0.177093	−	0.412278i
$75$		0			0
$76$	−0.113223	−	4.34780i	−0.0129875	−	0.498727i
$77$	17.6943	+	17.6943i	2.01645	+	2.01645i
$78$		0			0
$79$	−0.0383076			−0.00430994			−0.00215497	−	0.999998i	$-0.500686\pi$
$79$	−0.0383076			−0.00430994			−0.00215497	+	0.999998i	$0.500686\pi$
$80$	4.80309	+	4.32724i	0.537002	+	0.483800i
$81$		0			0
$82$	1.34154	+	0.535333i	0.148148	+	0.0591176i
$83$	−8.61127	−	8.61127i	−0.945210	−	0.945210i	0.0533652	−	0.998575i	$-0.483005\pi$
$83$	−8.61127	−	8.61127i	−0.945210	−	0.945210i	−0.998575	+	0.0533652i	$0.983005\pi$
$84$		0			0
$85$	3.74384	−	3.74384i	0.406076	−	0.406076i
$86$	−0.947647	−	2.20615i	−0.102187	−	0.237895i
$87$		0			0
$88$	5.56980	−	15.0875i	0.593743	−	1.60834i
$89$		−	10.6312i		−	1.12690i	−0.826150	−	0.563450i	$-0.809474\pi$
$89$		−	10.6312i		−	1.12690i	0.826150	−	0.563450i	$-0.190526\pi$
$90$		0			0
$91$	8.72773	−	8.72773i	0.914915	−	0.914915i
$92$	11.0500	−	11.6409i	1.15204	−	1.21364i
$93$		0			0
$94$	2.18174	−	5.46744i	0.225030	−	0.563923i
$95$	3.51469			0.360600
$96$		0			0
$97$	−5.18703			−0.526663			−0.263332	−	0.964705i	$-0.584821\pi$
$97$	−5.18703			−0.526663			−0.263332	+	0.964705i	$0.584821\pi$
$98$	6.48204	−	16.2440i	0.654785	−	1.64089i
$99$		0			0
$100$	3.28785	−	3.46367i	0.328785	−	0.346367i
$101$	−3.60642	+	3.60642i	−0.358852	+	0.358852i	−0.863390	−	0.504538i	$-0.831663\pi$
$101$	−3.60642	+	3.60642i	−0.358852	+	0.358852i	0.504538	+	0.863390i	$0.331663\pi$
$102$		0			0
$103$			10.3856i			1.02332i	0.859188	+	0.511659i	$0.170969\pi$
$103$			10.3856i			1.02332i	−0.859188	+	0.511659i	$0.829031\pi$
$104$	−7.44196	−	2.74732i	−0.729745	−	0.269397i
$105$		0			0
$106$	0.858715	+	1.99911i	0.0834058	+	0.194171i
$107$	−3.98900	+	3.98900i	−0.385631	+	0.385631i	−0.873126	−	0.487495i	$-0.837911\pi$
$107$	−3.98900	+	3.98900i	−0.385631	+	0.385631i	0.487495	+	0.873126i	$0.337911\pi$
$108$		0			0
$109$	−1.40487	−	1.40487i	−0.134562	−	0.134562i	0.636617	−	0.771180i	$-0.280333\pi$
$109$	−1.40487	−	1.40487i	−0.134562	−	0.134562i	−0.771180	+	0.636617i	$0.780333\pi$
$110$	12.0711	+	4.81688i	1.15093	+	0.459272i
$111$		0			0
$112$	−17.5793	+	0.916200i	−1.66109	+	0.0865728i
$113$	−12.8259			−1.20656			−0.603282	−	0.797528i	$-0.706140\pi$
$113$	−12.8259			−1.20656			−0.603282	+	0.797528i	$0.706140\pi$
$114$		0			0
$115$	9.17144	+	9.17144i	0.855241	+	0.855241i
$116$	−0.0383031	−	1.47085i	−0.00355635	−	0.136565i
$117$		0			0
$118$	5.77134	+	13.4358i	0.531295	+	1.23687i
$119$			14.4166i			1.32157i
$120$		0			0
$121$		−	21.3320i		−	1.93928i
$122$	10.2905	−	4.42027i	0.931659	−	0.400193i
$123$		0			0
$124$	−14.4633	−	13.7291i	−1.29884	−	1.23291i
$125$	8.44311	+	8.44311i	0.755175	+	0.755175i
$126$		0			0
$127$	1.36993			0.121561			0.0607806	−	0.998151i	$-0.480641\pi$
$127$	1.36993			0.121561			0.0607806	+	0.998151i	$0.480641\pi$
$128$	5.26276	+	10.0152i	0.465167	+	0.885223i
$129$		0			0
$130$	2.37594	−	5.95409i	0.208384	−	0.522208i
$131$	6.72910	+	6.72910i	0.587924	+	0.587924i	0.937069	−	0.349145i	$-0.113528\pi$
$131$	6.72910	+	6.72910i	0.587924	+	0.587924i	−0.349145	+	0.937069i	$0.613528\pi$
$132$		0			0
$133$	−6.76710	+	6.76710i	−0.586782	+	0.586782i
$134$	−7.79373	+	3.34778i	−0.673275	+	0.289204i
$135$		0			0
$136$	8.41539	−	3.87734i	0.721614	−	0.332479i
$137$		−	22.2550i		−	1.90137i	−0.310156	−	0.950686i	$-0.600381\pi$
$137$		−	22.2550i		−	1.90137i	0.310156	−	0.950686i	$-0.399619\pi$
$138$		0			0
$139$	−7.77425	+	7.77425i	−0.659403	+	0.659403i	−0.955239	−	0.295836i	$-0.904402\pi$
$139$	−7.77425	+	7.77425i	−0.659403	+	0.659403i	0.295836	+	0.955239i	$0.404402\pi$
$140$	−0.370321	−	14.2205i	−0.0312978	−	1.20185i
$141$		0			0
$142$	11.8456	+	4.72692i	0.994064	+	0.396674i
$143$	−15.9479			−1.33363
$144$		0			0
$145$	1.18901			0.0987422
$146$	3.22877	+	1.28842i	0.267215	+	0.106630i
$147$		0			0
$148$	5.45687	−	0.142104i	0.448552	−	0.0116809i
$149$	3.84216	−	3.84216i	0.314762	−	0.314762i	−0.531989	−	0.846751i	$-0.678555\pi$
$149$	3.84216	−	3.84216i	0.314762	−	0.314762i	0.846751	+	0.531989i	$0.178555\pi$
$150$		0			0
$151$			3.96169i			0.322398i	0.986922	+	0.161199i	$0.0515361\pi$
$151$			3.96169i			0.322398i	−0.986922	+	0.161199i	$0.948464\pi$
$152$	5.77017	+	2.13015i	0.468022	+	0.172778i
$153$		0			0
$154$	−32.5157	+	13.9670i	−2.62019	+	1.12550i
$155$	11.3952	−	11.3952i	0.915281	−	0.915281i
$156$		0			0
$157$	−4.00887	−	4.00887i	−0.319943	−	0.319943i	0.528802	−	0.848745i	$-0.322641\pi$
$157$	−4.00887	−	4.00887i	−0.319943	−	0.319943i	−0.848745	+	0.528802i	$0.822641\pi$
$158$	0.0200786	−	0.0503170i	0.00159737	−	0.00400300i
$159$		0			0
$160$	−8.20132	+	4.04076i	−0.648371	+	0.319450i
$161$	−35.3169			−2.78336
$162$		0			0
$163$	−14.8476	−	14.8476i	−1.16295	−	1.16295i	−0.983826	−	0.179126i	$-0.942673\pi$
$163$	−14.8476	−	14.8476i	−1.16295	−	1.16295i	−0.179126	−	0.983826i	$-0.557327\pi$
$164$	−1.40632	+	1.48152i	−0.109815	+	0.115687i
$165$		0			0
$166$	15.8244	−	6.79735i	1.22821	−	0.527577i
$167$			10.5791i			0.818635i	0.912392	+	0.409317i	$0.134233\pi$
$167$			10.5791i			0.818635i	−0.912392	+	0.409317i	$0.865767\pi$
$168$		0			0
$169$		−	5.13368i		−	0.394898i
$170$	2.95522	+	6.87983i	0.226655	+	0.527659i
$171$		0			0
$172$	3.39447	−	0.0883968i	0.258826	−	0.00674019i
$173$	−8.39876	−	8.39876i	−0.638546	−	0.638546i	0.311651	−	0.950197i	$-0.399118\pi$
$173$	−8.39876	−	8.39876i	−0.638546	−	0.638546i	−0.950197	+	0.311651i	$0.899118\pi$
$174$		0			0
$175$	−10.5084			−0.794357
$176$	16.8981	+	15.2239i	1.27374	+	1.14755i
$177$		0			0
$178$	13.9640	+	5.57223i	1.04665	+	0.417657i
$179$	−2.96025	−	2.96025i	−0.221260	−	0.221260i	0.587769	−	0.809029i	$-0.300006\pi$
$179$	−2.96025	−	2.96025i	−0.221260	−	0.221260i	−0.809029	+	0.587769i	$0.800006\pi$
$180$		0			0
$181$	−3.76128	+	3.76128i	−0.279574	+	0.279574i	−0.832939	−	0.553365i	$-0.813343\pi$
$181$	−3.76128	+	3.76128i	−0.279574	+	0.279574i	0.553365	+	0.832939i	$0.313343\pi$
$182$	6.88928	+	16.0384i	0.510667	+	1.18885i
$183$		0			0
$184$	9.49848	+	20.6155i	0.700237	+	1.51980i
$185$			4.41124i			0.324321i
$186$		0			0
$187$	13.1714	−	13.1714i	0.963191	−	0.963191i
$188$	6.03792	+	5.73143i	0.440361	+	0.418007i
$189$		0			0
$190$	−1.84220	+	4.61654i	−0.133647	+	0.334919i
$191$	−19.1339			−1.38448			−0.692242	−	0.721666i	$-0.743377\pi$
$191$	−19.1339			−1.38448			−0.692242	+	0.721666i	$0.743377\pi$
$192$		0			0
$193$	18.8020			1.35340			0.676698	−	0.736261i	$-0.263410\pi$
$193$	18.8020			1.35340			0.676698	+	0.736261i	$0.263410\pi$
$194$	2.71874	−	6.81315i	0.195194	−	0.489156i
$195$		0			0
$196$	17.9389	+	17.0283i	1.28135	+	1.21631i
$197$	−3.32506	+	3.32506i	−0.236901	+	0.236901i	−0.815565	−	0.578665i	$-0.803574\pi$
$197$	−3.32506	+	3.32506i	−0.236901	+	0.236901i	0.578665	+	0.815565i	$0.303574\pi$
$198$		0			0
$199$			4.94198i			0.350328i	0.984539	+	0.175164i	$0.0560455\pi$
$199$			4.94198i			0.350328i	−0.984539	+	0.175164i	$0.943954\pi$
$200$	2.82622	+	6.13404i	0.199844	+	0.433742i
$201$		0			0
$202$	−2.84674	−	6.62730i	−0.200296	−	0.466295i
$203$	−2.28930	+	2.28930i	−0.160677	+	0.160677i
$204$		0			0
$205$	−1.16724	−	1.16724i	−0.0815236	−	0.0815236i
$206$	−13.6414	−	5.44351i	−0.950441	−	0.379267i
$207$		0			0
$208$	7.50924	−	8.33501i	0.520672	−	0.577929i
$209$	12.3653			0.855323
$210$		0			0
$211$	16.6698	+	16.6698i	1.14759	+	1.14759i	0.987025	+	0.160569i	$0.0513329\pi$
$211$	16.6698	+	16.6698i	1.14759	+	1.14759i	0.160569	+	0.987025i	$0.448667\pi$
$212$	−3.07592	+	0.0801011i	−0.211255	+	0.00550137i
$213$		0			0
$214$	−3.14873	−	7.33034i	−0.215243	−	0.501092i
$215$			2.74404i			0.187142i
$216$		0			0
$217$			43.8799i			2.97876i
$218$	2.58165	−	1.10894i	0.174851	−	0.0751072i
$219$		0			0
$220$	−12.6539	+	13.3306i	−0.853128	+	0.898749i
$221$	−6.49685	−	6.49685i	−0.437025	−	0.437025i
$222$		0			0
$223$	8.43910			0.565124			0.282562	−	0.959249i	$-0.408816\pi$
$223$	8.43910			0.565124			0.282562	+	0.959249i	$0.408816\pi$
$224$	8.01063	−	23.5706i	0.535233	−	1.57488i
$225$		0			0
$226$	6.72262	−	16.8468i	0.447182	−	1.12064i
$227$	−13.7762	−	13.7762i	−0.914356	−	0.914356i	0.0822551	−	0.996611i	$-0.473788\pi$
$227$	−13.7762	−	13.7762i	−0.914356	−	0.914356i	−0.996611	+	0.0822551i	$0.973788\pi$
$228$		0			0
$229$	−8.24202	+	8.24202i	−0.544648	+	0.544648i	−0.924888	−	0.380240i	$-0.875841\pi$
$229$	−8.24202	+	8.24202i	−0.544648	+	0.544648i	0.380240	+	0.924888i	$0.375841\pi$
$230$	−16.8538	+	7.23952i	−1.11131	+	0.477360i
$231$		0			0
$232$	1.95204	+	0.720625i	0.128158	+	0.0473113i
$233$			5.50905i			0.360910i	0.983583	+	0.180455i	$0.0577570\pi$
$233$			5.50905i			0.360910i	−0.983583	+	0.180455i	$0.942243\pi$
$234$		0			0
$235$	−4.75708	+	4.75708i	−0.310317	+	0.310317i
$236$	−20.6729	+	0.538352i	−1.34569	+	0.0350437i
$237$		0			0
$238$	−18.9361	−	7.55634i	−1.22745	−	0.489805i
$239$	−22.6716			−1.46650			−0.733251	−	0.679959i	$-0.761998\pi$
$239$	−22.6716			−1.46650			−0.733251	+	0.679959i	$0.761998\pi$
$240$		0			0
$241$	0.0533528			0.00343676			0.00171838	−	0.999999i	$-0.499453\pi$
$241$	0.0533528			0.00343676			0.00171838	+	0.999999i	$0.499453\pi$
$242$	28.0196	+	11.1810i	1.80117	+	0.718744i
$243$		0			0
$244$	0.412324	+	15.8334i	0.0263964	+	1.01363i
$245$	−14.1334	+	14.1334i	−0.902953	+	0.902953i
$246$		0			0
$247$		−	6.09919i		−	0.388082i
$248$	25.6140	−	11.8015i	1.62649	−	0.749395i
$249$		0			0
$250$	−15.5154	+	6.66461i	−0.981280	+	0.421507i
$251$	11.4159	−	11.4159i	0.720566	−	0.720566i	−0.248154	−	0.968720i	$-0.579824\pi$
$251$	11.4159	−	11.4159i	0.720566	−	0.720566i	0.968720	+	0.248154i	$0.0798241\pi$
$252$		0			0
$253$	32.2666	+	32.2666i	2.02859	+	2.02859i
$254$	−0.718036	+	1.79939i	−0.0450536	+	0.112904i
$255$		0			0
$256$	−15.9133	+	1.66326i	−0.994582	+	0.103954i
$257$	12.8857			0.803788			0.401894	−	0.915686i	$-0.368352\pi$
$257$	12.8857			0.803788			0.401894	+	0.915686i	$0.368352\pi$
$258$		0			0
$259$	−8.49330	−	8.49330i	−0.527748	−	0.527748i
$260$	6.57535	+	6.24158i	0.407786	+	0.387086i
$261$		0			0
$262$	−12.3657	+	5.31165i	−0.763953	+	0.328155i
$263$			26.2126i			1.61634i	0.588953	+	0.808168i	$0.299540\pi$
$263$			26.2126i			1.61634i	−0.588953	+	0.808168i	$0.700460\pi$
$264$		0			0
$265$		−	2.48652i		−	0.152746i
$266$	−5.34164	−	12.4355i	−0.327517	−	0.762468i
$267$		0			0
$268$	−0.312282	−	11.9918i	−0.0190757	−	0.732513i
$269$	13.1408	+	13.1408i	0.801208	+	0.801208i	0.983284	−	0.182077i	$-0.0582819\pi$
$269$	13.1408	+	13.1408i	0.801208	+	0.801208i	−0.182077	+	0.983284i	$0.558282\pi$
$270$		0			0
$271$	−10.2489			−0.622576			−0.311288	−	0.950316i	$-0.600760\pi$
$271$	−10.2489			−0.622576			−0.311288	+	0.950316i	$0.600760\pi$
$272$	0.682011	+	13.0859i	0.0413530	+	0.793448i
$273$		0			0
$274$	29.2319	+	11.6648i	1.76596	+	0.704695i
$275$	9.60076	+	9.60076i	0.578948	+	0.578948i
$276$		0			0
$277$	17.2698	−	17.2698i	1.03764	−	1.03764i	0.0383797	−	0.999263i	$-0.487780\pi$
$277$	17.2698	−	17.2698i	1.03764	−	1.03764i	0.999263	−	0.0383797i	$-0.0122197\pi$
$278$	−6.13664	−	14.2863i	−0.368051	−	0.856833i
$279$		0			0
$280$	18.8726	+	6.96713i	1.12786	+	0.416366i
$281$			13.0834i			0.780487i	0.920712	+	0.390244i	$0.127609\pi$
$281$			13.0834i			0.780487i	−0.920712	+	0.390244i	$0.872391\pi$
$282$		0			0
$283$	−5.95147	+	5.95147i	−0.353778	+	0.353778i	−0.861513	−	0.507735i	$-0.830483\pi$
$283$	−5.95147	+	5.95147i	−0.353778	+	0.353778i	0.507735	+	0.861513i	$0.330483\pi$
$284$	−12.4176	+	13.0816i	−0.736849	+	0.776252i
$285$		0			0
$286$	8.35895	−	20.9475i	0.494275	−	1.23865i
$287$	4.49475			0.265317
$288$		0			0
$289$	−6.26843			−0.368731
$290$	−0.623212	+	1.56177i	−0.0365963	+	0.0917101i
$291$		0			0
$292$	−3.38467	+	3.56566i	−0.198073	+	0.208665i
$293$	−8.16327	+	8.16327i	−0.476903	+	0.476903i	−0.904140	−	0.427236i	$-0.859487\pi$
$293$	−8.16327	+	8.16327i	−0.476903	+	0.476903i	0.427236	+	0.904140i	$0.359487\pi$
$294$		0			0
$295$		−	16.7117i		−	0.972991i
$296$	−2.67352	+	7.24206i	−0.155395	+	0.420936i
$297$		0			0
$298$	3.03283	+	7.06051i	0.175687	+	0.409005i
$299$	15.9156	−	15.9156i	0.920423	−	0.920423i
$300$		0			0
$301$	−5.28330	−	5.28330i	−0.304524	−	0.304524i
$302$	−5.20367	−	2.07649i	−0.299438	−	0.119489i
$303$		0			0
$304$	−5.82233	+	6.46260i	−0.333934	+	0.370655i
$305$	−12.7995			−0.732896
$306$		0			0
$307$	−8.89022	−	8.89022i	−0.507391	−	0.507391i	0.406333	−	0.913725i	$-0.366807\pi$
$307$	−8.89022	−	8.89022i	−0.507391	−	0.507391i	−0.913725	+	0.406333i	$0.866807\pi$
$308$	−1.30285	−	50.0299i	−0.0742367	−	2.85072i
$309$		0			0
$310$	8.99482	+	20.9402i	0.510872	+	1.18932i
$311$		−	26.1862i		−	1.48489i	−0.669909	−	0.742443i	$-0.733667\pi$
$311$		−	26.1862i		−	1.48489i	0.669909	−	0.742443i	$-0.266333\pi$
$312$		0			0
$313$		−	8.60708i		−	0.486501i	−0.969963	−	0.243251i	$-0.921786\pi$
$313$		−	8.60708i		−	0.486501i	0.969963	−	0.243251i	$-0.0782137\pi$
$314$	7.36686	−	3.16442i	0.415736	−	0.178579i
$315$		0			0
$316$	0.0555671	+	0.0527465i	0.00312590	+	0.00296722i
$317$	−11.0091	−	11.0091i	−0.618334	−	0.618334i	0.326770	−	0.945104i	$-0.394040\pi$
$317$	−11.0091	−	11.0091i	−0.618334	−	0.618334i	−0.945104	+	0.326770i	$0.894040\pi$
$318$		0			0
$319$	4.18315			0.234211
$320$	−1.00887	−	12.8903i	−0.0563977	−	0.720592i
$321$		0			0
$322$	18.5111	−	46.3887i	1.03158	−	2.58514i
$323$	5.03736	+	5.03736i	0.280286	+	0.280286i
$324$		0			0
$325$	4.73560	−	4.73560i	0.262684	−	0.262684i
$326$	27.2845	−	11.7200i	1.51115	−	0.649111i
$327$		0			0
$328$	−1.20886	−	2.62372i	−0.0667482	−	0.144871i
$329$		−	18.3183i		−	1.00992i
$330$		0			0
$331$	−20.4754	+	20.4754i	−1.12543	+	1.12543i	−0.134518	+	0.990911i	$0.542949\pi$
$331$	−20.4754	+	20.4754i	−1.12543	+	1.12543i	−0.990911	+	0.134518i	$0.957051\pi$
$332$	0.634058	+	24.3481i	0.0347985	+	1.33628i
$333$		0			0
$334$	−13.8956	−	5.54495i	−0.760334	−	0.303406i
$335$	9.69394			0.529636
$336$		0			0
$337$	−18.2159			−0.992281			−0.496141	−	0.868242i	$-0.665250\pi$
$337$	−18.2159			−0.992281			−0.496141	+	0.868242i	$0.665250\pi$
$338$	6.74307	+	2.69078i	0.366775	+	0.146359i
$339$		0			0
$340$	−10.5856	+	0.275663i	−0.574084	+	0.0149499i
$341$	40.0900	−	40.0900i	2.17100	−	2.17100i
$342$		0			0
$343$		−	23.6188i		−	1.27530i
$344$	−1.66308	+	4.50496i	−0.0896671	+	0.242891i
$345$		0			0
$346$	15.4339	−	6.62960i	0.829731	−	0.356410i
$347$	−4.43980	+	4.43980i	−0.238341	+	0.238341i	−0.816163	−	0.577822i	$-0.803903\pi$
$347$	−4.43980	+	4.43980i	−0.238341	+	0.238341i	0.577822	+	0.816163i	$0.303903\pi$
$348$		0			0
$349$	10.3495	+	10.3495i	0.553996	+	0.553996i	0.927592	−	0.373595i	$-0.121875\pi$
$349$	10.3495	+	10.3495i	0.553996	+	0.553996i	−0.373595	+	0.927592i	$0.621875\pi$
$350$	5.50787	−	13.8027i	0.294408	−	0.737785i
$351$		0			0
$352$	−28.8536	+	14.2161i	−1.53790	+	0.757719i
$353$	25.5873			1.36188			0.680938	−	0.732341i	$-0.261572\pi$
$353$	25.5873			1.36188			0.680938	+	0.732341i	$0.261572\pi$
$354$		0			0
$355$	−10.3066	−	10.3066i	−0.547017	−	0.547017i
$356$	−14.6382	+	15.4210i	−0.775825	+	0.817312i
$357$		0			0
$358$	5.43988	−	2.33669i	0.287507	−	0.123498i
$359$		−	4.65858i		−	0.245871i	−0.992415	−	0.122935i	$-0.960769\pi$
$359$		−	4.65858i		−	0.245871i	0.992415	−	0.122935i	$-0.0392308\pi$
$360$		0			0
$361$		−	14.2710i		−	0.751103i
$362$	−2.96899	−	6.91188i	−0.156047	−	0.363280i
$363$		0			0
$364$	−24.6774	+	0.642634i	−1.29345	+	0.0336832i
$365$	−2.80927	−	2.80927i	−0.147044	−	0.147044i
$366$		0			0
$367$	−20.8994			−1.09094			−0.545469	−	0.838131i	$-0.683648\pi$
$367$	−20.8994			−1.09094			−0.545469	+	0.838131i	$0.683648\pi$
$368$	−32.0570	+	1.67075i	−1.67109	+	0.0870940i
$369$		0			0
$370$	−5.79416	−	2.31212i	−0.301224	−	0.120201i
$371$	4.78748	+	4.78748i	0.248554	+	0.248554i
$372$		0			0
$373$	22.2131	−	22.2131i	1.15015	−	1.15015i	0.163627	−	0.986522i	$-0.447681\pi$
$373$	22.2131	−	22.2131i	1.15015	−	1.15015i	0.986522	−	0.163627i	$-0.0523193\pi$
$374$	10.3969	+	24.2044i	0.537613	+	1.25158i
$375$		0			0
$376$	−10.6929	+	4.92671i	−0.551446	+	0.254075i
$377$		−	2.06335i		−	0.106268i
$378$		0			0
$379$	−13.2327	+	13.2327i	−0.679717	+	0.679717i	−0.959936	−	0.280219i	$-0.909593\pi$
$379$	−13.2327	+	13.2327i	−0.679717	+	0.679717i	0.280219	+	0.959936i	$0.409593\pi$
$380$	−5.09823	−	4.83944i	−0.261534	−	0.248258i
$381$		0			0
$382$	10.0289	−	25.1324i	0.513123	−	1.28588i
$383$	13.6857			0.699306			0.349653	−	0.936879i	$-0.386299\pi$
$383$	13.6857			0.699306			0.349653	+	0.936879i	$0.386299\pi$
$384$		0			0
$385$	40.4434			2.06119
$386$	−9.85491	+	24.6963i	−0.501602	+	1.25701i
$387$		0			0
$388$	7.52405	+	7.14212i	0.381976	+	0.362586i
$389$	−2.59662	+	2.59662i	−0.131654	+	0.131654i	−0.769863	−	0.638209i	$-0.779675\pi$
$389$	−2.59662	+	2.59662i	−0.131654	+	0.131654i	0.638209	+	0.769863i	$0.279675\pi$
$390$		0			0
$391$			26.2896i			1.32952i
$392$	−31.7691	+	14.6374i	−1.60458	+	0.739302i
$393$		0			0
$394$	−2.62465	−	6.11026i	−0.132228	−	0.307830i
$395$	−0.0437795	+	0.0437795i	−0.00220279	+	0.00220279i
$396$		0			0
$397$	−17.6682	−	17.6682i	−0.886742	−	0.886742i	0.107466	−	0.994209i	$-0.465726\pi$
$397$	−17.6682	−	17.6682i	−0.886742	−	0.886742i	−0.994209	+	0.107466i	$0.965726\pi$
$398$	−6.49128	−	2.59030i	−0.325378	−	0.129840i
$399$		0			0
$400$	−9.53839	+	0.497123i	−0.476919	+	0.0248561i
$401$	−5.27444			−0.263393			−0.131696	−	0.991290i	$-0.542042\pi$
$401$	−5.27444			−0.263393			−0.131696	+	0.991290i	$0.542042\pi$
$402$		0			0
$403$	−19.7745	−	19.7745i	−0.985038	−	0.985038i
$404$	10.1970	−	0.265545i	0.507321	−	0.0132114i
$405$		0			0
$406$	−1.80707	−	4.20690i	−0.0896833	−	0.208785i
$407$			15.5195i			0.769272i
$408$		0			0
$409$			26.5988i			1.31523i	0.753356	+	0.657613i	$0.228434\pi$
$409$			26.5988i			1.31523i	−0.753356	+	0.657613i	$0.771566\pi$
$410$	2.14497	−	0.921367i	0.105932	−	0.0455031i
$411$		0			0
$412$	14.3001	−	15.0648i	0.704513	−	0.742188i
$413$	32.1762	+	32.1762i	1.58329	+	1.58329i
$414$		0			0
$415$	−19.6826			−0.966181
$416$	7.01211	+	14.2321i	0.343797	+	0.697786i
$417$		0			0
$418$	−6.48116	+	16.2417i	−0.317004	+	0.794409i
$419$	−19.8536	−	19.8536i	−0.969911	−	0.969911i	0.0296493	−	0.999560i	$-0.490561\pi$
$419$	−19.8536	−	19.8536i	−0.969911	−	0.969911i	−0.999560	+	0.0296493i	$0.990561\pi$
$420$		0			0
$421$	5.81162	−	5.81162i	0.283241	−	0.283241i	−0.551159	−	0.834400i	$-0.685814\pi$
$421$	5.81162	−	5.81162i	0.283241	−	0.283241i	0.834400	+	0.551159i	$0.185814\pi$
$422$	−30.6330	+	13.1584i	−1.49119	+	0.640539i
$423$		0			0
$424$	1.50700	−	4.08219i	0.0731866	−	0.198249i
$425$			7.82232i			0.379438i
$426$		0			0
$427$	24.6438	−	24.6438i	1.19260	−	1.19260i
$428$	11.2788	−	0.293715i	0.545180	−	0.0141972i
$429$		0			0
$430$	−3.60428	−	1.43827i	−0.173814	−	0.0693593i
$431$	26.1479			1.25950			0.629750	−	0.776798i	$-0.283157\pi$
$431$	26.1479			1.25950			0.629750	+	0.776798i	$0.283157\pi$
$432$		0			0
$433$	39.2763			1.88750			0.943748	−	0.330665i	$-0.107273\pi$
$433$	39.2763			1.88750			0.943748	+	0.330665i	$0.107273\pi$
$434$	−57.6361	−	22.9993i	−2.76662	−	1.10400i
$435$		0			0
$436$	0.103443	+	3.97224i	0.00495400	+	0.190236i
$437$	−12.3402	+	12.3402i	−0.590314	+	0.590314i
$438$		0			0
$439$			4.25236i			0.202954i	0.994838	+	0.101477i	$0.0323568\pi$
$439$			4.25236i			0.202954i	−0.994838	+	0.101477i	$0.967643\pi$
$440$	−10.8772	−	23.6080i	−0.518553	−	1.12547i
$441$		0			0
$442$	11.9389	−	5.12832i	0.567874	−	0.243929i
$443$	−14.2988	+	14.2988i	−0.679357	+	0.679357i	−0.959855	−	0.280497i	$-0.909501\pi$
$443$	−14.2988	+	14.2988i	−0.679357	+	0.679357i	0.280497	+	0.959855i	$0.409501\pi$
$444$		0			0
$445$	−12.1497	−	12.1497i	−0.575951	−	0.575951i
$446$	−4.42329	+	11.0847i	−0.209449	+	0.524877i
$447$		0			0
$448$	26.7612	+	22.8763i	1.26435	+	1.08080i
$449$	−20.7419			−0.978869			−0.489434	−	0.872040i	$-0.662797\pi$
$449$	−20.7419			−0.978869			−0.489434	+	0.872040i	$0.662797\pi$
$450$		0			0
$451$	−4.10654	−	4.10654i	−0.193370	−	0.193370i
$452$	18.6047	+	17.6603i	0.875090	+	0.830670i
$453$		0			0
$454$	25.3156	−	10.8743i	1.18812	−	0.510356i
$455$		−	19.9488i		−	0.935214i
$456$		0			0
$457$		−	3.83369i		−	0.179333i	−0.995972	−	0.0896663i	$-0.971420\pi$
$457$		−	3.83369i		−	0.179333i	0.995972	−	0.0896663i	$-0.0285801\pi$
$458$	−6.50588	−	15.1459i	−0.304000	−	0.707720i
$459$		0			0
$460$	−0.675304	−	25.9320i	−0.0314862	−	1.20908i
$461$	11.8553	+	11.8553i	0.552155	+	0.552155i	0.927062	−	0.374908i	$-0.122326\pi$
$461$	11.8553	+	11.8553i	0.552155	+	0.552155i	−0.374908	+	0.927062i	$0.622326\pi$
$462$		0			0
$463$	6.91516			0.321375			0.160687	−	0.987005i	$-0.448629\pi$
$463$	6.91516			0.321375			0.160687	+	0.987005i	$0.448629\pi$
$464$	−1.96968	+	2.18629i	−0.0914403	+	0.101496i
$465$		0			0
$466$	−7.23613	−	2.88753i	−0.335207	−	0.133762i
$467$	18.7210	+	18.7210i	0.866304	+	0.866304i	0.992061	−	0.125757i	$-0.0401360\pi$
$467$	18.7210	+	18.7210i	0.866304	+	0.866304i	−0.125757	+	0.992061i	$0.540136\pi$
$468$		0			0
$469$	−18.6645	+	18.6645i	−0.861845	+	0.861845i
$470$	−3.75502	−	8.74179i	−0.173206	−	0.403229i
$471$		0			0
$472$	10.1284	−	27.4360i	0.466199	−	1.26284i
$473$			9.65397i			0.443890i
$474$		0			0
$475$	−3.67177	+	3.67177i	−0.168472	+	0.168472i
$476$	19.8505	−	20.9120i	0.909844	−	0.958499i
$477$		0			0
$478$	11.8831	−	29.7790i	0.543521	−	1.36206i
$479$	18.0704			0.825657			0.412829	−	0.910809i	$-0.364541\pi$
$479$	18.0704			0.825657			0.412829	+	0.910809i	$0.364541\pi$
$480$		0			0
$481$	7.65502			0.349039
$482$	−0.0279645	+	0.0700788i	−0.00127375	+	0.00319200i
$483$		0			0
$484$	−29.3725	+	30.9432i	−1.33511	+	1.40651i
$485$	−5.92795	+	5.92795i	−0.269174	+	0.269174i
$486$		0			0
$487$		−	20.2269i		−	0.916569i	−0.888806	−	0.458284i	$-0.848464\pi$
$487$		−	20.2269i		−	0.916569i	0.888806	−	0.458284i	$-0.151536\pi$
$488$	−21.0133	−	7.75737i	−0.951226	−	0.351160i
$489$		0			0
$490$	−11.1563	−	25.9722i	−0.503991	−	1.17330i
$491$	−13.1245	+	13.1245i	−0.592300	+	0.592300i	−0.938252	−	0.345952i	$-0.887556\pi$
$491$	−13.1245	+	13.1245i	−0.592300	+	0.592300i	0.345952	+	0.938252i	$0.387556\pi$
$492$		0			0
$493$	1.70413	+	1.70413i	0.0767502	+	0.0767502i
$494$	8.01128	+	3.19685i	0.360444	+	0.143833i
$495$		0			0
$496$	2.07584	+	39.8296i	0.0932081	+	1.78840i
$497$	39.6881			1.78025
$498$		0			0
$499$	−25.4295	−	25.4295i	−1.13838	−	1.13838i	−0.988741	−	0.149640i	$-0.952189\pi$
$499$	−25.4295	−	25.4295i	−1.13838	−	1.13838i	−0.149640	−	0.988741i	$-0.547811\pi$
$500$	−0.621677	−	23.8726i	−0.0278022	−	1.06762i
$501$		0			0
$502$	9.01121	+	20.9783i	0.402190	+	0.936309i
$503$		−	24.5234i		−	1.09344i	−0.837314	−	0.546722i	$-0.815875\pi$
$503$		−	24.5234i		−	1.09344i	0.837314	−	0.546722i	$-0.184125\pi$
$504$		0			0
$505$			8.24312i			0.366814i
$506$	−59.2945	+	25.4698i	−2.63596	+	1.13227i
$507$		0			0
$508$	−1.98715	−	1.88628i	−0.0881653	−	0.0836900i
$509$	−12.2303	−	12.2303i	−0.542099	−	0.542099i	0.382045	−	0.924144i	$-0.375220\pi$
$509$	−12.2303	−	12.2303i	−0.542099	−	0.542099i	−0.924144	+	0.382045i	$0.875220\pi$
$510$		0			0
$511$	10.8178			0.478550
$512$	6.15615	−	21.7739i	0.272066	−	0.962279i
$513$		0			0
$514$	−6.75394	+	16.9253i	−0.297904	+	0.746545i
$515$	11.8690	+	11.8690i	0.523012	+	0.523012i
$516$		0			0
$517$	−16.7362	+	16.7362i	−0.736056	+	0.736056i
$518$	15.6076	−	6.70423i	0.685759	−	0.294567i
$519$		0			0
$520$	−11.6447	+	5.36523i	−0.510655	+	0.235281i
$521$		−	2.65067i		−	0.116128i	−0.998313	−	0.0580640i	$-0.981507\pi$
$521$		−	2.65067i		−	0.116128i	0.998313	−	0.0580640i	$-0.0184927\pi$
$522$		0			0
$523$	22.6853	−	22.6853i	0.991961	−	0.991961i	−0.00800717	−	0.999968i	$-0.502549\pi$
$523$	22.6853	−	22.6853i	0.991961	−	0.991961i	0.999968	+	0.00800717i	$0.00254879\pi$
$524$	−0.495472	−	19.0263i	−0.0216448	−	0.831169i
$525$		0			0
$526$	−34.4301	−	13.7391i	−1.50122	−	0.599053i
$527$	32.6638			1.42286
$528$		0			0
$529$	−41.4027			−1.80012
$530$	3.26604	+	1.30329i	0.141868	+	0.0566113i
$531$		0			0
$532$	19.1338	−	0.498270i	0.829553	−	0.0216027i
$533$	−2.02556	+	2.02556i	−0.0877368	+	0.0877368i
$534$		0			0
$535$			9.11757i			0.394187i
$536$	15.9148	+	5.87520i	0.687415	+	0.253770i
$537$		0			0
$538$	−24.1480	+	10.3727i	−1.04110	+	0.447201i
$539$	−49.7238	+	49.7238i	−2.14176	+	2.14176i
$540$		0			0
$541$	23.2345	+	23.2345i	0.998930	+	0.998930i	0.999999	−	0.00106969i	$-0.000340495\pi$
$541$	23.2345	+	23.2345i	0.998930	+	0.998930i	−0.00106969	+	0.999999i	$0.500340\pi$
$542$	5.37188	−	13.4619i	0.230742	−	0.578238i
$543$		0			0
$544$	−17.5457	−	5.96304i	−0.752267	−	0.255663i
$545$	−3.21109			−0.137548
$546$		0			0
$547$	20.8516	+	20.8516i	0.891551	+	0.891551i	0.994669	−	0.103118i	$-0.0328819\pi$
$547$	20.8516	+	20.8516i	0.891551	+	0.891551i	−0.103118	+	0.994669i	$0.532882\pi$
$548$	−30.6433	+	32.2820i	−1.30902	+	1.37902i
$549$		0			0
$550$	−17.6427	+	7.57841i	−0.752289	+	0.323144i
$551$			1.59983i			0.0681549i
$552$		0			0
$553$		−	0.168584i		−	0.00716891i
$554$	13.6320	+	31.7357i	0.579169	+	1.34832i
$555$		0			0
$556$	21.9814	−	0.572428i	0.932221	−	0.0242763i
$557$	−25.1470	−	25.1470i	−1.06551	−	1.06551i	−0.997698	−	0.0678126i	$-0.978398\pi$
$557$	−25.1470	−	25.1470i	−1.06551	−	1.06551i	−0.0678126	−	0.997698i	$-0.521602\pi$
$558$		0			0
$559$	4.76184			0.201405
$560$	−19.0433	+	21.1374i	−0.804725	+	0.893218i
$561$		0			0
$562$	−17.1849	−	6.85754i	−0.724903	−	0.289268i
$563$	8.46453	+	8.46453i	0.356737	+	0.356737i	0.862609	−	0.505871i	$-0.168829\pi$
$563$	8.46453	+	8.46453i	0.356737	+	0.356737i	−0.505871	+	0.862609i	$0.668829\pi$
$564$		0			0
$565$	−14.6580	+	14.6580i	−0.616667	+	0.616667i
$566$	−4.69782	−	10.9367i	−0.197464	−	0.459702i
$567$		0			0
$568$	−10.6741	−	23.1671i	−0.447875	−	0.972071i
$569$			0.889656i			0.0372963i	0.999826	+	0.0186482i	$0.00593624\pi$
$569$			0.889656i			0.0372963i	−0.999826	+	0.0186482i	$0.994064\pi$
$570$		0			0
$571$	−8.51710	+	8.51710i	−0.356429	+	0.356429i	−0.862495	−	0.506066i	$-0.831099\pi$
$571$	−8.51710	+	8.51710i	−0.356429	+	0.356429i	0.506066	+	0.862495i	$0.331099\pi$
$572$	23.1332	+	21.9589i	0.967246	+	0.918148i
$573$		0			0
$574$	−2.35589	+	5.90384i	−0.0983328	+	0.246422i
$575$	−19.1627			−0.799139
$576$		0			0
$577$	4.88759			0.203473			0.101736	−	0.994811i	$-0.467560\pi$
$577$	4.88759			0.203473			0.101736	+	0.994811i	$0.467560\pi$
$578$	3.28555	−	8.23356i	0.136661	−	0.342471i
$579$		0			0
$580$	−1.72472	−	1.63718i	−0.0716152	−	0.0679800i
$581$	37.8964	−	37.8964i	1.57221	−	1.57221i
$582$		0			0
$583$		−	8.74799i		−	0.362305i
$584$	−2.90944	−	6.31466i	−0.120394	−	0.261303i
$585$		0			0
$586$	−6.44372	−	15.0012i	−0.266188	−	0.619692i
$587$	28.4721	−	28.4721i	1.17517	−	1.17517i	0.194209	−	0.980960i	$-0.437786\pi$
$587$	28.4721	−	28.4721i	1.17517	−	1.17517i	0.980960	−	0.194209i	$-0.0622139\pi$
$588$		0			0
$589$	15.3323	+	15.3323i	0.631755	+	0.631755i
$590$	21.9507	+	8.75929i	0.903697	+	0.360614i
$591$		0			0
$592$	−8.11113	−	7.30753i	−0.333365	−	0.300338i
$593$	11.7815			0.483808			0.241904	−	0.970300i	$-0.422228\pi$
$593$	11.7815			0.483808			0.241904	+	0.970300i	$0.422228\pi$
$594$		0			0
$595$	16.4758	+	16.4758i	0.675444	+	0.675444i
$596$	−10.8636	+	0.282903i	−0.444990	+	0.0115882i
$597$		0			0
$598$	12.5631	+	29.2471i	0.513742	+	1.19600i
$599$		−	15.9520i		−	0.651780i	−0.945408	−	0.325890i	$-0.894336\pi$
$599$		−	15.9520i		−	0.651780i	0.945408	−	0.325890i	$-0.105664\pi$
$600$		0			0
$601$			25.0500i			1.02181i	0.859637	+	0.510905i	$0.170690\pi$
$601$			25.0500i			1.02181i	−0.859637	+	0.510905i	$0.829310\pi$
$602$	9.70880	−	4.17040i	0.395701	−	0.169973i
$603$		0			0
$604$	5.45493	−	5.74663i	0.221958	−	0.233827i
$605$	−24.3791	−	24.3791i	−0.991152	−	0.991152i
$606$		0			0
$607$	−26.5877			−1.07916			−0.539580	−	0.841934i	$-0.681417\pi$
$607$	−26.5877			−1.07916			−0.539580	+	0.841934i	$0.681417\pi$
$608$	−5.43688	−	11.0349i	−0.220494	−	0.447526i
$609$		0			0
$610$	6.70875	−	16.8121i	0.271629	−	0.680701i
$611$	8.25516	+	8.25516i	0.333968	+	0.333968i
$612$		0			0
$613$	6.29751	−	6.29751i	0.254354	−	0.254354i	−0.568399	−	0.822753i	$-0.692437\pi$
$613$	6.29751	−	6.29751i	0.254354	−	0.254354i	0.822753	+	0.568399i	$0.192437\pi$
$614$	16.3370	−	7.01754i	0.659308	−	0.283205i
$615$		0			0
$616$	66.3971	+	24.5115i	2.67521	+	0.987597i
$617$		−	14.0208i		−	0.564456i	−0.959347	−	0.282228i	$-0.908927\pi$
$617$		−	14.0208i		−	0.564456i	0.959347	−	0.282228i	$-0.0910735\pi$
$618$		0			0
$619$	−3.36830	+	3.36830i	−0.135383	+	0.135383i	−0.771551	−	0.636168i	$-0.780519\pi$
$619$	−3.36830	+	3.36830i	−0.135383	+	0.135383i	0.636168	+	0.771551i	$0.280519\pi$
$620$	−32.2194	+	0.839039i	−1.29396	+	0.0336966i
$621$		0			0
$622$	34.3956	+	13.7253i	1.37914	+	0.550335i
$623$	46.7855			1.87442
$624$		0			0
$625$	7.35909			0.294363
$626$	11.3054	+	4.51134i	0.451854	+	0.180309i
$627$		0			0
$628$	0.295178	+	11.3350i	0.0117789	+	0.452314i
$629$	−6.32233	+	6.32233i	−0.252088	+	0.252088i
$630$		0			0
$631$			15.7665i			0.627655i	0.949480	+	0.313827i	$0.101611\pi$
$631$			15.7665i			0.627655i	−0.949480	+	0.313827i	$0.898389\pi$
$632$	−0.0984074	+	0.0453406i	−0.00391444	+	0.00180355i
$633$		0			0
$634$	20.2308	−	8.69011i	0.803468	−	0.345128i
$635$	1.56561	−	1.56561i	0.0621292	−	0.0621292i
$636$		0			0
$637$	24.5264	+	24.5264i	0.971771	+	0.971771i
$638$	−2.19256	+	5.49455i	−0.0868044	+	0.217531i
$639$		0			0
$640$	17.4602	+	5.43122i	0.690176	+	0.214688i
$641$	36.9165			1.45811			0.729057	−	0.684453i	$-0.239959\pi$
$641$	36.9165			1.45811			0.729057	+	0.684453i	$0.239959\pi$
$642$		0			0
$643$	29.1072	+	29.1072i	1.14787	+	1.14787i	0.986970	+	0.160904i	$0.0514410\pi$
$643$	29.1072	+	29.1072i	1.14787	+	1.14787i	0.160904	+	0.986970i	$0.448559\pi$
$644$	51.2290	+	48.6285i	2.01870	+	1.91623i
$645$		0			0
$646$	−9.25686	+	3.97627i	−0.364206	+	0.156444i
$647$		−	24.5298i		−	0.964364i	−0.876071	−	0.482182i	$-0.839844\pi$
$647$		−	24.5298i		−	0.964364i	0.876071	−	0.482182i	$-0.160156\pi$
$648$		0			0
$649$		−	58.7944i		−	2.30788i
$650$	3.73807	+	8.70232i	0.146619	+	0.341333i
$651$		0			0
$652$	1.09325	+	41.9811i	0.0428148	+	1.64410i
$653$	−12.2674	−	12.2674i	−0.480060	−	0.480060i	0.425091	−	0.905151i	$-0.360242\pi$
$653$	−12.2674	−	12.2674i	−0.480060	−	0.480060i	−0.905151	+	0.425091i	$0.860242\pi$
$654$		0			0
$655$	15.3806			0.600969
$656$	4.07986	−	0.212635i	0.159292	−	0.00830200i
$657$		0			0
$658$	24.0610	+	9.60140i	0.937997	+	0.374301i
$659$	−28.8769	−	28.8769i	−1.12488	−	1.12488i	−0.990997	−	0.133886i	$-0.957254\pi$
$659$	−28.8769	−	28.8769i	−1.12488	−	1.12488i	−0.133886	−	0.990997i	$-0.542746\pi$
$660$		0			0
$661$	29.5186	−	29.5186i	1.14814	−	1.14814i	0.161222	−	0.986918i	$-0.448456\pi$
$661$	29.5186	−	29.5186i	1.14814	−	1.14814i	0.986918	−	0.161222i	$-0.0515435\pi$
$662$	−16.1624	−	37.6264i	−0.628168	−	1.46239i
$663$		0			0
$664$	−32.3135	−	11.9290i	−1.25401	−	0.462936i
$665$			15.4674i			0.599801i
$666$		0			0
$667$	−4.17468	+	4.17468i	−0.161644	+	0.161644i
$668$	14.5666	−	15.3455i	0.563597	−	0.593735i
$669$		0			0
$670$	−5.08100	+	12.7330i	−0.196296	+	0.491917i
$671$	−45.0307			−1.73839
$672$		0			0
$673$	−29.9500			−1.15449			−0.577243	−	0.816572i	$-0.695872\pi$
$673$	−29.9500			−1.15449			−0.577243	+	0.816572i	$0.695872\pi$
$674$	9.54770	−	23.9265i	0.367764	−	0.921614i
$675$		0			0
$676$	−7.06866	+	7.44666i	−0.271872	+	0.286410i
$677$	−30.3970	+	30.3970i	−1.16825	+	1.16825i	−0.185633	+	0.982619i	$0.559434\pi$
$677$	−30.3970	+	30.3970i	−1.16825	+	1.16825i	−0.982619	+	0.185633i	$0.940566\pi$
$678$		0			0
$679$		−	22.8270i		−	0.876021i
$680$	5.18627	−	14.0486i	0.198884	−	0.538740i
$681$		0			0
$682$	31.6453	+	73.6710i	1.21176	+	2.82101i
$683$	−14.1557	+	14.1557i	−0.541653	+	0.541653i	−0.924013	−	0.382360i	$-0.875111\pi$
$683$	−14.1557	+	14.1557i	−0.541653	+	0.541653i	0.382360	+	0.924013i	$0.375111\pi$
$684$		0			0
$685$	−25.4339	−	25.4339i	−0.971779	−	0.971779i
$686$	31.0233	+	12.3796i	1.18447	+	0.472656i
$687$		0			0
$688$	−5.04557	−	4.54569i	−0.192360	−	0.173303i
$689$	−4.31497			−0.164387
$690$		0			0
$691$	9.52007	+	9.52007i	0.362161	+	0.362161i	0.864608	−	0.502447i	$-0.167567\pi$
$691$	9.52007	+	9.52007i	0.362161	+	0.362161i	−0.502447	+	0.864608i	$0.667567\pi$
$692$	0.618411	+	23.7472i	0.0235085	+	0.902734i
$693$		0			0
$694$	−3.50458	−	8.15876i	−0.133032	−	0.309702i
$695$			17.7694i			0.674034i
$696$		0			0
$697$		−	3.34585i		−	0.126733i
$698$	−19.0187	+	8.16944i	−0.719867	+	0.309218i
$699$		0			0
$700$	15.2429	+	14.4691i	0.576127	+	0.546882i
$701$	−28.7521	−	28.7521i	−1.08595	−	1.08595i	−0.995941	−	0.0900099i	$-0.971310\pi$
$701$	−28.7521	−	28.7521i	−1.08595	−	1.08595i	−0.0900099	−	0.995941i	$-0.528690\pi$
$702$		0			0
$703$	−5.93536			−0.223856
$704$	−3.54938	−	45.3503i	−0.133772	−	1.70921i
$705$		0			0
$706$	−13.4114	+	33.6089i	−0.504744	+	1.26489i
$707$	−15.8711	−	15.8711i	−0.596894	−	0.596894i
$708$		0			0
$709$	−19.2256	+	19.2256i	−0.722034	+	0.722034i	−0.969019	−	0.246985i	$-0.920560\pi$
$709$	−19.2256	+	19.2256i	−0.722034	+	0.722034i	0.246985	+	0.969019i	$0.420560\pi$
$710$	18.9398	−	8.13555i	0.710797	−	0.305322i
$711$		0			0
$712$	−12.5829	−	27.3101i	−0.471566	−	1.02349i
$713$			80.0179i			2.99669i
$714$		0			0
$715$	−18.2259	+	18.2259i	−0.681608	+	0.681608i
$716$	0.217967	+	8.37003i	0.00814581	+	0.312803i
$717$		0			0
$718$	6.11904	+	2.44176i	0.228360	+	0.0911257i
$719$	15.5795			0.581017			0.290508	−	0.956872i	$-0.406176\pi$
$719$	15.5795			0.581017			0.290508	+	0.956872i	$0.406176\pi$
$720$		0			0
$721$	−45.7046			−1.70213
$722$	18.7449	+	7.48001i	0.697611	+	0.278377i
$723$		0			0
$724$	10.6349	−	0.276948i	0.395243	−	0.0102927i
$725$	−1.24215	+	1.24215i	−0.0461324	+	0.0461324i
$726$		0			0
$727$			36.2519i			1.34451i	0.740320	+	0.672255i	$0.234674\pi$
$727$			36.2519i			1.34451i	−0.740320	+	0.672255i	$0.765326\pi$
$728$	12.0904	−	32.7505i	0.448099	−	1.21381i
$729$		0			0
$730$	5.16242	−	2.21751i	0.191070	−	0.0820737i
$731$	−3.93284	+	3.93284i	−0.145461	+	0.145461i
$732$		0			0
$733$	2.83390	+	2.83390i	0.104673	+	0.104673i	0.757504	−	0.652831i	$-0.226419\pi$
$733$	2.83390	+	2.83390i	0.104673	+	0.104673i	−0.652831	+	0.757504i	$0.726419\pi$
$734$	10.9542	−	27.4513i	0.404328	−	1.01324i
$735$		0			0
$736$	14.6079	−	42.9825i	0.538455	−	1.58436i
$737$	34.1049			1.25627
$738$		0			0
$739$	10.1067	+	10.1067i	0.371782	+	0.371782i	0.868126	−	0.496344i	$-0.165325\pi$
$739$	10.1067	+	10.1067i	0.371782	+	0.371782i	−0.496344	+	0.868126i	$0.665325\pi$
$740$	6.07392	−	6.39873i	0.223282	−	0.235222i
$741$		0			0
$742$	−8.79767	+	3.77902i	−0.322973	+	0.138732i
$743$			29.6504i			1.08777i	0.839161	+	0.543884i	$0.183047\pi$
$743$			29.6504i			1.08777i	−0.839161	+	0.543884i	$0.816953\pi$
$744$		0			0
$745$		−	8.78196i		−	0.321746i
$746$	17.5340	+	40.8196i	0.641965	+	1.49451i
$747$		0			0
$748$	−37.2418	+	0.969829i	−1.36170	+	0.0354605i
$749$	−17.5547	−	17.5547i	−0.641436	−	0.641436i
$750$		0			0
$751$	3.55537			0.129737			0.0648687	−	0.997894i	$-0.479337\pi$
$751$	3.55537			0.129737			0.0648687	+	0.997894i	$0.479337\pi$
$752$	−0.866591	−	16.6274i	−0.0316013	−	0.606341i
$753$		0			0
$754$	2.71020	+	1.08149i	0.0986997	+	0.0393854i
$755$	4.52758	+	4.52758i	0.164776	+	0.164776i
$756$		0			0
$757$	22.4898	−	22.4898i	0.817407	−	0.817407i	−0.168325	−	0.985732i	$-0.553836\pi$
$757$	22.4898	−	22.4898i	0.817407	−	0.817407i	0.985732	+	0.168325i	$0.0538358\pi$
$758$	−10.4453	−	24.3169i	−0.379390	−	0.883229i
$759$		0			0
$760$	9.02880	−	4.15996i	0.327509	−	0.150898i
$761$			25.4350i			0.922017i	0.887396	+	0.461009i	$0.152512\pi$
$761$			25.4350i			0.922017i	−0.887396	+	0.461009i	$0.847488\pi$
$762$		0			0
$763$	6.18255	−	6.18255i	0.223823	−	0.223823i
$764$	27.7547	+	26.3459i	1.00413	+	0.953161i
$765$		0			0
$766$	−7.17325	+	17.9761i	−0.259180	+	0.649504i
$767$	−29.0005			−1.04715
$768$		0			0
$769$	47.4685			1.71176			0.855879	−	0.517176i	$-0.173017\pi$
$769$	47.4685			1.71176			0.855879	+	0.517176i	$0.173017\pi$
$770$	−21.1981	+	53.1223i	−0.763926	+	1.91439i
$771$		0			0
$772$	−27.2732	−	25.8888i	−0.981584	−	0.931758i
$773$	2.12004	−	2.12004i	0.0762527	−	0.0762527i	−0.667952	−	0.744205i	$-0.732829\pi$
$773$	2.12004	−	2.12004i	0.0762527	−	0.0762527i	0.744205	+	0.667952i	$0.232829\pi$
$774$		0			0
$775$			23.8089i			0.855240i
$776$	−13.3248	+	6.13933i	−0.478333	+	0.220389i
$777$		0			0
$778$	−2.04965	−	4.77164i	−0.0734836	−	0.171072i
$779$	1.57053	−	1.57053i	0.0562701	−	0.0562701i
$780$		0			0
$781$	−36.2603	−	36.2603i	−1.29749	−	1.29749i
$782$	−34.5313	−	13.7795i	−1.23484	−	0.492753i
$783$		0			0
$784$	−2.57468	−	49.4008i	−0.0919527	−	1.76431i
$785$	−9.16300			−0.327042
$786$		0			0
$787$	0.616222	+	0.616222i	0.0219659	+	0.0219659i	0.718004	−	0.696039i	$-0.245056\pi$
$787$	0.616222	+	0.616222i	0.0219659	+	0.0219659i	−0.696039	+	0.718004i	$0.745056\pi$
$788$	9.40150	−	0.244828i	0.334915	−	0.00872164i
$789$		0			0
$790$	−0.0345576	−	0.0804509i	−0.00122950	−	0.00286232i
$791$		−	56.4443i		−	2.00693i
$792$		0			0
$793$			22.2115i			0.788753i
$794$	32.4678	−	13.9465i	1.15224	−	0.494943i
$795$		0			0
$796$	6.80471	−	7.16859i	0.241186	−	0.254084i
$797$	−7.38372	−	7.38372i	−0.261545	−	0.261545i	0.564137	−	0.825681i	$-0.309209\pi$
$797$	−7.38372	−	7.38372i	−0.261545	−	0.261545i	−0.825681	+	0.564137i	$0.809209\pi$
$798$		0			0
$799$	−13.6360			−0.482406
$800$	4.34650	−	12.7892i	0.153672	−	0.452167i
$801$		0			0
$802$	2.76456	−	6.92796i	0.0976198	−	0.244635i
$803$	−9.88346	−	9.88346i	−0.348780	−	0.348780i
$804$		0			0
$805$	−40.3616	+	40.3616i	−1.42256	+	1.42256i
$806$	36.3384	−	15.6091i	1.27997	−	0.549807i
$807$		0			0
$808$	−4.99590	+	13.5330i	−0.175755	+	0.476088i
$809$			41.6071i			1.46283i	0.681934	+	0.731413i	$0.261139\pi$
$809$			41.6071i			1.46283i	−0.681934	+	0.731413i	$0.738861\pi$
$810$		0			0
$811$	4.26526	−	4.26526i	0.149773	−	0.149773i	−0.628243	−	0.778017i	$-0.716226\pi$
$811$	4.26526	−	4.26526i	0.149773	−	0.149773i	0.778017	+	0.628243i	$0.216226\pi$
$812$	6.47291	−	0.168564i	0.227155	−	0.00591543i
$813$		0			0
$814$	−20.3848	−	8.13442i	−0.714487	−	0.285111i
$815$	−33.9368			−1.18875
$816$		0			0
$817$	−3.69212			−0.129171
$818$	−34.9374	−	13.9415i	−1.22156	−	0.487455i
$819$		0			0
$820$	0.0859453	+	3.30033i	0.00300134	+	0.115253i
$821$	−5.03247	+	5.03247i	−0.175634	+	0.175634i	−0.789450	−	0.613815i	$-0.789634\pi$
$821$	−5.03247	+	5.03247i	−0.175634	+	0.175634i	0.613815	+	0.789450i	$0.289634\pi$
$822$		0			0
$823$		−	15.8921i		−	0.553964i	−0.960875	−	0.276982i	$-0.910666\pi$
$823$		−	15.8921i		−	0.553964i	0.960875	−	0.276982i	$-0.0893343\pi$
$824$	12.2923	+	26.6792i	0.428221	+	0.929413i
$825$		0			0
$826$	−59.1283	+	25.3985i	−2.05734	+	0.883725i
$827$	−4.30482	+	4.30482i	−0.149693	+	0.149693i	−0.777981	−	0.628288i	$-0.783756\pi$
$827$	−4.30482	+	4.30482i	−0.149693	+	0.149693i	0.628288	+	0.777981i	$0.283756\pi$
$828$		0			0
$829$	−20.3218	−	20.3218i	−0.705804	−	0.705804i	0.259846	−	0.965650i	$-0.416328\pi$
$829$	−20.3218	−	20.3218i	−0.705804	−	0.705804i	−0.965650	+	0.259846i	$0.916328\pi$
$830$	10.3165	−	25.8531i	0.358091	−	0.897373i
$831$		0			0
$832$	−22.3692	+	1.75074i	−0.775511	+	0.0606960i
$833$	−40.5130			−1.40369
$834$		0			0
$835$	12.0902	+	12.0902i	0.418399	+	0.418399i
$836$	−17.9364	−	17.0260i	−0.620344	−	0.588855i
$837$		0			0
$838$	36.4837	−	15.6715i	1.26031	−	0.541364i
$839$			18.4813i			0.638046i	0.947747	+	0.319023i	$0.103355\pi$
$839$			18.4813i			0.638046i	−0.947747	+	0.319023i	$0.896645\pi$
$840$		0			0
$841$		−	28.4588i		−	0.981337i
$842$	4.58743	+	10.6797i	0.158093	+	0.368045i
$843$		0			0
$844$	−1.22741	−	47.1332i	−0.0422494	−	1.62239i
$845$	−5.86697	−	5.86697i	−0.201830	−	0.201830i
$846$		0			0
$847$	93.8779			3.22568
$848$	4.57206	+	4.11910i	0.157005	+	0.141450i
$849$		0			0
$850$	−10.2746	−	4.10001i	−0.352416	−	0.140629i
$851$	−15.4881	−	15.4881i	−0.530925	−	0.530925i
$852$		0			0
$853$	8.16310	−	8.16310i	0.279499	−	0.279499i	−0.553410	−	0.832909i	$-0.686674\pi$
$853$	8.16310	−	8.16310i	0.279499	−	0.279499i	0.832909	+	0.553410i	$0.186674\pi$
$854$	19.4527	+	45.2864i	0.665658	+	1.54967i
$855$		0			0
$856$	−5.52588	+	14.9686i	−0.188871	+	0.511615i
$857$		−	33.5755i		−	1.14692i	−0.819234	−	0.573459i	$-0.805601\pi$
$857$		−	33.5755i		−	1.14692i	0.819234	−	0.573459i	$-0.194399\pi$
$858$		0			0
$859$	20.3288	−	20.3288i	0.693609	−	0.693609i	−0.269415	−	0.963024i	$-0.586830\pi$
$859$	20.3288	−	20.3288i	0.693609	−	0.693609i	0.963024	+	0.269415i	$0.0868305\pi$
$860$	3.77832	−	3.98036i	0.128839	−	0.135729i
$861$		0			0
$862$	−13.7052	+	34.3452i	−0.466802	+	1.16980i
$863$	14.3176			0.487375			0.243688	−	0.969854i	$-0.421643\pi$
$863$	14.3176			0.487375			0.243688	+	0.969854i	$0.421643\pi$
$864$		0			0
$865$	−19.1969			−0.652713
$866$	−20.5863	+	51.5893i	−0.699553	+	1.75307i
$867$		0			0
$868$	60.4190	−	63.6499i	2.05076	−	2.16042i
$869$	−0.154023	+	0.154023i	−0.00522489	+	0.00522489i
$870$		0			0
$871$		−	16.8223i		−	0.570002i
$872$	−5.27174	−	1.94614i	−0.178524	−	0.0659048i
$873$		0			0
$874$	−9.74084	−	22.6769i	−0.329489	−	0.767058i
$875$	−37.1564	+	37.1564i	−1.25611	+	1.25611i
$876$		0			0
$877$	−3.60409	−	3.60409i	−0.121702	−	0.121702i	0.643633	−	0.765334i	$-0.277426\pi$
$877$	−3.60409	−	3.60409i	−0.121702	−	0.121702i	−0.765334	+	0.643633i	$0.777426\pi$
$878$	−5.58546	−	2.22884i	−0.188500	−	0.0752197i
$879$		0			0
$880$	36.7103	−	1.91327i	1.23750	−	0.0644964i
$881$	6.93242			0.233559			0.116780	−	0.993158i	$-0.462743\pi$
$881$	6.93242			0.233559			0.116780	+	0.993158i	$0.462743\pi$
$882$		0			0
$883$	9.50145	+	9.50145i	0.319749	+	0.319749i	0.848671	−	0.528922i	$-0.177403\pi$
$883$	9.50145	+	9.50145i	0.319749	+	0.319749i	−0.528922	+	0.848671i	$0.677403\pi$
$884$	0.478371	+	18.3696i	0.0160893	+	0.617837i
$885$		0			0
$886$	−11.2868	−	26.2761i	−0.379189	−	0.882762i
$887$		−	16.8549i		−	0.565933i	−0.959130	−	0.282967i	$-0.908681\pi$
$887$		−	16.8549i		−	0.565933i	0.959130	−	0.282967i	$-0.0913186\pi$
$888$		0			0
$889$			6.02875i			0.202198i
$890$	22.3268	−	9.59043i	0.748395	−	0.321472i
$891$		0			0
$892$	−12.2413	−	11.6200i	−0.409870	−	0.389065i
$893$	−6.40068	−	6.40068i	−0.214191	−	0.214191i
$894$		0			0
$895$	−6.76619			−0.226169
$896$	−44.0746	+	23.1603i	−1.47243	+	0.773732i
$897$		0			0
$898$	10.8717	−	27.2444i	0.362793	−	0.909156i
$899$	5.18688	+	5.18688i	0.172992	+	0.172992i
$900$		0			0
$901$	3.56376	−	3.56376i	0.118726	−	0.118726i
$902$	7.54635	−	3.24152i	0.251266	−	0.107931i
$903$		0			0
$904$	−32.9482	+	15.1807i	−1.09584	+	0.504902i
$905$			8.59709i			0.285777i
$906$		0			0
$907$	28.0494	−	28.0494i	0.931367	−	0.931367i	−0.0664249	−	0.997791i	$-0.521159\pi$
$907$	28.0494	−	28.0494i	0.931367	−	0.931367i	0.997791	+	0.0664249i	$0.0211593\pi$
$908$	1.01436	+	38.9517i	0.0336626	+	1.29266i
$909$		0			0
$910$	26.2027	+	10.4560i	0.868611	+	0.346613i
$911$	−26.0100			−0.861748			−0.430874	−	0.902412i	$-0.641795\pi$
$911$	−26.0100			−0.861748			−0.430874	+	0.902412i	$0.641795\pi$
$912$		0			0
$913$	−69.2467			−2.29173
$914$	5.03555	+	2.00940i	0.166561	+	0.0664651i
$915$		0			0
$916$	23.3041	−	0.606870i	0.769988	−	0.0200516i
$917$	−29.6134	+	29.6134i	−0.977919	+	0.977919i
$918$		0			0
$919$			44.5283i			1.46885i	0.678688	+	0.734426i	$0.262549\pi$
$919$			44.5283i			1.46885i	−0.678688	+	0.734426i	$0.737451\pi$
$920$	34.4155	+	12.7050i	1.13465	+	0.418872i
$921$		0			0
$922$	−21.7857	+	9.35801i	−0.717474	+	0.308190i
$923$	−17.8855	+	17.8855i	−0.588707	+	0.588707i
$924$		0			0
$925$	−4.60839	−	4.60839i	−0.151523	−	0.151523i
$926$	−3.62453	+	9.08305i	−0.119109	+	0.298487i
$927$		0			0
$928$	−1.83929	−	3.73310i	−0.0603775	−	0.122545i
$929$	5.00362			0.164163			0.0820817	−	0.996626i	$-0.473843\pi$
$929$	5.00362			0.164163			0.0820817	+	0.996626i	$0.473843\pi$
$930$		0			0
$931$	−19.0167	−	19.0167i	−0.623246	−	0.623246i
$932$	7.58552	−	7.99116i	0.248472	−	0.261759i
$933$		0			0
$934$	−34.4024	+	14.7775i	−1.12568	+	0.483535i
$935$		−	30.1057i		−	0.984562i
$936$		0			0
$937$		−	0.197040i		−	0.00643700i	−0.999995	−	0.00321850i	$-0.998976\pi$
$937$		−	0.197040i		−	0.00643700i	0.999995	−	0.00321850i	$-0.00102448\pi$
$938$	−14.7329	−	34.2986i	−0.481046	−	1.11989i
$939$		0			0
$940$	13.4505	−	0.350269i	0.438706	−	0.0114245i
$941$	−21.0406	−	21.0406i	−0.685902	−	0.685902i	0.275421	−	0.961324i	$-0.411183\pi$
$941$	−21.0406	−	21.0406i	−0.685902	−	0.685902i	−0.961324	+	0.275421i	$0.911183\pi$
$942$		0			0
$943$	8.19647			0.266914
$944$	30.7284	+	27.6840i	1.00012	+	0.901039i
$945$		0			0
$946$	−12.6805	−	5.06005i	−0.412277	−	0.164517i
$947$	−1.19798	−	1.19798i	−0.0389291	−	0.0389291i	0.687374	−	0.726303i	$-0.258763\pi$
$947$	−1.19798	−	1.19798i	−0.0389291	−	0.0389291i	−0.726303	+	0.687374i	$0.758763\pi$
$948$		0			0
$949$	−4.87504	+	4.87504i	−0.158251	+	0.158251i
$950$	−2.89833	−	6.74739i	−0.0940343	−	0.218914i
$951$		0			0
$952$	17.0634	+	37.0344i	0.553026	+	1.20029i
$953$		−	22.4857i		−	0.728383i	−0.931324	−	0.364191i	$-0.881345\pi$
$953$		−	22.4857i		−	0.728383i	0.931324	−	0.364191i	$-0.118655\pi$
$954$		0			0
$955$	−21.8670	+	21.8670i	−0.707601	+	0.707601i
$956$	32.8862	+	31.2169i	1.06362	+	1.00963i
$957$		0			0
$958$	−9.47145	+	23.7354i	−0.306009	+	0.766856i
$959$	97.9395			3.16263
$960$		0			0
$961$	68.4190			2.20706
$962$	−4.01232	+	10.0549i	−0.129362	+	0.324181i
$963$		0			0
$964$	−0.0773909	−	0.0734625i	−0.00249259	−	0.00236607i
$965$	21.4877	−	21.4877i	0.691712	−	0.691712i
$966$		0			0
$967$		−	53.3321i		−	1.71504i	−0.514447	−	0.857522i	$-0.672003\pi$
$967$		−	53.3321i		−	1.71504i	0.514447	−	0.857522i	$-0.327997\pi$
$968$	−25.2484	−	54.7993i	−0.811516	−	1.76132i
$969$		0			0
$970$	−4.67926	−	10.8934i	−0.150242	−	0.349767i
$971$	−21.5658	+	21.5658i	−0.692079	+	0.692079i	−0.962689	−	0.270610i	$-0.912775\pi$
$971$	−21.5658	+	21.5658i	−0.692079	+	0.692079i	0.270610	+	0.962689i	$0.412775\pi$
$972$		0			0
$973$	−34.2128	−	34.2128i	−1.09681	−	1.09681i
$974$	26.5680	+	10.6018i	0.851293	+	0.339703i
$975$		0			0
$976$	21.2032	−	23.5349i	0.678699	−	0.753334i
$977$	5.49655			0.175850			0.0879251	−	0.996127i	$-0.471976\pi$
$977$	5.49655			0.175850			0.0879251	+	0.996127i	$0.471976\pi$
$978$		0			0
$979$	−42.7447	−	42.7447i	−1.36613	−	1.36613i
$980$	39.9619	−	1.04066i	1.27654	−	0.0332428i
$981$		0			0
$982$	−10.3599	−	24.1181i	−0.330597	−	0.769639i
$983$			25.3192i			0.807556i	0.914857	+	0.403778i	$0.132303\pi$
$983$			25.3192i			0.807556i	−0.914857	+	0.403778i	$0.867697\pi$
$984$		0			0
$985$			7.60002i			0.242157i
$986$	−3.13158	+	1.34516i	−0.0997298	+	0.0428388i
$987$		0			0
$988$	−8.39810	+	8.84719i	−0.267179	+	0.281466i
$989$	−9.63444	−	9.63444i	−0.306357	−	0.306357i
$990$		0			0
$991$	−11.4022			−0.362203			−0.181102	−	0.983464i	$-0.557966\pi$
$991$	−11.4022			−0.362203			−0.181102	+	0.983464i	$0.557966\pi$
$992$	−53.4041	−	18.1497i	−1.69558	−	0.576255i
$993$		0			0
$994$	−20.8022	+	52.1302i	−0.659805	+	1.65347i
$995$	5.64790	+	5.64790i	0.179050	+	0.179050i
$996$		0			0
$997$	−34.2501	+	34.2501i	−1.08471	+	1.08471i	−0.0886501	+	0.996063i	$0.528255\pi$
$997$	−34.2501	+	34.2501i	−1.08471	+	1.08471i	−0.996063	+	0.0886501i	$0.971745\pi$
$998$	46.7302	−	20.0729i	1.47922	−	0.635397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.109.6	✓	32
3.2	odd	2	inner	432.2.k.d.109.11	yes	32
4.3	odd	2		1728.2.k.d.1297.11		32
12.11	even	2		1728.2.k.d.1297.6		32
16.5	even	4	inner	432.2.k.d.325.6	yes	32
16.11	odd	4		1728.2.k.d.433.11		32
48.5	odd	4	inner	432.2.k.d.325.11	yes	32
48.11	even	4		1728.2.k.d.433.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.6	✓	32	1.1	even	1	trivial
432.2.k.d.109.11	yes	32	3.2	odd	2	inner
432.2.k.d.325.6	yes	32	16.5	even	4	inner
432.2.k.d.325.11	yes	32	48.5	odd	4	inner
1728.2.k.d.433.6		32	48.11	even	4
1728.2.k.d.433.11		32	16.11	odd	4
1728.2.k.d.1297.6		32	12.11	even	2
1728.2.k.d.1297.11		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.524142 + 1.31350i) q^{2} +(-1.45055 - 1.37692i) q^{4} +(1.14284 - 1.14284i) q^{5} +4.40079i q^{7} +(2.56887 - 1.18359i) q^{8} +O(q^{10})\)	\(q+(-0.524142 + 1.31350i) q^{2} +(-1.45055 - 1.37692i) q^{4} +(1.14284 - 1.14284i) q^{5} +4.40079i q^{7} +(2.56887 - 1.18359i) q^{8} +(0.902107 + 2.10013i) q^{10} +(4.02070 - 4.02070i) q^{11} +(-1.98322 - 1.98322i) q^{13} +(-5.78043 - 2.30664i) q^{14} +(0.208190 + 3.99458i) q^{16} +3.27591 q^{17} +(1.53770 + 1.53770i) q^{19} +(-3.23134 + 0.0841487i) q^{20} +(3.17376 + 7.38860i) q^{22} +8.02513i q^{23} +2.38783i q^{25} +(3.64444 - 1.56546i) q^{26} +(6.05953 - 6.38357i) q^{28} +(0.520201 + 0.520201i) q^{29} +9.97091 q^{31} +(-5.35599 - 1.82027i) q^{32} +(-1.71704 + 4.30290i) q^{34} +(5.02940 + 5.02940i) q^{35} +(-1.92995 + 1.92995i) q^{37} +(-2.82574 + 1.21379i) q^{38} +(1.58315 - 4.28847i) q^{40} -1.02135i q^{41} +(-1.20053 + 1.20053i) q^{43} +(-11.3684 + 0.296049i) q^{44} +(-10.5410 - 4.20631i) q^{46} -4.16250 q^{47} -12.3670 q^{49} +(-3.13641 - 1.25156i) q^{50} +(0.146027 + 5.60749i) q^{52} +(1.08787 - 1.08787i) q^{53} -9.19003i q^{55} +(5.20874 + 11.3051i) q^{56} +(-0.955942 + 0.410623i) q^{58} +(7.31146 - 7.31146i) q^{59} +(-5.59986 - 5.59986i) q^{61} +(-5.22617 + 13.0968i) q^{62} +(5.19822 - 6.08100i) q^{64} -4.53301 q^{65} +(4.24116 + 4.24116i) q^{67} +(-4.75187 - 4.51066i) q^{68} +(-9.24222 + 3.96998i) q^{70} -9.01840i q^{71} -2.45814i q^{73} +(-1.52341 - 3.54655i) q^{74} +(-0.113223 - 4.34780i) q^{76} +(17.6943 + 17.6943i) q^{77} -0.0383076 q^{79} +(4.80309 + 4.32724i) q^{80} +(1.34154 + 0.535333i) q^{82} +(-8.61127 - 8.61127i) q^{83} +(3.74384 - 3.74384i) q^{85} +(-0.947647 - 2.20615i) q^{86} +(5.56980 - 15.0875i) q^{88} -10.6312i q^{89} +(8.72773 - 8.72773i) q^{91} +(11.0500 - 11.6409i) q^{92} +(2.18174 - 5.46744i) q^{94} +3.51469 q^{95} -5.18703 q^{97} +(6.48204 - 16.2440i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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