LMFDB - Embedded newform 900.2.k.n.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(307,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("900.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Root			$1.19252 + 0.760198i$ of defining polynomial
Character	$\chi$	$=$	900.307
Dual form			900.2.k.n.343.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760198 - 1.19252i) q^{2} +(-0.844199 - 1.81310i) q^{4} +(-0.611393 + 0.611393i) q^{7} +(-2.80391 - 0.371591i) q^{8} +O(q^{10})$	\(q+(0.760198 - 1.19252i) q^{2} +(-0.844199 - 1.81310i) q^{4} +(-0.611393 + 0.611393i) q^{7} +(-2.80391 - 0.371591i) q^{8} -5.12822i q^{11} +(-1.76156 + 1.76156i) q^{13} +(0.264318 + 1.19388i) q^{14} +(-2.57466 + 3.06123i) q^{16} +(-3.76156 - 3.76156i) q^{17} -1.22279 q^{19} +(-6.11549 - 3.89846i) q^{22} +(-1.07700 - 1.07700i) q^{23} +(0.761557 + 3.43982i) q^{26} +(1.62465 + 0.592379i) q^{28} +0.864641i q^{29} -7.81086i q^{31} +(1.69333 + 5.39747i) q^{32} +(-7.34525 + 1.62620i) q^{34} +(1.76156 + 1.76156i) q^{37} +(-0.929560 + 1.45820i) q^{38} -5.52311 q^{41} +(-6.20522 - 6.20522i) q^{43} +(-9.29797 + 4.32924i) q^{44} +(-2.10308 + 0.465611i) q^{46} +(2.29979 - 2.29979i) q^{47} +6.25240i q^{49} +(4.68098 + 1.70677i) q^{52} +(-2.62620 + 2.62620i) q^{53} +(1.94148 - 1.48710i) q^{56} +(1.03110 + 0.657298i) q^{58} +0.528636 q^{59} +4.98168 q^{61} +(-9.31460 - 5.93780i) q^{62} +(7.72384 + 2.08382i) q^{64} +(6.20522 - 6.20522i) q^{67} +(-3.64457 + 9.99558i) q^{68} +8.10243i q^{71} +(2.25240 - 2.25240i) q^{73} +(3.43982 - 0.761557i) q^{74} +(1.03228 + 2.21703i) q^{76} +(3.13536 + 3.13536i) q^{77} +15.9133 q^{79} +(-4.19866 + 6.58641i) q^{82} +(-7.95665 - 7.95665i) q^{83} +(-12.1170 + 2.68264i) q^{86} +(-1.90560 + 14.3791i) q^{88} +7.25240i q^{89} -2.15401i q^{91} +(-1.04351 + 2.86192i) q^{92} +(-0.994247 - 4.49084i) q^{94} +(-0.793833 - 0.793833i) q^{97} +(7.45610 + 4.75306i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^8	$ 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61} - 56 q^{62} - 16 q^{68} - 44 q^{73} + 8 q^{76} + 48 q^{77} - 16 q^{82} - 64 q^{86} - 60 q^{88} + 56 q^{92} + 20 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 12 * q^8 + 4 * q^13 + 12 * q^16 - 20 * q^17 - 12 * q^22 - 16 * q^26 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 40 * q^46 + 8 * q^52 + 4 * q^53 + 64 * q^56 + 20 * q^58 - 32 * q^61 - 56 * q^62 - 16 * q^68 - 44 * q^73 + 8 * q^76 + 48 * q^77 - 16 * q^82 - 64 * q^86 - 60 * q^88 + 56 * q^92 + 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.760198	−	1.19252i	0.537541	−	0.843238i
$2$	0.760198	−	1.19252i	0.537541	−	0.843238i
$3$		0			0
$3$		0			0
$4$	−0.844199	−	1.81310i	−0.422099	−	0.906550i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.611393	+	0.611393i	−0.231085	+	0.231085i	−0.813145	−	0.582060i	$-0.802247\pi$
$7$	−0.611393	+	0.611393i	−0.231085	+	0.231085i	0.582060	+	0.813145i	$0.302247\pi$
$8$	−2.80391	−	0.371591i	−0.991332	−	0.131377i
$9$		0			0
$10$		0			0
$11$		−	5.12822i		−	1.54622i	−0.634274	−	0.773108i	$-0.718701\pi$
$11$		−	5.12822i		−	1.54622i	0.634274	−	0.773108i	$-0.281299\pi$
$12$		0			0
$13$	−1.76156	+	1.76156i	−0.488568	+	0.488568i	−0.907854	−	0.419286i	$-0.862280\pi$
$13$	−1.76156	+	1.76156i	−0.488568	+	0.488568i	0.419286	+	0.907854i	$0.362280\pi$
$14$	0.264318	+	1.19388i	0.0706419	+	0.319077i
$15$		0			0
$16$	−2.57466	+	3.06123i	−0.643664	+	0.765308i
$17$	−3.76156	−	3.76156i	−0.912312	−	0.912312i	0.0841421	−	0.996454i	$-0.473185\pi$
$17$	−3.76156	−	3.76156i	−0.912312	−	0.912312i	−0.996454	+	0.0841421i	$0.973185\pi$
$18$		0			0
$19$	−1.22279			−0.280527			−0.140263	−	0.990114i	$-0.544795\pi$
$19$	−1.22279			−0.280527			−0.140263	+	0.990114i	$0.544795\pi$
$20$		0			0
$21$		0			0
$22$	−6.11549	−	3.89846i	−1.30383	−	0.831154i
$23$	−1.07700	−	1.07700i	−0.224571	−	0.224571i	0.585849	−	0.810420i	$-0.300761\pi$
$23$	−1.07700	−	1.07700i	−0.224571	−	0.224571i	−0.810420	+	0.585849i	$0.800761\pi$
$24$		0			0
$25$		0			0
$26$	0.761557	+	3.43982i	0.149354	+	0.674604i
$27$		0			0
$28$	1.62465	+	0.592379i	0.307031	+	0.111949i
$29$			0.864641i			0.160560i	0.996772	+	0.0802799i	$0.0255814\pi$
$29$			0.864641i			0.160560i	−0.996772	+	0.0802799i	$0.974419\pi$
$30$		0			0
$31$		−	7.81086i		−	1.40287i	−0.712732	−	0.701436i	$-0.752543\pi$
$31$		−	7.81086i		−	1.40287i	0.712732	−	0.701436i	$-0.247457\pi$
$32$	1.69333	+	5.39747i	0.299341	+	0.954146i
$33$		0			0
$34$	−7.34525	+	1.62620i	−1.25970	+	0.278891i
$35$		0			0
$36$		0			0
$37$	1.76156	+	1.76156i	0.289598	+	0.289598i	0.836921	−	0.547323i	$-0.184353\pi$
$37$	1.76156	+	1.76156i	0.289598	+	0.289598i	−0.547323	+	0.836921i	$0.684353\pi$
$38$	−0.929560	+	1.45820i	−0.150795	+	0.236551i
$39$		0			0
$40$		0			0
$41$	−5.52311			−0.862566			−0.431283	−	0.902217i	$-0.641939\pi$
$41$	−5.52311			−0.862566			−0.431283	+	0.902217i	$0.641939\pi$
$42$		0			0
$43$	−6.20522	−	6.20522i	−0.946288	−	0.946288i	0.0523416	−	0.998629i	$-0.483332\pi$
$43$	−6.20522	−	6.20522i	−0.946288	−	0.946288i	−0.998629	+	0.0523416i	$0.983332\pi$
$44$	−9.29797	+	4.32924i	−1.40172	+	0.652657i
$45$		0			0
$46$	−2.10308	+	0.465611i	−0.310083	+	0.0686506i
$47$	2.29979	−	2.29979i	0.335459	−	0.335459i	−0.519196	−	0.854655i	$-0.673769\pi$
$47$	2.29979	−	2.29979i	0.335459	−	0.335459i	0.854655	+	0.519196i	$0.173769\pi$
$48$		0			0
$49$			6.25240i			0.893199i
$50$		0			0
$51$		0			0
$52$	4.68098	+	1.70677i	0.649135	+	0.236687i
$53$	−2.62620	+	2.62620i	−0.360736	+	0.360736i	−0.864084	−	0.503348i	$-0.832101\pi$
$53$	−2.62620	+	2.62620i	−0.360736	+	0.360736i	0.503348	+	0.864084i	$0.332101\pi$
$54$		0			0
$55$		0			0
$56$	1.94148	−	1.48710i	0.259441	−	0.198723i
$57$		0			0
$58$	1.03110	+	0.657298i	0.135390	+	0.0863075i
$59$	0.528636			0.0688225			0.0344113	−	0.999408i	$-0.489044\pi$
$59$	0.528636			0.0688225			0.0344113	+	0.999408i	$0.489044\pi$
$60$		0			0
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	−9.31460	−	5.93780i	−1.18295	−	0.754101i
$63$		0			0
$64$	7.72384	+	2.08382i	0.965480	+	0.260477i
$65$		0			0
$66$		0			0
$67$	6.20522	−	6.20522i	0.758089	−	0.758089i	−0.217886	−	0.975974i	$-0.569916\pi$
$67$	6.20522	−	6.20522i	0.758089	−	0.758089i	0.975974	+	0.217886i	$0.0699160\pi$
$68$	−3.64457	+	9.99558i	−0.441969	+	1.21214i
$69$		0			0
$70$		0			0
$71$			8.10243i			0.961581i	0.876835	+	0.480791i	$0.159650\pi$
$71$			8.10243i			0.961581i	−0.876835	+	0.480791i	$0.840350\pi$
$72$		0			0
$73$	2.25240	−	2.25240i	0.263623	−	0.263623i	−0.562901	−	0.826524i	$-0.690315\pi$
$73$	2.25240	−	2.25240i	0.263623	−	0.263623i	0.826524	+	0.562901i	$0.190315\pi$
$74$	3.43982	−	0.761557i	0.399871	−	0.0885292i
$75$		0			0
$76$	1.03228	+	2.21703i	0.118410	+	0.254311i
$77$	3.13536	+	3.13536i	0.357307	+	0.357307i
$78$		0			0
$79$	15.9133			1.79039			0.895193	−	0.445680i	$-0.147038\pi$
$79$	15.9133			1.79039			0.895193	+	0.445680i	$0.147038\pi$
$80$		0			0
$81$		0			0
$82$	−4.19866	+	6.58641i	−0.463664	+	0.727348i
$83$	−7.95665	−	7.95665i	−0.873355	−	0.873355i	0.119481	−	0.992836i	$-0.461877\pi$
$83$	−7.95665	−	7.95665i	−0.873355	−	0.873355i	−0.992836	+	0.119481i	$0.961877\pi$
$84$		0			0
$85$		0			0
$86$	−12.1170	+	2.68264i	−1.30661	+	0.289277i
$87$		0			0
$88$	−1.90560	+	14.3791i	−0.203138	+	1.53281i
$89$			7.25240i			0.768752i	0.923177	+	0.384376i	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$		0			0
$91$		−	2.15401i		−	0.225801i
$92$	−1.04351	+	2.86192i	−0.108793	+	0.298376i
$93$		0			0
$94$	−0.994247	−	4.49084i	−0.102549	−	0.463195i
$95$		0			0
$96$		0			0
$97$	−0.793833	−	0.793833i	−0.0806015	−	0.0806015i	0.665657	−	0.746258i	$-0.268152\pi$
$97$	−0.793833	−	0.793833i	−0.0806015	−	0.0806015i	−0.746258	+	0.665657i	$0.768152\pi$
$98$	7.45610	+	4.75306i	0.753179	+	0.480131i
$99$		0			0
$100$		0			0
$101$	10.1170			1.00668			0.503341	−	0.864088i	$-0.332104\pi$
$101$	10.1170			1.00668			0.503341	+	0.864088i	$0.332104\pi$
$102$		0			0
$103$	−3.82267	−	3.82267i	−0.376659	−	0.376659i	0.493236	−	0.869895i	$-0.335814\pi$
$103$	−3.82267	−	3.82267i	−0.376659	−	0.376659i	−0.869895	+	0.493236i	$0.835814\pi$
$104$	5.59383	−	4.28467i	0.548520	−	0.420147i
$105$		0			0
$106$	1.13536	+	5.12822i	0.110276	+	0.498097i
$107$	5.51107	−	5.51107i	0.532775	−	0.532775i	−0.388622	−	0.921397i	$-0.627049\pi$
$107$	5.51107	−	5.51107i	0.532775	−	0.532775i	0.921397	+	0.388622i	$0.127049\pi$
$108$		0			0
$109$		−	7.31695i		−	0.700836i	−0.936593	−	0.350418i	$-0.886039\pi$
$109$		−	7.31695i		−	0.700836i	0.936593	−	0.350418i	$-0.113961\pi$
$110$		0			0
$111$		0			0
$112$	−0.297490	−	3.44575i	−0.0281101	−	0.325592i
$113$	−0.509161	+	0.509161i	−0.0478978	+	0.0478978i	−0.730650	−	0.682752i	$-0.760783\pi$
$113$	−0.509161	+	0.509161i	−0.0478978	+	0.0478978i	0.682752	+	0.730650i	$0.260783\pi$
$114$		0			0
$115$		0			0
$116$	1.56768	−	0.729929i	0.145555	−	0.0677722i
$117$		0			0
$118$	0.401868	−	0.630408i	0.0369949	−	0.0580337i
$119$	4.59958			0.421643
$120$		0			0
$121$	−15.2986			−1.39078
$122$	3.78706	−	5.94074i	0.342864	−	0.537849i
$123$		0			0
$124$	−14.1619	+	6.59392i	−1.27177	+	0.592152i
$125$		0			0
$126$		0			0
$127$	7.49103	−	7.49103i	0.664722	−	0.664722i	−0.291767	−	0.956489i	$-0.594243\pi$
$127$	7.49103	−	7.49103i	0.664722	−	0.664722i	0.956489	+	0.291767i	$0.0942433\pi$
$128$	8.35664	−	7.62671i	0.738629	−	0.674112i
$129$		0			0
$130$		0			0
$131$		−	13.9964i		−	1.22287i	−0.791296	−	0.611434i	$-0.790593\pi$
$131$		−	13.9964i		−	1.22287i	0.791296	−	0.611434i	$-0.209407\pi$
$132$		0			0
$133$	0.747604	−	0.747604i	0.0648255	−	0.0648255i
$134$	−2.68264	−	12.1170i	−0.231745	−	1.04675i
$135$		0			0
$136$	9.14931	+	11.9448i	0.784547	+	1.02426i
$137$	7.01395	+	7.01395i	0.599242	+	0.599242i	0.940111	−	0.340869i	$-0.110721\pi$
$137$	7.01395	+	7.01395i	0.599242	+	0.599242i	−0.340869	+	0.940111i	$0.610721\pi$
$138$		0			0
$139$	−2.28006			−0.193392			−0.0966960	−	0.995314i	$-0.530827\pi$
$139$	−2.28006			−0.193392			−0.0966960	+	0.995314i	$0.530827\pi$
$140$		0			0
$141$		0			0
$142$	9.66229	+	6.15945i	0.810842	+	0.516889i
$143$	9.03365	+	9.03365i	0.755432	+	0.755432i
$144$		0			0
$145$		0			0
$146$	−0.973757	−	4.39829i	−0.0805887	−	0.364005i
$147$		0			0
$148$	1.70677	−	4.68098i	0.140296	−	0.384774i
$149$		−	10.1170i		−	0.828820i	−0.910090	−	0.414410i	$-0.863988\pi$
$149$		−	10.1170i		−	0.828820i	0.910090	−	0.414410i	$-0.136012\pi$
$150$		0			0
$151$		−	7.93691i		−	0.645897i	−0.946417	−	0.322948i	$-0.895326\pi$
$151$		−	7.93691i		−	0.645897i	0.946417	−	0.322948i	$-0.104674\pi$
$152$	3.42859	+	0.454377i	0.278095	+	0.0368548i
$153$		0			0
$154$	6.12247	−	1.35548i	0.493362	−	0.109228i
$155$		0			0
$156$		0			0
$157$	−9.01395	−	9.01395i	−0.719392	−	0.719392i	0.249089	−	0.968481i	$-0.419869\pi$
$157$	−9.01395	−	9.01395i	−0.719392	−	0.719392i	−0.968481	+	0.249089i	$0.919869\pi$
$158$	12.0972	−	18.9769i	0.962405	−	1.50972i
$159$		0			0
$160$		0			0
$161$	1.31695			0.103790
$162$		0			0
$163$	13.0849	+	13.0849i	1.02489	+	1.02489i	0.999682	+	0.0252033i	$0.00802331\pi$
$163$	13.0849	+	13.0849i	1.02489	+	1.02489i	0.0252033	+	0.999682i	$0.491977\pi$
$164$	4.66261	+	10.0140i	0.364088	+	0.781958i
$165$		0			0
$166$	−15.5371	+	3.43982i	−1.20591	+	0.266982i
$167$	−11.3334	+	11.3334i	−0.877008	+	0.877008i	−0.993224	−	0.116216i	$-0.962924\pi$
$167$	−11.3334	+	11.3334i	−0.877008	+	0.877008i	0.116216	+	0.993224i	$0.462924\pi$
$168$		0			0
$169$			6.79383i			0.522603i
$170$		0			0
$171$		0			0
$172$	−6.01224	+	16.4891i	−0.458429	+	1.25728i
$173$	7.96772	−	7.96772i	0.605775	−	0.605775i	−0.336064	−	0.941839i	$-0.609096\pi$
$173$	7.96772	−	7.96772i	0.605775	−	0.605775i	0.941839	+	0.336064i	$0.109096\pi$
$174$		0			0
$175$		0			0
$176$	15.6987	+	13.2034i	1.18333	+	0.995244i
$177$		0			0
$178$	8.64861	+	5.51325i	0.648241	+	0.413236i
$179$	12.6475			0.945320			0.472660	−	0.881245i	$-0.343294\pi$
$179$	12.6475			0.945320			0.472660	+	0.881245i	$0.343294\pi$
$180$		0			0
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	−2.56869	−	1.63747i	−0.190404	−	0.121378i
$183$		0			0
$184$	2.61962	+	3.42003i	0.193121	+	0.252128i
$185$		0			0
$186$		0			0
$187$	−19.2901	+	19.2901i	−1.41063	+	1.41063i
$188$	−6.11123	−	2.22827i	−0.445707	−	0.162513i
$189$		0			0
$190$		0			0
$191$		−	7.04516i		−	0.509770i	−0.966971	−	0.254885i	$-0.917962\pi$
$191$		−	7.04516i		−	0.509770i	0.966971	−	0.254885i	$-0.0820376\pi$
$192$		0			0
$193$	11.5048	−	11.5048i	0.828133	−	0.828133i	−0.159125	−	0.987258i	$-0.550867\pi$
$193$	11.5048	−	11.5048i	0.828133	−	0.828133i	0.987258	+	0.159125i	$0.0508674\pi$
$194$	−1.55013	+	0.343190i	−0.111293	+	0.0246396i
$195$		0			0
$196$	11.3362	−	5.27827i	0.809730	−	0.377019i
$197$	7.87859	+	7.87859i	0.561327	+	0.561327i	0.929684	−	0.368358i	$-0.120080\pi$
$197$	7.87859	+	7.87859i	0.561327	+	0.561327i	−0.368358	+	0.929684i	$0.620080\pi$
$198$		0			0
$199$	−11.4792			−0.813741			−0.406870	−	0.913486i	$-0.633380\pi$
$199$	−11.4792			−0.813741			−0.406870	+	0.913486i	$0.633380\pi$
$200$		0			0
$201$		0			0
$202$	7.69095	−	12.0648i	0.541133	−	0.848873i
$203$	−0.528636	−	0.528636i	−0.0371030	−	0.0371030i
$204$		0			0
$205$		0			0
$206$	−7.46460	+	1.65262i	−0.520083	+	0.115143i
$207$		0			0
$208$	−0.857132	−	9.92794i	−0.0594314	−	0.688379i
$209$			6.27072i			0.433755i
$210$		0			0
$211$			5.49134i			0.378039i	0.981973	+	0.189020i	$0.0605310\pi$
$211$			5.49134i			0.378039i	−0.981973	+	0.189020i	$0.939469\pi$
$212$	6.97859	+	2.54452i	0.479292	+	0.174759i
$213$		0			0
$214$	−2.38255	−	10.7616i	−0.162868	−	0.735645i
$215$		0			0
$216$		0			0
$217$	4.77551	+	4.77551i	0.324183	+	0.324183i
$218$	−8.72559	−	5.56233i	−0.590972	−	0.376728i
$219$		0			0
$220$		0			0
$221$	13.2524			0.891453
$222$		0			0
$223$	−10.8678	−	10.8678i	−0.727764	−	0.727764i	0.242410	−	0.970174i	$-0.422062\pi$
$223$	−10.8678	−	10.8678i	−0.727764	−	0.727764i	−0.970174	+	0.242410i	$0.922062\pi$
$224$	−4.33526	−	2.26469i	−0.289662	−	0.151316i
$225$		0			0
$226$	0.220121	+	0.994247i	0.0146422	+	0.0661363i
$227$	−4.98244	+	4.98244i	−0.330696	+	0.330696i	−0.852851	−	0.522155i	$-0.825128\pi$
$227$	−4.98244	+	4.98244i	−0.330696	+	0.330696i	0.522155	+	0.852851i	$0.325128\pi$
$228$		0			0
$229$		−	25.7572i		−	1.70208i	−0.525098	−	0.851041i	$-0.675972\pi$
$229$		−	25.7572i		−	1.70208i	0.525098	−	0.851041i	$-0.324028\pi$
$230$		0			0
$231$		0			0
$232$	0.321293	−	2.42438i	0.0210939	−	0.159168i
$233$	−0.715328	+	0.715328i	−0.0468627	+	0.0468627i	−0.730150	−	0.683287i	$-0.760550\pi$
$233$	−0.715328	+	0.715328i	−0.0468627	+	0.0468627i	0.683287	+	0.730150i	$0.260550\pi$
$234$		0			0
$235$		0			0
$236$	−0.446274	−	0.958469i	−0.0290499	−	0.0623910i
$237$		0			0
$238$	3.49659	−	5.48509i	0.226650	−	0.355545i
$239$	−26.9354			−1.74231			−0.871154	−	0.491009i	$-0.836628\pi$
$239$	−26.9354			−1.74231			−0.871154	+	0.491009i	$0.836628\pi$
$240$		0			0
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	−11.6300	+	18.2439i	−0.747603	+	1.17276i
$243$		0			0
$244$	−4.20553	−	9.03228i	−0.269231	−	0.578232i
$245$		0			0
$246$		0			0
$247$	2.15401	−	2.15401i	0.137056	−	0.137056i
$248$	−2.90245	+	21.9010i	−0.184306	+	1.39071i
$249$		0			0
$250$		0			0
$251$			17.2471i			1.08863i	0.838882	+	0.544314i	$0.183210\pi$
$251$			17.2471i			1.08863i	−0.838882	+	0.544314i	$0.816790\pi$
$252$		0			0
$253$	−5.52311	+	5.52311i	−0.347235	+	0.347235i
$254$	−3.23853	−	14.6279i	−0.203203	−	0.917834i
$255$		0			0
$256$	−2.74229	−	15.7632i	−0.171393	−	0.985203i
$257$	−15.0140	−	15.0140i	−0.936545	−	0.936545i	0.0615588	−	0.998103i	$-0.480393\pi$
$257$	−15.0140	−	15.0140i	−0.936545	−	0.936545i	−0.998103	+	0.0615588i	$0.980393\pi$
$258$		0			0
$259$	−2.15401			−0.133844
$260$		0			0
$261$		0			0
$262$	−16.6909	−	10.6400i	−1.03117	−	0.657341i
$263$	6.73386	+	6.73386i	0.415228	+	0.415228i	0.883555	−	0.468327i	$-0.155143\pi$
$263$	6.73386	+	6.73386i	0.415228	+	0.415228i	−0.468327	+	0.883555i	$0.655143\pi$
$264$		0			0
$265$		0			0
$266$	−0.323204	−	1.45986i	−0.0198169	−	0.0895096i
$267$		0			0
$268$	−16.4891	−	6.01224i	−1.00723	−	0.367256i
$269$		−	25.7047i		−	1.56724i	−0.621238	−	0.783622i	$-0.713370\pi$
$269$		−	25.7047i		−	1.56724i	0.621238	−	0.783622i	$-0.286630\pi$
$270$		0			0
$271$			0.931222i			0.0565677i	0.999600	+	0.0282839i	$0.00900423\pi$
$271$			0.931222i			0.0565677i	−0.999600	+	0.0282839i	$0.990996\pi$
$272$	21.1997	−	1.83029i	1.28542	−	0.110977i
$273$		0			0
$274$	13.6963	−	3.03228i	0.827421	−	0.183186i
$275$		0			0
$276$		0			0
$277$	22.0602	+	22.0602i	1.32547	+	1.32547i	0.909277	+	0.416190i	$0.136635\pi$
$277$	22.0602	+	22.0602i	1.32547	+	1.32547i	0.416190	+	0.909277i	$0.363365\pi$
$278$	−1.73330	+	2.71901i	−0.103956	+	0.163075i
$279$		0			0
$280$		0			0
$281$	−8.56934			−0.511204			−0.255602	−	0.966782i	$-0.582274\pi$
$281$	−8.56934			−0.511204			−0.255602	+	0.966782i	$0.582274\pi$
$282$		0			0
$283$	11.5705	+	11.5705i	0.687796	+	0.687796i	0.961744	−	0.273949i	$-0.0883299\pi$
$283$	11.5705	+	11.5705i	0.687796	+	0.687796i	−0.273949	+	0.961744i	$0.588330\pi$
$284$	14.6905	−	6.84006i	0.871721	−	0.405883i
$285$		0			0
$286$	17.6402	−	3.90543i	1.04308	−	0.230933i
$287$	3.37680	−	3.37680i	0.199326	−	0.199326i
$288$		0			0
$289$			11.2986i			0.664625i
$290$		0			0
$291$		0			0
$292$	−5.98529	−	2.18235i	−0.350262	−	0.127712i
$293$	12.8969	−	12.8969i	0.753446	−	0.753446i	−0.221675	−	0.975121i	$-0.571152\pi$
$293$	12.8969	−	12.8969i	0.753446	−	0.753446i	0.975121	+	0.221675i	$0.0711523\pi$
$294$		0			0
$295$		0			0
$296$	−4.28467	−	5.59383i	−0.249041	−	0.325135i
$297$		0			0
$298$	−12.0648	−	7.69095i	−0.698892	−	0.445525i
$299$	3.79441			0.219436
$300$		0			0
$301$	7.58767			0.437346
$302$	−9.46491	−	6.03362i	−0.544644	−	0.347196i
$303$		0			0
$304$	3.14826	−	3.74324i	0.180565	−	0.214689i
$305$		0			0
$306$		0			0
$307$	1.60564	−	1.60564i	0.0916387	−	0.0916387i	−0.659801	−	0.751440i	$-0.729360\pi$
$307$	1.60564	−	1.60564i	0.0916387	−	0.0916387i	0.751440	+	0.659801i	$0.229360\pi$
$308$	3.03785	−	8.33158i	0.173098	−	0.474736i
$309$		0			0
$310$		0			0
$311$			19.4161i			1.10099i	0.834839	+	0.550494i	$0.185561\pi$
$311$			19.4161i			1.10099i	−0.834839	+	0.550494i	$0.814439\pi$
$312$		0			0
$313$	−17.7110	+	17.7110i	−1.00108	+	1.00108i	−0.00108322	+	0.999999i	$0.500345\pi$
$313$	−17.7110	+	17.7110i	−1.00108	+	1.00108i	−0.999999	+	0.00108322i	$0.999655\pi$
$314$	−17.6017	+	3.89692i	−0.993321	+	0.219916i
$315$		0			0
$316$	−13.4340	−	28.8524i	−0.755721	−	1.62307i
$317$	−7.78946	−	7.78946i	−0.437500	−	0.437500i	0.453670	−	0.891170i	$-0.350115\pi$
$317$	−7.78946	−	7.78946i	−0.437500	−	0.437500i	−0.891170	+	0.453670i	$0.850115\pi$
$318$		0			0
$319$	4.43407			0.248260
$320$		0			0
$321$		0			0
$322$	1.00114	−	1.57048i	0.0557914	−	0.0875196i
$323$	4.59958	+	4.59958i	0.255928	+	0.255928i
$324$		0			0
$325$		0			0
$326$	25.5510	−	5.65685i	1.41514	−	0.313304i
$327$		0			0
$328$	15.4863	+	2.05234i	0.855089	+	0.113322i
$329$			2.81215i			0.155039i
$330$		0			0
$331$			31.7005i			1.74242i	0.490912	+	0.871209i	$0.336664\pi$
$331$			31.7005i			1.74242i	−0.490912	+	0.871209i	$0.663336\pi$
$332$	−7.70919	+	21.1432i	−0.423097	+	1.16038i
$333$		0			0
$334$	4.89968	+	22.1310i	0.268098	+	1.21095i
$335$		0			0
$336$		0			0
$337$	−18.9634	−	18.9634i	−1.03300	−	1.03300i	−0.999437	−	0.0335632i	$-0.989314\pi$
$337$	−18.9634	−	18.9634i	−1.03300	−	1.03300i	−0.0335632	−	0.999437i	$-0.510686\pi$
$338$	8.10177	+	5.16466i	0.440678	+	0.280920i
$339$		0			0
$340$		0			0
$341$	−40.0558			−2.16914
$342$		0			0
$343$	−8.10243	−	8.10243i	−0.437490	−	0.437490i
$344$	15.0931	+	19.7047i	0.813765	+	1.06241i
$345$		0			0
$346$	−3.44461	−	15.5587i	−0.185183	−	0.836441i
$347$	7.71957	−	7.71957i	0.414408	−	0.414408i	−0.468863	−	0.883271i	$-0.655336\pi$
$347$	7.71957	−	7.71957i	0.414408	−	0.414408i	0.883271	+	0.468863i	$0.155336\pi$
$348$		0			0
$349$			27.0741i			1.44925i	0.689146	+	0.724623i	$0.257986\pi$
$349$			27.0741i			1.44925i	−0.689146	+	0.724623i	$0.742014\pi$
$350$		0			0
$351$		0			0
$352$	27.6794	−	8.68375i	1.47532	−	0.462846i
$353$	−9.96772	+	9.96772i	−0.530528	+	0.530528i	−0.920730	−	0.390201i	$-0.872405\pi$
$353$	−9.96772	+	9.96772i	−0.530528	+	0.530528i	0.390201	+	0.920730i	$0.372405\pi$
$354$		0			0
$355$		0			0
$356$	13.1493	−	6.12247i	0.696912	−	0.324490i
$357$		0			0
$358$	9.61461	−	15.0824i	0.508148	−	0.797129i
$359$	14.2334			0.751211			0.375606	−	0.926780i	$-0.377435\pi$
$359$	14.2334			0.751211			0.375606	+	0.926780i	$0.377435\pi$
$360$		0			0
$361$	−17.5048			−0.921305
$362$	5.87578	−	9.21731i	0.308824	−	0.484451i
$363$		0			0
$364$	−3.90543	+	1.81841i	−0.204700	+	0.0953107i
$365$		0			0
$366$		0			0
$367$	2.89145	−	2.89145i	0.150933	−	0.150933i	−0.627602	−	0.778534i	$-0.715963\pi$
$367$	2.89145	−	2.89145i	0.150933	−	0.150933i	0.778534	+	0.627602i	$0.215963\pi$
$368$	6.06988	−	0.524045i	0.316414	−	0.0273177i
$369$		0			0
$370$		0			0
$371$		−	3.21128i		−	0.166721i
$372$		0			0
$373$	11.2847	−	11.2847i	0.584298	−	0.584298i	−0.351783	−	0.936081i	$-0.614425\pi$
$373$	11.2847	−	11.2847i	0.584298	−	0.584298i	0.936081	+	0.351783i	$0.114425\pi$
$374$	8.33950	+	37.6681i	0.431225	+	1.94777i
$375$		0			0
$376$	−7.30299	+	5.59383i	−0.376623	+	0.288480i
$377$	−1.52311	−	1.52311i	−0.0784444	−	0.0784444i
$378$		0			0
$379$	−15.4562			−0.793932			−0.396966	−	0.917833i	$-0.629937\pi$
$379$	−15.4562			−0.793932			−0.396966	+	0.917833i	$0.629937\pi$
$380$		0			0
$381$		0			0
$382$	−8.40148	−	5.35571i	−0.429857	−	0.274022i
$383$	−12.5562	−	12.5562i	−0.641593	−	0.641593i	0.309354	−	0.950947i	$-0.399887\pi$
$383$	−12.5562	−	12.5562i	−0.641593	−	0.641593i	−0.950947	+	0.309354i	$0.899887\pi$
$384$		0			0
$385$		0			0
$386$	−4.97376	−	22.4656i	−0.253158	−	1.14347i
$387$		0			0
$388$	−0.769144	+	2.10945i	−0.0390474	+	0.107091i
$389$			5.16327i			0.261788i	0.991396	+	0.130894i	$0.0417848\pi$
$389$			5.16327i			0.261788i	−0.991396	+	0.130894i	$0.958215\pi$
$390$		0			0
$391$			8.10243i			0.409757i
$392$	2.32333	−	17.5312i	0.117346	−	0.885458i
$393$		0			0
$394$	15.3847	−	3.40608i	0.775068	−	0.171596i
$395$		0			0
$396$		0			0
$397$	3.46293	+	3.46293i	0.173800	+	0.173800i	0.788646	−	0.614847i	$-0.210782\pi$
$397$	3.46293	+	3.46293i	0.173800	+	0.173800i	−0.614847	+	0.788646i	$0.710782\pi$
$398$	−8.72648	+	13.6892i	−0.437419	+	0.686177i
$399$		0			0
$400$		0			0
$401$	−3.49521			−0.174542			−0.0872712	−	0.996185i	$-0.527815\pi$
$401$	−3.49521			−0.174542			−0.0872712	+	0.996185i	$0.527815\pi$
$402$		0			0
$403$	13.7593	+	13.7593i	0.685399	+	0.685399i
$404$	−8.54079	−	18.3432i	−0.424920	−	0.912608i
$405$		0			0
$406$	−1.03228	+	0.228540i	−0.0512310	+	0.0113423i
$407$	9.03365	−	9.03365i	0.447781	−	0.447781i
$408$		0			0
$409$		−	14.8034i		−	0.731982i	−0.930618	−	0.365991i	$-0.880730\pi$
$409$		−	14.8034i		−	0.731982i	0.930618	−	0.365991i	$-0.119270\pi$
$410$		0			0
$411$		0			0
$412$	−3.70379	+	10.1580i	−0.182473	+	0.500448i
$413$	−0.323204	+	0.323204i	−0.0159039	+	0.0159039i
$414$		0			0
$415$		0			0
$416$	−12.4908	−	6.52505i	−0.612414	−	0.319917i
$417$		0			0
$418$	7.47795	+	4.76699i	0.365758	+	0.233161i
$419$	−19.0701			−0.931634			−0.465817	−	0.884881i	$-0.654240\pi$
$419$	−19.0701			−0.931634			−0.465817	+	0.884881i	$0.654240\pi$
$420$		0			0
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	6.54852	+	4.17450i	0.318777	+	0.203212i
$423$		0			0
$424$	8.33950	−	6.38776i	0.405002	−	0.310217i
$425$		0			0
$426$		0			0
$427$	−3.04577	+	3.04577i	−0.147395	+	0.147395i
$428$	−14.6446	−	5.33968i	−0.707872	−	0.258103i
$429$		0			0
$430$		0			0
$431$			15.3302i			0.738428i	0.929344	+	0.369214i	$0.120373\pi$
$431$			15.3302i			0.738428i	−0.929344	+	0.369214i	$0.879627\pi$
$432$		0			0
$433$	−16.2803	+	16.2803i	−0.782381	+	0.782381i	−0.980232	−	0.197851i	$-0.936604\pi$
$433$	−16.2803	+	16.2803i	−0.782381	+	0.782381i	0.197851	+	0.980232i	$0.436604\pi$
$434$	9.32521	−	2.06455i	0.447625	−	0.0991016i
$435$		0			0
$436$	−13.2663	+	6.17696i	−0.635343	+	0.295823i
$437$	1.31695	+	1.31695i	0.0629981	+	0.0629981i
$438$		0			0
$439$	−24.6554			−1.17674			−0.588368	−	0.808593i	$-0.700230\pi$
$439$	−24.6554			−1.17674			−0.588368	+	0.808593i	$0.700230\pi$
$440$		0			0
$441$		0			0
$442$	10.0744	−	15.8037i	0.479192	−	0.751706i
$443$	−1.77116	−	1.77116i	−0.0841501	−	0.0841501i	0.663779	−	0.747929i	$-0.268952\pi$
$443$	−1.77116	−	1.77116i	−0.0841501	−	0.0841501i	−0.747929	+	0.663779i	$0.768952\pi$
$444$		0			0
$445$		0			0
$446$	−21.2218	+	4.69839i	−1.00488	+	0.222475i
$447$		0			0
$448$	−5.99634	+	3.44827i	−0.283300	+	0.162916i
$449$			33.1512i			1.56450i	0.622963	+	0.782251i	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$		0			0
$451$			28.3237i			1.33371i
$452$	1.35299	+	0.493326i	0.0636394	+	0.0232041i
$453$		0			0
$454$	2.15401	+	9.72928i	0.101093	+	0.456618i
$455$		0			0
$456$		0			0
$457$	7.50479	+	7.50479i	0.351059	+	0.351059i	0.860504	−	0.509444i	$-0.170149\pi$
$457$	7.50479	+	7.50479i	0.351059	+	0.351059i	−0.509444	+	0.860504i	$0.670149\pi$
$458$	−30.7159	−	19.5806i	−1.43526	−	0.914939i
$459$		0			0
$460$		0			0
$461$	27.0216			1.25852			0.629262	−	0.777193i	$-0.283357\pi$
$461$	27.0216			1.25852			0.629262	+	0.777193i	$0.283357\pi$
$462$		0			0
$463$	27.7123	+	27.7123i	1.28790	+	1.28790i	0.936059	+	0.351843i	$0.114445\pi$
$463$	27.7123	+	27.7123i	1.28790	+	1.28790i	0.351843	+	0.936059i	$0.385555\pi$
$464$	−2.64687	−	2.22615i	−0.122878	−	0.103347i
$465$		0			0
$466$	0.309251	+	1.39683i	0.0143258	+	0.0647070i
$467$	2.00823	−	2.00823i	0.0929296	−	0.0929296i	−0.659114	−	0.752043i	$-0.729068\pi$
$467$	2.00823	−	2.00823i	0.0929296	−	0.0929296i	0.752043	+	0.659114i	$0.229068\pi$
$468$		0			0
$469$			7.58767i			0.350366i
$470$		0			0
$471$		0			0
$472$	−1.48225	−	0.196436i	−0.0682260	−	0.00904172i
$473$	−31.8217	+	31.8217i	−1.46317	+	1.46317i
$474$		0			0
$475$		0			0
$476$	−3.88296	−	8.33950i	−0.177975	−	0.382240i
$477$		0			0
$478$	−20.4763	+	32.1210i	−0.936562	+	1.46918i
$479$	−13.7593			−0.628678			−0.314339	−	0.949311i	$-0.601783\pi$
$479$	−13.7593			−0.628678			−0.314339	+	0.949311i	$0.601783\pi$
$480$		0			0
$481$	−6.20617			−0.282977
$482$	10.7131	−	16.8055i	0.487966	−	0.765470i
$483$		0			0
$484$	12.9151	+	27.7379i	0.587049	+	1.26081i
$485$		0			0
$486$		0			0
$487$	−24.3355	+	24.3355i	−1.10275	+	1.10275i	−0.108671	+	0.994078i	$0.534660\pi$
$487$	−24.3355	+	24.3355i	−1.10275	+	1.10275i	−0.994078	+	0.108671i	$0.965340\pi$
$488$	−13.9682	−	1.85115i	−0.632310	−	0.0837975i
$489$		0			0
$490$		0			0
$491$		−	28.8918i		−	1.30387i	−0.758275	−	0.651935i	$-0.773957\pi$
$491$		−	28.8918i		−	1.30387i	0.758275	−	0.651935i	$-0.226043\pi$
$492$		0			0
$493$	3.25240	−	3.25240i	0.146481	−	0.146481i
$494$	−0.931222	−	4.20617i	−0.0418977	−	0.189244i
$495$		0			0
$496$	23.9109	+	20.1103i	1.07363	+	0.902979i
$497$	−4.95377	−	4.95377i	−0.222207	−	0.222207i
$498$		0			0
$499$	12.5365			0.561211			0.280605	−	0.959823i	$-0.409465\pi$
$499$	12.5365			0.561211			0.280605	+	0.959823i	$0.409465\pi$
$500$		0			0
$501$		0			0
$502$	20.5675	+	13.1112i	0.917972	+	0.585182i
$503$	9.01392	+	9.01392i	0.401911	+	0.401911i	0.878906	−	0.476995i	$-0.158274\pi$
$503$	9.01392	+	9.01392i	0.401911	+	0.401911i	−0.476995	+	0.878906i	$0.658274\pi$
$504$		0			0
$505$		0			0
$506$	2.38776	+	10.7851i	0.106149	+	0.479455i
$507$		0			0
$508$	−19.9059	−	7.25806i	−0.883182	−	0.322025i
$509$			22.5448i			0.999279i	0.866233	+	0.499640i	$0.166534\pi$
$509$			22.5448i			0.999279i	−0.866233	+	0.499640i	$0.833466\pi$
$510$		0			0
$511$			2.75420i			0.121839i
$512$	−20.8826	−	8.71295i	−0.922891	−	0.385062i
$513$		0			0
$514$	−29.3180	+	6.49084i	−1.29316	+	0.286299i
$515$		0			0
$516$		0			0
$517$	−11.7938	−	11.7938i	−0.518692	−	0.518692i
$518$	−1.63747	+	2.56869i	−0.0719464	+	0.112862i
$519$		0			0
$520$		0			0
$521$	18.9046			0.828226			0.414113	−	0.910225i	$-0.364092\pi$
$521$	18.9046			0.828226			0.414113	+	0.910225i	$0.364092\pi$
$522$		0			0
$523$	−21.8269	−	21.8269i	−0.954426	−	0.954426i	0.0445800	−	0.999006i	$-0.485805\pi$
$523$	−21.8269	−	21.8269i	−0.954426	−	0.954426i	−0.999006	+	0.0445800i	$0.985805\pi$
$524$	−25.3768	+	11.8157i	−1.10859	+	0.516172i
$525$		0			0
$526$	13.1493	−	2.91118i	0.573337	−	0.126934i
$527$	−29.3810	+	29.3810i	−1.27986	+	1.27986i
$528$		0			0
$529$		−	20.6801i		−	0.899136i
$530$		0			0
$531$		0			0
$532$	−1.98661	−	0.724353i	−0.0861303	−	0.0314047i
$533$	9.72928	−	9.72928i	0.421422	−	0.421422i
$534$		0			0
$535$		0			0
$536$	−19.7047	+	15.0931i	−0.851114	+	0.651922i
$537$		0			0
$538$	−30.6533	−	19.5407i	−1.32156	−	0.842457i
$539$	32.0637			1.38108
$540$		0			0
$541$	7.85838			0.337858			0.168929	−	0.985628i	$-0.445969\pi$
$541$	7.85838			0.337858			0.168929	+	0.985628i	$0.445969\pi$
$542$	1.11050	+	0.707913i	0.0477000	+	0.0304075i
$543$		0			0
$544$	13.9333	−	26.6724i	0.597387	−	1.14357i
$545$		0			0
$546$		0			0
$547$	17.8105	−	17.8105i	0.761522	−	0.761522i	−0.215076	−	0.976597i	$-0.569000\pi$
$547$	17.8105	−	17.8105i	0.761522	−	0.761522i	0.976597	+	0.215076i	$0.0689998\pi$
$548$	6.79582	−	18.6382i	0.290303	−	0.796183i
$549$		0			0
$550$		0			0
$551$		−	1.05727i		−	0.0450413i
$552$		0			0
$553$	−9.72928	+	9.72928i	−0.413731	+	0.413731i
$554$	43.0773	−	9.53707i	1.83018	−	0.405191i
$555$		0			0
$556$	1.92482	+	4.13397i	0.0816307	+	0.175319i
$557$	23.3372	+	23.3372i	0.988827	+	0.988827i	0.999938	−	0.0111112i	$-0.00353686\pi$
$557$	23.3372	+	23.3372i	0.988827	+	0.988827i	−0.0111112	+	0.999938i	$0.503537\pi$
$558$		0			0
$559$	21.8617			0.924652
$560$		0			0
$561$		0			0
$562$	−6.51439	+	10.2191i	−0.274793	+	0.431067i
$563$	5.27400	+	5.27400i	0.222273	+	0.222273i	0.809455	−	0.587182i	$-0.199763\pi$
$563$	5.27400	+	5.27400i	0.222273	+	0.222273i	−0.587182	+	0.809455i	$0.699763\pi$
$564$		0			0
$565$		0			0
$566$	22.5939	−	5.00217i	0.949693	−	0.210257i
$567$		0			0
$568$	3.01079	−	22.7185i	0.126330	−	0.953247i
$569$		−	28.5606i		−	1.19732i	−0.801002	−	0.598661i	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$		0			0
$571$		−	32.2837i		−	1.35103i	−0.737347	−	0.675515i	$-0.763922\pi$
$571$		−	32.2837i		−	1.35103i	0.737347	−	0.675515i	$-0.236078\pi$
$572$	8.75270	−	24.0051i	0.365969	−	1.00370i
$573$		0			0
$574$	−1.45986	−	6.59392i	−0.0609333	−	0.275225i
$575$		0			0
$576$		0			0
$577$	−27.0279	−	27.0279i	−1.12519	−	1.12519i	−0.990949	−	0.134237i	$-0.957142\pi$
$577$	−27.0279	−	27.0279i	−1.12519	−	1.12519i	−0.134237	−	0.990949i	$-0.542858\pi$
$578$	13.4738	+	8.58919i	0.560437	+	0.357263i
$579$		0			0
$580$		0			0
$581$	9.72928			0.403639
$582$		0			0
$583$	13.4677	+	13.4677i	0.557776	+	0.557776i
$584$	−7.15249	+	5.47855i	−0.295972	+	0.226704i
$585$		0			0
$586$	−5.57560	−	25.1840i	−0.230326	−	1.04034i
$587$	−17.1558	+	17.1558i	−0.708096	+	0.708096i	−0.966135	−	0.258039i	$-0.916924\pi$
$587$	−17.1558	+	17.1558i	−0.708096	+	0.708096i	0.258039	+	0.966135i	$0.416924\pi$
$588$		0			0
$589$			9.55102i			0.393543i
$590$		0			0
$591$		0			0
$592$	−9.92794	+	0.857132i	−0.408036	+	0.0352279i
$593$	−21.5833	+	21.5833i	−0.886320	+	0.886320i	−0.994167	−	0.107848i	$-0.965604\pi$
$593$	−21.5833	+	21.5833i	−0.886320	+	0.886320i	0.107848	+	0.994167i	$0.465604\pi$
$594$		0			0
$595$		0			0
$596$	−18.3432	+	8.54079i	−0.751366	+	0.349844i
$597$		0			0
$598$	2.88450	−	4.52490i	0.117956	−	0.185037i
$599$	−23.7636			−0.970955			−0.485478	−	0.874249i	$-0.661354\pi$
$599$	−23.7636			−0.970955			−0.485478	+	0.874249i	$0.661354\pi$
$600$		0			0
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	5.76813	−	9.04843i	0.235091	−	0.368786i
$603$		0			0
$604$	−14.3904	+	6.70033i	−0.585537	+	0.272633i
$605$		0			0
$606$		0			0
$607$	9.35348	−	9.35348i	0.379646	−	0.379646i	−0.491328	−	0.870974i	$-0.663489\pi$
$607$	9.35348	−	9.35348i	0.379646	−	0.379646i	0.870974	+	0.491328i	$0.163489\pi$
$608$	−2.07058	−	6.59995i	−0.0839731	−	0.267663i
$609$		0			0
$610$		0			0
$611$			8.10243i			0.327789i
$612$		0			0
$613$	24.1247	−	24.1247i	0.974389	−	0.974389i	−0.0252913	−	0.999680i	$-0.508051\pi$
$613$	24.1247	−	24.1247i	0.974389	−	0.974389i	0.999680	+	0.0252913i	$0.00805134\pi$
$614$	−0.694151	−	3.13536i	−0.0280137	−	0.126533i
$615$		0			0
$616$	−7.62620	−	9.95634i	−0.307268	−	0.401152i
$617$	3.82611	+	3.82611i	0.154033	+	0.154033i	0.779917	−	0.625883i	$-0.215261\pi$
$617$	3.82611	+	3.82611i	0.154033	+	0.154033i	−0.625883	+	0.779917i	$0.715261\pi$
$618$		0			0
$619$	−30.1297			−1.21101			−0.605507	−	0.795840i	$-0.707029\pi$
$619$	−30.1297			−1.21101			−0.605507	+	0.795840i	$0.707029\pi$
$620$		0			0
$621$		0			0
$622$	23.1541	+	14.7601i	0.928395	+	0.591826i
$623$	−4.43407	−	4.43407i	−0.177647	−	0.177647i
$624$		0			0
$625$		0			0
$626$	7.65681	+	34.5845i	0.306028	+	1.38227i
$627$		0			0
$628$	−8.73362	+	23.9528i	−0.348509	+	0.955819i
$629$		−	13.2524i		−	0.528408i
$630$		0			0
$631$		−	21.5701i		−	0.858694i	−0.903140	−	0.429347i	$-0.858744\pi$
$631$		−	21.5701i		−	0.858694i	0.903140	−	0.429347i	$-0.141256\pi$
$632$	−44.6195	−	5.91324i	−1.77487	−	0.235216i
$633$		0			0
$634$	−15.2106	+	3.36754i	−0.604090	+	0.133742i
$635$		0			0
$636$		0			0
$637$	−11.0140	−	11.0140i	−0.436389	−	0.436389i
$638$	3.37077	−	5.28771i	0.133450	−	0.209342i
$639$		0			0
$640$		0			0
$641$	−48.3911			−1.91133			−0.955666	−	0.294452i	$-0.904863\pi$
$641$	−48.3911			−1.91133			−0.955666	+	0.294452i	$0.904863\pi$
$642$		0			0
$643$	−23.3413	−	23.3413i	−0.920491	−	0.920491i	0.0765729	−	0.997064i	$-0.475602\pi$
$643$	−23.3413	−	23.3413i	−0.920491	−	0.920491i	−0.997064	+	0.0765729i	$0.975602\pi$
$644$	−1.11177	−	2.38776i	−0.0438097	−	0.0940907i
$645$		0			0
$646$	8.98168	−	1.98849i	0.353379	−	0.0782362i
$647$	32.4465	−	32.4465i	1.27560	−	1.27560i	0.332501	−	0.943103i	$-0.392108\pi$
$647$	32.4465	−	32.4465i	1.27560	−	1.27560i	0.943103	−	0.332501i	$-0.107892\pi$
$648$		0			0
$649$		−	2.71096i		−	0.106414i
$650$		0			0
$651$		0			0
$652$	12.6779	−	34.7704i	0.496506	−	1.36171i
$653$	18.4725	−	18.4725i	0.722885	−	0.722885i	−0.246307	−	0.969192i	$-0.579217\pi$
$653$	18.4725	−	18.4725i	0.722885	−	0.722885i	0.969192	+	0.246307i	$0.0792170\pi$
$654$		0			0
$655$		0			0
$656$	14.2201	−	16.9075i	0.555202	−	0.660128i
$657$		0			0
$658$	3.35355	+	2.13779i	0.130735	+	0.0833399i
$659$	−47.5028			−1.85045			−0.925223	−	0.379423i	$-0.876122\pi$
$659$	−47.5028			−1.85045			−0.925223	+	0.379423i	$0.876122\pi$
$660$		0			0
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	37.8035	+	24.0987i	1.46927	+	0.936621i
$663$		0			0
$664$	19.3531	+	25.2663i	0.751046	+	0.980525i
$665$		0			0
$666$		0			0
$667$	0.931222	−	0.931222i	0.0360571	−	0.0360571i
$668$	30.1163	+	10.9810i	1.16524	+	0.424867i
$669$		0			0
$670$		0			0
$671$		−	25.5471i		−	0.986236i
$672$		0			0
$673$	−3.60599	+	3.60599i	−0.139001	+	0.139001i	−0.773183	−	0.634183i	$-0.781337\pi$
$673$	−3.60599	+	3.60599i	−0.139001	+	0.139001i	0.634183	+	0.773183i	$0.281337\pi$
$674$	−37.0300	+	8.19825i	−1.42634	+	0.315785i
$675$		0			0
$676$	12.3179	−	5.73535i	0.473765	−	0.220590i
$677$	−8.26635	−	8.26635i	−0.317702	−	0.317702i	0.530182	−	0.847884i	$-0.322124\pi$
$677$	−8.26635	−	8.26635i	−0.317702	−	0.317702i	−0.847884	+	0.530182i	$0.822124\pi$
$678$		0			0
$679$	0.970688			0.0372516
$680$		0			0
$681$		0			0
$682$	−30.4503	+	47.7673i	−1.16600	+	1.82910i
$683$	8.43079	+	8.43079i	0.322595	+	0.322595i	0.849762	−	0.527167i	$-0.176746\pi$
$683$	8.43079	+	8.43079i	0.322595	+	0.322595i	−0.527167	+	0.849762i	$0.676746\pi$
$684$		0			0
$685$		0			0
$686$	−15.8217	+	3.50285i	−0.604077	+	0.133739i
$687$		0			0
$688$	34.9719	−	3.01932i	1.33329	−	0.115110i
$689$		−	9.25240i		−	0.352488i
$690$		0			0
$691$		−	21.9182i		−	0.833809i	−0.908950	−	0.416905i	$-0.863115\pi$
$691$		−	21.9182i		−	0.833809i	0.908950	−	0.416905i	$-0.136885\pi$
$692$	−21.1726	−	7.71993i	−0.804862	−	0.293468i
$693$		0			0
$694$	−3.33733	−	15.0741i	−0.126683	−	0.572206i
$695$		0			0
$696$		0			0
$697$	20.7755	+	20.7755i	0.786929	+	0.786929i
$698$	32.2864	+	20.5817i	1.22206	+	0.779029i
$699$		0			0
$700$		0			0
$701$	21.8184			0.824070			0.412035	−	0.911168i	$-0.364818\pi$
$701$	21.8184			0.824070			0.412035	+	0.911168i	$0.364818\pi$
$702$		0			0
$703$	−2.15401	−	2.15401i	−0.0812400	−	0.0812400i
$704$	10.6863	−	39.6095i	0.402754	−	1.49284i
$705$		0			0
$706$	4.30925	+	19.4641i	0.162181	+	0.732542i
$707$	−6.18549	+	6.18549i	−0.232629	+	0.232629i
$708$		0			0
$709$		−	31.7938i		−	1.19404i	−0.802225	−	0.597021i	$-0.796351\pi$
$709$		−	31.7938i		−	1.19404i	0.802225	−	0.597021i	$-0.203649\pi$
$710$		0			0
$711$		0			0
$712$	2.69493	−	20.3351i	0.100997	−	0.762089i
$713$	−8.41233	+	8.41233i	−0.315044	+	0.315044i
$714$		0			0
$715$		0			0
$716$	−10.6770	−	22.9312i	−0.399019	−	0.856979i
$717$		0			0
$718$	10.8202	−	16.9736i	0.403807	−	0.633450i
$719$	52.0874			1.94253			0.971265	−	0.237999i	$-0.0764916\pi$
$719$	52.0874			1.94253			0.971265	+	0.237999i	$0.0764916\pi$
$720$		0			0
$721$	4.67432			0.174081
$722$	−13.3071	+	20.8748i	−0.495239	+	0.776879i
$723$		0			0
$724$	−6.52505	−	14.0140i	−0.242502	−	0.520824i
$725$		0			0
$726$		0			0
$727$	−8.13069	+	8.13069i	−0.301551	+	0.301551i	−0.841620	−	0.540070i	$-0.818398\pi$
$727$	−8.13069	+	8.13069i	−0.301551	+	0.301551i	0.540070	+	0.841620i	$0.318398\pi$
$728$	−0.800411	+	6.03965i	−0.0296652	+	0.223844i
$729$		0			0
$730$		0			0
$731$			46.6826i			1.72662i
$732$		0			0
$733$	29.9956	−	29.9956i	1.10791	−	1.10791i	0.114489	−	0.993424i	$-0.463477\pi$
$733$	29.9956	−	29.9956i	1.10791	−	1.10791i	0.993424	−	0.114489i	$-0.0365232\pi$
$734$	−1.25003	−	5.64618i	−0.0461396	−	0.208404i
$735$		0			0
$736$	3.98937	−	7.63682i	0.147050	−	0.281497i
$737$	−31.8217	−	31.8217i	−1.17217	−	1.17217i
$738$		0			0
$739$	39.4719			1.45200			0.725999	−	0.687696i	$-0.241378\pi$
$739$	39.4719			1.45200			0.725999	+	0.687696i	$0.241378\pi$
$740$		0			0
$741$		0			0
$742$	−3.82951	−	2.44121i	−0.140586	−	0.0896196i
$743$	−12.2252	−	12.2252i	−0.448499	−	0.448499i	0.446356	−	0.894855i	$-0.352721\pi$
$743$	−12.2252	−	12.2252i	−0.448499	−	0.448499i	−0.894855	+	0.446356i	$0.852721\pi$
$744$		0			0
$745$		0			0
$746$	−4.87859	−	22.0358i	−0.178618	−	0.806786i
$747$		0			0
$748$	51.2595	+	18.6902i	1.87423	+	0.683380i
$749$			6.73887i			0.246233i
$750$		0			0
$751$			28.9069i			1.05483i	0.849609	+	0.527413i	$0.176838\pi$
$751$			28.9069i			1.05483i	−0.849609	+	0.527413i	$0.823162\pi$
$752$	1.11902	+	12.9614i	0.0408066	+	0.472652i
$753$		0			0
$754$	−2.97421	+	0.658473i	−0.108314	+	0.0239802i
$755$		0			0
$756$		0			0
$757$	16.2018	+	16.2018i	0.588864	+	0.588864i	0.937324	−	0.348459i	$-0.113295\pi$
$757$	16.2018	+	16.2018i	0.588864	+	0.588864i	−0.348459	+	0.937324i	$0.613295\pi$
$758$	−11.7498	+	18.4318i	−0.426771	+	0.669474i
$759$		0			0
$760$		0			0
$761$	6.64641			0.240932			0.120466	−	0.992717i	$-0.461561\pi$
$761$	6.64641			0.240932			0.120466	+	0.992717i	$0.461561\pi$
$762$		0			0
$763$	4.47353	+	4.47353i	0.161953	+	0.161953i
$764$	−12.7736	+	5.94751i	−0.462131	+	0.215173i
$765$		0			0
$766$	−24.5187	+	5.42831i	−0.885898	+	0.196133i
$767$	−0.931222	+	0.931222i	−0.0336245	+	0.0336245i
$768$		0			0
$769$			29.3449i			1.05820i	0.848559	+	0.529101i	$0.177471\pi$
$769$			29.3449i			1.05820i	−0.848559	+	0.529101i	$0.822529\pi$
$770$		0			0
$771$		0			0
$772$	−30.5717	−	11.1470i	−1.10030	−	0.401189i
$773$	37.5833	−	37.5833i	1.35178	−	1.35178i	0.468104	−	0.883674i	$-0.344937\pi$
$773$	37.5833	−	37.5833i	1.35178	−	1.35178i	0.883674	−	0.468104i	$-0.155063\pi$
$774$		0			0
$775$		0			0
$776$	1.93086	+	2.52082i	0.0693137	+	0.0904921i
$777$		0			0
$778$	6.15729	+	3.92510i	0.220749	+	0.140722i
$779$	6.75359			0.241973
$780$		0			0
$781$	41.5510			1.48681
$782$	9.66229	+	6.15945i	0.345523	+	0.220261i
$783$		0			0
$784$	−19.1400	−	16.0978i	−0.683573	−	0.574920i
$785$		0			0
$786$		0			0
$787$	−7.59353	+	7.59353i	−0.270680	+	0.270680i	−0.829374	−	0.558694i	$-0.811303\pi$
$787$	−7.59353	+	7.59353i	−0.270680	+	0.270680i	0.558694	+	0.829374i	$0.311303\pi$
$788$	7.63357	−	20.9358i	0.271935	−	0.745806i
$789$		0			0
$790$		0			0
$791$		−	0.622595i		−	0.0221369i
$792$		0			0
$793$	−8.77551	+	8.77551i	−0.311628	+	0.311628i
$794$	6.76212	−	1.49710i	0.239979	−	0.0531300i
$795$		0			0
$796$	9.69075	+	20.8130i	0.343479	+	0.737696i
$797$	27.4908	+	27.4908i	0.973775	+	0.973775i	0.999665	−	0.0258893i	$-0.00824175\pi$
$797$	27.4908	+	27.4908i	0.973775	+	0.973775i	−0.0258893	+	0.999665i	$0.508242\pi$
$798$		0			0
$799$	−17.3016			−0.612086
$800$		0			0
$801$		0			0
$802$	−2.65705	+	4.16810i	−0.0938237	+	0.147181i
$803$	−11.5508	−	11.5508i	−0.407618	−	0.407618i
$804$		0			0
$805$		0			0
$806$	26.8680	−	5.94842i	0.946384	−	0.209524i
$807$		0			0
$808$	−28.3673	−	3.75940i	−0.997957	−	0.132255i
$809$			47.7205i			1.67776i	0.544313	+	0.838882i	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$		0			0
$811$		−	37.3179i		−	1.31041i	−0.755451	−	0.655205i	$-0.772582\pi$
$811$		−	37.3179i		−	1.31041i	0.755451	−	0.655205i	$-0.227418\pi$
$812$	−0.512195	+	1.40474i	−0.0179745	+	0.0492968i
$813$		0			0
$814$	−3.90543	−	17.6402i	−0.136885	−	0.618287i
$815$		0			0
$816$		0			0
$817$	7.58767	+	7.58767i	0.265459	+	0.265459i
$818$	−17.6533	−	11.2535i	−0.617235	−	0.393470i
$819$		0			0
$820$		0			0
$821$	0.686380			0.0239548			0.0119774	−	0.999928i	$-0.496187\pi$
$821$	0.686380			0.0239548			0.0119774	+	0.999928i	$0.496187\pi$
$822$		0			0
$823$	−27.2553	−	27.2553i	−0.950059	−	0.950059i	0.0487521	−	0.998811i	$-0.484476\pi$
$823$	−27.2553	−	27.2553i	−0.950059	−	0.950059i	−0.998811	+	0.0487521i	$0.984476\pi$
$824$	9.29797	+	12.1389i	0.323910	+	0.422879i
$825$		0			0
$826$	0.139728	+	0.631126i	0.00486175	+	0.0219597i
$827$	31.4437	−	31.4437i	1.09341	−	1.09341i	0.0982432	−	0.995162i	$-0.468678\pi$
$827$	31.4437	−	31.4437i	1.09341	−	1.09341i	0.995162	−	0.0982432i	$-0.0313223\pi$
$828$		0			0
$829$		−	0.270718i		−	0.00940243i	−0.999989	−	0.00470122i	$-0.998504\pi$
$829$		−	0.270718i		−	0.00940243i	0.999989	−	0.00470122i	$-0.00149645\pi$
$830$		0			0
$831$		0			0
$832$	−17.2767	+	9.93522i	−0.598964	+	0.344442i
$833$	23.5187	−	23.5187i	0.814876	−	0.814876i
$834$		0			0
$835$		0			0
$836$	11.3694	−	5.29373i	0.393220	−	0.183088i
$837$		0			0
$838$	−14.4970	+	22.7414i	−0.500792	+	0.785589i
$839$	31.0214			1.07098			0.535489	−	0.844542i	$-0.320127\pi$
$839$	31.0214			1.07098			0.535489	+	0.844542i	$0.320127\pi$
$840$		0			0
$841$	28.2524			0.974221
$842$	−15.8147	+	24.8085i	−0.545011	+	0.854956i
$843$		0			0
$844$	9.95634	−	4.63578i	0.342711	−	0.159570i
$845$		0			0
$846$		0			0
$847$	9.35348	−	9.35348i	0.321389	−	0.321389i
$848$	−1.27785	−	14.8010i	−0.0438814	−	0.508267i
$849$		0			0
$850$		0			0
$851$		−	3.79441i		−	0.130071i
$852$		0			0
$853$	−3.82611	+	3.82611i	−0.131003	+	0.131003i	−0.769568	−	0.638565i	$-0.779528\pi$
$853$	−3.82611	+	3.82611i	−0.131003	+	0.131003i	0.638565	+	0.769568i	$0.279528\pi$
$854$	1.31675	+	5.94751i	0.0450581	+	0.203520i
$855$		0			0
$856$	−17.5004	+	13.4047i	−0.598152	+	0.458163i
$857$	20.7711	+	20.7711i	0.709529	+	0.709529i	0.966436	−	0.256907i	$-0.0827035\pi$
$857$	20.7711	+	20.7711i	0.709529	+	0.709529i	−0.256907	+	0.966436i	$0.582704\pi$
$858$		0			0
$859$	−1.69693			−0.0578985			−0.0289492	−	0.999581i	$-0.509216\pi$
$859$	−1.69693			−0.0578985			−0.0289492	+	0.999581i	$0.509216\pi$
$860$		0			0
$861$		0			0
$862$	18.2815	+	11.6540i	0.622670	+	0.396935i
$863$	−5.92869	−	5.92869i	−0.201815	−	0.201815i	0.598962	−	0.800777i	$-0.295580\pi$
$863$	−5.92869	−	5.92869i	−0.201815	−	0.201815i	−0.800777	+	0.598962i	$0.795580\pi$
$864$		0			0
$865$		0			0
$866$	7.03831	+	31.7908i	0.239171	+	1.08030i
$867$		0			0
$868$	4.62699	−	12.6900i	0.157050	−	0.430725i
$869$		−	81.6068i		−	2.76832i
$870$		0			0
$871$			21.8617i			0.740756i
$872$	−2.71891	+	20.5161i	−0.0920740	+	0.694762i
$873$		0			0
$874$	2.57162	−	0.569343i	0.0869865	−	0.0192583i
$875$		0			0
$876$		0			0
$877$	10.0323	+	10.0323i	0.338766	+	0.338766i	0.855903	−	0.517137i	$-0.173002\pi$
$877$	10.0323	+	10.0323i	0.338766	+	0.338766i	−0.517137	+	0.855903i	$0.673002\pi$
$878$	−18.7430	+	29.4020i	−0.632544	+	0.992269i
$879$		0			0
$880$		0			0
$881$	29.8130			1.00443			0.502213	−	0.864744i	$-0.332519\pi$
$881$	29.8130			1.00443			0.502213	+	0.864744i	$0.332519\pi$
$882$		0			0
$883$	−5.56557	−	5.56557i	−0.187296	−	0.187296i	0.607230	−	0.794526i	$-0.292281\pi$
$883$	−5.56557	−	5.56557i	−0.187296	−	0.187296i	−0.794526	+	0.607230i	$0.792281\pi$
$884$	−11.1877	−	24.0279i	−0.376282	−	0.808146i
$885$		0			0
$886$	−3.45856	+	0.765707i	−0.116193	+	0.0257244i
$887$	−8.59630	+	8.59630i	−0.288636	+	0.288636i	−0.836541	−	0.547905i	$-0.815426\pi$
$887$	−8.59630	+	8.59630i	−0.288636	+	0.288636i	0.547905	+	0.836541i	$0.315426\pi$
$888$		0			0
$889$			9.15994i			0.307214i
$890$		0			0
$891$		0			0
$892$	−10.5298	+	28.8791i	−0.352565	+	0.966943i
$893$	−2.81215	+	2.81215i	−0.0941052	+	0.0941052i
$894$		0			0
$895$		0			0
$896$	−0.446274	+	9.77211i	−0.0149090	+	0.326463i
$897$		0			0
$898$	39.5334	+	25.2015i	1.31925	+	0.840984i
$899$	6.75359			0.225245
$900$		0			0
$901$	19.7572			0.658207
$902$	33.7766	+	21.5316i	1.12464	+	0.716925i
$903$		0			0
$904$	1.61684	−	1.23844i	0.0537754	−	0.0411900i
$905$		0			0
$906$		0			0
$907$	31.6263	−	31.6263i	1.05013	−	1.05013i	0.0514592	−	0.998675i	$-0.483613\pi$
$907$	31.6263	−	31.6263i	1.05013	−	1.05013i	0.998675	−	0.0514592i	$-0.0163872\pi$
$908$	13.2398	+	4.82748i	0.439379	+	0.160206i
$909$		0			0
$910$		0			0
$911$		−	42.2656i		−	1.40032i	−0.713985	−	0.700161i	$-0.753112\pi$
$911$		−	42.2656i		−	1.40032i	0.713985	−	0.700161i	$-0.246888\pi$
$912$		0			0
$913$	−40.8034	+	40.8034i	−1.35040	+	1.35040i
$914$	14.6547	−	3.24448i	0.484735	−	0.107318i
$915$		0			0
$916$	−46.7003	+	21.7442i	−1.54302	+	0.718448i
$917$	8.55728	+	8.55728i	0.282586	+	0.282586i
$918$		0			0
$919$	31.2829			1.03193			0.515964	−	0.856610i	$-0.327434\pi$
$919$	31.2829			1.03193			0.515964	+	0.856610i	$0.327434\pi$
$920$		0			0
$921$		0			0
$922$	20.5418	−	32.2238i	0.676508	−	1.06123i
$923$	−14.2729	−	14.2729i	−0.469798	−	0.469798i
$924$		0			0
$925$		0			0
$926$	54.1143	−	11.9806i	1.77831	−	0.393707i
$927$		0			0
$928$	−4.66687	+	1.46412i	−0.153198	+	0.0480621i
$929$		−	22.1050i		−	0.725241i	−0.931937	−	0.362620i	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$		0			0
$931$		−	7.64535i		−	0.250566i
$932$	1.90084	+	0.693082i	0.0622641	+	0.0227026i
$933$		0			0
$934$	−0.868197	−	3.92150i	−0.0284083	−	0.128315i
$935$		0			0
$936$		0			0
$937$	15.2986	+	15.2986i	0.499784	+	0.499784i	0.911371	−	0.411586i	$-0.135025\pi$
$937$	15.2986	+	15.2986i	0.499784	+	0.499784i	−0.411586	+	0.911371i	$0.635025\pi$
$938$	9.04843	+	5.76813i	0.295442	+	0.188336i
$939$		0			0
$940$		0			0
$941$	−25.5264			−0.832138			−0.416069	−	0.909333i	$-0.636593\pi$
$941$	−25.5264			−0.832138			−0.416069	+	0.909333i	$0.636593\pi$
$942$		0			0
$943$	5.94842	+	5.94842i	0.193707	+	0.193707i
$944$	−1.36106	+	1.61828i	−0.0442986	+	0.0526704i
$945$		0			0
$946$	13.7572	+	62.1388i	0.447285	+	2.02031i
$947$	−11.9881	+	11.9881i	−0.389562	+	0.389562i	−0.874531	−	0.484969i	$-0.838831\pi$
$947$	−11.9881	+	11.9881i	−0.389562	+	0.389562i	0.484969	+	0.874531i	$0.338831\pi$
$948$		0			0
$949$			7.93545i			0.257596i
$950$		0			0
$951$		0			0
$952$	−12.8968	−	1.70916i	−0.417988	−	0.0553943i
$953$	5.99563	−	5.99563i	0.194218	−	0.194218i	−0.603298	−	0.797516i	$-0.706147\pi$
$953$	5.99563	−	5.99563i	0.194218	−	0.194218i	0.797516	+	0.603298i	$0.206147\pi$
$954$		0			0
$955$		0			0
$956$	22.7389	+	48.8366i	0.735427	+	1.57949i
$957$		0			0
$958$	−10.4598	+	16.4082i	−0.337940	+	0.530125i
$959$	−8.57657			−0.276952
$960$		0			0
$961$	−30.0096			−0.968051
$962$	−4.71791	+	7.40097i	−0.152112	+	0.238617i
$963$		0			0
$964$	−11.8968	−	25.5510i	−0.383171	−	0.822943i
$965$		0			0
$966$		0			0
$967$	−1.66866	+	1.66866i	−0.0536606	+	0.0536606i	−0.733428	−	0.679767i	$-0.762081\pi$
$967$	−1.66866	+	1.66866i	−0.0536606	+	0.0536606i	0.679767	+	0.733428i	$0.262081\pi$
$968$	42.8960	+	5.68483i	1.37873	+	0.182717i
$969$		0			0
$970$		0			0
$971$			4.79719i			0.153949i	0.997033	+	0.0769745i	$0.0245260\pi$
$971$			4.79719i			0.153949i	−0.997033	+	0.0769745i	$0.975474\pi$
$972$		0			0
$973$	1.39401	−	1.39401i	0.0446900	−	0.0446900i
$974$	10.5208	+	47.5204i	0.337107	+	1.52265i
$975$		0			0
$976$	−12.8261	+	15.2501i	−0.410554	+	0.488143i
$977$	−25.0140	−	25.0140i	−0.800267	−	0.800267i	0.182870	−	0.983137i	$-0.441461\pi$
$977$	−25.0140	−	25.0140i	−0.800267	−	0.800267i	−0.983137	+	0.182870i	$0.941461\pi$
$978$		0			0
$979$	37.1919			1.18866
$980$		0			0
$981$		0			0
$982$	−34.4540	−	21.9635i	−1.09947	−	0.700884i
$983$	30.9151	+	30.9151i	0.986038	+	0.986038i	0.999904	−	0.0138655i	$-0.00441368\pi$
$983$	30.9151	+	30.9151i	0.986038	+	0.986038i	−0.0138655	+	0.999904i	$0.504414\pi$
$984$		0			0
$985$		0			0
$986$	−1.40608	−	6.35101i	−0.0447786	−	0.202257i
$987$		0			0
$988$	−5.72384	−	2.08702i	−0.182100	−	0.0663969i
$989$			13.3661i			0.425017i
$990$		0			0
$991$			26.5873i			0.844575i	0.906462	+	0.422287i	$0.138773\pi$
$991$			26.5873i			0.844575i	−0.906462	+	0.422287i	$0.861227\pi$
$992$	42.1589	−	13.2264i	1.33855	−	0.419937i
$993$		0			0
$994$	−9.67331	+	2.14162i	−0.306819	+	0.0679280i
$995$		0			0
$996$		0			0
$997$	2.47252	+	2.47252i	0.0783054	+	0.0783054i	0.745175	−	0.666869i	$-0.232366\pi$
$997$	2.47252	+	2.47252i	0.0783054	+	0.0783054i	−0.666869	+	0.745175i	$0.732366\pi$
$998$	9.53021	−	14.9500i	0.301674	−	0.473234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.k.n.307.5		12
3.2	odd	2		300.2.j.d.7.2		12
4.3	odd	2	inner	900.2.k.n.307.2		12
5.2	odd	4		180.2.k.e.163.5		12
5.3	odd	4	inner	900.2.k.n.343.2		12
5.4	even	2		180.2.k.e.127.2		12
12.11	even	2		300.2.j.d.7.5		12
15.2	even	4		60.2.j.a.43.2	yes	12
15.8	even	4		300.2.j.d.43.5		12
15.14	odd	2		60.2.j.a.7.5	yes	12
20.3	even	4	inner	900.2.k.n.343.5		12
20.7	even	4		180.2.k.e.163.2		12
20.19	odd	2		180.2.k.e.127.5		12
60.23	odd	4		300.2.j.d.43.2		12
60.47	odd	4		60.2.j.a.43.5	yes	12
60.59	even	2		60.2.j.a.7.2	✓	12
120.29	odd	2		960.2.w.g.127.5		12
120.59	even	2		960.2.w.g.127.2		12
120.77	even	4		960.2.w.g.703.2		12
120.107	odd	4		960.2.w.g.703.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.2	✓	12	60.59	even	2
60.2.j.a.7.5	yes	12	15.14	odd	2
60.2.j.a.43.2	yes	12	15.2	even	4
60.2.j.a.43.5	yes	12	60.47	odd	4
180.2.k.e.127.2		12	5.4	even	2
180.2.k.e.127.5		12	20.19	odd	2
180.2.k.e.163.2		12	20.7	even	4
180.2.k.e.163.5		12	5.2	odd	4
300.2.j.d.7.2		12	3.2	odd	2
300.2.j.d.7.5		12	12.11	even	2
300.2.j.d.43.2		12	60.23	odd	4
300.2.j.d.43.5		12	15.8	even	4
900.2.k.n.307.2		12	4.3	odd	2	inner
900.2.k.n.307.5		12	1.1	even	1	trivial
900.2.k.n.343.2		12	5.3	odd	4	inner
900.2.k.n.343.5		12	20.3	even	4	inner
960.2.w.g.127.2		12	120.59	even	2
960.2.w.g.127.5		12	120.29	odd	2
960.2.w.g.703.2		12	120.77	even	4
960.2.w.g.703.5		12	120.107	odd	4

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

\(f(q)\)	\(=\)	\(q+(0.760198 - 1.19252i) q^{2} +(-0.844199 - 1.81310i) q^{4} +(-0.611393 + 0.611393i) q^{7} +(-2.80391 - 0.371591i) q^{8} +O(q^{10})\)	\(q+(0.760198 - 1.19252i) q^{2} +(-0.844199 - 1.81310i) q^{4} +(-0.611393 + 0.611393i) q^{7} +(-2.80391 - 0.371591i) q^{8} -5.12822i q^{11} +(-1.76156 + 1.76156i) q^{13} +(0.264318 + 1.19388i) q^{14} +(-2.57466 + 3.06123i) q^{16} +(-3.76156 - 3.76156i) q^{17} -1.22279 q^{19} +(-6.11549 - 3.89846i) q^{22} +(-1.07700 - 1.07700i) q^{23} +(0.761557 + 3.43982i) q^{26} +(1.62465 + 0.592379i) q^{28} +0.864641i q^{29} -7.81086i q^{31} +(1.69333 + 5.39747i) q^{32} +(-7.34525 + 1.62620i) q^{34} +(1.76156 + 1.76156i) q^{37} +(-0.929560 + 1.45820i) q^{38} -5.52311 q^{41} +(-6.20522 - 6.20522i) q^{43} +(-9.29797 + 4.32924i) q^{44} +(-2.10308 + 0.465611i) q^{46} +(2.29979 - 2.29979i) q^{47} +6.25240i q^{49} +(4.68098 + 1.70677i) q^{52} +(-2.62620 + 2.62620i) q^{53} +(1.94148 - 1.48710i) q^{56} +(1.03110 + 0.657298i) q^{58} +0.528636 q^{59} +4.98168 q^{61} +(-9.31460 - 5.93780i) q^{62} +(7.72384 + 2.08382i) q^{64} +(6.20522 - 6.20522i) q^{67} +(-3.64457 + 9.99558i) q^{68} +8.10243i q^{71} +(2.25240 - 2.25240i) q^{73} +(3.43982 - 0.761557i) q^{74} +(1.03228 + 2.21703i) q^{76} +(3.13536 + 3.13536i) q^{77} +15.9133 q^{79} +(-4.19866 + 6.58641i) q^{82} +(-7.95665 - 7.95665i) q^{83} +(-12.1170 + 2.68264i) q^{86} +(-1.90560 + 14.3791i) q^{88} +7.25240i q^{89} -2.15401i q^{91} +(-1.04351 + 2.86192i) q^{92} +(-0.994247 - 4.49084i) q^{94} +(-0.793833 - 0.793833i) q^{97} +(7.45610 + 4.75306i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^8	\( 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61} - 56 q^{62} - 16 q^{68} - 44 q^{73} + 8 q^{76} + 48 q^{77} - 16 q^{82} - 64 q^{86} - 60 q^{88} + 56 q^{92} + 20 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 12 * q^8 + 4 * q^13 + 12 * q^16 - 20 * q^17 - 12 * q^22 - 16 * q^26 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 40 * q^46 + 8 * q^52 + 4 * q^53 + 64 * q^56 + 20 * q^58 - 32 * q^61 - 56 * q^62 - 16 * q^68 - 44 * q^73 + 8 * q^76 + 48 * q^77 - 16 * q^82 - 64 * q^86 - 60 * q^88 + 56 * q^92 + 20 * q^97 + 24 * q^98

Introduction

L-functions

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