LMFDB - Embedded newform 900.2.k.n.307.2

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			307.2
Root			$-0.760198 - 1.19252i$ of defining polynomial
Character	$\chi$	$=$	900.307
Dual form			900.2.k.n.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−1.19252	+	0.760198i	−0.843238	+	0.537541i
$2$	−1.19252	+	0.760198i	−0.843238	+	0.537541i
$3$		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	−0.582060	−	0.813145i	$-0.697753\pi$
$7$	0.611393	−	0.611393i	0.231085	−	0.231085i	0.813145	+	0.582060i	$0.197753\pi$
$8$	0.371591	+	2.80391i	0.131377	+	0.991332i
$9$		0			0
$10$		0			0
$11$			5.12822i			1.54622i	0.634274	+	0.773108i	$0.281299\pi$
$11$			5.12822i			1.54622i	−0.634274	+	0.773108i	$0.718701\pi$
$12$		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	$-0.455205\pi$
$19$	1.22279			0.280527			0.140263	+	0.990114i	$0.455205\pi$
$20$		0			0
$21$		0			0
$22$	−3.89846	−	6.11549i	−0.831154	−	1.30383i
$23$	1.07700	+	1.07700i	0.224571	+	0.224571i	0.810420	−	0.585849i	$-0.199239\pi$
$23$	1.07700	+	1.07700i	0.224571	+	0.224571i	−0.585849	+	0.810420i	$0.699239\pi$
$24$		0			0
$25$		0			0
$26$	0.761557	−	3.43982i	0.149354	−	0.674604i
$27$		0			0
$28$	−0.592379	−	1.62465i	−0.111949	−	0.307031i
$29$			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	$0.247457\pi$
$31$			7.81086i			1.40287i	−0.712732	+	0.701436i	$0.752543\pi$
$32$	5.39747	+	1.69333i	0.954146	+	0.299341i
$33$		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	$0.684353\pi$
$38$	−1.45820	+	0.929560i	−0.236551	+	0.150795i
$39$		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	0.998629	−	0.0523416i	$-0.0166685\pi$
$43$	6.20522	+	6.20522i	0.946288	+	0.946288i	−0.0523416	+	0.998629i	$0.516668\pi$
$44$	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	−0.854655	−	0.519196i	$-0.826231\pi$
$47$	−2.29979	+	2.29979i	−0.335459	+	0.335459i	0.519196	+	0.854655i	$0.326231\pi$
$48$		0			0
$49$			6.25240i			0.893199i
$50$		0			0
$51$		0			0
$52$	1.70677	+	4.68098i	0.236687	+	0.649135i
$53$	−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
$58$	−0.657298	−	1.03110i	−0.0863075	−	0.135390i
$59$	−0.528636			−0.0688225			−0.0344113	−	0.999408i	$-0.510956\pi$
$59$	−0.528636			−0.0688225			−0.0344113	+	0.999408i	$0.510956\pi$
$60$		0			0
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	−5.93780	−	9.31460i	−0.754101	−	1.18295i
$63$		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	−0.975974	−	0.217886i	$-0.930084\pi$
$67$	−6.20522	+	6.20522i	−0.758089	+	0.758089i	0.217886	+	0.975974i	$0.430084\pi$
$68$	−9.99558	+	3.64457i	−1.21214	+	0.441969i
$69$		0			0
$70$		0			0
$71$		−	8.10243i		−	0.961581i	−0.876835	−	0.480791i	$-0.840350\pi$
$71$		−	8.10243i		−	0.961581i	0.876835	−	0.480791i	$-0.159650\pi$
$72$		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	$-0.852962\pi$
$79$	−15.9133			−1.79039			−0.895193	+	0.445680i	$0.852962\pi$
$80$		0			0
$81$		0			0
$82$	6.58641	−	4.19866i	0.727348	−	0.463664i
$83$	7.95665	+	7.95665i	0.873355	+	0.873355i	0.992836	−	0.119481i	$-0.0381231\pi$
$83$	7.95665	+	7.95665i	0.873355	+	0.873355i	−0.119481	+	0.992836i	$0.538123\pi$
$84$		0			0
$85$		0			0
$86$	−12.1170	−	2.68264i	−1.30661	−	0.289277i
$87$		0			0
$88$	−14.3791	+	1.90560i	−1.53281	+	0.203138i
$89$			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
$92$	2.86192	−	1.04351i	0.298376	−	0.108793i
$93$		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	$0.768152\pi$
$98$	−4.75306	−	7.45610i	−0.480131	−	0.753179i
$99$		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	0.869895	−	0.493236i	$-0.164186\pi$
$103$	3.82267	+	3.82267i	0.376659	+	0.376659i	−0.493236	+	0.869895i	$0.664186\pi$
$104$	−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	−0.921397	−	0.388622i	$-0.872951\pi$
$107$	−5.51107	+	5.51107i	−0.532775	+	0.532775i	0.388622	+	0.921397i	$0.372951\pi$
$108$		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
$112$	−3.44575	−	0.297490i	−0.325592	−	0.0281101i
$113$	−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
$118$	0.630408	−	0.401868i	0.0580337	−	0.0369949i
$119$	−4.59958			−0.421643
$120$		0			0
$121$	−15.2986			−1.39078
$122$	−5.94074	+	3.78706i	−0.537849	+	0.342864i
$123$		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	−0.956489	−	0.291767i	$-0.905757\pi$
$127$	−7.49103	+	7.49103i	−0.664722	+	0.664722i	0.291767	+	0.956489i	$0.405757\pi$
$128$	7.62671	−	8.35664i	0.674112	−	0.738629i
$129$		0			0
$130$		0			0
$131$			13.9964i			1.22287i	0.791296	+	0.611434i	$0.209407\pi$
$131$			13.9964i			1.22287i	−0.791296	+	0.611434i	$0.790593\pi$
$132$		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	$-0.469173\pi$
$139$	2.28006			0.193392			0.0966960	+	0.995314i	$0.469173\pi$
$140$		0			0
$141$		0			0
$142$	6.15945	+	9.66229i	0.516889	+	0.810842i
$143$	−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
$148$	4.68098	−	1.70677i	0.384774	−	0.140296i
$149$		−	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	$0.104674\pi$
$151$			7.93691i			0.645897i	−0.946417	+	0.322948i	$0.895326\pi$
$152$	0.454377	+	3.42859i	0.0368548	+	0.278095i
$153$		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	$0.919869\pi$
$158$	18.9769	−	12.0972i	1.50972	−	0.962405i
$159$		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	$-0.991977\pi$
$163$	−13.0849	−	13.0849i	−1.02489	−	1.02489i	−0.0252033	−	0.999682i	$-0.508023\pi$
$164$	−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	−0.116216	−	0.993224i	$-0.537076\pi$
$167$	11.3334	−	11.3334i	0.877008	−	0.877008i	0.993224	+	0.116216i	$0.0370765\pi$
$168$		0			0
$169$			6.79383i			0.522603i
$170$		0			0
$171$		0			0
$172$	16.4891	−	6.01224i	1.25728	−	0.458429i
$173$	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
$178$	−5.51325	−	8.64861i	−0.413236	−	0.648241i
$179$	−12.6475			−0.945320			−0.472660	−	0.881245i	$-0.656706\pi$
$179$	−12.6475			−0.945320			−0.472660	+	0.881245i	$0.656706\pi$
$180$		0			0
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	−1.63747	−	2.56869i	−0.121378	−	0.190404i
$183$		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
$188$	2.22827	+	6.11123i	0.162513	+	0.445707i
$189$		0			0
$190$		0			0
$191$			7.04516i			0.509770i	0.966971	+	0.254885i	$0.0820376\pi$
$191$			7.04516i			0.509770i	−0.966971	+	0.254885i	$0.917962\pi$
$192$		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	$-0.366620\pi$
$199$	11.4792			0.813741			0.406870	+	0.913486i	$0.366620\pi$
$200$		0			0
$201$		0			0
$202$	−12.0648	+	7.69095i	−0.848873	+	0.541133i
$203$	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
$208$	9.92794	+	0.857132i	0.688379	+	0.0594314i
$209$			6.27072i			0.433755i
$210$		0			0
$211$		−	5.49134i		−	0.378039i	−0.981973	−	0.189020i	$-0.939469\pi$
$211$		−	5.49134i		−	0.378039i	0.981973	−	0.189020i	$-0.0605310\pi$
$212$	2.54452	+	6.97859i	0.174759	+	0.479292i
$213$		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
$218$	5.56233	+	8.72559i	0.376728	+	0.590972i
$219$		0			0
$220$		0			0
$221$	13.2524			0.891453
$222$		0			0
$223$	10.8678	+	10.8678i	0.727764	+	0.727764i	0.970174	−	0.242410i	$-0.0779380\pi$
$223$	10.8678	+	10.8678i	0.727764	+	0.727764i	−0.242410	+	0.970174i	$0.577938\pi$
$224$	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	−0.522155	−	0.852851i	$-0.674872\pi$
$227$	4.98244	−	4.98244i	0.330696	−	0.330696i	0.852851	+	0.522155i	$0.174872\pi$
$228$		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
$232$	−2.42438	+	0.321293i	−0.159168	+	0.0210939i
$233$	−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
$238$	5.48509	−	3.49659i	0.355545	−	0.226650i
$239$	26.9354			1.74231			0.871154	−	0.491009i	$-0.163372\pi$
$239$	26.9354			1.74231			0.871154	+	0.491009i	$0.163372\pi$
$240$		0			0
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	18.2439	−	11.6300i	1.17276	−	0.747603i
$243$		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
$248$	−21.9010	+	2.90245i	−1.39071	+	0.184306i
$249$		0			0
$250$		0			0
$251$		−	17.2471i		−	1.08863i	−0.838882	−	0.544314i	$-0.816790\pi$
$251$		−	17.2471i		−	1.08863i	0.838882	−	0.544314i	$-0.183210\pi$
$252$		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
$262$	−10.6400	−	16.6909i	−0.657341	−	1.03117i
$263$	−6.73386	−	6.73386i	−0.415228	−	0.415228i	0.468327	−	0.883555i	$-0.344857\pi$
$263$	−6.73386	−	6.73386i	−0.415228	−	0.415228i	−0.883555	+	0.468327i	$0.844857\pi$
$264$		0			0
$265$		0			0
$266$	−0.323204	+	1.45986i	−0.0198169	+	0.0895096i
$267$		0			0
$268$	6.01224	+	16.4891i	0.367256	+	1.00723i
$269$		−	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	$-0.990996\pi$
$271$		−	0.931222i		−	0.0565677i	0.999600	−	0.0282839i	$-0.00900423\pi$
$272$	−1.83029	+	21.1997i	−0.110977	+	1.28542i
$273$		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	$0.363365\pi$
$278$	−2.71901	+	1.73330i	−0.163075	+	0.103956i
$279$		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	0.273949	−	0.961744i	$-0.411670\pi$
$283$	−11.5705	−	11.5705i	−0.687796	−	0.687796i	−0.961744	+	0.273949i	$0.911670\pi$
$284$	−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
$292$	−2.18235	−	5.98529i	−0.127712	−	0.350262i
$293$	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
$298$	7.69095	+	12.0648i	0.445525	+	0.698892i
$299$	−3.79441			−0.219436
$300$		0			0
$301$	7.58767			0.437346
$302$	−6.03362	−	9.46491i	−0.347196	−	0.544644i
$303$		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	−0.751440	−	0.659801i	$-0.770640\pi$
$307$	−1.60564	+	1.60564i	−0.0916387	+	0.0916387i	0.659801	+	0.751440i	$0.270640\pi$
$308$	8.33158	−	3.03785i	0.474736	−	0.173098i
$309$		0			0
$310$		0			0
$311$		−	19.4161i		−	1.10099i	−0.834839	−	0.550494i	$-0.814439\pi$
$311$		−	19.4161i		−	1.10099i	0.834839	−	0.550494i	$-0.185561\pi$
$312$		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
$322$	−1.57048	+	1.00114i	−0.0875196	+	0.0557914i
$323$	−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
$328$	−2.05234	−	15.4863i	−0.113322	−	0.855089i
$329$			2.81215i			0.155039i
$330$		0			0
$331$		−	31.7005i		−	1.74242i	−0.490912	−	0.871209i	$-0.663336\pi$
$331$		−	31.7005i		−	1.74242i	0.490912	−	0.871209i	$-0.336664\pi$
$332$	21.1432	−	7.70919i	1.16038	−	0.423097i
$333$		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	$-0.510686\pi$
$338$	−5.16466	−	8.10177i	−0.280920	−	0.440678i
$339$		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	−0.883271	−	0.468863i	$-0.844664\pi$
$347$	−7.71957	+	7.71957i	−0.414408	+	0.414408i	0.468863	+	0.883271i	$0.344664\pi$
$348$		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
$352$	−8.68375	+	27.6794i	−0.462846	+	1.47532i
$353$	−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
$358$	15.0824	−	9.61461i	0.797129	−	0.508148i
$359$	−14.2334			−0.751211			−0.375606	−	0.926780i	$-0.622565\pi$
$359$	−14.2334			−0.751211			−0.375606	+	0.926780i	$0.622565\pi$
$360$		0			0
$361$	−17.5048			−0.921305
$362$	−9.21731	+	5.87578i	−0.484451	+	0.308824i
$363$		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	−0.778534	−	0.627602i	$-0.784037\pi$
$367$	−2.89145	+	2.89145i	−0.150933	+	0.150933i	0.627602	+	0.778534i	$0.284037\pi$
$368$	0.524045	−	6.06988i	0.0273177	−	0.316414i
$369$		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	$-0.370063\pi$
$379$	15.4562			0.793932			0.396966	+	0.917833i	$0.370063\pi$
$380$		0			0
$381$		0			0
$382$	−5.35571	−	8.40148i	−0.274022	−	0.429857i
$383$	12.5562	+	12.5562i	0.641593	+	0.641593i	0.950947	−	0.309354i	$-0.100113\pi$
$383$	12.5562	+	12.5562i	0.641593	+	0.641593i	−0.309354	+	0.950947i	$0.600113\pi$
$384$		0			0
$385$		0			0
$386$	−4.97376	+	22.4656i	−0.253158	+	1.14347i
$387$		0			0
$388$	−2.10945	+	0.769144i	−0.107091	+	0.0390474i
$389$			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
$392$	−17.5312	+	2.32333i	−0.885458	+	0.117346i
$393$		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	$0.710782\pi$
$398$	−13.6892	+	8.72648i	−0.686177	+	0.437419i
$399$		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
$412$	10.1580	−	3.70379i	0.500448	−	0.182473i
$413$	−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
$418$	−4.76699	−	7.47795i	−0.233161	−	0.365758i
$419$	19.0701			0.931634			0.465817	−	0.884881i	$-0.345760\pi$
$419$	19.0701			0.931634			0.465817	+	0.884881i	$0.345760\pi$
$420$		0			0
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	4.17450	+	6.54852i	0.203212	+	0.318777i
$423$		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
$428$	5.33968	+	14.6446i	0.258103	+	0.707872i
$429$		0			0
$430$		0			0
$431$		−	15.3302i		−	0.738428i	−0.929344	−	0.369214i	$-0.879627\pi$
$431$		−	15.3302i		−	0.738428i	0.929344	−	0.369214i	$-0.120373\pi$
$432$		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	$-0.299770\pi$
$439$	24.6554			1.17674			0.588368	+	0.808593i	$0.299770\pi$
$440$		0			0
$441$		0			0
$442$	−15.8037	+	10.0744i	−0.751706	+	0.479192i
$443$	1.77116	+	1.77116i	0.0841501	+	0.0841501i	0.747929	−	0.663779i	$-0.231048\pi$
$443$	1.77116	+	1.77116i	0.0841501	+	0.0841501i	−0.663779	+	0.747929i	$0.731048\pi$
$444$		0			0
$445$		0			0
$446$	−21.2218	−	4.69839i	−1.00488	−	0.222475i
$447$		0			0
$448$	−3.44827	+	5.99634i	−0.162916	+	0.283300i
$449$			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
$452$	0.493326	+	1.35299i	0.0232041	+	0.0636394i
$453$		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	$0.670149\pi$
$458$	19.5806	+	30.7159i	0.914939	+	1.43526i
$459$		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	$-0.885555\pi$
$463$	−27.7123	−	27.7123i	−1.28790	−	1.28790i	−0.351843	−	0.936059i	$-0.614445\pi$
$464$	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	−0.752043	−	0.659114i	$-0.770932\pi$
$467$	−2.00823	+	2.00823i	−0.0929296	+	0.0929296i	0.659114	+	0.752043i	$0.270932\pi$
$468$		0			0
$469$			7.58767i			0.350366i
$470$		0			0
$471$		0			0
$472$	−0.196436	−	1.48225i	−0.00904172	−	0.0682260i
$473$	−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
$478$	−32.1210	+	20.4763i	−1.46918	+	0.936562i
$479$	13.7593			0.628678			0.314339	−	0.949311i	$-0.398217\pi$
$479$	13.7593			0.628678			0.314339	+	0.949311i	$0.398217\pi$
$480$		0			0
$481$	−6.20617			−0.282977
$482$	−16.8055	+	10.7131i	−0.765470	+	0.487966i
$483$		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	$-0.465340\pi$
$487$	24.3355	−	24.3355i	1.10275	−	1.10275i	0.994078	−	0.108671i	$-0.0346596\pi$
$488$	1.85115	+	13.9682i	0.0837975	+	0.632310i
$489$		0			0
$490$		0			0
$491$			28.8918i			1.30387i	0.758275	+	0.651935i	$0.226043\pi$
$491$			28.8918i			1.30387i	−0.758275	+	0.651935i	$0.773957\pi$
$492$		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	$-0.590535\pi$
$499$	−12.5365			−0.561211			−0.280605	+	0.959823i	$0.590535\pi$
$500$		0			0
$501$		0			0
$502$	13.1112	+	20.5675i	0.585182	+	0.917972i
$503$	−9.01392	−	9.01392i	−0.401911	−	0.401911i	0.476995	−	0.878906i	$-0.341726\pi$
$503$	−9.01392	−	9.01392i	−0.401911	−	0.401911i	−0.878906	+	0.476995i	$0.841726\pi$
$504$		0			0
$505$		0			0
$506$	2.38776	−	10.7851i	0.106149	−	0.479455i
$507$		0			0
$508$	7.25806	+	19.9059i	0.322025	+	0.883182i
$509$			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
$512$	−8.71295	−	20.8826i	−0.385062	−	0.922891i
$513$		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
$518$	−2.56869	+	1.63747i	−0.112862	+	0.0719464i
$519$		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	0.999006	−	0.0445800i	$-0.0141949\pi$
$523$	21.8269	+	21.8269i	0.954426	+	0.954426i	−0.0445800	+	0.999006i	$0.514195\pi$
$524$	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
$532$	−0.724353	−	1.98661i	−0.0314047	−	0.0861303i
$533$	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
$538$	19.5407	+	30.6533i	0.842457	+	1.32156i
$539$	−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	$0.445969\pi$
$542$	0.707913	+	1.11050i	0.0304075	+	0.0477000i
$543$		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	−0.976597	−	0.215076i	$-0.931000\pi$
$547$	−17.8105	+	17.8105i	−0.761522	+	0.761522i	0.215076	+	0.976597i	$0.431000\pi$
$548$	18.6382	−	6.79582i	0.796183	−	0.290303i
$549$		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
$562$	10.2191	−	6.51439i	0.431067	−	0.274793i
$563$	−5.27400	−	5.27400i	−0.222273	−	0.222273i	0.587182	−	0.809455i	$-0.300237\pi$
$563$	−5.27400	−	5.27400i	−0.222273	−	0.222273i	−0.809455	+	0.587182i	$0.800237\pi$
$564$		0			0
$565$		0			0
$566$	22.5939	+	5.00217i	0.949693	+	0.210257i
$567$		0			0
$568$	22.7185	−	3.01079i	0.953247	−	0.126330i
$569$		−	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	$0.236078\pi$
$571$			32.2837i			1.35103i	−0.737347	+	0.675515i	$0.763922\pi$
$572$	−24.0051	+	8.75270i	−1.00370	+	0.365969i
$573$		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	$-0.542858\pi$
$578$	−8.58919	−	13.4738i	−0.357263	−	0.560437i
$579$		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	−0.258039	−	0.966135i	$-0.583076\pi$
$587$	17.1558	−	17.1558i	0.708096	−	0.708096i	0.966135	+	0.258039i	$0.0830761\pi$
$588$		0			0
$589$			9.55102i			0.393543i
$590$		0			0
$591$		0			0
$592$	0.857132	−	9.92794i	0.0352279	−	0.408036i
$593$	−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
$598$	4.52490	−	2.88450i	0.185037	−	0.117956i
$599$	23.7636			0.970955			0.485478	−	0.874249i	$-0.338646\pi$
$599$	23.7636			0.970955			0.485478	+	0.874249i	$0.338646\pi$
$600$		0			0
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	−9.04843	+	5.76813i	−0.368786	+	0.235091i
$603$		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	−0.870974	−	0.491328i	$-0.836511\pi$
$607$	−9.35348	+	9.35348i	−0.379646	+	0.379646i	0.491328	+	0.870974i	$0.336511\pi$
$608$	6.59995	+	2.07058i	0.267663	+	0.0839731i
$609$		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	$-0.292971\pi$
$619$	30.1297			1.21101			0.605507	+	0.795840i	$0.292971\pi$
$620$		0			0
$621$		0			0
$622$	14.7601	+	23.1541i	0.591826	+	0.928395i
$623$	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
$628$	−23.9528	+	8.73362i	−0.955819	+	0.348509i
$629$		−	13.2524i		−	0.528408i
$630$		0			0
$631$			21.5701i			0.858694i	0.903140	+	0.429347i	$0.141256\pi$
$631$			21.5701i			0.858694i	−0.903140	+	0.429347i	$0.858744\pi$
$632$	−5.91324	−	44.6195i	−0.235216	−	1.77487i
$633$		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
$638$	5.28771	−	3.37077i	0.209342	−	0.133450i
$639$		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	0.997064	−	0.0765729i	$-0.0243978\pi$
$643$	23.3413	+	23.3413i	0.920491	+	0.920491i	−0.0765729	+	0.997064i	$0.524398\pi$
$644$	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	$0.607892\pi$
$647$	−32.4465	+	32.4465i	−1.27560	+	1.27560i	−0.943103	+	0.332501i	$0.892108\pi$
$648$		0			0
$649$		−	2.71096i		−	0.106414i
$650$		0			0
$651$		0			0
$652$	−34.7704	+	12.6779i	−1.36171	+	0.496506i
$653$	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
$658$	−2.13779	−	3.35355i	−0.0833399	−	0.130735i
$659$	47.5028			1.85045			0.925223	−	0.379423i	$-0.123878\pi$
$659$	47.5028			1.85045			0.925223	+	0.379423i	$0.123878\pi$
$660$		0			0
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	24.0987	+	37.8035i	0.936621	+	1.46927i
$663$		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
$668$	−10.9810	−	30.1163i	−0.424867	−	1.16524i
$669$		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
$682$	47.7673	−	30.4503i	1.82910	−	1.16600i
$683$	−8.43079	−	8.43079i	−0.322595	−	0.322595i	0.527167	−	0.849762i	$-0.323254\pi$
$683$	−8.43079	−	8.43079i	−0.322595	−	0.322595i	−0.849762	+	0.527167i	$0.823254\pi$
$684$		0			0
$685$		0			0
$686$	−15.8217	−	3.50285i	−0.604077	−	0.133739i
$687$		0			0
$688$	3.01932	−	34.9719i	0.115110	−	1.33329i
$689$		−	9.25240i		−	0.352488i
$690$		0			0
$691$			21.9182i			0.833809i	0.908950	+	0.416905i	$0.136885\pi$
$691$			21.9182i			0.833809i	−0.908950	+	0.416905i	$0.863115\pi$
$692$	−7.71993	−	21.1726i	−0.293468	−	0.804862i
$693$		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
$698$	−20.5817	−	32.2864i	−0.779029	−	1.22206i
$699$		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
$712$	−20.3351	+	2.69493i	−0.762089	+	0.100997i
$713$	−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
$718$	16.9736	−	10.8202i	0.633450	−	0.403807i
$719$	−52.0874			−1.94253			−0.971265	−	0.237999i	$-0.923508\pi$
$719$	−52.0874			−1.94253			−0.971265	+	0.237999i	$0.923508\pi$
$720$		0			0
$721$	4.67432			0.174081
$722$	20.8748	−	13.3071i	0.776879	−	0.495239i
$723$		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	−0.540070	−	0.841620i	$-0.681602\pi$
$727$	8.13069	−	8.13069i	0.301551	−	0.301551i	0.841620	+	0.540070i	$0.181602\pi$
$728$	−6.03965	+	0.800411i	−0.223844	+	0.0296652i
$729$		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	$-0.758622\pi$
$739$	−39.4719			−1.45200			−0.725999	+	0.687696i	$0.758622\pi$
$740$		0			0
$741$		0			0
$742$	−2.44121	−	3.82951i	−0.0896196	−	0.140586i
$743$	12.2252	+	12.2252i	0.448499	+	0.448499i	0.894855	−	0.446356i	$-0.147279\pi$
$743$	12.2252	+	12.2252i	0.448499	+	0.448499i	−0.446356	+	0.894855i	$0.647279\pi$
$744$		0			0
$745$		0			0
$746$	−4.87859	+	22.0358i	−0.178618	+	0.806786i
$747$		0			0
$748$	−18.6902	−	51.2595i	−0.683380	−	1.87423i
$749$			6.73887i			0.246233i
$750$		0			0
$751$		−	28.9069i		−	1.05483i	−0.849609	−	0.527413i	$-0.823162\pi$
$751$		−	28.9069i		−	1.05483i	0.849609	−	0.527413i	$-0.176838\pi$
$752$	12.9614	+	1.11902i	0.472652	+	0.0408066i
$753$		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	$0.613295\pi$
$758$	−18.4318	+	11.7498i	−0.669474	+	0.426771i
$759$		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
$772$	−11.1470	−	30.5717i	−0.401189	−	1.10030i
$773$	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
$778$	−3.92510	−	6.15729i	−0.140722	−	0.220749i
$779$	−6.75359			−0.241973
$780$		0			0
$781$	41.5510			1.48681
$782$	6.15945	+	9.66229i	0.220261	+	0.345523i
$783$		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	−0.558694	−	0.829374i	$-0.688697\pi$
$787$	7.59353	−	7.59353i	0.270680	−	0.270680i	0.829374	+	0.558694i	$0.188697\pi$
$788$	20.9358	−	7.63357i	0.745806	−	0.271935i
$789$		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
$802$	4.16810	−	2.65705i	0.147181	−	0.0938237i
$803$	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
$808$	3.75940	+	28.3673i	0.132255	+	0.997957i
$809$			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	$0.227418\pi$
$811$			37.3179i			1.31041i	−0.755451	+	0.655205i	$0.772582\pi$
$812$	1.40474	−	0.512195i	0.0492968	−	0.0179745i
$813$		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
$818$	11.2535	+	17.6533i	0.393470	+	0.617235i
$819$		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	0.998811	−	0.0487521i	$-0.0155244\pi$
$823$	27.2553	+	27.2553i	0.950059	+	0.950059i	−0.0487521	+	0.998811i	$0.515524\pi$
$824$	−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	$0.531322\pi$
$827$	−31.4437	+	31.4437i	−1.09341	+	1.09341i	−0.995162	+	0.0982432i	$0.968678\pi$
$828$		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
$832$	9.93522	−	17.2767i	0.344442	−	0.598964i
$833$	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
$838$	−22.7414	+	14.4970i	−0.785589	+	0.500792i
$839$	−31.0214			−1.07098			−0.535489	−	0.844542i	$-0.679873\pi$
$839$	−31.0214			−1.07098			−0.535489	+	0.844542i	$0.679873\pi$
$840$		0			0
$841$	28.2524			0.974221
$842$	24.8085	−	15.8147i	0.854956	−	0.545011i
$843$		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
$848$	14.8010	+	1.27785i	0.508267	+	0.0438814i
$849$		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	$-0.490784\pi$
$859$	1.69693			0.0578985			0.0289492	+	0.999581i	$0.490784\pi$
$860$		0			0
$861$		0			0
$862$	11.6540	+	18.2815i	0.396935	+	0.622670i
$863$	5.92869	+	5.92869i	0.201815	+	0.201815i	0.800777	−	0.598962i	$-0.204420\pi$
$863$	5.92869	+	5.92869i	0.201815	+	0.201815i	−0.598962	+	0.800777i	$0.704420\pi$
$864$		0			0
$865$		0			0
$866$	7.03831	−	31.7908i	0.239171	−	1.08030i
$867$		0			0
$868$	12.6900	−	4.62699i	0.430725	−	0.157050i
$869$		−	81.6068i		−	2.76832i
$870$		0			0
$871$		−	21.8617i		−	0.740756i
$872$	20.5161	−	2.71891i	0.694762	−	0.0920740i
$873$		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	$0.673002\pi$
$878$	−29.4020	+	18.7430i	−0.992269	+	0.632544i
$879$		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	0.794526	−	0.607230i	$-0.207719\pi$
$883$	5.56557	+	5.56557i	0.187296	+	0.187296i	−0.607230	+	0.794526i	$0.707719\pi$
$884$	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	−0.547905	−	0.836541i	$-0.684574\pi$
$887$	8.59630	−	8.59630i	0.288636	−	0.288636i	0.836541	+	0.547905i	$0.184574\pi$
$888$		0			0
$889$			9.15994i			0.307214i
$890$		0			0
$891$		0			0
$892$	28.8791	−	10.5298i	0.966943	−	0.352565i
$893$	−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
$898$	−25.2015	−	39.5334i	−0.840984	−	1.31925i
$899$	−6.75359			−0.225245
$900$		0			0
$901$	19.7572			0.658207
$902$	21.5316	+	33.7766i	0.716925	+	1.12464i
$903$		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	$0.516387\pi$
$907$	−31.6263	+	31.6263i	−1.05013	+	1.05013i	−0.998675	+	0.0514592i	$0.983613\pi$
$908$	−4.82748	−	13.2398i	−0.160206	−	0.439379i
$909$		0			0
$910$		0			0
$911$			42.2656i			1.40032i	0.713985	+	0.700161i	$0.246888\pi$
$911$			42.2656i			1.40032i	−0.713985	+	0.700161i	$0.753112\pi$
$912$		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	$-0.672566\pi$
$919$	−31.2829			−1.03193			−0.515964	+	0.856610i	$0.672566\pi$
$920$		0			0
$921$		0			0
$922$	−32.2238	+	20.5418i	−1.06123	+	0.676508i
$923$	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
$928$	−1.46412	+	4.66687i	−0.0480621	+	0.153198i
$929$		−	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
$932$	0.693082	+	1.90084i	0.0227026	+	0.0622641i
$933$		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	$0.635025\pi$
$938$	−5.76813	−	9.04843i	−0.188336	−	0.295442i
$939$		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	−0.484969	−	0.874531i	$-0.661169\pi$
$947$	11.9881	−	11.9881i	0.389562	−	0.389562i	0.874531	+	0.484969i	$0.161169\pi$
$948$		0			0
$949$			7.93545i			0.257596i
$950$		0			0
$951$		0			0
$952$	−1.70916	−	12.8968i	−0.0553943	−	0.417988i
$953$	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
$958$	−16.4082	+	10.4598i	−0.530125	+	0.337940i
$959$	8.57657			0.276952
$960$		0			0
$961$	−30.0096			−0.968051
$962$	7.40097	−	4.71791i	0.238617	−	0.152112i
$963$		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	−0.679767	−	0.733428i	$-0.737919\pi$
$967$	1.66866	−	1.66866i	0.0536606	−	0.0536606i	0.733428	+	0.679767i	$0.237919\pi$
$968$	−5.68483	−	42.8960i	−0.182717	−	1.37873i
$969$		0			0
$970$		0			0
$971$		−	4.79719i		−	0.153949i	−0.997033	−	0.0769745i	$-0.975474\pi$
$971$		−	4.79719i		−	0.153949i	0.997033	−	0.0769745i	$-0.0245260\pi$
$972$		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
$982$	−21.9635	−	34.4540i	−0.700884	−	1.09947i
$983$	−30.9151	−	30.9151i	−0.986038	−	0.986038i	0.0138655	−	0.999904i	$-0.495586\pi$
$983$	−30.9151	−	30.9151i	−0.986038	−	0.986038i	−0.999904	+	0.0138655i	$0.995586\pi$
$984$		0			0
$985$		0			0
$986$	−1.40608	+	6.35101i	−0.0447786	+	0.202257i
$987$		0			0
$988$	2.08702	+	5.72384i	0.0663969	+	0.182100i
$989$			13.3661i			0.425017i
$990$		0			0
$991$		−	26.5873i		−	0.844575i	−0.906462	−	0.422287i	$-0.861227\pi$
$991$		−	26.5873i		−	0.844575i	0.906462	−	0.422287i	$-0.138773\pi$
$992$	−13.2264	+	42.1589i	−0.419937	+	1.33855i
$993$		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	$0.732366\pi$
$998$	14.9500	−	9.53021i	0.473234	−	0.301674i
$999$		0			0

Twists

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

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

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