LMFDB - Embedded newform 3150.2.bp.g.899.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bp (of order $6$, degree $2$, not 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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.4
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.g.1349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.16005 - 1.52781i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.16005 - 1.52781i) q^{7} +1.00000 q^{8} +(-4.29783 - 2.48135i) q^{11} -5.49388 q^{13} +(-0.243099 + 2.63456i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.66237 - 1.53712i) q^{17} +(2.68622 - 1.55089i) q^{19} +4.96270i q^{22} +(3.08810 + 5.34875i) q^{23} +(2.74694 + 4.75784i) q^{26} +(2.40314 - 1.10675i) q^{28} +6.67885i q^{29} +(-1.01653 - 0.586893i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.07424i q^{34} +(-9.27339 + 5.35400i) q^{37} +(-2.68622 - 1.55089i) q^{38} +8.39427 q^{41} -8.81025i q^{43} +(4.29783 - 2.48135i) q^{44} +(3.08810 - 5.34875i) q^{46} +(-3.59075 + 2.07312i) q^{47} +(2.33160 + 6.60028i) q^{49} +(2.74694 - 4.75784i) q^{52} +(2.22536 - 3.85443i) q^{53} +(-2.16005 - 1.52781i) q^{56} +(5.78405 - 3.33943i) q^{58} +(3.00381 - 5.20275i) q^{59} +(9.05018 - 5.22512i) q^{61} +1.17379i q^{62} +1.00000 q^{64} +(10.3529 + 5.97727i) q^{67} +(2.66237 - 1.53712i) q^{68} -0.973522i q^{71} +(8.34916 - 14.4612i) q^{73} +(9.27339 + 5.35400i) q^{74} +3.10178i q^{76} +(5.49247 + 11.9261i) q^{77} +(-2.12328 - 3.67763i) q^{79} +(-4.19713 - 7.26965i) q^{82} +14.2841i q^{83} +(-7.62990 + 4.40513i) q^{86} +(-4.29783 - 2.48135i) q^{88} +(7.38517 + 12.7915i) q^{89} +(11.8670 + 8.39360i) q^{91} -6.17620 q^{92} +(3.59075 + 2.07312i) q^{94} -4.41643 q^{97} +(4.55021 - 5.31936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.16005	−	1.52781i	−0.816421	−	0.577458i
$7$	−2.16005	−	1.52781i	−0.816421	−	0.577458i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−4.29783	−	2.48135i	−1.29584	−	0.748156i	−0.316160	−	0.948706i	$-0.602394\pi$
$11$	−4.29783	−	2.48135i	−1.29584	−	0.748156i	−0.979683	+	0.200550i	$0.935727\pi$
$12$		0			0
$13$	−5.49388			−1.52373			−0.761864	−	0.647737i	$-0.775715\pi$
$13$	−5.49388			−1.52373			−0.761864	+	0.647737i	$0.775715\pi$
$14$	−0.243099	+	2.63456i	−0.0649709	+	0.704116i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.66237	−	1.53712i	−0.645719	−	0.372806i	0.141095	−	0.989996i	$-0.454938\pi$
$17$	−2.66237	−	1.53712i	−0.645719	−	0.372806i	−0.786814	+	0.617190i	$0.788271\pi$
$18$		0			0
$19$	2.68622	−	1.55089i	0.616261	−	0.355798i	−0.159151	−	0.987254i	$-0.550876\pi$
$19$	2.68622	−	1.55089i	0.616261	−	0.355798i	0.775412	+	0.631456i	$0.217542\pi$
$20$		0			0
$21$		0			0
$22$			4.96270i			1.05805i
$23$	3.08810	+	5.34875i	0.643914	+	1.11529i	0.984551	+	0.175097i	$0.0560238\pi$
$23$	3.08810	+	5.34875i	0.643914	+	1.11529i	−0.340638	+	0.940195i	$0.610643\pi$
$24$		0			0
$25$		0			0
$26$	2.74694	+	4.75784i	0.538719	+	0.933089i
$27$		0			0
$28$	2.40314	−	1.10675i	0.454152	−	0.209156i
$29$			6.67885i			1.24023i	0.784510	+	0.620116i	$0.212914\pi$
$29$			6.67885i			1.24023i	−0.784510	+	0.620116i	$0.787086\pi$
$30$		0			0
$31$	−1.01653	−	0.586893i	−0.182574	−	0.105409i	0.405928	−	0.913905i	$-0.366949\pi$
$31$	−1.01653	−	0.586893i	−0.182574	−	0.105409i	−0.588501	+	0.808496i	$0.700282\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			3.07424i			0.527228i
$35$		0			0
$36$		0			0
$37$	−9.27339	+	5.35400i	−1.52454	+	0.880192i	−0.524959	+	0.851128i	$0.675919\pi$
$37$	−9.27339	+	5.35400i	−1.52454	+	0.880192i	−0.999578	+	0.0290640i	$0.990747\pi$
$38$	−2.68622	−	1.55089i	−0.435762	−	0.251587i
$39$		0			0
$40$		0			0
$41$	8.39427			1.31096			0.655482	−	0.755211i	$-0.272466\pi$
$41$	8.39427			1.31096			0.655482	+	0.755211i	$0.272466\pi$
$42$		0			0
$43$		−	8.81025i		−	1.34355i	−0.740755	−	0.671776i	$-0.765532\pi$
$43$		−	8.81025i		−	1.34355i	0.740755	−	0.671776i	$-0.234468\pi$
$44$	4.29783	−	2.48135i	0.647922	−	0.374078i
$45$		0			0
$46$	3.08810	−	5.34875i	0.455316	−	0.788630i
$47$	−3.59075	+	2.07312i	−0.523765	+	0.302396i	−0.738474	−	0.674282i	$-0.764453\pi$
$47$	−3.59075	+	2.07312i	−0.523765	+	0.302396i	0.214709	+	0.976678i	$0.431120\pi$
$48$		0			0
$49$	2.33160	+	6.60028i	0.333085	+	0.942897i
$50$		0			0
$51$		0			0
$52$	2.74694	−	4.75784i	0.380932	−	0.659793i
$53$	2.22536	−	3.85443i	0.305676	−	0.529446i	−0.671736	−	0.740791i	$-0.734451\pi$
$53$	2.22536	−	3.85443i	0.305676	−	0.529446i	0.977412	+	0.211345i	$0.0677842\pi$
$54$		0			0
$55$		0			0
$56$	−2.16005	−	1.52781i	−0.288648	−	0.204162i
$57$		0			0
$58$	5.78405	−	3.33943i	0.759484	−	0.438488i
$59$	3.00381	−	5.20275i	0.391062	−	0.677340i	−0.601528	−	0.798852i	$-0.705441\pi$
$59$	3.00381	−	5.20275i	0.391062	−	0.677340i	0.992590	+	0.121512i	$0.0387743\pi$
$60$		0			0
$61$	9.05018	−	5.22512i	1.15876	−	0.669008i	0.207751	−	0.978182i	$-0.433386\pi$
$61$	9.05018	−	5.22512i	1.15876	−	0.669008i	0.951006	+	0.309173i	$0.100052\pi$
$62$			1.17379i			0.149071i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	10.3529	+	5.97727i	1.26481	+	0.730240i	0.974002	−	0.226540i	$-0.0727414\pi$
$67$	10.3529	+	5.97727i	1.26481	+	0.730240i	0.290811	+	0.956780i	$0.406075\pi$
$68$	2.66237	−	1.53712i	0.322860	−	0.186403i
$69$		0			0
$70$		0			0
$71$		−	0.973522i		−	0.115536i	−0.998330	−	0.0577679i	$-0.981602\pi$
$71$		−	0.973522i		−	0.115536i	0.998330	−	0.0577679i	$-0.0183983\pi$
$72$		0			0
$73$	8.34916	−	14.4612i	0.977196	−	1.69255i	0.304706	−	0.952446i	$-0.401442\pi$
$73$	8.34916	−	14.4612i	0.977196	−	1.69255i	0.672490	−	0.740106i	$-0.265225\pi$
$74$	9.27339	+	5.35400i	1.07801	+	0.622389i
$75$		0			0
$76$			3.10178i			0.355798i
$77$	5.49247	+	11.9261i	0.625925	+	1.35910i
$78$		0			0
$79$	−2.12328	−	3.67763i	−0.238887	−	0.413765i	0.721508	−	0.692406i	$-0.243449\pi$
$79$	−2.12328	−	3.67763i	−0.238887	−	0.413765i	−0.960395	+	0.278641i	$0.910116\pi$
$80$		0			0
$81$		0			0
$82$	−4.19713	−	7.26965i	−0.463496	−	0.802798i
$83$			14.2841i			1.56789i	0.620831	+	0.783944i	$0.286795\pi$
$83$			14.2841i			1.56789i	−0.620831	+	0.783944i	$0.713205\pi$
$84$		0			0
$85$		0			0
$86$	−7.62990	+	4.40513i	−0.822754	+	0.475017i
$87$		0			0
$88$	−4.29783	−	2.48135i	−0.458150	−	0.264513i
$89$	7.38517	+	12.7915i	0.782826	+	1.35590i	0.930289	+	0.366827i	$0.119556\pi$
$89$	7.38517	+	12.7915i	0.782826	+	1.35590i	−0.147463	+	0.989068i	$0.547111\pi$
$90$		0			0
$91$	11.8670	+	8.39360i	1.24400	+	0.879888i
$92$	−6.17620			−0.643914
$93$		0			0
$94$	3.59075	+	2.07312i	0.370358	+	0.213826i
$95$		0			0
$96$		0			0
$97$	−4.41643			−0.448420			−0.224210	−	0.974541i	$-0.571980\pi$
$97$	−4.41643			−0.448420			−0.224210	+	0.974541i	$0.571980\pi$
$98$	4.55021	−	5.31936i	0.459641	−	0.537336i
$99$		0			0
$100$		0			0
$101$	−5.19825	+	9.00364i	−0.517245	+	0.895895i	0.482554	+	0.875866i	$0.339709\pi$
$101$	−5.19825	+	9.00364i	−0.517245	+	0.895895i	−0.999799	+	0.0200290i	$0.993624\pi$
$102$		0			0
$103$	−5.11942	−	8.86709i	−0.504431	−	0.873701i	−0.999987	−	0.00512447i	$-0.998369\pi$
$103$	−5.11942	−	8.86709i	−0.504431	−	0.873701i	0.495556	−	0.868576i	$-0.334965\pi$
$104$	−5.49388			−0.538719
$105$		0			0
$106$	−4.45071			−0.432291
$107$	−3.28972	−	5.69797i	−0.318030	−	0.550844i	0.662047	−	0.749462i	$-0.269688\pi$
$107$	−3.28972	−	5.69797i	−0.318030	−	0.550844i	−0.980077	+	0.198619i	$0.936355\pi$
$108$		0			0
$109$	1.34219	−	2.32474i	0.128558	−	0.222669i	−0.794560	−	0.607186i	$-0.792298\pi$
$109$	1.34219	−	2.32474i	0.128558	−	0.222669i	0.923118	+	0.384516i	$0.125632\pi$
$110$		0			0
$111$		0			0
$112$	−0.243099	+	2.63456i	−0.0229707	+	0.248942i
$113$	3.55031			0.333985			0.166992	−	0.985958i	$-0.446594\pi$
$113$	3.55031			0.333985			0.166992	+	0.985958i	$0.446594\pi$
$114$		0			0
$115$		0			0
$116$	−5.78405	−	3.33943i	−0.537036	−	0.310058i
$117$		0			0
$118$	−6.00761			−0.553046
$119$	3.40241	+	7.38784i	0.311899	+	0.677242i
$120$		0			0
$121$	6.81421	+	11.8026i	0.619474	+	1.07296i
$122$	−9.05018	−	5.22512i	−0.819365	−	0.473060i
$123$		0			0
$124$	1.01653	−	0.586893i	0.0912869	−	0.0527045i
$125$		0			0
$126$		0			0
$127$		−	5.51567i		−	0.489437i	−0.969594	−	0.244719i	$-0.921304\pi$
$127$		−	5.51567i		−	0.489437i	0.969594	−	0.244719i	$-0.0786955\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	10.3068	+	17.8519i	0.900510	+	1.55973i	0.826833	+	0.562447i	$0.190140\pi$
$131$	10.3068	+	17.8519i	0.900510	+	1.55973i	0.0736773	+	0.997282i	$0.476527\pi$
$132$		0			0
$133$	−8.17182	−	0.754039i	−0.708586	−	0.0653835i
$134$		−	11.9545i		−	1.03272i
$135$		0			0
$136$	−2.66237	−	1.53712i	−0.228296	−	0.131807i
$137$	−5.72807	+	9.92131i	−0.489382	+	0.847635i	−0.999925	−	0.0122175i	$-0.996111\pi$
$137$	−5.72807	+	9.92131i	−0.489382	+	0.847635i	0.510543	+	0.859852i	$0.329444\pi$
$138$		0			0
$139$			1.16700i			0.0989840i	0.998775	+	0.0494920i	$0.0157602\pi$
$139$			1.16700i			0.0989840i	−0.998775	+	0.0494920i	$0.984240\pi$
$140$		0			0
$141$		0			0
$142$	−0.843095	+	0.486761i	−0.0707509	+	0.0408481i
$143$	23.6117	+	13.6322i	1.97451	+	1.13999i
$144$		0			0
$145$		0			0
$146$	−16.6983			−1.38196
$147$		0			0
$148$		−	10.7080i		−	0.880192i
$149$	−13.3404	+	7.70205i	−1.09288	+	0.630977i	−0.934343	−	0.356375i	$-0.884012\pi$
$149$	−13.3404	+	7.70205i	−1.09288	+	0.630977i	−0.158541	+	0.987352i	$0.550679\pi$
$150$		0			0
$151$	−0.511281	+	0.885565i	−0.0416075	+	0.0720663i	−0.886079	−	0.463534i	$-0.846581\pi$
$151$	−0.511281	+	0.885565i	−0.0416075	+	0.0720663i	0.844472	+	0.535600i	$0.179915\pi$
$152$	2.68622	−	1.55089i	0.217881	−	0.125794i
$153$		0			0
$154$	7.58207	−	10.7197i	0.610980	−	0.863815i
$155$		0			0
$156$		0			0
$157$	−2.68294	+	4.64699i	−0.214122	+	0.370871i	−0.953001	−	0.302968i	$-0.902022\pi$
$157$	−2.68294	+	4.64699i	−0.214122	+	0.370871i	0.738878	+	0.673839i	$0.235356\pi$
$158$	−2.12328	+	3.67763i	−0.168919	+	0.292576i
$159$		0			0
$160$		0			0
$161$	1.50143	−	16.2716i	0.118329	−	1.28238i
$162$		0			0
$163$	−8.69677	+	5.02108i	−0.681184	+	0.393282i	−0.800301	−	0.599599i	$-0.795327\pi$
$163$	−8.69677	+	5.02108i	−0.681184	+	0.393282i	0.119117	+	0.992880i	$0.461994\pi$
$164$	−4.19713	+	7.26965i	−0.327741	+	0.567664i
$165$		0			0
$166$	12.3704	−	7.14207i	0.960131	−	0.554332i
$167$			2.46005i			0.190364i	0.995460	+	0.0951822i	$0.0303434\pi$
$167$			2.46005i			0.190364i	−0.995460	+	0.0951822i	$0.969657\pi$
$168$		0			0
$169$	17.1827			1.32175
$170$		0			0
$171$		0			0
$172$	7.62990	+	4.40513i	0.581775	+	0.335888i
$173$	2.59880	−	1.50042i	0.197583	−	0.114075i	−0.397944	−	0.917410i	$-0.630276\pi$
$173$	2.59880	−	1.50042i	0.197583	−	0.114075i	0.595528	+	0.803335i	$0.296943\pi$
$174$		0			0
$175$		0			0
$176$			4.96270i			0.374078i
$177$		0			0
$178$	7.38517	−	12.7915i	0.553542	−	0.958763i
$179$	3.18036	+	1.83618i	0.237711	+	0.137243i	0.614124	−	0.789209i	$-0.289509\pi$
$179$	3.18036	+	1.83618i	0.237711	+	0.137243i	−0.376413	+	0.926452i	$0.622843\pi$
$180$		0			0
$181$		−	6.13560i		−	0.456056i	−0.973655	−	0.228028i	$-0.926772\pi$
$181$		−	6.13560i		−	0.456056i	0.973655	−	0.228028i	$-0.0732278\pi$
$182$	1.33556	−	14.4739i	0.0989980	−	1.07288i
$183$		0			0
$184$	3.08810	+	5.34875i	0.227658	+	0.394315i
$185$		0			0
$186$		0			0
$187$	7.62827	+	13.2125i	0.557834	+	0.966197i
$188$		−	4.14624i		−	0.302396i
$189$		0			0
$190$		0			0
$191$	4.95227	−	2.85920i	0.358334	−	0.206884i	−0.310016	−	0.950731i	$-0.600334\pi$
$191$	4.95227	−	2.85920i	0.358334	−	0.206884i	0.668350	+	0.743847i	$0.267001\pi$
$192$		0			0
$193$	5.39819	+	3.11665i	0.388570	+	0.224341i	0.681541	−	0.731780i	$-0.261310\pi$
$193$	5.39819	+	3.11665i	0.388570	+	0.224341i	−0.292970	+	0.956122i	$0.594644\pi$
$194$	2.20821	+	3.82474i	0.158540	+	0.274600i
$195$		0			0
$196$	−6.88181	−	1.28092i	−0.491558	−	0.0914941i
$197$	1.32234			0.0942128			0.0471064	−	0.998890i	$-0.485000\pi$
$197$	1.32234			0.0942128			0.0471064	+	0.998890i	$0.485000\pi$
$198$		0			0
$199$	8.27163	+	4.77563i	0.586360	+	0.338535i	0.763657	−	0.645622i	$-0.223402\pi$
$199$	8.27163	+	4.77563i	0.586360	+	0.338535i	−0.177297	+	0.984157i	$0.556735\pi$
$200$		0			0
$201$		0			0
$202$	10.3965			0.731495
$203$	10.2040	−	14.4266i	0.716181	−	1.01255i
$204$		0			0
$205$		0			0
$206$	−5.11942	+	8.86709i	−0.356687	+	0.617800i
$207$		0			0
$208$	2.74694	+	4.75784i	0.190466	+	0.329897i
$209$	−15.3932			−1.06477
$210$		0			0
$211$	26.0219			1.79142			0.895711	−	0.444636i	$-0.146667\pi$
$211$	26.0219			1.79142			0.895711	+	0.444636i	$0.146667\pi$
$212$	2.22536	+	3.85443i	0.152838	+	0.264723i
$213$		0			0
$214$	−3.28972	+	5.69797i	−0.224881	+	0.389505i
$215$		0			0
$216$		0			0
$217$	1.29909	+	2.82078i	0.0881878	+	0.191487i
$218$	−2.68437			−0.181809
$219$		0			0
$220$		0			0
$221$	14.6267	+	8.44475i	0.983900	+	0.568055i
$222$		0			0
$223$	7.25222			0.485644			0.242822	−	0.970071i	$-0.421927\pi$
$223$	7.25222			0.485644			0.242822	+	0.970071i	$0.421927\pi$
$224$	2.40314	−	1.10675i	0.160567	−	0.0739478i
$225$		0			0
$226$	−1.77515	−	3.07466i	−0.118081	−	0.204523i
$227$	23.1409	+	13.3604i	1.53592	+	0.886762i	0.999072	+	0.0430820i	$0.0137177\pi$
$227$	23.1409	+	13.3604i	1.53592	+	0.886762i	0.536846	+	0.843680i	$0.319616\pi$
$228$		0			0
$229$	−21.0473	+	12.1517i	−1.39085	+	0.803006i	−0.993409	−	0.114622i	$-0.963434\pi$
$229$	−21.0473	+	12.1517i	−1.39085	+	0.803006i	−0.397439	+	0.917629i	$0.630101\pi$
$230$		0			0
$231$		0			0
$232$			6.67885i			0.438488i
$233$	−4.62788	−	8.01573i	−0.303183	−	0.525128i	0.673672	−	0.739030i	$-0.264716\pi$
$233$	−4.62788	−	8.01573i	−0.303183	−	0.525128i	−0.976855	+	0.213902i	$0.931383\pi$
$234$		0			0
$235$		0			0
$236$	3.00381	+	5.20275i	0.195531	+	0.338670i
$237$		0			0
$238$	4.69685	−	6.64050i	0.304452	−	0.430439i
$239$		−	0.253367i		−	0.0163889i	−0.999966	−	0.00819446i	$-0.997392\pi$
$239$		−	0.253367i		−	0.0163889i	0.999966	−	0.00819446i	$-0.00260841\pi$
$240$		0			0
$241$	2.57538	+	1.48689i	0.165895	+	0.0957792i	0.580649	−	0.814154i	$-0.302799\pi$
$241$	2.57538	+	1.48689i	0.165895	+	0.0957792i	−0.414754	+	0.909934i	$0.636132\pi$
$242$	6.81421	−	11.8026i	0.438034	−	0.758698i
$243$		0			0
$244$			10.4502i			0.669008i
$245$		0			0
$246$		0			0
$247$	−14.7578	+	8.52039i	−0.939013	+	0.542140i
$248$	−1.01653	−	0.586893i	−0.0645496	−	0.0372677i
$249$		0			0
$250$		0			0
$251$	13.0800			0.825599			0.412800	−	0.910822i	$-0.364551\pi$
$251$	13.0800			0.825599			0.412800	+	0.910822i	$0.364551\pi$
$252$		0			0
$253$		−	30.6507i		−	1.92699i
$254$	−4.77671	+	2.75784i	−0.299718	+	0.173042i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.9084	+	6.29797i	−0.680447	+	0.392856i	−0.800023	−	0.599969i	$-0.795180\pi$
$257$	−10.9084	+	6.29797i	−0.680447	+	0.392856i	0.119576	+	0.992825i	$0.461846\pi$
$258$		0			0
$259$	28.2108	+	2.60310i	1.75294	+	0.161749i
$260$		0			0
$261$		0			0
$262$	10.3068	−	17.8519i	0.636757	−	1.10290i
$263$	8.33594	−	14.4383i	0.514016	−	0.890302i	−0.485852	−	0.874041i	$-0.661490\pi$
$263$	8.33594	−	14.4383i	0.514016	−	0.890302i	0.999868	−	0.0162609i	$-0.00517625\pi$
$264$		0			0
$265$		0			0
$266$	3.43289	+	7.45402i	0.210484	+	0.457035i
$267$		0			0
$268$	−10.3529	+	5.97727i	−0.632407	+	0.365120i
$269$	−10.0035	+	17.3265i	−0.609923	+	1.05642i	0.381330	+	0.924439i	$0.375466\pi$
$269$	−10.0035	+	17.3265i	−0.609923	+	1.05642i	−0.991253	+	0.131978i	$0.957867\pi$
$270$		0			0
$271$	−15.4684	+	8.93068i	−0.939638	+	0.542500i	−0.889847	−	0.456259i	$-0.849189\pi$
$271$	−15.4684	+	8.93068i	−0.939638	+	0.542500i	−0.0497914	+	0.998760i	$0.515856\pi$
$272$			3.07424i			0.186403i
$273$		0			0
$274$	11.4561			0.692091
$275$		0			0
$276$		0			0
$277$	−15.7167	−	9.07406i	−0.944327	−	0.545207i	−0.0530128	−	0.998594i	$-0.516882\pi$
$277$	−15.7167	−	9.07406i	−0.944327	−	0.545207i	−0.891314	+	0.453386i	$0.850216\pi$
$278$	1.01066	−	0.583502i	0.0606151	−	0.0349961i
$279$		0			0
$280$		0			0
$281$		−	15.5129i		−	0.925425i	−0.886508	−	0.462713i	$-0.846876\pi$
$281$		−	15.5129i		−	0.925425i	0.886508	−	0.462713i	$-0.153124\pi$
$282$		0			0
$283$	−8.82268	+	15.2813i	−0.524454	+	0.908381i	0.475141	+	0.879910i	$0.342397\pi$
$283$	−8.82268	+	15.2813i	−0.524454	+	0.908381i	−0.999595	+	0.0284708i	$0.990936\pi$
$284$	0.843095	+	0.486761i	0.0500285	+	0.0288840i
$285$		0			0
$286$		−	27.2645i		−	1.61218i
$287$	−18.1320	−	12.8248i	−1.07030	−	0.757026i
$288$		0			0
$289$	−3.77453	−	6.53767i	−0.222031	−	0.384569i
$290$		0			0
$291$		0			0
$292$	8.34916	+	14.4612i	0.488598	+	0.846276i
$293$			10.4489i			0.610432i	0.952283	+	0.305216i	$0.0987287\pi$
$293$			10.4489i			0.610432i	−0.952283	+	0.305216i	$0.901271\pi$
$294$		0			0
$295$		0			0
$296$	−9.27339	+	5.35400i	−0.539005	+	0.311195i
$297$		0			0
$298$	13.3404	+	7.70205i	0.772786	+	0.446168i
$299$	−16.9657	−	29.3854i	−0.981149	−	1.69940i
$300$		0			0
$301$	−13.4604	+	19.0306i	−0.775844	+	1.09690i
$302$	1.02256			0.0588419
$303$		0			0
$304$	−2.68622	−	1.55089i	−0.154065	−	0.0889496i
$305$		0			0
$306$		0			0
$307$	0.724648			0.0413579			0.0206789	−	0.999786i	$-0.493417\pi$
$307$	0.724648			0.0413579			0.0206789	+	0.999786i	$0.493417\pi$
$308$	−13.0745	−	1.20643i	−0.744991	−	0.0687426i
$309$		0			0
$310$		0			0
$311$	14.1225	−	24.4609i	0.800813	−	1.38705i	−0.118268	−	0.992982i	$-0.537734\pi$
$311$	14.1225	−	24.4609i	0.800813	−	1.38705i	0.919081	−	0.394068i	$-0.128932\pi$
$312$		0			0
$313$	10.2651	+	17.7797i	0.580218	+	1.00497i	0.995453	+	0.0952528i	$0.0303659\pi$
$313$	10.2651	+	17.7797i	0.580218	+	1.00497i	−0.415235	+	0.909714i	$0.636301\pi$
$314$	5.36589			0.302815
$315$		0			0
$316$	4.24656			0.238887
$317$	−1.13674	−	1.96890i	−0.0638459	−	0.110584i	0.832336	−	0.554272i	$-0.187003\pi$
$317$	−1.13674	−	1.96890i	−0.0638459	−	0.110584i	−0.896181	+	0.443688i	$0.853670\pi$
$318$		0			0
$319$	16.5726	−	28.7045i	0.927886	−	1.60715i
$320$		0			0
$321$		0			0
$322$	−14.8423	+	6.83551i	−0.827130	+	0.380928i
$323$	−9.53560			−0.530575
$324$		0			0
$325$		0			0
$326$	8.69677	+	5.02108i	0.481670	+	0.278092i
$327$		0			0
$328$	8.39427			0.463496
$329$	10.9235	+	1.00795i	0.602233	+	0.0555699i
$330$		0			0
$331$	18.0646	+	31.2889i	0.992922	+	1.71979i	0.599317	+	0.800512i	$0.295439\pi$
$331$	18.0646	+	31.2889i	0.992922	+	1.71979i	0.393605	+	0.919280i	$0.371228\pi$
$332$	−12.3704	−	7.14207i	−0.678915	−	0.391972i
$333$		0			0
$334$	2.13047	−	1.23003i	0.116574	−	0.0673040i
$335$		0			0
$336$		0			0
$337$		−	3.76361i		−	0.205017i	−0.994732	−	0.102508i	$-0.967313\pi$
$337$		−	3.76361i		−	0.205017i	0.994732	−	0.102508i	$-0.0326869\pi$
$338$	−8.59134	−	14.8806i	−0.467308	−	0.809400i
$339$		0			0
$340$		0			0
$341$	2.91258	+	5.04473i	0.157725	+	0.273187i
$342$		0			0
$343$	5.04761	−	17.8191i	0.272546	−	0.962143i
$344$		−	8.81025i		−	0.475017i
$345$		0			0
$346$	−2.59880	−	1.50042i	−0.139713	−	0.0806631i
$347$	−2.02389	+	3.50549i	−0.108648	+	0.188184i	−0.915223	−	0.402948i	$-0.867986\pi$
$347$	−2.02389	+	3.50549i	−0.108648	+	0.188184i	0.806575	+	0.591132i	$0.201319\pi$
$348$		0			0
$349$		−	23.9364i		−	1.28129i	−0.767838	−	0.640644i	$-0.778667\pi$
$349$		−	23.9364i		−	1.28129i	0.767838	−	0.640644i	$-0.221333\pi$
$350$		0			0
$351$		0			0
$352$	4.29783	−	2.48135i	0.229075	−	0.132256i
$353$	22.0679	+	12.7409i	1.17455	+	0.678129i	0.954748	−	0.297415i	$-0.0961244\pi$
$353$	22.0679	+	12.7409i	1.17455	+	0.678129i	0.219805	+	0.975544i	$0.429458\pi$
$354$		0			0
$355$		0			0
$356$	−14.7703			−0.782826
$357$		0			0
$358$		−	3.67236i		−	0.194091i
$359$	15.4893	−	8.94277i	0.817496	−	0.471981i	−0.0320565	−	0.999486i	$-0.510206\pi$
$359$	15.4893	−	8.94277i	0.817496	−	0.471981i	0.849552	+	0.527505i	$0.176872\pi$
$360$		0			0
$361$	−4.68949	+	8.12243i	−0.246815	+	0.427496i
$362$	−5.31359	+	3.06780i	−0.279276	+	0.161240i
$363$		0			0
$364$	−13.2026	+	6.08035i	−0.692003	+	0.318697i
$365$		0			0
$366$		0			0
$367$	2.63851	−	4.57004i	0.137729	−	0.238554i	−0.788907	−	0.614512i	$-0.789353\pi$
$367$	2.63851	−	4.57004i	0.137729	−	0.238554i	0.926637	+	0.375958i	$0.122686\pi$
$368$	3.08810	−	5.34875i	0.160978	−	0.278823i
$369$		0			0
$370$		0			0
$371$	−10.6957	+	4.92582i	−0.555293	+	0.255736i
$372$		0			0
$373$	−12.5988	+	7.27390i	−0.652339	+	0.376628i	−0.789352	−	0.613941i	$-0.789583\pi$
$373$	−12.5988	+	7.27390i	−0.652339	+	0.376628i	0.137013	+	0.990569i	$0.456250\pi$
$374$	7.62827	−	13.2125i	0.394448	−	0.683205i
$375$		0			0
$376$	−3.59075	+	2.07312i	−0.185179	+	0.106913i
$377$		−	36.6928i		−	1.88977i
$378$		0			0
$379$	−3.66669			−0.188345			−0.0941726	−	0.995556i	$-0.530021\pi$
$379$	−3.66669			−0.188345			−0.0941726	+	0.995556i	$0.530021\pi$
$380$		0			0
$381$		0			0
$382$	−4.95227	−	2.85920i	−0.253380	−	0.146289i
$383$	16.9091	−	9.76247i	0.864015	−	0.498839i	−0.00134002	−	0.999999i	$-0.500427\pi$
$383$	16.9091	−	9.76247i	0.864015	−	0.498839i	0.865355	+	0.501160i	$0.167093\pi$
$384$		0			0
$385$		0			0
$386$		−	6.23330i		−	0.317266i
$387$		0			0
$388$	2.20821	−	3.82474i	0.112105	−	0.194172i
$389$	−14.9711	−	8.64356i	−0.759064	−	0.438246i	0.0698956	−	0.997554i	$-0.477733\pi$
$389$	−14.9711	−	8.64356i	−0.759064	−	0.438246i	−0.828960	+	0.559309i	$0.811067\pi$
$390$		0			0
$391$		−	18.9871i		−	0.960220i
$392$	2.33160	+	6.60028i	0.117763	+	0.333364i
$393$		0			0
$394$	−0.661170	−	1.14518i	−0.0333092	−	0.0576933i
$395$		0			0
$396$		0			0
$397$	13.8423	+	23.9755i	0.694724	+	1.20330i	0.970274	+	0.242011i	$0.0778069\pi$
$397$	13.8423	+	23.9755i	0.694724	+	1.20330i	−0.275549	+	0.961287i	$0.588860\pi$
$398$		−	9.55125i		−	0.478761i
$399$		0			0
$400$		0			0
$401$	−32.7521	+	18.9095i	−1.63556	+	0.944293i	−0.653229	+	0.757161i	$0.726586\pi$
$401$	−32.7521	+	18.9095i	−1.63556	+	0.944293i	−0.982335	+	0.187132i	$0.940081\pi$
$402$		0			0
$403$	5.58468	+	3.22432i	0.278193	+	0.160615i
$404$	−5.19825	−	9.00364i	−0.258623	−	0.447948i
$405$		0			0
$406$	−17.5958	−	1.62362i	−0.873266	−	0.0805790i
$407$	53.1406			2.63408
$408$		0			0
$409$	−31.6028	−	18.2459i	−1.56266	−	0.902202i	−0.996987	−	0.0775719i	$-0.975283\pi$
$409$	−31.6028	−	18.2459i	−1.56266	−	0.902202i	−0.565673	−	0.824630i	$-0.691383\pi$
$410$		0			0
$411$		0			0
$412$	10.2388			0.504431
$413$	−14.4372	+	6.64893i	−0.710407	+	0.327172i
$414$		0			0
$415$		0			0
$416$	2.74694	−	4.75784i	0.134680	−	0.233272i
$417$		0			0
$418$	7.69660	+	13.3309i	0.376453	+	0.652036i
$419$	−21.6669			−1.05850			−0.529249	−	0.848466i	$-0.677526\pi$
$419$	−21.6669			−1.05850			−0.529249	+	0.848466i	$0.677526\pi$
$420$		0			0
$421$	−8.84193			−0.430929			−0.215465	−	0.976512i	$-0.569127\pi$
$421$	−8.84193			−0.430929			−0.215465	+	0.976512i	$0.569127\pi$
$422$	−13.0110	−	22.5356i	−0.633363	−	1.09702i
$423$		0			0
$424$	2.22536	−	3.85443i	0.108073	−	0.187188i
$425$		0			0
$426$		0			0
$427$	−27.5318	−	2.54044i	−1.33236	−	0.122941i
$428$	6.57945			0.318030
$429$		0			0
$430$		0			0
$431$	25.7481	+	14.8656i	1.24024	+	0.716053i	0.969143	−	0.246499i	$-0.0792802\pi$
$431$	25.7481	+	14.8656i	1.24024	+	0.716053i	0.271097	+	0.962552i	$0.412614\pi$
$432$		0			0
$433$	−26.5666			−1.27671			−0.638356	−	0.769741i	$-0.720385\pi$
$433$	−26.5666			−1.27671			−0.638356	+	0.769741i	$0.720385\pi$
$434$	1.79332	−	2.53543i	0.0860822	−	0.121705i
$435$		0			0
$436$	1.34219	+	2.32474i	0.0642791	+	0.111335i
$437$	16.5906	+	9.57860i	0.793637	+	0.458207i
$438$		0			0
$439$	−14.4067	+	8.31774i	−0.687597	+	0.396984i	−0.802711	−	0.596368i	$-0.796610\pi$
$439$	−14.4067	+	8.31774i	−0.687597	+	0.396984i	0.115114	+	0.993352i	$0.463277\pi$
$440$		0			0
$441$		0			0
$442$		−	16.8895i		−	0.803351i
$443$	1.63637	+	2.83428i	0.0777464	+	0.134661i	0.902277	−	0.431156i	$-0.141894\pi$
$443$	1.63637	+	2.83428i	0.0777464	+	0.134661i	−0.824531	+	0.565817i	$0.808561\pi$
$444$		0			0
$445$		0			0
$446$	−3.62611	−	6.28060i	−0.171701	−	0.297395i
$447$		0			0
$448$	−2.16005	−	1.52781i	−0.102053	−	0.0721822i
$449$		−	10.4322i		−	0.492324i	−0.969229	−	0.246162i	$-0.920831\pi$
$449$		−	10.4322i		−	0.492324i	0.969229	−	0.246162i	$-0.0791695\pi$
$450$		0			0
$451$	−36.0771	−	20.8291i	−1.69880	−	0.980805i
$452$	−1.77515	+	3.07466i	−0.0834962	+	0.144620i
$453$		0			0
$454$		−	26.7208i		−	1.25407i
$455$		0			0
$456$		0			0
$457$	28.6471	−	16.5394i	1.34005	−	0.773680i	0.353238	−	0.935533i	$-0.385080\pi$
$457$	28.6471	−	16.5394i	1.34005	−	0.773680i	0.986815	+	0.161853i	$0.0517471\pi$
$458$	21.0473	+	12.1517i	0.983478	+	0.567811i
$459$		0			0
$460$		0			0
$461$	11.5639			0.538585			0.269293	−	0.963058i	$-0.413210\pi$
$461$	11.5639			0.538585			0.269293	+	0.963058i	$0.413210\pi$
$462$		0			0
$463$			38.6061i			1.79418i	0.441848	+	0.897090i	$0.354323\pi$
$463$			38.6061i			1.79418i	−0.441848	+	0.897090i	$0.645677\pi$
$464$	5.78405	−	3.33943i	0.268518	−	0.155029i
$465$		0			0
$466$	−4.62788	+	8.01573i	−0.214383	+	0.371322i
$467$	−4.08230	+	2.35692i	−0.188906	+	0.109065i	−0.591471	−	0.806327i	$-0.701452\pi$
$467$	−4.08230	+	2.35692i	−0.188906	+	0.109065i	0.402564	+	0.915392i	$0.368119\pi$
$468$		0			0
$469$	−13.2307	−	28.7285i	−0.610937	−	1.32656i
$470$		0			0
$471$		0			0
$472$	3.00381	−	5.20275i	0.138261	−	0.239476i
$473$	−21.8613	+	37.8649i	−1.00519	+	1.74103i
$474$		0			0
$475$		0			0
$476$	−8.09926	−	0.747344i	−0.371229	−	0.0342545i
$477$		0			0
$478$	−0.219422	+	0.126683i	−0.0100361	+	0.00579436i
$479$	−10.0096	+	17.3371i	−0.457349	+	0.792152i	−0.998820	−	0.0485678i	$-0.984534\pi$
$479$	−10.0096	+	17.3371i	−0.457349	+	0.792152i	0.541471	+	0.840720i	$0.317868\pi$
$480$		0			0
$481$	50.9469	−	29.4142i	2.32298	−	1.34117i
$482$		−	2.97379i		−	0.135452i
$483$		0			0
$484$	−13.6284			−0.619474
$485$		0			0
$486$		0			0
$487$	−4.09706	−	2.36544i	−0.185656	−	0.107188i	0.404292	−	0.914630i	$-0.367518\pi$
$487$	−4.09706	−	2.36544i	−0.185656	−	0.107188i	−0.589947	+	0.807442i	$0.700851\pi$
$488$	9.05018	−	5.22512i	0.409682	−	0.236530i
$489$		0			0
$490$		0			0
$491$		−	16.0027i		−	0.722190i	−0.932529	−	0.361095i	$-0.882403\pi$
$491$		−	16.0027i		−	0.722190i	0.932529	−	0.361095i	$-0.117597\pi$
$492$		0			0
$493$	10.2662	−	17.7816i	0.462366	−	0.800841i
$494$	14.7578	+	8.52039i	0.663983	+	0.383351i
$495$		0			0
$496$			1.17379i			0.0527045i
$497$	−1.48736	+	2.10285i	−0.0667170	+	0.0943258i
$498$		0			0
$499$	3.18097	+	5.50961i	0.142400	+	0.246644i	0.928400	−	0.371583i	$-0.121185\pi$
$499$	3.18097	+	5.50961i	0.142400	+	0.246644i	−0.786000	+	0.618227i	$0.787851\pi$
$500$		0			0
$501$		0			0
$502$	−6.53998	−	11.3276i	−0.291893	−	0.505574i
$503$			36.3826i			1.62222i	0.584895	+	0.811109i	$0.301136\pi$
$503$			36.3826i			1.62222i	−0.584895	+	0.811109i	$0.698864\pi$
$504$		0			0
$505$		0			0
$506$	−26.5443	+	15.3253i	−1.18004	+	0.681294i
$507$		0			0
$508$	4.77671	+	2.75784i	0.211932	+	0.122359i
$509$	8.55353	+	14.8151i	0.379128	+	0.656670i	0.990936	−	0.134337i	$-0.0428905\pi$
$509$	8.55353	+	14.8151i	0.379128	+	0.656670i	−0.611807	+	0.791007i	$0.709557\pi$
$510$		0			0
$511$	−40.1285	+	18.4809i	−1.77518	+	0.817546i
$512$	1.00000			0.0441942
$513$		0			0
$514$	10.9084	+	6.29797i	0.481149	+	0.277791i
$515$		0			0
$516$		0			0
$517$	20.5766			0.904956
$518$	−11.8511	−	25.7329i	−0.520706	−	1.13064i
$519$		0			0
$520$		0			0
$521$	20.2375	−	35.0524i	0.886622	−	1.53567i	0.0427789	−	0.999085i	$-0.486379\pi$
$521$	20.2375	−	35.0524i	0.886622	−	1.53567i	0.843843	−	0.536590i	$-0.180288\pi$
$522$		0			0
$523$	21.8420	+	37.8314i	0.955083	+	1.65425i	0.734178	+	0.678957i	$0.237568\pi$
$523$	21.8420	+	37.8314i	0.955083	+	1.65425i	0.220905	+	0.975295i	$0.429099\pi$
$524$	−20.6136			−0.900510
$525$		0			0
$526$	−16.6719			−0.726929
$527$	1.80425	+	3.12505i	0.0785943	+	0.136129i
$528$		0			0
$529$	−7.57274	+	13.1164i	−0.329250	+	0.570277i
$530$		0			0
$531$		0			0
$532$	4.73893	−	6.69998i	0.205458	−	0.290481i
$533$	−46.1171			−1.99755
$534$		0			0
$535$		0			0
$536$	10.3529	+	5.97727i	0.447179	+	0.258179i
$537$		0			0
$538$	20.0069			0.862561
$539$	6.35681	−	34.1524i	0.273807	−	1.47105i
$540$		0			0
$541$	5.85601	+	10.1429i	0.251770	+	0.436078i	0.964013	−	0.265855i	$-0.0856541\pi$
$541$	5.85601	+	10.1429i	0.251770	+	0.436078i	−0.712243	+	0.701933i	$0.752321\pi$
$542$	15.4684	+	8.93068i	0.664425	+	0.383606i
$543$		0			0
$544$	2.66237	−	1.53712i	0.114148	−	0.0659035i
$545$		0			0
$546$		0			0
$547$			34.6501i			1.48153i	0.671764	+	0.740765i	$0.265537\pi$
$547$			34.6501i			1.48153i	−0.671764	+	0.740765i	$0.734463\pi$
$548$	−5.72807	−	9.92131i	−0.244691	−	0.423817i
$549$		0			0
$550$		0			0
$551$	10.3582	+	17.9409i	0.441272	+	0.764306i
$552$		0			0
$553$	−1.03233	+	11.1878i	−0.0438993	+	0.475754i
$554$			18.1481i			0.771040i
$555$		0			0
$556$	−1.01066	−	0.583502i	−0.0428613	−	0.0247460i
$557$	−17.6567	+	30.5822i	−0.748137	+	1.29581i	0.200578	+	0.979678i	$0.435718\pi$
$557$	−17.6567	+	30.5822i	−0.748137	+	1.29581i	−0.948715	+	0.316134i	$0.897615\pi$
$558$		0			0
$559$			48.4025i			2.04721i
$560$		0			0
$561$		0			0
$562$	−13.4346	+	7.75647i	−0.566705	+	0.327187i
$563$	−33.5143	−	19.3495i	−1.41246	−	0.815483i	−0.416839	−	0.908981i	$-0.636862\pi$
$563$	−33.5143	−	19.3495i	−1.41246	−	0.815483i	−0.995620	+	0.0934975i	$0.970195\pi$
$564$		0			0
$565$		0			0
$566$	17.6454			0.741690
$567$		0			0
$568$		−	0.973522i		−	0.0408481i
$569$	6.20799	−	3.58419i	0.260253	−	0.150257i	−0.364197	−	0.931322i	$-0.618657\pi$
$569$	6.20799	−	3.58419i	0.260253	−	0.150257i	0.624450	+	0.781065i	$0.285323\pi$
$570$		0			0
$571$	10.7717	−	18.6571i	0.450781	−	0.780776i	−0.547653	−	0.836705i	$-0.684479\pi$
$571$	10.7717	−	18.6571i	0.450781	−	0.780776i	0.998435	+	0.0559290i	$0.0178121\pi$
$572$	−23.6117	+	13.6322i	−0.987256	+	0.569993i
$573$		0			0
$574$	−2.04064	+	22.1152i	−0.0851746	+	0.923070i
$575$		0			0
$576$		0			0
$577$	7.86230	−	13.6179i	0.327312	−	0.566921i	−0.654666	−	0.755919i	$-0.727191\pi$
$577$	7.86230	−	13.6179i	0.327312	−	0.566921i	0.981978	+	0.188998i	$0.0605239\pi$
$578$	−3.77453	+	6.53767i	−0.157000	+	0.271931i
$579$		0			0
$580$		0			0
$581$	21.8234	−	30.8544i	0.905389	−	1.28006i
$582$		0			0
$583$	−19.1284	+	11.0438i	−0.792217	+	0.457387i
$584$	8.34916	−	14.4612i	0.345491	−	0.598408i
$585$		0			0
$586$	9.04902	−	5.22446i	0.373812	−	0.215820i
$587$		−	4.59252i		−	0.189554i	−0.995499	−	0.0947769i	$-0.969786\pi$
$587$		−	4.59252i		−	0.189554i	0.995499	−	0.0947769i	$-0.0302138\pi$
$588$		0			0
$589$	−3.64082			−0.150017
$590$		0			0
$591$		0			0
$592$	9.27339	+	5.35400i	0.381134	+	0.220048i
$593$	3.31317	−	1.91286i	0.136055	−	0.0785516i	−0.430427	−	0.902625i	$-0.641637\pi$
$593$	3.31317	−	1.91286i	0.136055	−	0.0785516i	0.566483	+	0.824074i	$0.308304\pi$
$594$		0			0
$595$		0			0
$596$		−	15.4041i		−	0.630977i
$597$		0			0
$598$	−16.9657	+	29.3854i	−0.693777	+	1.20166i
$599$	−13.6589	−	7.88600i	−0.558089	−	0.322213i	0.194289	−	0.980944i	$-0.437760\pi$
$599$	−13.6589	−	7.88600i	−0.558089	−	0.322213i	−0.752378	+	0.658731i	$0.771093\pi$
$600$		0			0
$601$		−	1.39673i		−	0.0569740i	−0.999594	−	0.0284870i	$-0.990931\pi$
$601$		−	1.39673i		−	0.0569740i	0.999594	−	0.0284870i	$-0.00906892\pi$
$602$	23.2111	+	2.14176i	0.946015	+	0.0872918i
$603$		0			0
$604$	−0.511281	−	0.885565i	−0.0208037	−	0.0360331i
$605$		0			0
$606$		0			0
$607$	−5.16682	−	8.94920i	−0.209715	−	0.363237i	0.741910	−	0.670500i	$-0.233920\pi$
$607$	−5.16682	−	8.94920i	−0.209715	−	0.363237i	−0.951625	+	0.307263i	$0.900587\pi$
$608$			3.10178i			0.125794i
$609$		0			0
$610$		0			0
$611$	19.7271	−	11.3895i	0.798075	−	0.460769i
$612$		0			0
$613$	10.6482	+	6.14772i	0.430075	+	0.248304i	0.699379	−	0.714751i	$-0.253460\pi$
$613$	10.6482	+	6.14772i	0.430075	+	0.248304i	−0.269303	+	0.963055i	$0.586793\pi$
$614$	−0.362324	−	0.627564i	−0.0146222	−	0.0253264i
$615$		0			0
$616$	5.49247	+	11.9261i	0.221298	+	0.480516i
$617$	−8.10935			−0.326470			−0.163235	−	0.986587i	$-0.552193\pi$
$617$	−8.10935			−0.326470			−0.163235	+	0.986587i	$0.552193\pi$
$618$		0			0
$619$	−7.03506	−	4.06170i	−0.282763	−	0.163253i	0.351911	−	0.936034i	$-0.385532\pi$
$619$	−7.03506	−	4.06170i	−0.282763	−	0.163253i	−0.634674	+	0.772780i	$0.718865\pi$
$620$		0			0
$621$		0			0
$622$	−28.2450			−1.13252
$623$	3.59065	−	38.9133i	0.143857	−	1.55903i
$624$		0			0
$625$		0			0
$626$	10.2651	−	17.7797i	0.410276	−	0.710619i
$627$		0			0
$628$	−2.68294	−	4.64699i	−0.107061	−	0.185435i
$629$	32.9189			1.31256
$630$		0			0
$631$	−40.6011			−1.61630			−0.808151	−	0.588975i	$-0.799532\pi$
$631$	−40.6011			−1.61630			−0.808151	+	0.588975i	$0.799532\pi$
$632$	−2.12328	−	3.67763i	−0.0844595	−	0.146288i
$633$		0			0
$634$	−1.13674	+	1.96890i	−0.0451459	+	0.0781950i
$635$		0			0
$636$		0			0
$637$	−12.8095	−	36.2611i	−0.507531	−	1.43672i
$638$	−33.1452			−1.31223
$639$		0			0
$640$		0			0
$641$	−32.0260	−	18.4902i	−1.26495	−	0.730319i	−0.290922	−	0.956747i	$-0.593962\pi$
$641$	−32.0260	−	18.4902i	−1.26495	−	0.730319i	−0.974028	+	0.226427i	$0.927295\pi$
$642$		0			0
$643$	−4.86696			−0.191934			−0.0959671	−	0.995385i	$-0.530594\pi$
$643$	−4.86696			−0.191934			−0.0959671	+	0.995385i	$0.530594\pi$
$644$	13.3409	+	9.43606i	0.525704	+	0.371833i
$645$		0			0
$646$	4.76780	+	8.25808i	0.187587	+	0.324910i
$647$	21.6217	+	12.4833i	0.850037	+	0.490769i	0.860663	−	0.509175i	$-0.170049\pi$
$647$	21.6217	+	12.4833i	0.850037	+	0.490769i	−0.0106266	+	0.999944i	$0.503383\pi$
$648$		0			0
$649$	−25.8197	+	14.9070i	−1.01351	+	0.585151i
$650$		0			0
$651$		0			0
$652$		−	10.0422i		−	0.393282i
$653$	−7.29496	−	12.6352i	−0.285474	−	0.494455i	0.687250	−	0.726421i	$-0.258818\pi$
$653$	−7.29496	−	12.6352i	−0.285474	−	0.494455i	−0.972724	+	0.231966i	$0.925484\pi$
$654$		0			0
$655$		0			0
$656$	−4.19713	−	7.26965i	−0.163870	−	0.283832i
$657$		0			0
$658$	−4.58885	−	9.96402i	−0.178892	−	0.388438i
$659$		−	33.8468i		−	1.31848i	−0.751931	−	0.659242i	$-0.770877\pi$
$659$		−	33.8468i		−	1.31848i	0.751931	−	0.659242i	$-0.229123\pi$
$660$		0			0
$661$	−14.9053	−	8.60557i	−0.579749	−	0.334718i	0.181285	−	0.983431i	$-0.441974\pi$
$661$	−14.9053	−	8.60557i	−0.579749	−	0.334718i	−0.761034	+	0.648713i	$0.775308\pi$
$662$	18.0646	−	31.2889i	0.702102	−	1.21608i
$663$		0			0
$664$			14.2841i			0.554332i
$665$		0			0
$666$		0			0
$667$	−35.7235	+	20.6250i	−1.38322	+	0.798602i
$668$	−2.13047	−	1.23003i	−0.0824302	−	0.0475911i
$669$		0			0
$670$		0			0
$671$	−51.8615			−2.00209
$672$		0			0
$673$			1.47971i			0.0570387i	0.999593	+	0.0285193i	$0.00907922\pi$
$673$			1.47971i			0.0570387i	−0.999593	+	0.0285193i	$0.990921\pi$
$674$	−3.25938	+	1.88181i	−0.125547	+	0.0724844i
$675$		0			0
$676$	−8.59134	+	14.8806i	−0.330436	+	0.572333i
$677$	−10.2632	+	5.92549i	−0.394448	+	0.227735i	−0.684086	−	0.729402i	$-0.739799\pi$
$677$	−10.2632	+	5.92549i	−0.394448	+	0.227735i	0.289637	+	0.957136i	$0.406465\pi$
$678$		0			0
$679$	9.53968	+	6.74746i	0.366099	+	0.258944i
$680$		0			0
$681$		0			0
$682$	2.91258	−	5.04473i	0.111528	−	0.193173i
$683$	5.26389	−	9.11732i	0.201417	−	0.348865i	−0.747568	−	0.664185i	$-0.768779\pi$
$683$	5.26389	−	9.11732i	0.201417	−	0.348865i	0.948985	+	0.315320i	$0.102112\pi$
$684$		0			0
$685$		0			0
$686$	−17.9556	+	4.53821i	−0.685549	+	0.173270i
$687$		0			0
$688$	−7.62990	+	4.40513i	−0.290887	+	0.167944i
$689$	−12.2258	+	21.1758i	−0.465767	+	0.806732i
$690$		0			0
$691$	6.61628	−	3.81991i	0.251695	−	0.145316i	−0.368845	−	0.929491i	$-0.620247\pi$
$691$	6.61628	−	3.81991i	0.251695	−	0.145316i	0.620540	+	0.784175i	$0.286913\pi$
$692$			3.00084i			0.114075i
$693$		0			0
$694$	4.04779			0.153652
$695$		0			0
$696$		0			0
$697$	−22.3486	−	12.9030i	−0.846515	−	0.488736i
$698$	−20.7296	+	11.9682i	−0.784626	+	0.453004i
$699$		0			0
$700$		0			0
$701$		−	35.2007i		−	1.32951i	−0.747060	−	0.664757i	$-0.768535\pi$
$701$		−	35.2007i		−	1.32951i	0.747060	−	0.664757i	$-0.231465\pi$
$702$		0			0
$703$	−16.6069	+	28.7640i	−0.626341	+	1.08485i
$704$	−4.29783	−	2.48135i	−0.161980	−	0.0935195i
$705$		0			0
$706$		−	25.4818i		−	0.959019i
$707$	24.9843	−	11.5063i	0.939631	−	0.432740i
$708$		0			0
$709$	−18.1846	−	31.4966i	−0.682936	−	1.18288i	−0.974081	−	0.226201i	$-0.927369\pi$
$709$	−18.1846	−	31.4966i	−0.682936	−	1.18288i	0.291145	−	0.956679i	$-0.405964\pi$
$710$		0			0
$711$		0			0
$712$	7.38517	+	12.7915i	0.276771	+	0.479381i
$713$		−	7.24954i		−	0.271497i
$714$		0			0
$715$		0			0
$716$	−3.18036	+	1.83618i	−0.118856	+	0.0686214i
$717$		0			0
$718$	−15.4893	−	8.94277i	−0.578057	−	0.333741i
$719$	0.772550	+	1.33810i	0.0288113	+	0.0499026i	0.880072	−	0.474841i	$-0.157494\pi$
$719$	0.772550	+	1.33810i	0.0288113	+	0.0499026i	−0.851260	+	0.524744i	$0.824161\pi$
$720$		0			0
$721$	−2.48905	+	26.9748i	−0.0926971	+	1.00460i
$722$	9.37898			0.349049
$723$		0			0
$724$	5.31359	+	3.06780i	0.197478	+	0.114014i
$725$		0			0
$726$		0			0
$727$	34.1857			1.26788			0.633939	−	0.773383i	$-0.281437\pi$
$727$	34.1857			1.26788			0.633939	+	0.773383i	$0.281437\pi$
$728$	11.8670	+	8.39360i	0.439821	+	0.311087i
$729$		0			0
$730$		0			0
$731$	−13.5424	+	23.4561i	−0.500884	+	0.867557i
$732$		0			0
$733$	21.9095	+	37.9485i	0.809248	+	1.40166i	0.913386	+	0.407095i	$0.133458\pi$
$733$	21.9095	+	37.9485i	0.809248	+	1.40166i	−0.104138	+	0.994563i	$0.533208\pi$
$734$	−5.27703			−0.194779
$735$		0			0
$736$	−6.17620			−0.227658
$737$	−29.6634	−	51.3786i	−1.09267	−	1.89255i
$738$		0			0
$739$	−6.86403	+	11.8888i	−0.252497	+	0.437338i	−0.964213	−	0.265130i	$-0.914585\pi$
$739$	−6.86403	+	11.8888i	−0.252497	+	0.437338i	0.711715	+	0.702468i	$0.247919\pi$
$740$		0			0
$741$		0			0
$742$	9.61374	+	6.79984i	0.352931	+	0.249630i
$743$	20.8393			0.764520			0.382260	−	0.924055i	$-0.375146\pi$
$743$	20.8393			0.764520			0.382260	+	0.924055i	$0.375146\pi$
$744$		0			0
$745$		0			0
$746$	12.5988	+	7.27390i	0.461274	+	0.266316i
$747$		0			0
$748$	−15.2565			−0.557834
$749$	−1.59946	+	17.3339i	−0.0584429	+	0.633369i
$750$		0			0
$751$	21.8346	+	37.8186i	0.796755	+	1.38002i	0.921719	+	0.387859i	$0.126785\pi$
$751$	21.8346	+	37.8186i	0.796755	+	1.38002i	−0.124964	+	0.992161i	$0.539881\pi$
$752$	3.59075	+	2.07312i	0.130941	+	0.0755989i
$753$		0			0
$754$	−31.7769	+	18.3464i	−1.15725	+	0.668136i
$755$		0			0
$756$		0			0
$757$		−	40.4115i		−	1.46878i	−0.678727	−	0.734391i	$-0.737468\pi$
$757$		−	40.4115i		−	1.46878i	0.678727	−	0.734391i	$-0.262532\pi$
$758$	1.83335	+	3.17545i	0.0665901	+	0.115337i
$759$		0			0
$760$		0			0
$761$	18.3292	+	31.7471i	0.664432	+	1.15083i	0.979439	+	0.201741i	$0.0646598\pi$
$761$	18.3292	+	31.7471i	0.664432	+	1.15083i	−0.315007	+	0.949089i	$0.602007\pi$
$762$		0			0
$763$	−6.45094	+	2.97093i	−0.233540	+	0.107555i
$764$			5.71839i			0.206884i
$765$		0			0
$766$	−16.9091	−	9.76247i	−0.610951	−	0.352732i
$767$	−16.5025	+	28.5833i	−0.595872	+	1.03208i
$768$		0			0
$769$			20.4304i			0.736738i	0.929680	+	0.368369i	$0.120084\pi$
$769$			20.4304i			0.736738i	−0.929680	+	0.368369i	$0.879916\pi$
$770$		0			0
$771$		0			0
$772$	−5.39819	+	3.11665i	−0.194285	+	0.112171i
$773$	−11.8586	−	6.84657i	−0.426525	−	0.246254i	0.271340	−	0.962483i	$-0.412533\pi$
$773$	−11.8586	−	6.84657i	−0.426525	−	0.246254i	−0.697865	+	0.716229i	$0.745866\pi$
$774$		0			0
$775$		0			0
$776$	−4.41643			−0.158540
$777$		0			0
$778$			17.2871i			0.619773i
$779$	22.5488	−	13.0186i	0.807896	−	0.466439i
$780$		0			0
$781$	−2.41565	+	4.18403i	−0.0864388	+	0.149716i
$782$	−16.4433	+	9.49356i	−0.588012	+	0.339489i
$783$		0			0
$784$	4.55021	−	5.31936i	0.162507	−	0.189977i
$785$		0			0
$786$		0			0
$787$	6.70701	−	11.6169i	0.239079	−	0.414097i	−0.721371	−	0.692549i	$-0.756488\pi$
$787$	6.70701	−	11.6169i	0.239079	−	0.414097i	0.960450	+	0.278451i	$0.0898211\pi$
$788$	−0.661170	+	1.14518i	−0.0235532	+	0.0407953i
$789$		0			0
$790$		0			0
$791$	−7.66883	−	5.42419i	−0.272672	−	0.192862i
$792$		0			0
$793$	−49.7206	+	28.7062i	−1.76563	+	1.01939i
$794$	13.8423	−	23.9755i	0.491244	−	0.850860i
$795$		0			0
$796$	−8.27163	+	4.77563i	−0.293180	+	0.169268i
$797$			53.8858i			1.90873i	0.298636	+	0.954367i	$0.403468\pi$
$797$			53.8858i			1.90873i	−0.298636	+	0.954367i	$0.596532\pi$
$798$		0			0
$799$	12.7465			0.450940
$800$		0			0
$801$		0			0
$802$	32.7521	+	18.9095i	1.15652	+	0.667716i
$803$	−71.7665	+	41.4344i	−2.53259	+	1.46219i
$804$		0			0
$805$		0			0
$806$		−	6.44864i		−	0.227144i
$807$		0			0
$808$	−5.19825	+	9.00364i	−0.182874	+	0.316747i
$809$	10.1762	+	5.87522i	0.357775	+	0.206562i	0.668104	−	0.744068i	$-0.267106\pi$
$809$	10.1762	+	5.87522i	0.357775	+	0.206562i	−0.310329	+	0.950629i	$0.600439\pi$
$810$		0			0
$811$		−	22.8579i		−	0.802649i	−0.915936	−	0.401325i	$-0.868550\pi$
$811$		−	22.8579i		−	0.802649i	0.915936	−	0.401325i	$-0.131450\pi$
$812$	7.39182	+	16.0502i	0.259402	+	0.563253i
$813$		0			0
$814$	−26.5703	−	46.0211i	−0.931288	−	1.61304i
$815$		0			0
$816$		0			0
$817$	−13.6637	−	23.6663i	−0.478033	−	0.827978i
$818$			36.4918i			1.27591i
$819$		0			0
$820$		0			0
$821$	−9.58876	+	5.53607i	−0.334650	+	0.193210i	−0.657904	−	0.753102i	$-0.728557\pi$
$821$	−9.58876	+	5.53607i	−0.334650	+	0.193210i	0.323254	+	0.946312i	$0.395223\pi$
$822$		0			0
$823$	−0.612108	−	0.353401i	−0.0213368	−	0.0123188i	0.489294	−	0.872119i	$-0.337255\pi$
$823$	−0.612108	−	0.353401i	−0.0213368	−	0.0123188i	−0.510630	+	0.859800i	$0.670588\pi$
$824$	−5.11942	−	8.86709i	−0.178343	−	0.308900i
$825$		0			0
$826$	12.9767	+	9.17849i	0.451518	+	0.319361i
$827$	−18.8230			−0.654540			−0.327270	−	0.944931i	$-0.606129\pi$
$827$	−18.8230			−0.654540			−0.327270	+	0.944931i	$0.606129\pi$
$828$		0			0
$829$	26.7423	+	15.4397i	0.928800	+	0.536243i	0.886432	−	0.462859i	$-0.153176\pi$
$829$	26.7423	+	15.4397i	0.928800	+	0.536243i	0.0423683	+	0.999102i	$0.486510\pi$
$830$		0			0
$831$		0			0
$832$	−5.49388			−0.190466
$833$	3.93785	−	21.1563i	0.136438	−	0.733023i
$834$		0			0
$835$		0			0
$836$	7.69660	−	13.3309i	0.266193	−	0.461059i
$837$		0			0
$838$	10.8335	+	18.7641i	0.374236	+	0.648195i
$839$	−20.9932			−0.724766			−0.362383	−	0.932029i	$-0.618037\pi$
$839$	−20.9932			−0.724766			−0.362383	+	0.932029i	$0.618037\pi$
$840$		0			0
$841$	−15.6071			−0.538174
$842$	4.42096	+	7.65733i	0.152356	+	0.263889i
$843$		0			0
$844$	−13.0110	+	22.5356i	−0.447856	+	0.775709i
$845$		0			0
$846$		0			0
$847$	3.31306	−	35.9049i	0.113838	−	1.23371i
$848$	−4.45071			−0.152838
$849$		0			0
$850$		0			0
$851$	−57.2744	−	33.0674i	−1.96334	−	1.13353i
$852$		0			0
$853$	−18.2167			−0.623729			−0.311864	−	0.950127i	$-0.600953\pi$
$853$	−18.2167			−0.623729			−0.311864	+	0.950127i	$0.600953\pi$
$854$	11.5658	+	25.1135i	0.395774	+	0.859365i
$855$		0			0
$856$	−3.28972	−	5.69797i	−0.112440	−	0.194753i
$857$	10.7382	+	6.19973i	0.366812	+	0.211779i	0.672065	−	0.740493i	$-0.265408\pi$
$857$	10.7382	+	6.19973i	0.366812	+	0.211779i	−0.305253	+	0.952271i	$0.598741\pi$
$858$		0			0
$859$	−6.67438	+	3.85345i	−0.227727	+	0.131478i	−0.609523	−	0.792768i	$-0.708639\pi$
$859$	−6.67438	+	3.85345i	−0.227727	+	0.131478i	0.381796	+	0.924247i	$0.375306\pi$
$860$		0			0
$861$		0			0
$862$		−	29.7313i		−	1.01265i
$863$	3.77821	+	6.54406i	0.128612	+	0.222762i	0.923139	−	0.384466i	$-0.125615\pi$
$863$	3.77821	+	6.54406i	0.128612	+	0.222762i	−0.794527	+	0.607229i	$0.792281\pi$
$864$		0			0
$865$		0			0
$866$	13.2833	+	23.0074i	0.451386	+	0.781823i
$867$		0			0
$868$	−3.09241	−	0.285346i	−0.104963	−	0.00968528i
$869$			21.0744i			0.714900i
$870$		0			0
$871$	−56.8778	−	32.8384i	−1.92723	−	1.11269i
$872$	1.34219	−	2.32474i	0.0454522	−	0.0787255i
$873$		0			0
$874$		−	19.1572i		−	0.648002i
$875$		0			0
$876$		0			0
$877$	−26.0843	+	15.0598i	−0.880803	+	0.508532i	−0.870923	−	0.491420i	$-0.836478\pi$
$877$	−26.0843	+	15.0598i	−0.880803	+	0.508532i	−0.00987971	+	0.999951i	$0.503145\pi$
$878$	14.4067	+	8.31774i	0.486204	+	0.280710i
$879$		0			0
$880$		0			0
$881$	29.6642			0.999411			0.499706	−	0.866195i	$-0.333442\pi$
$881$	29.6642			0.999411			0.499706	+	0.866195i	$0.333442\pi$
$882$		0			0
$883$		−	38.9643i		−	1.31125i	−0.755086	−	0.655626i	$-0.772405\pi$
$883$		−	38.9643i		−	1.31125i	0.755086	−	0.655626i	$-0.227595\pi$
$884$	−14.6267	+	8.44475i	−0.491950	+	0.284028i
$885$		0			0
$886$	1.63637	−	2.83428i	0.0549750	−	0.0952195i
$887$	17.9134	−	10.3423i	0.601472	−	0.347260i	−0.168149	−	0.985762i	$-0.553779\pi$
$887$	17.9134	−	10.3423i	0.601472	−	0.347260i	0.769620	+	0.638502i	$0.220446\pi$
$888$		0			0
$889$	−8.42690	+	11.9141i	−0.282629	+	0.399586i
$890$		0			0
$891$		0			0
$892$	−3.62611	+	6.28060i	−0.121411	+	0.210290i
$893$	−6.43036	+	11.1377i	−0.215184	+	0.372709i
$894$		0			0
$895$		0			0
$896$	−0.243099	+	2.63456i	−0.00812137	+	0.0880144i
$897$		0			0
$898$	−9.03451	+	5.21608i	−0.301485	+	0.174063i
$899$	3.91977	−	6.78924i	0.130732	−	0.226434i
$900$		0			0
$901$	−11.8494	+	6.84127i	−0.394762	+	0.227916i
$902$			41.6583i			1.38707i
$903$		0			0
$904$	3.55031			0.118081
$905$		0			0
$906$		0			0
$907$	10.5076	+	6.06658i	0.348900	+	0.201437i	0.664201	−	0.747554i	$-0.268772\pi$
$907$	10.5076	+	6.06658i	0.348900	+	0.201437i	−0.315301	+	0.948992i	$0.602105\pi$
$908$	−23.1409	+	13.3604i	−0.767959	+	0.443381i
$909$		0			0
$910$		0			0
$911$			24.5869i			0.814600i	0.913294	+	0.407300i	$0.133530\pi$
$911$			24.5869i			0.814600i	−0.913294	+	0.407300i	$0.866470\pi$
$912$		0			0
$913$	35.4440	−	61.3908i	1.17302	−	2.03174i
$914$	−28.6471	−	16.5394i	−0.947561	−	0.547074i
$915$		0			0
$916$		−	24.3034i		−	0.803006i
$917$	5.01115	−	54.3078i	0.165483	−	1.79340i
$918$		0			0
$919$	−11.5230	−	19.9585i	−0.380110	−	0.658369i	0.610968	−	0.791655i	$-0.290780\pi$
$919$	−11.5230	−	19.9585i	−0.380110	−	0.658369i	−0.991078	+	0.133286i	$0.957447\pi$
$920$		0			0
$921$		0			0
$922$	−5.78196	−	10.0146i	−0.190419	−	0.329815i
$923$			5.34841i			0.176045i
$924$		0			0
$925$		0			0
$926$	33.4339	−	19.3031i	1.09871	−	0.634338i
$927$		0			0
$928$	−5.78405	−	3.33943i	−0.189871	−	0.109622i
$929$	20.1685	+	34.9328i	0.661706	+	1.14611i	0.980167	+	0.198173i	$0.0635007\pi$
$929$	20.1685	+	34.9328i	0.661706	+	1.14611i	−0.318461	+	0.947936i	$0.603166\pi$
$930$		0			0
$931$	16.4995	+	14.1137i	0.540748	+	0.462559i
$932$	9.25577			0.303183
$933$		0			0
$934$	4.08230	+	2.35692i	0.133577	+	0.0771207i
$935$		0			0
$936$		0			0
$937$	41.4861			1.35529			0.677646	−	0.735389i	$-0.263000\pi$
$937$	41.4861			1.35529			0.677646	+	0.735389i	$0.263000\pi$
$938$	−18.2643	+	25.8224i	−0.596350	+	0.843130i
$939$		0			0
$940$		0			0
$941$	−9.37786	+	16.2429i	−0.305710	+	0.529505i	−0.977419	−	0.211310i	$-0.932227\pi$
$941$	−9.37786	+	16.2429i	−0.305710	+	0.529505i	0.671709	+	0.740815i	$0.265560\pi$
$942$		0			0
$943$	25.9223	+	44.8988i	0.844148	+	1.46211i
$944$	−6.00761			−0.195531
$945$		0			0
$946$	43.7227			1.42155
$947$	21.6910	+	37.5699i	0.704862	+	1.22086i	0.966741	+	0.255756i	$0.0823244\pi$
$947$	21.6910	+	37.5699i	0.704862	+	1.22086i	−0.261879	+	0.965101i	$0.584342\pi$
$948$		0			0
$949$	−45.8693	+	79.4479i	−1.48898	+	2.57899i
$950$		0			0
$951$		0			0
$952$	3.40241	+	7.38784i	0.110273	+	0.239441i
$953$	−18.1672			−0.588492			−0.294246	−	0.955730i	$-0.595069\pi$
$953$	−18.1672			−0.588492			−0.294246	+	0.955730i	$0.595069\pi$
$954$		0			0
$955$		0			0
$956$	0.219422	+	0.126683i	0.00709661	+	0.00409723i
$957$		0			0
$958$	20.0191			0.646789
$959$	27.5308	−	12.6791i	0.889015	−	0.409429i
$960$		0			0
$961$	−14.8111	−	25.6536i	−0.477778	−	0.827536i
$962$	−50.9469	−	29.4142i	−1.64259	−	0.948352i
$963$		0			0
$964$	−2.57538	+	1.48689i	−0.0829473	+	0.0478896i
$965$		0			0
$966$		0			0
$967$			29.7712i			0.957378i	0.877985	+	0.478689i	$0.158888\pi$
$967$			29.7712i			0.957378i	−0.877985	+	0.478689i	$0.841112\pi$
$968$	6.81421	+	11.8026i	0.219017	+	0.379349i
$969$		0			0
$970$		0			0
$971$	18.5472	+	32.1247i	0.595209	+	1.03093i	0.993517	+	0.113680i	$0.0362640\pi$
$971$	18.5472	+	32.1247i	0.595209	+	1.03093i	−0.398309	+	0.917251i	$0.630403\pi$
$972$		0			0
$973$	1.78296	−	2.52078i	0.0571591	−	0.0808126i
$974$			4.73088i			0.151587i
$975$		0			0
$976$	−9.05018	−	5.22512i	−0.289689	−	0.167252i
$977$	0.505165	−	0.874971i	0.0161617	−	0.0279928i	−0.857831	−	0.513931i	$-0.828189\pi$
$977$	0.505165	−	0.874971i	0.0161617	−	0.0279928i	0.873993	+	0.485938i	$0.161522\pi$
$978$		0			0
$979$		−	73.3008i		−	2.34270i
$980$		0			0
$981$		0			0
$982$	−13.8587	+	8.00133i	−0.442249	+	0.255333i
$983$	21.9623	+	12.6799i	0.700487	+	0.404427i	0.807529	−	0.589828i	$-0.200804\pi$
$983$	21.9623	+	12.6799i	0.700487	+	0.404427i	−0.107042	+	0.994255i	$0.534138\pi$
$984$		0			0
$985$		0			0
$986$	−20.5324			−0.653884
$987$		0			0
$988$		−	17.0408i		−	0.542140i
$989$	47.1238	−	27.2070i	1.49845	−	0.865131i
$990$		0			0
$991$	21.3875	−	37.0442i	0.679396	−	1.17675i	−0.295767	−	0.955260i	$-0.595575\pi$
$991$	21.3875	−	37.0442i	0.679396	−	1.17675i	0.975163	−	0.221488i	$-0.0710914\pi$
$992$	1.01653	−	0.586893i	0.0322748	−	0.0186339i
$993$		0			0
$994$	2.56480	+	0.236662i	0.0813506	+	0.00750647i
$995$		0			0
$996$		0			0
$997$	12.6906	−	21.9808i	0.401916	−	0.696139i	−0.592041	−	0.805908i	$-0.701678\pi$
$997$	12.6906	−	21.9808i	0.401916	−	0.696139i	0.993957	+	0.109769i	$0.0350111\pi$
$998$	3.18097	−	5.50961i	0.100692	−	0.174404i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.g.899.4		24
3.2	odd	2		3150.2.bp.h.899.4		24
5.2	odd	4		3150.2.bf.e.1151.12	yes	24
5.3	odd	4		3150.2.bf.d.1151.1	✓	24
5.4	even	2		3150.2.bp.h.899.9		24
7.5	odd	6	inner	3150.2.bp.g.1349.9		24
15.2	even	4		3150.2.bf.e.1151.1	yes	24
15.8	even	4		3150.2.bf.d.1151.12	yes	24
15.14	odd	2	inner	3150.2.bp.g.899.9		24
21.5	even	6		3150.2.bp.h.1349.9		24
35.12	even	12		3150.2.bf.e.1601.1	yes	24
35.19	odd	6		3150.2.bp.h.1349.4		24
35.33	even	12		3150.2.bf.d.1601.12	yes	24
105.47	odd	12		3150.2.bf.e.1601.12	yes	24
105.68	odd	12		3150.2.bf.d.1601.1	yes	24
105.89	even	6	inner	3150.2.bp.g.1349.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.1	✓	24	5.3	odd	4
3150.2.bf.d.1151.12	yes	24	15.8	even	4
3150.2.bf.d.1601.1	yes	24	105.68	odd	12
3150.2.bf.d.1601.12	yes	24	35.33	even	12
3150.2.bf.e.1151.1	yes	24	15.2	even	4
3150.2.bf.e.1151.12	yes	24	5.2	odd	4
3150.2.bf.e.1601.1	yes	24	35.12	even	12
3150.2.bf.e.1601.12	yes	24	105.47	odd	12
3150.2.bp.g.899.4		24	1.1	even	1	trivial
3150.2.bp.g.899.9		24	15.14	odd	2	inner
3150.2.bp.g.1349.4		24	105.89	even	6	inner
3150.2.bp.g.1349.9		24	7.5	odd	6	inner
3150.2.bp.h.899.4		24	3.2	odd	2
3150.2.bp.h.899.9		24	5.4	even	2
3150.2.bp.h.1349.4		24	35.19	odd	6
3150.2.bp.h.1349.9		24	21.5	even	6

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.16005 - 1.52781i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.16005 - 1.52781i) q^{7} +1.00000 q^{8} +(-4.29783 - 2.48135i) q^{11} -5.49388 q^{13} +(-0.243099 + 2.63456i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.66237 - 1.53712i) q^{17} +(2.68622 - 1.55089i) q^{19} +4.96270i q^{22} +(3.08810 + 5.34875i) q^{23} +(2.74694 + 4.75784i) q^{26} +(2.40314 - 1.10675i) q^{28} +6.67885i q^{29} +(-1.01653 - 0.586893i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.07424i q^{34} +(-9.27339 + 5.35400i) q^{37} +(-2.68622 - 1.55089i) q^{38} +8.39427 q^{41} -8.81025i q^{43} +(4.29783 - 2.48135i) q^{44} +(3.08810 - 5.34875i) q^{46} +(-3.59075 + 2.07312i) q^{47} +(2.33160 + 6.60028i) q^{49} +(2.74694 - 4.75784i) q^{52} +(2.22536 - 3.85443i) q^{53} +(-2.16005 - 1.52781i) q^{56} +(5.78405 - 3.33943i) q^{58} +(3.00381 - 5.20275i) q^{59} +(9.05018 - 5.22512i) q^{61} +1.17379i q^{62} +1.00000 q^{64} +(10.3529 + 5.97727i) q^{67} +(2.66237 - 1.53712i) q^{68} -0.973522i q^{71} +(8.34916 - 14.4612i) q^{73} +(9.27339 + 5.35400i) q^{74} +3.10178i q^{76} +(5.49247 + 11.9261i) q^{77} +(-2.12328 - 3.67763i) q^{79} +(-4.19713 - 7.26965i) q^{82} +14.2841i q^{83} +(-7.62990 + 4.40513i) q^{86} +(-4.29783 - 2.48135i) q^{88} +(7.38517 + 12.7915i) q^{89} +(11.8670 + 8.39360i) q^{91} -6.17620 q^{92} +(3.59075 + 2.07312i) q^{94} -4.41643 q^{97} +(4.55021 - 5.31936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Introduction

L-functions

Modular forms

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