LMFDB - Embedded newform 756.2.be.c.107.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(107,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-4,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	756.107
Dual form			756.2.be.c.431.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.994183 + 1.00578i) q^{2} +(-0.0232006 - 1.99987i) q^{4} +(1.28692 + 0.743002i) q^{5} +(-1.36953 + 2.26371i) q^{7} +(2.03450 + 1.96490i) q^{8} +(-2.02673 + 0.555680i) q^{10} +(1.37284 + 2.37783i) q^{11} -5.10488 q^{13} +(-0.915240 - 3.62799i) q^{14} +(-3.99892 + 0.0927963i) q^{16} +(4.52837 - 2.61446i) q^{17} +(1.30598 + 0.754009i) q^{19} +(1.45605 - 2.59090i) q^{20} +(-3.75644 - 0.983219i) q^{22} +(-4.49024 + 7.77732i) q^{23} +(-1.39590 - 2.41776i) q^{25} +(5.07518 - 5.13440i) q^{26} +(4.55889 + 2.68636i) q^{28} -2.11100i q^{29} +(0.202986 - 0.117194i) q^{31} +(3.88233 - 4.11431i) q^{32} +(-1.87245 + 7.15381i) q^{34} +(-3.44441 + 1.89564i) q^{35} +(-2.50604 + 4.34059i) q^{37} +(-2.05675 + 0.563912i) q^{38} +(1.15831 + 4.04029i) q^{40} +7.96878i q^{41} +6.52611i q^{43} +(4.72350 - 2.80067i) q^{44} +(-3.35818 - 12.2483i) q^{46} +(-2.12744 + 3.68483i) q^{47} +(-3.24878 - 6.20044i) q^{49} +(3.81952 + 0.999730i) q^{50} +(0.118437 + 10.2091i) q^{52} +(-3.44333 + 1.98801i) q^{53} +4.08010i q^{55} +(-7.23426 + 1.91453i) q^{56} +(2.12321 + 2.09872i) q^{58} +(0.339358 + 0.587784i) q^{59} +(-5.29992 + 9.17972i) q^{61} +(-0.0839334 + 0.320672i) q^{62} +(0.278358 + 7.99516i) q^{64} +(-6.56955 - 3.79293i) q^{65} +(9.34860 - 5.39742i) q^{67} +(-5.33362 - 8.99548i) q^{68} +(1.51777 - 5.34895i) q^{70} +1.32129 q^{71} +(-1.75041 - 3.03179i) q^{73} +(-1.87423 - 6.83587i) q^{74} +(1.47762 - 2.62928i) q^{76} +(-7.26288 - 0.148795i) q^{77} +(-14.4759 - 8.35768i) q^{79} +(-5.21523 - 2.85179i) q^{80} +(-8.01487 - 7.92242i) q^{82} -15.2915 q^{83} +7.77018 q^{85} +(-6.56385 - 6.48815i) q^{86} +(-1.87915 + 7.53519i) q^{88} +(10.8625 + 6.27147i) q^{89} +(6.99129 - 11.5560i) q^{91} +(15.6578 + 8.79944i) q^{92} +(-1.59108 - 5.80314i) q^{94} +(1.12046 + 1.94069i) q^{95} +14.2065 q^{97} +(9.46618 + 2.89681i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.994183	+	1.00578i	−0.702993	+	0.711196i
$2$	−0.994183	+	1.00578i	−0.702993	+	0.711196i
$3$		0			0
$3$		0			0
$4$	−0.0232006	−	1.99987i	−0.0116003	−	0.999933i
$5$	1.28692	+	0.743002i	0.575527	+	0.332280i	0.759354	−	0.650678i	$-0.225515\pi$
$5$	1.28692	+	0.743002i	0.575527	+	0.332280i	−0.183827	+	0.982959i	$0.558849\pi$
$6$		0			0
$7$	−1.36953	+	2.26371i	−0.517634	+	0.855602i
$7$	−1.36953	+	2.26371i	−0.517634	+	0.855602i
$8$	2.03450	+	1.96490i	0.719303	+	0.694696i
$9$		0			0
$10$	−2.02673	+	0.555680i	−0.640908	+	0.175721i
$11$	1.37284	+	2.37783i	0.413928	+	0.716944i	0.995315	−	0.0966827i	$-0.0308232\pi$
$11$	1.37284	+	2.37783i	0.413928	+	0.716944i	−0.581387	+	0.813627i	$0.697490\pi$
$12$		0			0
$13$	−5.10488			−1.41584			−0.707919	−	0.706293i	$-0.750366\pi$
$13$	−5.10488			−1.41584			−0.707919	+	0.706293i	$0.750366\pi$
$14$	−0.915240	−	3.62799i	−0.244608	−	0.969622i
$15$		0			0
$16$	−3.99892	+	0.0927963i	−0.999731	+	0.0231991i
$17$	4.52837	−	2.61446i	1.09829	−	0.634099i	0.162520	−	0.986705i	$-0.448038\pi$
$17$	4.52837	−	2.61446i	1.09829	−	0.634099i	0.935772	+	0.352606i	$0.114704\pi$
$18$		0			0
$19$	1.30598	+	0.754009i	0.299613	+	0.172982i	0.642269	−	0.766479i	$-0.277993\pi$
$19$	1.30598	+	0.754009i	0.299613	+	0.172982i	−0.342656	+	0.939461i	$0.611327\pi$
$20$	1.45605	−	2.59090i	0.325582	−	0.579342i
$21$		0			0
$22$	−3.75644	−	0.983219i	−0.800877	−	0.209623i
$23$	−4.49024	+	7.77732i	−0.936280	+	1.62168i	−0.163944	+	0.986470i	$0.552422\pi$
$23$	−4.49024	+	7.77732i	−0.936280	+	1.62168i	−0.772336	+	0.635214i	$0.780912\pi$
$24$		0			0
$25$	−1.39590	−	2.41776i	−0.279179	−	0.483553i
$26$	5.07518	−	5.13440i	0.995325	−	1.00694i
$27$		0			0
$28$	4.55889	+	2.68636i	0.861550	+	0.507674i
$29$		−	2.11100i		−	0.392004i	−0.980604	−	0.196002i	$-0.937204\pi$
$29$		−	2.11100i		−	0.392004i	0.980604	−	0.196002i	$-0.0627958\pi$
$30$		0			0
$31$	0.202986	−	0.117194i	0.0364574	−	0.0210487i	−0.481661	−	0.876358i	$-0.659966\pi$
$31$	0.202986	−	0.117194i	0.0364574	−	0.0210487i	0.518118	+	0.855309i	$0.326633\pi$
$32$	3.88233	−	4.11431i	0.686305	−	0.727314i
$33$		0			0
$34$	−1.87245	+	7.15381i	−0.321123	+	1.22687i
$35$	−3.44441	+	1.89564i	−0.582212	+	0.320422i
$36$		0			0
$37$	−2.50604	+	4.34059i	−0.411990	+	0.713588i	−0.995107	−	0.0988002i	$-0.968500\pi$
$37$	−2.50604	+	4.34059i	−0.411990	+	0.713588i	0.583117	+	0.812388i	$0.301833\pi$
$38$	−2.05675	+	0.563912i	−0.333650	+	0.0914786i
$39$		0			0
$40$	1.15831	+	4.04029i	0.183144	+	0.638827i
$41$			7.96878i			1.24451i	0.782813	+	0.622257i	$0.213784\pi$
$41$			7.96878i			1.24451i	−0.782813	+	0.622257i	$0.786216\pi$
$42$		0			0
$43$			6.52611i			0.995222i	0.867400	+	0.497611i	$0.165789\pi$
$43$			6.52611i			0.995222i	−0.867400	+	0.497611i	$0.834211\pi$
$44$	4.72350	−	2.80067i	0.712094	−	0.422217i
$45$		0			0
$46$	−3.35818	−	12.2483i	−0.495137	−	1.80591i
$47$	−2.12744	+	3.68483i	−0.310319	+	0.537488i	−0.978431	−	0.206572i	$-0.933769\pi$
$47$	−2.12744	+	3.68483i	−0.310319	+	0.537488i	0.668112	+	0.744060i	$0.267103\pi$
$48$		0			0
$49$	−3.24878	−	6.20044i	−0.464111	−	0.885777i
$50$	3.81952	+	0.999730i	0.540162	+	0.141383i
$51$		0			0
$52$	0.118437	+	10.2091i	0.0164242	+	1.41574i
$53$	−3.44333	+	1.98801i	−0.472978	+	0.273074i	−0.717485	−	0.696573i	$-0.754707\pi$
$53$	−3.44333	+	1.98801i	−0.472978	+	0.273074i	0.244508	+	0.969647i	$0.421374\pi$
$54$		0			0
$55$			4.08010i			0.550161i
$56$	−7.23426	+	1.91453i	−0.966719	+	0.255840i
$57$		0			0
$58$	2.12321	+	2.09872i	0.278791	+	0.275576i
$59$	0.339358	+	0.587784i	0.0441806	+	0.0765230i	0.887270	−	0.461250i	$-0.152599\pi$
$59$	0.339358	+	0.587784i	0.0441806	+	0.0765230i	−0.843089	+	0.537773i	$0.819266\pi$
$60$		0			0
$61$	−5.29992	+	9.17972i	−0.678585	+	1.17534i	0.296822	+	0.954933i	$0.404073\pi$
$61$	−5.29992	+	9.17972i	−0.678585	+	1.17534i	−0.975407	+	0.220411i	$0.929260\pi$
$62$	−0.0839334	+	0.320672i	−0.0106596	+	0.0407254i
$63$		0			0
$64$	0.278358	+	7.99516i	0.0347947	+	0.999394i
$65$	−6.56955	−	3.79293i	−0.814853	−	0.470456i
$66$		0			0
$67$	9.34860	−	5.39742i	1.14211	−	0.659399i	0.195160	−	0.980771i	$-0.437477\pi$
$67$	9.34860	−	5.39742i	1.14211	−	0.659399i	0.946953	+	0.321372i	$0.104144\pi$
$68$	−5.33362	−	8.99548i	−0.646797	−	1.09086i
$69$		0			0
$70$	1.51777	−	5.34895i	0.181408	−	0.639322i
$71$	1.32129			0.156808			0.0784040	−	0.996922i	$-0.475018\pi$
$71$	1.32129			0.156808			0.0784040	+	0.996922i	$0.475018\pi$
$72$		0			0
$73$	−1.75041	−	3.03179i	−0.204870	−	0.354844i	0.745222	−	0.666817i	$-0.232344\pi$
$73$	−1.75041	−	3.03179i	−0.204870	−	0.354844i	−0.950091	+	0.311972i	$0.899010\pi$
$74$	−1.87423	−	6.83587i	−0.217875	−	0.794654i
$75$		0			0
$76$	1.47762	−	2.62928i	0.169494	−	0.301599i
$77$	−7.26288	−	0.148795i	−0.827682	−	0.0169567i
$78$		0			0
$79$	−14.4759	−	8.35768i	−1.62867	−	0.940313i	−0.984490	−	0.175438i	$-0.943866\pi$
$79$	−14.4759	−	8.35768i	−1.62867	−	0.940313i	−0.644179	−	0.764874i	$-0.722801\pi$
$80$	−5.21523	−	2.85179i	−0.583080	−	0.318839i
$81$		0			0
$82$	−8.01487	−	7.92242i	−0.885094	−	0.874885i
$83$	−15.2915			−1.67846			−0.839232	−	0.543773i	$-0.816995\pi$
$83$	−15.2915			−1.67846			−0.839232	+	0.543773i	$0.816995\pi$
$84$		0			0
$85$	7.77018			0.842795
$86$	−6.56385	−	6.48815i	−0.707798	−	0.699635i
$87$		0			0
$88$	−1.87915	+	7.53519i	−0.200319	+	0.803254i
$89$	10.8625	+	6.27147i	1.15142	+	0.664775i	0.949234	−	0.314572i	$-0.101861\pi$
$89$	10.8625	+	6.27147i	1.15142	+	0.664775i	0.202190	+	0.979346i	$0.435194\pi$
$90$		0			0
$91$	6.99129	−	11.5560i	0.732886	−	1.21140i
$92$	15.6578	+	8.79944i	1.63244	+	0.917405i
$93$		0			0
$94$	−1.59108	−	5.80314i	−0.164107	−	0.598549i
$95$	1.12046	+	1.94069i	0.114957	+	0.199111i
$96$		0			0
$97$	14.2065			1.44245			0.721226	−	0.692700i	$-0.243579\pi$
$97$	14.2065			1.44245			0.721226	+	0.692700i	$0.243579\pi$
$98$	9.46618	+	2.89681i	0.956228	+	0.292622i
$99$		0			0
$100$	−4.80282	+	2.84770i	−0.480282	+	0.284770i
$101$	9.74384	−	5.62561i	0.969549	−	0.559769i	0.0704500	−	0.997515i	$-0.477556\pi$
$101$	9.74384	−	5.62561i	0.969549	−	0.559769i	0.899099	+	0.437746i	$0.144223\pi$
$102$		0			0
$103$	0.396421	+	0.228874i	0.0390605	+	0.0225516i	0.519403	−	0.854529i	$-0.326154\pi$
$103$	0.396421	+	0.228874i	0.0390605	+	0.0225516i	−0.480343	+	0.877081i	$0.659488\pi$
$104$	−10.3859	−	10.0306i	−1.01842	−	0.983578i
$105$		0			0
$106$	1.42380	−	5.43969i	0.138291	−	0.528349i
$107$	−4.44784	+	7.70389i	−0.429989	+	0.744763i	−0.996872	−	0.0790354i	$-0.974816\pi$
$107$	−4.44784	+	7.70389i	−0.429989	+	0.744763i	0.566883	+	0.823799i	$0.308149\pi$
$108$		0			0
$109$	−3.34680	−	5.79684i	−0.320566	−	0.555236i	0.660039	−	0.751231i	$-0.270540\pi$
$109$	−3.34680	−	5.79684i	−0.320566	−	0.555236i	−0.980605	+	0.195995i	$0.937206\pi$
$110$	−4.10370	−	4.05637i	−0.391272	−	0.386759i
$111$		0			0
$112$	5.26658	−	9.17949i	0.497645	−	0.867381i
$113$			15.7093i			1.47781i	0.673811	+	0.738903i	$0.264656\pi$
$113$			15.7093i			1.47781i	−0.673811	+	0.738903i	$0.735344\pi$
$114$		0			0
$115$	−11.5571	+	6.67251i	−1.07771	+	0.622215i
$116$	−4.22172	+	0.0489767i	−0.391977	+	0.00454737i
$117$		0			0
$118$	−0.928567	−	0.243045i	−0.0854816	−	0.0223741i
$119$	−0.283366	+	13.8315i	−0.0259761	+	1.26793i
$120$		0			0
$121$	1.73060	−	2.99749i	0.157327	−	0.272499i
$122$	−3.96373	−	14.4569i	−0.358859	−	1.30887i
$123$		0			0
$124$	−0.239082	−	0.403226i	−0.0214702	−	0.0362107i
$125$		−	11.5786i		−	1.03562i
$126$		0			0
$127$			0.423756i			0.0376022i	0.999823	+	0.0188011i	$0.00598493\pi$
$127$			0.423756i			0.0376022i	−0.999823	+	0.0188011i	$0.994015\pi$
$128$	−8.31813	−	7.66868i	−0.735226	−	0.677822i
$129$		0			0
$130$	10.3462	−	2.83668i	0.907423	−	0.248793i
$131$	3.93433	−	6.81447i	0.343744	−	0.595383i	−0.641380	−	0.767223i	$-0.721638\pi$
$131$	3.93433	−	6.81447i	0.343744	−	0.595383i	0.985125	+	0.171840i	$0.0549713\pi$
$132$		0			0
$133$	−3.49544	+	1.92373i	−0.303093	+	0.166808i
$134$	−3.86559	+	14.7687i	−0.333936	+	1.27582i
$135$		0			0
$136$	14.3501	+	3.57868i	1.23051	+	0.306869i
$137$	−3.91743	+	2.26173i	−0.334689	+	0.193233i	−0.657921	−	0.753087i	$-0.728564\pi$
$137$	−3.91743	+	2.26173i	−0.334689	+	0.193233i	0.323232	+	0.946320i	$0.395231\pi$
$138$		0			0
$139$			9.12345i			0.773841i	0.922113	+	0.386921i	$0.126461\pi$
$139$			9.12345i			0.773841i	−0.922113	+	0.386921i	$0.873539\pi$
$140$	3.87095	+	6.84438i	0.327155	+	0.578456i
$141$		0			0
$142$	−1.31360	+	1.32893i	−0.110235	+	0.111521i
$143$	−7.00820	−	12.1386i	−0.586055	−	1.01508i
$144$		0			0
$145$	1.56848	−	2.71669i	0.130255	−	0.225608i
$146$	4.78955	+	1.25363i	0.396386	+	0.103751i
$147$		0			0
$148$	8.73873	+	4.91104i	0.718319	+	0.403685i
$149$	17.4629	+	10.0822i	1.43062	+	0.825967i	0.997168	−	0.0752118i	$-0.0239633\pi$
$149$	17.4629	+	10.0822i	1.43062	+	0.825967i	0.433448	+	0.901178i	$0.357297\pi$
$150$		0			0
$151$	6.33048	−	3.65491i	0.515168	−	0.297432i	−0.219788	−	0.975548i	$-0.570536\pi$
$151$	6.33048	−	3.65491i	0.515168	−	0.297432i	0.734955	+	0.678116i	$0.237203\pi$
$152$	1.17547	+	4.10015i	0.0953429	+	0.332566i
$153$		0			0
$154$	7.37029	−	7.15696i	0.593915	−	0.576724i
$155$	0.348301			0.0279762
$156$		0			0
$157$	4.80178	+	8.31693i	0.383224	+	0.663763i	0.991521	−	0.129946i	$-0.0414805\pi$
$157$	4.80178	+	8.31693i	0.383224	+	0.663763i	−0.608297	+	0.793709i	$0.708147\pi$
$158$	22.7977	−	6.25059i	1.81369	−	0.497270i
$159$		0			0
$160$	8.05317	−	2.41019i	0.636659	−	0.190543i
$161$	−11.4561	−	20.8159i	−0.902867	−	1.64052i
$162$		0			0
$163$	−2.51601	−	1.45262i	−0.197069	−	0.113778i	0.398219	−	0.917291i	$-0.369629\pi$
$163$	−2.51601	−	1.45262i	−0.197069	−	0.113778i	−0.595288	+	0.803513i	$0.702962\pi$
$164$	15.9365	−	0.184881i	1.24443	−	0.0144368i
$165$		0			0
$166$	15.2026	−	15.3800i	1.17995	−	1.19372i
$167$	11.3739			0.880141			0.440071	−	0.897963i	$-0.354953\pi$
$167$	11.3739			0.880141			0.440071	+	0.897963i	$0.354953\pi$
$168$		0			0
$169$	13.0598			1.00460
$170$	−7.72498	+	7.81512i	−0.592479	+	0.599393i
$171$		0			0
$172$	13.0513	−	0.151410i	0.995155	−	0.0115449i
$173$	7.37811	+	4.25976i	0.560948	+	0.323863i	0.753526	−	0.657418i	$-0.228352\pi$
$173$	7.37811	+	4.25976i	0.560948	+	0.323863i	−0.192578	+	0.981282i	$0.561685\pi$
$174$		0			0
$175$	7.38484	+	0.151293i	0.558242	+	0.0114367i
$176$	−5.71055	−	9.38138i	−0.430449	−	0.707148i
$177$		0			0
$178$	−17.1071	+	4.69034i	−1.28223	+	0.351556i
$179$	4.80491	+	8.32235i	0.359136	+	0.622042i	0.987817	−	0.155622i	$-0.0497381\pi$
$179$	4.80491	+	8.32235i	0.359136	+	0.622042i	−0.628681	+	0.777664i	$0.716405\pi$
$180$		0			0
$181$	19.0553			1.41637			0.708184	−	0.706028i	$-0.249515\pi$
$181$	19.0553			1.41637			0.708184	+	0.706028i	$0.249515\pi$
$182$	4.67219	+	18.5205i	0.346326	+	1.37283i
$183$		0			0
$184$	−24.4170	+	7.00008i	−1.80005	+	0.516053i
$185$	−6.45012	+	3.72398i	−0.474223	+	0.273793i
$186$		0			0
$187$	12.4335	+	7.17848i	0.909227	+	0.524943i
$188$	7.41853	+	4.16910i	0.541052	+	0.304063i
$189$		0			0
$190$	−3.06586	−	0.802464i	−0.222421	−	0.0582169i
$191$	8.56327	−	14.8320i	0.619617	−	1.07321i	−0.369939	−	0.929056i	$-0.620621\pi$
$191$	8.56327	−	14.8320i	0.619617	−	1.07321i	0.989556	−	0.144152i	$-0.0460453\pi$
$192$		0			0
$193$	2.32947	+	4.03475i	0.167679	+	0.290428i	0.937603	−	0.347707i	$-0.113040\pi$
$193$	2.32947	+	4.03475i	0.167679	+	0.290428i	−0.769925	+	0.638135i	$0.779706\pi$
$194$	−14.1239	+	14.2887i	−1.01403	+	1.02587i
$195$		0			0
$196$	−12.3247	+	6.64097i	−0.880334	+	0.474355i
$197$		−	23.1622i		−	1.65024i	−0.564957	−	0.825121i	$-0.691107\pi$
$197$		−	23.1622i		−	1.65024i	0.564957	−	0.825121i	$-0.308893\pi$
$198$		0			0
$199$	1.81444	−	1.04757i	0.128622	−	0.0742602i	−0.434308	−	0.900764i	$-0.643007\pi$
$199$	1.81444	−	1.04757i	0.128622	−	0.0742602i	0.562931	+	0.826504i	$0.309674\pi$
$200$	1.91071	−	7.66173i	0.135108	−	0.541766i
$201$		0			0
$202$	−4.02902	+	15.3931i	−0.283481	+	1.08305i
$203$	4.77870	+	2.89108i	0.335399	+	0.202914i
$204$		0			0
$205$	−5.92082	+	10.2552i	−0.413528	+	0.716251i
$206$	−0.624312	+	0.171171i	−0.0434979	+	0.0119261i
$207$		0			0
$208$	20.4140	−	0.473714i	1.41546	−	0.0328462i
$209$			4.14055i			0.286408i
$210$		0			0
$211$		−	23.1812i		−	1.59586i	−0.602751	−	0.797929i	$-0.705929\pi$
$211$		−	23.1812i		−	1.59586i	0.602751	−	0.797929i	$-0.294071\pi$
$212$	4.05564	+	6.84007i	0.278542	+	0.469778i
$213$		0			0
$214$	−3.32648	−	12.1326i	−0.227393	−	0.829370i
$215$	−4.84891	+	8.39856i	−0.330693	+	0.572777i
$216$		0			0
$217$	−0.0127020	+	0.620003i	−0.000862268	+	0.0420885i
$218$	9.15770	+	2.39695i	0.620237	+	0.162342i
$219$		0			0
$220$	8.15965	−	0.0946610i	0.550124	−	0.00638204i
$221$	−23.1168	+	13.3465i	−1.55500	+	0.897782i
$222$		0			0
$223$			4.82210i			0.322912i	0.986880	+	0.161456i	$0.0516190\pi$
$223$			4.82210i			0.322912i	−0.986880	+	0.161456i	$0.948381\pi$
$224$	3.99664	+	14.4231i	0.267037	+	0.963686i
$225$		0			0
$226$	−15.8002	−	15.6179i	−1.05101	−	1.03889i
$227$	5.14352	+	8.90884i	0.341387	+	0.591300i	0.984691	−	0.174311i	$-0.0557699\pi$
$227$	5.14352	+	8.90884i	0.341387	+	0.591300i	−0.643303	+	0.765611i	$0.722437\pi$
$228$		0			0
$229$	5.55931	−	9.62901i	0.367370	−	0.636303i	−0.621784	−	0.783189i	$-0.713592\pi$
$229$	5.55931	−	9.62901i	0.367370	−	0.636303i	0.989153	+	0.146886i	$0.0469250\pi$
$230$	4.77880	−	18.2577i	0.315105	−	1.20387i
$231$		0			0
$232$	4.14791	−	4.29483i	0.272323	−	0.281970i
$233$	−6.62526	−	3.82509i	−0.434035	−	0.250590i	0.267029	−	0.963688i	$-0.413958\pi$
$233$	−6.62526	−	3.82509i	−0.434035	−	0.250590i	−0.701064	+	0.713098i	$0.747291\pi$
$234$		0			0
$235$	−5.47568	+	3.16138i	−0.357194	+	0.206226i
$236$	1.16762	−	0.692306i	0.0760054	−	0.0450653i
$237$		0			0
$238$	−13.6298	−	14.0361i	−0.883487	−	0.909822i
$239$	5.59222			0.361731			0.180865	−	0.983508i	$-0.442110\pi$
$239$	5.59222			0.361731			0.180865	+	0.983508i	$0.442110\pi$
$240$		0			0
$241$	−2.07295	−	3.59046i	−0.133531	−	0.231282i	0.791505	−	0.611163i	$-0.209298\pi$
$241$	−2.07295	−	3.59046i	−0.133531	−	0.231282i	−0.925035	+	0.379882i	$0.875965\pi$
$242$	1.29429	+	4.72066i	0.0832002	+	0.303456i
$243$		0			0
$244$	18.4812	+	10.3861i	1.18314	+	0.664905i
$245$	0.426034	−	10.3933i	0.0272183	−	0.664003i
$246$		0			0
$247$	−6.66688	−	3.84913i	−0.424203	−	0.244914i
$248$	0.643249	+	0.160416i	0.0408463	+	0.0101864i
$249$		0			0
$250$	11.6456	+	11.5113i	0.736532	+	0.728037i
$251$	11.7863			0.743943			0.371972	−	0.928244i	$-0.378682\pi$
$251$	11.7863			0.743943			0.371972	+	0.928244i	$0.378682\pi$
$252$		0			0
$253$	−24.6576			−1.55021
$254$	−0.426206	−	0.421291i	−0.0267426	−	0.0264341i
$255$		0			0
$256$	15.9828	−	0.742171i	0.998924	−	0.0463857i
$257$	26.2593	+	15.1608i	1.63801	+	0.945707i	0.981516	+	0.191379i	$0.0612958\pi$
$257$	26.2593	+	15.1608i	1.63801	+	0.945707i	0.656497	+	0.754329i	$0.272037\pi$
$258$		0			0
$259$	−6.39374	−	11.6175i	−0.397288	−	0.721877i
$260$	−7.43294	+	13.2262i	−0.460971	+	0.820256i
$261$		0			0
$262$	2.94243	+	10.7319i	0.181784	+	0.663020i
$263$	−9.23981	−	16.0038i	−0.569751	−	0.986838i	−0.996590	−	0.0825101i	$-0.973706\pi$
$263$	−9.23981	−	16.0038i	−0.569751	−	0.986838i	0.426839	−	0.904328i	$-0.359627\pi$
$264$		0			0
$265$	−5.90837			−0.362948
$266$	1.54025	−	5.42819i	0.0944390	−	0.332824i
$267$		0			0
$268$	−11.0110	−	18.5707i	−0.672604	−	1.13439i
$269$	0.629904	−	0.363675i	0.0384059	−	0.0221737i	−0.480674	−	0.876899i	$-0.659608\pi$
$269$	0.629904	−	0.363675i	0.0384059	−	0.0221737i	0.519080	+	0.854726i	$0.326275\pi$
$270$		0			0
$271$	−7.21987	−	4.16839i	−0.438576	−	0.253212i	0.264418	−	0.964408i	$-0.414820\pi$
$271$	−7.21987	−	4.16839i	−0.438576	−	0.253212i	−0.702993	+	0.711197i	$0.748154\pi$
$272$	−17.8660	+	10.8752i	−1.08329	+	0.659408i
$273$		0			0
$274$	1.61983	−	6.18866i	0.0978576	−	0.373871i
$275$	3.83270	−	6.63843i	0.231120	−	0.400312i
$276$		0			0
$277$	6.26885	+	10.8580i	0.376659	+	0.652392i	0.990574	−	0.136980i	$-0.0437396\pi$
$277$	6.26885	+	10.8580i	0.376659	+	0.652392i	−0.613915	+	0.789372i	$0.710406\pi$
$278$	−9.17622	−	9.07038i	−0.550353	−	0.544005i
$279$		0			0
$280$	−10.7324	−	2.91123i	−0.641383	−	0.173979i
$281$		−	14.8047i		−	0.883173i	−0.897219	−	0.441586i	$-0.854416\pi$
$281$		−	14.8047i		−	0.883173i	0.897219	−	0.441586i	$-0.145584\pi$
$282$		0			0
$283$	−12.9064	+	7.45154i	−0.767208	+	0.442948i	−0.831878	−	0.554959i	$-0.812734\pi$
$283$	−12.9064	+	7.45154i	−0.767208	+	0.442948i	0.0646694	+	0.997907i	$0.479401\pi$
$284$	−0.0306547	−	2.64240i	−0.00181902	−	0.156797i
$285$		0			0
$286$	19.1762	+	5.01922i	1.13391	+	0.296793i
$287$	−18.0390	−	10.9135i	−1.06481	−	0.644202i
$288$		0			0
$289$	5.17077	−	8.95604i	0.304163	−	0.526826i
$290$	1.17304	+	4.27843i	0.0688834	+	0.251238i
$291$		0			0
$292$	−6.02257	+	3.57092i	−0.352444	+	0.208972i
$293$			15.0676i			0.880258i	0.897934	+	0.440129i	$0.145067\pi$
$293$			15.0676i			0.880258i	−0.897934	+	0.440129i	$0.854933\pi$
$294$		0			0
$295$			1.00857i			0.0587214i
$296$	−13.6273	+	3.90680i	−0.792073	+	0.227078i
$297$		0			0
$298$	−27.5018	+	7.54033i	−1.59314	+	0.436800i
$299$	22.9221	−	39.7023i	1.32562	−	2.29604i
$300$		0			0
$301$	−14.7732	−	8.93770i	−0.851515	−	0.515161i
$302$	−2.61761	+	10.0007i	−0.150627	+	0.575478i
$303$		0			0
$304$	−5.29249	−	2.89403i	−0.303545	−	0.165984i
$305$	−13.6411	+	7.87569i	−0.781087	+	0.450961i
$306$		0			0
$307$			4.78619i			0.273162i	0.990629	+	0.136581i	$0.0436114\pi$
$307$			4.78619i			0.273162i	−0.990629	+	0.136581i	$0.956389\pi$
$308$	−0.129066	+	14.5282i	−0.00735421	+	0.827823i
$309$		0			0
$310$	−0.346275	+	0.350316i	−0.0196671	+	0.0198966i
$311$	−8.06864	−	13.9753i	−0.457530	−	0.792466i	0.541299	−	0.840830i	$-0.317933\pi$
$311$	−8.06864	−	13.9753i	−0.457530	−	0.792466i	−0.998830	+	0.0483640i	$0.984599\pi$
$312$		0			0
$313$	13.2748	−	22.9926i	0.750336	−	1.29962i	−0.197324	−	0.980338i	$-0.563225\pi$
$313$	13.2748	−	22.9926i	0.750336	−	1.29962i	0.947660	−	0.319282i	$-0.103442\pi$
$314$	−13.1389	−	3.43900i	−0.741470	−	0.194074i
$315$		0			0
$316$	−16.3784	+	29.1438i	−0.921357	+	1.63947i
$317$	−8.35634	−	4.82453i	−0.469339	−	0.270973i	0.246624	−	0.969111i	$-0.420679\pi$
$317$	−8.35634	−	4.82453i	−0.469339	−	0.270973i	−0.715963	+	0.698138i	$0.754012\pi$
$318$		0			0
$319$	5.01962	−	2.89808i	0.281045	−	0.162261i
$320$	−5.58219	+	10.4959i	−0.312054	+	0.586740i
$321$		0			0
$322$	32.3257	+	9.17244i	1.80144	+	0.511160i
$323$	7.88530			0.438750
$324$		0			0
$325$	7.12589	+	12.3424i	0.395273	+	0.684633i
$326$	3.96239	−	1.08639i	0.219456	−	0.0601696i
$327$		0			0
$328$	−15.6578	+	16.2125i	−0.864559	+	0.895183i
$329$	−5.42781	−	9.86240i	−0.299245	−	0.543732i
$330$		0			0
$331$	−0.992363	−	0.572941i	−0.0545452	−	0.0314917i	0.472479	−	0.881342i	$-0.343359\pi$
$331$	−0.992363	−	0.572941i	−0.0545452	−	0.0314917i	−0.527025	+	0.849850i	$0.676692\pi$
$332$	0.354774	+	30.5810i	0.0194707	+	1.67835i
$333$		0			0
$334$	−11.3078	+	11.4397i	−0.618734	+	0.625953i
$335$	16.0412			0.876422
$336$		0			0
$337$	−1.89202			−0.103065			−0.0515324	−	0.998671i	$-0.516411\pi$
$337$	−1.89202			−0.103065			−0.0515324	+	0.998671i	$0.516411\pi$
$338$	−12.9838	+	13.1353i	−0.706227	+	0.714467i
$339$		0			0
$340$	−0.180273	−	15.5393i	−0.00977669	−	0.842738i
$341$	0.557336	+	0.321778i	0.0301814	+	0.0174253i
$342$		0			0
$343$	18.4853	+	1.13740i	0.998112	+	0.0614138i
$344$	−12.8231	+	13.2774i	−0.691377	+	0.715867i
$345$		0			0
$346$	−11.6196	+	3.18581i	−0.624673	+	0.171270i
$347$	−1.96885	−	3.41015i	−0.105693	−	0.183066i	0.808328	−	0.588733i	$-0.200373\pi$
$347$	−1.96885	−	3.41015i	−0.105693	−	0.183066i	−0.914021	+	0.405666i	$0.867040\pi$
$348$		0			0
$349$	−22.8441			−1.22282			−0.611409	−	0.791315i	$-0.709397\pi$
$349$	−22.8441			−1.22282			−0.611409	+	0.791315i	$0.709397\pi$
$350$	−7.49405	+	7.27714i	−0.400574	+	0.388979i
$351$		0			0
$352$	15.1130	+	3.58324i	0.805524	+	0.190987i
$353$	28.5246	−	16.4687i	1.51821	−	0.876541i	0.518442	−	0.855113i	$-0.326512\pi$
$353$	28.5246	−	16.4687i	1.51821	−	0.876541i	0.999770	−	0.0214280i	$-0.00682128\pi$
$354$		0			0
$355$	1.70039	+	0.981719i	0.0902472	+	0.0521042i
$356$	12.2901	−	21.8691i	0.651373	−	1.15906i
$357$		0			0
$358$	−13.1474	−	3.44124i	−0.694864	−	0.181875i
$359$	11.8409	−	20.5090i	0.624939	−	1.08243i	−0.363614	−	0.931550i	$-0.618457\pi$
$359$	11.8409	−	20.5090i	0.624939	−	1.08243i	0.988553	−	0.150876i	$-0.0482094\pi$
$360$		0			0
$361$	−8.36294	−	14.4850i	−0.440155	−	0.762370i
$362$	−18.9444	+	19.1655i	−0.995697	+	1.00732i
$363$		0			0
$364$	−23.2726	−	13.7135i	−1.21982	−	0.718784i
$365$		−	5.20222i		−	0.272297i
$366$		0			0
$367$	22.3566	−	12.9076i	1.16701	−	0.673772i	0.214034	−	0.976826i	$-0.431340\pi$
$367$	22.3566	−	12.9076i	1.16701	−	0.673772i	0.952973	+	0.303054i	$0.0980063\pi$
$368$	17.2344	−	31.5176i	0.898406	−	1.64297i
$369$		0			0
$370$	2.66709	−	10.1897i	0.138655	−	0.529740i
$371$	0.215469	−	10.5173i	0.0111866	−	0.546033i
$372$		0			0
$373$	−18.6182	+	32.2476i	−0.964013	+	1.66972i	−0.251770	+	0.967787i	$0.581013\pi$
$373$	−18.6182	+	32.2476i	−0.964013	+	1.66972i	−0.712243	+	0.701933i	$0.752321\pi$
$374$	−19.5812	+	5.36868i	−1.01252	+	0.277608i
$375$		0			0
$376$	−11.5686	+	3.31658i	−0.596605	+	0.171040i
$377$			10.7764i			0.555014i
$378$		0			0
$379$			29.8599i			1.53380i	0.641766	+	0.766901i	$0.278202\pi$
$379$			29.8599i			1.53380i	−0.641766	+	0.766901i	$0.721798\pi$
$380$	3.85513	−	2.28579i	0.197764	−	0.117259i
$381$		0			0
$382$	6.40434	+	23.3585i	0.327675	+	1.19513i
$383$	6.22015	−	10.7736i	0.317835	−	0.550506i	−0.662201	−	0.749326i	$-0.730378\pi$
$383$	6.22015	−	10.7736i	0.317835	−	0.550506i	0.980036	+	0.198820i	$0.0637109\pi$
$384$		0			0
$385$	−9.23617	−	5.58782i	−0.470719	−	0.284782i
$386$	−6.37400	−	1.66834i	−0.324428	−	0.0849165i
$387$		0			0
$388$	−0.329600	−	28.4111i	−0.0167329	−	1.44235i
$389$	−30.7387	+	17.7470i	−1.55851	+	0.899808i	−0.561114	+	0.827738i	$0.689627\pi$
$389$	−30.7387	+	17.7470i	−1.55851	+	0.899808i	−0.997400	+	0.0720702i	$0.977039\pi$
$390$		0			0
$391$			46.9582i			2.37478i
$392$	5.57360	−	18.9983i	0.281509	−	0.959558i
$393$		0			0
$394$	23.2962	+	23.0275i	1.17365	+	1.16011i
$395$	−12.4195	−	21.5113i	−0.624895	−	1.08235i
$396$		0			0
$397$	−7.77378	+	13.4646i	−0.390155	+	0.675768i	−0.992470	−	0.122490i	$-0.960912\pi$
$397$	−7.77378	+	13.4646i	−0.390155	+	0.675768i	0.602315	+	0.798259i	$0.294245\pi$
$398$	−0.750260	+	2.86641i	−0.0376071	+	0.143680i
$399$		0			0
$400$	5.80645	+	9.53892i	0.290322	+	0.476946i
$401$	−7.50098	−	4.33070i	−0.374581	−	0.216265i	0.300877	−	0.953663i	$-0.402721\pi$
$401$	−7.50098	−	4.33070i	−0.374581	−	0.216265i	−0.675458	+	0.737398i	$0.736054\pi$
$402$		0			0
$403$	−1.03622	+	0.598261i	−0.0516178	+	0.0298015i
$404$	−11.4765	−	19.3559i	−0.570979	−	0.962990i
$405$		0			0
$406$	−7.65871	+	1.93207i	−0.380095	+	0.0958873i
$407$	−13.7616			−0.682137
$408$		0			0
$409$	−1.74788	−	3.02741i	−0.0864270	−	0.149696i	0.819571	−	0.572977i	$-0.194212\pi$
$409$	−1.74788	−	3.02741i	−0.0864270	−	0.149696i	−0.905998	+	0.423281i	$0.860878\pi$
$410$	−4.42809	−	16.1506i	−0.218688	−	0.797619i
$411$		0			0
$412$	0.448519	−	0.798098i	0.0220969	−	0.0393195i
$413$	−1.79533	−	0.0367810i	−0.0883426	−	0.00180988i
$414$		0			0
$415$	−19.6789	−	11.3616i	−0.966001	−	0.557721i
$416$	−19.8188	+	21.0030i	−0.971698	+	1.02976i
$417$		0			0
$418$	−4.16449	−	4.11646i	−0.203692	−	0.201343i
$419$	12.3776			0.604685			0.302342	−	0.953199i	$-0.402231\pi$
$419$	12.3776			0.604685			0.302342	+	0.953199i	$0.402231\pi$
$420$		0			0
$421$	−22.1948			−1.08171			−0.540855	−	0.841116i	$-0.681899\pi$
$421$	−22.1948			−1.08171			−0.540855	+	0.841116i	$0.681899\pi$
$422$	23.3153	+	23.0463i	1.13497	+	1.12188i
$423$		0			0
$424$	−10.9117	−	2.72119i	−0.529918	−	0.132153i
$425$	−12.6423	−	7.29903i	−0.613241	−	0.354055i
$426$		0			0
$427$	−13.5218	−	24.5694i	−0.654368	−	1.18900i
$428$	15.5099	+	8.71635i	0.749701	+	0.421321i
$429$		0			0
$430$	−3.62643	−	13.2267i	−0.174882	−	0.637846i
$431$	8.07284	+	13.9826i	0.388855	+	0.673517i	0.992296	−	0.123891i	$-0.0395374\pi$
$431$	8.07284	+	13.9826i	0.388855	+	0.673517i	−0.603441	+	0.797408i	$0.706204\pi$
$432$		0			0
$433$	11.6739			0.561014			0.280507	−	0.959852i	$-0.409497\pi$
$433$	11.6739			0.561014			0.280507	+	0.959852i	$0.409497\pi$
$434$	−0.610960	−	0.629171i	−0.0293270	−	0.0302012i
$435$		0			0
$436$	−11.5152	+	6.82765i	−0.551480	+	0.326985i
$437$	−11.7283	+	6.77136i	−0.561043	+	0.323918i
$438$		0			0
$439$	15.4132	+	8.89883i	0.735633	+	0.424718i	0.820479	−	0.571676i	$-0.193707\pi$
$439$	15.4132	+	8.89883i	0.735633	+	0.424718i	−0.0848464	+	0.996394i	$0.527040\pi$
$440$	−8.01698	+	8.30095i	−0.382194	+	0.395732i
$441$		0			0
$442$	9.55865	−	36.5193i	0.454658	−	1.73705i
$443$	−7.77644	+	13.4692i	−0.369470	+	0.639941i	−0.989483	−	0.144651i	$-0.953794\pi$
$443$	−7.77644	+	13.4692i	−0.369470	+	0.639941i	0.620013	+	0.784592i	$0.287127\pi$
$444$		0			0
$445$	9.31943	+	16.1417i	0.441783	+	0.765191i
$446$	−4.84999	−	4.79405i	−0.229654	−	0.227005i
$447$		0			0
$448$	−18.4799	−	10.3195i	−0.873095	−	0.487550i
$449$		−	32.4167i		−	1.52984i	−0.644127	−	0.764918i	$-0.722779\pi$
$449$		−	32.4167i		−	1.52984i	0.644127	−	0.764918i	$-0.277221\pi$
$450$		0			0
$451$	−18.9484	+	10.9399i	−0.892247	+	0.515139i
$452$	31.4165	−	0.364466i	1.47771	−	0.0171430i
$453$		0			0
$454$	−14.0740	−	3.68375i	−0.660524	−	0.172887i
$455$	17.5833	−	9.67704i	0.824318	−	0.453666i
$456$		0			0
$457$	3.46804	−	6.00683i	0.162228	−	0.280988i	−0.773439	−	0.633870i	$-0.781465\pi$
$457$	3.46804	−	6.00683i	0.162228	−	0.280988i	0.935668	+	0.352883i	$0.114799\pi$
$458$	4.15773	+	15.1645i	0.194278	+	0.708589i
$459$		0			0
$460$	13.6123	+	22.9579i	0.634675	+	1.07042i
$461$			33.0129i			1.53757i	0.639510	+	0.768783i	$0.279137\pi$
$461$			33.0129i			1.53757i	−0.639510	+	0.768783i	$0.720863\pi$
$462$		0			0
$463$			25.8834i			1.20291i	0.798909	+	0.601453i	$0.205411\pi$
$463$			25.8834i			1.20291i	−0.798909	+	0.601453i	$0.794589\pi$
$464$	0.195893	+	8.44174i	0.00909412	+	0.391898i
$465$		0			0
$466$	10.4339	−	2.86073i	0.483343	−	0.132521i
$467$	−12.0722	+	20.9097i	−0.558636	+	0.967586i	0.438974	+	0.898500i	$0.355342\pi$
$467$	−12.0722	+	20.9097i	−0.558636	+	0.967586i	−0.997611	+	0.0690867i	$0.977991\pi$
$468$		0			0
$469$	−0.584995	+	28.5545i	−0.0270126	+	1.31852i
$470$	2.26416	−	8.65034i	0.104438	−	0.399010i
$471$		0			0
$472$	−0.464514	+	1.86265i	−0.0213810	+	0.0857353i
$473$	−15.5180	+	8.95933i	−0.713519	+	0.411950i
$474$		0			0
$475$		−	4.21008i		−	0.193172i
$476$	27.6677	+	0.245794i	1.26815	+	0.0112660i
$477$		0			0
$478$	−5.55969	+	5.62456i	−0.254294	+	0.257262i
$479$	20.5106	+	35.5254i	0.937154	+	1.62320i	0.770748	+	0.637140i	$0.219883\pi$
$479$	20.5106	+	35.5254i	0.937154	+	1.62320i	0.166406	+	0.986057i	$0.446784\pi$
$480$		0			0
$481$	12.7930	−	22.1582i	0.583312	−	1.01033i
$482$	5.67211	+	1.48463i	0.258358	+	0.0676231i
$483$		0			0
$484$	−6.03473	−	3.39143i	−0.274306	−	0.154156i
$485$	18.2826	+	10.5555i	0.830169	+	0.479298i
$486$		0			0
$487$	13.0964	−	7.56120i	0.593454	−	0.342631i	−0.173008	−	0.984920i	$-0.555349\pi$
$487$	13.0964	−	7.56120i	0.593454	−	0.342631i	0.766462	+	0.642290i	$0.222015\pi$
$488$	−28.8199	+	8.26233i	−1.30461	+	0.374018i
$489$		0			0
$490$	10.0298	+	10.7613i	0.453102	+	0.486148i
$491$	−36.9285			−1.66656			−0.833280	−	0.552852i	$-0.813540\pi$
$491$	−36.9285			−1.66656			−0.833280	+	0.552852i	$0.813540\pi$
$492$		0			0
$493$	−5.51913	−	9.55941i	−0.248569	−	0.430534i
$494$	10.4995	−	2.87870i	0.472394	−	0.129519i
$495$		0			0
$496$	−0.800850	+	0.487486i	−0.0359592	+	0.0218888i
$497$	−1.80954	+	2.99101i	−0.0811691	+	0.134165i
$498$		0			0
$499$	1.47958	+	0.854238i	0.0662353	+	0.0382409i	0.532752	−	0.846271i	$-0.321158\pi$
$499$	1.47958	+	0.854238i	0.0662353	+	0.0382409i	−0.466517	+	0.884512i	$0.654491\pi$
$500$	−23.1557	+	0.268632i	−1.03555	+	0.0120136i
$501$		0			0
$502$	−11.7177	+	11.8544i	−0.522987	+	0.529090i
$503$	−0.0425771			−0.00189842			−0.000949210	−	1.00000i	$-0.500302\pi$
$503$	−0.0425771			−0.00189842			−0.000949210		1.00000i	$0.500302\pi$
$504$		0			0
$505$	16.7194			0.744001
$506$	24.5142	−	24.8002i	1.08979	−	1.10250i
$507$		0			0
$508$	0.847454	−	0.00983141i	0.0375997	−	0.000436198i
$509$	8.98568	+	5.18789i	0.398283	+	0.229949i	0.685743	−	0.727844i	$-0.259477\pi$
$509$	8.98568	+	5.18789i	0.398283	+	0.229949i	−0.287460	+	0.957793i	$0.592811\pi$
$510$		0			0
$511$	9.26034	+	0.189717i	0.409653	+	0.00839257i
$512$	−15.1433	+	16.8131i	−0.669247	+	0.743040i
$513$		0			0
$514$	−41.3551	+	11.3386i	−1.82410	+	0.500123i
$515$	0.340107	+	0.589082i	0.0149869	+	0.0259581i
$516$		0			0
$517$	−11.6826			−0.513799
$518$	18.0412	+	5.11921i	0.792687	+	0.224925i
$519$		0			0
$520$	−5.91301	−	20.6252i	−0.259303	−	0.904475i
$521$	−1.18275	+	0.682859i	−0.0518171	+	0.0299166i	−0.525685	−	0.850679i	$-0.676191\pi$
$521$	−1.18275	+	0.682859i	−0.0518171	+	0.0299166i	0.473868	+	0.880596i	$0.342858\pi$
$522$		0			0
$523$	9.31535	+	5.37822i	0.407332	+	0.235173i	0.689643	−	0.724150i	$-0.257768\pi$
$523$	9.31535	+	5.37822i	0.407332	+	0.235173i	−0.282311	+	0.959323i	$0.591101\pi$
$524$	−13.7193	−	7.71004i	−0.599330	−	0.336815i
$525$		0			0
$526$	25.2824	+	6.61748i	1.10237	+	0.288536i
$527$	0.612798	−	1.06140i	0.0266939	−	0.0462352i
$528$		0			0
$529$	−28.8245	−	49.9255i	−1.25324	−	2.17067i
$530$	5.87400	−	5.94254i	0.255150	−	0.258128i
$531$		0			0
$532$	3.92829	+	6.94578i	0.170313	+	0.301138i
$533$		−	40.6797i		−	1.76203i
$534$		0			0
$535$	−11.4480	+	6.60951i	−0.494940	+	0.285754i
$536$	29.6251	+	7.38801i	1.27961	+	0.319113i
$537$		0			0
$538$	−0.260461	+	0.995107i	−0.0112293	+	0.0429021i
$539$	10.2836	−	16.2373i	0.442944	−	0.699389i
$540$		0			0
$541$	−8.24296	+	14.2772i	−0.354393	+	0.613826i	−0.987014	−	0.160635i	$-0.948646\pi$
$541$	−8.24296	+	14.2772i	−0.354393	+	0.613826i	0.632621	+	0.774461i	$0.281979\pi$
$542$	11.3704	−	3.11748i	0.488399	−	0.133907i
$543$		0			0
$544$	6.82395	−	28.7813i	0.292574	−	1.23399i
$545$		−	9.94672i		−	0.426071i
$546$		0			0
$547$			4.03690i			0.172605i	0.996269	+	0.0863027i	$0.0275052\pi$
$547$			4.03690i			0.172605i	−0.996269	+	0.0863027i	$0.972495\pi$
$548$	4.61404	+	7.78186i	0.197102	+	0.332425i
$549$		0			0
$550$	2.86642	+	10.4547i	0.122224	+	0.445789i
$551$	1.59172	−	2.75693i	0.0678094	−	0.117449i
$552$		0			0
$553$	38.7446	−	21.3232i	1.64759	−	0.906756i
$554$	−17.1532	−	4.48970i	−0.728768	−	0.190749i
$555$		0			0
$556$	18.2457	−	0.211670i	0.773789	−	0.00897681i
$557$	9.29133	−	5.36435i	0.393686	−	0.227295i	−0.290070	−	0.957005i	$-0.593679\pi$
$557$	9.29133	−	5.36435i	0.393686	−	0.227295i	0.683756	+	0.729711i	$0.260345\pi$
$558$		0			0
$559$		−	33.3150i		−	1.40907i
$560$	13.5980	−	7.90017i	0.574622	−	0.333843i
$561$		0			0
$562$	14.8903	+	14.7186i	0.628109	+	0.620865i
$563$	7.14776	+	12.3803i	0.301242	+	0.521766i	0.976418	−	0.215891i	$-0.0692655\pi$
$563$	7.14776	+	12.3803i	0.301242	+	0.521766i	−0.675176	+	0.737657i	$0.735932\pi$
$564$		0			0
$565$	−11.6720	+	20.2166i	−0.491046	+	0.850517i
$566$	5.33673	−	20.3893i	0.224320	−	0.857025i
$567$		0			0
$568$	2.68816	+	2.59619i	0.112792	+	0.108934i
$569$	21.8632	+	12.6227i	0.916552	+	0.529172i	0.882534	−	0.470249i	$-0.155836\pi$
$569$	21.8632	+	12.6227i	0.916552	+	0.529172i	0.0340189	+	0.999421i	$0.489169\pi$
$570$		0			0
$571$	−4.21404	+	2.43298i	−0.176352	+	0.101817i	−0.585578	−	0.810616i	$-0.699132\pi$
$571$	−4.21404	+	2.43298i	−0.176352	+	0.101817i	0.409226	+	0.912433i	$0.365799\pi$
$572$	−24.1129	+	14.2971i	−1.00821	+	0.597791i
$573$		0			0
$574$	28.9107	−	7.29334i	1.20671	−	0.304418i
$575$	25.0717			1.04556
$576$		0			0
$577$	−1.36238	−	2.35972i	−0.0567168	−	0.0982364i	0.836273	−	0.548313i	$-0.184730\pi$
$577$	−1.36238	−	2.35972i	−0.0567168	−	0.0982364i	−0.892990	+	0.450077i	$0.851397\pi$
$578$	3.86714	+	14.1046i	0.160852	+	0.586675i
$579$		0			0
$580$	−5.46940	−	3.07372i	−0.227104	−	0.127629i
$581$	20.9422	−	34.6156i	0.868830	−	1.43610i
$582$		0			0
$583$	−9.45431	−	5.45845i	−0.391557	−	0.226066i
$584$	2.39596	−	9.60754i	0.0991457	−	0.397563i
$585$		0			0
$586$	−15.1547	−	14.9799i	−0.626036	−	0.618816i
$587$	−24.4237			−1.00807			−0.504037	−	0.863682i	$-0.668153\pi$
$587$	−24.4237			−1.00807			−0.504037	+	0.863682i	$0.668153\pi$
$588$		0			0
$589$	0.353461			0.0145641
$590$	−1.01441	−	1.00271i	−0.0417624	−	0.0412807i
$591$		0			0
$592$	9.61867	−	17.5902i	0.395325	−	0.722954i
$593$	28.8809	+	16.6744i	1.18600	+	0.684736i	0.957394	−	0.288784i	$-0.0932508\pi$
$593$	28.8809	+	16.6744i	1.18600	+	0.684736i	0.228603	+	0.973520i	$0.426584\pi$
$594$		0			0
$595$	−10.6415	+	17.5895i	−0.436259	+	0.721097i
$596$	19.7579	−	35.1574i	0.809315	−	1.44010i
$597$		0			0
$598$	17.1431	+	62.5261i	0.701034	+	2.55688i
$599$	22.3518	+	38.7144i	0.913268	+	1.58183i	0.809417	+	0.587235i	$0.199783\pi$
$599$	22.3518	+	38.7144i	0.913268	+	1.58183i	0.103852	+	0.994593i	$0.466883\pi$
$600$		0			0
$601$	44.1640			1.80149			0.900745	−	0.434349i	$-0.143022\pi$
$601$	44.1640			1.80149			0.900745	+	0.434349i	$0.143022\pi$
$602$	23.6767	−	5.97296i	0.964989	−	0.243439i
$603$		0			0
$604$	−7.45619	−	12.5753i	−0.303388	−	0.511683i
$605$	4.45428	−	2.57168i	0.181092	−	0.104554i
$606$		0			0
$607$	−29.9771	−	17.3073i	−1.21673	−	0.702481i	−0.252515	−	0.967593i	$-0.581258\pi$
$607$	−29.9771	−	17.3073i	−1.21673	−	0.702481i	−0.964218	+	0.265112i	$0.914591\pi$
$608$	8.17248	−	2.44590i	0.331438	−	0.0991944i
$609$		0			0
$610$	5.64051	−	21.5499i	0.228377	−	0.872529i
$611$	10.8603	−	18.8106i	0.439362	−	0.760997i
$612$		0			0
$613$	−8.76124	−	15.1749i	−0.353863	−	0.612909i	0.633060	−	0.774103i	$-0.281799\pi$
$613$	−8.76124	−	15.1749i	−0.353863	−	0.612909i	−0.986923	+	0.161194i	$0.948465\pi$
$614$	−4.81387	−	4.75835i	−0.194272	−	0.192031i
$615$		0			0
$616$	−14.4839	−	14.5735i	−0.583575	−	0.587185i
$617$		−	28.5501i		−	1.14938i	−0.818370	−	0.574692i	$-0.805122\pi$
$617$		−	28.5501i		−	1.14938i	0.818370	−	0.574692i	$-0.194878\pi$
$618$		0			0
$619$	30.8176	−	17.7925i	1.23866	−	0.715142i	0.269842	−	0.962905i	$-0.413029\pi$
$619$	30.8176	−	17.7925i	1.23866	−	0.715142i	0.968821	+	0.247762i	$0.0796952\pi$
$620$	−0.00808082	−	0.696556i	−0.000324534	−	0.0279744i
$621$		0			0
$622$	22.0778	+	5.77869i	0.885240	+	0.231704i
$623$	−29.0733	+	16.0006i	−1.16480	+	0.641051i
$624$		0			0
$625$	1.62346	−	2.81191i	0.0649383	−	0.112476i
$626$	9.92803	+	36.2105i	0.396804	+	1.44726i
$627$		0			0
$628$	16.5213	−	9.79587i	0.659273	−	0.390898i
$629$			26.2077i			1.04497i
$630$		0			0
$631$		−	36.8187i		−	1.46573i	−0.680374	−	0.732865i	$-0.738183\pi$
$631$		−	36.8187i		−	1.46573i	0.680374	−	0.732865i	$-0.261817\pi$
$632$	−13.0293	−	45.4474i	−0.518276	−	1.80780i
$633$		0			0
$634$	13.1602	−	3.60820i	0.522657	−	0.143300i
$635$	−0.314851	+	0.545338i	−0.0124945	+	0.0216411i
$636$		0			0
$637$	16.5846	+	31.6525i	0.657106	+	1.25412i
$638$	−2.07558	+	7.92987i	−0.0821730	+	0.313947i
$639$		0			0
$640$	−5.00690	−	16.0493i	−0.197915	−	0.634406i
$641$	−26.4156	+	15.2511i	−1.04335	+	0.602381i	−0.920781	−	0.390079i	$-0.872448\pi$
$641$	−26.4156	+	15.2511i	−1.04335	+	0.602381i	−0.122572	+	0.992460i	$0.539114\pi$
$642$		0			0
$643$		−	33.6298i		−	1.32623i	−0.748518	−	0.663114i	$-0.769234\pi$
$643$		−	33.6298i		−	1.32623i	0.748518	−	0.663114i	$-0.230766\pi$
$644$	−41.3632	+	23.3936i	−1.62994	+	0.921837i
$645$		0			0
$646$	−7.83943	+	7.93090i	−0.308438	+	0.312037i
$647$	−5.27521	−	9.13694i	−0.207390	−	0.359210i	0.743502	−	0.668734i	$-0.233164\pi$
$647$	−5.27521	−	9.13694i	−0.207390	−	0.359210i	−0.950892	+	0.309524i	$0.899830\pi$
$648$		0			0
$649$	−0.931770	+	1.61387i	−0.0365752	+	0.0633500i
$650$	−19.4982	−	5.10350i	−0.764783	−	0.200176i
$651$		0			0
$652$	−2.84667	+	5.06538i	−0.111484	+	0.198375i
$653$	10.9097	+	6.29874i	0.426931	+	0.246489i	0.698038	−	0.716060i	$-0.254056\pi$
$653$	10.9097	+	6.29874i	0.426931	+	0.246489i	−0.271107	+	0.962549i	$0.587390\pi$
$654$		0			0
$655$	10.1263	−	5.84643i	0.395668	−	0.228439i
$656$	−0.739474	−	31.8665i	−0.0288716	−	1.24418i
$657$		0			0
$658$	15.3157	+	4.34583i	0.597067	+	0.169418i
$659$	−31.4057			−1.22339			−0.611696	−	0.791093i	$-0.709512\pi$
$659$	−31.4057			−1.22339			−0.611696	+	0.791093i	$0.709512\pi$
$660$		0			0
$661$	13.6942	+	23.7190i	0.532642	+	0.922563i	0.999274	+	0.0381112i	$0.0121341\pi$
$661$	13.6942	+	23.7190i	0.532642	+	0.922563i	−0.466631	+	0.884452i	$0.654533\pi$
$662$	1.56285	−	0.428494i	0.0607417	−	0.0166539i
$663$		0			0
$664$	−31.1106	−	30.0463i	−1.20733	−	1.16602i
$665$	−5.92767	−	0.121440i	−0.229865	−	0.00470925i
$666$		0			0
$667$	16.4180	+	9.47891i	0.635706	+	0.367025i
$668$	−0.263883	−	22.7463i	−0.0102099	−	0.880082i
$669$		0			0
$670$	−15.9478	+	16.1339i	−0.616119	+	0.623308i
$671$	−29.1038			−1.12354
$672$		0			0
$673$	−7.59866			−0.292907			−0.146453	−	0.989218i	$-0.546786\pi$
$673$	−7.59866			−0.292907			−0.146453	+	0.989218i	$0.546786\pi$
$674$	1.88101	−	1.90296i	0.0724539	−	0.0732993i
$675$		0			0
$676$	−0.302996	−	26.1178i	−0.0116537	−	1.00453i
$677$	27.4847	+	15.8683i	1.05632	+	0.609868i	0.924413	−	0.381394i	$-0.124556\pi$
$677$	27.4847	+	15.8683i	1.05632	+	0.609868i	0.131910	+	0.991262i	$0.457889\pi$
$678$		0			0
$679$	−19.4562	+	32.1594i	−0.746661	+	1.23416i
$680$	15.8084	+	15.2676i	0.606225	+	0.585486i
$681$		0			0
$682$	−0.877733	+	0.240653i	−0.0336101	+	0.00921508i
$683$	13.5207	+	23.4185i	0.517355	+	0.896085i	0.999797	+	0.0201567i	$0.00641651\pi$
$683$	13.5207	+	23.4185i	0.517355	+	0.896085i	−0.482442	+	0.875928i	$0.660250\pi$
$684$		0			0
$685$	−6.72187			−0.256830
$686$	−19.5217	+	17.4614i	−0.745344	+	0.666680i
$687$		0			0
$688$	−0.605599	−	26.0974i	−0.0230882	−	0.994954i
$689$	17.5778	−	10.1485i	0.669660	−	0.386629i
$690$		0			0
$691$	−1.85489	−	1.07092i	−0.0705634	−	0.0407398i	0.464303	−	0.885676i	$-0.346305\pi$
$691$	−1.85489	−	1.07092i	−0.0705634	−	0.0407398i	−0.534867	+	0.844937i	$0.679638\pi$
$692$	8.34776	−	14.8541i	0.317334	−	0.564667i
$693$		0			0
$694$	5.38726	+	1.41007i	0.204498	+	0.0535257i
$695$	−6.77874	+	11.7411i	−0.257132	+	0.445366i
$696$		0			0
$697$	20.8340	+	36.0856i	0.789145	+	1.36684i
$698$	22.7112	−	22.9762i	0.859633	−	0.869663i
$699$		0			0
$700$	0.131233	−	14.7722i	0.00496015	−	0.558337i
$701$			26.8988i			1.01596i	0.861370	+	0.507978i	$0.169607\pi$
$701$			26.8988i			1.01596i	−0.861370	+	0.507978i	$0.830393\pi$
$702$		0			0
$703$	−6.54568	+	3.77915i	−0.246875	+	0.142533i
$704$	−18.6290	+	11.6380i	−0.702108	+	0.438623i
$705$		0			0
$706$	−11.7948	+	45.0625i	−0.443901	+	1.69595i
$707$	−0.609728	+	29.7617i	−0.0229312	+	1.11930i
$708$		0			0
$709$	19.7791	−	34.2583i	0.742818	−	1.28660i	−0.208389	−	0.978046i	$-0.566822\pi$
$709$	19.7791	−	34.2583i	0.742818	−	1.28660i	0.951207	−	0.308553i	$-0.0998447\pi$
$710$	−2.67789	+	0.734213i	−0.100499	+	0.0275545i
$711$		0			0
$712$	9.77694	+	34.1030i	0.366406	+	1.27806i
$713$			2.10492i			0.0788298i
$714$		0			0
$715$		−	20.8284i		−	0.778939i
$716$	16.5321	−	9.80226i	0.617834	−	0.366328i
$717$		0			0
$718$	8.85563	+	32.2991i	0.330489	+	1.20539i
$719$	−20.7863	+	36.0030i	−0.775199	+	1.34268i	0.159484	+	0.987201i	$0.449017\pi$
$719$	−20.7863	+	36.0030i	−0.775199	+	1.34268i	−0.934683	+	0.355483i	$0.884316\pi$
$720$		0			0
$721$	−1.06101	+	0.583933i	−0.0395142	+	0.0217468i
$722$	22.8831	+	5.98947i	0.851621	+	0.222905i
$723$		0			0
$724$	−0.442095	−	38.1080i	−0.0164303	−	1.41627i
$725$	−5.10391	+	2.94674i	−0.189554	+	0.109439i
$726$		0			0
$727$		−	40.5449i		−	1.50373i	−0.659320	−	0.751863i	$-0.729156\pi$
$727$		−	40.5449i		−	1.50373i	0.659320	−	0.751863i	$-0.270844\pi$
$728$	36.9300	−	9.77344i	1.36872	−	0.362228i
$729$		0			0
$730$	5.23231	+	5.17196i	0.193656	+	0.191423i
$731$	17.0622	+	29.5527i	0.631069	+	1.09304i
$732$		0			0
$733$	−4.10278	+	7.10622i	−0.151539	+	0.262474i	−0.931794	−	0.362989i	$-0.881756\pi$
$733$	−4.10278	+	7.10622i	−0.151539	+	0.262474i	0.780254	+	0.625463i	$0.215090\pi$
$734$	−9.24433	+	35.3185i	−0.341214	+	1.30363i
$735$		0			0
$736$	14.5657	+	48.6684i	0.536899	+	1.79394i
$737$	25.6683	+	14.8196i	0.945505	+	0.545888i
$738$		0			0
$739$	−26.5794	+	15.3456i	−0.977739	+	0.564498i	−0.901587	−	0.432598i	$-0.857597\pi$
$739$	−26.5794	+	15.3456i	−0.977739	+	0.564498i	−0.0761523	+	0.997096i	$0.524264\pi$
$740$	7.59711	+	12.8130i	0.279275	+	0.471015i
$741$		0			0
$742$	10.3640	+	10.6729i	0.380473	+	0.391814i
$743$	−38.6297			−1.41719			−0.708593	−	0.705617i	$-0.750670\pi$
$743$	−38.6297			−1.41719			−0.708593	+	0.705617i	$0.750670\pi$
$744$		0			0
$745$	14.9822	+	25.9499i	0.548905	+	0.950731i
$746$	−13.9243	−	50.7859i	−0.509804	−	1.85940i
$747$		0			0
$748$	14.0675	−	25.0319i	0.514360	−	0.915256i
$749$	−11.3479	−	20.6193i	−0.414644	−	0.753414i
$750$		0			0
$751$	37.1150	+	21.4284i	1.35435	+	0.781932i	0.988855	−	0.148883i	$-0.0475678\pi$
$751$	37.1150	+	21.4284i	1.35435	+	0.781932i	0.365491	+	0.930815i	$0.380901\pi$
$752$	8.16553	−	14.9328i	0.297766	−	0.544543i
$753$		0			0
$754$	−10.8387	−	10.7137i	−0.394724	−	0.390171i
$755$	10.8624			0.395323
$756$		0			0
$757$	28.1662			1.02372			0.511860	−	0.859069i	$-0.328957\pi$
$757$	28.1662			1.02372			0.511860	+	0.859069i	$0.328957\pi$
$758$	−30.0326	−	29.6862i	−1.09083	−	1.07825i
$759$		0			0
$760$	−1.53369	+	6.14992i	−0.0556328	+	0.223081i
$761$	−25.6364	−	14.8012i	−0.929319	−	0.536542i	−0.0427226	−	0.999087i	$-0.513603\pi$
$761$	−25.6364	−	14.8012i	−0.929319	−	0.536542i	−0.886596	+	0.462545i	$0.846937\pi$
$762$		0			0
$763$	17.7059	+	0.362741i	0.640997	+	0.0131321i
$764$	−29.8607	−	16.7813i	−1.08032	−	0.607125i
$765$		0			0
$766$	4.65196	+	16.9671i	0.168082	+	0.613045i
$767$	−1.73238	−	3.00057i	−0.0625526	−	0.108344i
$768$		0			0
$769$	−51.3103			−1.85030			−0.925148	−	0.379606i	$-0.876060\pi$
$769$	−51.3103			−1.85030			−0.925148	+	0.379606i	$0.876060\pi$
$770$	14.8026	−	3.73427i	0.533448	−	0.134574i
$771$		0			0
$772$	8.01492	−	4.75223i	0.288463	−	0.171036i
$773$	−39.3596	+	22.7243i	−1.41567	+	0.817335i	−0.995914	−	0.0903047i	$-0.971216\pi$
$773$	−39.3596	+	22.7243i	−1.41567	+	0.817335i	−0.419751	+	0.907639i	$0.637883\pi$
$774$		0			0
$775$	−0.566695	−	0.327182i	−0.0203563	−	0.0117527i
$776$	28.9031	+	27.9143i	1.03756	+	1.00207i
$777$		0			0
$778$	12.7103	−	48.5602i	0.455685	−	1.74097i
$779$	−6.00853	+	10.4071i	−0.215278	+	0.372872i
$780$		0			0
$781$	1.81392	+	3.14180i	0.0649072	+	0.112423i
$782$	−47.2297	−	46.6850i	−1.68893	−	1.66945i
$783$		0			0
$784$	13.5670	+	24.4936i	0.484535	+	0.874772i
$785$			14.2709i			0.509351i
$786$		0			0
$787$	40.2785	−	23.2548i	1.43577	−	0.828943i	0.438220	−	0.898868i	$-0.355609\pi$
$787$	40.2785	−	23.2548i	1.43577	−	0.828943i	0.997552	+	0.0699244i	$0.0222758\pi$
$788$	−46.3214	+	0.537379i	−1.65013	+	0.0191433i
$789$		0			0
$790$	33.9830	+	8.89478i	1.20906	+	0.316462i
$791$	−35.5613	−	21.5144i	−1.26441	−	0.764962i
$792$		0			0
$793$	27.0554	−	46.8614i	0.960767	−	1.66410i
$794$	−5.81390	−	21.2050i	−0.206327	−	0.752538i
$795$		0			0
$796$	−2.13709	−	3.60434i	−0.0757472	−	0.127752i
$797$		−	6.75950i		−	0.239434i	−0.992808	−	0.119717i	$-0.961801\pi$
$797$		−	6.75950i		−	0.239434i	0.992808	−	0.119717i	$-0.0381987\pi$
$798$		0			0
$799$			22.2484i			0.787092i
$800$	−15.3668	−	3.64341i	−0.543297	−	0.128814i
$801$		0			0
$802$	11.8131	−	3.23886i	0.417135	−	0.114368i
$803$	4.80607	−	8.32435i	0.169602	−	0.293760i
$804$		0			0
$805$	0.723195	−	35.3002i	0.0254893	−	1.24417i
$806$	0.428470	−	1.63699i	0.0150922	−	0.0576606i
$807$		0			0
$808$	30.8776	+	7.70036i	1.08627	+	0.270898i
$809$	−24.0673	+	13.8953i	−0.846160	+	0.488531i	−0.859354	−	0.511382i	$-0.829134\pi$
$809$	−24.0673	+	13.8953i	−0.846160	+	0.488531i	0.0131930	+	0.999913i	$0.495800\pi$
$810$		0			0
$811$			24.9697i			0.876804i	0.898779	+	0.438402i	$0.144455\pi$
$811$			24.9697i			0.876804i	−0.898779	+	0.438402i	$0.855545\pi$
$812$	5.67091	−	9.62384i	0.199010	−	0.337730i
$813$		0			0
$814$	13.6815	−	13.8412i	0.479538	−	0.485133i
$815$	−2.15859	−	3.73879i	−0.0756122	−	0.130964i
$816$		0			0
$817$	−4.92074	+	8.52298i	−0.172155	+	0.298181i
$818$	4.78263	+	1.25182i	0.167221	+	0.0437687i
$819$		0			0
$820$	20.6463	+	11.6029i	0.721000	+	0.405191i
$821$	−0.455422	−	0.262938i	−0.0158943	−	0.00917659i	0.492032	−	0.870577i	$-0.336254\pi$
$821$	−0.455422	−	0.262938i	−0.0158943	−	0.00917659i	−0.507926	+	0.861401i	$0.669588\pi$
$822$		0			0
$823$	15.0707	−	8.70110i	0.525333	−	0.303301i	−0.213781	−	0.976882i	$-0.568578\pi$
$823$	15.0707	−	8.70110i	0.525333	−	0.303301i	0.739114	+	0.673580i	$0.235245\pi$
$824$	0.356804	+	1.24457i	0.0124298	+	0.0433566i
$825$		0			0
$826$	1.82188	−	1.76915i	0.0633915	−	0.0615566i
$827$	1.24740			0.0433765			0.0216883	−	0.999765i	$-0.493096\pi$
$827$	1.24740			0.0433765			0.0216883	+	0.999765i	$0.493096\pi$
$828$		0			0
$829$	−5.51372	−	9.55004i	−0.191499	−	0.331687i	0.754248	−	0.656590i	$-0.228002\pi$
$829$	−5.51372	−	9.55004i	−0.191499	−	0.331687i	−0.945747	+	0.324903i	$0.894668\pi$
$830$	30.9918	−	8.49720i	1.07574	−	0.294942i
$831$		0			0
$832$	−1.42098	−	40.8143i	−0.0492637	−	1.41498i
$833$	−30.9225	−	19.5841i	−1.07140	−	0.678550i
$834$		0			0
$835$	14.6373	+	8.45085i	0.506545	+	0.292454i
$836$	8.28053	−	0.0960633i	0.286388	−	0.00332242i
$837$		0			0
$838$	−12.3056	+	12.4492i	−0.425089	+	0.430050i
$839$	20.3758			0.703452			0.351726	−	0.936103i	$-0.385595\pi$
$839$	20.3758			0.703452			0.351726	+	0.936103i	$0.385595\pi$
$840$		0			0
$841$	24.5437			0.846333
$842$	22.0657	−	22.3232i	0.760435	−	0.769308i
$843$		0			0
$844$	−46.3593	+	0.537818i	−1.59575	+	0.0185125i
$845$	16.8069	+	9.70345i	0.578174	+	0.333809i
$846$		0			0
$847$	4.41534	+	8.02273i	0.151713	+	0.275664i
$848$	13.5851	−	8.26942i	0.466515	−	0.283973i
$849$		0			0
$850$	19.9100	−	5.45883i	0.682907	−	0.187236i
$851$	−22.5054	−	38.9805i	−0.771476	−	1.33624i
$852$		0			0
$853$	5.32415			0.182295			0.0911477	−	0.995837i	$-0.470946\pi$
$853$	5.32415			0.182295			0.0911477	+	0.995837i	$0.470946\pi$
$854$	38.1547	+	10.8264i	1.30563	+	0.370472i
$855$		0			0
$856$	−24.1865	+	6.93399i	−0.826677	+	0.236999i
$857$	−31.3685	+	18.1106i	−1.07153	+	0.618647i	−0.928599	−	0.371086i	$-0.878986\pi$
$857$	−31.3685	+	18.1106i	−1.07153	+	0.618647i	−0.142930	+	0.989733i	$0.545652\pi$
$858$		0			0
$859$	−25.1177	−	14.5017i	−0.857004	−	0.494791i	0.00600391	−	0.999982i	$-0.498089\pi$
$859$	−25.1177	−	14.5017i	−0.857004	−	0.494791i	−0.863008	+	0.505191i	$0.831422\pi$
$860$	16.9085	+	9.50231i	0.576574	+	0.324026i
$861$		0			0
$862$	−22.0893	−	5.78170i	−0.752365	−	0.196926i
$863$	−6.76369	+	11.7151i	−0.230239	+	0.398785i	−0.957878	−	0.287174i	$-0.907284\pi$
$863$	−6.76369	+	11.7151i	−0.230239	+	0.398785i	0.727640	+	0.685960i	$0.240617\pi$
$864$		0			0
$865$	6.33001	+	10.9639i	0.215227	+	0.372784i
$866$	−11.6060	+	11.7415i	−0.394389	+	0.398991i
$867$		0			0
$868$	1.24022	+	0.0110178i	0.0420957	+	0.000373969i
$869$		−	45.8952i		−	1.55689i
$870$		0			0
$871$	−47.7235	+	27.5532i	−1.61705	+	0.933603i
$872$	4.58112	−	18.3698i	0.155136	−	0.622079i
$873$		0			0
$874$	4.84960	−	18.5281i	0.164040	−	0.626724i
$875$	26.2107	+	15.8573i	0.886083	+	0.536074i
$876$		0			0
$877$	−12.6825	+	21.9668i	−0.428258	+	0.741765i	−0.996718	−	0.0809459i	$-0.974206\pi$
$877$	−12.6825	+	21.9668i	−0.428258	+	0.741765i	0.568460	+	0.822711i	$0.307539\pi$
$878$	−24.2739	+	6.65530i	−0.819203	+	0.224606i
$879$		0			0
$880$	−0.378618	−	16.3160i	−0.0127632	−	0.550013i
$881$		−	6.65140i		−	0.224091i	−0.993703	−	0.112046i	$-0.964260\pi$
$881$		−	6.65140i		−	0.224091i	0.993703	−	0.112046i	$-0.0357403\pi$
$882$		0			0
$883$		−	21.5373i		−	0.724789i	−0.932025	−	0.362394i	$-0.881959\pi$
$883$		−	21.5373i		−	0.724789i	0.932025	−	0.362394i	$-0.118041\pi$
$884$	27.2275	+	45.9208i	0.915760	+	1.54448i
$885$		0			0
$886$	−5.81589	−	21.2123i	−0.195389	−	0.712640i
$887$	−6.11983	+	10.5999i	−0.205484	+	0.355908i	−0.950287	−	0.311376i	$-0.899210\pi$
$887$	−6.11983	+	10.5999i	−0.205484	+	0.355908i	0.744803	+	0.667284i	$0.232543\pi$
$888$		0			0
$889$	−0.959260	−	0.580346i	−0.0321726	−	0.0194642i
$890$	−25.5003	−	6.67450i	−0.854772	−	0.223730i
$891$		0			0
$892$	9.64356	−	0.111876i	0.322890	−	0.00374588i
$893$	−5.55680	+	3.20822i	−0.185951	+	0.107359i
$894$		0			0
$895$			14.2802i			0.477336i
$896$	28.7516	−	8.32737i	0.960524	−	0.278198i
$897$		0			0
$898$	32.6041	+	32.2281i	1.08801	+	1.07547i
$899$	−0.247397	−	0.428504i	−0.00825115	−	0.0142914i
$900$		0			0
$901$	−10.3951	+	18.0049i	−0.346312	+	0.599830i
$902$	7.83506	−	29.9343i	0.260879	−	0.996702i
$903$		0			0
$904$	−30.8672	+	31.9605i	−1.02663	+	1.06299i
$905$	24.5226	+	14.1581i	0.815157	+	0.470631i
$906$		0			0
$907$	−33.1072	+	19.1145i	−1.09931	+	0.634685i	−0.936039	−	0.351897i	$-0.885537\pi$
$907$	−33.1072	+	19.1145i	−1.09931	+	0.634685i	−0.163268	+	0.986582i	$0.552203\pi$
$908$	17.6971	−	10.4930i	0.587300	−	0.348224i
$909$		0			0
$910$	−7.74802	+	27.3057i	−0.256844	+	0.905177i
$911$	−6.62085			−0.219359			−0.109679	−	0.993967i	$-0.534982\pi$
$911$	−6.62085			−0.219359			−0.109679	+	0.993967i	$0.534982\pi$
$912$		0			0
$913$	−20.9929	−	36.3608i	−0.694763	−	1.20337i
$914$	2.59370	+	9.45999i	0.0857919	+	0.312909i
$915$		0			0
$916$	−19.3857	−	10.8945i	−0.640522	−	0.359964i
$917$	10.0378	+	18.2388i	0.331477	+	0.602299i
$918$		0			0
$919$	−10.6505	−	6.14908i	−0.351328	−	0.202839i	0.313942	−	0.949442i	$-0.398350\pi$
$919$	−10.6505	−	6.14908i	−0.351328	−	0.202839i	−0.665270	+	0.746603i	$0.731684\pi$
$920$	−36.6237	−	9.13336i	−1.20745	−	0.301118i
$921$		0			0
$922$	−33.2039	−	32.8209i	−1.09351	−	1.08090i
$923$	−6.74501			−0.222015
$924$		0			0
$925$	13.9927			0.460077
$926$	−26.0331	−	25.7329i	−0.855502	−	0.845634i
$927$		0			0
$928$	−8.68532	−	8.19561i	−0.285110	−	0.269034i
$929$	18.6376	+	10.7604i	0.611480	+	0.353038i	0.773545	−	0.633742i	$-0.218482\pi$
$929$	18.6376	+	10.7604i	0.611480	+	0.353038i	−0.162064	+	0.986780i	$0.551815\pi$
$930$		0			0
$931$	0.432345	−	10.5473i	0.0141695	−	0.345673i
$932$	−7.49596	+	13.3384i	−0.245538	+	0.436913i
$933$		0			0
$934$	−9.02864	−	32.9301i	−0.295426	−	1.07751i
$935$	10.6672	+	18.4762i	0.348856	+	0.604237i
$936$		0			0
$937$	19.0315			0.621733			0.310866	−	0.950454i	$-0.399381\pi$
$937$	19.0315			0.621733			0.310866	+	0.950454i	$0.399381\pi$
$938$	−28.1380	−	28.9767i	−0.918738	−	0.946124i
$939$		0			0
$940$	6.44938	+	10.8773i	0.210356	+	0.354777i
$941$	22.4940	−	12.9869i	0.733283	−	0.423361i	−0.0863390	−	0.996266i	$-0.527517\pi$
$941$	22.4940	−	12.9869i	0.733283	−	0.423361i	0.819622	+	0.572905i	$0.194183\pi$
$942$		0			0
$943$	−61.9758	−	35.7817i	−2.01821	−	1.16521i
$944$	−1.41161	−	2.31901i	−0.0459440	−	0.0754775i
$945$		0			0
$946$	6.41660	−	24.5150i	0.208622	−	0.797050i
$947$	−3.23409	+	5.60161i	−0.105094	+	0.182028i	−0.913777	−	0.406217i	$-0.866848\pi$
$947$	−3.23409	+	5.60161i	−0.105094	+	0.182028i	0.808683	+	0.588245i	$0.200181\pi$
$948$		0			0
$949$	8.93561	+	15.4769i	0.290062	+	0.502403i
$950$	4.23442	+	4.18559i	0.137383	+	0.135798i
$951$		0			0
$952$	−27.7540	+	27.5834i	−0.899512	+	0.893982i
$953$			17.4347i			0.564765i	0.959302	+	0.282382i	$0.0911247\pi$
$953$			17.4347i			0.564765i	−0.959302	+	0.282382i	$0.908875\pi$
$954$		0			0
$955$	22.0404	−	12.7251i	0.713212	−	0.411773i
$956$	−0.129743	−	11.1837i	−0.00419619	−	0.361706i
$957$		0			0
$958$	−56.1222	−	14.6895i	−1.81323	−	0.474597i
$959$	0.245136	−	11.9654i	0.00791585	−	0.386384i
$960$		0			0
$961$	−15.4725	+	26.7992i	−0.499114	+	0.864491i
$962$	9.56771	+	34.8963i	0.308475	+	1.12510i
$963$		0			0
$964$	−7.13234	+	4.22892i	−0.229717	+	0.136204i
$965$			6.92319i			0.222865i
$966$		0			0
$967$			11.5622i			0.371814i	0.982567	+	0.185907i	$0.0595223\pi$
$967$			11.5622i			0.371814i	−0.982567	+	0.185907i	$0.940478\pi$
$968$	9.41066	−	2.69793i	0.302470	−	0.0867147i
$969$		0			0
$970$	−28.7927	+	7.89426i	−0.924479	+	0.253470i
$971$	−27.0715	+	46.8892i	−0.868766	+	1.50475i	−0.00550751	+	0.999985i	$0.501753\pi$
$971$	−27.0715	+	46.8892i	−0.868766	+	1.50475i	−0.863259	+	0.504762i	$0.831580\pi$
$972$		0			0
$973$	−20.6529	−	12.4948i	−0.662100	−	0.400566i
$974$	−5.41527	+	20.6893i	−0.173516	+	0.662929i
$975$		0			0
$976$	20.3421	−	37.2008i	0.651135	−	1.19077i
$977$	20.1006	−	11.6051i	0.643076	−	0.371280i	−0.142722	−	0.989763i	$-0.545586\pi$
$977$	20.1006	−	11.6051i	0.643076	−	0.371280i	0.785798	+	0.618483i	$0.212252\pi$
$978$		0			0
$979$			34.4390i			1.10068i
$980$	−20.7951	−	0.610879i	−0.664274	−	0.0195138i
$981$		0			0
$982$	36.7137	−	37.1421i	1.17158	−	1.18525i
$983$	−18.5294	−	32.0939i	−0.590996	−	1.02363i	−0.994099	−	0.108480i	$-0.965402\pi$
$983$	−18.5294	−	32.0939i	−0.590996	−	1.02363i	0.403103	−	0.915155i	$-0.367932\pi$
$984$		0			0
$985$	17.2096	−	29.8079i	0.548343	−	0.949758i
$986$	15.1017	+	3.95276i	0.480937	+	0.125881i
$987$		0			0
$988$	−7.54306	+	13.4222i	−0.239977	+	0.427016i
$989$	−50.7557	−	29.3038i	−1.61394	−	0.931806i
$990$		0			0
$991$	−6.39309	+	3.69105i	−0.203083	+	0.117250i	−0.598093	−	0.801427i	$-0.704075\pi$
$991$	−6.39309	+	3.69105i	−0.203083	+	0.117250i	0.395010	+	0.918677i	$0.370741\pi$
$992$	0.305886	−	1.29013i	0.00971189	−	0.0409618i
$993$		0			0
$994$	−1.20929	−	4.79362i	−0.0383565	−	0.152044i
$995$	3.11338			0.0987008
$996$		0			0
$997$	−3.53100	−	6.11587i	−0.111828	−	0.193692i	0.804679	−	0.593710i	$-0.202337\pi$
$997$	−3.53100	−	6.11587i	−0.111828	−	0.193692i	−0.916507	+	0.400018i	$0.869004\pi$
$998$	−2.33016	+	0.638872i	−0.0737598	+	0.0202231i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.c.107.4	✓	28
3.2	odd	2	inner	756.2.be.c.107.11	yes	28
4.3	odd	2		756.2.be.d.107.9	yes	28
7.4	even	3		756.2.be.d.431.6	yes	28
12.11	even	2		756.2.be.d.107.6	yes	28
21.11	odd	6		756.2.be.d.431.9	yes	28
28.11	odd	6	inner	756.2.be.c.431.11	yes	28
84.11	even	6	inner	756.2.be.c.431.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.4	✓	28	1.1	even	1	trivial
756.2.be.c.107.11	yes	28	3.2	odd	2	inner
756.2.be.c.431.4	yes	28	84.11	even	6	inner
756.2.be.c.431.11	yes	28	28.11	odd	6	inner
756.2.be.d.107.6	yes	28	12.11	even	2
756.2.be.d.107.9	yes	28	4.3	odd	2
756.2.be.d.431.6	yes	28	7.4	even	3
756.2.be.d.431.9	yes	28	21.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994183 + 1.00578i) q^{2} +(-0.0232006 - 1.99987i) q^{4} +(1.28692 + 0.743002i) q^{5} +(-1.36953 + 2.26371i) q^{7} +(2.03450 + 1.96490i) q^{8} +(-2.02673 + 0.555680i) q^{10} +(1.37284 + 2.37783i) q^{11} -5.10488 q^{13} +(-0.915240 - 3.62799i) q^{14} +(-3.99892 + 0.0927963i) q^{16} +(4.52837 - 2.61446i) q^{17} +(1.30598 + 0.754009i) q^{19} +(1.45605 - 2.59090i) q^{20} +(-3.75644 - 0.983219i) q^{22} +(-4.49024 + 7.77732i) q^{23} +(-1.39590 - 2.41776i) q^{25} +(5.07518 - 5.13440i) q^{26} +(4.55889 + 2.68636i) q^{28} -2.11100i q^{29} +(0.202986 - 0.117194i) q^{31} +(3.88233 - 4.11431i) q^{32} +(-1.87245 + 7.15381i) q^{34} +(-3.44441 + 1.89564i) q^{35} +(-2.50604 + 4.34059i) q^{37} +(-2.05675 + 0.563912i) q^{38} +(1.15831 + 4.04029i) q^{40} +7.96878i q^{41} +6.52611i q^{43} +(4.72350 - 2.80067i) q^{44} +(-3.35818 - 12.2483i) q^{46} +(-2.12744 + 3.68483i) q^{47} +(-3.24878 - 6.20044i) q^{49} +(3.81952 + 0.999730i) q^{50} +(0.118437 + 10.2091i) q^{52} +(-3.44333 + 1.98801i) q^{53} +4.08010i q^{55} +(-7.23426 + 1.91453i) q^{56} +(2.12321 + 2.09872i) q^{58} +(0.339358 + 0.587784i) q^{59} +(-5.29992 + 9.17972i) q^{61} +(-0.0839334 + 0.320672i) q^{62} +(0.278358 + 7.99516i) q^{64} +(-6.56955 - 3.79293i) q^{65} +(9.34860 - 5.39742i) q^{67} +(-5.33362 - 8.99548i) q^{68} +(1.51777 - 5.34895i) q^{70} +1.32129 q^{71} +(-1.75041 - 3.03179i) q^{73} +(-1.87423 - 6.83587i) q^{74} +(1.47762 - 2.62928i) q^{76} +(-7.26288 - 0.148795i) q^{77} +(-14.4759 - 8.35768i) q^{79} +(-5.21523 - 2.85179i) q^{80} +(-8.01487 - 7.92242i) q^{82} -15.2915 q^{83} +7.77018 q^{85} +(-6.56385 - 6.48815i) q^{86} +(-1.87915 + 7.53519i) q^{88} +(10.8625 + 6.27147i) q^{89} +(6.99129 - 11.5560i) q^{91} +(15.6578 + 8.79944i) q^{92} +(-1.59108 - 5.80314i) q^{94} +(1.12046 + 1.94069i) q^{95} +14.2065 q^{97} +(9.46618 + 2.89681i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Introduction

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