LMFDB - Embedded newform 756.2.be.d.431.6

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			431.6
Character	$\chi$	$=$	756.431
Dual form			756.2.be.d.107.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.373943 - 1.36388i) q^{2} +(-1.72033 + 1.02003i) q^{4} +(-1.28692 + 0.743002i) q^{5} +(1.36953 + 2.26371i) q^{7} +(2.03450 + 1.96490i) q^{8} +(1.49460 + 1.47736i) q^{10} +(1.37284 - 2.37783i) q^{11} -5.10488 q^{13} +(2.57530 - 2.71437i) q^{14} +(1.91910 - 3.50957i) q^{16} +(-4.52837 - 2.61446i) q^{17} +(-1.30598 + 0.754009i) q^{19} +(1.45605 - 2.59090i) q^{20} +(-3.75644 - 0.983219i) q^{22} +(-4.49024 - 7.77732i) q^{23} +(-1.39590 + 2.41776i) q^{25} +(1.90893 + 6.96244i) q^{26} +(-4.66509 - 2.49738i) q^{28} -2.11100i q^{29} +(-0.202986 - 0.117194i) q^{31} +(-5.50426 - 1.30504i) q^{32} +(-1.87245 + 7.15381i) q^{34} +(-3.44441 - 1.89564i) q^{35} +(-2.50604 - 4.34059i) q^{37} +(1.51674 + 1.49925i) q^{38} +(-4.07815 - 1.01702i) q^{40} +7.96878i q^{41} +6.52611i q^{43} +(0.0637017 + 5.49100i) q^{44} +(-8.92824 + 9.03242i) q^{46} +(-2.12744 - 3.68483i) q^{47} +(-3.24878 + 6.20044i) q^{49} +(3.81952 + 0.999730i) q^{50} +(8.78210 - 5.20710i) q^{52} +(3.44333 + 1.98801i) q^{53} +4.08010i q^{55} +(-1.66165 + 7.29650i) q^{56} +(-2.87915 + 0.789394i) q^{58} +(0.339358 - 0.587784i) q^{59} +(-5.29992 - 9.17972i) q^{61} +(-0.0839334 + 0.320672i) q^{62} +(0.278358 + 7.99516i) q^{64} +(6.56955 - 3.79293i) q^{65} +(-9.34860 - 5.39742i) q^{67} +(10.4571 - 0.121314i) q^{68} +(-1.29742 + 5.40662i) q^{70} +1.32129 q^{71} +(-1.75041 + 3.03179i) q^{73} +(-4.98292 + 5.04106i) q^{74} +(1.47762 - 2.62928i) q^{76} +(7.26288 - 0.148795i) q^{77} +(14.4759 - 8.35768i) q^{79} +(0.137896 + 5.94241i) q^{80} +(10.8685 - 2.97987i) q^{82} -15.2915 q^{83} +7.77018 q^{85} +(8.90083 - 2.44039i) q^{86} +(7.46525 - 2.14020i) q^{88} +(-10.8625 + 6.27147i) q^{89} +(-6.99129 - 11.5560i) q^{91} +(15.6578 + 8.79944i) q^{92} +(-4.23013 + 4.27949i) q^{94} +(1.12046 - 1.94069i) q^{95} +14.2065 q^{97} +(9.67151 + 2.11233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64}+ \cdots - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.373943	−	1.36388i	−0.264417	−	0.964408i
$2$	−0.373943	−	1.36388i	−0.264417	−	0.964408i
$3$		0			0
$3$		0			0
$4$	−1.72033	+	1.02003i	−0.860167	+	0.510013i
$5$	−1.28692	+	0.743002i	−0.575527	+	0.332280i	−0.759354	−	0.650678i	$-0.774485\pi$
$5$	−1.28692	+	0.743002i	−0.575527	+	0.332280i	0.183827	+	0.982959i	$0.441151\pi$
$6$		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
$10$	1.49460	+	1.47736i	0.472633	+	0.467182i
$11$	1.37284	−	2.37783i	0.413928	−	0.716944i	−0.581387	−	0.813627i	$-0.697490\pi$
$11$	1.37284	−	2.37783i	0.413928	−	0.716944i	0.995315	+	0.0966827i	$0.0308232\pi$
$12$		0			0
$13$	−5.10488			−1.41584			−0.707919	−	0.706293i	$-0.750366\pi$
$13$	−5.10488			−1.41584			−0.707919	+	0.706293i	$0.750366\pi$
$14$	2.57530	−	2.71437i	0.688279	−	0.725446i
$15$		0			0
$16$	1.91910	−	3.50957i	0.479774	−	0.877392i
$17$	−4.52837	−	2.61446i	−1.09829	−	0.634099i	−0.162520	−	0.986705i	$-0.551962\pi$
$17$	−4.52837	−	2.61446i	−1.09829	−	0.634099i	−0.935772	+	0.352606i	$0.885296\pi$
$18$		0			0
$19$	−1.30598	+	0.754009i	−0.299613	+	0.172982i	−0.642269	−	0.766479i	$-0.722007\pi$
$19$	−1.30598	+	0.754009i	−0.299613	+	0.172982i	0.342656	+	0.939461i	$0.388673\pi$
$20$	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	−0.772336	−	0.635214i	$-0.780912\pi$
$23$	−4.49024	−	7.77732i	−0.936280	−	1.62168i	−0.163944	−	0.986470i	$-0.552422\pi$
$24$		0			0
$25$	−1.39590	+	2.41776i	−0.279179	+	0.483553i
$26$	1.90893	+	6.96244i	0.374372	+	1.36545i
$27$		0			0
$28$	−4.66509	−	2.49738i	−0.881619	−	0.471961i
$29$		−	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	$-0.340034\pi$
$31$	−0.202986	−	0.117194i	−0.0364574	−	0.0210487i	−0.518118	+	0.855309i	$0.673367\pi$
$32$	−5.50426	−	1.30504i	−0.973025	−	0.230701i
$33$		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	0.583117	−	0.812388i	$-0.301833\pi$
$37$	−2.50604	−	4.34059i	−0.411990	−	0.713588i	−0.995107	+	0.0988002i	$0.968500\pi$
$38$	1.51674	+	1.49925i	0.246048	+	0.243210i
$39$		0			0
$40$	−4.07815	−	1.01702i	−0.644812	−	0.160806i
$41$			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	$0.834211\pi$
$44$	0.0637017	+	5.49100i	0.00960340	+	0.827800i
$45$		0			0
$46$	−8.92824	+	9.03242i	−1.31640	+	1.33176i
$47$	−2.12744	−	3.68483i	−0.310319	−	0.537488i	0.668112	−	0.744060i	$-0.267103\pi$
$47$	−2.12744	−	3.68483i	−0.310319	−	0.537488i	−0.978431	+	0.206572i	$0.933769\pi$
$48$		0			0
$49$	−3.24878	+	6.20044i	−0.464111	+	0.885777i
$50$	3.81952	+	0.999730i	0.540162	+	0.141383i
$51$		0			0
$52$	8.78210	−	5.20710i	1.21786	−	0.722096i
$53$	3.44333	+	1.98801i	0.472978	+	0.273074i	0.717485	−	0.696573i	$-0.245293\pi$
$53$	3.44333	+	1.98801i	0.472978	+	0.273074i	−0.244508	+	0.969647i	$0.578626\pi$
$54$		0			0
$55$			4.08010i			0.550161i
$56$	−1.66165	+	7.29650i	−0.222048	+	0.975036i
$57$		0			0
$58$	−2.87915	+	0.789394i	−0.378052	+	0.103653i
$59$	0.339358	−	0.587784i	0.0441806	−	0.0765230i	−0.843089	−	0.537773i	$-0.819266\pi$
$59$	0.339358	−	0.587784i	0.0441806	−	0.0765230i	0.887270	+	0.461250i	$0.152599\pi$
$60$		0			0
$61$	−5.29992	−	9.17972i	−0.678585	−	1.17534i	−0.975407	−	0.220411i	$-0.929260\pi$
$61$	−5.29992	−	9.17972i	−0.678585	−	1.17534i	0.296822	−	0.954933i	$-0.404073\pi$
$62$	−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	$-0.562523\pi$
$67$	−9.34860	−	5.39742i	−1.14211	−	0.659399i	−0.946953	+	0.321372i	$0.895856\pi$
$68$	10.4571	−	0.121314i	1.26811	−	0.0147115i
$69$		0			0
$70$	−1.29742	+	5.40662i	−0.155071	+	0.646215i
$71$	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	−0.950091	−	0.311972i	$-0.899010\pi$
$73$	−1.75041	+	3.03179i	−0.204870	+	0.354844i	0.745222	+	0.666817i	$0.232344\pi$
$74$	−4.98292	+	5.04106i	−0.579253	+	0.586012i
$75$		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	0.644179	−	0.764874i	$-0.277199\pi$
$79$	14.4759	−	8.35768i	1.62867	−	0.940313i	0.984490	−	0.175438i	$-0.0561343\pi$
$80$	0.137896	+	5.94241i	0.0154172	+	0.664382i
$81$		0			0
$82$	10.8685	−	2.97987i	1.20022	−	0.329071i
$83$	−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
$86$	8.90083	−	2.44039i	0.959801	−	0.263154i
$87$		0			0
$88$	7.46525	−	2.14020i	0.795798	−	0.228146i
$89$	−10.8625	+	6.27147i	−1.15142	+	0.664775i	−0.949234	−	0.314572i	$-0.898139\pi$
$89$	−10.8625	+	6.27147i	−1.15142	+	0.664775i	−0.202190	+	0.979346i	$0.564806\pi$
$90$		0			0
$91$	−6.99129	−	11.5560i	−0.732886	−	1.21140i
$92$	15.6578	+	8.79944i	1.63244	+	0.917405i
$93$		0			0
$94$	−4.23013	+	4.27949i	−0.436305	+	0.441396i
$95$	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	$0.243579\pi$
$98$	9.67151	+	2.11233i	0.976970	+	0.213378i
$99$		0			0
$100$	−0.0647714	−	5.58321i	−0.00647714	−	0.558321i
$101$	−9.74384	−	5.62561i	−0.969549	−	0.559769i	−0.0704500	−	0.997515i	$-0.522444\pi$
$101$	−9.74384	−	5.62561i	−0.969549	−	0.559769i	−0.899099	+	0.437746i	$0.855777\pi$
$102$		0			0
$103$	−0.396421	+	0.228874i	−0.0390605	+	0.0225516i	−0.519403	−	0.854529i	$-0.673846\pi$
$103$	−0.396421	+	0.228874i	−0.0390605	+	0.0225516i	0.480343	+	0.877081i	$0.340512\pi$
$104$	−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	0.566883	−	0.823799i	$-0.308149\pi$
$107$	−4.44784	−	7.70389i	−0.429989	−	0.744763i	−0.996872	+	0.0790354i	$0.974816\pi$
$108$		0			0
$109$	−3.34680	+	5.79684i	−0.320566	+	0.555236i	−0.980605	−	0.195995i	$-0.937206\pi$
$109$	−3.34680	+	5.79684i	−0.320566	+	0.555236i	0.660039	+	0.751231i	$0.270540\pi$
$110$	5.56476	−	1.52572i	0.530579	−	0.145472i
$111$		0			0
$112$	10.5729	−	0.462175i	0.999046	−	0.0436714i
$113$			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
$116$	2.15328	+	3.63163i	0.199927	+	0.337189i
$117$		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
$122$	−10.5382	+	10.6611i	−0.954081	+	0.965214i
$123$		0			0
$124$	0.468745	−	0.00543796i	0.0420945	−	0.000488343i
$125$		−	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	$0.994015\pi$
$128$	10.8003	−	3.36938i	0.954624	−	0.297814i
$129$		0			0
$130$	−7.62974	−	7.54174i	−0.669172	−	0.661454i
$131$	3.93433	+	6.81447i	0.343744	+	0.595383i	0.985125	−	0.171840i	$-0.0549713\pi$
$131$	3.93433	+	6.81447i	0.343744	+	0.595383i	−0.641380	+	0.767223i	$0.721638\pi$
$132$		0			0
$133$	−3.49544	−	1.92373i	−0.303093	−	0.166808i
$134$	−3.86559	+	14.7687i	−0.333936	+	1.27582i
$135$		0			0
$136$	−4.07582	−	14.2169i	−0.349499	−	1.21909i
$137$	3.91743	+	2.26173i	0.334689	+	0.193233i	0.657921	−	0.753087i	$-0.271436\pi$
$137$	3.91743	+	2.26173i	0.334689	+	0.193233i	−0.323232	+	0.946320i	$0.604769\pi$
$138$		0			0
$139$			9.12345i			0.773841i	0.922113	+	0.386921i	$0.126461\pi$
$139$			9.12345i			0.773841i	−0.922113	+	0.386921i	$0.873539\pi$
$140$	7.85914	−	0.252245i	0.664219	−	0.0213186i
$141$		0			0
$142$	−0.494086	−	1.80208i	−0.0414627	−	0.151227i
$143$	−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	$-0.976037\pi$
$149$	−17.4629	+	10.0822i	−1.43062	+	0.825967i	−0.433448	+	0.901178i	$0.642703\pi$
$150$		0			0
$151$	−6.33048	−	3.65491i	−0.515168	−	0.297432i	0.219788	−	0.975548i	$-0.429464\pi$
$151$	−6.33048	−	3.65491i	−0.515168	−	0.297432i	−0.734955	+	0.678116i	$0.762797\pi$
$152$	−4.13857	−	1.03209i	−0.335682	−	0.0837136i
$153$		0			0
$154$	−2.91884	−	9.85005i	−0.235207	−	0.793740i
$155$	0.348301			0.0279762
$156$		0			0
$157$	4.80178	−	8.31693i	0.383224	−	0.663763i	−0.608297	−	0.793709i	$-0.708147\pi$
$157$	4.80178	−	8.31693i	0.383224	−	0.663763i	0.991521	+	0.129946i	$0.0414805\pi$
$158$	−16.8120	−	16.6181i	−1.33749	−	1.32207i
$159$		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	$-0.630371\pi$
$163$	2.51601	−	1.45262i	0.197069	−	0.113778i	0.595288	+	0.803513i	$0.297038\pi$
$164$	−8.12836	−	13.7090i	−0.634718	−	1.07049i
$165$		0			0
$166$	5.71816	+	20.8558i	0.443815	+	1.61873i
$167$	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
$170$	−2.90560	−	10.5976i	−0.222850	−	0.812798i
$171$		0			0
$172$	−6.65679	−	11.2271i	−0.507576	−	0.856057i
$173$	−7.37811	+	4.25976i	−0.560948	+	0.323863i	−0.753526	−	0.657418i	$-0.771648\pi$
$173$	−7.37811	+	4.25976i	−0.560948	+	0.323863i	0.192578	+	0.981282i	$0.438315\pi$
$174$		0			0
$175$	−7.38484	+	0.151293i	−0.558242	+	0.0114367i
$176$	−5.71055	−	9.38138i	−0.430449	−	0.707148i
$177$		0			0
$178$	12.6155	+	12.4700i	0.945570	+	0.934664i
$179$	4.80491	−	8.32235i	0.359136	−	0.622042i	−0.628681	−	0.777664i	$-0.716405\pi$
$179$	4.80491	−	8.32235i	0.359136	−	0.622042i	0.987817	+	0.155622i	$0.0497381\pi$
$180$		0			0
$181$	19.0553			1.41637			0.708184	−	0.706028i	$-0.249515\pi$
$181$	19.0553			1.41637			0.708184	+	0.706028i	$0.249515\pi$
$182$	−13.1466	+	13.8565i	−0.974492	+	1.02712i
$183$		0			0
$184$	6.14626	−	24.6458i	0.453108	−	1.81691i
$185$	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	0.989556	+	0.144152i	$0.0460453\pi$
$191$	8.56327	+	14.8320i	0.619617	+	1.07321i	−0.369939	+	0.929056i	$0.620621\pi$
$192$		0			0
$193$	2.32947	−	4.03475i	0.167679	−	0.290428i	−0.769925	−	0.638135i	$-0.779706\pi$
$193$	2.32947	−	4.03475i	0.167679	−	0.290428i	0.937603	+	0.347707i	$0.113040\pi$
$194$	−5.31241	−	19.3759i	−0.381409	−	1.39111i
$195$		0			0
$196$	−0.735625	−	13.9807i	−0.0525447	−	0.998619i
$197$		−	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	$-0.356993\pi$
$199$	−1.81444	−	1.04757i	−0.128622	−	0.0742602i	−0.562931	+	0.826504i	$0.690326\pi$
$200$	−7.59061	+	2.17614i	−0.536737	+	0.153876i
$201$		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
$206$	0.460394	+	0.455084i	0.0320772	+	0.0317072i
$207$		0			0
$208$	−9.79676	+	17.9159i	−0.679283	+	1.24225i
$209$			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	$-0.294071\pi$
$212$	−7.95150	+	0.0922461i	−0.546111	+	0.00633549i
$213$		0			0
$214$	−8.84394	+	8.94713i	−0.604559	+	0.611613i
$215$	−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
$220$	−4.16180	−	7.01913i	−0.280589	−	0.473230i
$221$	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	$0.948381\pi$
$224$	−4.58401	−	14.2473i	−0.306282	−	0.951941i
$225$		0			0
$226$	21.4256	−	5.87438i	1.42521	−	0.390758i
$227$	5.14352	−	8.90884i	0.341387	−	0.591300i	−0.643303	−	0.765611i	$-0.722437\pi$
$227$	5.14352	−	8.90884i	0.341387	−	0.591300i	0.984691	+	0.174311i	$0.0557699\pi$
$228$		0			0
$229$	5.55931	+	9.62901i	0.367370	+	0.636303i	0.989153	−	0.146886i	$-0.0469250\pi$
$229$	5.55931	+	9.62901i	0.367370	+	0.636303i	−0.621784	+	0.783189i	$0.713592\pi$
$230$	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	$-0.586042\pi$
$233$	6.62526	−	3.82509i	0.434035	−	0.250590i	0.701064	+	0.713098i	$0.252709\pi$
$234$		0			0
$235$	5.47568	+	3.16138i	0.357194	+	0.206226i
$236$	0.0157466	+	1.35734i	0.00102502	+	0.0883552i
$237$		0			0
$238$	−18.7585	+	5.55867i	−1.21594	+	0.360315i
$239$	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	−0.925035	−	0.379882i	$-0.875965\pi$
$241$	−2.07295	+	3.59046i	−0.133531	+	0.231282i	0.791505	+	0.611163i	$0.209298\pi$
$242$	3.44107	−	3.48122i	0.221200	−	0.223781i
$243$		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
$248$	−0.182700	−	0.637278i	−0.0116015	−	0.0404672i
$249$		0			0
$250$	−15.7919	+	4.32974i	−0.998765	+	0.273837i
$251$	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
$254$	0.577952	−	0.158460i	0.0362639	−	0.00994268i
$255$		0			0
$256$	−8.63413	−	13.4704i	−0.539633	−	0.841900i
$257$	−26.2593	+	15.1608i	−1.63801	+	0.945707i	−0.656497	+	0.754329i	$0.727963\pi$
$257$	−26.2593	+	15.1608i	−1.63801	+	0.945707i	−0.981516	+	0.191379i	$0.938704\pi$
$258$		0			0
$259$	6.39374	−	11.6175i	0.397288	−	0.721877i
$260$	−7.43294	+	13.2262i	−0.460971	+	0.820256i
$261$		0			0
$262$	7.82290	−	7.91418i	0.483300	−	0.488940i
$263$	−9.23981	+	16.0038i	−0.569751	+	0.986838i	0.426839	+	0.904328i	$0.359627\pi$
$263$	−9.23981	+	16.0038i	−0.569751	+	0.986838i	−0.996590	+	0.0825101i	$0.973706\pi$
$264$		0			0
$265$	−5.90837			−0.362948
$266$	−1.31664	+	5.48672i	−0.0807283	+	0.336413i
$267$		0			0
$268$	21.5882	−	0.250447i	1.31871	−	0.0152985i
$269$	−0.629904	−	0.363675i	−0.0384059	−	0.0221737i	0.480674	−	0.876899i	$-0.340392\pi$
$269$	−0.629904	−	0.363675i	−0.0384059	−	0.0221737i	−0.519080	+	0.854726i	$0.673725\pi$
$270$		0			0
$271$	7.21987	−	4.16839i	0.438576	−	0.253212i	−0.264418	−	0.964408i	$-0.585180\pi$
$271$	7.21987	−	4.16839i	0.438576	−	0.253212i	0.702993	+	0.711197i	$0.251846\pi$
$272$	−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	−0.613915	−	0.789372i	$-0.710406\pi$
$277$	6.26885	−	10.8580i	0.376659	−	0.652392i	0.990574	+	0.136980i	$0.0437396\pi$
$278$	12.4433	−	3.41165i	0.746299	−	0.204617i
$279$		0			0
$280$	−3.28290	−	10.6246i	−0.196191	−	0.634941i
$281$		−	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	$-0.187266\pi$
$283$	12.9064	+	7.45154i	0.767208	+	0.442948i	−0.0646694	+	0.997907i	$0.520599\pi$
$284$	−2.27306	+	1.34775i	−0.134881	+	0.0799740i
$285$		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
$290$	3.11871	−	3.15510i	0.183137	−	0.185274i
$291$		0			0
$292$	−0.0812211	−	7.00115i	−0.00475311	−	0.409712i
$293$			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
$296$	3.43028	−	13.7550i	0.199381	−	0.799494i
$297$		0			0
$298$	20.2810	+	20.0471i	1.17485	+	1.16130i
$299$	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
$304$	0.139939	+	6.03045i	0.00802603	+	0.345870i
$305$	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	$0.956389\pi$
$308$	−12.3428	+	7.66430i	−0.703297	+	0.436714i
$309$		0			0
$310$	−0.130245	−	0.475041i	−0.00739740	−	0.0269805i
$311$	−8.06864	+	13.9753i	−0.457530	+	0.792466i	−0.998830	−	0.0483640i	$-0.984599\pi$
$311$	−8.06864	+	13.9753i	−0.457530	+	0.792466i	0.541299	+	0.840830i	$0.317933\pi$
$312$		0			0
$313$	13.2748	+	22.9926i	0.750336	+	1.29962i	0.947660	+	0.319282i	$0.103442\pi$
$313$	13.2748	+	22.9926i	0.750336	+	1.29962i	−0.197324	+	0.980338i	$0.563225\pi$
$314$	−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	$-0.579321\pi$
$317$	8.35634	−	4.82453i	0.469339	−	0.270973i	0.715963	+	0.698138i	$0.245988\pi$
$318$		0			0
$319$	−5.01962	−	2.89808i	−0.281045	−	0.162261i
$320$	−6.29864	−	10.0823i	−0.352105	−	0.563617i
$321$		0			0
$322$	−32.6743	−	7.84079i	−1.82087	−	0.436950i
$323$	7.88530			0.438750
$324$		0			0
$325$	7.12589	−	12.3424i	0.395273	−	0.684633i
$326$	−2.92204	−	2.88833i	−0.161837	−	0.159970i
$327$		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	$-0.656641\pi$
$331$	0.992363	−	0.572941i	0.0545452	−	0.0314917i	0.527025	+	0.849850i	$0.323308\pi$
$332$	26.3066	−	15.5978i	1.44376	−	0.856038i
$333$		0			0
$334$	−4.25320	−	15.5127i	−0.232725	−	0.848816i
$335$	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	$0.516411\pi$
$338$	−4.88361	−	17.8120i	−0.265634	−	0.968844i
$339$		0			0
$340$	−13.3673	+	7.92578i	−0.724944	+	0.429836i
$341$	−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
$346$	8.56878	+	8.46995i	0.460661	+	0.455348i
$347$	−1.96885	+	3.41015i	−0.105693	+	0.183066i	−0.914021	−	0.405666i	$-0.867040\pi$
$347$	−1.96885	+	3.41015i	−0.105693	+	0.183066i	0.808328	+	0.588733i	$0.200373\pi$
$348$		0			0
$349$	−22.8441			−1.22282			−0.611409	−	0.791315i	$-0.709397\pi$
$349$	−22.8441			−1.22282			−0.611409	+	0.791315i	$0.709397\pi$
$350$	2.96785	+	10.0155i	0.158638	+	0.535349i
$351$		0			0
$352$	−10.6597	+	11.2966i	−0.568162	+	0.602111i
$353$	−28.5246	−	16.4687i	−1.51821	−	0.876541i	−0.999770	−	0.0214280i	$-0.993179\pi$
$353$	−28.5246	−	16.4687i	−1.51821	−	0.876541i	−0.518442	−	0.855113i	$-0.673488\pi$
$354$		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	0.988553	+	0.150876i	$0.0482094\pi$
$359$	11.8409	+	20.5090i	0.624939	+	1.08243i	−0.363614	+	0.931550i	$0.618457\pi$
$360$		0			0
$361$	−8.36294	+	14.4850i	−0.440155	+	0.762370i
$362$	−7.12558	−	25.9891i	−0.374512	−	1.36596i
$363$		0			0
$364$	23.8147	+	12.7488i	1.24823	+	0.668221i
$365$		−	5.20222i		−	0.272297i
$366$		0			0
$367$	−22.3566	−	12.9076i	−1.16701	−	0.673772i	−0.214034	−	0.976826i	$-0.568660\pi$
$367$	−22.3566	−	12.9076i	−1.16701	−	0.673772i	−0.952973	+	0.303054i	$0.901994\pi$
$368$	−35.9123	+	0.833356i	−1.87206	+	0.0434417i
$369$		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	−0.712243	−	0.701933i	$-0.752321\pi$
$373$	−18.6182	−	32.2476i	−0.964013	−	1.66972i	−0.251770	−	0.967787i	$-0.581013\pi$
$374$	14.4400	+	14.2734i	0.746674	+	0.738062i
$375$		0			0
$376$	2.91205	−	11.6770i	0.150178	−	0.602195i
$377$			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	$0.721798\pi$
$380$	0.0519908	+	4.48154i	0.00266707	+	0.229898i
$381$		0			0
$382$	17.0269	−	17.2256i	0.871173	−	0.881338i
$383$	6.22015	+	10.7736i	0.317835	+	0.550506i	0.980036	−	0.198820i	$-0.0637109\pi$
$383$	6.22015	+	10.7736i	0.317835	+	0.550506i	−0.662201	+	0.749326i	$0.730378\pi$
$384$		0			0
$385$	−9.23617	+	5.58782i	−0.470719	+	0.284782i
$386$	−6.37400	−	1.66834i	−0.324428	−	0.0849165i
$387$		0			0
$388$	−24.4399	+	14.4910i	−1.24075	+	0.735668i
$389$	30.7387	+	17.7470i	1.55851	+	0.899808i	0.997400	+	0.0720702i	$0.0229606\pi$
$389$	30.7387	+	17.7470i	1.55851	+	0.899808i	0.561114	+	0.827738i	$0.310373\pi$
$390$		0			0
$391$			46.9582i			2.37478i
$392$	−18.7929	+	6.23127i	−0.949182	+	0.314727i
$393$		0			0
$394$	−31.5905	+	8.66135i	−1.59151	+	0.436352i
$395$	−12.4195	+	21.5113i	−0.624895	+	1.08235i
$396$		0			0
$397$	−7.77378	−	13.4646i	−0.390155	−	0.675768i	0.602315	−	0.798259i	$-0.294245\pi$
$397$	−7.77378	−	13.4646i	−0.390155	−	0.675768i	−0.992470	+	0.122490i	$0.960912\pi$
$398$	−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	$-0.597279\pi$
$401$	7.50098	−	4.33070i	0.374581	−	0.216265i	0.675458	+	0.737398i	$0.263946\pi$
$402$		0			0
$403$	1.03622	+	0.598261i	0.0516178	+	0.0298015i
$404$	22.5009	−	0.261036i	1.11946	−	0.0129870i
$405$		0			0
$406$	−5.73005	−	5.43648i	−0.284378	−	0.269808i
$407$	−13.7616			−0.682137
$408$		0			0
$409$	−1.74788	+	3.02741i	−0.0864270	+	0.149696i	−0.905998	−	0.423281i	$-0.860878\pi$
$409$	−1.74788	+	3.02741i	−0.0864270	+	0.149696i	0.819571	+	0.572977i	$0.194212\pi$
$410$	−11.7727	+	11.9101i	−0.581415	+	0.588199i
$411$		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
$416$	28.0986	+	6.66208i	1.37765	+	0.326635i
$417$		0			0
$418$	5.64721	−	1.54833i	0.276214	−	0.0757311i
$419$	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	$0.681899\pi$
$422$	−31.6163	+	8.66843i	−1.53906	+	0.421973i
$423$		0			0
$424$	3.09922	+	10.8104i	0.150511	+	0.524999i
$425$	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
$430$	−9.64141	+	9.75391i	−0.464950	+	0.470375i
$431$	8.07284	−	13.9826i	0.388855	−	0.673517i	−0.603441	−	0.797408i	$-0.706204\pi$
$431$	8.07284	−	13.9826i	0.388855	−	0.673517i	0.992296	+	0.123891i	$0.0395374\pi$
$432$		0			0
$433$	11.6739			0.561014			0.280507	−	0.959852i	$-0.409497\pi$
$433$	11.6739			0.561014			0.280507	+	0.959852i	$0.409497\pi$
$434$	−0.840859	+	0.249169i	−0.0403625	+	0.0119605i
$435$		0			0
$436$	−0.155296	−	13.3863i	−0.00743733	−	0.641088i
$437$	11.7283	+	6.77136i	0.561043	+	0.323918i
$438$		0			0
$439$	−15.4132	+	8.89883i	−0.735633	+	0.424718i	−0.820479	−	0.571676i	$-0.806293\pi$
$439$	−15.4132	+	8.89883i	−0.735633	+	0.424718i	0.0848464	+	0.996394i	$0.472960\pi$
$440$	−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	0.620013	−	0.784592i	$-0.287127\pi$
$443$	−7.77644	−	13.4692i	−0.369470	−	0.639941i	−0.989483	+	0.144651i	$0.953794\pi$
$444$		0			0
$445$	9.31943	−	16.1417i	0.441783	−	0.765191i
$446$	6.57677	−	1.80319i	0.311419	−	0.0853835i
$447$		0			0
$448$	−17.7175	+	11.5797i	−0.837073	+	0.547091i
$449$		−	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
$452$	−16.0239	−	27.0252i	−0.753700	−	1.27116i
$453$		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	0.935668	−	0.352883i	$-0.114799\pi$
$457$	3.46804	+	6.00683i	0.162228	+	0.280988i	−0.773439	+	0.633870i	$0.781465\pi$
$458$	11.0540	−	11.1829i	0.516517	−	0.522544i
$459$		0			0
$460$	−26.6882	+	0.309613i	−1.24435	+	0.0144358i
$461$			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	$0.794589\pi$
$464$	−7.40871	−	4.05122i	−0.343941	−	0.188073i
$465$		0			0
$466$	−7.69443	−	7.60569i	−0.356438	−	0.352327i
$467$	−12.0722	−	20.9097i	−0.558636	−	0.967586i	−0.997611	−	0.0690867i	$-0.977991\pi$
$467$	−12.0722	−	20.9097i	−0.558636	−	0.967586i	0.438974	−	0.898500i	$-0.355342\pi$
$468$		0			0
$469$	−0.584995	−	28.5545i	−0.0270126	−	1.31852i
$470$	2.26416	−	8.65034i	0.104438	−	0.399010i
$471$		0			0
$472$	1.84536	−	0.529043i	0.0849395	−	0.0243512i
$473$	15.5180	+	8.95933i	0.713519	+	0.411950i
$474$		0			0
$475$		−	4.21008i		−	0.193172i
$476$	14.5960	+	23.5058i	0.669005	+	1.07739i
$477$		0			0
$478$	−2.09117	−	7.62711i	−0.0956479	−	0.348856i
$479$	20.5106	−	35.5254i	0.937154	−	1.62320i	0.166406	−	0.986057i	$-0.446784\pi$
$479$	20.5106	−	35.5254i	0.937154	−	1.62320i	0.770748	−	0.637140i	$-0.219883\pi$
$480$		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	$-0.444651\pi$
$487$	−13.0964	−	7.56120i	−0.593454	−	0.342631i	−0.766462	+	0.642290i	$0.777985\pi$
$488$	7.25455	−	29.0899i	0.328398	−	1.31684i
$489$		0			0
$490$	−14.0159	+	4.46755i	−0.633173	+	0.201824i
$491$	−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
$494$	−7.74277	−	7.65347i	−0.348364	−	0.344346i
$495$		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	$-0.678842\pi$
$499$	−1.47958	+	0.854238i	−0.0662353	+	0.0382409i	0.466517	+	0.884512i	$0.345509\pi$
$500$	11.8105	+	19.9191i	0.528181	+	0.890810i
$501$		0			0
$502$	−4.40739	−	16.0751i	−0.196711	−	0.717465i
$503$	−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
$506$	9.22052	+	33.6300i	0.409902	+	1.49503i
$507$		0			0
$508$	−0.432241	−	0.729001i	−0.0191776	−	0.0323442i
$509$	−8.98568	+	5.18789i	−0.398283	+	0.229949i	−0.685743	−	0.727844i	$-0.740523\pi$
$509$	−8.98568	+	5.18789i	−0.398283	+	0.229949i	0.287460	+	0.957793i	$0.407189\pi$
$510$		0			0
$511$	−9.26034	+	0.189717i	−0.409653	+	0.00839257i
$512$	−15.1433	+	16.8131i	−0.669247	+	0.743040i
$513$		0			0
$514$	30.4970	+	30.1453i	1.34517	+	1.32965i
$515$	0.340107	−	0.589082i	0.0149869	−	0.0259581i
$516$		0			0
$517$	−11.6826			−0.513799
$518$	−18.2358	−	4.37601i	−0.801234	−	0.192271i
$519$		0			0
$520$	20.8185	+	5.19179i	0.912950	+	0.227675i
$521$	1.18275	+	0.682859i	0.0518171	+	0.0299166i	0.525685	−	0.850679i	$-0.323809\pi$
$521$	1.18275	+	0.682859i	0.0518171	+	0.0299166i	−0.473868	+	0.880596i	$0.657142\pi$
$522$		0			0
$523$	−9.31535	+	5.37822i	−0.407332	+	0.235173i	−0.689643	−	0.724150i	$-0.742232\pi$
$523$	−9.31535	+	5.37822i	−0.407332	+	0.235173i	0.282311	+	0.959323i	$0.408899\pi$
$524$	−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
$530$	2.20939	+	8.05831i	0.0959698	+	0.350030i
$531$		0			0
$532$	7.97557	−	0.255982i	0.345785	−	0.0110982i
$533$		−	40.6797i		−	1.76203i
$534$		0			0
$535$	11.4480	+	6.60951i	0.494940	+	0.285754i
$536$	−8.41433	−	29.3501i	−0.363444	−	1.26773i
$537$		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	0.632621	−	0.774461i	$-0.281979\pi$
$541$	−8.24296	−	14.2772i	−0.354393	−	0.613826i	−0.987014	+	0.160635i	$0.948646\pi$
$542$	−8.38500	−	8.28829i	−0.360167	−	0.356012i
$543$		0			0
$544$	21.5134	+	20.3004i	0.922378	+	0.870371i
$545$		−	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	$0.972495\pi$
$548$	−9.04631	+	0.104947i	−0.386439	+	0.00448312i
$549$		0			0
$550$	7.62080	−	7.70973i	0.324952	−	0.328744i
$551$	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
$556$	−9.30615	−	15.6954i	−0.394669	−	0.665633i
$557$	−9.29133	−	5.36435i	−0.393686	−	0.227295i	0.290070	−	0.957005i	$-0.406321\pi$
$557$	−9.29133	−	5.36435i	−0.393686	−	0.227295i	−0.683756	+	0.729711i	$0.739655\pi$
$558$		0			0
$559$		−	33.3150i		−	1.40907i
$560$	−13.2631	+	8.45047i	−0.560466	+	0.357097i
$561$		0			0
$562$	−20.1918	+	5.53610i	−0.851739	+	0.233526i
$563$	7.14776	−	12.3803i	0.301242	−	0.521766i	−0.675176	−	0.737657i	$-0.735932\pi$
$563$	7.14776	−	12.3803i	0.301242	−	0.521766i	0.976418	+	0.215891i	$0.0692655\pi$
$564$		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	$-0.844164\pi$
$569$	−21.8632	+	12.6227i	−0.916552	+	0.529172i	−0.0340189	+	0.999421i	$0.510831\pi$
$570$		0			0
$571$	4.21404	+	2.43298i	0.176352	+	0.101817i	0.585578	−	0.810616i	$-0.300868\pi$
$571$	4.21404	+	2.43298i	0.176352	+	0.101817i	−0.409226	+	0.912433i	$0.634201\pi$
$572$	−0.325190	−	28.0309i	−0.0135969	−	1.17203i
$573$		0			0
$574$	21.6302	+	20.5220i	0.902828	+	0.856573i
$575$	25.0717			1.04556
$576$		0			0
$577$	−1.36238	+	2.35972i	−0.0567168	+	0.0982364i	−0.892990	−	0.450077i	$-0.851397\pi$
$577$	−1.36238	+	2.35972i	−0.0567168	+	0.0982364i	0.836273	+	0.548313i	$0.184730\pi$
$578$	10.2814	−	10.4014i	0.427649	−	0.432639i
$579$		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
$584$	−9.51836	+	2.72881i	−0.393872	+	0.112919i
$585$		0			0
$586$	20.5504	−	5.63441i	0.848928	−	0.232756i
$587$	−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
$590$	1.37557	−	0.377148i	0.0566314	−	0.0155269i
$591$		0			0
$592$	−20.0429	+	0.465102i	−0.823759	+	0.0191156i
$593$	−28.8809	+	16.6744i	−1.18600	+	0.684736i	−0.957394	−	0.288784i	$-0.906749\pi$
$593$	−28.8809	+	16.6744i	−1.18600	+	0.684736i	−0.228603	+	0.973520i	$0.573416\pi$
$594$		0			0
$595$	10.6415	+	17.5895i	0.436259	+	0.721097i
$596$	19.7579	−	35.1574i	0.809315	−	1.44010i
$597$		0			0
$598$	45.5776	−	46.1094i	1.86381	−	1.88555i
$599$	22.3518	−	38.7144i	0.913268	−	1.58183i	0.103852	−	0.994593i	$-0.466883\pi$
$599$	22.3518	−	38.7144i	0.913268	−	1.58183i	0.809417	−	0.587235i	$-0.199783\pi$
$600$		0			0
$601$	44.1640			1.80149			0.900745	−	0.434349i	$-0.143022\pi$
$601$	44.1640			1.80149			0.900745	+	0.434349i	$0.143022\pi$
$602$	17.7143	+	16.8067i	0.721980	+	0.684990i
$603$		0			0
$604$	14.6186	−	0.169592i	0.594824	−	0.00690062i
$605$	−4.45428	−	2.57168i	−0.181092	−	0.104554i
$606$		0			0
$607$	29.9771	−	17.3073i	1.21673	−	0.702481i	0.252515	−	0.967593i	$-0.418742\pi$
$607$	29.9771	−	17.3073i	1.21673	−	0.702481i	0.964218	+	0.265112i	$0.0854091\pi$
$608$	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	−0.986923	−	0.161194i	$-0.948465\pi$
$613$	−8.76124	+	15.1749i	−0.353863	+	0.612909i	0.633060	+	0.774103i	$0.281799\pi$
$614$	6.52779	−	1.78976i	0.263440	−	0.0722288i
$615$		0			0
$616$	15.0687	+	13.9681i	0.607134	+	0.562791i
$617$		−	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	$-0.586971\pi$
$619$	−30.8176	−	17.7925i	−1.23866	−	0.715142i	−0.968821	+	0.247762i	$0.920305\pi$
$620$	−0.599195	+	0.355276i	−0.0240642	+	0.0142682i
$621$		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
$626$	26.3952	−	26.7032i	1.05496	−	1.06727i
$627$		0			0
$628$	0.222809	+	19.2058i	0.00889104	+	0.766396i
$629$			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	$-0.261817\pi$
$632$	45.8732	+	11.4400i	1.82474	+	0.455060i
$633$		0			0
$634$	−9.70487	−	9.59294i	−0.385430	−	0.380984i
$635$	−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
$640$	−11.3957	+	12.3608i	−0.450454	+	0.488603i
$641$	26.4156	+	15.2511i	1.04335	+	0.602381i	0.920781	−	0.390079i	$-0.127552\pi$
$641$	26.4156	+	15.2511i	1.04335	+	0.602381i	0.122572	+	0.992460i	$0.460886\pi$
$642$		0			0
$643$		−	33.6298i		−	1.32623i	−0.748518	−	0.663114i	$-0.769234\pi$
$643$		−	33.6298i		−	1.32623i	0.748518	−	0.663114i	$-0.230766\pi$
$644$	1.52441	+	47.4958i	0.0600702	+	1.87160i
$645$		0			0
$646$	−2.94865	−	10.7546i	−0.116013	−	0.423134i
$647$	−5.27521	+	9.13694i	−0.207390	+	0.359210i	−0.950892	−	0.309524i	$-0.899830\pi$
$647$	−5.27521	+	9.13694i	−0.207390	+	0.359210i	0.743502	+	0.668734i	$0.233164\pi$
$648$		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	$-0.745944\pi$
$653$	−10.9097	+	6.29874i	−0.426931	+	0.246489i	0.271107	+	0.962549i	$0.412610\pi$
$654$		0			0
$655$	−10.1263	−	5.84643i	−0.395668	−	0.228439i
$656$	27.9670	+	15.2929i	1.09193	+	0.597086i
$657$		0			0
$658$	−15.4808	−	3.71490i	−0.603505	−	0.144822i
$659$	−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	−0.466631	−	0.884452i	$-0.654533\pi$
$661$	13.6942	−	23.7190i	0.532642	−	0.922563i	0.999274	−	0.0381112i	$-0.0121341\pi$
$662$	−1.15251	−	1.13922i	−0.0447936	−	0.0442769i
$663$		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
$668$	−19.5670	+	11.6017i	−0.757068	+	0.448883i
$669$		0			0
$670$	−5.99847	−	21.8782i	−0.231741	−	0.845229i
$671$	−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	$0.546786\pi$
$674$	0.707506	+	2.58048i	0.0272521	+	0.0993965i
$675$		0			0
$676$	−22.4672	+	13.3213i	−0.864123	+	0.512358i
$677$	−27.4847	+	15.8683i	−1.05632	+	0.609868i	−0.924413	−	0.381394i	$-0.875444\pi$
$677$	−27.4847	+	15.8683i	−1.05632	+	0.609868i	−0.131910	+	0.991262i	$0.542111\pi$
$678$		0			0
$679$	19.4562	+	32.1594i	0.746661	+	1.23416i
$680$	15.8084	+	15.2676i	0.606225	+	0.585486i
$681$		0			0
$682$	0.647278	+	0.639813i	0.0247856	+	0.0244997i
$683$	13.5207	−	23.4185i	0.517355	−	0.896085i	−0.482442	−	0.875928i	$-0.660250\pi$
$683$	13.5207	−	23.4185i	0.517355	−	0.896085i	0.999797	−	0.0201567i	$-0.00641651\pi$
$684$		0			0
$685$	−6.72187			−0.256830
$686$	8.46371	+	24.7864i	0.323146	+	0.946349i
$687$		0			0
$688$	22.9038	+	12.5242i	0.873200	+	0.477482i
$689$	−17.5778	−	10.1485i	−0.669660	−	0.386629i
$690$		0			0
$691$	1.85489	−	1.07092i	0.0705634	−	0.0407398i	−0.464303	−	0.885676i	$-0.653695\pi$
$691$	1.85489	−	1.07092i	0.0705634	−	0.0407398i	0.534867	+	0.844937i	$0.320362\pi$
$692$	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
$698$	8.54239	+	31.1566i	0.323334	+	1.17930i
$699$		0			0
$700$	12.5501	−	7.79300i	0.474348	−	0.294548i
$701$			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
$704$	19.3933	+	10.3142i	0.730913	+	0.388731i
$705$		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	0.951207	+	0.308553i	$0.0998447\pi$
$709$	19.7791	+	34.2583i	0.742818	+	1.28660i	−0.208389	+	0.978046i	$0.566822\pi$
$710$	1.97479	+	1.95202i	0.0741127	+	0.0732579i
$711$		0			0
$712$	−34.4225	−	8.58442i	−1.29004	−	0.321715i
$713$			2.10492i			0.0788298i
$714$		0			0
$715$		−	20.8284i		−	0.778939i
$716$	0.222954	+	19.2184i	0.00833219	+	0.718224i
$717$		0			0
$718$	23.5440	−	23.8188i	0.878656	−	0.888908i
$719$	−20.7863	−	36.0030i	−0.775199	−	1.34268i	−0.934683	−	0.355483i	$-0.884316\pi$
$719$	−20.7863	−	36.0030i	−0.775199	−	1.34268i	0.159484	−	0.987201i	$-0.449017\pi$
$720$		0			0
$721$	−1.06101	−	0.583933i	−0.0395142	−	0.0217468i
$722$	22.8831	+	5.98947i	0.851621	+	0.222905i
$723$		0			0
$724$	−32.7814	+	19.4369i	−1.21831	+	0.722365i
$725$	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	$-0.270844\pi$
$728$	8.48255	−	37.2477i	0.314384	−	1.38049i
$729$		0			0
$730$	−7.09520	+	1.94533i	−0.262605	+	0.0719999i
$731$	17.0622	−	29.5527i	0.631069	−	1.09304i
$732$		0			0
$733$	−4.10278	−	7.10622i	−0.151539	−	0.262474i	0.780254	−	0.625463i	$-0.215090\pi$
$733$	−4.10278	−	7.10622i	−0.151539	−	0.262474i	−0.931794	+	0.362989i	$0.881756\pi$
$734$	−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	$-0.142403\pi$
$739$	26.5794	+	15.3456i	0.977739	+	0.564498i	0.0761523	+	0.997096i	$0.475736\pi$
$740$	−14.8949	+	0.172798i	−0.547548	+	0.00635216i
$741$		0			0
$742$	14.2638	−	4.22675i	0.523641	−	0.155169i
$743$	−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
$746$	−37.0198	+	37.4517i	−1.35539	+	1.37121i
$747$		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	$-0.952432\pi$
$751$	−37.1150	+	21.4284i	−1.35435	+	0.781932i	−0.365491	+	0.930815i	$0.619099\pi$
$752$	−17.0149	+	0.394837i	−0.620471	+	0.0143982i
$753$		0			0
$754$	14.6977	−	4.02976i	0.535260	−	0.146755i
$755$	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	$0.328957\pi$
$758$	40.7253	−	11.1659i	1.47921	−	0.405564i
$759$		0			0
$760$	6.09284	−	1.74675i	0.221010	−	0.0633612i
$761$	25.6364	−	14.8012i	0.929319	−	0.536542i	0.0427226	−	0.999087i	$-0.486397\pi$
$761$	25.6364	−	14.8012i	0.929319	−	0.536542i	0.886596	+	0.462545i	$0.153063\pi$
$762$		0			0
$763$	−17.7059	+	0.362741i	−0.640997	+	0.0131321i
$764$	−29.8607	−	16.7813i	−1.08032	−	0.607125i
$765$		0			0
$766$	12.3679	−	12.5123i	0.446872	−	0.452086i
$767$	−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	$0.876060\pi$
$770$	11.0749	+	10.5075i	0.399112	+	0.378664i
$771$		0			0
$772$	0.108090	+	9.31724i	0.00389025	+	0.335335i
$773$	39.3596	+	22.7243i	1.41567	+	0.817335i	0.995914	−	0.0903047i	$-0.0287841\pi$
$773$	39.3596	+	22.7243i	1.41567	+	0.817335i	0.419751	+	0.907639i	$0.362117\pi$
$774$		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
$782$	64.0453	−	17.5597i	2.29025	−	0.627932i
$783$		0			0
$784$	15.5261	+	23.3010i	0.554505	+	0.832180i
$785$			14.2709i			0.509351i
$786$		0			0
$787$	−40.2785	−	23.2548i	−1.43577	−	0.828943i	−0.438220	−	0.898868i	$-0.644391\pi$
$787$	−40.2785	−	23.2548i	−1.43577	−	0.828943i	−0.997552	+	0.0699244i	$0.977724\pi$
$788$	23.6261	+	39.8468i	0.841644	+	1.41948i
$789$		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
$794$	−15.4571	+	15.6375i	−0.548553	+	0.554954i
$795$		0			0
$796$	4.18999	−	0.0486085i	0.148510	−	0.00172288i
$797$		−	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
$800$	10.8387	−	11.4863i	0.383205	−	0.406102i
$801$		0			0
$802$	−8.71148	−	8.61101i	−0.307613	−	0.304065i
$803$	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
$808$	−8.77008	−	30.5909i	−0.308530	−	1.07619i
$809$	24.0673	+	13.8953i	0.846160	+	0.488531i	0.859354	−	0.511382i	$-0.170866\pi$
$809$	24.0673	+	13.8953i	0.846160	+	0.488531i	−0.0131930	+	0.999913i	$0.504200\pi$
$810$		0			0
$811$			24.9697i			0.876804i	0.898779	+	0.438402i	$0.144455\pi$
$811$			24.9697i			0.876804i	−0.898779	+	0.438402i	$0.855545\pi$
$812$	−5.27199	+	9.84802i	−0.185010	+	0.345598i
$813$		0			0
$814$	5.14605	+	18.7692i	0.180369	+	0.657859i
$815$	−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	$-0.663746\pi$
$821$	0.455422	−	0.262938i	0.0158943	−	0.00917659i	0.507926	+	0.861401i	$0.330412\pi$
$822$		0			0
$823$	−15.0707	−	8.70110i	−0.525333	−	0.303301i	0.213781	−	0.976882i	$-0.431422\pi$
$823$	−15.0707	−	8.70110i	−0.525333	−	0.303301i	−0.739114	+	0.673580i	$0.764755\pi$
$824$	−1.25623	−	0.313283i	−0.0437628	−	0.0109137i
$825$		0			0
$826$	−0.721517	−	2.43487i	−0.0251048	−	0.0847198i
$827$	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	−0.945747	−	0.324903i	$-0.894668\pi$
$829$	−5.51372	+	9.55004i	−0.191499	+	0.331687i	0.754248	+	0.656590i	$0.228002\pi$
$830$	−22.8547	−	22.5911i	−0.793298	−	0.784148i
$831$		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
$836$	−4.22346	−	7.12312i	−0.146071	−	0.246358i
$837$		0			0
$838$	−4.62851	−	16.8815i	−0.159889	−	0.583163i
$839$	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
$842$	8.29960	+	30.2711i	0.286023	+	1.04321i
$843$		0			0
$844$	23.6454	+	39.8794i	0.813908	+	1.37270i
$845$	−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
$850$	−14.6825	−	14.5131i	−0.503605	−	0.497796i
$851$	−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	$0.470946\pi$
$854$	−38.5661	−	9.25463i	−1.31970	−	0.316687i
$855$		0			0
$856$	6.08823	−	24.4131i	0.208091	−	0.834422i
$857$	31.3685	+	18.1106i	1.07153	+	0.618647i	0.928599	−	0.371086i	$-0.121014\pi$
$857$	31.3685	+	18.1106i	1.07153	+	0.618647i	0.142930	+	0.989733i	$0.454348\pi$
$858$		0			0
$859$	25.1177	−	14.5017i	0.857004	−	0.494791i	−0.00600391	−	0.999982i	$-0.501911\pi$
$859$	25.1177	−	14.5017i	0.857004	−	0.494791i	0.863008	+	0.505191i	$0.168578\pi$
$860$	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	0.727640	−	0.685960i	$-0.240617\pi$
$863$	−6.76369	−	11.7151i	−0.230239	−	0.398785i	−0.957878	+	0.287174i	$0.907284\pi$
$864$		0			0
$865$	6.33001	−	10.9639i	0.215227	−	0.372784i
$866$	−4.36538	−	15.9218i	−0.148342	−	0.541046i
$867$		0			0
$868$	0.654270	+	1.05366i	0.0222074	+	0.0357634i
$869$		−	45.8952i		−	1.55689i
$870$		0			0
$871$	47.7235	+	27.5532i	1.61705	+	0.933603i
$872$	−18.1992	+	5.21752i	−0.616304	+	0.176687i
$873$		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	0.568460	−	0.822711i	$-0.307539\pi$
$877$	−12.6825	−	21.9668i	−0.428258	−	0.741765i	−0.996718	+	0.0809459i	$0.974206\pi$
$878$	17.9006	+	17.6941i	0.604116	+	0.597148i
$879$		0			0
$880$	14.3194	+	7.83011i	0.482706	+	0.263953i
$881$		−	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	$-0.118041\pi$
$884$	−53.3824	+	0.619294i	−1.79544	+	0.0208291i
$885$		0			0
$886$	−15.4624	+	15.6428i	−0.519470	+	0.525531i
$887$	−6.11983	−	10.5999i	−0.205484	−	0.355908i	0.744803	−	0.667284i	$-0.232543\pi$
$887$	−6.11983	−	10.5999i	−0.205484	−	0.355908i	−0.950287	+	0.311376i	$0.899210\pi$
$888$		0			0
$889$	−0.959260	+	0.580346i	−0.0321726	+	0.0194642i
$890$	−25.5003	−	6.67450i	−0.854772	−	0.223730i
$891$		0			0
$892$	−4.91867	−	8.29563i	−0.164689	−	0.277758i
$893$	5.55680	+	3.20822i	0.185951	+	0.107359i
$894$		0			0
$895$			14.2802i			0.477336i
$896$	22.4187	+	19.8344i	0.748955	+	0.662620i
$897$		0			0
$898$	−44.2124	+	12.1220i	−1.47539	+	0.404515i
$899$	−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	$-0.114463\pi$
$907$	33.1072	+	19.1145i	1.09931	+	0.634685i	0.163268	+	0.986582i	$0.447797\pi$
$908$	0.238666	+	20.5727i	0.00792041	+	0.682729i
$909$		0			0
$910$	6.62316	−	27.6002i	0.219556	−	0.914937i
$911$	−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
$914$	6.89574	−	6.97620i	0.228091	−	0.230752i
$915$		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	$-0.601650\pi$
$919$	10.6505	−	6.14908i	0.351328	−	0.202839i	0.665270	+	0.746603i	$0.268316\pi$
$920$	10.4021	+	36.2838i	0.342949	+	1.19624i
$921$		0			0
$922$	45.0257	−	12.3449i	1.48284	−	0.406559i
$923$	−6.74501			−0.222015
$924$		0			0
$925$	13.9927			0.460077
$926$	35.3019	−	9.67892i	1.16009	−	0.318069i
$927$		0			0
$928$	−2.75495	+	11.6195i	−0.0904356	+	0.381429i
$929$	−18.6376	+	10.7604i	−0.611480	+	0.353038i	−0.773545	−	0.633742i	$-0.781518\pi$
$929$	−18.6376	+	10.7604i	−0.611480	+	0.353038i	0.162064	+	0.986780i	$0.448185\pi$
$930$		0			0
$931$	−0.432345	−	10.5473i	−0.0141695	−	0.345673i
$932$	−7.49596	+	13.3384i	−0.245538	+	0.436913i
$933$		0			0
$934$	−24.0040	+	24.2841i	−0.785435	+	0.794600i
$935$	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	$0.399381\pi$
$938$	−38.7261	+	11.4756i	−1.26445	+	0.374691i
$939$		0			0
$940$	−12.6447	+	0.146692i	−0.412424	+	0.00478457i
$941$	−22.4940	−	12.9869i	−0.733283	−	0.423361i	0.0863390	−	0.996266i	$-0.472483\pi$
$941$	−22.4940	−	12.9869i	−0.733283	−	0.423361i	−0.819622	+	0.572905i	$0.805817\pi$
$942$		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	0.808683	−	0.588245i	$-0.200181\pi$
$947$	−3.23409	−	5.60161i	−0.105094	−	0.182028i	−0.913777	+	0.406217i	$0.866848\pi$
$948$		0			0
$949$	8.93561	−	15.4769i	0.290062	−	0.502403i
$950$	−5.74204	+	1.57433i	−0.186296	+	0.0510779i
$951$		0			0
$952$	26.6010	−	28.6969i	0.862143	−	0.930073i
$953$			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
$956$	−9.62049	+	5.70420i	−0.311149	+	0.184487i
$957$		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
$962$	25.4372	−	25.7340i	0.820129	−	0.829698i
$963$		0			0
$964$	−0.0961876	−	8.29125i	−0.00309799	−	0.267043i
$965$			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	$0.940478\pi$
$968$	−2.36885	+	9.49884i	−0.0761379	+	0.305304i
$969$		0			0
$970$	21.2330	+	20.9881i	0.681750	+	0.673887i
$971$	−27.0715	−	46.8892i	−0.868766	−	1.50475i	−0.863259	−	0.504762i	$-0.831580\pi$
$971$	−27.0715	−	46.8892i	−0.868766	−	1.50475i	−0.00550751	−	0.999985i	$-0.501753\pi$
$972$		0			0
$973$	−20.6529	+	12.4948i	−0.662100	+	0.400566i
$974$	−5.41527	+	20.6893i	−0.173516	+	0.662929i
$975$		0			0
$976$	−42.3879	+	0.983626i	−1.35680	+	0.0314851i
$977$	−20.1006	−	11.6051i	−0.643076	−	0.371280i	0.142722	−	0.989763i	$-0.454414\pi$
$977$	−20.1006	−	11.6051i	−0.643076	−	0.371280i	−0.785798	+	0.618483i	$0.787748\pi$
$978$		0			0
$979$			34.4390i			1.10068i
$980$	11.3343	+	17.4454i	0.362062	+	0.557272i
$981$		0			0
$982$	13.8091	+	50.3660i	0.440667	+	1.60724i
$983$	−18.5294	+	32.0939i	−0.590996	+	1.02363i	0.403103	+	0.915155i	$0.367932\pi$
$983$	−18.5294	+	32.0939i	−0.590996	+	1.02363i	−0.994099	+	0.108480i	$0.965402\pi$
$984$		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	$-0.295925\pi$
$991$	6.39309	+	3.69105i	0.203083	+	0.117250i	−0.395010	+	0.918677i	$0.629259\pi$
$992$	0.964345	+	0.909972i	0.0306180	+	0.0288916i
$993$		0			0
$994$	3.40272	−	3.58646i	0.107928	−	0.113756i
$995$	3.11338			0.0987008
$996$		0			0
$997$	−3.53100	+	6.11587i	−0.111828	+	0.193692i	−0.916507	−	0.400018i	$-0.869004\pi$
$997$	−3.53100	+	6.11587i	−0.111828	+	0.193692i	0.804679	+	0.593710i	$0.202337\pi$
$998$	1.71836	+	1.69854i	0.0543936	+	0.0537663i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.4	✓	28	7.2	even	3
756.2.be.c.107.11	yes	28	21.2	odd	6
756.2.be.c.431.4	yes	28	12.11	even	2
756.2.be.c.431.11	yes	28	4.3	odd	2
756.2.be.d.107.6	yes	28	84.23	even	6	inner
756.2.be.d.107.9	yes	28	28.23	odd	6	inner
756.2.be.d.431.6	yes	28	1.1	even	1	trivial
756.2.be.d.431.9	yes	28	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.373943 - 1.36388i) q^{2} +(-1.72033 + 1.02003i) q^{4} +(-1.28692 + 0.743002i) q^{5} +(1.36953 + 2.26371i) q^{7} +(2.03450 + 1.96490i) q^{8} +(1.49460 + 1.47736i) q^{10} +(1.37284 - 2.37783i) q^{11} -5.10488 q^{13} +(2.57530 - 2.71437i) q^{14} +(1.91910 - 3.50957i) q^{16} +(-4.52837 - 2.61446i) q^{17} +(-1.30598 + 0.754009i) q^{19} +(1.45605 - 2.59090i) q^{20} +(-3.75644 - 0.983219i) q^{22} +(-4.49024 - 7.77732i) q^{23} +(-1.39590 + 2.41776i) q^{25} +(1.90893 + 6.96244i) q^{26} +(-4.66509 - 2.49738i) q^{28} -2.11100i q^{29} +(-0.202986 - 0.117194i) q^{31} +(-5.50426 - 1.30504i) q^{32} +(-1.87245 + 7.15381i) q^{34} +(-3.44441 - 1.89564i) q^{35} +(-2.50604 - 4.34059i) q^{37} +(1.51674 + 1.49925i) q^{38} +(-4.07815 - 1.01702i) q^{40} +7.96878i q^{41} +6.52611i q^{43} +(0.0637017 + 5.49100i) q^{44} +(-8.92824 + 9.03242i) q^{46} +(-2.12744 - 3.68483i) q^{47} +(-3.24878 + 6.20044i) q^{49} +(3.81952 + 0.999730i) q^{50} +(8.78210 - 5.20710i) q^{52} +(3.44333 + 1.98801i) q^{53} +4.08010i q^{55} +(-1.66165 + 7.29650i) q^{56} +(-2.87915 + 0.789394i) q^{58} +(0.339358 - 0.587784i) q^{59} +(-5.29992 - 9.17972i) q^{61} +(-0.0839334 + 0.320672i) q^{62} +(0.278358 + 7.99516i) q^{64} +(6.56955 - 3.79293i) q^{65} +(-9.34860 - 5.39742i) q^{67} +(10.4571 - 0.121314i) q^{68} +(-1.29742 + 5.40662i) q^{70} +1.32129 q^{71} +(-1.75041 + 3.03179i) q^{73} +(-4.98292 + 5.04106i) q^{74} +(1.47762 - 2.62928i) q^{76} +(7.26288 - 0.148795i) q^{77} +(14.4759 - 8.35768i) q^{79} +(0.137896 + 5.94241i) q^{80} +(10.8685 - 2.97987i) q^{82} -15.2915 q^{83} +7.77018 q^{85} +(8.90083 - 2.44039i) q^{86} +(7.46525 - 2.14020i) q^{88} +(-10.8625 + 6.27147i) q^{89} +(-6.99129 - 11.5560i) q^{91} +(15.6578 + 8.79944i) q^{92} +(-4.23013 + 4.27949i) q^{94} +(1.12046 - 1.94069i) q^{95} +14.2065 q^{97} +(9.67151 + 2.11233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64}+ \cdots - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Introduction

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