LMFDB - Embedded newform 756.2.n.a.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	756.199
Dual form			756.2.n.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -3.46410i q^{5} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -3.46410i q^{5} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.26795 + 4.73205i) q^{10} -2.00000i q^{11} +(4.50000 + 2.59808i) q^{13} +(-1.63397 + 3.36603i) q^{14} +(2.00000 - 3.46410i) q^{16} +(4.50000 + 2.59808i) q^{17} +(-0.866025 - 1.50000i) q^{19} +(-3.46410 - 6.00000i) q^{20} +(0.732051 + 2.73205i) q^{22} -4.00000i q^{23} -7.00000 q^{25} +(-7.09808 - 1.90192i) q^{26} +(1.00000 - 5.19615i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-2.59808 - 4.50000i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-7.09808 - 1.90192i) q^{34} +(-6.92820 - 6.00000i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.73205 + 1.73205i) q^{38} +(6.92820 + 6.92820i) q^{40} +(-1.50000 - 0.866025i) q^{41} +(-9.52628 + 5.50000i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.46410 + 5.46410i) q^{46} +(0.866025 - 1.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(9.56218 - 2.56218i) q^{50} +10.3923 q^{52} +(0.500000 - 0.866025i) q^{53} -6.92820 q^{55} +(0.535898 + 7.46410i) q^{56} +(-5.00000 - 5.00000i) q^{58} +(-0.866025 - 1.50000i) q^{59} +(4.50000 + 2.59808i) q^{61} +(5.19615 + 5.19615i) q^{62} -8.00000i q^{64} +(9.00000 - 15.5885i) q^{65} +(7.79423 - 4.50000i) q^{67} +10.3923 q^{68} +(11.6603 + 5.66025i) q^{70} +2.00000i q^{71} +(-10.5000 - 6.06218i) q^{73} +(3.00000 + 3.00000i) q^{74} +(-3.00000 - 1.73205i) q^{76} +(-4.00000 - 3.46410i) q^{77} +(2.59808 + 1.50000i) q^{79} +(-12.0000 - 6.92820i) q^{80} +(2.36603 + 0.633975i) q^{82} +(2.59808 + 4.50000i) q^{83} +(9.00000 - 15.5885i) q^{85} +(11.0000 - 11.0000i) q^{86} +(4.00000 + 4.00000i) q^{88} +(-7.50000 + 4.33013i) q^{89} +(12.9904 - 4.50000i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(-0.633975 + 2.36603i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(1.50000 - 0.866025i) q^{97} +(3.90192 + 9.09808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 8 * q^8	$ 4 q - 2 q^{2} - 8 q^{8} + 12 q^{10} + 18 q^{13} - 10 q^{14} + 8 q^{16} + 18 q^{17} - 4 q^{22} - 28 q^{25} - 18 q^{26} + 4 q^{28} + 10 q^{29} + 8 q^{32} - 18 q^{34} - 6 q^{37} - 6 q^{41} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 14 q^{50} + 2 q^{53} + 16 q^{56} - 20 q^{58} + 18 q^{61} + 36 q^{65} + 12 q^{70} - 42 q^{73} + 12 q^{74} - 12 q^{76} - 16 q^{77} - 48 q^{80} + 6 q^{82} + 36 q^{85} + 44 q^{86} + 16 q^{88} - 30 q^{89} - 16 q^{92} - 6 q^{94} + 6 q^{97} + 26 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 8 * q^8 + 12 * q^10 + 18 * q^13 - 10 * q^14 + 8 * q^16 + 18 * q^17 - 4 * q^22 - 28 * q^25 - 18 * q^26 + 4 * q^28 + 10 * q^29 + 8 * q^32 - 18 * q^34 - 6 * q^37 - 6 * q^41 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 14 * q^50 + 2 * q^53 + 16 * q^56 - 20 * q^58 + 18 * q^61 + 36 * q^65 + 12 * q^70 - 42 * q^73 + 12 * q^74 - 12 * q^76 - 16 * q^77 - 48 * q^80 + 6 * q^82 + 36 * q^85 + 44 * q^86 + 16 * q^88 - 30 * q^89 - 16 * q^92 - 6 * q^94 + 6 * q^97 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$		−	3.46410i		−	1.54919i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$		−	3.46410i		−	1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$		0			0
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	1.26795	+	4.73205i	0.400961	+	1.49641i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$	4.50000	+	2.59808i	1.24808	+	0.720577i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	4.50000	+	2.59808i	1.24808	+	0.720577i	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.63397	+	3.36603i	−0.436698	+	0.899608i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	4.50000	+	2.59808i	1.09141	+	0.630126i	0.933952	−	0.357400i	$-0.116337\pi$
$17$	4.50000	+	2.59808i	1.09141	+	0.630126i	0.157459	+	0.987526i	$0.449670\pi$
$18$		0			0
$19$	−0.866025	−	1.50000i	−0.198680	−	0.344124i	0.749421	−	0.662094i	$-0.230332\pi$
$19$	−0.866025	−	1.50000i	−0.198680	−	0.344124i	−0.948101	+	0.317970i	$0.896999\pi$
$20$	−3.46410	−	6.00000i	−0.774597	−	1.34164i
$21$		0			0
$22$	0.732051	+	2.73205i	0.156074	+	0.582475i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	−7.00000			−1.40000
$26$	−7.09808	−	1.90192i	−1.39205	−	0.372998i
$27$		0			0
$28$	1.00000	−	5.19615i	0.188982	−	0.981981i
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$	−2.59808	−	4.50000i	−0.466628	−	0.808224i	0.532645	−	0.846339i	$-0.321198\pi$
$31$	−2.59808	−	4.50000i	−0.466628	−	0.808224i	−0.999273	+	0.0381148i	$0.987865\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		0			0
$34$	−7.09808	−	1.90192i	−1.21731	−	0.326177i
$35$	−6.92820	−	6.00000i	−1.17108	−	1.01419i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	1.73205	+	1.73205i	0.280976	+	0.280976i
$39$		0			0
$40$	6.92820	+	6.92820i	1.09545	+	1.09545i
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	0.378275	−	0.925693i	$-0.376517\pi$
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	−0.612536	+	0.790443i	$0.709851\pi$
$42$		0			0
$43$	−9.52628	+	5.50000i	−1.45274	+	0.838742i	−0.998636	−	0.0522047i	$-0.983375\pi$
$43$	−9.52628	+	5.50000i	−1.45274	+	0.838742i	−0.454108	+	0.890947i	$0.650042\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$		0			0
$46$	1.46410	+	5.46410i	0.215870	+	0.805638i
$47$	0.866025	−	1.50000i	0.126323	−	0.218797i	−0.795926	−	0.605393i	$-0.793016\pi$
$47$	0.866025	−	1.50000i	0.126323	−	0.218797i	0.922249	+	0.386596i	$0.126349\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	9.56218	−	2.56218i	1.35230	−	0.362347i
$51$		0			0
$52$	10.3923			1.44115
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$		0			0
$55$	−6.92820			−0.934199
$56$	0.535898	+	7.46410i	0.0716124	+	0.997433i
$57$		0			0
$58$	−5.00000	−	5.00000i	−0.656532	−	0.656532i
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	0.804130	−	0.594454i	$-0.202632\pi$
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	−0.916877	+	0.399170i	$0.869298\pi$
$60$		0			0
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	0.759608	−	0.650381i	$-0.225391\pi$
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	−0.183442	+	0.983030i	$0.558724\pi$
$62$	5.19615	+	5.19615i	0.659912	+	0.659912i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	9.00000	−	15.5885i	1.11631	−	1.93351i
$66$		0			0
$67$	7.79423	−	4.50000i	0.952217	−	0.549762i	0.0584478	−	0.998290i	$-0.481385\pi$
$67$	7.79423	−	4.50000i	0.952217	−	0.549762i	0.893769	+	0.448528i	$0.148052\pi$
$68$	10.3923			1.26025
$69$		0			0
$70$	11.6603	+	5.66025i	1.39367	+	0.676530i
$71$			2.00000i			0.237356i	0.992933	+	0.118678i	$0.0378657\pi$
$71$			2.00000i			0.237356i	−0.992933	+	0.118678i	$0.962134\pi$
$72$		0			0
$73$	−10.5000	−	6.06218i	−1.22893	−	0.709524i	−0.262126	−	0.965034i	$-0.584423\pi$
$73$	−10.5000	−	6.06218i	−1.22893	−	0.709524i	−0.966807	+	0.255510i	$0.917757\pi$
$74$	3.00000	+	3.00000i	0.348743	+	0.348743i
$75$		0			0
$76$	−3.00000	−	1.73205i	−0.344124	−	0.198680i
$77$	−4.00000	−	3.46410i	−0.455842	−	0.394771i
$78$		0			0
$79$	2.59808	+	1.50000i	0.292306	+	0.168763i	0.638982	−	0.769222i	$-0.279356\pi$
$79$	2.59808	+	1.50000i	0.292306	+	0.168763i	−0.346675	+	0.937985i	$0.612689\pi$
$80$	−12.0000	−	6.92820i	−1.34164	−	0.774597i
$81$		0			0
$82$	2.36603	+	0.633975i	0.261284	+	0.0700108i
$83$	2.59808	+	4.50000i	0.285176	+	0.493939i	0.972652	−	0.232268i	$-0.0746146\pi$
$83$	2.59808	+	4.50000i	0.285176	+	0.493939i	−0.687476	+	0.726207i	$0.741281\pi$
$84$		0			0
$85$	9.00000	−	15.5885i	0.976187	−	1.69081i
$86$	11.0000	−	11.0000i	1.18616	−	1.18616i
$87$		0			0
$88$	4.00000	+	4.00000i	0.426401	+	0.426401i
$89$	−7.50000	+	4.33013i	−0.794998	+	0.458993i	−0.841719	−	0.539915i	$-0.818456\pi$
$89$	−7.50000	+	4.33013i	−0.794998	+	0.458993i	0.0467209	+	0.998908i	$0.485123\pi$
$90$		0			0
$91$	12.9904	−	4.50000i	1.36176	−	0.471728i
$92$	−4.00000	−	6.92820i	−0.417029	−	0.722315i
$93$		0			0
$94$	−0.633975	+	2.36603i	−0.0653895	+	0.244037i
$95$	−5.19615	+	3.00000i	−0.533114	+	0.307794i
$96$		0			0
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	−0.421912	−	0.906637i	$-0.638641\pi$
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	0.574214	+	0.818705i	$0.305308\pi$
$98$	3.90192	+	9.09808i	0.394154	+	0.919044i
$99$		0			0
$100$	−12.1244	+	7.00000i	−1.21244	+	0.700000i
$101$			17.3205i			1.72345i	0.507371	+	0.861727i	$0.330617\pi$
$101$			17.3205i			1.72345i	−0.507371	+	0.861727i	$0.669383\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−14.1962	+	3.80385i	−1.39205	+	0.372998i
$105$		0			0
$106$	−0.366025	+	1.36603i	−0.0355515	+	0.132680i
$107$	6.06218	−	3.50000i	0.586053	−	0.338358i	−0.177482	−	0.984124i	$-0.556795\pi$
$107$	6.06218	−	3.50000i	0.586053	−	0.338358i	0.763535	+	0.645766i	$0.223462\pi$
$108$		0			0
$109$	−1.50000	+	2.59808i	−0.143674	+	0.248851i	−0.928877	−	0.370387i	$-0.879225\pi$
$109$	−1.50000	+	2.59808i	−0.143674	+	0.248851i	0.785203	+	0.619238i	$0.212558\pi$
$110$	9.46410	−	2.53590i	0.902367	−	0.241788i
$111$		0			0
$112$	−3.46410	−	10.0000i	−0.327327	−	0.944911i
$113$	9.50000	−	16.4545i	0.893685	−	1.54791i	0.0582609	−	0.998301i	$-0.481444\pi$
$113$	9.50000	−	16.4545i	0.893685	−	1.54791i	0.835424	−	0.549606i	$-0.185222\pi$
$114$		0			0
$115$	−13.8564			−1.29212
$116$	8.66025	+	5.00000i	0.804084	+	0.464238i
$117$		0			0
$118$	1.73205	+	1.73205i	0.159448	+	0.159448i
$119$	12.9904	−	4.50000i	1.19083	−	0.412514i
$120$		0			0
$121$	7.00000			0.636364
$122$	−7.09808	−	1.90192i	−0.642630	−	0.172192i
$123$		0			0
$124$	−9.00000	−	5.19615i	−0.808224	−	0.466628i
$125$			6.92820i			0.619677i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$		0			0
$130$	−6.58846	+	24.5885i	−0.577846	+	2.15655i
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	−4.50000	−	0.866025i	−0.390199	−	0.0750939i
$134$	−9.00000	+	9.00000i	−0.777482	+	0.777482i
$135$		0			0
$136$	−14.1962	+	3.80385i	−1.21731	+	0.326177i
$137$	−8.00000			−0.683486			−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000			−0.683486			−0.341743	+	0.939793i	$0.611017\pi$
$138$		0			0
$139$	−11.2583	+	19.5000i	−0.954919	+	1.65397i	−0.220366	+	0.975417i	$0.570725\pi$
$139$	−11.2583	+	19.5000i	−0.954919	+	1.65397i	−0.734553	+	0.678551i	$0.762608\pi$
$140$	−18.0000	−	3.46410i	−1.52128	−	0.292770i
$141$		0			0
$142$	−0.732051	−	2.73205i	−0.0614323	−	0.229269i
$143$	5.19615	−	9.00000i	0.434524	−	0.752618i
$144$		0			0
$145$	15.0000	−	8.66025i	1.24568	−	0.719195i
$146$	16.5622	+	4.43782i	1.37070	+	0.367277i
$147$		0			0
$148$	−5.19615	−	3.00000i	−0.427121	−	0.246598i
$149$	4.00000			0.327693			0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000			0.327693			0.163846	+	0.986486i	$0.447610\pi$
$150$		0			0
$151$			14.0000i			1.13930i	0.821886	+	0.569652i	$0.192922\pi$
$151$			14.0000i			1.13930i	−0.821886	+	0.569652i	$0.807078\pi$
$152$	4.73205	+	1.26795i	0.383820	+	0.102844i
$153$		0			0
$154$	6.73205	+	3.26795i	0.542484	+	0.263339i
$155$	−15.5885	+	9.00000i	−1.25210	+	0.722897i
$156$		0			0
$157$	−10.5000	+	6.06218i	−0.837991	+	0.483814i	−0.856581	−	0.516013i	$-0.827416\pi$
$157$	−10.5000	+	6.06218i	−0.837991	+	0.483814i	0.0185897	+	0.999827i	$0.494082\pi$
$158$	−4.09808	−	1.09808i	−0.326025	−	0.0873583i
$159$		0			0
$160$	18.9282	+	5.07180i	1.49641	+	0.400961i
$161$	−8.00000	−	6.92820i	−0.630488	−	0.546019i
$162$		0			0
$163$	7.79423	−	4.50000i	0.610491	−	0.352467i	−0.162667	−	0.986681i	$-0.552009\pi$
$163$	7.79423	−	4.50000i	0.610491	−	0.352467i	0.773158	+	0.634214i	$0.218676\pi$
$164$	−3.46410			−0.270501
$165$		0			0
$166$	−5.19615	−	5.19615i	−0.403300	−	0.403300i
$167$	2.59808	−	4.50000i	0.201045	−	0.348220i	−0.747820	−	0.663901i	$-0.768900\pi$
$167$	2.59808	−	4.50000i	0.201045	−	0.348220i	0.948865	+	0.315681i	$0.102233\pi$
$168$		0			0
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$	−6.58846	+	24.5885i	−0.505312	+	1.88585i
$171$		0			0
$172$	−11.0000	+	19.0526i	−0.838742	+	1.45274i
$173$	16.5000	+	9.52628i	1.25447	+	0.724270i	0.971994	−	0.235004i	$-0.0755104\pi$
$173$	16.5000	+	9.52628i	1.25447	+	0.724270i	0.282477	+	0.959274i	$0.408844\pi$
$174$		0			0
$175$	−12.1244	+	14.0000i	−0.916515	+	1.05830i
$176$	−6.92820	−	4.00000i	−0.522233	−	0.301511i
$177$		0			0
$178$	8.66025	−	8.66025i	0.649113	−	0.649113i
$179$	−4.33013	−	2.50000i	−0.323649	−	0.186859i	0.329369	−	0.944201i	$-0.393164\pi$
$179$	−4.33013	−	2.50000i	−0.323649	−	0.186859i	−0.653018	+	0.757343i	$0.726497\pi$
$180$		0			0
$181$			17.3205i			1.28742i	0.765268	+	0.643712i	$0.222606\pi$
$181$			17.3205i			1.28742i	−0.765268	+	0.643712i	$0.777394\pi$
$182$	−16.0981	+	10.9019i	−1.19327	+	0.808104i
$183$		0			0
$184$	8.00000	+	8.00000i	0.589768	+	0.589768i
$185$	−9.00000	+	5.19615i	−0.661693	+	0.382029i
$186$		0			0
$187$	5.19615	−	9.00000i	0.379980	−	0.658145i
$188$		−	3.46410i		−	0.252646i
$189$		0			0
$190$	6.00000	−	6.00000i	0.435286	−	0.435286i
$191$	−6.06218	−	3.50000i	−0.438644	−	0.253251i	0.264378	−	0.964419i	$-0.414833\pi$
$191$	−6.06218	−	3.50000i	−0.438644	−	0.253251i	−0.703022	+	0.711168i	$0.748167\pi$
$192$		0			0
$193$	4.50000	+	7.79423i	0.323917	+	0.561041i	0.981293	−	0.192522i	$-0.0616668\pi$
$193$	4.50000	+	7.79423i	0.323917	+	0.561041i	−0.657376	+	0.753563i	$0.728333\pi$
$194$	−1.73205	+	1.73205i	−0.124354	+	0.124354i
$195$		0			0
$196$	−8.66025	−	11.0000i	−0.618590	−	0.785714i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$		0			0
$199$	−0.866025	+	1.50000i	−0.0613909	+	0.106332i	−0.895087	−	0.445891i	$-0.852887\pi$
$199$	−0.866025	+	1.50000i	−0.0613909	+	0.106332i	0.833696	+	0.552223i	$0.186220\pi$
$200$	14.0000	−	14.0000i	0.989949	−	0.989949i
$201$		0			0
$202$	−6.33975	−	23.6603i	−0.446063	−	1.66473i
$203$	12.9904	+	2.50000i	0.911746	+	0.175466i
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$		0			0
$208$	18.0000	−	10.3923i	1.24808	−	0.720577i
$209$	−3.00000	+	1.73205i	−0.207514	+	0.119808i
$210$		0			0
$211$	21.6506	+	12.5000i	1.49049	+	0.860535i	0.999941	−	0.0108774i	$-0.00346244\pi$
$211$	21.6506	+	12.5000i	1.49049	+	0.860535i	0.490550	+	0.871413i	$0.336796\pi$
$212$		−	2.00000i		−	0.137361i
$213$		0			0
$214$	−7.00000	+	7.00000i	−0.478510	+	0.478510i
$215$	19.0526	+	33.0000i	1.29937	+	2.25058i
$216$		0			0
$217$	−13.5000	−	2.59808i	−0.916440	−	0.176369i
$218$	1.09808	−	4.09808i	0.0743711	−	0.277557i
$219$		0			0
$220$	−12.0000	+	6.92820i	−0.809040	+	0.467099i
$221$	13.5000	+	23.3827i	0.908108	+	1.57289i
$222$		0			0
$223$	−7.79423	−	13.5000i	−0.521940	−	0.904027i	−0.999674	−	0.0255224i	$-0.991875\pi$
$223$	−7.79423	−	13.5000i	−0.521940	−	0.904027i	0.477734	−	0.878504i	$-0.341458\pi$
$224$	8.39230	+	12.3923i	0.560734	+	0.827996i
$225$		0			0
$226$	−6.95448	+	25.9545i	−0.462605	+	1.72647i
$227$	−6.92820			−0.459841			−0.229920	−	0.973209i	$-0.573847\pi$
$227$	−6.92820			−0.459841			−0.229920	+	0.973209i	$0.573847\pi$
$228$		0			0
$229$		−	3.46410i		−	0.228914i	−0.993428	−	0.114457i	$-0.963487\pi$
$229$		−	3.46410i		−	0.228914i	0.993428	−	0.114457i	$-0.0365129\pi$
$230$	18.9282	−	5.07180i	1.24809	−	0.334424i
$231$		0			0
$232$	−13.6603	−	3.66025i	−0.896840	−	0.240307i
$233$	0.500000	+	0.866025i	0.0327561	+	0.0567352i	0.881939	−	0.471364i	$-0.156238\pi$
$233$	0.500000	+	0.866025i	0.0327561	+	0.0567352i	−0.849183	+	0.528099i	$0.822905\pi$
$234$		0			0
$235$	−5.19615	−	3.00000i	−0.338960	−	0.195698i
$236$	−3.00000	−	1.73205i	−0.195283	−	0.112747i
$237$		0			0
$238$	−16.0981	+	10.9019i	−1.04348	+	0.706667i
$239$	9.52628	+	5.50000i	0.616204	+	0.355765i	0.775390	−	0.631483i	$-0.217554\pi$
$239$	9.52628	+	5.50000i	0.616204	+	0.355765i	−0.159186	+	0.987249i	$0.550887\pi$
$240$		0			0
$241$		−	3.46410i		−	0.223142i	−0.993756	−	0.111571i	$-0.964412\pi$
$241$		−	3.46410i		−	0.223142i	0.993756	−	0.111571i	$-0.0355883\pi$
$242$	−9.56218	+	2.56218i	−0.614680	+	0.164703i
$243$		0			0
$244$	10.3923			0.665299
$245$	−24.0000	+	3.46410i	−1.53330	+	0.221313i
$246$		0			0
$247$		−	9.00000i		−	0.572656i
$248$	14.1962	+	3.80385i	0.901457	+	0.241545i
$249$		0			0
$250$	−2.53590	−	9.46410i	−0.160384	−	0.598562i
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$	2.19615	+	8.19615i	0.137799	+	0.514272i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		−	13.8564i		−	0.864339i	−0.901792	−	0.432169i	$-0.857748\pi$
$257$		−	13.8564i		−	0.864339i	0.901792	−	0.432169i	$-0.142252\pi$
$258$		0			0
$259$	−7.79423	−	1.50000i	−0.484310	−	0.0932055i
$260$		−	36.0000i		−	2.23263i
$261$		0			0
$262$	18.9282	−	5.07180i	1.16939	−	0.313337i
$263$			26.0000i			1.60323i	0.597841	+	0.801614i	$0.296025\pi$
$263$			26.0000i			1.60323i	−0.597841	+	0.801614i	$0.703975\pi$
$264$		0			0
$265$	−3.00000	−	1.73205i	−0.184289	−	0.106399i
$266$	6.46410	−	0.464102i	0.396339	−	0.0284559i
$267$		0			0
$268$	9.00000	−	15.5885i	0.549762	−	0.952217i
$269$	−25.5000	−	14.7224i	−1.55476	−	0.897643i	−0.997743	−	0.0671428i	$-0.978612\pi$
$269$	−25.5000	−	14.7224i	−1.55476	−	0.897643i	−0.557019	−	0.830500i	$-0.688055\pi$
$270$		0			0
$271$	−2.59808	−	4.50000i	−0.157822	−	0.273356i	0.776261	−	0.630412i	$-0.217114\pi$
$271$	−2.59808	−	4.50000i	−0.157822	−	0.273356i	−0.934083	+	0.357056i	$0.883781\pi$
$272$	18.0000	−	10.3923i	1.09141	−	0.630126i
$273$		0			0
$274$	10.9282	−	2.92820i	0.660197	−	0.176899i
$275$			14.0000i			0.844232i
$276$		0			0
$277$	−4.00000			−0.240337			−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000			−0.240337			−0.120168	+	0.992754i	$0.538343\pi$
$278$	8.24167	−	30.7583i	0.494303	−	1.84476i
$279$		0			0
$280$	25.8564	−	1.85641i	1.54522	−	0.110942i
$281$	−2.50000	−	4.33013i	−0.149137	−	0.258314i	0.781771	−	0.623565i	$-0.214316\pi$
$281$	−2.50000	−	4.33013i	−0.149137	−	0.258314i	−0.930909	+	0.365251i	$0.880983\pi$
$282$		0			0
$283$	4.33013	+	7.50000i	0.257399	+	0.445829i	0.965544	−	0.260238i	$-0.0838011\pi$
$283$	4.33013	+	7.50000i	0.257399	+	0.445829i	−0.708145	+	0.706067i	$0.750468\pi$
$284$	2.00000	+	3.46410i	0.118678	+	0.205557i
$285$		0			0
$286$	−3.80385	+	14.1962i	−0.224926	+	0.839436i
$287$	−4.33013	+	1.50000i	−0.255599	+	0.0885422i
$288$		0			0
$289$	5.00000	+	8.66025i	0.294118	+	0.509427i
$290$	−17.3205	+	17.3205i	−1.01710	+	1.01710i
$291$		0			0
$292$	−24.2487			−1.41905
$293$	−4.50000	−	2.59808i	−0.262893	−	0.151781i	0.362761	−	0.931882i	$-0.381834\pi$
$293$	−4.50000	−	2.59808i	−0.262893	−	0.151781i	−0.625653	+	0.780101i	$0.715168\pi$
$294$		0			0
$295$	−5.19615	+	3.00000i	−0.302532	+	0.174667i
$296$	8.19615	+	2.19615i	0.476392	+	0.127649i
$297$		0			0
$298$	−5.46410	+	1.46410i	−0.316527	+	0.0848131i
$299$	10.3923	−	18.0000i	0.601003	−	1.04097i
$300$		0			0
$301$	−5.50000	+	28.5788i	−0.317015	+	1.64726i
$302$	−5.12436	−	19.1244i	−0.294874	−	1.10048i
$303$		0			0
$304$	−6.92820			−0.397360
$305$	9.00000	−	15.5885i	0.515339	−	0.892592i
$306$		0			0
$307$	17.3205			0.988534			0.494267	−	0.869310i	$-0.335437\pi$
$307$	17.3205			0.988534			0.494267	+	0.869310i	$0.335437\pi$
$308$	−10.3923	−	2.00000i	−0.592157	−	0.113961i
$309$		0			0
$310$	18.0000	−	18.0000i	1.02233	−	1.02233i
$311$	11.2583	+	19.5000i	0.638401	+	1.10574i	0.985784	+	0.168020i	$0.0537373\pi$
$311$	11.2583	+	19.5000i	0.638401	+	1.10574i	−0.347382	+	0.937724i	$0.612929\pi$
$312$		0			0
$313$	19.5000	+	11.2583i	1.10221	+	0.636358i	0.936799	−	0.349867i	$-0.113773\pi$
$313$	19.5000	+	11.2583i	1.10221	+	0.636358i	0.165406	+	0.986226i	$0.447107\pi$
$314$	12.1244	−	12.1244i	0.684217	−	0.684217i
$315$		0			0
$316$	6.00000			0.337526
$317$	9.50000	−	16.4545i	0.533573	−	0.924176i	−0.465658	−	0.884965i	$-0.654182\pi$
$317$	9.50000	−	16.4545i	0.533573	−	0.924176i	0.999231	−	0.0392110i	$-0.0124844\pi$
$318$		0			0
$319$	8.66025	−	5.00000i	0.484881	−	0.279946i
$320$	−27.7128			−1.54919
$321$		0			0
$322$	13.4641	+	6.53590i	0.750325	+	0.364231i
$323$		−	9.00000i		−	0.500773i
$324$		0			0
$325$	−31.5000	−	18.1865i	−1.74731	−	1.00881i
$326$	−9.00000	+	9.00000i	−0.498464	+	0.498464i
$327$		0			0
$328$	4.73205	−	1.26795i	0.261284	−	0.0700108i
$329$	−1.50000	−	4.33013i	−0.0826977	−	0.238728i
$330$		0			0
$331$	−0.866025	−	0.500000i	−0.0476011	−	0.0274825i	0.476011	−	0.879440i	$-0.342082\pi$
$331$	−0.866025	−	0.500000i	−0.0476011	−	0.0274825i	−0.523612	+	0.851957i	$0.675416\pi$
$332$	9.00000	+	5.19615i	0.493939	+	0.285176i
$333$		0			0
$334$	−1.90192	+	7.09808i	−0.104069	+	0.388389i
$335$	−15.5885	−	27.0000i	−0.851688	−	1.47517i
$336$		0			0
$337$	13.5000	−	23.3827i	0.735392	−	1.27374i	−0.219159	−	0.975689i	$-0.570331\pi$
$337$	13.5000	−	23.3827i	0.735392	−	1.27374i	0.954551	−	0.298047i	$-0.0963352\pi$
$338$	−14.0000	−	14.0000i	−0.761500	−	0.761500i
$339$		0			0
$340$		−	36.0000i		−	1.95237i
$341$	−9.00000	+	5.19615i	−0.487377	+	0.281387i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	8.05256	−	30.0526i	0.434165	−	1.62033i
$345$		0			0
$346$	−26.0263	−	6.97372i	−1.39918	−	0.374910i
$347$	25.1147	−	14.5000i	1.34823	−	0.778401i	0.360231	−	0.932863i	$-0.382698\pi$
$347$	25.1147	−	14.5000i	1.34823	−	0.778401i	0.987999	+	0.154462i	$0.0493645\pi$
$348$		0			0
$349$	13.5000	−	7.79423i	0.722638	−	0.417215i	−0.0930846	−	0.995658i	$-0.529673\pi$
$349$	13.5000	−	7.79423i	0.722638	−	0.417215i	0.815723	+	0.578443i	$0.196339\pi$
$350$	11.4378	−	23.5622i	0.611377	−	1.25945i
$351$		0			0
$352$	10.9282	+	2.92820i	0.582475	+	0.156074i
$353$		−	10.3923i		−	0.553127i	−0.960996	−	0.276563i	$-0.910804\pi$
$353$		−	10.3923i		−	0.553127i	0.960996	−	0.276563i	$-0.0891955\pi$
$354$		0			0
$355$	6.92820			0.367711
$356$	−8.66025	+	15.0000i	−0.458993	+	0.794998i
$357$		0			0
$358$	6.83013	+	1.83013i	0.360983	+	0.0967252i
$359$	−14.7224	+	8.50000i	−0.777020	+	0.448613i	−0.835373	−	0.549683i	$-0.814748\pi$
$359$	−14.7224	+	8.50000i	−0.777020	+	0.448613i	0.0583530	+	0.998296i	$0.481415\pi$
$360$		0			0
$361$	8.00000	−	13.8564i	0.421053	−	0.729285i
$362$	−6.33975	−	23.6603i	−0.333210	−	1.24356i
$363$		0			0
$364$	18.0000	−	20.7846i	0.943456	−	1.08941i
$365$	−21.0000	+	36.3731i	−1.09919	+	1.90385i
$366$		0			0
$367$	34.6410			1.80825			0.904123	−	0.427272i	$-0.140525\pi$
$367$	34.6410			1.80825			0.904123	+	0.427272i	$0.140525\pi$
$368$	−13.8564	−	8.00000i	−0.722315	−	0.417029i
$369$		0			0
$370$	10.3923	−	10.3923i	0.540270	−	0.540270i
$371$	−0.866025	−	2.50000i	−0.0449618	−	0.129794i
$372$		0			0
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	−3.80385	+	14.1962i	−0.196692	+	0.734066i
$375$		0			0
$376$	1.26795	+	4.73205i	0.0653895	+	0.244037i
$377$			25.9808i			1.33808i
$378$		0			0
$379$			14.0000i			0.719132i	0.933120	+	0.359566i	$0.117075\pi$
$379$			14.0000i			0.719132i	−0.933120	+	0.359566i	$0.882925\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$		0			0
$382$	9.56218	+	2.56218i	0.489244	+	0.131092i
$383$	−6.92820			−0.354015			−0.177007	−	0.984210i	$-0.556642\pi$
$383$	−6.92820			−0.354015			−0.177007	+	0.984210i	$0.556642\pi$
$384$		0			0
$385$	−12.0000	+	13.8564i	−0.611577	+	0.706188i
$386$	−9.00000	−	9.00000i	−0.458088	−	0.458088i
$387$		0			0
$388$	1.73205	−	3.00000i	0.0879316	−	0.152302i
$389$	32.0000			1.62246			0.811232	−	0.584724i	$-0.198797\pi$
$389$	32.0000			1.62246			0.811232	+	0.584724i	$0.198797\pi$
$390$		0			0
$391$	10.3923	−	18.0000i	0.525561	−	0.910299i
$392$	15.8564	+	11.8564i	0.800869	+	0.598839i
$393$		0			0
$394$	−13.6603	+	3.66025i	−0.688194	+	0.184401i
$395$	5.19615	−	9.00000i	0.261447	−	0.452839i
$396$		0			0
$397$	−16.5000	+	9.52628i	−0.828111	+	0.478110i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−16.5000	+	9.52628i	−0.828111	+	0.478110i	0.0250943	+	0.999685i	$0.492011\pi$
$398$	0.633975	−	2.36603i	0.0317783	−	0.118598i
$399$		0			0
$400$	−14.0000	+	24.2487i	−0.700000	+	1.21244i
$401$	−8.00000			−0.399501			−0.199750	−	0.979847i	$-0.564013\pi$
$401$	−8.00000			−0.399501			−0.199750	+	0.979847i	$0.564013\pi$
$402$		0			0
$403$		−	27.0000i		−	1.34497i
$404$	17.3205	+	30.0000i	0.861727	+	1.49256i
$405$		0			0
$406$	−18.6603	+	1.33975i	−0.926093	+	0.0664905i
$407$	−5.19615	+	3.00000i	−0.257564	+	0.148704i
$408$		0			0
$409$	13.5000	−	7.79423i	0.667532	−	0.385400i	−0.127609	−	0.991825i	$-0.540730\pi$
$409$	13.5000	−	7.79423i	0.667532	−	0.385400i	0.795141	+	0.606425i	$0.207397\pi$
$410$	2.19615	−	8.19615i	0.108460	−	0.404779i
$411$		0			0
$412$		0			0
$413$	−4.50000	−	0.866025i	−0.221431	−	0.0426143i
$414$		0			0
$415$	15.5885	−	9.00000i	0.765207	−	0.441793i
$416$	−20.7846	+	20.7846i	−1.01905	+	1.01905i
$417$		0			0
$418$	3.46410	−	3.46410i	0.169435	−	0.169435i
$419$	−7.79423	+	13.5000i	−0.380773	+	0.659518i	−0.991173	−	0.132575i	$-0.957675\pi$
$419$	−7.79423	+	13.5000i	−0.380773	+	0.659518i	0.610400	+	0.792093i	$0.291009\pi$
$420$		0			0
$421$	11.5000	+	19.9186i	0.560476	+	0.970772i	0.997455	+	0.0713008i	$0.0227150\pi$
$421$	11.5000	+	19.9186i	0.560476	+	0.970772i	−0.436979	+	0.899472i	$0.643952\pi$
$422$	−34.1506	−	9.15064i	−1.66243	−	0.445446i
$423$		0			0
$424$	0.732051	+	2.73205i	0.0355515	+	0.132680i
$425$	−31.5000	−	18.1865i	−1.52797	−	0.882176i
$426$		0			0
$427$	12.9904	−	4.50000i	0.628649	−	0.217770i
$428$	7.00000	−	12.1244i	0.338358	−	0.586053i
$429$		0			0
$430$	−38.1051	−	38.1051i	−1.83759	−	1.83759i
$431$	4.33013	+	2.50000i	0.208575	+	0.120421i	0.600649	−	0.799513i	$-0.294909\pi$
$431$	4.33013	+	2.50000i	0.208575	+	0.120421i	−0.392074	+	0.919934i	$0.628242\pi$
$432$		0			0
$433$			27.7128i			1.33179i	0.746044	+	0.665896i	$0.231951\pi$
$433$			27.7128i			1.33179i	−0.746044	+	0.665896i	$0.768049\pi$
$434$	19.3923	−	1.39230i	0.930860	−	0.0668328i
$435$		0			0
$436$			6.00000i			0.287348i
$437$	−6.00000	+	3.46410i	−0.287019	+	0.165710i
$438$		0			0
$439$	6.06218	−	10.5000i	0.289332	−	0.501138i	−0.684318	−	0.729183i	$-0.739900\pi$
$439$	6.06218	−	10.5000i	0.289332	−	0.501138i	0.973650	+	0.228046i	$0.0732335\pi$
$440$	13.8564	−	13.8564i	0.660578	−	0.660578i
$441$		0			0
$442$	−27.0000	−	27.0000i	−1.28426	−	1.28426i
$443$	26.8468	+	15.5000i	1.27553	+	0.736427i	0.976023	−	0.217667i	$-0.0698447\pi$
$443$	26.8468	+	15.5000i	1.27553	+	0.736427i	0.299506	+	0.954094i	$0.403178\pi$
$444$		0			0
$445$	15.0000	+	25.9808i	0.711068	+	1.23161i
$446$	15.5885	+	15.5885i	0.738135	+	0.738135i
$447$		0			0
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$		0			0
$451$	−1.73205	+	3.00000i	−0.0815591	+	0.141264i
$452$		−	38.0000i		−	1.78737i
$453$		0			0
$454$	9.46410	−	2.53590i	0.444172	−	0.119016i
$455$	−15.5885	−	45.0000i	−0.730798	−	2.10963i
$456$		0			0
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	−0.898974	−	0.438001i	$-0.855687\pi$
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	0.828807	+	0.559534i	$0.189020\pi$
$458$	1.26795	+	4.73205i	0.0592474	+	0.221114i
$459$		0			0
$460$	−24.0000	+	13.8564i	−1.11901	+	0.646058i
$461$	−28.5000	+	16.4545i	−1.32738	+	0.766362i	−0.984893	−	0.173162i	$-0.944602\pi$
$461$	−28.5000	+	16.4545i	−1.32738	+	0.766362i	−0.342484	+	0.939524i	$0.611268\pi$
$462$		0			0
$463$	28.5788	+	16.5000i	1.32817	+	0.766820i	0.985017	−	0.172459i	$-0.0551712\pi$
$463$	28.5788	+	16.5000i	1.32817	+	0.766820i	0.343155	+	0.939279i	$0.388505\pi$
$464$	20.0000			0.928477
$465$		0			0
$466$	−1.00000	−	1.00000i	−0.0463241	−	0.0463241i
$467$	−0.866025	−	1.50000i	−0.0400749	−	0.0694117i	0.845292	−	0.534304i	$-0.179426\pi$
$467$	−0.866025	−	1.50000i	−0.0400749	−	0.0694117i	−0.885367	+	0.464892i	$0.846093\pi$
$468$		0			0
$469$	4.50000	−	23.3827i	0.207791	−	1.07971i
$470$	8.19615	+	2.19615i	0.378060	+	0.101301i
$471$		0			0
$472$	4.73205	+	1.26795i	0.217810	+	0.0583621i
$473$	11.0000	+	19.0526i	0.505781	+	0.876038i
$474$		0			0
$475$	6.06218	+	10.5000i	0.278152	+	0.481773i
$476$	18.0000	−	20.7846i	0.825029	−	0.952661i
$477$		0			0
$478$	−15.0263	−	4.02628i	−0.687286	−	0.184158i
$479$	20.7846			0.949673			0.474837	−	0.880074i	$-0.342507\pi$
$479$	20.7846			0.949673			0.474837	+	0.880074i	$0.342507\pi$
$480$		0			0
$481$		−	15.5885i		−	0.710772i
$482$	1.26795	+	4.73205i	0.0577535	+	0.215539i
$483$		0			0
$484$	12.1244	−	7.00000i	0.551107	−	0.318182i
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$		0			0
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.878042	−	0.478584i	$-0.158850\pi$
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.0245553	+	0.999698i	$0.492183\pi$
$488$	−14.1962	+	3.80385i	−0.642630	+	0.172192i
$489$		0			0
$490$	31.5167	−	13.5167i	1.42378	−	0.610620i
$491$	−16.4545	−	9.50000i	−0.742580	−	0.428729i	0.0804264	−	0.996761i	$-0.474372\pi$
$491$	−16.4545	−	9.50000i	−0.742580	−	0.428729i	−0.823007	+	0.568032i	$0.807705\pi$
$492$		0			0
$493$			25.9808i			1.17011i
$494$	3.29423	+	12.2942i	0.148214	+	0.553143i
$495$		0			0
$496$	−20.7846			−0.933257
$497$	4.00000	+	3.46410i	0.179425	+	0.155386i
$498$		0			0
$499$			2.00000i			0.0895323i	0.998997	+	0.0447661i	$0.0142543\pi$
$499$			2.00000i			0.0895323i	−0.998997	+	0.0447661i	$0.985746\pi$
$500$	6.92820	+	12.0000i	0.309839	+	0.536656i
$501$		0			0
$502$	4.73205	−	1.26795i	0.211202	−	0.0565913i
$503$	−41.5692			−1.85348			−0.926740	−	0.375703i	$-0.877401\pi$
$503$	−41.5692			−1.85348			−0.926740	+	0.375703i	$0.877401\pi$
$504$		0			0
$505$	60.0000			2.66996
$506$	10.9282	−	2.92820i	0.485818	−	0.130175i
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$			6.92820i			0.307087i	0.988142	+	0.153544i	$0.0490686\pi$
$509$			6.92820i			0.307087i	−0.988142	+	0.153544i	$0.950931\pi$
$510$		0			0
$511$	−30.3109	+	10.5000i	−1.34087	+	0.464493i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	5.07180	+	18.9282i	0.223707	+	0.834887i
$515$		0			0
$516$		0			0
$517$	−3.00000	−	1.73205i	−0.131940	−	0.0761755i
$518$	11.1962	−	0.803848i	0.491931	−	0.0353190i
$519$		0			0
$520$	13.1769	+	49.1769i	0.577846	+	2.15655i
$521$	19.5000	+	11.2583i	0.854311	+	0.493236i	0.862103	−	0.506733i	$-0.169147\pi$
$521$	19.5000	+	11.2583i	0.854311	+	0.493236i	−0.00779240	+	0.999970i	$0.502480\pi$
$522$		0			0
$523$	16.4545	+	28.5000i	0.719504	+	1.24622i	0.961196	+	0.275865i	$0.0889643\pi$
$523$	16.4545	+	28.5000i	0.719504	+	1.24622i	−0.241692	+	0.970353i	$0.577702\pi$
$524$	−24.0000	+	13.8564i	−1.04844	+	0.605320i
$525$		0			0
$526$	−9.51666	−	35.5167i	−0.414946	−	1.54860i
$527$		−	27.0000i		−	1.17614i
$528$		0			0
$529$	7.00000			0.304348
$530$	4.73205	+	1.26795i	0.205547	+	0.0550762i
$531$		0			0
$532$	−8.66025	+	3.00000i	−0.375470	+	0.130066i
$533$	−4.50000	−	7.79423i	−0.194917	−	0.337606i
$534$		0			0
$535$	−12.1244	−	21.0000i	−0.524182	−	0.907909i
$536$	−6.58846	+	24.5885i	−0.284578	+	1.06206i
$537$		0			0
$538$	40.2224	+	10.7776i	1.73411	+	0.464654i
$539$	−13.8564	+	2.00000i	−0.596838	+	0.0861461i
$540$		0			0
$541$	−20.5000	−	35.5070i	−0.881364	−	1.52657i	−0.849825	−	0.527064i	$-0.823293\pi$
$541$	−20.5000	−	35.5070i	−0.881364	−	1.52657i	−0.0315385	−	0.999503i	$-0.510041\pi$
$542$	5.19615	+	5.19615i	0.223194	+	0.223194i
$543$		0			0
$544$	−20.7846	+	20.7846i	−0.891133	+	0.891133i
$545$	9.00000	+	5.19615i	0.385518	+	0.222579i
$546$		0			0
$547$	2.59808	−	1.50000i	0.111086	−	0.0641354i	−0.443428	−	0.896310i	$-0.646238\pi$
$547$	2.59808	−	1.50000i	0.111086	−	0.0641354i	0.554513	+	0.832175i	$0.312904\pi$
$548$	−13.8564	+	8.00000i	−0.591916	+	0.341743i
$549$		0			0
$550$	−5.12436	−	19.1244i	−0.218503	−	0.815465i
$551$	4.33013	−	7.50000i	0.184470	−	0.319511i
$552$		0			0
$553$	7.50000	−	2.59808i	0.318932	−	0.110481i
$554$	5.46410	−	1.46410i	0.232147	−	0.0622037i
$555$		0			0
$556$			45.0333i			1.90984i
$557$	2.50000	−	4.33013i	0.105928	−	0.183473i	−0.808189	−	0.588924i	$-0.799552\pi$
$557$	2.50000	−	4.33013i	0.105928	−	0.183473i	0.914117	+	0.405450i	$0.132885\pi$
$558$		0			0
$559$	−57.1577			−2.41751
$560$	−34.6410	+	12.0000i	−1.46385	+	0.507093i
$561$		0			0
$562$	5.00000	+	5.00000i	0.210912	+	0.210912i
$563$	11.2583	+	19.5000i	0.474482	+	0.821827i	0.999573	−	0.0292191i	$-0.00930205\pi$
$563$	11.2583	+	19.5000i	0.474482	+	0.821827i	−0.525091	+	0.851046i	$0.675969\pi$
$564$		0			0
$565$	−57.0000	−	32.9090i	−2.39801	−	1.38449i
$566$	−8.66025	−	8.66025i	−0.364018	−	0.364018i
$567$		0			0
$568$	−4.00000	−	4.00000i	−0.167836	−	0.167836i
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	−0.855355	−	0.518043i	$-0.826661\pi$
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	0.876316	+	0.481737i	$0.159994\pi$
$570$		0			0
$571$	−23.3827	+	13.5000i	−0.978535	+	0.564957i	−0.901828	−	0.432096i	$-0.857774\pi$
$571$	−23.3827	+	13.5000i	−0.978535	+	0.564957i	−0.0767074	+	0.997054i	$0.524441\pi$
$572$		−	20.7846i		−	0.869048i
$573$		0			0
$574$	5.36603	−	3.63397i	0.223974	−	0.151679i
$575$			28.0000i			1.16768i
$576$		0			0
$577$	19.5000	+	11.2583i	0.811796	+	0.468690i	0.847579	−	0.530669i	$-0.178059\pi$
$577$	19.5000	+	11.2583i	0.811796	+	0.468690i	−0.0357834	+	0.999360i	$0.511393\pi$
$578$	−10.0000	−	10.0000i	−0.415945	−	0.415945i
$579$		0			0
$580$	17.3205	−	30.0000i	0.719195	−	1.24568i
$581$	13.5000	+	2.59808i	0.560074	+	0.107786i
$582$		0			0
$583$	−1.73205	−	1.00000i	−0.0717342	−	0.0414158i
$584$	33.1244	−	8.87564i	1.37070	−	0.367277i
$585$		0			0
$586$	7.09808	+	1.90192i	0.293219	+	0.0785677i
$587$	−16.4545	−	28.5000i	−0.679149	−	1.17632i	−0.975237	−	0.221160i	$-0.929016\pi$
$587$	−16.4545	−	28.5000i	−0.679149	−	1.17632i	0.296088	−	0.955161i	$-0.404318\pi$
$588$		0			0
$589$	−4.50000	+	7.79423i	−0.185419	+	0.321156i
$590$	6.00000	−	6.00000i	0.247016	−	0.247016i
$591$		0			0
$592$	−12.0000			−0.493197
$593$	13.5000	−	7.79423i	0.554379	−	0.320071i	−0.196508	−	0.980502i	$-0.562960\pi$
$593$	13.5000	−	7.79423i	0.554379	−	0.320071i	0.750886	+	0.660432i	$0.229627\pi$
$594$		0			0
$595$	−15.5885	−	45.0000i	−0.639064	−	1.84482i
$596$	6.92820	−	4.00000i	0.283790	−	0.163846i
$597$		0			0
$598$	−7.60770	+	28.3923i	−0.311102	+	1.16105i
$599$	−19.9186	+	11.5000i	−0.813851	+	0.469877i	−0.848292	−	0.529529i	$-0.822368\pi$
$599$	−19.9186	+	11.5000i	−0.813851	+	0.469877i	0.0344402	+	0.999407i	$0.489035\pi$
$600$		0			0
$601$	−1.50000	+	0.866025i	−0.0611863	+	0.0353259i	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−1.50000	+	0.866025i	−0.0611863	+	0.0353259i	0.469095	+	0.883148i	$0.344580\pi$
$602$	−2.94744	−	41.0526i	−0.120129	−	1.67318i
$603$		0			0
$604$	14.0000	+	24.2487i	0.569652	+	0.986666i
$605$		−	24.2487i		−	0.985850i
$606$		0			0
$607$	−27.7128			−1.12483			−0.562414	−	0.826856i	$-0.690127\pi$
$607$	−27.7128			−1.12483			−0.562414	+	0.826856i	$0.690127\pi$
$608$	9.46410	−	2.53590i	0.383820	−	0.102844i
$609$		0			0
$610$	−6.58846	+	24.5885i	−0.266759	+	0.995558i
$611$	7.79423	−	4.50000i	0.315321	−	0.182051i
$612$		0			0
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$	−23.6603	+	6.33975i	−0.954850	+	0.255851i
$615$		0			0
$616$	14.9282	−	1.07180i	0.601474	−	0.0431839i
$617$	6.50000	−	11.2583i	0.261680	−	0.453243i	−0.705008	−	0.709199i	$-0.749057\pi$
$617$	6.50000	−	11.2583i	0.261680	−	0.453243i	0.966689	+	0.255956i	$0.0823901\pi$
$618$		0			0
$619$	13.8564			0.556936			0.278468	−	0.960446i	$-0.410173\pi$
$619$	13.8564			0.556936			0.278468	+	0.960446i	$0.410173\pi$
$620$	−18.0000	+	31.1769i	−0.722897	+	1.25210i
$621$		0			0
$622$	−22.5167	−	22.5167i	−0.902836	−	0.902836i
$623$	−4.33013	+	22.5000i	−0.173483	+	0.901443i
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−30.7583	−	8.24167i	−1.22935	−	0.329403i
$627$		0			0
$628$	−12.1244	+	21.0000i	−0.483814	+	0.837991i
$629$		−	15.5885i		−	0.621552i
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$	−8.19615	+	2.19615i	−0.326025	+	0.0873583i
$633$		0			0
$634$	−6.95448	+	25.9545i	−0.276198	+	1.03078i
$635$	−20.7846			−0.824812
$636$		0			0
$637$	13.5000	−	33.7750i	0.534889	−	1.33821i
$638$	−10.0000	+	10.0000i	−0.395904	+	0.395904i
$639$		0			0
$640$	37.8564	−	10.1436i	1.49641	−	0.400961i
$641$	−4.00000			−0.157991			−0.0789953	−	0.996875i	$-0.525171\pi$
$641$	−4.00000			−0.157991			−0.0789953	+	0.996875i	$0.525171\pi$
$642$		0			0
$643$	−7.79423	+	13.5000i	−0.307374	+	0.532388i	−0.977787	−	0.209600i	$-0.932784\pi$
$643$	−7.79423	+	13.5000i	−0.307374	+	0.532388i	0.670413	+	0.741988i	$0.266117\pi$
$644$	−20.7846	−	4.00000i	−0.819028	−	0.157622i
$645$		0			0
$646$	3.29423	+	12.2942i	0.129610	+	0.483710i
$647$	7.79423	−	13.5000i	0.306423	−	0.530740i	−0.671154	−	0.741318i	$-0.734201\pi$
$647$	7.79423	−	13.5000i	0.306423	−	0.530740i	0.977577	+	0.210578i	$0.0675346\pi$
$648$		0			0
$649$	−3.00000	+	1.73205i	−0.117760	+	0.0679889i
$650$	49.6865	+	13.3135i	1.94887	+	0.522197i
$651$		0			0
$652$	9.00000	−	15.5885i	0.352467	−	0.610491i
$653$	−26.0000			−1.01746			−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000			−1.01746			−0.508729	+	0.860927i	$0.669885\pi$
$654$		0			0
$655$			48.0000i			1.87552i
$656$	−6.00000	+	3.46410i	−0.234261	+	0.135250i
$657$		0			0
$658$	3.63397	+	5.36603i	0.141667	+	0.209189i
$659$	−16.4545	+	9.50000i	−0.640976	+	0.370067i	−0.784990	−	0.619508i	$-0.787332\pi$
$659$	−16.4545	+	9.50000i	−0.640976	+	0.370067i	0.144015	+	0.989576i	$0.453999\pi$
$660$		0			0
$661$	10.5000	−	6.06218i	0.408403	−	0.235791i	−0.281701	−	0.959502i	$-0.590898\pi$
$661$	10.5000	−	6.06218i	0.408403	−	0.235791i	0.690103	+	0.723711i	$0.257565\pi$
$662$	1.36603	+	0.366025i	0.0530921	+	0.0142260i
$663$		0			0
$664$	−14.1962	−	3.80385i	−0.550918	−	0.147618i
$665$	−3.00000	+	15.5885i	−0.116335	+	0.604494i
$666$		0			0
$667$	17.3205	−	10.0000i	0.670653	−	0.387202i
$668$		−	10.3923i		−	0.402090i
$669$		0			0
$670$	31.1769	+	31.1769i	1.20447	+	1.20447i
$671$	5.19615	−	9.00000i	0.200595	−	0.347441i
$672$		0			0
$673$	−19.5000	−	33.7750i	−0.751670	−	1.30193i	−0.947013	−	0.321195i	$-0.895915\pi$
$673$	−19.5000	−	33.7750i	−0.751670	−	1.30193i	0.195343	−	0.980735i	$-0.437418\pi$
$674$	−9.88269	+	36.8827i	−0.380667	+	1.42067i
$675$		0			0
$676$	24.2487	+	14.0000i	0.932643	+	0.538462i
$677$	19.5000	+	11.2583i	0.749446	+	0.432693i	0.825494	−	0.564411i	$-0.190897\pi$
$677$	19.5000	+	11.2583i	0.749446	+	0.432693i	−0.0760478	+	0.997104i	$0.524230\pi$
$678$		0			0
$679$	0.866025	−	4.50000i	0.0332350	−	0.172694i
$680$	13.1769	+	49.1769i	0.505312	+	1.88585i
$681$		0			0
$682$	10.3923	−	10.3923i	0.397942	−	0.397942i
$683$	40.7032	+	23.5000i	1.55746	+	0.899203i	0.997499	+	0.0706868i	$0.0225191\pi$
$683$	40.7032	+	23.5000i	1.55746	+	0.899203i	0.559966	+	0.828516i	$0.310814\pi$
$684$		0			0
$685$			27.7128i			1.05885i
$686$	24.9545	+	7.95448i	0.952767	+	0.303704i
$687$		0			0
$688$			44.0000i			1.67748i
$689$	4.50000	−	2.59808i	0.171436	−	0.0989788i
$690$		0			0
$691$	−14.7224	+	25.5000i	−0.560068	+	0.970066i	0.437422	+	0.899256i	$0.355892\pi$
$691$	−14.7224	+	25.5000i	−0.560068	+	0.970066i	−0.997490	+	0.0708094i	$0.977442\pi$
$692$	38.1051			1.44854
$693$		0			0
$694$	−29.0000	+	29.0000i	−1.10082	+	1.10082i
$695$	67.5500	+	39.0000i	2.56232	+	1.47935i
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	−15.5885	+	15.5885i	−0.590032	+	0.590032i
$699$		0			0
$700$	−7.00000	+	36.3731i	−0.264575	+	1.37477i
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$		0			0
$703$	−2.59808	+	4.50000i	−0.0979883	+	0.169721i
$704$	−16.0000			−0.603023
$705$		0			0
$706$	3.80385	+	14.1962i	0.143160	+	0.534279i
$707$	34.6410	+	30.0000i	1.30281	+	1.12827i
$708$		0			0
$709$	16.5000	−	28.5788i	0.619671	−	1.07330i	−0.369875	−	0.929081i	$-0.620600\pi$
$709$	16.5000	−	28.5788i	0.619671	−	1.07330i	0.989546	−	0.144219i	$-0.0460671\pi$
$710$	−9.46410	+	2.53590i	−0.355181	+	0.0951706i
$711$		0			0
$712$	6.33975	−	23.6603i	0.237592	−	0.886706i
$713$	−18.0000	+	10.3923i	−0.674105	+	0.389195i
$714$		0			0
$715$	−31.1769	−	18.0000i	−1.16595	−	0.673162i
$716$	−10.0000			−0.373718
$717$		0			0
$718$	17.0000	−	17.0000i	0.634434	−	0.634434i
$719$	−9.52628	−	16.5000i	−0.355270	−	0.615346i	0.631894	−	0.775055i	$-0.282278\pi$
$719$	−9.52628	−	16.5000i	−0.355270	−	0.615346i	−0.987164	+	0.159709i	$0.948944\pi$
$720$		0			0
$721$		0			0
$722$	−5.85641	+	21.8564i	−0.217953	+	0.813411i
$723$		0			0
$724$	17.3205	+	30.0000i	0.643712	+	1.11494i
$725$	−17.5000	−	30.3109i	−0.649934	−	1.12572i
$726$		0			0
$727$	−4.33013	−	7.50000i	−0.160596	−	0.278160i	0.774487	−	0.632590i	$-0.218008\pi$
$727$	−4.33013	−	7.50000i	−0.160596	−	0.278160i	−0.935082	+	0.354430i	$0.884675\pi$
$728$	−16.9808	+	34.9808i	−0.629349	+	1.29647i
$729$		0			0
$730$	15.3731	−	57.3731i	0.568983	−	2.12347i
$731$	−57.1577			−2.11405
$732$		0			0
$733$			20.7846i			0.767697i	0.923396	+	0.383849i	$0.125402\pi$
$733$			20.7846i			0.767697i	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−47.3205	+	12.6795i	−1.74663	+	0.468009i
$735$		0			0
$736$	21.8564	+	5.85641i	0.805638	+	0.215870i
$737$	−9.00000	−	15.5885i	−0.331519	−	0.574208i
$738$		0			0
$739$	−44.1673	−	25.5000i	−1.62472	−	0.938033i	−0.985634	−	0.168898i	$-0.945979\pi$
$739$	−44.1673	−	25.5000i	−1.62472	−	0.938033i	−0.639087	−	0.769135i	$-0.720687\pi$
$740$	−10.3923	+	18.0000i	−0.382029	+	0.661693i
$741$		0			0
$742$	2.09808	+	3.09808i	0.0770228	+	0.113734i
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.884072	−	0.467351i	$-0.154791\pi$
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.0372984	+	0.999304i	$0.488125\pi$
$744$		0			0
$745$		−	13.8564i		−	0.507659i
$746$	35.5167	−	9.51666i	1.30036	−	0.348430i
$747$		0			0
$748$		−	20.7846i		−	0.759961i
$749$	3.50000	−	18.1865i	0.127887	−	0.664521i
$750$		0			0
$751$		−	2.00000i		−	0.0729810i	−0.999334	−	0.0364905i	$-0.988382\pi$
$751$		−	2.00000i		−	0.0729810i	0.999334	−	0.0364905i	$-0.0116179\pi$
$752$	−3.46410	−	6.00000i	−0.126323	−	0.218797i
$753$		0			0
$754$	−9.50962	−	35.4904i	−0.346320	−	1.29248i
$755$	48.4974			1.76500
$756$		0			0
$757$	−24.0000			−0.872295			−0.436147	−	0.899875i	$-0.643657\pi$
$757$	−24.0000			−0.872295			−0.436147	+	0.899875i	$0.643657\pi$
$758$	−5.12436	−	19.1244i	−0.186125	−	0.694628i
$759$		0			0
$760$	4.39230	−	16.3923i	0.159326	−	0.594611i
$761$		−	10.3923i		−	0.376721i	−0.982100	−	0.188360i	$-0.939683\pi$
$761$		−	10.3923i		−	0.376721i	0.982100	−	0.188360i	$-0.0603173\pi$
$762$		0			0
$763$	2.59808	+	7.50000i	0.0940567	+	0.271518i
$764$	−14.0000			−0.506502
$765$		0			0
$766$	9.46410	−	2.53590i	0.341952	−	0.0916257i
$767$		−	9.00000i		−	0.324971i
$768$		0			0
$769$	−7.50000	−	4.33013i	−0.270457	−	0.156148i	0.358638	−	0.933477i	$-0.383241\pi$
$769$	−7.50000	−	4.33013i	−0.270457	−	0.156148i	−0.629095	+	0.777328i	$0.716574\pi$
$770$	11.3205	−	23.3205i	0.407963	−	0.840413i
$771$		0			0
$772$	15.5885	+	9.00000i	0.561041	+	0.323917i
$773$	−1.50000	−	0.866025i	−0.0539513	−	0.0311488i	0.472782	−	0.881180i	$-0.343250\pi$
$773$	−1.50000	−	0.866025i	−0.0539513	−	0.0311488i	−0.526733	+	0.850031i	$0.676583\pi$
$774$		0			0
$775$	18.1865	+	31.5000i	0.653280	+	1.13151i
$776$	−1.26795	+	4.73205i	−0.0455167	+	0.169871i
$777$		0			0
$778$	−43.7128	+	11.7128i	−1.56718	+	0.419925i
$779$			3.00000i			0.107486i
$780$		0			0
$781$	4.00000			0.143131
$782$	−7.60770	+	28.3923i	−0.272051	+	1.01531i
$783$		0			0
$784$	−26.0000	−	10.3923i	−0.928571	−	0.371154i
$785$	21.0000	+	36.3731i	0.749522	+	1.29821i
$786$		0			0
$787$	−25.1147	−	43.5000i	−0.895244	−	1.55061i	−0.833503	−	0.552515i	$-0.813668\pi$
$787$	−25.1147	−	43.5000i	−0.895244	−	1.55061i	−0.0617409	−	0.998092i	$-0.519665\pi$
$788$	17.3205	−	10.0000i	0.617018	−	0.356235i
$789$		0			0
$790$	−3.80385	+	14.1962i	−0.135335	+	0.505076i
$791$	−16.4545	−	47.5000i	−0.585054	−	1.68891i
$792$		0			0
$793$	13.5000	+	23.3827i	0.479399	+	0.830344i
$794$	19.0526	−	19.0526i	0.676150	−	0.676150i
$795$		0			0
$796$			3.46410i			0.122782i
$797$	22.5000	+	12.9904i	0.796991	+	0.460143i	0.842418	−	0.538825i	$-0.181132\pi$
$797$	22.5000	+	12.9904i	0.796991	+	0.460143i	−0.0454270	+	0.998968i	$0.514465\pi$
$798$		0			0
$799$	7.79423	−	4.50000i	0.275740	−	0.159199i
$800$	10.2487	−	38.2487i	0.362347	−	1.35230i
$801$		0			0
$802$	10.9282	−	2.92820i	0.385888	−	0.103398i
$803$	−12.1244	+	21.0000i	−0.427859	+	0.741074i
$804$		0			0
$805$	−24.0000	+	27.7128i	−0.845889	+	0.976748i
$806$	9.88269	+	36.8827i	0.348103	+	1.29914i
$807$		0			0
$808$	−34.6410	−	34.6410i	−1.21867	−	1.21867i
$809$	11.5000	−	19.9186i	0.404318	−	0.700300i	−0.589923	−	0.807459i	$-0.700842\pi$
$809$	11.5000	−	19.9186i	0.404318	−	0.700300i	0.994242	+	0.107159i	$0.0341754\pi$
$810$		0			0
$811$	−6.92820			−0.243282			−0.121641	−	0.992574i	$-0.538816\pi$
$811$	−6.92820			−0.243282			−0.121641	+	0.992574i	$0.538816\pi$
$812$	25.0000	−	8.66025i	0.877328	−	0.303915i
$813$		0			0
$814$	6.00000	−	6.00000i	0.210300	−	0.210300i
$815$	−15.5885	−	27.0000i	−0.546040	−	0.945769i
$816$		0			0
$817$	16.5000	+	9.52628i	0.577262	+	0.333282i
$818$	−15.5885	+	15.5885i	−0.545038	+	0.545038i
$819$		0			0
$820$			12.0000i			0.419058i
$821$	−27.5000	+	47.6314i	−0.959757	+	1.66235i	−0.236670	+	0.971590i	$0.576056\pi$
$821$	−27.5000	+	47.6314i	−0.959757	+	1.66235i	−0.723087	+	0.690757i	$0.757277\pi$
$822$		0			0
$823$	18.1865	−	10.5000i	0.633943	−	0.366007i	−0.148335	−	0.988937i	$-0.547391\pi$
$823$	18.1865	−	10.5000i	0.633943	−	0.366007i	0.782277	+	0.622930i	$0.214058\pi$
$824$		0			0
$825$		0			0
$826$	6.46410	−	0.464102i	0.224915	−	0.0161482i
$827$		−	10.0000i		−	0.347734i	−0.984769	−	0.173867i	$-0.944374\pi$
$827$		−	10.0000i		−	0.347734i	0.984769	−	0.173867i	$-0.0556263\pi$
$828$		0			0
$829$	10.5000	+	6.06218i	0.364680	+	0.210548i	0.671132	−	0.741338i	$-0.265808\pi$
$829$	10.5000	+	6.06218i	0.364680	+	0.210548i	−0.306452	+	0.951886i	$0.599142\pi$
$830$	−18.0000	+	18.0000i	−0.624789	+	0.624789i
$831$		0			0
$832$	20.7846	−	36.0000i	0.720577	−	1.24808i
$833$	13.5000	−	33.7750i	0.467747	−	1.17023i
$834$		0			0
$835$	−15.5885	−	9.00000i	−0.539461	−	0.311458i
$836$	−3.46410	+	6.00000i	−0.119808	+	0.207514i
$837$		0			0
$838$	5.70577	−	21.2942i	0.197103	−	0.735597i
$839$	−9.52628	−	16.5000i	−0.328884	−	0.569643i	0.653407	−	0.757007i	$-0.273339\pi$
$839$	−9.52628	−	16.5000i	−0.328884	−	0.569643i	−0.982291	+	0.187364i	$0.940006\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	−23.0000	−	23.0000i	−0.792632	−	0.792632i
$843$		0			0
$844$	50.0000			1.72107
$845$	42.0000	−	24.2487i	1.44484	−	0.834181i
$846$		0			0
$847$	12.1244	−	14.0000i	0.416598	−	0.481046i
$848$	−2.00000	−	3.46410i	−0.0686803	−	0.118958i
$849$		0			0
$850$	49.6865	+	13.3135i	1.70423	+	0.456648i
$851$	−10.3923	+	6.00000i	−0.356244	+	0.205677i
$852$		0			0
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	−0.833012	−	0.553255i	$-0.813386\pi$
$853$	−22.5000	+	12.9904i	−0.770385	+	0.444782i	0.0626267	+	0.998037i	$0.480052\pi$
$854$	−16.0981	+	10.9019i	−0.550865	+	0.373056i
$855$		0			0
$856$	−5.12436	+	19.1244i	−0.175147	+	0.653657i
$857$		−	24.2487i		−	0.828320i	−0.910204	−	0.414160i	$-0.864075\pi$
$857$		−	24.2487i		−	0.828320i	0.910204	−	0.414160i	$-0.135925\pi$
$858$		0			0
$859$	−27.7128			−0.945549			−0.472774	−	0.881183i	$-0.656747\pi$
$859$	−27.7128			−0.945549			−0.472774	+	0.881183i	$0.656747\pi$
$860$	66.0000	+	38.1051i	2.25058	+	1.29937i
$861$		0			0
$862$	−6.83013	−	1.83013i	−0.232635	−	0.0623344i
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.114296	−	0.993447i	$-0.463539\pi$
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.917498	+	0.397740i	$0.130205\pi$
$864$		0			0
$865$	33.0000	−	57.1577i	1.12203	−	1.94342i
$866$	−10.1436	−	37.8564i	−0.344693	−	1.28641i
$867$		0			0
$868$	−25.9808	+	9.00000i	−0.881845	+	0.305480i
$869$	3.00000	−	5.19615i	0.101768	−	0.176267i
$870$		0			0
$871$	46.7654			1.58458
$872$	−2.19615	−	8.19615i	−0.0743711	−	0.277557i
$873$		0			0
$874$	6.92820	−	6.92820i	0.234350	−	0.234350i
$875$	13.8564	+	12.0000i	0.468432	+	0.405674i
$876$		0			0
$877$	16.0000			0.540282			0.270141	−	0.962821i	$-0.412930\pi$
$877$	16.0000			0.540282			0.270141	+	0.962821i	$0.412930\pi$
$878$	−4.43782	+	16.5622i	−0.149769	+	0.558946i
$879$		0			0
$880$	−13.8564	+	24.0000i	−0.467099	+	0.809040i
$881$		−	24.2487i		−	0.816960i	−0.912767	−	0.408480i	$-0.866059\pi$
$881$		−	24.2487i		−	0.816960i	0.912767	−	0.408480i	$-0.133941\pi$
$882$		0			0
$883$		−	14.0000i		−	0.471138i	−0.971858	−	0.235569i	$-0.924305\pi$
$883$		−	14.0000i		−	0.471138i	0.971858	−	0.235569i	$-0.0756953\pi$
$884$	46.7654	+	27.0000i	1.57289	+	0.908108i
$885$		0			0
$886$	−42.3468	−	11.3468i	−1.42267	−	0.381203i
$887$	−38.1051			−1.27944			−0.639722	−	0.768606i	$-0.720951\pi$
$887$	−38.1051			−1.27944			−0.639722	+	0.768606i	$0.720951\pi$
$888$		0			0
$889$	−12.0000	−	10.3923i	−0.402467	−	0.348547i
$890$	−30.0000	−	30.0000i	−1.00560	−	1.00560i
$891$		0			0
$892$	−27.0000	−	15.5885i	−0.904027	−	0.521940i
$893$	−3.00000			−0.100391
$894$		0			0
$895$	−8.66025	+	15.0000i	−0.289480	+	0.501395i
$896$	26.9282	+	13.0718i	0.899608	+	0.436698i
$897$		0			0
$898$	−35.5167	+	9.51666i	−1.18521	+	0.317575i
$899$	12.9904	−	22.5000i	0.433253	−	0.750417i
$900$		0			0
$901$	4.50000	−	2.59808i	0.149917	−	0.0865545i
$902$	1.26795	−	4.73205i	0.0422181	−	0.157560i
$903$		0			0
$904$	13.9090	+	51.9090i	0.462605	+	1.72647i
$905$	60.0000			1.99447
$906$		0			0
$907$		−	2.00000i		−	0.0664089i	−0.999449	−	0.0332045i	$-0.989429\pi$
$907$		−	2.00000i		−	0.0664089i	0.999449	−	0.0332045i	$-0.0105712\pi$
$908$	−12.0000	+	6.92820i	−0.398234	+	0.229920i
$909$		0			0
$910$	37.7654	+	55.7654i	1.25191	+	1.84860i
$911$	−11.2583	+	6.50000i	−0.373005	+	0.215355i	−0.674771	−	0.738028i	$-0.735757\pi$
$911$	−11.2583	+	6.50000i	−0.373005	+	0.215355i	0.301765	+	0.953382i	$0.402424\pi$
$912$		0			0
$913$	9.00000	−	5.19615i	0.297857	−	0.171968i
$914$	1.09808	−	4.09808i	0.0363211	−	0.135552i
$915$		0			0
$916$	−3.46410	−	6.00000i	−0.114457	−	0.198246i
$917$	−24.0000	+	27.7128i	−0.792550	+	0.915158i
$918$		0			0
$919$	−4.33013	+	2.50000i	−0.142838	+	0.0824674i	−0.569716	−	0.821842i	$-0.692947\pi$
$919$	−4.33013	+	2.50000i	−0.142838	+	0.0824674i	0.426878	+	0.904309i	$0.359613\pi$
$920$	27.7128	−	27.7128i	0.913664	−	0.913664i
$921$		0			0
$922$	32.9090	−	32.9090i	1.08380	−	1.08380i
$923$	−5.19615	+	9.00000i	−0.171033	+	0.296239i
$924$		0			0
$925$	10.5000	+	18.1865i	0.345238	+	0.597970i
$926$	−45.0788	−	12.0788i	−1.48138	−	0.396935i
$927$		0			0
$928$	−27.3205	+	7.32051i	−0.896840	+	0.240307i
$929$	19.5000	+	11.2583i	0.639774	+	0.369374i	0.784528	−	0.620094i	$-0.212906\pi$
$929$	19.5000	+	11.2583i	0.639774	+	0.369374i	−0.144753	+	0.989468i	$0.546239\pi$
$930$		0			0
$931$	−9.52628	+	7.50000i	−0.312211	+	0.245803i
$932$	1.73205	+	1.00000i	0.0567352	+	0.0327561i
$933$		0			0
$934$	1.73205	+	1.73205i	0.0566744	+	0.0566744i
$935$	−31.1769	−	18.0000i	−1.01959	−	0.588663i
$936$		0			0
$937$		−	3.46410i		−	0.113167i	−0.998398	−	0.0565836i	$-0.981979\pi$
$937$		−	3.46410i		−	0.113167i	0.998398	−	0.0565836i	$-0.0180208\pi$
$938$	2.41154	+	33.5885i	0.0787397	+	1.09670i
$939$		0			0
$940$	−12.0000			−0.391397
$941$	22.5000	−	12.9904i	0.733479	−	0.423474i	−0.0862145	−	0.996277i	$-0.527477\pi$
$941$	22.5000	−	12.9904i	0.733479	−	0.423474i	0.819694	+	0.572802i	$0.194144\pi$
$942$		0			0
$943$	−3.46410	+	6.00000i	−0.112807	+	0.195387i
$944$	−6.92820			−0.225494
$945$		0			0
$946$	−22.0000	−	22.0000i	−0.715282	−	0.715282i
$947$	−37.2391	−	21.5000i	−1.21011	−	0.698656i	−0.247325	−	0.968933i	$-0.579552\pi$
$947$	−37.2391	−	21.5000i	−1.21011	−	0.698656i	−0.962783	+	0.270276i	$0.912885\pi$
$948$		0			0
$949$	−31.5000	−	54.5596i	−1.02253	−	1.77108i
$950$	−12.1244	−	12.1244i	−0.393366	−	0.393366i
$951$		0			0
$952$	−16.9808	+	34.9808i	−0.550350	+	1.13373i
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$		0			0
$955$	−12.1244	+	21.0000i	−0.392335	+	0.679544i
$956$	22.0000			0.711531
$957$		0			0
$958$	−28.3923	+	7.60770i	−0.917314	+	0.245793i
$959$	−13.8564	+	16.0000i	−0.447447	+	0.516667i
$960$		0			0
$961$	2.00000	−	3.46410i	0.0645161	−	0.111745i
$962$	5.70577	+	21.2942i	0.183961	+	0.686553i
$963$		0			0
$964$	−3.46410	−	6.00000i	−0.111571	−	0.193247i
$965$	27.0000	−	15.5885i	0.869161	−	0.501810i
$966$		0			0
$967$	−49.3634	−	28.5000i	−1.58742	−	0.916498i	−0.993730	−	0.111805i	$-0.964337\pi$
$967$	−49.3634	−	28.5000i	−1.58742	−	0.916498i	−0.593691	−	0.804693i	$-0.702330\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$		0			0
$970$	6.00000	+	6.00000i	0.192648	+	0.192648i
$971$	2.59808	+	4.50000i	0.0833762	+	0.144412i	0.904698	−	0.426053i	$-0.140096\pi$
$971$	2.59808	+	4.50000i	0.0833762	+	0.144412i	−0.821322	+	0.570465i	$0.806763\pi$
$972$		0			0
$973$	19.5000	+	56.2917i	0.625141	+	1.80463i
$974$	−31.4186	−	8.41858i	−1.00672	−	0.269749i
$975$		0			0
$976$	18.0000	−	10.3923i	0.576166	−	0.332650i
$977$	−23.5000	−	40.7032i	−0.751832	−	1.30221i	−0.946934	−	0.321428i	$-0.895837\pi$
$977$	−23.5000	−	40.7032i	−0.751832	−	1.30221i	0.195103	−	0.980783i	$-0.437496\pi$
$978$		0			0
$979$	8.66025	+	15.0000i	0.276783	+	0.479402i
$980$	−38.1051	+	30.0000i	−1.21722	+	0.958315i
$981$		0			0
$982$	25.9545	+	6.95448i	0.828241	+	0.221926i
$983$	17.3205			0.552438			0.276219	−	0.961095i	$-0.410918\pi$
$983$	17.3205			0.552438			0.276219	+	0.961095i	$0.410918\pi$
$984$		0			0
$985$		−	34.6410i		−	1.10375i
$986$	−9.50962	−	35.4904i	−0.302848	−	1.13024i
$987$		0			0
$988$	−9.00000	−	15.5885i	−0.286328	−	0.495935i
$989$	22.0000	+	38.1051i	0.699559	+	1.21167i
$990$		0			0
$991$	42.4352	+	24.5000i	1.34800	+	0.778268i	0.987966	−	0.154671i	$-0.0494318\pi$
$991$	42.4352	+	24.5000i	1.34800	+	0.778268i	0.360034	+	0.932939i	$0.382765\pi$
$992$	28.3923	−	7.60770i	0.901457	−	0.241545i
$993$		0			0
$994$	−6.73205	−	3.26795i	−0.213528	−	0.103653i
$995$	5.19615	+	3.00000i	0.164729	+	0.0951064i
$996$		0			0
$997$			24.2487i			0.767964i	0.923340	+	0.383982i	$0.125448\pi$
$997$			24.2487i			0.767964i	−0.923340	+	0.383982i	$0.874552\pi$
$998$	−0.732051	−	2.73205i	−0.0231727	−	0.0864816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.a.199.1		4
3.2	odd	2		252.2.n.a.31.2	yes	4
4.3	odd	2	inner	756.2.n.a.199.2		4
7.5	odd	6		756.2.bj.a.523.2		4
9.2	odd	6		252.2.bj.a.115.1	yes	4
9.7	even	3		756.2.bj.a.451.2		4
12.11	even	2		252.2.n.a.31.1	✓	4
21.5	even	6		252.2.bj.a.103.1	yes	4
28.19	even	6		756.2.bj.a.523.1		4
36.7	odd	6		756.2.bj.a.451.1		4
36.11	even	6		252.2.bj.a.115.2	yes	4
63.47	even	6		252.2.n.a.187.1	yes	4
63.61	odd	6	inner	756.2.n.a.19.2		4
84.47	odd	6		252.2.bj.a.103.2	yes	4
252.47	odd	6		252.2.n.a.187.2	yes	4
252.187	even	6	inner	756.2.n.a.19.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.a.31.1	✓	4	12.11	even	2
252.2.n.a.31.2	yes	4	3.2	odd	2
252.2.n.a.187.1	yes	4	63.47	even	6
252.2.n.a.187.2	yes	4	252.47	odd	6
252.2.bj.a.103.1	yes	4	21.5	even	6
252.2.bj.a.103.2	yes	4	84.47	odd	6
252.2.bj.a.115.1	yes	4	9.2	odd	6
252.2.bj.a.115.2	yes	4	36.11	even	6
756.2.n.a.19.1		4	252.187	even	6	inner
756.2.n.a.19.2		4	63.61	odd	6	inner
756.2.n.a.199.1		4	1.1	even	1	trivial
756.2.n.a.199.2		4	4.3	odd	2	inner
756.2.bj.a.451.1		4	36.7	odd	6
756.2.bj.a.451.2		4	9.7	even	3
756.2.bj.a.523.1		4	28.19	even	6
756.2.bj.a.523.2		4	7.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -3.46410i q^{5} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -3.46410i q^{5} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.26795 + 4.73205i) q^{10} -2.00000i q^{11} +(4.50000 + 2.59808i) q^{13} +(-1.63397 + 3.36603i) q^{14} +(2.00000 - 3.46410i) q^{16} +(4.50000 + 2.59808i) q^{17} +(-0.866025 - 1.50000i) q^{19} +(-3.46410 - 6.00000i) q^{20} +(0.732051 + 2.73205i) q^{22} -4.00000i q^{23} -7.00000 q^{25} +(-7.09808 - 1.90192i) q^{26} +(1.00000 - 5.19615i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-2.59808 - 4.50000i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-7.09808 - 1.90192i) q^{34} +(-6.92820 - 6.00000i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.73205 + 1.73205i) q^{38} +(6.92820 + 6.92820i) q^{40} +(-1.50000 - 0.866025i) q^{41} +(-9.52628 + 5.50000i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.46410 + 5.46410i) q^{46} +(0.866025 - 1.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(9.56218 - 2.56218i) q^{50} +10.3923 q^{52} +(0.500000 - 0.866025i) q^{53} -6.92820 q^{55} +(0.535898 + 7.46410i) q^{56} +(-5.00000 - 5.00000i) q^{58} +(-0.866025 - 1.50000i) q^{59} +(4.50000 + 2.59808i) q^{61} +(5.19615 + 5.19615i) q^{62} -8.00000i q^{64} +(9.00000 - 15.5885i) q^{65} +(7.79423 - 4.50000i) q^{67} +10.3923 q^{68} +(11.6603 + 5.66025i) q^{70} +2.00000i q^{71} +(-10.5000 - 6.06218i) q^{73} +(3.00000 + 3.00000i) q^{74} +(-3.00000 - 1.73205i) q^{76} +(-4.00000 - 3.46410i) q^{77} +(2.59808 + 1.50000i) q^{79} +(-12.0000 - 6.92820i) q^{80} +(2.36603 + 0.633975i) q^{82} +(2.59808 + 4.50000i) q^{83} +(9.00000 - 15.5885i) q^{85} +(11.0000 - 11.0000i) q^{86} +(4.00000 + 4.00000i) q^{88} +(-7.50000 + 4.33013i) q^{89} +(12.9904 - 4.50000i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(-0.633975 + 2.36603i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(1.50000 - 0.866025i) q^{97} +(3.90192 + 9.09808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 8 * q^8	\( 4 q - 2 q^{2} - 8 q^{8} + 12 q^{10} + 18 q^{13} - 10 q^{14} + 8 q^{16} + 18 q^{17} - 4 q^{22} - 28 q^{25} - 18 q^{26} + 4 q^{28} + 10 q^{29} + 8 q^{32} - 18 q^{34} - 6 q^{37} - 6 q^{41} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 14 q^{50} + 2 q^{53} + 16 q^{56} - 20 q^{58} + 18 q^{61} + 36 q^{65} + 12 q^{70} - 42 q^{73} + 12 q^{74} - 12 q^{76} - 16 q^{77} - 48 q^{80} + 6 q^{82} + 36 q^{85} + 44 q^{86} + 16 q^{88} - 30 q^{89} - 16 q^{92} - 6 q^{94} + 6 q^{97} + 26 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 8 * q^8 + 12 * q^10 + 18 * q^13 - 10 * q^14 + 8 * q^16 + 18 * q^17 - 4 * q^22 - 28 * q^25 - 18 * q^26 + 4 * q^28 + 10 * q^29 + 8 * q^32 - 18 * q^34 - 6 * q^37 - 6 * q^41 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 14 * q^50 + 2 * q^53 + 16 * q^56 - 20 * q^58 + 18 * q^61 + 36 * q^65 + 12 * q^70 - 42 * q^73 + 12 * q^74 - 12 * q^76 - 16 * q^77 - 48 * q^80 + 6 * q^82 + 36 * q^85 + 44 * q^86 + 16 * q^88 - 30 * q^89 - 16 * q^92 - 6 * q^94 + 6 * q^97 + 26 * q^98

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