LMFDB - Embedded newform 363.2.e.a.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, 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:	$2.89856959337$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			124.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.a.202.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80902 + 1.31433i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.61803 - 1.17557i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-1.38197 + 4.25325i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.80902 + 1.31433i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.61803 - 1.17557i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-1.38197 + 4.25325i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +4.47214 q^{10} +3.00000 q^{12} +(-3.09017 - 9.51057i) q^{14} +(0.618034 - 1.90211i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-3.61803 - 2.62866i) q^{17} +(0.690983 - 2.12663i) q^{18} +(-1.38197 - 4.25325i) q^{19} +(-4.85410 + 3.52671i) q^{20} -4.47214 q^{21} -4.00000 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(10.8541 + 7.88597i) q^{28} +(1.38197 - 4.25325i) q^{29} +(1.38197 + 4.25325i) q^{30} -6.70820 q^{32} +10.0000 q^{34} +(7.23607 - 5.25731i) q^{35} +(0.927051 + 2.85317i) q^{36} +(0.618034 - 1.90211i) q^{37} +(8.09017 + 5.87785i) q^{38} +(1.38197 - 4.25325i) q^{40} +(-1.38197 - 4.25325i) q^{41} +(8.09017 - 5.87785i) q^{42} +4.47214 q^{43} +2.00000 q^{45} +(7.23607 - 5.25731i) q^{46} +(2.47214 + 7.60845i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-10.5172 - 7.64121i) q^{49} +(1.80902 + 1.31433i) q^{50} +(1.38197 - 4.25325i) q^{51} +(-4.85410 + 3.52671i) q^{53} +2.23607 q^{54} -10.0000 q^{56} +(3.61803 - 2.62866i) q^{57} +(3.09017 + 9.51057i) q^{58} +(-4.85410 - 3.52671i) q^{60} +(-7.23607 - 5.25731i) q^{61} +(-1.38197 - 4.25325i) q^{63} +(10.5172 - 7.64121i) q^{64} -12.0000 q^{67} +(-10.8541 + 7.88597i) q^{68} +(-1.23607 - 3.80423i) q^{69} +(-6.18034 + 19.0211i) q^{70} +(6.47214 + 4.70228i) q^{71} +(-1.80902 - 1.31433i) q^{72} +(-2.76393 + 8.50651i) q^{73} +(1.38197 + 4.25325i) q^{74} +(0.809017 - 0.587785i) q^{75} -13.4164 q^{76} +(-10.8541 + 7.88597i) q^{79} +(-0.618034 - 1.90211i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.09017 + 5.87785i) q^{82} +(7.23607 + 5.25731i) q^{83} +(-4.14590 + 12.7598i) q^{84} +(2.76393 + 8.50651i) q^{85} +(-8.09017 + 5.87785i) q^{86} +4.47214 q^{87} -14.0000 q^{89} +(-3.61803 + 2.62866i) q^{90} +(-3.70820 + 11.4127i) q^{92} +(-14.4721 - 10.5146i) q^{94} +(-2.76393 + 8.50651i) q^{95} +(-2.07295 - 6.37988i) q^{96} +(-1.61803 + 1.17557i) q^{97} +29.0689 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} - 5 q^{6} - 10 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - q^3 - 3 * q^4 - 2 * q^5 - 5 * q^6 - 10 * q^7 + 5 * q^8 - q^9	$ 4 q - 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} - 5 q^{6} - 10 q^{7} + 5 q^{8} - q^{9} + 12 q^{12} + 10 q^{14} - 2 q^{15} + q^{16} - 10 q^{17} + 5 q^{18} - 10 q^{19} - 6 q^{20} - 16 q^{23} - 5 q^{24} + q^{25} - q^{27} + 30 q^{28} + 10 q^{29} + 10 q^{30} + 40 q^{34} + 20 q^{35} - 3 q^{36} - 2 q^{37} + 10 q^{38} + 10 q^{40} - 10 q^{41} + 10 q^{42} + 8 q^{45} + 20 q^{46} - 8 q^{47} + q^{48} - 13 q^{49} + 5 q^{50} + 10 q^{51} - 6 q^{53} - 40 q^{56} + 10 q^{57} - 10 q^{58} - 6 q^{60} - 20 q^{61} - 10 q^{63} + 13 q^{64} - 48 q^{67} - 30 q^{68} + 4 q^{69} + 20 q^{70} + 8 q^{71} - 5 q^{72} - 20 q^{73} + 10 q^{74} + q^{75} - 30 q^{79} + 2 q^{80} - q^{81} + 10 q^{82} + 20 q^{83} - 30 q^{84} + 20 q^{85} - 10 q^{86} - 56 q^{89} - 10 q^{90} + 12 q^{92} - 40 q^{94} - 20 q^{95} - 15 q^{96} - 2 q^{97}+O(q^{100}) $ 4 * q - 5 * q^2 - q^3 - 3 * q^4 - 2 * q^5 - 5 * q^6 - 10 * q^7 + 5 * q^8 - q^9 + 12 * q^12 + 10 * q^14 - 2 * q^15 + q^16 - 10 * q^17 + 5 * q^18 - 10 * q^19 - 6 * q^20 - 16 * q^23 - 5 * q^24 + q^25 - q^27 + 30 * q^28 + 10 * q^29 + 10 * q^30 + 40 * q^34 + 20 * q^35 - 3 * q^36 - 2 * q^37 + 10 * q^38 + 10 * q^40 - 10 * q^41 + 10 * q^42 + 8 * q^45 + 20 * q^46 - 8 * q^47 + q^48 - 13 * q^49 + 5 * q^50 + 10 * q^51 - 6 * q^53 - 40 * q^56 + 10 * q^57 - 10 * q^58 - 6 * q^60 - 20 * q^61 - 10 * q^63 + 13 * q^64 - 48 * q^67 - 30 * q^68 + 4 * q^69 + 20 * q^70 + 8 * q^71 - 5 * q^72 - 20 * q^73 + 10 * q^74 + q^75 - 30 * q^79 + 2 * q^80 - q^81 + 10 * q^82 + 20 * q^83 - 30 * q^84 + 20 * q^85 - 10 * q^86 - 56 * q^89 - 10 * q^90 + 12 * q^92 - 40 * q^94 - 20 * q^95 - 15 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.80902	+	1.31433i	−1.27917	+	0.929370i	−0.999528	−	0.0307347i	$-0.990215\pi$
$2$	−1.80902	+	1.31433i	−1.27917	+	0.929370i	−0.279641	+	0.960105i	$0.590215\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.927051	−	2.85317i	0.463525	−	1.42658i
$5$	−1.61803	−	1.17557i	−0.723607	−	0.525731i	0.163928	−	0.986472i	$-0.447584\pi$
$5$	−1.61803	−	1.17557i	−0.723607	−	0.525731i	−0.887535	+	0.460741i	$0.847584\pi$
$6$	−1.80902	−	1.31433i	−0.738528	−	0.536572i
$7$	−1.38197	+	4.25325i	−0.522334	+	1.60758i	0.247194	+	0.968966i	$0.420491\pi$
$7$	−1.38197	+	4.25325i	−0.522334	+	1.60758i	−0.769528	+	0.638613i	$0.779509\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	4.47214			1.41421
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$13$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$14$	−3.09017	−	9.51057i	−0.825883	−	2.54181i
$15$	0.618034	−	1.90211i	0.159576	−	0.491123i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−3.61803	−	2.62866i	−0.877502	−	0.637543i	0.0550873	−	0.998482i	$-0.482456\pi$
$17$	−3.61803	−	2.62866i	−0.877502	−	0.637543i	−0.932589	+	0.360939i	$0.882456\pi$
$18$	0.690983	−	2.12663i	0.162866	−	0.501251i
$19$	−1.38197	−	4.25325i	−0.317045	−	0.975763i	−0.974905	−	0.222623i	$-0.928538\pi$
$19$	−1.38197	−	4.25325i	−0.317045	−	0.975763i	0.657860	−	0.753140i	$-0.271462\pi$
$20$	−4.85410	+	3.52671i	−1.08541	+	0.788597i
$21$	−4.47214			−0.975900
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.80902	+	1.31433i	−0.369264	+	0.268286i
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	10.8541	+	7.88597i	2.05123	+	1.49031i
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	−0.736881	−	0.676023i	$-0.763702\pi$
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	0.993505	−	0.113787i	$-0.0362980\pi$
$30$	1.38197	+	4.25325i	0.252311	+	0.776534i
$31$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$31$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	10.0000			1.71499
$35$	7.23607	−	5.25731i	1.22312	−	0.888648i
$36$	0.927051	+	2.85317i	0.154508	+	0.475528i
$37$	0.618034	−	1.90211i	0.101604	−	0.312705i	−0.887314	−	0.461165i	$-0.847432\pi$
$37$	0.618034	−	1.90211i	0.101604	−	0.312705i	0.988918	+	0.148460i	$0.0474315\pi$
$38$	8.09017	+	5.87785i	1.31240	+	0.953514i
$39$		0			0
$40$	1.38197	−	4.25325i	0.218508	−	0.672499i
$41$	−1.38197	−	4.25325i	−0.215827	−	0.664247i	−0.999094	−	0.0425613i	$-0.986448\pi$
$41$	−1.38197	−	4.25325i	−0.215827	−	0.664247i	0.783267	−	0.621685i	$-0.213552\pi$
$42$	8.09017	−	5.87785i	1.24834	−	0.906972i
$43$	4.47214			0.681994			0.340997	−	0.940064i	$-0.389235\pi$
$43$	4.47214			0.681994			0.340997	+	0.940064i	$0.389235\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$	7.23607	−	5.25731i	1.06690	−	0.775148i
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	0.952692	+	0.303938i	$0.0983015\pi$
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	−0.592094	+	0.805869i	$0.701699\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−10.5172	−	7.64121i	−1.50246	−	1.09160i
$50$	1.80902	+	1.31433i	0.255834	+	0.185874i
$51$	1.38197	−	4.25325i	0.193514	−	0.595575i
$52$		0			0
$53$	−4.85410	+	3.52671i	−0.666762	+	0.484431i	−0.868940	−	0.494918i	$-0.835198\pi$
$53$	−4.85410	+	3.52671i	−0.666762	+	0.484431i	0.202178	+	0.979349i	$0.435198\pi$
$54$	2.23607			0.304290
$55$		0			0
$56$	−10.0000			−1.33631
$57$	3.61803	−	2.62866i	0.479220	−	0.348174i
$58$	3.09017	+	9.51057i	0.405759	+	1.24880i
$59$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$59$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$60$	−4.85410	−	3.52671i	−0.626662	−	0.455296i
$61$	−7.23607	−	5.25731i	−0.926484	−	0.673130i	0.0186458	−	0.999826i	$-0.494065\pi$
$61$	−7.23607	−	5.25731i	−0.926484	−	0.673130i	−0.945129	+	0.326696i	$0.894065\pi$
$62$		0			0
$63$	−1.38197	−	4.25325i	−0.174111	−	0.535860i
$64$	10.5172	−	7.64121i	1.31465	−	0.955151i
$65$		0			0
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−10.8541	+	7.88597i	−1.31625	+	0.956314i
$69$	−1.23607	−	3.80423i	−0.148805	−	0.457975i
$70$	−6.18034	+	19.0211i	−0.738692	+	2.27346i
$71$	6.47214	+	4.70228i	0.768101	+	0.558058i	0.901384	−	0.433020i	$-0.142552\pi$
$71$	6.47214	+	4.70228i	0.768101	+	0.558058i	−0.133283	+	0.991078i	$0.542552\pi$
$72$	−1.80902	−	1.31433i	−0.213195	−	0.154895i
$73$	−2.76393	+	8.50651i	−0.323494	+	0.995611i	0.648622	+	0.761111i	$0.275346\pi$
$73$	−2.76393	+	8.50651i	−0.323494	+	0.995611i	−0.972116	+	0.234501i	$0.924654\pi$
$74$	1.38197	+	4.25325i	0.160650	+	0.494431i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	−13.4164			−1.53897
$77$		0			0
$78$		0			0
$79$	−10.8541	+	7.88597i	−1.22118	+	0.887241i	−0.996198	−	0.0871218i	$-0.972233\pi$
$79$	−10.8541	+	7.88597i	−1.22118	+	0.887241i	−0.224984	+	0.974362i	$0.572233\pi$
$80$	−0.618034	−	1.90211i	−0.0690983	−	0.212663i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	8.09017	+	5.87785i	0.893410	+	0.649100i
$83$	7.23607	+	5.25731i	0.794262	+	0.577065i	0.909225	−	0.416305i	$-0.136675\pi$
$83$	7.23607	+	5.25731i	0.794262	+	0.577065i	−0.114963	+	0.993370i	$0.536675\pi$
$84$	−4.14590	+	12.7598i	−0.452355	+	1.39220i
$85$	2.76393	+	8.50651i	0.299791	+	0.922660i
$86$	−8.09017	+	5.87785i	−0.872385	+	0.633825i
$87$	4.47214			0.479463
$88$		0			0
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$	−3.61803	+	2.62866i	−0.381374	+	0.277085i
$91$		0			0
$92$	−3.70820	+	11.4127i	−0.386607	+	1.18985i
$93$		0			0
$94$	−14.4721	−	10.5146i	−1.49269	−	1.08450i
$95$	−2.76393	+	8.50651i	−0.283573	+	0.872749i
$96$	−2.07295	−	6.37988i	−0.211569	−	0.651144i
$97$	−1.61803	+	1.17557i	−0.164286	+	0.119361i	−0.666891	−	0.745155i	$-0.732375\pi$
$97$	−1.61803	+	1.17557i	−0.164286	+	0.119361i	0.502604	+	0.864517i	$0.332375\pi$
$98$	29.0689			2.93640
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−3.61803	+	2.62866i	−0.360008	+	0.261561i	−0.753055	−	0.657957i	$-0.771421\pi$
$101$	−3.61803	+	2.62866i	−0.360008	+	0.261561i	0.393048	+	0.919518i	$0.371421\pi$
$102$	3.09017	+	9.51057i	0.305972	+	0.941686i
$103$	4.94427	−	15.2169i	0.487174	−	1.49937i	−0.341634	−	0.939833i	$-0.610980\pi$
$103$	4.94427	−	15.2169i	0.487174	−	1.49937i	0.828808	−	0.559533i	$-0.189020\pi$
$104$		0			0
$105$	7.23607	+	5.25731i	0.706168	+	0.513061i
$106$	4.14590	−	12.7598i	0.402685	−	1.23934i
$107$	2.76393	+	8.50651i	0.267199	+	0.822355i	0.991179	+	0.132533i	$0.0423112\pi$
$107$	2.76393	+	8.50651i	0.267199	+	0.822355i	−0.723979	+	0.689822i	$0.757689\pi$
$108$	−2.42705	+	1.76336i	−0.233543	+	0.169679i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$	−3.61803	+	2.62866i	−0.341872	+	0.248385i
$113$	1.85410	+	5.70634i	0.174419	+	0.536807i	0.999606	−	0.0280521i	$-0.00893043\pi$
$113$	1.85410	+	5.70634i	0.174419	+	0.536807i	−0.825187	+	0.564859i	$0.808930\pi$
$114$	−3.09017	+	9.51057i	−0.289421	+	0.890746i
$115$	6.47214	+	4.70228i	0.603530	+	0.438490i
$116$	−10.8541	−	7.88597i	−1.00778	−	0.732194i
$117$		0			0
$118$		0			0
$119$	16.1803	−	11.7557i	1.48325	−	1.07764i
$120$	4.47214			0.408248
$121$		0			0
$122$	20.0000			1.81071
$123$	3.61803	−	2.62866i	0.326227	−	0.237018i
$124$		0			0
$125$	−3.70820	+	11.4127i	−0.331672	+	1.02078i
$126$	8.09017	+	5.87785i	0.720730	+	0.523641i
$127$	−10.8541	−	7.88597i	−0.963146	−	0.699766i	−0.00926659	−	0.999957i	$-0.502950\pi$
$127$	−10.8541	−	7.88597i	−0.963146	−	0.699766i	−0.953879	+	0.300191i	$0.902950\pi$
$128$	−4.83688	+	14.8864i	−0.427524	+	1.31578i
$129$	1.38197	+	4.25325i	0.121675	+	0.374478i
$130$		0			0
$131$	−17.8885			−1.56293			−0.781465	−	0.623949i	$-0.785527\pi$
$131$	−17.8885			−1.56293			−0.781465	+	0.623949i	$0.785527\pi$
$132$		0			0
$133$	20.0000			1.73422
$134$	21.7082	−	15.7719i	1.87530	−	1.36249i
$135$	0.618034	+	1.90211i	0.0531919	+	0.163708i
$136$	3.09017	−	9.51057i	0.264980	−	0.815524i
$137$	−17.7984	−	12.9313i	−1.52062	−	1.10479i	−0.961180	−	0.275921i	$-0.911017\pi$
$137$	−17.7984	−	12.9313i	−1.52062	−	1.10479i	−0.559437	−	0.828873i	$-0.688983\pi$
$138$	7.23607	+	5.25731i	0.615975	+	0.447532i
$139$	4.14590	−	12.7598i	0.351650	−	1.08227i	−0.606276	−	0.795254i	$-0.707337\pi$
$139$	4.14590	−	12.7598i	0.351650	−	1.08227i	0.957926	−	0.287014i	$-0.0926628\pi$
$140$	−8.29180	−	25.5195i	−0.700785	−	2.15679i
$141$	−6.47214	+	4.70228i	−0.545052	+	0.396004i
$142$	−17.8885			−1.50117
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−7.23607	+	5.25731i	−0.600923	+	0.436596i
$146$	−6.18034	−	19.0211i	−0.511489	−	1.57420i
$147$	4.01722	−	12.3637i	0.331335	−	1.01974i
$148$	−4.85410	−	3.52671i	−0.399005	−	0.289894i
$149$	18.0902	+	13.1433i	1.48200	+	1.07674i	0.976904	+	0.213679i	$0.0685446\pi$
$149$	18.0902	+	13.1433i	1.48200	+	1.07674i	0.505100	+	0.863061i	$0.331455\pi$
$150$	−0.690983	+	2.12663i	−0.0564185	+	0.173638i
$151$	4.14590	+	12.7598i	0.337388	+	1.03837i	0.965534	+	0.260279i	$0.0838144\pi$
$151$	4.14590	+	12.7598i	0.337388	+	1.03837i	−0.628145	+	0.778096i	$0.716186\pi$
$152$	8.09017	−	5.87785i	0.656199	−	0.476757i
$153$	4.47214			0.361551
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.618034	+	1.90211i	0.0493245	+	0.151805i	0.972685	−	0.232129i	$-0.0745691\pi$
$157$	0.618034	+	1.90211i	0.0493245	+	0.151805i	−0.923361	+	0.383934i	$0.874569\pi$
$158$	9.27051	−	28.5317i	0.737522	−	2.26986i
$159$	−4.85410	−	3.52671i	−0.384955	−	0.279686i
$160$	10.8541	+	7.88597i	0.858092	+	0.623440i
$161$	5.52786	−	17.0130i	0.435657	−	1.34081i
$162$	0.690983	+	2.12663i	0.0542888	+	0.167084i
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	−0.707263	−	0.706951i	$-0.750070\pi$
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	0.453794	+	0.891107i	$0.350070\pi$
$164$	−13.4164			−1.04765
$165$		0			0
$166$	−20.0000			−1.55230
$167$	−7.23607	+	5.25731i	−0.559944	+	0.406823i	−0.831438	−	0.555617i	$-0.812482\pi$
$167$	−7.23607	+	5.25731i	−0.559944	+	0.406823i	0.271495	+	0.962440i	$0.412482\pi$
$168$	−3.09017	−	9.51057i	−0.238412	−	0.733756i
$169$	−4.01722	+	12.3637i	−0.309017	+	0.951057i
$170$	−16.1803	−	11.7557i	−1.24098	−	0.901621i
$171$	3.61803	+	2.62866i	0.276678	+	0.201018i
$172$	4.14590	−	12.7598i	0.316122	−	0.972923i
$173$	−4.14590	−	12.7598i	−0.315207	−	0.970107i	−0.975669	−	0.219248i	$-0.929640\pi$
$173$	−4.14590	−	12.7598i	−0.315207	−	0.970107i	0.660462	−	0.750859i	$-0.270360\pi$
$174$	−8.09017	+	5.87785i	−0.613314	+	0.445599i
$175$	4.47214			0.338062
$176$		0			0
$177$		0			0
$178$	25.3262	−	18.4006i	1.89828	−	1.37918i
$179$	−1.23607	−	3.80423i	−0.0923881	−	0.284341i	0.894176	−	0.447715i	$-0.147762\pi$
$179$	−1.23607	−	3.80423i	−0.0923881	−	0.284341i	−0.986564	+	0.163374i	$0.947762\pi$
$180$	1.85410	−	5.70634i	0.138197	−	0.425325i
$181$	8.09017	+	5.87785i	0.601338	+	0.436897i	0.846353	−	0.532622i	$-0.178793\pi$
$181$	8.09017	+	5.87785i	0.601338	+	0.436897i	−0.245016	+	0.969519i	$0.578793\pi$
$182$		0			0
$183$	2.76393	−	8.50651i	0.204316	−	0.628819i
$184$	−2.76393	−	8.50651i	−0.203760	−	0.627108i
$185$	−3.23607	+	2.35114i	−0.237920	+	0.172859i
$186$		0			0
$187$		0			0
$188$	24.0000			1.75038
$189$	3.61803	−	2.62866i	0.263173	−	0.191207i
$190$	−6.18034	−	19.0211i	−0.448369	−	1.37994i
$191$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$191$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$192$	10.5172	+	7.64121i	0.759015	+	0.551457i
$193$	14.4721	+	10.5146i	1.04173	+	0.756859i	0.970622	−	0.240610i	$-0.0773474\pi$
$193$	14.4721	+	10.5146i	1.04173	+	0.756859i	0.0711052	+	0.997469i	$0.477347\pi$
$194$	1.38197	−	4.25325i	0.0992194	−	0.305366i
$195$		0			0
$196$	−31.5517	+	22.9236i	−2.25369	+	1.63740i
$197$	22.3607			1.59313			0.796566	−	0.604551i	$-0.206648\pi$
$197$	22.3607			1.59313			0.796566	+	0.604551i	$0.206648\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	1.80902	−	1.31433i	0.127917	−	0.0929370i
$201$	−3.70820	−	11.4127i	−0.261557	−	0.804988i
$202$	3.09017	−	9.51057i	0.217424	−	0.669161i
$203$	16.1803	+	11.7557i	1.13564	+	0.825089i
$204$	−10.8541	−	7.88597i	−0.759939	−	0.552128i
$205$	−2.76393	+	8.50651i	−0.193041	+	0.594120i
$206$	11.0557	+	34.0260i	0.770289	+	2.37071i
$207$	3.23607	−	2.35114i	0.224922	−	0.163416i
$208$		0			0
$209$		0			0
$210$	−20.0000			−1.38013
$211$	3.61803	−	2.62866i	0.249076	−	0.180964i	−0.456241	−	0.889856i	$-0.650805\pi$
$211$	3.61803	−	2.62866i	0.249076	−	0.180964i	0.705317	+	0.708892i	$0.250805\pi$
$212$	5.56231	+	17.1190i	0.382021	+	1.17574i
$213$	−2.47214	+	7.60845i	−0.169388	+	0.521323i
$214$	−16.1803	−	11.7557i	−1.10607	−	0.803603i
$215$	−7.23607	−	5.25731i	−0.493496	−	0.358546i
$216$	0.690983	−	2.12663i	0.0470154	−	0.144699i
$217$		0			0
$218$		0			0
$219$	−8.94427			−0.604398
$220$		0			0
$221$		0			0
$222$	−3.61803	+	2.62866i	−0.242827	+	0.176424i
$223$	−4.94427	−	15.2169i	−0.331093	−	1.01900i	−0.968615	−	0.248567i	$-0.920040\pi$
$223$	−4.94427	−	15.2169i	−0.331093	−	1.01900i	0.637522	−	0.770432i	$-0.279960\pi$
$224$	9.27051	−	28.5317i	0.619412	−	1.90635i
$225$	0.809017	+	0.587785i	0.0539345	+	0.0391857i
$226$	−10.8541	−	7.88597i	−0.722004	−	0.524567i
$227$	2.76393	−	8.50651i	0.183449	−	0.564597i	−0.816470	−	0.577388i	$-0.804072\pi$
$227$	2.76393	−	8.50651i	0.183449	−	0.564597i	0.999918	+	0.0127917i	$0.00407183\pi$
$228$	−4.14590	−	12.7598i	−0.274569	−	0.845036i
$229$	−8.09017	+	5.87785i	−0.534613	+	0.388419i	−0.822081	−	0.569371i	$-0.807187\pi$
$229$	−8.09017	+	5.87785i	−0.534613	+	0.388419i	0.287467	+	0.957790i	$0.407187\pi$
$230$	−17.8885			−1.17954
$231$		0			0
$232$	10.0000			0.656532
$233$	3.61803	−	2.62866i	0.237025	−	0.172209i	−0.462932	−	0.886394i	$-0.653202\pi$
$233$	3.61803	−	2.62866i	0.237025	−	0.172209i	0.699957	+	0.714185i	$0.253202\pi$
$234$		0			0
$235$	4.94427	−	15.2169i	0.322529	−	0.992641i
$236$		0			0
$237$	−10.8541	−	7.88597i	−0.705050	−	0.512249i
$238$	−13.8197	+	42.5325i	−0.895796	+	2.75698i
$239$	2.76393	+	8.50651i	0.178784	+	0.550240i	0.999786	−	0.0206848i	$-0.00658466\pi$
$239$	2.76393	+	8.50651i	0.178784	+	0.550240i	−0.821002	+	0.570925i	$0.806585\pi$
$240$	1.61803	−	1.17557i	0.104444	−	0.0758827i
$241$	8.94427			0.576151			0.288076	−	0.957608i	$-0.406985\pi$
$241$	8.94427			0.576151			0.288076	+	0.957608i	$0.406985\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−21.7082	+	15.7719i	−1.38973	+	1.00969i
$245$	8.03444	+	24.7275i	0.513302	+	1.57978i
$246$	−3.09017	+	9.51057i	−0.197022	+	0.606371i
$247$		0			0
$248$		0			0
$249$	−2.76393	+	8.50651i	−0.175157	+	0.539078i
$250$	−8.29180	−	25.5195i	−0.524419	−	1.61400i
$251$	9.70820	−	7.05342i	0.612776	−	0.445208i	−0.237614	−	0.971360i	$-0.576365\pi$
$251$	9.70820	−	7.05342i	0.612776	−	0.445208i	0.850391	+	0.526151i	$0.176365\pi$
$252$	−13.4164			−0.845154
$253$		0			0
$254$	30.0000			1.88237
$255$	−7.23607	+	5.25731i	−0.453140	+	0.329226i
$256$	−2.78115	−	8.55951i	−0.173822	−	0.534969i
$257$	−6.79837	+	20.9232i	−0.424071	+	1.30516i	0.479810	+	0.877372i	$0.340706\pi$
$257$	−6.79837	+	20.9232i	−0.424071	+	1.30516i	−0.903881	+	0.427784i	$0.859294\pi$
$258$	−8.09017	−	5.87785i	−0.503672	−	0.365939i
$259$	7.23607	+	5.25731i	0.449627	+	0.326673i
$260$		0			0
$261$	1.38197	+	4.25325i	0.0855415	+	0.263270i
$262$	32.3607	−	23.5114i	1.99925	−	1.45254i
$263$	8.94427			0.551527			0.275764	−	0.961225i	$-0.411069\pi$
$263$	8.94427			0.551527			0.275764	+	0.961225i	$0.411069\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$	−36.1803	+	26.2866i	−2.21836	+	1.61173i
$267$	−4.32624	−	13.3148i	−0.264761	−	0.814852i
$268$	−11.1246	+	34.2380i	−0.679544	+	2.09142i
$269$	8.09017	+	5.87785i	0.493266	+	0.358379i	0.806439	−	0.591317i	$-0.201392\pi$
$269$	8.09017	+	5.87785i	0.493266	+	0.358379i	−0.313173	+	0.949696i	$0.601392\pi$
$270$	−3.61803	−	2.62866i	−0.220187	−	0.159975i
$271$	−4.14590	+	12.7598i	−0.251845	+	0.775100i	0.742589	+	0.669747i	$0.233597\pi$
$271$	−4.14590	+	12.7598i	−0.251845	+	0.775100i	−0.994435	+	0.105353i	$0.966403\pi$
$272$	−1.38197	−	4.25325i	−0.0837940	−	0.257891i
$273$		0			0
$274$	49.1935			2.97189
$275$		0			0
$276$	−12.0000			−0.722315
$277$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$277$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$278$	9.27051	+	28.5317i	0.556008	+	1.71122i
$279$		0			0
$280$	16.1803	+	11.7557i	0.966960	+	0.702538i
$281$	−25.3262	−	18.4006i	−1.51084	−	1.09769i	−0.965804	−	0.259272i	$-0.916517\pi$
$281$	−25.3262	−	18.4006i	−1.51084	−	1.09769i	−0.545032	−	0.838415i	$-0.683483\pi$
$282$	5.52786	−	17.0130i	0.329180	−	1.01311i
$283$	−4.14590	−	12.7598i	−0.246448	−	0.758489i	−0.995395	−	0.0958591i	$-0.969440\pi$
$283$	−4.14590	−	12.7598i	−0.246448	−	0.758489i	0.748947	−	0.662630i	$-0.230560\pi$
$284$	19.4164	−	14.1068i	1.15215	−	0.837087i
$285$	−8.94427			−0.529813
$286$		0			0
$287$	20.0000			1.18056
$288$	5.42705	−	3.94298i	0.319792	−	0.232343i
$289$	0.927051	+	2.85317i	0.0545324	+	0.167834i
$290$	6.18034	−	19.0211i	0.362922	−	1.11696i
$291$	−1.61803	−	1.17557i	−0.0948508	−	0.0689132i
$292$	21.7082	+	15.7719i	1.27038	+	0.922983i
$293$	−6.90983	+	21.2663i	−0.403677	+	1.24239i	0.518319	+	0.855188i	$0.326558\pi$
$293$	−6.90983	+	21.2663i	−0.403677	+	1.24239i	−0.921995	+	0.387201i	$0.873442\pi$
$294$	8.98278	+	27.6462i	0.523886	+	1.61236i
$295$		0			0
$296$	4.47214			0.259938
$297$		0			0
$298$	−50.0000			−2.89642
$299$		0			0
$300$	−0.927051	−	2.85317i	−0.0535233	−	0.164728i
$301$	−6.18034	+	19.0211i	−0.356229	+	1.09636i
$302$	−24.2705	−	17.6336i	−1.39661	−	1.01470i
$303$	−3.61803	−	2.62866i	−0.207851	−	0.151012i
$304$	1.38197	−	4.25325i	0.0792612	−	0.243941i
$305$	5.52786	+	17.0130i	0.316525	+	0.974162i
$306$	−8.09017	+	5.87785i	−0.462484	+	0.336014i
$307$	−4.47214			−0.255238			−0.127619	−	0.991823i	$-0.540734\pi$
$307$	−4.47214			−0.255238			−0.127619	+	0.991823i	$0.540734\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$		0			0
$311$	−3.70820	−	11.4127i	−0.210273	−	0.647154i	−0.999456	−	0.0329949i	$-0.989495\pi$
$311$	−3.70820	−	11.4127i	−0.210273	−	0.647154i	0.789183	−	0.614159i	$-0.210505\pi$
$312$		0			0
$313$	−11.3262	−	8.22899i	−0.640197	−	0.465130i	0.219721	−	0.975563i	$-0.429485\pi$
$313$	−11.3262	−	8.22899i	−0.640197	−	0.465130i	−0.859918	+	0.510433i	$0.829485\pi$
$314$	−3.61803	−	2.62866i	−0.204177	−	0.148344i
$315$	−2.76393	+	8.50651i	−0.155730	+	0.479287i
$316$	12.4377	+	38.2793i	0.699675	+	2.15338i
$317$	−14.5623	+	10.5801i	−0.817901	+	0.594240i	−0.916110	−	0.400926i	$-0.868688\pi$
$317$	−14.5623	+	10.5801i	−0.817901	+	0.594240i	0.0982098	+	0.995166i	$0.468688\pi$
$318$	13.4164			0.752355
$319$		0			0
$320$	−26.0000			−1.45344
$321$	−7.23607	+	5.25731i	−0.403878	+	0.293434i
$322$	12.3607	+	38.0423i	0.688834	+	2.12001i
$323$	−6.18034	+	19.0211i	−0.343883	+	1.05836i
$324$	−2.42705	−	1.76336i	−0.134836	−	0.0979642i
$325$		0			0
$326$	2.76393	−	8.50651i	0.153080	−	0.471132i
$327$		0			0
$328$	8.09017	−	5.87785i	0.446705	−	0.324550i
$329$	−35.7771			−1.97245
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	21.7082	−	15.7719i	1.19139	−	0.865597i
$333$	0.618034	+	1.90211i	0.0338681	+	0.104235i
$334$	6.18034	−	19.0211i	0.338173	−	1.04079i
$335$	19.4164	+	14.1068i	1.06083	+	0.770739i
$336$	−3.61803	−	2.62866i	−0.197380	−	0.143405i
$337$	2.76393	−	8.50651i	0.150561	−	0.463379i	−0.847123	−	0.531397i	$-0.821667\pi$
$337$	2.76393	−	8.50651i	0.150561	−	0.463379i	0.997684	+	0.0680176i	$0.0216674\pi$
$338$	−8.98278	−	27.6462i	−0.488599	−	1.50375i
$339$	−4.85410	+	3.52671i	−0.263639	+	0.191545i
$340$	26.8328			1.45521
$341$		0			0
$342$	−10.0000			−0.540738
$343$	21.7082	−	15.7719i	1.17213	−	0.851604i
$344$	3.09017	+	9.51057i	0.166611	+	0.512775i
$345$	−2.47214	+	7.60845i	−0.133095	+	0.409625i
$346$	24.2705	+	17.6336i	1.30479	+	0.947986i
$347$	−7.23607	−	5.25731i	−0.388452	−	0.282227i	0.376369	−	0.926470i	$-0.377173\pi$
$347$	−7.23607	−	5.25731i	−0.388452	−	0.282227i	−0.764821	+	0.644243i	$0.777173\pi$
$348$	4.14590	−	12.7598i	0.222243	−	0.683995i
$349$	−8.29180	−	25.5195i	−0.443850	−	1.36603i	−0.883740	−	0.467978i	$-0.844983\pi$
$349$	−8.29180	−	25.5195i	−0.443850	−	1.36603i	0.439891	−	0.898051i	$-0.355017\pi$
$350$	−8.09017	+	5.87785i	−0.432438	+	0.314184i
$351$		0			0
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$		0			0
$355$	−4.94427	−	15.2169i	−0.262415	−	0.807629i
$356$	−12.9787	+	39.9444i	−0.687870	+	2.11705i
$357$	16.1803	+	11.7557i	0.856354	+	0.622178i
$358$	7.23607	+	5.25731i	0.382438	+	0.277858i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$	1.38197	+	4.25325i	0.0728360	+	0.224166i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−22.3607			−1.17525
$363$		0			0
$364$		0			0
$365$	14.4721	−	10.5146i	0.757506	−	0.550360i
$366$	6.18034	+	19.0211i	0.323052	+	0.994250i
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	0.994616	+	0.103627i	$0.0330448\pi$
$368$	−3.23607	−	2.35114i	−0.168692	−	0.122562i
$369$	3.61803	+	2.62866i	0.188347	+	0.136842i
$370$	2.76393	−	8.50651i	0.143690	−	0.442232i
$371$	−8.29180	−	25.5195i	−0.430489	−	1.32491i
$372$		0			0
$373$	−26.8328			−1.38935			−0.694675	−	0.719323i	$-0.744452\pi$
$373$	−26.8328			−1.38935			−0.694675	+	0.719323i	$0.744452\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$	−14.4721	+	10.5146i	−0.746343	+	0.542250i
$377$		0			0
$378$	−3.09017	+	9.51057i	−0.158941	+	0.489171i
$379$	16.1803	+	11.7557i	0.831128	+	0.603850i	0.919878	−	0.392204i	$-0.128287\pi$
$379$	16.1803	+	11.7557i	0.831128	+	0.603850i	−0.0887501	+	0.996054i	$0.528287\pi$
$380$	21.7082	+	15.7719i	1.11361	+	0.809083i
$381$	4.14590	−	12.7598i	0.212401	−	0.653702i
$382$		0			0
$383$	29.1246	−	21.1603i	1.48820	−	1.08124i	0.513400	−	0.858149i	$-0.328386\pi$
$383$	29.1246	−	21.1603i	1.48820	−	1.08124i	0.974798	−	0.223090i	$-0.0716144\pi$
$384$	−15.6525			−0.798762
$385$		0			0
$386$	−40.0000			−2.03595
$387$	−3.61803	+	2.62866i	−0.183915	+	0.133622i
$388$	1.85410	+	5.70634i	0.0941278	+	0.289695i
$389$	3.09017	−	9.51057i	0.156678	−	0.482205i	−0.841649	−	0.540025i	$-0.818415\pi$
$389$	3.09017	−	9.51057i	0.156678	−	0.482205i	0.998327	+	0.0578199i	$0.0184149\pi$
$390$		0			0
$391$	14.4721	+	10.5146i	0.731887	+	0.531747i
$392$	8.98278	−	27.6462i	0.453699	−	1.39634i
$393$	−5.52786	−	17.0130i	−0.278844	−	0.858193i
$394$	−40.4508	+	29.3893i	−2.03788	+	1.48061i
$395$	26.8328			1.35011
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$		0			0
$399$	6.18034	+	19.0211i	0.309404	+	0.952248i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−24.2705	−	17.6336i	−1.21201	−	0.880578i	−0.216600	−	0.976261i	$-0.569497\pi$
$401$	−24.2705	−	17.6336i	−1.21201	−	0.880578i	−0.995412	+	0.0956827i	$0.969497\pi$
$402$	21.7082	+	15.7719i	1.08271	+	0.786633i
$403$		0			0
$404$	4.14590	+	12.7598i	0.206266	+	0.634822i
$405$	−1.61803	+	1.17557i	−0.0804008	+	0.0584146i
$406$	−44.7214			−2.21948
$407$		0			0
$408$	10.0000			0.495074
$409$	21.7082	−	15.7719i	1.07340	−	0.779872i	0.0968810	−	0.995296i	$-0.469113\pi$
$409$	21.7082	−	15.7719i	1.07340	−	0.779872i	0.976521	+	0.215424i	$0.0691134\pi$
$410$	−6.18034	−	19.0211i	−0.305225	−	0.939387i
$411$	6.79837	−	20.9232i	0.335339	−	1.03207i
$412$	−38.8328	−	28.2137i	−1.91316	−	1.38999i
$413$		0			0
$414$	−2.76393	+	8.50651i	−0.135840	+	0.418072i
$415$	−5.52786	−	17.0130i	−0.271352	−	0.835136i
$416$		0			0
$417$	13.4164			0.657004
$418$		0			0
$419$	4.00000			0.195413			0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000			0.195413			0.0977064	+	0.995215i	$0.468849\pi$
$420$	21.7082	−	15.7719i	1.05925	−	0.769592i
$421$	3.09017	+	9.51057i	0.150606	+	0.463517i	0.997689	−	0.0679432i	$-0.0216437\pi$
$421$	3.09017	+	9.51057i	0.150606	+	0.463517i	−0.847084	+	0.531460i	$0.821644\pi$
$422$	−3.09017	+	9.51057i	−0.150427	+	0.462967i
$423$	−6.47214	−	4.70228i	−0.314686	−	0.228633i
$424$	−10.8541	−	7.88597i	−0.527122	−	0.382976i
$425$	−1.38197	+	4.25325i	−0.0670352	+	0.206313i
$426$	−5.52786	−	17.0130i	−0.267826	−	0.824283i
$427$	32.3607	−	23.5114i	1.56604	−	1.13780i
$428$	26.8328			1.29701
$429$		0			0
$430$	20.0000			0.964486
$431$	7.23607	−	5.25731i	0.348549	−	0.253236i	−0.399711	−	0.916641i	$-0.630890\pi$
$431$	7.23607	−	5.25731i	0.348549	−	0.253236i	0.748260	+	0.663405i	$0.230890\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	−0.985672	−	0.168674i	$-0.946051\pi$
$433$	−1.85410	+	5.70634i	−0.0891025	+	0.274229i	0.896569	+	0.442903i	$0.146051\pi$
$434$		0			0
$435$	−7.23607	−	5.25731i	−0.346943	−	0.252069i
$436$		0			0
$437$	5.52786	+	17.0130i	0.264434	+	0.813843i
$438$	16.1803	−	11.7557i	0.773127	−	0.561709i
$439$	−13.4164			−0.640330			−0.320165	−	0.947362i	$-0.603738\pi$
$439$	−13.4164			−0.640330			−0.320165	+	0.947362i	$0.603738\pi$
$440$		0			0
$441$	13.0000			0.619048
$442$		0			0
$443$	−7.41641	−	22.8254i	−0.352364	−	1.08447i	−0.957522	−	0.288360i	$-0.906890\pi$
$443$	−7.41641	−	22.8254i	−0.352364	−	1.08447i	0.605158	−	0.796105i	$-0.293110\pi$
$444$	1.85410	−	5.70634i	0.0879918	−	0.270811i
$445$	22.6525	+	16.4580i	1.07383	+	0.780183i
$446$	28.9443	+	21.0292i	1.37055	+	0.995764i
$447$	−6.90983	+	21.2663i	−0.326824	+	1.00586i
$448$	17.9656	+	55.2923i	0.848793	+	2.61232i
$449$	4.85410	−	3.52671i	0.229079	−	0.166436i	−0.467325	−	0.884086i	$-0.654782\pi$
$449$	4.85410	−	3.52671i	0.229079	−	0.166436i	0.696404	+	0.717650i	$0.254782\pi$
$450$	−2.23607			−0.105409
$451$		0			0
$452$	18.0000			0.846649
$453$	−10.8541	+	7.88597i	−0.509970	+	0.370515i
$454$	6.18034	+	19.0211i	0.290058	+	0.892706i
$455$		0			0
$456$	8.09017	+	5.87785i	0.378857	+	0.275256i
$457$	−21.7082	−	15.7719i	−1.01547	−	0.737780i	−0.0501182	−	0.998743i	$-0.515960\pi$
$457$	−21.7082	−	15.7719i	−1.01547	−	0.737780i	−0.965349	+	0.260963i	$0.915960\pi$
$458$	6.90983	−	21.2663i	0.322875	−	0.993708i
$459$	1.38197	+	4.25325i	0.0645046	+	0.198525i
$460$	19.4164	−	14.1068i	0.905295	−	0.657735i
$461$	13.4164			0.624864			0.312432	−	0.949940i	$-0.398856\pi$
$461$	13.4164			0.624864			0.312432	+	0.949940i	$0.398856\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	3.61803	−	2.62866i	0.167963	−	0.122032i
$465$		0			0
$466$	−3.09017	+	9.51057i	−0.143149	+	0.440568i
$467$	6.47214	+	4.70228i	0.299495	+	0.217596i	0.727376	−	0.686239i	$-0.240740\pi$
$467$	6.47214	+	4.70228i	0.299495	+	0.217596i	−0.427881	+	0.903835i	$0.640740\pi$
$468$		0			0
$469$	16.5836	−	51.0390i	0.765759	−	2.35676i
$470$	11.0557	+	34.0260i	0.509963	+	1.56950i
$471$	−1.61803	+	1.17557i	−0.0745551	+	0.0541674i
$472$		0			0
$473$		0			0
$474$	30.0000			1.37795
$475$	−3.61803	+	2.62866i	−0.166007	+	0.120611i
$476$	−18.5410	−	57.0634i	−0.849826	−	2.61550i
$477$	1.85410	−	5.70634i	0.0848935	−	0.261275i
$478$	−16.1803	−	11.7557i	−0.740072	−	0.537693i
$479$	7.23607	+	5.25731i	0.330624	+	0.240213i	0.740696	−	0.671841i	$-0.234496\pi$
$479$	7.23607	+	5.25731i	0.330624	+	0.240213i	−0.410071	+	0.912054i	$0.634496\pi$
$480$	−4.14590	+	12.7598i	−0.189233	+	0.582401i
$481$		0			0
$482$	−16.1803	+	11.7557i	−0.736994	+	0.535458i
$483$	17.8885			0.813957
$484$		0			0
$485$	4.00000			0.181631
$486$	−1.80902	+	1.31433i	−0.0820587	+	0.0596191i
$487$	2.47214	+	7.60845i	0.112023	+	0.344772i	0.991315	−	0.131512i	$-0.0419833\pi$
$487$	2.47214	+	7.60845i	0.112023	+	0.344772i	−0.879291	+	0.476284i	$0.841983\pi$
$488$	6.18034	−	19.0211i	0.279771	−	0.861046i
$489$	−3.23607	−	2.35114i	−0.146340	−	0.106322i
$490$	−47.0344	−	34.1725i	−2.12480	−	1.54376i
$491$	−8.29180	+	25.5195i	−0.374204	+	1.15168i	0.569811	+	0.821776i	$0.307016\pi$
$491$	−8.29180	+	25.5195i	−0.374204	+	1.15168i	−0.944014	+	0.329904i	$0.892984\pi$
$492$	−4.14590	−	12.7598i	−0.186912	−	0.575255i
$493$	−16.1803	+	11.7557i	−0.728726	+	0.529450i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−28.9443	+	21.0292i	−1.29833	+	0.943291i
$498$	−6.18034	−	19.0211i	−0.276948	−	0.852357i
$499$	−6.18034	+	19.0211i	−0.276670	+	0.851503i	0.712103	+	0.702075i	$0.247743\pi$
$499$	−6.18034	+	19.0211i	−0.276670	+	0.851503i	−0.988773	+	0.149427i	$0.952257\pi$
$500$	29.1246	+	21.1603i	1.30249	+	0.946316i
$501$	−7.23607	−	5.25731i	−0.323284	−	0.234879i
$502$	−8.29180	+	25.5195i	−0.370081	+	1.13899i
$503$	−8.29180	−	25.5195i	−0.369713	−	1.13786i	−0.946977	−	0.321302i	$-0.895880\pi$
$503$	−8.29180	−	25.5195i	−0.369713	−	1.13786i	0.577264	−	0.816558i	$-0.304120\pi$
$504$	8.09017	−	5.87785i	0.360365	−	0.261820i
$505$	8.94427			0.398015
$506$		0			0
$507$	−13.0000			−0.577350
$508$	−32.5623	+	23.6579i	−1.44472	+	1.04965i
$509$	9.27051	+	28.5317i	0.410908	+	1.26465i	0.915860	+	0.401498i	$0.131510\pi$
$509$	9.27051	+	28.5317i	0.410908	+	1.26465i	−0.504952	+	0.863147i	$0.668490\pi$
$510$	6.18034	−	19.0211i	0.273670	−	0.842270i
$511$	−32.3607	−	23.5114i	−1.43155	−	1.04008i
$512$	−9.04508	−	6.57164i	−0.399740	−	0.290428i
$513$	−1.38197	+	4.25325i	−0.0610153	+	0.187786i
$514$	−15.2016	−	46.7858i	−0.670515	−	2.06363i
$515$	−25.8885	+	18.8091i	−1.14079	+	0.828829i
$516$	13.4164			0.590624
$517$		0			0
$518$	−20.0000			−0.878750
$519$	10.8541	−	7.88597i	0.476442	−	0.346156i
$520$		0			0
$521$	9.27051	−	28.5317i	0.406148	−	1.25000i	−0.513784	−	0.857920i	$-0.671757\pi$
$521$	9.27051	−	28.5317i	0.406148	−	1.25000i	0.919933	−	0.392077i	$-0.128243\pi$
$522$	−8.09017	−	5.87785i	−0.354097	−	0.257267i
$523$	−3.61803	−	2.62866i	−0.158206	−	0.114943i	0.505866	−	0.862612i	$-0.331173\pi$
$523$	−3.61803	−	2.62866i	−0.158206	−	0.114943i	−0.664072	+	0.747669i	$0.731173\pi$
$524$	−16.5836	+	51.0390i	−0.724458	+	2.22965i
$525$	1.38197	+	4.25325i	0.0603139	+	0.185627i
$526$	−16.1803	+	11.7557i	−0.705496	+	0.512573i
$527$		0			0
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−21.7082	+	15.7719i	−0.942944	+	0.685089i
$531$		0			0
$532$	18.5410	−	57.0634i	0.803855	−	2.47401i
$533$		0			0
$534$	25.3262	+	18.4006i	1.09597	+	0.796271i
$535$	5.52786	−	17.0130i	0.238990	−	0.735537i
$536$	−8.29180	−	25.5195i	−0.358151	−	1.10228i
$537$	3.23607	−	2.35114i	0.139647	−	0.101459i
$538$	−22.3607			−0.964037
$539$		0			0
$540$	6.00000			0.258199
$541$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$541$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$542$	−9.27051	−	28.5317i	−0.398202	−	1.22554i
$543$	−3.09017	+	9.51057i	−0.132612	+	0.408137i
$544$	24.2705	+	17.6336i	1.04059	+	0.756033i
$545$		0			0
$546$		0			0
$547$	12.4377	+	38.2793i	0.531797	+	1.63670i	0.750469	+	0.660906i	$0.229828\pi$
$547$	12.4377	+	38.2793i	0.531797	+	1.63670i	−0.218672	+	0.975798i	$0.570172\pi$
$548$	−53.3951	+	38.7938i	−2.28093	+	1.65719i
$549$	8.94427			0.381732
$550$		0			0
$551$	−20.0000			−0.852029
$552$	7.23607	−	5.25731i	0.307988	−	0.223766i
$553$	−18.5410	−	57.0634i	−0.788444	−	2.42658i
$554$		0			0
$555$	−3.23607	−	2.35114i	−0.137363	−	0.0998004i
$556$	−32.5623	−	23.6579i	−1.38095	−	1.00332i
$557$	−12.4377	+	38.2793i	−0.527002	+	1.62195i	0.233321	+	0.972400i	$0.425041\pi$
$557$	−12.4377	+	38.2793i	−0.527002	+	1.62195i	−0.760323	+	0.649546i	$0.774959\pi$
$558$		0			0
$559$		0			0
$560$	8.94427			0.377964
$561$		0			0
$562$	70.0000			2.95277
$563$	−14.4721	+	10.5146i	−0.609928	+	0.443138i	−0.849389	−	0.527767i	$-0.823029\pi$
$563$	−14.4721	+	10.5146i	−0.609928	+	0.443138i	0.239461	+	0.970906i	$0.423029\pi$
$564$	7.41641	+	22.8254i	0.312287	+	0.961121i
$565$	3.70820	−	11.4127i	0.156005	−	0.480135i
$566$	24.2705	+	17.6336i	1.02017	+	0.741194i
$567$	3.61803	+	2.62866i	0.151943	+	0.110393i
$568$	−5.52786	+	17.0130i	−0.231944	+	0.713850i
$569$	1.38197	+	4.25325i	0.0579350	+	0.178306i	0.975836	−	0.218503i	$-0.0701175\pi$
$569$	1.38197	+	4.25325i	0.0579350	+	0.178306i	−0.917901	+	0.396809i	$0.870117\pi$
$570$	16.1803	−	11.7557i	0.677720	−	0.492392i
$571$	−13.4164			−0.561459			−0.280730	−	0.959787i	$-0.590576\pi$
$571$	−13.4164			−0.561459			−0.280730	+	0.959787i	$0.590576\pi$
$572$		0			0
$573$		0			0
$574$	−36.1803	+	26.2866i	−1.51014	+	1.09718i
$575$	1.23607	+	3.80423i	0.0515476	+	0.158647i
$576$	−4.01722	+	12.3637i	−0.167384	+	0.515156i
$577$	1.61803	+	1.17557i	0.0673596	+	0.0489396i	0.620956	−	0.783846i	$-0.286745\pi$
$577$	1.61803	+	1.17557i	0.0673596	+	0.0489396i	−0.553596	+	0.832785i	$0.686745\pi$
$578$	−5.42705	−	3.94298i	−0.225736	−	0.164006i
$579$	−5.52786	+	17.0130i	−0.229730	+	0.707037i
$580$	8.29180	+	25.5195i	0.344298	+	1.05964i
$581$	−32.3607	+	23.5114i	−1.34255	+	0.975418i
$582$	4.47214			0.185376
$583$		0			0
$584$	−20.0000			−0.827606
$585$		0			0
$586$	−15.4508	−	47.5528i	−0.638269	−	1.96439i
$587$	−2.47214	+	7.60845i	−0.102036	+	0.314034i	−0.989023	−	0.147759i	$-0.952794\pi$
$587$	−2.47214	+	7.60845i	−0.102036	+	0.314034i	0.886987	+	0.461794i	$0.152794\pi$
$588$	−31.5517	−	22.9236i	−1.30117	−	0.945354i
$589$		0			0
$590$		0			0
$591$	6.90983	+	21.2663i	0.284232	+	0.874777i
$592$	1.61803	−	1.17557i	0.0665008	−	0.0483157i
$593$	−22.3607			−0.918243			−0.459122	−	0.888373i	$-0.651836\pi$
$593$	−22.3607			−0.918243			−0.459122	+	0.888373i	$0.651836\pi$
$594$		0			0
$595$	−40.0000			−1.63984
$596$	54.2705	−	39.4298i	2.22301	−	1.61511i
$597$		0			0
$598$		0			0
$599$	29.1246	+	21.1603i	1.19000	+	0.864585i	0.993264	−	0.115872i	$-0.0369661\pi$
$599$	29.1246	+	21.1603i	1.19000	+	0.864585i	0.196735	+	0.980457i	$0.436966\pi$
$600$	1.80902	+	1.31433i	0.0738528	+	0.0536572i
$601$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$601$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$602$	−13.8197	−	42.5325i	−0.563247	−	1.73350i
$603$	9.70820	−	7.05342i	0.395349	−	0.287238i
$604$	40.2492			1.63772
$605$		0			0
$606$	10.0000			0.406222
$607$	3.61803	−	2.62866i	0.146851	−	0.106694i	−0.511934	−	0.859025i	$-0.671071\pi$
$607$	3.61803	−	2.62866i	0.146851	−	0.106694i	0.658785	+	0.752331i	$0.271071\pi$
$608$	9.27051	+	28.5317i	0.375969	+	1.15711i
$609$	−6.18034	+	19.0211i	−0.250440	+	0.770775i
$610$	−32.3607	−	23.5114i	−1.31025	−	0.951949i
$611$		0			0
$612$	4.14590	−	12.7598i	0.167588	−	0.515783i
$613$	13.8197	+	42.5325i	0.558171	+	1.71787i	0.687419	+	0.726261i	$0.258744\pi$
$613$	13.8197	+	42.5325i	0.558171	+	1.71787i	−0.129248	+	0.991612i	$0.541256\pi$
$614$	8.09017	−	5.87785i	0.326493	−	0.237211i
$615$	−8.94427			−0.360668
$616$		0			0
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$	−28.9443	+	21.0292i	−1.16431	+	0.845920i
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	0.717398	+	0.696664i	$0.245333\pi$
$619$	13.5967	+	41.8465i	0.546499	+	1.68195i	−0.170898	+	0.985289i	$0.554667\pi$
$620$		0			0
$621$	3.23607	+	2.35114i	0.129859	+	0.0943480i
$622$	21.7082	+	15.7719i	0.870420	+	0.632397i
$623$	19.3475	−	59.5456i	0.775142	−	2.38564i
$624$		0			0
$625$	15.3713	−	11.1679i	0.614853	−	0.446717i
$626$	31.3050			1.25120
$627$		0			0
$628$	6.00000			0.239426
$629$	−7.23607	+	5.25731i	−0.288521	+	0.209623i
$630$	−6.18034	−	19.0211i	−0.246231	−	0.757820i
$631$	9.88854	−	30.4338i	0.393657	−	1.21155i	−0.536346	−	0.843998i	$-0.680196\pi$
$631$	9.88854	−	30.4338i	0.393657	−	1.21155i	0.930003	−	0.367553i	$-0.119804\pi$
$632$	−24.2705	−	17.6336i	−0.965429	−	0.701425i
$633$	3.61803	+	2.62866i	0.143804	+	0.104480i
$634$	12.4377	−	38.2793i	0.493964	−	1.52026i
$635$	8.29180	+	25.5195i	0.329050	+	1.01271i
$636$	−14.5623	+	10.5801i	−0.577433	+	0.419530i
$637$		0			0
$638$		0			0
$639$	−8.00000			−0.316475
$640$	25.3262	−	18.4006i	1.00111	−	0.727347i
$641$	−9.27051	−	28.5317i	−0.366163	−	1.12693i	−0.949250	−	0.314524i	$-0.898155\pi$
$641$	−9.27051	−	28.5317i	−0.366163	−	1.12693i	0.583086	−	0.812410i	$-0.301845\pi$
$642$	6.18034	−	19.0211i	0.243919	−	0.750704i
$643$	−29.1246	−	21.1603i	−1.14856	−	0.834480i	−0.160273	−	0.987073i	$-0.551238\pi$
$643$	−29.1246	−	21.1603i	−1.14856	−	0.834480i	−0.988289	+	0.152593i	$0.951238\pi$
$644$	−43.4164	−	31.5439i	−1.71085	−	1.24300i
$645$	2.76393	−	8.50651i	0.108830	−	0.334943i
$646$	−13.8197	−	42.5325i	−0.543727	−	1.67342i
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	−0.380364	−	0.924837i	$-0.624201\pi$
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	0.762033	+	0.647538i	$0.224201\pi$
$648$	2.23607			0.0878410
$649$		0			0
$650$		0			0
$651$		0			0
$652$	3.70820	+	11.4127i	0.145224	+	0.446955i
$653$	14.2148	−	43.7486i	0.556267	−	1.71202i	−0.136305	−	0.990667i	$-0.543523\pi$
$653$	14.2148	−	43.7486i	0.556267	−	1.71202i	0.692573	−	0.721348i	$-0.256477\pi$
$654$		0			0
$655$	28.9443	+	21.0292i	1.13095	+	0.821681i
$656$	1.38197	−	4.25325i	0.0539567	−	0.166062i
$657$	−2.76393	−	8.50651i	−0.107831	−	0.331870i
$658$	64.7214	−	47.0228i	2.52310	−	1.83314i
$659$	17.8885			0.696839			0.348419	−	0.937339i	$-0.386719\pi$
$659$	17.8885			0.696839			0.348419	+	0.937339i	$0.386719\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	36.1803	−	26.2866i	1.40619	−	1.02166i
$663$		0			0
$664$	−6.18034	+	19.0211i	−0.239844	+	0.738163i
$665$	−32.3607	−	23.5114i	−1.25489	−	0.911733i
$666$	−3.61803	−	2.62866i	−0.140196	−	0.101858i
$667$	−5.52786	+	17.0130i	−0.214040	+	0.658747i
$668$	8.29180	+	25.5195i	0.320819	+	0.987380i
$669$	12.9443	−	9.40456i	0.500454	−	0.363601i
$670$	−53.6656			−2.07328
$671$		0			0
$672$	30.0000			1.15728
$673$	14.4721	−	10.5146i	0.557860	−	0.405309i	−0.272815	−	0.962066i	$-0.587955\pi$
$673$	14.4721	−	10.5146i	0.557860	−	0.405309i	0.830675	+	0.556758i	$0.187955\pi$
$674$	6.18034	+	19.0211i	0.238058	+	0.732667i
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$	31.5517	+	22.9236i	1.21353	+	0.881678i
$677$	25.3262	+	18.4006i	0.973366	+	0.707192i	0.956216	−	0.292661i	$-0.0945407\pi$
$677$	25.3262	+	18.4006i	0.973366	+	0.707192i	0.0171501	+	0.999853i	$0.494541\pi$
$678$	4.14590	−	12.7598i	0.159222	−	0.490036i
$679$	−2.76393	−	8.50651i	−0.106070	−	0.326450i
$680$	−16.1803	+	11.7557i	−0.620488	+	0.450811i
$681$	8.94427			0.342745
$682$		0			0
$683$	44.0000			1.68361			0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000			1.68361			0.841807	+	0.539779i	$0.181492\pi$
$684$	10.8541	−	7.88597i	0.415017	−	0.301527i
$685$	13.5967	+	41.8465i	0.519505	+	1.59887i
$686$	−18.5410	+	57.0634i	−0.707899	+	2.17869i
$687$	−8.09017	−	5.87785i	−0.308659	−	0.224254i
$688$	3.61803	+	2.62866i	0.137936	+	0.100217i
$689$		0			0
$690$	−5.52786	−	17.0130i	−0.210442	−	0.647674i
$691$	−9.70820	+	7.05342i	−0.369317	+	0.268325i	−0.756928	−	0.653498i	$-0.773301\pi$
$691$	−9.70820	+	7.05342i	−0.369317	+	0.268325i	0.387610	+	0.921823i	$0.373301\pi$
$692$	−40.2492			−1.53005
$693$		0			0
$694$	20.0000			0.759190
$695$	−21.7082	+	15.7719i	−0.823439	+	0.598264i
$696$	3.09017	+	9.51057i	0.117133	+	0.360497i
$697$	−6.18034	+	19.0211i	−0.234097	+	0.720477i
$698$	48.5410	+	35.2671i	1.83730	+	1.33488i
$699$	3.61803	+	2.62866i	0.136847	+	0.0994249i
$700$	4.14590	−	12.7598i	0.156700	−	0.482274i
$701$	−6.90983	−	21.2663i	−0.260981	−	0.803216i	−0.992592	−	0.121494i	$-0.961231\pi$
$701$	−6.90983	−	21.2663i	−0.260981	−	0.803216i	0.731611	−	0.681722i	$-0.238769\pi$
$702$		0			0
$703$	−8.94427			−0.337340
$704$		0			0
$705$	16.0000			0.602595
$706$	25.3262	−	18.4006i	0.953166	−	0.692515i
$707$	−6.18034	−	19.0211i	−0.232436	−	0.715363i
$708$		0			0
$709$	4.85410	+	3.52671i	0.182300	+	0.132448i	0.675192	−	0.737642i	$-0.264061\pi$
$709$	4.85410	+	3.52671i	0.182300	+	0.132448i	−0.492893	+	0.870090i	$0.664061\pi$
$710$	28.9443	+	21.0292i	1.08626	+	0.789213i
$711$	4.14590	−	12.7598i	0.155483	−	0.478528i
$712$	−9.67376	−	29.7728i	−0.362540	−	1.11578i
$713$		0			0
$714$	−44.7214			−1.67365
$715$		0			0
$716$	−12.0000			−0.448461
$717$	−7.23607	+	5.25731i	−0.270236	+	0.196338i
$718$		0			0
$719$	−7.41641	+	22.8254i	−0.276585	+	0.851242i	0.712210	+	0.701966i	$0.247694\pi$
$719$	−7.41641	+	22.8254i	−0.276585	+	0.851242i	−0.988796	+	0.149276i	$0.952306\pi$
$720$	1.61803	+	1.17557i	0.0603006	+	0.0438109i
$721$	57.8885	+	42.0585i	2.15588	+	1.56634i
$722$	0.690983	−	2.12663i	0.0257157	−	0.0791449i
$723$	2.76393	+	8.50651i	0.102792	+	0.316360i
$724$	24.2705	−	17.6336i	0.902006	−	0.655346i
$725$	−4.47214			−0.166091
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−12.3607	+	38.0423i	−0.457489	+	1.40801i
$731$	−16.1803	−	11.7557i	−0.598451	−	0.434800i
$732$	−21.7082	−	15.7719i	−0.802358	−	0.582947i
$733$	−5.52786	+	17.0130i	−0.204176	+	0.628390i	0.795570	+	0.605862i	$0.207172\pi$
$733$	−5.52786	+	17.0130i	−0.204176	+	0.628390i	−0.999746	+	0.0225283i	$0.992828\pi$
$734$	5.52786	+	17.0130i	0.204037	+	0.627962i
$735$	−21.0344	+	15.2824i	−0.775867	+	0.563700i
$736$	26.8328			0.989071
$737$		0			0
$738$	−10.0000			−0.368105
$739$	−3.61803	+	2.62866i	−0.133092	+	0.0966967i	−0.652339	−	0.757927i	$-0.726212\pi$
$739$	−3.61803	+	2.62866i	−0.133092	+	0.0966967i	0.519248	+	0.854624i	$0.326212\pi$
$740$	3.70820	+	11.4127i	0.136316	+	0.419538i
$741$		0			0
$742$	48.5410	+	35.2671i	1.78200	+	1.29470i
$743$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$743$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$744$		0			0
$745$	−13.8197	−	42.5325i	−0.506313	−	1.55827i
$746$	48.5410	−	35.2671i	1.77721	−	1.29122i
$747$	−8.94427			−0.327254
$748$		0			0
$749$	−40.0000			−1.46157
$750$	21.7082	−	15.7719i	0.792672	−	0.575910i
$751$	9.88854	+	30.4338i	0.360838	+	1.11055i	0.952546	+	0.304393i	$0.0984537\pi$
$751$	9.88854	+	30.4338i	0.360838	+	1.11055i	−0.591708	+	0.806152i	$0.701546\pi$
$752$	−2.47214	+	7.60845i	−0.0901495	+	0.277452i
$753$	9.70820	+	7.05342i	0.353787	+	0.257041i
$754$		0			0
$755$	8.29180	−	25.5195i	0.301769	−	0.928751i
$756$	−4.14590	−	12.7598i	−0.150785	−	0.464068i
$757$	−33.9787	+	24.6870i	−1.23498	+	0.897264i	−0.997253	−	0.0740691i	$-0.976401\pi$
$757$	−33.9787	+	24.6870i	−1.23498	+	0.897264i	−0.237724	+	0.971333i	$0.576401\pi$
$758$	−44.7214			−1.62435
$759$		0			0
$760$	−20.0000			−0.725476
$761$	25.3262	−	18.4006i	0.918075	−	0.667021i	−0.0249688	−	0.999688i	$-0.507949\pi$
$761$	25.3262	−	18.4006i	0.918075	−	0.667021i	0.943044	+	0.332667i	$0.107949\pi$
$762$	9.27051	+	28.5317i	0.335835	+	1.03359i
$763$		0			0
$764$		0			0
$765$	−7.23607	−	5.25731i	−0.261621	−	0.190078i
$766$	−24.8754	+	76.5586i	−0.898784	+	2.76617i
$767$		0			0
$768$	7.28115	−	5.29007i	0.262736	−	0.190889i
$769$	35.7771			1.29015			0.645077	−	0.764117i	$-0.276825\pi$
$769$	35.7771			1.29015			0.645077	+	0.764117i	$0.276825\pi$
$770$		0			0
$771$	−22.0000			−0.792311
$772$	43.4164	−	31.5439i	1.56259	−	1.13529i
$773$	4.32624	+	13.3148i	0.155604	+	0.478900i	0.998222	−	0.0596126i	$-0.0189865\pi$
$773$	4.32624	+	13.3148i	0.155604	+	0.478900i	−0.842618	+	0.538512i	$0.818987\pi$
$774$	3.09017	−	9.51057i	0.111074	−	0.341850i
$775$		0			0
$776$	−3.61803	−	2.62866i	−0.129880	−	0.0943632i
$777$	−2.76393	+	8.50651i	−0.0991555	+	0.305169i
$778$	6.90983	+	21.2663i	0.247729	+	0.762433i
$779$	−16.1803	+	11.7557i	−0.579721	+	0.421192i
$780$		0			0
$781$		0			0
$782$	−40.0000			−1.43040
$783$	−3.61803	+	2.62866i	−0.129298	+	0.0939405i
$784$	−4.01722	−	12.3637i	−0.143472	−	0.441562i
$785$	1.23607	−	3.80423i	0.0441172	−	0.135779i
$786$	32.3607	+	23.5114i	1.15427	+	0.838624i
$787$	−32.5623	−	23.6579i	−1.16072	−	0.843313i	−0.170852	−	0.985297i	$-0.554652\pi$
$787$	−32.5623	−	23.6579i	−1.16072	−	0.843313i	−0.989869	+	0.141984i	$0.954652\pi$
$788$	20.7295	−	63.7988i	0.738458	−	2.27274i
$789$	2.76393	+	8.50651i	0.0983986	+	0.302840i
$790$	−48.5410	+	35.2671i	−1.72701	+	1.25475i
$791$	−26.8328			−0.954065
$792$		0			0
$793$		0			0
$794$	−39.7984	+	28.9152i	−1.41239	+	1.02616i
$795$	3.70820	+	11.4127i	0.131516	+	0.404766i
$796$		0			0
$797$	−33.9787	−	24.6870i	−1.20359	−	0.874458i	−0.208955	−	0.977925i	$-0.567006\pi$
$797$	−33.9787	−	24.6870i	−1.20359	−	0.874458i	−0.994633	+	0.103468i	$0.967006\pi$
$798$	−36.1803	−	26.2866i	−1.28077	−	0.930534i
$799$	11.0557	−	34.0260i	0.391124	−	1.20375i
$800$	2.07295	+	6.37988i	0.0732898	+	0.225563i
$801$	11.3262	−	8.22899i	0.400193	−	0.290757i
$802$	67.0820			2.36875
$803$		0			0
$804$	−36.0000			−1.26962
$805$	−28.9443	+	21.0292i	−1.02015	+	0.741183i
$806$		0			0
$807$	−3.09017	+	9.51057i	−0.108779	+	0.334788i
$808$	−8.09017	−	5.87785i	−0.284611	−	0.206782i
$809$	10.8541	+	7.88597i	0.381610	+	0.277256i	0.762009	−	0.647567i	$-0.224213\pi$
$809$	10.8541	+	7.88597i	0.381610	+	0.277256i	−0.380399	+	0.924823i	$0.624213\pi$
$810$	1.38197	−	4.25325i	0.0485573	−	0.149444i
$811$	−1.38197	−	4.25325i	−0.0485274	−	0.149352i	0.923857	−	0.382739i	$-0.125019\pi$
$811$	−1.38197	−	4.25325i	−0.0485274	−	0.149352i	−0.972384	+	0.233387i	$0.925019\pi$
$812$	48.5410	−	35.2671i	1.70346	−	1.23763i
$813$	−13.4164			−0.470534
$814$		0			0
$815$	8.00000			0.280228
$816$	3.61803	−	2.62866i	0.126657	−	0.0920214i
$817$	−6.18034	−	19.0211i	−0.216223	−	0.665465i
$818$	−18.5410	+	57.0634i	−0.648272	+	1.99517i
$819$		0			0
$820$	21.7082	+	15.7719i	0.758083	+	0.550780i
$821$	6.90983	−	21.2663i	0.241155	−	0.742198i	−0.755090	−	0.655621i	$-0.772407\pi$
$821$	6.90983	−	21.2663i	0.241155	−	0.742198i	0.996245	−	0.0865773i	$-0.0275929\pi$
$822$	15.2016	+	46.7858i	0.530218	+	1.63184i
$823$	−12.9443	+	9.40456i	−0.451209	+	0.327822i	−0.790073	−	0.613013i	$-0.789957\pi$
$823$	−12.9443	+	9.40456i	−0.451209	+	0.327822i	0.338864	+	0.940835i	$0.389957\pi$
$824$	35.7771			1.24635
$825$		0			0
$826$		0			0
$827$	−36.1803	+	26.2866i	−1.25811	+	0.914073i	−0.998664	−	0.0516834i	$-0.983541\pi$
$827$	−36.1803	+	26.2866i	−1.25811	+	0.914073i	−0.259450	+	0.965756i	$0.583541\pi$
$828$	−3.70820	−	11.4127i	−0.128869	−	0.396618i
$829$	4.32624	−	13.3148i	0.150256	−	0.462442i	−0.847393	−	0.530966i	$-0.821829\pi$
$829$	4.32624	−	13.3148i	0.150256	−	0.462442i	0.997649	+	0.0685244i	$0.0218291\pi$
$830$	32.3607	+	23.5114i	1.12326	+	0.816093i
$831$		0			0
$832$		0			0
$833$	17.9656	+	55.2923i	0.622470	+	1.91576i
$834$	−24.2705	+	17.6336i	−0.840419	+	0.610600i
$835$	17.8885			0.619059
$836$		0			0
$837$		0			0
$838$	−7.23607	+	5.25731i	−0.249966	+	0.181611i
$839$	−6.18034	−	19.0211i	−0.213369	−	0.656682i	−0.999265	−	0.0383241i	$-0.987798\pi$
$839$	−6.18034	−	19.0211i	−0.213369	−	0.656682i	0.785896	−	0.618358i	$-0.212202\pi$
$840$	−6.18034	+	19.0211i	−0.213242	+	0.656291i
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$	−18.0902	−	13.1433i	−0.623428	−	0.452947i
$843$	9.67376	−	29.7728i	0.333182	−	1.02543i
$844$	−4.14590	−	12.7598i	−0.142708	−	0.439209i
$845$	21.0344	−	15.2824i	0.723607	−	0.525731i
$846$	17.8885			0.615021
$847$		0			0
$848$	−6.00000			−0.206041
$849$	10.8541	−	7.88597i	0.372512	−	0.270646i
$850$	−3.09017	−	9.51057i	−0.105992	−	0.326210i
$851$	−2.47214	+	7.60845i	−0.0847437	+	0.260814i
$852$	19.4164	+	14.1068i	0.665195	+	0.483293i
$853$	−7.23607	−	5.25731i	−0.247758	−	0.180007i	0.456974	−	0.889480i	$-0.348933\pi$
$853$	−7.23607	−	5.25731i	−0.247758	−	0.180007i	−0.704733	+	0.709473i	$0.748933\pi$
$854$	−27.6393	+	85.0651i	−0.945798	+	2.91087i
$855$	−2.76393	−	8.50651i	−0.0945245	−	0.290916i
$856$	−16.1803	+	11.7557i	−0.553033	+	0.401802i
$857$	40.2492			1.37489			0.687444	−	0.726238i	$-0.258733\pi$
$857$	40.2492			1.37489			0.687444	+	0.726238i	$0.258733\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−21.7082	+	15.7719i	−0.740244	+	0.537818i
$861$	6.18034	+	19.0211i	0.210625	+	0.648238i
$862$	−6.18034	+	19.0211i	−0.210503	+	0.647862i
$863$	−3.23607	−	2.35114i	−0.110157	−	0.0800338i	0.531343	−	0.847157i	$-0.321688\pi$
$863$	−3.23607	−	2.35114i	−0.110157	−	0.0800338i	−0.641500	+	0.767123i	$0.721688\pi$
$864$	5.42705	+	3.94298i	0.184632	+	0.134143i
$865$	−8.29180	+	25.5195i	−0.281930	+	0.867690i
$866$	−4.14590	−	12.7598i	−0.140883	−	0.433594i
$867$	−2.42705	+	1.76336i	−0.0824270	+	0.0598867i
$868$		0			0
$869$		0			0
$870$	20.0000			0.678064
$871$		0			0
$872$		0			0
$873$	0.618034	−	1.90211i	0.0209173	−	0.0643768i
$874$	−32.3607	−	23.5114i	−1.09462	−	0.795285i
$875$	−43.4164	−	31.5439i	−1.46774	−	1.06638i
$876$	−8.29180	+	25.5195i	−0.280154	+	0.862225i
$877$	−2.76393	−	8.50651i	−0.0933314	−	0.287244i	0.893484	−	0.449095i	$-0.148254\pi$
$877$	−2.76393	−	8.50651i	−0.0933314	−	0.287244i	−0.986815	+	0.161851i	$0.948254\pi$
$878$	24.2705	−	17.6336i	0.819090	−	0.595104i
$879$	−22.3607			−0.754207
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	−23.5172	+	17.0863i	−0.791866	+	0.575324i
$883$	13.5967	+	41.8465i	0.457567	+	1.40825i	0.868095	+	0.496398i	$0.165344\pi$
$883$	13.5967	+	41.8465i	0.457567	+	1.40825i	−0.410528	+	0.911848i	$0.634656\pi$
$884$		0			0
$885$		0			0
$886$	43.4164	+	31.5439i	1.45860	+	1.05974i
$887$	−16.5836	+	51.0390i	−0.556823	+	1.71372i	0.134259	+	0.990946i	$0.457135\pi$
$887$	−16.5836	+	51.0390i	−0.556823	+	1.71372i	−0.691081	+	0.722777i	$0.742865\pi$
$888$	1.38197	+	4.25325i	0.0463757	+	0.142730i
$889$	48.5410	−	35.2671i	1.62801	−	1.18282i
$890$	−62.6099			−2.09869
$891$		0			0
$892$	−48.0000			−1.60716
$893$	28.9443	−	21.0292i	0.968583	−	0.703717i
$894$	−15.4508	−	47.5528i	−0.516754	−	1.59040i
$895$	−2.47214	+	7.60845i	−0.0826344	+	0.254323i
$896$	−56.6312	−	41.1450i	−1.89192	−	1.37456i
$897$		0			0
$898$	−4.14590	+	12.7598i	−0.138350	+	0.425799i
$899$		0			0
$900$	2.42705	−	1.76336i	0.0809017	−	0.0587785i
$901$	26.8328			0.893931
$902$		0			0
$903$	−20.0000			−0.665558
$904$	−10.8541	+	7.88597i	−0.361002	+	0.262283i
$905$	−6.18034	−	19.0211i	−0.205441	−	0.632284i
$906$	9.27051	−	28.5317i	0.307992	−	0.947902i
$907$	9.70820	+	7.05342i	0.322356	+	0.234205i	0.737180	−	0.675696i	$-0.236157\pi$
$907$	9.70820	+	7.05342i	0.322356	+	0.234205i	−0.414824	+	0.909902i	$0.636157\pi$
$908$	−21.7082	−	15.7719i	−0.720412	−	0.523410i
$909$	1.38197	−	4.25325i	0.0458369	−	0.141072i
$910$		0			0
$911$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$911$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$912$	4.47214			0.148087
$913$		0			0
$914$	60.0000			1.98462
$915$	−14.4721	+	10.5146i	−0.478434	+	0.347603i
$916$	9.27051	+	28.5317i	0.306306	+	0.942714i
$917$	24.7214	−	76.0845i	0.816371	−	2.51253i
$918$	−8.09017	−	5.87785i	−0.267015	−	0.193998i
$919$	−18.0902	−	13.1433i	−0.596740	−	0.433557i	0.247980	−	0.968765i	$-0.420233\pi$
$919$	−18.0902	−	13.1433i	−0.596740	−	0.433557i	−0.844720	+	0.535208i	$0.820233\pi$
$920$	−5.52786	+	17.0130i	−0.182248	+	0.560903i
$921$	−1.38197	−	4.25325i	−0.0455373	−	0.140149i
$922$	−24.2705	+	17.6336i	−0.799307	+	0.580730i
$923$		0			0
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	−43.4164	+	31.5439i	−1.42675	+	1.03660i
$927$	4.94427	+	15.2169i	0.162391	+	0.499789i
$928$	−9.27051	+	28.5317i	−0.304319	+	0.936599i
$929$	−24.2705	−	17.6336i	−0.796290	−	0.578538i	0.113534	−	0.993534i	$-0.463783\pi$
$929$	−24.2705	−	17.6336i	−0.796290	−	0.578538i	−0.909823	+	0.414996i	$0.863783\pi$
$930$		0			0
$931$	−17.9656	+	55.2923i	−0.588797	+	1.81213i
$932$	−4.14590	−	12.7598i	−0.135803	−	0.417960i
$933$	9.70820	−	7.05342i	0.317832	−	0.230919i
$934$	−17.8885			−0.585331
$935$		0			0
$936$		0			0
$937$	−43.4164	+	31.5439i	−1.41835	+	1.03049i	−0.426311	+	0.904576i	$0.640187\pi$
$937$	−43.4164	+	31.5439i	−1.41835	+	1.03049i	−0.992041	+	0.125917i	$0.959813\pi$
$938$	37.0820	+	114.127i	1.21077	+	3.72637i
$939$	4.32624	−	13.3148i	0.141181	−	0.434512i
$940$	−38.8328	−	28.2137i	−1.26659	−	0.920229i
$941$	−18.0902	−	13.1433i	−0.589723	−	0.428459i	0.252493	−	0.967599i	$-0.418749\pi$
$941$	−18.0902	−	13.1433i	−0.589723	−	0.428459i	−0.842216	+	0.539140i	$0.818749\pi$
$942$	1.38197	−	4.25325i	0.0450269	−	0.138579i
$943$	5.52786	+	17.0130i	0.180012	+	0.554020i
$944$		0			0
$945$	−8.94427			−0.290957
$946$		0			0
$947$	52.0000			1.68977			0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000			1.68977			0.844886	+	0.534946i	$0.179668\pi$
$948$	−32.5623	+	23.6579i	−1.05757	+	0.768373i
$949$		0			0
$950$	3.09017	−	9.51057i	0.100258	−	0.308563i
$951$	−14.5623	−	10.5801i	−0.472215	−	0.343084i
$952$	36.1803	+	26.2866i	1.17261	+	0.851952i
$953$	6.90983	−	21.2663i	0.223831	−	0.688882i	−0.774577	−	0.632480i	$-0.782037\pi$
$953$	6.90983	−	21.2663i	0.223831	−	0.688882i	0.998408	−	0.0564022i	$-0.0179629\pi$
$954$	4.14590	+	12.7598i	0.134228	+	0.413113i
$955$		0			0
$956$	26.8328			0.867835
$957$		0			0
$958$	−20.0000			−0.646171
$959$	79.5967	−	57.8304i	2.57031	−	1.86744i
$960$	−8.03444	−	24.7275i	−0.259310	−	0.798076i
$961$	−9.57953	+	29.4828i	−0.309017	+	0.951057i
$962$		0			0
$963$	−7.23607	−	5.25731i	−0.233179	−	0.169414i
$964$	8.29180	−	25.5195i	0.267061	−	0.821929i
$965$	−11.0557	−	34.0260i	−0.355896	−	1.09534i
$966$	−32.3607	+	23.5114i	−1.04119	+	0.756467i
$967$	13.4164			0.431443			0.215721	−	0.976455i	$-0.430790\pi$
$967$	13.4164			0.431443			0.215721	+	0.976455i	$0.430790\pi$
$968$		0			0
$969$	−20.0000			−0.642493
$970$	−7.23607	+	5.25731i	−0.232336	+	0.168802i
$971$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$971$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$972$	0.927051	−	2.85317i	0.0297352	−	0.0915155i
$973$	48.5410	+	35.2671i	1.55615	+	1.13061i
$974$	−14.4721	−	10.5146i	−0.463717	−	0.336910i
$975$		0			0
$976$	−2.76393	−	8.50651i	−0.0884713	−	0.272287i
$977$	33.9787	−	24.6870i	1.08708	−	0.789806i	0.108172	−	0.994132i	$-0.465500\pi$
$977$	33.9787	−	24.6870i	1.08708	−	0.789806i	0.978903	+	0.204326i	$0.0655002\pi$
$978$	8.94427			0.286006
$979$		0			0
$980$	78.0000			2.49162
$981$		0			0
$982$	−18.5410	−	57.0634i	−0.591668	−	1.82097i
$983$	11.1246	−	34.2380i	0.354820	−	1.09202i	−0.601294	−	0.799028i	$-0.705348\pi$
$983$	11.1246	−	34.2380i	0.354820	−	1.09202i	0.956114	−	0.292996i	$-0.0946522\pi$
$984$	8.09017	+	5.87785i	0.257905	+	0.187379i
$985$	−36.1803	−	26.2866i	−1.15280	−	0.837559i
$986$	13.8197	−	42.5325i	0.440108	−	1.35451i
$987$	−11.0557	−	34.0260i	−0.351908	−	1.08306i
$988$		0			0
$989$	−17.8885			−0.568823
$990$		0			0
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$		0			0
$993$	−6.18034	−	19.0211i	−0.196127	−	0.603617i
$994$	24.7214	−	76.0845i	0.784114	−	2.41325i
$995$		0			0
$996$	21.7082	+	15.7719i	0.687851	+	0.499753i
$997$	−8.29180	+	25.5195i	−0.262604	+	0.808211i	0.729632	+	0.683840i	$0.239691\pi$
$997$	−8.29180	+	25.5195i	−0.262604	+	0.808211i	−0.992236	+	0.124371i	$0.960309\pi$
$998$	−13.8197	−	42.5325i	−0.437454	−	1.34634i
$999$	−1.61803	+	1.17557i	−0.0511923	+	0.0371934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.a.124.1		4
11.2	odd	10		363.2.a.g.1.1	✓	2
11.3	even	5		363.2.e.l.148.1		4
11.4	even	5	inner	363.2.e.a.202.1		4
11.5	even	5		363.2.e.l.130.1		4
11.6	odd	10	inner	363.2.e.a.130.1		4
11.7	odd	10		363.2.e.l.202.1		4
11.8	odd	10	inner	363.2.e.a.148.1		4
11.9	even	5		363.2.a.g.1.2	yes	2
11.10	odd	2		363.2.e.l.124.1		4
33.2	even	10		1089.2.a.p.1.2		2
33.20	odd	10		1089.2.a.p.1.1		2
44.31	odd	10		5808.2.a.bx.1.2		2
44.35	even	10		5808.2.a.bx.1.1		2
55.9	even	10		9075.2.a.bi.1.1		2
55.24	odd	10		9075.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.a.g.1.1	✓	2	11.2	odd	10
363.2.a.g.1.2	yes	2	11.9	even	5
363.2.e.a.124.1		4	1.1	even	1	trivial
363.2.e.a.130.1		4	11.6	odd	10	inner
363.2.e.a.148.1		4	11.8	odd	10	inner
363.2.e.a.202.1		4	11.4	even	5	inner
363.2.e.l.124.1		4	11.10	odd	2
363.2.e.l.130.1		4	11.5	even	5
363.2.e.l.148.1		4	11.3	even	5
363.2.e.l.202.1		4	11.7	odd	10
1089.2.a.p.1.1		2	33.20	odd	10
1089.2.a.p.1.2		2	33.2	even	10
5808.2.a.bx.1.1		2	44.35	even	10
5808.2.a.bx.1.2		2	44.31	odd	10
9075.2.a.bi.1.1		2	55.9	even	10
9075.2.a.bi.1.2		2	55.24	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80902 + 1.31433i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.61803 - 1.17557i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-1.38197 + 4.25325i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.80902 + 1.31433i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.61803 - 1.17557i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-1.38197 + 4.25325i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +4.47214 q^{10} +3.00000 q^{12} +(-3.09017 - 9.51057i) q^{14} +(0.618034 - 1.90211i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-3.61803 - 2.62866i) q^{17} +(0.690983 - 2.12663i) q^{18} +(-1.38197 - 4.25325i) q^{19} +(-4.85410 + 3.52671i) q^{20} -4.47214 q^{21} -4.00000 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(10.8541 + 7.88597i) q^{28} +(1.38197 - 4.25325i) q^{29} +(1.38197 + 4.25325i) q^{30} -6.70820 q^{32} +10.0000 q^{34} +(7.23607 - 5.25731i) q^{35} +(0.927051 + 2.85317i) q^{36} +(0.618034 - 1.90211i) q^{37} +(8.09017 + 5.87785i) q^{38} +(1.38197 - 4.25325i) q^{40} +(-1.38197 - 4.25325i) q^{41} +(8.09017 - 5.87785i) q^{42} +4.47214 q^{43} +2.00000 q^{45} +(7.23607 - 5.25731i) q^{46} +(2.47214 + 7.60845i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-10.5172 - 7.64121i) q^{49} +(1.80902 + 1.31433i) q^{50} +(1.38197 - 4.25325i) q^{51} +(-4.85410 + 3.52671i) q^{53} +2.23607 q^{54} -10.0000 q^{56} +(3.61803 - 2.62866i) q^{57} +(3.09017 + 9.51057i) q^{58} +(-4.85410 - 3.52671i) q^{60} +(-7.23607 - 5.25731i) q^{61} +(-1.38197 - 4.25325i) q^{63} +(10.5172 - 7.64121i) q^{64} -12.0000 q^{67} +(-10.8541 + 7.88597i) q^{68} +(-1.23607 - 3.80423i) q^{69} +(-6.18034 + 19.0211i) q^{70} +(6.47214 + 4.70228i) q^{71} +(-1.80902 - 1.31433i) q^{72} +(-2.76393 + 8.50651i) q^{73} +(1.38197 + 4.25325i) q^{74} +(0.809017 - 0.587785i) q^{75} -13.4164 q^{76} +(-10.8541 + 7.88597i) q^{79} +(-0.618034 - 1.90211i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.09017 + 5.87785i) q^{82} +(7.23607 + 5.25731i) q^{83} +(-4.14590 + 12.7598i) q^{84} +(2.76393 + 8.50651i) q^{85} +(-8.09017 + 5.87785i) q^{86} +4.47214 q^{87} -14.0000 q^{89} +(-3.61803 + 2.62866i) q^{90} +(-3.70820 + 11.4127i) q^{92} +(-14.4721 - 10.5146i) q^{94} +(-2.76393 + 8.50651i) q^{95} +(-2.07295 - 6.37988i) q^{96} +(-1.61803 + 1.17557i) q^{97} +29.0689 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} - 5 q^{6} - 10 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - q^3 - 3 * q^4 - 2 * q^5 - 5 * q^6 - 10 * q^7 + 5 * q^8 - q^9	\( 4 q - 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} - 5 q^{6} - 10 q^{7} + 5 q^{8} - q^{9} + 12 q^{12} + 10 q^{14} - 2 q^{15} + q^{16} - 10 q^{17} + 5 q^{18} - 10 q^{19} - 6 q^{20} - 16 q^{23} - 5 q^{24} + q^{25} - q^{27} + 30 q^{28} + 10 q^{29} + 10 q^{30} + 40 q^{34} + 20 q^{35} - 3 q^{36} - 2 q^{37} + 10 q^{38} + 10 q^{40} - 10 q^{41} + 10 q^{42} + 8 q^{45} + 20 q^{46} - 8 q^{47} + q^{48} - 13 q^{49} + 5 q^{50} + 10 q^{51} - 6 q^{53} - 40 q^{56} + 10 q^{57} - 10 q^{58} - 6 q^{60} - 20 q^{61} - 10 q^{63} + 13 q^{64} - 48 q^{67} - 30 q^{68} + 4 q^{69} + 20 q^{70} + 8 q^{71} - 5 q^{72} - 20 q^{73} + 10 q^{74} + q^{75} - 30 q^{79} + 2 q^{80} - q^{81} + 10 q^{82} + 20 q^{83} - 30 q^{84} + 20 q^{85} - 10 q^{86} - 56 q^{89} - 10 q^{90} + 12 q^{92} - 40 q^{94} - 20 q^{95} - 15 q^{96} - 2 q^{97}+O(q^{100}) \) 4 * q - 5 * q^2 - q^3 - 3 * q^4 - 2 * q^5 - 5 * q^6 - 10 * q^7 + 5 * q^8 - q^9 + 12 * q^12 + 10 * q^14 - 2 * q^15 + q^16 - 10 * q^17 + 5 * q^18 - 10 * q^19 - 6 * q^20 - 16 * q^23 - 5 * q^24 + q^25 - q^27 + 30 * q^28 + 10 * q^29 + 10 * q^30 + 40 * q^34 + 20 * q^35 - 3 * q^36 - 2 * q^37 + 10 * q^38 + 10 * q^40 - 10 * q^41 + 10 * q^42 + 8 * q^45 + 20 * q^46 - 8 * q^47 + q^48 - 13 * q^49 + 5 * q^50 + 10 * q^51 - 6 * q^53 - 40 * q^56 + 10 * q^57 - 10 * q^58 - 6 * q^60 - 20 * q^61 - 10 * q^63 + 13 * q^64 - 48 * q^67 - 30 * q^68 + 4 * q^69 + 20 * q^70 + 8 * q^71 - 5 * q^72 - 20 * q^73 + 10 * q^74 + q^75 - 30 * q^79 + 2 * q^80 - q^81 + 10 * q^82 + 20 * q^83 - 30 * q^84 + 20 * q^85 - 10 * q^86 - 56 * q^89 - 10 * q^90 + 12 * q^92 - 40 * q^94 - 20 * q^95 - 15 * q^96 - 2 * q^97

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