LMFDB - Embedded newform 363.2.e.a.202.1

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			202.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.202
Dual form			363.2.e.a.124.1

$q$-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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

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

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	−0.279641	−	0.960105i	$-0.590215\pi$
$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.999528	+	0.0307347i	$0.990215\pi$
$3$	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	−0.887535	−	0.460741i	$-0.847584\pi$
$5$	−1.61803	+	1.17557i	−0.723607	+	0.525731i	0.163928	+	0.986472i	$0.447584\pi$
$6$	−1.80902	+	1.31433i	−0.738528	+	0.536572i
$7$	−1.38197	−	4.25325i	−0.522334	−	1.60758i	−0.769528	−	0.638613i	$-0.779509\pi$
$7$	−1.38197	−	4.25325i	−0.522334	−	1.60758i	0.247194	−	0.968966i	$-0.420491\pi$
$8$	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	$-0.300000\pi$
$13$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$14$	−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	−0.932589	−	0.360939i	$-0.882456\pi$
$17$	−3.61803	+	2.62866i	−0.877502	+	0.637543i	0.0550873	+	0.998482i	$0.482456\pi$
$18$	0.690983	+	2.12663i	0.162866	+	0.501251i
$19$	−1.38197	+	4.25325i	−0.317045	+	0.975763i	0.657860	+	0.753140i	$0.271462\pi$
$19$	−1.38197	+	4.25325i	−0.317045	+	0.975763i	−0.974905	+	0.222623i	$0.928538\pi$
$20$	−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	0.993505	+	0.113787i	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$	1.38197	−	4.25325i	0.252311	−	0.776534i
$31$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$31$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$32$	−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	0.988918	−	0.148460i	$-0.0474315\pi$
$37$	0.618034	+	1.90211i	0.101604	+	0.312705i	−0.887314	+	0.461165i	$0.847432\pi$
$38$	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	0.783267	+	0.621685i	$0.213552\pi$
$41$	−1.38197	+	4.25325i	−0.215827	+	0.664247i	−0.999094	+	0.0425613i	$0.986448\pi$
$42$	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	−0.592094	−	0.805869i	$-0.701699\pi$
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	0.952692	−	0.303938i	$-0.0983015\pi$
$48$	−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	0.202178	−	0.979349i	$-0.435198\pi$
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	−0.868940	+	0.494918i	$0.835198\pi$
$54$	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	$-0.100000\pi$
$59$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$60$	−4.85410	+	3.52671i	−0.626662	+	0.455296i
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	−0.945129	−	0.326696i	$-0.894065\pi$
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	0.0186458	+	0.999826i	$0.494065\pi$
$62$		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	−0.133283	−	0.991078i	$-0.542552\pi$
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	0.901384	+	0.433020i	$0.142552\pi$
$72$	−1.80902	+	1.31433i	−0.213195	+	0.154895i
$73$	−2.76393	−	8.50651i	−0.323494	−	0.995611i	−0.972116	−	0.234501i	$-0.924654\pi$
$73$	−2.76393	−	8.50651i	−0.323494	−	0.995611i	0.648622	−	0.761111i	$-0.275346\pi$
$74$	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	−0.224984	−	0.974362i	$-0.572233\pi$
$79$	−10.8541	−	7.88597i	−1.22118	−	0.887241i	−0.996198	+	0.0871218i	$0.972233\pi$
$80$	−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	−0.114963	−	0.993370i	$-0.536675\pi$
$83$	7.23607	−	5.25731i	0.794262	−	0.577065i	0.909225	+	0.416305i	$0.136675\pi$
$84$	−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	0.502604	−	0.864517i	$-0.332375\pi$
$97$	−1.61803	−	1.17557i	−0.164286	−	0.119361i	−0.666891	+	0.745155i	$0.732375\pi$
$98$	29.0689			2.93640
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−3.61803	−	2.62866i	−0.360008	−	0.261561i	0.393048	−	0.919518i	$-0.371421\pi$
$101$	−3.61803	−	2.62866i	−0.360008	−	0.261561i	−0.753055	+	0.657957i	$0.771421\pi$
$102$	3.09017	−	9.51057i	0.305972	−	0.941686i
$103$	4.94427	+	15.2169i	0.487174	+	1.49937i	0.828808	+	0.559533i	$0.189020\pi$
$103$	4.94427	+	15.2169i	0.487174	+	1.49937i	−0.341634	+	0.939833i	$0.610980\pi$
$104$		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	−0.723979	−	0.689822i	$-0.757689\pi$
$107$	2.76393	−	8.50651i	0.267199	−	0.822355i	0.991179	−	0.132533i	$-0.0423112\pi$
$108$	−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	−0.825187	−	0.564859i	$-0.808930\pi$
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	0.999606	+	0.0280521i	$0.00893043\pi$
$114$	−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	−0.953879	−	0.300191i	$-0.902950\pi$
$127$	−10.8541	+	7.88597i	−0.963146	+	0.699766i	−0.00926659	+	0.999957i	$0.502950\pi$
$128$	−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	−0.559437	+	0.828873i	$0.688983\pi$
$137$	−17.7984	+	12.9313i	−1.52062	+	1.10479i	−0.961180	+	0.275921i	$0.911017\pi$
$138$	7.23607	−	5.25731i	0.615975	−	0.447532i
$139$	4.14590	+	12.7598i	0.351650	+	1.08227i	0.957926	+	0.287014i	$0.0926628\pi$
$139$	4.14590	+	12.7598i	0.351650	+	1.08227i	−0.606276	+	0.795254i	$0.707337\pi$
$140$	−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	0.505100	−	0.863061i	$-0.331455\pi$
$149$	18.0902	−	13.1433i	1.48200	−	1.07674i	0.976904	−	0.213679i	$-0.0685446\pi$
$150$	−0.690983	−	2.12663i	−0.0564185	−	0.173638i
$151$	4.14590	−	12.7598i	0.337388	−	1.03837i	−0.628145	−	0.778096i	$-0.716186\pi$
$151$	4.14590	−	12.7598i	0.337388	−	1.03837i	0.965534	−	0.260279i	$-0.0838144\pi$
$152$	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	−0.923361	−	0.383934i	$-0.874569\pi$
$157$	0.618034	−	1.90211i	0.0493245	−	0.151805i	0.972685	+	0.232129i	$0.0745691\pi$
$158$	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	0.453794	−	0.891107i	$-0.350070\pi$
$163$	−3.23607	−	2.35114i	−0.253468	−	0.184156i	−0.707263	+	0.706951i	$0.750070\pi$
$164$	−13.4164			−1.04765
$165$		0			0
$166$	−20.0000			−1.55230
$167$	−7.23607	−	5.25731i	−0.559944	−	0.406823i	0.271495	−	0.962440i	$-0.412482\pi$
$167$	−7.23607	−	5.25731i	−0.559944	−	0.406823i	−0.831438	+	0.555617i	$0.812482\pi$
$168$	−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	0.660462	+	0.750859i	$0.270360\pi$
$173$	−4.14590	+	12.7598i	−0.315207	+	0.970107i	−0.975669	+	0.219248i	$0.929640\pi$
$174$	−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	−0.986564	−	0.163374i	$-0.947762\pi$
$179$	−1.23607	+	3.80423i	−0.0923881	+	0.284341i	0.894176	+	0.447715i	$0.147762\pi$
$180$	1.85410	+	5.70634i	0.138197	+	0.425325i
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	−0.245016	−	0.969519i	$-0.578793\pi$
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	0.846353	+	0.532622i	$0.178793\pi$
$182$		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	$-0.100000\pi$
$191$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$192$	10.5172	−	7.64121i	0.759015	−	0.551457i
$193$	14.4721	−	10.5146i	1.04173	−	0.756859i	0.0711052	−	0.997469i	$-0.477347\pi$
$193$	14.4721	−	10.5146i	1.04173	−	0.756859i	0.970622	+	0.240610i	$0.0773474\pi$
$194$	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	0.705317	−	0.708892i	$-0.250805\pi$
$211$	3.61803	+	2.62866i	0.249076	+	0.180964i	−0.456241	+	0.889856i	$0.650805\pi$
$212$	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	0.637522	+	0.770432i	$0.279960\pi$
$223$	−4.94427	+	15.2169i	−0.331093	+	1.01900i	−0.968615	+	0.248567i	$0.920040\pi$
$224$	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	0.999918	−	0.0127917i	$-0.00407183\pi$
$227$	2.76393	+	8.50651i	0.183449	+	0.564597i	−0.816470	+	0.577388i	$0.804072\pi$
$228$	−4.14590	+	12.7598i	−0.274569	+	0.845036i
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	0.287467	−	0.957790i	$-0.407187\pi$
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	−0.822081	+	0.569371i	$0.807187\pi$
$230$	−17.8885			−1.17954
$231$		0			0
$232$	10.0000			0.656532
$233$	3.61803	+	2.62866i	0.237025	+	0.172209i	0.699957	−	0.714185i	$-0.253202\pi$
$233$	3.61803	+	2.62866i	0.237025	+	0.172209i	−0.462932	+	0.886394i	$0.653202\pi$
$234$		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	−0.821002	−	0.570925i	$-0.806585\pi$
$239$	2.76393	−	8.50651i	0.178784	−	0.550240i	0.999786	+	0.0206848i	$0.00658466\pi$
$240$	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	0.850391	−	0.526151i	$-0.176365\pi$
$251$	9.70820	+	7.05342i	0.612776	+	0.445208i	−0.237614	+	0.971360i	$0.576365\pi$
$252$	−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	−0.903881	−	0.427784i	$-0.859294\pi$
$257$	−6.79837	−	20.9232i	−0.424071	−	1.30516i	0.479810	−	0.877372i	$-0.340706\pi$
$258$	−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	−0.313173	−	0.949696i	$-0.601392\pi$
$269$	8.09017	−	5.87785i	0.493266	−	0.358379i	0.806439	+	0.591317i	$0.201392\pi$
$270$	−3.61803	+	2.62866i	−0.220187	+	0.159975i
$271$	−4.14590	−	12.7598i	−0.251845	−	0.775100i	−0.994435	−	0.105353i	$-0.966403\pi$
$271$	−4.14590	−	12.7598i	−0.251845	−	0.775100i	0.742589	−	0.669747i	$-0.233597\pi$
$272$	−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	$-0.300000\pi$
$277$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$278$	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	−0.545032	+	0.838415i	$0.683483\pi$
$281$	−25.3262	+	18.4006i	−1.51084	+	1.09769i	−0.965804	+	0.259272i	$0.916517\pi$
$282$	5.52786	+	17.0130i	0.329180	+	1.01311i
$283$	−4.14590	+	12.7598i	−0.246448	+	0.758489i	0.748947	+	0.662630i	$0.230560\pi$
$283$	−4.14590	+	12.7598i	−0.246448	+	0.758489i	−0.995395	+	0.0958591i	$0.969440\pi$
$284$	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	−0.921995	−	0.387201i	$-0.873442\pi$
$293$	−6.90983	−	21.2663i	−0.403677	−	1.24239i	0.518319	−	0.855188i	$-0.326558\pi$
$294$	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	0.789183	+	0.614159i	$0.210505\pi$
$311$	−3.70820	+	11.4127i	−0.210273	+	0.647154i	−0.999456	+	0.0329949i	$0.989495\pi$
$312$		0			0
$313$	−11.3262	+	8.22899i	−0.640197	+	0.465130i	−0.859918	−	0.510433i	$-0.829485\pi$
$313$	−11.3262	+	8.22899i	−0.640197	+	0.465130i	0.219721	+	0.975563i	$0.429485\pi$
$314$	−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	0.0982098	−	0.995166i	$-0.468688\pi$
$317$	−14.5623	−	10.5801i	−0.817901	−	0.594240i	−0.916110	+	0.400926i	$0.868688\pi$
$318$	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	0.997684	−	0.0680176i	$-0.0216674\pi$
$337$	2.76393	+	8.50651i	0.150561	+	0.463379i	−0.847123	+	0.531397i	$0.821667\pi$
$338$	−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	−0.764821	−	0.644243i	$-0.777173\pi$
$347$	−7.23607	+	5.25731i	−0.388452	+	0.282227i	0.376369	+	0.926470i	$0.377173\pi$
$348$	4.14590	+	12.7598i	0.222243	+	0.683995i
$349$	−8.29180	+	25.5195i	−0.443850	+	1.36603i	0.439891	+	0.898051i	$0.355017\pi$
$349$	−8.29180	+	25.5195i	−0.443850	+	1.36603i	−0.883740	+	0.467978i	$0.844983\pi$
$350$	−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	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$	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	0.994616	−	0.103627i	$-0.0330448\pi$
$367$	2.47214	+	7.60845i	0.129044	+	0.397158i	−0.865572	+	0.500785i	$0.833045\pi$
$368$	−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	−0.0887501	−	0.996054i	$-0.528287\pi$
$379$	16.1803	−	11.7557i	0.831128	−	0.603850i	0.919878	+	0.392204i	$0.128287\pi$
$380$	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	0.974798	+	0.223090i	$0.0716144\pi$
$383$	29.1246	+	21.1603i	1.48820	+	1.08124i	0.513400	+	0.858149i	$0.328386\pi$
$384$	−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	0.998327	−	0.0578199i	$-0.0184149\pi$
$389$	3.09017	+	9.51057i	0.156678	+	0.482205i	−0.841649	+	0.540025i	$0.818415\pi$
$390$		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	−0.995412	−	0.0956827i	$-0.969497\pi$
$401$	−24.2705	+	17.6336i	−1.21201	+	0.880578i	−0.216600	+	0.976261i	$0.569497\pi$
$402$	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	0.976521	−	0.215424i	$-0.0691134\pi$
$409$	21.7082	+	15.7719i	1.07340	+	0.779872i	0.0968810	+	0.995296i	$0.469113\pi$
$410$	−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	−0.847084	−	0.531460i	$-0.821644\pi$
$421$	3.09017	−	9.51057i	0.150606	−	0.463517i	0.997689	+	0.0679432i	$0.0216437\pi$
$422$	−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	0.748260	−	0.663405i	$-0.230890\pi$
$431$	7.23607	+	5.25731i	0.348549	+	0.253236i	−0.399711	+	0.916641i	$0.630890\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$		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	0.605158	+	0.796105i	$0.293110\pi$
$443$	−7.41641	+	22.8254i	−0.352364	+	1.08447i	−0.957522	+	0.288360i	$0.906890\pi$
$444$	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	0.696404	−	0.717650i	$-0.254782\pi$
$449$	4.85410	+	3.52671i	0.229079	+	0.166436i	−0.467325	+	0.884086i	$0.654782\pi$
$450$	−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	−0.965349	−	0.260963i	$-0.915960\pi$
$457$	−21.7082	+	15.7719i	−1.01547	+	0.737780i	−0.0501182	+	0.998743i	$0.515960\pi$
$458$	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	−0.427881	−	0.903835i	$-0.640740\pi$
$467$	6.47214	−	4.70228i	0.299495	−	0.217596i	0.727376	+	0.686239i	$0.240740\pi$
$468$		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	−0.410071	−	0.912054i	$-0.634496\pi$
$479$	7.23607	−	5.25731i	0.330624	−	0.240213i	0.740696	+	0.671841i	$0.234496\pi$
$480$	−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	−0.879291	−	0.476284i	$-0.841983\pi$
$487$	2.47214	−	7.60845i	0.112023	−	0.344772i	0.991315	+	0.131512i	$0.0419833\pi$
$488$	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	−0.944014	−	0.329904i	$-0.892984\pi$
$491$	−8.29180	−	25.5195i	−0.374204	−	1.15168i	0.569811	−	0.821776i	$-0.307016\pi$
$492$	−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	−0.988773	−	0.149427i	$-0.952257\pi$
$499$	−6.18034	−	19.0211i	−0.276670	−	0.851503i	0.712103	−	0.702075i	$-0.247743\pi$
$500$	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	0.577264	+	0.816558i	$0.304120\pi$
$503$	−8.29180	+	25.5195i	−0.369713	+	1.13786i	−0.946977	+	0.321302i	$0.895880\pi$
$504$	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	−0.504952	−	0.863147i	$-0.668490\pi$
$509$	9.27051	−	28.5317i	0.410908	−	1.26465i	0.915860	−	0.401498i	$-0.131510\pi$
$510$	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	0.919933	+	0.392077i	$0.128243\pi$
$521$	9.27051	+	28.5317i	0.406148	+	1.25000i	−0.513784	+	0.857920i	$0.671757\pi$
$522$	−8.09017	+	5.87785i	−0.354097	+	0.257267i
$523$	−3.61803	+	2.62866i	−0.158206	+	0.114943i	−0.664072	−	0.747669i	$-0.731173\pi$
$523$	−3.61803	+	2.62866i	−0.158206	+	0.114943i	0.505866	+	0.862612i	$0.331173\pi$
$524$	−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	$-0.300000\pi$
$541$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$542$	−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	−0.218672	−	0.975798i	$-0.570172\pi$
$547$	12.4377	−	38.2793i	0.531797	−	1.63670i	0.750469	−	0.660906i	$-0.229828\pi$
$548$	−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	−0.760323	−	0.649546i	$-0.774959\pi$
$557$	−12.4377	−	38.2793i	−0.527002	−	1.62195i	0.233321	−	0.972400i	$-0.425041\pi$
$558$		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	0.239461	−	0.970906i	$-0.423029\pi$
$563$	−14.4721	−	10.5146i	−0.609928	−	0.443138i	−0.849389	+	0.527767i	$0.823029\pi$
$564$	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	−0.917901	−	0.396809i	$-0.870117\pi$
$569$	1.38197	−	4.25325i	0.0579350	−	0.178306i	0.975836	+	0.218503i	$0.0701175\pi$
$570$	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	−0.553596	−	0.832785i	$-0.686745\pi$
$577$	1.61803	−	1.17557i	0.0673596	−	0.0489396i	0.620956	+	0.783846i	$0.286745\pi$
$578$	−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	0.886987	−	0.461794i	$-0.152794\pi$
$587$	−2.47214	−	7.60845i	−0.102036	−	0.314034i	−0.989023	+	0.147759i	$0.952794\pi$
$588$	−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	0.196735	−	0.980457i	$-0.436966\pi$
$599$	29.1246	−	21.1603i	1.19000	−	0.864585i	0.993264	+	0.115872i	$0.0369661\pi$
$600$	1.80902	−	1.31433i	0.0738528	−	0.0536572i
$601$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$601$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$602$	−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	0.658785	−	0.752331i	$-0.271071\pi$
$607$	3.61803	+	2.62866i	0.146851	+	0.106694i	−0.511934	+	0.859025i	$0.671071\pi$
$608$	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	−0.129248	−	0.991612i	$-0.541256\pi$
$613$	13.8197	−	42.5325i	0.558171	−	1.71787i	0.687419	−	0.726261i	$-0.258744\pi$
$614$	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	−0.170898	−	0.985289i	$-0.554667\pi$
$619$	13.5967	−	41.8465i	0.546499	−	1.68195i	0.717398	−	0.696664i	$-0.245333\pi$
$620$		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	0.930003	+	0.367553i	$0.119804\pi$
$631$	9.88854	+	30.4338i	0.393657	+	1.21155i	−0.536346	+	0.843998i	$0.680196\pi$
$632$	−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	0.583086	+	0.812410i	$0.301845\pi$
$641$	−9.27051	+	28.5317i	−0.366163	+	1.12693i	−0.949250	+	0.314524i	$0.898155\pi$
$642$	6.18034	+	19.0211i	0.243919	+	0.750704i
$643$	−29.1246	+	21.1603i	−1.14856	+	0.834480i	−0.988289	−	0.152593i	$-0.951238\pi$
$643$	−29.1246	+	21.1603i	−1.14856	+	0.834480i	−0.160273	+	0.987073i	$0.551238\pi$
$644$	−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	0.762033	−	0.647538i	$-0.224201\pi$
$647$	9.70820	+	7.05342i	0.381669	+	0.277299i	−0.380364	+	0.924837i	$0.624201\pi$
$648$	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	0.692573	+	0.721348i	$0.256477\pi$
$653$	14.2148	+	43.7486i	0.556267	+	1.71202i	−0.136305	+	0.990667i	$0.543523\pi$
$654$		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	0.830675	−	0.556758i	$-0.187955\pi$
$673$	14.4721	+	10.5146i	0.557860	+	0.405309i	−0.272815	+	0.962066i	$0.587955\pi$
$674$	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	0.0171501	−	0.999853i	$-0.494541\pi$
$677$	25.3262	−	18.4006i	0.973366	−	0.707192i	0.956216	+	0.292661i	$0.0945407\pi$
$678$	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	0.387610	−	0.921823i	$-0.373301\pi$
$691$	−9.70820	−	7.05342i	−0.369317	−	0.268325i	−0.756928	+	0.653498i	$0.773301\pi$
$692$	−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	0.731611	+	0.681722i	$0.238769\pi$
$701$	−6.90983	+	21.2663i	−0.260981	+	0.803216i	−0.992592	+	0.121494i	$0.961231\pi$
$702$		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	−0.492893	−	0.870090i	$-0.664061\pi$
$709$	4.85410	−	3.52671i	0.182300	−	0.132448i	0.675192	+	0.737642i	$0.264061\pi$
$710$	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	−0.988796	−	0.149276i	$-0.952306\pi$
$719$	−7.41641	−	22.8254i	−0.276585	−	0.851242i	0.712210	−	0.701966i	$-0.247694\pi$
$720$	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	−0.999746	−	0.0225283i	$-0.992828\pi$
$733$	−5.52786	−	17.0130i	−0.204176	−	0.628390i	0.795570	−	0.605862i	$-0.207172\pi$
$734$	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	0.519248	−	0.854624i	$-0.326212\pi$
$739$	−3.61803	−	2.62866i	−0.133092	−	0.0966967i	−0.652339	+	0.757927i	$0.726212\pi$
$740$	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	$-0.700000\pi$
$743$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$744$		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	−0.591708	−	0.806152i	$-0.701546\pi$
$751$	9.88854	−	30.4338i	0.360838	−	1.11055i	0.952546	−	0.304393i	$-0.0984537\pi$
$752$	−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	−0.237724	−	0.971333i	$-0.576401\pi$
$757$	−33.9787	−	24.6870i	−1.23498	−	0.897264i	−0.997253	+	0.0740691i	$0.976401\pi$
$758$	−44.7214			−1.62435
$759$		0			0
$760$	−20.0000			−0.725476
$761$	25.3262	+	18.4006i	0.918075	+	0.667021i	0.943044	−	0.332667i	$-0.107949\pi$
$761$	25.3262	+	18.4006i	0.918075	+	0.667021i	−0.0249688	+	0.999688i	$0.507949\pi$
$762$	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	−0.842618	−	0.538512i	$-0.818987\pi$
$773$	4.32624	−	13.3148i	0.155604	−	0.478900i	0.998222	+	0.0596126i	$0.0189865\pi$
$774$	3.09017	+	9.51057i	0.111074	+	0.341850i
$775$		0			0
$776$	−3.61803

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more