LMFDB - Embedded newform 444.2.g.a.443.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(443,444)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("444.443"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - x^{2} + 2x + 22 $ x^4 - 2x^3 - x^2 + 2x + 22
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			443.4
Root			$-1.23205 - 1.32288i$ of defining polynomial
Character	$\chi$	$=$	444.443
Dual form			444.2.g.a.443.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 1.32288i) q^{2} +1.73205 q^{3} +(-1.50000 - 1.32288i) q^{4} -2.00000 q^{5} +(-0.866025 + 2.29129i) q^{6} -2.64575i q^{7} +(2.50000 - 1.32288i) q^{8} +3.00000 q^{9} +(1.00000 - 2.64575i) q^{10} +1.73205 q^{11} +(-2.59808 - 2.29129i) q^{12} -4.58258i q^{13} +(3.50000 + 1.32288i) q^{14} -3.46410 q^{15} +(0.500000 + 3.96863i) q^{16} +5.00000 q^{17} +(-1.50000 + 3.96863i) q^{18} +1.73205 q^{19} +(3.00000 + 2.64575i) q^{20} -4.58258i q^{21} +(-0.866025 + 2.29129i) q^{22} +2.64575i q^{23} +(4.33013 - 2.29129i) q^{24} -1.00000 q^{25} +(6.06218 + 2.29129i) q^{26} +5.19615 q^{27} +(-3.50000 + 3.96863i) q^{28} +4.00000 q^{29} +(1.73205 - 4.58258i) q^{30} -3.46410 q^{31} +(-5.50000 - 1.32288i) q^{32} +3.00000 q^{33} +(-2.50000 + 6.61438i) q^{34} +5.29150i q^{35} +(-4.50000 - 3.96863i) q^{36} +(4.00000 - 4.58258i) q^{37} +(-0.866025 + 2.29129i) q^{38} -7.93725i q^{39} +(-5.00000 + 2.64575i) q^{40} -9.16515i q^{41} +(6.06218 + 2.29129i) q^{42} -3.46410 q^{43} +(-2.59808 - 2.29129i) q^{44} -6.00000 q^{45} +(-3.50000 - 1.32288i) q^{46} -10.3923 q^{47} +(0.866025 + 6.87386i) q^{48} +(0.500000 - 1.32288i) q^{50} +8.66025 q^{51} +(-6.06218 + 6.87386i) q^{52} +13.7477i q^{53} +(-2.59808 + 6.87386i) q^{54} -3.46410 q^{55} +(-3.50000 - 6.61438i) q^{56} +3.00000 q^{57} +(-2.00000 + 5.29150i) q^{58} +5.29150i q^{59} +(5.19615 + 4.58258i) q^{60} -9.16515i q^{61} +(1.73205 - 4.58258i) q^{62} -7.93725i q^{63} +(4.50000 - 6.61438i) q^{64} +9.16515i q^{65} +(-1.50000 + 3.96863i) q^{66} +10.5830i q^{67} +(-7.50000 - 6.61438i) q^{68} +4.58258i q^{69} +(-7.00000 - 2.64575i) q^{70} -3.46410 q^{71} +(7.50000 - 3.96863i) q^{72} +9.00000 q^{73} +(4.06218 + 7.58279i) q^{74} -1.73205 q^{75} +(-2.59808 - 2.29129i) q^{76} -4.58258i q^{77} +(10.5000 + 3.96863i) q^{78} +13.8564 q^{79} +(-1.00000 - 7.93725i) q^{80} +9.00000 q^{81} +(12.1244 + 4.58258i) q^{82} -8.66025 q^{83} +(-6.06218 + 6.87386i) q^{84} -10.0000 q^{85} +(1.73205 - 4.58258i) q^{86} +6.92820 q^{87} +(4.33013 - 2.29129i) q^{88} -5.00000 q^{89} +(3.00000 - 7.93725i) q^{90} -12.1244 q^{91} +(3.50000 - 3.96863i) q^{92} -6.00000 q^{93} +(5.19615 - 13.7477i) q^{94} -3.46410 q^{95} +(-9.52628 - 2.29129i) q^{96} +5.19615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{4} - 8 q^{5} + 10 q^{8} + 12 q^{9} + 4 q^{10} + 14 q^{14} + 2 q^{16} + 20 q^{17} - 6 q^{18} + 12 q^{20} - 4 q^{25} - 14 q^{28} + 16 q^{29} - 22 q^{32} + 12 q^{33} - 10 q^{34} - 18 q^{36}+ \cdots - 24 q^{93}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^4 - 8 * q^5 + 10 * q^8 + 12 * q^9 + 4 * q^10 + 14 * q^14 + 2 * q^16 + 20 * q^17 - 6 * q^18 + 12 * q^20 - 4 * q^25 - 14 * q^28 + 16 * q^29 - 22 * q^32 + 12 * q^33 - 10 * q^34 - 18 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 - 14 * q^46 + 2 * q^50 - 14 * q^56 + 12 * q^57 - 8 * q^58 + 18 * q^64 - 6 * q^66 - 30 * q^68 - 28 * q^70 + 30 * q^72 + 36 * q^73 - 8 * q^74 + 42 * q^78 - 4 * q^80 + 36 * q^81 - 40 * q^85 - 20 * q^89 + 12 * q^90 + 14 * q^92 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	1.32288i	−0.353553	+	0.935414i
$2$	−0.500000	+	1.32288i	−0.353553	+	0.935414i
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$	−1.50000	−	1.32288i	−0.750000	−	0.661438i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	−0.866025	+	2.29129i	−0.353553	+	0.935414i
$7$		−	2.64575i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$		−	2.64575i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$8$	2.50000	−	1.32288i	0.883883	−	0.467707i
$9$	3.00000			1.00000
$10$	1.00000	−	2.64575i	0.316228	−	0.836660i
$11$	1.73205			0.522233			0.261116	−	0.965307i	$-0.415909\pi$
$11$	1.73205			0.522233			0.261116	+	0.965307i	$0.415909\pi$
$12$	−2.59808	−	2.29129i	−0.750000	−	0.661438i
$13$		−	4.58258i		−	1.27098i	−0.772110	−	0.635489i	$-0.780799\pi$
$13$		−	4.58258i		−	1.27098i	0.772110	−	0.635489i	$-0.219201\pi$
$14$	3.50000	+	1.32288i	0.935414	+	0.353553i
$15$	−3.46410			−0.894427
$16$	0.500000	+	3.96863i	0.125000	+	0.992157i
$17$	5.00000			1.21268			0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000			1.21268			0.606339	+	0.795206i	$0.292637\pi$
$18$	−1.50000	+	3.96863i	−0.353553	+	0.935414i
$19$	1.73205			0.397360			0.198680	−	0.980064i	$-0.436335\pi$
$19$	1.73205			0.397360			0.198680	+	0.980064i	$0.436335\pi$
$20$	3.00000	+	2.64575i	0.670820	+	0.591608i
$21$		−	4.58258i		−	1.00000i
$22$	−0.866025	+	2.29129i	−0.184637	+	0.488504i
$23$			2.64575i			0.551677i	0.961204	+	0.275839i	$0.0889555\pi$
$23$			2.64575i			0.551677i	−0.961204	+	0.275839i	$0.911044\pi$
$24$	4.33013	−	2.29129i	0.883883	−	0.467707i
$25$	−1.00000			−0.200000
$26$	6.06218	+	2.29129i	1.18889	+	0.449359i
$27$	5.19615			1.00000
$28$	−3.50000	+	3.96863i	−0.661438	+	0.750000i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$	1.73205	−	4.58258i	0.316228	−	0.836660i
$31$	−3.46410			−0.622171			−0.311086	−	0.950382i	$-0.600693\pi$
$31$	−3.46410			−0.622171			−0.311086	+	0.950382i	$0.600693\pi$
$32$	−5.50000	−	1.32288i	−0.972272	−	0.233854i
$33$	3.00000			0.522233
$34$	−2.50000	+	6.61438i	−0.428746	+	1.13436i
$35$			5.29150i			0.894427i
$36$	−4.50000	−	3.96863i	−0.750000	−	0.661438i
$37$	4.00000	−	4.58258i	0.657596	−	0.753371i
$37$	4.00000	−	4.58258i	0.657596	−	0.753371i
$38$	−0.866025	+	2.29129i	−0.140488	+	0.371696i
$39$		−	7.93725i		−	1.27098i
$40$	−5.00000	+	2.64575i	−0.790569	+	0.418330i
$41$		−	9.16515i		−	1.43136i	−0.698430	−	0.715678i	$-0.746118\pi$
$41$		−	9.16515i		−	1.43136i	0.698430	−	0.715678i	$-0.253882\pi$
$42$	6.06218	+	2.29129i	0.935414	+	0.353553i
$43$	−3.46410			−0.528271			−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410			−0.528271			−0.264135	+	0.964486i	$0.585087\pi$
$44$	−2.59808	−	2.29129i	−0.391675	−	0.345425i
$45$	−6.00000			−0.894427
$46$	−3.50000	−	1.32288i	−0.516047	−	0.195047i
$47$	−10.3923			−1.51587			−0.757937	−	0.652328i	$-0.773792\pi$
$47$	−10.3923			−1.51587			−0.757937	+	0.652328i	$0.773792\pi$
$48$	0.866025	+	6.87386i	0.125000	+	0.992157i
$49$		0			0
$50$	0.500000	−	1.32288i	0.0707107	−	0.187083i
$51$	8.66025			1.21268
$52$	−6.06218	+	6.87386i	−0.840673	+	0.953233i
$53$			13.7477i			1.88840i	0.329379	+	0.944198i	$0.393161\pi$
$53$			13.7477i			1.88840i	−0.329379	+	0.944198i	$0.606839\pi$
$54$	−2.59808	+	6.87386i	−0.353553	+	0.935414i
$55$	−3.46410			−0.467099
$56$	−3.50000	−	6.61438i	−0.467707	−	0.883883i
$57$	3.00000			0.397360
$58$	−2.00000	+	5.29150i	−0.262613	+	0.694808i
$59$			5.29150i			0.688895i	0.938806	+	0.344447i	$0.111934\pi$
$59$			5.29150i			0.688895i	−0.938806	+	0.344447i	$0.888066\pi$
$60$	5.19615	+	4.58258i	0.670820	+	0.591608i
$61$		−	9.16515i		−	1.17348i	−0.809776	−	0.586739i	$-0.800412\pi$
$61$		−	9.16515i		−	1.17348i	0.809776	−	0.586739i	$-0.199588\pi$
$62$	1.73205	−	4.58258i	0.219971	−	0.581988i
$63$		−	7.93725i		−	1.00000i
$64$	4.50000	−	6.61438i	0.562500	−	0.826797i
$65$			9.16515i			1.13680i
$66$	−1.50000	+	3.96863i	−0.184637	+	0.488504i
$67$			10.5830i			1.29292i	0.762948	+	0.646460i	$0.223751\pi$
$67$			10.5830i			1.29292i	−0.762948	+	0.646460i	$0.776249\pi$
$68$	−7.50000	−	6.61438i	−0.909509	−	0.802111i
$69$			4.58258i			0.551677i
$70$	−7.00000	−	2.64575i	−0.836660	−	0.316228i
$71$	−3.46410			−0.411113			−0.205557	−	0.978645i	$-0.565900\pi$
$71$	−3.46410			−0.411113			−0.205557	+	0.978645i	$0.565900\pi$
$72$	7.50000	−	3.96863i	0.883883	−	0.467707i
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$	4.06218	+	7.58279i	0.472219	+	0.881481i
$75$	−1.73205			−0.200000
$76$	−2.59808	−	2.29129i	−0.298020	−	0.262829i
$77$		−	4.58258i		−	0.522233i
$78$	10.5000	+	3.96863i	1.18889	+	0.449359i
$79$	13.8564			1.55897			0.779484	−	0.626422i	$-0.215481\pi$
$79$	13.8564			1.55897			0.779484	+	0.626422i	$0.215481\pi$
$80$	−1.00000	−	7.93725i	−0.111803	−	0.887412i
$81$	9.00000			1.00000
$82$	12.1244	+	4.58258i	1.33891	+	0.506061i
$83$	−8.66025			−0.950586			−0.475293	−	0.879827i	$-0.657658\pi$
$83$	−8.66025			−0.950586			−0.475293	+	0.879827i	$0.657658\pi$
$84$	−6.06218	+	6.87386i	−0.661438	+	0.750000i
$85$	−10.0000			−1.08465
$86$	1.73205	−	4.58258i	0.186772	−	0.494152i
$87$	6.92820			0.742781
$88$	4.33013	−	2.29129i	0.461593	−	0.244252i
$89$	−5.00000			−0.529999			−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000			−0.529999			−0.264999	+	0.964249i	$0.585372\pi$
$90$	3.00000	−	7.93725i	0.316228	−	0.836660i
$91$	−12.1244			−1.27098
$92$	3.50000	−	3.96863i	0.364900	−	0.413758i
$93$	−6.00000			−0.622171
$94$	5.19615	−	13.7477i	0.535942	−	1.41797i
$95$	−3.46410			−0.355409
$96$	−9.52628	−	2.29129i	−0.972272	−	0.233854i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		0			0
$99$	5.19615			0.522233
$100$	1.50000	+	1.32288i	0.150000	+	0.132288i
$101$			9.16515i			0.911967i	0.889988	+	0.455983i	$0.150712\pi$
$101$			9.16515i			0.911967i	−0.889988	+	0.455983i	$0.849288\pi$
$102$	−4.33013	+	11.4564i	−0.428746	+	1.13436i
$103$	−13.8564			−1.36531			−0.682656	−	0.730740i	$-0.739175\pi$
$103$	−13.8564			−1.36531			−0.682656	+	0.730740i	$0.739175\pi$
$104$	−6.06218	−	11.4564i	−0.594445	−	1.12340i
$105$			9.16515i			0.894427i
$106$	−18.1865	−	6.87386i	−1.76643	−	0.667649i
$107$	1.73205			0.167444			0.0837218	−	0.996489i	$-0.473319\pi$
$107$	1.73205			0.167444			0.0837218	+	0.996489i	$0.473319\pi$
$108$	−7.79423	−	6.87386i	−0.750000	−	0.661438i
$109$			13.7477i			1.31679i	0.752671	+	0.658397i	$0.228765\pi$
$109$			13.7477i			1.31679i	−0.752671	+	0.658397i	$0.771235\pi$
$110$	1.73205	−	4.58258i	0.165145	−	0.436931i
$111$	6.92820	−	7.93725i	0.657596	−	0.753371i
$112$	10.5000	−	1.32288i	0.992157	−	0.125000i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	−1.50000	+	3.96863i	−0.140488	+	0.371696i
$115$		−	5.29150i		−	0.493435i
$116$	−6.00000	−	5.29150i	−0.557086	−	0.491304i
$117$		−	13.7477i		−	1.27098i
$118$	−7.00000	−	2.64575i	−0.644402	−	0.243561i
$119$		−	13.2288i		−	1.21268i
$120$	−8.66025	+	4.58258i	−0.790569	+	0.418330i
$121$	−8.00000			−0.727273
$122$	12.1244	+	4.58258i	1.09769	+	0.414887i
$123$		−	15.8745i		−	1.43136i
$124$	5.19615	+	4.58258i	0.466628	+	0.411527i
$125$	12.0000			1.07331
$126$	10.5000	+	3.96863i	0.935414	+	0.353553i
$127$		−	7.93725i		−	0.704317i	−0.935940	−	0.352159i	$-0.885448\pi$
$127$		−	7.93725i		−	0.704317i	0.935940	−	0.352159i	$-0.114552\pi$
$128$	6.50000	+	9.26013i	0.574524	+	0.818488i
$129$	−6.00000			−0.528271
$130$	−12.1244	−	4.58258i	−1.06338	−	0.401918i
$131$			5.29150i			0.462321i	0.972916	+	0.231160i	$0.0742522\pi$
$131$			5.29150i			0.462321i	−0.972916	+	0.231160i	$0.925748\pi$
$132$	−4.50000	−	3.96863i	−0.391675	−	0.345425i
$133$		−	4.58258i		−	0.397360i
$134$	−14.0000	−	5.29150i	−1.20942	−	0.457116i
$135$	−10.3923			−0.894427
$136$	12.5000	−	6.61438i	1.07187	−	0.567178i
$137$		−	9.16515i		−	0.783032i	−0.920171	−	0.391516i	$-0.871951\pi$
$137$		−	9.16515i		−	0.783032i	0.920171	−	0.391516i	$-0.128049\pi$
$138$	−6.06218	−	2.29129i	−0.516047	−	0.195047i
$139$			5.29150i			0.448819i	0.974495	+	0.224410i	$0.0720454\pi$
$139$			5.29150i			0.448819i	−0.974495	+	0.224410i	$0.927955\pi$
$140$	7.00000	−	7.93725i	0.591608	−	0.670820i
$141$	−18.0000			−1.51587
$142$	1.73205	−	4.58258i	0.145350	−	0.384561i
$143$		−	7.93725i		−	0.663747i
$144$	1.50000	+	11.9059i	0.125000	+	0.992157i
$145$	−8.00000			−0.664364
$146$	−4.50000	+	11.9059i	−0.372423	+	0.985338i
$147$		0			0
$148$	−12.0622	+	1.58236i	−0.991505	+	0.130069i
$149$		−	9.16515i		−	0.750838i	−0.926855	−	0.375419i	$-0.877499\pi$
$149$		−	9.16515i		−	0.750838i	0.926855	−	0.375419i	$-0.122501\pi$
$150$	0.866025	−	2.29129i	0.0707107	−	0.187083i
$151$			7.93725i			0.645925i	0.946412	+	0.322962i	$0.104679\pi$
$151$			7.93725i			0.645925i	−0.946412	+	0.322962i	$0.895321\pi$
$152$	4.33013	−	2.29129i	0.351220	−	0.185848i
$153$	15.0000			1.21268
$154$	6.06218	+	2.29129i	0.488504	+	0.184637i
$155$	6.92820			0.556487
$156$	−10.5000	+	11.9059i	−0.840673	+	0.953233i
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$	−6.92820	+	18.3303i	−0.551178	+	1.45828i
$159$			23.8118i			1.88840i
$160$	11.0000	+	2.64575i	0.869626	+	0.209165i
$161$	7.00000			0.551677
$162$	−4.50000	+	11.9059i	−0.353553	+	0.935414i
$163$	8.66025			0.678323			0.339162	−	0.940728i	$-0.389857\pi$
$163$	8.66025			0.678323			0.339162	+	0.940728i	$0.389857\pi$
$164$	−12.1244	+	13.7477i	−0.946753	+	1.07352i
$165$	−6.00000			−0.467099
$166$	4.33013	−	11.4564i	0.336083	−	0.889192i
$167$			2.64575i			0.204734i	0.994747	+	0.102367i	$0.0326417\pi$
$167$			2.64575i			0.204734i	−0.994747	+	0.102367i	$0.967358\pi$
$168$	−6.06218	−	11.4564i	−0.467707	−	0.883883i
$169$	−8.00000			−0.615385
$170$	5.00000	−	13.2288i	0.383482	−	1.01460i
$171$	5.19615			0.397360
$172$	5.19615	+	4.58258i	0.396203	+	0.349418i
$173$			4.58258i			0.348407i	0.984710	+	0.174203i	$0.0557350\pi$
$173$			4.58258i			0.348407i	−0.984710	+	0.174203i	$0.944265\pi$
$174$	−3.46410	+	9.16515i	−0.262613	+	0.694808i
$175$			2.64575i			0.200000i
$176$	0.866025	+	6.87386i	0.0652791	+	0.518137i
$177$			9.16515i			0.688895i
$178$	2.50000	−	6.61438i	0.187383	−	0.495769i
$179$			5.29150i			0.395505i	0.980252	+	0.197753i	$0.0633643\pi$
$179$			5.29150i			0.395505i	−0.980252	+	0.197753i	$0.936636\pi$
$180$	9.00000	+	7.93725i	0.670820	+	0.591608i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	6.06218	−	16.0390i	0.449359	−	1.18889i
$183$		−	15.8745i		−	1.17348i
$184$	3.50000	+	6.61438i	0.258023	+	0.487618i
$185$	−8.00000	+	9.16515i	−0.588172	+	0.673835i
$186$	3.00000	−	7.93725i	0.219971	−	0.581988i
$187$	8.66025			0.633300
$188$	15.5885	+	13.7477i	1.13691	+	1.00266i
$189$		−	13.7477i		−	1.00000i
$190$	1.73205	−	4.58258i	0.125656	−	0.332455i
$191$			18.5203i			1.34008i	0.742325	+	0.670039i	$0.233723\pi$
$191$			18.5203i			1.34008i	−0.742325	+	0.670039i	$0.766277\pi$
$192$	7.79423	−	11.4564i	0.562500	−	0.826797i
$193$			18.3303i			1.31944i	0.751510	+	0.659722i	$0.229326\pi$
$193$			18.3303i			1.31944i	−0.751510	+	0.659722i	$0.770674\pi$
$194$		0			0
$195$			15.8745i			1.13680i
$196$		0			0
$197$		−	4.58258i		−	0.326495i	−0.986585	−	0.163247i	$-0.947803\pi$
$197$		−	4.58258i		−	0.326495i	0.986585	−	0.163247i	$-0.0521969\pi$
$198$	−2.59808	+	6.87386i	−0.184637	+	0.488504i
$199$	24.2487			1.71895			0.859473	−	0.511182i	$-0.170792\pi$
$199$	24.2487			1.71895			0.859473	+	0.511182i	$0.170792\pi$
$200$	−2.50000	+	1.32288i	−0.176777	+	0.0935414i
$201$			18.3303i			1.29292i
$202$	−12.1244	−	4.58258i	−0.853067	−	0.322429i
$203$		−	10.5830i		−	0.742781i
$204$	−12.9904	−	11.4564i	−0.909509	−	0.802111i
$205$			18.3303i			1.28024i
$206$	6.92820	−	18.3303i	0.482711	−	1.27713i
$207$			7.93725i			0.551677i
$208$	18.1865	−	2.29129i	1.26101	−	0.158872i
$209$	3.00000			0.207514
$210$	−12.1244	−	4.58258i	−0.836660	−	0.316228i
$211$			15.8745i			1.09285i	0.837509	+	0.546423i	$0.184011\pi$
$211$			15.8745i			1.09285i	−0.837509	+	0.546423i	$0.815989\pi$
$212$	18.1865	−	20.6216i	1.24906	−	1.41630i
$213$	−6.00000			−0.411113
$214$	−0.866025	+	2.29129i	−0.0592003	+	0.156629i
$215$	6.92820			0.472500
$216$	12.9904	−	6.87386i	0.883883	−	0.467707i
$217$			9.16515i			0.622171i
$218$	−18.1865	−	6.87386i	−1.23175	−	0.465557i
$219$	15.5885			1.05337
$220$	5.19615	+	4.58258i	0.350325	+	0.308957i
$221$		−	22.9129i		−	1.54129i
$222$	7.03590	+	13.1338i	0.472219	+	0.881481i
$223$		−	15.8745i		−	1.06304i	−0.847047	−	0.531518i	$-0.821622\pi$
$223$		−	15.8745i		−	1.06304i	0.847047	−	0.531518i	$-0.178378\pi$
$224$	−3.50000	+	14.5516i	−0.233854	+	0.972272i
$225$	−3.00000			−0.200000
$226$	7.00000	−	18.5203i	0.465633	−	1.23195i
$227$			21.1660i			1.40484i	0.711764	+	0.702419i	$0.247897\pi$
$227$			21.1660i			1.40484i	−0.711764	+	0.702419i	$0.752103\pi$
$228$	−4.50000	−	3.96863i	−0.298020	−	0.262829i
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	7.00000	+	2.64575i	0.461566	+	0.174456i
$231$		−	7.93725i		−	0.522233i
$232$	10.0000	−	5.29150i	0.656532	−	0.347404i
$233$		−	18.3303i		−	1.20086i	−0.799678	−	0.600429i	$-0.794996\pi$
$233$		−	18.3303i		−	1.20086i	0.799678	−	0.600429i	$-0.205004\pi$
$234$	18.1865	+	6.87386i	1.18889	+	0.449359i
$235$	20.7846			1.35584
$236$	7.00000	−	7.93725i	0.455661	−	0.516671i
$237$	24.0000			1.55897
$238$	17.5000	+	6.61438i	1.13436	+	0.428746i
$239$		−	5.29150i		−	0.342279i	−0.985247	−	0.171139i	$-0.945255\pi$
$239$		−	5.29150i		−	0.342279i	0.985247	−	0.171139i	$-0.0547449\pi$
$240$	−1.73205	−	13.7477i	−0.111803	−	0.887412i
$241$			9.16515i			0.590379i	0.955439	+	0.295190i	$0.0953828\pi$
$241$			9.16515i			0.590379i	−0.955439	+	0.295190i	$0.904617\pi$
$242$	4.00000	−	10.5830i	0.257130	−	0.680301i
$243$	15.5885			1.00000
$244$	−12.1244	+	13.7477i	−0.776182	+	0.880108i
$245$		0			0
$246$	21.0000	+	7.93725i	1.33891	+	0.506061i
$247$		−	7.93725i		−	0.505035i
$248$	−8.66025	+	4.58258i	−0.549927	+	0.290994i
$249$	−15.0000			−0.950586
$250$	−6.00000	+	15.8745i	−0.379473	+	1.00399i
$251$			21.1660i			1.33599i	0.744167	+	0.667993i	$0.232847\pi$
$251$			21.1660i			1.33599i	−0.744167	+	0.667993i	$0.767153\pi$
$252$	−10.5000	+	11.9059i	−0.661438	+	0.750000i
$253$			4.58258i			0.288104i
$254$	10.5000	+	3.96863i	0.658829	+	0.249014i
$255$	−17.3205			−1.08465
$256$	−15.5000	+	3.96863i	−0.968750	+	0.248039i
$257$	5.00000			0.311891			0.155946	−	0.987766i	$-0.450158\pi$
$257$	5.00000			0.311891			0.155946	+	0.987766i	$0.450158\pi$
$258$	3.00000	−	7.93725i	0.186772	−	0.494152i
$259$	−12.1244	−	10.5830i	−0.753371	−	0.657596i
$260$	12.1244	−	13.7477i	0.751921	−	0.852598i
$261$	12.0000			0.742781
$262$	−7.00000	−	2.64575i	−0.432461	−	0.163455i
$263$	−13.8564			−0.854423			−0.427211	−	0.904152i	$-0.640504\pi$
$263$	−13.8564			−0.854423			−0.427211	+	0.904152i	$0.640504\pi$
$264$	7.50000	−	3.96863i	0.461593	−	0.244252i
$265$		−	27.4955i		−	1.68903i
$266$	6.06218	+	2.29129i	0.371696	+	0.140488i
$267$	−8.66025			−0.529999
$268$	14.0000	−	15.8745i	0.855186	−	0.969690i
$269$			22.9129i			1.39702i	0.715599	+	0.698511i	$0.246154\pi$
$269$			22.9129i			1.39702i	−0.715599	+	0.698511i	$0.753846\pi$
$270$	5.19615	−	13.7477i	0.316228	−	0.836660i
$271$			26.4575i			1.60718i	0.595184	+	0.803590i	$0.297079\pi$
$271$			26.4575i			1.60718i	−0.595184	+	0.803590i	$0.702921\pi$
$272$	2.50000	+	19.8431i	0.151585	+	1.20317i
$273$	−21.0000			−1.27098
$274$	12.1244	+	4.58258i	0.732459	+	0.276844i
$275$	−1.73205			−0.104447
$276$	6.06218	−	6.87386i	0.364900	−	0.413758i
$277$			4.58258i			0.275340i	0.990478	+	0.137670i	$0.0439614\pi$
$277$			4.58258i			0.275340i	−0.990478	+	0.137670i	$0.956039\pi$
$278$	−7.00000	−	2.64575i	−0.419832	−	0.158682i
$279$	−10.3923			−0.622171
$280$	7.00000	+	13.2288i	0.418330	+	0.790569i
$281$	11.0000			0.656205			0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000			0.656205			0.328102	+	0.944642i	$0.393591\pi$
$282$	9.00000	−	23.8118i	0.535942	−	1.41797i
$283$	−29.4449			−1.75032			−0.875158	−	0.483838i	$-0.839242\pi$
$283$	−29.4449			−1.75032			−0.875158	+	0.483838i	$0.839242\pi$
$284$	5.19615	+	4.58258i	0.308335	+	0.271926i
$285$	−6.00000			−0.355409
$286$	10.5000	+	3.96863i	0.620878	+	0.234670i
$287$	−24.2487			−1.43136
$288$	−16.5000	−	3.96863i	−0.972272	−	0.233854i
$289$	8.00000			0.470588
$290$	4.00000	−	10.5830i	0.234888	−	0.621455i
$291$		0			0
$292$	−13.5000	−	11.9059i	−0.790028	−	0.696739i
$293$		−	4.58258i		−	0.267717i	−0.991000	−	0.133858i	$-0.957263\pi$
$293$		−	4.58258i		−	0.267717i	0.991000	−	0.133858i	$-0.0427368\pi$
$294$		0			0
$295$		−	10.5830i		−	0.616166i
$296$	3.93782	−	16.7479i	0.228881	−	0.973454i
$297$	9.00000			0.522233
$298$	12.1244	+	4.58258i	0.702345	+	0.265461i
$299$	12.1244			0.701170
$300$	2.59808	+	2.29129i	0.150000	+	0.132288i
$301$			9.16515i			0.528271i
$302$	−10.5000	−	3.96863i	−0.604207	−	0.228369i
$303$			15.8745i			0.911967i
$304$	0.866025	+	6.87386i	0.0496700	+	0.394243i
$305$			18.3303i			1.04959i
$306$	−7.50000	+	19.8431i	−0.428746	+	1.13436i
$307$		−	31.7490i		−	1.81201i	−0.423265	−	0.906006i	$-0.639116\pi$
$307$		−	31.7490i		−	1.81201i	0.423265	−	0.906006i	$-0.360884\pi$
$308$	−6.06218	+	6.87386i	−0.345425	+	0.391675i
$309$	−24.0000			−1.36531
$310$	−3.46410	+	9.16515i	−0.196748	+	0.520546i
$311$			5.29150i			0.300054i	0.988682	+	0.150027i	$0.0479360\pi$
$311$			5.29150i			0.300054i	−0.988682	+	0.150027i	$0.952064\pi$
$312$	−10.5000	−	19.8431i	−0.594445	−	1.12340i
$313$		−	27.4955i		−	1.55413i	−0.629417	−	0.777067i	$-0.716706\pi$
$313$		−	27.4955i		−	1.55413i	0.629417	−	0.777067i	$-0.283294\pi$
$314$	−6.00000	+	15.8745i	−0.338600	+	0.895850i
$315$			15.8745i			0.894427i
$316$	−20.7846	−	18.3303i	−1.16923	−	1.03116i
$317$			9.16515i			0.514766i	0.966309	+	0.257383i	$0.0828602\pi$
$317$			9.16515i			0.514766i	−0.966309	+	0.257383i	$0.917140\pi$
$318$	−31.5000	−	11.9059i	−1.76643	−	0.667649i
$319$	6.92820			0.387905
$320$	−9.00000	+	13.2288i	−0.503115	+	0.739510i
$321$	3.00000			0.167444
$322$	−3.50000	+	9.26013i	−0.195047	+	0.516047i
$323$	8.66025			0.481869
$324$	−13.5000	−	11.9059i	−0.750000	−	0.661438i
$325$			4.58258i			0.254196i
$326$	−4.33013	+	11.4564i	−0.239824	+	0.634513i
$327$			23.8118i			1.31679i
$328$	−12.1244	−	22.9129i	−0.669456	−	1.26515i
$329$			27.4955i			1.51587i
$330$	3.00000	−	7.93725i	0.165145	−	0.436931i
$331$	10.3923			0.571213			0.285606	−	0.958347i	$-0.407805\pi$
$331$	10.3923			0.571213			0.285606	+	0.958347i	$0.407805\pi$
$332$	12.9904	+	11.4564i	0.712940	+	0.628754i
$333$	12.0000	−	13.7477i	0.657596	−	0.753371i
$334$	−3.50000	−	1.32288i	−0.191511	−	0.0723845i
$335$		−	21.1660i		−	1.15642i
$336$	18.1865	−	2.29129i	0.992157	−	0.125000i
$337$	19.0000			1.03500			0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000			1.03500			0.517498	+	0.855684i	$0.326864\pi$
$338$	4.00000	−	10.5830i	0.217571	−	0.575640i
$339$	−24.2487			−1.31701
$340$	15.0000	+	13.2288i	0.813489	+	0.717430i
$341$	−6.00000			−0.324918
$342$	−2.59808	+	6.87386i	−0.140488	+	0.371696i
$343$		−	18.5203i		−	1.00000i
$344$	−8.66025	+	4.58258i	−0.466930	+	0.247076i
$345$		−	9.16515i		−	0.493435i
$346$	−6.06218	−	2.29129i	−0.325905	−	0.123180i
$347$		−	5.29150i		−	0.284063i	−0.989862	−	0.142031i	$-0.954637\pi$
$347$		−	5.29150i		−	0.284063i	0.989862	−	0.142031i	$-0.0453634\pi$
$348$	−10.3923	−	9.16515i	−0.557086	−	0.491304i
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$	−3.50000	−	1.32288i	−0.187083	−	0.0707107i
$351$		−	23.8118i		−	1.27098i
$352$	−9.52628	−	2.29129i	−0.507752	−	0.122126i
$353$	2.00000			0.106449			0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000			0.106449			0.0532246	+	0.998583i	$0.483050\pi$
$354$	−12.1244	−	4.58258i	−0.644402	−	0.243561i
$355$	6.92820			0.367711
$356$	7.50000	+	6.61438i	0.397499	+	0.350561i
$357$		−	22.9129i		−	1.21268i
$358$	−7.00000	−	2.64575i	−0.369961	−	0.139832i
$359$	−27.7128			−1.46263			−0.731313	−	0.682042i	$-0.761092\pi$
$359$	−27.7128			−1.46263			−0.731313	+	0.682042i	$0.761092\pi$
$360$	−15.0000	+	7.93725i	−0.790569	+	0.418330i
$361$	−16.0000			−0.842105
$362$	3.00000	−	7.93725i	0.157676	−	0.417173i
$363$	−13.8564			−0.727273
$364$	18.1865	+	16.0390i	0.953233	+	0.840673i
$365$	−18.0000			−0.942163
$366$	21.0000	+	7.93725i	1.09769	+	0.414887i
$367$			23.8118i			1.24296i	0.783429	+	0.621482i	$0.213469\pi$
$367$			23.8118i			1.24296i	−0.783429	+	0.621482i	$0.786531\pi$
$368$	−10.5000	+	1.32288i	−0.547350	+	0.0689597i
$369$		−	27.4955i		−	1.43136i
$370$	−8.12436	−	15.1656i	−0.422365	−	0.788421i
$371$	36.3731			1.88840
$372$	9.00000	+	7.93725i	0.466628	+	0.411527i
$373$	−12.0000			−0.621336			−0.310668	−	0.950518i	$-0.600553\pi$
$373$	−12.0000			−0.621336			−0.310668	+	0.950518i	$0.600553\pi$
$374$	−4.33013	+	11.4564i	−0.223906	+	0.592398i
$375$	20.7846			1.07331
$376$	−25.9808	+	13.7477i	−1.33986	+	0.708985i
$377$		−	18.3303i		−	0.944059i
$378$	18.1865	+	6.87386i	0.935414	+	0.353553i
$379$		−	10.5830i		−	0.543612i	−0.962352	−	0.271806i	$-0.912379\pi$
$379$		−	10.5830i		−	0.543612i	0.962352	−	0.271806i	$-0.0876210\pi$
$380$	5.19615	+	4.58258i	0.266557	+	0.235081i
$381$		−	13.7477i		−	0.704317i
$382$	−24.5000	−	9.26013i	−1.25353	−	0.473789i
$383$		−	34.3948i		−	1.75749i	−0.477291	−	0.878745i	$-0.658381\pi$
$383$		−	34.3948i		−	1.75749i	0.477291	−	0.878745i	$-0.341619\pi$
$384$	11.2583	+	16.0390i	0.574524	+	0.818488i
$385$			9.16515i			0.467099i
$386$	−24.2487	−	9.16515i	−1.23423	−	0.466494i
$387$	−10.3923			−0.528271
$388$		0			0
$389$	32.0000			1.62246			0.811232	−	0.584724i	$-0.198797\pi$
$389$	32.0000			1.62246			0.811232	+	0.584724i	$0.198797\pi$
$390$	−21.0000	−	7.93725i	−1.06338	−	0.401918i
$391$			13.2288i			0.669007i
$392$		0			0
$393$			9.16515i			0.462321i
$394$	6.06218	+	2.29129i	0.305408	+	0.115433i
$395$	−27.7128			−1.39438
$396$	−7.79423	−	6.87386i	−0.391675	−	0.345425i
$397$	30.0000			1.50566			0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000			1.50566			0.752828	+	0.658217i	$0.228689\pi$
$398$	−12.1244	+	32.0780i	−0.607739	+	1.60793i
$399$		−	7.93725i		−	0.397360i
$400$	−0.500000	−	3.96863i	−0.0250000	−	0.198431i
$401$	13.0000			0.649189			0.324595	−	0.945853i	$-0.394772\pi$
$401$	13.0000			0.649189			0.324595	+	0.945853i	$0.394772\pi$
$402$	−24.2487	−	9.16515i	−1.20942	−	0.457116i
$403$			15.8745i			0.790766i
$404$	12.1244	−	13.7477i	0.603209	−	0.683975i
$405$	−18.0000			−0.894427
$406$	14.0000	+	5.29150i	0.694808	+	0.262613i
$407$	6.92820	−	7.93725i	0.343418	−	0.393435i
$408$	21.6506	−	11.4564i	1.07187	−	0.567178i
$409$		−	27.4955i		−	1.35956i	−0.733415	−	0.679781i	$-0.762075\pi$
$409$		−	27.4955i		−	1.35956i	0.733415	−	0.679781i	$-0.237925\pi$
$410$	−24.2487	−	9.16515i	−1.19756	−	0.452635i
$411$		−	15.8745i		−	0.783032i
$412$	20.7846	+	18.3303i	1.02398	+	0.903069i
$413$	14.0000			0.688895
$414$	−10.5000	−	3.96863i	−0.516047	−	0.195047i
$415$	17.3205			0.850230
$416$	−6.06218	+	25.2042i	−0.297223	+	1.23574i
$417$			9.16515i			0.448819i
$418$	−1.50000	+	3.96863i	−0.0733674	+	0.194112i
$419$	39.8372			1.94617			0.973087	−	0.230440i	$-0.0740166\pi$
$419$	39.8372			1.94617			0.973087	+	0.230440i	$0.0740166\pi$
$420$	12.1244	−	13.7477i	0.591608	−	0.670820i
$421$			9.16515i			0.446682i	0.974740	+	0.223341i	$0.0716964\pi$
$421$			9.16515i			0.446682i	−0.974740	+	0.223341i	$0.928304\pi$
$422$	−21.0000	−	7.93725i	−1.02226	−	0.386379i
$423$	−31.1769			−1.51587
$424$	18.1865	+	34.3693i	0.883216	+	1.66912i
$425$	−5.00000			−0.242536
$426$	3.00000	−	7.93725i	0.145350	−	0.384561i
$427$	−24.2487			−1.17348
$428$	−2.59808	−	2.29129i	−0.125583	−	0.110754i
$429$		−	13.7477i		−	0.663747i
$430$	−3.46410	+	9.16515i	−0.167054	+	0.441983i
$431$		−	34.3948i		−	1.65674i	−0.560183	−	0.828369i	$-0.689269\pi$
$431$		−	34.3948i		−	1.65674i	0.560183	−	0.828369i	$-0.310731\pi$
$432$	2.59808	+	20.6216i	0.125000	+	0.992157i
$433$	3.00000			0.144171			0.0720854	−	0.997398i	$-0.477035\pi$
$433$	3.00000			0.144171			0.0720854	+	0.997398i	$0.477035\pi$
$434$	−12.1244	−	4.58258i	−0.581988	−	0.219971i
$435$	−13.8564			−0.664364
$436$	18.1865	−	20.6216i	0.870977	−	0.987595i
$437$			4.58258i			0.219214i
$438$	−7.79423	+	20.6216i	−0.372423	+	0.985338i
$439$	−10.3923			−0.495998			−0.247999	−	0.968760i	$-0.579773\pi$
$439$	−10.3923			−0.495998			−0.247999	+	0.968760i	$0.579773\pi$
$440$	−8.66025	+	4.58258i	−0.412861	+	0.218466i
$441$		0			0
$442$	30.3109	+	11.4564i	1.44174	+	0.544927i
$443$	3.46410			0.164584			0.0822922	−	0.996608i	$-0.473776\pi$
$443$	3.46410			0.164584			0.0822922	+	0.996608i	$0.473776\pi$
$444$	−20.8923	+	2.74073i	−0.991505	+	0.130069i
$445$	10.0000			0.474045
$446$	21.0000	+	7.93725i	0.994379	+	0.375840i
$447$		−	15.8745i		−	0.750838i
$448$	−17.5000	−	11.9059i	−0.826797	−	0.562500i
$449$	−38.0000			−1.79333			−0.896665	−	0.442709i	$-0.854018\pi$
$449$	−38.0000			−1.79333			−0.896665	+	0.442709i	$0.854018\pi$
$450$	1.50000	−	3.96863i	0.0707107	−	0.187083i
$451$		−	15.8745i		−	0.747501i
$452$	21.0000	+	18.5203i	0.987757	+	0.871120i
$453$			13.7477i			0.645925i
$454$	−28.0000	−	10.5830i	−1.31411	−	0.496685i
$455$	24.2487			1.13680
$456$	7.50000	−	3.96863i	0.351220	−	0.185848i
$457$			18.3303i			0.857455i	0.903434	+	0.428728i	$0.141038\pi$
$457$			18.3303i			0.857455i	−0.903434	+	0.428728i	$0.858962\pi$
$458$	5.00000	−	13.2288i	0.233635	−	0.618139i
$459$	25.9808			1.21268
$460$	−7.00000	+	7.93725i	−0.326377	+	0.370076i
$461$	−10.0000			−0.465746			−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000			−0.465746			−0.232873	+	0.972507i	$0.574813\pi$
$462$	10.5000	+	3.96863i	0.488504	+	0.184637i
$463$	6.92820			0.321981			0.160990	−	0.986956i	$-0.448531\pi$
$463$	6.92820			0.321981			0.160990	+	0.986956i	$0.448531\pi$
$464$	2.00000	+	15.8745i	0.0928477	+	0.736956i
$465$	12.0000			0.556487
$466$	24.2487	+	9.16515i	1.12330	+	0.424567i
$467$			37.0405i			1.71403i	0.515291	+	0.857015i	$0.327684\pi$
$467$			37.0405i			1.71403i	−0.515291	+	0.857015i	$0.672316\pi$
$468$	−18.1865	+	20.6216i	−0.840673	+	0.953233i
$469$	28.0000			1.29292
$470$	−10.3923	+	27.4955i	−0.479361	+	1.26827i
$471$	20.7846			0.957704
$472$	7.00000	+	13.2288i	0.322201	+	0.608903i
$473$	−6.00000			−0.275880
$474$	−12.0000	+	31.7490i	−0.551178	+	1.45828i
$475$	−1.73205			−0.0794719
$476$	−17.5000	+	19.8431i	−0.802111	+	0.909509i
$477$			41.2432i			1.88840i
$478$	7.00000	+	2.64575i	0.320173	+	0.121014i
$479$		−	13.2288i		−	0.604437i	−0.953239	−	0.302219i	$-0.902273\pi$
$479$		−	13.2288i		−	0.604437i	0.953239	−	0.302219i	$-0.0977273\pi$
$480$	19.0526	+	4.58258i	0.869626	+	0.209165i
$481$	−21.0000	−	18.3303i	−0.957518	−	0.835790i
$482$	−12.1244	−	4.58258i	−0.552249	−	0.208731i
$483$	12.1244			0.551677
$484$	12.0000	+	10.5830i	0.545455	+	0.481046i
$485$		0			0
$486$	−7.79423	+	20.6216i	−0.353553	+	0.935414i
$487$	−34.6410			−1.56973			−0.784867	−	0.619664i	$-0.787269\pi$
$487$	−34.6410			−1.56973			−0.784867	+	0.619664i	$0.787269\pi$
$488$	−12.1244	−	22.9129i	−0.548844	−	1.03722i
$489$	15.0000			0.678323
$490$		0			0
$491$	−19.0526			−0.859830			−0.429915	−	0.902869i	$-0.641456\pi$
$491$	−19.0526			−0.859830			−0.429915	+	0.902869i	$0.641456\pi$
$492$	−21.0000	+	23.8118i	−0.946753	+	1.07352i
$493$	20.0000			0.900755
$494$	10.5000	+	3.96863i	0.472417	+	0.178557i
$495$	−10.3923			−0.467099
$496$	−1.73205	−	13.7477i	−0.0777714	−	0.617291i
$497$			9.16515i			0.411113i
$498$	7.50000	−	19.8431i	0.336083	−	0.889192i
$499$	1.73205			0.0775372			0.0387686	−	0.999248i	$-0.487656\pi$
$499$	1.73205			0.0775372			0.0387686	+	0.999248i	$0.487656\pi$
$500$	−18.0000	−	15.8745i	−0.804984	−	0.709930i
$501$			4.58258i			0.204734i
$502$	−28.0000	−	10.5830i	−1.24970	−	0.472343i
$503$			5.29150i			0.235936i	0.993017	+	0.117968i	$0.0376381\pi$
$503$			5.29150i			0.235936i	−0.993017	+	0.117968i	$0.962362\pi$
$504$	−10.5000	−	19.8431i	−0.467707	−	0.883883i
$505$		−	18.3303i		−	0.815688i
$506$	−6.06218	−	2.29129i	−0.269497	−	0.101860i
$507$	−13.8564			−0.615385
$508$	−10.5000	+	11.9059i	−0.465862	+	0.528238i
$509$		−	13.7477i		−	0.609357i	−0.952455	−	0.304679i	$-0.901451\pi$
$509$		−	13.7477i		−	0.609357i	0.952455	−	0.304679i	$-0.0985491\pi$
$510$	8.66025	−	22.9129i	0.383482	−	1.01460i
$511$		−	23.8118i		−	1.05337i
$512$	2.50000	−	22.4889i	0.110485	−	0.993878i
$513$	9.00000			0.397360
$514$	−2.50000	+	6.61438i	−0.110270	+	0.291748i
$515$	27.7128			1.22117
$516$	9.00000	+	7.93725i	0.396203	+	0.349418i
$517$	−18.0000			−0.791639
$518$	20.0622	−	10.7475i	0.881481	−	0.472219i
$519$			7.93725i			0.348407i
$520$	12.1244	+	22.9129i	0.531688	+	1.00480i
$521$		−	27.4955i		−	1.20460i	−0.798271	−	0.602299i	$-0.794252\pi$
$521$		−	27.4955i		−	1.20460i	0.798271	−	0.602299i	$-0.205748\pi$
$522$	−6.00000	+	15.8745i	−0.262613	+	0.694808i
$523$	−10.3923			−0.454424			−0.227212	−	0.973845i	$-0.572961\pi$
$523$	−10.3923			−0.454424			−0.227212	+	0.973845i	$0.572961\pi$
$524$	7.00000	−	7.93725i	0.305796	−	0.346741i
$525$			4.58258i			0.200000i
$526$	6.92820	−	18.3303i	0.302084	−	0.799239i
$527$	−17.3205			−0.754493
$528$	1.50000	+	11.9059i	0.0652791	+	0.518137i
$529$	16.0000			0.695652
$530$	36.3731	+	13.7477i	1.57995	+	0.597163i
$531$			15.8745i			0.688895i
$532$	−6.06218	+	6.87386i	−0.262829	+	0.298020i
$533$	−42.0000			−1.81922
$534$	4.33013	−	11.4564i	0.187383	−	0.495769i
$535$	−3.46410			−0.149766
$536$	14.0000	+	26.4575i	0.604708	+	1.14279i
$537$			9.16515i			0.395505i
$538$	−30.3109	−	11.4564i	−1.30680	−	0.493922i
$539$		0			0
$540$	15.5885	+	13.7477i	0.670820	+	0.591608i
$541$			32.0780i			1.37914i	0.724218	+	0.689571i	$0.242201\pi$
$541$			32.0780i			1.37914i	−0.724218	+	0.689571i	$0.757799\pi$
$542$	−35.0000	−	13.2288i	−1.50338	−	0.568224i
$543$	−10.3923			−0.445976
$544$	−27.5000	−	6.61438i	−1.17905	−	0.283589i
$545$		−	27.4955i		−	1.17778i
$546$	10.5000	−	27.7804i	0.449359	−	1.18889i
$547$	43.3013			1.85143			0.925714	−	0.378224i	$-0.123465\pi$
$547$	43.3013			1.85143			0.925714	+	0.378224i	$0.123465\pi$
$548$	−12.1244	+	13.7477i	−0.517927	+	0.587274i
$549$		−	27.4955i		−	1.17348i
$550$	0.866025	−	2.29129i	0.0369274	−	0.0977008i
$551$	6.92820			0.295151
$552$	6.06218	+	11.4564i	0.258023	+	0.487618i
$553$		−	36.6606i		−	1.55897i
$554$	−6.06218	−	2.29129i	−0.257557	−	0.0973475i
$555$	−13.8564	+	15.8745i	−0.588172	+	0.673835i
$556$	7.00000	−	7.93725i	0.296866	−	0.336615i
$557$	−28.0000			−1.18640			−0.593199	−	0.805056i	$-0.702135\pi$
$557$	−28.0000			−1.18640			−0.593199	+	0.805056i	$0.702135\pi$
$558$	5.19615	−	13.7477i	0.219971	−	0.581988i
$559$			15.8745i			0.671420i
$560$	−21.0000	+	2.64575i	−0.887412	+	0.111803i
$561$	15.0000			0.633300
$562$	−5.50000	+	14.5516i	−0.232003	+	0.613824i
$563$		−	37.0405i		−	1.56107i	−0.625111	−	0.780536i	$-0.714946\pi$
$563$		−	37.0405i		−	1.56107i	0.625111	−	0.780536i	$-0.285054\pi$
$564$	27.0000	+	23.8118i	1.13691	+	1.00266i
$565$	28.0000			1.17797
$566$	14.7224	−	38.9519i	0.618830	−	1.63727i
$567$		−	23.8118i		−	1.00000i
$568$	−8.66025	+	4.58258i	−0.363376	+	0.192281i
$569$	7.00000			0.293455			0.146728	−	0.989177i	$-0.453126\pi$
$569$	7.00000			0.293455			0.146728	+	0.989177i	$0.453126\pi$
$570$	3.00000	−	7.93725i	0.125656	−	0.332455i
$571$			5.29150i			0.221442i	0.993852	+	0.110721i	$0.0353161\pi$
$571$			5.29150i			0.221442i	−0.993852	+	0.110721i	$0.964684\pi$
$572$	−10.5000	+	11.9059i	−0.439027	+	0.497810i
$573$			32.0780i			1.34008i
$574$	12.1244	−	32.0780i	0.506061	−	1.33891i
$575$		−	2.64575i		−	0.110335i
$576$	13.5000	−	19.8431i	0.562500	−	0.826797i
$577$		−	45.8258i		−	1.90775i	−0.300202	−	0.953876i	$-0.597054\pi$
$577$		−	45.8258i		−	1.90775i	0.300202	−	0.953876i	$-0.402946\pi$
$578$	−4.00000	+	10.5830i	−0.166378	+	0.440195i
$579$			31.7490i			1.31944i
$580$	12.0000	+	10.5830i	0.498273	+	0.439435i
$581$			22.9129i			0.950586i
$582$		0			0
$583$			23.8118i			0.986182i
$584$	22.5000	−	11.9059i	0.931057	−	0.492669i
$585$			27.4955i			1.13680i
$586$	6.06218	+	2.29129i	0.250426	+	0.0946522i
$587$		−	42.3320i		−	1.74723i	−0.486618	−	0.873615i	$-0.661770\pi$
$587$		−	42.3320i		−	1.74723i	0.486618	−	0.873615i	$-0.338230\pi$
$588$		0			0
$589$	−6.00000			−0.247226
$590$	14.0000	+	5.29150i	0.576371	+	0.217848i
$591$		−	7.93725i		−	0.326495i
$592$	20.1865	+	13.5832i	0.829661	+	0.558267i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−4.50000	+	11.9059i	−0.184637	+	0.488504i
$595$			26.4575i			1.08465i
$596$	−12.1244	+	13.7477i	−0.496633	+	0.563129i
$597$	42.0000			1.71895
$598$	−6.06218	+	16.0390i	−0.247901	+	0.655884i
$599$	17.3205			0.707697			0.353848	−	0.935303i	$-0.384873\pi$
$599$	17.3205			0.707697			0.353848	+	0.935303i	$0.384873\pi$
$600$	−4.33013	+	2.29129i	−0.176777	+	0.0935414i
$601$	−39.0000			−1.59084			−0.795422	−	0.606057i	$-0.792751\pi$
$601$	−39.0000			−1.59084			−0.795422	+	0.606057i	$0.792751\pi$
$602$	−12.1244	−	4.58258i	−0.494152	−	0.186772i
$603$			31.7490i			1.29292i
$604$	10.5000	−	11.9059i	0.427239	−	0.484443i
$605$	16.0000			0.650493
$606$	−21.0000	−	7.93725i	−0.853067	−	0.322429i
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	−9.52628	−	2.29129i	−0.386342	−	0.0929240i
$609$		−	18.3303i		−	0.742781i
$610$	−24.2487	−	9.16515i	−0.981802	−	0.371086i
$611$			47.6235i			1.92664i
$612$	−22.5000	−	19.8431i	−0.909509	−	0.802111i
$613$	−14.0000			−0.565455			−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000			−0.565455			−0.282727	+	0.959200i	$0.591239\pi$
$614$	42.0000	+	15.8745i	1.69498	+	0.640643i
$615$			31.7490i			1.28024i
$616$	−6.06218	−	11.4564i	−0.244252	−	0.461593i
$617$			9.16515i			0.368975i	0.982835	+	0.184488i	$0.0590625\pi$
$617$			9.16515i			0.368975i	−0.982835	+	0.184488i	$0.940937\pi$
$618$	12.0000	−	31.7490i	0.482711	−	1.27713i
$619$		−	31.7490i		−	1.27610i	−0.769995	−	0.638050i	$-0.779741\pi$
$619$		−	31.7490i		−	1.27610i	0.769995	−	0.638050i	$-0.220259\pi$
$620$	−10.3923	−	9.16515i	−0.417365	−	0.368081i
$621$			13.7477i			0.551677i
$622$	−7.00000	−	2.64575i	−0.280674	−	0.106085i
$623$			13.2288i			0.529999i
$624$	31.5000	−	3.96863i	1.26101	−	0.158872i
$625$	−19.0000			−0.760000
$626$	36.3731	+	13.7477i	1.45376	+	0.549470i
$627$	5.19615			0.207514
$628$	−18.0000	−	15.8745i	−0.718278	−	0.633462i
$629$	20.0000	−	22.9129i	0.797452	−	0.913596i
$630$	−21.0000	−	7.93725i	−0.836660	−	0.316228i
$631$	−41.5692			−1.65484			−0.827422	−	0.561580i	$-0.810194\pi$
$631$	−41.5692			−1.65484			−0.827422	+	0.561580i	$0.810194\pi$
$632$	34.6410	−	18.3303i	1.37795	−	0.729140i
$633$			27.4955i			1.09285i
$634$	−12.1244	−	4.58258i	−0.481520	−	0.181997i
$635$			15.8745i			0.629961i
$636$	31.5000	−	35.7176i	1.24906	−	1.41630i
$637$		0			0
$638$	−3.46410	+	9.16515i	−0.137145	+	0.362852i
$639$	−10.3923			−0.411113
$640$	−13.0000	−	18.5203i	−0.513870	−	0.732078i
$641$		−	36.6606i		−	1.44801i	−0.689796	−	0.724003i	$-0.742300\pi$
$641$		−	36.6606i		−	1.44801i	0.689796	−	0.724003i	$-0.257700\pi$
$642$	−1.50000	+	3.96863i	−0.0592003	+	0.156629i
$643$	−12.1244			−0.478138			−0.239069	−	0.971003i	$-0.576842\pi$
$643$	−12.1244			−0.478138			−0.239069	+	0.971003i	$0.576842\pi$
$644$	−10.5000	−	9.26013i	−0.413758	−	0.364900i
$645$	12.0000			0.472500
$646$	−4.33013	+	11.4564i	−0.170367	+	0.450748i
$647$			34.3948i			1.35220i	0.736811	+	0.676099i	$0.236331\pi$
$647$			34.3948i			1.35220i	−0.736811	+	0.676099i	$0.763669\pi$
$648$	22.5000	−	11.9059i	0.883883	−	0.467707i
$649$			9.16515i			0.359764i
$650$	−6.06218	−	2.29129i	−0.237778	−	0.0898717i
$651$			15.8745i			0.622171i
$652$	−12.9904	−	11.4564i	−0.508743	−	0.448669i
$653$	−28.0000			−1.09572			−0.547862	−	0.836569i	$-0.684558\pi$
$653$	−28.0000			−1.09572			−0.547862	+	0.836569i	$0.684558\pi$
$654$	−31.5000	−	11.9059i	−1.23175	−	0.465557i
$655$		−	10.5830i		−	0.413512i
$656$	36.3731	−	4.58258i	1.42013	−	0.178920i
$657$	27.0000			1.05337
$658$	−36.3731	−	13.7477i	−1.41797	−	0.535942i
$659$	−3.46410			−0.134942			−0.0674711	−	0.997721i	$-0.521493\pi$
$659$	−3.46410			−0.134942			−0.0674711	+	0.997721i	$0.521493\pi$
$660$	9.00000	+	7.93725i	0.350325	+	0.308957i
$661$			22.9129i			0.891208i	0.895230	+	0.445604i	$0.147011\pi$
$661$			22.9129i			0.891208i	−0.895230	+	0.445604i	$0.852989\pi$
$662$	−5.19615	+	13.7477i	−0.201954	+	0.534321i
$663$		−	39.6863i		−	1.54129i
$664$	−21.6506	+	11.4564i	−0.840208	+	0.444596i
$665$			9.16515i			0.355409i
$666$	12.1865	+	22.7484i	0.472219	+	0.881481i
$667$			10.5830i			0.409776i
$668$	3.50000	−	3.96863i	0.135419	−	0.153551i
$669$		−	27.4955i		−	1.06304i
$670$	28.0000	+	10.5830i	1.08173	+	0.408857i
$671$		−	15.8745i		−	0.612829i
$672$	−6.06218	+	25.2042i	−0.233854	+	0.972272i
$673$	−21.0000			−0.809491			−0.404745	−	0.914429i	$-0.632640\pi$
$673$	−21.0000			−0.809491			−0.404745	+	0.914429i	$0.632640\pi$
$674$	−9.50000	+	25.1346i	−0.365926	+	0.968150i
$675$	−5.19615			−0.200000
$676$	12.0000	+	10.5830i	0.461538	+	0.407039i
$677$		−	22.9129i		−	0.880613i	−0.897847	−	0.440307i	$-0.854870\pi$
$677$		−	22.9129i		−	0.880613i	0.897847	−	0.440307i	$-0.145130\pi$
$678$	12.1244	−	32.0780i	0.465633	−	1.23195i
$679$		0			0
$680$	−25.0000	+	13.2288i	−0.958706	+	0.507300i
$681$			36.6606i			1.40484i
$682$	3.00000	−	7.93725i	0.114876	−	0.303933i
$683$		−	10.5830i		−	0.404947i	−0.979288	−	0.202474i	$-0.935102\pi$
$683$		−	10.5830i		−	0.404947i	0.979288	−	0.202474i	$-0.0648981\pi$
$684$	−7.79423	−	6.87386i	−0.298020	−	0.262829i
$685$			18.3303i			0.700365i
$686$	24.5000	+	9.26013i	0.935414	+	0.353553i
$687$	−17.3205			−0.660819
$688$	−1.73205	−	13.7477i	−0.0660338	−	0.524127i
$689$	63.0000			2.40011
$690$	12.1244	+	4.58258i	0.461566	+	0.174456i
$691$		−	5.29150i		−	0.201298i	−0.994922	−	0.100649i	$-0.967908\pi$
$691$		−	5.29150i		−	0.201298i	0.994922	−	0.100649i	$-0.0320920\pi$
$692$	6.06218	−	6.87386i	0.230449	−	0.261305i
$693$		−	13.7477i		−	0.522233i
$694$	7.00000	+	2.64575i	0.265716	+	0.100431i
$695$		−	10.5830i		−	0.401436i
$696$	17.3205	−	9.16515i	0.656532	−	0.347404i
$697$		−	45.8258i		−	1.73577i
$698$	−9.00000	+	23.8118i	−0.340655	+	0.901288i
$699$		−	31.7490i		−	1.20086i
$700$	3.50000	−	3.96863i	0.132288	−	0.150000i
$701$	28.0000			1.05755			0.528773	−	0.848763i	$-0.322652\pi$
$701$	28.0000			1.05755			0.528773	+	0.848763i	$0.322652\pi$
$702$	31.5000	+	11.9059i	1.18889	+	0.449359i
$703$	6.92820	−	7.93725i	0.261302	−	0.299359i
$704$	7.79423	−	11.4564i	0.293756	−	0.431781i
$705$	36.0000			1.35584
$706$	−1.00000	+	2.64575i	−0.0376355	+	0.0995742i
$707$	24.2487			0.911967
$708$	12.1244	−	13.7477i	0.455661	−	0.516671i
$709$		−	13.7477i		−	0.516307i	−0.966104	−	0.258153i	$-0.916886\pi$
$709$		−	13.7477i		−	0.516307i	0.966104	−	0.258153i	$-0.0831140\pi$
$710$	−3.46410	+	9.16515i	−0.130005	+	0.343962i
$711$	41.5692			1.55897
$712$	−12.5000	+	6.61438i	−0.468457	+	0.247884i
$713$		−	9.16515i		−	0.343238i
$714$	30.3109	+	11.4564i	1.13436	+	0.428746i
$715$			15.8745i			0.593673i
$716$	7.00000	−	7.93725i	0.261602	−	0.296629i
$717$		−	9.16515i		−	0.342279i
$718$	13.8564	−	36.6606i	0.517116	−	1.36816i
$719$	−13.8564			−0.516757			−0.258378	−	0.966044i	$-0.583188\pi$
$719$	−13.8564			−0.516757			−0.258378	+	0.966044i	$0.583188\pi$
$720$	−3.00000	−	23.8118i	−0.111803	−	0.887412i
$721$			36.6606i			1.36531i
$722$	8.00000	−	21.1660i	0.297729	−	0.787717i
$723$			15.8745i			0.590379i
$724$	9.00000	+	7.93725i	0.334482	+	0.294986i
$725$	−4.00000			−0.148556
$726$	6.92820	−	18.3303i	0.257130	−	0.680301i
$727$	−10.3923			−0.385429			−0.192715	−	0.981255i	$-0.561729\pi$
$727$	−10.3923			−0.385429			−0.192715	+	0.981255i	$0.561729\pi$
$728$	−30.3109	+	16.0390i	−1.12340	+	0.594445i
$729$	27.0000			1.00000
$730$	9.00000	−	23.8118i	0.333105	−	0.881313i
$731$	−17.3205			−0.640622
$732$	−21.0000	+	23.8118i	−0.776182	+	0.880108i
$733$	26.0000			0.960332			0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000			0.960332			0.480166	+	0.877178i	$0.340576\pi$
$734$	−31.5000	−	11.9059i	−1.16269	−	0.439454i
$735$		0			0
$736$	3.50000	−	14.5516i	0.129012	−	0.536380i
$737$			18.3303i			0.675205i
$738$	36.3731	+	13.7477i	1.33891	+	0.506061i
$739$			31.7490i			1.16791i	0.811787	+	0.583953i	$0.198495\pi$
$739$			31.7490i			1.16791i	−0.811787	+	0.583953i	$0.801505\pi$
$740$	24.1244	−	3.16472i	0.886829	−	0.116337i
$741$		−	13.7477i		−	0.505035i
$742$	−18.1865	+	48.1170i	−0.667649	+	1.76643i
$743$	41.5692			1.52503			0.762513	−	0.646972i	$-0.223965\pi$
$743$	41.5692			1.52503			0.762513	+	0.646972i	$0.223965\pi$
$744$	−15.0000	+	7.93725i	−0.549927	+	0.290994i
$745$			18.3303i			0.671570i
$746$	6.00000	−	15.8745i	0.219676	−	0.581207i
$747$	−25.9808			−0.950586
$748$	−12.9904	−	11.4564i	−0.474975	−	0.418889i
$749$		−	4.58258i		−	0.167444i
$750$	−10.3923	+	27.4955i	−0.379473	+	1.00399i
$751$		−	37.0405i		−	1.35163i	−0.737072	−	0.675814i	$-0.763792\pi$
$751$		−	37.0405i		−	1.35163i	0.737072	−	0.675814i	$-0.236208\pi$
$752$	−5.19615	−	41.2432i	−0.189484	−	1.50398i
$753$			36.6606i			1.33599i
$754$	24.2487	+	9.16515i	0.883086	+	0.333775i
$755$		−	15.8745i		−	0.577732i
$756$	−18.1865	+	20.6216i	−0.661438	+	0.750000i
$757$		−	32.0780i		−	1.16590i	−0.812510	−	0.582948i	$-0.801899\pi$
$757$		−	32.0780i		−	1.16590i	0.812510	−	0.582948i	$-0.198101\pi$
$758$	14.0000	+	5.29150i	0.508503	+	0.192196i
$759$			7.93725i			0.288104i
$760$	−8.66025	+	4.58258i	−0.314140	+	0.166227i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	18.1865	+	6.87386i	0.658829	+	0.249014i
$763$	36.3731			1.31679
$764$	24.5000	−	27.7804i	0.886379	−	1.00506i
$765$	−30.0000			−1.08465
$766$	45.5000	+	17.1974i	1.64398	+	0.621367i
$767$	24.2487			0.875570
$768$	−26.8468	+	6.87386i	−0.968750	+	0.248039i
$769$			36.6606i			1.32202i	0.750379	+	0.661008i	$0.229871\pi$
$769$			36.6606i			1.32202i	−0.750379	+	0.661008i	$0.770129\pi$
$770$	−12.1244	−	4.58258i	−0.436931	−	0.165145i
$771$	8.66025			0.311891
$772$	24.2487	−	27.4955i	0.872730	−	0.989583i
$773$		−	4.58258i		−	0.164824i	−0.996598	−	0.0824119i	$-0.973738\pi$
$773$		−	4.58258i		−	0.164824i	0.996598	−	0.0824119i	$-0.0262623\pi$
$774$	5.19615	−	13.7477i	0.186772	−	0.494152i
$775$	3.46410			0.124434
$776$		0			0
$777$	−21.0000	−	18.3303i	−0.753371	−	0.657596i
$778$	−16.0000	+	42.3320i	−0.573628	+	1.51768i
$779$		−	15.8745i		−	0.568763i
$780$	21.0000	−	23.8118i	0.751921	−	0.852598i
$781$	−6.00000			−0.214697
$782$	−17.5000	−	6.61438i	−0.625799	−	0.236530i
$783$	20.7846			0.742781
$784$		0			0
$785$	−24.0000			−0.856597
$786$	−12.1244	−	4.58258i	−0.432461	−	0.163455i
$787$		−	15.8745i		−	0.565865i	−0.959140	−	0.282933i	$-0.908693\pi$
$787$		−	15.8745i		−	0.565865i	0.959140	−	0.282933i	$-0.0913073\pi$
$788$	−6.06218	+	6.87386i	−0.215956	+	0.244871i
$789$	−24.0000			−0.854423
$790$	13.8564	−	36.6606i	0.492989	−	1.30433i
$791$			37.0405i			1.31701i
$792$	12.9904	−	6.87386i	0.461593	−	0.244252i
$793$	−42.0000			−1.49146
$794$	−15.0000	+	39.6863i	−0.532330	+	1.40841i
$795$		−	47.6235i		−	1.68903i
$796$	−36.3731	−	32.0780i	−1.28921	−	1.13698i
$797$	−22.0000			−0.779280			−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000			−0.779280			−0.389640	+	0.920967i	$0.627401\pi$
$798$	10.5000	+	3.96863i	0.371696	+	0.140488i
$799$	−51.9615			−1.83827
$800$	5.50000	+	1.32288i	0.194454	+	0.0467707i
$801$	−15.0000			−0.529999
$802$	−6.50000	+	17.1974i	−0.229523	+	0.607261i
$803$	15.5885			0.550105
$804$	24.2487	−	27.4955i	0.855186	−	0.969690i
$805$	−14.0000			−0.493435
$806$	−21.0000	−	7.93725i	−0.739693	−	0.279578i
$807$			39.6863i			1.39702i
$808$	12.1244	+	22.9129i	0.426533	+	0.806072i
$809$	−13.0000			−0.457056			−0.228528	−	0.973537i	$-0.573391\pi$
$809$	−13.0000			−0.457056			−0.228528	+	0.973537i	$0.573391\pi$
$810$	9.00000	−	23.8118i	0.316228	−	0.836660i
$811$			42.3320i			1.48648i	0.669026	+	0.743239i	$0.266712\pi$
$811$			42.3320i			1.48648i	−0.669026	+	0.743239i	$0.733288\pi$
$812$	−14.0000	+	15.8745i	−0.491304	+	0.557086i
$813$			45.8258i			1.60718i
$814$	7.03590	+	13.1338i	0.246608	+	0.460339i
$815$	−17.3205			−0.606711
$816$	4.33013	+	34.3693i	0.151585	+	1.20317i
$817$	−6.00000			−0.209913
$818$	36.3731	+	13.7477i	1.27175	+	0.480678i
$819$	−36.3731			−1.27098
$820$	24.2487	−	27.4955i	0.846802	−	0.960183i
$821$			32.0780i			1.11953i	0.828651	+	0.559765i	$0.189109\pi$
$821$			32.0780i			1.11953i	−0.828651	+	0.559765i	$0.810891\pi$
$822$	21.0000	+	7.93725i	0.732459	+	0.276844i
$823$			39.6863i			1.38338i	0.722196	+	0.691688i	$0.243133\pi$
$823$			39.6863i			1.38338i	−0.722196	+	0.691688i	$0.756867\pi$
$824$	−34.6410	+	18.3303i	−1.20678	+	0.638566i
$825$	−3.00000			−0.104447
$826$	−7.00000	+	18.5203i	−0.243561	+	0.644402i
$827$		−	37.0405i		−	1.28803i	−0.765015	−	0.644013i	$-0.777268\pi$
$827$		−	37.0405i		−	1.28803i	0.765015	−	0.644013i	$-0.222732\pi$
$828$	10.5000	−	11.9059i	0.364900	−	0.413758i
$829$			32.0780i			1.11412i	0.830474	+	0.557058i	$0.188070\pi$
$829$			32.0780i			1.11412i	−0.830474	+	0.557058i	$0.811930\pi$
$830$	−8.66025	+	22.9129i	−0.300602	+	0.795318i
$831$			7.93725i			0.275340i
$832$	−30.3109	−	20.6216i	−1.05084	−	0.714925i
$833$		0			0
$834$	−12.1244	−	4.58258i	−0.419832	−	0.158682i
$835$		−	5.29150i		−	0.183120i
$836$	−4.50000	−	3.96863i	−0.155636	−	0.137258i
$837$	−18.0000			−0.622171
$838$	−19.9186	+	52.6996i	−0.688076	+	1.82048i
$839$	20.7846			0.717564			0.358782	−	0.933421i	$-0.383192\pi$
$839$	20.7846			0.717564			0.358782	+	0.933421i	$0.383192\pi$
$840$	12.1244	+	22.9129i	0.418330	+	0.790569i
$841$	−13.0000			−0.448276
$842$	−12.1244	−	4.58258i	−0.417833	−	0.157926i
$843$	19.0526			0.656205
$844$	21.0000	−	23.8118i	0.722850	−	0.819635i
$845$	16.0000			0.550417
$846$	15.5885	−	41.2432i	0.535942	−	1.41797i
$847$			21.1660i			0.727273i
$848$	−54.5596	+	6.87386i	−1.87358	+	0.236049i
$849$	−51.0000			−1.75032
$850$	2.50000	−	6.61438i	0.0857493	−	0.226871i
$851$	12.1244	+	10.5830i	0.415618	+	0.362781i
$852$	9.00000	+	7.93725i	0.308335	+	0.271926i
$853$		−	13.7477i		−	0.470713i	−0.971909	−	0.235357i	$-0.924374\pi$
$853$		−	13.7477i		−	0.470713i	0.971909	−	0.235357i	$-0.0756258\pi$
$854$	12.1244	−	32.0780i	0.414887	−	1.09769i
$855$	−10.3923			−0.355409
$856$	4.33013	−	2.29129i	0.148001	−	0.0783146i
$857$	−37.0000			−1.26390			−0.631948	−	0.775011i	$-0.717744\pi$
$857$	−37.0000			−1.26390			−0.631948	+	0.775011i	$0.717744\pi$
$858$	18.1865	+	6.87386i	0.620878	+	0.234670i
$859$	12.1244			0.413678			0.206839	−	0.978375i	$-0.433682\pi$
$859$	12.1244			0.413678			0.206839	+	0.978375i	$0.433682\pi$
$860$	−10.3923	−	9.16515i	−0.354375	−	0.312529i
$861$	−42.0000			−1.43136
$862$	45.5000	+	17.1974i	1.54974	+	0.585745i
$863$	−10.3923			−0.353758			−0.176879	−	0.984233i	$-0.556600\pi$
$863$	−10.3923			−0.353758			−0.176879	+	0.984233i	$0.556600\pi$
$864$	−28.5788	−	6.87386i	−0.972272	−	0.233854i
$865$		−	9.16515i		−	0.311624i
$866$	−1.50000	+	3.96863i	−0.0509721	+	0.134859i
$867$	13.8564			0.470588
$868$	12.1244	−	13.7477i	0.411527	−	0.466628i
$869$	24.0000			0.814144
$870$	6.92820	−	18.3303i	0.234888	−	0.621455i
$871$	48.4974			1.64327
$872$	18.1865	+	34.3693i	0.615874	+	1.16389i
$873$		0			0
$874$	−6.06218	−	2.29129i	−0.205056	−	0.0775040i
$875$		−	31.7490i		−	1.07331i
$876$	−23.3827	−	20.6216i	−0.790028	−	0.696739i
$877$	−30.0000			−1.01303			−0.506514	−	0.862232i	$-0.669066\pi$
$877$	−30.0000			−1.01303			−0.506514	+	0.862232i	$0.669066\pi$
$878$	5.19615	−	13.7477i	0.175362	−	0.463963i
$879$		−	7.93725i		−	0.267717i
$880$	−1.73205	−	13.7477i	−0.0583874	−	0.463436i
$881$			27.4955i			0.926345i	0.886268	+	0.463173i	$0.153289\pi$
$881$			27.4955i			0.926345i	−0.886268	+	0.463173i	$0.846711\pi$
$882$		0			0
$883$	29.4449			0.990899			0.495449	−	0.868637i	$-0.335003\pi$
$883$	29.4449			0.990899			0.495449	+	0.868637i	$0.335003\pi$
$884$	−30.3109	+	34.3693i	−1.01947	+	1.15597i
$885$		−	18.3303i		−	0.616166i
$886$	−1.73205	+	4.58258i	−0.0581894	+	0.153955i
$887$	31.1769			1.04682			0.523409	−	0.852081i	$-0.324660\pi$
$887$	31.1769			1.04682			0.523409	+	0.852081i	$0.324660\pi$
$888$	6.82051	−	29.0083i	0.228881	−	0.973454i
$889$	−21.0000			−0.704317
$890$	−5.00000	+	13.2288i	−0.167600	+	0.443429i
$891$	15.5885			0.522233
$892$	−21.0000	+	23.8118i	−0.703132	+	0.797277i
$893$	−18.0000			−0.602347
$894$	21.0000	+	7.93725i	0.702345	+	0.265461i
$895$		−	10.5830i		−	0.353751i
$896$	24.5000	−	17.1974i	0.818488	−	0.574524i
$897$	21.0000			0.701170
$898$	19.0000	−	50.2693i	0.634038	−	1.67751i
$899$	−13.8564			−0.462137
$900$	4.50000	+	3.96863i	0.150000	+	0.132288i
$901$			68.7386i			2.29002i
$902$	21.0000	+	7.93725i	0.699224	+	0.264282i
$903$			15.8745i			0.528271i
$904$	−35.0000	+	18.5203i	−1.16408	+	0.615975i
$905$	12.0000			0.398893
$906$	−18.1865	−	6.87386i	−0.604207	−	0.228369i
$907$	−29.4449			−0.977701			−0.488850	−	0.872368i	$-0.662584\pi$
$907$	−29.4449			−0.977701			−0.488850	+	0.872368i	$0.662584\pi$
$908$	28.0000	−	31.7490i	0.929213	−	1.05363i
$909$			27.4955i			0.911967i
$910$	−12.1244	+	32.0780i	−0.401918	+	1.06338i
$911$		−	26.4575i		−	0.876577i	−0.898834	−	0.438288i	$-0.855585\pi$
$911$		−	26.4575i		−	0.876577i	0.898834	−	0.438288i	$-0.144415\pi$
$912$	1.50000	+	11.9059i	0.0496700	+	0.394243i
$913$	−15.0000			−0.496428
$914$	−24.2487	−	9.16515i	−0.802076	−	0.303156i
$915$			31.7490i			1.04959i
$916$	15.0000	+	13.2288i	0.495614	+	0.437090i
$917$	14.0000			0.462321
$918$	−12.9904	+	34.3693i	−0.428746	+	1.13436i
$919$	20.7846			0.685621			0.342811	−	0.939405i	$-0.388621\pi$
$919$	20.7846			0.685621			0.342811	+	0.939405i	$0.388621\pi$
$920$	−7.00000	−	13.2288i	−0.230783	−	0.436139i
$921$		−	54.9909i		−	1.81201i
$922$	5.00000	−	13.2288i	0.164666	−	0.435666i
$923$			15.8745i			0.522516i
$924$	−10.5000	+	11.9059i	−0.345425	+	0.391675i
$925$	−4.00000	+	4.58258i	−0.131519	+	0.150674i
$926$	−3.46410	+	9.16515i	−0.113837	+	0.301186i
$927$	−41.5692			−1.36531
$928$	−22.0000	−	5.29150i	−0.722185	−	0.173702i
$929$			27.4955i			0.902097i	0.892500	+	0.451048i	$0.148950\pi$
$929$			27.4955i			0.902097i	−0.892500	+	0.451048i	$0.851050\pi$
$930$	−6.00000	+	15.8745i	−0.196748	+	0.520546i
$931$		0			0
$932$	−24.2487	+	27.4955i	−0.794293	+	0.900644i
$933$			9.16515i			0.300054i
$934$	−49.0000	−	18.5203i	−1.60333	−	0.606001i
$935$	−17.3205			−0.566441
$936$	−18.1865	−	34.3693i	−0.594445	−	1.12340i
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	−14.0000	+	37.0405i	−0.457116	+	1.20942i
$939$		−	47.6235i		−	1.55413i
$940$	−31.1769	−	27.4955i	−1.01688	−	0.896803i
$941$			9.16515i			0.298775i	0.988779	+	0.149388i	$0.0477302\pi$
$941$			9.16515i			0.298775i	−0.988779	+	0.149388i	$0.952270\pi$
$942$	−10.3923	+	27.4955i	−0.338600	+	0.895850i
$943$	24.2487			0.789647
$944$	−21.0000	+	2.64575i	−0.683492	+	0.0861119i
$945$			27.4955i			0.894427i
$946$	3.00000	−	7.93725i	0.0975384	−	0.258062i
$947$		−	5.29150i		−	0.171951i	−0.996297	−	0.0859754i	$-0.972599\pi$
$947$		−	5.29150i		−	0.171951i	0.996297	−	0.0859754i	$-0.0274006\pi$
$948$	−36.0000	−	31.7490i	−1.16923	−	1.03116i
$949$		−	41.2432i		−	1.33881i
$950$	0.866025	−	2.29129i	0.0280976	−	0.0743392i
$951$			15.8745i			0.514766i
$952$	−17.5000	−	33.0719i	−0.567178	−	1.07187i
$953$			54.9909i			1.78133i	0.454660	+	0.890665i	$0.349761\pi$
$953$			54.9909i			1.78133i	−0.454660	+	0.890665i	$0.650239\pi$
$954$	−54.5596	−	20.6216i	−1.76643	−	0.667649i
$955$		−	37.0405i		−	1.19860i
$956$	−7.00000	+	7.93725i	−0.226396	+	0.256709i
$957$	12.0000			0.387905
$958$	17.5000	+	6.61438i	0.565399	+	0.213701i
$959$	−24.2487			−0.783032
$960$	−15.5885	+	22.9129i	−0.503115	+	0.739510i
$961$	−19.0000			−0.612903
$962$	34.7487	−	18.6152i	1.12034	−	0.600179i
$963$	5.19615			0.167444
$964$	12.1244	−	13.7477i	0.390499	−	0.442784i
$965$		−	36.6606i		−	1.18015i
$966$	−6.06218	+	16.0390i	−0.195047	+	0.516047i
$967$	31.1769			1.00258			0.501291	−	0.865279i	$-0.332859\pi$
$967$	31.1769			1.00258			0.501291	+	0.865279i	$0.332859\pi$
$968$	−20.0000	+	10.5830i	−0.642824	+	0.340151i
$969$	15.0000			0.481869
$970$		0			0
$971$	−38.1051			−1.22285			−0.611426	−	0.791302i	$-0.709404\pi$
$971$	−38.1051			−1.22285			−0.611426	+	0.791302i	$0.709404\pi$
$972$	−23.3827	−	20.6216i	−0.750000	−	0.661438i
$973$	14.0000			0.448819
$974$	17.3205	−	45.8258i	0.554985	−	1.46835i
$975$			7.93725i			0.254196i
$976$	36.3731	−	4.58258i	1.16427	−	0.146685i
$977$	13.0000			0.415907			0.207953	−	0.978139i	$-0.433320\pi$
$977$	13.0000			0.415907			0.207953	+	0.978139i	$0.433320\pi$
$978$	−7.50000	+	19.8431i	−0.239824	+	0.634513i
$979$	−8.66025			−0.276783
$980$		0			0
$981$			41.2432i			1.31679i
$982$	9.52628	−	25.2042i	0.303996	−	0.804297i
$983$	−6.92820			−0.220975			−0.110488	−	0.993877i	$-0.535241\pi$
$983$	−6.92820			−0.220975			−0.110488	+	0.993877i	$0.535241\pi$
$984$	−21.0000	−	39.6863i	−0.669456	−	1.26515i
$985$			9.16515i			0.292026i
$986$	−10.0000	+	26.4575i	−0.318465	+	0.842579i
$987$			47.6235i			1.51587i
$988$	−10.5000	+	11.9059i	−0.334050	+	0.378777i
$989$		−	9.16515i		−	0.291435i
$990$	5.19615	−	13.7477i	0.165145	−	0.436931i
$991$	−13.8564			−0.440163			−0.220082	−	0.975481i	$-0.570632\pi$
$991$	−13.8564			−0.440163			−0.220082	+	0.975481i	$0.570632\pi$
$992$	19.0526	+	4.58258i	0.604919	+	0.145497i
$993$	18.0000			0.571213
$994$	−12.1244	−	4.58258i	−0.384561	−	0.145350i
$995$	−48.4974			−1.53747
$996$	22.5000	+	19.8431i	0.712940	+	0.628754i
$997$		−	32.0780i		−	1.01592i	−0.861380	−	0.507961i	$-0.830400\pi$
$997$		−	32.0780i		−	1.01592i	0.861380	−	0.507961i	$-0.169600\pi$
$998$	−0.866025	+	2.29129i	−0.0274136	+	0.0725294i
$999$	20.7846	−	23.8118i	0.657596	−	0.753371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.g.a.443.4	yes	4
3.2	odd	2		444.2.g.b.443.1	yes	4
4.3	odd	2	inner	444.2.g.a.443.1	✓	4
12.11	even	2		444.2.g.b.443.4	yes	4
37.36	even	2		444.2.g.b.443.2	yes	4
111.110	odd	2	inner	444.2.g.a.443.3	yes	4
148.147	odd	2		444.2.g.b.443.3	yes	4
444.443	even	2	inner	444.2.g.a.443.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.g.a.443.1	✓	4	4.3	odd	2	inner
444.2.g.a.443.2	yes	4	444.443	even	2	inner
444.2.g.a.443.3	yes	4	111.110	odd	2	inner
444.2.g.a.443.4	yes	4	1.1	even	1	trivial
444.2.g.b.443.1	yes	4	3.2	odd	2
444.2.g.b.443.2	yes	4	37.36	even	2
444.2.g.b.443.3	yes	4	148.147	odd	2
444.2.g.b.443.4	yes	4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.32288i) q^{2} +1.73205 q^{3} +(-1.50000 - 1.32288i) q^{4} -2.00000 q^{5} +(-0.866025 + 2.29129i) q^{6} -2.64575i q^{7} +(2.50000 - 1.32288i) q^{8} +3.00000 q^{9} +(1.00000 - 2.64575i) q^{10} +1.73205 q^{11} +(-2.59808 - 2.29129i) q^{12} -4.58258i q^{13} +(3.50000 + 1.32288i) q^{14} -3.46410 q^{15} +(0.500000 + 3.96863i) q^{16} +5.00000 q^{17} +(-1.50000 + 3.96863i) q^{18} +1.73205 q^{19} +(3.00000 + 2.64575i) q^{20} -4.58258i q^{21} +(-0.866025 + 2.29129i) q^{22} +2.64575i q^{23} +(4.33013 - 2.29129i) q^{24} -1.00000 q^{25} +(6.06218 + 2.29129i) q^{26} +5.19615 q^{27} +(-3.50000 + 3.96863i) q^{28} +4.00000 q^{29} +(1.73205 - 4.58258i) q^{30} -3.46410 q^{31} +(-5.50000 - 1.32288i) q^{32} +3.00000 q^{33} +(-2.50000 + 6.61438i) q^{34} +5.29150i q^{35} +(-4.50000 - 3.96863i) q^{36} +(4.00000 - 4.58258i) q^{37} +(-0.866025 + 2.29129i) q^{38} -7.93725i q^{39} +(-5.00000 + 2.64575i) q^{40} -9.16515i q^{41} +(6.06218 + 2.29129i) q^{42} -3.46410 q^{43} +(-2.59808 - 2.29129i) q^{44} -6.00000 q^{45} +(-3.50000 - 1.32288i) q^{46} -10.3923 q^{47} +(0.866025 + 6.87386i) q^{48} +(0.500000 - 1.32288i) q^{50} +8.66025 q^{51} +(-6.06218 + 6.87386i) q^{52} +13.7477i q^{53} +(-2.59808 + 6.87386i) q^{54} -3.46410 q^{55} +(-3.50000 - 6.61438i) q^{56} +3.00000 q^{57} +(-2.00000 + 5.29150i) q^{58} +5.29150i q^{59} +(5.19615 + 4.58258i) q^{60} -9.16515i q^{61} +(1.73205 - 4.58258i) q^{62} -7.93725i q^{63} +(4.50000 - 6.61438i) q^{64} +9.16515i q^{65} +(-1.50000 + 3.96863i) q^{66} +10.5830i q^{67} +(-7.50000 - 6.61438i) q^{68} +4.58258i q^{69} +(-7.00000 - 2.64575i) q^{70} -3.46410 q^{71} +(7.50000 - 3.96863i) q^{72} +9.00000 q^{73} +(4.06218 + 7.58279i) q^{74} -1.73205 q^{75} +(-2.59808 - 2.29129i) q^{76} -4.58258i q^{77} +(10.5000 + 3.96863i) q^{78} +13.8564 q^{79} +(-1.00000 - 7.93725i) q^{80} +9.00000 q^{81} +(12.1244 + 4.58258i) q^{82} -8.66025 q^{83} +(-6.06218 + 6.87386i) q^{84} -10.0000 q^{85} +(1.73205 - 4.58258i) q^{86} +6.92820 q^{87} +(4.33013 - 2.29129i) q^{88} -5.00000 q^{89} +(3.00000 - 7.93725i) q^{90} -12.1244 q^{91} +(3.50000 - 3.96863i) q^{92} -6.00000 q^{93} +(5.19615 - 13.7477i) q^{94} -3.46410 q^{95} +(-9.52628 - 2.29129i) q^{96} +5.19615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{4} - 8 q^{5} + 10 q^{8} + 12 q^{9} + 4 q^{10} + 14 q^{14} + 2 q^{16} + 20 q^{17} - 6 q^{18} + 12 q^{20} - 4 q^{25} - 14 q^{28} + 16 q^{29} - 22 q^{32} + 12 q^{33} - 10 q^{34} - 18 q^{36}+ \cdots - 24 q^{93}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^4 - 8 * q^5 + 10 * q^8 + 12 * q^9 + 4 * q^10 + 14 * q^14 + 2 * q^16 + 20 * q^17 - 6 * q^18 + 12 * q^20 - 4 * q^25 - 14 * q^28 + 16 * q^29 - 22 * q^32 + 12 * q^33 - 10 * q^34 - 18 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 - 14 * q^46 + 2 * q^50 - 14 * q^56 + 12 * q^57 - 8 * q^58 + 18 * q^64 - 6 * q^66 - 30 * q^68 - 28 * q^70 + 30 * q^72 + 36 * q^73 - 8 * q^74 + 42 * q^78 - 4 * q^80 + 36 * q^81 - 40 * q^85 - 20 * q^89 + 12 * q^90 + 14 * q^92 - 24 * q^93

Introduction

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