LMFDB - Embedded newform 700.2.t.a.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(199,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("700.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.199
Dual form			700.2.t.a.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.866025 + 0.500000i) q^{11} +(1.73205 + 3.00000i) q^{12} -3.46410 q^{13} +(-3.09808 + 2.09808i) q^{14} +(2.00000 + 3.46410i) q^{16} +(0.866025 - 1.50000i) q^{17} +(2.59808 + 4.50000i) q^{19} +(1.50000 + 4.33013i) q^{21} +(1.00000 - 1.00000i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(4.73205 - 1.26795i) q^{24} +(-1.26795 + 4.73205i) q^{26} +5.19615i q^{27} +(1.73205 + 5.00000i) q^{28} -4.00000 q^{29} +(-0.866025 + 1.50000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-0.866025 - 1.50000i) q^{33} +(-1.73205 - 1.73205i) q^{34} +(2.59808 - 1.50000i) q^{37} +(7.09808 - 1.90192i) q^{38} +(5.19615 + 3.00000i) q^{39} +3.46410i q^{41} +(6.46410 - 0.464102i) q^{42} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(-7.50000 + 4.33013i) q^{47} -6.92820i q^{48} +(1.00000 + 6.92820i) q^{49} +(-2.59808 + 1.50000i) q^{51} +(6.00000 + 3.46410i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(7.09808 + 1.90192i) q^{54} +(7.46410 - 0.535898i) q^{56} -9.00000i q^{57} +(-1.46410 + 5.46410i) q^{58} +(2.59808 - 4.50000i) q^{59} +(-4.50000 + 2.59808i) q^{61} +(1.73205 + 1.73205i) q^{62} -8.00000i q^{64} +(-2.36603 + 0.633975i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-3.00000 + 1.73205i) q^{68} +1.73205i q^{69} -14.0000i q^{71} +(4.33013 - 7.50000i) q^{73} +(-1.09808 - 4.09808i) q^{74} -10.3923i q^{76} +(-0.866025 - 2.50000i) q^{77} +(6.00000 - 6.00000i) q^{78} +(-7.79423 + 4.50000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(4.73205 + 1.26795i) q^{82} +13.8564i q^{83} +(1.73205 - 9.00000i) q^{84} +(0.732051 - 2.73205i) q^{86} +(6.00000 + 3.46410i) q^{87} +(-2.73205 + 0.732051i) q^{88} +(-13.5000 + 7.79423i) q^{89} +(6.92820 + 6.00000i) q^{91} +2.00000i q^{92} +(2.59808 - 1.50000i) q^{93} +(3.16987 + 11.8301i) q^{94} +(-9.46410 - 2.53590i) q^{96} -17.3205 q^{97} +(9.83013 + 1.16987i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 8 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^7 - 8 * q^8	$ 4 q - 2 q^{2} - 6 q^{3} - 8 q^{7} - 8 q^{8} - 2 q^{14} + 8 q^{16} + 6 q^{21} + 4 q^{22} - 2 q^{23} + 12 q^{24} - 12 q^{26} - 16 q^{29} + 8 q^{32} + 18 q^{38} + 12 q^{42} + 8 q^{43} - 4 q^{44} - 2 q^{46} - 30 q^{47} + 4 q^{49} + 24 q^{52} + 18 q^{54} + 16 q^{56} + 8 q^{58} - 18 q^{61} - 6 q^{66} - 6 q^{67} - 12 q^{68} + 6 q^{74} + 24 q^{78} + 18 q^{81} + 12 q^{82} - 4 q^{86} + 24 q^{87} - 4 q^{88} - 54 q^{89} + 30 q^{94} - 24 q^{96} + 22 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^7 - 8 * q^8 - 2 * q^14 + 8 * q^16 + 6 * q^21 + 4 * q^22 - 2 * q^23 + 12 * q^24 - 12 * q^26 - 16 * q^29 + 8 * q^32 + 18 * q^38 + 12 * q^42 + 8 * q^43 - 4 * q^44 - 2 * q^46 - 30 * q^47 + 4 * q^49 + 24 * q^52 + 18 * q^54 + 16 * q^56 + 8 * q^58 - 18 * q^61 - 6 * q^66 - 6 * q^67 - 12 * q^68 + 6 * q^74 + 24 * q^78 + 18 * q^81 + 12 * q^82 - 4 * q^86 + 24 * q^87 - 4 * q^88 - 54 * q^89 + 30 * q^94 - 24 * q^96 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$	−1.73205	+	1.73205i	−0.707107	+	0.707107i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$		0			0
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i	0.624844	−	0.780750i	$-0.285163\pi$
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i	−0.363727	+	0.931505i	$0.618496\pi$
$12$	1.73205	+	3.00000i	0.500000	+	0.866025i
$13$	−3.46410			−0.960769			−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410			−0.960769			−0.480384	+	0.877058i	$0.659503\pi$
$14$	−3.09808	+	2.09808i	−0.827996	+	0.560734i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	0.866025	−	1.50000i	0.210042	−	0.363803i	−0.741685	−	0.670748i	$-0.765973\pi$
$17$	0.866025	−	1.50000i	0.210042	−	0.363803i	0.951727	+	0.306944i	$0.0993066\pi$
$18$		0			0
$19$	2.59808	+	4.50000i	0.596040	+	1.03237i	0.993399	+	0.114708i	$0.0365932\pi$
$19$	2.59808	+	4.50000i	0.596040	+	1.03237i	−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$	1.50000	+	4.33013i	0.327327	+	0.944911i
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$	4.73205	−	1.26795i	0.965926	−	0.258819i
$25$		0			0
$26$	−1.26795	+	4.73205i	−0.248665	+	0.928032i
$27$			5.19615i			1.00000i
$28$	1.73205	+	5.00000i	0.327327	+	0.944911i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−0.866025	+	1.50000i	−0.155543	+	0.269408i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$	−0.866025	+	1.50000i	−0.155543	+	0.269408i	0.777714	+	0.628619i	$0.216379\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	−0.866025	−	1.50000i	−0.150756	−	0.261116i
$34$	−1.73205	−	1.73205i	−0.297044	−	0.297044i
$35$		0			0
$36$		0			0
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$	7.09808	−	1.90192i	1.15146	−	0.308533i
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$		0			0
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$	6.46410	−	0.464102i	0.997433	−	0.0716124i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	−1.36603	+	0.366025i	−0.201409	+	0.0539675i
$47$	−7.50000	+	4.33013i	−1.09399	+	0.631614i	−0.934635	−	0.355608i	$-0.884274\pi$
$47$	−7.50000	+	4.33013i	−1.09399	+	0.631614i	−0.159352	+	0.987222i	$0.550941\pi$
$48$		−	6.92820i		−	1.00000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−2.59808	+	1.50000i	−0.363803	+	0.210042i
$52$	6.00000	+	3.46410i	0.832050	+	0.480384i
$53$	−0.866025	−	0.500000i	−0.118958	−	0.0686803i	0.439340	−	0.898321i	$-0.355212\pi$
$53$	−0.866025	−	0.500000i	−0.118958	−	0.0686803i	−0.558298	+	0.829640i	$0.688546\pi$
$54$	7.09808	+	1.90192i	0.965926	+	0.258819i
$55$		0			0
$56$	7.46410	−	0.535898i	0.997433	−	0.0716124i
$57$		−	9.00000i		−	1.19208i
$58$	−1.46410	+	5.46410i	−0.192246	+	0.717472i
$59$	2.59808	−	4.50000i	0.338241	−	0.585850i	−0.645861	−	0.763455i	$-0.723502\pi$
$59$	2.59808	−	4.50000i	0.338241	−	0.585850i	0.984102	+	0.177605i	$0.0568349\pi$
$60$		0			0
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	−0.759608	−	0.650381i	$-0.774609\pi$
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	0.183442	+	0.983030i	$0.441276\pi$
$62$	1.73205	+	1.73205i	0.219971	+	0.219971i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−2.36603	+	0.633975i	−0.291238	+	0.0780369i
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	−3.00000	+	1.73205i	−0.363803	+	0.210042i
$69$			1.73205i			0.208514i
$70$		0			0
$71$		−	14.0000i		−	1.66149i	−0.556650	−	0.830747i	$-0.687914\pi$
$71$		−	14.0000i		−	1.66149i	0.556650	−	0.830747i	$-0.312086\pi$
$72$		0			0
$73$	4.33013	−	7.50000i	0.506803	−	0.877809i	−0.493166	−	0.869935i	$-0.664160\pi$
$73$	4.33013	−	7.50000i	0.506803	−	0.877809i	0.999969	−	0.00787336i	$-0.00250619\pi$
$74$	−1.09808	−	4.09808i	−0.127649	−	0.476392i
$75$		0			0
$76$		−	10.3923i		−	1.19208i
$77$	−0.866025	−	2.50000i	−0.0986928	−	0.284901i
$78$	6.00000	−	6.00000i	0.679366	−	0.679366i
$79$	−7.79423	+	4.50000i	−0.876919	+	0.506290i	−0.869641	−	0.493684i	$-0.835650\pi$
$79$	−7.79423	+	4.50000i	−0.876919	+	0.506290i	−0.00727784	+	0.999974i	$0.502317\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	4.73205	+	1.26795i	0.522568	+	0.140022i
$83$			13.8564i			1.52094i	0.649374	+	0.760469i	$0.275031\pi$
$83$			13.8564i			1.52094i	−0.649374	+	0.760469i	$0.724969\pi$
$84$	1.73205	−	9.00000i	0.188982	−	0.981981i
$85$		0			0
$86$	0.732051	−	2.73205i	0.0789391	−	0.294605i
$87$	6.00000	+	3.46410i	0.643268	+	0.371391i
$88$	−2.73205	+	0.732051i	−0.291238	+	0.0780369i
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.997197	−	0.0748225i	$-0.976161\pi$
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.433800	+	0.901009i	$0.642828\pi$
$90$		0			0
$91$	6.92820	+	6.00000i	0.726273	+	0.628971i
$92$			2.00000i			0.208514i
$93$	2.59808	−	1.50000i	0.269408	−	0.155543i
$94$	3.16987	+	11.8301i	0.326947	+	1.22018i
$95$		0			0
$96$	−9.46410	−	2.53590i	−0.965926	−	0.258819i
$97$	−17.3205			−1.75863			−0.879316	−	0.476240i	$-0.842000\pi$
$97$	−17.3205			−1.75863			−0.879316	+	0.476240i	$0.842000\pi$
$98$	9.83013	+	1.16987i	0.992993	+	0.118175i
$99$		0			0
$100$		0			0
$101$	−7.50000	−	4.33013i	−0.746278	−	0.430864i	0.0780696	−	0.996948i	$-0.475124\pi$
$101$	−7.50000	−	4.33013i	−0.746278	−	0.430864i	−0.824347	+	0.566084i	$0.808458\pi$
$102$	1.09808	+	4.09808i	0.108726	+	0.405770i
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	−0.821705	−	0.569914i	$-0.806977\pi$
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	0.0827075	+	0.996574i	$0.473643\pi$
$104$	6.92820	−	6.92820i	0.679366	−	0.679366i
$105$		0			0
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$	−6.50000	−	11.2583i	−0.628379	−	1.08838i	−0.987877	−	0.155238i	$-0.950386\pi$
$107$	−6.50000	−	11.2583i	−0.628379	−	1.08838i	0.359498	−	0.933146i	$-0.382948\pi$
$108$	5.19615	−	9.00000i	0.500000	−	0.866025i
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$		0			0
$111$	−5.19615			−0.493197
$112$	2.00000	−	10.3923i	0.188982	−	0.981981i
$113$			16.0000i			1.50515i	0.658505	+	0.752577i	$0.271189\pi$
$113$			16.0000i			1.50515i	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−12.2942	−	3.29423i	−1.15146	−	0.308533i
$115$		0			0
$116$	6.92820	+	4.00000i	0.643268	+	0.371391i
$117$		0			0
$118$	−5.19615	−	5.19615i	−0.478345	−	0.478345i
$119$	−4.33013	+	1.50000i	−0.396942	+	0.137505i
$120$		0			0
$121$	−5.00000	−	8.66025i	−0.454545	−	0.787296i
$122$	1.90192	+	7.09808i	0.172192	+	0.642630i
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$		0			0
$126$		0			0
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$		0			0
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	0.956916	−	0.290365i	$-0.0937766\pi$
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	−0.729921	+	0.683531i	$0.760443\pi$
$132$			3.46410i			0.301511i
$133$	2.59808	−	13.5000i	0.225282	−	1.17060i
$134$	3.00000	+	3.00000i	0.259161	+	0.259161i
$135$		0			0
$136$	1.26795	+	4.73205i	0.108726	+	0.405770i
$137$	−0.866025	−	0.500000i	−0.0739895	−	0.0427179i	0.462549	−	0.886594i	$-0.346935\pi$
$137$	−0.866025	−	0.500000i	−0.0739895	−	0.0427179i	−0.536538	+	0.843876i	$0.680268\pi$
$138$	2.36603	+	0.633975i	0.201409	+	0.0539675i
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$		0			0
$141$	15.0000			1.26323
$142$	−19.1244	−	5.12436i	−1.60488	−	0.430026i
$143$	−3.00000	−	1.73205i	−0.250873	−	0.144841i
$144$		0			0
$145$		0			0
$146$	−8.66025	−	8.66025i	−0.716728	−	0.716728i
$147$	4.50000	−	11.2583i	0.371154	−	0.928571i
$148$	−6.00000			−0.493197
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$		0			0
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	0.232623	−	0.972567i	$-0.425269\pi$
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	−0.725956	+	0.687741i	$0.758602\pi$
$152$	−14.1962	−	3.80385i	−1.15146	−	0.308533i
$153$		0			0
$154$	−3.73205	+	0.267949i	−0.300737	+	0.0215920i
$155$		0			0
$156$	−6.00000	−	10.3923i	−0.480384	−	0.832050i
$157$	−0.866025	+	1.50000i	−0.0691164	+	0.119713i	−0.898513	−	0.438948i	$-0.855351\pi$
$157$	−0.866025	+	1.50000i	−0.0691164	+	0.119713i	0.829396	+	0.558661i	$0.188685\pi$
$158$	3.29423	+	12.2942i	0.262075	+	0.978076i
$159$	0.866025	+	1.50000i	0.0686803	+	0.118958i
$160$		0			0
$161$	−0.500000	+	2.59808i	−0.0394055	+	0.204757i
$162$	−9.00000	−	9.00000i	−0.707107	−	0.707107i
$163$	−10.5000	−	18.1865i	−0.822423	−	1.42448i	−0.903873	−	0.427802i	$-0.859288\pi$
$163$	−10.5000	−	18.1865i	−0.822423	−	1.42448i	0.0814491	−	0.996678i	$-0.474045\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$		0			0
$166$	18.9282	+	5.07180i	1.46911	+	0.393648i
$167$			17.3205i			1.34030i	0.742225	+	0.670151i	$0.233770\pi$
$167$			17.3205i			1.34030i	−0.742225	+	0.670151i	$0.766230\pi$
$168$	−11.6603	−	5.66025i	−0.899608	−	0.436698i
$169$	−1.00000			−0.0769231
$170$		0			0
$171$		0			0
$172$	−3.46410	−	2.00000i	−0.264135	−	0.152499i
$173$	6.06218	+	10.5000i	0.460899	+	0.798300i	0.999006	−	0.0445762i	$-0.0141938\pi$
$173$	6.06218	+	10.5000i	0.460899	+	0.798300i	−0.538107	+	0.842876i	$0.680860\pi$
$174$	6.92820	−	6.92820i	0.525226	−	0.525226i
$175$		0			0
$176$			4.00000i			0.301511i
$177$	−7.79423	+	4.50000i	−0.585850	+	0.338241i
$178$	5.70577	+	21.2942i	0.427666	+	1.59607i
$179$	16.4545	+	9.50000i	1.22987	+	0.710063i	0.967002	−	0.254770i	$-0.0819996\pi$
$179$	16.4545	+	9.50000i	1.22987	+	0.710063i	0.262864	+	0.964833i	$0.415333\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$	10.7321	−	7.26795i	0.795513	−	0.538736i
$183$	9.00000			0.665299
$184$	2.73205	+	0.732051i	0.201409	+	0.0539675i
$185$		0			0
$186$	−1.09808	−	4.09808i	−0.0805149	−	0.300486i
$187$	1.50000	−	0.866025i	0.109691	−	0.0633300i
$188$	17.3205			1.26323
$189$	9.00000	−	10.3923i	0.654654	−	0.755929i
$190$		0			0
$191$	−0.866025	+	0.500000i	−0.0626634	+	0.0361787i	−0.531004	−	0.847369i	$-0.678185\pi$
$191$	−0.866025	+	0.500000i	−0.0626634	+	0.0361787i	0.468341	+	0.883548i	$0.344852\pi$
$192$	−6.92820	+	12.0000i	−0.500000	+	0.866025i
$193$	−12.9904	−	7.50000i	−0.935068	−	0.539862i	−0.0466572	−	0.998911i	$-0.514857\pi$
$193$	−12.9904	−	7.50000i	−0.935068	−	0.539862i	−0.888411	+	0.459049i	$0.848190\pi$
$194$	−6.33975	+	23.6603i	−0.455167	+	1.69871i
$195$		0			0
$196$	5.19615	−	13.0000i	0.371154	−	0.928571i
$197$			16.0000i			1.13995i	0.821661	+	0.569976i	$0.193048\pi$
$197$			16.0000i			1.13995i	−0.821661	+	0.569976i	$0.806952\pi$
$198$		0			0
$199$	11.2583	−	19.5000i	0.798082	−	1.38232i	−0.122782	−	0.992434i	$-0.539182\pi$
$199$	11.2583	−	19.5000i	0.798082	−	1.38232i	0.920864	−	0.389885i	$-0.127485\pi$
$200$		0			0
$201$	4.50000	−	2.59808i	0.317406	−	0.183254i
$202$	−8.66025	+	8.66025i	−0.609333	+	0.609333i
$203$	8.00000	+	6.92820i	0.561490	+	0.486265i
$204$	6.00000			0.420084
$205$		0			0
$206$	3.16987	+	11.8301i	0.220856	+	0.824244i
$207$		0			0
$208$	−6.92820	−	12.0000i	−0.480384	−	0.832050i
$209$			5.19615i			0.359425i
$210$		0			0
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$	1.00000	+	1.73205i	0.0686803	+	0.118958i
$213$	−12.1244	+	21.0000i	−0.830747	+	1.43890i
$214$	−17.7583	+	4.75833i	−1.21393	+	0.325273i
$215$		0			0
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$	4.33013	−	1.50000i	0.293948	−	0.101827i
$218$	−9.00000	−	9.00000i	−0.609557	−	0.609557i
$219$	−12.9904	+	7.50000i	−0.877809	+	0.506803i
$220$		0			0
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$	−1.90192	+	7.09808i	−0.127649	+	0.476392i
$223$			6.92820i			0.463947i	0.972722	+	0.231973i	$0.0745182\pi$
$223$			6.92820i			0.463947i	−0.972722	+	0.231973i	$0.925482\pi$
$224$	−13.4641	−	6.53590i	−0.899608	−	0.436698i
$225$		0			0
$226$	21.8564	+	5.85641i	1.45387	+	0.389562i
$227$	16.5000	+	9.52628i	1.09514	+	0.632281i	0.934941	−	0.354803i	$-0.115452\pi$
$227$	16.5000	+	9.52628i	1.09514	+	0.632281i	0.160202	+	0.987084i	$0.448785\pi$
$228$	−9.00000	+	15.5885i	−0.596040	+	1.03237i
$229$	13.5000	−	7.79423i	0.892105	−	0.515057i	0.0174746	−	0.999847i	$-0.494437\pi$
$229$	13.5000	−	7.79423i	0.892105	−	0.515057i	0.874630	+	0.484790i	$0.161104\pi$
$230$		0			0
$231$	−0.866025	+	4.50000i	−0.0569803	+	0.296078i
$232$	8.00000	−	8.00000i	0.525226	−	0.525226i
$233$	6.06218	−	3.50000i	0.397146	−	0.229293i	−0.288106	−	0.957599i	$-0.593025\pi$
$233$	6.06218	−	3.50000i	0.397146	−	0.229293i	0.685252	+	0.728306i	$0.259692\pi$
$234$		0			0
$235$		0			0
$236$	−9.00000	+	5.19615i	−0.585850	+	0.338241i
$237$	15.5885			1.01258
$238$	0.464102	+	6.46410i	0.0300832	+	0.419005i
$239$		−	20.0000i		−	1.29369i	−0.762620	−	0.646846i	$-0.776088\pi$
$239$		−	20.0000i		−	1.29369i	0.762620	−	0.646846i	$-0.223912\pi$
$240$		0			0
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	0.348013	−	0.937490i	$-0.386857\pi$
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	−0.637883	+	0.770133i	$0.720190\pi$
$242$	−13.6603	+	3.66025i	−0.878114	+	0.235290i
$243$		0			0
$244$	10.3923			0.665299
$245$		0			0
$246$	−6.00000	−	6.00000i	−0.382546	−	0.382546i
$247$	−9.00000	−	15.5885i	−0.572656	−	0.991870i
$248$	−1.26795	−	4.73205i	−0.0805149	−	0.300486i
$249$	12.0000	−	20.7846i	0.760469	−	1.31717i
$250$		0			0
$251$	3.46410			0.218652			0.109326	−	0.994006i	$-0.465131\pi$
$251$	3.46410			0.218652			0.109326	+	0.994006i	$0.465131\pi$
$252$		0			0
$253$		−	1.00000i		−	0.0628695i
$254$	−2.19615	+	8.19615i	−0.137799	+	0.514272i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	2.59808	+	4.50000i	0.162064	+	0.280702i	0.935609	−	0.353039i	$-0.114852\pi$
$257$	2.59808	+	4.50000i	0.162064	+	0.280702i	−0.773545	+	0.633741i	$0.781518\pi$
$258$	−3.46410	+	3.46410i	−0.215666	+	0.215666i
$259$	−7.79423	−	1.50000i	−0.484310	−	0.0932055i
$260$		0			0
$261$		0			0
$262$	7.09808	−	1.90192i	0.438521	−	0.117501i
$263$	11.5000	−	19.9186i	0.709120	−	1.22823i	−0.256063	−	0.966660i	$-0.582426\pi$
$263$	11.5000	−	19.9186i	0.709120	−	1.22823i	0.965184	−	0.261573i	$-0.0842411\pi$
$264$	4.73205	+	1.26795i	0.291238	+	0.0780369i
$265$		0			0
$266$	−17.4904	−	8.49038i	−1.07240	−	0.520579i
$267$	27.0000			1.65237
$268$	5.19615	−	3.00000i	0.317406	−	0.183254i
$269$	−19.5000	−	11.2583i	−1.18894	−	0.686433i	−0.230871	−	0.972984i	$-0.574158\pi$
$269$	−19.5000	−	11.2583i	−1.18894	−	0.686433i	−0.958065	+	0.286552i	$0.907491\pi$
$270$		0			0
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	0.526073	−	0.850439i	$-0.323664\pi$
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	−0.999539	+	0.0303728i	$0.990331\pi$
$272$	6.92820			0.420084
$273$	−5.19615	−	15.0000i	−0.314485	−	0.907841i
$274$	−1.00000	+	1.00000i	−0.0604122	+	0.0604122i
$275$		0			0
$276$	1.73205	−	3.00000i	0.104257	−	0.180579i
$277$	11.2583	+	6.50000i	0.676448	+	0.390547i	0.798515	−	0.601975i	$-0.205619\pi$
$277$	11.2583	+	6.50000i	0.676448	+	0.390547i	−0.122068	+	0.992522i	$0.538953\pi$
$278$	−2.53590	+	9.46410i	−0.152093	+	0.567619i
$279$		0			0
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	5.49038	−	20.4904i	0.326947	−	1.22018i
$283$	−10.5000	−	6.06218i	−0.624160	−	0.360359i	0.154327	−	0.988020i	$-0.450679\pi$
$283$	−10.5000	−	6.06218i	−0.624160	−	0.360359i	−0.778487	+	0.627661i	$0.784012\pi$
$284$	−14.0000	+	24.2487i	−0.830747	+	1.43890i
$285$		0			0
$286$	−3.46410	+	3.46410i	−0.204837	+	0.204837i
$287$	6.00000	−	6.92820i	0.354169	−	0.408959i
$288$		0			0
$289$	7.00000	+	12.1244i	0.411765	+	0.713197i
$290$		0			0
$291$	25.9808	+	15.0000i	1.52302	+	0.879316i
$292$	−15.0000	+	8.66025i	−0.877809	+	0.506803i
$293$	20.7846			1.21425			0.607125	−	0.794606i	$-0.292323\pi$
$293$	20.7846			1.21425			0.607125	+	0.794606i	$0.292323\pi$
$294$	−13.7321	−	10.2679i	−0.800869	−	0.598839i
$295$		0			0
$296$	−2.19615	+	8.19615i	−0.127649	+	0.476392i
$297$	−2.59808	+	4.50000i	−0.150756	+	0.261116i
$298$	1.36603	−	0.366025i	0.0791317	−	0.0212033i
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	−7.00000	+	7.00000i	−0.402805	+	0.402805i
$303$	7.50000	+	12.9904i	0.430864	+	0.746278i
$304$	−10.3923	+	18.0000i	−0.596040	+	1.03237i
$305$		0			0
$306$		0			0
$307$		−	20.7846i		−	1.18624i	−0.805114	−	0.593120i	$-0.797896\pi$
$307$		−	20.7846i		−	1.18624i	0.805114	−	0.593120i	$-0.202104\pi$
$308$	−1.00000	+	5.19615i	−0.0569803	+	0.296078i
$309$	15.0000			0.853320
$310$		0			0
$311$	4.33013	−	7.50000i	0.245539	−	0.425286i	−0.716744	−	0.697336i	$-0.754368\pi$
$311$	4.33013	−	7.50000i	0.245539	−	0.425286i	0.962283	+	0.272050i	$0.0877017\pi$
$312$	−16.3923	+	4.39230i	−0.928032	+	0.248665i
$313$	−0.866025	−	1.50000i	−0.0489506	−	0.0847850i	0.840512	−	0.541793i	$-0.182254\pi$
$313$	−0.866025	−	1.50000i	−0.0489506	−	0.0847850i	−0.889463	+	0.457008i	$0.848921\pi$
$314$	1.73205	+	1.73205i	0.0977453	+	0.0977453i
$315$		0			0
$316$	18.0000			1.01258
$317$	9.52628	−	5.50000i	0.535049	−	0.308911i	−0.208021	−	0.978124i	$-0.566702\pi$
$317$	9.52628	−	5.50000i	0.535049	−	0.308911i	0.743070	+	0.669214i	$0.233369\pi$
$318$	2.36603	−	0.633975i	0.132680	−	0.0355515i
$319$	−3.46410	−	2.00000i	−0.193952	−	0.111979i
$320$		0			0
$321$			22.5167i			1.25676i
$322$	3.36603	+	1.63397i	0.187581	+	0.0910578i
$323$	9.00000			0.500773
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$		0			0
$326$	−28.6865	+	7.68653i	−1.58880	+	0.425718i
$327$	−13.5000	+	7.79423i	−0.746552	+	0.431022i
$328$	−6.92820	−	6.92820i	−0.382546	−	0.382546i
$329$	22.5000	+	4.33013i	1.24047	+	0.238728i
$330$		0			0
$331$	−6.06218	+	3.50000i	−0.333207	+	0.192377i	−0.657264	−	0.753660i	$-0.728286\pi$
$331$	−6.06218	+	3.50000i	−0.333207	+	0.192377i	0.324057	+	0.946038i	$0.394953\pi$
$332$	13.8564	−	24.0000i	0.760469	−	1.31717i
$333$		0			0
$334$	23.6603	+	6.33975i	1.29463	+	0.346895i
$335$		0			0
$336$	−12.0000	+	13.8564i	−0.654654	+	0.755929i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−0.366025	+	1.36603i	−0.0199092	+	0.0743020i
$339$	13.8564	−	24.0000i	0.752577	−	1.30350i
$340$		0			0
$341$	−1.50000	+	0.866025i	−0.0812296	+	0.0468979i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−4.00000	+	4.00000i	−0.215666	+	0.215666i
$345$		0			0
$346$	16.5622	−	4.43782i	0.890388	−	0.238579i
$347$	6.50000	−	11.2583i	0.348938	−	0.604379i	−0.637123	−	0.770762i	$-0.719876\pi$
$347$	6.50000	−	11.2583i	0.348938	−	0.604379i	0.986061	+	0.166383i	$0.0532089\pi$
$348$	−6.92820	−	12.0000i	−0.371391	−	0.643268i
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$	5.46410	+	1.46410i	0.291238	+	0.0780369i
$353$	−14.7224	+	25.5000i	−0.783596	+	1.35723i	0.146238	+	0.989249i	$0.453283\pi$
$353$	−14.7224	+	25.5000i	−0.783596	+	1.35723i	−0.929834	+	0.367979i	$0.880050\pi$
$354$	3.29423	+	12.2942i	0.175086	+	0.653431i
$355$		0			0
$356$	31.1769			1.65237
$357$	7.79423	+	1.50000i	0.412514	+	0.0793884i
$358$	19.0000	−	19.0000i	1.00418	−	1.00418i
$359$	−19.9186	+	11.5000i	−1.05126	+	0.606947i	−0.923003	−	0.384794i	$-0.874273\pi$
$359$	−19.9186	+	11.5000i	−1.05126	+	0.606947i	−0.128260	+	0.991741i	$0.540939\pi$
$360$		0			0
$361$	−4.00000	+	6.92820i	−0.210526	+	0.364642i
$362$	−9.46410	−	2.53590i	−0.497422	−	0.133284i
$363$			17.3205i			0.909091i
$364$	−6.00000	−	17.3205i	−0.314485	−	0.907841i
$365$		0			0
$366$	3.29423	−	12.2942i	0.172192	−	0.642630i
$367$	1.50000	+	0.866025i	0.0782994	+	0.0452062i	0.538639	−	0.842537i	$-0.318939\pi$
$367$	1.50000	+	0.866025i	0.0782994	+	0.0452062i	−0.460339	+	0.887743i	$0.652272\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$		0			0
$371$	0.866025	+	2.50000i	0.0449618	+	0.129794i
$372$	−6.00000			−0.311086
$373$	25.1147	−	14.5000i	1.30039	−	0.750782i	0.319921	−	0.947444i	$-0.396344\pi$
$373$	25.1147	−	14.5000i	1.30039	−	0.750782i	0.980471	+	0.196663i	$0.0630104\pi$
$374$	−0.633975	−	2.36603i	−0.0327820	−	0.122344i
$375$		0			0
$376$	6.33975	−	23.6603i	0.326947	−	1.22018i
$377$	13.8564			0.713641
$378$	−10.9019	−	16.0981i	−0.560734	−	0.827996i
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$		0			0
$381$	9.00000	+	5.19615i	0.461084	+	0.266207i
$382$	0.366025	+	1.36603i	0.0187275	+	0.0698919i
$383$	−4.50000	+	2.59808i	−0.229939	+	0.132755i	−0.610544	−	0.791982i	$-0.709049\pi$
$383$	−4.50000	+	2.59808i	−0.229939	+	0.132755i	0.380605	+	0.924738i	$0.375716\pi$
$384$	13.8564	+	13.8564i	0.707107	+	0.707107i
$385$		0			0
$386$	−15.0000	+	15.0000i	−0.763480	+	0.763480i
$387$		0			0
$388$	30.0000	+	17.3205i	1.52302	+	0.879316i
$389$	−9.50000	+	16.4545i	−0.481669	+	0.834275i	−0.999779	−	0.0210389i	$-0.993303\pi$
$389$	−9.50000	+	16.4545i	−0.481669	+	0.834275i	0.518110	+	0.855314i	$0.326636\pi$
$390$		0			0
$391$	−1.73205			−0.0875936
$392$	−15.8564	−	11.8564i	−0.800869	−	0.598839i
$393$		−	9.00000i		−	0.453990i
$394$	21.8564	+	5.85641i	1.10111	+	0.295041i
$395$		0			0
$396$		0			0
$397$	9.52628	+	16.5000i	0.478110	+	0.828111i	0.999685	−	0.0250943i	$-0.00798860\pi$
$397$	9.52628	+	16.5000i	0.478110	+	0.828111i	−0.521575	+	0.853206i	$0.674655\pi$
$398$	−22.5167	−	22.5167i	−1.12866	−	1.12866i
$399$	−15.5885	+	18.0000i	−0.780399	+	0.901127i
$400$		0			0
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	0.996119	+	0.0880147i	$0.0280523\pi$
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	−0.421837	+	0.906672i	$0.638614\pi$
$402$	−1.90192	−	7.09808i	−0.0948593	−	0.354020i
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$	8.66025	+	15.0000i	0.430864	+	0.746278i
$405$		0			0
$406$	12.3923	−	8.39230i	0.615020	−	0.416503i
$407$	3.00000			0.148704
$408$	2.19615	−	8.19615i	0.108726	−	0.405770i
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.939490	+	0.342578i	$0.888700\pi$
$410$		0			0
$411$	0.866025	+	1.50000i	0.0427179	+	0.0739895i
$412$	17.3205			0.853320
$413$	−12.9904	+	4.50000i	−0.639215	+	0.221431i
$414$		0			0
$415$		0			0
$416$	−18.9282	+	5.07180i	−0.928032	+	0.248665i
$417$	10.3923	+	6.00000i	0.508913	+	0.293821i
$418$	7.09808	+	1.90192i	0.347178	+	0.0930261i
$419$	−20.7846			−1.01539			−0.507697	−	0.861536i	$-0.669503\pi$
$419$	−20.7846			−1.01539			−0.507697	+	0.861536i	$0.669503\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	13.6603	+	3.66025i	0.664971	+	0.178178i
$423$		0			0
$424$	2.73205	−	0.732051i	0.132680	−	0.0355515i
$425$		0			0
$426$	24.2487	+	24.2487i	1.17485	+	1.17485i
$427$	13.5000	+	2.59808i	0.653311	+	0.125730i
$428$			26.0000i			1.25676i
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	−19.9186	−	11.5000i	−0.959444	−	0.553936i	−0.0634424	−	0.997985i	$-0.520208\pi$
$431$	−19.9186	−	11.5000i	−0.959444	−	0.553936i	−0.896002	+	0.444050i	$0.853541\pi$
$432$	−18.0000	+	10.3923i	−0.866025	+	0.500000i
$433$	10.3923			0.499422			0.249711	−	0.968320i	$-0.419664\pi$
$433$	10.3923			0.499422			0.249711	+	0.968320i	$0.419664\pi$
$434$	−0.464102	−	6.46410i	−0.0222776	−	0.310287i
$435$		0			0
$436$	−15.5885	+	9.00000i	−0.746552	+	0.431022i
$437$	2.59808	−	4.50000i	0.124283	−	0.215264i
$438$	5.49038	+	20.4904i	0.262341	+	0.979068i
$439$	−11.2583	−	19.5000i	−0.537331	−	0.930684i	−0.999047	−	0.0436563i	$-0.986099\pi$
$439$	−11.2583	−	19.5000i	−0.537331	−	0.930684i	0.461716	−	0.887028i	$-0.347234\pi$
$440$		0			0
$441$		0			0
$442$	6.00000	+	6.00000i	0.285391	+	0.285391i
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	0.994187	−	0.107671i	$-0.0343394\pi$
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	−0.590339	+	0.807155i	$0.701006\pi$
$444$	9.00000	+	5.19615i	0.427121	+	0.246598i
$445$		0			0
$446$	9.46410	+	2.53590i	0.448138	+	0.120078i
$447$		−	1.73205i		−	0.0819232i
$448$	−13.8564	+	16.0000i	−0.654654	+	0.755929i
$449$	−8.00000			−0.377543			−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000			−0.377543			−0.188772	+	0.982021i	$0.560451\pi$
$450$		0			0
$451$	−1.73205	+	3.00000i	−0.0815591	+	0.141264i
$452$	16.0000	−	27.7128i	0.752577	−	1.30350i
$453$	6.06218	+	10.5000i	0.284826	+	0.493333i
$454$	19.0526	−	19.0526i	0.894181	−	0.894181i
$455$		0			0
$456$	18.0000	+	18.0000i	0.842927	+	0.842927i
$457$	12.9904	−	7.50000i	0.607664	−	0.350835i	−0.164386	−	0.986396i	$-0.552564\pi$
$457$	12.9904	−	7.50000i	0.607664	−	0.350835i	0.772051	+	0.635561i	$0.219231\pi$
$458$	−5.70577	−	21.2942i	−0.266613	−	0.995014i
$459$	7.79423	+	4.50000i	0.363803	+	0.210042i
$460$		0			0
$461$			17.3205i			0.806696i	0.915047	+	0.403348i	$0.132154\pi$
$461$			17.3205i			0.806696i	−0.915047	+	0.403348i	$0.867846\pi$
$462$	5.83013	+	2.83013i	0.271242	+	0.131669i
$463$	−30.0000			−1.39422			−0.697109	−	0.716965i	$-0.745531\pi$
$463$	−30.0000			−1.39422			−0.697109	+	0.716965i	$0.745531\pi$
$464$	−8.00000	−	13.8564i	−0.371391	−	0.643268i
$465$		0			0
$466$	−2.56218	−	9.56218i	−0.118691	−	0.442959i
$467$	7.50000	−	4.33013i	0.347059	−	0.200374i	−0.316330	−	0.948649i	$-0.602451\pi$
$467$	7.50000	−	4.33013i	0.347059	−	0.200374i	0.663389	+	0.748275i	$0.269117\pi$
$468$		0			0
$469$	7.50000	−	2.59808i	0.346318	−	0.119968i
$470$		0			0
$471$	2.59808	−	1.50000i	0.119713	−	0.0691164i
$472$	3.80385	+	14.1962i	0.175086	+	0.653431i
$473$	1.73205	+	1.00000i	0.0796398	+	0.0459800i
$474$	5.70577	−	21.2942i	0.262075	−	0.978076i
$475$		0			0
$476$	9.00000	+	1.73205i	0.412514	+	0.0793884i
$477$		0			0
$478$	−27.3205	−	7.32051i	−1.24961	−	0.334832i
$479$	6.06218	−	10.5000i	0.276988	−	0.479757i	−0.693647	−	0.720315i	$-0.743997\pi$
$479$	6.06218	−	10.5000i	0.276988	−	0.479757i	0.970635	+	0.240558i	$0.0773304\pi$
$480$		0			0
$481$	−9.00000	+	5.19615i	−0.410365	+	0.236924i
$482$	−5.19615	+	5.19615i	−0.236678	+	0.236678i
$483$	3.00000	−	3.46410i	0.136505	−	0.157622i
$484$			20.0000i			0.909091i
$485$		0			0
$486$		0			0
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$	3.80385	−	14.1962i	0.172192	−	0.642630i
$489$			36.3731i			1.64485i
$490$		0			0
$491$			32.0000i			1.44414i	0.691820	+	0.722070i	$0.256809\pi$
$491$			32.0000i			1.44414i	−0.691820	+	0.722070i	$0.743191\pi$
$492$	−10.3923	+	6.00000i	−0.468521	+	0.270501i
$493$	−3.46410	+	6.00000i	−0.156015	+	0.270226i
$494$	−24.5885	+	6.58846i	−1.10629	+	0.296429i
$495$		0			0
$496$	−6.92820			−0.311086
$497$	−24.2487	+	28.0000i	−1.08770	+	1.25597i
$498$	−24.0000	−	24.0000i	−1.07547	−	1.07547i
$499$	30.3109	−	17.5000i	1.35690	−	0.783408i	0.367697	−	0.929946i	$-0.380146\pi$
$499$	30.3109	−	17.5000i	1.35690	−	0.783408i	0.989205	+	0.146538i	$0.0468131\pi$
$500$		0			0
$501$	15.0000	−	25.9808i	0.670151	−	1.16073i
$502$	1.26795	−	4.73205i	0.0565913	−	0.211202i
$503$		−	6.92820i		−	0.308913i	−0.988000	−	0.154457i	$-0.950637\pi$
$503$		−	6.92820i		−	0.308913i	0.988000	−	0.154457i	$-0.0493627\pi$
$504$		0			0
$505$		0			0
$506$	−1.36603	−	0.366025i	−0.0607272	−	0.0162718i
$507$	1.50000	+	0.866025i	0.0666173	+	0.0384615i
$508$	10.3923	+	6.00000i	0.461084	+	0.266207i
$509$	−10.5000	+	6.06218i	−0.465404	+	0.268701i	−0.714314	−	0.699825i	$-0.753261\pi$
$509$	−10.5000	+	6.06218i	−0.465404	+	0.268701i	0.248910	+	0.968527i	$0.419928\pi$
$510$		0			0
$511$	−21.6506	+	7.50000i	−0.957768	+	0.331780i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−23.3827	+	13.5000i	−1.03237	+	0.596040i
$514$	7.09808	−	1.90192i	0.313083	−	0.0838903i
$515$		0			0
$516$	3.46410	+	6.00000i	0.152499	+	0.264135i
$517$	−8.66025			−0.380878
$518$	−4.90192	+	10.0981i	−0.215378	+	0.443684i
$519$		−	21.0000i		−	0.921798i
$520$		0			0
$521$	1.50000	+	0.866025i	0.0657162	+	0.0379413i	0.532498	−	0.846431i	$-0.321253\pi$
$521$	1.50000	+	0.866025i	0.0657162	+	0.0379413i	−0.466782	+	0.884372i	$0.654587\pi$
$522$		0			0
$523$	−22.5000	+	12.9904i	−0.983856	+	0.568030i	−0.903432	−	0.428731i	$-0.858961\pi$
$523$	−22.5000	+	12.9904i	−0.983856	+	0.568030i	−0.0804241	+	0.996761i	$0.525627\pi$
$524$		−	10.3923i		−	0.453990i
$525$		0			0
$526$	−23.0000	−	23.0000i	−1.00285	−	1.00285i
$527$	1.50000	+	2.59808i	0.0653410	+	0.113174i
$528$	3.46410	−	6.00000i	0.150756	−	0.261116i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$		0			0
$532$	−18.0000	+	20.7846i	−0.780399	+	0.901127i
$533$		−	12.0000i		−	0.519778i
$534$	9.88269	−	36.8827i	0.427666	−	1.59607i
$535$		0			0
$536$	−2.19615	−	8.19615i	−0.0948593	−	0.354020i
$537$	−16.4545	−	28.5000i	−0.710063	−	1.22987i
$538$	−22.5167	+	22.5167i	−0.970762	+	0.970762i
$539$	−2.59808	+	6.50000i	−0.111907	+	0.279975i
$540$		0			0
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	−21.2942	+	5.70577i	−0.914665	+	0.245084i
$543$	−6.00000	+	10.3923i	−0.257485	+	0.445976i
$544$	2.53590	−	9.46410i	0.108726	−	0.405770i
$545$		0			0
$546$	−22.3923	+	1.60770i	−0.958302	+	0.0688030i
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$		0			0
$550$		0			0
$551$	−10.3923	−	18.0000i	−0.442727	−	0.766826i
$552$	−3.46410	−	3.46410i	−0.147442	−	0.147442i
$553$	23.3827	+	4.50000i	0.994333	+	0.191359i
$554$	13.0000	−	13.0000i	0.552317	−	0.552317i
$555$		0			0
$556$	12.0000	+	6.92820i	0.508913	+	0.293821i
$557$	−32.0429	−	18.5000i	−1.35770	−	0.783870i	−0.368389	−	0.929672i	$-0.620091\pi$
$557$	−32.0429	−	18.5000i	−1.35770	−	0.783870i	−0.989314	+	0.145802i	$0.953424\pi$
$558$		0			0
$559$	−6.92820			−0.293032
$560$		0			0
$561$	−3.00000			−0.126660
$562$	−1.46410	+	5.46410i	−0.0617594	+	0.230489i
$563$	−19.5000	−	11.2583i	−0.821827	−	0.474482i	0.0292191	−	0.999573i	$-0.490698\pi$
$563$	−19.5000	−	11.2583i	−0.821827	−	0.474482i	−0.851046	+	0.525091i	$0.824031\pi$
$564$	−25.9808	−	15.0000i	−1.09399	−	0.631614i
$565$		0			0
$566$	−12.1244	+	12.1244i	−0.509625	+	0.509625i
$567$	−22.5000	+	7.79423i	−0.944911	+	0.327327i
$568$	28.0000	+	28.0000i	1.17485	+	1.17485i
$569$	−6.50000	−	11.2583i	−0.272494	−	0.471974i	0.697006	−	0.717066i	$-0.254515\pi$
$569$	−6.50000	−	11.2583i	−0.272494	−	0.471974i	−0.969500	+	0.245092i	$0.921182\pi$
$570$		0			0
$571$	18.1865	+	10.5000i	0.761083	+	0.439411i	0.829684	−	0.558233i	$-0.188520\pi$
$571$	18.1865	+	10.5000i	0.761083	+	0.439411i	−0.0686016	+	0.997644i	$0.521854\pi$
$572$	3.46410	+	6.00000i	0.144841	+	0.250873i
$573$	1.73205			0.0723575
$574$	−7.26795	−	10.7321i	−0.303358	−	0.447947i
$575$		0			0
$576$		0			0
$577$	16.4545	−	28.5000i	0.685009	−	1.18647i	−0.288425	−	0.957503i	$-0.593132\pi$
$577$	16.4545	−	28.5000i	0.685009	−	1.18647i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$	19.1244	−	5.12436i	0.795468	−	0.213145i
$579$	12.9904	+	22.5000i	0.539862	+	0.935068i
$580$		0			0
$581$	24.0000	−	27.7128i	0.995688	−	1.14972i
$582$	30.0000	−	30.0000i	1.24354	−	1.24354i
$583$	−0.500000	−	0.866025i	−0.0207079	−	0.0358671i
$584$	6.33975	+	23.6603i	0.262341	+	0.979068i
$585$		0			0
$586$	7.60770	−	28.3923i	0.314271	−	1.17288i
$587$		−	6.92820i		−	0.285958i	−0.989726	−	0.142979i	$-0.954332\pi$
$587$		−	6.92820i		−	0.285958i	0.989726	−	0.142979i	$-0.0456681\pi$
$588$	−19.0526	+	15.0000i	−0.785714	+	0.618590i
$589$	−9.00000			−0.370839
$590$		0			0
$591$	13.8564	−	24.0000i	0.569976	−	0.987228i
$592$	10.3923	+	6.00000i	0.427121	+	0.246598i
$593$	7.79423	+	13.5000i	0.320071	+	0.554379i	0.980502	−	0.196508i	$-0.0629600\pi$
$593$	7.79423	+	13.5000i	0.320071	+	0.554379i	−0.660432	+	0.750886i	$0.729627\pi$
$594$	5.19615	+	5.19615i	0.213201	+	0.213201i
$595$		0			0
$596$		−	2.00000i		−	0.0819232i
$597$	−33.7750	+	19.5000i	−1.38232	+	0.798082i
$598$	4.73205	−	1.26795i	0.193508	−	0.0518503i
$599$	14.7224	+	8.50000i	0.601542	+	0.347301i	0.769648	−	0.638468i	$-0.220432\pi$
$599$	14.7224	+	8.50000i	0.601542	+	0.347301i	−0.168106	+	0.985769i	$0.553765\pi$
$600$		0			0
$601$		−	38.1051i		−	1.55434i	−0.629291	−	0.777170i	$-0.716654\pi$
$601$		−	38.1051i		−	1.55434i	0.629291	−	0.777170i	$-0.283346\pi$
$602$	−6.19615	+	4.19615i	−0.252536	+	0.171022i
$603$		0			0
$604$	7.00000	+	12.1244i	0.284826	+	0.493333i
$605$		0			0
$606$	20.4904	−	5.49038i	0.832365	−	0.223031i
$607$	−13.5000	+	7.79423i	−0.547948	+	0.316358i	−0.748294	−	0.663367i	$-0.769127\pi$
$607$	−13.5000	+	7.79423i	−0.547948	+	0.316358i	0.200346	+	0.979725i	$0.435793\pi$
$608$	20.7846	+	20.7846i	0.842927	+	0.842927i
$609$	−6.00000	−	17.3205i	−0.243132	−	0.701862i
$610$		0			0
$611$	25.9808	−	15.0000i	1.05107	−	0.606835i
$612$		0			0
$613$	−26.8468	−	15.5000i	−1.08433	−	0.626039i	−0.152270	−	0.988339i	$-0.548658\pi$
$613$	−26.8468	−	15.5000i	−1.08433	−	0.626039i	−0.932062	+	0.362300i	$0.881992\pi$
$614$	−28.3923	−	7.60770i	−1.14582	−	0.307022i
$615$		0			0
$616$	6.73205	+	3.26795i	0.271242	+	0.131669i
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$	5.49038	−	20.4904i	0.220856	−	0.824244i
$619$	−7.79423	+	13.5000i	−0.313276	+	0.542611i	−0.979070	−	0.203526i	$-0.934760\pi$
$619$	−7.79423	+	13.5000i	−0.313276	+	0.542611i	0.665793	+	0.746136i	$0.268093\pi$
$620$		0			0
$621$	4.50000	−	2.59808i	0.180579	−	0.104257i
$622$	−8.66025	−	8.66025i	−0.347245	−	0.347245i
$623$	40.5000	+	7.79423i	1.62260	+	0.312269i
$624$			24.0000i			0.960769i
$625$		0			0
$626$	−2.36603	+	0.633975i	−0.0945654	+	0.0253387i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	3.00000	−	1.73205i	0.119713	−	0.0691164i
$629$		−	5.19615i		−	0.207184i
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$	6.58846	−	24.5885i	0.262075	−	0.978076i
$633$	8.66025	−	15.0000i	0.344214	−	0.596196i
$634$	−4.02628	−	15.0263i	−0.159904	−	0.596770i
$635$		0			0
$636$		−	3.46410i		−	0.137361i
$637$	−3.46410	−	24.0000i	−0.137253	−	0.950915i
$638$	−4.00000	+	4.00000i	−0.158362	+	0.158362i
$639$		0			0
$640$		0			0
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	−0.708631	−	0.705580i	$-0.750687\pi$
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	0.965365	+	0.260902i	$0.0840201\pi$
$642$	30.7583	+	8.24167i	1.21393	+	0.325273i
$643$		−	13.8564i		−	0.546443i	−0.961951	−	0.273222i	$-0.911911\pi$
$643$		−	13.8564i		−	0.546443i	0.961951	−	0.273222i	$-0.0880892\pi$
$644$	3.46410	−	4.00000i	0.136505	−	0.157622i
$645$		0			0
$646$	3.29423	−	12.2942i	0.129610	−	0.483710i
$647$	−28.5000	−	16.4545i	−1.12045	−	0.646892i	−0.178935	−	0.983861i	$-0.557265\pi$
$647$	−28.5000	−	16.4545i	−1.12045	−	0.646892i	−0.941516	+	0.336968i	$0.890598\pi$
$648$	6.58846	+	24.5885i	0.258819	+	0.965926i
$649$	4.50000	−	2.59808i	0.176640	−	0.101983i
$650$		0			0
$651$	−7.79423	−	1.50000i	−0.305480	−	0.0587896i
$652$			42.0000i			1.64485i
$653$	−26.8468	+	15.5000i	−1.05060	+	0.606562i	−0.922816	−	0.385241i	$-0.874118\pi$
$653$	−26.8468	+	15.5000i	−1.05060	+	0.606562i	−0.127780	+	0.991803i	$0.540785\pi$
$654$	5.70577	+	21.2942i	0.223113	+	0.832670i
$655$		0			0
$656$	−12.0000	+	6.92820i	−0.468521	+	0.270501i
$657$		0			0
$658$	14.1506	−	29.1506i	0.551649	−	1.13641i
$659$			38.0000i			1.48027i	0.672458	+	0.740135i	$0.265238\pi$
$659$			38.0000i			1.48027i	−0.672458	+	0.740135i	$0.734762\pi$
$660$		0			0
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.354809	−	0.934939i	$-0.615454\pi$
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.987085	+	0.160196i	$0.948788\pi$
$662$	2.56218	+	9.56218i	0.0995819	+	0.371645i
$663$	9.00000	−	5.19615i	0.349531	−	0.201802i
$664$	−27.7128	−	27.7128i	−1.07547	−	1.07547i
$665$		0			0
$666$		0			0
$667$	2.00000	+	3.46410i	0.0774403	+	0.134131i
$668$	17.3205	−	30.0000i	0.670151	−	1.16073i
$669$	6.00000	−	10.3923i	0.231973	−	0.401790i
$670$		0			0
$671$	−5.19615			−0.200595
$672$	14.5359	+	21.4641i	0.560734	+	0.827996i
$673$		−	24.0000i		−	0.925132i	−0.886585	−	0.462566i	$-0.846929\pi$
$673$		−	24.0000i		−	0.925132i	0.886585	−	0.462566i	$-0.153071\pi$
$674$		0			0
$675$		0			0
$676$	1.73205	+	1.00000i	0.0666173	+	0.0384615i
$677$	−21.6506	−	37.5000i	−0.832102	−	1.44124i	−0.896369	−	0.443309i	$-0.853804\pi$
$677$	−21.6506	−	37.5000i	−0.832102	−	1.44124i	0.0642672	−	0.997933i	$-0.479529\pi$
$678$	−27.7128	−	27.7128i	−1.06430	−	1.06430i
$679$	34.6410	+	30.0000i	1.32940	+	1.15129i
$680$		0			0
$681$	−16.5000	−	28.5788i	−0.632281	−	1.09514i
$682$	0.633975	+	2.36603i	0.0242761	+	0.0905998i
$683$	12.5000	−	21.6506i	0.478299	−	0.828439i	−0.521391	−	0.853318i	$-0.674587\pi$
$683$	12.5000	−	21.6506i	0.478299	−	0.828439i	0.999690	+	0.0248792i	$0.00792011\pi$
$684$		0			0
$685$		0			0
$686$	−17.6340	−	19.3660i	−0.673268	−	0.739398i
$687$	−27.0000			−1.03011
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	3.00000	+	1.73205i	0.114291	+	0.0659859i
$690$		0			0
$691$	6.06218	+	10.5000i	0.230616	+	0.399439i	0.957990	−	0.286803i	$-0.0925925\pi$
$691$	6.06218	+	10.5000i	0.230616	+	0.399439i	−0.727373	+	0.686242i	$0.759259\pi$
$692$		−	24.2487i		−	0.921798i
$693$		0			0
$694$	−13.0000	−	13.0000i	−0.493473	−	0.493473i
$695$		0			0
$696$	−18.9282	+	5.07180i	−0.717472	+	0.192246i
$697$	5.19615	+	3.00000i	0.196818	+	0.113633i
$698$	14.1962	+	3.80385i	0.537332	+	0.143978i
$699$	−12.1244			−0.458585
$700$		0			0
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$	−24.5885	−	6.58846i	−0.928032	−	0.248665i
$703$	13.5000	+	7.79423i	0.509162	+	0.293965i
$704$	4.00000	−	6.92820i	0.150756	−	0.261116i
$705$		0			0
$706$	29.4449	+	29.4449i	1.10817	+	1.10817i
$707$	7.50000	+	21.6506i	0.282067	+	0.814256i
$708$	18.0000			0.676481
$709$	−4.50000	−	7.79423i	−0.169001	−	0.292718i	0.769068	−	0.639167i	$-0.220721\pi$
$709$	−4.50000	−	7.79423i	−0.169001	−	0.292718i	−0.938069	+	0.346449i	$0.887387\pi$
$710$		0			0
$711$		0			0
$712$	11.4115	−	42.5885i	0.427666	−	1.59607i
$713$	1.73205			0.0648658
$714$	4.90192	−	10.0981i	0.183450	−	0.377911i
$715$		0			0
$716$	−19.0000	−	32.9090i	−0.710063	−	1.22987i
$717$	−17.3205	+	30.0000i	−0.646846	+	1.12037i
$718$	8.41858	+	31.4186i	0.314179	+	1.17253i
$719$	−12.9904	−	22.5000i	−0.484459	−	0.839108i	0.515381	−	0.856961i	$-0.327650\pi$
$719$	−12.9904	−	22.5000i	−0.484459	−	0.839108i	−0.999841	+	0.0178527i	$0.994317\pi$
$720$		0			0
$721$	22.5000	+	4.33013i	0.837944	+	0.161262i
$722$	8.00000	+	8.00000i	0.297729	+	0.297729i
$723$	4.50000	+	7.79423i	0.167357	+	0.289870i
$724$	−6.92820	+	12.0000i	−0.257485	+	0.445976i
$725$		0			0
$726$	23.6603	+	6.33975i	0.878114	+	0.235290i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−25.8564	+	1.85641i	−0.958302	+	0.0688030i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	1.73205	−	3.00000i	0.0640622	−	0.110959i
$732$	−15.5885	−	9.00000i	−0.576166	−	0.332650i
$733$	−21.6506	−	37.5000i	−0.799684	−	1.38509i	−0.919822	−	0.392337i	$-0.871667\pi$
$733$	−21.6506	−	37.5000i	−0.799684	−	1.38509i	0.120137	−	0.992757i	$-0.461667\pi$
$734$	1.73205	−	1.73205i	0.0639312	−	0.0639312i
$735$		0			0
$736$	−4.00000	−	4.00000i	−0.147442	−	0.147442i
$737$	−2.59808	+	1.50000i	−0.0957014	+	0.0552532i
$738$		0			0
$739$	44.1673	+	25.5000i	1.62472	+	0.938033i	0.985634	+	0.168898i	$0.0540208\pi$
$739$	44.1673	+	25.5000i	1.62472	+	0.938033i	0.639087	+	0.769135i	$0.279313\pi$
$740$		0			0
$741$			31.1769i			1.14531i
$742$	3.73205	−	0.267949i	0.137008	−	0.00983672i
$743$	−34.0000			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$744$	−2.19615	+	8.19615i	−0.0805149	+	0.300486i
$745$		0			0
$746$	−10.6147	−	39.6147i	−0.388633	−	1.45040i
$747$		0			0
$748$	−3.46410			−0.126660
$749$	−6.50000	+	33.7750i	−0.237505	+	1.23411i
$750$		0			0
$751$	−21.6506	+	12.5000i	−0.790043	+	0.456131i	−0.839978	−	0.542621i	$-0.817432\pi$
$751$	−21.6506	+	12.5000i	−0.790043	+	0.456131i	0.0499348	+	0.998752i	$0.484099\pi$
$752$	−30.0000	−	17.3205i	−1.09399	−	0.631614i
$753$	−5.19615	−	3.00000i	−0.189358	−	0.109326i
$754$	5.07180	−	18.9282i	0.184704	−	0.689325i
$755$		0			0
$756$	−25.9808	+	9.00000i	−0.944911	+	0.327327i
$757$		−	48.0000i		−	1.74459i	−0.488980	−	0.872295i	$-0.662631\pi$
$757$		−	48.0000i		−	1.74459i	0.488980	−	0.872295i	$-0.337369\pi$
$758$	10.9282	+	2.92820i	0.396930	+	0.106357i
$759$	−0.866025	+	1.50000i	−0.0314347	+	0.0544466i
$760$		0			0
$761$	16.5000	−	9.52628i	0.598125	−	0.345327i	−0.170179	−	0.985413i	$-0.554435\pi$
$761$	16.5000	−	9.52628i	0.598125	−	0.345327i	0.768303	+	0.640086i	$0.221101\pi$
$762$	10.3923	−	10.3923i	0.376473	−	0.376473i
$763$	−22.5000	+	7.79423i	−0.814555	+	0.282170i
$764$	2.00000			0.0723575
$765$		0			0
$766$	1.90192	+	7.09808i	0.0687193	+	0.256464i
$767$	−9.00000	+	15.5885i	−0.324971	+	0.562867i
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$		−	3.46410i		−	0.124919i	−0.998048	−	0.0624593i	$-0.980106\pi$
$769$		−	3.46410i		−	0.124919i	0.998048	−	0.0624593i	$-0.0198944\pi$
$770$		0			0
$771$		−	9.00000i		−	0.324127i
$772$	15.0000	+	25.9808i	0.539862	+	0.935068i
$773$	12.9904	−	22.5000i	0.467232	−	0.809269i	−0.532068	−	0.846702i	$-0.678585\pi$
$773$	12.9904	−	22.5000i	0.467232	−	0.809269i	0.999299	+	0.0374331i	$0.0119181\pi$
$774$		0			0
$775$		0			0
$776$	34.6410	−	34.6410i	1.24354	−	1.24354i
$777$	10.3923	+	9.00000i	0.372822	+	0.322873i
$778$	19.0000	+	19.0000i	0.681183	+	0.681183i
$779$	−15.5885	+	9.00000i	−0.558514	+	0.322458i
$780$		0			0
$781$	7.00000	−	12.1244i	0.250480	−	0.433844i
$782$	−0.633975	+	2.36603i	−0.0226709	+	0.0846089i
$783$		−	20.7846i		−	0.742781i
$784$	−22.0000	+	17.3205i	−0.785714	+	0.618590i
$785$		0			0
$786$	−12.2942	−	3.29423i	−0.438521	−	0.117501i
$787$	−4.50000	−	2.59808i	−0.160408	−	0.0926114i	0.417647	−	0.908609i	$-0.362855\pi$
$787$	−4.50000	−	2.59808i	−0.160408	−	0.0926114i	−0.578055	+	0.815998i	$0.696188\pi$
$788$	16.0000	−	27.7128i	0.569976	−	0.987228i
$789$	−34.5000	+	19.9186i	−1.22823	+	0.709120i
$790$		0			0
$791$	27.7128	−	32.0000i	0.985354	−	1.13779i
$792$		0			0
$793$	15.5885	−	9.00000i	0.553562	−	0.319599i
$794$	26.0263	−	6.97372i	0.923638	−	0.247488i
$795$		0			0
$796$	−39.0000	+	22.5167i	−1.38232	+	0.798082i
$797$	−10.3923			−0.368114			−0.184057	−	0.982916i	$-0.558923\pi$
$797$	−10.3923			−0.368114			−0.184057	+	0.982916i	$0.558923\pi$
$798$	18.8827	+	27.8827i	0.668440	+	0.987036i
$799$			15.0000i			0.530662i
$800$		0			0
$801$		0			0
$802$	31.4186	−	8.41858i	1.10943	−	0.297271i
$803$	7.50000	−	4.33013i	0.264669	−	0.152807i
$804$	−10.3923			−0.366508
$805$		0			0
$806$	−6.00000	−	6.00000i	−0.211341	−	0.211341i
$807$	19.5000	+	33.7750i	0.686433	+	1.18894i
$808$	23.6603	−	6.33975i	0.832365	−	0.223031i
$809$	21.5000	−	37.2391i	0.755900	−	1.30926i	−0.189026	−	0.981972i	$-0.560533\pi$
$809$	21.5000	−	37.2391i	0.755900	−	1.30926i	0.944926	−	0.327285i	$-0.106134\pi$
$810$		0			0
$811$	−13.8564			−0.486564			−0.243282	−	0.969956i	$-0.578224\pi$
$811$	−13.8564			−0.486564			−0.243282	+	0.969956i	$0.578224\pi$
$812$	−6.92820	−	20.0000i	−0.243132	−	0.701862i
$813$			27.0000i			0.946931i
$814$	1.09808	−	4.09808i	0.0384876	−	0.143637i
$815$		0			0
$816$	−10.3923	−	6.00000i	−0.363803	−	0.210042i
$817$	5.19615	+	9.00000i	0.181790	+	0.314870i
$818$	−25.9808	+	25.9808i	−0.908396	+	0.908396i
$819$		0			0
$820$		0			0
$821$	5.50000	+	9.52628i	0.191951	+	0.332469i	0.945897	−	0.324468i	$-0.105185\pi$
$821$	5.50000	+	9.52628i	0.191951	+	0.332469i	−0.753946	+	0.656937i	$0.771852\pi$
$822$	2.36603	−	0.633975i	0.0825246	−	0.0221124i
$823$	−4.50000	+	7.79423i	−0.156860	+	0.271690i	−0.933735	−	0.357966i	$-0.883471\pi$
$823$	−4.50000	+	7.79423i	−0.156860	+	0.271690i	0.776875	+	0.629655i	$0.216804\pi$
$824$	6.33975	−	23.6603i	0.220856	−	0.824244i
$825$		0			0
$826$	1.39230	+	19.3923i	0.0484445	+	0.674745i
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$		0			0
$829$	7.50000	+	4.33013i	0.260486	+	0.150392i	0.624556	−	0.780980i	$-0.285280\pi$
$829$	7.50000	+	4.33013i	0.260486	+	0.150392i	−0.364070	+	0.931371i	$0.618613\pi$
$830$		0			0
$831$	−11.2583	−	19.5000i	−0.390547	−	0.676448i
$832$			27.7128i			0.960769i
$833$	11.2583	+	4.50000i	0.390078	+	0.155916i
$834$	12.0000	−	12.0000i	0.415526	−	0.415526i
$835$		0			0
$836$	5.19615	−	9.00000i	0.179713	−	0.311272i
$837$	−7.79423	−	4.50000i	−0.269408	−	0.155543i
$838$	−7.60770	+	28.3923i	−0.262803	+	0.980796i
$839$	48.4974			1.67432			0.837158	−	0.546960i	$-0.184215\pi$
$839$	48.4974			1.67432			0.837158	+	0.546960i	$0.184215\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−7.32051	+	27.3205i	−0.252281	+	0.941527i
$843$	6.00000	+	3.46410i	0.206651	+	0.119310i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$		0			0
$846$		0			0
$847$	−5.00000	+	25.9808i	−0.171802	+	0.892710i
$848$		−	4.00000i		−	0.137361i
$849$	10.5000	+	18.1865i	0.360359	+	0.624160i
$850$		0			0
$851$	−2.59808	−	1.50000i	−0.0890609	−	0.0514193i
$852$	42.0000	−	24.2487i	1.43890	−	0.830747i
$853$	24.2487			0.830260			0.415130	−	0.909762i	$-0.363736\pi$
$853$	24.2487			0.830260			0.415130	+	0.909762i	$0.363736\pi$
$854$	8.49038	−	17.4904i	0.290535	−	0.598509i
$855$		0			0
$856$	35.5167	+	9.51666i	1.21393	+	0.325273i
$857$	12.9904	−	22.5000i	0.443743	−	0.768585i	−0.554221	−	0.832370i	$-0.686984\pi$
$857$	12.9904	−	22.5000i	0.443743	−	0.768585i	0.997964	+	0.0637844i	$0.0203170\pi$
$858$	8.19615	−	2.19615i	0.279812	−	0.0749754i
$859$	−25.1147	−	43.5000i	−0.856904	−	1.48420i	−0.874868	−	0.484362i	$-0.839052\pi$
$859$	−25.1147	−	43.5000i	−0.856904	−	1.48420i	0.0179638	−	0.999839i	$-0.494282\pi$
$860$		0			0
$861$	−15.0000	+	5.19615i	−0.511199	+	0.177084i
$862$	−23.0000	+	23.0000i	−0.783383	+	0.783383i
$863$	17.5000	+	30.3109i	0.595707	+	1.03179i	0.993447	+	0.114296i	$0.0364614\pi$
$863$	17.5000	+	30.3109i	0.595707	+	1.03179i	−0.397740	+	0.917498i	$0.630205\pi$
$864$	7.60770	+	28.3923i	0.258819	+	0.965926i
$865$		0			0
$866$	3.80385	−	14.1962i	0.129260	−	0.482405i
$867$		−	24.2487i		−	0.823529i
$868$	−9.00000	−	1.73205i	−0.305480	−	0.0587896i
$869$	−9.00000			−0.305304
$870$		0			0
$871$	5.19615	−	9.00000i	0.176065	−	0.304953i
$872$	6.58846	+	24.5885i	0.223113	+	0.832670i
$873$		0			0
$874$	−5.19615	−	5.19615i	−0.175762	−	0.175762i
$875$		0			0
$876$	30.0000			1.01361
$877$	0.866025	−	0.500000i	0.0292436	−	0.0168838i	−0.485307	−	0.874344i	$-0.661292\pi$
$877$	0.866025	−	0.500000i	0.0292436	−	0.0168838i	0.514551	+	0.857460i	$0.327959\pi$
$878$	−30.7583	+	8.24167i	−1.03804	+	0.278143i
$879$	−31.1769	−	18.0000i	−1.05157	−	0.607125i
$880$		0			0
$881$		−	13.8564i		−	0.466834i	−0.972377	−	0.233417i	$-0.925009\pi$
$881$		−	13.8564i		−	0.466834i	0.972377	−	0.233417i	$-0.0749907\pi$
$882$		0			0
$883$	−10.0000			−0.336527			−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000			−0.336527			−0.168263	+	0.985742i	$0.553816\pi$
$884$	10.3923	−	6.00000i	0.349531	−	0.201802i
$885$		0			0
$886$	23.2224	−	6.22243i	0.780173	−	0.209047i
$887$	22.5000	−	12.9904i	0.755476	−	0.436174i	−0.0721931	−	0.997391i	$-0.523000\pi$
$887$	22.5000	−	12.9904i	0.755476	−	0.436174i	0.827669	+	0.561216i	$0.189666\pi$
$888$	10.3923	−	10.3923i	0.348743	−	0.348743i
$889$	12.0000	+	10.3923i	0.402467	+	0.348547i
$890$		0			0
$891$	7.79423	−	4.50000i	0.261116	−	0.150756i
$892$	6.92820	−	12.0000i	0.231973	−	0.401790i
$893$	−38.9711	−	22.5000i	−1.30412	−	0.752934i
$894$	−2.36603	−	0.633975i	−0.0791317	−	0.0212033i
$895$		0			0
$896$	16.7846	+	24.7846i	0.560734	+	0.827996i
$897$		−	6.00000i		−	0.200334i
$898$	−2.92820	+	10.9282i	−0.0977154	+	0.364679i
$899$	3.46410	−	6.00000i	0.115534	−	0.200111i
$900$		0			0
$901$	−1.50000	+	0.866025i	−0.0499722	+	0.0288515i
$902$	3.46410	+	3.46410i	0.115342	+	0.115342i
$903$	3.00000	+	8.66025i	0.0998337	+	0.288195i
$904$	−32.0000	−	32.0000i	−1.06430	−	1.06430i
$905$		0			0
$906$	16.5622	−	4.43782i	0.550242	−	0.147437i
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$	−19.0526	−	33.0000i	−0.632281	−	1.09514i
$909$		0			0
$910$		0			0
$911$		−	26.0000i		−	0.861418i	−0.902491	−	0.430709i	$-0.858263\pi$
$911$		−	26.0000i		−	0.861418i	0.902491	−	0.430709i	$-0.141737\pi$
$912$	31.1769	−	18.0000i	1.03237	−	0.596040i
$913$	−6.92820	+	12.0000i	−0.229290	+	0.397142i
$914$	−5.49038	−	20.4904i	−0.181606	−	0.677762i
$915$		0			0
$916$	−31.1769			−1.03011
$917$	2.59808	−	13.5000i	0.0857960	−	0.445809i
$918$	9.00000	−	9.00000i	0.297044	−	0.297044i
$919$	0.866025	−	0.500000i	0.0285675	−	0.0164935i	−0.485648	−	0.874154i	$-0.661416\pi$
$919$	0.866025	−	0.500000i	0.0285675	−	0.0164935i	0.514216	+	0.857661i	$0.328083\pi$
$920$		0			0
$921$	−18.0000	+	31.1769i	−0.593120	+	1.02731i
$922$	23.6603	+	6.33975i	0.779209	+	0.208788i
$923$			48.4974i			1.59631i
$924$	6.00000	−	6.92820i	0.197386	−	0.227921i
$925$		0			0
$926$	−10.9808	+	40.9808i	−0.360850	+	1.34671i
$927$		0			0
$928$	−21.8564	+	5.85641i	−0.717472	+	0.192246i
$929$	−7.50000	+	4.33013i	−0.246067	+	0.142067i	−0.617962	−	0.786208i	$-0.712041\pi$
$929$	−7.50000	+	4.33013i	−0.246067	+	0.142067i	0.371895	+	0.928275i	$0.378708\pi$
$930$		0			0
$931$	−28.5788	+	22.5000i	−0.936634	+	0.737408i
$932$	−14.0000			−0.458585
$933$	−12.9904	+	7.50000i	−0.425286	+	0.245539i
$934$	−3.16987	−	11.8301i	−0.103721	−	0.387094i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−0.803848	−	11.1962i	−0.0262466	−	0.365567i
$939$			3.00000i			0.0979013i
$940$		0			0
$941$	49.5000	+	28.5788i	1.61365	+	0.931644i	0.988514	+	0.151131i	$0.0482915\pi$
$941$	49.5000	+	28.5788i	1.61365	+	0.931644i	0.625140	+	0.780513i	$0.285042\pi$
$942$	−1.09808	−	4.09808i	−0.0357773	−	0.133523i
$943$	3.00000	−	1.73205i	0.0976934	−	0.0564033i
$944$	20.7846			0.676481
$945$		0			0
$946$	2.00000	−	2.00000i	0.0650256	−	0.0650256i
$947$	14.5000	+	25.1147i	0.471187	+	0.816119i	0.999457	−	0.0329571i	$-0.0104925\pi$
$947$	14.5000	+	25.1147i	0.471187	+	0.816119i	−0.528270	+	0.849076i	$0.677159\pi$
$948$	−27.0000	−	15.5885i	−0.876919	−	0.506290i
$949$	−15.0000	+	25.9808i	−0.486921	+	0.843371i
$950$		0			0
$951$	−19.0526			−0.617822
$952$	5.66025	−	11.6603i	0.183450	−	0.377911i
$953$			8.00000i			0.259145i	0.991570	+	0.129573i	$0.0413606\pi$
$953$			8.00000i			0.259145i	−0.991570	+	0.129573i	$0.958639\pi$
$954$		0			0
$955$		0			0
$956$	−20.0000	+	34.6410i	−0.646846	+	1.12037i
$957$	3.46410	+	6.00000i	0.111979	+	0.193952i
$958$	−12.1244	−	12.1244i	−0.391720	−	0.391720i
$959$	0.866025	+	2.50000i	0.0279654	+	0.0807292i
$960$		0			0
$961$	14.0000	+	24.2487i	0.451613	+	0.782216i
$962$	3.80385	+	14.1962i	0.122641	+	0.457702i
$963$		0			0
$964$	5.19615	+	9.00000i	0.167357	+	0.289870i
$965$		0			0
$966$	−3.63397	−	5.36603i	−0.116921	−	0.172649i
$967$	6.00000			0.192947			0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000			0.192947			0.0964735	+	0.995336i	$0.469244\pi$
$968$	27.3205	+	7.32051i	0.878114	+	0.235290i
$969$	−13.5000	−	7.79423i	−0.433682	−	0.250387i
$970$		0			0
$971$	30.3109	+	52.5000i	0.972723	+	1.68481i	0.687254	+	0.726417i	$0.258816\pi$
$971$	30.3109	+	52.5000i	0.972723	+	1.68481i	0.285469	+	0.958388i	$0.407851\pi$
$972$		0			0
$973$	13.8564	+	12.0000i	0.444216	+	0.384702i
$974$	31.0000	+	31.0000i	0.993304	+	0.993304i
$975$		0			0
$976$	−18.0000	−	10.3923i	−0.576166	−	0.332650i
$977$	26.8468	+	15.5000i	0.858905	+	0.495889i	0.863645	−	0.504100i	$-0.168176\pi$
$977$	26.8468	+	15.5000i	0.858905	+	0.495889i	−0.00474056	+	0.999989i	$0.501509\pi$
$978$	49.6865	+	13.3135i	1.58880	+	0.425718i
$979$	−15.5885			−0.498209
$980$		0			0
$981$		0			0
$982$	43.7128	+	11.7128i	1.39493	+	0.373771i
$983$	−52.5000	−	30.3109i	−1.67449	−	0.966767i	−0.965074	−	0.261977i	$-0.915626\pi$
$983$	−52.5000	−	30.3109i	−1.67449	−	0.966767i	−0.709416	−	0.704790i	$-0.751041\pi$
$984$	4.39230	+	16.3923i	0.140022	+	0.522568i
$985$		0			0
$986$	6.92820	+	6.92820i	0.220639	+	0.220639i
$987$	−30.0000	−	25.9808i	−0.954911	−	0.826977i
$988$			36.0000i			1.14531i
$989$	−1.00000	−	1.73205i	−0.0317982	−	0.0550760i
$990$		0			0
$991$	19.9186	+	11.5000i	0.632735	+	0.365310i	0.781810	−	0.623516i	$-0.214296\pi$
$991$	19.9186	+	11.5000i	0.632735	+	0.365310i	−0.149076	+	0.988826i	$0.547630\pi$
$992$	−2.53590	+	9.46410i	−0.0805149	+	0.300486i
$993$	12.1244			0.384755
$994$	29.3731	+	43.3731i	0.931657	+	1.37571i
$995$		0			0
$996$	−41.5692	+	24.0000i	−1.31717	+	0.760469i
$997$	−11.2583	+	19.5000i	−0.356555	+	0.617571i	−0.987383	−	0.158352i	$-0.949382\pi$
$997$	−11.2583	+	19.5000i	−0.356555	+	0.617571i	0.630828	+	0.775923i	$0.282715\pi$
$998$	−12.8109	−	47.8109i	−0.405522	−	1.51343i
$999$	7.79423	+	13.5000i	0.246598	+	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.a.199.2		4
4.3	odd	2		700.2.t.b.199.2		4
5.2	odd	4		700.2.p.a.451.2		4
5.3	odd	4		28.2.f.a.3.1	✓	4
5.4	even	2		700.2.t.b.199.1		4
7.5	odd	6	inner	700.2.t.a.299.1		4
15.8	even	4		252.2.bf.e.199.2		4
20.3	even	4		28.2.f.a.3.2	yes	4
20.7	even	4		700.2.p.a.451.1		4
20.19	odd	2	inner	700.2.t.a.199.1		4
28.19	even	6		700.2.t.b.299.1		4
35.3	even	12		196.2.d.b.195.2		4
35.12	even	12		700.2.p.a.551.1		4
35.13	even	4		196.2.f.a.31.1		4
35.18	odd	12		196.2.d.b.195.1		4
35.19	odd	6		700.2.t.b.299.2		4
35.23	odd	12		196.2.f.a.19.2		4
35.33	even	12		28.2.f.a.19.2	yes	4
40.3	even	4		448.2.p.d.255.2		4
40.13	odd	4		448.2.p.d.255.1		4
60.23	odd	4		252.2.bf.e.199.1		4
105.38	odd	12		1764.2.b.a.1567.3		4
105.53	even	12		1764.2.b.a.1567.4		4
105.68	odd	12		252.2.bf.e.19.1		4
140.3	odd	12		196.2.d.b.195.3		4
140.19	even	6	inner	700.2.t.a.299.2		4
140.23	even	12		196.2.f.a.19.1		4
140.47	odd	12		700.2.p.a.551.2		4
140.83	odd	4		196.2.f.a.31.2		4
140.103	odd	12		28.2.f.a.19.1	yes	4
140.123	even	12		196.2.d.b.195.4		4
280.3	odd	12		3136.2.f.e.3135.3		4
280.53	odd	12		3136.2.f.e.3135.4		4
280.123	even	12		3136.2.f.e.3135.2		4
280.173	even	12		448.2.p.d.383.2		4
280.213	even	12		3136.2.f.e.3135.1		4
280.243	odd	12		448.2.p.d.383.1		4
420.143	even	12		1764.2.b.a.1567.1		4
420.263	odd	12		1764.2.b.a.1567.2		4
420.383	even	12		252.2.bf.e.19.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.f.a.3.1	✓	4	5.3	odd	4
28.2.f.a.3.2	yes	4	20.3	even	4
28.2.f.a.19.1	yes	4	140.103	odd	12
28.2.f.a.19.2	yes	4	35.33	even	12
196.2.d.b.195.1		4	35.18	odd	12
196.2.d.b.195.2		4	35.3	even	12
196.2.d.b.195.3		4	140.3	odd	12
196.2.d.b.195.4		4	140.123	even	12
196.2.f.a.19.1		4	140.23	even	12
196.2.f.a.19.2		4	35.23	odd	12
196.2.f.a.31.1		4	35.13	even	4
196.2.f.a.31.2		4	140.83	odd	4
252.2.bf.e.19.1		4	105.68	odd	12
252.2.bf.e.19.2		4	420.383	even	12
252.2.bf.e.199.1		4	60.23	odd	4
252.2.bf.e.199.2		4	15.8	even	4
448.2.p.d.255.1		4	40.13	odd	4
448.2.p.d.255.2		4	40.3	even	4
448.2.p.d.383.1		4	280.243	odd	12
448.2.p.d.383.2		4	280.173	even	12
700.2.p.a.451.1		4	20.7	even	4
700.2.p.a.451.2		4	5.2	odd	4
700.2.p.a.551.1		4	35.12	even	12
700.2.p.a.551.2		4	140.47	odd	12
700.2.t.a.199.1		4	20.19	odd	2	inner
700.2.t.a.199.2		4	1.1	even	1	trivial
700.2.t.a.299.1		4	7.5	odd	6	inner
700.2.t.a.299.2		4	140.19	even	6	inner
700.2.t.b.199.1		4	5.4	even	2
700.2.t.b.199.2		4	4.3	odd	2
700.2.t.b.299.1		4	28.19	even	6
700.2.t.b.299.2		4	35.19	odd	6
1764.2.b.a.1567.1		4	420.143	even	12
1764.2.b.a.1567.2		4	420.263	odd	12
1764.2.b.a.1567.3		4	105.38	odd	12
1764.2.b.a.1567.4		4	105.53	even	12
3136.2.f.e.3135.1		4	280.213	even	12
3136.2.f.e.3135.2		4	280.123	even	12
3136.2.f.e.3135.3		4	280.3	odd	12
3136.2.f.e.3135.4		4	280.53	odd	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.866025 + 0.500000i) q^{11} +(1.73205 + 3.00000i) q^{12} -3.46410 q^{13} +(-3.09808 + 2.09808i) q^{14} +(2.00000 + 3.46410i) q^{16} +(0.866025 - 1.50000i) q^{17} +(2.59808 + 4.50000i) q^{19} +(1.50000 + 4.33013i) q^{21} +(1.00000 - 1.00000i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(4.73205 - 1.26795i) q^{24} +(-1.26795 + 4.73205i) q^{26} +5.19615i q^{27} +(1.73205 + 5.00000i) q^{28} -4.00000 q^{29} +(-0.866025 + 1.50000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-0.866025 - 1.50000i) q^{33} +(-1.73205 - 1.73205i) q^{34} +(2.59808 - 1.50000i) q^{37} +(7.09808 - 1.90192i) q^{38} +(5.19615 + 3.00000i) q^{39} +3.46410i q^{41} +(6.46410 - 0.464102i) q^{42} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(-7.50000 + 4.33013i) q^{47} -6.92820i q^{48} +(1.00000 + 6.92820i) q^{49} +(-2.59808 + 1.50000i) q^{51} +(6.00000 + 3.46410i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(7.09808 + 1.90192i) q^{54} +(7.46410 - 0.535898i) q^{56} -9.00000i q^{57} +(-1.46410 + 5.46410i) q^{58} +(2.59808 - 4.50000i) q^{59} +(-4.50000 + 2.59808i) q^{61} +(1.73205 + 1.73205i) q^{62} -8.00000i q^{64} +(-2.36603 + 0.633975i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-3.00000 + 1.73205i) q^{68} +1.73205i q^{69} -14.0000i q^{71} +(4.33013 - 7.50000i) q^{73} +(-1.09808 - 4.09808i) q^{74} -10.3923i q^{76} +(-0.866025 - 2.50000i) q^{77} +(6.00000 - 6.00000i) q^{78} +(-7.79423 + 4.50000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(4.73205 + 1.26795i) q^{82} +13.8564i q^{83} +(1.73205 - 9.00000i) q^{84} +(0.732051 - 2.73205i) q^{86} +(6.00000 + 3.46410i) q^{87} +(-2.73205 + 0.732051i) q^{88} +(-13.5000 + 7.79423i) q^{89} +(6.92820 + 6.00000i) q^{91} +2.00000i q^{92} +(2.59808 - 1.50000i) q^{93} +(3.16987 + 11.8301i) q^{94} +(-9.46410 - 2.53590i) q^{96} -17.3205 q^{97} +(9.83013 + 1.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^7 - 8 * q^8	\( 4 q - 2 q^{2} - 6 q^{3} - 8 q^{7} - 8 q^{8} - 2 q^{14} + 8 q^{16} + 6 q^{21} + 4 q^{22} - 2 q^{23} + 12 q^{24} - 12 q^{26} - 16 q^{29} + 8 q^{32} + 18 q^{38} + 12 q^{42} + 8 q^{43} - 4 q^{44} - 2 q^{46} - 30 q^{47} + 4 q^{49} + 24 q^{52} + 18 q^{54} + 16 q^{56} + 8 q^{58} - 18 q^{61} - 6 q^{66} - 6 q^{67} - 12 q^{68} + 6 q^{74} + 24 q^{78} + 18 q^{81} + 12 q^{82} - 4 q^{86} + 24 q^{87} - 4 q^{88} - 54 q^{89} + 30 q^{94} - 24 q^{96} + 22 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^7 - 8 * q^8 - 2 * q^14 + 8 * q^16 + 6 * q^21 + 4 * q^22 - 2 * q^23 + 12 * q^24 - 12 * q^26 - 16 * q^29 + 8 * q^32 + 18 * q^38 + 12 * q^42 + 8 * q^43 - 4 * q^44 - 2 * q^46 - 30 * q^47 + 4 * q^49 + 24 * q^52 + 18 * q^54 + 16 * q^56 + 8 * q^58 - 18 * q^61 - 6 * q^66 - 6 * q^67 - 12 * q^68 + 6 * q^74 + 24 * q^78 + 18 * q^81 + 12 * q^82 - 4 * q^86 + 24 * q^87 - 4 * q^88 - 54 * q^89 + 30 * q^94 - 24 * q^96 + 22 * q^98

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