LMFDB - Embedded newform 637.2.h.a.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.a.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} -1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 - 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} -1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 - 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +(1.50000 + 2.59808i) q^{12} +(1.00000 + 3.46410i) q^{13} +(4.50000 - 7.79423i) q^{15} -1.00000 q^{16} +2.00000 q^{17} +(-3.00000 + 5.19615i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 3.46410i) q^{26} +9.00000 q^{27} +(-3.50000 + 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} +(1.50000 - 2.59808i) q^{31} +5.00000 q^{32} +(4.50000 - 7.79423i) q^{33} +2.00000 q^{34} +(3.00000 - 5.19615i) q^{36} +2.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(7.50000 - 7.79423i) q^{39} +(-4.50000 - 7.79423i) q^{40} +(1.50000 - 2.59808i) q^{41} +(3.50000 + 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{44} -18.0000 q^{45} +(0.500000 + 0.866025i) q^{47} +(1.50000 + 2.59808i) q^{48} +(-2.00000 + 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{54} +(-4.50000 + 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +4.00000 q^{59} +(-4.50000 + 7.79423i) q^{60} +(-6.50000 + 11.2583i) q^{61} +(1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-7.50000 + 7.79423i) q^{65} +(4.50000 - 7.79423i) q^{66} +(1.50000 + 2.59808i) q^{67} -2.00000 q^{68} +(-6.50000 - 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} +(-6.50000 + 11.2583i) q^{73} +2.00000 q^{74} +12.0000 q^{75} +(0.500000 - 0.866025i) q^{76} +(7.50000 - 7.79423i) q^{78} +(1.50000 + 2.59808i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +(3.00000 + 5.19615i) q^{85} +(3.50000 + 6.06218i) q^{86} +21.0000 q^{87} +(-4.50000 - 7.79423i) q^{88} -6.00000 q^{89} -18.0000 q^{90} -9.00000 q^{93} +(0.500000 + 0.866025i) q^{94} -3.00000 q^{95} +(-7.50000 - 12.9904i) q^{96} +(-2.50000 - 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 - 6 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 2 q^{13} + 9 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{24} - 4 q^{25} + 2 q^{26} + 18 q^{27} - 7 q^{29} + 9 q^{30} + 3 q^{31} + 10 q^{32} + 9 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{37} - q^{38} + 15 q^{39} - 9 q^{40} + 3 q^{41} + 7 q^{43} - 3 q^{44} - 36 q^{45} + q^{47} + 3 q^{48} - 4 q^{50} - 6 q^{51} - 2 q^{52} - 3 q^{53} + 18 q^{54} - 9 q^{55} + 6 q^{57} - 7 q^{58} + 8 q^{59} - 9 q^{60} - 13 q^{61} + 3 q^{62} + 14 q^{64} - 15 q^{65} + 9 q^{66} + 3 q^{67} - 4 q^{68} - 13 q^{71} + 18 q^{72} - 13 q^{73} + 4 q^{74} + 24 q^{75} + q^{76} + 15 q^{78} + 3 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 6 q^{85} + 7 q^{86} + 42 q^{87} - 9 q^{88} - 12 q^{89} - 36 q^{90} - 18 q^{93} + q^{94} - 6 q^{95} - 15 q^{96} - 5 q^{97} - 36 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 2 * q^13 + 9 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^18 - q^19 - 3 * q^20 + 3 * q^22 + 9 * q^24 - 4 * q^25 + 2 * q^26 + 18 * q^27 - 7 * q^29 + 9 * q^30 + 3 * q^31 + 10 * q^32 + 9 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^37 - q^38 + 15 * q^39 - 9 * q^40 + 3 * q^41 + 7 * q^43 - 3 * q^44 - 36 * q^45 + q^47 + 3 * q^48 - 4 * q^50 - 6 * q^51 - 2 * q^52 - 3 * q^53 + 18 * q^54 - 9 * q^55 + 6 * q^57 - 7 * q^58 + 8 * q^59 - 9 * q^60 - 13 * q^61 + 3 * q^62 + 14 * q^64 - 15 * q^65 + 9 * q^66 + 3 * q^67 - 4 * q^68 - 13 * q^71 + 18 * q^72 - 13 * q^73 + 4 * q^74 + 24 * q^75 + q^76 + 15 * q^78 + 3 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 6 * q^85 + 7 * q^86 + 42 * q^87 - 9 * q^88 - 12 * q^89 - 36 * q^90 - 18 * q^93 + q^94 - 6 * q^95 - 15 * q^96 - 5 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$4$	−1.00000			−0.500000
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	−1.50000	−	2.59808i	−0.612372	−	1.06066i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$	4.50000	−	7.79423i	1.16190	−	2.01246i
$16$	−1.00000			−0.250000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	4.50000	+	7.79423i	0.918559	+	1.59099i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$	9.00000			1.73205
$28$		0			0
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$	4.50000	−	7.79423i	0.821584	−	1.42302i
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	−0.699301	−	0.714827i	$-0.746505\pi$
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	0.968709	+	0.248199i	$0.0798387\pi$
$32$	5.00000			0.883883
$33$	4.50000	−	7.79423i	0.783349	−	1.35680i
$34$	2.00000			0.342997
$35$		0			0
$36$	3.00000	−	5.19615i	0.500000	−	0.866025i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	7.50000	−	7.79423i	1.20096	−	1.24808i
$40$	−4.50000	−	7.79423i	−0.711512	−	1.23238i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	0.999223	+	0.0394140i	$0.0125491\pi$
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	−0.465478	+	0.885059i	$0.654118\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	−18.0000			−2.68328
$46$		0			0
$47$	0.500000	+	0.866025i	0.0729325	+	0.126323i	0.900185	−	0.435507i	$-0.143431\pi$
$47$	0.500000	+	0.866025i	0.0729325	+	0.126323i	−0.827253	+	0.561830i	$0.810098\pi$
$48$	1.50000	+	2.59808i	0.216506	+	0.375000i
$49$		0			0
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	9.00000			1.22474
$55$	−4.50000	+	7.79423i	−0.606780	+	1.05097i
$56$		0			0
$57$	3.00000			0.397360
$58$	−3.50000	+	6.06218i	−0.459573	+	0.796003i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$	−4.50000	+	7.79423i	−0.580948	+	1.00623i
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	0.0640184	+	0.997949i	$0.479608\pi$
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	1.50000	−	2.59808i	0.190500	−	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$	−7.50000	+	7.79423i	−0.930261	+	0.966755i
$66$	4.50000	−	7.79423i	0.553912	−	0.959403i
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	−2.00000			−0.242536
$69$		0			0
$70$		0			0
$71$	−6.50000	−	11.2583i	−0.771408	−	1.33612i	−0.936791	−	0.349889i	$-0.886219\pi$
$71$	−6.50000	−	11.2583i	−0.771408	−	1.33612i	0.165383	−	0.986229i	$-0.447114\pi$
$72$	9.00000	−	15.5885i	1.06066	−	1.83712i
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	0.181688	+	0.983356i	$0.441844\pi$
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	−0.942455	+	0.334332i	$0.891489\pi$
$74$	2.00000			0.232495
$75$	12.0000			1.38564
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$		0			0
$78$	7.50000	−	7.79423i	0.849208	−	0.882523i
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$	21.0000			2.25144
$88$	−4.50000	−	7.79423i	−0.479702	−	0.830868i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−18.0000			−1.89737
$91$		0			0
$92$		0			0
$93$	−9.00000			−0.933257
$94$	0.500000	+	0.866025i	0.0515711	+	0.0893237i
$95$	−3.00000			−0.307794
$96$	−7.50000	−	12.9904i	−0.765466	−	1.32583i
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	0.710742	−	0.703452i	$-0.248359\pi$
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$	−18.0000			−1.80907
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	0.714423	−	0.699715i	$-0.246689\pi$
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	−0.963182	+	0.268851i	$0.913356\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	−3.00000	−	10.3923i	−0.294174	−	1.01905i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	8.00000			0.773389			0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000			0.773389			0.386695	+	0.922208i	$0.373617\pi$
$108$	−9.00000			−0.866025
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$	−4.50000	+	7.79423i	−0.429058	+	0.743151i
$111$	−3.00000	−	5.19615i	−0.284747	−	0.493197i
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$	3.00000			0.280976
$115$		0			0
$116$	3.50000	−	6.06218i	0.324967	−	0.562859i
$117$	−21.0000	−	5.19615i	−1.94145	−	0.480384i
$118$	4.00000			0.368230
$119$		0			0
$120$	−13.5000	+	23.3827i	−1.23238	+	2.13454i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−6.50000	+	11.2583i	−0.588482	+	1.01928i
$123$	−9.00000			−0.811503
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$	3.00000			0.268328
$126$		0			0
$127$	−5.50000	+	9.52628i	−0.488046	+	0.845321i	−0.999905	−	0.0137486i	$-0.995624\pi$
$127$	−5.50000	+	9.52628i	−0.488046	+	0.845321i	0.511859	+	0.859069i	$0.328957\pi$
$128$	−3.00000			−0.265165
$129$	10.5000	−	18.1865i	0.924473	−	1.60123i
$130$	−7.50000	+	7.79423i	−0.657794	+	0.683599i
$131$	2.50000	+	4.33013i	0.218426	+	0.378325i	0.954327	−	0.298764i	$-0.0965744\pi$
$131$	2.50000	+	4.33013i	0.218426	+	0.378325i	−0.735901	+	0.677089i	$0.763241\pi$
$132$	−4.50000	+	7.79423i	−0.391675	+	0.678401i
$133$		0			0
$134$	1.50000	+	2.59808i	0.129580	+	0.224440i
$135$	13.5000	+	23.3827i	1.16190	+	2.01246i
$136$	−6.00000			−0.514496
$137$	10.0000			0.854358			0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000			0.854358			0.427179	+	0.904167i	$0.359507\pi$
$138$		0			0
$139$	−7.50000	−	12.9904i	−0.636142	−	1.10183i	−0.986272	−	0.165129i	$-0.947196\pi$
$139$	−7.50000	−	12.9904i	−0.636142	−	1.10183i	0.350130	−	0.936701i	$-0.386137\pi$
$140$		0			0
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$	−6.50000	−	11.2583i	−0.545468	−	0.944778i
$143$	−7.50000	+	7.79423i	−0.627182	+	0.651786i
$144$	3.00000	−	5.19615i	0.250000	−	0.433013i
$145$	−21.0000			−1.74396
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$	12.0000			0.979796
$151$	10.5000	−	18.1865i	0.854478	−	1.48000i	−0.0226507	−	0.999743i	$-0.507211\pi$
$151$	10.5000	−	18.1865i	0.854478	−	1.48000i	0.877129	−	0.480256i	$-0.159456\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$	−6.00000	+	10.3923i	−0.485071	+	0.840168i
$154$		0			0
$155$	9.00000			0.722897
$156$	−7.50000	+	7.79423i	−0.600481	+	0.624038i
$157$	9.50000	−	16.4545i	0.758183	−	1.31321i	−0.185594	−	0.982627i	$-0.559421\pi$
$157$	9.50000	−	16.4545i	0.758183	−	1.31321i	0.943777	−	0.330584i	$-0.107246\pi$
$158$	1.50000	+	2.59808i	0.119334	+	0.206692i
$159$	9.00000			0.713746
$160$	7.50000	+	12.9904i	0.592927	+	1.02698i
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$	27.0000			2.10195
$166$		0			0
$167$	−6.50000	+	11.2583i	−0.502985	+	0.871196i	0.497009	+	0.867745i	$0.334432\pi$
$167$	−6.50000	+	11.2583i	−0.502985	+	0.871196i	−0.999994	+	0.00345033i	$0.998902\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−3.50000	−	6.06218i	−0.266872	−	0.462237i
$173$	9.50000	−	16.4545i	0.722272	−	1.25101i	−0.237816	−	0.971310i	$-0.576431\pi$
$173$	9.50000	−	16.4545i	0.722272	−	1.25101i	0.960087	−	0.279701i	$-0.0902353\pi$
$174$	21.0000			1.59201
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	−6.00000			−0.449719
$179$	−8.50000	−	14.7224i	−0.635320	−	1.10041i	−0.986447	−	0.164079i	$-0.947535\pi$
$179$	−8.50000	−	14.7224i	−0.635320	−	1.10041i	0.351127	−	0.936328i	$-0.385798\pi$
$180$	18.0000			1.34164
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	39.0000			2.88296
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$	−9.00000			−0.659912
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	−0.500000	−	0.866025i	−0.0364662	−	0.0631614i
$189$		0			0
$190$	−3.00000			−0.217643
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	−0.375339	−	0.926887i	$-0.622474\pi$
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	0.990378	−	0.138390i	$-0.0441928\pi$
$192$	−10.5000	−	18.1865i	−0.757772	−	1.31250i
$193$	−3.50000	−	6.06218i	−0.251936	−	0.436365i	0.712123	−	0.702055i	$-0.247734\pi$
$193$	−3.50000	−	6.06218i	−0.251936	−	0.436365i	−0.964059	+	0.265689i	$0.914400\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$	31.5000	+	7.79423i	2.25576	+	0.558156i
$196$		0			0
$197$	0.500000	−	0.866025i	0.0356235	−	0.0617018i	−0.847664	−	0.530534i	$-0.821992\pi$
$197$	0.500000	−	0.866025i	0.0356235	−	0.0617018i	0.883287	+	0.468832i	$0.155325\pi$
$198$	−18.0000			−1.27920
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	6.00000	−	10.3923i	0.424264	−	0.734847i
$201$	4.50000	−	7.79423i	0.317406	−	0.549762i
$202$	−2.50000	−	4.33013i	−0.175899	−	0.304667i
$203$		0			0
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	9.00000			0.628587
$206$	2.50000	+	4.33013i	0.174183	+	0.301694i
$207$		0			0
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−3.50000	+	6.06218i	−0.240950	+	0.417338i	−0.960985	−	0.276600i	$-0.910792\pi$
$211$	−3.50000	+	6.06218i	−0.240950	+	0.417338i	0.720035	+	0.693938i	$0.244126\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−19.5000	+	33.7750i	−1.33612	+	2.31422i
$214$	8.00000			0.546869
$215$	−10.5000	+	18.1865i	−0.716094	+	1.24031i
$216$	−27.0000			−1.83712
$217$		0			0
$218$	−3.50000	+	6.06218i	−0.237050	+	0.410582i
$219$	39.0000			2.63538
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$	2.00000	+	6.92820i	0.134535	+	0.466041i
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	−0.976440	−	0.215788i	$-0.930768\pi$
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	0.675098	+	0.737728i	$0.264101\pi$
$224$		0			0
$225$	−12.0000	−	20.7846i	−0.800000	−	1.38564i
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$	−3.00000			−0.198680
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$		0			0
$231$		0			0
$232$	10.5000	−	18.1865i	0.689359	−	1.19400i
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$	−21.0000	−	5.19615i	−1.37281	−	0.339683i
$235$	−1.50000	+	2.59808i	−0.0978492	+	0.169480i
$236$	−4.00000			−0.260378
$237$	4.50000	−	7.79423i	0.292306	−	0.506290i
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−4.50000	+	7.79423i	−0.290474	+	0.503115i
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	6.50000	−	11.2583i	0.416120	−	0.720741i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	−3.50000	−	0.866025i	−0.222700	−	0.0551039i
$248$	−4.50000	+	7.79423i	−0.285750	+	0.494934i
$249$		0			0
$250$	3.00000			0.189737
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	−0.958613	−	0.284711i	$-0.908102\pi$
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	0.232740	−	0.972539i	$-0.425231\pi$
$252$		0			0
$253$		0			0
$254$	−5.50000	+	9.52628i	−0.345101	+	0.597732i
$255$	9.00000	−	15.5885i	0.563602	−	0.976187i
$256$	−17.0000			−1.06250
$257$	2.00000			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$258$	10.5000	−	18.1865i	0.653701	−	1.13224i
$259$		0			0
$260$	7.50000	−	7.79423i	0.465130	−	0.483378i
$261$	−21.0000	−	36.3731i	−1.29987	−	2.25144i
$262$	2.50000	+	4.33013i	0.154451	+	0.267516i
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$	−13.5000	+	23.3827i	−0.830868	+	1.43910i
$265$	−9.00000			−0.552866
$266$		0			0
$267$	9.00000	+	15.5885i	0.550791	+	0.953998i
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$	13.5000	+	23.3827i	0.821584	+	1.42302i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	−12.0000			−0.723627
$276$		0			0
$277$	22.0000			1.32185			0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000			1.32185			0.660926	+	0.750451i	$0.270164\pi$
$278$	−7.50000	−	12.9904i	−0.449820	−	0.779111i
$279$	9.00000	+	15.5885i	0.538816	+	0.933257i
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	0.500000	+	0.866025i	0.0297219	+	0.0514799i	0.880504	−	0.474039i	$-0.157204\pi$
$283$	0.500000	+	0.866025i	0.0297219	+	0.0514799i	−0.850782	+	0.525519i	$0.823871\pi$
$284$	6.50000	+	11.2583i	0.385704	+	0.668059i
$285$	4.50000	+	7.79423i	0.266557	+	0.461690i
$286$	−7.50000	+	7.79423i	−0.443484	+	0.460882i
$287$		0			0
$288$	−15.0000	+	25.9808i	−0.883883	+	1.53093i
$289$	−13.0000			−0.764706
$290$	−21.0000			−1.23316
$291$	−7.50000	+	12.9904i	−0.439658	+	0.761510i
$292$	6.50000	−	11.2583i	0.380384	−	0.658844i
$293$	5.50000	+	9.52628i	0.321313	+	0.556531i	0.980759	−	0.195221i	$-0.0625424\pi$
$293$	5.50000	+	9.52628i	0.321313	+	0.556531i	−0.659446	+	0.751752i	$0.729209\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$	−6.00000			−0.348743
$297$	13.5000	+	23.3827i	0.783349	+	1.35680i
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$		0			0
$300$	−12.0000			−0.692820
$301$		0			0
$302$	10.5000	−	18.1865i	0.604207	−	1.04652i
$303$	−7.50000	+	12.9904i	−0.430864	+	0.746278i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	−39.0000			−2.23313
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$	9.00000			0.511166
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	−0.964942	−	0.262463i	$-0.915465\pi$
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	0.709771	+	0.704433i	$0.248799\pi$
$312$	−22.5000	+	23.3827i	−1.27381	+	1.32378i
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$	9.50000	−	16.4545i	0.536116	−	0.928580i
$315$		0			0
$316$	−1.50000	−	2.59808i	−0.0843816	−	0.146153i
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$	9.00000			0.504695
$319$	−21.0000			−1.17577
$320$	10.5000	+	18.1865i	0.586968	+	1.01666i
$321$	−12.0000	−	20.7846i	−0.669775	−	1.16008i
$322$		0			0
$323$	−1.00000	+	1.73205i	−0.0556415	+	0.0963739i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−14.0000	−	3.46410i	−0.776580	−	0.192154i
$326$	0.500000	−	0.866025i	0.0276924	−	0.0479647i
$327$	21.0000			1.16130
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$		0			0
$330$	27.0000			1.48630
$331$	14.5000	−	25.1147i	0.796992	−	1.38043i	−0.124574	−	0.992210i	$-0.539757\pi$
$331$	14.5000	−	25.1147i	0.796992	−	1.38043i	0.921567	−	0.388221i	$-0.126910\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$	−6.50000	+	11.2583i	−0.355664	+	0.616028i
$335$	−4.50000	+	7.79423i	−0.245861	+	0.425844i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	−22.5000	+	38.9711i	−1.22203	+	2.11662i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	9.00000			0.487377
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$		0			0
$344$	−10.5000	−	18.1865i	−0.566122	−	0.980552i
$345$		0			0
$346$	9.50000	−	16.4545i	0.510723	−	0.884598i
$347$	−8.00000			−0.429463			−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000			−0.429463			−0.214731	+	0.976673i	$0.568888\pi$
$348$	−21.0000			−1.12572
$349$	11.5000	−	19.9186i	0.615581	−	1.06622i	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	11.5000	−	19.9186i	0.615581	−	1.06622i	0.990282	−	0.139072i	$-0.0444119\pi$
$350$		0			0
$351$	9.00000	+	31.1769i	0.480384	+	1.66410i
$352$	7.50000	+	12.9904i	0.399751	+	0.692390i
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	−0.979202	−	0.202889i	$-0.934967\pi$
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	0.313894	−	0.949458i	$-0.398366\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	19.5000	−	33.7750i	1.03495	−	1.79259i
$356$	6.00000			0.317999
$357$		0			0
$358$	−8.50000	−	14.7224i	−0.449239	−	0.778105i
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	0.549683	−	0.835373i	$-0.314748\pi$
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	−0.998296	+	0.0583530i	$0.981415\pi$
$360$	54.0000			2.84605
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	22.0000			1.15629
$363$	−6.00000			−0.314918
$364$		0			0
$365$	−39.0000			−2.04135
$366$	39.0000			2.03856
$367$	−15.5000	−	26.8468i	−0.809093	−	1.40139i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−15.5000	−	26.8468i	−0.809093	−	1.40139i	0.104399	−	0.994535i	$-0.466708\pi$
$368$		0			0
$369$	9.00000	+	15.5885i	0.468521	+	0.811503i
$370$	3.00000	+	5.19615i	0.155963	+	0.270135i
$371$		0			0
$372$	9.00000			0.466628
$373$	4.50000	−	7.79423i	0.233001	−	0.403570i	−0.725689	−	0.688023i	$-0.758479\pi$
$373$	4.50000	−	7.79423i	0.233001	−	0.403570i	0.958690	+	0.284453i	$0.0918121\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−1.50000	−	2.59808i	−0.0773566	−	0.133986i
$377$	−24.5000	−	6.06218i	−1.26181	−	0.312218i
$378$		0			0
$379$	16.5000	−	28.5788i	0.847548	−	1.46800i	−0.0358418	−	0.999357i	$-0.511411\pi$
$379$	16.5000	−	28.5788i	0.847548	−	1.46800i	0.883390	−	0.468639i	$-0.155255\pi$
$380$	3.00000			0.153897
$381$	33.0000			1.69064
$382$	8.50000	−	14.7224i	0.434898	−	0.753265i
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$	4.50000	+	7.79423i	0.229640	+	0.397748i
$385$		0			0
$386$	−3.50000	−	6.06218i	−0.178145	−	0.308557i
$387$	−42.0000			−2.13498
$388$	2.50000	+	4.33013i	0.126918	+	0.219829i
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	−0.0561516	−	0.998422i	$-0.517883\pi$
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	0.892735	−	0.450582i	$-0.148784\pi$
$390$	31.5000	+	7.79423i	1.59506	+	0.394676i
$391$		0			0
$392$		0			0
$393$	7.50000	−	12.9904i	0.378325	−	0.655278i
$394$	0.500000	−	0.866025i	0.0251896	−	0.0436297i
$395$	−4.50000	+	7.79423i	−0.226420	+	0.392170i
$396$	18.0000			0.904534
$397$	−0.500000	+	0.866025i	−0.0250943	+	0.0434646i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−0.500000	+	0.866025i	−0.0250943	+	0.0434646i	0.853206	+	0.521575i	$0.174655\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$	4.50000	−	7.79423i	0.224440	−	0.388741i
$403$	10.5000	+	2.59808i	0.523042	+	0.129419i
$404$	2.50000	+	4.33013i	0.124380	+	0.215432i
$405$	13.5000	−	23.3827i	0.670820	−	1.16190i
$406$		0			0
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$	9.00000	+	15.5885i	0.445566	+	0.771744i
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$	9.00000			0.444478
$411$	−15.0000	−	25.9808i	−0.739895	−	1.28154i
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	5.00000	+	17.3205i	0.245145	+	0.849208i
$417$	−22.5000	+	38.9711i	−1.10183	+	1.90843i
$418$	−3.00000			−0.146735
$419$	−12.5000	+	21.6506i	−0.610665	+	1.05770i	0.380464	+	0.924796i	$0.375764\pi$
$419$	−12.5000	+	21.6506i	−0.610665	+	1.05770i	−0.991129	+	0.132907i	$0.957569\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	−3.50000	+	6.06218i	−0.170377	+	0.295102i
$423$	−6.00000			−0.291730
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	−4.00000	+	6.92820i	−0.194029	+	0.336067i
$426$	−19.5000	+	33.7750i	−0.944778	+	1.63640i
$427$		0			0
$428$	−8.00000			−0.386695
$429$	31.5000	+	7.79423i	1.52083	+	0.376309i
$430$	−10.5000	+	18.1865i	−0.506355	+	0.877033i
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	0.737057	−	0.675830i	$-0.236215\pi$
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	−0.953815	+	0.300395i	$0.902881\pi$
$432$	−9.00000			−0.433013
$433$	13.5000	+	23.3827i	0.648769	+	1.12370i	0.983417	+	0.181357i	$0.0580490\pi$
$433$	13.5000	+	23.3827i	0.648769	+	1.12370i	−0.334649	+	0.942343i	$0.608618\pi$
$434$		0			0
$435$	31.5000	+	54.5596i	1.51031	+	2.61593i
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$		0			0
$438$	39.0000			1.86349
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$	13.5000	−	23.3827i	0.643587	−	1.11473i
$441$		0			0
$442$	2.00000	+	6.92820i	0.0951303	+	0.329541i
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	0.966591	−	0.256323i	$-0.0825112\pi$
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	−0.705278	+	0.708931i	$0.749178\pi$
$444$	3.00000	+	5.19615i	0.142374	+	0.246598i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$	45.0000			2.12843
$448$		0			0
$449$	−7.50000	−	12.9904i	−0.353947	−	0.613054i	0.632990	−	0.774160i	$-0.281827\pi$
$449$	−7.50000	−	12.9904i	−0.353947	−	0.613054i	−0.986937	+	0.161106i	$0.948494\pi$
$450$	−12.0000	−	20.7846i	−0.565685	−	0.979796i
$451$	9.00000			0.423793
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$	−63.0000			−2.96000
$454$	4.00000			0.187729
$455$		0			0
$456$	−9.00000			−0.421464
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	18.0000			0.840168
$460$		0			0
$461$	17.5000	+	30.3109i	0.815056	+	1.41172i	0.909288	+	0.416169i	$0.136627\pi$
$461$	17.5000	+	30.3109i	0.815056	+	1.41172i	−0.0942312	+	0.995550i	$0.530039\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	3.50000	−	6.06218i	0.162483	−	0.281430i
$465$	−13.5000	−	23.3827i	−0.626048	−	1.08435i
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	0.773611	−	0.633661i	$-0.218448\pi$
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	−0.935572	+	0.353137i	$0.885115\pi$
$468$	21.0000	+	5.19615i	0.970725	+	0.240192i
$469$		0			0
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	−57.0000			−2.62642
$472$	−12.0000			−0.552345
$473$	−10.5000	+	18.1865i	−0.482791	+	0.836218i
$474$	4.50000	−	7.79423i	0.206692	−	0.358001i
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$	−9.00000	−	15.5885i	−0.412082	−	0.713746i
$478$	−4.00000			−0.182956
$479$	−17.5000	−	30.3109i	−0.799595	−	1.38494i	−0.919880	−	0.392200i	$-0.871714\pi$
$479$	−17.5000	−	30.3109i	−0.799595	−	1.38494i	0.120284	−	0.992739i	$-0.461619\pi$
$480$	22.5000	−	38.9711i	1.02698	−	1.77878i
$481$	2.00000	+	6.92820i	0.0911922	+	0.315899i
$482$	26.0000			1.18427
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$	7.50000	−	12.9904i	0.340557	−	0.589863i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	19.5000	−	33.7750i	0.882724	−	1.52892i
$489$	−3.00000			−0.135665
$490$		0			0
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$	9.00000			0.405751
$493$	−7.00000	+	12.1244i	−0.315264	+	0.546054i
$494$	−3.50000	−	0.866025i	−0.157472	−	0.0389643i
$495$	−27.0000	−	46.7654i	−1.21356	−	2.10195i
$496$	−1.50000	+	2.59808i	−0.0673520	+	0.116657i
$497$		0			0
$498$		0			0
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	0.970558	+	0.240866i	$0.0774314\pi$
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	−0.276683	+	0.960961i	$0.589235\pi$
$500$	−3.00000			−0.134164
$501$	39.0000			1.74239
$502$	−11.5000	−	19.9186i	−0.513270	−	0.889010i
$503$	−15.5000	−	26.8468i	−0.691111	−	1.19704i	−0.971474	−	0.237145i	$-0.923788\pi$
$503$	−15.5000	−	26.8468i	−0.691111	−	1.19704i	0.280363	−	0.959894i	$-0.409545\pi$
$504$		0			0
$505$	7.50000	−	12.9904i	0.333746	−	0.578064i
$506$		0			0
$507$	34.5000	+	18.1865i	1.53220	+	0.807692i
$508$	5.50000	−	9.52628i	0.244023	−	0.422660i
$509$	34.0000			1.50702			0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000			1.50702			0.753512	+	0.657434i	$0.228358\pi$
$510$	9.00000	−	15.5885i	0.398527	−	0.690268i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	−4.50000	+	7.79423i	−0.198680	+	0.344124i
$514$	2.00000			0.0882162
$515$	−7.50000	+	12.9904i	−0.330489	+	0.572425i
$516$	−10.5000	+	18.1865i	−0.462237	+	0.800617i
$517$	−1.50000	+	2.59808i	−0.0659699	+	0.114263i
$518$		0			0
$519$	−57.0000			−2.50202
$520$	22.5000	−	23.3827i	0.986690	−	1.02540i
$521$	−8.50000	+	14.7224i	−0.372392	+	0.645001i	−0.989933	−	0.141537i	$-0.954796\pi$
$521$	−8.50000	+	14.7224i	−0.372392	+	0.645001i	0.617541	+	0.786539i	$0.288129\pi$
$522$	−21.0000	−	36.3731i	−0.919145	−	1.59201i
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−2.50000	−	4.33013i	−0.109213	−	0.189162i
$525$		0			0
$526$	13.5000	+	23.3827i	0.588628	+	1.01953i
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$	−4.50000	+	7.79423i	−0.195837	+	0.339200i
$529$	−23.0000			−1.00000
$530$	−9.00000			−0.390935
$531$	−12.0000	+	20.7846i	−0.520756	+	0.901975i
$532$		0			0
$533$	10.5000	+	2.59808i	0.454805	+	0.112535i
$534$	9.00000	+	15.5885i	0.389468	+	0.674579i
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	−25.5000	+	44.1673i	−1.10041	+	1.90596i
$538$	−18.0000			−0.776035
$539$		0			0
$540$	−13.5000	−	23.3827i	−0.580948	−	1.00623i
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	0.922599	+	0.385759i	$0.126061\pi$
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	−0.127222	+	0.991874i	$0.540606\pi$
$542$	16.0000			0.687259
$543$	−33.0000	−	57.1577i	−1.41617	−	2.45287i
$544$	10.0000			0.428746
$545$	−21.0000			−0.899541
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−10.0000			−0.427179
$549$	−39.0000	−	67.5500i	−1.66448	−	2.88296i
$550$	−12.0000			−0.511682
$551$	−3.50000	−	6.06218i	−0.149105	−	0.258257i
$552$		0			0
$553$		0			0
$554$	22.0000			0.934690
$555$	9.00000	−	15.5885i	0.382029	−	0.661693i
$556$	7.50000	+	12.9904i	0.318071	+	0.550915i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$	9.00000	+	15.5885i	0.381000	+	0.659912i
$559$	−17.5000	+	18.1865i	−0.740171	+	0.769208i
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−18.0000			−0.759284
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$	−1.50000	+	2.59808i	−0.0631614	+	0.109399i
$565$	22.5000	−	38.9711i	0.946582	−	1.63953i
$566$	0.500000	+	0.866025i	0.0210166	+	0.0364018i
$567$		0			0
$568$	19.5000	+	33.7750i	0.818202	+	1.41717i
$569$	10.0000			0.419222			0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000			0.419222			0.209611	+	0.977785i	$0.432780\pi$
$570$	4.50000	+	7.79423i	0.188484	+	0.326464i
$571$	−21.5000	+	37.2391i	−0.899747	+	1.55841i	−0.0719297	+	0.997410i	$0.522916\pi$
$571$	−21.5000	+	37.2391i	−0.899747	+	1.55841i	−0.827817	+	0.560998i	$0.810418\pi$
$572$	7.50000	−	7.79423i	0.313591	−	0.325893i
$573$	−51.0000			−2.13056
$574$		0			0
$575$		0			0
$576$	−21.0000	+	36.3731i	−0.875000	+	1.51554i
$577$	−0.500000	+	0.866025i	−0.0208153	+	0.0360531i	−0.876245	−	0.481865i	$-0.839960\pi$
$577$	−0.500000	+	0.866025i	−0.0208153	+	0.0360531i	0.855430	+	0.517918i	$0.173293\pi$
$578$	−13.0000			−0.540729
$579$	−10.5000	+	18.1865i	−0.436365	+	0.755807i
$580$	21.0000			0.871978
$581$		0			0
$582$	−7.50000	+	12.9904i	−0.310885	+	0.538469i
$583$	−9.00000			−0.372742
$584$	19.5000	−	33.7750i	0.806916	−	1.39762i
$585$	−18.0000	−	62.3538i	−0.744208	−	2.57801i
$586$	5.50000	+	9.52628i	0.227203	+	0.393527i
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	0.293640	+	0.955916i	$0.405133\pi$
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	−0.974668	+	0.223659i	$0.928200\pi$
$588$		0			0
$589$	1.50000	+	2.59808i	0.0618064	+	0.107052i
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$	−3.00000			−0.123404
$592$	−2.00000			−0.0821995
$593$	13.5000	+	23.3827i	0.554379	+	0.960212i	0.997952	+	0.0639736i	$0.0203773\pi$
$593$	13.5000	+	23.3827i	0.554379	+	0.960212i	−0.443573	+	0.896238i	$0.646289\pi$
$594$	13.5000	+	23.3827i	0.553912	+	0.959403i
$595$		0			0
$596$	7.50000	−	12.9904i	0.307212	−	0.532107i
$597$	−30.0000	−	51.9615i	−1.22782	−	2.12664i
$598$		0			0
$599$	12.5000	−	21.6506i	0.510736	−	0.884621i	−0.489186	−	0.872179i	$-0.662706\pi$
$599$	12.5000	−	21.6506i	0.510736	−	0.884621i	0.999923	−	0.0124417i	$-0.00396043\pi$
$600$	−36.0000			−1.46969
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$		0			0
$603$	−18.0000			−0.733017
$604$	−10.5000	+	18.1865i	−0.427239	+	0.740000i
$605$	6.00000			0.243935
$606$	−7.50000	+	12.9904i	−0.304667	+	0.527698i
$607$	5.50000	−	9.52628i	0.223238	−	0.386660i	−0.732551	−	0.680712i	$-0.761671\pi$
$607$	5.50000	−	9.52628i	0.223238	−	0.386660i	0.955789	+	0.294052i	$0.0950039\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	−39.0000			−1.57906
$611$	−2.50000	+	2.59808i	−0.101139	+	0.105107i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	−12.0000			−0.484281
$615$	−13.5000	−	23.3827i	−0.544373	−	0.942881i
$616$		0			0
$617$	16.5000	+	28.5788i	0.664265	+	1.15054i	0.979484	+	0.201522i	$0.0645887\pi$
$617$	16.5000	+	28.5788i	0.664265	+	1.15054i	−0.315219	+	0.949019i	$0.602078\pi$
$618$	7.50000	−	12.9904i	0.301694	−	0.522550i
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	−9.00000			−0.361449
$621$		0			0
$622$	−4.50000	+	7.79423i	−0.180434	+	0.312520i
$623$		0			0
$624$	−7.50000	+	7.79423i	−0.300240	+	0.312019i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	−9.50000	+	16.4545i	−0.379091	+	0.656605i
$629$	4.00000			0.159490
$630$		0			0
$631$	−12.5000	−	21.6506i	−0.497617	−	0.861898i	0.502379	−	0.864647i	$-0.332458\pi$
$631$	−12.5000	−	21.6506i	−0.497617	−	0.861898i	−0.999996	+	0.00274930i	$0.999125\pi$
$632$	−4.50000	−	7.79423i	−0.179000	−	0.310038i
$633$	21.0000			0.834675
$634$	4.50000	+	7.79423i	0.178718	+	0.309548i
$635$	−33.0000			−1.30957
$636$	−9.00000			−0.356873
$637$		0			0
$638$	−21.0000			−0.831398
$639$	78.0000			3.08563
$640$	−4.50000	−	7.79423i	−0.177878	−	0.308094i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−12.0000	−	20.7846i	−0.473602	−	0.820303i
$643$	−9.50000	−	16.4545i	−0.374643	−	0.648901i	0.615630	−	0.788035i	$-0.288902\pi$
$643$	−9.50000	−	16.4545i	−0.374643	−	0.648901i	−0.990274	+	0.139134i	$0.955568\pi$
$644$		0			0
$645$	63.0000			2.48062
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$	13.5000	+	23.3827i	0.530330	+	0.918559i
$649$	6.00000	+	10.3923i	0.235521	+	0.407934i
$650$	−14.0000	−	3.46410i	−0.549125	−	0.135873i
$651$		0			0
$652$	−0.500000	+	0.866025i	−0.0195815	+	0.0339162i
$653$	18.0000			0.704394			0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000			0.704394			0.352197	+	0.935926i	$0.385435\pi$
$654$	21.0000			0.821165
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	−39.0000	−	67.5500i	−1.52153	−	2.63538i
$658$		0			0
$659$	−14.5000	−	25.1147i	−0.564840	−	0.978331i	−0.997065	−	0.0765653i	$-0.975605\pi$
$659$	−14.5000	−	25.1147i	−0.564840	−	0.978331i	0.432225	−	0.901766i	$-0.357729\pi$
$660$	−27.0000			−1.05097
$661$	−4.50000	−	7.79423i	−0.175030	−	0.303160i	0.765142	−	0.643862i	$-0.222669\pi$
$661$	−4.50000	−	7.79423i	−0.175030	−	0.303160i	−0.940172	+	0.340701i	$0.889335\pi$
$662$	14.5000	−	25.1147i	0.563559	−	0.976112i
$663$	15.0000	−	15.5885i	0.582552	−	0.605406i
$664$		0			0
$665$		0			0
$666$	−6.00000	+	10.3923i	−0.232495	+	0.402694i
$667$		0			0
$668$	6.50000	−	11.2583i	0.251493	−	0.435598i
$669$	27.0000			1.04388
$670$	−4.50000	+	7.79423i	−0.173850	+	0.301117i
$671$	−39.0000			−1.50558
$672$		0			0
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	−0.135615	−	0.990762i	$-0.543301\pi$
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	0.925832	−	0.377934i	$-0.123365\pi$
$674$	14.0000			0.539260
$675$	−18.0000	+	31.1769i	−0.692820	+	1.20000i
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	3.50000	+	6.06218i	0.134516	+	0.232988i	0.925412	−	0.378962i	$-0.123719\pi$
$677$	3.50000	+	6.06218i	0.134516	+	0.232988i	−0.790897	+	0.611950i	$0.790385\pi$
$678$	−22.5000	+	38.9711i	−0.864107	+	1.49668i
$679$		0			0
$680$	−9.00000	−	15.5885i	−0.345134	−	0.597790i
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$	9.00000			0.344628
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	3.00000	+	5.19615i	0.114708	+	0.198680i
$685$	15.0000	+	25.9808i	0.573121	+	0.992674i
$686$		0			0
$687$	−19.5000	+	33.7750i	−0.743971	+	1.28860i
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$	−10.5000	−	2.59808i	−0.400018	−	0.0989788i
$690$		0			0
$691$	4.00000			0.152167			0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000			0.152167			0.0760836	+	0.997101i	$0.475758\pi$
$692$	−9.50000	+	16.4545i	−0.361136	+	0.625506i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	22.5000	−	38.9711i	0.853474	−	1.47826i
$696$	−63.0000			−2.38801
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	11.5000	−	19.9186i	0.435281	−	0.753930i
$699$	31.5000	−	54.5596i	1.19144	−	2.06363i
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	9.00000	+	31.1769i	0.339683	+	1.17670i
$703$	−1.00000	+	1.73205i	−0.0377157	+	0.0653255i
$704$	10.5000	+	18.1865i	0.395734	+	0.685431i
$705$	9.00000			0.338960
$706$	−12.5000	−	21.6506i	−0.470444	−	0.814832i
$707$		0			0
$708$	6.00000	+	10.3923i	0.225494	+	0.390567i
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$	19.5000	−	33.7750i	0.731822	−	1.26755i
$711$	−18.0000			−0.675053
$712$	18.0000			0.674579
$713$		0			0
$714$		0			0
$715$	−31.5000	−	7.79423i	−1.17803	−	0.291488i
$716$	8.50000	+	14.7224i	0.317660	+	0.550203i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	−8.50000	−	14.7224i	−0.317217	−	0.549436i
$719$	−4.50000	+	7.79423i	−0.167822	+	0.290676i	−0.937654	−	0.347571i	$-0.887007\pi$
$719$	−4.50000	+	7.79423i	−0.167822	+	0.290676i	0.769832	+	0.638247i	$0.220340\pi$
$720$	18.0000			0.670820
$721$		0			0
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	−39.0000	−	67.5500i	−1.45043	−	2.51221i
$724$	−22.0000			−0.817624
$725$	−14.0000	−	24.2487i	−0.519947	−	0.900575i
$726$	−6.00000			−0.222681
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−39.0000			−1.44345
$731$	7.00000	+	12.1244i	0.258904	+	0.448435i
$732$	−39.0000			−1.44148
$733$	−4.50000	−	7.79423i	−0.166211	−	0.287886i	0.770873	−	0.636988i	$-0.219820\pi$
$733$	−4.50000	−	7.79423i	−0.166211	−	0.287886i	−0.937085	+	0.349102i	$0.886487\pi$
$734$	−15.5000	−	26.8468i	−0.572115	−	0.990933i
$735$		0			0
$736$		0			0
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$	9.00000	+	15.5885i	0.331295	+	0.573819i
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	3.00000	+	10.3923i	0.110208	+	0.381771i
$742$		0			0
$743$	−25.5000	+	44.1673i	−0.935504	+	1.62034i	−0.161772	+	0.986828i	$0.551721\pi$
$743$	−25.5000	+	44.1673i	−0.935504	+	1.62034i	−0.773732	+	0.633513i	$0.781612\pi$
$744$	27.0000			0.989868
$745$	−45.0000			−1.64867
$746$	4.50000	−	7.79423i	0.164757	−	0.285367i
$747$		0			0
$748$	−3.00000	−	5.19615i	−0.109691	−	0.189990i
$749$		0			0
$750$	−4.50000	−	7.79423i	−0.164317	−	0.284605i
$751$	28.0000			1.02173			0.510867	−	0.859660i	$-0.329324\pi$
$751$	28.0000			1.02173			0.510867	+	0.859660i	$0.329324\pi$
$752$	−0.500000	−	0.866025i	−0.0182331	−	0.0315807i
$753$	−34.5000	+	59.7558i	−1.25725	+	2.17762i
$754$	−24.5000	−	6.06218i	−0.892237	−	0.220771i
$755$	63.0000			2.29280
$756$		0			0
$757$	−1.50000	+	2.59808i	−0.0545184	+	0.0944287i	−0.891997	−	0.452042i	$-0.850696\pi$
$757$	−1.50000	+	2.59808i	−0.0545184	+	0.0944287i	0.837478	+	0.546471i	$0.184029\pi$
$758$	16.5000	−	28.5788i	0.599307	−	1.03803i
$759$		0			0
$760$	9.00000			0.326464
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	−0.935988	−	0.352032i	$-0.885491\pi$
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	0.772863	+	0.634573i	$0.218824\pi$
$762$	33.0000			1.19546
$763$		0			0
$764$	−8.50000	+	14.7224i	−0.307519	+	0.532639i
$765$	−36.0000			−1.30158
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$	4.00000	+	13.8564i	0.144432	+	0.500326i
$768$	25.5000	+	44.1673i	0.920152	+	1.59375i
$769$	9.50000	−	16.4545i	0.342579	−	0.593364i	−0.642332	−	0.766426i	$-0.722033\pi$
$769$	9.50000	−	16.4545i	0.342579	−	0.593364i	0.984911	+	0.173063i	$0.0553663\pi$
$770$		0			0
$771$	−3.00000	−	5.19615i	−0.108042	−	0.187135i
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$	−42.0000			−1.50966
$775$	6.00000	+	10.3923i	0.215526	+	0.373303i

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} -1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 - 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} -1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 - 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +(1.50000 + 2.59808i) q^{12} +(1.00000 + 3.46410i) q^{13} +(4.50000 - 7.79423i) q^{15} -1.00000 q^{16} +2.00000 q^{17} +(-3.00000 + 5.19615i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 3.46410i) q^{26} +9.00000 q^{27} +(-3.50000 + 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} +(1.50000 - 2.59808i) q^{31} +5.00000 q^{32} +(4.50000 - 7.79423i) q^{33} +2.00000 q^{34} +(3.00000 - 5.19615i) q^{36} +2.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(7.50000 - 7.79423i) q^{39} +(-4.50000 - 7.79423i) q^{40} +(1.50000 - 2.59808i) q^{41} +(3.50000 + 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{44} -18.0000 q^{45} +(0.500000 + 0.866025i) q^{47} +(1.50000 + 2.59808i) q^{48} +(-2.00000 + 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{54} +(-4.50000 + 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +4.00000 q^{59} +(-4.50000 + 7.79423i) q^{60} +(-6.50000 + 11.2583i) q^{61} +(1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-7.50000 + 7.79423i) q^{65} +(4.50000 - 7.79423i) q^{66} +(1.50000 + 2.59808i) q^{67} -2.00000 q^{68} +(-6.50000 - 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} +(-6.50000 + 11.2583i) q^{73} +2.00000 q^{74} +12.0000 q^{75} +(0.500000 - 0.866025i) q^{76} +(7.50000 - 7.79423i) q^{78} +(1.50000 + 2.59808i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +(3.00000 + 5.19615i) q^{85} +(3.50000 + 6.06218i) q^{86} +21.0000 q^{87} +(-4.50000 - 7.79423i) q^{88} -6.00000 q^{89} -18.0000 q^{90} -9.00000 q^{93} +(0.500000 + 0.866025i) q^{94} -3.00000 q^{95} +(-7.50000 - 12.9904i) q^{96} +(-2.50000 - 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 2 q^{13} + 9 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{24} - 4 q^{25} + 2 q^{26} + 18 q^{27} - 7 q^{29} + 9 q^{30} + 3 q^{31} + 10 q^{32} + 9 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{37} - q^{38} + 15 q^{39} - 9 q^{40} + 3 q^{41} + 7 q^{43} - 3 q^{44} - 36 q^{45} + q^{47} + 3 q^{48} - 4 q^{50} - 6 q^{51} - 2 q^{52} - 3 q^{53} + 18 q^{54} - 9 q^{55} + 6 q^{57} - 7 q^{58} + 8 q^{59} - 9 q^{60} - 13 q^{61} + 3 q^{62} + 14 q^{64} - 15 q^{65} + 9 q^{66} + 3 q^{67} - 4 q^{68} - 13 q^{71} + 18 q^{72} - 13 q^{73} + 4 q^{74} + 24 q^{75} + q^{76} + 15 q^{78} + 3 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 6 q^{85} + 7 q^{86} + 42 q^{87} - 9 q^{88} - 12 q^{89} - 36 q^{90} - 18 q^{93} + q^{94} - 6 q^{95} - 15 q^{96} - 5 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 2 * q^13 + 9 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^18 - q^19 - 3 * q^20 + 3 * q^22 + 9 * q^24 - 4 * q^25 + 2 * q^26 + 18 * q^27 - 7 * q^29 + 9 * q^30 + 3 * q^31 + 10 * q^32 + 9 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^37 - q^38 + 15 * q^39 - 9 * q^40 + 3 * q^41 + 7 * q^43 - 3 * q^44 - 36 * q^45 + q^47 + 3 * q^48 - 4 * q^50 - 6 * q^51 - 2 * q^52 - 3 * q^53 + 18 * q^54 - 9 * q^55 + 6 * q^57 - 7 * q^58 + 8 * q^59 - 9 * q^60 - 13 * q^61 + 3 * q^62 + 14 * q^64 - 15 * q^65 + 9 * q^66 + 3 * q^67 - 4 * q^68 - 13 * q^71 + 18 * q^72 - 13 * q^73 + 4 * q^74 + 24 * q^75 + q^76 + 15 * q^78 + 3 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 6 * q^85 + 7 * q^86 + 42 * q^87 - 9 * q^88 - 12 * q^89 - 36 * q^90 - 18 * q^93 + q^94 - 6 * q^95 - 15 * q^96 - 5 * q^97 - 36 * q^99

Introduction

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