LMFDB - Embedded newform 91.2.h.a.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, 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:	$0.726638658394$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			74.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	91.74
Dual form			91.2.h.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.50000 + 2.59808i) q^{3} -1.00000 q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(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} +(2.00000 - 1.73205i) q^{7} -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} +(2.00000 - 1.73205i) q^{14} +(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} +(7.50000 + 2.59808i) q^{21} +(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} +(-2.00000 + 1.73205i) q^{28} +(-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} +(-7.50000 - 2.59808i) q^{35} +(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} +(7.50000 + 2.59808i) q^{42} +(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} +(1.00000 - 6.92820i) q^{49} +(-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} +(-6.00000 + 5.19615i) q^{56} +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} +(3.00000 + 15.5885i) q^{63} +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} +(-7.50000 - 2.59808i) q^{70} +(-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 + 2.59808i) q^{77} +(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} +(-7.50000 - 2.59808i) q^{84} +(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} +(-8.00000 - 5.19615i) q^{91} -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} +(1.00000 - 6.92820i) q^{98} -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} + 4 q^{7} - 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 + 4 * q^7 - 6 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + 4 q^{7} - 6 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 2 q^{13} + 4 q^{14} + 9 q^{15} - 2 q^{16} - 4 q^{17} - 6 q^{18} + q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} - 9 q^{24} - 4 q^{25} - 2 q^{26} - 18 q^{27} - 4 q^{28} - 7 q^{29} + 9 q^{30} - 3 q^{31} + 10 q^{32} - 9 q^{33} - 4 q^{34} - 15 q^{35} + 6 q^{36} + 4 q^{37} + q^{38} + 15 q^{39} + 9 q^{40} - 3 q^{41} + 15 q^{42} + 7 q^{43} - 3 q^{44} + 36 q^{45} - q^{47} - 3 q^{48} + 2 q^{49} - 4 q^{50} - 6 q^{51} + 2 q^{52} - 3 q^{53} - 18 q^{54} + 9 q^{55} - 12 q^{56} + 6 q^{57} - 7 q^{58} - 8 q^{59} - 9 q^{60} + 13 q^{61} - 3 q^{62} + 6 q^{63} + 14 q^{64} - 15 q^{65} - 9 q^{66} + 3 q^{67} + 4 q^{68} - 15 q^{70} - 13 q^{71} + 18 q^{72} + 13 q^{73} + 4 q^{74} - 24 q^{75} - q^{76} + 15 q^{77} + 15 q^{78} + 3 q^{79} + 3 q^{80} - 9 q^{81} - 3 q^{82} - 15 q^{84} + 6 q^{85} + 7 q^{86} - 42 q^{87} - 9 q^{88} + 12 q^{89} + 36 q^{90} - 16 q^{91} - 18 q^{93} - q^{94} - 6 q^{95} + 15 q^{96} + 5 q^{97} + 2 q^{98} - 36 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + 4 * q^7 - 6 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 2 * q^13 + 4 * q^14 + 9 * q^15 - 2 * q^16 - 4 * q^17 - 6 * q^18 + q^19 + 3 * q^20 + 15 * q^21 + 3 * q^22 - 9 * q^24 - 4 * q^25 - 2 * q^26 - 18 * q^27 - 4 * q^28 - 7 * q^29 + 9 * q^30 - 3 * q^31 + 10 * q^32 - 9 * q^33 - 4 * q^34 - 15 * q^35 + 6 * q^36 + 4 * q^37 + q^38 + 15 * q^39 + 9 * q^40 - 3 * q^41 + 15 * q^42 + 7 * q^43 - 3 * q^44 + 36 * q^45 - q^47 - 3 * q^48 + 2 * q^49 - 4 * q^50 - 6 * q^51 + 2 * q^52 - 3 * q^53 - 18 * q^54 + 9 * q^55 - 12 * q^56 + 6 * q^57 - 7 * q^58 - 8 * q^59 - 9 * q^60 + 13 * q^61 - 3 * q^62 + 6 * q^63 + 14 * q^64 - 15 * q^65 - 9 * q^66 + 3 * q^67 + 4 * q^68 - 15 * q^70 - 13 * q^71 + 18 * q^72 + 13 * q^73 + 4 * q^74 - 24 * q^75 - q^76 + 15 * q^77 + 15 * q^78 + 3 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 - 15 * q^84 + 6 * q^85 + 7 * q^86 - 42 * q^87 - 9 * q^88 + 12 * q^89 + 36 * q^90 - 16 * q^91 - 18 * q^93 - q^94 - 6 * q^95 + 15 * q^96 + 5 * q^97 + 2 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	$0.166667\pi$
$3$	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	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	1.50000	+	2.59808i	0.612372	+	1.06066i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	−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
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	4.50000	−	7.79423i	1.16190	−	2.01246i
$16$	−1.00000			−0.250000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$	7.50000	+	2.59808i	1.63663	+	0.566947i
$22$	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
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−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	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	5.00000			0.883883
$33$	−4.50000	+	7.79423i	−0.783349	+	1.35680i
$34$	−2.00000			−0.342997
$35$	−7.50000	−	2.59808i	−1.26773	−	0.439155i
$36$	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	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	7.50000	+	2.59808i	1.15728	+	0.400892i
$43$	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	0.827253	−	0.561830i	$-0.189902\pi$
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	−0.900185	+	0.435507i	$0.856569\pi$
$48$	−1.50000	−	2.59808i	−0.216506	−	0.375000i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−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
$56$	−6.00000	+	5.19615i	−0.801784	+	0.694365i
$57$	3.00000			0.397360
$58$	−3.50000	+	6.06218i	−0.459573	+	0.796003i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$	−4.50000	+	7.79423i	−0.580948	+	1.00623i
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	−1.50000	+	2.59808i	−0.190500	+	0.329956i
$63$	3.00000	+	15.5885i	0.377964	+	1.96396i
$64$	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
$70$	−7.50000	−	2.59808i	−0.896421	−	0.310530i
$71$	−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	$-0.558156\pi$
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	0.942455	−	0.334332i	$-0.108511\pi$
$74$	2.00000			0.232495
$75$	−12.0000			−1.38564
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$	7.50000	+	2.59808i	0.854704	+	0.296078i
$78$	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	$0.5\pi$
$84$	−7.50000	−	2.59808i	−0.818317	−	0.283473i
$85$	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	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	18.0000			1.89737
$91$	−8.00000	−	5.19615i	−0.838628	−	0.544705i
$92$		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	0.964579	−	0.263795i	$-0.0849741\pi$
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	−0.710742	+	0.703452i	$0.751641\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−18.0000			−1.80907
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$	3.00000	+	10.3923i	0.294174	+	1.01905i
$105$	−4.50000	−	23.3827i	−0.439155	−	2.28192i
$106$	−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
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−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
$119$	−4.00000	+	3.46410i	−0.366679	+	0.317554i
$120$	−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
$126$	3.00000	+	15.5885i	0.267261	+	1.38873i
$127$	−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	0.735901	−	0.677089i	$-0.236759\pi$
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	−0.954327	+	0.298764i	$0.903426\pi$
$132$	4.50000	−	7.79423i	0.391675	−	0.678401i
$133$	−0.500000	−	2.59808i	−0.0433555	−	0.225282i
$134$	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	$0.0528040\pi$
$139$	7.50000	+	12.9904i	0.636142	+	1.10183i	−0.350130	+	0.936701i	$0.613863\pi$
$140$	7.50000	+	2.59808i	0.633866	+	0.219578i
$141$	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
$147$	19.5000	−	7.79423i	1.60833	−	0.642857i
$148$	−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
$154$	7.50000	+	2.59808i	0.604367	+	0.209359i
$155$	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	$0.440579\pi$
$157$	−9.50000	+	16.4545i	−0.758183	+	1.31321i	−0.943777	+	0.330584i	$0.892754\pi$
$158$	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	$-0.665568\pi$
$167$	6.50000	−	11.2583i	0.502985	−	0.871196i	0.999994	−	0.00345033i	$-0.00109828\pi$
$168$	−22.5000	−	7.79423i	−1.73591	−	0.601338i
$169$	−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	$0.423569\pi$
$173$	−9.50000	+	16.4545i	−0.722272	+	1.25101i	−0.960087	+	0.279701i	$0.909765\pi$
$174$	−21.0000			−1.59201
$175$	2.00000	+	10.3923i	0.151186	+	0.785584i
$176$	−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	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−8.00000	−	5.19615i	−0.592999	−	0.385164i
$183$	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
$189$	−18.0000	+	15.5885i	−1.30931	+	1.13389i
$190$	−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
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$	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	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$	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
$203$	3.50000	+	18.1865i	0.245652	+	1.27644i
$204$	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
$210$	−4.50000	−	23.3827i	−0.310530	−	1.61356i
$211$	−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
$217$	1.50000	+	7.79423i	0.101827	+	0.529107i
$218$	−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	−0.675098	−	0.737728i	$-0.735899\pi$
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	0.976440	+	0.215788i	$0.0692320\pi$
$224$	10.0000	−	8.66025i	0.668153	−	0.578638i
$225$	−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	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$	−3.00000			−0.198680
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$		0			0
$231$	4.50000	+	23.3827i	0.296078	+	1.53847i
$232$	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
$238$	−4.00000	+	3.46410i	−0.259281	+	0.224544i
$239$	−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	$-0.815928\pi$
$241$	−26.0000			−1.67481			−0.837404	+	0.546585i	$0.815928\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	−6.50000	+	11.2583i	−0.416120	+	0.720741i
$245$	−19.5000	+	7.79423i	−1.24581	+	0.497955i
$246$	−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	$0.0918976\pi$
$251$	11.5000	+	19.9186i	0.725874	+	1.25725i	−0.232740	+	0.972539i	$0.574769\pi$
$252$	−3.00000	−	15.5885i	−0.188982	−	0.981981i
$253$		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	$-0.519869\pi$
$257$	−2.00000			−0.124757			−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−10.5000	+	18.1865i	−0.653701	+	1.13224i
$259$	4.00000	−	3.46410i	0.248548	−	0.215249i
$260$	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
$266$	−0.500000	−	2.59808i	−0.0306570	−	0.159298i
$267$	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	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$	13.5000	+	23.3827i	0.821584	+	1.42302i
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	2.00000			0.121268
$273$	1.50000	−	28.5788i	0.0907841	−	1.72967i
$274$	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
$280$	22.5000	+	7.79423i	1.34463	+	0.465794i
$281$	−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	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$	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
$287$	1.50000	+	7.79423i	0.0885422	+	0.460079i
$288$	−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	0.659446	−	0.751752i	$-0.270791\pi$
$293$	−5.50000	−	9.52628i	−0.321313	−	0.556531i	−0.980759	+	0.195221i	$0.937458\pi$
$294$	19.5000	−	7.79423i	1.13726	−	0.454569i
$295$	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
$301$	17.5000	+	6.06218i	1.00868	+	0.349418i
$302$	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	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	−7.50000	−	2.59808i	−0.427352	−	0.148039i
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$	9.00000			0.511166
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	−0.709771	−	0.704433i	$-0.751201\pi$
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	0.964942	+	0.262463i	$0.0845347\pi$
$312$	−22.5000	+	23.3827i	−1.27381	+	1.32378i
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$	−9.50000	+	16.4545i	−0.536116	+	0.928580i
$315$	36.0000	−	31.1769i	2.02837	−	1.75662i
$316$	−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
$329$	−2.50000	−	0.866025i	−0.137829	−	0.0477455i
$330$	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
$336$	−7.50000	−	2.59808i	−0.409159	−	0.141737i
$337$	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
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−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	$0.377745\pi$
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	2.00000	+	10.3923i	0.106904	+	0.555492i
$351$	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	$0.0650330\pi$
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	−0.313894	+	0.949458i	$0.601634\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	−19.5000	+	33.7750i	−1.03495	+	1.79259i
$356$	−6.00000			−0.317999
$357$	−15.0000	−	5.19615i	−0.793884	−	0.275010i
$358$	−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
$364$	8.00000	+	5.19615i	0.419314	+	0.272352i
$365$	−39.0000			−2.04135
$366$	39.0000			2.03856
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	0.913493	+	0.406855i	$0.133375\pi$
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	−0.104399	+	0.994535i	$0.533292\pi$
$368$		0			0
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	−3.00000	−	5.19615i	−0.155963	−	0.270135i
$371$	1.50000	+	7.79423i	0.0778761	+	0.404656i
$372$	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
$378$	−18.0000	+	15.5885i	−0.925820	+	0.801784i
$379$	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	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	−4.50000	−	7.79423i	−0.229640	−	0.397748i
$385$	−4.50000	−	23.3827i	−0.229341	−	1.19169i
$386$	−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
$392$	−3.00000	+	20.7846i	−0.151523	+	1.04978i
$393$	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	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	0.878300	+	0.478110i	$0.158678\pi$
$398$	−20.0000			−1.00251
$399$	6.00000	−	5.19615i	0.300376	−	0.260133i
$400$	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
$406$	3.50000	+	18.1865i	0.173702	+	0.902583i
$407$	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	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	9.00000			0.444478
$411$	15.0000	+	25.9808i	0.739895	+	1.28154i
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$	−8.00000	+	6.92820i	−0.393654	+	0.340915i
$414$		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	$-0.624236\pi$
$419$	12.5000	−	21.6506i	0.610665	−	1.05770i	0.991129	−	0.132907i	$-0.0424311\pi$
$420$	4.50000	+	23.3827i	0.219578	+	1.14096i
$421$	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
$427$	−6.50000	−	33.7750i	−0.314557	−	1.63449i
$428$	−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	$-0.941951\pi$
$433$	−13.5000	−	23.3827i	−0.648769	−	1.12370i	0.334649	−	0.942343i	$-0.391382\pi$
$434$	1.50000	+	7.79423i	0.0720023	+	0.374135i
$435$	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	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$	−13.5000	+	23.3827i	−0.643587	+	1.11473i
$441$	33.0000	+	25.9808i	1.57143	+	1.23718i
$442$	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
$448$	14.0000	−	12.1244i	0.661438	−	0.572822i
$449$	−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
$455$	−1.50000	+	28.5788i	−0.0703211	+	1.33980i
$456$	−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	$-0.863373\pi$
$461$	−17.5000	−	30.3109i	−0.815056	−	1.41172i	0.0942312	−	0.995550i	$-0.469961\pi$
$462$	4.50000	+	23.3827i	0.209359	+	1.08786i
$463$	−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	0.935572	−	0.353137i	$-0.114885\pi$
$467$	3.50000	+	6.06218i	0.161961	+	0.280524i	−0.773611	+	0.633661i	$0.781552\pi$
$468$	−21.0000	−	5.19615i	−0.970725	−	0.240192i
$469$	7.50000	+	2.59808i	0.346318	+	0.119968i
$470$	−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
$476$	4.00000	−	3.46410i	0.183340	−	0.158777i
$477$	−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	$0.128286\pi$
$479$	17.5000	+	30.3109i	0.799595	+	1.38494i	−0.120284	+	0.992739i	$0.538381\pi$
$480$	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
$490$	−19.5000	+	7.79423i	−0.880920	+	0.352107i
$491$	−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
$497$	−32.5000	−	11.2583i	−1.45782	−	0.505005i
$498$		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	$0.0762117\pi$
$503$	15.5000	+	26.8468i	0.691111	+	1.19704i	−0.280363	+	0.959894i	$0.590455\pi$
$504$	−9.00000	−	46.7654i	−0.400892	−	2.08310i
$505$	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	$-0.771642\pi$
$509$	−34.0000			−1.50702			−0.753512	+	0.657434i	$0.771642\pi$
$510$	−9.00000	+	15.5885i	−0.398527	+	0.690268i
$511$	−6.50000	−	33.7750i	−0.287543	−	1.49412i
$512$	−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
$518$	4.00000	−	3.46410i	0.175750	−	0.152204i
$519$	−57.0000			−2.50202
$520$	22.5000	−	23.3827i	0.986690	−	1.02540i
$521$	8.50000	−	14.7224i	0.372392	−	0.645001i	−0.617541	−	0.786539i	$-0.711871\pi$
$521$	8.50000	−	14.7224i	0.372392	−	0.645001i	0.989933	+	0.141537i	$0.0452044\pi$
$522$	−21.0000	−	36.3731i	−0.919145	−	1.59201i
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$	2.50000	+	4.33013i	0.109213	+	0.189162i
$525$	−24.0000	+	20.7846i	−1.04745	+	0.907115i
$526$	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
$532$	0.500000	+	2.59808i	0.0216777	+	0.112641i
$533$	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
$539$	19.5000	−	7.79423i	0.839924	−	0.335721i
$540$	−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
$546$	1.50000	−	28.5788i	0.0641941	−	1.22306i
$547$	−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
$553$	7.50000	+	2.59808i	0.318932	+	0.110481i
$554$	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
$560$	7.50000	+	2.59808i	0.316933	+	0.109789i
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−18.0000			−0.759284
$563$	4.00000			0.168580			0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000			0.168580			0.0842900	+	0.996441i	$0.473138\pi$
$564$	−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
$567$	−22.5000	−	7.79423i	−0.944911	−	0.327327i
$568$	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
$574$	1.50000	+	7.79423i	0.0626088	+	0.325325i
$575$		0			0
$576$	−21.0000	+	36.3731i	−0.875000	+	1.51554i
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	−0.855430	−	0.517918i	$-0.826707\pi$
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	0.876245	+	0.481865i	$0.160040\pi$
$578$	−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	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$	−19.5000	+	7.79423i	−0.804166	+	0.321429i
$589$	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	$-0.979623\pi$
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	0.443573	−	0.896238i	$-0.353711\pi$
$594$	−13.5000	−	23.3827i	−0.553912	−	0.959403i
$595$	15.0000	+	5.19615i	0.614940	+	0.213021i
$596$	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	$0.419712\pi$
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	−0.963405	+	0.268049i	$0.913621\pi$
$602$	17.5000	+	6.06218i	0.713247	+	0.247076i
$603$	−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	−0.955789	−	0.294052i	$-0.904996\pi$
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	0.732551	+	0.680712i	$0.238329\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$	−42.0000	+	36.3731i	−1.70193	+	1.47391i
$610$	−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
$616$	−22.5000	−	7.79423i	−0.906551	−	0.314038i
$617$	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	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$	−9.00000			−0.361449
$621$		0			0
$622$	4.50000	−	7.79423i	0.180434	−	0.312520i
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$	−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
$630$	36.0000	−	31.1769i	1.43427	−	1.24212i
$631$	−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
$637$	−25.0000	+	3.46410i	−0.990536	+	0.137253i
$638$	−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	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$		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	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	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
$651$	−18.0000	+	15.5885i	−0.705476	+	0.610960i
$652$	−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
$658$	−2.50000	−	0.866025i	−0.0974601	−	0.0337612i
$659$	−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	0.940172	−	0.340701i	$-0.110665\pi$
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	−0.765142	+	0.643862i	$0.777331\pi$
$662$	14.5000	−	25.1147i	0.563559	−	0.976112i
$663$	−15.0000	+	15.5885i	−0.582552	+	0.605406i
$664$		0			0
$665$	−6.00000	+	5.19615i	−0.232670	+	0.201498i
$666$	−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
$672$	37.5000	+	12.9904i	1.44659	+	0.501115i
$673$	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	0.790897	−	0.611950i	$-0.209615\pi$
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	−0.925412	+	0.378962i	$0.876281\pi$
$678$	22.5000	−	38.9711i	0.864107	−	1.49668i
$679$	12.5000	+	4.33013i	0.479706	+	0.166175i
$680$	−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
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$	−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	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$	9.50000	−	16.4545i	0.361136	−	0.625506i
$693$	−36.0000	+	31.1769i	−1.36753	+	1.18431i
$694$	−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
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	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
$707$	12.5000	+	4.33013i	0.470111	+	0.162851i
$708$	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
$714$	−15.0000	−	5.19615i	−0.561361	−	0.194461i
$715$	−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	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$	−18.0000			−0.670820
$721$	−12.5000	−	4.33013i	−0.465524	−	0.161262i
$722$	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	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	24.0000	+	15.5885i	0.889499	+	0.577747i
$729$	−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	0.937085	−	0.349102i	$-0.113513\pi$
$733$	4.50000	+	7.79423i	0.166211	+	0.287886i	−0.770873	+	0.636988i	$0.780180\pi$
$734$	15.5000	+	26.8468i	0.572115	+	0.990933i
$735$	−49.5000	−	38.9711i	−1.82584	−	1.43747i
$736$		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
$742$	1.50000	+	7.79423i	0.0550667	+	0.286135i
$743$	−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
$749$	16.0000	−	13.8564i	0.584627	−	0.506302i
$750$	−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
$756$	18.0000	−	15.5885i	0.654654	−	0.566947i
$757$	−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	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$	−33.0000			−1.19546
$763$	3.50000	+	18.1865i	0.126709	+	0.658397i
$764$	−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	−0.984911	−	0.173063i	$-0.944634\pi$
$769$	−9.50000	+	16.4545i	−0.342579	+	0.593364i	0.642332	+	0.766426i	$0.277967\pi$
$770$	−4.50000	−	23.3827i	−0.162169	−	0.842654i
$771$	−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	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$	−42.0000			−1.50966
$775$	−6.00000	−	10.3923i	−0.215526	−	0.373303i
$776$	−7.50000	−	12.9904i	−0.269234	−	0.466328i
$777$	15.0000	+	5.19615i	0.538122	+	0.186411i
$778$	16.5000	−	28.5788i	0.591554	−	1.02460i
$779$	1.50000	+	2.59808i	0.0537431	+	0.0930857i
$780$	31.5000	+	7.79423i	1.12788	+	0.279078i
$781$	19.5000	−	33.7750i	0.697765	−	1.20856i
$782$		0			0
$783$	31.5000	−	54.5596i	1.12572	−	1.94980i
$784$	−1.00000	+	6.92820i	−0.0357143	+	0.247436i
$785$	57.0000			2.03442
$786$	7.50000	−	12.9904i	0.267516	−	0.463352i
$787$	−20.0000			−0.712923			−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000			−0.712923			−0.356462	+	0.934310i	$0.616017\pi$
$788$	−0.500000	+	0.866025i	−0.0178118	+	0.0308509i
$789$	−40.5000	+	70.1481i	−1.44184	+	2.49734i
$790$	4.50000	−	7.79423i	0.160103	−	0.277306i
$791$	−37.5000	−	12.9904i	−1.33335	−	0.461885i
$792$	54.0000			1.91881
$793$	−45.5000	−	11.2583i	−1.61575	−	0.399795i
$794$	0.500000	−	0.866025i	0.0177443	−	0.0307341i
$795$	13.5000	+	23.3827i	0.478796	+	0.829298i
$796$	20.0000			0.708881
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$	6.00000	−	5.19615i	0.212398	−	0.183942i
$799$	1.00000	+	1.73205i	0.0353775	+	0.0612756i
$800$	−10.0000	+	17.3205i	−0.353553	+	0.612372i
$801$	−18.0000	+	31.1769i	−0.635999	+	1.10158i
$802$	−2.00000			−0.0706225
$803$	39.0000			1.37628
$804$	4.50000	−	7.79423i	0.158703	−	0.274881i
$805$		0			0
$806$	10.5000	+	2.59808i	0.369847	+	0.0915133i
$807$	27.0000	+	46.7654i	0.950445	+	1.64622i
$808$	−7.50000	−	12.9904i	−0.263849	−	0.457000i
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	0.752995	−	0.658026i	$-0.228608\pi$
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	−0.946365	+	0.323100i	$0.895275\pi$
$810$	−13.5000	+	23.3827i	−0.474342	+	0.821584i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−3.50000	−	18.1865i	−0.122826	−	0.638222i
$813$	−24.0000	−	41.5692i	−0.841717	−	1.45790i
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$	−3.00000			−0.105085
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	7.00000			0.244899
$818$	14.0000			0.489499
$819$	51.0000	−	25.9808i	1.78208	−	0.907841i
$820$	−9.00000			−0.314294
$821$	−54.0000			−1.88461			−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000			−1.88461			−0.942306	+	0.334751i	$0.891348\pi$
$822$	15.0000	+	25.9808i	0.523185	+	0.906183i
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$	7.50000	+	12.9904i	0.261275	+	0.452541i
$825$	−18.0000	−	31.1769i	−0.626680	−	1.08544i
$826$	−8.00000	+	6.92820i	−0.278356	+	0.241063i
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		0			0
$831$	33.0000	+	57.1577i	1.14476	+	1.98278i
$832$	−7.00000	−	24.2487i	−0.242681	−	0.840673i
$833$	−2.00000	+	13.8564i	−0.0692959	+	0.480096i
$834$	−22.5000	+	38.9711i	−0.779111	+	1.34946i
$835$	−39.0000			−1.34965
$836$	−3.00000			−0.103757
$837$	13.5000	−	23.3827i	0.466628	−	0.808224i
$838$	12.5000	−	21.6506i	0.431805	−	0.747909i
$839$	−18.5000	−	32.0429i	−0.638691	−	1.10625i	−0.985720	−	0.168391i	$-0.946143\pi$
$839$	−18.5000	−	32.0429i	−0.638691	−	1.10625i	0.347029	−	0.937854i	$-0.387190\pi$
$840$	13.5000	+	70.1481i	0.465794	+	2.42034i
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	18.0000			0.620321
$843$	−27.0000	−	46.7654i	−0.929929	−	1.61068i
$844$	3.50000	−	6.06218i	0.120475	−	0.208669i
$845$	34.5000	+	18.1865i	1.18684	+	0.625636i
$846$	6.00000			0.206284
$847$	−1.00000	−	5.19615i	−0.0343604	−	0.178542i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$	1.50000	−	2.59808i	0.0514799	−	0.0891657i
$850$	4.00000	−	6.92820i	0.137199	−	0.237635i
$851$		0			0
$852$	−19.5000	+	33.7750i	−0.668059	+	1.15711i
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$	−6.50000	−	33.7750i	−0.222425	−	1.15576i
$855$	9.00000	−	15.5885i	0.307794	−	0.533114i
$856$	−24.0000			−0.820303
$857$	16.5000	−	28.5788i	0.563629	−	0.976235i	−0.433546	−	0.901131i	$-0.642738\pi$
$857$	16.5000	−	28.5788i	0.563629	−	0.976235i	0.997176	−	0.0751033i	$-0.0239287\pi$
$858$	31.5000	+	7.79423i	1.07539	+	0.266091i
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	0.570064	−	0.821600i	$-0.306918\pi$
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	−0.996559	+	0.0828900i	$0.973585\pi$
$860$	−10.5000	+	18.1865i	−0.358047	+	0.620156i
$861$	−18.0000	+	15.5885i	−0.613438	+	0.531253i
$862$	−4.50000	−	7.79423i	−0.153271	−	0.265472i
$863$	−18.5000	−	32.0429i	−0.629747	−	1.09075i	−0.987602	−	0.156977i	$-0.949825\pi$
$863$	−18.5000	−	32.0429i	−0.629747	−	1.09075i	0.357855	−	0.933777i	$-0.383508\pi$
$864$	−45.0000			−1.53093
$865$	57.0000			1.93806
$866$	−13.5000	−	23.3827i	−0.458749	−	0.794576i
$867$	−19.5000	−	33.7750i	−0.662255	−	1.14706i
$868$	−1.50000	−	7.79423i	−0.0509133	−	0.264553i
$869$	−4.50000	+	7.79423i	−0.152652	+	0.264401i
$870$	31.5000	+	54.5596i	1.06795	+	1.84974i
$871$	7.50000	−	7.79423i	0.254128	−	0.264097i
$872$	10.5000	−	18.1865i	0.355575	−	0.615874i
$873$	−30.0000			−1.01535
$874$		0			0
$875$	−6.00000	+	5.19615i	−0.202837	+	0.175662i
$876$	−39.0000			−1.31769
$877$	22.5000	−	38.9711i	0.759771	−	1.31596i	−0.183196	−	0.983076i	$-0.558644\pi$
$877$	22.5000	−	38.9711i	0.759771	−	1.31596i	0.942967	−	0.332886i	$-0.108022\pi$
$878$	−16.0000			−0.539974
$879$	16.5000	−	28.5788i	0.556531	−	0.963940i
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	−0.964263	−	0.264946i	$-0.914646\pi$
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	0.711582	+	0.702603i	$0.247979\pi$
$882$	33.0000	+	25.9808i	1.11117	+	0.874818i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−2.00000	−	6.92820i	−0.0672673	−	0.233021i
$885$	−18.0000	+	31.1769i	−0.605063	+	1.04800i
$886$	5.50000	+	9.52628i	0.184776	+	0.320042i
$887$	24.0000			0.805841			0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000			0.805841			0.402921	+	0.915235i	$0.367995\pi$
$888$	−9.00000	−	15.5885i	−0.302020	−	0.523114i
$889$	5.50000	+	28.5788i	0.184464	+	0.958503i
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$	−4.50000	+	7.79423i	−0.150671	+	0.260970i
$893$	−1.00000			−0.0334637
$894$	−45.0000			−1.50503
$895$	−25.5000	+	44.1673i	−0.852371	+	1.47635i
$896$	−6.00000	+	5.19615i	−0.200446	+	0.173591i
$897$		0			0
$898$	−7.50000	−	12.9904i	−0.250278	−	0.433495i
$899$	−10.5000	−	18.1865i	−0.350195	−	0.606555i
$900$	12.0000	+	20.7846i	0.400000	+	0.692820i
$901$	3.00000	−	5.19615i	0.0999445	−	0.173109i
$902$	−9.00000			−0.299667
$903$	10.5000	+	54.5596i	0.349418	+	1.81563i
$904$	22.5000	+	38.9711i	0.748339	+	1.29616i
$905$	33.0000	+	57.1577i	1.09696	+	1.89999i
$906$	63.0000			2.09303
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	0.931764	+	0.363064i	$0.118269\pi$
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	−0.151460	+	0.988463i	$0.548397\pi$
$908$	4.00000			0.132745
$909$	−30.0000			−0.995037
$910$	−1.50000	+	28.5788i	−0.0497245	+	0.947379i
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−3.00000			−0.0993399
$913$		0			0
$914$	−18.0000			−0.595387
$915$	−58.5000	−	101.325i	−1.93395	−	3.34970i
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$	−12.5000	−	4.33013i	−0.412786	−	0.142993i
$918$	18.0000			0.594089
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	−0.582808	−	0.812610i	$-0.698046\pi$
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	0.995145	+	0.0984214i	$0.0313793\pi$
$920$		0			0
$921$	18.0000	+	31.1769i	0.593120	+	1.02731i
$922$	−17.5000	−	30.3109i	−0.576332	−	0.998236i
$923$	−32.5000	+	33.7750i	−1.06975	+	1.11172i
$924$	−4.50000	−	23.3827i	−0.148039	−	0.769234i
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	−8.00000			−0.262896
$927$	30.0000			0.985329
$928$	−17.5000	+	30.3109i	−0.574466	+	0.995004i
$929$	6.50000	−	11.2583i	0.213258	−	0.369374i	−0.739474	−	0.673185i	$-0.764926\pi$
$929$	6.50000	−	11.2583i	0.213258	−	0.369374i	0.952732	+	0.303811i	$0.0982592\pi$
$930$	13.5000	+	23.3827i	0.442682	+	0.766748i
$931$	−5.50000	−	4.33013i	−0.180255	−	0.141914i
$932$	−10.5000	−	18.1865i	−0.343939	−	0.595720i
$933$	27.0000			0.883940
$934$	3.50000	+	6.06218i	0.114523	+	0.198361i
$935$	−9.00000	+	15.5885i	−0.294331	+	0.509797i
$936$	−63.0000	−	15.5885i	−2.05922	−	0.509525i
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	7.50000	+	2.59808i	0.244884	+	0.0848302i
$939$	28.5000	−	49.3634i	0.930062	−	1.61092i
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$	8.50000	−	14.7224i	0.277092	−	0.479938i	−0.693569	−	0.720390i	$-0.743963\pi$
$941$	8.50000	−	14.7224i	0.277092	−	0.479938i	0.970661	+	0.240453i	$0.0772960\pi$
$942$	−57.0000			−1.85716
$943$		0			0
$944$	4.00000			0.130189
$945$	67.5000	+	23.3827i	2.19578	+	0.760639i
$946$	−10.5000	+	18.1865i	−0.341384	+	0.591295i
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	4.50000	−	7.79423i	0.146153	−	0.253145i
$949$	−45.5000	−	11.2583i	−1.47699	−	0.365461i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$	−13.5000	+	23.3827i	−0.437767	+	0.758236i
$952$	12.0000	−	10.3923i	0.388922	−	0.336817i
$953$	16.5000	+	28.5788i	0.534487	+	0.925759i	0.999188	+	0.0402915i	$0.0128286\pi$
$953$	16.5000	+	28.5788i	0.534487	+	0.925759i	−0.464701	+	0.885468i	$0.653838\pi$
$954$	−9.00000	−	15.5885i	−0.291386	−	0.504695i
$955$	−51.0000			−1.65032
$956$	4.00000			0.129369
$957$	−31.5000	−	54.5596i	−1.01825	−	1.76366i
$958$	17.5000	+	30.3109i	0.565399	+	0.979300i
$959$	20.0000	−	17.3205i	0.645834	−	0.559308i
$960$	31.5000	−	54.5596i	1.01666	−	1.76090i
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	−2.00000	−	6.92820i	−0.0644826	−	0.223374i
$963$	−24.0000	+	41.5692i	−0.773389	+	1.33955i
$964$	26.0000			0.837404
$965$	−10.5000	+	18.1865i	−0.338007	+	0.585445i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−3.00000	+	5.19615i	−0.0964237	+	0.167011i
$969$	−6.00000			−0.192748
$970$	7.50000	−	12.9904i	0.240810	−	0.417096i
$971$	0.500000	−	0.866025i	0.0160458	−	0.0277921i	−0.857891	−	0.513832i	$-0.828226\pi$
$971$	0.500000	−	0.866025i	0.0160458	−	0.0277921i	0.873937	+	0.486040i	$0.161559\pi$
$972$		0			0
$973$	37.5000	+	12.9904i	1.20219	+	0.416452i
$974$	16.0000			0.512673
$975$	12.0000	+	41.5692i	0.384308	+	1.33128i
$976$	−6.50000	+	11.2583i	−0.208060	+	0.360370i
$977$	2.50000	+	4.33013i	0.0799821	+	0.138533i	0.903242	−	0.429132i	$-0.141180\pi$
$977$	2.50000	+	4.33013i	0.0799821	+	0.138533i	−0.823260	+	0.567665i	$0.807847\pi$
$978$	3.00000			0.0959294
$979$	9.00000	+	15.5885i	0.287641	+	0.498209i
$980$	19.5000	−	7.79423i	0.622905	−	0.248978i
$981$	−21.0000	−	36.3731i	−0.670478	−	1.16130i
$982$	−7.50000	+	12.9904i	−0.239335	+	0.414540i
$983$	−23.5000	+	40.7032i	−0.749534	+	1.29823i	0.198513	+	0.980098i	$0.436389\pi$
$983$	−23.5000	+	40.7032i	−0.749534	+	1.29823i	−0.948046	+	0.318132i	$0.896944\pi$
$984$	27.0000			0.860729
$985$	−3.00000			−0.0955879
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$	−1.50000	−	7.79423i	−0.0477455	−	0.248093i
$988$	3.50000	+	0.866025i	0.111350	+	0.0275519i
$989$		0			0
$990$	27.0000	+	46.7654i	0.858116	+	1.48630i
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	0.744124	−	0.668042i	$-0.232867\pi$
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	−0.950603	+	0.310409i	$0.899534\pi$
$992$	−7.50000	+	12.9904i	−0.238125	+	0.412445i
$993$	87.0000			2.76086
$994$	−32.5000	−	11.2583i	−1.03084	−	0.357093i
$995$	30.0000	+	51.9615i	0.951064	+	1.64729i
$996$		0			0
$997$	2.00000			0.0633406			0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000			0.0633406			0.0316703	+	0.999498i	$0.489917\pi$
$998$	15.5000	+	26.8468i	0.490644	+	0.849820i
$999$	−18.0000			−0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.h.a.74.1	yes	2
3.2	odd	2		819.2.s.a.802.1		2
7.2	even	3		91.2.g.a.9.1	✓	2
7.3	odd	6		637.2.f.a.295.1		2
7.4	even	3		637.2.f.b.295.1		2
7.5	odd	6		637.2.g.a.373.1		2
7.6	odd	2		637.2.h.a.165.1		2
13.3	even	3		91.2.g.a.81.1	yes	2
13.4	even	6		1183.2.e.c.508.1		2
13.9	even	3		1183.2.e.a.508.1		2
21.2	odd	6		819.2.n.c.100.1		2
39.29	odd	6		819.2.n.c.172.1		2
91.3	odd	6		637.2.f.a.393.1		2
91.4	even	6		8281.2.a.c.1.1		1
91.9	even	3		1183.2.e.a.170.1		2
91.16	even	3	inner	91.2.h.a.16.1	yes	2
91.17	odd	6		8281.2.a.g.1.1		1
91.30	even	6		1183.2.e.c.170.1		2
91.55	odd	6		637.2.g.a.263.1		2
91.68	odd	6		637.2.h.a.471.1		2
91.74	even	3		8281.2.a.i.1.1		1
91.81	even	3		637.2.f.b.393.1		2
91.87	odd	6		8281.2.a.j.1.1		1
273.107	odd	6		819.2.s.a.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.a.9.1	✓	2	7.2	even	3
91.2.g.a.81.1	yes	2	13.3	even	3
91.2.h.a.16.1	yes	2	91.16	even	3	inner
91.2.h.a.74.1	yes	2	1.1	even	1	trivial
637.2.f.a.295.1		2	7.3	odd	6
637.2.f.a.393.1		2	91.3	odd	6
637.2.f.b.295.1		2	7.4	even	3
637.2.f.b.393.1		2	91.81	even	3
637.2.g.a.263.1		2	91.55	odd	6
637.2.g.a.373.1		2	7.5	odd	6
637.2.h.a.165.1		2	7.6	odd	2
637.2.h.a.471.1		2	91.68	odd	6
819.2.n.c.100.1		2	21.2	odd	6
819.2.n.c.172.1		2	39.29	odd	6
819.2.s.a.289.1		2	273.107	odd	6
819.2.s.a.802.1		2	3.2	odd	2
1183.2.e.a.170.1		2	91.9	even	3
1183.2.e.a.508.1		2	13.9	even	3
1183.2.e.c.170.1		2	91.30	even	6
1183.2.e.c.508.1		2	13.4	even	6
8281.2.a.c.1.1		1	91.4	even	6
8281.2.a.g.1.1		1	91.17	odd	6
8281.2.a.i.1.1		1	91.74	even	3
8281.2.a.j.1.1		1	91.87	odd	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.50000 + 2.59808i) q^{3} -1.00000 q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(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} +(2.00000 - 1.73205i) q^{7} -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} +(2.00000 - 1.73205i) q^{14} +(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} +(7.50000 + 2.59808i) q^{21} +(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} +(-2.00000 + 1.73205i) q^{28} +(-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} +(-7.50000 - 2.59808i) q^{35} +(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} +(7.50000 + 2.59808i) q^{42} +(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} +(1.00000 - 6.92820i) q^{49} +(-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} +(-6.00000 + 5.19615i) q^{56} +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} +(3.00000 + 15.5885i) q^{63} +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} +(-7.50000 - 2.59808i) q^{70} +(-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 + 2.59808i) q^{77} +(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} +(-7.50000 - 2.59808i) q^{84} +(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} +(-8.00000 - 5.19615i) q^{91} -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} +(1.00000 - 6.92820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + 4 * q^7 - 6 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + 4 q^{7} - 6 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 2 q^{13} + 4 q^{14} + 9 q^{15} - 2 q^{16} - 4 q^{17} - 6 q^{18} + q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} - 9 q^{24} - 4 q^{25} - 2 q^{26} - 18 q^{27} - 4 q^{28} - 7 q^{29} + 9 q^{30} - 3 q^{31} + 10 q^{32} - 9 q^{33} - 4 q^{34} - 15 q^{35} + 6 q^{36} + 4 q^{37} + q^{38} + 15 q^{39} + 9 q^{40} - 3 q^{41} + 15 q^{42} + 7 q^{43} - 3 q^{44} + 36 q^{45} - q^{47} - 3 q^{48} + 2 q^{49} - 4 q^{50} - 6 q^{51} + 2 q^{52} - 3 q^{53} - 18 q^{54} + 9 q^{55} - 12 q^{56} + 6 q^{57} - 7 q^{58} - 8 q^{59} - 9 q^{60} + 13 q^{61} - 3 q^{62} + 6 q^{63} + 14 q^{64} - 15 q^{65} - 9 q^{66} + 3 q^{67} + 4 q^{68} - 15 q^{70} - 13 q^{71} + 18 q^{72} + 13 q^{73} + 4 q^{74} - 24 q^{75} - q^{76} + 15 q^{77} + 15 q^{78} + 3 q^{79} + 3 q^{80} - 9 q^{81} - 3 q^{82} - 15 q^{84} + 6 q^{85} + 7 q^{86} - 42 q^{87} - 9 q^{88} + 12 q^{89} + 36 q^{90} - 16 q^{91} - 18 q^{93} - q^{94} - 6 q^{95} + 15 q^{96} + 5 q^{97} + 2 q^{98} - 36 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + 4 * q^7 - 6 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 2 * q^13 + 4 * q^14 + 9 * q^15 - 2 * q^16 - 4 * q^17 - 6 * q^18 + q^19 + 3 * q^20 + 15 * q^21 + 3 * q^22 - 9 * q^24 - 4 * q^25 - 2 * q^26 - 18 * q^27 - 4 * q^28 - 7 * q^29 + 9 * q^30 - 3 * q^31 + 10 * q^32 - 9 * q^33 - 4 * q^34 - 15 * q^35 + 6 * q^36 + 4 * q^37 + q^38 + 15 * q^39 + 9 * q^40 - 3 * q^41 + 15 * q^42 + 7 * q^43 - 3 * q^44 + 36 * q^45 - q^47 - 3 * q^48 + 2 * q^49 - 4 * q^50 - 6 * q^51 + 2 * q^52 - 3 * q^53 - 18 * q^54 + 9 * q^55 - 12 * q^56 + 6 * q^57 - 7 * q^58 - 8 * q^59 - 9 * q^60 + 13 * q^61 - 3 * q^62 + 6 * q^63 + 14 * q^64 - 15 * q^65 - 9 * q^66 + 3 * q^67 + 4 * q^68 - 15 * q^70 - 13 * q^71 + 18 * q^72 + 13 * q^73 + 4 * q^74 - 24 * q^75 - q^76 + 15 * q^77 + 15 * q^78 + 3 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 - 15 * q^84 + 6 * q^85 + 7 * q^86 - 42 * q^87 - 9 * q^88 + 12 * q^89 + 36 * q^90 - 16 * q^91 - 18 * q^93 - q^94 - 6 * q^95 + 15 * q^96 + 5 * q^97 + 2 * q^98 - 36 * q^99

Introduction

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