LMFDB - Embedded newform 91.2.g.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(9,91)]

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, 4]))

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

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

chi := DirichletCharacter("91.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.g (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:	$1$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	91.9
Dual form			91.2.g.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(-2.50000 + 0.866025i) q^{7} -3.00000 q^{8} +6.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(-2.50000 + 0.866025i) q^{7} -3.00000 q^{8} +6.00000 q^{9} +3.00000 q^{10} -3.00000 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} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} -1.00000 q^{19} +(1.50000 + 2.59808i) q^{20} +(7.50000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{22} +9.00000 q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 + 2.59808i) q^{26} -9.00000 q^{27} +(-0.500000 + 2.59808i) q^{28} +(-3.50000 + 6.06218i) q^{29} -9.00000 q^{30} +(-1.50000 - 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +9.00000 q^{33} -2.00000 q^{34} +(1.50000 - 7.79423i) q^{35} +(3.00000 - 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{38} +(3.00000 + 10.3923i) q^{39} +(4.50000 - 7.79423i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-6.00000 - 5.19615i) q^{42} +(3.50000 + 6.06218i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(-9.00000 + 15.5885i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-1.50000 - 2.59808i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 - 7.79423i) q^{55} +(7.50000 - 2.59808i) q^{56} +3.00000 q^{57} +7.00000 q^{58} +(2.00000 - 3.46410i) q^{59} +(-4.50000 - 7.79423i) q^{60} -13.0000 q^{61} +(-1.50000 + 2.59808i) q^{62} +(-15.0000 + 5.19615i) q^{63} +7.00000 q^{64} +(10.5000 + 2.59808i) q^{65} +(-4.50000 - 7.79423i) q^{66} -3.00000 q^{67} +(-1.00000 - 1.73205i) q^{68} +(-7.50000 + 2.59808i) q^{70} +(-6.50000 - 11.2583i) q^{71} -18.0000 q^{72} +(6.50000 + 11.2583i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) 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} -3.00000 q^{80} +9.00000 q^{81} +3.00000 q^{82} +(1.50000 - 7.79423i) q^{84} +(3.00000 + 5.19615i) q^{85} +(3.50000 - 6.06218i) q^{86} +(10.5000 - 18.1865i) q^{87} +9.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(5.50000 + 7.79423i) q^{91} +(4.50000 + 7.79423i) q^{93} +1.00000 q^{94} +(1.50000 - 2.59808i) q^{95} +(7.50000 - 12.9904i) q^{96} +(2.50000 + 4.33013i) q^{97} +(-6.50000 - 2.59808i) q^{98} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 6 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 2 * q - q^2 - 6 * q^3 + q^4 - 3 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 12 * q^9	\( 2 q - q^{2} - 6 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 12 q^{9} + 6 q^{10} - 6 q^{11} - 3 q^{12} - 2 q^{13} + 4 q^{14} + 9 q^{15} + q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} + 18 q^{24} - 4 q^{25} - 5 q^{26} - 18 q^{27} - q^{28} - 7 q^{29} - 18 q^{30} - 3 q^{31} - 5 q^{32} + 18 q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} + q^{38} + 6 q^{39} + 9 q^{40} - 3 q^{41} - 12 q^{42} + 7 q^{43} - 3 q^{44} - 18 q^{45} - q^{47} - 3 q^{48} + 11 q^{49} - 4 q^{50} - 6 q^{51} - 7 q^{52} - 3 q^{53} + 9 q^{54} + 9 q^{55} + 15 q^{56} + 6 q^{57} + 14 q^{58} + 4 q^{59} - 9 q^{60} - 26 q^{61} - 3 q^{62} - 30 q^{63} + 14 q^{64} + 21 q^{65} - 9 q^{66} - 6 q^{67} - 2 q^{68} - 15 q^{70} - 13 q^{71} - 36 q^{72} + 13 q^{73} - 2 q^{74} + 12 q^{75} - q^{76} + 15 q^{77} + 15 q^{78} + 3 q^{79} - 6 q^{80} + 18 q^{81} + 6 q^{82} + 3 q^{84} + 6 q^{85} + 7 q^{86} + 21 q^{87} + 18 q^{88} - 6 q^{89} + 36 q^{90} + 11 q^{91} + 9 q^{93} + 2 q^{94} + 3 q^{95} + 15 q^{96} + 5 q^{97} - 13 q^{98} - 36 q^{99}+O(q^{100}) \) 2 * q - q^2 - 6 * q^3 + q^4 - 3 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 12 * q^9 + 6 * q^10 - 6 * q^11 - 3 * q^12 - 2 * q^13 + 4 * q^14 + 9 * q^15 + q^16 + 2 * q^17 - 6 * q^18 - 2 * q^19 + 3 * q^20 + 15 * q^21 + 3 * q^22 + 18 * q^24 - 4 * q^25 - 5 * q^26 - 18 * q^27 - q^28 - 7 * q^29 - 18 * q^30 - 3 * q^31 - 5 * q^32 + 18 * q^33 - 4 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 + q^38 + 6 * q^39 + 9 * q^40 - 3 * q^41 - 12 * q^42 + 7 * q^43 - 3 * q^44 - 18 * q^45 - q^47 - 3 * q^48 + 11 * q^49 - 4 * q^50 - 6 * q^51 - 7 * q^52 - 3 * q^53 + 9 * q^54 + 9 * q^55 + 15 * q^56 + 6 * q^57 + 14 * q^58 + 4 * q^59 - 9 * q^60 - 26 * q^61 - 3 * q^62 - 30 * q^63 + 14 * q^64 + 21 * q^65 - 9 * q^66 - 6 * q^67 - 2 * q^68 - 15 * q^70 - 13 * q^71 - 36 * q^72 + 13 * q^73 - 2 * q^74 + 12 * q^75 - q^76 + 15 * q^77 + 15 * q^78 + 3 * q^79 - 6 * q^80 + 18 * q^81 + 6 * q^82 + 3 * q^84 + 6 * q^85 + 7 * q^86 + 21 * q^87 + 18 * q^88 - 6 * q^89 + 36 * q^90 + 11 * q^91 + 9 * q^93 + 2 * q^94 + 3 * q^95 + 15 * q^96 + 5 * q^97 - 13 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	−3.00000			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	1.50000	+	2.59808i	0.612372	+	1.06066i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−3.00000			−1.06066
$9$	6.00000			2.00000
$10$	3.00000			0.948683
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−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
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−3.00000	−	5.19615i	−0.707107	−	1.22474i
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	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		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	9.00000			1.83712
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−2.50000	+	2.59808i	−0.490290	+	0.509525i
$27$	−9.00000			−1.73205
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	−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	$0.941463\pi$
$30$	−9.00000			−1.64317
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$	9.00000			1.56670
$34$	−2.00000			−0.342997
$35$	1.50000	−	7.79423i	0.253546	−	1.31747i
$36$	3.00000	−	5.19615i	0.500000	−	0.866025i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	3.00000	+	10.3923i	0.480384	+	1.66410i
$40$	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	$0.241934\pi$
$42$	−6.00000	−	5.19615i	−0.925820	−	0.801784i
$43$	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
$45$	−9.00000	+	15.5885i	−1.34164	+	2.32379i
$46$		0			0
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$	−1.50000	−	2.59808i	−0.216506	−	0.375000i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$	4.50000	−	7.79423i	0.606780	−	1.05097i
$56$	7.50000	−	2.59808i	1.00223	−	0.347183i
$57$	3.00000			0.397360
$58$	7.00000			0.919145
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	−4.50000	−	7.79423i	−0.580948	−	1.00623i
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	−1.50000	+	2.59808i	−0.190500	+	0.329956i
$63$	−15.0000	+	5.19615i	−1.88982	+	0.654654i
$64$	7.00000			0.875000
$65$	10.5000	+	2.59808i	1.30236	+	0.322252i
$66$	−4.50000	−	7.79423i	−0.553912	−	0.959403i
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		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	$-0.447114\pi$
$72$	−18.0000			−2.12132
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	6.00000	+	10.3923i	0.692820	+	1.20000i
$76$	−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	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$	−3.00000			−0.335410
$81$	9.00000			1.00000
$82$	3.00000			0.331295
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	1.50000	−	7.79423i	0.163663	−	0.850420i
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$	3.50000	−	6.06218i	0.377415	−	0.653701i
$87$	10.5000	−	18.1865i	1.12572	−	1.94980i
$88$	9.00000			0.959403
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	18.0000			1.89737
$91$	5.50000	+	7.79423i	0.576557	+	0.817057i
$92$		0			0
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	1.00000			0.103142
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$	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	$0.751641\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	−18.0000			−1.80907
$100$	−4.00000			−0.400000
$101$	−5.00000			−0.497519			−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000			−0.497519			−0.248759	+	0.968565i	$0.580023\pi$
$102$	6.00000			0.594089
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	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
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	−4.50000	+	7.79423i	−0.433013	+	0.750000i
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$	−9.00000			−0.858116
$111$	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	$-0.415962\pi$
$114$	−1.50000	−	2.59808i	−0.140488	−	0.243332i
$115$		0			0
$116$	3.50000	+	6.06218i	0.324967	+	0.562859i
$117$	−6.00000	−	20.7846i	−0.554700	−	1.92154i
$118$	−4.00000			−0.368230
$119$	−1.00000	+	5.19615i	−0.0916698	+	0.476331i
$120$	−13.5000	+	23.3827i	−1.23238	+	2.13454i
$121$	−2.00000			−0.181818
$122$	6.50000	+	11.2583i	0.588482	+	1.01928i
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	−3.00000			−0.269408
$125$	−3.00000			−0.268328
$126$	12.0000	+	10.3923i	1.06904	+	0.925820i
$127$	−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	$0.328957\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	−10.5000	−	18.1865i	−0.924473	−	1.60123i
$130$	−3.00000	−	10.3923i	−0.263117	−	0.911465i
$131$	−2.50000	+	4.33013i	−0.218426	+	0.378325i	−0.954327	−	0.298764i	$-0.903426\pi$
$131$	−2.50000	+	4.33013i	−0.218426	+	0.378325i	0.735901	+	0.677089i	$0.236759\pi$
$132$	4.50000	−	7.79423i	0.391675	−	0.678401i
$133$	2.50000	−	0.866025i	0.216777	−	0.0750939i
$134$	1.50000	+	2.59808i	0.129580	+	0.224440i
$135$	13.5000	−	23.3827i	1.16190	−	2.01246i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$		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	$0.613863\pi$
$140$	−6.00000	−	5.19615i	−0.507093	−	0.439155i
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$	−6.50000	+	11.2583i	−0.545468	+	0.944778i
$143$	3.00000	+	10.3923i	0.250873	+	0.869048i
$144$	3.00000	+	5.19615i	0.250000	+	0.433013i
$145$	−10.5000	−	18.1865i	−0.871978	−	1.51031i
$146$	6.50000	−	11.2583i	0.537944	−	0.931746i
$147$	−16.5000	+	12.9904i	−1.36090	+	1.07143i
$148$	−2.00000			−0.164399
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	6.00000	−	10.3923i	0.489898	−	0.848528i
$151$	10.5000	+	18.1865i	0.854478	+	1.48000i	0.877129	+	0.480256i	$0.159456\pi$
$151$	10.5000	+	18.1865i	0.854478	+	1.48000i	−0.0226507	+	0.999743i	$0.507211\pi$
$152$	3.00000			0.243332
$153$	6.00000	−	10.3923i	0.485071	−	0.840168i
$154$	−6.00000	−	5.19615i	−0.483494	−	0.418718i
$155$	9.00000			0.722897
$156$	10.5000	+	2.59808i	0.840673	+	0.208013i
$157$	−9.50000	−	16.4545i	−0.758183	−	1.31321i	−0.943777	−	0.330584i	$-0.892754\pi$
$157$	−9.50000	−	16.4545i	−0.758183	−	1.31321i	0.185594	−	0.982627i	$-0.440579\pi$
$158$	−3.00000			−0.238667
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	−7.50000	−	12.9904i	−0.592927	−	1.02698i
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$	−13.5000	+	23.3827i	−1.05097	+	1.82034i
$166$		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
$171$	−6.00000			−0.458831
$172$	7.00000			0.533745
$173$	19.0000			1.44454			0.722272	−	0.691609i	$-0.243098\pi$
$173$	19.0000			1.44454			0.722272	+	0.691609i	$0.243098\pi$
$174$	−21.0000			−1.59201
$175$	8.00000	+	6.92820i	0.604743	+	0.523723i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	17.0000			1.27064			0.635320	−	0.772249i	$-0.280868\pi$
$179$	17.0000			1.27064			0.635320	+	0.772249i	$0.280868\pi$
$180$	9.00000	+	15.5885i	0.670820	+	1.16190i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	4.00000	−	8.66025i	0.296500	−	0.641941i
$183$	39.0000			2.88296
$184$		0			0
$185$	6.00000			0.441129
$186$	4.50000	−	7.79423i	0.329956	−	0.571501i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	0.500000	+	0.866025i	0.0364662	+	0.0631614i
$189$	22.5000	−	7.79423i	1.63663	−	0.566947i
$190$	−3.00000			−0.217643
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	−21.0000			−1.51554
$193$	7.00000			0.503871			0.251936	−	0.967744i	$-0.418933\pi$
$193$	7.00000			0.503871			0.251936	+	0.967744i	$0.418933\pi$
$194$	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	$0.155325\pi$
$198$	9.00000	+	15.5885i	0.639602	+	1.10782i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	6.00000	+	10.3923i	0.424264	+	0.734847i
$201$	9.00000			0.634811
$202$	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
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	5.00000			0.348367
$207$		0			0
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	3.00000			0.207514
$210$	22.5000	−	7.79423i	1.55265	−	0.537853i
$211$	−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	$0.244126\pi$
$212$	−3.00000			−0.206041
$213$	19.5000	+	33.7750i	1.33612	+	2.31422i
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	−21.0000			−1.43219
$216$	27.0000			1.83712
$217$	6.00000	+	5.19615i	0.407307	+	0.352738i
$218$	−3.50000	+	6.06218i	−0.237050	+	0.410582i
$219$	−19.5000	−	33.7750i	−1.31769	−	2.28230i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	−7.00000	−	1.73205i	−0.470871	−	0.116510i
$222$	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	$0.0692320\pi$
$224$	2.50000	−	12.9904i	0.167038	−	0.867956i
$225$	−12.0000	−	20.7846i	−0.800000	−	1.38564i
$226$	−7.50000	+	12.9904i	−0.498893	+	0.864107i
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$	1.50000	−	2.59808i	0.0993399	−	0.172062i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$	−22.5000	+	7.79423i	−1.48039	+	0.512823i
$232$	10.5000	−	18.1865i	0.689359	−	1.19400i
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	−0.284645	−	0.958633i	$-0.591876\pi$
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	0.972523	−	0.232806i	$-0.0747909\pi$
$234$	−15.0000	+	15.5885i	−0.980581	+	1.01905i
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	−4.50000	+	7.79423i	−0.292306	+	0.506290i
$238$	5.00000	−	1.73205i	0.324102	−	0.112272i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	9.00000			0.580948
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	−6.50000	+	11.2583i	−0.416120	+	0.720741i
$245$	3.00000	+	20.7846i	0.191663	+	1.32788i
$246$	−9.00000			−0.573819
$247$	1.00000	+	3.46410i	0.0636285	+	0.220416i
$248$	4.50000	+	7.79423i	0.285750	+	0.494934i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	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
$254$	11.0000			0.690201
$255$	−9.00000	−	15.5885i	−0.563602	−	0.976187i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$	−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
$262$	5.00000			0.308901
$263$	−27.0000			−1.66489			−0.832446	−	0.554107i	$-0.813060\pi$
$263$	−27.0000			−1.66489			−0.832446	+	0.554107i	$0.813060\pi$
$264$	−27.0000			−1.66174
$265$	9.00000			0.552866
$266$	−2.00000	−	1.73205i	−0.122628	−	0.106199i
$267$	9.00000	+	15.5885i	0.550791	+	0.953998i
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−27.0000			−1.64317
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	2.00000			0.121268
$273$	−16.5000	−	23.3827i	−0.998625	−	1.41518i
$274$	10.0000			0.604122
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	7.50000	−	12.9904i	0.449820	−	0.779111i
$279$	−9.00000	−	15.5885i	−0.538816	−	0.933257i
$280$	−4.50000	+	23.3827i	−0.268926	+	1.39738i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	−3.00000			−0.178647
$283$	1.00000			0.0594438			0.0297219	−	0.999558i	$-0.490538\pi$
$283$	1.00000			0.0594438			0.0297219	+	0.999558i	$0.490538\pi$
$284$	−13.0000			−0.771408
$285$	−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
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.5000	+	18.1865i	−0.616581	+	1.06795i
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$	13.0000			0.760767
$293$	−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
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$	27.0000			1.56670
$298$	−7.50000	−	12.9904i	−0.434463	−	0.752513i
$299$		0			0
$300$	12.0000			0.692820
$301$	−14.0000	−	12.1244i	−0.806947	−	0.698836i
$302$	10.5000	−	18.1865i	0.604207	−	1.04652i
$303$	15.0000			0.861727
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	19.5000	−	33.7750i	1.11657	−	1.93395i
$306$	−12.0000			−0.685994
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	1.50000	−	7.79423i	0.0854704	−	0.444117i
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$	−4.50000	−	7.79423i	−0.255583	−	0.442682i
$311$	4.50000	+	7.79423i	0.255172	+	0.441970i	0.964942	−	0.262463i	$-0.0845347\pi$
$311$	4.50000	+	7.79423i	0.255172	+	0.441970i	−0.709771	+	0.704433i	$0.751201\pi$
$312$	−9.00000	−	31.1769i	−0.509525	−	1.76505i
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	−9.50000	+	16.4545i	−0.536116	+	0.928580i
$315$	9.00000	−	46.7654i	0.507093	−	2.63493i
$316$	−1.50000	−	2.59808i	−0.0843816	−	0.146153i
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	−0.711535	−	0.702650i	$-0.752000\pi$
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	0.964281	+	0.264883i	$0.0853332\pi$
$318$	4.50000	−	7.79423i	0.252347	−	0.437079i
$319$	10.5000	−	18.1865i	0.587887	−	1.01825i
$320$	−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
$325$	−10.0000	+	10.3923i	−0.554700	+	0.576461i
$326$	0.500000	+	0.866025i	0.0276924	+	0.0479647i
$327$	10.5000	+	18.1865i	0.580651	+	1.00572i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	0.500000	−	2.59808i	0.0275659	−	0.143237i
$330$	27.0000			1.48630
$331$	−29.0000			−1.59398			−0.796992	−	0.603990i	$-0.793577\pi$
$331$	−29.0000			−1.59398			−0.796992	+	0.603990i	$0.793577\pi$
$332$		0			0
$333$	−6.00000	−	10.3923i	−0.328798	−	0.569495i
$334$	−13.0000			−0.711328
$335$	4.50000	−	7.79423i	0.245861	−	0.425844i
$336$	6.00000	+	5.19615i	0.327327	+	0.283473i
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	22.5000	+	38.9711i	1.22203	+	2.11662i
$340$	6.00000			0.325396
$341$	4.50000	+	7.79423i	0.243689	+	0.422081i
$342$	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
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	−0.738458	−	0.674299i	$-0.764446\pi$
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	0.953189	+	0.302374i	$0.0977791\pi$
$348$	−10.5000	−	18.1865i	−0.562859	−	0.974901i
$349$	−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
$353$	−25.0000			−1.33062			−0.665308	−	0.746569i	$-0.731700\pi$
$353$	−25.0000			−1.33062			−0.665308	+	0.746569i	$0.731700\pi$
$354$	12.0000			0.637793
$355$	39.0000			2.06991
$356$	−6.00000			−0.317999
$357$	3.00000	−	15.5885i	0.158777	−	0.825029i
$358$	−8.50000	−	14.7224i	−0.449239	−	0.778105i
$359$	−8.50000	+	14.7224i	−0.448613	+	0.777020i	−0.998296	−	0.0583530i	$-0.981415\pi$
$359$	−8.50000	+	14.7224i	−0.448613	+	0.777020i	0.549683	+	0.835373i	$0.314748\pi$
$360$	27.0000	−	46.7654i	1.42302	−	2.46475i
$361$	−18.0000			−0.947368
$362$	11.0000	+	19.0526i	0.578147	+	1.00138i
$363$	6.00000			0.314918
$364$	9.50000	−	0.866025i	0.497935	−	0.0453921i
$365$	−39.0000			−2.04135
$366$	−19.5000	−	33.7750i	−1.01928	−	1.76545i
$367$	−31.0000			−1.61819			−0.809093	−	0.587680i	$-0.800041\pi$
$367$	−31.0000			−1.61819			−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$	−3.00000	−	5.19615i	−0.155963	−	0.270135i
$371$	6.00000	+	5.19615i	0.311504	+	0.269771i
$372$	9.00000			0.466628
$373$	−9.00000			−0.466002			−0.233001	−	0.972476i	$-0.574855\pi$
$373$	−9.00000			−0.466002			−0.233001	+	0.972476i	$0.574855\pi$
$374$	6.00000			0.310253
$375$	9.00000			0.464758
$376$	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	$-0.155255\pi$
$380$	−1.50000	−	2.59808i	−0.0769484	−	0.133278i
$381$	16.5000	−	28.5788i	0.845321	−	1.46414i
$382$	8.50000	+	14.7224i	0.434898	+	0.753265i
$383$	−21.0000			−1.07305			−0.536525	−	0.843884i	$-0.680263\pi$
$383$	−21.0000			−1.07305			−0.536525	+	0.843884i	$0.680263\pi$
$384$	−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
$387$	21.0000	+	36.3731i	1.06749	+	1.84895i
$388$	5.00000			0.253837
$389$	16.5000	+	28.5788i	0.836583	+	1.44900i	0.892735	+	0.450582i	$0.148784\pi$
$389$	16.5000	+	28.5788i	0.836583	+	1.44900i	−0.0561516	+	0.998422i	$0.517883\pi$
$390$	9.00000	+	31.1769i	0.455733	+	1.57870i
$391$		0			0
$392$	−16.5000	+	12.9904i	−0.833376	+	0.656113i
$393$	7.50000	−	12.9904i	0.378325	−	0.655278i
$394$	−1.00000			−0.0503793
$395$	4.50000	+	7.79423i	0.226420	+	0.392170i
$396$	−9.00000	+	15.5885i	−0.452267	+	0.783349i
$397$	−1.00000			−0.0501886			−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000			−0.0501886			−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−20.0000			−1.00251
$399$	−7.50000	+	2.59808i	−0.375470	+	0.130066i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	0.889914	−	0.456129i	$-0.150764\pi$
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	−0.839976	+	0.542623i	$0.817431\pi$
$402$	−4.50000	−	7.79423i	−0.224440	−	0.388741i
$403$	−7.50000	+	7.79423i	−0.373602	+	0.388258i
$404$	−2.50000	+	4.33013i	−0.124380	+	0.215432i
$405$	−13.5000	+	23.3827i	−0.670820	+	1.16190i
$406$	−17.5000	+	6.06218i	−0.868510	+	0.300861i
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$	9.00000	−	15.5885i	0.445566	−	0.771744i
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	15.0000	−	25.9808i	0.739895	−	1.28154i
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$	−2.00000	+	10.3923i	−0.0984136	+	0.511372i
$414$		0			0
$415$		0			0
$416$	17.5000	+	4.33013i	0.858008	+	0.212302i
$417$	−22.5000	−	38.9711i	−1.10183	−	1.90843i
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	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	$-0.0424311\pi$
$420$	18.0000	+	15.5885i	0.878310	+	0.760639i
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	7.00000			0.340755
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−8.00000			−0.388057
$426$	19.5000	−	33.7750i	0.944778	−	1.63640i
$427$	32.5000	−	11.2583i	1.57279	−	0.544829i
$428$	−8.00000			−0.386695
$429$	−9.00000	−	31.1769i	−0.434524	−	1.50524i
$430$	10.5000	+	18.1865i	0.506355	+	0.877033i
$431$	9.00000			0.433515			0.216757	−	0.976226i	$-0.430452\pi$
$431$	9.00000			0.433515			0.216757	+	0.976226i	$0.430452\pi$
$432$	−4.50000	−	7.79423i	−0.216506	−	0.375000i
$433$	−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
$436$	−7.00000			−0.335239
$437$		0			0
$438$	−19.5000	+	33.7750i	−0.931746	+	1.61383i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−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	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$	6.00000			0.284747
$445$	18.0000			0.853282
$446$	−9.00000			−0.426162
$447$	−45.0000			−2.12843
$448$	−17.5000	+	6.06218i	−0.826797	+	0.286411i
$449$	−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
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	−15.0000			−0.705541
$453$	−31.5000	−	54.5596i	−1.48000	−	2.56343i
$454$	−4.00000			−0.187729
$455$	−28.5000	+	2.59808i	−1.33610	+	0.121800i
$456$	−9.00000			−0.421464
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	−13.0000			−0.607450
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		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	$-0.469961\pi$
$462$	18.0000	+	15.5885i	0.837436	+	0.725241i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−7.00000			−0.324967
$465$	−27.0000			−1.25210
$466$	−21.0000			−0.972806
$467$	3.50000	−	6.06218i	0.161961	−	0.280524i	−0.773611	−	0.633661i	$-0.781552\pi$
$467$	3.50000	−	6.06218i	0.161961	−	0.280524i	0.935572	+	0.353137i	$0.114885\pi$
$468$	−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
$471$	28.5000	+	49.3634i	1.31321	+	2.27455i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−10.5000	−	18.1865i	−0.482791	−	0.836218i
$474$	9.00000			0.413384
$475$	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
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	−35.0000			−1.59919			−0.799595	−	0.600539i	$-0.794953\pi$
$479$	−35.0000			−1.59919			−0.799595	+	0.600539i	$0.794953\pi$
$480$	22.5000	+	38.9711i	1.02698	+	1.77878i
$481$	−5.00000	+	5.19615i	−0.227980	+	0.236924i
$482$	−26.0000			−1.18427
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$	−15.0000			−0.681115
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	39.0000			1.76545
$489$	3.00000			0.135665
$490$	16.5000	−	12.9904i	0.745394	−	0.586846i
$491$	−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	$0.276576\pi$
$492$	−4.50000	−	7.79423i	−0.202876	−	0.351391i
$493$	7.00000	+	12.1244i	0.315264	+	0.546054i
$494$	2.50000	−	2.59808i	0.112480	−	0.116893i
$495$	27.0000	−	46.7654i	1.21356	−	2.10195i
$496$	1.50000	−	2.59808i	0.0673520	−	0.116657i
$497$	26.0000	+	22.5167i	1.16626	+	1.01001i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−19.5000	+	33.7750i	−0.871196	+	1.50896i
$502$	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	$0.590455\pi$
$504$	45.0000	−	15.5885i	2.00446	−	0.694365i
$505$	7.50000	−	12.9904i	0.333746	−	0.578064i
$506$		0			0
$507$	33.0000	−	20.7846i	1.46558	−	0.923077i
$508$	5.50000	+	9.52628i	0.244023	+	0.422660i
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$	−9.00000	+	15.5885i	−0.398527	+	0.690268i
$511$	−26.0000	−	22.5167i	−1.15017	−	0.996078i
$512$	−11.0000			−0.486136
$513$	9.00000			0.397360
$514$	1.00000	−	1.73205i	0.0441081	−	0.0763975i
$515$	−7.50000	−	12.9904i	−0.330489	−	0.572425i
$516$	−21.0000			−0.924473
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$	1.00000	−	5.19615i	0.0439375	−	0.228306i
$519$	−57.0000			−2.50202
$520$	−31.5000	−	7.79423i	−1.38137	−	0.341800i
$521$	8.50000	+	14.7224i	0.372392	+	0.645001i	0.989933	−	0.141537i	$-0.0452044\pi$
$521$	8.50000	+	14.7224i	0.372392	+	0.645001i	−0.617541	+	0.786539i	$0.711871\pi$
$522$	42.0000			1.83829
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	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
$527$	−6.00000			−0.261364
$528$	4.50000	+	7.79423i	0.195837	+	0.339200i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$	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
$535$	24.0000			1.03761
$536$	9.00000			0.388741
$537$	−51.0000			−2.20081
$538$	18.0000			0.776035
$539$	−16.5000	+	12.9904i	−0.710705	+	0.559535i
$540$	−13.5000	−	23.3827i	−0.580948	−	1.00623i
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	−0.127222	−	0.991874i	$-0.540606\pi$
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	0.922599	−	0.385759i	$-0.126061\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	66.0000			2.83233
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$	21.0000			0.899541
$546$	−12.0000	+	25.9808i	−0.513553	+	1.11187i
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	5.00000	+	8.66025i	0.213589	+	0.369948i
$549$	−78.0000			−3.32896
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	3.50000	−	6.06218i	0.149105	−	0.258257i
$552$		0			0
$553$	−1.50000	+	7.79423i	−0.0637865	+	0.331444i
$554$	22.0000			0.934690
$555$	−18.0000			−0.764057
$556$	15.0000			0.636142
$557$	3.00000			0.127114			0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000			0.127114			0.0635570	+	0.997978i	$0.479756\pi$
$558$	−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
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$	45.0000			1.89316
$566$	−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
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$	9.00000			0.376969
$571$	−21.5000	−	37.2391i	−0.899747	−	1.55841i	−0.827817	−	0.560998i	$-0.810418\pi$
$571$	−21.5000	−	37.2391i	−0.899747	−	1.55841i	−0.0719297	−	0.997410i	$-0.522916\pi$
$572$	10.5000	+	2.59808i	0.439027	+	0.108631i
$573$	51.0000			2.13056
$574$	−7.50000	+	2.59808i	−0.313044	+	0.108442i
$575$		0			0
$576$	42.0000			1.75000
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	0.876245	−	0.481865i	$-0.160040\pi$
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	−0.855430	+	0.517918i	$0.826707\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	−21.0000			−0.872730
$580$	−21.0000			−0.871978
$581$		0			0
$582$	−7.50000	+	12.9904i	−0.310885	+	0.538469i
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	−19.5000	−	33.7750i	−0.806916	−	1.39762i
$585$	63.0000	+	15.5885i	2.60473	+	0.644503i
$586$	−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	$-0.0718001\pi$
$588$	3.00000	+	20.7846i	0.123718	+	0.857143i
$589$	1.50000	+	2.59808i	0.0618064	+	0.107052i
$590$	6.00000	−	10.3923i	0.247016	−	0.427844i
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	0.443573	+	0.896238i	$0.353711\pi$
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	−0.997952	+	0.0639736i	$0.979623\pi$
$594$	−13.5000	−	23.3827i	−0.553912	−	0.959403i
$595$	−12.0000	−	10.3923i	−0.491952	−	0.426043i
$596$	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	0.999923	+	0.0124417i	$0.00396043\pi$
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	−0.489186	+	0.872179i	$0.662706\pi$
$600$	−18.0000	−	31.1769i	−0.734847	−	1.27279i
$601$	−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	$0.913621\pi$
$602$	−3.50000	+	18.1865i	−0.142649	+	0.741228i
$603$	−18.0000			−0.733017
$604$	21.0000			0.854478
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$	−7.50000	−	12.9904i	−0.304667	−	0.527698i
$607$	11.0000			0.446476			0.223238	−	0.974764i	$-0.428337\pi$
$607$	11.0000			0.446476			0.223238	+	0.974764i	$0.428337\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$	−10.5000	+	54.5596i	−0.425481	+	2.21087i
$610$	−39.0000			−1.57906
$611$	3.50000	+	0.866025i	0.141595	+	0.0350356i
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−25.0000			−1.00974			−0.504870	−	0.863195i	$-0.668460\pi$
$613$	−25.0000			−1.00974			−0.504870	+	0.863195i	$0.668460\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$	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	$0.602078\pi$
$618$	−15.0000			−0.603388
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	0.734068	−	0.679076i	$-0.237620\pi$
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	−0.955131	+	0.296183i	$0.904286\pi$
$620$	4.50000	−	7.79423i	0.180724	−	0.313024i
$621$		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
$626$	19.0000			0.759393
$627$	−9.00000			−0.359425
$628$	−19.0000			−0.758183
$629$	−4.00000			−0.159490
$630$	−45.0000	+	15.5885i	−1.79284	+	0.621059i
$631$	−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
$633$	10.5000	−	18.1865i	0.417338	−	0.722850i
$634$	−9.00000			−0.357436
$635$	−16.5000	−	28.5788i	−0.654783	−	1.13412i
$636$	9.00000			0.356873
$637$	−20.5000	−	14.7224i	−0.812240	−	0.583324i
$638$	−21.0000			−0.831398
$639$	−39.0000	−	67.5500i	−1.54282	−	2.67224i
$640$	−9.00000			−0.355756
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	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
$646$	2.00000			0.0786889
$647$	9.00000			0.353827			0.176913	−	0.984226i	$-0.443389\pi$
$647$	9.00000			0.353827			0.176913	+	0.984226i	$0.443389\pi$
$648$	−27.0000			−1.06066
$649$	−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
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	10.5000	−	18.1865i	0.410582	−	0.711150i
$655$	−7.50000	−	12.9904i	−0.293049	−	0.507576i
$656$	−3.00000			−0.117130
$657$	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	$-0.357729\pi$
$660$	13.5000	+	23.3827i	0.525487	+	0.910170i
$661$	−9.00000			−0.350059			−0.175030	−	0.984563i	$-0.556002\pi$
$661$	−9.00000			−0.350059			−0.175030	+	0.984563i	$0.556002\pi$
$662$	14.5000	+	25.1147i	0.563559	+	0.976112i
$663$	21.0000	+	5.19615i	0.815572	+	0.201802i
$664$		0			0
$665$	−1.50000	+	7.79423i	−0.0581675	+	0.302247i
$666$	−6.00000	+	10.3923i	−0.232495	+	0.402694i
$667$		0			0
$668$	−6.50000	−	11.2583i	−0.251493	−	0.435598i
$669$	−13.5000	+	23.3827i	−0.521940	+	0.904027i
$670$	−9.00000			−0.347700
$671$	39.0000			1.50558
$672$	−7.50000	+	38.9711i	−0.289319	+	1.50334i
$673$	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	$-0.123365\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$	18.0000	+	31.1769i	0.692820	+	1.20000i
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−3.50000	+	6.06218i	−0.134516	+	0.232988i	−0.925412	−	0.378962i	$-0.876281\pi$
$677$	−3.50000	+	6.06218i	−0.134516	+	0.232988i	0.790897	+	0.611950i	$0.209615\pi$
$678$	22.5000	−	38.9711i	0.864107	−	1.49668i
$679$	−10.0000	−	8.66025i	−0.383765	−	0.332350i
$680$	−9.00000	−	15.5885i	−0.345134	−	0.597790i
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$	4.50000	−	7.79423i	0.172314	−	0.298456i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−3.00000	+	5.19615i	−0.114708	+	0.198680i
$685$	−15.0000	−	25.9808i	−0.573121	−	0.992674i
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	−19.5000	+	33.7750i	−0.743971	+	1.28860i
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	−7.50000	+	7.79423i	−0.285727	+	0.296936i
$690$		0			0
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$	9.50000	−	16.4545i	0.361136	−	0.625506i
$693$	45.0000	−	15.5885i	1.70941	−	0.592157i
$694$	−8.00000			−0.303676
$695$	−45.0000			−1.70695
$696$	−31.5000	+	54.5596i	−1.19400	+	2.06808i
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	23.0000			0.870563
$699$	−31.5000	+	54.5596i	−1.19144	+	2.06363i
$700$	10.0000	−	3.46410i	0.377964	−	0.130931i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	22.5000	−	23.3827i	0.849208	−	0.882523i
$703$	1.00000	+	1.73205i	0.0377157	+	0.0653255i
$704$	−21.0000			−0.791467
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	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
$709$	11.0000			0.413114			0.206557	−	0.978435i	$-0.433774\pi$
$709$	11.0000			0.413114			0.206557	+	0.978435i	$0.433774\pi$
$710$	−19.5000	−	33.7750i	−0.731822	−	1.26755i
$711$	9.00000	−	15.5885i	0.337526	−	0.584613i
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$		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
$717$	12.0000			0.448148
$718$	17.0000			0.634434
$719$	−9.00000			−0.335643			−0.167822	−	0.985817i	$-0.553673\pi$
$719$	−9.00000			−0.335643			−0.167822	+	0.985817i	$0.553673\pi$
$720$	−18.0000			−0.670820
$721$	2.50000	−	12.9904i	0.0931049	−	0.483787i
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	−39.0000	+	67.5500i	−1.45043	+	2.51221i
$724$	−11.0000	+	19.0526i	−0.408812	+	0.708083i
$725$	28.0000			1.03989
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−16.5000	−	23.3827i	−0.611531	−	0.866620i
$729$	−27.0000			−1.00000
$730$	19.5000	+	33.7750i	0.721727	+	1.25007i
$731$	14.0000			0.517809
$732$	19.5000	−	33.7750i	0.720741	−	1.24836i
$733$	4.50000	−	7.79423i	0.166211	−	0.287886i	−0.770873	−	0.636988i	$-0.780180\pi$
$733$	4.50000	−	7.79423i	0.166211	−	0.287886i	0.937085	+	0.349102i	$0.113513\pi$
$734$	15.5000	+	26.8468i	0.572115	+	0.990933i
$735$	−9.00000	−	62.3538i	−0.331970	−	2.29996i
$736$		0			0
$737$	9.00000			0.331519
$738$	18.0000			0.662589
$739$	1.00000			0.0367856			0.0183928	−	0.999831i	$-0.494145\pi$
$739$	1.00000			0.0367856			0.0183928	+	0.999831i	$0.494145\pi$
$740$	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	$0.781612\pi$
$744$	−13.5000	−	23.3827i	−0.494934	−	0.857251i
$745$	−22.5000	+	38.9711i	−0.824336	+	1.42779i
$746$	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
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	−1.00000			−0.0364662
$753$	−34.5000	−	59.7558i	−1.25725	−	2.17762i
$754$	−7.00000	−	24.2487i	−0.254925	−	0.883086i
$755$	−63.0000			−2.29280
$756$	4.50000	−	23.3827i	0.163663	−	0.850420i
$757$	−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	$0.184029\pi$
$758$	−33.0000			−1.19861
$759$		0			0
$760$	−4.50000	+	7.79423i	−0.163232	+	0.282726i
$761$	−9.00000			−0.326250			−0.163125	−	0.986605i	$-0.552157\pi$
$761$	−9.00000			−0.326250			−0.163125	+	0.986605i	$0.552157\pi$
$762$	−33.0000			−1.19546
$763$	14.0000	+	12.1244i	0.506834	+	0.438931i
$764$	−8.50000	+	14.7224i	−0.307519	+	0.532639i
$765$	18.0000	+	31.1769i	0.650791	+	1.12720i
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$	−14.0000	−	3.46410i	−0.505511	−	0.125081i
$768$	−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

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.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(-2.50000 + 0.866025i) q^{7} -3.00000 q^{8} +6.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(-2.50000 + 0.866025i) q^{7} -3.00000 q^{8} +6.00000 q^{9} +3.00000 q^{10} -3.00000 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} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} -1.00000 q^{19} +(1.50000 + 2.59808i) q^{20} +(7.50000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{22} +9.00000 q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 + 2.59808i) q^{26} -9.00000 q^{27} +(-0.500000 + 2.59808i) q^{28} +(-3.50000 + 6.06218i) q^{29} -9.00000 q^{30} +(-1.50000 - 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +9.00000 q^{33} -2.00000 q^{34} +(1.50000 - 7.79423i) q^{35} +(3.00000 - 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{38} +(3.00000 + 10.3923i) q^{39} +(4.50000 - 7.79423i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-6.00000 - 5.19615i) q^{42} +(3.50000 + 6.06218i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(-9.00000 + 15.5885i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-1.50000 - 2.59808i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 - 7.79423i) q^{55} +(7.50000 - 2.59808i) q^{56} +3.00000 q^{57} +7.00000 q^{58} +(2.00000 - 3.46410i) q^{59} +(-4.50000 - 7.79423i) q^{60} -13.0000 q^{61} +(-1.50000 + 2.59808i) q^{62} +(-15.0000 + 5.19615i) q^{63} +7.00000 q^{64} +(10.5000 + 2.59808i) q^{65} +(-4.50000 - 7.79423i) q^{66} -3.00000 q^{67} +(-1.00000 - 1.73205i) q^{68} +(-7.50000 + 2.59808i) q^{70} +(-6.50000 - 11.2583i) q^{71} -18.0000 q^{72} +(6.50000 + 11.2583i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) 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} -3.00000 q^{80} +9.00000 q^{81} +3.00000 q^{82} +(1.50000 - 7.79423i) q^{84} +(3.00000 + 5.19615i) q^{85} +(3.50000 - 6.06218i) q^{86} +(10.5000 - 18.1865i) q^{87} +9.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(5.50000 + 7.79423i) q^{91} +(4.50000 + 7.79423i) q^{93} +1.00000 q^{94} +(1.50000 - 2.59808i) q^{95} +(7.50000 - 12.9904i) q^{96} +(2.50000 + 4.33013i) q^{97} +(-6.50000 - 2.59808i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 6 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 2 * q - q^2 - 6 * q^3 + q^4 - 3 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 12 * q^9	\( 2 q - q^{2} - 6 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 12 q^{9} + 6 q^{10} - 6 q^{11} - 3 q^{12} - 2 q^{13} + 4 q^{14} + 9 q^{15} + q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} + 18 q^{24} - 4 q^{25} - 5 q^{26} - 18 q^{27} - q^{28} - 7 q^{29} - 18 q^{30} - 3 q^{31} - 5 q^{32} + 18 q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} + q^{38} + 6 q^{39} + 9 q^{40} - 3 q^{41} - 12 q^{42} + 7 q^{43} - 3 q^{44} - 18 q^{45} - q^{47} - 3 q^{48} + 11 q^{49} - 4 q^{50} - 6 q^{51} - 7 q^{52} - 3 q^{53} + 9 q^{54} + 9 q^{55} + 15 q^{56} + 6 q^{57} + 14 q^{58} + 4 q^{59} - 9 q^{60} - 26 q^{61} - 3 q^{62} - 30 q^{63} + 14 q^{64} + 21 q^{65} - 9 q^{66} - 6 q^{67} - 2 q^{68} - 15 q^{70} - 13 q^{71} - 36 q^{72} + 13 q^{73} - 2 q^{74} + 12 q^{75} - q^{76} + 15 q^{77} + 15 q^{78} + 3 q^{79} - 6 q^{80} + 18 q^{81} + 6 q^{82} + 3 q^{84} + 6 q^{85} + 7 q^{86} + 21 q^{87} + 18 q^{88} - 6 q^{89} + 36 q^{90} + 11 q^{91} + 9 q^{93} + 2 q^{94} + 3 q^{95} + 15 q^{96} + 5 q^{97} - 13 q^{98} - 36 q^{99}+O(q^{100}) \) 2 * q - q^2 - 6 * q^3 + q^4 - 3 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 12 * q^9 + 6 * q^10 - 6 * q^11 - 3 * q^12 - 2 * q^13 + 4 * q^14 + 9 * q^15 + q^16 + 2 * q^17 - 6 * q^18 - 2 * q^19 + 3 * q^20 + 15 * q^21 + 3 * q^22 + 18 * q^24 - 4 * q^25 - 5 * q^26 - 18 * q^27 - q^28 - 7 * q^29 - 18 * q^30 - 3 * q^31 - 5 * q^32 + 18 * q^33 - 4 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 + q^38 + 6 * q^39 + 9 * q^40 - 3 * q^41 - 12 * q^42 + 7 * q^43 - 3 * q^44 - 18 * q^45 - q^47 - 3 * q^48 + 11 * q^49 - 4 * q^50 - 6 * q^51 - 7 * q^52 - 3 * q^53 + 9 * q^54 + 9 * q^55 + 15 * q^56 + 6 * q^57 + 14 * q^58 + 4 * q^59 - 9 * q^60 - 26 * q^61 - 3 * q^62 - 30 * q^63 + 14 * q^64 + 21 * q^65 - 9 * q^66 - 6 * q^67 - 2 * q^68 - 15 * q^70 - 13 * q^71 - 36 * q^72 + 13 * q^73 - 2 * q^74 + 12 * q^75 - q^76 + 15 * q^77 + 15 * q^78 + 3 * q^79 - 6 * q^80 + 18 * q^81 + 6 * q^82 + 3 * q^84 + 6 * q^85 + 7 * q^86 + 21 * q^87 + 18 * q^88 - 6 * q^89 + 36 * q^90 + 11 * q^91 + 9 * q^93 + 2 * q^94 + 3 * q^95 + 15 * q^96 + 5 * q^97 - 13 * q^98 - 36 * q^99

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