LMFDB - Embedded newform 45.2.e.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.e (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:	$0.359326809096$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.2.e.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)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.50000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(1.50000 - 2.59808i) q^{18} -8.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} -5.19615i q^{21} +(1.00000 - 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{26} -5.19615i q^{27} +3.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(1.50000 + 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{32} -3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +3.00000 q^{35} +3.00000 q^{36} -4.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-4.50000 + 2.59808i) q^{42} +(4.00000 + 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{45} +3.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} -1.73205i q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} -2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +2.00000 q^{55} +(-4.50000 - 7.79423i) q^{56} +(12.0000 + 6.92820i) q^{57} +(0.500000 - 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{59} +1.73205i q^{60} +(-3.50000 - 6.06218i) q^{61} +(-4.50000 + 7.79423i) q^{63} +7.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(-3.00000 + 1.73205i) q^{66} +(1.50000 - 2.59808i) q^{67} +(2.00000 - 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-1.50000 - 2.59808i) q^{70} +2.00000 q^{71} +(-4.50000 - 7.79423i) q^{72} +4.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +1.73205i q^{75} +(-4.00000 + 6.92820i) q^{76} +(-3.00000 + 5.19615i) q^{77} +(3.00000 + 1.73205i) q^{78} +(3.00000 + 5.19615i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(2.00000 - 3.46410i) q^{85} +(4.00000 - 6.92820i) q^{86} -1.73205i q^{87} +(-3.00000 - 5.19615i) q^{88} -15.0000 q^{89} +(-1.50000 - 2.59808i) q^{90} +6.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(7.50000 - 4.33013i) q^{96} +(-1.00000 - 1.73205i) q^{97} +2.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 + q^4 + q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9	$ 2 q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} - 3 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{15} + q^{16} + 8 q^{17} + 3 q^{18} - 16 q^{19} - q^{20} + 2 q^{22} - 3 q^{23} + 9 q^{24} - q^{25} - 4 q^{26} + 6 q^{28} + q^{29} + 3 q^{30} - 5 q^{32} - 4 q^{34} + 6 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} - 6 q^{39} - 3 q^{40} - 5 q^{41} - 9 q^{42} + 8 q^{43} + 4 q^{44} + 6 q^{45} + 6 q^{46} - 7 q^{47} - 2 q^{49} - q^{50} - 12 q^{51} - 2 q^{52} - 4 q^{53} - 9 q^{54} + 4 q^{55} - 9 q^{56} + 24 q^{57} + q^{58} + 14 q^{59} - 7 q^{61} - 9 q^{63} + 14 q^{64} - 2 q^{65} - 6 q^{66} + 3 q^{67} + 4 q^{68} + 9 q^{69} - 3 q^{70} + 4 q^{71} - 9 q^{72} + 8 q^{73} + 4 q^{74} - 8 q^{76} - 6 q^{77} + 6 q^{78} + 6 q^{79} + 2 q^{80} - 9 q^{81} + 10 q^{82} - 9 q^{83} - 9 q^{84} + 4 q^{85} + 8 q^{86} - 6 q^{88} - 30 q^{89} - 3 q^{90} + 12 q^{91} + 3 q^{92} - 7 q^{94} - 8 q^{95} + 15 q^{96} - 2 q^{97} + 4 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 + q^4 + q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 2 * q^11 - 3 * q^12 + 2 * q^13 + 3 * q^14 - 3 * q^15 + q^16 + 8 * q^17 + 3 * q^18 - 16 * q^19 - q^20 + 2 * q^22 - 3 * q^23 + 9 * q^24 - q^25 - 4 * q^26 + 6 * q^28 + q^29 + 3 * q^30 - 5 * q^32 - 4 * q^34 + 6 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 - 6 * q^39 - 3 * q^40 - 5 * q^41 - 9 * q^42 + 8 * q^43 + 4 * q^44 + 6 * q^45 + 6 * q^46 - 7 * q^47 - 2 * q^49 - q^50 - 12 * q^51 - 2 * q^52 - 4 * q^53 - 9 * q^54 + 4 * q^55 - 9 * q^56 + 24 * q^57 + q^58 + 14 * q^59 - 7 * q^61 - 9 * q^63 + 14 * q^64 - 2 * q^65 - 6 * q^66 + 3 * q^67 + 4 * q^68 + 9 * q^69 - 3 * q^70 + 4 * q^71 - 9 * q^72 + 8 * q^73 + 4 * q^74 - 8 * q^76 - 6 * q^77 + 6 * q^78 + 6 * q^79 + 2 * q^80 - 9 * q^81 + 10 * q^82 - 9 * q^83 - 9 * q^84 + 4 * q^85 + 8 * q^86 - 6 * q^88 - 30 * q^89 - 3 * q^90 + 12 * q^91 + 3 * q^92 - 7 * q^94 - 8 * q^95 + 15 * q^96 - 2 * q^97 + 4 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	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	$0.948360\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$			1.73205i			0.707107i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	−3.00000			−1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.00000			−0.316228
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		−	5.19615i		−	1.13389i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	4.50000	+	2.59808i	0.918559	+	0.530330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.00000			−0.392232
$27$		−	5.19615i		−	1.00000i
$28$	3.00000			0.566947
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	1.50000	+	0.866025i	0.273861	+	0.158114i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$		−	3.46410i		−	0.603023i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$	3.00000			0.507093
$36$	3.00000			0.500000
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	4.00000	+	6.92820i	0.648886	+	1.12390i
$39$	−3.00000	+	1.73205i	−0.480384	+	0.277350i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	−4.50000	+	2.59808i	−0.694365	+	0.400892i
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	2.00000			0.301511
$45$	3.00000			0.447214
$46$	3.00000			0.442326
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$		−	1.73205i		−	0.250000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−6.00000	−	3.46410i	−0.840168	−	0.485071i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	2.00000			0.269680
$56$	−4.50000	−	7.79423i	−0.601338	−	1.04155i
$57$	12.0000	+	6.92820i	1.58944	+	0.917663i
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.0991242	−	0.995075i	$-0.468396\pi$
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.812198	−	0.583382i	$-0.198271\pi$
$60$			1.73205i			0.223607i
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$	−4.50000	+	7.79423i	−0.566947	+	0.981981i
$64$	7.00000			0.875000
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$	−3.00000	+	1.73205i	−0.369274	+	0.213201i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$	−1.50000	−	2.59808i	−0.179284	−	0.310530i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−4.50000	−	7.79423i	−0.530330	−	0.918559i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$			1.73205i			0.200000i
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$	−3.00000	+	5.19615i	−0.341882	+	0.592157i
$78$	3.00000	+	1.73205i	0.339683	+	0.196116i
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$	1.00000			0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.00000			0.552158
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$	−4.50000	−	2.59808i	−0.490990	−	0.283473i
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$		−	1.73205i		−	0.185695i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$	6.00000			0.628971
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	2.00000			0.202031
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$	−1.00000			−0.100000
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$			6.92820i			0.685994i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−3.00000	+	5.19615i	−0.294174	+	0.509525i
$105$	−4.50000	−	2.59808i	−0.439155	−	0.253546i
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	−1.50000	+	2.59808i	−0.141737	+	0.245495i
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$		−	13.8564i		−	1.29777i
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	1.00000			0.0928477
$117$	6.00000			0.554700
$118$	−14.0000			−1.28880
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−3.50000	+	6.06218i	−0.316875	+	0.548844i
$123$	7.50000	−	4.33013i	0.676252	−	0.390434i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$	9.00000			0.801784
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$		−	13.8564i		−	1.21999i
$130$	−1.00000	+	1.73205i	−0.0877058	+	0.151911i
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	−3.00000	−	1.73205i	−0.261116	−	0.150756i
$133$	−12.0000	−	20.7846i	−1.04053	−	1.80225i
$134$	−3.00000			−0.259161
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$	−12.0000			−1.02899
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	−4.50000	−	2.59808i	−0.383065	−	0.221163i
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	1.50000	−	2.59808i	0.126773	−	0.219578i
$141$			12.1244i			1.02105i
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$	4.00000			0.334497
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	1.00000			0.0830455
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	3.00000	−	1.73205i	0.247436	−	0.142857i
$148$	−2.00000	+	3.46410i	−0.164399	+	0.284747i
$149$	−8.50000	+	14.7224i	−0.696347	+	1.20611i	0.273377	+	0.961907i	$0.411859\pi$
$149$	−8.50000	+	14.7224i	−0.696347	+	1.20611i	−0.969724	+	0.244202i	$0.921474\pi$
$150$	1.50000	−	0.866025i	0.122474	−	0.0707107i
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	24.0000			1.94666
$153$	6.00000	+	10.3923i	0.485071	+	0.840168i
$154$	6.00000			0.483494
$155$		0			0
$156$			3.46410i			0.277350i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$	3.00000	+	1.73205i	0.237915	+	0.137361i
$160$	2.50000	+	4.33013i	0.197642	+	0.342327i
$161$	−9.00000			−0.709299
$162$	9.00000			0.707107
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.50000	+	4.33013i	0.195217	+	0.338126i
$165$	−3.00000	−	1.73205i	−0.233550	−	0.134840i
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$			15.5885i			1.20268i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−4.00000			−0.306786
$171$	−12.0000	−	20.7846i	−0.917663	−	1.58944i
$172$	8.00000			0.609994
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−1.50000	+	0.866025i	−0.113715	+	0.0656532i
$175$	1.50000	−	2.59808i	0.113389	−	0.196396i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	−21.0000	+	12.1244i	−1.57846	+	0.911322i
$178$	7.50000	+	12.9904i	0.562149	+	0.973670i
$179$	−2.00000			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−3.00000	−	5.19615i	−0.222375	−	0.385164i
$183$			12.1244i			0.896258i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$	−7.00000			−0.510527
$189$	13.5000	−	7.79423i	0.981981	−	0.566947i
$190$	8.00000			0.580381
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	−10.5000	−	6.06218i	−0.757772	−	0.437500i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$			3.46410i			0.248069i
$196$	1.00000	+	1.73205i	0.0714286	+	0.123718i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	6.00000			0.426401
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$	−4.50000	+	2.59808i	−0.317406	+	0.183254i
$202$	9.00000	−	15.5885i	0.633238	−	1.09680i
$203$	−1.50000	+	2.59808i	−0.105279	+	0.182349i
$204$	−6.00000	+	3.46410i	−0.420084	+	0.242536i
$205$	2.50000	+	4.33013i	0.174608	+	0.302429i
$206$	8.00000			0.557386
$207$	−9.00000			−0.625543
$208$	2.00000			0.138675
$209$	−8.00000	−	13.8564i	−0.553372	−	0.958468i
$210$			5.19615i			0.358569i
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	−1.00000	+	1.73205i	−0.0686803	+	0.118958i
$213$	−3.00000	−	1.73205i	−0.205557	−	0.118678i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	8.00000			0.545595
$216$			15.5885i			1.06066i
$217$		0			0
$218$	−2.50000	−	4.33013i	−0.169321	−	0.293273i
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$		−	6.92820i		−	0.464991i
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	−15.0000			−1.00223
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$	−8.00000			−0.532152
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	0.924734	−	0.380615i	$-0.124288\pi$
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	−0.791989	+	0.610535i	$0.790954\pi$
$228$	12.0000	−	6.92820i	0.794719	−	0.458831i
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	−0.999987	−	0.00505719i	$-0.998390\pi$
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	0.504373	+	0.863486i	$0.331724\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$	9.00000	−	5.19615i	0.592157	−	0.341882i
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	−7.00000			−0.456630
$236$	−7.00000	−	12.1244i	−0.455661	−	0.789228i
$237$		−	10.3923i		−	0.675053i
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$	4.00000	−	6.92820i	0.258738	−	0.448148i	−0.707166	−	0.707048i	$-0.750027\pi$
$239$	4.00000	−	6.92820i	0.258738	−	0.448148i	0.965904	+	0.258900i	$0.0833599\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	−7.00000			−0.449977
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−7.00000			−0.448129
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$	−7.50000	−	4.33013i	−0.478183	−	0.276079i
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$		0			0
$249$			15.5885i			0.987878i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	4.50000	+	7.79423i	0.283473	+	0.490990i
$253$	−6.00000			−0.377217
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$	−6.00000	+	3.46410i	−0.375735	+	0.216930i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	−12.0000	+	6.92820i	−0.747087	+	0.431331i
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$	−2.00000			−0.124035
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	−6.00000			−0.370681
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$			10.3923i			0.639602i
$265$	−1.00000	+	1.73205i	−0.0614295	+	0.106399i
$266$	−12.0000	+	20.7846i	−0.735767	+	1.27439i
$267$	22.5000	+	12.9904i	1.37698	+	0.794998i
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	25.0000			1.52428			0.762138	−	0.647414i	$-0.224150\pi$
$269$	25.0000			1.52428			0.762138	+	0.647414i	$0.224150\pi$
$270$			5.19615i			0.316228i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$	−9.00000	−	5.19615i	−0.544705	−	0.314485i
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		−	5.19615i		−	0.312772i
$277$	−6.00000	−	10.3923i	−0.360505	−	0.624413i	0.627539	−	0.778585i	$-0.284062\pi$
$277$	−6.00000	−	10.3923i	−0.360505	−	0.624413i	−0.988044	+	0.154172i	$0.950729\pi$
$278$	−16.0000			−0.959616
$279$		0			0
$280$	−9.00000			−0.537853
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$	10.5000	−	6.06218i	0.625266	−	0.360997i
$283$	−10.5000	+	18.1865i	−0.624160	+	1.08108i	0.364542	+	0.931187i	$0.381225\pi$
$283$	−10.5000	+	18.1865i	−0.624160	+	1.08108i	−0.988703	+	0.149890i	$0.952108\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	12.0000	−	6.92820i	0.710819	−	0.410391i
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	−15.0000			−0.885422
$288$	−15.0000			−0.883883
$289$	−1.00000			−0.0588235
$290$	−0.500000	−	0.866025i	−0.0293610	−	0.0508548i
$291$			3.46410i			0.203069i
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$	−3.00000	−	1.73205i	−0.174964	−	0.101015i
$295$	−7.00000	−	12.1244i	−0.407556	−	0.705907i
$296$	12.0000			0.697486
$297$	9.00000	−	5.19615i	0.522233	−	0.301511i
$298$	17.0000			0.984784
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$	1.50000	+	0.866025i	0.0866025	+	0.0500000i
$301$	−12.0000	+	20.7846i	−0.691669	+	1.19800i
$302$	1.00000	−	1.73205i	0.0575435	−	0.0996683i
$303$		−	31.1769i		−	1.79107i
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$	−7.00000			−0.400819
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	12.0000	−	6.92820i	0.682656	−	0.394132i
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	9.00000	−	5.19615i	0.509525	−	0.294174i
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	14.0000			0.790066
$315$	4.50000	+	7.79423i	0.253546	+	0.439155i
$316$	6.00000			0.337526
$317$	17.0000	+	29.4449i	0.954815	+	1.65379i	0.734791	+	0.678294i	$0.237280\pi$
$317$	17.0000	+	29.4449i	0.954815	+	1.65379i	0.220024	+	0.975494i	$0.429386\pi$
$318$		−	3.46410i		−	0.194257i
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	3.50000	−	6.06218i	0.195656	−	0.338886i
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	4.50000	+	7.79423i	0.250775	+	0.434355i
$323$	−32.0000			−1.78053
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−2.00000			−0.110940
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	−7.50000	−	4.33013i	−0.414751	−	0.239457i
$328$	7.50000	−	12.9904i	0.414118	−	0.717274i
$329$	10.5000	−	18.1865i	0.578884	−	1.00266i
$330$			3.46410i			0.190693i
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	0.936618	−	0.350352i	$-0.113938\pi$
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	−0.771723	+	0.635959i	$0.780605\pi$
$332$	−9.00000			−0.493939
$333$	−6.00000	−	10.3923i	−0.328798	−	0.569495i
$334$	−9.00000			−0.492458
$335$	−1.50000	−	2.59808i	−0.0819538	−	0.141948i
$336$	4.50000	−	2.59808i	0.245495	−	0.141737i
$337$	4.00000	−	6.92820i	0.217894	−	0.377403i	−0.736270	−	0.676688i	$-0.763415\pi$
$337$	4.00000	−	6.92820i	0.217894	−	0.377403i	0.954164	+	0.299285i	$0.0967480\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−12.0000	+	6.92820i	−0.651751	+	0.376288i
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$		0			0
$342$	−12.0000	+	20.7846i	−0.648886	+	1.12390i
$343$	15.0000			0.809924
$344$	−12.0000	−	20.7846i	−0.646997	−	1.12063i
$345$		−	5.19615i		−	0.279751i
$346$		0			0
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$	−1.50000	−	0.866025i	−0.0804084	−	0.0464238i
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$	−3.00000			−0.160357
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$	−10.0000			−0.533002
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	21.0000	+	12.1244i	1.11614	+	0.644402i
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$		−	20.7846i		−	1.10004i
$358$	1.00000	+	1.73205i	0.0528516	+	0.0915417i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	−9.00000			−0.474342
$361$	45.0000			2.36842
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$	−10.5000	+	6.06218i	−0.551107	+	0.318182i
$364$	3.00000	−	5.19615i	0.157243	−	0.272352i
$365$	2.00000	−	3.46410i	0.104685	−	0.181319i
$366$	10.5000	−	6.06218i	0.548844	−	0.316875i
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	−0.988269	−	0.152721i	$-0.951196\pi$
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	0.361874	−	0.932227i	$-0.382137\pi$
$368$	−3.00000			−0.156386
$369$	−15.0000			−0.780869
$370$	4.00000			0.207950
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	−0.965945	−	0.258748i	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$	10.5000	+	18.1865i	0.541496	+	0.937899i
$377$	2.00000			0.103005
$378$	−13.5000	−	7.79423i	−0.694365	−	0.400892i
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$	7.50000	+	4.33013i	0.384237	+	0.221839i
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$		−	5.19615i		−	0.265165i
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$	−10.0000			−0.508987
$387$	−12.0000	+	20.7846i	−0.609994	+	1.05654i
$388$	−2.00000			−0.101535
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	−0.892735	−	0.450582i	$-0.851216\pi$
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	0.0561516	−	0.998422i	$-0.482117\pi$
$390$	3.00000	−	1.73205i	0.151911	−	0.0877058i
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	−9.00000	+	5.19615i	−0.453990	+	0.262111i
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	6.00000			0.301893
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$	−2.00000	−	3.46410i	−0.100251	−	0.173640i
$399$			41.5692i			2.08106i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$	4.50000	+	2.59808i	0.224440	+	0.129580i
$403$		0			0
$404$	18.0000			0.895533
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$	3.00000			0.148888
$407$	−4.00000	−	6.92820i	−0.198273	−	0.343418i
$408$	18.0000	+	10.3923i	0.891133	+	0.514496i
$409$	−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	$0.279170\pi$
$410$	2.50000	−	4.33013i	0.123466	−	0.213850i
$411$			20.7846i			1.02523i
$412$	4.00000	+	6.92820i	0.197066	+	0.341328i
$413$	42.0000			2.06668
$414$	4.50000	+	7.79423i	0.221163	+	0.383065i
$415$	−9.00000			−0.441793
$416$	5.00000	+	8.66025i	0.245145	+	0.424604i
$417$	−24.0000	+	13.8564i	−1.17529	+	0.678551i
$418$	−8.00000	+	13.8564i	−0.391293	+	0.677739i
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	0.351404	+	0.936224i	$0.385704\pi$
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	−0.986496	+	0.163787i	$0.947629\pi$
$420$	−4.50000	+	2.59808i	−0.219578	+	0.126773i
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	−0.899192	−	0.437555i	$-0.855845\pi$
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	0.0706626	−	0.997500i	$-0.477489\pi$
$422$	−22.0000			−1.07094
$423$	10.5000	−	18.1865i	0.510527	−	0.884260i
$424$	6.00000			0.291386
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$			3.46410i			0.167836i
$427$	10.5000	−	18.1865i	0.508131	−	0.880108i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$	−6.00000	−	3.46410i	−0.289683	−	0.167248i
$430$	−4.00000	−	6.92820i	−0.192897	−	0.334108i
$431$	−30.0000			−1.44505			−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000			−1.44505			−0.722525	+	0.691345i	$0.757018\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$		0			0
$435$	−1.50000	−	0.866025i	−0.0719195	−	0.0415227i
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$			6.92820i			0.331042i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$	−6.00000			−0.286039
$441$	−6.00000			−0.285714
$442$	−8.00000			−0.380521
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	0.631010	−	0.775775i	$-0.282641\pi$
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	−0.987346	+	0.158583i	$0.949307\pi$
$444$	6.00000	−	3.46410i	0.284747	−	0.164399i
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$	25.5000	−	14.7224i	1.20611	−	0.696347i
$448$	10.5000	+	18.1865i	0.496078	+	0.859233i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$	−3.00000			−0.141421
$451$	−10.0000			−0.470882
$452$	−4.00000	−	6.92820i	−0.188144	−	0.325875i
$453$		−	3.46410i		−	0.162758i
$454$	2.00000	−	3.46410i	0.0938647	−	0.162578i
$455$	3.00000	−	5.19615i	0.140642	−	0.243599i
$456$	−36.0000	−	20.7846i	−1.68585	−	0.973329i
$457$	10.0000	+	17.3205i	0.467780	+	0.810219i	0.999322	−	0.0368128i	$-0.0117205\pi$
$457$	10.0000	+	17.3205i	0.467780	+	0.810219i	−0.531542	+	0.847032i	$0.678387\pi$
$458$	15.0000			0.700904
$459$		−	20.7846i		−	0.970143i
$460$	3.00000			0.139876
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	0.741998	−	0.670402i	$-0.233878\pi$
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	−0.951584	+	0.307388i	$0.900545\pi$
$462$	−9.00000	−	5.19615i	−0.418718	−	0.241747i
$463$	18.0000	−	31.1769i	0.836531	−	1.44891i	−0.0562469	−	0.998417i	$-0.517913\pi$
$463$	18.0000	−	31.1769i	0.836531	−	1.44891i	0.892778	−	0.450497i	$-0.148753\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$	3.00000	−	5.19615i	0.138675	−	0.240192i
$469$	9.00000			0.415581
$470$	3.50000	+	6.06218i	0.161443	+	0.279627i
$471$	21.0000	−	12.1244i	0.967629	−	0.558661i
$472$	−21.0000	+	36.3731i	−0.966603	+	1.67421i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$	−9.00000	+	5.19615i	−0.413384	+	0.238667i
$475$	4.00000	+	6.92820i	0.183533	+	0.317888i
$476$	12.0000			0.550019
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−8.00000			−0.365911
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		−	8.66025i		−	0.395285i
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$	5.50000	−	9.52628i	0.250518	−	0.433910i
$483$	13.5000	+	7.79423i	0.614271	+	0.354650i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	−2.00000			−0.0908153
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	10.5000	+	18.1865i	0.475313	+	0.823266i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$		−	8.66025i		−	0.390434i
$493$	2.00000	+	3.46410i	0.0900755	+	0.156015i
$494$	16.0000			0.719874
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$		0			0
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	13.5000	−	7.79423i	0.604949	−	0.349268i
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−13.5000	+	7.79423i	−0.603136	+	0.348220i
$502$		0			0
$503$	−7.00000			−0.312115			−0.156057	−	0.987748i	$-0.549878\pi$
$503$	−7.00000			−0.312115			−0.156057	+	0.987748i	$0.549878\pi$
$504$	13.5000	−	23.3827i	0.601338	−	1.04155i
$505$	18.0000			0.800989
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		−	15.5885i		−	0.692308i
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	−21.5000	+	37.2391i	−0.952971	+	1.65059i	−0.214026	+	0.976828i	$0.568658\pi$
$509$	−21.5000	+	37.2391i	−0.952971	+	1.65059i	−0.738945	+	0.673766i	$0.764676\pi$
$510$	6.00000	+	3.46410i	0.265684	+	0.153393i
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	−11.0000			−0.486136
$513$			41.5692i			1.83533i
$514$	−6.00000			−0.264649
$515$	4.00000	+	6.92820i	0.176261	+	0.305293i
$516$	−12.0000	−	6.92820i	−0.528271	−	0.304997i
$517$	7.00000	−	12.1244i	0.307860	−	0.533229i
$518$	−6.00000	+	10.3923i	−0.263625	+	0.456612i
$519$		0			0
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$	3.00000			0.131306
$523$	−29.0000			−1.26808			−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000			−1.26808			−0.634041	+	0.773300i	$0.718605\pi$
$524$	−3.00000	−	5.19615i	−0.131056	−	0.226995i
$525$	−4.50000	+	2.59808i	−0.196396	+	0.113389i
$526$	8.00000	−	13.8564i	0.348817	−	0.604168i
$527$		0			0
$528$	3.00000	−	1.73205i	0.130558	−	0.0753778i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	2.00000			0.0868744
$531$	42.0000			1.82264
$532$	−24.0000			−1.04053
$533$	5.00000	+	8.66025i	0.216574	+	0.375117i
$534$		−	25.9808i		−	1.12430i
$535$	1.50000	−	2.59808i	0.0648507	−	0.112325i
$536$	−4.50000	+	7.79423i	−0.194370	+	0.336659i
$537$	3.00000	+	1.73205i	0.129460	+	0.0747435i
$538$	−12.5000	−	21.6506i	−0.538913	−	0.933425i
$539$	−4.00000			−0.172292
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	−39.0000			−1.67674			−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000			−1.67674			−0.838370	+	0.545101i	$0.816491\pi$
$542$	4.00000	+	6.92820i	0.171815	+	0.297592i
$543$	10.5000	+	6.06218i	0.450598	+	0.260153i
$544$	−10.0000	+	17.3205i	−0.428746	+	0.742611i
$545$	2.50000	−	4.33013i	0.107088	−	0.185482i
$546$			10.3923i			0.444750i
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	−12.0000			−0.512615
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$	−2.00000			−0.0852803
$551$	−4.00000	−	6.92820i	−0.170406	−	0.295151i
$552$	−13.5000	+	7.79423i	−0.574598	+	0.331744i
$553$	−9.00000	+	15.5885i	−0.382719	+	0.662889i
$554$	−6.00000	+	10.3923i	−0.254916	+	0.441527i
$555$	6.00000	−	3.46410i	0.254686	−	0.147043i
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$	1.50000	+	2.59808i	0.0633866	+	0.109789i
$561$		−	13.8564i		−	0.585018i
$562$	7.50000	−	12.9904i	0.316368	−	0.547966i
$563$	10.5000	−	18.1865i	0.442522	−	0.766471i	−0.555354	−	0.831614i	$-0.687417\pi$
$563$	10.5000	−	18.1865i	0.442522	−	0.766471i	0.997876	+	0.0651433i	$0.0207504\pi$
$564$	10.5000	+	6.06218i	0.442130	+	0.255264i
$565$	−4.00000	−	6.92820i	−0.168281	−	0.291472i
$566$	21.0000			0.882696
$567$	−27.0000			−1.13389
$568$	−6.00000			−0.251754
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−12.0000	−	6.92820i	−0.502625	−	0.290191i
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$			13.8564i			0.578860i
$574$	7.50000	+	12.9904i	0.313044	+	0.542208i
$575$	3.00000			0.125109
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	−15.0000	+	8.66025i	−0.623379	+	0.359908i
$580$	0.500000	−	0.866025i	0.0207614	−	0.0359597i
$581$	13.5000	−	23.3827i	0.560074	−	0.970077i
$582$	3.00000	−	1.73205i	0.124354	−	0.0717958i
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	−12.0000			−0.496564
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$	12.0000			0.495715
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$		−	3.46410i		−	0.142857i
$589$		0			0
$590$	−7.00000	+	12.1244i	−0.288185	+	0.499152i
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	20.0000			0.821302			0.410651	−	0.911793i	$-0.365302\pi$
$593$	20.0000			0.821302			0.410651	+	0.911793i	$0.365302\pi$
$594$	−9.00000	−	5.19615i	−0.369274	−	0.213201i
$595$	12.0000			0.491952
$596$	8.50000	+	14.7224i	0.348174	+	0.603054i
$597$	−6.00000	−	3.46410i	−0.245564	−	0.141776i
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	−0.745613	−	0.666379i	$-0.767843\pi$
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	0.949908	+	0.312531i	$0.101177\pi$
$600$		−	5.19615i		−	0.212132i
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$	24.0000			0.978167
$603$	9.00000			0.366508
$604$	2.00000			0.0813788
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$	−27.0000	+	15.5885i	−1.09680	+	0.633238i
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	−0.0643251	−	0.997929i	$-0.520489\pi$
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	0.896394	−	0.443257i	$-0.146177\pi$
$608$	20.0000	−	34.6410i	0.811107	−	1.40488i
$609$	4.50000	−	2.59808i	0.182349	−	0.105279i
$610$	3.50000	+	6.06218i	0.141711	+	0.245450i
$611$	−14.0000			−0.566379
$612$	12.0000			0.485071
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		−	8.66025i		−	0.349215i
$616$	9.00000	−	15.5885i	0.362620	−	0.628077i
$617$	18.0000	−	31.1769i	0.724653	−	1.25514i	−0.234464	−	0.972125i	$-0.575334\pi$
$617$	18.0000	−	31.1769i	0.724653	−	1.25514i	0.959117	−	0.283011i	$-0.0913331\pi$
$618$	−12.0000	−	6.92820i	−0.482711	−	0.278693i
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$		0			0
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		0			0
$623$	−22.5000	−	38.9711i	−0.901443	−	1.56135i
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$			27.7128i			1.10674i
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	−16.0000			−0.637962
$630$	4.50000	−	7.79423i	0.179284	−	0.310530i
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	−9.00000	−	15.5885i	−0.358001	−	0.620076i
$633$	−33.0000	+	19.0526i	−1.31163	+	0.757271i
$634$	17.0000	−	29.4449i	0.675156	−	1.16940i
$635$	−2.50000	+	4.33013i	−0.0992095	+	0.171836i
$636$	3.00000	−	1.73205i	0.118958	−	0.0686803i
$637$	2.00000	+	3.46410i	0.0792429	+	0.137253i
$638$	2.00000			0.0791808
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	3.00000			0.118585
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$			5.19615i			0.205076i
$643$	4.50000	−	7.79423i	0.177463	−	0.307374i	−0.763548	−	0.645751i	$-0.776544\pi$
$643$	4.50000	−	7.79423i	0.177463	−	0.307374i	0.941011	+	0.338377i	$0.109878\pi$
$644$	−4.50000	+	7.79423i	−0.177325	+	0.307136i
$645$	−12.0000	−	6.92820i	−0.472500	−	0.272798i
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	−17.0000			−0.668339			−0.334169	−	0.942513i	$-0.608456\pi$
$647$	−17.0000			−0.668339			−0.334169	+	0.942513i	$0.608456\pi$
$648$	13.5000	−	23.3827i	0.530330	−	0.918559i
$649$	28.0000			1.09910
$650$	1.00000	+	1.73205i	0.0392232	+	0.0679366i
$651$		0			0
$652$	−2.00000	+	3.46410i	−0.0783260	+	0.135665i
$653$	2.00000	−	3.46410i	0.0782660	−	0.135561i	−0.824236	−	0.566247i	$-0.808395\pi$
$653$	2.00000	−	3.46410i	0.0782660	−	0.135561i	0.902502	+	0.430686i	$0.141728\pi$
$654$			8.66025i			0.338643i
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$	−5.00000			−0.195217
$657$	6.00000	+	10.3923i	0.234082	+	0.405442i
$658$	−21.0000			−0.818665
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	0.933357	−	0.358951i	$-0.116865\pi$
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	−0.777539	+	0.628835i	$0.783532\pi$
$660$	−3.00000	+	1.73205i	−0.116775	+	0.0674200i
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	3.00000	−	5.19615i	0.116598	−	0.201954i
$663$	−12.0000	+	6.92820i	−0.466041	+	0.269069i
$664$	13.5000	+	23.3827i	0.523902	+	0.907424i
$665$	−24.0000			−0.930680
$666$	−6.00000	+	10.3923i	−0.232495	+	0.402694i
$667$	−3.00000			−0.116160
$668$	−4.50000	−	7.79423i	−0.174110	−	0.301568i
$669$		−	32.9090i		−	1.27233i
$670$	−1.50000	+	2.59808i	−0.0579501	+	0.100372i
$671$	7.00000	−	12.1244i	0.270232	−	0.468056i
$672$	22.5000	+	12.9904i	0.867956	+	0.501115i
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	0.802395	−	0.596794i	$-0.203559\pi$
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	−0.918036	+	0.396497i	$0.870226\pi$
$674$	−8.00000			−0.308148
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$	9.00000			0.346154
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$	12.0000	+	6.92820i	0.460857	+	0.266076i
$679$	3.00000	−	5.19615i	0.115129	−	0.199410i
$680$	−6.00000	+	10.3923i	−0.230089	+	0.398527i
$681$		−	6.92820i		−	0.265489i
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−24.0000			−0.917663
$685$	−12.0000			−0.458496
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	22.5000	−	12.9904i	0.858429	−	0.495614i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$	−4.50000	+	2.59808i	−0.171312	+	0.0989071i
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	0.967901	−	0.251330i	$-0.0808679\pi$
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	−0.701609	+	0.712562i	$0.747535\pi$
$692$		0			0
$693$	−18.0000			−0.683763
$694$	4.00000			0.151838
$695$	−8.00000	−	13.8564i	−0.303457	−	0.525603i
$696$			5.19615i			0.196960i
$697$	−10.0000	+	17.3205i	−0.378777	+	0.656061i
$698$	2.50000	−	4.33013i	0.0946264	−	0.163898i
$699$	−36.0000	−	20.7846i	−1.36165	−	0.786146i
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	23.0000			0.868698			0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000			0.868698			0.434349	+	0.900745i	$0.356978\pi$
$702$			10.3923i			0.392232i
$703$	32.0000			1.20690
$704$	7.00000	+	12.1244i	0.263822	+	0.456954i
$705$	10.5000	+	6.06218i	0.395453	+	0.228315i
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−27.0000	+	46.7654i	−1.01544	+	1.75879i
$708$			24.2487i			0.911322i
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	0.937620	+	0.347661i	$0.113024\pi$
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	−0.167727	+	0.985834i	$0.553643\pi$
$710$	−2.00000			−0.0750587
$711$	−9.00000	+	15.5885i	−0.337526	+	0.584613i
$712$	45.0000			1.68645
$713$		0			0
$714$	−18.0000	+	10.3923i	−0.673633	+	0.388922i
$715$	2.00000	−	3.46410i	0.0747958	−	0.129550i
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	−12.0000	+	6.92820i	−0.448148	+	0.258738i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$	1.50000	+	2.59808i	0.0559017	+	0.0968246i
$721$	−24.0000			−0.893807
$722$	−22.5000	−	38.9711i	−0.837363	−	1.45036i
$723$		−	19.0526i		−	0.708572i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	0.500000	−	0.866025i	0.0185695	−	0.0321634i
$726$	10.5000	+	6.06218i	0.389692	+	0.224989i
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	0.570049	−	0.821611i	$-0.306924\pi$
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	−0.996560	+	0.0828714i	$0.973591\pi$
$728$	−18.0000			−0.667124
$729$	−27.0000			−1.00000
$730$	−4.00000			−0.148047
$731$	16.0000	+	27.7128i	0.591781	+	1.02500i
$732$	10.5000	+	6.06218i	0.388091	+	0.224065i
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	−0.360061	−	0.932929i	$-0.617244\pi$
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	0.987971	−	0.154642i	$-0.0494225\pi$
$734$	−12.0000	+	20.7846i	−0.442928	+	0.767174i
$735$		−	3.46410i		−	0.127775i
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	6.00000			0.221013
$738$	7.50000	+	12.9904i	0.276079	+	0.478183i
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$	24.0000	−	13.8564i	0.881662	−	0.509028i
$742$	−3.00000	+	5.19615i	−0.110133	+	0.190757i
$743$	14.5000	−	25.1147i	0.531953	−	0.921370i	−0.467351	−	0.884072i	$-0.654791\pi$
$743$	14.5000	−	25.1147i	0.531953	−	0.921370i	0.999304	−	0.0372984i	$-0.0118752\pi$
$744$		0			0
$745$	8.50000	+	14.7224i	0.311416	+	0.539388i
$746$	10.0000			0.366126
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$	8.00000			0.292509
$749$	4.50000	+	7.79423i	0.164426	+	0.284795i
$750$		−	1.73205i		−	0.0632456i
$751$	−5.00000	+	8.66025i	−0.182453	+	0.316017i	−0.942715	−	0.333599i	$-0.891737\pi$
$751$	−5.00000	+	8.66025i	−0.182453	+	0.316017i	0.760263	+	0.649616i	$0.225070\pi$
$752$	3.50000	−	6.06218i	0.127632	−	0.221065i
$753$		0			0
$754$	−1.00000	−	1.73205i	−0.0364179	−	0.0630776i
$755$	2.00000			0.0727875
$756$		−	15.5885i		−	0.566947i
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	13.0000	+	22.5167i	0.472181	+	0.817842i
$759$	9.00000	+	5.19615i	0.326679	+	0.188608i
$760$	12.0000	−	20.7846i	0.435286	−	0.753937i
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	−0.969342	−	0.245716i	$-0.920977\pi$
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	0.697467	+	0.716617i	$0.254310\pi$
$762$		−	8.66025i		−	0.313728i
$763$	7.50000	+	12.9904i	0.271518	+	0.470283i
$764$	−8.00000			−0.289430
$765$	12.0000			0.433861
$766$	36.0000			1.30073
$767$	−14.0000	−	24.2487i	−0.505511	−	0.875570i
$768$	−25.5000	+	14.7224i	−0.920152	+	0.531250i
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$	3.00000	−	5.19615i	0.108112	−	0.187256i
$771$	−9.00000	+	5.19615i	−0.324127	+	0.187135i
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$	24.0000			0.862662
$775$		0			0
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$			20.7846i			0.745644i
$778$	−16.5000	+	28.5788i	−0.591554	+	1.02460i
$779$	20.0000	−	34.6410i	0.716574	−	1.24114i
$780$	3.00000	+	1.73205i	0.107417	+	0.0620174i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	12.0000			0.429119
$783$	4.50000	−	2.59808i	0.160817	−	0.0928477i
$784$	−2.00000			−0.0714286
$785$	7.00000	+	12.1244i	0.249841	+	0.432737i
$786$	9.00000	+	5.19615i	0.321019	+	0.185341i
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$		−	27.7128i		−	0.986602i
$790$	−3.00000	−	5.19615i	−0.106735	−	0.184871i
$791$	24.0000			0.853342
$792$	9.00000	−	15.5885i	0.319801	−	0.553912i
$793$	−14.0000			−0.497155
$794$	−17.0000	−	29.4449i	−0.603307	−	1.04496i
$795$	3.00000	−	1.73205i	0.106399	−	0.0614295i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−13.0000	+	22.5167i	−0.460484	+	0.797581i	−0.998985	−	0.0450436i	$-0.985657\pi$
$797$	−13.0000	+	22.5167i	−0.460484	+	0.797581i	0.538501	+	0.842625i	$0.318991\pi$
$798$	36.0000	−	20.7846i	1.27439	−	0.735767i
$799$	−14.0000	−	24.2487i	−0.495284	−	0.857858i
$800$	5.00000			0.176777
$801$	−22.5000	−	38.9711i	−0.794998	−	1.37698i
$802$	−18.0000			−0.635602
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$			5.19615i			0.183254i
$805$	−4.50000	+	7.79423i	−0.158604	+	0.274710i
$806$		0			0
$807$	−37.5000	−	21.6506i	−1.32006	−	0.762138i
$808$	−27.0000	−	46.7654i	−0.949857	−	1.64520i
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	−42.0000			−1.47482			−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000			−1.47482			−0.737410	+	0.675446i	$0.763951\pi$
$812$	1.50000	+	2.59808i	0.0526397	+	0.0911746i
$813$	12.0000	+	6.92820i	0.420858	+	0.242983i
$814$	−4.00000	+	6.92820i	−0.140200	+	0.242833i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$		−	6.92820i		−	0.242536i
$817$	−32.0000	−	55.4256i	−1.11954	−	1.93910i
$818$	14.0000			0.489499
$819$	9.00000	+	15.5885i	0.314485	+	0.544705i
$820$	5.00000			0.174608
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	0.704956	−	0.709251i	$-0.250967\pi$
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	−0.966708	+	0.255884i	$0.917634\pi$
$822$	18.0000	−	10.3923i	0.627822	−	0.362473i
$823$	−26.5000	+	45.8993i	−0.923732	+	1.59995i	−0.130144	+	0.991495i	$0.541544\pi$
$823$	−26.5000	+	45.8993i	−0.923732	+	1.59995i	−0.793588	+	0.608456i	$0.791789\pi$
$824$	12.0000	−	20.7846i	0.418040	−	0.724066i
$825$	−3.00000	+	1.73205i	−0.104447	+	0.0603023i
$826$	−21.0000	−	36.3731i	−0.730683	−	1.26558i
$827$	37.0000			1.28662			0.643308	−	0.765607i	$-0.277561\pi$
$827$	37.0000			1.28662			0.643308	+	0.765607i	$0.277561\pi$
$828$	−4.50000	+	7.79423i	−0.156386	+	0.270868i
$829$	−3.00000			−0.104194			−0.0520972	−	0.998642i	$-0.516591\pi$
$829$	−3.00000			−0.104194			−0.0520972	+	0.998642i	$0.516591\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$			20.7846i			0.721010i
$832$	7.00000	−	12.1244i	0.242681	−	0.420336i
$833$	−4.00000	+	6.92820i	−0.138592	+	0.240048i
$834$	24.0000	+	13.8564i	0.831052	+	0.479808i
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$	−16.0000			−0.553372
$837$		0			0
$838$	26.0000			0.898155
$839$	20.0000	+	34.6410i	0.690477	+	1.19594i	0.971682	+	0.236293i	$0.0759325\pi$
$839$	20.0000	+	34.6410i	0.690477	+	1.19594i	−0.281205	+	0.959648i	$0.590734\pi$
$840$	13.5000	+	7.79423i	0.465794	+	0.268926i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	−17.0000	+	29.4449i	−0.585859	+	1.01474i
$843$		−	25.9808i		−	0.894825i
$844$	−11.0000	−	19.0526i	−0.378636	−	0.655816i
$845$	9.00000			0.309609
$846$	−21.0000			−0.721995
$847$	21.0000			0.721569
$848$	−1.00000	−	1.73205i	−0.0343401	−	0.0594789i
$849$	31.5000	−	18.1865i	1.08108	−	0.624160i
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	−3.00000	+	1.73205i	−0.102778	+	0.0593391i
$853$	27.0000	+	46.7654i	0.924462	+	1.60122i	0.792424	+	0.609971i	$0.208819\pi$
$853$	27.0000	+	46.7654i	0.924462	+	1.60122i	0.132039	+	0.991245i	$0.457848\pi$
$854$	−21.0000			−0.718605
$855$	−24.0000			−0.820783
$856$	−9.00000			−0.307614
$857$	−5.00000	−	8.66025i	−0.170797	−	0.295829i	0.767902	−	0.640567i	$-0.221301\pi$
$857$	−5.00000	−	8.66025i	−0.170797	−	0.295829i	−0.938699	+	0.344739i	$0.887967\pi$
$858$			6.92820i			0.236525i
$859$	−11.0000	+	19.0526i	−0.375315	+	0.650065i	−0.990374	−	0.138416i	$-0.955799\pi$
$859$	−11.0000	+	19.0526i	−0.375315	+	0.650065i	0.615059	+	0.788481i	$0.289132\pi$
$860$	4.00000	−	6.92820i	0.136399	−	0.236250i
$861$	22.5000	+	12.9904i	0.766798	+	0.442711i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	17.0000			0.578687			0.289343	−	0.957225i	$-0.406563\pi$
$863$	17.0000			0.578687			0.289343	+	0.957225i	$0.406563\pi$
$864$	22.5000	+	12.9904i	0.765466	+	0.441942i
$865$		0			0
$866$	−14.0000	−	24.2487i	−0.475739	−	0.824005i
$867$	1.50000	+	0.866025i	0.0509427	+	0.0294118i
$868$		0			0
$869$	−6.00000	+	10.3923i	−0.203536	+	0.352535i
$870$			1.73205i			0.0587220i
$871$	−3.00000	−	5.19615i	−0.101651	−	0.176065i
$872$	−15.0000			−0.507964
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$	−24.0000			−0.811812
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$	−6.00000	+	3.46410i	−0.202721	+	0.117041i
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$	−14.0000	+	24.2487i	−0.472477	+	0.818354i
$879$	18.0000	−	10.3923i	0.607125	−	0.350524i
$880$	1.00000	+	1.73205i	0.0337100	+	0.0583874i
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	3.00000	+	5.19615i	0.101015	+	0.174964i
$883$	23.0000			0.774012			0.387006	−	0.922077i	$-0.373509\pi$
$883$	23.0000			0.774012			0.387006	+	0.922077i	$0.373509\pi$
$884$	−4.00000	−	6.92820i	−0.134535	−	0.233021i
$885$			24.2487i			0.815112i
$886$	−7.50000	+	12.9904i	−0.251967	+	0.436420i
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$	−18.0000	−	10.3923i	−0.604040	−	0.348743i
$889$	−7.50000	−	12.9904i	−0.251542	−	0.435683i
$890$	15.0000			0.502801
$891$	−18.0000			−0.603023
$892$	19.0000			0.636167
$893$	28.0000	+	48.4974i	0.936984	+	1.62290i
$894$	−25.5000	−	14.7224i	−0.852848	−	0.492392i
$895$	−1.00000	+	1.73205i	−0.0334263	+	0.0578961i
$896$	−4.50000	+	7.79423i	−0.150334	+	0.260387i
$897$		−	10.3923i		−	0.346989i
$898$	13.0000	+	22.5167i	0.433816	+	0.751391i
$899$		0			0
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	−8.00000			−0.266519
$902$	5.00000	+	8.66025i	0.166482	+	0.288355i
$903$	36.0000	−	20.7846i	1.19800	−	0.691669i
$904$	−12.0000	+	20.7846i	−0.399114	+	0.691286i
$905$	−3.50000	+	6.06218i	−0.116344	+	0.201514i
$906$	−3.00000	+	1.73205i	−0.0996683	+	0.0575435i
$907$	25.5000	+	44.1673i	0.846714	+	1.46655i	0.884125	+	0.467251i	$0.154756\pi$
$907$	25.5000	+	44.1673i	0.846714	+	1.46655i	−0.0374111	+	0.999300i	$0.511911\pi$
$908$	4.00000			0.132745
$909$	−27.0000	+	46.7654i	−0.895533	+	1.55111i
$910$	−6.00000			−0.198898
$911$	25.0000	+	43.3013i	0.828287	+	1.43464i	0.899381	+	0.437165i	$0.144018\pi$
$911$	25.0000	+	43.3013i	0.828287	+	1.43464i	−0.0710941	+	0.997470i	$0.522649\pi$
$912$			13.8564i			0.458831i
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	10.0000	−	17.3205i	0.330771	−	0.572911i
$915$	10.5000	+	6.06218i	0.347119	+	0.200409i
$916$	7.50000	+	12.9904i	0.247807	+	0.429214i
$917$	18.0000			0.594412
$918$	−18.0000	+	10.3923i	−0.594089	+	0.342997i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$	−10.5000	−	6.06218i	−0.345987	−	0.199756i
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$	2.00000	−	3.46410i	0.0658308	−	0.114022i
$924$		−	10.3923i		−	0.341882i
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	−36.0000			−1.18303
$927$	−24.0000			−0.788263
$928$	−5.00000			−0.164133
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$	8.00000	−	13.8564i	0.262189	−	0.454125i
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$		0			0
$934$	−10.0000	−	17.3205i	−0.327210	−	0.566744i
$935$	8.00000			0.261628
$936$	−18.0000			−0.588348
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−4.50000	−	7.79423i	−0.146930	−	0.254491i
$939$			24.2487i			0.791327i
$940$	−3.50000	+	6.06218i	−0.114157	+	0.197726i
$941$	3.50000	−	6.06218i	0.114097	−	0.197621i	−0.803322	−	0.595545i	$-0.796936\pi$
$941$	3.50000	−	6.06218i	0.114097	−	0.197621i	0.917418	+	0.397924i	$0.130269\pi$
$942$	−21.0000	−	12.1244i	−0.684217	−	0.395033i
$943$	−7.50000	−	12.9904i	−0.244234	−	0.423025i
$944$	14.0000			0.455661
$945$		−	15.5885i		−	0.507093i
$946$	16.0000			0.520205
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.789741	−	0.613441i	$-0.789785\pi$
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.136385	−	0.990656i	$-0.543548\pi$
$948$	−9.00000	−	5.19615i	−0.292306	−	0.168763i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	4.00000	−	6.92820i	0.129777	−	0.224781i
$951$		−	58.8897i		−	1.90963i
$952$	−18.0000	−	31.1769i	−0.583383	−	1.01045i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	−8.00000			−0.258874
$956$	−4.00000	−	6.92820i	−0.129369	−	0.224074i
$957$	3.00000	−	1.73205i	0.0969762	−	0.0559893i
$958$	9.00000	−	15.5885i	0.290777	−	0.503640i
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$	−10.5000	+	6.06218i	−0.338886	+	0.195656i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	8.00000			0.257930
$963$	4.50000	+	7.79423i	0.145010	+	0.251166i
$964$	11.0000			0.354286
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$		−	15.5885i		−	0.501550i
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	0.321578	+	0.946883i	$0.395787\pi$
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	−0.980814	+	0.194946i	$0.937547\pi$
$968$	−10.5000	+	18.1865i	−0.337483	+	0.584537i
$969$	48.0000	+	27.7128i	1.54198	+	0.890264i
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		−	15.5885i		−	0.500000i
$973$	48.0000			1.53881
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$	3.00000	+	1.73205i	0.0960769	+	0.0554700i
$976$	3.50000	−	6.06218i	0.112032	−	0.194046i
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	−0.383728	−	0.923446i	$-0.625360\pi$
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	0.991592	−	0.129405i	$-0.0413067\pi$
$978$		−	6.92820i		−	0.221540i
$979$	−15.0000	−	25.9808i	−0.479402	−	0.830349i
$980$	2.00000			0.0638877
$981$	7.50000	+	12.9904i	0.239457	+	0.414751i
$982$	20.0000			0.638226
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$	−22.5000	+	12.9904i	−0.717274	+	0.414118i
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$	2.00000	−	3.46410i	0.0636930	−	0.110319i
$987$	−31.5000	+	18.1865i	−1.00266	+	0.578884i
$988$	8.00000	+	13.8564i	0.254514	+	0.440831i
$989$	−24.0000			−0.763156
$990$	3.00000	−	5.19615i	0.0953463	−	0.165145i
$991$	26.0000			0.825917			0.412959	−	0.910750i	$-0.364495\pi$
$991$	26.0000			0.825917			0.412959	+	0.910750i	$0.364495\pi$
$992$		0			0
$993$		−	10.3923i		−	0.329790i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$	2.00000	−	3.46410i	0.0634043	−	0.109819i
$996$	13.5000	+	7.79423i	0.427764	+	0.246970i
$997$	9.00000	+	15.5885i	0.285033	+	0.493691i	0.972617	−	0.232413i	$-0.0746622\pi$
$997$	9.00000	+	15.5885i	0.285033	+	0.493691i	−0.687584	+	0.726105i	$0.741329\pi$
$998$	−32.0000			−1.01294
$999$			20.7846i			0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.e.a.31.1	yes	2
3.2	odd	2		135.2.e.a.91.1		2
4.3	odd	2		720.2.q.d.481.1		2
5.2	odd	4		225.2.k.a.49.2		4
5.3	odd	4		225.2.k.a.49.1		4
5.4	even	2		225.2.e.a.76.1		2
9.2	odd	6		135.2.e.a.46.1		2
9.4	even	3		405.2.a.e.1.1		1
9.5	odd	6		405.2.a.b.1.1		1
9.7	even	3	inner	45.2.e.a.16.1	✓	2
12.11	even	2		2160.2.q.a.1441.1		2
15.2	even	4		675.2.k.a.199.1		4
15.8	even	4		675.2.k.a.199.2		4
15.14	odd	2		675.2.e.a.226.1		2
36.7	odd	6		720.2.q.d.241.1		2
36.11	even	6		2160.2.q.a.721.1		2
36.23	even	6		6480.2.a.x.1.1		1
36.31	odd	6		6480.2.a.k.1.1		1
45.2	even	12		675.2.k.a.424.2		4
45.4	even	6		2025.2.a.b.1.1		1
45.7	odd	12		225.2.k.a.124.1		4
45.13	odd	12		2025.2.b.c.649.1		2
45.14	odd	6		2025.2.a.e.1.1		1
45.22	odd	12		2025.2.b.c.649.2		2
45.23	even	12		2025.2.b.d.649.2		2
45.29	odd	6		675.2.e.a.451.1		2
45.32	even	12		2025.2.b.d.649.1		2
45.34	even	6		225.2.e.a.151.1		2
45.38	even	12		675.2.k.a.424.1		4
45.43	odd	12		225.2.k.a.124.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.a.16.1	✓	2	9.7	even	3	inner
45.2.e.a.31.1	yes	2	1.1	even	1	trivial
135.2.e.a.46.1		2	9.2	odd	6
135.2.e.a.91.1		2	3.2	odd	2
225.2.e.a.76.1		2	5.4	even	2
225.2.e.a.151.1		2	45.34	even	6
225.2.k.a.49.1		4	5.3	odd	4
225.2.k.a.49.2		4	5.2	odd	4
225.2.k.a.124.1		4	45.7	odd	12
225.2.k.a.124.2		4	45.43	odd	12
405.2.a.b.1.1		1	9.5	odd	6
405.2.a.e.1.1		1	9.4	even	3
675.2.e.a.226.1		2	15.14	odd	2
675.2.e.a.451.1		2	45.29	odd	6
675.2.k.a.199.1		4	15.2	even	4
675.2.k.a.199.2		4	15.8	even	4
675.2.k.a.424.1		4	45.38	even	12
675.2.k.a.424.2		4	45.2	even	12
720.2.q.d.241.1		2	36.7	odd	6
720.2.q.d.481.1		2	4.3	odd	2
2025.2.a.b.1.1		1	45.4	even	6
2025.2.a.e.1.1		1	45.14	odd	6
2025.2.b.c.649.1		2	45.13	odd	12
2025.2.b.c.649.2		2	45.22	odd	12
2025.2.b.d.649.1		2	45.32	even	12
2025.2.b.d.649.2		2	45.23	even	12
2160.2.q.a.721.1		2	36.11	even	6
2160.2.q.a.1441.1		2	12.11	even	2
6480.2.a.k.1.1		1	36.31	odd	6
6480.2.a.x.1.1		1	36.23	even	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-1.50000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(1.50000 - 2.59808i) q^{18} -8.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} -5.19615i q^{21} +(1.00000 - 1.73205i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{26} -5.19615i q^{27} +3.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(1.50000 + 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{32} -3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +3.00000 q^{35} +3.00000 q^{36} -4.00000 q^{37} +(4.00000 + 6.92820i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-4.50000 + 2.59808i) q^{42} +(4.00000 + 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{45} +3.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} -1.73205i q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} -2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +2.00000 q^{55} +(-4.50000 - 7.79423i) q^{56} +(12.0000 + 6.92820i) q^{57} +(0.500000 - 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{59} +1.73205i q^{60} +(-3.50000 - 6.06218i) q^{61} +(-4.50000 + 7.79423i) q^{63} +7.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(-3.00000 + 1.73205i) q^{66} +(1.50000 - 2.59808i) q^{67} +(2.00000 - 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-1.50000 - 2.59808i) q^{70} +2.00000 q^{71} +(-4.50000 - 7.79423i) q^{72} +4.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +1.73205i q^{75} +(-4.00000 + 6.92820i) q^{76} +(-3.00000 + 5.19615i) q^{77} +(3.00000 + 1.73205i) q^{78} +(3.00000 + 5.19615i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(2.00000 - 3.46410i) q^{85} +(4.00000 - 6.92820i) q^{86} -1.73205i q^{87} +(-3.00000 - 5.19615i) q^{88} -15.0000 q^{89} +(-1.50000 - 2.59808i) q^{90} +6.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(7.50000 - 4.33013i) q^{96} +(-1.00000 - 1.73205i) q^{97} +2.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 + q^4 + q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9	\( 2 q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} - 3 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{15} + q^{16} + 8 q^{17} + 3 q^{18} - 16 q^{19} - q^{20} + 2 q^{22} - 3 q^{23} + 9 q^{24} - q^{25} - 4 q^{26} + 6 q^{28} + q^{29} + 3 q^{30} - 5 q^{32} - 4 q^{34} + 6 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} - 6 q^{39} - 3 q^{40} - 5 q^{41} - 9 q^{42} + 8 q^{43} + 4 q^{44} + 6 q^{45} + 6 q^{46} - 7 q^{47} - 2 q^{49} - q^{50} - 12 q^{51} - 2 q^{52} - 4 q^{53} - 9 q^{54} + 4 q^{55} - 9 q^{56} + 24 q^{57} + q^{58} + 14 q^{59} - 7 q^{61} - 9 q^{63} + 14 q^{64} - 2 q^{65} - 6 q^{66} + 3 q^{67} + 4 q^{68} + 9 q^{69} - 3 q^{70} + 4 q^{71} - 9 q^{72} + 8 q^{73} + 4 q^{74} - 8 q^{76} - 6 q^{77} + 6 q^{78} + 6 q^{79} + 2 q^{80} - 9 q^{81} + 10 q^{82} - 9 q^{83} - 9 q^{84} + 4 q^{85} + 8 q^{86} - 6 q^{88} - 30 q^{89} - 3 q^{90} + 12 q^{91} + 3 q^{92} - 7 q^{94} - 8 q^{95} + 15 q^{96} - 2 q^{97} + 4 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 + q^4 + q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 2 * q^11 - 3 * q^12 + 2 * q^13 + 3 * q^14 - 3 * q^15 + q^16 + 8 * q^17 + 3 * q^18 - 16 * q^19 - q^20 + 2 * q^22 - 3 * q^23 + 9 * q^24 - q^25 - 4 * q^26 + 6 * q^28 + q^29 + 3 * q^30 - 5 * q^32 - 4 * q^34 + 6 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 - 6 * q^39 - 3 * q^40 - 5 * q^41 - 9 * q^42 + 8 * q^43 + 4 * q^44 + 6 * q^45 + 6 * q^46 - 7 * q^47 - 2 * q^49 - q^50 - 12 * q^51 - 2 * q^52 - 4 * q^53 - 9 * q^54 + 4 * q^55 - 9 * q^56 + 24 * q^57 + q^58 + 14 * q^59 - 7 * q^61 - 9 * q^63 + 14 * q^64 - 2 * q^65 - 6 * q^66 + 3 * q^67 + 4 * q^68 + 9 * q^69 - 3 * q^70 + 4 * q^71 - 9 * q^72 + 8 * q^73 + 4 * q^74 - 8 * q^76 - 6 * q^77 + 6 * q^78 + 6 * q^79 + 2 * q^80 - 9 * q^81 + 10 * q^82 - 9 * q^83 - 9 * q^84 + 4 * q^85 + 8 * q^86 - 6 * q^88 - 30 * q^89 - 3 * q^90 + 12 * q^91 + 3 * q^92 - 7 * q^94 - 8 * q^95 + 15 * q^96 - 2 * q^97 + 4 * q^98 - 6 * q^99

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