LMFDB - Embedded newform 603.2.f.b.238.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(238,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("603.238");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.f (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:	$4.81497924188$
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			238.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	603.238
Dual form			603.2.f.b.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} +3.00000 q^{8} -3.00000 q^{9} +(-0.500000 - 0.866025i) q^{10} +5.00000 q^{11} +(1.50000 - 0.866025i) q^{12} -1.00000 q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +1.00000 q^{20} -1.73205i q^{21} +(2.50000 - 4.33013i) q^{22} +3.00000 q^{23} -5.19615i q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} -5.00000 q^{29} +(-1.50000 + 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(2.50000 + 4.33013i) q^{32} -8.66025i q^{33} -3.00000 q^{34} +(0.500000 - 0.866025i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(-5.50000 - 9.52628i) q^{37} -1.00000 q^{38} +1.73205i q^{39} +(1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-1.50000 - 0.866025i) q^{42} +(2.50000 + 4.33013i) q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} -7.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} -6.00000 q^{49} +4.00000 q^{50} +(-4.50000 + 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +10.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(2.50000 - 4.33013i) q^{55} +3.00000 q^{56} +(-1.50000 + 0.866025i) q^{57} +(-2.50000 + 4.33013i) q^{58} +(-4.50000 + 7.79423i) q^{59} -1.73205i q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000 q^{62} -3.00000 q^{63} +7.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-7.50000 - 4.33013i) q^{66} +(5.50000 + 6.06218i) q^{67} +(1.50000 - 2.59808i) q^{68} -5.19615i q^{69} +(-0.500000 - 0.866025i) q^{70} +(-1.50000 + 2.59808i) q^{71} -9.00000 q^{72} +(-5.50000 - 9.52628i) q^{73} -11.0000 q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +5.00000 q^{77} +(1.50000 + 0.866025i) q^{78} +1.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +6.00000 q^{82} +(4.00000 - 6.92820i) q^{83} +(1.50000 - 0.866025i) q^{84} -3.00000 q^{85} +5.00000 q^{86} +8.66025i q^{87} +15.0000 q^{88} -2.00000 q^{89} +(1.50000 + 2.59808i) q^{90} -1.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-12.0000 + 6.92820i) q^{93} +(-3.50000 + 6.06218i) q^{94} -1.00000 q^{95} +(7.50000 - 4.33013i) q^{96} +(-3.00000 + 5.19615i) q^{97} +(-3.00000 + 5.19615i) q^{98} -15.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 + q^4 + q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 6 * q^9	$ 2 q + q^{2} + q^{4} + q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 6 q^{9} - q^{10} + 10 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - 3 q^{18} - q^{19} + 2 q^{20} + 5 q^{22} + 6 q^{23} + 4 q^{25} - q^{26} + q^{28} - 10 q^{29} - 3 q^{30} - 8 q^{31} + 5 q^{32} - 6 q^{34} + q^{35} - 3 q^{36} - 11 q^{37} - 2 q^{38} + 3 q^{40} + 6 q^{41} - 3 q^{42} + 5 q^{43} + 5 q^{44} - 3 q^{45} + 3 q^{46} - 14 q^{47} - 3 q^{48} - 12 q^{49} + 8 q^{50} - 9 q^{51} - q^{52} + 20 q^{53} + 9 q^{54} + 5 q^{55} + 6 q^{56} - 3 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{61} - 16 q^{62} - 6 q^{63} + 14 q^{64} - q^{65} - 15 q^{66} + 11 q^{67} + 3 q^{68} - q^{70} - 3 q^{71} - 18 q^{72} - 11 q^{73} - 22 q^{74} + 12 q^{75} + q^{76} + 10 q^{77} + 3 q^{78} + 2 q^{79} - q^{80} + 18 q^{81} + 12 q^{82} + 8 q^{83} + 3 q^{84} - 6 q^{85} + 10 q^{86} + 30 q^{88} - 4 q^{89} + 3 q^{90} - 2 q^{91} + 3 q^{92} - 24 q^{93} - 7 q^{94} - 2 q^{95} + 15 q^{96} - 6 q^{97} - 6 q^{98} - 30 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^4 + q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 6 * q^9 - q^10 + 10 * q^11 + 3 * q^12 - 2 * q^13 + q^14 - 3 * q^15 + q^16 - 3 * q^17 - 3 * q^18 - q^19 + 2 * q^20 + 5 * q^22 + 6 * q^23 + 4 * q^25 - q^26 + q^28 - 10 * q^29 - 3 * q^30 - 8 * q^31 + 5 * q^32 - 6 * q^34 + q^35 - 3 * q^36 - 11 * q^37 - 2 * q^38 + 3 * q^40 + 6 * q^41 - 3 * q^42 + 5 * q^43 + 5 * q^44 - 3 * q^45 + 3 * q^46 - 14 * q^47 - 3 * q^48 - 12 * q^49 + 8 * q^50 - 9 * q^51 - q^52 + 20 * q^53 + 9 * q^54 + 5 * q^55 + 6 * q^56 - 3 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^61 - 16 * q^62 - 6 * q^63 + 14 * q^64 - q^65 - 15 * q^66 + 11 * q^67 + 3 * q^68 - q^70 - 3 * q^71 - 18 * q^72 - 11 * q^73 - 22 * q^74 + 12 * q^75 + q^76 + 10 * q^77 + 3 * q^78 + 2 * q^79 - q^80 + 18 * q^81 + 12 * q^82 + 8 * q^83 + 3 * q^84 - 6 * q^85 + 10 * q^86 + 30 * q^88 - 4 * q^89 + 3 * q^90 - 2 * q^91 + 3 * q^92 - 24 * q^93 - 7 * q^94 - 2 * q^95 + 15 * q^96 - 6 * q^97 - 6 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	3.00000			1.06066
$9$	−3.00000			−1.00000
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.00000			0.223607
$21$		−	1.73205i		−	0.377964i
$22$	2.50000	−	4.33013i	0.533002	−	0.923186i
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$		−	5.19615i		−	1.06066i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$			5.19615i			1.00000i
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	−1.50000	+	0.866025i	−0.273861	+	0.158114i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		−	8.66025i		−	1.50756i
$34$	−3.00000			−0.514496
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.0821995	−	0.996616i	$-0.526194\pi$
$38$	−1.00000			−0.162221
$39$			1.73205i			0.277350i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$	−1.50000	−	0.866025i	−0.231455	−	0.133631i
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−7.00000			−1.02105			−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000			−1.02105			−0.510527	+	0.859861i	$0.670550\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	−6.00000			−0.857143
$50$	4.00000			0.565685
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	2.50000	−	4.33013i	0.337100	−	0.583874i
$56$	3.00000			0.400892
$57$	−1.50000	+	0.866025i	−0.198680	+	0.114708i
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	−8.00000			−1.01600
$63$	−3.00000			−0.377964
$64$	7.00000			0.875000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−7.50000	−	4.33013i	−0.923186	−	0.533002i
$67$	5.50000	+	6.06218i	0.671932	+	0.740613i
$67$	5.50000	+	6.06218i	0.671932	+	0.740613i
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		−	5.19615i		−	0.625543i
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$	−9.00000			−1.06066
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	−11.0000			−1.27872
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$	5.00000			0.569803
$78$	1.50000	+	0.866025i	0.169842	+	0.0980581i
$79$	1.00000			0.112509			0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000			0.112509			0.0562544	+	0.998416i	$0.482084\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	9.00000			1.00000
$82$	6.00000			0.662589
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	−0.558560	−	0.829464i	$-0.688646\pi$
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	0.997617	+	0.0689950i	$0.0219793\pi$
$84$	1.50000	−	0.866025i	0.163663	−	0.0944911i
$85$	−3.00000			−0.325396
$86$	5.00000			0.539164
$87$			8.66025i			0.928477i
$88$	15.0000			1.59901
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$	−1.00000			−0.104828
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$	−12.0000	+	6.92820i	−1.24434	+	0.718421i
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	−1.00000			−0.102598
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	−0.977173	−	0.212445i	$-0.931857\pi$
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	0.672569	+	0.740034i	$0.265191\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−15.0000			−1.50756
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	11.0000			1.09454			0.547270	−	0.836956i	$-0.315667\pi$
$101$	11.0000			1.09454			0.547270	+	0.836956i	$0.315667\pi$
$102$			5.19615i			0.514496i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−3.00000			−0.294174
$105$	−1.50000	−	0.866025i	−0.146385	−	0.0845154i
$106$	5.00000	−	8.66025i	0.485643	−	0.841158i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$	−16.5000	+	9.52628i	−1.56611	+	0.904194i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	0.884182	+	0.467143i	$0.154717\pi$
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	−0.0375328	+	0.999295i	$0.511950\pi$
$114$			1.73205i			0.162221i
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$	3.00000			0.277350
$118$	4.50000	+	7.79423i	0.414259	+	0.717517i
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$	−4.50000	−	2.59808i	−0.410792	−	0.237171i
$121$	14.0000			1.27273
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$	9.00000	−	5.19615i	0.811503	−	0.468521i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	9.00000			0.804984
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	2.50000	−	4.33013i	0.221839	−	0.384237i	−0.733527	−	0.679660i	$-0.762127\pi$
$127$	2.50000	−	4.33013i	0.221839	−	0.384237i	0.955366	+	0.295423i	$0.0954607\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	7.50000	−	4.33013i	0.660338	−	0.381246i
$130$	0.500000	+	0.866025i	0.0438529	+	0.0759555i
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$	7.50000	−	4.33013i	0.652791	−	0.376889i
$133$	−0.500000	−	0.866025i	−0.0433555	−	0.0750939i
$134$	8.00000	−	1.73205i	0.691095	−	0.149626i
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	−4.50000	−	7.79423i	−0.385872	−	0.668350i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−4.50000	−	2.59808i	−0.383065	−	0.221163i
$139$	−0.500000	+	0.866025i	−0.0424094	+	0.0734553i	−0.886451	−	0.462822i	$-0.846837\pi$
$139$	−0.500000	+	0.866025i	−0.0424094	+	0.0734553i	0.844042	+	0.536278i	$0.180170\pi$
$140$	1.00000			0.0845154
$141$			12.1244i			1.02105i
$142$	1.50000	+	2.59808i	0.125877	+	0.218026i
$143$	−5.00000			−0.418121
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−2.50000	+	4.33013i	−0.207614	+	0.359597i
$146$	−11.0000			−0.910366
$147$			10.3923i			0.857143i
$148$	5.50000	−	9.52628i	0.452097	−	0.783055i
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		−	6.92820i		−	0.565685i
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$	−1.50000	−	2.59808i	−0.121666	−	0.210732i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	2.50000	−	4.33013i	0.201456	−	0.348932i
$155$	−8.00000			−0.642575
$156$	−1.50000	+	0.866025i	−0.120096	+	0.0693375i
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$	0.500000	−	0.866025i	0.0397779	−	0.0688973i
$159$		−	17.3205i		−	1.37361i
$160$	5.00000			0.395285
$161$	3.00000			0.236433
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	0.206518	+	0.978443i	$0.433787\pi$
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	−0.950615	+	0.310372i	$0.899546\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$	−7.50000	−	4.33013i	−0.583874	−	0.337100i
$166$	−4.00000	−	6.92820i	−0.310460	−	0.537733i
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.785687	+	0.618624i	$0.212310\pi$
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.142901	+	0.989737i	$0.454357\pi$
$168$		−	5.19615i		−	0.400892i
$169$	−12.0000			−0.923077
$170$	−1.50000	+	2.59808i	−0.115045	+	0.199263i
$171$	1.50000	+	2.59808i	0.114708	+	0.198680i
$172$	−2.50000	+	4.33013i	−0.190623	+	0.330169i
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$	7.50000	+	4.33013i	0.568574	+	0.328266i
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$	13.5000	+	7.79423i	1.01472	+	0.585850i
$178$	−1.00000	+	1.73205i	−0.0749532	+	0.129823i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−3.00000			−0.223607
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	0.706129	+	0.708083i	$0.250440\pi$
$182$	−0.500000	+	0.866025i	−0.0370625	+	0.0641941i
$183$	15.0000	+	8.66025i	1.10883	+	0.640184i
$184$	9.00000			0.663489
$185$	−11.0000			−0.808736
$186$			13.8564i			1.01600i
$187$	−7.50000	−	12.9904i	−0.548454	−	0.949951i
$188$	−3.50000	−	6.06218i	−0.255264	−	0.442130i
$189$			5.19615i			0.377964i
$190$	−0.500000	+	0.866025i	−0.0362738	+	0.0628281i
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$		−	12.1244i		−	0.875000i
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	−0.761911	−	0.647682i	$-0.775738\pi$
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	0.941865	+	0.335993i	$0.109072\pi$
$194$	3.00000	+	5.19615i	0.215387	+	0.373062i
$195$	1.50000	+	0.866025i	0.107417	+	0.0620174i
$196$	−3.00000	−	5.19615i	−0.214286	−	0.371154i
$197$	2.50000	−	4.33013i	0.178118	−	0.308509i	−0.763118	−	0.646259i	$-0.776333\pi$
$197$	2.50000	−	4.33013i	0.178118	−	0.308509i	0.941236	+	0.337750i	$0.109666\pi$
$198$	−7.50000	+	12.9904i	−0.533002	+	0.923186i
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.844446	−	0.535641i	$-0.820070\pi$
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.0416556	−	0.999132i	$-0.513263\pi$
$200$	6.00000	+	10.3923i	0.424264	+	0.734847i
$201$	10.5000	−	9.52628i	0.740613	−	0.671932i
$202$	5.50000	−	9.52628i	0.386979	−	0.670267i
$203$	−5.00000			−0.350931
$204$	−4.50000	−	2.59808i	−0.315063	−	0.181902i
$205$	6.00000			0.419058
$206$	4.00000			0.278693
$207$	−9.00000			−0.625543
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−2.50000	−	4.33013i	−0.172929	−	0.299521i
$210$	−1.50000	+	0.866025i	−0.103510	+	0.0597614i
$211$	−21.0000			−1.44570			−0.722850	−	0.691005i	$-0.757168\pi$
$211$	−21.0000			−1.44570			−0.722850	+	0.691005i	$0.757168\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	4.50000	+	2.59808i	0.308335	+	0.178017i
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$	5.00000			0.340997
$216$			15.5885i			1.06066i
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−16.5000	+	9.52628i	−1.11497	+	0.643726i
$220$	5.00000			0.337100
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$			19.0526i			1.27872i
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	2.50000	+	4.33013i	0.167038	+	0.289319i
$225$	−6.00000	−	10.3923i	−0.400000	−	0.692820i
$226$	18.0000			1.19734
$227$	−27.0000			−1.79205			−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000			−1.79205			−0.896026	+	0.444001i	$0.853559\pi$
$228$	−1.50000	−	0.866025i	−0.0993399	−	0.0573539i
$229$	−5.00000			−0.330409			−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000			−0.330409			−0.165205	+	0.986259i	$0.552828\pi$
$230$	−1.50000	−	2.59808i	−0.0989071	−	0.171312i
$231$		−	8.66025i		−	0.569803i
$232$	−15.0000			−0.984798
$233$	8.50000	−	14.7224i	0.556854	−	0.964499i	−0.440903	−	0.897555i	$-0.645342\pi$
$233$	8.50000	−	14.7224i	0.556854	−	0.964499i	0.997757	−	0.0669439i	$-0.0213249\pi$
$234$	1.50000	−	2.59808i	0.0980581	−	0.169842i
$235$	−3.50000	+	6.06218i	−0.228315	+	0.395453i
$236$	−9.00000			−0.585850
$237$		−	1.73205i		−	0.112509i
$238$	−3.00000			−0.194461
$239$	−8.00000	−	13.8564i	−0.517477	−	0.896296i	−0.999794	−	0.0202996i	$-0.993538\pi$
$239$	−8.00000	−	13.8564i	−0.517477	−	0.896296i	0.482317	−	0.875997i	$-0.339795\pi$
$240$	−1.50000	+	0.866025i	−0.0968246	+	0.0559017i
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$		−	15.5885i		−	1.00000i
$244$	−10.0000			−0.640184
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		−	10.3923i		−	0.662589i
$247$	0.500000	+	0.866025i	0.0318142	+	0.0551039i
$248$	−12.0000	−	20.7846i	−0.762001	−	1.31982i
$249$	−12.0000	−	6.92820i	−0.760469	−	0.439057i
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	−12.5000	−	21.6506i	−0.788993	−	1.36658i	−0.926584	−	0.376087i	$-0.877269\pi$
$251$	−12.5000	−	21.6506i	−0.788993	−	1.36658i	0.137591	−	0.990489i	$-0.456064\pi$
$252$	−1.50000	−	2.59808i	−0.0944911	−	0.163663i
$253$	15.0000			0.943042
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$			5.19615i			0.325396i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$		−	8.66025i		−	0.539164i
$259$	−5.50000	−	9.52628i	−0.341753	−	0.591934i
$260$	−1.00000			−0.0620174
$261$	15.0000			0.928477
$262$	4.50000	+	7.79423i	0.278011	+	0.481529i
$263$	2.50000	+	4.33013i	0.154157	+	0.267007i	0.932752	−	0.360520i	$-0.117401\pi$
$263$	2.50000	+	4.33013i	0.154157	+	0.267007i	−0.778595	+	0.627527i	$0.784067\pi$
$264$		−	25.9808i		−	1.59901i
$265$	5.00000	−	8.66025i	0.307148	−	0.531995i
$266$	−1.00000			−0.0613139
$267$			3.46410i			0.212000i
$268$	−2.50000	+	7.79423i	−0.152712	+	0.476108i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$	4.50000	−	2.59808i	0.273861	−	0.158114i
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	−3.00000			−0.181902
$273$			1.73205i			0.104828i
$274$	9.00000			0.543710
$275$	10.0000	+	17.3205i	0.603023	+	1.04447i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	0.999923	+	0.0124177i	$0.00395278\pi$
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	−0.489207	+	0.872167i	$0.662714\pi$
$278$	0.500000	+	0.866025i	0.0299880	+	0.0519408i
$279$	12.0000	+	20.7846i	0.718421	+	1.24434i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$	10.5000	+	6.06218i	0.625266	+	0.360997i
$283$	1.50000	−	2.59808i	0.0891657	−	0.154440i	−0.817993	−	0.575228i	$-0.804913\pi$
$283$	1.50000	−	2.59808i	0.0891657	−	0.154440i	0.907159	+	0.420789i	$0.138247\pi$
$284$	−3.00000			−0.178017
$285$			1.73205i			0.102598i
$286$	−2.50000	+	4.33013i	−0.147828	+	0.256046i
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$	−7.50000	−	12.9904i	−0.441942	−	0.765466i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	2.50000	+	4.33013i	0.146805	+	0.254274i
$291$	9.00000	+	5.19615i	0.527589	+	0.304604i
$292$	5.50000	−	9.52628i	0.321863	−	0.557483i
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	0.990660	−	0.136355i	$-0.0435386\pi$
$294$	9.00000	+	5.19615i	0.524891	+	0.303046i
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$	−16.5000	−	28.5788i	−0.959043	−	1.66111i
$297$			25.9808i			1.50756i
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$	−3.00000			−0.173494
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$	2.50000	+	4.33013i	0.144098	+	0.249584i
$302$		0			0
$303$		−	19.0526i		−	1.09454i
$304$	−1.00000			−0.0573539
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$	9.00000			0.514496
$307$	−2.50000	−	4.33013i	−0.142683	−	0.247133i	0.785823	−	0.618451i	$-0.212239\pi$
$307$	−2.50000	−	4.33013i	−0.142683	−	0.247133i	−0.928506	+	0.371318i	$0.878906\pi$
$308$	2.50000	+	4.33013i	0.142451	+	0.246732i
$309$	6.00000	−	3.46410i	0.341328	−	0.197066i
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	−0.964942	−	0.262463i	$-0.915465\pi$
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	0.709771	+	0.704433i	$0.248799\pi$
$312$			5.19615i			0.294174i
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$	1.50000	−	2.59808i	0.0846499	−	0.146618i
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−15.0000	−	8.66025i	−0.841158	−	0.485643i
$319$	−25.0000			−1.39973
$320$	3.50000	−	6.06218i	0.195656	−	0.338886i
$321$			6.92820i			0.386695i
$322$	1.50000	−	2.59808i	0.0835917	−	0.144785i
$323$	−1.50000	+	2.59808i	−0.0834622	+	0.144561i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	9.50000	+	16.4545i	0.526156	+	0.911330i
$327$		−	3.46410i		−	0.191565i
$328$	9.00000	+	15.5885i	0.496942	+	0.860729i
$329$	−7.00000			−0.385922
$330$	−7.50000	+	4.33013i	−0.412861	+	0.238366i
$331$	−27.0000			−1.48405			−0.742027	−	0.670370i	$-0.766135\pi$
$331$	−27.0000			−1.48405			−0.742027	+	0.670370i	$0.766135\pi$
$332$	8.00000			0.439057
$333$	16.5000	+	28.5788i	0.904194	+	1.56611i
$334$	24.0000			1.31322
$335$	8.00000	−	1.73205i	0.437087	−	0.0946320i
$336$	−1.50000	−	0.866025i	−0.0818317	−	0.0472456i
$337$	7.00000			0.381314			0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000			0.381314			0.190657	+	0.981657i	$0.438938\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	27.0000	−	15.5885i	1.46644	−	0.846649i
$340$	−1.50000	−	2.59808i	−0.0813489	−	0.140900i
$341$	−20.0000	−	34.6410i	−1.08306	−	1.87592i
$342$	3.00000			0.162221
$343$	−13.0000			−0.701934
$344$	7.50000	+	12.9904i	0.404373	+	0.700394i
$345$	−4.50000	−	2.59808i	−0.242272	−	0.139876i
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$	−7.50000	+	4.33013i	−0.402042	+	0.232119i
$349$	−7.50000	−	12.9904i	−0.401466	−	0.695359i	0.592437	−	0.805617i	$-0.298166\pi$
$349$	−7.50000	−	12.9904i	−0.401466	−	0.695359i	−0.993903	+	0.110257i	$0.964832\pi$
$350$	4.00000			0.213809
$351$		−	5.19615i		−	0.277350i
$352$	12.5000	+	21.6506i	0.666252	+	1.15398i
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	13.5000	−	7.79423i	0.717517	−	0.414259i
$355$	1.50000	+	2.59808i	0.0796117	+	0.137892i
$356$	−1.00000	−	1.73205i	−0.0529999	−	0.0917985i
$357$	−4.50000	+	2.59808i	−0.238165	+	0.137505i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	−4.50000	+	7.79423i	−0.237171	+	0.410792i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$		−	24.2487i		−	1.27273i
$364$	−0.500000	−	0.866025i	−0.0262071	−	0.0453921i
$365$	−11.0000			−0.575766
$366$	15.0000	−	8.66025i	0.784063	−	0.452679i
$367$	25.0000			1.30499			0.652495	−	0.757793i	$-0.273722\pi$
$367$	25.0000			1.30499			0.652495	+	0.757793i	$0.273722\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	−5.50000	+	9.52628i	−0.285931	+	0.495248i
$371$	10.0000			0.519174
$372$	−12.0000	−	6.92820i	−0.622171	−	0.359211i
$373$	3.00000	+	5.19615i	0.155334	+	0.269047i	0.933181	−	0.359408i	$-0.117021\pi$
$373$	3.00000	+	5.19615i	0.155334	+	0.269047i	−0.777847	+	0.628454i	$0.783688\pi$
$374$	−15.0000			−0.775632
$375$		−	15.5885i		−	0.804984i
$376$	−21.0000			−1.08299
$377$	5.00000			0.257513
$378$	4.50000	+	2.59808i	0.231455	+	0.133631i
$379$	7.50000	+	12.9904i	0.385249	+	0.667271i	0.991804	−	0.127771i	$-0.0407822\pi$
$379$	7.50000	+	12.9904i	0.385249	+	0.667271i	−0.606555	+	0.795042i	$0.707449\pi$
$380$	−0.500000	−	0.866025i	−0.0256495	−	0.0444262i
$381$	−7.50000	−	4.33013i	−0.384237	−	0.221839i
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	23.0000			1.17525			0.587623	−	0.809135i	$-0.300064\pi$
$383$	23.0000			1.17525			0.587623	+	0.809135i	$0.300064\pi$
$384$	4.50000	+	2.59808i	0.229640	+	0.132583i
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	−2.50000	−	4.33013i	−0.127247	−	0.220398i
$387$	−7.50000	−	12.9904i	−0.381246	−	0.660338i
$388$	−6.00000			−0.304604
$389$	11.0000	−	19.0526i	0.557722	−	0.966003i	−0.439964	−	0.898015i	$-0.645009\pi$
$389$	11.0000	−	19.0526i	0.557722	−	0.966003i	0.997686	−	0.0679877i	$-0.0216579\pi$
$390$	1.50000	−	0.866025i	0.0759555	−	0.0438529i
$391$	−4.50000	−	7.79423i	−0.227575	−	0.394171i
$392$	−18.0000			−0.909137
$393$	13.5000	+	7.79423i	0.680985	+	0.393167i
$394$	−2.50000	−	4.33013i	−0.125948	−	0.218149i
$395$	0.500000	−	0.866025i	0.0251577	−	0.0435745i
$396$	−7.50000	−	12.9904i	−0.376889	−	0.652791i
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$	−25.0000			−1.25314
$399$	−1.50000	+	0.866025i	−0.0750939	+	0.0433555i
$400$	4.00000			0.200000
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	−0.571901	−	0.820323i	$-0.693794\pi$
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	0.996371	+	0.0851195i	$0.0271272\pi$
$402$	−3.00000	−	13.8564i	−0.149626	−	0.691095i
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	5.50000	+	9.52628i	0.273635	+	0.473950i
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$	−2.50000	+	4.33013i	−0.124073	+	0.214901i
$407$	−27.5000	−	47.6314i	−1.36312	−	2.36100i
$408$	−13.5000	+	7.79423i	−0.668350	+	0.385872i
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$	13.5000	−	7.79423i	0.665906	−	0.384461i
$412$	−2.00000	+	3.46410i	−0.0985329	+	0.170664i
$413$	−4.50000	+	7.79423i	−0.221431	+	0.383529i
$414$	−4.50000	+	7.79423i	−0.221163	+	0.383065i
$415$	−4.00000	−	6.92820i	−0.196352	−	0.340092i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$	1.50000	+	0.866025i	0.0734553	+	0.0424094i
$418$	−5.00000			−0.244558
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		−	1.73205i		−	0.0845154i
$421$	3.00000	−	5.19615i	0.146211	−	0.253245i	−0.783613	−	0.621249i	$-0.786625\pi$
$421$	3.00000	−	5.19615i	0.146211	−	0.253245i	0.929824	+	0.368004i	$0.119959\pi$
$422$	−10.5000	+	18.1865i	−0.511132	+	0.885307i
$423$	21.0000			1.02105
$424$	30.0000			1.45693
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	4.50000	−	2.59808i	0.218026	−	0.125877i
$427$	−5.00000	+	8.66025i	−0.241967	+	0.419099i
$428$	−2.00000	−	3.46410i	−0.0966736	−	0.167444i
$429$			8.66025i			0.418121i
$430$	2.50000	−	4.33013i	0.120561	−	0.208817i
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−7.50000	+	12.9904i	−0.360427	+	0.624278i	−0.988031	−	0.154255i	$-0.950702\pi$
$433$	−7.50000	+	12.9904i	−0.360427	+	0.624278i	0.627604	+	0.778533i	$0.284036\pi$
$434$	−8.00000			−0.384012
$435$	7.50000	+	4.33013i	0.359597	+	0.207614i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−1.50000	−	2.59808i	−0.0717547	−	0.124283i
$438$			19.0526i			0.910366i
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	−0.999661	−	0.0260459i	$-0.991708\pi$
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	0.522387	+	0.852709i	$0.325042\pi$
$440$	7.50000	−	12.9904i	0.357548	−	0.619292i
$441$	18.0000			0.857143
$442$	3.00000			0.142695
$443$	−19.0000			−0.902717			−0.451359	−	0.892343i	$-0.649060\pi$
$443$	−19.0000			−0.902717			−0.451359	+	0.892343i	$0.649060\pi$
$444$	−16.5000	−	9.52628i	−0.783055	−	0.452097i
$445$	−1.00000	+	1.73205i	−0.0474045	+	0.0821071i
$446$	1.00000			0.0473514
$447$	−13.5000	−	7.79423i	−0.638528	−	0.368654i
$448$	7.00000			0.330719
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$450$	−12.0000			−0.565685
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$		0			0
$454$	−13.5000	+	23.3827i	−0.633586	+	1.09740i
$455$	−0.500000	+	0.866025i	−0.0234404	+	0.0405999i
$456$	−4.50000	+	2.59808i	−0.210732	+	0.121666i
$457$	−25.0000			−1.16945			−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000			−1.16945			−0.584725	+	0.811231i	$0.698798\pi$
$458$	−2.50000	+	4.33013i	−0.116817	+	0.202334i
$459$	13.5000	−	7.79423i	0.630126	−	0.363803i
$460$	3.00000			0.139876
$461$	2.50000	+	4.33013i	0.116437	+	0.201674i	0.918353	−	0.395762i	$-0.129519\pi$
$461$	2.50000	+	4.33013i	0.116437	+	0.201674i	−0.801917	+	0.597436i	$0.796186\pi$
$462$	−7.50000	−	4.33013i	−0.348932	−	0.201456i
$463$	31.0000			1.44069			0.720346	−	0.693615i	$-0.243983\pi$
$463$	31.0000			1.44069			0.720346	+	0.693615i	$0.243983\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$			13.8564i			0.642575i
$466$	−8.50000	−	14.7224i	−0.393755	−	0.682003i
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$	1.50000	+	2.59808i	0.0693375	+	0.120096i
$469$	5.50000	+	6.06218i	0.253966	+	0.279925i
$470$	3.50000	+	6.06218i	0.161443	+	0.279627i
$471$		−	5.19615i		−	0.239426i
$472$	−13.5000	+	23.3827i	−0.621388	+	1.07628i
$473$	12.5000	+	21.6506i	0.574751	+	0.995497i
$474$	−1.50000	−	0.866025i	−0.0688973	−	0.0397779i
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	1.50000	−	2.59808i	0.0687524	−	0.119083i
$477$	−30.0000			−1.37361
$478$	−16.0000			−0.731823
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		−	8.66025i		−	0.395285i
$481$	5.50000	+	9.52628i	0.250778	+	0.434361i
$482$	25.0000			1.13872
$483$		−	5.19615i		−	0.236433i
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	21.5000	+	37.2391i	0.974258	+	1.68746i	0.682362	+	0.731014i	$0.260953\pi$
$487$	21.5000	+	37.2391i	0.974258	+	1.68746i	0.291896	+	0.956450i	$0.405714\pi$
$488$	−15.0000	+	25.9808i	−0.679018	+	1.17609i
$489$	28.5000	+	16.4545i	1.28881	+	0.744097i
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$	19.5000	−	33.7750i	0.880023	−	1.52424i	0.0287085	−	0.999588i	$-0.490861\pi$
$491$	19.5000	−	33.7750i	0.880023	−	1.52424i	0.851314	−	0.524656i	$-0.175806\pi$
$492$	9.00000	+	5.19615i	0.405751	+	0.234261i
$493$	7.50000	+	12.9904i	0.337783	+	0.585057i
$494$	1.00000			0.0449921
$495$	−7.50000	+	12.9904i	−0.337100	+	0.583874i
$496$	−8.00000			−0.359211
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$	−12.0000	+	6.92820i	−0.537733	+	0.310460i
$499$	−33.0000			−1.47728			−0.738641	−	0.674099i	$-0.764532\pi$
$499$	−33.0000			−1.47728			−0.738641	+	0.674099i	$0.764532\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$	36.0000	−	20.7846i	1.60836	−	0.928588i
$502$	−25.0000			−1.11580
$503$	−3.50000	+	6.06218i	−0.156057	+	0.270299i	−0.933444	−	0.358724i	$-0.883212\pi$
$503$	−3.50000	+	6.06218i	−0.156057	+	0.270299i	0.777386	+	0.629024i	$0.216545\pi$
$504$	−9.00000			−0.400892
$505$	5.50000	−	9.52628i	0.244747	−	0.423914i
$506$	7.50000	−	12.9904i	0.333416	−	0.577493i
$507$			20.7846i			0.923077i
$508$	5.00000			0.221839
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$	4.50000	+	2.59808i	0.199263	+	0.115045i
$511$	−5.50000	−	9.52628i	−0.243306	−	0.421418i
$512$	11.0000			0.486136
$513$	4.50000	−	2.59808i	0.198680	−	0.114708i
$514$	−14.0000			−0.617514
$515$	4.00000			0.176261
$516$	7.50000	+	4.33013i	0.330169	+	0.190623i
$517$	−35.0000			−1.53930
$518$	−11.0000			−0.483312
$519$	21.0000	+	12.1244i	0.921798	+	0.532200i
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$	7.50000	−	12.9904i	0.328266	−	0.568574i
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	0.975652	+	0.219326i	$0.0703858\pi$
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	−0.297884	+	0.954602i	$0.596281\pi$
$524$	−9.00000			−0.393167
$525$	6.00000	−	3.46410i	0.261861	−	0.151186i
$526$	5.00000			0.218010
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$	−7.50000	−	4.33013i	−0.326396	−	0.188445i
$529$	−14.0000			−0.608696
$530$	−5.00000	−	8.66025i	−0.217186	−	0.376177i
$531$	13.5000	−	23.3827i	0.585850	−	1.01472i
$532$	0.500000	−	0.866025i	0.0216777	−	0.0375470i
$533$	−3.00000	−	5.19615i	−0.129944	−	0.225070i
$534$	3.00000	+	1.73205i	0.129823	+	0.0749532i
$535$	−2.00000	+	3.46410i	−0.0864675	+	0.149766i
$536$	16.5000	+	18.1865i	0.712691	+	0.785539i
$537$			20.7846i			0.896922i
$538$	7.00000	−	12.1244i	0.301791	−	0.522718i
$539$	−30.0000			−1.29219
$540$			5.19615i			0.223607i
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	−14.0000	+	24.2487i	−0.601351	+	1.04157i
$543$	10.5000	+	6.06218i	0.450598	+	0.260153i
$544$	7.50000	−	12.9904i	0.321560	−	0.556958i
$545$	1.00000	−	1.73205i	0.0428353	−	0.0741929i
$546$	1.50000	+	0.866025i	0.0641941	+	0.0370625i
$547$	−7.00000			−0.299298			−0.149649	−	0.988739i	$-0.547814\pi$
$547$	−7.00000			−0.299298			−0.149649	+	0.988739i	$0.547814\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$	20.0000			0.852803
$551$	2.50000	+	4.33013i	0.106504	+	0.184470i
$552$		−	15.5885i		−	0.663489i
$553$	1.00000			0.0425243
$554$	17.0000			0.722261
$555$			19.0526i			0.808736i
$556$	−1.00000			−0.0424094
$557$	14.5000	−	25.1147i	0.614385	−	1.06415i	−0.376107	−	0.926576i	$-0.622738\pi$
$557$	14.5000	−	25.1147i	0.614385	−	1.06415i	0.990492	−	0.137569i	$-0.0439290\pi$
$558$	24.0000			1.01600
$559$	−2.50000	−	4.33013i	−0.105739	−	0.183145i
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	−22.5000	+	12.9904i	−0.949951	+	0.548454i
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$	−10.5000	+	6.06218i	−0.442130	+	0.255264i
$565$	18.0000			0.757266
$566$	−1.50000	−	2.59808i	−0.0630497	−	0.109205i
$567$	9.00000			0.377964
$568$	−4.50000	+	7.79423i	−0.188816	+	0.327039i
$569$	27.0000			1.13190			0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000			1.13190			0.565949	+	0.824440i	$0.308510\pi$
$570$	1.50000	+	0.866025i	0.0628281	+	0.0362738i
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	−2.50000	−	4.33013i	−0.104530	−	0.181052i
$573$	−36.0000	−	20.7846i	−1.50392	−	0.868290i
$574$	6.00000			0.250435
$575$	6.00000	+	10.3923i	0.250217	+	0.433389i
$576$	−21.0000			−0.875000
$577$	−13.5000	+	23.3827i	−0.562012	+	0.973434i	0.435308	+	0.900281i	$0.356639\pi$
$577$	−13.5000	+	23.3827i	−0.562012	+	0.973434i	−0.997321	+	0.0731526i	$0.976694\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−7.50000	−	4.33013i	−0.311689	−	0.179954i
$580$	−5.00000			−0.207614
$581$	4.00000	−	6.92820i	0.165948	−	0.287430i
$582$	9.00000	−	5.19615i	0.373062	−	0.215387i
$583$	50.0000			2.07079
$584$	−16.5000	−	28.5788i	−0.682775	−	1.18260i
$585$	1.50000	−	2.59808i	0.0620174	−	0.107417i
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	−0.715226	−	0.698893i	$-0.753676\pi$
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	0.962872	+	0.269957i	$0.0870095\pi$
$588$	−9.00000	+	5.19615i	−0.371154	+	0.214286i
$589$	−4.00000	+	6.92820i	−0.164817	+	0.285472i
$590$	9.00000			0.370524
$591$	−7.50000	−	4.33013i	−0.308509	−	0.178118i
$592$	−11.0000			−0.452097
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$	22.5000	+	12.9904i	0.923186	+	0.533002i
$595$	−3.00000			−0.122988
$596$	9.00000			0.368654
$597$	−37.5000	+	21.6506i	−1.53477	+	0.886102i
$598$	−1.50000	+	2.59808i	−0.0613396	+	0.106243i
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	0.936099	−	0.351738i	$-0.114409\pi$
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	−0.772663	+	0.634816i	$0.781076\pi$
$600$	18.0000	−	10.3923i	0.734847	−	0.424264i
$601$	19.0000	−	32.9090i	0.775026	−	1.34238i	−0.159754	−	0.987157i	$-0.551070\pi$
$601$	19.0000	−	32.9090i	0.775026	−	1.34238i	0.934780	−	0.355228i	$-0.115597\pi$
$602$	5.00000			0.203785
$603$	−16.5000	−	18.1865i	−0.671932	−	0.740613i
$604$		0			0
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$	−16.5000	−	9.52628i	−0.670267	−	0.386979i
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$			8.66025i			0.350931i
$610$	10.0000			0.404888
$611$	7.00000			0.283190
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	0.942478	−	0.334269i	$-0.108489\pi$
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	−0.760724	+	0.649075i	$0.775156\pi$
$614$	−5.00000			−0.201784
$615$		−	10.3923i		−	0.419058i
$616$	15.0000			0.604367
$617$	−11.5000	+	19.9186i	−0.462973	+	0.801892i	−0.999107	−	0.0422403i	$-0.986550\pi$
$617$	−11.5000	+	19.9186i	−0.462973	+	0.801892i	0.536135	+	0.844132i	$0.319884\pi$
$618$		−	6.92820i		−	0.278693i
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	−0.993959	−	0.109749i	$-0.964995\pi$
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	0.592025	+	0.805919i	$0.298329\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$			15.5885i			0.625543i
$622$	4.50000	+	7.79423i	0.180434	+	0.312520i
$623$	−2.00000			−0.0801283
$624$	1.50000	+	0.866025i	0.0600481	+	0.0346688i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−11.0000			−0.439648
$627$	−7.50000	+	4.33013i	−0.299521	+	0.172929i
$628$	1.50000	+	2.59808i	0.0598565	+	0.103675i
$629$	−16.5000	+	28.5788i	−0.657898	+	1.13951i
$630$	1.50000	+	2.59808i	0.0597614	+	0.103510i
$631$	−0.500000	−	0.866025i	−0.0199047	−	0.0344759i	0.855901	−	0.517139i	$-0.173003\pi$
$631$	−0.500000	−	0.866025i	−0.0199047	−	0.0344759i	−0.875806	+	0.482663i	$0.839670\pi$
$632$	3.00000			0.119334
$633$			36.3731i			1.44570i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−2.50000	−	4.33013i	−0.0992095	−	0.171836i
$636$	15.0000	−	8.66025i	0.594789	−	0.343401i
$637$	6.00000			0.237729
$638$	−12.5000	+	21.6506i	−0.494880	+	0.857157i
$639$	4.50000	−	7.79423i	0.178017	−	0.308335i
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	35.0000			1.38242			0.691208	−	0.722655i	$-0.257079\pi$
$641$	35.0000			1.38242			0.691208	+	0.722655i	$0.257079\pi$
$642$	6.00000	+	3.46410i	0.236801	+	0.136717i
$643$	13.5000	−	23.3827i	0.532388	−	0.922123i	−0.466897	−	0.884312i	$-0.654628\pi$
$643$	13.5000	−	23.3827i	0.532388	−	0.922123i	0.999285	−	0.0378113i	$-0.0120386\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$		−	8.66025i		−	0.340997i
$646$	1.50000	+	2.59808i	0.0590167	+	0.102220i
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	27.0000			1.06066
$649$	−22.5000	+	38.9711i	−0.883202	+	1.52975i
$650$	−4.00000			−0.156893
$651$	−12.0000	+	6.92820i	−0.470317	+	0.271538i
$652$	−19.0000			−0.744097
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$	−3.00000	−	1.73205i	−0.117309	−	0.0677285i
$655$	4.50000	+	7.79423i	0.175830	+	0.304546i
$656$	6.00000			0.234261
$657$	16.5000	+	28.5788i	0.643726	+	1.11497i
$658$	−3.50000	+	6.06218i	−0.136444	+	0.236328i
$659$	−15.0000			−0.584317			−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000			−0.584317			−0.292159	+	0.956370i	$0.594373\pi$
$660$		−	8.66025i		−	0.337100i
$661$	10.5000	−	18.1865i	0.408403	−	0.707374i	−0.586308	−	0.810088i	$-0.699419\pi$
$661$	10.5000	−	18.1865i	0.408403	−	0.707374i	0.994711	+	0.102714i	$0.0327526\pi$
$662$	−13.5000	+	23.3827i	−0.524692	+	0.908794i
$663$	4.50000	−	2.59808i	0.174766	−	0.100901i
$664$	12.0000	−	20.7846i	0.465690	−	0.806599i
$665$	−1.00000			−0.0387783
$666$	33.0000			1.27872
$667$	−15.0000			−0.580802
$668$	−12.0000	+	20.7846i	−0.464294	+	0.804181i
$669$	1.50000	−	0.866025i	0.0579934	−	0.0334825i
$670$	2.50000	−	7.79423i	0.0965834	−	0.301117i
$671$	−25.0000	+	43.3013i	−0.965114	+	1.67163i
$672$	7.50000	−	4.33013i	0.289319	−	0.167038i
$673$	−15.5000	−	26.8468i	−0.597481	−	1.03487i	−0.993192	−	0.116492i	$-0.962835\pi$
$673$	−15.5000	−	26.8468i	−0.597481	−	1.03487i	0.395711	−	0.918375i	$-0.370498\pi$
$674$	3.50000	−	6.06218i	0.134815	−	0.233506i
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	27.0000			1.03769			0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000			1.03769			0.518847	+	0.854867i	$0.326361\pi$
$678$		−	31.1769i		−	1.19734i
$679$	−3.00000	+	5.19615i	−0.115129	+	0.199410i
$680$	−9.00000			−0.345134
$681$			46.7654i			1.79205i
$682$	−40.0000			−1.53168
$683$	7.50000	+	12.9904i	0.286980	+	0.497063i	0.973087	−	0.230437i	$-0.0740155\pi$
$683$	7.50000	+	12.9904i	0.286980	+	0.497063i	−0.686108	+	0.727500i	$0.740682\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$	9.00000			0.343872
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$			8.66025i			0.330409i
$688$	5.00000			0.190623
$689$	−10.0000			−0.380970
$690$	−4.50000	+	2.59808i	−0.171312	+	0.0989071i
$691$	45.0000			1.71188			0.855940	−	0.517075i	$-0.172979\pi$
$691$	45.0000			1.71188			0.855940	+	0.517075i	$0.172979\pi$
$692$	−14.0000			−0.532200
$693$	−15.0000			−0.569803
$694$	−24.0000			−0.911028
$695$	0.500000	+	0.866025i	0.0189661	+	0.0328502i
$696$			25.9808i			0.984798i
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$	−15.0000			−0.567758
$699$	−25.5000	−	14.7224i	−0.964499	−	0.556854i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	12.5000	−	21.6506i	0.472118	−	0.817733i	−0.527373	−	0.849634i	$-0.676823\pi$
$701$	12.5000	−	21.6506i	0.472118	−	0.817733i	0.999491	+	0.0319010i	$0.0101561\pi$
$702$	−4.50000	−	2.59808i	−0.169842	−	0.0980581i
$703$	−5.50000	+	9.52628i	−0.207436	+	0.359290i
$704$	35.0000			1.31911
$705$	10.5000	+	6.06218i	0.395453	+	0.228315i
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	11.0000			0.413698
$708$			15.5885i			0.585850i
$709$	−25.0000	+	43.3013i	−0.938895	+	1.62621i	−0.171358	+	0.985209i	$0.554815\pi$
$709$	−25.0000	+	43.3013i	−0.938895	+	1.62621i	−0.767537	+	0.641004i	$0.778518\pi$
$710$	3.00000			0.112588
$711$	−3.00000			−0.112509
$712$	−6.00000			−0.224860
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$			5.19615i			0.194461i
$715$	−2.50000	+	4.33013i	−0.0934947	+	0.161938i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−24.0000	+	13.8564i	−0.896296	+	0.517477i
$718$	8.00000	−	13.8564i	0.298557	−	0.517116i
$719$	11.5000	+	19.9186i	0.428878	+	0.742838i	0.996774	−	0.0802624i	$-0.0255758\pi$
$719$	11.5000	+	19.9186i	0.428878	+	0.742838i	−0.567896	+	0.823100i	$0.692242\pi$
$720$	1.50000	+	2.59808i	0.0559017	+	0.0968246i
$721$	2.00000	+	3.46410i	0.0744839	+	0.129010i
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$	37.5000	−	21.6506i	1.39464	−	0.805196i
$724$	−7.00000			−0.260153
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$	−21.0000	−	12.1244i	−0.779383	−	0.449977i
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	−0.400362	−	0.916357i	$-0.631116\pi$
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	0.993770	−	0.111454i	$-0.0355509\pi$
$728$	−3.00000			−0.111187
$729$	−27.0000			−1.00000
$730$	−5.50000	+	9.52628i	−0.203564	+	0.352583i
$731$	7.50000	−	12.9904i	0.277398	−	0.480467i
$732$			17.3205i			0.640184i
$733$	−15.0000	−	25.9808i	−0.554038	−	0.959621i	−0.997978	−	0.0635649i	$-0.979753\pi$
$733$	−15.0000	−	25.9808i	−0.554038	−	0.959621i	0.443940	−	0.896056i	$-0.353580\pi$
$734$	12.5000	−	21.6506i	0.461383	−	0.799140i
$735$	9.00000	+	5.19615i	0.331970	+	0.191663i
$736$	7.50000	+	12.9904i	0.276454	+	0.478832i
$737$	27.5000	+	30.3109i	1.01298	+	1.11652i
$738$	−18.0000			−0.662589
$739$	−12.5000	−	21.6506i	−0.459820	−	0.796431i	0.539131	−	0.842222i	$-0.318753\pi$
$739$	−12.5000	−	21.6506i	−0.459820	−	0.796431i	−0.998951	+	0.0457903i	$0.985419\pi$
$740$	−5.50000	−	9.52628i	−0.202184	−	0.350193i
$741$	1.50000	−	0.866025i	0.0551039	−	0.0318142i
$742$	5.00000	−	8.66025i	0.183556	−	0.317928i
$743$	−21.0000			−0.770415			−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000			−0.770415			−0.385208	+	0.922830i	$0.625870\pi$
$744$	−36.0000	+	20.7846i	−1.31982	+	0.762001i
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$	6.00000			0.219676
$747$	−12.0000	+	20.7846i	−0.439057	+	0.760469i
$748$	7.50000	−	12.9904i	0.274227	−	0.474975i
$749$	−4.00000			−0.146157
$750$	−13.5000	−	7.79423i	−0.492950	−	0.284605i
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	−0.795075	−	0.606511i	$-0.792568\pi$
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	0.922792	+	0.385299i	$0.125902\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$	−37.5000	+	21.6506i	−1.36658	+	0.788993i
$754$	2.50000	−	4.33013i	0.0910446	−	0.157694i
$755$		0			0
$756$	−4.50000	+	2.59808i	−0.163663	+	0.0944911i
$757$	14.5000	−	25.1147i	0.527011	−	0.912811i	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	14.5000	−	25.1147i	0.527011	−	0.912811i	0.999505	−	0.0314762i	$-0.0100208\pi$
$758$	15.0000			0.544825
$759$		−	25.9808i		−	0.943042i
$760$	−3.00000			−0.108821
$761$	−5.50000	+	9.52628i	−0.199375	+	0.345327i	−0.948326	−	0.317298i	$-0.897224\pi$
$761$	−5.50000	+	9.52628i	−0.199375	+	0.345327i	0.748951	+	0.662625i	$0.230558\pi$
$762$	−7.50000	+	4.33013i	−0.271696	+	0.156864i
$763$	2.00000			0.0724049
$764$	24.0000			0.868290
$765$	9.00000			0.325396
$766$	11.5000	−	19.9186i	0.415512	−	0.719688i
$767$	4.50000	−	7.79423i	0.162486	−	0.281433i
$768$	25.5000	−	14.7224i	0.920152	−	0.531250i
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	0.998852	+	0.0479061i	$0.0152548\pi$
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	−0.457938	+	0.888984i	$0.651412\pi$
$770$	−2.50000	−	4.33013i	−0.0900937	−	0.156047i
$771$	−21.0000	+	12.1244i	−0.756297	+	0.436648i
$772$	5.00000			0.179954
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$	−15.0000			−0.539164
$775$	16.0000	−	27.7128i	0.574737	−	0.995474i
$776$	−9.00000	+	15.5885i	−0.323081	+	0.559593i
$777$	−16.5000	+	9.52628i	−0.591934	+	0.341753i
$778$	−11.0000	−	19.0526i	−0.394369	−	0.683067i
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$			1.73205i			0.0620174i
$781$	−7.50000	+	12.9904i	−0.268371	+	0.464832i
$782$	−9.00000			−0.321839
$783$		−	25.9808i		−	0.928477i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$	1.50000	−	2.59808i	0.0535373	−	0.0927293i
$786$	13.5000	−	7.79423i	0.481529	−	0.278011i
$787$	−5.00000			−0.178231			−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000			−0.178231			−0.0891154	+	0.996021i	$0.528404\pi$
$788$	5.00000			0.178118
$789$	7.50000	−	4.33013i	0.267007	−	0.154157i
$790$	−0.500000	−	0.866025i	−0.0177892	−	0.0308118i
$791$	9.00000	+	15.5885i	0.320003	+	0.554262i
$792$	−45.0000			−1.59901
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$	−15.0000	−	8.66025i	−0.531995	−	0.307148i
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	−0.950726	−	0.310031i	$-0.899660\pi$
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	0.206868	−	0.978369i	$-0.433673\pi$
$798$			1.73205i			0.0613139i
$799$	10.5000	+	18.1865i	0.371463	+	0.643393i
$800$	−10.0000	+	17.3205i	−0.353553	+	0.612372i
$801$	6.00000			0.212000
$802$	−8.50000	−	14.7224i	−0.300145	−	0.519867i
$803$	−27.5000	−	47.6314i	−0.970454	−	1.68088i
$804$	13.5000	+	4.33013i	0.476108	+	0.152712i
$805$	1.50000	−	2.59808i	0.0528681	−	0.0915702i
$806$	8.00000			0.281788
$807$		−	24.2487i		−	0.853595i
$808$	33.0000			1.16094
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	18.5000	−	32.0429i	0.649623	−	1.12518i	−0.333590	−	0.942718i	$-0.608260\pi$
$811$	18.5000	−	32.0429i	0.649623	−	1.12518i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$	−2.50000	−	4.33013i	−0.0877328	−	0.151958i
$813$			48.4974i			1.70088i
$814$	−55.0000			−1.92775
$815$	9.50000	+	16.4545i	0.332770	+	0.576375i
$816$			5.19615i			0.181902i
$817$	2.50000	−	4.33013i	0.0874639	−	0.151492i
$818$	−14.0000			−0.489499
$819$	3.00000			0.104828
$820$	3.00000	+	5.19615i	0.104765	+	0.181458i
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	−0.882948	−	0.469471i	$-0.844445\pi$
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	0.848048	+	0.529920i	$0.177778\pi$
$822$		−	15.5885i		−	0.543710i
$823$	3.00000			0.104573			0.0522867	−	0.998632i	$-0.483349\pi$
$823$	3.00000			0.104573			0.0522867	+	0.998632i	$0.483349\pi$
$824$	6.00000	+	10.3923i	0.209020	+	0.362033i
$825$	30.0000	−	17.3205i	1.04447	−	0.603023i
$826$	4.50000	+	7.79423i	0.156575	+	0.271196i
$827$	1.50000	+	2.59808i	0.0521601	+	0.0903440i	0.890927	−	0.454147i	$-0.150056\pi$
$827$	1.50000	+	2.59808i	0.0521601	+	0.0903440i	−0.838766	+	0.544491i	$0.816723\pi$
$828$	−4.50000	−	7.79423i	−0.156386	−	0.270868i
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$	−8.00000			−0.277684
$831$	25.5000	−	14.7224i	0.884585	−	0.510716i
$832$	−7.00000			−0.242681
$833$	9.00000	+	15.5885i	0.311832	+	0.540108i
$834$	1.50000	−	0.866025i	0.0519408	−	0.0299880i
$835$	24.0000			0.830554
$836$	2.50000	−	4.33013i	0.0864643	−	0.149761i
$837$	36.0000	−	20.7846i	1.24434	−	0.718421i
$838$	1.50000	−	2.59808i	0.0518166	−	0.0897491i
$839$	−23.0000			−0.794048			−0.397024	−	0.917808i	$-0.629957\pi$
$839$	−23.0000			−0.794048			−0.397024	+	0.917808i	$0.629957\pi$
$840$	−4.50000	−	2.59808i	−0.155265	−	0.0896421i
$841$	−4.00000			−0.137931
$842$	−3.00000	−	5.19615i	−0.103387	−	0.179071i
$843$	9.00000	+	5.19615i	0.309976	+	0.178965i
$844$	−10.5000	−	18.1865i	−0.361425	−	0.626006i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$	10.5000	−	18.1865i	0.360997	−	0.625266i
$847$	14.0000			0.481046
$848$	5.00000	−	8.66025i	0.171701	−	0.297394i
$849$	−4.50000	−	2.59808i	−0.154440	−	0.0891657i
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	−16.5000	−	28.5788i	−0.565613	−	0.979670i
$852$			5.19615i			0.178017i
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$	5.00000	+	8.66025i	0.171096	+	0.296348i
$855$	3.00000			0.102598
$856$	−12.0000			−0.410152
$857$	28.5000	+	49.3634i	0.973541	+	1.68622i	0.684667	+	0.728856i	$0.259948\pi$
$857$	28.5000	+	49.3634i	0.973541	+	1.68622i	0.288875	+	0.957367i	$0.406719\pi$
$858$	7.50000	+	4.33013i	0.256046	+	0.147828i
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$	2.50000	+	4.33013i	0.0852493	+	0.147656i
$861$	9.00000	−	5.19615i	0.306719	−	0.177084i
$862$	−4.50000	−	7.79423i	−0.153271	−	0.265472i
$863$	−56.0000			−1.90626			−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000			−1.90626			−0.953131	+	0.302558i	$0.902160\pi$
$864$	−22.5000	+	12.9904i	−0.765466	+	0.441942i
$865$	7.00000	+	12.1244i	0.238007	+	0.412240i
$866$	7.50000	+	12.9904i	0.254860	+	0.441431i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$	5.00000			0.169613
$870$	7.50000	−	4.33013i	0.254274	−	0.146805i
$871$	−5.50000	−	6.06218i	−0.186360	−	0.205409i
$872$	6.00000			0.203186
$873$	9.00000	−	15.5885i	0.304604	−	0.527589i
$874$	−3.00000			−0.101477
$875$	9.00000			0.304256
$876$	−16.5000	−	9.52628i	−0.557483	−	0.321863i
$877$	47.0000			1.58708			0.793539	−	0.608520i	$-0.208236\pi$
$877$	47.0000			1.58708			0.793539	+	0.608520i	$0.208236\pi$
$878$	10.0000	+	17.3205i	0.337484	+	0.584539i
$879$	−31.5000	−	18.1865i	−1.06247	−	0.613417i
$880$	−2.50000	−	4.33013i	−0.0842750	−	0.145969i
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	0.711582	−	0.702603i	$-0.247979\pi$
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	−0.964263	+	0.264946i	$0.914646\pi$
$882$	9.00000	−	15.5885i	0.303046	−	0.524891i
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	−0.281996	−	0.959415i	$-0.590997\pi$
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	0.971876	−	0.235492i	$-0.0756700\pi$
$884$	−1.50000	+	2.59808i	−0.0504505	+	0.0873828i
$885$	13.5000	−	7.79423i	0.453798	−	0.262000i
$886$	−9.50000	+	16.4545i	−0.319159	+	0.552799i
$887$	−13.0000			−0.436497			−0.218249	−	0.975893i	$-0.570034\pi$
$887$	−13.0000			−0.436497			−0.218249	+	0.975893i	$0.570034\pi$
$888$	−49.5000	+	28.5788i	−1.66111	+	0.959043i
$889$	2.50000	−	4.33013i	0.0838473	−	0.145228i
$890$	1.00000	+	1.73205i	0.0335201	+	0.0580585i
$891$	45.0000			1.50756
$892$	−0.500000	+	0.866025i	−0.0167412	+	0.0289967i
$893$	3.50000	+	6.06218i	0.117123	+	0.202863i
$894$	−13.5000	+	7.79423i	−0.451508	+	0.260678i
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	−1.50000	+	2.59808i	−0.0501115	+	0.0867956i
$897$			5.19615i			0.173494i
$898$	7.50000	+	12.9904i	0.250278	+	0.433495i
$899$	20.0000	+	34.6410i	0.667037	+	1.15534i
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	−15.0000	−	25.9808i	−0.499722	−	0.865545i
$902$	30.0000			0.998891
$903$	7.50000	−	4.33013i	0.249584	−	0.144098i
$904$	27.0000	+	46.7654i	0.898007	+	1.55539i
$905$	3.50000	+	6.06218i	0.116344	+	0.201514i
$906$		0			0
$907$	−31.0000			−1.02934			−0.514669	−	0.857389i	$-0.672085\pi$
$907$	−31.0000			−1.02934			−0.514669	+	0.857389i	$0.672085\pi$
$908$	−13.5000	−	23.3827i	−0.448013	−	0.775982i
$909$	−33.0000			−1.09454
$910$	0.500000	+	0.866025i	0.0165748	+	0.0287085i
$911$	16.5000	+	28.5788i	0.546669	+	0.946859i	0.998500	+	0.0547553i	$0.0174379\pi$
$911$	16.5000	+	28.5788i	0.546669	+	0.946859i	−0.451830	+	0.892104i	$0.649229\pi$
$912$			1.73205i			0.0573539i
$913$	20.0000	−	34.6410i	0.661903	−	1.14645i
$914$	−12.5000	+	21.6506i	−0.413463	+	0.716139i
$915$	15.0000	−	8.66025i	0.495885	−	0.286299i
$916$	−2.50000	−	4.33013i	−0.0826023	−	0.143071i
$917$	−4.50000	+	7.79423i	−0.148603	+	0.257388i
$918$		−	15.5885i		−	0.514496i
$919$	−22.5000	−	38.9711i	−0.742207	−	1.28554i	−0.951489	−	0.307684i	$-0.900446\pi$
$919$	−22.5000	−	38.9711i	−0.742207	−	1.28554i	0.209282	−	0.977855i	$-0.432887\pi$
$920$	4.50000	−	7.79423i	0.148361	−	0.256968i
$921$	−7.50000	+	4.33013i	−0.247133	+	0.142683i
$922$	5.00000			0.164666
$923$	1.50000	−	2.59808i	0.0493731	−	0.0855167i
$924$	7.50000	−	4.33013i	0.246732	−	0.142451i
$925$	22.0000	−	38.1051i	0.723356	−	1.25289i
$926$	15.5000	−	26.8468i	0.509362	−	0.882240i
$927$	−6.00000	−	10.3923i	−0.197066	−	0.341328i
$928$	−12.5000	−	21.6506i	−0.410333	−	0.710717i
$929$	0.500000	+	0.866025i	0.0164045	+	0.0284134i	0.874111	−	0.485726i	$-0.161445\pi$
$929$	0.500000	+	0.866025i	0.0164045	+	0.0284134i	−0.857707	+	0.514139i	$0.828111\pi$
$930$	12.0000	+	6.92820i	0.393496	+	0.227185i
$931$	3.00000	+	5.19615i	0.0983210	+	0.170297i
$932$	17.0000			0.556854
$933$	13.5000	+	7.79423i	0.441970	+	0.255172i
$934$	3.00000			0.0981630
$935$	−15.0000			−0.490552
$936$	9.00000			0.294174
$937$	54.0000			1.76410			0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000			1.76410			0.882052	+	0.471153i	$0.156162\pi$
$938$	8.00000	−	1.73205i	0.261209	−	0.0565535i
$939$	−16.5000	+	9.52628i	−0.538457	+	0.310878i
$940$	−7.00000			−0.228315
$941$	0.500000	−	0.866025i	0.0162995	−	0.0282316i	−0.857761	−	0.514049i	$-0.828145\pi$
$941$	0.500000	−	0.866025i	0.0162995	−	0.0282316i	0.874060	+	0.485818i	$0.161478\pi$
$942$	−4.50000	−	2.59808i	−0.146618	−	0.0846499i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	4.50000	+	7.79423i	0.146463	+	0.253681i
$945$	4.50000	+	2.59808i	0.146385	+	0.0845154i
$946$	25.0000			0.812820
$947$	−19.5000	−	33.7750i	−0.633665	−	1.09754i	−0.986796	−	0.161966i	$-0.948217\pi$
$947$	−19.5000	−	33.7750i	−0.633665	−	1.09754i	0.353131	−	0.935574i	$-0.385117\pi$
$948$	1.50000	−	0.866025i	0.0487177	−	0.0281272i
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	27.0000	+	15.5885i	0.875535	+	0.505490i
$952$	−4.50000	−	7.79423i	−0.145846	−	0.252612i
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$	−15.0000	+	25.9808i	−0.485643	+	0.841158i
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$			43.3013i			1.39973i
$958$	2.00000	+	3.46410i	0.0646171	+	0.111920i
$959$	4.50000	+	7.79423i	0.145313	+	0.251689i
$960$	−10.5000	−	6.06218i	−0.338886	−	0.195656i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	11.0000			0.354654
$963$	12.0000			0.386695
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$	−2.50000	−	4.33013i	−0.0804778	−	0.139392i
$966$	−4.50000	−	2.59808i	−0.144785	−	0.0835917i
$967$	−24.0000	−	41.5692i	−0.771788	−	1.33678i	−0.936582	−	0.350448i	$-0.886029\pi$
$967$	−24.0000	−	41.5692i	−0.771788	−	1.33678i	0.164794	−	0.986328i	$-0.447304\pi$
$968$	42.0000			1.34993
$969$	4.50000	+	2.59808i	0.144561	+	0.0834622i
$970$	6.00000			0.192648
$971$	4.50000	−	7.79423i	0.144412	−	0.250129i	−0.784741	−	0.619823i	$-0.787204\pi$
$971$	4.50000	−	7.79423i	0.144412	−	0.250129i	0.929153	+	0.369694i	$0.120538\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	−0.500000	+	0.866025i	−0.0160293	+	0.0277635i
$974$	43.0000			1.37781
$975$	−6.00000	+	3.46410i	−0.192154	+	0.110940i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	−13.0000			−0.415907			−0.207953	−	0.978139i	$-0.566680\pi$
$977$	−13.0000			−0.415907			−0.207953	+	0.978139i	$0.566680\pi$
$978$	28.5000	−	16.4545i	0.911330	−	0.526156i
$979$	−10.0000			−0.319601
$980$	−6.00000			−0.191663
$981$	−6.00000			−0.191565
$982$	−19.5000	−	33.7750i	−0.622270	−	1.07780i
$983$	−21.5000	−	37.2391i	−0.685744	−	1.18774i	−0.973203	−	0.229950i	$-0.926144\pi$
$983$	−21.5000	−	37.2391i	−0.685744	−	1.18774i	0.287459	−	0.957793i	$-0.407189\pi$
$984$	27.0000	−	15.5885i	0.860729	−	0.496942i
$985$	−2.50000	−	4.33013i	−0.0796566	−	0.137969i
$986$	15.0000			0.477697
$987$			12.1244i			0.385922i
$988$	−0.500000	+	0.866025i	−0.0159071	+	0.0275519i
$989$	7.50000	+	12.9904i	0.238486	+	0.413070i
$990$	7.50000	+	12.9904i	0.238366	+	0.412861i
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	20.0000	−	34.6410i	0.635001	−	1.09985i
$993$			46.7654i			1.48405i
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$	−25.0000			−0.792553
$996$		−	13.8564i		−	0.439057i
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	0.841295	−	0.540576i	$-0.181794\pi$
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	−0.888800	+	0.458295i	$0.848460\pi$
$998$	−16.5000	+	28.5788i	−0.522298	+	0.904647i
$999$	49.5000	−	28.5788i	1.56611	−	0.904194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.f.b.238.1	✓	2
9.7	even	3		603.2.h.b.439.1	yes	2
67.29	even	3		603.2.h.b.364.1	yes	2
603.565	even	3	inner	603.2.f.b.565.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.f.b.238.1	✓	2	1.1	even	1	trivial
603.2.f.b.565.1	yes	2	603.565	even	3	inner
603.2.h.b.364.1	yes	2	67.29	even	3
603.2.h.b.439.1	yes	2	9.7	even	3

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.00000 q^{7} +3.00000 q^{8} -3.00000 q^{9} +(-0.500000 - 0.866025i) q^{10} +5.00000 q^{11} +(1.50000 - 0.866025i) q^{12} -1.00000 q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +1.00000 q^{20} -1.73205i q^{21} +(2.50000 - 4.33013i) q^{22} +3.00000 q^{23} -5.19615i q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} -5.00000 q^{29} +(-1.50000 + 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(2.50000 + 4.33013i) q^{32} -8.66025i q^{33} -3.00000 q^{34} +(0.500000 - 0.866025i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(-5.50000 - 9.52628i) q^{37} -1.00000 q^{38} +1.73205i q^{39} +(1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-1.50000 - 0.866025i) q^{42} +(2.50000 + 4.33013i) q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} -7.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} -6.00000 q^{49} +4.00000 q^{50} +(-4.50000 + 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +10.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(2.50000 - 4.33013i) q^{55} +3.00000 q^{56} +(-1.50000 + 0.866025i) q^{57} +(-2.50000 + 4.33013i) q^{58} +(-4.50000 + 7.79423i) q^{59} -1.73205i q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000 q^{62} -3.00000 q^{63} +7.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-7.50000 - 4.33013i) q^{66} +(5.50000 + 6.06218i) q^{67} +(1.50000 - 2.59808i) q^{68} -5.19615i q^{69} +(-0.500000 - 0.866025i) q^{70} +(-1.50000 + 2.59808i) q^{71} -9.00000 q^{72} +(-5.50000 - 9.52628i) q^{73} -11.0000 q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +5.00000 q^{77} +(1.50000 + 0.866025i) q^{78} +1.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +6.00000 q^{82} +(4.00000 - 6.92820i) q^{83} +(1.50000 - 0.866025i) q^{84} -3.00000 q^{85} +5.00000 q^{86} +8.66025i q^{87} +15.0000 q^{88} -2.00000 q^{89} +(1.50000 + 2.59808i) q^{90} -1.00000 q^{91} +(1.50000 + 2.59808i) q^{92} +(-12.0000 + 6.92820i) q^{93} +(-3.50000 + 6.06218i) q^{94} -1.00000 q^{95} +(7.50000 - 4.33013i) q^{96} +(-3.00000 + 5.19615i) q^{97} +(-3.00000 + 5.19615i) q^{98} -15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 + q^4 + q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 6 * q^9	\( 2 q + q^{2} + q^{4} + q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 6 q^{9} - q^{10} + 10 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - 3 q^{18} - q^{19} + 2 q^{20} + 5 q^{22} + 6 q^{23} + 4 q^{25} - q^{26} + q^{28} - 10 q^{29} - 3 q^{30} - 8 q^{31} + 5 q^{32} - 6 q^{34} + q^{35} - 3 q^{36} - 11 q^{37} - 2 q^{38} + 3 q^{40} + 6 q^{41} - 3 q^{42} + 5 q^{43} + 5 q^{44} - 3 q^{45} + 3 q^{46} - 14 q^{47} - 3 q^{48} - 12 q^{49} + 8 q^{50} - 9 q^{51} - q^{52} + 20 q^{53} + 9 q^{54} + 5 q^{55} + 6 q^{56} - 3 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{61} - 16 q^{62} - 6 q^{63} + 14 q^{64} - q^{65} - 15 q^{66} + 11 q^{67} + 3 q^{68} - q^{70} - 3 q^{71} - 18 q^{72} - 11 q^{73} - 22 q^{74} + 12 q^{75} + q^{76} + 10 q^{77} + 3 q^{78} + 2 q^{79} - q^{80} + 18 q^{81} + 12 q^{82} + 8 q^{83} + 3 q^{84} - 6 q^{85} + 10 q^{86} + 30 q^{88} - 4 q^{89} + 3 q^{90} - 2 q^{91} + 3 q^{92} - 24 q^{93} - 7 q^{94} - 2 q^{95} + 15 q^{96} - 6 q^{97} - 6 q^{98} - 30 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^4 + q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 6 * q^9 - q^10 + 10 * q^11 + 3 * q^12 - 2 * q^13 + q^14 - 3 * q^15 + q^16 - 3 * q^17 - 3 * q^18 - q^19 + 2 * q^20 + 5 * q^22 + 6 * q^23 + 4 * q^25 - q^26 + q^28 - 10 * q^29 - 3 * q^30 - 8 * q^31 + 5 * q^32 - 6 * q^34 + q^35 - 3 * q^36 - 11 * q^37 - 2 * q^38 + 3 * q^40 + 6 * q^41 - 3 * q^42 + 5 * q^43 + 5 * q^44 - 3 * q^45 + 3 * q^46 - 14 * q^47 - 3 * q^48 - 12 * q^49 + 8 * q^50 - 9 * q^51 - q^52 + 20 * q^53 + 9 * q^54 + 5 * q^55 + 6 * q^56 - 3 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^61 - 16 * q^62 - 6 * q^63 + 14 * q^64 - q^65 - 15 * q^66 + 11 * q^67 + 3 * q^68 - q^70 - 3 * q^71 - 18 * q^72 - 11 * q^73 - 22 * q^74 + 12 * q^75 + q^76 + 10 * q^77 + 3 * q^78 + 2 * q^79 - q^80 + 18 * q^81 + 12 * q^82 + 8 * q^83 + 3 * q^84 - 6 * q^85 + 10 * q^86 + 30 * q^88 - 4 * q^89 + 3 * q^90 - 2 * q^91 + 3 * q^92 - 24 * q^93 - 7 * q^94 - 2 * q^95 + 15 * q^96 - 6 * q^97 - 6 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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