LMFDB - Embedded newform 603.2.h.b.439.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(364,603)]

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, 4]))

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

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

chi := DirichletCharacter("603.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.81497924188$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	603.439
Dual form			603.2.h.b.364.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} -1.73205i q^{12} +(0.500000 - 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.50000 + 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +3.00000 q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.50000 - 0.866025i) q^{21} +(2.50000 + 4.33013i) q^{22} +(-1.50000 + 2.59808i) 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} +(2.50000 + 4.33013i) q^{29} +(1.50000 - 0.866025i) q^{30} +8.00000 q^{31} -5.00000 q^{32} +(7.50000 - 4.33013i) q^{33} +(1.50000 + 2.59808i) q^{34} +(0.500000 - 0.866025i) q^{35} +3.00000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(0.500000 + 0.866025i) q^{38} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{40} -6.00000 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} +(3.50000 + 6.06218i) q^{47} -1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(4.50000 - 2.59808i) q^{51} +(-0.500000 + 0.866025i) q^{52} +10.0000 q^{53} +5.19615i q^{54} +(2.50000 - 4.33013i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(1.50000 - 0.866025i) q^{57} +(-2.50000 - 4.33013i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(1.50000 - 0.866025i) q^{60} +10.0000 q^{61} -8.00000 q^{62} +(1.50000 + 2.59808i) q^{63} +7.00000 q^{64} +1.00000 q^{65} +(-7.50000 + 4.33013i) q^{66} +(-8.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.50000 - 2.59808i) q^{69} +(-0.500000 + 0.866025i) q^{70} +(-1.50000 + 2.59808i) q^{71} -9.00000 q^{72} +(-5.50000 - 9.52628i) q^{73} +(5.50000 + 9.52628i) q^{74} +(6.00000 + 3.46410i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-2.50000 + 4.33013i) q^{77} +(-1.50000 - 0.866025i) q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +6.00000 q^{82} -8.00000 q^{83} +(-1.50000 + 0.866025i) q^{84} +(1.50000 - 2.59808i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(-7.50000 + 4.33013i) q^{87} +(-7.50000 - 12.9904i) q^{88} -2.00000 q^{89} +(1.50000 + 2.59808i) q^{90} -1.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +13.8564i q^{93} +(-3.50000 - 6.06218i) q^{94} +(0.500000 - 0.866025i) q^{95} -8.66025i q^{96} +6.00000 q^{97} +(-3.00000 + 5.19615i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 + 6 * q^8 - 6 * q^9	$ 2 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} + 6 q^{8} - 6 q^{9} - q^{10} - 5 q^{11} + q^{13} + q^{14} - 3 q^{15} - 2 q^{16} - 3 q^{17} + 6 q^{18} - q^{19} - q^{20} + 3 q^{21} + 5 q^{22} - 3 q^{23} + 4 q^{25} - q^{26} + q^{28} + 5 q^{29} + 3 q^{30} + 16 q^{31} - 10 q^{32} + 15 q^{33} + 3 q^{34} + q^{35} + 6 q^{36} - 11 q^{37} + q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{41} - 3 q^{42} + 5 q^{43} + 5 q^{44} - 3 q^{45} + 3 q^{46} + 7 q^{47} + 6 q^{49} - 4 q^{50} + 9 q^{51} - q^{52} + 20 q^{53} + 5 q^{55} - 3 q^{56} + 3 q^{57} - 5 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} - 16 q^{62} + 3 q^{63} + 14 q^{64} + 2 q^{65} - 15 q^{66} - 16 q^{67} + 3 q^{68} - 9 q^{69} - q^{70} - 3 q^{71} - 18 q^{72} - 11 q^{73} + 11 q^{74} + 12 q^{75} + q^{76} - 5 q^{77} - 3 q^{78} - q^{79} - q^{80} + 18 q^{81} + 12 q^{82} - 16 q^{83} - 3 q^{84} + 3 q^{85} - 5 q^{86} - 15 q^{87} - 15 q^{88} - 4 q^{89} + 3 q^{90} - 2 q^{91} + 3 q^{92} - 7 q^{94} + q^{95} + 12 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 + 6 * q^8 - 6 * q^9 - q^10 - 5 * q^11 + q^13 + q^14 - 3 * q^15 - 2 * q^16 - 3 * q^17 + 6 * q^18 - q^19 - q^20 + 3 * q^21 + 5 * q^22 - 3 * q^23 + 4 * q^25 - q^26 + q^28 + 5 * q^29 + 3 * q^30 + 16 * q^31 - 10 * q^32 + 15 * q^33 + 3 * q^34 + q^35 + 6 * q^36 - 11 * q^37 + q^38 + 3 * q^39 + 3 * q^40 - 12 * q^41 - 3 * q^42 + 5 * q^43 + 5 * q^44 - 3 * q^45 + 3 * q^46 + 7 * q^47 + 6 * q^49 - 4 * q^50 + 9 * q^51 - q^52 + 20 * q^53 + 5 * q^55 - 3 * q^56 + 3 * q^57 - 5 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 - 16 * q^62 + 3 * q^63 + 14 * q^64 + 2 * q^65 - 15 * q^66 - 16 * q^67 + 3 * q^68 - 9 * q^69 - q^70 - 3 * q^71 - 18 * q^72 - 11 * q^73 + 11 * q^74 + 12 * q^75 + q^76 - 5 * q^77 - 3 * q^78 - q^79 - q^80 + 18 * q^81 + 12 * q^82 - 16 * q^83 - 3 * q^84 + 3 * q^85 - 5 * q^86 - 15 * q^87 - 15 * q^88 - 4 * q^89 + 3 * q^90 - 2 * q^91 + 3 * q^92 - 7 * q^94 + q^95 + 12 * q^97 - 6 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		−	1.73205i		−	0.707107i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	3.00000			1.06066
$9$	−3.00000			−1.00000
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		−	1.73205i		−	0.500000i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$	−1.00000			−0.250000
$17$	−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	$0.951855\pi$
$18$	3.00000			0.707107
$19$	−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	$0.869927\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.50000	−	0.866025i	0.327327	−	0.188982i
$22$	2.50000	+	4.33013i	0.533002	+	0.923186i
$23$	−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	$0.267924\pi$
$24$			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
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	−5.00000			−0.883883
$33$	7.50000	−	4.33013i	1.30558	−	0.753778i
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	3.00000			0.500000
$37$	−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	$-0.526194\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.50000	+	0.866025i	−0.231455	+	0.133631i
$43$	2.50000	−	4.33013i	0.381246	−	0.660338i	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	2.50000	−	4.33013i	0.381246	−	0.660338i	0.991241	+	0.132068i	$0.0421616\pi$
$44$	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
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	0.999926	+	0.0121990i	$0.00388317\pi$
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	−0.489398	+	0.872060i	$0.662783\pi$
$48$		−	1.73205i		−	0.250000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	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	$0.259014\pi$
$54$			5.19615i			0.707107i
$55$	2.50000	−	4.33013i	0.337100	−	0.583874i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	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	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$	1.50000	−	0.866025i	0.193649	−	0.111803i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	−8.00000			−1.01600
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	7.00000			0.875000
$65$	1.00000			0.124035
$66$	−7.50000	+	4.33013i	−0.923186	+	0.533002i
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$	−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	$-0.389279\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$	6.00000	+	3.46410i	0.692820	+	0.400000i
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$	−2.50000	+	4.33013i	−0.284901	+	0.493464i
$78$	−1.50000	−	0.866025i	−0.169842	−	0.0980581i
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	9.00000			1.00000
$82$	6.00000			0.662589
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	−1.50000	+	0.866025i	−0.163663	+	0.0944911i
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	−2.50000	+	4.33013i	−0.269582	+	0.466930i
$87$	−7.50000	+	4.33013i	−0.804084	+	0.464238i
$88$	−7.50000	−	12.9904i	−0.799503	−	1.38478i
$89$	−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
$93$			13.8564i			1.43684i
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		−	8.66025i		−	0.883883i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	7.50000	+	12.9904i	0.753778	+	1.30558i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−5.50000	−	9.52628i	−0.547270	−	0.947900i	−0.998460	−	0.0554722i	$-0.982334\pi$
$101$	−5.50000	−	9.52628i	−0.547270	−	0.947900i	0.451190	−	0.892428i	$-0.351000\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	1.50000	−	2.59808i	0.147087	−	0.254762i
$105$	1.50000	+	0.866025i	0.146385	+	0.0845154i
$106$	−10.0000			−0.971286
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$			5.19615i			0.500000i
$109$	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
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$	−1.50000	+	0.866025i	−0.140488	+	0.0811107i
$115$	−3.00000			−0.279751
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$	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
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−10.0000			−0.905357
$123$		−	10.3923i		−	0.937043i
$124$	−8.00000			−0.718421
$125$	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	$0.0954607\pi$
$128$	3.00000			0.265165
$129$	7.50000	+	4.33013i	0.660338	+	0.381246i
$130$	−1.00000			−0.0877058
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$	−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	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	4.50000	+	2.59808i	0.383065	+	0.221163i
$139$	−0.500000	−	0.866025i	−0.0424094	−	0.0734553i	0.844042	−	0.536278i	$-0.180170\pi$
$139$	−0.500000	−	0.866025i	−0.0424094	−	0.0734553i	−0.886451	+	0.462822i	$0.846837\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	−10.5000	+	6.06218i	−0.884260	+	0.510527i
$142$	1.50000	−	2.59808i	0.125877	−	0.218026i
$143$	−5.00000			−0.418121
$144$	3.00000			0.250000
$145$	−2.50000	+	4.33013i	−0.207614	+	0.359597i
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$	9.00000	+	5.19615i	0.742307	+	0.428571i
$148$	5.50000	+	9.52628i	0.452097	+	0.783055i
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$	−6.00000	−	3.46410i	−0.489898	−	0.282843i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−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
$155$	4.00000	+	6.92820i	0.321288	+	0.556487i
$156$	−1.50000	−	0.866025i	−0.120096	−	0.0693375i
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	−0.919654	−	0.392730i	$-0.871531\pi$
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	0.799941	+	0.600079i	$0.204864\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$			17.3205i			1.37361i
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$	3.00000			0.236433
$162$	−9.00000			−0.707107
$163$	−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	$0.899546\pi$
$164$	6.00000			0.468521
$165$	7.50000	+	4.33013i	0.583874	+	0.337100i
$166$	8.00000			0.620920
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$	4.50000	−	2.59808i	0.347183	−	0.200446i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−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
$173$	14.0000			1.06440			0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000			1.06440			0.532200	+	0.846619i	$0.321365\pi$
$174$	7.50000	−	4.33013i	0.568574	−	0.328266i
$175$	−4.00000			−0.302372
$176$	2.50000	+	4.33013i	0.188445	+	0.326396i
$177$	13.5000	−	7.79423i	1.01472	−	0.585850i
$178$	2.00000			0.149906
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	−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	$0.250440\pi$
$182$	1.00000			0.0741249
$183$			17.3205i			1.28037i
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	5.50000	−	9.52628i	0.404368	−	0.700386i
$186$		−	13.8564i		−	1.01600i
$187$	−7.50000	+	12.9904i	−0.548454	+	0.949951i
$188$	−3.50000	−	6.06218i	−0.255264	−	0.442130i
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$	−0.500000	+	0.866025i	−0.0362738	+	0.0628281i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$			12.1244i			0.875000i
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$	−6.00000			−0.430775
$195$			1.73205i			0.124035i
$196$	−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
$201$	−3.00000	−	13.8564i	−0.211604	−	0.977356i
$202$	5.50000	+	9.52628i	0.386979	+	0.670267i
$203$	2.50000	−	4.33013i	0.175466	−	0.303915i
$204$	−4.50000	+	2.59808i	−0.315063	+	0.181902i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	4.00000			0.278693
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$	−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
$211$	10.5000	−	18.1865i	0.722850	−	1.25201i	−0.237003	−	0.971509i	$-0.576165\pi$
$211$	10.5000	−	18.1865i	0.722850	−	1.25201i	0.959853	−	0.280504i	$-0.0905015\pi$
$212$	−10.0000			−0.686803
$213$	−4.50000	−	2.59808i	−0.308335	−	0.178017i
$214$	4.00000			0.273434
$215$	5.00000			0.340997
$216$		−	15.5885i		−	1.06066i
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$	−2.00000			−0.135457
$219$	16.5000	−	9.52628i	1.11497	−	0.643726i
$220$	−2.50000	+	4.33013i	−0.168550	+	0.291937i
$221$	−3.00000			−0.201802
$222$	−16.5000	+	9.52628i	−1.10741	+	0.639362i
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	2.50000	+	4.33013i	0.167038	+	0.289319i
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	18.0000			1.19734
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.832529	+	0.553981i	$0.186892\pi$
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.0634974	+	0.997982i	$0.479775\pi$
$228$	−1.50000	+	0.866025i	−0.0993399	+	0.0573539i
$229$	2.50000	−	4.33013i	0.165205	−	0.286143i	−0.771523	−	0.636201i	$-0.780505\pi$
$229$	2.50000	−	4.33013i	0.165205	−	0.286143i	0.936728	+	0.350058i	$0.113838\pi$
$230$	3.00000			0.197814
$231$	−7.50000	−	4.33013i	−0.493464	−	0.284901i
$232$	7.50000	+	12.9904i	0.492399	+	0.852860i
$233$	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
$236$	4.50000	+	7.79423i	0.292925	+	0.507361i
$237$	1.50000	−	0.866025i	0.0974355	−	0.0562544i
$238$	1.50000	−	2.59808i	0.0972306	−	0.168408i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$			15.5885i			1.00000i
$244$	−10.0000			−0.640184
$245$	6.00000			0.383326
$246$			10.3923i			0.662589i
$247$	−1.00000			−0.0636285
$248$	24.0000			1.52400
$249$		−	13.8564i		−	0.878114i
$250$	−9.00000			−0.569210
$251$	−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
$255$	4.50000	+	2.59808i	0.281801	+	0.162698i
$256$	−17.0000			−1.06250
$257$	14.0000			0.873296			0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000			0.873296			0.436648	+	0.899632i	$0.356166\pi$
$258$	−7.50000	−	4.33013i	−0.466930	−	0.269582i
$259$	−5.50000	+	9.52628i	−0.341753	+	0.591934i
$260$	−1.00000			−0.0620174
$261$	−7.50000	−	12.9904i	−0.464238	−	0.804084i
$262$	4.50000	+	7.79423i	0.278011	+	0.481529i
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	−0.778595	−	0.627527i	$-0.784067\pi$
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	0.932752	+	0.360520i	$0.117401\pi$
$264$	22.5000	−	12.9904i	1.38478	−	0.799503i
$265$	5.00000	+	8.66025i	0.307148	+	0.531995i
$266$	0.500000	−	0.866025i	0.0306570	−	0.0530994i
$267$		−	3.46410i		−	0.212000i
$268$	8.00000	−	1.73205i	0.488678	−	0.105802i
$269$	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	$0.823664\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		−	1.73205i		−	0.104828i
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	−20.0000			−1.20605
$276$	4.50000	+	2.59808i	0.270868	+	0.156386i
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	−0.489207	−	0.872167i	$-0.662714\pi$
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	0.999923	−	0.0124177i	$-0.00395278\pi$
$278$	0.500000	+	0.866025i	0.0299880	+	0.0519408i
$279$	−24.0000			−1.43684
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	10.5000	−	6.06218i	0.625266	−	0.360997i
$283$	1.50000	+	2.59808i	0.0891657	+	0.154440i	0.907159	−	0.420789i	$-0.138247\pi$
$283$	1.50000	+	2.59808i	0.0891657	+	0.154440i	−0.817993	+	0.575228i	$0.804913\pi$
$284$	1.50000	−	2.59808i	0.0890086	−	0.154167i
$285$	1.50000	+	0.866025i	0.0888523	+	0.0512989i
$286$	5.00000			0.295656
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$	15.0000			0.883883
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	2.50000	−	4.33013i	0.146805	−	0.254274i
$291$			10.3923i			0.609208i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	10.5000	+	18.1865i	0.613417	+	1.06247i	0.990660	+	0.136355i	$0.0435386\pi$
$293$	10.5000	+	18.1865i	0.613417	+	1.06247i	−0.377244	+	0.926114i	$0.623128\pi$
$294$	−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
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$	1.50000	+	2.59808i	0.0867472	+	0.150251i
$300$	−6.00000	−	3.46410i	−0.346410	−	0.200000i
$301$	−5.00000			−0.288195
$302$		0			0
$303$	16.5000	−	9.52628i	0.947900	−	0.547270i
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$	−4.50000	−	7.79423i	−0.257248	−	0.445566i
$307$	−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
$309$		−	6.92820i		−	0.394132i
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	0.709771	−	0.704433i	$-0.248799\pi$
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	−0.964942	+	0.262463i	$0.915465\pi$
$312$	4.50000	+	2.59808i	0.254762	+	0.147087i
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$	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
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		−	17.3205i		−	0.971286i
$319$	12.5000	−	21.6506i	0.699866	−	1.21220i
$320$	3.50000	+	6.06218i	0.195656	+	0.338886i
$321$		−	6.92820i		−	0.386695i
$322$	−3.00000			−0.167183
$323$	−1.50000	+	2.59808i	−0.0834622	+	0.144561i
$324$	−9.00000			−0.500000
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	9.50000	−	16.4545i	0.526156	−	0.911330i
$327$			3.46410i			0.191565i
$328$	−18.0000			−0.993884
$329$	3.50000	−	6.06218i	0.192961	−	0.334219i
$330$	−7.50000	−	4.33013i	−0.412861	−	0.238366i
$331$	13.5000	+	23.3827i	0.742027	+	1.28523i	0.951571	+	0.307429i	$0.0994688\pi$
$331$	13.5000	+	23.3827i	0.742027	+	1.28523i	−0.209544	+	0.977799i	$0.567198\pi$
$332$	8.00000			0.439057
$333$	16.5000	+	28.5788i	0.904194	+	1.56611i
$334$	24.0000			1.31322
$335$	−5.50000	−	6.06218i	−0.300497	−	0.331212i
$336$	−1.50000	+	0.866025i	−0.0818317	+	0.0472456i
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	−0.945468	−	0.325714i	$-0.894395\pi$
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	0.754811	+	0.655942i	$0.227729\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$		−	31.1769i		−	1.69330i
$340$	−1.50000	+	2.59808i	−0.0813489	+	0.140900i
$341$	−20.0000	−	34.6410i	−1.08306	−	1.87592i
$342$	−1.50000	−	2.59808i	−0.0811107	−	0.140488i
$343$	−13.0000			−0.701934
$344$	7.50000	−	12.9904i	0.404373	−	0.700394i
$345$		−	5.19615i		−	0.279751i
$346$	−14.0000			−0.752645
$347$	24.0000			1.28839			0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000			1.28839			0.644194	+	0.764862i	$0.277193\pi$
$348$	7.50000	−	4.33013i	0.402042	−	0.232119i
$349$	−7.50000	+	12.9904i	−0.401466	+	0.695359i	−0.993903	−	0.110257i	$-0.964832\pi$
$349$	−7.50000	+	12.9904i	−0.401466	+	0.695359i	0.592437	+	0.805617i	$0.298166\pi$
$350$	4.00000			0.213809
$351$	−4.50000	−	2.59808i	−0.240192	−	0.138675i
$352$	12.5000	+	21.6506i	0.666252	+	1.15398i
$353$	−18.0000			−0.958043			−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000			−0.958043			−0.479022	+	0.877803i	$0.659008\pi$
$354$	−13.5000	+	7.79423i	−0.717517	+	0.414259i
$355$	−3.00000			−0.159223
$356$	2.00000			0.106000
$357$	−4.50000	−	2.59808i	−0.238165	−	0.137505i
$358$	12.0000			0.634220
$359$	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
$363$	−21.0000	−	12.1244i	−1.10221	−	0.636364i
$364$	1.00000			0.0524142
$365$	5.50000	−	9.52628i	0.287883	−	0.498628i
$366$		−	17.3205i		−	0.905357i
$367$	−12.5000	−	21.6506i	−0.652495	−	1.13015i	−0.982516	−	0.186180i	$-0.940389\pi$
$367$	−12.5000	−	21.6506i	−0.652495	−	1.13015i	0.330021	−	0.943974i	$-0.392944\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	18.0000			0.937043
$370$	−5.50000	+	9.52628i	−0.285931	+	0.495248i
$371$	−5.00000	−	8.66025i	−0.259587	−	0.449618i
$372$		−	13.8564i		−	0.718421i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$	7.50000	−	12.9904i	0.387816	−	0.671717i
$375$			15.5885i			0.804984i
$376$	10.5000	+	18.1865i	0.541496	+	0.937899i
$377$	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
$382$	24.0000			1.22795
$383$	−11.5000	+	19.9186i	−0.587623	+	1.01779i	0.406920	+	0.913464i	$0.366603\pi$
$383$	−11.5000	+	19.9186i	−0.587623	+	1.01779i	−0.994543	+	0.104328i	$0.966731\pi$
$384$			5.19615i			0.265165i
$385$	−5.00000			−0.254824
$386$	−2.50000	−	4.33013i	−0.127247	−	0.220398i
$387$	−7.50000	+	12.9904i	−0.381246	+	0.660338i
$388$	−6.00000			−0.304604
$389$	−22.0000			−1.11544			−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000			−1.11544			−0.557722	+	0.830028i	$0.688325\pi$
$390$		−	1.73205i		−	0.0877058i
$391$	9.00000			0.455150
$392$	9.00000	−	15.5885i	0.454569	−	0.787336i
$393$	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	$0.686163\pi$
$398$	12.5000	+	21.6506i	0.626568	+	1.08525i
$399$	−1.50000	−	0.866025i	−0.0750939	−	0.0433555i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	8.50000	+	14.7224i	0.424470	+	0.735203i	0.996371	−	0.0851195i	$-0.0271272\pi$
$401$	8.50000	+	14.7224i	0.424470	+	0.735203i	−0.571901	+	0.820323i	$0.693794\pi$
$402$	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
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	13.5000	+	7.79423i	0.665906	+	0.384461i
$412$	4.00000			0.197066
$413$	−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
$418$	2.50000	−	4.33013i	0.122279	−	0.211793i
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	−0.900337	−	0.435194i	$-0.856680\pi$
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	0.827057	+	0.562118i	$0.190013\pi$
$420$	−1.50000	−	0.866025i	−0.0731925	−	0.0422577i
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	−10.5000	+	18.1865i	−0.511132	+	0.885307i
$423$	−10.5000	−	18.1865i	−0.510527	−	0.884260i
$424$	30.0000			1.45693
$425$	−12.0000			−0.582086
$426$	4.50000	+	2.59808i	0.218026	+	0.125877i
$427$	−5.00000	−	8.66025i	−0.241967	−	0.419099i
$428$	4.00000			0.193347
$429$		−	8.66025i		−	0.418121i
$430$	−5.00000			−0.241121
$431$	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	$0.0971186\pi$
$432$			5.19615i			0.250000i
$433$	−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	$0.284036\pi$
$434$	4.00000	+	6.92820i	0.192006	+	0.332564i
$435$	−7.50000	−	4.33013i	−0.359597	−	0.207614i
$436$	−2.00000			−0.0957826
$437$	3.00000			0.143509
$438$	−16.5000	+	9.52628i	−0.788400	+	0.455183i
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$	7.50000	−	12.9904i	0.357548	−	0.619292i
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$	3.00000			0.142695
$443$	9.50000	+	16.4545i	0.451359	+	0.781776i	0.998471	−	0.0552833i	$-0.0176062\pi$
$443$	9.50000	+	16.4545i	0.451359	+	0.781776i	−0.547112	+	0.837059i	$0.684273\pi$
$444$	−16.5000	+	9.52628i	−0.783055	+	0.452097i
$445$	−1.00000	−	1.73205i	−0.0474045	−	0.0821071i
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$	−13.5000	+	7.79423i	−0.638528	+	0.368654i
$448$	−3.50000	−	6.06218i	−0.165359	−	0.286411i
$449$	−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	$0.281827\pi$
$450$	6.00000	−	10.3923i	0.282843	−	0.489898i
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$	18.0000			0.846649
$453$		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
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$	−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	−0.801917	−	0.597436i	$-0.796186\pi$
$461$	2.50000	−	4.33013i	0.116437	−	0.201674i	0.918353	+	0.395762i	$0.129519\pi$
$462$	7.50000	+	4.33013i	0.348932	+	0.201456i
$463$	−15.5000	+	26.8468i	−0.720346	+	1.24768i	0.240515	+	0.970645i	$0.422684\pi$
$463$	−15.5000	+	26.8468i	−0.720346	+	1.24768i	−0.960861	+	0.277031i	$0.910650\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$	−12.0000	+	6.92820i	−0.556487	+	0.321288i
$466$	−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
$471$	−4.50000	−	2.59808i	−0.207349	−	0.119713i
$472$	−13.5000	−	23.3827i	−0.621388	−	1.07628i
$473$	−25.0000			−1.14950
$474$	−1.50000	+	0.866025i	−0.0688973	+	0.0397779i
$475$	−4.00000			−0.183533
$476$	1.50000	−	2.59808i	0.0687524	−	0.119083i
$477$	−30.0000			−1.37361
$478$	−16.0000			−0.731823
$479$	4.00000			0.182765			0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000			0.182765			0.0913823	+	0.995816i	$0.470871\pi$
$480$	7.50000	−	4.33013i	0.342327	−	0.197642i
$481$	−11.0000			−0.501557
$482$	−12.5000	+	21.6506i	−0.569359	+	0.986159i
$483$			5.19615i			0.236433i
$484$	7.00000	−	12.1244i	0.318182	−	0.551107i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		−	15.5885i		−	0.707107i
$487$	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	$0.405714\pi$
$488$	30.0000			1.35804
$489$	−28.5000	−	16.4545i	−1.28881	−	0.744097i
$490$	−6.00000			−0.271052
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.851314	+	0.524656i	$0.175806\pi$
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.0287085	+	0.999588i	$0.490861\pi$
$492$			10.3923i			0.468521i
$493$	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
$497$	3.00000			0.134568
$498$			13.8564i			0.620920i
$499$	16.5000	−	28.5788i	0.738641	−	1.27936i	−0.214466	−	0.976732i	$-0.568801\pi$
$499$	16.5000	−	28.5788i	0.738641	−	1.27936i	0.953107	−	0.302633i	$-0.0978656\pi$
$500$	−9.00000			−0.402492
$501$		−	41.5692i		−	1.85718i
$502$	12.5000	+	21.6506i	0.557902	+	0.966315i
$503$	−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	$0.216545\pi$
$504$	4.50000	+	7.79423i	0.200446	+	0.347183i
$505$	5.50000	−	9.52628i	0.244747	−	0.423914i
$506$	−15.0000			−0.666831
$507$	−18.0000	+	10.3923i	−0.799408	+	0.461538i
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	0.999220	−	0.0394971i	$-0.0125756\pi$
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	−0.533815	+	0.845601i	$0.679242\pi$
$510$	−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
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	−7.50000	−	4.33013i	−0.330169	−	0.190623i
$517$	17.5000	−	30.3109i	0.769649	−	1.33307i
$518$	5.50000	−	9.52628i	0.241656	−	0.418561i
$519$			24.2487i			1.06440i
$520$	3.00000			0.131559
$521$	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	$0.596281\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$		−	6.92820i		−	0.302372i
$526$	−2.50000	+	4.33013i	−0.109005	+	0.188803i
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$	−7.50000	+	4.33013i	−0.326396	+	0.188445i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−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
$534$			3.46410i			0.149906i
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	−24.0000	+	5.19615i	−1.03664	+	0.224440i
$537$		−	20.7846i		−	0.896922i
$538$	−14.0000			−0.603583
$539$	−30.0000			−1.29219
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	28.0000			1.20270
$543$	−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
$546$			1.73205i			0.0741249i
$547$	3.50000	+	6.06218i	0.149649	+	0.259200i	0.931098	−	0.364770i	$-0.118852\pi$
$547$	3.50000	+	6.06218i	0.149649	+	0.259200i	−0.781449	+	0.623970i	$0.785519\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$	−30.0000			−1.28037
$550$	20.0000			0.852803
$551$	2.50000	−	4.33013i	0.106504	−	0.184470i
$552$	−13.5000	−	7.79423i	−0.574598	−	0.331744i
$553$	−0.500000	+	0.866025i	−0.0212622	+	0.0368271i
$554$	−8.50000	+	14.7224i	−0.361130	+	0.625496i
$555$	16.5000	+	9.52628i	0.700386	+	0.404368i
$556$	0.500000	+	0.866025i	0.0212047	+	0.0367277i
$557$	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
$562$	−6.00000			−0.253095
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	0.895902	−	0.444252i	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$	10.5000	−	6.06218i	0.442130	−	0.255264i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	−1.50000	−	2.59808i	−0.0630497	−	0.109205i
$567$	−4.50000	−	7.79423i	−0.188982	−	0.327327i
$568$	−4.50000	+	7.79423i	−0.188816	+	0.327039i
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	−0.996961	−	0.0779066i	$-0.975176\pi$
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	0.431011	−	0.902347i	$-0.358157\pi$
$570$	−1.50000	−	0.866025i	−0.0628281	−	0.0362738i
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	5.00000			0.209061
$573$		−	41.5692i		−	1.73658i
$574$	−3.00000	−	5.19615i	−0.125218	−	0.216883i
$575$	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
$580$	2.50000	−	4.33013i	0.103807	−	0.179799i
$581$	4.00000	+	6.92820i	0.165948	+	0.287430i
$582$		−	10.3923i		−	0.430775i
$583$	−25.0000	−	43.3013i	−1.03539	−	1.79336i
$584$	−16.5000	−	28.5788i	−0.682775	−	1.18260i
$585$	−3.00000			−0.124035
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	−9.00000	−	5.19615i	−0.371154	−	0.214286i
$589$	−4.00000	−	6.92820i	−0.164817	−	0.285472i
$590$	−4.50000	+	7.79423i	−0.185262	+	0.320883i
$591$	7.50000	+	4.33013i	0.308509	+	0.178118i
$592$	5.50000	+	9.52628i	0.226049	+	0.391528i
$593$	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
$596$	−4.50000	−	7.79423i	−0.184327	−	0.319264i
$597$	37.5000	−	21.6506i	1.53477	−	0.886102i
$598$	−1.50000	−	2.59808i	−0.0613396	−	0.106243i
$599$	−8.00000			−0.326871			−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000			−0.326871			−0.163436	+	0.986554i	$0.552258\pi$
$600$	18.0000	+	10.3923i	0.734847	+	0.424264i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	5.00000			0.203785
$603$	24.0000	−	5.19615i	0.977356	−	0.211604i
$604$		0			0
$605$	−14.0000			−0.569181
$606$	−16.5000	+	9.52628i	−0.670267	+	0.386979i
$607$	8.00000			0.324710			0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000			0.324710			0.162355	+	0.986732i	$0.448091\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$	7.50000	+	4.33013i	0.303915	+	0.175466i
$610$	−5.00000	−	8.66025i	−0.202444	−	0.350643i
$611$	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	$0.775156\pi$
$614$	2.50000	+	4.33013i	0.100892	+	0.174750i
$615$	9.00000	−	5.19615i	0.362915	−	0.209529i
$616$	−7.50000	+	12.9904i	−0.302184	+	0.523397i
$617$	−11.5000	−	19.9186i	−0.462973	−	0.801892i	0.536135	−	0.844132i	$-0.319884\pi$
$617$	−11.5000	−	19.9186i	−0.462973	−	0.801892i	−0.999107	+	0.0422403i	$0.986550\pi$
$618$			6.92820i			0.278693i
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$	4.50000	+	7.79423i	0.180434	+	0.312520i
$623$	1.00000	+	1.73205i	0.0400642	+	0.0693932i
$624$	−1.50000	−	0.866025i	−0.0600481	−	0.0346688i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	5.50000	−	9.52628i	0.219824	−	0.380747i
$627$	−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	$0.839670\pi$
$632$	−1.50000	−	2.59808i	−0.0596668	−	0.103346i
$633$	31.5000	+	18.1865i	1.25201	+	0.722850i
$634$	−18.0000			−0.714871
$635$	5.00000			0.198419
$636$		−	17.3205i		−	0.686803i
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$	−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
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	−0.971442	−	0.237276i	$-0.923745\pi$
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	0.280234	−	0.959932i	$-0.409588\pi$
$642$			6.92820i			0.273434i
$643$	13.5000	+	23.3827i	0.532388	+	0.922123i	0.999285	+	0.0378113i	$0.0120386\pi$
$643$	13.5000	+	23.3827i	0.532388	+	0.922123i	−0.466897	+	0.884312i	$0.654628\pi$
$644$	−3.00000			−0.118217
$645$			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
$650$	2.00000	+	3.46410i	0.0784465	+	0.135873i
$651$	12.0000	−	6.92820i	0.470317	−	0.271538i
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		−	3.46410i		−	0.135457i
$655$	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
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	0.974320	−	0.225168i	$-0.0722932\pi$
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	−0.682161	+	0.731202i	$0.738960\pi$
$660$	−7.50000	−	4.33013i	−0.291937	−	0.168550i
$661$	10.5000	+	18.1865i	0.408403	+	0.707374i	0.994711	−	0.102714i	$-0.0327526\pi$
$661$	10.5000	+	18.1865i	0.408403	+	0.707374i	−0.586308	+	0.810088i	$0.699419\pi$
$662$	−13.5000	−	23.3827i	−0.524692	−	0.908794i
$663$		−	5.19615i		−	0.201802i
$664$	−24.0000			−0.931381
$665$	−1.00000			−0.0387783
$666$	−16.5000	−	28.5788i	−0.639362	−	1.10741i
$667$	−15.0000			−0.580802
$668$	24.0000			0.928588
$669$	1.50000	+	0.866025i	0.0579934	+	0.0334825i
$670$	5.50000	+	6.06218i	0.212484	+	0.234202i
$671$	−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	0.395711	+	0.918375i	$0.370498\pi$
$673$	−15.5000	+	26.8468i	−0.597481	+	1.03487i	−0.993192	+	0.116492i	$0.962835\pi$
$674$	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
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$			31.1769i			1.19734i
$679$	−3.00000	−	5.19615i	−0.115129	−	0.199410i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	−40.5000	+	23.3827i	−1.55196	+	0.896026i
$682$	20.0000	+	34.6410i	0.765840	+	1.32647i
$683$	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
$686$	13.0000			0.496342
$687$	7.50000	+	4.33013i	0.286143	+	0.165205i
$688$	−2.50000	+	4.33013i	−0.0953116	+	0.165085i
$689$	5.00000	−	8.66025i	0.190485	−	0.329929i
$690$			5.19615i			0.197814i
$691$	−22.5000	−	38.9711i	−0.855940	−	1.48253i	−0.875770	−	0.482729i	$-0.839646\pi$
$691$	−22.5000	−	38.9711i	−0.855940	−	1.48253i	0.0198296	−	0.999803i	$-0.493688\pi$
$692$	−14.0000			−0.532200
$693$	7.50000	−	12.9904i	0.284901	−	0.493464i
$694$	−24.0000			−0.911028
$695$	0.500000	−	0.866025i	0.0189661	−	0.0328502i
$696$	−22.5000	+	12.9904i	−0.852860	+	0.492399i
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	7.50000	−	12.9904i	0.283879	−	0.491693i
$699$	25.5000	+	14.7224i	0.964499	+	0.556854i
$700$	4.00000			0.151186
$701$	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
$704$	−17.5000	−	30.3109i	−0.659556	−	1.14238i
$705$	−10.5000	−	6.06218i	−0.395453	−	0.228315i
$706$	18.0000			0.677439
$707$	−5.50000	+	9.52628i	−0.206849	+	0.358273i
$708$	−13.5000	+	7.79423i	−0.507361	+	0.292925i
$709$	50.0000			1.87779			0.938895	−	0.344204i	$-0.111851\pi$
$709$	50.0000			1.87779			0.938895	+	0.344204i	$0.111851\pi$
$710$	3.00000			0.112588
$711$	1.50000	+	2.59808i	0.0562544	+	0.0974355i
$712$	−6.00000			−0.224860
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$	4.50000	+	2.59808i	0.168408	+	0.0972306i
$715$	−2.50000	−	4.33013i	−0.0934947	−	0.161938i
$716$	12.0000			0.448461
$717$			27.7128i			1.03495i
$718$	−16.0000			−0.597115
$719$	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
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$	20.0000			0.742781
$726$	21.0000	+	12.1244i	0.779383	+	0.449977i
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$	−3.00000			−0.111187
$729$	−27.0000			−1.00000
$730$	−5.50000	+	9.52628i	−0.203564	+	0.352583i
$731$	−15.0000			−0.554795
$732$		−	17.3205i		−	0.640184i
$733$	30.0000			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$734$	12.5000	+	21.6506i	0.461383	+	0.799140i
$735$			10.3923i			0.383326i
$736$	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
$741$		−	1.73205i		−	0.0636285i
$742$	5.00000	+	8.66025i	0.183556	+	0.317928i
$743$	10.5000	−	18.1865i	0.385208	−	0.667199i	−0.606590	−	0.795015i	$-0.707463\pi$
$743$	10.5000	−	18.1865i	0.385208	−	0.667199i	0.991798	+	0.127815i	$0.0407965\pi$
$744$			41.5692i			1.52400i
$745$	−4.50000	+	7.79423i	−0.164867	+	0.285558i
$746$	6.00000			0.219676
$747$	24.0000			0.878114
$748$	7.50000	−	12.9904i	0.274227	−	0.474975i
$749$	2.00000	+	3.46410i	0.0730784	+	0.126576i
$750$		−	15.5885i		−	0.569210i
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	−3.50000	−	6.06218i	−0.127632	−	0.221065i
$753$	37.5000	−	21.6506i	1.36658	−	0.788993i
$754$	−5.00000			−0.182089
$755$		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	$-0.0100208\pi$
$758$	−7.50000	−	12.9904i	−0.272412	−	0.471832i
$759$			25.9808i			0.943042i
$760$	1.50000	−	2.59808i	0.0544107	−	0.0942421i
$761$	−5.50000	−	9.52628i	−0.199375	−	0.345327i	0.748951	−	0.662625i	$-0.230558\pi$
$761$	−5.50000	−	9.52628i	−0.199375	−	0.345327i	−0.948326	+	0.317298i	$0.897224\pi$
$762$	−7.50000	−	4.33013i	−0.271696	−	0.156864i
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$	24.0000			0.868290
$765$	−4.50000	+	7.79423i	−0.162698	+	0.281801i
$766$	11.5000	−	19.9186i	0.415512	−	0.719688i
$767$	−9.00000			−0.324971
$768$		−	29.4449i		−	1.06250i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$	5.00000			0.180187
$771$			24.2487i			0.873296i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	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	$0.0433959\pi$
$774$	7.50000	−	12.9904i	0.269582	−	0.466930i
$775$	16.0000	−	27.7128i	0.574737	−	0.995474i
$776$	18.0000			0.646162
$777$	−16.5000	−	9.52628i	−0.591934	−	0.341753i
$778$	22.0000			0.788738
$779$	3.00000	+	5.19615i	0.107486	+	0.186171i
$780$		−	1.73205i		−	0.0620174i
$781$	15.0000			0.536742
$782$	−9.00000			−0.321839
$783$	22.5000	−	12.9904i	0.804084	−	0.464238i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$	−3.00000			−0.107075
$786$	−13.5000	+	7.79423i	−0.481529	+	0.278011i
$787$	2.50000	−	4.33013i	0.0891154	−	0.154352i	−0.818022	−	0.575187i	$-0.804929\pi$
$787$	2.50000	−	4.33013i	0.0891154	−	0.154352i	0.907137	+	0.420834i	$0.138263\pi$
$788$	−2.50000	+	4.33013i	−0.0890588	+	0.154254i
$789$	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
$792$	22.5000	+	38.9711i	0.799503	+	1.38478i
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$	22.0000			0.780751
$795$	−15.0000	+	8.66025i	−0.531995	+	0.307148i
$796$	12.5000	+	21.6506i	0.443051	+	0.767386i
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$	1.50000	+	0.866025i	0.0530994	+	0.0306570i
$799$	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
$804$	3.00000	+	13.8564i	0.105802	+	0.488678i
$805$	1.50000	+	2.59808i	0.0528681	+	0.0915702i
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$			24.2487i			0.853595i
$808$	−16.5000	−	28.5788i	−0.580468	−	1.00540i
$809$	−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
$814$	27.5000	−	47.6314i	0.963875	−	1.66948i
$815$	−19.0000			−0.665541
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	−5.00000			−0.174928
$818$	−14.0000			−0.489499
$819$	3.00000			0.104828
$820$	3.00000	+	5.19615i	0.104765	+	0.181458i
$821$	2.00000			0.0698005			0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000			0.0698005			0.0349002	+	0.999391i	$0.488889\pi$
$822$	−13.5000	−	7.79423i	−0.470867	−	0.271855i
$823$	−1.50000	+	2.59808i	−0.0522867	+	0.0905632i	−0.890984	−	0.454034i	$-0.849984\pi$
$823$	−1.50000	+	2.59808i	−0.0522867	+	0.0905632i	0.838697	+	0.544598i	$0.183318\pi$
$824$	−12.0000			−0.418040
$825$		−	34.6410i		−	1.20605i
$826$	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	$0.350886\pi$
$830$	4.00000	+	6.92820i	0.138842	+	0.240481i
$831$	25.5000	+	14.7224i	0.884585	+	0.510716i
$832$	3.50000	−	6.06218i	0.121341	−	0.210168i
$833$	−18.0000			−0.623663
$834$	−1.50000	+	0.866025i	−0.0519408	+	0.0299880i
$835$	−12.0000	−	20.7846i	−0.415277	−	0.719281i
$836$	2.50000	−	4.33013i	0.0864643	−	0.149761i
$837$		−	41.5692i		−	1.43684i
$838$	1.50000	−	2.59808i	0.0518166	−	0.0897491i
$839$	11.5000	+	19.9186i	0.397024	+	0.687666i	0.993357	−	0.115071i	$-0.0367096\pi$
$839$	11.5000	+	19.9186i	0.397024	+	0.687666i	−0.596333	+	0.802737i	$0.703376\pi$
$840$	4.50000	+	2.59808i	0.155265	+	0.0896421i
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	6.00000			0.206774
$843$			10.3923i			0.357930i
$844$	−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
$848$	−10.0000			−0.343401
$849$	−4.50000	+	2.59808i	−0.154440	+	0.0891657i
$850$	12.0000			0.411597
$851$	33.0000			1.13123
$852$	4.50000	+	2.59808i	0.154167	+	0.0890086i
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$	5.00000	+	8.66025i	0.171096	+	0.296348i
$855$	−1.50000	+	2.59808i	−0.0512989	+	0.0888523i
$856$	−12.0000			−0.410152
$857$	28.5000	−	49.3634i	0.973541	−	1.68622i	0.288875	−	0.957367i	$-0.406719\pi$
$857$	28.5000	−	49.3634i	0.973541	−	1.68622i	0.684667	−	0.728856i	$-0.259948\pi$
$858$			8.66025i			0.295656i
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−5.00000			−0.170499
$861$	−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	$0.902160\pi$
$864$			25.9808i			0.883883i
$865$	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
$869$	−2.50000	+	4.33013i	−0.0848067	+	0.146889i
$870$	7.50000	+	4.33013i	0.254274	+	0.146805i
$871$	−2.50000	+	7.79423i	−0.0847093	+	0.264097i
$872$	6.00000			0.203186
$873$	−18.0000			−0.609208
$874$	−3.00000			−0.101477
$875$	−4.50000	−	7.79423i	−0.152128	−	0.263493i
$876$	−16.5000	+	9.52628i	−0.557483	+	0.321863i
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	0.130224	+	0.991485i	$0.458430\pi$
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	−0.923763	+	0.382965i	$0.874903\pi$
$878$	−20.0000			−0.674967
$879$	−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	$-0.0756700\pi$
$884$	3.00000			0.100901
$885$	13.5000	+	7.79423i	0.453798	+	0.262000i
$886$	−9.50000	−	16.4545i	−0.319159	−	0.552799i
$887$	6.50000	−	11.2583i	0.218249	−	0.378018i	−0.736024	−	0.676955i	$-0.763299\pi$
$887$	6.50000	−	11.2583i	0.218249	−	0.378018i	0.954273	+	0.298938i	$0.0966323\pi$
$888$	49.5000	−	28.5788i	1.66111	−	0.959043i
$889$	−5.00000			−0.167695
$890$	1.00000	+	1.73205i	0.0335201	+	0.0580585i
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$	−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
$897$	−4.50000	+	2.59808i	−0.150251	+	0.0867472i
$898$	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
$902$	−15.0000	−	25.9808i	−0.499445	−	0.865065i
$903$		−	8.66025i		−	0.288195i
$904$	−54.0000			−1.79601
$905$	−7.00000			−0.232688
$906$		0			0
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	0.999855	+	0.0170220i	$0.00541854\pi$
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	−0.485186	+	0.874411i	$0.661248\pi$
$908$	−13.5000	−	23.3827i	−0.448013	−	0.775982i
$909$	16.5000	+	28.5788i	0.547270	+	0.947900i
$910$	0.500000	+	0.866025i	0.0165748	+	0.0287085i
$911$	16.5000	−	28.5788i	0.546669	−	0.946859i	−0.451830	−	0.892104i	$-0.649229\pi$
$911$	16.5000	−	28.5788i	0.546669	−	0.946859i	0.998500	−	0.0547553i	$-0.0174379\pi$
$912$	−1.50000	+	0.866025i	−0.0496700	+	0.0286770i
$913$	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
$918$	13.5000	−	7.79423i	0.445566	−	0.257248i
$919$	−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	$-0.432887\pi$
$920$	−9.00000			−0.296721
$921$	7.50000	−	4.33013i	0.247133	−	0.142683i
$922$	−2.50000	+	4.33013i	−0.0823331	+	0.142605i
$923$	1.50000	+	2.59808i	0.0493731	+	0.0855167i
$924$	7.50000	+	4.33013i	0.246732	+	0.142451i
$925$	−44.0000			−1.44671
$926$	15.5000	−	26.8468i	0.509362	−	0.882240i
$927$	12.0000			0.394132
$928$	−12.5000	−	21.6506i	−0.410333	−	0.710717i
$929$	0.500000	−	0.866025i	0.0164045	−	0.0284134i	−0.857707	−	0.514139i	$-0.828111\pi$
$929$	0.500000	−	0.866025i	0.0164045	−	0.0284134i	0.874111	+	0.485726i	$0.161445\pi$
$930$	12.0000	−	6.92820i	0.393496	−	0.227185i
$931$	−6.00000			−0.196642
$932$	−8.50000	+	14.7224i	−0.278427	+	0.482249i
$933$	13.5000	−	7.79423i	0.441970	−	0.255172i
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$	−15.0000			−0.490552
$936$	−4.50000	+	7.79423i	−0.147087	+	0.254762i
$937$	54.0000			1.76410			0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000			1.76410			0.882052	+	0.471153i	$0.156162\pi$
$938$	−5.50000	−	6.06218i	−0.179581	−	0.197937i
$939$	−16.5000	−	9.52628i	−0.538457	−	0.310878i
$940$	3.50000	−	6.06218i	0.114157	−	0.197726i
$941$	0.500000	+	0.866025i	0.0162995	+	0.0282316i	0.874060	−	0.485818i	$-0.161478\pi$
$941$	0.500000	+	0.866025i	0.0162995	+	0.0282316i	−0.857761	+	0.514049i	$0.828145\pi$
$942$	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	0.353131	+	0.935574i	$0.385117\pi$
$947$	−19.5000	+	33.7750i	−0.633665	+	1.09754i	−0.986796	+	0.161966i	$0.948217\pi$
$948$	−1.50000	+	0.866025i	−0.0487177	+	0.0281272i
$949$	−11.0000			−0.357075
$950$	4.00000			0.129777
$951$			31.1769i			1.01098i
$952$	−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	$0.685633\pi$
$954$	30.0000			0.971286
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−16.0000			−0.517477
$957$	37.5000	+	21.6506i	1.21220	+	0.699866i
$958$	−4.00000			−0.129234
$959$	−9.00000			−0.290625
$960$	−10.5000	+	6.06218i	−0.338886	+	0.195656i
$961$	33.0000			1.06452
$962$	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
$966$		−	5.19615i		−	0.167183i
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$	−21.0000	+	36.3731i	−0.674966	+	1.16907i
$969$	−4.50000	−	2.59808i	−0.144561	−	0.0834622i
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	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	$0.120538\pi$
$972$		−	15.5885i		−	0.500000i
$973$	−0.500000	+	0.866025i	−0.0160293	+	0.0277635i
$974$	−21.5000	−	37.2391i	−0.688904	−	1.19322i
$975$	6.00000	−	3.46410i	0.192154	−	0.110940i
$976$	−10.0000			−0.320092
$977$	6.50000	−	11.2583i	0.207953	−	0.360186i	−0.743116	−	0.669162i	$-0.766653\pi$
$977$	6.50000	−	11.2583i	0.207953	−	0.360186i	0.951070	+	0.308976i	$0.0999864\pi$
$978$	28.5000	+	16.4545i	0.911330	+	0.526156i
$979$	5.00000	+	8.66025i	0.159801	+	0.276783i
$980$	−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	0.287459	+	0.957793i	$0.407189\pi$
$983$	−21.5000	+	37.2391i	−0.685744	+	1.18774i	−0.973203	+	0.229950i	$0.926144\pi$
$984$		−	31.1769i		−	0.993884i
$985$	5.00000			0.159313
$986$	−7.50000	+	12.9904i	−0.238849	+	0.413698i
$987$	10.5000	+	6.06218i	0.334219	+	0.192961i
$988$	1.00000			0.0318142
$989$	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	$0.459445\pi$
$992$	−40.0000			−1.27000
$993$	−40.5000	+	23.3827i	−1.28523	+	0.742027i
$994$	−3.00000			−0.0951542
$995$	12.5000	−	21.6506i	0.396277	−	0.686371i
$996$			13.8564i			0.439057i
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	−0.888800	−	0.458295i	$-0.848460\pi$
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	0.841295	+	0.540576i	$0.181794\pi$
$998$	−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.h.b.439.1	yes	2
9.4	even	3		603.2.f.b.238.1	✓	2
67.29	even	3		603.2.f.b.565.1	yes	2
603.364	even	3	inner	603.2.h.b.364.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.f.b.238.1	✓	2	9.4	even	3
603.2.f.b.565.1	yes	2	67.29	even	3
603.2.h.b.364.1	yes	2	603.364	even	3	inner
603.2.h.b.439.1	yes	2	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} -3.00000 q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} -1.73205i q^{12} +(0.500000 - 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.50000 + 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +3.00000 q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.50000 - 0.866025i) q^{21} +(2.50000 + 4.33013i) q^{22} +(-1.50000 + 2.59808i) 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} +(2.50000 + 4.33013i) q^{29} +(1.50000 - 0.866025i) q^{30} +8.00000 q^{31} -5.00000 q^{32} +(7.50000 - 4.33013i) q^{33} +(1.50000 + 2.59808i) q^{34} +(0.500000 - 0.866025i) q^{35} +3.00000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(0.500000 + 0.866025i) q^{38} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{40} -6.00000 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} +(3.50000 + 6.06218i) q^{47} -1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(4.50000 - 2.59808i) q^{51} +(-0.500000 + 0.866025i) q^{52} +10.0000 q^{53} +5.19615i q^{54} +(2.50000 - 4.33013i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(1.50000 - 0.866025i) q^{57} +(-2.50000 - 4.33013i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(1.50000 - 0.866025i) q^{60} +10.0000 q^{61} -8.00000 q^{62} +(1.50000 + 2.59808i) q^{63} +7.00000 q^{64} +1.00000 q^{65} +(-7.50000 + 4.33013i) q^{66} +(-8.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.50000 - 2.59808i) q^{69} +(-0.500000 + 0.866025i) q^{70} +(-1.50000 + 2.59808i) q^{71} -9.00000 q^{72} +(-5.50000 - 9.52628i) q^{73} +(5.50000 + 9.52628i) q^{74} +(6.00000 + 3.46410i) q^{75} +(0.500000 + 0.866025i) q^{76} +(-2.50000 + 4.33013i) q^{77} +(-1.50000 - 0.866025i) q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +6.00000 q^{82} -8.00000 q^{83} +(-1.50000 + 0.866025i) q^{84} +(1.50000 - 2.59808i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(-7.50000 + 4.33013i) q^{87} +(-7.50000 - 12.9904i) q^{88} -2.00000 q^{89} +(1.50000 + 2.59808i) q^{90} -1.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +13.8564i q^{93} +(-3.50000 - 6.06218i) q^{94} +(0.500000 - 0.866025i) q^{95} -8.66025i q^{96} +6.00000 q^{97} +(-3.00000 + 5.19615i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 + 6 * q^8 - 6 * q^9	\( 2 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} + 6 q^{8} - 6 q^{9} - q^{10} - 5 q^{11} + q^{13} + q^{14} - 3 q^{15} - 2 q^{16} - 3 q^{17} + 6 q^{18} - q^{19} - q^{20} + 3 q^{21} + 5 q^{22} - 3 q^{23} + 4 q^{25} - q^{26} + q^{28} + 5 q^{29} + 3 q^{30} + 16 q^{31} - 10 q^{32} + 15 q^{33} + 3 q^{34} + q^{35} + 6 q^{36} - 11 q^{37} + q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{41} - 3 q^{42} + 5 q^{43} + 5 q^{44} - 3 q^{45} + 3 q^{46} + 7 q^{47} + 6 q^{49} - 4 q^{50} + 9 q^{51} - q^{52} + 20 q^{53} + 5 q^{55} - 3 q^{56} + 3 q^{57} - 5 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} - 16 q^{62} + 3 q^{63} + 14 q^{64} + 2 q^{65} - 15 q^{66} - 16 q^{67} + 3 q^{68} - 9 q^{69} - q^{70} - 3 q^{71} - 18 q^{72} - 11 q^{73} + 11 q^{74} + 12 q^{75} + q^{76} - 5 q^{77} - 3 q^{78} - q^{79} - q^{80} + 18 q^{81} + 12 q^{82} - 16 q^{83} - 3 q^{84} + 3 q^{85} - 5 q^{86} - 15 q^{87} - 15 q^{88} - 4 q^{89} + 3 q^{90} - 2 q^{91} + 3 q^{92} - 7 q^{94} + q^{95} + 12 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 + 6 * q^8 - 6 * q^9 - q^10 - 5 * q^11 + q^13 + q^14 - 3 * q^15 - 2 * q^16 - 3 * q^17 + 6 * q^18 - q^19 - q^20 + 3 * q^21 + 5 * q^22 - 3 * q^23 + 4 * q^25 - q^26 + q^28 + 5 * q^29 + 3 * q^30 + 16 * q^31 - 10 * q^32 + 15 * q^33 + 3 * q^34 + q^35 + 6 * q^36 - 11 * q^37 + q^38 + 3 * q^39 + 3 * q^40 - 12 * q^41 - 3 * q^42 + 5 * q^43 + 5 * q^44 - 3 * q^45 + 3 * q^46 + 7 * q^47 + 6 * q^49 - 4 * q^50 + 9 * q^51 - q^52 + 20 * q^53 + 5 * q^55 - 3 * q^56 + 3 * q^57 - 5 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 - 16 * q^62 + 3 * q^63 + 14 * q^64 + 2 * q^65 - 15 * q^66 - 16 * q^67 + 3 * q^68 - 9 * q^69 - q^70 - 3 * q^71 - 18 * q^72 - 11 * q^73 + 11 * q^74 + 12 * q^75 + q^76 - 5 * q^77 - 3 * q^78 - q^79 - q^80 + 18 * q^81 + 12 * q^82 - 16 * q^83 - 3 * q^84 + 3 * q^85 - 5 * q^86 - 15 * q^87 - 15 * q^88 - 4 * q^89 + 3 * q^90 - 2 * q^91 + 3 * q^92 - 7 * q^94 + q^95 + 12 * q^97 - 6 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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