LMFDB - Embedded newform 858.2.i.c.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [858,2,Mod(133,858)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(858, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("858.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 858 = 2 \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	858.i (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:	$6.85116449343$
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			529.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	858.529
Dual form			858.2.i.c.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +1.00000 q^{14} +(1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +1.00000 q^{18} +(3.00000 + 5.19615i) q^{19} +(-1.50000 - 2.59808i) q^{20} -1.00000 q^{21} +(0.500000 + 0.866025i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +(1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-5.00000 + 8.66025i) q^{29} +(1.50000 + 2.59808i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +7.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.00000 - 5.19615i) q^{37} -6.00000 q^{38} +(-1.00000 - 3.46410i) q^{39} +3.00000 q^{40} +(-0.500000 + 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-5.00000 - 8.66025i) q^{43} -1.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +(2.00000 + 3.46410i) q^{46} -3.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.00000 + 3.46410i) q^{50} -7.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} +11.0000 q^{53} +(0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-0.500000 - 0.866025i) q^{56} +6.00000 q^{57} +(-5.00000 - 8.66025i) q^{58} +(4.00000 + 6.92820i) q^{59} -3.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(7.50000 - 7.79423i) q^{65} +1.00000 q^{66} +(-6.00000 + 10.3923i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-2.00000 - 3.46410i) q^{69} +3.00000 q^{70} +(4.00000 + 6.92820i) q^{71} +(-0.500000 - 0.866025i) q^{72} +16.0000 q^{73} +(3.00000 + 5.19615i) q^{74} +(2.00000 - 3.46410i) q^{75} +(3.00000 - 5.19615i) q^{76} -1.00000 q^{77} +(3.50000 + 0.866025i) q^{78} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} -7.00000 q^{83} +(0.500000 + 0.866025i) q^{84} +(-10.5000 - 18.1865i) q^{85} +10.0000 q^{86} +(5.00000 + 8.66025i) q^{87} +(0.500000 - 0.866025i) q^{88} +(6.00000 - 10.3923i) q^{89} +3.00000 q^{90} +(-3.50000 - 0.866025i) q^{91} -4.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(9.00000 + 15.5885i) q^{95} -1.00000 q^{96} +(-4.50000 - 7.79423i) q^{97} +(3.00000 + 5.19615i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 - q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{10} + q^{11} - 2 q^{12} + 5 q^{13} + 2 q^{14} + 3 q^{15} - q^{16} - 7 q^{17} + 2 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 4 q^{23} + q^{24} + 8 q^{25} + 2 q^{26} - 2 q^{27} - q^{28} - 10 q^{29} + 3 q^{30} - q^{32} - q^{33} + 14 q^{34} - 3 q^{35} - q^{36} + 6 q^{37} - 12 q^{38} - 2 q^{39} + 6 q^{40} - q^{41} + q^{42} - 10 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 6 q^{47} + q^{48} + 6 q^{49} - 4 q^{50} - 14 q^{51} - 7 q^{52} + 22 q^{53} + q^{54} + 3 q^{55} - q^{56} + 12 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} - 2 q^{61} - q^{63} + 2 q^{64} + 15 q^{65} + 2 q^{66} - 12 q^{67} - 7 q^{68} - 4 q^{69} + 6 q^{70} + 8 q^{71} - q^{72} + 32 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} - 2 q^{77} + 7 q^{78} - 3 q^{80} - q^{81} - q^{82} - 14 q^{83} + q^{84} - 21 q^{85} + 20 q^{86} + 10 q^{87} + q^{88} + 12 q^{89} + 6 q^{90} - 7 q^{91} - 8 q^{92} + 3 q^{94} + 18 q^{95} - 2 q^{96} - 9 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^10 + q^11 - 2 * q^12 + 5 * q^13 + 2 * q^14 + 3 * q^15 - q^16 - 7 * q^17 + 2 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 4 * q^23 + q^24 + 8 * q^25 + 2 * q^26 - 2 * q^27 - q^28 - 10 * q^29 + 3 * q^30 - q^32 - q^33 + 14 * q^34 - 3 * q^35 - q^36 + 6 * q^37 - 12 * q^38 - 2 * q^39 + 6 * q^40 - q^41 + q^42 - 10 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 6 * q^47 + q^48 + 6 * q^49 - 4 * q^50 - 14 * q^51 - 7 * q^52 + 22 * q^53 + q^54 + 3 * q^55 - q^56 + 12 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 - 2 * q^61 - q^63 + 2 * q^64 + 15 * q^65 + 2 * q^66 - 12 * q^67 - 7 * q^68 - 4 * q^69 + 6 * q^70 + 8 * q^71 - q^72 + 32 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 - 2 * q^77 + 7 * q^78 - 3 * q^80 - q^81 - q^82 - 14 * q^83 + q^84 - 21 * q^85 + 20 * q^86 + 10 * q^87 + q^88 + 12 * q^89 + 6 * q^90 - 7 * q^91 - 8 * q^92 + 3 * q^94 + 18 * q^95 - 2 * q^96 - 9 * q^97 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/858\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−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	$0.893852\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.00000			−0.288675
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$	1.00000			0.267261
$15$	1.50000	−	2.59808i	0.387298	−	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$	1.00000			0.235702
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$	−1.00000			−0.218218
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.00000			0.800000
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$	−1.00000			−0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.142605	+	0.989780i	$0.545548\pi$
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.785872	+	0.618389i	$0.787786\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	7.00000			1.20049
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	−6.00000			−0.973329
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$	3.00000			0.474342
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	−0.902424	−	0.430848i	$-0.858214\pi$
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	0.824338	+	0.566099i	$0.191548\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$	−1.00000			−0.150756
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	−7.00000			−0.980196
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	11.0000			1.51097			0.755483	−	0.655168i	$-0.227402\pi$
$53$	11.0000			1.51097			0.755483	+	0.655168i	$0.227402\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	6.00000			0.794719
$58$	−5.00000	−	8.66025i	−0.656532	−	1.13715i
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$	−3.00000			−0.387298
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	7.50000	−	7.79423i	0.930261	−	0.966755i
$66$	1.00000			0.123091
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	−3.50000	+	6.06218i	−0.424437	+	0.735147i
$69$	−2.00000	−	3.46410i	−0.240772	−	0.417029i
$70$	3.00000			0.358569
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	0.999581	−	0.0289572i	$-0.00921865\pi$
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	−0.524868	+	0.851184i	$0.675885\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	16.0000			1.87266			0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000			1.87266			0.936329	+	0.351123i	$0.114200\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$	3.00000	−	5.19615i	0.344124	−	0.596040i
$77$	−1.00000			−0.113961
$78$	3.50000	+	0.866025i	0.396297	+	0.0980581i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.500000	−	0.866025i	−0.0552158	−	0.0956365i
$83$	−7.00000			−0.768350			−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000			−0.768350			−0.384175	+	0.923260i	$0.625514\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−10.5000	−	18.1865i	−1.13888	−	1.97261i
$86$	10.0000			1.07833
$87$	5.00000	+	8.66025i	0.536056	+	0.928477i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$	3.00000			0.316228
$91$	−3.50000	−	0.866025i	−0.366900	−	0.0907841i
$92$	−4.00000			−0.417029
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	9.00000	+	15.5885i	0.923381	+	1.59934i
$96$	−1.00000			−0.102062
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	0.541890	−	0.840450i	$-0.317709\pi$
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	−0.998796	+	0.0490655i	$0.984376\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	−1.00000			−0.100504
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$	3.50000	−	6.06218i	0.346552	−	0.600245i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$	−3.00000			−0.292770
$106$	−5.50000	+	9.52628i	−0.534207	+	0.925274i
$107$	−4.50000	+	7.79423i	−0.435031	+	0.753497i	−0.997298	−	0.0734594i	$-0.976596\pi$
$107$	−4.50000	+	7.79423i	−0.435031	+	0.753497i	0.562267	+	0.826956i	$0.309929\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	−3.00000	−	5.19615i	−0.284747	−	0.493197i
$112$	1.00000			0.0944911
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$	6.00000	−	10.3923i	0.559503	−	0.969087i
$116$	10.0000			0.928477
$117$	−3.50000	−	0.866025i	−0.323575	−	0.0800641i
$118$	−8.00000			−0.736460
$119$	−3.50000	+	6.06218i	−0.320844	+	0.555719i
$120$	1.50000	−	2.59808i	0.136931	−	0.237171i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.00000			0.181071
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$		0			0
$125$	−3.00000			−0.268328
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−2.50000	+	4.33013i	−0.221839	+	0.384237i	−0.955366	−	0.295423i	$-0.904539\pi$
$127$	−2.50000	+	4.33013i	−0.221839	+	0.384237i	0.733527	+	0.679660i	$0.237873\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−10.0000			−0.880451
$130$	3.00000	+	10.3923i	0.263117	+	0.911465i
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$	−0.500000	+	0.866025i	−0.0435194	+	0.0753778i
$133$	3.00000	−	5.19615i	0.260133	−	0.450564i
$134$	−6.00000	−	10.3923i	−0.518321	−	0.897758i
$135$	−3.00000			−0.258199
$136$	−3.50000	−	6.06218i	−0.300123	−	0.519827i
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$	4.00000			0.340503
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$	−1.50000	+	2.59808i	−0.126773	+	0.219578i
$141$	−1.50000	+	2.59808i	−0.126323	+	0.218797i
$142$	−8.00000			−0.671345
$143$	−1.00000	−	3.46410i	−0.0836242	−	0.289683i
$144$	1.00000			0.0833333
$145$	−15.0000	+	25.9808i	−1.24568	+	2.15758i
$146$	−8.00000	+	13.8564i	−0.662085	+	1.14676i
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$	−6.00000			−0.493197
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−7.00000			−0.569652			−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000			−0.569652			−0.284826	+	0.958579i	$0.591936\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	−3.50000	+	6.06218i	−0.282958	+	0.490098i
$154$	0.500000	−	0.866025i	0.0402911	−	0.0697863i
$155$		0			0
$156$	−2.50000	+	2.59808i	−0.200160	+	0.208013i
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$		0			0
$159$	5.50000	−	9.52628i	0.436178	−	0.755483i
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$	−4.00000			−0.315244
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	1.00000			0.0780869
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	3.50000	−	6.06218i	0.271653	−	0.470516i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$	−1.00000			−0.0771517
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	21.0000			1.61063
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	10.0000	+	17.3205i	0.760286	+	1.31685i	0.942703	+	0.333633i	$0.108275\pi$
$173$	10.0000	+	17.3205i	0.760286	+	1.31685i	−0.182417	+	0.983221i	$0.558392\pi$
$174$	−10.0000			−0.758098
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	8.00000			0.601317
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	−9.00000	+	15.5885i	−0.672692	+	1.16514i	0.304446	+	0.952529i	$0.401529\pi$
$179$	−9.00000	+	15.5885i	−0.672692	+	1.16514i	−0.977138	+	0.212607i	$0.931805\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$	2.50000	−	2.59808i	0.185312	−	0.192582i
$183$	−2.00000			−0.147844
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	9.00000	−	15.5885i	0.661693	−	1.14609i
$186$		0			0
$187$	−7.00000			−0.511891
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−18.0000			−1.30586
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−8.00000	+	13.8564i	−0.575853	+	0.997406i	0.420096	+	0.907480i	$0.361996\pi$
$193$	−8.00000	+	13.8564i	−0.575853	+	0.997406i	−0.995948	+	0.0899262i	$0.971337\pi$
$194$	9.00000			0.646162
$195$	−3.00000	−	10.3923i	−0.214834	−	0.744208i
$196$	−6.00000			−0.428571
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	4.00000			0.282843
$201$	6.00000	+	10.3923i	0.423207	+	0.733017i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	10.0000			0.701862
$204$	3.50000	+	6.06218i	0.245049	+	0.424437i
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$	−4.00000			−0.278019
$208$	1.00000	+	3.46410i	0.0693375	+	0.240192i
$209$	6.00000			0.415029
$210$	1.50000	−	2.59808i	0.103510	−	0.179284i
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	−0.640996	−	0.767544i	$-0.721479\pi$
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	0.985211	+	0.171347i	$0.0548120\pi$
$212$	−5.50000	−	9.52628i	−0.377742	−	0.654268i
$213$	8.00000			0.548151
$214$	−4.50000	−	7.79423i	−0.307614	−	0.532803i
$215$	−15.0000	−	25.9808i	−1.02299	−	1.77187i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−8.50000	+	14.7224i	−0.575693	+	0.997129i
$219$	8.00000	−	13.8564i	0.540590	−	0.936329i
$220$	−3.00000			−0.202260
$221$	−24.5000	−	6.06218i	−1.64805	−	0.407786i
$222$	6.00000			0.402694
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$	−6.00000			−0.399114
$227$	−8.50000	−	14.7224i	−0.564165	−	0.977162i	−0.997127	−	0.0757500i	$-0.975865\pi$
$227$	−8.50000	−	14.7224i	−0.564165	−	0.977162i	0.432962	−	0.901412i	$-0.357468\pi$
$228$	−3.00000	−	5.19615i	−0.198680	−	0.344124i
$229$	−24.0000			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$230$	6.00000	+	10.3923i	0.395628	+	0.685248i
$231$	−0.500000	+	0.866025i	−0.0328976	+	0.0569803i
$232$	−5.00000	+	8.66025i	−0.328266	+	0.568574i
$233$	−17.0000			−1.11371			−0.556854	−	0.830611i	$-0.687992\pi$
$233$	−17.0000			−1.11371			−0.556854	+	0.830611i	$0.687992\pi$
$234$	2.50000	−	2.59808i	0.163430	−	0.169842i
$235$	−9.00000			−0.587095
$236$	4.00000	−	6.92820i	0.260378	−	0.450988i
$237$		0			0
$238$	−3.50000	−	6.06218i	−0.226871	−	0.392953i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	1.50000	+	2.59808i	0.0968246	+	0.167705i
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$	1.00000			0.0642824
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$	−1.00000			−0.0637577
$247$	21.0000	+	5.19615i	1.33620	+	0.330623i
$248$		0			0
$249$	−3.50000	+	6.06218i	−0.221803	+	0.384175i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	1.00000			0.0629941
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$	−21.0000			−1.31507
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	−0.833150	−	0.553047i	$-0.813465\pi$
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	0.895528	+	0.445005i	$0.146798\pi$
$258$	5.00000	−	8.66025i	0.311286	−	0.539164i
$259$	−6.00000			−0.372822
$260$	−10.5000	−	2.59808i	−0.651182	−	0.161126i
$261$	10.0000			0.618984
$262$	10.0000	−	17.3205i	0.617802	−	1.07006i
$263$	−14.0000	+	24.2487i	−0.863277	+	1.49524i	0.00547092	+	0.999985i	$0.498259\pi$
$263$	−14.0000	+	24.2487i	−0.863277	+	1.49524i	−0.868748	+	0.495255i	$0.835075\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	33.0000			2.02717
$266$	3.00000	+	5.19615i	0.183942	+	0.318597i
$267$	−6.00000	−	10.3923i	−0.367194	−	0.635999i
$268$	12.0000			0.733017
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$	1.50000	−	2.59808i	0.0912871	−	0.158114i
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	7.00000			0.424437
$273$	−2.50000	+	2.59808i	−0.151307	+	0.157243i
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	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	$0.662714\pi$
$278$	−8.00000			−0.479808
$279$		0			0
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	0.464169	+	0.885747i	$0.346353\pi$
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	−0.999164	+	0.0408910i	$0.986980\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$	18.0000			1.06623
$286$	3.50000	+	0.866025i	0.206959	+	0.0512092i
$287$	1.00000			0.0590281
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$	−15.0000	−	25.9808i	−0.880830	−	1.52564i
$291$	−9.00000			−0.527589
$292$	−8.00000	−	13.8564i	−0.468165	−	0.810885i
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$	6.00000			0.349927
$295$	12.0000	+	20.7846i	0.698667	+	1.21013i
$296$	3.00000	−	5.19615i	0.174371	−	0.302020i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	14.0000			0.810998
$299$	−4.00000	−	13.8564i	−0.231326	−	0.801337i
$300$	−4.00000			−0.230940
$301$	−5.00000	+	8.66025i	−0.288195	+	0.499169i
$302$	3.50000	−	6.06218i	0.201402	−	0.348839i
$303$	9.00000	+	15.5885i	0.517036	+	0.895533i
$304$	−6.00000			−0.344124
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	−3.50000	−	6.06218i	−0.200082	−	0.346552i
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	0.500000	+	0.866025i	0.0284901	+	0.0493464i
$309$	7.00000	−	12.1244i	0.398216	−	0.689730i
$310$		0			0
$311$	17.0000			0.963982			0.481991	−	0.876176i	$-0.339914\pi$
$311$	17.0000			0.963982			0.481991	+	0.876176i	$0.339914\pi$
$312$	−1.00000	−	3.46410i	−0.0566139	−	0.196116i
$313$	−7.00000			−0.395663			−0.197832	−	0.980236i	$-0.563390\pi$
$313$	−7.00000			−0.395663			−0.197832	+	0.980236i	$0.563390\pi$
$314$	−4.00000	+	6.92820i	−0.225733	+	0.390981i
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$		0			0
$317$	−23.0000			−1.29181			−0.645904	−	0.763418i	$-0.723520\pi$
$317$	−23.0000			−1.29181			−0.645904	+	0.763418i	$0.723520\pi$
$318$	5.50000	+	9.52628i	0.308425	+	0.534207i
$319$	5.00000	+	8.66025i	0.279946	+	0.484881i
$320$	3.00000			0.167705
$321$	4.50000	+	7.79423i	0.251166	+	0.435031i
$322$	2.00000	−	3.46410i	0.111456	−	0.193047i
$323$	21.0000	−	36.3731i	1.16847	−	2.02385i
$324$	1.00000			0.0555556
$325$	10.0000	−	10.3923i	0.554700	−	0.576461i
$326$	−8.00000			−0.443079
$327$	8.50000	−	14.7224i	0.470051	−	0.814152i
$328$	−0.500000	+	0.866025i	−0.0276079	+	0.0478183i
$329$	1.50000	+	2.59808i	0.0826977	+	0.143237i
$330$	3.00000			0.165145
$331$	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	$0.567198\pi$
$332$	3.50000	+	6.06218i	0.192087	+	0.332705i
$333$	−6.00000			−0.328798
$334$	−9.00000	−	15.5885i	−0.492458	−	0.852962i
$335$	−18.0000	+	31.1769i	−0.983445	+	1.70338i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	6.00000			0.325875
$340$	−10.5000	+	18.1865i	−0.569442	+	0.986303i
$341$		0			0
$342$	3.00000	+	5.19615i	0.162221	+	0.280976i
$343$	−13.0000			−0.701934
$344$	−5.00000	−	8.66025i	−0.269582	−	0.466930i
$345$	−6.00000	−	10.3923i	−0.323029	−	0.559503i
$346$	−20.0000			−1.07521
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$	5.00000	−	8.66025i	0.268028	−	0.464238i
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	−0.274011	−	0.961727i	$-0.588351\pi$
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$	4.00000			0.213809
$351$	−2.50000	+	2.59808i	−0.133440	+	0.138675i
$352$	−1.00000			−0.0533002
$353$	−2.00000	+	3.46410i	−0.106449	+	0.184376i	−0.914329	−	0.404971i	$-0.867282\pi$
$353$	−2.00000	+	3.46410i	−0.106449	+	0.184376i	0.807880	+	0.589347i	$0.200615\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$	12.0000	+	20.7846i	0.636894	+	1.10313i
$356$	−12.0000			−0.635999
$357$	3.50000	+	6.06218i	0.185240	+	0.320844i
$358$	−9.00000	−	15.5885i	−0.475665	−	0.823876i
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	4.00000	−	6.92820i	0.210235	−	0.364138i
$363$	−1.00000			−0.0524864
$364$	1.00000	+	3.46410i	0.0524142	+	0.181568i
$365$	48.0000			2.51243
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	1.00000			0.0520579
$370$	9.00000	+	15.5885i	0.467888	+	0.810405i
$371$	−5.50000	−	9.52628i	−0.285546	−	0.494580i
$372$		0			0
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	0.972556	−	0.232671i	$-0.0747464\pi$
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	−0.687776	+	0.725923i	$0.741413\pi$
$374$	3.50000	−	6.06218i	0.180981	−	0.313468i
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$	−3.00000			−0.154713
$377$	10.0000	+	34.6410i	0.515026	+	1.78410i
$378$	−1.00000			−0.0514344
$379$	−10.0000	+	17.3205i	−0.513665	+	0.889695i	0.486209	+	0.873843i	$0.338379\pi$
$379$	−10.0000	+	17.3205i	−0.513665	+	0.889695i	−0.999874	+	0.0158521i	$0.994954\pi$
$380$	9.00000	−	15.5885i	0.461690	−	0.799671i
$381$	2.50000	+	4.33013i	0.128079	+	0.221839i
$382$	8.00000			0.409316
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−3.00000			−0.152894
$386$	−8.00000	−	13.8564i	−0.407189	−	0.705273i
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$	−4.50000	+	7.79423i	−0.228453	+	0.395692i
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$	10.5000	+	2.59808i	0.531688	+	0.131559i
$391$	−28.0000			−1.41602
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	−10.0000	+	17.3205i	−0.504433	+	0.873704i
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$	4.00000			0.200502
$399$	−3.00000	−	5.19615i	−0.150188	−	0.260133i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$	−12.0000			−0.598506
$403$		0			0
$404$	18.0000			0.895533
$405$	−1.50000	+	2.59808i	−0.0745356	+	0.129099i
$406$	−5.00000	+	8.66025i	−0.248146	+	0.429801i
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$	−7.00000			−0.346552
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	0.889689	−	0.456566i	$-0.150921\pi$
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	−0.840243	+	0.542211i	$0.817588\pi$
$410$	−1.50000	−	2.59808i	−0.0740797	−	0.128310i
$411$		0			0
$412$	−7.00000	−	12.1244i	−0.344865	−	0.597324i
$413$	4.00000	−	6.92820i	0.196827	−	0.340915i
$414$	2.00000	−	3.46410i	0.0982946	−	0.170251i
$415$	−21.0000			−1.03085
$416$	−3.50000	−	0.866025i	−0.171602	−	0.0424604i
$417$	8.00000			0.391762
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	4.00000	−	6.92820i	0.195413	−	0.338465i	−0.751623	−	0.659593i	$-0.770729\pi$
$419$	4.00000	−	6.92820i	0.195413	−	0.338465i	0.947036	+	0.321128i	$0.104062\pi$
$420$	1.50000	+	2.59808i	0.0731925	+	0.126773i
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	5.00000	+	8.66025i	0.243396	+	0.421575i
$423$	1.50000	+	2.59808i	0.0729325	+	0.126323i
$424$	11.0000			0.534207
$425$	−14.0000	−	24.2487i	−0.679100	−	1.17624i
$426$	−4.00000	+	6.92820i	−0.193801	+	0.335673i
$427$	−1.00000	+	1.73205i	−0.0483934	+	0.0838198i
$428$	9.00000			0.435031
$429$	−3.50000	−	0.866025i	−0.168982	−	0.0418121i
$430$	30.0000			1.44673
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−3.00000	−	5.19615i	−0.144171	−	0.249711i	0.784892	−	0.619632i	$-0.212718\pi$
$433$	−3.00000	−	5.19615i	−0.144171	−	0.249711i	−0.929063	+	0.369921i	$0.879385\pi$
$434$		0			0
$435$	15.0000	+	25.9808i	0.719195	+	1.24568i
$436$	−8.50000	−	14.7224i	−0.407076	−	0.705077i
$437$	24.0000			1.14808
$438$	8.00000	+	13.8564i	0.382255	+	0.662085i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	−6.00000			−0.285714
$442$	17.5000	−	18.1865i	0.832390	−	0.865045i
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$	18.0000	−	31.1769i	0.853282	−	1.47793i
$446$	−4.00000	−	6.92820i	−0.189405	−	0.328060i
$447$	−14.0000			−0.662177
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	10.0000	+	17.3205i	0.471929	+	0.817405i	0.999484	−	0.0321156i	$-0.0102245\pi$
$449$	10.0000	+	17.3205i	0.471929	+	0.817405i	−0.527555	+	0.849521i	$0.676891\pi$
$450$	4.00000			0.188562
$451$	0.500000	+	0.866025i	0.0235441	+	0.0407795i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	−3.50000	+	6.06218i	−0.164444	+	0.284826i
$454$	17.0000			0.797850
$455$	−10.5000	−	2.59808i	−0.492248	−	0.121800i
$456$	6.00000			0.280976
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	−0.200118	−	0.979772i	$-0.564132\pi$
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	0.948566	−	0.316579i	$-0.102534\pi$
$458$	12.0000	−	20.7846i	0.560723	−	0.971201i
$459$	3.50000	+	6.06218i	0.163366	+	0.282958i
$460$	−12.0000			−0.559503
$461$	1.00000	+	1.73205i	0.0465746	+	0.0806696i	0.888373	−	0.459123i	$-0.151836\pi$
$461$	1.00000	+	1.73205i	0.0465746	+	0.0806696i	−0.841798	+	0.539792i	$0.818503\pi$
$462$	−0.500000	−	0.866025i	−0.0232621	−	0.0402911i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−5.00000	−	8.66025i	−0.232119	−	0.402042i
$465$		0			0
$466$	8.50000	−	14.7224i	0.393755	−	0.682003i
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$	1.00000	+	3.46410i	0.0462250	+	0.160128i
$469$	12.0000			0.554109
$470$	4.50000	−	7.79423i	0.207570	−	0.359521i
$471$	4.00000	−	6.92820i	0.184310	−	0.319235i
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$	−10.0000			−0.459800
$474$		0			0
$475$	12.0000	+	20.7846i	0.550598	+	0.953663i
$476$	7.00000			0.320844
$477$	−5.50000	−	9.52628i	−0.251828	−	0.436178i
$478$	−2.00000	+	3.46410i	−0.0914779	+	0.158444i
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.105208	−	0.994450i	$-0.466449\pi$
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.808615	−	0.588338i	$-0.200218\pi$
$480$	−3.00000			−0.136931
$481$	−6.00000	−	20.7846i	−0.273576	−	0.947697i
$482$	−2.00000			−0.0910975
$483$	−2.00000	+	3.46410i	−0.0910032	+	0.157622i
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	−13.5000	−	23.3827i	−0.613003	−	1.06175i
$486$	−1.00000			−0.0453609
$487$	−2.00000	−	3.46410i	−0.0906287	−	0.156973i	0.817147	−	0.576429i	$-0.195554\pi$
$487$	−2.00000	−	3.46410i	−0.0906287	−	0.156973i	−0.907776	+	0.419456i	$0.862221\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	8.00000			0.361773
$490$	9.00000	+	15.5885i	0.406579	+	0.704215i
$491$	−14.5000	+	25.1147i	−0.654376	+	1.13341i	0.327674	+	0.944791i	$0.393735\pi$
$491$	−14.5000	+	25.1147i	−0.654376	+	1.13341i	−0.982050	+	0.188621i	$0.939598\pi$
$492$	0.500000	−	0.866025i	0.0225417	−	0.0390434i
$493$	70.0000			3.15264
$494$	−15.0000	+	15.5885i	−0.674882	+	0.701358i
$495$	−3.00000			−0.134840
$496$		0			0
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$	−3.50000	−	6.06218i	−0.156839	−	0.271653i
$499$	35.0000			1.56682			0.783408	−	0.621508i	$-0.213480\pi$
$499$	35.0000			1.56682			0.783408	+	0.621508i	$0.213480\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	−12.0000			−0.535586
$503$	−21.0000	−	36.3731i	−0.936344	−	1.62179i	−0.772220	−	0.635355i	$-0.780854\pi$
$503$	−21.0000	−	36.3731i	−0.936344	−	1.62179i	−0.164124	−	0.986440i	$-0.552480\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	−27.0000	+	46.7654i	−1.20148	+	2.08103i
$506$	4.00000			0.177822
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	5.00000			0.221839
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$	10.5000	−	18.1865i	0.464948	−	0.805313i
$511$	−8.00000	−	13.8564i	−0.353899	−	0.612971i
$512$	1.00000			0.0441942
$513$	−3.00000	−	5.19615i	−0.132453	−	0.229416i
$514$	1.00000	+	1.73205i	0.0441081	+	0.0763975i
$515$	42.0000			1.85074
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$	−1.50000	+	2.59808i	−0.0659699	+	0.114263i
$518$	3.00000	−	5.19615i	0.131812	−	0.228306i
$519$	20.0000			0.877903
$520$	7.50000	−	7.79423i	0.328897	−	0.341800i
$521$	24.0000			1.05146			0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000			1.05146			0.525730	+	0.850652i	$0.323792\pi$
$522$	−5.00000	+	8.66025i	−0.218844	+	0.379049i
$523$	19.0000	−	32.9090i	0.830812	−	1.43901i	−0.0665832	−	0.997781i	$-0.521210\pi$
$523$	19.0000	−	32.9090i	0.830812	−	1.43901i	0.897395	−	0.441228i	$-0.145457\pi$
$524$	10.0000	+	17.3205i	0.436852	+	0.756650i
$525$	−4.00000			−0.174574
$526$	−14.0000	−	24.2487i	−0.610429	−	1.05729i
$527$		0			0
$528$	1.00000			0.0435194
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−16.5000	+	28.5788i	−0.716714	+	1.24139i
$531$	4.00000	−	6.92820i	0.173585	−	0.300658i
$532$	−6.00000			−0.260133
$533$	1.00000	+	3.46410i	0.0433148	+	0.150047i
$534$	12.0000			0.519291
$535$	−13.5000	+	23.3827i	−0.583656	+	1.01092i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$	9.00000	+	15.5885i	0.388379	+	0.672692i
$538$	−9.00000			−0.388018
$539$	−3.00000	−	5.19615i	−0.129219	−	0.223814i
$540$	1.50000	+	2.59808i	0.0645497	+	0.111803i
$541$	−26.0000			−1.11783			−0.558914	−	0.829226i	$-0.688782\pi$
$541$	−26.0000			−1.11783			−0.558914	+	0.829226i	$0.688782\pi$
$542$		0			0
$543$	−4.00000	+	6.92820i	−0.171656	+	0.297318i
$544$	−3.50000	+	6.06218i	−0.150061	+	0.259914i
$545$	51.0000			2.18460
$546$	−1.00000	−	3.46410i	−0.0427960	−	0.148250i
$547$	−10.0000			−0.427569			−0.213785	−	0.976881i	$-0.568579\pi$
$547$	−10.0000			−0.427569			−0.213785	+	0.976881i	$0.568579\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	−60.0000			−2.55609
$552$	−2.00000	−	3.46410i	−0.0851257	−	0.147442i
$553$		0			0
$554$	−17.0000			−0.722261
$555$	−9.00000	−	15.5885i	−0.382029	−	0.661693i
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$	−16.0000	+	27.7128i	−0.677942	+	1.17423i	0.297658	+	0.954673i	$0.403795\pi$
$557$	−16.0000	+	27.7128i	−0.677942	+	1.17423i	−0.975600	+	0.219557i	$0.929539\pi$
$558$		0			0
$559$	−35.0000	−	8.66025i	−1.48034	−	0.366290i
$560$	3.00000			0.126773
$561$	−3.50000	+	6.06218i	−0.147770	+	0.255945i
$562$	2.50000	−	4.33013i	0.105456	−	0.182655i
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	−0.996669	−	0.0815478i	$-0.974014\pi$
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	0.427712	−	0.903915i	$-0.359320\pi$
$564$	3.00000			0.126323
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$	−9.00000	−	15.5885i	−0.378298	−	0.655232i
$567$	1.00000			0.0419961
$568$	4.00000	+	6.92820i	0.167836	+	0.290701i
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	−0.855355	−	0.518043i	$-0.826661\pi$
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	0.876316	+	0.481737i	$0.159994\pi$
$570$	−9.00000	+	15.5885i	−0.376969	+	0.652929i
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	−2.50000	+	2.59808i	−0.104530	+	0.108631i
$573$	−8.00000			−0.334205
$574$	−0.500000	+	0.866025i	−0.0208696	+	0.0361472i
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	−16.0000	−	27.7128i	−0.665512	−	1.15270i
$579$	8.00000	+	13.8564i	0.332469	+	0.575853i
$580$	30.0000			1.24568
$581$	3.50000	+	6.06218i	0.145204	+	0.251502i
$582$	4.50000	−	7.79423i	0.186531	−	0.323081i
$583$	5.50000	−	9.52628i	0.227787	−	0.394538i
$584$	16.0000			0.662085
$585$	−10.5000	−	2.59808i	−0.434122	−	0.107417i
$586$	6.00000			0.247858
$587$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$587$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$588$	−3.00000	+	5.19615i	−0.123718	+	0.214286i
$589$		0			0
$590$	−24.0000			−0.988064
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	3.00000	+	5.19615i	0.123299	+	0.213561i
$593$	19.0000			0.780236			0.390118	−	0.920765i	$-0.372434\pi$
$593$	19.0000			0.780236			0.390118	+	0.920765i	$0.372434\pi$
$594$	−0.500000	−	0.866025i	−0.0205152	−	0.0355335i
$595$	−10.5000	+	18.1865i	−0.430458	+	0.745575i
$596$	−7.00000	+	12.1244i	−0.286731	+	0.496633i
$597$	−4.00000			−0.163709
$598$	14.0000	+	3.46410i	0.572503	+	0.141658i
$599$	−25.0000			−1.02147			−0.510736	−	0.859738i	$-0.670627\pi$
$599$	−25.0000			−1.02147			−0.510736	+	0.859738i	$0.670627\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$	−5.00000	−	8.66025i	−0.203785	−	0.352966i
$603$	12.0000			0.488678
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$	−18.0000			−0.731200
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	0.732551	−	0.680712i	$-0.238329\pi$
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	−0.955789	+	0.294052i	$0.904996\pi$
$608$	3.00000	−	5.19615i	0.121666	−	0.210732i
$609$	5.00000	−	8.66025i	0.202610	−	0.350931i
$610$	6.00000			0.242933
$611$	−7.50000	+	7.79423i	−0.303418	+	0.315321i
$612$	7.00000			0.282958
$613$	−1.50000	+	2.59808i	−0.0605844	+	0.104935i	−0.894727	−	0.446614i	$-0.852630\pi$
$613$	−1.50000	+	2.59808i	−0.0605844	+	0.104935i	0.834142	+	0.551549i	$0.185963\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	1.50000	+	2.59808i	0.0604858	+	0.104765i
$616$	−1.00000			−0.0402911
$617$	−13.0000	−	22.5167i	−0.523360	−	0.906487i	−0.999630	−	0.0271876i	$-0.991345\pi$
$617$	−13.0000	−	22.5167i	−0.523360	−	0.906487i	0.476270	−	0.879299i	$-0.341988\pi$
$618$	7.00000	+	12.1244i	0.281581	+	0.487713i
$619$	−27.0000			−1.08522			−0.542611	−	0.839984i	$-0.682564\pi$
$619$	−27.0000			−1.08522			−0.542611	+	0.839984i	$0.682564\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	−8.50000	+	14.7224i	−0.340819	+	0.590316i
$623$	−12.0000			−0.480770
$624$	3.50000	+	0.866025i	0.140112	+	0.0346688i
$625$	−29.0000			−1.16000
$626$	3.50000	−	6.06218i	0.139888	−	0.242293i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	−4.00000	−	6.92820i	−0.159617	−	0.276465i
$629$	−42.0000			−1.67465
$630$	−1.50000	−	2.59808i	−0.0597614	−	0.103510i
$631$	−11.0000	−	19.0526i	−0.437903	−	0.758470i	0.559625	−	0.828746i	$-0.310945\pi$
$631$	−11.0000	−	19.0526i	−0.437903	−	0.758470i	−0.997528	+	0.0702759i	$0.977612\pi$
$632$		0			0
$633$	−5.00000	−	8.66025i	−0.198732	−	0.344214i
$634$	11.5000	−	19.9186i	0.456723	−	0.791068i
$635$	−7.50000	+	12.9904i	−0.297628	+	0.515508i
$636$	−11.0000			−0.436178
$637$	−6.00000	−	20.7846i	−0.237729	−	0.823516i
$638$	−10.0000			−0.395904
$639$	4.00000	−	6.92820i	0.158238	−	0.274075i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$	−9.00000			−0.355202
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	0.999967	−	0.00811944i	$-0.00258453\pi$
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	−0.507015	+	0.861937i	$0.669251\pi$
$644$	2.00000	+	3.46410i	0.0788110	+	0.136505i
$645$	−30.0000			−1.18125
$646$	21.0000	+	36.3731i	0.826234	+	1.43108i
$647$	8.00000	−	13.8564i	0.314512	−	0.544752i	−0.664821	−	0.747002i	$-0.731492\pi$
$647$	8.00000	−	13.8564i	0.314512	−	0.544752i	0.979334	+	0.202251i	$0.0648256\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	8.00000			0.314027
$650$	4.00000	+	13.8564i	0.156893	+	0.543493i
$651$		0			0
$652$	4.00000	−	6.92820i	0.156652	−	0.271329i
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	8.50000	+	14.7224i	0.332376	+	0.575693i
$655$	−60.0000			−2.34439
$656$	−0.500000	−	0.866025i	−0.0195217	−	0.0338126i
$657$	−8.00000	−	13.8564i	−0.312110	−	0.540590i
$658$	−3.00000			−0.116952
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	10.0000	−	17.3205i	0.388955	−	0.673690i	−0.603354	−	0.797473i	$-0.706170\pi$
$661$	10.0000	−	17.3205i	0.388955	−	0.673690i	0.992309	+	0.123784i	$0.0395028\pi$
$662$	−27.0000			−1.04938
$663$	−17.5000	+	18.1865i	−0.679644	+	0.706306i
$664$	−7.00000			−0.271653
$665$	9.00000	−	15.5885i	0.349005	−	0.604494i
$666$	3.00000	−	5.19615i	0.116248	−	0.201347i
$667$	20.0000	+	34.6410i	0.774403	+	1.34131i
$668$	18.0000			0.696441
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$	−18.0000	−	31.1769i	−0.695401	−	1.20447i
$671$	−2.00000			−0.0772091
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	−12.0000	+	20.7846i	−0.462566	+	0.801188i	−0.999088	−	0.0426985i	$-0.986405\pi$
$673$	−12.0000	+	20.7846i	−0.462566	+	0.801188i	0.536522	+	0.843886i	$0.319738\pi$
$674$	−16.0000	+	27.7128i	−0.616297	+	1.06746i
$675$	−4.00000			−0.153960
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	−12.0000			−0.461197			−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000			−0.461197			−0.230599	+	0.973049i	$0.574068\pi$
$678$	−3.00000	+	5.19615i	−0.115214	+	0.199557i
$679$	−4.50000	+	7.79423i	−0.172694	+	0.299115i
$680$	−10.5000	−	18.1865i	−0.402657	−	0.697422i
$681$	−17.0000			−0.651441
$682$		0			0
$683$	−9.00000	−	15.5885i	−0.344375	−	0.596476i	0.640865	−	0.767654i	$-0.278576\pi$
$683$	−9.00000	−	15.5885i	−0.344375	−	0.596476i	−0.985240	+	0.171178i	$0.945243\pi$
$684$	−6.00000			−0.229416
$685$		0			0
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	−12.0000	+	20.7846i	−0.457829	+	0.792982i
$688$	10.0000			0.381246
$689$	27.5000	−	28.5788i	1.04767	−	1.08877i
$690$	12.0000			0.456832
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	10.0000	−	17.3205i	0.380143	−	0.658427i
$693$	0.500000	+	0.866025i	0.0189934	+	0.0328976i
$694$	−24.0000			−0.911028
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$	5.00000	+	8.66025i	0.189525	+	0.328266i
$697$	7.00000			0.265144
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$	−8.50000	+	14.7224i	−0.321500	+	0.556854i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	8.00000			0.302156			0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000			0.302156			0.151078	+	0.988522i	$0.451726\pi$
$702$	−1.00000	−	3.46410i	−0.0377426	−	0.130744i
$703$	36.0000			1.35777
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−4.50000	+	7.79423i	−0.169480	+	0.293548i
$706$	−2.00000	−	3.46410i	−0.0752710	−	0.130373i
$707$	18.0000			0.676960
$708$	−4.00000	−	6.92820i	−0.150329	−	0.260378i
$709$	−9.00000	−	15.5885i	−0.338002	−	0.585437i	0.646055	−	0.763291i	$-0.276418\pi$
$709$	−9.00000	−	15.5885i	−0.338002	−	0.585437i	−0.984057	+	0.177854i	$0.943084\pi$
$710$	−24.0000			−0.900704
$711$		0			0
$712$	6.00000	−	10.3923i	0.224860	−	0.389468i
$713$		0			0
$714$	−7.00000			−0.261968
$715$	−3.00000	−	10.3923i	−0.112194	−	0.388650i
$716$	18.0000			0.672692
$717$	2.00000	−	3.46410i	0.0746914	−	0.129369i
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	−11.5000	−	19.9186i	−0.428878	−	0.742838i	0.567896	−	0.823100i	$-0.307758\pi$
$719$	−11.5000	−	19.9186i	−0.428878	−	0.742838i	−0.996774	+	0.0802624i	$0.974424\pi$
$720$	3.00000			0.111803
$721$	−7.00000	−	12.1244i	−0.260694	−	0.451535i
$722$	−8.50000	−	14.7224i	−0.316337	−	0.547912i
$723$	2.00000			0.0743808
$724$	4.00000	+	6.92820i	0.148659	+	0.257485i
$725$	−20.0000	+	34.6410i	−0.742781	+	1.28654i
$726$	0.500000	−	0.866025i	0.0185567	−	0.0321412i
$727$	−20.0000			−0.741759			−0.370879	−	0.928681i	$-0.620944\pi$
$727$	−20.0000			−0.741759			−0.370879	+	0.928681i	$0.620944\pi$
$728$	−3.50000	−	0.866025i	−0.129719	−	0.0320970i
$729$	1.00000			0.0370370
$730$	−24.0000	+	41.5692i	−0.888280	+	1.53855i
$731$	−35.0000	+	60.6218i	−1.29452	+	2.24218i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$	34.0000			1.25582			0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000			1.25582			0.627909	+	0.778287i	$0.283911\pi$
$734$	14.0000	+	24.2487i	0.516749	+	0.895036i
$735$	−9.00000	−	15.5885i	−0.331970	−	0.574989i
$736$	−4.00000			−0.147442
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$	−0.500000	+	0.866025i	−0.0184053	+	0.0318788i
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	−0.943215	−	0.332184i	$-0.892215\pi$
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	0.759287	+	0.650756i	$0.225548\pi$
$740$	−18.0000			−0.661693
$741$	15.0000	−	15.5885i	0.551039	−	0.572656i
$742$	11.0000			0.403823
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.113455	−	0.993543i	$-0.463808\pi$
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.803706	−	0.595026i	$-0.202858\pi$
$744$		0			0
$745$	−21.0000	−	36.3731i	−0.769380	−	1.33261i
$746$	−11.0000			−0.402739
$747$	3.50000	+	6.06218i	0.128058	+	0.221803i
$748$	3.50000	+	6.06218i	0.127973	+	0.221655i
$749$	9.00000			0.328853
$750$	−1.50000	−	2.59808i	−0.0547723	−	0.0948683i
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	−0.883694	−	0.468065i	$-0.844951\pi$
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	0.847203	+	0.531269i	$0.178285\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	12.0000			0.437304
$754$	−35.0000	−	8.66025i	−1.27462	−	0.315388i
$755$	−21.0000			−0.764268
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	0.413768	+	0.910382i	$0.364212\pi$
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	−0.995298	+	0.0968571i	$0.969121\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$	−4.00000			−0.145191
$760$	9.00000	+	15.5885i	0.326464	+	0.565453i
$761$	22.5000	+	38.9711i	0.815624	+	1.41270i	0.908879	+	0.417061i	$0.136940\pi$
$761$	22.5000	+	38.9711i	0.815624	+	1.41270i	−0.0932544	+	0.995642i	$0.529727\pi$
$762$	−5.00000			−0.181131
$763$	−8.50000	−	14.7224i	−0.307721	−	0.532988i
$764$	−4.00000	+	6.92820i	−0.144715	+	0.250654i
$765$	−10.5000	+	18.1865i	−0.379628	+	0.657536i
$766$	−15.0000			−0.541972
$767$	28.0000	+	6.92820i	1.01102	+	0.250163i
$768$	−1.00000			−0.0360844
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$	1.50000	−	2.59808i	0.0540562	−	0.0936282i
$771$	−1.00000	−	1.73205i	−0.0360141	−	0.0623783i
$772$	16.0000			0.575853
$773$	−5.50000	−	9.52628i	−0.197821	−	0.342636i	0.750000	−	0.661437i	$-0.230053\pi$
$773$	−5.50000	−	9.52628i	−0.197821	−	0.342636i	−0.947822	+	0.318801i	$0.896720\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$		0			0
$776$	−4.50000	−	7.79423i	−0.161541	−	0.279797i
$777$	−3.00000	+	5.19615i	−0.107624	+	0.186411i
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	−6.00000			−0.214972
$780$	−7.50000	+	7.79423i	−0.268543	+	0.279078i
$781$	8.00000			0.286263
$782$	14.0000	−	24.2487i	0.500639	−	0.867132i
$783$	5.00000	−	8.66025i	0.178685	−	0.309492i
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	24.0000			0.856597
$786$	−10.0000	−	17.3205i	−0.356688	−	0.617802i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	−6.00000			−0.213741
$789$	14.0000	+	24.2487i	0.498413	+	0.863277i
$790$		0			0
$791$	3.00000	−	5.19615i	0.106668	−	0.184754i
$792$	−1.00000			−0.0355335
$793$	−7.00000	−	1.73205i	−0.248577	−	0.0615069i
$794$	34.0000			1.20661
$795$	16.5000	−	28.5788i	0.585195	−	1.01359i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−7.50000	−	12.9904i	−0.265664	−	0.460143i	0.702074	−	0.712104i	$-0.252258\pi$
$797$	−7.50000	−	12.9904i	−0.265664	−	0.460143i	−0.967737	+	0.251961i	$0.918924\pi$
$798$	6.00000			0.212398
$799$	10.5000	+	18.1865i	0.371463	+	0.643393i
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	−12.0000			−0.423999
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	8.00000	−	13.8564i	0.282314	−	0.488982i
$804$	6.00000	−	10.3923i	0.211604	−	0.366508i
$805$	−12.0000			−0.422944
$806$		0			0
$807$	9.00000			0.316815
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	−0.134255	−	0.990947i	$-0.542864\pi$
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	0.925312	−	0.379206i	$-0.123803\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	−5.00000	−	8.66025i	−0.175466	−	0.303915i
$813$		0			0
$814$	6.00000			0.210300
$815$	12.0000	+	20.7846i	0.420342	+	0.728053i
$816$	3.50000	−	6.06218i	0.122525	−	0.212219i
$817$	30.0000	−	51.9615i	1.04957	−	1.81790i
$818$	−2.00000			−0.0699284
$819$	1.00000	+	3.46410i	0.0349428	+	0.121046i
$820$	3.00000			0.104765
$821$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$821$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$822$		0			0
$823$	9.00000	+	15.5885i	0.313720	+	0.543379i	0.979165	−	0.203068i	$-0.0650912\pi$
$823$	9.00000	+	15.5885i	0.313720	+	0.543379i	−0.665444	+	0.746447i	$0.731758\pi$
$824$	14.0000			0.487713
$825$	−2.00000	−	3.46410i	−0.0696311	−	0.120605i
$826$	4.00000	+	6.92820i	0.139178	+	0.241063i
$827$	23.0000			0.799788			0.399894	−	0.916561i	$-0.369047\pi$
$827$	23.0000			0.799788			0.399894	+	0.916561i	$0.369047\pi$
$828$	2.00000	+	3.46410i	0.0695048	+	0.120386i
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	10.5000	−	18.1865i	0.364460	−	0.631264i
$831$	17.0000			0.589723
$832$	2.50000	−	2.59808i	0.0866719	−	0.0900721i
$833$	−42.0000			−1.45521
$834$	−4.00000	+	6.92820i	−0.138509	+	0.239904i
$835$	−27.0000	+	46.7654i	−0.934374	+	1.61838i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$		0			0
$838$	4.00000	+	6.92820i	0.138178	+	0.239331i
$839$	−22.0000	−	38.1051i	−0.759524	−	1.31553i	−0.943093	−	0.332528i	$-0.892098\pi$
$839$	−22.0000	−	38.1051i	−0.759524	−	1.31553i	0.183569	−	0.983007i	$-0.441235\pi$
$840$	−3.00000			−0.103510
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	−3.00000	+	5.19615i	−0.103387	+	0.179071i
$843$	−2.50000	+	4.33013i	−0.0861046	+	0.149137i
$844$	−10.0000			−0.344214
$845$	−1.50000	−	38.9711i	−0.0516016	−	1.34065i
$846$	−3.00000			−0.103142
$847$	−0.500000	+	0.866025i	−0.0171802	+	0.0297570i
$848$	−5.50000	+	9.52628i	−0.188871	+	0.327134i
$849$	9.00000	+	15.5885i	0.308879	+	0.534994i
$850$	28.0000			0.960392
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−4.00000	−	6.92820i	−0.137038	−	0.237356i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	−1.00000	−	1.73205i	−0.0342193	−	0.0592696i
$855$	9.00000	−	15.5885i	0.307794	−	0.533114i
$856$	−4.50000	+	7.79423i	−0.153807	+	0.266401i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$	2.50000	−	2.59808i	0.0853486	−	0.0886969i
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−15.0000	+	25.9808i	−0.511496	+	0.885937i
$861$	0.500000	−	0.866025i	0.0170400	−	0.0295141i
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	30.0000	+	51.9615i	1.02003	+	1.76674i
$866$	6.00000			0.203888
$867$	16.0000	+	27.7128i	0.543388	+	0.941176i
$868$		0			0
$869$		0			0
$870$	−30.0000			−1.01710
$871$	12.0000	+	41.5692i	0.406604	+	1.40852i
$872$	17.0000			0.575693
$873$	−4.50000	+	7.79423i	−0.152302	+	0.263795i
$874$	−12.0000	+	20.7846i	−0.405906	+	0.703050i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$	−16.0000			−0.540590
$877$	13.5000	+	23.3827i	0.455863	+	0.789577i	0.998737	−	0.0502365i	$-0.0159975\pi$
$877$	13.5000	+	23.3827i	0.455863	+	0.789577i	−0.542875	+	0.839814i	$0.682664\pi$
$878$		0			0
$879$	−6.00000			−0.202375
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−23.0000	+	39.8372i	−0.774890	+	1.34215i	0.159967	+	0.987122i	$0.448861\pi$
$881$	−23.0000	+	39.8372i	−0.774890	+	1.34215i	−0.934856	+	0.355026i	$0.884472\pi$
$882$	3.00000	−	5.19615i	0.101015	−	0.174964i
$883$	21.0000			0.706706			0.353353	−	0.935490i	$-0.385041\pi$
$883$	21.0000			0.706706			0.353353	+	0.935490i	$0.385041\pi$
$884$	7.00000	+	24.2487i	0.235435	+	0.815572i
$885$	24.0000			0.806751
$886$		0			0
$887$	17.0000	−	29.4449i	0.570804	−	0.988662i	−0.425679	−	0.904874i	$-0.639965\pi$
$887$	17.0000	−	29.4449i	0.570804	−	0.988662i	0.996484	−	0.0837878i	$-0.0267018\pi$
$888$	−3.00000	−	5.19615i	−0.100673	−	0.174371i
$889$	5.00000			0.167695
$890$	18.0000	+	31.1769i	0.603361	+	1.04505i
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	8.00000			0.267860
$893$	−9.00000	−	15.5885i	−0.301174	−	0.521648i
$894$	7.00000	−	12.1244i	0.234115	−	0.405499i
$895$	−27.0000	+	46.7654i	−0.902510	+	1.56319i
$896$	1.00000			0.0334077
$897$	−14.0000	−	3.46410i	−0.467446	−	0.115663i
$898$	−20.0000			−0.667409
$899$		0			0
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	−38.5000	−	66.6840i	−1.28262	−	2.22156i
$902$	−1.00000			−0.0332964
$903$	5.00000	+	8.66025i	0.166390	+	0.288195i
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	−24.0000			−0.797787
$906$	−3.50000	−	6.06218i	−0.116280	−	0.201402i
$907$	10.5000	−	18.1865i	0.348647	−	0.603874i	−0.637363	−	0.770564i	$-0.719975\pi$
$907$	10.5000	−	18.1865i	0.348647	−	0.603874i	0.986009	+	0.166690i	$0.0533080\pi$
$908$	−8.50000	+	14.7224i	−0.282082	+	0.488581i
$909$	18.0000			0.597022
$910$	7.50000	−	7.79423i	0.248623	−	0.258376i
$911$	−19.0000			−0.629498			−0.314749	−	0.949175i	$-0.601920\pi$
$911$	−19.0000			−0.629498			−0.314749	+	0.949175i	$0.601920\pi$
$912$	−3.00000	+	5.19615i	−0.0993399	+	0.172062i
$913$	−3.50000	+	6.06218i	−0.115833	+	0.200629i
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$	−6.00000			−0.198354
$916$	12.0000	+	20.7846i	0.396491	+	0.686743i
$917$	10.0000	+	17.3205i	0.330229	+	0.571974i
$918$	−7.00000			−0.231034
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	0.821842	−	0.569716i	$-0.192947\pi$
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	−0.904309	+	0.426878i	$0.859613\pi$
$920$	6.00000	−	10.3923i	0.197814	−	0.342624i
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$	−2.00000			−0.0658665
$923$	28.0000	+	6.92820i	0.921631	+	0.228045i
$924$	1.00000			0.0328976
$925$	12.0000	−	20.7846i	0.394558	−	0.683394i
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	−7.00000	−	12.1244i	−0.229910	−	0.398216i
$928$	10.0000			0.328266
$929$	20.0000	+	34.6410i	0.656179	+	1.13653i	0.981597	+	0.190965i	$0.0611616\pi$
$929$	20.0000	+	34.6410i	0.656179	+	1.13653i	−0.325418	+	0.945570i	$0.605505\pi$
$930$		0			0
$931$	36.0000			1.17985
$932$	8.50000	+	14.7224i	0.278427	+	0.482249i
$933$	8.50000	−	14.7224i	0.278278	−	0.481991i
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$	−21.0000			−0.686773
$936$	−3.50000	−	0.866025i	−0.114401	−	0.0283069i
$937$	−16.0000			−0.522697			−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000			−0.522697			−0.261349	+	0.965244i	$0.584167\pi$
$938$	−6.00000	+	10.3923i	−0.195907	+	0.339321i
$939$	−3.50000	+	6.06218i	−0.114218	+	0.197832i
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$	4.00000	+	6.92820i	0.130327	+	0.225733i
$943$	2.00000	+	3.46410i	0.0651290	+	0.112807i
$944$	−8.00000			−0.260378
$945$	1.50000	+	2.59808i	0.0487950	+	0.0845154i
$946$	5.00000	−	8.66025i	0.162564	−	0.281569i
$947$	23.0000	−	39.8372i	0.747400	−	1.29453i	−0.201666	−	0.979454i	$-0.564635\pi$
$947$	23.0000	−	39.8372i	0.747400	−	1.29453i	0.949065	−	0.315080i	$-0.102031\pi$
$948$		0			0
$949$	40.0000	−	41.5692i	1.29845	−	1.34939i
$950$	−24.0000			−0.778663
$951$	−11.5000	+	19.9186i	−0.372913	+	0.645904i
$952$	−3.50000	+	6.06218i	−0.113436	+	0.196476i
$953$	−7.50000	−	12.9904i	−0.242949	−	0.420800i	0.718604	−	0.695419i	$-0.244781\pi$
$953$	−7.50000	−	12.9904i	−0.242949	−	0.420800i	−0.961553	+	0.274620i	$0.911448\pi$
$954$	11.0000			0.356138
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−2.00000	−	3.46410i	−0.0646846	−	0.112037i
$957$	10.0000			0.323254
$958$	20.0000	+	34.6410i	0.646171	+	1.11920i
$959$		0			0
$960$	1.50000	−	2.59808i	0.0484123	−	0.0838525i
$961$	−31.0000			−1.00000
$962$	21.0000	+	5.19615i	0.677067	+	0.167531i
$963$	9.00000			0.290021
$964$	1.00000	−	1.73205i	0.0322078	−	0.0557856i
$965$	−24.0000	+	41.5692i	−0.772587	+	1.33816i
$966$	−2.00000	−	3.46410i	−0.0643489	−	0.111456i
$967$	−33.0000			−1.06121			−0.530604	−	0.847620i	$-0.678035\pi$
$967$	−33.0000			−1.06121			−0.530604	+	0.847620i	$0.678035\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−21.0000	−	36.3731i	−0.674617	−	1.16847i
$970$	27.0000			0.866918
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	0.633768	−	0.773523i	$-0.281507\pi$
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	−0.986775	+	0.162098i	$0.948174\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	4.00000	−	6.92820i	0.128234	−	0.222108i
$974$	4.00000			0.128168
$975$	−4.00000	−	13.8564i	−0.128103	−	0.443760i
$976$	2.00000			0.0640184
$977$	−19.0000	+	32.9090i	−0.607864	+	1.05285i	0.383728	+	0.923446i	$0.374640\pi$
$977$	−19.0000	+	32.9090i	−0.607864	+	1.05285i	−0.991592	+	0.129405i	$0.958693\pi$
$978$	−4.00000	+	6.92820i	−0.127906	+	0.221540i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$	−18.0000			−0.574989
$981$	−8.50000	−	14.7224i	−0.271384	−	0.470051i
$982$	−14.5000	−	25.1147i	−0.462714	−	0.801443i
$983$	5.00000			0.159475			0.0797376	−	0.996816i	$-0.474592\pi$
$983$	5.00000			0.159475			0.0797376	+	0.996816i	$0.474592\pi$
$984$	0.500000	+	0.866025i	0.0159394	+	0.0276079i
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	−35.0000	+	60.6218i	−1.11463	+	1.93059i
$987$	3.00000			0.0954911
$988$	−6.00000	−	20.7846i	−0.190885	−	0.661247i
$989$	−40.0000			−1.27193
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$		0			0
$993$	27.0000			0.856819
$994$	4.00000	+	6.92820i	0.126872	+	0.219749i
$995$	−6.00000	−	10.3923i	−0.190213	−	0.329458i
$996$	7.00000			0.221803
$997$	19.5000	+	33.7750i	0.617571	+	1.06966i	0.989928	+	0.141575i	$0.0452166\pi$
$997$	19.5000	+	33.7750i	0.617571	+	1.06966i	−0.372356	+	0.928090i	$0.621450\pi$
$998$	−17.5000	+	30.3109i	−0.553953	+	0.959474i
$999$	−3.00000	+	5.19615i	−0.0949158	+	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	858.2.i.c.529.1	yes	2
13.3	even	3	inner	858.2.i.c.133.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
858.2.i.c.133.1	✓	2	13.3	even	3	inner
858.2.i.c.529.1	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:	\( N \)	\(=\)	\( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	858.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +1.00000 q^{14} +(1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +1.00000 q^{18} +(3.00000 + 5.19615i) q^{19} +(-1.50000 - 2.59808i) q^{20} -1.00000 q^{21} +(0.500000 + 0.866025i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +(1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-5.00000 + 8.66025i) q^{29} +(1.50000 + 2.59808i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +7.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.00000 - 5.19615i) q^{37} -6.00000 q^{38} +(-1.00000 - 3.46410i) q^{39} +3.00000 q^{40} +(-0.500000 + 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-5.00000 - 8.66025i) q^{43} -1.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +(2.00000 + 3.46410i) q^{46} -3.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.00000 + 3.46410i) q^{50} -7.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} +11.0000 q^{53} +(0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-0.500000 - 0.866025i) q^{56} +6.00000 q^{57} +(-5.00000 - 8.66025i) q^{58} +(4.00000 + 6.92820i) q^{59} -3.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(7.50000 - 7.79423i) q^{65} +1.00000 q^{66} +(-6.00000 + 10.3923i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-2.00000 - 3.46410i) q^{69} +3.00000 q^{70} +(4.00000 + 6.92820i) q^{71} +(-0.500000 - 0.866025i) q^{72} +16.0000 q^{73} +(3.00000 + 5.19615i) q^{74} +(2.00000 - 3.46410i) q^{75} +(3.00000 - 5.19615i) q^{76} -1.00000 q^{77} +(3.50000 + 0.866025i) q^{78} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} -7.00000 q^{83} +(0.500000 + 0.866025i) q^{84} +(-10.5000 - 18.1865i) q^{85} +10.0000 q^{86} +(5.00000 + 8.66025i) q^{87} +(0.500000 - 0.866025i) q^{88} +(6.00000 - 10.3923i) q^{89} +3.00000 q^{90} +(-3.50000 - 0.866025i) q^{91} -4.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(9.00000 + 15.5885i) q^{95} -1.00000 q^{96} +(-4.50000 - 7.79423i) q^{97} +(3.00000 + 5.19615i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 - q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{10} + q^{11} - 2 q^{12} + 5 q^{13} + 2 q^{14} + 3 q^{15} - q^{16} - 7 q^{17} + 2 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 4 q^{23} + q^{24} + 8 q^{25} + 2 q^{26} - 2 q^{27} - q^{28} - 10 q^{29} + 3 q^{30} - q^{32} - q^{33} + 14 q^{34} - 3 q^{35} - q^{36} + 6 q^{37} - 12 q^{38} - 2 q^{39} + 6 q^{40} - q^{41} + q^{42} - 10 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 6 q^{47} + q^{48} + 6 q^{49} - 4 q^{50} - 14 q^{51} - 7 q^{52} + 22 q^{53} + q^{54} + 3 q^{55} - q^{56} + 12 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} - 2 q^{61} - q^{63} + 2 q^{64} + 15 q^{65} + 2 q^{66} - 12 q^{67} - 7 q^{68} - 4 q^{69} + 6 q^{70} + 8 q^{71} - q^{72} + 32 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} - 2 q^{77} + 7 q^{78} - 3 q^{80} - q^{81} - q^{82} - 14 q^{83} + q^{84} - 21 q^{85} + 20 q^{86} + 10 q^{87} + q^{88} + 12 q^{89} + 6 q^{90} - 7 q^{91} - 8 q^{92} + 3 q^{94} + 18 q^{95} - 2 q^{96} - 9 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^10 + q^11 - 2 * q^12 + 5 * q^13 + 2 * q^14 + 3 * q^15 - q^16 - 7 * q^17 + 2 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 4 * q^23 + q^24 + 8 * q^25 + 2 * q^26 - 2 * q^27 - q^28 - 10 * q^29 + 3 * q^30 - q^32 - q^33 + 14 * q^34 - 3 * q^35 - q^36 + 6 * q^37 - 12 * q^38 - 2 * q^39 + 6 * q^40 - q^41 + q^42 - 10 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 6 * q^47 + q^48 + 6 * q^49 - 4 * q^50 - 14 * q^51 - 7 * q^52 + 22 * q^53 + q^54 + 3 * q^55 - q^56 + 12 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 - 2 * q^61 - q^63 + 2 * q^64 + 15 * q^65 + 2 * q^66 - 12 * q^67 - 7 * q^68 - 4 * q^69 + 6 * q^70 + 8 * q^71 - q^72 + 32 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 - 2 * q^77 + 7 * q^78 - 3 * q^80 - q^81 - q^82 - 14 * q^83 + q^84 - 21 * q^85 + 20 * q^86 + 10 * q^87 + q^88 + 12 * q^89 + 6 * q^90 - 7 * q^91 - 8 * q^92 + 3 * q^94 + 18 * q^95 - 2 * q^96 - 9 * q^97 + 6 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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