LMFDB - Embedded newform 930.2.i.f.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.f.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.500000 - 0.866025i) q^{21} +(-2.50000 + 4.33013i) q^{22} -4.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +3.00000 q^{29} +1.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +1.00000 q^{32} +5.00000 q^{33} +(1.00000 + 1.73205i) q^{34} -1.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.00000 + 3.46410i) q^{37} +(1.00000 + 1.73205i) q^{38} +4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{45} -4.00000 q^{46} +2.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.00000 - 1.73205i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +1.00000 q^{54} +(-2.50000 - 4.33013i) q^{55} +(0.500000 + 0.866025i) q^{56} +(1.00000 - 1.73205i) q^{57} +3.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +1.00000 q^{60} +(3.50000 - 4.33013i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +5.00000 q^{66} +(2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(2.00000 + 3.46410i) q^{69} -1.00000 q^{70} +(-4.00000 + 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(1.00000 + 1.73205i) q^{76} -5.00000 q^{77} +4.00000 q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(0.500000 - 0.866025i) q^{84} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-2.50000 + 4.33013i) q^{88} +18.0000 q^{89} +(-0.500000 - 0.866025i) q^{90} -4.00000 q^{91} -4.00000 q^{92} +(-5.50000 - 0.866025i) q^{93} +2.00000 q^{94} -2.00000 q^{95} +(-0.500000 - 0.866025i) q^{96} -1.00000 q^{97} +(3.00000 - 5.19615i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{10} - 5 q^{11} - q^{12} - 4 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - q^{20} + q^{21} - 5 q^{22} - 8 q^{23} - q^{24} - q^{25} - 4 q^{26} + 2 q^{27} + q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} + 10 q^{33} + 2 q^{34} - 2 q^{35} - q^{36} + 4 q^{37} + 2 q^{38} + 8 q^{39} - q^{40} - 4 q^{41} + q^{42} + 4 q^{43} - 5 q^{44} - q^{45} - 8 q^{46} + 4 q^{47} - q^{48} + 6 q^{49} - q^{50} + 2 q^{51} - 4 q^{52} - 3 q^{53} + 2 q^{54} - 5 q^{55} + q^{56} + 2 q^{57} + 6 q^{58} - 3 q^{59} + 2 q^{60} + 7 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{65} + 10 q^{66} + 4 q^{67} + 2 q^{68} + 4 q^{69} - 2 q^{70} - 8 q^{71} - q^{72} - 2 q^{73} + 4 q^{74} - q^{75} + 2 q^{76} - 10 q^{77} + 8 q^{78} - q^{80} - q^{81} - 4 q^{82} - 9 q^{83} + q^{84} - 4 q^{85} + 4 q^{86} - 3 q^{87} - 5 q^{88} + 36 q^{89} - q^{90} - 8 q^{91} - 8 q^{92} - 11 q^{93} + 4 q^{94} - 4 q^{95} - q^{96} - 2 q^{97} + 6 q^{98} - 5 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - q^9 - q^10 - 5 * q^11 - q^12 - 4 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 - q^18 + 2 * q^19 - q^20 + q^21 - 5 * q^22 - 8 * q^23 - q^24 - q^25 - 4 * q^26 + 2 * q^27 + q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 + 2 * q^32 + 10 * q^33 + 2 * q^34 - 2 * q^35 - q^36 + 4 * q^37 + 2 * q^38 + 8 * q^39 - q^40 - 4 * q^41 + q^42 + 4 * q^43 - 5 * q^44 - q^45 - 8 * q^46 + 4 * q^47 - q^48 + 6 * q^49 - q^50 + 2 * q^51 - 4 * q^52 - 3 * q^53 + 2 * q^54 - 5 * q^55 + q^56 + 2 * q^57 + 6 * q^58 - 3 * q^59 + 2 * q^60 + 7 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^65 + 10 * q^66 + 4 * q^67 + 2 * q^68 + 4 * q^69 - 2 * q^70 - 8 * q^71 - q^72 - 2 * q^73 + 4 * q^74 - q^75 + 2 * q^76 - 10 * q^77 + 8 * q^78 - q^80 - q^81 - 4 * q^82 - 9 * q^83 + q^84 - 4 * q^85 + 4 * q^86 - 3 * q^87 - 5 * q^88 + 36 * q^89 - q^90 - 8 * q^91 - 8 * q^92 - 11 * q^93 + 4 * q^94 - 4 * q^95 - q^96 - 2 * q^97 + 6 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.500000	−	0.866025i	0.109109	−	0.188982i
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$	1.00000			0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	1.00000			0.182574
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$32$	1.00000			0.176777
$33$	5.00000			0.870388
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	−1.00000			−0.169031
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	4.00000			0.640513
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	−0.978870	−	0.204483i	$-0.934449\pi$
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	0.666523	+	0.745485i	$0.267782\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−4.00000			−0.589768
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	1.00000			0.136083
$55$	−2.50000	−	4.33013i	−0.337100	−	0.583874i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	1.00000	−	1.73205i	0.132453	−	0.229416i
$58$	3.00000			0.393919
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	1.00000			0.129099
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$	3.50000	−	4.33013i	0.444500	−	0.549927i
$63$	−1.00000			−0.125988
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	5.00000			0.615457
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$	2.00000	+	3.46410i	0.240772	+	0.417029i
$70$	−1.00000			−0.119523
$71$	−4.00000	+	6.92820i	−0.474713	+	0.822226i	−0.999581	−	0.0289572i	$-0.990781\pi$
$71$	−4.00000	+	6.92820i	−0.474713	+	0.822226i	0.524868	+	0.851184i	$0.324115\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$	−5.00000			−0.569803
$78$	4.00000			0.452911
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$	0.500000	−	0.866025i	0.0545545	−	0.0944911i
$85$	−2.00000			−0.216930
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	18.0000			1.90800			0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000			1.90800			0.953998	+	0.299813i	$0.0969242\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−4.00000			−0.419314
$92$	−4.00000			−0.417029
$93$	−5.50000	−	0.866025i	−0.570323	−	0.0898027i
$94$	2.00000			0.206284
$95$	−2.00000			−0.205196
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$	−2.50000	−	4.33013i	−0.251259	−	0.435194i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.00000			−0.497519			−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000			−0.497519			−0.248759	+	0.968565i	$0.580023\pi$
$102$	1.00000	−	1.73205i	0.0990148	−	0.171499i
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	−0.716173	−	0.697923i	$-0.754108\pi$
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	0.962505	+	0.271263i	$0.0874412\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$	0.500000	+	0.866025i	0.0487950	+	0.0845154i
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	−0.904396	−	0.426694i	$-0.859678\pi$
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	0.0826699	−	0.996577i	$-0.473655\pi$
$108$	1.00000			0.0962250
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	2.00000	−	3.46410i	0.188144	−	0.325875i	−0.756487	−	0.654008i	$-0.773086\pi$
$113$	2.00000	−	3.46410i	0.188144	−	0.325875i	0.944632	+	0.328133i	$0.106419\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	3.00000			0.278543
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	−1.50000	−	2.59808i	−0.138086	−	0.239172i
$119$	−1.00000	+	1.73205i	−0.0916698	+	0.158777i
$120$	1.00000			0.0912871
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$	4.00000			0.360668
$124$	3.50000	−	4.33013i	0.314309	−	0.388857i
$125$	1.00000			0.0894427
$126$	−1.00000			−0.0890871
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	−0.945745	−	0.324910i	$-0.894666\pi$
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	0.191492	−	0.981494i	$-0.438667\pi$
$128$	1.00000			0.0883883
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$	5.00000			0.435194
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−7.00000	+	12.1244i	−0.598050	+	1.03585i	0.395058	+	0.918656i	$0.370724\pi$
$137$	−7.00000	+	12.1244i	−0.598050	+	1.03585i	−0.993109	+	0.117198i	$0.962609\pi$
$138$	2.00000	+	3.46410i	0.170251	+	0.294884i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$	−1.00000			−0.0845154
$141$	−1.00000	−	1.73205i	−0.0842152	−	0.145865i
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	−10.0000	−	17.3205i	−0.836242	−	1.44841i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.50000	+	2.59808i	−0.124568	+	0.215758i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	−6.00000			−0.494872
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	5.50000	+	9.52628i	0.450578	+	0.780423i	0.998422	−	0.0561570i	$-0.0178847\pi$
$149$	5.50000	+	9.52628i	0.450578	+	0.780423i	−0.547844	+	0.836580i	$0.684551\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	−2.00000			−0.161690
$154$	−5.00000			−0.402911
$155$	2.00000	+	5.19615i	0.160644	+	0.417365i
$156$	4.00000			0.320256
$157$	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
$159$	3.00000			0.237915
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−2.00000	−	3.46410i	−0.157622	−	0.273009i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−8.00000			−0.626608			−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000			−0.626608			−0.313304	+	0.949653i	$0.601436\pi$
$164$	−2.00000	+	3.46410i	−0.156174	+	0.270501i
$165$	−2.50000	+	4.33013i	−0.194625	+	0.337100i
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−8.00000	−	13.8564i	−0.619059	−	1.07224i	−0.989658	−	0.143448i	$-0.954181\pi$
$167$	−8.00000	−	13.8564i	−0.619059	−	1.07224i	0.370599	−	0.928793i	$-0.379152\pi$
$168$	0.500000	−	0.866025i	0.0385758	−	0.0668153i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−2.00000			−0.153393
$171$	−2.00000			−0.152944
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$	−1.50000	−	2.59808i	−0.113715	−	0.196960i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−2.50000	+	4.33013i	−0.188445	+	0.326396i
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$	18.0000			1.34916
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	11.0000	−	19.0526i	0.817624	−	1.41617i	−0.0898051	−	0.995959i	$-0.528624\pi$
$181$	11.0000	−	19.0526i	0.817624	−	1.41617i	0.907429	−	0.420206i	$-0.138042\pi$
$182$	−4.00000			−0.296500
$183$		0			0
$184$	−4.00000			−0.294884
$185$	−4.00000			−0.294086
$186$	−5.50000	−	0.866025i	−0.403280	−	0.0635001i
$187$	−10.0000			−0.731272
$188$	2.00000			0.145865
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−2.00000			−0.145095
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$	−1.00000			−0.0717958
$195$	−2.00000	+	3.46410i	−0.143223	+	0.248069i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−13.0000	+	22.5167i	−0.926212	+	1.60425i	−0.136611	+	0.990625i	$0.543621\pi$
$197$	−13.0000	+	22.5167i	−0.926212	+	1.60425i	−0.789601	+	0.613621i	$0.789712\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	2.50000	−	4.33013i	0.177220	−	0.306955i	−0.763707	−	0.645563i	$-0.776623\pi$
$199$	2.50000	−	4.33013i	0.177220	−	0.306955i	0.940927	+	0.338608i	$0.109956\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−4.00000			−0.282138
$202$	−5.00000			−0.351799
$203$	1.50000	+	2.59808i	0.105279	+	0.182349i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	−2.00000	−	3.46410i	−0.139686	−	0.241943i
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	−10.0000			−0.691714
$210$	0.500000	+	0.866025i	0.0345033	+	0.0597614i
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	−0.944237	−	0.329266i	$-0.893199\pi$
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	0.186966	−	0.982366i	$-0.440135\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$	8.00000			0.548151
$214$	−8.50000	−	14.7224i	−0.581048	−	1.00640i
$215$	−4.00000			−0.272798
$216$	1.00000			0.0680414
$217$	5.50000	+	0.866025i	0.373364	+	0.0587896i
$218$	14.0000			0.948200
$219$	2.00000			0.135147
$220$	−2.50000	−	4.33013i	−0.168550	−	0.291937i
$221$	−8.00000			−0.538138
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	0.811422	−	0.584461i	$-0.198694\pi$
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	−0.911869	+	0.410481i	$0.865361\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	1.00000			0.0666667
$226$	2.00000	−	3.46410i	0.133038	−	0.230429i
$227$	−2.50000	+	4.33013i	−0.165931	+	0.287401i	−0.936985	−	0.349368i	$-0.886396\pi$
$227$	−2.50000	+	4.33013i	−0.165931	+	0.287401i	0.771055	+	0.636769i	$0.219730\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	14.0000	+	24.2487i	0.925146	+	1.60240i	0.791326	+	0.611394i	$0.209391\pi$
$229$	14.0000	+	24.2487i	0.925146	+	1.60240i	0.133820	+	0.991006i	$0.457276\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$	2.50000	+	4.33013i	0.164488	+	0.284901i
$232$	3.00000			0.196960
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	−1.00000	+	1.73205i	−0.0652328	+	0.112987i
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$	−1.00000	+	1.73205i	−0.0648204	+	0.112272i
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	−0.157893	−	0.987456i	$-0.550470\pi$
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	0.934109	−	0.356988i	$-0.116196\pi$
$240$	1.00000			0.0645497
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	−7.00000	−	12.1244i	−0.449977	−	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$	4.00000			0.255031
$247$	−8.00000			−0.509028
$248$	3.50000	−	4.33013i	0.222250	−	0.274963i
$249$	9.00000			0.570352
$250$	1.00000			0.0632456
$251$	14.0000	+	24.2487i	0.883672	+	1.53057i	0.847228	+	0.531229i	$0.178270\pi$
$251$	14.0000	+	24.2487i	0.883672	+	1.53057i	0.0364441	+	0.999336i	$0.488397\pi$
$252$	−1.00000			−0.0629941
$253$	10.0000	−	17.3205i	0.628695	−	1.08893i
$254$	−8.50000	−	14.7224i	−0.533337	−	0.923768i
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$	1.00000			0.0625000
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	2.00000	−	3.46410i	0.124515	−	0.215666i
$259$	−2.00000	+	3.46410i	−0.124274	+	0.215249i
$260$	−2.00000	−	3.46410i	−0.124035	−	0.214834i
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	−14.0000			−0.863277			−0.431638	−	0.902047i	$-0.642064\pi$
$263$	−14.0000			−0.863277			−0.431638	+	0.902047i	$0.642064\pi$
$264$	5.00000			0.307729
$265$	−1.50000	−	2.59808i	−0.0921443	−	0.159599i
$266$	−1.00000	+	1.73205i	−0.0613139	+	0.106199i
$267$	−9.00000	−	15.5885i	−0.550791	−	0.953998i
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	−0.977229	−	0.212187i	$-0.931941\pi$
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	0.672374	+	0.740212i	$0.265275\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	15.0000			0.911185			0.455593	−	0.890188i	$-0.349427\pi$
$271$	15.0000			0.911185			0.455593	+	0.890188i	$0.349427\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$	2.00000	+	3.46410i	0.121046	+	0.209657i
$274$	−7.00000	+	12.1244i	−0.422885	+	0.732459i
$275$	5.00000			0.301511
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	18.0000			1.08152			0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000			1.08152			0.540758	+	0.841178i	$0.318138\pi$
$278$	10.0000			0.599760
$279$	2.00000	+	5.19615i	0.119737	+	0.311086i
$280$	−1.00000			−0.0597614
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	−1.00000	−	1.73205i	−0.0595491	−	0.103142i
$283$	12.0000			0.713326			0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000			0.713326			0.356663	+	0.934233i	$0.383914\pi$
$284$	−4.00000	+	6.92820i	−0.237356	+	0.411113i
$285$	1.00000	+	1.73205i	0.0592349	+	0.102598i
$286$	−10.0000	−	17.3205i	−0.591312	−	1.02418i
$287$	−4.00000			−0.236113
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$	0.500000	+	0.866025i	0.0293105	+	0.0507673i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−9.50000	−	16.4545i	−0.554996	−	0.961281i	−0.997904	−	0.0647140i	$-0.979386\pi$
$293$	−9.50000	−	16.4545i	−0.554996	−	0.961281i	0.442908	−	0.896567i	$-0.353947\pi$
$294$	−6.00000			−0.349927
$295$	3.00000			0.174667
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−2.50000	+	4.33013i	−0.145065	+	0.251259i
$298$	5.50000	+	9.52628i	0.318606	+	0.551843i
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$	−5.00000			−0.287718
$303$	2.50000	+	4.33013i	0.143621	+	0.248759i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$		0			0
$306$	−2.00000			−0.114332
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	0.836077	−	0.548612i	$-0.184843\pi$
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	−0.893150	+	0.449758i	$0.851510\pi$
$308$	−5.00000			−0.284901
$309$	−5.00000			−0.284440
$310$	2.00000	+	5.19615i	0.113592	+	0.295122i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$	4.00000			0.226455
$313$	17.5000	+	30.3109i	0.989158	+	1.71327i	0.621757	+	0.783210i	$0.286419\pi$
$313$	17.5000	+	30.3109i	0.989158	+	1.71327i	0.367402	+	0.930062i	$0.380247\pi$
$314$	8.00000			0.451466
$315$	0.500000	−	0.866025i	0.0281718	−	0.0487950i
$316$		0			0
$317$	0.500000	+	0.866025i	0.0280828	+	0.0486408i	0.879725	−	0.475482i	$-0.157726\pi$
$317$	0.500000	+	0.866025i	0.0280828	+	0.0486408i	−0.851642	+	0.524123i	$0.824393\pi$
$318$	3.00000			0.168232
$319$	−7.50000	+	12.9904i	−0.419919	+	0.727322i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−8.50000	+	14.7224i	−0.474424	+	0.821726i
$322$	−2.00000	−	3.46410i	−0.111456	−	0.193047i
$323$	−2.00000	+	3.46410i	−0.111283	+	0.192748i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	4.00000			0.221880
$326$	−8.00000			−0.443079
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$	−2.00000	+	3.46410i	−0.110432	+	0.191273i
$329$	1.00000	+	1.73205i	0.0551318	+	0.0954911i
$330$	−2.50000	+	4.33013i	−0.137620	+	0.238366i
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	−4.00000			−0.219199
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	−3.00000			−0.163420			−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000			−0.163420			−0.0817102	+	0.996656i	$0.526038\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−4.00000			−0.217250
$340$	−2.00000			−0.108465
$341$	10.0000	+	25.9808i	0.541530	+	1.40694i
$342$	−2.00000			−0.108148
$343$	13.0000			0.701934
$344$	2.00000	+	3.46410i	0.107833	+	0.186772i
$345$	−4.00000			−0.215353
$346$	1.50000	−	2.59808i	0.0806405	−	0.139673i
$347$	0.500000	+	0.866025i	0.0268414	+	0.0464907i	0.879134	−	0.476575i	$-0.158122\pi$
$347$	0.500000	+	0.866025i	0.0268414	+	0.0464907i	−0.852293	+	0.523065i	$0.824788\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$	0.500000	−	0.866025i	0.0267261	−	0.0462910i
$351$	−2.00000	+	3.46410i	−0.106752	+	0.184900i
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	0.989960	−	0.141344i	$-0.0451425\pi$
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	−0.617388	+	0.786659i	$0.711809\pi$
$354$	−1.50000	+	2.59808i	−0.0797241	+	0.138086i
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	18.0000			0.953998
$357$	2.00000			0.105851
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	11.0000	−	19.0526i	0.578147	−	1.00138i
$363$	−7.00000	+	12.1244i	−0.367405	+	0.636364i
$364$	−4.00000			−0.209657
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$		0			0
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	−4.00000			−0.208514
$369$	−2.00000	−	3.46410i	−0.104116	−	0.180334i
$370$	−4.00000			−0.207950
$371$	−3.00000			−0.155752
$372$	−5.50000	−	0.866025i	−0.285162	−	0.0449013i
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$	−10.0000			−0.517088
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	2.00000			0.103142
$377$	−6.00000	+	10.3923i	−0.309016	+	0.535231i
$378$	0.500000	+	0.866025i	0.0257172	+	0.0445435i
$379$	−1.00000	−	1.73205i	−0.0513665	−	0.0889695i	0.839199	−	0.543825i	$-0.183024\pi$
$379$	−1.00000	−	1.73205i	−0.0513665	−	0.0889695i	−0.890565	+	0.454855i	$0.849691\pi$
$380$	−2.00000			−0.102598
$381$	−8.50000	+	14.7224i	−0.435468	+	0.754253i
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	−0.500000	−	0.866025i	−0.0254493	−	0.0440795i
$387$	−4.00000			−0.203331
$388$	−1.00000			−0.0507673
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$	−2.00000	+	3.46410i	−0.101274	+	0.175412i
$391$	−4.00000	−	6.92820i	−0.202289	−	0.350374i
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	−2.00000	+	3.46410i	−0.100887	+	0.174741i
$394$	−13.0000	+	22.5167i	−0.654931	+	1.13437i
$395$		0			0
$396$	−2.50000	−	4.33013i	−0.125630	−	0.217597i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	2.50000	−	4.33013i	0.125314	−	0.217050i
$399$	2.00000			0.100125
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$	−4.00000			−0.199502
$403$	8.00000	+	20.7846i	0.398508	+	1.03536i
$404$	−5.00000			−0.248759
$405$	1.00000			0.0496904
$406$	1.50000	+	2.59808i	0.0744438	+	0.128940i
$407$	−20.0000			−0.991363
$408$	1.00000	−	1.73205i	0.0495074	−	0.0857493i
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	0.995968	−	0.0897044i	$-0.0285922\pi$
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	−0.575670	+	0.817682i	$0.695259\pi$
$410$	−2.00000	−	3.46410i	−0.0987730	−	0.171080i
$411$	14.0000			0.690569
$412$	2.50000	−	4.33013i	0.123166	−	0.213330i
$413$	1.50000	−	2.59808i	0.0738102	−	0.127843i
$414$	2.00000	−	3.46410i	0.0982946	−	0.170251i
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	−5.00000	−	8.66025i	−0.244851	−	0.424094i
$418$	−10.0000			−0.489116
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$	0.500000	+	0.866025i	0.0243975	+	0.0422577i
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	−0.999895	−	0.0145228i	$-0.995377\pi$
$421$	−10.0000	+	17.3205i	−0.487370	+	0.844150i	0.512524	+	0.858673i	$0.328710\pi$
$422$	−11.0000	−	19.0526i	−0.535472	−	0.927464i
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	8.00000			0.387601
$427$		0			0
$428$	−8.50000	−	14.7224i	−0.410863	−	0.711636i
$429$	−10.0000	+	17.3205i	−0.482805	+	0.836242i
$430$	−4.00000			−0.192897
$431$	11.0000	+	19.0526i	0.529851	+	0.917729i	0.999394	+	0.0348195i	$0.0110856\pi$
$431$	11.0000	+	19.0526i	0.529851	+	0.917729i	−0.469542	+	0.882910i	$0.655581\pi$
$432$	1.00000			0.0481125
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$	5.50000	+	0.866025i	0.264008	+	0.0415705i
$435$	3.00000			0.143839
$436$	14.0000			0.670478
$437$	−4.00000	−	6.92820i	−0.191346	−	0.331421i
$438$	2.00000			0.0955637
$439$	4.50000	−	7.79423i	0.214773	−	0.371998i	−0.738429	−	0.674331i	$-0.764432\pi$
$439$	4.50000	−	7.79423i	0.214773	−	0.371998i	0.953202	+	0.302333i	$0.0977654\pi$
$440$	−2.50000	−	4.33013i	−0.119183	−	0.206431i
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$	−8.00000			−0.380521
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	−0.909618	−	0.415445i	$-0.863626\pi$
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	0.814595	+	0.580030i	$0.196959\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−1.50000	−	2.59808i	−0.0710271	−	0.123022i
$447$	5.50000	−	9.52628i	0.260141	−	0.450578i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$	1.00000			0.0471405
$451$	−10.0000	−	17.3205i	−0.470882	−	0.815591i
$452$	2.00000	−	3.46410i	0.0940721	−	0.162938i
$453$	2.50000	+	4.33013i	0.117460	+	0.203447i
$454$	−2.50000	+	4.33013i	−0.117331	+	0.203223i
$455$	2.00000	−	3.46410i	0.0937614	−	0.162400i
$456$	1.00000	−	1.73205i	0.0468293	−	0.0811107i
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	14.0000	+	24.2487i	0.654177	+	1.13307i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$	21.0000			0.978068			0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000			0.978068			0.489034	+	0.872265i	$0.337349\pi$
$462$	2.50000	+	4.33013i	0.116311	+	0.201456i
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	3.00000			0.139272
$465$	3.50000	−	4.33013i	0.162309	−	0.200805i
$466$	4.00000			0.185296
$467$	33.0000			1.52706			0.763529	−	0.645774i	$-0.223465\pi$
$467$	33.0000			1.52706			0.763529	+	0.645774i	$0.223465\pi$
$468$	−2.00000	−	3.46410i	−0.0924500	−	0.160128i
$469$	4.00000			0.184703
$470$	−1.00000	+	1.73205i	−0.0461266	+	0.0798935i
$471$	−4.00000	−	6.92820i	−0.184310	−	0.319235i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	−20.0000			−0.919601
$474$		0			0
$475$	1.00000	−	1.73205i	0.0458831	−	0.0794719i
$476$	−1.00000	+	1.73205i	−0.0458349	+	0.0793884i
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	12.0000	−	20.7846i	0.548867	−	0.950666i
$479$	−7.00000	−	12.1244i	−0.319838	−	0.553976i	0.660616	−	0.750724i	$-0.270295\pi$
$479$	−7.00000	−	12.1244i	−0.319838	−	0.553976i	−0.980454	+	0.196748i	$0.936962\pi$
$480$	1.00000			0.0456435
$481$	−16.0000			−0.729537
$482$	−3.50000	−	6.06218i	−0.159421	−	0.276125i
$483$	−2.00000	+	3.46410i	−0.0910032	+	0.157622i
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	0.500000	−	0.866025i	0.0227038	−	0.0393242i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−21.5000	+	37.2391i	−0.974258	+	1.68746i	−0.291896	+	0.956450i	$0.594286\pi$
$487$	−21.5000	+	37.2391i	−0.974258	+	1.68746i	−0.682362	+	0.731014i	$0.739047\pi$
$488$		0			0
$489$	4.00000	+	6.92820i	0.180886	+	0.313304i
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$	4.00000			0.180334
$493$	3.00000	+	5.19615i	0.135113	+	0.234023i
$494$	−8.00000			−0.359937
$495$	5.00000			0.224733
$496$	3.50000	−	4.33013i	0.157155	−	0.194428i
$497$	−8.00000			−0.358849
$498$	9.00000			0.403300
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$	1.00000			0.0447214
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	14.0000	+	24.2487i	0.624851	+	1.08227i
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	−0.917912	−	0.396783i	$-0.870127\pi$
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	0.115332	−	0.993327i	$-0.463207\pi$
$504$	−1.00000			−0.0445435
$505$	2.50000	−	4.33013i	0.111249	−	0.192688i
$506$	10.0000	−	17.3205i	0.444554	−	0.769991i
$507$	−1.50000	+	2.59808i	−0.0666173	+	0.115385i
$508$	−8.50000	−	14.7224i	−0.377127	−	0.653202i
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	−0.748894	−	0.662690i	$-0.769415\pi$
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	0.948353	+	0.317217i	$0.102748\pi$
$510$	1.00000	+	1.73205i	0.0442807	+	0.0766965i
$511$	−2.00000			−0.0884748
$512$	1.00000			0.0441942
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$	2.50000	+	4.33013i	0.110163	+	0.190808i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−5.00000	+	8.66025i	−0.219900	+	0.380878i
$518$	−2.00000	+	3.46410i	−0.0878750	+	0.152204i
$519$	−3.00000			−0.131685
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	14.0000	+	24.2487i	0.613351	+	1.06236i	0.990671	+	0.136272i	$0.0435123\pi$
$521$	14.0000	+	24.2487i	0.613351	+	1.06236i	−0.377320	+	0.926083i	$0.623154\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−24.0000			−1.04945			−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000			−1.04945			−0.524723	+	0.851273i	$0.675831\pi$
$524$	−2.00000	−	3.46410i	−0.0873704	−	0.151330i
$525$	−1.00000			−0.0436436
$526$	−14.0000			−0.610429
$527$	11.0000	+	1.73205i	0.479168	+	0.0754493i
$528$	5.00000			0.217597
$529$	−7.00000			−0.304348
$530$	−1.50000	−	2.59808i	−0.0651558	−	0.112853i
$531$	3.00000			0.130189
$532$	−1.00000	+	1.73205i	−0.0433555	+	0.0750939i
$533$	−8.00000	−	13.8564i	−0.346518	−	0.600188i
$534$	−9.00000	−	15.5885i	−0.389468	−	0.674579i
$535$	17.0000			0.734974
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$	4.50000	−	7.79423i	0.194189	−	0.336346i
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	15.0000	+	25.9808i	0.646096	+	1.11907i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	−0.972518	−	0.232828i	$-0.925202\pi$
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	0.284624	−	0.958639i	$-0.408131\pi$
$542$	15.0000			0.644305
$543$	−22.0000			−0.944110
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	−7.00000	+	12.1244i	−0.299847	+	0.519350i
$546$	2.00000	+	3.46410i	0.0855921	+	0.148250i
$547$	−21.0000	+	36.3731i	−0.897895	+	1.55520i	−0.0677151	+	0.997705i	$0.521571\pi$
$547$	−21.0000	+	36.3731i	−0.897895	+	1.55520i	−0.830180	+	0.557495i	$0.811762\pi$
$548$	−7.00000	+	12.1244i	−0.299025	+	0.517927i
$549$		0			0
$550$	5.00000			0.213201
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$	2.00000	+	3.46410i	0.0851257	+	0.147442i
$553$		0			0
$554$	18.0000			0.764747
$555$	2.00000	+	3.46410i	0.0848953	+	0.147043i
$556$	10.0000			0.424094
$557$	13.0000			0.550828			0.275414	−	0.961326i	$-0.411185\pi$
$557$	13.0000			0.550828			0.275414	+	0.961326i	$0.411185\pi$
$558$	2.00000	+	5.19615i	0.0846668	+	0.219971i
$559$	−16.0000			−0.676728
$560$	−1.00000			−0.0422577
$561$	5.00000	+	8.66025i	0.211100	+	0.365636i
$562$	−10.0000			−0.421825
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$	−1.00000	−	1.73205i	−0.0421076	−	0.0729325i
$565$	2.00000	+	3.46410i	0.0841406	+	0.145736i
$566$	12.0000			0.504398
$567$	0.500000	−	0.866025i	0.0209980	−	0.0363696i
$568$	−4.00000	+	6.92820i	−0.167836	+	0.290701i
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$	−10.0000	−	17.3205i	−0.418121	−	0.724207i
$573$	−8.00000			−0.334205
$574$	−4.00000			−0.166957
$575$	2.00000	+	3.46410i	0.0834058	+	0.144463i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	0.990278	−	0.139100i	$-0.0444210\pi$
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	−0.615603	+	0.788056i	$0.711088\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	−0.500000	+	0.866025i	−0.0207793	+	0.0359908i
$580$	−1.50000	+	2.59808i	−0.0622841	+	0.107879i
$581$	−9.00000			−0.373383
$582$	0.500000	+	0.866025i	0.0207257	+	0.0358979i
$583$	−7.50000	−	12.9904i	−0.310618	−	0.538007i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	4.00000			0.165380
$586$	−9.50000	−	16.4545i	−0.392441	−	0.679728i
$587$	27.0000			1.11441			0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000			1.11441			0.557205	+	0.830375i	$0.311874\pi$
$588$	−6.00000			−0.247436
$589$	11.0000	+	1.73205i	0.453247	+	0.0713679i
$590$	3.00000			0.123508
$591$	26.0000			1.06950
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	22.0000			0.903432			0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$	−2.50000	+	4.33013i	−0.102576	+	0.177667i
$595$	−1.00000	−	1.73205i	−0.0409960	−	0.0710072i
$596$	5.50000	+	9.52628i	0.225289	+	0.390212i
$597$	−5.00000			−0.204636
$598$	8.00000	−	13.8564i	0.327144	−	0.566631i
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	−0.219061	−	0.975711i	$-0.570299\pi$
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	0.954521	−	0.298143i	$-0.0963673\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	21.0000	+	36.3731i	0.856608	+	1.48369i	0.875145	+	0.483860i	$0.160766\pi$
$601$	21.0000	+	36.3731i	0.856608	+	1.48369i	−0.0185374	+	0.999828i	$0.505901\pi$
$602$	−2.00000	+	3.46410i	−0.0815139	+	0.141186i
$603$	2.00000	+	3.46410i	0.0814463	+	0.141069i
$604$	−5.00000			−0.203447
$605$	14.0000			0.569181
$606$	2.50000	+	4.33013i	0.101556	+	0.175899i
$607$	−24.0000	+	41.5692i	−0.974130	+	1.68724i	−0.291353	+	0.956616i	$0.594105\pi$
$607$	−24.0000	+	41.5692i	−0.974130	+	1.68724i	−0.682777	+	0.730627i	$0.739228\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	1.50000	−	2.59808i	0.0607831	−	0.105279i
$610$		0			0
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$	−2.00000			−0.0808452
$613$	−12.0000	−	20.7846i	−0.484675	−	0.839482i	0.515170	−	0.857088i	$-0.327729\pi$
$613$	−12.0000	−	20.7846i	−0.484675	−	0.839482i	−0.999845	+	0.0176058i	$0.994396\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$	−2.00000	+	3.46410i	−0.0806478	+	0.139686i
$616$	−5.00000			−0.201456
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	0.719605	−	0.694383i	$-0.244323\pi$
$617$	−6.00000	−	10.3923i	−0.241551	−	0.418378i	−0.961156	+	0.276005i	$0.910989\pi$
$618$	−5.00000			−0.201129
$619$	−34.0000			−1.36658			−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000			−1.36658			−0.683288	+	0.730149i	$0.739451\pi$
$620$	2.00000	+	5.19615i	0.0803219	+	0.208683i
$621$	−4.00000			−0.160514
$622$	20.0000			0.801927
$623$	9.00000	+	15.5885i	0.360577	+	0.624538i
$624$	4.00000			0.160128
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.5000	+	30.3109i	0.699441	+	1.21147i
$627$	5.00000	+	8.66025i	0.199681	+	0.345857i
$628$	8.00000			0.319235
$629$	−4.00000	+	6.92820i	−0.159490	+	0.276246i
$630$	0.500000	−	0.866025i	0.0199205	−	0.0345033i
$631$	−5.50000	+	9.52628i	−0.218952	+	0.379235i	−0.954488	−	0.298250i	$-0.903597\pi$
$631$	−5.50000	+	9.52628i	−0.218952	+	0.379235i	0.735536	+	0.677485i	$0.236930\pi$
$632$		0			0
$633$	−11.0000	+	19.0526i	−0.437211	+	0.757271i
$634$	0.500000	+	0.866025i	0.0198575	+	0.0343943i
$635$	17.0000			0.674624
$636$	3.00000			0.118958
$637$	12.0000	+	20.7846i	0.475457	+	0.823516i
$638$	−7.50000	+	12.9904i	−0.296928	+	0.514294i
$639$	−4.00000	−	6.92820i	−0.158238	−	0.274075i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	0.722862	+	0.690992i	$0.242826\pi$
$642$	−8.50000	+	14.7224i	−0.335468	+	0.581048i
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$	−2.00000	−	3.46410i	−0.0788110	−	0.136505i
$645$	2.00000	+	3.46410i	0.0787499	+	0.136399i
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	15.0000			0.588802
$650$	4.00000			0.156893
$651$	−2.00000	−	5.19615i	−0.0783862	−	0.203653i
$652$	−8.00000			−0.313304
$653$	21.0000			0.821794			0.410897	−	0.911682i	$-0.365216\pi$
$653$	21.0000			0.821794			0.410897	+	0.911682i	$0.365216\pi$
$654$	−7.00000	−	12.1244i	−0.273722	−	0.474100i
$655$	4.00000			0.156293
$656$	−2.00000	+	3.46410i	−0.0780869	+	0.135250i
$657$	−1.00000	−	1.73205i	−0.0390137	−	0.0675737i
$658$	1.00000	+	1.73205i	0.0389841	+	0.0675224i
$659$	15.0000			0.584317			0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000			0.584317			0.292159	+	0.956370i	$0.405627\pi$
$660$	−2.50000	+	4.33013i	−0.0973124	+	0.168550i
$661$	18.0000	−	31.1769i	0.700119	−	1.21264i	−0.268306	−	0.963334i	$-0.586464\pi$
$661$	18.0000	−	31.1769i	0.700119	−	1.21264i	0.968424	−	0.249308i	$-0.0802030\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$	4.00000	+	6.92820i	0.155347	+	0.269069i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	−1.00000	−	1.73205i	−0.0387783	−	0.0671660i
$666$	−4.00000			−0.154997
$667$	−12.0000			−0.464642
$668$	−8.00000	−	13.8564i	−0.309529	−	0.536120i
$669$	−1.50000	+	2.59808i	−0.0579934	+	0.100447i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$		0			0
$672$	0.500000	−	0.866025i	0.0192879	−	0.0334077i
$673$	−16.5000	+	28.5788i	−0.636028	+	1.10163i	0.350268	+	0.936650i	$0.386091\pi$
$673$	−16.5000	+	28.5788i	−0.636028	+	1.10163i	−0.986296	+	0.164984i	$0.947243\pi$
$674$	−3.00000			−0.115556
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	23.5000	−	40.7032i	0.903178	−	1.56435i	0.0798344	−	0.996808i	$-0.474561\pi$
$677$	23.5000	−	40.7032i	0.903178	−	1.56435i	0.823344	−	0.567543i	$-0.192106\pi$
$678$	−4.00000			−0.153619
$679$	−0.500000	−	0.866025i	−0.0191882	−	0.0332350i
$680$	−2.00000			−0.0766965
$681$	5.00000			0.191600
$682$	10.0000	+	25.9808i	0.382920	+	0.994855i
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$	−2.00000			−0.0764719
$685$	−7.00000	−	12.1244i	−0.267456	−	0.463248i
$686$	13.0000			0.496342
$687$	14.0000	−	24.2487i	0.534133	−	0.925146i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$	−4.00000			−0.152277
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	−0.945319	−	0.326146i	$-0.894250\pi$
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	0.755110	+	0.655598i	$0.227583\pi$
$692$	1.50000	−	2.59808i	0.0570214	−	0.0987640i
$693$	2.50000	−	4.33013i	0.0949671	−	0.164488i
$694$	0.500000	+	0.866025i	0.0189797	+	0.0328739i
$695$	−5.00000	+	8.66025i	−0.189661	+	0.328502i
$696$	−1.50000	−	2.59808i	−0.0568574	−	0.0984798i
$697$	−8.00000			−0.303022
$698$	34.0000			1.28692
$699$	−2.00000	−	3.46410i	−0.0756469	−	0.131024i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	4.50000	+	7.79423i	0.169963	+	0.294384i	0.938406	−	0.345533i	$-0.112302\pi$
$701$	4.50000	+	7.79423i	0.169963	+	0.294384i	−0.768444	+	0.639917i	$0.778969\pi$
$702$	−2.00000	+	3.46410i	−0.0754851	+	0.130744i
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	2.00000			0.0753244
$706$	7.00000	+	12.1244i	0.263448	+	0.456306i
$707$	−2.50000	−	4.33013i	−0.0940222	−	0.162851i
$708$	−1.50000	+	2.59808i	−0.0563735	+	0.0976417i
$709$	12.0000			0.450669			0.225335	−	0.974281i	$-0.427652\pi$
$709$	12.0000			0.450669			0.225335	+	0.974281i	$0.427652\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$		0			0
$712$	18.0000			0.674579
$713$	−14.0000	+	17.3205i	−0.524304	+	0.648658i
$714$	2.00000			0.0748481
$715$	20.0000			0.747958
$716$	4.50000	+	7.79423i	0.168173	+	0.291284i
$717$	−24.0000			−0.896296
$718$	−10.0000	+	17.3205i	−0.373197	+	0.646396i
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	−0.930087	−	0.367338i	$-0.880269\pi$
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	0.146920	−	0.989148i	$-0.453064\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	5.00000			0.186210
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	−3.50000	+	6.06218i	−0.130166	+	0.225455i
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$	−7.00000	+	12.1244i	−0.259794	+	0.449977i
$727$	13.5000	+	23.3827i	0.500687	+	0.867216i	1.00000		0.000793791i	$0.000252672\pi$
$727$	13.5000	+	23.3827i	0.500687	+	0.867216i	−0.499312	+	0.866422i	$0.666414\pi$
$728$	−4.00000			−0.148250
$729$	1.00000			0.0370370
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	12.0000	−	20.7846i	0.442928	−	0.767174i
$735$	3.00000	−	5.19615i	0.110657	−	0.191663i
$736$	−4.00000			−0.147442
$737$	10.0000	+	17.3205i	0.368355	+	0.638009i
$738$	−2.00000	−	3.46410i	−0.0736210	−	0.127515i
$739$	−21.0000	+	36.3731i	−0.772497	+	1.33800i	0.163693	+	0.986511i	$0.447659\pi$
$739$	−21.0000	+	36.3731i	−0.772497	+	1.33800i	−0.936190	+	0.351494i	$0.885674\pi$
$740$	−4.00000			−0.147043
$741$	4.00000	+	6.92820i	0.146944	+	0.254514i
$742$	−3.00000			−0.110133
$743$	−46.0000			−1.68758			−0.843788	−	0.536676i	$-0.819680\pi$
$743$	−46.0000			−1.68758			−0.843788	+	0.536676i	$0.819680\pi$
$744$	−5.50000	−	0.866025i	−0.201640	−	0.0317500i
$745$	−11.0000			−0.403009
$746$	2.00000			0.0732252
$747$	−4.50000	−	7.79423i	−0.164646	−	0.285176i
$748$	−10.0000			−0.365636
$749$	8.50000	−	14.7224i	0.310583	−	0.537946i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$	2.00000			0.0729325
$753$	14.0000	−	24.2487i	0.510188	−	0.883672i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	2.50000	−	4.33013i	0.0909843	−	0.157589i
$756$	0.500000	+	0.866025i	0.0181848	+	0.0314970i
$757$	10.0000	−	17.3205i	0.363456	−	0.629525i	−0.625071	−	0.780568i	$-0.714930\pi$
$757$	10.0000	−	17.3205i	0.363456	−	0.629525i	0.988527	+	0.151043i	$0.0482633\pi$
$758$	−1.00000	−	1.73205i	−0.0363216	−	0.0629109i
$759$	−20.0000			−0.725954
$760$	−2.00000			−0.0725476
$761$	−25.0000	−	43.3013i	−0.906249	−	1.56967i	−0.819231	−	0.573463i	$-0.805600\pi$
$761$	−25.0000	−	43.3013i	−0.906249	−	1.56967i	−0.0870179	−	0.996207i	$-0.527734\pi$
$762$	−8.50000	+	14.7224i	−0.307923	+	0.533337i
$763$	7.00000	+	12.1244i	0.253417	+	0.438931i
$764$	4.00000	−	6.92820i	0.144715	−	0.250654i
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	14.0000	−	24.2487i	0.505841	−	0.876142i
$767$	12.0000			0.433295
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$	2.50000	−	4.33013i	0.0900937	−	0.156047i
$771$	12.0000			0.432169
$772$	−0.500000	−	0.866025i	−0.0179954	−	0.0311689i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	−4.00000			−0.143777
$775$	−5.50000	−	0.866025i	−0.197566	−	0.0311086i
$776$	−1.00000			−0.0358979
$777$	4.00000			0.143499
$778$	9.00000	+	15.5885i	0.322666	+	0.558873i
$779$	−8.00000			−0.286630
$780$	−2.00000	+	3.46410i	−0.0716115	+	0.124035i
$781$	−20.0000	−	34.6410i	−0.715656	−	1.23955i
$782$	−4.00000	−	6.92820i	−0.143040	−	0.247752i
$783$	3.00000			0.107211
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−4.00000	+	6.92820i	−0.142766	+	0.247278i
$786$	−2.00000	+	3.46410i	−0.0713376	+	0.123560i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−13.0000	+	22.5167i	−0.463106	+	0.802123i
$789$	7.00000	+	12.1244i	0.249207	+	0.431638i
$790$		0			0
$791$	4.00000			0.142224
$792$	−2.50000	−	4.33013i	−0.0888336	−	0.153864i
$793$		0			0
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	−1.50000	+	2.59808i	−0.0531995	+	0.0921443i
$796$	2.50000	−	4.33013i	0.0886102	−	0.153477i
$797$	−6.50000	+	11.2583i	−0.230242	+	0.398791i	−0.957879	−	0.287171i	$-0.907285\pi$
$797$	−6.50000	+	11.2583i	−0.230242	+	0.398791i	0.727637	+	0.685962i	$0.240618\pi$
$798$	2.00000			0.0707992
$799$	2.00000	+	3.46410i	0.0707549	+	0.122551i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$		0			0
$803$	−5.00000	−	8.66025i	−0.176446	−	0.305614i
$804$	−4.00000			−0.141069
$805$	4.00000			0.140981
$806$	8.00000	+	20.7846i	0.281788	+	0.732107i
$807$	10.0000			0.352017
$808$	−5.00000			−0.175899
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.746968	−	0.664860i	$-0.768491\pi$
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.202301	−	0.979323i	$-0.564842\pi$
$810$	1.00000			0.0351364
$811$	−3.00000	+	5.19615i	−0.105344	+	0.182462i	−0.913879	−	0.405987i	$-0.866928\pi$
$811$	−3.00000	+	5.19615i	−0.105344	+	0.182462i	0.808535	+	0.588449i	$0.200261\pi$
$812$	1.50000	+	2.59808i	0.0526397	+	0.0911746i
$813$	−7.50000	−	12.9904i	−0.263036	−	0.455593i
$814$	−20.0000			−0.701000
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	−4.00000	+	6.92820i	−0.139942	+	0.242387i
$818$	8.50000	+	14.7224i	0.297196	+	0.514758i
$819$	2.00000	−	3.46410i	0.0698857	−	0.121046i
$820$	−2.00000	−	3.46410i	−0.0698430	−	0.120972i
$821$	−45.0000			−1.57051			−0.785255	−	0.619172i	$-0.787468\pi$
$821$	−45.0000			−1.57051			−0.785255	+	0.619172i	$0.787468\pi$
$822$	14.0000			0.488306
$823$	5.50000	+	9.52628i	0.191718	+	0.332065i	0.945820	−	0.324692i	$-0.105261\pi$
$823$	5.50000	+	9.52628i	0.191718	+	0.332065i	−0.754102	+	0.656758i	$0.771927\pi$
$824$	2.50000	−	4.33013i	0.0870916	−	0.150847i
$825$	−2.50000	−	4.33013i	−0.0870388	−	0.150756i
$826$	1.50000	−	2.59808i	0.0521917	−	0.0903986i
$827$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$827$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$	−9.00000	−	15.5885i	−0.312207	−	0.540758i
$832$	−2.00000	+	3.46410i	−0.0693375	+	0.120096i
$833$	12.0000			0.415775
$834$	−5.00000	−	8.66025i	−0.173136	−	0.299880i
$835$	16.0000			0.553703
$836$	−10.0000			−0.345857
$837$	3.50000	−	4.33013i	0.120978	−	0.149671i
$838$	9.00000			0.310900
$839$	−26.0000			−0.897620			−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000			−0.897620			−0.448810	+	0.893627i	$0.648152\pi$
$840$	0.500000	+	0.866025i	0.0172516	+	0.0298807i
$841$	−20.0000			−0.689655
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$	5.00000	+	8.66025i	0.172209	+	0.298275i
$844$	−11.0000	−	19.0526i	−0.378636	−	0.655816i
$845$	3.00000			0.103203
$846$	−1.00000	+	1.73205i	−0.0343807	+	0.0595491i
$847$	7.00000	−	12.1244i	0.240523	−	0.416598i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$	−6.00000	−	10.3923i	−0.205919	−	0.356663i
$850$	1.00000	−	1.73205i	0.0342997	−	0.0594089i
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$	8.00000			0.274075
$853$	−12.0000			−0.410872			−0.205436	−	0.978671i	$-0.565861\pi$
$853$	−12.0000			−0.410872			−0.205436	+	0.978671i	$0.565861\pi$
$854$		0			0
$855$	1.00000	−	1.73205i	0.0341993	−	0.0592349i
$856$	−8.50000	−	14.7224i	−0.290524	−	0.503202i
$857$	14.0000	−	24.2487i	0.478231	−	0.828320i	−0.521458	−	0.853277i	$-0.674612\pi$
$857$	14.0000	−	24.2487i	0.478231	−	0.828320i	0.999689	+	0.0249570i	$0.00794488\pi$
$858$	−10.0000	+	17.3205i	−0.341394	+	0.591312i
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	−4.00000			−0.136399
$861$	2.00000	+	3.46410i	0.0681598	+	0.118056i
$862$	11.0000	+	19.0526i	0.374661	+	0.648933i
$863$	24.0000	−	41.5692i	0.816970	−	1.41503i	−0.0909355	−	0.995857i	$-0.528986\pi$
$863$	24.0000	−	41.5692i	0.816970	−	1.41503i	0.907905	−	0.419176i	$-0.137681\pi$
$864$	1.00000			0.0340207
$865$	1.50000	+	2.59808i	0.0510015	+	0.0883372i
$866$	−22.0000			−0.747590
$867$	−13.0000			−0.441503
$868$	5.50000	+	0.866025i	0.186682	+	0.0293948i
$869$		0			0
$870$	3.00000			0.101710
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$	14.0000			0.474100
$873$	0.500000	−	0.866025i	0.0169224	−	0.0293105i
$874$	−4.00000	−	6.92820i	−0.135302	−	0.234350i
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	2.00000			0.0675737
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	−0.301014	−	0.953620i	$-0.597325\pi$
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	0.976366	−	0.216124i	$-0.0693416\pi$
$878$	4.50000	−	7.79423i	0.151868	−	0.263042i
$879$	−9.50000	+	16.4545i	−0.320427	+	0.554996i
$880$	−2.50000	−	4.33013i	−0.0842750	−	0.145969i
$881$	10.0000	−	17.3205i	0.336909	−	0.583543i	−0.646941	−	0.762540i	$-0.723952\pi$
$881$	10.0000	−	17.3205i	0.336909	−	0.583543i	0.983850	+	0.178997i	$0.0572853\pi$
$882$	3.00000	+	5.19615i	0.101015	+	0.174964i
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$	−8.00000			−0.269069
$885$	−1.50000	−	2.59808i	−0.0504219	−	0.0873334i
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$	−19.0000	−	32.9090i	−0.637958	−	1.10497i	−0.985880	−	0.167452i	$-0.946446\pi$
$887$	−19.0000	−	32.9090i	−0.637958	−	1.10497i	0.347923	−	0.937523i	$-0.386887\pi$
$888$	2.00000	−	3.46410i	0.0671156	−	0.116248i
$889$	8.50000	−	14.7224i	0.285081	−	0.493775i
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$	5.00000			0.167506
$892$	−1.50000	−	2.59808i	−0.0502237	−	0.0869900i
$893$	2.00000	+	3.46410i	0.0669274	+	0.115922i
$894$	5.50000	−	9.52628i	0.183948	−	0.318606i
$895$	−9.00000			−0.300837
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−16.0000			−0.534224
$898$	−34.0000			−1.13459
$899$	10.5000	−	12.9904i	0.350195	−	0.433253i
$900$	1.00000			0.0333333
$901$	−6.00000			−0.199889
$902$	−10.0000	−	17.3205i	−0.332964	−	0.576710i
$903$	4.00000			0.133112
$904$	2.00000	−	3.46410i	0.0665190	−	0.115214i
$905$	11.0000	+	19.0526i	0.365652	+	0.633328i
$906$	2.50000	+	4.33013i	0.0830569	+	0.143859i
$907$	48.0000			1.59381			0.796907	−	0.604102i	$-0.206468\pi$
$907$	48.0000			1.59381			0.796907	+	0.604102i	$0.206468\pi$
$908$	−2.50000	+	4.33013i	−0.0829654	+	0.143700i
$909$	2.50000	−	4.33013i	0.0829198	−	0.143621i
$910$	2.00000	−	3.46410i	0.0662994	−	0.114834i
$911$	−11.0000	−	19.0526i	−0.364446	−	0.631239i	0.624241	−	0.781232i	$-0.285408\pi$
$911$	−11.0000	−	19.0526i	−0.364446	−	0.631239i	−0.988687	+	0.149992i	$0.952075\pi$
$912$	1.00000	−	1.73205i	0.0331133	−	0.0573539i
$913$	−22.5000	−	38.9711i	−0.744641	−	1.28976i
$914$	−18.0000			−0.595387
$915$		0			0
$916$	14.0000	+	24.2487i	0.462573	+	0.801200i
$917$	2.00000	−	3.46410i	0.0660458	−	0.114395i
$918$	1.00000	+	1.73205i	0.0330049	+	0.0571662i
$919$	21.5000	−	37.2391i	0.709220	−	1.22840i	−0.255927	−	0.966696i	$-0.582381\pi$
$919$	21.5000	−	37.2391i	0.709220	−	1.22840i	0.965147	−	0.261708i	$-0.0842858\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	−1.00000	+	1.73205i	−0.0329511	+	0.0570730i
$922$	21.0000			0.691598
$923$	−16.0000	−	27.7128i	−0.526646	−	0.912178i
$924$	2.50000	+	4.33013i	0.0822440	+	0.142451i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	5.00000			0.164310
$927$	2.50000	+	4.33013i	0.0821108	+	0.142220i
$928$	3.00000			0.0984798
$929$	42.0000			1.37798			0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000			1.37798			0.688988	+	0.724773i	$0.258055\pi$
$930$	3.50000	−	4.33013i	0.114770	−	0.141990i
$931$	12.0000			0.393284
$932$	4.00000			0.131024
$933$	−10.0000	−	17.3205i	−0.327385	−	0.567048i
$934$	33.0000			1.07979
$935$	5.00000	−	8.66025i	0.163517	−	0.283221i
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	5.00000	+	8.66025i	0.163343	+	0.282918i	0.936066	−	0.351826i	$-0.114439\pi$
$937$	5.00000	+	8.66025i	0.163343	+	0.282918i	−0.772723	+	0.634744i	$0.781106\pi$
$938$	4.00000			0.130605
$939$	17.5000	−	30.3109i	0.571091	−	0.989158i
$940$	−1.00000	+	1.73205i	−0.0326164	+	0.0564933i
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	−0.984858	−	0.173365i	$-0.944536\pi$
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	0.642567	+	0.766229i	$0.277869\pi$
$942$	−4.00000	−	6.92820i	−0.130327	−	0.225733i
$943$	8.00000	−	13.8564i	0.260516	−	0.451227i
$944$	−1.50000	−	2.59808i	−0.0488208	−	0.0845602i
$945$	−1.00000			−0.0325300
$946$	−20.0000			−0.650256
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	0.500000	−	0.866025i	0.0162136	−	0.0280828i
$952$	−1.00000	+	1.73205i	−0.0324102	+	0.0561361i
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$	−1.50000	−	2.59808i	−0.0485643	−	0.0841158i
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$	15.0000			0.484881
$958$	−7.00000	−	12.1244i	−0.226160	−	0.391720i
$959$	−14.0000			−0.452084
$960$	1.00000			0.0322749
$961$	−6.50000	−	30.3109i	−0.209677	−	0.977771i
$962$	−16.0000			−0.515861
$963$	17.0000			0.547817
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$	1.00000			0.0321911
$966$	−2.00000	+	3.46410i	−0.0643489	+	0.111456i
$967$	−28.0000	−	48.4974i	−0.900419	−	1.55957i	−0.826951	−	0.562274i	$-0.809926\pi$
$967$	−28.0000	−	48.4974i	−0.900419	−	1.55957i	−0.0734686	−	0.997298i	$-0.523407\pi$
$968$	−7.00000	−	12.1244i	−0.224989	−	0.389692i
$969$	4.00000			0.128499
$970$	0.500000	−	0.866025i	0.0160540	−	0.0278064i
$971$	−1.50000	+	2.59808i	−0.0481373	+	0.0833762i	−0.889090	−	0.457732i	$-0.848662\pi$
$971$	−1.50000	+	2.59808i	−0.0481373	+	0.0833762i	0.840953	+	0.541108i	$0.181995\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	5.00000	+	8.66025i	0.160293	+	0.277635i
$974$	−21.5000	+	37.2391i	−0.688904	+	1.19322i
$975$	−2.00000	−	3.46410i	−0.0640513	−	0.110940i
$976$		0			0
$977$	56.0000			1.79160			0.895799	−	0.444459i	$-0.146604\pi$
$977$	56.0000			1.79160			0.895799	+	0.444459i	$0.146604\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	−45.0000	+	77.9423i	−1.43821	+	2.49105i
$980$	3.00000	+	5.19615i	0.0958315	+	0.165985i
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	17.0000	−	29.4449i	0.542216	−	0.939145i	−0.456561	−	0.889692i	$-0.650919\pi$
$983$	17.0000	−	29.4449i	0.542216	−	0.939145i	0.998776	−	0.0494530i	$-0.0157478\pi$
$984$	4.00000			0.127515
$985$	−13.0000	−	22.5167i	−0.414214	−	0.717440i
$986$	3.00000	+	5.19615i	0.0955395	+	0.165479i
$987$	1.00000	−	1.73205i	0.0318304	−	0.0551318i
$988$	−8.00000			−0.254514
$989$	−8.00000	−	13.8564i	−0.254385	−	0.440608i
$990$	5.00000			0.158910
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$	3.50000	−	4.33013i	0.111125	−	0.137482i
$993$	4.00000			0.126936
$994$	−8.00000			−0.253745
$995$	2.50000	+	4.33013i	0.0792553	+	0.137274i
$996$	9.00000			0.285176
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	−0.755235	−	0.655454i	$-0.772477\pi$
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	0.945257	+	0.326326i	$0.105811\pi$
$998$	16.0000	+	27.7128i	0.506471	+	0.877234i
$999$	2.00000	+	3.46410i	0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.f.211.1	✓	2
31.5	even	3	inner	930.2.i.f.811.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.f.211.1	✓	2	1.1	even	1	trivial
930.2.i.f.811.1	yes	2	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.500000 - 0.866025i) q^{21} +(-2.50000 + 4.33013i) q^{22} -4.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +3.00000 q^{29} +1.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +1.00000 q^{32} +5.00000 q^{33} +(1.00000 + 1.73205i) q^{34} -1.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.00000 + 3.46410i) q^{37} +(1.00000 + 1.73205i) q^{38} +4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{45} -4.00000 q^{46} +2.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.00000 - 1.73205i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +1.00000 q^{54} +(-2.50000 - 4.33013i) q^{55} +(0.500000 + 0.866025i) q^{56} +(1.00000 - 1.73205i) q^{57} +3.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +1.00000 q^{60} +(3.50000 - 4.33013i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +5.00000 q^{66} +(2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(2.00000 + 3.46410i) q^{69} -1.00000 q^{70} +(-4.00000 + 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(1.00000 + 1.73205i) q^{76} -5.00000 q^{77} +4.00000 q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(0.500000 - 0.866025i) q^{84} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-2.50000 + 4.33013i) q^{88} +18.0000 q^{89} +(-0.500000 - 0.866025i) q^{90} -4.00000 q^{91} -4.00000 q^{92} +(-5.50000 - 0.866025i) q^{93} +2.00000 q^{94} -2.00000 q^{95} +(-0.500000 - 0.866025i) q^{96} -1.00000 q^{97} +(3.00000 - 5.19615i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{10} - 5 q^{11} - q^{12} - 4 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - q^{20} + q^{21} - 5 q^{22} - 8 q^{23} - q^{24} - q^{25} - 4 q^{26} + 2 q^{27} + q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} + 10 q^{33} + 2 q^{34} - 2 q^{35} - q^{36} + 4 q^{37} + 2 q^{38} + 8 q^{39} - q^{40} - 4 q^{41} + q^{42} + 4 q^{43} - 5 q^{44} - q^{45} - 8 q^{46} + 4 q^{47} - q^{48} + 6 q^{49} - q^{50} + 2 q^{51} - 4 q^{52} - 3 q^{53} + 2 q^{54} - 5 q^{55} + q^{56} + 2 q^{57} + 6 q^{58} - 3 q^{59} + 2 q^{60} + 7 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{65} + 10 q^{66} + 4 q^{67} + 2 q^{68} + 4 q^{69} - 2 q^{70} - 8 q^{71} - q^{72} - 2 q^{73} + 4 q^{74} - q^{75} + 2 q^{76} - 10 q^{77} + 8 q^{78} - q^{80} - q^{81} - 4 q^{82} - 9 q^{83} + q^{84} - 4 q^{85} + 4 q^{86} - 3 q^{87} - 5 q^{88} + 36 q^{89} - q^{90} - 8 q^{91} - 8 q^{92} - 11 q^{93} + 4 q^{94} - 4 q^{95} - q^{96} - 2 q^{97} + 6 q^{98} - 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - q^9 - q^10 - 5 * q^11 - q^12 - 4 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 - q^18 + 2 * q^19 - q^20 + q^21 - 5 * q^22 - 8 * q^23 - q^24 - q^25 - 4 * q^26 + 2 * q^27 + q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 + 2 * q^32 + 10 * q^33 + 2 * q^34 - 2 * q^35 - q^36 + 4 * q^37 + 2 * q^38 + 8 * q^39 - q^40 - 4 * q^41 + q^42 + 4 * q^43 - 5 * q^44 - q^45 - 8 * q^46 + 4 * q^47 - q^48 + 6 * q^49 - q^50 + 2 * q^51 - 4 * q^52 - 3 * q^53 + 2 * q^54 - 5 * q^55 + q^56 + 2 * q^57 + 6 * q^58 - 3 * q^59 + 2 * q^60 + 7 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^65 + 10 * q^66 + 4 * q^67 + 2 * q^68 + 4 * q^69 - 2 * q^70 - 8 * q^71 - q^72 - 2 * q^73 + 4 * q^74 - q^75 + 2 * q^76 - 10 * q^77 + 8 * q^78 - q^80 - q^81 - 4 * q^82 - 9 * q^83 + q^84 - 4 * q^85 + 4 * q^86 - 3 * q^87 - 5 * q^88 + 36 * q^89 - q^90 - 8 * q^91 - 8 * q^92 - 11 * q^93 + 4 * q^94 - 4 * q^95 - q^96 - 2 * q^97 + 6 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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