LMFDB - Embedded newform 630.2.i.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 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("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.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:	$5.03057532734$
Analytic rank:	$1$
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			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(2.00000 + 1.73205i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 + 4.33013i) q^{21} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.00000 - 3.46410i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +1.73205i q^{30} -2.00000 q^{31} -1.00000 q^{32} +(-6.00000 + 3.46410i) q^{33} +(2.00000 + 3.46410i) q^{34} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-5.00000 + 8.66025i) q^{37} +(1.00000 - 1.73205i) q^{38} +(6.00000 - 3.46410i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.00000 + 8.66025i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(1.50000 + 2.59808i) q^{43} +(2.00000 - 3.46410i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-0.500000 - 0.866025i) q^{46} -7.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} +(1.00000 + 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{50} +6.92820i q^{51} +(-2.00000 + 3.46410i) q^{52} +(-3.00000 - 5.19615i) q^{53} +5.19615i q^{54} +4.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(3.00000 - 1.73205i) q^{57} +(3.00000 + 5.19615i) q^{58} -4.00000 q^{59} -1.73205i q^{60} -11.0000 q^{61} +2.00000 q^{62} +(1.50000 - 7.79423i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +(6.00000 - 3.46410i) q^{66} -9.00000 q^{67} +(-2.00000 - 3.46410i) q^{68} -1.73205i q^{69} +(-0.500000 + 2.59808i) q^{70} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(7.00000 + 12.1244i) q^{73} +(5.00000 - 8.66025i) q^{74} +(1.50000 - 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +(-10.0000 + 3.46410i) q^{77} +(-6.00000 + 3.46410i) q^{78} +(0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.00000 - 8.66025i) q^{82} +(6.00000 + 10.3923i) q^{83} +(1.50000 + 4.33013i) q^{84} +(2.00000 - 3.46410i) q^{85} +(-1.50000 - 2.59808i) q^{86} +10.3923i q^{87} +(-2.00000 + 3.46410i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(1.50000 - 2.59808i) q^{90} +(10.0000 - 3.46410i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.00000 + 1.73205i) q^{93} +7.00000 q^{94} -2.00000 q^{95} +(1.50000 + 0.866025i) q^{96} +(-5.00000 - 8.66025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + q^{5} + 3 q^{6} - 4 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + q^5 + 3 * q^6 - 4 * q^7 - 2 * q^8 + 3 * q^9	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + q^{5} + 3 q^{6} - 4 q^{7} - 2 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 3 q^{12} - 4 q^{13} + 4 q^{14} + 2 q^{16} - 4 q^{17} - 3 q^{18} - 2 q^{19} + q^{20} + 3 q^{21} - 4 q^{22} + q^{23} + 3 q^{24} - q^{25} + 4 q^{26} - 4 q^{28} - 6 q^{29} - 4 q^{31} - 2 q^{32} - 12 q^{33} + 4 q^{34} + q^{35} + 3 q^{36} - 10 q^{37} + 2 q^{38} + 12 q^{39} - q^{40} - 10 q^{41} - 3 q^{42} + 3 q^{43} + 4 q^{44} - 3 q^{45} - q^{46} - 14 q^{47} - 3 q^{48} + 2 q^{49} + q^{50} - 4 q^{52} - 6 q^{53} + 8 q^{55} + 4 q^{56} + 6 q^{57} + 6 q^{58} - 8 q^{59} - 22 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} - 8 q^{65} + 12 q^{66} - 18 q^{67} - 4 q^{68} - q^{70} - 16 q^{71} - 3 q^{72} + 14 q^{73} + 10 q^{74} + 3 q^{75} - 2 q^{76} - 20 q^{77} - 12 q^{78} + q^{80} - 9 q^{81} + 10 q^{82} + 12 q^{83} + 3 q^{84} + 4 q^{85} - 3 q^{86} - 4 q^{88} - q^{89} + 3 q^{90} + 20 q^{91} + q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} + 3 q^{96} - 10 q^{97} - 2 q^{98} + 24 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + q^5 + 3 * q^6 - 4 * q^7 - 2 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 3 * q^12 - 4 * q^13 + 4 * q^14 + 2 * q^16 - 4 * q^17 - 3 * q^18 - 2 * q^19 + q^20 + 3 * q^21 - 4 * q^22 + q^23 + 3 * q^24 - q^25 + 4 * q^26 - 4 * q^28 - 6 * q^29 - 4 * q^31 - 2 * q^32 - 12 * q^33 + 4 * q^34 + q^35 + 3 * q^36 - 10 * q^37 + 2 * q^38 + 12 * q^39 - q^40 - 10 * q^41 - 3 * q^42 + 3 * q^43 + 4 * q^44 - 3 * q^45 - q^46 - 14 * q^47 - 3 * q^48 + 2 * q^49 + q^50 - 4 * q^52 - 6 * q^53 + 8 * q^55 + 4 * q^56 + 6 * q^57 + 6 * q^58 - 8 * q^59 - 22 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 - 8 * q^65 + 12 * q^66 - 18 * q^67 - 4 * q^68 - q^70 - 16 * q^71 - 3 * q^72 + 14 * q^73 + 10 * q^74 + 3 * q^75 - 2 * q^76 - 20 * q^77 - 12 * q^78 + q^80 - 9 * q^81 + 10 * q^82 + 12 * q^83 + 3 * q^84 + 4 * q^85 - 3 * q^86 - 4 * q^88 - q^89 + 3 * q^90 + 20 * q^91 + q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 + 3 * q^96 - 10 * q^97 - 2 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	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
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	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	$0.979500\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$		−	1.73205i		−	0.447214i
$16$	1.00000			0.250000
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.50000	+	4.33013i	0.327327	+	0.944911i
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$		−	5.19615i		−	1.00000i
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$			1.73205i			0.316228i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000			−0.176777
$33$	−6.00000	+	3.46410i	−1.04447	+	0.603023i
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−5.00000	+	8.66025i	−0.821995	+	1.42374i	0.0821995	+	0.996616i	$0.473806\pi$
$37$	−5.00000	+	8.66025i	−0.821995	+	1.42374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	6.00000	−	3.46410i	0.960769	−	0.554700i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	−1.50000	−	4.33013i	−0.231455	−	0.668153i
$43$	1.50000	+	2.59808i	0.228748	+	0.396203i	0.957437	−	0.288641i	$-0.0932035\pi$
$43$	1.50000	+	2.59808i	0.228748	+	0.396203i	−0.728689	+	0.684844i	$0.759870\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−7.00000			−1.02105			−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000			−1.02105			−0.510527	+	0.859861i	$0.670550\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$			6.92820i			0.970143i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$			5.19615i			0.707107i
$55$	4.00000			0.539360
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$	3.00000	−	1.73205i	0.397360	−	0.229416i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−11.0000			−1.40841			−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000			−1.40841			−0.704203	+	0.709999i	$0.748695\pi$
$62$	2.00000			0.254000
$63$	1.50000	−	7.79423i	0.188982	−	0.981981i
$64$	1.00000			0.125000
$65$	−4.00000			−0.496139
$66$	6.00000	−	3.46410i	0.738549	−	0.426401i
$67$	−9.00000			−1.09952			−0.549762	−	0.835321i	$-0.685282\pi$
$67$	−9.00000			−1.09952			−0.549762	+	0.835321i	$0.685282\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		−	1.73205i		−	0.208514i
$70$	−0.500000	+	2.59808i	−0.0597614	+	0.310530i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$	1.50000	−	0.866025i	0.173205	−	0.100000i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−10.0000	+	3.46410i	−1.13961	+	0.394771i
$78$	−6.00000	+	3.46410i	−0.679366	+	0.392232i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$	1.50000	+	4.33013i	0.163663	+	0.472456i
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	−1.50000	−	2.59808i	−0.161749	−	0.280158i
$87$			10.3923i			1.11417i
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$	1.50000	−	2.59808i	0.158114	−	0.273861i
$91$	10.0000	−	3.46410i	1.04828	−	0.363137i
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	7.00000			0.721995
$95$	−2.00000			−0.205196
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$	12.0000			1.20605
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		−	6.92820i		−	0.685994i
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	−0.998793	−	0.0491146i	$-0.984360\pi$
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	0.456862	−	0.889538i	$-0.348973\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$	−3.00000	+	3.46410i	−0.292770	+	0.338062i
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	8.00000	−	13.8564i	0.773389	−	1.33955i	−0.162306	−	0.986740i	$-0.551893\pi$
$107$	8.00000	−	13.8564i	0.773389	−	1.33955i	0.935695	−	0.352809i	$-0.114773\pi$
$108$		−	5.19615i		−	0.500000i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	−4.00000			−0.381385
$111$	15.0000	−	8.66025i	1.42374	−	0.821995i
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	−0.529065	−	0.848581i	$-0.677457\pi$
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	0.999425	+	0.0338931i	$0.0107906\pi$
$114$	−3.00000	+	1.73205i	−0.280976	+	0.162221i
$115$	−0.500000	+	0.866025i	−0.0466252	+	0.0807573i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−12.0000			−1.10940
$118$	4.00000			0.368230
$119$	−2.00000	+	10.3923i	−0.183340	+	0.952661i
$120$			1.73205i			0.158114i
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	11.0000			0.995893
$123$	15.0000	−	8.66025i	1.35250	−	0.780869i
$124$	−2.00000			−0.179605
$125$	−1.00000			−0.0894427
$126$	−1.50000	+	7.79423i	−0.133631	+	0.694365i
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	−1.00000			−0.0883883
$129$		−	5.19615i		−	0.457496i
$130$	4.00000			0.350823
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$	−6.00000	+	3.46410i	−0.522233	+	0.301511i
$133$	5.00000	−	1.73205i	0.433555	−	0.150188i
$134$	9.00000			0.777482
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$			1.73205i			0.147442i
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	0.500000	−	2.59808i	0.0422577	−	0.219578i
$141$	10.5000	+	6.06218i	0.884260	+	0.510527i
$142$	8.00000			0.671345
$143$	8.00000	+	13.8564i	0.668994	+	1.15873i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	−7.00000	−	12.1244i	−0.579324	−	1.00342i
$147$	4.50000	−	11.2583i	0.371154	−	0.928571i
$148$	−5.00000	+	8.66025i	−0.410997	+	0.711868i
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	0.871742	+	0.489966i	$0.162991\pi$
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	−0.0115483	+	0.999933i	$0.503676\pi$
$150$	−1.50000	+	0.866025i	−0.122474	+	0.0707107i
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	6.00000	−	10.3923i	0.485071	−	0.840168i
$154$	10.0000	−	3.46410i	0.805823	−	0.279145i
$155$	−1.00000	−	1.73205i	−0.0803219	−	0.139122i
$156$	6.00000	−	3.46410i	0.480384	−	0.277350i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$			10.3923i			0.824163i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.500000	−	2.59808i	0.0394055	−	0.204757i
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$	−5.00000	+	8.66025i	−0.390434	+	0.676252i
$165$	−6.00000	−	3.46410i	−0.467099	−	0.269680i
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	8.50000	−	14.7224i	0.657750	−	1.13926i	−0.323447	−	0.946246i	$-0.604842\pi$
$167$	8.50000	−	14.7224i	0.657750	−	1.13926i	0.981197	−	0.193010i	$-0.0618249\pi$
$168$	−1.50000	−	4.33013i	−0.115728	−	0.334077i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$	−6.00000			−0.458831
$172$	1.50000	+	2.59808i	0.114374	+	0.198101i
$173$	4.00000			0.304114			0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000			0.304114			0.152057	+	0.988372i	$0.451410\pi$
$174$		−	10.3923i		−	0.787839i
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$	2.00000	−	3.46410i	0.150756	−	0.261116i
$177$	6.00000	+	3.46410i	0.450988	+	0.260378i
$178$	0.500000	−	0.866025i	0.0374766	−	0.0649113i
$179$	−7.00000	−	12.1244i	−0.523205	−	0.906217i	−0.999635	−	0.0270049i	$-0.991403\pi$
$179$	−7.00000	−	12.1244i	−0.523205	−	0.906217i	0.476431	−	0.879212i	$-0.341930\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−10.0000	+	3.46410i	−0.741249	+	0.256776i
$183$	16.5000	+	9.52628i	1.21972	+	0.704203i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−10.0000			−0.735215
$186$	−3.00000	−	1.73205i	−0.219971	−	0.127000i
$187$	−16.0000			−1.17004
$188$	−7.00000			−0.510527
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	2.00000			0.145095
$191$	−14.0000			−1.01300			−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000			−1.01300			−0.506502	+	0.862239i	$0.669062\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	22.0000			1.58359			0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000			1.58359			0.791797	+	0.610784i	$0.209146\pi$
$194$	5.00000	+	8.66025i	0.358979	+	0.621770i
$195$	6.00000	+	3.46410i	0.429669	+	0.248069i
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−12.0000			−0.852803
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	13.5000	+	7.79423i	0.952217	+	0.549762i
$202$	−4.50000	+	7.79423i	−0.316619	+	0.548400i
$203$	−3.00000	+	15.5885i	−0.210559	+	1.09410i
$204$			6.92820i			0.485071i
$205$	−10.0000			−0.698430
$206$	5.50000	+	9.52628i	0.383203	+	0.663727i
$207$	−1.50000	+	2.59808i	−0.104257	+	0.180579i
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	4.00000	+	6.92820i	0.276686	+	0.479234i
$210$	3.00000	−	3.46410i	0.207020	−	0.239046i
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	12.0000	+	6.92820i	0.822226	+	0.474713i
$214$	−8.00000	+	13.8564i	−0.546869	+	0.947204i
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$			5.19615i			0.353553i
$217$	4.00000	+	3.46410i	0.271538	+	0.235159i
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$		−	24.2487i		−	1.63858i
$220$	4.00000			0.269680
$221$	16.0000			1.07628
$222$	−15.0000	+	8.66025i	−1.00673	+	0.581238i
$223$	−7.50000	−	12.9904i	−0.502237	−	0.869900i	−0.999997	−	0.00258516i	$-0.999177\pi$
$223$	−7.50000	−	12.9904i	−0.502237	−	0.869900i	0.497760	−	0.867315i	$-0.334156\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$	−3.00000			−0.200000
$226$	−5.00000	+	8.66025i	−0.332595	+	0.576072i
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$	3.00000	−	1.73205i	0.198680	−	0.114708i
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	0.500000	−	0.866025i	0.0329690	−	0.0571040i
$231$	18.0000	+	3.46410i	1.18431	+	0.227921i
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	−0.998886	−	0.0471787i	$-0.984977\pi$
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	0.540301	+	0.841472i	$0.318310\pi$
$234$	12.0000			0.784465
$235$	−3.50000	−	6.06218i	−0.228315	−	0.395453i
$236$	−4.00000			−0.260378
$237$		0			0
$238$	2.00000	−	10.3923i	0.129641	−	0.673633i
$239$	4.00000	−	6.92820i	0.258738	−	0.448148i	−0.707166	−	0.707048i	$-0.750027\pi$
$239$	4.00000	−	6.92820i	0.258738	−	0.448148i	0.965904	+	0.258900i	$0.0833599\pi$
$240$		−	1.73205i		−	0.111803i
$241$	1.50000	−	2.59808i	0.0966235	−	0.167357i	−0.813662	−	0.581339i	$-0.802529\pi$
$241$	1.50000	−	2.59808i	0.0966235	−	0.167357i	0.910285	+	0.413982i	$0.135862\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−11.0000			−0.704203
$245$	−5.50000	+	4.33013i	−0.351382	+	0.276642i
$246$	−15.0000	+	8.66025i	−0.956365	+	0.552158i
$247$	−4.00000	−	6.92820i	−0.254514	−	0.440831i
$248$	2.00000			0.127000
$249$		−	20.7846i		−	1.31717i
$250$	1.00000			0.0632456
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$	1.50000	−	7.79423i	0.0944911	−	0.490990i
$253$	4.00000			0.251478
$254$	−9.00000			−0.564710
$255$	−6.00000	+	3.46410i	−0.375735	+	0.216930i
$256$	1.00000			0.0625000
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$			5.19615i			0.323498i
$259$	25.0000	−	8.66025i	1.55342	−	0.538122i
$260$	−4.00000			−0.248069
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	−0.908560	−	0.417755i	$-0.862817\pi$
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	0.816066	+	0.577959i	$0.196151\pi$
$264$	6.00000	−	3.46410i	0.369274	−	0.213201i
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	−5.00000	+	1.73205i	−0.306570	+	0.106199i
$267$	1.50000	−	0.866025i	0.0917985	−	0.0529999i
$268$	−9.00000			−0.549762
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$	−4.50000	+	2.59808i	−0.273861	+	0.158114i
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	−0.624218	−	0.781251i	$-0.714582\pi$
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	0.988692	+	0.149963i	$0.0479155\pi$
$272$	−2.00000	−	3.46410i	−0.121268	−	0.210042i
$273$	−18.0000	−	3.46410i	−1.08941	−	0.209657i
$274$	−8.00000	+	13.8564i	−0.483298	+	0.837096i
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		−	1.73205i		−	0.104257i
$277$	−10.0000	+	17.3205i	−0.600842	+	1.04069i	0.391852	+	0.920028i	$0.371834\pi$
$277$	−10.0000	+	17.3205i	−0.600842	+	1.04069i	−0.992694	+	0.120660i	$0.961499\pi$
$278$	4.00000	−	6.92820i	0.239904	−	0.415526i
$279$	−3.00000	−	5.19615i	−0.179605	−	0.311086i
$280$	−0.500000	+	2.59808i	−0.0298807	+	0.155265i
$281$	−14.5000	−	25.1147i	−0.864997	−	1.49822i	−0.867050	−	0.498222i	$-0.833987\pi$
$281$	−14.5000	−	25.1147i	−0.864997	−	1.49822i	0.00205220	−	0.999998i	$-0.499347\pi$
$282$	−10.5000	−	6.06218i	−0.625266	−	0.360997i
$283$	29.0000			1.72387			0.861936	−	0.507018i	$-0.169252\pi$
$283$	29.0000			1.72387			0.861936	+	0.507018i	$0.169252\pi$
$284$	−8.00000			−0.474713
$285$	3.00000	+	1.73205i	0.177705	+	0.102598i
$286$	−8.00000	−	13.8564i	−0.473050	−	0.819346i
$287$	25.0000	−	8.66025i	1.47570	−	0.511199i
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$			17.3205i			1.01535i
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$	−4.50000	+	11.2583i	−0.262445	+	0.656599i
$295$	−2.00000	−	3.46410i	−0.116445	−	0.201688i
$296$	5.00000	−	8.66025i	0.290619	−	0.503367i
$297$	−18.0000	−	10.3923i	−1.04447	−	0.603023i
$298$	−10.5000	−	18.1865i	−0.608249	−	1.05352i
$299$	−4.00000			−0.231326
$300$	1.50000	−	0.866025i	0.0866025	−	0.0500000i
$301$	1.50000	−	7.79423i	0.0864586	−	0.449252i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$	−13.5000	+	7.79423i	−0.775555	+	0.447767i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	−5.50000	−	9.52628i	−0.314929	−	0.545473i
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−10.0000	+	3.46410i	−0.569803	+	0.197386i
$309$			19.0526i			1.08386i
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$	−6.00000	+	3.46410i	−0.339683	+	0.196116i
$313$	22.0000			1.24351			0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000			1.24351			0.621757	+	0.783210i	$0.286419\pi$
$314$	22.0000			1.24153
$315$	7.50000	−	2.59808i	0.422577	−	0.146385i
$316$		0			0
$317$	10.0000			0.561656			0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000			0.561656			0.280828	+	0.959758i	$0.409391\pi$
$318$		−	10.3923i		−	0.582772i
$319$	−24.0000			−1.34374
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−24.0000	+	13.8564i	−1.33955	+	0.773389i
$322$	−0.500000	+	2.59808i	−0.0278639	+	0.144785i
$323$	8.00000			0.445132
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$			17.3205i			0.957826i
$328$	5.00000	−	8.66025i	0.276079	−	0.478183i
$329$	14.0000	+	12.1244i	0.771845	+	0.668437i
$330$	6.00000	+	3.46410i	0.330289	+	0.190693i
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−30.0000			−1.64399
$334$	−8.50000	+	14.7224i	−0.465099	+	0.805576i
$335$	−4.50000	−	7.79423i	−0.245861	−	0.425844i
$336$	1.50000	+	4.33013i	0.0818317	+	0.236228i
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.0112091	+	0.999937i	$0.503568\pi$
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.860366	+	0.509676i	$0.829765\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$	−15.0000	+	8.66025i	−0.814688	+	0.470360i
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$	6.00000			0.324443
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−1.50000	−	2.59808i	−0.0808746	−	0.140079i
$345$	1.50000	−	0.866025i	0.0807573	−	0.0466252i
$346$	−4.00000			−0.215041
$347$	21.0000			1.12734			0.563670	−	0.826000i	$-0.309389\pi$
$347$	21.0000			1.12734			0.563670	+	0.826000i	$0.309389\pi$
$348$			10.3923i			0.557086i
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	0.999951	+	0.00987003i	$0.00314178\pi$
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	−0.491428	+	0.870918i	$0.663525\pi$
$350$	−2.50000	+	0.866025i	−0.133631	+	0.0462910i
$351$	18.0000	+	10.3923i	0.960769	+	0.554700i
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	−0.980352	−	0.197256i	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$	−6.00000	−	3.46410i	−0.318896	−	0.184115i
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	−0.500000	+	0.866025i	−0.0264999	+	0.0458993i
$357$	12.0000	−	13.8564i	0.635107	−	0.733359i
$358$	7.00000	+	12.1244i	0.369961	+	0.640792i
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	−0.703382	−	0.710812i	$-0.748328\pi$
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	0.967272	+	0.253741i	$0.0816611\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−2.00000			−0.105118
$363$			8.66025i			0.454545i
$364$	10.0000	−	3.46410i	0.524142	−	0.181568i
$365$	−7.00000	+	12.1244i	−0.366397	+	0.634618i
$366$	−16.5000	−	9.52628i	−0.862469	−	0.497947i
$367$	14.5000	−	25.1147i	0.756894	−	1.31098i	−0.187533	−	0.982258i	$-0.560049\pi$
$367$	14.5000	−	25.1147i	0.756894	−	1.31098i	0.944427	−	0.328720i	$-0.106617\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−30.0000			−1.56174
$370$	10.0000			0.519875
$371$	−3.00000	+	15.5885i	−0.155752	+	0.809312i
$372$	3.00000	+	1.73205i	0.155543	+	0.0898027i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	16.0000			0.827340
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$	7.00000			0.360997
$377$	24.0000			1.23606
$378$	9.00000	−	10.3923i	0.462910	−	0.534522i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−2.00000			−0.102598
$381$	−13.5000	−	7.79423i	−0.691626	−	0.399310i
$382$	14.0000			0.716302
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	0.727851	−	0.685736i	$-0.240519\pi$
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	−0.957790	+	0.287469i	$0.907186\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	−8.00000	−	6.92820i	−0.407718	−	0.353094i
$386$	−22.0000			−1.11977
$387$	−4.50000	+	7.79423i	−0.228748	+	0.396203i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	−0.991100	−	0.133120i	$-0.957501\pi$
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	0.610835	+	0.791758i	$0.290834\pi$
$390$	−6.00000	−	3.46410i	−0.303822	−	0.175412i
$391$	2.00000	−	3.46410i	0.101144	−	0.175187i
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$		−	20.7846i		−	1.04844i
$394$		0			0
$395$		0			0
$396$	12.0000			0.603023
$397$	4.00000	−	6.92820i	0.200754	−	0.347717i	−0.748017	−	0.663679i	$-0.768994\pi$
$397$	4.00000	−	6.92820i	0.200754	−	0.347717i	0.948772	+	0.315963i	$0.102327\pi$
$398$	4.00000	+	6.92820i	0.200502	+	0.347279i
$399$	−9.00000	−	1.73205i	−0.450564	−	0.0867110i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	4.50000	+	7.79423i	0.224719	+	0.389225i	0.956235	−	0.292599i	$-0.0945202\pi$
$401$	4.50000	+	7.79423i	0.224719	+	0.389225i	−0.731516	+	0.681824i	$0.761187\pi$
$402$	−13.5000	−	7.79423i	−0.673319	−	0.388741i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	−9.00000			−0.447214
$406$	3.00000	−	15.5885i	0.148888	−	0.773642i
$407$	20.0000	+	34.6410i	0.991363	+	1.71709i
$408$		−	6.92820i		−	0.342997i
$409$	31.0000			1.53285			0.766426	−	0.642333i	$-0.222033\pi$
$409$	31.0000			1.53285			0.766426	+	0.642333i	$0.222033\pi$
$410$	10.0000			0.493865
$411$	−24.0000	+	13.8564i	−1.18383	+	0.683486i
$412$	−5.50000	−	9.52628i	−0.270966	−	0.469326i
$413$	8.00000	+	6.92820i	0.393654	+	0.340915i
$414$	1.50000	−	2.59808i	0.0737210	−	0.127688i
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$	12.0000	−	6.92820i	0.587643	−	0.339276i
$418$	−4.00000	−	6.92820i	−0.195646	−	0.338869i
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$	−3.00000	+	3.46410i	−0.146385	+	0.169031i
$421$	−18.5000	−	32.0429i	−0.901635	−	1.56168i	−0.825372	−	0.564590i	$-0.809034\pi$
$421$	−18.5000	−	32.0429i	−0.901635	−	1.56168i	−0.0762630	−	0.997088i	$-0.524299\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$	−10.5000	−	18.1865i	−0.510527	−	0.884260i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	4.00000			0.194029
$426$	−12.0000	−	6.92820i	−0.581402	−	0.335673i
$427$	22.0000	+	19.0526i	1.06465	+	0.922018i
$428$	8.00000	−	13.8564i	0.386695	−	0.669775i
$429$		−	27.7128i		−	1.33799i
$430$	1.50000	−	2.59808i	0.0723364	−	0.125290i
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−36.0000			−1.73005			−0.865025	−	0.501729i	$-0.832697\pi$
$433$	−36.0000			−1.73005			−0.865025	+	0.501729i	$0.832697\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$	−9.00000	+	5.19615i	−0.431517	+	0.249136i
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$	−2.00000			−0.0956730
$438$			24.2487i			1.15865i
$439$	−4.00000			−0.190910			−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000			−0.190910			−0.0954548	+	0.995434i	$0.530431\pi$
$440$	−4.00000			−0.190693
$441$	−16.5000	+	12.9904i	−0.785714	+	0.618590i
$442$	−16.0000			−0.761042
$443$	−32.0000			−1.52037			−0.760183	−	0.649709i	$-0.774891\pi$
$443$	−32.0000			−1.52037			−0.760183	+	0.649709i	$0.774891\pi$
$444$	15.0000	−	8.66025i	0.711868	−	0.410997i
$445$	−1.00000			−0.0474045
$446$	7.50000	+	12.9904i	0.355135	+	0.615112i
$447$		−	36.3731i		−	1.72039i
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	−1.00000			−0.0471929			−0.0235965	−	0.999722i	$-0.507512\pi$
$449$	−1.00000			−0.0471929			−0.0235965	+	0.999722i	$0.507512\pi$
$450$	3.00000			0.141421
$451$	20.0000	+	34.6410i	0.941763	+	1.63118i
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$	−15.0000	+	8.66025i	−0.704761	+	0.406894i
$454$	12.0000	−	20.7846i	0.563188	−	0.975470i
$455$	8.00000	+	6.92820i	0.375046	+	0.324799i
$456$	−3.00000	+	1.73205i	−0.140488	+	0.0811107i
$457$	34.0000			1.59045			0.795226	−	0.606313i	$-0.207352\pi$
$457$	34.0000			1.59045			0.795226	+	0.606313i	$0.207352\pi$
$458$	0.500000	+	0.866025i	0.0233635	+	0.0404667i
$459$	−18.0000	+	10.3923i	−0.840168	+	0.485071i
$460$	−0.500000	+	0.866025i	−0.0233126	+	0.0403786i
$461$	−3.50000	−	6.06218i	−0.163011	−	0.282344i	0.772936	−	0.634484i	$-0.218787\pi$
$461$	−3.50000	−	6.06218i	−0.163011	−	0.282344i	−0.935947	+	0.352140i	$0.885454\pi$
$462$	−18.0000	−	3.46410i	−0.837436	−	0.161165i
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$			3.46410i			0.160644i
$466$	7.00000	−	12.1244i	0.324269	−	0.561650i
$467$	3.50000	−	6.06218i	0.161961	−	0.280524i	−0.773611	−	0.633661i	$-0.781552\pi$
$467$	3.50000	−	6.06218i	0.161961	−	0.280524i	0.935572	+	0.353137i	$0.114885\pi$
$468$	−12.0000			−0.554700
$469$	18.0000	+	15.5885i	0.831163	+	0.719808i
$470$	3.50000	+	6.06218i	0.161443	+	0.279627i
$471$	33.0000	+	19.0526i	1.52056	+	0.877896i
$472$	4.00000			0.184115
$473$	12.0000			0.551761
$474$		0			0
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$	−2.00000	+	10.3923i	−0.0916698	+	0.476331i
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$	−4.00000	+	6.92820i	−0.182956	+	0.316889i
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$			1.73205i			0.0790569i
$481$	−20.0000	−	34.6410i	−0.911922	−	1.57949i
$482$	−1.50000	+	2.59808i	−0.0683231	+	0.118339i
$483$	−3.00000	+	3.46410i	−0.136505	+	0.157622i
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	5.00000	−	8.66025i	0.227038	−	0.393242i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	6.00000	+	10.3923i	0.271886	+	0.470920i	0.969345	−	0.245705i	$-0.0790193\pi$
$487$	6.00000	+	10.3923i	0.271886	+	0.470920i	−0.697459	+	0.716625i	$0.745686\pi$
$488$	11.0000			0.497947
$489$	18.0000	−	10.3923i	0.813988	−	0.469956i
$490$	5.50000	−	4.33013i	0.248465	−	0.195615i
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$	15.0000	−	8.66025i	0.676252	−	0.390434i
$493$	−12.0000	+	20.7846i	−0.540453	+	0.936092i
$494$	4.00000	+	6.92820i	0.179969	+	0.311715i
$495$	6.00000	+	10.3923i	0.269680	+	0.467099i
$496$	−2.00000			−0.0898027
$497$	16.0000	+	13.8564i	0.717698	+	0.621545i
$498$			20.7846i			0.931381i
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$	−1.00000			−0.0447214
$501$	−25.5000	+	14.7224i	−1.13926	+	0.657750i
$502$	28.0000			1.24970
$503$	8.00000			0.356702			0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000			0.356702			0.178351	+	0.983967i	$0.442924\pi$
$504$	−1.50000	+	7.79423i	−0.0668153	+	0.347183i
$505$	9.00000			0.400495
$506$	−4.00000			−0.177822
$507$			5.19615i			0.230769i
$508$	9.00000			0.399310
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$	6.00000	−	3.46410i	0.265684	−	0.153393i
$511$	7.00000	−	36.3731i	0.309662	−	1.60905i
$512$	−1.00000			−0.0441942
$513$	9.00000	+	5.19615i	0.397360	+	0.229416i
$514$	−1.00000	−	1.73205i	−0.0441081	−	0.0763975i
$515$	5.50000	−	9.52628i	0.242359	−	0.419778i
$516$		−	5.19615i		−	0.228748i
$517$	−14.0000	+	24.2487i	−0.615719	+	1.06646i
$518$	−25.0000	+	8.66025i	−1.09844	+	0.380510i
$519$	−6.00000	−	3.46410i	−0.263371	−	0.152057i
$520$	4.00000			0.175412
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	−0.688196	−	0.725525i	$-0.741597\pi$
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	0.972421	+	0.233233i	$0.0749303\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$	−4.50000	−	0.866025i	−0.196396	−	0.0377964i
$526$	1.50000	−	2.59808i	0.0654031	−	0.113282i
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$	−6.00000	+	3.46410i	−0.261116	+	0.150756i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	5.00000	−	1.73205i	0.216777	−	0.0750939i
$533$	−20.0000	−	34.6410i	−0.866296	−	1.50047i
$534$	−1.50000	+	0.866025i	−0.0649113	+	0.0374766i
$535$	16.0000			0.691740
$536$	9.00000			0.388741
$537$			24.2487i			1.04641i
$538$	7.50000	+	12.9904i	0.323348	+	0.560055i
$539$	26.0000	+	10.3923i	1.11990	+	0.447628i
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	−0.691793	−	0.722096i	$-0.743179\pi$
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	0.971250	+	0.238062i	$0.0765123\pi$
$542$	−6.00000	+	10.3923i	−0.257722	+	0.446388i
$543$	−3.00000	−	1.73205i	−0.128742	−	0.0743294i
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	5.00000	−	8.66025i	0.214176	−	0.370965i
$546$	18.0000	+	3.46410i	0.770329	+	0.148250i
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$	8.00000	−	13.8564i	0.341743	−	0.591916i
$549$	−16.5000	−	28.5788i	−0.704203	−	1.21972i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	12.0000			0.511217
$552$			1.73205i			0.0737210i
$553$		0			0
$554$	10.0000	−	17.3205i	0.424859	−	0.735878i
$555$	15.0000	+	8.66025i	0.636715	+	0.367607i
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	−1.00000	−	1.73205i	−0.0423714	−	0.0733893i	0.844062	−	0.536246i	$-0.180158\pi$
$557$	−1.00000	−	1.73205i	−0.0423714	−	0.0733893i	−0.886433	+	0.462856i	$0.846825\pi$
$558$	3.00000	+	5.19615i	0.127000	+	0.219971i
$559$	−12.0000			−0.507546
$560$	0.500000	−	2.59808i	0.0211289	−	0.109789i
$561$	24.0000	+	13.8564i	1.01328	+	0.585018i
$562$	14.5000	+	25.1147i	0.611646	+	1.05940i
$563$	−39.0000			−1.64365			−0.821827	−	0.569737i	$-0.807045\pi$
$563$	−39.0000			−1.64365			−0.821827	+	0.569737i	$0.807045\pi$
$564$	10.5000	+	6.06218i	0.442130	+	0.255264i
$565$	10.0000			0.420703
$566$	−29.0000			−1.21896
$567$	22.5000	−	7.79423i	0.944911	−	0.327327i
$568$	8.00000			0.335673
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$	−3.00000	−	1.73205i	−0.125656	−	0.0725476i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	8.00000	+	13.8564i	0.334497	+	0.579365i
$573$	21.0000	+	12.1244i	0.877288	+	0.506502i
$574$	−25.0000	+	8.66025i	−1.04348	+	0.361472i
$575$	−1.00000			−0.0417029
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	14.0000	+	24.2487i	0.582828	+	1.00949i	0.995142	+	0.0984456i	$0.0313871\pi$
$577$	14.0000	+	24.2487i	0.582828	+	1.00949i	−0.412315	+	0.911041i	$0.635280\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	−33.0000	−	19.0526i	−1.37143	−	0.791797i
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	6.00000	−	31.1769i	0.248922	−	1.29344i
$582$		−	17.3205i		−	0.717958i
$583$	−24.0000			−0.993978
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$	−6.00000	−	10.3923i	−0.248069	−	0.429669i
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$	4.50000	−	11.2583i	0.185577	−	0.464286i
$589$	2.00000	−	3.46410i	0.0824086	−	0.142736i
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$		0			0
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	−0.507184	−	0.861838i	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$	18.0000	+	10.3923i	0.738549	+	0.426401i
$595$	−10.0000	+	3.46410i	−0.409960	+	0.142014i
$596$	10.5000	+	18.1865i	0.430097	+	0.744949i
$597$			13.8564i			0.567105i
$598$	4.00000			0.163572
$599$	−14.0000			−0.572024			−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000			−0.572024			−0.286012	+	0.958226i	$0.592330\pi$
$600$	−1.50000	+	0.866025i	−0.0612372	+	0.0353553i
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$	−1.50000	+	7.79423i	−0.0611354	+	0.317669i
$603$	−13.5000	−	23.3827i	−0.549762	−	0.952217i
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$	2.50000	−	4.33013i	0.101639	−	0.176045i
$606$	13.5000	−	7.79423i	0.548400	−	0.316619i
$607$	−24.0000	−	41.5692i	−0.974130	−	1.68724i	−0.682777	−	0.730627i	$-0.739228\pi$
$607$	−24.0000	−	41.5692i	−0.974130	−	1.68724i	−0.291353	−	0.956616i	$-0.594105\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	18.0000	−	20.7846i	0.729397	−	0.842235i
$610$	5.50000	+	9.52628i	0.222688	+	0.385708i
$611$	14.0000	−	24.2487i	0.566379	−	0.980998i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	28.0000			1.12999
$615$	15.0000	+	8.66025i	0.604858	+	0.349215i
$616$	10.0000	−	3.46410i	0.402911	−	0.139573i
$617$	23.0000	−	39.8372i	0.925945	−	1.60378i	0.135911	−	0.990721i	$-0.456604\pi$
$617$	23.0000	−	39.8372i	0.925945	−	1.60378i	0.790034	−	0.613063i	$-0.210063\pi$
$618$		−	19.0526i		−	0.766406i
$619$	1.00000	−	1.73205i	0.0401934	−	0.0696170i	−0.845229	−	0.534404i	$-0.820536\pi$
$619$	1.00000	−	1.73205i	0.0401934	−	0.0696170i	0.885422	+	0.464787i	$0.153869\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$	4.50000	−	2.59808i	0.180579	−	0.104257i
$622$	8.00000			0.320771
$623$	2.50000	−	0.866025i	0.100160	−	0.0346966i
$624$	6.00000	−	3.46410i	0.240192	−	0.138675i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−22.0000			−0.879297
$627$		−	13.8564i		−	0.553372i
$628$	−22.0000			−0.877896
$629$	40.0000			1.59490
$630$	−7.50000	+	2.59808i	−0.298807	+	0.103510i
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$		0			0
$633$	−6.00000	+	3.46410i	−0.238479	+	0.137686i
$634$	−10.0000			−0.397151
$635$	4.50000	+	7.79423i	0.178577	+	0.309305i
$636$			10.3923i			0.412082i
$637$	−26.0000	−	10.3923i	−1.03016	−	0.411758i
$638$	24.0000			0.950169
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$	24.0000	−	13.8564i	0.947204	−	0.546869i
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	−0.990274	−	0.139134i	$-0.955568\pi$
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	0.615630	+	0.788035i	$0.288902\pi$
$644$	0.500000	−	2.59808i	0.0197028	−	0.102379i
$645$	4.50000	−	2.59808i	0.177187	−	0.102299i
$646$	−8.00000			−0.314756
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	0.776622	−	0.629967i	$-0.216932\pi$
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	−0.933878	+	0.357591i	$0.883598\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$	2.00000	+	3.46410i	0.0784465	+	0.135873i
$651$	−3.00000	−	8.66025i	−0.117579	−	0.339422i
$652$	−6.00000	+	10.3923i	−0.234978	+	0.406994i
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	0.969865	−	0.243643i	$-0.0783426\pi$
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	−0.695934	+	0.718106i	$0.745009\pi$
$654$		−	17.3205i		−	0.677285i
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$	−21.0000	+	36.3731i	−0.819288	+	1.41905i
$658$	−14.0000	−	12.1244i	−0.545777	−	0.472657i
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$	−6.00000	−	3.46410i	−0.233550	−	0.134840i
$661$	17.0000			0.661223			0.330612	−	0.943767i	$-0.392745\pi$
$661$	17.0000			0.661223			0.330612	+	0.943767i	$0.392745\pi$
$662$	−10.0000			−0.388661
$663$	−24.0000	−	13.8564i	−0.932083	−	0.538138i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	4.00000	+	3.46410i	0.155113	+	0.134332i
$666$	30.0000			1.16248
$667$	3.00000	−	5.19615i	0.116160	−	0.201196i
$668$	8.50000	−	14.7224i	0.328875	−	0.569628i
$669$			25.9808i			1.00447i
$670$	4.50000	+	7.79423i	0.173850	+	0.301117i
$671$	−22.0000	+	38.1051i	−0.849301	+	1.47103i
$672$	−1.50000	−	4.33013i	−0.0578638	−	0.167038i
$673$	14.0000	+	24.2487i	0.539660	+	0.934719i	0.998922	+	0.0464181i	$0.0147807\pi$
$673$	14.0000	+	24.2487i	0.539660	+	0.934719i	−0.459262	+	0.888301i	$0.651886\pi$
$674$	16.0000	−	27.7128i	0.616297	−	1.06746i
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	36.0000			1.38359			0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000			1.38359			0.691796	+	0.722093i	$0.256820\pi$
$678$	15.0000	−	8.66025i	0.576072	−	0.332595i
$679$	−5.00000	+	25.9808i	−0.191882	+	0.997050i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$	36.0000	−	20.7846i	1.37952	−	0.796468i
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	17.5000	+	30.3109i	0.669619	+	1.15981i	0.978011	+	0.208555i	$0.0668759\pi$
$683$	17.5000	+	30.3109i	0.669619	+	1.15981i	−0.308392	+	0.951259i	$0.599791\pi$
$684$	−6.00000			−0.229416
$685$	16.0000			0.611329
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$			1.73205i			0.0660819i
$688$	1.50000	+	2.59808i	0.0571870	+	0.0990507i
$689$	24.0000			0.914327
$690$	−1.50000	+	0.866025i	−0.0571040	+	0.0329690i
$691$	34.0000			1.29342			0.646710	−	0.762736i	$-0.276144\pi$
$691$	34.0000			1.29342			0.646710	+	0.762736i	$0.276144\pi$
$692$	4.00000			0.152057
$693$	−24.0000	−	20.7846i	−0.911685	−	0.789542i
$694$	−21.0000			−0.797149
$695$	−8.00000			−0.303457
$696$		−	10.3923i		−	0.393919i
$697$	40.0000			1.51511
$698$	−9.50000	−	16.4545i	−0.359580	−	0.622811i
$699$	21.0000	−	12.1244i	0.794293	−	0.458585i
$700$	2.50000	−	0.866025i	0.0944911	−	0.0327327i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$	−18.0000	−	10.3923i	−0.679366	−	0.392232i
$703$	−10.0000	−	17.3205i	−0.377157	−	0.653255i
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$			12.1244i			0.456630i
$706$	6.00000	−	10.3923i	0.225813	−	0.391120i
$707$	−22.5000	+	7.79423i	−0.846200	+	0.293132i
$708$	6.00000	+	3.46410i	0.225494	+	0.130189i
$709$	1.00000			0.0375558			0.0187779	−	0.999824i	$-0.494022\pi$
$709$	1.00000			0.0375558			0.0187779	+	0.999824i	$0.494022\pi$
$710$	4.00000	+	6.92820i	0.150117	+	0.260011i
$711$		0			0
$712$	0.500000	−	0.866025i	0.0187383	−	0.0324557i
$713$	−1.00000	−	1.73205i	−0.0374503	−	0.0648658i
$714$	−12.0000	+	13.8564i	−0.449089	+	0.518563i
$715$	−8.00000	+	13.8564i	−0.299183	+	0.518200i
$716$	−7.00000	−	12.1244i	−0.261602	−	0.453108i
$717$	−12.0000	+	6.92820i	−0.448148	+	0.258738i
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	0.146920	+	0.989148i	$0.453064\pi$
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	−0.930087	+	0.367338i	$0.880269\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	−5.50000	+	28.5788i	−0.204831	+	1.06433i
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	−4.50000	+	2.59808i	−0.167357	+	0.0966235i
$724$	2.00000			0.0743294
$725$	6.00000			0.222834
$726$		−	8.66025i		−	0.321412i
$727$	10.5000	+	18.1865i	0.389423	+	0.674501i	0.992372	−	0.123279i	$-0.0393409\pi$
$727$	10.5000	+	18.1865i	0.389423	+	0.674501i	−0.602949	+	0.797780i	$0.706008\pi$
$728$	−10.0000	+	3.46410i	−0.370625	+	0.128388i
$729$	−27.0000			−1.00000
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$	16.5000	+	9.52628i	0.609858	+	0.352101i
$733$	−12.0000	−	20.7846i	−0.443230	−	0.767697i	0.554697	−	0.832052i	$-0.312834\pi$
$733$	−12.0000	−	20.7846i	−0.443230	−	0.767697i	−0.997927	+	0.0643554i	$0.979501\pi$
$734$	−14.5000	+	25.1147i	−0.535205	+	0.927002i
$735$	12.0000	−	1.73205i	0.442627	−	0.0638877i
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	−18.0000	+	31.1769i	−0.663039	+	1.14842i
$738$	30.0000			1.10432
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	−0.980052	−	0.198741i	$-0.936315\pi$
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	0.317911	−	0.948120i	$-0.397019\pi$
$740$	−10.0000			−0.367607
$741$			13.8564i			0.509028i
$742$	3.00000	−	15.5885i	0.110133	−	0.572270i
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$	−3.00000	−	1.73205i	−0.109985	−	0.0635001i
$745$	−10.5000	+	18.1865i	−0.384690	+	0.666303i
$746$	−5.00000	−	8.66025i	−0.183063	−	0.317074i
$747$	−18.0000	+	31.1769i	−0.658586	+	1.14070i
$748$	−16.0000			−0.585018
$749$	−40.0000	+	13.8564i	−1.46157	+	0.506302i
$750$	−1.50000	−	0.866025i	−0.0547723	−	0.0316228i
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	0.965013	−	0.262201i	$-0.0844484\pi$
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	−0.709580	+	0.704625i	$0.751115\pi$
$752$	−7.00000			−0.255264
$753$	42.0000	+	24.2487i	1.53057	+	0.883672i
$754$	−24.0000			−0.874028
$755$	10.0000			0.363937
$756$	−9.00000	+	10.3923i	−0.327327	+	0.377964i
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$	20.0000			0.726433
$759$	−6.00000	−	3.46410i	−0.217786	−	0.125739i
$760$	2.00000			0.0725476
$761$	−15.5000	−	26.8468i	−0.561875	−	0.973195i	−0.997333	−	0.0729864i	$-0.976747\pi$
$761$	−15.5000	−	26.8468i	−0.561875	−	0.973195i	0.435458	−	0.900209i	$-0.356586\pi$
$762$	13.5000	+	7.79423i	0.489053	+	0.282355i
$763$	−5.00000	+	25.9808i	−0.181012	+	0.940567i
$764$	−14.0000			−0.506502
$765$	12.0000			0.433861
$766$	4.50000	+	7.79423i	0.162592	+	0.281617i
$767$	8.00000	−	13.8564i	0.288863	−	0.500326i
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	−0.959097	−	0.283078i	$-0.908645\pi$
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	0.724701	+	0.689063i	$0.241978\pi$
$770$	8.00000	+	6.92820i	0.288300	+	0.249675i
$771$		−	3.46410i		−	0.124757i
$772$	22.0000			0.791797
$773$	−1.00000	−	1.73205i	−0.0359675	−	0.0622975i	0.847481	−	0.530825i	$-0.178118\pi$
$773$	−1.00000	−	1.73205i	−0.0359675	−	0.0622975i	−0.883449	+	0.468528i	$0.844785\pi$
$774$	4.50000	−	7.79423i	0.161749	−	0.280158i
$775$	1.00000	−	1.73205i	0.0359211	−	0.0622171i
$776$	5.00000	+	8.66025i	0.179490	+	0.310885i
$777$	−45.0000	−	8.66025i	−1.61437	−	0.310685i
$778$	7.50000	−	12.9904i	0.268888	−	0.465728i
$779$	−10.0000	−	17.3205i	−0.358287	−	0.620572i
$780$	6.00000	+	3.46410i	0.214834	+	0.124035i
$781$	−16.0000	+	27.7128i	−0.572525	+	0.991642i
$782$	−2.00000	+	3.46410i	−0.0715199	+	0.123876i
$783$	−27.0000	+	15.5885i	−0.964901	+	0.557086i
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−11.0000	−	19.0526i	−0.392607	−	0.680015i
$786$			20.7846i			0.741362i
$787$	−31.0000			−1.10503			−0.552515	−	0.833503i	$-0.686332\pi$
$787$	−31.0000			−1.10503			−0.552515	+	0.833503i	$0.686332\pi$
$788$		0			0
$789$	4.50000	−	2.59808i	0.160204	−	0.0924940i
$790$		0			0
$791$	−25.0000	+	8.66025i	−0.888898	+	0.307923i
$792$	−12.0000			−0.426401
$793$	22.0000	−	38.1051i	0.781243	−	1.35315i
$794$	−4.00000	+	6.92820i	−0.141955	+	0.245873i
$795$	−9.00000	+	5.19615i	−0.319197	+	0.184289i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	−0.914255	−	0.405140i	$-0.867223\pi$
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	0.807989	+	0.589197i	$0.200556\pi$
$798$	9.00000	+	1.73205i	0.318597	+	0.0613139i
$799$	14.0000	+	24.2487i	0.495284	+	0.857858i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.00000			−0.106000
$802$	−4.50000	−	7.79423i	−0.158901	−	0.275224i
$803$	56.0000			1.97620
$804$	13.5000	+	7.79423i	0.476108	+	0.274881i
$805$	2.50000	−	0.866025i	0.0881134	−	0.0305234i
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$			25.9808i			0.914566i
$808$	−4.50000	+	7.79423i	−0.158309	+	0.274200i
$809$	−8.50000	−	14.7224i	−0.298844	−	0.517613i	0.677028	−	0.735958i	$-0.263268\pi$
$809$	−8.50000	−	14.7224i	−0.298844	−	0.517613i	−0.975872	+	0.218344i	$0.929934\pi$
$810$	9.00000			0.316228
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	−3.00000	+	15.5885i	−0.105279	+	0.547048i
$813$	−18.0000	+	10.3923i	−0.631288	+	0.364474i
$814$	−20.0000	−	34.6410i	−0.701000	−	1.21417i
$815$	−12.0000			−0.420342
$816$			6.92820i			0.242536i
$817$	−6.00000			−0.209913
$818$	−31.0000			−1.08389
$819$	24.0000	+	20.7846i	0.838628	+	0.726273i
$820$	−10.0000			−0.349215
$821$	−55.0000			−1.91951			−0.959757	−	0.280833i	$-0.909389\pi$
$821$	−55.0000			−1.91951			−0.959757	+	0.280833i	$0.909389\pi$
$822$	24.0000	−	13.8564i	0.837096	−	0.483298i
$823$	−32.0000			−1.11545			−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000			−1.11545			−0.557725	+	0.830026i	$0.688326\pi$
$824$	5.50000	+	9.52628i	0.191602	+	0.331864i
$825$		−	6.92820i		−	0.241209i
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	−1.50000	+	2.59808i	−0.0521286	+	0.0902894i
$829$	18.5000	+	32.0429i	0.642532	+	1.11290i	0.984866	+	0.173319i	$0.0554492\pi$
$829$	18.5000	+	32.0429i	0.642532	+	1.11290i	−0.342334	+	0.939578i	$0.611217\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$	30.0000	−	17.3205i	1.04069	−	0.600842i
$832$	−2.00000	+	3.46410i	−0.0693375	+	0.120096i
$833$	22.0000	−	17.3205i	0.762255	−	0.600120i
$834$	−12.0000	+	6.92820i	−0.415526	+	0.239904i
$835$	17.0000			0.588309
$836$	4.00000	+	6.92820i	0.138343	+	0.239617i
$837$			10.3923i			0.359211i
$838$		0			0
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	−0.999785	−	0.0207443i	$-0.993396\pi$
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	0.481927	−	0.876211i	$-0.339937\pi$
$840$	3.00000	−	3.46410i	0.103510	−	0.119523i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	18.5000	+	32.0429i	0.637552	+	1.10427i
$843$			50.2295i			1.72999i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	1.50000	−	2.59808i	0.0516016	−	0.0893765i
$846$	10.5000	+	18.1865i	0.360997	+	0.625266i
$847$	−2.50000	+	12.9904i	−0.0859010	+	0.446355i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$	−43.5000	−	25.1147i	−1.49292	−	0.861936i
$850$	−4.00000			−0.137199
$851$	−10.0000			−0.342796
$852$	12.0000	+	6.92820i	0.411113	+	0.237356i
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	0.946232	+	0.323489i	$0.104856\pi$
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	−0.192966	+	0.981205i	$0.561811\pi$
$854$	−22.0000	−	19.0526i	−0.752825	−	0.651965i
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$	−8.00000	+	13.8564i	−0.273434	+	0.473602i
$857$	19.0000	−	32.9090i	0.649028	−	1.12415i	−0.334328	−	0.942457i	$-0.608509\pi$
$857$	19.0000	−	32.9090i	0.649028	−	1.12415i	0.983355	−	0.181692i	$-0.0581574\pi$
$858$			27.7128i			0.946100i
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	0.554396	−	0.832253i	$-0.312949\pi$
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	−0.997950	+	0.0639945i	$0.979616\pi$
$860$	−1.50000	+	2.59808i	−0.0511496	+	0.0885937i
$861$	−45.0000	−	8.66025i	−1.53360	−	0.295141i
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	−28.5000	+	49.3634i	−0.970151	+	1.68035i	−0.275064	+	0.961426i	$0.588699\pi$
$863$	−28.5000	+	49.3634i	−0.970151	+	1.68035i	−0.695087	+	0.718925i	$0.744634\pi$
$864$			5.19615i			0.176777i
$865$	2.00000	+	3.46410i	0.0680020	+	0.117783i
$866$	36.0000			1.22333
$867$	−1.50000	+	0.866025i	−0.0509427	+	0.0294118i
$868$	4.00000	+	3.46410i	0.135769	+	0.117579i
$869$		0			0
$870$	9.00000	−	5.19615i	0.305129	−	0.176166i
$871$	18.0000	−	31.1769i	0.609907	−	1.05639i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	15.0000	−	25.9808i	0.507673	−	0.879316i
$874$	2.00000			0.0676510
$875$	2.00000	+	1.73205i	0.0676123	+	0.0585540i
$876$		−	24.2487i		−	0.819288i
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	4.00000			0.134993
$879$	27.0000	−	15.5885i	0.910687	−	0.525786i
$880$	4.00000			0.134840
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$	16.5000	−	12.9904i	0.555584	−	0.437409i
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$	16.0000			0.538138
$885$			6.92820i			0.232889i
$886$	32.0000			1.07506
$887$	−17.5000	−	30.3109i	−0.587592	−	1.01774i	−0.994547	−	0.104292i	$-0.966743\pi$
$887$	−17.5000	−	30.3109i	−0.587592	−	1.01774i	0.406954	−	0.913449i	$-0.366591\pi$
$888$	−15.0000	+	8.66025i	−0.503367	+	0.290619i
$889$	−18.0000	−	15.5885i	−0.603701	−	0.522820i
$890$	1.00000			0.0335201
$891$	18.0000	+	31.1769i	0.603023	+	1.04447i
$892$	−7.50000	−	12.9904i	−0.251119	−	0.434950i
$893$	7.00000	−	12.1244i	0.234246	−	0.405726i
$894$			36.3731i			1.21650i
$895$	7.00000	−	12.1244i	0.233984	−	0.405273i
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	6.00000	+	3.46410i	0.200334	+	0.115663i
$898$	1.00000			0.0333704
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$	−3.00000			−0.100000
$901$	−12.0000	+	20.7846i	−0.399778	+	0.692436i
$902$	−20.0000	−	34.6410i	−0.665927	−	1.15342i
$903$	−9.00000	+	10.3923i	−0.299501	+	0.345834i
$904$	−5.00000	+	8.66025i	−0.166298	+	0.288036i
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	15.0000	−	8.66025i	0.498342	−	0.287718i
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	27.0000			0.895533
$910$	−8.00000	−	6.92820i	−0.265197	−	0.229668i
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	0.999994	−	0.00349271i	$-0.00111177\pi$
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$912$	3.00000	−	1.73205i	0.0993399	−	0.0573539i
$913$	48.0000			1.58857
$914$	−34.0000			−1.12462
$915$			19.0526i			0.629858i
$916$	−0.500000	−	0.866025i	−0.0165205	−	0.0286143i
$917$	6.00000	−	31.1769i	0.198137	−	1.02955i
$918$	18.0000	−	10.3923i	0.594089	−	0.342997i
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	−0.652616	−	0.757689i	$-0.726329\pi$
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	0.982486	+	0.186338i	$0.0596619\pi$
$920$	0.500000	−	0.866025i	0.0164845	−	0.0285520i
$921$	42.0000	+	24.2487i	1.38395	+	0.799022i
$922$	3.50000	+	6.06218i	0.115266	+	0.199647i
$923$	16.0000	−	27.7128i	0.526646	−	0.912178i
$924$	18.0000	+	3.46410i	0.592157	+	0.113961i
$925$	−5.00000	−	8.66025i	−0.164399	−	0.284747i
$926$	−0.500000	+	0.866025i	−0.0164310	+	0.0284594i
$927$	16.5000	−	28.5788i	0.541931	−	0.938652i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	47.0000			1.54202			0.771010	−	0.636823i	$-0.219752\pi$
$929$	47.0000			1.54202			0.771010	+	0.636823i	$0.219752\pi$
$930$		−	3.46410i		−	0.113592i
$931$	−13.0000	−	5.19615i	−0.426058	−	0.170297i
$932$	−7.00000	+	12.1244i	−0.229293	+	0.397146i
$933$	12.0000	+	6.92820i	0.392862	+	0.226819i
$934$	−3.50000	+	6.06218i	−0.114523	+	0.198361i
$935$	−8.00000	−	13.8564i	−0.261628	−	0.453153i
$936$	12.0000			0.392232
$937$	24.0000			0.784046			0.392023	−	0.919955i	$-0.371775\pi$
$937$	24.0000			0.784046			0.392023	+	0.919955i	$0.371775\pi$
$938$	−18.0000	−	15.5885i	−0.587721	−	0.508981i
$939$	−33.0000	−	19.0526i	−1.07691	−	0.621757i
$940$	−3.50000	−	6.06218i	−0.114157	−	0.197726i
$941$	−45.0000			−1.46696			−0.733479	−	0.679712i	$-0.762105\pi$
$941$	−45.0000			−1.46696			−0.733479	+	0.679712i	$0.762105\pi$
$942$	−33.0000	−	19.0526i	−1.07520	−	0.620766i
$943$	−10.0000			−0.325645
$944$	−4.00000			−0.130189
$945$	−13.5000	−	2.59808i	−0.439155	−	0.0845154i
$946$	−12.0000			−0.390154
$947$	27.0000			0.877382			0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000			0.877382			0.438691	+	0.898638i	$0.355442\pi$
$948$		0			0
$949$	−56.0000			−1.81784
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$	−15.0000	−	8.66025i	−0.486408	−	0.280828i
$952$	2.00000	−	10.3923i	0.0648204	−	0.336817i
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$	−7.00000	−	12.1244i	−0.226515	−	0.392335i
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$	36.0000	+	20.7846i	1.16371	+	0.671871i
$958$	3.00000	−	5.19615i	0.0969256	−	0.167880i
$959$	−40.0000	+	13.8564i	−1.29167	+	0.447447i
$960$		−	1.73205i		−	0.0559017i
$961$	−27.0000			−0.870968
$962$	20.0000	+	34.6410i	0.644826	+	1.11687i
$963$	48.0000			1.54678
$964$	1.50000	−	2.59808i	0.0483117	−	0.0836784i
$965$	11.0000	+	19.0526i	0.354103	+	0.613324i
$966$	3.00000	−	3.46410i	0.0965234	−	0.111456i
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$	2.50000	+	4.33013i	0.0803530	+	0.139176i
$969$	−12.0000	−	6.92820i	−0.385496	−	0.222566i
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	20.0000	−	6.92820i	0.641171	−	0.222108i
$974$	−6.00000	−	10.3923i	−0.192252	−	0.332991i
$975$			6.92820i			0.221880i
$976$	−11.0000			−0.352101
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$	−18.0000	+	10.3923i	−0.575577	+	0.332309i
$979$	2.00000	+	3.46410i	0.0639203	+	0.110713i
$980$	−5.50000	+	4.33013i	−0.175691	+	0.138321i
$981$	15.0000	−	25.9808i	0.478913	−	0.829502i
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	4.00000	−	6.92820i	0.127580	−	0.220975i	−0.795158	−	0.606402i	$-0.792612\pi$
$983$	4.00000	−	6.92820i	0.127580	−	0.220975i	0.922739	+	0.385426i	$0.125946\pi$
$984$	−15.0000	+	8.66025i	−0.478183	+	0.276079i
$985$		0			0
$986$	12.0000	−	20.7846i	0.382158	−	0.661917i
$987$	−10.5000	−	30.3109i	−0.334219	−	0.964806i
$988$	−4.00000	−	6.92820i	−0.127257	−	0.220416i
$989$	−1.50000	+	2.59808i	−0.0476972	+	0.0826140i
$990$	−6.00000	−	10.3923i	−0.190693	−	0.330289i
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	2.00000			0.0635001
$993$	−15.0000	−	8.66025i	−0.476011	−	0.274825i
$994$	−16.0000	−	13.8564i	−0.507489	−	0.439499i
$995$	4.00000	−	6.92820i	0.126809	−	0.219639i
$996$		−	20.7846i		−	0.658586i
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	2.00000	+	3.46410i	0.0633089	+	0.109654i
$999$	45.0000	+	25.9808i	1.42374	+	0.821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.b.121.1	✓	2
3.2	odd	2		1890.2.i.c.1171.1		2
7.4	even	3		630.2.l.c.571.1	yes	2
9.2	odd	6		1890.2.l.b.1801.1		2
9.7	even	3		630.2.l.c.331.1	yes	2
21.11	odd	6		1890.2.l.b.361.1		2
63.11	odd	6		1890.2.i.c.991.1		2
63.25	even	3	inner	630.2.i.b.151.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.b.121.1	✓	2	1.1	even	1	trivial
630.2.i.b.151.1	yes	2	63.25	even	3	inner
630.2.l.c.331.1	yes	2	9.7	even	3
630.2.l.c.571.1	yes	2	7.4	even	3
1890.2.i.c.991.1		2	63.11	odd	6
1890.2.i.c.1171.1		2	3.2	odd	2
1890.2.l.b.361.1		2	21.11	odd	6
1890.2.l.b.1801.1		2	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(2.00000 + 1.73205i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 + 4.33013i) q^{21} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.00000 - 3.46410i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +1.73205i q^{30} -2.00000 q^{31} -1.00000 q^{32} +(-6.00000 + 3.46410i) q^{33} +(2.00000 + 3.46410i) q^{34} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-5.00000 + 8.66025i) q^{37} +(1.00000 - 1.73205i) q^{38} +(6.00000 - 3.46410i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.00000 + 8.66025i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(1.50000 + 2.59808i) q^{43} +(2.00000 - 3.46410i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-0.500000 - 0.866025i) q^{46} -7.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} +(1.00000 + 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{50} +6.92820i q^{51} +(-2.00000 + 3.46410i) q^{52} +(-3.00000 - 5.19615i) q^{53} +5.19615i q^{54} +4.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(3.00000 - 1.73205i) q^{57} +(3.00000 + 5.19615i) q^{58} -4.00000 q^{59} -1.73205i q^{60} -11.0000 q^{61} +2.00000 q^{62} +(1.50000 - 7.79423i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +(6.00000 - 3.46410i) q^{66} -9.00000 q^{67} +(-2.00000 - 3.46410i) q^{68} -1.73205i q^{69} +(-0.500000 + 2.59808i) q^{70} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(7.00000 + 12.1244i) q^{73} +(5.00000 - 8.66025i) q^{74} +(1.50000 - 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +(-10.0000 + 3.46410i) q^{77} +(-6.00000 + 3.46410i) q^{78} +(0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.00000 - 8.66025i) q^{82} +(6.00000 + 10.3923i) q^{83} +(1.50000 + 4.33013i) q^{84} +(2.00000 - 3.46410i) q^{85} +(-1.50000 - 2.59808i) q^{86} +10.3923i q^{87} +(-2.00000 + 3.46410i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(1.50000 - 2.59808i) q^{90} +(10.0000 - 3.46410i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.00000 + 1.73205i) q^{93} +7.00000 q^{94} -2.00000 q^{95} +(1.50000 + 0.866025i) q^{96} +(-5.00000 - 8.66025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + q^{5} + 3 q^{6} - 4 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + q^5 + 3 * q^6 - 4 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + q^{5} + 3 q^{6} - 4 q^{7} - 2 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 3 q^{12} - 4 q^{13} + 4 q^{14} + 2 q^{16} - 4 q^{17} - 3 q^{18} - 2 q^{19} + q^{20} + 3 q^{21} - 4 q^{22} + q^{23} + 3 q^{24} - q^{25} + 4 q^{26} - 4 q^{28} - 6 q^{29} - 4 q^{31} - 2 q^{32} - 12 q^{33} + 4 q^{34} + q^{35} + 3 q^{36} - 10 q^{37} + 2 q^{38} + 12 q^{39} - q^{40} - 10 q^{41} - 3 q^{42} + 3 q^{43} + 4 q^{44} - 3 q^{45} - q^{46} - 14 q^{47} - 3 q^{48} + 2 q^{49} + q^{50} - 4 q^{52} - 6 q^{53} + 8 q^{55} + 4 q^{56} + 6 q^{57} + 6 q^{58} - 8 q^{59} - 22 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} - 8 q^{65} + 12 q^{66} - 18 q^{67} - 4 q^{68} - q^{70} - 16 q^{71} - 3 q^{72} + 14 q^{73} + 10 q^{74} + 3 q^{75} - 2 q^{76} - 20 q^{77} - 12 q^{78} + q^{80} - 9 q^{81} + 10 q^{82} + 12 q^{83} + 3 q^{84} + 4 q^{85} - 3 q^{86} - 4 q^{88} - q^{89} + 3 q^{90} + 20 q^{91} + q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} + 3 q^{96} - 10 q^{97} - 2 q^{98} + 24 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + q^5 + 3 * q^6 - 4 * q^7 - 2 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 3 * q^12 - 4 * q^13 + 4 * q^14 + 2 * q^16 - 4 * q^17 - 3 * q^18 - 2 * q^19 + q^20 + 3 * q^21 - 4 * q^22 + q^23 + 3 * q^24 - q^25 + 4 * q^26 - 4 * q^28 - 6 * q^29 - 4 * q^31 - 2 * q^32 - 12 * q^33 + 4 * q^34 + q^35 + 3 * q^36 - 10 * q^37 + 2 * q^38 + 12 * q^39 - q^40 - 10 * q^41 - 3 * q^42 + 3 * q^43 + 4 * q^44 - 3 * q^45 - q^46 - 14 * q^47 - 3 * q^48 + 2 * q^49 + q^50 - 4 * q^52 - 6 * q^53 + 8 * q^55 + 4 * q^56 + 6 * q^57 + 6 * q^58 - 8 * q^59 - 22 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 - 8 * q^65 + 12 * q^66 - 18 * q^67 - 4 * q^68 - q^70 - 16 * q^71 - 3 * q^72 + 14 * q^73 + 10 * q^74 + 3 * q^75 - 2 * q^76 - 20 * q^77 - 12 * q^78 + q^80 - 9 * q^81 + 10 * q^82 + 12 * q^83 + 3 * q^84 + 4 * q^85 - 3 * q^86 - 4 * q^88 - q^89 + 3 * q^90 + 20 * q^91 + q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 + 3 * q^96 - 10 * q^97 - 2 * q^98 + 24 * q^99

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