LMFDB - Embedded newform 770.2.i.a.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.a.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -5.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(0.500000 - 2.59808i) q^{35} -2.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +12.0000 q^{41} +(2.50000 - 0.866025i) q^{42} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{46} +(6.00000 - 10.3923i) q^{47} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} -4.00000 q^{62} +(1.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(6.50000 + 11.2583i) q^{67} -6.00000 q^{69} +(2.00000 + 1.73205i) q^{70} +(1.00000 - 1.73205i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} -1.00000 q^{78} +(-8.50000 + 14.7224i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +6.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(5.00000 - 8.66025i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +2.00000 q^{90} +(-2.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(6.00000 + 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} + 2 q^{8} + 2 q^{9} + q^{10} - q^{11} - q^{12} - 2 q^{13} - q^{14} - 2 q^{15} - q^{16} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 4 q^{21} + 2 q^{22} + 6 q^{23} - q^{24} - q^{25} + q^{26} - 10 q^{27} - 4 q^{28} - 18 q^{29} + q^{30} + 4 q^{31} - q^{32} - q^{33} + q^{35} - 4 q^{36} + 4 q^{37} - 2 q^{38} + q^{39} + q^{40} + 24 q^{41} + 5 q^{42} - 20 q^{43} - q^{44} - 2 q^{45} + 6 q^{46} + 12 q^{47} + 2 q^{48} + 11 q^{49} + 2 q^{50} + q^{52} - 6 q^{53} + 5 q^{54} - 2 q^{55} + 5 q^{56} + 4 q^{57} + 9 q^{58} - 3 q^{59} + q^{60} + 7 q^{61} - 8 q^{62} + 2 q^{63} + 2 q^{64} - q^{65} - q^{66} + 13 q^{67} - 12 q^{69} + 4 q^{70} + 2 q^{72} - 14 q^{73} + 4 q^{74} - q^{75} + 4 q^{76} - 4 q^{77} - 2 q^{78} - 17 q^{79} + q^{80} - q^{81} - 12 q^{82} + 12 q^{83} - q^{84} + 10 q^{86} + 9 q^{87} - q^{88} + 6 q^{89} + 4 q^{90} - 5 q^{91} - 12 q^{92} + 4 q^{93} + 12 q^{94} + 2 q^{95} - q^{96} + 10 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 + 2 * q^8 + 2 * q^9 + q^10 - q^11 - q^12 - 2 * q^13 - q^14 - 2 * q^15 - q^16 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 4 * q^21 + 2 * q^22 + 6 * q^23 - q^24 - q^25 + q^26 - 10 * q^27 - 4 * q^28 - 18 * q^29 + q^30 + 4 * q^31 - q^32 - q^33 + q^35 - 4 * q^36 + 4 * q^37 - 2 * q^38 + q^39 + q^40 + 24 * q^41 + 5 * q^42 - 20 * q^43 - q^44 - 2 * q^45 + 6 * q^46 + 12 * q^47 + 2 * q^48 + 11 * q^49 + 2 * q^50 + q^52 - 6 * q^53 + 5 * q^54 - 2 * q^55 + 5 * q^56 + 4 * q^57 + 9 * q^58 - 3 * q^59 + q^60 + 7 * q^61 - 8 * q^62 + 2 * q^63 + 2 * q^64 - q^65 - q^66 + 13 * q^67 - 12 * q^69 + 4 * q^70 + 2 * q^72 - 14 * q^73 + 4 * q^74 - q^75 + 4 * q^76 - 4 * q^77 - 2 * q^78 - 17 * q^79 + q^80 - q^81 - 12 * q^82 + 12 * q^83 - q^84 + 10 * q^86 + 9 * q^87 - q^88 + 6 * q^89 + 4 * q^90 - 5 * q^91 - 12 * q^92 + 4 * q^93 + 12 * q^94 + 2 * q^95 - q^96 + 10 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	−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	$0.240348\pi$
$20$	−1.00000			−0.223607
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$	1.00000			0.213201
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−5.00000			−0.962250
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$	−2.00000			−0.333333
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$	2.50000	−	0.866025i	0.385758	−	0.133631i
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.0186297	−	0.999826i	$-0.494070\pi$
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.856560	−	0.516047i	$-0.172597\pi$
$48$	1.00000			0.144338
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	1.00000			0.141421
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−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	$0.968532\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$	−1.00000			−0.134840
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$	2.00000			0.264906
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	−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	$0.895896\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−4.00000			−0.508001
$63$	1.00000	−	5.19615i	0.125988	−	0.654654i
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$	2.00000	+	1.73205i	0.239046	+	0.207020i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	2.00000			0.229416
$77$	−2.00000	−	1.73205i	−0.227921	−	0.197386i
$78$	−1.00000			−0.113228
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.225018	+	0.974355i	$0.572244\pi$
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−0.500000	+	2.59808i	−0.0545545	+	0.283473i
$85$		0			0
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	2.00000			0.210819
$91$	−2.50000	+	0.866025i	−0.262071	+	0.0907841i
$92$	−6.00000			−0.625543
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	5.00000			0.507673			0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$	−2.00000			−0.201008
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−1.00000			−0.0980581
$105$	−2.50000	+	0.866025i	−0.243975	+	0.0845154i
$106$	6.00000			0.582772
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	−4.00000			−0.379663
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	−9.00000			−0.846649			−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000			−0.846649			−0.423324	+	0.905978i	$0.639137\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	4.50000	+	7.79423i	0.417815	+	0.723676i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	3.00000			0.276172
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.50000	+	6.06218i	0.316875	+	0.548844i
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−1.00000			−0.0894427
$126$	4.00000	+	3.46410i	0.356348	+	0.308607i
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.00000	+	8.66025i	0.440225	+	0.762493i
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$	1.00000			0.0870388
$133$	−1.00000	+	5.19615i	−0.0867110	+	0.450564i
$134$	−13.0000			−1.12303
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$	3.00000	−	5.19615i	0.255377	−	0.442326i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$	−2.50000	+	0.866025i	−0.211289	+	0.0731925i
$141$	−12.0000			−1.01058
$142$		0			0
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	14.0000			1.15865
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$	−4.00000			−0.328798
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$	2.50000	−	0.866025i	0.201456	−	0.0697863i
$155$	4.00000			0.321288
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	−8.50000	−	14.7224i	−0.676224	−	1.17125i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−1.00000			−0.0790569
$161$	3.00000	−	15.5885i	0.236433	−	1.22854i
$162$	1.00000			0.0785674
$163$	−2.50000	+	4.33013i	−0.195815	+	0.339162i	−0.947167	−	0.320740i	$-0.896069\pi$
$163$	−2.50000	+	4.33013i	−0.195815	+	0.339162i	0.751352	+	0.659901i	$0.229402\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$	−2.00000	−	1.73205i	−0.154303	−	0.133631i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127601\pi$
$174$	−9.00000			−0.682288
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$	1.00000			0.0753778
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	0.929114	+	0.369792i	$0.120571\pi$
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	−0.144308	+	0.989533i	$0.546095\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	0.500000	−	2.59808i	0.0370625	−	0.192582i
$183$	−7.00000			−0.517455
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$		0			0
$188$	−12.0000			−0.875190
$189$	−12.5000	+	4.33013i	−0.909241	+	0.314970i
$190$	−2.00000			−0.145095
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	−2.50000	+	4.33013i	−0.179490	+	0.310885i
$195$	1.00000			0.0716115
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	6.50000	−	11.2583i	0.458475	−	0.794101i
$202$	−9.00000			−0.633238
$203$	−22.5000	+	7.79423i	−1.57919	+	0.547048i
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$	−6.00000	−	10.3923i	−0.417029	−	0.722315i
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	2.00000			0.138343
$210$	0.500000	−	2.59808i	0.0345033	−	0.179284i
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$	−5.00000			−0.340207
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	−10.0000			−0.677285
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$		0			0
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$	−2.00000			−0.133333
$226$	4.50000	−	7.79423i	0.299336	−	0.518464i
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	6.00000			0.395628
$231$	−0.500000	+	2.59808i	−0.0328976	+	0.170941i
$232$	−9.00000			−0.590879
$233$	6.00000	−	10.3923i	0.393073	−	0.680823i	−0.599780	−	0.800165i	$-0.704745\pi$
$233$	6.00000	−	10.3923i	0.393073	−	0.680823i	0.992853	+	0.119342i	$0.0380786\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	−6.00000	−	10.3923i	−0.391397	−	0.677919i
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	17.0000			1.10427
$238$		0			0
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−7.00000			−0.448129
$245$	−1.00000	−	6.92820i	−0.0638877	−	0.442627i
$246$	12.0000			0.765092
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−5.00000	+	1.73205i	−0.314970	+	0.109109i
$253$	−6.00000			−0.377217
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	−0.971558	−	0.236802i	$-0.923901\pi$
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	0.690856	+	0.722993i	$0.257234\pi$
$258$	−10.0000			−0.622573
$259$	2.00000	−	10.3923i	0.124274	−	0.645746i
$260$	1.00000			0.0620174
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$	−9.00000	−	15.5885i	−0.556022	−	0.963058i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	−6.00000			−0.368577
$266$	−4.00000	−	3.46410i	−0.245256	−	0.212398i
$267$	−6.00000			−0.367194
$268$	6.50000	−	11.2583i	0.397051	−	0.687712i
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$	−2.50000	−	4.33013i	−0.152145	−	0.263523i
$271$	−14.5000	+	25.1147i	−0.880812	+	1.52561i	−0.0303728	+	0.999539i	$0.509669\pi$
$271$	−14.5000	+	25.1147i	−0.880812	+	1.52561i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$	2.00000	+	1.73205i	0.121046	+	0.104828i
$274$	9.00000			0.543710
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$	−10.0000	+	17.3205i	−0.599760	+	1.03882i
$279$	8.00000			0.478947
$280$	0.500000	−	2.59808i	0.0298807	−	0.155265i
$281$	24.0000			1.43172			0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000			1.43172			0.715860	+	0.698244i	$0.246035\pi$
$282$	6.00000	−	10.3923i	0.357295	−	0.618853i
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	0.982173	+	0.187980i	$0.0601941\pi$
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	−0.328291	+	0.944577i	$0.606473\pi$
$284$		0			0
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$	−1.00000			−0.0591312
$287$	30.0000	−	10.3923i	1.77084	−	0.613438i
$288$	−2.00000			−0.117851
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$	−2.50000	−	4.33013i	−0.146553	−	0.253837i
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	5.50000	−	4.33013i	0.320767	−	0.252538i
$295$	−3.00000			−0.174667
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	1.00000			0.0577350
$301$	−25.0000	+	8.66025i	−1.44098	+	0.499169i
$302$	−19.0000			−1.09333
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	−3.50000	−	6.06218i	−0.200409	−	0.347119i
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−0.500000	+	2.59808i	−0.0284901	+	0.148039i
$309$	−4.00000			−0.227552
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−10.0000			−0.564333
$315$	−4.00000	−	3.46410i	−0.225374	−	0.195180i
$316$	17.0000			0.956325
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−6.00000			−0.334887
$322$	12.0000	+	10.3923i	0.668734	+	0.579141i
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$	−2.50000	−	4.33013i	−0.138462	−	0.239824i
$327$	5.00000	−	8.66025i	0.276501	−	0.478913i
$328$	12.0000			0.662589
$329$	6.00000	−	31.1769i	0.330791	−	1.71884i
$330$	−1.00000			−0.0550482
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	−4.00000	−	6.92820i	−0.219199	−	0.379663i
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	13.0000			0.710266
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	4.50000	+	7.79423i	0.244406	+	0.423324i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$	−4.00000			−0.216295
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−10.0000			−0.539164
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	2.50000	−	0.866025i	0.133631	−	0.0462910i
$351$	5.00000			0.266880
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$	−1.50000	−	2.59808i	−0.0797241	−	0.138086i
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−21.0000			−1.10988
$359$	13.5000	−	23.3827i	0.712503	−	1.23409i	−0.251412	−	0.967880i	$-0.580895\pi$
$359$	13.5000	−	23.3827i	0.712503	−	1.23409i	0.963915	−	0.266211i	$-0.0857717\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	8.00000	−	13.8564i	0.420471	−	0.728277i
$363$	1.00000			0.0524864
$364$	2.00000	+	1.73205i	0.104828	+	0.0907841i
$365$	−14.0000			−0.732793
$366$	3.50000	−	6.06218i	0.182948	−	0.316875i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	12.0000	−	20.7846i	0.624695	−	1.08200i
$370$	4.00000			0.207950
$371$	−12.0000	−	10.3923i	−0.623009	−	0.539542i
$372$	−4.00000			−0.207390
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	9.00000			0.463524
$378$	2.50000	−	12.9904i	0.128586	−	0.668153i
$379$	5.00000			0.256833			0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000			0.256833			0.128416	+	0.991720i	$0.459011\pi$
$380$	1.00000	−	1.73205i	0.0512989	−	0.0888523i
$381$	6.50000	+	11.2583i	0.333005	+	0.576782i
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$	1.00000			0.0510310
$385$	−2.50000	+	0.866025i	−0.127412	+	0.0441367i
$386$	−4.00000			−0.203595
$387$	−10.0000	+	17.3205i	−0.508329	+	0.880451i
$388$	−2.50000	−	4.33013i	−0.126918	−	0.219829i
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	0.672874	−	0.739758i	$-0.265060\pi$
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931726\pi$
$390$	−0.500000	+	0.866025i	−0.0253185	+	0.0438529i
$391$		0			0
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	18.0000			0.907980
$394$	−4.50000	+	7.79423i	−0.226707	+	0.392668i
$395$	8.50000	+	14.7224i	0.427681	+	0.740766i
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	−10.0000			−0.501255
$399$	5.00000	−	1.73205i	0.250313	−	0.0867110i
$400$	1.00000			0.0500000
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$	6.50000	+	11.2583i	0.324191	+	0.561514i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	−1.00000			−0.0496904
$406$	4.50000	−	23.3827i	0.223331	−	1.16046i
$407$	−4.00000			−0.198273
$408$		0			0
$409$	−10.0000	−	17.3205i	−0.494468	−	0.856444i	0.505511	−	0.862820i	$-0.331304\pi$
$409$	−10.0000	−	17.3205i	−0.494468	−	0.856444i	−0.999980	+	0.00637586i	$0.997970\pi$
$410$	6.00000	+	10.3923i	0.296319	+	0.513239i
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$	−4.00000			−0.197066
$413$	−6.00000	−	5.19615i	−0.295241	−	0.255686i
$414$	12.0000			0.589768
$415$	3.00000	−	5.19615i	0.147264	−	0.255069i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−10.0000	−	17.3205i	−0.489702	−	0.848189i
$418$	−1.00000	+	1.73205i	−0.0489116	+	0.0847174i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	2.00000	+	1.73205i	0.0975900	+	0.0845154i
$421$	32.0000			1.55958			0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000			1.55958			0.779792	+	0.626038i	$0.215325\pi$
$422$	8.00000	−	13.8564i	0.389434	−	0.674519i
$423$	−12.0000	−	20.7846i	−0.583460	−	1.01058i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$		0			0
$426$		0			0
$427$	3.50000	−	18.1865i	0.169377	−	0.880108i
$428$	−6.00000			−0.290021
$429$	0.500000	−	0.866025i	0.0241402	−	0.0418121i
$430$	−5.00000	−	8.66025i	−0.241121	−	0.417635i
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−10.0000	+	3.46410i	−0.480015	+	0.166282i
$435$	9.00000			0.431517
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$	−7.00000	−	12.1244i	−0.334473	−	0.579324i
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	0.978412	+	0.206666i	$0.0662612\pi$
$440$	−1.00000			−0.0476731
$441$	−2.00000	−	13.8564i	−0.0952381	−	0.659829i
$442$		0			0
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	−10.0000	+	17.3205i	−0.473514	+	0.820150i
$447$	−6.00000			−0.283790
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	4.50000	+	7.79423i	0.211662	+	0.366610i
$453$	9.50000	−	16.4545i	0.446349	−	0.773099i
$454$	−12.0000			−0.563188
$455$	−0.500000	+	2.59808i	−0.0234404	+	0.121800i
$456$	2.00000			0.0936586
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	−0.815449	−	0.578829i	$-0.803510\pi$
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	0.909005	+	0.416785i	$0.136843\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$		0			0
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	15.0000			0.698620			0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000			0.698620			0.349310	+	0.937007i	$0.386416\pi$
$462$	−2.00000	−	1.73205i	−0.0930484	−	0.0805823i
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	2.00000			0.0924500
$469$	26.0000	+	22.5167i	1.20057	+	1.03972i
$470$	12.0000			0.553519
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$	−8.50000	+	14.7224i	−0.390418	+	0.676224i
$475$	2.00000			0.0917663
$476$		0			0
$477$	−12.0000			−0.549442
$478$	−1.50000	+	2.59808i	−0.0686084	+	0.118833i
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	0.999730	−	0.0232187i	$-0.00739140\pi$
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	−0.519973	+	0.854183i	$0.674058\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	−10.0000			−0.455488
$483$	−15.0000	+	5.19615i	−0.682524	+	0.236433i
$484$	1.00000			0.0454545
$485$	2.50000	−	4.33013i	0.113519	−	0.196621i
$486$	−8.00000	−	13.8564i	−0.362887	−	0.628539i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	3.50000	−	6.06218i	0.158438	−	0.274422i
$489$	5.00000			0.226108
$490$	6.50000	+	2.59808i	0.293640	+	0.117369i
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$		0			0
$494$	1.00000	+	1.73205i	0.0449921	+	0.0779287i
$495$	−1.00000	+	1.73205i	−0.0449467	+	0.0778499i
$496$	−4.00000			−0.179605
$497$		0			0
$498$	6.00000			0.268866
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$	−6.00000	+	10.3923i	−0.267793	+	0.463831i
$503$	−3.00000			−0.133763			−0.0668817	−	0.997761i	$-0.521305\pi$
$503$	−3.00000			−0.133763			−0.0668817	+	0.997761i	$0.521305\pi$
$504$	1.00000	−	5.19615i	0.0445435	−	0.231455i
$505$	9.00000			0.400495
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$	−28.0000	−	24.2487i	−1.23865	−	1.07270i
$512$	1.00000			0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	−4.50000	−	7.79423i	−0.198486	−	0.343789i
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−12.0000			−0.527759
$518$	8.00000	+	6.92820i	0.351500	+	0.304408i
$519$	−21.0000			−0.921798
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	−9.00000	−	15.5885i	−0.393919	−	0.682288i
$523$	−1.00000	+	1.73205i	−0.0437269	+	0.0757373i	−0.887061	−	0.461653i	$-0.847256\pi$
$523$	−1.00000	+	1.73205i	−0.0437269	+	0.0757373i	0.843334	+	0.537390i	$0.180590\pi$
$524$	18.0000			0.786334
$525$	−0.500000	+	2.59808i	−0.0218218	+	0.113389i
$526$	9.00000			0.392419
$527$		0			0
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$	−6.00000			−0.260378
$532$	5.00000	−	1.73205i	0.216777	−	0.0750939i
$533$	−12.0000			−0.519778
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$	−3.00000	−	5.19615i	−0.129701	−	0.224649i
$536$	6.50000	+	11.2583i	0.280757	+	0.486286i
$537$	10.5000	−	18.1865i	0.453108	−	0.784807i
$538$	6.00000			0.258678
$539$	−6.50000	−	2.59808i	−0.279975	−	0.111907i
$540$	5.00000			0.215166
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	−14.5000	−	25.1147i	−0.622828	−	1.07877i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$		0			0
$545$	10.0000			0.428353
$546$	−2.50000	+	0.866025i	−0.106990	+	0.0370625i
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$	−7.00000	−	12.1244i	−0.298753	−	0.517455i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$	−6.00000			−0.255377
$553$	−8.50000	+	44.1673i	−0.361457	+	1.87818i
$554$	−19.0000			−0.807233
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	−4.00000	+	6.92820i	−0.169334	+	0.293294i
$559$	10.0000			0.422955
$560$	2.00000	+	1.73205i	0.0845154	+	0.0731925i
$561$		0			0
$562$	−12.0000	+	20.7846i	−0.506189	+	0.876746i
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	0.795858	−	0.605483i	$-0.207020\pi$
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	−0.922293	+	0.386492i	$0.873687\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$	−4.50000	+	7.79423i	−0.189316	+	0.327906i
$566$	−22.0000			−0.924729
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$		0			0
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.0294311	+	0.999567i	$0.509370\pi$
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.850935	+	0.525271i	$0.823964\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	0.500000	−	0.866025i	0.0209061	−	0.0362103i
$573$	12.0000			0.501307
$574$	−6.00000	+	31.1769i	−0.250435	+	1.30130i
$575$	−6.00000			−0.250217
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$	9.00000			0.373705
$581$	15.0000	−	5.19615i	0.622305	−	0.215573i
$582$	5.00000			0.207257
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$	−3.00000	+	5.19615i	−0.123929	+	0.214651i
$587$	−15.0000			−0.619116			−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000			−0.619116			−0.309558	+	0.950881i	$0.600181\pi$
$588$	1.00000	+	6.92820i	0.0412393	+	0.285714i
$589$	−8.00000			−0.329634
$590$	1.50000	−	2.59808i	0.0617540	−	0.106961i
$591$	−4.50000	−	7.79423i	−0.185105	−	0.320612i
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$	−5.00000			−0.205152
$595$		0			0
$596$	−6.00000			−0.245770
$597$	5.00000	−	8.66025i	0.204636	−	0.354441i
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	5.00000	−	25.9808i	0.203785	−	1.05890i
$603$	26.0000			1.05880
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	4.50000	+	7.79423i	0.182800	+	0.316619i
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	2.00000			0.0811107
$609$	18.0000	+	15.5885i	0.729397	+	0.631676i
$610$	7.00000			0.283422
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$		0			0
$613$	−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	$0.846193\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$	−12.0000			−0.483887
$616$	−2.00000	−	1.73205i	−0.0805823	−	0.0697863i
$617$	15.0000			0.603877			0.301939	−	0.953327i	$-0.402366\pi$
$617$	15.0000			0.603877			0.301939	+	0.953327i	$0.402366\pi$
$618$	2.00000	−	3.46410i	0.0804518	−	0.139347i
$619$	−4.00000	−	6.92820i	−0.160774	−	0.278468i	0.774373	−	0.632730i	$-0.218066\pi$
$619$	−4.00000	−	6.92820i	−0.160774	−	0.278468i	−0.935146	+	0.354262i	$0.884732\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$	24.0000			0.962312
$623$	3.00000	−	15.5885i	0.120192	−	0.624538i
$624$	−1.00000			−0.0400320
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$	−1.00000	−	1.73205i	−0.0399362	−	0.0691714i
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$		0			0
$630$	5.00000	−	1.73205i	0.199205	−	0.0690066i
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−8.50000	+	14.7224i	−0.338112	+	0.585627i
$633$	8.00000	+	13.8564i	0.317971	+	0.550743i
$634$		0			0
$635$	−6.50000	+	11.2583i	−0.257945	+	0.446773i
$636$	6.00000			0.237915
$637$	−5.50000	+	4.33013i	−0.217918	+	0.171566i
$638$	−9.00000			−0.356313
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$	3.00000	−	5.19615i	0.118401	−	0.205076i
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$	−15.0000	+	5.19615i	−0.591083	+	0.204757i
$645$	10.0000			0.393750
$646$		0			0
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$	−1.00000			−0.0392232
$651$	2.00000	−	10.3923i	0.0783862	−	0.407307i
$652$	5.00000			0.195815
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	5.00000	+	8.66025i	0.195515	+	0.338643i
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−28.0000			−1.09238
$658$	24.0000	+	20.7846i	0.935617	+	0.810268i
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	0.500000	−	0.866025i	0.0194625	−	0.0337100i
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	−0.999979	−	0.00652642i	$-0.997923\pi$
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	0.494337	−	0.869270i	$-0.335411\pi$
$662$	3.50000	+	6.06218i	0.136031	+	0.235613i
$663$		0			0
$664$	6.00000			0.232845
$665$	4.00000	+	3.46410i	0.155113	+	0.134332i
$666$	8.00000			0.309994
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$	−10.0000	−	17.3205i	−0.386622	−	0.669650i
$670$	−6.50000	+	11.2583i	−0.251117	+	0.434947i
$671$	−7.00000			−0.270232
$672$	−0.500000	+	2.59808i	−0.0192879	+	0.100223i
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−16.0000	+	27.7128i	−0.616297	+	1.06746i
$675$	2.50000	+	4.33013i	0.0962250	+	0.166667i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$	−9.00000			−0.345643
$679$	12.5000	−	4.33013i	0.479706	−	0.166175i
$680$		0			0
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	−19.5000	−	33.7750i	−0.746147	−	1.29236i	−0.949657	−	0.313291i	$-0.898568\pi$
$683$	−19.5000	−	33.7750i	−0.746147	−	1.29236i	0.203510	−	0.979073i	$-0.434765\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	−9.00000			−0.343872
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−10.0000			−0.381524
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$	−3.00000	−	5.19615i	−0.114208	−	0.197814i
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$	−21.0000			−0.798300
$693$	−5.00000	+	1.73205i	−0.189934	+	0.0657952i
$694$	18.0000			0.683271
$695$	10.0000	−	17.3205i	0.379322	−	0.657004i
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$		0			0
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$	−12.0000			−0.453882
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	21.0000			0.793159			0.396580	−	0.918000i	$-0.370197\pi$
$701$	21.0000			0.793159			0.396580	+	0.918000i	$0.370197\pi$
$702$	−2.50000	+	4.33013i	−0.0943564	+	0.163430i
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$	−6.00000			−0.225813
$707$	18.0000	+	15.5885i	0.676960	+	0.586264i
$708$	3.00000			0.112747
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$	17.0000	+	29.4449i	0.637550	+	1.10427i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	24.0000			0.898807
$714$		0			0
$715$	1.00000			0.0373979
$716$	10.5000	−	18.1865i	0.392403	−	0.679663i
$717$	−1.50000	−	2.59808i	−0.0560185	−	0.0970269i
$718$	13.5000	+	23.3827i	0.503816	+	0.872634i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$	2.00000			0.0745356
$721$	2.00000	−	10.3923i	0.0744839	−	0.387030i
$722$	−15.0000			−0.558242
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$	4.50000	+	7.79423i	0.167126	+	0.289470i
$726$	−0.500000	+	0.866025i	−0.0185567	+	0.0321412i
$727$	−34.0000			−1.26099			−0.630495	−	0.776193i	$-0.717148\pi$
$727$	−34.0000			−1.26099			−0.630495	+	0.776193i	$0.717148\pi$
$728$	−2.50000	+	0.866025i	−0.0926562	+	0.0320970i
$729$	13.0000			0.481481
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$		0			0
$732$	3.50000	+	6.06218i	0.129364	+	0.224065i
$733$	−5.50000	+	9.52628i	−0.203147	+	0.351861i	−0.949541	−	0.313644i	$-0.898450\pi$
$733$	−5.50000	+	9.52628i	−0.203147	+	0.351861i	0.746394	+	0.665505i	$0.231784\pi$
$734$	−28.0000			−1.03350
$735$	−5.50000	+	4.33013i	−0.202871	+	0.159719i
$736$	−6.00000			−0.221163
$737$	6.50000	−	11.2583i	0.239431	−	0.414706i
$738$	12.0000	+	20.7846i	0.441726	+	0.765092i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	−2.00000	+	3.46410i	−0.0735215	+	0.127343i
$741$	−2.00000			−0.0734718
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	−14.5000	−	25.1147i	−0.530883	−	0.919516i
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$	3.00000	−	15.5885i	0.109618	−	0.569590i
$750$	−1.00000			−0.0365148
$751$	23.0000	−	39.8372i	0.839282	−	1.45368i	−0.0512140	−	0.998688i	$-0.516309\pi$
$751$	23.0000	−	39.8372i	0.839282	−	1.45368i	0.890496	−	0.454991i	$-0.150358\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$	−4.50000	+	7.79423i	−0.163880	+	0.283849i
$755$	19.0000			0.691481
$756$	10.0000	+	8.66025i	0.363696	+	0.314970i
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$	−2.50000	+	4.33013i	−0.0908041	+	0.157277i
$759$	3.00000	+	5.19615i	0.108893	+	0.188608i
$760$	1.00000	+	1.73205i	0.0362738	+	0.0628281i
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	−13.0000			−0.470940
$763$	20.0000	+	17.3205i	0.724049	+	0.627044i
$764$	12.0000			0.434145
$765$		0			0
$766$	−18.0000	−	31.1769i	−0.650366	−	1.12647i
$767$	1.50000	+	2.59808i	0.0541619	+	0.0938111i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$	0.500000	−	2.59808i	0.0180187	−	0.0936282i
$771$	9.00000			0.324127
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	27.0000	+	46.7654i	0.971123	+	1.68203i	0.692179	+	0.721726i	$0.256651\pi$
$773$	27.0000	+	46.7654i	0.971123	+	1.68203i	0.278944	+	0.960307i	$0.410016\pi$
$774$	−10.0000	−	17.3205i	−0.359443	−	0.622573i
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	5.00000			0.179490
$777$	−10.0000	+	3.46410i	−0.358748	+	0.124274i
$778$	12.0000			0.430221
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$	−0.500000	−	0.866025i	−0.0179029	−	0.0310087i
$781$		0			0
$782$		0			0
$783$	45.0000			1.60817
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	10.0000			0.356915
$786$	−9.00000	+	15.5885i	−0.321019	+	0.556022i
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	0.713871	−	0.700278i	$-0.246941\pi$
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	−0.963394	+	0.268091i	$0.913607\pi$
$788$	−4.50000	−	7.79423i	−0.160306	−	0.277658i
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$	−17.0000			−0.604833
$791$	−22.5000	+	7.79423i	−0.800008	+	0.277131i
$792$	−2.00000			−0.0710669
$793$	−3.50000	+	6.06218i	−0.124289	+	0.215274i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	24.0000			0.850124			0.425062	−	0.905164i	$-0.360252\pi$
$797$	24.0000			0.850124			0.425062	+	0.905164i	$0.360252\pi$
$798$	−1.00000	+	5.19615i	−0.0353996	+	0.183942i
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−6.00000	−	10.3923i	−0.212000	−	0.367194i
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$	−7.00000	+	12.1244i	−0.247025	+	0.427859i
$804$	−13.0000			−0.458475
$805$	−12.0000	−	10.3923i	−0.422944	−	0.366281i
$806$	4.00000			0.140894
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$	4.50000	+	7.79423i	0.158309	+	0.274200i
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	18.0000	+	15.5885i	0.631676	+	0.547048i
$813$	29.0000			1.01707
$814$	2.00000	−	3.46410i	0.0701000	−	0.121417i
$815$	2.50000	+	4.33013i	0.0875712	+	0.151678i
$816$		0			0
$817$	10.0000	−	17.3205i	0.349856	−	0.605968i
$818$	20.0000			0.699284
$819$	−1.00000	+	5.19615i	−0.0349428	+	0.181568i
$820$	−12.0000			−0.419058
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	−0.891013	−	0.453978i	$-0.850005\pi$
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	0.838663	+	0.544651i	$0.183338\pi$
$822$	−4.50000	−	7.79423i	−0.156956	−	0.271855i
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$	1.00000			0.0348155
$826$	7.50000	−	2.59808i	0.260958	−	0.0903986i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	0.638457	−	0.769657i	$-0.279573\pi$
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	−0.985771	+	0.168091i	$0.946240\pi$
$830$	3.00000	+	5.19615i	0.104132	+	0.180361i
$831$	9.50000	−	16.4545i	0.329551	−	0.570800i
$832$	−1.00000			−0.0346688
$833$		0			0
$834$	20.0000			0.692543
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	−1.00000	−	1.73205i	−0.0345857	−	0.0599042i
$837$	−10.0000	−	17.3205i	−0.345651	−	0.598684i
$838$		0			0
$839$	42.0000			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$840$	−2.50000	+	0.866025i	−0.0862582	+	0.0298807i
$841$	52.0000			1.79310
$842$	−16.0000	+	27.7128i	−0.551396	+	0.955047i
$843$	−12.0000	−	20.7846i	−0.413302	−	0.715860i
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$	24.0000			0.825137
$847$	−0.500000	+	2.59808i	−0.0171802	+	0.0892710i
$848$	6.00000			0.206041
$849$	11.0000	−	19.0526i	0.377519	−	0.653882i
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$		0			0
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	14.0000	+	12.1244i	0.479070	+	0.414887i
$855$	4.00000			0.136797
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$	0.500000	+	0.866025i	0.0170697	+	0.0295656i
$859$	−2.50000	+	4.33013i	−0.0852989	+	0.147742i	−0.905519	−	0.424307i	$-0.860518\pi$
$859$	−2.50000	+	4.33013i	−0.0852989	+	0.147742i	0.820220	+	0.572049i	$0.193851\pi$
$860$	10.0000			0.340997
$861$	−24.0000	−	20.7846i	−0.817918	−	0.708338i
$862$	−15.0000			−0.510902
$863$	−18.0000	+	31.1769i	−0.612727	+	1.06127i	0.378052	+	0.925785i	$0.376594\pi$
$863$	−18.0000	+	31.1769i	−0.612727	+	1.06127i	−0.990779	+	0.135490i	$0.956739\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$	−10.5000	−	18.1865i	−0.357011	−	0.618361i
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$	−17.0000			−0.577350
$868$	2.00000	−	10.3923i	0.0678844	−	0.352738i
$869$	17.0000			0.576686
$870$	−4.50000	+	7.79423i	−0.152564	+	0.264249i
$871$	−6.50000	−	11.2583i	−0.220244	−	0.381474i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$	−12.0000			−0.405906
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	14.0000			0.473016
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$	6.50000	+	11.2583i	0.219364	+	0.379950i
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	−51.0000			−1.71823			−0.859117	−	0.511780i	$-0.828986\pi$
$881$	−51.0000			−1.71823			−0.859117	+	0.511780i	$0.828986\pi$
$882$	13.0000	+	5.19615i	0.437733	+	0.174964i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$		0			0
$885$	1.50000	+	2.59808i	0.0504219	+	0.0873334i
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	−0.712203	−	0.701974i	$-0.752302\pi$
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	0.964028	+	0.265799i	$0.0856358\pi$
$888$	−4.00000			−0.134231
$889$	−32.5000	+	11.2583i	−1.09002	+	0.377592i
$890$	6.00000			0.201120
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−10.0000	−	17.3205i	−0.334825	−	0.579934i
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$	21.0000			0.701953
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$	6.00000			0.200334
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$		0			0
$902$	12.0000			0.399556
$903$	20.0000	+	17.3205i	0.665558	+	0.576390i
$904$	−9.00000			−0.299336
$905$	−8.00000	+	13.8564i	−0.265929	+	0.460603i
$906$	9.50000	+	16.4545i	0.315616	+	0.546664i
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	0.650868	−	0.759191i	$-0.274405\pi$
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	−0.982913	+	0.184073i	$0.941072\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$	18.0000			0.597022
$910$	−2.00000	−	1.73205i	−0.0662994	−	0.0574169i
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	−3.00000	−	5.19615i	−0.0992855	−	0.171968i
$914$	2.00000	+	3.46410i	0.0661541	+	0.114582i
$915$	−3.50000	+	6.06218i	−0.115706	+	0.200409i
$916$	−10.0000			−0.330409
$917$	−9.00000	+	46.7654i	−0.297206	+	1.54433i
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	−3.00000	−	5.19615i	−0.0989071	−	0.171312i
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$	−7.50000	+	12.9904i	−0.246999	+	0.427815i
$923$		0			0
$924$	2.50000	−	0.866025i	0.0822440	−	0.0284901i
$925$	−4.00000			−0.131519
$926$	−10.0000	+	17.3205i	−0.328620	+	0.569187i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$	4.00000			0.131165
$931$	2.00000	+	13.8564i	0.0655474	+	0.454125i
$932$	−12.0000			−0.393073
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$		0			0
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	−32.5000	+	11.2583i	−1.06116	+	0.367598i
$939$	−1.00000			−0.0326338
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	0.889439	−	0.457054i	$-0.151096\pi$
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	−0.840540	+	0.541749i	$0.817762\pi$
$942$	5.00000	+	8.66025i	0.162909	+	0.282166i
$943$	36.0000	−	62.3538i	1.17232	−	2.03052i
$944$	3.00000			0.0976417
$945$	−2.50000	+	12.9904i	−0.0813250	+	0.422577i
$946$	−10.0000			−0.325128
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	−0.152106	−	0.988364i	$-0.548606\pi$
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	0.932002	−	0.362454i	$-0.118061\pi$
$948$	−8.50000	−	14.7224i	−0.276067	−	0.478162i
$949$	7.00000	+	12.1244i	0.227230	+	0.393573i
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$		0			0
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	−1.50000	−	2.59808i	−0.0485135	−	0.0840278i
$957$	4.50000	−	7.79423i	0.145464	−	0.251952i
$958$	−21.0000			−0.678479
$959$	−18.0000	−	15.5885i	−0.581250	−	0.503378i
$960$	−1.00000			−0.0322749
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−2.00000	−	3.46410i	−0.0644826	−	0.111687i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	4.00000			0.128765
$966$	3.00000	−	15.5885i	0.0965234	−	0.501550i
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$		0			0
$970$	2.50000	+	4.33013i	0.0802702	+	0.139032i
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$	16.0000			0.513200
$973$	50.0000	−	17.3205i	1.60293	−	0.555270i
$974$	2.00000			0.0640841
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$	−2.50000	+	4.33013i	−0.0799412	+	0.138462i
$979$	−6.00000			−0.191761
$980$	−5.50000	+	4.33013i	−0.175691	+	0.138321i
$981$	20.0000			0.638551
$982$	12.0000	−	20.7846i	0.382935	−	0.663264i
$983$	−15.0000	−	25.9808i	−0.478426	−	0.828658i	0.521268	−	0.853393i	$-0.325459\pi$
$983$	−15.0000	−	25.9808i	−0.478426	−	0.828658i	−0.999694	+	0.0247352i	$0.992126\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$	4.50000	−	7.79423i	0.143382	−	0.248345i
$986$		0			0
$987$	−30.0000	+	10.3923i	−0.954911	+	0.330791i
$988$	−2.00000			−0.0636285
$989$	−30.0000	+	51.9615i	−0.953945	+	1.65228i
$990$	−1.00000	−	1.73205i	−0.0317821	−	0.0550482i
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−7.00000			−0.222138
$994$		0			0
$995$	10.0000			0.317021
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−10.0000	−	17.3205i	−0.316544	−	0.548271i
$999$	−10.0000	+	17.3205i	−0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.a.331.1	yes	2
7.2	even	3		5390.2.a.be.1.1		1
7.4	even	3	inner	770.2.i.a.221.1	✓	2
7.5	odd	6		5390.2.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.a.221.1	✓	2	7.4	even	3	inner
770.2.i.a.331.1	yes	2	1.1	even	1	trivial
5390.2.a.z.1.1		1	7.5	odd	6
5390.2.a.be.1.1		1	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -5.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(0.500000 - 2.59808i) q^{35} -2.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +12.0000 q^{41} +(2.50000 - 0.866025i) q^{42} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{46} +(6.00000 - 10.3923i) q^{47} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} -4.00000 q^{62} +(1.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(6.50000 + 11.2583i) q^{67} -6.00000 q^{69} +(2.00000 + 1.73205i) q^{70} +(1.00000 - 1.73205i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} -1.00000 q^{78} +(-8.50000 + 14.7224i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +6.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(5.00000 - 8.66025i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +2.00000 q^{90} +(-2.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(6.00000 + 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} + 2 q^{8} + 2 q^{9} + q^{10} - q^{11} - q^{12} - 2 q^{13} - q^{14} - 2 q^{15} - q^{16} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 4 q^{21} + 2 q^{22} + 6 q^{23} - q^{24} - q^{25} + q^{26} - 10 q^{27} - 4 q^{28} - 18 q^{29} + q^{30} + 4 q^{31} - q^{32} - q^{33} + q^{35} - 4 q^{36} + 4 q^{37} - 2 q^{38} + q^{39} + q^{40} + 24 q^{41} + 5 q^{42} - 20 q^{43} - q^{44} - 2 q^{45} + 6 q^{46} + 12 q^{47} + 2 q^{48} + 11 q^{49} + 2 q^{50} + q^{52} - 6 q^{53} + 5 q^{54} - 2 q^{55} + 5 q^{56} + 4 q^{57} + 9 q^{58} - 3 q^{59} + q^{60} + 7 q^{61} - 8 q^{62} + 2 q^{63} + 2 q^{64} - q^{65} - q^{66} + 13 q^{67} - 12 q^{69} + 4 q^{70} + 2 q^{72} - 14 q^{73} + 4 q^{74} - q^{75} + 4 q^{76} - 4 q^{77} - 2 q^{78} - 17 q^{79} + q^{80} - q^{81} - 12 q^{82} + 12 q^{83} - q^{84} + 10 q^{86} + 9 q^{87} - q^{88} + 6 q^{89} + 4 q^{90} - 5 q^{91} - 12 q^{92} + 4 q^{93} + 12 q^{94} + 2 q^{95} - q^{96} + 10 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 + 2 * q^8 + 2 * q^9 + q^10 - q^11 - q^12 - 2 * q^13 - q^14 - 2 * q^15 - q^16 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 4 * q^21 + 2 * q^22 + 6 * q^23 - q^24 - q^25 + q^26 - 10 * q^27 - 4 * q^28 - 18 * q^29 + q^30 + 4 * q^31 - q^32 - q^33 + q^35 - 4 * q^36 + 4 * q^37 - 2 * q^38 + q^39 + q^40 + 24 * q^41 + 5 * q^42 - 20 * q^43 - q^44 - 2 * q^45 + 6 * q^46 + 12 * q^47 + 2 * q^48 + 11 * q^49 + 2 * q^50 + q^52 - 6 * q^53 + 5 * q^54 - 2 * q^55 + 5 * q^56 + 4 * q^57 + 9 * q^58 - 3 * q^59 + q^60 + 7 * q^61 - 8 * q^62 + 2 * q^63 + 2 * q^64 - q^65 - q^66 + 13 * q^67 - 12 * q^69 + 4 * q^70 + 2 * q^72 - 14 * q^73 + 4 * q^74 - q^75 + 4 * q^76 - 4 * q^77 - 2 * q^78 - 17 * q^79 + q^80 - q^81 - 12 * q^82 + 12 * q^83 - q^84 + 10 * q^86 + 9 * q^87 - q^88 + 6 * q^89 + 4 * q^90 - 5 * q^91 - 12 * q^92 + 4 * q^93 + 12 * q^94 + 2 * q^95 - q^96 + 10 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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