LMFDB - Embedded newform 770.2.i.b.221.1

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			221.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.b.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(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} +(-0.500000 - 2.59808i) 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} -2.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +5.00000 q^{27} +(2.50000 + 0.866025i) q^{28} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} -4.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} -2.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -1.00000 q^{41} +(0.500000 + 2.59808i) q^{42} +1.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.00000 - 6.92820i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(-2.00000 - 3.46410i) q^{51} +(1.00000 - 1.73205i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -8.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +(4.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(6.50000 - 11.2583i) q^{67} +(2.00000 + 3.46410i) q^{68} +1.00000 q^{69} +(2.50000 + 0.866025i) q^{70} -16.0000 q^{71} +(1.00000 + 1.73205i) q^{72} +(2.00000 - 3.46410i) q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +8.00000 q^{76} +(-2.50000 - 0.866025i) q^{77} +2.00000 q^{78} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} -1.00000 q^{83} +(2.00000 - 1.73205i) q^{84} -4.00000 q^{85} +(-0.500000 - 0.866025i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} -2.00000 q^{90} +(1.00000 + 5.19615i) q^{91} -1.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(5.50000 + 4.33013i) 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} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - q^{10} + q^{11} + q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 4 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{20} - 5 q^{21} - 2 q^{22} + q^{23} + q^{24} - q^{25} + 2 q^{26} + 10 q^{27} + 5 q^{28} - 18 q^{29} + q^{30} - 2 q^{31} - q^{32} - q^{33} - 8 q^{34} - 4 q^{35} - 4 q^{36} + 2 q^{37} - 8 q^{38} - 2 q^{39} - q^{40} - 2 q^{41} + q^{42} + 2 q^{43} + q^{44} + 2 q^{45} + q^{46} - 8 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} - 4 q^{51} + 2 q^{52} - 2 q^{53} - 5 q^{54} - 2 q^{55} - q^{56} - 16 q^{57} + 9 q^{58} + 6 q^{59} + q^{60} + 5 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} + 2 q^{65} - q^{66} + 13 q^{67} + 4 q^{68} + 2 q^{69} + 5 q^{70} - 32 q^{71} + 2 q^{72} + 4 q^{73} + 2 q^{74} + q^{75} + 16 q^{76} - 5 q^{77} + 4 q^{78} + 14 q^{79} - q^{80} - q^{81} + q^{82} - 2 q^{83} + 4 q^{84} - 8 q^{85} - q^{86} - 9 q^{87} + q^{88} - q^{89} - 4 q^{90} + 2 q^{91} - 2 q^{92} + 2 q^{93} - 8 q^{94} - 8 q^{95} + q^{96} - 16 q^{97} + 11 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - q^10 + q^11 + q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - q^16 + 4 * q^17 + 2 * q^18 - 8 * q^19 + 2 * q^20 - 5 * q^21 - 2 * q^22 + q^23 + q^24 - q^25 + 2 * q^26 + 10 * q^27 + 5 * q^28 - 18 * q^29 + q^30 - 2 * q^31 - q^32 - q^33 - 8 * q^34 - 4 * q^35 - 4 * q^36 + 2 * q^37 - 8 * q^38 - 2 * q^39 - q^40 - 2 * q^41 + q^42 + 2 * q^43 + q^44 + 2 * q^45 + q^46 - 8 * q^47 - 2 * q^48 - 13 * q^49 + 2 * q^50 - 4 * q^51 + 2 * q^52 - 2 * q^53 - 5 * q^54 - 2 * q^55 - q^56 - 16 * q^57 + 9 * q^58 + 6 * q^59 + q^60 + 5 * q^61 + 4 * q^62 + 8 * q^63 + 2 * q^64 + 2 * q^65 - q^66 + 13 * q^67 + 4 * q^68 + 2 * q^69 + 5 * q^70 - 32 * q^71 + 2 * q^72 + 4 * q^73 + 2 * q^74 + q^75 + 16 * q^76 - 5 * q^77 + 4 * q^78 + 14 * q^79 - q^80 - q^81 + q^82 - 2 * q^83 + 4 * q^84 - 8 * q^85 - q^86 - 9 * q^87 + q^88 - q^89 - 4 * q^90 + 2 * q^91 - 2 * q^92 + 2 * q^93 - 8 * q^94 - 8 * q^95 + q^96 - 16 * q^97 + 11 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−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	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−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
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	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
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	1.00000	−	1.73205i	0.235702	−	0.408248i
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$	1.00000			0.223607
$21$	−2.50000	−	0.866025i	−0.545545	−	0.188982i
$22$	−1.00000			−0.213201
$23$	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	$0.800087\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	5.00000			0.962250
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	−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
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	−4.00000			−0.685994
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$	−2.00000			−0.333333
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	−4.00000	+	6.92820i	−0.648886	+	1.12390i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.00000			−0.156174			−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000			−0.156174			−0.0780869	+	0.996947i	$0.524881\pi$
$42$	0.500000	+	2.59808i	0.0771517	+	0.400892i
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	1.00000			0.141421
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$	−1.00000			−0.134840
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$	−8.00000			−1.05963
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	2.00000			0.254000
$63$	4.00000	−	3.46410i	0.503953	−	0.436436i
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	1.00000			0.120386
$70$	2.50000	+	0.866025i	0.298807	+	0.103510i
$71$	−16.0000			−1.89885			−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000			−1.89885			−0.949425	+	0.313993i	$0.898333\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	8.00000			0.917663
$77$	−2.50000	−	0.866025i	−0.284901	−	0.0986928i
$78$	2.00000			0.226455
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	0.927457	+	0.373930i	$0.121990\pi$
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	−0.139895	+	0.990166i	$0.544677\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.500000	+	0.866025i	0.0552158	+	0.0956365i
$83$	−1.00000			−0.109764			−0.0548821	−	0.998493i	$-0.517478\pi$
$83$	−1.00000			−0.109764			−0.0548821	+	0.998493i	$0.517478\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$	−4.00000			−0.433861
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	0.838308	−	0.545197i	$-0.183545\pi$
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	−0.891308	+	0.453398i	$0.850212\pi$
$90$	−2.00000			−0.210819
$91$	1.00000	+	5.19615i	0.104828	+	0.544705i
$92$	−1.00000			−0.104257
$93$	1.00000	+	1.73205i	0.103695	+	0.179605i
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	2.00000			0.201008
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	−2.00000	+	3.46410i	−0.198030	+	0.342997i
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.772728	+	0.634738i	$0.218892\pi$
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.163335	+	0.986571i	$0.447775\pi$
$104$	−2.00000			−0.196116
$105$	0.500000	+	2.59808i	0.0487950	+	0.253546i
$106$	2.00000			0.194257
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	9.50000	−	16.4545i	0.909935	−	1.57605i	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	9.50000	−	16.4545i	0.909935	−	1.57605i	0.814152	−	0.580651i	$-0.197202\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$	2.00000			0.189832
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	16.0000			1.50515			0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000			1.50515			0.752577	+	0.658505i	$0.228811\pi$
$114$	4.00000	+	6.92820i	0.374634	+	0.648886i
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	−6.00000			−0.552345
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$	−1.00000			−0.0912871
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.50000	−	4.33013i	0.226339	−	0.392031i
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	1.00000			0.0894427
$126$	−5.00000	−	1.73205i	−0.445435	−	0.154303i
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.500000	−	0.866025i	0.0440225	−	0.0762493i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	1.00000			0.0870388
$133$	−16.0000	+	13.8564i	−1.38738	+	1.20150i
$134$	−13.0000			−1.12303
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	18.0000			1.52674			0.763370	−	0.645961i	$-0.223543\pi$
$139$	18.0000			1.52674			0.763370	+	0.645961i	$0.223543\pi$
$140$	−0.500000	−	2.59808i	−0.0422577	−	0.219578i
$141$	−8.00000			−0.673722
$142$	8.00000	+	13.8564i	0.671345	+	1.16280i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	−4.00000			−0.331042
$147$	−1.00000	+	6.92820i	−0.0824786	+	0.571429i
$148$	−2.00000			−0.164399
$149$	3.50000	+	6.06218i	0.286731	+	0.496633i	0.973028	−	0.230689i	$-0.0740980\pi$
$149$	3.50000	+	6.06218i	0.286731	+	0.496633i	−0.686296	+	0.727322i	$0.740765\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$	−4.00000	−	6.92820i	−0.324443	−	0.561951i
$153$	8.00000			0.646762
$154$	0.500000	+	2.59808i	0.0402911	+	0.209359i
$155$	2.00000			0.160644
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	6.00000	−	10.3923i	0.478852	−	0.829396i	−0.520854	−	0.853646i	$-0.674386\pi$
$157$	6.00000	−	10.3923i	0.478852	−	0.829396i	0.999706	+	0.0242497i	$0.00771967\pi$
$158$	7.00000	−	12.1244i	0.556890	−	0.964562i
$159$	1.00000	+	1.73205i	0.0793052	+	0.137361i
$160$	1.00000			0.0790569
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$	1.00000			0.0785674
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	0.500000	−	0.866025i	0.0390434	−	0.0676252i
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$	0.500000	+	0.866025i	0.0388075	+	0.0672166i
$167$	9.00000			0.696441			0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000			0.696441			0.348220	+	0.937413i	$0.386786\pi$
$168$	−2.50000	−	0.866025i	−0.192879	−	0.0668153i
$169$	−9.00000			−0.692308
$170$	2.00000	+	3.46410i	0.153393	+	0.265684i
$171$	8.00000	−	13.8564i	0.611775	−	1.05963i
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	9.00000			0.682288
$175$	2.50000	+	0.866025i	0.188982	+	0.0654654i
$176$	−1.00000			−0.0753778
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	−0.500000	+	0.866025i	−0.0374766	+	0.0649113i
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	4.00000	−	3.46410i	0.296500	−	0.256776i
$183$	5.00000			0.369611
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	8.00000			0.583460
$189$	−2.50000	−	12.9904i	−0.181848	−	0.944911i
$190$	8.00000			0.580381
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	2.00000			0.143223
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−6.50000	−	11.2583i	−0.458475	−	0.794101i
$202$	−3.00000			−0.211079
$203$	4.50000	+	23.3827i	0.315838	+	1.64114i
$204$	4.00000			0.280056
$205$	0.500000	+	0.866025i	0.0349215	+	0.0604858i
$206$	9.50000	−	16.4545i	0.661896	−	1.14644i
$207$	−1.00000	+	1.73205i	−0.0695048	+	0.120386i
$208$	1.00000	+	1.73205i	0.0693375	+	0.120096i
$209$	−8.00000			−0.553372
$210$	2.00000	−	1.73205i	0.138013	−	0.119523i
$211$	−6.00000			−0.413057			−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000			−0.413057			−0.206529	+	0.978441i	$0.566217\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$	−8.00000	+	13.8564i	−0.548151	+	0.949425i
$214$	−4.50000	+	7.79423i	−0.307614	+	0.532803i
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$	5.00000			0.340207
$217$	5.00000	+	1.73205i	0.339422	+	0.117579i
$218$	−19.0000			−1.28684
$219$	−2.00000	−	3.46410i	−0.135147	−	0.234082i
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	−4.00000	+	6.92820i	−0.269069	+	0.466041i
$222$	−1.00000	−	1.73205i	−0.0671156	−	0.116248i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$	−2.00000			−0.133333
$226$	−8.00000	−	13.8564i	−0.532152	−	0.921714i
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$	4.00000	−	6.92820i	0.264906	−	0.458831i
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	0.947960	−	0.318390i	$-0.103142\pi$
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	−0.749714	+	0.661762i	$0.769809\pi$
$230$	−1.00000			−0.0659380
$231$	−2.00000	+	1.73205i	−0.131590	+	0.113961i
$232$	−9.00000			−0.590879
$233$	−11.0000	−	19.0526i	−0.720634	−	1.24817i	−0.960746	−	0.277429i	$-0.910518\pi$
$233$	−11.0000	−	19.0526i	−0.720634	−	1.24817i	0.240112	−	0.970745i	$-0.422816\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	14.0000			0.909398
$238$	2.00000	+	10.3923i	0.129641	+	0.673633i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−5.00000			−0.320092
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$	1.00000			0.0637577
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$	−0.500000	+	0.866025i	−0.0316862	+	0.0548821i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	1.00000	+	5.19615i	0.0629941	+	0.327327i
$253$	1.00000			0.0628695
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	−2.00000	+	3.46410i	−0.125245	+	0.216930i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	0.666880	−	0.745165i	$-0.267629\pi$
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	−0.978772	+	0.204953i	$0.934296\pi$
$258$	−1.00000			−0.0622573
$259$	4.00000	−	3.46410i	0.248548	−	0.215249i
$260$	−2.00000			−0.124035
$261$	−9.00000	−	15.5885i	−0.557086	−	0.964901i
$262$	−9.00000	+	15.5885i	−0.556022	+	0.963058i
$263$	−3.50000	+	6.06218i	−0.215819	+	0.373810i	−0.953526	−	0.301312i	$-0.902576\pi$
$263$	−3.50000	+	6.06218i	−0.215819	+	0.373810i	0.737706	+	0.675122i	$0.235909\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	2.00000			0.122859
$266$	20.0000	+	6.92820i	1.22628	+	0.424795i
$267$	−1.00000			−0.0611990
$268$	6.50000	+	11.2583i	0.397051	+	0.687712i
$269$	−9.50000	+	16.4545i	−0.579225	+	1.00325i	0.416343	+	0.909208i	$0.363311\pi$
$269$	−9.50000	+	16.4545i	−0.579225	+	1.00325i	−0.995568	+	0.0940400i	$0.970022\pi$
$270$	−2.50000	+	4.33013i	−0.152145	+	0.263523i
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	−4.00000			−0.242536
$273$	5.00000	+	1.73205i	0.302614	+	0.104828i
$274$	−2.00000			−0.120824
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	−9.00000	−	15.5885i	−0.539784	−	0.934934i
$279$	−4.00000			−0.239474
$280$	−2.00000	+	1.73205i	−0.119523	+	0.103510i
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	4.00000	+	6.92820i	0.238197	+	0.412568i
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	8.00000	−	13.8564i	0.474713	−	0.822226i
$285$	4.00000	+	6.92820i	0.236940	+	0.410391i
$286$	2.00000			0.118262
$287$	0.500000	+	2.59808i	0.0295141	+	0.153360i
$288$	−2.00000			−0.117851
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	−2.00000			−0.116841			−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000			−0.116841			−0.0584206	+	0.998292i	$0.518606\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$	−6.00000			−0.349334
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$	3.50000	−	6.06218i	0.202750	−	0.351173i
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$	−1.00000			−0.0577350
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	−12.0000			−0.690522
$303$	−1.50000	−	2.59808i	−0.0861727	−	0.149256i
$304$	−4.00000	+	6.92820i	−0.229416	+	0.397360i
$305$	2.50000	−	4.33013i	0.143150	−	0.247942i
$306$	−4.00000	−	6.92820i	−0.228665	−	0.396059i
$307$	−23.0000			−1.31268			−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000			−1.31268			−0.656340	+	0.754466i	$0.727896\pi$
$308$	2.00000	−	1.73205i	0.113961	−	0.0986928i
$309$	19.0000			1.08087
$310$	−1.00000	−	1.73205i	−0.0567962	−	0.0983739i
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$	−1.00000	+	1.73205i	−0.0566139	+	0.0980581i
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−12.0000			−0.677199
$315$	−5.00000	−	1.73205i	−0.281718	−	0.0975900i
$316$	−14.0000			−0.787562
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	1.00000	−	1.73205i	0.0560772	−	0.0971286i
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−9.00000			−0.502331
$322$	−2.50000	−	0.866025i	−0.139320	−	0.0482617i
$323$	−32.0000			−1.78053
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$	−9.50000	−	16.4545i	−0.525351	−	0.909935i
$328$	−1.00000			−0.0552158
$329$	−16.0000	+	13.8564i	−0.882109	+	0.763928i
$330$	1.00000			0.0550482
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	0.500000	−	0.866025i	0.0274411	−	0.0475293i
$333$	−2.00000	+	3.46410i	−0.109599	+	0.189832i
$334$	−4.50000	−	7.79423i	−0.246229	−	0.426481i
$335$	−13.0000			−0.710266
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$	8.00000			0.435788			0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000			0.435788			0.217894	+	0.975972i	$0.430081\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	8.00000	−	13.8564i	0.434500	−	0.752577i
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	1.00000	+	1.73205i	0.0541530	+	0.0937958i
$342$	−16.0000			−0.865181
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	1.00000			0.0539164
$345$	−0.500000	−	0.866025i	−0.0269191	−	0.0466252i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	−0.822951	−	0.568112i	$-0.807674\pi$
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	0.903475	+	0.428640i	$0.141007\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	19.0000			1.01705			0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000			1.01705			0.508523	+	0.861048i	$0.330192\pi$
$350$	−0.500000	−	2.59808i	−0.0267261	−	0.138873i
$351$	−10.0000			−0.533761
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	1.00000			0.0529999
$357$	−8.00000	+	6.92820i	−0.423405	+	0.366679i
$358$	−4.00000			−0.211407
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	−1.00000			−0.0524864
$364$	−5.00000	−	1.73205i	−0.262071	−	0.0907841i
$365$	−4.00000			−0.209370
$366$	−2.50000	−	4.33013i	−0.130677	−	0.226339i
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	−0.824217	−	0.566274i	$-0.808384\pi$
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	0.902516	+	0.430656i	$0.141718\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−1.00000	−	1.73205i	−0.0520579	−	0.0901670i
$370$	−2.00000			−0.103975
$371$	5.00000	+	1.73205i	0.259587	+	0.0899236i
$372$	−2.00000			−0.103695
$373$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$373$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$	18.0000			0.927047
$378$	−10.0000	+	8.66025i	−0.514344	+	0.445435i
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$	6.00000	−	10.3923i	0.307389	−	0.532414i
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	0.957790	−	0.287469i	$-0.0928139\pi$
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	−0.727851	+	0.685736i	$0.759481\pi$
$384$	−1.00000			−0.0510310
$385$	0.500000	+	2.59808i	0.0254824	+	0.132410i
$386$	−14.0000			−0.712581
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	−17.0000	+	29.4449i	−0.861934	+	1.49291i	0.00812520	+	0.999967i	$0.497414\pi$
$389$	−17.0000	+	29.4449i	−0.861934	+	1.49291i	−0.870059	+	0.492947i	$0.835920\pi$
$390$	−1.00000	−	1.73205i	−0.0506370	−	0.0877058i
$391$	4.00000			0.202289
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$	−18.0000			−0.907980
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	7.00000	−	12.1244i	0.352208	−	0.610043i
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	−6.00000	−	10.3923i	−0.301131	−	0.521575i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	−6.00000	−	10.3923i	−0.301131	−	0.521575i	−0.976392	+	0.216004i	$0.930698\pi$
$398$	−24.0000			−1.20301
$399$	4.00000	+	20.7846i	0.200250	+	1.04053i
$400$	1.00000			0.0500000
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$	−6.50000	+	11.2583i	−0.324191	+	0.561514i
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	1.00000			0.0496904
$406$	18.0000	−	15.5885i	0.893325	−	0.773642i
$407$	2.00000			0.0991363
$408$	−2.00000	−	3.46410i	−0.0990148	−	0.171499i
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$	0.500000	−	0.866025i	0.0246932	−	0.0427699i
$411$	−1.00000	−	1.73205i	−0.0493264	−	0.0854358i
$412$	−19.0000			−0.936063
$413$	−15.0000	−	5.19615i	−0.738102	−	0.255686i
$414$	2.00000			0.0982946
$415$	0.500000	+	0.866025i	0.0245440	+	0.0425115i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	9.00000	−	15.5885i	0.440732	−	0.763370i
$418$	4.00000	+	6.92820i	0.195646	+	0.338869i
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$	−2.50000	−	0.866025i	−0.121988	−	0.0422577i
$421$	−35.0000			−1.70580			−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000			−1.70580			−0.852898	+	0.522078i	$0.825157\pi$
$422$	3.00000	+	5.19615i	0.146038	+	0.252945i
$423$	8.00000	−	13.8564i	0.388973	−	0.673722i
$424$	−1.00000	+	1.73205i	−0.0485643	+	0.0841158i
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$	16.0000			0.775203
$427$	10.0000	−	8.66025i	0.483934	−	0.419099i
$428$	9.00000			0.435031
$429$	1.00000	+	1.73205i	0.0482805	+	0.0836242i
$430$	−0.500000	+	0.866025i	−0.0241121	+	0.0417635i
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	0.302300	+	0.953213i	$0.402245\pi$
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	−0.976657	+	0.214807i	$0.931088\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$	−1.00000	−	5.19615i	−0.0480015	−	0.249423i
$435$	9.00000			0.431517
$436$	9.50000	+	16.4545i	0.454967	+	0.788027i
$437$	4.00000	−	6.92820i	0.191346	−	0.331421i
$438$	−2.00000	+	3.46410i	−0.0955637	+	0.165521i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$	−1.00000			−0.0476731
$441$	−11.0000	−	8.66025i	−0.523810	−	0.412393i
$442$	8.00000			0.380521
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	−0.500000	+	0.866025i	−0.0237023	+	0.0410535i
$446$	−12.0000	−	20.7846i	−0.568216	−	0.984180i
$447$	7.00000			0.331089
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$	1.00000	+	1.73205i	0.0471405	+	0.0816497i
$451$	−0.500000	+	0.866025i	−0.0235441	+	0.0407795i
$452$	−8.00000	+	13.8564i	−0.376288	+	0.651751i
$453$	−6.00000	−	10.3923i	−0.281905	−	0.488273i
$454$	−4.00000			−0.187729
$455$	4.00000	−	3.46410i	0.187523	−	0.162400i
$456$	−8.00000			−0.374634
$457$	4.00000	+	6.92820i	0.187112	+	0.324088i	0.944286	−	0.329125i	$-0.106754\pi$
$457$	4.00000	+	6.92820i	0.187112	+	0.324088i	−0.757174	+	0.653213i	$0.773421\pi$
$458$	3.00000	−	5.19615i	0.140181	−	0.242800i
$459$	10.0000	−	17.3205i	0.466760	−	0.808452i
$460$	0.500000	+	0.866025i	0.0233126	+	0.0403786i
$461$	−34.0000			−1.58354			−0.791769	−	0.610821i	$-0.790840\pi$
$461$	−34.0000			−1.58354			−0.791769	+	0.610821i	$0.790840\pi$
$462$	2.50000	+	0.866025i	0.116311	+	0.0402911i
$463$	−35.0000			−1.62659			−0.813294	−	0.581853i	$-0.802328\pi$
$463$	−35.0000			−1.62659			−0.813294	+	0.581853i	$0.802328\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$	1.00000	−	1.73205i	0.0463739	−	0.0803219i
$466$	−11.0000	+	19.0526i	−0.509565	+	0.882593i
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	0.638667	−	0.769483i	$-0.279486\pi$
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	−0.985726	+	0.168360i	$0.946153\pi$
$468$	4.00000			0.184900
$469$	−32.5000	−	11.2583i	−1.50071	−	0.519861i
$470$	8.00000			0.369012
$471$	−6.00000	−	10.3923i	−0.276465	−	0.478852i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	0.500000	−	0.866025i	0.0229900	−	0.0398199i
$474$	−7.00000	−	12.1244i	−0.321521	−	0.556890i
$475$	8.00000			0.367065
$476$	8.00000	−	6.92820i	0.366679	−	0.317554i
$477$	−4.00000			−0.183147
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.235833	−	0.971794i	$-0.424218\pi$
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.723681	−	0.690134i	$-0.242449\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	14.0000			0.637683
$483$	−0.500000	−	2.59808i	−0.0227508	−	0.118217i
$484$	1.00000			0.0454545
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	−18.0000	+	31.1769i	−0.815658	+	1.41276i	0.0931967	+	0.995648i	$0.470291\pi$
$487$	−18.0000	+	31.1769i	−0.815658	+	1.41276i	−0.908855	+	0.417113i	$0.863042\pi$
$488$	2.50000	+	4.33013i	0.113170	+	0.196016i
$489$	16.0000			0.723545
$490$	1.00000	−	6.92820i	0.0451754	−	0.312984i
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$	−0.500000	−	0.866025i	−0.0225417	−	0.0390434i
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$	8.00000	−	13.8564i	0.359937	−	0.623429i
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$	2.00000			0.0898027
$497$	8.00000	+	41.5692i	0.358849	+	1.86463i
$498$	1.00000			0.0448111
$499$	−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	$0.861871\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	4.50000	−	7.79423i	0.201045	−	0.348220i
$502$	−9.00000	−	15.5885i	−0.401690	−	0.695747i
$503$	−39.0000			−1.73892			−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000			−1.73892			−0.869462	+	0.494000i	$0.835534\pi$
$504$	4.00000	−	3.46410i	0.178174	−	0.154303i
$505$	−3.00000			−0.133498
$506$	−0.500000	−	0.866025i	−0.0222277	−	0.0384995i
$507$	−4.50000	+	7.79423i	−0.199852	+	0.346154i
$508$	−6.00000	+	10.3923i	−0.266207	+	0.461084i
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	0.897352	−	0.441315i	$-0.145488\pi$
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	−0.830866	+	0.556473i	$0.812154\pi$
$510$	4.00000			0.177123
$511$	−10.0000	−	3.46410i	−0.442374	−	0.153243i
$512$	1.00000			0.0441942
$513$	−20.0000	−	34.6410i	−0.883022	−	1.52944i
$514$	−5.00000	+	8.66025i	−0.220541	+	0.381987i
$515$	9.50000	−	16.4545i	0.418620	−	0.725071i
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	−8.00000			−0.351840
$518$	−5.00000	−	1.73205i	−0.219687	−	0.0761019i
$519$	6.00000			0.263371
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	1.00000	−	1.73205i	0.0438108	−	0.0758825i	−0.843288	−	0.537461i	$-0.819383\pi$
$521$	1.00000	−	1.73205i	0.0438108	−	0.0758825i	0.887099	+	0.461579i	$0.152717\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$523$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$524$	18.0000			0.786334
$525$	2.00000	−	1.73205i	0.0872872	−	0.0755929i
$526$	7.00000			0.305215
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$	−0.500000	+	0.866025i	−0.0217597	+	0.0376889i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−1.00000	−	1.73205i	−0.0434372	−	0.0752355i
$531$	12.0000			0.520756
$532$	−4.00000	−	20.7846i	−0.173422	−	0.901127i
$533$	2.00000			0.0866296
$534$	0.500000	+	0.866025i	0.0216371	+	0.0374766i
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$	6.50000	−	11.2583i	0.280757	−	0.486286i
$537$	−2.00000	−	3.46410i	−0.0863064	−	0.149487i
$538$	19.0000			0.819148
$539$	−1.00000	+	6.92820i	−0.0430730	+	0.298419i
$540$	5.00000			0.215166
$541$	−0.500000	−	0.866025i	−0.0214967	−	0.0372333i	0.855077	−	0.518501i	$-0.173510\pi$
$541$	−0.500000	−	0.866025i	−0.0214967	−	0.0372333i	−0.876574	+	0.481268i	$0.840176\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$	3.50000	−	6.06218i	0.150199	−	0.260153i
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	−19.0000			−0.813871
$546$	−1.00000	−	5.19615i	−0.0427960	−	0.222375i
$547$	37.0000			1.58201			0.791003	−	0.611812i	$-0.209559\pi$
$547$	37.0000			1.58201			0.791003	+	0.611812i	$0.209559\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	36.0000	+	62.3538i	1.53365	+	2.65636i
$552$	1.00000			0.0425628
$553$	28.0000	−	24.2487i	1.19068	−	1.03116i
$554$	22.0000			0.934690
$555$	−1.00000	−	1.73205i	−0.0424476	−	0.0735215i
$556$	−9.00000	+	15.5885i	−0.381685	+	0.661098i
$557$	22.0000	−	38.1051i	0.932170	−	1.61457i	0.152566	−	0.988293i	$-0.451246\pi$
$557$	22.0000	−	38.1051i	0.932170	−	1.61457i	0.779604	−	0.626272i	$-0.215420\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	−2.00000			−0.0845910
$560$	2.50000	+	0.866025i	0.105644	+	0.0365963i
$561$	−4.00000			−0.168880
$562$	5.00000	+	8.66025i	0.210912	+	0.365311i
$563$	−7.50000	+	12.9904i	−0.316087	+	0.547479i	−0.979668	−	0.200625i	$-0.935703\pi$
$563$	−7.50000	+	12.9904i	−0.316087	+	0.547479i	0.663581	+	0.748105i	$0.269036\pi$
$564$	4.00000	−	6.92820i	0.168430	−	0.291730i
$565$	−8.00000	−	13.8564i	−0.336563	−	0.582943i
$566$	−20.0000			−0.840663
$567$	2.50000	+	0.866025i	0.104990	+	0.0363696i
$568$	−16.0000			−0.671345
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	0.998608	+	0.0527519i	$0.0167993\pi$
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	−0.453619	+	0.891196i	$0.649867\pi$
$570$	4.00000	−	6.92820i	0.167542	−	0.290191i
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	−0.990571	−	0.137002i	$-0.956253\pi$
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	0.613933	+	0.789359i	$0.289587\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$	16.0000			0.668410
$574$	2.00000	−	1.73205i	0.0834784	−	0.0722944i
$575$	−1.00000			−0.0417029
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−15.0000	+	25.9808i	−0.624458	+	1.08159i	0.364187	+	0.931326i	$0.381347\pi$
$577$	−15.0000	+	25.9808i	−0.624458	+	1.08159i	−0.988645	+	0.150268i	$0.951987\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	−7.00000	−	12.1244i	−0.290910	−	0.503871i
$580$	−9.00000			−0.373705
$581$	0.500000	+	2.59808i	0.0207435	+	0.107786i
$582$	8.00000			0.331611
$583$	1.00000	+	1.73205i	0.0414158	+	0.0717342i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$	1.00000	+	1.73205i	0.0413096	+	0.0715504i
$587$	36.0000			1.48588			0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000			1.48588			0.742940	+	0.669359i	$0.233431\pi$
$588$	−5.50000	−	4.33013i	−0.226816	−	0.178571i
$589$	16.0000			0.659269
$590$	3.00000	+	5.19615i	0.123508	+	0.213922i
$591$	−1.00000	+	1.73205i	−0.0411345	+	0.0712470i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−2.00000	−	3.46410i	−0.0821302	−	0.142254i	0.822035	−	0.569438i	$-0.192839\pi$
$593$	−2.00000	−	3.46410i	−0.0821302	−	0.142254i	−0.904165	+	0.427184i	$0.859506\pi$
$594$	−5.00000			−0.205152
$595$	2.00000	+	10.3923i	0.0819920	+	0.426043i
$596$	−7.00000			−0.286731
$597$	−12.0000	−	20.7846i	−0.491127	−	0.850657i
$598$	−1.00000	+	1.73205i	−0.0408930	+	0.0708288i
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	−2.00000	+	1.73205i	−0.0815139	+	0.0705931i
$603$	26.0000			1.05880
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	−1.50000	+	2.59808i	−0.0609333	+	0.105540i
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	8.00000			0.324443
$609$	22.5000	+	7.79423i	0.911746	+	0.315838i
$610$	−5.00000			−0.202444
$611$	8.00000	+	13.8564i	0.323645	+	0.560570i
$612$	−4.00000	+	6.92820i	−0.161690	+	0.280056i
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	−0.386073	−	0.922468i	$-0.626169\pi$
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	0.991917	−	0.126885i	$-0.0404979\pi$
$614$	11.5000	+	19.9186i	0.464102	+	0.803849i
$615$	1.00000			0.0403239
$616$	−2.50000	−	0.866025i	−0.100728	−	0.0348932i
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$	−9.50000	−	16.4545i	−0.382146	−	0.661896i
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	−0.477143	−	0.878826i	$-0.658328\pi$
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	0.999657	−	0.0261952i	$-0.00833914\pi$
$620$	−1.00000	+	1.73205i	−0.0401610	+	0.0695608i
$621$	2.50000	+	4.33013i	0.100322	+	0.173762i
$622$	−18.0000			−0.721734
$623$	−2.00000	+	1.73205i	−0.0801283	+	0.0693932i
$624$	2.00000			0.0800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−4.00000	+	6.92820i	−0.159745	+	0.276686i
$628$	6.00000	+	10.3923i	0.239426	+	0.414698i
$629$	8.00000			0.318981
$630$	1.00000	+	5.19615i	0.0398410	+	0.207020i
$631$	−22.0000			−0.875806			−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000			−0.875806			−0.437903	+	0.899022i	$0.644279\pi$
$632$	7.00000	+	12.1244i	0.278445	+	0.482281i
$633$	−3.00000	+	5.19615i	−0.119239	+	0.206529i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$	−2.00000			−0.0793052
$637$	13.0000	−	5.19615i	0.515079	−	0.205879i
$638$	9.00000			0.356313
$639$	−16.0000	−	27.7128i	−0.632950	−	1.09630i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$	4.50000	+	7.79423i	0.177601	+	0.307614i
$643$	−12.0000			−0.473234			−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000			−0.473234			−0.236617	+	0.971603i	$0.576039\pi$
$644$	0.500000	+	2.59808i	0.0197028	+	0.102379i
$645$	−1.00000			−0.0393750
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	7.50000	−	12.9904i	0.294855	−	0.510705i	−0.680096	−	0.733123i	$-0.738062\pi$
$647$	7.50000	−	12.9904i	0.294855	−	0.510705i	0.974951	+	0.222419i	$0.0713952\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−3.00000	−	5.19615i	−0.117760	−	0.203967i
$650$	−2.00000			−0.0784465
$651$	4.00000	−	3.46410i	0.156772	−	0.135769i
$652$	−16.0000			−0.626608
$653$	−13.0000	−	22.5167i	−0.508729	−	0.881145i	−0.999949	−	0.0101092i	$-0.996782\pi$
$653$	−13.0000	−	22.5167i	−0.508729	−	0.881145i	0.491220	−	0.871036i	$-0.336551\pi$
$654$	−9.50000	+	16.4545i	−0.371479	+	0.643421i
$655$	−9.00000	+	15.5885i	−0.351659	+	0.609091i
$656$	0.500000	+	0.866025i	0.0195217	+	0.0338126i
$657$	8.00000			0.312110
$658$	20.0000	+	6.92820i	0.779681	+	0.270089i
$659$	−48.0000			−1.86981			−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000			−1.86981			−0.934907	+	0.354892i	$0.884518\pi$
$660$	−0.500000	−	0.866025i	−0.0194625	−	0.0337100i
$661$	−6.50000	+	11.2583i	−0.252821	+	0.437898i	−0.964301	−	0.264807i	$-0.914692\pi$
$661$	−6.50000	+	11.2583i	−0.252821	+	0.437898i	0.711481	+	0.702706i	$0.248025\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$	4.00000	+	6.92820i	0.155347	+	0.269069i
$664$	−1.00000			−0.0388075
$665$	20.0000	+	6.92820i	0.775567	+	0.268664i
$666$	4.00000			0.154997
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$	−4.50000	+	7.79423i	−0.174110	+	0.301568i
$669$	12.0000	−	20.7846i	0.463947	−	0.803579i
$670$	6.50000	+	11.2583i	0.251117	+	0.434947i
$671$	5.00000			0.193023
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	−4.00000	−	6.92820i	−0.154074	−	0.266864i
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−14.0000	−	24.2487i	−0.538064	−	0.931954i	−0.999008	−	0.0445248i	$-0.985823\pi$
$677$	−14.0000	−	24.2487i	−0.538064	−	0.931954i	0.460945	−	0.887429i	$-0.347511\pi$
$678$	−16.0000			−0.614476
$679$	4.00000	+	20.7846i	0.153506	+	0.797640i
$680$	−4.00000			−0.153393
$681$	−2.00000	−	3.46410i	−0.0766402	−	0.132745i
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$	8.00000	+	13.8564i	0.305888	+	0.529813i
$685$	−2.00000			−0.0764161
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	6.00000			0.228914
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$	−0.500000	+	0.866025i	−0.0190347	+	0.0329690i
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$	−6.00000			−0.228086
$693$	−1.00000	−	5.19615i	−0.0379869	−	0.197386i
$694$	−3.00000			−0.113878
$695$	−9.00000	−	15.5885i	−0.341389	−	0.591304i
$696$	−4.50000	+	7.79423i	−0.170572	+	0.295439i
$697$	−2.00000	+	3.46410i	−0.0757554	+	0.131212i
$698$	−9.50000	−	16.4545i	−0.359580	−	0.622811i
$699$	−22.0000			−0.832116
$700$	−2.00000	+	1.73205i	−0.0755929	+	0.0654654i
$701$	11.0000			0.415464			0.207732	−	0.978186i	$-0.433392\pi$
$701$	11.0000			0.415464			0.207732	+	0.978186i	$0.433392\pi$
$702$	5.00000	+	8.66025i	0.188713	+	0.326860i
$703$	8.00000	−	13.8564i	0.301726	−	0.522604i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	4.00000	+	6.92820i	0.150649	+	0.260931i
$706$	−12.0000			−0.451626
$707$	−7.50000	−	2.59808i	−0.282067	−	0.0977107i
$708$	6.00000			0.225494
$709$	13.5000	+	23.3827i	0.507003	+	0.878155i	0.999967	+	0.00810550i	$0.00258009\pi$
$709$	13.5000	+	23.3827i	0.507003	+	0.878155i	−0.492964	+	0.870050i	$0.664087\pi$
$710$	8.00000	−	13.8564i	0.300235	−	0.520022i
$711$	−14.0000	+	24.2487i	−0.525041	+	0.909398i
$712$	−0.500000	−	0.866025i	−0.0187383	−	0.0324557i
$713$	−2.00000			−0.0749006
$714$	10.0000	+	3.46410i	0.374241	+	0.129641i
$715$	2.00000			0.0747958
$716$	2.00000	+	3.46410i	0.0747435	+	0.129460i
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$	−2.00000			−0.0745356
$721$	38.0000	−	32.9090i	1.41519	−	1.22559i
$722$	45.0000			1.67473
$723$	7.00000	+	12.1244i	0.260333	+	0.450910i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$	0.500000	+	0.866025i	0.0185567	+	0.0321412i
$727$	51.0000			1.89149			0.945743	−	0.324917i	$-0.105336\pi$
$727$	51.0000			1.89149			0.945743	+	0.324917i	$0.105336\pi$
$728$	1.00000	+	5.19615i	0.0370625	+	0.192582i
$729$	13.0000			0.481481
$730$	2.00000	+	3.46410i	0.0740233	+	0.128212i
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$	−2.50000	+	4.33013i	−0.0924027	+	0.160046i
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	−0.881633	−	0.471935i	$-0.843556\pi$
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	0.0321090	−	0.999484i	$-0.489778\pi$
$734$	−3.00000			−0.110732
$735$	6.50000	−	2.59808i	0.239756	−	0.0958315i
$736$	−1.00000			−0.0368605
$737$	−6.50000	−	11.2583i	−0.239431	−	0.414706i
$738$	−1.00000	+	1.73205i	−0.0368105	+	0.0637577i
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	−0.104078	−	0.994569i	$-0.533189\pi$
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	0.913361	−	0.407150i	$-0.133477\pi$
$740$	1.00000	+	1.73205i	0.0367607	+	0.0636715i
$741$	16.0000			0.587775
$742$	−1.00000	−	5.19615i	−0.0367112	−	0.190757i
$743$	19.0000			0.697042			0.348521	−	0.937301i	$-0.386684\pi$
$743$	19.0000			0.697042			0.348521	+	0.937301i	$0.386684\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$	3.50000	−	6.06218i	0.128230	−	0.222101i
$746$		0			0
$747$	−1.00000	−	1.73205i	−0.0365881	−	0.0633724i
$748$	4.00000			0.146254
$749$	−18.0000	+	15.5885i	−0.657706	+	0.569590i
$750$	−1.00000			−0.0365148
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$	9.00000	−	15.5885i	0.327978	−	0.568075i
$754$	−9.00000	−	15.5885i	−0.327761	−	0.567698i
$755$	−12.0000			−0.436725
$756$	12.5000	+	4.33013i	0.454621	+	0.157485i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−2.00000	−	3.46410i	−0.0726433	−	0.125822i
$759$	0.500000	−	0.866025i	0.0181489	−	0.0314347i
$760$	−4.00000	+	6.92820i	−0.145095	+	0.251312i
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	0.998684	+	0.0512772i	$0.0163292\pi$
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	−0.454935	+	0.890525i	$0.650337\pi$
$762$	−12.0000			−0.434714
$763$	−47.5000	−	16.4545i	−1.71962	−	0.595692i
$764$	−16.0000			−0.578860
$765$	−4.00000	−	6.92820i	−0.144620	−	0.250490i
$766$	4.50000	−	7.79423i	0.162592	−	0.281617i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$	2.00000	−	1.73205i	0.0720750	−	0.0624188i
$771$	−10.0000			−0.360141
$772$	7.00000	+	12.1244i	0.251936	+	0.436365i
$773$	26.0000	−	45.0333i	0.935155	−	1.61974i	0.160798	−	0.986987i	$-0.448593\pi$
$773$	26.0000	−	45.0333i	0.935155	−	1.61974i	0.774357	−	0.632749i	$-0.218073\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$	−8.00000			−0.287183
$777$	−1.00000	−	5.19615i	−0.0358748	−	0.186411i
$778$	34.0000			1.21896
$779$	4.00000	+	6.92820i	0.143315	+	0.248229i
$780$	−1.00000	+	1.73205i	−0.0358057	+	0.0620174i
$781$	−8.00000	+	13.8564i	−0.286263	+	0.495821i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$	−45.0000			−1.60817
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−12.0000			−0.428298
$786$	9.00000	+	15.5885i	0.321019	+	0.556022i
$787$	−16.5000	+	28.5788i	−0.588161	+	1.01873i	0.406312	+	0.913735i	$0.366815\pi$
$787$	−16.5000	+	28.5788i	−0.588161	+	1.01873i	−0.994473	+	0.104991i	$0.966519\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$	3.50000	+	6.06218i	0.124603	+	0.215819i
$790$	−14.0000			−0.498098
$791$	−8.00000	−	41.5692i	−0.284447	−	1.47803i
$792$	2.00000			0.0710669
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	−6.00000	+	10.3923i	−0.212932	+	0.368809i
$795$	1.00000	−	1.73205i	0.0354663	−	0.0614295i
$796$	12.0000	+	20.7846i	0.425329	+	0.736691i
$797$	40.0000			1.41687			0.708436	−	0.705775i	$-0.249401\pi$
$797$	40.0000			1.41687			0.708436	+	0.705775i	$0.249401\pi$
$798$	16.0000	−	13.8564i	0.566394	−	0.490511i
$799$	−32.0000			−1.13208
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	1.00000	−	1.73205i	0.0353333	−	0.0611990i
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$	−2.00000	−	3.46410i	−0.0705785	−	0.122245i
$804$	13.0000			0.458475
$805$	−2.50000	−	0.866025i	−0.0881134	−	0.0305234i
$806$	−4.00000			−0.140894
$807$	9.50000	+	16.4545i	0.334416	+	0.579225i
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	−22.5000	−	7.79423i	−0.789595	−	0.273524i
$813$	20.0000			0.701431
$814$	−1.00000	−	1.73205i	−0.0350500	−	0.0607083i
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	−4.00000	−	6.92820i	−0.139942	−	0.242387i
$818$	17.0000			0.594391
$819$	−8.00000	+	6.92820i	−0.279543	+	0.242091i
$820$	−1.00000			−0.0349215
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	−1.00000	+	1.73205i	−0.0348790	+	0.0604122i
$823$	2.50000	−	4.33013i	0.0871445	−	0.150939i	−0.819159	−	0.573567i	$-0.805559\pi$
$823$	2.50000	−	4.33013i	0.0871445	−	0.150939i	0.906303	+	0.422628i	$0.138892\pi$
$824$	9.50000	+	16.4545i	0.330948	+	0.573219i
$825$	1.00000			0.0348155
$826$	3.00000	+	15.5885i	0.104383	+	0.542392i
$827$	43.0000			1.49526			0.747628	−	0.664117i	$-0.231193\pi$
$827$	43.0000			1.49526			0.747628	+	0.664117i	$0.231193\pi$
$828$	−1.00000	−	1.73205i	−0.0347524	−	0.0601929i
$829$	19.0000	−	32.9090i	0.659897	−	1.14298i	−0.320745	−	0.947166i	$-0.603933\pi$
$829$	19.0000	−	32.9090i	0.659897	−	1.14298i	0.980642	−	0.195810i	$-0.0627335\pi$
$830$	0.500000	−	0.866025i	0.0173553	−	0.0300602i
$831$	11.0000	+	19.0526i	0.381586	+	0.660926i
$832$	−2.00000			−0.0693375
$833$	−4.00000	+	27.7128i	−0.138592	+	0.960192i
$834$	−18.0000			−0.623289
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$	4.00000	−	6.92820i	0.138343	−	0.239617i
$837$	−5.00000	+	8.66025i	−0.172825	+	0.299342i
$838$	−1.00000	−	1.73205i	−0.0345444	−	0.0598327i
$839$	−18.0000			−0.621429			−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000			−0.621429			−0.310715	+	0.950503i	$0.600568\pi$
$840$	0.500000	+	2.59808i	0.0172516	+	0.0896421i
$841$	52.0000			1.79310
$842$	17.5000	+	30.3109i	0.603090	+	1.04458i
$843$	−5.00000	+	8.66025i	−0.172209	+	0.298275i
$844$	3.00000	−	5.19615i	0.103264	−	0.178859i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$	−16.0000			−0.550091
$847$	−2.00000	+	1.73205i	−0.0687208	+	0.0595140i
$848$	2.00000			0.0686803
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	−1.00000	+	1.73205i	−0.0342796	+	0.0593739i
$852$	−8.00000	−	13.8564i	−0.274075	−	0.474713i
$853$	4.00000			0.136957			0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000			0.136957			0.0684787	+	0.997653i	$0.478185\pi$
$854$	−12.5000	−	4.33013i	−0.427741	−	0.148174i
$855$	−16.0000			−0.547188
$856$	−4.50000	−	7.79423i	−0.153807	−	0.266401i
$857$	−12.0000	+	20.7846i	−0.409912	+	0.709989i	−0.994880	−	0.101068i	$-0.967774\pi$
$857$	−12.0000	+	20.7846i	−0.409912	+	0.709989i	0.584967	+	0.811057i	$0.301107\pi$
$858$	1.00000	−	1.73205i	0.0341394	−	0.0591312i
$859$	−1.00000	−	1.73205i	−0.0341196	−	0.0590968i	0.848461	−	0.529257i	$-0.177529\pi$
$859$	−1.00000	−	1.73205i	−0.0341196	−	0.0590968i	−0.882581	+	0.470160i	$0.844196\pi$
$860$	1.00000			0.0340997
$861$	2.50000	+	0.866025i	0.0851998	+	0.0295141i
$862$	28.0000			0.953684
$863$	−0.500000	−	0.866025i	−0.0170202	−	0.0294798i	0.857390	−	0.514667i	$-0.172085\pi$
$863$	−0.500000	−	0.866025i	−0.0170202	−	0.0294798i	−0.874410	+	0.485188i	$0.838751\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	13.0000	+	22.5167i	0.441758	+	0.765147i
$867$	1.00000			0.0339618
$868$	−4.00000	+	3.46410i	−0.135769	+	0.117579i
$869$	14.0000			0.474917
$870$	−4.50000	−	7.79423i	−0.152564	−	0.264249i
$871$	−13.0000	+	22.5167i	−0.440488	+	0.762948i
$872$	9.50000	−	16.4545i	0.321711	−	0.557219i
$873$	−8.00000	−	13.8564i	−0.270759	−	0.468968i
$874$	−8.00000			−0.270604
$875$	−0.500000	−	2.59808i	−0.0169031	−	0.0878310i
$876$	4.00000			0.135147
$877$	−4.00000	−	6.92820i	−0.135070	−	0.233949i	0.790554	−	0.612392i	$-0.209793\pi$
$877$	−4.00000	−	6.92820i	−0.135070	−	0.233949i	−0.925624	+	0.378444i	$0.876459\pi$
$878$	7.00000	−	12.1244i	0.236239	−	0.409177i
$879$	−1.00000	+	1.73205i	−0.0337292	+	0.0584206i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	−11.0000			−0.370599			−0.185300	−	0.982682i	$-0.559326\pi$
$881$	−11.0000			−0.370599			−0.185300	+	0.982682i	$0.559326\pi$
$882$	−2.00000	+	13.8564i	−0.0673435	+	0.466569i
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$	−4.00000	−	6.92820i	−0.134535	−	0.233021i
$885$	−3.00000	+	5.19615i	−0.100844	+	0.174667i
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	−7.50000	−	12.9904i	−0.251825	−	0.436174i	0.712203	−	0.701974i	$-0.247698\pi$
$887$	−7.50000	−	12.9904i	−0.251825	−	0.436174i	−0.964028	+	0.265799i	$0.914364\pi$
$888$	2.00000			0.0671156
$889$	−6.00000	−	31.1769i	−0.201234	−	1.04564i
$890$	1.00000			0.0335201
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	−12.0000	+	20.7846i	−0.401790	+	0.695920i
$893$	−32.0000	+	55.4256i	−1.07084	+	1.85475i
$894$	−3.50000	−	6.06218i	−0.117058	−	0.202750i
$895$	−4.00000			−0.133705
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$	−2.00000			−0.0667781
$898$	−7.50000	−	12.9904i	−0.250278	−	0.433495i
$899$	9.00000	−	15.5885i	0.300167	−	0.519904i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	4.00000	+	6.92820i	0.133259	+	0.230812i
$902$	1.00000			0.0332964
$903$	−2.50000	−	0.866025i	−0.0831948	−	0.0288195i
$904$	16.0000			0.532152
$905$	−3.50000	−	6.06218i	−0.116344	−	0.201514i
$906$	−6.00000	+	10.3923i	−0.199337	+	0.345261i
$907$	17.5000	−	30.3109i	0.581078	−	1.00646i	−0.414274	−	0.910152i	$-0.635964\pi$
$907$	17.5000	−	30.3109i	0.581078	−	1.00646i	0.995352	−	0.0963043i	$-0.0307022\pi$
$908$	2.00000	+	3.46410i	0.0663723	+	0.114960i
$909$	6.00000			0.199007
$910$	−5.00000	−	1.73205i	−0.165748	−	0.0574169i
$911$	−46.0000			−1.52405			−0.762024	−	0.647549i	$-0.775794\pi$
$911$	−46.0000			−1.52405			−0.762024	+	0.647549i	$0.775794\pi$
$912$	4.00000	+	6.92820i	0.132453	+	0.229416i
$913$	−0.500000	+	0.866025i	−0.0165476	+	0.0286613i
$914$	4.00000	−	6.92820i	0.132308	−	0.229165i
$915$	−2.50000	−	4.33013i	−0.0826475	−	0.143150i
$916$	−6.00000			−0.198246
$917$	−36.0000	+	31.1769i	−1.18882	+	1.02955i
$918$	−20.0000			−0.660098
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	0.993208	−	0.116348i	$-0.0371189\pi$
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	−0.597365	+	0.801970i	$0.703786\pi$
$920$	0.500000	−	0.866025i	0.0164845	−	0.0285520i
$921$	−11.5000	+	19.9186i	−0.378938	+	0.656340i
$922$	17.0000	+	29.4449i	0.559865	+	0.969715i
$923$	32.0000			1.05329
$924$	−0.500000	−	2.59808i	−0.0164488	−	0.0854704i
$925$	−2.00000			−0.0657596
$926$	17.5000	+	30.3109i	0.575086	+	0.996078i
$927$	−19.0000	+	32.9090i	−0.624042	+	1.08087i
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$	−2.00000			−0.0655826
$931$	44.0000	+	34.6410i	1.44204	+	1.13531i
$932$	22.0000			0.720634
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$	−7.50000	+	12.9904i	−0.245407	+	0.425058i
$935$	−2.00000	+	3.46410i	−0.0654070	+	0.113288i
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	6.50000	+	33.7750i	0.212233	+	1.10279i
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	−11.0000	+	19.0526i	−0.358590	+	0.621096i	−0.987725	−	0.156200i	$-0.950076\pi$
$941$	−11.0000	+	19.0526i	−0.358590	+	0.621096i	0.629136	+	0.777295i	$0.283409\pi$
$942$	−6.00000	+	10.3923i	−0.195491	+	0.338600i
$943$	−0.500000	−	0.866025i	−0.0162822	−	0.0282017i
$944$	−6.00000			−0.195283
$945$	−10.0000	+	8.66025i	−0.325300	+	0.281718i
$946$	−1.00000			−0.0325128
$947$	−15.5000	−	26.8468i	−0.503682	−	0.872403i	−0.999991	−	0.00425721i	$-0.998645\pi$
$947$	−15.5000	−	26.8468i	−0.503682	−	0.872403i	0.496309	−	0.868146i	$-0.334688\pi$
$948$	−7.00000	+	12.1244i	−0.227349	+	0.393781i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$	−12.0000			−0.389127
$952$	−10.0000	−	3.46410i	−0.324102	−	0.112272i
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$	2.00000	+	3.46410i	0.0647524	+	0.112154i
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$	4.50000	+	7.79423i	0.145464	+	0.251952i
$958$	−42.0000			−1.35696
$959$	−5.00000	−	1.73205i	−0.161458	−	0.0559308i
$960$	−1.00000			−0.0322749
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−2.00000	+	3.46410i	−0.0644826	+	0.111687i
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$	−14.0000			−0.450676
$966$	−2.00000	+	1.73205i	−0.0643489	+	0.0557278i
$967$	−25.0000			−0.803946			−0.401973	−	0.915652i	$-0.631675\pi$
$967$	−25.0000			−0.803946			−0.401973	+	0.915652i	$0.631675\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−16.0000	+	27.7128i	−0.513994	+	0.890264i
$970$	4.00000	−	6.92820i	0.128432	−	0.222451i
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$	−16.0000			−0.513200
$973$	−9.00000	−	46.7654i	−0.288527	−	1.49923i
$974$	36.0000			1.15351
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	2.50000	−	4.33013i	0.0800230	−	0.138604i
$977$	−4.00000	+	6.92820i	−0.127971	+	0.221653i	−0.922890	−	0.385063i	$-0.874180\pi$
$977$	−4.00000	+	6.92820i	−0.127971	+	0.221653i	0.794919	+	0.606715i	$0.207513\pi$
$978$	−8.00000	−	13.8564i	−0.255812	−	0.443079i
$979$	−1.00000			−0.0319601
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$	38.0000			1.21325
$982$	−13.0000	−	22.5167i	−0.414847	−	0.718536i
$983$	−10.5000	+	18.1865i	−0.334898	+	0.580060i	−0.983465	−	0.181097i	$-0.942035\pi$
$983$	−10.5000	+	18.1865i	−0.334898	+	0.580060i	0.648567	+	0.761157i	$0.275369\pi$
$984$	−0.500000	+	0.866025i	−0.0159394	+	0.0276079i
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$	36.0000			1.14647
$987$	4.00000	+	20.7846i	0.127321	+	0.661581i
$988$	−16.0000			−0.509028
$989$	0.500000	+	0.866025i	0.0158991	+	0.0275380i
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$	−4.00000			−0.126936
$994$	32.0000	−	27.7128i	1.01498	−	0.878997i
$995$	−24.0000			−0.760851
$996$	−0.500000	−	0.866025i	−0.0158431	−	0.0274411i
$997$	−28.0000	+	48.4974i	−0.886769	+	1.53593i	−0.0430962	+	0.999071i	$0.513722\pi$
$997$	−28.0000	+	48.4974i	−0.886769	+	1.53593i	−0.843673	+	0.536858i	$0.819611\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.b.221.1	✓	2	1.1	even	1	trivial
770.2.i.b.331.1	yes	2	7.2	even	3	inner
5390.2.a.w.1.1		1	7.4	even	3
5390.2.a.bd.1.1		1	7.3	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(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} +(-0.500000 - 2.59808i) 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} -2.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +5.00000 q^{27} +(2.50000 + 0.866025i) q^{28} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} -4.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} -2.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -1.00000 q^{41} +(0.500000 + 2.59808i) q^{42} +1.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.00000 - 6.92820i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(-2.00000 - 3.46410i) q^{51} +(1.00000 - 1.73205i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -8.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +(4.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(6.50000 - 11.2583i) q^{67} +(2.00000 + 3.46410i) q^{68} +1.00000 q^{69} +(2.50000 + 0.866025i) q^{70} -16.0000 q^{71} +(1.00000 + 1.73205i) q^{72} +(2.00000 - 3.46410i) q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +8.00000 q^{76} +(-2.50000 - 0.866025i) q^{77} +2.00000 q^{78} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} -1.00000 q^{83} +(2.00000 - 1.73205i) q^{84} -4.00000 q^{85} +(-0.500000 - 0.866025i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} -2.00000 q^{90} +(1.00000 + 5.19615i) q^{91} -1.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(5.50000 + 4.33013i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - q^{10} + q^{11} + q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 4 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{20} - 5 q^{21} - 2 q^{22} + q^{23} + q^{24} - q^{25} + 2 q^{26} + 10 q^{27} + 5 q^{28} - 18 q^{29} + q^{30} - 2 q^{31} - q^{32} - q^{33} - 8 q^{34} - 4 q^{35} - 4 q^{36} + 2 q^{37} - 8 q^{38} - 2 q^{39} - q^{40} - 2 q^{41} + q^{42} + 2 q^{43} + q^{44} + 2 q^{45} + q^{46} - 8 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} - 4 q^{51} + 2 q^{52} - 2 q^{53} - 5 q^{54} - 2 q^{55} - q^{56} - 16 q^{57} + 9 q^{58} + 6 q^{59} + q^{60} + 5 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} + 2 q^{65} - q^{66} + 13 q^{67} + 4 q^{68} + 2 q^{69} + 5 q^{70} - 32 q^{71} + 2 q^{72} + 4 q^{73} + 2 q^{74} + q^{75} + 16 q^{76} - 5 q^{77} + 4 q^{78} + 14 q^{79} - q^{80} - q^{81} + q^{82} - 2 q^{83} + 4 q^{84} - 8 q^{85} - q^{86} - 9 q^{87} + q^{88} - q^{89} - 4 q^{90} + 2 q^{91} - 2 q^{92} + 2 q^{93} - 8 q^{94} - 8 q^{95} + q^{96} - 16 q^{97} + 11 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - q^10 + q^11 + q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - q^16 + 4 * q^17 + 2 * q^18 - 8 * q^19 + 2 * q^20 - 5 * q^21 - 2 * q^22 + q^23 + q^24 - q^25 + 2 * q^26 + 10 * q^27 + 5 * q^28 - 18 * q^29 + q^30 - 2 * q^31 - q^32 - q^33 - 8 * q^34 - 4 * q^35 - 4 * q^36 + 2 * q^37 - 8 * q^38 - 2 * q^39 - q^40 - 2 * q^41 + q^42 + 2 * q^43 + q^44 + 2 * q^45 + q^46 - 8 * q^47 - 2 * q^48 - 13 * q^49 + 2 * q^50 - 4 * q^51 + 2 * q^52 - 2 * q^53 - 5 * q^54 - 2 * q^55 - q^56 - 16 * q^57 + 9 * q^58 + 6 * q^59 + q^60 + 5 * q^61 + 4 * q^62 + 8 * q^63 + 2 * q^64 + 2 * q^65 - q^66 + 13 * q^67 + 4 * q^68 + 2 * q^69 + 5 * q^70 - 32 * q^71 + 2 * q^72 + 4 * q^73 + 2 * q^74 + q^75 + 16 * q^76 - 5 * q^77 + 4 * q^78 + 14 * q^79 - q^80 - q^81 + q^82 - 2 * q^83 + 4 * q^84 - 8 * q^85 - q^86 - 9 * q^87 + q^88 - q^89 - 4 * q^90 + 2 * q^91 - 2 * q^92 + 2 * q^93 - 8 * q^94 - 8 * q^95 + q^96 - 16 * q^97 + 11 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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