LMFDB - Embedded newform 342.2.h.a.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (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:	$2.73088374913$
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			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} -1.73205i q^{12} +(-1.00000 + 1.73205i) q^{13} -3.00000 q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +5.19615i q^{21} +5.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(-1.50000 + 0.866025i) q^{24} -4.00000 q^{25} +2.00000 q^{26} +5.19615i q^{27} +(1.50000 + 2.59808i) q^{28} -5.00000 q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} -8.66025i q^{33} +3.00000 q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +10.0000 q^{37} +(3.50000 + 2.59808i) q^{38} -3.46410i q^{39} -1.00000 q^{40} +7.00000 q^{41} +(4.50000 - 2.59808i) q^{42} +(4.00000 + 6.92820i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +8.00000 q^{46} -1.00000 q^{47} +(1.50000 + 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} -5.19615i q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.50000 - 9.52628i) q^{53} +(4.50000 - 2.59808i) q^{54} +(2.50000 - 4.33013i) q^{55} +(1.50000 - 2.59808i) q^{56} +(4.50000 - 6.06218i) q^{57} +(2.50000 + 4.33013i) q^{58} -3.00000 q^{59} +1.73205i q^{60} -1.00000 q^{61} +(-3.50000 + 6.06218i) q^{62} +(-4.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-7.50000 + 4.33013i) q^{66} +(-6.00000 + 10.3923i) q^{67} +(-1.50000 - 2.59808i) q^{68} -13.8564i q^{69} +3.00000 q^{70} +(0.500000 - 0.866025i) q^{71} +(1.50000 - 2.59808i) q^{72} +(-1.50000 + 2.59808i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 4.33013i) q^{76} +(7.50000 + 12.9904i) q^{77} +(-3.00000 + 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(1.50000 - 2.59808i) q^{85} +(4.00000 - 6.92820i) q^{86} +(7.50000 - 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-7.50000 - 12.9904i) q^{89} +3.00000 q^{90} +(3.00000 + 5.19615i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(10.5000 + 6.06218i) q^{93} +(0.500000 + 0.866025i) q^{94} +(4.00000 - 1.73205i) q^{95} -1.73205i q^{96} +(1.00000 + 1.73205i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 3 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 3 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 3 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} - 5 q^{11} - 2 q^{13} - 6 q^{14} + 3 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} - 8 q^{19} + q^{20} + 10 q^{22} - 8 q^{23} - 3 q^{24} - 8 q^{25} + 4 q^{26} + 3 q^{28} - 10 q^{29} - 3 q^{30} - 7 q^{31} - q^{32} + 6 q^{34} - 3 q^{35} + 3 q^{36} + 20 q^{37} + 7 q^{38} - 2 q^{40} + 14 q^{41} + 9 q^{42} + 8 q^{43} - 5 q^{44} - 3 q^{45} + 16 q^{46} - 2 q^{47} + 3 q^{48} - 2 q^{49} + 4 q^{50} - 2 q^{52} - 11 q^{53} + 9 q^{54} + 5 q^{55} + 3 q^{56} + 9 q^{57} + 5 q^{58} - 6 q^{59} - 2 q^{61} - 7 q^{62} - 9 q^{63} + 2 q^{64} + 2 q^{65} - 15 q^{66} - 12 q^{67} - 3 q^{68} + 6 q^{70} + q^{71} + 3 q^{72} - 3 q^{73} - 10 q^{74} + 12 q^{75} + q^{76} + 15 q^{77} - 6 q^{78} + 4 q^{79} + q^{80} - 9 q^{81} - 7 q^{82} - 9 q^{83} - 9 q^{84} + 3 q^{85} + 8 q^{86} + 15 q^{87} - 5 q^{88} - 15 q^{89} + 6 q^{90} + 6 q^{91} - 8 q^{92} + 21 q^{93} + q^{94} + 8 q^{95} + 2 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 3 * q^7 + 2 * q^8 + 3 * q^9 + q^10 - 5 * q^11 - 2 * q^13 - 6 * q^14 + 3 * q^15 - q^16 - 3 * q^17 - 6 * q^18 - 8 * q^19 + q^20 + 10 * q^22 - 8 * q^23 - 3 * q^24 - 8 * q^25 + 4 * q^26 + 3 * q^28 - 10 * q^29 - 3 * q^30 - 7 * q^31 - q^32 + 6 * q^34 - 3 * q^35 + 3 * q^36 + 20 * q^37 + 7 * q^38 - 2 * q^40 + 14 * q^41 + 9 * q^42 + 8 * q^43 - 5 * q^44 - 3 * q^45 + 16 * q^46 - 2 * q^47 + 3 * q^48 - 2 * q^49 + 4 * q^50 - 2 * q^52 - 11 * q^53 + 9 * q^54 + 5 * q^55 + 3 * q^56 + 9 * q^57 + 5 * q^58 - 6 * q^59 - 2 * q^61 - 7 * q^62 - 9 * q^63 + 2 * q^64 + 2 * q^65 - 15 * q^66 - 12 * q^67 - 3 * q^68 + 6 * q^70 + q^71 + 3 * q^72 - 3 * q^73 - 10 * q^74 + 12 * q^75 + q^76 + 15 * q^77 - 6 * q^78 + 4 * q^79 + q^80 - 9 * q^81 - 7 * q^82 - 9 * q^83 - 9 * q^84 + 3 * q^85 + 8 * q^86 + 15 * q^87 - 5 * q^88 - 15 * q^89 + 6 * q^90 + 6 * q^91 - 8 * q^92 + 21 * q^93 + q^94 + 8 * q^95 + 2 * q^97 - 2 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−3.00000			−0.801784
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−3.00000			−0.707107
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$			5.19615i			1.13389i
$22$	5.00000			1.06600
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−4.00000			−0.800000
$26$	2.00000			0.392232
$27$			5.19615i			1.00000i
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	−1.50000	−	0.866025i	−0.273861	−	0.158114i
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		−	8.66025i		−	1.50756i
$34$	3.00000			0.514496
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$	3.50000	+	2.59808i	0.567775	+	0.421464i
$39$		−	3.46410i		−	0.554700i
$40$	−1.00000			−0.158114
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$	4.50000	−	2.59808i	0.694365	−	0.400892i
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	8.00000			1.17954
$47$	−1.00000			−0.145865			−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000			−0.145865			−0.0729325	+	0.997337i	$0.523236\pi$
$48$	1.50000	+	0.866025i	0.216506	+	0.125000i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		−	5.19615i		−	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−5.50000	−	9.52628i	−0.755483	−	1.30854i	−0.945134	−	0.326683i	$-0.894069\pi$
$53$	−5.50000	−	9.52628i	−0.755483	−	1.30854i	0.189651	−	0.981852i	$-0.439264\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	2.50000	−	4.33013i	0.337100	−	0.583874i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	4.50000	−	6.06218i	0.596040	−	0.802955i
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	−3.00000			−0.390567			−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000			−0.390567			−0.195283	+	0.980747i	$0.562563\pi$
$60$			1.73205i			0.223607i
$61$	−1.00000			−0.128037			−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000			−0.128037			−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−3.50000	+	6.06218i	−0.444500	+	0.769897i
$63$	−4.50000	−	7.79423i	−0.566947	−	0.981981i
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	−7.50000	+	4.33013i	−0.923186	+	0.533002i
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		−	13.8564i		−	1.66812i
$70$	3.00000			0.358569
$71$	0.500000	−	0.866025i	0.0593391	−	0.102778i	−0.834830	−	0.550508i	$-0.814434\pi$
$71$	0.500000	−	0.866025i	0.0593391	−	0.102778i	0.894169	+	0.447730i	$0.147767\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$	−5.00000	−	8.66025i	−0.581238	−	1.00673i
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$	7.50000	+	12.9904i	0.854704	+	1.48039i
$78$	−3.00000	+	1.73205i	−0.339683	+	0.196116i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$	−4.50000	−	2.59808i	−0.490990	−	0.283473i
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	7.50000	−	4.33013i	0.804084	−	0.464238i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$	3.00000			0.316228
$91$	3.00000	+	5.19615i	0.314485	+	0.544705i
$92$	−4.00000	−	6.92820i	−0.417029	−	0.722315i
$93$	10.5000	+	6.06218i	1.08880	+	0.628619i
$94$	0.500000	+	0.866025i	0.0515711	+	0.0893237i
$95$	4.00000	−	1.73205i	0.410391	−	0.177705i
$96$		−	1.73205i		−	0.176777i
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$	7.50000	+	12.9904i	0.753778	+	1.30558i
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	11.0000			1.09454			0.547270	−	0.836956i	$-0.315667\pi$
$101$	11.0000			1.09454			0.547270	+	0.836956i	$0.315667\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	−7.50000	−	12.9904i	−0.738997	−	1.27998i	−0.952947	−	0.303136i	$-0.901966\pi$
$103$	−7.50000	−	12.9904i	−0.738997	−	1.27998i	0.213950	−	0.976845i	$-0.431367\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		−	5.19615i		−	0.507093i
$106$	−5.50000	+	9.52628i	−0.534207	+	0.925274i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$	−5.00000			−0.476731
$111$	−15.0000	+	8.66025i	−1.42374	+	0.821995i
$112$	−3.00000			−0.283473
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$	−7.50000	−	0.866025i	−0.702439	−	0.0811107i
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	1.50000	+	2.59808i	0.138086	+	0.239172i
$119$	4.50000	+	7.79423i	0.412514	+	0.714496i
$120$	1.50000	−	0.866025i	0.136931	−	0.0790569i
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	0.500000	+	0.866025i	0.0452679	+	0.0784063i
$123$	−10.5000	+	6.06218i	−0.946753	+	0.546608i
$124$	7.00000			0.628619
$125$	9.00000			0.804984
$126$	−4.50000	+	7.79423i	−0.400892	+	0.694365i
$127$	7.50000	+	12.9904i	0.665517	+	1.15271i	0.979145	+	0.203164i	$0.0651224\pi$
$127$	7.50000	+	12.9904i	0.665517	+	1.15271i	−0.313627	+	0.949546i	$0.601544\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−12.0000	−	6.92820i	−1.05654	−	0.609994i
$130$	−2.00000			−0.175412
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$	7.50000	+	4.33013i	0.652791	+	0.376889i
$133$	−1.50000	+	12.9904i	−0.130066	+	1.12641i
$134$	12.0000			1.03664
$135$		−	5.19615i		−	0.447214i
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	19.0000			1.62328			0.811640	−	0.584158i	$-0.198575\pi$
$137$	19.0000			1.62328			0.811640	+	0.584158i	$0.198575\pi$
$138$	−12.0000	+	6.92820i	−1.02151	+	0.589768i
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$	1.50000	−	0.866025i	0.126323	−	0.0729325i
$142$	−1.00000			−0.0839181
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$	−3.00000			−0.250000
$145$	5.00000			0.415227
$146$	3.00000			0.248282
$147$	3.00000	+	1.73205i	0.247436	+	0.142857i
$148$	−5.00000	+	8.66025i	−0.410997	+	0.711868i
$149$	3.00000			0.245770			0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000			0.245770			0.122885	+	0.992421i	$0.460785\pi$
$150$	−6.00000	−	3.46410i	−0.489898	−	0.282843i
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$	−4.00000	+	1.73205i	−0.324443	+	0.140488i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	7.50000	−	12.9904i	0.604367	−	1.04679i
$155$	3.50000	+	6.06218i	0.281127	+	0.486926i
$156$	3.00000	+	1.73205i	0.240192	+	0.138675i
$157$	−17.0000			−1.35675			−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000			−1.35675			−0.678374	+	0.734717i	$0.737315\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	16.5000	+	9.52628i	1.30854	+	0.755483i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	12.0000	+	20.7846i	0.945732	+	1.63806i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−3.50000	+	6.06218i	−0.273304	+	0.473377i
$165$			8.66025i			0.674200i
$166$	9.00000			0.698535
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$			5.19615i			0.400892i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.00000			−0.230089
$171$	−1.50000	+	12.9904i	−0.114708	+	0.993399i
$172$	−8.00000			−0.609994
$173$	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	$0.760087\pi$
$174$	−7.50000	−	4.33013i	−0.568574	−	0.328266i
$175$	−6.00000	+	10.3923i	−0.453557	+	0.785584i
$176$	5.00000			0.376889
$177$	4.50000	−	2.59808i	0.338241	−	0.195283i
$178$	−7.50000	+	12.9904i	−0.562149	+	0.973670i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−9.50000	−	16.4545i	−0.706129	−	1.22305i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−9.50000	−	16.4545i	−0.706129	−	1.22305i	0.260153	−	0.965567i	$-0.416227\pi$
$182$	3.00000	−	5.19615i	0.222375	−	0.385164i
$183$	1.50000	−	0.866025i	0.110883	−	0.0640184i
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	−10.0000			−0.735215
$186$		−	12.1244i		−	0.889001i
$187$	−7.50000	−	12.9904i	−0.548454	−	0.949951i
$188$	0.500000	−	0.866025i	0.0364662	−	0.0631614i
$189$	13.5000	+	7.79423i	0.981981	+	0.566947i
$190$	−3.50000	−	2.59808i	−0.253917	−	0.188484i
$191$	−0.500000	+	0.866025i	−0.0361787	+	0.0626634i	−0.883548	−	0.468341i	$-0.844852\pi$
$191$	−0.500000	+	0.866025i	−0.0361787	+	0.0626634i	0.847369	+	0.531004i	$0.178185\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	−9.00000			−0.647834			−0.323917	−	0.946085i	$-0.605000\pi$
$193$	−9.00000			−0.647834			−0.323917	+	0.946085i	$0.605000\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$			3.46410i			0.248069i
$196$	2.00000			0.142857
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	7.50000	−	12.9904i	0.533002	−	0.923186i
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$	−4.00000			−0.282843
$201$		−	20.7846i		−	1.46603i
$202$	−5.50000	−	9.52628i	−0.386979	−	0.670267i
$203$	−7.50000	+	12.9904i	−0.526397	+	0.911746i
$204$	4.50000	+	2.59808i	0.315063	+	0.181902i
$205$	−7.00000			−0.488901
$206$	−7.50000	+	12.9904i	−0.522550	+	0.905083i
$207$	12.0000	+	20.7846i	0.834058	+	1.44463i
$208$	2.00000			0.138675
$209$	2.50000	−	21.6506i	0.172929	−	1.49761i
$210$	−4.50000	+	2.59808i	−0.310530	+	0.179284i
$211$	9.00000			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$212$	11.0000			0.755483
$213$			1.73205i			0.118678i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$			5.19615i			0.353553i
$217$	−21.0000			−1.42557
$218$	−9.00000			−0.609557
$219$		−	5.19615i		−	0.351123i
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$	15.0000	+	8.66025i	1.00673	+	0.581238i
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	5.50000	−	9.52628i	0.365048	−	0.632281i	−0.623736	−	0.781635i	$-0.714386\pi$
$227$	5.50000	−	9.52628i	0.365048	−	0.632281i	0.988784	+	0.149354i	$0.0477193\pi$
$228$	3.00000	+	6.92820i	0.198680	+	0.458831i
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$	−8.00000			−0.527504
$231$	−22.5000	−	12.9904i	−1.48039	−	0.854704i
$232$	−5.00000			−0.328266
$233$	−7.50000	+	12.9904i	−0.491341	+	0.851028i	−0.999950	−	0.00996947i	$-0.996827\pi$
$233$	−7.50000	+	12.9904i	−0.491341	+	0.851028i	0.508609	+	0.860998i	$0.330160\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	1.00000			0.0652328
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$	−6.00000	−	3.46410i	−0.389742	−	0.225018i
$238$	4.50000	−	7.79423i	0.291692	−	0.505225i
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.858623	−	0.512607i	$-0.828680\pi$
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.0146191	−	0.999893i	$-0.504654\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	−17.0000			−1.09507			−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000			−1.09507			−0.547533	+	0.836784i	$0.684433\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$	10.5000	+	6.06218i	0.669456	+	0.386510i
$247$	1.00000	−	8.66025i	0.0636285	−	0.551039i
$248$	−3.50000	−	6.06218i	−0.222250	−	0.384949i
$249$		−	15.5885i		−	0.987878i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−2.50000	−	4.33013i	−0.157799	−	0.273315i	0.776276	−	0.630393i	$-0.217106\pi$
$251$	−2.50000	−	4.33013i	−0.157799	−	0.273315i	−0.934075	+	0.357078i	$0.883773\pi$
$252$	9.00000			0.566947
$253$	−20.0000	−	34.6410i	−1.25739	−	2.17786i
$254$	7.50000	−	12.9904i	0.470592	−	0.815089i
$255$			5.19615i			0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$			13.8564i			0.862662i
$259$	15.0000	−	25.9808i	0.932055	−	1.61437i
$260$	1.00000	+	1.73205i	0.0620174	+	0.107417i
$261$	−7.50000	+	12.9904i	−0.464238	+	0.804084i
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		−	8.66025i		−	0.533002i
$265$	5.50000	+	9.52628i	0.337862	+	0.585195i
$266$	12.0000	−	5.19615i	0.735767	−	0.318597i
$267$	22.5000	+	12.9904i	1.37698	+	0.794998i
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$	−4.50000	+	2.59808i	−0.273861	+	0.158114i
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	−0.952531	−	0.304443i	$-0.901530\pi$
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	0.739921	+	0.672694i	$0.234863\pi$
$272$	3.00000			0.181902
$273$	−9.00000	−	5.19615i	−0.544705	−	0.314485i
$274$	−9.50000	−	16.4545i	−0.573916	−	0.994052i
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$	12.0000	+	6.92820i	0.722315	+	0.417029i
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$	−12.0000			−0.719712
$279$	−21.0000			−1.25724
$280$	−1.50000	+	2.59808i	−0.0896421	+	0.155265i
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$	−1.50000	−	0.866025i	−0.0893237	−	0.0515711i
$283$	−3.00000			−0.178331			−0.0891657	−	0.996017i	$-0.528420\pi$
$283$	−3.00000			−0.178331			−0.0891657	+	0.996017i	$0.528420\pi$
$284$	0.500000	+	0.866025i	0.0296695	+	0.0513892i
$285$	−4.50000	+	6.06218i	−0.266557	+	0.359092i
$286$	−5.00000	+	8.66025i	−0.295656	+	0.512092i
$287$	10.5000	−	18.1865i	0.619795	−	1.07352i
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−2.50000	−	4.33013i	−0.146805	−	0.254274i
$291$	−3.00000	−	1.73205i	−0.175863	−	0.101535i
$292$	−1.50000	−	2.59808i	−0.0877809	−	0.152041i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$		−	3.46410i		−	0.202031i
$295$	3.00000			0.174667
$296$	10.0000			0.581238
$297$	−22.5000	−	12.9904i	−1.30558	−	0.753778i
$298$	−1.50000	−	2.59808i	−0.0868927	−	0.150503i
$299$	−8.00000	−	13.8564i	−0.462652	−	0.801337i
$300$			6.92820i			0.400000i
$301$	24.0000			1.38334
$302$	5.00000			0.287718
$303$	−16.5000	+	9.52628i	−0.947900	+	0.547270i
$304$	3.50000	+	2.59808i	0.200739	+	0.149010i
$305$	1.00000			0.0572598
$306$	4.50000	−	7.79423i	0.257248	−	0.445566i
$307$	16.5000	−	28.5788i	0.941705	−	1.63108i	0.179486	−	0.983760i	$-0.442556\pi$
$307$	16.5000	−	28.5788i	0.941705	−	1.63108i	0.762218	−	0.647320i	$-0.224110\pi$
$308$	−15.0000			−0.854704
$309$	22.5000	+	12.9904i	1.27998	+	0.738997i
$310$	3.50000	−	6.06218i	0.198787	−	0.344309i
$311$	−3.50000	−	6.06218i	−0.198467	−	0.343755i	0.749565	−	0.661931i	$-0.230263\pi$
$311$	−3.50000	−	6.06218i	−0.198467	−	0.343755i	−0.948031	+	0.318177i	$0.896930\pi$
$312$		−	3.46410i		−	0.196116i
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	8.50000	+	14.7224i	0.479683	+	0.830835i
$315$	4.50000	+	7.79423i	0.253546	+	0.439155i
$316$	−4.00000			−0.225018
$317$	3.00000			0.168497			0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000			0.168497			0.0842484	+	0.996445i	$0.473151\pi$
$318$		−	19.0526i		−	1.06841i
$319$	12.5000	−	21.6506i	0.699866	−	1.21220i
$320$	−1.00000			−0.0559017
$321$	6.00000	−	3.46410i	0.334887	−	0.193347i
$322$	12.0000	−	20.7846i	0.668734	−	1.15828i
$323$	1.50000	−	12.9904i	0.0834622	−	0.722804i
$324$	9.00000			0.500000
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$			15.5885i			0.862044i
$328$	7.00000			0.386510
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$	7.50000	−	4.33013i	0.412861	−	0.238366i
$331$	−14.5000	+	25.1147i	−0.796992	+	1.38043i	0.124574	+	0.992210i	$0.460243\pi$
$331$	−14.5000	+	25.1147i	−0.796992	+	1.38043i	−0.921567	+	0.388221i	$0.873090\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$	15.0000	−	25.9808i	0.821995	−	1.42374i
$334$	−12.0000			−0.656611
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$	4.50000	−	2.59808i	0.245495	−	0.141737i
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−1.50000	−	0.866025i	−0.0814688	−	0.0470360i
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$	35.0000			1.89536
$342$	12.0000	−	5.19615i	0.648886	−	0.280976i
$343$	15.0000			0.809924
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$			13.8564i			0.746004i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−23.0000			−1.23470			−0.617352	−	0.786687i	$-0.711795\pi$
$347$	−23.0000			−1.23470			−0.617352	+	0.786687i	$0.711795\pi$
$348$			8.66025i			0.464238i
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	−0.791325	−	0.611396i	$-0.790608\pi$
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$350$	12.0000			0.641427
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$	−4.50000	−	2.59808i	−0.239172	−	0.138086i
$355$	−0.500000	+	0.866025i	−0.0265372	+	0.0459639i
$356$	15.0000			0.794998
$357$	−13.5000	−	7.79423i	−0.714496	−	0.412514i
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	−0.993207	−	0.116358i	$-0.962878\pi$
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	0.597372	+	0.801964i	$0.296211\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	−9.50000	+	16.4545i	−0.499309	+	0.864828i
$363$	21.0000	+	12.1244i	1.10221	+	0.636364i
$364$	−6.00000			−0.314485
$365$	1.50000	−	2.59808i	0.0785136	−	0.135990i
$366$	−1.50000	−	0.866025i	−0.0784063	−	0.0452679i
$367$	−17.0000			−0.887393			−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000			−0.887393			−0.443696	+	0.896177i	$0.646333\pi$
$368$	8.00000			0.417029
$369$	10.5000	−	18.1865i	0.546608	−	0.946753i
$370$	5.00000	+	8.66025i	0.259938	+	0.450225i
$371$	−33.0000			−1.71327
$372$	−10.5000	+	6.06218i	−0.544400	+	0.314309i
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	0.983783	+	0.179364i	$0.0574041\pi$
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	−0.336557	+	0.941663i	$0.609263\pi$
$374$	−7.50000	+	12.9904i	−0.387816	+	0.671717i
$375$	−13.5000	+	7.79423i	−0.697137	+	0.402492i
$376$	−1.00000			−0.0515711
$377$	5.00000	−	8.66025i	0.257513	−	0.446026i
$378$		−	15.5885i		−	0.801784i
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	−0.500000	+	4.33013i	−0.0256495	+	0.222131i
$381$	−22.5000	−	12.9904i	−1.15271	−	0.665517i
$382$	1.00000			0.0511645
$383$	13.0000			0.664269			0.332134	−	0.943232i	$-0.392231\pi$
$383$	13.0000			0.664269			0.332134	+	0.943232i	$0.392231\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	−7.50000	−	12.9904i	−0.382235	−	0.662051i
$386$	4.50000	+	7.79423i	0.229044	+	0.396716i
$387$	24.0000			1.21999
$388$	−2.00000			−0.101535
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$	3.00000	−	1.73205i	0.151911	−	0.0877058i
$391$	−12.0000	−	20.7846i	−0.606866	−	1.05112i
$392$	−1.00000	−	1.73205i	−0.0505076	−	0.0874818i
$393$	22.5000	−	12.9904i	1.13497	−	0.655278i
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−2.00000	−	3.46410i	−0.100631	−	0.174298i
$396$	−15.0000			−0.753778
$397$	−17.5000	+	30.3109i	−0.878300	+	1.52126i	−0.0250943	+	0.999685i	$0.507989\pi$
$397$	−17.5000	+	30.3109i	−0.878300	+	1.52126i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	3.50000	−	6.06218i	0.175439	−	0.303870i
$399$	−9.00000	−	20.7846i	−0.450564	−	1.04053i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	31.0000			1.54807			0.774033	−	0.633145i	$-0.218236\pi$
$401$	31.0000			1.54807			0.774033	+	0.633145i	$0.218236\pi$
$402$	−18.0000	+	10.3923i	−0.897758	+	0.518321i
$403$	14.0000			0.697390
$404$	−5.50000	+	9.52628i	−0.273635	+	0.473950i
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$	15.0000			0.744438
$407$	−25.0000	+	43.3013i	−1.23920	+	2.14636i
$408$		−	5.19615i		−	0.257248i
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	3.50000	+	6.06218i	0.172853	+	0.299390i
$411$	−28.5000	+	16.4545i	−1.40580	+	0.811640i
$412$	15.0000			0.738997
$413$	−4.50000	+	7.79423i	−0.221431	+	0.383529i
$414$	12.0000	−	20.7846i	0.589768	−	1.02151i
$415$	4.50000	−	7.79423i	0.220896	−	0.382604i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$			20.7846i			1.01783i
$418$	−20.0000	+	8.66025i	−0.978232	+	0.423587i
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$	4.50000	+	2.59808i	0.219578	+	0.126773i
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	−4.50000	−	7.79423i	−0.219057	−	0.379417i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	−5.50000	−	9.52628i	−0.267104	−	0.462637i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	1.50000	−	0.866025i	0.0726752	−	0.0419591i
$427$	−1.50000	+	2.59808i	−0.0725901	+	0.125730i
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$	15.0000	+	8.66025i	0.724207	+	0.418121i
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	0.899888	−	0.436121i	$-0.143648\pi$
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	−0.827636	+	0.561266i	$0.810315\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	18.5000	+	32.0429i	0.889053	+	1.53989i	0.840996	+	0.541041i	$0.181970\pi$
$433$	18.5000	+	32.0429i	0.889053	+	1.53989i	0.0480569	+	0.998845i	$0.484697\pi$
$434$	10.5000	+	18.1865i	0.504016	+	0.872982i
$435$	−7.50000	+	4.33013i	−0.359597	+	0.207614i
$436$	4.50000	+	7.79423i	0.215511	+	0.373276i
$437$	4.00000	−	34.6410i	0.191346	−	1.65710i
$438$	−4.50000	+	2.59808i	−0.215018	+	0.124141i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	2.50000	−	4.33013i	0.119183	−	0.206431i
$441$	−6.00000			−0.285714
$442$	−3.00000	+	5.19615i	−0.142695	+	0.247156i
$443$	31.0000			1.47285			0.736427	−	0.676517i	$-0.236511\pi$
$443$	31.0000			1.47285			0.736427	+	0.676517i	$0.236511\pi$
$444$		−	17.3205i		−	0.821995i
$445$	7.50000	+	12.9904i	0.355534	+	0.615803i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$	−4.50000	+	2.59808i	−0.212843	+	0.122885i
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$	12.0000			0.565685
$451$	−17.5000	+	30.3109i	−0.824043	+	1.42728i
$452$	−1.00000			−0.0470360
$453$		−	8.66025i		−	0.406894i
$454$	−11.0000			−0.516256
$455$	−3.00000	−	5.19615i	−0.140642	−	0.243599i
$456$	4.50000	−	6.06218i	0.210732	−	0.283887i
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	−0.672994	−	0.739648i	$-0.734992\pi$
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	0.977051	+	0.213006i	$0.0683253\pi$
$458$	6.50000	−	11.2583i	0.303725	−	0.526067i
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$	4.00000	+	6.92820i	0.186501	+	0.323029i
$461$	−13.0000	−	22.5167i	−0.605470	−	1.04871i	−0.991977	−	0.126419i	$-0.959652\pi$
$461$	−13.0000	−	22.5167i	−0.605470	−	1.04871i	0.386507	−	0.922287i	$-0.373682\pi$
$462$			25.9808i			1.20873i
$463$	14.5000	+	25.1147i	0.673872	+	1.16718i	0.976797	+	0.214166i	$0.0687035\pi$
$463$	14.5000	+	25.1147i	0.673872	+	1.16718i	−0.302925	+	0.953014i	$0.597963\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$	−10.5000	−	6.06218i	−0.486926	−	0.281127i
$466$	15.0000			0.694862
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	−6.00000			−0.277350
$469$	18.0000	+	31.1769i	0.831163	+	1.43962i
$470$	−0.500000	−	0.866025i	−0.0230633	−	0.0399468i
$471$	25.5000	−	14.7224i	1.17498	−	0.678374i
$472$	−3.00000			−0.138086
$473$	−40.0000			−1.83920
$474$			6.92820i			0.318223i
$475$	16.0000	−	6.92820i	0.734130	−	0.317888i
$476$	−9.00000			−0.412514
$477$	−33.0000			−1.51097
$478$	−13.5000	+	23.3827i	−0.617476	+	1.06950i
$479$	−17.0000			−0.776750			−0.388375	−	0.921501i	$-0.626963\pi$
$479$	−17.0000			−0.776750			−0.388375	+	0.921501i	$0.626963\pi$
$480$			1.73205i			0.0790569i
$481$	−10.0000	+	17.3205i	−0.455961	+	0.789747i
$482$	8.50000	+	14.7224i	0.387164	+	0.670588i
$483$	−36.0000	−	20.7846i	−1.63806	−	0.945732i
$484$	14.0000			0.636364
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$		−	15.5885i		−	0.707107i
$487$	40.0000			1.81257			0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000			1.81257			0.906287	+	0.422664i	$0.138905\pi$
$488$	−1.00000			−0.0452679
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	−19.0000			−0.857458			−0.428729	−	0.903433i	$-0.641038\pi$
$491$	−19.0000			−0.857458			−0.428729	+	0.903433i	$0.641038\pi$
$492$		−	12.1244i		−	0.546608i
$493$	7.50000	−	12.9904i	0.337783	−	0.585057i
$494$	−8.00000	+	3.46410i	−0.359937	+	0.155857i
$495$	−7.50000	−	12.9904i	−0.337100	−	0.583874i
$496$	−3.50000	+	6.06218i	−0.157155	+	0.272200i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$	−13.5000	+	7.79423i	−0.604949	+	0.349268i
$499$	−11.0000			−0.492428			−0.246214	−	0.969216i	$-0.579187\pi$
$499$	−11.0000			−0.492428			−0.246214	+	0.969216i	$0.579187\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$			20.7846i			0.928588i
$502$	−2.50000	+	4.33013i	−0.111580	+	0.193263i
$503$	−16.5000	−	28.5788i	−0.735699	−	1.27427i	−0.954416	−	0.298479i	$-0.903521\pi$
$503$	−16.5000	−	28.5788i	−0.735699	−	1.27427i	0.218718	−	0.975788i	$-0.429813\pi$
$504$	−4.50000	−	7.79423i	−0.200446	−	0.347183i
$505$	−11.0000			−0.489494
$506$	−20.0000	+	34.6410i	−0.889108	+	1.53998i
$507$	−13.5000	−	7.79423i	−0.599556	−	0.346154i
$508$	−15.0000			−0.665517
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.148866	+	0.988857i	$0.547562\pi$
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.781943	+	0.623350i	$0.785771\pi$
$510$	4.50000	−	2.59808i	0.199263	−	0.115045i
$511$	4.50000	+	7.79423i	0.199068	+	0.344796i
$512$	1.00000			0.0441942
$513$	−9.00000	−	20.7846i	−0.397360	−	0.917663i
$514$	14.0000			0.617514
$515$	7.50000	+	12.9904i	0.330489	+	0.572425i
$516$	12.0000	−	6.92820i	0.528271	−	0.304997i
$517$	2.50000	−	4.33013i	0.109950	−	0.190439i
$518$	−30.0000			−1.31812
$519$	−9.00000	−	5.19615i	−0.395056	−	0.228086i
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$	15.0000			0.656532
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		−	20.7846i		−	0.907115i
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	21.0000			0.914774
$528$	−7.50000	+	4.33013i	−0.326396	+	0.188445i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	5.50000	−	9.52628i	0.238905	−	0.413795i
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$	−10.5000	−	7.79423i	−0.455233	−	0.337923i
$533$	−7.00000	+	12.1244i	−0.303204	+	0.525164i
$534$		−	25.9808i		−	1.12430i
$535$	4.00000			0.172935
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$	−18.0000	+	10.3923i	−0.776757	+	0.448461i
$538$	3.00000			0.129339
$539$	10.0000			0.430730
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	7.00000			0.300676
$543$	28.5000	+	16.4545i	1.22305	+	0.706129i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−4.50000	+	7.79423i	−0.192759	+	0.333868i
$546$			10.3923i			0.444750i
$547$	−5.00000			−0.213785			−0.106892	−	0.994271i	$-0.534090\pi$
$547$	−5.00000			−0.213785			−0.106892	+	0.994271i	$0.534090\pi$
$548$	−9.50000	+	16.4545i	−0.405820	+	0.702901i
$549$	−1.50000	+	2.59808i	−0.0640184	+	0.110883i
$550$	−20.0000			−0.852803
$551$	20.0000	−	8.66025i	0.852029	−	0.368939i
$552$		−	13.8564i		−	0.589768i
$553$	12.0000			0.510292
$554$	19.0000			0.807233
$555$	15.0000	−	8.66025i	0.636715	−	0.367607i
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	8.50000	+	14.7224i	0.360157	+	0.623809i	0.987986	−	0.154541i	$-0.0493899\pi$
$557$	8.50000	+	14.7224i	0.360157	+	0.623809i	−0.627830	+	0.778351i	$0.716057\pi$
$558$	10.5000	+	18.1865i	0.444500	+	0.769897i
$559$	−16.0000			−0.676728
$560$	3.00000			0.126773
$561$	22.5000	+	12.9904i	0.949951	+	0.548454i
$562$	2.50000	+	4.33013i	0.105456	+	0.182655i
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$			1.73205i			0.0729325i
$565$	−0.500000	−	0.866025i	−0.0210352	−	0.0364340i
$566$	1.50000	+	2.59808i	0.0630497	+	0.109205i
$567$	−27.0000			−1.13389
$568$	0.500000	−	0.866025i	0.0209795	−	0.0363376i
$569$	20.5000	−	35.5070i	0.859405	−	1.48853i	−0.0130929	−	0.999914i	$-0.504168\pi$
$569$	20.5000	−	35.5070i	0.859405	−	1.48853i	0.872498	−	0.488618i	$-0.162499\pi$
$570$	7.50000	+	0.866025i	0.314140	+	0.0362738i
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	0.727690	−	0.685907i	$-0.240594\pi$
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	−0.957857	+	0.287244i	$0.907261\pi$
$572$	10.0000			0.418121
$573$		−	1.73205i		−	0.0723575i
$574$	−21.0000			−0.876523
$575$	16.0000	−	27.7128i	0.667246	−	1.15570i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	13.5000	−	7.79423i	0.561041	−	0.323917i
$580$	−2.50000	+	4.33013i	−0.103807	+	0.179799i
$581$	13.5000	+	23.3827i	0.560074	+	0.970077i
$582$			3.46410i			0.143592i
$583$	55.0000			2.27787
$584$	−1.50000	+	2.59808i	−0.0620704	+	0.107509i
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	0.715226	−	0.698893i	$-0.246324\pi$
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	−0.962872	+	0.269957i	$0.912990\pi$
$588$	−3.00000	+	1.73205i	−0.123718	+	0.0714286i
$589$	24.5000	+	18.1865i	1.00950	+	0.749363i
$590$	−1.50000	−	2.59808i	−0.0617540	−	0.106961i
$591$	−3.00000	+	1.73205i	−0.123404	+	0.0712470i
$592$	−5.00000	−	8.66025i	−0.205499	−	0.355934i
$593$	20.5000	+	35.5070i	0.841834	+	1.45810i	0.888342	+	0.459182i	$0.151857\pi$
$593$	20.5000	+	35.5070i	0.841834	+	1.45810i	−0.0465084	+	0.998918i	$0.514809\pi$
$594$			25.9808i			1.06600i
$595$	−4.50000	−	7.79423i	−0.184482	−	0.319532i
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$	−10.5000	−	6.06218i	−0.429736	−	0.248108i
$598$	−8.00000	+	13.8564i	−0.327144	+	0.566631i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$	6.00000	−	3.46410i	0.244949	−	0.141421i
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	−0.810522	−	0.585708i	$-0.800816\pi$
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	0.912499	+	0.409079i	$0.134150\pi$
$602$	−12.0000	−	20.7846i	−0.489083	−	0.847117i
$603$	18.0000	+	31.1769i	0.733017	+	1.26962i
$604$	−2.50000	−	4.33013i	−0.101724	−	0.176190i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	16.5000	+	9.52628i	0.670267	+	0.386979i
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$	0.500000	−	4.33013i	0.0202777	−	0.175610i
$609$		−	25.9808i		−	1.05279i
$610$	−0.500000	−	0.866025i	−0.0202444	−	0.0350643i
$611$	1.00000	−	1.73205i	0.0404557	−	0.0700713i
$612$	−9.00000			−0.363803
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	−0.991588	−	0.129433i	$-0.958684\pi$
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	0.607887	+	0.794024i	$0.292017\pi$
$614$	−33.0000			−1.33177
$615$	10.5000	−	6.06218i	0.423401	−	0.244451i
$616$	7.50000	+	12.9904i	0.302184	+	0.523397i
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		−	25.9808i		−	1.04510i
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	−7.00000			−0.281127
$621$	−36.0000	−	20.7846i	−1.44463	−	0.834058i
$622$	−3.50000	+	6.06218i	−0.140337	+	0.243071i
$623$	−45.0000			−1.80289
$624$	−3.00000	+	1.73205i	−0.120096	+	0.0693375i
$625$	11.0000			0.440000
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$	15.0000	+	34.6410i	0.599042	+	1.38343i
$628$	8.50000	−	14.7224i	0.339187	−	0.587489i
$629$	−15.0000	+	25.9808i	−0.598089	+	1.03592i
$630$	4.50000	−	7.79423i	0.179284	−	0.310530i
$631$	21.5000	+	37.2391i	0.855901	+	1.48246i	0.875806	+	0.482663i	$0.160330\pi$
$631$	21.5000	+	37.2391i	0.855901	+	1.48246i	−0.0199047	+	0.999802i	$0.506336\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−13.5000	+	7.79423i	−0.536577	+	0.309793i
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	−7.50000	−	12.9904i	−0.297628	−	0.515508i
$636$	−16.5000	+	9.52628i	−0.654268	+	0.377742i
$637$	4.00000			0.158486
$638$	−25.0000			−0.989759
$639$	−1.50000	−	2.59808i	−0.0593391	−	0.102778i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	−6.00000	−	3.46410i	−0.236801	−	0.136717i
$643$	49.0000			1.93237			0.966186	−	0.257847i	$-0.0830131\pi$
$643$	49.0000			1.93237			0.966186	+	0.257847i	$0.0830131\pi$
$644$	−24.0000			−0.945732
$645$	12.0000	+	6.92820i	0.472500	+	0.272798i
$646$	−12.0000	+	5.19615i	−0.472134	+	0.204440i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	7.50000	−	12.9904i	0.294401	−	0.509917i
$650$	−8.00000			−0.313786
$651$	31.5000	−	18.1865i	1.23458	−	0.712786i
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$	13.5000	−	7.79423i	0.527892	−	0.304778i
$655$	15.0000			0.586098
$656$	−3.50000	−	6.06218i	−0.136652	−	0.236688i
$657$	4.50000	+	7.79423i	0.175562	+	0.304082i
$658$	3.00000			0.116952
$659$	23.0000			0.895953			0.447976	−	0.894045i	$-0.352145\pi$
$659$	23.0000			0.895953			0.447976	+	0.894045i	$0.352145\pi$
$660$	−7.50000	−	4.33013i	−0.291937	−	0.168550i
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$	29.0000			1.12712
$663$	9.00000	+	5.19615i	0.349531	+	0.201802i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	1.50000	−	12.9904i	0.0581675	−	0.503745i
$666$	−30.0000			−1.16248
$667$	20.0000	−	34.6410i	0.774403	−	1.34131i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	−24.0000	−	13.8564i	−0.927894	−	0.535720i
$670$	−12.0000			−0.463600
$671$	2.50000	−	4.33013i	0.0965114	−	0.167163i
$672$	−4.50000	−	2.59808i	−0.173591	−	0.100223i
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	2.50000	+	4.33013i	0.0962964	+	0.166790i
$675$		−	20.7846i		−	0.800000i
$676$	−9.00000			−0.346154
$677$	−3.50000	+	6.06218i	−0.134516	+	0.232988i	−0.925412	−	0.378962i	$-0.876281\pi$
$677$	−3.50000	+	6.06218i	−0.134516	+	0.232988i	0.790897	+	0.611950i	$0.209615\pi$
$678$			1.73205i			0.0665190i
$679$	6.00000			0.230259
$680$	1.50000	−	2.59808i	0.0575224	−	0.0996317i
$681$			19.0526i			0.730096i
$682$	−17.5000	−	30.3109i	−0.670110	−	1.16066i
$683$	−44.0000			−1.68361			−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000			−1.68361			−0.841807	+	0.539779i	$0.818508\pi$
$684$	−10.5000	−	7.79423i	−0.401478	−	0.298020i
$685$	−19.0000			−0.725953
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	−19.5000	−	11.2583i	−0.743971	−	0.429532i
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	22.0000			0.838133
$690$	12.0000	−	6.92820i	0.456832	−	0.263752i
$691$	−10.5000	+	18.1865i	−0.399439	+	0.691848i	−0.993657	−	0.112456i	$-0.964128\pi$
$691$	−10.5000	+	18.1865i	−0.399439	+	0.691848i	0.594218	+	0.804304i	$0.297462\pi$
$692$	−6.00000			−0.228086
$693$	45.0000			1.70941
$694$	11.5000	+	19.9186i	0.436534	+	0.756099i
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$	7.50000	−	4.33013i	0.284287	−	0.164133i
$697$	−10.5000	+	18.1865i	−0.397716	+	0.688864i
$698$	−5.00000			−0.189253
$699$		−	25.9808i		−	0.982683i
$700$	−6.00000	−	10.3923i	−0.226779	−	0.392792i
$701$	0.500000	−	0.866025i	0.0188847	−	0.0327093i	−0.856429	−	0.516265i	$-0.827322\pi$
$701$	0.500000	−	0.866025i	0.0188847	−	0.0327093i	0.875313	+	0.483556i	$0.160655\pi$
$702$			10.3923i			0.392232i
$703$	−40.0000	+	17.3205i	−1.50863	+	0.653255i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	−1.50000	+	0.866025i	−0.0564933	+	0.0326164i
$706$	3.00000			0.112906
$707$	16.5000	−	28.5788i	0.620546	−	1.07482i
$708$			5.19615i			0.195283i
$709$	3.00000			0.112667			0.0563337	−	0.998412i	$-0.482059\pi$
$709$	3.00000			0.112667			0.0563337	+	0.998412i	$0.482059\pi$
$710$	1.00000			0.0375293
$711$	12.0000			0.450035
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	56.0000			2.09722
$714$			15.5885i			0.583383i
$715$	5.00000	+	8.66025i	0.186989	+	0.323875i
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	40.5000	+	23.3827i	1.51250	+	0.873242i
$718$	15.0000			0.559795
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	−0.923880	−	0.382682i	$-0.875001\pi$
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	0.793352	+	0.608763i	$0.208334\pi$
$720$	3.00000			0.111803
$721$	−45.0000			−1.67589
$722$	−18.5000	−	4.33013i	−0.688499	−	0.161151i
$723$	25.5000	−	14.7224i	0.948355	−	0.547533i
$724$	19.0000			0.706129
$725$	20.0000			0.742781
$726$		−	24.2487i		−	0.899954i
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	−0.951694	−	0.307049i	$-0.900659\pi$
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	0.209935	−	0.977715i	$-0.432675\pi$
$728$	3.00000	+	5.19615i	0.111187	+	0.192582i
$729$	−27.0000			−1.00000
$730$	−3.00000			−0.111035
$731$	−24.0000			−0.887672
$732$			1.73205i			0.0640184i
$733$	−7.50000	−	12.9904i	−0.277019	−	0.479811i	0.693624	−	0.720338i	$-0.256013\pi$
$733$	−7.50000	−	12.9904i	−0.277019	−	0.479811i	−0.970642	+	0.240527i	$0.922680\pi$
$734$	8.50000	+	14.7224i	0.313741	+	0.543415i
$735$	−3.00000	−	1.73205i	−0.110657	−	0.0638877i
$736$	−4.00000	−	6.92820i	−0.147442	−	0.255377i
$737$	−30.0000	−	51.9615i	−1.10506	−	1.91403i
$738$	−21.0000			−0.773021
$739$	18.5000	−	32.0429i	0.680534	−	1.17872i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	18.5000	−	32.0429i	0.680534	−	1.17872i	0.974818	−	0.223001i	$-0.0715853\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$	6.00000	+	13.8564i	0.220416	+	0.509028i
$742$	16.5000	+	28.5788i	0.605734	+	1.04916i
$743$	−19.0000			−0.697042			−0.348521	−	0.937301i	$-0.613316\pi$
$743$	−19.0000			−0.697042			−0.348521	+	0.937301i	$0.613316\pi$
$744$	10.5000	+	6.06218i	0.384949	+	0.222250i
$745$	−3.00000			−0.109911
$746$	12.5000	−	21.6506i	0.457658	−	0.792686i
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$	15.0000			0.548454
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$	13.5000	+	7.79423i	0.492950	+	0.284605i
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$	0.500000	+	0.866025i	0.0182331	+	0.0315807i
$753$	7.50000	+	4.33013i	0.273315	+	0.157799i
$754$	−10.0000			−0.364179
$755$	2.50000	−	4.33013i	0.0909843	−	0.157589i
$756$	−13.5000	+	7.79423i	−0.490990	+	0.283473i
$757$	14.5000	−	25.1147i	0.527011	−	0.912811i	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	14.5000	−	25.1147i	0.527011	−	0.912811i	0.999505	−	0.0314762i	$-0.0100208\pi$
$758$	6.00000	+	10.3923i	0.217930	+	0.377466i
$759$	60.0000	+	34.6410i	2.17786	+	1.25739i
$760$	4.00000	−	1.73205i	0.145095	−	0.0628281i
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	0.697467	−	0.716617i	$-0.254310\pi$
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	−0.969342	+	0.245716i	$0.920977\pi$
$762$			25.9808i			0.941184i
$763$	−13.5000	−	23.3827i	−0.488733	−	0.846510i
$764$	−0.500000	−	0.866025i	−0.0180894	−	0.0313317i
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	−6.50000	−	11.2583i	−0.234855	−	0.406780i
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$		−	1.73205i		−	0.0625000i
$769$	13.0000	−	22.5167i	0.468792	−	0.811972i	−0.530572	−	0.847640i	$-0.678023\pi$
$769$	13.0000	−	22.5167i	0.468792	−	0.811972i	0.999364	+	0.0356685i	$0.0113561\pi$
$770$	−7.50000	+	12.9904i	−0.270281	+	0.468141i
$771$		−	24.2487i		−	0.873296i
$772$	4.50000	−	7.79423i	0.161959	−	0.280520i
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$	−12.0000	−	20.7846i	−0.431331	−	0.747087i
$775$	14.0000	+	24.2487i	0.502895	+	0.871039i
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$			51.9615i			1.86411i
$778$	4.50000	+	7.79423i	0.161333	+	0.279437i
$779$	−28.0000	+	12.1244i	−1.00320	+	0.434400i
$780$	−3.00000	−	1.73205i	−0.107417	−	0.0620174i
$781$	2.50000	+	4.33013i	0.0894570	+	0.154944i
$782$	−12.0000	+	20.7846i	−0.429119	+	0.743256i
$783$		−	25.9808i		−	0.928477i
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	17.0000			0.606756
$786$	−22.5000	−	12.9904i	−0.802548	−	0.463352i
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	0.796878	−	0.604140i	$-0.206483\pi$
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	−0.921640	+	0.388047i	$0.873150\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$	−36.0000	−	20.7846i	−1.28163	−	0.739952i
$790$	−2.00000	+	3.46410i	−0.0711568	+	0.123247i
$791$	3.00000			0.106668
$792$	7.50000	+	12.9904i	0.266501	+	0.461593i
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$	35.0000			1.24210
$795$	−16.5000	−	9.52628i	−0.585195	−	0.337862i
$796$	−7.00000			−0.248108
$797$	4.50000	+	7.79423i	0.159398	+	0.276086i	0.934652	−	0.355564i	$-0.115711\pi$
$797$	4.50000	+	7.79423i	0.159398	+	0.276086i	−0.775254	+	0.631650i	$0.782378\pi$
$798$	−13.5000	+	18.1865i	−0.477895	+	0.643796i
$799$	1.50000	−	2.59808i	0.0530662	−	0.0919133i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−45.0000			−1.59000
$802$	−15.5000	−	26.8468i	−0.547324	−	0.947993i
$803$	−7.50000	−	12.9904i	−0.264669	−	0.458421i
$804$	18.0000	+	10.3923i	0.634811	+	0.366508i
$805$	−12.0000	−	20.7846i	−0.422944	−	0.732561i
$806$	−7.00000	−	12.1244i	−0.246564	−	0.427062i
$807$		−	5.19615i		−	0.182913i
$808$	11.0000			0.386979
$809$	54.0000			1.89854			0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000			1.89854			0.949269	+	0.314464i	$0.101825\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	−16.5000	−	28.5788i	−0.579393	−	1.00354i	−0.995549	−	0.0942453i	$-0.969956\pi$
$811$	−16.5000	−	28.5788i	−0.579393	−	1.00354i	0.416156	−	0.909293i	$-0.363377\pi$
$812$	−7.50000	−	12.9904i	−0.263198	−	0.455873i
$813$		−	12.1244i		−	0.425220i
$814$	50.0000			1.75250
$815$	4.00000			0.140114
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	−28.0000	−	20.7846i	−0.979596	−	0.727161i
$818$	10.0000			0.349642
$819$	18.0000			0.628971
$820$	3.50000	−	6.06218i	0.122225	−	0.211700i
$821$	3.00000			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$822$	28.5000	+	16.4545i	0.994052	+	0.573916i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−7.50000	−	12.9904i	−0.261275	−	0.452541i
$825$			34.6410i			1.20605i
$826$	9.00000			0.313150
$827$	−20.5000	−	35.5070i	−0.712855	−	1.23470i	−0.963781	−	0.266695i	$-0.914068\pi$
$827$	−20.5000	−	35.5070i	−0.712855	−	1.23470i	0.250926	−	0.968006i	$-0.419265\pi$
$828$	−24.0000			−0.834058
$829$	18.0000			0.625166			0.312583	−	0.949890i	$-0.398806\pi$
$829$	18.0000			0.625166			0.312583	+	0.949890i	$0.398806\pi$
$830$	−9.00000			−0.312395
$831$		−	32.9090i		−	1.14160i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	6.00000			0.207888
$834$	18.0000	−	10.3923i	0.623289	−	0.359856i
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$	17.5000	+	12.9904i	0.605250	+	0.449282i
$837$	31.5000	−	18.1865i	1.08880	−	0.628619i
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$	8.00000	+	13.8564i	0.276191	+	0.478376i	0.970435	−	0.241363i	$-0.0775945\pi$
$839$	8.00000	+	13.8564i	0.276191	+	0.478376i	−0.694244	+	0.719740i	$0.744261\pi$
$840$		−	5.19615i		−	0.179284i
$841$	−4.00000			−0.137931
$842$	11.0000	−	19.0526i	0.379085	−	0.656595i
$843$	7.50000	−	4.33013i	0.258314	−	0.149137i
$844$	−4.50000	+	7.79423i	−0.154896	+	0.268288i
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$	3.00000			0.103142
$847$	−42.0000			−1.44314
$848$	−5.50000	+	9.52628i	−0.188871	+	0.327134i
$849$	4.50000	−	2.59808i	0.154440	−	0.0891657i
$850$	−12.0000			−0.411597
$851$	−40.0000	+	69.2820i	−1.37118	+	2.37496i
$852$	−1.50000	−	0.866025i	−0.0513892	−	0.0296695i
$853$	15.0000	+	25.9808i	0.513590	+	0.889564i	0.999876	+	0.0157644i	$0.00501816\pi$
$853$	15.0000	+	25.9808i	0.513590	+	0.889564i	−0.486286	+	0.873800i	$0.661649\pi$
$854$	3.00000			0.102658
$855$	1.50000	−	12.9904i	0.0512989	−	0.444262i
$856$	−4.00000			−0.136717
$857$	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	$0.578690\pi$
$858$		−	17.3205i		−	0.591312i
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	−0.999672	−	0.0255910i	$-0.991853\pi$
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	0.521999	+	0.852946i	$0.325187\pi$
$860$	8.00000			0.272798
$861$			36.3731i			1.23959i
$862$	1.50000	−	2.59808i	0.0510902	−	0.0884908i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	18.5000	−	32.0429i	0.628656	−	1.08886i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$	10.5000	−	18.1865i	0.356393	−	0.617291i
$869$	−20.0000			−0.678454
$870$	7.50000	+	4.33013i	0.254274	+	0.146805i
$871$	−12.0000	−	20.7846i	−0.406604	−	0.704260i
$872$	4.50000	−	7.79423i	0.152389	−	0.263946i
$873$	6.00000			0.203069
$874$	−32.0000	+	13.8564i	−1.08242	+	0.468700i
$875$	13.5000	−	23.3827i	0.456383	−	0.790479i
$876$	4.50000	+	2.59808i	0.152041	+	0.0877809i
$877$	−53.0000			−1.78968			−0.894841	−	0.446384i	$-0.852711\pi$
$877$	−53.0000			−1.78968			−0.894841	+	0.446384i	$0.852711\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$	−13.5000	−	7.79423i	−0.455344	−	0.262893i
$880$	−5.00000			−0.168550
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	3.00000	+	5.19615i	0.101015	+	0.174964i
$883$	−6.50000	−	11.2583i	−0.218742	−	0.378873i	0.735681	−	0.677328i	$-0.236862\pi$
$883$	−6.50000	−	11.2583i	−0.218742	−	0.378873i	−0.954424	+	0.298455i	$0.903529\pi$
$884$	6.00000			0.201802
$885$	−4.50000	+	2.59808i	−0.151266	+	0.0873334i
$886$	−15.5000	−	26.8468i	−0.520733	−	0.901935i
$887$	28.0000	−	48.4974i	0.940148	−	1.62838i	0.174962	−	0.984575i	$-0.444020\pi$
$887$	28.0000	−	48.4974i	0.940148	−	1.62838i	0.765186	−	0.643809i	$-0.222647\pi$
$888$	−15.0000	+	8.66025i	−0.503367	+	0.290619i
$889$	45.0000			1.50925
$890$	7.50000	−	12.9904i	0.251401	−	0.435439i
$891$	45.0000			1.50756
$892$	−16.0000			−0.535720
$893$	4.00000	−	1.73205i	0.133855	−	0.0579609i
$894$	4.50000	+	2.59808i	0.150503	+	0.0868927i
$895$	−12.0000			−0.401116
$896$	−3.00000			−0.100223
$897$	24.0000	+	13.8564i	0.801337	+	0.462652i
$898$	13.0000	+	22.5167i	0.433816	+	0.751391i
$899$	17.5000	+	30.3109i	0.583658	+	1.01092i
$900$	−6.00000	−	10.3923i	−0.200000	−	0.346410i
$901$	33.0000			1.09939
$902$	35.0000			1.16537
$903$	−36.0000	+	20.7846i	−1.19800	+	0.691669i
$904$	0.500000	+	0.866025i	0.0166298	+	0.0288036i
$905$	9.50000	+	16.4545i	0.315791	+	0.546966i
$906$	−7.50000	+	4.33013i	−0.249171	+	0.143859i
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	−0.999334	−	0.0364935i	$-0.988381\pi$
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	0.468063	−	0.883695i	$-0.344952\pi$
$908$	5.50000	+	9.52628i	0.182524	+	0.316141i
$909$	16.5000	−	28.5788i	0.547270	−	0.947900i
$910$	−3.00000	+	5.19615i	−0.0994490	+	0.172251i
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$	−7.50000	−	0.866025i	−0.248350	−	0.0286770i
$913$	−22.5000	−	38.9711i	−0.744641	−	1.28976i
$914$	−13.0000			−0.430002
$915$	−1.50000	+	0.866025i	−0.0495885	+	0.0286299i
$916$	−13.0000			−0.429532
$917$	−22.5000	+	38.9711i	−0.743015	+	1.28694i
$918$			15.5885i			0.514496i
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	4.00000	−	6.92820i	0.131876	−	0.228416i
$921$			57.1577i			1.88341i
$922$	−13.0000	+	22.5167i	−0.428132	+	0.741547i
$923$	1.00000	+	1.73205i	0.0329154	+	0.0570111i
$924$	22.5000	−	12.9904i	0.740196	−	0.427352i
$925$	−40.0000			−1.31519
$926$	14.5000	−	25.1147i	0.476500	−	0.825321i
$927$	−45.0000			−1.47799
$928$	2.50000	−	4.33013i	0.0820665	−	0.142143i
$929$	−25.0000	−	43.3013i	−0.820223	−	1.42067i	−0.905516	−	0.424313i	$-0.860516\pi$
$929$	−25.0000	−	43.3013i	−0.820223	−	1.42067i	0.0852924	−	0.996356i	$-0.472818\pi$
$930$			12.1244i			0.397573i
$931$	7.00000	+	5.19615i	0.229416	+	0.170297i
$932$	−7.50000	−	12.9904i	−0.245671	−	0.425514i
$933$	10.5000	+	6.06218i	0.343755	+	0.198467i
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$	7.50000	+	12.9904i	0.245276	+	0.424831i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	−23.5000	−	40.7032i	−0.767712	−	1.32972i	−0.938801	−	0.344460i	$-0.888062\pi$
$937$	−23.5000	−	40.7032i	−0.767712	−	1.32972i	0.171089	−	0.985255i	$-0.445271\pi$
$938$	18.0000	−	31.1769i	0.587721	−	1.01796i
$939$	1.50000	−	0.866025i	0.0489506	−	0.0282617i
$940$	−0.500000	+	0.866025i	−0.0163082	+	0.0282466i
$941$	−5.00000	+	8.66025i	−0.162995	+	0.282316i	−0.935942	−	0.352155i	$-0.885449\pi$
$941$	−5.00000	+	8.66025i	−0.162995	+	0.282316i	0.772946	+	0.634472i	$0.218782\pi$
$942$	−25.5000	−	14.7224i	−0.830835	−	0.479683i
$943$	−28.0000	+	48.4974i	−0.911805	+	1.57929i
$944$	1.50000	+	2.59808i	0.0488208	+	0.0845602i
$945$	−13.5000	−	7.79423i	−0.439155	−	0.253546i
$946$	20.0000	+	34.6410i	0.650256	+	1.12628i
$947$	30.0000	+	51.9615i	0.974869	+	1.68852i	0.680367	+	0.732872i	$0.261821\pi$
$947$	30.0000	+	51.9615i	0.974869	+	1.68852i	0.294502	+	0.955651i	$0.404846\pi$
$948$	6.00000	−	3.46410i	0.194871	−	0.112509i
$949$	−3.00000	−	5.19615i	−0.0973841	−	0.168674i
$950$	−14.0000	−	10.3923i	−0.454220	−	0.337171i
$951$	−4.50000	+	2.59808i	−0.145922	+	0.0842484i
$952$	4.50000	+	7.79423i	0.145846	+	0.252612i
$953$	0.500000	−	0.866025i	0.0161966	−	0.0280533i	−0.857814	−	0.513961i	$-0.828178\pi$
$953$	0.500000	−	0.866025i	0.0161966	−	0.0280533i	0.874010	+	0.485908i	$0.161511\pi$
$954$	16.5000	+	28.5788i	0.534207	+	0.925274i
$955$	0.500000	−	0.866025i	0.0161796	−	0.0280239i
$956$	27.0000			0.873242
$957$			43.3013i			1.39973i
$958$	8.50000	+	14.7224i	0.274623	+	0.475660i
$959$	28.5000	−	49.3634i	0.920313	−	1.59403i
$960$	1.50000	−	0.866025i	0.0484123	−	0.0279508i
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	20.0000			0.644826
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	9.00000			0.289720
$966$			41.5692i			1.33747i
$967$	9.00000			0.289420			0.144710	−	0.989474i	$-0.453775\pi$
$967$	9.00000			0.289420			0.144710	+	0.989474i	$0.453775\pi$
$968$	−7.00000	−	12.1244i	−0.224989	−	0.389692i
$969$	9.00000	+	20.7846i	0.289122	+	0.667698i
$970$	−1.00000	+	1.73205i	−0.0321081	+	0.0556128i
$971$	−17.5000	+	30.3109i	−0.561602	+	0.972723i	0.435755	+	0.900065i	$0.356481\pi$
$971$	−17.5000	+	30.3109i	−0.561602	+	0.972723i	−0.997357	+	0.0726575i	$0.976852\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	−18.0000	−	31.1769i	−0.577054	−	0.999486i
$974$	−20.0000	−	34.6410i	−0.640841	−	1.10997i
$975$			13.8564i			0.443760i
$976$	0.500000	+	0.866025i	0.0160046	+	0.0277208i
$977$	−5.50000	−	9.52628i	−0.175961	−	0.304773i	0.764533	−	0.644585i	$-0.222970\pi$
$977$	−5.50000	−	9.52628i	−0.175961	−	0.304773i	−0.940493	+	0.339812i	$0.889636\pi$
$978$	−6.00000	−	3.46410i	−0.191859	−	0.110770i
$979$	75.0000			2.39701
$980$	−2.00000			−0.0638877
$981$	−13.5000	−	23.3827i	−0.431022	−	0.746552i
$982$	9.50000	+	16.4545i	0.303157	+	0.525084i
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	−10.5000	+	6.06218i	−0.334728	+	0.193255i
$985$	−2.00000			−0.0637253
$986$	−15.0000			−0.477697
$987$		−	5.19615i		−	0.165395i
$988$	7.00000	+	5.19615i	0.222700	+	0.165312i
$989$	−64.0000			−2.03508
$990$	−7.50000	+	12.9904i	−0.238366	+	0.412861i
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	−0.976539	−	0.215342i	$-0.930913\pi$
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	0.674761	+	0.738036i	$0.264247\pi$
$992$	7.00000			0.222250
$993$		−	50.2295i		−	1.59398i
$994$	−1.50000	+	2.59808i	−0.0475771	+	0.0824060i
$995$	−3.50000	−	6.06218i	−0.110957	−	0.192184i
$996$	13.5000	+	7.79423i	0.427764	+	0.246970i
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$	5.50000	+	9.52628i	0.174099	+	0.301549i
$999$			51.9615i			1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.a.277.1	yes	2
3.2	odd	2		1026.2.h.d.505.1		2
9.4	even	3		342.2.f.c.49.1	yes	2
9.5	odd	6		1026.2.f.a.847.1		2
19.7	even	3		342.2.f.c.7.1	✓	2
57.26	odd	6		1026.2.f.a.235.1		2
171.121	even	3	inner	342.2.h.a.121.1	yes	2
171.140	odd	6		1026.2.h.d.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.c.7.1	✓	2	19.7	even	3
342.2.f.c.49.1	yes	2	9.4	even	3
342.2.h.a.121.1	yes	2	171.121	even	3	inner
342.2.h.a.277.1	yes	2	1.1	even	1	trivial
1026.2.f.a.235.1		2	57.26	odd	6
1026.2.f.a.847.1		2	9.5	odd	6
1026.2.h.d.505.1		2	3.2	odd	2
1026.2.h.d.577.1		2	171.140	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} -1.73205i q^{12} +(-1.00000 + 1.73205i) q^{13} -3.00000 q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +5.19615i q^{21} +5.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(-1.50000 + 0.866025i) q^{24} -4.00000 q^{25} +2.00000 q^{26} +5.19615i q^{27} +(1.50000 + 2.59808i) q^{28} -5.00000 q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} -8.66025i q^{33} +3.00000 q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +10.0000 q^{37} +(3.50000 + 2.59808i) q^{38} -3.46410i q^{39} -1.00000 q^{40} +7.00000 q^{41} +(4.50000 - 2.59808i) q^{42} +(4.00000 + 6.92820i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +8.00000 q^{46} -1.00000 q^{47} +(1.50000 + 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} -5.19615i q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.50000 - 9.52628i) q^{53} +(4.50000 - 2.59808i) q^{54} +(2.50000 - 4.33013i) q^{55} +(1.50000 - 2.59808i) q^{56} +(4.50000 - 6.06218i) q^{57} +(2.50000 + 4.33013i) q^{58} -3.00000 q^{59} +1.73205i q^{60} -1.00000 q^{61} +(-3.50000 + 6.06218i) q^{62} +(-4.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-7.50000 + 4.33013i) q^{66} +(-6.00000 + 10.3923i) q^{67} +(-1.50000 - 2.59808i) q^{68} -13.8564i q^{69} +3.00000 q^{70} +(0.500000 - 0.866025i) q^{71} +(1.50000 - 2.59808i) q^{72} +(-1.50000 + 2.59808i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 4.33013i) q^{76} +(7.50000 + 12.9904i) q^{77} +(-3.00000 + 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(1.50000 - 2.59808i) q^{85} +(4.00000 - 6.92820i) q^{86} +(7.50000 - 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-7.50000 - 12.9904i) q^{89} +3.00000 q^{90} +(3.00000 + 5.19615i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(10.5000 + 6.06218i) q^{93} +(0.500000 + 0.866025i) q^{94} +(4.00000 - 1.73205i) q^{95} -1.73205i q^{96} +(1.00000 + 1.73205i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 3 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 3 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 3 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} - 5 q^{11} - 2 q^{13} - 6 q^{14} + 3 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} - 8 q^{19} + q^{20} + 10 q^{22} - 8 q^{23} - 3 q^{24} - 8 q^{25} + 4 q^{26} + 3 q^{28} - 10 q^{29} - 3 q^{30} - 7 q^{31} - q^{32} + 6 q^{34} - 3 q^{35} + 3 q^{36} + 20 q^{37} + 7 q^{38} - 2 q^{40} + 14 q^{41} + 9 q^{42} + 8 q^{43} - 5 q^{44} - 3 q^{45} + 16 q^{46} - 2 q^{47} + 3 q^{48} - 2 q^{49} + 4 q^{50} - 2 q^{52} - 11 q^{53} + 9 q^{54} + 5 q^{55} + 3 q^{56} + 9 q^{57} + 5 q^{58} - 6 q^{59} - 2 q^{61} - 7 q^{62} - 9 q^{63} + 2 q^{64} + 2 q^{65} - 15 q^{66} - 12 q^{67} - 3 q^{68} + 6 q^{70} + q^{71} + 3 q^{72} - 3 q^{73} - 10 q^{74} + 12 q^{75} + q^{76} + 15 q^{77} - 6 q^{78} + 4 q^{79} + q^{80} - 9 q^{81} - 7 q^{82} - 9 q^{83} - 9 q^{84} + 3 q^{85} + 8 q^{86} + 15 q^{87} - 5 q^{88} - 15 q^{89} + 6 q^{90} + 6 q^{91} - 8 q^{92} + 21 q^{93} + q^{94} + 8 q^{95} + 2 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 3 * q^7 + 2 * q^8 + 3 * q^9 + q^10 - 5 * q^11 - 2 * q^13 - 6 * q^14 + 3 * q^15 - q^16 - 3 * q^17 - 6 * q^18 - 8 * q^19 + q^20 + 10 * q^22 - 8 * q^23 - 3 * q^24 - 8 * q^25 + 4 * q^26 + 3 * q^28 - 10 * q^29 - 3 * q^30 - 7 * q^31 - q^32 + 6 * q^34 - 3 * q^35 + 3 * q^36 + 20 * q^37 + 7 * q^38 - 2 * q^40 + 14 * q^41 + 9 * q^42 + 8 * q^43 - 5 * q^44 - 3 * q^45 + 16 * q^46 - 2 * q^47 + 3 * q^48 - 2 * q^49 + 4 * q^50 - 2 * q^52 - 11 * q^53 + 9 * q^54 + 5 * q^55 + 3 * q^56 + 9 * q^57 + 5 * q^58 - 6 * q^59 - 2 * q^61 - 7 * q^62 - 9 * q^63 + 2 * q^64 + 2 * q^65 - 15 * q^66 - 12 * q^67 - 3 * q^68 + 6 * q^70 + q^71 + 3 * q^72 - 3 * q^73 - 10 * q^74 + 12 * q^75 + q^76 + 15 * q^77 - 6 * q^78 + 4 * q^79 + q^80 - 9 * q^81 - 7 * q^82 - 9 * q^83 - 9 * q^84 + 3 * q^85 + 8 * q^86 + 15 * q^87 - 5 * q^88 - 15 * q^89 + 6 * q^90 + 6 * q^91 - 8 * q^92 + 21 * q^93 + q^94 + 8 * q^95 + 2 * q^97 - 2 * q^98 + 15 * q^99

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