LMFDB - Embedded newform 483.2.i.d.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
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			415.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.d.277.1

$q$-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} +(1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} -3.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +3.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +2.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(2.50000 + 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{33} -1.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} -1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{39} +(4.50000 - 7.79423i) q^{40} +4.00000 q^{41} +(0.500000 + 2.59808i) q^{42} +4.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(1.50000 + 2.59808i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-3.50000 + 6.06218i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-0.500000 + 0.866025i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +6.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +(2.00000 + 3.46410i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} -10.0000 q^{62} +(2.50000 + 0.866025i) q^{63} +7.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(1.50000 + 2.59808i) q^{67} +(0.500000 - 0.866025i) q^{68} +1.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} -15.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(6.50000 + 11.2583i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(4.00000 - 3.46410i) q^{77} +1.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.00000 - 3.46410i) q^{82} +6.00000 q^{83} +(-2.50000 - 0.866025i) q^{84} -3.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{88} +(3.00000 - 5.19615i) q^{89} +3.00000 q^{90} +(0.500000 + 2.59808i) q^{91} -1.00000 q^{92} +(-5.00000 + 8.66025i) q^{93} +(3.50000 + 6.06218i) q^{94} +(2.50000 - 4.33013i) q^{96} +16.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} + q^{4} + 3 q^{5} - 2 q^{6} - q^{7} + 6 q^{8} - q^{9} - 3 q^{10} + 2 q^{11} + q^{12} - 2 q^{13} - 5 q^{14} - 6 q^{15} + q^{16} - q^{17} + q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{22}+ \cdots - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 + q^4 + 3 * q^5 - 2 * q^6 - q^7 + 6 * q^8 - q^9 - 3 * q^10 + 2 * q^11 + q^12 - 2 * q^13 - 5 * q^14 - 6 * q^15 + q^16 - q^17 + q^18 + 6 * q^20 - 4 * q^21 + 4 * q^22 - q^23 - 3 * q^24 - 4 * q^25 - q^26 + 2 * q^27 + 4 * q^28 - 3 * q^30 - 10 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 - 15 * q^35 - 2 * q^36 + 2 * q^37 + q^39 + 9 * q^40 + 8 * q^41 + q^42 + 8 * q^43 - 2 * q^44 + 3 * q^45 + q^46 - 7 * q^47 - 2 * q^48 - 13 * q^49 - 8 * q^50 - q^51 - q^52 + 9 * q^53 + q^54 + 12 * q^55 - 3 * q^56 + 4 * q^59 - 3 * q^60 + 2 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 - 3 * q^65 - 2 * q^66 + 3 * q^67 + q^68 + 2 * q^69 - 12 * q^70 - 30 * q^71 - 3 * q^72 + 13 * q^73 - 2 * q^74 - 4 * q^75 + 8 * q^77 + 2 * q^78 - 4 * q^79 - 3 * q^80 - q^81 + 4 * q^82 + 12 * q^83 - 5 * q^84 - 6 * q^85 + 4 * q^86 + 6 * q^88 + 6 * q^89 + 6 * q^90 + q^91 - 2 * q^92 - 10 * q^93 + 7 * q^94 + 5 * q^96 + 32 * q^97 - 2 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$	−1.00000			−0.408248
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	3.00000			1.06066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$	−3.00000			−0.774597
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	3.00000			0.670820
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	2.00000			0.426401
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$	−1.00000			−0.171499
$35$	−7.50000	−	2.59808i	−1.26773	−	0.439155i
$36$	−1.00000			−0.166667
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	4.50000	−	7.79423i	0.711512	−	1.23238i
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$	0.500000	+	2.59808i	0.0771517	+	0.400892i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	0.489398	+	0.872060i	$0.337217\pi$
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	−0.999926	+	0.0121990i	$0.996117\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−4.00000			−0.565685
$51$	−0.500000	+	0.866025i	−0.0700140	+	0.121268i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	6.00000			0.809040
$56$	−1.50000	−	7.79423i	−0.200446	−	1.04155i
$57$		0			0
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−1.50000	−	2.59808i	−0.193649	−	0.335410i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	−10.0000			−1.27000
$63$	2.50000	+	0.866025i	0.314970	+	0.109109i
$64$	7.00000			0.875000
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	0.500000	−	0.866025i	0.0606339	−	0.105021i
$69$	1.00000			0.120386
$70$	−6.00000	+	5.19615i	−0.717137	+	0.621059i
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$		0			0
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$	1.00000			0.113228
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.00000	−	3.46410i	0.220863	−	0.382546i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−2.50000	−	0.866025i	−0.272772	−	0.0944911i
$85$	−3.00000			−0.325396
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		0			0
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	3.00000			0.316228
$91$	0.500000	+	2.59808i	0.0524142	+	0.272352i
$92$	−1.00000			−0.104257
$93$	−5.00000	+	8.66025i	−0.518476	+	0.898027i
$94$	3.50000	+	6.06218i	0.360997	+	0.625266i
$95$		0			0
$96$	2.50000	−	4.33013i	0.255155	−	0.441942i
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$	−2.00000			−0.201008
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$	0.500000	+	0.866025i	0.0495074	+	0.0857493i
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	0.456862	+	0.889538i	$0.348973\pi$
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	−0.998793	+	0.0491146i	$0.984360\pi$
$104$	−3.00000			−0.294174
$105$	1.50000	+	7.79423i	0.146385	+	0.760639i
$106$	9.00000			0.874157
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	−0.946357	−	0.323122i	$-0.895268\pi$
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	0.753010	+	0.658009i	$0.228601\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−4.00000	−	6.92820i	−0.383131	−	0.663602i	0.608377	−	0.793648i	$-0.291821\pi$
$109$	−4.00000	−	6.92820i	−0.383131	−	0.663602i	−0.991508	+	0.130046i	$0.958487\pi$
$110$	3.00000	−	5.19615i	0.286039	−	0.495434i
$111$	−2.00000			−0.189832
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	7.00000			0.658505			0.329252	−	0.944242i	$-0.393203\pi$
$113$	7.00000			0.658505			0.329252	+	0.944242i	$0.393203\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	4.00000			0.368230
$119$	−2.00000	+	1.73205i	−0.183340	+	0.158777i
$120$	−9.00000			−0.821584
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$	−2.00000	−	3.46410i	−0.180334	−	0.312348i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	3.00000			0.268328
$126$	2.00000	−	1.73205i	0.178174	−	0.154303i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	1.50000	+	2.59808i	0.131559	+	0.227866i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	3.00000			0.259161
$135$	1.50000	−	2.59808i	0.129099	−	0.223607i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	0.958477	+	0.285171i	$0.0920506\pi$
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	−0.232273	+	0.972651i	$0.574616\pi$
$138$	0.500000	−	0.866025i	0.0425628	−	0.0737210i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	−1.50000	−	7.79423i	−0.126773	−	0.658733i
$141$	7.00000			0.589506
$142$	−7.50000	+	12.9904i	−0.629386	+	1.09013i
$143$	−1.00000	−	1.73205i	−0.0836242	−	0.144841i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	13.0000			1.07589
$147$	5.50000	+	4.33013i	0.453632	+	0.357143i
$148$	2.00000			0.164399
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	−0.950072	−	0.312032i	$-0.898990\pi$
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	0.745264	+	0.666770i	$0.232324\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$	1.00000			0.0808452
$154$	−1.00000	−	5.19615i	−0.0805823	−	0.418718i
$155$	−30.0000			−2.40966
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$	4.50000	−	7.79423i	0.356873	−	0.618123i
$160$	15.0000			1.18585
$161$	2.50000	+	0.866025i	0.197028	+	0.0682524i
$162$	−1.00000			−0.0785674
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	2.00000	+	3.46410i	0.156174	+	0.270501i
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−19.0000			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$168$	−6.00000	+	5.19615i	−0.462910	+	0.400892i
$169$	−12.0000			−0.923077
$170$	−1.50000	+	2.59808i	−0.115045	+	0.199263i
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	8.00000	−	13.8564i	0.608229	−	1.05348i	−0.383304	−	0.923622i	$-0.625214\pi$
$173$	8.00000	−	13.8564i	0.608229	−	1.05348i	0.991532	−	0.129861i	$-0.0414530\pi$
$174$		0			0
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	2.00000			0.150756
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	0.995009	−	0.0997838i	$-0.0318151\pi$
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	−0.583920	+	0.811811i	$0.698482\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	−26.0000			−1.93256			−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000			−1.93256			−0.966282	+	0.257485i	$0.917106\pi$
$182$	2.50000	+	0.866025i	0.185312	+	0.0641941i
$183$	−2.00000			−0.147844
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$	5.00000	+	8.66025i	0.366618	+	0.635001i
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	−7.00000			−0.510527
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−3.50000	−	6.06218i	−0.252591	−	0.437500i
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$	8.00000	−	13.8564i	0.574367	−	0.994832i
$195$	3.00000			0.214834
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−1.00000	+	1.73205i	−0.0710669	+	0.123091i
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$	−6.00000	−	10.3923i	−0.424264	−	0.734847i
$201$	1.50000	−	2.59808i	0.105802	−	0.183254i
$202$	18.0000			1.26648
$203$		0			0
$204$	−1.00000			−0.0700140
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$	5.50000	+	9.52628i	0.383203	+	0.663727i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$		0			0
$210$	7.50000	+	2.59808i	0.517549	+	0.179284i
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$	7.50000	+	12.9904i	0.513892	+	0.890086i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$	3.00000			0.204124
$217$	−20.0000	+	17.3205i	−1.35769	+	1.17579i
$218$	−8.00000			−0.541828
$219$	6.50000	−	11.2583i	0.439229	−	0.760767i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	0.500000	+	0.866025i	0.0336336	+	0.0582552i
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	10.0000	−	8.66025i	0.668153	−	0.578638i
$225$	4.00000			0.266667
$226$	3.50000	−	6.06218i	0.232817	−	0.403250i
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	0.999184	−	0.0403978i	$-0.0128625\pi$
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	−0.534577	+	0.845120i	$0.679529\pi$
$228$		0			0
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.133820	+	0.991006i	$0.542724\pi$
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.791326	+	0.611394i	$0.790609\pi$
$230$	3.00000			0.197814
$231$	−5.00000	−	1.73205i	−0.328976	−	0.113961i
$232$		0			0
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	−0.142166	−	0.989843i	$-0.545407\pi$
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	0.928312	−	0.371802i	$-0.121260\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	10.5000	+	18.1865i	0.684944	+	1.18636i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$	4.00000			0.259828
$238$	0.500000	+	2.59808i	0.0324102	+	0.168408i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	−1.50000	+	2.59808i	−0.0968246	+	0.167705i
$241$	−3.00000	−	5.19615i	−0.193247	−	0.334714i	0.753077	−	0.657932i	$-0.228569\pi$
$241$	−3.00000	−	5.19615i	−0.193247	−	0.334714i	−0.946324	+	0.323218i	$0.895235\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.00000			0.128037
$245$	−3.00000	+	20.7846i	−0.191663	+	1.32788i
$246$	−4.00000			−0.255031
$247$		0			0
$248$	−15.0000	−	25.9808i	−0.952501	−	1.64978i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	10.0000			0.631194			0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000			0.631194			0.315597	+	0.948893i	$0.397795\pi$
$252$	0.500000	+	2.59808i	0.0314970	+	0.163663i
$253$	−2.00000			−0.125739
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$	1.50000	+	2.59808i	0.0939336	+	0.162698i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−4.00000			−0.249029
$259$	−5.00000	−	1.73205i	−0.310685	−	0.107624i
$260$	−3.00000			−0.186052
$261$		0			0
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	27.0000			1.65860
$266$		0			0
$267$	−6.00000			−0.367194
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−2.00000	−	3.46410i	−0.121942	−	0.211210i	0.798591	−	0.601874i	$-0.205579\pi$
$269$	−2.00000	−	3.46410i	−0.121942	−	0.211210i	−0.920534	+	0.390664i	$0.872246\pi$
$270$	−1.50000	−	2.59808i	−0.0912871	−	0.158114i
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	−0.996441	−	0.0842940i	$-0.973137\pi$
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	0.571221	+	0.820796i	$0.306470\pi$
$272$	−1.00000			−0.0606339
$273$	2.00000	−	1.73205i	0.121046	−	0.104828i
$274$	17.0000			1.02701
$275$	4.00000	−	6.92820i	0.241209	−	0.417786i
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$	−5.00000	+	8.66025i	−0.299880	+	0.519408i
$279$	10.0000			0.598684
$280$	−22.5000	−	7.79423i	−1.34463	−	0.465794i
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$	3.50000	−	6.06218i	0.208422	−	0.360997i
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.797283	−	0.603606i	$-0.793730\pi$
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.124096	−	0.992270i	$-0.539603\pi$
$284$	−7.50000	−	12.9904i	−0.445043	−	0.770837i
$285$		0			0
$286$	−2.00000			−0.118262
$287$	−2.00000	−	10.3923i	−0.118056	−	0.613438i
$288$	−5.00000			−0.294628
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$	−8.00000	−	13.8564i	−0.468968	−	0.812277i
$292$	−6.50000	+	11.2583i	−0.380384	+	0.658844i
$293$	−13.0000			−0.759468			−0.379734	−	0.925096i	$-0.623985\pi$
$293$	−13.0000			−0.759468			−0.379734	+	0.925096i	$0.623985\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$	12.0000			0.698667
$296$	3.00000	−	5.19615i	0.174371	−	0.302020i
$297$	1.00000	+	1.73205i	0.0580259	+	0.100504i
$298$	2.50000	+	4.33013i	0.144821	+	0.250838i
$299$	0.500000	−	0.866025i	0.0289157	−	0.0500835i
$300$	−4.00000			−0.230940
$301$	−2.00000	−	10.3923i	−0.115278	−	0.599002i
$302$	−4.00000			−0.230174
$303$	9.00000	−	15.5885i	0.517036	−	0.895533i
$304$		0			0
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	0.500000	−	0.866025i	0.0285831	−	0.0495074i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$	5.00000	+	1.73205i	0.284901	+	0.0986928i
$309$	11.0000			0.625768
$310$	−15.0000	+	25.9808i	−0.851943	+	1.47561i
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$	1.50000	+	2.59808i	0.0849208	+	0.147087i
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	−10.0000			−0.564333
$315$	6.00000	−	5.19615i	0.338062	−	0.292770i
$316$	−4.00000			−0.225018
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	−0.971589	−	0.236675i	$-0.923942\pi$
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	0.690761	+	0.723083i	$0.257276\pi$
$318$	−4.50000	−	7.79423i	−0.252347	−	0.437079i
$319$		0			0
$320$	10.5000	−	18.1865i	0.586968	−	1.01666i
$321$	4.00000			0.223258
$322$	2.00000	−	1.73205i	0.111456	−	0.0965234i
$323$		0			0
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$	−4.00000	+	6.92820i	−0.221201	+	0.383131i
$328$	12.0000			0.662589
$329$	17.5000	+	6.06218i	0.964806	+	0.334219i
$330$	−6.00000			−0.330289
$331$	17.0000	−	29.4449i	0.934405	−	1.61844i	0.158712	−	0.987325i	$-0.449266\pi$
$331$	17.0000	−	29.4449i	0.934405	−	1.61844i	0.775692	−	0.631111i	$-0.217401\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	1.00000	+	1.73205i	0.0547997	+	0.0949158i
$334$	−9.50000	+	16.4545i	−0.519817	+	0.900349i
$335$	9.00000			0.491723
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	−3.50000	−	6.06218i	−0.190094	−	0.329252i
$340$	−1.50000	−	2.59808i	−0.0813489	−	0.140900i
$341$	10.0000	−	17.3205i	0.541530	−	0.937958i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	12.0000			0.646997
$345$	1.50000	−	2.59808i	0.0807573	−	0.139876i
$346$	−8.00000	−	13.8564i	−0.430083	−	0.744925i
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	0.822951	−	0.568112i	$-0.192326\pi$
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	−0.903475	+	0.428640i	$0.858993\pi$
$348$		0			0
$349$	−5.00000			−0.267644			−0.133822	−	0.991005i	$-0.542725\pi$
$349$	−5.00000			−0.267644			−0.133822	+	0.991005i	$0.542725\pi$
$350$	2.00000	+	10.3923i	0.106904	+	0.555492i
$351$	−1.00000			−0.0533761
$352$	−5.00000	+	8.66025i	−0.266501	+	0.461593i
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	0.914329	−	0.404971i	$-0.132718\pi$
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	−0.807880	+	0.589347i	$0.799385\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	−22.5000	+	38.9711i	−1.19418	+	2.06837i
$356$	6.00000			0.317999
$357$	2.50000	+	0.866025i	0.132314	+	0.0458349i
$358$	11.0000			0.581368
$359$	−11.0000	+	19.0526i	−0.580558	+	1.00556i	0.414855	+	0.909887i	$0.363832\pi$
$359$	−11.0000	+	19.0526i	−0.580558	+	1.00556i	−0.995413	+	0.0956683i	$0.969501\pi$
$360$	4.50000	+	7.79423i	0.237171	+	0.410792i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−13.0000	+	22.5167i	−0.683265	+	1.18345i
$363$	−7.00000			−0.367405
$364$	−2.00000	+	1.73205i	−0.104828	+	0.0907841i
$365$	39.0000			2.04135
$366$	−1.00000	+	1.73205i	−0.0522708	+	0.0905357i
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−2.00000	+	3.46410i	−0.104116	+	0.180334i
$370$	−6.00000			−0.311925
$371$	18.0000	−	15.5885i	0.934513	−	0.809312i
$372$	−10.0000			−0.518476
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$	−10.5000	+	18.1865i	−0.541496	+	0.937899i
$377$		0			0
$378$	−2.50000	−	0.866025i	−0.128586	−	0.0445435i
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$		0			0
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$		0			0
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	3.00000			0.153093
$385$	−3.00000	−	15.5885i	−0.152894	−	0.794461i
$386$	11.0000			0.559885
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$	8.00000	+	13.8564i	0.406138	+	0.703452i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$	1.50000	−	2.59808i	0.0759555	−	0.131559i
$391$	1.00000			0.0505722
$392$	−19.5000	+	7.79423i	−0.984899	+	0.393668i
$393$	−3.00000			−0.151330
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	6.00000	+	10.3923i	0.301893	+	0.522894i
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−10.5000	+	18.1865i	−0.526980	+	0.912756i	0.472526	+	0.881317i	$0.343342\pi$
$397$	−10.5000	+	18.1865i	−0.526980	+	0.912756i	−0.999506	+	0.0314391i	$0.989991\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	−4.00000			−0.200000
$401$	5.50000	−	9.52628i	0.274657	−	0.475720i	−0.695392	−	0.718631i	$-0.744769\pi$
$401$	5.50000	−	9.52628i	0.274657	−	0.475720i	0.970049	+	0.242911i	$0.0781024\pi$
$402$	−1.50000	−	2.59808i	−0.0748132	−	0.129580i
$403$	5.00000	+	8.66025i	0.249068	+	0.431398i
$404$	−9.00000	+	15.5885i	−0.447767	+	0.775555i
$405$	−3.00000			−0.149071
$406$		0			0
$407$	4.00000			0.198273
$408$	−1.50000	+	2.59808i	−0.0742611	+	0.128624i
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	0.173064	−	0.984911i	$-0.444633\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	8.50000	−	14.7224i	0.419274	−	0.726204i
$412$	−11.0000			−0.541931
$413$	8.00000	−	6.92820i	0.393654	−	0.340915i
$414$	−1.00000			−0.0491473
$415$	9.00000	−	15.5885i	0.441793	−	0.765207i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$	5.00000	+	8.66025i	0.244851	+	0.424094i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$	−6.00000	+	5.19615i	−0.292770	+	0.253546i
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	−11.0000	+	19.0526i	−0.535472	+	0.927464i
$423$	−3.50000	−	6.06218i	−0.170176	−	0.294753i
$424$	13.5000	+	23.3827i	0.655618	+	1.13556i
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	15.0000			0.726752
$427$	−5.00000	−	1.73205i	−0.241967	−	0.0838198i
$428$	−4.00000			−0.193347
$429$	−1.00000	+	1.73205i	−0.0482805	+	0.0836242i
$430$	−6.00000	−	10.3923i	−0.289346	−	0.501161i
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$	5.00000	+	25.9808i	0.240008	+	1.24712i
$435$		0			0
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$		0			0
$438$	−6.50000	−	11.2583i	−0.310582	−	0.537944i
$439$	−11.0000	+	19.0526i	−0.525001	+	0.909329i	0.474575	+	0.880215i	$0.342602\pi$
$439$	−11.0000	+	19.0526i	−0.525001	+	0.909329i	−0.999576	+	0.0291138i	$0.990731\pi$
$440$	18.0000			0.858116
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	1.00000			0.0475651
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$	5.00000			0.236492
$448$	−3.50000	−	18.1865i	−0.165359	−	0.859233i
$449$	14.0000			0.660701			0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000			0.660701			0.330350	+	0.943858i	$0.392833\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	3.50000	+	6.06218i	0.164626	+	0.285141i
$453$	−2.00000	+	3.46410i	−0.0939682	+	0.162758i
$454$	14.0000			0.657053
$455$	7.50000	+	2.59808i	0.351605	+	0.121800i
$456$		0			0
$457$	−8.00000	+	13.8564i	−0.374224	+	0.648175i	−0.990211	−	0.139581i	$-0.955424\pi$
$457$	−8.00000	+	13.8564i	−0.374224	+	0.648175i	0.615986	+	0.787757i	$0.288758\pi$
$458$	14.0000	+	24.2487i	0.654177	+	1.13307i
$459$	−0.500000	−	0.866025i	−0.0233380	−	0.0404226i
$460$	−1.50000	+	2.59808i	−0.0699379	+	0.121136i
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$	−4.00000	+	3.46410i	−0.186097	+	0.161165i
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$	15.0000	+	25.9808i	0.695608	+	1.20483i
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	−0.335794	−	0.941935i	$-0.609005\pi$
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	0.983637	−	0.180161i	$-0.0576619\pi$
$468$	1.00000			0.0462250
$469$	6.00000	−	5.19615i	0.277054	−	0.239936i
$470$	21.0000			0.968658
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$		0			0
$476$	−2.50000	−	0.866025i	−0.114587	−	0.0396942i
$477$	−9.00000			−0.412082
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$	−7.50000	−	12.9904i	−0.342327	−	0.592927i
$481$	−1.00000	+	1.73205i	−0.0455961	+	0.0789747i
$482$	−6.00000			−0.273293
$483$	−0.500000	−	2.59808i	−0.0227508	−	0.118217i
$484$	7.00000			0.318182
$485$	24.0000	−	41.5692i	1.08978	−	1.88756i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$	−20.0000			−0.904431
$490$	16.5000	+	12.9904i	0.745394	+	0.586846i
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$	2.00000	−	3.46410i	0.0901670	−	0.156174i
$493$		0			0
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$	−10.0000			−0.449013
$497$	7.50000	+	38.9711i	0.336421	+	1.74809i
$498$	−6.00000			−0.268866
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	0.109965	+	0.993935i	$0.464926\pi$
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	−0.915756	+	0.401735i	$0.868407\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	9.50000	+	16.4545i	0.424429	+	0.735132i
$502$	5.00000	−	8.66025i	0.223161	−	0.386526i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	7.50000	+	2.59808i	0.334077	+	0.115728i
$505$	54.0000			2.40297
$506$	−1.00000	+	1.73205i	−0.0444554	+	0.0769991i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	1.00000	+	1.73205i	0.0443678	+	0.0768473i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$	3.00000			0.132842
$511$	26.0000	−	22.5167i	1.15017	−	0.996078i
$512$	11.0000			0.486136
$513$		0			0
$514$	−9.00000	−	15.5885i	−0.396973	−	0.687577i
$515$	16.5000	+	28.5788i	0.727077	+	1.25933i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−14.0000			−0.615719
$518$	−4.00000	+	3.46410i	−0.175750	+	0.152204i
$519$	−16.0000			−0.702322
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	14.5000	+	25.1147i	0.635257	+	1.10030i	0.986461	+	0.163998i	$0.0524390\pi$
$521$	14.5000	+	25.1147i	0.635257	+	1.10030i	−0.351204	+	0.936299i	$0.614228\pi$
$522$		0			0
$523$	−8.50000	+	14.7224i	−0.371679	+	0.643767i	−0.989824	−	0.142297i	$-0.954551\pi$
$523$	−8.50000	+	14.7224i	−0.371679	+	0.643767i	0.618145	+	0.786064i	$0.287884\pi$
$524$	3.00000			0.131056
$525$	10.0000	+	3.46410i	0.436436	+	0.151186i
$526$	16.0000			0.697633
$527$	−5.00000	+	8.66025i	−0.217803	+	0.377247i
$528$	−1.00000	−	1.73205i	−0.0435194	−	0.0753778i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	13.5000	−	23.3827i	0.586403	−	1.01568i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−4.00000			−0.173259
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	4.50000	+	7.79423i	0.194370	+	0.336659i
$537$	5.50000	−	9.52628i	0.237343	−	0.411089i
$538$	−4.00000			−0.172452
$539$	−11.0000	−	8.66025i	−0.473804	−	0.373024i
$540$	3.00000			0.129099
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	7.00000	+	12.1244i	0.300676	+	0.520786i
$543$	13.0000	+	22.5167i	0.557883	+	0.966282i
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	−24.0000			−1.02805
$546$	−0.500000	−	2.59808i	−0.0213980	−	0.111187i
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	−8.50000	+	14.7224i	−0.363102	+	0.628911i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$		0			0
$552$	3.00000			0.127688
$553$	10.0000	+	3.46410i	0.425243	+	0.147309i
$554$	−13.0000			−0.552317
$555$	−3.00000	+	5.19615i	−0.127343	+	0.220564i
$556$	−5.00000	−	8.66025i	−0.212047	−	0.367277i
$557$	7.00000	+	12.1244i	0.296600	+	0.513725i	0.975356	−	0.220638i	$-0.0708140\pi$
$557$	7.00000	+	12.1244i	0.296600	+	0.513725i	−0.678756	+	0.734364i	$0.737481\pi$
$558$	5.00000	−	8.66025i	0.211667	−	0.366618i
$559$	−4.00000			−0.169182
$560$	−6.00000	+	5.19615i	−0.253546	+	0.219578i
$561$	−2.00000			−0.0844401
$562$	13.5000	−	23.3827i	0.569463	−	0.986339i
$563$	−20.0000	−	34.6410i	−0.842900	−	1.45994i	−0.887433	−	0.460937i	$-0.847513\pi$
$563$	−20.0000	−	34.6410i	−0.842900	−	1.45994i	0.0445334	−	0.999008i	$-0.485820\pi$
$564$	3.50000	+	6.06218i	0.147377	+	0.255264i
$565$	10.5000	−	18.1865i	0.441738	−	0.765113i
$566$	−31.0000			−1.30303
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−45.0000			−1.88816
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	0.279559	+	0.960128i	$0.409812\pi$
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	−0.971275	+	0.237959i	$0.923522\pi$
$570$		0			0
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	0.783450	−	0.621455i	$-0.213458\pi$
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	−0.929921	+	0.367760i	$0.880125\pi$
$572$	1.00000	−	1.73205i	0.0418121	−	0.0724207i
$573$		0			0
$574$	−10.0000	−	3.46410i	−0.417392	−	0.144589i
$575$	4.00000			0.166812
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	−8.00000	−	13.8564i	−0.332756	−	0.576351i
$579$	5.50000	−	9.52628i	0.228572	−	0.395899i
$580$		0			0
$581$	−3.00000	−	15.5885i	−0.124461	−	0.646718i
$582$	−16.0000			−0.663221
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$	19.5000	+	33.7750i	0.806916	+	1.39762i
$585$	−1.50000	−	2.59808i	−0.0620174	−	0.107417i
$586$	−6.50000	+	11.2583i	−0.268513	+	0.465077i
$587$	−37.0000			−1.52715			−0.763577	−	0.645717i	$-0.776559\pi$
$587$	−37.0000			−1.52715			−0.763577	+	0.645717i	$0.776559\pi$
$588$	−1.00000	+	6.92820i	−0.0412393	+	0.285714i
$589$		0			0
$590$	6.00000	−	10.3923i	0.247016	−	0.427844i
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−13.0000	+	22.5167i	−0.533846	+	0.924648i	0.465372	+	0.885115i	$0.345920\pi$
$593$	−13.0000	+	22.5167i	−0.533846	+	0.924648i	−0.999218	+	0.0395334i	$0.987413\pi$
$594$	2.00000			0.0820610
$595$	1.50000	+	7.79423i	0.0614940	+	0.319532i
$596$	−5.00000			−0.204808
$597$	−8.00000	+	13.8564i	−0.327418	+	0.567105i
$598$	−0.500000	−	0.866025i	−0.0204465	−	0.0354144i
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	−0.921723	−	0.387849i	$-0.873218\pi$
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	0.124975	−	0.992160i	$-0.460115\pi$
$600$	−6.00000	+	10.3923i	−0.244949	+	0.424264i
$601$	18.0000			0.734235			0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000			0.734235			0.367118	+	0.930175i	$0.380345\pi$
$602$	−10.0000	−	3.46410i	−0.407570	−	0.141186i
$603$	−3.00000			−0.122169
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	−10.5000	−	18.1865i	−0.426886	−	0.739388i
$606$	−9.00000	−	15.5885i	−0.365600	−	0.633238i
$607$	−3.00000	+	5.19615i	−0.121766	+	0.210905i	−0.920464	−	0.390827i	$-0.872189\pi$
$607$	−3.00000	+	5.19615i	−0.121766	+	0.210905i	0.798698	+	0.601732i	$0.205522\pi$
$608$		0			0
$609$		0			0
$610$	−6.00000			−0.242933
$611$	3.50000	−	6.06218i	0.141595	−	0.245249i
$612$	0.500000	+	0.866025i	0.0202113	+	0.0350070i
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$	−12.0000			−0.483887
$616$	12.0000	−	10.3923i	0.483494	−	0.418718i
$617$	−29.0000			−1.16750			−0.583748	−	0.811935i	$-0.698414\pi$
$617$	−29.0000			−1.16750			−0.583748	+	0.811935i	$0.698414\pi$
$618$	5.50000	−	9.52628i	0.221242	−	0.383203i
$619$	13.5000	+	23.3827i	0.542611	+	0.939829i	0.998753	+	0.0499226i	$0.0158975\pi$
$619$	13.5000	+	23.3827i	0.542611	+	0.939829i	−0.456142	+	0.889907i	$0.650769\pi$
$620$	−15.0000	−	25.9808i	−0.602414	−	1.04341i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	−21.0000			−0.842023
$623$	−15.0000	−	5.19615i	−0.600962	−	0.208179i
$624$	1.00000			0.0400320
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$		0			0
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	−2.00000			−0.0797452
$630$	−1.50000	−	7.79423i	−0.0597614	−	0.310530i
$631$	−5.00000			−0.199047			−0.0995234	−	0.995035i	$-0.531732\pi$
$631$	−5.00000			−0.199047			−0.0995234	+	0.995035i	$0.531732\pi$
$632$	−6.00000	+	10.3923i	−0.238667	+	0.413384i
$633$	11.0000	+	19.0526i	0.437211	+	0.757271i
$634$	5.00000	+	8.66025i	0.198575	+	0.343943i
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$	9.00000			0.356873
$637$	6.50000	−	2.59808i	0.257539	−	0.102940i
$638$		0			0
$639$	7.50000	−	12.9904i	0.296695	−	0.513892i
$640$	4.50000	+	7.79423i	0.177878	+	0.308094i
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$	2.00000	−	3.46410i	0.0789337	−	0.136717i
$643$	12.0000			0.473234			0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$644$	0.500000	+	2.59808i	0.0197028	+	0.102379i
$645$	−12.0000			−0.472500
$646$		0			0
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	0.776622	−	0.629967i	$-0.216932\pi$
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	−0.933878	+	0.357591i	$0.883598\pi$
$648$	−1.50000	−	2.59808i	−0.0589256	−	0.102062i
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	4.00000			0.156893
$651$	25.0000	+	8.66025i	0.979827	+	0.339422i
$652$	20.0000			0.783260
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$	4.00000	+	6.92820i	0.156412	+	0.270914i
$655$	−4.50000	−	7.79423i	−0.175830	−	0.304546i
$656$	2.00000	−	3.46410i	0.0780869	−	0.135250i
$657$	−13.0000			−0.507178
$658$	14.0000	−	12.1244i	0.545777	−	0.472657i
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	0.933271	−	0.359174i	$-0.116941\pi$
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	−0.777689	+	0.628649i	$0.783608\pi$
$662$	−17.0000	−	29.4449i	−0.660724	−	1.14441i
$663$	0.500000	−	0.866025i	0.0194184	−	0.0336336i
$664$	18.0000			0.698535
$665$		0			0
$666$	2.00000			0.0774984
$667$		0			0
$668$	−9.50000	−	16.4545i	−0.367566	−	0.636643i
$669$	−2.00000	−	3.46410i	−0.0773245	−	0.133930i
$670$	4.50000	−	7.79423i	0.173850	−	0.301117i
$671$	4.00000			0.154418
$672$	−12.5000	−	4.33013i	−0.482198	−	0.167038i
$673$	50.0000			1.92736			0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000			1.92736			0.963679	+	0.267063i	$0.0860531\pi$
$674$	−6.00000	+	10.3923i	−0.231111	+	0.400297i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	5.50000	−	9.52628i	0.211382	−	0.366125i	−0.740765	−	0.671764i	$-0.765537\pi$
$677$	5.50000	−	9.52628i	0.211382	−	0.366125i	0.952147	+	0.305639i	$0.0988702\pi$
$678$	−7.00000			−0.268833
$679$	−8.00000	−	41.5692i	−0.307012	−	1.59528i
$680$	−9.00000			−0.345134
$681$	7.00000	−	12.1244i	0.268241	−	0.464606i
$682$	−10.0000	−	17.3205i	−0.382920	−	0.663237i
$683$	−20.5000	−	35.5070i	−0.784411	−	1.35864i	−0.929350	−	0.369199i	$-0.879632\pi$
$683$	−20.5000	−	35.5070i	−0.784411	−	1.35864i	0.144940	−	0.989440i	$-0.453701\pi$
$684$		0			0
$685$	51.0000			1.94861
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$	28.0000			1.06827
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$	−1.50000	−	2.59808i	−0.0571040	−	0.0989071i
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	−0.577325	−	0.816514i	$-0.695903\pi$
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	0.995785	+	0.0917209i	$0.0292368\pi$
$692$	16.0000			0.608229
$693$	1.00000	+	5.19615i	0.0379869	+	0.197386i
$694$	−3.00000			−0.113878
$695$	−15.0000	+	25.9808i	−0.568982	+	0.985506i
$696$		0			0
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$	−2.50000	+	4.33013i	−0.0946264	+	0.163898i
$699$	−24.0000			−0.907763
$700$	−10.0000	−	3.46410i	−0.377964	−	0.130931i
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$	−0.500000	+	0.866025i	−0.0188713	+	0.0326860i
$703$		0			0
$704$	7.00000	+	12.1244i	0.263822	+	0.456954i
$705$	10.5000	−	18.1865i	0.395453	−	0.684944i
$706$	4.00000			0.150542
$707$	36.0000	−	31.1769i	1.35392	−	1.17253i
$708$	4.00000			0.150329
$709$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$709$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$710$	22.5000	+	38.9711i	0.844410	+	1.46256i
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$	10.0000			0.374503
$714$	2.00000	−	1.73205i	0.0748481	−	0.0648204i
$715$	−6.00000			−0.224387
$716$	−5.50000	+	9.52628i	−0.205545	+	0.356014i
$717$	8.00000	+	13.8564i	0.298765	+	0.517477i
$718$	11.0000	+	19.0526i	0.410516	+	0.711035i
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$	3.00000			0.111803
$721$	27.5000	+	9.52628i	1.02415	+	0.354777i
$722$	19.0000			0.707107
$723$	−3.00000	+	5.19615i	−0.111571	+	0.193247i
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$		0			0
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$	1.50000	+	7.79423i	0.0555937	+	0.288873i
$729$	1.00000			0.0370370
$730$	19.5000	−	33.7750i	0.721727	−	1.25007i
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$	−1.00000	−	1.73205i	−0.0369611	−	0.0640184i
$733$	12.0000	−	20.7846i	0.443230	−	0.767697i	−0.554697	−	0.832052i	$-0.687166\pi$
$733$	12.0000	−	20.7846i	0.443230	−	0.767697i	0.997927	+	0.0643554i	$0.0204991\pi$
$734$	19.0000			0.701303
$735$	19.5000	−	7.79423i	0.719268	−	0.287494i
$736$	−5.00000			−0.184302
$737$	−3.00000	+	5.19615i	−0.110506	+	0.191403i
$738$	2.00000	+	3.46410i	0.0736210	+	0.127515i
$739$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$739$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$740$	3.00000	−	5.19615i	0.110282	−	0.191014i
$741$		0			0
$742$	−4.50000	−	23.3827i	−0.165200	−	0.858405i
$743$	−18.0000			−0.660356			−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000			−0.660356			−0.330178	+	0.943919i	$0.607109\pi$
$744$	−15.0000	+	25.9808i	−0.549927	+	0.952501i
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	2.00000			0.0731272
$749$	10.0000	+	3.46410i	0.365392	+	0.126576i
$750$	−3.00000			−0.109545
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	3.50000	+	6.06218i	0.127632	+	0.221065i
$753$	−5.00000	−	8.66025i	−0.182210	−	0.315597i
$754$		0			0
$755$	−12.0000			−0.436725
$756$	2.00000	−	1.73205i	0.0727393	−	0.0629941i
$757$	12.0000			0.436147			0.218074	−	0.975932i	$-0.430023\pi$
$757$	12.0000			0.436147			0.218074	+	0.975932i	$0.430023\pi$
$758$	−9.50000	+	16.4545i	−0.345056	+	0.597654i
$759$	1.00000	+	1.73205i	0.0362977	+	0.0628695i
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	−2.00000			−0.0724524
$763$	−16.0000	+	13.8564i	−0.579239	+	0.501636i
$764$		0			0
$765$	1.50000	−	2.59808i	0.0542326	−	0.0939336i
$766$	−3.00000	−	5.19615i	−0.108394	−	0.187745i
$767$	−2.00000	−	3.46410i	−0.0722158	−	0.125081i
$768$	8.50000	−	14.7224i	0.306717	−	0.531250i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$	−15.0000	−	5.19615i	−0.540562	−	0.187256i
$771$	−18.0000			−0.648254
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	−4.50000	−	7.79423i	−0.161854	−	0.280339i	0.773680	−	0.633577i	$-0.218414\pi$
$773$	−4.50000	−	7.79423i	−0.161854	−	0.280339i	−0.935534	+	0.353238i	$0.885081\pi$
$774$	2.00000	+	3.46410i	0.0718885

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.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} +(1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} -3.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +3.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +2.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(2.50000 + 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{33} -1.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} -1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{39} +(4.50000 - 7.79423i) q^{40} +4.00000 q^{41} +(0.500000 + 2.59808i) q^{42} +4.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(1.50000 + 2.59808i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-3.50000 + 6.06218i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-0.500000 + 0.866025i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +6.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +(2.00000 + 3.46410i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} -10.0000 q^{62} +(2.50000 + 0.866025i) q^{63} +7.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(1.50000 + 2.59808i) q^{67} +(0.500000 - 0.866025i) q^{68} +1.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} -15.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(6.50000 + 11.2583i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(4.00000 - 3.46410i) q^{77} +1.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.00000 - 3.46410i) q^{82} +6.00000 q^{83} +(-2.50000 - 0.866025i) q^{84} -3.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{88} +(3.00000 - 5.19615i) q^{89} +3.00000 q^{90} +(0.500000 + 2.59808i) q^{91} -1.00000 q^{92} +(-5.00000 + 8.66025i) q^{93} +(3.50000 + 6.06218i) q^{94} +(2.50000 - 4.33013i) q^{96} +16.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} + q^{4} + 3 q^{5} - 2 q^{6} - q^{7} + 6 q^{8} - q^{9} - 3 q^{10} + 2 q^{11} + q^{12} - 2 q^{13} - 5 q^{14} - 6 q^{15} + q^{16} - q^{17} + q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{22}+ \cdots - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 + q^4 + 3 * q^5 - 2 * q^6 - q^7 + 6 * q^8 - q^9 - 3 * q^10 + 2 * q^11 + q^12 - 2 * q^13 - 5 * q^14 - 6 * q^15 + q^16 - q^17 + q^18 + 6 * q^20 - 4 * q^21 + 4 * q^22 - q^23 - 3 * q^24 - 4 * q^25 - q^26 + 2 * q^27 + 4 * q^28 - 3 * q^30 - 10 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 - 15 * q^35 - 2 * q^36 + 2 * q^37 + q^39 + 9 * q^40 + 8 * q^41 + q^42 + 8 * q^43 - 2 * q^44 + 3 * q^45 + q^46 - 7 * q^47 - 2 * q^48 - 13 * q^49 - 8 * q^50 - q^51 - q^52 + 9 * q^53 + q^54 + 12 * q^55 - 3 * q^56 + 4 * q^59 - 3 * q^60 + 2 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 - 3 * q^65 - 2 * q^66 + 3 * q^67 + q^68 + 2 * q^69 - 12 * q^70 - 30 * q^71 - 3 * q^72 + 13 * q^73 - 2 * q^74 - 4 * q^75 + 8 * q^77 + 2 * q^78 - 4 * q^79 - 3 * q^80 - q^81 + 4 * q^82 + 12 * q^83 - 5 * q^84 - 6 * q^85 + 4 * q^86 + 6 * q^88 + 6 * q^89 + 6 * q^90 + q^91 - 2 * q^92 - 10 * q^93 + 7 * q^94 + 5 * q^96 + 32 * q^97 - 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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