LMFDB - Embedded newform 483.2.i.d.277.1

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			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.d.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 2 * q + q^2 - q^3 + q^4 + 3 * q^5 - 2 * q^6 - q^7 + 6 * q^8 - q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	−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	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	−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	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	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	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	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	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	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	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		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	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$	−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	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$	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	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−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	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	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	−0.181688	−	0.983356i	$-0.558156\pi$
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	0.942455	−	0.334332i	$-0.108511\pi$
$74$	−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	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	−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	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	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	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$	0.500000	−	0.866025i	0.0495074	−	0.0857493i
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	−0.998793	−	0.0491146i	$-0.984360\pi$
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	0.456862	−	0.889538i	$-0.348973\pi$
$104$	−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	0.753010	−	0.658009i	$-0.228601\pi$
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	−0.991508	−	0.130046i	$-0.958487\pi$
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	0.608377	+	0.793648i	$0.291821\pi$
$110$	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	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$	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	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$	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	0.745264	−	0.666770i	$-0.232324\pi$
$149$	−2.50000	−	4.33013i	−0.204808	−	0.354738i	−0.950072	+	0.312032i	$0.898990\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	0.773099	+	0.634285i	$0.218706\pi$
$152$		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	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$	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	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	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	0.991532	+	0.129861i	$0.0414530\pi$
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	−0.383304	+	0.923622i	$0.625214\pi$
$174$		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	−0.583920	−	0.811811i	$-0.698482\pi$
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	0.995009	+	0.0997838i	$0.0318151\pi$
$180$	−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	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−3.50000	+	6.06218i	−0.252591	+	0.437500i
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$	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	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$	−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	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	−14.0000	−	24.2487i	−0.925146	−	1.60240i	−0.791326	−	0.611394i	$-0.790609\pi$
$229$	−14.0000	−	24.2487i	−0.925146	−	1.60240i	−0.133820	−	0.991006i	$-0.542724\pi$
$230$	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	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$	−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	−0.946324	−	0.323218i	$-0.895235\pi$
$241$	−3.00000	+	5.19615i	−0.193247	+	0.334714i	0.753077	+	0.657932i	$0.228569\pi$
$242$	−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	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	−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	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$	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	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$	−1.50000	+	2.59808i	−0.0912871	+	0.158114i
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	0.571221	−	0.820796i	$-0.306470\pi$
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	−0.996441	+	0.0842940i	$0.973137\pi$
$272$	−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	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$	−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	−0.124096	+	0.992270i	$0.539603\pi$
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.797283	+	0.603606i	$0.793730\pi$
$284$	−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	0.398090	+	0.917346i	$0.369673\pi$
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	−0.993490	+	0.113917i	$0.963660\pi$
$312$	1.50000	−	2.59808i	0.0849208	−	0.147087i
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	−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	0.690761	−	0.723083i	$-0.257276\pi$
$317$	−5.00000	−	8.66025i	−0.280828	−	0.486408i	−0.971589	+	0.236675i	$0.923942\pi$
$318$	−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	0.775692	+	0.631111i	$0.217401\pi$
$331$	17.0000	+	29.4449i	0.934405	+	1.61844i	0.158712	+	0.987325i	$0.449266\pi$
$332$	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	−0.903475	−	0.428640i	$-0.858993\pi$
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	0.822951	+	0.568112i	$0.192326\pi$
$348$		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	−0.807880	−	0.589347i	$-0.799385\pi$
$353$	2.00000	−	3.46410i	0.106449	−	0.184376i	0.914329	+	0.404971i	$0.132718\pi$
$354$	−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	−0.995413	−	0.0956683i	$-0.969501\pi$
$359$	−11.0000	−	19.0526i	−0.580558	−	1.00556i	0.414855	−	0.909887i	$-0.363832\pi$
$360$	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	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$	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	0.977016	+	0.213165i	$0.0683772\pi$
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$374$	−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	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$	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	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$	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	−0.999506	−	0.0314391i	$-0.989991\pi$
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	0.472526	−	0.881317i	$-0.343342\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	−4.00000			−0.200000
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	0.970049	−	0.242911i	$-0.0781024\pi$
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	−0.695392	+	0.718631i	$0.744769\pi$
$402$	−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	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−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	−0.166491	−	0.986043i	$-0.553244\pi$
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	0.937184	−	0.348836i	$-0.113423\pi$
$432$	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	−0.999576	−	0.0291138i	$-0.990731\pi$
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	0.474575	−	0.880215i	$-0.342602\pi$
$440$	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	0.966591	−	0.256323i	$-0.0825112\pi$
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	−0.705278	+	0.708931i	$0.749178\pi$
$444$	−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	0.615986	−	0.787757i	$-0.288758\pi$
$457$	−8.00000	−	13.8564i	−0.374224	−	0.648175i	−0.990211	+	0.139581i	$0.955424\pi$
$458$	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	0.983637	+	0.180161i	$0.0576619\pi$
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	−0.335794	+	0.941935i	$0.609005\pi$
$468$	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	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$	−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	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	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	−0.915756	−	0.401735i	$-0.868407\pi$
$499$	−18.0000	−	31.1769i	−0.805791	−	1.39567i	0.109965	−	0.993935i	$-0.464926\pi$
$500$	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	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$	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	−0.351204	−	0.936299i	$-0.614228\pi$
$521$	14.5000	−	25.1147i	0.635257	−	1.10030i	0.986461	−	0.163998i	$-0.0524390\pi$
$522$		0			0
$523$	−8.50000	−	14.7224i	−0.371679	−	0.643767i	0.618145	−	0.786064i	$-0.287884\pi$
$523$	−8.50000	−	14.7224i	−0.371679	−	0.643767i	−0.989824	+	0.142297i	$0.954551\pi$
$524$	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	0.807267	−	0.590187i	$-0.200946\pi$
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	−0.914750	+	0.404020i	$0.867613\pi$
$542$	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	−0.678756	−	0.734364i	$-0.737481\pi$
$557$	7.00000	−	12.1244i	0.296600	−	0.513725i	0.975356	+	0.220638i	$0.0708140\pi$
$558$	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	0.0445334	+	0.999008i	$0.485820\pi$
$563$	−20.0000	+	34.6410i	−0.842900	+	1.45994i	−0.887433	+	0.460937i	$0.847513\pi$
$564$	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	−0.971275	−	0.237959i	$-0.923522\pi$
$569$	−16.5000	−	28.5788i	−0.691716	−	1.19809i	0.279559	−	0.960128i	$-0.409812\pi$
$570$		0			0
$571$	−3.50000	+	6.06218i	−0.146470	+	0.253694i	−0.929921	−	0.367760i	$-0.880125\pi$
$571$	−3.50000	+	6.06218i	−0.146470	+	0.253694i	0.783450	+	0.621455i	$0.213458\pi$
$572$	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	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−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	−0.999218	−	0.0395334i	$-0.987413\pi$
$593$	−13.0000	−	22.5167i	−0.533846	−	0.924648i	0.465372	−	0.885115i	$-0.345920\pi$
$594$	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	0.124975	+	0.992160i	$0.460115\pi$
$599$	−19.5000	+	33.7750i	−0.796748	+	1.38001i	−0.921723	+	0.387849i	$0.873218\pi$
$600$	−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	0.798698	−	0.601732i	$-0.205522\pi$
$607$	−3.00000	−	5.19615i	−0.121766	−	0.210905i	−0.920464	+	0.390827i	$0.872189\pi$
$608$		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	−0.845124	−	0.534570i	$-0.820473\pi$
$613$	1.00000	−	1.73205i	0.0403896	−	0.0699569i	0.885514	+	0.464614i	$0.153807\pi$
$614$	−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	−0.456142	−	0.889907i	$-0.650769\pi$
$619$	13.5000	−	23.3827i	0.542611	−	0.939829i	0.998753	−	0.0499226i	$-0.0158975\pi$
$620$	−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	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$	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	−0.933878	−	0.357591i	$-0.883598\pi$
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	0.776622	+	0.629967i	$0.216932\pi$
$648$	−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	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$	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	−0.777689	−	0.628649i	$-0.783608\pi$
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	0.933271	+	0.359174i	$0.116941\pi$
$662$	−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	0.952147	−	0.305639i	$-0.0988702\pi$
$677$	5.50000	+	9.52628i	0.211382	+	0.366125i	−0.740765	+	0.671764i	$0.765537\pi$
$678$	−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	0.144940	+	0.989440i	$0.453701\pi$
$683$	−20.5000	+	35.5070i	−0.784411	+	1.35864i	−0.929350	+	0.369199i	$0.879632\pi$
$684$		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	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$	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	$-0.166667\pi$
$709$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$710$	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	0.691608	−	0.722273i	$-0.256903\pi$
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	−0.971311	+	0.237814i	$0.923569\pi$
$720$	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	0.997927	−	0.0643554i	$-0.0204991\pi$
$733$	12.0000	+	20.7846i	0.443230	+	0.767697i	−0.554697	+	0.832052i	$0.687166\pi$
$734$	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	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$	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	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	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	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$	−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	−0.935534	−	0.353238i	$-0.885081\pi$
$773$	−4.50000	+	7.79423i	−0.161854	+	0.280339i	0.773680	+	0.633577i	$0.218414\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$	−20.0000	−	34.6410i	−0.718421	−	1.24434i
$776$	48.0000			1.72310
$777$	1.00000	−	5.19615i	0.0358748	−	0.186411i
$778$	6.00000			0.215110
$779$		0			0
$780$	1.50000	−	2.59808i	0.0537086	−	0.0930261i
$781$	−15.0000	+	25.9808i	−0.536742	+	0.929665i
$782$	0.500000	+	0.866025i	0.0178800	+	0.0309690i
$783$		0			0
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$	−30.0000			−1.07075
$786$	−1.50000	−	2.59808i	−0.0535032	−	0.0926703i
$787$	−25.5000	+	44.1673i	−0.908977	+	1.57439i	−0.0934886	+	0.995620i	$0.529802\pi$
$787$	−25.5000	+	44.1673i	−0.908977	+	1.57439i	−0.815488	+	0.578774i	$0.803531\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	8.00000	+	13.8564i	0.284808	+	0.493301i
$790$	12.0000			0.426941
$791$	−3.50000	+	18.1865i	−0.124446	+	0.646639i
$792$	−6.00000			−0.213201
$793$	−1.00000	−	1.73205i	−0.0355110	−	0.0615069i
$794$	10.5000	−	18.1865i	0.372631	−	0.645416i
$795$	−13.5000	+	23.3827i	−0.478796	+	0.829298i
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	19.0000			0.673015			0.336507	−	0.941681i	$-0.390754\pi$
$797$	19.0000			0.673015			0.336507	+	0.941681i	$0.390754\pi$
$798$		0			0
$799$	7.00000			0.247642
$800$	10.0000	+	17.3205i	0.353553	+	0.612372i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	−5.50000	+	9.52628i	−0.194212	+	0.336385i
$803$	−13.0000	−	22.5167i	−0.458760	−	0.794596i
$804$	3.00000			0.105802
$805$	6.00000	+	5.19615i	0.211472	+	0.183140i
$806$	10.0000			0.352235
$807$	−2.00000	−	3.46410i	−0.0704033	−	0.121942i
$808$	27.0000	−	46.7654i	0.949857	−	1.64520i
$809$	27.0000	−	46.7654i	0.949269	−	1.64418i	0.202301	−	0.979323i	$-0.435158\pi$
$809$	27.0000	−	46.7654i	0.949269	−	1.64418i	0.746968	−	0.664860i	$-0.231509\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$	−30.0000			−1.05344			−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000			−1.05344			−0.526721	+	0.850038i	$0.676579\pi$
$812$		0			0
$813$	14.0000			0.491001
$814$	2.00000	+	3.46410i	0.0701000	+	0.121417i
$815$	−30.0000	+	51.9615i	−1.05085	+	1.82013i
$816$	0.500000	−	0.866025i	0.0175035	−	0.0303170i
$817$		0			0
$818$	−31.0000			−1.08389
$819$	−2.50000	+	0.866025i	−0.0873571	+	0.0302614i
$820$	12.0000			0.419058
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	−8.50000	+	14.7224i	−0.296472	+	0.513504i
$823$	13.0000	−	22.5167i	0.453152	−	0.784881i	−0.545428	−	0.838157i	$-0.683633\pi$
$823$	13.0000	−	22.5167i	0.453152	−	0.784881i	0.998580	+	0.0532760i	$0.0169663\pi$
$824$	−16.5000	−	28.5788i	−0.574805	−	0.995591i
$825$	−8.00000			−0.278524
$826$	−2.00000	+	10.3923i	−0.0695889	+	0.361595i
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	1.50000	−	2.59808i	0.0520972	−	0.0902349i	−0.838801	−	0.544438i	$-0.816743\pi$
$829$	1.50000	−	2.59808i	0.0520972	−	0.0902349i	0.890898	+	0.454204i	$0.150076\pi$
$830$	−9.00000	+	15.5885i	−0.312395	+	0.541083i
$831$	−6.50000	−	11.2583i	−0.225483	−	0.390547i
$832$	−7.00000			−0.242681
$833$	5.50000	−	4.33013i	0.190564	−	0.150030i
$834$	10.0000			0.346272
$835$	−28.5000	−	49.3634i	−0.986283	−	1.70829i
$836$		0			0
$837$	−5.00000	+	8.66025i	−0.172825	+	0.299342i
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	20.0000			0.690477			0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000			0.690477			0.345238	+	0.938515i	$0.387798\pi$
$840$	4.50000	−	23.3827i	0.155265	−	0.806779i
$841$	−29.0000			−1.00000
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$	−13.5000	+	23.3827i	−0.464965	+	0.805342i
$844$	−11.0000	+	19.0526i	−0.378636	+	0.655816i
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$	−7.00000			−0.240665
$847$	−17.5000	+	6.06218i	−0.601307	+	0.208299i
$848$	9.00000			0.309061
$849$	−15.5000	−	26.8468i	−0.531959	−	0.921379i
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$	−7.50000	−	12.9904i	−0.256946	−	0.445043i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	−4.00000	−	3.46410i	−0.136877	−	0.118539i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	23.0000	−	39.8372i	0.785665	−	1.36081i	−0.142936	−	0.989732i	$-0.545654\pi$
$857$	23.0000	−	39.8372i	0.785665	−	1.36081i	0.928601	−	0.371080i	$-0.121012\pi$
$858$	1.00000	−	1.73205i	0.0341394	−	0.0591312i
$859$	−4.00000	−	6.92820i	−0.136478	−	0.236387i	0.789683	−	0.613515i	$-0.210245\pi$
$859$	−4.00000	−	6.92820i	−0.136478	−	0.236387i	−0.926161	+	0.377128i	$0.876912\pi$
$860$	12.0000			0.409197
$861$	−8.00000	−	6.92820i	−0.272639	−	0.236113i
$862$	32.0000			1.08992
$863$	10.5000	+	18.1865i	0.357424	+	0.619077i	0.987530	−	0.157433i	$-0.0503217\pi$
$863$	10.5000	+	18.1865i	0.357424	+	0.619077i	−0.630106	+	0.776509i	$0.716988\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$	−24.0000	+	41.5692i	−0.816024	+	1.41340i
$866$	−11.0000	−	19.0526i	−0.373795	−	0.647432i
$867$	−16.0000			−0.543388
$868$	−25.0000	+	8.66025i	−0.848555	+	0.293948i
$869$	−8.00000			−0.271381
$870$		0			0
$871$	−1.50000	+	2.59808i	−0.0508256	+	0.0880325i
$872$	−12.0000	+	20.7846i	−0.406371	+	0.703856i
$873$	−8.00000	−	13.8564i	−0.270759	−	0.468968i
$874$		0			0
$875$	−1.50000	+	7.79423i	−0.0507093	+	0.263493i
$876$	13.0000			0.439229
$877$	−9.50000	−	16.4545i	−0.320792	−	0.555628i	0.659860	−	0.751389i	$-0.270616\pi$
$877$	−9.50000	−	16.4545i	−0.320792	−	0.555628i	−0.980652	+	0.195761i	$0.937282\pi$
$878$	11.0000	−	19.0526i	0.371232	−	0.642993i
$879$	6.50000	−	11.2583i	0.219240	−	0.379734i
$880$	3.00000	+	5.19615i	0.101130	+	0.175162i
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$	−5.50000	+	4.33013i	−0.185195	+	0.145803i
$883$	24.0000			0.807664			0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000			0.807664			0.403832	+	0.914833i	$0.367678\pi$
$884$	−0.500000	−	0.866025i	−0.0168168	−	0.0291276i
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	−5.50000	+	9.52628i	−0.184776	+	0.320042i
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$	−6.00000			−0.201347
$889$	−1.00000	+	5.19615i	−0.0335389	+	0.174273i
$890$	−18.0000			−0.603361
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	2.00000	−	3.46410i	0.0669650	−	0.115987i
$893$		0			0
$894$	2.50000	+	4.33013i	0.0836125	+	0.144821i
$895$	33.0000			1.10307
$896$	7.50000	−	2.59808i	0.250557	−	0.0867956i
$897$	−1.00000			−0.0333890
$898$	7.00000	+	12.1244i	0.233593	+	0.404595i
$899$		0			0
$900$	2.00000	−	3.46410i	0.0666667	−	0.115470i
$901$	4.50000	+	7.79423i	0.149917	+	0.259663i
$902$	8.00000			0.266371
$903$	−8.00000	−	6.92820i	−0.266223	−	0.230556i
$904$	21.0000			0.698450
$905$	−39.0000	−	67.5500i	−1.29640	−	2.24544i
$906$	2.00000	−	3.46410i	0.0664455	−	0.115087i
$907$	10.5000	−	18.1865i	0.348647	−	0.603874i	−0.637363	−	0.770564i	$-0.719975\pi$
$907$	10.5000	−	18.1865i	0.348647	−	0.603874i	0.986009	+	0.166690i	$0.0533080\pi$
$908$	−7.00000	−	12.1244i	−0.232303	−	0.402361i
$909$	−18.0000			−0.597022
$910$	6.00000	+	5.19615i	0.198898	+	0.172251i
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	8.00000	−	13.8564i	0.264616	−	0.458329i
$915$	−3.00000	−	5.19615i	−0.0991769	−	0.171780i
$916$	−28.0000			−0.925146
$917$	−7.50000	+	2.59808i	−0.247672	+	0.0857960i
$918$	−1.00000			−0.0330049
$919$	24.5000	+	42.4352i	0.808180	+	1.39981i	0.914123	+	0.405437i	$0.132881\pi$
$919$	24.5000	+	42.4352i	0.808180	+	1.39981i	−0.105942	+	0.994372i	$0.533786\pi$
$920$	4.50000	−	7.79423i	0.148361	−	0.256968i
$921$	10.0000	−	17.3205i	0.329511	−	0.570730i
$922$	−21.0000	−	36.3731i	−0.691598	−	1.19788i
$923$	15.0000			0.493731
$924$	−1.00000	+	5.19615i	−0.0328976	+	0.170941i
$925$	−8.00000			−0.263038
$926$	20.0000	+	34.6410i	0.657241	+	1.13837i
$927$	−5.50000	+	9.52628i	−0.180644	+	0.312884i
$928$		0			0
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	0.599228	−	0.800578i	$-0.295474\pi$
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	−0.992935	+	0.118657i	$0.962141\pi$
$930$	30.0000			0.983739
$931$		0			0
$932$	24.0000			0.786146
$933$	−10.5000	−	18.1865i	−0.343755	−	0.595400i
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	−3.00000	+	5.19615i	−0.0981105	+	0.169932i
$936$	1.50000	+	2.59808i	0.0490290	+	0.0849208i
$937$	−8.00000			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$938$	−1.50000	+	7.79423i	−0.0489767	+	0.254491i
$939$	−8.00000			−0.261070
$940$	−10.5000	−	18.1865i	−0.342472	−	0.593179i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$	5.00000	−	8.66025i	0.162909	−	0.282166i
$943$	−2.00000	−	3.46410i	−0.0651290	−	0.112807i
$944$	4.00000			0.130189
$945$	−7.50000	+	2.59808i	−0.243975	+	0.0845154i
$946$	8.00000			0.260102
$947$	−23.5000	−	40.7032i	−0.763647	−	1.32268i	−0.940959	−	0.338521i	$-0.890073\pi$
$947$	−23.5000	−	40.7032i	−0.763647	−	1.32268i	0.177311	−	0.984155i	$-0.443260\pi$
$948$	2.00000	−	3.46410i	0.0649570	−	0.112509i
$949$	−6.50000	+	11.2583i	−0.210999	+	0.365461i
$950$		0			0
$951$	10.0000			0.324272
$952$	−6.00000	−	5.19615i	−0.194461	−	0.168408i
$953$	−14.0000			−0.453504			−0.226752	−	0.973952i	$-0.572811\pi$
$953$	−14.0000			−0.453504			−0.226752	+	0.973952i	$0.572811\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$		0			0
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$	−16.0000			−0.516937
$959$	34.0000	+	29.4449i	1.09792	+	0.950824i
$960$	−21.0000			−0.677772
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	1.00000	−	1.73205i	0.0322413	−	0.0558436i
$963$	−2.00000	+	3.46410i	−0.0644491	+	0.111629i
$964$	3.00000	+	5.19615i	0.0966235	+	0.167357i
$965$	33.0000			1.06231
$966$	−2.50000	+	0.866025i	−0.0804362	+	0.0278639i
$967$	4.00000			0.128631			0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000			0.128631			0.0643157	+	0.997930i	$0.479514\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$		0			0
$970$	−24.0000	+	41.5692i	−0.770594	+	1.33471i
$971$	2.00000	+	3.46410i	0.0641831	+	0.111168i	0.896331	−	0.443385i	$-0.146223\pi$
$971$	2.00000	+	3.46410i	0.0641831	+	0.111168i	−0.832148	+	0.554553i	$0.812889\pi$
$972$	−1.00000			−0.0320750
$973$	5.00000	−	25.9808i	0.160293	−	0.832905i
$974$	−16.0000			−0.512673
$975$	2.00000	+	3.46410i	0.0640513	+	0.110940i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	0.364900	+	0.931047i	$0.381103\pi$
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	−0.988760	+	0.149511i	$0.952230\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	12.0000			0.383522
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$	8.00000			0.255420
$982$	4.50000	+	7.79423i	0.143601	+	0.248724i
$983$	7.00000	−	12.1244i	0.223265	−	0.386707i	−0.732532	−	0.680732i	$-0.761662\pi$
$983$	7.00000	−	12.1244i	0.223265	−	0.386707i	0.955798	+	0.294025i	$0.0949950\pi$
$984$	−6.00000	+	10.3923i	−0.191273	+	0.331295i
$985$	−27.0000	−	46.7654i	−0.860292	−	1.49007i
$986$		0			0
$987$	−3.50000	+	18.1865i	−0.111406	+	0.578884i
$988$		0			0
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$	3.00000	−	5.19615i	0.0953463	−	0.165145i
$991$	25.0000	−	43.3013i	0.794151	−	1.37551i	−0.129226	−	0.991615i	$-0.541249\pi$
$991$	25.0000	−	43.3013i	0.794151	−	1.37551i	0.923377	−	0.383895i	$-0.125418\pi$
$992$	25.0000	+	43.3013i	0.793751	+	1.37482i
$993$	−34.0000			−1.07896
$994$	37.5000	−	12.9904i	1.18943	−	0.412030i
$995$	−48.0000			−1.52170
$996$	3.00000	+	5.19615i	0.0950586	+	0.164646i
$997$	−21.0000	+	36.3731i	−0.665077	+	1.15195i	0.314188	+	0.949361i	$0.398268\pi$
$997$	−21.0000	+	36.3731i	−0.665077	+	1.15195i	−0.979265	+	0.202586i	$0.935066\pi$
$998$	18.0000	−	31.1769i	0.569780	−	0.986888i
$999$	1.00000	+	1.73205i	0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.d.277.1	✓	2
7.2	even	3	inner	483.2.i.d.415.1	yes	2
7.3	odd	6		3381.2.a.b.1.1		1
7.4	even	3		3381.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.d.277.1	✓	2	1.1	even	1	trivial
483.2.i.d.415.1	yes	2	7.2	even	3	inner
3381.2.a.b.1.1		1	7.3	odd	6
3381.2.a.c.1.1		1	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

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

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