LMFDB - Embedded newform 1690.2.e.a.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(191,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1690.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not 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:	$13.4947179416$
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:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.a.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +2.00000 q^{12} -4.00000 q^{14} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} -8.00000 q^{21} +(1.00000 + 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.00000 + 1.73205i) q^{24} +1.00000 q^{25} -4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(1.00000 + 1.73205i) q^{30} -6.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +2.00000 q^{34} +(-2.00000 - 3.46410i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 - 1.73205i) q^{37} +6.00000 q^{38} -1.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +(4.00000 - 6.92820i) q^{42} +(5.00000 + 8.66025i) q^{43} -2.00000 q^{44} +(0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{46} -12.0000 q^{47} +(-1.00000 - 1.73205i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +4.00000 q^{51} +2.00000 q^{53} +(2.00000 - 3.46410i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(2.00000 + 3.46410i) q^{56} +12.0000 q^{57} +(-1.00000 - 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{59} -2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} -4.00000 q^{66} +(6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-6.00000 - 10.3923i) q^{69} +4.00000 q^{70} +(-5.00000 - 8.66025i) q^{71} +(-0.500000 - 0.866025i) q^{72} +10.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-3.00000 + 5.19615i) q^{76} +8.00000 q^{77} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.00000 - 8.66025i) q^{82} +(4.00000 + 6.92820i) q^{84} +(1.00000 + 1.73205i) q^{85} -10.0000 q^{86} +(-2.00000 - 3.46410i) q^{87} +(1.00000 - 1.73205i) q^{88} +(7.00000 - 12.1244i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(6.00000 - 10.3923i) q^{93} +(6.00000 - 10.3923i) q^{94} +(3.00000 + 5.19615i) q^{95} +2.00000 q^{96} +(-7.00000 - 12.1244i) q^{97} +(-4.50000 - 7.79423i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} - 6 q^{19} + q^{20} - 16 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} + 2 q^{25} - 8 q^{27} + 4 q^{28} - 2 q^{29} + 2 q^{30} - 12 q^{31} - q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 2 q^{37} + 12 q^{38} - 2 q^{40} - 10 q^{41} + 8 q^{42} + 10 q^{43} - 4 q^{44} + q^{45} - 6 q^{46} - 24 q^{47} - 2 q^{48} - 9 q^{49} - q^{50} + 8 q^{51} + 4 q^{53} + 4 q^{54} - 2 q^{55} + 4 q^{56} + 24 q^{57} - 2 q^{58} - 10 q^{59} - 4 q^{60} - 2 q^{61} + 6 q^{62} + 4 q^{63} + 2 q^{64} - 8 q^{66} + 12 q^{67} - 2 q^{68} - 12 q^{69} + 8 q^{70} - 10 q^{71} - q^{72} + 20 q^{73} + 2 q^{74} - 2 q^{75} - 6 q^{76} + 16 q^{77} - 8 q^{79} + q^{80} + 11 q^{81} - 10 q^{82} + 8 q^{84} + 2 q^{85} - 20 q^{86} - 4 q^{87} + 2 q^{88} + 14 q^{89} - 2 q^{90} + 12 q^{92} + 12 q^{93} + 12 q^{94} + 6 q^{95} + 4 q^{96} - 14 q^{97} - 9 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^14 + 2 * q^15 - q^16 - 2 * q^17 + 2 * q^18 - 6 * q^19 + q^20 - 16 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 + 2 * q^25 - 8 * q^27 + 4 * q^28 - 2 * q^29 + 2 * q^30 - 12 * q^31 - q^32 + 4 * q^33 + 4 * q^34 - 4 * q^35 - q^36 + 2 * q^37 + 12 * q^38 - 2 * q^40 - 10 * q^41 + 8 * q^42 + 10 * q^43 - 4 * q^44 + q^45 - 6 * q^46 - 24 * q^47 - 2 * q^48 - 9 * q^49 - q^50 + 8 * q^51 + 4 * q^53 + 4 * q^54 - 2 * q^55 + 4 * q^56 + 24 * q^57 - 2 * q^58 - 10 * q^59 - 4 * q^60 - 2 * q^61 + 6 * q^62 + 4 * q^63 + 2 * q^64 - 8 * q^66 + 12 * q^67 - 2 * q^68 - 12 * q^69 + 8 * q^70 - 10 * q^71 - q^72 + 20 * q^73 + 2 * q^74 - 2 * q^75 - 6 * q^76 + 16 * q^77 - 8 * q^79 + q^80 + 11 * q^81 - 10 * q^82 + 8 * q^84 + 2 * q^85 - 20 * q^86 - 4 * q^87 + 2 * q^88 + 14 * q^89 - 2 * q^90 + 12 * q^92 + 12 * q^93 + 12 * q^94 + 6 * q^95 + 4 * q^96 - 14 * q^97 - 9 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000	−	1.73205i	−0.408248	−	0.707107i
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	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	$0.0691756\pi$
$12$	2.00000			0.577350
$13$		0			0
$13$		0			0
$14$	−4.00000			−1.06904
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	1.00000			0.235702
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−8.00000			−1.74574
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	1.00000			0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$	1.00000	+	1.73205i	0.182574	+	0.316228i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$	2.00000			0.342997
$35$	−2.00000	−	3.46410i	−0.338062	−	0.585540i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	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	$0.114098\pi$
$38$	6.00000			0.973329
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	4.00000	−	6.92820i	0.617213	−	1.06904i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	−2.00000			−0.301511
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$	−1.00000	−	1.73205i	−0.144338	−	0.250000i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	4.00000			0.560112
$52$		0			0
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$	12.0000			1.58944
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$	−2.00000			−0.258199
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	3.00000	−	5.19615i	0.381000	−	0.659912i
$63$	2.00000	−	3.46410i	0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.00000			−0.492366
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$	4.00000			0.478091
$71$	−5.00000	−	8.66025i	−0.593391	−	1.02778i	−0.993772	−	0.111434i	$-0.964456\pi$
$71$	−5.00000	−	8.66025i	−0.593391	−	1.02778i	0.400381	−	0.916349i	$-0.368878\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	8.00000			0.911685
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−5.00000	−	8.66025i	−0.552158	−	0.956365i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	4.00000	+	6.92820i	0.436436	+	0.755929i
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$	−10.0000			−1.07833
$87$	−2.00000	−	3.46410i	−0.214423	−	0.371391i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	6.00000	−	10.3923i	0.622171	−	1.07763i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	2.00000			0.204124
$97$	−7.00000	−	12.1244i	−0.710742	−	1.23104i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−7.00000	−	12.1244i	−0.710742	−	1.23104i	0.253837	−	0.967247i	$-0.418307\pi$
$98$	−4.50000	−	7.79423i	−0.454569	−	0.787336i
$99$	−2.00000			−0.201008
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$	−2.00000	+	3.46410i	−0.198030	+	0.342997i
$103$	−18.0000			−1.77359			−0.886796	−	0.462160i	$-0.847074\pi$
$103$	−18.0000			−1.77359			−0.886796	+	0.462160i	$0.847074\pi$
$104$		0			0
$105$	8.00000			0.780720
$106$	−1.00000	+	1.73205i	−0.0971286	+	0.168232i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$	2.00000	+	3.46410i	0.189832	+	0.328798i
$112$	−4.00000			−0.377964
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	0.815149	−	0.579252i	$-0.196655\pi$
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	−0.909221	+	0.416314i	$0.863322\pi$
$114$	−6.00000	+	10.3923i	−0.561951	+	0.973329i
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	2.00000			0.185695
$117$		0			0
$118$	10.0000			0.920575
$119$	4.00000	−	6.92820i	0.366679	−	0.635107i
$120$	1.00000	−	1.73205i	0.0912871	−	0.158114i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	2.00000			0.181071
$123$	−10.0000	−	17.3205i	−0.901670	−	1.56174i
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	−1.00000			−0.0894427
$126$	2.00000	+	3.46410i	0.178174	+	0.308607i
$127$	7.00000	−	12.1244i	0.621150	−	1.07586i	−0.368122	−	0.929777i	$-0.619999\pi$
$127$	7.00000	−	12.1244i	0.621150	−	1.07586i	0.989272	−	0.146085i	$-0.0466674\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−20.0000			−1.76090
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	2.00000	−	3.46410i	0.174078	−	0.301511i
$133$	12.0000	−	20.7846i	1.04053	−	1.80225i
$134$	6.00000	+	10.3923i	0.518321	+	0.897758i
$135$	4.00000			0.344265
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$	12.0000			1.02151
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$	−2.00000	+	3.46410i	−0.169031	+	0.292770i
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$	10.0000			0.839181
$143$		0			0
$144$	1.00000			0.0833333
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	−5.00000	+	8.66025i	−0.413803	+	0.716728i
$147$	−9.00000	−	15.5885i	−0.742307	−	1.28571i
$148$	−2.00000			−0.164399
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	0.822153	−	0.569267i	$-0.192773\pi$
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	−0.904076	+	0.427372i	$0.859440\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	6.00000			0.488273			0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000			0.488273			0.244137	+	0.969741i	$0.421495\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	−1.00000	+	1.73205i	−0.0808452	+	0.140028i
$154$	−4.00000	+	6.92820i	−0.322329	+	0.558291i
$155$	6.00000			0.481932
$156$		0			0
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−2.00000	+	3.46410i	−0.158610	+	0.274721i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−24.0000			−1.89146
$162$	5.50000	+	9.52628i	0.432121	+	0.748455i
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	10.0000			0.780869
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$		0			0
$167$	−10.0000	+	17.3205i	−0.773823	+	1.34030i	0.161630	+	0.986851i	$0.448325\pi$
$167$	−10.0000	+	17.3205i	−0.773823	+	1.34030i	−0.935454	+	0.353450i	$0.885009\pi$
$168$	−8.00000			−0.617213
$169$		0			0
$170$	−2.00000			−0.153393
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	0.610939	−	0.791677i	$-0.290792\pi$
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	−0.991082	+	0.133250i	$0.957459\pi$
$174$	4.00000			0.303239
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	20.0000			1.50329
$178$	7.00000	+	12.1244i	0.524672	+	0.908759i
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$	6.00000	+	10.3923i	0.439941	+	0.762001i
$187$	−4.00000			−0.292509
$188$	6.00000	+	10.3923i	0.437595	+	0.757937i
$189$	−8.00000	−	13.8564i	−0.581914	−	1.00791i
$190$	−6.00000			−0.435286
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	14.0000			1.00514
$195$		0			0
$196$	9.00000			0.642857
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	1.00000			0.0707107
$201$	12.0000	+	20.7846i	0.846415	+	1.46603i
$202$	−7.00000	−	12.1244i	−0.492518	−	0.853067i
$203$	−8.00000			−0.561490
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$	9.00000	−	15.5885i	0.627060	−	1.08610i
$207$	6.00000			0.417029
$208$		0			0
$209$	−12.0000			−0.830057
$210$	−4.00000	+	6.92820i	−0.276026	+	0.478091i
$211$	−14.0000	+	24.2487i	−0.963800	+	1.66935i	−0.250994	+	0.967989i	$0.580757\pi$
$211$	−14.0000	+	24.2487i	−0.963800	+	1.66935i	−0.712806	+	0.701361i	$0.752576\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$	20.0000			1.37038
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$	−5.00000	−	8.66025i	−0.340997	−	0.590624i
$216$	−4.00000			−0.272166
$217$	−12.0000	−	20.7846i	−0.814613	−	1.41095i
$218$	3.00000	−	5.19615i	0.203186	−	0.351928i
$219$	−10.0000	+	17.3205i	−0.675737	+	1.17041i
$220$	2.00000			0.134840
$221$		0			0
$222$	−4.00000			−0.268462
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$	2.00000	−	3.46410i	0.133631	−	0.231455i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	2.00000			0.133038
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	0.924734	−	0.380615i	$-0.124288\pi$
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	−0.791989	+	0.610535i	$0.790954\pi$
$228$	−6.00000	−	10.3923i	−0.397360	−	0.688247i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$	−8.00000	+	13.8564i	−0.526361	+	0.911685i
$232$	−1.00000	+	1.73205i	−0.0656532	+	0.113715i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$	4.00000	+	6.92820i	0.259281	+	0.449089i
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$	−7.00000			−0.449977
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	4.50000	−	7.79423i	0.287494	−	0.497955i
$246$	20.0000			1.27515
$247$		0			0
$248$	−6.00000			−0.381000
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	−4.00000			−0.251976
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	7.00000	+	12.1244i	0.439219	+	0.760750i
$255$	−4.00000			−0.250490
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.162247	−	0.986750i	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$	10.0000	−	17.3205i	0.622573	−	1.07833i
$259$	8.00000			0.497096
$260$		0			0
$261$	2.00000			0.123797
$262$	−2.00000	+	3.46410i	−0.123560	+	0.214013i
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$	2.00000	+	3.46410i	0.123091	+	0.213201i
$265$	−2.00000			−0.122859
$266$	12.0000	+	20.7846i	0.735767	+	1.27439i
$267$	14.0000	+	24.2487i	0.856786	+	1.48400i
$268$	−12.0000			−0.733017
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$	−2.00000	+	3.46410i	−0.121716	+	0.210819i
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	−18.0000			−1.08742
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−8.00000			−0.479808
$279$	3.00000	+	5.19615i	0.179605	+	0.311086i
$280$	−2.00000	−	3.46410i	−0.119523	−	0.207020i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	12.0000	+	20.7846i	0.714590	+	1.23771i
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	−5.00000	+	8.66025i	−0.296695	+	0.513892i
$285$	−12.0000			−0.710819
$286$		0			0
$287$	−40.0000			−2.36113
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	1.00000	+	1.73205i	0.0587220	+	0.101710i
$291$	28.0000			1.64139
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−11.0000	−	19.0526i	−0.642627	−	1.11306i	−0.984844	−	0.173442i	$-0.944511\pi$
$293$	−11.0000	−	19.0526i	−0.642627	−	1.11306i	0.342217	−	0.939621i	$-0.388822\pi$
$294$	18.0000			1.04978
$295$	5.00000	+	8.66025i	0.291111	+	0.504219i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−4.00000	+	6.92820i	−0.232104	+	0.402015i
$298$	2.00000			0.115857
$299$		0			0
$300$	2.00000			0.115470
$301$	−20.0000	+	34.6410i	−1.15278	+	1.99667i
$302$	−3.00000	+	5.19615i	−0.172631	+	0.299005i
$303$	−14.0000	−	24.2487i	−0.804279	−	1.39305i
$304$	6.00000			0.344124
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$	24.0000			1.36975			0.684876	−	0.728659i	$-0.259856\pi$
$307$	24.0000			1.36975			0.684876	+	0.728659i	$0.259856\pi$
$308$	−4.00000	−	6.92820i	−0.227921	−	0.394771i
$309$	18.0000	−	31.1769i	1.02398	−	1.77359i
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−5.00000	+	8.66025i	−0.282166	+	0.488726i
$315$	−2.00000	+	3.46410i	−0.112687	+	0.195180i
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	−2.00000	−	3.46410i	−0.112154	−	0.194257i
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	−1.00000			−0.0559017
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$	12.0000	−	20.7846i	0.668734	−	1.15828i
$323$	−6.00000	+	10.3923i	−0.333849	+	0.578243i
$324$	−11.0000			−0.611111
$325$		0			0
$326$	−4.00000			−0.221540
$327$	6.00000	−	10.3923i	0.331801	−	0.574696i
$328$	−5.00000	+	8.66025i	−0.276079	+	0.478183i
$329$	−24.0000	−	41.5692i	−1.32316	−	2.29179i
$330$	4.00000			0.220193
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	0.991735	−	0.128302i	$-0.0409527\pi$
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	−0.606980	+	0.794717i	$0.707619\pi$
$332$		0			0
$333$	−2.00000			−0.109599
$334$	−10.0000	−	17.3205i	−0.547176	−	0.947736i
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$	4.00000	−	6.92820i	0.218218	−	0.377964i
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$		0			0
$339$	4.00000			0.217250
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$	−8.00000			−0.431959
$344$	5.00000	+	8.66025i	0.269582	+	0.466930i
$345$	6.00000	+	10.3923i	0.323029	+	0.559503i
$346$	10.0000			0.537603
$347$	−3.00000	−	5.19615i	−0.161048	−	0.278944i	0.774197	−	0.632945i	$-0.218154\pi$
$347$	−3.00000	−	5.19615i	−0.161048	−	0.278944i	−0.935245	+	0.354001i	$0.884821\pi$
$348$	−2.00000	+	3.46410i	−0.107211	+	0.185695i
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	−0.891548	−	0.452926i	$-0.850380\pi$
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	0.838019	+	0.545640i	$0.183714\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	−2.00000			−0.106600
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.0836583	+	0.996495i	$0.526660\pi$
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.821160	+	0.570697i	$0.806673\pi$
$354$	−10.0000	+	17.3205i	−0.531494	+	0.920575i
$355$	5.00000	+	8.66025i	0.265372	+	0.459639i
$356$	−14.0000			−0.741999
$357$	8.00000	+	13.8564i	0.423405	+	0.733359i
$358$	2.00000	+	3.46410i	0.105703	+	0.183083i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−14.0000			−0.734809
$364$		0			0
$365$	−10.0000			−0.523424
$366$	−2.00000	+	3.46410i	−0.104542	+	0.181071i
$367$	−15.0000	+	25.9808i	−0.782994	+	1.35618i	0.147197	+	0.989107i	$0.452975\pi$
$367$	−15.0000	+	25.9808i	−0.782994	+	1.35618i	−0.930190	+	0.367078i	$0.880358\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	10.0000			0.520579
$370$	−1.00000	−	1.73205i	−0.0519875	−	0.0900450i
$371$	4.00000	+	6.92820i	0.207670	+	0.359694i
$372$	−12.0000			−0.622171
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$	−12.0000			−0.618853
$377$		0			0
$378$	16.0000			0.822951
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	−0.932731	−	0.360573i	$-0.882581\pi$
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	0.778631	+	0.627482i	$0.215914\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	14.0000	+	24.2487i	0.717242	+	1.24230i
$382$		0			0
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$	−1.00000	−	1.73205i	−0.0510310	−	0.0883883i
$385$	−8.00000			−0.407718
$386$	−7.00000	−	12.1244i	−0.356291	−	0.617113i
$387$	5.00000	−	8.66025i	0.254164	−	0.440225i
$388$	−7.00000	+	12.1244i	−0.355371	+	0.615521i
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$	−4.00000	+	6.92820i	−0.201773	+	0.349482i
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	4.00000			0.201262
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−19.0000	−	32.9090i	−0.953583	−	1.65165i	−0.737579	−	0.675261i	$-0.764031\pi$
$397$	−19.0000	−	32.9090i	−0.953583	−	1.65165i	−0.216004	−	0.976392i	$-0.569302\pi$
$398$		0			0
$399$	24.0000	+	41.5692i	1.20150	+	2.08106i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−24.0000			−1.19701
$403$		0			0
$404$	14.0000			0.696526
$405$	−5.50000	+	9.52628i	−0.273297	+	0.473365i
$406$	4.00000	−	6.92820i	0.198517	−	0.343841i
$407$	−2.00000	−	3.46410i	−0.0991363	−	0.171709i
$408$	4.00000			0.198030
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	−0.889392	−	0.457146i	$-0.848872\pi$
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	0.0487958	−	0.998809i	$-0.484462\pi$
$410$	5.00000	+	8.66025i	0.246932	+	0.427699i
$411$	−36.0000			−1.77575
$412$	9.00000	+	15.5885i	0.443398	+	0.767988i
$413$	20.0000	−	34.6410i	0.984136	−	1.70457i
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$		0			0
$416$		0			0
$417$	−16.0000			−0.783523
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	−0.992559	−	0.121768i	$-0.961144\pi$
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	0.601733	+	0.798697i	$0.294477\pi$
$420$	−4.00000	−	6.92820i	−0.195180	−	0.338062i
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−14.0000	−	24.2487i	−0.681509	−	1.18041i
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$	2.00000			0.0971286
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	−10.0000	+	17.3205i	−0.484502	+	0.839181i
$427$	4.00000	−	6.92820i	0.193574	−	0.335279i
$428$	6.00000			0.290021
$429$		0			0
$430$	10.0000			0.482243
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	19.0000	+	32.9090i	0.913082	+	1.58150i	0.809686	+	0.586864i	$0.199638\pi$
$433$	19.0000	+	32.9090i	0.913082	+	1.58150i	0.103396	+	0.994640i	$0.467029\pi$
$434$	24.0000			1.15204
$435$	2.00000	+	3.46410i	0.0958927	+	0.166091i
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$	36.0000			1.72211
$438$	−10.0000	−	17.3205i	−0.477818	−	0.827606i
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$	−1.00000	+	1.73205i	−0.0476731	+	0.0825723i
$441$	9.00000			0.428571
$442$		0			0
$443$	−14.0000			−0.665160			−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000			−0.665160			−0.332580	+	0.943075i	$0.607919\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$	−7.00000	+	12.1244i	−0.331832	+	0.574750i
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$	4.00000			0.189194
$448$	2.00000	+	3.46410i	0.0944911	+	0.163663i
$449$	3.00000	+	5.19615i	0.141579	+	0.245222i	0.928091	−	0.372353i	$-0.121449\pi$
$449$	3.00000	+	5.19615i	0.141579	+	0.245222i	−0.786513	+	0.617574i	$0.788115\pi$
$450$	1.00000			0.0471405
$451$	10.0000	+	17.3205i	0.470882	+	0.815591i
$452$	−1.00000	+	1.73205i	−0.0470360	+	0.0814688i
$453$	−6.00000	+	10.3923i	−0.281905	+	0.488273i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	12.0000			0.561951
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−5.00000	+	8.66025i	−0.233635	+	0.404667i
$459$	4.00000	+	6.92820i	0.186704	+	0.323381i
$460$	−6.00000			−0.279751
$461$	3.00000	+	5.19615i	0.139724	+	0.242009i	0.927392	−	0.374091i	$-0.122045\pi$
$461$	3.00000	+	5.19615i	0.139724	+	0.242009i	−0.787668	+	0.616100i	$0.788712\pi$
$462$	−8.00000	−	13.8564i	−0.372194	−	0.644658i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	10.0000			0.462745			0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000			0.462745			0.231372	+	0.972865i	$0.425678\pi$
$468$		0			0
$469$	48.0000			2.21643
$470$	−6.00000	+	10.3923i	−0.276759	+	0.479361i
$471$	−10.0000	+	17.3205i	−0.460776	+	0.798087i
$472$	−5.00000	−	8.66025i	−0.230144	−	0.398621i
$473$	20.0000			0.919601
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$	−3.00000	−	5.19615i	−0.137649	−	0.238416i
$476$	−8.00000			−0.366679
$477$	−1.00000	−	1.73205i	−0.0457869	−	0.0793052i
$478$	13.0000	−	22.5167i	0.594606	−	1.02989i
$479$	−1.00000	+	1.73205i	−0.0456912	+	0.0791394i	−0.887967	−	0.459908i	$-0.847882\pi$
$479$	−1.00000	+	1.73205i	−0.0456912	+	0.0791394i	0.842275	+	0.539048i	$0.181216\pi$
$480$	−2.00000			−0.0912871
$481$		0			0
$482$	−22.0000			−1.00207
$483$	24.0000	−	41.5692i	1.09204	−	1.89146i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$	−10.0000			−0.453609
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	0.988374	−	0.152042i	$-0.0485850\pi$
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	−0.625859	+	0.779936i	$0.715252\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	−8.00000			−0.361773
$490$	4.50000	+	7.79423i	0.203289	+	0.352107i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	−10.0000	+	17.3205i	−0.450835	+	0.780869i
$493$	4.00000			0.180151
$494$		0			0
$495$	2.00000			0.0898933
$496$	3.00000	−	5.19615i	0.134704	−	0.233314i
$497$	20.0000	−	34.6410i	0.897123	−	1.55386i
$498$		0			0
$499$	38.0000			1.70111			0.850557	−	0.525883i	$-0.176265\pi$
$499$	38.0000			1.70111			0.850557	+	0.525883i	$0.176265\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−20.0000	−	34.6410i	−0.893534	−	1.54765i
$502$		0			0
$503$	7.00000	+	12.1244i	0.312115	+	0.540598i	0.978820	−	0.204723i	$-0.0656294\pi$
$503$	7.00000	+	12.1244i	0.312115	+	0.540598i	−0.666705	+	0.745321i	$0.732296\pi$
$504$	2.00000	−	3.46410i	0.0890871	−	0.154303i
$505$	7.00000	−	12.1244i	0.311496	−	0.539527i
$506$	−12.0000			−0.533465
$507$		0			0
$508$	−14.0000			−0.621150
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$	2.00000	−	3.46410i	0.0885615	−	0.153393i
$511$	20.0000	+	34.6410i	0.884748	+	1.53243i
$512$	1.00000			0.0441942
$513$	12.0000	+	20.7846i	0.529813	+	0.917663i
$514$	15.0000	+	25.9808i	0.661622	+	1.14596i
$515$	18.0000			0.793175
$516$	10.0000	+	17.3205i	0.440225	+	0.762493i
$517$	−12.0000	+	20.7846i	−0.527759	+	0.914106i
$518$	−4.00000	+	6.92820i	−0.175750	+	0.304408i
$519$	20.0000			0.877903
$520$		0			0
$521$	−26.0000			−1.13908			−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000			−1.13908			−0.569540	+	0.821963i	$0.692879\pi$
$522$	−1.00000	+	1.73205i	−0.0437688	+	0.0758098i
$523$	3.00000	−	5.19615i	0.131181	−	0.227212i	−0.792951	−	0.609285i	$-0.791456\pi$
$523$	3.00000	−	5.19615i	0.131181	−	0.227212i	0.924132	+	0.382073i	$0.124790\pi$
$524$	−2.00000	−	3.46410i	−0.0873704	−	0.151330i
$525$	−8.00000			−0.349149
$526$	−1.00000	−	1.73205i	−0.0436021	−	0.0755210i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	−4.00000			−0.174078
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	1.00000	−	1.73205i	0.0434372	−	0.0752355i
$531$	−5.00000	+	8.66025i	−0.216982	+	0.375823i
$532$	−24.0000			−1.04053
$533$		0			0
$534$	−28.0000			−1.21168
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	4.00000	+	6.92820i	0.172613	+	0.298974i
$538$	6.00000			0.258678
$539$	9.00000	+	15.5885i	0.387657	+	0.671442i
$540$	−2.00000	−	3.46410i	−0.0860663	−	0.149071i
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$	1.00000	+	1.73205i	0.0429537	+	0.0743980i
$543$	−10.0000	+	17.3205i	−0.429141	+	0.743294i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	6.00000			0.257012
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	12.0000			0.511217
$552$	−6.00000	−	10.3923i	−0.255377	−	0.442326i
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$	2.00000			0.0849719
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$	−19.0000	+	32.9090i	−0.805056	+	1.39440i	0.111198	+	0.993798i	$0.464531\pi$
$557$	−19.0000	+	32.9090i	−0.805056	+	1.39440i	−0.916253	+	0.400599i	$0.868802\pi$
$558$	−6.00000			−0.254000
$559$		0			0
$560$	4.00000			0.169031
$561$	4.00000	−	6.92820i	0.168880	−	0.292509i
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	0.795858	−	0.605483i	$-0.207020\pi$
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	−0.922293	+	0.386492i	$0.873687\pi$
$564$	−24.0000			−1.01058
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$	−7.00000	−	12.1244i	−0.294232	−	0.509625i
$567$	44.0000			1.84783
$568$	−5.00000	−	8.66025i	−0.209795	−	0.363376i
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$	6.00000	−	10.3923i	0.251312	−	0.435286i
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$		0			0
$574$	20.0000	−	34.6410i	0.834784	−	1.44589i
$575$	−3.00000	+	5.19615i	−0.125109	+	0.216695i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−14.0000	−	24.2487i	−0.581820	−	1.00774i
$580$	−2.00000			−0.0830455
$581$		0			0
$582$	−14.0000	+	24.2487i	−0.580319	+	1.00514i
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	10.0000			0.413803
$585$		0			0
$586$	22.0000			0.908812
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	−0.962872	−	0.269957i	$-0.912990\pi$
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	0.715226	+	0.698893i	$0.246324\pi$
$588$	−9.00000	+	15.5885i	−0.371154	+	0.642857i
$589$	18.0000	+	31.1769i	0.741677	+	1.28462i
$590$	−10.0000			−0.411693
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−2.00000			−0.0821302			−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000			−0.0821302			−0.0410651	+	0.999156i	$0.513075\pi$
$594$	−4.00000	−	6.92820i	−0.164122	−	0.284268i
$595$	−4.00000	+	6.92820i	−0.163984	+	0.284029i
$596$	−1.00000	+	1.73205i	−0.0409616	+	0.0709476i
$597$		0			0
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	−1.00000	+	1.73205i	−0.0408248	+	0.0707107i
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$	−20.0000	−	34.6410i	−0.815139	−	1.41186i
$603$	−12.0000			−0.488678
$604$	−3.00000	−	5.19615i	−0.122068	−	0.211428i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$	28.0000			1.13742
$607$	17.0000	+	29.4449i	0.690009	+	1.19513i	0.971834	+	0.235665i	$0.0757267\pi$
$607$	17.0000	+	29.4449i	0.690009	+	1.19513i	−0.281826	+	0.959466i	$0.590940\pi$
$608$	−3.00000	+	5.19615i	−0.121666	+	0.210732i
$609$	8.00000	−	13.8564i	0.324176	−	0.561490i
$610$	−2.00000			−0.0809776
$611$		0			0
$612$	2.00000			0.0808452
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	−12.0000	+	20.7846i	−0.484281	+	0.838799i
$615$	10.0000	+	17.3205i	0.403239	+	0.698430i
$616$	8.00000			0.322329
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$	18.0000	+	31.1769i	0.724066	+	1.25412i
$619$	−46.0000			−1.84890			−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000			−1.84890			−0.924448	+	0.381308i	$0.875474\pi$
$620$	−3.00000	−	5.19615i	−0.120483	−	0.208683i
$621$	12.0000	−	20.7846i	0.481543	−	0.834058i
$622$	6.00000	−	10.3923i	0.240578	−	0.416693i
$623$	56.0000			2.24359
$624$		0			0
$625$	1.00000			0.0400000
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	12.0000	−	20.7846i	0.479234	−	0.830057i
$628$	−5.00000	−	8.66025i	−0.199522	−	0.345582i
$629$	−4.00000			−0.159490
$630$	−2.00000	−	3.46410i	−0.0796819	−	0.138013i
$631$	−15.0000	−	25.9808i	−0.597141	−	1.03428i	−0.993241	−	0.116071i	$-0.962970\pi$
$631$	−15.0000	−	25.9808i	−0.597141	−	1.03428i	0.396100	−	0.918207i	$-0.370363\pi$
$632$	−4.00000			−0.159111
$633$	−28.0000	−	48.4974i	−1.11290	−	1.92760i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	−7.00000	+	12.1244i	−0.277787	+	0.481140i
$636$	4.00000			0.158610
$637$		0			0
$638$	−4.00000			−0.158362
$639$	−5.00000	+	8.66025i	−0.197797	+	0.342594i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	12.0000			0.473602
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	0.979541	−	0.201243i	$-0.0644981\pi$
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	−0.664052	+	0.747686i	$0.731165\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$	20.0000			0.787499
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−21.0000	+	36.3731i	−0.825595	+	1.42997i	0.0758684	+	0.997118i	$0.475827\pi$
$647$	−21.0000	+	36.3731i	−0.825595	+	1.42997i	−0.901464	+	0.432855i	$0.857506\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$	−20.0000			−0.785069
$650$		0			0
$651$	48.0000			1.88127
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$	6.00000	+	10.3923i	0.234619	+	0.406371i
$655$	−4.00000			−0.156293
$656$	−5.00000	−	8.66025i	−0.195217	−	0.338126i
$657$	−5.00000	−	8.66025i	−0.195069	−	0.337869i
$658$	48.0000			1.87123
$659$	−4.00000	−	6.92820i	−0.155818	−	0.269884i	0.777539	−	0.628835i	$-0.216468\pi$
$659$	−4.00000	−	6.92820i	−0.155818	−	0.269884i	−0.933357	+	0.358951i	$0.883135\pi$
$660$	−2.00000	+	3.46410i	−0.0778499	+	0.134840i
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	−0.411636	−	0.911348i	$-0.635043\pi$
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	0.995069	−	0.0991864i	$-0.0316240\pi$
$662$	−14.0000			−0.544125
$663$		0			0
$664$		0			0
$665$	−12.0000	+	20.7846i	−0.465340	+	0.805993i
$666$	1.00000	−	1.73205i	0.0387492	−	0.0671156i
$667$	−6.00000	−	10.3923i	−0.232321	−	0.402392i
$668$	20.0000			0.773823
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	−4.00000			−0.154418
$672$	4.00000	+	6.92820i	0.154303	+	0.267261i
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$	11.0000	−	19.0526i	0.423704	−	0.733877i
$675$	−4.00000			−0.153960
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$	−2.00000	+	3.46410i	−0.0768095	+	0.133038i
$679$	28.0000	−	48.4974i	1.07454	−	1.86116i
$680$	1.00000	+	1.73205i	0.0383482	+	0.0664211i
$681$	−8.00000			−0.306561
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	0.888366	+	0.459136i	$0.151841\pi$
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	−0.0465592	+	0.998916i	$0.514826\pi$
$684$	6.00000			0.229416
$685$	−9.00000	−	15.5885i	−0.343872	−	0.595604i
$686$	4.00000	−	6.92820i	0.152721	−	0.264520i
$687$	−10.0000	+	17.3205i	−0.381524	+	0.660819i
$688$	−10.0000			−0.381246
$689$		0			0
$690$	−12.0000			−0.456832
$691$	19.0000	−	32.9090i	0.722794	−	1.25192i	−0.237082	−	0.971490i	$-0.576191\pi$
$691$	19.0000	−	32.9090i	0.722794	−	1.25192i	0.959876	−	0.280426i	$-0.0904758\pi$
$692$	−5.00000	+	8.66025i	−0.190071	+	0.329213i
$693$	−4.00000	−	6.92820i	−0.151947	−	0.263181i
$694$	6.00000			0.227757
$695$	−4.00000	−	6.92820i	−0.151729	−	0.262802i
$696$	−2.00000	−	3.46410i	−0.0758098	−	0.131306i
$697$	20.0000			0.757554
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$	6.00000	−	10.3923i	0.226941	−	0.393073i
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	38.0000			1.43524			0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000			1.43524			0.717620	+	0.696435i	$0.245231\pi$
$702$		0			0
$703$	−12.0000			−0.452589
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	−12.0000	+	20.7846i	−0.451946	+	0.782794i
$706$	−17.0000	−	29.4449i	−0.639803	−	1.10817i
$707$	−56.0000			−2.10610
$708$	−10.0000	−	17.3205i	−0.375823	−	0.650945i
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	0.995228	−	0.0975728i	$-0.0311079\pi$
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	−0.582115	+	0.813107i	$0.697775\pi$
$710$	−10.0000			−0.375293
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	7.00000	−	12.1244i	0.262336	−	0.454379i
$713$	18.0000	−	31.1769i	0.674105	−	1.16758i
$714$	−16.0000			−0.598785
$715$		0			0
$716$	−4.00000			−0.149487
$717$	26.0000	−	45.0333i	0.970988	−	1.68180i
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$	−1.00000			−0.0372678
$721$	−36.0000	−	62.3538i	−1.34071	−	2.32218i
$722$	−8.50000	−	14.7224i	−0.316337	−	0.547912i
$723$	−44.0000			−1.63638
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	−1.00000	+	1.73205i	−0.0371391	+	0.0643268i
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	5.00000	−	8.66025i	0.185058	−	0.320530i
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$	−2.00000	−	3.46410i	−0.0739221	−	0.128037i
$733$	2.00000			0.0738717			0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000			0.0738717			0.0369358	+	0.999318i	$0.488240\pi$
$734$	−15.0000	−	25.9808i	−0.553660	−	0.958967i
$735$	9.00000	+	15.5885i	0.331970	+	0.574989i
$736$	6.00000			0.221163
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$	−5.00000	+	8.66025i	−0.184053	+	0.318788i
$739$	−21.0000	+	36.3731i	−0.772497	+	1.33800i	0.163693	+	0.986511i	$0.447659\pi$
$739$	−21.0000	+	36.3731i	−0.772497	+	1.33800i	−0.936190	+	0.351494i	$0.885674\pi$
$740$	2.00000			0.0735215
$741$		0			0
$742$	−8.00000			−0.293689
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$	6.00000	−	10.3923i	0.219971	−	0.381000i
$745$	1.00000	+	1.73205i	0.0366372	+	0.0634574i
$746$	−14.0000			−0.512576
$747$		0			0
$748$	2.00000	+	3.46410i	0.0731272	+	0.126660i
$749$	−24.0000			−0.876941
$750$	1.00000	+	1.73205i	0.0365148	+	0.0632456i
$751$	−22.0000	+	38.1051i	−0.802791	+	1.39048i	0.114981	+	0.993368i	$0.463319\pi$
$751$	−22.0000	+	38.1051i	−0.802791	+	1.39048i	−0.917772	+	0.397108i	$0.870014\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$		0			0
$754$		0			0
$755$	−6.00000			−0.218362
$756$	−8.00000	+	13.8564i	−0.290957	+	0.503953i
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	0.654827	+	0.755779i	$0.272742\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$	−24.0000			−0.871145
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	7.00000	+	12.1244i	0.253750	+	0.439508i	0.964555	−	0.263881i	$-0.0850027\pi$
$761$	7.00000	+	12.1244i	0.253750	+	0.439508i	−0.710805	+	0.703389i	$0.751669\pi$
$762$	−28.0000			−1.01433
$763$	−12.0000	−	20.7846i	−0.434429	−	0.752453i
$764$		0			0
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	12.0000			0.433578
$767$		0			0
$768$	2.00000			0.0721688
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	−0.941984	−	0.335657i	$-0.891042\pi$
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	0.761680	+	0.647954i	$0.224375\pi$
$770$	4.00000	−	6.92820i	0.144150	−	0.249675i
$771$	30.0000	+	51.9615i	1.08042	+	1.87135i
$772$	14.0000			0.503871
$773$	17.0000	+	29.4449i	0.611448	+	1.05906i	0.990997	+	0.133887i	$0.0427458\pi$
$773$	17.0000	+	29.4449i	0.611448	+	1.05906i	−0.379549	+	0.925172i	$0.623921\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$	−6.00000			−0.215526
$776$	−7.00000	−	12.1244i	−0.251285	−	0.435239i
$777$	−8.00000	+	13.8564i	−0.286998	+	0.497096i
$778$	5.00000	−	8.66025i	0.179259	−	0.310485i
$779$	60.0000			2.14972
$780$		0			0
$781$	−20.0000			−0.715656
$782$	−6.00000	+	10.3923i	−0.214560	+	0.371628i
$783$	4.00000	−	6.92820i	0.142948	−	0.247594i
$784$	−4.50000	−	7.79423i	−0.160714	−	0.278365i
$785$	−10.0000			−0.356915
$786$	−4.00000	−	6.92820i	−0.142675	−	0.247121i
$787$	4.00000	+	6.92820i	0.142585	+	0.246964i	0.928469	−	0.371409i	$-0.121125\pi$
$787$	4.00000	+	6.92820i	0.142585	+	0.246964i	−0.785885	+	0.618373i	$0.787792\pi$
$788$	−6.00000			−0.213741
$789$	−2.00000	−	3.46410i	−0.0712019	−	0.123325i
$790$	−2.00000	+	3.46410i	−0.0711568	+	0.123247i
$791$	4.00000	−	6.92820i	0.142224	−	0.246339i
$792$	−2.00000			−0.0710669
$793$		0			0
$794$	38.0000			1.34857
$795$	2.00000	−	3.46410i	0.0709327	−	0.122859i
$796$		0			0
$797$	11.0000	+	19.0526i	0.389640	+	0.674876i	0.992401	−	0.123045i	$-0.0392661\pi$
$797$	11.0000	+	19.0526i	0.389640	+	0.674876i	−0.602761	+	0.797922i	$0.705933\pi$
$798$	−48.0000			−1.69918
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−14.0000			−0.494666
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	10.0000	−	17.3205i	0.352892	−	0.611227i
$804$	12.0000	−	20.7846i	0.423207	−	0.733017i
$805$	24.0000			0.845889
$806$		0			0
$807$	12.0000			0.422420
$808$	−7.00000	+	12.1244i	−0.246259	+	0.426533i
$809$	17.0000	−	29.4449i	0.597688	−	1.03523i	−0.395473	−	0.918477i	$-0.629419\pi$
$809$	17.0000	−	29.4449i	0.597688	−	1.03523i	0.993161	−	0.116749i	$-0.0372472\pi$
$810$	−5.50000	−	9.52628i	−0.193250	−	0.334719i
$811$	−38.0000			−1.33436			−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000			−1.33436			−0.667180	+	0.744896i	$0.732499\pi$
$812$	4.00000	+	6.92820i	0.140372	+	0.243132i
$813$	2.00000	+	3.46410i	0.0701431	+	0.121491i
$814$	4.00000			0.140200
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	30.0000	−	51.9615i	1.04957	−	1.81790i
$818$	34.0000			1.18878
$819$		0			0
$820$	−10.0000			−0.349215
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.0131101	+	0.999914i	$0.504173\pi$
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.859396	+	0.511311i	$0.829160\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−18.0000			−0.627060
$825$	2.00000	+	3.46410i	0.0696311	+	0.120605i
$826$	20.0000	+	34.6410i	0.695889	+	1.20532i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$		0			0
$831$	4.00000			0.138758
$832$		0			0
$833$	18.0000			0.623663
$834$	8.00000	−	13.8564i	0.277017	−	0.479808i
$835$	10.0000	−	17.3205i	0.346064	−	0.599401i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	24.0000			0.829561
$838$	−8.00000	−	13.8564i	−0.276355	−	0.478662i
$839$	−13.0000	−	22.5167i	−0.448810	−	0.777361i	0.549499	−	0.835494i	$-0.314819\pi$
$839$	−13.0000	−	22.5167i	−0.448810	−	0.777361i	−0.998309	+	0.0581329i	$0.981485\pi$
$840$	8.00000			0.276026
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	28.0000			0.963800
$845$		0			0
$846$	−12.0000			−0.412568
$847$	−14.0000	+	24.2487i	−0.481046	+	0.833196i
$848$	−1.00000	+	1.73205i	−0.0343401	+	0.0594789i
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$	2.00000			0.0685994
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	−10.0000	−	17.3205i	−0.342594	−	0.593391i
$853$	−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	+	6.92820i	0.136877	+	0.237078i
$855$	3.00000	−	5.19615i	0.102598	−	0.177705i
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−14.0000			−0.478231			−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000			−0.478231			−0.239115	+	0.970991i	$0.576857\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$	−5.00000	+	8.66025i	−0.170499	+	0.295312i
$861$	40.0000	−	69.2820i	1.36320	−	2.36113i
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$	5.00000	+	8.66025i	0.170005	+	0.294457i
$866$	−38.0000			−1.29129
$867$	13.0000	+	22.5167i	0.441503	+	0.764706i
$868$	−12.0000	+	20.7846i	−0.407307	+	0.705476i
$869$	−4.00000	+	6.92820i	−0.135691	+	0.235023i
$870$	−4.00000			−0.135613
$871$		0			0
$872$	−6.00000			−0.203186
$873$	−7.00000	+	12.1244i	−0.236914	+	0.410347i
$874$	−18.0000	+	31.1769i	−0.608859	+	1.05457i
$875$	−2.00000	−	3.46410i	−0.0676123	−	0.117108i
$876$	20.0000			0.675737
$877$	7.00000	+	12.1244i	0.236373	+	0.409410i	0.959671	−	0.281126i	$-0.0907079\pi$
$877$	7.00000	+	12.1244i	0.236373	+	0.409410i	−0.723298	+	0.690536i	$0.757375\pi$
$878$	16.0000	+	27.7128i	0.539974	+	0.935262i
$879$	44.0000			1.48408
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	−3.00000	+	5.19615i	−0.101073	+	0.175063i	−0.912127	−	0.409908i	$-0.865561\pi$
$881$	−3.00000	+	5.19615i	−0.101073	+	0.175063i	0.811054	+	0.584971i	$0.198894\pi$
$882$	−4.50000	+	7.79423i	−0.151523	+	0.262445i
$883$	38.0000			1.27880			0.639401	−	0.768874i	$-0.279182\pi$
$883$	38.0000			1.27880			0.639401	+	0.768874i	$0.279182\pi$
$884$		0			0
$885$	−20.0000			−0.672293
$886$	7.00000	−	12.1244i	0.235170	−	0.407326i
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	−0.989463	−	0.144785i	$-0.953751\pi$
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	0.620119	+	0.784508i	$0.287084\pi$
$888$	2.00000	+	3.46410i	0.0671156	+	0.116248i
$889$	56.0000			1.87818
$890$	−7.00000	−	12.1244i	−0.234641	−	0.406409i
$891$	−11.0000	−	19.0526i	−0.368514	−	0.638285i
$892$	4.00000			0.133930
$893$	36.0000	+	62.3538i	1.20469	+	2.08659i
$894$	−2.00000	+	3.46410i	−0.0668900	+	0.115857i
$895$	−2.00000	+	3.46410i	−0.0668526	+	0.115792i
$896$	−4.00000			−0.133631
$897$		0			0
$898$	−6.00000			−0.200223
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$	−20.0000			−0.665927
$903$	−40.0000	−	69.2820i	−1.33112	−	2.30556i
$904$	−1.00000	−	1.73205i	−0.0332595	−	0.0576072i
$905$	−10.0000			−0.332411
$906$	−6.00000	−	10.3923i	−0.199337	−	0.345261i
$907$	7.00000	−	12.1244i	0.232431	−	0.402583i	−0.726092	−	0.687598i	$-0.758665\pi$
$907$	7.00000	−	12.1244i	0.232431	−	0.402583i	0.958523	+	0.285015i	$0.0919986\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$	14.0000			0.464351
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	−6.00000	+	10.3923i	−0.198680	+	0.344124i
$913$		0			0
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$	−4.00000			−0.132236
$916$	−5.00000	−	8.66025i	−0.165205	−	0.286143i
$917$	8.00000	+	13.8564i	0.264183	+	0.457579i
$918$	−8.00000			−0.264039
$919$	−2.00000	−	3.46410i	−0.0659739	−	0.114270i	0.831152	−	0.556046i	$-0.187682\pi$
$919$	−2.00000	−	3.46410i	−0.0659739	−	0.114270i	−0.897126	+	0.441776i	$0.854349\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	−24.0000	+	41.5692i	−0.790827	+	1.36975i
$922$	−6.00000			−0.197599
$923$		0			0
$924$	16.0000			0.526361
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	9.00000	+	15.5885i	0.295599	+	0.511992i
$928$	2.00000			0.0656532
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$	−6.00000	−	10.3923i	−0.196748	−	0.340777i
$931$	54.0000			1.76978
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$	−5.00000	+	8.66025i	−0.163605	+	0.283372i
$935$	4.00000			0.130814
$936$		0			0
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$	−24.0000	+	41.5692i	−0.783628	+	1.35728i
$939$	6.00000	−	10.3923i	0.195803	−	0.339140i
$940$	−6.00000	−	10.3923i	−0.195698	−	0.338960i
$941$	50.0000			1.62995			0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000			1.62995			0.814977	+	0.579494i	$0.196750\pi$
$942$	−10.0000	−	17.3205i	−0.325818	−	0.564333i
$943$	−30.0000	−	51.9615i	−0.976934	−	1.69210i
$944$	10.0000			0.325472
$945$	8.00000	+	13.8564i	0.260240	+	0.450749i
$946$	−10.0000	+	17.3205i	−0.325128	+	0.563138i
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	0.923670	+	0.383190i	$0.125175\pi$
$948$	−8.00000			−0.259828
$949$		0			0
$950$	6.00000			0.194666
$951$	18.0000	−	31.1769i	0.583690	−	1.01098i
$952$	4.00000	−	6.92820i	0.129641	−	0.224544i
$953$	−9.00000	−	15.5885i	−0.291539	−	0.504960i	0.682635	−	0.730759i	$-0.260834\pi$
$953$	−9.00000	−	15.5885i	−0.291539	−	0.504960i	−0.974174	+	0.225800i	$0.927501\pi$
$954$	2.00000			0.0647524
$955$		0			0
$956$	13.0000	+	22.5167i	0.420450	+	0.728241i
$957$	−8.00000			−0.258603
$958$	−1.00000	−	1.73205i	−0.0323085	−	0.0559600i
$959$	−36.0000	+	62.3538i	−1.16250	+	2.01351i
$960$	1.00000	−	1.73205i	0.0322749	−	0.0559017i
$961$	5.00000			0.161290
$962$		0			0
$963$	6.00000			0.193347
$964$	11.0000	−	19.0526i	0.354286	−	0.613642i
$965$	7.00000	−	12.1244i	0.225338	−	0.390297i
$966$	24.0000	+	41.5692i	0.772187	+	1.33747i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	−12.0000	−	20.7846i	−0.385496	−	0.667698i
$970$	−14.0000			−0.449513
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	0.659762	−	0.751475i	$-0.270657\pi$
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	−0.980677	+	0.195633i	$0.937324\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$	−16.0000	+	27.7128i	−0.512936	+	0.888432i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	2.00000			0.0640184
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$	−9.00000			−0.287494
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$		0			0
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$	−10.0000	−	17.3205i	−0.318788	−	0.552158i
$985$	−3.00000	+	5.19615i	−0.0955879	+	0.165563i
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$	96.0000			3.05571
$988$		0			0
$989$	−60.0000			−1.90789
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$	3.00000	+	5.19615i	0.0952501	+	0.164978i
$993$	−28.0000			−0.888553
$994$	20.0000	+	34.6410i	0.634361	+	1.09875i
$995$		0			0
$996$		0			0
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$	−19.0000	+	32.9090i	−0.601434	+	1.04172i
$999$	−4.00000	+	6.92820i	−0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.a.191.1		2
13.2	odd	12		1690.2.l.a.361.1		4
13.3	even	3	inner	1690.2.e.a.991.1		2
13.4	even	6		1690.2.a.e.1.1		1
13.5	odd	4		1690.2.l.a.1161.2		4
13.6	odd	12		1690.2.d.e.1351.1		2
13.7	odd	12		1690.2.d.e.1351.2		2
13.8	odd	4		1690.2.l.a.1161.1		4
13.9	even	3		130.2.a.c.1.1	✓	1
13.10	even	6		1690.2.e.g.991.1		2
13.11	odd	12		1690.2.l.a.361.2		4
13.12	even	2		1690.2.e.g.191.1		2
39.35	odd	6		1170.2.a.d.1.1		1
52.35	odd	6		1040.2.a.b.1.1		1
65.4	even	6		8450.2.a.n.1.1		1
65.9	even	6		650.2.a.c.1.1		1
65.22	odd	12		650.2.b.g.599.2		2
65.48	odd	12		650.2.b.g.599.1		2
91.48	odd	6		6370.2.a.l.1.1		1
104.35	odd	6		4160.2.a.t.1.1		1
104.61	even	6		4160.2.a.c.1.1		1
156.35	even	6		9360.2.a.by.1.1		1
195.74	odd	6		5850.2.a.cb.1.1		1
195.113	even	12		5850.2.e.u.5149.2		2
195.152	even	12		5850.2.e.u.5149.1		2
260.139	odd	6		5200.2.a.bd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.a.c.1.1	✓	1	13.9	even	3
650.2.a.c.1.1		1	65.9	even	6
650.2.b.g.599.1		2	65.48	odd	12
650.2.b.g.599.2		2	65.22	odd	12
1040.2.a.b.1.1		1	52.35	odd	6
1170.2.a.d.1.1		1	39.35	odd	6
1690.2.a.e.1.1		1	13.4	even	6
1690.2.d.e.1351.1		2	13.6	odd	12
1690.2.d.e.1351.2		2	13.7	odd	12
1690.2.e.a.191.1		2	1.1	even	1	trivial
1690.2.e.a.991.1		2	13.3	even	3	inner
1690.2.e.g.191.1		2	13.12	even	2
1690.2.e.g.991.1		2	13.10	even	6
1690.2.l.a.361.1		4	13.2	odd	12
1690.2.l.a.361.2		4	13.11	odd	12
1690.2.l.a.1161.1		4	13.8	odd	4
1690.2.l.a.1161.2		4	13.5	odd	4
4160.2.a.c.1.1		1	104.61	even	6
4160.2.a.t.1.1		1	104.35	odd	6
5200.2.a.bd.1.1		1	260.139	odd	6
5850.2.a.cb.1.1		1	195.74	odd	6
5850.2.e.u.5149.1		2	195.152	even	12
5850.2.e.u.5149.2		2	195.113	even	12
6370.2.a.l.1.1		1	91.48	odd	6
8450.2.a.n.1.1		1	65.4	even	6
9360.2.a.by.1.1		1	156.35	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +2.00000 q^{12} -4.00000 q^{14} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} -8.00000 q^{21} +(1.00000 + 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.00000 + 1.73205i) q^{24} +1.00000 q^{25} -4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(1.00000 + 1.73205i) q^{30} -6.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +2.00000 q^{34} +(-2.00000 - 3.46410i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 - 1.73205i) q^{37} +6.00000 q^{38} -1.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +(4.00000 - 6.92820i) q^{42} +(5.00000 + 8.66025i) q^{43} -2.00000 q^{44} +(0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{46} -12.0000 q^{47} +(-1.00000 - 1.73205i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +4.00000 q^{51} +2.00000 q^{53} +(2.00000 - 3.46410i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(2.00000 + 3.46410i) q^{56} +12.0000 q^{57} +(-1.00000 - 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{59} -2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} -4.00000 q^{66} +(6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-6.00000 - 10.3923i) q^{69} +4.00000 q^{70} +(-5.00000 - 8.66025i) q^{71} +(-0.500000 - 0.866025i) q^{72} +10.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-3.00000 + 5.19615i) q^{76} +8.00000 q^{77} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.00000 - 8.66025i) q^{82} +(4.00000 + 6.92820i) q^{84} +(1.00000 + 1.73205i) q^{85} -10.0000 q^{86} +(-2.00000 - 3.46410i) q^{87} +(1.00000 - 1.73205i) q^{88} +(7.00000 - 12.1244i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(6.00000 - 10.3923i) q^{93} +(6.00000 - 10.3923i) q^{94} +(3.00000 + 5.19615i) q^{95} +2.00000 q^{96} +(-7.00000 - 12.1244i) q^{97} +(-4.50000 - 7.79423i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} - 6 q^{19} + q^{20} - 16 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} + 2 q^{25} - 8 q^{27} + 4 q^{28} - 2 q^{29} + 2 q^{30} - 12 q^{31} - q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 2 q^{37} + 12 q^{38} - 2 q^{40} - 10 q^{41} + 8 q^{42} + 10 q^{43} - 4 q^{44} + q^{45} - 6 q^{46} - 24 q^{47} - 2 q^{48} - 9 q^{49} - q^{50} + 8 q^{51} + 4 q^{53} + 4 q^{54} - 2 q^{55} + 4 q^{56} + 24 q^{57} - 2 q^{58} - 10 q^{59} - 4 q^{60} - 2 q^{61} + 6 q^{62} + 4 q^{63} + 2 q^{64} - 8 q^{66} + 12 q^{67} - 2 q^{68} - 12 q^{69} + 8 q^{70} - 10 q^{71} - q^{72} + 20 q^{73} + 2 q^{74} - 2 q^{75} - 6 q^{76} + 16 q^{77} - 8 q^{79} + q^{80} + 11 q^{81} - 10 q^{82} + 8 q^{84} + 2 q^{85} - 20 q^{86} - 4 q^{87} + 2 q^{88} + 14 q^{89} - 2 q^{90} + 12 q^{92} + 12 q^{93} + 12 q^{94} + 6 q^{95} + 4 q^{96} - 14 q^{97} - 9 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^14 + 2 * q^15 - q^16 - 2 * q^17 + 2 * q^18 - 6 * q^19 + q^20 - 16 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 + 2 * q^25 - 8 * q^27 + 4 * q^28 - 2 * q^29 + 2 * q^30 - 12 * q^31 - q^32 + 4 * q^33 + 4 * q^34 - 4 * q^35 - q^36 + 2 * q^37 + 12 * q^38 - 2 * q^40 - 10 * q^41 + 8 * q^42 + 10 * q^43 - 4 * q^44 + q^45 - 6 * q^46 - 24 * q^47 - 2 * q^48 - 9 * q^49 - q^50 + 8 * q^51 + 4 * q^53 + 4 * q^54 - 2 * q^55 + 4 * q^56 + 24 * q^57 - 2 * q^58 - 10 * q^59 - 4 * q^60 - 2 * q^61 + 6 * q^62 + 4 * q^63 + 2 * q^64 - 8 * q^66 + 12 * q^67 - 2 * q^68 - 12 * q^69 + 8 * q^70 - 10 * q^71 - q^72 + 20 * q^73 + 2 * q^74 - 2 * q^75 - 6 * q^76 + 16 * q^77 - 8 * q^79 + q^80 + 11 * q^81 - 10 * q^82 + 8 * q^84 + 2 * q^85 - 20 * q^86 - 4 * q^87 + 2 * q^88 + 14 * q^89 - 2 * q^90 + 12 * q^92 + 12 * q^93 + 12 * q^94 + 6 * q^95 + 4 * q^96 - 14 * q^97 - 9 * q^98 - 4 * q^99

Introduction

L-functions

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