LMFDB - Embedded newform 845.2.e.b.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
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 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.b.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(2.00000 + 3.46410i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +3.00000 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} +(3.00000 - 5.19615i) 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} -10.0000 q^{31} +(2.50000 + 4.33013i) 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} -3.00000 q^{40} +(3.00000 - 5.19615i) 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} +4.00000 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} +(6.00000 + 10.3923i) q^{56} +12.0000 q^{57} +(1.00000 + 1.73205i) q^{58} +(-3.00000 - 5.19615i) q^{59} -2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-5.00000 + 8.66025i) q^{62} +(2.00000 - 3.46410i) q^{63} +7.00000 q^{64} +4.00000 q^{66} +(2.00000 - 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-6.00000 - 10.3923i) q^{69} -4.00000 q^{70} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -6.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-3.00000 + 5.19615i) q^{76} -8.00000 q^{77} -12.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} -16.0000 q^{83} +(4.00000 + 6.92820i) q^{84} +(1.00000 + 1.73205i) q^{85} -10.0000 q^{86} +(2.00000 + 3.46410i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-1.00000 + 1.73205i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(-10.0000 + 17.3205i) q^{93} +(2.00000 - 3.46410i) q^{94} +(-3.00000 - 5.19615i) q^{95} +10.0000 q^{96} +(1.00000 + 1.73205i) 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} + 6 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 + 6 * q^8 - q^9	$ 2 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 6 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} + 6 q^{24} + 2 q^{25} + 8 q^{27} - 4 q^{28} - 2 q^{29} + 2 q^{30} - 20 q^{31} + 5 q^{32} + 4 q^{33} - 4 q^{34} - 4 q^{35} + q^{36} + 2 q^{37} + 12 q^{38} - 6 q^{40} + 6 q^{41} + 8 q^{42} - 10 q^{43} - 4 q^{44} + q^{45} - 6 q^{46} + 8 q^{47} - 2 q^{48} - 9 q^{49} + q^{50} - 8 q^{51} + 4 q^{53} + 4 q^{54} + 2 q^{55} + 12 q^{56} + 24 q^{57} + 2 q^{58} - 6 q^{59} - 4 q^{60} - 2 q^{61} - 10 q^{62} + 4 q^{63} + 14 q^{64} + 8 q^{66} + 4 q^{67} + 2 q^{68} - 12 q^{69} - 8 q^{70} - 6 q^{71} - 3 q^{72} - 12 q^{73} - 2 q^{74} + 2 q^{75} - 6 q^{76} - 16 q^{77} - 24 q^{79} - q^{80} + 11 q^{81} - 6 q^{82} - 32 q^{83} + 8 q^{84} + 2 q^{85} - 20 q^{86} + 4 q^{87} - 6 q^{88} - 2 q^{89} + 2 q^{90} + 12 q^{92} - 20 q^{93} + 4 q^{94} - 6 q^{95} + 20 q^{96} + 2 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 + 6 * 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 + 6 * q^24 + 2 * q^25 + 8 * q^27 - 4 * q^28 - 2 * q^29 + 2 * q^30 - 20 * q^31 + 5 * q^32 + 4 * q^33 - 4 * q^34 - 4 * q^35 + q^36 + 2 * q^37 + 12 * q^38 - 6 * q^40 + 6 * q^41 + 8 * q^42 - 10 * q^43 - 4 * q^44 + q^45 - 6 * q^46 + 8 * q^47 - 2 * q^48 - 9 * q^49 + q^50 - 8 * q^51 + 4 * q^53 + 4 * q^54 + 2 * q^55 + 12 * q^56 + 24 * q^57 + 2 * q^58 - 6 * q^59 - 4 * q^60 - 2 * q^61 - 10 * q^62 + 4 * q^63 + 14 * q^64 + 8 * q^66 + 4 * q^67 + 2 * q^68 - 12 * q^69 - 8 * q^70 - 6 * q^71 - 3 * q^72 - 12 * q^73 - 2 * q^74 + 2 * q^75 - 6 * q^76 - 16 * q^77 - 24 * q^79 - q^80 + 11 * q^81 - 6 * q^82 - 32 * q^83 + 8 * q^84 + 2 * q^85 - 20 * q^86 + 4 * q^87 - 6 * q^88 - 2 * q^89 + 2 * q^90 + 12 * q^92 - 20 * q^93 + 4 * q^94 - 6 * q^95 + 20 * q^96 + 2 * q^97 + 9 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

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	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$	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	$0.560519\pi$
$8$	3.00000			1.06066
$9$	−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	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	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	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−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	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	3.00000	−	5.19615i	0.612372	−	1.06066i
$25$	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
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$	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
$40$	−3.00000			−0.474342
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$	4.00000	−	6.92820i	0.617213	−	1.06904i
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$	−2.00000			−0.301511
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$	−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
$56$	6.00000	+	10.3923i	0.801784	+	1.38873i
$57$	12.0000			1.58944
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−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	$0.874201\pi$
$62$	−5.00000	+	8.66025i	−0.635001	+	1.09985i
$63$	2.00000	−	3.46410i	0.251976	−	0.436436i
$64$	7.00000			0.875000
$65$		0			0
$66$	4.00000			0.492366
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$	−4.00000			−0.478091
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	−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
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$	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
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	−10.0000	+	17.3205i	−1.03695	+	1.79605i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$	10.0000			1.02062
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	4.50000	+	7.79423i	0.454569	+	0.787336i
$99$	2.00000			0.201008
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	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	$-0.186539\pi$
$102$	−2.00000	+	3.46410i	−0.198030	+	0.342997i
$103$	2.00000			0.197066			0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000			0.197066			0.0985329	+	0.995134i	$0.468585\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	1.00000	−	1.73205i	0.0971286	−	0.168232i
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	−0.999818	−	0.0190994i	$-0.993920\pi$
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	0.516449	+	0.856318i	$0.327253\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$	−2.00000	−	3.46410i	−0.189832	−	0.328798i
$112$	4.00000			0.377964
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$	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
$118$	−6.00000			−0.552345
$119$	4.00000	−	6.92820i	0.366679	−	0.635107i
$120$	−3.00000	+	5.19615i	−0.273861	+	0.474342i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−2.00000			−0.181071
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$	−1.00000			−0.0894427
$126$	−2.00000	−	3.46410i	−0.178174	−	0.308607i
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	−20.0000			−1.76090
$130$		0			0
$131$	20.0000			1.74741			0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000			1.74741			0.873704	+	0.486458i	$0.161711\pi$
$132$	−2.00000	+	3.46410i	−0.174078	+	0.301511i
$133$	−12.0000	+	20.7846i	−1.04053	+	1.80225i
$134$	−2.00000	−	3.46410i	−0.172774	−	0.299253i
$135$	−4.00000			−0.344265
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	−12.0000			−1.02151
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$	2.00000	−	3.46410i	0.169031	−	0.292770i
$141$	4.00000	−	6.92820i	0.336861	−	0.583460i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	−3.00000	+	5.19615i	−0.248282	+	0.430037i
$147$	9.00000	+	15.5885i	0.742307	+	1.28571i
$148$	2.00000			0.164399
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$	9.00000	+	15.5885i	0.729996	+	1.26439i
$153$	−1.00000	+	1.73205i	−0.0808452	+	0.140028i
$154$	−4.00000	+	6.92820i	−0.322329	+	0.558291i
$155$	10.0000			0.803219
$156$		0			0
$157$	−6.00000			−0.478852			−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000			−0.478852			−0.239426	+	0.970915i	$0.576959\pi$
$158$	−6.00000	+	10.3923i	−0.477334	+	0.826767i
$159$	2.00000	−	3.46410i	0.158610	−	0.274721i
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$	24.0000			1.89146
$162$	−5.50000	−	9.52628i	−0.432121	−	0.748455i
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	0.999410	−	0.0343508i	$-0.0109363\pi$
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	−0.529454	+	0.848339i	$0.677603\pi$
$164$	6.00000			0.468521
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	−8.00000	+	13.8564i	−0.620920	+	1.07547i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$	24.0000			1.85164
$169$		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
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	4.00000			0.303239
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	−12.0000			−0.901975
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	−4.00000			−0.295689
$184$	9.00000	−	15.5885i	0.663489	−	1.14920i
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$	10.0000	+	17.3205i	0.733236	+	1.27000i
$187$	4.00000			0.292509
$188$	2.00000	+	3.46410i	0.145865	+	0.252646i
$189$	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	$0.833333\pi$
$192$	7.00000	−	12.1244i	0.505181	−	0.875000i
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$	2.00000			0.143592
$195$		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
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	3.00000			0.212132
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	−8.00000			−0.561490
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	1.00000	−	1.73205i	0.0696733	−	0.120678i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−12.0000			−0.830057
$210$	−4.00000	+	6.92820i	−0.276026	+	0.478091i
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	−0.995222	−	0.0976347i	$-0.968872\pi$
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	0.582165	+	0.813070i	$0.302206\pi$
$212$	1.00000	+	1.73205i	0.0686803	+	0.118958i
$213$	−12.0000			−0.822226
$214$	5.00000	+	8.66025i	0.341793	+	0.592003i
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$	12.0000			0.816497
$217$	−20.0000	−	34.6410i	−1.35769	−	2.35159i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	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	$0.209426\pi$
$224$	−10.0000	+	17.3205i	−0.668153	+	1.15728i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	14.0000			0.931266
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	0.791989	−	0.610535i	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$	−8.00000	+	13.8564i	−0.526361	+	0.911685i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$		0			0
$235$	−4.00000			−0.260931
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	−12.0000	+	20.7846i	−0.779484	+	1.35011i
$238$	−4.00000	−	6.92820i	−0.259281	−	0.449089i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	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
$246$	−12.0000			−0.765092
$247$		0			0
$248$	−30.0000			−1.90500
$249$	−16.0000	+	27.7128i	−1.01396	+	1.75623i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−12.0000	−	20.7846i	−0.757433	−	1.31191i	−0.944156	−	0.329500i	$-0.893120\pi$
$251$	−12.0000	−	20.7846i	−0.757433	−	1.31191i	0.186722	−	0.982413i	$-0.440214\pi$
$252$	4.00000			0.251976
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$	4.00000			0.250490
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	−10.0000	+	17.3205i	−0.622573	+	1.07833i
$259$	8.00000			0.497096
$260$		0			0
$261$	2.00000			0.123797
$262$	10.0000	−	17.3205i	0.617802	−	1.07006i
$263$	−7.00000	+	12.1244i	−0.431638	+	0.747620i	−0.997015	−	0.0772134i	$-0.975398\pi$
$263$	−7.00000	+	12.1244i	−0.431638	+	0.747620i	0.565376	+	0.824833i	$0.308731\pi$
$264$	6.00000	+	10.3923i	0.369274	+	0.639602i
$265$	−2.00000			−0.122859
$266$	12.0000	+	20.7846i	0.735767	+	1.27439i
$267$	2.00000	+	3.46410i	0.122398	+	0.212000i
$268$	4.00000			0.244339
$269$	−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	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	2.00000			0.120824
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	6.00000	−	10.3923i	0.361158	−	0.625543i
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	0.995997	−	0.0893846i	$-0.0284900\pi$
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	−0.575408	+	0.817867i	$0.695157\pi$
$278$		0			0
$279$	5.00000	+	8.66025i	0.299342	+	0.518476i
$280$	−6.00000	−	10.3923i	−0.358569	−	0.621059i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−4.00000	−	6.92820i	−0.238197	−	0.412568i
$283$	−1.00000	+	1.73205i	−0.0594438	+	0.102960i	−0.894216	−	0.447636i	$-0.852266\pi$
$283$	−1.00000	+	1.73205i	−0.0594438	+	0.102960i	0.834772	+	0.550596i	$0.185599\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−12.0000			−0.710819
$286$		0			0
$287$	24.0000			1.41668
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$	4.00000			0.234484
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	−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
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	3.00000	−	5.19615i	0.174371	−	0.302020i
$297$	−4.00000	+	6.92820i	−0.232104	+	0.402015i
$298$	−18.0000			−1.04271
$299$		0			0
$300$	2.00000			0.115470
$301$	20.0000	−	34.6410i	1.15278	−	1.99667i
$302$	5.00000	−	8.66025i	0.287718	−	0.498342i
$303$	−18.0000	−	31.1769i	−1.03407	−	1.79107i
$304$	6.00000			0.344124
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	1.00000	+	1.73205i	0.0571662	+	0.0990148i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−4.00000	−	6.92820i	−0.227921	−	0.394771i
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$	5.00000	−	8.66025i	0.283981	−	0.491869i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−3.00000	+	5.19615i	−0.169300	+	0.293236i
$315$	−2.00000	+	3.46410i	−0.112687	+	0.195180i
$316$	−6.00000	−	10.3923i	−0.337526	−	0.584613i
$317$	−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
$320$	−7.00000			−0.391312
$321$	10.0000	+	17.3205i	0.558146	+	0.966736i
$322$	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
$326$	12.0000			0.664619
$327$	10.0000	−	17.3205i	0.553001	−	0.957826i
$328$	9.00000	−	15.5885i	0.496942	−	0.860729i
$329$	8.00000	+	13.8564i	0.441054	+	0.763928i
$330$	−4.00000			−0.220193
$331$	9.00000	+	15.5885i	0.494685	+	0.856819i	0.999981	−	0.00612670i	$-0.00195020\pi$
$331$	9.00000	+	15.5885i	0.494685	+	0.856819i	−0.505296	+	0.862946i	$0.668617\pi$
$332$	−8.00000	−	13.8564i	−0.439057	−	0.760469i
$333$	−2.00000			−0.109599
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	−2.00000	+	3.46410i	−0.109272	+	0.189264i
$336$	4.00000	−	6.92820i	0.218218	−	0.377964i
$337$	26.0000			1.41631			0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000			1.41631			0.708155	+	0.706057i	$0.249528\pi$
$338$		0			0
$339$	28.0000			1.52075
$340$	−1.00000	+	1.73205i	−0.0542326	+	0.0939336i
$341$	10.0000	−	17.3205i	0.541530	−	0.937958i
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$	−8.00000			−0.431959
$344$	−15.0000	−	25.9808i	−0.808746	−	1.40079i
$345$	6.00000	+	10.3923i	0.323029	+	0.559503i
$346$	6.00000			0.322562
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	0.994164	+	0.107883i	$0.0344071\pi$
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	−0.403653	+	0.914912i	$0.632260\pi$
$348$	−2.00000	+	3.46410i	−0.107211	+	0.185695i
$349$	15.0000	−	25.9808i	0.802932	−	1.39072i	−0.114747	−	0.993395i	$-0.536606\pi$
$349$	15.0000	−	25.9808i	0.802932	−	1.39072i	0.917679	−	0.397324i	$-0.130061\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−10.0000			−0.533002
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	−2.00000			−0.106000
$357$	−8.00000	−	13.8564i	−0.423405	−	0.733359i
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−10.0000			−0.527780			−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000			−0.527780			−0.263890	+	0.964553i	$0.585006\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$	14.0000			0.734809
$364$		0			0
$365$	6.00000			0.314054
$366$	−2.00000	+	3.46410i	−0.104542	+	0.181071i
$367$	7.00000	−	12.1244i	0.365397	−	0.632886i	−0.623443	−	0.781869i	$-0.714267\pi$
$367$	7.00000	−	12.1244i	0.365397	−	0.632886i	0.988840	+	0.148983i	$0.0475999\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	−6.00000			−0.312348
$370$	1.00000	+	1.73205i	0.0519875	+	0.0900450i
$371$	4.00000	+	6.92820i	0.207670	+	0.359694i
$372$	−20.0000			−1.03695
$373$	−17.0000	−	29.4449i	−0.880227	−	1.52460i	−0.851089	−	0.525022i	$-0.824057\pi$
$373$	−17.0000	−	29.4449i	−0.880227	−	1.52460i	−0.0291379	−	0.999575i	$-0.509276\pi$
$374$	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
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	−0.965392	−	0.260804i	$-0.916012\pi$
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	0.708559	+	0.705652i	$0.249346\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	−2.00000	−	3.46410i	−0.102463	−	0.177471i
$382$		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	$0.932520\pi$
$384$	3.00000	+	5.19615i	0.153093	+	0.265165i
$385$	8.00000			0.407718
$386$	−1.00000	−	1.73205i	−0.0508987	−	0.0881591i
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	−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
$392$	−13.5000	+	23.3827i	−0.681853	+	1.18100i
$393$	20.0000	−	34.6410i	1.00887	−	1.74741i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	12.0000			0.603786
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	0.780870	−	0.624694i	$-0.214776\pi$
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	−0.931436	+	0.363906i	$0.881443\pi$
$398$	16.0000			0.802008
$399$	24.0000	+	41.5692i	1.20150	+	2.08106i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	−0.963439	−	0.267927i	$-0.913661\pi$
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	0.713751	+	0.700399i	$0.246995\pi$
$402$	−8.00000			−0.399004
$403$		0			0
$404$	18.0000			0.895533
$405$	−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
$408$	−12.0000			−0.594089
$409$	−9.00000	−	15.5885i	−0.445021	−	0.770800i	0.553032	−	0.833160i	$-0.313471\pi$
$409$	−9.00000	−	15.5885i	−0.445021	−	0.770800i	−0.998054	+	0.0623602i	$0.980137\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	4.00000			0.197305
$412$	1.00000	+	1.73205i	0.0492665	+	0.0853320i
$413$	12.0000	−	20.7846i	0.590481	−	1.02274i
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	16.0000			0.785409
$416$		0			0
$417$		0			0
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	20.0000	−	34.6410i	0.977064	−	1.69232i	0.304115	−	0.952635i	$-0.401639\pi$
$419$	20.0000	−	34.6410i	0.977064	−	1.69232i	0.672949	−	0.739689i	$-0.265027\pi$
$420$	−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	$0.421644\pi$
$422$	6.00000	+	10.3923i	0.292075	+	0.505889i
$423$	−2.00000	−	3.46410i	−0.0972433	−	0.168430i
$424$	6.00000			0.291386
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$	4.00000	−	6.92820i	0.193574	−	0.335279i
$428$	−10.0000			−0.483368
$429$		0			0
$430$	10.0000			0.482243
$431$	−7.00000	+	12.1244i	−0.337178	+	0.584010i	−0.983901	−	0.178716i	$-0.942806\pi$
$431$	−7.00000	+	12.1244i	−0.337178	+	0.584010i	0.646723	+	0.762725i	$0.276139\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−5.00000	−	8.66025i	−0.240285	−	0.416185i	0.720511	−	0.693444i	$-0.243907\pi$
$433$	−5.00000	−	8.66025i	−0.240285	−	0.416185i	−0.960795	+	0.277259i	$0.910574\pi$
$434$	−40.0000			−1.92006
$435$	−2.00000	−	3.46410i	−0.0958927	−	0.166091i
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	36.0000			1.72211
$438$	6.00000	+	10.3923i	0.286691	+	0.496564i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	3.00000	−	5.19615i	0.143019	−	0.247717i
$441$	9.00000			0.428571
$442$		0			0
$443$	14.0000			0.665160			0.332580	−	0.943075i	$-0.392081\pi$
$443$	14.0000			0.665160			0.332580	+	0.943075i	$0.392081\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$	1.00000	−	1.73205i	0.0474045	−	0.0821071i
$446$	2.00000	+	3.46410i	0.0947027	+	0.164030i
$447$	−36.0000			−1.70274
$448$	14.0000	+	24.2487i	0.661438	+	1.14564i
$449$	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
$451$	6.00000	+	10.3923i	0.282529	+	0.489355i
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	36.0000			1.68585
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.0474665	+	0.998873i	$0.515115\pi$
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.841316	+	0.540544i	$0.818219\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$	−4.00000	−	6.92820i	−0.186704	−	0.323381i
$460$	−6.00000			−0.279751
$461$	−5.00000	−	8.66025i	−0.232873	−	0.403348i	0.725779	−	0.687928i	$-0.241479\pi$
$461$	−5.00000	−	8.66025i	−0.232873	−	0.403348i	−0.958652	+	0.284579i	$0.908146\pi$
$462$	8.00000	+	13.8564i	0.372194	+	0.644658i
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$	10.0000	−	17.3205i	0.463739	−	0.803219i
$466$	5.00000	−	8.66025i	0.231621	−	0.401179i
$467$	−10.0000			−0.462745			−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000			−0.462745			−0.231372	+	0.972865i	$0.574322\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	−6.00000	+	10.3923i	−0.276465	+	0.478852i
$472$	−9.00000	−	15.5885i	−0.414259	−	0.717517i
$473$	20.0000			0.919601
$474$	12.0000	+	20.7846i	0.551178	+	0.954669i
$475$	3.00000	+	5.19615i	0.137649	+	0.238416i
$476$	8.00000			0.366679
$477$	−1.00000	−	1.73205i	−0.0457869	−	0.0793052i
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$	−10.0000			−0.456435
$481$		0			0
$482$	−10.0000			−0.455488
$483$	24.0000	−	41.5692i	1.09204	−	1.89146i
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$	−10.0000			−0.453609
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$	24.0000			1.08532
$490$	−4.50000	−	7.79423i	−0.203289	−	0.352107i
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	−0.457263	−	0.889332i	$-0.651170\pi$
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	0.998815	−	0.0486647i	$-0.0154966\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	4.00000			0.180151
$494$		0			0
$495$	−2.00000			−0.0898933
$496$	−5.00000	+	8.66025i	−0.224507	+	0.388857i
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$	16.0000	+	27.7128i	0.716977	+	1.24184i
$499$	10.0000			0.447661			0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000			0.447661			0.223831	+	0.974628i	$0.428144\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−12.0000	−	20.7846i	−0.536120	−	0.928588i
$502$	−24.0000			−1.07117
$503$	9.00000	+	15.5885i	0.401290	+	0.695055i	0.993882	−	0.110448i	$-0.0352286\pi$
$503$	9.00000	+	15.5885i	0.401290	+	0.695055i	−0.592592	+	0.805503i	$0.701895\pi$
$504$	6.00000	−	10.3923i	0.267261	−	0.462910i
$505$	−9.00000	+	15.5885i	−0.400495	+	0.693677i
$506$	12.0000			0.533465
$507$		0			0
$508$	2.00000			0.0887357
$509$	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
$511$	−12.0000	−	20.7846i	−0.530849	−	0.919457i
$512$	11.0000			0.486136
$513$	12.0000	+	20.7846i	0.529813	+	0.917663i
$514$	1.00000	+	1.73205i	0.0441081	+	0.0763975i
$515$	−2.00000			−0.0881305
$516$	−10.0000	−	17.3205i	−0.440225	−	0.762493i
$517$	−4.00000	+	6.92820i	−0.175920	+	0.304702i
$518$	4.00000	−	6.92820i	0.175750	−	0.304408i
$519$	12.0000			0.526742
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	1.00000	−	1.73205i	0.0437688	−	0.0758098i
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	−0.924132	−	0.382073i	$-0.875210\pi$
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	0.792951	+	0.609285i	$0.208544\pi$
$524$	10.0000	+	17.3205i	0.436852	+	0.756650i
$525$	8.00000			0.349149
$526$	7.00000	+	12.1244i	0.305215	+	0.528647i
$527$	10.0000	+	17.3205i	0.435607	+	0.754493i
$528$	4.00000			0.174078
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−1.00000	+	1.73205i	−0.0434372	+	0.0752355i
$531$	−3.00000	+	5.19615i	−0.130189	+	0.225494i
$532$	−24.0000			−1.04053
$533$		0			0
$534$	4.00000			0.173097
$535$	5.00000	−	8.66025i	0.216169	−	0.374415i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	12.0000	+	20.7846i	0.517838	+	0.896922i
$538$	−6.00000			−0.258678
$539$	−9.00000	−	15.5885i	−0.387657	−	0.671442i
$540$	−2.00000	−	3.46410i	−0.0860663	−	0.149071i
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$	1.00000	+	1.73205i	0.0429537	+	0.0743980i
$543$	−22.0000	+	38.1051i	−0.944110	+	1.63525i
$544$	5.00000	−	8.66025i	0.214373	−	0.371305i
$545$	−10.0000			−0.428353
$546$		0			0
$547$	−6.00000			−0.256541			−0.128271	−	0.991739i	$-0.540943\pi$
$547$	−6.00000			−0.256541			−0.128271	+	0.991739i	$0.540943\pi$
$548$	−1.00000	+	1.73205i	−0.0427179	+	0.0739895i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−12.0000			−0.511217
$552$	−18.0000	−	31.1769i	−0.766131	−	1.32698i
$553$	−24.0000	−	41.5692i	−1.02058	−	1.76770i
$554$	14.0000			0.594803
$555$	2.00000	+	3.46410i	0.0848953	+	0.147043i
$556$		0			0
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	−0.447387	−	0.894340i	$-0.647645\pi$
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	0.998215	−	0.0597213i	$-0.0190212\pi$
$558$	10.0000			0.423334
$559$		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
$563$	11.0000	+	19.0526i	0.463595	+	0.802970i	0.999137	−	0.0415389i	$-0.0132260\pi$
$563$	11.0000	+	19.0526i	0.463595	+	0.802970i	−0.535542	+	0.844508i	$0.679893\pi$
$564$	8.00000			0.336861
$565$	−7.00000	−	12.1244i	−0.294492	−	0.510075i
$566$	1.00000	+	1.73205i	0.0420331	+	0.0728035i
$567$	44.0000			1.84783
$568$	−9.00000	−	15.5885i	−0.377632	−	0.654077i
$569$	13.0000	−	22.5167i	0.544988	−	0.943948i	−0.453619	−	0.891196i	$-0.649867\pi$
$569$	13.0000	−	22.5167i	0.544988	−	0.943948i	0.998608	−	0.0527519i	$-0.0167993\pi$
$570$	−6.00000	+	10.3923i	−0.251312	+	0.435286i
$571$	24.0000			1.00437			0.502184	−	0.864761i	$-0.332530\pi$
$571$	24.0000			1.00437			0.502184	+	0.864761i	$0.332530\pi$
$572$		0			0
$573$		0			0
$574$	12.0000	−	20.7846i	0.500870	−	0.867533i
$575$	3.00000	−	5.19615i	0.125109	−	0.216695i
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	2.00000			0.0830455
$581$	−32.0000	−	55.4256i	−1.32758	−	2.29944i
$582$	2.00000	−	3.46410i	0.0829027	−	0.143592i
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−18.0000			−0.744845
$585$		0			0
$586$	−22.0000			−0.908812
$587$	22.0000	−	38.1051i	0.908037	−	1.57277i	0.0912496	−	0.995828i	$-0.470914\pi$
$587$	22.0000	−	38.1051i	0.908037	−	1.57277i	0.816788	−	0.576938i	$-0.195753\pi$
$588$	−9.00000	+	15.5885i	−0.371154	+	0.642857i
$589$	−30.0000	−	51.9615i	−1.23613	−	2.14104i
$590$	6.00000			0.247016
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$	4.00000	+	6.92820i	0.164122	+	0.284268i
$595$	−4.00000	+	6.92820i	−0.163984	+	0.284029i
$596$	9.00000	−	15.5885i	0.368654	−	0.638528i
$597$	32.0000			1.30967
$598$		0			0
$599$	−4.00000			−0.163436			−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000			−0.163436			−0.0817178	+	0.996656i	$0.526041\pi$
$600$	3.00000	−	5.19615i	0.122474	−	0.212132i
$601$	−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
$603$	−4.00000			−0.162893
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$	−36.0000			−1.46240
$607$	−17.0000	−	29.4449i	−0.690009	−	1.19513i	−0.971834	−	0.235665i	$-0.924273\pi$
$607$	−17.0000	−	29.4449i	−0.690009	−	1.19513i	0.281826	−	0.959466i	$-0.409060\pi$
$608$	−15.0000	+	25.9808i	−0.608330	+	1.05366i
$609$	−8.00000	+	13.8564i	−0.324176	+	0.561490i
$610$	2.00000			0.0809776
$611$		0			0
$612$	−2.00000			−0.0808452
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	−0.799060	−	0.601251i	$-0.794669\pi$
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	0.920229	+	0.391381i	$0.128002\pi$
$614$	4.00000	−	6.92820i	0.161427	−	0.279600i
$615$	6.00000	+	10.3923i	0.241943	+	0.419058i
$616$	−24.0000			−0.966988
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	0.885249	+	0.465118i	$0.153988\pi$
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	−0.0398207	+	0.999207i	$0.512679\pi$
$618$	−2.00000	−	3.46410i	−0.0804518	−	0.139347i
$619$	−2.00000			−0.0803868			−0.0401934	−	0.999192i	$-0.512797\pi$
$619$	−2.00000			−0.0803868			−0.0401934	+	0.999192i	$0.512797\pi$
$620$	5.00000	+	8.66025i	0.200805	+	0.347804i
$621$	12.0000	−	20.7846i	0.481543	−	0.834058i
$622$	−2.00000	+	3.46410i	−0.0801927	+	0.138898i
$623$	−8.00000			−0.320513
$624$		0			0
$625$	1.00000			0.0400000
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$	−12.0000	+	20.7846i	−0.479234	+	0.830057i
$628$	−3.00000	−	5.19615i	−0.119713	−	0.207349i
$629$	−4.00000			−0.159490
$630$	2.00000	+	3.46410i	0.0796819	+	0.138013i
$631$	7.00000	+	12.1244i	0.278666	+	0.482663i	0.971053	−	0.238863i	$-0.0767746\pi$
$631$	7.00000	+	12.1244i	0.278666	+	0.482663i	−0.692388	+	0.721526i	$0.743441\pi$
$632$	−36.0000			−1.43200
$633$	12.0000	+	20.7846i	0.476957	+	0.826114i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−1.00000	+	1.73205i	−0.0396838	+	0.0687343i
$636$	4.00000			0.158610
$637$		0			0
$638$	−4.00000			−0.158362
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	23.0000	+	39.8372i	0.908445	+	1.57347i	0.816224	+	0.577735i	$0.196063\pi$
$641$	23.0000	+	39.8372i	0.908445	+	1.57347i	0.0922210	+	0.995739i	$0.470603\pi$
$642$	20.0000			0.789337
$643$	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
$647$	−19.0000	+	32.9090i	−0.746967	+	1.29378i	0.202303	+	0.979323i	$0.435157\pi$
$647$	−19.0000	+	32.9090i	−0.746967	+	1.29378i	−0.949270	+	0.314462i	$0.898176\pi$
$648$	16.5000	−	28.5788i	0.648181	−	1.12268i
$649$	12.0000			0.471041
$650$		0			0
$651$	−80.0000			−3.13545
$652$	−6.00000	+	10.3923i	−0.234978	+	0.406994i
$653$	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	$0.129211\pi$
$654$	−10.0000	−	17.3205i	−0.391031	−	0.677285i
$655$	−20.0000			−0.781465
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	3.00000	+	5.19615i	0.117041	+	0.202721i
$658$	16.0000			0.623745
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	18.0000			0.699590
$663$		0			0
$664$	−48.0000			−1.86276
$665$	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
$668$	12.0000			0.464294
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$	4.00000			0.154418
$672$	20.0000	+	34.6410i	0.771517	+	1.33631i
$673$	15.0000	−	25.9808i	0.578208	−	1.00148i	−0.417477	−	0.908687i	$-0.637086\pi$
$673$	15.0000	−	25.9808i	0.578208	−	1.00148i	0.995685	−	0.0927975i	$-0.0295809\pi$
$674$	13.0000	−	22.5167i	0.500741	−	0.867309i
$675$	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	$0.536783\pi$
$678$	14.0000	−	24.2487i	0.537667	−	0.931266i
$679$	−4.00000	+	6.92820i	−0.153506	+	0.265880i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$	−8.00000			−0.306561
$682$	−10.0000	−	17.3205i	−0.382920	−	0.663237i
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	0.991439	−	0.130573i	$-0.0416818\pi$
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	−0.608799	+	0.793324i	$0.708349\pi$
$684$	6.00000			0.229416
$685$	−1.00000	−	1.73205i	−0.0382080	−	0.0661783i
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$	−22.0000	+	38.1051i	−0.839352	+	1.45380i
$688$	−10.0000			−0.381246
$689$		0			0
$690$	12.0000			0.456832
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	−0.995785	−	0.0917209i	$-0.970763\pi$
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	0.577325	+	0.816514i	$0.304097\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$	4.00000	+	6.92820i	0.151947	+	0.263181i
$694$	22.0000			0.835109
$695$		0			0
$696$	6.00000	+	10.3923i	0.227429	+	0.393919i
$697$	−12.0000			−0.454532
$698$	−15.0000	−	25.9808i	−0.567758	−	0.983386i
$699$	10.0000	−	17.3205i	0.378235	−	0.655122i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$		0			0
$703$	12.0000			0.452589
$704$	−7.00000	+	12.1244i	−0.263822	+	0.456954i
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$	72.0000			2.70784
$708$	−6.00000	−	10.3923i	−0.225494	−	0.390567i
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	6.00000			0.225176
$711$	6.00000	+	10.3923i	0.225018	+	0.389742i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	−30.0000	+	51.9615i	−1.12351	+	1.94597i
$714$	−16.0000			−0.598785
$715$		0			0
$716$	−12.0000			−0.448461
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	16.0000	+	27.7128i	0.596699	+	1.03351i	0.993305	+	0.115524i	$0.0368548\pi$
$719$	16.0000	+	27.7128i	0.596699	+	1.03351i	−0.396605	+	0.917989i	$0.629812\pi$
$720$	1.00000			0.0372678
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$	−20.0000			−0.743808
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	−1.00000	+	1.73205i	−0.0371391	+	0.0643268i
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	−18.0000			−0.667583			−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000			−0.667583			−0.333792	+	0.942647i	$0.608328\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$	−2.00000	−	3.46410i	−0.0739221	−	0.128037i
$733$	34.0000			1.25582			0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000			1.25582			0.627909	+	0.778287i	$0.283911\pi$
$734$	−7.00000	−	12.1244i	−0.258375	−	0.447518i
$735$	−9.00000	−	15.5885i	−0.331970	−	0.574989i
$736$	30.0000			1.10581
$737$	4.00000	+	6.92820i	0.147342	+	0.255204i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	−3.00000	+	5.19615i	−0.110357	+	0.191144i	−0.915914	−	0.401374i	$-0.868533\pi$
$739$	−3.00000	+	5.19615i	−0.110357	+	0.191144i	0.805557	+	0.592518i	$0.201866\pi$
$740$	−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	$0.0960222\pi$
$744$	−30.0000	+	51.9615i	−1.09985	+	1.90500i
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	−34.0000			−1.24483
$747$	8.00000	+	13.8564i	0.292705	+	0.506979i
$748$	2.00000	+	3.46410i	0.0731272	+	0.126660i
$749$	−40.0000			−1.46157
$750$	1.00000	+	1.73205i	0.0365148	+	0.0632456i
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	−0.489053	−	0.872254i	$-0.662658\pi$
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	0.999921	−	0.0125942i	$-0.00400897\pi$
$752$	2.00000	−	3.46410i	0.0729325	−	0.126323i
$753$	−48.0000			−1.74922
$754$		0			0
$755$	−10.0000			−0.363937
$756$	−8.00000	+	13.8564i	−0.290957	+	0.503953i
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	−0.883626	−	0.468193i	$-0.844905\pi$
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	0.847280	+	0.531146i	$0.178238\pi$
$758$	5.00000	+	8.66025i	0.181608	+	0.314555i
$759$	24.0000			0.871145
$760$	−9.00000	−	15.5885i	−0.326464	−	0.565453i
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$	−4.00000			−0.144905
$763$	20.0000	+	34.6410i	0.724049	+	1.25409i
$764$		0			0
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−12.0000			−0.433578
$767$		0			0
$768$	34.0000			1.22687
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	−0.999364	−	0.0356685i	$-0.988644\pi$
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	0.530572	+	0.847640i	$0.321977\pi$
$770$	4.00000	−	6.92820i	0.144150	−	0.249675i
$771$	2.00000	+	3.46410i	0.0720282	+	0.124757i
$772$	2.00000			0.0719816
$773$	1.00000	+	1.73205i	0.0359675	+	0.0622975i	0.883449	−	0.468528i	$-0.155215\pi$
$773$	1.00000	+	1.73205i	0.0359675	+	0.0622975i	−0.847481	+	0.530825i	$0.821882\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$	−10.0000			−0.359211
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	8.00000	−	13.8564i	0.286998	−	0.497096i
$778$	−5.00000	+	8.66025i	−0.179259	+	0.310485i
$779$	36.0000			1.28983
$780$		0			0
$781$	12.0000			0.429394
$782$	−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
$785$	6.00000			0.214149
$786$	−20.0000	−	34.6410i	−0.713376	−	1.23560i
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	0.785885	−	0.618373i	$-0.212208\pi$
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	−0.928469	+	0.371409i	$0.878875\pi$
$788$	6.00000			0.213741
$789$	14.0000	+	24.2487i	0.498413	+	0.863277i
$790$	6.00000	−	10.3923i	0.213470	−	0.369742i
$791$	−28.0000	+	48.4974i	−0.995565	+	1.72437i
$792$	6.00000			0.213201
$793$		0			0
$794$	−6.00000			−0.212932
$795$	−2.00000	+	3.46410i	−0.0709327	+	0.122859i
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	−0.950726	−	0.310031i	$-0.899660\pi$
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	0.206868	−	0.978369i	$-0.433673\pi$
$798$	48.0000			1.69918
$799$	−4.00000	−	6.92820i	−0.141510	−	0.245102i
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	2.00000			0.0706665
$802$	5.00000	+	8.66025i	0.176556	+	0.305804i
$803$	6.00000	−	10.3923i	0.211735	−	0.366736i
$804$	4.00000	−	6.92820i	0.141069	−	0.244339i
$805$	−24.0000			−0.845889
$806$		0			0
$807$	−12.0000			−0.422420
$808$	27.0000	−	46.7654i	0.949857	−	1.64520i
$809$	1.00000	−	1.73205i	0.0351581	−	0.0608957i	−0.847911	−	0.530139i	$-0.822140\pi$
$809$	1.00000	−	1.73205i	0.0351581	−	0.0608957i	0.883069	+	0.469243i	$0.155473\pi$
$810$	5.50000	+	9.52628i	0.193250	+	0.334719i
$811$	−42.0000			−1.47482			−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000			−1.47482			−0.737410	+	0.675446i	$0.763951\pi$
$812$	−4.00000	−	6.92820i	−0.140372	−	0.243132i
$813$	2.00000	+	3.46410i	0.0701431	+	0.121491i
$814$	4.00000			0.140200
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	30.0000	−	51.9615i	1.04957	−	1.81790i
$818$	−18.0000			−0.629355
$819$		0			0
$820$	−6.00000			−0.209529
$821$	−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	$0.829160\pi$
$822$	2.00000	−	3.46410i	0.0697580	−	0.120824i
$823$	23.0000	+	39.8372i	0.801730	+	1.38864i	0.918477	+	0.395475i	$0.129420\pi$
$823$	23.0000	+	39.8372i	0.801730	+	1.38864i	−0.116747	+	0.993162i	$0.537247\pi$
$824$	6.00000			0.209020
$825$	2.00000	+	3.46410i	0.0696311	+	0.120605i
$826$	−12.0000	−	20.7846i	−0.417533	−	0.723189i
$827$	−32.0000			−1.11275			−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000			−1.11275			−0.556375	+	0.830932i	$0.687808\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$	8.00000	−	13.8564i	0.277684	−	0.480963i
$831$	28.0000			0.971309
$832$		0			0
$833$	18.0000			0.623663
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	−40.0000			−1.38260
$838$	−20.0000	−	34.6410i	−0.690889	−	1.19665i
$839$	−19.0000	−	32.9090i	−0.655953	−	1.13614i	−0.981654	−	0.190671i	$-0.938934\pi$
$839$	−19.0000	−	32.9090i	−0.655953	−	1.13614i	0.325701	−	0.945473i	$-0.394400\pi$
$840$	−24.0000			−0.828079
$841$	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
$844$	−12.0000			−0.413057
$845$		0			0
$846$	−4.00000			−0.137523
$847$	−14.0000	+	24.2487i	−0.481046	+	0.833196i
$848$	1.00000	−	1.73205i	0.0343401	−	0.0594789i
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$	−2.00000			−0.0685994
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	−4.00000	−	6.92820i	−0.136877	−	0.237078i
$855$	−3.00000	+	5.19615i	−0.102598	+	0.177705i
$856$	−15.0000	+	25.9808i	−0.512689	+	0.888004i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	−5.00000	+	8.66025i	−0.170499	+	0.295312i
$861$	24.0000	−	41.5692i	0.817918	−	1.41668i
$862$	7.00000	+	12.1244i	0.238421	+	0.412957i
$863$	12.0000			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$864$	10.0000	+	17.3205i	0.340207	+	0.589256i
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	−10.0000			−0.339814
$867$	−13.0000	−	22.5167i	−0.441503	−	0.764706i
$868$	20.0000	−	34.6410i	0.678844	−	1.17579i
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$	−4.00000			−0.135613
$871$		0			0
$872$	30.0000			1.01593
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$	18.0000	−	31.1769i	0.608859	−	1.05457i
$875$	−2.00000	−	3.46410i	−0.0676123	−	0.117108i
$876$	−12.0000			−0.405442
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	0.673109	−	0.739543i	$-0.264958\pi$
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	−0.977018	+	0.213158i	$0.931625\pi$
$878$		0			0
$879$	−44.0000			−1.48408
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	−19.0000	+	32.9090i	−0.640126	+	1.10873i	0.345278	+	0.938500i	$0.387785\pi$
$881$	−19.0000	+	32.9090i	−0.640126	+	1.10873i	−0.985404	+	0.170231i	$0.945549\pi$
$882$	4.50000	−	7.79423i	0.151523	−	0.262445i
$883$	−22.0000			−0.740359			−0.370179	−	0.928960i	$-0.620704\pi$
$883$	−22.0000			−0.740359			−0.370179	+	0.928960i	$0.620704\pi$
$884$		0			0
$885$	12.0000			0.403376
$886$	7.00000	−	12.1244i	0.235170	−	0.407326i
$887$	−29.0000	+	50.2295i	−0.973725	+	1.68654i	−0.289644	+	0.957135i	$0.593537\pi$
$887$	−29.0000	+	50.2295i	−0.973725	+	1.68654i	−0.684081	+	0.729406i	$0.739796\pi$
$888$	−6.00000	−	10.3923i	−0.201347	−	0.348743i
$889$	8.00000			0.268311
$890$	−1.00000	−	1.73205i	−0.0335201	−	0.0580585i
$891$	11.0000	+	19.0526i	0.368514	+	0.638285i
$892$	−4.00000			−0.133930
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$	−18.0000	+	31.1769i	−0.602010	+	1.04271i
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$	−12.0000			−0.400892
$897$		0			0
$898$	6.00000			0.200223
$899$	10.0000	−	17.3205i	0.333519	−	0.577671i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$	12.0000			0.399556
$903$	−40.0000	−	69.2820i	−1.33112	−	2.30556i
$904$	21.0000	+	36.3731i	0.698450	+	1.20975i
$905$	22.0000			0.731305
$906$	−10.0000	−	17.3205i	−0.332228	−	0.575435i
$907$	17.0000	−	29.4449i	0.564476	−	0.977701i	−0.432623	−	0.901575i	$-0.642412\pi$
$907$	17.0000	−	29.4449i	0.564476	−	0.977701i	0.997098	−	0.0761255i	$-0.0242550\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	6.00000	−	10.3923i	0.198680	−	0.344124i
$913$	16.0000	−	27.7128i	0.529523	−	0.917160i
$914$	19.0000	+	32.9090i	0.628464	+	1.08853i
$915$	4.00000			0.132236
$916$	−11.0000	−	19.0526i	−0.363450	−	0.629514i
$917$	40.0000	+	69.2820i	1.32092	+	2.28789i
$918$	−8.00000			−0.264039
$919$	26.0000	+	45.0333i	0.857661	+	1.48551i	0.874154	+	0.485648i	$0.161416\pi$
$919$	26.0000	+	45.0333i	0.857661	+	1.48551i	−0.0164935	+	0.999864i	$0.505250\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	−10.0000			−0.329332
$923$		0			0
$924$	−16.0000			−0.526361
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	−12.0000	+	20.7846i	−0.394344	+	0.683025i
$927$	−1.00000	−	1.73205i	−0.0328443	−	0.0568880i
$928$	−10.0000			−0.328266
$929$	19.0000	+	32.9090i	0.623370	+	1.07971i	0.988854	+	0.148890i	$0.0475702\pi$
$929$	19.0000	+	32.9090i	0.623370	+	1.07971i	−0.365484	+	0.930818i	$0.619096\pi$
$930$	−10.0000	−	17.3205i	−0.327913	−	0.567962i
$931$	−54.0000			−1.76978
$932$	5.00000	+	8.66025i	0.163780	+	0.283676i
$933$	−4.00000	+	6.92820i	−0.130954	+	0.226819i
$934$	−5.00000	+	8.66025i	−0.163605	+	0.283372i
$935$	−4.00000			−0.130814
$936$		0			0
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	8.00000	−	13.8564i	0.261209	−	0.452428i
$939$	−22.0000	+	38.1051i	−0.717943	+	1.24351i
$940$	−2.00000	−	3.46410i	−0.0652328	−	0.112987i
$941$	18.0000			0.586783			0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000			0.586783			0.293392	+	0.955992i	$0.405216\pi$
$942$	6.00000	+	10.3923i	0.195491	+	0.338600i
$943$	−18.0000	−	31.1769i	−0.586161	−	1.01526i
$944$	−6.00000			−0.195283
$945$	−8.00000	−	13.8564i	−0.260240	−	0.450749i
$946$	10.0000	−	17.3205i	0.325128	−	0.563138i
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$	−24.0000			−0.779484
$949$		0			0
$950$	6.00000			0.194666
$951$	−18.0000	+	31.1769i	−0.583690	+	1.01098i
$952$	12.0000	−	20.7846i	0.388922	−	0.673633i
$953$	−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
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	−8.00000			−0.258603
$958$	15.0000	+	25.9808i	0.484628	+	0.839400i
$959$	−4.00000	+	6.92820i	−0.129167	+	0.223723i
$960$	−7.00000	+	12.1244i	−0.225924	+	0.391312i
$961$	69.0000			2.22581
$962$		0			0
$963$	10.0000			0.322245
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	−1.00000	+	1.73205i	−0.0321911	+	0.0557567i
$966$	−24.0000	−	41.5692i	−0.772187	−	1.33747i
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$	−12.0000	−	20.7846i	−0.385496	−	0.667698i
$970$	−2.00000			−0.0642161
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	0.998339	−	0.0576061i	$-0.0183467\pi$
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	−0.549058	+	0.835784i	$0.685013\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$		0			0
$974$	40.0000			1.28168
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$	12.0000	−	20.7846i	0.383718	−	0.664619i
$979$	−2.00000	−	3.46410i	−0.0639203	−	0.110713i
$980$	9.00000			0.287494
$981$	−5.00000	−	8.66025i	−0.159638	−	0.276501i
$982$	−12.0000	−	20.7846i	−0.382935	−	0.663264i
$983$	56.0000			1.78612			0.893061	−	0.449935i	$-0.148553\pi$
$983$	56.0000			1.78612			0.893061	+	0.449935i	$0.148553\pi$
$984$	−18.0000	−	31.1769i	−0.573819	−	0.993884i
$985$	−3.00000	+	5.19615i	−0.0955879	+	0.165563i
$986$	2.00000	−	3.46410i	0.0636930	−	0.110319i
$987$	32.0000			1.01857
$988$		0			0
$989$	−60.0000			−1.90789
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$	−24.0000	+	41.5692i	−0.762385	+	1.32049i	0.179233	+	0.983807i	$0.442638\pi$
$991$	−24.0000	+	41.5692i	−0.762385	+	1.32049i	−0.941618	+	0.336683i	$0.890695\pi$
$992$	−25.0000	−	43.3013i	−0.793751	−	1.37482i
$993$	36.0000			1.14243
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$	−8.00000	−	13.8564i	−0.253617	−	0.439278i
$996$	−32.0000			−1.01396
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$	5.00000	−	8.66025i	0.158272	−	0.274136i
$999$	4.00000	−	6.92820i	0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.b.191.1		2
13.2	odd	12		845.2.m.b.361.2		4
13.3	even	3	inner	845.2.e.b.146.1		2
13.4	even	6		845.2.a.a.1.1		1
13.5	odd	4		845.2.m.b.316.1		4
13.6	odd	12		845.2.c.a.506.2		2
13.7	odd	12		845.2.c.a.506.1		2
13.8	odd	4		845.2.m.b.316.2		4
13.9	even	3		65.2.a.a.1.1	✓	1
13.10	even	6		845.2.e.a.146.1		2
13.11	odd	12		845.2.m.b.361.1		4
13.12	even	2		845.2.e.a.191.1		2
39.17	odd	6		7605.2.a.f.1.1		1
39.35	odd	6		585.2.a.h.1.1		1
52.35	odd	6		1040.2.a.f.1.1		1
65.4	even	6		4225.2.a.g.1.1		1
65.9	even	6		325.2.a.d.1.1		1
65.22	odd	12		325.2.b.b.274.1		2
65.48	odd	12		325.2.b.b.274.2		2
91.48	odd	6		3185.2.a.e.1.1		1
104.35	odd	6		4160.2.a.f.1.1		1
104.61	even	6		4160.2.a.q.1.1		1
143.87	odd	6		7865.2.a.c.1.1		1
156.35	even	6		9360.2.a.ca.1.1		1
195.74	odd	6		2925.2.a.f.1.1		1
195.113	even	12		2925.2.c.h.2224.1		2
195.152	even	12		2925.2.c.h.2224.2		2
260.139	odd	6		5200.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.a.1.1	✓	1	13.9	even	3
325.2.a.d.1.1		1	65.9	even	6
325.2.b.b.274.1		2	65.22	odd	12
325.2.b.b.274.2		2	65.48	odd	12
585.2.a.h.1.1		1	39.35	odd	6
845.2.a.a.1.1		1	13.4	even	6
845.2.c.a.506.1		2	13.7	odd	12
845.2.c.a.506.2		2	13.6	odd	12
845.2.e.a.146.1		2	13.10	even	6
845.2.e.a.191.1		2	13.12	even	2
845.2.e.b.146.1		2	13.3	even	3	inner
845.2.e.b.191.1		2	1.1	even	1	trivial
845.2.m.b.316.1		4	13.5	odd	4
845.2.m.b.316.2		4	13.8	odd	4
845.2.m.b.361.1		4	13.11	odd	12
845.2.m.b.361.2		4	13.2	odd	12
1040.2.a.f.1.1		1	52.35	odd	6
2925.2.a.f.1.1		1	195.74	odd	6
2925.2.c.h.2224.1		2	195.113	even	12
2925.2.c.h.2224.2		2	195.152	even	12
3185.2.a.e.1.1		1	91.48	odd	6
4160.2.a.f.1.1		1	104.35	odd	6
4160.2.a.q.1.1		1	104.61	even	6
4225.2.a.g.1.1		1	65.4	even	6
5200.2.a.d.1.1		1	260.139	odd	6
7605.2.a.f.1.1		1	39.17	odd	6
7865.2.a.c.1.1		1	143.87	odd	6
9360.2.a.ca.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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.00000 - 1.73205i) q^{6} +(2.00000 + 3.46410i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +3.00000 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} +(3.00000 - 5.19615i) 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} -10.0000 q^{31} +(2.50000 + 4.33013i) 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} -3.00000 q^{40} +(3.00000 - 5.19615i) 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} +4.00000 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} +(6.00000 + 10.3923i) q^{56} +12.0000 q^{57} +(1.00000 + 1.73205i) q^{58} +(-3.00000 - 5.19615i) q^{59} -2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-5.00000 + 8.66025i) q^{62} +(2.00000 - 3.46410i) q^{63} +7.00000 q^{64} +4.00000 q^{66} +(2.00000 - 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-6.00000 - 10.3923i) q^{69} -4.00000 q^{70} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -6.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-3.00000 + 5.19615i) q^{76} -8.00000 q^{77} -12.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} -16.0000 q^{83} +(4.00000 + 6.92820i) q^{84} +(1.00000 + 1.73205i) q^{85} -10.0000 q^{86} +(2.00000 + 3.46410i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-1.00000 + 1.73205i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(-10.0000 + 17.3205i) q^{93} +(2.00000 - 3.46410i) q^{94} +(-3.00000 - 5.19615i) q^{95} +10.0000 q^{96} +(1.00000 + 1.73205i) q^{97} +(4.50000 + 7.79423i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 + q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - q^9	\( 2 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - q^{9} - q^{10} - 2 q^{11} + 4 q^{12} + 8 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} - 2 q^{18} + 6 q^{19} - q^{20} + 16 q^{21} + 2 q^{22} + 6 q^{23} + 6 q^{24} + 2 q^{25} + 8 q^{27} - 4 q^{28} - 2 q^{29} + 2 q^{30} - 20 q^{31} + 5 q^{32} + 4 q^{33} - 4 q^{34} - 4 q^{35} + q^{36} + 2 q^{37} + 12 q^{38} - 6 q^{40} + 6 q^{41} + 8 q^{42} - 10 q^{43} - 4 q^{44} + q^{45} - 6 q^{46} + 8 q^{47} - 2 q^{48} - 9 q^{49} + q^{50} - 8 q^{51} + 4 q^{53} + 4 q^{54} + 2 q^{55} + 12 q^{56} + 24 q^{57} + 2 q^{58} - 6 q^{59} - 4 q^{60} - 2 q^{61} - 10 q^{62} + 4 q^{63} + 14 q^{64} + 8 q^{66} + 4 q^{67} + 2 q^{68} - 12 q^{69} - 8 q^{70} - 6 q^{71} - 3 q^{72} - 12 q^{73} - 2 q^{74} + 2 q^{75} - 6 q^{76} - 16 q^{77} - 24 q^{79} - q^{80} + 11 q^{81} - 6 q^{82} - 32 q^{83} + 8 q^{84} + 2 q^{85} - 20 q^{86} + 4 q^{87} - 6 q^{88} - 2 q^{89} + 2 q^{90} + 12 q^{92} - 20 q^{93} + 4 q^{94} - 6 q^{95} + 20 q^{96} + 2 q^{97} + 9 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 + q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 + 6 * 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 + 6 * q^24 + 2 * q^25 + 8 * q^27 - 4 * q^28 - 2 * q^29 + 2 * q^30 - 20 * q^31 + 5 * q^32 + 4 * q^33 - 4 * q^34 - 4 * q^35 + q^36 + 2 * q^37 + 12 * q^38 - 6 * q^40 + 6 * q^41 + 8 * q^42 - 10 * q^43 - 4 * q^44 + q^45 - 6 * q^46 + 8 * q^47 - 2 * q^48 - 9 * q^49 + q^50 - 8 * q^51 + 4 * q^53 + 4 * q^54 + 2 * q^55 + 12 * q^56 + 24 * q^57 + 2 * q^58 - 6 * q^59 - 4 * q^60 - 2 * q^61 - 10 * q^62 + 4 * q^63 + 14 * q^64 + 8 * q^66 + 4 * q^67 + 2 * q^68 - 12 * q^69 - 8 * q^70 - 6 * q^71 - 3 * q^72 - 12 * q^73 - 2 * q^74 + 2 * q^75 - 6 * q^76 - 16 * q^77 - 24 * q^79 - q^80 + 11 * q^81 - 6 * q^82 - 32 * q^83 + 8 * q^84 + 2 * q^85 - 20 * q^86 + 4 * q^87 - 6 * q^88 - 2 * q^89 + 2 * q^90 + 12 * q^92 - 20 * q^93 + 4 * q^94 - 6 * q^95 + 20 * q^96 + 2 * q^97 + 9 * q^98 + 4 * q^99

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