LMFDB - Embedded newform 195.2.i.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(16,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("195.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	195.16
Dual form			195.2.i.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -1.00000 q^{5} +(-1.00000 + 1.73205i) q^{6} +(-2.50000 + 4.33013i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -1.00000 q^{5} +(-1.00000 + 1.73205i) q^{6} +(-2.50000 + 4.33013i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-1.00000 - 1.73205i) q^{11} +2.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +10.0000 q^{14} +(0.500000 + 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +2.00000 q^{18} +(1.00000 - 1.73205i) q^{20} +5.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(-3.00000 - 5.19615i) q^{23} +1.00000 q^{25} +(-2.00000 + 6.92820i) q^{26} +1.00000 q^{27} +(-5.00000 - 8.66025i) q^{28} +(2.00000 + 3.46410i) q^{29} +(1.00000 - 1.73205i) q^{30} -7.00000 q^{31} +(4.00000 - 6.92820i) q^{32} +(-1.00000 + 1.73205i) q^{33} +4.00000 q^{34} +(2.50000 - 4.33013i) q^{35} +(-1.00000 - 1.73205i) q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.00000 + 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(-5.00000 - 8.66025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +4.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(-6.00000 + 10.3923i) q^{46} -8.00000 q^{47} +(2.00000 - 3.46410i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(-1.00000 - 1.73205i) q^{50} +2.00000 q^{51} +(7.00000 - 1.73205i) q^{52} -4.00000 q^{53} +(-1.00000 - 1.73205i) q^{54} +(1.00000 + 1.73205i) q^{55} +(4.00000 - 6.92820i) q^{58} +(-6.00000 + 10.3923i) q^{59} -2.00000 q^{60} +(6.50000 - 11.2583i) q^{61} +(7.00000 + 12.1244i) q^{62} +(-2.50000 - 4.33013i) q^{63} -8.00000 q^{64} +(2.50000 + 2.59808i) q^{65} +4.00000 q^{66} +(3.50000 + 6.06218i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-3.00000 + 5.19615i) q^{69} -10.0000 q^{70} +(-6.00000 + 10.3923i) q^{71} +15.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(-0.500000 - 0.866025i) q^{75} +10.0000 q^{77} +(7.00000 - 1.73205i) q^{78} +3.00000 q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +8.00000 q^{83} +(-5.00000 + 8.66025i) q^{84} +(1.00000 - 1.73205i) q^{85} +2.00000 q^{86} +(2.00000 - 3.46410i) q^{87} +(-7.00000 - 12.1244i) q^{89} -2.00000 q^{90} +(17.5000 - 4.33013i) q^{91} +12.0000 q^{92} +(3.50000 + 6.06218i) q^{93} +(8.00000 + 13.8564i) q^{94} -8.00000 q^{96} +(2.50000 - 4.33013i) q^{97} +(-18.0000 + 31.1769i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 5 * q^7 - q^9	$ 2 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 5 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 5 q^{13} + 20 q^{14} + q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} + 10 q^{21} - 4 q^{22} - 6 q^{23} + 2 q^{25} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{30} - 14 q^{31} + 8 q^{32} - 2 q^{33} + 8 q^{34} + 5 q^{35} - 2 q^{36} + 2 q^{37} - 2 q^{39} - 6 q^{41} - 10 q^{42} - q^{43} + 8 q^{44} + q^{45} - 12 q^{46} - 16 q^{47} + 4 q^{48} - 18 q^{49} - 2 q^{50} + 4 q^{51} + 14 q^{52} - 8 q^{53} - 2 q^{54} + 2 q^{55} + 8 q^{58} - 12 q^{59} - 4 q^{60} + 13 q^{61} + 14 q^{62} - 5 q^{63} - 16 q^{64} + 5 q^{65} + 8 q^{66} + 7 q^{67} - 4 q^{68} - 6 q^{69} - 20 q^{70} - 12 q^{71} + 30 q^{73} + 4 q^{74} - q^{75} + 20 q^{77} + 14 q^{78} + 6 q^{79} - 4 q^{80} - q^{81} - 12 q^{82} + 16 q^{83} - 10 q^{84} + 2 q^{85} + 4 q^{86} + 4 q^{87} - 14 q^{89} - 4 q^{90} + 35 q^{91} + 24 q^{92} + 7 q^{93} + 16 q^{94} - 16 q^{96} + 5 q^{97} - 36 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 5 * q^7 - q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 - 5 * q^13 + 20 * q^14 + q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^20 + 10 * q^21 - 4 * q^22 - 6 * q^23 + 2 * q^25 - 4 * q^26 + 2 * q^27 - 10 * q^28 + 4 * q^29 + 2 * q^30 - 14 * q^31 + 8 * q^32 - 2 * q^33 + 8 * q^34 + 5 * q^35 - 2 * q^36 + 2 * q^37 - 2 * q^39 - 6 * q^41 - 10 * q^42 - q^43 + 8 * q^44 + q^45 - 12 * q^46 - 16 * q^47 + 4 * q^48 - 18 * q^49 - 2 * q^50 + 4 * q^51 + 14 * q^52 - 8 * q^53 - 2 * q^54 + 2 * q^55 + 8 * q^58 - 12 * q^59 - 4 * q^60 + 13 * q^61 + 14 * q^62 - 5 * q^63 - 16 * q^64 + 5 * q^65 + 8 * q^66 + 7 * q^67 - 4 * q^68 - 6 * q^69 - 20 * q^70 - 12 * q^71 + 30 * q^73 + 4 * q^74 - q^75 + 20 * q^77 + 14 * q^78 + 6 * q^79 - 4 * q^80 - q^81 - 12 * q^82 + 16 * q^83 - 10 * q^84 + 2 * q^85 + 4 * q^86 + 4 * q^87 - 14 * q^89 - 4 * q^90 + 35 * q^91 + 24 * q^92 + 7 * q^93 + 16 * q^94 - 16 * q^96 + 5 * q^97 - 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.188982	+	0.981981i	$0.560519\pi$
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	2.00000			0.577350
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	10.0000			2.67261
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	2.00000			0.471405
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	5.00000			1.09109
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.00000	+	6.92820i	−0.392232	+	1.35873i
$27$	1.00000			0.192450
$28$	−5.00000	−	8.66025i	−0.944911	−	1.63663i
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	4.00000			0.685994
$35$	2.50000	−	4.33013i	0.422577	−	0.731925i
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	−5.00000	−	8.66025i	−0.771517	−	1.33631i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$	4.00000			0.603023
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−6.00000	+	10.3923i	−0.884652	+	1.53226i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	2.00000	−	3.46410i	0.288675	−	0.500000i
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$	−1.00000	−	1.73205i	−0.141421	−	0.244949i
$51$	2.00000			0.280056
$52$	7.00000	−	1.73205i	0.970725	−	0.240192i
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$		0			0
$57$		0			0
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$	−2.00000			−0.258199
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	7.00000	+	12.1244i	0.889001	+	1.53979i
$63$	−2.50000	−	4.33013i	−0.314970	−	0.545545i
$64$	−8.00000			−1.00000
$65$	2.50000	+	2.59808i	0.310087	+	0.322252i
$66$	4.00000			0.492366
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	−10.0000			−1.19523
$71$	−6.00000	+	10.3923i	−0.712069	+	1.23334i	0.252010	+	0.967725i	$0.418908\pi$
$71$	−6.00000	+	10.3923i	−0.712069	+	1.23334i	−0.964079	+	0.265615i	$0.914425\pi$
$72$		0			0
$73$	15.0000			1.75562			0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000			1.75562			0.877809	+	0.479012i	$0.159005\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	10.0000			1.13961
$78$	7.00000	−	1.73205i	0.792594	−	0.196116i
$79$	3.00000			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$	−5.00000	+	8.66025i	−0.545545	+	0.944911i
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	2.00000			0.215666
$87$	2.00000	−	3.46410i	0.214423	−	0.371391i
$88$		0			0
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	−2.00000			−0.210819
$91$	17.5000	−	4.33013i	1.83450	−	0.453921i
$92$	12.0000			1.25109
$93$	3.50000	+	6.06218i	0.362933	+	0.628619i
$94$	8.00000	+	13.8564i	0.825137	+	1.42918i
$95$		0			0
$96$	−8.00000			−0.816497
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$	−18.0000	+	31.1769i	−1.81827	+	3.14934i
$99$	2.00000			0.201008
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$	−5.00000			−0.487950
$106$	4.00000	+	6.92820i	0.388514	+	0.672927i
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	0.753010	−	0.658009i	$-0.228601\pi$
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	1.00000	−	1.73205i	0.0949158	−	0.164399i
$112$	−20.0000			−1.88982
$113$	1.00000	−	1.73205i	0.0940721	−	0.162938i	−0.815149	−	0.579252i	$-0.803345\pi$
$113$	1.00000	−	1.73205i	0.0940721	−	0.162938i	0.909221	+	0.416314i	$0.136678\pi$
$114$		0			0
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$	−8.00000			−0.742781
$117$	3.50000	−	0.866025i	0.323575	−	0.0800641i
$118$	24.0000			2.20938
$119$	−5.00000	−	8.66025i	−0.458349	−	0.793884i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−26.0000			−2.35393
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	7.00000	−	12.1244i	0.628619	−	1.08880i
$125$	−1.00000			−0.0894427
$126$	−5.00000	+	8.66025i	−0.445435	+	0.771517i
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	0.999905	−	0.0137486i	$-0.00437646\pi$
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	−0.511859	+	0.859069i	$0.671043\pi$
$128$		0			0
$129$	1.00000			0.0880451
$130$	2.00000	−	6.92820i	0.175412	−	0.607644i
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$	−2.00000	−	3.46410i	−0.174078	−	0.301511i
$133$		0			0
$134$	7.00000	−	12.1244i	0.604708	−	1.04738i
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$	12.0000			1.02151
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	−0.795373	−	0.606120i	$-0.792725\pi$
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	0.922602	+	0.385754i	$0.126059\pi$
$140$	5.00000	+	8.66025i	0.422577	+	0.731925i
$141$	4.00000	+	6.92820i	0.336861	+	0.583460i
$142$	24.0000			2.01404
$143$	−2.00000	+	6.92820i	−0.167248	+	0.579365i
$144$	−4.00000			−0.333333
$145$	−2.00000	−	3.46410i	−0.166091	−	0.287678i
$146$	−15.0000	−	25.9808i	−1.24141	−	2.15018i
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$	−4.00000			−0.328798
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	−0.508413	−	0.861113i	$-0.669768\pi$
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	0.999953	+	0.00974235i	$0.00310113\pi$
$150$	−1.00000	+	1.73205i	−0.0816497	+	0.141421i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$	−10.0000	−	17.3205i	−0.805823	−	1.39573i
$155$	7.00000			0.562254
$156$	−5.00000	−	5.19615i	−0.400320	−	0.416025i
$157$	−15.0000			−1.19713			−0.598565	−	0.801074i	$-0.704262\pi$
$157$	−15.0000			−1.19713			−0.598565	+	0.801074i	$0.704262\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$	2.00000	+	3.46410i	0.158610	+	0.274721i
$160$	−4.00000	+	6.92820i	−0.316228	+	0.547723i
$161$	30.0000			2.36433
$162$	−1.00000	+	1.73205i	−0.0785674	+	0.136083i
$163$	7.50000	−	12.9904i	0.587445	−	1.01749i	−0.407120	−	0.913375i	$-0.633467\pi$
$163$	7.50000	−	12.9904i	0.587445	−	1.01749i	0.994566	−	0.104111i	$-0.0331996\pi$
$164$	12.0000			0.937043
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	−8.00000	−	13.8564i	−0.620920	−	1.07547i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	−8.00000			−0.606478
$175$	−2.50000	+	4.33013i	−0.188982	+	0.327327i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	12.0000			0.901975
$178$	−14.0000	+	24.2487i	−1.04934	+	1.81752i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−25.0000	−	25.9808i	−1.85312	−	1.92582i
$183$	−13.0000			−0.960988
$184$		0			0
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	7.00000	−	12.1244i	0.513265	−	0.889001i
$187$	4.00000			0.292509
$188$	8.00000	−	13.8564i	0.583460	−	1.01058i
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$	−10.0000			−0.717958
$195$	1.00000	−	3.46410i	0.0716115	−	0.248069i
$196$	36.0000			2.57143
$197$	6.00000	+	10.3923i	0.427482	+	0.740421i	0.996649	−	0.0818013i	$-0.0260673\pi$
$197$	6.00000	+	10.3923i	0.427482	+	0.740421i	−0.569166	+	0.822222i	$0.692734\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	0.389885	+	0.920864i	$0.372515\pi$
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$	18.0000	−	31.1769i	1.26648	−	2.19360i
$203$	−20.0000			−1.40372
$204$	−2.00000	+	3.46410i	−0.140028	+	0.242536i
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	6.00000			0.417029
$208$	4.00000	−	13.8564i	0.277350	−	0.960769i
$209$		0			0
$210$	5.00000	+	8.66025i	0.345033	+	0.597614i
$211$	−7.50000	−	12.9904i	−0.516321	−	0.894295i	−0.999820	−	0.0189499i	$-0.993968\pi$
$211$	−7.50000	−	12.9904i	−0.516321	−	0.894295i	0.483499	−	0.875345i	$-0.339366\pi$
$212$	4.00000	−	6.92820i	0.274721	−	0.475831i
$213$	12.0000			0.822226
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		0			0
$217$	17.5000	−	30.3109i	1.18798	−	2.05764i
$218$	11.0000	+	19.0526i	0.745014	+	1.29040i
$219$	−7.50000	−	12.9904i	−0.506803	−	0.877809i
$220$	−4.00000			−0.269680
$221$	7.00000	−	1.73205i	0.470871	−	0.116510i
$222$	−4.00000			−0.268462
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$	20.0000	+	34.6410i	1.33631	+	2.31455i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−4.00000			−0.266076
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	−0.982877	−	0.184263i	$-0.941010\pi$
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	0.651015	+	0.759065i	$0.274343\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	6.00000	−	10.3923i	0.395628	−	0.685248i
$231$	−5.00000	−	8.66025i	−0.328976	−	0.569803i
$232$		0			0
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$	−5.00000	−	5.19615i	−0.326860	−	0.339683i
$235$	8.00000			0.521862
$236$	−12.0000	−	20.7846i	−0.781133	−	1.35296i
$237$	−1.50000	−	2.59808i	−0.0974355	−	0.168763i
$238$	−10.0000	+	17.3205i	−0.648204	+	1.12272i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	−2.00000	+	3.46410i	−0.129099	+	0.223607i
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−14.0000			−0.899954
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	13.0000	+	22.5167i	0.832240	+	1.44148i
$245$	9.00000	+	15.5885i	0.574989	+	0.995910i
$246$	12.0000			0.765092
$247$		0			0
$248$		0			0
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$	1.00000	+	1.73205i	0.0632456	+	0.109545i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	10.0000			0.629941
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$	11.0000	−	19.0526i	0.690201	−	1.19546i
$255$	−2.00000			−0.125245
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	0.973070	+	0.230508i	$0.0740389\pi$
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	−0.286909	+	0.957958i	$0.592628\pi$
$258$	−1.00000	−	1.73205i	−0.0622573	−	0.107833i
$259$	−10.0000			−0.621370
$260$	−7.00000	+	1.73205i	−0.434122	+	0.107417i
$261$	−4.00000			−0.247594
$262$	4.00000	+	6.92820i	0.247121	+	0.428026i
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	0.977993	−	0.208635i	$-0.0669022\pi$
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	−0.669680	+	0.742650i	$0.733569\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	−7.00000	+	12.1244i	−0.428393	+	0.741999i
$268$	−14.0000			−0.855186
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$	1.00000	+	1.73205i	0.0608581	+	0.105409i
$271$	−14.5000	−	25.1147i	−0.880812	−	1.52561i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−14.5000	−	25.1147i	−0.880812	−	1.52561i	−0.0303728	−	0.999539i	$-0.509669\pi$
$272$	−8.00000			−0.485071
$273$	−12.5000	−	12.9904i	−0.756534	−	0.786214i
$274$	−4.00000			−0.241649
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	−0.976231	−	0.216731i	$-0.930460\pi$
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	0.675810	+	0.737075i	$0.263794\pi$
$278$	−6.00000			−0.359856
$279$	3.50000	−	6.06218i	0.209540	−	0.362933i
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	8.00000	−	13.8564i	0.476393	−	0.825137i
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	0.782104	−	0.623148i	$-0.214146\pi$
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	−0.930714	+	0.365748i	$0.880813\pi$
$284$	−12.0000	−	20.7846i	−0.712069	−	1.23334i
$285$		0			0
$286$	14.0000	−	3.46410i	0.827837	−	0.204837i
$287$	30.0000			1.77084
$288$	4.00000	+	6.92820i	0.235702	+	0.408248i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−4.00000	+	6.92820i	−0.234888	+	0.406838i
$291$	−5.00000			−0.293105
$292$	−15.0000	+	25.9808i	−0.877809	+	1.52041i
$293$	−8.00000	+	13.8564i	−0.467365	+	0.809500i	−0.999305	−	0.0372823i	$-0.988130\pi$
$293$	−8.00000	+	13.8564i	−0.467365	+	0.809500i	0.531940	+	0.846782i	$0.321463\pi$
$294$	36.0000			2.09956
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$		0			0
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	−24.0000			−1.39028
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	2.00000			0.115470
$301$	−2.50000	−	4.33013i	−0.144098	−	0.249584i
$302$	8.00000	+	13.8564i	0.460348	+	0.797347i
$303$	9.00000	−	15.5885i	0.517036	−	0.895533i
$304$		0			0
$305$	−6.50000	+	11.2583i	−0.372189	+	0.644650i
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	−31.0000			−1.76926			−0.884632	−	0.466290i	$-0.845590\pi$
$307$	−31.0000			−1.76926			−0.884632	+	0.466290i	$0.845590\pi$
$308$	−10.0000	+	17.3205i	−0.569803	+	0.986928i
$309$	3.50000	+	6.06218i	0.199108	+	0.344865i
$310$	−7.00000	−	12.1244i	−0.397573	−	0.688617i
$311$	−22.0000			−1.24751			−0.623753	−	0.781622i	$-0.714393\pi$
$311$	−22.0000			−1.24751			−0.623753	+	0.781622i	$0.714393\pi$
$312$		0			0
$313$	−31.0000			−1.75222			−0.876112	−	0.482108i	$-0.839871\pi$
$313$	−31.0000			−1.75222			−0.876112	+	0.482108i	$0.839871\pi$
$314$	15.0000	+	25.9808i	0.846499	+	1.46618i
$315$	2.50000	+	4.33013i	0.140859	+	0.243975i
$316$	−3.00000	+	5.19615i	−0.168763	+	0.292306i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$	4.00000	−	6.92820i	0.224309	−	0.388514i
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$	8.00000			0.447214
$321$	−2.00000	+	3.46410i	−0.111629	+	0.193347i
$322$	−30.0000	−	51.9615i	−1.67183	−	2.89570i
$323$		0			0
$324$	2.00000			0.111111
$325$	−2.50000	−	2.59808i	−0.138675	−	0.144115i
$326$	−30.0000			−1.66155
$327$	5.50000	+	9.52628i	0.304151	+	0.526804i
$328$		0			0
$329$	20.0000	−	34.6410i	1.10264	−	1.90982i
$330$	−4.00000			−0.220193
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	−0.962788	−	0.270259i	$-0.912891\pi$
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	0.715445	+	0.698669i	$0.246224\pi$
$332$	−8.00000	+	13.8564i	−0.439057	+	0.760469i
$333$	−2.00000			−0.109599
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$	−3.50000	−	6.06218i	−0.191225	−	0.331212i
$336$	10.0000	+	17.3205i	0.545545	+	0.944911i
$337$	−1.00000			−0.0544735			−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000			−0.0544735			−0.0272367	+	0.999629i	$0.508671\pi$
$338$	23.0000	−	12.1244i	1.25104	−	0.659478i
$339$	−2.00000			−0.108625
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	7.00000	+	12.1244i	0.379071	+	0.656571i
$342$		0			0
$343$	55.0000			2.96972
$344$		0			0
$345$	3.00000	−	5.19615i	0.161515	−	0.279751i
$346$		0			0
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$	4.00000	+	6.92820i	0.214423	+	0.371391i
$349$	−1.50000	−	2.59808i	−0.0802932	−	0.139072i	0.823083	−	0.567922i	$-0.192252\pi$
$349$	−1.50000	−	2.59808i	−0.0802932	−	0.139072i	−0.903376	+	0.428850i	$0.858919\pi$
$350$	10.0000			0.534522
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$	−16.0000			−0.852803
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	28.0000			1.48400
$357$	−5.00000	+	8.66025i	−0.264628	+	0.458349i
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	2.00000			0.105556			0.0527780	−	0.998606i	$-0.483192\pi$
$359$	2.00000			0.105556			0.0527780	+	0.998606i	$0.483192\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	22.0000	+	38.1051i	1.15629	+	2.00276i
$363$	−7.00000			−0.367405
$364$	−10.0000	+	34.6410i	−0.524142	+	1.81568i
$365$	−15.0000			−0.785136
$366$	13.0000	+	22.5167i	0.679521	+	1.17696i
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	0.760100	−	0.649806i	$-0.225150\pi$
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	−0.942799	+	0.333363i	$0.891817\pi$
$368$	12.0000	−	20.7846i	0.625543	−	1.08347i
$369$	6.00000			0.312348
$370$	−2.00000	+	3.46410i	−0.103975	+	0.180090i
$371$	10.0000	−	17.3205i	0.519174	−	0.899236i
$372$	−14.0000			−0.725866
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	0.647225	+	0.762299i	$0.275929\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	4.00000	−	13.8564i	0.206010	−	0.713641i
$378$	10.0000			0.514344
$379$	2.50000	+	4.33013i	0.128416	+	0.222424i	0.923063	−	0.384648i	$-0.125677\pi$
$379$	2.50000	+	4.33013i	0.128416	+	0.222424i	−0.794647	+	0.607072i	$0.792344\pi$
$380$		0			0
$381$	5.50000	−	9.52628i	0.281774	−	0.488046i
$382$	24.0000			1.22795
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	−0.539076	−	0.842257i	$-0.681226\pi$
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	0.998954	+	0.0457244i	$0.0145596\pi$
$384$		0			0
$385$	−10.0000			−0.509647
$386$	11.0000	−	19.0526i	0.559885	−	0.969750i
$387$	−0.500000	−	0.866025i	−0.0254164	−	0.0440225i
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	8.00000			0.405616			0.202808	−	0.979219i	$-0.434993\pi$
$389$	8.00000			0.405616			0.202808	+	0.979219i	$0.434993\pi$
$390$	−7.00000	+	1.73205i	−0.354459	+	0.0877058i
$391$	12.0000			0.606866
$392$		0			0
$393$	2.00000	+	3.46410i	0.100887	+	0.174741i
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	−3.00000			−0.150946
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	7.50000	−	12.9904i	0.376414	−	0.651969i	−0.614123	−	0.789210i	$-0.710490\pi$
$397$	7.50000	−	12.9904i	0.376414	−	0.651969i	0.990538	+	0.137241i	$0.0438236\pi$
$398$	34.0000			1.70427
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−8.00000	−	13.8564i	−0.399501	−	0.691956i	0.594163	−	0.804344i	$-0.297483\pi$
$401$	−8.00000	−	13.8564i	−0.399501	−	0.691956i	−0.993664	+	0.112388i	$0.964150\pi$
$402$	−14.0000			−0.698257
$403$	17.5000	+	18.1865i	0.871737	+	0.905936i
$404$	−36.0000			−1.79107
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	20.0000	+	34.6410i	0.992583	+	1.71920i
$407$	2.00000	−	3.46410i	0.0991363	−	0.171709i
$408$		0			0
$409$	7.50000	−	12.9904i	0.370851	−	0.642333i	−0.618846	−	0.785513i	$-0.712399\pi$
$409$	7.50000	−	12.9904i	0.370851	−	0.642333i	0.989697	+	0.143180i	$0.0457327\pi$
$410$	6.00000	−	10.3923i	0.296319	−	0.513239i
$411$	−2.00000			−0.0986527
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$	−30.0000	−	51.9615i	−1.47620	−	2.55686i
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$	−8.00000			−0.392705
$416$	−28.0000	+	6.92820i	−1.37281	+	0.339683i
$417$	−3.00000			−0.146911
$418$		0			0
$419$	−19.0000	−	32.9090i	−0.928211	−	1.60771i	−0.786314	−	0.617827i	$-0.788013\pi$
$419$	−19.0000	−	32.9090i	−0.928211	−	1.60771i	−0.141896	−	0.989882i	$-0.545320\pi$
$420$	5.00000	−	8.66025i	0.243975	−	0.422577i
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	−15.0000	+	25.9808i	−0.730189	+	1.26472i
$423$	4.00000	−	6.92820i	0.194487	−	0.336861i
$424$		0			0
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	−12.0000	−	20.7846i	−0.581402	−	1.00702i
$427$	32.5000	+	56.2917i	1.57279	+	2.72414i
$428$	8.00000			0.386695
$429$	7.00000	−	1.73205i	0.337963	−	0.0836242i
$430$	−2.00000			−0.0964486
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	0.976657	+	0.214807i	$0.0689121\pi$
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	−0.302300	+	0.953213i	$0.597755\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	−0.877790	−	0.479046i	$-0.840983\pi$
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	0.853761	+	0.520665i	$0.174316\pi$
$434$	−70.0000			−3.36011
$435$	−2.00000	+	3.46410i	−0.0958927	+	0.166091i
$436$	11.0000	−	19.0526i	0.526804	−	0.912452i
$437$		0			0
$438$	−15.0000	+	25.9808i	−0.716728	+	1.24141i
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	0.629664	−	0.776868i	$-0.283193\pi$
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	−0.987619	+	0.156871i	$0.949859\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$	−10.0000	−	10.3923i	−0.475651	−	0.494312i
$443$	26.0000			1.23530			0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000			1.23530			0.617649	+	0.786454i	$0.288085\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	7.00000	+	12.1244i	0.331832	+	0.574750i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$	−12.0000			−0.567581
$448$	20.0000	−	34.6410i	0.944911	−	1.63663i
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	−0.996396	−	0.0848262i	$-0.972967\pi$
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	0.571660	+	0.820491i	$0.306300\pi$
$450$	2.00000			0.0942809
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$	20.0000			0.938647
$455$	−17.5000	+	4.33013i	−0.820413	+	0.202999i
$456$		0			0
$457$	−17.5000	−	30.3109i	−0.818615	−	1.41788i	−0.906702	−	0.421771i	$-0.861409\pi$
$457$	−17.5000	−	30.3109i	−0.818615	−	1.41788i	0.0880870	−	0.996113i	$-0.471925\pi$
$458$	−14.0000	−	24.2487i	−0.654177	−	1.13307i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−12.0000			−0.559503
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	−0.841798	−	0.539792i	$-0.818503\pi$
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	0.888373	+	0.459123i	$0.151836\pi$
$462$	−10.0000	+	17.3205i	−0.465242	+	0.805823i
$463$	3.00000			0.139422			0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000			0.139422			0.0697109	+	0.997567i	$0.477792\pi$
$464$	−8.00000	+	13.8564i	−0.371391	+	0.643268i
$465$	−3.50000	−	6.06218i	−0.162309	−	0.281127i
$466$	14.0000	+	24.2487i	0.648537	+	1.12330i
$467$	−4.00000			−0.185098			−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000			−0.185098			−0.0925490	+	0.995708i	$0.529501\pi$
$468$	−2.00000	+	6.92820i	−0.0924500	+	0.320256i
$469$	−35.0000			−1.61615
$470$	−8.00000	−	13.8564i	−0.369012	−	0.639148i
$471$	7.50000	+	12.9904i	0.345582	+	0.598565i
$472$		0			0
$473$	2.00000			0.0919601
$474$	−3.00000	+	5.19615i	−0.137795	+	0.238667i
$475$		0			0
$476$	20.0000			0.916698
$477$	2.00000	−	3.46410i	0.0915737	−	0.158610i
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	−21.0000	−	36.3731i	−0.959514	−	1.66193i	−0.723681	−	0.690134i	$-0.757551\pi$
$479$	−21.0000	−	36.3731i	−0.959514	−	1.66193i	−0.235833	−	0.971794i	$-0.575782\pi$
$480$	8.00000			0.365148
$481$	2.00000	−	6.92820i	0.0911922	−	0.315899i
$482$	20.0000			0.910975
$483$	−15.0000	−	25.9808i	−0.682524	−	1.18217i
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	−2.50000	+	4.33013i	−0.113519	+	0.196621i
$486$	2.00000			0.0907218
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	−0.352241	−	0.935909i	$-0.614580\pi$
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	0.986642	−	0.162905i	$-0.0520863\pi$
$488$		0			0
$489$	−15.0000			−0.678323
$490$	18.0000	−	31.1769i	0.813157	−	1.40843i
$491$	12.0000	+	20.7846i	0.541552	+	0.937996i	0.998815	+	0.0486647i	$0.0154966\pi$
$491$	12.0000	+	20.7846i	0.541552	+	0.937996i	−0.457263	+	0.889332i	$0.651170\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$	−8.00000			−0.360302
$494$		0			0
$495$	−2.00000			−0.0898933
$496$	−14.0000	−	24.2487i	−0.628619	−	1.08880i
$497$	−30.0000	−	51.9615i	−1.34568	−	2.33079i
$498$	−8.00000	+	13.8564i	−0.358489	+	0.620920i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$		0			0
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	−0.791361	−	0.611349i	$-0.790627\pi$
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	0.925124	+	0.379664i	$0.123960\pi$
$504$		0			0
$505$	−9.00000	−	15.5885i	−0.400495	−	0.693677i
$506$	24.0000			1.06693
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	−22.0000			−0.976092
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	−37.5000	+	64.9519i	−1.65890	+	2.87330i
$512$	32.0000			1.41421
$513$		0			0
$514$	22.0000	−	38.1051i	0.970378	−	1.68074i
$515$	7.00000			0.308457
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	8.00000	+	13.8564i	0.351840	+	0.609404i
$518$	10.0000	+	17.3205i	0.439375	+	0.761019i
$519$		0			0
$520$		0			0
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	4.00000	+	6.92820i	0.175075	+	0.303239i
$523$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$523$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$	5.00000			0.218218
$526$	10.0000	−	17.3205i	0.436021	−	0.755210i
$527$	7.00000	−	12.1244i	0.304925	−	0.528145i
$528$	−8.00000			−0.348155
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−4.00000	−	6.92820i	−0.173749	−	0.300942i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$		0			0
$533$	−6.00000	+	20.7846i	−0.259889	+	0.900281i
$534$	28.0000			1.21168
$535$	2.00000	+	3.46410i	0.0864675	+	0.149766i
$536$		0			0
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$	−12.0000			−0.517357
$539$	−18.0000	+	31.1769i	−0.775315	+	1.34288i
$540$	1.00000	−	1.73205i	0.0430331	−	0.0745356i
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	−29.0000	+	50.2295i	−1.24566	+	2.15754i
$543$	11.0000	+	19.0526i	0.472055	+	0.817624i
$544$	8.00000	+	13.8564i	0.342997	+	0.594089i
$545$	11.0000			0.471188
$546$	−10.0000	+	34.6410i	−0.427960	+	1.48250i
$547$	−9.00000			−0.384812			−0.192406	−	0.981315i	$-0.561629\pi$
$547$	−9.00000			−0.384812			−0.192406	+	0.981315i	$0.561629\pi$
$548$	2.00000	+	3.46410i	0.0854358	+	0.147979i
$549$	6.50000	+	11.2583i	0.277413	+	0.480494i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$		0			0
$552$		0			0
$553$	−7.50000	+	12.9904i	−0.318932	+	0.552407i
$554$	20.0000			0.849719
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	3.00000	+	5.19615i	0.127228	+	0.220366i
$557$	10.0000	+	17.3205i	0.423714	+	0.733893i	0.996299	−	0.0859514i	$-0.0273930\pi$
$557$	10.0000	+	17.3205i	0.423714	+	0.733893i	−0.572586	+	0.819845i	$0.694060\pi$
$558$	−14.0000			−0.592667
$559$	3.50000	−	0.866025i	0.148034	−	0.0366290i
$560$	20.0000			0.845154
$561$	−2.00000	−	3.46410i	−0.0844401	−	0.146254i
$562$	12.0000	+	20.7846i	0.506189	+	0.876746i
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	0.450535	+	0.892759i	$0.351233\pi$
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	−0.998419	+	0.0562051i	$0.982100\pi$
$564$	−16.0000			−0.673722
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$	−5.00000	+	8.66025i	−0.210166	+	0.364018i
$567$	5.00000			0.209980
$568$		0			0
$569$	10.0000	+	17.3205i	0.419222	+	0.726113i	0.995861	−	0.0908852i	$-0.0289696\pi$
$569$	10.0000	+	17.3205i	0.419222	+	0.726113i	−0.576640	+	0.816999i	$0.695636\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	−10.0000	−	10.3923i	−0.418121	−	0.434524i
$573$	12.0000			0.501307
$574$	−30.0000	−	51.9615i	−1.25218	−	2.16883i
$575$	−3.00000	−	5.19615i	−0.125109	−	0.216695i
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	13.0000	−	22.5167i	0.540729	−	0.936570i
$579$	5.50000	−	9.52628i	0.228572	−	0.395899i
$580$	8.00000			0.332182
$581$	−20.0000	+	34.6410i	−0.829740	+	1.43715i
$582$	5.00000	+	8.66025i	0.207257	+	0.358979i
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$		0			0
$585$	−3.50000	+	0.866025i	−0.144707	+	0.0358057i
$586$	32.0000			1.32191
$587$	−14.0000	−	24.2487i	−0.577842	−	1.00085i	−0.995726	−	0.0923513i	$-0.970562\pi$
$587$	−14.0000	−	24.2487i	−0.577842	−	1.00085i	0.417885	−	0.908500i	$-0.362772\pi$
$588$	−18.0000	−	31.1769i	−0.742307	−	1.28571i
$589$		0			0
$590$	−24.0000			−0.988064
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−10.0000			−0.410651			−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000			−0.410651			−0.205325	+	0.978694i	$0.565825\pi$
$594$	−2.00000	+	3.46410i	−0.0820610	+	0.142134i
$595$	5.00000	+	8.66025i	0.204980	+	0.355036i
$596$	12.0000	+	20.7846i	0.491539	+	0.851371i
$597$	17.0000			0.695764
$598$	42.0000	−	10.3923i	1.71751	−	0.424973i
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$		0			0
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	0.549602	−	0.835426i	$-0.314779\pi$
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	−0.998302	+	0.0582563i	$0.981446\pi$
$602$	−5.00000	+	8.66025i	−0.203785	+	0.352966i
$603$	−7.00000			−0.285062
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$	−36.0000			−1.46240
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$		0			0
$609$	10.0000	+	17.3205i	0.405220	+	0.701862i
$610$	26.0000			1.05271
$611$	20.0000	+	20.7846i	0.809113	+	0.840855i
$612$	4.00000			0.161690
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	0.976797	−	0.214169i	$-0.0687045\pi$
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	−0.673874	+	0.738846i	$0.735371\pi$
$614$	31.0000	+	53.6936i	1.25106	+	2.16690i
$615$	3.00000	−	5.19615i	0.120972	−	0.209529i
$616$		0			0
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	37.0000			1.48716			0.743578	−	0.668649i	$-0.233127\pi$
$619$	37.0000			1.48716			0.743578	+	0.668649i	$0.233127\pi$
$620$	−7.00000	+	12.1244i	−0.281127	+	0.486926i
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	22.0000	+	38.1051i	0.882120	+	1.52788i
$623$	70.0000			2.80449
$624$	−14.0000	+	3.46410i	−0.560449	+	0.138675i
$625$	1.00000			0.0400000
$626$	31.0000	+	53.6936i	1.23901	+	2.14603i
$627$		0			0
$628$	15.0000	−	25.9808i	0.598565	−	1.03675i
$629$	−4.00000			−0.159490
$630$	5.00000	−	8.66025i	0.199205	−	0.345033i
$631$	−3.50000	+	6.06218i	−0.139333	+	0.241331i	−0.927244	−	0.374457i	$-0.877829\pi$
$631$	−3.50000	+	6.06218i	−0.139333	+	0.241331i	0.787911	+	0.615789i	$0.211162\pi$
$632$		0			0
$633$	−7.50000	+	12.9904i	−0.298098	+	0.516321i
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$	−5.50000	−	9.52628i	−0.218261	−	0.378039i
$636$	−8.00000			−0.317221
$637$	−18.0000	+	62.3538i	−0.713186	+	2.47055i
$638$	−16.0000			−0.633446
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$		0			0
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$	8.00000			0.315735
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$	−30.0000	+	51.9615i	−1.18217	+	2.04757i
$645$	−1.00000			−0.0393750
$646$		0			0
$647$	−19.0000	−	32.9090i	−0.746967	−	1.29378i	−0.949270	−	0.314462i	$-0.898176\pi$
$647$	−19.0000	−	32.9090i	−0.746967	−	1.29378i	0.202303	−	0.979323i	$-0.435157\pi$
$648$		0			0
$649$	24.0000			0.942082
$650$	−2.00000	+	6.92820i	−0.0784465	+	0.271746i
$651$	−35.0000			−1.37176
$652$	15.0000	+	25.9808i	0.587445	+	1.01749i
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$	11.0000	−	19.0526i	0.430134	−	0.745014i
$655$	4.00000			0.156293
$656$	12.0000	−	20.7846i	0.468521	−	0.811503i
$657$	−7.50000	+	12.9904i	−0.292603	+	0.506803i
$658$	−80.0000			−3.11872
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	−0.531855	−	0.846836i	$-0.678505\pi$
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	0.999309	+	0.0371821i	$0.0118382\pi$
$660$	2.00000	+	3.46410i	0.0778499	+	0.134840i
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	−0.974776	−	0.223184i	$-0.928355\pi$
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	0.294105	−	0.955773i	$-0.404978\pi$
$662$	18.0000			0.699590
$663$	−5.00000	−	5.19615i	−0.194184	−	0.201802i
$664$		0			0
$665$		0			0
$666$	2.00000	+	3.46410i	0.0774984	+	0.134231i
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$	24.0000			0.928588
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$	−7.00000	+	12.1244i	−0.270434	+	0.468405i
$671$	−26.0000			−1.00372
$672$	20.0000	−	34.6410i	0.771517	−	1.33631i
$673$	−16.5000	−	28.5788i	−0.636028	−	1.10163i	−0.986296	−	0.164984i	$-0.947243\pi$
$673$	−16.5000	−	28.5788i	−0.636028	−	1.10163i	0.350268	−	0.936650i	$-0.386091\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$	1.00000			0.0384900
$676$	−22.0000	−	13.8564i	−0.846154	−	0.532939i
$677$	−12.0000			−0.461197			−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000			−0.461197			−0.230599	+	0.973049i	$0.574068\pi$
$678$	2.00000	+	3.46410i	0.0768095	+	0.133038i
$679$	12.5000	+	21.6506i	0.479706	+	0.830875i
$680$		0			0
$681$	10.0000			0.383201
$682$	14.0000	−	24.2487i	0.536088	−	0.928531i
$683$	10.0000	−	17.3205i	0.382639	−	0.662751i	−0.608799	−	0.793324i	$-0.708349\pi$
$683$	10.0000	−	17.3205i	0.382639	−	0.662751i	0.991439	+	0.130573i	$0.0416818\pi$
$684$		0			0
$685$	−1.00000	+	1.73205i	−0.0382080	+	0.0661783i
$686$	−55.0000	−	95.2628i	−2.09991	−	3.63715i
$687$	−7.00000	−	12.1244i	−0.267067	−	0.462573i
$688$	−4.00000			−0.152499
$689$	10.0000	+	10.3923i	0.380970	+	0.395915i
$690$	−12.0000			−0.456832
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	−0.967132	−	0.254273i	$-0.918164\pi$
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	0.263359	−	0.964698i	$-0.415170\pi$
$692$		0			0
$693$	−5.00000	+	8.66025i	−0.189934	+	0.328976i
$694$	−32.0000			−1.21470
$695$	−1.50000	+	2.59808i	−0.0568982	+	0.0985506i
$696$		0			0
$697$	12.0000			0.454532
$698$	−3.00000	+	5.19615i	−0.113552	+	0.196677i
$699$	7.00000	+	12.1244i	0.264764	+	0.458585i
$700$	−5.00000	−	8.66025i	−0.188982	−	0.327327i
$701$	40.0000			1.51078			0.755390	−	0.655276i	$-0.227448\pi$
$701$	40.0000			1.51078			0.755390	+	0.655276i	$0.227448\pi$
$702$	−2.00000	+	6.92820i	−0.0754851	+	0.261488i
$703$		0			0
$704$	8.00000	+	13.8564i	0.301511	+	0.522233i
$705$	−4.00000	−	6.92820i	−0.150649	−	0.260931i
$706$	−6.00000	+	10.3923i	−0.225813	+	0.391120i
$707$	−90.0000			−3.38480
$708$	−12.0000	+	20.7846i	−0.450988	+	0.781133i
$709$	11.5000	−	19.9186i	0.431892	−	0.748058i	−0.565145	−	0.824992i	$-0.691180\pi$
$709$	11.5000	−	19.9186i	0.431892	−	0.748058i	0.997036	+	0.0769337i	$0.0245130\pi$
$710$	−24.0000			−0.900704
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$		0			0
$713$	21.0000	+	36.3731i	0.786456	+	1.36218i
$714$	20.0000			0.748481
$715$	2.00000	−	6.92820i	0.0747958	−	0.259100i
$716$	−12.0000			−0.448461
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	−2.00000	−	3.46410i	−0.0746393	−	0.129279i
$719$	−20.0000	+	34.6410i	−0.745874	+	1.29189i	0.203911	+	0.978989i	$0.434635\pi$
$719$	−20.0000	+	34.6410i	−0.745874	+	1.29189i	−0.949785	+	0.312903i	$0.898699\pi$
$720$	4.00000			0.149071
$721$	17.5000	−	30.3109i	0.651734	−	1.12884i
$722$	19.0000	−	32.9090i	0.707107	−	1.22474i
$723$	10.0000			0.371904
$724$	22.0000	−	38.1051i	0.817624	−	1.41617i
$725$	2.00000	+	3.46410i	0.0742781	+	0.128654i
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$	9.00000			0.333792			0.166896	−	0.985975i	$-0.446626\pi$
$727$	9.00000			0.333792			0.166896	+	0.985975i	$0.446626\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	15.0000	+	25.9808i	0.555175	+	0.961591i
$731$	−1.00000	−	1.73205i	−0.0369863	−	0.0640622i
$732$	13.0000	−	22.5167i	0.480494	−	0.832240i
$733$	7.00000			0.258551			0.129275	−	0.991609i	$-0.458735\pi$
$733$	7.00000			0.258551			0.129275	+	0.991609i	$0.458735\pi$
$734$	−7.00000	+	12.1244i	−0.258375	+	0.447518i
$735$	9.00000	−	15.5885i	0.331970	−	0.574989i
$736$	−48.0000			−1.76930
$737$	7.00000	−	12.1244i	0.257848	−	0.446606i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	18.0000	+	31.1769i	0.662141	+	1.14686i	0.980052	+	0.198741i	$0.0636852\pi$
$739$	18.0000	+	31.1769i	0.662141	+	1.14686i	−0.317911	+	0.948120i	$0.602981\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	−40.0000			−1.46845
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	0.557470	−	0.830197i	$-0.311772\pi$
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	−0.997707	+	0.0676840i	$0.978439\pi$
$744$		0			0
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	26.0000			0.951928
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$	−4.00000	+	6.92820i	−0.146254	+	0.253320i
$749$	20.0000			0.730784
$750$	1.00000	−	1.73205i	0.0365148	−	0.0632456i
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$	−16.0000	−	27.7128i	−0.583460	−	1.01058i
$753$		0			0
$754$	−28.0000	+	6.92820i	−1.01970	+	0.252310i
$755$	8.00000			0.291150
$756$	−5.00000	−	8.66025i	−0.181848	−	0.314970i
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	0.847280	−	0.531146i	$-0.178238\pi$
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	−0.883626	+	0.468193i	$0.844905\pi$
$758$	5.00000	−	8.66025i	0.181608	−	0.314555i
$759$	12.0000			0.435572
$760$		0			0
$761$	18.0000	−	31.1769i	0.652499	−	1.13016i	−0.330015	−	0.943976i	$-0.607054\pi$
$761$	18.0000	−	31.1769i	0.652499	−	1.13016i	0.982514	−	0.186187i	$-0.0596129\pi$
$762$	−22.0000			−0.796976
$763$	27.5000	−	47.6314i	0.995567	−	1.72437i
$764$	−12.0000	−	20.7846i	−0.434145	−	0.751961i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	−36.0000			−1.30073
$767$	42.0000	−	10.3923i	1.51653	−	0.375244i
$768$	16.0000			0.577350
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	0.990726	+	0.135877i	$0.0433852\pi$
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	−0.377690	+	0.925932i	$0.623282\pi$
$770$	10.0000	+	17.3205i	0.360375	+	0.624188i
$771$	11.0000	−	19.0526i	0.396155	−	0.686161i
$772$	−22.0000			−0.791797
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	0.0729331	+	0.997337i	$0.476764\pi$
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	−0.900186	+	0.435507i	$0.856569\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	−7.00000			−0.251447
$776$		0			0
$777$	5.00000	+	8.66025i	0.179374	+	0.310685i
$778$	−8.00000	−	13.8564i	−0.286814	−	0.496776i
$779$		0			0
$780$	5.00000	+	5.19615i	0.179029	+	0.186052i
$781$	24.0000			0.858788
$782$	−12.0000	−	20.7846i	−0.429119	−	0.743256i
$783$	2.00000	+	3.46410i	0.0714742	+	0.123797i
$784$	36.0000	−	62.3538i	1.28571	−	2.22692i
$785$	15.0000			0.535373
$786$	4.00000	−	6.92820i	0.142675	−	0.247121i
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	−0.976812	−	0.214097i	$-0.931319\pi$
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	0.673820	+	0.738896i	$0.264652\pi$
$788$	−24.0000			−0.854965
$789$	5.00000	−	8.66025i	0.178005	−	0.308313i
$790$	3.00000	+	5.19615i	0.106735	+	0.184871i
$791$	5.00000	+	8.66025i	0.177780	+	0.307923i
$792$		0			0
$793$	−45.5000	+	11.2583i	−1.61575	+	0.399795i
$794$	−30.0000			−1.06466
$795$	−2.00000	−	3.46410i	−0.0709327	−	0.122859i
$796$	−17.0000	−	29.4449i	−0.602549	−	1.04365i
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$		0			0
$799$	8.00000	−	13.8564i	0.283020	−	0.490204i
$800$	4.00000	−	6.92820i	0.141421	−	0.244949i
$801$	14.0000			0.494666
$802$	−16.0000	+	27.7128i	−0.564980	+	0.978573i
$803$	−15.0000	−	25.9808i	−0.529339	−	0.916841i
$804$	7.00000	+	12.1244i	0.246871	+	0.427593i
$805$	−30.0000			−1.05736
$806$	14.0000	−	48.4974i	0.493129	−	1.70825i
$807$	−6.00000			−0.211210
$808$		0			0
$809$	−2.00000	−	3.46410i	−0.0703163	−	0.121791i	0.828724	−	0.559658i	$-0.189068\pi$
$809$	−2.00000	−	3.46410i	−0.0703163	−	0.121791i	−0.899040	+	0.437867i	$0.855734\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$	45.0000			1.58016			0.790082	−	0.613001i	$-0.210038\pi$
$811$	45.0000			1.58016			0.790082	+	0.613001i	$0.210038\pi$
$812$	20.0000	−	34.6410i	0.701862	−	1.21566i
$813$	−14.5000	+	25.1147i	−0.508537	+	0.880812i
$814$	−8.00000			−0.280400
$815$	−7.50000	+	12.9904i	−0.262714	+	0.455033i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$		0			0
$818$	−30.0000			−1.04893
$819$	−5.00000	+	17.3205i	−0.174714	+	0.605228i
$820$	−12.0000			−0.419058
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$	2.00000	+	3.46410i	0.0697580	+	0.120824i
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	−0.985997	−	0.166762i	$-0.946669\pi$
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	0.637419	+	0.770517i	$0.280002\pi$
$824$		0			0
$825$	−1.00000	+	1.73205i	−0.0348155	+	0.0603023i
$826$	−60.0000	+	103.923i	−2.08767	+	3.61595i
$827$	46.0000			1.59958			0.799788	−	0.600282i	$-0.204945\pi$
$827$	46.0000			1.59958			0.799788	+	0.600282i	$0.204945\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	5.50000	+	9.52628i	0.191023	+	0.330861i	0.945589	−	0.325362i	$-0.105486\pi$
$829$	5.50000	+	9.52628i	0.191023	+	0.330861i	−0.754567	+	0.656223i	$0.772153\pi$
$830$	8.00000	+	13.8564i	0.277684	+	0.480963i
$831$	10.0000			0.346896
$832$	20.0000	+	20.7846i	0.693375	+	0.720577i
$833$	36.0000			1.24733
$834$	3.00000	+	5.19615i	0.103882	+	0.179928i
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$		0			0
$837$	−7.00000			−0.241955
$838$	−38.0000	+	65.8179i	−1.31269	+	2.27364i
$839$	17.0000	−	29.4449i	0.586905	−	1.01655i	−0.407730	−	0.913103i	$-0.633679\pi$
$839$	17.0000	−	29.4449i	0.586905	−	1.01655i	0.994635	−	0.103447i	$-0.0329872\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	23.0000	+	39.8372i	0.792632	+	1.37288i
$843$	6.00000	+	10.3923i	0.206651	+	0.357930i
$844$	30.0000			1.03264
$845$	0.500000	−	12.9904i	0.0172005	−	0.446883i
$846$	−16.0000			−0.550091
$847$	17.5000	+	30.3109i	0.601307	+	1.04149i
$848$	−8.00000	−	13.8564i	−0.274721	−	0.475831i
$849$	−2.50000	+	4.33013i	−0.0857998	+	0.148610i
$850$	4.00000			0.137199
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	−12.0000	+	20.7846i	−0.411113	+	0.712069i
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$	65.0000	−	112.583i	2.22425	−	3.85252i
$855$		0			0
$856$		0			0
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$	−10.0000	−	10.3923i	−0.341394	−	0.354787i
$859$	43.0000			1.46714			0.733571	−	0.679613i	$-0.237852\pi$
$859$	43.0000			1.46714			0.733571	+	0.679613i	$0.237852\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$	−15.0000	−	25.9808i	−0.511199	−	0.885422i
$862$	28.0000	−	48.4974i	0.953684	−	1.65183i
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	4.00000	−	6.92820i	0.136083	−	0.235702i
$865$		0			0
$866$	2.00000			0.0679628
$867$	6.50000	−	11.2583i	0.220752	−	0.382353i
$868$	35.0000	+	60.6218i	1.18798	+	2.05764i
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$	8.00000			0.271225
$871$	7.00000	−	24.2487i	0.237186	−	0.821636i
$872$		0			0
$873$	2.50000	+	4.33013i	0.0846122	+	0.146553i
$874$		0			0
$875$	2.50000	−	4.33013i	0.0845154	−	0.146385i
$876$	30.0000			1.01361
$877$	−3.00000	+	5.19615i	−0.101303	+	0.175462i	−0.912222	−	0.409697i	$-0.865634\pi$
$877$	−3.00000	+	5.19615i	−0.101303	+	0.175462i	0.810919	+	0.585159i	$0.198968\pi$
$878$	−15.0000	+	25.9808i	−0.506225	+	0.876808i
$879$	16.0000			0.539667
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	−10.0000	−	17.3205i	−0.336909	−	0.583543i	0.646941	−	0.762540i	$-0.276048\pi$
$881$	−10.0000	−	17.3205i	−0.336909	−	0.583543i	−0.983850	+	0.178997i	$0.942715\pi$
$882$	−18.0000	−	31.1769i	−0.606092	−	1.04978i
$883$	−25.0000			−0.841317			−0.420658	−	0.907219i	$-0.638201\pi$
$883$	−25.0000			−0.841317			−0.420658	+	0.907219i	$0.638201\pi$
$884$	−4.00000	+	13.8564i	−0.134535	+	0.466041i
$885$	−12.0000			−0.403376
$886$	−26.0000	−	45.0333i	−0.873487	−	1.51292i
$887$	22.0000	+	38.1051i	0.738688	+	1.27944i	0.953086	+	0.302698i	$0.0978875\pi$
$887$	22.0000	+	38.1051i	0.738688	+	1.27944i	−0.214399	+	0.976746i	$0.568779\pi$
$888$		0			0
$889$	−55.0000			−1.84464
$890$	14.0000	−	24.2487i	0.469281	−	0.812819i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−16.0000			−0.535720
$893$		0			0
$894$	12.0000	+	20.7846i	0.401340	+	0.695141i
$895$	−3.00000	−	5.19615i	−0.100279	−	0.173688i
$896$		0			0
$897$	21.0000	−	5.19615i	0.701170	−	0.173494i
$898$	36.0000			1.20134
$899$	−14.0000	−	24.2487i	−0.466926	−	0.808740i
$900$	−1.00000	−	1.73205i	−0.0333333	−	0.0577350i
$901$	4.00000	−	6.92820i	0.133259	−	0.230812i
$902$	24.0000			0.799113
$903$	−2.50000	+	4.33013i	−0.0831948	+	0.144098i
$904$		0			0
$905$	22.0000			0.731305
$906$	8.00000	−	13.8564i	0.265782	−	0.460348i
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	0.650868	−	0.759191i	$-0.274405\pi$
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	−0.982913	+	0.184073i	$0.941072\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$	−18.0000			−0.597022
$910$	25.0000	+	25.9808i	0.828742	+	0.861254i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$	−35.0000	+	60.6218i	−1.15770	+	2.00519i
$915$	13.0000			0.429767
$916$	−14.0000	+	24.2487i	−0.462573	+	0.801200i
$917$	10.0000	−	17.3205i	0.330229	−	0.571974i
$918$	4.00000			0.132020
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$	15.5000	+	26.8468i	0.510742	+	0.884632i
$922$	−4.00000			−0.131733
$923$	42.0000	−	10.3923i	1.38245	−	0.342067i
$924$	20.0000			0.657952
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	−3.00000	−	5.19615i	−0.0985861	−	0.170756i
$927$	3.50000	−	6.06218i	0.114955	−	0.199108i
$928$	32.0000			1.05045
$929$	−26.0000	+	45.0333i	−0.853032	+	1.47750i	0.0254262	+	0.999677i	$0.491906\pi$
$929$	−26.0000	+	45.0333i	−0.853032	+	1.47750i	−0.878459	+	0.477819i	$0.841428\pi$
$930$	−7.00000	+	12.1244i	−0.229539	+	0.397573i
$931$		0			0
$932$	14.0000	−	24.2487i	0.458585	−	0.794293i
$933$	11.0000	+	19.0526i	0.360124	+	0.623753i
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$	−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	$0.663014\pi$
$938$	35.0000	+	60.6218i	1.14279	+	1.97937i
$939$	15.5000	+	26.8468i	0.505823	+	0.876112i
$940$	−8.00000	+	13.8564i	−0.260931	+	0.451946i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	15.0000	−	25.9808i	0.488726	−	0.846499i
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$	−48.0000			−1.56227
$945$	2.50000	−	4.33013i	0.0813250	−	0.140859i
$946$	−2.00000	−	3.46410i	−0.0650256	−	0.112628i
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$	6.00000			0.194871
$949$	−37.5000	−	38.9711i	−1.21730	−	1.26506i
$950$		0			0
$951$	−6.00000	−	10.3923i	−0.194563	−	0.336994i
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$	−8.00000			−0.259010
$955$	6.00000	−	10.3923i	0.194155	−	0.336287i
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$	−8.00000			−0.258603
$958$	−42.0000	+	72.7461i	−1.35696	+	2.35032i
$959$	5.00000	+	8.66025i	0.161458	+	0.279654i
$960$	−4.00000	−	6.92820i	−0.129099	−	0.223607i
$961$	18.0000			0.580645
$962$	−14.0000	+	3.46410i	−0.451378	+	0.111687i
$963$	4.00000			0.128898
$964$	−10.0000	−	17.3205i	−0.322078	−	0.557856i
$965$	−5.50000	−	9.52628i	−0.177051	−	0.306662i
$966$	−30.0000	+	51.9615i	−0.965234	+	1.67183i
$967$	−56.0000			−1.80084			−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000			−1.80084			−0.900419	+	0.435023i	$0.856740\pi$
$968$		0			0
$969$		0			0
$970$	10.0000			0.321081
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	−0.980677	−	0.195633i	$-0.937324\pi$
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	0.659762	+	0.751475i	$0.270657\pi$
$972$	−1.00000	−	1.73205i	−0.0320750	−	0.0555556i
$973$	7.50000	+	12.9904i	0.240439	+	0.416452i
$974$	−56.0000			−1.79436
$975$	−1.00000	+	3.46410i	−0.0320256	+	0.110940i
$976$	52.0000			1.66448
$977$	−30.0000	−	51.9615i	−0.959785	−	1.66240i	−0.723017	−	0.690830i	$-0.757245\pi$
$977$	−30.0000	−	51.9615i	−0.959785	−	1.66240i	−0.236768	−	0.971566i	$-0.576088\pi$
$978$	15.0000	+	25.9808i	0.479647	+	0.830773i
$979$	−14.0000	+	24.2487i	−0.447442	+	0.774992i
$980$	−36.0000			−1.14998
$981$	5.50000	−	9.52628i	0.175601	−	0.304151i
$982$	24.0000	−	41.5692i	0.765871	−	1.32653i
$983$	38.0000			1.21201			0.606006	−	0.795460i	$-0.292771\pi$
$983$	38.0000			1.21201			0.606006	+	0.795460i	$0.292771\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$	8.00000	+	13.8564i	0.254772	+	0.441278i
$987$	−40.0000			−1.27321
$988$		0			0
$989$	6.00000			0.190789
$990$	2.00000	+	3.46410i	0.0635642	+	0.110096i
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$	−28.0000	+	48.4974i	−0.889001	+	1.53979i
$993$	9.00000			0.285606
$994$	−60.0000	+	103.923i	−1.90308	+	3.29624i
$995$	8.50000	−	14.7224i	0.269468	−	0.466732i
$996$	16.0000			0.506979
$997$	−14.5000	+	25.1147i	−0.459220	+	0.795392i	−0.998920	−	0.0464655i	$-0.985204\pi$
$997$	−14.5000	+	25.1147i	−0.459220	+	0.795392i	0.539700	+	0.841857i	$0.318538\pi$
$998$	−4.00000	−	6.92820i	−0.126618	−	0.219308i
$999$	1.00000	+	1.73205i	0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.i.a.16.1	✓	2
3.2	odd	2		585.2.j.b.406.1		2
5.2	odd	4		975.2.bb.f.874.2		4
5.3	odd	4		975.2.bb.f.874.1		4
5.4	even	2		975.2.i.i.601.1		2
13.3	even	3		2535.2.a.m.1.1		1
13.9	even	3	inner	195.2.i.a.61.1	yes	2
13.10	even	6		2535.2.a.c.1.1		1
39.23	odd	6		7605.2.a.s.1.1		1
39.29	odd	6		7605.2.a.a.1.1		1
39.35	odd	6		585.2.j.b.451.1		2
65.9	even	6		975.2.i.i.451.1		2
65.22	odd	12		975.2.bb.f.724.1		4
65.48	odd	12		975.2.bb.f.724.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.a.16.1	✓	2	1.1	even	1	trivial
195.2.i.a.61.1	yes	2	13.9	even	3	inner
585.2.j.b.406.1		2	3.2	odd	2
585.2.j.b.451.1		2	39.35	odd	6
975.2.i.i.451.1		2	65.9	even	6
975.2.i.i.601.1		2	5.4	even	2
975.2.bb.f.724.1		4	65.22	odd	12
975.2.bb.f.724.2		4	65.48	odd	12
975.2.bb.f.874.1		4	5.3	odd	4
975.2.bb.f.874.2		4	5.2	odd	4
2535.2.a.c.1.1		1	13.10	even	6
2535.2.a.m.1.1		1	13.3	even	3
7605.2.a.a.1.1		1	39.29	odd	6
7605.2.a.s.1.1		1	39.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -1.00000 q^{5} +(-1.00000 + 1.73205i) q^{6} +(-2.50000 + 4.33013i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -1.00000 q^{5} +(-1.00000 + 1.73205i) q^{6} +(-2.50000 + 4.33013i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-1.00000 - 1.73205i) q^{11} +2.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +10.0000 q^{14} +(0.500000 + 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +2.00000 q^{18} +(1.00000 - 1.73205i) q^{20} +5.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(-3.00000 - 5.19615i) q^{23} +1.00000 q^{25} +(-2.00000 + 6.92820i) q^{26} +1.00000 q^{27} +(-5.00000 - 8.66025i) q^{28} +(2.00000 + 3.46410i) q^{29} +(1.00000 - 1.73205i) q^{30} -7.00000 q^{31} +(4.00000 - 6.92820i) q^{32} +(-1.00000 + 1.73205i) q^{33} +4.00000 q^{34} +(2.50000 - 4.33013i) q^{35} +(-1.00000 - 1.73205i) q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.00000 + 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(-5.00000 - 8.66025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +4.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(-6.00000 + 10.3923i) q^{46} -8.00000 q^{47} +(2.00000 - 3.46410i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(-1.00000 - 1.73205i) q^{50} +2.00000 q^{51} +(7.00000 - 1.73205i) q^{52} -4.00000 q^{53} +(-1.00000 - 1.73205i) q^{54} +(1.00000 + 1.73205i) q^{55} +(4.00000 - 6.92820i) q^{58} +(-6.00000 + 10.3923i) q^{59} -2.00000 q^{60} +(6.50000 - 11.2583i) q^{61} +(7.00000 + 12.1244i) q^{62} +(-2.50000 - 4.33013i) q^{63} -8.00000 q^{64} +(2.50000 + 2.59808i) q^{65} +4.00000 q^{66} +(3.50000 + 6.06218i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-3.00000 + 5.19615i) q^{69} -10.0000 q^{70} +(-6.00000 + 10.3923i) q^{71} +15.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(-0.500000 - 0.866025i) q^{75} +10.0000 q^{77} +(7.00000 - 1.73205i) q^{78} +3.00000 q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +8.00000 q^{83} +(-5.00000 + 8.66025i) q^{84} +(1.00000 - 1.73205i) q^{85} +2.00000 q^{86} +(2.00000 - 3.46410i) q^{87} +(-7.00000 - 12.1244i) q^{89} -2.00000 q^{90} +(17.5000 - 4.33013i) q^{91} +12.0000 q^{92} +(3.50000 + 6.06218i) q^{93} +(8.00000 + 13.8564i) q^{94} -8.00000 q^{96} +(2.50000 - 4.33013i) q^{97} +(-18.0000 + 31.1769i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 5 * q^7 - q^9	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 5 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 5 q^{13} + 20 q^{14} + q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} + 10 q^{21} - 4 q^{22} - 6 q^{23} + 2 q^{25} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{30} - 14 q^{31} + 8 q^{32} - 2 q^{33} + 8 q^{34} + 5 q^{35} - 2 q^{36} + 2 q^{37} - 2 q^{39} - 6 q^{41} - 10 q^{42} - q^{43} + 8 q^{44} + q^{45} - 12 q^{46} - 16 q^{47} + 4 q^{48} - 18 q^{49} - 2 q^{50} + 4 q^{51} + 14 q^{52} - 8 q^{53} - 2 q^{54} + 2 q^{55} + 8 q^{58} - 12 q^{59} - 4 q^{60} + 13 q^{61} + 14 q^{62} - 5 q^{63} - 16 q^{64} + 5 q^{65} + 8 q^{66} + 7 q^{67} - 4 q^{68} - 6 q^{69} - 20 q^{70} - 12 q^{71} + 30 q^{73} + 4 q^{74} - q^{75} + 20 q^{77} + 14 q^{78} + 6 q^{79} - 4 q^{80} - q^{81} - 12 q^{82} + 16 q^{83} - 10 q^{84} + 2 q^{85} + 4 q^{86} + 4 q^{87} - 14 q^{89} - 4 q^{90} + 35 q^{91} + 24 q^{92} + 7 q^{93} + 16 q^{94} - 16 q^{96} + 5 q^{97} - 36 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 5 * q^7 - q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 - 5 * q^13 + 20 * q^14 + q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^20 + 10 * q^21 - 4 * q^22 - 6 * q^23 + 2 * q^25 - 4 * q^26 + 2 * q^27 - 10 * q^28 + 4 * q^29 + 2 * q^30 - 14 * q^31 + 8 * q^32 - 2 * q^33 + 8 * q^34 + 5 * q^35 - 2 * q^36 + 2 * q^37 - 2 * q^39 - 6 * q^41 - 10 * q^42 - q^43 + 8 * q^44 + q^45 - 12 * q^46 - 16 * q^47 + 4 * q^48 - 18 * q^49 - 2 * q^50 + 4 * q^51 + 14 * q^52 - 8 * q^53 - 2 * q^54 + 2 * q^55 + 8 * q^58 - 12 * q^59 - 4 * q^60 + 13 * q^61 + 14 * q^62 - 5 * q^63 - 16 * q^64 + 5 * q^65 + 8 * q^66 + 7 * q^67 - 4 * q^68 - 6 * q^69 - 20 * q^70 - 12 * q^71 + 30 * q^73 + 4 * q^74 - q^75 + 20 * q^77 + 14 * q^78 + 6 * q^79 - 4 * q^80 - q^81 - 12 * q^82 + 16 * q^83 - 10 * q^84 + 2 * q^85 + 4 * q^86 + 4 * q^87 - 14 * q^89 - 4 * q^90 + 35 * q^91 + 24 * q^92 + 7 * q^93 + 16 * q^94 - 16 * q^96 + 5 * q^97 - 36 * q^98 + 4 * q^99

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