LMFDB - Embedded newform 195.2.i.d.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:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.385124i$ of defining polynomial
Character	$\chi$	$=$	195.16
Dual form			195.2.i.d.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30084 - 2.25312i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +1.00000 q^{5} +(1.30084 - 2.25312i) q^{6} +(-1.80084 + 3.11915i) q^{7} +7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.30084 - 2.25312i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +1.00000 q^{5} +(1.30084 - 2.25312i) q^{6} +(-1.80084 + 3.11915i) q^{7} +7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.30084 - 2.25312i) q^{10} +(2.60168 + 4.50624i) q^{11} -4.76873 q^{12} +(3.01815 - 1.97250i) q^{13} +9.37041 q^{14} +(0.500000 + 0.866025i) q^{15} +(-4.60168 - 7.97034i) q^{16} +(1.46789 - 2.54247i) q^{17} +2.60168 q^{18} +(-3.38437 + 5.86190i) q^{19} +(-2.38437 + 4.12985i) q^{20} -3.60168 q^{21} +(6.76873 - 11.7238i) q^{22} +(-2.76873 - 4.79559i) q^{23} +(3.60168 + 6.23829i) q^{24} +1.00000 q^{25} +(-8.37041 - 4.23435i) q^{26} -1.00000 q^{27} +(-8.58773 - 14.8744i) q^{28} +(-0.916472 - 1.58738i) q^{29} +(1.30084 - 2.25312i) q^{30} +4.10284 q^{31} +(-4.76873 + 8.25969i) q^{32} +(-2.60168 + 4.50624i) q^{33} -7.63798 q^{34} +(-1.80084 + 3.11915i) q^{35} +(-2.38437 - 4.12985i) q^{36} +(1.76873 + 3.06354i) q^{37} +17.6101 q^{38} +(3.21731 + 1.62755i) q^{39} +7.20336 q^{40} +(2.68521 + 4.65091i) q^{41} +(4.68521 + 8.11502i) q^{42} +(-1.58353 + 2.74275i) q^{43} -24.8134 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-7.20336 + 12.4766i) q^{46} +3.80504 q^{47} +(4.60168 - 7.97034i) q^{48} +(-2.98605 - 5.17198i) q^{49} +(-1.30084 - 2.25312i) q^{50} +2.93579 q^{51} +(0.949743 + 17.1677i) q^{52} -5.20336 q^{53} +(1.30084 + 2.25312i) q^{54} +(2.60168 + 4.50624i) q^{55} +(-12.9721 + 22.4683i) q^{56} -6.76873 q^{57} +(-2.38437 + 4.12985i) q^{58} +(3.68521 - 6.38297i) q^{59} -4.76873 q^{60} +(1.71731 - 2.97447i) q^{61} +(-5.33714 - 9.24420i) q^{62} +(-1.80084 - 3.11915i) q^{63} +6.40672 q^{64} +(3.01815 - 1.97250i) q^{65} +13.5375 q^{66} +(-1.75058 - 3.03210i) q^{67} +(7.00000 + 12.1244i) q^{68} +(2.76873 - 4.79559i) q^{69} +9.37041 q^{70} +(4.85226 - 8.40436i) q^{71} +(-3.60168 + 6.23829i) q^{72} -0.805037 q^{73} +(4.60168 - 7.97034i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-16.1391 - 27.9538i) q^{76} -18.7408 q^{77} +(-0.518152 - 9.36617i) q^{78} -4.10284 q^{79} +(-4.60168 - 7.97034i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.98605 - 12.1002i) q^{82} -11.5375 q^{83} +(8.58773 - 14.8744i) q^{84} +(1.46789 - 2.54247i) q^{85} +8.23966 q^{86} +(0.916472 - 1.58738i) q^{87} +(18.7408 + 32.4601i) q^{88} +(-4.91647 - 8.51558i) q^{89} +2.60168 q^{90} +(0.717312 + 12.9662i) q^{91} +26.4067 q^{92} +(2.05142 + 3.55317i) q^{93} +(-4.94974 - 8.57321i) q^{94} +(-3.38437 + 5.86190i) q^{95} -9.53747 q^{96} +(2.78689 - 4.82703i) q^{97} +(-7.76873 + 13.4558i) q^{98} -5.20336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9} - 12 q^{12} + 3 q^{13} + 24 q^{14} + 3 q^{15} - 12 q^{16} - 12 q^{19} - 6 q^{20} - 6 q^{21} + 24 q^{22} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 12 q^{28} - 6 q^{29} + 6 q^{31} - 12 q^{32} - 3 q^{35} - 6 q^{36} - 6 q^{37} + 12 q^{38} + 12 q^{39} + 12 q^{40} + 12 q^{42} - 9 q^{43} - 24 q^{44} - 3 q^{45} - 12 q^{46} - 24 q^{47} + 12 q^{48} + 6 q^{49} + 12 q^{52} - 30 q^{56} - 24 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{60} + 3 q^{61} + 6 q^{62} - 3 q^{63} - 24 q^{64} + 3 q^{65} + 48 q^{66} - 9 q^{67} + 42 q^{68} + 24 q^{70} + 12 q^{71} - 6 q^{72} + 42 q^{73} + 12 q^{74} + 3 q^{75} - 48 q^{76} - 48 q^{77} + 12 q^{78} - 6 q^{79} - 12 q^{80} - 3 q^{81} + 18 q^{82} - 36 q^{83} + 12 q^{84} - 12 q^{86} + 6 q^{87} + 48 q^{88} - 30 q^{89} - 3 q^{91} + 96 q^{92} + 3 q^{93} - 36 q^{94} - 12 q^{95} - 24 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) $ 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9 - 12 * q^12 + 3 * q^13 + 24 * q^14 + 3 * q^15 - 12 * q^16 - 12 * q^19 - 6 * q^20 - 6 * q^21 + 24 * q^22 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 + 6 * q^31 - 12 * q^32 - 3 * q^35 - 6 * q^36 - 6 * q^37 + 12 * q^38 + 12 * q^39 + 12 * q^40 + 12 * q^42 - 9 * q^43 - 24 * q^44 - 3 * q^45 - 12 * q^46 - 24 * q^47 + 12 * q^48 + 6 * q^49 + 12 * q^52 - 30 * q^56 - 24 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^60 + 3 * q^61 + 6 * q^62 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 48 * q^66 - 9 * q^67 + 42 * q^68 + 24 * q^70 + 12 * q^71 - 6 * q^72 + 42 * q^73 + 12 * q^74 + 3 * q^75 - 48 * q^76 - 48 * q^77 + 12 * q^78 - 6 * q^79 - 12 * q^80 - 3 * q^81 + 18 * q^82 - 36 * q^83 + 12 * q^84 - 12 * q^86 + 6 * q^87 + 48 * q^88 - 30 * q^89 - 3 * q^91 + 96 * q^92 + 3 * q^93 - 36 * q^94 - 12 * q^95 - 24 * q^96 - 15 * q^97 - 30 * q^98

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 $

$2$	−1.30084	−	2.25312i	−0.919832	−	1.59320i	−0.799668	−	0.600443i	$-0.794991\pi$
$2$	−1.30084	−	2.25312i	−0.919832	−	1.59320i	−0.120165	−	0.992754i	$-0.538342\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.38437	+	4.12985i	−1.19218	+	2.06492i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.30084	−	2.25312i	0.531066	−	0.919832i
$7$	−1.80084	+	3.11915i	−0.680653	+	1.17893i	0.294128	+	0.955766i	$0.404971\pi$
$7$	−1.80084	+	3.11915i	−0.680653	+	1.17893i	−0.974782	+	0.223160i	$0.928363\pi$
$8$	7.20336			2.54677
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.30084	−	2.25312i	−0.411362	−	0.712499i
$11$	2.60168	+	4.50624i	0.784436	+	1.35868i	0.929336	+	0.369236i	$0.120381\pi$
$11$	2.60168	+	4.50624i	0.784436	+	1.35868i	−0.144900	+	0.989446i	$0.546286\pi$
$12$	−4.76873			−1.37662
$13$	3.01815	−	1.97250i	0.837085	−	0.547073i
$13$	3.01815	−	1.97250i	0.837085	−	0.547073i
$14$	9.37041			2.50435
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−4.60168	−	7.97034i	−1.15042	−	1.99259i
$17$	1.46789	−	2.54247i	0.356017	−	0.616639i	−0.631275	−	0.775559i	$-0.717468\pi$
$17$	1.46789	−	2.54247i	0.356017	−	0.616639i	0.987291	+	0.158920i	$0.0508013\pi$
$18$	2.60168			0.613222
$19$	−3.38437	+	5.86190i	−0.776427	+	1.34481i	0.157562	+	0.987509i	$0.449637\pi$
$19$	−3.38437	+	5.86190i	−0.776427	+	1.34481i	−0.933989	+	0.357302i	$0.883697\pi$
$20$	−2.38437	+	4.12985i	−0.533161	+	0.923461i
$21$	−3.60168			−0.785951
$22$	6.76873	−	11.7238i	1.44310	−	2.49952i
$23$	−2.76873	−	4.79559i	−0.577321	−	0.999949i	−0.995785	−	0.0917160i	$-0.970765\pi$
$23$	−2.76873	−	4.79559i	−0.577321	−	0.999949i	0.418464	−	0.908233i	$-0.362569\pi$
$24$	3.60168	+	6.23829i	0.735190	+	1.27339i
$25$	1.00000			0.200000
$26$	−8.37041	−	4.23435i	−1.64157	−	0.830424i
$27$	−1.00000			−0.192450
$28$	−8.58773	−	14.8744i	−1.62293	−	2.81099i
$29$	−0.916472	−	1.58738i	−0.170185	−	0.294768i	0.768300	−	0.640090i	$-0.221103\pi$
$29$	−0.916472	−	1.58738i	−0.170185	−	0.294768i	−0.938484	+	0.345322i	$0.887770\pi$
$30$	1.30084	−	2.25312i	0.237500	−	0.411362i
$31$	4.10284			0.736893			0.368446	−	0.929649i	$-0.379890\pi$
$31$	4.10284			0.736893			0.368446	+	0.929649i	$0.379890\pi$
$32$	−4.76873	+	8.25969i	−0.843001	+	1.46012i
$33$	−2.60168	+	4.50624i	−0.452894	+	0.784436i
$34$	−7.63798			−1.30990
$35$	−1.80084	+	3.11915i	−0.304397	+	0.527232i
$36$	−2.38437	−	4.12985i	−0.397395	−	0.688308i
$37$	1.76873	+	3.06354i	0.290778	+	0.503642i	0.973994	−	0.226574i	$-0.0727525\pi$
$37$	1.76873	+	3.06354i	0.290778	+	0.503642i	−0.683216	+	0.730217i	$0.739419\pi$
$38$	17.6101			2.85673
$39$	3.21731	+	1.62755i	0.515182	+	0.260616i
$40$	7.20336			1.13895
$41$	2.68521	+	4.65091i	0.419359	+	0.726351i	0.995875	−	0.0907349i	$-0.0289216\pi$
$41$	2.68521	+	4.65091i	0.419359	+	0.726351i	−0.576516	+	0.817086i	$0.695588\pi$
$42$	4.68521	+	8.11502i	0.722943	+	1.25217i
$43$	−1.58353	+	2.74275i	−0.241486	+	0.418265i	−0.961138	−	0.276069i	$-0.910968\pi$
$43$	−1.58353	+	2.74275i	−0.241486	+	0.418265i	0.719652	+	0.694335i	$0.244301\pi$
$44$	−24.8134			−3.74077
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−7.20336	+	12.4766i	−1.06208	+	1.83957i
$47$	3.80504			0.555022			0.277511	−	0.960722i	$-0.410491\pi$
$47$	3.80504			0.555022			0.277511	+	0.960722i	$0.410491\pi$
$48$	4.60168	−	7.97034i	0.664195	−	1.15042i
$49$	−2.98605	−	5.17198i	−0.426578	−	0.738855i
$50$	−1.30084	−	2.25312i	−0.183966	−	0.318639i
$51$	2.93579			0.411093
$52$	0.949743	+	17.1677i	0.131706	+	2.38073i
$53$	−5.20336			−0.714736			−0.357368	−	0.933964i	$-0.616326\pi$
$53$	−5.20336			−0.714736			−0.357368	+	0.933964i	$0.616326\pi$
$54$	1.30084	+	2.25312i	0.177022	+	0.306611i
$55$	2.60168	+	4.50624i	0.350810	+	0.607621i
$56$	−12.9721	+	22.4683i	−1.73347	+	3.00246i
$57$	−6.76873			−0.896541
$58$	−2.38437	+	4.12985i	−0.313083	+	0.542275i
$59$	3.68521	−	6.38297i	0.479773	−	0.830991i	−0.519958	−	0.854192i	$-0.674052\pi$
$59$	3.68521	−	6.38297i	0.479773	−	0.830991i	0.999731	+	0.0232007i	$0.00738566\pi$
$60$	−4.76873			−0.615641
$61$	1.71731	−	2.97447i	0.219879	−	0.380842i	−0.734892	−	0.678185i	$-0.762767\pi$
$61$	1.71731	−	2.97447i	0.219879	−	0.380842i	0.954771	+	0.297343i	$0.0961003\pi$
$62$	−5.33714	−	9.24420i	−0.677818	−	1.17401i
$63$	−1.80084	−	3.11915i	−0.226884	−	0.392975i
$64$	6.40672			0.800840
$65$	3.01815	−	1.97250i	0.374356	−	0.244659i
$66$	13.5375			1.66635
$67$	−1.75058	−	3.03210i	−0.213868	−	0.370430i	0.739054	−	0.673646i	$-0.235273\pi$
$67$	−1.75058	−	3.03210i	−0.213868	−	0.370430i	−0.952922	+	0.303216i	$0.901939\pi$
$68$	7.00000	+	12.1244i	0.848875	+	1.47029i
$69$	2.76873	−	4.79559i	0.333316	−	0.577321i
$70$	9.37041			1.11998
$71$	4.85226	−	8.40436i	0.575858	−	0.997415i	−0.420090	−	0.907482i	$-0.638002\pi$
$71$	4.85226	−	8.40436i	0.575858	−	0.997415i	0.995948	−	0.0899322i	$-0.0286650\pi$
$72$	−3.60168	+	6.23829i	−0.424462	+	0.735190i
$73$	−0.805037			−0.0942225			−0.0471113	−	0.998890i	$-0.515002\pi$
$73$	−0.805037			−0.0942225			−0.0471113	+	0.998890i	$0.515002\pi$
$74$	4.60168	−	7.97034i	0.534934	−	0.926533i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−16.1391	−	27.9538i	−1.85129	−	3.20652i
$77$	−18.7408			−2.13572
$78$	−0.518152	−	9.36617i	−0.0586691	−	1.06051i
$79$	−4.10284			−0.461606			−0.230803	−	0.973000i	$-0.574135\pi$
$79$	−4.10284			−0.461606			−0.230803	+	0.973000i	$0.574135\pi$
$80$	−4.60168	−	7.97034i	−0.514483	−	0.891111i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.98605	−	12.1002i	0.771480	−	1.33624i
$83$	−11.5375			−1.26640			−0.633201	−	0.773988i	$-0.718259\pi$
$83$	−11.5375			−1.26640			−0.633201	+	0.773988i	$0.718259\pi$
$84$	8.58773	−	14.8744i	0.936998	−	1.62293i
$85$	1.46789	−	2.54247i	0.159216	−	0.275769i
$86$	8.23966			0.888506
$87$	0.916472	−	1.58738i	0.0982562	−	0.170185i
$88$	18.7408	+	32.4601i	1.99778	+	3.46025i
$89$	−4.91647	−	8.51558i	−0.521145	−	0.902650i	−0.999698	−	0.0245908i	$-0.992172\pi$
$89$	−4.91647	−	8.51558i	−0.521145	−	0.902650i	0.478553	−	0.878059i	$-0.341162\pi$
$90$	2.60168			0.274241
$91$	0.717312	+	12.9662i	0.0751947	+	1.35923i
$92$	26.4067			2.75309
$93$	2.05142	+	3.55317i	0.212723	+	0.368446i
$94$	−4.94974	−	8.57321i	−0.510527	−	0.884259i
$95$	−3.38437	+	5.86190i	−0.347229	+	0.601418i
$96$	−9.53747			−0.973414
$97$	2.78689	−	4.82703i	0.282965	−	0.490110i	−0.689148	−	0.724620i	$-0.742015\pi$
$97$	2.78689	−	4.82703i	0.282965	−	0.490110i	0.972114	+	0.234510i	$0.0753485\pi$
$98$	−7.76873	+	13.4558i	−0.784761	+	1.35925i
$99$	−5.20336			−0.522957
$100$	−2.38437	+	4.12985i	−0.238437	+	0.412985i
$101$	−1.20336	−	2.08428i	−0.119739	−	0.207393i	0.799925	−	0.600099i	$-0.204872\pi$
$101$	−1.20336	−	2.08428i	−0.119739	−	0.207393i	−0.919664	+	0.392706i	$0.871539\pi$
$102$	−3.81899	−	6.61469i	−0.378136	−	0.654952i
$103$	18.4430			1.81724			0.908622	−	0.417619i	$-0.137135\pi$
$103$	18.4430			1.81724			0.908622	+	0.417619i	$0.137135\pi$
$104$	21.7408	−	14.2086i	2.13186	−	1.39327i
$105$	−3.60168			−0.351488
$106$	6.76873	+	11.7238i	0.657438	+	1.13872i
$107$	−5.46789	−	9.47067i	−0.528601	−	0.915564i	−0.999444	−	0.0333471i	$-0.989383\pi$
$107$	−5.46789	−	9.47067i	−0.528601	−	0.915564i	0.470842	−	0.882217i	$-0.343950\pi$
$108$	2.38437	−	4.12985i	0.229436	−	0.397395i
$109$	13.8692			1.32843			0.664217	−	0.747540i	$-0.268765\pi$
$109$	13.8692			1.32843			0.664217	+	0.747540i	$0.268765\pi$
$110$	6.76873	−	11.7238i	0.645373	−	1.11782i
$111$	−1.76873	+	3.06354i	−0.167881	+	0.290778i
$112$	33.1475			3.13215
$113$	5.60168	−	9.70239i	0.526962	−	0.912724i	−0.472545	−	0.881307i	$-0.656664\pi$
$113$	5.60168	−	9.70239i	0.526962	−	0.912724i	0.999506	−	0.0314176i	$-0.0100022\pi$
$114$	8.80504	+	15.2508i	0.824667	+	1.42837i
$115$	−2.76873	−	4.79559i	−0.258186	−	0.447191i
$116$	8.74083			0.811565
$117$	0.199160	+	3.60005i	0.0184124	+	0.332824i
$118$	−19.1755			−1.76524
$119$	5.28689	+	9.15715i	0.484648	+	0.839435i
$120$	3.60168	+	6.23829i	0.328787	+	0.569475i
$121$	−8.03747	+	13.9213i	−0.730679	+	1.26557i
$122$	−8.93579			−0.809008
$123$	−2.68521	+	4.65091i	−0.242117	+	0.419359i
$124$	−9.78269	+	16.9441i	−0.878511	+	1.52163i
$125$	1.00000			0.0894427
$126$	−4.68521	+	8.11502i	−0.417391	+	0.722943i
$127$	1.59748	+	2.76692i	0.141754	+	0.245524i	0.928157	−	0.372189i	$-0.121393\pi$
$127$	1.59748	+	2.76692i	0.141754	+	0.245524i	−0.786403	+	0.617713i	$0.788059\pi$
$128$	1.20336	+	2.08428i	0.106363	+	0.184226i
$129$	−3.16706			−0.278844
$130$	−8.37041	−	4.23435i	−0.734134	−	0.371377i
$131$	−4.57377			−0.399612			−0.199806	−	0.979835i	$-0.564031\pi$
$131$	−4.57377			−0.399612			−0.199806	+	0.979835i	$0.564031\pi$
$132$	−12.4067	−	21.4891i	−1.07987	−	1.87038i
$133$	−12.1894	−	21.1127i	−1.05696	−	1.83070i
$134$	−4.55445	+	7.88855i	−0.393445	+	0.681467i
$135$	−1.00000			−0.0860663
$136$	10.5738	−	18.3143i	0.906693	−	1.57044i
$137$	−5.33714	+	9.24420i	−0.455983	+	0.789785i	−0.998744	−	0.0501015i	$-0.984046\pi$
$137$	−5.33714	+	9.24420i	−0.455983	+	0.789785i	0.542761	+	0.839887i	$0.317379\pi$
$138$	−14.4067			−1.22638
$139$	8.07377	−	13.9842i	0.684808	−	1.18612i	−0.288689	−	0.957423i	$-0.593219\pi$
$139$	8.07377	−	13.9842i	0.684808	−	1.18612i	0.973497	−	0.228700i	$-0.0734474\pi$
$140$	−8.58773	−	14.8744i	−0.725795	−	1.25711i
$141$	1.90252	+	3.29526i	0.160221	+	0.277511i
$142$	−25.2481			−2.11877
$143$	16.7408	+	8.46870i	1.39994	+	0.708188i
$144$	9.20336			0.766947
$145$	−0.916472	−	1.58738i	−0.0761089	−	0.131824i
$146$	1.04722	+	1.81385i	0.0866689	+	0.150115i
$147$	2.98605	−	5.17198i	0.246285	−	0.426578i
$148$	−16.8692			−1.38664
$149$	4.83294	−	8.37091i	0.395930	−	0.685771i	−0.597289	−	0.802026i	$-0.703756\pi$
$149$	4.83294	−	8.37091i	0.395930	−	0.685771i	0.993219	+	0.116255i	$0.0370889\pi$
$150$	1.30084	−	2.25312i	0.106213	−	0.183966i
$151$	−18.7129			−1.52284			−0.761418	−	0.648261i	$-0.775496\pi$
$151$	−18.7129			−1.52284			−0.761418	+	0.648261i	$0.775496\pi$
$152$	−24.3788	+	42.2253i	−1.97738	+	3.42493i
$153$	1.46789	+	2.54247i	0.118672	+	0.205546i
$154$	24.3788	+	42.2253i	1.96450	+	3.40261i
$155$	4.10284			0.329548
$156$	−14.3928	+	9.40633i	−1.15234	+	0.753109i
$157$	−10.3704			−0.827649			−0.413825	−	0.910357i	$-0.635807\pi$
$157$	−10.3704			−0.827649			−0.413825	+	0.910357i	$0.635807\pi$
$158$	5.33714	+	9.24420i	0.424600	+	0.735429i
$159$	−2.60168	−	4.50624i	−0.206327	−	0.357368i
$160$	−4.76873	+	8.25969i	−0.377002	+	0.652986i
$161$	19.9442			1.57182
$162$	−1.30084	+	2.25312i	−0.102204	+	0.177022i
$163$	5.73663	−	9.93613i	0.449327	−	0.778258i	−0.549015	−	0.835813i	$-0.684997\pi$
$163$	5.73663	−	9.93613i	0.449327	−	0.778258i	0.998342	+	0.0575546i	$0.0183303\pi$
$164$	−25.6101			−1.99981
$165$	−2.60168	+	4.50624i	−0.202540	+	0.350810i
$166$	15.0084	+	25.9953i	1.16488	+	2.01763i
$167$	1.56538	+	2.71131i	0.121132	+	0.209808i	0.920215	−	0.391414i	$-0.128014\pi$
$167$	1.56538	+	2.71131i	0.121132	+	0.209808i	−0.799082	+	0.601222i	$0.794681\pi$
$168$	−25.9442			−2.00164
$169$	5.21848	−	11.9066i	0.401421	−	0.915893i
$170$	−7.63798			−0.585806
$171$	−3.38437	−	5.86190i	−0.258809	−	0.448270i
$172$	−7.55142	−	13.0794i	−0.575791	−	0.997298i
$173$	−4.13378	+	7.15992i	−0.314286	+	0.544359i	−0.979285	−	0.202485i	$-0.935098\pi$
$173$	−4.13378	+	7.15992i	−0.314286	+	0.544359i	0.665000	+	0.746844i	$0.268432\pi$
$174$	−4.76873			−0.361517
$175$	−1.80084	+	3.11915i	−0.136131	+	0.235785i
$176$	23.9442	−	41.4725i	1.80486	−	3.12611i
$177$	7.37041			0.553994
$178$	−12.7911	+	22.1548i	−0.958732	+	1.66057i
$179$	9.22268	+	15.9741i	0.689335	+	1.19396i	0.972053	+	0.234760i	$0.0754306\pi$
$179$	9.22268	+	15.9741i	0.689335	+	1.19396i	−0.282718	+	0.959203i	$0.591236\pi$
$180$	−2.38437	−	4.12985i	−0.177720	−	0.307820i
$181$	21.1028			1.56856			0.784281	−	0.620406i	$-0.213032\pi$
$181$	21.1028			1.56856			0.784281	+	0.620406i	$0.213032\pi$
$182$	28.2813	−	18.4832i	2.09635	−	1.37006i
$183$	3.43462			0.253895
$184$	−19.9442	−	34.5443i	−1.47030	−	2.54664i
$185$	1.76873	+	3.06354i	0.130040	+	0.225236i
$186$	5.33714	−	9.24420i	0.391338	−	0.677818i
$187$	15.2760			1.11709
$188$	−9.07261	+	15.7142i	−0.661688	+	1.14608i
$189$	1.80084	−	3.11915i	0.130992	−	0.226884i
$190$	17.6101			1.27757
$191$	4.35110	−	7.53632i	0.314834	−	0.545309i	−0.664568	−	0.747228i	$-0.731384\pi$
$191$	4.35110	−	7.53632i	0.314834	−	0.545309i	0.979402	+	0.201919i	$0.0647177\pi$
$192$	3.20336	+	5.54838i	0.231182	+	0.400420i
$193$	−9.63378	−	16.6862i	−0.693455	−	1.20110i	−0.970699	−	0.240300i	$-0.922754\pi$
$193$	−9.63378	−	16.6862i	−0.693455	−	1.20110i	0.277244	−	0.960800i	$-0.410579\pi$
$194$	−14.5012			−1.04112
$195$	3.21731	+	1.62755i	0.230396	+	0.116551i
$196$	28.4793			2.03424
$197$	7.57377	+	13.1182i	0.539609	+	0.934630i	0.998925	+	0.0463571i	$0.0147612\pi$
$197$	7.57377	+	13.1182i	0.539609	+	0.934630i	−0.459316	+	0.888273i	$0.651905\pi$
$198$	6.76873	+	11.7238i	0.481033	+	0.833174i
$199$	2.26873	−	3.92956i	0.160826	−	0.278559i	−0.774339	−	0.632771i	$-0.781917\pi$
$199$	2.26873	−	3.92956i	0.160826	−	0.278559i	0.935165	+	0.354212i	$0.115251\pi$
$200$	7.20336			0.509354
$201$	1.75058	−	3.03210i	0.123477	−	0.213868i
$202$	−3.13075	+	5.42262i	−0.220279	+	0.381534i
$203$	6.60168			0.463347
$204$	−7.00000	+	12.1244i	−0.490098	+	0.848875i
$205$	2.68521	+	4.65091i	0.187543	+	0.324834i
$206$	−23.9914	−	41.5543i	−1.67156	−	2.89523i
$207$	5.53747			0.384881
$208$	−29.6101	−	14.9789i	−2.05309	−	1.03860i
$209$	−35.2201			−2.43623
$210$	4.68521	+	8.11502i	0.323310	+	0.559989i
$211$	11.0738	+	19.1803i	0.762350	+	1.32043i	0.941636	+	0.336632i	$0.109288\pi$
$211$	11.0738	+	19.1803i	0.762350	+	1.32043i	−0.179286	+	0.983797i	$0.557379\pi$
$212$	12.4067	−	21.4891i	0.852097	−	1.47587i
$213$	9.70452			0.664943
$214$	−14.2257	+	24.6396i	−0.972449	+	1.68433i
$215$	−1.58353	+	2.74275i	−0.107996	+	0.187054i
$216$	−7.20336			−0.490126
$217$	−7.38856	+	12.7974i	−0.501568	+	0.868742i
$218$	−18.0417	−	31.2491i	−1.22194	−	2.11645i
$219$	−0.402519	−	0.697183i	−0.0271997	−	0.0471113i
$220$	−24.8134			−1.67292
$221$	−0.584693	−	10.5690i	−0.0393307	−	0.710946i
$222$	9.20336			0.617689
$223$	3.80504	+	6.59052i	0.254804	+	0.441334i	0.964842	−	0.262829i	$-0.0846557\pi$
$223$	3.80504	+	6.59052i	0.254804	+	0.441334i	−0.710038	+	0.704163i	$0.751322\pi$
$224$	−17.1755	−	29.7488i	−1.14758	−	1.98767i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−29.1475			−1.93887
$227$	−11.6713	+	20.2152i	−0.774648	+	1.34173i	0.160344	+	0.987061i	$0.448740\pi$
$227$	−11.6713	+	20.2152i	−0.774648	+	1.34173i	−0.934992	+	0.354669i	$0.884594\pi$
$228$	16.1391	−	27.9538i	1.06884	−	1.85129i
$229$	0.824549			0.0544877			0.0272439	−	0.999629i	$-0.491327\pi$
$229$	0.824549			0.0544877			0.0272439	+	0.999629i	$0.491327\pi$
$230$	−7.20336	+	12.4766i	−0.474975	+	0.822681i
$231$	−9.37041	−	16.2300i	−0.616528	−	1.06786i
$232$	−6.60168	−	11.4344i	−0.433421	−	0.750708i
$233$	−13.4044			−0.878150			−0.439075	−	0.898450i	$-0.644694\pi$
$233$	−13.4044			−0.878150			−0.439075	+	0.898450i	$0.644694\pi$
$234$	7.85226	−	5.13182i	0.513318	−	0.335477i
$235$	3.80504			0.248213
$236$	17.5738	+	30.4387i	1.14396	+	1.98139i
$237$	−2.05142	−	3.55317i	−0.133254	−	0.230803i
$238$	13.7548	−	23.8240i	0.891590	−	1.54428i
$239$	12.7966			0.827746			0.413873	−	0.910335i	$-0.364176\pi$
$239$	12.7966			0.827746			0.413873	+	0.910335i	$0.364176\pi$
$240$	4.60168	−	7.97034i	0.297037	−	0.514483i
$241$	−6.38437	+	11.0580i	−0.411253	+	0.712312i	−0.995027	−	0.0996048i	$-0.968242\pi$
$241$	−6.38437	+	11.0580i	−0.411253	+	0.712312i	0.583774	+	0.811916i	$0.301575\pi$
$242$	41.8218			2.68841
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	8.18940	+	14.1845i	0.524273	+	0.908067i
$245$	−2.98605	−	5.17198i	−0.190771	−	0.330426i
$246$	13.9721			0.890828
$247$	1.34806	+	24.3678i	0.0857753	+	1.55048i
$248$	29.5543			1.87670
$249$	−5.76873	−	9.99174i	−0.365579	−	0.633201i
$250$	−1.30084	−	2.25312i	−0.0822723	−	0.142500i
$251$	4.20336	−	7.28043i	0.265314	−	0.459537i	−0.702332	−	0.711849i	$-0.747858\pi$
$251$	4.20336	−	7.28043i	0.265314	−	0.459537i	0.967646	+	0.252313i	$0.0811912\pi$
$252$	17.1755			1.08195
$253$	14.4067	−	24.9532i	0.905743	−	1.56879i
$254$	4.15613	−	7.19863i	0.260779	−	0.451683i
$255$	2.93579			0.183846
$256$	9.53747	−	16.5194i	0.596092	−	1.03246i
$257$	−3.06957	−	5.31666i	−0.191475	−	0.331644i	0.754264	−	0.656571i	$-0.227994\pi$
$257$	−3.06957	−	5.31666i	−0.191475	−	0.331644i	−0.945739	+	0.324927i	$0.894660\pi$
$258$	4.11983	+	7.13576i	0.256489	+	0.444253i
$259$	−12.7408			−0.791676
$260$	0.949743	+	17.1677i	0.0589006	+	1.06469i
$261$	1.83294			0.113456
$262$	5.94974	+	10.3053i	0.367576	+	0.636661i
$263$	2.36505	+	4.09639i	0.145835	+	0.252594i	0.929684	−	0.368357i	$-0.120080\pi$
$263$	2.36505	+	4.09639i	0.145835	+	0.252594i	−0.783849	+	0.620951i	$0.786746\pi$
$264$	−18.7408	+	32.4601i	−1.15342	+	1.99778i
$265$	−5.20336			−0.319640
$266$	−31.7129	+	54.9284i	−1.94444	+	3.36788i
$267$	4.91647	−	8.51558i	0.300883	−	0.521145i
$268$	16.6961			1.01988
$269$	2.72151	−	4.71379i	0.165933	−	0.287405i	−0.771053	−	0.636771i	$-0.780270\pi$
$269$	2.72151	−	4.71379i	0.165933	−	0.287405i	0.936986	+	0.349366i	$0.113603\pi$
$270$	1.30084	+	2.25312i	0.0791666	+	0.137121i
$271$	−12.7397	−	22.0657i	−0.773879	−	1.34040i	−0.935422	−	0.353533i	$-0.884980\pi$
$271$	−12.7397	−	22.0657i	−0.773879	−	1.34040i	0.161543	−	0.986866i	$-0.448353\pi$
$272$	−27.0191			−1.63827
$273$	−10.8704	+	7.10432i	−0.657907	+	0.429973i
$274$	27.7711			1.67771
$275$	2.60168	+	4.50624i	0.156887	+	0.271737i
$276$	13.2034	+	22.8689i	0.794749	+	1.37655i
$277$	11.4067	−	19.7570i	0.685363	−	1.18708i	−0.287959	−	0.957643i	$-0.592977\pi$
$277$	11.4067	−	19.7570i	0.685363	−	1.18708i	0.973323	−	0.229441i	$-0.0736899\pi$
$278$	−42.0107			−2.51964
$279$	−2.05142	+	3.55317i	−0.122815	+	0.212723i
$280$	−12.9721	+	22.4683i	−0.775231	+	1.34274i
$281$	−2.16706			−0.129276			−0.0646378	−	0.997909i	$-0.520589\pi$
$281$	−2.16706			−0.129276			−0.0646378	+	0.997909i	$0.520589\pi$
$282$	4.94974	−	8.57321i	0.294753	−	0.510527i
$283$	14.8734	+	25.7616i	0.884135	+	1.53137i	0.846702	+	0.532067i	$0.178584\pi$
$283$	14.8734	+	25.7616i	0.884135	+	1.53137i	0.0374322	+	0.999299i	$0.488082\pi$
$284$	23.1391	+	40.0782i	1.37306	+	2.37820i
$285$	−6.76873			−0.400945
$286$	−2.69613	−	48.7355i	−0.159425	−	2.88179i
$287$	−19.3425			−1.14175
$288$	−4.76873	−	8.25969i	−0.281000	−	0.486707i
$289$	4.19057	+	7.25828i	0.246504	+	0.426958i
$290$	−2.38437	+	4.12985i	−0.140015	+	0.242513i
$291$	5.57377			0.326740
$292$	1.91950	−	3.32468i	0.112331	−	0.194562i
$293$	−16.5428	+	28.6530i	−0.966443	+	1.67393i	−0.260754	+	0.965405i	$0.583971\pi$
$293$	−16.5428	+	28.6530i	−0.966443	+	1.67393i	−0.705688	+	0.708522i	$0.749362\pi$
$294$	−15.5375			−0.906164
$295$	3.68521	−	6.38297i	0.214561	−	0.371631i
$296$	12.7408	+	22.0678i	0.740546	+	1.28266i
$297$	−2.60168	−	4.50624i	−0.150965	−	0.261479i
$298$	−25.1475			−1.45676
$299$	−17.8158	−	9.01248i	−1.03031	−	0.521205i
$300$	−4.76873			−0.275323
$301$	−5.70336	−	9.87851i	−0.328736	−	0.569388i
$302$	24.3425	+	42.1625i	1.40075	+	2.42618i
$303$	1.20336	−	2.08428i	0.0691311	−	0.119739i
$304$	62.2951			3.57287
$305$	1.71731	−	2.97447i	0.0983330	−	0.170318i
$306$	3.81899	−	6.61469i	0.218317	−	0.378136i
$307$	−14.3704			−0.820163			−0.410081	−	0.912049i	$-0.634500\pi$
$307$	−14.3704			−0.820163			−0.410081	+	0.912049i	$0.634500\pi$
$308$	44.6850	−	77.3967i	2.54616	−	4.41009i
$309$	9.22151	+	15.9721i	0.524593	+	0.908622i
$310$	−5.33714	−	9.24420i	−0.303129	−	0.525035i
$311$	−8.70685			−0.493720			−0.246860	−	0.969051i	$-0.579399\pi$
$311$	−8.70685			−0.493720			−0.246860	+	0.969051i	$0.579399\pi$
$312$	23.1755	+	11.7238i	1.31205	+	0.663729i
$313$	−8.16472			−0.461497			−0.230749	−	0.973013i	$-0.574118\pi$
$313$	−8.16472			−0.461497			−0.230749	+	0.973013i	$0.574118\pi$
$314$	13.4902	+	23.3658i	0.761299	+	1.31861i
$315$	−1.80084	−	3.11915i	−0.101466	−	0.175744i
$316$	9.78269	−	16.9441i	0.550319	−	0.953181i
$317$	13.4090			0.753127			0.376564	−	0.926391i	$-0.377106\pi$
$317$	13.4090			0.753127			0.376564	+	0.926391i	$0.377106\pi$
$318$	−6.76873	+	11.7238i	−0.379572	+	0.657438i
$319$	4.76873	−	8.25969i	0.266998	−	0.462454i
$320$	6.40672			0.358146
$321$	5.46789	−	9.47067i	0.305188	−	0.528601i
$322$	−25.9442	−	44.9366i	−1.44581	−	2.50422i
$323$	9.93579	+	17.2093i	0.552842	+	0.957551i
$324$	4.76873			0.264930
$325$	3.01815	−	1.97250i	0.167417	−	0.109415i
$326$	−29.8497			−1.65322
$327$	6.93462	+	12.0111i	0.383486	+	0.664217i
$328$	19.3425	+	33.5022i	1.06801	+	1.84985i
$329$	−6.85226	+	11.8685i	−0.377777	+	0.654330i
$330$	13.5375			0.745213
$331$	−10.7397	+	18.6016i	−0.590305	+	1.02244i	0.403886	+	0.914809i	$0.367659\pi$
$331$	−10.7397	+	18.6016i	−0.590305	+	1.02244i	−0.994191	+	0.107629i	$0.965674\pi$
$332$	27.5096	−	47.6480i	1.50978	−	2.61502i
$333$	−3.53747			−0.193852
$334$	4.07261	−	7.05396i	0.222843	−	0.385976i
$335$	−1.75058	−	3.03210i	−0.0956446	−	0.165661i
$336$	16.5738	+	28.7066i	0.904173	+	1.56607i
$337$	−7.44535			−0.405574			−0.202787	−	0.979223i	$-0.565000\pi$
$337$	−7.44535			−0.405574			−0.202787	+	0.979223i	$0.565000\pi$
$338$	−33.6154	+	3.73074i	−1.82844	+	0.202925i
$339$	11.2034			0.608483
$340$	7.00000	+	12.1244i	0.379628	+	0.657536i
$341$	10.6743	+	18.4884i	0.578045	+	1.00120i
$342$	−8.80504	+	15.2508i	−0.476122	+	0.824667i
$343$	−3.70219			−0.199900
$344$	−11.4067	+	19.7570i	−0.615009	+	1.06523i
$345$	2.76873	−	4.79559i	0.149064	−	0.258186i
$346$	21.5096			1.15636
$347$	12.4733	−	21.6043i	0.669600	−	1.15978i	−0.308417	−	0.951251i	$-0.599799\pi$
$347$	12.4733	−	21.6043i	0.669600	−	1.15978i	0.978016	−	0.208529i	$-0.0668676\pi$
$348$	4.37041	+	7.56978i	0.234279	+	0.405783i
$349$	−1.05142	−	1.82112i	−0.0562813	−	0.0974822i	0.836512	−	0.547949i	$-0.184591\pi$
$349$	−1.05142	−	1.82112i	−0.0562813	−	0.0974822i	−0.892793	+	0.450466i	$0.851258\pi$
$350$	9.37041			0.500870
$351$	−3.01815	+	1.97250i	−0.161097	+	0.105284i
$352$	−49.6269			−2.64512
$353$	−9.26990	−	16.0559i	−0.493387	−	0.854571i	0.506584	−	0.862191i	$-0.330908\pi$
$353$	−9.26990	−	16.0559i	−0.493387	−	0.854571i	−0.999971	+	0.00761929i	$0.997575\pi$
$354$	−9.58773	−	16.6064i	−0.509582	−	0.882622i
$355$	4.85226	−	8.40436i	0.257531	−	0.446057i
$356$	46.8907			2.48520
$357$	−5.28689	+	9.15715i	−0.279812	+	0.484648i
$358$	23.9944	−	41.5596i	1.26815	−	2.19649i
$359$	−4.75801			−0.251118			−0.125559	−	0.992086i	$-0.540072\pi$
$359$	−4.75801			−0.251118			−0.125559	+	0.992086i	$0.540072\pi$
$360$	−3.60168	+	6.23829i	−0.189825	+	0.328787i
$361$	−13.4079	−	23.2231i	−0.705678	−	1.22227i
$362$	−27.4514	−	47.5472i	−1.44281	−	2.49903i
$363$	−16.0749			−0.843715
$364$	−55.2588	−	27.9538i	−2.89635	−	1.46518i
$365$	−0.805037			−0.0421376
$366$	−4.46789	−	7.73862i	−0.233541	−	0.404504i
$367$	5.12100	+	8.86983i	0.267314	+	0.463001i	0.968167	−	0.250304i	$-0.0805306\pi$
$367$	5.12100	+	8.86983i	0.267314	+	0.463001i	−0.700853	+	0.713305i	$0.747197\pi$
$368$	−25.4817	+	44.1355i	−1.32832	+	2.30072i
$369$	−5.37041			−0.279573
$370$	4.60168	−	7.97034i	0.239230	−	0.414358i
$371$	9.37041	−	16.2300i	0.486488	−	0.842621i
$372$	−19.5654			−1.01442
$373$	11.6701	−	20.2132i	0.604254	−	1.04660i	−0.387915	−	0.921695i	$-0.626804\pi$
$373$	11.6701	−	20.2132i	0.604254	−	1.04660i	0.992169	−	0.124904i	$-0.0398622\pi$
$374$	−19.8716	−	34.4186i	−1.02753	−	1.77974i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	27.4090			1.41351
$377$	−5.89716	−	2.98320i	−0.303719	−	0.153643i
$378$	−9.37041			−0.481962
$379$	17.8286	+	30.8800i	0.915791	+	1.58620i	0.805739	+	0.592271i	$0.201769\pi$
$379$	17.8286	+	30.8800i	0.915791	+	1.58620i	0.110052	+	0.993926i	$0.464898\pi$
$380$	−16.1391	−	27.9538i	−0.827921	−	1.43400i
$381$	−1.59748	+	2.76692i	−0.0818414	+	0.141754i
$382$	−22.6403			−1.15838
$383$	15.3092	−	26.5164i	0.782265	−	1.35492i	−0.148354	−	0.988934i	$-0.547397\pi$
$383$	15.3092	−	26.5164i	0.782265	−	1.35492i	0.930619	−	0.365989i	$-0.119269\pi$
$384$	−1.20336	+	2.08428i	−0.0614086	+	0.106363i
$385$	−18.7408			−0.955121
$386$	−25.0640	+	43.4121i	−1.27572	+	2.20962i
$387$	−1.58353	−	2.74275i	−0.0804952	−	0.139422i
$388$	13.2899	+	23.0188i	0.674693	+	1.16860i
$389$	25.0191			1.26852			0.634260	−	0.773120i	$-0.281305\pi$
$389$	25.0191			1.26852			0.634260	+	0.773120i	$0.281305\pi$
$390$	−0.518152	−	9.36617i	−0.0262376	−	0.474274i
$391$	−16.2568			−0.822144
$392$	−21.5096	−	37.2557i	−1.08640	−	1.88169i
$393$	−2.28689	−	3.96100i	−0.115358	−	0.199806i
$394$	19.7045	−	34.1292i	0.992700	−	1.71941i
$395$	−4.10284			−0.206437
$396$	12.4067	−	21.4891i	0.623461	−	1.07987i
$397$	−5.41647	+	9.38161i	−0.271845	+	0.470849i	−0.969334	−	0.245746i	$-0.920967\pi$
$397$	−5.41647	+	9.38161i	−0.271845	+	0.470849i	0.697489	+	0.716595i	$0.254300\pi$
$398$	−11.8050			−0.591733
$399$	12.1894	−	21.1127i	0.610233	−	1.05696i
$400$	−4.60168	−	7.97034i	−0.230084	−	0.398517i
$401$	12.2397	+	21.1997i	0.611220	+	1.05866i	0.991035	+	0.133601i	$0.0426541\pi$
$401$	12.2397	+	21.1997i	0.611220	+	1.05866i	−0.379816	+	0.925062i	$0.624013\pi$
$402$	−9.10891			−0.454311
$403$	12.3830	−	8.09287i	0.616842	−	0.403134i
$404$	11.4770			0.571002
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−8.58773	−	14.8744i	−0.426202	−	0.738203i
$407$	−9.20336	+	15.9407i	−0.456194	+	0.790150i
$408$	21.1475			1.04696
$409$	−13.3553	+	23.1320i	−0.660377	+	1.14381i	0.320140	+	0.947370i	$0.396270\pi$
$409$	−13.3553	+	23.1320i	−0.660377	+	1.14381i	−0.980517	+	0.196436i	$0.937063\pi$
$410$	6.98605	−	12.1002i	0.345016	−	0.597586i
$411$	−10.6743			−0.526524
$412$	−43.9749	+	76.1668i	−2.16649	+	3.75247i
$413$	13.2729	+	22.9894i	0.653118	+	1.13123i
$414$	−7.20336	−	12.4766i	−0.354026	−	0.613191i
$415$	−11.5375			−0.566352
$416$	1.89949	+	34.3353i	0.0931300	+	1.68343i
$417$	16.1475			0.790749
$418$	45.8158	+	79.3552i	2.24092	+	3.88139i
$419$	−7.51815	−	13.0218i	−0.367286	−	0.636158i	0.621854	−	0.783133i	$-0.286380\pi$
$419$	−7.51815	−	13.0218i	−0.367286	−	0.636158i	−0.989140	+	0.146975i	$0.953046\pi$
$420$	8.58773	−	14.8744i	0.419038	−	0.725795i
$421$	−5.90182			−0.287637			−0.143818	−	0.989604i	$-0.545938\pi$
$421$	−5.90182			−0.287637			−0.143818	+	0.989604i	$0.545938\pi$
$422$	28.8104	−	49.9011i	1.40247	−	2.42915i
$423$	−1.90252	+	3.29526i	−0.0925036	+	0.160221i
$424$	−37.4817			−1.82027
$425$	1.46789	−	2.54247i	0.0712034	−	0.123328i
$426$	−12.6240	−	21.8655i	−0.611636	−	1.05938i
$427$	6.18521	+	10.7131i	0.299323	+	0.518443i
$428$	52.1499			2.52076
$429$	1.03630	+	18.7323i	0.0500332	+	0.904406i
$430$	8.23966			0.397352
$431$	−19.6743	−	34.0769i	−0.947677	−	1.64142i	−0.750301	−	0.661097i	$-0.770091\pi$
$431$	−19.6743	−	34.0769i	−0.947677	−	1.64142i	−0.197376	−	0.980328i	$-0.563242\pi$
$432$	4.60168	+	7.97034i	0.221398	+	0.383473i
$433$	−6.20756	+	10.7518i	−0.298316	+	0.516699i	−0.975751	−	0.218884i	$-0.929758\pi$
$433$	−6.20756	+	10.7518i	−0.298316	+	0.516699i	0.677435	+	0.735583i	$0.263092\pi$
$434$	38.4454			1.84544
$435$	0.916472	−	1.58738i	0.0439415	−	0.0761089i
$436$	−33.0694	+	57.2778i	−1.58374	+	2.74311i
$437$	37.4817			1.79299
$438$	−1.04722	+	1.81385i	−0.0500383	+	0.0866689i
$439$	−15.9207	−	27.5754i	−0.759852	−	1.31610i	−0.942926	−	0.333003i	$-0.891938\pi$
$439$	−15.9207	−	27.5754i	−0.759852	−	1.31610i	0.183074	−	0.983099i	$-0.441395\pi$
$440$	18.7408	+	32.4601i	0.893434	+	1.54747i
$441$	5.97209			0.284385
$442$	−23.0526	+	15.0659i	−1.09650	+	0.716613i
$443$	−1.06421			−0.0505622			−0.0252811	−	0.999680i	$-0.508048\pi$
$443$	−1.06421			−0.0505622			−0.0252811	+	0.999680i	$0.508048\pi$
$444$	−8.43462	−	14.6092i	−0.400290	−	0.693322i
$445$	−4.91647	−	8.51558i	−0.233063	−	0.403677i
$446$	9.89949	−	17.1464i	0.468754	−	0.811906i
$447$	9.66589			0.457181
$448$	−11.5375	+	19.9835i	−0.545094	+	0.944131i
$449$	−7.70219	+	13.3406i	−0.363489	+	0.629581i	−0.988532	−	0.151009i	$-0.951748\pi$
$449$	−7.70219	+	13.3406i	−0.363489	+	0.629581i	0.625044	+	0.780590i	$0.285081\pi$
$450$	2.60168			0.122644
$451$	−13.9721	+	24.2004i	−0.657920	+	1.13955i
$452$	26.7129	+	46.2681i	1.25647	+	2.17627i
$453$	−9.35646	−	16.2059i	−0.439605	−	0.761418i
$454$	60.7297			2.85019
$455$	0.717312	+	12.9662i	0.0336281	+	0.607865i
$456$	−48.7576			−2.28328
$457$	4.78689	+	8.29113i	0.223921	+	0.387843i	0.955995	−	0.293382i	$-0.0947809\pi$
$457$	4.78689	+	8.29113i	0.223921	+	0.387843i	−0.732074	+	0.681225i	$0.761448\pi$
$458$	−1.07261	−	1.85781i	−0.0501196	−	0.0868097i
$459$	−1.46789	+	2.54247i	−0.0685155	+	0.118672i
$460$	26.4067			1.23122
$461$	−8.18637	+	14.1792i	−0.381277	+	0.660392i	−0.991245	−	0.132034i	$-0.957849\pi$
$461$	−8.18637	+	14.1792i	−0.381277	+	0.660392i	0.609968	+	0.792426i	$0.291182\pi$
$462$	−24.3788	+	42.2253i	−1.13420	+	1.96450i
$463$	−24.6487			−1.14552			−0.572761	−	0.819722i	$-0.694128\pi$
$463$	−24.6487			−1.14552			−0.572761	+	0.819722i	$0.694128\pi$
$464$	−8.43462	+	14.6092i	−0.391568	+	0.678215i
$465$	2.05142	+	3.55317i	0.0951324	+	0.164774i
$466$	17.4370	+	30.2017i	0.807751	+	1.39907i
$467$	−20.3402			−0.941231			−0.470616	−	0.882338i	$-0.655968\pi$
$467$	−20.3402			−0.941231			−0.470616	+	0.882338i	$0.655968\pi$
$468$	−15.3425	−	7.76133i	−0.709208	−	0.358768i
$469$	12.6101			0.582279
$470$	−4.94974	−	8.57321i	−0.228315	−	0.395453i
$471$	−5.18521	−	8.98104i	−0.238922	−	0.413825i
$472$	26.5459	−	45.9788i	1.22187	−	2.11635i
$473$	−16.4793			−0.757720
$474$	−5.33714	+	9.24420i	−0.245143	+	0.424600i
$475$	−3.38437	+	5.86190i	−0.155285	+	0.268962i
$476$	−50.4235			−2.31116
$477$	2.60168	−	4.50624i	0.119123	−	0.206327i
$478$	−16.6464	−	28.8324i	−0.761388	−	1.31876i
$479$	0.0811965	+	0.140637i	0.00370996	+	0.00642585i	0.867874	−	0.496784i	$-0.165486\pi$
$479$	0.0811965	+	0.140637i	0.00370996	+	0.00642585i	−0.864164	+	0.503209i	$0.832152\pi$
$480$	−9.53747			−0.435324
$481$	11.3811	+	5.75739i	0.518935	+	0.262514i
$482$	33.2201			1.51314
$483$	9.97209	+	17.2722i	0.453746	+	0.785911i
$484$	−38.3286	−	66.3870i	−1.74221	−	3.01759i
$485$	2.78689	−	4.82703i	0.126546	−	0.219184i
$486$	−2.60168			−0.118015
$487$	−1.28152	+	2.21966i	−0.0580713	+	0.100582i	−0.893600	−	0.448865i	$-0.851828\pi$
$487$	−1.28152	+	2.21966i	−0.0580713	+	0.100582i	0.835528	+	0.549447i	$0.185162\pi$
$488$	12.3704	−	21.4262i	0.559982	−	0.969918i
$489$	11.4733			0.518839
$490$	−7.76873	+	13.4558i	−0.350956	+	0.607873i
$491$	−14.2203	−	24.6304i	−0.641755	−	1.11155i	−0.985041	−	0.172321i	$-0.944873\pi$
$491$	−14.2203	−	24.6304i	−0.641755	−	1.11155i	0.343286	−	0.939231i	$-0.388460\pi$
$492$	−12.8050	−	22.1790i	−0.577296	−	0.999905i
$493$	−5.38114			−0.242354
$494$	53.1499	−	34.7359i	2.39133	−	1.56284i
$495$	−5.20336			−0.233874
$496$	−18.8800	−	32.7011i	−0.847736	−	1.46832i
$497$	17.4763	+	30.2698i	0.783919	+	1.35779i
$498$	−15.0084	+	25.9953i	−0.672542	+	1.16488i
$499$	−27.8605			−1.24721			−0.623603	−	0.781741i	$-0.714332\pi$
$499$	−27.8605			−1.24721			−0.623603	+	0.781741i	$0.714332\pi$
$500$	−2.38437	+	4.12985i	−0.106632	+	0.184692i
$501$	−1.56538	+	2.71131i	−0.0699358	+	0.121132i
$502$	−21.8716			−0.976176
$503$	−15.7129	+	27.2156i	−0.700604	+	1.21348i	0.267650	+	0.963516i	$0.413753\pi$
$503$	−15.7129	+	27.2156i	−0.700604	+	1.21348i	−0.968255	+	0.249966i	$0.919580\pi$
$504$	−12.9721	−	22.4683i	−0.577823	−	1.00082i
$505$	−1.20336	−	2.08428i	−0.0535487	−	0.0927491i
$506$	−74.9633			−3.33253
$507$	12.9207	−	1.43397i	0.573827	−	0.0636850i
$508$	−15.2359			−0.675985
$509$	−8.11124	−	14.0491i	−0.359524	−	0.622715i	0.628357	−	0.777925i	$-0.283728\pi$
$509$	−8.11124	−	14.0491i	−0.359524	−	0.622715i	−0.987881	+	0.155211i	$0.950394\pi$
$510$	−3.81899	−	6.61469i	−0.169108	−	0.292903i
$511$	1.44974	−	2.51103i	0.0641329	−	0.111081i
$512$	−44.8134			−1.98049
$513$	3.38437	−	5.86190i	0.149423	−	0.258809i
$514$	−7.98605	+	13.8322i	−0.352249	+	0.610114i
$515$	18.4430			0.812697
$516$	7.55142	−	13.0794i	0.332433	−	0.575791i
$517$	9.89949	+	17.1464i	0.435379	+	0.754098i
$518$	16.5738	+	28.7066i	0.728210	+	1.26130i
$519$	−8.26757			−0.362906
$520$	21.7408	−	14.2086i	0.953398	−	0.623090i
$521$	−20.0386			−0.877909			−0.438954	−	0.898509i	$-0.644651\pi$
$521$	−20.0386			−0.877909			−0.438954	+	0.898509i	$0.644651\pi$
$522$	−2.38437	−	4.12985i	−0.104361	−	0.180758i
$523$	6.62959	+	11.4828i	0.289892	+	0.502107i	0.973784	−	0.227476i	$-0.0730474\pi$
$523$	6.62959	+	11.4828i	0.289892	+	0.502107i	−0.683892	+	0.729583i	$0.739714\pi$
$524$	10.9056	−	18.8890i	0.476411	−	0.825168i
$525$	−3.60168			−0.157190
$526$	6.15310	−	10.6575i	0.268288	−	0.464688i
$527$	6.02254	−	10.4314i	0.262346	−	0.454397i
$528$	47.8884			2.08407
$529$	−3.83178	+	6.63684i	−0.166599	+	0.288558i
$530$	6.76873	+	11.7238i	0.294015	+	0.509249i
$531$	3.68521	+	6.38297i	0.159924	+	0.276997i
$532$	116.256			5.04034
$533$	17.2783	+	8.74059i	0.748406	+	0.378597i
$534$	−25.5822			−1.10705
$535$	−5.46789	−	9.47067i	−0.236398	−	0.409453i
$536$	−12.6101	−	21.8413i	−0.544672	−	0.943400i
$537$	−9.22268	+	15.9741i	−0.397988	+	0.689335i
$538$	−14.1610			−0.610524
$539$	15.5375	−	26.9117i	0.669246	−	1.15917i
$540$	2.38437	−	4.12985i	0.102607	−	0.177720i
$541$	35.6850			1.53422			0.767109	−	0.641516i	$-0.221694\pi$
$541$	35.6850			1.53422			0.767109	+	0.641516i	$0.221694\pi$
$542$	−33.1445	+	57.4080i	−1.42368	+	2.46588i
$543$	10.5514	+	18.2756i	0.452805	+	0.784281i
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$	13.8692			0.594093
$546$	30.1475	+	15.2508i	1.29020	+	0.652673i
$547$	−0.627256			−0.0268195			−0.0134098	−	0.999910i	$-0.504269\pi$
$547$	−0.627256			−0.0268195			−0.0134098	+	0.999910i	$0.504269\pi$
$548$	−25.4514	−	44.0831i	−1.08723	−	1.88314i
$549$	1.71731	+	2.97447i	0.0732931	+	0.126947i
$550$	6.76873	−	11.7238i	0.288620	−	0.499904i
$551$	12.4067			0.528544
$552$	19.9442	−	34.5443i	0.848881	−	1.47030i
$553$	7.38856	−	12.7974i	0.314194	−	0.544200i
$554$	−59.3532			−2.52168
$555$	−1.76873	+	3.06354i	−0.0750786	+	0.130040i
$556$	38.5017	+	66.6869i	1.63283	+	2.82815i
$557$	−4.60401	−	7.97438i	−0.195078	−	0.337885i	0.751848	−	0.659337i	$-0.229163\pi$
$557$	−4.60401	−	7.97438i	−0.195078	−	0.337885i	−0.946926	+	0.321451i	$0.895829\pi$
$558$	10.6743			0.451879
$559$	0.630752	+	11.4015i	0.0266780	+	0.482234i
$560$	33.1475			1.40074
$561$	7.63798	+	13.2294i	0.322476	+	0.558545i
$562$	2.81899	+	4.88264i	0.118912	+	0.205962i
$563$	−1.33411	+	2.31075i	−0.0562260	+	0.0973864i	−0.892768	−	0.450516i	$-0.851240\pi$
$563$	−1.33411	+	2.31075i	−0.0562260	+	0.0973864i	0.836542	+	0.547902i	$0.184573\pi$
$564$	−18.1452			−0.764051
$565$	5.60168	−	9.70239i	0.235664	−	0.408183i
$566$	38.6959	−	67.0233i	1.62651	−	2.81720i
$567$	3.60168			0.151256
$568$	34.9526	−	60.5396i	1.46658	−	2.54019i
$569$	13.0919	+	22.6759i	0.548842	+	0.950622i	0.998354	+	0.0573480i	$0.0182645\pi$
$569$	13.0919	+	22.6759i	0.548842	+	0.950622i	−0.449512	+	0.893274i	$0.648402\pi$
$570$	8.80504	+	15.2508i	0.368802	+	0.638785i
$571$	−19.2481			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$571$	−19.2481			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$572$	−74.8907	+	48.9445i	−3.13134	+	2.04647i
$573$	8.70219			0.363539
$574$	25.1615	+	43.5810i	1.05022	+	1.81904i
$575$	−2.76873	−	4.79559i	−0.115464	−	0.199990i
$576$	−3.20336	+	5.54838i	−0.133473	+	0.231182i
$577$	23.8716			0.993787			0.496893	−	0.867812i	$-0.334474\pi$
$577$	23.8716			0.993787			0.496893	+	0.867812i	$0.334474\pi$
$578$	10.9025	−	18.8837i	0.453485	−	0.785459i
$579$	9.63378	−	16.6862i	0.400366	−	0.693455i
$580$	8.74083			0.362943
$581$	20.7771	−	35.9870i	0.861981	−	1.49299i
$582$	−7.25058	−	12.5584i	−0.300546	−	0.520562i
$583$	−13.5375	−	23.4476i	−0.560665	−	0.971100i
$584$	−5.79897			−0.239963
$585$	0.199160	+	3.60005i	0.00823427	+	0.148844i
$586$	86.0783			3.55586
$587$	−14.4377	−	25.0068i	−0.595906	−	1.03214i	−0.993418	−	0.114542i	$-0.963460\pi$
$587$	−14.4377	−	25.0068i	−0.595906	−	1.03214i	0.397513	−	0.917597i	$-0.369874\pi$
$588$	14.2397	+	24.6638i	0.587234	+	1.01712i
$589$	−13.8855	+	24.0504i	−0.572143	+	0.990981i
$590$	−19.1755			−0.789441
$591$	−7.57377	+	13.1182i	−0.311543	+	0.539609i
$592$	16.2783	−	28.1948i	0.669034	−	1.15880i
$593$	−8.74083			−0.358943			−0.179471	−	0.983763i	$-0.557439\pi$
$593$	−8.74083			−0.358943			−0.179471	+	0.983763i	$0.557439\pi$
$594$	−6.76873	+	11.7238i	−0.277725	+	0.481033i
$595$	5.28689	+	9.15715i	0.216741	+	0.375407i
$596$	23.0470	+	39.9186i	0.944043	+	1.63513i
$597$	4.53747			0.185706
$598$	2.86925	+	51.8649i	0.117332	+	2.12091i
$599$	21.5929			0.882262			0.441131	−	0.897443i	$-0.354577\pi$
$599$	21.5929			0.882262			0.441131	+	0.897443i	$0.354577\pi$
$600$	3.60168	+	6.23829i	0.147038	+	0.254677i
$601$	−15.1252	−	26.1976i	−0.616970	−	1.06862i	−0.990036	−	0.140818i	$-0.955027\pi$
$601$	−15.1252	−	26.1976i	−0.616970	−	1.06862i	0.373066	−	0.927805i	$-0.378306\pi$
$602$	−14.8383	+	25.7007i	−0.604764	+	1.04748i
$603$	3.50117			0.142578
$604$	44.6185	−	77.2815i	1.81550	−	3.14454i
$605$	−8.03747	+	13.9213i	−0.326770	+	0.565981i
$606$	−6.26150			−0.254356
$607$	11.2536	−	19.4918i	0.456770	−	0.791149i	−0.542018	−	0.840367i	$-0.682340\pi$
$607$	11.2536	−	19.4918i	0.456770	−	0.791149i	0.998788	+	0.0492178i	$0.0156729\pi$
$608$	−32.2783	−	55.9076i	−1.30906	−	2.26735i
$609$	3.30084	+	5.71722i	0.133757	+	0.231674i
$610$	−8.93579			−0.361800
$611$	11.4842	−	7.50544i	0.464600	−	0.303638i
$612$	−14.0000			−0.565916
$613$	−9.38856	−	16.2615i	−0.379201	−	0.656795i	0.611746	−	0.791055i	$-0.290468\pi$
$613$	−9.38856	−	16.2615i	−0.379201	−	0.656795i	−0.990946	+	0.134260i	$0.957134\pi$
$614$	18.6936	+	32.3783i	0.754412	+	1.30668i
$615$	−2.68521	+	4.65091i	−0.108278	+	0.187543i
$616$	−134.997			−5.43918
$617$	1.80504	−	3.12642i	0.0726681	−	0.125865i	−0.827402	−	0.561610i	$-0.810182\pi$
$617$	1.80504	−	3.12642i	0.0726681	−	0.125865i	0.900070	+	0.435746i	$0.143515\pi$
$618$	23.9914	−	41.5543i	0.965076	−	1.67156i
$619$	2.87158			0.115419			0.0577093	−	0.998333i	$-0.481620\pi$
$619$	2.87158			0.115419			0.0577093	+	0.998333i	$0.481620\pi$
$620$	−9.78269	+	16.9441i	−0.392882	+	0.680492i
$621$	2.76873	+	4.79559i	0.111105	+	0.192440i
$622$	11.3262	+	19.6176i	0.454140	+	0.786594i
$623$	35.4151			1.41888
$624$	−1.83294	−	33.1325i	−0.0733765	−	1.32636i
$625$	1.00000			0.0400000
$626$	10.6210	+	18.3961i	0.424500	+	0.735256i
$627$	−17.6101	−	30.5015i	−0.703279	−	1.21811i
$628$	24.7269	−	42.8282i	0.986710	−	1.70903i
$629$	10.3853			0.414088
$630$	−4.68521	+	8.11502i	−0.186663	+	0.323310i
$631$	−8.49444	+	14.7128i	−0.338158	+	0.585708i	−0.984086	−	0.177691i	$-0.943137\pi$
$631$	−8.49444	+	14.7128i	−0.338158	+	0.585708i	0.645928	+	0.763398i	$0.276471\pi$
$632$	−29.5543			−1.17561
$633$	−11.0738	+	19.1803i	−0.440143	+	0.762350i
$634$	−17.4430	−	30.2122i	−0.692751	−	1.19988i
$635$	1.59748	+	2.76692i	0.0633941	+	0.109802i
$636$	24.8134			0.983917
$637$	−19.2141	−	9.71985i	−0.761290	−	0.385115i
$638$	−24.8134			−0.982373
$639$	4.85226	+	8.40436i	0.191953	+	0.332472i
$640$	1.20336	+	2.08428i	0.0475669	+	0.0823883i
$641$	8.30620	−	14.3868i	0.328075	−	0.568243i	−0.654055	−	0.756447i	$-0.726933\pi$
$641$	8.30620	−	14.3868i	0.328075	−	0.568243i	0.982130	+	0.188204i	$0.0602667\pi$
$642$	−28.4514			−1.12289
$643$	−22.6701	+	39.2657i	−0.894021	+	1.54849i	−0.0590094	+	0.998257i	$0.518794\pi$
$643$	−22.6701	+	39.2657i	−0.894021	+	1.54849i	−0.835012	+	0.550232i	$0.814539\pi$
$644$	−47.5543	+	82.3664i	−1.87390	+	3.24569i
$645$	−3.16706			−0.124703
$646$	25.8497	−	44.7731i	1.01704	−	1.76157i
$647$	−2.43462	−	4.21689i	−0.0957149	−	0.165783i	0.814192	−	0.580596i	$-0.197180\pi$
$647$	−2.43462	−	4.21689i	−0.0957149	−	0.165783i	−0.909907	+	0.414813i	$0.863847\pi$
$648$	−3.60168	−	6.23829i	−0.141487	−	0.245063i
$649$	38.3509			1.50540
$650$	−8.37041	−	4.23435i	−0.328315	−	0.166085i
$651$	−14.7771			−0.579161
$652$	27.3565	+	47.3828i	1.07136	+	1.85565i
$653$	−9.63495	−	16.6882i	−0.377045	−	0.653061i	0.613586	−	0.789628i	$-0.289726\pi$
$653$	−9.63495	−	16.6882i	−0.377045	−	0.653061i	−0.990631	+	0.136567i	$0.956393\pi$
$654$	18.0417	−	31.2491i	0.705485	−	1.22194i
$655$	−4.57377			−0.178712
$656$	24.7129	−	42.8040i	0.964877	−	1.67122i
$657$	0.402519	−	0.697183i	0.0157038	−	0.0271997i
$658$	35.6548			1.38997
$659$	−0.167055	+	0.289348i	−0.00650755	+	0.0112714i	−0.869261	−	0.494354i	$-0.835405\pi$
$659$	−0.167055	+	0.289348i	−0.00650755	+	0.0112714i	0.862753	+	0.505625i	$0.168738\pi$
$660$	−12.4067	−	21.4891i	−0.482931	−	0.836461i
$661$	6.83411	+	11.8370i	0.265816	+	0.460407i	0.967777	−	0.251808i	$-0.0810253\pi$
$661$	6.83411	+	11.8370i	0.265816	+	0.460407i	−0.701961	+	0.712215i	$0.747692\pi$
$662$	55.8823			2.17193
$663$	8.86066	−	5.79085i	0.344119	−	0.224898i
$664$	−83.1085			−3.22524
$665$	−12.1894	−	21.1127i	−0.472685	−	0.818714i
$666$	4.60168	+	7.97034i	0.178311	+	0.308844i
$667$	−5.07494	+	8.79005i	−0.196502	+	0.340352i
$668$	−14.9297			−0.577648
$669$	−3.80504	+	6.59052i	−0.147111	+	0.254804i
$670$	−4.55445	+	7.88855i	−0.175954	+	0.304761i
$671$	17.8716			0.689925
$672$	17.1755	−	29.7488i	0.662557	−	1.14758i
$673$	10.9400	+	18.9486i	0.421706	+	0.730415i	0.996106	−	0.0881587i	$-0.0280983\pi$
$673$	10.9400	+	18.9486i	0.421706	+	0.730415i	−0.574401	+	0.818574i	$0.694765\pi$
$674$	9.68521	+	16.7753i	0.373060	+	0.646159i
$675$	−1.00000			−0.0384900
$676$	36.7297	+	49.9412i	1.41268	+	1.92082i
$677$	−17.0749			−0.656243			−0.328122	−	0.944636i	$-0.606416\pi$
$677$	−17.0749			−0.656243			−0.328122	+	0.944636i	$0.606416\pi$
$678$	−14.5738	−	25.2425i	−0.559702	−	0.969433i
$679$	10.0375	+	17.3854i	0.385203	+	0.667191i
$680$	10.5738	−	18.3143i	0.405486	−	0.702322i
$681$	−23.3425			−0.894487
$682$	27.7711	−	48.1009i	1.06341	−	1.84188i
$683$	13.3651	−	23.1489i	0.511399	−	0.885770i	−0.488513	−	0.872556i	$-0.662461\pi$
$683$	13.3651	−	23.1489i	0.511399	−	0.885770i	0.999913	−	0.0132133i	$-0.00420606\pi$
$684$	32.2783			1.23419
$685$	−5.33714	+	9.24420i	−0.203922	+	0.353203i
$686$	4.81596	+	8.34149i	0.183874	+	0.318479i
$687$	0.412275	+	0.714081i	0.0157293	+	0.0272439i
$688$	29.1475			1.11124
$689$	−15.7045	+	10.2636i	−0.598295	+	0.391013i
$690$	−14.4067			−0.548454
$691$	−24.3576	−	42.1886i	−0.926608	−	1.60493i	−0.788955	−	0.614451i	$-0.789378\pi$
$691$	−24.3576	−	42.1886i	−0.926608	−	1.60493i	−0.137653	−	0.990481i	$-0.543956\pi$
$692$	−19.7129	−	34.1438i	−0.749373	−	1.29795i
$693$	9.37041	−	16.2300i	0.355953	−	0.616528i
$694$	−64.9028			−2.46368
$695$	8.07377	−	13.9842i	0.306256	−	0.530450i
$696$	6.60168	−	11.4344i	0.250236	−	0.433421i
$697$	15.7664			0.597195
$698$	−2.73546	+	4.73796i	−0.103539	+	0.179334i
$699$	−6.70219	−	11.6085i	−0.253500	−	0.439075i
$700$	−8.58773	−	14.8744i	−0.324586	−	0.562199i
$701$	22.9419			0.866502			0.433251	−	0.901273i	$-0.357366\pi$
$701$	22.9419			0.866502			0.433251	+	0.901273i	$0.357366\pi$
$702$	8.37041	+	4.23435i	0.315921	+	0.159815i
$703$	−23.9442			−0.903072
$704$	16.6682	+	28.8702i	0.628207	+	1.08809i
$705$	1.90252	+	3.29526i	0.0716530	+	0.124107i
$706$	−24.1173	+	41.7724i	−0.907667	+	1.57212i
$707$	8.66822			0.326002
$708$	−17.5738	+	30.4387i	−0.660463	+	1.14396i
$709$	3.57261	−	6.18794i	0.134172	−	0.232393i	−0.791109	−	0.611675i	$-0.790496\pi$
$709$	3.57261	−	6.18794i	0.134172	−	0.232393i	0.925281	+	0.379283i	$0.123829\pi$
$710$	−25.2481			−0.947543
$711$	2.05142	−	3.55317i	0.0769343	−	0.133254i
$712$	−35.4151	−	61.3408i	−1.32724	−	2.29884i
$713$	−11.3597	−	19.6756i	−0.425424	−	0.736855i
$714$	27.5096			1.02952
$715$	16.7408	+	8.46870i	0.626071	+	0.316711i
$716$	−87.9610			−3.28726
$717$	6.39832	+	11.0822i	0.238950	+	0.413873i
$718$	6.18940	+	10.7204i	0.230987	+	0.400080i
$719$	−20.9891	+	36.3542i	−0.782761	+	1.35578i	0.147567	+	0.989052i	$0.452856\pi$
$719$	−20.9891	+	36.3542i	−0.782761	+	1.35578i	−0.930328	+	0.366729i	$0.880478\pi$
$720$	9.20336			0.342989
$721$	−33.2129	+	57.5265i	−1.23691	+	2.14240i
$722$	−34.8830	+	60.4191i	−1.29821	+	2.24857i
$723$	−12.7687			−0.474874
$724$	−50.3169	+	87.1515i	−1.87001	+	3.23896i
$725$	−0.916472	−	1.58738i	−0.0340369	−	0.0589537i
$726$	20.9109	+	36.2188i	0.776077	+	1.34420i
$727$	−11.4965			−0.426382			−0.213191	−	0.977011i	$-0.568386\pi$
$727$	−11.4965			−0.426382			−0.213191	+	0.977011i	$0.568386\pi$
$728$	5.16706	+	93.4003i	0.191504	+	3.46164i
$729$	1.00000			0.0370370
$730$	1.04722	+	1.81385i	0.0387595	+	0.0671335i
$731$	4.64890	+	8.05214i	0.171946	+	0.297819i
$732$	−8.18940	+	14.1845i	−0.302689	+	0.524273i
$733$	46.1136			1.70324			0.851622	−	0.524157i	$-0.175619\pi$
$733$	46.1136			1.70324			0.851622	+	0.524157i	$0.175619\pi$
$734$	13.3232	−	23.0764i	0.491768	−	0.851767i
$735$	2.98605	−	5.17198i	0.110142	−	0.190771i
$736$	52.8134			1.94673
$737$	9.10891	−	15.7771i	0.335531	−	0.581157i
$738$	6.98605	+	12.1002i	0.257160	+	0.445414i
$739$	5.80504	+	10.0546i	0.213542	+	0.369865i	0.952820	−	0.303534i	$-0.0981667\pi$
$739$	5.80504	+	10.0546i	0.213542	+	0.369865i	−0.739279	+	0.673400i	$0.764833\pi$
$740$	−16.8692			−0.620126
$741$	−20.4291	+	13.3513i	−0.750480	+	0.490474i
$742$	−48.7576			−1.78995
$743$	−6.70756	−	11.6178i	−0.246076	−	0.426217i	0.716357	−	0.697734i	$-0.245808\pi$
$743$	−6.70756	−	11.6178i	−0.246076	−	0.426217i	−0.962434	+	0.271517i	$0.912475\pi$
$744$	14.7771	+	25.5947i	0.541756	+	0.938349i
$745$	4.83294	−	8.37091i	0.177065	−	0.306686i
$746$	−60.7236			−2.22325
$747$	5.76873	−	9.99174i	0.211067	−	0.365579i
$748$	−36.4235	+	63.0874i	−1.33178	+	2.30670i
$749$	39.3872			1.43918
$750$	1.30084	−	2.25312i	0.0474999	−	0.0822723i
$751$	−22.0866	−	38.2550i	−0.805950	−	1.39595i	−0.915648	−	0.401981i	$-0.868322\pi$
$751$	−22.0866	−	38.2550i	−0.805950	−	1.39595i	0.109698	−	0.993965i	$-0.465012\pi$
$752$	−17.5096	−	30.3274i	−0.638508	−	1.10593i
$753$	8.40672			0.306358
$754$	0.949743	+	17.1677i	0.0345876	+	0.625210i
$755$	−18.7129			−0.681033
$756$	8.58773	+	14.8744i	0.312333	+	0.540976i
$757$	−3.98605	−	6.90403i	−0.144875	−	0.250931i	0.784451	−	0.620191i	$-0.212945\pi$
$757$	−3.98605	−	6.90403i	−0.144875	−	0.250931i	−0.929326	+	0.369259i	$0.879611\pi$
$758$	46.3842	−	80.3397i	1.68475	−	2.91807i
$759$	28.8134			1.04586
$760$	−24.3788	+	42.2253i	−0.884312	+	1.53167i
$761$	−6.83294	+	11.8350i	−0.247694	+	0.429019i	−0.962886	−	0.269910i	$-0.913006\pi$
$761$	−6.83294	+	11.8350i	−0.247694	+	0.429019i	0.715192	+	0.698928i	$0.246339\pi$
$762$	8.31227			0.301122
$763$	−24.9763	+	43.2602i	−0.904202	+	1.56612i
$764$	20.7492	+	35.9387i	0.750681	+	1.30022i
$765$	1.46789	+	2.54247i	0.0530718	+	0.0919231i
$766$	−79.6594			−2.87821
$767$	−1.46789	−	26.5338i	−0.0530026	−	0.958081i
$768$	19.0749			0.688308
$769$	−8.24522	−	14.2811i	−0.297330	−	0.514991i	0.678194	−	0.734883i	$-0.262763\pi$
$769$	−8.24522	−	14.2811i	−0.297330	−	0.514991i	−0.975524	+	0.219892i	$0.929430\pi$
$770$	24.3788	+	42.2253i	0.878551	+	1.52170i
$771$	3.06957	−	5.31666i	0.110548	−	0.191475i
$772$	91.8819			3.30690
$773$	22.8521	−	39.5809i	0.821932	−	1.42363i	−0.0823101	−	0.996607i	$-0.526230\pi$
$773$	22.8521	−	39.5809i	0.821932	−	1.42363i	0.904242	−	0.427021i	$-0.140437\pi$
$774$	−4.11983	+	7.13576i	−0.148084	+	0.256489i
$775$	4.10284			0.147379
$776$	20.0749	−	34.7708i	0.720648	−	1.24820i
$777$	−6.37041	−	11.0339i	−0.228537	−	0.395838i
$778$	−32.5459	−	56.3711i	−1.16683	−	2.02100i
$779$	−36.3509			−1.30241
$780$	−14.3928	+	9.40633i	−0.515344	+	0.336801i
$781$	50.4961			1.80689
$782$	21.1475	+	36.6286i	0.756235	+	1.30984i
$783$	0.916472	+	1.58738i	0.0327521	+	0.0567282i
$784$	−27.4817	+	47.5996i	−0.981488	+	1.69999i
$785$	−10.3704			−0.370136
$786$	−5.94974	+	10.3053i	−0.212220	+	0.367576i
$787$	24.4109	−	42.2809i	0.870155	−	1.50715i	0.00831938	−	0.999965i	$-0.497352\pi$
$787$	24.4109	−	42.2809i	0.870155	−	1.50715i	0.861836	−	0.507187i	$-0.169315\pi$
$788$	−72.2346			−2.57325
$789$	−2.36505	+	4.09639i	−0.0841980	+	0.145835i
$790$	5.33714	+	9.24420i	0.189887	+	0.328894i
$791$	20.1755	+	34.9449i	0.717356	+	1.24250i
$792$	−37.4817			−1.33185
$793$	−0.684041	−	12.3648i	−0.0242910	−	0.439087i
$794$	28.1838			1.00021
$795$	−2.60168	−	4.50624i	−0.0922720	−	0.159820i
$796$	10.8190	+	18.7390i	0.383469	+	0.664188i
$797$	−6.87461	+	11.9072i	−0.243511	+	0.421774i	−0.961712	−	0.274062i	$-0.911633\pi$
$797$	−6.87461	+	11.9072i	−0.243511	+	0.421774i	0.718201	+	0.695836i	$0.244966\pi$
$798$	−63.4258			−2.24525
$799$	5.58539	−	9.67419i	0.197597	−	0.342248i
$800$	−4.76873	+	8.25969i	−0.168600	+	0.292024i
$801$	9.83294			0.347430
$802$	31.8437	−	55.1549i	1.12444	−	1.94759i
$803$	−2.09445	−	3.62769i	−0.0739115	−	0.128018i
$804$	8.34806	+	14.4593i	0.294414	+	0.509939i
$805$	19.9442			0.702940
$806$	−34.3425	−	17.3729i	−1.20966	−	0.611934i
$807$	5.44302			0.191603
$808$	−8.66822	−	15.0138i	−0.304947	−	0.528184i
$809$	−10.1671	−	17.6099i	−0.357455	−	0.619130i	0.630080	−	0.776530i	$-0.283022\pi$
$809$	−10.1671	−	17.6099i	−0.357455	−	0.619130i	−0.987535	+	0.157400i	$0.949689\pi$
$810$	−1.30084	+	2.25312i	−0.0457068	+	0.0791666i
$811$	22.4817			0.789438			0.394719	−	0.918802i	$-0.370842\pi$
$811$	22.4817			0.789438			0.394719	+	0.918802i	$0.370842\pi$
$812$	−15.7408	+	27.2639i	−0.552395	+	0.956776i
$813$	12.7397	−	22.0657i	0.446799	−	0.773879i
$814$	47.8884			1.67849
$815$	5.73663	−	9.93613i	0.200945	−	0.348048i
$816$	−13.5096	−	23.3992i	−0.472929	−	0.819137i
$817$	−10.7185	−	18.5649i	−0.374992	−	0.649505i
$818$	69.4924			2.42974
$819$	−11.5877	−	5.86190i	−0.404908	−	0.204831i
$820$	−25.6101			−0.894343
$821$	16.3039	+	28.2391i	0.569009	+	0.985553i	0.996664	+	0.0816107i	$0.0260064\pi$
$821$	16.3039	+	28.2391i	0.569009	+	0.985553i	−0.427655	+	0.903942i	$0.640660\pi$
$822$	13.8855	+	24.0504i	0.484314	+	0.838856i
$823$	−16.7408	+	28.9960i	−0.583549	+	1.01074i	0.411506	+	0.911407i	$0.365003\pi$
$823$	−16.7408	+	28.9960i	−0.583549	+	1.01074i	−0.995055	+	0.0993287i	$0.968330\pi$
$824$	132.852			4.62811
$825$	−2.60168	+	4.50624i	−0.0905788	+	0.156887i
$826$	34.5319	−	59.8110i	1.20152	−	2.08109i
$827$	−51.0298			−1.77448			−0.887241	−	0.461306i	$-0.847381\pi$
$827$	−51.0298			−1.77448			−0.887241	+	0.461306i	$0.847381\pi$
$828$	−13.2034	+	22.8689i	−0.458848	+	0.794749i
$829$	−10.5973	−	18.3550i	−0.368059	−	0.637497i	0.621203	−	0.783650i	$-0.286644\pi$
$829$	−10.5973	−	18.3550i	−0.368059	−	0.637497i	−0.989262	+	0.146153i	$0.953311\pi$
$830$	15.0084	+	25.9953i	0.520949	+	0.902310i
$831$	22.8134			0.791389
$832$	19.3364	−	12.6373i	0.670370	−	0.438118i
$833$	−17.5328			−0.607476
$834$	−21.0054	−	36.3824i	−0.727356	−	1.25982i
$835$	1.56538	+	2.71131i	0.0541721	+	0.0938288i
$836$	83.9778	−	145.454i	2.90443	−	5.03062i
$837$	−4.10284			−0.141815
$838$	−19.5598	+	33.8786i	−0.675683	+	1.17032i
$839$	−26.9419	+	46.6647i	−0.930136	+	1.61104i	−0.147051	+	0.989129i	$0.546978\pi$
$839$	−26.9419	+	46.6647i	−0.930136	+	1.61104i	−0.783086	+	0.621914i	$0.786355\pi$
$840$	−25.9442			−0.895159
$841$	12.8202	−	22.2052i	0.442074	−	0.765695i
$842$	7.67732	+	13.2975i	0.264578	+	0.458262i
$843$	−1.08353	−	1.87672i	−0.0373187	−	0.0646378i
$844$	−105.616			−3.63544
$845$	5.21848	−	11.9066i	0.179521	−	0.409600i
$846$	9.89949			0.340351
$847$	−28.9484	−	50.1401i	−0.994678	−	1.72283i
$848$	23.9442	+	41.4725i	0.822247	+	1.42417i
$849$	−14.8734	+	25.7616i	−0.510455	+	0.884135i
$850$	−7.63798			−0.261981
$851$	9.79431	−	16.9642i	0.335745	−	0.581527i
$852$	−23.1391	+	40.0782i	−0.792734	+	1.37306i
$853$	−4.06421			−0.139156			−0.0695780	−	0.997577i	$-0.522165\pi$
$853$	−4.06421			−0.139156			−0.0695780	+	0.997577i	$0.522165\pi$
$854$	16.0919	−	27.8720i	0.550654	−	0.953761i
$855$	−3.38437	−	5.86190i	−0.115743	−	0.200473i
$856$	−39.3872	−	68.2206i	−1.34623	−	2.33173i
$857$	−39.2141			−1.33953			−0.669764	−	0.742574i	$-0.733605\pi$
$857$	−39.2141			−1.33953			−0.669764	+	0.742574i	$0.733605\pi$
$858$	40.8581	−	26.7027i	1.39487	−	0.911614i
$859$	−5.64031			−0.192445			−0.0962225	−	0.995360i	$-0.530676\pi$
$859$	−5.64031			−0.192445			−0.0962225	+	0.995360i	$0.530676\pi$
$860$	−7.55142	−	13.0794i	−0.257501	−	0.446005i
$861$	−9.67125	−	16.7511i	−0.329595	−	0.570876i
$862$	−51.1862	+	88.6571i	−1.74341	+	3.01967i
$863$	−9.66589			−0.329031			−0.164515	−	0.986375i	$-0.552606\pi$
$863$	−9.66589			−0.329031			−0.164515	+	0.986375i	$0.552606\pi$
$864$	4.76873	−	8.25969i	0.162236	−	0.281000i
$865$	−4.13378	+	7.15992i	−0.140553	+	0.243445i
$866$	32.3001			1.09760
$867$	−4.19057	+	7.25828i	−0.142319	+	0.246504i
$868$	−35.2341	−	61.0273i	−1.19592	−	2.07140i
$869$	−10.6743	−	18.4884i	−0.362100	−	0.627176i
$870$	−4.76873			−0.161675
$871$	−11.2643	−	5.69831i	−0.381678	−	0.193080i
$872$	99.9052			3.38322
$873$	2.78689	+	4.82703i	0.0943218	+	0.163370i
$874$	−48.7576	−	84.4507i	−1.64925	−	2.85659i
$875$	−1.80084	+	3.11915i	−0.0608795	+	0.105446i
$876$	3.83901			0.129708
$877$	−7.93579	+	13.7452i	−0.267973	+	0.464142i	−0.968338	−	0.249642i	$-0.919687\pi$
$877$	−7.93579	+	13.7452i	−0.267973	+	0.464142i	0.700366	+	0.713784i	$0.253020\pi$
$878$	−41.4205	+	71.7424i	−1.39787	+	2.42119i
$879$	−33.0857			−1.11595
$880$	23.9442	−	41.4725i	0.807158	−	1.39804i
$881$	14.6017	+	25.2909i	0.491943	+	0.852070i	0.999957	−	0.00927849i	$-0.00295348\pi$
$881$	14.6017	+	25.2909i	0.491943	+	0.852070i	−0.508014	+	0.861349i	$0.669620\pi$
$882$	−7.76873	−	13.4558i	−0.261587	−	0.453082i
$883$	30.4598			1.02505			0.512527	−	0.858671i	$-0.328709\pi$
$883$	30.4598			1.02505			0.512527	+	0.858671i	$0.328709\pi$
$884$	45.0424	+	22.7856i	1.51494	+	0.766364i
$885$	7.37041			0.247754
$886$	1.38437	+	2.39779i	0.0465087	+	0.0805555i
$887$	−5.79967	−	10.0453i	−0.194734	−	0.337289i	0.752079	−	0.659073i	$-0.229051\pi$
$887$	−5.79967	−	10.0453i	−0.194734	−	0.337289i	−0.946813	+	0.321783i	$0.895718\pi$
$888$	−12.7408	+	22.0678i	−0.427554	+	0.740546i
$889$	−11.5072			−0.385940
$890$	−12.7911	+	22.1548i	−0.428758	+	0.742631i
$891$	2.60168	−	4.50624i	0.0871595	−	0.150965i
$892$	−36.2904			−1.21509
$893$	−12.8776	+	22.3047i	−0.430934	+	0.746399i
$894$	−12.5738	−	21.7784i	−0.420530	−	0.728379i
$895$	9.22268	+	15.9741i	0.308280	+	0.533957i
$896$	−8.66822			−0.289585
$897$	−1.10284	−	19.9351i	−0.0368229	−	0.665615i
$898$	40.0773			1.33740
$899$	−3.76014	−	6.51276i	−0.125408	−	0.217213i
$900$	−2.38437	−	4.12985i	−0.0794789	−	0.137662i
$901$	−7.63798	+	13.2294i	−0.254458	+	0.440734i
$902$	72.7018			2.42071
$903$	5.70336	−	9.87851i	0.189796	−	0.328736i
$904$	40.3509	−	69.8898i	1.34205	−	2.32450i
$905$	21.1028			0.701482
$906$	−24.3425	+	42.1625i	−0.808726	+	1.40075i
$907$	−21.4593	−	37.1686i	−0.712545	−	1.23416i	−0.963899	−	0.266268i	$-0.914209\pi$
$907$	−21.4593	−	37.1686i	−0.712545	−	1.23416i	0.251354	−	0.967895i	$-0.419124\pi$
$908$	−55.6571	−	96.4009i	−1.84705	−	3.19918i
$909$	2.40672			0.0798257
$910$	28.2813	−	18.4832i	0.937517	−	0.612711i
$911$	42.0726			1.39393			0.696964	−	0.717106i	$-0.254534\pi$
$911$	42.0726			1.39393			0.696964	+	0.717106i	$0.254534\pi$
$912$	31.1475	+	53.9491i	1.03140	+	1.78643i
$913$	−30.0168	−	51.9906i	−0.993411	−	1.72064i
$914$	12.4539	−	21.5709i	0.411940	−	0.713501i
$915$	3.43462			0.113545
$916$	−1.96603	+	3.40526i	−0.0649594	+	0.112513i
$917$	8.23663	−	14.2663i	0.271997	−	0.471113i
$918$	7.63798			0.252091
$919$	−19.5575	+	33.8746i	−0.645142	+	1.11742i	0.339127	+	0.940741i	$0.389868\pi$
$919$	−19.5575	+	33.8746i	−0.645142	+	1.11742i	−0.984269	+	0.176678i	$0.943465\pi$
$920$	−19.9442	−	34.5443i	−0.657540	−	1.13889i
$921$	−7.18521	−	12.4451i	−0.236761	−	0.410081i
$922$	42.5966			1.40285
$923$	−1.93276	−	34.9367i	−0.0636175	−	1.14996i
$924$	89.3700			2.94006
$925$	1.76873	+	3.06354i	0.0581556	+	0.100728i
$926$	32.0640	+	55.5365i	1.05369	+	1.82504i
$927$	−9.22151	+	15.9721i	−0.302874	+	0.524593i
$928$	17.4817			0.573863
$929$	−5.23127	+	9.06082i	−0.171632	+	0.297276i	−0.938991	−	0.343943i	$-0.888237\pi$
$929$	−5.23127	+	9.06082i	−0.171632	+	0.297276i	0.767358	+	0.641218i	$0.221571\pi$
$930$	5.33714	−	9.24420i	0.175012	−	0.303129i
$931$	40.4235			1.32483
$932$	31.9610	−	55.3580i	1.04692	−	1.81331i
$933$	−4.35343	−	7.54036i	−0.142525	−	0.246860i
$934$	26.4593	+	45.8289i	0.865775	+	1.49957i
$935$	15.2760			0.499577
$936$	1.43462	+	25.9324i	0.0468922	+	0.847628i
$937$	39.6269			1.29455			0.647277	−	0.762255i	$-0.275908\pi$
$937$	39.6269			1.29455			0.647277	+	0.762255i	$0.275908\pi$
$938$	−16.4037	−	28.4120i	−0.535599	−	0.927685i
$939$	−4.08236	−	7.07086i	−0.133223	−	0.230749i
$940$	−9.07261	+	15.7142i	−0.295916	+	0.512541i
$941$	15.3146			0.499242			0.249621	−	0.968344i	$-0.419694\pi$
$941$	15.3146			0.499242			0.249621	+	0.968344i	$0.419694\pi$
$942$	−13.4902	+	23.3658i	−0.439536	+	0.761299i
$943$	14.8692	−	25.7543i	0.484209	−	0.838675i
$944$	−67.8326			−2.20776
$945$	1.80084	−	3.11915i	0.0585813	−	0.101466i
$946$	21.4370	+	37.1299i	0.696976	+	1.20720i
$947$	16.6433	+	28.8271i	0.540836	+	0.936756i	0.998856	+	0.0478138i	$0.0152254\pi$
$947$	16.6433	+	28.8271i	0.540836	+	0.936756i	−0.458020	+	0.888942i	$0.651441\pi$
$948$	19.5654			0.635454
$949$	−2.42972	+	1.58794i	−0.0788722	+	0.0515466i
$950$	17.6101			0.571346
$951$	6.70452	+	11.6126i	0.217409	+	0.376564i
$952$	38.0833	+	65.9623i	1.23429	+	2.13785i
$953$	−11.7045	+	20.2728i	−0.379147	+	0.656701i	−0.990938	−	0.134318i	$-0.957116\pi$
$953$	−11.7045	+	20.2728i	−0.379147	+	0.656701i	0.611792	+	0.791019i	$0.290449\pi$
$954$	−13.5375			−0.438292
$955$	4.35110	−	7.53632i	0.140798	−	0.243870i
$956$	−30.5119	+	52.8481i	−0.986825	+	1.70923i
$957$	9.53747			0.308303
$958$	0.211247	−	0.365891i	0.00682509	−	0.0118214i
$959$	−19.2227	−	33.2947i	−0.620733	−	1.07514i
$960$	3.20336	+	5.54838i	0.103388	+	0.179073i
$961$	−14.1667			−0.456989
$962$	−1.83294	−	33.1325i	−0.0590965	−	1.06824i
$963$	10.9358			0.352401
$964$	−30.4454	−	52.7329i	−0.980579	−	1.69841i
$965$	−9.63378	−	16.6862i	−0.310122	−	0.537148i
$966$	25.9442	−	44.9366i	0.834740	−	1.44581i
$967$	27.8669			0.896140			0.448070	−	0.893999i	$-0.352112\pi$
$967$	27.8669			0.896140			0.448070	+	0.893999i	$0.352112\pi$
$968$	−57.8968	+	100.280i	−1.86087	+	3.22313i
$969$	−9.93579	+	17.2093i	−0.319184	+	0.552842i
$970$	−14.5012			−0.465604
$971$	2.25917	−	3.91300i	0.0725003	−	0.125574i	−0.827496	−	0.561471i	$-0.810236\pi$
$971$	2.25917	−	3.91300i	0.0725003	−	0.125574i	0.899997	+	0.435897i	$0.143569\pi$
$972$	2.38437	+	4.12985i	0.0764786	+	0.132465i
$973$	29.0791	+	50.3665i	0.932234	+	1.61468i
$974$	6.66822			0.213664
$975$	3.21731	+	1.62755i	0.103036	+	0.0521232i
$976$	−31.6101			−1.01181
$977$	21.2420	+	36.7922i	0.679592	+	1.17709i	0.975104	+	0.221748i	$0.0711763\pi$
$977$	21.2420	+	36.7922i	0.679592	+	1.17709i	−0.295512	+	0.955339i	$0.595490\pi$
$978$	−14.9249	−	25.8506i	−0.477245	−	0.826612i
$979$	25.5822	−	44.3096i	0.817610	−	1.41614i
$980$	28.4793			0.909739
$981$	−6.93462	+	12.0111i	−0.221406	+	0.383486i
$982$	−36.9968	+	64.0803i	−1.18061	+	2.04488i
$983$	9.87158			0.314854			0.157427	−	0.987531i	$-0.449680\pi$
$983$	9.87158			0.314854			0.157427	+	0.987531i	$0.449680\pi$
$984$	−19.3425	+	33.5022i	−0.616617	+	1.06801i
$985$	7.57377	+	13.1182i	0.241320	+	0.417979i
$986$	7.00000	+	12.1244i	0.222925	+	0.386118i
$987$	−13.7045			−0.436220
$988$	−103.849	−	52.5344i	−3.30389	−	1.67134i
$989$	17.5375			0.557659
$990$	6.76873	+	11.7238i	0.215124	+	0.372607i
$991$	−10.5598	−	18.2901i	−0.335444	−	0.581005i	0.648126	−	0.761533i	$-0.275553\pi$
$991$	−10.5598	−	18.2901i	−0.335444	−	0.581005i	−0.983570	+	0.180527i	$0.942220\pi$
$992$	−19.5654	+	33.8882i	−0.621201	+	1.07595i
$993$	−21.4793			−0.681626
$994$	45.4677	−	78.7524i	1.44215	−	2.49787i
$995$	2.26873	−	3.92956i	0.0719237	−	0.124576i
$996$	55.0191			1.74335
$997$	−8.54167	+	14.7946i	−0.270517	+	0.468550i	−0.968994	−	0.247083i	$-0.920528\pi$
$997$	−8.54167	+	14.7946i	−0.270517	+	0.468550i	0.698477	+	0.715632i	$0.253861\pi$
$998$	36.2420	+	62.7730i	1.14722	+	1.98704i
$999$	−1.76873	−	3.06354i	−0.0559603	−	0.0969260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.i.d.16.1	✓	6
3.2	odd	2		585.2.j.f.406.3		6
5.2	odd	4		975.2.bb.k.874.6		12
5.3	odd	4		975.2.bb.k.874.1		12
5.4	even	2		975.2.i.l.601.3		6
13.3	even	3		2535.2.a.bb.1.3		3
13.9	even	3	inner	195.2.i.d.61.1	yes	6
13.10	even	6		2535.2.a.ba.1.1		3
39.23	odd	6		7605.2.a.bw.1.3		3
39.29	odd	6		7605.2.a.bv.1.1		3
39.35	odd	6		585.2.j.f.451.3		6
65.9	even	6		975.2.i.l.451.3		6
65.22	odd	12		975.2.bb.k.724.1		12
65.48	odd	12		975.2.bb.k.724.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.1	✓	6	1.1	even	1	trivial
195.2.i.d.61.1	yes	6	13.9	even	3	inner
585.2.j.f.406.3		6	3.2	odd	2
585.2.j.f.451.3		6	39.35	odd	6
975.2.i.l.451.3		6	65.9	even	6
975.2.i.l.601.3		6	5.4	even	2
975.2.bb.k.724.1		12	65.22	odd	12
975.2.bb.k.724.6		12	65.48	odd	12
975.2.bb.k.874.1		12	5.3	odd	4
975.2.bb.k.874.6		12	5.2	odd	4
2535.2.a.ba.1.1		3	13.10	even	6
2535.2.a.bb.1.3		3	13.3	even	3
7605.2.a.bv.1.1		3	39.29	odd	6
7605.2.a.bw.1.3		3	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)

\(f(q)\)	\(=\)	\(q+(-1.30084 - 2.25312i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +1.00000 q^{5} +(1.30084 - 2.25312i) q^{6} +(-1.80084 + 3.11915i) q^{7} +7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.30084 - 2.25312i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +1.00000 q^{5} +(1.30084 - 2.25312i) q^{6} +(-1.80084 + 3.11915i) q^{7} +7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.30084 - 2.25312i) q^{10} +(2.60168 + 4.50624i) q^{11} -4.76873 q^{12} +(3.01815 - 1.97250i) q^{13} +9.37041 q^{14} +(0.500000 + 0.866025i) q^{15} +(-4.60168 - 7.97034i) q^{16} +(1.46789 - 2.54247i) q^{17} +2.60168 q^{18} +(-3.38437 + 5.86190i) q^{19} +(-2.38437 + 4.12985i) q^{20} -3.60168 q^{21} +(6.76873 - 11.7238i) q^{22} +(-2.76873 - 4.79559i) q^{23} +(3.60168 + 6.23829i) q^{24} +1.00000 q^{25} +(-8.37041 - 4.23435i) q^{26} -1.00000 q^{27} +(-8.58773 - 14.8744i) q^{28} +(-0.916472 - 1.58738i) q^{29} +(1.30084 - 2.25312i) q^{30} +4.10284 q^{31} +(-4.76873 + 8.25969i) q^{32} +(-2.60168 + 4.50624i) q^{33} -7.63798 q^{34} +(-1.80084 + 3.11915i) q^{35} +(-2.38437 - 4.12985i) q^{36} +(1.76873 + 3.06354i) q^{37} +17.6101 q^{38} +(3.21731 + 1.62755i) q^{39} +7.20336 q^{40} +(2.68521 + 4.65091i) q^{41} +(4.68521 + 8.11502i) q^{42} +(-1.58353 + 2.74275i) q^{43} -24.8134 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-7.20336 + 12.4766i) q^{46} +3.80504 q^{47} +(4.60168 - 7.97034i) q^{48} +(-2.98605 - 5.17198i) q^{49} +(-1.30084 - 2.25312i) q^{50} +2.93579 q^{51} +(0.949743 + 17.1677i) q^{52} -5.20336 q^{53} +(1.30084 + 2.25312i) q^{54} +(2.60168 + 4.50624i) q^{55} +(-12.9721 + 22.4683i) q^{56} -6.76873 q^{57} +(-2.38437 + 4.12985i) q^{58} +(3.68521 - 6.38297i) q^{59} -4.76873 q^{60} +(1.71731 - 2.97447i) q^{61} +(-5.33714 - 9.24420i) q^{62} +(-1.80084 - 3.11915i) q^{63} +6.40672 q^{64} +(3.01815 - 1.97250i) q^{65} +13.5375 q^{66} +(-1.75058 - 3.03210i) q^{67} +(7.00000 + 12.1244i) q^{68} +(2.76873 - 4.79559i) q^{69} +9.37041 q^{70} +(4.85226 - 8.40436i) q^{71} +(-3.60168 + 6.23829i) q^{72} -0.805037 q^{73} +(4.60168 - 7.97034i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-16.1391 - 27.9538i) q^{76} -18.7408 q^{77} +(-0.518152 - 9.36617i) q^{78} -4.10284 q^{79} +(-4.60168 - 7.97034i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.98605 - 12.1002i) q^{82} -11.5375 q^{83} +(8.58773 - 14.8744i) q^{84} +(1.46789 - 2.54247i) q^{85} +8.23966 q^{86} +(0.916472 - 1.58738i) q^{87} +(18.7408 + 32.4601i) q^{88} +(-4.91647 - 8.51558i) q^{89} +2.60168 q^{90} +(0.717312 + 12.9662i) q^{91} +26.4067 q^{92} +(2.05142 + 3.55317i) q^{93} +(-4.94974 - 8.57321i) q^{94} +(-3.38437 + 5.86190i) q^{95} -9.53747 q^{96} +(2.78689 - 4.82703i) q^{97} +(-7.76873 + 13.4558i) q^{98} -5.20336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9} - 12 q^{12} + 3 q^{13} + 24 q^{14} + 3 q^{15} - 12 q^{16} - 12 q^{19} - 6 q^{20} - 6 q^{21} + 24 q^{22} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 12 q^{28} - 6 q^{29} + 6 q^{31} - 12 q^{32} - 3 q^{35} - 6 q^{36} - 6 q^{37} + 12 q^{38} + 12 q^{39} + 12 q^{40} + 12 q^{42} - 9 q^{43} - 24 q^{44} - 3 q^{45} - 12 q^{46} - 24 q^{47} + 12 q^{48} + 6 q^{49} + 12 q^{52} - 30 q^{56} - 24 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{60} + 3 q^{61} + 6 q^{62} - 3 q^{63} - 24 q^{64} + 3 q^{65} + 48 q^{66} - 9 q^{67} + 42 q^{68} + 24 q^{70} + 12 q^{71} - 6 q^{72} + 42 q^{73} + 12 q^{74} + 3 q^{75} - 48 q^{76} - 48 q^{77} + 12 q^{78} - 6 q^{79} - 12 q^{80} - 3 q^{81} + 18 q^{82} - 36 q^{83} + 12 q^{84} - 12 q^{86} + 6 q^{87} + 48 q^{88} - 30 q^{89} - 3 q^{91} + 96 q^{92} + 3 q^{93} - 36 q^{94} - 12 q^{95} - 24 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) \) 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9 - 12 * q^12 + 3 * q^13 + 24 * q^14 + 3 * q^15 - 12 * q^16 - 12 * q^19 - 6 * q^20 - 6 * q^21 + 24 * q^22 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 + 6 * q^31 - 12 * q^32 - 3 * q^35 - 6 * q^36 - 6 * q^37 + 12 * q^38 + 12 * q^39 + 12 * q^40 + 12 * q^42 - 9 * q^43 - 24 * q^44 - 3 * q^45 - 12 * q^46 - 24 * q^47 + 12 * q^48 + 6 * q^49 + 12 * q^52 - 30 * q^56 - 24 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^60 + 3 * q^61 + 6 * q^62 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 48 * q^66 - 9 * q^67 + 42 * q^68 + 24 * q^70 + 12 * q^71 - 6 * q^72 + 42 * q^73 + 12 * q^74 + 3 * q^75 - 48 * q^76 - 48 * q^77 + 12 * q^78 - 6 * q^79 - 12 * q^80 - 3 * q^81 + 18 * q^82 - 36 * q^83 + 12 * q^84 - 12 * q^86 + 6 * q^87 + 48 * q^88 - 30 * q^89 - 3 * q^91 + 96 * q^92 + 3 * q^93 - 36 * q^94 - 12 * q^95 - 24 * q^96 - 15 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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