LMFDB - Embedded newform 195.2.v.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(4,195)]

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, 3, 1]))

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

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

chi := DirichletCharacter("195.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.v (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	195.49
Dual form			195.2.v.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00561 - 1.74177i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.02251 + 1.77105i) q^{4} +(-1.28334 - 1.83113i) q^{5} +(1.74177 + 1.00561i) q^{6} +(1.11175 - 1.92561i) q^{7} +0.0905636 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00561 - 1.74177i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.02251 + 1.77105i) q^{4} +(-1.28334 - 1.83113i) q^{5} +(1.74177 + 1.00561i) q^{6} +(1.11175 - 1.92561i) q^{7} +0.0905636 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.89887 + 4.07669i) q^{10} +(-4.40935 + 2.54574i) q^{11} -2.04503i q^{12} +(-1.22803 + 3.38998i) q^{13} -4.47196 q^{14} +(2.02697 + 0.944138i) q^{15} +(1.95396 + 3.38435i) q^{16} +(-2.00356 - 1.15676i) q^{17} -2.01123 q^{18} +(-6.07004 - 3.50454i) q^{19} +(4.55525 - 0.400493i) q^{20} +2.22350i q^{21} +(8.86820 + 5.12006i) q^{22} +(4.77307 - 2.75574i) q^{23} +(-0.0784304 + 0.0452818i) q^{24} +(-1.70609 + 4.69992i) q^{25} +(7.13949 - 1.27006i) q^{26} +1.00000i q^{27} +(2.27356 + 3.93792i) q^{28} +(0.503549 + 0.872172i) q^{29} +(-0.393873 - 4.47996i) q^{30} -9.55876i q^{31} +(4.02041 - 6.96356i) q^{32} +(2.54574 - 4.40935i) q^{33} +4.65300i q^{34} +(-4.95279 + 0.435444i) q^{35} +(1.02251 + 1.77105i) q^{36} +(-0.579795 - 1.00423i) q^{37} +14.0968i q^{38} +(-0.631485 - 3.54982i) q^{39} +(-0.116224 - 0.165834i) q^{40} +(1.42586 - 0.823222i) q^{41} +(3.87283 - 2.23598i) q^{42} +(-7.97844 - 4.60635i) q^{43} -10.4122i q^{44} +(-2.22748 + 0.195838i) q^{45} +(-9.59973 - 5.54241i) q^{46} -1.34816 q^{47} +(-3.38435 - 1.95396i) q^{48} +(1.02803 + 1.78060i) q^{49} +(9.90186 - 1.75469i) q^{50} +2.31351 q^{51} +(-4.74813 - 5.64120i) q^{52} -9.36564i q^{53} +(1.74177 - 1.00561i) q^{54} +(10.3203 + 4.80706i) q^{55} +(0.100684 - 0.174390i) q^{56} +7.00908 q^{57} +(1.01275 - 1.75413i) q^{58} +(0.894540 + 0.516463i) q^{59} +(-3.74472 + 2.62446i) q^{60} +(5.32768 - 9.22782i) q^{61} +(-16.6492 + 9.61241i) q^{62} +(-1.11175 - 1.92561i) q^{63} -8.35609 q^{64} +(7.78347 - 2.10180i) q^{65} -10.2401 q^{66} +(1.66583 + 2.88530i) q^{67} +(4.09734 - 2.36560i) q^{68} +(-2.75574 + 4.77307i) q^{69} +(5.73903 + 8.18874i) q^{70} +(1.54037 + 0.889333i) q^{71} +(0.0452818 - 0.0784304i) q^{72} +4.49399 q^{73} +(-1.16610 + 2.01974i) q^{74} +(-0.872447 - 4.92330i) q^{75} +(12.4134 - 7.16688i) q^{76} +11.3209i q^{77} +(-5.54795 + 4.66965i) q^{78} -7.05606 q^{79} +(3.68961 - 7.92122i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.86773 - 1.65568i) q^{82} -2.25488 q^{83} +(-3.93792 - 2.27356i) q^{84} +(0.453072 + 5.15329i) q^{85} +18.5288i q^{86} +(-0.872172 - 0.503549i) q^{87} +(-0.399327 + 0.230551i) q^{88} +(-7.03934 + 4.06416i) q^{89} +(2.58108 + 3.68282i) q^{90} +(5.16250 + 6.13350i) q^{91} +11.2711i q^{92} +(4.77938 + 8.27813i) q^{93} +(1.35573 + 2.34819i) q^{94} +(1.37264 + 15.6126i) q^{95} +8.04083i q^{96} +(3.01787 - 5.22710i) q^{97} +(2.06760 - 3.58118i) q^{98} +5.09148i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q - 20 * q^4 + 16 * q^9	$ 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) $ 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.00561	−	1.74177i	−0.711076	−	1.23162i	−0.964454	−	0.264252i	$-0.914875\pi$
$2$	−1.00561	−	1.74177i	−0.711076	−	1.23162i	0.253378	−	0.967367i	$-0.418458\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−1.02251	+	1.77105i	−0.511257	+	0.885524i
$5$	−1.28334	−	1.83113i	−0.573926	−	0.818907i
$5$	−1.28334	−	1.83113i	−0.573926	−	0.818907i
$6$	1.74177	+	1.00561i	0.711076	+	0.410540i
$7$	1.11175	−	1.92561i	0.420202	−	0.727811i	−0.575757	−	0.817621i	$-0.695293\pi$
$7$	1.11175	−	1.92561i	0.420202	−	0.727811i	0.995959	+	0.0898101i	$0.0286260\pi$
$8$	0.0905636			0.0320191
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.89887	+	4.07669i	−0.600477	+	1.28916i
$11$	−4.40935	+	2.54574i	−1.32947	+	0.767569i	−0.985217	−	0.171308i	$-0.945201\pi$
$11$	−4.40935	+	2.54574i	−1.32947	+	0.767569i	−0.344251	+	0.938877i	$0.611867\pi$
$12$		−	2.04503i		−	0.590349i
$13$	−1.22803	+	3.38998i	−0.340594	+	0.940211i
$13$	−1.22803	+	3.38998i	−0.340594	+	0.940211i
$14$	−4.47196			−1.19518
$15$	2.02697	+	0.944138i	0.523361	+	0.243775i
$16$	1.95396	+	3.38435i	0.488489	+	0.846088i
$17$	−2.00356	−	1.15676i	−0.485935	−	0.280555i	0.236952	−	0.971521i	$-0.423852\pi$
$17$	−2.00356	−	1.15676i	−0.485935	−	0.280555i	−0.722886	+	0.690967i	$0.757185\pi$
$18$	−2.01123			−0.474050
$19$	−6.07004	−	3.50454i	−1.39256	−	0.803996i	−0.398964	−	0.916967i	$-0.630630\pi$
$19$	−6.07004	−	3.50454i	−1.39256	−	0.803996i	−0.993598	+	0.112970i	$0.963964\pi$
$20$	4.55525	−	0.400493i	1.01859	−	0.0895531i
$21$			2.22350i			0.485207i
$22$	8.86820	+	5.12006i	1.89071	+	1.09160i
$23$	4.77307	−	2.75574i	0.995255	−	0.574611i	0.0884139	−	0.996084i	$-0.471820\pi$
$23$	4.77307	−	2.75574i	0.995255	−	0.574611i	0.906841	+	0.421473i	$0.138487\pi$
$24$	−0.0784304	+	0.0452818i	−0.0160095	+	0.00924311i
$25$	−1.70609	+	4.69992i	−0.341217	+	0.939984i
$26$	7.13949	−	1.27006i	1.40017	−	0.249079i
$27$			1.00000i			0.192450i
$28$	2.27356	+	3.93792i	0.429662	+	0.744197i
$29$	0.503549	+	0.872172i	0.0935066	+	0.161958i	0.908984	−	0.416830i	$-0.136859\pi$
$29$	0.503549	+	0.872172i	0.0935066	+	0.161958i	−0.815478	+	0.578788i	$0.803526\pi$
$30$	−0.393873	−	4.47996i	−0.0719111	−	0.817924i
$31$		−	9.55876i		−	1.71680i	−0.512977	−	0.858402i	$-0.671458\pi$
$31$		−	9.55876i		−	1.71680i	0.512977	−	0.858402i	$-0.328542\pi$
$32$	4.02041	−	6.96356i	0.710715	−	1.23099i
$33$	2.54574	−	4.40935i	0.443156	−	0.767569i
$34$			4.65300i			0.797982i
$35$	−4.95279	+	0.435444i	−0.837174	+	0.0736035i
$36$	1.02251	+	1.77105i	0.170419	+	0.295175i
$37$	−0.579795	−	1.00423i	−0.0953178	−	0.165095i	0.814423	−	0.580271i	$-0.197053\pi$
$37$	−0.579795	−	1.00423i	−0.0953178	−	0.165095i	−0.909741	+	0.415176i	$0.863720\pi$
$38$			14.0968i			2.28681i
$39$	−0.631485	−	3.54982i	−0.101118	−	0.568426i
$40$	−0.116224	−	0.165834i	−0.0183766	−	0.0262206i
$41$	1.42586	−	0.823222i	0.222682	−	0.128566i	−0.384509	−	0.923121i	$-0.625629\pi$
$41$	1.42586	−	0.823222i	0.222682	−	0.128566i	0.607192	+	0.794555i	$0.292296\pi$
$42$	3.87283	−	2.23598i	0.597590	−	0.345019i
$43$	−7.97844	−	4.60635i	−1.21670	−	0.702462i	−0.252490	−	0.967600i	$-0.581249\pi$
$43$	−7.97844	−	4.60635i	−1.21670	−	0.702462i	−0.964211	+	0.265137i	$0.914583\pi$
$44$		−	10.4122i		−	1.56970i
$45$	−2.22748	+	0.195838i	−0.332052	+	0.0291937i
$46$	−9.59973	−	5.54241i	−1.41540	−	0.817183i
$47$	−1.34816			−0.196649			−0.0983246	−	0.995154i	$-0.531348\pi$
$47$	−1.34816			−0.196649			−0.0983246	+	0.995154i	$0.531348\pi$
$48$	−3.38435	−	1.95396i	−0.488489	−	0.282029i
$49$	1.02803	+	1.78060i	0.146861	+	0.254371i
$50$	9.90186	−	1.75469i	1.40033	−	0.248150i
$51$	2.31351			0.323956
$52$	−4.74813	−	5.64120i	−0.658447	−	0.782293i
$53$		−	9.36564i		−	1.28647i	−0.765669	−	0.643235i	$-0.777592\pi$
$53$		−	9.36564i		−	1.28647i	0.765669	−	0.643235i	$-0.222408\pi$
$54$	1.74177	−	1.00561i	0.237025	−	0.136847i
$55$	10.3203	+	4.80706i	1.39158	+	0.648183i
$56$	0.100684	−	0.174390i	0.0134545	−	0.0233038i
$57$	7.00908			0.928375
$58$	1.01275	−	1.75413i	0.132981	−	0.230329i
$59$	0.894540	+	0.516463i	0.116459	+	0.0672377i	0.557098	−	0.830447i	$-0.311915\pi$
$59$	0.894540	+	0.516463i	0.116459	+	0.0672377i	−0.440639	+	0.897684i	$0.645248\pi$
$60$	−3.74472	+	2.62446i	−0.483441	+	0.338817i
$61$	5.32768	−	9.22782i	0.682140	−	1.18150i	−0.292187	−	0.956361i	$-0.594383\pi$
$61$	5.32768	−	9.22782i	0.682140	−	1.18150i	0.974327	−	0.225140i	$-0.0722838\pi$
$62$	−16.6492	+	9.61241i	−2.11445	+	1.22078i
$63$	−1.11175	−	1.92561i	−0.140067	−	0.242604i
$64$	−8.35609			−1.04451
$65$	7.78347	−	2.10180i	0.965421	−	0.260697i
$66$	−10.2401			−1.26047
$67$	1.66583	+	2.88530i	0.203513	+	0.352495i	0.949658	−	0.313288i	$-0.101431\pi$
$67$	1.66583	+	2.88530i	0.203513	+	0.352495i	−0.746145	+	0.665784i	$0.768097\pi$
$68$	4.09734	−	2.36560i	0.496875	−	0.286871i
$69$	−2.75574	+	4.77307i	−0.331752	+	0.574611i
$70$	5.73903	+	8.18874i	0.685946	+	0.978742i
$71$	1.54037	+	0.889333i	0.182808	+	0.105544i	0.588611	−	0.808416i	$-0.299675\pi$
$71$	1.54037	+	0.889333i	0.182808	+	0.105544i	−0.405803	+	0.913961i	$0.633008\pi$
$72$	0.0452818	−	0.0784304i	0.00533651	−	0.00924311i
$73$	4.49399			0.525982			0.262991	−	0.964798i	$-0.415291\pi$
$73$	4.49399			0.525982			0.262991	+	0.964798i	$0.415291\pi$
$74$	−1.16610	+	2.01974i	−0.135556	+	0.234790i
$75$	−0.872447	−	4.92330i	−0.100741	−	0.568493i
$76$	12.4134	−	7.16688i	1.42392	−	0.822098i
$77$			11.3209i			1.29014i
$78$	−5.54795	+	4.66965i	−0.628182	+	0.528734i
$79$	−7.05606			−0.793868			−0.396934	−	0.917847i	$-0.629926\pi$
$79$	−7.05606			−0.793868			−0.396934	+	0.917847i	$0.629926\pi$
$80$	3.68961	−	7.92122i	0.412511	−	0.885620i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.86773	−	1.65568i	−0.316688	−	0.182840i
$83$	−2.25488			−0.247505			−0.123752	−	0.992313i	$-0.539493\pi$
$83$	−2.25488			−0.247505			−0.123752	+	0.992313i	$0.539493\pi$
$84$	−3.93792	−	2.27356i	−0.429662	−	0.248066i
$85$	0.453072	+	5.15329i	0.0491426	+	0.558953i
$86$			18.5288i			1.99802i
$87$	−0.872172	−	0.503549i	−0.0935066	−	0.0539861i
$88$	−0.399327	+	0.230551i	−0.0425684	+	0.0245769i
$89$	−7.03934	+	4.06416i	−0.746168	+	0.430800i	−0.824308	−	0.566142i	$-0.808435\pi$
$89$	−7.03934	+	4.06416i	−0.746168	+	0.430800i	0.0781395	+	0.996942i	$0.475102\pi$
$90$	2.58108	+	3.68282i	0.272070	+	0.388203i
$91$	5.16250	+	6.13350i	0.541177	+	0.642966i
$92$			11.2711i			1.17510i
$93$	4.77938	+	8.27813i	0.495599	+	0.858402i
$94$	1.35573	+	2.34819i	0.139833	+	0.242197i
$95$	1.37264	+	15.6126i	0.140830	+	1.60181i
$96$			8.04083i			0.820663i
$97$	3.01787	−	5.22710i	0.306418	−	0.530731i	−0.671158	−	0.741314i	$-0.734203\pi$
$97$	3.01787	−	5.22710i	0.306418	−	0.530731i	0.977576	+	0.210583i	$0.0675362\pi$
$98$	2.06760	−	3.58118i	0.208859	−	0.361754i
$99$			5.09148i			0.511713i
$100$	−6.57929	−	7.82730i	−0.657929	−	0.782730i
$101$	4.13627	+	7.16422i	0.411574	+	0.712867i	0.995062	−	0.0992549i	$-0.0316459\pi$
$101$	4.13627	+	7.16422i	0.411574	+	0.712867i	−0.583488	+	0.812122i	$0.698313\pi$
$102$	−2.32650	−	4.02961i	−0.230358	−	0.398991i
$103$		−	12.4746i		−	1.22916i	−0.788854	−	0.614581i	$-0.789325\pi$
$103$		−	12.4746i		−	1.22916i	0.788854	−	0.614581i	$-0.210675\pi$
$104$	−0.111215	+	0.307009i	−0.0109055	+	0.0301047i
$105$	4.07152	−	2.85350i	0.397339	−	0.278473i
$106$	−16.3128	+	9.41821i	−1.58444	+	0.914777i
$107$	−6.13972	+	3.54477i	−0.593549	+	0.342686i	−0.766500	−	0.642245i	$-0.778003\pi$
$107$	−6.13972	+	3.54477i	−0.593549	+	0.342686i	0.172951	+	0.984931i	$0.444670\pi$
$108$	−1.77105	−	1.02251i	−0.170419	−	0.0983915i
$109$			8.37275i			0.801964i	0.916086	+	0.400982i	$0.131331\pi$
$109$			8.37275i			0.801964i	−0.916086	+	0.400982i	$0.868669\pi$
$110$	−2.00540	−	22.8096i	−0.191207	−	2.17481i
$111$	1.00423	+	0.579795i	0.0953178	+	0.0550317i
$112$	8.68924			0.821056
$113$	2.22760	+	1.28611i	0.209555	+	0.120987i	0.601105	−	0.799170i	$-0.294727\pi$
$113$	2.22760	+	1.28611i	0.209555	+	0.120987i	−0.391549	+	0.920157i	$0.628061\pi$
$114$	−7.04842	−	12.2082i	−0.660145	−	1.14340i
$115$	−11.1716	−	5.20359i	−1.04176	−	0.485237i
$116$	−2.05954			−0.191224
$117$	2.32179	+	2.75849i	0.214650	+	0.255023i
$118$		−	2.07745i		−	0.191244i
$119$	−4.45491	+	2.57204i	−0.408381	+	0.235779i
$120$	0.183570	+	0.0855045i	0.0167575	+	0.00780546i
$121$	7.46158	−	12.9238i	0.678325	−	1.17489i
$122$	−21.4303			−1.94021
$123$	−0.823222	+	1.42586i	−0.0742274	+	0.128566i
$124$	16.9290	+	9.77397i	1.52027	+	0.877729i
$125$	10.7957	−	2.90752i	0.965593	−	0.260056i
$126$	−2.23598	+	3.87283i	−0.199197	+	0.345019i
$127$	−17.7037	+	10.2212i	−1.57095	+	0.906986i	−0.574892	+	0.818229i	$0.694956\pi$
$127$	−17.7037	+	10.2212i	−1.57095	+	0.906986i	−0.996053	+	0.0887562i	$0.971711\pi$
$128$	0.362163	+	0.627284i	0.0320110	+	0.0554446i
$129$	9.21271			0.811134
$130$	−11.4880	−	11.4434i	−1.00757	−	1.00366i
$131$	−3.75523			−0.328096			−0.164048	−	0.986452i	$-0.552455\pi$
$131$	−3.75523			−0.328096			−0.164048	+	0.986452i	$0.552455\pi$
$132$	5.20611	+	9.01725i	0.453134	+	0.784851i
$133$	−13.4967	+	7.79234i	−1.17031	+	0.675681i
$134$	3.35036	−	5.80299i	0.289427	−	0.501302i
$135$	1.83113	−	1.28334i	0.157599	−	0.110452i
$136$	−0.181450	−	0.104760i	−0.0155592	−	0.00898310i
$137$	1.03777	−	1.79746i	0.0886623	−	0.153568i	−0.818284	−	0.574815i	$-0.805074\pi$
$137$	1.03777	−	1.79746i	0.0886623	−	0.153568i	0.906946	+	0.421247i	$0.138407\pi$
$138$	11.0848			0.943602
$139$	10.7917	−	18.6917i	0.915337	−	1.58541i	0.108931	−	0.994049i	$-0.465257\pi$
$139$	10.7917	−	18.6917i	0.915337	−	1.58541i	0.806406	−	0.591362i	$-0.201409\pi$
$140$	4.29310	−	9.21687i	0.362834	−	0.778968i
$141$	1.16754	−	0.674080i	0.0983246	−	0.0567678i
$142$		−	3.57730i		−	0.300200i
$143$	−3.21519	−	18.0738i	−0.268868	−	1.51141i
$144$	3.90791			0.325660
$145$	0.950838	−	2.04136i	0.0789628	−	0.169525i
$146$	−4.51921	−	7.82751i	−0.374013	−	0.647809i
$147$	−1.78060	−	1.02803i	−0.146861	−	0.0847904i
$148$	2.37140			0.194928
$149$	16.1862	+	9.34512i	1.32603	+	0.765582i	0.984683	−	0.174357i	$-0.0557845\pi$
$149$	16.1862	+	9.34512i	1.32603	+	0.765582i	0.341344	+	0.939938i	$0.389118\pi$
$150$	−7.69792	+	6.47053i	−0.628532	+	0.528317i
$151$			1.70343i			0.138623i	0.997595	+	0.0693117i	$0.0220803\pi$
$151$			1.70343i			0.138623i	−0.997595	+	0.0693117i	$0.977920\pi$
$152$	−0.549725	−	0.317384i	−0.0445886	−	0.0257432i
$153$	−2.00356	+	1.15676i	−0.161978	+	0.0935182i
$154$	19.7184	−	11.3844i	1.58896	−	0.917384i
$155$	−17.5034	+	12.2671i	−1.40590	+	0.985319i
$156$	6.93260	+	2.51135i	0.555052	+	0.201069i
$157$			9.10906i			0.726982i	0.931598	+	0.363491i	$0.118415\pi$
$157$			9.10906i			0.726982i	−0.931598	+	0.363491i	$0.881585\pi$
$158$	7.09566	+	12.2900i	0.564501	+	0.977744i
$159$	4.68282	+	8.11088i	0.371372	+	0.643235i
$160$	−17.9107	+	1.57470i	−1.41597	+	0.124491i
$161$		−	12.2547i		−	0.965809i
$162$	−1.00561	+	1.74177i	−0.0790084	+	0.136847i
$163$	4.08138	−	7.06916i	0.319679	−	0.553700i	−0.660742	−	0.750613i	$-0.729758\pi$
$163$	4.08138	−	7.06916i	0.319679	−	0.553700i	0.980421	+	0.196913i	$0.0630917\pi$
$164$			3.36702i			0.262920i
$165$	−11.3411	+	0.997103i	−0.882907	+	0.0776243i
$166$	2.26753	+	3.92748i	0.175995	+	0.304832i
$167$	−1.22032	−	2.11365i	−0.0944309	−	0.163559i	0.814940	−	0.579545i	$-0.196770\pi$
$167$	−1.22032	−	2.11365i	−0.0944309	−	0.163559i	−0.909371	+	0.415986i	$0.863436\pi$
$168$			0.201368i			0.0155359i
$169$	−9.98389	−	8.32598i	−0.767992	−	0.640460i
$170$	8.52025	−	5.97137i	0.653473	−	0.457983i
$171$	−6.07004	+	3.50454i	−0.464188	+	0.267999i
$172$	16.3161	−	9.42013i	1.24409	−	0.718278i
$173$	−7.86899	−	4.54317i	−0.598269	−	0.345411i	0.170092	−	0.985428i	$-0.445594\pi$
$173$	−7.86899	−	4.54317i	−0.598269	−	0.345411i	−0.768360	+	0.640018i	$0.778927\pi$
$174$			2.02550i			0.153553i
$175$	7.15346	+	8.51038i	0.540750	+	0.643325i
$176$	−17.2314	−	9.94853i	−1.29886	−	0.749899i
$177$	−1.03293			−0.0776394
$178$	14.1577	+	8.17395i	1.06116	+	0.612663i
$179$	−9.86590	−	17.0882i	−0.737412	−	1.27724i	−0.953657	−	0.300896i	$-0.902714\pi$
$179$	−9.86590	−	17.0882i	−0.737412	−	1.27724i	0.216245	−	0.976339i	$-0.430619\pi$
$180$	1.93079	−	4.14521i	0.143912	−	0.308966i
$181$	5.17994			0.385022			0.192511	−	0.981295i	$-0.438337\pi$
$181$	5.17994			0.385022			0.192511	+	0.981295i	$0.438337\pi$
$182$	5.49169	−	15.1598i	0.407071	−	1.12372i
$183$			10.6554i			0.787667i
$184$	0.432267	−	0.249569i	0.0318671	−	0.0183985i
$185$	−1.09481	+	2.35045i	−0.0804922	+	0.172809i
$186$	9.61241	−	16.6492i	0.704816	−	1.22078i
$187$	11.7792			0.861380
$188$	1.37851	−	2.38765i	0.100538	−	0.174138i
$189$	1.92561	+	1.11175i	0.140067	+	0.0808678i
$190$	25.8132	−	18.0910i	1.87268	−	1.31246i
$191$	0.477649	−	0.827312i	0.0345614	−	0.0598622i	−0.848227	−	0.529632i	$-0.822330\pi$
$191$	0.477649	−	0.827312i	0.0345614	−	0.0598622i	0.882789	+	0.469770i	$0.155663\pi$
$192$	7.23658	−	4.17804i	0.522255	−	0.301524i
$193$	4.92814	+	8.53580i	0.354736	+	0.614420i	0.987073	−	0.160273i	$-0.0512376\pi$
$193$	4.92814	+	8.53580i	0.354736	+	0.614420i	−0.632337	+	0.774693i	$0.717904\pi$
$194$	−12.1392			−0.871545
$195$	−5.68978	+	5.71195i	−0.407454	+	0.409041i
$196$	−4.20470			−0.300335
$197$	1.60088	+	2.77281i	0.114058	+	0.197554i	0.917403	−	0.397960i	$-0.130282\pi$
$197$	1.60088	+	2.77281i	0.114058	+	0.197554i	−0.803345	+	0.595514i	$0.796948\pi$
$198$	8.86820	−	5.12006i	0.630235	−	0.363867i
$199$	−9.62676	+	16.6740i	−0.682423	+	1.18199i	0.291816	+	0.956474i	$0.405740\pi$
$199$	−9.62676	+	16.6740i	−0.682423	+	1.18199i	−0.974239	+	0.225517i	$0.927593\pi$
$200$	−0.154509	+	0.425642i	−0.0109255	+	0.0300974i
$201$	−2.88530	−	1.66583i	−0.203513	−	0.117498i
$202$	8.31896	−	14.4089i	0.585320	−	1.01380i
$203$	2.23928			0.157167
$204$	−2.36560	+	4.09734i	−0.165625	+	0.286871i
$205$	−3.33729	−	1.55447i	−0.233086	−	0.108569i
$206$	−21.7280	+	12.5446i	−1.51386	+	0.874027i
$207$		−	5.51147i		−	0.383074i
$208$	−13.8724	+	2.46779i	−0.961878	+	0.171110i
$209$	35.6866			2.46849
$210$	−9.06452	−	4.22214i	−0.625511	−	0.291355i
$211$	7.58883	+	13.1442i	0.522436	+	0.904887i	0.999659	+	0.0261042i	$0.00831015\pi$
$211$	7.58883	+	13.1442i	0.522436	+	0.904887i	−0.477223	+	0.878782i	$0.658357\pi$
$212$	16.5870	+	9.57650i	1.13920	+	0.657717i
$213$	−1.77867			−0.121872
$214$	12.3484	+	7.12933i	0.844116	+	0.487351i
$215$	1.80419	+	20.5211i	0.123045	+	1.39953i
$216$			0.0905636i			0.00616207i
$217$	−18.4064	−	10.6269i	−1.24951	−	0.721404i
$218$	14.5834	−	8.41975i	0.987714	−	0.570257i
$219$	−3.89191	+	2.24699i	−0.262991	+	0.151838i
$220$	−19.0661	+	13.3624i	−1.28544	+	0.900893i
$221$	6.38181	−	5.37149i	0.429287	−	0.361326i
$222$		−	2.33220i		−	0.156527i
$223$	−0.557533	−	0.965676i	−0.0373352	−	0.0646665i	0.846754	−	0.531985i	$-0.178554\pi$
$223$	−0.557533	−	0.965676i	−0.0373352	−	0.0646665i	−0.884089	+	0.467318i	$0.845220\pi$
$224$	−8.93938	−	15.4835i	−0.597287	−	1.03453i
$225$	3.21721	+	3.82748i	0.214481	+	0.255165i
$226$		−	5.17330i		−	0.344123i
$227$	−7.65390	+	13.2569i	−0.508007	+	0.879894i	0.491950	+	0.870623i	$0.336284\pi$
$227$	−7.65390	+	13.2569i	−0.508007	+	0.879894i	−0.999957	+	0.00927048i	$0.997049\pi$
$228$	−7.16688	+	12.4134i	−0.474638	+	0.822098i
$229$		−	9.57447i		−	0.632699i	−0.948643	−	0.316349i	$-0.897543\pi$
$229$		−	9.57447i		−	0.632699i	0.948643	−	0.316349i	$-0.102457\pi$
$230$	2.17082	+	24.6912i	0.143140	+	1.62809i
$231$	−5.66045	−	9.80418i	−0.372430	−	0.645068i
$232$	0.0456032	+	0.0789870i	0.00299400	+	0.00518575i
$233$			22.9693i			1.50477i	0.658724	+	0.752384i	$0.271096\pi$
$233$			22.9693i			1.50477i	−0.658724	+	0.752384i	$0.728904\pi$
$234$	2.46984	−	6.81801i	0.161459	−	0.445707i
$235$	1.73014	+	2.46866i	0.112862	+	0.161037i
$236$	−1.82936	+	1.05618i	−0.119081	+	0.0687516i
$237$	6.11072	−	3.52803i	0.396934	−	0.229170i
$238$	8.95983	+	5.17296i	0.580780	+	0.335313i
$239$			11.5257i			0.745538i	0.927924	+	0.372769i	$0.121592\pi$
$239$			11.5257i			0.745538i	−0.927924	+	0.372769i	$0.878408\pi$
$240$	0.765316	+	8.70478i	0.0494010	+	0.561891i
$241$	−13.2207	−	7.63297i	−0.851620	−	0.491683i	0.00957728	−	0.999954i	$-0.496951\pi$
$241$	−13.2207	−	7.63297i	−0.851620	−	0.491683i	−0.861197	+	0.508271i	$0.830285\pi$
$242$	−30.0138			−1.92936
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	10.8953	+	18.8712i	0.697498	+	1.20810i
$245$	1.94120	−	4.16756i	0.124019	−	0.266256i
$246$	3.31137			0.211125
$247$	19.3345	−	16.2736i	1.23022	−	1.03547i
$248$		−	0.865676i		−	0.0549705i
$249$	1.95278	−	1.12744i	0.123752	−	0.0714485i
$250$	−15.9205	−	15.8797i	−1.00690	−	1.00432i
$251$	14.6941	−	25.4509i	0.927483	−	1.60645i	0.139965	−	0.990157i	$-0.455301\pi$
$251$	14.6941	−	25.4509i	0.927483	−	1.60645i	0.787518	−	0.616291i	$-0.211366\pi$
$252$	4.54712			0.286442
$253$	−14.0308	+	24.3020i	−0.882107	+	1.52785i
$254$	35.6060	+	20.5572i	2.23412	+	1.28987i
$255$	−2.96902	−	4.23635i	−0.185927	−	0.265290i
$256$	−7.62770	+	13.2116i	−0.476731	+	0.825722i
$257$	27.0314	−	15.6066i	1.68617	−	0.973513i	0.728772	−	0.684757i	$-0.240092\pi$
$257$	27.0314	−	15.6066i	1.68617	−	0.973513i	0.957403	−	0.288756i	$-0.0932417\pi$
$258$	−9.26442	−	16.0464i	−0.576777	−	0.999008i
$259$	−2.57835			−0.160211
$260$	−4.23632	+	15.9340i	−0.262725	+	0.988186i
$261$	1.00710			0.0623378
$262$	3.77630	+	6.54075i	0.233301	+	0.404089i
$263$	4.83518	−	2.79159i	0.298150	−	0.172137i	−0.343462	−	0.939167i	$-0.611600\pi$
$263$	4.83518	−	2.79159i	0.298150	−	0.172137i	0.641611	+	0.767030i	$0.278266\pi$
$264$	0.230551	−	0.399327i	0.0141895	−	0.0245769i
$265$	−17.1497	+	12.0193i	−1.05350	+	0.738339i
$266$	27.1450	+	15.6721i	1.66436	+	0.960921i
$267$	4.06416	−	7.03934i	0.248723	−	0.430800i
$268$	−6.81333			−0.416191
$269$	−8.99744	+	15.5840i	−0.548584	+	0.950175i	0.449788	+	0.893135i	$0.351499\pi$
$269$	−8.99744	+	15.5840i	−0.548584	+	0.950175i	−0.998372	+	0.0570394i	$0.981834\pi$
$270$	−4.07669	−	1.89887i	−0.248100	−	0.115562i
$271$	−14.1527	+	8.17105i	−0.859714	+	0.496356i	−0.863916	−	0.503635i	$-0.831996\pi$
$271$	−14.1527	+	8.17105i	−0.859714	+	0.496356i	0.00420268	+	0.999991i	$0.498662\pi$
$272$		−	9.04101i		−	0.548192i
$273$	−7.53761	−	2.73052i	−0.456197	−	0.165259i
$274$	−4.17436			−0.252182
$275$	−4.44204	−	25.0669i	−0.267865	−	1.51159i
$276$	−5.63556	−	9.76108i	−0.339221	−	0.587548i
$277$	−0.0829507	−	0.0478916i	−0.00498402	−	0.00287753i	0.497506	−	0.867461i	$-0.334249\pi$
$277$	−0.0829507	−	0.0478916i	−0.00498402	−	0.00287753i	−0.502490	+	0.864583i	$0.667583\pi$
$278$	−43.4090			−2.60350
$279$	−8.27813	−	4.77938i	−0.495599	−	0.286134i
$280$	−0.448542	+	0.0394354i	−0.0268055	+	0.00235672i
$281$		−	29.8592i		−	1.78125i	−0.454735	−	0.890627i	$-0.650266\pi$
$281$		−	29.8592i		−	1.78125i	0.454735	−	0.890627i	$-0.349734\pi$
$282$	−2.34819	−	1.35573i	−0.139833	−	0.0807324i
$283$	1.83492	−	1.05939i	0.109075	−	0.0629744i	−0.444470	−	0.895794i	$-0.646608\pi$
$283$	1.83492	−	1.05939i	0.109075	−	0.0629744i	0.553545	+	0.832819i	$0.313275\pi$
$284$	−3.15010	+	1.81871i	−0.186924	+	0.107921i
$285$	−8.99502	−	12.8345i	−0.532819	−	0.760253i
$286$	−28.2473	+	23.7754i	−1.67030	+	1.40587i
$287$		−	3.66086i		−	0.216094i
$288$	−4.02041	−	6.96356i	−0.236905	−	0.410332i
$289$	−5.82383	−	10.0872i	−0.342578	−	0.593363i
$290$	−4.51175	+	0.396669i	−0.264939	+	0.0232932i
$291$			6.03573i			0.353821i
$292$	−4.59517	+	7.95907i	−0.268912	+	0.465769i
$293$	9.27529	−	16.0653i	0.541868	−	0.938544i	−0.456928	−	0.889503i	$-0.651050\pi$
$293$	9.27529	−	16.0653i	0.541868	−	0.938544i	0.998797	−	0.0490402i	$-0.0156162\pi$
$294$			4.13519i			0.241169i
$295$	−0.202286	−	2.30082i	−0.0117775	−	0.133959i
$296$	−0.0525084	−	0.0909471i	−0.00305199	−	0.00528620i
$297$	−2.54574	−	4.40935i	−0.147719	−	0.255856i
$298$		−	37.5903i		−	2.17755i
$299$	3.48041	+	19.5647i	0.201277	+	1.13146i
$300$	9.61148	+	3.48900i	0.554919	+	0.201437i
$301$	−17.7400	+	10.2422i	−1.02252	+	0.590352i
$302$	2.96699	−	1.71299i	0.170731	−	0.0985718i
$303$	−7.16422	−	4.13627i	−0.411574	−	0.237622i
$304$		−	27.3909i		−	1.57097i
$305$	−23.7346	+	2.08672i	−1.35904	+	0.119485i
$306$	4.02961	+	2.32650i	0.230358	+	0.132997i
$307$	−2.19278			−0.125148			−0.0625742	−	0.998040i	$-0.519931\pi$
$307$	−2.19278			−0.125148			−0.0625742	+	0.998040i	$0.519931\pi$
$308$	−20.0498	−	11.5758i	−1.14245	−	0.659591i
$309$	6.23732	+	10.8033i	0.354828	+	0.614581i
$310$	38.9681	+	18.1509i	2.21324	+	1.03090i
$311$	6.95530			0.394399			0.197199	−	0.980363i	$-0.436815\pi$
$311$	6.95530			0.394399			0.197199	+	0.980363i	$0.436815\pi$
$312$	−0.0571895	−	0.321485i	−0.00323772	−	0.0182005i
$313$		−	6.01866i		−	0.340195i	−0.985427	−	0.170097i	$-0.945592\pi$
$313$		−	6.01866i		−	0.340195i	0.985427	−	0.170097i	$-0.0544082\pi$
$314$	15.8659	−	9.16019i	0.895366	−	0.516940i
$315$	−2.09929	+	4.50696i	−0.118281	+	0.253939i
$316$	7.21492	−	12.4966i	0.405871	−	0.702989i
$317$	−11.8288			−0.664373			−0.332187	−	0.943214i	$-0.607786\pi$
$317$	−11.8288			−0.664373			−0.332187	+	0.943214i	$0.607786\pi$
$318$	9.41821	−	16.3128i	0.528147	−	0.914777i
$319$	−4.44064	−	2.56381i	−0.248628	−	0.143546i
$320$	10.7237	+	15.3011i	0.599472	+	0.855357i
$321$	3.54477	−	6.13972i	0.197850	−	0.342686i
$322$	−21.3450	+	12.3235i	−1.18951	+	0.686763i
$323$	8.10779	+	14.0431i	0.451130	+	0.781380i
$324$	2.04503			0.113613
$325$	−13.8375	−	11.5552i	−0.767567	−	0.640969i
$326$	−16.4172			−0.909263
$327$	−4.18638	−	7.25101i	−0.231507	−	0.400982i
$328$	0.129131	−	0.0745539i	0.00713008	−	0.00411655i
$329$	−1.49882	+	2.59602i	−0.0826324	+	0.143123i
$330$	13.1415	+	18.7510i	0.723417	+	1.03221i
$331$	30.1726	+	17.4202i	1.65844	+	0.957499i	0.973437	+	0.228956i	$0.0735313\pi$
$331$	30.1726	+	17.4202i	1.65844	+	0.957499i	0.685000	+	0.728543i	$0.259802\pi$
$332$	2.30564	−	3.99349i	0.126539	−	0.219171i
$333$	−1.15959			−0.0635452
$334$	−2.45433	+	4.25103i	−0.134295	+	0.232606i
$335$	3.14554	−	6.75316i	0.171859	−	0.368965i
$336$	−7.52510	+	4.34462i	−0.410528	+	0.237018i
$337$			6.74322i			0.367327i	0.982989	+	0.183663i	$0.0587957\pi$
$337$			6.74322i			0.367327i	−0.982989	+	0.183663i	$0.941204\pi$
$338$	−4.46203	+	25.7624i	−0.242703	+	1.40129i
$339$	−2.57221			−0.139703
$340$	−9.59000	−	4.46690i	−0.520091	−	0.242252i
$341$	24.3341	+	42.1479i	1.31777	+	2.28244i
$342$	12.2082	+	7.04842i	0.660145	+	0.381135i
$343$	20.1361			1.08725
$344$	−0.722556	−	0.417168i	−0.0389576	−	0.0224922i
$345$	12.2767	−	1.07935i	0.660954	−	0.0581104i
$346$			18.2747i			0.982452i
$347$	18.6877	+	10.7893i	1.00321	+	0.579202i	0.909196	−	0.416369i	$-0.136698\pi$
$347$	18.6877	+	10.7893i	1.00321	+	0.579202i	0.0940118	+	0.995571i	$0.470031\pi$
$348$	1.78362	−	1.02977i	0.0956119	−	0.0552016i
$349$	−1.11343	+	0.642839i	−0.0596005	+	0.0344104i	−0.529504	−	0.848307i	$-0.677622\pi$
$349$	−1.11343	+	0.642839i	−0.0596005	+	0.0344104i	0.469904	+	0.882718i	$0.344289\pi$
$350$	7.62955	−	21.0178i	0.407816	−	1.12345i
$351$	−3.38998	−	1.22803i	−0.180944	−	0.0655473i
$352$			40.9397i			2.18209i
$353$	−0.808410	−	1.40021i	−0.0430273	−	0.0745255i	0.843710	−	0.536800i	$-0.180367\pi$
$353$	−0.808410	−	1.40021i	−0.0430273	−	0.0745255i	−0.886737	+	0.462274i	$0.847034\pi$
$354$	1.03872	+	1.79912i	0.0552075	+	0.0956222i
$355$	−0.348330	−	3.96194i	−0.0184874	−	0.210278i
$356$		−	16.6227i		−	0.880999i
$357$	2.57204	−	4.45491i	0.136127	−	0.235779i
$358$	−19.8426	+	34.3683i	−1.04871	+	1.81642i
$359$		−	22.7418i		−	1.20026i	−0.799901	−	0.600132i	$-0.795115\pi$
$359$		−	22.7418i		−	1.20026i	0.799901	−	0.600132i	$-0.204885\pi$
$360$	−0.201728	+	0.0177358i	−0.0106320	+	0.000934756i
$361$	15.0636	+	26.0909i	0.792820	+	1.37321i
$362$	−5.20902	−	9.02228i	−0.273780	−	0.474201i
$363$			14.9232i			0.783262i
$364$	−16.1415	+	2.87143i	−0.846042	+	0.150504i
$365$	−5.76731	−	8.22909i	−0.301875	−	0.430730i
$366$	18.5592	−	10.7152i	0.970106	−	0.560091i
$367$	23.2533	−	13.4253i	1.21381	−	0.700795i	0.250225	−	0.968188i	$-0.419495\pi$
$367$	23.2533	−	13.4253i	1.21381	−	0.700795i	0.963588	+	0.267393i	$0.0861621\pi$
$368$	18.6528	+	10.7692i	0.972343	+	0.561382i
$369$		−	1.64644i		−	0.0857104i
$370$	5.19492	−	0.456732i	0.270071	−	0.0237444i
$371$	−18.0345	−	10.4122i	−0.936306	−	0.540577i
$372$	−19.5479			−1.01351
$373$	−2.46918	−	1.42558i	−0.127849	−	0.0738138i	0.434711	−	0.900570i	$-0.356850\pi$
$373$	−2.46918	−	1.42558i	−0.127849	−	0.0738138i	−0.562561	+	0.826756i	$0.690184\pi$
$374$	−11.8453	−	20.5167i	−0.612507	−	1.06089i
$375$	−7.89556	+	7.91582i	−0.407725	+	0.408771i
$376$	−0.122094			−0.00629653
$377$	−3.57502	+	0.635966i	−0.184123	+	0.0327539i
$378$		−	4.47196i		−	0.230013i
$379$	−2.73248	+	1.57760i	−0.140358	+	0.0810357i	−0.568535	−	0.822659i	$-0.692489\pi$
$379$	−2.73248	+	1.57760i	−0.140358	+	0.0810357i	0.428177	+	0.903695i	$0.359156\pi$
$380$	−29.0541	−	13.5330i	−1.49044	−	0.694231i
$381$	10.2212	−	17.7037i	0.523648	−	0.906986i
$382$	−1.92132			−0.0983032
$383$	1.76378	−	3.05495i	0.0901248	−	0.156101i	−0.817439	−	0.576016i	$-0.804607\pi$
$383$	1.76378	−	3.05495i	0.0901248	−	0.156101i	0.907563	+	0.419915i	$0.137940\pi$
$384$	−0.627284	−	0.362163i	−0.0320110	−	0.0184815i
$385$	20.7300	−	14.5285i	1.05650	−	0.740443i
$386$	9.91161	−	17.1674i	0.504488	−	0.873798i
$387$	−7.97844	+	4.60635i	−0.405567	+	0.234154i
$388$	6.17163	+	10.6896i	0.313317	+	0.542681i
$389$	−10.2877			−0.521608			−0.260804	−	0.965392i	$-0.583988\pi$
$389$	−10.2877			−0.521608			−0.260804	+	0.965392i	$0.583988\pi$
$390$	15.6706	+	4.16629i	0.793514	+	0.210968i
$391$	−12.7509			−0.644838
$392$	0.0931020	+	0.161257i	0.00470236	+	0.00814473i
$393$	3.25212	−	1.87761i	0.164048	−	0.0947130i
$394$	3.21973	−	5.57674i	0.162208	−	0.280952i
$395$	9.05531	+	12.9206i	0.455622	+	0.650104i
$396$	−9.01725	−	5.20611i	−0.453134	−	0.261617i
$397$	4.43523	−	7.68204i	0.222598	−	0.385550i	−0.732998	−	0.680230i	$-0.761880\pi$
$397$	4.43523	−	7.68204i	0.222598	−	0.385550i	0.955596	+	0.294680i	$0.0952131\pi$
$398$	38.7232			1.94102
$399$	7.79234	−	13.4967i	0.390105	−	0.675681i
$400$	−19.2398	+	3.40945i	−0.961991	+	0.170472i
$401$	−18.1333	+	10.4693i	−0.905533	+	0.522810i	−0.878991	−	0.476838i	$-0.841783\pi$
$401$	−18.1333	+	10.4693i	−0.905533	+	0.522810i	−0.0265418	+	0.999648i	$0.508450\pi$
$402$			6.70071i			0.334201i
$403$	32.4040	+	11.7384i	1.61416	+	0.584733i
$404$	−16.9176			−0.841680
$405$	−0.944138	+	2.02697i	−0.0469146	+	0.100721i
$406$	−2.25185	−	3.90031i	−0.111757	−	0.193569i
$407$	5.11304	+	2.95202i	0.253444	+	0.146326i
$408$	0.209520			0.0103728
$409$	−5.25909	−	3.03634i	−0.260045	−	0.150137i	0.364310	−	0.931278i	$-0.381305\pi$
$409$	−5.25909	−	3.03634i	−0.260045	−	0.150137i	−0.624355	+	0.781141i	$0.714638\pi$
$410$	0.648490	+	7.37600i	0.0320267	+	0.364274i
$411$			2.07553i			0.102378i
$412$	22.0932	+	12.7555i	1.08845	+	0.628418i
$413$	1.98901	−	1.14835i	0.0978727	−	0.0565068i
$414$	−9.59973	+	5.54241i	−0.471801	+	0.272394i
$415$	2.89377	+	4.12897i	0.142049	+	0.202683i
$416$	18.6691	+	22.1806i	0.915329	+	1.08749i
$417$			21.5833i			1.05694i
$418$	−35.8869	−	62.1579i	−1.75528	−	3.04024i
$419$	−14.1532	−	24.5140i	−0.691428	−	1.19759i	−0.971370	−	0.237571i	$-0.923649\pi$
$419$	−14.1532	−	24.5140i	−0.691428	−	1.19759i	0.279942	−	0.960017i	$-0.409685\pi$
$420$	0.890496	+	10.1286i	0.0434518	+	0.494225i
$421$		−	6.60307i		−	0.321814i	−0.986970	−	0.160907i	$-0.948558\pi$
$421$		−	6.60307i		−	0.321814i	0.986970	−	0.160907i	$-0.0514419\pi$
$422$	15.2628	−	26.4360i	0.742984	−	1.28689i
$423$	−0.674080	+	1.16754i	−0.0327749	+	0.0567678i
$424$		−	0.848186i		−	0.0411916i
$425$	8.85491	−	7.44305i	0.429526	−	0.361041i
$426$	1.78865	+	3.09803i	0.0866604	+	0.150100i
$427$	−11.8461	−	20.5180i	−0.573273	−	0.992937i
$428$		−	14.4983i		−	0.700802i
$429$	11.8214	+	14.0448i	0.570740	+	0.678090i
$430$	33.9287	−	23.7788i	1.63619	−	1.14671i
$431$	0.428160	−	0.247198i	0.0206238	−	0.0119071i	−0.489653	−	0.871918i	$-0.662876\pi$
$431$	0.428160	−	0.247198i	0.0206238	−	0.0119071i	0.510276	+	0.860010i	$0.329543\pi$
$432$	−3.38435	+	1.95396i	−0.162830	+	0.0940098i
$433$	18.2568	+	10.5406i	0.877366	+	0.506547i	0.869789	−	0.493424i	$-0.164255\pi$
$433$	18.2568	+	10.5406i	0.877366	+	0.506547i	0.00757691	+	0.999971i	$0.497588\pi$
$434$			42.7464i			2.05189i
$435$	0.197227	+	2.24328i	0.00945633	+	0.107557i
$436$	−14.8285	−	8.56126i	−0.710158	−	0.410010i
$437$	−38.6303			−1.84794
$438$	7.82751	+	4.51921i	0.374013	+	0.215936i
$439$	−10.9328	−	18.9362i	−0.521794	−	0.903774i	−0.999679	−	0.0253511i	$-0.991930\pi$
$439$	−10.9328	−	18.9362i	−0.521794	−	0.903774i	0.477885	−	0.878423i	$-0.341404\pi$
$440$	0.934641	+	0.435344i	0.0445573	+	0.0207542i
$441$	2.05606			0.0979075
$442$	−15.7735	−	5.71401i	−0.750271	−	0.271788i
$443$		−	8.83792i		−	0.419902i	−0.977712	−	0.209951i	$-0.932669\pi$
$443$		−	8.83792i		−	0.419902i	0.977712	−	0.209951i	$-0.0673305\pi$
$444$	−2.05369	+	1.18570i	−0.0974638	+	0.0562707i
$445$	16.4759	+	7.67426i	0.781031	+	0.363795i
$446$	−1.12133	+	1.94219i	−0.0530963	+	0.0919655i
$447$	−18.6902			−0.884018
$448$	−9.28987	+	16.0905i	−0.438905	+	0.760206i
$449$	−14.9282	−	8.61882i	−0.704507	−	0.406747i	0.104517	−	0.994523i	$-0.466670\pi$
$449$	−14.9282	−	8.61882i	−0.704507	−	0.406747i	−0.809024	+	0.587776i	$0.800004\pi$
$450$	3.43133	−	9.45260i	0.161754	−	0.445600i
$451$	−4.19142	+	7.25975i	−0.197366	+	0.341848i
$452$	−4.55551	+	2.63013i	−0.214273	+	0.123711i
$453$	−0.851717	−	1.47522i	−0.0400171	−	0.0693117i
$454$	30.7874			1.44493
$455$	4.60602	−	17.3246i	0.215933	−	0.812189i
$456$	0.634767			0.0297257
$457$	15.9248	+	27.5826i	0.744933	+	1.29026i	0.950226	+	0.311561i	$0.100852\pi$
$457$	15.9248	+	27.5826i	0.744933	+	1.29026i	−0.205294	+	0.978700i	$0.565815\pi$
$458$	−16.6766	+	9.62821i	−0.779244	+	0.449897i
$459$	1.15676	−	2.00356i	0.0539927	−	0.0935182i
$460$	20.6389	−	14.4647i	0.962294	−	0.674418i
$461$	−30.9451	−	17.8662i	−1.44126	−	0.832110i	−0.443324	−	0.896362i	$-0.646201\pi$
$461$	−30.9451	−	17.8662i	−1.44126	−	0.832110i	−0.997934	+	0.0642514i	$0.979534\pi$
$462$	−11.3844	+	19.7184i	−0.529652	+	0.917384i
$463$	−27.4133			−1.27401			−0.637003	−	0.770862i	$-0.719826\pi$
$463$	−27.4133			−1.27401			−0.637003	+	0.770862i	$0.719826\pi$
$464$	−1.96783	+	3.40837i	−0.0913540	+	0.158230i
$465$	9.02479	−	19.3753i	0.418514	−	0.898509i
$466$	40.0073	−	23.0982i	1.85330	−	1.07000i
$467$		−	13.6947i		−	0.633716i	−0.948473	−	0.316858i	$-0.897372\pi$
$467$		−	13.6947i		−	0.633716i	0.948473	−	0.316858i	$-0.102628\pi$
$468$	−7.25949	+	1.29140i	−0.335570	+	0.0596952i
$469$	7.40793			0.342066
$470$	2.55998	−	5.49603i	0.118083	−	0.253513i
$471$	−4.55453	−	7.88868i	−0.209862	−	0.363491i
$472$	0.0810128	+	0.0467727i	0.00372891	+	0.00215289i
$473$	46.9063			2.15675
$474$	−12.2900	−	7.09566i	−0.564501	−	0.325915i
$475$	26.8271	−	22.5497i	1.23091	−	1.03465i
$476$		−	10.5198i		−	0.482175i
$477$	−8.11088	−	4.68282i	−0.371372	−	0.214412i
$478$	20.0752	−	11.5904i	0.918219	−	0.530134i
$479$	11.1837	−	6.45690i	0.510996	−	0.295023i	−0.222247	−	0.974990i	$-0.571339\pi$
$479$	11.1837	−	6.45690i	0.510996	−	0.295023i	0.733243	+	0.679967i	$0.238006\pi$
$480$	14.7238	−	10.3191i	0.672047	−	0.471000i
$481$	4.11634	−	0.732263i	0.187689	−	0.0333883i
$482$			30.7033i			1.39850i
$483$	6.12737	+	10.6129i	0.278805	+	0.482905i
$484$	15.2591	+	26.4296i	0.693597	+	1.20135i
$485$	−13.4445	+	1.18202i	−0.610481	+	0.0536729i
$486$		−	2.01123i		−	0.0912311i
$487$	−18.1268	+	31.3965i	−0.821403	+	1.42271i	0.0832337	+	0.996530i	$0.473475\pi$
$487$	−18.1268	+	31.3965i	−0.821403	+	1.42271i	−0.904637	+	0.426183i	$0.859858\pi$
$488$	0.482494	−	0.835705i	0.0218415	−	0.0378306i
$489$			8.16277i			0.369133i
$490$	−9.21105	+	0.809826i	−0.416113	+	0.0365842i
$491$	−1.60516	−	2.78022i	−0.0724400	−	0.125470i	0.827530	−	0.561421i	$-0.189745\pi$
$491$	−1.60516	−	2.78022i	−0.0724400	−	0.125470i	−0.899970	+	0.435952i	$0.856412\pi$
$492$	−1.68351	−	2.91593i	−0.0758986	−	0.131460i
$493$		−	2.32993i		−	0.104935i
$494$	−47.7880	−	17.3113i	−2.15008	−	0.778873i
$495$	9.32317	−	6.53409i	0.419045	−	0.293685i
$496$	32.3502	−	18.6774i	1.45257	−	0.838640i
$497$	3.42501	−	1.97743i	0.153633	−	0.0886999i
$498$	−3.92748	−	2.26753i	−0.175995	−	0.101611i
$499$			13.6867i			0.612703i	0.951918	+	0.306351i	$0.0991083\pi$
$499$			13.6867i			0.612703i	−0.951918	+	0.306351i	$0.900892\pi$
$500$	−5.88937	+	22.0926i	−0.263381	+	0.988011i
$501$	2.11365	+	1.22032i	0.0944309	+	0.0545197i
$502$	−59.1063			−2.63804
$503$	−21.8447	−	12.6120i	−0.974006	−	0.562343i	−0.0735511	−	0.997291i	$-0.523433\pi$
$503$	−21.8447	−	12.6120i	−0.974006	−	0.562343i	−0.900455	+	0.434949i	$0.856767\pi$
$504$	−0.100684	−	0.174390i	−0.00448482	−	0.00776794i
$505$	7.81041	−	16.7682i	0.347559	−	0.746174i
$506$	56.4381			2.50898
$507$	12.8093	+	2.21856i	0.568881	+	0.0985299i
$508$		−	41.8053i		−	1.85481i
$509$	−29.1852	+	16.8501i	−1.29361	+	0.746866i	−0.979292	−	0.202452i	$-0.935109\pi$
$509$	−29.1852	+	16.8501i	−1.29361	+	0.746866i	−0.314318	+	0.949318i	$0.601776\pi$
$510$	−4.39307	+	9.43148i	−0.194528	+	0.417633i
$511$	4.99619	−	8.65365i	0.221018	−	0.382815i
$512$	32.1307			1.41999
$513$	3.50454	−	6.07004i	0.154729	−	0.267999i
$514$	−54.3663	−	31.3884i	−2.39799	−	1.38448i
$515$	−22.8427	+	16.0092i	−1.00657	+	0.705448i
$516$	−9.42013	+	16.3161i	−0.414698	+	0.718278i
$517$	5.94451	−	3.43206i	0.261439	−	0.150942i
$518$	2.59282	+	4.49089i	0.113922	+	0.197319i
$519$	9.08633			0.398846
$520$	0.704899	−	0.190347i	0.0309119	−	0.00834727i
$521$	−2.79900			−0.122627			−0.0613133	−	0.998119i	$-0.519529\pi$
$521$	−2.79900			−0.122627			−0.0613133	+	0.998119i	$0.519529\pi$
$522$	−1.01275	−	1.75413i	−0.0443269	−	0.0767764i
$523$	−24.3895	+	14.0813i	−1.06648	+	0.615731i	−0.927217	−	0.374525i	$-0.877806\pi$
$523$	−24.3895	+	14.0813i	−1.06648	+	0.615731i	−0.139260	+	0.990256i	$0.544473\pi$
$524$	3.83977	−	6.65068i	0.167741	−	0.290536i
$525$	−10.4503	−	3.79348i	−0.456087	−	0.165561i
$526$	−9.72463	−	5.61452i	−0.424014	−	0.244805i
$527$	−11.0572	+	19.1516i	−0.481657	+	0.834255i
$528$	19.8971			0.865908
$529$	3.68816	−	6.38808i	0.160355	−	0.277743i
$530$	38.1808	+	17.7842i	1.65847	+	0.772495i
$531$	0.894540	−	0.516463i	0.0388197	−	0.0224126i
$532$		−	31.8711i		−	1.38179i
$533$	1.03970	+	5.84458i	0.0450346	+	0.253157i
$534$	−16.3479			−0.707443
$535$	14.3703	+	6.69350i	0.621281	+	0.289385i
$536$	0.150863	+	0.261303i	0.00651631	+	0.0112866i
$537$	17.0882	+	9.86590i	0.737412	+	0.425745i
$538$	36.1918			1.56034
$539$	−9.06587	−	5.23418i	−0.390495	−	0.225452i
$540$	0.400493	+	4.55525i	0.0172345	+	0.196027i
$541$		−	5.41109i		−	0.232641i	−0.993212	−	0.116320i	$-0.962890\pi$
$541$		−	5.41109i		−	0.232641i	0.993212	−	0.116320i	$-0.0371100\pi$
$542$	28.4642	+	16.4338i	1.22264	+	0.705893i
$543$	−4.48596	+	2.58997i	−0.192511	+	0.111146i
$544$	−16.1103	+	9.30127i	−0.690722	+	0.398789i
$545$	15.3316	−	10.7451i	0.656734	−	0.460268i
$546$	2.82397	+	15.8746i	0.120855	+	0.679372i
$547$		−	41.1838i		−	1.76089i	−0.474147	−	0.880446i	$-0.657243\pi$
$547$		−	41.1838i		−	1.76089i	0.474147	−	0.880446i	$-0.342757\pi$
$548$	2.12226	+	3.67586i	0.0906585	+	0.157025i
$549$	−5.32768	−	9.22782i	−0.227380	−	0.393834i
$550$	−39.1938	+	32.9446i	−1.67123	+	1.40476i
$551$		−	7.05882i		−	0.300716i
$552$	−0.249569	+	0.432267i	−0.0106224	+	0.0183985i
$553$	−7.84456	+	13.5872i	−0.333585	+	0.577786i
$554$			0.192642i			0.00818456i
$555$	−0.227091	−	2.58296i	−0.00963949	−	0.109641i
$556$	22.0693	+	38.2251i	0.935946	+	1.62111i
$557$	−16.1698	−	28.0070i	−0.685137	−	1.18669i	−0.973394	−	0.229139i	$-0.926409\pi$
$557$	−16.1698	−	28.0070i	−0.685137	−	1.18669i	0.288256	−	0.957553i	$-0.406924\pi$
$558$			19.2248i			0.813852i
$559$	25.4132	−	21.3900i	1.07486	−	0.904700i
$560$	−11.1512	−	15.9111i	−0.471226	−	0.672368i
$561$	−10.2011	+	5.88960i	−0.430690	+	0.248659i
$562$	−52.0080	+	30.0268i	−2.19383	+	1.26661i
$563$	−38.9114	−	22.4655i	−1.63992	−	0.946809i	−0.980858	−	0.194722i	$-0.937619\pi$
$563$	−38.9114	−	22.4655i	−1.63992	−	0.946809i	−0.659064	−	0.752087i	$-0.729047\pi$
$564$			2.75703i			0.116092i
$565$	−0.503736	−	5.72954i	−0.0211923	−	0.241044i
$566$	−3.69044	−	2.13068i	−0.155121	−	0.0895591i
$567$	−2.22350			−0.0933781
$568$	0.139501	+	0.0805412i	0.00585335	+	0.00337943i
$569$	14.5891	+	25.2691i	0.611608	+	1.05934i	0.990969	+	0.134088i	$0.0428103\pi$
$569$	14.5891	+	25.2691i	0.611608	+	1.05934i	−0.379362	+	0.925249i	$0.623856\pi$
$570$	−13.3094	+	28.5739i	−0.557467	+	1.19683i
$571$	−8.45655			−0.353895			−0.176948	−	0.984220i	$-0.556622\pi$
$571$	−8.45655			−0.353895			−0.176948	+	0.984220i	$0.556622\pi$
$572$	35.2972	+	12.7865i	1.47585	+	0.534631i
$573$			0.955297i			0.0399081i
$574$	−6.37639	+	3.68141i	−0.266145	+	0.153659i
$575$	4.80846	+	27.1346i	0.200527	+	1.13159i
$576$	−4.17804	+	7.23658i	−0.174085	+	0.301524i
$577$	−27.2027			−1.13246			−0.566232	−	0.824246i	$-0.691599\pi$
$577$	−27.2027			−1.13246			−0.566232	+	0.824246i	$0.691599\pi$
$578$	−11.7130	+	20.2876i	−0.487198	+	0.843852i
$579$	−8.53580	−	4.92814i	−0.354736	−	0.204807i
$580$	2.64309	+	3.77130i	0.109748	+	0.156595i
$581$	−2.50686	+	4.34200i	−0.104002	+	0.180137i
$582$	10.5129	−	6.06961i	0.435773	−	0.251594i
$583$	23.8425	+	41.2964i	0.987454	+	1.71032i
$584$	0.406992			0.0168414
$585$	2.07152	−	7.79159i	0.0856468	−	0.322142i
$586$	−37.3094			−1.54124
$587$	15.4477	+	26.7561i	0.637593	+	1.10434i	0.985959	+	0.166986i	$0.0534033\pi$
$587$	15.4477	+	26.7561i	0.637593	+	1.10434i	−0.348366	+	0.937359i	$0.613263\pi$
$588$	3.64137	−	2.10235i	0.150168	−	0.0866994i
$589$	−33.4991	+	58.0221i	−1.38030	+	2.39076i
$590$	−3.80408	+	2.66607i	−0.156611	+	0.109760i
$591$	−2.77281	−	1.60088i	−0.114058	−	0.0658515i
$592$	2.26579	−	3.92446i	0.0931234	−	0.161294i
$593$	−14.6049			−0.599750			−0.299875	−	0.953979i	$-0.596945\pi$
$593$	−14.6049			−0.599750			−0.299875	+	0.953979i	$0.596945\pi$
$594$	−5.12006	+	8.86820i	−0.210078	+	0.363867i
$595$	10.4269	+	4.85673i	0.427462	+	0.199106i
$596$	−33.1013	+	19.1110i	−1.35588	+	0.782819i
$597$		−	19.2535i		−	0.787994i
$598$	30.5774	−	25.7366i	1.25040	−	1.05245i
$599$	21.9911			0.898532			0.449266	−	0.893398i	$-0.351686\pi$
$599$	21.9911			0.898532			0.449266	+	0.893398i	$0.351686\pi$
$600$	−0.0790119	−	0.445871i	−0.00322565	−	0.0182026i
$601$	−22.3908	−	38.7820i	−0.913339	−	1.58195i	−0.809314	−	0.587376i	$-0.800161\pi$
$601$	−22.3908	−	38.7820i	−0.913339	−	1.58195i	−0.104025	−	0.994575i	$-0.533172\pi$
$602$	35.6792	+	20.5994i	1.45418	+	0.839569i
$603$	3.33166			0.135676
$604$	−3.01686	−	1.74179i	−0.122754	−	0.0708723i
$605$	−33.2410	+	2.92251i	−1.35144	+	0.118817i
$606$			16.6379i			0.675870i
$607$	11.3649	+	6.56151i	0.461285	+	0.266323i	0.712585	−	0.701586i	$-0.247524\pi$
$607$	11.3649	+	6.56151i	0.461285	+	0.266323i	−0.251299	+	0.967909i	$0.580858\pi$
$608$	−48.8081	+	28.1794i	−1.97943	+	1.14282i
$609$	−1.93927	+	1.11964i	−0.0785833	+	0.0453701i
$610$	27.5024	+	39.2418i	1.11354	+	1.58885i
$611$	1.65558	−	4.57023i	0.0669775	−	0.184892i
$612$		−	4.73120i		−	0.191247i
$613$	−8.64874	−	14.9801i	−0.349320	−	0.605039i	0.636809	−	0.771021i	$-0.280254\pi$
$613$	−8.64874	−	14.9801i	−0.349320	−	0.605039i	−0.986129	+	0.165982i	$0.946921\pi$
$614$	2.20508	+	3.81932i	0.0889900	+	0.154135i
$615$	3.66741	−	0.322435i	0.147884	−	0.0130019i
$616$			1.02526i			0.0413089i
$617$	8.09910	−	14.0281i	0.326058	−	0.564748i	−0.655668	−	0.755049i	$-0.727613\pi$
$617$	8.09910	−	14.0281i	0.326058	−	0.564748i	0.981726	+	0.190301i	$0.0609463\pi$
$618$	12.5446	−	21.7280i	0.504620	−	0.874027i
$619$		−	10.8858i		−	0.437539i	−0.975777	−	0.218770i	$-0.929796\pi$
$619$		−	10.8858i		−	0.437539i	0.975777	−	0.218770i	$-0.0702043\pi$
$620$	−3.82822	−	43.5426i	−0.153745	−	1.74871i
$621$	2.75574	+	4.77307i	0.110584	+	0.191537i
$622$	−6.99434	−	12.1145i	−0.280447	−	0.485749i
$623$			18.0733i			0.724092i
$624$	10.7800	−	9.07336i	0.431543	−	0.363225i
$625$	−19.1785	−	16.0369i	−0.767141	−	0.641478i
$626$	−10.4831	+	6.05244i	−0.418990	+	0.241904i
$627$	−30.9055	+	17.8433i	−1.23425	+	0.712592i
$628$	−16.1326	−	9.31415i	−0.643760	−	0.371675i
$629$			2.68273i			0.106967i
$630$	9.96117	−	0.875777i	0.396863	−	0.0348918i
$631$	29.1425	+	16.8254i	1.16014	+	0.669810i	0.951339	−	0.308147i	$-0.0997090\pi$
$631$	29.1425	+	16.8254i	1.16014	+	0.669810i	0.208806	+	0.977957i	$0.433042\pi$
$632$	−0.639022			−0.0254189
$633$	−13.1442	−	7.58883i	−0.522436	−	0.301629i
$634$	11.8952	+	20.6031i	0.472420	+	0.818255i
$635$	41.4362	+	19.3005i	1.64434	+	0.765915i
$636$	−19.1530			−0.759466
$637$	−7.29863	+	1.29837i	−0.289182	+	0.0514432i
$638$			10.3128i			0.408287i
$639$	1.54037	−	0.889333i	0.0609361	−	0.0351815i
$640$	0.683863	−	1.46819i	0.0270320	−	0.0580351i
$641$	−14.7514	+	25.5501i	−0.582643	+	1.00917i	0.412521	+	0.910948i	$0.364648\pi$
$641$	−14.7514	+	25.5501i	−0.582643	+	1.00917i	−0.995165	+	0.0982199i	$0.968685\pi$
$642$	−14.2587			−0.562744
$643$	12.7206	−	22.0327i	0.501651	−	0.868885i	−0.498347	−	0.866978i	$-0.666059\pi$
$643$	12.7206	−	22.0327i	0.501651	−	0.868885i	0.999998	−	0.00190769i	$-0.000607237\pi$
$644$	21.7037	+	12.5307i	0.855247	+	0.493777i
$645$	−11.8230	−	16.8697i	−0.465531	−	0.664243i
$646$	16.3066	−	28.2439i	0.641575	−	1.11124i
$647$	4.27889	−	2.47042i	0.168221	−	0.0971222i	−0.413526	−	0.910492i	$-0.635703\pi$
$647$	4.27889	−	2.47042i	0.168221	−	0.0971222i	0.581747	+	0.813370i	$0.302370\pi$
$648$	−0.0452818	−	0.0784304i	−0.00177884	−	0.00308104i
$649$	−5.25912			−0.206438
$650$	−6.21142	+	35.7219i	−0.243632	+	1.40113i
$651$	21.2539			0.833005
$652$	8.34655	+	14.4566i	0.326876	+	0.566166i
$653$	12.5981	−	7.27351i	0.493001	−	0.284634i	−0.232818	−	0.972520i	$-0.574795\pi$
$653$	12.5981	−	7.27351i	0.493001	−	0.284634i	0.725819	+	0.687886i	$0.241461\pi$
$654$	−8.41975	+	14.5834i	−0.329238	+	0.570257i
$655$	4.81922	+	6.87631i	0.188303	+	0.268680i
$656$	5.57215	+	3.21708i	0.217556	+	0.125606i
$657$	2.24699	−	3.89191i	0.0876636	−	0.151838i
$658$	6.02891			0.235031
$659$	4.47698	−	7.75435i	0.174398	−	0.302067i	−0.765555	−	0.643371i	$-0.777535\pi$
$659$	4.47698	−	7.75435i	0.174398	−	0.302067i	0.939953	+	0.341304i	$0.110869\pi$
$660$	9.83057	−	21.1053i	0.382654	−	0.821521i
$661$	−10.3161	+	5.95599i	−0.401249	+	0.231661i	−0.687023	−	0.726636i	$-0.741083\pi$
$661$	−10.3161	+	5.95599i	−0.401249	+	0.231661i	0.285774	+	0.958297i	$0.407749\pi$
$662$		−	70.0718i		−	2.72342i
$663$	−2.84106	+	7.84275i	−0.110338	+	0.304587i
$664$	−0.204210			−0.00792487
$665$	31.5896	+	14.7141i	1.22499	+	0.570587i
$666$	1.16610	+	2.01974i	0.0451854	+	0.0782635i
$667$	4.80695	+	2.77529i	0.186126	+	0.107460i
$668$	4.99116			0.193114
$669$	0.965676	+	0.557533i	0.0373352	+	0.0215555i
$670$	−14.9257	+	1.31225i	−0.576629	+	0.0506967i
$671$			54.2516i			2.09436i
$672$	15.4835	+	8.93938i	0.597287	+	0.344844i
$673$	−2.25576	+	1.30236i	−0.0869532	+	0.0502025i	−0.542846	−	0.839832i	$-0.682653\pi$
$673$	−2.25576	+	1.30236i	−0.0869532	+	0.0502025i	0.455893	+	0.890035i	$0.349320\pi$
$674$	11.7452	−	6.78107i	0.452407	−	0.261197i
$675$	−4.69992	−	1.70609i	−0.180900	−	0.0656673i
$676$	24.9544	−	9.16851i	0.959784	−	0.352635i
$677$			15.6343i			0.600877i	0.953801	+	0.300438i	$0.0971329\pi$
$677$			15.6343i			0.600877i	−0.953801	+	0.300438i	$0.902867\pi$
$678$	2.58665	+	4.48021i	0.0993397	+	0.172061i
$679$	−6.71022	−	11.6224i	−0.257515	−	0.446028i
$680$	0.0410319	+	0.466701i	0.00157350	+	0.0178972i
$681$		−	15.3078i		−	0.586596i
$682$	48.9414	−	84.7690i	1.87406	−	3.24597i
$683$	−16.7155	+	28.9520i	−0.639599	+	1.10782i	0.345921	+	0.938264i	$0.387566\pi$
$683$	−16.7155	+	28.9520i	−0.639599	+	1.10782i	−0.985521	+	0.169555i	$0.945767\pi$
$684$		−	14.3338i		−	0.548065i
$685$	−4.62320	+	0.406467i	−0.176643	+	0.0155303i
$686$	−20.2491	−	35.0725i	−0.773116	−	1.33908i
$687$	4.78724	+	8.29173i	0.182644	+	0.316349i
$688$		−	36.0025i		−	1.37258i
$689$	31.7493	+	11.5013i	1.20955	+	0.438164i
$690$	−14.2256	−	20.2978i	−0.541558	−	0.772722i
$691$	23.4855	−	13.5594i	0.893431	−	0.515823i	0.0183678	−	0.999831i	$-0.494153\pi$
$691$	23.4855	−	13.5594i	0.893431	−	0.515823i	0.875063	+	0.484009i	$0.160820\pi$
$692$	16.0923	−	9.29091i	0.611738	−	0.353187i
$693$	9.80418	+	5.66045i	0.372430	+	0.215023i
$694$		−	43.3996i		−	1.64743i
$695$	−48.0764	+	4.22683i	−1.82364	+	0.160333i
$696$	−0.0789870	−	0.0456032i	−0.00299400	−	0.00172858i
$697$	−3.80907			−0.144279
$698$	2.23936	+	1.29289i	0.0847610	+	0.0489368i
$699$	−11.4846	−	19.8920i	−0.434389	−	0.752384i
$700$	−22.3868	+	3.96712i	−0.846142	+	0.149943i
$701$	31.5261			1.19072			0.595362	−	0.803457i	$-0.297008\pi$
$701$	31.5261			1.19072			0.595362	+	0.803457i	$0.297008\pi$
$702$	1.27006	+	7.13949i	0.0479352	+	0.269463i
$703$			8.12766i			0.306541i
$704$	36.8449	−	21.2724i	1.38864	−	0.801734i
$705$	−2.73268	−	1.27285i	−0.102919	−	0.0479382i
$706$	−1.62590	+	2.81613i	−0.0611914	+	0.105987i
$707$	18.3940			0.691776
$708$	1.05618	−	1.82936i	0.0396937	−	0.0687516i
$709$	16.0354	+	9.25806i	0.602223	+	0.347694i	0.769916	−	0.638146i	$-0.220298\pi$
$709$	16.0354	+	9.25806i	0.602223	+	0.347694i	−0.167692	+	0.985839i	$0.553632\pi$
$710$	−6.55051	+	4.59088i	−0.245836	+	0.172293i
$711$	−3.52803	+	6.11072i	−0.132311	+	0.229170i
$712$	−0.637508	+	0.368065i	−0.0238916	+	0.0137938i
$713$	−26.3414	−	45.6247i	−0.986494	−	1.70866i
$714$	−10.3459			−0.387187
$715$	−28.9694	+	29.0823i	−1.08339	+	1.08762i
$716$	40.3521			1.50803
$717$	−5.76287	−	9.98158i	−0.215218	−	0.372769i
$718$	−39.6110	+	22.8694i	−1.47827	+	0.853479i
$719$	8.35147	−	14.4652i	0.311457	−	0.539460i	−0.667221	−	0.744860i	$-0.732516\pi$
$719$	8.35147	−	14.4652i	0.311457	−	0.539460i	0.978678	+	0.205400i	$0.0658496\pi$
$720$	−5.01518	−	7.15591i	−0.186905	−	0.266685i
$721$	−24.0212	−	13.8687i	−0.894597	−	0.516496i
$722$	30.2963	−	52.4747i	1.12751	−	1.95291i
$723$	15.2659			0.567747
$724$	−5.29657	+	9.17392i	−0.196845	+	0.340946i
$725$	−4.95824	+	0.878639i	−0.184144	+	0.0326318i
$726$	25.9927	−	15.0069i	0.964681	−	0.556959i
$727$			9.38173i			0.347949i	0.984750	+	0.173974i	$0.0556610\pi$
$727$			9.38173i			0.347949i	−0.984750	+	0.173974i	$0.944339\pi$
$728$	0.467535	+	0.555472i	0.0173280	+	0.0205872i
$729$	−1.00000			−0.0370370
$730$	−8.53352	+	18.3206i	−0.315840	+	0.678076i
$731$	10.6569	+	18.4582i	0.394158	+	0.682702i
$732$	−18.8712	−	10.8953i	−0.697498	−	0.402701i
$733$	−8.06377			−0.297842			−0.148921	−	0.988849i	$-0.547580\pi$
$733$	−8.06377			−0.297842			−0.148921	+	0.988849i	$0.547580\pi$
$734$	−46.7676	−	27.0013i	−1.72623	−	0.996637i
$735$	0.402653	+	4.57982i	0.0148521	+	0.168929i
$736$		−	44.3168i		−	1.63354i
$737$	−14.6904	−	8.48153i	−0.541129	−	0.312421i
$738$	−2.86773	+	1.65568i	−0.105563	+	0.0609466i
$739$	8.05917	−	4.65297i	0.296461	−	0.171162i	−0.344391	−	0.938826i	$-0.611914\pi$
$739$	8.05917	−	4.65297i	0.296461	−	0.171162i	0.640852	+	0.767664i	$0.278581\pi$
$740$	−3.04330	−	4.34234i	−0.111874	−	0.159628i
$741$	−8.60735	+	23.7606i	−0.316199	+	0.872868i
$742$			41.8827i			1.53756i
$743$	−17.2420	−	29.8641i	−0.632549	−	1.09561i	−0.987029	−	0.160543i	$-0.948676\pi$
$743$	−17.2420	−	29.8641i	−0.632549	−	1.09561i	0.354480	−	0.935064i	$-0.384658\pi$
$744$	0.432838	+	0.749697i	0.0158686	+	0.0274852i
$745$	−3.66025	−	41.6320i	−0.134101	−	1.52528i
$746$			5.73433i			0.209949i
$747$	−1.12744	+	1.95278i	−0.0412508	+	0.0714485i
$748$	−12.0444	+	20.8615i	−0.440387	+	0.762772i
$749$			15.7636i			0.575988i
$750$	21.7274	+	5.79202i	0.793374	+	0.211495i
$751$	13.5823	+	23.5253i	0.495626	+	0.858450i	0.999987	−	0.00504305i	$-0.00160526\pi$
$751$	13.5823	+	23.5253i	0.495626	+	0.858450i	−0.504361	+	0.863493i	$0.668272\pi$
$752$	−2.63425	−	4.56265i	−0.0960611	−	0.166383i
$753$			29.3882i			1.07097i
$754$	4.70279	+	5.58733i	0.171266	+	0.203478i
$755$	3.11921	−	2.18608i	0.113520	−	0.0795596i
$756$	−3.93792	+	2.27356i	−0.143221	+	0.0826885i
$757$	28.9507	−	16.7147i	1.05223	−	0.607506i	0.128958	−	0.991650i	$-0.458837\pi$
$757$	28.9507	−	16.7147i	1.05223	−	0.607506i	0.923273	+	0.384144i	$0.125503\pi$
$758$	5.49563	+	3.17290i	0.199610	+	0.115245i
$759$		−	28.0615i		−	1.01857i
$760$	0.124311	+	1.41393i	0.00450924	+	0.0512886i
$761$	−6.95046	−	4.01285i	−0.251954	−	0.145466i	0.368705	−	0.929547i	$-0.379801\pi$
$761$	−6.95046	−	4.01285i	−0.251954	−	0.145466i	−0.620659	+	0.784081i	$0.713135\pi$
$762$	−41.1143			−1.48941
$763$	16.1226	+	9.30840i	0.583678	+	0.336987i
$764$	0.976805	+	1.69188i	0.0353396	+	0.0612099i
$765$	4.68942	+	2.18427i	0.169546	+	0.0789726i
$766$	−7.09471			−0.256342
$767$	−2.84932	+	2.39824i	−0.102883	+	0.0865954i
$768$		−	15.2554i		−	0.550481i
$769$	16.7658	−	9.67974i	0.604590	−	0.349060i	−0.166255	−	0.986083i	$-0.553167\pi$
$769$	16.7658	−	9.67974i	0.604590	−	0.349060i	0.770845	+	0.637022i	$0.219834\pi$
$770$	−46.1518	−	21.4969i	−1.66320	−	0.774696i
$771$	−15.6066	+	27.0314i	−0.562058	+	0.973513i
$772$	−20.1564			−0.725445
$773$	23.2735	−	40.3109i	0.837090	−	1.44988i	−0.0552265	−	0.998474i	$-0.517588\pi$
$773$	23.2735	−	40.3109i	0.837090	−	1.44988i	0.892317	−	0.451409i	$-0.149079\pi$
$774$	16.0464	+	9.26442i	0.576777	+	0.333003i
$775$	44.9254	+	16.3081i	1.61377	+	0.585803i
$776$	0.273309	−	0.473385i	0.00981122	−	0.0169935i
$777$	2.23291	−	1.28917i	0.0801053	−	0.0462488i
$778$	10.3455	+	17.9189i	0.370903	+	0.642423i
$779$	−11.5401			−0.413465
$780$	−4.29825	−	15.9174i	−0.153902	−	0.569935i
$781$	−9.05604			−0.324051
$782$	12.8224	+	22.2091i	0.458529	+	0.794195i
$783$	−0.872172	+	0.503549i	−0.0311689	+	0.0179954i
$784$	−4.01745	+	6.95842i	−0.143480	+	0.248515i
$785$	16.6799	−	11.6900i	0.595331	−	0.417234i
$786$	−6.54075	−	3.77630i	−0.233301	−	0.134696i
$787$	10.8493	−	18.7915i	0.386735	−	0.669845i	−0.605273	−	0.796018i	$-0.706936\pi$
$787$	10.8493	−	18.7915i	0.386735	−	0.669845i	0.992008	+	0.126173i	$0.0402693\pi$
$788$	−6.54770			−0.233252
$789$	−2.79159	+	4.83518i	−0.0993833	+	0.172137i
$790$	13.3986	−	28.7654i	0.476699	−	1.02343i
$791$	4.95307	−	2.85965i	0.176111	−	0.101678i
$792$			0.461103i			0.0163846i
$793$	24.7395	+	29.3927i	0.878527	+	1.04377i
$794$	−17.8405			−0.633135
$795$	8.84245	−	18.9839i	0.313609	−	0.673288i
$796$	−19.6870	−	34.0989i	−0.697787	−	1.20860i
$797$	−2.95547	−	1.70634i	−0.104688	−	0.0604418i	0.446742	−	0.894663i	$-0.352584\pi$
$797$	−2.95547	−	1.70634i	−0.104688	−	0.0604418i	−0.551430	+	0.834221i	$0.685918\pi$
$798$	−31.3443			−1.10958
$799$	2.70112	+	1.55949i	0.0955587	+	0.0551709i
$800$	25.8690	+	30.7761i	0.914608	+	1.08810i
$801$			8.12833i			0.287200i
$802$	36.4701	+	21.0560i	1.28780	+	0.743515i
$803$	−19.8156	+	11.4405i	−0.699276	+	0.403727i
$804$	5.90052	−	3.40667i	0.208095	−	0.120144i
$805$	−22.4401	+	15.7270i	−0.790908	+	0.554303i
$806$	−12.1402	−	68.2447i	−0.427620	−	2.40382i
$807$		−	17.9949i		−	0.633450i
$808$	0.374595	+	0.648818i	0.0131782	+	0.0228253i
$809$	−9.89881	−	17.1452i	−0.348024	−	0.602795i	0.637875	−	0.770140i	$-0.279814\pi$
$809$	−9.89881	−	17.1452i	−0.348024	−	0.602795i	−0.985898	+	0.167345i	$0.946480\pi$
$810$	4.47996	−	0.393873i	0.157410	−	0.0138393i
$811$			6.24712i			0.219366i	0.993967	+	0.109683i	$0.0349836\pi$
$811$			6.24712i			0.219366i	−0.993967	+	0.109683i	$0.965016\pi$
$812$	−2.28970	+	3.96587i	−0.0803526	+	0.139175i
$813$	8.17105	−	14.1527i	0.286571	−	0.496356i
$814$		−	11.8743i		−	0.416195i
$815$	−18.1824	+	1.59858i	−0.636900	+	0.0559957i
$816$	4.52050	+	7.82974i	0.158249	+	0.274096i
$817$	32.2863	+	55.9215i	1.12955	+	1.95645i
$818$			12.2135i			0.427036i
$819$	7.89302	−	1.40410i	0.275804	−	0.0490634i
$820$	6.16547	−	4.32103i	0.215307	−	0.150897i
$821$	−17.2097	+	9.93601i	−0.600622	+	0.346769i	−0.769286	−	0.638904i	$-0.779388\pi$
$821$	−17.2097	+	9.93601i	−0.600622	+	0.346769i	0.168664	+	0.985674i	$0.446055\pi$
$822$	3.61510	−	2.08718i	0.126091	−	0.0727988i
$823$	24.0465	+	13.8832i	0.838207	+	0.483939i	0.856654	−	0.515891i	$-0.172539\pi$
$823$	24.0465	+	13.8832i	0.838207	+	0.483939i	−0.0184475	+	0.999830i	$0.505872\pi$
$824$		−	1.12975i		−	0.0393566i
$825$	16.3803	+	19.4875i	0.570291	+	0.678468i
$826$	−4.00034	−	2.30960i	−0.139190	−	0.0803612i
$827$	24.0957			0.837889			0.418944	−	0.908012i	$-0.362400\pi$
$827$	24.0957			0.837889			0.418944	+	0.908012i	$0.362400\pi$
$828$	9.76108	+	5.63556i	0.339221	+	0.195849i
$829$	18.5805	+	32.1824i	0.645329	+	1.11774i	0.984225	+	0.176919i	$0.0566130\pi$
$829$	18.5805	+	32.1824i	0.645329	+	1.11774i	−0.338896	+	0.940824i	$0.610054\pi$
$830$	4.28172	−	9.19243i	0.148621	−	0.319074i
$831$	0.0957832			0.00332268
$832$	10.2615	−	28.3269i	0.355754	−	0.982060i
$833$		−	4.75671i		−	0.164810i
$834$	37.5933	−	21.7045i	1.30175	−	0.751565i
$835$	−2.30429	+	4.94709i	−0.0797433	+	0.171201i
$836$	−36.4900	+	63.2026i	−1.26203	+	2.18591i
$837$	9.55876			0.330399
$838$	−28.4652	+	49.3032i	−0.983315	+	1.70315i
$839$	−27.2829	−	15.7518i	−0.941912	−	0.543813i	−0.0513528	−	0.998681i	$-0.516353\pi$
$839$	−27.2829	−	15.7518i	−0.941912	−	0.543813i	−0.890559	+	0.454867i	$0.849687\pi$
$840$	0.368731	−	0.258423i	0.0127224	−	0.00891645i
$841$	13.9929	−	24.2364i	0.482513	−	0.835737i
$842$	−11.5011	+	6.64014i	−0.396353	+	0.228834i
$843$	14.9296	+	25.8589i	0.514204	+	0.890627i
$844$	−31.0387			−1.06840
$845$	−2.43326	+	28.9669i	−0.0837066	+	0.996490i
$846$	2.71145			0.0932217
$847$	−16.5908	−	28.7361i	−0.570067	−	0.987384i
$848$	31.6966	−	18.3001i	1.08847	−	0.628427i
$849$	−1.05939	+	1.83492i	−0.0363583	+	0.0629744i
$850$	−21.8687	−	7.93841i	−0.750091	−	0.272285i
$851$	−5.53481	−	3.19553i	−0.189731	−	0.109541i
$852$	1.81871	−	3.15010i	0.0623080	−	0.107921i
$853$	−50.8047			−1.73952			−0.869760	−	0.493474i	$-0.835727\pi$
$853$	−50.8047			−1.73952			−0.869760	+	0.493474i	$0.835727\pi$
$854$	−23.8252	+	41.2664i	−0.815280	+	1.41211i
$855$	14.2072	+	6.61753i	0.485875	+	0.226315i
$856$	−0.556035	+	0.321027i	−0.0190049	+	0.0109725i
$857$		−	9.65725i		−	0.329885i	−0.986303	−	0.164943i	$-0.947256\pi$
$857$		−	9.65725i		−	0.329885i	0.986303	−	0.164943i	$-0.0527439\pi$
$858$	12.5752	−	34.7137i	0.429309	−	1.18511i
$859$	8.60606			0.293635			0.146817	−	0.989164i	$-0.453097\pi$
$859$	8.60606			0.293635			0.146817	+	0.989164i	$0.453097\pi$
$860$	−38.1886	−	17.7878i	−1.30222	−	0.606559i
$861$	1.83043	+	3.17040i	0.0623810	+	0.108047i
$862$	−0.861127	−	0.497172i	−0.0293301	−	0.0169337i
$863$	40.2071			1.36866			0.684332	−	0.729170i	$-0.260094\pi$
$863$	40.2071			1.36866			0.684332	+	0.729170i	$0.260094\pi$
$864$	6.96356	+	4.02041i	0.236905	+	0.136777i
$865$	1.77944	+	20.2396i	0.0605029	+	0.688166i
$866$		−	42.3989i		−	1.44077i
$867$	10.0872	+	5.82383i	0.342578	+	0.197788i
$868$	37.6416	−	21.7324i	1.27764	−	0.737646i
$869$	31.1126	−	17.9629i	1.05542	−	0.609349i
$870$	3.70896	−	2.59940i	0.125745	−	0.0881280i
$871$	−11.8268	+	2.10389i	−0.400735	+	0.0712876i
$872$			0.758267i			0.0256781i
$873$	−3.01787	−	5.22710i	−0.102139	−	0.176910i
$874$	38.8472	+	67.2853i	1.31402	+	2.27596i
$875$	6.40333	−	24.0206i	0.216472	−	0.812045i
$876$		−	9.19034i		−	0.310513i
$877$	−16.9984	+	29.4421i	−0.573995	+	0.994189i	0.422155	+	0.906524i	$0.361274\pi$
$877$	−16.9984	+	29.4421i	−0.573995	+	0.994189i	−0.996150	+	0.0876652i	$0.972059\pi$
$878$	−21.9883	+	38.0849i	−0.742070	+	1.28530i
$879$			18.5506i			0.625696i
$880$	3.89659	+	44.3202i	0.131354	+	1.49403i
$881$	−1.29166	−	2.23722i	−0.0435172	−	0.0753740i	0.843446	−	0.537213i	$-0.180523\pi$
$881$	−1.29166	−	2.23722i	−0.0435172	−	0.0753740i	−0.886964	+	0.461839i	$0.847190\pi$
$882$	−2.06760	−	3.58118i	−0.0696196	−	0.120585i
$883$		−	41.6034i		−	1.40007i	−0.714110	−	0.700034i	$-0.753168\pi$
$883$		−	41.6034i		−	1.40007i	0.714110	−	0.700034i	$-0.246832\pi$
$884$	2.98768	+	16.7949i	0.100487	+	0.564874i
$885$	1.32559	+	1.89142i	0.0445593	+	0.0635795i
$886$	−15.3937	+	8.88753i	−0.517160	+	0.298582i
$887$	36.1779	−	20.8873i	1.21473	−	0.701328i	0.250948	−	0.968001i	$-0.419258\pi$
$887$	36.1779	−	20.8873i	1.21473	−	0.701328i	0.963787	+	0.266673i	$0.0859244\pi$
$888$	0.0909471	+	0.0525084i	0.00305199	+	0.00176207i
$889$			45.4537i			1.52447i
$890$	−3.20153	−	36.4145i	−0.107316	−	1.22062i
$891$	4.40935	+	2.54574i	0.147719	+	0.0852855i
$892$	2.28034			0.0763516
$893$	8.18338	+	4.72468i	0.273846	+	0.158105i
$894$	18.7951	+	32.5541i	0.628604	+	1.08877i
$895$	−18.6295	+	39.9958i	−0.622717	+	1.33691i
$896$	1.61054			0.0538042
$897$	−12.7965	−	15.2034i	−0.427262	−	0.507625i
$898$			34.6688i			1.15691i
$899$	8.33688	−	4.81330i	0.278051	−	0.160533i
$900$	−10.0683	+	1.78418i	−0.335609	+	0.0594726i
$901$	−10.8338	+	18.7646i	−0.360925	+	0.625140i
$902$	16.8598			0.561369
$903$	10.2422	−	17.7400i	0.340840	−	0.590352i
$904$	0.201740	+	0.116474i	0.00670976	+	0.00387388i
$905$	−6.64762	−	9.48516i	−0.220974	−	0.315297i
$906$	−1.71299	+	2.96699i	−0.0569104	+	0.0985718i
$907$	−39.4345	+	22.7675i	−1.30940	+	0.755984i	−0.981996	−	0.188900i	$-0.939508\pi$
$907$	−39.4345	+	22.7675i	−1.30940	+	0.755984i	−0.327406	+	0.944884i	$0.606174\pi$
$908$	−15.6524	−	27.1108i	−0.519445	−	0.899704i
$909$	8.27253			0.274383
$910$	−34.8073	+	9.39918i	−1.15385	+	0.311580i
$911$	11.6856			0.387163			0.193581	−	0.981084i	$-0.437990\pi$
$911$	11.6856			0.387163			0.193581	+	0.981084i	$0.437990\pi$
$912$	13.6954	+	23.7212i	0.453501	+	0.785487i
$913$	9.94253	−	5.74032i	0.329050	−	0.189977i
$914$	32.0285	−	55.4749i	1.05941	−	1.83495i
$915$	19.5114	−	13.6744i	0.645026	−	0.452063i
$916$	16.9568	+	9.79004i	0.560270	+	0.323472i
$917$	−4.17487	+	7.23108i	−0.137866	+	0.238791i
$918$	−4.65300			−0.153572
$919$	12.0274	−	20.8320i	0.396747	−	0.687186i	−0.596576	−	0.802557i	$-0.703472\pi$
$919$	12.0274	−	20.8320i	0.396747	−	0.687186i	0.993322	+	0.115371i	$0.0368058\pi$
$920$	−1.01174	−	0.471256i	−0.0333560	−	0.0155368i
$921$	1.89900	−	1.09639i	0.0625742	−	0.0361272i
$922$			71.8658i			2.36677i
$923$	−4.90644	+	4.12969i	−0.161497	+	0.135931i
$924$	23.1516			0.761630
$925$	5.70901	−	1.01168i	0.187711	−	0.0332639i
$926$	27.5672	+	47.7478i	0.905914	+	1.56909i
$927$	−10.8033	−	6.23732i	−0.354828	−	0.204860i
$928$	8.09789			0.265826
$929$	37.6020	+	21.7095i	1.23368	+	0.712266i	0.967795	−	0.251738i	$-0.0810022\pi$
$929$	37.6020	+	21.7095i	1.23368	+	0.712266i	0.265886	+	0.964004i	$0.414336\pi$
$930$	−42.8228	+	3.76494i	−1.40422	+	0.123457i
$931$		−	14.4111i		−	0.472304i
$932$	−40.6797	−	23.4864i	−1.33251	−	0.769324i
$933$	−6.02346	+	3.47765i	−0.197199	+	0.113853i
$934$	−23.8531	+	13.7716i	−0.780497	+	0.450620i
$935$	−15.1167	−	21.5693i	−0.494369	−	0.705390i
$936$	0.210270	+	0.249819i	0.00687289	+	0.00816559i
$937$			16.9942i			0.555177i	0.960700	+	0.277588i	$0.0895352\pi$
$937$			16.9942i			0.555177i	−0.960700	+	0.277588i	$0.910465\pi$
$938$	−7.44951	−	12.9029i	−0.243235	−	0.421296i
$939$	3.00933	+	5.21231i	0.0982057	+	0.170097i
$940$	−6.14121	+	0.539929i	−0.200304	+	0.0176105i
$941$			33.1512i			1.08070i	0.841440	+	0.540350i	$0.181708\pi$
$941$			33.1512i			1.08070i	−0.841440	+	0.540350i	$0.818292\pi$
$942$	−9.16019	+	15.8659i	−0.298455	+	0.516940i
$943$	4.53716	−	7.85860i	0.147750	−	0.255911i
$944$			4.03659i			0.131380i
$945$	−0.435444	−	4.95279i	−0.0141650	−	0.161114i
$946$	−47.1696	−	81.7001i	−1.53362	−	2.65630i
$947$	8.19555	+	14.1951i	0.266319	+	0.461279i	0.967908	−	0.251303i	$-0.0808590\pi$
$947$	8.19555	+	14.1951i	0.266319	+	0.461279i	−0.701589	+	0.712582i	$0.747526\pi$
$948$			14.4298i			0.468659i
$949$	−5.51875	+	15.2345i	−0.179146	+	0.494533i
$950$	−66.2540	−	24.0504i	−2.14956	−	0.780299i
$951$	10.2441	−	5.91442i	0.332187	−	0.191788i
$952$	−0.403453	+	0.232934i	−0.0130760	+	0.00754942i
$953$	−29.3515	−	16.9461i	−0.950788	−	0.548938i	−0.0574626	−	0.998348i	$-0.518301\pi$
$953$	−29.3515	−	16.9461i	−0.950788	−	0.548938i	−0.893326	+	0.449410i	$0.851634\pi$
$954$			18.8364i			0.609851i
$955$	−2.12790	+	0.187083i	−0.0688573	+	0.00605387i
$956$	−20.4126	−	11.7852i	−0.660191	−	0.381162i
$957$	5.12761			0.165752
$958$	−22.4929	−	12.9863i	−0.726713	−	0.419568i
$959$	−2.30747	−	3.99666i	−0.0745121	−	0.129059i
$960$	−16.9375	−	7.88929i	−0.546656	−	0.254626i
$961$	−60.3699			−1.94742
$962$	−5.41488	−	6.43335i	−0.174583	−	0.207420i
$963$			7.08954i			0.228457i
$964$	27.0367	−	15.6096i	0.870794	−	0.502753i
$965$	9.30569	−	19.9784i	0.299561	−	0.643127i
$966$	12.3235	−	21.3450i	0.396503	−	0.686763i
$967$	−39.0470			−1.25567			−0.627833	−	0.778348i	$-0.716058\pi$
$967$	−39.0470			−1.25567			−0.627833	+	0.778348i	$0.716058\pi$
$968$	0.675747	−	1.17043i	0.0217193	−	0.0376190i
$969$	−14.0431	−	8.10779i	−0.451130	−	0.260460i
$970$	15.5787	+	22.2285i	0.500203	+	0.713715i
$971$	−13.5561	+	23.4799i	−0.435037	+	0.753506i	−0.997299	−	0.0734533i	$-0.976598\pi$
$971$	−13.5561	+	23.4799i	−0.435037	+	0.753506i	0.562262	+	0.826959i	$0.309931\pi$
$972$	−1.77105	+	1.02251i	−0.0568064	+	0.0327972i
$973$	−23.9953	−	41.5610i	−0.769253	−	1.33238i
$974$	72.9142			2.33632
$975$	17.7612	+	3.08837i	0.568815	+	0.0989071i
$976$	41.6403			1.33287
$977$	−8.93848	−	15.4819i	−0.285967	−	0.495310i	0.686876	−	0.726775i	$-0.258982\pi$
$977$	−8.93848	−	15.4819i	−0.285967	−	0.495310i	−0.972843	+	0.231465i	$0.925648\pi$
$978$	14.2177	−	8.20858i	0.454631	−	0.262482i
$979$	20.6926	−	35.8406i	0.661338	−	1.14547i
$980$	5.39605	+	7.69935i	0.172370	+	0.245947i
$981$	7.25101	+	4.18638i	0.231507	+	0.133661i
$982$	−3.22834	+	5.59166i	−0.103021	+	0.178437i
$983$	18.6955			0.596293			0.298146	−	0.954520i	$-0.403632\pi$
$983$	18.6955			0.596293			0.298146	+	0.954520i	$0.403632\pi$
$984$	−0.0745539	+	0.129131i	−0.00237669	+	0.00411655i
$985$	3.02291	−	6.48988i	0.0963178	−	0.206785i
$986$	−4.05821	+	2.34301i	−0.129240	+	0.0746166i
$987$		−	2.99763i		−	0.0954156i
$988$	9.05155	+	50.8823i	0.287968	+	1.61878i
$989$	−50.7756			−1.61457
$990$	−20.7564	−	9.66807i	−0.659681	−	0.307272i
$991$	−13.5235	−	23.4234i	−0.429588	−	0.744068i	0.567248	−	0.823547i	$-0.308008\pi$
$991$	−13.5235	−	23.4234i	−0.429588	−	0.744068i	−0.996837	+	0.0794782i	$0.974675\pi$
$992$	−66.5630	−	38.4302i	−2.11338	−	1.22016i
$993$	−34.8403			−1.10562
$994$	−6.88847	−	3.97706i	−0.218489	−	0.126145i
$995$	42.8867	−	3.77056i	1.35960	−	0.119535i
$996$			4.61129i			0.146114i
$997$	−24.6028	−	14.2044i	−0.779179	−	0.449859i	0.0569605	−	0.998376i	$-0.481859\pi$
$997$	−24.6028	−	14.2044i	−0.779179	−	0.449859i	−0.836139	+	0.548517i	$0.815192\pi$
$998$	23.8392	−	13.7636i	0.754617	−	0.435678i
$999$	1.00423	−	0.579795i	0.0317726	−	0.0183439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.v.a.49.3	yes	32
3.2	odd	2		585.2.bf.c.244.14		32
5.2	odd	4		975.2.bc.n.751.7		16
5.3	odd	4		975.2.bc.m.751.2		16
5.4	even	2	inner	195.2.v.a.49.14	yes	32
13.4	even	6	inner	195.2.v.a.4.14	yes	32
15.14	odd	2		585.2.bf.c.244.3		32
39.17	odd	6		585.2.bf.c.199.3		32
65.4	even	6	inner	195.2.v.a.4.3	✓	32
65.17	odd	12		975.2.bc.n.901.7		16
65.43	odd	12		975.2.bc.m.901.2		16
195.134	odd	6		585.2.bf.c.199.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.3	✓	32	65.4	even	6	inner
195.2.v.a.4.14	yes	32	13.4	even	6	inner
195.2.v.a.49.3	yes	32	1.1	even	1	trivial
195.2.v.a.49.14	yes	32	5.4	even	2	inner
585.2.bf.c.199.3		32	39.17	odd	6
585.2.bf.c.199.14		32	195.134	odd	6
585.2.bf.c.244.3		32	15.14	odd	2
585.2.bf.c.244.14		32	3.2	odd	2
975.2.bc.m.751.2		16	5.3	odd	4
975.2.bc.m.901.2		16	65.43	odd	12
975.2.bc.n.751.7		16	5.2	odd	4
975.2.bc.n.901.7		16	65.17	odd	12

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.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00561 - 1.74177i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.02251 + 1.77105i) q^{4} +(-1.28334 - 1.83113i) q^{5} +(1.74177 + 1.00561i) q^{6} +(1.11175 - 1.92561i) q^{7} +0.0905636 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00561 - 1.74177i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.02251 + 1.77105i) q^{4} +(-1.28334 - 1.83113i) q^{5} +(1.74177 + 1.00561i) q^{6} +(1.11175 - 1.92561i) q^{7} +0.0905636 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.89887 + 4.07669i) q^{10} +(-4.40935 + 2.54574i) q^{11} -2.04503i q^{12} +(-1.22803 + 3.38998i) q^{13} -4.47196 q^{14} +(2.02697 + 0.944138i) q^{15} +(1.95396 + 3.38435i) q^{16} +(-2.00356 - 1.15676i) q^{17} -2.01123 q^{18} +(-6.07004 - 3.50454i) q^{19} +(4.55525 - 0.400493i) q^{20} +2.22350i q^{21} +(8.86820 + 5.12006i) q^{22} +(4.77307 - 2.75574i) q^{23} +(-0.0784304 + 0.0452818i) q^{24} +(-1.70609 + 4.69992i) q^{25} +(7.13949 - 1.27006i) q^{26} +1.00000i q^{27} +(2.27356 + 3.93792i) q^{28} +(0.503549 + 0.872172i) q^{29} +(-0.393873 - 4.47996i) q^{30} -9.55876i q^{31} +(4.02041 - 6.96356i) q^{32} +(2.54574 - 4.40935i) q^{33} +4.65300i q^{34} +(-4.95279 + 0.435444i) q^{35} +(1.02251 + 1.77105i) q^{36} +(-0.579795 - 1.00423i) q^{37} +14.0968i q^{38} +(-0.631485 - 3.54982i) q^{39} +(-0.116224 - 0.165834i) q^{40} +(1.42586 - 0.823222i) q^{41} +(3.87283 - 2.23598i) q^{42} +(-7.97844 - 4.60635i) q^{43} -10.4122i q^{44} +(-2.22748 + 0.195838i) q^{45} +(-9.59973 - 5.54241i) q^{46} -1.34816 q^{47} +(-3.38435 - 1.95396i) q^{48} +(1.02803 + 1.78060i) q^{49} +(9.90186 - 1.75469i) q^{50} +2.31351 q^{51} +(-4.74813 - 5.64120i) q^{52} -9.36564i q^{53} +(1.74177 - 1.00561i) q^{54} +(10.3203 + 4.80706i) q^{55} +(0.100684 - 0.174390i) q^{56} +7.00908 q^{57} +(1.01275 - 1.75413i) q^{58} +(0.894540 + 0.516463i) q^{59} +(-3.74472 + 2.62446i) q^{60} +(5.32768 - 9.22782i) q^{61} +(-16.6492 + 9.61241i) q^{62} +(-1.11175 - 1.92561i) q^{63} -8.35609 q^{64} +(7.78347 - 2.10180i) q^{65} -10.2401 q^{66} +(1.66583 + 2.88530i) q^{67} +(4.09734 - 2.36560i) q^{68} +(-2.75574 + 4.77307i) q^{69} +(5.73903 + 8.18874i) q^{70} +(1.54037 + 0.889333i) q^{71} +(0.0452818 - 0.0784304i) q^{72} +4.49399 q^{73} +(-1.16610 + 2.01974i) q^{74} +(-0.872447 - 4.92330i) q^{75} +(12.4134 - 7.16688i) q^{76} +11.3209i q^{77} +(-5.54795 + 4.66965i) q^{78} -7.05606 q^{79} +(3.68961 - 7.92122i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.86773 - 1.65568i) q^{82} -2.25488 q^{83} +(-3.93792 - 2.27356i) q^{84} +(0.453072 + 5.15329i) q^{85} +18.5288i q^{86} +(-0.872172 - 0.503549i) q^{87} +(-0.399327 + 0.230551i) q^{88} +(-7.03934 + 4.06416i) q^{89} +(2.58108 + 3.68282i) q^{90} +(5.16250 + 6.13350i) q^{91} +11.2711i q^{92} +(4.77938 + 8.27813i) q^{93} +(1.35573 + 2.34819i) q^{94} +(1.37264 + 15.6126i) q^{95} +8.04083i q^{96} +(3.01787 - 5.22710i) q^{97} +(2.06760 - 3.58118i) q^{98} +5.09148i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q - 20 * q^4 + 16 * q^9	\( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Introduction

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