LMFDB - Embedded newform 273.2.cc.a.50.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.20
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06694 + 0.285886i) q^{2} +(-1.02855 + 1.39358i) q^{3} +(-0.675418 - 0.389953i) q^{4} +(-1.84315 + 1.84315i) q^{5} +(-1.49581 + 1.19282i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.17126 - 2.17126i) q^{8} +(-0.884154 - 2.86675i) q^{9} +O(q^{10})$	\(q+(1.06694 + 0.285886i) q^{2} +(-1.02855 + 1.39358i) q^{3} +(-0.675418 - 0.389953i) q^{4} +(-1.84315 + 1.84315i) q^{5} +(-1.49581 + 1.19282i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.17126 - 2.17126i) q^{8} +(-0.884154 - 2.86675i) q^{9} +(-2.49346 + 1.43960i) q^{10} +(-0.401664 + 1.49903i) q^{11} +(1.23814 - 0.540164i) q^{12} +(-3.57492 + 0.468987i) q^{13} +1.10458i q^{14} +(-0.672805 - 4.46435i) q^{15} +(-0.915969 - 1.58650i) q^{16} +(-2.15597 + 3.73425i) q^{17} +(-0.123776 - 3.31142i) q^{18} +(-0.00571206 + 0.00153054i) q^{19} +(1.96363 - 0.526154i) q^{20} +(-1.61231 - 0.632820i) q^{21} +(-0.857104 + 1.48455i) q^{22} +(1.39691 + 2.41952i) q^{23} +(5.25909 - 0.792576i) q^{24} -1.79437i q^{25} +(-3.94831 - 0.521638i) q^{26} +(4.90446 + 1.71647i) q^{27} +(0.201854 - 0.753331i) q^{28} +(1.24986 - 0.721605i) q^{29} +(0.558454 - 4.95555i) q^{30} +(5.54090 + 5.54090i) q^{31} +(1.06575 + 3.97742i) q^{32} +(-1.67589 - 2.10159i) q^{33} +(-3.36786 + 3.36786i) q^{34} +(-2.25738 - 1.30330i) q^{35} +(-0.520724 + 2.28103i) q^{36} +(4.39332 + 1.17719i) q^{37} -0.00653200 q^{38} +(3.02342 - 5.46433i) q^{39} +8.00390 q^{40} +(9.42057 + 2.52423i) q^{41} +(-1.53932 - 1.13612i) q^{42} +(-8.60368 - 4.96734i) q^{43} +(0.855842 - 0.855842i) q^{44} +(6.91347 + 3.65422i) q^{45} +(0.798713 + 2.98084i) q^{46} +(-9.54450 - 9.54450i) q^{47} +(3.15305 + 0.355325i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.512986 - 1.91449i) q^{50} +(-2.98646 - 6.84540i) q^{51} +(2.59745 + 1.07729i) q^{52} +1.15682i q^{53} +(4.74206 + 3.23349i) q^{54} +(-2.02261 - 3.50326i) q^{55} +(1.53531 - 2.65924i) q^{56} +(0.00374222 - 0.00953449i) q^{57} +(1.53982 - 0.412593i) q^{58} +(1.54072 - 0.412835i) q^{59} +(-1.28646 + 3.27767i) q^{60} +(-5.02356 + 8.70107i) q^{61} +(4.32775 + 7.49588i) q^{62} +(2.54023 - 1.59600i) q^{63} +8.21223i q^{64} +(5.72469 - 7.45351i) q^{65} +(-1.18727 - 2.72138i) q^{66} +(-3.68250 + 13.7433i) q^{67} +(2.91236 - 1.68145i) q^{68} +(-4.80859 - 0.541893i) q^{69} +(-2.03590 - 2.03590i) q^{70} +(-3.17093 - 11.8341i) q^{71} +(-4.30474 + 8.14419i) q^{72} +(-4.96743 + 4.96743i) q^{73} +(4.35087 + 2.51198i) q^{74} +(2.50061 + 1.84561i) q^{75} +(0.00445487 + 0.00119368i) q^{76} -1.55191 q^{77} +(4.78799 - 4.96577i) q^{78} +4.21684 q^{79} +(4.61242 + 1.23589i) q^{80} +(-7.43654 + 5.06930i) q^{81} +(9.32955 + 5.38642i) q^{82} +(5.19558 - 5.19558i) q^{83} +(0.842212 + 1.05614i) q^{84} +(-2.90900 - 10.8565i) q^{85} +(-7.75953 - 7.75953i) q^{86} +(-0.279927 + 2.48399i) q^{87} +(4.12690 - 2.38267i) q^{88} +(0.181404 - 0.677010i) q^{89} +(6.33158 + 5.87530i) q^{90} +(-1.37826 - 3.33172i) q^{91} -2.17891i q^{92} +(-13.4208 + 2.02260i) q^{93} +(-7.45478 - 12.9121i) q^{94} +(0.00770715 - 0.0133492i) q^{95} +(-6.63905 - 2.60578i) q^{96} +(-2.44137 + 0.654164i) q^{97} +(-1.06694 + 0.285886i) q^{98} +(4.65248 - 0.173903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.06694	+	0.285886i	0.754441	+	0.202152i	0.615487	−	0.788147i	$-0.288959\pi$
$2$	1.06694	+	0.285886i	0.754441	+	0.202152i	0.138954	+	0.990299i	$0.455626\pi$
$3$	−1.02855	+	1.39358i	−0.593836	+	0.804586i
$3$	−1.02855	+	1.39358i	−0.593836	+	0.804586i
$4$	−0.675418	−	0.389953i	−0.337709	−	0.194976i
$5$	−1.84315	+	1.84315i	−0.824280	+	0.824280i	−0.986719	−	0.162439i	$-0.948064\pi$
$5$	−1.84315	+	1.84315i	−0.824280	+	0.824280i	0.162439	+	0.986719i	$0.448064\pi$
$6$	−1.49581	+	1.19282i	−0.610663	+	0.486968i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	−2.17126	−	2.17126i	−0.767656	−	0.767656i
$9$	−0.884154	−	2.86675i	−0.294718	−	0.955584i
$10$	−2.49346	+	1.43960i	−0.788501	+	0.455241i
$11$	−0.401664	+	1.49903i	−0.121106	+	0.451975i	−0.999671	−	0.0256484i	$-0.991835\pi$
$11$	−0.401664	+	1.49903i	−0.121106	+	0.451975i	0.878565	+	0.477623i	$0.158502\pi$
$12$	1.23814	−	0.540164i	0.357419	−	0.155932i
$13$	−3.57492	+	0.468987i	−0.991504	+	0.130074i
$13$	−3.57492	+	0.468987i	−0.991504	+	0.130074i
$14$			1.10458i			0.295211i
$15$	−0.672805	−	4.46435i	−0.173717	−	1.15269i
$16$	−0.915969	−	1.58650i	−0.228992	−	0.396626i
$17$	−2.15597	+	3.73425i	−0.522899	+	0.905688i	0.476746	+	0.879041i	$0.341816\pi$
$17$	−2.15597	+	3.73425i	−0.522899	+	0.905688i	−0.999645	+	0.0266468i	$0.991517\pi$
$18$	−0.123776	−	3.31142i	−0.0291743	−	0.780510i
$19$	−0.00571206	+	0.00153054i	−0.00131044	+	0.000351131i	−0.259474	−	0.965750i	$-0.583549\pi$
$19$	−0.00571206	+	0.00153054i	−0.00131044	+	0.000351131i	0.258164	+	0.966101i	$0.416883\pi$
$20$	1.96363	−	0.526154i	0.439082	−	0.117652i
$21$	−1.61231	−	0.632820i	−0.351835	−	0.138093i
$22$	−0.857104	+	1.48455i	−0.182735	+	0.316507i
$23$	1.39691	+	2.41952i	0.291276	+	0.504504i	0.974112	−	0.226068i	$-0.0725870\pi$
$23$	1.39691	+	2.41952i	0.291276	+	0.504504i	−0.682836	+	0.730572i	$0.739254\pi$
$24$	5.25909	−	0.792576i	1.07351	−	0.161784i
$25$		−	1.79437i		−	0.358875i
$26$	−3.94831	−	0.521638i	−0.774327	−	0.102302i
$27$	4.90446	+	1.71647i	0.943864	+	0.330334i
$28$	0.201854	−	0.753331i	0.0381469	−	0.142366i
$29$	1.24986	−	0.721605i	0.232092	−	0.133999i	−0.379445	−	0.925214i	$-0.623885\pi$
$29$	1.24986	−	0.721605i	0.232092	−	0.133999i	0.611537	+	0.791216i	$0.290552\pi$
$30$	0.558454	−	4.95555i	0.101959	−	0.904755i
$31$	5.54090	+	5.54090i	0.995174	+	0.995174i	0.999988	−	0.00481424i	$-0.00153243\pi$
$31$	5.54090	+	5.54090i	0.995174	+	0.995174i	−0.00481424	+	0.999988i	$0.501532\pi$
$32$	1.06575	+	3.97742i	0.188399	+	0.703116i
$33$	−1.67589	−	2.10159i	−0.291736	−	0.365839i
$34$	−3.36786	+	3.36786i	−0.577584	+	0.577584i
$35$	−2.25738	−	1.30330i	−0.381567	−	0.220298i
$36$	−0.520724	+	2.28103i	−0.0867874	+	0.380172i
$37$	4.39332	+	1.17719i	0.722257	+	0.193528i	0.601179	−	0.799115i	$-0.294698\pi$
$37$	4.39332	+	1.17719i	0.722257	+	0.193528i	0.121079	+	0.992643i	$0.461365\pi$
$38$	−0.00653200			−0.00105963
$39$	3.02342	−	5.46433i	0.484135	−	0.874993i
$40$	8.00390			1.26553
$41$	9.42057	+	2.52423i	1.47125	+	0.394219i	0.903358	−	0.428887i	$-0.141094\pi$
$41$	9.42057	+	2.52423i	1.47125	+	0.394219i	0.567888	+	0.823106i	$0.307761\pi$
$42$	−1.53932	−	1.13612i	−0.237523	−	0.175307i
$43$	−8.60368	−	4.96734i	−1.31205	−	0.757512i	−0.329614	−	0.944116i	$-0.606919\pi$
$43$	−8.60368	−	4.96734i	−1.31205	−	0.757512i	−0.982435	+	0.186604i	$0.940252\pi$
$44$	0.855842	−	0.855842i	0.129023	−	0.129023i
$45$	6.91347	+	3.65422i	1.03060	+	0.544739i
$46$	0.798713	+	2.98084i	0.117764	+	0.439501i
$47$	−9.54450	−	9.54450i	−1.39221	−	1.39221i	−0.820357	−	0.571852i	$-0.806225\pi$
$47$	−9.54450	−	9.54450i	−1.39221	−	1.39221i	−0.571852	−	0.820357i	$-0.693775\pi$
$48$	3.15305	+	0.355325i	0.455104	+	0.0512868i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.512986	−	1.91449i	0.0725472	−	0.270750i
$51$	−2.98646	−	6.84540i	−0.418188	−	0.958548i
$52$	2.59745	+	1.07729i	0.360201	+	0.149393i
$53$			1.15682i			0.158901i	0.996839	+	0.0794505i	$0.0253166\pi$
$53$			1.15682i			0.158901i	−0.996839	+	0.0794505i	$0.974683\pi$
$54$	4.74206	+	3.23349i	0.645313	+	0.440022i
$55$	−2.02261	−	3.50326i	−0.272728	−	0.472379i
$56$	1.53531	−	2.65924i	0.205165	−	0.355356i
$57$	0.00374222	−	0.00953449i	0.000495670	−	0.00126287i
$58$	1.53982	−	0.412593i	0.202188	−	0.0541762i
$59$	1.54072	−	0.412835i	0.200585	−	0.0537465i	−0.157128	−	0.987578i	$-0.550223\pi$
$59$	1.54072	−	0.412835i	0.200585	−	0.0537465i	0.357712	+	0.933832i	$0.383557\pi$
$60$	−1.28646	+	3.27767i	−0.166082	+	0.423145i
$61$	−5.02356	+	8.70107i	−0.643202	+	1.11406i	0.341512	+	0.939877i	$0.389061\pi$
$61$	−5.02356	+	8.70107i	−0.643202	+	1.11406i	−0.984714	+	0.174180i	$0.944272\pi$
$62$	4.32775	+	7.49588i	0.549624	+	0.951977i
$63$	2.54023	−	1.59600i	0.320039	−	0.201077i
$64$			8.21223i			1.02653i
$65$	5.72469	−	7.45351i	0.710060	−	0.924494i
$66$	−1.18727	−	2.72138i	−0.146142	−	0.334979i
$67$	−3.68250	+	13.7433i	−0.449889	+	1.67901i	0.252804	+	0.967517i	$0.418647\pi$
$67$	−3.68250	+	13.7433i	−0.449889	+	1.67901i	−0.702694	+	0.711492i	$0.748020\pi$
$68$	2.91236	−	1.68145i	0.353175	−	0.203906i
$69$	−4.80859	−	0.541893i	−0.578887	−	0.0652362i
$70$	−2.03590	−	2.03590i	−0.243337	−	0.243337i
$71$	−3.17093	−	11.8341i	−0.376321	−	1.40445i	−0.851406	−	0.524508i	$-0.824249\pi$
$71$	−3.17093	−	11.8341i	−0.376321	−	1.40445i	0.475085	−	0.879940i	$-0.342417\pi$
$72$	−4.30474	+	8.14419i	−0.507318	+	0.959802i
$73$	−4.96743	+	4.96743i	−0.581394	+	0.581394i	−0.935286	−	0.353892i	$-0.884858\pi$
$73$	−4.96743	+	4.96743i	−0.581394	+	0.581394i	0.353892	+	0.935286i	$0.384858\pi$
$74$	4.35087	+	2.51198i	0.505779	+	0.292011i
$75$	2.50061	+	1.84561i	0.288746	+	0.213113i
$76$	0.00445487	+	0.00119368i	0.000511008	+	0.000136924i
$77$	−1.55191			−0.176857
$78$	4.78799	−	4.96577i	0.542133	−	0.562262i
$79$	4.21684			0.474431			0.237216	−	0.971457i	$-0.423765\pi$
$79$	4.21684			0.474431			0.237216	+	0.971457i	$0.423765\pi$
$80$	4.61242	+	1.23589i	0.515685	+	0.138177i
$81$	−7.43654	+	5.06930i	−0.826282	+	0.563256i
$82$	9.32955	+	5.38642i	1.03028	+	0.594831i
$83$	5.19558	−	5.19558i	0.570289	−	0.570289i	−0.361920	−	0.932209i	$-0.617879\pi$
$83$	5.19558	−	5.19558i	0.570289	−	0.570289i	0.932209	+	0.361920i	$0.117879\pi$
$84$	0.842212	+	1.05614i	0.0918928	+	0.115235i
$85$	−2.90900	−	10.8565i	−0.315525	−	1.17756i
$86$	−7.75953	−	7.75953i	−0.836732	−	0.836732i
$87$	−0.279927	+	2.48399i	−0.0300113	+	0.266312i
$88$	4.12690	−	2.38267i	0.439929	−	0.253993i
$89$	0.181404	−	0.677010i	0.0192288	−	0.0717629i	−0.955645	−	0.294522i	$-0.904840\pi$
$89$	0.181404	−	0.677010i	0.0192288	−	0.0717629i	0.974874	+	0.222759i	$0.0715063\pi$
$90$	6.33158	+	5.87530i	0.667407	+	0.619311i
$91$	−1.37826	−	3.33172i	−0.144481	−	0.349260i
$92$		−	2.17891i		−	0.227167i
$93$	−13.4208	+	2.02260i	−1.39167	+	0.209733i
$94$	−7.45478	−	12.9121i	−0.768902	−	1.33178i
$95$	0.00770715	−	0.0133492i	0.000790737	−	0.00136960i
$96$	−6.63905	−	2.60578i	−0.677595	−	0.265952i
$97$	−2.44137	+	0.654164i	−0.247884	+	0.0664203i	−0.380622	−	0.924731i	$-0.624290\pi$
$97$	−2.44137	+	0.654164i	−0.247884	+	0.0664203i	0.132738	+	0.991151i	$0.457623\pi$
$98$	−1.06694	+	0.285886i	−0.107777	+	0.0288789i
$99$	4.65248	−	0.173903i	0.467592	−	0.0174779i
$100$	−0.699721	+	1.21195i	−0.0699721	+	0.121195i
$101$	1.82995	+	3.16957i	0.182087	+	0.315384i	0.942591	−	0.333949i	$-0.108381\pi$
$101$	1.82995	+	3.16957i	0.182087	+	0.315384i	−0.760504	+	0.649333i	$0.775048\pi$
$102$	−1.22937	−	8.15743i	−0.121726	−	0.807706i
$103$		−	17.9654i		−	1.77018i	−0.465415	−	0.885092i	$-0.654095\pi$
$103$		−	17.9654i		−	1.77018i	0.465415	−	0.885092i	$-0.345905\pi$
$104$	8.78037	+	6.74379i	0.860986	+	0.661283i
$105$	4.13810	−	1.80534i	0.403837	−	0.176183i
$106$	−0.330718	+	1.23426i	−0.0321221	+	0.119881i
$107$	−7.21858	+	4.16765i	−0.697846	+	0.402902i	−0.806545	−	0.591173i	$-0.798665\pi$
$107$	−7.21858	+	4.16765i	−0.697846	+	0.402902i	0.108698	+	0.994075i	$0.465332\pi$
$108$	−2.64322	−	3.07184i	−0.254344	−	0.295588i
$109$	3.33933	+	3.33933i	0.319850	+	0.319850i	0.848709	−	0.528860i	$-0.177380\pi$
$109$	3.33933	+	3.33933i	0.319850	+	0.319850i	−0.528860	+	0.848709i	$0.677380\pi$
$110$	−1.15647	−	4.31601i	−0.110265	−	0.411515i
$111$	−6.15927	+	4.91166i	−0.584612	+	0.466194i
$112$	1.29538	−	1.29538i	0.122401	−	0.122401i
$113$	6.62305	+	3.82382i	0.623044	+	0.359715i	0.778053	−	0.628198i	$-0.216207\pi$
$113$	6.62305	+	3.82382i	0.623044	+	0.359715i	−0.155009	+	0.987913i	$0.549541\pi$
$114$	0.00671851	−	0.00910289i	0.000629246	−	0.000852564i
$115$	−7.03423	−	1.88482i	−0.655945	−	0.175760i
$116$	−1.12557			−0.104506
$117$	4.50525	+	9.83375i	0.416511	+	0.909131i
$118$	1.76188			0.162194
$119$	−4.16501	−	1.11601i	−0.381806	−	0.102305i
$120$	−8.23244	+	11.1541i	−0.751515	+	1.01823i
$121$	7.44052	+	4.29579i	0.676411	+	0.390526i
$122$	−7.84736	+	7.84736i	−0.710467	+	0.710467i
$123$	−13.2073	+	10.5320i	−1.19086	+	0.949643i
$124$	−1.58173	−	5.90311i	−0.142044	−	0.530115i
$125$	−5.90844	−	5.90844i	−0.528467	−	0.528467i
$126$	3.16655	−	0.976618i	0.282099	−	0.0870041i
$127$	1.92088	−	1.10902i	0.170451	−	0.0984099i	−0.412348	−	0.911027i	$-0.635291\pi$
$127$	1.92088	−	1.10902i	0.170451	−	0.0984099i	0.582798	+	0.812617i	$0.301958\pi$
$128$	−0.216269	+	0.807127i	−0.0191157	+	0.0713406i
$129$	15.7718	−	6.88078i	1.38863	−	0.605819i
$130$	8.23876	−	6.31585i	0.722587	−	0.553937i
$131$			4.01679i			0.350949i	0.984484	+	0.175474i	$0.0561459\pi$
$131$			4.01679i			0.350949i	−0.984484	+	0.175474i	$0.943854\pi$
$132$	0.312409	+	2.07297i	0.0271917	+	0.180429i
$133$	−0.00295678	−	0.00512130i	−0.000256385	−	0.000444073i
$134$	−7.85803	+	13.6105i	−0.678830	+	1.17577i
$135$	−12.2033	+	5.87594i	−1.05030	+	0.505721i
$136$	12.7892	−	3.42685i	1.09666	−	0.293850i
$137$	3.82886	−	1.02594i	0.327121	−	0.0876519i	−0.0915208	−	0.995803i	$-0.529173\pi$
$137$	3.82886	−	1.02594i	0.327121	−	0.0876519i	0.418642	+	0.908151i	$0.362506\pi$
$138$	−4.97557	−	1.95288i	−0.423549	−	0.166240i
$139$	−5.76149	+	9.97920i	−0.488683	+	0.846424i	−0.999915	−	0.0130185i	$-0.995856\pi$
$139$	−5.76149	+	9.97920i	−0.488683	+	0.846424i	0.511232	+	0.859443i	$0.329189\pi$
$140$	1.01645	+	1.76055i	0.0859058	+	0.148793i
$141$	23.1181	−	3.48403i	1.94690	−	0.293409i
$142$		−	13.5328i		−	1.13565i
$143$	0.732891	−	5.54729i	0.0612874	−	0.463888i
$144$	−3.73826	+	4.02857i	−0.311521	+	0.335714i
$145$	−0.973644	+	3.63369i	−0.0808567	+	0.301761i
$146$	−6.72007	+	3.87984i	−0.556157	+	0.321098i
$147$	0.193962	−	1.72116i	0.0159977	−	0.141959i
$148$	−2.50828	−	2.50828i	−0.206179	−	0.206179i
$149$	2.80262	+	10.4595i	0.229599	+	0.856876i	0.980509	+	0.196472i	$0.0629484\pi$
$149$	2.80262	+	10.4595i	0.229599	+	0.856876i	−0.750910	+	0.660404i	$0.770385\pi$
$150$	2.14037	+	2.68405i	0.174761	+	0.219152i
$151$	16.3158	−	16.3158i	1.32776	−	1.32776i	0.420440	−	0.907320i	$-0.361876\pi$
$151$	16.3158	−	16.3158i	1.32776	−	1.32776i	0.907320	−	0.420440i	$-0.138124\pi$
$152$	0.0157256	+	0.00907917i	0.00127551	+	0.000736418i
$153$	12.6114	+	2.87898i	1.01957	+	0.232752i
$154$	−1.65580	−	0.443670i	−0.133428	−	0.0357519i
$155$	−20.4254			−1.64060
$156$	−4.17290	+	2.51171i	−0.334100	+	0.201098i
$157$	−17.7555			−1.41704			−0.708522	−	0.705689i	$-0.750638\pi$
$157$	−17.7555			−1.41704			−0.708522	+	0.705689i	$0.750638\pi$
$158$	4.49912	+	1.20554i	0.357931	+	0.0959072i
$159$	−1.61212	−	1.18985i	−0.127850	−	0.0943611i
$160$	−9.29530	−	5.36664i	−0.734858	−	0.424270i
$161$	−1.97553	+	1.97553i	−0.155693	+	0.155693i
$162$	−9.38360	+	3.28265i	−0.737245	+	0.257909i
$163$	0.728654	+	2.71937i	0.0570726	+	0.212998i	0.988573	−	0.150742i	$-0.0481663\pi$
$163$	0.728654	+	2.71937i	0.0570726	+	0.212998i	−0.931501	+	0.363740i	$0.881500\pi$
$164$	−5.37849	−	5.37849i	−0.419989	−	0.419989i
$165$	6.96245	+	0.784616i	0.542026	+	0.0610823i
$166$	7.02872	−	4.05804i	0.545535	−	0.314965i
$167$	−2.99427	+	11.1748i	−0.231704	+	0.864730i	0.747903	+	0.663808i	$0.231061\pi$
$167$	−2.99427	+	11.1748i	−0.231704	+	0.864730i	−0.979607	+	0.200923i	$0.935606\pi$
$168$	2.12672	+	4.87476i	0.164080	+	0.376096i
$169$	12.5601	−	3.35318i	0.966162	−	0.257937i
$170$		−	12.4149i		−	0.952181i
$171$	0.00943803	+	0.0150218i	0.000721744	+	0.00114875i
$172$	3.87405	+	6.71006i	0.295394	+	0.511637i
$173$	−4.31563	+	7.47489i	−0.328111	+	0.568305i	−0.982137	−	0.188167i	$-0.939745\pi$
$173$	−4.31563	+	7.47489i	−0.328111	+	0.568305i	0.654026	+	0.756472i	$0.273079\pi$
$174$	−1.00880	+	2.57024i	−0.0764772	+	0.194850i
$175$	1.73323	−	0.464418i	0.131020	−	0.0351067i
$176$	2.74613	−	0.735824i	0.206997	−	0.0554648i
$177$	−1.00939	+	2.57175i	−0.0758707	+	0.193304i
$178$	0.387095	−	0.670469i	0.0290140	−	0.0502537i
$179$	−5.24013	−	9.07617i	−0.391665	−	0.678384i	0.601004	−	0.799246i	$-0.294768\pi$
$179$	−5.24013	−	9.07617i	−0.391665	−	0.678384i	−0.992669	+	0.120862i	$0.961434\pi$
$180$	−3.24451	−	5.16405i	−0.241831	−	0.384905i
$181$			12.0872i			0.898436i	0.893422	+	0.449218i	$0.148297\pi$
$181$			12.0872i			0.898436i	−0.893422	+	0.449218i	$0.851703\pi$
$182$	−0.518034	−	3.94878i	−0.0383992	−	0.292703i
$183$	−6.95867	−	15.9503i	−0.514399	−	1.17908i
$184$	2.22035	−	8.28645i	0.163686	−	0.610885i
$185$	−10.2673	+	5.92780i	−0.754864	+	0.435821i
$186$	−14.8975	−	1.67883i	−1.09233	−	0.123098i
$187$	−4.73178	−	4.73178i	−0.346022	−	0.346022i
$188$	2.72462	+	10.1684i	0.198714	+	0.741609i
$189$	−0.388610	+	5.18160i	−0.0282672	+	0.376906i
$190$	0.0120394	−	0.0120394i	0.000873432	−	0.000873432i
$191$	4.58803	+	2.64890i	0.331978	+	0.191668i	0.656719	−	0.754135i	$-0.271944\pi$
$191$	4.58803	+	2.64890i	0.331978	+	0.191668i	−0.324741	+	0.945803i	$0.605277\pi$
$192$	−11.4444	−	8.44672i	−0.825931	−	0.609590i
$193$	−7.83056	−	2.09819i	−0.563656	−	0.151031i	−0.0342707	−	0.999413i	$-0.510911\pi$
$193$	−7.83056	−	2.09819i	−0.563656	−	0.151031i	−0.529386	+	0.848381i	$0.677578\pi$
$194$	−2.79182			−0.200441
$195$	4.49895	+	15.6442i	0.322176	+	1.12030i
$196$	0.779905			0.0557075
$197$	7.49830	+	2.00916i	0.534232	+	0.143147i	0.515842	−	0.856684i	$-0.327479\pi$
$197$	7.49830	+	2.00916i	0.534232	+	0.143147i	0.0183900	+	0.999831i	$0.494146\pi$
$198$	5.01364	+	1.14454i	0.356304	+	0.0813387i
$199$	−6.88342	−	3.97415i	−0.487953	−	0.281720i	0.235772	−	0.971808i	$-0.424238\pi$
$199$	−6.88342	−	3.97415i	−0.487953	−	0.281720i	−0.723725	+	0.690089i	$0.757571\pi$
$200$	−3.89605	+	3.89605i	−0.275492	+	0.275492i
$201$	−15.3648	−	19.2676i	−1.08375	−	1.35903i
$202$	1.04631	+	3.90490i	0.0736184	+	0.274748i
$203$	1.02050	+	1.02050i	0.0716253	+	0.0716253i
$204$	−0.652274	+	5.78808i	−0.0456683	+	0.405247i
$205$	−22.0160	+	12.7110i	−1.53767	+	0.887771i
$206$	5.13606	−	19.1680i	0.357846	−	1.33550i
$207$	5.70107	−	6.14382i	0.396252	−	0.427025i
$208$	4.01856	+	5.24205i	0.278637	+	0.363471i
$209$		−	0.00917732i		−	0.000634809i
$210$	4.93123	−	0.743166i	0.340287	−	0.0512833i
$211$	5.13161	+	8.88820i	0.353274	+	0.611889i	0.986821	−	0.161815i	$-0.0517349\pi$
$211$	5.13161	+	8.88820i	0.353274	+	0.611889i	−0.633547	+	0.773704i	$0.718402\pi$
$212$	0.451104	−	0.781334i	0.0309819	−	0.0536623i
$213$	19.7533	+	7.75303i	1.35347	+	0.531229i
$214$	−8.89327	+	2.38295i	−0.607932	+	0.162895i
$215$	25.0134	−	6.70231i	1.70590	−	0.457094i
$216$	−6.92197	−	14.3758i	−0.470980	−	0.978146i
$217$	−3.91800	+	6.78618i	−0.265971	+	0.460676i
$218$	2.60820	+	4.51753i	0.176650	+	0.305966i
$219$	−1.81326	−	12.0318i	−0.122529	−	0.813034i
$220$			3.15488i			0.212702i
$221$	5.95610	−	14.3608i	0.400651	−	0.966009i
$222$	−7.97576	+	3.47960i	−0.535298	+	0.233536i
$223$	2.12358	−	7.92529i	0.142205	−	0.530717i	−0.857659	−	0.514219i	$-0.828082\pi$
$223$	2.12358	−	7.92529i	0.142205	−	0.530717i	0.999864	−	0.0164977i	$-0.00525160\pi$
$224$	−3.56606	+	2.05887i	−0.238267	+	0.137564i
$225$	−5.14403	+	1.58650i	−0.342935	+	0.105767i
$226$	5.97323	+	5.97323i	0.397333	+	0.397333i
$227$	3.19682	+	11.9307i	0.212180	+	0.791867i	0.987140	+	0.159857i	$0.0511033\pi$
$227$	3.19682	+	11.9307i	0.212180	+	0.791867i	−0.774960	+	0.632010i	$0.782230\pi$
$228$	−0.00624556	+	0.00498047i	−0.000413622	+	0.000329840i
$229$	−1.46663	+	1.46663i	−0.0969179	+	0.0969179i	−0.753903	−	0.656985i	$-0.771831\pi$
$229$	−1.46663	+	1.46663i	−0.0969179	+	0.0969179i	0.656985	+	0.753903i	$0.271831\pi$
$230$	−6.96627	−	4.02198i	−0.459342	−	0.265201i
$231$	1.59622	−	2.16272i	0.105024	−	0.142296i
$232$	−4.28055	−	1.14697i	−0.281032	−	0.0753023i
$233$	13.1944			0.864396			0.432198	−	0.901779i	$-0.357738\pi$
$233$	13.1944			0.864396			0.432198	+	0.901779i	$0.357738\pi$
$234$	1.99551	+	11.7800i	0.130450	+	0.770084i
$235$	35.1838			2.29514
$236$	−1.20162	−	0.321972i	−0.0782185	−	0.0209586i
$237$	−4.33724	+	5.87652i	−0.281734	+	0.381721i
$238$	−4.12477	−	2.38144i	−0.267369	−	0.154366i
$239$	8.02729	−	8.02729i	0.519242	−	0.519242i	−0.398100	−	0.917342i	$-0.630330\pi$
$239$	8.02729	−	8.02729i	0.519242	−	0.519242i	0.917342	+	0.398100i	$0.130330\pi$
$240$	−6.46645	+	5.15662i	−0.417407	+	0.332858i
$241$	−6.05224	−	22.5873i	−0.389859	−	1.45497i	−0.830363	−	0.557223i	$-0.811867\pi$
$241$	−6.05224	−	22.5873i	−0.389859	−	1.45497i	0.440503	−	0.897751i	$-0.354800\pi$
$242$	6.71049	+	6.71049i	0.431367	+	0.431367i
$243$	0.584381	−	15.5775i	0.0374881	−	0.999297i
$244$	6.78601	−	3.91790i	0.434430	−	0.250818i
$245$	0.674638	−	2.51778i	0.0431011	−	0.160855i
$246$	−17.1024	+	7.46130i	−1.09041	+	0.475715i
$247$	0.0197024	−	0.00815045i	0.00125363	−	0.000518601i
$248$		−	24.0614i		−	1.52790i
$249$	1.89655	+	12.5844i	0.120189	+	0.797505i
$250$	−4.61482	−	7.99310i	−0.291867	−	0.505528i
$251$	3.97283	−	6.88114i	0.250763	−	0.434334i	−0.712973	−	0.701191i	$-0.752652\pi$
$251$	3.97283	−	6.88114i	0.250763	−	0.434334i	0.963736	+	0.266857i	$0.0859853\pi$
$252$	−2.33808	+	0.0873941i	−0.147285	+	0.00550531i
$253$	−4.18802	+	1.12218i	−0.263298	+	0.0705506i
$254$	2.36652	−	0.634108i	0.148489	−	0.0397875i
$255$	18.1215	+	7.11259i	1.13482	+	0.445408i
$256$	7.75074	−	13.4247i	0.484421	−	0.839042i
$257$	15.0874	+	26.1322i	0.941129	+	1.63008i	0.763322	+	0.646018i	$0.223567\pi$
$257$	15.0874	+	26.1322i	0.941129	+	1.63008i	0.177807	+	0.984065i	$0.443100\pi$
$258$	18.7947	−	2.83247i	1.17010	−	0.176342i
$259$			4.54830i			0.282618i
$260$	−6.77307	+	2.80188i	−0.420048	+	0.173765i
$261$	−3.17373	−	2.94502i	−0.196449	−	0.182292i
$262$	−1.14834	+	4.28568i	−0.0709450	+	0.264770i
$263$	−15.9506	+	9.20907i	−0.983554	+	0.567855i	−0.903341	−	0.428922i	$-0.858893\pi$
$263$	−15.9506	+	9.20907i	−0.983554	+	0.567855i	−0.0802129	+	0.996778i	$0.525560\pi$
$264$	−0.924292	+	8.20189i	−0.0568862	+	0.504791i
$265$	−2.13218	−	2.13218i	−0.130979	−	0.130979i
$266$	−0.00169061	−	0.00630942i	−0.000103658	−	0.000386856i
$267$	0.756886	+	0.949143i	0.0463207	+	0.0580866i
$268$	7.84646	−	7.84646i	0.479299	−	0.479299i
$269$	14.9997	+	8.66006i	0.914546	+	0.528013i	0.881891	−	0.471453i	$-0.156270\pi$
$269$	14.9997	+	8.66006i	0.914546	+	0.528013i	0.0326548	+	0.999467i	$0.489604\pi$
$270$	−14.7001	+	2.78052i	−0.894619	+	0.169217i
$271$	19.3494	+	5.18465i	1.17539	+	0.314945i	0.793097	−	0.609095i	$-0.208467\pi$
$271$	19.3494	+	5.18465i	1.17539	+	0.314945i	0.382295	+	0.924040i	$0.375134\pi$
$272$	7.89920			0.478959
$273$	6.06066	+	1.50613i	0.366808	+	0.0911551i
$274$	4.37847			0.264513
$275$	2.68982	+	0.720736i	0.162202	+	0.0434620i
$276$	3.03650	+	2.24113i	0.182776	+	0.134900i
$277$	26.2922	+	15.1798i	1.57975	+	0.912067i	0.994894	+	0.100928i	$0.0321812\pi$
$277$	26.2922	+	15.1798i	1.57975	+	0.912067i	0.584853	+	0.811139i	$0.301152\pi$
$278$	−9.00009	+	9.00009i	−0.539789	+	0.539789i
$279$	10.9854	−	20.7834i	0.657677	−	1.24427i
$280$	2.07156	+	7.73117i	0.123799	+	0.462026i
$281$	12.2037	+	12.2037i	0.728014	+	0.728014i	0.970224	−	0.242210i	$-0.0778723\pi$
$281$	12.2037	+	12.2037i	0.728014	+	0.728014i	−0.242210	+	0.970224i	$0.577872\pi$
$282$	25.6617	+	2.89188i	1.52813	+	0.172209i
$283$	−21.2557	+	12.2720i	−1.26352	+	0.729493i	−0.973753	−	0.227605i	$-0.926910\pi$
$283$	−21.2557	+	12.2720i	−1.26352	+	0.729493i	−0.289765	+	0.957098i	$0.593577\pi$
$284$	−2.47303	+	9.22947i	−0.146747	+	0.547668i
$285$	0.0106760	+	0.0244709i	0.000632391	+	0.00144953i
$286$	2.36784	−	5.70911i	0.140014	−	0.337587i
$287$			9.75289i			0.575695i
$288$	10.4600	−	6.57189i	0.616361	−	0.387252i
$289$	−0.796403	−	1.37941i	−0.0468472	−	0.0811418i
$290$	−2.07764	+	3.59858i	−0.122003	+	0.211316i
$291$	1.59945	−	4.07510i	0.0937615	−	0.238887i
$292$	5.29215	−	1.41803i	0.309700	−	0.0829838i
$293$	16.9504	−	4.54184i	0.990251	−	0.265337i	0.272895	−	0.962044i	$-0.412019\pi$
$293$	16.9504	−	4.54184i	0.990251	−	0.265337i	0.717356	+	0.696707i	$0.245352\pi$
$294$	0.699000	−	1.78092i	0.0407665	−	0.103865i
$295$	−2.07886	+	3.60069i	−0.121036	+	0.209640i
$296$	−6.98306	−	12.0950i	−0.405882	−	0.703008i
$297$	−4.54298	+	6.66250i	−0.263611	+	0.386597i
$298$			11.9609i			0.692877i
$299$	−6.12856	−	7.99444i	−0.354424	−	0.462331i
$300$	−0.969257	−	2.22168i	−0.0559601	−	0.128269i
$301$	2.57128	−	9.59616i	0.148206	−	0.553113i
$302$	22.0725	−	12.7435i	1.27013	−	0.733308i
$303$	−6.29926	−	0.709880i	−0.361883	−	0.0407815i
$304$	0.00766028	+	0.00766028i	0.000439347	+	0.000439347i
$305$	−6.77818	−	25.2965i	−0.388117	−	1.44847i
$306$	12.6325	+	6.67712i	0.722154	+	0.381705i
$307$	13.1019	−	13.1019i	0.747762	−	0.747762i	−0.226296	−	0.974059i	$-0.572662\pi$
$307$	13.1019	−	13.1019i	0.747762	−	0.747762i	0.974059	+	0.226296i	$0.0726618\pi$
$308$	1.04819	+	0.605172i	0.0597261	+	0.0344829i
$309$	25.0363	+	18.4784i	1.42427	+	1.05120i
$310$	−21.7927	−	5.83933i	−1.23774	−	0.331651i
$311$	−31.4176			−1.78153			−0.890765	−	0.454464i	$-0.849831\pi$
$311$	−31.4176			−1.78153			−0.890765	+	0.454464i	$0.849831\pi$
$312$	−18.4291	+	5.29984i	−1.04334	+	0.300045i
$313$	−20.7707			−1.17403			−0.587016	−	0.809576i	$-0.699697\pi$
$313$	−20.7707			−1.17403			−0.587016	+	0.809576i	$0.699697\pi$
$314$	−18.9441	−	5.07605i	−1.06908	−	0.286458i
$315$	−1.74037	+	7.62368i	−0.0980585	+	0.429546i
$316$	−2.84813	−	1.64437i	−0.160220	−	0.0925029i
$317$	5.74701	−	5.74701i	0.322784	−	0.322784i	−0.527050	−	0.849834i	$-0.676702\pi$
$317$	5.74701	−	5.74701i	0.322784	−	0.322784i	0.849834	+	0.527050i	$0.176702\pi$
$318$	−1.37988	−	1.73038i	−0.0773797	−	0.0970349i
$319$	0.579685	+	2.16342i	0.0324562	+	0.121128i
$320$	−15.1363	−	15.1363i	−0.846147	−	0.846147i
$321$	1.61673	−	14.3464i	0.0902369	−	0.800735i
$322$	−2.67255	+	1.54300i	−0.148935	+	0.0859878i
$323$	0.00659960	−	0.0246301i	0.000367212	−	0.00137045i
$324$	6.99956	−	0.523999i	0.388864	−	0.0291110i
$325$	0.841538	+	6.41474i	0.0466802	+	0.355826i
$326$			3.10972i			0.172232i
$327$	−8.08831	+	1.21896i	−0.447285	+	0.0674085i
$328$	−14.9737	−	25.9353i	−0.826786	−	1.43204i
$329$	6.74898	−	11.6896i	0.372083	−	0.644467i
$330$	7.20421	+	2.82761i	0.396579	+	0.155655i
$331$	29.9778	−	8.03254i	1.64773	−	0.441508i	0.688755	−	0.724994i	$-0.258158\pi$
$331$	29.9778	−	8.03254i	1.64773	−	0.441508i	0.958976	+	0.283486i	$0.0914910\pi$
$332$	−5.53522	+	1.48316i	−0.303785	+	0.0813988i
$333$	−0.509670	−	13.6354i	−0.0279298	−	0.747214i
$334$	−6.38943	+	11.0668i	−0.349614	+	0.605549i
$335$	−18.5435	−	32.1183i	−1.01314	−	1.75481i
$336$	0.472852	+	3.13758i	0.0257962	+	0.171169i
$337$			6.37141i			0.347073i	0.984827	+	0.173536i	$0.0555194\pi$
$337$			6.37141i			0.347073i	−0.984827	+	0.173536i	$0.944481\pi$
$338$	14.3595	+	0.0131074i	0.781055	+	0.000712947i
$339$	−12.1410	+	5.29678i	−0.659408	+	0.287681i
$340$	−2.26874	+	8.46706i	−0.123040	+	0.459191i
$341$	−10.5316	+	6.08040i	−0.570316	+	0.329272i
$342$	0.00577529	+	0.0187256i	0.000312292	+	0.00101257i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	7.89545	+	29.4662i	0.425694	+	1.58871i
$345$	9.86173	−	7.86415i	0.530938	−	0.423392i
$346$	−6.74149	+	6.74149i	−0.362425	+	0.362425i
$347$	4.72469	+	2.72780i	0.253634	+	0.146436i	0.621427	−	0.783472i	$-0.286553\pi$
$347$	4.72469	+	2.72780i	0.253634	+	0.146436i	−0.367793	+	0.929908i	$0.619886\pi$
$348$	1.15771	−	1.56857i	0.0620595	−	0.0840843i
$349$	−26.4194	−	7.07905i	−1.41420	−	0.378933i	−0.530775	−	0.847513i	$-0.678099\pi$
$349$	−26.4194	−	7.07905i	−1.41420	−	0.378933i	−0.883421	+	0.468580i	$0.844766\pi$
$350$	1.98203			0.105944
$351$	−18.3381	−	3.83610i	−0.978813	−	0.204756i
$352$	−6.39035			−0.340607
$353$	26.7723	+	7.17361i	1.42494	+	0.381813i	0.887235	−	0.461318i	$-0.152623\pi$
$353$	26.7723	+	7.17361i	1.42494	+	0.381813i	0.537709	+	0.843131i	$0.319290\pi$
$354$	−1.81219	+	2.45533i	−0.0963168	+	0.130499i
$355$	27.6564	+	15.9675i	1.46785	+	0.847465i
$356$	−0.386525	+	0.386525i	−0.0204858	+	0.0204858i
$357$	5.83919	−	4.65642i	0.309043	−	0.246444i
$358$	−2.99616	−	11.1818i	−0.158352	−	0.590977i
$359$	2.20895	+	2.20895i	0.116584	+	0.116584i	0.762992	−	0.646408i	$-0.223730\pi$
$359$	2.20895	+	2.20895i	0.116584	+	0.116584i	−0.646408	+	0.762992i	$0.723730\pi$
$360$	−7.07668	−	22.9452i	−0.372974	−	1.20932i
$361$	−16.4545	+	9.49998i	−0.866024	+	0.499999i
$362$	−3.45557	+	12.8964i	−0.181621	+	0.677817i
$363$	−13.6395	+	5.95054i	−0.715889	+	0.312323i
$364$	−0.368311	+	2.78776i	−0.0193047	+	0.146119i
$365$		−	18.3114i		−	0.958462i
$366$	−2.86453	−	19.0074i	−0.149731	−	0.993533i
$367$	−3.14106	−	5.44048i	−0.163962	−	0.283991i	0.772324	−	0.635229i	$-0.219094\pi$
$367$	−3.14106	−	5.44048i	−0.163962	−	0.283991i	−0.936286	+	0.351238i	$0.885761\pi$
$368$	2.55905	−	4.43240i	0.133400	−	0.231055i
$369$	−1.09288	−	29.2383i	−0.0568932	−	1.52208i
$370$	−12.6492	+	3.38935i	−0.657602	+	0.176204i
$371$	−1.11740	+	0.299406i	−0.0580125	+	0.0155444i
$372$	9.85337	+	3.86738i	0.510874	+	0.200515i
$373$	−5.15274	+	8.92481i	−0.266799	+	0.462109i	−0.968033	−	0.250822i	$-0.919299\pi$
$373$	−5.15274	+	8.92481i	−0.266799	+	0.462109i	0.701235	+	0.712931i	$0.252633\pi$
$374$	−3.69578	−	6.40128i	−0.191104	−	0.331002i
$375$	14.3111	−	2.15676i	0.739019	−	0.111375i
$376$			41.4472i			2.13748i
$377$	−4.12971	+	3.16584i	−0.212691	+	0.163049i
$378$	−1.89597	+	5.41737i	−0.0975183	+	0.278639i
$379$	−4.09252	+	15.2735i	−0.210219	+	0.784547i	0.777576	+	0.628788i	$0.216449\pi$
$379$	−4.09252	+	15.2735i	−0.210219	+	0.784547i	−0.987795	+	0.155759i	$0.950218\pi$
$380$	−0.0104111	+	0.00601085i	−0.000534078	+	0.000308350i
$381$	−0.430216	+	3.81760i	−0.0220406	+	0.195582i
$382$	4.13788	+	4.13788i	0.211712	+	0.211712i
$383$	3.71877	+	13.8786i	0.190020	+	0.709165i	0.993500	+	0.113833i	$0.0363129\pi$
$383$	3.71877	+	13.8786i	0.190020	+	0.709165i	−0.803480	+	0.595332i	$0.797020\pi$
$384$	−0.902355	−	1.13156i	−0.0460481	−	0.0577448i
$385$	2.86040	−	2.86040i	0.145779	−	0.145779i
$386$	−7.75491	−	4.47730i	−0.394714	−	0.227888i
$387$	−6.63315	+	29.0565i	−0.337182	+	1.47703i
$388$	1.90404	+	0.510186i	0.0966630	+	0.0259008i
$389$	−36.1530			−1.83303			−0.916515	−	0.400001i	$-0.869010\pi$
$389$	−36.1530			−1.83303			−0.916515	+	0.400001i	$0.869010\pi$
$390$	0.327663	+	17.9776i	0.0165919	+	0.910331i
$391$	−12.0468			−0.609231
$392$	2.96600	+	0.794736i	0.149805	+	0.0401402i
$393$	−5.59774	−	4.13149i	−0.282369	−	0.208406i
$394$	7.42585	+	4.28732i	0.374109	+	0.215992i
$395$	−7.77225	+	7.77225i	−0.391064	+	0.391064i
$396$	−3.21018	−	1.69679i	−0.161318	−	0.0852670i
$397$	−4.68757	−	17.4943i	−0.235263	−	0.878012i	−0.978030	−	0.208463i	$-0.933154\pi$
$397$	−4.68757	−	17.4943i	−0.235263	−	0.878012i	0.742768	−	0.669549i	$-0.233513\pi$
$398$	−6.20806	−	6.20806i	−0.311182	−	0.311182i
$399$	0.0101782	+	0.00114700i	0.000509546	+	5.74220e-5i
$400$	−2.84678	+	1.64359i	−0.142339	+	0.0821795i
$401$	−4.82450	+	18.0053i	−0.240924	+	0.899140i	0.734465	+	0.678647i	$0.237433\pi$
$401$	−4.82450	+	18.0053i	−0.240924	+	0.899140i	−0.975388	+	0.220493i	$0.929233\pi$
$402$	−10.8850	−	24.9500i	−0.542894	−	1.24439i
$403$	−22.4069	−	17.2096i	−1.11617	−	0.857274i
$404$		−	2.85438i		−	0.142011i
$405$	4.36317	−	23.0501i	0.216807	−	1.14537i
$406$	0.797069	+	1.38056i	0.0395579	+	0.0685163i
$407$	−3.52928	+	6.11289i	−0.174940	+	0.303005i
$408$	−8.37876	+	21.3475i	−0.414810	+	1.05686i
$409$	34.1514	−	9.15083i	1.68868	−	0.452480i	0.718629	−	0.695394i	$-0.244770\pi$
$409$	34.1514	−	9.15083i	1.68868	−	0.452480i	0.970048	+	0.242914i	$0.0781032\pi$
$410$	−27.1237	+	7.26777i	−1.33954	+	0.358930i
$411$	−2.50845	+	6.39107i	−0.123733	+	0.315248i
$412$	−7.00566	+	12.1342i	−0.345144	+	0.597807i
$413$	0.797536	+	1.38137i	0.0392442	+	0.0679729i
$414$	7.83914	−	4.92523i	0.385273	−	0.242062i
$415$			19.1524i			0.940156i
$416$	−5.67532	−	13.7191i	−0.278255	−	0.672636i
$417$	−7.98085	−	18.2933i	−0.390824	−	0.895825i
$418$	0.00262367	−	0.00979167i	0.000128328	−	0.000478926i
$419$	0.727549	−	0.420051i	0.0355431	−	0.0205208i	−0.482123	−	0.876103i	$-0.660134\pi$
$419$	0.727549	−	0.420051i	0.0355431	−	0.0205208i	0.517666	+	0.855583i	$0.326801\pi$
$420$	−3.49894	−	0.394305i	−0.170731	−	0.0192401i
$421$	−18.8700	−	18.8700i	−0.919666	−	0.919666i	0.0773384	−	0.997005i	$-0.475358\pi$
$421$	−18.8700	−	18.8700i	−0.919666	−	0.919666i	−0.997005	+	0.0773384i	$0.975358\pi$
$422$	2.93411	+	10.9502i	0.142830	+	0.533050i
$423$	−18.9229	+	35.8005i	−0.920064	+	1.74068i
$424$	2.51175	−	2.51175i	0.121981	−	0.121981i
$425$	6.70064	+	3.86861i	0.325029	+	0.187655i
$426$	18.8591	+	13.9192i	0.913727	+	0.674388i
$427$	−9.70478	−	2.60039i	−0.469647	−	0.125842i
$428$	6.50074			0.314225
$429$	6.97680	+	6.72703i	0.336843	+	0.324784i
$430$	28.6039			1.37940
$431$	−15.4635	−	4.14344i	−0.744852	−	0.199582i	−0.133618	−	0.991033i	$-0.542660\pi$
$431$	−15.4635	−	4.14344i	−0.744852	−	0.199582i	−0.611233	+	0.791450i	$0.709326\pi$
$432$	−1.76915	−	9.35318i	−0.0851184	−	0.450005i
$433$	6.06372	+	3.50089i	0.291404	+	0.168242i	0.638575	−	0.769560i	$-0.279524\pi$
$433$	6.06372	+	3.50089i	0.291404	+	0.168242i	−0.347171	+	0.937802i	$0.612858\pi$
$434$	−6.12036	+	6.12036i	−0.293787	+	0.293787i
$435$	−4.06241	−	5.09430i	−0.194777	−	0.244253i
$436$	−0.953262	−	3.55762i	−0.0456530	−	0.170379i
$437$	−0.0116824	−	0.0116824i	−0.000558845	−	0.000558845i
$438$	1.50508	−	13.3556i	0.0719154	−	0.638156i
$439$	4.10819	−	2.37186i	0.196073	−	0.113203i	−0.398749	−	0.917060i	$-0.630556\pi$
$439$	4.10819	−	2.37186i	0.196073	−	0.113203i	0.594823	+	0.803857i	$0.297222\pi$
$440$	−3.21488	+	11.9981i	−0.153263	+	0.571987i
$441$	2.19908	+	2.04060i	0.104718	+	0.0971716i
$442$	10.4604	−	13.6193i	0.497548	−	0.647805i
$443$			32.0561i			1.52303i	0.648147	+	0.761516i	$0.275544\pi$
$443$			32.0561i			1.52303i	−0.648147	+	0.761516i	$0.724456\pi$
$444$	6.07540	−	0.915598i	0.288326	−	0.0434524i
$445$	0.913473	+	1.58218i	0.0433028	+	0.0750026i
$446$	4.53146	−	7.84872i	0.214571	−	0.371648i
$447$	−17.4588	−	6.85248i	−0.825775	−	0.324111i
$448$	−7.93241	+	2.12548i	−0.374771	+	0.100420i
$449$	−26.4815	+	7.09569i	−1.24974	+	0.334866i	−0.822235	−	0.569148i	$-0.807273\pi$
$449$	−26.4815	+	7.09569i	−1.24974	+	0.334866i	−0.427503	+	0.904014i	$0.640606\pi$
$450$	−5.94193	+	0.222101i	−0.280105	+	0.0104699i
$451$	−7.56781	+	13.1078i	−0.356354	+	0.617224i
$452$	−2.98222	−	5.16535i	−0.140272	−	0.242958i
$453$	5.95576	+	39.5191i	0.279826	+	1.85677i
$454$			13.6433i			0.640310i
$455$	8.68120	+	3.60051i	0.406981	+	0.168795i
$456$	−0.0288272	+	0.0125765i	−0.00134996	+	0.000588949i
$457$	−6.44991	+	24.0714i	−0.301714	+	1.12601i	0.634023	+	0.773314i	$0.281403\pi$
$457$	−6.44991	+	24.0714i	−0.301714	+	1.12601i	−0.935737	+	0.352698i	$0.885264\pi$
$458$	−1.98410	+	1.14552i	−0.0927111	+	0.0535268i
$459$	−16.9836	+	14.6138i	−0.792725	+	0.682115i
$460$	4.01605	+	4.01605i	0.187249	+	0.187249i
$461$	−2.60510	−	9.72237i	−0.121332	−	0.452816i	0.878351	−	0.478017i	$-0.158644\pi$
$461$	−2.60510	−	9.72237i	−0.121332	−	0.452816i	−0.999682	+	0.0252009i	$0.991977\pi$
$462$	2.32137	−	1.85116i	0.108000	−	0.0861236i
$463$	−19.2333	+	19.2333i	−0.893848	+	0.893848i	−0.994883	−	0.101035i	$-0.967784\pi$
$463$	−19.2333	+	19.2333i	−0.893848	+	0.893848i	0.101035	+	0.994883i	$0.467784\pi$
$464$	−2.28966	−	1.32193i	−0.106295	−	0.0613693i
$465$	21.0086	−	28.4645i	0.974249	−	1.32001i
$466$	14.0777	+	3.77210i	0.652136	+	0.174739i
$467$	38.0381			1.76019			0.880097	−	0.474795i	$-0.157478\pi$
$467$	38.0381			1.76019			0.880097	+	0.474795i	$0.157478\pi$
$468$	0.791771	−	8.39873i	0.0365996	−	0.388231i
$469$	−14.2281			−0.656993
$470$	37.5391	+	10.0586i	1.73155	+	0.463967i
$471$	18.2625	−	24.7438i	0.841491	−	1.14013i
$472$	−4.24168	−	2.44893i	−0.195239	−	0.112721i
$473$	10.9020	−	10.9020i	0.501274	−	0.501274i
$474$	−6.30760	+	5.02994i	−0.289718	+	0.231033i
$475$	0.00274637	+	0.0102496i	0.000126012	+	0.000470283i
$476$	2.37793	+	2.37793i	0.108992	+	0.108992i
$477$	3.31631	−	1.02280i	0.151843	−	0.0468310i
$478$	10.8595	−	6.26976i	0.496704	−	0.286772i
$479$	7.55852	−	28.2088i	0.345358	−	1.28889i	−0.546836	−	0.837240i	$-0.684168\pi$
$479$	7.55852	−	28.2088i	0.345358	−	1.28889i	0.892194	−	0.451653i	$-0.149165\pi$
$480$	17.0396	−	7.43390i	0.777747	−	0.339310i
$481$	−16.2579	−	2.14794i	−0.741294	−	0.0979374i
$482$		−	25.8296i		−	1.17650i
$483$	−0.721128	−	4.78500i	−0.0328124	−	0.217725i
$484$	−3.35031	−	5.80290i	−0.152287	−	0.263768i
$485$	3.29409	−	5.70553i	0.149577	−	0.259075i
$486$	5.07689	−	16.4532i	0.230292	−	0.746333i
$487$	10.4381	−	2.79687i	0.472994	−	0.126738i	−0.0144447	−	0.999896i	$-0.504598\pi$
$487$	10.4381	−	2.79687i	0.472994	−	0.126738i	0.487438	+	0.873157i	$0.337931\pi$
$488$	29.7997	−	7.98482i	1.34897	−	0.361456i
$489$	−4.53914	−	1.78158i	−0.205267	−	0.0805659i
$490$	1.43960	−	2.49346i	0.0650344	−	0.112643i
$491$	−8.33872	−	14.4431i	−0.376321	−	0.651807i	0.614203	−	0.789148i	$-0.289478\pi$
$491$	−8.33872	−	14.4431i	−0.376321	−	0.651807i	−0.990524	+	0.137341i	$0.956144\pi$
$492$	13.0274	−	1.96331i	0.587322	−	0.0885130i
$493$			6.22303i			0.280271i
$494$	0.0233514	−	0.00306342i	0.00105063	−	0.000137830i
$495$	−8.25468	+	8.89574i	−0.371020	+	0.399834i
$496$	3.71537	−	13.8659i	0.166825	−	0.622599i
$497$	10.6102	−	6.12577i	0.475930	−	0.274779i
$498$	−1.57421	+	13.9690i	−0.0705418	+	0.625967i
$499$	−1.79186	−	1.79186i	−0.0802148	−	0.0802148i	0.665861	−	0.746076i	$-0.268064\pi$
$499$	−1.79186	−	1.79186i	−0.0802148	−	0.0802148i	−0.746076	+	0.665861i	$0.768064\pi$
$500$	1.68665	+	6.29467i	0.0754294	+	0.281506i
$501$	−12.4932	−	15.6666i	−0.558156	−	0.699933i
$502$	6.20600	−	6.20600i	0.276987	−	0.276987i
$503$	−24.8090	−	14.3235i	−1.10618	−	0.638651i	−0.168340	−	0.985729i	$-0.553841\pi$
$503$	−24.8090	−	14.3235i	−1.10618	−	0.638651i	−0.937836	+	0.347077i	$0.887174\pi$
$504$	−8.98083	−	2.05018i	−0.400038	−	0.0913224i
$505$	−9.21484	−	2.46911i	−0.410055	−	0.109874i
$506$	−4.78918			−0.212905
$507$	−8.24580	+	20.9525i	−0.366209	+	0.930533i
$508$	−1.72987			−0.0767504
$509$	−21.1337	−	5.66276i	−0.936735	−	0.250997i	−0.242011	−	0.970274i	$-0.577807\pi$
$509$	−21.1337	−	5.66276i	−0.936735	−	0.250997i	−0.694724	+	0.719276i	$0.744474\pi$
$510$	17.3012	+	12.7694i	0.766112	+	0.565439i
$511$	−6.08383	−	3.51250i	−0.269133	−	0.155384i
$512$	13.2892	−	13.2892i	0.587307	−	0.587307i
$513$	−0.0306417	−	0.00229807i	−0.00135286	−	0.000101462i
$514$	8.62658	+	32.1948i	0.380502	+	1.42005i
$515$	33.1129	+	33.1129i	1.45913	+	1.45913i
$516$	−13.3357	−	1.50283i	−0.587071	−	0.0661586i
$517$	18.1412	−	10.4738i	0.797849	−	0.460638i
$518$	−1.30030	+	4.85277i	−0.0571317	+	0.213218i
$519$	−5.97803	−	13.7025i	−0.262406	−	0.601474i
$520$	−28.6133	+	3.75373i	−1.25478	+	0.164612i
$521$			29.3442i			1.28559i	0.766038	+	0.642795i	$0.222225\pi$
$521$			29.3442i			1.28559i	−0.766038	+	0.642795i	$0.777775\pi$
$522$	−2.54424	−	4.04949i	−0.111358	−	0.177241i
$523$	−2.67845	−	4.63921i	−0.117120	−	0.202858i	0.801505	−	0.597988i	$-0.204033\pi$
$523$	−2.67845	−	4.63921i	−0.117120	−	0.202858i	−0.918625	+	0.395130i	$0.870700\pi$
$524$	1.56636	−	2.71301i	0.0684267	−	0.118519i
$525$	−1.13552	+	2.89308i	−0.0495580	+	0.126265i
$526$	−19.6511	+	5.26549i	−0.856827	+	0.229586i
$527$	−32.6371	+	8.74508i	−1.42169	+	0.380942i
$528$	−1.79911	+	4.58380i	−0.0782963	+	0.199484i
$529$	7.59729	−	13.1589i	0.330317	−	0.572126i
$530$	−1.66535	−	2.88447i	−0.0723382	−	0.125294i
$531$	−2.54573	−	4.05185i	−0.110475	−	0.175836i
$532$			0.00461202i			0.000199956i
$533$	−34.8616	−	4.60581i	−1.51002	−	0.199500i
$534$	0.536206	+	1.22906i	0.0232039	+	0.0531867i
$535$	5.62331	−	20.9865i	0.243117	−	0.907325i
$536$	37.8359	−	21.8446i	1.63426	−	0.943542i
$537$	18.0382	+	2.03277i	0.778404	+	0.0877203i
$538$	13.5280	+	13.5280i	0.583232	+	0.583232i
$539$	−0.401664	−	1.49903i	−0.0173009	−	0.0645678i
$540$	10.5337	+	0.790007i	0.453298	+	0.0339965i
$541$	10.4003	−	10.4003i	0.447143	−	0.447143i	−0.447261	−	0.894404i	$-0.647600\pi$
$541$	10.4003	−	10.4003i	0.447143	−	0.447143i	0.894404	+	0.447261i	$0.147600\pi$
$542$	19.1624	+	11.0634i	0.823098	+	0.475216i
$543$	−16.8446	−	12.4324i	−0.722869	−	0.533523i
$544$	−17.1504	−	4.59543i	−0.735317	−	0.197028i
$545$	−12.3097			−0.527291
$546$	6.03578	+	3.33961i	0.258308	+	0.142922i
$547$	18.8749			0.807035			0.403517	−	0.914972i	$-0.367788\pi$
$547$	18.8749			0.807035			0.403517	+	0.914972i	$0.367788\pi$
$548$	−2.98615	−	0.800135i	−0.127562	−	0.0341801i
$549$	29.3854	+	6.70823i	1.25414	+	0.286300i
$550$	2.66383	+	1.53797i	0.113586	+	0.0655791i
$551$	−0.00603481	+	0.00603481i	−0.000257091	+	0.000257091i
$552$	9.26412	+	11.6173i	0.394307	+	0.494465i
$553$	1.09140	+	4.07315i	0.0464110	+	0.173208i
$554$	23.7126	+	23.7126i	1.00745	+	1.00745i
$555$	2.29953	−	20.4053i	0.0976097	−	0.866159i
$556$	7.78283	−	4.49342i	0.330065	−	0.190563i
$557$	10.6709	−	39.8245i	0.452142	−	1.68742i	−0.244213	−	0.969722i	$-0.578530\pi$
$557$	10.6709	−	39.8245i	0.452142	−	1.68742i	0.696355	−	0.717697i	$-0.254804\pi$
$558$	17.6624	−	19.0341i	0.747710	−	0.805777i
$559$	33.0871	+	13.7228i	1.39943	+	0.580413i
$560$			4.77513i			0.201786i
$561$	11.4610	−	1.72724i	0.483885	−	0.0729243i
$562$	9.53179	+	16.5095i	0.402074	+	0.696413i
$563$	3.40782	−	5.90253i	0.143623	−	0.248762i	−0.785236	−	0.619197i	$-0.787458\pi$
$563$	3.40782	−	5.90253i	0.143623	−	0.248762i	0.928858	+	0.370435i	$0.120791\pi$
$564$	−16.9730	−	6.66179i	−0.714692	−	0.280512i
$565$	−19.2551	+	5.15939i	−0.810069	+	0.217057i
$566$	−26.1869	+	7.01677i	−1.10072	+	0.294937i
$567$	−6.82129	−	5.87112i	−0.286467	−	0.246564i
$568$	−18.8100	+	32.5798i	−0.789248	+	1.36702i
$569$	−8.56471	−	14.8345i	−0.359051	−	0.621895i	0.628751	−	0.777606i	$-0.283566\pi$
$569$	−8.56471	−	14.8345i	−0.359051	−	0.621895i	−0.987803	+	0.155711i	$0.950233\pi$
$570$	0.00439476	+	0.0291611i	0.000184076	+	0.00122143i
$571$		−	31.5919i		−	1.32208i	−0.750351	−	0.661040i	$-0.770115\pi$
$571$		−	31.5919i		−	1.32208i	0.750351	−	0.661040i	$-0.229885\pi$
$572$	−2.65819	+	3.46095i	−0.111144	+	0.144709i
$573$	−8.41050	+	3.66927i	−0.351354	+	0.153286i
$574$	−2.78822	+	10.4058i	−0.116378	+	0.434328i
$575$	4.34152	−	2.50658i	0.181054	−	0.104531i
$576$	23.5424	−	7.26088i	0.980935	−	0.302537i
$577$	−3.79649	−	3.79649i	−0.158050	−	0.158050i	0.623652	−	0.781702i	$-0.285648\pi$
$577$	−3.79649	−	3.79649i	−0.158050	−	0.158050i	−0.781702	+	0.623652i	$0.785648\pi$
$578$	−0.455361	−	1.69943i	−0.0189405	−	0.0706870i
$579$	10.9782	−	8.75445i	0.456237	−	0.363822i
$580$	2.07458	−	2.07458i	0.0861424	−	0.0861424i
$581$	6.36326	+	3.67383i	0.263993	+	0.152416i
$582$	2.87154	−	3.89064i	0.119029	−	0.161272i
$583$	−1.73410	−	0.464652i	−0.0718192	−	0.0192439i
$584$	21.5712			0.892621
$585$	−26.4289	−	9.82121i	−1.09270	−	0.406057i
$586$	19.3835			0.800725
$587$	6.35206	+	1.70203i	0.262178	+	0.0702503i	0.387513	−	0.921864i	$-0.373334\pi$
$587$	6.35206	+	1.70203i	0.262178	+	0.0702503i	−0.125336	+	0.992114i	$0.540001\pi$
$588$	−0.802174	+	1.08686i	−0.0330811	+	0.0448215i
$589$	−0.0401305	−	0.0231694i	−0.00165355	−	0.000954677i
$590$	−3.24741	+	3.24741i	−0.133694	+	0.133694i
$591$	−10.5123	+	8.38298i	−0.432420	+	0.344830i
$592$	−2.15653	−	8.04829i	−0.0886329	−	0.330783i
$593$	−6.76326	−	6.76326i	−0.277734	−	0.277734i	0.554470	−	0.832204i	$-0.312921\pi$
$593$	−6.76326	−	6.76326i	−0.277734	−	0.277734i	−0.832204	+	0.554470i	$0.812921\pi$
$594$	−6.75181	+	5.80972i	−0.277030	+	0.238376i
$595$	9.73370	−	5.61975i	0.399043	−	0.230387i
$596$	2.18578	−	8.15742i	0.0895328	−	0.334141i
$597$	12.6183	−	5.50501i	0.516432	−	0.225305i
$598$	−4.25331	−	10.2817i	−0.173931	−	0.420449i
$599$			36.4081i			1.48759i	0.668406	+	0.743797i	$0.266977\pi$
$599$			36.4081i			1.48759i	−0.668406	+	0.743797i	$0.733023\pi$
$600$	−1.42218	−	9.43677i	−0.0580602	−	0.385255i
$601$	12.1576	+	21.0576i	0.495920	+	0.858959i	0.999989	−	0.00470479i	$-0.00149759\pi$
$601$	12.1576	+	21.0576i	0.495920	+	0.858959i	−0.504069	+	0.863663i	$0.668164\pi$
$602$	5.48682	−	9.50345i	0.223626	−	0.387332i
$603$	42.6545	−	1.59436i	1.73703	−	0.0649275i
$604$	−17.3824	+	4.65759i	−0.707278	+	0.189515i
$605$	−21.6317	+	5.79620i	−0.879455	+	0.235649i
$606$	−6.51800	−	2.55827i	−0.264776	−	0.103923i
$607$	11.8231	−	20.4782i	0.479884	−	0.831184i	−0.519849	−	0.854258i	$-0.674012\pi$
$607$	11.8231	−	20.4782i	0.479884	−	0.831184i	0.999734	+	0.0230737i	$0.00734524\pi$
$608$	−0.0121752	−	0.0210881i	−0.000493771	−	0.000855236i
$609$	−2.47180	+	0.372515i	−0.100162	+	0.0150951i
$610$		−	28.9277i		−	1.17125i
$611$	38.5971	+	29.6446i	1.56147	+	1.19929i
$612$	−7.39528	−	6.86235i	−0.298936	−	0.277394i
$613$	−2.09200	+	7.80744i	−0.0844950	+	0.315340i	−0.995218	−	0.0976779i	$-0.968859\pi$
$613$	−2.09200	+	7.80744i	−0.0844950	+	0.315340i	0.910723	+	0.413017i	$0.135525\pi$
$614$	17.7245	−	10.2333i	0.715304	−	0.412981i
$615$	4.93087	−	43.7551i	0.198832	−	1.76437i
$616$	3.36960	+	3.36960i	0.135765	+	0.135765i
$617$	−0.591212	−	2.20643i	−0.0238013	−	0.0888277i	0.953004	−	0.302959i	$-0.0979746\pi$
$617$	−0.591212	−	2.20643i	−0.0238013	−	0.0888277i	−0.976805	+	0.214131i	$0.931308\pi$
$618$	21.4296	+	26.8729i	0.862024	+	1.08099i
$619$	−9.86129	+	9.86129i	−0.396359	+	0.396359i	−0.876947	−	0.480588i	$-0.840423\pi$
$619$	−9.86129	+	9.86129i	−0.396359	+	0.396359i	0.480588	+	0.876947i	$0.340423\pi$
$620$	13.7956	+	7.96492i	0.554047	+	0.319879i
$621$	2.69807	+	14.2642i	0.108270	+	0.572401i
$622$	−33.5208	−	8.98186i	−1.34406	−	0.360140i
$623$	0.700892			0.0280806
$624$	−11.4385	+	0.208481i	−0.457908	+	0.00834592i
$625$	30.7521			1.23008
$626$	−22.1612	−	5.93806i	−0.885738	−	0.237333i
$627$	0.0127894	+	0.00943937i	0.000510758	+	0.000376972i
$628$	11.9924	+	6.92381i	0.478548	+	0.276290i
$629$	−13.8678	+	13.8678i	−0.552944	+	0.552944i
$630$	−4.03637	+	7.63647i	−0.160813	+	0.304244i
$631$	8.34121	+	31.1298i	0.332058	+	1.23926i	0.907023	+	0.421081i	$0.138349\pi$
$631$	8.34121	+	31.1298i	0.332058	+	1.23926i	−0.574965	+	0.818178i	$0.694984\pi$
$632$	−9.15585	−	9.15585i	−0.364200	−	0.364200i
$633$	−17.6646	−	1.99067i	−0.702105	−	0.0791220i
$634$	7.77472	−	4.48873i	0.308773	−	0.178270i
$635$	−1.49638	+	5.58456i	−0.0593820	+	0.221617i
$636$	0.624871	+	1.43230i	0.0247777	+	0.0567942i
$637$	2.86148	−	2.19361i	0.113376	−	0.0869142i
$638$			2.47396i			0.0979451i
$639$	−31.1218	+	19.5534i	−1.23116	+	0.773522i
$640$	−1.08904	−	1.88627i	−0.0430480	−	0.0745613i
$641$	0.901500	−	1.56144i	0.0356071	−	0.0616733i	−0.847673	−	0.530520i	$-0.821997\pi$
$641$	0.901500	−	1.56144i	0.0356071	−	0.0616733i	0.883280	+	0.468846i	$0.155330\pi$
$642$	5.82638	−	14.8445i	0.229949	−	0.585866i
$643$	9.74493	−	2.61115i	0.384303	−	0.102974i	−0.0614949	−	0.998107i	$-0.519587\pi$
$643$	9.74493	−	2.61115i	0.384303	−	0.102974i	0.445798	+	0.895134i	$0.352920\pi$
$644$	2.10467	−	0.563944i	0.0829355	−	0.0222225i
$645$	−16.3874	+	41.7519i	−0.645252	+	1.64398i
$646$	0.0140828	−	0.0243921i	0.000554080	−	0.000959694i
$647$	12.5828	+	21.7941i	0.494682	+	0.856814i	0.999981	−	0.00613024i	$-0.00195133\pi$
$647$	12.5828	+	21.7941i	0.494682	+	0.856814i	−0.505300	+	0.862944i	$0.668618\pi$
$648$	27.1534	+	5.13989i	1.06669	+	0.201914i
$649$			2.47541i			0.0971683i
$650$	−0.936013	+	7.08474i	−0.0367135	+	0.277886i
$651$	−5.42724	−	12.4400i	−0.212710	−	0.487563i
$652$	0.568281	−	2.12085i	0.0222556	−	0.0830591i
$653$	−23.4753	+	13.5535i	−0.918659	+	0.530388i	−0.883207	−	0.468984i	$-0.844620\pi$
$653$	−23.4753	+	13.5535i	−0.918659	+	0.530388i	−0.0354518	+	0.999371i	$0.511287\pi$
$654$	−8.97824	−	1.01178i	−0.351077	−	0.0395638i
$655$	−7.40353	−	7.40353i	−0.289280	−	0.289280i
$656$	−4.62424	−	17.2579i	−0.180546	−	0.673807i
$657$	18.6324	+	9.84842i	0.726918	+	0.384223i
$658$	10.5427	−	10.5427i	0.410996	−	0.410996i
$659$	−19.2179	−	11.0954i	−0.748622	−	0.432217i	0.0765736	−	0.997064i	$-0.475602\pi$
$659$	−19.2179	−	11.0954i	−0.748622	−	0.432217i	−0.825196	+	0.564847i	$0.808935\pi$
$660$	−4.39660	−	3.24497i	−0.171137	−	0.126310i
$661$	−13.8276	−	3.70509i	−0.537830	−	0.144111i	−0.0203285	−	0.999793i	$-0.506471\pi$
$661$	−13.8276	−	3.70509i	−0.537830	−	0.144111i	−0.517502	+	0.855682i	$0.673138\pi$
$662$	34.2810			1.33237
$663$	13.8868	+	23.0711i	0.539317	+	0.896009i
$664$	−22.5619			−0.875572
$665$	0.0148891	+	0.00398952i	0.000577374	+	0.000154707i
$666$	3.35438	−	14.6939i	0.129979	−	0.569375i
$667$	3.49187	+	2.01603i	0.135206	+	0.0780610i
$668$	6.38002	−	6.38002i	0.246850	−	0.246850i
$669$	8.86035	+	11.1110i	0.342561	+	0.429575i
$670$	−10.6027	−	39.5696i	−0.409616	−	1.52871i
$671$	−11.0254	−	11.0254i	−0.425630	−	0.425630i
$672$	0.798681	−	7.08726i	0.0308098	−	0.273397i
$673$	40.2120	−	23.2164i	1.55006	−	0.894928i	0.551925	−	0.833894i	$-0.313894\pi$
$673$	40.2120	−	23.2164i	1.55006	−	0.894928i	0.998136	−	0.0610337i	$-0.0194397\pi$
$674$	−1.82150	+	6.79792i	−0.0701614	+	0.261846i
$675$	3.07998	−	8.80044i	0.118549	−	0.338729i
$676$	−9.79090	−	2.63304i	−0.376573	−	0.101271i
$677$			11.0386i			0.424249i	0.977243	+	0.212125i	$0.0680383\pi$
$677$			11.0386i			0.424249i	−0.977243	+	0.212125i	$0.931962\pi$
$678$	−14.4680	+	2.18041i	−0.555640	+	0.0837382i
$679$	−1.26375	−	2.18888i	−0.0484982	−	0.0840013i
$680$	−17.2562	+	29.8885i	−0.661743	+	1.14617i
$681$	−19.9145	−	7.81631i	−0.763126	−	0.299522i
$682$	−12.9749	+	3.47660i	−0.496833	+	0.133126i
$683$	11.9131	−	3.19211i	0.455843	−	0.122143i	−0.0235890	−	0.999722i	$-0.507509\pi$
$683$	11.9131	−	3.19211i	0.455843	−	0.122143i	0.479432	+	0.877579i	$0.340843\pi$
$684$	−0.000516810	−	0.0138264i	−1.97607e−5	−	0.000528666i
$685$	−5.16619	+	8.94810i	−0.197390	+	0.341889i
$686$	−0.552289	−	0.956593i	−0.0210865	−	0.0365229i
$687$	−0.535366	−	3.55239i	−0.0204255	−	0.135532i
$688$			18.1997i			0.693857i
$689$	−0.542532	−	4.13553i	−0.0206688	−	0.157551i
$690$	12.7701	−	5.57126i	0.486151	−	0.212094i
$691$	1.97905	−	7.38591i	0.0752866	−	0.280973i	−0.918012	−	0.396554i	$-0.870206\pi$
$691$	1.97905	−	7.38591i	0.0752866	−	0.280973i	0.993298	+	0.115580i	$0.0368727\pi$
$692$	5.82970	−	3.36578i	0.221612	−	0.127948i
$693$	1.37213	+	4.44895i	0.0521229	+	0.169001i
$694$	4.26112	+	4.26112i	0.161750	+	0.161750i
$695$	−7.77384	−	29.0124i	−0.294879	−	1.10050i
$696$	6.00118	−	4.78559i	0.227474	−	0.181397i
$697$	−29.7366	+	29.7366i	−1.12635	+	1.12635i
$698$	−26.1641	−	15.1059i	−0.990326	−	0.571765i
$699$	−13.5712	+	18.3875i	−0.513309	+	0.695481i
$700$	−1.35176	−	0.362202i	−0.0510916	−	0.0136900i
$701$	−15.7657			−0.595462			−0.297731	−	0.954650i	$-0.596230\pi$
$701$	−15.7657			−0.595462			−0.297731	+	0.954650i	$0.596230\pi$
$702$	−18.4689	−	9.33549i	−0.697065	−	0.352345i
$703$	−0.0268967			−0.00101443
$704$	−12.3104	−	3.29856i	−0.463965	−	0.124319i
$705$	−36.1885	+	49.0316i	−1.36294	+	1.84664i
$706$	26.5136	+	15.3076i	0.997853	+	0.576110i
$707$	−2.58794	+	2.58794i	−0.0973295	+	0.0973295i
$708$	1.68462	−	1.34339i	0.0633120	−	0.0504876i
$709$	−5.77258	−	21.5436i	−0.216794	−	0.809086i	−0.985527	−	0.169516i	$-0.945779\pi$
$709$	−5.77258	−	21.5436i	−0.216794	−	0.809086i	0.768734	−	0.639569i	$-0.220887\pi$
$710$	24.9429	+	24.9429i	0.936092	+	0.936092i
$711$	−3.72833	−	12.0886i	−0.139823	−	0.453359i
$712$	−1.86384	+	1.07609i	−0.0698503	+	0.0403281i
$713$	−5.66616	+	21.1464i	−0.212199	+	0.791939i
$714$	7.56128	−	3.29878i	0.282974	−	0.123454i
$715$	8.87364	+	11.5753i	0.331855	+	0.432891i
$716$			8.17360i			0.305462i
$717$	2.93021	+	19.4432i	0.109431	+	0.726120i
$718$	1.72532	+	2.98833i	0.0643882	+	0.111524i
$719$	21.3671	−	37.0088i	0.796857	−	1.38020i	−0.124796	−	0.992182i	$-0.539828\pi$
$719$	21.3671	−	37.0088i	0.796857	−	1.38020i	0.921653	−	0.388015i	$-0.126839\pi$
$720$	−0.535088	−	14.3154i	−0.0199416	−	0.533503i
$721$	17.3533	−	4.64979i	0.646269	−	0.173167i
$722$	−20.2718	+	5.43183i	−0.754440	+	0.202152i
$723$	37.7023	+	14.7979i	1.40216	+	0.550340i
$724$	4.71344	−	8.16392i	0.175174	−	0.303410i
$725$	−1.29483	−	2.24271i	−0.0480887	−	0.0832921i
$726$	−16.2537	+	2.44953i	−0.603233	+	0.0909108i
$727$		−	27.7622i		−	1.02964i	−0.857297	−	0.514822i	$-0.827858\pi$
$727$		−	27.7622i		−	1.02964i	0.857297	−	0.514822i	$-0.172142\pi$
$728$	−4.24147	+	10.2266i	−0.157199	+	0.379023i
$729$	21.1075	+	16.8367i	0.781759	+	0.623581i
$730$	5.23497	−	19.5372i	0.193755	−	0.723104i
$731$	37.0985	−	21.4189i	1.37214	−	0.792205i
$732$	−1.51985	+	13.4867i	−0.0561751	+	0.498481i
$733$	11.9570	+	11.9570i	0.441642	+	0.441642i	0.892564	−	0.450922i	$-0.148905\pi$
$733$	11.9570	+	11.9570i	0.441642	+	0.441642i	−0.450922	+	0.892564i	$0.648905\pi$
$734$	−1.79597	−	6.70266i	−0.0662905	−	0.247400i
$735$	2.81484	+	3.52984i	0.103827	+	0.130200i
$736$	−8.13469	+	8.13469i	−0.299849	+	0.299849i
$737$	−19.1225	−	11.0404i	−0.704386	−	0.406677i
$738$	7.19277	−	31.5079i	0.264769	−	1.15982i
$739$	−19.8061	−	5.30703i	−0.728579	−	0.195222i	−0.124583	−	0.992209i	$-0.539759\pi$
$739$	−19.8061	−	5.30703i	−0.728579	−	0.195222i	−0.603996	+	0.796987i	$0.706426\pi$
$740$	9.24625			0.339899
$741$	−0.00890660	+	0.0358401i	−0.000327192	+	0.00131662i
$742$	−1.27780			−0.0469093
$743$	−22.0160	−	5.89917i	−0.807689	−	0.216420i	−0.168732	−	0.985662i	$-0.553967\pi$
$743$	−22.0160	−	5.89917i	−0.807689	−	0.216420i	−0.638957	+	0.769242i	$0.720634\pi$
$744$	33.5317	+	24.7485i	1.22933	+	0.907324i
$745$	−24.4440	−	14.1128i	−0.895560	−	0.517052i
$746$	−8.04915	+	8.04915i	−0.294700	+	0.294700i
$747$	−19.4881	−	10.3007i	−0.713034	−	0.376885i
$748$	1.35076	+	5.04110i	0.0493886	+	0.184321i
$749$	−5.89395	−	5.89395i	−0.215360	−	0.215360i
$750$	15.8856	+	1.79019i	0.580062	+	0.0653686i
$751$	−1.22016	+	0.704461i	−0.0445243	+	0.0257061i	−0.522097	−	0.852886i	$-0.674850\pi$
$751$	−1.22016	+	0.704461i	−0.0445243	+	0.0257061i	0.477573	+	0.878592i	$0.341517\pi$
$752$	−6.39993	+	23.8849i	−0.233381	+	0.870991i
$753$	5.50318	+	12.6141i	0.200547	+	0.459683i
$754$	−5.31123	+	2.19714i	−0.193424	+	0.0800153i
$755$			60.1448i			2.18889i
$756$	2.28305	−	3.34821i	0.0830338	−	0.121773i
$757$	−6.57285	−	11.3845i	−0.238894	−	0.413777i	0.721503	−	0.692411i	$-0.243452\pi$
$757$	−6.57285	−	11.3845i	−0.238894	−	0.413777i	−0.960397	+	0.278634i	$0.910118\pi$
$758$	−8.73296	+	15.1259i	−0.317195	+	0.549399i
$759$	2.74375	−	6.99057i	0.0995920	−	0.253742i
$760$	−0.0457188	+	0.0122503i	−0.00165839	+	0.000444365i
$761$	−1.90846	+	0.511371i	−0.0691817	+	0.0185372i	−0.293244	−	0.956038i	$-0.594735\pi$
$761$	−1.90846	+	0.511371i	−0.0691817	+	0.0185372i	0.224062	+	0.974575i	$0.428068\pi$
$762$	−1.55041	+	3.95017i	−0.0561656	+	0.143099i
$763$	−2.36126	+	4.08982i	−0.0854834	+	0.148062i
$764$	−2.06589	−	3.57823i	−0.0747413	−	0.129456i
$765$	−28.5510	+	17.9382i	−1.03226	+	0.648558i
$766$			15.8708i			0.573437i
$767$	−5.31434	+	2.19843i	−0.191890	+	0.0793807i
$768$	10.7364	+	24.6093i	0.387415	+	0.888012i
$769$	5.95528	−	22.2254i	0.214753	−	0.801469i	−0.771500	−	0.636229i	$-0.780493\pi$
$769$	5.95528	−	22.2254i	0.214753	−	0.801469i	0.986253	−	0.165240i	$-0.0528399\pi$
$770$	3.86963	−	2.23413i	0.139452	−	0.0805124i
$771$	−51.9357	−	5.85277i	−1.87042	−	0.210782i
$772$	4.47071	+	4.47071i	0.160904	+	0.160904i
$773$	−6.27243	−	23.4090i	−0.225603	−	0.841964i	−0.982162	−	0.188037i	$-0.939787\pi$
$773$	−6.27243	−	23.4090i	−0.225603	−	0.841964i	0.756558	−	0.653926i	$-0.226879\pi$
$774$	−15.3840	+	29.1053i	−0.552968	+	1.04617i
$775$	9.94244	−	9.94244i	0.357143	−	0.357143i
$776$	6.72122	+	3.88050i	0.241278	+	0.139302i
$777$	−6.33844	−	4.67817i	−0.227390	−	0.167828i
$778$	−38.5731	−	10.3356i	−1.38291	−	0.370550i
$779$	−0.0576743			−0.00206640
$780$	3.06182	−	12.3207i	0.109631	−	0.441153i
$781$	19.0133			0.680350
$782$	−12.8532	−	3.44400i	−0.459629	−	0.123157i
$783$	7.36848	−	1.39375i	0.263328	−	0.0498085i
$784$	1.58650	+	0.915969i	0.0566609	+	0.0327132i
$785$	32.7260	−	32.7260i	1.16804	−	1.16804i
$786$	−4.79132	−	6.00837i	−0.170901	−	0.214311i
$787$	−1.34398	−	5.01579i	−0.0479076	−	0.178794i	0.937826	−	0.347105i	$-0.112835\pi$
$787$	−1.34398	−	5.01579i	−0.0479076	−	0.178794i	−0.985734	+	0.168311i	$0.946169\pi$
$788$	−4.28101	−	4.28101i	−0.152504	−	0.152504i
$789$	3.57241	−	31.7005i	0.127181	−	1.12857i
$790$	−10.5145	+	6.07055i	−0.374089	+	0.215981i
$791$	−1.97936	+	7.38706i	−0.0703778	+	0.262653i
$792$	−10.4793	−	9.72416i	−0.372367	−	0.345533i
$793$	13.8781	−	33.4616i	0.492828	−	1.18826i
$794$		−	20.0055i		−	0.709967i
$795$	5.16444	−	0.778311i	0.183164	−	0.0276039i
$796$	3.09946	+	5.36842i	0.109857	+	0.190279i
$797$	19.3260	−	33.4736i	0.684561	−	1.18569i	−0.289013	−	0.957325i	$-0.593327\pi$
$797$	19.3260	−	33.4736i	0.684561	−	1.18569i	0.973574	−	0.228370i	$-0.0733395\pi$
$798$	0.0105316	+	0.00413358i	0.000372814	+	0.000146327i
$799$	56.2192	−	15.0639i	1.98889	−	0.532922i
$800$	7.13698	−	1.91235i	0.252330	−	0.0676117i
$801$	−2.10121	+	0.0785401i	−0.0742425	+	0.00277508i
$802$	−10.2949	+	17.8313i	−0.363526	+	0.629645i
$803$	−5.45109	−	9.44157i	−0.192365	−	0.333186i
$804$	2.86420	+	19.0052i	0.101012	+	0.670262i
$805$		−	7.28237i		−	0.256670i
$806$	−18.9868	−	24.7675i	−0.668782	−	0.872398i
$807$	−27.4965	+	11.9960i	−0.967922	+	0.422278i
$808$	2.90866	−	10.8553i	0.102326	−	0.381886i
$809$	−1.06177	+	0.613016i	−0.0373300	+	0.0215525i	−0.518549	−	0.855048i	$-0.673528\pi$
$809$	−1.06177	+	0.613016i	−0.0373300	+	0.0215525i	0.481219	+	0.876600i	$0.340194\pi$
$810$	11.2449	−	23.3457i	0.395107	−	0.820286i
$811$	−8.02360	−	8.02360i	−0.281747	−	0.281747i	0.552059	−	0.833805i	$-0.313842\pi$
$811$	−8.02360	−	8.02360i	−0.281747	−	0.281747i	−0.833805	+	0.552059i	$0.813842\pi$
$812$	−0.291318	−	1.08721i	−0.0102233	−	0.0381537i
$813$	−27.1271	+	21.6323i	−0.951391	+	0.758678i
$814$	−5.51312	+	5.51312i	−0.193235	+	0.193235i
$815$	−6.35522	−	3.66919i	−0.222614	−	0.128526i
$816$	−8.12475	+	11.0082i	−0.284423	+	0.385364i
$817$	0.0567475	+	0.0152054i	0.00198534	+	0.000531971i
$818$	39.0536			1.36548
$819$	−8.33263	+	6.89690i	−0.291166	+	0.240997i
$820$	19.8267			0.692378
$821$	7.50392	+	2.01067i	0.261888	+	0.0701728i	0.387374	−	0.921923i	$-0.373382\pi$
$821$	7.50392	+	2.01067i	0.261888	+	0.0701728i	−0.125486	+	0.992095i	$0.540049\pi$
$822$	−4.50349	+	6.10176i	−0.157077	+	0.212823i
$823$	16.3362	+	9.43172i	0.569444	+	0.328769i	0.756927	−	0.653499i	$-0.226700\pi$
$823$	16.3362	+	9.43172i	0.569444	+	0.328769i	−0.187483	+	0.982268i	$0.560033\pi$
$824$	−39.0076	+	39.0076i	−1.35889	+	1.35889i
$825$	−3.77103	+	3.00718i	−0.131290	+	0.104697i
$826$	0.456009	+	1.70185i	0.0158666	+	0.0592148i
$827$	28.6638	+	28.6638i	0.996738	+	0.996738i	0.999995	−	0.00325631i	$-0.00103652\pi$
$827$	28.6638	+	28.6638i	0.996738	+	0.996738i	−0.00325631	+	0.999995i	$0.501037\pi$
$828$	−6.24640	+	1.92649i	−0.217077	+	0.0669503i
$829$	8.24532	−	4.76044i	0.286372	−	0.165337i	−0.349933	−	0.936775i	$-0.613796\pi$
$829$	8.24532	−	4.76044i	0.286372	−	0.165337i	0.636304	+	0.771438i	$0.280462\pi$
$830$	−5.47541	+	20.4345i	−0.190054	+	0.709292i
$831$	−48.1973	+	21.0272i	−1.67195	+	0.729424i
$832$	−3.85143	−	29.3581i	−0.133524	−	1.01781i
$833$		−	4.31194i		−	0.149400i
$834$	−3.28531	−	21.7995i	−0.113761	−	0.754853i
$835$	−15.0779	−	26.1156i	−0.521791	−	0.903768i
$836$	−0.00357872	+	0.00619853i	−0.000123773	+	0.000214381i
$837$	17.6644	+	36.6859i	0.610569	+	1.26805i
$838$	0.896339	−	0.240173i	0.0309635	−	0.00829665i
$839$	31.6174	−	8.47186i	1.09155	−	0.292481i	0.332234	−	0.943197i	$-0.392198\pi$
$839$	31.6174	−	8.47186i	1.09155	−	0.292481i	0.759321	+	0.650716i	$0.225531\pi$
$840$	−12.9047	−	5.06503i	−0.445256	−	0.174760i
$841$	−13.4586	+	23.3109i	−0.464089	+	0.803825i
$842$	−14.7385	−	25.5278i	−0.507922	−	0.879747i
$843$	−29.5591	+	4.45474i	−1.01807	+	0.153429i
$844$		−	8.00433i		−	0.275521i
$845$	−16.9697	+	29.3305i	−0.583775	+	1.00900i
$846$	−30.4245	+	32.7873i	−1.04602	+	1.12725i
$847$	−2.22366	+	8.29882i	−0.0764059	+	0.285151i
$848$	1.83529	−	1.05961i	0.0630243	−	0.0363871i
$849$	4.76058	−	42.2439i	0.163383	−	1.44981i
$850$	6.04320	+	6.04320i	0.207280	+	0.207280i
$851$	3.28884	+	12.2741i	0.112740	+	0.420752i
$852$	−10.3184	−	12.9394i	−0.353503	−	0.443296i
$853$	−6.48798	+	6.48798i	−0.222144	+	0.222144i	−0.809401	−	0.587257i	$-0.800208\pi$
$853$	−6.48798	+	6.48798i	−0.222144	+	0.222144i	0.587257	+	0.809401i	$0.300208\pi$
$854$	−9.61102	−	5.54892i	−0.328882	−	0.189880i
$855$	−0.0450831	−	0.0102918i	−0.00154181	−	0.000351971i
$856$	24.7225	+	6.62436i	0.844996	+	0.226416i
$857$	−48.8055			−1.66716			−0.833582	−	0.552396i	$-0.813714\pi$
$857$	−48.8055			−1.66716			−0.833582	+	0.552396i	$0.813714\pi$
$858$	5.52067	+	9.17192i	0.188473	+	0.313124i
$859$	−12.3805			−0.422417			−0.211209	−	0.977441i	$-0.567740\pi$
$859$	−12.3805			−0.422417			−0.211209	+	0.977441i	$0.567740\pi$
$860$	−19.5081	−	5.22717i	−0.665219	−	0.178245i
$861$	−13.5915	−	10.0314i	−0.463196	−	0.341868i
$862$	−15.3141	−	8.84161i	−0.521601	−	0.301146i
$863$	34.1599	−	34.1599i	1.16282	−	1.16282i	0.178959	−	0.983857i	$-0.442727\pi$
$863$	34.1599	−	34.1599i	1.16282	−	1.16282i	0.983857	−	0.178959i	$-0.0572730\pi$
$864$	−1.60019	+	21.3364i	−0.0544397	+	0.725880i
$865$	−5.82298	−	21.7316i	−0.197987	−	0.738898i
$866$	5.46878	+	5.46878i	0.185837	+	0.185837i
$867$	2.74147	+	0.308943i	0.0931052	+	0.0104923i
$868$	5.29258	−	3.05567i	0.179642	−	0.103716i
$869$	−1.69375	+	6.32117i	−0.0574566	+	0.214431i
$870$	−2.87796	−	6.59670i	−0.0975720	−	0.223649i
$871$	6.71922	−	50.8582i	0.227672	−	1.72326i
$872$		−	14.5011i		−	0.491069i
$873$	4.03388	+	6.42043i	0.136526	+	0.217299i
$874$	−0.00912460	−	0.0158043i	−0.000308644	−	0.000534587i
$875$	4.17790	−	7.23633i	0.141239	−	0.244633i
$876$	−3.46712	+	8.83358i	−0.117143	+	0.298459i
$877$	5.39979	−	1.44687i	0.182338	−	0.0488573i	−0.166495	−	0.986042i	$-0.553245\pi$
$877$	5.39979	−	1.44687i	0.182338	−	0.0488573i	0.348833	+	0.937185i	$0.386578\pi$
$878$	5.06128	−	1.35617i	0.170810	−	0.0457684i
$879$	−11.1049	+	28.2933i	−0.374560	+	0.954309i
$880$	−3.70529	+	6.41775i	−0.124905	+	0.216342i
$881$	23.1247	+	40.0531i	0.779090	+	1.34942i	0.932467	+	0.361255i	$0.117652\pi$
$881$	23.1247	+	40.0531i	0.779090	+	1.34942i	−0.153377	+	0.988168i	$0.549015\pi$
$882$	1.76291	+	2.80589i	0.0593601	+	0.0944792i
$883$		−	38.1738i		−	1.28465i	−0.766432	−	0.642325i	$-0.777970\pi$
$883$		−	38.1738i		−	1.28465i	0.766432	−	0.642325i	$-0.222030\pi$
$884$	−9.62287	+	7.37691i	−0.323652	+	0.248112i
$885$	−2.87964	−	6.60056i	−0.0967982	−	0.221876i
$886$	−9.16439	+	34.2020i	−0.307884	+	1.14904i
$887$	30.9055	−	17.8433i	1.03771	−	0.599120i	0.118523	−	0.992951i	$-0.462184\pi$
$887$	30.9055	−	17.8433i	1.03771	−	0.599120i	0.919183	+	0.393831i	$0.128851\pi$
$888$	24.0379	+	2.70889i	0.806658	+	0.0909044i
$889$	1.56840	+	1.56840i	0.0526023	+	0.0526023i
$890$	0.522298	+	1.94924i	0.0175075	+	0.0653388i
$891$	−4.61205	−	13.1838i	−0.154510	−	0.441673i
$892$	−4.52479	+	4.52479i	−0.151501	+	0.151501i
$893$	0.0691271	+	0.0399105i	0.00231325	+	0.00133555i
$894$	−16.6685	−	12.3024i	−0.557479	−	0.411455i
$895$	26.3870	+	7.07038i	0.882021	+	0.236337i
$896$	−0.835599			−0.0279154
$897$	17.4445	−	0.317946i	0.582454	−	0.0106159i
$898$	−30.2827			−1.01055
$899$	10.9237	+	2.92698i	0.364324	+	0.0976204i
$900$	4.09303	+	0.934374i	0.136434	+	0.0311458i
$901$	−4.31984	−	2.49406i	−0.143915	−	0.0830892i
$902$	−11.8218	+	11.8218i	−0.393621	+	0.393621i
$903$	10.7284	+	13.4535i	0.357017	+	0.447703i
$904$	−6.07786	−	22.6829i	−0.202147	−	0.754421i
$905$	−22.2785	−	22.2785i	−0.740563	−	0.740563i
$906$	−4.94351	+	43.8672i	−0.164237	+	1.45739i
$907$	−32.4659	+	18.7442i	−1.07801	+	0.622390i	−0.930359	−	0.366649i	$-0.880505\pi$
$907$	−32.4659	+	18.7442i	−1.07801	+	0.622390i	−0.147652	+	0.989039i	$0.547172\pi$
$908$	2.49321	−	9.30480i	0.0827402	−	0.308791i
$909$	7.46841	−	8.04840i	0.247711	−	0.266949i
$910$	8.23299	+	6.32337i	0.272921	+	0.209618i
$911$		−	47.7033i		−	1.58048i	−0.612796	−	0.790241i	$-0.709955\pi$
$911$		−	47.7033i		−	1.58048i	0.612796	−	0.790241i	$-0.290045\pi$
$912$	−0.0185543	+	0.00279624i	−0.000614393	+	9.25927e-5i
$913$	5.70146	+	9.87522i	0.188691	+	0.326822i
$914$	−13.7634	+	23.8388i	−0.455251	+	0.788519i
$915$	42.2245	+	16.5729i	1.39590	+	0.547882i
$916$	1.56251	−	0.418673i	0.0516268	−	0.0138333i
$917$	−3.87992	+	1.03962i	−0.128126	+	0.0343314i
$918$	−22.2984	+	10.7367i	−0.735956	+	0.354365i
$919$	8.58476	−	14.8692i	0.283185	−	0.490491i	−0.688982	−	0.724778i	$-0.741942\pi$
$919$	8.58476	−	14.8692i	0.283185	−	0.490491i	0.972167	+	0.234287i	$0.0752756\pi$
$920$	11.1807	+	19.3656i	0.368617	+	0.638464i
$921$	4.78258	+	31.7345i	0.157591	+	1.04569i
$922$		−	11.1180i		−	0.366150i
$923$	16.8859	+	40.8188i	0.555805	+	1.34357i
$924$	−1.92148	+	0.838287i	−0.0632119	+	0.0275776i
$925$	2.11231	−	7.88326i	0.0694524	−	0.259200i
$926$	−26.0193	+	15.0223i	−0.855049	+	0.493663i
$927$	−51.5024	+	15.8842i	−1.69156	+	0.521706i
$928$	4.20216	+	4.20216i	0.137943	+	0.137943i
$929$	0.409533	+	1.52840i	0.0134363	+	0.0501451i	0.972319	−	0.233659i	$-0.0750700\pi$
$929$	0.409533	+	1.52840i	0.0134363	+	0.0501451i	−0.958882	+	0.283804i	$0.908403\pi$
$930$	30.5525	−	24.3638i	1.00186	−	0.798922i
$931$	0.00418152	−	0.00418152i	0.000137044	−	0.000137044i
$932$	−8.91175	−	5.14520i	−0.291914	−	0.168537i
$933$	32.3147	−	43.7831i	1.05794	−	1.43340i
$934$	40.5844	+	10.8746i	1.32796	+	0.355827i
$935$	17.4427			0.570438
$936$	11.5696	−	31.1337i	0.378163	−	1.01764i
$937$	16.8424			0.550217			0.275109	−	0.961413i	$-0.411286\pi$
$937$	16.8424			0.550217			0.275109	+	0.961413i	$0.411286\pi$
$938$	−15.1805	−	4.06762i	−0.495662	−	0.132812i
$939$	21.3638	−	28.9458i	0.697182	−	0.944609i
$940$	−23.7638	−	13.7200i	−0.775089	−	0.447498i
$941$	25.9171	−	25.9171i	0.844873	−	0.844873i	−0.144615	−	0.989488i	$-0.546194\pi$
$941$	25.9171	−	25.9171i	0.844873	−	0.844873i	0.989488	+	0.144615i	$0.0461943\pi$
$942$	26.5589	−	21.1792i	0.865336	−	0.690055i
$943$	7.05225	+	26.3193i	0.229653	+	0.857076i
$944$	−2.06622	−	2.06622i	−0.0672496	−	0.0672496i
$945$	−8.83418	−	10.2667i	−0.287376	−	0.333976i
$946$	14.7485	−	8.51505i	0.479515	−	0.276848i
$947$	−1.79821	+	6.71101i	−0.0584339	+	0.218078i	−0.988969	−	0.148125i	$-0.952676\pi$
$947$	−1.79821	+	6.71101i	−0.0584339	+	0.218078i	0.930535	+	0.366204i	$0.119343\pi$
$948$	5.22102	−	2.27779i	0.169571	−	0.0739790i
$949$	15.4285	−	20.0878i	0.500830	−	0.652078i
$950$			0.0117208i			0.000380274i
$951$	2.09784	+	13.9201i	0.0680270	+	0.451389i
$952$	6.62017	+	11.4665i	0.214561	+	0.371631i
$953$	−27.0528	+	46.8568i	−0.876325	+	1.51784i	−0.0209813	+	0.999780i	$0.506679\pi$
$953$	−27.0528	+	46.8568i	−0.876325	+	1.51784i	−0.855344	+	0.518060i	$0.826654\pi$
$954$	3.83071	−	0.143186i	0.124024	−	0.00463583i
$955$	−13.3387	+	3.57410i	−0.431631	+	0.115655i
$956$	−8.55204	+	2.29151i	−0.276593	+	0.0741128i
$957$	−3.61114	−	1.41735i	−0.116732	−	0.0458164i
$958$	16.1290	−	27.9363i	0.521104	−	0.902579i
$959$	1.98196	+	3.43286i	0.0640009	+	0.110853i
$960$	36.6623	−	5.52523i	1.18327	−	0.178326i
$961$			30.4030i			0.980743i
$962$	−16.7321	−	6.93961i	−0.539465	−	0.223742i
$963$	18.3300	+	17.0090i	0.590675	+	0.548109i
$964$	−4.72018	+	17.6159i	−0.152027	+	0.567371i
$965$	18.3001	−	10.5656i	0.589103	−	0.340119i
$966$	0.598564	−	5.31147i	0.0192585	−	0.170894i
$967$	34.2743	+	34.2743i	1.10219	+	1.10219i	0.994146	+	0.108041i	$0.0344578\pi$
$967$	34.2743	+	34.2743i	1.10219	+	1.10219i	0.108041	+	0.994146i	$0.465542\pi$
$968$	−6.82803	−	25.4826i	−0.219461	−	0.819041i
$969$	0.0275360	+	0.0345304i	0.000884584	+	0.00110928i
$970$	5.14573	−	5.14573i	0.165219	−	0.165219i
$971$	−1.38163	−	0.797687i	−0.0443388	−	0.0255990i	0.477667	−	0.878541i	$-0.341483\pi$
$971$	−1.38163	−	0.797687i	−0.0443388	−	0.0255990i	−0.522006	+	0.852942i	$0.674816\pi$
$972$	−6.46919	+	10.2934i	−0.207499	+	0.330162i
$973$	−11.1303	−	2.98237i	−0.356823	−	0.0956103i
$974$	11.9364			0.382466
$975$	−9.80505	−	5.42515i	−0.314013	−	0.173744i
$976$	18.4057			0.589152
$977$	−40.5959	−	10.8776i	−1.29878	−	0.348007i	−0.457791	−	0.889060i	$-0.651359\pi$
$977$	−40.5959	−	10.8776i	−1.29878	−	0.348007i	−0.840988	+	0.541053i	$0.818026\pi$
$978$	−4.33366	−	3.19852i	−0.138575	−	0.102277i
$979$	0.941995	+	0.543861i	0.0301063	+	0.0173819i
$980$	−1.43748	+	1.43748i	−0.0459186	+	0.0459186i
$981$	6.62055	−	12.5255i	0.211378	−	0.399909i
$982$	−4.76785	−	17.7938i	−0.152148	−	0.567824i
$983$	24.8338	+	24.8338i	0.792076	+	0.792076i	0.981831	−	0.189756i	$-0.0607696\pi$
$983$	24.8338	+	24.8338i	0.792076	+	0.792076i	−0.189756	+	0.981831i	$0.560770\pi$
$984$	51.5443	+	5.80866i	1.64317	+	0.185173i
$985$	−17.5236	+	10.1173i	−0.558350	+	0.322363i
$986$	−1.77908	+	6.63961i	−0.0566574	+	0.211448i
$987$	9.34872	+	21.4286i	0.297573	+	0.682081i
$988$	−0.0164856	−	0.00217803i	−0.000524477	−	6.92923e-5i
$989$		−	27.7557i		−	0.882579i
$990$	−11.3504	+	7.13133i	−0.360740	+	0.226649i
$991$	−3.07746	−	5.33031i	−0.0977587	−	0.169323i	0.812998	−	0.582267i	$-0.197834\pi$
$991$	−3.07746	−	5.33031i	−0.0977587	−	0.169323i	−0.910757	+	0.412944i	$0.864501\pi$
$992$	−16.1333	+	27.9437i	−0.512232	+	0.887212i
$993$	−19.6398	+	50.0385i	−0.623250	+	1.58793i
$994$	13.0717	−	3.50255i	0.414609	−	0.111094i
$995$	20.0121	−	5.36222i	0.634426	−	0.169994i
$996$	3.62636	−	9.23930i	0.114906	−	0.292758i
$997$	−14.2460	+	24.6747i	−0.451174	+	0.781456i	−0.998459	−	0.0554900i	$-0.982328\pi$
$997$	−14.2460	+	24.6747i	−0.451174	+	0.781456i	0.547285	+	0.836946i	$0.315661\pi$
$998$	−1.39954	−	2.42408i	−0.0443018	−	0.0767330i
$999$	19.5263	+	13.3144i	0.617784	+	0.421250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.20	yes	112
3.2	odd	2	inner	273.2.cc.a.50.9	✓	112
13.6	odd	12	inner	273.2.cc.a.71.9	yes	112
39.32	even	12	inner	273.2.cc.a.71.20	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.9	✓	112	3.2	odd	2	inner
273.2.cc.a.50.20	yes	112	1.1	even	1	trivial
273.2.cc.a.71.9	yes	112	13.6	odd	12	inner
273.2.cc.a.71.20	yes	112	39.32	even	12	inner

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06694 + 0.285886i) q^{2} +(-1.02855 + 1.39358i) q^{3} +(-0.675418 - 0.389953i) q^{4} +(-1.84315 + 1.84315i) q^{5} +(-1.49581 + 1.19282i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.17126 - 2.17126i) q^{8} +(-0.884154 - 2.86675i) q^{9} +O(q^{10})\)	\(q+(1.06694 + 0.285886i) q^{2} +(-1.02855 + 1.39358i) q^{3} +(-0.675418 - 0.389953i) q^{4} +(-1.84315 + 1.84315i) q^{5} +(-1.49581 + 1.19282i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.17126 - 2.17126i) q^{8} +(-0.884154 - 2.86675i) q^{9} +(-2.49346 + 1.43960i) q^{10} +(-0.401664 + 1.49903i) q^{11} +(1.23814 - 0.540164i) q^{12} +(-3.57492 + 0.468987i) q^{13} +1.10458i q^{14} +(-0.672805 - 4.46435i) q^{15} +(-0.915969 - 1.58650i) q^{16} +(-2.15597 + 3.73425i) q^{17} +(-0.123776 - 3.31142i) q^{18} +(-0.00571206 + 0.00153054i) q^{19} +(1.96363 - 0.526154i) q^{20} +(-1.61231 - 0.632820i) q^{21} +(-0.857104 + 1.48455i) q^{22} +(1.39691 + 2.41952i) q^{23} +(5.25909 - 0.792576i) q^{24} -1.79437i q^{25} +(-3.94831 - 0.521638i) q^{26} +(4.90446 + 1.71647i) q^{27} +(0.201854 - 0.753331i) q^{28} +(1.24986 - 0.721605i) q^{29} +(0.558454 - 4.95555i) q^{30} +(5.54090 + 5.54090i) q^{31} +(1.06575 + 3.97742i) q^{32} +(-1.67589 - 2.10159i) q^{33} +(-3.36786 + 3.36786i) q^{34} +(-2.25738 - 1.30330i) q^{35} +(-0.520724 + 2.28103i) q^{36} +(4.39332 + 1.17719i) q^{37} -0.00653200 q^{38} +(3.02342 - 5.46433i) q^{39} +8.00390 q^{40} +(9.42057 + 2.52423i) q^{41} +(-1.53932 - 1.13612i) q^{42} +(-8.60368 - 4.96734i) q^{43} +(0.855842 - 0.855842i) q^{44} +(6.91347 + 3.65422i) q^{45} +(0.798713 + 2.98084i) q^{46} +(-9.54450 - 9.54450i) q^{47} +(3.15305 + 0.355325i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.512986 - 1.91449i) q^{50} +(-2.98646 - 6.84540i) q^{51} +(2.59745 + 1.07729i) q^{52} +1.15682i q^{53} +(4.74206 + 3.23349i) q^{54} +(-2.02261 - 3.50326i) q^{55} +(1.53531 - 2.65924i) q^{56} +(0.00374222 - 0.00953449i) q^{57} +(1.53982 - 0.412593i) q^{58} +(1.54072 - 0.412835i) q^{59} +(-1.28646 + 3.27767i) q^{60} +(-5.02356 + 8.70107i) q^{61} +(4.32775 + 7.49588i) q^{62} +(2.54023 - 1.59600i) q^{63} +8.21223i q^{64} +(5.72469 - 7.45351i) q^{65} +(-1.18727 - 2.72138i) q^{66} +(-3.68250 + 13.7433i) q^{67} +(2.91236 - 1.68145i) q^{68} +(-4.80859 - 0.541893i) q^{69} +(-2.03590 - 2.03590i) q^{70} +(-3.17093 - 11.8341i) q^{71} +(-4.30474 + 8.14419i) q^{72} +(-4.96743 + 4.96743i) q^{73} +(4.35087 + 2.51198i) q^{74} +(2.50061 + 1.84561i) q^{75} +(0.00445487 + 0.00119368i) q^{76} -1.55191 q^{77} +(4.78799 - 4.96577i) q^{78} +4.21684 q^{79} +(4.61242 + 1.23589i) q^{80} +(-7.43654 + 5.06930i) q^{81} +(9.32955 + 5.38642i) q^{82} +(5.19558 - 5.19558i) q^{83} +(0.842212 + 1.05614i) q^{84} +(-2.90900 - 10.8565i) q^{85} +(-7.75953 - 7.75953i) q^{86} +(-0.279927 + 2.48399i) q^{87} +(4.12690 - 2.38267i) q^{88} +(0.181404 - 0.677010i) q^{89} +(6.33158 + 5.87530i) q^{90} +(-1.37826 - 3.33172i) q^{91} -2.17891i q^{92} +(-13.4208 + 2.02260i) q^{93} +(-7.45478 - 12.9121i) q^{94} +(0.00770715 - 0.0133492i) q^{95} +(-6.63905 - 2.60578i) q^{96} +(-2.44137 + 0.654164i) q^{97} +(-1.06694 + 0.285886i) q^{98} +(4.65248 - 0.173903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

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