LMFDB - Embedded newform 273.2.bh.a.248.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			248.6
Character	$\chi$	$=$	273.248
Dual form			273.2.bh.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71340 + 0.989233i) q^{2} +(-1.24374 + 1.20545i) q^{3} +(0.957162 - 1.65785i) q^{4} +(-0.830302 - 1.43813i) q^{5} +(0.938561 - 3.29577i) q^{6} +(2.61452 + 0.405294i) q^{7} -0.169506i q^{8} +(0.0937900 - 2.99853i) q^{9} +O(q^{10})$	\(q+(-1.71340 + 0.989233i) q^{2} +(-1.24374 + 1.20545i) q^{3} +(0.957162 - 1.65785i) q^{4} +(-0.830302 - 1.43813i) q^{5} +(0.938561 - 3.29577i) q^{6} +(2.61452 + 0.405294i) q^{7} -0.169506i q^{8} +(0.0937900 - 2.99853i) q^{9} +(2.84528 + 1.64272i) q^{10} +(3.87356 + 2.23640i) q^{11} +(0.807993 + 3.21575i) q^{12} -1.00000i q^{13} +(-4.88066 + 1.89194i) q^{14} +(2.76627 + 0.787772i) q^{15} +(2.08201 + 3.60614i) q^{16} +(1.83031 - 3.17019i) q^{17} +(2.80555 + 5.23047i) q^{18} +(-6.48934 + 3.74662i) q^{19} -3.17894 q^{20} +(-3.74036 + 2.64759i) q^{21} -8.84927 q^{22} +(2.05223 - 1.18486i) q^{23} +(0.204331 + 0.210822i) q^{24} +(1.12120 - 1.94197i) q^{25} +(0.989233 + 1.71340i) q^{26} +(3.49793 + 3.84246i) q^{27} +(3.17444 - 3.94657i) q^{28} +9.21663i q^{29} +(-5.51902 + 1.38671i) q^{30} +(8.16879 + 4.71625i) q^{31} +(-6.84103 - 3.94967i) q^{32} +(-7.51357 + 1.88787i) q^{33} +7.24240i q^{34} +(-1.58798 - 4.09653i) q^{35} +(-4.88136 - 3.02557i) q^{36} +(-1.46979 - 2.54575i) q^{37} +(7.41256 - 12.8389i) q^{38} +(1.20545 + 1.24374i) q^{39} +(-0.243771 + 0.140741i) q^{40} +0.239057 q^{41} +(3.78964 - 8.23647i) q^{42} +8.76234 q^{43} +(7.41524 - 4.28119i) q^{44} +(-4.39014 + 2.35481i) q^{45} +(-2.34419 + 4.06026i) q^{46} +(-1.89098 - 3.27527i) q^{47} +(-6.93649 - 1.97536i) q^{48} +(6.67147 + 2.11930i) q^{49} +4.43649i q^{50} +(1.54506 + 6.14924i) q^{51} +(-1.65785 - 0.957162i) q^{52} +(8.34639 + 4.81879i) q^{53} +(-9.79444 - 3.12342i) q^{54} -7.42755i q^{55} +(0.0686999 - 0.443178i) q^{56} +(3.55471 - 12.4824i) q^{57} +(-9.11740 - 15.7918i) q^{58} +(0.145711 - 0.252379i) q^{59} +(3.95378 - 3.83204i) q^{60} +(6.89332 - 3.97986i) q^{61} -18.6619 q^{62} +(1.46050 - 7.80173i) q^{63} +7.30054 q^{64} +(-1.43813 + 0.830302i) q^{65} +(11.0062 - 10.6673i) q^{66} +(-0.989788 + 1.71436i) q^{67} +(-3.50380 - 6.06877i) q^{68} +(-1.12416 + 3.94751i) q^{69} +(6.77327 + 5.44812i) q^{70} -3.23478i q^{71} +(-0.508270 - 0.0158980i) q^{72} +(-7.09914 - 4.09869i) q^{73} +(5.03667 + 2.90792i) q^{74} +(0.946463 + 3.76685i) q^{75} +14.3445i q^{76} +(9.22110 + 7.41705i) q^{77} +(-3.29577 - 0.938561i) q^{78} +(-3.44782 - 5.97180i) q^{79} +(3.45739 - 5.98837i) q^{80} +(-8.98241 - 0.562465i) q^{81} +(-0.409600 + 0.236483i) q^{82} +2.91828 q^{83} +(0.809193 + 8.73514i) q^{84} -6.07884 q^{85} +(-15.0134 + 8.66799i) q^{86} +(-11.1102 - 11.4631i) q^{87} +(0.379083 - 0.656592i) q^{88} +(1.32756 + 2.29940i) q^{89} +(5.19262 - 8.37760i) q^{90} +(0.405294 - 2.61452i) q^{91} -4.53639i q^{92} +(-15.8451 + 3.98125i) q^{93} +(6.48001 + 3.74123i) q^{94} +(10.7762 + 6.22165i) q^{95} +(13.2696 - 3.33413i) q^{96} +2.45844i q^{97} +(-13.5274 + 2.96842i) q^{98} +(7.06922 - 11.4052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.71340	+	0.989233i	−1.21156	+	0.699493i	−0.963098	−	0.269149i	$-0.913257\pi$
$2$	−1.71340	+	0.989233i	−1.21156	+	0.699493i	−0.248459	+	0.968642i	$0.579924\pi$
$3$	−1.24374	+	1.20545i	−0.718075	+	0.695966i
$3$	−1.24374	+	1.20545i	−0.718075	+	0.695966i
$4$	0.957162	−	1.65785i	0.478581	−	0.828927i
$5$	−0.830302	−	1.43813i	−0.371323	−	0.643150i	0.618447	−	0.785827i	$-0.287762\pi$
$5$	−0.830302	−	1.43813i	−0.371323	−	0.643150i	−0.989769	+	0.142677i	$0.954429\pi$
$6$	0.938561	−	3.29577i	0.383166	−	1.34549i
$7$	2.61452	+	0.405294i	0.988197	+	0.153187i
$7$	2.61452	+	0.405294i	0.988197	+	0.153187i
$8$		−	0.169506i		−	0.0599295i
$9$	0.0937900	−	2.99853i	0.0312633	−	0.999511i
$10$	2.84528	+	1.64272i	0.899757	+	0.519475i
$11$	3.87356	+	2.23640i	1.16792	+	0.674299i	0.953189	−	0.302374i	$-0.0977791\pi$
$11$	3.87356	+	2.23640i	1.16792	+	0.674299i	0.214731	+	0.976673i	$0.431112\pi$
$12$	0.807993	+	3.21575i	0.233248	+	0.928308i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−4.88066	+	1.89194i	−1.30441	+	0.505643i
$15$	2.76627	+	0.787772i	0.714247	+	0.203402i
$16$	2.08201	+	3.60614i	0.520501	+	0.901535i
$17$	1.83031	−	3.17019i	0.443915	−	0.768883i	−0.554061	−	0.832476i	$-0.686923\pi$
$17$	1.83031	−	3.17019i	0.443915	−	0.768883i	0.997976	+	0.0635927i	$0.0202558\pi$
$18$	2.80555	+	5.23047i	0.661274	+	1.23283i
$19$	−6.48934	+	3.74662i	−1.48876	+	0.859533i	−0.999918	−	0.0128411i	$-0.995912\pi$
$19$	−6.48934	+	3.74662i	−1.48876	+	0.859533i	−0.488838	+	0.872375i	$0.662579\pi$
$20$	−3.17894			−0.710832
$21$	−3.74036	+	2.64759i	−0.816212	+	0.577752i
$22$	−8.84927			−1.88667
$23$	2.05223	−	1.18486i	0.427919	−	0.247059i	−0.270540	−	0.962709i	$-0.587202\pi$
$23$	2.05223	−	1.18486i	0.427919	−	0.247059i	0.698460	+	0.715649i	$0.253869\pi$
$24$	0.204331	+	0.210822i	0.0417089	+	0.0430339i
$25$	1.12120	−	1.94197i	0.224239	−	0.388394i
$26$	0.989233	+	1.71340i	0.194004	+	0.336026i
$27$	3.49793	+	3.84246i	0.673176	+	0.739482i
$28$	3.17444	−	3.94657i	0.599913	−	0.745831i
$29$			9.21663i			1.71149i	0.517401	+	0.855743i	$0.326900\pi$
$29$			9.21663i			1.71149i	−0.517401	+	0.855743i	$0.673100\pi$
$30$	−5.51902	+	1.38671i	−1.00763	+	0.253178i
$31$	8.16879	+	4.71625i	1.46716	+	0.847064i	0.999324	−	0.0367524i	$-0.0117013\pi$
$31$	8.16879	+	4.71625i	1.46716	+	0.847064i	0.467834	+	0.883817i	$0.345035\pi$
$32$	−6.84103	−	3.94967i	−1.20933	−	0.698209i
$33$	−7.51357	+	1.88787i	−1.30794	+	0.328635i
$34$			7.24240i			1.24206i
$35$	−1.58798	−	4.09653i	−0.268418	−	0.692440i
$36$	−4.88136	−	3.02557i	−0.813560	−	0.504262i
$37$	−1.46979	−	2.54575i	−0.241632	−	0.418518i	0.719548	−	0.694443i	$-0.244349\pi$
$37$	−1.46979	−	2.54575i	−0.241632	−	0.418518i	−0.961179	+	0.275925i	$0.911016\pi$
$38$	7.41256	−	12.8389i	1.20248	−	2.08275i
$39$	1.20545	+	1.24374i	0.193026	+	0.199158i
$40$	−0.243771	+	0.140741i	−0.0385436	+	0.0222532i
$41$	0.239057			0.0373344			0.0186672	−	0.999826i	$-0.494058\pi$
$41$	0.239057			0.0373344			0.0186672	+	0.999826i	$0.494058\pi$
$42$	3.78964	−	8.23647i	0.584755	−	1.27091i
$43$	8.76234			1.33624			0.668122	−	0.744052i	$-0.267098\pi$
$43$	8.76234			1.33624			0.668122	+	0.744052i	$0.267098\pi$
$44$	7.41524	−	4.28119i	1.11789	−	0.645414i
$45$	−4.39014	+	2.35481i	−0.654444	+	0.351034i
$46$	−2.34419	+	4.06026i	−0.345633	+	0.598653i
$47$	−1.89098	−	3.27527i	−0.275828	−	0.477747i	0.694516	−	0.719477i	$-0.255619\pi$
$47$	−1.89098	−	3.27527i	−0.275828	−	0.477747i	−0.970344	+	0.241730i	$0.922285\pi$
$48$	−6.93649	−	1.97536i	−1.00120	−	0.285118i
$49$	6.67147	+	2.11930i	0.953068	+	0.302757i
$50$			4.43649i			0.627415i
$51$	1.54506	+	6.14924i	0.216352	+	0.861066i
$52$	−1.65785	−	0.957162i	−0.229903	−	0.132735i
$53$	8.34639	+	4.81879i	1.14646	+	0.661912i	0.948023	−	0.318201i	$-0.103079\pi$
$53$	8.34639	+	4.81879i	1.14646	+	0.661912i	0.198441	+	0.980113i	$0.436412\pi$
$54$	−9.79444	−	3.12342i	−1.33285	−	0.425043i
$55$		−	7.42755i		−	1.00153i
$56$	0.0686999	−	0.443178i	0.00918040	−	0.0592222i
$57$	3.55471	−	12.4824i	0.470832	−	1.65333i
$58$	−9.11740	−	15.7918i	−1.19717	−	2.07356i
$59$	0.145711	−	0.252379i	0.0189700	−	0.0328570i	−0.856385	−	0.516339i	$-0.827295\pi$
$59$	0.145711	−	0.252379i	0.0189700	−	0.0328570i	0.875355	+	0.483482i	$0.160628\pi$
$60$	3.95378	−	3.83204i	0.510431	−	0.494715i
$61$	6.89332	−	3.97986i	0.882599	−	0.509569i	0.0110847	−	0.999939i	$-0.496472\pi$
$61$	6.89332	−	3.97986i	0.882599	−	0.509569i	0.871515	+	0.490370i	$0.163138\pi$
$62$	−18.6619			−2.37006
$63$	1.46050	−	7.80173i	0.184006	−	0.982925i
$64$	7.30054			0.912568
$65$	−1.43813	+	0.830302i	−0.178378	+	0.102986i
$66$	11.0062	−	10.6673i	1.35477	−	1.31306i
$67$	−0.989788	+	1.71436i	−0.120922	+	0.209443i	−0.920131	−	0.391610i	$-0.871918\pi$
$67$	−0.989788	+	1.71436i	−0.120922	+	0.209443i	0.799210	+	0.601052i	$0.205252\pi$
$68$	−3.50380	−	6.06877i	−0.424899	−	0.735946i
$69$	−1.12416	+	3.94751i	−0.135333	+	0.475224i
$70$	6.77327	+	5.44812i	0.809561	+	0.651175i
$71$		−	3.23478i		−	0.383898i	−0.981405	−	0.191949i	$-0.938519\pi$
$71$		−	3.23478i		−	0.383898i	0.981405	−	0.191949i	$-0.0614807\pi$
$72$	−0.508270	−	0.0158980i	−0.0599002	−	0.00187360i
$73$	−7.09914	−	4.09869i	−0.830892	−	0.479716i	0.0232660	−	0.999729i	$-0.492594\pi$
$73$	−7.09914	−	4.09869i	−0.830892	−	0.479716i	−0.854158	+	0.520014i	$0.825927\pi$
$74$	5.03667	+	2.90792i	0.585501	+	0.338039i
$75$	0.946463	+	3.76685i	0.109288	+	0.434958i
$76$			14.3445i			1.64543i
$77$	9.22110	+	7.41705i	1.05084	+	0.845251i
$78$	−3.29577	−	0.938561i	−0.373172	−	0.106271i
$79$	−3.44782	−	5.97180i	−0.387910	−	0.671880i	0.604258	−	0.796789i	$-0.293470\pi$
$79$	−3.44782	−	5.97180i	−0.387910	−	0.671880i	−0.992168	+	0.124909i	$0.960136\pi$
$80$	3.45739	−	5.98837i	0.386548	−	0.669520i
$81$	−8.98241	−	0.562465i	−0.998045	−	0.0624961i
$82$	−0.409600	+	0.236483i	−0.0452327	+	0.0261151i
$83$	2.91828			0.320322			0.160161	−	0.987091i	$-0.448799\pi$
$83$	2.91828			0.320322			0.160161	+	0.987091i	$0.448799\pi$
$84$	0.809193	+	8.73514i	0.0882902	+	0.953081i
$85$	−6.07884			−0.659343
$86$	−15.0134	+	8.66799i	−1.61894	+	0.934693i
$87$	−11.1102	−	11.4631i	−1.19114	−	1.22898i
$88$	0.379083	−	0.656592i	0.0404104	−	0.0699929i
$89$	1.32756	+	2.29940i	0.140721	+	0.243736i	0.927768	−	0.373157i	$-0.121725\pi$
$89$	1.32756	+	2.29940i	0.140721	+	0.243736i	−0.787047	+	0.616892i	$0.788391\pi$
$90$	5.19262	−	8.37760i	0.547351	−	0.883077i
$91$	0.405294	−	2.61452i	0.0424864	−	0.274077i
$92$		−	4.53639i		−	0.472952i
$93$	−15.8451	+	3.98125i	−1.64306	+	0.412836i
$94$	6.48001	+	3.74123i	0.668362	+	0.385879i
$95$	10.7762	+	6.22165i	1.10562	+	0.638328i
$96$	13.2696	−	3.33413i	1.35432	−	0.340288i
$97$			2.45844i			0.249617i	0.992181	+	0.124808i	$0.0398316\pi$
$97$			2.45844i			0.249617i	−0.992181	+	0.124808i	$0.960168\pi$
$98$	−13.5274	+	2.96842i	−1.36647	+	0.299856i
$99$	7.06922	−	11.4052i	0.710483	−	1.14627i
$100$	−2.14633	−	3.71756i	−0.214633	−	0.371756i
$101$	−1.15781	+	2.00538i	−0.115206	+	0.199543i	−0.917862	−	0.396899i	$-0.870086\pi$
$101$	−1.15781	+	2.00538i	−0.115206	+	0.199543i	0.802656	+	0.596442i	$0.203420\pi$
$102$	−8.73034	−	9.00768i	−0.864433	−	0.891894i
$103$	−9.92266	+	5.72885i	−0.977709	+	0.564480i	−0.901578	−	0.432617i	$-0.857590\pi$
$103$	−9.92266	+	5.72885i	−0.977709	+	0.564480i	−0.0761311	+	0.997098i	$0.524257\pi$
$104$	−0.169506			−0.0166215
$105$	6.91320	+	3.18080i	0.674659	+	0.310414i
$106$	−19.0676			−1.85201
$107$	12.1992	−	7.04322i	1.17934	−	0.680894i	0.223480	−	0.974709i	$-0.428258\pi$
$107$	12.1992	−	7.04322i	1.17934	−	0.680894i	0.955862	+	0.293815i	$0.0949249\pi$
$108$	9.71832	−	2.12119i	0.935146	−	0.204112i
$109$	−1.91428	+	3.31564i	−0.183355	+	0.317580i	−0.943021	−	0.332733i	$-0.892029\pi$
$109$	−1.91428	+	3.31564i	−0.183355	+	0.317580i	0.759666	+	0.650314i	$0.225362\pi$
$110$	7.34757	+	12.7264i	0.700563	+	1.21341i
$111$	4.89680	+	1.39450i	0.464784	+	0.132360i
$112$	3.98191	+	10.2722i	0.376255	+	0.970628i
$113$			11.3396i			1.06674i	0.845882	+	0.533370i	$0.179075\pi$
$113$			11.3396i			1.06674i	−0.845882	+	0.533370i	$0.820925\pi$
$114$	6.25735	+	24.9038i	0.586054	+	2.33245i
$115$	−3.40794	−	1.96758i	−0.317792	−	0.183477i
$116$	15.2798	+	8.82181i	1.41870	+	0.819085i
$117$	−2.99853	−	0.0937900i	−0.277215	−	0.00867089i
$118$			0.576569i			0.0530775i
$119$	6.07024	−	7.54672i	0.556458	−	0.691807i
$120$	0.133532	−	0.468900i	0.0121898	−	0.0428045i
$121$	4.50295	+	7.79934i	0.409359	+	0.709031i
$122$	−7.87402	+	13.6382i	−0.712880	+	1.23474i
$123$	−0.297325	+	0.288170i	−0.0268089	+	0.0259834i
$124$	15.6377	−	9.02844i	1.40431	−	0.810778i
$125$	−12.0268			−1.07571
$126$	5.21529	+	14.8123i	0.464615	+	1.31958i
$127$	15.1376			1.34324			0.671621	−	0.740895i	$-0.265598\pi$
$127$	15.1376			1.34324			0.671621	+	0.740895i	$0.265598\pi$
$128$	1.17330	−	0.677403i	0.103706	−	0.0598745i
$129$	−10.8981	+	10.5625i	−0.959523	+	0.929980i
$130$	1.64272	−	2.84528i	0.144076	−	0.249548i
$131$	2.84546	+	4.92847i	0.248609	+	0.430603i	0.963140	−	0.269001i	$-0.0866934\pi$
$131$	2.84546	+	4.92847i	0.248609	+	0.430603i	−0.714531	+	0.699603i	$0.753360\pi$
$132$	−4.06190	+	14.2634i	−0.353543	+	1.24147i
$133$	−18.4850	+	7.16554i	−1.60285	+	0.621331i
$134$		−	3.91652i		−	0.338336i
$135$	2.62161	−	8.22086i	0.225632	−	0.707539i
$136$	−0.537367	−	0.310249i	−0.0460788	−	0.0266036i
$137$	−4.66128	−	2.69119i	−0.398240	−	0.229924i	0.287484	−	0.957785i	$-0.407181\pi$
$137$	−4.66128	−	2.69119i	−0.398240	−	0.229924i	−0.685724	+	0.727861i	$0.740514\pi$
$138$	−1.97886	−	7.87573i	−0.168452	−	0.670426i
$139$		−	7.92393i		−	0.672099i	−0.941844	−	0.336049i	$-0.890909\pi$
$139$		−	7.92393i		−	0.672099i	0.941844	−	0.336049i	$-0.109091\pi$
$140$	−8.31141	−	1.28840i	−0.702442	−	0.108890i
$141$	6.30006	+	1.79412i	0.530561	+	0.151092i
$142$	3.19995	+	5.54247i	0.268534	+	0.465114i
$143$	2.23640	−	3.87356i	0.187017	−	0.323923i
$144$	11.0084	−	5.90474i	0.917367	−	0.492062i
$145$	13.2547	−	7.65259i	1.10074	−	0.635513i
$146$	16.2182			1.34223
$147$	−10.8523	+	5.40625i	−0.895083	+	0.445900i
$148$	−5.62730			−0.462561
$149$	−11.7312	+	6.77301i	−0.961057	+	0.554866i	−0.896498	−	0.443047i	$-0.853897\pi$
$149$	−11.7312	+	6.77301i	−0.961057	+	0.554866i	−0.0645587	+	0.997914i	$0.520564\pi$
$150$	−5.34796	−	5.51785i	−0.436659	−	0.450531i
$151$	−1.63095	+	2.82488i	−0.132725	+	0.229886i	−0.924726	−	0.380634i	$-0.875706\pi$
$151$	−1.63095	+	2.82488i	−0.132725	+	0.229886i	0.792001	+	0.610519i	$0.209039\pi$
$152$	0.635075	+	1.09998i	0.0515114	+	0.0892204i
$153$	−9.33425	−	5.78557i	−0.754629	−	0.467736i
$154$	−23.1366	−	3.58656i	−1.86440	−	0.289013i
$155$		−	15.6637i		−	1.25814i
$156$	3.21575	−	0.807993i	0.257466	−	0.0646912i
$157$	−3.60598	−	2.08191i	−0.287789	−	0.166155i	0.349156	−	0.937065i	$-0.386468\pi$
$157$	−3.60598	−	2.08191i	−0.287789	−	0.166155i	−0.636944	+	0.770910i	$0.719802\pi$
$158$	11.8150	+	6.82139i	0.939951	+	0.542681i
$159$	−16.1896	+	4.06780i	−1.28392	+	0.322598i
$160$			13.1177i			1.03704i
$161$	5.84582	−	2.26608i	0.460715	−	0.178592i
$162$	15.9469	−	7.92196i	1.25290	−	0.622408i
$163$	−2.60571	−	4.51321i	−0.204095	−	0.353502i	0.745749	−	0.666227i	$-0.232092\pi$
$163$	−2.60571	−	4.51321i	−0.204095	−	0.353502i	−0.949844	+	0.312724i	$0.898758\pi$
$164$	0.228816	−	0.396321i	0.0178675	−	0.0309475i
$165$	8.95352	+	9.23796i	0.697031	+	0.719174i
$166$	−5.00018	+	2.88685i	−0.388089	+	0.224063i
$167$	−20.6748			−1.59986			−0.799931	−	0.600092i	$-0.795131\pi$
$167$	−20.6748			−1.59986			−0.799931	+	0.600092i	$0.795131\pi$
$168$	0.448783	+	0.634014i	0.0346244	+	0.0489152i
$169$	−1.00000			−0.0769231
$170$	10.4155	−	6.01339i	0.798832	−	0.461206i
$171$	10.6257	+	19.8099i	0.812570	+	1.51490i
$172$	8.38698	−	14.5267i	0.639501	−	1.10765i
$173$	−9.06403	−	15.6994i	−0.689125	−	1.19360i	−0.972121	−	0.234479i	$-0.924662\pi$
$173$	−9.06403	−	15.6994i	−0.689125	−	1.19360i	0.282996	−	0.959121i	$-0.408672\pi$
$174$	30.3759	+	8.65037i	2.30279	+	0.655783i
$175$	3.71846	−	4.62291i	0.281089	−	0.349459i
$176$			18.6248i			1.40390i
$177$	0.123003	+	0.489542i	0.00924546	+	0.0367962i
$178$	−4.54928	−	2.62653i	−0.340983	−	0.196867i
$179$	−8.61227	−	4.97230i	−0.643711	−	0.371647i	0.142331	−	0.989819i	$-0.454540\pi$
$179$	−8.61227	−	4.97230i	−0.643711	−	0.371647i	−0.786043	+	0.618172i	$0.787873\pi$
$180$	−0.298152	+	9.53215i	−0.0222230	+	0.710484i
$181$		−	9.37972i		−	0.697189i	−0.937274	−	0.348595i	$-0.886659\pi$
$181$		−	9.37972i		−	0.697189i	0.937274	−	0.348595i	$-0.113341\pi$
$182$	1.89194	+	4.88066i	0.140240	+	0.361778i
$183$	−3.77600	+	13.2595i	−0.279130	+	0.980168i
$184$	−0.200840	−	0.347866i	−0.0148061	−	0.0256450i
$185$	−2.44074	+	4.22748i	−0.179447	+	0.310811i
$186$	23.2106	−	22.4959i	1.70188	−	1.64948i
$187$	14.1796	−	8.18660i	1.03692	−	0.598663i
$188$	−7.23989			−0.528023
$189$	7.58808	+	11.4639i	0.551952	+	0.833876i
$190$	−24.6187			−1.78602
$191$	13.0628	−	7.54180i	0.945189	−	0.545705i	0.0536062	−	0.998562i	$-0.482928\pi$
$191$	13.0628	−	7.54180i	0.945189	−	0.545705i	0.891583	+	0.452857i	$0.149595\pi$
$192$	−9.07999	+	8.80043i	−0.655292	+	0.635116i
$193$	6.39611	−	11.0784i	0.460402	−	0.797440i	−0.538579	−	0.842575i	$-0.681039\pi$
$193$	6.39611	−	11.0784i	0.460402	−	0.797440i	0.998981	+	0.0451353i	$0.0143719\pi$
$194$	−2.43197	−	4.21230i	−0.174605	−	0.302425i
$195$	0.787772	−	2.76627i	0.0564135	−	0.198097i
$196$	9.89917	−	9.03181i	0.707084	−	0.645129i
$197$			0.683281i			0.0486818i	0.999704	+	0.0243409i	$0.00774871\pi$
$197$			0.683281i			0.0486818i	−0.999704	+	0.0243409i	$0.992251\pi$
$198$	−0.829973	+	26.5348i	−0.0589836	+	1.88575i
$199$	−11.1348	−	6.42866i	−0.789322	−	0.455716i	0.0504015	−	0.998729i	$-0.483950\pi$
$199$	−11.1348	−	6.42866i	−0.789322	−	0.455716i	−0.839724	+	0.543013i	$0.817283\pi$
$200$	−0.329176	−	0.190050i	−0.0232762	−	0.0134385i
$201$	−0.835534	−	3.32536i	−0.0589340	−	0.234553i
$202$		−	4.58136i		−	0.322343i
$203$	−3.73545	+	24.0971i	−0.262177	+	1.69129i
$204$	11.6734	+	3.32433i	0.817303	+	0.232750i
$205$	−0.198489	−	0.343794i	−0.0138631	−	0.0240116i
$206$	11.3343	−	19.6316i	0.789700	−	1.36780i
$207$	−3.36035	−	6.26481i	−0.233560	−	0.435434i
$208$	3.60614	−	2.08201i	0.250041	−	0.144361i
$209$	−33.5157			−2.31833
$210$	−14.9916	+	1.38877i	−1.03452	+	0.0958344i
$211$	−5.22713			−0.359851			−0.179925	−	0.983680i	$-0.557586\pi$
$211$	−5.22713			−0.359851			−0.179925	+	0.983680i	$0.557586\pi$
$212$	15.9777	−	9.22473i	1.09735	−	0.633557i
$213$	3.89936	+	4.02323i	0.267180	+	0.275667i
$214$	−13.9348	+	24.1357i	−0.952561	+	1.64988i
$215$	−7.27539	−	12.6013i	−0.496178	−	0.859405i
$216$	0.651321	−	0.592920i	0.0443168	−	0.0403431i
$217$	19.4460	+	15.6415i	1.32008	+	1.06182i
$218$		−	7.57469i		−	0.513022i
$219$	13.7703	−	3.45993i	0.930508	−	0.233801i
$220$	−12.3138	−	7.10937i	−0.830195	−	0.479313i
$221$	−3.17019	−	1.83031i	−0.213250	−	0.123120i
$222$	−9.76967	+	2.45474i	−0.655698	+	0.164751i
$223$		−	3.56027i		−	0.238413i	−0.992869	−	0.119207i	$-0.961965\pi$
$223$		−	3.56027i		−	0.238413i	0.992869	−	0.119207i	$-0.0380351\pi$
$224$	−16.2853	−	13.0991i	−1.08810	−	0.875223i
$225$	−5.71790	−	3.54408i	−0.381193	−	0.236272i
$226$	−11.2175	−	19.4293i	−0.746178	−	1.29242i
$227$	−2.51486	+	4.35586i	−0.166917	+	0.289109i	−0.937334	−	0.348431i	$-0.886715\pi$
$227$	−2.51486	+	4.35586i	−0.166917	+	0.289109i	0.770417	+	0.637540i	$0.220048\pi$
$228$	−17.2915	−	17.8408i	−1.14516	−	1.18154i
$229$	7.82163	−	4.51582i	0.516868	−	0.298414i	−0.218784	−	0.975773i	$-0.570209\pi$
$229$	7.82163	−	4.51582i	0.516868	−	0.298414i	0.735652	+	0.677359i	$0.236876\pi$
$230$	7.78556			0.513365
$231$	−20.4095	+	1.89067i	−1.34285	+	0.124397i
$232$	1.56228			0.102569
$233$	10.3939	−	6.00093i	0.680929	−	0.393134i	−0.119276	−	0.992861i	$-0.538057\pi$
$233$	10.3939	−	6.00093i	0.680929	−	0.393134i	0.800205	+	0.599727i	$0.204724\pi$
$234$	5.23047	−	2.80555i	0.341927	−	0.183404i
$235$	−3.14017	+	5.43893i	−0.204842	+	0.354797i
$236$	−0.278939	−	0.483136i	−0.0181574	−	0.0314495i
$237$	11.4869	+	3.27121i	0.746154	+	0.212488i
$238$	−2.93530	+	18.9354i	−0.190267	+	1.22740i
$239$			6.71827i			0.434569i	0.976108	+	0.217284i	$0.0697199\pi$
$239$			6.71827i			0.434569i	−0.976108	+	0.217284i	$0.930280\pi$
$240$	2.91857	+	11.6157i	0.188393	+	0.749790i
$241$	−4.22933	−	2.44180i	−0.272435	−	0.157290i	0.357559	−	0.933891i	$-0.383609\pi$
$241$	−4.22933	−	2.44180i	−0.272435	−	0.157290i	−0.629994	+	0.776600i	$0.716943\pi$
$242$	−15.4307	−	8.90894i	−0.991925	−	0.572688i
$243$	11.8498	−	10.1283i	0.760166	−	0.649728i
$244$		−	15.2375i		−	0.975480i
$245$	−2.49152	−	11.3541i	−0.159177	−	0.725386i
$246$	0.224369	−	0.787875i	0.0143053	−	0.0502331i
$247$	3.74662	+	6.48934i	0.238392	+	0.412907i
$248$	0.799434	−	1.38466i	0.0507641	−	0.0879261i
$249$	−3.62958	+	3.51783i	−0.230016	+	0.222933i
$250$	20.6066	−	11.8973i	1.30328	−	0.752448i
$251$	25.1424			1.58697			0.793486	−	0.608589i	$-0.208264\pi$
$251$	25.1424			1.58697			0.793486	+	0.608589i	$0.208264\pi$
$252$	−11.5362	−	9.88882i	−0.726711	−	0.622937i
$253$	10.5992			0.666368
$254$	−25.9367	+	14.9746i	−1.62742	+	0.939589i
$255$	7.56051	−	7.32773i	0.473458	−	0.458880i
$256$	−8.64076	+	14.9662i	−0.540048	+	0.935390i
$257$	−3.51489	−	6.08797i	−0.219253	−	0.379757i	0.735327	−	0.677713i	$-0.237029\pi$
$257$	−3.51489	−	6.08797i	−0.219253	−	0.379757i	−0.954580	+	0.297955i	$0.903695\pi$
$258$	8.22399	−	28.8786i	0.512003	−	1.79790i
$259$	−2.81102	−	7.25161i	−0.174668	−	0.450593i
$260$			3.17894i			0.197149i
$261$	27.6364	+	0.864428i	1.71065	+	0.0535068i
$262$	−9.75081	−	5.62963i	−0.602407	−	0.347800i
$263$	−15.5382	−	8.97100i	−0.958128	−	0.553175i	−0.0625315	−	0.998043i	$-0.519917\pi$
$263$	−15.5382	−	8.97100i	−0.958128	−	0.553175i	−0.895596	+	0.444868i	$0.853251\pi$
$264$	0.320005	+	1.27360i	0.0196950	+	0.0783844i
$265$		−	16.0042i		−	0.983131i
$266$	24.5838	−	30.5634i	1.50733	−	1.87396i
$267$	−4.42294	−	1.25956i	−0.270680	−	0.0770836i
$268$	1.89477	+	3.28185i	0.115742	+	0.200471i
$269$	9.26511	−	16.0476i	0.564904	−	0.978442i	−0.432155	−	0.901799i	$-0.642247\pi$
$269$	9.26511	−	16.0476i	0.564904	−	0.978442i	0.997059	−	0.0766428i	$-0.0244201\pi$
$270$	3.64048	+	16.6790i	0.221553	+	1.01505i
$271$	−8.71622	+	5.03231i	−0.529472	+	0.305691i	−0.740802	−	0.671724i	$-0.765554\pi$
$271$	−8.71622	+	5.03231i	−0.529472	+	0.305691i	0.211329	+	0.977415i	$0.432221\pi$
$272$	15.2429			0.924234
$273$	2.64759	+	3.74036i	0.160240	+	0.226377i
$274$	10.6489			0.643321
$275$	8.68603	−	5.01488i	0.523787	−	0.302409i
$276$	5.46839	+	5.64211i	0.329158	+	0.339615i
$277$	−12.6513	+	21.9127i	−0.760144	+	1.31661i	0.182632	+	0.983181i	$0.441538\pi$
$277$	−12.6513	+	21.9127i	−0.760144	+	1.31661i	−0.942776	+	0.333427i	$0.891795\pi$
$278$	7.83861	+	13.5769i	0.470128	+	0.814286i
$279$	14.9080	−	24.0521i	0.892518	−	1.43996i
$280$	−0.694388	+	0.269173i	−0.0414976	+	0.0160862i
$281$		−	0.566180i		−	0.0337755i	−0.999857	−	0.0168877i	$-0.994624\pi$
$281$		−	0.566180i		−	0.0337755i	0.999857	−	0.0168877i	$-0.00537579\pi$
$282$	−12.5693	+	3.15818i	−0.748492	+	0.188067i
$283$	−12.3001	−	7.10146i	−0.731165	−	0.422138i	0.0876833	−	0.996148i	$-0.472054\pi$
$283$	−12.3001	−	7.10146i	−0.731165	−	0.422138i	−0.818848	+	0.574010i	$0.805387\pi$
$284$	−5.36279	−	3.09621i	−0.318223	−	0.183726i
$285$	−20.9027	+	5.25204i	−1.23817	+	0.311104i
$286$			8.84927i			0.523268i
$287$	0.625019	+	0.0968882i	0.0368937	+	0.00571913i
$288$	−12.4848	+	20.1426i	−0.735676	+	1.18691i
$289$	1.79994	+	3.11759i	0.105879	+	0.183387i
$290$	−15.1404	+	26.2239i	−0.889074	+	1.53992i
$291$	−2.96352	−	3.05767i	−0.173725	−	0.179244i
$292$	−13.5901	+	7.84623i	−0.795298	+	0.459166i
$293$	−14.1555			−0.826971			−0.413486	−	0.910511i	$-0.635689\pi$
$293$	−14.1555			−0.826971			−0.413486	+	0.910511i	$0.635689\pi$
$294$	13.2463	−	19.9985i	0.772540	−	1.16634i
$295$	−0.483938			−0.0281759
$296$	−0.431520	+	0.249138i	−0.0250816	+	0.0144809i
$297$	4.95613	+	22.7067i	0.287584	+	1.31758i
$298$	13.4002	−	23.2098i	0.776250	−	1.34451i
$299$	−1.18486	−	2.05223i	−0.0685219	−	0.118683i
$300$	7.15081	+	2.03639i	0.412852	+	0.117571i
$301$	22.9093	+	3.55132i	1.32047	+	0.204695i
$302$		−	6.45354i		−	0.371360i
$303$	−0.977368	−	3.88985i	−0.0561483	−	0.223466i
$304$	−27.0217	−	15.6010i	−1.54980	−	0.894777i
$305$	−11.4471	−	6.60898i	−0.655458	−	0.378429i
$306$	21.7166	+	0.679265i	1.24145	+	0.0388310i
$307$			23.7299i			1.35434i	0.735828	+	0.677169i	$0.236793\pi$
$307$			23.7299i			1.35434i	−0.735828	+	0.677169i	$0.763207\pi$
$308$	21.1225	−	8.18793i	1.20356	−	0.466550i
$309$	5.43540	−	19.0865i	0.309209	−	1.08579i
$310$	15.4950	+	26.8381i	0.880057	+	1.52430i
$311$	−0.593615	+	1.02817i	−0.0336608	+	0.0583023i	−0.882365	−	0.470566i	$-0.844050\pi$
$311$	−0.593615	+	1.02817i	−0.0336608	+	0.0583023i	0.848704	+	0.528868i	$0.177383\pi$
$312$	0.210822	−	0.204331i	0.0119354	−	0.0115680i
$313$	−16.6913	+	9.63675i	−0.943450	+	0.544701i	−0.891040	−	0.453924i	$-0.850024\pi$
$313$	−16.6913	+	9.63675i	−0.943450	+	0.544701i	−0.0524100	+	0.998626i	$0.516690\pi$
$314$	8.23799			0.464896
$315$	−12.4325	+	4.37740i	−0.700493	+	0.246639i
$316$	−13.2005			−0.742586
$317$	−16.9147	+	9.76571i	−0.950025	+	0.548497i	−0.893089	−	0.449881i	$-0.851466\pi$
$317$	−16.9147	+	9.76571i	−0.950025	+	0.548497i	−0.0569360	+	0.998378i	$0.518133\pi$
$318$	23.7152	−	22.9850i	1.32988	−	1.28894i
$319$	−20.6121	+	35.7011i	−1.15405	+	1.99888i
$320$	−6.06166	−	10.4991i	−0.338857	−	0.586918i
$321$	−6.68244	+	23.4655i	−0.372978	+	1.30971i
$322$	−7.77455	+	9.66557i	−0.433259	+	0.538641i
$323$			27.4299i			1.52624i
$324$	−9.53010	+	14.3531i	−0.529450	+	0.797397i
$325$	−1.94197	−	1.12120i	−0.107721	−	0.0621927i
$326$	8.92924	+	5.15530i	0.494545	+	0.285526i
$327$	−1.61595	−	6.43137i	−0.0893623	−	0.355655i
$328$		−	0.0405216i		−	0.00223743i
$329$	−3.61656	−	9.32968i	−0.199387	−	0.514362i
$330$	−24.4795	−	6.97121i	−1.34755	−	0.383752i
$331$	14.9745	+	25.9366i	0.823073	+	1.42560i	0.903383	+	0.428834i	$0.141076\pi$
$331$	14.9745	+	25.9366i	0.823073	+	1.42560i	−0.0803101	+	0.996770i	$0.525591\pi$
$332$	2.79326	−	4.83808i	0.153300	−	0.265524i
$333$	−7.77136	+	4.16844i	−0.425868	+	0.228429i
$334$	35.4242	−	20.4522i	1.93833	−	1.11909i
$335$	3.28729			0.179604
$336$	−17.3350	−	7.97594i	−0.945703	−	0.435123i
$337$	−2.19666			−0.119660			−0.0598299	−	0.998209i	$-0.519056\pi$
$337$	−2.19666			−0.119660			−0.0598299	+	0.998209i	$0.519056\pi$
$338$	1.71340	−	0.989233i	0.0931967	−	0.0538072i
$339$	−13.6693	−	14.1036i	−0.742415	−	0.766000i
$340$	−5.81844	+	10.0778i	−0.315549	+	0.546547i
$341$	21.0948	+	36.5373i	1.14235	+	1.97861i
$342$	−37.8027	−	23.4310i	−2.04414	−	1.26700i
$343$	16.5838	+	8.24487i	0.895440	+	0.445181i
$344$		−	1.48527i		−	0.0800804i
$345$	6.61041	−	1.66094i	0.355893	−	0.0894220i
$346$	31.0606	+	17.9329i	1.66983	+	0.964077i
$347$	−19.5066	−	11.2622i	−1.04717	−	0.604584i	−0.125315	−	0.992117i	$-0.539994\pi$
$347$	−19.5066	−	11.2622i	−1.04717	−	0.604584i	−0.921856	+	0.387533i	$0.873327\pi$
$348$	−29.6384	+	7.44698i	−1.58879	+	0.399200i
$349$			15.2888i			0.818392i	0.912446	+	0.409196i	$0.134191\pi$
$349$			15.2888i			0.818392i	−0.912446	+	0.409196i	$0.865809\pi$
$350$	−1.79808	+	11.5993i	−0.0961116	+	0.620010i
$351$	3.84246	−	3.49793i	0.205095	−	0.186705i
$352$	−17.6661	−	30.5985i	−0.941604	−	1.63091i
$353$	1.68278	−	2.91467i	0.0895656	−	0.155132i	−0.817762	−	0.575557i	$-0.804785\pi$
$353$	1.68278	−	2.91467i	0.0895656	−	0.155132i	0.907328	+	0.420424i	$0.138119\pi$
$354$	−0.695024	−	0.717104i	−0.0369401	−	0.0381136i
$355$	−4.65202	+	2.68584i	−0.246904	+	0.142550i
$356$	5.08275			0.269385
$357$	1.54736	+	16.7035i	0.0818949	+	0.884045i
$358$	19.6750			1.03986
$359$	−5.81709	+	3.35850i	−0.307014	+	0.177255i	−0.645590	−	0.763685i	$-0.723388\pi$
$359$	−5.81709	+	3.35850i	−0.307014	+	0.177255i	0.338575	+	0.940939i	$0.390055\pi$
$360$	0.399155	+	0.744157i	0.0210373	+	0.0392205i
$361$	18.5743	−	32.1717i	0.977596	−	1.69325i
$362$	9.27873	+	16.0712i	0.487679	+	0.844685i
$363$	−15.0022	−	4.27230i	−0.787412	−	0.224237i
$364$	−3.94657	−	3.17444i	−0.206856	−	0.166386i
$365$			13.6126i			0.712517i
$366$	−6.64689	−	26.4541i	−0.347438	−	1.38278i
$367$	21.3627	+	12.3337i	1.11512	+	0.643816i	0.940151	−	0.340757i	$-0.110683\pi$
$367$	21.3627	+	12.3337i	1.11512	+	0.643816i	0.174971	+	0.984574i	$0.444017\pi$
$368$	8.54550	+	4.93375i	0.445465	+	0.257189i
$369$	0.0224211	−	0.716819i	0.00116720	−	0.0373161i
$370$		−	9.65783i		−	0.502086i
$371$	19.8688	+	15.9816i	1.03154	+	0.829722i
$372$	−8.56597	+	30.0795i	−0.444125	+	1.55955i
$373$	−12.6042	−	21.8310i	−0.652618	−	1.13037i	−0.982485	−	0.186340i	$-0.940337\pi$
$373$	−12.6042	−	21.8310i	−0.652618	−	1.13037i	0.329867	−	0.944027i	$-0.392996\pi$
$374$	−16.1969	+	28.0539i	−0.837522	+	1.45063i
$375$	14.9582	−	14.4976i	0.772437	−	0.748654i
$376$	−0.555179	+	0.320533i	−0.0286312	+	0.0165302i
$377$	9.21663			0.474681
$378$	−24.3419	−	12.1359i	−1.25201	−	0.624202i
$379$	6.55272			0.336591			0.168295	−	0.985737i	$-0.446174\pi$
$379$	6.55272			0.336591			0.168295	+	0.985737i	$0.446174\pi$
$380$	20.6292	−	11.9103i	1.05825	−	0.610984i
$381$	−18.8272	+	18.2476i	−0.964549	+	0.934851i
$382$	−14.9212	+	25.8443i	−0.763434	+	1.32231i
$383$	9.75860	+	16.9024i	0.498641	+	0.863672i	0.999999	−	0.00156853i	$-0.000499279\pi$
$383$	9.75860	+	16.9024i	0.498641	+	0.863672i	−0.501358	+	0.865240i	$0.667166\pi$
$384$	−0.642704	+	2.25686i	−0.0327979	+	0.115170i
$385$	3.01034	−	19.4195i	0.153421	−	0.989709i
$386$			25.3090i			1.28819i
$387$	0.821820	−	26.2742i	0.0417754	−	1.33559i
$388$	4.07574	+	2.35313i	0.206914	+	0.119462i
$389$	7.87564	+	4.54700i	0.399311	+	0.230542i	0.686186	−	0.727426i	$-0.259283\pi$
$389$	7.87564	+	4.54700i	0.399311	+	0.230542i	−0.286876	+	0.957968i	$0.592617\pi$
$390$	1.38671	+	5.51902i	0.0702190	+	0.279466i
$391$		−	8.67460i		−	0.438694i
$392$	0.359235	−	1.13086i	0.0181441	−	0.0571169i
$393$	−9.48003	−	2.69970i	−0.478204	−	0.136182i
$394$	−0.675924	−	1.17073i	−0.0340526	−	0.0589807i
$395$	−5.72547	+	9.91680i	−0.288080	+	0.498968i
$396$	−12.1418	−	22.6364i	−0.610149	−	1.13752i
$397$	10.5125	−	6.06939i	0.527607	−	0.304614i	−0.212435	−	0.977175i	$-0.568139\pi$
$397$	10.5125	−	6.06939i	0.527607	−	0.304614i	0.740041	+	0.672561i	$0.234806\pi$
$398$	25.4378			1.27508
$399$	14.3529	−	31.1948i	0.718544	−	1.56169i
$400$	9.33734			0.466867
$401$	16.2882	−	9.40398i	0.813393	−	0.469612i	−0.0347400	−	0.999396i	$-0.511060\pi$
$401$	16.2882	−	9.40398i	0.813393	−	0.469612i	0.848133	+	0.529784i	$0.177727\pi$
$402$	4.72116	+	4.87114i	0.235470	+	0.242951i
$403$	4.71625	−	8.16879i	0.234933	−	0.406916i
$404$	2.21642	+	3.83895i	0.110271	+	0.190995i
$405$	6.64922	+	13.3848i	0.330402	+	0.665099i
$406$	−17.4373	−	44.9832i	−0.865400	−	2.23248i
$407$		−	13.1481i		−	0.651728i
$408$	1.04233	−	0.261898i	0.0516032	−	0.0129659i
$409$	20.8615	+	12.0444i	1.03154	+	0.595558i	0.917425	−	0.397910i	$-0.130264\pi$
$409$	20.8615	+	12.0444i	1.03154	+	0.595558i	0.114112	+	0.993468i	$0.463598\pi$
$410$	0.680184	+	0.392704i	0.0335919	+	0.0193943i
$411$	9.04152	−	2.27178i	0.445985	−	0.112059i
$412$			21.9338i			1.08060i
$413$	0.483253	−	0.600796i	0.0237793	−	0.0295632i
$414$	11.9550	+	7.40996i	0.587555	+	0.364180i
$415$	−2.42305	−	4.19685i	−0.118943	−	0.206015i
$416$	−3.94967	+	6.84103i	−0.193648	+	0.335409i
$417$	9.55188	+	9.85532i	0.467758	+	0.482617i
$418$	57.4259	−	33.1549i	2.80879	−	1.62166i
$419$	4.00341			0.195579			0.0977896	−	0.995207i	$-0.468823\pi$
$419$	4.00341			0.195579			0.0977896	+	0.995207i	$0.468823\pi$
$420$	11.8904	−	8.41653i	0.580190	−	0.410684i
$421$	−37.6994			−1.83736			−0.918678	−	0.395008i	$-0.870742\pi$
$421$	−37.6994			−1.83736			−0.918678	+	0.395008i	$0.870742\pi$
$422$	8.95618	−	5.17085i	0.435980	−	0.251713i
$423$	−9.99836	+	5.36297i	−0.486137	+	0.260757i
$424$	0.816815	−	1.41476i	0.0396680	−	0.0687070i
$425$	−4.10427	−	7.10880i	−0.199086	−	0.344828i
$426$	−10.6611	−	3.03604i	−0.516531	−	0.147096i
$427$	19.6358	−	7.61162i	0.950241	−	0.368352i
$428$		−	26.9660i		−	1.30345i
$429$	1.88787	+	7.51357i	0.0911471	+	0.362758i
$430$	24.9313	+	14.3941i	1.20230	+	0.694145i
$431$	−28.6874	−	16.5627i	−1.38182	−	0.797797i	−0.389449	−	0.921048i	$-0.627335\pi$
$431$	−28.6874	−	16.5627i	−1.38182	−	0.797797i	−0.992376	+	0.123251i	$0.960668\pi$
$432$	−6.57375	+	20.6140i	−0.316280	+	0.991793i
$433$		−	19.1277i		−	0.919220i	−0.888121	−	0.459610i	$-0.847989\pi$
$433$		−	19.1277i		−	0.919220i	0.888121	−	0.459610i	$-0.152011\pi$
$434$	−48.7920	−	7.56355i	−2.34209	−	0.363062i
$435$	−7.26060	+	25.4957i	−0.348119	+	1.22242i
$436$	3.66456	+	6.34720i	0.175501	+	0.303976i
$437$	−8.87840	+	15.3778i	−0.424712	+	0.735622i
$438$	−20.1713	+	19.5502i	−0.963823	+	0.934147i
$439$	−23.7149	+	13.6918i	−1.13185	+	0.653475i	−0.944400	−	0.328799i	$-0.893356\pi$
$439$	−23.7149	+	13.6918i	−1.13185	+	0.653475i	−0.187451	+	0.982274i	$0.560023\pi$
$440$	−1.25902			−0.0600212
$441$	6.98052	−	19.8059i	0.332406	−	0.943137i
$442$	7.24240			0.344486
$443$	−26.8557	+	15.5052i	−1.27595	+	0.736673i	−0.976102	−	0.217313i	$-0.930271\pi$
$443$	−26.8557	+	15.5052i	−1.27595	+	0.736673i	−0.299853	+	0.953985i	$0.596938\pi$
$444$	6.99891	−	6.78342i	0.332154	−	0.321927i
$445$	2.20455	−	3.81839i	0.104506	−	0.181009i
$446$	3.52194	+	6.10017i	0.166768	+	0.288851i
$447$	6.42607	−	22.5652i	0.303943	−	1.06730i
$448$	19.0874	+	2.95887i	0.901797	+	0.139793i
$449$		−	24.0940i		−	1.13707i	−0.822660	−	0.568534i	$-0.807511\pi$
$449$		−	24.0940i		−	1.13707i	0.822660	−	0.568534i	$-0.192489\pi$
$450$	13.3030	+	0.416099i	0.627108	+	0.0196151i
$451$	0.925999	+	0.534626i	0.0436036	+	0.0251745i
$452$	18.7994	+	10.8538i	0.884250	+	0.510522i
$453$	−1.37677	−	5.47945i	−0.0646864	−	0.257447i
$454$		−	9.95112i		−	0.467029i
$455$	−4.09653	+	1.58798i	−0.192048	+	0.0744457i
$456$	−2.11584	−	0.602545i	−0.0990834	−	0.0282167i
$457$	−16.2472	−	28.1409i	−0.760010	−	1.31638i	−0.942845	−	0.333232i	$-0.891861\pi$
$457$	−16.2472	−	28.1409i	−0.760010	−	1.31638i	0.182835	−	0.983144i	$-0.441473\pi$
$458$	−8.93440	+	15.4748i	−0.417477	+	0.723091i
$459$	18.5836	−	4.05619i	0.867409	−	0.189327i
$460$	−6.52391	+	3.76658i	−0.304179	+	0.175618i
$461$	−1.83092			−0.0852744			−0.0426372	−	0.999091i	$-0.513576\pi$
$461$	−1.83092			−0.0852744			−0.0426372	+	0.999091i	$0.513576\pi$
$462$	33.0994	−	23.4293i	1.53992	−	1.09003i
$463$	−1.94725			−0.0904963			−0.0452482	−	0.998976i	$-0.514408\pi$
$463$	−1.94725			−0.0904963			−0.0452482	+	0.998976i	$0.514408\pi$
$464$	−33.2365	+	19.1891i	−1.54296	+	0.890831i
$465$	18.8817	+	19.4816i	0.875620	+	0.903436i
$466$	−11.8726	+	20.5640i	−0.549989	+	0.952610i
$467$	6.90469	+	11.9593i	0.319511	+	0.553409i	0.980386	−	0.197087i	$-0.0631480\pi$
$467$	6.90469	+	11.9593i	0.319511	+	0.553409i	−0.660875	+	0.750496i	$0.729815\pi$
$468$	−3.02557	+	4.88136i	−0.139857	+	0.225641i
$469$	−3.28264	+	4.08109i	−0.151578	+	0.188447i
$470$		−	12.4254i		−	0.573142i
$471$	6.99455	−	1.75746i	0.322292	−	0.0809794i
$472$	−0.0427799	−	0.0246990i	−0.00196910	−	0.00113686i
$473$	33.9414	+	19.5961i	1.56063	+	0.901029i
$474$	−22.9177	+	5.75831i	−1.05264	+	0.264488i
$475$			16.8028i			0.770964i
$476$	−6.70115	−	17.2870i	−0.307147	−	0.792349i
$477$	15.2321	−	24.5750i	0.697430	−	1.12521i
$478$	−6.64593	−	11.5111i	−0.303978	−	0.526505i
$479$	4.56382	−	7.90478i	0.208526	−	0.361178i	−0.742724	−	0.669598i	$-0.766467\pi$
$479$	4.56382	−	7.90478i	0.208526	−	0.361178i	0.951251	+	0.308419i	$0.0997999\pi$
$480$	−15.8127	−	16.3150i	−0.721747	−	0.744675i
$481$	−2.54575	+	1.46979i	−0.116076	+	0.0670166i
$482$	9.66205			0.440094
$483$	−4.53905	+	9.86524i	−0.206534	+	0.448884i
$484$	17.2402			0.783647
$485$	3.53555	−	2.04125i	0.160541	−	0.0926884i
$486$	−10.2843	+	29.0760i	−0.466505	+	1.31891i
$487$	−0.594466	+	1.02965i	−0.0269378	+	0.0466577i	−0.879180	−	0.476490i	$-0.841909\pi$
$487$	−0.594466	+	1.02965i	−0.0269378	+	0.0466577i	0.852242	+	0.523147i	$0.175242\pi$
$488$	−0.674611	−	1.16846i	−0.0305382	−	0.0528937i
$489$	8.68127	+	2.47223i	0.392581	+	0.111798i
$490$	15.5008	+	16.9894i	0.700255	+	0.767503i
$491$			12.4760i			0.563036i	0.959556	+	0.281518i	$0.0908379\pi$
$491$			12.4760i			0.563036i	−0.959556	+	0.281518i	$0.909162\pi$
$492$	0.193156	+	0.768747i	0.00870815	+	0.0346578i
$493$	29.2185	+	16.8693i	1.31593	+	0.759754i
$494$	−12.8389	−	7.41256i	−0.577650	−	0.333507i
$495$	−22.2718	−	0.696630i	−1.00104	−	0.0313112i
$496$			39.2771i			1.76359i
$497$	1.31104	−	8.45741i	0.0588080	−	0.379366i
$498$	2.73898	−	9.61796i	0.122737	−	0.430991i
$499$	−11.2646	−	19.5109i	−0.504273	−	0.873426i	−0.999988	−	0.00494058i	$-0.998427\pi$
$499$	−11.2646	−	19.5109i	−0.504273	−	0.873426i	0.495715	−	0.868485i	$-0.334906\pi$
$500$	−11.5116	+	19.9386i	−0.514812	+	0.891681i
$501$	25.7141	−	24.9224i	1.14882	−	1.11345i
$502$	−43.0789	+	24.8716i	−1.92271	+	1.11008i
$503$	−1.98498			−0.0885057			−0.0442529	−	0.999020i	$-0.514091\pi$
$503$	−1.98498			−0.0885057			−0.0442529	+	0.999020i	$0.514091\pi$
$504$	−1.32244	−	0.247565i	−0.0589062	−	0.0110274i
$505$	3.84532			0.171114
$506$	−18.1607	+	10.4851i	−0.807343	+	0.466120i
$507$	1.24374	−	1.20545i	0.0552365	−	0.0535358i
$508$	14.4891	−	25.0959i	0.642851	−	1.11345i
$509$	−7.39959	−	12.8165i	−0.327981	−	0.568080i	0.654130	−	0.756382i	$-0.273035\pi$
$509$	−7.39959	−	12.8165i	−0.327981	−	0.568080i	−0.982111	+	0.188302i	$0.939702\pi$
$510$	−5.70536	+	20.0344i	−0.252638	+	0.887140i
$511$	−16.8997	−	13.5934i	−0.747599	−	0.601335i
$512$		−	31.4813i		−	1.39129i
$513$	−37.0955	−	11.8296i	−1.63780	−	0.522291i
$514$	12.0448	+	6.95409i	0.531275	+	0.306732i
$515$	16.4776	+	9.51336i	0.726091	+	0.419209i
$516$	7.07991	+	28.1775i	0.311676	+	1.24045i
$517$		−	16.9159i		−	0.743961i
$518$	11.9899	+	9.64417i	0.526808	+	0.423741i
$519$	30.1981	+	8.59974i	1.32555	+	0.377487i
$520$	0.140741	+	0.243771i	0.00617192	+	0.0106901i
$521$	−21.2426	+	36.7933i	−0.930655	+	1.61194i	−0.148451	+	0.988920i	$0.547429\pi$
$521$	−21.2426	+	36.7933i	−0.930655	+	1.61194i	−0.782204	+	0.623022i	$0.785905\pi$
$522$	−48.2073	+	25.8577i	−2.10998	+	1.13176i
$523$	−32.8045	+	18.9397i	−1.43444	+	0.828176i	−0.997455	−	0.0712925i	$-0.977288\pi$
$523$	−32.8045	+	18.9397i	−1.43444	+	0.828176i	−0.436987	+	0.899468i	$0.643954\pi$
$524$	10.8942			0.475917
$525$	0.947868	+	10.2321i	0.0413683	+	0.446566i
$526$	35.4976			1.54777
$527$	29.9028	−	17.2644i	1.30259	−	0.752049i
$528$	−22.4512	−	23.1644i	−0.977063	−	1.00810i
$529$	−8.69224	+	15.0554i	−0.377923	+	0.654582i
$530$	15.8319	+	27.4216i	0.687693	+	1.19112i
$531$	−0.743101	−	0.460591i	−0.0322479	−	0.0199879i
$532$	−5.81374	+	37.5040i	−0.252057	+	1.62601i
$533$		−	0.239057i		−	0.0103547i
$534$	8.82427	−	2.21720i	0.381864	−	0.0959474i
$535$	−20.2581	−	11.6960i	−0.875833	−	0.505662i
$536$	0.290595	+	0.167775i	0.0125518	+	0.00724678i
$537$	16.7053	−	4.19739i	0.720887	−	0.181131i
$538$			36.6614i			1.58059i
$539$	21.1027	+	23.1293i	0.908958	+	0.996250i
$540$	−11.1197	−	12.2149i	−0.478515	−	0.525647i
$541$	−13.3516	−	23.1257i	−0.574031	−	0.994251i	−0.996146	−	0.0877087i	$-0.972046\pi$
$541$	−13.3516	−	23.1257i	−0.574031	−	0.994251i	0.422115	−	0.906542i	$-0.361288\pi$
$542$	9.95625	−	17.2447i	0.427658	−	0.740725i
$543$	11.3068	+	11.6660i	0.485220	+	0.500634i
$544$	−25.0424	+	14.4582i	−1.07368	+	0.619891i
$545$	6.35774			0.272336
$546$	−8.23647	−	3.78964i	−0.352488	−	0.162182i
$547$	16.6645			0.712522			0.356261	−	0.934386i	$-0.384051\pi$
$547$	16.6645			0.712522			0.356261	+	0.934386i	$0.384051\pi$
$548$	−8.92320	+	5.15181i	−0.381180	+	0.220075i
$549$	−11.2872	−	21.0431i	−0.481727	−	0.898099i
$550$	−9.92176	+	17.1850i	−0.423065	+	0.732771i
$551$	−34.5312	−	59.8098i	−1.47108	−	2.54798i
$552$	0.669128	+	0.190553i	0.0284800	+	0.00811046i
$553$	−6.59408	−	17.0108i	−0.280409	−	0.723373i
$554$		−	50.0604i		−	2.12686i
$555$	−2.06036	−	8.20008i	−0.0874574	−	0.348074i
$556$	−13.1367	−	7.58448i	−0.557121	−	0.321654i
$557$	−39.4422	−	22.7720i	−1.67122	−	0.964880i	−0.966956	−	0.254942i	$-0.917944\pi$
$557$	−39.4422	−	22.7720i	−1.67122	−	0.964880i	−0.704264	−	0.709938i	$-0.748723\pi$
$558$	−1.75030	+	55.9583i	−0.0740960	+	2.36890i
$559$		−	8.76234i		−	0.370607i
$560$	11.4665	−	14.2555i	0.484547	−	0.602404i
$561$	−7.76726	+	27.2748i	−0.327934	+	1.15154i
$562$	0.560084	+	0.970094i	0.0236257	+	0.0409210i
$563$	7.84648	−	13.5905i	0.330690	−	0.572772i	−0.651957	−	0.758256i	$-0.726052\pi$
$563$	7.84648	−	13.5905i	0.330690	−	0.572772i	0.982647	+	0.185484i	$0.0593853\pi$
$564$	9.00456	−	8.72731i	0.379160	−	0.367486i
$565$	16.3078	−	9.41531i	0.686074	−	0.396105i
$566$	28.1000			1.18113
$567$	−23.2568	−	5.11109i	−0.976692	−	0.214646i
$568$	−0.548315			−0.0230068
$569$	0.145164	−	0.0838103i	0.00608558	−	0.00351351i	−0.496954	−	0.867777i	$-0.665548\pi$
$569$	0.145164	−	0.0838103i	0.00608558	−	0.00351351i	0.503040	+	0.864263i	$0.332215\pi$
$570$	30.6193	−	29.6765i	1.28250	−	1.24301i
$571$	−13.7193	+	23.7625i	−0.574135	+	0.994431i	0.422000	+	0.906596i	$0.361328\pi$
$571$	−13.7193	+	23.7625i	−0.574135	+	0.994431i	−0.996135	+	0.0878352i	$0.972005\pi$
$572$	−4.28119	−	7.41524i	−0.179006	−	0.310047i
$573$	−7.15548	+	25.1266i	−0.298925	+	1.04968i
$574$	−1.16675	+	0.452281i	−0.0486994	+	0.0188779i
$575$		−	5.31382i		−	0.221602i
$576$	0.684718	−	21.8909i	0.0285299	−	0.912122i
$577$	28.4050	+	16.3996i	1.18252	+	0.682726i	0.956595	−	0.291420i	$-0.0941276\pi$
$577$	28.4050	+	16.3996i	1.18252	+	0.682726i	0.225921	+	0.974146i	$0.427461\pi$
$578$	−6.16804	−	3.56112i	−0.256556	−	0.148123i
$579$	5.39931	+	21.4888i	0.224388	+	0.893046i
$580$		−	29.2991i		−	1.21658i
$581$	7.62990	+	1.18276i	0.316542	+	0.0490692i
$582$	8.10245	+	2.30740i	0.335857	+	0.0956447i
$583$	21.5535	+	37.3317i	0.892653	+	1.54612i
$584$	−0.694754	+	1.20335i	−0.0287491	+	0.0497949i
$585$	2.35481	+	4.39014i	0.0973593	+	0.181510i
$586$	24.2540	−	14.0030i	1.00192	−	0.578461i
$587$	13.6770			0.564509			0.282255	−	0.959340i	$-0.408918\pi$
$587$	13.6770			0.564509			0.282255	+	0.959340i	$0.408918\pi$
$588$	−1.42464	+	23.1662i	−0.0587513	+	0.955357i
$589$	−70.6800			−2.91232
$590$	0.829179	−	0.478727i	0.0341368	−	0.0197089i
$591$	−0.823660	−	0.849826i	−0.0338808	−	0.0349572i
$592$	6.12021	−	10.6005i	0.251539	−	0.435679i
$593$	6.16297	+	10.6746i	0.253083	+	0.438353i	0.964373	−	0.264546i	$-0.0852221\pi$
$593$	6.16297	+	10.6746i	0.253083	+	0.438353i	−0.711290	+	0.702899i	$0.751889\pi$
$594$	−30.9541	−	34.0030i	−1.27006	−	1.39516i
$595$	−15.8933	−	2.46372i	−0.651561	−	0.101003i
$596$			25.9315i			1.06219i
$597$	21.5982	−	5.42678i	0.883955	−	0.222103i
$598$	4.06026	+	2.34419i	0.166037	+	0.0958612i
$599$	−8.51459	−	4.91590i	−0.347897	−	0.200858i	0.315862	−	0.948805i	$-0.397706\pi$
$599$	−8.51459	−	4.91590i	−0.347897	−	0.200858i	−0.663759	+	0.747947i	$0.731040\pi$
$600$	0.638505	−	0.160431i	0.0260668	−	0.00654958i
$601$		−	2.02669i		−	0.0826703i	−0.999145	−	0.0413351i	$-0.986839\pi$
$601$		−	2.02669i		−	0.0826703i	0.999145	−	0.0413351i	$-0.0131611\pi$
$602$	−42.7660	+	16.5778i	−1.74301	+	0.675662i
$603$	5.04774	+	3.12870i	0.205560	+	0.127411i
$604$	3.12216	+	5.40774i	0.127039	+	0.220038i
$605$	7.47763	−	12.9516i	0.304009	−	0.526559i
$606$	5.52259	+	5.69803i	0.224340	+	0.231467i
$607$	−2.33089	+	1.34574i	−0.0946078	+	0.0546218i	−0.546557	−	0.837422i	$-0.684062\pi$
$607$	−2.33089	+	1.34574i	−0.0946078	+	0.0546218i	0.451950	+	0.892043i	$0.350729\pi$
$608$	59.1916			2.40054
$609$	−24.4019	−	34.4735i	−0.988814	−	1.39694i
$610$	26.1513			1.05883
$611$	−3.27527	+	1.89098i	−0.132503	+	0.0765008i
$612$	−18.5260	+	9.93709i	−0.748870	+	0.401683i
$613$	−0.665332	+	1.15239i	−0.0268725	+	0.0465445i	−0.879149	−	0.476547i	$-0.841888\pi$
$613$	−0.665332	+	1.15239i	−0.0268725	+	0.0465445i	0.852276	+	0.523092i	$0.175221\pi$
$614$	−23.4744	−	40.6589i	−0.947350	−	1.64086i
$615$	0.661295	+	0.188322i	0.0266660	+	0.00759388i
$616$	1.25724	−	1.56303i	0.0506555	−	0.0629765i
$617$		−	13.2786i		−	0.534576i	−0.963617	−	0.267288i	$-0.913873\pi$
$617$		−	13.2786i		−	0.534576i	0.963617	−	0.267288i	$-0.0861274\pi$
$618$	9.56793	+	38.0796i	0.384879	+	1.53179i
$619$	9.75477	+	5.63192i	0.392077	+	0.226366i	0.683060	−	0.730362i	$-0.260649\pi$
$619$	9.75477	+	5.63192i	0.392077	+	0.226366i	−0.290982	+	0.956728i	$0.593982\pi$
$620$	−25.9681	−	14.9927i	−1.04290	−	0.602120i
$621$	11.7313	+	3.74108i	0.470761	+	0.150124i
$622$		−	2.34889i		−	0.0941821i
$623$	2.53900	+	6.54988i	0.101723	+	0.262415i
$624$	−1.97536	+	6.93649i	−0.0790776	+	0.277682i
$625$	4.37986	+	7.58614i	0.175194	+	0.303446i
$626$	19.0660	−	33.0232i	0.762029	−	1.31987i
$627$	41.6849	−	40.4015i	1.66474	−	1.61348i
$628$	−6.90302	+	3.98546i	−0.275460	+	0.159037i
$629$	−10.7607			−0.429056
$630$	16.9716	−	19.7989i	0.676166	−	0.788807i
$631$	−17.1242			−0.681703			−0.340851	−	0.940117i	$-0.610715\pi$
$631$	−17.1242			−0.681703			−0.340851	+	0.940117i	$0.610715\pi$
$632$	−1.01226	+	0.584427i	−0.0402654	+	0.0232473i
$633$	6.50121	−	6.30104i	0.258400	−	0.250444i
$634$	19.3211	−	33.4652i	0.767340	−	1.32907i
$635$	−12.5688	−	21.7697i	−0.498776	−	0.863906i
$636$	−8.75221	+	30.7335i	−0.347048	+	1.21866i
$637$	2.11930	−	6.67147i	0.0839698	−	0.264333i
$638$		−	81.5605i		−	3.22901i
$639$	−9.69959	−	0.303390i	−0.383710	−	0.0120019i
$640$	−1.94838	−	1.12490i	−0.0770165	−	0.0444655i
$641$	−35.5658	−	20.5339i	−1.40476	−	0.811041i	−0.409888	−	0.912136i	$-0.634432\pi$
$641$	−35.5658	−	20.5339i	−1.40476	−	0.811041i	−0.994877	+	0.101095i	$0.967766\pi$
$642$	−11.7631	−	46.8162i	−0.464252	−	1.84769i
$643$		−	2.30359i		−	0.0908449i	−0.998968	−	0.0454224i	$-0.985537\pi$
$643$		−	2.30359i		−	0.0908449i	0.998968	−	0.0454224i	$-0.0144634\pi$
$644$	1.83857	−	11.8605i	0.0724499	−	0.467370i
$645$	24.2390	+	6.90272i	0.954409	+	0.271794i
$646$	−27.1345	−	46.9984i	−1.06759	−	1.84913i
$647$	13.5444	−	23.4597i	0.532487	−	0.922294i	−0.466794	−	0.884366i	$-0.654591\pi$
$647$	13.5444	−	23.4597i	0.532487	−	0.922294i	0.999280	−	0.0379281i	$-0.0120758\pi$
$648$	−0.0953413	+	1.52257i	−0.00374536	+	0.0598124i
$649$	1.12884	−	0.651737i	0.0443109	−	0.0255829i
$650$	4.43649			0.174014
$651$	−43.0409	+	3.98716i	−1.68691	+	0.156269i
$652$	−9.97633			−0.390703
$653$	−17.8995	+	10.3343i	−0.700462	+	0.404412i	−0.807519	−	0.589841i	$-0.799190\pi$
$653$	−17.8995	+	10.3343i	−0.700462	+	0.404412i	0.107058	+	0.994253i	$0.465857\pi$
$654$	9.13089	+	9.42096i	0.357046	+	0.368389i
$655$	4.72518	−	8.18425i	0.184628	−	0.319785i
$656$	0.497717	+	0.862072i	0.0194326	+	0.0336582i
$657$	−12.9559	+	20.9026i	−0.505458	+	0.815488i
$658$	15.4258	+	12.4079i	0.601362	+	0.483709i
$659$			46.8367i			1.82450i	0.409635	+	0.912250i	$0.365656\pi$
$659$			46.8367i			1.82450i	−0.409635	+	0.912250i	$0.634344\pi$
$660$	23.8852	−	6.00141i	0.929728	−	0.233604i
$661$	−7.06585	−	4.07947i	−0.274830	−	0.158673i	0.356251	−	0.934390i	$-0.384055\pi$
$661$	−7.06585	−	4.07947i	−0.274830	−	0.158673i	−0.631080	+	0.775717i	$0.717388\pi$
$662$	−51.3147	−	29.6265i	−1.99440	−	1.15147i
$663$	6.14924	−	1.54506i	0.238817	−	0.0600053i
$664$		−	0.494666i		−	0.0191968i
$665$	25.6531	+	20.6342i	0.994784	+	0.800160i
$666$	9.19190	−	14.8299i	0.356179	−	0.574647i
$667$	10.9204	+	18.9146i	0.422839	+	0.732378i
$668$	−19.7891	+	34.2758i	−0.765664	+	1.32617i
$669$	4.29172	+	4.42806i	0.165928	+	0.171199i
$670$	−5.63245	+	3.25190i	−0.217601	+	0.125632i
$671$	35.6022			1.37441
$672$	36.0450	−	3.33908i	1.39047	−	0.128808i
$673$	31.6586			1.22035			0.610175	−	0.792267i	$-0.291099\pi$
$673$	31.6586			1.22035			0.610175	+	0.792267i	$0.291099\pi$
$674$	3.76376	−	2.17301i	0.144975	−	0.0837012i
$675$	11.3838	−	2.48471i	0.438163	−	0.0956364i
$676$	−0.957162	+	1.65785i	−0.0368139	+	0.0637636i
$677$	18.9079	+	32.7494i	0.726688	+	1.25866i	0.958275	+	0.285846i	$0.0922747\pi$
$677$	18.9079	+	32.7494i	0.726688	+	1.25866i	−0.231588	+	0.972814i	$0.574392\pi$
$678$	37.3727	+	10.6429i	1.43529	+	0.408739i
$679$	−0.996392	+	6.42765i	−0.0382380	+	0.246671i
$680$			1.03040i			0.0395141i
$681$	−2.12293	−	8.44911i	−0.0813509	−	0.323770i
$682$	−72.2878	−	41.7354i	−2.76804	−	1.59813i
$683$	−11.5610	−	6.67474i	−0.442369	−	0.255402i	0.262233	−	0.965005i	$-0.415541\pi$
$683$	−11.5610	−	6.67474i	−0.442369	−	0.255402i	−0.704602	+	0.709603i	$0.748874\pi$
$684$	43.0124	+	1.34537i	1.64462	+	0.0514415i
$685$			8.93801i			0.341504i
$686$	−36.5708	+	2.27845i	−1.39628	+	0.0869915i
$687$	−4.28451	+	15.0451i	−0.163464	+	0.574006i
$688$	18.2432	+	31.5982i	0.695517	+	1.20467i
$689$	4.81879	−	8.34639i	0.183581	−	0.317972i
$690$	−9.68323	+	9.38509i	−0.368634	+	0.357284i
$691$	35.0206	−	20.2192i	1.33225	−	0.769173i	0.346604	−	0.938012i	$-0.387335\pi$
$691$	35.0206	−	20.2192i	1.33225	−	0.769173i	0.985644	+	0.168838i	$0.0540016\pi$
$692$	−34.7030			−1.31921
$693$	23.1051	−	26.9541i	0.877690	−	1.02390i
$694$	44.5636			1.69161
$695$	−11.3956	+	6.57926i	−0.432260	+	0.249565i
$696$	−1.94307	+	1.88324i	−0.0736519	+	0.0713842i
$697$	0.437547	−	0.757854i	0.0165733	−	0.0287058i
$698$	−15.1242	−	26.1959i	−0.572460	−	0.991529i
$699$	−5.69355	+	19.9930i	−0.215350	+	0.756203i
$700$	−4.10493	−	10.5895i	−0.155152	−	0.400247i
$701$			11.5327i			0.435583i	0.975995	+	0.217791i	$0.0698853\pi$
$701$			11.5327i			0.435583i	−0.975995	+	0.217791i	$0.930115\pi$
$702$	−3.12342	+	9.79444i	−0.117886	+	0.369667i
$703$	19.0759	+	11.0135i	0.719461	+	0.415381i
$704$	28.2791	+	16.3269i	1.06581	+	0.615344i
$705$	−2.65079	−	10.5499i	−0.0998345	−	0.397334i
$706$			6.65866i			0.250602i
$707$	−3.83988	+	4.77386i	−0.144414	+	0.179540i
$708$	0.929323	+	0.264650i	0.0349261	+	0.00994617i
$709$	−22.2958	−	38.6174i	−0.837335	−	1.45031i	−0.892115	−	0.451809i	$-0.850779\pi$
$709$	−22.2958	−	38.6174i	−0.837335	−	1.45031i	0.0547793	−	0.998498i	$-0.482554\pi$
$710$	5.31385	−	9.20386i	0.199425	−	0.345415i
$711$	−18.2300	+	9.77831i	−0.683679	+	0.366715i
$712$	0.389762	−	0.225029i	0.0146070	−	0.00843333i
$713$	22.3523			0.837100
$714$	−19.1749	−	27.0892i	−0.717604	−	1.01379i
$715$	−7.42755			−0.277775
$716$	−16.4867	+	9.51859i	−0.616136	+	0.355726i
$717$	−8.09852	−	8.35579i	−0.302445	−	0.312053i
$718$	6.64467	−	11.5089i	0.247977	−	0.429509i
$719$	15.4830	+	26.8174i	0.577420	+	1.00012i	0.995774	+	0.0918369i	$0.0292739\pi$
$719$	15.4830	+	26.8174i	0.577420	+	1.00012i	−0.418354	+	0.908284i	$0.637393\pi$
$720$	−17.6321	−	10.9287i	−0.657108	−	0.407290i
$721$	−28.2649	+	10.9566i	−1.05264	+	0.408046i
$722$			73.4973i			2.73529i
$723$	8.20366	−	2.06126i	0.305098	−	0.0766591i
$724$	−15.5502	−	8.97791i	−0.577919	−	0.333662i
$725$	17.8984	+	10.3337i	0.664730	+	0.383782i
$726$	29.9311	−	7.52052i	1.11085	−	0.279113i
$727$		−	38.9378i		−	1.44412i	−0.691828	−	0.722062i	$-0.743194\pi$
$727$		−	38.9378i		−	1.44412i	0.691828	−	0.722062i	$-0.256806\pi$
$728$	−0.443178	−	0.0686999i	−0.0164253	−	0.00254619i
$729$	−2.52903	+	26.8813i	−0.0936678	+	0.995604i
$730$	−13.4660	−	23.3239i	−0.498401	−	0.863255i
$731$	16.0378	−	27.7783i	0.593179	−	1.02742i
$732$	18.3680	+	18.9515i	0.678901	+	0.700468i
$733$	−4.16409	+	2.40414i	−0.153804	+	0.0887989i	−0.574927	−	0.818205i	$-0.694970\pi$
$733$	−4.16409	+	2.40414i	−0.153804	+	0.0887989i	0.421123	+	0.907004i	$0.361636\pi$
$734$	−48.8038			−1.80138
$735$	16.7856	+	11.1182i	0.619145	+	0.410099i
$736$	−18.7191			−0.689997
$737$	−7.66799	+	4.42712i	−0.282454	+	0.163075i
$738$	0.670685	+	1.25038i	0.0246882	+	0.0460271i
$739$	21.9639	−	38.0427i	0.807957	−	1.39942i	−0.106320	−	0.994332i	$-0.533907\pi$
$739$	21.9639	−	38.0427i	0.807957	−	1.39942i	0.914277	−	0.405090i	$-0.132760\pi$
$740$	4.67236	+	8.09277i	0.171759	+	0.297496i
$741$	−12.4824	−	3.55471i	−0.458552	−	0.130585i
$742$	−49.8527	−	7.72799i	−1.83015	−	0.283703i
$743$			4.52890i			0.166149i	0.996543	+	0.0830746i	$0.0264740\pi$
$743$			4.52890i			0.166149i	−0.996543	+	0.0830746i	$0.973526\pi$
$744$	0.674846	+	2.68584i	0.0247411	+	0.0984676i
$745$	19.4809	+	11.2473i	0.713724	+	0.412069i
$746$	43.1919	+	24.9369i	1.58137	+	0.913004i
$747$	0.273705	−	8.75055i	0.0100143	−	0.320166i
$748$		−	31.3436i		−	1.14604i
$749$	34.7497	−	13.4704i	1.26973	−	0.492198i
$750$	−11.2878	+	39.6374i	−0.412174	+	1.44735i
$751$	20.7065	+	35.8648i	0.755592	+	1.30872i	0.945080	+	0.326840i	$0.105984\pi$
$751$	20.7065	+	35.8648i	0.755592	+	1.30872i	−0.189488	+	0.981883i	$0.560683\pi$
$752$	7.87405	−	13.6383i	0.287137	−	0.497336i
$753$	−31.2706	+	30.3078i	−1.13956	+	1.10448i
$754$	−15.7918	+	9.11740i	−0.575103	+	0.332036i
$755$	5.41671			0.197134
$756$	26.2685	−	1.60712i	0.955376	−	0.0584505i
$757$	−1.73067			−0.0629024			−0.0314512	−	0.999505i	$-0.510013\pi$
$757$	−1.73067			−0.0629024			−0.0314512	+	0.999505i	$0.510013\pi$
$758$	−11.2274	+	6.48216i	−0.407799	+	0.235443i
$759$	−13.1827	+	12.7768i	−0.478502	+	0.463769i
$760$	1.05461	−	1.82664i	0.0382547	−	0.0662591i
$761$	−9.40838	−	16.2958i	−0.341053	−	0.590722i	0.643575	−	0.765383i	$-0.277450\pi$
$761$	−9.40838	−	16.2958i	−0.341053	−	0.590722i	−0.984629	+	0.174661i	$0.944117\pi$
$762$	14.2075	−	49.8899i	0.514685	−	1.80732i
$763$	−6.34875	+	7.89296i	−0.229840	+	0.285744i
$764$		−	28.8749i		−	1.04466i
$765$	−0.570134	+	18.2276i	−0.0206133	+	0.659020i
$766$	−33.4408	−	19.3070i	−1.20826	−	0.697592i
$767$	−0.252379	−	0.145711i	−0.00911289	−	0.00526133i
$768$	−7.29414	−	29.0301i	−0.263205	−	1.04753i
$769$			14.7929i			0.533447i	0.963773	+	0.266724i	$0.0859411\pi$
$769$			14.7929i			0.533447i	−0.963773	+	0.266724i	$0.914059\pi$
$770$	14.0525	+	36.2513i	0.506416	+	1.30641i
$771$	11.7104	+	3.33485i	0.421738	+	0.120102i
$772$	−12.2442	−	21.2076i	−0.440679	−	0.763279i
$773$	23.9317	−	41.4509i	0.860763	−	1.49088i	−0.0104316	−	0.999946i	$-0.503321\pi$
$773$	23.9317	−	41.4509i	0.860763	−	1.49088i	0.871194	−	0.490939i	$-0.163346\pi$
$774$	24.5832	+	45.8312i	0.883623	+	1.64737i
$775$	18.3176	−	10.5757i	0.657989	−	0.379890i
$776$	0.416721			0.0149594
$777$	12.2376	+	5.63060i	0.439022	+	0.201997i
$778$	−17.9922			−0.645050
$779$	−1.55132	+	0.895654i	−0.0555818	+	0.0320901i
$780$	−3.83204	−	3.95378i	−0.137209	−	0.141568i
$781$	7.23425	−	12.5301i	0.258862	−	0.448362i
$782$	8.58120	+	14.8631i	0.306863	+	0.531502i
$783$	−35.4146	+	32.2391i	−1.26561	+	1.15213i
$784$	6.24755	+	28.4707i	0.223127	+	1.01681i
$785$			6.91447i			0.246788i
$786$	18.9137	−	4.75228i	0.674630	−	0.169508i
$787$	10.6854	+	6.16922i	0.380894	+	0.219909i	0.678207	−	0.734871i	$-0.262757\pi$
$787$	10.6854	+	6.16922i	0.380894	+	0.219909i	−0.297313	+	0.954780i	$0.596091\pi$
$788$	1.13278	+	0.654011i	0.0403536	+	0.0232982i
$789$	30.1396	−	7.57291i	1.07300	−	0.269603i
$790$		−	22.6553i		−	0.806039i
$791$	−4.59588	+	29.6477i	−0.163411	+	1.05415i
$792$	−1.93326	−	1.19828i	−0.0686953	−	0.0425789i
$793$	−3.97986	−	6.89332i	−0.141329	−	0.244789i
$794$	−12.0081	+	20.7986i	−0.426151	+	0.738114i
$795$	19.2922	+	19.9051i	0.684225	+	0.705962i
$796$	−21.3155	+	12.3065i	−0.755510	+	0.436194i
$797$	0.539135			0.0190971			0.00954857	−	0.999954i	$-0.496961\pi$
$797$	0.539135			0.0190971			0.00954857	+	0.999954i	$0.496961\pi$
$798$	6.26664	+	67.6476i	0.221836	+	2.39470i
$799$	−13.8443			−0.489776
$800$	−15.3403	+	8.85670i	−0.542360	+	0.313132i
$801$	7.01933	−	3.76507i	0.248016	−	0.133032i
$802$	−18.6054	+	32.2256i	−0.656981	+	1.13792i
$803$	−18.3326	−	31.7530i	−0.646944	−	1.12054i
$804$	−6.31271	−	1.79772i	−0.222632	−	0.0634006i
$805$	−8.11270	−	6.52549i	−0.285935	−	0.229993i
$806$			18.6619i			0.657337i
$807$	7.82119	+	31.1278i	0.275319	+	1.09575i
$808$	0.339924	+	0.196255i	0.0119585	+	0.00690424i
$809$	8.52331	+	4.92094i	0.299664	+	0.173011i	0.642292	−	0.766460i	$-0.277984\pi$
$809$	8.52331	+	4.92094i	0.299664	+	0.173011i	−0.342628	+	0.939471i	$0.611317\pi$
$810$	−24.6335	−	16.3560i	−0.865533	−	0.574691i
$811$			50.1090i			1.75956i	0.475377	+	0.879782i	$0.342312\pi$
$811$			50.1090i			1.75956i	−0.475377	+	0.879782i	$0.657688\pi$
$812$	36.3741	+	29.2577i	1.27648	+	1.02674i
$813$	4.77454	−	16.7658i	0.167450	−	0.588004i
$814$	13.0066	+	22.5280i	0.455879	+	0.789606i
$815$	−4.32705	+	7.49467i	−0.151570	+	0.262527i
$816$	−18.9582	+	18.3745i	−0.663669	+	0.643235i
$817$	−56.8617	+	32.8291i	−1.98934	+	1.14855i
$818$	−47.6589			−1.66636
$819$	−7.80173	−	1.46050i	−0.272614	−	0.0510341i
$820$	−0.759946			−0.0265385
$821$	−20.6335	+	11.9128i	−0.720115	+	0.415758i	−0.814795	−	0.579749i	$-0.803150\pi$
$821$	−20.6335	+	11.9128i	−0.720115	+	0.415758i	0.0946802	+	0.995508i	$0.469817\pi$
$822$	−13.2444	+	12.8366i	−0.461953	+	0.447729i
$823$	11.5270	−	19.9654i	0.401806	−	0.695949i	−0.592138	−	0.805837i	$-0.701716\pi$
$823$	11.5270	−	19.9654i	0.401806	−	0.695949i	0.993944	+	0.109888i	$0.0350492\pi$
$824$	0.971076	+	1.68195i	0.0338290	+	0.0585936i
$825$	−4.75800	+	16.7078i	−0.165652	+	0.581690i
$826$	−0.233680	+	1.50745i	−0.00813077	+	0.0524510i
$827$			42.2725i			1.46996i	0.678089	+	0.734980i	$0.262809\pi$
$827$			42.2725i			1.46996i	−0.678089	+	0.734980i	$0.737191\pi$
$828$	−13.6025	−	0.425468i	−0.472721	−	0.0147860i
$829$	−25.4744	−	14.7077i	−0.884763	−	0.510818i	−0.0125370	−	0.999921i	$-0.503991\pi$
$829$	−25.4744	−	14.7077i	−0.884763	−	0.510818i	−0.872226	+	0.489103i	$0.837324\pi$
$830$	8.30332	+	4.79392i	0.288212	+	0.166400i
$831$	−10.6797	−	42.5043i	−0.370474	−	1.47446i
$832$		−	7.30054i		−	0.253101i
$833$	18.9294	−	17.2708i	0.655866	−	0.598399i
$834$	−26.1154	−	7.43709i	−0.904303	−	0.257525i
$835$	17.1663	+	29.7329i	0.594065	+	1.02895i
$836$	−32.0800	+	55.5642i	−1.10951	+	1.92173i
$837$	10.4518	+	47.8854i	0.361267	+	1.65516i
$838$	−6.85944	+	3.96030i	−0.236955	+	0.136806i
$839$	39.4335			1.36140			0.680698	−	0.732564i	$-0.261677\pi$
$839$	39.4335			1.36140			0.680698	+	0.732564i	$0.261677\pi$
$840$	0.539165	−	1.17183i	0.0186030	−	0.0404320i
$841$	−55.9464			−1.92918
$842$	64.5942	−	37.2935i	2.22606	−	1.28522i
$843$	0.682501	+	0.704183i	0.0235066	+	0.0242533i
$844$	−5.00321	+	8.66582i	−0.172218	+	0.298290i
$845$	0.830302	+	1.43813i	0.0285633	+	0.0494730i
$846$	11.8260	−	19.0796i	0.406585	−	0.655971i
$847$	8.61205	+	22.2166i	0.295914	+	0.763371i
$848$			40.1310i			1.37810i
$849$	23.8586	−	5.99474i	0.818825	−	0.205739i
$850$	14.0645	+	8.12015i	0.482409	+	0.278519i
$851$	−6.03268	−	3.48297i	−0.206798	−	0.119395i
$852$	10.4022	−	2.61368i	0.356375	−	0.0895432i
$853$			28.3504i			0.970699i	0.874320	+	0.485349i	$0.161308\pi$
$853$			28.3504i			0.970699i	−0.874320	+	0.485349i	$0.838692\pi$
$854$	−26.1143	+	32.4661i	−0.893612	+	1.11097i
$855$	19.6665	−	31.7293i	0.672582	−	1.08512i
$856$	−1.19387	−	2.06784i	−0.0408056	−	0.0706774i
$857$	−11.0549	+	19.1477i	−0.377630	+	0.654074i	−0.990717	−	0.135942i	$-0.956594\pi$
$857$	−11.0549	+	19.1477i	−0.377630	+	0.654074i	0.613087	+	0.790015i	$0.289927\pi$
$858$	−10.6673	−	11.0062i	−0.364177	−	0.375746i
$859$	3.70612	−	2.13973i	0.126451	−	0.0730066i	−0.435440	−	0.900218i	$-0.643407\pi$
$859$	3.70612	−	2.13973i	0.126451	−	0.0730066i	0.561891	+	0.827211i	$0.310074\pi$
$860$	−27.8549			−0.949845
$861$	−0.894157	+	0.632924i	−0.0304728	+	0.0215700i
$862$	65.5374			2.23221
$863$	24.0770	−	13.9009i	0.819591	−	0.473191i	−0.0306846	−	0.999529i	$-0.509769\pi$
$863$	24.0770	−	13.9009i	0.819591	−	0.473191i	0.850275	+	0.526338i	$0.176435\pi$
$864$	−8.75295	−	40.1020i	−0.297782	−	1.36430i
$865$	−15.0518	+	26.0704i	−0.511776	+	0.886421i
$866$	18.9218	+	32.7735i	0.642988	+	1.11369i
$867$	−5.99675	−	1.70774i	−0.203660	−	0.0579979i
$868$	44.5444	−	17.2672i	1.51193	−	0.586087i
$869$		−	30.8428i		−	1.04627i
$870$	−12.7808	−	50.8668i	−0.433311	−	1.72454i
$871$	1.71436	+	0.989788i	0.0580890	+	0.0335377i
$872$	0.562021	+	0.324483i	0.0190324	+	0.0109884i
$873$	7.37172	+	0.230577i	0.249495	+	0.00780386i
$874$		−	35.1312i		−	1.18833i
$875$	−31.4442	−	4.87437i	−1.06301	−	0.164784i
$876$	7.44432	−	26.1408i	0.251520	−	0.883216i
$877$	−3.38044	−	5.85509i	−0.114149	−	0.197713i	0.803290	−	0.595588i	$-0.203081\pi$
$877$	−3.38044	−	5.85509i	−0.114149	−	0.197713i	−0.917439	+	0.397876i	$0.869748\pi$
$878$	27.0888	−	46.9191i	0.914202	−	1.58344i
$879$	17.6057	−	17.0637i	0.593827	−	0.575544i
$880$	26.7848	−	15.4642i	0.902914	−	0.521298i
$881$	38.5496			1.29877			0.649384	−	0.760461i	$-0.275027\pi$
$881$	38.5496			1.29877			0.649384	+	0.760461i	$0.275027\pi$
$882$	7.63219	+	40.8407i	0.256989	+	1.37518i
$883$	−33.9159			−1.14136			−0.570680	−	0.821172i	$-0.693320\pi$
$883$	−33.9159			−1.14136			−0.570680	+	0.821172i	$0.693320\pi$
$884$	−6.06877	+	3.50380i	−0.204115	+	0.117846i
$885$	0.601894	−	0.583362i	0.0202324	−	0.0196095i
$886$	30.6764	−	53.1332i	1.03060	−	1.78504i
$887$	0.410584	+	0.711152i	0.0137861	+	0.0238782i	0.872836	−	0.488013i	$-0.162278\pi$
$887$	0.410584	+	0.711152i	0.0137861	+	0.0238782i	−0.859050	+	0.511892i	$0.828945\pi$
$888$	0.236377	−	0.830039i	0.00793228	−	0.0278543i
$889$	39.5776	+	6.13517i	1.32739	+	0.205767i
$890$			8.72325i			0.292404i
$891$	−33.5360	−	22.2670i	−1.12350	−	0.745972i
$892$	−5.90241	−	3.40776i	−0.197627	−	0.114100i
$893$	24.5424	+	14.1696i	0.821280	+	0.474166i
$894$	11.3118	+	45.0202i	0.378324	+	1.50570i
$895$			16.5140i			0.552004i
$896$	3.34216	−	1.29556i	0.111654	−	0.0432815i
$897$	3.94751	+	1.12416i	0.131804	+	0.0375347i
$898$	23.8346	+	41.2828i	0.795371	+	1.37762i
$899$	−43.4680	+	75.2888i	−1.44974	+	2.51102i
$900$	−11.3485	+	6.08718i	−0.378284	+	0.202906i
$901$	30.5529	−	17.6397i	1.01787	−	0.587665i
$902$	−2.11548			−0.0704377
$903$	−32.7743	+	23.1991i	−1.09066	+	0.772017i
$904$	1.92213			0.0639292
$905$	−13.4892	+	7.78801i	−0.448397	+	0.258882i
$906$	7.77941	+	8.02654i	0.258454	+	0.266664i
$907$	3.48054	−	6.02847i	0.115569	−	0.200172i	−0.802438	−	0.596736i	$-0.796464\pi$
$907$	3.48054	−	6.02847i	0.115569	−	0.200172i	0.918007	+	0.396564i	$0.129797\pi$
$908$	4.81426	+	8.33854i	0.159767	+	0.276724i
$909$	5.90461	+	3.65981i	0.195843	+	0.121388i
$910$	5.44812	−	6.77327i	0.180603	−	0.224532i
$911$		−	56.4091i		−	1.86892i	−0.356073	−	0.934458i	$-0.615885\pi$
$911$		−	56.4091i		−	1.86892i	0.356073	−	0.934458i	$-0.384115\pi$
$912$	52.4141	−	13.1696i	1.73561	−	0.436090i
$913$	11.3041	+	6.52643i	0.374111	+	0.215993i
$914$	55.6758	+	32.1444i	1.84159	+	1.06324i
$915$	22.2040	−	5.57900i	0.734042	−	0.184436i
$916$		−	17.2895i		−	0.571261i
$917$	5.44203	+	14.0389i	0.179712	+	0.463604i
$918$	−27.8287	+	25.3334i	−0.918483	+	0.836127i
$919$	10.2330	+	17.7241i	0.337556	+	0.584664i	0.983972	−	0.178321i	$-0.0570664\pi$
$919$	10.2330	+	17.7241i	0.337556	+	0.584664i	−0.646416	+	0.762985i	$0.723733\pi$
$920$	−0.333516	+	0.577667i	−0.0109957	+	0.0190451i
$921$	−28.6052	−	29.5139i	−0.942573	−	0.972516i
$922$	3.13710	−	1.81121i	0.103315	−	0.0596489i
$923$	−3.23478			−0.106474
$924$	−16.4008	+	35.6457i	−0.539546	+	1.17266i
$925$	−6.59168			−0.216733
$926$	3.33642	−	1.92628i	0.109641	−	0.0633015i
$927$	16.2475	+	30.2907i	0.533638	+	0.994878i
$928$	36.4027	−	63.0512i	1.19498	−	2.06976i
$929$	18.0062	+	31.1876i	0.590764	+	1.02323i	0.994130	+	0.108194i	$0.0345067\pi$
$929$	18.0062	+	31.1876i	0.590764	+	1.02323i	−0.403366	+	0.915039i	$0.632160\pi$
$930$	−51.6238	−	14.7013i	−1.69281	−	0.482075i
$931$	−51.2336	+	11.2426i	−1.67911	+	0.368462i
$932$		−	22.9755i		−	0.752587i
$933$	−0.501103	−	1.99435i	−0.0164054	−	0.0652922i
$934$	−23.6610	−	13.6607i	−0.774212	−	0.446991i
$935$	−23.5467	−	13.5947i	−0.770060	−	0.444594i
$936$	−0.0158980	+	0.508270i	−0.000519642	+	0.0166133i
$937$		−	37.4715i		−	1.22414i	−0.790803	−	0.612070i	$-0.790337\pi$
$937$		−	37.4715i		−	1.22414i	0.790803	−	0.612070i	$-0.209663\pi$
$938$	1.58734	−	10.2398i	0.0518286	−	0.334343i
$939$	9.14312	−	32.1062i	0.298375	−	1.04775i
$940$	6.01130	+	10.4119i	0.196067	+	0.339598i
$941$	10.4636	−	18.1234i	0.341103	−	0.590807i	−0.643535	−	0.765417i	$-0.722533\pi$
$941$	10.4636	−	18.1234i	0.341103	−	0.590807i	0.984638	+	0.174609i	$0.0558662\pi$
$942$	−10.2459	+	9.93047i	−0.333831	+	0.323552i
$943$	0.490599	−	0.283247i	0.0159761	−	0.00922381i
$944$	1.21349			0.0394956
$945$	10.1861	−	20.4311i	0.331355	−	0.664625i
$946$	−77.5403			−2.52105
$947$	−20.0140	+	11.5551i	−0.650369	+	0.375490i	−0.788597	−	0.614910i	$-0.789192\pi$
$947$	−20.0140	+	11.5551i	−0.650369	+	0.375490i	0.138229	+	0.990400i	$0.455859\pi$
$948$	16.4180	−	15.9125i	0.533232	−	0.516814i
$949$	−4.09869	+	7.09914i	−0.133049	+	0.230448i
$950$	−16.6219	−	28.7899i	−0.539284	−	0.934067i
$951$	9.26548	−	32.5358i	0.300454	−	1.05505i
$952$	−1.27922	−	1.02894i	−0.0414596	−	0.0333483i
$953$		−	37.9078i		−	1.22795i	−0.789325	−	0.613976i	$-0.789569\pi$
$953$		−	37.9078i		−	1.22795i	0.789325	−	0.613976i	$-0.210431\pi$
$954$	−1.78835	+	57.1749i	−0.0579000	+	1.85110i
$955$	−21.6921	−	12.5239i	−0.701940	−	0.405265i
$956$	11.1379	+	6.43047i	0.360225	+	0.207976i
$957$	−17.3998	−	69.2498i	−0.562455	−	2.23853i
$958$			18.0587i			0.583451i
$959$	−11.0963	−	8.92537i	−0.358318	−	0.288215i
$960$	20.1953	+	5.75116i	0.651799	+	0.185618i
$961$	28.9861	+	50.2054i	0.935035	+	1.61953i
$962$	2.90792	−	5.03667i	0.0937552	−	0.162389i
$963$	−19.9752	−	37.2403i	−0.643691	−	1.20005i
$964$	−8.09631	+	4.67441i	−0.260765	+	0.150552i
$965$	−21.2428			−0.683831
$966$	−1.98180	−	21.3933i	−0.0637634	−	0.688318i
$967$	−30.0334			−0.965810			−0.482905	−	0.875673i	$-0.660418\pi$
$967$	−30.0334			−0.965810			−0.482905	+	0.875673i	$0.660418\pi$
$968$	1.32204	−	0.763279i	0.0424919	−	0.0245327i
$969$	−33.0653	−	34.1157i	−1.06221	−	1.09595i
$970$	−4.03854	+	6.99496i	−0.129670	+	0.224595i
$971$	−2.37387	−	4.11167i	−0.0761812	−	0.131950i	0.825418	−	0.564522i	$-0.190939\pi$
$971$	−2.37387	−	4.11167i	−0.0761812	−	0.131950i	−0.901599	+	0.432572i	$0.857606\pi$
$972$	−5.44898	−	29.3397i	−0.174776	−	0.941070i
$973$	3.21152	−	20.7173i	0.102957	−	0.664166i
$974$		−	2.35226i		−	0.0753713i
$975$	3.76685	−	0.946463i	0.120636	−	0.0303111i
$976$	28.7039	+	16.5722i	0.918788	+	0.530463i
$977$	32.3951	+	18.7033i	1.03641	+	0.598373i	0.918815	−	0.394689i	$-0.129148\pi$
$977$	32.3951	+	18.7033i	1.03641	+	0.598373i	0.117597	+	0.993061i	$0.462481\pi$
$978$	−17.3201	+	4.35187i	−0.553836	+	0.139157i
$979$			11.8758i			0.379552i
$980$	−21.2082	−	6.73713i	−0.677471	−	0.215210i
$981$	9.76251	+	6.05102i	0.311693	+	0.193194i
$982$	−12.3417	−	21.3765i	−0.393840	−	0.682150i
$983$	−0.697795	+	1.20862i	−0.0222562	+	0.0385489i	−0.876939	−	0.480602i	$-0.840418\pi$
$983$	−0.697795	+	1.20862i	−0.0222562	+	0.0385489i	0.854683	+	0.519151i	$0.173752\pi$
$984$	0.0488467	+	0.0503984i	0.00155718	+	0.00160664i
$985$	0.982644	−	0.567330i	0.0313096	−	0.0180766i
$986$	−66.7506			−2.12577
$987$	15.7445	+	7.24414i	0.501153	+	0.230583i
$988$	14.3445			0.456359
$989$	17.9823	−	10.3821i	0.571805	−	0.330132i
$990$	38.8496	−	20.8383i	1.23472	−	0.662286i
$991$	3.56377	−	6.17263i	0.113207	−	0.196080i	−0.803855	−	0.594826i	$-0.797221\pi$
$991$	3.56377	−	6.17263i	0.113207	−	0.196080i	0.917062	+	0.398746i	$0.130554\pi$
$992$	−37.2553	−	64.5280i	−1.18286	−	2.04877i
$993$	−49.8896	−	14.2075i	−1.58320	−	0.450860i
$994$	6.12001	+	15.7878i	0.194115	+	0.500760i
$995$			21.3509i			0.676870i
$996$	2.35795	+	9.38445i	0.0747144	+	0.297358i
$997$	−51.5527	−	29.7640i	−1.63269	−	0.942634i	−0.983259	−	0.182215i	$-0.941673\pi$
$997$	−51.5527	−	29.7640i	−1.63269	−	0.942634i	−0.649432	−	0.760420i	$-0.724993\pi$
$998$	38.6015	+	22.2866i	1.22191	+	0.705470i
$999$	4.64073	−	14.5524i	0.146826	−	0.460419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.248.6	yes	64
3.2	odd	2	inner	273.2.bh.a.248.27	yes	64
7.5	odd	6	inner	273.2.bh.a.131.27	yes	64
21.5	even	6	inner	273.2.bh.a.131.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.6	✓	64	21.5	even	6	inner
273.2.bh.a.131.27	yes	64	7.5	odd	6	inner
273.2.bh.a.248.6	yes	64	1.1	even	1	trivial
273.2.bh.a.248.27	yes	64	3.2	odd	2	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.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71340 + 0.989233i) q^{2} +(-1.24374 + 1.20545i) q^{3} +(0.957162 - 1.65785i) q^{4} +(-0.830302 - 1.43813i) q^{5} +(0.938561 - 3.29577i) q^{6} +(2.61452 + 0.405294i) q^{7} -0.169506i q^{8} +(0.0937900 - 2.99853i) q^{9} +O(q^{10})\)	\(q+(-1.71340 + 0.989233i) q^{2} +(-1.24374 + 1.20545i) q^{3} +(0.957162 - 1.65785i) q^{4} +(-0.830302 - 1.43813i) q^{5} +(0.938561 - 3.29577i) q^{6} +(2.61452 + 0.405294i) q^{7} -0.169506i q^{8} +(0.0937900 - 2.99853i) q^{9} +(2.84528 + 1.64272i) q^{10} +(3.87356 + 2.23640i) q^{11} +(0.807993 + 3.21575i) q^{12} -1.00000i q^{13} +(-4.88066 + 1.89194i) q^{14} +(2.76627 + 0.787772i) q^{15} +(2.08201 + 3.60614i) q^{16} +(1.83031 - 3.17019i) q^{17} +(2.80555 + 5.23047i) q^{18} +(-6.48934 + 3.74662i) q^{19} -3.17894 q^{20} +(-3.74036 + 2.64759i) q^{21} -8.84927 q^{22} +(2.05223 - 1.18486i) q^{23} +(0.204331 + 0.210822i) q^{24} +(1.12120 - 1.94197i) q^{25} +(0.989233 + 1.71340i) q^{26} +(3.49793 + 3.84246i) q^{27} +(3.17444 - 3.94657i) q^{28} +9.21663i q^{29} +(-5.51902 + 1.38671i) q^{30} +(8.16879 + 4.71625i) q^{31} +(-6.84103 - 3.94967i) q^{32} +(-7.51357 + 1.88787i) q^{33} +7.24240i q^{34} +(-1.58798 - 4.09653i) q^{35} +(-4.88136 - 3.02557i) q^{36} +(-1.46979 - 2.54575i) q^{37} +(7.41256 - 12.8389i) q^{38} +(1.20545 + 1.24374i) q^{39} +(-0.243771 + 0.140741i) q^{40} +0.239057 q^{41} +(3.78964 - 8.23647i) q^{42} +8.76234 q^{43} +(7.41524 - 4.28119i) q^{44} +(-4.39014 + 2.35481i) q^{45} +(-2.34419 + 4.06026i) q^{46} +(-1.89098 - 3.27527i) q^{47} +(-6.93649 - 1.97536i) q^{48} +(6.67147 + 2.11930i) q^{49} +4.43649i q^{50} +(1.54506 + 6.14924i) q^{51} +(-1.65785 - 0.957162i) q^{52} +(8.34639 + 4.81879i) q^{53} +(-9.79444 - 3.12342i) q^{54} -7.42755i q^{55} +(0.0686999 - 0.443178i) q^{56} +(3.55471 - 12.4824i) q^{57} +(-9.11740 - 15.7918i) q^{58} +(0.145711 - 0.252379i) q^{59} +(3.95378 - 3.83204i) q^{60} +(6.89332 - 3.97986i) q^{61} -18.6619 q^{62} +(1.46050 - 7.80173i) q^{63} +7.30054 q^{64} +(-1.43813 + 0.830302i) q^{65} +(11.0062 - 10.6673i) q^{66} +(-0.989788 + 1.71436i) q^{67} +(-3.50380 - 6.06877i) q^{68} +(-1.12416 + 3.94751i) q^{69} +(6.77327 + 5.44812i) q^{70} -3.23478i q^{71} +(-0.508270 - 0.0158980i) q^{72} +(-7.09914 - 4.09869i) q^{73} +(5.03667 + 2.90792i) q^{74} +(0.946463 + 3.76685i) q^{75} +14.3445i q^{76} +(9.22110 + 7.41705i) q^{77} +(-3.29577 - 0.938561i) q^{78} +(-3.44782 - 5.97180i) q^{79} +(3.45739 - 5.98837i) q^{80} +(-8.98241 - 0.562465i) q^{81} +(-0.409600 + 0.236483i) q^{82} +2.91828 q^{83} +(0.809193 + 8.73514i) q^{84} -6.07884 q^{85} +(-15.0134 + 8.66799i) q^{86} +(-11.1102 - 11.4631i) q^{87} +(0.379083 - 0.656592i) q^{88} +(1.32756 + 2.29940i) q^{89} +(5.19262 - 8.37760i) q^{90} +(0.405294 - 2.61452i) q^{91} -4.53639i q^{92} +(-15.8451 + 3.98125i) q^{93} +(6.48001 + 3.74123i) q^{94} +(10.7762 + 6.22165i) q^{95} +(13.2696 - 3.33413i) q^{96} +2.45844i q^{97} +(-13.5274 + 2.96842i) q^{98} +(7.06922 - 11.4052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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