LMFDB - Embedded newform 546.2.bv.a.317.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.36
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.70468 - 0.306679i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.82490 + 0.488980i) q^{5} +(1.56722 - 0.737434i) q^{6} +(2.57215 + 0.619719i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.81190 - 1.04558i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.70468 - 0.306679i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.82490 + 0.488980i) q^{5} +(1.56722 - 0.737434i) q^{6} +(2.57215 + 0.619719i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.81190 - 1.04558i) q^{9} +(-1.63616 + 0.944637i) q^{10} +(-1.71267 - 0.458908i) q^{11} +(1.32296 - 1.11793i) q^{12} +(1.62200 - 3.22011i) q^{13} +(2.64490 - 0.0671181i) q^{14} +(-2.96091 + 1.39321i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.01432 + 3.48891i) q^{17} +(2.44547 - 1.73773i) q^{18} +(-0.854328 - 3.18839i) q^{19} +(-1.33592 + 1.33592i) q^{20} +(4.57476 + 0.267603i) q^{21} -1.77308 q^{22} +(-3.75204 + 6.49873i) q^{23} +(0.988539 - 1.42225i) q^{24} +(-1.23898 + 0.715324i) q^{25} +(0.733303 - 3.53019i) q^{26} +(4.47274 - 2.64473i) q^{27} +(2.53741 - 0.749382i) q^{28} -2.36532i q^{29} +(-2.49943 + 2.11208i) q^{30} +(7.49138 + 2.00731i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-3.06029 - 0.257054i) q^{33} +(2.84869 + 2.84869i) q^{34} +(-4.99694 + 0.126804i) q^{35} +(1.91238 - 2.31145i) q^{36} +(-7.18011 + 1.92390i) q^{37} +(-1.65043 - 2.85864i) q^{38} +(1.77745 - 5.98671i) q^{39} +(-0.944637 + 1.63616i) q^{40} +(-1.16845 - 1.16845i) q^{41} +(4.48814 - 0.925549i) q^{42} -1.15824i q^{43} +(-1.71267 + 0.458908i) q^{44} +(-4.62016 + 3.28304i) q^{45} +(-1.94220 + 7.24839i) q^{46} +(-2.55755 - 9.54491i) q^{47} +(0.586751 - 1.62964i) q^{48} +(6.23190 + 3.18802i) q^{49} +(-1.01162 + 1.01162i) q^{50} +(4.50376 + 5.32974i) q^{51} +(-0.205365 - 3.59970i) q^{52} +(-8.17176 + 4.71797i) q^{53} +(3.63583 - 3.71225i) q^{54} +3.34984 q^{55} +(2.25699 - 1.38058i) q^{56} +(-2.43417 - 5.17320i) q^{57} +(-0.612191 - 2.28473i) q^{58} +(-12.1981 - 3.26848i) q^{59} +(-1.86762 + 2.68702i) q^{60} +(-5.96460 + 10.3310i) q^{61} +7.75565 q^{62} +(7.88058 - 0.946802i) q^{63} -1.00000i q^{64} +(-1.38541 + 6.66950i) q^{65} +(-3.02255 + 0.543767i) q^{66} +(-10.6271 - 2.84753i) q^{67} +(3.48891 + 2.01432i) q^{68} +(-4.40303 + 12.2290i) q^{69} +(-4.79385 + 1.41579i) q^{70} +(1.54553 + 1.54553i) q^{71} +(1.24897 - 2.72765i) q^{72} +(0.439791 - 1.64132i) q^{73} +(-6.43751 + 3.71670i) q^{74} +(-1.89269 + 1.59937i) q^{75} +(-2.33407 - 2.33407i) q^{76} +(-4.12084 - 2.24175i) q^{77} +(0.167415 - 6.24275i) q^{78} +(-3.34611 + 5.79563i) q^{79} +(-0.488980 + 1.82490i) q^{80} +(6.81352 - 5.88013i) q^{81} +(-1.43105 - 0.826218i) q^{82} +(4.17139 + 4.17139i) q^{83} +(4.09566 - 2.05563i) q^{84} +(-5.38194 - 5.38194i) q^{85} +(-0.299774 - 1.11877i) q^{86} +(-0.725394 - 4.03213i) q^{87} +(-1.53553 + 0.886542i) q^{88} +(0.853770 + 3.18631i) q^{89} +(-3.61301 + 4.36696i) q^{90} +(6.16759 - 7.27742i) q^{91} +7.50409i q^{92} +(13.3860 + 1.12438i) q^{93} +(-4.94081 - 8.55773i) q^{94} +(3.11812 + 5.40074i) q^{95} +(0.144976 - 1.72597i) q^{96} +(5.14678 - 5.14678i) q^{97} +(6.84467 + 1.46646i) q^{98} +(-5.29567 + 0.500330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.70468	−	0.306679i	0.984200	−	0.177061i
$3$	1.70468	−	0.306679i	0.984200	−	0.177061i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.82490	+	0.488980i	−0.816119	+	0.218678i	−0.642649	−	0.766161i	$-0.722165\pi$
$5$	−1.82490	+	0.488980i	−0.816119	+	0.218678i	−0.173470	+	0.984839i	$0.555498\pi$
$6$	1.56722	−	0.737434i	0.639817	−	0.301056i
$7$	2.57215	+	0.619719i	0.972181	+	0.234232i
$7$	2.57215	+	0.619719i	0.972181	+	0.234232i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.81190	−	1.04558i	0.937299	−	0.348527i
$10$	−1.63616	+	0.944637i	−0.517399	+	0.298720i
$11$	−1.71267	−	0.458908i	−0.516388	−	0.138366i	−0.00879290	−	0.999961i	$-0.502799\pi$
$11$	−1.71267	−	0.458908i	−0.516388	−	0.138366i	−0.507596	+	0.861595i	$0.669466\pi$
$12$	1.32296	−	1.11793i	0.381906	−	0.322720i
$13$	1.62200	−	3.22011i	0.449861	−	0.893098i
$13$	1.62200	−	3.22011i	0.449861	−	0.893098i
$14$	2.64490	−	0.0671181i	0.706879	−	0.0179381i
$15$	−2.96091	+	1.39321i	−0.764505	+	0.359726i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.01432	+	3.48891i	0.488545	+	0.846186i	0.999913	−	0.0131764i	$-0.00419430\pi$
$17$	2.01432	+	3.48891i	0.488545	+	0.846186i	−0.511368	+	0.859362i	$0.670861\pi$
$18$	2.44547	−	1.73773i	0.576402	−	0.409586i
$19$	−0.854328	−	3.18839i	−0.195996	−	0.731468i	−0.992007	−	0.126185i	$-0.959727\pi$
$19$	−0.854328	−	3.18839i	−0.195996	−	0.731468i	0.796011	−	0.605283i	$-0.206940\pi$
$20$	−1.33592	+	1.33592i	−0.298720	+	0.298720i
$21$	4.57476	+	0.267603i	0.998294	+	0.0583957i
$22$	−1.77308			−0.378023
$23$	−3.75204	+	6.49873i	−0.782355	+	1.35508i	0.148211	+	0.988956i	$0.452648\pi$
$23$	−3.75204	+	6.49873i	−0.782355	+	1.35508i	−0.930566	+	0.366123i	$0.880685\pi$
$24$	0.988539	−	1.42225i	0.201785	−	0.290315i
$25$	−1.23898	+	0.715324i	−0.247795	+	0.143065i
$26$	0.733303	−	3.53019i	0.143813	−	0.692328i
$27$	4.47274	−	2.64473i	0.860779	−	0.508979i
$28$	2.53741	−	0.749382i	0.479525	−	0.141620i
$29$		−	2.36532i		−	0.439230i	−0.975587	−	0.219615i	$-0.929520\pi$
$29$		−	2.36532i		−	0.439230i	0.975587	−	0.219615i	$-0.0704800\pi$
$30$	−2.49943	+	2.11208i	−0.456332	+	0.385612i
$31$	7.49138	+	2.00731i	1.34549	+	0.360523i	0.858469	−	0.512866i	$-0.171416\pi$
$31$	7.49138	+	2.00731i	1.34549	+	0.360523i	0.487023	+	0.873389i	$0.338083\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−3.06029	−	0.257054i	−0.532729	−	0.0447474i
$34$	2.84869	+	2.84869i	0.488545	+	0.488545i
$35$	−4.99694	+	0.126804i	−0.844637	+	0.0214338i
$36$	1.91238	−	2.31145i	0.318731	−	0.385241i
$37$	−7.18011	+	1.92390i	−1.18040	+	0.316288i	−0.795086	−	0.606497i	$-0.792574\pi$
$37$	−7.18011	+	1.92390i	−1.18040	+	0.316288i	−0.385316	+	0.922785i	$0.625908\pi$
$38$	−1.65043	−	2.85864i	−0.267736	−	0.463732i
$39$	1.77745	−	5.98671i	0.284620	−	0.958640i
$40$	−0.944637	+	1.63616i	−0.149360	+	0.258699i
$41$	−1.16845	−	1.16845i	−0.182481	−	0.182481i	0.609955	−	0.792436i	$-0.291188\pi$
$41$	−1.16845	−	1.16845i	−0.182481	−	0.182481i	−0.792436	+	0.609955i	$0.791188\pi$
$42$	4.48814	−	0.925549i	0.692534	−	0.142815i
$43$		−	1.15824i		−	0.176630i	−0.996093	−	0.0883149i	$-0.971852\pi$
$43$		−	1.15824i		−	0.176630i	0.996093	−	0.0883149i	$-0.0281482\pi$
$44$	−1.71267	+	0.458908i	−0.258194	+	0.0691829i
$45$	−4.62016	+	3.28304i	−0.688732	+	0.489406i
$46$	−1.94220	+	7.24839i	−0.286362	+	1.06872i
$47$	−2.55755	−	9.54491i	−0.373057	−	1.39227i	−0.856163	−	0.516706i	$-0.827158\pi$
$47$	−2.55755	−	9.54491i	−0.373057	−	1.39227i	0.483106	−	0.875562i	$-0.339509\pi$
$48$	0.586751	−	1.62964i	0.0846902	−	0.235218i
$49$	6.23190	+	3.18802i	0.890271	+	0.455432i
$50$	−1.01162	+	1.01162i	−0.143065	+	0.143065i
$51$	4.50376	+	5.32974i	0.630653	+	0.746313i
$52$	−0.205365	−	3.59970i	−0.0284790	−	0.499188i
$53$	−8.17176	+	4.71797i	−1.12248	+	0.648063i	−0.942032	−	0.335522i	$-0.891087\pi$
$53$	−8.17176	+	4.71797i	−1.12248	+	0.648063i	−0.180445	+	0.983585i	$0.557754\pi$
$54$	3.63583	−	3.71225i	0.494773	−	0.505173i
$55$	3.34984			0.451692
$56$	2.25699	−	1.38058i	0.301603	−	0.184487i
$57$	−2.43417	−	5.17320i	−0.322414	−	0.685207i
$58$	−0.612191	−	2.28473i	−0.0803846	−	0.299999i
$59$	−12.1981	−	3.26848i	−1.58806	−	0.425520i	−0.646652	−	0.762785i	$-0.723831\pi$
$59$	−12.1981	−	3.26848i	−1.58806	−	0.425520i	−0.941410	+	0.337265i	$0.890498\pi$
$60$	−1.86762	+	2.68702i	−0.241109	+	0.346892i
$61$	−5.96460	+	10.3310i	−0.763689	+	1.32275i	0.177249	+	0.984166i	$0.443280\pi$
$61$	−5.96460	+	10.3310i	−0.763689	+	1.32275i	−0.940937	+	0.338581i	$0.890053\pi$
$62$	7.75565			0.984968
$63$	7.88058	−	0.946802i	0.992860	−	0.119286i
$64$		−	1.00000i		−	0.125000i
$65$	−1.38541	+	6.66950i	−0.171839	+	0.827250i
$66$	−3.02255	+	0.543767i	−0.372050	+	0.0669331i
$67$	−10.6271	−	2.84753i	−1.29831	−	0.347881i	−0.457498	−	0.889211i	$-0.651254\pi$
$67$	−10.6271	−	2.84753i	−1.29831	−	0.347881i	−0.840810	+	0.541330i	$0.817921\pi$
$68$	3.48891	+	2.01432i	0.423093	+	0.244273i
$69$	−4.40303	+	12.2290i	−0.530062	+	1.47219i
$70$	−4.79385	+	1.41579i	−0.572975	+	0.169219i
$71$	1.54553	+	1.54553i	0.183421	+	0.183421i	0.792845	−	0.609424i	$-0.208599\pi$
$71$	1.54553	+	1.54553i	0.183421	+	0.183421i	−0.609424	+	0.792845i	$0.708599\pi$
$72$	1.24897	−	2.72765i	0.147193	−	0.321456i
$73$	0.439791	−	1.64132i	0.0514736	−	0.192102i	−0.935402	−	0.353587i	$-0.884962\pi$
$73$	0.439791	−	1.64132i	0.0514736	−	0.192102i	0.986875	+	0.161485i	$0.0516284\pi$
$74$	−6.43751	+	3.71670i	−0.748345	+	0.432057i
$75$	−1.89269	+	1.59937i	−0.218549	+	0.184679i
$76$	−2.33407	−	2.33407i	−0.267736	−	0.267736i
$77$	−4.12084	−	2.24175i	−0.469613	−	0.255471i
$78$	0.167415	−	6.24275i	0.0189560	−	0.706853i
$79$	−3.34611	+	5.79563i	−0.376467	+	0.652059i	−0.990545	−	0.137185i	$-0.956194\pi$
$79$	−3.34611	+	5.79563i	−0.376467	+	0.652059i	0.614079	+	0.789245i	$0.289528\pi$
$80$	−0.488980	+	1.82490i	−0.0546696	+	0.204030i
$81$	6.81352	−	5.88013i	0.757058	−	0.653348i
$82$	−1.43105	−	0.826218i	−0.158033	−	0.0912405i
$83$	4.17139	+	4.17139i	0.457869	+	0.457869i	0.897956	−	0.440086i	$-0.145052\pi$
$83$	4.17139	+	4.17139i	0.457869	+	0.457869i	−0.440086	+	0.897956i	$0.645052\pi$
$84$	4.09566	−	2.05563i	0.446873	−	0.224287i
$85$	−5.38194	−	5.38194i	−0.583754	−	0.583754i
$86$	−0.299774	−	1.11877i	−0.0323255	−	0.120640i
$87$	−0.725394	−	4.03213i	−0.0777704	−	0.432290i
$88$	−1.53553	+	0.886542i	−0.163689	+	0.0945056i
$89$	0.853770	+	3.18631i	0.0904994	+	0.337748i	0.996299	−	0.0859586i	$-0.0273953\pi$
$89$	0.853770	+	3.18631i	0.0904994	+	0.337748i	−0.905799	+	0.423707i	$0.860729\pi$
$90$	−3.61301	+	4.36696i	−0.380845	+	0.460318i
$91$	6.16759	−	7.27742i	0.646539	−	0.762881i
$92$			7.50409i			0.782355i
$93$	13.3860	+	1.12438i	1.38807	+	0.116593i
$94$	−4.94081	−	8.55773i	−0.509605	−	0.882662i
$95$	3.11812	+	5.40074i	0.319912	+	0.554105i
$96$	0.144976	−	1.72597i	0.0147965	−	0.176156i
$97$	5.14678	−	5.14678i	0.522576	−	0.522576i	−0.395772	−	0.918349i	$-0.629523\pi$
$97$	5.14678	−	5.14678i	0.522576	−	0.522576i	0.918349	+	0.395772i	$0.129523\pi$
$98$	6.84467	+	1.46646i	0.691416	+	0.148135i
$99$	−5.29567	+	0.500330i	−0.532234	+	0.0502851i
$100$	−0.715324	+	1.23898i	−0.0715324	+	0.123898i
$101$	1.23524	+	2.13950i	0.122911	+	0.212888i	0.920914	−	0.389765i	$-0.127444\pi$
$101$	1.23524	+	2.13950i	0.122911	+	0.212888i	−0.798003	+	0.602653i	$0.794110\pi$
$102$	5.72974	+	3.98248i	0.567329	+	0.394324i
$103$	2.64117	+	1.52488i	0.260242	+	0.150251i	0.624445	−	0.781069i	$-0.285325\pi$
$103$	2.64117	+	1.52488i	0.260242	+	0.150251i	−0.364203	+	0.931320i	$0.618659\pi$
$104$	−1.13004	−	3.42389i	−0.110809	−	0.335740i
$105$	−8.47931	+	1.74862i	−0.827496	+	0.170647i
$106$	−6.67222	+	6.67222i	−0.648063	+	0.648063i
$107$	13.5598	+	7.82877i	1.31088	+	0.756836i	0.982242	−	0.187621i	$-0.0600776\pi$
$107$	13.5598	+	7.82877i	1.31088	+	0.756836i	0.328636	+	0.944457i	$0.393411\pi$
$108$	2.55114	−	4.52678i	0.245483	−	0.435589i
$109$	4.88654	+	1.30934i	0.468045	+	0.125412i	0.485131	−	0.874442i	$-0.338772\pi$
$109$	4.88654	+	1.30934i	0.468045	+	0.125412i	−0.0170853	+	0.999854i	$0.505439\pi$
$110$	3.23570	−	0.867002i	0.308511	−	0.0826654i
$111$	−11.6498	+	5.48163i	−1.10575	+	0.520294i
$112$	1.82277	−	1.91769i	0.172235	−	0.181204i
$113$		−	10.8278i		−	1.01859i	−0.860592	−	0.509296i	$-0.829906\pi$
$113$		−	10.8278i		−	1.01859i	0.860592	−	0.509296i	$-0.170094\pi$
$114$	−3.69015	−	4.36692i	−0.345614	−	0.408999i
$115$	3.66935	−	13.6942i	0.342168	−	1.27699i
$116$	−1.18266	−	2.04843i	−0.109807	−	0.190192i
$117$	1.19400	−	10.7506i	0.110386	−	0.993889i
$118$	−12.6284			−1.16254
$119$	3.01900	+	10.2223i	0.276751	+	0.937078i
$120$	−1.10853	+	3.07883i	−0.101195	+	0.281058i
$121$	−6.80365	−	3.92809i	−0.618513	−	0.357099i
$122$	−3.08750	+	11.5227i	−0.279529	+	1.04322i
$123$	−2.35018	−	1.63350i	−0.211908	−	0.147288i
$124$	7.49138	−	2.00731i	0.672746	−	0.180262i
$125$	8.59082	−	8.59082i	0.768386	−	0.768386i
$126$	7.36701	−	2.95418i	0.656305	−	0.263180i
$127$			19.2052i			1.70419i	0.523390	+	0.852093i	$0.324667\pi$
$127$			19.2052i			1.70419i	−0.523390	+	0.852093i	$0.675333\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−0.355207	−	1.97443i	−0.0312743	−	0.173839i
$130$	0.387990	+	6.80081i	0.0340290	+	0.596471i
$131$	−3.71710	−	2.14607i	−0.324764	−	0.187503i	0.328750	−	0.944417i	$-0.393373\pi$
$131$	−3.71710	−	2.14607i	−0.324764	−	0.187503i	−0.653514	+	0.756914i	$0.726706\pi$
$132$	−2.77882	+	1.30753i	−0.241865	+	0.113806i
$133$	−0.221548	−	8.73047i	−0.0192106	−	0.757027i
$134$	−11.0020			−0.950428
$135$	−6.86907	+	7.01345i	−0.591195	+	0.603621i
$136$	3.89138	+	1.04269i	0.333683	+	0.0894100i
$137$	6.46244	+	1.73161i	0.552124	+	0.147941i	0.524085	−	0.851666i	$-0.324407\pi$
$137$	6.46244	+	1.73161i	0.552124	+	0.147941i	0.0280384	+	0.999607i	$0.491074\pi$
$138$	−1.08791	+	12.9518i	−0.0926092	+	1.10253i
$139$	12.9517			1.09855			0.549275	−	0.835642i	$-0.314904\pi$
$139$	12.9517			1.09855			0.549275	+	0.835642i	$0.314904\pi$
$140$	−4.26407	+	2.60828i	−0.360380	+	0.220440i
$141$	−7.28703	−	15.4867i	−0.613679	−	1.30422i
$142$	1.89288	+	1.09285i	0.158847	+	0.0917103i
$143$	−4.25568	+	4.77063i	−0.355877	+	0.398940i
$144$	0.500449	−	2.95796i	0.0417041	−	0.246497i
$145$	1.15660	+	4.31647i	0.0960500	+	0.358464i
$146$		−	1.69922i		−	0.140629i
$147$	11.6011	+	3.52338i	0.956844	+	0.290603i
$148$	−5.25620	+	5.25620i	−0.432057	+	0.432057i
$149$	1.67431	−	0.448629i	0.137165	−	0.0367531i	−0.189584	−	0.981865i	$-0.560714\pi$
$149$	1.67431	−	0.448629i	0.137165	−	0.0367531i	0.326748	+	0.945111i	$0.394047\pi$
$150$	−1.41425	+	2.03474i	−0.115473	+	0.166135i
$151$	−1.36199	+	5.08300i	−0.110837	+	0.413648i	−0.998942	−	0.0459921i	$-0.985355\pi$
$151$	−1.36199	+	5.08300i	−0.110837	+	0.413648i	0.888105	+	0.459641i	$0.152022\pi$
$152$	−2.85864	−	1.65043i	−0.231866	−	0.133868i
$153$	9.31201	+	7.70432i	0.752831	+	0.622858i
$154$	−4.56063	−	1.09881i	−0.367506	−	0.0885449i
$155$	−14.6525			−1.17692
$156$	−1.45403	−	6.07337i	−0.116416	−	0.486259i
$157$	−9.16996	−	15.8828i	−0.731843	−	1.26759i	−0.956095	−	0.293057i	$-0.905327\pi$
$157$	−9.16996	−	15.8828i	−0.731843	−	1.26759i	0.224252	−	0.974531i	$-0.428006\pi$
$158$	−1.73207	+	6.46419i	−0.137796	+	0.514263i
$159$	−12.4834	+	10.5488i	−0.989996	+	0.836570i
$160$			1.88927i			0.149360i
$161$	−13.6782	+	14.3905i	−1.07799	+	1.13413i
$162$	5.05947	−	7.44324i	0.397509	−	0.584796i
$163$	−16.4100	+	4.39704i	−1.28533	+	0.344403i	−0.835884	−	0.548906i	$-0.815045\pi$
$163$	−16.4100	+	4.39704i	−1.28533	+	0.344403i	−0.449444	+	0.893308i	$0.648378\pi$
$164$	−1.59613	−	0.427682i	−0.124637	−	0.0333964i
$165$	5.71042	−	1.02732i	0.444555	−	0.0799770i
$166$	5.10889	+	2.94962i	0.396527	+	0.228935i
$167$	−7.54305	+	7.54305i	−0.583698	+	0.583698i	−0.935918	−	0.352219i	$-0.885427\pi$
$167$	−7.54305	+	7.54305i	−0.583698	+	0.583698i	0.352219	+	0.935918i	$0.385427\pi$
$168$	3.42406	−	3.04562i	0.264172	−	0.234974i
$169$	−7.73825	−	10.4460i	−0.595250	−	0.803541i
$170$	−6.59151	−	3.80561i	−0.505546	−	0.291877i
$171$	−5.73600	−	8.07216i	−0.438643	−	0.617294i
$172$	−0.579120	−	1.00306i	−0.0441575	−	0.0764830i
$173$	7.40149	−	12.8198i	0.562725	−	0.974668i	−0.434533	−	0.900656i	$-0.643086\pi$
$173$	7.40149	−	12.8198i	0.562725	−	0.974668i	0.997257	−	0.0740116i	$-0.0235802\pi$
$174$	−1.74427	−	3.70699i	−0.132233	−	0.281026i
$175$	−3.63013	+	1.07210i	−0.274412	+	0.0810432i
$176$	−1.25376	+	1.25376i	−0.0945056	+	0.0945056i
$177$	−21.7963	−	1.83082i	−1.63831	−	0.137613i
$178$	1.64936	+	2.85677i	0.123624	+	0.214124i
$179$	−9.29037	−	16.0914i	−0.694395	−	1.20273i	−0.970384	−	0.241567i	$-0.922339\pi$
$179$	−9.29037	−	16.0914i	−0.694395	−	1.20273i	0.275989	−	0.961161i	$-0.410995\pi$
$180$	−2.35965	+	5.15327i	−0.175878	+	0.384102i
$181$			19.2547i			1.43119i	0.698515	+	0.715595i	$0.253844\pi$
$181$			19.2547i			1.43119i	−0.698515	+	0.715595i	$0.746156\pi$
$182$	4.07389	−	8.62574i	0.301977	−	0.639382i
$183$	−6.99946	+	19.4403i	−0.517415	+	1.43707i
$184$	1.94220	+	7.24839i	0.143181	+	0.534358i
$185$	12.1622	−	7.02186i	0.894183	−	0.516257i
$186$	13.2209	−	2.37849i	0.969405	−	0.174399i
$187$	−1.84878	−	6.89973i	−0.135196	−	0.504558i
$188$	−6.98736	−	6.98736i	−0.509605	−	0.509605i
$189$	13.1435	−	4.03080i	0.956052	−	0.293198i
$190$	4.40969	+	4.40969i	0.319912	+	0.319912i
$191$	13.2016	+	7.62196i	0.955236	+	0.551506i	0.894704	−	0.446660i	$-0.147387\pi$
$191$	13.2016	+	7.62196i	0.955236	+	0.551506i	0.0605325	+	0.998166i	$0.480720\pi$
$192$	−0.306679	−	1.70468i	−0.0221326	−	0.123025i
$193$	5.43309	−	20.2766i	0.391083	−	1.45954i	−0.437269	−	0.899331i	$-0.644054\pi$
$193$	5.43309	−	20.2766i	0.391083	−	1.45954i	0.828351	−	0.560209i	$-0.189279\pi$
$194$	3.63932	−	6.30349i	0.261288	−	0.452565i
$195$	−0.316293	+	11.7943i	−0.0226502	+	0.844605i
$196$	6.99099	−	0.355041i	0.499356	−	0.0253601i
$197$	7.65448	+	7.65448i	0.545359	+	0.545359i	0.925095	−	0.379736i	$-0.123985\pi$
$197$	7.65448	+	7.65448i	0.545359	+	0.545359i	−0.379736	+	0.925095i	$0.623985\pi$
$198$	−4.98573	+	1.85390i	−0.354320	+	0.131751i
$199$	10.0996	−	5.83099i	0.715940	−	0.413348i	−0.0973164	−	0.995253i	$-0.531026\pi$
$199$	10.0996	−	5.83099i	0.715940	−	0.413348i	0.813257	+	0.581905i	$0.197693\pi$
$200$	−0.370279	+	1.38190i	−0.0261827	+	0.0977150i
$201$	−18.9891	−	1.59502i	−1.33939	−	0.112504i
$202$	1.74689	+	1.74689i	0.122911	+	0.122911i
$203$	1.46584	−	6.08396i	0.102882	−	0.427011i
$204$	6.56524	+	2.36381i	0.459659	+	0.165500i
$205$	2.70365	+	1.56095i	0.188831	+	0.109022i
$206$	2.94584	+	0.789336i	0.205247	+	0.0549957i
$207$	−3.75541	+	22.1968i	−0.261019	+	1.54279i
$208$	−1.97770	−	3.01475i	−0.137129	−	0.209035i
$209$			5.85271i			0.404841i
$210$	−7.73781	+	3.88364i	−0.533960	+	0.267997i
$211$	9.45867			0.651162			0.325581	−	0.945514i	$-0.394440\pi$
$211$	9.45867			0.651162			0.325581	+	0.945514i	$0.394440\pi$
$212$	−4.71797	+	8.17176i	−0.324031	+	0.561239i
$213$	3.10862	+	2.16066i	0.212999	+	0.148046i
$214$	15.1240	+	4.05247i	1.03386	+	0.277021i
$215$	0.566356	+	2.11367i	0.0386251	+	0.144151i
$216$	1.29259	−	5.03281i	0.0879499	−	0.342439i
$217$	18.0250	+	9.80565i	1.22361	+	0.665651i
$218$	5.05892			0.342633
$219$	0.246346	−	2.93281i	0.0166465	−	0.198181i
$220$	2.90104	−	1.67492i	0.195588	−	0.112923i
$221$	14.5019	−	0.827343i	0.975505	−	0.0556531i
$222$	−9.83409	+	8.31004i	−0.660021	+	0.557733i
$223$	8.24792	−	8.24792i	0.552321	−	0.552321i	−0.374789	−	0.927110i	$-0.622285\pi$
$223$	8.24792	−	8.24792i	0.552321	−	0.552321i	0.927110	+	0.374789i	$0.122285\pi$
$224$	1.26432	−	2.32411i	0.0844762	−	0.155286i
$225$	−2.73595	+	3.30687i	−0.182396	+	0.220458i
$226$	−2.80243	−	10.4588i	−0.186415	−	0.695711i
$227$	2.40458	−	8.97401i	0.159597	−	0.595626i	−0.839070	−	0.544023i	$-0.816900\pi$
$227$	2.40458	−	8.97401i	0.159597	−	0.595626i	0.998668	−	0.0516026i	$-0.0164329\pi$
$228$	−4.69465	−	3.26304i	−0.310911	−	0.216100i
$229$	19.3307	−	5.17964i	1.27741	−	0.342281i	0.444544	−	0.895757i	$-0.353366\pi$
$229$	19.3307	−	5.17964i	1.27741	−	0.342281i	0.832865	+	0.553477i	$0.186699\pi$
$230$		−	14.1773i		−	0.934821i
$231$	−7.71223	−	2.55770i	−0.507427	−	0.168285i
$232$	−1.67254	−	1.67254i	−0.109807	−	0.109807i
$233$	11.6047	−	20.0999i	0.760248	−	1.31679i	−0.182475	−	0.983210i	$-0.558411\pi$
$233$	11.6047	−	20.0999i	0.760248	−	1.31679i	0.942723	−	0.333577i	$-0.108256\pi$
$234$	−1.62913	−	10.6933i	−0.106500	−	0.699041i
$235$	9.33453	+	16.1679i	0.608918	+	1.05468i
$236$	−12.1981	+	3.26848i	−0.794031	+	0.212760i
$237$	−3.92666	+	10.9059i	−0.255064	+	0.708414i
$238$	5.56186	+	9.09263i	0.360522	+	0.589387i
$239$	−5.31141	−	5.31141i	−0.343567	−	0.343567i	0.514140	−	0.857706i	$-0.328111\pi$
$239$	−5.31141	−	5.31141i	−0.343567	−	0.343567i	−0.857706	+	0.514140i	$0.828111\pi$
$240$	−0.273899	+	3.26083i	−0.0176801	+	0.210486i
$241$	5.43462	−	20.2823i	0.350075	−	1.30650i	−0.536496	−	0.843903i	$-0.680252\pi$
$241$	5.43462	−	20.2823i	0.350075	−	1.30650i	0.886570	−	0.462594i	$-0.153081\pi$
$242$	−7.58848	−	2.03333i	−0.487806	−	0.130707i
$243$	9.81160	−	12.1133i	0.629414	−	0.777070i
$244$			11.9292i			0.763689i
$245$	−12.9314	−	2.77054i	−0.826160	−	0.177003i
$246$	−2.69288	−	0.969568i	−0.171691	−	0.0618174i
$247$	−11.6527	−	2.42054i	−0.741444	−	0.154015i
$248$	6.71659	−	3.87782i	0.426504	−	0.246242i
$249$	8.39018	+	5.83163i	0.531706	+	0.369564i
$250$	6.07462	−	10.5216i	0.384193	−	0.665442i
$251$	2.44319			0.154213			0.0771063	−	0.997023i	$-0.475432\pi$
$251$	2.44319			0.154213			0.0771063	+	0.997023i	$0.475432\pi$
$252$	6.35138	−	4.76024i	0.400100	−	0.299867i
$253$	9.40832	−	9.40832i	0.591496	−	0.591496i
$254$	4.97067	+	18.5508i	0.311888	+	1.16398i
$255$	−10.8250	−	7.52399i	−0.677890	−	0.471170i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.17304	+	3.76382i	−0.135551	+	0.234780i	−0.925808	−	0.377995i	$-0.876614\pi$
$257$	−2.17304	+	3.76382i	−0.135551	+	0.234780i	0.790257	+	0.612775i	$0.209947\pi$
$258$	−0.854125	−	1.81522i	−0.0531755	−	0.113011i
$259$	−19.6606	+	0.498915i	−1.22165	+	0.0310011i
$260$	2.13495	+	6.46866i	0.132404	+	0.401169i
$261$	−2.47314	−	6.65105i	−0.153083	−	0.411689i
$262$	−4.14588	−	1.11089i	−0.256134	−	0.0686308i
$263$	−9.85510	+	5.68984i	−0.607691	+	0.350851i	−0.772061	−	0.635548i	$-0.780774\pi$
$263$	−9.85510	+	5.68984i	−0.607691	+	0.350851i	0.164370	+	0.986399i	$0.447441\pi$
$264$	−2.34572	+	1.98219i	−0.144369	+	0.121995i
$265$	12.6056	−	12.6056i	0.774358	−	0.774358i
$266$	−2.47361	−	8.37564i	−0.151667	−	0.513544i
$267$	2.43258	+	5.16982i	0.148872	+	0.316388i
$268$	−10.6271	+	2.84753i	−0.649154	+	0.173940i
$269$	18.3630	−	10.6019i	1.11961	−	0.646408i	0.178310	−	0.983974i	$-0.442937\pi$
$269$	18.3630	−	10.6019i	1.11961	−	0.646408i	0.941302	+	0.337566i	$0.109604\pi$
$270$	−4.81980	+	8.55231i	−0.293324	+	0.520477i
$271$	−14.2899	+	3.82897i	−0.868051	+	0.232594i	−0.665245	−	0.746625i	$-0.731673\pi$
$271$	−14.2899	+	3.82897i	−0.868051	+	0.232594i	−0.202806	+	0.979219i	$0.565006\pi$
$272$	4.02865			0.244273
$273$	8.28195	−	14.2972i	0.501247	−	0.865304i
$274$	6.69041			0.404183
$275$	2.45022	−	0.656535i	0.147754	−	0.0395905i
$276$	2.30134	+	12.7921i	0.138525	+	0.769994i
$277$	−17.8363	+	10.2978i	−1.07168	+	0.618735i	−0.928640	−	0.370982i	$-0.879021\pi$
$277$	−17.8363	+	10.2978i	−1.07168	+	0.618735i	−0.143040	+	0.989717i	$0.545688\pi$
$278$	12.5104	−	3.35215i	0.750323	−	0.201049i
$279$	23.1638	−	2.18849i	1.38678	−	0.131022i
$280$	−3.44370	+	3.62303i	−0.205801	+	0.216518i
$281$	−8.00943	+	8.00943i	−0.477803	+	0.477803i	−0.904428	−	0.426626i	$-0.859702\pi$
$281$	−8.00943	+	8.00943i	−0.477803	+	0.477803i	0.426626	+	0.904428i	$0.359702\pi$
$282$	−11.0470	−	13.0730i	−0.657839	−	0.778485i
$283$	1.97537	−	1.14048i	0.117423	−	0.0677945i	−0.440138	−	0.897930i	$-0.645070\pi$
$283$	1.97537	−	1.14048i	0.117423	−	0.0677945i	0.557561	+	0.830136i	$0.311737\pi$
$284$	2.11123	+	0.565703i	0.125279	+	0.0335683i
$285$	6.97170	+	8.25030i	0.412968	+	0.488706i
$286$	−2.87594	+	5.70953i	−0.170058	+	0.337611i
$287$	−2.28131	−	3.72954i	−0.134662	−	0.220148i
$288$	−0.282181	−	2.98670i	−0.0166277	−	0.175993i
$289$	0.384992	−	0.666826i	0.0226466	−	0.0392251i
$290$	2.23437	+	3.87004i	0.131207	+	0.227257i
$291$	7.19523	−	10.3520i	0.421792	−	0.606848i
$292$	−0.439791	−	1.64132i	−0.0257368	−	0.0960511i
$293$	19.4879	−	19.4879i	1.13850	−	1.13850i	0.149775	−	0.988720i	$-0.452145\pi$
$293$	19.4879	−	19.4879i	1.13850	−	1.13850i	0.988720	−	0.149775i	$-0.0478550\pi$
$294$	12.1177	+	0.400734i	0.706720	+	0.0233713i
$295$	23.8586			1.38910
$296$	−3.71670	+	6.43751i	−0.216029	+	0.374173i
$297$	−8.87400	+	2.47697i	−0.514922	+	0.143729i
$298$	1.50114	−	0.866685i	0.0869589	−	0.0502057i
$299$	14.8408	+	22.6229i	0.858268	+	1.30832i
$300$	−0.839433	+	2.33144i	−0.0484647	+	0.134606i
$301$	0.717784	−	2.97916i	0.0413724	−	0.171716i
$302$			5.26231i			0.302812i
$303$	2.76183	+	3.26835i	0.158663	+	0.187762i
$304$	−3.18839	−	0.854328i	−0.182867	−	0.0489990i
$305$	5.83314	−	21.7696i	0.334004	−	1.24652i
$306$	10.9887	+	5.03168i	0.628184	+	0.287642i
$307$	4.22431	+	4.22431i	0.241094	+	0.241094i	0.817303	−	0.576209i	$-0.195468\pi$
$307$	4.22431	+	4.22431i	0.241094	+	0.241094i	−0.576209	+	0.817303i	$0.695468\pi$
$308$	−4.68963	+	0.119006i	−0.267216	+	0.00678099i
$309$	4.97001	+	1.78945i	0.282734	+	0.101798i
$310$	−14.1533	+	3.79235i	−0.803851	+	0.215391i
$311$	−1.39800	−	2.42141i	−0.0792733	−	0.137305i	0.823663	−	0.567079i	$-0.191927\pi$
$311$	−1.39800	−	2.42141i	−0.0792733	−	0.137305i	−0.902937	+	0.429774i	$0.858593\pi$
$312$	−2.97639	−	5.49009i	−0.168505	−	0.310815i
$313$	4.51429	−	7.81899i	0.255163	−	0.441955i	−0.709777	−	0.704427i	$-0.751204\pi$
$313$	4.51429	−	7.81899i	0.255163	−	0.441955i	0.964940	+	0.262471i	$0.0845375\pi$
$314$	−12.9683	−	12.9683i	−0.731843	−	0.731843i
$315$	−13.9183	+	5.58126i	−0.784207	+	0.314468i
$316$			6.69222i			0.376467i
$317$	−6.73660	+	1.80507i	−0.378365	+	0.101383i	−0.442989	−	0.896527i	$-0.646082\pi$
$317$	−6.73660	+	1.80507i	−0.378365	+	0.101383i	0.0646238	+	0.997910i	$0.479415\pi$
$318$	−9.32779	+	13.4202i	−0.523077	+	0.752570i
$319$	−1.08547	+	4.05101i	−0.0607744	+	0.226813i
$320$	0.488980	+	1.82490i	0.0273348	+	0.102015i
$321$	25.5161	+	9.18707i	1.42417	+	0.512772i
$322$	−9.48760	+	17.4403i	−0.528723	+	0.971911i
$323$	9.40313	−	9.40313i	0.523204	−	0.523204i
$324$	2.96062	−	8.49910i	0.164479	−	0.472172i
$325$	0.293805	+	5.14990i	0.0162974	+	0.285665i
$326$	−14.7128	+	8.49443i	−0.814865	+	0.470463i
$327$	8.73155	+	0.733421i	0.482856	+	0.0405583i
$328$	−1.65244			−0.0912405
$329$	−0.663235	−	26.1359i	−0.0365653	−	1.44092i
$330$	5.24995	−	2.47028i	0.289000	−	0.135985i
$331$	3.70810	+	13.8388i	0.203816	+	0.760650i	0.989807	+	0.142413i	$0.0454861\pi$
$331$	3.70810	+	13.8388i	0.203816	+	0.760650i	−0.785992	+	0.618237i	$0.787847\pi$
$332$	5.69822	+	1.52683i	0.312731	+	0.0837959i
$333$	−18.1781	+	12.9172i	−0.996155	+	0.707858i
$334$	−5.33374	+	9.23831i	−0.291849	+	0.505498i
$335$	20.7858			1.13565
$336$	2.51913	−	3.82805i	0.137430	−	0.208837i
$337$		−	1.28563i		−	0.0700326i	−0.999387	−	0.0350163i	$-0.988852\pi$
$337$		−	1.28563i		−	0.0700326i	0.999387	−	0.0350163i	$-0.0111483\pi$
$338$	−10.1782	−	8.08728i	−0.553621	−	0.439890i
$339$	−3.32065	−	18.4579i	−0.180353	−	1.00250i
$340$	−7.35187	−	1.96993i	−0.398711	−	0.106834i
$341$	−11.9091	−	6.87570i	−0.644912	−	0.372340i
$342$	−7.62978	−	6.31253i	−0.412571	−	0.341342i
$343$	14.0537	+	12.0621i	0.758828	+	0.651292i
$344$	−0.818999	−	0.818999i	−0.0441575	−	0.0441575i
$345$	2.05536	−	24.4696i	0.110657	−	1.31740i
$346$	3.83129	−	14.2986i	0.205972	−	0.768696i
$347$	18.9998	−	10.9696i	1.01997	−	0.588877i	0.105871	−	0.994380i	$-0.466237\pi$
$347$	18.9998	−	10.9696i	1.01997	−	0.588877i	0.914094	+	0.405503i	$0.132904\pi$
$348$	−2.64427	−	3.12923i	−0.141748	−	0.167744i
$349$	−17.9380	−	17.9380i	−0.960198	−	0.960198i	0.0390397	−	0.999238i	$-0.487570\pi$
$349$	−17.9380	−	17.9380i	−0.960198	−	0.960198i	−0.999238	+	0.0390397i	$0.987570\pi$
$350$	−3.22896	+	1.97512i	−0.172595	+	0.105574i
$351$	−1.26157	−	18.6925i	−0.0673374	−	0.997730i
$352$	−0.886542	+	1.53553i	−0.0472528	+	0.0818443i
$353$	−5.94830	+	22.1994i	−0.316596	+	1.18155i	0.605898	+	0.795542i	$0.292814\pi$
$353$	−5.94830	+	22.1994i	−0.316596	+	1.18155i	−0.922494	+	0.386011i	$0.873853\pi$
$354$	−21.5275	+	3.87287i	−1.14417	+	0.205841i
$355$	−3.57617	−	2.06470i	−0.189803	−	0.109583i
$356$	2.33254	+	2.33254i	0.123624	+	0.123624i
$357$	8.28140	+	16.5000i	0.438298	+	0.873271i
$358$	−13.1386	−	13.1386i	−0.694395	−	0.694395i
$359$	5.49845	+	20.5205i	0.290197	+	1.08303i	0.944957	+	0.327193i	$0.106103\pi$
$359$	5.49845	+	20.5205i	0.290197	+	1.08303i	−0.654761	+	0.755836i	$0.727231\pi$
$360$	−0.945485	+	5.58840i	−0.0498314	+	0.294535i
$361$	7.01850	−	4.05213i	0.369395	−	0.213270i
$362$	4.98348	+	18.5986i	0.261926	+	0.977521i
$363$	−12.8027	−	4.60962i	−0.671969	−	0.241942i
$364$	1.70257	−	9.38623i	0.0892391	−	0.491972i
$365$			3.21029i			0.168034i
$366$	−1.72945	+	20.5895i	−0.0903996	+	1.07623i
$367$	12.2557	+	21.2274i	0.639740	+	1.10806i	0.985490	+	0.169735i	$0.0542913\pi$
$367$	12.2557	+	21.2274i	0.639740	+	1.10806i	−0.345750	+	0.938327i	$0.612375\pi$
$368$	3.75204	+	6.49873i	0.195589	+	0.338770i
$369$	−4.50727	−	2.06385i	−0.234639	−	0.107440i
$370$	9.93040	−	9.93040i	0.516257	−	0.516257i
$371$	−23.9428	+	7.07112i	−1.24305	+	0.367114i
$372$	12.1548	−	5.71927i	0.630199	−	0.296531i
$373$	8.95144	−	15.5044i	0.463488	−	0.802785i	−0.535644	−	0.844444i	$-0.679931\pi$
$373$	8.95144	−	15.5044i	0.463488	−	0.802785i	0.999132	+	0.0416590i	$0.0132643\pi$
$374$	−3.57156	−	6.18613i	−0.184681	−	0.319877i
$375$	12.0100	−	17.2792i	0.620194	−	0.892297i
$376$	−8.55773	−	4.94081i	−0.441331	−	0.254803i
$377$	−7.61661	−	3.83655i	−0.392275	−	0.197592i
$378$	11.6524	−	7.29526i	0.599337	−	0.375227i
$379$	−18.5922	+	18.5922i	−0.955019	+	0.955019i	−0.999031	−	0.0440116i	$-0.985986\pi$
$379$	−18.5922	+	18.5922i	−0.955019	+	0.955019i	0.0440116	+	0.999031i	$0.485986\pi$
$380$	5.40074	+	3.11812i	0.277052	+	0.159956i
$381$	5.88983	+	32.7388i	0.301745	+	1.67726i
$382$	14.7245	+	3.94542i	0.753371	+	0.201865i
$383$	−20.5305	+	5.50114i	−1.04906	+	0.281095i	−0.741864	−	0.670551i	$-0.766058\pi$
$383$	−20.5305	+	5.50114i	−1.04906	+	0.281095i	−0.307197	+	0.951646i	$0.599391\pi$
$384$	−0.737434	−	1.56722i	−0.0376320	−	0.0799771i
$385$	8.61628	+	2.07596i	0.439126	+	0.105801i
$386$		−	20.9919i		−	1.06846i
$387$	−1.21103	−	3.25685i	−0.0615603	−	0.165555i
$388$	1.88385	−	7.03063i	0.0956381	−	0.356926i
$389$	6.58614	+	11.4075i	0.333931	+	0.578385i	0.983279	−	0.182106i	$-0.0582915\pi$
$389$	6.58614	+	11.4075i	0.333931	+	0.578385i	−0.649348	+	0.760491i	$0.724958\pi$
$390$	2.74707	+	11.4742i	0.139103	+	0.581021i
$391$	−30.2313			−1.52886
$392$	6.66089	−	2.15234i	0.336426	−	0.108710i
$393$	−6.99463	−	2.51841i	−0.352833	−	0.127037i
$394$	9.37479	+	5.41253i	0.472295	+	0.272680i
$395$	3.27236	−	12.2126i	0.164650	−	0.614483i
$396$	−4.33602	+	3.08113i	−0.217893	+	0.154833i
$397$	−22.5853	+	6.05173i	−1.13353	+	0.303727i	−0.776345	−	0.630308i	$-0.782929\pi$
$397$	−22.5853	+	6.05173i	−1.13353	+	0.303727i	−0.357181	+	0.934035i	$0.616262\pi$
$398$	8.24627	−	8.24627i	0.413348	−	0.413348i
$399$	−3.05512	−	14.8147i	−0.152947	−	0.741665i
$400$			1.43065i			0.0715324i
$401$	2.69059	+	10.0414i	0.134362	+	0.501444i	1.00000		0.000774026i	$0.000246380\pi$
$401$	2.69059	+	10.0414i	0.134362	+	0.501444i	−0.865638	+	0.500670i	$0.833087\pi$
$402$	−18.7549	+	3.37408i	−0.935411	+	0.168284i
$403$	18.6148	−	20.8672i	0.927267	−	1.03947i
$404$	2.13950	+	1.23524i	0.106444	+	0.0614555i
$405$	−9.55872	+	14.0623i	−0.474977	+	0.698762i
$406$	−0.158756	−	6.25604i	−0.00787892	−	0.310482i
$407$	13.1800			0.653310
$408$	6.95334	+	0.584057i	0.344242	+	0.0289151i
$409$	−2.65150	−	0.710467i	−0.131108	−	0.0351304i	0.192668	−	0.981264i	$-0.438286\pi$
$409$	−2.65150	−	0.710467i	−0.131108	−	0.0351304i	−0.323776	+	0.946134i	$0.604953\pi$
$410$	3.01553	+	0.808008i	0.148926	+	0.0399047i
$411$	11.5475	+	0.969949i	0.569595	+	0.0478440i
$412$	3.04976			0.150251
$413$	−29.3499	−	15.9664i	−1.44421	−	0.785657i
$414$	2.11751	+	22.4125i	0.104070	+	1.10151i
$415$	−9.65208	−	5.57263i	−0.473802	−	0.273550i
$416$	−2.69059	−	2.40016i	−0.131917	−	0.117677i
$417$	22.0786	−	3.97201i	1.08119	−	0.194510i
$418$	1.51479	+	5.65329i	0.0740910	+	0.276511i
$419$		−	36.6360i		−	1.78979i	−0.446281	−	0.894893i	$-0.647252\pi$
$419$		−	36.6360i		−	1.78979i	0.446281	−	0.894893i	$-0.352748\pi$
$420$	−6.46899	+	5.75400i	−0.315655	+	0.280767i
$421$	−8.20942	+	8.20942i	−0.400103	+	0.400103i	−0.878269	−	0.478167i	$-0.841302\pi$
$421$	−8.20942	+	8.20942i	−0.400103	+	0.400103i	0.478167	+	0.878269i	$0.341302\pi$
$422$	9.13638	−	2.44808i	0.444752	−	0.119171i
$423$	−17.1715	−	24.1652i	−0.834908	−	1.17495i
$424$	−2.44220	+	9.11442i	−0.118604	+	0.442635i
$425$	−4.99140	−	2.88179i	−0.242119	−	0.139787i
$426$	3.56192	+	1.28247i	0.172575	+	0.0621357i
$427$	−21.7441	+	22.8765i	−1.05227	+	1.10707i
$428$	15.6575			0.756836
$429$	−5.79153	+	9.43755i	−0.279618	+	0.455649i
$430$	1.09412	+	1.89506i	0.0527629	+	0.0913881i
$431$	3.40340	−	12.7016i	0.163936	−	0.611817i	−0.834238	−	0.551405i	$-0.814092\pi$
$431$	3.40340	−	12.7016i	0.163936	−	0.611817i	0.998174	−	0.0604118i	$-0.0192414\pi$
$432$	−0.0540370	−	5.19587i	−0.00259985	−	0.249986i
$433$			20.3113i			0.976097i	0.872816	+	0.488049i	$0.162291\pi$
$433$			20.3113i			0.976097i	−0.872816	+	0.488049i	$0.837709\pi$
$434$	19.9487	+	4.80632i	0.957567	+	0.230711i
$435$	3.29540	+	7.00352i	0.158002	+	0.335793i
$436$	4.88654	−	1.30934i	0.234023	−	0.0627062i
$437$	23.9260	+	6.41095i	1.14453	+	0.306677i
$438$	−0.521115	−	2.89664i	−0.0248998	−	0.138407i
$439$	25.1485	+	14.5195i	1.20027	+	0.692977i	0.960615	−	0.277881i	$-0.0896321\pi$
$439$	25.1485	+	14.5195i	1.20027	+	0.692977i	0.239656	+	0.970858i	$0.422965\pi$
$440$	2.36869	−	2.36869i	0.112923	−	0.112923i
$441$	20.8568	+	2.44844i	0.993180	+	0.116592i
$442$	13.7936	−	4.55253i	0.656097	−	0.216542i
$443$	21.6793	+	12.5166i	1.03002	+	0.594680i	0.916989	−	0.398912i	$-0.130612\pi$
$443$	21.6793	+	12.5166i	1.03002	+	0.594680i	0.113026	+	0.993592i	$0.463946\pi$
$444$	−7.34820	+	10.5721i	−0.348730	+	0.501731i
$445$	−3.11608	−	5.39722i	−0.147717	−	0.255853i
$446$	5.83216	−	10.1016i	0.276161	−	0.478324i
$447$	2.71658	−	1.27825i	0.128490	−	0.0604589i
$448$	0.619719	−	2.57215i	0.0292790	−	0.121523i
$449$	23.3615	−	23.3615i	1.10250	−	1.10250i	0.108386	−	0.994109i	$-0.465432\pi$
$449$	23.3615	−	23.3615i	1.10250	−	1.10250i	0.994109	−	0.108386i	$-0.0345684\pi$
$450$	−1.78684	+	3.90230i	−0.0842325	+	0.183956i
$451$	1.46495	+	2.53737i	0.0689820	+	0.119480i
$452$	−5.41389	−	9.37713i	−0.254648	−	0.441063i
$453$	−0.762908	+	9.08260i	−0.0358445	+	0.426738i
$454$		−	9.29057i		−	0.436028i
$455$	−7.69670	+	16.2964i	−0.360827	+	0.763986i
$456$	−5.37922	−	1.93679i	−0.251905	−	0.0906983i
$457$	−3.96263	−	14.7887i	−0.185364	−	0.691788i	−0.994552	−	0.104239i	$-0.966759\pi$
$457$	−3.96263	−	14.7887i	−0.185364	−	0.691788i	0.809188	−	0.587550i	$-0.199907\pi$
$458$	17.3314	−	10.0063i	0.809845	−	0.467564i
$459$	18.2368	+	10.2776i	0.851220	+	0.479719i
$460$	−3.66935	−	13.6942i	−0.171084	−	0.638495i
$461$	20.4542	+	20.4542i	0.952648	+	0.952648i	0.998929	−	0.0462800i	$-0.0147367\pi$
$461$	20.4542	+	20.4542i	0.952648	+	0.952648i	−0.0462800	+	0.998929i	$0.514737\pi$
$462$	−8.11142	−	0.474482i	−0.377377	−	0.0220749i
$463$	11.4042	+	11.4042i	0.530000	+	0.530000i	0.920572	−	0.390572i	$-0.127723\pi$
$463$	11.4042	+	11.4042i	0.530000	+	0.530000i	−0.390572	+	0.920572i	$0.627723\pi$
$464$	−2.04843	−	1.18266i	−0.0950960	−	0.0549037i
$465$	−24.9779	+	4.49362i	−1.15832	+	0.208387i
$466$	6.00702	−	22.4185i	0.278270	−	1.03852i
$467$	−7.70434	+	13.3443i	−0.356514	+	0.617501i	−0.987376	−	0.158394i	$-0.949368\pi$
$467$	−7.70434	+	13.3443i	−0.356514	+	0.617501i	0.630861	+	0.775895i	$0.282702\pi$
$468$	−4.34124	−	9.90725i	−0.200674	−	0.457963i
$469$	−25.5698	−	13.9101i	−1.18071	−	0.642308i
$470$	13.2010	+	13.2010i	0.608918	+	0.608918i
$471$	−20.5028	−	24.2630i	−0.944720	−	1.11798i
$472$	−10.9365	+	6.31422i	−0.503395	+	0.290636i
$473$	−0.531525	+	1.98368i	−0.0244395	+	0.0912096i
$474$	−0.970211	+	11.5506i	−0.0445632	+	0.530536i
$475$	3.33923	+	3.33923i	0.153214	+	0.153214i
$476$	7.72569	+	7.34329i	0.354106	+	0.336579i
$477$	−18.0451	+	21.8107i	−0.826230	+	0.998642i
$478$	−6.50513	−	3.75574i	−0.297538	−	0.171783i
$479$	−10.6367	−	2.85010i	−0.486004	−	0.130224i	0.00749277	−	0.999972i	$-0.497615\pi$
$479$	−10.6367	−	2.85010i	−0.486004	−	0.130224i	−0.493497	+	0.869747i	$0.664282\pi$
$480$	0.579400	+	3.22061i	0.0264459	+	0.147000i
$481$	−5.45093	+	26.2413i	−0.248541	+	1.19650i
$482$		−	20.9978i		−	0.956422i
$483$	−18.9038	+	28.7260i	−0.860151	+	1.30708i
$484$	−7.85618			−0.357099
$485$	−6.87568	+	11.9090i	−0.312208	+	0.540761i
$486$	6.34211	−	14.2400i	0.287684	−	0.645939i
$487$	−28.1534	−	7.54368i	−1.27575	−	0.341837i	−0.443521	−	0.896264i	$-0.646271\pi$
$487$	−28.1534	−	7.54368i	−1.27575	−	0.341837i	−0.832232	+	0.554427i	$0.812937\pi$
$488$	3.08750	+	11.5227i	0.139765	+	0.521609i
$489$	−26.6253	+	12.5282i	−1.20404	+	0.566543i
$490$	−13.2079	+	0.670770i	−0.596672	+	0.0303023i
$491$	17.6204			0.795198			0.397599	−	0.917559i	$-0.369844\pi$
$491$	17.6204			0.795198			0.397599	+	0.917559i	$0.369844\pi$
$492$	−2.85206	−	0.239563i	−0.128581	−	0.0108004i
$493$	8.25241	−	4.76453i	0.371670	−	0.214584i
$494$	−11.8821	+	0.677883i	−0.534602	+	0.0304994i
$495$	9.41940	−	3.50253i	0.423370	−	0.157427i
$496$	5.48407	−	5.48407i	0.246242	−	0.246242i
$497$	3.01754	+	4.93313i	0.135355	+	0.221281i
$498$	9.61363	+	3.46138i	0.430797	+	0.155108i
$499$	−1.57562	−	5.88028i	−0.0705343	−	0.263238i	0.921649	−	0.388024i	$-0.126842\pi$
$499$	−1.57562	−	5.88028i	−0.0705343	−	0.263238i	−0.992184	+	0.124786i	$0.960175\pi$
$500$	3.14446	−	11.7353i	0.140624	−	0.524817i
$501$	−10.5452	+	15.1718i	−0.471126	+	0.677826i
$502$	2.35994	−	0.632344i	0.105329	−	0.0282229i
$503$			38.6506i			1.72334i	0.507466	+	0.861671i	$0.330582\pi$
$503$			38.6506i			1.72334i	−0.507466	+	0.861671i	$0.669418\pi$
$504$	4.90292	−	6.24190i	0.218394	−	0.278036i
$505$	−3.30036	−	3.30036i	−0.146864	−	0.146864i
$506$	6.65268	−	11.5228i	0.295748	−	0.512250i
$507$	−16.3948	−	15.4340i	−0.728120	−	0.685449i
$508$	9.60260	+	16.6322i	0.426047	+	0.737934i
$509$	−1.77675	+	0.476080i	−0.0787532	+	0.0211019i	−0.297981	−	0.954572i	$-0.596313\pi$
$509$	−1.77675	+	0.476080i	−0.0787532	+	0.0211019i	0.219227	+	0.975674i	$0.429646\pi$
$510$	−12.4035	−	4.46589i	−0.549238	−	0.197753i
$511$	2.14837	−	3.94918i	0.0950381	−	0.174701i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−12.2536	−	12.0014i	−0.541011	−	0.529874i
$514$	−1.12485	+	4.19799i	−0.0496149	+	0.185166i
$515$	−5.56550	−	1.49127i	−0.245245	−	0.0657133i
$516$	−1.29483	−	1.53231i	−0.0570019	−	0.0674560i
$517$			17.5209i			0.770569i
$518$	−18.8615	+	5.57045i	−0.828728	+	0.244751i
$519$	8.68565	−	24.1235i	0.381258	−	1.05890i
$520$	3.73642	+	5.69568i	0.163853	+	0.249772i
$521$	−11.5622	+	6.67544i	−0.506549	+	0.292456i	−0.731414	−	0.681934i	$-0.761139\pi$
$521$	−11.5622	+	6.67544i	−0.506549	+	0.292456i	0.224865	+	0.974390i	$0.427806\pi$
$522$	−4.11028	−	5.78432i	−0.179902	−	0.253173i
$523$	−7.83685	+	13.5738i	−0.342681	+	0.593542i	−0.984930	−	0.172955i	$-0.944668\pi$
$523$	−7.83685	+	13.5738i	−0.342681	+	0.593542i	0.642248	+	0.766497i	$0.278002\pi$
$524$	−4.29214			−0.187503
$525$	−5.85944	+	2.94088i	−0.255727	+	0.128350i
$526$	−8.04665	+	8.04665i	−0.350851	+	0.350851i
$527$	8.08674	+	30.1801i	0.352264	+	1.31467i
$528$	−1.75276	+	2.52176i	−0.0762792	+	0.109746i
$529$	−16.6557	−	28.8484i	−0.724159	−	1.25428i
$530$	8.91353	−	15.4387i	0.387179	−	0.670614i
$531$	−37.7174	+	3.56350i	−1.63679	+	0.154643i
$532$	−4.55710	−	7.45003i	−0.197575	−	0.323000i
$533$	−5.65776	+	1.86732i	−0.245065	+	0.0808824i
$534$	3.68774	+	4.36407i	0.159584	+	0.188852i
$535$	−28.5734	−	7.65622i	−1.23534	−	0.331007i
$536$	−9.52801	+	5.50100i	−0.411547	+	0.237607i
$537$	−20.7720	−	24.5816i	−0.896380	−	1.06077i
$538$	14.9933	−	14.9933i	0.646408	−	0.646408i
$539$	−9.21015	−	8.31988i	−0.396709	−	0.358363i
$540$	−2.44206	+	9.50836i	−0.105090	+	0.409175i
$541$	28.0736	−	7.52229i	1.20698	−	0.323409i	0.401402	−	0.915902i	$-0.368523\pi$
$541$	28.0736	−	7.52229i	1.20698	−	0.323409i	0.805575	+	0.592493i	$0.201856\pi$
$542$	−12.8120	+	7.39701i	−0.550322	+	0.317729i
$543$	5.90500	+	32.8232i	0.253408	+	1.40858i
$544$	3.89138	−	1.04269i	0.166841	−	0.0447050i
$545$	−9.55767			−0.409406
$546$	4.29937	−	15.9535i	0.183996	−	0.682748i
$547$	−30.9427			−1.32301			−0.661506	−	0.749939i	$-0.730083\pi$
$547$	−30.9427			−1.32301			−0.661506	+	0.749939i	$0.730083\pi$
$548$	6.46244	−	1.73161i	0.276062	−	0.0739706i
$549$	−5.96995	+	35.2861i	−0.254791	+	1.50598i
$550$	2.19681	−	1.26833i	0.0936722	−	0.0540817i
$551$	−7.54158	+	2.02076i	−0.321282	+	0.0860873i
$552$	5.53377	+	11.7606i	0.235533	+	0.500564i
$553$	−12.1984	+	12.8336i	−0.518727	+	0.545739i
$554$	−14.5633	+	14.5633i	−0.618735	+	0.618735i
$555$	18.5793	−	15.6999i	0.788646	−	0.666425i
$556$	11.2165	−	6.47585i	0.475686	−	0.274637i
$557$	−6.35250	−	1.70215i	−0.269164	−	0.0721223i	0.121713	−	0.992565i	$-0.461161\pi$
$557$	−6.35250	−	1.70215i	−0.269164	−	0.0721223i	−0.390877	+	0.920443i	$0.627828\pi$
$558$	21.8081	−	8.10915i	0.923209	−	0.343288i
$559$	−3.72966	−	1.87866i	−0.157748	−	0.0794589i
$560$	−2.38865	+	4.39088i	−0.100939	+	0.185548i
$561$	−5.26758	−	11.1949i	−0.222398	−	0.472648i
$562$	−5.66353	+	9.80951i	−0.238901	+	0.413789i
$563$	−22.8101	−	39.5083i	−0.961332	−	1.66508i	−0.719163	−	0.694842i	$-0.755474\pi$
$563$	−22.8101	−	39.5083i	−0.961332	−	1.66508i	−0.242169	−	0.970234i	$-0.577859\pi$
$564$	−14.0541	−	9.76836i	−0.591785	−	0.411322i
$565$	5.29456	+	19.7596i	0.222744	+	0.831292i
$566$	1.61288	−	1.61288i	0.0677945	−	0.0677945i
$567$	21.1694	−	10.9021i	0.889032	−	0.457845i
$568$	2.18571			0.0917103
$569$	5.55993	−	9.63007i	0.233084	−	0.403714i	−0.725630	−	0.688085i	$-0.758452\pi$
$569$	5.55993	−	9.63007i	0.233084	−	0.403714i	0.958714	+	0.284371i	$0.0917849\pi$
$570$	8.86948	+	6.16477i	0.371502	+	0.258214i
$571$	−14.9711	+	8.64357i	−0.626521	+	0.361722i	−0.779404	−	0.626522i	$-0.784478\pi$
$571$	−14.9711	+	8.64357i	−0.626521	+	0.361722i	0.152882	+	0.988244i	$0.451144\pi$
$572$	−1.30021	+	6.25933i	−0.0543644	+	0.261716i
$573$	24.8421	+	8.94438i	1.03779	+	0.373657i
$574$	−3.16885	−	3.01201i	−0.132265	−	0.125719i
$575$		−	10.7357i		−	0.447710i
$576$	−1.04558	−	2.81190i	−0.0435659	−	0.117162i
$577$	−2.99074	−	0.801367i	−0.124506	−	0.0333613i	0.196028	−	0.980598i	$-0.437196\pi$
$577$	−2.99074	−	0.801367i	−0.124506	−	0.0333613i	−0.320534	+	0.947237i	$0.603862\pi$
$578$	0.199287	−	0.743748i	0.00828923	−	0.0309358i
$579$	3.04331	−	36.2314i	0.126476	−	1.50572i
$580$	3.15988	+	3.15988i	0.131207	+	0.131207i
$581$	8.14434	+	13.3145i	0.337884	+	0.552380i
$582$	4.27075	−	11.8616i	0.177028	−	0.491678i
$583$	16.1606	−	4.33022i	0.669304	−	0.179340i
$584$	−0.849611	−	1.47157i	−0.0351571	−	0.0608940i
$585$	3.07787	+	20.2025i	0.127254	+	0.835271i
$586$	13.7800	−	23.8677i	0.569248	−	0.985966i
$587$	17.5046	+	17.5046i	0.722490	+	0.722490i	0.969112	−	0.246621i	$-0.0793204\pi$
$587$	17.5046	+	17.5046i	0.722490	+	0.722490i	−0.246621	+	0.969112i	$0.579320\pi$
$588$	11.8085	−	2.74922i	0.486976	−	0.113376i
$589$		−	25.6004i		−	1.05484i
$590$	23.0456	−	6.17505i	0.948773	−	0.254223i
$591$	15.3959	+	10.7010i	0.633304	+	0.440181i
$592$	−1.92390	+	7.18011i	−0.0790720	+	0.295101i
$593$	1.20868	+	4.51085i	0.0496345	+	0.185238i	0.986292	−	0.165007i	$-0.0527648\pi$
$593$	1.20868	+	4.51085i	0.0496345	+	0.185238i	−0.936658	+	0.350246i	$0.886098\pi$
$594$	−7.93054	+	4.68933i	−0.325394	+	0.192406i
$595$	−10.5079	−	17.1785i	−0.430780	−	0.704248i
$596$	1.22568	−	1.22568i	0.0502057	−	0.0502057i
$597$	15.4284	−	13.0373i	0.631440	−	0.533582i
$598$	20.1904	+	18.0110i	0.825646	+	0.736524i
$599$	−30.3818	+	17.5409i	−1.24137	+	0.716703i	−0.969372	−	0.245596i	$-0.921016\pi$
$599$	−30.3818	+	17.5409i	−1.24137	+	0.716703i	−0.271994	+	0.962299i	$0.587683\pi$
$600$	−0.207409	+	2.46926i	−0.00846745	+	0.100807i
$601$	−31.5161			−1.28557			−0.642784	−	0.766048i	$-0.722221\pi$
$601$	−31.5161			−1.28557			−0.642784	+	0.766048i	$0.722221\pi$
$602$	−0.0777388	−	3.06343i	−0.00316840	−	0.124856i
$603$	−32.8597	+	3.10455i	−1.33815	+	0.126427i
$604$	1.36199	+	5.08300i	0.0554184	+	0.206824i
$605$	14.3367	+	3.84151i	0.582870	+	0.156180i
$606$	3.51364	+	2.44217i	0.142732	+	0.0992063i
$607$	−4.82277	+	8.35328i	−0.195750	+	0.339049i	−0.947146	−	0.320802i	$-0.896047\pi$
$607$	−4.82277	+	8.35328i	−0.195750	+	0.339049i	0.751396	+	0.659851i	$0.229381\pi$
$608$	−3.30087			−0.133868
$609$	0.632967	−	10.8208i	0.0256491	−	0.438480i
$610$		−	22.5375i		−	0.912517i
$611$	−34.8840	−	7.24622i	−1.41126	−	0.293151i
$612$	11.9166	+	2.01613i	0.481700	+	0.0814974i
$613$	6.27588	+	1.68162i	0.253480	+	0.0679198i	0.383322	−	0.923615i	$-0.374780\pi$
$613$	6.27588	+	1.68162i	0.253480	+	0.0679198i	−0.129841	+	0.991535i	$0.541447\pi$
$614$	5.17370	+	2.98704i	0.208794	+	0.120547i
$615$	5.08758	+	1.83178i	0.205151	+	0.0738645i
$616$	−4.49903	+	1.32872i	−0.181271	+	0.0535355i
$617$	−15.3887	−	15.3887i	−0.619527	−	0.619527i	0.325883	−	0.945410i	$-0.394339\pi$
$617$	−15.3887	−	15.3887i	−0.619527	−	0.619527i	−0.945410	+	0.325883i	$0.894339\pi$
$618$	5.26380	+	0.442142i	0.211741	+	0.0177856i
$619$	−10.0159	+	37.3800i	−0.402575	+	1.50243i	0.405911	+	0.913913i	$0.366954\pi$
$619$	−10.0159	+	37.3800i	−0.402575	+	1.50243i	−0.808485	+	0.588516i	$0.799712\pi$
$620$	−12.6895	+	7.32627i	−0.509621	+	0.294230i
$621$	0.405498	+	38.9903i	0.0162721	+	1.56463i
$622$	−1.97707	−	1.97707i	−0.0792733	−	0.0792733i
$623$	0.221403	+	8.72476i	0.00887033	+	0.349550i
$624$	−4.29591	−	4.53267i	−0.171974	−	0.181452i
$625$	−7.90001	+	13.6832i	−0.316000	+	0.547328i
$626$	2.33677	−	8.72095i	0.0933961	−	0.348559i
$627$	1.79490	+	9.97703i	0.0716815	+	0.398444i
$628$	−15.8828	−	9.16996i	−0.633794	−	0.365921i
$629$	−21.1754	−	21.1754i	−0.844318	−	0.844318i
$630$	−11.9995	+	8.99340i	−0.478071	+	0.358306i
$631$	−0.880984	−	0.880984i	−0.0350714	−	0.0350714i	0.689354	−	0.724425i	$-0.257895\pi$
$631$	−0.880984	−	0.880984i	−0.0350714	−	0.0350714i	−0.724425	+	0.689354i	$0.757895\pi$
$632$	1.73207	+	6.46419i	0.0688982	+	0.257132i
$633$	16.1240	−	2.90077i	0.640873	−	0.115295i
$634$	−6.03987	+	3.48712i	−0.239874	+	0.138491i
$635$	−9.39096	−	35.0475i	−0.372669	−	1.39082i
$636$	−5.53654	+	15.3772i	−0.219538	+	0.609745i
$637$	20.3739	−	14.8964i	0.807244	−	0.590219i
$638$			4.19392i			0.166039i
$639$	5.96184	+	2.72989i	0.235847	+	0.107993i
$640$	0.944637	+	1.63616i	0.0373400	+	0.0646748i
$641$	−20.8196	−	36.0606i	−0.822326	−	1.42431i	−0.903946	−	0.427646i	$-0.859343\pi$
$641$	−20.8196	−	36.0606i	−0.822326	−	1.42431i	0.0816205	−	0.996663i	$-0.473990\pi$
$642$	27.0245	+	2.26997i	1.06657	+	0.0895884i
$643$	6.49542	−	6.49542i	0.256154	−	0.256154i	−0.567334	−	0.823488i	$-0.692025\pi$
$643$	6.49542	−	6.49542i	0.256154	−	0.256154i	0.823488	+	0.567334i	$0.192025\pi$
$644$	−4.65043	+	19.3016i	−0.183253	+	0.760591i
$645$	1.61367	+	3.42945i	0.0635384	+	0.135034i
$646$	6.64902	−	11.5164i	0.261602	−	0.453108i
$647$	12.5131	+	21.6734i	0.491941	+	0.852068i	0.999957	−	0.00928034i	$-0.00295406\pi$
$647$	12.5131	+	21.6734i	0.491941	+	0.852068i	−0.508015	+	0.861348i	$0.669621\pi$
$648$	0.660010	−	8.97577i	0.0259276	−	0.352601i
$649$	19.3914	+	11.1956i	0.761179	+	0.439467i
$650$	1.61669	+	4.89838i	0.0634116	+	0.192130i
$651$	33.7341	+	11.1877i	1.32214	+	0.438479i
$652$	−12.0129	+	12.0129i	−0.470463	+	0.470463i
$653$	−6.96251	−	4.01981i	−0.272464	−	0.157307i	0.357543	−	0.933897i	$-0.383615\pi$
$653$	−6.96251	−	4.01981i	−0.272464	−	0.157307i	−0.630007	+	0.776590i	$0.716948\pi$
$654$	8.62386	−	1.55146i	0.337219	−	0.0606670i
$655$	7.83271	+	2.09877i	0.306049	+	0.0820056i
$656$	−1.59613	+	0.427682i	−0.0623185	+	0.0166982i
$657$	−0.479488	−	5.07506i	−0.0187066	−	0.197997i
$658$	−7.40510	−	25.0737i	−0.288681	−	0.977473i
$659$			9.01704i			0.351254i	0.984457	+	0.175627i	$0.0561953\pi$
$659$			9.01704i			0.351254i	−0.984457	+	0.175627i	$0.943805\pi$
$660$	4.43170	−	3.74490i	0.172504	−	0.145770i
$661$	−7.64816	+	28.5433i	−0.297479	+	1.11021i	0.641749	+	0.766914i	$0.278209\pi$
$661$	−7.64816	+	28.5433i	−0.297479	+	1.11021i	−0.939228	+	0.343293i	$0.888458\pi$
$662$	7.16350	+	12.4075i	0.278417	+	0.482233i
$663$	24.4675	−	5.85779i	0.950238	−	0.227498i
$664$	5.89924			0.228935
$665$	4.67332	+	15.8239i	0.181224	+	0.613623i
$666$	−14.2155	+	17.1819i	−0.550839	+	0.665785i
$667$	15.3716	+	8.87480i	0.595191	+	0.343633i
$668$	−2.76095	+	10.3040i	−0.106824	+	0.398673i
$669$	11.5306	−	16.5896i	0.445800	−	0.641389i
$670$	20.0775	−	5.37975i	0.775662	−	0.207838i
$671$	14.9563	−	14.9563i	0.577383	−	0.577383i
$672$	1.44252	−	4.34961i	0.0556464	−	0.167790i
$673$			22.6718i			0.873933i	0.899478	+	0.436967i	$0.143947\pi$
$673$			22.6718i			0.873933i	−0.899478	+	0.436967i	$0.856053\pi$
$674$	−0.332745	−	1.24182i	−0.0128169	−	0.0478332i
$675$	−3.64978	+	6.47622i	−0.140480	+	0.249270i
$676$	−11.9245	−	5.17740i	−0.458636	−	0.199131i
$677$	−35.2952	−	20.3777i	−1.35650	−	0.783178i	−0.367354	−	0.930081i	$-0.619736\pi$
$677$	−35.2952	−	20.3777i	−1.35650	−	0.783178i	−0.989151	+	0.146903i	$0.953070\pi$
$678$	−7.98476	−	16.9696i	−0.306653	−	0.651712i
$679$	16.4278	−	10.0487i	0.630443	−	0.385635i
$680$	−7.61122			−0.291877
$681$	1.34691	−	16.0353i	0.0516137	−	0.614473i
$682$	−13.2828	−	3.55913i	−0.508626	−	0.136286i
$683$	32.6006	+	8.73532i	1.24743	+	0.334248i	0.821343	−	0.570435i	$-0.193225\pi$
$683$	32.6006	+	8.73532i	1.24743	+	0.334248i	0.426086	+	0.904683i	$0.359892\pi$
$684$	−9.00361	−	4.12270i	−0.344261	−	0.157635i
$685$	−12.6400			−0.482950
$686$	16.6967	+	8.01372i	0.637483	+	0.305965i
$687$	31.3642	−	14.7580i	1.19662	−	0.563052i
$688$	−1.00306	−	0.579120i	−0.0382415	−	0.0220787i
$689$	1.93781	+	33.9665i	0.0738247	+	1.29402i
$690$	−4.34787	−	24.1678i	−0.165520	−	0.920051i
$691$	3.33672	+	12.4528i	0.126935	+	0.473728i	0.999901	−	0.0140528i	$-0.00447329\pi$
$691$	3.33672	+	12.4528i	0.126935	+	0.473728i	−0.872966	+	0.487781i	$0.837807\pi$
$692$		−	14.8030i		−	0.562725i
$693$	−13.9313	−	1.99490i	−0.529206	−	0.0757801i
$694$	15.5133	−	15.5133i	0.588877	−	0.588877i
$695$	−23.6355	+	6.33312i	−0.896547	+	0.240229i
$696$	−3.36408	−	2.33822i	−0.127515	−	0.0886298i
$697$	1.72298	−	6.43025i	0.0652626	−	0.243563i
$698$	−21.9694	−	12.6841i	−0.831556	−	0.480099i
$699$	13.6181	−	37.8229i	0.515084	−	1.43059i
$700$	−2.60774	+	2.74353i	−0.0985632	+	0.103696i
$701$	−7.08221			−0.267492			−0.133746	−	0.991016i	$-0.542701\pi$
$701$	−7.08221			−0.267492			−0.133746	+	0.991016i	$0.542701\pi$
$702$	−6.05655	−	17.7290i	−0.228590	−	0.669139i
$703$	12.2683	+	21.2494i	0.462709	+	0.801435i
$704$	−0.458908	+	1.71267i	−0.0172957	+	0.0645486i
$705$	20.8708	+	24.6984i	0.786039	+	0.930197i
$706$			22.9825i			0.864957i
$707$	1.85133	+	6.26861i	0.0696265	+	0.235755i
$708$	−19.7916	+	9.31263i	−0.743814	+	0.349990i
$709$	24.3392	−	6.52166i	0.914076	−	0.244926i	0.229025	−	0.973421i	$-0.426446\pi$
$709$	24.3392	−	6.52166i	0.914076	−	0.244926i	0.685052	+	0.728495i	$0.259780\pi$
$710$	−3.98869	−	1.06877i	−0.149693	−	0.0401101i
$711$	−3.34911	+	19.7953i	−0.125602	+	0.742383i
$712$	2.85677	+	1.64936i	0.107062	+	0.0618122i
$713$	−41.1529	+	41.1529i	−1.54119	+	1.54119i
$714$	12.2697	+	13.7944i	0.459183	+	0.516241i
$715$	5.43343	−	10.7869i	0.203199	−	0.403405i
$716$	−16.0914	−	9.29037i	−0.601364	−	0.347197i
$717$	−10.6832	−	7.42539i	−0.398971	−	0.277306i
$718$	10.6222	+	18.3982i	0.396416	+	0.686613i
$719$	8.08257	−	13.9994i	0.301429	−	0.522090i	−0.675031	−	0.737789i	$-0.735870\pi$
$719$	8.08257	−	13.9994i	0.301429	−	0.522090i	0.976460	+	0.215699i	$0.0692031\pi$
$720$	0.533117	+	5.64269i	0.0198681	+	0.210291i
$721$	5.84848	+	5.55900i	0.217809	+	0.207028i
$722$	5.73058	−	5.73058i	0.213270	−	0.213270i
$723$	3.04417	−	36.2416i	0.113214	−	1.34784i
$724$	9.62735	+	16.6751i	0.357798	+	0.619724i
$725$	1.69197	+	2.93058i	0.0628383	+	0.108839i
$726$	−13.5595	−	1.13896i	−0.503242	−	0.0422706i
$727$			13.8986i			0.515470i	0.966216	+	0.257735i	$0.0829762\pi$
$727$			13.8986i			0.515470i	−0.966216	+	0.257735i	$0.917024\pi$
$728$	−0.784774	−	9.50706i	−0.0290857	−	0.352355i
$729$	13.0108	−	23.6584i	0.481881	−	0.876237i
$730$	0.830885	+	3.10091i	0.0307524	+	0.114770i
$731$	4.04100	−	2.33307i	0.149462	−	0.0862917i
$732$	3.65843	+	20.3355i	0.135219	+	0.751622i
$733$	−13.4604	−	50.2347i	−0.497170	−	1.85546i	−0.517522	−	0.855670i	$-0.673146\pi$
$733$	−13.4604	−	50.2347i	−0.497170	−	1.85546i	0.0203527	−	0.999793i	$-0.493521\pi$
$734$	17.3321	+	17.3321i	0.639740	+	0.639740i
$735$	−22.8937	−	0.757096i	−0.844447	−	0.0279259i
$736$	5.30619	+	5.30619i	0.195589	+	0.195589i
$737$	16.8939	+	9.75373i	0.622297	+	0.359283i
$738$	−4.88785	−	0.826960i	−0.179924	−	0.0304408i
$739$	10.6200	−	39.6342i	0.390662	−	1.45797i	−0.438384	−	0.898788i	$-0.644449\pi$
$739$	10.6200	−	39.6342i	0.390662	−	1.45797i	0.829045	−	0.559181i	$-0.188884\pi$
$740$	7.02186	−	12.1622i	0.258129	−	0.447092i
$741$	−20.6065	−	0.552615i	−0.756999	−	0.0203008i
$742$	−21.2968	+	13.0270i	−0.781831	+	0.478237i
$743$	−22.9626	−	22.9626i	−0.842414	−	0.842414i	0.146758	−	0.989172i	$-0.453116\pi$
$743$	−22.9626	−	22.9626i	−0.842414	−	0.842414i	−0.989172	+	0.146758i	$0.953116\pi$
$744$	10.2604	−	8.67030i	0.376165	−	0.317869i
$745$	−2.83607	+	1.63741i	−0.103906	+	0.0599899i
$746$	4.63361	−	17.2929i	0.169648	−	0.633137i
$747$	16.0910	+	7.36799i	0.588740	+	0.269581i
$748$	−5.05096	−	5.05096i	−0.184681	−	0.184681i
$749$	30.0262	+	28.5400i	1.09714	+	1.04283i
$750$	7.12858	−	19.7989i	0.260299	−	0.722953i
$751$	13.1524	+	7.59356i	0.479939	+	0.277093i	0.720391	−	0.693568i	$-0.243962\pi$
$751$	13.1524	+	7.59356i	0.479939	+	0.277093i	−0.240452	+	0.970661i	$0.577296\pi$
$752$	−9.54491	−	2.55755i	−0.348067	−	0.0932642i
$753$	4.16486	−	0.749274i	0.151776	−	0.0273051i
$754$	−8.35005	−	1.73450i	−0.304091	−	0.0631667i
$755$		−	9.94193i		−	0.361824i
$756$	9.36724	−	10.0625i	0.340683	−	0.365971i
$757$	31.0409			1.12820			0.564100	−	0.825706i	$-0.309223\pi$
$757$	31.0409			1.12820			0.564100	+	0.825706i	$0.309223\pi$
$758$	−13.1467	+	22.7708i	−0.477510	+	0.827071i
$759$	13.1529	−	18.9235i	0.477419	−	0.686881i
$760$	6.02375	+	1.61406i	0.218504	+	0.0585480i
$761$	−3.13377	−	11.6954i	−0.113599	−	0.423958i	0.885579	−	0.464489i	$-0.153762\pi$
$761$	−3.13377	−	11.6954i	−0.113599	−	0.423958i	−0.999178	+	0.0405307i	$0.987095\pi$
$762$	14.1626	+	30.0989i	0.513055	+	1.09037i
$763$	11.7575	+	6.39611i	0.425649	+	0.231555i
$764$	15.2439			0.551506
$765$	−20.7607	−	9.50621i	−0.750606	−	0.343698i
$766$	−18.4072	+	10.6274i	−0.665078	+	0.383983i
$767$	−30.3102	+	33.9779i	−1.09444	+	1.22687i
$768$	−1.11793	−	1.32296i	−0.0403400	−	0.0477382i
$769$	8.07445	−	8.07445i	0.291172	−	0.291172i	−0.546371	−	0.837543i	$-0.683991\pi$
$769$	8.07445	−	8.07445i	0.291172	−	0.291172i	0.837543	+	0.546371i	$0.183991\pi$
$770$	8.85999	−	0.224835i	0.319292	−	0.00810248i
$771$	−2.55007	+	7.08254i	−0.0918384	+	0.255072i
$772$	−5.43309	−	20.2766i	−0.195541	−	0.729770i
$773$	2.09730	−	7.82723i	0.0754346	−	0.281526i	−0.917897	−	0.396819i	$-0.870114\pi$
$773$	2.09730	−	7.82723i	0.0754346	−	0.281526i	0.993332	+	0.115293i	$0.0367807\pi$
$774$	−2.01270	−	2.83244i	−0.0723451	−	0.101810i
$775$	−10.7175	+	2.87175i	−0.384985	+	0.103156i
$776$		−	7.27865i		−	0.261288i
$777$	−33.3621	+	6.87997i	−1.19686	+	0.246818i
$778$	9.31421	+	9.31421i	0.333931	+	0.333931i
$779$	−2.72724	+	4.72371i	−0.0977134	+	0.169245i
$780$	5.62322	+	10.3723i	0.201343	+	0.371387i
$781$	−1.93772	−	3.35623i	−0.0693371	−	0.120095i
$782$	−29.2012	+	7.82444i	−1.04423	+	0.279802i
$783$	−6.25565	−	10.5795i	−0.223559	−	0.378080i
$784$	5.87685	−	3.80297i	0.209888	−	0.135820i
$785$	24.5006	+	24.5006i	0.874465	+	0.874465i
$786$	−7.40811	−	0.622256i	−0.264239	−	0.0221951i
$787$	−8.66577	+	32.3411i	−0.308901	+	1.15284i	0.620633	+	0.784101i	$0.286876\pi$
$787$	−8.66577	+	32.3411i	−0.308901	+	1.15284i	−0.929535	+	0.368735i	$0.879791\pi$
$788$	10.4562	+	2.80173i	0.372487	+	0.0998076i
$789$	−15.0549	+	12.7217i	−0.535968	+	0.452906i
$790$		−	12.6434i		−	0.449833i
$791$	6.71018	−	27.8506i	0.238587	−	0.990255i
$792$	−3.39081	+	4.09839i	−0.120487	+	0.145630i
$793$	23.5924	+	35.9635i	0.837790	+	1.27710i
$794$	−20.2495	+	11.6910i	−0.718627	+	0.414899i
$795$	17.6227	−	25.3545i	0.625015	−	0.899232i
$796$	5.83099	−	10.0996i	0.206674	−	0.357970i
$797$	−31.3484			−1.11042			−0.555208	−	0.831712i	$-0.687361\pi$
$797$	−31.3484			−1.11042			−0.555208	+	0.831712i	$0.687361\pi$
$798$	−6.78535	−	13.5192i	−0.240199	−	0.478575i
$799$	28.1496	−	28.1496i	0.995861	−	0.995861i
$800$	0.370279	+	1.38190i	0.0130913	+	0.0488575i
$801$	5.73226	+	8.06689i	0.202539	+	0.285030i
$802$	5.19782	+	9.00288i	0.183541	+	0.317903i
$803$	−1.50643	+	2.60921i	−0.0531608	+	0.0920772i
$804$	−17.2426	+	8.11324i	−0.608099	+	0.286132i
$805$	17.9247	−	32.9495i	0.631761	−	1.16132i
$806$	12.5796	−	24.9741i	0.443099	−	0.879673i
$807$	28.0517	−	23.7044i	0.987468	−	0.834435i
$808$	2.38630	+	0.639408i	0.0839498	+	0.0224943i
$809$	−21.7614	+	12.5640i	−0.765091	+	0.441725i	−0.831121	−	0.556092i	$-0.812300\pi$
$809$	−21.7614	+	12.5640i	−0.765091	+	0.441725i	0.0660299	+	0.997818i	$0.478967\pi$
$810$	−5.59342	+	16.0571i	−0.196533	+	0.564190i
$811$	−9.57492	+	9.57492i	−0.336221	+	0.336221i	−0.854943	−	0.518722i	$-0.826408\pi$
$811$	−9.57492	+	9.57492i	−0.336221	+	0.336221i	0.518722	+	0.854943i	$0.326408\pi$
$812$	−1.77253	−	6.00179i	−0.0622036	−	0.210621i
$813$	−23.1855	+	10.9096i	−0.813152	+	0.382616i
$814$	12.7309	−	3.41124i	0.446219	−	0.119564i
$815$	27.7965	−	16.0483i	0.973667	−	0.562147i
$816$	6.86757	−	1.23550i	0.240413	−	0.0432512i
$817$	−3.69292	+	0.989516i	−0.129199	+	0.0346188i
$818$	−2.74504			−0.0959779
$819$	9.73348	−	26.9121i	0.340115	−	0.940384i
$820$	3.12190			0.109022
$821$	40.0306	−	10.7262i	1.39708	−	0.374346i	0.519783	−	0.854298i	$-0.326013\pi$
$821$	40.0306	−	10.7262i	1.39708	−	0.374346i	0.877294	+	0.479952i	$0.159346\pi$
$822$	11.4050	−	2.05181i	0.397797	−	0.0715650i
$823$	37.9165	−	21.8911i	1.32168	−	0.763075i	0.337687	−	0.941258i	$-0.390355\pi$
$823$	37.9165	−	21.8911i	1.32168	−	0.763075i	0.983997	+	0.178183i	$0.0570221\pi$
$824$	2.94584	−	0.789336i	0.102623	−	0.0274978i
$825$	3.97551	−	1.87062i	0.138409	−	0.0651265i
$826$	−32.4822	−	7.82609i	−1.13020	−	0.272304i
$827$	−2.95104	+	2.95104i	−0.102618	+	0.102618i	−0.756552	−	0.653934i	$-0.773117\pi$
$827$	−2.95104	+	2.95104i	−0.102618	+	0.102618i	0.653934	+	0.756552i	$0.273117\pi$
$828$	7.84613	+	21.1007i	0.272672	+	0.733300i
$829$	20.6401	−	11.9166i	0.716860	−	0.413879i	−0.0967360	−	0.995310i	$-0.530840\pi$
$829$	20.6401	−	11.9166i	0.716860	−	0.413879i	0.813596	+	0.581431i	$0.197507\pi$
$830$	−10.7655	−	2.88461i	−0.373676	−	0.100126i
$831$	−27.2472	+	23.0245i	−0.945194	+	0.798712i
$832$	−3.22011	−	1.62200i	−0.111637	−	0.0562327i
$833$	1.43034	+	28.1642i	0.0495582	+	0.975833i
$834$	20.2982	−	9.55103i	0.702870	−	0.330725i
$835$	10.0769	−	17.4537i	0.348725	−	0.604010i
$836$	2.92636	+	5.06860i	0.101210	+	0.175301i
$837$	38.8158	−	10.8345i	1.34167	−	0.374496i
$838$	−9.48209	−	35.3877i	−0.327553	−	1.22245i
$839$	29.0248	−	29.0248i	1.00205	−	1.00205i	0.00204922	−	0.999998i	$-0.499348\pi$
$839$	29.0248	−	29.0248i	1.00205	−	1.00205i	0.999998	−	0.00204922i	$-0.000652287\pi$
$840$	−4.75932	+	7.23224i	−0.164212	+	0.249536i
$841$	23.4052			0.807077
$842$	−5.80494	+	10.0544i	−0.200051	+	0.346499i
$843$	−11.1972	+	16.1099i	−0.385653	+	0.554854i
$844$	8.19145	−	4.72934i	0.281961	−	0.162790i
$845$	19.2294	+	15.2791i	0.661512	+	0.525617i
$846$	−22.8408	−	18.8974i	−0.785284	−	0.649707i
$847$	−15.0657	−	14.3200i	−0.517663	−	0.492040i
$848$			9.43594i			0.324031i
$849$	3.01762	−	2.54996i	0.103564	−	0.0875144i
$850$	−5.56719	−	1.49172i	−0.190953	−	0.0511657i
$851$	14.4371	−	53.8801i	0.494899	−	1.84699i
$852$	3.77247	+	0.316875i	0.129243	+	0.0108560i
$853$	−22.1862	−	22.1862i	−0.759640	−	0.759640i	0.216616	−	0.976257i	$-0.430498\pi$
$853$	−22.1862	−	22.1862i	−0.759640	−	0.759640i	−0.976257	+	0.216616i	$0.930498\pi$
$854$	−15.0824	+	27.7248i	−0.516108	+	0.948722i
$855$	14.4147	+	11.9261i	0.492974	+	0.407863i
$856$	15.1240	−	4.05247i	0.516928	−	0.138511i
$857$	8.80481	+	15.2504i	0.300767	+	0.520943i	0.976310	−	0.216377i	$-0.0694242\pi$
$857$	8.80481	+	15.2504i	0.300767	+	0.520943i	−0.675543	+	0.737320i	$0.736091\pi$
$858$	−3.15157	+	10.6149i	−0.107593	+	0.362388i
$859$	6.64921	−	11.5168i	0.226868	−	0.392947i	−0.730010	−	0.683436i	$-0.760485\pi$
$859$	6.64921	−	11.5168i	0.226868	−	0.392947i	0.956878	+	0.290489i	$0.0938180\pi$
$860$	1.54731	+	1.54731i	0.0527629	+	0.0527629i
$861$	−5.03269	−	5.65805i	−0.171514	−	0.192826i
$862$		−	13.1497i		−	0.447881i
$863$	−39.9496	+	10.7045i	−1.35990	+	0.364384i	−0.863780	−	0.503869i	$-0.831909\pi$
$863$	−39.9496	+	10.7045i	−1.35990	+	0.364384i	−0.496121	+	0.868254i	$0.665243\pi$
$864$	−1.39699	−	5.00484i	−0.0475264	−	0.170268i
$865$	−7.23836	+	27.0139i	−0.246111	+	0.918501i
$866$	5.25694	+	19.6192i	0.178638	+	0.666687i
$867$	0.451789	−	1.25480i	0.0153436	−	0.0426151i
$868$	20.5129	−	0.520544i	0.696253	−	0.0176684i
$869$	8.39043	−	8.39043i	0.284626	−	0.284626i
$870$	4.99576	+	5.91197i	0.169372	+	0.200435i
$871$	−26.4065	+	29.6018i	−0.894750	+	1.00302i
$872$	4.38115	−	2.52946i	0.148364	−	0.0856583i
$873$	9.09084	−	19.8536i	0.307678	−	0.671942i
$874$	24.7700			0.837858
$875$	27.4208	−	16.7730i	0.926991	−	0.567030i
$876$	−1.25306	−	2.66306i	−0.0423371	−	0.0899765i
$877$	−5.37547	−	20.0615i	−0.181517	−	0.677429i	−0.995349	−	0.0963301i	$-0.969290\pi$
$877$	−5.37547	−	20.0615i	−0.181517	−	0.677429i	0.813833	−	0.581099i	$-0.197377\pi$
$878$	28.0495	+	7.51583i	0.946624	+	0.253647i
$879$	27.2442	−	39.1972i	0.918924	−	1.32209i
$880$	1.67492	−	2.90104i	0.0564615	−	0.0977942i
$881$	−14.9464			−0.503556			−0.251778	−	0.967785i	$-0.581015\pi$
$881$	−14.9464			−0.503556			−0.251778	+	0.967785i	$0.581015\pi$
$882$	20.7798	−	3.03312i	0.699692	−	0.102131i
$883$			25.4257i			0.855642i	0.903863	+	0.427821i	$0.140719\pi$
$883$			25.4257i			0.855642i	−0.903863	+	0.427821i	$0.859281\pi$
$884$	12.1454	−	7.96746i	0.408493	−	0.267975i
$885$	40.6713	−	7.31691i	1.36715	−	0.245955i
$886$	24.1801	+	6.47905i	0.812348	+	0.217668i
$887$	−9.09755	−	5.25247i	−0.305466	−	0.176361i	0.339430	−	0.940631i	$-0.389766\pi$
$887$	−9.09755	−	5.25247i	−0.305466	−	0.176361i	−0.644896	+	0.764271i	$0.723099\pi$
$888$	−4.36155	+	12.1137i	−0.146364	+	0.406511i
$889$	−11.9018	+	49.3986i	−0.399175	+	1.65678i
$890$	−4.40681	−	4.40681i	−0.147717	−	0.147717i
$891$	−14.3677	+	6.94392i	−0.481337	+	0.232630i
$892$	3.01895	−	11.2669i	0.101082	−	0.377242i
$893$	−28.2479	+	16.3090i	−0.945281	+	0.545758i
$894$	2.29318	−	1.93779i	0.0766954	−	0.0648095i
$895$	24.8223	+	24.8223i	0.829719	+	0.829719i
$896$	−0.0671181	−	2.64490i	−0.00224226	−	0.0883599i
$897$	32.2369	+	34.0136i	1.07636	+	1.13568i
$898$	16.5190	−	28.6118i	0.551248	−	0.954789i
$899$	4.74793	−	17.7195i	0.158352	−	0.590980i
$900$	−0.715966	+	4.23180i	−0.0238655	+	0.141060i
$901$	−32.9212	−	19.0070i	−1.09676	−	0.633216i
$902$	2.07176	+	2.07176i	0.0689820	+	0.0689820i
$903$	0.309948	−	5.29866i	0.0103144	−	0.176328i
$904$	−7.65639	−	7.65639i	−0.254648	−	0.254648i
$905$	−9.41516	−	35.1378i	−0.312970	−	1.16802i
$906$	1.61384	+	8.97057i	0.0536161	+	0.298027i
$907$	−28.6605	+	16.5472i	−0.951657	+	0.549439i	−0.893595	−	0.448874i	$-0.851825\pi$
$907$	−28.6605	+	16.5472i	−0.951657	+	0.549439i	−0.0580616	+	0.998313i	$0.518492\pi$
$908$	−2.40458	−	8.97401i	−0.0797987	−	0.297813i
$909$	5.71039	+	4.72451i	0.189402	+	0.156702i
$910$	−3.21663	+	17.7331i	−0.106630	+	0.587848i
$911$			6.36943i			0.211029i	0.994418	+	0.105514i	$0.0336489\pi$
$911$			6.36943i			0.211029i	−0.994418	+	0.105514i	$0.966351\pi$
$912$	−5.69721	−	0.478546i	−0.188653	−	0.0158463i
$913$	−5.22992	−	9.05848i	−0.173085	−	0.299792i
$914$	−7.65522	−	13.2592i	−0.253212	−	0.438576i
$915$	3.26740	−	38.8991i	0.108017	−	1.28597i
$916$	14.1511	−	14.1511i	0.467564	−	0.467564i
$917$	−8.23097	−	7.82356i	−0.271811	−	0.258357i
$918$	20.2754	+	5.20741i	0.669189	+	0.171870i
$919$	−3.77646	+	6.54103i	−0.124574	+	0.215769i	−0.921566	−	0.388221i	$-0.873090\pi$
$919$	−3.77646	+	6.54103i	−0.124574	+	0.215769i	0.796992	+	0.603989i	$0.206423\pi$
$920$	−7.08863	−	12.2779i	−0.233705	−	0.404790i
$921$	8.49662	+	5.90561i	0.279973	+	0.194596i
$922$	25.0512	+	14.4633i	0.825018	+	0.476324i
$923$	7.48362	−	2.46993i	0.246326	−	0.0812988i
$924$	−7.95784	+	1.64108i	−0.261794	+	0.0539874i
$925$	7.51977	−	7.51977i	0.247249	−	0.247249i
$926$	13.9673	+	8.06402i	0.458993	+	0.265000i
$927$	9.02108	+	1.52625i	0.296291	+	0.0501286i
$928$	−2.28473	−	0.612191i	−0.0749998	−	0.0200961i
$929$	50.1073	−	13.4262i	1.64397	−	0.440500i	0.686053	−	0.727552i	$-0.259342\pi$
$929$	50.1073	−	13.4262i	1.64397	−	0.440500i	0.957915	+	0.287052i	$0.0926753\pi$
$930$	−22.9638	+	10.8053i	−0.753013	+	0.354319i
$931$	4.84058	−	22.5934i	0.158644	−	0.740467i
$932$		−	23.2094i		−	0.760248i
$933$	−3.12574	−	3.69900i	−0.102332	−	0.121100i
$934$	−3.98806	+	14.8836i	−0.130493	+	0.487008i
$935$	6.74766	+	11.6873i	0.220672	+	0.382215i
$936$	−6.75750	−	8.44608i	−0.220876	−	0.276069i
$937$	−1.69179			−0.0552683			−0.0276341	−	0.999618i	$-0.508797\pi$
$937$	−1.69179			−0.0552683			−0.0276341	+	0.999618i	$0.508797\pi$
$938$	−28.2988	−	6.81815i	−0.923987	−	0.222620i
$939$	5.29753	−	14.7133i	0.172878	−	0.480152i
$940$	16.1679	+	9.33453i	0.527338	+	0.304459i
$941$	−13.4576	+	50.2245i	−0.438706	+	1.63727i	0.293335	+	0.956010i	$0.405235\pi$
$941$	−13.4576	+	50.2245i	−0.438706	+	1.63727i	−0.732040	+	0.681261i	$0.761432\pi$
$942$	−26.0839	−	18.1297i	−0.849860	−	0.590699i
$943$	11.9775	−	3.20936i	0.390041	−	0.104511i
$944$	−8.92965	+	8.92965i	−0.290636	+	0.290636i
$945$	−22.0146	+	13.7827i	−0.716136	+	0.448352i
$946$			2.05365i			0.0667701i
$947$	2.76512	+	10.3196i	0.0898542	+	0.335340i	0.996189	−	0.0872197i	$-0.0277982\pi$
$947$	2.76512	+	10.3196i	0.0898542	+	0.335340i	−0.906335	+	0.422560i	$0.861132\pi$
$948$	2.05236	+	11.4081i	0.0666576	+	0.370518i
$949$	−4.57190	−	4.07840i	−0.148410	−	0.132390i
$950$	4.08970	+	2.36119i	0.132687	+	0.0766071i
$951$	−10.9302	+	5.14304i	−0.354436	+	0.166774i
$952$	9.36302	+	5.09352i	0.303457	+	0.165082i
$953$	11.9865			0.388282			0.194141	−	0.980974i	$-0.437808\pi$
$953$	11.9865			0.388282			0.194141	+	0.980974i	$0.437808\pi$
$954$	−11.7852	+	25.7379i	−0.381561	+	0.833296i
$955$	−27.8186	−	7.45397i	−0.900189	−	0.241205i
$956$	−7.25553	−	1.94411i	−0.234661	−	0.0628771i
$957$	−0.608017	+	7.23858i	−0.0196544	+	0.233990i
$958$	−11.0119			−0.355780
$959$	15.5493	+	8.45885i	0.502112	+	0.273151i
$960$	1.39321	+	2.96091i	0.0449658	+	0.0955631i
$961$	25.2447	+	14.5750i	0.814344	+	0.470162i
$962$	1.52656	+	26.7580i	0.0492182	+	0.862712i
$963$	46.3144	+	7.83580i	1.49246	+	0.252505i
$964$	−5.43462	−	20.2823i	−0.175037	−	0.653248i
$965$			39.6593i			1.27668i
$966$	−10.8248	+	32.6399i	−0.348282	+	1.05017i
$967$	−29.6610	+	29.6610i	−0.953833	+	0.953833i	−0.998980	−	0.0451476i	$-0.985624\pi$
$967$	−29.6610	+	29.6610i	−0.953833	+	0.953833i	0.0451476	+	0.998980i	$0.485624\pi$
$968$	−7.58848	+	2.03333i	−0.243903	+	0.0653536i
$969$	13.1456	−	18.9131i	0.422299	−	0.607577i
$970$	−3.55911	+	13.2828i	−0.114276	+	0.426485i
$971$	−4.19572	−	2.42240i	−0.134647	−	0.0777385i	0.431163	−	0.902274i	$-0.358103\pi$
$971$	−4.19572	−	2.42240i	−0.134647	−	0.0777385i	−0.565810	+	0.824535i	$0.691437\pi$
$972$	2.44043	−	15.3962i	0.0782768	−	0.493835i
$973$	33.3137	+	8.02643i	1.06799	+	0.257315i
$974$	−29.1466			−0.933916
$975$	2.08021	+	8.68885i	0.0666200	+	0.278266i
$976$	5.96460	+	10.3310i	0.190922	+	0.330687i
$977$	−2.41792	+	9.02380i	−0.0773561	+	0.288697i	−0.993757	−	0.111564i	$-0.964414\pi$
$977$	−2.41792	+	9.02380i	−0.0773561	+	0.288697i	0.916401	+	0.400261i	$0.131081\pi$
$978$	−22.4756	+	18.9924i	−0.718690	+	0.607310i
$979$		−	5.84889i		−	0.186931i
$980$	−12.5842	+	4.06637i	−0.401989	+	0.129895i
$981$	15.1095	−	1.42753i	0.482408	−	0.0455775i
$982$	17.0200	−	4.56050i	0.543130	−	0.145531i
$983$	−4.75954	−	1.27531i	−0.151806	−	0.0406762i	0.182116	−	0.983277i	$-0.441705\pi$
$983$	−4.75954	−	1.27531i	−0.151806	−	0.0406762i	−0.333922	+	0.942601i	$0.608372\pi$
$984$	−2.81688	+	0.506767i	−0.0897989	+	0.0161551i
$985$	−17.7115	−	10.2258i	−0.564336	−	0.325820i
$986$	6.73806	−	6.73806i	0.214584	−	0.214584i
$987$	−9.14592	−	44.3500i	−0.291118	−	1.41168i
$988$	−11.3018	+	3.73011i	−0.359558	+	0.118670i
$989$	7.52709	+	4.34577i	0.239347	+	0.138187i
$990$	8.19192	−	5.82110i	0.260356	−	0.185007i
$991$	−27.0543	−	46.8594i	−0.859408	−	1.48854i	−0.872494	−	0.488625i	$-0.837499\pi$
$991$	−27.0543	−	46.8594i	−0.859408	−	1.48854i	0.0130855	−	0.999914i	$-0.495835\pi$
$992$	3.87782	−	6.71659i	0.123121	−	0.213252i
$993$	10.5652	+	22.4536i	0.335277	+	0.712544i
$994$	4.19150	+	3.98404i	0.132946	+	0.126366i
$995$	−15.5795	+	15.5795i	−0.493902	+	0.493902i
$996$	10.1819	+	0.855247i	0.322626	+	0.0270995i
$997$	1.60113	+	2.77325i	0.0507084	+	0.0878296i	0.890265	−	0.455442i	$-0.150519\pi$
$997$	1.60113	+	2.77325i	0.0507084	+	0.0878296i	−0.839557	+	0.543272i	$0.817185\pi$
$998$	−3.04386	−	5.27212i	−0.0963516	−	0.166886i
$999$	−27.0265	+	27.5946i	−0.855081	+	0.873054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.36	yes	144
3.2	odd	2	inner	546.2.bv.a.317.5	✓	144
7.4	even	3	inner	546.2.bv.a.473.5	yes	144
13.8	odd	4	inner	546.2.bv.a.359.36	yes	144
21.11	odd	6	inner	546.2.bv.a.473.36	yes	144
39.8	even	4	inner	546.2.bv.a.359.5	yes	144
91.60	odd	12	inner	546.2.bv.a.515.5	yes	144
273.242	even	12	inner	546.2.bv.a.515.36	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.5	✓	144	3.2	odd	2	inner
546.2.bv.a.317.36	yes	144	1.1	even	1	trivial
546.2.bv.a.359.5	yes	144	39.8	even	4	inner
546.2.bv.a.359.36	yes	144	13.8	odd	4	inner
546.2.bv.a.473.5	yes	144	7.4	even	3	inner
546.2.bv.a.473.36	yes	144	21.11	odd	6	inner
546.2.bv.a.515.5	yes	144	91.60	odd	12	inner
546.2.bv.a.515.36	yes	144	273.242	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.70468 - 0.306679i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.82490 + 0.488980i) q^{5} +(1.56722 - 0.737434i) q^{6} +(2.57215 + 0.619719i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.81190 - 1.04558i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.70468 - 0.306679i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.82490 + 0.488980i) q^{5} +(1.56722 - 0.737434i) q^{6} +(2.57215 + 0.619719i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.81190 - 1.04558i) q^{9} +(-1.63616 + 0.944637i) q^{10} +(-1.71267 - 0.458908i) q^{11} +(1.32296 - 1.11793i) q^{12} +(1.62200 - 3.22011i) q^{13} +(2.64490 - 0.0671181i) q^{14} +(-2.96091 + 1.39321i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.01432 + 3.48891i) q^{17} +(2.44547 - 1.73773i) q^{18} +(-0.854328 - 3.18839i) q^{19} +(-1.33592 + 1.33592i) q^{20} +(4.57476 + 0.267603i) q^{21} -1.77308 q^{22} +(-3.75204 + 6.49873i) q^{23} +(0.988539 - 1.42225i) q^{24} +(-1.23898 + 0.715324i) q^{25} +(0.733303 - 3.53019i) q^{26} +(4.47274 - 2.64473i) q^{27} +(2.53741 - 0.749382i) q^{28} -2.36532i q^{29} +(-2.49943 + 2.11208i) q^{30} +(7.49138 + 2.00731i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-3.06029 - 0.257054i) q^{33} +(2.84869 + 2.84869i) q^{34} +(-4.99694 + 0.126804i) q^{35} +(1.91238 - 2.31145i) q^{36} +(-7.18011 + 1.92390i) q^{37} +(-1.65043 - 2.85864i) q^{38} +(1.77745 - 5.98671i) q^{39} +(-0.944637 + 1.63616i) q^{40} +(-1.16845 - 1.16845i) q^{41} +(4.48814 - 0.925549i) q^{42} -1.15824i q^{43} +(-1.71267 + 0.458908i) q^{44} +(-4.62016 + 3.28304i) q^{45} +(-1.94220 + 7.24839i) q^{46} +(-2.55755 - 9.54491i) q^{47} +(0.586751 - 1.62964i) q^{48} +(6.23190 + 3.18802i) q^{49} +(-1.01162 + 1.01162i) q^{50} +(4.50376 + 5.32974i) q^{51} +(-0.205365 - 3.59970i) q^{52} +(-8.17176 + 4.71797i) q^{53} +(3.63583 - 3.71225i) q^{54} +3.34984 q^{55} +(2.25699 - 1.38058i) q^{56} +(-2.43417 - 5.17320i) q^{57} +(-0.612191 - 2.28473i) q^{58} +(-12.1981 - 3.26848i) q^{59} +(-1.86762 + 2.68702i) q^{60} +(-5.96460 + 10.3310i) q^{61} +7.75565 q^{62} +(7.88058 - 0.946802i) q^{63} -1.00000i q^{64} +(-1.38541 + 6.66950i) q^{65} +(-3.02255 + 0.543767i) q^{66} +(-10.6271 - 2.84753i) q^{67} +(3.48891 + 2.01432i) q^{68} +(-4.40303 + 12.2290i) q^{69} +(-4.79385 + 1.41579i) q^{70} +(1.54553 + 1.54553i) q^{71} +(1.24897 - 2.72765i) q^{72} +(0.439791 - 1.64132i) q^{73} +(-6.43751 + 3.71670i) q^{74} +(-1.89269 + 1.59937i) q^{75} +(-2.33407 - 2.33407i) q^{76} +(-4.12084 - 2.24175i) q^{77} +(0.167415 - 6.24275i) q^{78} +(-3.34611 + 5.79563i) q^{79} +(-0.488980 + 1.82490i) q^{80} +(6.81352 - 5.88013i) q^{81} +(-1.43105 - 0.826218i) q^{82} +(4.17139 + 4.17139i) q^{83} +(4.09566 - 2.05563i) q^{84} +(-5.38194 - 5.38194i) q^{85} +(-0.299774 - 1.11877i) q^{86} +(-0.725394 - 4.03213i) q^{87} +(-1.53553 + 0.886542i) q^{88} +(0.853770 + 3.18631i) q^{89} +(-3.61301 + 4.36696i) q^{90} +(6.16759 - 7.27742i) q^{91} +7.50409i q^{92} +(13.3860 + 1.12438i) q^{93} +(-4.94081 - 8.55773i) q^{94} +(3.11812 + 5.40074i) q^{95} +(0.144976 - 1.72597i) q^{96} +(5.14678 - 5.14678i) q^{97} +(6.84467 + 1.46646i) q^{98} +(-5.29567 + 0.500330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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