LMFDB - Embedded newform 546.2.bv.a.473.5

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			473.5
Character	$\chi$	$=$	546.473
Dual form			546.2.bv.a.359.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.488980 - 1.82490i) q^{5} +(1.56722 - 0.737434i) q^{6} +(0.619719 + 2.57215i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.488980 - 1.82490i) q^{5} +(1.56722 - 0.737434i) q^{6} +(0.619719 + 2.57215i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +(1.63616 + 0.944637i) q^{10} +(0.458908 + 1.71267i) q^{11} +(0.306679 + 1.70468i) 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} +(-2.72765 - 1.24897i) q^{18} +(3.18839 + 0.854328i) q^{19} +(-1.33592 + 1.33592i) q^{20} +(2.71005 - 3.69536i) q^{21} -1.77308 q^{22} +(-3.75204 - 6.49873i) q^{23} +(-1.72597 - 0.144976i) q^{24} +(1.23898 + 0.715324i) q^{25} +(2.69059 + 2.40016i) q^{26} +(4.47274 - 2.64473i) q^{27} +(0.749382 - 2.53741i) q^{28} -2.36532i q^{29} +(-0.579400 - 3.22061i) q^{30} +(-2.00731 - 7.49138i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.75276 - 2.52176i) q^{33} +(2.84869 + 2.84869i) q^{34} +(4.99694 + 0.126804i) q^{35} +(1.91238 - 2.31145i) q^{36} +(1.92390 - 7.18011i) q^{37} +(-1.65043 + 2.85864i) q^{38} +(-6.07337 + 1.45403i) q^{39} +(-0.944637 - 1.63616i) q^{40} +(-1.16845 - 1.16845i) q^{41} +(2.86803 + 3.57413i) q^{42} -1.15824i q^{43} +(0.458908 - 1.71267i) q^{44} +(5.15327 + 2.35965i) q^{45} +(7.24839 - 1.94220i) q^{46} +(9.54491 + 2.55755i) q^{47} +(0.586751 - 1.62964i) q^{48} +(-6.23190 + 3.18802i) q^{49} +(-1.01162 + 1.01162i) q^{50} +(-6.86757 + 1.23550i) q^{51} +(-3.01475 + 1.97770i) q^{52} +(8.17176 + 4.71797i) q^{53} +(1.39699 + 5.00484i) q^{54} +3.34984 q^{55} +(2.25699 + 1.38058i) q^{56} +(-2.43417 - 5.17320i) q^{57} +(2.28473 + 0.612191i) q^{58} +(3.26848 + 12.1981i) q^{59} +(3.26083 + 0.273899i) q^{60} +(-5.96460 - 10.3310i) q^{61} +7.75565 q^{62} +(-7.91846 + 0.545879i) q^{63} -1.00000i q^{64} +(-5.08325 - 4.53455i) q^{65} +(1.98219 + 2.34572i) q^{66} +(2.84753 + 10.6271i) q^{67} +(-3.48891 + 2.01432i) q^{68} +(-4.40303 + 12.2290i) q^{69} +(-1.41579 + 4.79385i) q^{70} +(1.54553 + 1.54553i) q^{71} +(1.73773 + 2.44547i) q^{72} +(-1.64132 + 0.439791i) q^{73} +(6.43751 + 3.71670i) q^{74} +(-0.438749 - 2.43880i) 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} +(1.82490 - 0.488980i) q^{80} +(-8.49910 - 2.96062i) q^{81} +(1.43105 - 0.826218i) q^{82} +(4.17139 + 4.17139i) q^{83} +(-4.19465 + 1.84525i) q^{84} +(-5.38194 - 5.38194i) q^{85} +(1.11877 + 0.299774i) q^{86} +(-3.12923 + 2.64427i) q^{87} +(1.53553 + 0.886542i) q^{88} +(-3.18631 - 0.853770i) q^{89} +(-3.61301 + 4.36696i) q^{90} +(9.28779 + 2.17645i) q^{91} +7.50409i q^{92} +(-7.66676 + 11.0305i) q^{93} +(-4.94081 + 8.55773i) q^{94} +(3.11812 - 5.40074i) q^{95} +(1.42225 + 0.988539i) q^{96} +(5.14678 - 5.14678i) q^{97} +(-1.46646 - 6.84467i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.11793	−	1.32296i	−0.645439	−	0.763812i
$3$	−1.11793	−	1.32296i	−0.645439	−	0.763812i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.488980	−	1.82490i	0.218678	−	0.816119i	−0.766161	−	0.642649i	$-0.777835\pi$
$5$	0.488980	−	1.82490i	0.218678	−	0.816119i	0.984839	−	0.173470i	$-0.0554980\pi$
$6$	1.56722	−	0.737434i	0.639817	−	0.301056i
$7$	0.619719	+	2.57215i	0.234232	+	0.972181i
$7$	0.619719	+	2.57215i	0.234232	+	0.972181i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.500449	+	2.95796i	−0.166816	+	0.985988i
$10$	1.63616	+	0.944637i	0.517399	+	0.298720i
$11$	0.458908	+	1.71267i	0.138366	+	0.516388i	0.999961	+	0.00879290i	$0.00279890\pi$
$11$	0.458908	+	1.71267i	0.138366	+	0.516388i	−0.861595	+	0.507596i	$0.830534\pi$
$12$	0.306679	+	1.70468i	0.0885305	+	0.492100i
$13$	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	−0.511368	−	0.859362i	$-0.670861\pi$
$17$	2.01432	−	3.48891i	0.488545	−	0.846186i	0.999913	+	0.0131764i	$0.00419430\pi$
$18$	−2.72765	−	1.24897i	−0.642913	−	0.294386i
$19$	3.18839	+	0.854328i	0.731468	+	0.195996i	0.605283	−	0.796011i	$-0.293060\pi$
$19$	3.18839	+	0.854328i	0.731468	+	0.195996i	0.126185	+	0.992007i	$0.459727\pi$
$20$	−1.33592	+	1.33592i	−0.298720	+	0.298720i
$21$	2.71005	−	3.69536i	0.591380	−	0.806393i
$22$	−1.77308			−0.378023
$23$	−3.75204	−	6.49873i	−0.782355	−	1.35508i	−0.930566	−	0.366123i	$-0.880685\pi$
$23$	−3.75204	−	6.49873i	−0.782355	−	1.35508i	0.148211	−	0.988956i	$-0.452648\pi$
$24$	−1.72597	−	0.144976i	−0.352313	−	0.0295931i
$25$	1.23898	+	0.715324i	0.247795	+	0.143065i
$26$	2.69059	+	2.40016i	0.527667	+	0.470709i
$27$	4.47274	−	2.64473i	0.860779	−	0.508979i
$28$	0.749382	−	2.53741i	0.141620	−	0.479525i
$29$		−	2.36532i		−	0.439230i	−0.975587	−	0.219615i	$-0.929520\pi$
$29$		−	2.36532i		−	0.439230i	0.975587	−	0.219615i	$-0.0704800\pi$
$30$	−0.579400	−	3.22061i	−0.105783	−	0.588001i
$31$	−2.00731	−	7.49138i	−0.360523	−	1.34549i	−0.873389	−	0.487023i	$-0.838083\pi$
$31$	−2.00731	−	7.49138i	−0.360523	−	1.34549i	0.512866	−	0.858469i	$-0.328584\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.75276	−	2.52176i	0.305117	−	0.438983i
$34$	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
$37$	1.92390	−	7.18011i	0.316288	−	1.18040i	−0.606497	−	0.795086i	$-0.707426\pi$
$37$	1.92390	−	7.18011i	0.316288	−	1.18040i	0.922785	−	0.385316i	$-0.125908\pi$
$38$	−1.65043	+	2.85864i	−0.267736	+	0.463732i
$39$	−6.07337	+	1.45403i	−0.972517	+	0.232832i
$40$	−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	$0.791188\pi$
$42$	2.86803	+	3.57413i	0.442546	+	0.551500i
$43$		−	1.15824i		−	0.176630i	−0.996093	−	0.0883149i	$-0.971852\pi$
$43$		−	1.15824i		−	0.176630i	0.996093	−	0.0883149i	$-0.0281482\pi$
$44$	0.458908	−	1.71267i	0.0691829	−	0.258194i
$45$	5.15327	+	2.35965i	0.768204	+	0.351756i
$46$	7.24839	−	1.94220i	1.06872	−	0.286362i
$47$	9.54491	+	2.55755i	1.39227	+	0.373057i	0.875562	−	0.483106i	$-0.160491\pi$
$47$	9.54491	+	2.55755i	1.39227	+	0.373057i	0.516706	+	0.856163i	$0.327158\pi$
$48$	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
$51$	−6.86757	+	1.23550i	−0.961653	+	0.173005i
$52$	−3.01475	+	1.97770i	−0.418070	+	0.274258i
$53$	8.17176	+	4.71797i	1.12248	+	0.648063i	0.942032	−	0.335522i	$-0.108913\pi$
$53$	8.17176	+	4.71797i	1.12248	+	0.648063i	0.180445	+	0.983585i	$0.442246\pi$
$54$	1.39699	+	5.00484i	0.190106	+	0.681073i
$55$	3.34984			0.451692
$56$	2.25699	+	1.38058i	0.301603	+	0.184487i
$57$	−2.43417	−	5.17320i	−0.322414	−	0.685207i
$58$	2.28473	+	0.612191i	0.299999	+	0.0803846i
$59$	3.26848	+	12.1981i	0.425520	+	1.58806i	0.762785	+	0.646652i	$0.223831\pi$
$59$	3.26848	+	12.1981i	0.425520	+	1.58806i	−0.337265	+	0.941410i	$0.609502\pi$
$60$	3.26083	+	0.273899i	0.420972	+	0.0353602i
$61$	−5.96460	−	10.3310i	−0.763689	−	1.32275i	−0.940937	−	0.338581i	$-0.890053\pi$
$61$	−5.96460	−	10.3310i	−0.763689	−	1.32275i	0.177249	−	0.984166i	$-0.443280\pi$
$62$	7.75565			0.984968
$63$	−7.91846	+	0.545879i	−0.997632	+	0.0687742i
$64$		−	1.00000i		−	0.125000i
$65$	−5.08325	−	4.53455i	−0.630500	−	0.562442i
$66$	1.98219	+	2.34572i	0.243991	+	0.288738i
$67$	2.84753	+	10.6271i	0.347881	+	1.29831i	0.889211	+	0.457498i	$0.151254\pi$
$67$	2.84753	+	10.6271i	0.347881	+	1.29831i	−0.541330	+	0.840810i	$0.682079\pi$
$68$	−3.48891	+	2.01432i	−0.423093	+	0.244273i
$69$	−4.40303	+	12.2290i	−0.530062	+	1.47219i
$70$	−1.41579	+	4.79385i	−0.169219	+	0.572975i
$71$	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	$0.708599\pi$
$72$	1.73773	+	2.44547i	0.204793	+	0.288201i
$73$	−1.64132	+	0.439791i	−0.192102	+	0.0514736i	−0.353587	−	0.935402i	$-0.615038\pi$
$73$	−1.64132	+	0.439791i	−0.192102	+	0.0514736i	0.161485	+	0.986875i	$0.448372\pi$
$74$	6.43751	+	3.71670i	0.748345	+	0.432057i
$75$	−0.438749	−	2.43880i	−0.0506624	−	0.281609i
$76$	−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	0.614079	−	0.789245i	$-0.289528\pi$
$79$	−3.34611	−	5.79563i	−0.376467	−	0.652059i	−0.990545	+	0.137185i	$0.956194\pi$
$80$	1.82490	−	0.488980i	0.204030	−	0.0546696i
$81$	−8.49910	−	2.96062i	−0.944345	−	0.328958i
$82$	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	$0.645052\pi$
$84$	−4.19465	+	1.84525i	−0.457673	+	0.201333i
$85$	−5.38194	−	5.38194i	−0.583754	−	0.583754i
$86$	1.11877	+	0.299774i	0.120640	+	0.0323255i
$87$	−3.12923	+	2.64427i	−0.335489	+	0.283496i
$88$	1.53553	+	0.886542i	0.163689	+	0.0945056i
$89$	−3.18631	−	0.853770i	−0.337748	−	0.0904994i	0.0859586	−	0.996299i	$-0.472605\pi$
$89$	−3.18631	−	0.853770i	−0.337748	−	0.0904994i	−0.423707	+	0.905799i	$0.639271\pi$
$90$	−3.61301	+	4.36696i	−0.380845	+	0.460318i
$91$	9.28779	+	2.17645i	0.973625	+	0.228154i
$92$			7.50409i			0.782355i
$93$	−7.66676	+	11.0305i	−0.795006	+	1.14380i
$94$	−4.94081	+	8.55773i	−0.509605	+	0.882662i
$95$	3.11812	−	5.40074i	0.319912	−	0.554105i
$96$	1.42225	+	0.988539i	0.145158	+	0.100892i
$97$	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	$0.129523\pi$
$98$	−1.46646	−	6.84467i	−0.148135	−	0.691416i
$99$	−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	−0.798003	−	0.602653i	$-0.794110\pi$
$101$	1.23524	−	2.13950i	0.122911	−	0.212888i	0.920914	+	0.389765i	$0.127444\pi$
$102$	0.584057	−	6.95334i	0.0578303	−	0.688483i
$103$	−2.64117	+	1.52488i	−0.260242	+	0.150251i	−0.624445	−	0.781069i	$-0.714675\pi$
$103$	−2.64117	+	1.52488i	−0.260242	+	0.150251i	0.364203	+	0.931320i	$0.381341\pi$
$104$	−1.13004	−	3.42389i	−0.110809	−	0.335740i
$105$	−5.41849	−	6.75251i	−0.528790	−	0.658978i
$106$	−6.67222	+	6.67222i	−0.648063	+	0.648063i
$107$	−13.5598	+	7.82877i	−1.31088	+	0.756836i	−0.982242	−	0.187621i	$-0.939922\pi$
$107$	−13.5598	+	7.82877i	−1.31088	+	0.756836i	−0.328636	+	0.944457i	$0.606589\pi$
$108$	−5.19587	+	0.0540370i	−0.499973	+	0.00519971i
$109$	−1.30934	−	4.88654i	−0.125412	−	0.468045i	0.874442	−	0.485131i	$-0.161228\pi$
$109$	−1.30934	−	4.88654i	−0.125412	−	0.468045i	−0.999854	+	0.0170853i	$0.994561\pi$
$110$	−0.867002	+	3.23570i	−0.0826654	+	0.308511i
$111$	−11.6498	+	5.48163i	−1.10575	+	0.520294i
$112$	−1.91769	+	1.82277i	−0.181204	+	0.172235i
$113$		−	10.8278i		−	1.01859i	−0.860592	−	0.509296i	$-0.829906\pi$
$113$		−	10.8278i		−	1.01859i	0.860592	−	0.509296i	$-0.170094\pi$
$114$	5.62694	−	1.01231i	0.527011	−	0.0948111i
$115$	−13.6942	+	3.66935i	−1.27699	+	0.342168i
$116$	−1.18266	+	2.04843i	−0.109807	+	0.190192i
$117$	8.71325	+	6.40931i	0.805540	+	0.592541i
$118$	−12.6284			−1.16254
$119$	10.2223	+	3.01900i	0.937078	+	0.276751i
$120$	−1.10853	+	3.07883i	−0.101195	+	0.281058i
$121$	6.80365	−	3.92809i	0.618513	−	0.357099i
$122$	11.5227	−	3.08750i	1.04322	−	0.279529i
$123$	−0.239563	+	2.85206i	−0.0216007	+	0.257162i
$124$	−2.00731	+	7.49138i	−0.180262	+	0.672746i
$125$	8.59082	−	8.59082i	0.768386	−	0.768386i
$126$	1.52217	−	7.78993i	0.135606	−	0.693982i
$127$			19.2052i			1.70419i	0.523390	+	0.852093i	$0.324667\pi$
$127$			19.2052i			1.70419i	−0.523390	+	0.852093i	$0.675333\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−1.53231	+	1.29483i	−0.134912	+	0.114004i
$130$	5.69568	−	3.73642i	0.499544	−	0.327705i
$131$	3.71710	−	2.14607i	0.324764	−	0.187503i	−0.328750	−	0.944417i	$-0.606627\pi$
$131$	3.71710	−	2.14607i	0.324764	−	0.187503i	0.653514	+	0.756914i	$0.273294\pi$
$132$	−2.77882	+	1.30753i	−0.241865	+	0.113806i
$133$	−0.221548	+	8.73047i	−0.0192106	+	0.757027i
$134$	−11.0020			−0.950428
$135$	−2.63929	−	9.45551i	−0.227154	−	0.813801i
$136$	−1.04269	−	3.89138i	−0.0894100	−	0.333683i
$137$	−1.73161	−	6.46244i	−0.147941	−	0.552124i	−0.999607	−	0.0280384i	$-0.991074\pi$
$137$	−1.73161	−	6.46244i	−0.147941	−	0.552124i	0.851666	−	0.524085i	$-0.175593\pi$
$138$	−10.6727	−	7.41808i	−0.908518	−	0.631469i
$139$	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
$143$	6.25933	+	1.30021i	0.523431	+	0.108729i
$144$	−2.81190	+	1.04558i	−0.234325	+	0.0871317i
$145$	−4.31647	−	1.15660i	−0.358464	−	0.0960500i
$146$		−	1.69922i		−	0.140629i
$147$	11.1845	+	4.68056i	0.922480	+	0.386046i
$148$	−5.25620	+	5.25620i	−0.432057	+	0.432057i
$149$	−0.448629	+	1.67431i	−0.0367531	+	0.137165i	−0.981865	−	0.189584i	$-0.939286\pi$
$149$	−0.448629	+	1.67431i	−0.0367531	+	0.137165i	0.945111	+	0.326748i	$0.105953\pi$
$150$	2.46926	+	0.207409i	0.201614	+	0.0169349i
$151$	5.08300	−	1.36199i	0.413648	−	0.110837i	−0.0459921	−	0.998942i	$-0.514645\pi$
$151$	5.08300	−	1.36199i	0.413648	−	0.110837i	0.459641	+	0.888105i	$0.347978\pi$
$152$	2.85864	−	1.65043i	0.231866	−	0.133868i
$153$	9.31201	+	7.70432i	0.752831	+	0.622858i
$154$	−1.09881	−	4.56063i	−0.0885449	−	0.367506i
$155$	−14.6525			−1.17692
$156$	5.98671	+	1.77745i	0.479320	+	0.142310i
$157$	−9.16996	+	15.8828i	−0.731843	+	1.26759i	0.224252	+	0.974531i	$0.428006\pi$
$157$	−9.16996	+	15.8828i	−0.731843	+	1.26759i	−0.956095	+	0.293057i	$0.905327\pi$
$158$	6.46419	−	1.73207i	0.514263	−	0.137796i
$159$	−2.89380	−	16.0853i	−0.229493	−	1.27565i
$160$			1.88927i			0.149360i
$161$	14.3905	−	13.6782i	1.13413	−	1.07799i
$162$	5.05947	−	7.44324i	0.397509	−	0.584796i
$163$	4.39704	−	16.4100i	0.344403	−	1.28533i	−0.548906	−	0.835884i	$-0.684955\pi$
$163$	4.39704	−	16.4100i	0.344403	−	1.28533i	0.893308	−	0.449444i	$-0.148378\pi$
$164$	0.427682	+	1.59613i	0.0333964	+	0.124637i
$165$	−3.74490	−	4.43170i	−0.291540	−	0.345008i
$166$	−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	$0.385427\pi$
$168$	−0.696719	−	4.52930i	−0.0537531	−	0.349443i
$169$	−7.73825	−	10.4460i	−0.595250	−	0.803541i
$170$	6.59151	−	3.80561i	0.505546	−	0.291877i
$171$	−4.12270	+	9.00361i	−0.315271	+	0.688523i
$172$	−0.579120	+	1.00306i	−0.0441575	+	0.0764830i
$173$	7.40149	+	12.8198i	0.562725	+	0.974668i	0.997257	+	0.0740116i	$0.0235802\pi$
$173$	7.40149	+	12.8198i	0.562725	+	0.974668i	−0.434533	+	0.900656i	$0.643086\pi$
$174$	−1.74427	−	3.70699i	−0.132233	−	0.281026i
$175$	−1.07210	+	3.63013i	−0.0810432	+	0.274412i
$176$	−1.25376	+	1.25376i	−0.0945056	+	0.0945056i
$177$	12.4837	−	17.9608i	0.938333	−	1.35001i
$178$	1.64936	−	2.85677i	0.123624	−	0.214124i
$179$	−9.29037	+	16.0914i	−0.694395	+	1.20273i	0.275989	+	0.961161i	$0.410995\pi$
$179$	−9.29037	+	16.0914i	−0.694395	+	1.20273i	−0.970384	+	0.241567i	$0.922339\pi$
$180$	−3.28304	−	4.62016i	−0.244703	−	0.344366i
$181$			19.2547i			1.43119i	0.698515	+	0.715595i	$0.253844\pi$
$181$			19.2547i			1.43119i	−0.698515	+	0.715595i	$0.746156\pi$
$182$	−4.50615	+	8.40801i	−0.334018	+	0.623243i
$183$	−6.99946	+	19.4403i	−0.517415	+	1.43707i
$184$	−7.24839	−	1.94220i	−0.534358	−	0.143181i
$185$	−12.1622	−	7.02186i	−0.894183	−	0.516257i
$186$	−8.67030	−	10.2604i	−0.635737	−	0.752330i
$187$	6.89973	+	1.84878i	0.504558	+	0.135196i
$188$	−6.98736	−	6.98736i	−0.509605	−	0.509605i
$189$	9.57449	+	9.86555i	0.696442	+	0.717613i
$190$	4.40969	+	4.40969i	0.319912	+	0.319912i
$191$	−13.2016	+	7.62196i	−0.955236	+	0.551506i	−0.894704	−	0.446660i	$-0.852613\pi$
$191$	−13.2016	+	7.62196i	−0.955236	+	0.551506i	−0.0605325	+	0.998166i	$0.519280\pi$
$192$	−1.32296	+	1.11793i	−0.0954764	+	0.0806799i
$193$	−20.2766	+	5.43309i	−1.45954	+	0.391083i	−0.899331	−	0.437269i	$-0.855946\pi$
$193$	−20.2766	+	5.43309i	−1.45954	+	0.391083i	−0.560209	+	0.828351i	$0.689279\pi$
$194$	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	$0.623985\pi$
$198$	0.887338	−	5.24472i	0.0630603	−	0.372726i
$199$	−10.0996	−	5.83099i	−0.715940	−	0.413348i	0.0973164	−	0.995253i	$-0.468974\pi$
$199$	−10.0996	−	5.83099i	−0.715940	−	0.413348i	−0.813257	+	0.581905i	$0.802307\pi$
$200$	1.38190	−	0.370279i	0.0977150	−	0.0261827i
$201$	10.8759	−	15.6476i	0.767127	−	1.10369i
$202$	1.74689	+	1.74689i	0.122911	+	0.122911i
$203$	6.08396	−	1.46584i	0.427011	−	0.102882i
$204$	6.56524	+	2.36381i	0.459659	+	0.165500i
$205$	−2.70365	+	1.56095i	−0.188831	+	0.109022i
$206$	−0.789336	−	2.94584i	−0.0549957	−	0.205247i
$207$	21.1007	−	7.84613i	1.46660	−	0.545343i
$208$	3.59970	−	0.205365i	0.249594	−	0.0142395i
$209$			5.85271i			0.404841i
$210$	7.92483	−	3.48618i	0.546865	−	0.240569i
$211$	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
$213$	0.316875	−	3.77247i	0.0217119	−	0.258486i
$214$	−4.05247	−	15.1240i	−0.277021	−	1.03386i
$215$	−2.11367	−	0.566356i	−0.144151	−	0.0386251i
$216$	1.29259	−	5.03281i	0.0879499	−	0.342439i
$217$	18.0250	−	9.80565i	1.22361	−	0.665651i
$218$	5.05892			0.342633
$219$	2.41671	+	1.67975i	0.163306	+	0.113507i
$220$	−2.90104	−	1.67492i	−0.195588	−	0.112923i
$221$	−7.96746	−	12.1454i	−0.535949	−	0.816985i
$222$	−2.27966	−	12.6716i	−0.153001	−	0.850461i
$223$	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
$226$	10.4588	+	2.80243i	0.695711	+	0.186415i
$227$	−8.97401	+	2.40458i	−0.595626	+	0.159597i	−0.544023	−	0.839070i	$-0.683100\pi$
$227$	−8.97401	+	2.40458i	−0.595626	+	0.159597i	−0.0516026	+	0.998668i	$0.516433\pi$
$228$	−0.478546	+	5.69721i	−0.0316925	+	0.377307i
$229$	−5.17964	+	19.3307i	−0.342281	+	1.27741i	0.553477	+	0.832865i	$0.313301\pi$
$229$	−5.17964	+	19.3307i	−0.342281	+	1.27741i	−0.895757	+	0.444544i	$0.853366\pi$
$230$		−	14.1773i		−	0.934821i
$231$	7.57257	+	2.94558i	0.498239	+	0.193805i
$232$	−1.67254	−	1.67254i	−0.109807	−	0.109807i
$233$	11.6047	+	20.0999i	0.760248	+	1.31679i	0.942723	+	0.333577i	$0.108256\pi$
$233$	11.6047	+	20.0999i	0.760248	+	1.31679i	−0.182475	+	0.983210i	$0.558411\pi$
$234$	−8.44608	+	6.75750i	−0.552137	+	0.441752i
$235$	9.33453	−	16.1679i	0.608918	−	1.05468i
$236$	3.26848	−	12.1981i	0.212760	−	0.794031i
$237$	−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	$0.828111\pi$
$240$	−2.68702	−	1.86762i	−0.173446	−	0.120554i
$241$	−20.2823	+	5.43462i	−1.30650	+	0.350075i	−0.843903	−	0.536496i	$-0.819748\pi$
$241$	−20.2823	+	5.43462i	−1.30650	+	0.350075i	−0.462594	+	0.886570i	$0.653081\pi$
$242$	2.03333	+	7.58848i	0.130707	+	0.487806i
$243$	5.58465	+	14.5538i	0.358255	+	0.933624i
$244$			11.9292i			0.763689i
$245$	2.77054	+	12.9314i	0.177003	+	0.826160i
$246$	−2.69288	−	0.969568i	−0.171691	−	0.0618174i
$247$	7.92260	−	8.88127i	0.504103	−	0.565102i
$248$	−6.71659	−	3.87782i	−0.426504	−	0.246242i
$249$	0.855247	−	10.1819i	0.0541991	−	0.645253i
$250$	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	$0.475432\pi$
$252$	7.13053	+	3.48649i	0.449181	+	0.219628i
$253$	9.40832	−	9.40832i	0.591496	−	0.591496i
$254$	−18.5508	−	4.97067i	−1.16398	−	0.311888i
$255$	−1.10344	+	13.1368i	−0.0691003	+	0.822656i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.17304	−	3.76382i	−0.135551	−	0.234780i	0.790257	−	0.612775i	$-0.209947\pi$
$257$	−2.17304	−	3.76382i	−0.135551	−	0.234780i	−0.925808	+	0.377995i	$0.876614\pi$
$258$	−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
$261$	6.99654	+	1.18372i	0.433075	+	0.0732707i
$262$	1.11089	+	4.14588i	0.0686308	+	0.256134i
$263$	9.85510	+	5.68984i	0.607691	+	0.350851i	0.772061	−	0.635548i	$-0.219226\pi$
$263$	9.85510	+	5.68984i	0.607691	+	0.350851i	−0.164370	+	0.986399i	$0.552559\pi$
$264$	−0.543767	−	3.02255i	−0.0334665	−	0.186025i
$265$	12.6056	−	12.6056i	0.774358	−	0.774358i
$266$	−8.37564	−	2.47361i	−0.513544	−	0.151667i
$267$	2.43258	+	5.16982i	0.148872	+	0.316388i
$268$	2.84753	−	10.6271i	0.173940	−	0.649154i
$269$	−18.3630	−	10.6019i	−1.11961	−	0.646408i	−0.178310	−	0.983974i	$-0.557063\pi$
$269$	−18.3630	−	10.6019i	−1.11961	−	0.646408i	−0.941302	+	0.337566i	$0.890396\pi$
$270$	9.81642	−	0.102091i	0.597408	−	0.00621304i
$271$	3.82897	−	14.2899i	0.232594	−	0.868051i	−0.746625	−	0.665245i	$-0.768327\pi$
$271$	3.82897	−	14.2899i	0.232594	−	0.868051i	0.979219	−	0.202806i	$-0.0650061\pi$
$272$	4.02865			0.244273
$273$	−7.50377	−	14.7205i	−0.454149	−	0.890926i
$274$	6.69041			0.404183
$275$	−0.656535	+	2.45022i	−0.0395905	+	0.147754i
$276$	9.92761	−	8.38907i	0.597572	−	0.504963i
$277$	17.8363	+	10.2978i	1.07168	+	0.618735i	0.928640	−	0.370982i	$-0.120979\pi$
$277$	17.8363	+	10.2978i	1.07168	+	0.618735i	0.143040	+	0.989717i	$0.454312\pi$
$278$	−3.35215	+	12.5104i	−0.201049	+	0.750323i
$279$	23.1638	−	2.18849i	1.38678	−	0.131022i
$280$	3.62303	−	3.44370i	0.216518	−	0.205801i
$281$	−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	$0.359702\pi$
$282$	16.8450	−	3.03048i	1.00311	−	0.180462i
$283$	−1.97537	−	1.14048i	−0.117423	−	0.0677945i	0.440138	−	0.897930i	$-0.354930\pi$
$283$	−1.97537	−	1.14048i	−0.117423	−	0.0677945i	−0.557561	+	0.830136i	$0.688263\pi$
$284$	−0.565703	−	2.11123i	−0.0335683	−	0.125279i
$285$	−10.6308	+	1.91252i	−0.629716	+	0.113288i
$286$	−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
$291$	−12.5627	−	1.05523i	−0.736441	−	0.0618586i
$292$	1.64132	+	0.439791i	0.0960511	+	0.0257368i
$293$	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	$-0.0478550\pi$
$294$	−7.41582	+	9.59195i	−0.432500	+	0.559414i
$295$	23.8586			1.38910
$296$	−3.71670	−	6.43751i	−0.216029	−	0.374173i
$297$	6.58212	+	6.44662i	0.381933	+	0.374071i
$298$	−1.50114	−	0.866685i	−0.0869589	−	0.0502057i
$299$	−27.0124	+	1.54108i	−1.56217	+	0.0891227i
$300$	−0.839433	+	2.33144i	−0.0484647	+	0.134606i
$301$	2.97916	−	0.717784i	0.171716	−	0.0413724i
$302$			5.26231i			0.302812i
$303$	−4.21139	+	0.757644i	−0.241938	+	0.0435255i
$304$	0.854328	+	3.18839i	0.0489990	+	0.182867i
$305$	−21.7696	+	5.83314i	−1.24652	+	0.334004i
$306$	−9.85193	+	7.00069i	−0.563197	+	0.400203i
$307$	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
$310$	3.79235	−	14.1533i	0.215391	−	0.803851i
$311$	−1.39800	+	2.42141i	−0.0792733	+	0.137305i	−0.902937	−	0.429774i	$-0.858593\pi$
$311$	−1.39800	+	2.42141i	−0.0792733	+	0.137305i	0.823663	+	0.567079i	$0.191927\pi$
$312$	−3.26636	+	5.32268i	−0.184921	+	0.301337i
$313$	4.51429	+	7.81899i	0.255163	+	0.441955i	0.964940	−	0.262471i	$-0.0845375\pi$
$313$	4.51429	+	7.81899i	0.255163	+	0.441955i	−0.709777	+	0.704427i	$0.751204\pi$
$314$	−12.9683	−	12.9683i	−0.731843	−	0.731843i
$315$	−2.87580	+	14.7173i	−0.162033	+	0.829226i
$316$			6.69222i			0.376467i
$317$	1.80507	−	6.73660i	0.101383	−	0.378365i	−0.896527	−	0.442989i	$-0.853918\pi$
$317$	1.80507	−	6.73660i	0.101383	−	0.378365i	0.997910	+	0.0646238i	$0.0205847\pi$
$318$	16.2862	+	1.36798i	0.913283	+	0.0767127i
$319$	4.05101	−	1.08547i	0.226813	−	0.0607744i
$320$	−1.82490	−	0.488980i	−0.102015	−	0.0273348i
$321$	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
$324$	5.88013	+	6.81352i	0.326674	+	0.378529i
$325$	4.31304	−	2.82939i	0.239244	−	0.156946i
$326$	14.7128	+	8.49443i	0.814865	+	0.470463i
$327$	−5.00094	+	7.19504i	−0.276552	+	0.397886i
$328$	−1.65244			−0.0912405
$329$	−0.663235	+	26.1359i	−0.0365653	+	1.44092i
$330$	5.24995	−	2.47028i	0.289000	−	0.135985i
$331$	−13.8388	−	3.70810i	−0.760650	−	0.203816i	−0.142413	−	0.989807i	$-0.545486\pi$
$331$	−13.8388	−	3.70810i	−0.760650	−	0.203816i	−0.618237	+	0.785992i	$0.712153\pi$
$332$	−1.52683	−	5.69822i	−0.0837959	−	0.312731i
$333$	20.2757	+	9.28412i	1.11110	+	0.508766i
$334$	−5.33374	−	9.23831i	−0.291849	−	0.505498i
$335$	20.7858			1.13565
$336$	4.55529	+	0.499291i	0.248512	+	0.0272385i
$337$		−	1.28563i		−	0.0700326i	−0.999387	−	0.0350163i	$-0.988852\pi$
$337$		−	1.28563i		−	0.0700326i	0.999387	−	0.0350163i	$-0.0111483\pi$
$338$	12.0929	−	4.77094i	0.657767	−	0.259505i
$339$	−14.3247	+	12.1047i	−0.778012	+	0.657439i
$340$	1.96993	+	7.35187i	0.106834	+	0.398711i
$341$	11.9091	−	6.87570i	0.644912	−	0.372340i
$342$	−7.62978	−	6.31253i	−0.412571	−	0.341342i
$343$	−12.0621	−	14.0537i	−0.651292	−	0.758828i
$344$	−0.818999	−	0.818999i	−0.0441575	−	0.0441575i
$345$	20.1636	+	14.0148i	1.08557	+	0.754531i
$346$	−14.2986	+	3.83129i	−0.768696	+	0.205972i
$347$	−18.9998	−	10.9696i	−1.01997	−	0.588877i	−0.105871	−	0.994380i	$-0.533763\pi$
$347$	−18.9998	−	10.9696i	−1.01997	−	0.588877i	−0.914094	+	0.405503i	$0.867096\pi$
$348$	4.03213	−	0.725394i	0.216145	−	0.0388852i
$349$	−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
$353$	22.1994	−	5.94830i	1.18155	−	0.316596i	0.386011	−	0.922494i	$-0.373853\pi$
$353$	22.1994	−	5.94830i	1.18155	−	0.316596i	0.795542	+	0.605898i	$0.207186\pi$
$354$	14.1178	+	16.7069i	0.750350	+	0.887963i
$355$	3.57617	−	2.06470i	0.189803	−	0.109583i
$356$	2.33254	+	2.33254i	0.123624	+	0.123624i
$357$	−7.43386	−	16.8988i	−0.393442	−	0.894377i
$358$	−13.1386	−	13.1386i	−0.694395	−	0.694395i
$359$	−20.5205	−	5.49845i	−1.08303	−	0.290197i	−0.327193	−	0.944957i	$-0.606103\pi$
$359$	−20.5205	−	5.49845i	−1.08303	−	0.290197i	−0.755836	+	0.654761i	$0.772769\pi$
$360$	5.31244	−	1.97539i	0.279990	−	0.104112i
$361$	−7.01850	−	4.05213i	−0.369395	−	0.213270i
$362$	−18.5986	−	4.98348i	−0.977521	−	0.261926i
$363$	−12.8027	−	4.60962i	−0.671969	−	0.241942i
$364$	−6.95524	−	6.52876i	−0.364553	−	0.342200i
$365$			3.21029i			0.168034i
$366$	−16.9663	−	11.7925i	−0.886842	−	0.616403i
$367$	12.2557	−	21.2274i	0.639740	−	1.10806i	−0.345750	−	0.938327i	$-0.612375\pi$
$367$	12.2557	−	21.2274i	0.639740	−	1.10806i	0.985490	−	0.169735i	$-0.0542913\pi$
$368$	3.75204	−	6.49873i	0.195589	−	0.338770i
$369$	4.04098	−	2.87148i	0.210365	−	0.149483i
$370$	9.93040	−	9.93040i	0.516257	−	0.516257i
$371$	−7.07112	+	23.9428i	−0.367114	+	1.24305i
$372$	12.1548	−	5.71927i	0.630199	−	0.296531i
$373$	8.95144	+	15.5044i	0.463488	+	0.802785i	0.999132	−	0.0416590i	$-0.0132643\pi$
$373$	8.95144	+	15.5044i	0.463488	+	0.802785i	−0.535644	+	0.844444i	$0.679931\pi$
$374$	−3.57156	+	6.18613i	−0.184681	+	0.319877i
$375$	−20.9693	−	1.76135i	−1.08285	−	0.0909556i
$376$	8.55773	−	4.94081i	0.441331	−	0.254803i
$377$	−7.61661	−	3.83655i	−0.392275	−	0.197592i
$378$	−12.0075	+	6.69485i	−0.617597	+	0.344346i
$379$	−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
$381$	25.4077	−	21.4701i	1.30168	−	1.09995i
$382$	−3.94542	−	14.7245i	−0.201865	−	0.753371i
$383$	5.50114	−	20.5305i	0.281095	−	1.04906i	−0.670551	−	0.741864i	$-0.733942\pi$
$383$	5.50114	−	20.5305i	0.281095	−	1.04906i	0.951646	−	0.307197i	$-0.0993911\pi$
$384$	−0.737434	−	1.56722i	−0.0376320	−	0.0799771i
$385$	2.07596	+	8.61628i	0.105801	+	0.439126i
$386$		−	20.9919i		−	1.06846i
$387$	3.42603	+	0.579640i	0.174155	+	0.0294647i
$388$	−7.03063	+	1.88385i	−0.356926	+	0.0956381i
$389$	6.58614	−	11.4075i	0.333931	−	0.578385i	−0.649348	−	0.760491i	$-0.724958\pi$
$389$	6.58614	−	11.4075i	0.333931	−	0.578385i	0.983279	+	0.182106i	$0.0582915\pi$
$390$	−11.3105	−	3.35810i	−0.572731	−	0.170044i
$391$	−30.2313			−1.52886
$392$	−2.15234	+	6.66089i	−0.108710	+	0.336426i
$393$	−6.99463	−	2.51841i	−0.352833	−	0.127037i
$394$	−9.37479	+	5.41253i	−0.472295	+	0.272680i
$395$	−12.2126	+	3.27236i	−0.614483	+	0.164650i
$396$	4.83635	+	2.21453i	0.243036	+	0.111285i
$397$	6.05173	−	22.5853i	0.303727	−	1.13353i	−0.630308	−	0.776345i	$-0.717071\pi$
$397$	6.05173	−	22.5853i	0.303727	−	1.13353i	0.934035	−	0.357181i	$-0.116262\pi$
$398$	8.24627	−	8.24627i	0.413348	−	0.413348i
$399$	11.7977	−	9.46698i	0.590626	−	0.473942i
$400$			1.43065i			0.0715324i
$401$	−10.0414	−	2.69059i	−0.501444	−	0.134362i	−0.000774026	−	1.00000i	$-0.500246\pi$
$401$	−10.0414	−	2.69059i	−0.501444	−	0.134362i	−0.500670	+	0.865638i	$0.666913\pi$
$402$	12.2995	+	14.5552i	0.613443	+	0.725948i
$403$	−27.3789	−	5.68724i	−1.36384	−	0.283302i
$404$	−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
$408$	−3.98248	+	5.72974i	−0.197162	+	0.283664i
$409$	0.710467	+	2.65150i	0.0351304	+	0.131108i	0.981264	−	0.192668i	$-0.0617141\pi$
$409$	0.710467	+	2.65150i	0.0351304	+	0.131108i	−0.946134	+	0.323776i	$0.895047\pi$
$410$	−0.808008	−	3.01553i	−0.0399047	−	0.148926i
$411$	−6.61374	+	9.51543i	−0.326232	+	0.469362i
$412$	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
$416$	−0.733303	+	3.53019i	−0.0359531	+	0.173082i
$417$	−14.4792	−	17.1346i	−0.709047	−	0.839085i
$418$	−5.65329	−	1.51479i	−0.276511	−	0.0740910i
$419$		−	36.6360i		−	1.78979i	−0.446281	−	0.894893i	$-0.647252\pi$
$419$		−	36.6360i		−	1.78979i	0.446281	−	0.894893i	$-0.352748\pi$
$420$	1.31629	+	8.55709i	0.0642285	+	0.417543i
$421$	−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	$0.341302\pi$
$422$	−2.44808	+	9.13638i	−0.119171	+	0.444752i
$423$	−12.3419	+	26.9536i	−0.600083	+	1.31053i
$424$	9.11442	−	2.44220i	0.442635	−	0.118604i
$425$	4.99140	−	2.88179i	0.242119	−	0.139787i
$426$	3.56192	+	1.28247i	0.172575	+	0.0621357i
$427$	22.8765	−	21.7441i	1.10707	−	1.05227i
$428$	15.6575			0.756836
$429$	−5.27739	−	9.73439i	−0.254795	−	0.469981i
$430$	1.09412	−	1.89506i	0.0527629	−	0.0913881i
$431$	−12.7016	+	3.40340i	−0.611817	+	0.163936i	−0.551405	−	0.834238i	$-0.685908\pi$
$431$	−12.7016	+	3.40340i	−0.611817	+	0.163936i	−0.0604118	+	0.998174i	$0.519241\pi$
$432$	4.52678	+	2.55114i	0.217795	+	0.122742i
$433$			20.3113i			0.976097i	0.872816	+	0.488049i	$0.162291\pi$
$433$			20.3113i			0.976097i	−0.872816	+	0.488049i	$0.837709\pi$
$434$	4.80632	+	19.9487i	0.230711	+	0.957567i
$435$	3.29540	+	7.00352i	0.158002	+	0.335793i
$436$	−1.30934	+	4.88654i	−0.0627062	+	0.234023i
$437$	−6.41095	−	23.9260i	−0.306677	−	1.14453i
$438$	−2.24800	+	1.89962i	−0.107414	+	0.0907672i
$439$	−25.1485	+	14.5195i	−1.20027	+	0.692977i	−0.960615	−	0.277881i	$-0.910368\pi$
$439$	−25.1485	+	14.5195i	−1.20027	+	0.692977i	−0.239656	+	0.970858i	$0.577035\pi$
$440$	2.36869	−	2.36869i	0.112923	−	0.112923i
$441$	−6.31130	−	20.0292i	−0.300538	−	0.953770i
$442$	13.7936	−	4.55253i	0.656097	−	0.216542i
$443$	−21.6793	+	12.5166i	−1.03002	+	0.594680i	−0.916989	−	0.398912i	$-0.869388\pi$
$443$	−21.6793	+	12.5166i	−1.03002	+	0.594680i	−0.113026	+	0.993592i	$0.536054\pi$
$444$	12.8298	+	1.07766i	0.608877	+	0.0511436i
$445$	−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
$448$	2.57215	−	0.619719i	0.121523	−	0.0292790i
$449$	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	$-0.0345684\pi$
$450$	−2.48607	−	3.49860i	−0.117195	−	0.164926i
$451$	1.46495	−	2.53737i	0.0689820	−	0.119480i
$452$	−5.41389	+	9.37713i	−0.254648	+	0.441063i
$453$	−7.48431	−	5.20200i	−0.351643	−	0.244411i
$454$		−	9.29057i		−	0.436028i
$455$	8.51335	−	15.8850i	0.399112	−	0.744701i
$456$	−5.37922	−	1.93679i	−0.251905	−	0.0906983i
$457$	14.7887	+	3.96263i	0.691788	+	0.185364i	0.587550	−	0.809188i	$-0.300093\pi$
$457$	14.7887	+	3.96263i	0.691788	+	0.185364i	0.104239	+	0.994552i	$0.466759\pi$
$458$	−17.3314	−	10.0063i	−0.809845	−	0.467564i
$459$	−0.217696	−	20.9323i	−0.0101612	−	0.977038i
$460$	13.6942	+	3.66935i	0.638495	+	0.171084i
$461$	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	$0.514737\pi$
$462$	−4.80514	+	6.55217i	−0.223555	+	0.304835i
$463$	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
$465$	16.3806	+	19.3847i	0.759630	+	0.898945i
$466$	−22.4185	+	6.00702i	−1.03852	+	0.278270i
$467$	−7.70434	−	13.3443i	−0.356514	−	0.617501i	0.630861	−	0.775895i	$-0.282702\pi$
$467$	−7.70434	−	13.3443i	−0.356514	−	0.617501i	−0.987376	+	0.158394i	$0.949368\pi$
$468$	−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
$471$	31.2638	−	5.62446i	1.44056	−	0.259162i
$472$	10.9365	+	6.31422i	0.503395	+	0.290636i
$473$	1.98368	−	0.531525i	0.0912096	−	0.0244395i
$474$	−9.51800	−	6.61552i	−0.437176	−	0.303861i
$475$	3.33923	+	3.33923i	0.153214	+	0.153214i
$476$	−7.34329	−	7.72569i	−0.336579	−	0.354106i
$477$	−18.0451	+	21.8107i	−0.826230	+	0.998642i
$478$	6.50513	−	3.75574i	0.297538	−	0.171783i
$479$	2.85010	+	10.6367i	0.130224	+	0.486004i	0.999972	−	0.00749277i	$-0.00238504\pi$
$479$	2.85010	+	10.6367i	0.130224	+	0.486004i	−0.869747	+	0.493497i	$0.835718\pi$
$480$	2.49943	−	2.11208i	0.114083	−	0.0964029i
$481$	−20.0002	−	17.8413i	−0.911930	−	0.813493i
$482$		−	20.9978i		−	0.956422i
$483$	−34.1833	−	3.74672i	−1.55540	−	0.170482i
$484$	−7.85618			−0.357099
$485$	−6.87568	−	11.9090i	−0.312208	−	0.540761i
$486$	−15.5033	+	1.62757i	−0.703242	+	0.0738280i
$487$	7.54368	+	28.1534i	0.341837	+	1.27575i	0.896264	+	0.443521i	$0.146271\pi$
$487$	7.54368	+	28.1534i	0.341837	+	1.27575i	−0.554427	+	0.832232i	$0.687063\pi$
$488$	−11.5227	−	3.08750i	−0.521609	−	0.139765i
$489$	−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	$0.369844\pi$
$492$	1.63350	−	2.35018i	0.0736438	−	0.105954i
$493$	−8.25241	−	4.76453i	−0.371670	−	0.214584i
$494$	6.52813	+	9.95128i	0.293714	+	0.447729i
$495$	−1.67642	+	9.90870i	−0.0753496	+	0.445363i
$496$	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
$499$	5.88028	+	1.57562i	0.263238	+	0.0705343i	0.388024	−	0.921649i	$-0.373158\pi$
$499$	5.88028	+	1.57562i	0.263238	+	0.0705343i	−0.124786	+	0.992184i	$0.539825\pi$
$500$	−11.7353	+	3.14446i	−0.524817	+	0.140624i
$501$	18.4118	+	1.54653i	0.822577	+	0.0690937i
$502$	−0.632344	+	2.35994i	−0.0282229	+	0.105329i
$503$			38.6506i			1.72334i	0.507466	+	0.861671i	$0.330582\pi$
$503$			38.6506i			1.72334i	−0.507466	+	0.861671i	$0.669418\pi$
$504$	−5.21320	+	5.98519i	−0.232215	+	0.266602i
$505$	−3.30036	−	3.30036i	−0.146864	−	0.146864i
$506$	6.65268	+	11.5228i	0.295748	+	0.512250i
$507$	−5.16884	+	21.9154i	−0.229556	+	0.973295i
$508$	9.60260	−	16.6322i	0.426047	−	0.737934i
$509$	0.476080	−	1.77675i	0.0211019	−	0.0787532i	−0.954572	−	0.297981i	$-0.903687\pi$
$509$	0.476080	−	1.77675i	0.0211019	−	0.0787532i	0.975674	+	0.219227i	$0.0703536\pi$
$510$	−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
$513$	16.5203	−	4.61127i	0.729390	−	0.203592i
$514$	4.19799	−	1.12485i	0.185166	−	0.0496149i
$515$	1.49127	+	5.56550i	0.0657133	+	0.245245i
$516$	1.97443	−	0.355207i	0.0869196	−	0.0156371i
$517$			17.5209i			0.770569i
$518$	−5.57045	+	18.8615i	−0.244751	+	0.828728i
$519$	8.68565	−	24.1235i	0.381258	−	1.05890i
$520$	−6.80081	+	0.387990i	−0.298235	+	0.0170145i
$521$	11.5622	+	6.67544i	0.506549	+	0.292456i	0.731414	−	0.681934i	$-0.238861\pi$
$521$	11.5622	+	6.67544i	0.506549	+	0.292456i	−0.224865	+	0.974390i	$0.572194\pi$
$522$	−2.95423	+	6.45177i	−0.129303	+	0.282386i
$523$	−7.83685	−	13.5738i	−0.342681	−	0.593542i	0.642248	−	0.766497i	$-0.278002\pi$
$523$	−7.83685	−	13.5738i	−0.342681	−	0.593542i	−0.984930	+	0.172955i	$0.944668\pi$
$524$	−4.29214			−0.187503
$525$	6.00106	−	2.63990i	0.261908	−	0.115215i
$526$	−8.04665	+	8.04665i	−0.350851	+	0.350851i
$527$	−30.1801	−	8.08674i	−1.31467	−	0.352264i
$528$	3.06029	+	0.257054i	0.133182	+	0.0111869i
$529$	−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
$534$	−5.62326	+	1.01164i	−0.243342	+	0.0437781i
$535$	7.65622	+	28.5734i	0.331007	+	1.23534i
$536$	9.52801	+	5.50100i	0.411547	+	0.237607i
$537$	31.6743	−	5.69832i	1.36685	−	0.245901i
$538$	14.9933	−	14.9933i	0.646408	−	0.646408i
$539$	−8.31988	−	9.21015i	−0.358363	−	0.396709i
$540$	−2.44206	+	9.50836i	−0.105090	+	0.409175i
$541$	−7.52229	+	28.0736i	−0.323409	+	1.20698i	0.592493	+	0.805575i	$0.298144\pi$
$541$	−7.52229	+	28.0736i	−0.323409	+	1.20698i	−0.915902	+	0.401402i	$0.868523\pi$
$542$	12.8120	+	7.39701i	0.550322	+	0.317729i
$543$	25.4732	−	21.5255i	1.09316	−	0.923746i
$544$	−1.04269	+	3.89138i	−0.0447050	+	0.166841i
$545$	−9.55767			−0.409406
$546$	16.1610	−	3.43814i	0.691629	−	0.147139i
$547$	−30.9427			−1.32301			−0.661506	−	0.749939i	$-0.730083\pi$
$547$	−30.9427			−1.32301			−0.661506	+	0.749939i	$0.730083\pi$
$548$	−1.73161	+	6.46244i	−0.0739706	+	0.276062i
$549$	33.5437	−	12.4729i	1.43161	−	0.532332i
$550$	−2.19681	−	1.26833i	−0.0936722	−	0.0540817i
$551$	2.02076	−	7.54158i	0.0860873	−	0.321282i
$552$	5.53377	+	11.7606i	0.235533	+	0.500564i
$553$	12.8336	−	12.1984i	0.545739	−	0.518727i
$554$	−14.5633	+	14.5633i	−0.618735	+	0.618735i
$555$	4.30691	+	23.9401i	0.182818	+	1.01620i
$556$	−11.2165	−	6.47585i	−0.475686	−	0.274637i
$557$	1.70215	+	6.35250i	0.0721223	+	0.269164i	0.992565	−	0.121713i	$-0.0388386\pi$
$557$	1.70215	+	6.35250i	0.0721223	+	0.269164i	−0.920443	+	0.390877i	$0.872172\pi$
$558$	−3.88130	+	22.9409i	−0.164309	+	0.971167i
$559$	−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	−0.242169	+	0.970234i	$0.577859\pi$
$563$	−22.8101	+	39.5083i	−0.961332	+	1.66508i	−0.719163	+	0.694842i	$0.755474\pi$
$564$	−1.43260	+	17.0554i	−0.0603232	+	0.718162i
$565$	−19.7596	−	5.29456i	−0.831292	−	0.222744i
$566$	1.61288	−	1.61288i	0.0677945	−	0.0677945i
$567$	2.34810	−	23.6957i	0.0986108	−	0.995126i
$568$	2.18571			0.0917103
$569$	5.55993	+	9.63007i	0.233084	+	0.403714i	0.958714	−	0.284371i	$-0.0917849\pi$
$569$	5.55993	+	9.63007i	0.233084	+	0.403714i	−0.725630	+	0.688085i	$0.758452\pi$
$570$	0.904105	−	10.7636i	0.0378688	−	0.450837i
$571$	14.9711	+	8.64357i	0.626521	+	0.361722i	0.779404	−	0.626522i	$-0.215522\pi$
$571$	14.9711	+	8.64357i	0.626521	+	0.361722i	−0.152882	+	0.988244i	$0.548856\pi$
$572$	−4.77063	−	4.25568i	−0.199470	−	0.177939i
$573$	24.8421	+	8.94438i	1.03779	+	0.373657i
$574$	3.01201	+	3.16885i	0.125719	+	0.132265i
$575$		−	10.7357i		−	0.447710i
$576$	2.95796	+	0.500449i	0.123248	+	0.0208520i
$577$	0.801367	+	2.99074i	0.0333613	+	0.124506i	0.980598	−	0.196028i	$-0.0628043\pi$
$577$	0.801367	+	2.99074i	0.0333613	+	0.124506i	−0.947237	+	0.320534i	$0.896138\pi$
$578$	−0.743748	+	0.199287i	−0.0309358	+	0.00828923i
$579$	29.8556	+	20.7513i	1.24076	+	0.862393i
$580$	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
$583$	−4.33022	+	16.1606i	−0.179340	+	0.669304i
$584$	−0.849611	+	1.47157i	−0.0351571	+	0.0608940i
$585$	15.9569	−	12.7668i	0.659738	−	0.527841i
$586$	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	$0.579320\pi$
$588$	−7.34576	−	9.64572i	−0.302934	−	0.397783i
$589$		−	25.6004i		−	1.05484i
$590$	−6.17505	+	23.0456i	−0.254223	+	0.948773i
$591$	1.56937	−	18.6838i	0.0645554	−	0.768548i
$592$	7.18011	−	1.92390i	0.295101	−	0.0790720i
$593$	−4.51085	−	1.20868i	−0.185238	−	0.0496345i	0.165007	−	0.986292i	$-0.447235\pi$
$593$	−4.51085	−	1.20868i	−0.185238	−	0.0496345i	−0.350246	+	0.936658i	$0.613902\pi$
$594$	−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
$597$	3.57648	+	19.8800i	0.146376	+	0.813635i
$598$	5.50277	−	26.4909i	0.225025	−	1.08329i
$599$	30.3818	+	17.5409i	1.24137	+	0.716703i	0.969372	−	0.245596i	$-0.0789835\pi$
$599$	30.3818	+	17.5409i	1.24137	+	0.716703i	0.271994	+	0.962299i	$0.412317\pi$
$600$	−2.03474	−	1.41425i	−0.0830677	−	0.0577366i
$601$	−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
$604$	−5.08300	−	1.36199i	−0.206824	−	0.0554184i
$605$	−3.84151	−	14.3367i	−0.156180	−	0.582870i
$606$	0.358160	−	4.26398i	0.0145493	−	0.173212i
$607$	−4.82277	−	8.35328i	−0.195750	−	0.339049i	0.751396	−	0.659851i	$-0.229381\pi$
$607$	−4.82277	−	8.35328i	−0.195750	−	0.339049i	−0.947146	+	0.320802i	$0.896047\pi$
$608$	−3.30087			−0.133868
$609$	−8.74071	−	6.41014i	−0.354192	−	0.259752i
$610$		−	22.5375i		−	0.912517i
$611$	23.7174	−	26.5873i	0.959504	−	1.07561i
$612$	−4.21228	−	11.3281i	−0.170271	−	0.457913i
$613$	−1.68162	−	6.27588i	−0.0679198	−	0.253480i	0.923615	−	0.383322i	$-0.125220\pi$
$613$	−1.68162	−	6.27588i	−0.0679198	−	0.253480i	−0.991535	+	0.129841i	$0.958553\pi$
$614$	−5.17370	+	2.98704i	−0.208794	+	0.120547i
$615$	5.08758	+	1.83178i	0.205151	+	0.0738645i
$616$	−1.32872	+	4.49903i	−0.0535355	+	0.181271i
$617$	−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	$0.894339\pi$
$618$	−3.01481	+	4.33752i	−0.121273	+	0.174481i
$619$	37.3800	−	10.0159i	1.50243	−	0.402575i	0.588516	−	0.808485i	$-0.299712\pi$
$619$	37.3800	−	10.0159i	1.50243	−	0.402575i	0.913913	+	0.405911i	$0.133046\pi$
$620$	12.6895	+	7.32627i	0.509621	+	0.294230i
$621$	−33.9693	−	19.1440i	−1.36314	−	0.768221i
$622$	−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
$626$	−8.72095	+	2.33677i	−0.348559	+	0.0933961i
$627$	7.74291	−	6.54294i	0.309222	−	0.261300i
$628$	15.8828	−	9.16996i	0.633794	−	0.365921i
$629$	−21.1754	−	21.1754i	−0.844318	−	0.844318i
$630$	−13.4715	−	6.58692i	−0.536718	−	0.262429i
$631$	−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	$0.757895\pi$
$632$	−6.46419	−	1.73207i	−0.257132	−	0.0688982i
$633$	−10.5742	−	12.5134i	−0.420285	−	0.497365i
$634$	6.03987	+	3.48712i	0.239874	+	0.138491i
$635$	35.0475	+	9.39096i	1.39082	+	0.372669i
$636$	−5.53654	+	15.3772i	−0.219538	+	0.609745i
$637$	0.157664	+	25.2384i	0.00624686	+	0.999980i
$638$			4.19392i			0.166039i
$639$	−5.34508	+	3.79816i	−0.211448	+	0.150253i
$640$	0.944637	−	1.63616i	0.0373400	−	0.0646748i
$641$	−20.8196	+	36.0606i	−0.822326	+	1.42431i	0.0816205	+	0.996663i	$0.473990\pi$
$641$	−20.8196	+	36.0606i	−0.822326	+	1.42431i	−0.903946	+	0.427646i	$0.859343\pi$
$642$	−15.4781	+	22.2689i	−0.610872	+	0.878884i
$643$	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	$0.192025\pi$
$644$	−19.3016	+	4.65043i	−0.760591	+	0.183253i
$645$	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	−0.508015	−	0.861348i	$-0.669621\pi$
$647$	12.5131	−	21.6734i	0.491941	−	0.852068i	0.999957	+	0.00928034i	$0.00295406\pi$
$648$	−8.10325	+	3.91630i	−0.318326	+	0.153847i
$649$	−19.3914	+	11.1956i	−0.761179	+	0.439467i
$650$	1.61669	+	4.89838i	0.0634116	+	0.192130i
$651$	−33.1232	−	12.8843i	−1.29820	−	0.504974i
$652$	−12.0129	+	12.0129i	−0.470463	+	0.470463i
$653$	6.96251	−	4.01981i	0.272464	−	0.157307i	−0.357543	−	0.933897i	$-0.616385\pi$
$653$	6.96251	−	4.01981i	0.272464	−	0.157307i	0.630007	+	0.776590i	$0.283052\pi$
$654$	−5.65553	−	6.69275i	−0.221149	−	0.261707i
$655$	−2.09877	−	7.83271i	−0.0820056	−	0.306049i
$656$	0.427682	−	1.59613i	0.0166982	−	0.0623185i
$657$	−0.479488	−	5.07506i	−0.0187066	−	0.197997i
$658$	−25.0737	−	7.40510i	−0.977473	−	0.288681i
$659$			9.01704i			0.351254i	0.984457	+	0.175627i	$0.0561953\pi$
$659$			9.01704i			0.351254i	−0.984457	+	0.175627i	$0.943805\pi$
$660$	1.02732	+	5.71042i	0.0399885	+	0.222278i
$661$	28.5433	−	7.64816i	1.11021	−	0.297479i	0.343293	−	0.939228i	$-0.388458\pi$
$661$	28.5433	−	7.64816i	1.11021	−	0.297479i	0.766914	+	0.641749i	$0.221791\pi$
$662$	7.16350	−	12.4075i	0.278417	−	0.482233i
$663$	−7.16074	+	24.1183i	−0.278100	+	0.936679i
$664$	5.89924			0.228935
$665$	15.8239	+	4.67332i	0.613623	+	0.181224i
$666$	−14.2155	+	17.1819i	−0.550839	+	0.665785i
$667$	−15.3716	+	8.87480i	−0.595191	+	0.343633i
$668$	10.3040	−	2.76095i	0.398673	−	0.106824i
$669$	−20.1323	−	1.69104i	−0.778359	−	0.0653796i
$670$	−5.37975	+	20.0775i	−0.207838	+	0.775662i
$671$	14.9563	−	14.9563i	0.577383	−	0.577383i
$672$	−1.66127	+	4.27085i	−0.0640851	+	0.164752i
$673$			22.6718i			0.873933i	0.899478	+	0.436967i	$0.143947\pi$
$673$			22.6718i			0.873933i	−0.899478	+	0.436967i	$0.856053\pi$
$674$	1.24182	+	0.332745i	0.0478332	+	0.0128169i
$675$	7.43346	−	0.0773078i	0.286114	−	0.00297558i
$676$	1.47850	+	12.9157i	0.0568655	+	0.496756i
$677$	35.2952	−	20.3777i	1.35650	−	0.783178i	0.367354	−	0.930081i	$-0.380264\pi$
$677$	35.2952	−	20.3777i	1.35650	−	0.783178i	0.989151	+	0.146903i	$0.0469304\pi$
$678$	−7.98476	−	16.9696i	−0.306653	−	0.651712i
$679$	16.4278	+	10.0487i	0.630443	+	0.385635i
$680$	−7.61122			−0.291877
$681$	13.2135	+	9.18410i	0.506343	+	0.351935i
$682$	3.55913	+	13.2828i	0.136286	+	0.508626i
$683$	−8.73532	−	32.6006i	−0.334248	−	1.24743i	−0.904683	−	0.426086i	$-0.859892\pi$
$683$	−8.73532	−	32.6006i	−0.334248	−	1.24743i	0.570435	−	0.821343i	$-0.306775\pi$
$684$	8.07216	−	5.73600i	0.308647	−	0.219322i
$685$	−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
$689$	28.4470	−	18.6615i	1.08374	−	0.710945i
$690$	−18.7560	+	15.8492i	−0.714027	+	0.603370i
$691$	−12.4528	−	3.33672i	−0.473728	−	0.126935i	0.0140528	−	0.999901i	$-0.495527\pi$
$691$	−12.4528	−	3.33672i	−0.473728	−	0.126935i	−0.487781	+	0.872966i	$0.662193\pi$
$692$		−	14.8030i		−	0.562725i
$693$	−4.56875	−	13.3112i	−0.173552	−	0.505650i
$694$	15.5133	−	15.5133i	0.588877	−	0.588877i
$695$	6.33312	−	23.6355i	0.240229	−	0.896547i
$696$	−0.342915	+	4.08248i	−0.0129982	+	0.154746i
$697$	−6.43025	+	1.72298i	−0.243563	+	0.0652626i
$698$	21.9694	−	12.6841i	0.831556	−	0.480099i
$699$	13.6181	−	37.8229i	0.515084	−	1.43059i
$700$	2.74353	−	2.60774i	0.103696	−	0.0985632i
$701$	−7.08221			−0.267492			−0.133746	−	0.991016i	$-0.542701\pi$
$701$	−7.08221			−0.267492			−0.133746	+	0.991016i	$0.542701\pi$
$702$	18.3821	+	3.61939i	0.693786	+	0.136605i
$703$	12.2683	−	21.2494i	0.462709	−	0.801435i
$704$	1.71267	−	0.458908i	0.0645486	−	0.0172957i
$705$	−31.8249	+	5.72540i	−1.19859	+	0.215631i
$706$			22.9825i			0.864957i
$707$	6.26861	+	1.85133i	0.235755	+	0.0696265i
$708$	−19.7916	+	9.31263i	−0.743814	+	0.349990i
$709$	−6.52166	+	24.3392i	−0.244926	+	0.914076i	0.728495	+	0.685052i	$0.240220\pi$
$709$	−6.52166	+	24.3392i	−0.244926	+	0.914076i	−0.973421	+	0.229025i	$0.926446\pi$
$710$	1.06877	+	3.98869i	0.0401101	+	0.149693i
$711$	18.8178	−	6.99725i	0.705724	−	0.262418i
$712$	−2.85677	+	1.64936i	−0.107062	+	0.0618122i
$713$	−41.1529	+	41.1529i	−1.54119	+	1.54119i
$714$	18.2470	−	2.80684i	0.682876	−	0.105043i
$715$	5.43343	−	10.7869i	0.203199	−	0.403405i
$716$	16.0914	−	9.29037i	0.601364	−	0.347197i
$717$	−1.08898	+	12.9646i	−0.0406688	+	0.484172i
$718$	10.6222	−	18.3982i	0.396416	−	0.686613i
$719$	8.08257	+	13.9994i	0.301429	+	0.522090i	0.976460	−	0.215699i	$-0.0692031\pi$
$719$	8.08257	+	13.9994i	0.301429	+	0.522090i	−0.675031	+	0.737789i	$0.735870\pi$
$720$	0.533117	+	5.64269i	0.0198681	+	0.210291i
$721$	−5.55900	−	5.84848i	−0.207028	−	0.217809i
$722$	5.73058	−	5.73058i	0.213270	−	0.213270i
$723$	29.8640	+	20.7571i	1.11066	+	0.771965i
$724$	9.62735	−	16.6751i	0.357798	−	0.619724i
$725$	1.69197	−	2.93058i	0.0628383	−	0.108839i
$726$	7.76614	−	11.1734i	0.288228	−	0.414685i
$727$			13.8986i			0.515470i	0.966216	+	0.257735i	$0.0829762\pi$
$727$			13.8986i			0.515470i	−0.966216	+	0.257735i	$0.917024\pi$
$728$	8.10644	−	5.02848i	0.300445	−	0.186368i
$729$	13.0108	−	23.6584i	0.481881	−	0.876237i
$730$	−3.10091	−	0.830885i	−0.114770	−	0.0307524i
$731$	−4.04100	−	2.33307i	−0.149462	−	0.0862917i
$732$	15.7819	−	13.3361i	0.583314	−	0.492915i
$733$	50.2347	+	13.4604i	1.85546	+	0.497170i	0.999793	−	0.0203527i	$-0.00647891\pi$
$733$	50.2347	+	13.4604i	1.85546	+	0.497170i	0.855670	+	0.517522i	$0.173146\pi$
$734$	17.3321	+	17.3321i	0.639740	+	0.639740i
$735$	14.0105	−	18.1218i	0.516786	−	0.668433i
$736$	5.30619	+	5.30619i	0.195589	+	0.195589i
$737$	−16.8939	+	9.75373i	−0.622297	+	0.359283i
$738$	1.72776	+	4.64648i	0.0635996	+	0.171039i
$739$	−39.6342	+	10.6200i	−1.45797	+	0.390662i	−0.898788	−	0.438384i	$-0.855551\pi$
$739$	−39.6342	+	10.6200i	−1.45797	+	0.390662i	−0.559181	+	0.829045i	$0.688884\pi$
$740$	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	$0.953116\pi$
$744$	2.37849	+	13.2209i	0.0871997	+	0.484703i
$745$	2.83607	+	1.63741i	0.103906	+	0.0599899i
$746$	−17.2929	+	4.63361i	−0.633137	+	0.169648i
$747$	−14.4264	+	10.2513i	−0.527834	+	0.375074i
$748$	−5.05096	−	5.05096i	−0.184681	−	0.184681i
$749$	−28.5400	−	30.0262i	−1.04283	−	1.09714i
$750$	7.12858	−	19.7989i	0.260299	−	0.722953i
$751$	−13.1524	+	7.59356i	−0.479939	+	0.277093i	−0.720391	−	0.693568i	$-0.756038\pi$
$751$	−13.1524	+	7.59356i	−0.479939	+	0.277093i	0.240452	+	0.970661i	$0.422704\pi$
$752$	2.55755	+	9.54491i	0.0932642	+	0.348067i
$753$	−2.73132	−	3.23224i	−0.0995349	−	0.117789i
$754$	5.67715	−	6.36411i	0.206749	−	0.231767i
$755$		−	9.94193i		−	0.361824i
$756$	−3.35897	−	13.3311i	−0.122165	−	0.484846i
$757$	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
$759$	−22.9647	−	1.92896i	−0.833566	−	0.0700167i
$760$	−1.61406	−	6.02375i	−0.0585480	−	0.218504i
$761$	11.6954	+	3.13377i	0.423958	+	0.113599i	0.464489	−	0.885579i	$-0.346238\pi$
$761$	11.6954	+	3.13377i	0.423958	+	0.113599i	−0.0405307	+	0.999178i	$0.512905\pi$
$762$	14.1626	+	30.0989i	0.513055	+	1.09037i
$763$	11.7575	−	6.39611i	0.425649	−	0.231555i
$764$	15.2439			0.551506
$765$	18.6130	−	13.2262i	0.672954	−	0.478195i
$766$	18.4072	+	10.6274i	0.665078	+	0.383983i
$767$	44.5808	+	9.26047i	1.60972	+	0.334376i
$768$	1.70468	−	0.306679i	0.0615125	−	0.0110663i
$769$	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
$772$	20.2766	+	5.43309i	0.729770	+	0.195541i
$773$	−7.82723	+	2.09730i	−0.281526	+	0.0754346i	−0.396819	−	0.917897i	$-0.629886\pi$
$773$	−7.82723	+	2.09730i	−0.281526	+	0.0754346i	0.115293	+	0.993332i	$0.463219\pi$
$774$	−1.44661	+	3.15927i	−0.0519974	+	0.113558i
$775$	2.87175	−	10.7175i	0.103156	−	0.384985i
$776$		−	7.27865i		−	0.261288i
$777$	−21.3192	−	26.5679i	−0.764821	−	0.953119i
$778$	9.31421	+	9.31421i	0.333931	+	0.333931i
$779$	−2.72724	−	4.72371i	−0.0977134	−	0.169245i
$780$	6.17105	−	10.0560i	0.220959	−	0.360062i
$781$	−1.93772	+	3.35623i	−0.0693371	+	0.120095i
$782$	7.82444	−	29.2012i	0.279802	−	1.04423i
$783$	−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
$786$	4.24294	−	6.10448i	0.151341	−	0.217740i
$787$	32.3411	−	8.66577i	1.15284	−	0.308901i	0.368735	−	0.929535i	$-0.379791\pi$
$787$	32.3411	−	8.66577i	1.15284	−	0.308901i	0.784101	+	0.620633i	$0.213124\pi$
$788$	−2.80173	−	10.4562i	−0.0998076	−	0.372487i
$789$	−3.48991	−	19.3988i	−0.124244	−	0.690615i
$790$		−	12.6434i		−	0.449833i
$791$	27.8506	−	6.71018i	0.990255	−	0.238587i
$792$	−3.39081	+	4.09839i	−0.120487	+	0.145630i
$793$	−42.9415	+	2.44984i	−1.52490	+	0.0869963i
$794$	20.2495	+	11.6910i	0.718627	+	0.414899i
$795$	−30.7690	−	2.58449i	−1.09126	−	0.0916626i
$796$	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	$0.687361\pi$
$798$	6.09092	+	13.8460i	0.215616	+	0.490142i
$799$	28.1496	−	28.1496i	0.995861	−	0.995861i
$800$	−1.38190	−	0.370279i	−0.0488575	−	0.0130913i
$801$	4.12001	−	8.99773i	0.145573	−	0.317919i
$802$	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
$807$	6.50274	+	36.1457i	0.228907	+	1.27239i
$808$	−0.639408	−	2.38630i	−0.0224943	−	0.0839498i
$809$	21.7614	+	12.5640i	0.765091	+	0.441725i	0.831121	−	0.556092i	$-0.187700\pi$
$809$	21.7614	+	12.5640i	0.765091	+	0.441725i	−0.0660299	+	0.997818i	$0.521033\pi$
$810$	−11.1092	−	12.8726i	−0.390336	−	0.452297i
$811$	−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	$0.326408\pi$
$812$	−6.00179	−	1.77253i	−0.210621	−	0.0622036i
$813$	−23.1855	+	10.9096i	−0.813152	+	0.382616i
$814$	−3.41124	+	12.7309i	−0.119564	+	0.446219i
$815$	−27.7965	−	16.0483i	−0.973667	−	0.562147i
$816$	−4.50376	−	5.32974i	−0.157663	−	0.186578i
$817$	0.989516	−	3.69292i	0.0346188	−	0.129199i
$818$	−2.74504			−0.0959779
$819$	−11.0859	+	26.3837i	−0.387374	+	0.921923i
$820$	3.12190			0.109022
$821$	−10.7262	+	40.0306i	−0.374346	+	1.39708i	0.479952	+	0.877294i	$0.340654\pi$
$821$	−10.7262	+	40.0306i	−0.374346	+	1.39708i	−0.854298	+	0.519783i	$0.826013\pi$
$822$	−7.47944	−	8.85115i	−0.260875	−	0.308719i
$823$	−37.9165	−	21.8911i	−1.32168	−	0.763075i	−0.337687	−	0.941258i	$-0.609645\pi$
$823$	−37.9165	−	21.8911i	−1.32168	−	0.763075i	−0.983997	+	0.178183i	$0.942978\pi$
$824$	−0.789336	+	2.94584i	−0.0274978	+	0.102623i
$825$	3.97551	−	1.87062i	0.138409	−	0.0651265i
$826$	−7.82609	−	32.4822i	−0.272304	−	1.13020i
$827$	−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	$0.273117\pi$
$828$	−22.1968	−	3.75541i	−0.771393	−	0.130510i
$829$	−20.6401	−	11.9166i	−0.716860	−	0.413879i	0.0967360	−	0.995310i	$-0.469160\pi$
$829$	−20.6401	−	11.9166i	−0.716860	−	0.413879i	−0.813596	+	0.581431i	$0.802493\pi$
$830$	2.88461	+	10.7655i	0.100126	+	0.373676i
$831$	−6.31623	−	35.1090i	−0.219108	−	1.21792i
$832$	−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
$837$	−28.7909	−	28.1982i	−0.995158	−	0.974672i
$838$	35.3877	+	9.48209i	1.22245	+	0.327553i
$839$	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	$-0.000652287\pi$
$840$	−8.60620	−	0.943296i	−0.296942	−	0.0325468i
$841$	23.4052			0.807077
$842$	−5.80494	−	10.0544i	−0.200051	−	0.346499i
$843$	19.5502	+	1.64215i	0.673344	+	0.0565586i
$844$	−8.19145	−	4.72934i	−0.281961	−	0.162790i
$845$	−22.8468	+	9.01361i	−0.785953	+	0.310078i
$846$	−22.8408	−	18.8974i	−0.785284	−	0.649707i
$847$	14.3200	+	15.0657i	0.492040	+	0.517663i
$848$			9.43594i			0.324031i
$849$	0.699522	+	3.88832i	0.0240075	+	0.133447i
$850$	1.49172	+	5.56719i	0.0511657	+	0.190953i
$851$	−53.8801	+	14.4371i	−1.84699	+	0.494899i
$852$	−2.16066	+	3.10862i	−0.0740229	+	0.106500i
$853$	−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
$856$	−4.05247	+	15.1240i	−0.138511	+	0.516928i
$857$	8.80481	−	15.2504i	0.300767	−	0.520943i	−0.675543	−	0.737320i	$-0.736091\pi$
$857$	8.80481	−	15.2504i	0.300767	−	0.520943i	0.976310	+	0.216377i	$0.0694242\pi$
$858$	10.7686	−	2.57812i	0.367633	−	0.0880156i
$859$	6.64921	+	11.5168i	0.226868	+	0.392947i	0.956878	−	0.290489i	$-0.0938180\pi$
$859$	6.64921	+	11.5168i	0.226868	+	0.392947i	−0.730010	+	0.683436i	$0.760485\pi$
$860$	1.54731	+	1.54731i	0.0527629	+	0.0527629i
$861$	−7.48439	+	1.15128i	−0.255067	+	0.0392357i
$862$		−	13.1497i		−	0.447881i
$863$	10.7045	−	39.9496i	0.364384	−	1.35990i	−0.503869	−	0.863780i	$-0.668091\pi$
$863$	10.7045	−	39.9496i	0.364384	−	1.35990i	0.868254	−	0.496121i	$-0.165243\pi$
$864$	−3.63583	+	3.71225i	−0.123693	+	0.126293i
$865$	27.0139	−	7.23836i	0.918501	−	0.246111i
$866$	−19.6192	−	5.25694i	−0.666687	−	0.178638i
$867$	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
$870$	−7.61779	+	1.37047i	−0.258267	+	0.0464632i
$871$	38.8392	+	8.06780i	1.31602	+	0.273367i
$872$	−4.38115	−	2.52946i	−0.148364	−	0.0856583i
$873$	12.6483	+	17.7997i	0.428080	+	0.602428i
$874$	24.7700			0.837858
$875$	27.4208	+	16.7730i	0.926991	+	0.567030i
$876$	−1.25306	−	2.66306i	−0.0423371	−	0.0899765i
$877$	20.0615	+	5.37547i	0.677429	+	0.181517i	0.581099	−	0.813833i	$-0.302623\pi$
$877$	20.0615	+	5.37547i	0.677429	+	0.181517i	0.0963301	+	0.995349i	$0.469290\pi$
$878$	−7.51583	−	28.0495i	−0.253647	−	0.946624i
$879$	−47.5679	−	3.99554i	−1.60443	−	0.134766i
$880$	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	$0.581015\pi$
$882$	20.9802	−	0.912323i	0.706439	−	0.0307195i
$883$			25.4257i			0.855642i	0.903863	+	0.427821i	$0.140719\pi$
$883$			25.4257i			0.855642i	−0.903863	+	0.427821i	$0.859281\pi$
$884$	0.827343	+	14.5019i	0.0278266	+	0.487752i
$885$	−26.6723	−	31.5639i	−0.896579	−	1.06101i
$886$	−6.47905	−	24.1801i	−0.217668	−	0.812348i
$887$	9.09755	−	5.25247i	0.305466	−	0.176361i	−0.339430	−	0.940631i	$-0.610234\pi$
$887$	9.09755	−	5.25247i	0.305466	−	0.176361i	0.644896	+	0.764271i	$0.276901\pi$
$888$	−4.36155	+	12.1137i	−0.146364	+	0.406511i
$889$	−49.3986	+	11.9018i	−1.65678	+	0.399175i
$890$	−4.40681	−	4.40681i	−0.147717	−	0.147717i
$891$	1.17025	−	15.9148i	0.0392049	−	0.533165i
$892$	−11.2669	+	3.01895i	−0.377242	+	0.101082i
$893$	28.2479	+	16.3090i	0.945281	+	0.545758i
$894$	0.531588	+	2.95485i	0.0177790	+	0.0988250i
$895$	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
$899$	−17.7195	+	4.74793i	−0.590980	+	0.158352i
$900$	4.02283	−	1.49586i	0.134094	−	0.0498619i
$901$	32.9212	−	19.0070i	1.09676	−	0.633216i
$902$	2.07176	+	2.07176i	0.0689820	+	0.0689820i
$903$	−4.28011	−	3.13888i	−0.142433	−	0.104455i
$904$	−7.65639	−	7.65639i	−0.254648	−	0.254648i
$905$	35.1378	+	9.41516i	1.16802	+	0.312970i
$906$	6.96182	−	5.88291i	0.231291	−	0.195447i
$907$	28.6605	+	16.5472i	0.951657	+	0.549439i	0.893595	−	0.448874i	$-0.148175\pi$
$907$	28.6605	+	16.5472i	0.951657	+	0.549439i	0.0580616	+	0.998313i	$0.481508\pi$
$908$	8.97401	+	2.40458i	0.297813	+	0.0797987i
$909$	5.71039	+	4.72451i	0.189402	+	0.156702i
$910$	13.1403	+	12.3346i	0.435598	+	0.408888i
$911$			6.36943i			0.211029i	0.994418	+	0.105514i	$0.0336489\pi$
$911$			6.36943i			0.211029i	−0.994418	+	0.105514i	$0.966351\pi$
$912$	3.26304	−	4.69465i	0.108050	−	0.155456i
$913$	−5.22992	+	9.05848i	−0.173085	+	0.299792i
$914$	−7.65522	+	13.2592i	−0.253212	+	0.438576i
$915$	32.0539	+	22.2792i	1.05967	+	0.736528i
$916$	14.1511	−	14.1511i	0.467564	−	0.467564i
$917$	7.82356	+	8.23097i	0.258357	+	0.271811i
$918$	20.2754	+	5.20741i	0.669189	+	0.171870i
$919$	−3.77646	−	6.54103i	−0.124574	−	0.215769i	0.796992	−	0.603989i	$-0.206423\pi$
$919$	−3.77646	−	6.54103i	−0.124574	−	0.215769i	−0.921566	+	0.388221i	$0.873090\pi$
$920$	−7.08863	+	12.2779i	−0.233705	+	0.404790i
$921$	0.866097	−	10.3111i	0.0285389	−	0.339762i
$922$	−25.0512	+	14.4633i	−0.825018	+	0.476324i
$923$	7.48362	−	2.46993i	0.246326	−	0.0812988i
$924$	−5.08525	−	6.33723i	−0.167292	−	0.208480i
$925$	7.51977	−	7.51977i	0.247249	−	0.247249i
$926$	−13.9673	+	8.06402i	−0.458993	+	0.265000i
$927$	−3.18877	−	8.57561i	−0.104733	−	0.281660i
$928$	0.612191	+	2.28473i	0.0200961	+	0.0749998i
$929$	−13.4262	+	50.1073i	−0.440500	+	1.64397i	0.287052	+	0.957915i	$0.407325\pi$
$929$	−13.4262	+	50.1073i	−0.440500	+	1.64397i	−0.727552	+	0.686053i	$0.759342\pi$
$930$	−22.9638	+	10.8053i	−0.753013	+	0.354319i
$931$	−22.5934	+	4.84058i	−0.740467	+	0.158644i
$932$		−	23.2094i		−	0.760248i
$933$	4.76629	−	0.857473i	0.156041	−	0.0280724i
$934$	14.8836	−	3.98806i	0.487008	−	0.130493i
$935$	6.74766	−	11.6873i	0.220672	−	0.382215i
$936$	10.6933	−	1.62913i	0.349520	−	0.0532498i
$937$	−1.69179			−0.0552683			−0.0276341	−	0.999618i	$-0.508797\pi$
$937$	−1.69179			−0.0552683			−0.0276341	+	0.999618i	$0.508797\pi$
$938$	−6.81815	−	28.2988i	−0.222620	−	0.923987i
$939$	5.29753	−	14.7133i	0.172878	−	0.480152i
$940$	−16.1679	+	9.33453i	−0.527338	+	0.304459i
$941$	50.2245	−	13.4576i	1.63727	−	0.438706i	0.681261	−	0.732040i	$-0.261432\pi$
$941$	50.2245	−	13.4576i	1.63727	−	0.438706i	0.956010	+	0.293335i	$0.0947650\pi$
$942$	−2.65885	+	31.6542i	−0.0866299	+	1.03135i
$943$	−3.20936	+	11.9775i	−0.104511	+	0.390041i
$944$	−8.92965	+	8.92965i	−0.290636	+	0.290636i
$945$	22.6854	−	12.6484i	0.737955	−	0.411453i
$946$			2.05365i			0.0667701i
$947$	−10.3196	−	2.76512i	−0.335340	−	0.0898542i	0.0872197	−	0.996189i	$-0.472202\pi$
$947$	−10.3196	−	2.76512i	−0.335340	−	0.0898542i	−0.422560	+	0.906335i	$0.638868\pi$
$948$	8.85354	−	7.48146i	0.287550	−	0.242986i
$949$	−1.24604	+	5.99858i	−0.0404483	+	0.194722i
$950$	−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	$0.437808\pi$
$954$	−16.3971	−	23.0753i	−0.530875	−	0.747090i
$955$	7.45397	+	27.8186i	0.241205	+	0.900189i
$956$	1.94411	+	7.25553i	0.0628771	+	0.234661i
$957$	−5.96479	−	4.14585i	−0.192814	−	0.134016i
$958$	−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
$962$	22.4098	−	14.7010i	0.722521	−	0.473980i
$963$	−16.3712	−	44.0274i	−0.527555	−	1.41876i
$964$	20.2823	+	5.43462i	0.653248	+	0.175037i
$965$			39.6593i			1.27668i
$966$	12.4663	−	32.0488i	0.401098	−	1.03115i
$967$	−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	$0.485624\pi$
$968$	2.03333	−	7.58848i	0.0653536	−	0.243903i
$969$	−22.9521	−	1.92790i	−0.737326	−	0.0619329i
$970$	13.2828	−	3.55911i	0.426485	−	0.114276i
$971$	4.19572	−	2.42240i	0.134647	−	0.0777385i	−0.431163	−	0.902274i	$-0.641897\pi$
$971$	4.19572	−	2.42240i	0.134647	−	0.0777385i	0.565810	+	0.824535i	$0.308563\pi$
$972$	2.44043	−	15.3962i	0.0782768	−	0.493835i
$973$	8.02643	+	33.3137i	0.257315	+	1.06799i
$974$	−29.1466			−0.933916
$975$	−8.56487	−	2.54291i	−0.274295	−	0.0814383i
$976$	5.96460	−	10.3310i	0.190922	−	0.330687i
$977$	9.02380	−	2.41792i	0.288697	−	0.0773561i	−0.111564	−	0.993757i	$-0.535586\pi$
$977$	9.02380	−	2.41792i	0.288697	−	0.0773561i	0.400261	+	0.916401i	$0.368919\pi$
$978$	−5.21012	−	28.9606i	−0.166601	−	0.926059i
$979$		−	5.84889i		−	0.186931i
$980$	4.06637	−	12.5842i	0.129895	−	0.401989i
$981$	15.1095	−	1.42753i	0.482408	−	0.0455775i
$982$	−4.56050	+	17.0200i	−0.145531	+	0.543130i
$983$	1.27531	+	4.75954i	0.0406762	+	0.151806i	0.983277	−	0.182116i	$-0.0582946\pi$
$983$	1.27531	+	4.75954i	0.0406762	+	0.151806i	−0.942601	+	0.333922i	$0.891628\pi$
$984$	1.84731	+	2.18611i	0.0588902	+	0.0696906i
$985$	17.7115	−	10.2258i	0.564336	−	0.325820i
$986$	6.73806	−	6.73806i	0.214584	−	0.214584i
$987$	35.3182	−	28.3407i	1.12419	−	0.902096i
$988$	−11.3018	+	3.73011i	−0.359558	+	0.118670i
$989$	−7.52709	+	4.34577i	−0.239347	+	0.138187i
$990$	−9.13718	−	4.18386i	−0.290399	−	0.132972i
$991$	−27.0543	+	46.8594i	−0.859408	+	1.48854i	0.0130855	+	0.999914i	$0.495835\pi$
$991$	−27.0543	+	46.8594i	−0.859408	+	1.48854i	−0.872494	+	0.488625i	$0.837499\pi$
$992$	3.87782	+	6.71659i	0.123121	+	0.213252i
$993$	10.5652	+	22.4536i	0.335277	+	0.712544i
$994$	−3.98404	−	4.19150i	−0.126366	−	0.132946i
$995$	−15.5795	+	15.5795i	−0.493902	+	0.493902i
$996$	−5.83163	+	8.39018i	−0.184782	+	0.265853i
$997$	1.60113	−	2.77325i	0.0507084	−	0.0878296i	−0.839557	−	0.543272i	$-0.817185\pi$
$997$	1.60113	−	2.77325i	0.0507084	−	0.0878296i	0.890265	+	0.455442i	$0.150519\pi$
$998$	−3.04386	+	5.27212i	−0.0963516	+	0.166886i
$999$	−10.3843	−	37.2030i	−0.328546	−	1.17705i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.5	✓	144	21.2	odd	6	inner
546.2.bv.a.317.36	yes	144	7.2	even	3	inner
546.2.bv.a.359.5	yes	144	273.86	even	12	inner
546.2.bv.a.359.36	yes	144	91.86	odd	12	inner
546.2.bv.a.473.5	yes	144	1.1	even	1	trivial
546.2.bv.a.473.36	yes	144	3.2	odd	2	inner
546.2.bv.a.515.5	yes	144	13.8	odd	4	inner
546.2.bv.a.515.36	yes	144	39.8	even	4	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.488980 - 1.82490i) q^{5} +(1.56722 - 0.737434i) q^{6} +(0.619719 + 2.57215i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.488980 - 1.82490i) q^{5} +(1.56722 - 0.737434i) q^{6} +(0.619719 + 2.57215i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +(1.63616 + 0.944637i) q^{10} +(0.458908 + 1.71267i) q^{11} +(0.306679 + 1.70468i) 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} +(-2.72765 - 1.24897i) q^{18} +(3.18839 + 0.854328i) q^{19} +(-1.33592 + 1.33592i) q^{20} +(2.71005 - 3.69536i) q^{21} -1.77308 q^{22} +(-3.75204 - 6.49873i) q^{23} +(-1.72597 - 0.144976i) q^{24} +(1.23898 + 0.715324i) q^{25} +(2.69059 + 2.40016i) q^{26} +(4.47274 - 2.64473i) q^{27} +(0.749382 - 2.53741i) q^{28} -2.36532i q^{29} +(-0.579400 - 3.22061i) q^{30} +(-2.00731 - 7.49138i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.75276 - 2.52176i) q^{33} +(2.84869 + 2.84869i) q^{34} +(4.99694 + 0.126804i) q^{35} +(1.91238 - 2.31145i) q^{36} +(1.92390 - 7.18011i) q^{37} +(-1.65043 + 2.85864i) q^{38} +(-6.07337 + 1.45403i) q^{39} +(-0.944637 - 1.63616i) q^{40} +(-1.16845 - 1.16845i) q^{41} +(2.86803 + 3.57413i) q^{42} -1.15824i q^{43} +(0.458908 - 1.71267i) q^{44} +(5.15327 + 2.35965i) q^{45} +(7.24839 - 1.94220i) q^{46} +(9.54491 + 2.55755i) q^{47} +(0.586751 - 1.62964i) q^{48} +(-6.23190 + 3.18802i) q^{49} +(-1.01162 + 1.01162i) q^{50} +(-6.86757 + 1.23550i) q^{51} +(-3.01475 + 1.97770i) q^{52} +(8.17176 + 4.71797i) q^{53} +(1.39699 + 5.00484i) q^{54} +3.34984 q^{55} +(2.25699 + 1.38058i) q^{56} +(-2.43417 - 5.17320i) q^{57} +(2.28473 + 0.612191i) q^{58} +(3.26848 + 12.1981i) q^{59} +(3.26083 + 0.273899i) q^{60} +(-5.96460 - 10.3310i) q^{61} +7.75565 q^{62} +(-7.91846 + 0.545879i) q^{63} -1.00000i q^{64} +(-5.08325 - 4.53455i) q^{65} +(1.98219 + 2.34572i) q^{66} +(2.84753 + 10.6271i) q^{67} +(-3.48891 + 2.01432i) q^{68} +(-4.40303 + 12.2290i) q^{69} +(-1.41579 + 4.79385i) q^{70} +(1.54553 + 1.54553i) q^{71} +(1.73773 + 2.44547i) q^{72} +(-1.64132 + 0.439791i) q^{73} +(6.43751 + 3.71670i) q^{74} +(-0.438749 - 2.43880i) 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} +(1.82490 - 0.488980i) q^{80} +(-8.49910 - 2.96062i) q^{81} +(1.43105 - 0.826218i) q^{82} +(4.17139 + 4.17139i) q^{83} +(-4.19465 + 1.84525i) q^{84} +(-5.38194 - 5.38194i) q^{85} +(1.11877 + 0.299774i) q^{86} +(-3.12923 + 2.64427i) q^{87} +(1.53553 + 0.886542i) q^{88} +(-3.18631 - 0.853770i) q^{89} +(-3.61301 + 4.36696i) q^{90} +(9.28779 + 2.17645i) q^{91} +7.50409i q^{92} +(-7.66676 + 11.0305i) q^{93} +(-4.94081 + 8.55773i) q^{94} +(3.11812 - 5.40074i) q^{95} +(1.42225 + 0.988539i) q^{96} +(5.14678 - 5.14678i) q^{97} +(-1.46646 - 6.84467i) 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

L-functions

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