LMFDB - Embedded newform 546.2.bv.a.515.5

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			515.5
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.82490 + 0.488980i) q^{5} +(0.737434 + 1.56722i) q^{6} +(2.57215 - 0.619719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.82490 + 0.488980i) q^{5} +(0.737434 + 1.56722i) q^{6} +(2.57215 - 0.619719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +(-1.63616 - 0.944637i) q^{10} +(1.71267 - 0.458908i) q^{11} +(-0.306679 - 1.70468i) q^{12} +(1.62200 + 3.22011i) q^{13} +(-2.64490 - 0.0671181i) q^{14} +(-1.39321 - 2.96091i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.01432 + 3.48891i) q^{17} +(1.24897 - 2.72765i) q^{18} +(-0.854328 + 3.18839i) q^{19} +(1.33592 + 1.33592i) q^{20} +(-3.69536 - 2.71005i) q^{21} -1.77308 q^{22} +(3.75204 + 6.49873i) q^{23} +(-0.144976 + 1.72597i) 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} +(0.579400 + 3.22061i) q^{30} +(7.49138 - 2.00731i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-2.52176 - 1.75276i) 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} +(2.44680 - 5.74571i) q^{39} +(-0.944637 - 1.63616i) q^{40} +(1.16845 - 1.16845i) q^{41} +(2.86803 + 3.57413i) q^{42} +1.15824i q^{43} +(1.71267 + 0.458908i) q^{44} +(-2.35965 + 5.15327i) 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} +(6.86757 - 1.23550i) q^{51} +(-0.205365 + 3.59970i) q^{52} +(8.17176 + 4.71797i) q^{53} +(-5.00484 + 1.39699i) q^{54} +3.34984 q^{55} +(-2.25699 - 1.38058i) q^{56} +(5.17320 - 2.43417i) q^{57} +(-0.612191 + 2.28473i) q^{58} +(12.1981 - 3.26848i) q^{59} +(0.273899 - 3.26083i) q^{60} +(-5.96460 - 10.3310i) q^{61} -7.75565 q^{62} +(0.545879 + 7.91846i) q^{63} +1.00000i q^{64} +(1.38541 + 6.66950i) q^{65} +(1.98219 + 2.34572i) 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} +(2.44547 - 1.73773i) q^{72} +(0.439791 + 1.64132i) 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} +(-3.85052 + 4.91665i) q^{78} +(-3.34611 - 5.79563i) q^{79} +(0.488980 + 1.82490i) q^{80} +(-8.49910 - 2.96062i) q^{81} +(-1.43105 + 0.826218i) q^{82} +(-4.17139 + 4.17139i) q^{83} +(-1.84525 - 4.19465i) q^{84} +(-5.38194 + 5.38194i) q^{85} +(0.299774 - 1.11877i) q^{86} +(-3.12923 + 2.64427i) 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} +(-11.0305 - 7.66676i) q^{93} +(-4.94081 + 8.55773i) q^{94} +(-3.11812 + 5.40074i) q^{95} +(-0.988539 + 1.42225i) q^{96} +(5.14678 + 5.14678i) q^{97} +(-6.84467 + 1.46646i) q^{98} +(0.500330 + 5.29567i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	−1.11793	−	1.32296i	−0.645439	−	0.763812i
$3$	−1.11793	−	1.32296i	−0.645439	−	0.763812i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.82490	+	0.488980i	0.816119	+	0.218678i	0.642649	−	0.766161i	$-0.277835\pi$
$5$	1.82490	+	0.488980i	0.816119	+	0.218678i	0.173470	+	0.984839i	$0.444502\pi$
$6$	0.737434	+	1.56722i	0.301056	+	0.639817i
$7$	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
$9$	−0.500449	+	2.95796i	−0.166816	+	0.985988i
$10$	−1.63616	−	0.944637i	−0.517399	−	0.298720i
$11$	1.71267	−	0.458908i	0.516388	−	0.138366i	0.00879290	−	0.999961i	$-0.497201\pi$
$11$	1.71267	−	0.458908i	0.516388	−	0.138366i	0.507596	+	0.861595i	$0.330534\pi$
$12$	−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
$15$	−1.39321	−	2.96091i	−0.359726	−	0.764505i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.01432	+	3.48891i	−0.488545	+	0.846186i	−0.999913	−	0.0131764i	$-0.995806\pi$
$17$	−2.01432	+	3.48891i	−0.488545	+	0.846186i	0.511368	+	0.859362i	$0.329139\pi$
$18$	1.24897	−	2.72765i	0.294386	−	0.642913i
$19$	−0.854328	+	3.18839i	−0.195996	+	0.731468i	0.796011	+	0.605283i	$0.206940\pi$
$19$	−0.854328	+	3.18839i	−0.195996	+	0.731468i	−0.992007	+	0.126185i	$0.959727\pi$
$20$	1.33592	+	1.33592i	0.298720	+	0.298720i
$21$	−3.69536	−	2.71005i	−0.806393	−	0.591380i
$22$	−1.77308			−0.378023
$23$	3.75204	+	6.49873i	0.782355	+	1.35508i	0.930566	+	0.366123i	$0.119315\pi$
$23$	3.75204	+	6.49873i	0.782355	+	1.35508i	−0.148211	+	0.988956i	$0.547352\pi$
$24$	−0.144976	+	1.72597i	−0.0295931	+	0.352313i
$25$	−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	$-0.0704800\pi$
$30$	0.579400	+	3.22061i	0.105783	+	0.588001i
$31$	7.49138	−	2.00731i	1.34549	−	0.360523i	0.487023	−	0.873389i	$-0.338083\pi$
$31$	7.49138	−	2.00731i	1.34549	−	0.360523i	0.858469	+	0.512866i	$0.171416\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−2.52176	−	1.75276i	−0.438983	−	0.305117i
$34$	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	−0.385316	−	0.922785i	$-0.625908\pi$
$37$	−7.18011	−	1.92390i	−1.18040	−	0.316288i	−0.795086	+	0.606497i	$0.792574\pi$
$38$	1.65043	−	2.85864i	0.267736	−	0.463732i
$39$	2.44680	−	5.74571i	0.391801	−	0.920050i
$40$	−0.944637	−	1.63616i	−0.149360	−	0.258699i
$41$	1.16845	−	1.16845i	0.182481	−	0.182481i	−0.609955	−	0.792436i	$-0.708812\pi$
$41$	1.16845	−	1.16845i	0.182481	−	0.182481i	0.792436	+	0.609955i	$0.208812\pi$
$42$	2.86803	+	3.57413i	0.442546	+	0.551500i
$43$			1.15824i			0.176630i	0.996093	+	0.0883149i	$0.0281482\pi$
$43$			1.15824i			0.176630i	−0.996093	+	0.0883149i	$0.971852\pi$
$44$	1.71267	+	0.458908i	0.258194	+	0.0691829i
$45$	−2.35965	+	5.15327i	−0.351756	+	0.768204i
$46$	−1.94220	−	7.24839i	−0.286362	−	1.06872i
$47$	2.55755	−	9.54491i	0.373057	−	1.39227i	−0.483106	−	0.875562i	$-0.660491\pi$
$47$	2.55755	−	9.54491i	0.373057	−	1.39227i	0.856163	−	0.516706i	$-0.172842\pi$
$48$	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
$52$	−0.205365	+	3.59970i	−0.0284790	+	0.499188i
$53$	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	$0.442246\pi$
$54$	−5.00484	+	1.39699i	−0.681073	+	0.190106i
$55$	3.34984			0.451692
$56$	−2.25699	−	1.38058i	−0.301603	−	0.184487i
$57$	5.17320	−	2.43417i	0.685207	−	0.322414i
$58$	−0.612191	+	2.28473i	−0.0803846	+	0.299999i
$59$	12.1981	−	3.26848i	1.58806	−	0.425520i	0.646652	−	0.762785i	$-0.276169\pi$
$59$	12.1981	−	3.26848i	1.58806	−	0.425520i	0.941410	+	0.337265i	$0.109502\pi$
$60$	0.273899	−	3.26083i	0.0353602	−	0.420972i
$61$	−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
$63$	0.545879	+	7.91846i	0.0687742	+	0.997632i
$64$			1.00000i			0.125000i
$65$	1.38541	+	6.66950i	0.171839	+	0.827250i
$66$	1.98219	+	2.34572i	0.243991	+	0.288738i
$67$	−10.6271	+	2.84753i	−1.29831	+	0.347881i	−0.840810	−	0.541330i	$-0.817921\pi$
$67$	−10.6271	+	2.84753i	−1.29831	+	0.347881i	−0.457498	+	0.889211i	$0.651254\pi$
$68$	−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	$-0.791401\pi$
$71$	−1.54553	+	1.54553i	−0.183421	+	0.183421i	0.609424	+	0.792845i	$0.291401\pi$
$72$	2.44547	−	1.73773i	0.288201	−	0.204793i
$73$	0.439791	+	1.64132i	0.0514736	+	0.192102i	0.986875	−	0.161485i	$-0.0516284\pi$
$73$	0.439791	+	1.64132i	0.0514736	+	0.192102i	−0.935402	+	0.353587i	$0.884962\pi$
$74$	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
$78$	−3.85052	+	4.91665i	−0.435986	+	0.556701i
$79$	−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	$0.956194\pi$
$80$	0.488980	+	1.82490i	0.0546696	+	0.204030i
$81$	−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	$-0.854948\pi$
$83$	−4.17139	+	4.17139i	−0.457869	+	0.457869i	0.440086	+	0.897956i	$0.354948\pi$
$84$	−1.84525	−	4.19465i	−0.201333	−	0.457673i
$85$	−5.38194	+	5.38194i	−0.583754	+	0.583754i
$86$	0.299774	−	1.11877i	0.0323255	−	0.120640i
$87$	−3.12923	+	2.64427i	−0.335489	+	0.283496i
$88$	−1.53553	−	0.886542i	−0.163689	−	0.0945056i
$89$	−0.853770	+	3.18631i	−0.0904994	+	0.337748i	−0.996299	−	0.0859586i	$-0.972605\pi$
$89$	−0.853770	+	3.18631i	−0.0904994	+	0.337748i	0.905799	+	0.423707i	$0.139271\pi$
$90$	3.61301	−	4.36696i	0.380845	−	0.460318i
$91$	6.16759	+	7.27742i	0.646539	+	0.762881i
$92$			7.50409i			0.782355i
$93$	−11.0305	−	7.66676i	−1.14380	−	0.795006i
$94$	−4.94081	+	8.55773i	−0.509605	+	0.882662i
$95$	−3.11812	+	5.40074i	−0.319912	+	0.554105i
$96$	−0.988539	+	1.42225i	−0.100892	+	0.145158i
$97$	5.14678	+	5.14678i	0.522576	+	0.522576i	0.918349	−	0.395772i	$-0.129523\pi$
$97$	5.14678	+	5.14678i	0.522576	+	0.522576i	−0.395772	+	0.918349i	$0.629523\pi$
$98$	−6.84467	+	1.46646i	−0.691416	+	0.148135i
$99$	0.500330	+	5.29567i	0.0502851	+	0.532234i
$100$	−0.715324	−	1.23898i	−0.0715324	−	0.123898i
$101$	−1.23524	+	2.13950i	−0.122911	+	0.212888i	−0.920914	−	0.389765i	$-0.872556\pi$
$101$	−1.23524	+	2.13950i	−0.122911	+	0.212888i	0.798003	+	0.602653i	$0.205890\pi$
$102$	−6.95334	−	0.584057i	−0.688483	−	0.0578303i
$103$	2.64117	−	1.52488i	0.260242	−	0.150251i	−0.364203	−	0.931320i	$-0.618659\pi$
$103$	2.64117	−	1.52488i	0.260242	−	0.150251i	0.624445	+	0.781069i	$0.285325\pi$
$104$	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
$109$	4.88654	−	1.30934i	0.468045	−	0.125412i	−0.0170853	−	0.999854i	$-0.505439\pi$
$109$	4.88654	−	1.30934i	0.468045	−	0.125412i	0.485131	+	0.874442i	$0.338772\pi$
$110$	−3.23570	−	0.867002i	−0.308511	−	0.0826654i
$111$	5.48163	+	11.6498i	0.520294	+	1.10575i
$112$	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	$-0.170094\pi$
$114$	−5.62694	+	1.01231i	−0.527011	+	0.0948111i
$115$	3.66935	+	13.6942i	0.342168	+	1.27699i
$116$	1.18266	−	2.04843i	0.109807	−	0.190192i
$117$	−10.3367	+	3.18631i	−0.955629	+	0.294574i
$118$	−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
$123$	−2.85206	−	0.239563i	−0.257162	−	0.0216007i
$124$	7.49138	+	2.00731i	0.672746	+	0.180262i
$125$	−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	$-0.675333\pi$
$127$		−	19.2052i		−	1.70419i	0.523390	−	0.852093i	$-0.324667\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	1.53231	−	1.29483i	0.134912	−	0.114004i
$130$	0.387990	−	6.80081i	0.0340290	−	0.596471i
$131$	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	$0.273294\pi$
$132$	−1.30753	−	2.77882i	−0.113806	−	0.241865i
$133$	−0.221548	+	8.73047i	−0.0192106	+	0.757027i
$134$	11.0020			0.950428
$135$	9.45551	−	2.63929i	0.813801	−	0.227154i
$136$	3.89138	−	1.04269i	0.333683	−	0.0894100i
$137$	−6.46244	+	1.73161i	−0.552124	+	0.147941i	−0.524085	−	0.851666i	$-0.675593\pi$
$137$	−6.46244	+	1.73161i	−0.552124	+	0.147941i	−0.0280384	+	0.999607i	$0.508926\pi$
$138$	−7.41808	+	10.6727i	−0.631469	+	0.908518i
$139$	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
$141$	−15.4867	+	7.28703i	−1.30422	+	0.613679i
$142$	1.89288	−	1.09285i	0.158847	−	0.0917103i
$143$	4.25568	+	4.77063i	0.355877	+	0.398940i
$144$	−2.81190	+	1.04558i	−0.234325	+	0.0871317i
$145$	1.15660	−	4.31647i	0.0960500	−	0.358464i
$146$		−	1.69922i		−	0.140629i
$147$	−11.1845	−	4.68056i	−0.922480	−	0.386046i
$148$	−5.25620	−	5.25620i	−0.432057	−	0.432057i
$149$	−1.67431	−	0.448629i	−0.137165	−	0.0367531i	0.189584	−	0.981865i	$-0.439286\pi$
$149$	−1.67431	−	0.448629i	−0.137165	−	0.0367531i	−0.326748	+	0.945111i	$0.605953\pi$
$150$	0.207409	−	2.46926i	0.0169349	−	0.201614i
$151$	−1.36199	−	5.08300i	−0.110837	−	0.413648i	0.888105	−	0.459641i	$-0.152022\pi$
$151$	−1.36199	−	5.08300i	−0.110837	−	0.413648i	−0.998942	+	0.0459921i	$0.985355\pi$
$152$	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
$156$	4.99184	−	3.75253i	0.399667	−	0.300443i
$157$	−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	$0.905327\pi$
$158$	1.73207	+	6.46419i	0.137796	+	0.514263i
$159$	−2.89380	−	16.0853i	−0.229493	−	1.27565i
$160$		−	1.88927i		−	0.149360i
$161$	13.6782	+	14.3905i	1.07799	+	1.13413i
$162$	7.44324	+	5.05947i	0.584796	+	0.397509i
$163$	−16.4100	−	4.39704i	−1.28533	−	0.344403i	−0.449444	−	0.893308i	$-0.648378\pi$
$163$	−16.4100	−	4.39704i	−1.28533	−	0.344403i	−0.835884	+	0.548906i	$0.815045\pi$
$164$	1.59613	−	0.427682i	0.124637	−	0.0333964i
$165$	−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	$-0.114573\pi$
$167$	7.54305	+	7.54305i	0.583698	+	0.583698i	−0.352219	+	0.935918i	$0.614573\pi$
$168$	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
$171$	−9.00361	−	4.12270i	−0.688523	−	0.315271i
$172$	−0.579120	+	1.00306i	−0.0441575	+	0.0764830i
$173$	−7.40149	−	12.8198i	−0.562725	−	0.974668i	−0.997257	−	0.0740116i	$-0.976420\pi$
$173$	−7.40149	−	12.8198i	−0.562725	−	0.974668i	0.434533	−	0.900656i	$-0.356914\pi$
$174$	3.70699	−	1.74427i	0.281026	−	0.132233i
$175$	−3.63013	−	1.07210i	−0.274412	−	0.0810432i
$176$	1.25376	+	1.25376i	0.0945056	+	0.0945056i
$177$	−17.9608	−	12.4837i	−1.35001	−	0.938333i
$178$	1.64936	−	2.85677i	0.123624	−	0.214124i
$179$	9.29037	−	16.0914i	0.694395	−	1.20273i	−0.275989	−	0.961161i	$-0.589005\pi$
$179$	9.29037	−	16.0914i	0.694395	−	1.20273i	0.970384	−	0.241567i	$-0.0776612\pi$
$180$	−4.62016	+	3.28304i	−0.344366	+	0.244703i
$181$		−	19.2547i		−	1.43119i	−0.698515	−	0.715595i	$-0.746156\pi$
$181$		−	19.2547i		−	1.43119i	0.698515	−	0.715595i	$-0.253844\pi$
$182$	−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
$186$	8.67030	+	10.2604i	0.635737	+	0.752330i
$187$	−1.84878	+	6.89973i	−0.135196	+	0.504558i
$188$	6.98736	−	6.98736i	0.509605	−	0.509605i
$189$	9.86555	−	9.57449i	0.717613	−	0.696442i
$190$	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
$193$	5.43309	+	20.2766i	0.391083	+	1.45954i	0.828351	+	0.560209i	$0.189279\pi$
$193$	5.43309	+	20.2766i	0.391083	+	1.45954i	−0.437269	+	0.899331i	$0.644054\pi$
$194$	−3.63932	−	6.30349i	−0.261288	−	0.452565i
$195$	7.27469	−	9.28890i	0.520951	−	0.665192i
$196$	6.99099	+	0.355041i	0.499356	+	0.0253601i
$197$	−7.65448	+	7.65448i	−0.545359	+	0.545359i	−0.925095	−	0.379736i	$-0.876015\pi$
$197$	−7.65448	+	7.65448i	−0.545359	+	0.545359i	0.379736	+	0.925095i	$0.376015\pi$
$198$	0.887338	−	5.24472i	0.0630603	−	0.372726i
$199$	10.0996	+	5.83099i	0.715940	+	0.413348i	0.813257	−	0.581905i	$-0.197693\pi$
$199$	10.0996	+	5.83099i	0.715940	+	0.413348i	−0.0973164	+	0.995253i	$0.531026\pi$
$200$	0.370279	+	1.38190i	0.0261827	+	0.0977150i
$201$	15.6476	+	10.8759i	1.10369	+	0.767127i
$202$	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
$207$	−21.1007	+	7.84613i	−1.46660	+	0.545343i
$208$	−1.97770	+	3.01475i	−0.137129	+	0.209035i
$209$			5.85271i			0.404841i
$210$	3.48618	+	7.92483i	0.240569	+	0.546865i
$211$	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
$213$	3.77247	+	0.316875i	0.258486	+	0.0217119i
$214$	15.1240	−	4.05247i	1.03386	−	0.277021i
$215$	−0.566356	+	2.11367i	−0.0386251	+	0.144151i
$216$	−5.03281	−	1.29259i	−0.342439	−	0.0879499i
$217$	18.0250	−	9.80565i	1.22361	−	0.665651i
$218$	−5.05892			−0.342633
$219$	1.67975	−	2.41671i	0.113507	−	0.163306i
$220$	2.90104	+	1.67492i	0.195588	+	0.112923i
$221$	−14.5019	−	0.827343i	−0.975505	−	0.0556531i
$222$	−2.27966	−	12.6716i	−0.153001	−	0.850461i
$223$	8.24792	+	8.24792i	0.552321	+	0.552321i	0.927110	−	0.374789i	$-0.122285\pi$
$223$	8.24792	+	8.24792i	0.552321	+	0.552321i	−0.374789	+	0.927110i	$0.622285\pi$
$224$	−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	−0.998668	−	0.0516026i	$-0.983567\pi$
$227$	−2.40458	−	8.97401i	−0.159597	−	0.595626i	0.839070	−	0.544023i	$-0.183100\pi$
$228$	5.69721	+	0.478546i	0.377307	+	0.0316925i
$229$	19.3307	+	5.17964i	1.27741	+	0.342281i	0.832865	−	0.553477i	$-0.186699\pi$
$229$	19.3307	+	5.17964i	1.27741	+	0.342281i	0.444544	+	0.895757i	$0.353366\pi$
$230$		−	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	$-0.891744\pi$
$233$	−11.6047	−	20.0999i	−0.760248	−	1.31679i	0.182475	−	0.983210i	$-0.441589\pi$
$234$	10.8092	−	0.402402i	0.706617	−	0.0263059i
$235$	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	$-0.671889\pi$
$239$	5.31141	−	5.31141i	0.343567	−	0.343567i	0.857706	+	0.514140i	$0.171889\pi$
$240$	1.86762	−	2.68702i	0.120554	−	0.173446i
$241$	5.43462	+	20.2823i	0.350075	+	1.30650i	0.886570	+	0.462594i	$0.153081\pi$
$241$	5.43462	+	20.2823i	0.350075	+	1.30650i	−0.536496	+	0.843903i	$0.680252\pi$
$242$	7.58848	−	2.03333i	0.487806	−	0.130707i
$243$	5.58465	+	14.5538i	0.358255	+	0.933624i
$244$		−	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
$249$	10.1819	+	0.855247i	0.645253	+	0.0541991i
$250$	6.07462	+	10.5216i	0.384193	+	0.665442i
$251$	−2.44319			−0.154213			−0.0771063	−	0.997023i	$-0.524568\pi$
$251$	−2.44319			−0.154213			−0.0771063	+	0.997023i	$0.524568\pi$
$252$	−3.48649	+	7.13053i	−0.219628	+	0.449181i
$253$	9.40832	+	9.40832i	0.591496	+	0.591496i
$254$	−4.97067	+	18.5508i	−0.311888	+	1.16398i
$255$	13.1368	+	1.10344i	0.822656	+	0.0691003i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.17304	+	3.76382i	0.135551	+	0.234780i	0.925808	−	0.377995i	$-0.123386\pi$
$257$	2.17304	+	3.76382i	0.135551	+	0.234780i	−0.790257	+	0.612775i	$0.790053\pi$
$258$	−1.81522	+	0.854125i	−0.113011	+	0.0531755i
$259$	−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
$262$	−4.14588	+	1.11089i	−0.256134	+	0.0686308i
$263$	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
$266$	2.47361	−	8.37564i	0.151667	−	0.513544i
$267$	5.16982	−	2.43258i	0.316388	−	0.148872i
$268$	−10.6271	−	2.84753i	−0.649154	−	0.173940i
$269$	−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
$271$	−14.2899	−	3.82897i	−0.868051	−	0.232594i	−0.202806	−	0.979219i	$-0.565006\pi$
$271$	−14.2899	−	3.82897i	−0.868051	−	0.232594i	−0.665245	+	0.746625i	$0.731673\pi$
$272$	−4.02865			−0.244273
$273$	2.73279	−	16.2951i	0.165396	−	0.986227i
$274$	6.69041			0.404183
$275$	−2.45022	−	0.656535i	−0.147754	−	0.0395905i
$276$	9.92761	−	8.38907i	0.597572	−	0.504963i
$277$	−17.8363	−	10.2978i	−1.07168	−	0.618735i	−0.143040	−	0.989717i	$-0.545688\pi$
$277$	−17.8363	−	10.2978i	−1.07168	−	0.618735i	−0.928640	+	0.370982i	$0.879021\pi$
$278$	−12.5104	−	3.35215i	−0.750323	−	0.201049i
$279$	2.18849	+	23.1638i	0.131022	+	1.38678i
$280$	−3.44370	−	3.62303i	−0.205801	−	0.216518i
$281$	8.00943	+	8.00943i	0.477803	+	0.477803i	0.904428	−	0.426626i	$-0.140298\pi$
$281$	8.00943	+	8.00943i	0.477803	+	0.477803i	−0.426626	+	0.904428i	$0.640298\pi$
$282$	16.8450	−	3.03048i	1.00311	−	0.180462i
$283$	1.97537	+	1.14048i	0.117423	+	0.0677945i	0.557561	−	0.830136i	$-0.311737\pi$
$283$	1.97537	+	1.14048i	0.117423	+	0.0677945i	−0.440138	+	0.897930i	$0.645070\pi$
$284$	−2.11123	+	0.565703i	−0.125279	+	0.0335683i
$285$	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
$288$	2.98670	−	0.282181i	0.175993	−	0.0166277i
$289$	0.384992	+	0.666826i	0.0226466	+	0.0392251i
$290$	−2.23437	+	3.87004i	−0.131207	+	0.227257i
$291$	1.05523	−	12.5627i	0.0618586	−	0.736441i
$292$	−0.439791	+	1.64132i	−0.0257368	+	0.0960511i
$293$	−19.4879	−	19.4879i	−1.13850	−	1.13850i	−0.988720	−	0.149775i	$-0.952145\pi$
$293$	−19.4879	−	19.4879i	−1.13850	−	1.13850i	−0.149775	−	0.988720i	$-0.547855\pi$
$294$	9.59195	+	7.41582i	0.559414	+	0.432500i
$295$	23.8586			1.38910
$296$	3.71670	+	6.43751i	0.216029	+	0.374173i
$297$	6.44662	−	6.58212i	0.374071	−	0.381933i
$298$	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
$303$	4.21139	−	0.757644i	0.241938	−	0.0435255i
$304$	−3.18839	+	0.854328i	−0.182867	+	0.0489990i
$305$	−5.83314	−	21.7696i	−0.334004	−	1.24652i
$306$	7.00069	+	9.85193i	0.400203	+	0.563197i
$307$	4.22431	−	4.22431i	0.241094	−	0.241094i	−0.576209	−	0.817303i	$-0.695468\pi$
$307$	4.22431	−	4.22431i	0.241094	−	0.241094i	0.817303	+	0.576209i	$0.195468\pi$
$308$	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	$-0.808073\pi$
$311$	1.39800	−	2.42141i	0.0792733	−	0.137305i	0.902937	+	0.429774i	$0.141407\pi$
$312$	−5.79298	+	2.33269i	−0.327963	+	0.132062i
$313$	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
$317$	6.73660	+	1.80507i	0.378365	+	0.101383i	0.442989	−	0.896527i	$-0.353918\pi$
$317$	6.73660	+	1.80507i	0.378365	+	0.101383i	−0.0646238	+	0.997910i	$0.520585\pi$
$318$	−1.36798	+	16.2862i	−0.0767127	+	0.913283i
$319$	−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
$324$	−5.88013	−	6.81352i	−0.326674	−	0.378529i
$325$	0.293805	−	5.14990i	0.0162974	−	0.285665i
$326$	14.7128	+	8.49443i	0.814865	+	0.470463i
$327$	−7.19504	−	5.00094i	−0.397886	−	0.276552i
$328$	−1.65244			−0.0912405
$329$	0.663235	−	26.1359i	0.0365653	−	1.44092i
$330$	2.47028	+	5.24995i	0.135985	+	0.289000i
$331$	3.70810	−	13.8388i	0.203816	−	0.760650i	−0.785992	−	0.618237i	$-0.787847\pi$
$331$	3.70810	−	13.8388i	0.203816	−	0.760650i	0.989807	−	0.142413i	$-0.0454861\pi$
$332$	−5.69822	+	1.52683i	−0.312731	+	0.0837959i
$333$	9.28412	−	20.2757i	0.508766	−	1.11110i
$334$	−5.33374	−	9.23831i	−0.291849	−	0.505498i
$335$	−20.7858			−1.13565
$336$	0.499291	−	4.55529i	0.0272385	−	0.248512i
$337$			1.28563i			0.0700326i	0.999387	+	0.0350163i	$0.0111483\pi$
$337$			1.28563i			0.0700326i	−0.999387	+	0.0350163i	$0.988852\pi$
$338$	10.1782	−	8.08728i	0.553621	−	0.439890i
$339$	−14.3247	+	12.1047i	−0.778012	+	0.657439i
$340$	−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
$345$	14.0148	−	20.1636i	0.754531	−	1.08557i
$346$	3.83129	+	14.2986i	0.205972	+	0.768696i
$347$	−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	−0.999238	−	0.0390397i	$-0.987570\pi$
$349$	−17.9380	+	17.9380i	−0.960198	+	0.960198i	0.0390397	+	0.999238i	$0.487570\pi$
$350$	3.22896	+	1.97512i	0.172595	+	0.105574i
$351$	15.7711	+	10.1130i	0.841800	+	0.539790i
$352$	−0.886542	−	1.53553i	−0.0472528	−	0.0818443i
$353$	5.94830	+	22.1994i	0.316596	+	1.18155i	0.922494	+	0.386011i	$0.126147\pi$
$353$	5.94830	+	22.1994i	0.316596	+	1.18155i	−0.605898	+	0.795542i	$0.707186\pi$
$354$	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
$357$	16.8988	−	7.43386i	0.894377	−	0.393442i
$358$	−13.1386	+	13.1386i	−0.694395	+	0.694395i
$359$	−5.49845	+	20.5205i	−0.290197	+	1.08303i	0.654761	+	0.755836i	$0.272769\pi$
$359$	−5.49845	+	20.5205i	−0.290197	+	1.08303i	−0.944957	+	0.327193i	$0.893897\pi$
$360$	5.31244	−	1.97539i	0.279990	−	0.104112i
$361$	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
$366$	11.7925	−	16.9663i	0.616403	−	0.886842i
$367$	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
$369$	2.87148	+	4.04098i	0.149483	+	0.210365i
$370$	9.93040	+	9.93040i	0.516257	+	0.516257i
$371$	23.9428	+	7.07112i	1.24305	+	0.367114i
$372$	−5.71927	−	12.1548i	−0.296531	−	0.630199i
$373$	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
$375$	−1.76135	+	20.9693i	−0.0909556	+	1.08285i
$376$	−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	0.0440116	−	0.999031i	$-0.485986\pi$
$379$	−18.5922	−	18.5922i	−0.955019	−	0.955019i	−0.999031	+	0.0440116i	$0.985986\pi$
$380$	−5.40074	+	3.11812i	−0.277052	+	0.159956i
$381$	−25.4077	+	21.4701i	−1.30168	+	1.09995i
$382$	14.7245	−	3.94542i	0.753371	−	0.201865i
$383$	20.5305	+	5.50114i	1.04906	+	0.281095i	0.741864	−	0.670551i	$-0.233942\pi$
$383$	20.5305	+	5.50114i	1.04906	+	0.281095i	0.307197	+	0.951646i	$0.400609\pi$
$384$	−1.56722	+	0.737434i	−0.0799771	+	0.0376320i
$385$	8.61628	−	2.07596i	0.439126	−	0.105801i
$386$		−	20.9919i		−	1.06846i
$387$	−3.42603	−	0.579640i	−0.174155	−	0.0294647i
$388$	1.88385	+	7.03063i	0.0956381	+	0.356926i
$389$	−6.58614	+	11.4075i	−0.333931	+	0.578385i	−0.983279	−	0.182106i	$-0.941708\pi$
$389$	−6.58614	+	11.4075i	−0.333931	+	0.578385i	0.649348	+	0.760491i	$0.275042\pi$
$390$	−9.43095	+	7.08956i	−0.477555	+	0.358994i
$391$	−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
$396$	−2.21453	+	4.83635i	−0.111285	+	0.243036i
$397$	−22.5853	−	6.05173i	−1.13353	−	0.303727i	−0.357181	−	0.934035i	$-0.616262\pi$
$397$	−22.5853	−	6.05173i	−1.13353	−	0.303727i	−0.776345	+	0.630308i	$0.782929\pi$
$398$	−8.24627	−	8.24627i	−0.413348	−	0.413348i
$399$	11.7977	−	9.46698i	0.590626	−	0.473942i
$400$		−	1.43065i		−	0.0715324i
$401$	−2.69059	+	10.0414i	−0.134362	+	0.501444i	0.865638	+	0.500670i	$0.166913\pi$
$401$	−2.69059	+	10.0414i	−0.134362	+	0.501444i	−1.00000		0.000774026i	$0.999754\pi$
$402$	−12.2995	−	14.5552i	−0.613443	−	0.725948i
$403$	18.6148	+	20.8672i	0.927267	+	1.03947i
$404$	−2.13950	+	1.23524i	−0.106444	+	0.0614555i
$405$	−14.0623	−	9.55872i	−0.698762	−	0.474977i
$406$	−0.158756	+	6.25604i	−0.00787892	+	0.310482i
$407$	−13.1800			−0.653310
$408$	−5.72974	−	3.98248i	−0.283664	−	0.197162i
$409$	−2.65150	+	0.710467i	−0.131108	+	0.0351304i	−0.323776	−	0.946134i	$-0.604953\pi$
$409$	−2.65150	+	0.710467i	−0.131108	+	0.0351304i	0.192668	+	0.981264i	$0.438286\pi$
$410$	−3.01553	+	0.808008i	−0.148926	+	0.0399047i
$411$	9.51543	+	6.61374i	0.469362	+	0.326232i
$412$	3.04976			0.150251
$413$	29.3499	−	15.9664i	1.44421	−	0.785657i
$414$	22.4125	−	2.11751i	1.10151	−	0.104070i
$415$	−9.65208	+	5.57263i	−0.473802	+	0.273550i
$416$	2.69059	−	2.40016i	0.131917	−	0.117677i
$417$	−14.4792	−	17.1346i	−0.709047	−	0.839085i
$418$	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	$-0.352748\pi$
$420$	−1.31629	−	8.55709i	−0.0642285	−	0.417543i
$421$	−8.20942	−	8.20942i	−0.400103	−	0.400103i	0.478167	−	0.878269i	$-0.341302\pi$
$421$	−8.20942	−	8.20942i	−0.400103	−	0.400103i	−0.878269	+	0.478167i	$0.841302\pi$
$422$	−9.13638	−	2.44808i	−0.444752	−	0.119171i
$423$	26.9536	+	12.3419i	1.31053	+	0.600083i
$424$	−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
$429$	1.55379	−	10.9633i	0.0750179	−	0.529315i
$430$	1.09412	−	1.89506i	0.0527629	−	0.0913881i
$431$	−3.40340	−	12.7016i	−0.163936	−	0.611817i	−0.998174	−	0.0604118i	$-0.980759\pi$
$431$	−3.40340	−	12.7016i	−0.163936	−	0.611817i	0.834238	−	0.551405i	$-0.185908\pi$
$432$	4.52678	+	2.55114i	0.217795	+	0.122742i
$433$		−	20.3113i		−	0.976097i	−0.872816	−	0.488049i	$-0.837709\pi$
$433$		−	20.3113i		−	0.976097i	0.872816	−	0.488049i	$-0.162291\pi$
$434$	−19.9487	+	4.80632i	−0.957567	+	0.230711i
$435$	−7.00352	+	3.29540i	−0.335793	+	0.158002i
$436$	4.88654	+	1.30934i	0.234023	+	0.0627062i
$437$	−23.9260	+	6.41095i	−1.14453	+	0.306677i
$438$	−2.24800	+	1.89962i	−0.107414	+	0.0907672i
$439$	25.1485	−	14.5195i	1.20027	−	0.692977i	0.239656	−	0.970858i	$-0.422965\pi$
$439$	25.1485	−	14.5195i	1.20027	−	0.692977i	0.960615	+	0.277881i	$0.0896321\pi$
$440$	−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	$0.536054\pi$
$444$	−1.07766	+	12.8298i	−0.0511436	+	0.608877i
$445$	−3.11608	+	5.39722i	−0.147717	+	0.255853i
$446$	−5.83216	−	10.1016i	−0.276161	−	0.478324i
$447$	1.27825	+	2.71658i	0.0604589	+	0.128490i
$448$	0.619719	+	2.57215i	0.0292790	+	0.121523i
$449$	−23.3615	−	23.3615i	−1.10250	−	1.10250i	−0.994109	−	0.108386i	$-0.965432\pi$
$449$	−23.3615	−	23.3615i	−1.10250	−	1.10250i	−0.108386	−	0.994109i	$-0.534568\pi$
$450$	−3.49860	+	2.48607i	−0.164926	+	0.117195i
$451$	1.46495	−	2.53737i	0.0689820	−	0.119480i
$452$	5.41389	−	9.37713i	0.254648	−	0.441063i
$453$	−5.20200	+	7.48431i	−0.244411	+	0.351643i
$454$			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	0.809188	+	0.587550i	$0.199907\pi$
$457$	−3.96263	+	14.7887i	−0.185364	+	0.691788i	−0.994552	+	0.104239i	$0.966759\pi$
$458$	−17.3314	−	10.0063i	−0.809845	−	0.467564i
$459$	0.217696	+	20.9323i	0.0101612	+	0.977038i
$460$	−3.66935	+	13.6942i	−0.171084	+	0.638495i
$461$	−20.4542	+	20.4542i	−0.952648	+	0.952648i	−0.998929	−	0.0462800i	$-0.985263\pi$
$461$	−20.4542	+	20.4542i	−0.952648	+	0.952648i	0.0462800	+	0.998929i	$0.485263\pi$
$462$	6.55217	+	4.80514i	0.304835	+	0.223555i
$463$	11.4042	−	11.4042i	0.530000	−	0.530000i	−0.390572	−	0.920572i	$-0.627723\pi$
$463$	11.4042	−	11.4042i	0.530000	−	0.530000i	0.920572	+	0.390572i	$0.127723\pi$
$464$	2.04843	−	1.18266i	0.0950960	−	0.0549037i
$465$	−16.3806	−	19.3847i	−0.759630	−	0.898945i
$466$	6.00702	+	22.4185i	0.278270	+	1.03852i
$467$	7.70434	+	13.3443i	0.356514	+	0.617501i	0.987376	−	0.158394i	$-0.0506317\pi$
$467$	7.70434	+	13.3443i	0.356514	+	0.617501i	−0.630861	+	0.775895i	$0.717298\pi$
$468$	−10.5450	−	2.40893i	−0.487443	−	0.111353i
$469$	−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
$473$	0.531525	+	1.98368i	0.0244395	+	0.0912096i
$474$	6.61552	−	9.51800i	0.303861	−	0.437176i
$475$	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	$-0.502385\pi$
$479$	10.6367	−	2.85010i	0.486004	−	0.130224i	0.493497	+	0.869747i	$0.335718\pi$
$480$	−2.49943	+	2.11208i	−0.114083	+	0.0964029i
$481$	−5.45093	−	26.2413i	−0.248541	−	1.19650i
$482$		−	20.9978i		−	0.956422i
$483$	3.74672	−	34.1833i	0.170482	−	1.55540i
$484$	−7.85618			−0.357099
$485$	6.87568	+	11.9090i	0.312208	+	0.540761i
$486$	−1.62757	−	15.5033i	−0.0738280	−	0.703242i
$487$	−28.1534	+	7.54368i	−1.27575	+	0.341837i	−0.832232	−	0.554427i	$-0.812937\pi$
$487$	−28.1534	+	7.54368i	−1.27575	+	0.341837i	−0.443521	+	0.896264i	$0.646271\pi$
$488$	−3.08750	+	11.5227i	−0.139765	+	0.521609i
$489$	12.5282	+	26.6253i	0.566543	+	1.20404i
$490$	−13.2079	−	0.670770i	−0.596672	−	0.0303023i
$491$	−17.6204			−0.795198			−0.397599	−	0.917559i	$-0.630156\pi$
$491$	−17.6204			−0.795198			−0.397599	+	0.917559i	$0.630156\pi$
$492$	−2.35018	−	1.63350i	−0.105954	−	0.0736438i
$493$	8.25241	+	4.76453i	0.371670	+	0.214584i
$494$	11.8821	+	0.677883i	0.534602	+	0.0304994i
$495$	−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
$499$	−1.57562	+	5.88028i	−0.0705343	+	0.263238i	−0.992184	−	0.124786i	$-0.960175\pi$
$499$	−1.57562	+	5.88028i	−0.0705343	+	0.263238i	0.921649	+	0.388024i	$0.126842\pi$
$500$	−3.14446	−	11.7353i	−0.140624	−	0.524817i
$501$	1.54653	−	18.4118i	0.0690937	−	0.822577i
$502$	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	$0.669418\pi$
$504$	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
$507$	22.4705	−	1.44057i	0.997951	−	0.0639781i
$508$	9.60260	−	16.6322i	0.426047	−	0.737934i
$509$	1.77675	+	0.476080i	0.0787532	+	0.0211019i	0.297981	−	0.954572i	$-0.403687\pi$
$509$	1.77675	+	0.476080i	0.0787532	+	0.0211019i	−0.219227	+	0.975674i	$0.570354\pi$
$510$	−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
$513$	4.61127	+	16.5203i	0.203592	+	0.729390i
$514$	−1.12485	−	4.19799i	−0.0496149	−	0.185166i
$515$	5.56550	−	1.49127i	0.245245	−	0.0657133i
$516$	1.97443	−	0.355207i	0.0869196	−	0.0156371i
$517$		−	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	$-0.238861\pi$
$521$	11.5622	+	6.67544i	0.506549	+	0.292456i	−0.224865	+	0.974390i	$0.572194\pi$
$522$	−6.45177	−	2.95423i	−0.282386	−	0.129303i
$523$	−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
$525$	2.63990	+	6.00106i	0.115215	+	0.261908i
$526$	−8.04665	−	8.04665i	−0.350851	−	0.350851i
$527$	−8.08674	+	30.1801i	−0.352264	+	1.31467i
$528$	0.257054	−	3.06029i	0.0111869	−	0.133182i
$529$	−16.6557	+	28.8484i	−0.724159	+	1.25428i
$530$	−8.91353	−	15.4387i	−0.387179	−	0.670614i
$531$	3.56350	+	37.7174i	0.154643	+	1.63679i
$532$	−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
$535$	−28.5734	+	7.65622i	−1.23534	+	0.331007i
$536$	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
$539$	9.21015	−	8.31988i	0.396709	−	0.358363i
$540$	9.50836	+	2.44206i	0.409175	+	0.105090i
$541$	28.0736	+	7.52229i	1.20698	+	0.323409i	0.805575	−	0.592493i	$-0.201856\pi$
$541$	28.0736	+	7.52229i	1.20698	+	0.323409i	0.401402	+	0.915902i	$0.368523\pi$
$542$	12.8120	+	7.39701i	0.550322	+	0.317729i
$543$	−25.4732	+	21.5255i	−1.09316	+	0.923746i
$544$	3.89138	+	1.04269i	0.166841	+	0.0447050i
$545$	9.55767			0.409406
$546$	−6.85717	+	15.0326i	−0.293460	+	0.643336i
$547$	−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
$549$	33.5437	−	12.4729i	1.43161	−	0.532332i
$550$	2.19681	+	1.26833i	0.0936722	+	0.0540817i
$551$	7.54158	+	2.02076i	0.321282	+	0.0860873i
$552$	−11.7606	+	5.53377i	−0.500564	+	0.235533i
$553$	−12.1984	−	12.8336i	−0.518727	−	0.545739i
$554$	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
$557$	6.35250	−	1.70215i	0.269164	−	0.0721223i	−0.121713	−	0.992565i	$-0.538839\pi$
$557$	6.35250	−	1.70215i	0.269164	−	0.0721223i	0.390877	+	0.920443i	$0.372172\pi$
$558$	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
$561$	11.1949	−	5.26758i	0.472648	−	0.222398i
$562$	−5.66353	−	9.80951i	−0.238901	−	0.413789i
$563$	22.8101	−	39.5083i	0.961332	−	1.66508i	0.242169	−	0.970234i	$-0.422141\pi$
$563$	22.8101	−	39.5083i	0.961332	−	1.66508i	0.719163	−	0.694842i	$-0.244526\pi$
$564$	−17.0554	−	1.43260i	−0.718162	−	0.0603232i
$565$	5.29456	−	19.7596i	0.222744	−	0.831292i
$566$	−1.61288	−	1.61288i	−0.0677945	−	0.0677945i
$567$	−23.6957	−	2.34810i	−0.995126	−	0.0986108i
$568$	2.18571			0.0917103
$569$	−5.55993	−	9.63007i	−0.233084	−	0.403714i	0.725630	−	0.688085i	$-0.241548\pi$
$569$	−5.55993	−	9.63007i	−0.233084	−	0.403714i	−0.958714	+	0.284371i	$0.908215\pi$
$570$	−10.7636	−	0.904105i	−0.450837	−	0.0378688i
$571$	−14.9711	−	8.64357i	−0.626521	−	0.361722i	0.152882	−	0.988244i	$-0.451144\pi$
$571$	−14.9711	−	8.64357i	−0.626521	−	0.361722i	−0.779404	+	0.626522i	$0.784478\pi$
$572$	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
$576$	−2.95796	−	0.500449i	−0.123248	−	0.0208520i
$577$	−2.99074	+	0.801367i	−0.124506	+	0.0333613i	−0.320534	−	0.947237i	$-0.603862\pi$
$577$	−2.99074	+	0.801367i	−0.124506	+	0.0333613i	0.196028	+	0.980598i	$0.437196\pi$
$578$	−0.199287	−	0.743748i	−0.00828923	−	0.0309358i
$579$	20.7513	−	29.8556i	0.862393	−	1.24076i
$580$	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
$585$	−20.4215	+	0.760248i	−0.844324	+	0.0314324i
$586$	13.7800	+	23.8677i	0.569248	+	0.985966i
$587$	−17.5046	+	17.5046i	−0.722490	+	0.722490i	−0.969112	−	0.246621i	$-0.920680\pi$
$587$	−17.5046	+	17.5046i	−0.722490	+	0.722490i	0.246621	+	0.969112i	$0.420680\pi$
$588$	−7.34576	−	9.64572i	−0.302934	−	0.397783i
$589$			25.6004i			1.05484i
$590$	−23.0456	−	6.17505i	−0.948773	−	0.254223i
$591$	18.6838	+	1.56937i	0.768548	+	0.0645554i
$592$	−1.92390	−	7.18011i	−0.0790720	−	0.295101i
$593$	−1.20868	+	4.51085i	−0.0496345	+	0.185238i	−0.986292	−	0.165007i	$-0.947235\pi$
$593$	−1.20868	+	4.51085i	−0.0496345	+	0.185238i	0.936658	+	0.350246i	$0.113902\pi$
$594$	−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
$598$	20.1904	−	18.0110i	0.825646	−	0.736524i
$599$	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	$0.412317\pi$
$600$	1.41425	−	2.03474i	0.0577366	−	0.0830677i
$601$	−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
$603$	−3.10455	−	32.8597i	−0.126427	−	1.33815i
$604$	1.36199	−	5.08300i	0.0554184	−	0.206824i
$605$	−14.3367	+	3.84151i	−0.582870	+	0.156180i
$606$	−4.26398	−	0.358160i	−0.173212	−	0.0145493i
$607$	−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
$609$	−6.41014	+	8.74071i	−0.259752	+	0.354192i
$610$			22.5375i			0.912517i
$611$	34.8840	−	7.24622i	1.41126	−	0.293151i
$612$	−4.21228	−	11.3281i	−0.170271	−	0.457913i
$613$	6.27588	−	1.68162i	0.253480	−	0.0679198i	−0.129841	−	0.991535i	$-0.541447\pi$
$613$	6.27588	−	1.68162i	0.253480	−	0.0679198i	0.383322	+	0.923615i	$0.374780\pi$
$614$	−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	$-0.605661\pi$
$617$	15.3887	−	15.3887i	0.619527	−	0.619527i	0.945410	+	0.325883i	$0.105661\pi$
$618$	4.33752	+	3.01481i	0.174481	+	0.121273i
$619$	−10.0159	−	37.3800i	−0.402575	−	1.50243i	−0.808485	−	0.588516i	$-0.799712\pi$
$619$	−10.0159	−	37.3800i	−0.402575	−	1.50243i	0.405911	−	0.913913i	$-0.366954\pi$
$620$	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
$624$	6.19933	−	0.753868i	0.248172	−	0.0301789i
$625$	−7.90001	−	13.6832i	−0.316000	−	0.547328i
$626$	−2.33677	−	8.72095i	−0.0933961	−	0.348559i
$627$	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
$630$	6.58692	−	13.4715i	0.262429	−	0.536718i
$631$	−0.880984	+	0.880984i	−0.0350714	+	0.0350714i	−0.724425	−	0.689354i	$-0.757895\pi$
$631$	−0.880984	+	0.880984i	−0.0350714	+	0.0350714i	0.689354	+	0.724425i	$0.257895\pi$
$632$	−1.73207	+	6.46419i	−0.0688982	+	0.257132i
$633$	−10.5742	−	12.5134i	−0.420285	−	0.497365i
$634$	−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
$639$	−3.79816	−	5.34508i	−0.150253	−	0.211448i
$640$	0.944637	−	1.63616i	0.0373400	−	0.0646748i
$641$	20.8196	−	36.0606i	0.822326	−	1.42431i	−0.0816205	−	0.996663i	$-0.526010\pi$
$641$	20.8196	−	36.0606i	0.822326	−	1.42431i	0.903946	−	0.427646i	$-0.140657\pi$
$642$	−22.2689	−	15.4781i	−0.878884	−	0.610872i
$643$	6.49542	+	6.49542i	0.256154	+	0.256154i	0.823488	−	0.567334i	$-0.192025\pi$
$643$	6.49542	+	6.49542i	0.256154	+	0.256154i	−0.567334	+	0.823488i	$0.692025\pi$
$644$	4.65043	+	19.3016i	0.183253	+	0.760591i
$645$	3.42945	−	1.61367i	0.135034	−	0.0635384i
$646$	6.64902	+	11.5164i	0.261602	+	0.453108i
$647$	−12.5131	+	21.6734i	−0.491941	+	0.852068i	−0.999957	−	0.00928034i	$-0.997046\pi$
$647$	−12.5131	+	21.6734i	−0.491941	+	0.852068i	0.508015	+	0.861348i	$0.330379\pi$
$648$	3.91630	+	8.10325i	0.153847	+	0.318326i
$649$	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
$655$	7.83271	−	2.09877i	0.306049	−	0.0820056i
$656$	1.59613	+	0.427682i	0.0623185	+	0.0166982i
$657$	−5.07506	+	0.479488i	−0.197997	+	0.0187066i
$658$	−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	$0.943805\pi$
$660$	−1.02732	−	5.71042i	−0.0399885	−	0.222278i
$661$	−7.64816	−	28.5433i	−0.297479	−	1.11021i	−0.939228	−	0.343293i	$-0.888458\pi$
$661$	−7.64816	−	28.5433i	−0.297479	−	1.11021i	0.641749	−	0.766914i	$-0.278209\pi$
$662$	−7.16350	+	12.4075i	−0.278417	+	0.482233i
$663$	15.1176	+	20.1104i	0.587121	+	0.781023i
$664$	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
$669$	1.69104	−	20.1323i	0.0653796	−	0.778359i
$670$	20.0775	+	5.37975i	0.775662	+	0.207838i
$671$	−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	$-0.856053\pi$
$673$		−	22.6718i		−	0.873933i	0.899478	−	0.436967i	$-0.143947\pi$
$674$	0.332745	−	1.24182i	0.0128169	−	0.0478332i
$675$	−7.43346	+	0.0773078i	−0.286114	+	0.00297558i
$676$	−11.9245	+	5.17740i	−0.458636	+	0.199131i
$677$	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	$0.0469304\pi$
$678$	16.9696	−	7.98476i	0.651712	−	0.306653i
$679$	16.4278	+	10.0487i	0.630443	+	0.385635i
$680$	7.61122			0.291877
$681$	−9.18410	+	13.2135i	−0.351935	+	0.506343i
$682$	−13.2828	+	3.55913i	−0.508626	+	0.136286i
$683$	−32.6006	+	8.73532i	−1.24743	+	0.334248i	−0.821343	−	0.570435i	$-0.806775\pi$
$683$	−32.6006	+	8.73532i	−1.24743	+	0.334248i	−0.426086	+	0.904683i	$0.640108\pi$
$684$	−5.73600	−	8.07216i	−0.219322	−	0.308647i
$685$	−12.6400			−0.482950
$686$	−16.6967	+	8.01372i	−0.637483	+	0.305965i
$687$	−14.7580	−	31.3642i	−0.563052	−	1.19662i
$688$	−1.00306	+	0.579120i	−0.0382415	+	0.0220787i
$689$	−1.93781	+	33.9665i	−0.0738247	+	1.29402i
$690$	−18.7560	+	15.8492i	−0.714027	+	0.603370i
$691$	3.33672	−	12.4528i	0.126935	−	0.473728i	−0.872966	−	0.487781i	$-0.837807\pi$
$691$	3.33672	−	12.4528i	0.126935	−	0.473728i	0.999901	+	0.0140528i	$0.00447329\pi$
$692$		−	14.8030i		−	0.562725i
$693$	4.56875	+	13.3112i	0.173552	+	0.505650i
$694$	15.5133	+	15.5133i	0.588877	+	0.588877i
$695$	23.6355	+	6.33312i	0.896547	+	0.240229i
$696$	4.08248	+	0.342915i	0.154746	+	0.0129982i
$697$	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	$-0.457299\pi$
$701$	7.08221			0.267492			0.133746	+	0.991016i	$0.457299\pi$
$702$	−12.6163	−	13.8502i	−0.476171	−	0.522744i
$703$	12.2683	−	21.2494i	0.462709	−	0.801435i
$704$	0.458908	+	1.71267i	0.0172957	+	0.0645486i
$705$	−31.8249	+	5.72540i	−1.19859	+	0.215631i
$706$		−	22.9825i		−	0.864957i
$707$	−1.85133	+	6.26861i	−0.0696265	+	0.235755i
$708$	−9.31263	−	19.7916i	−0.349990	−	0.743814i
$709$	24.3392	+	6.52166i	0.914076	+	0.244926i	0.685052	−	0.728495i	$-0.259780\pi$
$709$	24.3392	+	6.52166i	0.914076	+	0.244926i	0.229025	+	0.973421i	$0.426446\pi$
$710$	3.98869	−	1.06877i	0.149693	−	0.0401101i
$711$	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
$717$	−12.9646	−	1.08898i	−0.484172	−	0.0406688i
$718$	10.6222	−	18.3982i	0.396416	−	0.686613i
$719$	−8.08257	−	13.9994i	−0.301429	−	0.522090i	0.675031	−	0.737789i	$-0.264130\pi$
$719$	−8.08257	−	13.9994i	−0.301429	−	0.522090i	−0.976460	+	0.215699i	$0.930797\pi$
$720$	−5.64269	+	0.533117i	−0.210291	+	0.0198681i
$721$	5.84848	−	5.55900i	0.217809	−	0.207028i
$722$	−5.73058	−	5.73058i	−0.213270	−	0.213270i
$723$	20.7571	−	29.8640i	0.771965	−	1.11066i
$724$	9.62735	−	16.6751i	0.357798	−	0.619724i
$725$	−1.69197	+	2.93058i	−0.0628383	+	0.108839i
$726$	−11.1734	−	7.76614i	−0.414685	−	0.288228i
$727$		−	13.8986i		−	0.515470i	−0.966216	−	0.257735i	$-0.917024\pi$
$727$		−	13.8986i		−	0.515470i	0.966216	−	0.257735i	$-0.0829762\pi$
$728$	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
$732$	−15.7819	+	13.3361i	−0.583314	+	0.492915i
$733$	−13.4604	+	50.2347i	−0.497170	+	1.85546i	0.0203527	+	0.999793i	$0.493521\pi$
$733$	−13.4604	+	50.2347i	−0.497170	+	1.85546i	−0.517522	+	0.855670i	$0.673146\pi$
$734$	−17.3321	+	17.3321i	−0.639740	+	0.639740i
$735$	−18.1218	−	14.0105i	−0.668433	−	0.516786i
$736$	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
$739$	10.6200	+	39.6342i	0.390662	+	1.45797i	0.829045	+	0.559181i	$0.188884\pi$
$739$	10.6200	+	39.6342i	0.390662	+	1.45797i	−0.438384	+	0.898788i	$0.644449\pi$
$740$	−7.02186	−	12.1622i	−0.258129	−	0.447092i
$741$	16.2292	+	12.7101i	0.596195	+	0.466916i
$742$	−21.2968	−	13.0270i	−0.781831	−	0.478237i
$743$	22.9626	−	22.9626i	0.842414	−	0.842414i	−0.146758	−	0.989172i	$-0.546884\pi$
$743$	22.9626	−	22.9626i	0.842414	−	0.842414i	0.989172	+	0.146758i	$0.0468839\pi$
$744$	2.37849	+	13.2209i	0.0871997	+	0.484703i
$745$	−2.83607	−	1.63741i	−0.103906	−	0.0599899i
$746$	−4.63361	−	17.2929i	−0.169648	−	0.633137i
$747$	−10.2513	−	14.4264i	−0.375074	−	0.527834i
$748$	−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	−0.240452	−	0.970661i	$-0.577296\pi$
$751$	13.1524	−	7.59356i	0.479939	−	0.277093i	0.720391	+	0.693568i	$0.243962\pi$
$752$	9.54491	−	2.55755i	0.348067	−	0.0932642i
$753$	2.73132	+	3.23224i	0.0995349	+	0.117789i
$754$	−8.35005	+	1.73450i	−0.304091	+	0.0631667i
$755$		−	9.94193i		−	0.361824i
$756$	13.3311	−	3.35897i	0.484846	−	0.122165i
$757$	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
$759$	1.92896	−	22.9647i	0.0700167	−	0.833566i
$760$	6.02375	−	1.61406i	0.218504	−	0.0585480i
$761$	3.13377	−	11.6954i	0.113599	−	0.423958i	−0.885579	−	0.464489i	$-0.846238\pi$
$761$	3.13377	−	11.6954i	0.113599	−	0.423958i	0.999178	+	0.0405307i	$0.0129048\pi$
$762$	30.0989	−	14.1626i	1.09037	−	0.513055i
$763$	11.7575	−	6.39611i	0.425649	−	0.231555i
$764$	−15.2439			−0.551506
$765$	−13.2262	−	18.6130i	−0.478195	−	0.672954i
$766$	−18.4072	−	10.6274i	−0.665078	−	0.383983i
$767$	30.3102	+	33.9779i	1.09444	+	1.22687i
$768$	1.70468	−	0.306679i	0.0615125	−	0.0110663i
$769$	8.07445	+	8.07445i	0.291172	+	0.291172i	0.837543	−	0.546371i	$-0.183991\pi$
$769$	8.07445	+	8.07445i	0.291172	+	0.291172i	−0.546371	+	0.837543i	$0.683991\pi$
$770$	−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	$-0.129886\pi$
$773$	−2.09730	−	7.82723i	−0.0754346	−	0.281526i	−0.993332	+	0.115293i	$0.963219\pi$
$774$	3.15927	+	1.44661i	0.113558	+	0.0519974i
$775$	−10.7175	−	2.87175i	−0.384985	−	0.103156i
$776$		−	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
$780$	10.9445	−	4.40708i	0.391877	−	0.157799i
$781$	−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
$786$	6.10448	+	4.24294i	0.217740	+	0.151341i
$787$	−8.66577	−	32.3411i	−0.308901	−	1.15284i	−0.929535	−	0.368735i	$-0.879791\pi$
$787$	−8.66577	−	32.3411i	−0.308901	−	1.15284i	0.620633	−	0.784101i	$-0.286876\pi$
$788$	−10.4562	+	2.80173i	−0.372487	+	0.0998076i
$789$	−3.48991	−	19.3988i	−0.124244	−	0.690615i
$790$			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
$795$	2.58449	−	30.7690i	0.0916626	−	1.09126i
$796$	5.83099	+	10.0996i	0.206674	+	0.357970i
$797$	31.3484			1.11042			0.555208	−	0.831712i	$-0.312639\pi$
$797$	31.3484			1.11042			0.555208	+	0.831712i	$0.312639\pi$
$798$	−13.8460	+	6.09092i	−0.490142	+	0.215616i
$799$	28.1496	+	28.1496i	0.995861	+	0.995861i
$800$	−0.370279	+	1.38190i	−0.0130913	+	0.0488575i
$801$	−8.99773	−	4.12001i	−0.317919	−	0.145573i
$802$	5.19782	−	9.00288i	0.183541	−	0.317903i
$803$	1.50643	+	2.60921i	0.0531608	+	0.0920772i
$804$	8.11324	+	17.2426i	0.286132	+	0.608099i
$805$	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
$808$	2.38630	−	0.639408i	0.0839498	−	0.0224943i
$809$	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	0.518722	−	0.854943i	$-0.326408\pi$
$811$	−9.57492	−	9.57492i	−0.336221	−	0.336221i	−0.854943	+	0.518722i	$0.826408\pi$
$812$	1.77253	−	6.00179i	0.0622036	−	0.210621i
$813$	10.9096	+	23.1855i	0.382616	+	0.813152i
$814$	12.7309	+	3.41124i	0.446219	+	0.119564i
$815$	−27.7965	−	16.0483i	−0.973667	−	0.562147i
$816$	4.50376	+	5.32974i	0.157663	+	0.186578i
$817$	−3.69292	−	0.989516i	−0.129199	−	0.0346188i
$818$	2.74504			0.0959779
$819$	−24.6129	+	14.6015i	−0.860045	+	0.510218i
$820$	3.12190			0.109022
$821$	−40.0306	−	10.7262i	−1.39708	−	0.374346i	−0.519783	−	0.854298i	$-0.673987\pi$
$821$	−40.0306	−	10.7262i	−1.39708	−	0.374346i	−0.877294	+	0.479952i	$0.840654\pi$
$822$	−7.47944	−	8.85115i	−0.260875	−	0.308719i
$823$	37.9165	+	21.8911i	1.32168	+	0.763075i	0.983997	−	0.178183i	$-0.0570221\pi$
$823$	37.9165	+	21.8911i	1.32168	+	0.763075i	0.337687	+	0.941258i	$0.390355\pi$
$824$	−2.94584	−	0.789336i	−0.102623	−	0.0274978i
$825$	1.87062	+	3.97551i	0.0651265	+	0.138409i
$826$	−32.4822	+	7.82609i	−1.13020	+	0.272304i
$827$	2.95104	+	2.95104i	0.102618	+	0.102618i	0.756552	−	0.653934i	$-0.226883\pi$
$827$	2.95104	+	2.95104i	0.102618	+	0.102618i	−0.653934	+	0.756552i	$0.726883\pi$
$828$	−22.1968	−	3.75541i	−0.771393	−	0.130510i
$829$	20.6401	+	11.9166i	0.716860	+	0.413879i	0.813596	−	0.581431i	$-0.197507\pi$
$829$	20.6401	+	11.9166i	0.716860	+	0.413879i	−0.0967360	+	0.995310i	$0.530840\pi$
$830$	10.7655	−	2.88461i	0.373676	−	0.100126i
$831$	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
$834$	9.55103	+	20.2982i	0.330725	+	0.702870i
$835$	10.0769	+	17.4537i	0.348725	+	0.604010i
$836$	−2.92636	+	5.06860i	−0.101210	+	0.175301i
$837$	28.1982	−	28.7909i	0.974672	−	0.995158i
$838$	−9.48209	+	35.3877i	−0.327553	+	1.22245i
$839$	−29.0248	−	29.0248i	−1.00205	−	1.00205i	−0.999998	−	0.00204922i	$-0.999348\pi$
$839$	−29.0248	−	29.0248i	−1.00205	−	1.00205i	−0.00204922	−	0.999998i	$-0.500652\pi$
$840$	−0.943296	+	8.60620i	−0.0325468	+	0.296942i
$841$	23.4052			0.807077
$842$	5.80494	+	10.0544i	0.200051	+	0.346499i
$843$	1.64215	−	19.5502i	0.0565586	−	0.673344i
$844$	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
$849$	−0.699522	−	3.88832i	−0.0240075	−	0.133447i
$850$	−5.56719	+	1.49172i	−0.190953	+	0.0511657i
$851$	−14.4371	−	53.8801i	−0.494899	−	1.84699i
$852$	3.10862	+	2.16066i	0.106500	+	0.0740229i
$853$	−22.1862	+	22.1862i	−0.759640	+	0.759640i	−0.976257	−	0.216616i	$-0.930498\pi$
$853$	−22.1862	+	22.1862i	−0.759640	+	0.759640i	0.216616	+	0.976257i	$0.430498\pi$
$854$	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	$-0.930576\pi$
$857$	−8.80481	+	15.2504i	−0.300767	+	0.520943i	0.675543	+	0.737320i	$0.263909\pi$
$858$	−4.33837	+	10.1876i	−0.148110	+	0.347800i
$859$	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
$863$	39.9496	+	10.7045i	1.35990	+	0.364384i	0.863780	−	0.503869i	$-0.168091\pi$
$863$	39.9496	+	10.7045i	1.35990	+	0.364384i	0.496121	+	0.868254i	$0.334757\pi$
$864$	−3.71225	−	3.63583i	−0.126293	−	0.123693i
$865$	−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
$870$	7.61779	−	1.37047i	0.258267	−	0.0464632i
$871$	−26.4065	−	29.6018i	−0.894750	−	1.00302i
$872$	−4.38115	−	2.52946i	−0.148364	−	0.0856583i
$873$	−17.7997	+	12.6483i	−0.602428	+	0.428080i
$874$	24.7700			0.837858
$875$	−27.4208	−	16.7730i	−0.926991	−	0.567030i
$876$	2.66306	−	1.25306i	0.0899765	−	0.0423371i
$877$	−5.37547	+	20.0615i	−0.181517	+	0.677429i	0.813833	+	0.581099i	$0.197377\pi$
$877$	−5.37547	+	20.0615i	−0.181517	+	0.677429i	−0.995349	+	0.0963301i	$0.969290\pi$
$878$	−28.0495	+	7.51583i	−0.946624	+	0.253647i
$879$	−3.99554	+	47.5679i	−0.134766	+	1.60443i
$880$	1.67492	+	2.90104i	0.0564615	+	0.0977942i
$881$	14.9464			0.503556			0.251778	−	0.967785i	$-0.418985\pi$
$881$	14.9464			0.503556			0.251778	+	0.967785i	$0.418985\pi$
$882$	−0.912323	−	20.9802i	−0.0307195	−	0.706439i
$883$		−	25.4257i		−	0.855642i	−0.903863	−	0.427821i	$-0.859281\pi$
$883$		−	25.4257i		−	0.855642i	0.903863	−	0.427821i	$-0.140719\pi$
$884$	−12.1454	−	7.96746i	−0.408493	−	0.267975i
$885$	−26.6723	−	31.5639i	−0.896579	−	1.06101i
$886$	24.1801	−	6.47905i	0.812348	−	0.217668i
$887$	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
$889$	−11.9018	−	49.3986i	−0.399175	−	1.65678i
$890$	4.40681	−	4.40681i	0.147717	−	0.147717i
$891$	−15.9148	−	1.17025i	−0.533165	−	0.0392049i
$892$	3.01895	+	11.2669i	0.101082	+	0.377242i
$893$	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
$897$	46.5203	−	5.65709i	1.55327	−	0.188885i
$898$	16.5190	+	28.6118i	0.551248	+	0.954789i
$899$	−4.74793	−	17.7195i	−0.158352	−	0.590980i
$900$	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
$903$	3.13888	−	4.28011i	0.104455	−	0.142433i
$904$	−7.65639	+	7.65639i	−0.254648	+	0.254648i
$905$	9.41516	−	35.1378i	0.312970	−	1.16802i
$906$	6.96182	−	5.88291i	0.231291	−	0.195447i
$907$	−28.6605	−	16.5472i	−0.951657	−	0.549439i	−0.0580616	−	0.998313i	$-0.518492\pi$
$907$	−28.6605	−	16.5472i	−0.951657	−	0.549439i	−0.893595	+	0.448874i	$0.851825\pi$
$908$	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	$0.966351\pi$
$912$	4.69465	+	3.26304i	0.155456	+	0.108050i
$913$	−5.22992	+	9.05848i	−0.173085	+	0.299792i
$914$	7.65522	−	13.2592i	0.253212	−	0.438576i
$915$	−22.2792	+	32.0539i	−0.736528	+	1.05967i
$916$	14.1511	+	14.1511i	0.467564	+	0.467564i
$917$	8.23097	−	7.82356i	0.271811	−	0.258357i
$918$	5.20741	−	20.2754i	0.171870	−	0.669189i
$919$	−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
$921$	−10.3111	−	0.866097i	−0.339762	−	0.0285389i
$922$	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
$928$	−2.28473	+	0.612191i	−0.0749998	+	0.0200961i
$929$	−50.1073	−	13.4262i	−1.64397	−	0.440500i	−0.686053	−	0.727552i	$-0.740658\pi$
$929$	−50.1073	−	13.4262i	−1.64397	−	0.440500i	−0.957915	+	0.287052i	$0.907325\pi$
$930$	10.8053	+	22.9638i	0.354319	+	0.753013i
$931$	4.84058	+	22.5934i	0.158644	+	0.740467i
$932$		−	23.2094i		−	0.760248i
$933$	−4.76629	+	0.857473i	−0.156041	+	0.0280724i
$934$	−3.98806	−	14.8836i	−0.130493	−	0.487008i
$935$	−6.74766	+	11.6873i	−0.220672	+	0.382215i
$936$	9.56221	+	5.05609i	0.312551	+	0.165264i
$937$	−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	0.732040	+	0.681261i	$0.238568\pi$
$941$	13.4576	+	50.2245i	0.438706	+	1.63727i	−0.293335	+	0.956010i	$0.594765\pi$
$942$	−31.6542	−	2.65885i	−1.03135	−	0.0866299i
$943$	11.9775	+	3.20936i	0.390041	+	0.104511i
$944$	8.92965	+	8.92965i	0.290636	+	0.290636i
$945$	22.6854	−	12.6484i	0.737955	−	0.411453i
$946$		−	2.05365i		−	0.0667701i
$947$	−2.76512	+	10.3196i	−0.0898542	+	0.335340i	−0.996189	−	0.0872197i	$-0.972202\pi$
$947$	−2.76512	+	10.3196i	−0.0898542	+	0.335340i	0.906335	+	0.422560i	$0.138868\pi$
$948$	−8.85354	+	7.48146i	−0.287550	+	0.242986i
$949$	−4.57190	+	4.07840i	−0.148410	+	0.132390i
$950$	−4.08970	+	2.36119i	−0.132687	+	0.0766071i
$951$	−5.14304	−	10.9302i	−0.166774	−	0.354436i
$952$	9.36302	−	5.09352i	0.303457	−	0.165082i
$953$	−11.9865			−0.388282			−0.194141	−	0.980974i	$-0.562192\pi$
$953$	−11.9865			−0.388282			−0.194141	+	0.980974i	$0.562192\pi$
$954$	23.0753	−	16.3971i	0.747090	−	0.530875i
$955$	−27.8186	+	7.45397i	−0.900189	+	0.241205i
$956$	7.25553	−	1.94411i	0.234661	−	0.0628771i
$957$	−4.14585	+	5.96479i	−0.134016	+	0.192814i
$958$	−11.0119			−0.355780
$959$	−15.5493	+	8.45885i	−0.502112	+	0.273151i
$960$	2.96091	−	1.39321i	0.0955631	−	0.0449658i
$961$	25.2447	−	14.5750i	0.814344	−	0.470162i
$962$	−1.52656	+	26.7580i	−0.0492182	+	0.862712i
$963$	−16.3712	−	44.0274i	−0.527555	−	1.41876i
$964$	−5.43462	+	20.2823i	−0.175037	+	0.653248i
$965$			39.6593i			1.27668i
$966$	−12.4663	+	32.0488i	−0.401098	+	1.03115i
$967$	−29.6610	−	29.6610i	−0.953833	−	0.953833i	0.0451476	−	0.998980i	$-0.485624\pi$
$967$	−29.6610	−	29.6610i	−0.953833	−	0.953833i	−0.998980	+	0.0451476i	$0.985624\pi$
$968$	7.58848	+	2.03333i	0.243903	+	0.0653536i
$969$	−1.92790	+	22.9521i	−0.0619329	+	0.737326i
$970$	−3.55911	−	13.2828i	−0.114276	−	0.426485i
$971$	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
$973$	33.3137	−	8.02643i	1.06799	−	0.257315i
$974$	29.1466			0.933916
$975$	−7.14157	+	5.36855i	−0.228713	+	0.171931i
$976$	5.96460	−	10.3310i	0.190922	−	0.330687i
$977$	2.41792	+	9.02380i	0.0773561	+	0.288697i	0.993757	−	0.111564i	$-0.0355861\pi$
$977$	2.41792	+	9.02380i	0.0773561	+	0.288697i	−0.916401	+	0.400261i	$0.868919\pi$
$978$	−5.21012	−	28.9606i	−0.166601	−	0.926059i
$979$			5.84889i			0.186931i
$980$	12.5842	+	4.06637i	0.401989	+	0.129895i
$981$	1.42753	+	15.1095i	0.0455775	+	0.482408i
$982$	17.0200	+	4.56050i	0.543130	+	0.145531i
$983$	4.75954	−	1.27531i	0.151806	−	0.0406762i	−0.182116	−	0.983277i	$-0.558295\pi$
$983$	4.75954	−	1.27531i	0.151806	−	0.0406762i	0.333922	+	0.942601i	$0.391628\pi$
$984$	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
$990$	4.18386	−	9.13718i	0.132972	−	0.290399i
$991$	−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
$993$	−22.4536	+	10.5652i	−0.712544	+	0.335277i
$994$	4.19150	−	3.98404i	0.132946	−	0.126366i
$995$	15.5795	+	15.5795i	0.493902	+	0.493902i
$996$	8.39018	+	5.83163i	0.265853	+	0.184782i
$997$	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
$999$	−37.2030	+	10.3843i	−1.17705	+	0.328546i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.5	✓	144	273.44	even	12	inner
546.2.bv.a.317.36	yes	144	91.44	odd	12	inner
546.2.bv.a.359.5	yes	144	21.2	odd	6	inner
546.2.bv.a.359.36	yes	144	7.2	even	3	inner
546.2.bv.a.473.5	yes	144	13.5	odd	4	inner
546.2.bv.a.473.36	yes	144	39.5	even	4	inner
546.2.bv.a.515.5	yes	144	1.1	even	1	trivial
546.2.bv.a.515.36	yes	144	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.82490 + 0.488980i) q^{5} +(0.737434 + 1.56722i) q^{6} +(2.57215 - 0.619719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.11793 - 1.32296i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.82490 + 0.488980i) q^{5} +(0.737434 + 1.56722i) q^{6} +(2.57215 - 0.619719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.500449 + 2.95796i) q^{9} +(-1.63616 - 0.944637i) q^{10} +(1.71267 - 0.458908i) q^{11} +(-0.306679 - 1.70468i) q^{12} +(1.62200 + 3.22011i) q^{13} +(-2.64490 - 0.0671181i) q^{14} +(-1.39321 - 2.96091i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.01432 + 3.48891i) q^{17} +(1.24897 - 2.72765i) q^{18} +(-0.854328 + 3.18839i) q^{19} +(1.33592 + 1.33592i) q^{20} +(-3.69536 - 2.71005i) q^{21} -1.77308 q^{22} +(3.75204 + 6.49873i) q^{23} +(-0.144976 + 1.72597i) 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} +(0.579400 + 3.22061i) q^{30} +(7.49138 - 2.00731i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-2.52176 - 1.75276i) 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} +(2.44680 - 5.74571i) q^{39} +(-0.944637 - 1.63616i) q^{40} +(1.16845 - 1.16845i) q^{41} +(2.86803 + 3.57413i) q^{42} +1.15824i q^{43} +(1.71267 + 0.458908i) q^{44} +(-2.35965 + 5.15327i) 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} +(6.86757 - 1.23550i) q^{51} +(-0.205365 + 3.59970i) q^{52} +(8.17176 + 4.71797i) q^{53} +(-5.00484 + 1.39699i) q^{54} +3.34984 q^{55} +(-2.25699 - 1.38058i) q^{56} +(5.17320 - 2.43417i) q^{57} +(-0.612191 + 2.28473i) q^{58} +(12.1981 - 3.26848i) q^{59} +(0.273899 - 3.26083i) q^{60} +(-5.96460 - 10.3310i) q^{61} -7.75565 q^{62} +(0.545879 + 7.91846i) q^{63} +1.00000i q^{64} +(1.38541 + 6.66950i) q^{65} +(1.98219 + 2.34572i) 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} +(2.44547 - 1.73773i) q^{72} +(0.439791 + 1.64132i) 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} +(-3.85052 + 4.91665i) q^{78} +(-3.34611 - 5.79563i) q^{79} +(0.488980 + 1.82490i) q^{80} +(-8.49910 - 2.96062i) q^{81} +(-1.43105 + 0.826218i) q^{82} +(-4.17139 + 4.17139i) q^{83} +(-1.84525 - 4.19465i) q^{84} +(-5.38194 + 5.38194i) q^{85} +(0.299774 - 1.11877i) q^{86} +(-3.12923 + 2.64427i) 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} +(-11.0305 - 7.66676i) q^{93} +(-4.94081 + 8.55773i) q^{94} +(-3.11812 + 5.40074i) q^{95} +(-0.988539 + 1.42225i) q^{96} +(5.14678 + 5.14678i) q^{97} +(-6.84467 + 1.46646i) q^{98} +(0.500330 + 5.29567i) 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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