LMFDB - Embedded newform 770.2.bv.a.257.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			257.16
Character	$\chi$	$=$	770.257
Dual form			770.2.bv.a.3.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 - 0.358368i) q^{2} +(0.907325 + 0.589224i) q^{3} +(0.743145 + 0.669131i) q^{4} +(-1.48749 + 1.66954i) q^{5} +(-0.635902 - 0.875244i) q^{6} +(-0.0897121 - 2.64423i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.744156 - 1.67140i) q^{9} +O(q^{10})$	\(q+(-0.933580 - 0.358368i) q^{2} +(0.907325 + 0.589224i) q^{3} +(0.743145 + 0.669131i) q^{4} +(-1.48749 + 1.66954i) q^{5} +(-0.635902 - 0.875244i) q^{6} +(-0.0897121 - 2.64423i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.744156 - 1.67140i) q^{9} +(1.98700 - 1.02558i) q^{10} +(3.16826 - 0.980879i) q^{11} +(0.280006 + 1.04500i) q^{12} +(0.567508 + 3.58311i) q^{13} +(-0.863854 + 2.50075i) q^{14} +(-2.33337 + 0.638349i) q^{15} +(0.104528 + 0.994522i) q^{16} +(3.15829 - 1.21235i) q^{17} +(0.0957526 + 1.82707i) q^{18} +(2.20010 + 2.44346i) q^{19} +(-2.22256 + 0.245382i) q^{20} +(1.47665 - 2.45204i) q^{21} +(-3.30934 - 0.219674i) q^{22} +(-2.16180 - 8.06795i) q^{23} +(0.113085 - 1.07593i) q^{24} +(-0.574726 - 4.96686i) q^{25} +(0.754256 - 3.54849i) q^{26} +(0.817359 - 5.16060i) q^{27} +(1.70267 - 2.02507i) q^{28} +(-2.72355 + 0.884934i) q^{29} +(2.40715 + 0.240256i) q^{30} +(8.70218 + 0.914636i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.45260 + 0.976839i) q^{33} -3.38298 q^{34} +(4.54809 + 3.78350i) q^{35} +(0.565370 - 1.74003i) q^{36} +(5.68859 + 8.75966i) q^{37} +(-1.17831 - 3.06961i) q^{38} +(-1.59634 + 3.58543i) q^{39} +(2.16288 + 0.567411i) q^{40} +(4.04375 + 1.31389i) q^{41} +(-2.25730 + 1.75999i) q^{42} +(0.101811 - 0.101811i) q^{43} +(3.01081 + 1.39105i) q^{44} +(3.89740 + 1.24380i) q^{45} +(-0.873080 + 8.30680i) q^{46} +(-0.391558 - 0.0205207i) q^{47} +(-0.491155 + 0.963945i) q^{48} +(-6.98390 + 0.474439i) q^{49} +(-1.24341 + 4.84293i) q^{50} +(3.57994 + 0.760940i) q^{51} +(-1.97583 + 3.04250i) q^{52} +(3.33368 + 4.11676i) q^{53} +(-2.61247 + 4.52492i) q^{54} +(-3.07515 + 6.74859i) q^{55} +(-2.31530 + 1.28039i) q^{56} +(0.556463 + 3.51337i) q^{57} +(2.85978 + 0.149875i) q^{58} +(7.54793 - 8.38283i) q^{59} +(-2.16117 - 1.08695i) q^{60} +(13.4688 - 1.41562i) q^{61} +(-7.79641 - 3.97247i) q^{62} +(-4.35281 + 2.11766i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-6.82630 - 4.38237i) q^{65} +(-2.87321 - 2.14926i) q^{66} +(3.26997 - 12.2037i) q^{67} +(3.15829 + 1.21235i) q^{68} +(2.79237 - 8.59404i) q^{69} +(-2.89013 - 5.16209i) q^{70} +(-1.56525 + 1.13722i) q^{71} +(-1.15139 + 1.42185i) q^{72} +(-8.60268 + 0.450847i) q^{73} +(-2.17158 - 10.2165i) q^{74} +(2.40513 - 4.84520i) q^{75} +3.28800i q^{76} +(-2.87790 - 8.28961i) q^{77} +(2.77521 - 2.77521i) q^{78} +(6.72159 + 15.0969i) q^{79} +(-1.81588 - 1.30483i) q^{80} +(0.109684 - 0.121816i) q^{81} +(-3.30431 - 2.67578i) q^{82} +(-2.68493 - 0.425252i) q^{83} +(2.73809 - 0.834150i) q^{84} +(-2.67386 + 7.07625i) q^{85} +(-0.131535 + 0.0585632i) q^{86} +(-2.99257 - 0.801856i) q^{87} +(-2.31233 - 2.37763i) q^{88} +(-1.64065 + 2.84169i) q^{89} +(-3.19280 - 2.55789i) q^{90} +(9.42364 - 1.82207i) q^{91} +(3.79198 - 7.44218i) q^{92} +(7.35678 + 5.95741i) q^{93} +(0.358197 + 0.159479i) q^{94} +(-7.35210 + 0.0385253i) q^{95} +(0.803979 - 0.723906i) q^{96} +(-3.14577 + 0.498242i) q^{97} +(6.69006 + 2.05988i) q^{98} +(-3.99712 - 4.56551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.933580	−	0.358368i	−0.660141	−	0.253404i
$2$	−0.933580	−	0.358368i	−0.660141	−	0.253404i
$3$	0.907325	+	0.589224i	0.523844	+	0.340189i	0.779319	−	0.626627i	$-0.215565\pi$
$3$	0.907325	+	0.589224i	0.523844	+	0.340189i	−0.255475	+	0.966816i	$0.582232\pi$
$4$	0.743145	+	0.669131i	0.371572	+	0.334565i
$5$	−1.48749	+	1.66954i	−0.665227	+	0.746641i
$5$	−1.48749	+	1.66954i	−0.665227	+	0.746641i
$6$	−0.635902	−	0.875244i	−0.259606	−	0.357317i
$7$	−0.0897121	−	2.64423i	−0.0339080	−	0.999425i
$7$	−0.0897121	−	2.64423i	−0.0339080	−	0.999425i
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−0.744156	−	1.67140i	−0.248052	−	0.557134i
$10$	1.98700	−	1.02558i	0.628346	−	0.324317i
$11$	3.16826	−	0.980879i	0.955267	−	0.295746i
$11$	3.16826	−	0.980879i	0.955267	−	0.295746i
$12$	0.280006	+	1.04500i	0.0808308	+	0.301665i
$13$	0.567508	+	3.58311i	0.157398	+	0.993775i	0.932298	+	0.361691i	$0.117800\pi$
$13$	0.567508	+	3.58311i	0.157398	+	0.993775i	−0.774900	+	0.632084i	$0.782200\pi$
$14$	−0.863854	+	2.50075i	−0.230875	+	0.668354i
$15$	−2.33337	+	0.638349i	−0.602474	+	0.164821i
$16$	0.104528	+	0.994522i	0.0261321	+	0.248630i
$17$	3.15829	−	1.21235i	0.765997	−	0.294039i	0.0561761	−	0.998421i	$-0.482109\pi$
$17$	3.15829	−	1.21235i	0.765997	−	0.294039i	0.709821	+	0.704382i	$0.248776\pi$
$18$	0.0957526	+	1.82707i	0.0225691	+	0.430644i
$19$	2.20010	+	2.44346i	0.504738	+	0.560569i	0.940631	−	0.339430i	$-0.110234\pi$
$19$	2.20010	+	2.44346i	0.504738	+	0.560569i	−0.435893	+	0.899998i	$0.643567\pi$
$20$	−2.22256	+	0.245382i	−0.496980	+	0.0548691i
$21$	1.47665	−	2.45204i	0.322230	−	0.535078i
$22$	−3.30934	−	0.219674i	−0.705554	−	0.0468346i
$23$	−2.16180	−	8.06795i	−0.450767	−	1.68228i	−0.700244	−	0.713903i	$-0.746926\pi$
$23$	−2.16180	−	8.06795i	−0.450767	−	1.68228i	0.249478	−	0.968381i	$-0.419741\pi$
$24$	0.113085	−	1.07593i	0.0230834	−	0.219624i
$25$	−0.574726	−	4.96686i	−0.114945	−	0.993372i
$26$	0.754256	−	3.54849i	0.147922	−	0.695917i
$27$	0.817359	−	5.16060i	0.157301	−	0.993159i
$28$	1.70267	−	2.02507i	0.321774	−	0.382703i
$29$	−2.72355	+	0.884934i	−0.505750	+	0.164328i	−0.550769	−	0.834658i	$-0.685665\pi$
$29$	−2.72355	+	0.884934i	−0.505750	+	0.164328i	0.0450185	+	0.998986i	$0.485665\pi$
$30$	2.40715	+	0.240256i	0.439484	+	0.0438646i
$31$	8.70218	+	0.914636i	1.56296	+	0.164274i	0.846130	−	0.532976i	$-0.178926\pi$
$31$	8.70218	+	0.914636i	1.56296	+	0.164274i	0.716828	+	0.697250i	$0.245593\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	3.45260	+	0.976839i	0.601020	+	0.170046i
$34$	−3.38298			−0.580177
$35$	4.54809	+	3.78350i	0.768768	+	0.639528i
$36$	0.565370	−	1.74003i	0.0942284	−	0.290005i
$37$	5.68859	+	8.75966i	0.935199	+	1.44008i	0.897612	+	0.440786i	$0.145300\pi$
$37$	5.68859	+	8.75966i	0.935199	+	1.44008i	0.0375867	+	0.999293i	$0.488033\pi$
$38$	−1.17831	−	3.06961i	−0.191148	−	0.497957i
$39$	−1.59634	+	3.58543i	−0.255619	+	0.574129i
$40$	2.16288	+	0.567411i	0.341981	+	0.0897156i
$41$	4.04375	+	1.31389i	0.631528	+	0.205196i	0.607252	−	0.794510i	$-0.292272\pi$
$41$	4.04375	+	1.31389i	0.631528	+	0.205196i	0.0242760	+	0.999705i	$0.492272\pi$
$42$	−2.25730	+	1.75999i	−0.348309	+	0.271573i
$43$	0.101811	−	0.101811i	0.0155261	−	0.0155261i	−0.699301	−	0.714827i	$-0.746505\pi$
$43$	0.101811	−	0.101811i	0.0155261	−	0.0155261i	0.714827	+	0.699301i	$0.246505\pi$
$44$	3.01081	+	1.39105i	0.453897	+	0.209708i
$45$	3.89740	+	1.24380i	0.580990	+	0.185415i
$46$	−0.873080	+	8.30680i	−0.128729	+	1.22477i
$47$	−0.391558	−	0.0205207i	−0.0571145	−	0.00299325i	0.0237573	−	0.999718i	$-0.492437\pi$
$47$	−0.391558	−	0.0205207i	−0.0571145	−	0.00299325i	−0.0808718	+	0.996725i	$0.525770\pi$
$48$	−0.491155	+	0.963945i	−0.0708921	+	0.139134i
$49$	−6.98390	+	0.474439i	−0.997700	+	0.0677769i
$50$	−1.24341	+	4.84293i	−0.175845	+	0.684893i
$51$	3.57994	+	0.760940i	0.501292	+	0.106553i
$52$	−1.97583	+	3.04250i	−0.273998	+	0.421919i
$53$	3.33368	+	4.11676i	0.457917	+	0.565480i	0.952846	−	0.303453i	$-0.0981395\pi$
$53$	3.33368	+	4.11676i	0.457917	+	0.565480i	−0.494930	+	0.868933i	$0.664806\pi$
$54$	−2.61247	+	4.52492i	−0.355512	+	0.615764i
$55$	−3.07515	+	6.74859i	−0.414653	+	0.909979i
$56$	−2.31530	+	1.28039i	−0.309395	+	0.171099i
$57$	0.556463	+	3.51337i	0.0737053	+	0.465357i
$58$	2.85978	+	0.149875i	0.375508	+	0.0196795i
$59$	7.54793	−	8.38283i	0.982657	−	1.09135i	−0.0131540	−	0.999913i	$-0.504187\pi$
$59$	7.54793	−	8.38283i	0.982657	−	1.09135i	0.995811	−	0.0914375i	$-0.0291462\pi$
$60$	−2.16117	−	1.08695i	−0.279006	−	0.140324i
$61$	13.4688	−	1.41562i	1.72450	−	0.181252i	0.810161	−	0.586208i	$-0.199380\pi$
$61$	13.4688	−	1.41562i	1.72450	−	0.181252i	0.914336	+	0.404956i	$0.132713\pi$
$62$	−7.79641	−	3.97247i	−0.990145	−	0.504504i
$63$	−4.35281	+	2.11766i	−0.548402	+	0.266801i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−6.82630	−	4.38237i	−0.846699	−	0.543566i
$66$	−2.87321	−	2.14926i	−0.353668	−	0.264555i
$67$	3.26997	−	12.2037i	0.399490	−	1.49092i	−0.414506	−	0.910047i	$-0.636046\pi$
$67$	3.26997	−	12.2037i	0.399490	−	1.49092i	0.813996	−	0.580870i	$-0.197288\pi$
$68$	3.15829	+	1.21235i	0.382999	+	0.147019i
$69$	2.79237	−	8.59404i	0.336162	−	1.03460i
$70$	−2.89013	−	5.16209i	−0.345436	−	0.616988i
$71$	−1.56525	+	1.13722i	−0.185761	+	0.134963i	−0.676779	−	0.736186i	$-0.736625\pi$
$71$	−1.56525	+	1.13722i	−0.185761	+	0.134963i	0.491018	+	0.871149i	$0.336625\pi$
$72$	−1.15139	+	1.42185i	−0.135693	+	0.167566i
$73$	−8.60268	+	0.450847i	−1.00687	+	0.0527677i	−0.548633	−	0.836064i	$-0.684851\pi$
$73$	−8.60268	+	0.450847i	−1.00687	+	0.0527677i	−0.458235	+	0.888831i	$0.651518\pi$
$74$	−2.17158	−	10.2165i	−0.252441	−	1.18764i
$75$	2.40513	−	4.84520i	0.277720	−	0.559475i
$76$			3.28800i			0.377160i
$77$	−2.87790	−	8.28961i	−0.327967	−	0.944689i
$78$	2.77521	−	2.77521i	0.314231	−	0.314231i
$79$	6.72159	+	15.0969i	0.756238	+	1.69854i	0.714730	+	0.699401i	$0.246550\pi$
$79$	6.72159	+	15.0969i	0.756238	+	1.69854i	0.0415082	+	0.999138i	$0.486784\pi$
$80$	−1.81588	−	1.30483i	−0.203021	−	0.145884i
$81$	0.109684	−	0.121816i	0.0121871	−	0.0135351i
$82$	−3.30431	−	2.67578i	−0.364900	−	0.295490i
$83$	−2.68493	−	0.425252i	−0.294710	−	0.0466774i	0.00732885	−	0.999973i	$-0.497667\pi$
$83$	−2.68493	−	0.425252i	−0.294710	−	0.0466774i	−0.302039	+	0.953296i	$0.597667\pi$
$84$	2.73809	−	0.834150i	0.298751	−	0.0910132i
$85$	−2.67386	+	7.07625i	−0.290021	+	0.767527i
$86$	−0.131535	+	0.0585632i	−0.0141838	+	0.00631503i
$87$	−2.99257	−	0.801856i	−0.320837	−	0.0859680i
$88$	−2.31233	−	2.37763i	−0.246495	−	0.253456i
$89$	−1.64065	+	2.84169i	−0.173909	+	0.301219i	−0.939783	−	0.341771i	$-0.888973\pi$
$89$	−1.64065	+	2.84169i	−0.173909	+	0.301219i	0.765874	+	0.642990i	$0.222306\pi$
$90$	−3.19280	−	2.55789i	−0.336550	−	0.269625i
$91$	9.42364	−	1.82207i	0.987866	−	0.191005i
$92$	3.79198	−	7.44218i	0.395341	−	0.775901i
$93$	7.35678	+	5.95741i	0.762863	+	0.617754i
$94$	0.358197	+	0.159479i	0.0369452	+	0.0164490i
$95$	−7.35210	+	0.0385253i	−0.754309	+	0.00395261i
$96$	0.803979	−	0.723906i	0.0820558	−	0.0738834i
$97$	−3.14577	+	0.498242i	−0.319405	+	0.0505888i	−0.314078	−	0.949397i	$-0.601695\pi$
$97$	−3.14577	+	0.498242i	−0.319405	+	0.0505888i	−0.00532648	+	0.999986i	$0.501695\pi$
$98$	6.69006	+	2.05988i	0.675798	+	0.208079i
$99$	−3.99712	−	4.56551i	−0.401726	−	0.458851i
$100$	2.89637	−	4.07566i	0.289637	−	0.407566i
$101$	4.06551	+	0.427302i	0.404533	+	0.0425182i	0.304610	−	0.952477i	$-0.401474\pi$
$101$	4.06551	+	0.427302i	0.404533	+	0.0425182i	0.0999228	+	0.994995i	$0.468140\pi$
$102$	−3.06947	−	1.99333i	−0.303922	−	0.197369i
$103$	−8.07659	−	12.4369i	−0.795810	−	1.22544i	−0.970568	−	0.240828i	$-0.922581\pi$
$103$	−8.07659	−	12.4369i	−0.795810	−	1.22544i	0.174758	−	0.984611i	$-0.444086\pi$
$104$	2.93493	−	2.13235i	0.287793	−	0.209094i
$105$	1.89727	+	6.11271i	0.185155	+	0.596539i
$106$	−1.63695	−	5.03801i	−0.158995	−	0.489335i
$107$	−0.0978648	+	1.86737i	−0.00946095	+	0.180526i	0.989811	+	0.142385i	$0.0454770\pi$
$107$	−0.0978648	+	1.86737i	−0.00946095	+	0.180526i	−0.999272	+	0.0381411i	$0.987856\pi$
$108$	4.06053	−	3.28816i	0.390725	−	0.316403i
$109$	−7.23753	+	4.17859i	−0.693230	+	0.400237i	−0.804821	−	0.593518i	$-0.797739\pi$
$109$	−7.23753	+	4.17859i	−0.693230	+	0.400237i	0.111591	+	0.993754i	$0.464405\pi$
$110$	5.28938	−	5.19831i	0.504322	−	0.495640i
$111$			11.2997i			1.07252i
$112$	2.62037	−	0.365618i	0.247601	−	0.0345476i
$113$	−6.30452	−	12.3733i	−0.593079	−	1.16398i	−0.971209	−	0.238231i	$-0.923433\pi$
$113$	−6.30452	−	12.3733i	−0.593079	−	1.16398i	0.378129	−	0.925753i	$-0.376567\pi$
$114$	0.739576	−	3.47943i	0.0692676	−	0.325878i
$115$	16.6854	+	8.39181i	1.55592	+	0.782540i
$116$	−2.61613	−	1.16477i	−0.242901	−	0.108147i
$117$	5.56649	−	3.61492i	0.514623	−	0.334200i
$118$	−10.0507	+	5.12111i	−0.925245	+	0.471436i
$119$	−3.48908	−	8.24247i	−0.319843	−	0.755586i
$120$	1.62810	+	1.78925i	0.148625	+	0.163335i
$121$	9.07575	−	6.21536i	0.825068	−	0.565033i
$122$	−13.0815	−	3.50517i	−1.18434	−	0.317343i
$123$	2.89482	+	3.57480i	0.261017	+	0.322329i
$124$	5.85497	+	6.50261i	0.525792	+	0.583951i
$125$	9.14727	+	6.42864i	0.818157	+	0.574995i
$126$	4.82260	−	0.417102i	0.429631	−	0.0371584i
$127$	3.48472	+	0.551925i	0.309219	+	0.0489754i	0.309115	−	0.951025i	$-0.399967\pi$
$127$	3.48472	+	0.551925i	0.309219	+	0.0489754i	0.000103403		1.00000i	$0.499967\pi$
$128$	0.838671	−	0.544639i	0.0741287	−	0.0481397i
$129$	0.152366	−	0.0323863i	0.0134151	−	0.00285146i
$130$	4.80240	+	6.53762i	0.421199	+	0.573388i
$131$	−17.7457	−	10.2455i	−1.55045	−	0.895152i	−0.998105	−	0.0615359i	$-0.980400\pi$
$131$	−17.7457	−	10.2455i	−1.55045	−	0.895152i	−0.552344	−	0.833616i	$-0.686267\pi$
$132$	1.91215	+	3.03617i	0.166431	+	0.264265i
$133$	6.26370	−	6.03679i	0.543132	−	0.523456i
$134$	−7.42618	+	10.2213i	−0.641525	+	0.882983i
$135$	7.40002	+	9.04098i	0.636892	+	0.778124i
$136$	−2.51405	−	2.26366i	−0.215578	−	0.194107i
$137$	−5.63955	−	14.6915i	−0.481819	−	1.25518i	−0.932069	−	0.362280i	$-0.881998\pi$
$137$	−5.63955	−	14.6915i	−0.481819	−	1.25518i	0.450250	−	0.892903i	$-0.351335\pi$
$138$	−5.68673	+	7.02253i	−0.484087	+	0.597797i
$139$	2.68660	+	8.26850i	0.227874	+	0.701325i	0.997987	+	0.0634173i	$0.0201999\pi$
$139$	2.68660	+	8.26850i	0.227874	+	0.701325i	−0.770113	+	0.637908i	$0.779800\pi$
$140$	0.848238	+	5.85495i	0.0716892	+	0.494834i
$141$	−0.343179	−	0.249334i	−0.0289009	−	0.0209977i
$142$	1.86883	−	0.500751i	0.156829	−	0.0420221i
$143$	5.31261	+	10.7956i	0.444263	+	0.902770i
$144$	1.58446	−	0.914788i	0.132038	−	0.0762324i
$145$	2.57383	−	5.86341i	0.213745	−	0.486929i
$146$	8.19286	+	2.66202i	0.678046	+	0.220310i
$147$	−6.61622	−	3.68461i	−0.545697	−	0.303902i
$148$	−1.63391	+	10.3161i	−0.134307	+	0.847979i
$149$	−12.8361	+	1.34912i	−1.05157	+	0.110525i	−0.614511	−	0.788908i	$-0.710647\pi$
$149$	−12.8361	+	1.34912i	−1.05157	+	0.110525i	−0.437060	+	0.899433i	$0.643980\pi$
$150$	−3.98174	+	3.66146i	−0.325108	+	0.298957i
$151$	−3.73583	+	0.794075i	−0.304017	+	0.0646209i	−0.357394	−	0.933954i	$-0.616335\pi$
$151$	−3.73583	+	0.794075i	−0.304017	+	0.0646209i	0.0533770	+	0.998574i	$0.483001\pi$
$152$	1.17831	−	3.06961i	0.0955739	−	0.248979i
$153$	−4.37659	−	4.37659i	−0.353826	−	0.353826i
$154$	−0.283980	+	8.77037i	−0.0228838	+	0.706736i
$155$	−14.4715	+	13.1681i	−1.16238	+	1.05769i
$156$	−3.58543	+	1.59634i	−0.287064	+	0.127809i
$157$	−9.24389	+	14.2343i	−0.737743	+	1.13602i	0.248162	+	0.968718i	$0.420173\pi$
$157$	−9.24389	+	14.2343i	−0.737743	+	1.13602i	−0.985905	+	0.167306i	$0.946493\pi$
$158$	−0.864886	−	16.5030i	−0.0688067	−	1.31291i
$159$	0.599044	+	5.69952i	0.0475073	+	0.452002i
$160$	1.22766	+	1.86892i	0.0970550	+	0.147751i
$161$	−21.1396	+	6.44009i	−1.66603	+	0.507550i
$162$	−0.146054	+	0.0744181i	−0.0114751	+	0.00584684i
$163$	−0.871162	+	2.26945i	−0.0682347	+	0.177757i	−0.963457	−	0.267862i	$-0.913683\pi$
$163$	−0.871162	+	2.26945i	−0.0682347	+	0.177757i	0.895223	+	0.445619i	$0.147016\pi$
$164$	2.12593	+	3.68221i	0.166007	+	0.287532i
$165$	−6.76659	+	4.31121i	−0.526778	+	0.335627i
$166$	2.35420	+	1.35920i	0.182722	+	0.105494i
$167$	−14.3622	+	2.27475i	−1.11138	+	0.176026i	−0.685019	−	0.728526i	$-0.740206\pi$
$167$	−14.3622	+	2.27475i	−1.11138	+	0.176026i	−0.426365	+	0.904551i	$0.640206\pi$
$168$	−2.85516	−	0.202499i	−0.220281	−	0.0156231i
$169$	−0.152852	+	0.0496645i	−0.0117578	+	0.00382035i
$170$	5.03217	−	5.64802i	0.385950	−	0.433184i
$171$	2.44679	−	5.49557i	0.187110	−	0.420257i
$172$	0.143786	−	0.00753549i	0.0109636	−	0.000574576i
$173$	0.466056	−	8.89287i	0.0354335	−	0.676112i	−0.921953	−	0.387302i	$-0.873407\pi$
$173$	0.466056	−	8.89287i	0.0354335	−	0.676112i	0.957386	−	0.288810i	$-0.0932597\pi$
$174$	2.50644	+	1.82104i	0.190013	+	0.138052i
$175$	−13.0820	+	1.96529i	−0.988903	+	0.148562i
$176$	1.30668	+	3.04837i	0.0984946	+	0.229780i
$177$	11.7878	−	3.15853i	0.886024	−	0.237409i
$178$	2.55005	−	2.06499i	0.191135	−	0.154778i
$179$	4.12056	+	19.3857i	0.307985	+	1.44895i	0.811188	+	0.584786i	$0.198822\pi$
$179$	4.12056	+	19.3857i	0.307985	+	1.44895i	−0.503203	+	0.864168i	$0.667845\pi$
$180$	2.06407	+	3.53219i	0.153846	+	0.263274i
$181$	−5.91322	−	8.13885i	−0.439526	−	0.604956i	0.530580	−	0.847635i	$-0.321974\pi$
$181$	−5.91322	−	8.13885i	−0.439526	−	0.604956i	−0.970107	+	0.242678i	$0.921974\pi$
$182$	−9.45070	−	1.67608i	−0.700533	−	0.124240i
$183$	13.0547	+	6.65168i	0.965028	+	0.491706i
$184$	−6.20716	+	5.58895i	−0.457598	+	0.412023i
$185$	−23.0863	−	3.53261i	−1.69734	−	0.259723i
$186$	−4.73321	−	8.19815i	−0.347056	−	0.601118i
$187$	8.81711	−	6.93895i	0.644771	−	0.507426i
$188$	−0.277253	−	0.277253i	−0.0202208	−	0.0202208i
$189$	−13.7191	−	1.69832i	−0.997921	−	0.123534i
$190$	6.87758	+	2.59879i	0.498952	+	0.188536i
$191$	12.8449	+	2.73027i	0.929427	+	0.197556i	0.647662	−	0.761928i	$-0.275747\pi$
$191$	12.8449	+	2.73027i	0.929427	+	0.197556i	0.281765	+	0.959484i	$0.409080\pi$
$192$	−1.01000	+	0.387704i	−0.0728908	+	0.0279802i
$193$	5.90484	−	2.26665i	0.425040	−	0.163157i	−0.136439	−	0.990648i	$-0.543566\pi$
$193$	5.90484	−	2.26665i	0.425040	−	0.163157i	0.561479	+	0.827491i	$0.310233\pi$
$194$	3.11539	+	0.662196i	0.223672	+	0.0475429i
$195$	−3.61148	−	7.99845i	−0.258623	−	0.572781i
$196$	−5.50751	−	4.32057i	−0.393394	−	0.308612i
$197$	−18.1395	−	18.1395i	−1.29238	−	1.29238i	−0.933309	−	0.359074i	$-0.883093\pi$
$197$	−18.1395	−	18.1395i	−1.29238	−	1.29238i	−0.359074	−	0.933309i	$-0.616907\pi$
$198$	2.09550	+	5.69471i	0.148921	+	0.404705i
$199$	0.346442	+	0.600056i	0.0245587	+	0.0425368i	0.878044	−	0.478581i	$-0.158849\pi$
$199$	0.346442	+	0.600056i	0.0245587	+	0.0425368i	−0.853485	+	0.521118i	$0.825515\pi$
$200$	−4.16458	+	2.76699i	−0.294481	+	0.195656i
$201$	10.1576	−	9.14596i	0.716463	−	0.645107i
$202$	−3.64235	−	1.85587i	−0.256275	−	0.130578i
$203$	2.58431	+	7.12230i	0.181383	+	0.499887i
$204$	2.15125	+	2.96094i	0.150617	+	0.207307i
$205$	−8.20865	+	4.79679i	−0.573317	+	0.335023i
$206$	3.08317	+	14.5052i	0.214815	+	1.01062i
$207$	−11.8761	+	9.61705i	−0.825444	+	0.668431i
$208$	−3.50416	+	0.938936i	−0.242970	+	0.0651035i
$209$	9.36724	+	5.58349i	0.647946	+	0.386218i
$210$	0.419342	−	6.38662i	0.0289373	−	0.440719i
$211$	−0.214967	−	0.156183i	−0.0147989	−	0.0107520i	0.580361	−	0.814359i	$-0.302911\pi$
$211$	−0.214967	−	0.156183i	−0.0147989	−	0.0107520i	−0.595160	+	0.803607i	$0.702911\pi$
$212$	−0.277238	+	5.29002i	−0.0190408	+	0.363320i
$213$	−2.09027	+	0.109546i	−0.143223	+	0.00750598i
$214$	0.760571	−	1.70827i	0.0519916	−	0.116775i
$215$	0.0185344	+	0.321422i	0.00126403	+	0.0219208i
$216$	−4.96920	+	1.61459i	−0.338112	+	0.109859i
$217$	1.63782	−	23.0926i	0.111182	−	1.56763i
$218$	8.25429	−	1.30735i	0.559051	−	0.0885450i
$219$	−8.07107	−	4.65984i	−0.545393	−	0.314883i
$220$	−6.80097	+	2.95750i	−0.458521	+	0.199395i
$221$	6.13634	+	10.6285i	0.412775	+	0.714947i
$222$	4.04946	−	10.5492i	0.271782	−	0.708015i
$223$	3.13948	−	1.59965i	0.210235	−	0.107120i	−0.345702	−	0.938344i	$-0.612359\pi$
$223$	3.13948	−	1.59965i	0.210235	−	0.107120i	0.555938	+	0.831224i	$0.312359\pi$
$224$	−2.57735	−	0.597722i	−0.172206	−	0.0399370i
$225$	−7.87393	+	4.65671i	−0.524929	+	0.310448i
$226$	1.45158	+	13.8108i	0.0965574	+	0.918682i
$227$	1.36706	+	26.0851i	0.0907349	+	1.73133i	0.543252	+	0.839570i	$0.317193\pi$
$227$	1.36706	+	26.0851i	0.0907349	+	1.73133i	−0.452517	+	0.891756i	$0.649474\pi$
$228$	−1.93737	+	2.98329i	−0.128305	+	0.197573i
$229$	2.16039	−	0.961869i	0.142763	−	0.0635621i	−0.334112	−	0.942533i	$-0.608436\pi$
$229$	2.16039	−	0.961869i	0.142763	−	0.0635621i	0.476875	+	0.878971i	$0.341770\pi$
$230$	−12.5698	−	13.8140i	−0.828830	−	0.910865i
$231$	2.27325	−	9.21710i	0.149569	−	0.606441i
$232$	2.02495	+	2.02495i	0.132944	+	0.132944i
$233$	−0.0715248	+	0.186329i	−0.00468575	+	0.0122068i	−0.935903	−	0.352257i	$-0.885414\pi$
$233$	−0.0715248	+	0.186329i	−0.00468575	+	0.0122068i	0.931218	+	0.364464i	$0.118748\pi$
$234$	−6.49224	+	1.37997i	−0.424411	+	0.0902114i
$235$	0.616699	−	0.623197i	0.0402290	−	0.0406529i
$236$	11.2184	−	1.17910i	0.730256	−	0.0767530i
$237$	−2.79681	+	17.6584i	−0.181672	+	1.14703i
$238$	0.303494	+	8.94539i	0.0196726	+	0.579843i
$239$	17.2557	+	5.60673i	1.11618	+	0.362669i	0.808309	−	0.588759i	$-0.200383\pi$
$239$	17.2557	+	5.60673i	1.11618	+	0.362669i	0.307872	+	0.951428i	$0.400383\pi$
$240$	−0.878756	−	2.25386i	−0.0567234	−	0.145486i
$241$	10.8999	−	6.29303i	0.702121	−	0.405370i	−0.106016	−	0.994364i	$-0.533809\pi$
$241$	10.8999	−	6.29303i	0.702121	−	0.405370i	0.808137	+	0.588995i	$0.200476\pi$
$242$	−10.7003	+	2.55008i	−0.687843	+	0.163925i
$243$	−14.9694	+	4.01104i	−0.960287	+	0.257308i
$244$	10.9565	+	7.96034i	0.701416	+	0.509609i
$245$	9.59642	−	12.3656i	0.613093	−	0.790011i
$246$	−1.42145	−	4.37478i	−0.0906284	−	0.278926i
$247$	−7.50661	+	9.26989i	−0.477634	+	0.589829i
$248$	−3.13576	−	8.16894i	−0.199121	−	0.518728i
$249$	−2.18554	−	1.96787i	−0.138503	−	0.124709i
$250$	−6.23589	−	9.27974i	−0.394392	−	0.586903i
$251$	−17.9182	+	24.6623i	−1.13099	+	1.55667i	−0.344808	+	0.938673i	$0.612056\pi$
$251$	−17.9182	+	24.6623i	−1.13099	+	1.55667i	−0.786180	+	0.617998i	$0.787944\pi$
$252$	−4.65176	−	1.33887i	−0.293033	−	0.0843407i
$253$	−14.7628	−	23.4409i	−0.928131	−	1.47372i
$254$	−3.05547	−	1.76408i	−0.191717	−	0.110688i
$255$	−6.59556	+	4.84496i	−0.413030	+	0.303403i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−11.0247	+	7.15954i	−0.687704	+	0.446600i	−0.840610	−	0.541641i	$-0.817803\pi$
$257$	−11.0247	+	7.15954i	−0.687704	+	0.446600i	0.152906	+	0.988241i	$0.451137\pi$
$258$	−0.153852	−	0.0243677i	−0.00957840	−	0.00151707i
$259$	22.6522	−	15.8278i	1.40754	−	0.983491i
$260$	−2.14055	−	7.82442i	−0.132752	−	0.485250i
$261$	3.50582	+	3.89361i	0.217005	+	0.241009i
$262$	12.8954	+	15.9245i	0.796680	+	0.983817i
$263$	−17.3730	−	4.65509i	−1.07127	−	0.287045i	−0.320254	−	0.947332i	$-0.603768\pi$
$263$	−17.3730	−	4.65509i	−1.07127	−	0.287045i	−0.751014	+	0.660287i	$0.770435\pi$
$264$	−0.697078	−	3.51976i	−0.0429022	−	0.216627i
$265$	−11.8319	−	0.557932i	−0.726829	−	0.0342735i
$266$	−8.01106	+	3.39112i	−0.491189	+	0.207923i
$267$	−3.16300	+	1.61163i	−0.193572	+	0.0986301i
$268$	10.5959	−	6.88107i	0.647249	−	0.420328i
$269$	4.13980	+	1.84316i	0.252408	+	0.112379i	0.529041	−	0.848596i	$-0.322552\pi$
$269$	4.13980	+	1.84316i	0.252408	+	0.112379i	−0.276633	+	0.960976i	$0.589218\pi$
$270$	−3.66851	−	11.0924i	−0.223259	−	0.675063i
$271$	−0.901846	+	4.24285i	−0.0547832	+	0.257735i	−0.997013	−	0.0772320i	$-0.975392\pi$
$271$	−0.901846	+	4.24285i	−0.0547832	+	0.257735i	0.942230	+	0.334967i	$0.108725\pi$
$272$	1.53584	+	3.01426i	0.0931241	+	0.182766i
$273$	9.62392	+	3.89943i	0.582466	+	0.236004i
$274$			15.7368i			0.950693i
$275$	−6.69277	−	15.1726i	−0.403589	−	0.914940i
$276$	7.82567	−	4.51815i	0.471050	−	0.271961i
$277$	−1.06534	+	0.862699i	−0.0640103	+	0.0518345i	−0.660792	−	0.750569i	$-0.729779\pi$
$277$	−1.06534	+	0.862699i	−0.0640103	+	0.0518345i	0.596781	+	0.802404i	$0.296446\pi$
$278$	0.455010	−	8.68210i	0.0272897	−	0.520718i
$279$	−4.94706	−	15.2255i	−0.296173	−	0.911525i
$280$	1.30633	−	5.77005i	0.0780681	−	0.344827i
$281$	−4.08398	+	2.96719i	−0.243630	+	0.177007i	−0.702899	−	0.711290i	$-0.748111\pi$
$281$	−4.08398	+	2.96719i	−0.243630	+	0.177007i	0.459269	+	0.888297i	$0.348111\pi$
$282$	0.231032	+	0.355758i	0.0137577	+	0.0211851i
$283$	11.3430	+	7.36621i	0.674270	+	0.437876i	0.835831	−	0.548987i	$-0.184986\pi$
$283$	11.3430	+	7.36621i	0.674270	+	0.437876i	−0.161561	+	0.986863i	$0.551653\pi$
$284$	−1.92415	−	0.202237i	−0.114178	−	0.0120005i
$285$	−6.69344	−	4.29707i	−0.396485	−	0.254537i
$286$	−1.09096	−	11.9824i	−0.0645101	−	0.708534i
$287$	3.11146	−	10.8105i	0.183664	−	0.638122i
$288$	−1.80705	+	0.286209i	−0.106482	+	0.0168650i
$289$	−4.12849	+	3.71730i	−0.242852	+	0.218665i
$290$	−4.50413	+	4.55158i	−0.264492	+	0.267278i
$291$	−3.14781	−	1.40150i	−0.184528	−	0.0821572i
$292$	−6.69471	−	5.42127i	−0.391778	−	0.317256i
$293$	−4.60724	+	9.04221i	−0.269158	+	0.528252i	−0.985537	−	0.169459i	$-0.945798\pi$
$293$	−4.60724	+	9.04221i	−0.269158	+	0.528252i	0.716380	+	0.697711i	$0.245798\pi$
$294$	4.85633	+	5.81092i	0.283227	+	0.338900i
$295$	2.76796	+	25.0710i	0.161157	+	1.45969i
$296$	5.22235	−	9.04538i	0.303543	−	0.525752i
$297$	−2.47232	−	17.1519i	−0.143459	−	0.995252i
$298$	12.4670	+	3.34052i	0.722193	+	0.193511i
$299$	27.6815	−	12.3246i	1.60086	−	0.712749i
$300$	5.02943	−	1.99134i	0.290374	−	0.114970i
$301$	−0.278346	−	0.260079i	−0.0160436	−	0.0149907i
$302$	3.77227	+	0.597469i	0.217070	+	0.0343805i
$303$	3.43696	+	2.78320i	0.197448	+	0.159890i
$304$	−2.20010	+	2.44346i	−0.126185	+	0.140142i
$305$	−17.6712	+	24.5923i	−1.01185	+	1.40815i
$306$	2.51747	+	5.65432i	0.143914	+	0.323236i
$307$	18.4739	−	18.4739i	1.05436	−	1.05436i	0.0559289	−	0.998435i	$-0.482188\pi$
$307$	18.4739	−	18.4739i	1.05436	−	1.05436i	0.998435	−	0.0559289i	$-0.0178120\pi$
$308$	3.40814	−	8.08607i	0.194197	−	0.460747i
$309$		−	16.0432i		−	0.912665i
$310$	18.2293	−	7.10740i	1.03536	−	0.403673i
$311$	−2.35941	−	11.1001i	−0.133790	−	0.629431i	−0.993030	−	0.117859i	$-0.962397\pi$
$311$	−2.35941	−	11.1001i	−0.133790	−	0.629431i	0.859241	−	0.511572i	$-0.170936\pi$
$312$	3.91936	−	0.205405i	0.221890	−	0.0116288i
$313$	1.38727	−	1.71314i	0.0784133	−	0.0968323i	−0.736430	−	0.676514i	$-0.763490\pi$
$313$	1.38727	−	1.71314i	0.0784133	−	0.0968323i	0.814843	+	0.579682i	$0.196823\pi$
$314$	13.7310	−	9.97619i	0.774888	−	0.562989i
$315$	2.93925	−	10.4172i	0.165608	−	0.586943i
$316$	−5.10671	+	15.7168i	−0.287275	+	0.884141i
$317$	12.7829	+	4.90691i	0.717961	+	0.275599i	0.689796	−	0.724004i	$-0.257700\pi$
$317$	12.7829	+	4.90691i	0.717961	+	0.275599i	0.0281652	+	0.999603i	$0.491034\pi$
$318$	1.48327	−	5.53564i	0.0831777	−	0.310423i
$319$	−7.76090	+	5.47517i	−0.434527	+	0.306551i
$320$	−0.476359	−	2.18474i	−0.0266293	−	0.122131i
$321$	−1.18909	+	1.63665i	−0.0663688	+	0.0913488i
$322$	22.0434	+	1.56340i	1.22843	+	0.0871251i
$323$	9.91089	+	5.04985i	0.551457	+	0.280981i
$324$	0.163022	−	0.0171343i	0.00905677	−	0.000951905i
$325$	17.4706	−	4.87804i	0.969096	−	0.270585i
$326$	1.62660	−	1.80652i	0.0900890	−	0.100054i
$327$	−9.02892	−	0.473186i	−0.499301	−	0.0261672i
$328$	−0.665136	−	4.19950i	−0.0367260	−	0.231879i
$329$	−0.0191339	+	1.03721i	−0.00105489	+	0.0571832i
$330$	7.86216	−	1.59993i	0.432797	−	0.0880734i
$331$	2.50679	−	4.34189i	0.137786	−	0.238652i	−0.788872	−	0.614557i	$-0.789335\pi$
$331$	2.50679	−	4.34189i	0.137786	−	0.238652i	0.926658	+	0.375905i	$0.122668\pi$
$332$	−1.71075	−	2.11259i	−0.0938893	−	0.115944i
$333$	10.4077	−	16.0265i	0.570339	−	0.878245i
$334$	14.2235	+	3.02330i	0.778275	+	0.165428i
$335$	15.5105	+	23.6122i	0.847428	+	1.29007i
$336$	2.59296	+	1.21225i	0.141457	+	0.0661336i
$337$	−11.0749	+	21.7357i	−0.603289	+	1.18402i	0.364251	+	0.931301i	$0.381325\pi$
$337$	−11.0749	+	21.7357i	−0.603289	+	1.18402i	−0.967539	+	0.252720i	$0.918675\pi$
$338$	0.160498	+	0.00841132i	0.00872991	+	0.000457515i
$339$	1.57040	−	14.9414i	0.0852926	−	0.811505i
$340$	−6.72200	+	3.46952i	−0.364552	+	0.188161i
$341$	28.4679	−	5.63798i	1.54163	−	0.305314i
$342$	−4.25371	+	4.25371i	−0.230014	+	0.230014i
$343$	1.88107	+	18.4245i	0.101568	+	0.994829i
$344$	−0.136936	−	0.0444932i	−0.00738310	−	0.00239891i
$345$	10.1945	+	17.4456i	0.548851	+	0.939237i
$346$	−3.62202	+	8.13519i	−0.194721	+	0.437351i
$347$	4.95034	+	12.8961i	0.265748	+	0.692298i	0.999911	+	0.0133248i	$0.00424154\pi$
$347$	4.95034	+	12.8961i	0.265748	+	0.692298i	−0.734163	+	0.678973i	$0.762425\pi$
$348$	−1.68736	−	2.59831i	−0.0904522	−	0.139284i
$349$	−6.28937	+	19.3567i	−0.336662	+	1.03614i	0.629235	+	0.777215i	$0.283368\pi$
$349$	−6.28937	+	19.3567i	−0.336662	+	1.03614i	−0.965897	+	0.258925i	$0.916632\pi$
$350$	12.9174	+	2.85339i	0.690462	+	0.152520i
$351$	18.9548			1.01174
$352$	−0.127450	−	3.31418i	−0.00679311	−	0.176646i
$353$	2.30649	−	8.60794i	0.122762	−	0.458154i	−0.876988	−	0.480512i	$-0.840451\pi$
$353$	2.30649	−	8.60794i	0.122762	−	0.458154i	0.999750	+	0.0223580i	$0.00711736\pi$
$354$	−12.1368	−	1.27563i	−0.645062	−	0.0677987i
$355$	0.429664	−	4.30485i	0.0228042	−	0.228478i
$356$	−3.12071	+	1.01398i	−0.165397	+	0.0537408i
$357$	1.69094	−	9.53445i	0.0894938	−	0.504617i
$358$	3.10034	−	19.5748i	0.163858	−	1.03456i
$359$	3.52212	−	16.5703i	0.185890	−	0.874545i	−0.782021	−	0.623252i	$-0.785811\pi$
$359$	3.52212	−	16.5703i	0.185890	−	0.874545i	0.967911	−	0.251293i	$-0.0808557\pi$
$360$	−0.661147	−	4.03728i	−0.0348455	−	0.212783i
$361$	0.855988	−	8.14418i	0.0450520	−	0.428641i
$362$	2.60377	+	9.71738i	0.136851	+	0.510734i
$363$	11.8969	−	0.291703i	0.624425	−	0.0153104i
$364$	8.22234	+	4.95159i	0.430968	+	0.259534i
$365$	12.0437	−	15.0331i	0.630397	−	0.786871i
$366$	−9.80382	−	10.8882i	−0.512454	−	0.569138i
$367$	0.256098	+	4.88664i	0.0133682	+	0.255080i	0.997136	+	0.0756329i	$0.0240977\pi$
$367$	0.256098	+	4.88664i	0.0133682	+	0.255080i	−0.983768	+	0.179448i	$0.942569\pi$
$368$	7.79778	−	2.99329i	0.406488	−	0.156036i
$369$	−0.813136	−	7.73647i	−0.0423302	−	0.402745i
$370$	20.2870	+	11.5714i	1.05467	+	0.601568i
$371$	10.5866	−	9.18435i	0.549628	−	0.476828i
$372$	1.48087	+	9.34987i	0.0767797	+	0.484768i
$373$	7.04289	+	26.2844i	0.364667	+	1.36096i	0.867872	+	0.496788i	$0.165487\pi$
$373$	7.04289	+	26.2844i	0.364667	+	1.36096i	−0.503205	+	0.864167i	$0.667846\pi$
$374$	−10.7182	+	3.31830i	−0.554224	+	0.171585i
$375$	4.51164	+	11.2227i	0.232980	+	0.579536i
$376$	0.159479	+	0.358197i	0.00822452	+	0.0184726i
$377$	−4.71645	−	9.25655i	−0.242910	−	0.476737i
$378$	12.1993	+	6.50202i	0.627465	+	0.334428i
$379$	−19.7976	−	27.2491i	−1.01694	−	1.39969i	−0.914330	−	0.404970i	$-0.867282\pi$
$379$	−19.7976	−	27.2491i	−1.01694	−	1.39969i	−0.102606	−	0.994722i	$-0.532718\pi$
$380$	−5.48945	−	4.89088i	−0.281603	−	0.250897i
$381$	2.83656	+	2.55405i	0.145322	+	0.130848i
$382$	−11.0133	−	7.15214i	−0.563491	−	0.365935i
$383$	17.5375	+	6.73203i	0.896126	+	0.343991i	0.762460	−	0.647036i	$-0.223992\pi$
$383$	17.5375	+	6.73203i	0.896126	+	0.343991i	0.133666	+	0.991026i	$0.457325\pi$
$384$	1.08186			0.0552085
$385$	18.1207	+	7.52598i	0.923516	+	0.383559i
$386$	−6.32494			−0.321931
$387$	−0.245931	−	0.0944042i	−0.0125014	−	0.00479883i
$388$	−2.67115	−	1.73467i	−0.135607	−	0.0880644i
$389$	−17.8940	−	16.1118i	−0.907262	−	0.816902i	0.0763726	−	0.997079i	$-0.475666\pi$
$389$	−17.8940	−	16.1118i	−0.907262	−	0.816902i	−0.983634	+	0.180177i	$0.942333\pi$
$390$	0.505217	+	8.76144i	0.0255826	+	0.443653i
$391$	−16.6088	−	22.8600i	−0.839943	−	1.15608i
$392$	3.59335	+	6.00731i	0.181492	+	0.303415i
$393$	−10.0642	−	19.7522i	−0.507673	−	0.996365i
$394$	10.4340	+	23.4352i	0.525659	+	1.18065i
$395$	−35.2033	−	11.2346i	−1.77127	−	0.565276i
$396$	0.0844809	−	6.06743i	0.00424532	−	0.304900i
$397$	2.56491	+	9.57237i	0.128729	+	0.480423i	0.999945	−	0.0104763i	$-0.00333478\pi$
$397$	2.56491	+	9.57237i	0.128729	+	0.480423i	−0.871216	+	0.490900i	$0.836668\pi$
$398$	−0.108391	−	0.684354i	−0.00543315	−	0.0343036i
$399$	9.24023	−	1.78661i	0.462590	−	0.0894422i
$400$	4.87958	−	1.09076i	0.243979	−	0.0545378i
$401$	−0.486936	−	4.63289i	−0.0243164	−	0.231355i	−0.999930	−	0.0118587i	$-0.996225\pi$
$401$	−0.486936	−	4.63289i	−0.0243164	−	0.231355i	0.975613	−	0.219497i	$-0.0704415\pi$
$402$	−12.7606	+	4.89833i	−0.636440	+	0.244306i
$403$	1.66132	+	31.6999i	0.0827564	+	1.57909i
$404$	2.73534	+	3.03790i	0.136088	+	0.151141i
$405$	0.0402230	+	0.364322i	0.00199870	+	0.0181033i
$406$	0.139747	−	7.57537i	0.00693551	−	0.375959i
$407$	26.6151	+	22.1731i	1.31926	+	1.09908i
$408$	−0.947256	−	3.53521i	−0.0468962	−	0.175019i
$409$	1.70163	−	16.1899i	0.0841401	−	0.800540i	−0.868346	−	0.495958i	$-0.834817\pi$
$409$	1.70163	−	16.1899i	0.0841401	−	0.800540i	0.952486	−	0.304581i	$-0.0985165\pi$
$410$	9.38245	−	1.53647i	0.463366	−	0.0758811i
$411$	3.53970	−	16.6530i	0.174600	−	0.821430i
$412$	2.31981	−	14.6467i	0.114289	−	0.721590i
$413$	−22.8433	−	19.2064i	−1.12404	−	0.945086i
$414$	14.5337	−	4.72229i	0.714293	−	0.232088i
$415$	4.70380	−	3.85004i	0.230900	−	0.188991i
$416$	3.60790	+	0.379205i	0.176892	+	0.0185921i
$417$	−2.43438	+	9.08522i	−0.119212	+	0.444905i
$418$	−6.74413	−	8.56956i	−0.329866	−	0.419151i
$419$	−2.49226			−0.121755			−0.0608774	−	0.998145i	$-0.519390\pi$
$419$	−2.49226			−0.121755			−0.0608774	+	0.998145i	$0.519390\pi$
$420$	−2.68025	+	5.81215i	−0.130783	+	0.283604i
$421$	−2.20475	+	6.78552i	−0.107453	+	0.330706i	−0.990298	−	0.138958i	$-0.955625\pi$
$421$	−2.20475	+	6.78552i	−0.107453	+	0.330706i	0.882845	+	0.469664i	$0.155625\pi$
$422$	0.144718	+	0.222846i	0.00704476	+	0.0108480i
$423$	0.257082	+	0.669720i	0.0124997	+	0.0325629i
$424$	2.15460	−	4.83930i	0.104636	−	0.235017i
$425$	−7.83673	−	14.9900i	−0.380137	−	0.727122i
$426$	1.99069	+	0.646814i	0.0964492	+	0.0313382i
$427$	−4.95154	−	35.4875i	−0.239622	−	1.71736i
$428$	−1.32224	+	1.32224i	−0.0639130	+	0.0639130i
$429$	−1.54074	+	12.9254i	−0.0743875	+	0.624044i
$430$	0.0978840	−	0.306715i	0.00472039	−	0.0147911i
$431$	−2.79393	+	26.5825i	−0.134579	+	1.28043i	0.693760	+	0.720206i	$0.255953\pi$
$431$	−2.79393	+	26.5825i	−0.134579	+	1.28043i	−0.828339	+	0.560227i	$0.810714\pi$
$432$	5.21777	+	0.273452i	0.251040	+	0.0131565i
$433$	10.0296	−	19.6842i	0.481993	−	0.945964i	−0.514107	−	0.857726i	$-0.671876\pi$
$433$	10.0296	−	19.6842i	0.481993	−	0.945964i	0.996099	−	0.0882379i	$-0.0281236\pi$
$434$	−9.80469	+	20.9719i	−0.470640	+	1.00668i
$435$	5.79016	−	3.80345i	0.277617	−	0.182362i
$436$	−8.17456	−	1.73756i	−0.391490	−	0.0832139i
$437$	14.9575	−	23.0326i	0.715516	−	1.10180i
$438$	5.86506	+	7.24275i	0.280243	+	0.346072i
$439$	−4.24883	+	7.35919i	−0.202786	+	0.351235i	−0.949425	−	0.313994i	$-0.898333\pi$
$439$	−4.24883	+	7.35919i	−0.202786	+	0.351235i	0.746639	+	0.665229i	$0.231666\pi$
$440$	7.40913	−	0.323815i	0.353216	−	0.0154373i
$441$	5.99009	+	11.3198i	0.285242	+	0.539040i
$442$	−1.91987	−	12.1216i	−0.0913190	−	0.576565i
$443$	−1.47534	−	0.0773192i	−0.0700954	−	0.00367355i	0.0172560	−	0.999851i	$-0.494507\pi$
$443$	−1.47534	−	0.0773192i	−0.0700954	−	0.00367355i	−0.0873514	+	0.996178i	$0.527840\pi$
$444$	−7.56099	+	8.39732i	−0.358828	+	0.398519i
$445$	−2.30386	−	6.96614i	−0.109213	−	0.330227i
$446$	−3.50422	+	0.368308i	−0.165930	+	0.0174399i
$447$	−12.4414	−	6.33922i	−0.588459	−	0.299835i
$448$	2.19196	+	1.48166i	0.103560	+	0.0700019i
$449$	2.83285	−	3.89909i	0.133691	−	0.184009i	−0.736923	−	0.675977i	$-0.763722\pi$
$449$	2.83285	−	3.89909i	0.133691	−	0.184009i	0.870614	+	0.491967i	$0.163722\pi$
$450$	9.01976	−	1.52565i	0.425196	−	0.0719200i
$451$	14.1004	+	0.196330i	0.663963	+	0.00924480i
$452$	3.59419	−	13.4137i	0.169057	−	0.630928i
$453$	−3.85750	−	1.48076i	−0.181241	−	0.0695720i
$454$	8.07179	−	24.8424i	0.378828	−	1.16591i
$455$	−10.9756	+	18.4435i	−0.514544	+	0.864643i
$456$	2.87780	−	2.09085i	0.134766	−	0.0979129i
$457$	−16.9797	+	20.9681i	−0.794275	+	0.980847i	0.205723	+	0.978610i	$0.434045\pi$
$457$	−16.9797	+	20.9681i	−0.794275	+	0.980847i	−0.999997	+	0.00223714i	$0.999288\pi$
$458$	−2.36160	+	0.123766i	−0.110350	+	0.00578322i
$459$	−3.67502	−	17.2896i	−0.171535	−	0.807009i
$460$	6.78447	+	17.4011i	0.316328	+	0.811329i
$461$		−	31.7437i		−	1.47845i	−0.673457	−	0.739226i	$-0.735191\pi$
$461$		−	31.7437i		−	1.47845i	0.673457	−	0.739226i	$-0.264809\pi$
$462$	−5.42537	+	7.79025i	−0.252411	+	0.362435i
$463$	12.4148	−	12.4148i	0.576966	−	0.576966i	−0.357100	−	0.934066i	$-0.616235\pi$
$463$	12.4148	−	12.4148i	0.576966	−	0.576966i	0.934066	+	0.357100i	$0.116235\pi$
$464$	−1.16477	−	2.61613i	−0.0540733	−	0.121451i
$465$	−20.8893	+	3.42084i	−0.968718	+	0.158638i
$466$	0.133548	−	0.148321i	0.00618651	−	0.00687081i
$467$	17.5305	+	14.1959i	0.811215	+	0.656909i	0.942415	−	0.334447i	$-0.108550\pi$
$467$	17.5305	+	14.1959i	0.811215	+	0.656909i	−0.131200	+	0.991356i	$0.541883\pi$
$468$	6.55557	+	1.03830i	0.303031	+	0.0479954i
$469$	−32.5627	−	7.55173i	−1.50361	−	0.348706i
$470$	−0.799072	+	0.360799i	−0.0368585	+	0.0166424i
$471$	−16.7744	+	7.46846i	−0.772925	+	0.344128i
$472$	−10.8958	−	2.91953i	−0.501522	−	0.134382i
$473$	0.222700	−	0.422430i	0.0102398	−	0.0194233i
$474$	8.93923	−	15.4832i	0.410593	−	0.711167i
$475$	10.8719	−	12.3319i	0.498836	−	0.565827i
$476$	2.92240	−	8.46000i	0.133948	−	0.387763i
$477$	4.39997	−	8.63543i	0.201461	−	0.395389i
$478$	−14.1003	−	11.4182i	−0.644935	−	0.522258i
$479$	10.7948	+	4.80614i	0.493226	+	0.219598i	0.638249	−	0.769830i	$-0.279659\pi$
$479$	10.7948	+	4.80614i	0.493226	+	0.219598i	−0.145023	+	0.989428i	$0.546326\pi$
$480$	0.0126761	+	2.41908i	0.000578582	+	0.110415i
$481$	−28.1585	+	25.3540i	−1.28392	+	1.15604i
$482$	−12.4311	+	1.96889i	−0.566221	+	0.0896807i
$483$	−22.9751	−	6.61268i	−1.04540	−	0.300888i
$484$	10.9035	+	1.45395i	0.495613	+	0.0660887i
$485$	3.84748	−	5.99312i	0.174705	−	0.272134i
$486$	15.4126	+	1.61993i	0.699128	+	0.0734813i
$487$	23.3466	+	15.1615i	1.05794	+	0.687032i	0.951613	−	0.307300i	$-0.0994254\pi$
$487$	23.3466	+	15.1615i	1.05794	+	0.687032i	0.106324	+	0.994332i	$0.466092\pi$
$488$	−7.37601	−	11.3581i	−0.333896	−	0.514155i
$489$	−2.12764	+	1.54582i	−0.0962153	+	0.0699045i
$490$	−13.3905	+	8.10526i	−0.604920	+	0.366158i
$491$	10.7737	+	33.1581i	0.486212	+	1.49641i	0.830218	+	0.557438i	$0.188216\pi$
$491$	10.7737	+	33.1581i	0.486212	+	1.49641i	−0.344007	+	0.938967i	$0.611784\pi$
$492$	−0.240741	+	4.59361i	−0.0108534	+	0.207096i
$493$	−7.52889	+	6.09678i	−0.339084	+	0.274585i
$494$	10.3301	−	5.96406i	0.464771	−	0.268336i
$495$	13.5680	+	0.117811i	0.609836	+	0.00529520i
$496$			8.75012i			0.392892i
$497$	3.14749	+	4.03685i	0.141184	+	0.181078i
$498$	1.33516	+	2.62039i	0.0598297	+	0.117422i
$499$	−2.46306	+	11.5878i	−0.110262	+	0.518740i	0.888002	+	0.459839i	$0.152093\pi$
$499$	−2.46306	+	11.5878i	−0.110262	+	0.518740i	−0.998264	+	0.0589010i	$0.981240\pi$
$500$	2.49614	+	10.8981i	0.111631	+	0.487379i
$501$	−14.3716	−	6.39863i	−0.642074	−	0.285870i
$502$	25.5663	−	16.6029i	1.14108	−	0.741025i
$503$	0.838543	−	0.427259i	0.0373888	−	0.0190505i	−0.435196	−	0.900336i	$-0.643321\pi$
$503$	0.838543	−	0.427259i	0.0373888	−	0.0190505i	0.472585	+	0.881285i	$0.343321\pi$
$504$	3.86299	+	2.91698i	0.172071	+	0.129933i
$505$	−6.76082	+	6.15192i	−0.300852	+	0.273757i
$506$	5.38182	+	27.1745i	0.239251	+	1.20805i
$507$	−0.167950	−	0.0450020i	−0.00745891	−	0.00199861i
$508$	2.22034	+	2.74189i	0.0985117	+	0.121652i
$509$	−12.6327	−	14.0300i	−0.559934	−	0.621870i	0.395002	−	0.918680i	$-0.370744\pi$
$509$	−12.6327	−	14.0300i	−0.559934	−	0.621870i	−0.954937	+	0.296810i	$0.904077\pi$
$510$	7.89376	−	2.15952i	0.349542	−	0.0956253i
$511$	1.96391	+	22.7070i	0.0868782	+	1.00450i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	14.4080	−	9.35667i	0.636129	−	0.413107i
$514$	12.8582	−	2.73310i	0.567152	−	0.120552i
$515$	32.7777	+	5.01556i	1.44436	+	0.221012i
$516$	0.134901	+	0.0778848i	0.00593866	+	0.00342869i
$517$	−1.26068	+	0.319056i	−0.0554449	+	0.0140321i
$518$	−26.8198	+	6.65868i	−1.17840	+	0.292566i
$519$	5.66275	−	7.79411i	0.248567	−	0.342124i
$520$	−0.805644	+	8.07184i	−0.0353298	+	0.353973i
$521$	6.74614	+	6.07425i	0.295554	+	0.266118i	0.803544	−	0.595245i	$-0.202945\pi$
$521$	6.74614	+	6.07425i	0.295554	+	0.266118i	−0.507991	+	0.861363i	$0.669612\pi$
$522$	−1.87762	−	4.89138i	−0.0821813	−	0.214090i
$523$	−13.6515	+	16.8582i	−0.596939	+	0.737158i	−0.982652	−	0.185461i	$-0.940622\pi$
$523$	−13.6515	+	16.8582i	−0.596939	+	0.737158i	0.385713	+	0.922619i	$0.373956\pi$
$524$	−6.33206	−	19.4881i	−0.276617	−	0.851340i
$525$	−13.0276	−	5.92504i	−0.568570	−	0.258590i
$526$	14.5509	+	10.5718i	0.634449	+	0.460954i
$527$	28.5929	−	7.66143i	1.24552	−	0.333737i
$528$	−0.610592	+	3.53579i	−0.0265726	+	0.153876i
$529$	−40.4998	+	23.3826i	−1.76086	+	1.01663i
$530$	10.8461	+	4.76106i	0.471125	+	0.206807i
$531$	−19.6279	−	6.37749i	−0.851778	−	0.276760i
$532$	8.69423	−	0.294973i	0.376943	−	0.0127887i
$533$	−2.41296	+	15.2348i	−0.104517	+	0.659894i
$534$	3.53047	−	0.371067i	0.152778	−	0.0160577i
$535$	−2.97208	−	2.94109i	−0.128494	−	0.127155i
$536$	−12.3581	+	2.62679i	−0.533788	+	0.113460i
$537$	−7.68383	+	20.0171i	−0.331582	+	0.863800i
$538$	−3.20431	−	3.20431i	−0.138148	−	0.138148i
$539$	−21.6615	+	8.35351i	−0.933025	+	0.359811i
$540$	−0.550312	+	11.6703i	−0.0236817	+	0.502211i
$541$	−25.0772	+	11.1651i	−1.07815	+	0.480025i	−0.867450	−	0.497525i	$-0.834242\pi$
$541$	−25.0772	+	11.1651i	−1.07815	+	0.480025i	−0.210704	+	0.977550i	$0.567576\pi$
$542$	2.36245	−	3.63785i	0.101476	−	0.156259i
$543$	−0.569610	−	10.8688i	−0.0244443	−	0.466425i
$544$	−0.353618	−	3.36445i	−0.0151612	−	0.144250i
$545$	3.78946	−	18.2990i	0.162323	−	0.783842i
$546$	−7.58727	−	7.08933i	−0.324705	−	0.303395i
$547$	−12.3668	+	6.30122i	−0.528768	+	0.269421i	−0.697928	−	0.716168i	$-0.745895\pi$
$547$	−12.3668	+	6.30122i	−0.528768	+	0.269421i	0.169160	+	0.985589i	$0.445895\pi$
$548$	5.63955	−	14.6915i	0.240910	−	0.627591i
$549$	−12.3889	−	21.4582i	−0.528746	−	0.915816i
$550$	0.810875	+	16.5633i	0.0345758	+	0.706261i
$551$	−8.15439	−	4.70794i	−0.347389	−	0.200565i
$552$	−8.92505	+	1.41359i	−0.379876	+	0.0601664i
$553$	39.3168	−	19.1278i	1.67192	−	0.813397i
$554$	1.30375	−	0.423613i	0.0553909	−	0.0179976i
$555$	−18.8653	−	16.8083i	−0.800788	−	0.713471i
$556$	−3.53617	+	7.94238i	−0.149967	+	0.336832i
$557$	27.3091	−	1.43121i	1.15712	−	0.0606423i	0.535904	−	0.844279i	$-0.319971\pi$
$557$	27.3091	−	1.43121i	1.15712	−	0.0606423i	0.621219	+	0.783637i	$0.286638\pi$
$558$	−0.837847	+	15.9871i	−0.0354689	+	0.676787i
$559$	0.422580	+	0.307022i	0.0178732	+	0.0129857i
$560$	−3.28737	+	4.91866i	−0.138917	+	0.207851i
$561$	12.0886	−	1.10063i	0.510380	−	0.0464687i
$562$	4.87607	−	1.30654i	0.205685	−	0.0551130i
$563$	14.8938	−	12.0608i	0.627698	−	0.508300i	−0.261870	−	0.965103i	$-0.584339\pi$
$563$	14.8938	−	12.0608i	0.627698	−	0.508300i	0.889568	+	0.456803i	$0.151006\pi$
$564$	−0.0881945	−	0.414923i	−0.00371366	−	0.0174714i
$565$	30.0357	+	7.87958i	1.26361	+	0.331496i
$566$	−7.94976	−	10.9419i	−0.334153	−	0.459923i
$567$	−0.331950	−	0.279101i	−0.0139406	−	0.0117211i
$568$	1.72388	+	0.878360i	0.0723323	+	0.0368551i
$569$	5.57924	−	5.02357i	0.233894	−	0.210599i	−0.543846	−	0.839185i	$-0.683033\pi$
$569$	5.57924	−	5.02357i	0.233894	−	0.210599i	0.777740	+	0.628586i	$0.216366\pi$
$570$	4.70893	+	6.41038i	0.197235	+	0.268501i
$571$	−12.3230	−	21.3440i	−0.515700	−	0.893219i	−0.999834	−	0.0182250i	$-0.994198\pi$
$571$	−12.3230	−	21.3440i	−0.515700	−	0.893219i	0.484134	−	0.874994i	$-0.339135\pi$
$572$	−3.27560	+	11.5775i	−0.136960	+	0.484079i
$573$	10.0458	+	10.0458i	0.419669	+	0.419669i
$574$	−6.77893	+	8.97740i	−0.282947	+	0.374709i
$575$	−38.8299	+	15.3742i	−1.61932	+	0.641149i
$576$	1.78960	+	0.380390i	0.0745665	+	0.0158496i
$577$	8.50627	−	3.26525i	0.354121	−	0.135934i	−0.174803	−	0.984603i	$-0.555929\pi$
$577$	8.50627	−	3.26525i	0.354121	−	0.135934i	0.528924	+	0.848669i	$0.322596\pi$
$578$	5.18644	−	1.99089i	0.215727	−	0.0828099i
$579$	6.69317	+	1.42268i	0.278159	+	0.0591245i
$580$	5.83611	−	2.63513i	0.242331	−	0.109418i
$581$	−0.883592	+	7.13773i	−0.0366576	+	0.296123i
$582$	2.43649	+	2.43649i	0.100996	+	0.100996i
$583$	14.6000	+	9.77302i	0.604671	+	0.404757i
$584$	4.30724	+	7.46036i	0.178235	+	0.308712i
$585$	−2.24487	+	14.6707i	−0.0928138	+	0.606557i
$586$	7.54167	−	6.79055i	0.311543	−	0.280515i
$587$	−18.8389	−	9.59888i	−0.777563	−	0.396188i	0.0197107	−	0.999806i	$-0.493725\pi$
$587$	−18.8389	−	9.59888i	−0.777563	−	0.396188i	−0.797274	+	0.603617i	$0.793725\pi$
$588$	−2.45132	−	7.16532i	−0.101091	−	0.295493i
$589$	16.9108	+	23.2758i	0.696798	+	0.959061i
$590$	6.40052	−	24.3977i	0.263505	−	1.00444i
$591$	−5.77018	−	27.1466i	−0.237354	−	1.11666i
$592$	−8.11706	+	6.57306i	−0.333609	+	0.270151i
$593$	12.6041	−	3.37727i	0.517590	−	0.138688i	0.00943813	−	0.999955i	$-0.496996\pi$
$593$	12.6041	−	3.37727i	0.517590	−	0.138688i	0.508151	+	0.861268i	$0.330329\pi$
$594$	−3.83857	+	16.8986i	−0.157498	+	0.693360i
$595$	18.9511	+	6.43548i	0.776920	+	0.263829i
$596$	−10.4418	−	7.58641i	−0.427712	−	0.310751i
$597$	−0.0392313	+	0.748578i	−0.00160563	+	0.0306373i
$598$	−30.2596	+	1.58584i	−1.23741	+	0.0648498i
$599$	−5.18456	+	11.6447i	−0.211836	+	0.475790i	−0.987945	−	0.154808i	$-0.950524\pi$
$599$	−5.18456	+	11.6447i	−0.211836	+	0.475790i	0.776109	+	0.630599i	$0.217191\pi$
$600$	−5.40901	+	0.0566884i	−0.220822	+	0.00231429i
$601$	24.8176	−	8.06372i	1.01233	−	0.328926i	0.244548	−	0.969637i	$-0.421360\pi$
$601$	24.8176	−	8.06372i	1.01233	−	0.328926i	0.767782	+	0.640711i	$0.221360\pi$
$602$	0.166655	+	0.342555i	0.00679234	+	0.0139615i
$603$	−22.8306	+	3.61601i	−0.929734	+	0.147255i
$604$	−3.30760	−	1.90964i	−0.134584	−	0.0777024i
$605$	−3.12333	+	24.3976i	−0.126982	+	0.991905i
$606$	−2.21127	−	3.83003i	−0.0898268	−	0.155585i
$607$	−6.13032	+	15.9700i	−0.248822	+	0.648204i	−0.999928	−	0.0119776i	$-0.996187\pi$
$607$	−6.13032	+	15.9700i	−0.248822	+	0.648204i	0.751106	+	0.660182i	$0.229521\pi$
$608$	2.92963	−	1.49272i	0.118812	−	0.0605379i
$609$	−1.85182	+	7.98497i	−0.0750396	+	0.323567i
$610$	25.3106	−	16.6261i	1.02480	−	0.673172i
$611$	−0.148684	−	1.41464i	−0.00601513	−	0.0572301i
$612$	−0.323930	−	6.18094i	−0.0130941	−	0.249850i
$613$	−25.5343	+	39.3193i	−1.03132	+	1.58809i	−0.245736	+	0.969337i	$0.579030\pi$
$613$	−25.5343	+	39.3193i	−1.03132	+	1.58809i	−0.785583	+	0.618756i	$0.787637\pi$
$614$	−23.8674	+	10.6264i	−0.963209	+	0.428848i
$615$	−10.2743	−	0.484482i	−0.414300	−	0.0195362i
$616$	−6.07956	+	6.32763i	−0.244952	+	0.254948i
$617$	−18.8426	−	18.8426i	−0.758574	−	0.758574i	0.217489	−	0.976063i	$-0.430213\pi$
$617$	−18.8426	−	18.8426i	−0.758574	−	0.758574i	−0.976063	+	0.217489i	$0.930213\pi$
$618$	−5.74936	+	14.9776i	−0.231273	+	0.602488i
$619$	24.8377	−	5.27941i	0.998310	−	0.212197i	0.320353	−	0.947298i	$-0.396199\pi$
$619$	24.8377	−	5.27941i	0.998310	−	0.212197i	0.677958	+	0.735101i	$0.262865\pi$
$620$	−19.5656	+	0.102525i	−0.785773	+	0.00411748i
$621$	−43.4025	+	4.56178i	−1.74168	+	0.183058i
$622$	−1.77524	+	11.2084i	−0.0711805	+	0.449416i
$623$	7.66128	+	4.08333i	0.306943	+	0.163595i
$624$	−3.73265	−	1.21281i	−0.149426	−	0.0485514i
$625$	−24.3394	+	5.70916i	−0.973575	+	0.228366i
$626$	−1.90906	+	1.10220i	−0.0763015	+	0.0440527i
$627$	5.20921	+	10.5854i	0.208036	+	0.422742i
$628$	−16.3942	+	4.39281i	−0.654199	+	0.175292i
$629$	28.5860	+	20.7689i	1.13980	+	0.828112i
$630$	−6.47722	+	8.67196i	−0.258059	+	0.345499i
$631$	−0.593425	−	1.82637i	−0.0236239	−	0.0727068i	0.938550	−	0.345145i	$-0.112170\pi$
$631$	−0.593425	−	1.82637i	−0.0236239	−	0.0727068i	−0.962173	+	0.272438i	$0.912170\pi$
$632$	10.3999	−	12.8429i	0.413687	−	0.510861i
$633$	−0.103018	−	0.268372i	−0.00409461	−	0.0106668i
$634$	−10.1754	−	9.16199i	−0.404117	−	0.363869i
$635$	−6.10496	+	4.99689i	−0.242268	+	0.198296i
$636$	−3.36855	+	4.63641i	−0.133572	+	0.183846i
$637$	−5.66339	−	24.7548i	−0.224392	−	0.980822i
$638$	9.20755	−	2.33026i	0.364530	−	0.0922558i
$639$	3.06554	+	1.76989i	0.121271	+	0.0700157i
$640$	−0.338221	+	2.21034i	−0.0133693	+	0.0873714i
$641$	−1.50568	+	0.320042i	−0.0594708	+	0.0126409i	−0.237551	−	0.971375i	$-0.576345\pi$
$641$	−1.50568	+	0.320042i	−0.0594708	+	0.0126409i	0.178080	+	0.984016i	$0.443011\pi$
$642$	1.69664	−	1.10181i	0.0669610	−	0.0434850i
$643$	−21.8202	−	3.45598i	−0.860505	−	0.136291i	−0.289441	−	0.957196i	$-0.593469\pi$
$643$	−21.8202	−	3.45598i	−0.860505	−	0.136291i	−0.571064	+	0.820905i	$0.693469\pi$
$644$	−20.0190	−	9.35922i	−0.788860	−	0.368805i
$645$	−0.172573	+	0.302555i	−0.00679505	+	0.0119131i
$646$	−7.44291	−	8.26619i	−0.292837	−	0.325229i
$647$	10.3970	+	12.8392i	0.408748	+	0.504762i	0.939398	−	0.342829i	$-0.111385\pi$
$647$	10.3970	+	12.8392i	0.408748	+	0.504762i	−0.530649	+	0.847591i	$0.678052\pi$
$648$	−0.158334	−	0.0424256i	−0.00621996	−	0.00166663i
$649$	15.6913	−	33.9626i	0.615936	−	1.33315i
$650$	−18.0584	−	1.70687i	−0.708307	−	0.0669490i
$651$	15.0928	−	19.9875i	0.591532	−	0.783371i
$652$	−2.16596	+	1.10361i	−0.0848256	+	0.0432208i
$653$	−2.00007	+	1.29886i	−0.0782687	+	0.0508283i	−0.583180	−	0.812343i	$-0.698192\pi$
$653$	−2.00007	+	1.29886i	−0.0782687	+	0.0508283i	0.504911	+	0.863171i	$0.331525\pi$
$654$	8.25965	+	3.67743i	0.322978	+	0.143799i
$655$	43.5019	−	14.3871i	1.69976	−	0.562149i
$656$	−0.884009	+	4.15894i	−0.0345148	+	0.162379i
$657$	7.15528	+	14.0430i	0.279154	+	0.547871i
$658$	0.389566	−	0.961461i	0.0151868	−	0.0374817i
$659$			4.91779i			0.191570i	0.995402	+	0.0957850i	$0.0305361\pi$
$659$			4.91779i			0.191570i	−0.995402	+	0.0957850i	$0.969464\pi$
$660$	−7.91332	−	1.32388i	−0.308026	−	0.0515319i
$661$	1.06702	−	0.616046i	0.0415024	−	0.0239614i	−0.479105	−	0.877757i	$-0.659039\pi$
$661$	1.06702	−	0.616046i	0.0415024	−	0.0239614i	0.520608	+	0.853796i	$0.325705\pi$
$662$	−3.89629	+	3.15515i	−0.151433	+	0.122628i
$663$	−0.694882	+	13.2591i	−0.0269870	+	0.514943i
$664$	0.840032	+	2.58535i	0.0325996	+	0.100331i
$665$	0.761441	+	19.4372i	0.0295274	+	0.753741i
$666$	−15.4598	+	11.2322i	−0.599056	+	0.435239i
$667$	13.0274	+	20.0604i	0.504422	+	0.776742i
$668$	−12.1953	−	7.91974i	−0.471852	−	0.306424i
$669$	3.79108	+	0.398459i	0.146572	+	0.0154053i
$670$	−6.01841	−	27.6024i	−0.232511	−	1.06637i
$671$	41.2840	−	17.6963i	1.59375	−	0.683157i
$672$	−1.98630	−	2.06096i	−0.0766232	−	0.0795034i
$673$	−45.1436	+	7.15004i	−1.74016	+	0.275614i	−0.944113	−	0.329623i	$-0.893078\pi$
$673$	−45.1436	+	7.15004i	−1.74016	+	0.275614i	−0.796045	+	0.605237i	$0.793078\pi$
$674$	18.1287	−	16.3232i	0.698292	−	0.628745i
$675$	−26.1017	−	1.09378i	−1.00466	−	0.0420995i
$676$	−0.146823	−	0.0653698i	−0.00564704	−	0.00251422i
$677$	32.2328	+	26.1016i	1.23881	+	1.00316i	0.999481	+	0.0322253i	$0.0102594\pi$
$677$	32.2328	+	26.1016i	1.23881	+	1.00316i	0.239325	+	0.970940i	$0.423074\pi$
$678$	−6.82061	+	13.3862i	−0.261944	+	0.514094i
$679$	1.59968	+	8.27345i	0.0613900	+	0.317506i
$680$	7.51889	−	0.830124i	0.288336	−	0.0318338i
$681$	−14.1296	+	24.4731i	−0.541446	+	0.937812i
$682$	−28.5976	−	4.93849i	−1.09506	−	0.189104i
$683$	30.1397	+	8.07592i	1.15327	+	0.309016i	0.784273	−	0.620416i	$-0.213036\pi$
$683$	30.1397	+	8.07592i	1.15327	+	0.309016i	0.368992	+	0.929432i	$0.379703\pi$
$684$	5.49557	−	2.44679i	0.210128	−	0.0935552i
$685$	32.9169	+	12.4381i	1.25769	+	0.475236i
$686$	4.84662	−	17.8749i	0.185045	−	0.682465i
$687$	2.52693	+	0.400227i	0.0964086	+	0.0152696i
$688$	0.111896	+	0.0906115i	0.00426599	+	0.00345453i
$689$	−12.8589	+	14.2812i	−0.489885	+	0.544072i
$690$	−3.26541	−	19.9402i	−0.124312	−	0.759110i
$691$	−20.0144	−	44.9531i	−0.761385	−	1.71010i	−0.702339	−	0.711842i	$-0.747861\pi$
$691$	−20.0144	−	44.9531i	−0.761385	−	1.71010i	−0.0590453	−	0.998255i	$-0.518806\pi$
$692$	6.29684	−	6.29684i	0.239370	−	0.239370i
$693$	−11.7137	+	10.9789i	−0.444965	+	0.417054i
$694$		−	13.8136i		−	0.524356i
$695$	−17.8009	−	7.81396i	−0.675226	−	0.296400i
$696$	0.644138	+	3.03043i	0.0244160	+	0.114868i
$697$	14.3642	−	0.752797i	0.544084	−	0.0285142i
$698$	12.8084	−	15.8171i	0.484807	−	0.598687i
$699$	−0.174686	+	0.126916i	−0.00660721	+	0.00480042i
$700$	−11.0368	−	7.29304i	−0.417153	−	0.275651i
$701$	−4.83949	+	14.8944i	−0.182785	+	0.562554i	−0.999903	−	0.0139158i	$-0.995570\pi$
$701$	−4.83949	+	14.8944i	−0.182785	+	0.562554i	0.817118	+	0.576470i	$0.195570\pi$
$702$	−17.6959	−	6.79281i	−0.667888	−	0.256378i
$703$	−8.88842	+	33.1720i	−0.335233	+	1.25111i
$704$	−1.06871	+	3.13972i	−0.0402785	+	0.118333i
$705$	0.926749	−	0.202068i	0.0349034	−	0.00761032i
$706$	−5.23810	+	7.20963i	−0.197139	+	0.271338i
$707$	0.765160	−	10.7885i	0.0287768	−	0.405742i
$708$	10.8735	+	5.54032i	0.408651	+	0.208218i
$709$	−42.3568	+	4.45188i	−1.59074	+	0.167194i	−0.858123	−	0.513445i	$-0.828369\pi$
$709$	−42.3568	+	4.45188i	−1.59074	+	0.167194i	−0.732619	+	0.680638i	$0.761702\pi$
$710$	−1.94385	+	3.86495i	−0.0729512	+	0.145049i
$711$	20.2311	−	22.4690i	0.758727	−	0.842652i
$712$	3.27681	+	0.171730i	0.122804	+	0.00643587i
$713$	−11.4331	−	72.1861i	−0.428175	−	2.70339i
$714$	−4.99547	+	8.29520i	−0.186951	+	0.310440i
$715$	−25.9261	−	7.18871i	−0.969581	−	0.268843i
$716$	−9.90939	+	17.1636i	−0.370331	+	0.641433i
$717$	12.3529	+	15.2546i	0.461329	+	0.569694i
$718$	−9.22643	+	14.2075i	−0.344327	+	0.530218i
$719$	−6.09851	−	1.29628i	−0.227436	−	0.0483431i	0.0927837	−	0.995686i	$-0.470423\pi$
$719$	−6.09851	−	1.29628i	−0.227436	−	0.0483431i	−0.320220	+	0.947343i	$0.603757\pi$
$720$	−0.829598	+	4.00606i	−0.0309173	+	0.149297i
$721$	−32.1613	+	22.4721i	−1.19775	+	0.836904i
$722$	−3.71775	+	7.29649i	−0.138360	+	0.271547i
$723$	13.5977	+	0.712626i	0.505704	+	0.0265028i
$724$	1.05157	−	10.0051i	0.0390815	−	0.371835i
$725$	5.96064	+	13.0189i	0.221373	+	0.483509i
$726$	−11.2112	−	3.99114i	−0.416088	−	0.148125i
$727$	−20.3187	+	20.3187i	−0.753580	+	0.753580i	−0.975145	−	0.221566i	$-0.928883\pi$
$727$	−20.3187	+	20.3187i	−0.753580	+	0.753580i	0.221566	+	0.975145i	$0.428883\pi$
$728$	−5.90172	−	7.56933i	−0.218732	−	0.280538i
$729$	−16.4132	−	5.33297i	−0.607896	−	0.197517i
$730$	−16.6312	+	9.71856i	−0.615547	+	0.359700i
$731$	0.198118	−	0.444981i	0.00732767	−	0.0164582i
$732$	5.25066	+	13.6784i	0.194070	+	0.505569i
$733$	6.50615	+	10.0186i	0.240310	+	0.370045i	0.938162	−	0.346197i	$-0.112527\pi$
$733$	6.50615	+	10.0186i	0.240310	+	0.370045i	−0.697852	+	0.716242i	$0.745860\pi$
$734$	1.51213	−	4.65385i	0.0558136	−	0.171777i
$735$	15.9932	−	5.56521i	0.589918	−	0.205276i
$736$	−8.35256			−0.307879
$737$	−1.61023	−	41.8719i	−0.0593135	−	1.54237i
$738$	−2.01338	+	7.51402i	−0.0741134	+	0.276595i
$739$	−2.05989	−	0.216504i	−0.0757744	−	0.00796421i	0.0665654	−	0.997782i	$-0.478796\pi$
$739$	−2.05989	−	0.216504i	−0.0757744	−	0.00796421i	−0.142340	+	0.989818i	$0.545463\pi$
$740$	−14.7927	−	18.0730i	−0.543791	−	0.664378i
$741$	−12.2730	+	3.98773i	−0.450859	+	0.146493i
$742$	−13.1748	+	4.78044i	−0.483662	+	0.175495i
$743$	0.822230	−	5.19136i	0.0301647	−	0.190452i	−0.968005	−	0.250932i	$-0.919263\pi$
$743$	0.822230	−	5.19136i	0.0301647	−	0.190452i	0.998169	+	0.0604795i	$0.0192630\pi$
$744$	1.96818	−	9.25955i	0.0721569	−	0.339472i
$745$	16.8411	−	23.4371i	0.617012	−	0.858670i
$746$	2.84439	−	27.0626i	0.104140	−	0.990831i
$747$	1.28724	+	4.80405i	0.0470977	+	0.175771i
$748$	11.1954	+	0.743153i	0.409346	+	0.0271723i
$749$	4.94654	+	0.0912513i	0.180743	+	0.00333425i
$750$	−0.190134	−	12.0941i	−0.00694273	−	0.441613i
$751$	−30.9316	−	34.3530i	−1.12871	−	1.25356i	−0.963619	−	0.267281i	$-0.913875\pi$
$751$	−30.9316	−	34.3530i	−1.12871	−	1.25356i	−0.165091	−	0.986278i	$-0.552792\pi$
$752$	−0.0205207	−	0.391558i	−0.000748312	−	0.0142786i
$753$	−30.7893	+	11.8189i	−1.12202	+	0.430704i
$754$	1.08593	+	10.3320i	0.0395473	+	0.376268i
$755$	4.23128	−	7.41830i	0.153992	−	0.269979i
$756$	−9.05892	−	10.4420i	−0.329470	−	0.379772i
$757$	−0.197216	−	1.24517i	−0.00716795	−	0.0452566i	0.983845	−	0.179022i	$-0.0572932\pi$
$757$	−0.197216	−	1.24517i	−0.00716795	−	0.0452566i	−0.991013	+	0.133765i	$0.957293\pi$
$758$	8.71747	+	32.5341i	0.316633	+	1.18169i
$759$	0.417252	−	29.9671i	0.0151453	−	1.08774i
$760$	3.37211	+	6.53328i	0.122319	+	0.236987i
$761$	12.3654	+	27.7732i	0.448246	+	1.00678i	0.986465	+	0.163971i	$0.0524305\pi$
$761$	12.3654	+	27.7732i	0.448246	+	1.00678i	−0.538219	+	0.842805i	$0.680903\pi$
$762$	−1.73287	−	3.40095i	−0.0627753	−	0.123203i
$763$	11.6985	+	18.7628i	0.423512	+	0.679260i
$764$	7.71873	+	10.6239i	0.279254	+	0.384360i
$765$	13.8170	−	0.796740i	0.499556	−	0.0288062i
$766$	−13.9602	−	12.5698i	−0.504401	−	0.454165i
$767$	34.3201	+	22.2877i	1.23923	+	0.804763i
$768$	−1.01000	−	0.387704i	−0.0364454	−	0.0139901i
$769$	44.7153			1.61247			0.806237	−	0.591592i	$-0.201501\pi$
$769$	44.7153			1.61247			0.806237	+	0.591592i	$0.201501\pi$
$770$	−14.2201	−	13.5200i	−0.512455	−	0.487226i
$771$	−14.2216			−0.512178
$772$	5.90484	+	2.26665i	0.212520	+	0.0815787i
$773$	19.6071	+	12.7330i	0.705218	+	0.457974i	0.846772	−	0.531957i	$-0.178543\pi$
$773$	19.6071	+	12.7330i	0.705218	+	0.457974i	−0.141553	+	0.989931i	$0.545210\pi$
$774$	0.195765	+	0.176268i	0.00703663	+	0.00633581i
$775$	−0.458497	−	43.7482i	−0.0164697	−	1.57148i
$776$	1.87209	+	2.57671i	0.0672040	+	0.0924984i
$777$	29.8790	−	1.01372i	1.07190	−	0.0363670i
$778$	10.9315	+	21.4543i	0.391914	+	0.769175i
$779$	5.68622	+	12.7715i	0.203730	+	0.457585i
$780$	2.66816	−	8.36056i	0.0955354	−	0.299356i
$781$	−3.84364	+	5.13833i	−0.137536	+	0.183864i
$782$	7.31334	+	27.2937i	0.261524	+	0.976022i
$783$	2.34068	+	14.7785i	0.0836490	+	0.528139i
$784$	−1.20186	−	6.89605i	−0.0429234	−	0.246288i
$785$	−10.0146	−	36.6065i	−0.357435	−	1.30654i
$786$	2.31723	+	22.0469i	0.0826527	+	0.786388i
$787$	15.9994	−	6.14158i	0.570316	−	0.218924i	−0.0560834	−	0.998426i	$-0.517861\pi$
$787$	15.9994	−	6.14158i	0.570316	−	0.218924i	0.626399	+	0.779502i	$0.284528\pi$
$788$	−1.34258	−	25.6179i	−0.0478274	−	0.912600i
$789$	−13.0201	−	14.4603i	−0.463528	−	0.514800i
$790$	28.8389	+	23.1042i	1.02604	+	0.822009i
$791$	−32.1523	+	17.7806i	−1.14320	+	0.632206i
$792$	−2.25324	+	5.63416i	−0.0800655	+	0.200201i
$793$	12.7160	+	47.4566i	0.451557	+	1.68523i
$794$	1.03588	−	9.85576i	0.0367621	−	0.349768i
$795$	−10.4067	−	7.47788i	−0.369086	−	0.265213i
$796$	−0.144059	+	0.677744i	−0.00510603	+	0.0240220i
$797$	−1.91829	+	12.1116i	−0.0679493	+	0.429015i	0.930139	+	0.367208i	$0.119686\pi$
$797$	−1.91829	+	12.1116i	−0.0679493	+	0.429015i	−0.998088	+	0.0618068i	$0.980314\pi$
$798$	−9.26676	−	1.64346i	−0.328040	−	0.0581779i
$799$	−1.26153	+	0.409896i	−0.0446297	+	0.0145011i
$800$	−4.94637	−	0.730376i	−0.174881	−	0.0258227i
$801$	5.97051	+	0.627526i	0.210958	+	0.0221726i
$802$	−1.20568	+	4.49967i	−0.0425742	+	0.158889i
$803$	−26.8133	+	9.86659i	−0.946221	+	0.348184i
$804$	13.6684			0.482048
$805$	20.6930	−	44.8730i	0.729332	−	1.58156i
$806$	9.80926	−	30.1898i	0.345516	−	1.06339i
$807$	2.67011	+	4.11161i	0.0939925	+	0.144736i
$808$	−1.46497	−	3.81639i	−0.0515376	−	0.134260i
$809$	14.1022	−	31.6740i	0.495806	−	1.11360i	−0.476349	−	0.879257i	$-0.658040\pi$
$809$	14.1022	−	31.6740i	0.495806	−	1.11360i	0.972154	−	0.234341i	$-0.0752934\pi$
$810$	0.0930100	−	0.354539i	0.00326804	−	0.0124572i
$811$	17.3969	+	5.65261i	0.610889	+	0.198490i	0.598091	−	0.801428i	$-0.295926\pi$
$811$	17.3969	+	5.65261i	0.610889	+	0.198490i	0.0127982	+	0.999918i	$0.495926\pi$
$812$	−2.84523	+	7.02214i	−0.0998482	+	0.246429i
$813$	−3.31825	+	3.31825i	−0.116376	+	0.116376i
$814$	−16.9012	−	30.2384i	−0.592388	−	1.05985i
$815$	−2.49310	−	4.83024i	−0.0873293	−	0.169196i
$816$	−0.382566	+	3.63987i	−0.0133925	+	0.127421i
$817$	0.472768	+	0.0247767i	0.0165401	+	0.000866828i
$818$	−7.39055	+	14.5048i	−0.258405	+	0.507148i
$819$	−10.0581	−	14.3948i	−0.351457	−	0.502995i
$820$	−9.30990	−	1.92795i	−0.325116	−	0.0673269i
$821$	−28.0012	−	5.95184i	−0.977248	−	0.207721i	−0.308512	−	0.951220i	$-0.599831\pi$
$821$	−28.0012	−	5.95184i	−0.977248	−	0.207721i	−0.668736	+	0.743500i	$0.733164\pi$
$822$	−9.27248	+	14.2784i	−0.323415	+	0.498015i
$823$	21.1897	+	26.1671i	0.738627	+	0.912128i	0.998568	−	0.0534963i	$-0.0170365\pi$
$823$	21.1897	+	26.1671i	0.738627	+	0.912128i	−0.259941	+	0.965624i	$0.583703\pi$
$824$	−7.41462	+	12.8425i	−0.258301	+	0.447390i
$825$	2.86752	−	17.7100i	0.0998343	−	0.616583i
$826$	14.4431	+	26.1170i	0.502538	+	0.908728i
$827$	−2.99969	−	18.9393i	−0.104310	−	0.658585i	−0.983334	−	0.181808i	$-0.941805\pi$
$827$	−2.99969	−	18.9393i	−0.104310	−	0.658585i	0.879024	−	0.476777i	$-0.158195\pi$
$828$	−15.2607	−	0.799779i	−0.530346	−	0.0277943i
$829$	20.1101	−	22.3346i	0.698454	−	0.775712i	−0.284675	−	0.958624i	$-0.591886\pi$
$829$	20.1101	−	22.3346i	0.698454	−	0.775712i	0.983129	+	0.182912i	$0.0585524\pi$
$830$	−5.77110	+	1.90864i	−0.200318	+	0.0662497i
$831$	−1.47494	+	0.155022i	−0.0511650	+	0.00537765i
$832$	−3.23237	−	1.64697i	−0.112062	−	0.0570985i
$833$	−21.4820	+	9.96537i	−0.744307	+	0.345280i
$834$	5.52854	−	7.60938i	0.191438	−	0.263491i
$835$	17.5659	−	27.3620i	0.607895	−	0.946901i
$836$	3.22513	+	10.4172i	0.111544	+	0.360288i
$837$	11.8329	−	44.1609i	0.409004	−	1.52643i
$838$	2.32672	+	0.893145i	0.0803753	+	0.0308532i
$839$	−10.5509	+	32.4722i	−0.364256	+	1.12107i	0.586189	+	0.810174i	$0.300627\pi$
$839$	−10.5509	+	32.4722i	−0.364256	+	1.12107i	−0.950446	+	0.310891i	$0.899373\pi$
$840$	4.58512	−	4.46559i	0.158202	−	0.154078i
$841$	−16.8269	+	12.2254i	−0.580238	+	0.421567i
$842$	4.49002	−	5.54472i	0.154736	−	0.191084i
$843$	−5.45383	+	0.285823i	−0.187840	+	0.00984428i
$844$	−0.0552450	−	0.259907i	−0.00190161	−	0.00894637i
$845$	0.144449	−	0.329068i	0.00496920	−	0.0113203i
$846$		−	0.717368i		−	0.0246636i
$847$	−17.2490	−	23.4408i	−0.592684	−	0.805435i
$848$	−3.74574	+	3.74574i	−0.128629	+	0.128629i
$849$	5.95142	+	13.3671i	0.204252	+	0.458758i
$850$	1.94429	+	16.8028i	0.0666885	+	0.576331i
$851$	58.3749	−	64.8319i	2.00107	−	2.22241i
$852$	−1.62667	−	1.31725i	−0.0557288	−	0.0451283i
$853$	−34.9013	−	5.52782i	−1.19500	−	0.189269i	−0.472935	−	0.881097i	$-0.656805\pi$
$853$	−34.9013	−	5.52782i	−1.19500	−	0.189269i	−0.722062	+	0.691828i	$0.756805\pi$
$854$	−8.09491	+	34.9049i	−0.277002	+	1.19442i
$855$	5.53550	+	12.2596i	0.189310	+	0.419271i
$856$	1.70827	−	0.760571i	0.0583875	−	0.0259958i
$857$	22.4182	+	6.00694i	0.765792	+	0.205193i	0.620512	−	0.784197i	$-0.286925\pi$
$857$	22.4182	+	6.00694i	0.765792	+	0.205193i	0.145280	+	0.989391i	$0.453592\pi$
$858$	6.07045	−	11.5147i	0.207242	−	0.393107i
$859$	−14.7531	+	25.5530i	−0.503368	+	0.871858i	0.496625	+	0.867965i	$0.334573\pi$
$859$	−14.7531	+	25.5530i	−0.503368	+	0.871858i	−0.999992	+	0.00389305i	$0.998761\pi$
$860$	−0.201300	+	0.251265i	−0.00686426	+	0.00856807i
$861$	9.19290	−	7.97527i	0.313293	−	0.271796i
$862$	12.1347	−	23.8156i	0.413309	−	0.811164i
$863$	−21.5211	−	17.4274i	−0.732587	−	0.593237i	0.188740	−	0.982027i	$-0.439560\pi$
$863$	−21.5211	−	17.4274i	−0.732587	−	0.593237i	−0.921326	+	0.388790i	$0.872893\pi$
$864$	−4.77321	−	2.12517i	−0.162388	−	0.0722998i
$865$	14.1537	+	14.0062i	0.481242	+	0.476225i
$866$	−16.4177	+	14.7825i	−0.557895	+	0.502331i
$867$	−5.93620	+	0.940202i	−0.201604	+	0.0319309i
$868$	16.6691	−	16.0653i	0.565787	−	0.545290i
$869$	36.1040	+	41.2380i	1.22475	+	1.39890i
$870$	−6.76861	+	1.47582i	−0.229477	+	0.0500351i
$871$	45.5828	+	4.79095i	1.54451	+	0.162335i
$872$	7.00893	+	4.55165i	0.237352	+	0.154138i
$873$	3.17371	+	4.88708i	0.107414	+	0.165403i
$874$	−22.2182	+	16.1425i	−0.751542	+	0.546027i
$875$	16.1782	−	24.7642i	0.546923	−	0.837183i
$876$	−2.87994	−	8.86354i	−0.0973041	−	0.299471i
$877$	0.570966	−	10.8947i	0.0192802	−	0.367887i	−0.971902	−	0.235384i	$-0.924365\pi$
$877$	0.570966	−	10.8947i	0.0192802	−	0.367887i	0.991183	−	0.132503i	$-0.0423015\pi$
$878$	6.60392	−	5.34775i	0.222872	−	0.180478i
$879$	−9.50815	+	5.48953i	−0.320702	+	0.185157i
$880$	−7.03306	−	2.35289i	−0.237084	−	0.0793158i
$881$			46.6964i			1.57324i	0.617437	+	0.786620i	$0.288171\pi$
$881$			46.6964i			1.57324i	−0.617437	+	0.786620i	$0.711829\pi$
$882$	−1.53556	−	12.7146i	−0.0517050	−	0.428124i
$883$	−3.95723	−	7.76651i	−0.133172	−	0.261364i	0.814785	−	0.579763i	$-0.196855\pi$
$883$	−3.95723	−	7.76651i	−0.133172	−	0.261364i	−0.947957	+	0.318399i	$0.896855\pi$
$884$	−2.55163	+	12.0045i	−0.0858208	+	0.403755i
$885$	−12.2610	+	24.3785i	−0.412148	+	0.819473i
$886$	1.34964	+	0.600898i	0.0453420	+	0.0201876i
$887$	−27.7528	+	18.0229i	−0.931848	+	0.605149i	−0.918782	−	0.394766i	$-0.870826\pi$
$887$	−27.7528	+	18.0229i	−0.931848	+	0.605149i	−0.0130658	+	0.999915i	$0.504159\pi$
$888$	10.0681	−	5.12996i	0.337864	−	0.172150i
$889$	1.14680	−	9.26391i	0.0384623	−	0.310702i
$890$	−0.345601	+	7.32908i	−0.0115846	+	0.245671i
$891$	0.228020	−	0.493532i	0.00763896	−	0.0165339i
$892$	3.40346	+	0.911955i	0.113956	+	0.0305345i
$893$	−0.811326	−	1.00190i	−0.0271500	−	0.0335274i
$894$	9.34329	+	10.3768i	0.312486	+	0.347051i
$895$	−38.4945	−	21.9567i	−1.28673	−	0.733930i
$896$	−1.51539	−	2.16878i	−0.0506256	−	0.0724538i
$897$	32.3780	+	5.12818i	1.08107	+	0.171225i
$898$	−4.04200	+	2.62491i	−0.134883	+	0.0875943i
$899$	−24.5102	+	5.20981i	−0.817461	+	0.173757i
$900$	−8.96742	−	1.80807i	−0.298914	−	0.0602691i
$901$	15.5197	+	8.96030i	0.517036	+	0.298511i
$902$	−13.0935	−	5.23643i	−0.435967	−	0.174354i
$903$	−0.0993060	−	0.399985i	−0.00330470	−	0.0133107i
$904$	−8.16251	+	11.2347i	−0.271481	+	0.373662i
$905$	22.3840	+	2.23413i	0.744070	+	0.0742651i
$906$	3.07063	+	2.76481i	0.102015	+	0.0918546i
$907$	−16.4112	−	42.7525i	−0.544924	−	1.41957i	−0.878906	−	0.476995i	$-0.841726\pi$
$907$	−16.4112	−	42.7525i	−0.544924	−	1.41957i	0.333982	−	0.942579i	$-0.391607\pi$
$908$	−16.4384	+	20.2997i	−0.545527	+	0.673670i
$909$	−2.31118	−	7.11308i	−0.0766569	−	0.235926i
$910$	16.8561	−	13.2852i	0.558776	−	0.440399i
$911$	−11.8540	−	8.61244i	−0.392741	−	0.285343i	0.373837	−	0.927494i	$-0.378042\pi$
$911$	−11.8540	−	8.61244i	−0.392741	−	0.285343i	−0.766578	+	0.642152i	$0.778042\pi$
$912$	−3.43595	+	0.920661i	−0.113776	+	0.0304861i
$913$	−8.92369	+	1.28629i	−0.295331	+	0.0425699i
$914$	23.3662	−	13.4905i	0.772884	−	0.446225i
$915$	−30.5240	+	11.9009i	−1.00909	+	0.393433i
$916$	2.24910	+	0.730777i	0.0743124	+	0.0241456i
$917$	−25.4994	+	47.8429i	−0.842065	+	1.57991i
$918$	−2.76511	+	17.4582i	−0.0912623	+	0.576208i
$919$	−16.6218	+	1.74703i	−0.548304	+	0.0576291i	−0.374631	−	0.927174i	$-0.622230\pi$
$919$	−16.6218	+	1.74703i	−0.548304	+	0.0576291i	−0.173674	+	0.984803i	$0.555564\pi$
$920$	−0.0978663	−	18.6766i	−0.00322656	−	0.615750i
$921$	27.6472	−	5.87659i	0.911005	−	0.193640i
$922$	−11.3759	+	29.6353i	−0.374646	+	0.975987i
$923$	−4.96307	−	4.96307i	−0.163361	−	0.163361i
$924$	7.85680	−	5.32854i	0.258470	−	0.175296i
$925$	40.2386	−	33.2888i	1.32304	−	1.09453i
$926$	−16.0393	+	7.14116i	−0.527084	+	0.234673i
$927$	−14.7767	+	22.7542i	−0.485332	+	0.747345i
$928$	0.149875	+	2.85978i	0.00491988	+	0.0938770i
$929$	−3.43364	−	32.6689i	−0.112654	−	1.07183i	−0.894103	−	0.447861i	$-0.852186\pi$
$929$	−3.43364	−	32.6689i	−0.112654	−	1.07183i	0.781449	−	0.623969i	$-0.214481\pi$
$930$	20.7278	+	4.29243i	0.679690	+	0.140754i
$931$	−16.5246	−	16.0211i	−0.541571	−	0.525070i
$932$	−0.177831	+	0.0906097i	−0.00582506	+	0.00296802i
$933$	4.39971	−	11.4616i	0.144040	−	0.375237i
$934$	−11.2788	−	19.5354i	−0.369053	−	0.639218i
$935$	−1.53054	+	25.0421i	−0.0500540	+	0.818966i
$936$	−5.74806	−	3.31864i	−0.187881	−	0.108473i
$937$	−2.99541	+	0.474426i	−0.0978557	+	0.0154988i	−0.205170	−	0.978726i	$-0.565775\pi$
$937$	−2.99541	+	0.474426i	−0.0978557	+	0.0154988i	0.107315	+	0.994225i	$0.465775\pi$
$938$	27.6936	+	18.7196i	0.904228	+	0.611216i
$939$	2.26813	−	0.736960i	0.0740176	−	0.0240498i
$940$	0.875297	−	0.0504728i	0.0285490	−	0.00164624i
$941$	1.21579	−	2.73071i	0.0396336	−	0.0890186i	−0.892644	−	0.450763i	$-0.851152\pi$
$941$	1.21579	−	2.73071i	0.0396336	−	0.0890186i	0.932277	+	0.361744i	$0.117819\pi$
$942$	18.3367	−	0.960987i	0.597443	−	0.0313107i
$943$	1.85865	−	35.4652i	0.0605260	−	1.15490i
$944$	9.12588	+	6.63034i	0.297022	+	0.215799i
$945$	23.2426	−	20.3784i	0.756080	−	0.662910i
$946$	−0.359294	+	0.314563i	−0.0116817	+	0.0102273i
$947$	25.0412	−	6.70977i	0.813730	−	0.218038i	0.172126	−	0.985075i	$-0.444936\pi$
$947$	25.0412	−	6.70977i	0.813730	−	0.218038i	0.641603	+	0.767037i	$0.278270\pi$
$948$	−13.8942	+	11.2513i	−0.451262	+	0.365425i
$949$	−6.49752	−	30.5684i	−0.210919	−	0.992294i
$950$	−14.5691	+	7.61671i	−0.472685	+	0.247119i
$951$	8.70701	+	11.9842i	0.282344	+	0.388613i
$952$	−5.76009	+	6.85079i	−0.186686	+	0.222036i
$953$	36.2557	+	18.4732i	1.17444	+	0.598405i	0.928664	−	0.370922i	$-0.120958\pi$
$953$	36.2557	+	18.4732i	1.17444	+	0.598405i	0.245773	+	0.969328i	$0.420958\pi$
$954$	−7.20239	+	6.48506i	−0.233186	+	0.209962i
$955$	−23.6651	+	17.3839i	−0.765783	+	0.562528i
$956$	9.07188	+	15.7129i	0.293405	+	0.508193i
$957$	−10.2678	+	0.394857i	−0.331910	+	0.0127639i
$958$	−8.35542	−	8.35542i	−0.269951	−	0.269951i
$959$	−38.3419	+	16.2303i	−1.23812	+	0.524103i
$960$	0.855087	−	2.26295i	0.0275978	−	0.0730364i
$961$	44.5689	+	9.47341i	1.43771	+	0.305594i
$962$	35.3743	−	13.5789i	1.14051	−	0.437802i
$963$	3.19395	−	1.22604i	0.102924	−	0.0395087i
$964$	12.3110	+	2.61679i	0.396511	+	0.0842811i
$965$	−4.99914	+	13.2300i	−0.160928	+	0.425889i
$966$	19.0793	+	14.4070i	0.613868	+	0.463538i
$967$	23.6211	+	23.6211i	0.759602	+	0.759602i	0.976250	−	0.216648i	$-0.0695123\pi$
$967$	23.6211	+	23.6211i	0.759602	+	0.759602i	−0.216648	+	0.976250i	$0.569512\pi$
$968$	−9.65823	−	5.26484i	−0.310427	−	0.169218i
$969$	6.01691	+	10.4216i	0.193291	+	0.334790i
$970$	−5.73968	+	4.21625i	−0.184290	+	0.135376i
$971$	−39.7385	+	35.7807i	−1.27527	+	1.14826i	−0.293960	+	0.955818i	$0.594973\pi$
$971$	−39.7385	+	35.7807i	−1.27527	+	1.14826i	−0.981309	+	0.192439i	$0.938360\pi$
$972$	−13.8083	−	7.03570i	−0.442902	−	0.225670i
$973$	21.6228	−	7.84577i	0.693195	−	0.251524i
$974$	−16.3626	−	22.5211i	−0.524290	−	0.721624i
$975$	18.7258	+	5.86814i	0.599705	+	0.187931i
$976$	2.81574	+	13.2470i	0.0901295	+	0.424026i
$977$	16.8923	−	13.6791i	0.540433	−	0.437634i	−0.319837	−	0.947473i	$-0.603628\pi$
$977$	16.8923	−	13.6791i	0.540433	−	0.437634i	0.860270	+	0.509839i	$0.170295\pi$
$978$	2.54030	−	0.680671i	0.0812298	−	0.0217655i
$979$	−2.41066	+	10.6125i	−0.0770450	+	0.339177i
$980$	15.4057	−	2.76820i	0.492119	−	0.0884268i
$981$	12.3700	+	8.98730i	0.394942	+	0.286942i
$982$	1.82467	−	34.8167i	0.0582275	−	1.11105i
$983$	4.49880	−	0.235772i	0.143490	−	0.00751997i	0.0195441	−	0.999809i	$-0.493779\pi$
$983$	4.49880	−	0.235772i	0.143490	−	0.00751997i	0.123946	+	0.992289i	$0.460445\pi$
$984$	1.87095	−	4.20223i	0.0596438	−	0.133962i
$985$	57.2669	−	3.30222i	1.82467	−	0.105217i
$986$	9.21372	−	2.99372i	0.293425	−	0.0953394i
$987$	−0.628509	+	0.929812i	−0.0200057	+	0.0295962i
$988$	−11.7813	+	1.86597i	−0.374812	+	0.0593644i
$989$	−1.04151	−	0.601313i	−0.0331179	−	0.0191207i
$990$	−12.6246	−	4.97232i	−0.401236	−	0.158031i
$991$	−6.74516	−	11.6830i	−0.214267	−	0.371121i	0.738779	−	0.673948i	$-0.235403\pi$
$991$	−6.74516	−	11.6830i	−0.214267	−	0.371121i	−0.953046	+	0.302827i	$0.902070\pi$
$992$	3.13576	−	8.16894i	0.0995605	−	0.259364i
$993$	4.83282	−	2.46244i	0.153365	−	0.0781433i
$994$	−1.49176	−	4.89669i	−0.0473157	−	0.155313i
$995$	−1.51715	−	0.314180i	−0.0480968	−	0.00996017i
$996$	−0.307411	−	2.92482i	−0.00974070	−	0.0926765i
$997$	−0.544687	−	10.3933i	−0.0172504	−	0.329158i	−0.993600	−	0.112959i	$-0.963967\pi$
$997$	−0.544687	−	10.3933i	−0.0172504	−	0.329158i	0.976349	−	0.216199i	$-0.0693661\pi$
$998$	6.45215	−	9.93544i	0.204239	−	0.314501i
$999$	49.8548	−	22.1968i	1.57734	−	0.702275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.257.16	yes	768
5.3	odd	4	inner	770.2.bv.a.103.9	yes	768
7.3	odd	6	inner	770.2.bv.a.367.33	yes	768
11.3	even	5	inner	770.2.bv.a.47.9	yes	768
35.3	even	12	inner	770.2.bv.a.213.9	yes	768
55.3	odd	20	inner	770.2.bv.a.663.33	yes	768
77.3	odd	30	inner	770.2.bv.a.157.9	yes	768
385.3	even	60	inner	770.2.bv.a.3.16	✓	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.16	✓	768	385.3	even	60	inner
770.2.bv.a.47.9	yes	768	11.3	even	5	inner
770.2.bv.a.103.9	yes	768	5.3	odd	4	inner
770.2.bv.a.157.9	yes	768	77.3	odd	30	inner
770.2.bv.a.213.9	yes	768	35.3	even	12	inner
770.2.bv.a.257.16	yes	768	1.1	even	1	trivial
770.2.bv.a.367.33	yes	768	7.3	odd	6	inner
770.2.bv.a.663.33	yes	768	55.3	odd	20	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933580 - 0.358368i) q^{2} +(0.907325 + 0.589224i) q^{3} +(0.743145 + 0.669131i) q^{4} +(-1.48749 + 1.66954i) q^{5} +(-0.635902 - 0.875244i) q^{6} +(-0.0897121 - 2.64423i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.744156 - 1.67140i) q^{9} +O(q^{10})\)	\(q+(-0.933580 - 0.358368i) q^{2} +(0.907325 + 0.589224i) q^{3} +(0.743145 + 0.669131i) q^{4} +(-1.48749 + 1.66954i) q^{5} +(-0.635902 - 0.875244i) q^{6} +(-0.0897121 - 2.64423i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.744156 - 1.67140i) q^{9} +(1.98700 - 1.02558i) q^{10} +(3.16826 - 0.980879i) q^{11} +(0.280006 + 1.04500i) q^{12} +(0.567508 + 3.58311i) q^{13} +(-0.863854 + 2.50075i) q^{14} +(-2.33337 + 0.638349i) q^{15} +(0.104528 + 0.994522i) q^{16} +(3.15829 - 1.21235i) q^{17} +(0.0957526 + 1.82707i) q^{18} +(2.20010 + 2.44346i) q^{19} +(-2.22256 + 0.245382i) q^{20} +(1.47665 - 2.45204i) q^{21} +(-3.30934 - 0.219674i) q^{22} +(-2.16180 - 8.06795i) q^{23} +(0.113085 - 1.07593i) q^{24} +(-0.574726 - 4.96686i) q^{25} +(0.754256 - 3.54849i) q^{26} +(0.817359 - 5.16060i) q^{27} +(1.70267 - 2.02507i) q^{28} +(-2.72355 + 0.884934i) q^{29} +(2.40715 + 0.240256i) q^{30} +(8.70218 + 0.914636i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.45260 + 0.976839i) q^{33} -3.38298 q^{34} +(4.54809 + 3.78350i) q^{35} +(0.565370 - 1.74003i) q^{36} +(5.68859 + 8.75966i) q^{37} +(-1.17831 - 3.06961i) q^{38} +(-1.59634 + 3.58543i) q^{39} +(2.16288 + 0.567411i) q^{40} +(4.04375 + 1.31389i) q^{41} +(-2.25730 + 1.75999i) q^{42} +(0.101811 - 0.101811i) q^{43} +(3.01081 + 1.39105i) q^{44} +(3.89740 + 1.24380i) q^{45} +(-0.873080 + 8.30680i) q^{46} +(-0.391558 - 0.0205207i) q^{47} +(-0.491155 + 0.963945i) q^{48} +(-6.98390 + 0.474439i) q^{49} +(-1.24341 + 4.84293i) q^{50} +(3.57994 + 0.760940i) q^{51} +(-1.97583 + 3.04250i) q^{52} +(3.33368 + 4.11676i) q^{53} +(-2.61247 + 4.52492i) q^{54} +(-3.07515 + 6.74859i) q^{55} +(-2.31530 + 1.28039i) q^{56} +(0.556463 + 3.51337i) q^{57} +(2.85978 + 0.149875i) q^{58} +(7.54793 - 8.38283i) q^{59} +(-2.16117 - 1.08695i) q^{60} +(13.4688 - 1.41562i) q^{61} +(-7.79641 - 3.97247i) q^{62} +(-4.35281 + 2.11766i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-6.82630 - 4.38237i) q^{65} +(-2.87321 - 2.14926i) q^{66} +(3.26997 - 12.2037i) q^{67} +(3.15829 + 1.21235i) q^{68} +(2.79237 - 8.59404i) q^{69} +(-2.89013 - 5.16209i) q^{70} +(-1.56525 + 1.13722i) q^{71} +(-1.15139 + 1.42185i) q^{72} +(-8.60268 + 0.450847i) q^{73} +(-2.17158 - 10.2165i) q^{74} +(2.40513 - 4.84520i) q^{75} +3.28800i q^{76} +(-2.87790 - 8.28961i) q^{77} +(2.77521 - 2.77521i) q^{78} +(6.72159 + 15.0969i) q^{79} +(-1.81588 - 1.30483i) q^{80} +(0.109684 - 0.121816i) q^{81} +(-3.30431 - 2.67578i) q^{82} +(-2.68493 - 0.425252i) q^{83} +(2.73809 - 0.834150i) q^{84} +(-2.67386 + 7.07625i) q^{85} +(-0.131535 + 0.0585632i) q^{86} +(-2.99257 - 0.801856i) q^{87} +(-2.31233 - 2.37763i) q^{88} +(-1.64065 + 2.84169i) q^{89} +(-3.19280 - 2.55789i) q^{90} +(9.42364 - 1.82207i) q^{91} +(3.79198 - 7.44218i) q^{92} +(7.35678 + 5.95741i) q^{93} +(0.358197 + 0.159479i) q^{94} +(-7.35210 + 0.0385253i) q^{95} +(0.803979 - 0.723906i) q^{96} +(-3.14577 + 0.498242i) q^{97} +(6.69006 + 2.05988i) q^{98} +(-3.99712 - 4.56551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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