LMFDB - Embedded newform 966.2.bf.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(11,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 44, 27]))

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

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

chi := DirichletCharacter("966.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bf (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	966.11
Dual form			966.2.bf.a.527.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458227 + 0.888835i) q^{2} +(-1.59740 - 0.669558i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.48546 - 1.41639i) q^{5} +(1.32710 - 1.11302i) q^{6} +(0.598705 - 2.57712i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.10338 + 2.13911i) q^{9} +O(q^{10})$	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.59740 - 0.669558i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.48546 - 1.41639i) q^{5} +(1.32710 - 1.11302i) q^{6} +(0.598705 - 2.57712i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.10338 + 2.13911i) q^{9} +(1.93961 - 0.671307i) q^{10} +(-0.101677 + 0.0524182i) q^{11} +(0.381178 + 1.68959i) q^{12} +(1.76736 - 2.03964i) q^{13} +(2.01629 + 1.71306i) q^{14} +(1.42453 + 3.25714i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(3.84698 + 0.367342i) q^{17} +(-2.86514 + 0.889366i) q^{18} +(-0.472034 - 4.94337i) q^{19} +(-0.292101 + 2.03161i) q^{20} +(-2.68191 + 3.71583i) q^{21} -0.114394i q^{22} +(0.121496 + 4.79429i) q^{23} +(-1.67643 - 0.435409i) q^{24} +(-0.0374589 - 0.786358i) q^{25} +(1.00305 + 2.50551i) q^{26} +(-1.92769 - 4.82535i) q^{27} +(-2.44654 + 1.00719i) q^{28} +(-0.316072 + 0.144345i) q^{29} +(-3.54782 - 0.226338i) q^{30} +(-0.261068 - 0.104516i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(0.197516 - 0.0156541i) q^{33} +(-2.08930 + 3.25101i) q^{34} +(-4.53955 + 2.98022i) q^{35} +(0.522383 - 2.95417i) q^{36} +(-0.890439 + 0.216018i) q^{37} +(4.61014 + 1.84562i) q^{38} +(-4.18884 + 2.07478i) q^{39} +(-1.67192 - 1.19057i) q^{40} +(-1.51114 - 5.14647i) q^{41} +(-2.07384 - 4.08646i) q^{42} +(-10.2263 - 1.47031i) q^{43} +(0.101677 + 0.0524182i) q^{44} +(-0.0946959 - 6.15677i) q^{45} +(-4.31701 - 2.08888i) q^{46} +(-5.26560 + 3.04009i) q^{47} +(1.15519 - 1.29055i) q^{48} +(-6.28310 - 3.08587i) q^{49} +(0.716108 + 0.327035i) q^{50} +(-5.89922 - 3.16257i) q^{51} +(-2.68661 - 0.256540i) q^{52} +(0.533719 - 0.102866i) q^{53} +(5.17226 + 0.497705i) q^{54} +(0.225282 + 0.0661488i) q^{55} +(0.225848 - 2.63609i) q^{56} +(-2.55585 + 8.21260i) q^{57} +(0.0165334 - 0.347079i) q^{58} +(4.41573 - 1.52830i) q^{59} +(1.82688 - 3.04971i) q^{60} +(-2.40678 - 3.06047i) q^{61} +(0.212525 - 0.184154i) q^{62} +(6.77204 - 4.13998i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-5.51427 + 0.526549i) q^{65} +(-0.0765932 + 0.182733i) q^{66} +(-1.03280 + 0.0491981i) q^{67} +(-1.93224 - 3.34674i) q^{68} +(3.01598 - 7.73976i) q^{69} +(-0.568782 - 5.40053i) q^{70} +(-2.76089 - 4.29603i) q^{71} +(2.38640 + 1.81799i) q^{72} +(1.74464 + 2.45001i) q^{73} +(0.216018 - 0.890439i) q^{74} +(-0.466676 + 1.28121i) q^{75} +(-3.75294 + 3.25194i) q^{76} +(0.0742134 + 0.293417i) q^{77} +(0.0753039 - 4.67391i) q^{78} +(0.913684 - 4.74064i) q^{79} +(1.82433 - 0.940509i) q^{80} +(-0.151560 + 8.99872i) q^{81} +(5.26681 + 1.01509i) q^{82} +(-14.7165 - 4.32114i) q^{83} +(4.58248 + 0.0292232i) q^{84} +(-5.19425 - 5.99449i) q^{85} +(5.99281 - 8.41572i) q^{86} +(0.601542 - 0.0189486i) q^{87} +(-0.0931823 + 0.0663548i) q^{88} +(0.205529 - 0.0822812i) q^{89} +(5.51575 + 2.73703i) q^{90} +(-4.19828 - 5.77584i) q^{91} +(3.83484 - 2.87993i) q^{92} +(0.347051 + 0.341754i) q^{93} +(-0.289307 - 6.07330i) q^{94} +(-6.30053 + 8.01177i) q^{95} +(0.617751 + 1.61814i) q^{96} +(2.09794 + 7.14493i) q^{97} +(5.62192 - 4.17062i) q^{98} +(-0.325994 - 0.107243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$3$	−1.59740	−	0.669558i	−0.922260	−	0.386570i
$3$	−1.59740	−	0.669558i	−0.922260	−	0.386570i
$4$	−0.580057	−	0.814576i	−0.290028	−	0.407288i
$5$	−1.48546	−	1.41639i	−0.664319	−	0.633427i	0.280948	−	0.959723i	$-0.409351\pi$
$5$	−1.48546	−	1.41639i	−0.664319	−	0.633427i	−0.945268	+	0.326296i	$0.894199\pi$
$6$	1.32710	−	1.11302i	0.541786	−	0.454388i
$7$	0.598705	−	2.57712i	0.226289	−	0.974060i
$7$	0.598705	−	2.57712i	0.226289	−	0.974060i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	2.10338	+	2.13911i	0.701128	+	0.713036i
$10$	1.93961	−	0.671307i	0.613359	−	0.212286i
$11$	−0.101677	+	0.0524182i	−0.0306568	+	0.0158047i	−0.473487	−	0.880801i	$-0.657005\pi$
$11$	−0.101677	+	0.0524182i	−0.0306568	+	0.0158047i	0.442830	+	0.896606i	$0.353975\pi$
$12$	0.381178	+	1.68959i	0.110036	+	0.487742i
$13$	1.76736	−	2.03964i	0.490177	−	0.565695i	−0.455736	−	0.890115i	$-0.650624\pi$
$13$	1.76736	−	2.03964i	0.490177	−	0.565695i	0.945913	+	0.324420i	$0.105169\pi$
$14$	2.01629	+	1.71306i	0.538877	+	0.457833i
$15$	1.42453	+	3.25714i	0.367811	+	0.840990i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	3.84698	+	0.367342i	0.933030	+	0.0890936i	0.550487	−	0.834844i	$-0.314442\pi$
$17$	3.84698	+	0.367342i	0.933030	+	0.0890936i	0.382544	+	0.923937i	$0.375048\pi$
$18$	−2.86514	+	0.889366i	−0.675320	+	0.209626i
$19$	−0.472034	−	4.94337i	−0.108292	−	1.13409i	−0.872331	−	0.488916i	$-0.837392\pi$
$19$	−0.472034	−	4.94337i	−0.108292	−	1.13409i	0.764039	−	0.645170i	$-0.223214\pi$
$20$	−0.292101	+	2.03161i	−0.0653158	+	0.454281i
$21$	−2.68191	+	3.71583i	−0.585240	+	0.810860i
$22$		−	0.114394i		−	0.0243888i
$23$	0.121496	+	4.79429i	0.0253337	+	0.999679i
$23$	0.121496	+	4.79429i	0.0253337	+	0.999679i
$24$	−1.67643	−	0.435409i	−0.342200	−	0.0888776i
$25$	−0.0374589	−	0.786358i	−0.00749177	−	0.157272i
$26$	1.00305	+	2.50551i	0.196715	+	0.491371i
$27$	−1.92769	−	4.82535i	−0.370984	−	0.928639i
$28$	−2.44654	+	1.00719i	−0.462353	+	0.190340i
$29$	−0.316072	+	0.144345i	−0.0586931	+	0.0268042i	−0.444545	−	0.895756i	$-0.646635\pi$
$29$	−0.316072	+	0.144345i	−0.0586931	+	0.0268042i	0.385852	+	0.922561i	$0.373907\pi$
$30$	−3.54782	−	0.226338i	−0.647740	−	0.0413235i
$31$	−0.261068	−	0.104516i	−0.0468891	−	0.0187716i	0.348099	−	0.937458i	$-0.386827\pi$
$31$	−0.261068	−	0.104516i	−0.0468891	−	0.0187716i	−0.394988	+	0.918686i	$0.629251\pi$
$32$	−0.690079	−	0.723734i	−0.121990	−	0.127939i
$33$	0.197516	−	0.0156541i	0.0343832	−	0.00272503i
$34$	−2.08930	+	3.25101i	−0.358311	+	0.557543i
$35$	−4.53955	+	2.98022i	−0.767324	+	0.503749i
$36$	0.522383	−	2.95417i	0.0870639	−	0.492362i
$37$	−0.890439	+	0.216018i	−0.146387	+	0.0355132i	−0.308283	−	0.951295i	$-0.599754\pi$
$37$	−0.890439	+	0.216018i	−0.146387	+	0.0355132i	0.161896	+	0.986808i	$0.448239\pi$
$38$	4.61014	+	1.84562i	0.747863	+	0.299399i
$39$	−4.18884	+	2.07478i	−0.670751	+	0.332230i
$40$	−1.67192	−	1.19057i	−0.264353	−	0.188245i
$41$	−1.51114	−	5.14647i	−0.236000	−	0.803743i	−0.989279	−	0.146041i	$-0.953347\pi$
$41$	−1.51114	−	5.14647i	−0.236000	−	0.803743i	0.753278	−	0.657702i	$-0.228471\pi$
$42$	−2.07384	−	4.08646i	−0.320001	−	0.630555i
$43$	−10.2263	−	1.47031i	−1.55949	−	0.224221i	−0.692082	−	0.721819i	$-0.743306\pi$
$43$	−10.2263	−	1.47031i	−1.55949	−	0.224221i	−0.867408	+	0.497598i	$0.834216\pi$
$44$	0.101677	+	0.0524182i	0.0153284	+	0.00790234i
$45$	−0.0946959	−	6.15677i	−0.0141164	−	0.917797i
$46$	−4.31701	−	2.08888i	−0.636508	−	0.307989i
$47$	−5.26560	+	3.04009i	−0.768066	+	0.443443i	−0.832184	−	0.554499i	$-0.812910\pi$
$47$	−5.26560	+	3.04009i	−0.768066	+	0.443443i	0.0641183	+	0.997942i	$0.479577\pi$
$48$	1.15519	−	1.29055i	0.166738	−	0.186276i
$49$	−6.28310	−	3.08587i	−0.897586	−	0.440839i
$50$	0.716108	+	0.327035i	0.101273	+	0.0462498i
$51$	−5.89922	−	3.16257i	−0.826056	−	0.442849i
$52$	−2.68661	−	0.256540i	−0.372566	−	0.0355757i
$53$	0.533719	−	0.102866i	0.0733119	−	0.0141297i	−0.152463	−	0.988309i	$-0.548721\pi$
$53$	0.533719	−	0.102866i	0.0733119	−	0.0141297i	0.225775	+	0.974179i	$0.427508\pi$
$54$	5.17226	+	0.497705i	0.703856	+	0.0677290i
$55$	0.225282	+	0.0661488i	0.0303770	+	0.00891950i
$56$	0.225848	−	2.63609i	0.0301803	−	0.352263i
$57$	−2.55585	+	8.21260i	−0.338530	+	1.08779i
$58$	0.0165334	−	0.347079i	0.00217094	−	0.0455737i
$59$	4.41573	−	1.52830i	0.574879	−	0.198968i	−0.0241312	−	0.999709i	$-0.507682\pi$
$59$	4.41573	−	1.52830i	0.574879	−	0.198968i	0.599011	+	0.800741i	$0.295561\pi$
$60$	1.82688	−	3.04971i	0.235849	−	0.393716i
$61$	−2.40678	−	3.06047i	−0.308156	−	0.391853i	0.607166	−	0.794575i	$-0.292306\pi$
$61$	−2.40678	−	3.06047i	−0.308156	−	0.391853i	−0.915322	+	0.402722i	$0.868064\pi$
$62$	0.212525	−	0.184154i	0.0269908	−	0.0233876i
$63$	6.77204	−	4.13998i	0.853197	−	0.521588i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−5.51427	+	0.526549i	−0.683960	+	0.0653103i
$66$	−0.0765932	+	0.182733i	−0.00942797	+	0.0224928i
$67$	−1.03280	+	0.0491981i	−0.126176	+	0.00601051i	−0.110575	−	0.993868i	$-0.535269\pi$
$67$	−1.03280	+	0.0491981i	−0.126176	+	0.00601051i	−0.0156011	+	0.999878i	$0.504966\pi$
$68$	−1.93224	−	3.34674i	−0.234319	−	0.405852i
$69$	3.01598	−	7.73976i	0.363081	−	0.931757i
$70$	−0.568782	−	5.40053i	−0.0679825	−	0.645487i
$71$	−2.76089	−	4.29603i	−0.327657	−	0.509845i	0.637871	−	0.770143i	$-0.279815\pi$
$71$	−2.76089	−	4.29603i	−0.327657	−	0.509845i	−0.965528	+	0.260299i	$0.916179\pi$
$72$	2.38640	+	1.81799i	0.281240	+	0.214252i
$73$	1.74464	+	2.45001i	0.204195	+	0.286752i	0.903956	−	0.427625i	$-0.140650\pi$
$73$	1.74464	+	2.45001i	0.204195	+	0.286752i	−0.699761	+	0.714377i	$0.746710\pi$
$74$	0.216018	−	0.890439i	0.0251116	−	0.103511i
$75$	−0.466676	+	1.28121i	−0.0538871	+	0.147941i
$76$	−3.75294	+	3.25194i	−0.430492	+	0.373023i
$77$	0.0742134	+	0.293417i	0.00845741	+	0.0334380i
$78$	0.0753039	−	4.67391i	0.00852649	−	0.529216i
$79$	0.913684	−	4.74064i	0.102797	−	0.533364i	−0.893622	−	0.448820i	$-0.851845\pi$
$79$	0.913684	−	4.74064i	0.102797	−	0.533364i	0.996420	−	0.0845441i	$-0.0269434\pi$
$80$	1.82433	−	0.940509i	0.203967	−	0.105152i
$81$	−0.151560	+	8.99872i	−0.0168400	+	0.999858i
$82$	5.26681	+	1.01509i	0.581621	+	0.112098i
$83$	−14.7165	−	4.32114i	−1.61534	−	0.474307i	−0.655581	−	0.755125i	$-0.727576\pi$
$83$	−14.7165	−	4.32114i	−1.61534	−	0.474307i	−0.959761	+	0.280818i	$0.909394\pi$
$84$	4.58248	+	0.0292232i	0.499990	+	0.00318851i
$85$	−5.19425	−	5.99449i	−0.563396	−	0.650193i
$86$	5.99281	−	8.41572i	0.646221	−	0.907491i
$87$	0.601542	−	0.0189486i	0.0644920	−	0.00203151i
$88$	−0.0931823	+	0.0663548i	−0.00993327	+	0.00707345i
$89$	0.205529	−	0.0822812i	0.0217860	−	0.00872179i	−0.360744	−	0.932665i	$-0.617477\pi$
$89$	0.205529	−	0.0822812i	0.0217860	−	0.00872179i	0.382530	+	0.923943i	$0.375053\pi$
$90$	5.51575	+	2.73703i	0.581411	+	0.288508i
$91$	−4.19828	−	5.77584i	−0.440099	−	0.605473i
$92$	3.83484	−	2.87993i	0.399810	−	0.300253i
$93$	0.347051	+	0.341754i	0.0359875	+	0.0354382i
$94$	−0.289307	−	6.07330i	−0.0298397	−	0.626413i
$95$	−6.30053	+	8.01177i	−0.646421	+	0.821991i
$96$	0.617751	+	1.61814i	0.0630489	+	0.165151i
$97$	2.09794	+	7.14493i	0.213013	+	0.725457i	0.994794	+	0.101904i	$0.0324934\pi$
$97$	2.09794	+	7.14493i	0.213013	+	0.725457i	−0.781781	+	0.623553i	$0.785688\pi$
$98$	5.62192	−	4.17062i	0.567899	−	0.421296i
$99$	−0.325994	−	0.107243i	−0.0327636	−	0.0107783i
$100$	−0.618820	+	0.486646i	−0.0618820	+	0.0486646i
$101$	3.41770	+	3.58438i	0.340074	+	0.356660i	0.871457	−	0.490472i	$-0.163176\pi$
$101$	3.41770	+	3.58438i	0.340074	+	0.356660i	−0.531382	+	0.847132i	$0.678327\pi$
$102$	5.51419	−	3.79426i	0.545986	−	0.375688i
$103$	10.8810	+	0.518327i	1.07214	+	0.0510723i	0.576219	−	0.817296i	$-0.304528\pi$
$103$	10.8810	+	0.518327i	1.07214	+	0.0510723i	0.495921	+	0.868368i	$0.334831\pi$
$104$	1.45910	−	2.27040i	0.143076	−	0.222631i
$105$	9.24692	−	1.72111i	0.902407	−	0.167963i
$106$	−0.153133	+	0.521524i	−0.0148736	+	0.0506549i
$107$	−2.28303	+	1.79540i	−0.220709	+	0.173568i	−0.722391	−	0.691484i	$-0.756957\pi$
$107$	−2.28303	+	1.79540i	−0.220709	+	0.173568i	0.501682	+	0.865052i	$0.332715\pi$
$108$	−2.81245	+	4.36923i	−0.270628	+	0.420429i
$109$	0.223141	−	2.33684i	0.0213731	−	0.223829i	−0.978474	−	0.206368i	$-0.933836\pi$
$109$	0.223141	−	2.33684i	0.0213731	−	0.223829i	0.999848	−	0.0174610i	$-0.00555828\pi$
$110$	−0.162026	+	0.169927i	−0.0154485	+	0.0162020i
$111$	1.56703	+	0.251133i	0.148736	+	0.0238365i
$112$	2.23956	+	1.40867i	0.211619	+	0.133107i
$113$	3.17919	−	2.04314i	0.299073	−	0.192203i	−0.382494	−	0.923958i	$-0.624935\pi$
$113$	3.17919	−	2.04314i	0.299073	−	0.192203i	0.681568	+	0.731755i	$0.261299\pi$
$114$	−6.12849	−	6.03496i	−0.573986	−	0.565225i
$115$	6.61009	−	7.29383i	0.616394	−	0.680153i
$116$	0.300920	+	0.173736i	0.0279397	+	0.0161310i
$117$	8.08044	−	0.509576i	0.747037	−	0.0471103i
$118$	−0.664999	+	4.62517i	−0.0612181	+	0.425781i
$119$	3.24989	−	9.69421i	0.297917	−	0.888667i
$120$	1.87357	+	3.02126i	0.171033	+	0.275802i
$121$	−6.37304	+	8.94968i	−0.579367	+	0.813607i
$122$	3.82310	−	0.736842i	0.346127	−	0.0667106i
$123$	−1.03196	+	9.23277i	−0.0930491	+	0.832491i
$124$	0.0662981	+	0.273285i	0.00595375	+	0.0245417i
$125$	−7.77865	+	8.97704i	−0.695743	+	0.802931i
$126$	0.576630	+	7.91628i	0.0513702	+	0.705238i
$127$	−16.4339	−	10.5614i	−1.45828	−	0.937177i	−0.998799	−	0.0489870i	$-0.984401\pi$
$127$	−16.4339	−	10.5614i	−1.45828	−	0.937177i	−0.459476	−	0.888190i	$-0.651963\pi$
$128$	−0.189251	+	0.981929i	−0.0167276	+	0.0867911i
$129$	15.3510	+	9.19576i	1.35158	+	0.809642i
$130$	2.05877	−	5.14255i	0.180566	−	0.451032i
$131$	−2.03403	−	0.703984i	−0.177714	−	0.0615073i	0.236762	−	0.971568i	$-0.423914\pi$
$131$	−2.03403	−	0.703984i	−0.177714	−	0.0615073i	−0.414476	+	0.910060i	$0.636035\pi$
$132$	−0.127322	−	0.151812i	−0.0110820	−	0.0132135i
$133$	−13.0223	−	1.74313i	−1.12917	−	0.151148i
$134$	0.429525	−	0.940529i	0.0371053	−	0.0812494i
$135$	−3.97105	+	9.89823i	−0.341773	+	0.851904i
$136$	3.86010	−	0.183879i	0.331001	−	0.0157675i
$137$	−6.22793	+	10.7871i	−0.532088	+	0.921603i	0.467210	+	0.884146i	$0.345259\pi$
$137$	−6.22793	+	10.7871i	−0.532088	+	0.921603i	−0.999298	+	0.0374572i	$0.988074\pi$
$138$	5.49737	+	6.22727i	0.467967	+	0.530101i
$139$	2.30542			0.195543			0.0977717	−	0.995209i	$-0.468829\pi$
$139$	2.30542			0.195543			0.0977717	+	0.995209i	$0.468829\pi$
$140$	5.06081	+	1.96911i	0.427717	+	0.166420i
$141$	10.4468	−	1.33063i	0.879778	−	0.112059i
$142$	5.08357	−	0.485422i	0.426604	−	0.0407358i
$143$	−0.0727857	+	0.300027i	−0.00608664	+	0.0250895i
$144$	−2.70941	+	1.28807i	−0.225784	+	0.107339i
$145$	0.673962	+	0.233261i	0.0559695	+	0.0193712i
$146$	−2.97709	+	0.428042i	−0.246386	+	0.0354250i
$147$	7.97047	+	9.13628i	0.657393	+	0.753548i
$148$	0.692469	+	0.600028i	0.0569206	+	0.0493220i
$149$	0.466250	−	9.78780i	0.0381967	−	0.801848i	−0.895776	−	0.444505i	$-0.853380\pi$
$149$	0.466250	−	9.78780i	0.0381967	−	0.801848i	0.933973	−	0.357343i	$-0.116317\pi$
$150$	−0.924942	−	1.00188i	−0.0755212	−	0.0818034i
$151$	3.90992	+	11.2970i	0.318184	+	0.919334i	0.984763	+	0.173899i	$0.0556367\pi$
$151$	3.90992	+	11.2970i	0.318184	+	0.919334i	−0.666579	+	0.745434i	$0.732242\pi$
$152$	−1.17074	−	4.82587i	−0.0949599	−	0.391430i
$153$	7.30589	+	9.00177i	0.590647	+	0.727750i
$154$	−0.294806	−	0.0684880i	−0.0237562	−	0.00551892i
$155$	0.239772	+	0.525027i	0.0192589	+	0.0421712i
$156$	4.11983	+	2.20864i	0.329850	+	0.176833i
$157$	16.7774	−	11.9471i	1.33898	−	0.953483i	0.339060	−	0.940765i	$-0.389891\pi$
$157$	16.7774	−	11.9471i	1.33898	−	0.953483i	0.999919	−	0.0127181i	$-0.00404842\pi$
$158$	3.79498	+	2.98440i	0.301912	+	0.237426i
$159$	−0.921437	−	0.193038i	−0.0730747	−	0.0153089i
$160$			2.05250i			0.162264i
$161$	12.4282	+	2.55726i	0.979480	+	0.201540i
$162$	−7.92894	−	4.25817i	−0.622956	−	0.334553i
$163$	1.21075	+	0.624187i	0.0948335	+	0.0488901i	0.504991	−	0.863125i	$-0.331496\pi$
$163$	1.21075	+	0.624187i	0.0948335	+	0.0488901i	−0.410157	+	0.912015i	$0.634526\pi$
$164$	−3.31564	+	4.21618i	−0.258908	+	0.329228i
$165$	−0.315575	−	0.256506i	−0.0245675	−	0.0199689i
$166$	10.5843	−	11.1005i	0.821498	−	0.861562i
$167$	−19.7825	+	9.03438i	−1.53082	+	0.699101i	−0.989873	−	0.141956i	$-0.954661\pi$
$167$	−19.7825	+	9.03438i	−1.53082	+	0.699101i	−0.540945	+	0.841058i	$0.681933\pi$
$168$	−2.12579	+	4.05968i	−0.164008	+	0.313211i
$169$	0.813515	+	5.65812i	0.0625781	+	0.435240i
$170$	7.70826	−	1.87000i	0.591196	−	0.143423i
$171$	9.58153	−	11.4075i	0.732718	−	0.872356i
$172$	4.73413	+	9.18293i	0.360974	+	0.700192i
$173$	−17.5874	−	0.837793i	−1.33715	−	0.0636962i	−0.633223	−	0.773970i	$-0.718268\pi$
$173$	−17.5874	−	0.837793i	−1.33715	−	0.0636962i	−0.703926	+	0.710273i	$0.748571\pi$
$174$	−0.258800	+	0.543354i	−0.0196196	+	0.0411916i
$175$	−2.04897	−	0.374260i	−0.154887	−	0.0282914i
$176$	−0.0162799	−	0.113229i	−0.00122714	−	0.00853498i
$177$	−8.07698	−	0.515282i	−0.607103	−	0.0387310i
$178$	−0.0210442	+	0.220385i	−0.00157733	+	0.0165185i
$179$	−6.48413	−	1.57303i	−0.484647	−	0.117574i	−0.0140113	−	0.999902i	$-0.504460\pi$
$179$	−6.48413	−	1.57303i	−0.484647	−	0.117574i	−0.470635	+	0.882328i	$0.655975\pi$
$180$	−4.96023	+	3.64841i	−0.369713	+	0.271937i
$181$	−0.560572	−	0.0805980i	−0.0416670	−	0.00599080i	0.121450	−	0.992598i	$-0.461246\pi$
$181$	−0.560572	−	0.0805980i	−0.0416670	−	0.00599080i	−0.163117	+	0.986607i	$0.552155\pi$
$182$	7.05753	−	1.08493i	0.523139	−	0.0804205i
$183$	1.79543	+	6.50027i	0.132722	+	0.480514i
$184$	0.802558	+	4.72820i	0.0591654	+	0.348568i
$185$	1.62868	+	0.940319i	0.119743	+	0.0691336i
$186$	−0.462791	+	0.151870i	−0.0339335	+	0.0111357i
$187$	−0.410406	+	0.164302i	−0.0300118	+	0.0120149i
$188$	5.53073	+	2.52580i	0.403370	+	0.184213i
$189$	−13.5896	+	2.07893i	−0.988500	+	0.151220i
$190$	−4.23408	−	9.27134i	−0.307172	−	0.672614i
$191$	−5.58372	+	16.1331i	−0.404024	+	1.16735i	0.541191	+	0.840900i	$0.317974\pi$
$191$	−5.58372	+	16.1331i	−0.404024	+	1.16735i	−0.945214	+	0.326450i	$0.894148\pi$
$192$	−1.72133	−	0.192397i	−0.124226	−	0.0138850i
$193$	14.3147	−	13.6491i	1.03040	−	0.982480i	0.0305409	−	0.999534i	$-0.490277\pi$
$193$	14.3147	−	13.6491i	1.03040	−	0.982480i	0.999855	+	0.0170534i	$0.00542853\pi$
$194$	−7.31199	−	1.40927i	−0.524971	−	0.101180i
$195$	9.16105	+	2.85101i	0.656037	+	0.204165i
$196$	1.13088	+	6.90805i	0.0807774	+	0.493432i
$197$	−3.69992	−	3.20600i	−0.263608	−	0.228418i	0.513020	−	0.858376i	$-0.328526\pi$
$197$	−3.69992	−	3.20600i	−0.263608	−	0.228418i	−0.776629	+	0.629958i	$0.783072\pi$
$198$	0.244700	−	0.240614i	0.0173901	−	0.0170997i
$199$	10.3503	−	25.8537i	0.733712	−	1.83272i	0.218032	−	0.975942i	$-0.430036\pi$
$199$	10.3503	−	25.8537i	0.733712	−	1.83272i	0.515679	−	0.856782i	$-0.327540\pi$
$200$	−0.148988	−	0.773023i	−0.0105350	−	0.0546610i
$201$	1.68273	+	0.612928i	0.118691	+	0.0432326i
$202$	−4.75201	+	1.39532i	−0.334350	+	0.0981741i
$203$	0.182761	+	0.900976i	0.0128273	+	0.0632361i
$204$	0.845727	+	6.63983i	0.0592127	+	0.464881i
$205$	−5.04464	+	9.78524i	−0.352333	+	0.683431i
$206$	−5.44668	+	9.43393i	−0.379488	+	0.657293i
$207$	−9.99995	+	10.3441i	−0.695045	+	0.718966i
$208$	1.34942	+	2.33726i	0.0935652	+	0.162060i
$209$	0.307118	+	0.477884i	0.0212438	+	0.0330559i
$210$	−2.70740	+	9.00765i	−0.186828	+	0.621587i
$211$	−1.21696	+	2.66477i	−0.0837790	+	0.183450i	−0.946885	−	0.321572i	$-0.895789\pi$
$211$	−1.21696	+	2.66477i	−0.0837790	+	0.183450i	0.863106	+	0.505023i	$0.168516\pi$
$212$	−0.393379	−	0.375086i	−0.0270174	−	0.0257610i
$213$	1.53381	+	8.71106i	0.105095	+	0.596872i
$214$	−0.549666	−	2.85194i	−0.0375744	−	0.194954i
$215$	13.1082	+	16.6684i	0.893972	+	1.13678i
$216$	−2.59479	−	4.50190i	−0.176553	−	0.306315i
$217$	−0.425652	+	0.610229i	−0.0288952	+	0.0414250i
$218$	1.97482	+	1.26914i	0.133752	+	0.0859569i
$219$	−1.14647	−	5.08179i	−0.0774713	−	0.343395i
$220$	−0.0767932	−	0.221879i	−0.00517740	−	0.0149591i
$221$	7.54825	−	7.19724i	0.507750	−	0.484139i
$222$	−0.941269	+	1.27775i	−0.0631738	+	0.0857571i
$223$	1.74091	+	2.00912i	0.116580	+	0.134541i	0.811040	−	0.584991i	$-0.198902\pi$
$223$	1.74091	+	2.00912i	0.116580	+	0.134541i	−0.694460	+	0.719532i	$0.744356\pi$
$224$	−2.27830	+	1.34511i	−0.152226	+	0.0898742i
$225$	1.60331	−	1.73414i	0.106888	−	0.115609i
$226$	0.359228	+	3.76200i	0.0238955	+	0.250245i
$227$	−22.4903	−	17.6866i	−1.49274	−	1.17390i	−0.940301	−	0.340345i	$-0.889456\pi$
$227$	−22.4903	−	17.6866i	−1.49274	−	1.17390i	−0.552436	−	0.833556i	$-0.686301\pi$
$228$	8.17232	−	2.68184i	0.541225	−	0.177609i
$229$	18.5028	−	10.6826i	1.22270	−	0.705925i	0.257206	−	0.966357i	$-0.417198\pi$
$229$	18.5028	−	10.6826i	1.22270	−	0.705925i	0.965492	+	0.260431i	$0.0838647\pi$
$230$	3.45409	+	9.21751i	0.227756	+	0.607785i
$231$	0.0779113	−	0.518395i	0.00512619	−	0.0341079i
$232$	−0.292312	+	0.187858i	−0.0191913	+	0.0123335i
$233$	7.00532	+	17.4984i	0.458934	+	1.14636i	0.959762	+	0.280815i	$0.0906046\pi$
$233$	7.00532	+	17.4984i	0.458934	+	1.14636i	−0.500828	+	0.865547i	$0.666971\pi$
$234$	−3.24974	+	7.41569i	−0.212442	+	0.484779i
$235$	12.1278	+	2.94217i	0.791130	+	0.191926i
$236$	−3.80629	−	2.71045i	−0.247768	−	0.176435i
$237$	−4.63366	+	6.96094i	−0.300988	+	0.452162i
$238$	7.12737	+	7.33077i	0.461999	+	0.475183i
$239$	4.34822	−	14.8087i	0.281263	−	0.957893i	−0.690775	−	0.723069i	$-0.742731\pi$
$239$	4.34822	−	14.8087i	0.281263	−	0.957893i	0.972038	−	0.234823i	$-0.0754511\pi$
$240$	−3.54392	+	0.280873i	−0.228759	+	0.0181303i
$241$	11.7879	+	22.8654i	0.759326	+	1.47289i	0.877337	+	0.479875i	$0.159318\pi$
$241$	11.7879	+	22.8654i	0.759326	+	1.47289i	−0.118011	+	0.993012i	$0.537652\pi$
$242$	−5.03450	−	9.76556i	−0.323630	−	0.627754i
$243$	6.26727	−	14.2731i	0.402046	−	0.915620i
$244$	−1.09691	+	3.73575i	−0.0702228	+	0.239157i
$245$	4.96254	+	13.4832i	0.317045	+	0.861413i
$246$	−7.73354	−	5.14795i	−0.493072	−	0.328221i
$247$	−10.9170	−	7.77393i	−0.694629	−	0.494643i
$248$	−0.273285	−	0.0662981i	−0.0173536	−	0.00420993i
$249$	20.6148	+	16.7561i	1.30641	+	1.06188i
$250$	−4.41473	−	11.0275i	−0.279212	−	0.697437i
$251$	24.4198	−	15.6937i	1.54137	−	0.990576i	0.553929	−	0.832564i	$-0.313128\pi$
$251$	24.4198	−	15.6937i	1.54137	−	0.990576i	0.987437	−	0.158013i	$-0.0505086\pi$
$252$	−7.30050	−	3.11492i	−0.459888	−	0.196222i
$253$	−0.263661	−	0.481101i	−0.0165763	−	0.0302466i
$254$	16.9179	−	9.76753i	1.06152	−	0.612869i
$255$	4.28365	+	13.0535i	0.268252	+	0.817439i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	−0.654134	−	6.85040i	−0.0408038	−	0.427316i	−0.992675	−	0.120817i	$-0.961448\pi$
$257$	−0.654134	−	6.85040i	−0.0408038	−	0.427316i	0.951871	−	0.306499i	$-0.0991576\pi$
$258$	−15.2077	+	9.43075i	−0.946793	+	0.587133i
$259$	0.0235948	+	2.42410i	0.00146611	+	0.150626i
$260$	3.62750	+	4.18636i	0.224968	+	0.259627i
$261$	−0.973591	−	0.372499i	−0.0602638	−	0.0230571i
$262$	1.55777	−	1.48533i	0.0962394	−	0.0917641i
$263$	−0.419588	−	1.21232i	−0.0258729	−	0.0747548i	0.931325	−	0.364189i	$-0.118654\pi$
$263$	−0.419588	−	1.21232i	−0.0258729	−	0.0747548i	−0.957198	+	0.289435i	$0.906533\pi$
$264$	0.193278	−	0.0436043i	0.0118954	−	0.00268366i
$265$	−0.938517	−	0.603148i	−0.0576526	−	0.0370511i
$266$	7.51650	−	10.7759i	0.460866	−	0.660713i
$267$	−0.383404	−	0.00617723i	−0.0234639	−	0.000378040i
$268$	0.639156	+	0.812753i	0.0390427	+	0.0496468i
$269$	3.48452	+	18.0794i	0.212455	+	1.10232i	0.918881	+	0.394534i	$0.129094\pi$
$269$	3.48452	+	18.0794i	0.212455	+	1.10232i	−0.706426	+	0.707787i	$0.749694\pi$
$270$	−6.97826	−	8.06524i	−0.424683	−	0.490835i
$271$	−14.7977	−	14.1096i	−0.898896	−	0.857096i	0.0914359	−	0.995811i	$-0.470854\pi$
$271$	−14.7977	−	14.1096i	−0.898896	−	0.857096i	−0.990332	+	0.138715i	$0.955703\pi$
$272$	−1.60536	+	3.51526i	−0.0973395	+	0.213144i
$273$	2.83907	+	12.0373i	0.171828	+	0.728532i
$274$	−6.73415	−	10.4785i	−0.406825	−	0.633032i
$275$	0.0450282	+	0.0779911i	0.00271530	+	0.00470304i
$276$	−8.05406	+	2.03275i	−0.484798	+	0.122357i
$277$	−16.0800	+	27.8513i	−0.966152	+	1.67342i	−0.259665	+	0.965699i	$0.583612\pi$
$277$	−16.0800	+	27.8513i	−0.966152	+	1.67342i	−0.706487	+	0.707726i	$0.749721\pi$
$278$	−1.05641	+	2.04914i	−0.0633590	+	0.122899i
$279$	−0.325555	−	0.778289i	−0.0194905	−	0.0465949i
$280$	−4.06922	+	3.59593i	−0.243182	+	0.214898i
$281$	24.1075	−	7.07860i	1.43813	−	0.422274i	0.532534	−	0.846409i	$-0.321240\pi$
$281$	24.1075	−	7.07860i	1.43813	−	0.422274i	0.905599	+	0.424135i	$0.139422\pi$
$282$	−3.60429	+	9.89520i	−0.214632	+	0.589251i
$283$	1.38635	+	7.19304i	0.0824097	+	0.427582i	0.999577	+	0.0290799i	$0.00925773\pi$
$283$	1.38635	+	7.19304i	0.0824097	+	0.427582i	−0.917167	+	0.398502i	$0.869530\pi$
$284$	−1.89797	+	4.74089i	−0.112624	+	0.281320i
$285$	15.4288	−	8.57945i	0.913925	−	0.508203i
$286$	−0.233322	−	0.202175i	−0.0137966	−	0.0119548i
$287$	−14.1678	+	0.813173i	−0.836298	+	0.0480001i
$288$	0.0966443	−	2.99844i	0.00569482	−	0.176685i
$289$	−2.02845	−	0.390951i	−0.119321	−	0.0229971i
$290$	−0.516158	+	0.492155i	−0.0303098	+	0.0289003i
$291$	1.43269	−	12.8180i	0.0839860	−	0.751405i
$292$	0.983725	−	2.84229i	0.0575682	−	0.166332i
$293$	−5.61557	−	12.2964i	−0.328065	−	0.718362i	0.671682	−	0.740839i	$-0.265572\pi$
$293$	−5.61557	−	12.2964i	−0.328065	−	0.718362i	−0.999747	+	0.0224769i	$0.992845\pi$
$294$	−11.7729	+	2.89795i	−0.686611	+	0.169012i
$295$	−8.72407	−	3.98415i	−0.507935	−	0.231966i
$296$	−0.850633	+	0.340542i	−0.0494421	+	0.0197936i
$297$	0.448938	+	0.389582i	0.0260500	+	0.0226058i
$298$	8.48610	+	4.89945i	0.491586	+	0.283818i
$299$	9.99336	+	8.22543i	0.577931	+	0.475689i
$300$	1.31434	−	0.363032i	0.0758836	−	0.0209597i
$301$	−9.91169	+	25.4740i	−0.571300	+	1.46830i
$302$	−11.8328	−	1.70129i	−0.680899	−	0.0978985i
$303$	−3.05949	−	8.01405i	−0.175763	−	0.460395i
$304$	4.82587	+	1.17074i	0.276783	+	0.0671468i
$305$	−0.759624	+	7.95514i	−0.0434959	+	0.455510i
$306$	−11.3488	+	2.36889i	−0.648770	+	0.135420i
$307$	2.74268	+	19.0758i	0.156533	+	1.08871i	0.904961	+	0.425495i	$0.139900\pi$
$307$	2.74268	+	19.0758i	0.156533	+	1.08871i	−0.748428	+	0.663216i	$0.769191\pi$
$308$	0.195963	−	0.230651i	0.0111660	−	0.0131426i
$309$	−17.0343	−	8.11346i	−0.969048	−	0.461559i
$310$	−0.576532	−	0.0274636i	−0.0327448	−	0.00155983i
$311$	−11.6771	−	22.6503i	−0.662145	−	1.28438i	−0.945580	−	0.325391i	$-0.894504\pi$
$311$	−11.6771	−	22.6503i	−0.662145	−	1.28438i	0.283434	−	0.958992i	$-0.408526\pi$
$312$	−3.85093	+	2.64979i	−0.218016	+	0.150015i
$313$	−3.13285	+	0.760021i	−0.177079	+	0.0429589i	−0.323318	−	0.946290i	$-0.604798\pi$
$313$	−3.13285	+	0.760021i	−0.177079	+	0.0429589i	0.146239	+	0.989249i	$0.453283\pi$
$314$	2.93118	+	20.3868i	0.165416	+	1.15049i
$315$	−15.9234	−	3.44204i	−0.897184	−	0.193937i
$316$	−4.39160	+	2.00558i	−0.247047	+	0.112823i
$317$	11.5349	−	12.0974i	0.647864	−	0.679460i	−0.315110	−	0.949055i	$-0.602041\pi$
$317$	11.5349	−	12.0974i	0.647864	−	0.679460i	0.962974	+	0.269595i	$0.0868898\pi$
$318$	0.593806	−	0.730551i	0.0332990	−	0.0409673i
$319$	0.0245710	−	0.0312445i	0.00137571	−	0.00174936i
$320$	−1.82433	−	0.940509i	−0.101983	−	0.0525761i
$321$	4.84904	−	1.33935i	0.270647	−	0.0747550i
$322$	−7.96792	+	9.87483i	−0.444035	+	0.550303i
$323$		−	19.1905i		−	1.06779i
$324$	7.41806	−	5.09632i	0.412114	−	0.283129i
$325$	−1.67009	−	1.31337i	−0.0926400	−	0.0728529i
$326$	−1.10960	+	0.790142i	−0.0614550	+	0.0437619i
$327$	−1.92110	+	3.58347i	−0.106237	+	0.198166i
$328$	−2.22818	−	4.87903i	−0.123030	−	0.269399i
$329$	4.68215	+	15.3902i	0.258135	+	0.848489i
$330$	0.372596	−	0.162957i	0.0205107	−	0.00897048i
$331$	3.90269	+	16.0871i	0.214511	+	0.884227i	0.972677	+	0.232165i	$0.0745808\pi$
$331$	3.90269	+	16.0871i	0.214511	+	0.884227i	−0.758165	+	0.652062i	$0.773904\pi$
$332$	5.01649	+	14.4942i	0.275316	+	0.795472i
$333$	−2.33502	−	1.45038i	−0.127958	−	0.0794801i
$334$	1.03480	−	21.7232i	0.0566220	−	1.18864i
$335$	1.60386	+	1.38976i	0.0876284	+	0.0759305i
$336$	−2.63430	−	3.74973i	−0.143713	−	0.204565i
$337$	11.3588	−	1.63315i	0.618752	−	0.0889631i	0.174191	−	0.984712i	$-0.444269\pi$
$337$	11.3588	−	1.63315i	0.618752	−	0.0889631i	0.444561	+	0.895749i	$0.353360\pi$
$338$	−5.40191	−	1.86962i	−0.293825	−	0.101694i
$339$	−6.44645	+	1.13506i	−0.350123	+	0.0616482i
$340$	−1.87000	+	7.70826i	−0.101415	+	0.418039i
$341$	0.0320231	−	0.00305784i	0.00173415	−	0.000165591i
$342$	5.74891	+	13.7436i	0.310865	+	0.743171i
$343$	−11.7144	+	14.3448i	−0.632517	+	0.774546i
$344$	−10.3314			−0.557033
$345$	−15.4426	+	7.22533i	−0.831402	+	0.388999i
$346$	8.80369	−	15.2484i	0.473290	−	0.819762i
$347$	11.1566	−	0.531455i	0.598918	−	0.0285300i	0.254066	−	0.967187i	$-0.418232\pi$
$347$	11.1566	−	0.531455i	0.598918	−	0.0285300i	0.344852	+	0.938657i	$0.387929\pi$
$348$	−0.364363	−	0.479010i	−0.0195319	−	0.0256776i
$349$	8.68542	−	19.0184i	0.464920	−	1.01803i	−0.521419	−	0.853301i	$-0.674597\pi$
$349$	8.68542	−	19.0184i	0.464920	−	1.01803i	0.986338	−	0.164731i	$-0.0526757\pi$
$350$	1.27155	−	1.64970i	0.0679670	−	0.0881801i
$351$	−13.2489	−	4.59633i	−0.707174	−	0.245334i
$352$	0.108102	+	0.0374145i	0.00576186	+	0.00199420i
$353$	1.49899	−	3.74429i	0.0797830	−	0.199288i	−0.883113	−	0.469160i	$-0.844557\pi$
$353$	1.49899	−	3.74429i	0.0797830	−	0.199288i	0.962896	+	0.269871i	$0.0869811\pi$
$354$	4.15909	−	6.94299i	0.221053	−	0.369016i
$355$	−1.98363	+	10.2921i	−0.105280	+	0.546247i
$356$	−0.186243	−	0.119691i	−0.00987084	−	0.00634360i
$357$	−11.6822	+	13.3096i	−0.618289	+	0.704416i
$358$	4.36937	−	5.04252i	0.230928	−	0.266505i
$359$	−0.00686786	−	0.0283097i	−0.000362472	−	0.00149413i	0.971630	−	0.236506i	$-0.0760023\pi$
$359$	−0.00686786	−	0.0283097i	−0.000362472	−	0.00149413i	−0.971993	+	0.235012i	$0.924487\pi$
$360$	−0.969931	−	6.08062i	−0.0511199	−	0.320477i
$361$	−5.55743	+	1.07111i	−0.292496	+	0.0563740i
$362$	0.328507	−	0.461324i	0.0172660	−	0.0242466i
$363$	16.1726	−	10.0291i	0.848843	−	0.526392i
$364$	−2.26962	+	6.77013i	−0.118961	+	0.354851i
$365$	0.878555	−	6.11048i	0.0459857	−	0.319837i
$366$	−6.60039	−	1.38276i	−0.345008	−	0.0722779i
$367$	−16.9173	−	9.76720i	−0.883075	−	0.509843i	−0.0114038	−	0.999935i	$-0.503630\pi$
$367$	−16.9173	−	9.76720i	−0.883075	−	0.509843i	−0.871671	+	0.490091i	$0.836963\pi$
$368$	−4.57035	−	1.45325i	−0.238246	−	0.0757557i
$369$	7.83034	−	14.0575i	0.407631	−	0.731803i
$370$	−1.58209	+	1.01675i	−0.0822491	+	0.0528583i
$371$	0.0544422	−	1.43704i	0.00282650	−	0.0746076i
$372$	0.0770753	−	0.480936i	0.00399617	−	0.0249354i
$373$	12.1832	−	12.7774i	0.630822	−	0.661587i	−0.328302	−	0.944573i	$-0.606477\pi$
$373$	12.1832	−	12.7774i	0.630822	−	0.661587i	0.959124	+	0.282986i	$0.0913250\pi$
$374$	0.0420216	−	0.440070i	0.00217289	−	0.0227555i
$375$	18.4363	−	9.13167i	0.952045	−	0.471558i
$376$	−4.77935	+	3.75852i	−0.246476	+	0.193831i
$377$	−0.264200	+	0.899784i	−0.0136070	+	0.0463412i
$378$	4.37930	−	13.0316i	0.225247	−	0.670271i
$379$	14.0675	−	21.8895i	0.722599	−	1.12439i	−0.264517	−	0.964381i	$-0.585213\pi$
$379$	14.0675	−	21.8895i	0.722599	−	1.12439i	0.987116	−	0.160005i	$-0.0511510\pi$
$380$	10.1809	+	0.484974i	0.522267	+	0.0248787i
$381$	19.1801	+	27.8744i	0.982625	+	1.42805i
$382$	−11.7811	−	12.3556i	−0.602771	−	0.632168i
$383$	18.0039	−	14.1584i	0.919956	−	0.723461i	−0.0412920	−	0.999147i	$-0.513147\pi$
$383$	18.0039	−	14.1584i	0.919956	−	0.723461i	0.961248	+	0.275686i	$0.0889050\pi$
$384$	0.959769	−	1.44182i	0.0489780	−	0.0735775i
$385$	0.305351	−	0.540975i	0.0155621	−	0.0275707i
$386$	5.57238	+	18.9778i	0.283627	+	0.965944i
$387$	−18.3646	−	24.9677i	−0.933524	−	1.26918i
$388$	4.60316	−	5.85339i	0.233690	−	0.297161i
$389$	−0.154630	−	3.24608i	−0.00784005	−	0.164583i	−0.999392	−	0.0348713i	$-0.988898\pi$
$389$	−0.154630	−	3.24608i	−0.00784005	−	0.164583i	0.991552	−	0.129712i	$-0.0414052\pi$
$390$	−6.73192	+	6.83626i	−0.340884	+	0.346167i
$391$	−1.29375	+	18.4882i	−0.0654279	+	0.934988i
$392$	−6.65832	−	2.16028i	−0.336296	−	0.109111i
$393$	2.77780	+	2.48644i	0.140121	+	0.125425i
$394$	4.54501	−	1.81955i	0.228974	−	0.0916674i
$395$	−8.07182	+	5.74792i	−0.406137	+	0.289209i
$396$	0.101738	+	0.327754i	0.00511251	+	0.0164702i
$397$	−1.13386	+	1.59228i	−0.0569067	+	0.0799142i	−0.842049	−	0.539402i	$-0.818651\pi$
$397$	−1.13386	+	1.59228i	−0.0569067	+	0.0799142i	0.785142	+	0.619316i	$0.212590\pi$
$398$	18.2370	+	21.0466i	0.914136	+	1.05497i
$399$	19.6347	+	11.5036i	0.982963	+	0.575903i
$400$	0.755361	+	0.221794i	0.0377680	+	0.0110897i
$401$	−20.1222	−	3.87824i	−1.00485	−	0.193670i	−0.339826	−	0.940488i	$-0.610368\pi$
$401$	−20.1222	−	3.87824i	−1.00485	−	0.193670i	−0.665028	+	0.746818i	$0.731580\pi$
$402$	−1.31586	+	1.21481i	−0.0656293	+	0.0605892i
$403$	−0.674575	+	0.347768i	−0.0336030	+	0.0173235i
$404$	0.937291	−	4.86313i	0.0466320	−	0.241950i
$405$	12.9708	−	13.1526i	0.644524	−	0.653558i
$406$	−0.884566	−	0.250406i	−0.0439003	−	0.0124275i
$407$	0.0792140	−	0.0686393i	0.00392649	−	0.00340232i
$408$	−6.28925	−	2.29084i	−0.311365	−	0.113413i
$409$	6.94857	−	28.6424i	0.343585	−	1.41628i	−0.493759	−	0.869599i	$-0.664378\pi$
$409$	6.94857	−	28.6424i	0.343585	−	1.41628i	0.837344	−	0.546677i	$-0.184107\pi$
$410$	−6.38588	−	8.96771i	−0.315376	−	0.442884i
$411$	17.1711	−	13.0614i	0.846988	−	0.644269i
$412$	−5.88940	−	9.16408i	−0.290150	−	0.451482i
$413$	−1.29489	−	12.2949i	−0.0637175	−	0.604991i
$414$	−4.61198	−	13.6283i	−0.226667	−	0.669793i
$415$	15.7404	+	27.2631i	0.772664	+	1.33829i
$416$	−2.69578	+	0.128416i	−0.132171	+	0.00629609i
$417$	−3.68268	−	1.54361i	−0.180342	−	0.0755911i
$418$	−0.565490	+	0.0539977i	−0.0276590	+	0.00264112i
$419$	11.3500	−	3.33266i	0.554484	−	0.162811i	0.00752660	−	0.999972i	$-0.497604\pi$
$419$	11.3500	−	3.33266i	0.554484	−	0.162811i	0.546957	+	0.837161i	$0.315786\pi$
$420$	−6.76572	−	6.53397i	−0.330133	−	0.318825i
$421$	12.8967	−	11.1751i	0.628549	−	0.544641i	−0.281279	−	0.959626i	$-0.590759\pi$
$421$	12.8967	−	11.1751i	0.628549	−	0.544641i	0.909828	+	0.414985i	$0.136213\pi$
$422$	−1.81090	−	2.30274i	−0.0881532	−	0.112096i
$423$	−17.5786	−	4.86919i	−0.854703	−	0.236748i
$424$	0.513647	−	0.177775i	0.0249449	−	0.00863351i
$425$	0.144759	−	3.03887i	0.00702185	−	0.147407i
$426$	−8.44553	−	2.62834i	−0.409187	−	0.127343i
$427$	−9.32815	+	4.37024i	−0.451421	+	0.211491i
$428$	2.78678	+	0.818271i	0.134704	+	0.0395526i
$429$	0.317153	−	0.430529i	0.0153123	−	0.0207861i
$430$	−20.8220	+	4.01311i	−1.00413	+	0.193530i
$431$	−5.70751	−	0.545001i	−0.274921	−	0.0262518i	−0.0433151	−	0.999061i	$-0.513792\pi$
$431$	−5.70751	−	0.545001i	−0.274921	−	0.0262518i	−0.231606	+	0.972810i	$0.574398\pi$
$432$	5.19045	−	0.243451i	0.249725	−	0.0117130i
$433$	−0.205411	−	0.0938082i	−0.00987144	−	0.00450814i	0.410473	−	0.911873i	$-0.365364\pi$
$433$	−0.205411	−	0.0938082i	−0.00987144	−	0.00450814i	−0.420345	+	0.907365i	$0.638091\pi$
$434$	−0.347348	−	0.657958i	−0.0166732	−	0.0315830i
$435$	−0.920406	−	0.823868i	−0.0441301	−	0.0395014i
$436$	−2.03297	+	1.17374i	−0.0973616	+	0.0562117i
$437$	23.6426	−	2.86367i	1.13098	−	0.136988i
$438$	5.04221	+	1.30958i	0.240926	+	0.0625744i
$439$	1.86337	+	0.960632i	0.0889336	+	0.0458484i	0.502120	−	0.864798i	$-0.332554\pi$
$439$	1.86337	+	0.960632i	0.0889336	+	0.0458484i	−0.413186	+	0.910647i	$0.635584\pi$
$440$	0.232403	+	0.0334145i	0.0110794	+	0.00159297i
$441$	−6.61477	−	19.9310i	−0.314989	−	0.949095i
$442$	2.93835	+	10.0071i	0.139763	+	0.475990i
$443$	−20.8177	−	14.8242i	−0.989079	−	0.704320i	−0.0336170	−	0.999435i	$-0.510703\pi$
$443$	−20.8177	−	14.8242i	−0.989079	−	0.704320i	−0.955462	+	0.295115i	$0.904642\pi$
$444$	−0.704397	−	1.42213i	−0.0334292	−	0.0674915i
$445$	−0.421847	−	0.168882i	−0.0199975	−	0.00800578i
$446$	−2.58351	+	0.626753i	−0.122333	+	0.0296776i
$447$	−7.29829	+	15.3229i	−0.345197	+	0.724747i
$448$	−0.151606	−	2.64140i	−0.00716270	−	0.124795i
$449$	3.58135	−	5.57269i	0.169014	−	0.262992i	−0.746406	−	0.665491i	$-0.768222\pi$
$449$	3.58135	−	5.57269i	0.169014	−	0.262992i	0.915420	+	0.402500i	$0.131859\pi$
$450$	0.806685	+	2.21971i	0.0380275	+	0.104638i
$451$	0.423417	+	0.444067i	0.0199379	+	0.0209103i
$452$	−3.50841	−	1.40455i	−0.165022	−	0.0660647i
$453$	1.31827	−	20.6637i	0.0619377	−	0.970865i
$454$	26.0261	−	11.8857i	1.22147	−	0.557826i
$455$	−1.94444	+	14.5262i	−0.0911567	+	0.680998i
$456$	−1.36106	+	8.49274i	−0.0637373	+	0.397709i
$457$	13.5213	+	33.7747i	0.632502	+	1.57991i	0.803935	+	0.594717i	$0.202736\pi$
$457$	13.5213	+	33.7747i	0.632502	+	1.57991i	−0.171433	+	0.985196i	$0.554840\pi$
$458$	1.01660	+	21.3410i	0.0475024	+	0.997198i
$459$	−5.64323	−	19.2712i	−0.263404	−	0.899501i
$460$	−9.77561	−	1.15359i	−0.455790	−	0.0537862i
$461$		−	33.0996i		−	1.54160i	−0.637075	−	0.770802i	$-0.719856\pi$
$461$		−	33.0996i		−	1.54160i	0.637075	−	0.770802i	$-0.280144\pi$
$462$	0.425067	+	0.306793i	0.0197759	+	0.0142733i
$463$	2.79869	−	19.4653i	0.130066	−	0.904631i	−0.815397	−	0.578902i	$-0.803481\pi$
$463$	2.79869	−	19.4653i	0.130066	−	0.904631i	0.945463	−	0.325729i	$-0.105610\pi$
$464$	−0.0330294	−	0.345899i	−0.00153335	−	0.0160580i
$465$	−0.0314756	−	0.999220i	−0.00145964	−	0.0463377i
$466$	−18.7633	−	1.79167i	−0.869191	−	0.0829977i
$467$	−11.2661	+	32.5512i	−0.521333	+	1.50629i	0.310121	+	0.950697i	$0.399631\pi$
$467$	−11.2661	+	32.5512i	−0.521333	+	1.50629i	−0.831453	+	0.555595i	$0.812491\pi$
$468$	−5.10221	−	6.28655i	−0.235850	−	0.290596i
$469$	−0.491550	+	2.69109i	−0.0226977	+	0.124263i
$470$	−8.17238	+	9.43143i	−0.376964	+	0.435039i
$471$	−34.7995	+	7.85090i	−1.60347	+	0.361750i
$472$	4.15329	−	2.14117i	0.191170	−	0.0985552i
$473$	1.11685	−	0.386545i	0.0513527	−	0.0177733i
$474$	−4.06387	−	7.30825i	−0.186660	−	0.335679i
$475$	−3.86958	+	0.556361i	−0.177548	+	0.0255276i
$476$	−9.78179	+	2.97591i	−0.448348	+	0.136401i
$477$	1.34266	+	0.925315i	0.0614760	+	0.0423673i
$478$	11.1700	+	10.6506i	0.510904	+	0.487146i
$479$	4.50172	+	6.32178i	0.205689	+	0.288849i	0.904515	−	0.426442i	$-0.140233\pi$
$479$	4.50172	+	6.32178i	0.205689	+	0.288849i	−0.698826	+	0.715292i	$0.746294\pi$
$480$	1.37427	−	3.27866i	0.0627265	−	0.149650i
$481$	−1.13313	+	2.19796i	−0.0516661	+	0.100218i
$482$	−25.7251			−1.17174
$483$	−18.1406	−	12.4064i	−0.825426	−	0.564510i
$484$	10.9869			0.499405
$485$	7.00356	−	13.5850i	0.318015	−	0.616864i
$486$	9.81460	+	12.1109i	0.445199	+	0.549361i
$487$	−14.8015	−	20.7858i	−0.670718	−	0.941892i	0.329279	−	0.944233i	$-0.393194\pi$
$487$	−14.8015	−	20.7858i	−0.670718	−	0.941892i	−0.999997	+	0.00234049i	$0.999255\pi$
$488$	−2.81783	−	2.68680i	−0.127557	−	0.121626i
$489$	−1.51613	−	1.80775i	−0.0685618	−	0.0817492i
$490$	−14.2584	−	1.76750i	−0.644127	−	0.0798477i
$491$	35.6259	−	5.12223i	1.60777	−	0.231163i	0.720853	−	0.693088i	$-0.243750\pi$
$491$	35.6259	−	5.12223i	1.60777	−	0.231163i	0.886919	+	0.461925i	$0.152841\pi$
$492$	8.11939	−	4.51492i	0.366050	−	0.203548i
$493$	−1.26895	+	0.439187i	−0.0571505	+	0.0197800i
$494$	11.9122	−	6.14115i	0.535954	−	0.276304i
$495$	0.332355	+	0.621038i	0.0149382	+	0.0279136i
$496$	0.184154	−	0.212525i	0.00826877	−	0.00954268i
$497$	−12.7243	+	4.54309i	−0.570765	+	0.203786i
$498$	−24.3397	+	10.6451i	−1.09069	+	0.477018i
$499$	2.31474	−	6.68802i	0.103622	−	0.299397i	−0.881257	−	0.472637i	$-0.843302\pi$
$499$	2.31474	−	6.68802i	0.103622	−	0.299397i	0.984880	+	0.173240i	$0.0554236\pi$
$500$	11.8245	+	1.12911i	0.528809	+	0.0504952i
$501$	37.6497	−	1.18597i	1.68206	−	0.0529853i
$502$	2.75928	+	28.8965i	0.123153	+	1.28971i
$503$	5.26412	−	36.6128i	0.234716	−	1.63248i	−0.442550	−	0.896744i	$-0.645926\pi$
$503$	5.26412	−	36.6128i	0.234716	−	1.63248i	0.677265	−	0.735739i	$-0.263165\pi$
$504$	6.11393	−	5.06160i	0.272336	−	0.225462i
$505$		−	10.1653i		−	0.452348i
$506$	0.548436	−	0.0138984i	0.0243810	−	0.000617858i
$507$	2.48893	−	9.58299i	0.110537	−	0.425596i
$508$	0.929515	+	19.5129i	0.0412406	+	0.865746i
$509$	−12.8177	−	32.0170i	−0.568134	−	1.41913i	−0.882719	−	0.469901i	$-0.844290\pi$
$509$	−12.8177	−	32.0170i	−0.568134	−	1.41913i	0.314585	−	0.949229i	$-0.398135\pi$
$510$	−13.5653	−	2.17398i	−0.600680	−	0.0962656i
$511$	7.35849	−	3.02932i	0.325521	−	0.134009i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−22.9436	+	11.8070i	−1.01298	+	0.521292i
$514$	6.38862	+	2.55762i	0.281790	+	0.112812i
$515$	−15.4292	−	16.1817i	−0.679892	−	0.713050i
$516$	−1.41380	−	17.8386i	−0.0622390	−	0.785301i
$517$	0.376034	−	0.585121i	0.0165380	−	0.0257336i
$518$	−2.16544	−	1.08982i	−0.0951439	−	0.0478837i
$519$	27.5333	+	13.1141i	1.20858	+	0.575646i
$520$	−5.38320	+	1.30595i	−0.236069	+	0.0572697i
$521$	23.0402	+	9.22389i	1.00941	+	0.404106i	0.816646	−	0.577139i	$-0.195831\pi$
$521$	23.0402	+	9.22389i	1.00941	+	0.404106i	0.192762	+	0.981245i	$0.438255\pi$
$522$	0.777215	−	0.694673i	0.0340178	−	0.0304050i
$523$	−15.4023	−	10.9680i	−0.673497	−	0.479595i	0.191421	−	0.981508i	$-0.438690\pi$
$523$	−15.4023	−	10.9680i	−0.673497	−	0.479595i	−0.864918	+	0.501913i	$0.832630\pi$
$524$	0.606403	+	2.06522i	0.0264909	+	0.0902196i
$525$	3.02243	+	1.96975i	0.131910	+	0.0859668i
$526$	1.26982	+	0.182572i	0.0553667	+	0.00796053i
$527$	−0.965930	−	0.497972i	−0.0420766	−	0.0216920i
$528$	−0.0498081	+	0.191773i	−0.00216762	+	0.00834585i
$529$	−22.9705	+	1.16497i	−0.998716	+	0.0506511i
$530$	0.966153	−	0.557809i	0.0419670	−	0.0242297i
$531$	12.5572	+	6.23112i	0.544935	+	0.270408i
$532$	6.13375	+	11.6187i	0.265932	+	0.503736i
$533$	−13.1677	−	6.01347i	−0.570355	−	0.260472i
$534$	0.181176	−	0.337952i	0.00784027	−	0.0146246i
$535$	5.93433	+	0.566660i	0.256564	+	0.0244989i
$536$	−1.01528	+	0.195679i	−0.0438535	+	0.00845207i
$537$	9.30452	+	6.85427i	0.401520	+	0.295784i
$538$	−17.6663	−	5.18730i	−0.761649	−	0.223640i
$539$	0.800604	−	0.0155867i	0.0344844	−	0.000671366i
$540$	10.3663	−	2.50682i	0.446094	−	0.107876i
$541$	−1.67098	+	35.0782i	−0.0718410	+	1.50813i	0.619155	+	0.785269i	$0.287475\pi$
$541$	−1.67098	+	35.0782i	−0.0718410	+	1.50813i	−0.690996	+	0.722859i	$0.742828\pi$
$542$	19.3218	−	6.68734i	0.829942	−	0.287246i
$543$	0.841493	+	0.504083i	0.0361119	+	0.0216323i
$544$	−2.38886	−	3.03769i	−0.102422	−	0.130240i
$545$	−3.64134	+	3.15524i	−0.155978	+	0.135155i
$546$	−12.0001	−	2.99236i	−0.513559	−	0.128061i
$547$	8.79407	−	2.58217i	0.376007	−	0.110406i	−0.0882677	−	0.996097i	$-0.528133\pi$
$547$	8.79407	−	2.58217i	0.376007	−	0.110406i	0.464275	+	0.885691i	$0.346315\pi$
$548$	12.3995	−	1.18400i	0.529679	−	0.0505782i
$549$	1.48429	−	11.5857i	0.0633480	−	0.494465i
$550$	−0.0899544	+	0.00428505i	−0.00383567	+	0.000182715i
$551$	0.862749	+	1.49432i	0.0367543	+	0.0636604i
$552$	1.88380	−	8.09020i	0.0801799	−	0.344342i
$553$	−11.6702	−	5.19292i	−0.496267	−	0.220825i
$554$	−17.3870	−	27.0547i	−0.738702	−	1.14944i
$555$	−1.97206	−	2.59256i	−0.0837092	−	0.110048i
$556$	−1.33728	−	1.87794i	−0.0567131	−	0.0796425i
$557$	10.7993	−	44.5152i	0.457580	−	1.88617i	−0.00574804	−	0.999983i	$-0.501830\pi$
$557$	10.7993	−	44.5152i	0.457580	−	1.88617i	0.463328	−	0.886187i	$-0.346655\pi$
$558$	0.840948	+	0.0672676i	0.0356002	+	0.00284766i
$559$	−21.0724	+	18.2593i	−0.891267	+	0.772287i
$560$	−1.33157	−	5.26462i	−0.0562691	−	0.222471i
$561$	0.765592	+	0.0123349i	0.0323233	+	0.000520779i
$562$	−4.75498	+	24.6712i	−0.200577	+	1.04069i
$563$	−33.4297	+	17.2342i	−1.40889	+	0.726335i	−0.983876	−	0.178851i	$-0.942762\pi$
$563$	−33.4297	+	17.2342i	−1.40889	+	0.726335i	−0.425017	+	0.905186i	$0.639732\pi$
$564$	−7.14363	−	7.73786i	−0.300801	−	0.325823i
$565$	−7.61645	−	1.46795i	−0.320427	−	0.0617572i
$566$	−7.02869	−	2.06381i	−0.295438	−	0.0867484i
$567$	23.1001	+	5.77817i	0.970111	+	0.242660i
$568$	−3.34418	−	3.85938i	−0.140319	−	0.161936i
$569$	−11.9696	+	16.8089i	−0.501791	+	0.704666i	−0.985331	−	0.170656i	$-0.945411\pi$
$569$	−11.9696	+	16.8089i	−0.501791	+	0.704666i	0.483540	+	0.875322i	$0.339351\pi$
$570$	0.555820	+	17.6450i	0.0232808	+	0.739068i
$571$	26.3929	−	18.7943i	1.10451	−	0.786516i	0.125857	−	0.992048i	$-0.459832\pi$
$571$	26.3929	−	18.7943i	1.10451	−	0.786516i	0.978650	+	0.205533i	$0.0658927\pi$
$572$	0.286614	−	0.114743i	0.0119839	−	0.00479765i
$573$	19.7215	−	22.0324i	0.823877	−	0.920417i
$574$	5.76928	−	12.9655i	0.240805	−	0.541168i
$575$	3.76548	−	0.275128i	0.157031	−	0.0114736i
$576$	2.62084	+	1.45987i	0.109202	+	0.0608278i
$577$	−1.11439	−	23.3939i	−0.0463926	−	0.973900i	−0.895329	−	0.445405i	$-0.853060\pi$
$577$	−1.11439	−	23.3939i	−0.0463926	−	0.973900i	0.848937	−	0.528495i	$-0.177243\pi$
$578$	1.27698	−	1.62381i	0.0531154	−	0.0675417i
$579$	−32.0052	+	12.2185i	−1.33009	+	0.507783i
$580$	−0.200928	−	0.684298i	−0.00834308	−	0.0284139i
$581$	−19.9469	+	35.3390i	−0.827538	+	1.46611i
$582$	10.7366	+	7.14698i	0.445046	+	0.296252i
$583$	−0.0488749	+	0.0384357i	−0.00202419	+	0.00159184i
$584$	2.07556	+	2.17678i	0.0858872	+	0.0900759i
$585$	−12.7250	−	10.6881i	−0.526112	−	0.441897i
$586$	13.5027	+	0.643211i	0.557790	+	0.0265708i
$587$	−0.265481	+	0.413096i	−0.0109576	+	0.0170503i	−0.846689	−	0.532088i	$-0.821408\pi$
$587$	−0.265481	+	0.413096i	−0.0109576	+	0.0170503i	0.835732	+	0.549138i	$0.185044\pi$
$588$	2.81887	−	11.7921i	0.116248	−	0.486299i
$589$	−0.393427	+	1.33989i	−0.0162109	+	0.0552092i
$590$	7.53885	−	5.92862i	0.310370	−	0.244077i
$591$	3.76365	+	7.59858i	0.154816	+	0.312564i
$592$	0.0870968	−	0.912118i	0.00357965	−	0.0374878i
$593$	3.94949	−	4.14210i	0.162186	−	0.170096i	−0.637627	−	0.770346i	$-0.720084\pi$
$593$	3.94949	−	4.14210i	0.162186	−	0.170096i	0.799813	+	0.600250i	$0.204932\pi$
$594$	−0.551989	+	0.220515i	−0.0226484	+	0.00904786i
$595$	−18.5583	+	9.79729i	−0.760818	+	0.401650i
$596$	−8.24336	+	5.29769i	−0.337661	+	0.217002i
$597$	−33.8441	+	34.3687i	−1.38515	+	1.40662i
$598$	−11.8903	+	5.11335i	−0.486230	+	0.209100i
$599$	30.0046	+	17.3231i	1.22595	+	0.707805i	0.966181	−	0.257865i	$-0.0830190\pi$
$599$	30.0046	+	17.3231i	1.22595	+	0.707805i	0.259773	+	0.965670i	$0.416352\pi$
$600$	−0.279591	+	1.33458i	−0.0114142	+	0.0544842i
$601$	−5.37932	+	37.4140i	−0.219427	+	1.52615i	0.520734	+	0.853719i	$0.325658\pi$
$601$	−5.37932	+	37.4140i	−0.219427	+	1.52615i	−0.740161	+	0.672430i	$0.765251\pi$
$602$	−18.1004	−	20.4827i	−0.737718	−	0.834814i
$603$	−2.27760	−	2.10578i	−0.0927512	−	0.0857539i
$604$	6.93426	−	9.73780i	0.282151	−	0.396226i
$605$	22.1431	−	4.26773i	0.900245	−	0.173508i
$606$	8.52511	+	0.952869i	0.346309	+	0.0387076i
$607$	9.80512	+	40.4173i	0.397978	+	1.64049i	0.720159	+	0.693809i	$0.244069\pi$
$607$	9.80512	+	40.4173i	0.397978	+	1.64049i	−0.322182	+	0.946678i	$0.604416\pi$
$608$	−3.25194	+	3.75294i	−0.131884	+	0.152202i
$609$	0.311313	−	1.56159i	0.0126150	−	0.0632788i
$610$	−6.72273	−	4.32044i	−0.272195	−	0.174929i
$611$	−3.10550	+	16.1129i	−0.125635	+	0.651857i
$612$	3.09479	−	11.1727i	0.125100	−	0.451631i
$613$	−4.20124	+	10.4942i	−0.169687	+	0.423857i	−0.988698	−	0.149920i	$-0.952098\pi$
$613$	−4.20124	+	10.4942i	−0.169687	+	0.423857i	0.819011	+	0.573777i	$0.194522\pi$
$614$	−18.2120	−	6.30323i	−0.734976	−	0.254378i
$615$	14.6101	−	12.2533i	0.589137	−	0.494100i
$616$	0.115216	+	0.279869i	0.00464217	+	0.0112762i
$617$	−1.11974	+	2.45190i	−0.0450792	+	0.0987097i	−0.930832	−	0.365448i	$-0.880916\pi$
$617$	−1.11974	+	2.45190i	−0.0450792	+	0.0987097i	0.885752	+	0.464158i	$0.153643\pi$
$618$	15.0171	−	11.4229i	0.604077	−	0.459497i
$619$	−2.74381	+	0.130704i	−0.110283	+	0.00525343i	−0.102651	−	0.994717i	$-0.532732\pi$
$619$	−2.74381	+	0.130704i	−0.110283	+	0.00525343i	−0.00763220	+	0.999971i	$0.502429\pi$
$620$	0.288593	−	0.499858i	0.0115902	−	0.0200748i
$621$	22.8999	−	9.82817i	0.918943	−	0.394391i
$622$	25.4832			1.02178
$623$	−0.0889977	−	0.578934i	−0.00356562	−	0.0231945i
$624$	−0.590629	−	4.63705i	−0.0236441	−	0.185631i
$625$	20.3514	−	1.94332i	0.814057	−	0.0777330i
$626$	0.760021	−	3.13285i	0.0303766	−	0.125214i
$627$	−0.170619	−	0.969006i	−0.00681385	−	0.0386984i
$628$	−19.4636	−	6.73643i	−0.776684	−	0.268813i
$629$	−3.50486	+	0.503922i	−0.139748	+	0.0200927i
$630$	10.3559	−	12.5761i	0.412591	−	0.501043i
$631$	−17.1978	−	14.9019i	−0.684632	−	0.593237i	0.241516	−	0.970397i	$-0.422355\pi$
$631$	−17.1978	−	14.9019i	−0.684632	−	0.593237i	−0.926148	+	0.377160i	$0.876901\pi$
$632$	0.229720	−	4.82242i	0.00913778	−	0.191826i
$633$	3.72819	−	3.44188i	0.148182	−	0.136803i
$634$	5.46704	+	15.7960i	0.217124	+	0.627339i
$635$	9.45291	+	38.9654i	0.375127	+	1.54630i
$636$	0.377242	+	0.862554i	0.0149586	+	0.0342025i
$637$	−17.3986	+	7.36144i	−0.689356	+	0.291671i
$638$	0.0165122	+	0.0361566i	0.000653723	+	0.00143145i
$639$	3.38246	−	14.9420i	0.133808	−	0.591098i
$640$	1.67192	−	1.19057i	0.0660883	−	0.0470613i
$641$	12.5477	+	9.86760i	0.495603	+	0.389747i	0.834440	−	0.551098i	$-0.185791\pi$
$641$	12.5477	+	9.86760i	0.495603	+	0.389747i	−0.338837	+	0.940845i	$0.610034\pi$
$642$	−1.03150	+	4.92372i	−0.0407101	+	0.194324i
$643$		−	9.48702i		−	0.374131i	−0.982347	−	0.187066i	$-0.940102\pi$
$643$		−	9.48702i		−	0.374131i	0.982347	−	0.187066i	$-0.0598977\pi$
$644$	−5.12599	−	11.6071i	−0.201992	−	0.457383i
$645$	−9.77857	−	35.4029i	−0.385031	−	1.39399i
$646$	17.0572	+	8.79357i	0.671105	+	0.345979i
$647$	−15.7889	+	20.0772i	−0.620724	+	0.789315i	−0.990160	−	0.139941i	$-0.955309\pi$
$647$	−15.7889	+	20.0772i	−0.620724	+	0.789315i	0.369435	+	0.929256i	$0.379551\pi$
$648$	1.13063	+	8.92870i	0.0444155	+	0.350752i
$649$	−0.368868	+	0.386858i	−0.0144793	+	0.0151855i
$650$	1.93265	−	0.882614i	0.0758049	−	0.0346190i
$651$	1.08852	−	0.689782i	0.0426625	−	0.0270347i
$652$	−0.193858	−	1.34831i	−0.00759208	−	0.0528041i
$653$	−13.6823	+	3.31929i	−0.535429	+	0.129894i	−0.494351	−	0.869262i	$-0.664594\pi$
$653$	−13.6823	+	3.31929i	−0.535429	+	0.129894i	−0.0410780	+	0.999156i	$0.513079\pi$
$654$	−2.30481	−	3.34958i	−0.0901254	−	0.130979i
$655$	2.02436	+	3.92671i	0.0790983	+	0.153429i
$656$	5.35766	+	0.255217i	0.209181	+	0.00996454i
$657$	−1.57118	+	8.88528i	−0.0612975	+	0.346648i
$658$	−15.8248	−	2.89053i	−0.616916	−	0.112685i
$659$	4.65939	+	32.4067i	0.181504	+	1.26239i	0.853209	+	0.521569i	$0.174653\pi$
$659$	4.65939	+	32.4067i	0.181504	+	1.26239i	−0.671705	+	0.740819i	$0.734438\pi$
$660$	−0.0258916	+	0.405848i	−0.00100783	+	0.0157976i
$661$	−0.317453	+	3.32452i	−0.0123475	+	0.129309i	−0.999544	−	0.0302010i	$-0.990385\pi$
$661$	−0.317453	+	3.32452i	−0.0123475	+	0.129309i	0.987196	+	0.159510i	$0.0509913\pi$
$662$	−16.0871	−	3.90269i	−0.625243	−	0.151682i
$663$	−16.8766	+	6.44289i	−0.655431	+	0.250221i
$664$	−15.1816	−	2.18279i	−0.589162	−	0.0847087i
$665$	16.8752	+	21.0339i	0.654390	+	0.815660i
$666$	2.35911	−	1.41085i	0.0914138	−	0.0546693i
$667$	−0.730435	−	1.49780i	−0.0282826	−	0.0579952i
$668$	18.8342	+	10.8739i	0.728716	+	0.420725i
$669$	−1.43571	−	4.37502i	−0.0555079	−	0.169148i
$670$	−1.97020	+	0.788748i	−0.0761153	+	0.0304720i
$671$	0.405138	+	0.185021i	0.0156402	+	0.00714264i
$672$	4.54000	−	0.623230i	0.175134	−	0.0240416i
$673$	−17.4153	−	38.1343i	−0.671312	−	1.46997i	−0.871593	−	0.490230i	$-0.836913\pi$
$673$	−17.4153	−	38.1343i	−0.671312	−	1.46997i	0.200281	−	0.979738i	$-0.435814\pi$
$674$	−3.75329	+	10.8444i	−0.144572	+	0.417712i
$675$	−3.72225	+	1.69661i	−0.143269	+	0.0653024i
$676$	4.13709	−	3.94470i	0.159119	−	0.151719i
$677$	−32.7073	−	6.30382i	−1.25704	−	0.242275i	−0.483120	−	0.875554i	$-0.660497\pi$
$677$	−32.7073	−	6.30382i	−1.25704	−	0.242275i	−0.773924	+	0.633279i	$0.781709\pi$
$678$	1.94505	−	6.24995i	0.0746992	−	0.240028i
$679$	19.6694	−	1.12894i	0.754842	−	0.0433248i
$680$	−5.99449	−	5.19425i	−0.229878	−	0.199190i
$681$	24.0839	+	43.3112i	0.922897	+	1.65969i
$682$	−0.0119559	+	0.0298645i	−0.000457816	+	0.00114357i
$683$	5.04446	+	26.1731i	0.193021	+	1.00149i	0.941164	+	0.337950i	$0.109733\pi$
$683$	5.04446	+	26.1731i	0.193021	+	1.00149i	−0.748143	+	0.663537i	$0.769054\pi$
$684$	−14.8501	−	1.18786i	−0.567809	−	0.0454191i
$685$	24.5300	−	7.20267i	0.937245	−	0.275200i
$686$	−7.38232	−	16.9853i	−0.281858	−	0.648503i
$687$	−36.7090	+	4.67569i	−1.40054	+	0.178389i
$688$	4.73413	−	9.18293i	0.180487	−	0.350096i
$689$	0.733463	−	1.27040i	0.0279427	−	0.0483982i
$690$	0.654085	−	17.0368i	0.0249006	−	0.648579i
$691$	8.69518	+	15.0605i	0.330780	+	0.572928i	0.982665	−	0.185390i	$-0.0593547\pi$
$691$	8.69518	+	15.0605i	0.330780	+	0.572928i	−0.651885	+	0.758318i	$0.726021\pi$
$692$	9.51927	+	14.8123i	0.361868	+	0.563078i
$693$	−0.471552	+	0.775919i	−0.0179128	+	0.0294747i
$694$	−4.63988	+	10.1599i	−0.176127	+	0.385665i
$695$	−3.42462	−	3.26537i	−0.129903	−	0.123862i
$696$	0.592722	−	0.104364i	0.0224671	−	0.00395591i
$697$	−3.92281	−	20.3535i	−0.148587	−	0.770943i
$698$	12.9244	+	16.4346i	0.489194	+	0.622061i
$699$	0.525922	−	32.6425i	0.0198922	−	1.23465i
$700$	0.883654	+	1.88613i	0.0333990	+	0.0712891i
$701$	−17.5552	−	11.2821i	−0.663052	−	0.426117i	0.165363	−	0.986233i	$-0.447120\pi$
$701$	−17.5552	−	11.2821i	−0.663052	−	0.426117i	−0.828415	+	0.560115i	$0.810757\pi$
$702$	10.1564	−	9.66993i	0.383328	−	0.364968i
$703$	1.48818	+	4.29980i	0.0561276	+	0.162170i
$704$	−0.0827906	+	0.0789406i	−0.00312029	+	0.00297519i
$705$	−17.4030	−	12.8201i	−0.655435	−	0.482833i
$706$	2.64118	+	3.04808i	0.0994021	+	0.114716i
$707$	11.2836	−	6.66185i	0.424363	−	0.250545i
$708$	4.26537	+	6.87821i	0.160303	+	0.258499i
$709$	−3.45570	−	36.1897i	−0.129782	−	1.35913i	−0.792320	−	0.610106i	$-0.791127\pi$
$709$	−3.45570	−	36.1897i	−0.129782	−	1.35913i	0.662538	−	0.749028i	$-0.269479\pi$
$710$	−8.23901	−	6.47923i	−0.309204	−	0.243161i
$711$	12.0626	−	8.01692i	0.452382	−	0.300658i
$712$	0.191727	−	0.110694i	0.00718526	−	0.00414841i
$713$	0.469360	−	1.26433i	0.0175777	−	0.0473497i
$714$	−6.47690	−	16.4824i	−0.242392	−	0.616837i
$715$	0.533074	−	0.342586i	0.0199358	−	0.0128120i
$716$	2.47981	+	6.19426i	0.0926748	+	0.231491i
$717$	−16.8611	+	20.7440i	−0.629690	+	0.774699i
$718$	0.0283097	+	0.00686786i	0.00105651	+	0.000256306i
$719$	12.3776	+	8.81408i	0.461608	+	0.328710i	0.787090	−	0.616839i	$-0.211587\pi$
$719$	12.3776	+	8.81408i	0.461608	+	0.328710i	−0.325481	+	0.945548i	$0.605526\pi$
$720$	5.84912	+	1.92419i	0.217984	+	0.0717105i
$721$	7.85032	−	27.7314i	0.292361	−	1.03277i
$722$	1.59452	−	5.43045i	0.0593420	−	0.202100i
$723$	−3.52033	−	44.4178i	−0.130923	−	1.65192i
$724$	0.259510	+	0.503380i	0.00964462	+	0.0187080i
$725$	0.125347	+	0.243139i	0.00465526	+	0.00902995i
$726$	1.50350	+	18.9704i	0.0558001	+	0.704058i
$727$	3.89291	−	13.2580i	0.144380	−	0.491713i	−0.855270	−	0.518183i	$-0.826609\pi$
$727$	3.89291	−	13.2580i	0.144380	−	0.491713i	0.999650	+	0.0264702i	$0.00842672\pi$
$728$	−4.97753	−	5.11957i	−0.184480	−	0.189744i
$729$	−19.5680	+	18.6036i	−0.724742	+	0.689021i
$730$	5.02864	+	3.58088i	0.186118	+	0.132534i
$731$	−38.8001	−	9.41281i	−1.43507	−	0.348145i
$732$	4.25352	−	5.23304i	0.157214	−	0.193419i
$733$	−0.909895	−	2.27281i	−0.0336077	−	0.0839480i	0.910615	−	0.413256i	$-0.135609\pi$
$733$	−0.909895	−	2.27281i	−0.0336077	−	0.0839480i	−0.944222	+	0.329308i	$0.893184\pi$
$734$	16.4334	−	10.5611i	0.606567	−	0.389817i
$735$	1.10066	−	24.8609i	0.0405984	−	0.917007i
$736$	3.38595	−	3.39637i	0.124808	−	0.125192i
$737$	0.102433	−	0.0591396i	0.00377316	−	0.00217844i
$738$	8.90672	+	13.4014i	0.327861	+	0.493312i
$739$	31.1293	+	24.4804i	1.14511	+	0.900525i	0.996093	−	0.0883095i	$-0.0281464\pi$
$739$	31.1293	+	24.4804i	1.14511	+	0.900525i	0.149018	+	0.988835i	$0.452389\pi$
$740$	−0.178766	−	1.87212i	−0.00657157	−	0.0688206i
$741$	12.2337	+	19.7276i	0.449415	+	0.724712i
$742$	1.25235	+	0.706882i	0.0459752	+	0.0259504i
$743$	29.2184	+	33.7198i	1.07192	+	1.23706i	0.970215	+	0.242246i	$0.0778840\pi$
$743$	29.2184	+	33.7198i	1.07192	+	1.23706i	0.101704	+	0.994815i	$0.467571\pi$
$744$	0.392155	+	0.288885i	0.0143771	+	0.0105910i
$745$	−14.5559	+	13.8790i	−0.533287	+	0.508488i
$746$	5.77431	+	16.6838i	0.211413	+	0.610836i
$747$	−21.7110	−	40.5691i	−0.794363	−	1.48435i
$748$	0.371895	+	0.239002i	0.0135978	+	0.00873879i
$749$	3.26009	+	6.95856i	0.119121	+	0.254260i
$750$	−0.331434	+	20.5712i	−0.0121023	+	0.751154i
$751$	12.2219	+	15.5414i	0.445983	+	0.567113i	0.956118	−	0.292981i	$-0.0946472\pi$
$751$	12.2219	+	15.5414i	0.445983	+	0.567113i	−0.510135	+	0.860094i	$0.670405\pi$
$752$	−1.15068	−	5.97031i	−0.0419611	−	0.217715i
$753$	−49.5161	+	8.71859i	−1.80447	+	0.317723i
$754$	−0.678696	−	0.647135i	−0.0247166	−	0.0235673i
$755$	10.1928	−	22.3192i	0.370955	−	0.812278i
$756$	9.57620	+	9.86389i	0.348283	+	0.358746i
$757$	26.1984	+	40.7654i	0.952195	+	1.48164i	0.874707	+	0.484652i	$0.161054\pi$
$757$	26.1984	+	40.7654i	0.952195	+	1.48164i	0.0774881	+	0.996993i	$0.475310\pi$
$758$	13.0100	+	22.5340i	0.472545	+	0.818472i
$759$	0.0990479	+	0.945048i	0.00359521	+	0.0343031i
$760$	−5.09620	+	8.82688i	−0.184859	+	0.320185i
$761$	−14.7820	+	28.6731i	−0.535848	+	1.03940i	0.453145	+	0.891437i	$0.350302\pi$
$761$	−14.7820	+	28.6731i	−0.535848	+	1.03940i	−0.988993	+	0.147963i	$0.952728\pi$
$762$	−33.5645	+	4.27517i	−1.21591	+	0.154873i
$763$	−5.88873	−	1.97414i	−0.213186	−	0.0714687i
$764$	16.3805	−	4.80975i	0.592626	−	0.174011i
$765$	1.89735	−	23.7198i	0.0685988	−	0.857590i
$766$	4.33464	+	22.4903i	0.156617	+	0.812606i
$767$	4.68700	−	11.7076i	0.169238	−	0.422736i
$768$	0.841749	+	1.51376i	0.0303740	+	0.0546230i
$769$	−10.5159	−	9.11206i	−0.379212	−	0.328589i	0.444310	−	0.895873i	$-0.353449\pi$
$769$	−10.5159	−	9.11206i	−0.379212	−	0.328589i	−0.823522	+	0.567284i	$0.807994\pi$
$770$	0.340918	+	0.519296i	0.0122858	+	0.0187141i
$771$	−3.54183	+	11.3808i	−0.127556	+	0.409870i
$772$	−19.4215	−	3.74319i	−0.698996	−	0.134721i
$773$	30.6616	−	29.2357i	1.10282	−	1.05154i	0.104446	−	0.994531i	$-0.466693\pi$
$773$	30.6616	−	29.2357i	1.10282	−	1.05154i	0.998374	−	0.0570058i	$-0.0181554\pi$
$774$	30.6073	−	4.88223i	1.10016	−	0.175488i
$775$	−0.0724075	+	0.209208i	−0.00260095	+	0.00751497i
$776$	3.09341	+	6.77363i	0.111047	+	0.243159i
$777$	1.58539	−	3.88806i	0.0568754	−	0.139483i
$778$	2.95609	+	1.35000i	0.105981	+	0.0483999i
$779$	−24.7276	+	9.89943i	−0.885957	+	0.354684i
$780$	−2.99156	−	9.11612i	−0.107115	−	0.326410i
$781$	0.505909	+	0.292087i	0.0181029	+	0.0104517i
$782$	−15.8401	−	9.62171i	−0.566442	−	0.344072i
$783$	1.30581	+	1.24691i	0.0466657	+	0.0445608i
$784$	4.97115	−	4.92825i	0.177541	−	0.176009i
$785$	−41.8439	−	6.01624i	−1.49347	−	0.214729i
$786$	−3.48290	+	1.32965i	−0.124231	+	0.0474271i
$787$	−6.03729	−	1.46463i	−0.215206	−	0.0522084i	0.126706	−	0.991940i	$-0.459559\pi$
$787$	−6.03729	−	1.46463i	−0.215206	−	0.0522084i	−0.341912	+	0.939732i	$0.611075\pi$
$788$	−0.465366	+	4.87353i	−0.0165780	+	0.173612i
$789$	−0.141468	+	2.21750i	−0.00503641	+	0.0789450i
$790$	−1.41023	−	9.80837i	−0.0501738	−	0.348966i
$791$	−3.36203	−	9.41640i	−0.119540	−	0.334809i
$792$	−0.337938	−	0.0597573i	−0.0120081	−	0.00212338i
$793$	−10.4959	−	0.499981i	−0.372720	−	0.0177549i
$794$	−0.895711	−	1.73744i	−0.0317876	−	0.0616593i
$795$	1.09535	+	1.59186i	0.0388479	+	0.0564575i
$796$	−27.0636	+	6.56556i	−0.959243	+	0.232710i
$797$	2.44371	+	16.9963i	0.0865605	+	0.602041i	0.986219	+	0.165447i	$0.0529065\pi$
$797$	2.44371	+	16.9963i	0.0865605	+	0.602041i	−0.899658	+	0.436595i	$0.856184\pi$
$798$	−19.2220	+	12.1807i	−0.680450	+	0.431192i
$799$	−21.3734	+	9.76091i	−0.756137	+	0.345316i
$800$	−0.543265	+	0.569760i	−0.0192073	+	0.0201440i
$801$	0.608314	+	0.266579i	0.0214937	+	0.00941910i
$802$	12.6676	−	16.1082i	0.447310	−	0.568801i
$803$	−0.305815	−	0.157659i	−0.0107920	−	0.00556365i
$804$	−0.476803	−	1.72624i	−0.0168155	−	0.0608800i
$805$	−14.8396	−	21.4019i	−0.523027	−	0.754316i
$806$		−	0.758943i		−	0.0267326i
$807$	6.53904	−	31.2132i	0.230185	−	1.09876i
$808$	3.89303	+	3.06151i	0.136956	+	0.107704i
$809$	−5.55797	+	3.95781i	−0.195408	+	0.139149i	−0.673573	−	0.739121i	$-0.735241\pi$
$809$	−5.55797	+	3.95781i	−0.195408	+	0.139149i	0.478165	+	0.878270i	$0.341302\pi$
$810$	5.74693	+	17.5558i	0.201927	+	0.616847i
$811$	16.1179	+	35.2932i	0.565975	+	1.23931i	0.948913	+	0.315539i	$0.102185\pi$
$811$	16.1179	+	35.2932i	0.565975	+	1.23931i	−0.382937	+	0.923774i	$0.625087\pi$
$812$	0.627902	−	0.671490i	0.0220350	−	0.0235647i
$813$	14.1907	+	32.4466i	0.497689	+	1.13795i
$814$	0.0247111	+	0.101861i	0.000866124	+	0.00357021i
$815$	−0.914440	−	2.64210i	−0.0320314	−	0.0925488i
$816$	4.91808	−	4.54039i	0.172167	−	0.158945i
$817$	−2.44116	+	51.2462i	−0.0854053	+	1.79288i
$818$	22.2744	+	19.3008i	0.778805	+	0.674838i
$819$	3.52456	−	21.1294i	0.123158	−	0.738320i
$820$	10.8970	−	1.56675i	0.380540	−	0.0547134i
$821$	−51.4007	−	17.7899i	−1.79390	−	0.620873i	−0.999916	−	0.0129291i	$-0.995884\pi$
$821$	−51.4007	−	17.7899i	−1.79390	−	0.620873i	−0.793980	−	0.607944i	$-0.791994\pi$
$822$	3.74114	+	21.2473i	0.130487	+	0.741086i
$823$	2.42447	−	9.99381i	0.0845118	−	0.348362i	−0.913819	−	0.406122i	$-0.866881\pi$
$823$	2.42447	−	9.99381i	0.0845118	−	0.348362i	0.998330	+	0.0577600i	$0.0183958\pi$
$824$	10.8440	−	1.03548i	0.377770	−	0.0360727i
$825$	−0.0197085	−	0.154732i	−0.000686161	−	0.00538708i
$826$	11.5215	+	4.48289i	0.400883	+	0.155980i
$827$	−47.3197			−1.64547			−0.822734	−	0.568426i	$-0.807552\pi$
$827$	−47.3197			−1.64547			−0.822734	+	0.568426i	$0.807552\pi$
$828$	14.2266	+	2.14554i	0.494409	+	0.0745626i
$829$	4.92560	−	8.53140i	0.171073	−	0.296308i	−0.767722	−	0.640783i	$-0.778610\pi$
$829$	4.92560	−	8.53140i	0.171073	−	0.296308i	0.938795	+	0.344475i	$0.111943\pi$
$830$	−31.4451	+	1.49791i	−1.09147	+	0.0519933i
$831$	44.3343	−	33.7233i	1.53794	−	1.16985i
$832$	1.12114	−	2.45494i	0.0388684	−	0.0851099i
$833$	−23.0374	−	14.1793i	−0.798200	−	0.491285i
$834$	3.05952	−	2.56598i	0.105943	−	0.0888525i
$835$	42.1824	+	14.5995i	1.45978	+	0.505235i
$836$	0.211127	−	0.527371i	0.00730199	−	0.0182395i
$837$	−0.00106757	+	1.46122i	−3.69005e−5	+	0.0505071i
$838$	−2.23868	+	11.6154i	−0.0773341	+	0.401247i
$839$	−9.27955	−	5.96360i	−0.320366	−	0.205886i	0.370567	−	0.928806i	$-0.379163\pi$
$839$	−9.27955	−	5.96360i	−0.320366	−	0.205886i	−0.690932	+	0.722919i	$0.742800\pi$
$840$	8.90786	−	3.01957i	0.307350	−	0.104185i
$841$	−18.9119	+	21.8255i	−0.652134	+	0.752603i
$842$	4.02319	+	16.5838i	0.138648	+	0.571516i
$843$	−43.2489	−	4.83401i	−1.48957	−	0.166492i
$844$	2.87656	−	0.554412i	0.0990154	−	0.0190837i
$845$	6.80564	−	9.55718i	0.234121	−	0.328777i
$846$	12.3829	−	13.3933i	0.425733	−	0.460472i
$847$	19.2488	+	21.7823i	0.661398	+	0.748449i
$848$	−0.0773540	+	0.538009i	−0.00265635	+	0.0184753i
$849$	2.60161	−	12.4184i	0.0892871	−	0.426199i
$850$	2.63472	+	1.52116i	0.0903702	+	0.0521752i
$851$	−1.14384	−	4.24278i	−0.0392103	−	0.145441i
$852$	6.20612	−	6.30231i	0.212618	−	0.215914i
$853$	−19.8059	+	12.7285i	−0.678140	+	0.435814i	−0.833852	−	0.551988i	$-0.813869\pi$
$853$	−19.8059	+	12.7285i	−0.678140	+	0.435814i	0.155712	+	0.987803i	$0.450233\pi$
$854$	0.389978	−	10.2937i	0.0133448	−	0.352245i
$855$	−30.3905	+	3.37432i	−1.03933	+	0.115399i
$856$	−2.00428	+	2.10203i	−0.0685050	+	0.0718459i
$857$	−2.40557	+	25.1923i	−0.0821729	+	0.860553i	0.856592	+	0.515994i	$0.172577\pi$
$857$	−2.40557	+	25.1923i	−0.0821729	+	0.860553i	−0.938765	+	0.344559i	$0.888029\pi$
$858$	0.237341	+	0.479177i	0.00810269	+	0.0163588i
$859$	15.8935	−	12.4988i	0.542279	−	0.426453i	−0.309080	−	0.951036i	$-0.600021\pi$
$859$	15.8935	−	12.4988i	0.542279	−	0.426453i	0.851359	+	0.524583i	$0.175779\pi$
$860$	5.97420	−	20.3463i	0.203719	−	0.693802i
$861$	23.1761	+	8.18720i	0.789840	+	0.279019i
$862$	3.09975	−	4.82330i	0.105578	−	0.164282i
$863$	43.2065	+	2.05818i	1.47077	+	0.0700613i	0.767585	−	0.640947i	$-0.221458\pi$
$863$	43.2065	+	2.05818i	1.47077	+	0.0700613i	0.703183	+	0.711009i	$0.251761\pi$
$864$	−2.16201	+	4.72501i	−0.0735532	+	0.160748i
$865$	24.9389	+	26.1551i	0.847947	+	0.889301i
$866$	0.177505	−	0.139591i	0.00603187	−	0.00474351i
$867$	2.97848	+	1.98267i	0.101155	+	0.0673351i
$868$	0.743980	−	0.00724146i	0.0252523	−	0.000245791i
$869$	0.155595	+	0.529908i	0.00527820	+	0.0179759i
$870$	1.15404	−	0.440572i	0.0391255	−	0.0149368i
$871$	−1.72497	+	2.19348i	−0.0584485	+	0.0743233i
$872$	−0.111697	−	2.34481i	−0.00378254	−	0.0794053i
$873$	−10.8710	+	19.5162i	−0.367927	+	0.660524i
$874$	−8.28834	+	22.3266i	−0.280357	+	0.755208i
$875$	18.4778	+	25.4211i	0.624663	+	0.859390i
$876$	−3.47448	+	3.88161i	−0.117392	+	0.131148i
$877$	12.3852	−	4.95829i	0.418219	−	0.167430i	−0.153002	−	0.988226i	$-0.548894\pi$
$877$	12.3852	−	4.95829i	0.418219	−	0.167430i	0.571221	+	0.820796i	$0.306470\pi$
$878$	−1.70769	+	1.21604i	−0.0576316	+	0.0410393i
$879$	0.737173	+	23.4022i	0.0248642	+	0.789337i
$880$	−0.136193	+	0.191257i	−0.00459107	+	0.00644726i
$881$	18.3542	+	21.1818i	0.618368	+	0.713635i	0.975396	−	0.220459i	$-0.0707555\pi$
$881$	18.3542	+	21.1818i	0.618368	+	0.713635i	−0.357028	+	0.934094i	$0.616210\pi$
$882$	20.7464	+	3.25347i	0.698569	+	0.109550i
$883$	24.2439	+	7.11865i	0.815872	+	0.239562i	0.662938	−	0.748675i	$-0.269309\pi$
$883$	24.2439	+	7.11865i	0.815872	+	0.239562i	0.152935	+	0.988236i	$0.451128\pi$
$884$	−10.2411	−	1.97381i	−0.344446	−	0.0663865i
$885$	11.2682	+	12.2056i	0.378777	+	0.410285i
$886$	22.7155	−	11.7107i	0.763143	−	0.393427i
$887$	−4.45434	+	23.1113i	−0.149562	+	0.776002i	0.827239	+	0.561851i	$0.189910\pi$
$887$	−4.45434	+	23.1113i	−0.149562	+	0.776002i	−0.976801	+	0.214151i	$0.931302\pi$
$888$	1.58682	+	0.0255661i	0.0532500	+	0.000857941i
$889$	−37.0572	+	36.0290i	−1.24286	+	1.20838i
$890$	0.343410	−	0.297566i	0.0115111	−	0.00997445i
$891$	−0.456287	−	0.922909i	−0.0152862	−	0.0309186i
$892$	0.626753	−	2.58351i	0.0209853	−	0.0865024i
$893$	17.5138	+	24.5947i	0.586078	+	0.823032i
$894$	−10.2752	−	13.5083i	−0.343655	−	0.451786i
$895$	7.40391	+	11.5207i	0.247486	+	0.385095i
$896$	2.41724	+	1.07561i	0.0807544	+	0.0359336i
$897$	−10.4560	−	19.8305i	−0.349116	−	0.662119i
$898$	3.31214	+	5.73679i	0.110527	+	0.191439i
$899$	0.0976026	−	0.00464938i	0.00325523	−	0.000155066i
$900$	−2.34260	−	0.300121i	−0.0780868	−	0.0100040i
$901$	2.09099	−	0.199666i	0.0696611	−	0.00665183i
$902$	−0.588723	+	0.172865i	−0.0196023	+	0.00575576i
$903$	32.8893	−	34.0558i	1.09449	−	1.13331i
$904$	2.85606	−	2.47479i	0.0949913	−	0.0823104i
$905$	0.718550	+	0.913711i	0.0238854	+	0.0303728i
$906$	17.7626	+	10.6404i	0.590122	+	0.353503i
$907$	−51.6895	+	17.8899i	−1.71632	+	0.594025i	−0.995118	−	0.0986968i	$-0.968533\pi$
$907$	−51.6895	+	17.8899i	−1.71632	+	0.594025i	−0.721205	+	0.692722i	$0.756411\pi$
$908$	−1.36140	+	28.5793i	−0.0451797	+	0.948438i
$909$	−0.478643	+	14.8502i	−0.0158756	+	0.492549i
$910$	−12.0204	−	8.38457i	−0.398472	−	0.277946i
$911$	44.2574	+	12.9951i	1.46631	+	0.430548i	0.914899	−	0.403684i	$-0.132270\pi$
$911$	44.2574	+	12.9951i	1.46631	+	0.430548i	0.551414	+	0.834232i	$0.314089\pi$
$912$	−6.92498	−	5.10135i	−0.229309	−	0.168923i
$913$	1.72283	−	0.332049i	0.0570175	−	0.0109892i
$914$	−36.2160	−	3.45821i	−1.19792	−	0.114387i
$915$	6.53985	−	12.1989i	0.216201	−	0.403284i
$916$	−19.4345	−	8.87542i	−0.642132	−	0.293252i
$917$	−3.03203	+	4.82046i	−0.100127	+	0.159185i
$918$	19.7148	+	3.81465i	0.650685	+	0.125902i
$919$	44.6895	−	25.8015i	1.47417	−	0.851113i	0.474594	−	0.880205i	$-0.342595\pi$
$919$	44.6895	−	25.8015i	1.47417	−	0.851113i	0.999577	+	0.0290915i	$0.00926142\pi$
$920$	5.50479	−	8.16030i	0.181488	−	0.269037i
$921$	8.39117	−	32.3080i	0.276499	−	1.06459i
$922$	29.4201	+	15.1671i	0.968901	+	0.499503i
$923$	−13.6418	−	1.96140i	−0.449027	−	0.0645603i
$924$	−0.467465	+	0.237234i	−0.0153785	+	0.00780443i
$925$	0.203223	+	0.692112i	0.00668192	+	0.0227565i
$926$	16.0191	+	11.4071i	0.526419	+	0.374861i
$927$	21.7782	+	24.3659i	0.715290	+	0.800282i
$928$	0.322582	+	0.129142i	0.0105893	+	0.00423931i
$929$	43.2310	−	10.4877i	1.41836	−	0.344091i	0.547991	−	0.836484i	$-0.315393\pi$
$929$	43.2310	−	10.4877i	1.41836	−	0.344091i	0.870373	+	0.492393i	$0.163878\pi$
$930$	0.902565	+	0.429893i	0.0295963	+	0.0140967i
$931$	−12.2887	+	32.5163i	−0.402747	+	1.06568i
$932$	10.1903	−	15.8565i	0.333795	−	0.519396i
$933$	3.48723	+	44.0002i	0.114167	+	1.44050i
$934$	−23.7703	−	24.9295i	−0.777787	−	0.815720i
$935$	0.842357	+	0.337229i	0.0275480	+	0.0110286i
$936$	7.92568	−	1.65436i	0.259059	−	0.0540743i
$937$	−10.8821	+	4.96967i	−0.355502	+	0.162352i	−0.585157	−	0.810920i	$-0.698967\pi$
$937$	−10.8821	+	4.96967i	−0.355502	+	0.162352i	0.229656	+	0.973272i	$0.426240\pi$
$938$	−2.16670	−	1.67004i	−0.0707452	−	0.0545287i
$939$	5.51330	+	0.883567i	0.179920	+	0.0288341i
$940$	−4.63819	−	11.5856i	−0.151281	−	0.377882i
$941$	0.437814	+	9.19085i	0.0142723	+	0.299613i	0.994706	+	0.102763i	$0.0327683\pi$
$941$	0.437814	+	9.19085i	0.0142723	+	0.299613i	−0.980434	+	0.196850i	$0.936929\pi$
$942$	8.96788	−	34.5285i	0.292189	−	1.12500i
$943$	24.4901	−	7.87012i	0.797506	−	0.256286i
$944$			4.67273i			0.152084i
$945$	23.1315	+	16.1600i	0.752466	+	0.525685i
$946$	−0.168195	+	1.16982i	−0.00546848	+	0.0380341i
$947$	−5.79761	−	60.7153i	−0.188397	−	1.97298i	−0.227616	−	0.973751i	$-0.573093\pi$
$947$	−5.79761	−	60.7153i	−0.188397	−	1.97298i	0.0392195	−	0.999231i	$-0.487513\pi$
$948$	8.35800	−	0.263278i	0.271455	−	0.00855088i
$949$	8.08055	+	0.771599i	0.262306	+	0.0250471i
$950$	1.27863	−	3.69436i	0.0414842	−	0.119861i
$951$	−26.5258	+	11.6012i	−0.860158	+	0.376194i
$952$	1.83718	−	10.0580i	0.0595435	−	0.325983i
$953$	−9.85405	+	11.3722i	−0.319204	+	0.368381i	−0.892563	−	0.450923i	$-0.851095\pi$
$953$	−9.85405	+	11.3722i	−0.319204	+	0.368381i	0.573359	+	0.819305i	$0.305640\pi$
$954$	−1.43769	+	0.769396i	−0.0465470	+	0.0249101i
$955$	31.1451	−	16.0564i	1.00783	−	0.519573i
$956$	−14.5850	+	5.04791i	−0.471712	+	0.163261i
$957$	−0.0601698	+	0.0334584i	−0.00194501	+	0.00108156i
$958$	−7.68183	+	1.10448i	−0.248189	+	0.0356841i
$959$	24.0709	+	22.5084i	0.777291	+	0.726835i
$960$	2.28447	+	2.72387i	0.0737309	+	0.0879125i
$961$	−22.3785	−	21.3379i	−0.721888	−	0.688319i
$962$	−1.43439	−	2.01433i	−0.0462467	−	0.0649445i
$963$	−8.64264	−	1.10724i	−0.278505	−	0.0356805i
$964$	11.7879	−	22.8654i	0.379663	−	0.736444i
$965$	−40.5963			−1.30684
$966$	19.3397	−	10.4391i	0.622246	−	0.335872i
$967$	53.0293			1.70531			0.852654	−	0.522475i	$-0.174991\pi$
$967$	53.0293			1.70531			0.852654	+	0.522475i	$0.174991\pi$
$968$	−5.03450	+	9.76556i	−0.161815	+	0.313877i
$969$	−12.8491	+	30.6549i	−0.412774	+	0.984776i
$970$	8.86563	+	12.4500i	0.284658	+	0.399746i
$971$	39.4691	+	37.6337i	1.26662	+	1.20772i	0.967318	+	0.253568i	$0.0816040\pi$
$971$	39.4691	+	37.6337i	1.26662	+	1.20772i	0.299307	+	0.954157i	$0.403244\pi$
$972$	−15.2619	+	3.17404i	−0.489526	+	0.101807i
$973$	1.38027	−	5.94135i	0.0442493	−	0.190471i
$974$	25.2575	−	3.63149i	0.809304	−	0.116360i
$975$	1.78843	+	3.21621i	0.0572755	+	0.103001i
$976$	3.67932	−	1.27343i	0.117772	−	0.0407614i
$977$	31.9698	−	16.4816i	1.02281	−	0.527293i	0.136620	−	0.990624i	$-0.456376\pi$
$977$	31.9698	−	16.4816i	1.02281	−	0.527293i	0.886186	+	0.463331i	$0.153346\pi$
$978$	2.30152	−	0.519232i	0.0735945	−	0.0166032i
$979$	−0.0165845	+	0.0191396i	−0.000530044	+	0.000611703i
$980$	8.10458	−	11.8634i	0.258891	−	0.378963i
$981$	5.46810	−	4.43795i	0.174583	−	0.141693i
$982$	−11.7719	+	34.0127i	−0.375656	+	1.08539i
$983$	52.5411	+	5.01707i	1.67580	+	0.160020i	0.889224	−	0.457473i	$-0.151245\pi$
$983$	52.5411	+	5.01707i	1.67580	+	0.160020i	0.786577	+	0.617492i	$0.211851\pi$
$984$	0.292499	+	9.28566i	0.00932454	+	0.296016i
$985$	0.955162	+	10.0029i	0.0304340	+	0.318719i
$986$	0.191101	−	1.32913i	0.00608588	−	0.0423282i
$987$	2.82536	−	27.7193i	0.0899323	−	0.882315i
$988$			13.4020i			0.426375i
$989$	5.80667	−	49.2063i	0.184641	−	1.56467i
$990$	−0.704295	+	0.0108326i	−0.0223840	+	0.000344283i
$991$	−0.134774	−	2.82925i	−0.00428123	−	0.0898740i	0.995715	−	0.0924707i	$-0.0294765\pi$
$991$	−0.134774	−	2.82925i	−0.00428123	−	0.0898740i	−0.999997	+	0.00259674i	$0.999173\pi$
$992$	0.104516	+	0.261068i	0.00331838	+	0.00828891i
$993$	4.53709	−	28.3106i	0.143980	−	0.898411i
$994$	1.79257	−	13.3916i	0.0568568	−	0.424756i
$995$	−51.9938	+	23.7448i	−1.64832	+	0.752760i
$996$	1.69136	−	26.5119i	0.0535929	−	0.840061i
$997$	−44.7486	−	17.9146i	−1.41720	−	0.567362i	−0.468480	−	0.883474i	$-0.655198\pi$
$997$	−44.7486	−	17.9146i	−1.41720	−	0.567362i	−0.948722	+	0.316112i	$0.897622\pi$
$998$	4.88387	+	5.12205i	0.154596	+	0.162136i
$999$	2.75885	+	3.88027i	0.0872863	+	0.122766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bf.a.11.5	✓	1280
3.2	odd	2	inner	966.2.bf.a.11.42	yes	1280
7.2	even	3	inner	966.2.bf.a.149.58	yes	1280
21.2	odd	6	inner	966.2.bf.a.149.31	yes	1280
23.21	odd	22	inner	966.2.bf.a.389.31	yes	1280
69.44	even	22	inner	966.2.bf.a.389.58	yes	1280
161.44	odd	66	inner	966.2.bf.a.527.42	yes	1280
483.44	even	66	inner	966.2.bf.a.527.5	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.5	✓	1280	1.1	even	1	trivial
966.2.bf.a.11.42	yes	1280	3.2	odd	2	inner
966.2.bf.a.149.31	yes	1280	21.2	odd	6	inner
966.2.bf.a.149.58	yes	1280	7.2	even	3	inner
966.2.bf.a.389.31	yes	1280	23.21	odd	22	inner
966.2.bf.a.389.58	yes	1280	69.44	even	22	inner
966.2.bf.a.527.5	yes	1280	483.44	even	66	inner
966.2.bf.a.527.42	yes	1280	161.44	odd	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.59740 - 0.669558i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.48546 - 1.41639i) q^{5} +(1.32710 - 1.11302i) q^{6} +(0.598705 - 2.57712i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.10338 + 2.13911i) q^{9} +O(q^{10})\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.59740 - 0.669558i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.48546 - 1.41639i) q^{5} +(1.32710 - 1.11302i) q^{6} +(0.598705 - 2.57712i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.10338 + 2.13911i) q^{9} +(1.93961 - 0.671307i) q^{10} +(-0.101677 + 0.0524182i) q^{11} +(0.381178 + 1.68959i) q^{12} +(1.76736 - 2.03964i) q^{13} +(2.01629 + 1.71306i) q^{14} +(1.42453 + 3.25714i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(3.84698 + 0.367342i) q^{17} +(-2.86514 + 0.889366i) q^{18} +(-0.472034 - 4.94337i) q^{19} +(-0.292101 + 2.03161i) q^{20} +(-2.68191 + 3.71583i) q^{21} -0.114394i q^{22} +(0.121496 + 4.79429i) q^{23} +(-1.67643 - 0.435409i) q^{24} +(-0.0374589 - 0.786358i) q^{25} +(1.00305 + 2.50551i) q^{26} +(-1.92769 - 4.82535i) q^{27} +(-2.44654 + 1.00719i) q^{28} +(-0.316072 + 0.144345i) q^{29} +(-3.54782 - 0.226338i) q^{30} +(-0.261068 - 0.104516i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(0.197516 - 0.0156541i) q^{33} +(-2.08930 + 3.25101i) q^{34} +(-4.53955 + 2.98022i) q^{35} +(0.522383 - 2.95417i) q^{36} +(-0.890439 + 0.216018i) q^{37} +(4.61014 + 1.84562i) q^{38} +(-4.18884 + 2.07478i) q^{39} +(-1.67192 - 1.19057i) q^{40} +(-1.51114 - 5.14647i) q^{41} +(-2.07384 - 4.08646i) q^{42} +(-10.2263 - 1.47031i) q^{43} +(0.101677 + 0.0524182i) q^{44} +(-0.0946959 - 6.15677i) q^{45} +(-4.31701 - 2.08888i) q^{46} +(-5.26560 + 3.04009i) q^{47} +(1.15519 - 1.29055i) q^{48} +(-6.28310 - 3.08587i) q^{49} +(0.716108 + 0.327035i) q^{50} +(-5.89922 - 3.16257i) q^{51} +(-2.68661 - 0.256540i) q^{52} +(0.533719 - 0.102866i) q^{53} +(5.17226 + 0.497705i) q^{54} +(0.225282 + 0.0661488i) q^{55} +(0.225848 - 2.63609i) q^{56} +(-2.55585 + 8.21260i) q^{57} +(0.0165334 - 0.347079i) q^{58} +(4.41573 - 1.52830i) q^{59} +(1.82688 - 3.04971i) q^{60} +(-2.40678 - 3.06047i) q^{61} +(0.212525 - 0.184154i) q^{62} +(6.77204 - 4.13998i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-5.51427 + 0.526549i) q^{65} +(-0.0765932 + 0.182733i) q^{66} +(-1.03280 + 0.0491981i) q^{67} +(-1.93224 - 3.34674i) q^{68} +(3.01598 - 7.73976i) q^{69} +(-0.568782 - 5.40053i) q^{70} +(-2.76089 - 4.29603i) q^{71} +(2.38640 + 1.81799i) q^{72} +(1.74464 + 2.45001i) q^{73} +(0.216018 - 0.890439i) q^{74} +(-0.466676 + 1.28121i) q^{75} +(-3.75294 + 3.25194i) q^{76} +(0.0742134 + 0.293417i) q^{77} +(0.0753039 - 4.67391i) q^{78} +(0.913684 - 4.74064i) q^{79} +(1.82433 - 0.940509i) q^{80} +(-0.151560 + 8.99872i) q^{81} +(5.26681 + 1.01509i) q^{82} +(-14.7165 - 4.32114i) q^{83} +(4.58248 + 0.0292232i) q^{84} +(-5.19425 - 5.99449i) q^{85} +(5.99281 - 8.41572i) q^{86} +(0.601542 - 0.0189486i) q^{87} +(-0.0931823 + 0.0663548i) q^{88} +(0.205529 - 0.0822812i) q^{89} +(5.51575 + 2.73703i) q^{90} +(-4.19828 - 5.77584i) q^{91} +(3.83484 - 2.87993i) q^{92} +(0.347051 + 0.341754i) q^{93} +(-0.289307 - 6.07330i) q^{94} +(-6.30053 + 8.01177i) q^{95} +(0.617751 + 1.61814i) q^{96} +(2.09794 + 7.14493i) q^{97} +(5.62192 - 4.17062i) q^{98} +(-0.325994 - 0.107243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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