LMFDB - Embedded newform 228.2.m.a.83.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(11,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			83.4
Character	$\chi$	$=$	228.83
Dual form			228.2.m.a.11.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34509 + 0.436732i) q^{2} +(1.04438 + 1.38176i) q^{3} +(1.61853 - 1.17489i) q^{4} +(-1.24455 + 0.718541i) q^{5} +(-2.00825 - 1.40248i) q^{6} +1.00140i q^{7} +(-1.66396 + 2.28719i) q^{8} +(-0.818536 + 2.88617i) q^{9} +(1.36022 - 1.51004i) q^{10} +2.30738 q^{11} +(3.31378 + 1.00939i) q^{12} +(-1.89855 + 3.28839i) q^{13} +(-0.437344 - 1.34697i) q^{14} +(-2.29264 - 0.969241i) q^{15} +(1.23928 - 3.80318i) q^{16} +(-2.69636 + 1.55674i) q^{17} +(-0.159482 - 4.23964i) q^{18} +(3.95943 - 1.82288i) q^{19} +(-1.17014 + 2.62518i) q^{20} +(-1.38370 + 1.04584i) q^{21} +(-3.10363 + 1.00771i) q^{22} +(0.457022 - 0.791584i) q^{23} +(-4.89816 + 0.0895094i) q^{24} +(-1.46740 + 2.54161i) q^{25} +(1.11758 - 5.25234i) q^{26} +(-4.84287 + 1.88324i) q^{27} +(1.17653 + 1.62080i) q^{28} +(-1.05901 - 0.611420i) q^{29} +(3.50710 + 0.302447i) q^{30} +5.13118i q^{31} +(-0.00596757 + 5.65685i) q^{32} +(2.40978 + 3.18825i) q^{33} +(2.94696 - 3.27154i) q^{34} +(-0.719547 - 1.24629i) q^{35} +(2.06611 + 5.63305i) q^{36} -4.22366 q^{37} +(-4.52968 + 4.18115i) q^{38} +(-6.52659 + 0.810984i) q^{39} +(0.427433 - 4.04214i) q^{40} +(9.12867 - 5.27044i) q^{41} +(1.40444 - 2.01106i) q^{42} +(7.83509 - 4.52359i) q^{43} +(3.73456 - 2.71091i) q^{44} +(-1.05513 - 4.18014i) q^{45} +(-0.269024 + 1.26435i) q^{46} +(4.71344 - 8.16392i) q^{47} +(6.54937 - 2.25958i) q^{48} +5.99720 q^{49} +(0.863780 - 4.05955i) q^{50} +(-4.96707 - 2.09989i) q^{51} +(0.790625 + 7.55295i) q^{52} +(-2.17897 - 1.25803i) q^{53} +(5.69162 - 4.64817i) q^{54} +(-2.87165 + 1.65795i) q^{55} +(-2.29040 - 1.66629i) q^{56} +(6.65395 + 3.56721i) q^{57} +(1.69149 + 0.359910i) q^{58} +(0.176619 + 0.305912i) q^{59} +(-4.84945 + 1.12484i) q^{60} +(5.51674 - 9.55527i) q^{61} +(-2.24095 - 6.90190i) q^{62} +(-2.89022 - 0.819682i) q^{63} +(-2.46250 - 7.61158i) q^{64} -5.45675i q^{65} +(-4.63379 - 3.23605i) q^{66} +(-5.71202 - 3.29784i) q^{67} +(-2.53514 + 5.68755i) q^{68} +(1.57109 - 0.195221i) q^{69} +(1.51215 + 1.36212i) q^{70} +(5.35069 + 9.26766i) q^{71} +(-5.23923 - 6.67461i) q^{72} +(0.163973 + 0.284010i) q^{73} +(5.68120 - 1.84461i) q^{74} +(-5.04442 + 0.626812i) q^{75} +(4.26678 - 7.60228i) q^{76} +2.31061i q^{77} +(8.42467 - 3.94122i) q^{78} +(3.78812 - 2.18707i) q^{79} +(1.19040 + 5.62372i) q^{80} +(-7.66000 - 4.72487i) q^{81} +(-9.97710 + 11.0760i) q^{82} +14.9113 q^{83} +(-1.01081 + 3.31842i) q^{84} +(2.23716 - 3.87488i) q^{85} +(-8.56330 + 9.50647i) q^{86} +(-0.261173 - 2.10186i) q^{87} +(-3.83938 + 5.27742i) q^{88} +(8.48010 + 4.89599i) q^{89} +(3.24484 + 5.16185i) q^{90} +(-3.29300 - 1.90121i) q^{91} +(-0.190320 - 1.81815i) q^{92} +(-7.09007 + 5.35891i) q^{93} +(-2.77455 + 13.0397i) q^{94} +(-3.61789 + 5.11368i) q^{95} +(-7.82266 + 5.89966i) q^{96} +(-4.96660 - 8.60241i) q^{97} +(-8.06677 + 2.61917i) q^{98} +(-1.88867 + 6.65950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) $ 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.34509	+	0.436732i	−0.951122	+	0.308816i
$2$	−1.34509	+	0.436732i	−0.951122	+	0.308816i
$3$	1.04438	+	1.38176i	0.602974	+	0.797761i
$3$	1.04438	+	1.38176i	0.602974	+	0.797761i
$4$	1.61853	−	1.17489i	0.809265	−	0.587444i
$5$	−1.24455	+	0.718541i	−0.556579	+	0.321341i	−0.751771	−	0.659424i	$-0.770800\pi$
$5$	−1.24455	+	0.718541i	−0.556579	+	0.321341i	0.195192	+	0.980765i	$0.437467\pi$
$6$	−2.00825	−	1.40248i	−0.819863	−	0.572560i
$7$			1.00140i			0.378494i	0.981930	+	0.189247i	$0.0606046\pi$
$7$			1.00140i			0.378494i	−0.981930	+	0.189247i	$0.939395\pi$
$8$	−1.66396	+	2.28719i	−0.588297	+	0.808645i
$9$	−0.818536	+	2.88617i	−0.272845	+	0.962058i
$10$	1.36022	−	1.51004i	0.430139	−	0.477515i
$11$	2.30738			0.695701			0.347851	−	0.937550i	$-0.386912\pi$
$11$	2.30738			0.695701			0.347851	+	0.937550i	$0.386912\pi$
$12$	3.31378	+	1.00939i	0.956605	+	0.291387i
$13$	−1.89855	+	3.28839i	−0.526564	+	0.912036i	0.472957	+	0.881086i	$0.343187\pi$
$13$	−1.89855	+	3.28839i	−0.526564	+	0.912036i	−0.999521	+	0.0309503i	$0.990147\pi$
$14$	−0.437344	−	1.34697i	−0.116885	−	0.359994i
$15$	−2.29264	−	0.969241i	−0.591956	−	0.250257i
$16$	1.23928	−	3.80318i	0.309820	−	0.950795i
$17$	−2.69636	+	1.55674i	−0.653962	+	0.377565i	−0.789973	−	0.613142i	$-0.789905\pi$
$17$	−2.69636	+	1.55674i	−0.653962	+	0.377565i	0.136010	+	0.990707i	$0.456572\pi$
$18$	−0.159482	−	4.23964i	−0.0375902	−	0.999293i
$19$	3.95943	−	1.82288i	0.908356	−	0.418198i
$19$	3.95943	−	1.82288i	0.908356	−	0.418198i
$20$	−1.17014	+	2.62518i	−0.261650	+	0.587009i
$21$	−1.38370	+	1.04584i	−0.301948	+	0.228222i
$22$	−3.10363	+	1.00771i	−0.661696	+	0.214844i
$23$	0.457022	−	0.791584i	0.0952956	−	0.165057i	−0.814436	−	0.580253i	$-0.802954\pi$
$23$	0.457022	−	0.791584i	0.0952956	−	0.165057i	0.909732	+	0.415196i	$0.136287\pi$
$24$	−4.89816	+	0.0895094i	−0.999833	+	0.0182710i
$25$	−1.46740	+	2.54161i	−0.293480	+	0.508322i
$26$	1.11758	−	5.25234i	0.219175	−	1.03007i
$27$	−4.84287	+	1.88324i	−0.932011	+	0.362430i
$28$	1.17653	+	1.62080i	0.222344	+	0.306302i
$29$	−1.05901	−	0.611420i	−0.196653	−	0.113538i	0.398440	−	0.917194i	$-0.369552\pi$
$29$	−1.05901	−	0.611420i	−0.196653	−	0.113538i	−0.595094	+	0.803656i	$0.702885\pi$
$30$	3.50710	+	0.302447i	0.640306	+	0.0552190i
$31$			5.13118i			0.921587i	0.887507	+	0.460794i	$0.152435\pi$
$31$			5.13118i			0.921587i	−0.887507	+	0.460794i	$0.847565\pi$
$32$	−0.00596757	+	5.65685i	−0.00105493	+	0.999999i
$33$	2.40978	+	3.18825i	0.419489	+	0.555003i
$34$	2.94696	−	3.27154i	0.505399	−	0.561065i
$35$	−0.719547	−	1.24629i	−0.121626	−	0.210662i
$36$	2.06611	+	5.63305i	0.344351	+	0.938841i
$37$	−4.22366			−0.694365			−0.347183	−	0.937798i	$-0.612862\pi$
$37$	−4.22366			−0.694365			−0.347183	+	0.937798i	$0.612862\pi$
$38$	−4.52968	+	4.18115i	−0.734811	+	0.678272i
$39$	−6.52659	+	0.810984i	−1.04509	+	0.129861i
$40$	0.427433	−	4.04214i	0.0675831	−	0.639119i
$41$	9.12867	−	5.27044i	1.42566	−	0.823104i	0.428884	−	0.903360i	$-0.358907\pi$
$41$	9.12867	−	5.27044i	1.42566	−	0.823104i	0.996774	+	0.0802554i	$0.0255736\pi$
$42$	1.40444	−	2.01106i	0.216710	−	0.310313i
$43$	7.83509	−	4.52359i	1.19484	−	0.689841i	0.235440	−	0.971889i	$-0.424347\pi$
$43$	7.83509	−	4.52359i	1.19484	−	0.689841i	0.959400	+	0.282048i	$0.0910136\pi$
$44$	3.73456	−	2.71091i	0.563006	−	0.408685i
$45$	−1.05513	−	4.18014i	−0.157289	−	0.623138i
$46$	−0.269024	+	1.26435i	−0.0396655	+	0.186418i
$47$	4.71344	−	8.16392i	0.687526	−	1.19083i	−0.285110	−	0.958495i	$-0.592030\pi$
$47$	4.71344	−	8.16392i	0.687526	−	1.19083i	0.972636	−	0.232335i	$-0.0746365\pi$
$48$	6.54937	−	2.25958i	0.945321	−	0.326143i
$49$	5.99720			0.856742
$50$	0.863780	−	4.05955i	0.122157	−	0.574107i
$51$	−4.96707	−	2.09989i	−0.695529	−	0.294044i
$52$	0.790625	+	7.55295i	0.109640	+	1.04741i
$53$	−2.17897	−	1.25803i	−0.299305	−	0.172804i	0.342826	−	0.939399i	$-0.388616\pi$
$53$	−2.17897	−	1.25803i	−0.299305	−	0.172804i	−0.642131	+	0.766595i	$0.721949\pi$
$54$	5.69162	−	4.64817i	0.774531	−	0.632536i
$55$	−2.87165	+	1.65795i	−0.387213	+	0.223557i
$56$	−2.29040	−	1.66629i	−0.306067	−	0.222667i
$57$	6.65395	+	3.56721i	0.881337	+	0.472489i
$58$	1.69149	+	0.359910i	0.222104	+	0.0472586i
$59$	0.176619	+	0.305912i	0.0229938	+	0.0398264i	0.877293	−	0.479955i	$-0.159347\pi$
$59$	0.176619	+	0.305912i	0.0229938	+	0.0398264i	−0.854300	+	0.519781i	$0.826014\pi$
$60$	−4.84945	+	1.12484i	−0.626061	+	0.145217i
$61$	5.51674	−	9.55527i	0.706346	−	1.22343i	−0.259857	−	0.965647i	$-0.583676\pi$
$61$	5.51674	−	9.55527i	0.706346	−	1.22343i	0.966204	−	0.257780i	$-0.0829911\pi$
$62$	−2.24095	−	6.90190i	−0.284601	−	0.876542i
$63$	−2.89022	−	0.819682i	−0.364133	−	0.103270i
$64$	−2.46250	−	7.61158i	−0.307813	−	0.951447i
$65$		−	5.45675i		−	0.676827i
$66$	−4.63379	−	3.23605i	−0.570380	−	0.398330i
$67$	−5.71202	−	3.29784i	−0.697835	−	0.402895i	0.108706	−	0.994074i	$-0.465329\pi$
$67$	−5.71202	−	3.29784i	−0.697835	−	0.402895i	−0.806541	+	0.591179i	$0.798663\pi$
$68$	−2.53514	+	5.68755i	−0.307430	+	0.689717i
$69$	1.57109	−	0.195221i	0.189137	−	0.0235018i
$70$	1.51215	+	1.36212i	0.180737	+	0.162805i
$71$	5.35069	+	9.26766i	0.635010	+	1.09987i	0.986513	+	0.163683i	$0.0523373\pi$
$71$	5.35069	+	9.26766i	0.635010	+	1.09987i	−0.351503	+	0.936187i	$0.614329\pi$
$72$	−5.23923	−	6.67461i	−0.617449	−	0.786611i
$73$	0.163973	+	0.284010i	0.0191916	+	0.0332409i	0.875462	−	0.483287i	$-0.160557\pi$
$73$	0.163973	+	0.284010i	0.0191916	+	0.0332409i	−0.856270	+	0.516528i	$0.827224\pi$
$74$	5.68120	−	1.84461i	0.660426	−	0.214431i
$75$	−5.04442	+	0.626812i	−0.582480	+	0.0723780i
$76$	4.26678	−	7.60228i	0.489433	−	0.872041i
$77$			2.31061i			0.263318i
$78$	8.42467	−	3.94122i	0.953906	−	0.446255i
$79$	3.78812	−	2.18707i	0.426197	−	0.246065i	−0.271528	−	0.962431i	$-0.587529\pi$
$79$	3.78812	−	2.18707i	0.426197	−	0.246065i	0.697725	+	0.716365i	$0.254196\pi$
$80$	1.19040	+	5.62372i	0.133091	+	0.628751i
$81$	−7.66000	−	4.72487i	−0.851111	−	0.524986i
$82$	−9.97710	+	11.0760i	−1.10179	+	1.22314i
$83$	14.9113			1.63673			0.818364	−	0.574701i	$-0.194881\pi$
$83$	14.9113			1.63673			0.818364	+	0.574701i	$0.194881\pi$
$84$	−1.01081	+	3.31842i	−0.110288	+	0.362069i
$85$	2.23716	−	3.87488i	0.242655	−	0.420290i
$86$	−8.56330	+	9.50647i	−0.923404	+	1.02511i
$87$	−0.261173	−	2.10186i	−0.0280007	−	0.225343i
$88$	−3.83938	+	5.27742i	−0.409279	+	0.562575i
$89$	8.48010	+	4.89599i	0.898888	+	0.518973i	0.876839	−	0.480783i	$-0.159648\pi$
$89$	8.48010	+	4.89599i	0.898888	+	0.518973i	0.0220490	+	0.999757i	$0.492981\pi$
$90$	3.24484	+	5.16185i	0.342036	+	0.544107i
$91$	−3.29300	−	1.90121i	−0.345200	−	0.199301i
$92$	−0.190320	−	1.81815i	−0.0198422	−	0.189555i
$93$	−7.09007	+	5.35891i	−0.735206	+	0.555693i
$94$	−2.77455	+	13.0397i	−0.286173	+	1.34494i
$95$	−3.61789	+	5.11368i	−0.371188	+	0.524652i
$96$	−7.82266	+	5.89966i	−0.798397	+	0.602132i
$97$	−4.96660	−	8.60241i	−0.504282	−	0.873442i	−0.999988	−	0.00495141i	$-0.998424\pi$
$97$	−4.96660	−	8.60241i	−0.504282	−	0.873442i	0.495706	−	0.868490i	$-0.334909\pi$
$98$	−8.06677	+	2.61917i	−0.814866	+	0.264576i
$99$	−1.88867	+	6.65950i	−0.189819	+	0.669305i
$100$	0.611076	+	5.83770i	0.0611076	+	0.583770i
$101$	−12.4727	−	7.20112i	−1.24108	−	0.716539i	−0.271767	−	0.962363i	$-0.587608\pi$
$101$	−12.4727	−	7.20112i	−1.24108	−	0.716539i	−0.969314	+	0.245825i	$0.920941\pi$
$102$	7.59824	+	0.655262i	0.752338	+	0.0648806i
$103$			20.0454i			1.97513i	0.157209	+	0.987565i	$0.449750\pi$
$103$			20.0454i			1.97513i	−0.157209	+	0.987565i	$0.550250\pi$
$104$	−4.36208	−	9.81410i	−0.427737	−	0.962352i
$105$	0.970598	−	2.29585i	0.0947207	−	0.224052i
$106$	3.48033	+	0.740535i	0.338040	+	0.0719271i
$107$	6.46121			0.624629			0.312314	−	0.949979i	$-0.398896\pi$
$107$	6.46121			0.624629			0.312314	+	0.949979i	$0.398896\pi$
$108$	−5.62573	+	8.73791i	−0.541336	+	0.840806i
$109$	0.303425	+	0.525548i	0.0290629	+	0.0503384i	0.880191	−	0.474620i	$-0.157414\pi$
$109$	0.303425	+	0.525548i	0.0290629	+	0.0503384i	−0.851128	+	0.524958i	$0.824081\pi$
$110$	3.13854	−	3.48423i	0.299248	−	0.332208i
$111$	−4.41111	−	5.83609i	−0.418684	−	0.553937i
$112$	3.80851	+	1.24101i	0.359870	+	0.117265i
$113$			13.4479i			1.26507i	0.774531	+	0.632536i	$0.217986\pi$
$113$			13.4479i			1.26507i	−0.774531	+	0.632536i	$0.782014\pi$
$114$	−10.5081	−	1.89223i	−0.984171	−	0.177223i
$115$			1.31355i			0.122490i
$116$	−2.43239	+	0.254617i	−0.225842	+	0.0236406i
$117$	−7.93684	−	8.17122i	−0.733761	−	0.755430i
$118$	−0.371170	−	0.334345i	−0.0341689	−	0.0307789i
$119$	−1.55892	−	2.70013i	−0.142906	−	0.247521i
$120$	6.03169	−	3.63093i	0.550615	−	0.331457i
$121$	−5.67600			−0.516000
$122$	−3.24741	+	15.2620i	−0.294007	+	1.38176i
$123$	16.8163	+	7.10930i	1.51627	+	0.641024i
$124$	6.02856	+	8.30497i	0.541381	+	0.745808i
$125$		−	11.4029i		−	1.01991i
$126$	4.24558	−	0.159705i	0.378226	−	0.0142276i
$127$	−14.2542	−	8.22968i	−1.26486	−	0.730266i	−0.290847	−	0.956769i	$-0.593937\pi$
$127$	−14.2542	−	8.22968i	−1.26486	−	0.730266i	−0.974010	+	0.226504i	$0.927271\pi$
$128$	6.63651	+	9.16279i	0.586590	+	0.809884i
$129$	14.4334	+	6.10188i	1.27079	+	0.537241i
$130$	2.38314	+	7.33982i	0.209015	+	0.643745i
$131$	−6.64121	−	11.5029i	−0.580245	−	1.00501i	−0.995450	−	0.0952861i	$-0.969623\pi$
$131$	−6.64121	−	11.5029i	−0.580245	−	1.00501i	0.415205	−	0.909728i	$-0.363710\pi$
$132$	7.64614	+	2.32905i	0.665511	+	0.202718i
$133$	1.82543	+	3.96498i	0.158285	+	0.343807i
$134$	9.12346	+	1.94126i	0.788147	+	0.167700i
$135$	4.67400	−	5.82359i	0.402274	−	0.501215i
$136$	0.926048	−	8.75744i	0.0794080	−	0.750944i
$137$	6.92053	+	3.99557i	0.591261	+	0.341364i	0.765596	−	0.643322i	$-0.222444\pi$
$137$	6.92053	+	3.99557i	0.591261	+	0.341364i	−0.174335	+	0.984686i	$0.555778\pi$
$138$	−2.02799	+	0.948733i	−0.172634	+	0.0807616i
$139$	−9.72287	−	5.61350i	−0.824683	−	0.476131i	0.0273457	−	0.999626i	$-0.491295\pi$
$139$	−9.72287	−	5.61350i	−0.824683	−	0.476131i	−0.852029	+	0.523495i	$0.824628\pi$
$140$	−2.62886	−	1.17177i	−0.222179	−	0.0990329i
$141$	16.2032	−	2.01339i	1.36456	−	0.169558i
$142$	−11.2446	−	10.1290i	−0.943629	−	0.850008i
$143$	−4.38068	+	7.58757i	−0.366331	+	0.634504i
$144$	9.96225	+	6.68981i	0.830187	+	0.557484i
$145$	1.75732			0.145938
$146$	−0.344595	−	0.310407i	−0.0285189	−	0.0256894i
$147$	6.26336	+	8.28670i	0.516593	+	0.683476i
$148$	−6.83612	+	4.96232i	−0.561925	+	0.407901i
$149$	−17.8388	+	10.2993i	−1.46141	+	0.843748i	−0.999077	−	0.0429559i	$-0.986322\pi$
$149$	−17.8388	+	10.2993i	−1.46141	+	0.843748i	−0.462338	+	0.886704i	$0.652989\pi$
$150$	6.51145	−	3.04618i	0.531658	−	0.248720i
$151$		−	13.1949i		−	1.07378i	−0.843651	−	0.536892i	$-0.819598\pi$
$151$		−	13.1949i		−	1.07378i	0.843651	−	0.536892i	$-0.180402\pi$
$152$	−2.41904	+	12.0892i	−0.196210	+	0.980562i
$153$	−2.28596	−	9.05640i	−0.184809	−	0.732167i
$154$	−1.00912	−	3.10798i	−0.0813170	−	0.250448i
$155$	−3.68696	−	6.38600i	−0.296144	−	0.512936i
$156$	−9.61067	+	8.98061i	−0.769469	+	0.719025i
$157$	−0.358460	−	0.620871i	−0.0286082	−	0.0495509i	0.851367	−	0.524571i	$-0.175774\pi$
$157$	−0.358460	−	0.620871i	−0.0286082	−	0.0495509i	−0.879975	+	0.475020i	$0.842441\pi$
$158$	−4.14020	+	4.59621i	−0.329377	+	0.365655i
$159$	−0.537378	−	4.32468i	−0.0426169	−	0.342970i
$160$	−4.05725	−	7.04452i	−0.320754	−	0.556918i
$161$	0.792693	+	0.457662i	0.0624730	+	0.0360688i
$162$	12.3669	+	3.01001i	0.971634	+	0.236489i
$163$		−	8.71919i		−	0.682940i	−0.939893	−	0.341470i	$-0.889075\pi$
$163$		−	8.71919i		−	0.682940i	0.939893	−	0.341470i	$-0.110925\pi$
$164$	8.58285	−	19.2555i	0.670208	−	1.50360i
$165$	−5.28998	−	2.23641i	−0.411824	−	0.174104i
$166$	−20.0570	+	6.51224i	−1.55673	+	0.505448i
$167$	2.97617	−	5.15487i	0.230303	−	0.398896i	−0.727594	−	0.686008i	$-0.759362\pi$
$167$	2.97617	−	5.15487i	0.230303	−	0.398896i	0.957897	+	0.287112i	$0.0926950\pi$
$168$	−0.0896347	−	4.90502i	−0.00691547	−	0.378431i
$169$	−0.709017	−	1.22805i	−0.0545398	−	0.0944656i
$170$	−1.31690	+	6.18910i	−0.101002	+	0.474683i
$171$	2.02022	+	12.9197i	0.154490	+	0.987994i
$172$	7.36662	−	16.5269i	0.561699	−	1.26017i
$173$	1.92226	−	1.10982i	0.146147	−	0.0843780i	−0.425143	−	0.905126i	$-0.639776\pi$
$173$	1.92226	−	1.10982i	0.146147	−	0.0843780i	0.571290	+	0.820748i	$0.306443\pi$
$174$	1.26925	+	2.71312i	0.0962216	+	0.205681i
$175$	−2.54517	−	1.46945i	−0.192397	−	0.111080i
$176$	2.85948	−	8.77538i	0.215542	−	0.661469i
$177$	−0.238241	+	0.563534i	−0.0179073	+	0.0423578i
$178$	−13.5447	−	2.88201i	−1.01522	−	0.216015i
$179$	−19.2641			−1.43987			−0.719933	−	0.694043i	$-0.755828\pi$
$179$	−19.2641			−1.43987			−0.719933	+	0.694043i	$0.755828\pi$
$180$	−6.61894	−	5.52602i	−0.493347	−	0.411885i
$181$	−1.84634	+	3.19796i	−0.137238	+	0.237703i	−0.926450	−	0.376418i	$-0.877156\pi$
$181$	−1.84634	+	3.19796i	−0.137238	+	0.237703i	0.789212	+	0.614120i	$0.210489\pi$
$182$	5.25970	+	1.11914i	0.389875	+	0.0829564i
$183$	18.9647	−	2.35652i	1.40191	−	0.174199i
$184$	1.05004	+	2.36246i	0.0774102	+	0.174163i
$185$	5.25655	−	3.03487i	0.386469	−	0.223128i
$186$	7.19637	−	10.3047i	0.527664	−	0.755575i
$187$	−6.22152	+	3.59199i	−0.454962	+	0.262673i
$188$	−1.96284	−	18.7513i	−0.143155	−	1.36758i
$189$	−1.88588	−	4.84965i	−0.137178	−	0.352760i
$190$	2.63308	−	8.45840i	0.191024	−	0.613637i
$191$	−3.29172			−0.238180			−0.119090	−	0.992883i	$-0.537998\pi$
$191$	−3.29172			−0.238180			−0.119090	+	0.992883i	$0.537998\pi$
$192$	7.94560	−	11.3520i	0.573424	−	0.819259i
$193$	9.58514	+	16.6019i	0.689953	+	1.19503i	0.971852	+	0.235590i	$0.0757023\pi$
$193$	9.58514	+	16.6019i	0.689953	+	1.19503i	−0.281899	+	0.959444i	$0.590964\pi$
$194$	10.4375	+	9.40193i	0.749367	+	0.675019i
$195$	7.53994	−	5.69893i	0.539946	−	0.408109i
$196$	9.70664	−	7.04603i	0.693332	−	0.503288i
$197$			10.5191i			0.749458i	0.927134	+	0.374729i	$0.122264\pi$
$197$			10.5191i			0.749458i	−0.927134	+	0.374729i	$0.877736\pi$
$198$	−0.367984	−	9.78246i	−0.0261515	−	0.695209i
$199$	19.1120	+	11.0343i	1.35482	+	0.782203i	0.988919	−	0.148453i	$-0.0474294\pi$
$199$	19.1120	+	11.0343i	1.35482	+	0.782203i	0.365896	+	0.930656i	$0.380763\pi$
$200$	−3.37146	−	7.58535i	−0.238399	−	0.536365i
$201$	−1.40870	−	11.3369i	−0.0993621	−	0.799641i
$202$	19.9219	+	4.23892i	1.40170	+	0.298249i
$203$	0.612276	−	1.06049i	0.0429734	−	0.0744321i
$204$	−10.5065	+	2.43701i	−0.735601	+	0.170625i
$205$	−7.57405	+	13.1186i	−0.528994	+	0.916245i
$206$	−8.75447	−	26.9628i	−0.609953	−	1.87859i
$207$	1.91056	+	1.96698i	0.132793	+	0.136715i
$208$	10.1535	+	11.2958i	0.704020	+	0.783221i
$209$	9.13591	−	4.20608i	0.631944	−	0.290941i
$210$	−0.302871	+	3.51201i	−0.0209001	+	0.242352i
$211$	−7.45609	+	4.30478i	−0.513298	+	0.296353i	−0.734188	−	0.678946i	$-0.762437\pi$
$211$	−7.45609	+	4.30478i	−0.513298	+	0.296353i	0.220890	+	0.975299i	$0.429104\pi$
$212$	−5.00477	+	0.523888i	−0.343729	+	0.0359808i
$213$	−7.21755	+	17.0724i	−0.494539	+	1.16978i
$214$	−8.69090	+	2.82182i	−0.594098	+	0.192896i
$215$	−6.50077	+	11.2597i	−0.443349	+	0.767903i
$216$	3.75098	−	14.2102i	0.255222	−	0.966883i
$217$	−5.13837			−0.348815
$218$	−0.637658	−	0.574394i	−0.0431877	−	0.0389028i
$219$	−0.221184	+	0.523187i	−0.0149462	+	0.0353537i
$220$	−2.69995	+	6.05730i	−0.182030	+	0.408383i
$221$		−	11.8222i		−	0.795250i
$222$	8.48215	+	5.92359i	0.569284	+	0.397566i
$223$	8.22632	−	4.74947i	0.550875	−	0.318048i	−0.198600	−	0.980081i	$-0.563639\pi$
$223$	8.22632	−	4.74947i	0.550875	−	0.318048i	0.749475	+	0.662033i	$0.230306\pi$
$224$	−5.66477	−	0.00597592i	−0.378494	−	0.000399283i
$225$	−6.13441	−	6.31557i	−0.408961	−	0.421038i
$226$	−5.87313	−	18.0886i	−0.390675	−	1.20324i
$227$	8.76193			0.581550			0.290775	−	0.956792i	$-0.406087\pi$
$227$	8.76193			0.581550			0.290775	+	0.956792i	$0.406087\pi$
$228$	14.9607	−	2.04400i	0.990795	−	0.135367i
$229$	9.42160			0.622597			0.311299	−	0.950312i	$-0.399236\pi$
$229$	9.42160			0.622597			0.311299	+	0.950312i	$0.399236\pi$
$230$	−0.573671	−	1.76685i	−0.0378268	−	0.116502i
$231$	−3.19272	+	2.41316i	−0.210065	+	0.158774i
$232$	3.16058	−	1.40479i	0.207502	−	0.0922287i
$233$	11.3618	−	6.55974i	0.744336	−	0.429743i	−0.0793074	−	0.996850i	$-0.525271\pi$
$233$	11.3618	−	6.55974i	0.744336	−	0.429743i	0.823644	+	0.567107i	$0.191938\pi$
$234$	14.2444	+	7.52475i	0.931185	+	0.491908i
$235$			13.5472i			0.883721i
$236$	0.645275	+	0.287621i	0.0420038	+	0.0187226i
$237$	6.97826	+	2.95015i	0.453287	+	0.191633i
$238$	3.27612	+	2.95109i	0.212360	+	0.191291i
$239$	9.71365			0.628324			0.314162	−	0.949369i	$-0.398277\pi$
$239$	9.71365			0.628324			0.314162	+	0.949369i	$0.398277\pi$
$240$	−6.52741	+	7.51815i	−0.421343	+	0.485295i
$241$	−7.71523	+	13.3632i	−0.496982	+	0.860798i	−0.999994	−	0.00348172i	$-0.998892\pi$
$241$	−7.71523	+	13.3632i	−0.496982	+	0.860798i	0.503012	+	0.864279i	$0.332225\pi$
$242$	7.63473	−	2.47889i	0.490779	−	0.159349i
$243$	−1.47131	−	15.5189i	−0.0943843	−	0.995536i
$244$	−2.29736	−	21.9470i	−0.147074	−	1.40502i
$245$	−7.46380	+	4.30923i	−0.476845	+	0.275307i
$246$	−25.7243	−	2.21843i	−1.64012	−	0.141442i
$247$	−1.52285	+	16.4810i	−0.0968964	+	1.04866i
$248$	−11.7360	−	8.53806i	−0.745237	−	0.542167i
$249$	15.5731	+	20.6039i	0.986904	+	1.30572i
$250$	4.98004	+	15.3380i	0.314965	+	0.970059i
$251$	−13.3214	+	23.0733i	−0.840838	+	1.45637i	0.0483485	+	0.998831i	$0.484604\pi$
$251$	−13.3214	+	23.0733i	−0.840838	+	1.45637i	−0.889187	+	0.457544i	$0.848729\pi$
$252$	−5.64093	+	2.06900i	−0.355345	+	0.130335i
$253$	1.05452	−	1.82649i	0.0662972	−	0.114830i
$254$	22.7674	+	4.84437i	1.42855	+	0.303963i
$255$	7.69062	−	0.955624i	0.481605	−	0.0598435i
$256$	−12.9284	−	9.42640i	−0.808024	−	0.589150i
$257$	2.70402	+	1.56117i	0.168672	+	0.0973828i	0.581960	−	0.813218i	$-0.302286\pi$
$257$	2.70402	+	1.56117i	0.168672	+	0.0973828i	−0.413287	+	0.910601i	$0.635620\pi$
$258$	−22.0790	−	1.90406i	−1.37458	−	0.118542i
$259$		−	4.22957i		−	0.262813i
$260$	−6.41107	−	8.83192i	−0.397598	−	0.547732i
$261$	2.63150	−	2.55602i	0.162886	−	0.158214i
$262$	13.9567	+	12.5720i	0.862248	+	0.776701i
$263$	−14.3469	−	24.8496i	−0.884670	−	1.53229i	−0.846091	−	0.533039i	$-0.821050\pi$
$263$	−14.3469	−	24.8496i	−0.884670	−	1.53229i	−0.0385796	−	0.999256i	$-0.512283\pi$
$264$	−11.3019	+	0.206532i	−0.695585	+	0.0127112i
$265$	3.61578			0.222116
$266$	−4.18701	−	4.53602i	−0.256722	−	0.278121i
$267$	2.09136	+	16.8308i	0.127989	+	1.03003i
$268$	−13.1197	+	1.37334i	−0.801412	+	0.0838899i
$269$	−2.25352	+	1.30107i	−0.137400	+	0.0793277i	−0.567124	−	0.823632i	$-0.691944\pi$
$269$	−2.25352	+	1.30107i	−0.137400	+	0.0793277i	0.429725	+	0.902960i	$0.358611\pi$
$270$	−3.74360	+	9.87453i	−0.227828	+	0.600945i
$271$	26.7596	−	15.4497i	1.62553	−	0.938501i	0.640129	−	0.768268i	$-0.278881\pi$
$271$	26.7596	−	15.4497i	1.62553	−	0.938501i	0.985404	−	0.170234i	$-0.0544522\pi$
$272$	2.57904	+	12.1840i	0.156377	+	0.738762i
$273$	−0.812120	−	6.53573i	−0.0491517	−	0.395560i
$274$	−11.0537	−	2.35198i	−0.667780	−	0.142088i
$275$	−3.38585	+	5.86446i	−0.204174	+	0.353640i
$276$	2.31349	−	2.16182i	0.139256	−	0.130126i
$277$	−15.7913			−0.948805			−0.474402	−	0.880308i	$-0.657336\pi$
$277$	−15.7913			−0.948805			−0.474402	+	0.880308i	$0.657336\pi$
$278$	15.5297	+	3.30437i	0.931411	+	0.198183i
$279$	−14.8095	−	4.20005i	−0.886620	−	0.251451i
$280$	4.04780	+	0.428032i	0.241903	+	0.0255798i
$281$	−16.1977	−	9.35172i	−0.966271	−	0.557877i	−0.0681738	−	0.997673i	$-0.521717\pi$
$281$	−16.1977	−	9.35172i	−0.966271	−	0.557877i	−0.898097	+	0.439796i	$0.855051\pi$
$282$	−20.9155	+	9.78465i	−1.24550	+	0.582668i
$283$	−11.8095	+	6.81821i	−0.702001	+	0.405300i	−0.808092	−	0.589056i	$-0.799500\pi$
$283$	−11.8095	+	6.81821i	−0.702001	+	0.405300i	0.106091	+	0.994356i	$0.466166\pi$
$284$	19.5487	+	8.71353i	1.16000	+	0.517053i
$285$	−10.8443	+	0.341561i	−0.642364	+	0.0202323i
$286$	2.57868	−	12.1191i	0.152480	−	0.716620i
$287$	5.27782	+	9.14145i	0.311540	+	0.539603i
$288$	−16.3218	−	4.64756i	−0.961770	−	0.273860i
$289$	−3.65311	+	6.32737i	−0.214889	+	0.372198i
$290$	−2.36375	+	0.767479i	−0.138804	+	0.0450679i
$291$	6.69946	−	15.8469i	0.392729	−	0.928959i
$292$	0.599076	+	0.267029i	0.0350583	+	0.0156267i
$293$		−	12.3015i		−	0.718662i	−0.933210	−	0.359331i	$-0.883005\pi$
$293$		−	12.3015i		−	0.718662i	0.933210	−	0.359331i	$-0.116995\pi$
$294$	−12.0438	−	8.41094i	−0.702412	−	0.490536i
$295$	−0.439621	−	0.253815i	−0.0255957	−	0.0147777i
$296$	7.02798	−	9.66032i	0.408493	−	0.561495i
$297$	−11.1743	+	4.34536i	−0.648401	+	0.252143i
$298$	19.4968	−	21.6442i	1.12942	−	1.25382i
$299$	1.73536	+	3.00573i	0.100358	+	0.173826i
$300$	−7.42812	+	6.94115i	−0.428863	+	0.400747i
$301$	4.52993	+	7.84606i	0.261101	+	0.452240i
$302$	5.76263	+	17.7483i	0.331602	+	1.02130i
$303$	−3.07602	−	24.7550i	−0.176713	−	1.42214i
$304$	−2.02591	−	17.3175i	−0.116194	−	0.993227i
$305$			15.8560i			0.907912i
$306$	7.03005	+	11.1833i	0.401881	+	0.639307i
$307$	22.7799	−	13.1520i	1.30012	−	0.750623i	0.319693	−	0.947521i	$-0.396420\pi$
$307$	22.7799	−	13.1520i	1.30012	−	0.750623i	0.980424	+	0.196898i	$0.0630868\pi$
$308$	2.71471	+	3.73979i	0.154685	+	0.213094i
$309$	−27.6980	+	20.9350i	−1.57568	+	1.19095i
$310$	7.74827	+	6.97953i	0.440072	+	0.396411i
$311$	−16.1452			−0.915508			−0.457754	−	0.889079i	$-0.651346\pi$
$311$	−16.1452			−0.915508			−0.457754	+	0.889079i	$0.651346\pi$
$312$	9.00508	−	16.2770i	0.509812	−	0.921505i
$313$	6.59354	−	11.4203i	0.372689	−	0.645516i	−0.617289	−	0.786736i	$-0.711769\pi$
$313$	6.59354	−	11.4203i	0.372689	−	0.645516i	0.989978	+	0.141220i	$0.0451025\pi$
$314$	0.753315	+	0.678576i	0.0425120	+	0.0382943i
$315$	4.18599	−	1.05660i	0.235854	−	0.0595328i
$316$	3.56163	−	7.99047i	0.200357	−	0.449499i
$317$	3.04579	+	1.75849i	0.171069	+	0.0987665i	0.583090	−	0.812408i	$-0.301844\pi$
$317$	3.04579	+	1.75849i	0.171069	+	0.0987665i	−0.412021	+	0.911174i	$0.635177\pi$
$318$	2.61155	+	5.58240i	0.146449	+	0.313045i
$319$	−2.44354	−	1.41078i	−0.136812	−	0.0789884i
$320$	8.53393	+	7.70357i	0.477061	+	0.430643i
$321$	6.74796	+	8.92786i	0.376635	+	0.498304i
$322$	−1.26612	−	0.269401i	−0.0705580	−	0.0150131i
$323$	−7.83828	+	11.0790i	−0.436134	+	0.616449i
$324$	−17.9491	+	1.35229i	−0.997174	+	0.0751272i
$325$	−5.57187	−	9.65077i	−0.309072	−	0.535328i
$326$	3.80795	+	11.7281i	0.210903	+	0.649559i
$327$	−0.409291	+	0.968134i	−0.0226338	+	0.0535380i
$328$	−3.13519	+	29.6488i	−0.173112	+	1.63708i
$329$	8.17535	+	4.72004i	0.450722	+	0.260224i
$330$	8.09221	+	0.697860i	0.445461	+	0.0384159i
$331$			2.51103i			0.138019i	0.997616	+	0.0690094i	$0.0219838\pi$
$331$			2.51103i			0.138019i	−0.997616	+	0.0690094i	$0.978016\pi$
$332$	24.1344	−	17.5191i	1.32455	−	0.961485i
$333$	3.45722	−	12.1902i	0.189454	−	0.668020i
$334$	−1.75191	+	8.23355i	−0.0958603	+	0.450520i
$335$	9.47852			0.517867
$336$	2.26275	+	6.55854i	0.123443	+	0.357798i
$337$	−11.0338	−	19.1110i	−0.601047	−	1.04104i	−0.992663	−	0.120915i	$-0.961417\pi$
$337$	−11.0338	−	19.1110i	−0.601047	−	1.04104i	0.391616	−	0.920129i	$-0.371916\pi$
$338$	1.49002	+	1.34219i	0.0810465	+	0.0730055i
$339$	−18.5818	+	14.0447i	−1.00922	+	0.762805i
$340$	−0.931634	−	8.90003i	−0.0505249	−	0.482672i
$341$			11.8396i			0.641149i
$342$	−8.35982	−	16.4959i	−0.452047	−	0.891994i
$343$			13.0154i			0.702765i
$344$	−2.69092	+	25.4474i	−0.145085	+	1.37203i
$345$	−1.81502	+	1.37185i	−0.0977174	+	0.0738580i
$346$	−2.10092	+	2.33232i	−0.112946	+	0.125386i
$347$	−8.14062	−	14.1000i	−0.437011	−	0.756926i	0.560446	−	0.828191i	$-0.310630\pi$
$347$	−8.14062	−	14.1000i	−0.437011	−	0.756926i	−0.997457	+	0.0712651i	$0.977296\pi$
$348$	−2.89216	−	3.09507i	−0.155036	−	0.165913i
$349$	31.0024			1.65952			0.829759	−	0.558122i	$-0.188478\pi$
$349$	31.0024			1.65952			0.829759	+	0.558122i	$0.188478\pi$
$350$	4.06524	+	0.864989i	0.217296	+	0.0462356i
$351$	3.00161	−	19.5007i	0.160214	−	1.04087i
$352$	−0.0137694	+	13.0525i	−0.000733914	+	0.695701i
$353$			21.1820i			1.12740i	0.825979	+	0.563701i	$0.190623\pi$
$353$			21.1820i			1.12740i	−0.825979	+	0.563701i	$0.809377\pi$
$354$	0.0743421	−	0.862052i	0.00395124	−	0.0458175i
$355$	−13.3184	−	7.68937i	−0.706867	−	0.408110i
$356$	19.4775	−	2.03886i	1.03231	−	0.108059i
$357$	2.10283	−	4.97403i	0.111294	−	0.263253i
$358$	25.9119	−	8.41325i	1.36949	−	0.444654i
$359$	4.35846	+	7.54907i	0.230031	+	0.398425i	0.957817	−	0.287379i	$-0.0927841\pi$
$359$	4.35846	+	7.54907i	0.230031	+	0.398425i	−0.727786	+	0.685804i	$0.759451\pi$
$360$	11.3165	+	4.54229i	0.596430	+	0.239399i
$361$	12.3542	−	14.4352i	0.650221	−	0.759745i
$362$	1.08684	−	5.10790i	0.0571232	−	0.268465i
$363$	−5.92791	−	7.84289i	−0.311135	−	0.411645i
$364$	−7.56353	+	0.791732i	−0.396437	+	0.0414980i
$365$	−0.408146	−	0.235643i	−0.0213633	−	0.0123341i
$366$	−24.4800	+	11.4522i	−1.27959	+	0.598618i
$367$	21.3406	+	12.3210i	1.11397	+	0.643152i	0.939855	−	0.341573i	$-0.110960\pi$
$367$	21.3406	+	12.3210i	1.11397	+	0.643152i	0.174116	+	0.984725i	$0.444293\pi$
$368$	−2.44416	−	2.71913i	−0.127411	−	0.141744i
$369$	7.73926	+	30.6610i	0.402890	+	1.59615i
$370$	−5.74510	+	6.37788i	−0.298674	+	0.331570i
$371$	1.25979	−	2.18202i	0.0654051	−	0.113285i
$372$	−5.17938	+	17.0036i	−0.268538	+	0.881595i
$373$	10.0259			0.519120			0.259560	−	0.965727i	$-0.416422\pi$
$373$	10.0259			0.519120			0.259560	+	0.965727i	$0.416422\pi$
$374$	6.79975	−	7.54869i	0.351607	−	0.390333i
$375$	15.7562	−	11.9090i	0.813645	−	0.614979i
$376$	10.8295	+	24.3649i	0.558489	+	1.25653i
$377$	4.02118	−	2.32163i	0.207101	−	0.119570i
$378$	4.65468	+	5.69959i	0.239411	+	0.293155i
$379$		−	27.2904i		−	1.40181i	−0.713254	−	0.700906i	$-0.752779\pi$
$379$		−	27.2904i		−	1.40181i	0.713254	−	0.700906i	$-0.247221\pi$
$380$	0.152331	+	12.5273i	0.00781440	+	0.642635i
$381$	−3.51538	−	28.2909i	−0.180098	−	1.44939i
$382$	4.42765	−	1.43760i	0.226538	−	0.0735540i
$383$	−0.668270	−	1.15748i	−0.0341470	−	0.0591443i	0.848447	−	0.529281i	$-0.177538\pi$
$383$	−0.668270	−	1.15748i	−0.0341470	−	0.0591443i	−0.882594	+	0.470136i	$0.844205\pi$
$384$	−5.72976	+	18.7395i	−0.292396	+	0.956297i
$385$	−1.66027	−	2.87567i	−0.0846151	−	0.146558i
$386$	−20.1435	−	18.1450i	−1.02528	−	0.923554i
$387$	6.64257	+	26.3162i	0.337661	+	1.33773i
$388$	−18.1455	−	8.08805i	−0.921196	−	0.410609i
$389$	−8.84813	−	5.10847i	−0.448618	−	0.259010i	0.258628	−	0.965977i	$-0.416729\pi$
$389$	−8.84813	−	5.10847i	−0.448618	−	0.259010i	−0.707246	+	0.706967i	$0.750063\pi$
$390$	−7.65298	+	10.9585i	−0.387524	+	0.554905i
$391$			2.84586i			0.143921i
$392$	−9.97907	+	13.7167i	−0.504019	+	0.692800i
$393$	8.95834	−	21.1900i	0.451888	−	1.06889i
$394$	−4.59405	−	14.1492i	−0.231445	−	0.712826i
$395$	−3.14300	+	5.44384i	−0.158142	+	0.273909i
$396$	4.76729	+	12.9976i	0.239565	+	0.653153i
$397$	−15.1278	−	26.2020i	−0.759240	−	1.31504i	−0.943238	−	0.332116i	$-0.892237\pi$
$397$	−15.1278	−	26.2020i	−0.759240	−	1.31504i	0.183998	−	0.982927i	$-0.441096\pi$
$398$	−30.5264	−	6.49532i	−1.53015	−	0.325581i
$399$	−3.57221	+	6.66326i	−0.178834	+	0.333580i
$400$	7.84769	+	8.73054i	0.392384	+	0.436527i
$401$	−15.2383	+	8.79786i	−0.760967	+	0.439344i	−0.829643	−	0.558295i	$-0.811456\pi$
$401$	−15.2383	+	8.79786i	−0.760967	+	0.439344i	0.0686760	+	0.997639i	$0.478123\pi$
$402$	6.84600	+	14.6339i	0.341448	+	0.729871i
$403$	−16.8733	−	9.74182i	−0.840521	−	0.485275i
$404$	−28.6480	+	2.99880i	−1.42529	+	0.149196i
$405$	12.9283	+	0.376315i	0.642410	+	0.0186992i
$406$	−0.360414	+	1.69386i	−0.0178871	+	0.0840648i
$407$	−9.74558			−0.483071
$408$	13.0678	−	7.86652i	0.646955	−	0.389451i
$409$	−12.9914	+	22.5017i	−0.642381	+	1.11264i	0.342519	+	0.939511i	$0.388720\pi$
$409$	−12.9914	+	22.5017i	−0.642381	+	1.11264i	−0.984900	+	0.173126i	$0.944613\pi$
$410$	4.45844	−	20.9536i	0.220187	−	1.03482i
$411$	1.70674	+	13.7354i	0.0841874	+	0.677518i
$412$	23.5511	+	32.4441i	1.16028	+	1.59840i
$413$	−0.306341	+	0.176866i	−0.0150740	+	0.00870301i
$414$	−3.42892	−	1.81136i	−0.168522	−	0.0890237i
$415$	−18.5578	+	10.7144i	−0.910968	+	0.525948i
$416$	−18.5906	−	10.7595i	−0.911480	−	0.527526i
$417$	−2.39786	−	19.2973i	−0.117424	−	0.944994i
$418$	−10.4517	+	9.64750i	−0.511209	+	0.471875i
$419$	17.8340			0.871247			0.435624	−	0.900129i	$-0.356528\pi$
$419$	17.8340			0.871247			0.435624	+	0.900129i	$0.356528\pi$
$420$	−1.12642	−	4.85624i	−0.0549637	−	0.236960i
$421$	−6.60218	−	11.4353i	−0.321771	−	0.557323i	0.659083	−	0.752070i	$-0.270945\pi$
$421$	−6.60218	−	11.4353i	−0.321771	−	0.557323i	−0.980853	+	0.194747i	$0.937611\pi$
$422$	8.14907	−	9.04662i	0.396691	−	0.440383i
$423$	19.7044	+	20.2863i	0.958059	+	0.986352i
$424$	6.50307	−	2.89042i	0.315817	−	0.140371i
$425$		−	9.13744i		−	0.443231i
$426$	2.25220	−	26.1160i	0.109120	−	1.26532i
$427$	9.56866	+	5.52447i	0.463060	+	0.267348i
$428$	10.4577	−	7.59119i	0.505490	−	0.366934i
$429$	−15.0593	+	1.87125i	−0.727071	+	0.0903447i
$430$	3.82666	−	17.9843i	0.184538	−	0.867282i
$431$	−9.44236	+	16.3546i	−0.454822	+	0.787776i	−0.998678	−	0.0514033i	$-0.983631\pi$
$431$	−9.44236	+	16.3546i	−0.454822	+	0.787776i	0.543856	+	0.839179i	$0.316964\pi$
$432$	1.16065	+	20.7522i	0.0558420	+	0.998440i
$433$	4.87623	−	8.44588i	0.234337	−	0.405883i	−0.724743	−	0.689019i	$-0.758041\pi$
$433$	4.87623	−	8.44588i	0.234337	−	0.405883i	0.959080	+	0.283136i	$0.0913748\pi$
$434$	6.91156	−	2.24409i	0.331766	−	0.107720i
$435$	1.83531	+	2.42820i	0.0879965	+	0.116423i
$436$	1.10856	+	0.494125i	0.0530905	+	0.0236643i
$437$	0.366581	−	3.96732i	0.0175359	−	0.189783i
$438$	0.0690195	−	0.800332i	0.00329788	−	0.0382413i
$439$	−21.3464	+	12.3244i	−1.01881	+	0.588210i	−0.913759	−	0.406257i	$-0.866834\pi$
$439$	−21.3464	+	12.3244i	−1.01881	+	0.588210i	−0.105051	+	0.994467i	$0.533500\pi$
$440$	0.986251	−	9.32676i	0.0470177	−	0.444636i
$441$	−4.90892	+	17.3090i	−0.233758	+	0.824236i
$442$	5.16315	+	15.9020i	0.245586	+	0.756379i
$443$	0.221764	−	0.384106i	0.0105363	−	0.0182494i	−0.860709	−	0.509097i	$-0.829979\pi$
$443$	0.221764	−	0.384106i	0.0105363	−	0.0182494i	0.871245	+	0.490848i	$0.163313\pi$
$444$	−13.9963	−	4.26333i	−0.664233	−	0.202329i
$445$	−14.0719			−0.667070
$446$	−8.99089	+	9.98116i	−0.425731	+	0.472622i
$447$	−32.8617	−	13.8927i	−1.55430	−	0.657102i
$448$	7.62223	−	2.46595i	0.360117	−	0.116505i
$449$		−	7.13703i		−	0.336817i	−0.985717	−	0.168409i	$-0.946137\pi$
$449$		−	7.13703i		−	0.336817i	0.985717	−	0.168409i	$-0.0538628\pi$
$450$	11.0095	+	5.81591i	0.518995	+	0.274164i
$451$	21.0633	−	12.1609i	0.991832	−	0.572634i
$452$	15.7998	+	21.7658i	0.743158	+	1.02378i
$453$	18.2322	−	13.7805i	0.856623	−	0.647464i
$454$	−11.7856	+	3.82662i	−0.553124	+	0.179592i
$455$	5.46439			0.256175
$456$	−19.2308	+	9.28318i	−0.900563	+	0.434725i
$457$	−1.75502			−0.0820964			−0.0410482	−	0.999157i	$-0.513070\pi$
$457$	−1.75502			−0.0820964			−0.0410482	+	0.999157i	$0.513070\pi$
$458$	−12.6729	+	4.11472i	−0.592166	+	0.192268i
$459$	10.1264	−	12.6170i	0.472659	−	0.588911i
$460$	1.54328	+	2.12603i	0.0719557	+	0.0991265i
$461$	32.8900	−	18.9891i	1.53184	−	0.884409i	0.532565	−	0.846389i	$-0.321228\pi$
$461$	32.8900	−	18.9891i	1.53184	−	0.884409i	0.999277	−	0.0380204i	$-0.0121052\pi$
$462$	3.24058	−	4.64027i	0.150766	−	0.215885i
$463$			20.7854i			0.965978i	0.875626	+	0.482989i	$0.160449\pi$
$463$			20.7854i			0.965978i	−0.875626	+	0.482989i	$0.839551\pi$
$464$	−3.63775	+	3.26989i	−0.168878	+	0.151801i
$465$	4.97335	−	11.7639i	0.230634	−	0.545539i
$466$	−12.4178	+	13.7855i	−0.575243	+	0.638601i
$467$	−11.0036			−0.509187			−0.254593	−	0.967048i	$-0.581942\pi$
$467$	−11.0036			−0.509187			−0.254593	+	0.967048i	$0.581942\pi$
$468$	−22.4463	−	3.90048i	−1.03758	−	0.180300i
$469$	3.30246	−	5.72002i	0.152493	−	0.264126i
$470$	−5.91649	−	18.2222i	−0.272908	−	0.840526i
$471$	0.483528	−	1.14373i	0.0222798	−	0.0527004i
$472$	−0.993566	−	0.105064i	−0.0457326	−	0.00483596i
$473$	18.0785	−	10.4376i	0.831252	−	0.479923i
$474$	−10.6748	−	0.920581i	−0.490310	−	0.0422837i
$475$	−1.17701	+	12.7382i	−0.0540051	+	0.584470i
$476$	−5.69551	−	2.53869i	−0.261053	−	0.116360i
$477$	5.41446	−	5.25915i	0.247911	−	0.240800i
$478$	−13.0657	+	4.24226i	−0.597612	+	0.194037i
$479$	15.1267	−	26.2003i	0.691158	−	1.19712i	−0.280300	−	0.959912i	$-0.590434\pi$
$479$	15.1267	−	26.2003i	0.691158	−	1.19712i	0.971459	−	0.237209i	$-0.0762326\pi$
$480$	5.49653	−	12.9633i	0.250881	−	0.591692i
$481$	8.01885	−	13.8890i	0.365628	−	0.633286i
$482$	4.54155	−	21.3441i	0.206862	−	0.972199i
$483$	0.195494	+	1.57329i	0.00889529	+	0.0715870i
$484$	−9.18678	+	6.66866i	−0.417581	+	0.303121i
$485$	12.3624	+	7.13741i	0.561346	+	0.324093i
$486$	8.75663	+	20.2317i	0.397209	+	0.917728i
$487$		−	14.5904i		−	0.661155i	−0.943779	−	0.330578i	$-0.892756\pi$
$487$		−	14.5904i		−	0.661155i	0.943779	−	0.330578i	$-0.107244\pi$
$488$	12.6751	+	28.5174i	0.573777	+	1.29092i
$489$	12.0479	−	9.10616i	0.544823	−	0.411795i
$490$	8.15750	−	9.05598i	0.368518	−	0.409108i
$491$	6.77672	+	11.7376i	0.305829	+	0.529711i	0.977446	−	0.211188i	$-0.0677331\pi$
$491$	6.77672	+	11.7376i	0.305829	+	0.529711i	−0.671617	+	0.740899i	$0.734400\pi$
$492$	35.5703	−	8.25065i	1.60363	−	0.371968i
$493$	3.80729			0.171472
$494$	−5.14942	−	22.8335i	−0.231683	−	1.02733i
$495$	−2.43457	−	9.64516i	−0.109426	−	0.433518i
$496$	19.5148	+	6.35896i	0.876241	+	0.285526i
$497$	−9.28064	+	5.35818i	−0.416294	+	0.240347i
$498$	−29.9456	−	20.9128i	−1.34189	−	0.937124i
$499$	21.8167	−	12.5959i	0.976650	−	0.563869i	0.0753930	−	0.997154i	$-0.475979\pi$
$499$	21.8167	−	12.5959i	0.976650	−	0.563869i	0.901257	+	0.433285i	$0.142646\pi$
$500$	−13.3972	−	18.4560i	−0.599140	−	0.825378i
$501$	10.2311	−	1.27130i	0.457090	−	0.0567973i
$502$	7.84159	−	36.8535i	0.349987	−	1.64485i
$503$	0.757234	−	1.31157i	0.0337634	−	0.0584799i	−0.848650	−	0.528955i	$-0.822584\pi$
$503$	0.757234	−	1.31157i	0.0337634	−	0.0584799i	0.882413	+	0.470475i	$0.155917\pi$
$504$	6.68396	−	5.24657i	0.297727	−	0.233701i
$505$	20.6972			0.921013
$506$	−0.620741	+	2.91733i	−0.0275953	+	0.129691i
$507$	0.956394	−	2.26225i	0.0424749	−	0.100470i
$508$	−32.7398	+	3.42713i	−1.45260	+	0.152054i
$509$	−19.8666	−	11.4700i	−0.880571	−	0.508398i	−0.00972436	−	0.999953i	$-0.503095\pi$
$509$	−19.8666	−	11.4700i	−0.880571	−	0.508398i	−0.870847	+	0.491555i	$0.836429\pi$
$510$	−9.92722	+	4.64414i	−0.439585	+	0.205646i
$511$	−0.284408	+	0.164203i	−0.0125815	+	0.00726392i
$512$	21.5066	+	7.03311i	0.950468	+	0.310822i
$513$	−15.7421	+	16.2846i	−0.695030	+	0.718981i
$514$	−4.31896	−	0.918975i	−0.190501	−	0.0405343i
$515$	−14.4034	−	24.9475i	−0.634691	−	1.09932i
$516$	30.5298	−	7.08149i	1.34400	−	0.311745i
$517$	10.8757	−	18.8372i	0.478312	−	0.828461i
$518$	1.84719	+	5.68915i	0.0811609	+	0.249967i
$519$	3.54108	+	1.49704i	0.155436	+	0.0657126i
$520$	12.4806	+	9.07980i	0.547313	+	0.398175i
$521$		−	10.5938i		−	0.464123i	−0.972701	−	0.232061i	$-0.925453\pi$
$521$		−	10.5938i		−	0.464123i	0.972701	−	0.232061i	$-0.0745470\pi$
$522$	−2.42331	+	4.58734i	−0.106065	+	0.200782i
$523$	−16.8636	−	9.73621i	−0.737394	−	0.425735i	0.0837271	−	0.996489i	$-0.473318\pi$
$523$	−16.8636	−	9.73621i	−0.737394	−	0.425735i	−0.821121	+	0.570754i	$0.806651\pi$
$524$	−24.2636	−	10.8151i	−1.05996	−	0.472461i
$525$	−0.627690	−	5.05149i	−0.0273946	−	0.220465i
$526$	30.1506	+	27.1592i	1.31463	+	1.18420i
$527$	−7.98792	−	13.8355i	−0.347959	−	0.602683i
$528$	15.1119	−	5.21372i	0.657660	−	0.226898i
$529$	11.0823	+	19.1950i	0.481838	+	0.834567i
$530$	−4.86355	+	1.57913i	−0.211259	+	0.0685930i
$531$	−1.02749	+	0.259352i	−0.0445891	+	0.0112549i
$532$	7.61292	+	4.27275i	0.330062	+	0.185247i
$533$			40.0249i			1.73367i
$534$	−10.1636	−	21.7255i	−0.439822	−	0.940154i
$535$	−8.04129	+	4.64264i	−0.347655	+	0.200719i
$536$	17.0474	−	7.57704i	0.736333	−	0.327278i
$537$	−20.1191	−	26.6184i	−0.868202	−	1.14867i
$538$	2.46297	−	2.73424i	0.106186	−	0.117881i
$539$	13.8378			0.596037
$540$	0.722950	−	14.9171i	0.0311108	−	0.641929i
$541$	−9.48120	+	16.4219i	−0.407629	+	0.706034i	−0.994624	−	0.103557i	$-0.966978\pi$
$541$	−9.48120	+	16.4219i	−0.407629	+	0.706034i	0.586995	+	0.809591i	$0.300311\pi$
$542$	−29.2467	+	32.4680i	−1.25625	+	1.39462i
$543$	−6.34711	+	0.788682i	−0.272380	+	0.0338456i
$544$	−8.79017	−	15.2622i	−0.376875	−	0.654360i
$545$	−0.755255	−	0.436047i	−0.0323516	−	0.0186782i
$546$	3.94674	+	8.43646i	0.168905	+	0.361047i
$547$	−2.28136	−	1.31715i	−0.0975440	−	0.0563171i	0.450434	−	0.892809i	$-0.351269\pi$
$547$	−2.28136	−	1.31715i	−0.0975440	−	0.0563171i	−0.547978	+	0.836492i	$0.684602\pi$
$548$	15.8954	−	1.66390i	0.679019	−	0.0710781i
$549$	23.0625	+	23.7436i	0.984285	+	1.01335i
$550$	1.99307	−	9.36693i	0.0849847	−	0.399407i
$551$	−5.30763	−	0.490425i	−0.226113	−	0.0208928i
$552$	−2.16771	+	3.91822i	−0.0922639	+	0.166770i
$553$	2.19014	+	3.79343i	0.0931341	+	0.161313i
$554$	21.2406	−	6.89655i	0.902429	−	0.293006i
$555$	9.68331	+	4.09374i	0.411034	+	0.173770i
$556$	−22.3320	+	2.33766i	−0.947087	+	0.0991388i
$557$	17.9182	+	10.3451i	0.759220	+	0.438336i	0.829016	−	0.559225i	$-0.188901\pi$
$557$	17.9182	+	10.3451i	0.759220	+	0.438336i	−0.0697954	+	0.997561i	$0.522235\pi$
$558$	21.7544	−	0.818329i	0.920936	−	0.0346426i
$559$			34.3531i			1.45298i
$560$	−5.63159	+	1.19207i	−0.237978	+	0.0503740i
$561$	−11.4609	−	4.84525i	−0.483880	−	0.204566i
$562$	25.8715	+	5.50486i	1.09132	+	0.232209i
$563$	−18.4946			−0.779454			−0.389727	−	0.920930i	$-0.627431\pi$
$563$	−18.4946			−0.779454			−0.389727	+	0.920930i	$0.627431\pi$
$564$	23.8599	−	22.2957i	1.00468	−	0.938818i
$565$	−9.66286	−	16.7366i	−0.406519	−	0.704112i
$566$	12.9071	−	14.3287i	0.542525	−	0.602279i
$567$	4.73149	−	7.67073i	0.198704	−	0.322140i
$568$	−30.1002	−	3.18293i	−1.26298	−	0.133553i
$569$		−	17.6269i		−	0.738957i	−0.929239	−	0.369479i	$-0.879536\pi$
$569$		−	17.6269i		−	0.738957i	0.929239	−	0.369479i	$-0.120464\pi$
$570$	14.4374	−	5.19551i	0.604718	−	0.217616i
$571$		−	18.2535i		−	0.763887i	−0.924186	−	0.381943i	$-0.875255\pi$
$571$		−	18.2535i		−	0.763887i	0.924186	−	0.381943i	$-0.124745\pi$
$572$	1.82427	+	17.4275i	0.0762766	+	0.728681i
$573$	−3.43781	−	4.54837i	−0.143616	−	0.190011i
$574$	−11.0915	−	9.99107i	−0.462950	−	0.417019i
$575$	1.34127	+	2.32314i	0.0559346	+	0.0968816i
$576$	23.9840	−	0.876863i	0.999332	−	0.0365360i
$577$	−30.0748			−1.25203			−0.626015	−	0.779811i	$-0.715315\pi$
$577$	−30.0748			−1.25203			−0.626015	+	0.779811i	$0.715315\pi$
$578$	2.15039	−	10.1063i	0.0894445	−	0.420367i
$579$	−12.9294	+	30.5831i	−0.537328	+	1.27099i
$580$	2.84428	−	2.06465i	0.118102	−	0.0857301i
$581$			14.9322i			0.619491i
$582$	−2.09054	+	24.2413i	−0.0866555	+	1.00483i
$583$	−5.02771	−	2.90275i	−0.208227	−	0.120220i
$584$	−0.922431	−	0.0975418i	−0.0381705	−	0.00403631i
$585$	15.7491	+	4.46655i	0.651147	+	0.184669i
$586$	5.37246	+	16.5466i	0.221934	+	0.683535i
$587$	−1.32723	−	2.29883i	−0.0547807	−	0.0948830i	0.837335	−	0.546691i	$-0.184113\pi$
$587$	−1.32723	−	2.29883i	−0.0547807	−	0.0948830i	−0.892115	+	0.451808i	$0.850779\pi$
$588$	19.8734	+	6.05353i	0.819564	+	0.249643i
$589$	9.35353	+	20.3166i	0.385406	+	0.837129i
$590$	0.702179	+	0.149408i	0.0289082	+	0.00615101i
$591$	−14.5350	+	10.9860i	−0.597888	+	0.451903i
$592$	−5.23429	+	16.0633i	−0.215128	+	0.660199i
$593$	−36.0791	−	20.8303i	−1.48159	−	0.855398i	−0.481811	−	0.876275i	$-0.660021\pi$
$593$	−36.0791	−	20.8303i	−1.48159	−	0.855398i	−0.999782	+	0.0208774i	$0.993354\pi$
$594$	13.1327	−	10.7251i	0.538842	−	0.440056i
$595$	3.88031	+	2.24030i	0.159077	+	0.0918432i
$596$	−16.7722	+	37.6283i	−0.687017	+	1.54131i
$597$	4.71341	+	37.9323i	0.192907	+	1.55247i
$598$	−3.64691	−	3.28509i	−0.149133	−	0.134337i
$599$	11.0889	−	19.2065i	0.453078	−	0.784755i	−0.545497	−	0.838113i	$-0.683659\pi$
$599$	11.0889	−	19.2065i	0.453078	−	0.784755i	0.998575	+	0.0533579i	$0.0169924\pi$
$600$	6.96006	−	12.5806i	0.284143	−	0.513599i
$601$	11.6361			0.474648			0.237324	−	0.971431i	$-0.423730\pi$
$601$	11.6361			0.474648			0.237324	+	0.971431i	$0.423730\pi$
$602$	−9.51978	−	8.57529i	−0.387997	−	0.349503i
$603$	14.1936	−	13.7865i	0.578009	−	0.561430i
$604$	−15.5025	−	21.3563i	−0.630788	−	0.868976i
$605$	7.06406	−	4.07844i	0.287195	−	0.165812i
$606$	14.9488	+	31.9543i	0.607256	+	1.29806i
$607$		−	6.93356i		−	0.281424i	−0.990051	−	0.140712i	$-0.955061\pi$
$607$		−	6.93356i		−	0.281424i	0.990051	−	0.140712i	$-0.0449392\pi$
$608$	10.2881	+	22.4088i	0.417239	+	0.908797i
$609$	2.10480	−	0.261539i	0.0852908	−	0.0105981i
$610$	−6.92483	−	21.3277i	−0.280378	−	0.863535i
$611$	17.8974	+	30.9993i	0.724053	+	1.25410i
$612$	−14.3402	−	11.9723i	−0.579666	−	0.483952i
$613$	19.7921	+	34.2809i	0.799395	+	1.38459i	0.920011	+	0.391893i	$0.128180\pi$
$613$	19.7921	+	34.2809i	0.799395	+	1.38459i	−0.120616	+	0.992699i	$0.538487\pi$
$614$	−24.8971	+	27.6393i	−1.00477	+	1.11543i
$615$	−26.0370	+	3.23532i	−1.04991	+	0.130461i
$616$	−5.28481	−	3.84475i	−0.212931	−	0.154910i
$617$	−28.5834	−	16.5026i	−1.15072	−	0.664371i	−0.201661	−	0.979455i	$-0.564634\pi$
$617$	−28.5834	−	16.5026i	−1.15072	−	0.664371i	−0.949064	+	0.315084i	$0.897967\pi$
$618$	28.1132	−	40.2561i	1.13088	−	1.61934i
$619$		−	33.6634i		−	1.35304i	−0.736422	−	0.676522i	$-0.763486\pi$
$619$		−	33.6634i		−	1.35304i	0.736422	−	0.676522i	$-0.236514\pi$
$620$	−13.4703	−	6.00417i	−0.540980	−	0.241133i
$621$	−0.722550	+	4.69422i	−0.0289949	+	0.188373i
$622$	21.7167	−	7.05111i	0.870760	−	0.282724i
$623$	−4.90284	+	8.49197i	−0.196428	+	0.340224i
$624$	−5.00394	+	25.8268i	−0.200318	+	1.03390i
$625$	0.856487	+	1.48348i	0.0342595	+	0.0593392i
$626$	−3.88127	+	18.2410i	−0.155127	+	0.729057i
$627$	15.3532	+	8.23091i	0.613147	+	0.328711i
$628$	−1.30963	−	0.583748i	−0.0522600	−	0.0232941i
$629$	11.3885	−	6.57515i	0.454089	−	0.262168i
$630$	−5.16908	+	3.24938i	−0.205941	+	0.129458i
$631$	−7.96424	−	4.59816i	−0.317051	−	0.183050i	0.333026	−	0.942918i	$-0.391930\pi$
$631$	−7.96424	−	4.59816i	−0.317051	−	0.183050i	−0.650077	+	0.759868i	$0.725264\pi$
$632$	−1.30101	+	12.3034i	−0.0517514	+	0.489402i
$633$	−13.7352	−	5.80672i	−0.545924	−	0.230796i
$634$	−4.86484	−	1.03513i	−0.193208	−	0.0411102i
$635$	23.6534			0.938658
$636$	−5.95078	−	6.36827i	−0.235964	−	0.252518i
$637$	−11.3860	+	19.7211i	−0.451130	+	0.781380i
$638$	3.90291	+	0.830450i	0.154518	+	0.0328778i
$639$	−31.1278	+	7.85710i	−1.23140	+	0.310822i
$640$	−14.8433	−	6.63495i	−0.586733	−	0.262269i
$641$	−34.7983	+	20.0908i	−1.37445	+	0.793538i	−0.991484	−	0.130225i	$-0.958430\pi$
$641$	−34.7983	+	20.0908i	−1.37445	+	0.793538i	−0.382964	+	0.923763i	$0.625097\pi$
$642$	−12.9757	−	9.06171i	−0.512110	−	0.357637i
$643$	−15.3558	+	8.86568i	−0.605574	+	0.349628i	−0.771231	−	0.636555i	$-0.780359\pi$
$643$	−15.3558	+	8.86568i	−0.605574	+	0.349628i	0.165657	+	0.986183i	$0.447025\pi$
$644$	1.82070	−	0.190586i	0.0717456	−	0.00751015i
$645$	−22.3475	+	2.77686i	−0.879930	+	0.109339i
$646$	5.70465	−	18.3254i	0.224447	−	0.721004i
$647$	1.57416			0.0618867			0.0309434	−	0.999521i	$-0.490149\pi$
$647$	1.57416			0.0618867			0.0309434	+	0.999521i	$0.490149\pi$
$648$	23.5526	−	9.65791i	0.925233	−	0.379399i
$649$	0.407526	+	0.705856i	0.0159968	+	0.0277073i
$650$	11.7095	+	10.5477i	0.459283	+	0.413716i
$651$	−5.36641	−	7.10000i	−0.210326	−	0.278271i
$652$	−10.2441	−	14.1123i	−0.401189	−	0.552679i
$653$			14.0502i			0.549827i	0.961469	+	0.274914i	$0.0886493\pi$
$653$			14.0502i			0.549827i	−0.961469	+	0.274914i	$0.911351\pi$
$654$	0.127717	−	1.48098i	0.00499415	−	0.0579108i
$655$	16.5306	+	9.54396i	0.645905	+	0.372913i
$656$	−8.73148	−	41.2495i	−0.340907	−	1.61052i
$657$	−0.953921	+	0.240783i	−0.0372160	+	0.00939385i
$658$	−13.0580	−	2.77844i	−0.509053	−	0.108315i
$659$	11.3916	−	19.7309i	0.443755	−	0.768607i	−0.554209	−	0.832377i	$-0.686979\pi$
$659$	11.3916	−	19.7309i	0.443755	−	0.768607i	0.997965	+	0.0637705i	$0.0203126\pi$
$660$	−11.1895	+	2.59544i	−0.435551	+	0.101027i
$661$	−7.01939	+	12.1579i	−0.273023	+	0.472889i	−0.969634	−	0.244559i	$-0.921357\pi$
$661$	−7.01939	+	12.1579i	−0.273023	+	0.472889i	0.696612	+	0.717448i	$0.254690\pi$
$662$	−1.09665	−	3.37756i	−0.0426224	−	0.131273i
$663$	16.3355	−	12.3469i	0.634419	−	0.479515i
$664$	−24.8117	+	34.1050i	−0.962882	+	1.32353i
$665$	−5.12084	−	3.62296i	−0.198578	−	0.140492i
$666$	0.673596	+	17.9068i	0.0261013	+	0.693874i
$667$	−0.967981	+	0.558864i	−0.0374804	+	0.0216393i
$668$	−1.23938	−	11.8400i	−0.0479531	−	0.458102i
$669$	15.1541	+	6.40657i	0.585890	+	0.247692i
$670$	−12.7495	+	4.13958i	−0.492555	+	0.159926i
$671$	12.7292	−	22.0476i	0.491406	−	0.851140i
$672$	−5.90792	−	7.83361i	−0.227903	−	0.302188i
$673$	−29.7977			−1.14862			−0.574309	−	0.818639i	$-0.694729\pi$
$673$	−29.7977			−1.14862			−0.574309	+	0.818639i	$0.694729\pi$
$674$	23.1878	+	20.8872i	0.893160	+	0.804546i
$675$	2.31995	−	15.0722i	0.0892950	−	0.580127i
$676$	−2.59039	−	1.15463i	−0.0996304	−	0.0444087i
$677$			22.7987i			0.876226i	0.898920	+	0.438113i	$0.144353\pi$
$677$			22.7987i			0.876226i	−0.898920	+	0.438113i	$0.855647\pi$
$678$	18.8604	−	27.0067i	0.724329	−	1.03719i
$679$	8.61445	−	4.97356i	0.330592	−	0.190868i
$680$	5.14006	+	11.5645i	0.197112	+	0.443477i
$681$	9.15079	+	12.1069i	0.350659	+	0.463938i
$682$	−5.17073	−	15.9253i	−0.197997	−	0.609811i
$683$	18.1863			0.695881			0.347941	−	0.937517i	$-0.386881\pi$
$683$	18.1863			0.695881			0.347941	+	0.937517i	$0.386881\pi$
$684$	18.4490	+	18.5374i	0.705414	+	0.708795i
$685$	−11.4839			−0.438778
$686$	−5.68424	−	17.5069i	−0.217025	−	0.668415i
$687$	9.83975	+	13.0184i	0.375410	+	0.496684i
$688$	−7.49418	−	35.4043i	−0.285713	−	1.34977i
$689$	8.27379	−	4.77688i	0.315206	−	0.181984i
$690$	1.84223	−	2.63794i	0.0701326	−	0.100425i
$691$			1.40760i			0.0535478i	0.999642	+	0.0267739i	$0.00852341\pi$
$691$			1.40760i			0.0535478i	−0.999642	+	0.0267739i	$0.991477\pi$
$692$	1.80733	−	4.05472i	0.0687043	−	0.154137i
$693$	−6.66882	−	1.89132i	−0.253328	−	0.0718452i
$694$	17.1078	+	15.4104i	0.649402	+	0.584972i
$695$	16.1341			0.612002
$696$	5.24193	+	2.90004i	0.198695	+	0.109926i
$697$	−16.4094	+	28.4220i	−0.621551	+	1.07656i
$698$	−41.7009	+	13.5397i	−1.57840	+	0.512486i
$699$	20.9301	+	8.84845i	0.791647	+	0.334679i
$700$	−5.84587	+	0.611932i	−0.220953	+	0.0231289i
$701$	41.4092	−	23.9076i	1.56400	−	0.902977i	0.567157	−	0.823610i	$-0.308043\pi$
$701$	41.4092	−	23.9076i	1.56400	−	0.902977i	0.996845	−	0.0793675i	$-0.0252901\pi$
$702$	4.47915	+	27.5411i	0.169055	+	1.03947i
$703$	−16.7233	+	7.69923i	−0.630731	+	0.290382i
$704$	−5.68193	−	17.5628i	−0.214146	−	0.661923i
$705$	−18.7190	+	14.1484i	−0.704998	+	0.532861i
$706$	−9.25085	−	28.4916i	−0.348160	−	1.07230i
$707$	7.21121	−	12.4902i	0.271205	−	0.469741i
$708$	0.276489	+	1.19200i	0.0103911	+	0.0447982i
$709$	−13.1723	+	22.8150i	−0.494695	+	0.856836i	−0.999981	−	0.00611514i	$-0.998053\pi$
$709$	−13.1723	+	22.8150i	−0.494695	+	0.856836i	0.505287	+	0.862952i	$0.331387\pi$
$710$	21.2726	+	4.52632i	0.798347	+	0.169870i
$711$	3.21156	+	12.7234i	0.120443	+	0.477164i
$712$	−25.3086	+	11.2489i	−0.948479	+	0.421571i
$713$	4.06176	+	2.34506i	0.152114	+	0.0878232i
$714$	−0.656179	+	7.60888i	−0.0245569	+	0.284755i
$715$		−	12.5908i		−	0.470869i
$716$	−31.1795	+	22.6331i	−1.16523	+	0.845840i
$717$	10.1448	+	13.4220i	0.378863	+	0.501252i
$718$	−9.15944	−	8.25069i	−0.341827	−	0.307913i
$719$	18.4930	+	32.0309i	0.689674	+	1.19455i	0.971943	+	0.235216i	$0.0755797\pi$
$719$	18.4930	+	32.0309i	0.689674	+	1.19455i	−0.282269	+	0.959335i	$0.591087\pi$
$720$	−17.2054	−	1.16752i	−0.641208	−	0.0435108i
$721$	−20.0735			−0.747575
$722$	−10.3132	+	24.8120i	−0.383818	+	0.923409i
$723$	−26.5224	+	3.29563i	−0.986378	+	0.122566i
$724$	0.768882	+	7.34524i	0.0285753	+	0.272984i
$725$	3.10798	−	1.79439i	0.115428	−	0.0666421i
$726$	11.3988	+	7.96047i	0.423049	+	0.295441i
$727$	−13.5930	+	7.84792i	−0.504136	+	0.291063i	−0.730420	−	0.682998i	$-0.760676\pi$
$727$	−13.5930	+	7.84792i	−0.504136	+	0.291063i	0.226284	+	0.974061i	$0.427342\pi$
$728$	9.82784	−	4.36819i	0.364244	−	0.161896i
$729$	19.9068	−	18.2406i	0.737288	−	0.675578i
$730$	0.651906	+	0.138711i	0.0241281	+	0.00513391i
$731$	−14.0841	+	24.3944i	−0.520920	+	0.902260i
$732$	27.9263	−	26.0955i	1.03219	−	0.964517i
$733$	6.99386			0.258324			0.129162	−	0.991624i	$-0.458771\pi$
$733$	6.99386			0.258324			0.129162	+	0.991624i	$0.458771\pi$
$734$	−34.0860	−	7.25272i	−1.25814	−	0.267703i
$735$	−13.7494	−	5.81273i	−0.507154	−	0.214406i
$736$	4.47515	+	2.59003i	0.164956	+	0.0954696i
$737$	−13.1798	−	7.60937i	−0.485484	−	0.280295i
$738$	−23.8006	−	37.8617i	−0.876113	−	1.39371i
$739$	−14.5022	+	8.37285i	−0.533472	+	0.308000i	−0.742429	−	0.669924i	$-0.766326\pi$
$739$	−14.5022	+	8.37285i	−0.533472	+	0.308000i	0.208957	+	0.977925i	$0.432993\pi$
$740$	4.94225	−	11.0879i	0.181681	−	0.407599i
$741$	−24.3633	+	15.1082i	−0.895007	+	0.555015i
$742$	−0.741572	+	3.48521i	−0.0272240	+	0.127946i
$743$	17.7502	+	30.7443i	0.651192	+	1.12790i	0.982834	+	0.184492i	$0.0590640\pi$
$743$	17.7502	+	30.7443i	0.651192	+	1.12790i	−0.331642	+	0.943405i	$0.607603\pi$
$744$	−0.459289	−	25.1334i	−0.0168383	−	0.921433i
$745$	14.8009	−	25.6359i	0.542262	−	0.939225i
$746$	−13.4857	+	4.37863i	−0.493747	+	0.160313i
$747$	−12.2054	+	43.0366i	−0.446573	+	1.57463i
$748$	−5.84952	+	13.1233i	−0.213880	+	0.479837i
$749$			6.47026i			0.236418i
$750$	−15.9924	+	22.8999i	−0.583960	+	0.836187i
$751$	35.7193	+	20.6225i	1.30341	+	0.752526i	0.980988	−	0.194068i	$-0.0621683\pi$
$751$	35.7193	+	20.6225i	1.30341	+	0.752526i	0.322426	+	0.946595i	$0.395502\pi$
$752$	−25.2076	−	28.0434i	−0.919226	−	1.02264i
$753$	−45.7944	+	5.69035i	−1.66884	+	0.207368i
$754$	−4.39491	+	4.87898i	−0.160053	+	0.177682i
$755$	9.48106	+	16.4217i	0.345051	+	0.597646i
$756$	−8.75015	−	5.63361i	−0.318240	−	0.204892i
$757$	−0.898669	−	1.55654i	−0.0326627	−	0.0565734i	0.849232	−	0.528020i	$-0.177065\pi$
$757$	−0.898669	−	1.55654i	−0.0326627	−	0.0565734i	−0.881895	+	0.471447i	$0.843732\pi$
$758$	11.9186	+	36.7080i	0.432902	+	1.33329i
$759$	3.62509	−	0.450448i	0.131583	−	0.0163502i
$760$	−5.67596	−	16.7838i	−0.205889	−	0.608811i
$761$			21.6481i			0.784742i	0.919807	+	0.392371i	$0.128345\pi$
$761$			21.6481i			0.784742i	−0.919807	+	0.392371i	$0.871655\pi$
$762$	17.0840	+	36.5185i	0.618889	+	1.32292i
$763$	−0.526284	+	0.303850i	−0.0190528	+	0.0110001i
$764$	−5.32774	+	3.86740i	−0.192751	+	0.139918i
$765$	9.35238	+	9.62858i	0.338136	+	0.348122i
$766$	1.40439	+	1.26506i	0.0507427	+	0.0457083i
$767$	−1.34128			−0.0484308
$768$	−0.477111	−	27.7087i	−0.0172163	−	0.999852i
$769$	−1.36750	+	2.36857i	−0.0493132	+	0.0854130i	−0.889628	−	0.456685i	$-0.849037\pi$
$769$	−1.36750	+	2.36857i	−0.0493132	+	0.0854130i	0.840315	+	0.542098i	$0.182370\pi$
$770$	3.48910	+	3.14294i	0.125739	+	0.113264i
$771$	0.666865	+	5.36676i	0.0240166	+	0.193279i
$772$	35.0193	+	15.6093i	1.26037	+	0.561790i
$773$	−11.8179	−	6.82305i	−0.425059	−	0.245408i	0.272180	−	0.962246i	$-0.412255\pi$
$773$	−11.8179	−	6.82305i	−0.425059	−	0.245408i	−0.697240	+	0.716838i	$0.745589\pi$
$774$	−20.4280	−	32.4966i	−0.734268	−	1.16806i
$775$	−13.0415	−	7.52949i	−0.468463	−	0.270467i
$776$	27.9396	+	2.95445i	1.00297	+	0.106058i
$777$	5.84427	−	4.41729i	0.209662	−	0.158469i
$778$	14.1326	+	3.00708i	0.506677	+	0.107809i
$779$	26.5370	−	37.5084i	0.950785	−	1.34388i
$780$	5.50801	−	18.0825i	0.197218	−	0.647456i
$781$	12.3461	+	21.3840i	0.441777	+	0.765180i
$782$	−1.24288	−	3.82793i	−0.0444452	−	0.136887i
$783$	6.28010	+	0.966653i	0.224433	+	0.0345454i
$784$	7.43220	−	22.8084i	0.265436	−	0.814587i
$785$	0.892242	+	0.515136i	0.0318455	+	0.0183860i
$786$	−2.79541	+	32.4148i	−0.0997089	+	1.15620i
$787$		−	12.9782i		−	0.462624i	−0.972880	−	0.231312i	$-0.925698\pi$
$787$		−	12.9782i		−	0.462624i	0.972880	−	0.231312i	$-0.0743019\pi$
$788$	12.3588	+	17.0255i	0.440264	+	0.606510i
$789$	19.3526	−	45.7766i	0.688971	−	1.62969i
$790$	1.85012	−	8.69510i	0.0658243	−	0.309358i
$791$	−13.4667			−0.478822
$792$	−12.0889	−	15.4009i	−0.429560	−	0.547246i
$793$	20.9477	+	36.2824i	0.743873	+	1.28843i
$794$	31.7915	+	28.6373i	1.12824	+	1.01630i
$795$	3.77625	+	4.99615i	0.133930	+	0.177195i
$796$	43.8975	−	4.59508i	1.55590	−	0.162868i
$797$		−	36.7430i		−	1.30150i	−0.759290	−	0.650752i	$-0.774454\pi$
$797$		−	36.7430i		−	1.30150i	0.759290	−	0.650752i	$-0.225546\pi$
$798$	1.89487	−	10.5228i	0.0670778	−	0.372502i
$799$			29.3504i			1.03834i
$800$	−14.3687	−	8.31602i	−0.508012	−	0.294016i
$801$	−21.0719	+	20.4675i	−0.744540	+	0.723183i
$802$	16.6546	−	18.4890i	0.588095	−	0.652869i
$803$	0.378349	+	0.655320i	0.0133516	+	0.0231257i
$804$	−15.5996	−	16.6940i	−0.550154	−	0.588752i
$805$	−1.31539			−0.0463615
$806$	26.9507	+	5.73449i	0.949298	+	0.201989i
$807$	−4.15130	−	1.75502i	−0.146133	−	0.0617795i
$808$	37.2244	−	16.5451i	1.30955	−	0.582056i
$809$			1.63402i			0.0574491i	0.999587	+	0.0287245i	$0.00914456\pi$
$809$			1.63402i			0.0574491i	−0.999587	+	0.0287245i	$0.990855\pi$
$810$	−17.5540	+	5.14001i	−0.616785	+	0.180601i
$811$	−11.1637	−	6.44538i	−0.392011	−	0.226328i	0.291020	−	0.956717i	$-0.406005\pi$
$811$	−11.1637	−	6.44538i	−0.392011	−	0.226328i	−0.683031	+	0.730389i	$0.739339\pi$
$812$	−0.254973	−	2.43580i	−0.00894781	−	0.0854797i
$813$	49.2951	+	20.8401i	1.72885	+	0.730894i
$814$	13.1087	−	4.25621i	0.459459	−	0.149180i
$815$	6.26509	+	10.8515i	0.219457	+	0.380110i
$816$	−14.1419	+	16.2883i	−0.495064	+	0.570205i
$817$	22.7765	−	32.1933i	0.796850	−	1.12630i
$818$	7.64732	−	35.9405i	0.267382	−	1.25663i
$819$	8.18267	−	7.94795i	0.285926	−	0.277724i
$820$	3.15410	+	30.1316i	0.110146	+	1.05224i
$821$	6.42094	+	3.70713i	0.224092	+	0.129380i	0.607844	−	0.794057i	$-0.292035\pi$
$821$	6.42094	+	3.70713i	0.224092	+	0.129380i	−0.383751	+	0.923436i	$0.625368\pi$
$822$	−8.29442	−	17.7300i	−0.289301	−	0.618404i
$823$	−23.7798	−	13.7293i	−0.828913	−	0.478573i	0.0245673	−	0.999698i	$-0.492179\pi$
$823$	−23.7798	−	13.7293i	−0.828913	−	0.478573i	−0.853480	+	0.521125i	$0.825513\pi$
$824$	−45.8477	−	33.3546i	−1.59718	−	1.16196i
$825$	−11.6394	+	1.44629i	−0.405232	+	0.0503535i
$826$	0.334813	−	0.371689i	0.0116496	−	0.0129327i
$827$	−2.68955	+	4.65844i	−0.0935248	+	0.161990i	−0.908992	−	0.416814i	$-0.863147\pi$
$827$	−2.68955	+	4.65844i	−0.0935248	+	0.161990i	0.815467	+	0.578803i	$0.196480\pi$
$828$	5.40329	+	0.938926i	0.187777	+	0.0326299i
$829$	23.4951			0.816020			0.408010	−	0.912978i	$-0.366223\pi$
$829$	23.4951			0.816020			0.408010	+	0.912978i	$0.366223\pi$
$830$	20.2826	−	22.5166i	0.704021	−	0.781562i
$831$	−16.4921	−	21.8198i	−0.572104	−	0.756919i
$832$	29.7050	+	6.35332i	1.02984	+	0.220262i
$833$	−16.1706	+	9.33609i	−0.560277	+	0.323476i
$834$	11.6531	+	24.9094i	0.403514	+	0.862542i
$835$			8.55399i			0.296023i
$836$	9.84507	−	17.5413i	0.340499	−	0.606680i
$837$	−9.66326	−	24.8496i	−0.334011	−	0.858929i
$838$	−23.9883	+	7.78868i	−0.828662	+	0.269055i
$839$	−13.3854	−	23.1842i	−0.462115	−	0.800406i	0.536951	−	0.843613i	$-0.319576\pi$
$839$	−13.3854	−	23.1842i	−0.462115	−	0.800406i	−0.999066	+	0.0432070i	$0.986242\pi$
$840$	3.63601	+	6.04013i	0.125454	+	0.208404i
$841$	−13.7523	−	23.8197i	−0.474218	−	0.821370i
$842$	13.8747	+	12.4981i	0.478153	+	0.430714i
$843$	−3.99467	−	32.1481i	−0.137584	−	1.10724i
$844$	−7.01028	+	15.7275i	−0.241304	+	0.541362i
$845$	1.76481	+	1.01891i	0.0607114	+	0.0350517i
$846$	−35.3638	−	18.6813i	−1.21583	−	0.642276i
$847$		−	5.68395i		−	0.195303i
$848$	−7.48487	+	6.72798i	−0.257031	+	0.231040i
$849$	−21.7548	−	9.19709i	−0.746621	−	0.315643i
$850$	3.99062	+	12.2907i	0.136877	+	0.421567i
$851$	−1.93030	+	3.34338i	−0.0661699	+	0.114610i
$852$	8.37627	+	36.1119i	0.286966	+	1.23717i
$853$	−3.22288	−	5.58220i	−0.110349	−	0.191131i	0.805562	−	0.592512i	$-0.201864\pi$
$853$	−3.22288	−	5.58220i	−0.110349	−	0.191131i	−0.915911	+	0.401381i	$0.868530\pi$
$854$	−15.2834	−	3.25196i	−0.522987	−	0.111280i
$855$	−11.7976	−	14.6276i	−0.403469	−	0.500253i
$856$	−10.7512	+	14.7780i	−0.367467	+	0.505103i
$857$	35.7177	−	20.6216i	1.22009	−	0.704422i	0.255157	−	0.966900i	$-0.417873\pi$
$857$	35.7177	−	20.6216i	1.22009	−	0.704422i	0.964938	+	0.262478i	$0.0845396\pi$
$858$	19.4389	−	9.09389i	0.663633	−	0.310460i
$859$	−15.7997	−	9.12194i	−0.539078	−	0.311237i	0.205627	−	0.978630i	$-0.434077\pi$
$859$	−15.7997	−	9.12194i	−0.539078	−	0.311237i	−0.744705	+	0.667394i	$0.767410\pi$
$860$	2.70715	+	25.8618i	0.0923130	+	0.881879i
$861$	−7.11926	+	16.8399i	−0.242624	+	0.573901i
$862$	5.55821	−	26.1222i	0.189314	−	0.889727i
$863$	10.1599			0.345846			0.172923	−	0.984935i	$-0.444679\pi$
$863$	10.1599			0.345846			0.172923	+	0.984935i	$0.444679\pi$
$864$	−10.6243	−	27.4066i	−0.361447	−	0.932393i
$865$	−1.59490	+	2.76245i	−0.0542282	+	0.0939260i
$866$	−2.87038	+	13.4901i	−0.0975395	+	0.458411i
$867$	−12.5582	+	1.56046i	−0.426498	+	0.0529959i
$868$	−8.31660	+	6.03700i	−0.282284	+	0.204909i
$869$	8.74064	−	5.04641i	0.296506	−	0.171188i
$870$	−3.52913	−	2.46461i	−0.119649	−	0.0835579i
$871$	21.6892	−	12.5223i	0.734910	−	0.424300i
$872$	−1.70692	−	0.180497i	−0.0578035	−	0.00611238i
$873$	28.8934	−	7.29310i	0.977893	−	0.246834i
$874$	1.23957	+	5.49650i	0.0419292	+	0.185922i
$875$	11.4189			0.386030
$876$	0.256693	+	1.10666i	0.00867287	+	0.0373906i
$877$	−22.9501	−	39.7508i	−0.774971	−	1.34229i	−0.934811	−	0.355146i	$-0.884431\pi$
$877$	−22.9501	−	39.7508i	−0.774971	−	1.34229i	0.159840	−	0.987143i	$-0.448902\pi$
$878$	23.3304	−	25.9000i	0.787363	−	0.874084i
$879$	16.9978	−	12.8475i	0.573320	−	0.433334i
$880$	2.74670	+	12.9760i	0.0925912	+	0.437422i
$881$			22.4288i			0.755647i	0.925878	+	0.377823i	$0.123327\pi$
$881$			22.4288i			0.755647i	−0.925878	+	0.377823i	$0.876673\pi$
$882$	−0.956442	−	25.4260i	−0.0322051	−	0.856137i
$883$	27.2400	+	15.7270i	0.916698	+	0.529256i	0.882580	−	0.470162i	$-0.155805\pi$
$883$	27.2400	+	15.7270i	0.916698	+	0.529256i	0.0341177	+	0.999418i	$0.489138\pi$
$884$	−13.8898	−	19.1346i	−0.467164	−	0.643568i
$885$	−0.108419	−	0.872532i	−0.00364448	−	0.0293298i
$886$	−0.130541	+	0.613508i	−0.00438559	+	0.0206112i
$887$	28.9309	−	50.1098i	0.971406	−	1.68252i	0.280085	−	0.959975i	$-0.409637\pi$
$887$	28.9309	−	50.1098i	0.971406	−	1.68252i	0.691320	−	0.722549i	$-0.257029\pi$
$888$	20.6882	−	0.378057i	0.694249	−	0.0126868i
$889$	8.24120	−	14.2742i	0.276401	−	0.478741i
$890$	18.9279	−	6.14563i	0.634465	−	0.206002i
$891$	−17.6745	−	10.9021i	−0.592119	−	0.365233i
$892$	7.73446	−	17.3522i	0.258969	−	0.580994i
$893$	3.78069	−	40.9165i	0.126516	−	1.36922i
$894$	50.2693	+	4.33515i	1.68126	+	0.144989i
$895$	23.9751	−	13.8420i	0.801399	−	0.462688i
$896$	−9.17563	+	6.64580i	−0.306536	+	0.222021i
$897$	−2.34083	+	5.53699i	−0.0781581	+	0.184875i
$898$	3.11697	+	9.59995i	0.104015	+	0.320354i
$899$	3.13731	−	5.43397i	0.104635	−	0.181233i
$900$	−17.3488	−	3.01469i	−0.578293	−	0.100490i
$901$	7.83371			0.260979
$902$	−23.0210	+	25.5565i	−0.766514	+	0.850939i
$903$	−6.11043	+	14.4536i	−0.203342	+	0.480984i
$904$	−30.7579	−	22.3767i	−1.02299	−	0.744238i
$905$		−	5.30669i		−	0.176400i
$906$	−18.5055	+	26.4986i	−0.614805	+	0.880356i
$907$	−23.8069	+	13.7449i	−0.790494	+	0.456392i	−0.840136	−	0.542375i	$-0.817525\pi$
$907$	−23.8069	+	13.7449i	−0.790494	+	0.456392i	0.0496427	+	0.998767i	$0.484192\pi$
$908$	14.1814	−	10.2943i	0.470628	−	0.341628i
$909$	30.9931	−	30.1040i	1.02797	−	0.998488i
$910$	−7.35010	+	2.38648i	−0.243653	+	0.0791110i
$911$	−49.6451			−1.64482			−0.822408	−	0.568898i	$-0.807370\pi$
$911$	−49.6451			−1.64482			−0.822408	+	0.568898i	$0.807370\pi$
$912$	21.8128	−	20.8854i	0.722295	−	0.691585i
$913$	34.4060			1.13867
$914$	2.36066	−	0.766474i	0.0780837	−	0.0253527i
$915$	−21.9092	+	16.5597i	−0.724297	+	0.547447i
$916$	15.2491	−	11.0693i	0.503846	−	0.365741i
$917$	11.5190	−	6.65051i	0.380392	−	0.219619i
$918$	−8.11063	+	21.3935i	−0.267691	+	0.706091i
$919$		−	9.54949i		−	0.315009i	−0.987518	−	0.157504i	$-0.949655\pi$
$919$		−	9.54949i		−	0.315009i	0.987518	−	0.157504i	$-0.0503448\pi$
$920$	−3.00435	−	2.18570i	−0.0990505	−	0.0720603i
$921$	41.9638	+	17.7407i	1.38275	+	0.584577i
$922$	−35.9469	+	39.9061i	−1.18385	+	1.31424i
$923$	−40.6343			−1.33749
$924$	−2.33232	+	7.65685i	−0.0767275	+	0.251892i
$925$	6.19779	−	10.7349i	0.203782	−	0.352961i
$926$	−9.07764	−	27.9582i	−0.298310	−	0.918762i
$927$	−57.8545	−	16.4079i	−1.90019	−	0.538905i
$928$	3.46503	−	5.98702i	0.113745	−	0.196533i
$929$	−35.5696	+	20.5361i	−1.16700	+	0.673768i	−0.952971	−	0.303060i	$-0.901992\pi$
$929$	−35.5696	+	20.5361i	−1.16700	+	0.673768i	−0.214028	+	0.976828i	$0.568658\pi$
$930$	−1.55191	+	17.9956i	−0.0508892	+	0.590097i
$931$	23.7455	−	10.9322i	0.778227	−	0.358288i
$932$	10.6825	−	23.9660i	0.349916	−	0.785032i
$933$	−16.8617	−	22.3088i	−0.552027	−	0.730357i
$934$	14.8008	−	4.80563i	0.484298	−	0.157245i
$935$	5.16199	−	8.94082i	0.168815	−	0.292396i
$936$	31.8957	−	4.55652i	1.04254	−	0.148935i
$937$	4.17478	−	7.23092i	0.136384	−	0.236224i	−0.789741	−	0.613440i	$-0.789785\pi$
$937$	4.17478	−	7.23092i	0.136384	−	0.236224i	0.926125	+	0.377216i	$0.123119\pi$
$938$	−1.94398	+	9.13623i	−0.0634732	+	0.298309i
$939$	22.6664	−	2.81649i	0.739689	−	0.0919126i
$940$	15.9164	+	21.9265i	0.519137	+	0.715165i
$941$	43.2704	+	24.9822i	1.41057	+	0.814395i	0.995442	−	0.0953666i	$-0.0304023\pi$
$941$	43.2704	+	24.9822i	1.41057	+	0.814395i	0.415131	+	0.909762i	$0.363736\pi$
$942$	−0.150883	+	1.74960i	−0.00491602	+	0.0570049i
$943$		−	9.63481i		−	0.313753i
$944$	1.38232	−	0.292602i	0.0449907	−	0.00952339i
$945$	5.83174	+	4.68055i	0.189707	+	0.152258i
$946$	−19.7588	+	21.9350i	−0.642413	+	0.713169i
$947$	8.22190	+	14.2407i	0.267176	+	0.462762i	0.968131	−	0.250443i	$-0.0805762\pi$
$947$	8.22190	+	14.2407i	0.267176	+	0.462762i	−0.700956	+	0.713205i	$0.747243\pi$
$948$	14.7606	−	3.42377i	0.479403	−	0.111199i
$949$	−1.24525			−0.0404225
$950$	−3.98001	−	17.6481i	−0.129128	−	0.572580i
$951$	0.751153	+	6.04509i	0.0243578	+	0.196025i
$952$	8.76970	+	0.927345i	0.284228	+	0.0300554i
$953$	2.05142	−	1.18439i	0.0664520	−	0.0383661i	−0.466406	−	0.884571i	$-0.654451\pi$
$953$	2.05142	−	1.18439i	0.0664520	−	0.0383661i	0.532858	+	0.846205i	$0.321118\pi$
$954$	−4.98609	+	9.43869i	−0.161431	+	0.305589i
$955$	4.09670	−	2.36523i	0.132566	−	0.0765371i
$956$	15.7218	−	11.4124i	0.508480	−	0.369105i
$957$	−0.602626	−	4.84978i	−0.0194801	−	0.156771i
$958$	−8.90431	+	41.8481i	−0.287685	+	1.35205i
$959$	−4.00116	+	6.93022i	−0.129204	+	0.223788i
$960$	−1.73183	+	19.8373i	−0.0558945	+	0.640247i
$961$	4.67099			0.150677
$962$	−4.72027	+	22.1841i	−0.152188	+	0.715244i
$963$	−5.28873	+	18.6482i	−0.170427	+	0.600929i
$964$	3.21289	+	30.6932i	0.103480	+	0.988562i
$965$	−23.8583	−	13.7746i	−0.768027	−	0.443421i
$966$	−0.950062	−	2.03083i	−0.0305677	−	0.0653410i
$967$	7.54969	−	4.35882i	0.242782	−	0.140170i	−0.373673	−	0.927561i	$-0.621902\pi$
$967$	7.54969	−	4.35882i	0.242782	−	0.140170i	0.616455	+	0.787390i	$0.288568\pi$
$968$	9.44462	−	12.9821i	0.303561	−	0.417261i
$969$	−23.4946	+	0.740004i	−0.754756	+	0.0237724i
$970$	−19.7456	−	4.20141i	−0.633993	−	0.134899i
$971$	−7.88219	−	13.6523i	−0.252951	−	0.438125i	0.711386	−	0.702802i	$-0.248068\pi$
$971$	−7.88219	−	13.6523i	−0.252951	−	0.438125i	−0.964337	+	0.264677i	$0.914735\pi$
$972$	−20.6143	−	23.3891i	−0.661203	−	0.750207i
$973$	5.62136	−	9.73649i	0.180213	−	0.312137i
$974$	6.37211	+	19.6254i	0.204175	+	0.628839i
$975$	7.51591	−	17.7781i	0.240702	−	0.569354i
$976$	−29.5037	−	32.8228i	−0.944389	−	1.05063i
$977$		−	42.1932i		−	1.34988i	−0.737872	−	0.674941i	$-0.764169\pi$
$977$		−	42.1932i		−	1.34988i	0.737872	−	0.674941i	$-0.235831\pi$
$978$	−12.2285	+	17.5103i	−0.391024	+	0.559917i
$979$	19.5668	+	11.2969i	0.625357	+	0.361050i
$980$	−7.01753	+	15.7437i	−0.224167	+	0.502916i
$981$	−1.76519	+	0.445558i	−0.0563581	+	0.0142256i
$982$	−14.2415	−	12.8285i	−0.454464	−	0.409375i
$983$	−12.8051	−	22.1791i	−0.408420	−	0.707404i	0.586293	−	0.810099i	$-0.300587\pi$
$983$	−12.8051	−	22.1791i	−0.408420	−	0.707404i	−0.994713	+	0.102695i	$0.967254\pi$
$984$	−44.2419	+	26.6326i	−1.41038	+	0.849015i
$985$	−7.55843	−	13.0916i	−0.240832	−	0.417133i
$986$	−5.12115	+	1.66277i	−0.163091	+	0.0529533i
$987$	2.01621	+	16.2259i	0.0641765	+	0.516476i
$988$	16.8986	+	28.4642i	0.537615	+	0.905566i
$989$		−	8.26952i		−	0.262955i
$990$	7.48707	+	11.9103i	0.237955	+	0.378535i
$991$	−17.9972	+	10.3907i	−0.571699	+	0.330070i	−0.757828	−	0.652455i	$-0.773739\pi$
$991$	−17.9972	+	10.3907i	−0.571699	+	0.330070i	0.186129	+	0.982525i	$0.440406\pi$
$992$	−29.0263	−	0.0306207i	−0.921587	−	0.000972207i
$993$	−3.46965	+	2.62247i	−0.110106	+	0.0832217i
$994$	10.1432	−	11.2604i	0.321723	−	0.357158i
$995$	−31.7145			−1.00542
$996$	49.4127	+	15.0514i	1.56570	+	0.476921i
$997$	6.80677	−	11.7897i	0.215573	−	0.373383i	−0.737877	−	0.674935i	$-0.764172\pi$
$997$	6.80677	−	11.7897i	0.215573	−	0.373383i	0.953450	+	0.301552i	$0.0975048\pi$
$998$	−23.8444	+	26.4706i	−0.754781	+	0.837914i
$999$	20.4546	−	7.95418i	0.647156	−	0.251659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.m.a.83.4	yes	72
3.2	odd	2	inner	228.2.m.a.83.33	yes	72
4.3	odd	2	inner	228.2.m.a.83.9	yes	72
12.11	even	2	inner	228.2.m.a.83.28	yes	72
19.11	even	3	inner	228.2.m.a.11.28	yes	72
57.11	odd	6	inner	228.2.m.a.11.9	yes	72
76.11	odd	6	inner	228.2.m.a.11.33	yes	72
228.11	even	6	inner	228.2.m.a.11.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.m.a.11.4	✓	72	228.11	even	6	inner
228.2.m.a.11.9	yes	72	57.11	odd	6	inner
228.2.m.a.11.28	yes	72	19.11	even	3	inner
228.2.m.a.11.33	yes	72	76.11	odd	6	inner
228.2.m.a.83.4	yes	72	1.1	even	1	trivial
228.2.m.a.83.9	yes	72	4.3	odd	2	inner
228.2.m.a.83.28	yes	72	12.11	even	2	inner
228.2.m.a.83.33	yes	72	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34509 + 0.436732i) q^{2} +(1.04438 + 1.38176i) q^{3} +(1.61853 - 1.17489i) q^{4} +(-1.24455 + 0.718541i) q^{5} +(-2.00825 - 1.40248i) q^{6} +1.00140i q^{7} +(-1.66396 + 2.28719i) q^{8} +(-0.818536 + 2.88617i) q^{9} +(1.36022 - 1.51004i) q^{10} +2.30738 q^{11} +(3.31378 + 1.00939i) q^{12} +(-1.89855 + 3.28839i) q^{13} +(-0.437344 - 1.34697i) q^{14} +(-2.29264 - 0.969241i) q^{15} +(1.23928 - 3.80318i) q^{16} +(-2.69636 + 1.55674i) q^{17} +(-0.159482 - 4.23964i) q^{18} +(3.95943 - 1.82288i) q^{19} +(-1.17014 + 2.62518i) q^{20} +(-1.38370 + 1.04584i) q^{21} +(-3.10363 + 1.00771i) q^{22} +(0.457022 - 0.791584i) q^{23} +(-4.89816 + 0.0895094i) q^{24} +(-1.46740 + 2.54161i) q^{25} +(1.11758 - 5.25234i) q^{26} +(-4.84287 + 1.88324i) q^{27} +(1.17653 + 1.62080i) q^{28} +(-1.05901 - 0.611420i) q^{29} +(3.50710 + 0.302447i) q^{30} +5.13118i q^{31} +(-0.00596757 + 5.65685i) q^{32} +(2.40978 + 3.18825i) q^{33} +(2.94696 - 3.27154i) q^{34} +(-0.719547 - 1.24629i) q^{35} +(2.06611 + 5.63305i) q^{36} -4.22366 q^{37} +(-4.52968 + 4.18115i) q^{38} +(-6.52659 + 0.810984i) q^{39} +(0.427433 - 4.04214i) q^{40} +(9.12867 - 5.27044i) q^{41} +(1.40444 - 2.01106i) q^{42} +(7.83509 - 4.52359i) q^{43} +(3.73456 - 2.71091i) q^{44} +(-1.05513 - 4.18014i) q^{45} +(-0.269024 + 1.26435i) q^{46} +(4.71344 - 8.16392i) q^{47} +(6.54937 - 2.25958i) q^{48} +5.99720 q^{49} +(0.863780 - 4.05955i) q^{50} +(-4.96707 - 2.09989i) q^{51} +(0.790625 + 7.55295i) q^{52} +(-2.17897 - 1.25803i) q^{53} +(5.69162 - 4.64817i) q^{54} +(-2.87165 + 1.65795i) q^{55} +(-2.29040 - 1.66629i) q^{56} +(6.65395 + 3.56721i) q^{57} +(1.69149 + 0.359910i) q^{58} +(0.176619 + 0.305912i) q^{59} +(-4.84945 + 1.12484i) q^{60} +(5.51674 - 9.55527i) q^{61} +(-2.24095 - 6.90190i) q^{62} +(-2.89022 - 0.819682i) q^{63} +(-2.46250 - 7.61158i) q^{64} -5.45675i q^{65} +(-4.63379 - 3.23605i) q^{66} +(-5.71202 - 3.29784i) q^{67} +(-2.53514 + 5.68755i) q^{68} +(1.57109 - 0.195221i) q^{69} +(1.51215 + 1.36212i) q^{70} +(5.35069 + 9.26766i) q^{71} +(-5.23923 - 6.67461i) q^{72} +(0.163973 + 0.284010i) q^{73} +(5.68120 - 1.84461i) q^{74} +(-5.04442 + 0.626812i) q^{75} +(4.26678 - 7.60228i) q^{76} +2.31061i q^{77} +(8.42467 - 3.94122i) q^{78} +(3.78812 - 2.18707i) q^{79} +(1.19040 + 5.62372i) q^{80} +(-7.66000 - 4.72487i) q^{81} +(-9.97710 + 11.0760i) q^{82} +14.9113 q^{83} +(-1.01081 + 3.31842i) q^{84} +(2.23716 - 3.87488i) q^{85} +(-8.56330 + 9.50647i) q^{86} +(-0.261173 - 2.10186i) q^{87} +(-3.83938 + 5.27742i) q^{88} +(8.48010 + 4.89599i) q^{89} +(3.24484 + 5.16185i) q^{90} +(-3.29300 - 1.90121i) q^{91} +(-0.190320 - 1.81815i) q^{92} +(-7.09007 + 5.35891i) q^{93} +(-2.77455 + 13.0397i) q^{94} +(-3.61789 + 5.11368i) q^{95} +(-7.82266 + 5.89966i) q^{96} +(-4.96660 - 8.60241i) q^{97} +(-8.06677 + 2.61917i) q^{98} +(-1.88867 + 6.65950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) \) 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

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