LMFDB - Embedded newform 228.2.m.a.11.4

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			11.4
Character	$\chi$	$=$	228.11
Dual form			228.2.m.a.83.4

$q$-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 $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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	0.195192	−	0.980765i	$-0.437467\pi$
$5$	−1.24455	−	0.718541i	−0.556579	−	0.321341i	−0.751771	+	0.659424i	$0.770800\pi$
$6$	−2.00825	+	1.40248i	−0.819863	+	0.572560i
$7$		−	1.00140i		−	0.378494i	−0.981930	−	0.189247i	$-0.939395\pi$
$7$		−	1.00140i		−	0.378494i	0.981930	−	0.189247i	$-0.0606046\pi$
$8$	−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	−0.999521	−	0.0309503i	$-0.990147\pi$
$13$	−1.89855	−	3.28839i	−0.526564	−	0.912036i	0.472957	−	0.881086i	$-0.343187\pi$
$14$	−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	0.136010	−	0.990707i	$-0.456572\pi$
$17$	−2.69636	−	1.55674i	−0.653962	−	0.377565i	−0.789973	+	0.613142i	$0.789905\pi$
$18$	−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	0.909732	−	0.415196i	$-0.136287\pi$
$23$	0.457022	+	0.791584i	0.0952956	+	0.165057i	−0.814436	+	0.580253i	$0.802954\pi$
$24$	−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	−0.595094	−	0.803656i	$-0.702885\pi$
$29$	−1.05901	+	0.611420i	−0.196653	+	0.113538i	0.398440	+	0.917194i	$0.369552\pi$
$30$	3.50710	−	0.302447i	0.640306	−	0.0552190i
$31$		−	5.13118i		−	0.921587i	−0.887507	−	0.460794i	$-0.847565\pi$
$31$		−	5.13118i		−	0.921587i	0.887507	−	0.460794i	$-0.152435\pi$
$32$	−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	0.996774	−	0.0802554i	$-0.0255736\pi$
$41$	9.12867	+	5.27044i	1.42566	+	0.823104i	0.428884	+	0.903360i	$0.358907\pi$
$42$	1.40444	+	2.01106i	0.216710	+	0.310313i
$43$	7.83509	+	4.52359i	1.19484	+	0.689841i	0.959400	−	0.282048i	$-0.0910136\pi$
$43$	7.83509	+	4.52359i	1.19484	+	0.689841i	0.235440	+	0.971889i	$0.424347\pi$
$44$	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	0.972636	+	0.232335i	$0.0746365\pi$
$47$	4.71344	+	8.16392i	0.687526	+	1.19083i	−0.285110	+	0.958495i	$0.592030\pi$
$48$	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	−0.642131	−	0.766595i	$-0.721949\pi$
$53$	−2.17897	+	1.25803i	−0.299305	+	0.172804i	0.342826	+	0.939399i	$0.388616\pi$
$54$	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	−0.854300	−	0.519781i	$-0.826014\pi$
$59$	0.176619	−	0.305912i	0.0229938	−	0.0398264i	0.877293	+	0.479955i	$0.159347\pi$
$60$	−4.84945	−	1.12484i	−0.626061	−	0.145217i
$61$	5.51674	+	9.55527i	0.706346	+	1.22343i	0.966204	+	0.257780i	$0.0829911\pi$
$61$	5.51674	+	9.55527i	0.706346	+	1.22343i	−0.259857	+	0.965647i	$0.583676\pi$
$62$	−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	−0.806541	−	0.591179i	$-0.798663\pi$
$67$	−5.71202	+	3.29784i	−0.697835	+	0.402895i	0.108706	+	0.994074i	$0.465329\pi$
$68$	−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	−0.351503	−	0.936187i	$-0.614329\pi$
$71$	5.35069	−	9.26766i	0.635010	−	1.09987i	0.986513	−	0.163683i	$-0.0523373\pi$
$72$	−5.23923	+	6.67461i	−0.617449	+	0.786611i
$73$	0.163973	−	0.284010i	0.0191916	−	0.0332409i	−0.856270	−	0.516528i	$-0.827224\pi$
$73$	0.163973	−	0.284010i	0.0191916	−	0.0332409i	0.875462	+	0.483287i	$0.160557\pi$
$74$	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	0.697725	−	0.716365i	$-0.254196\pi$
$79$	3.78812	+	2.18707i	0.426197	+	0.246065i	−0.271528	+	0.962431i	$0.587529\pi$
$80$	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	0.0220490	−	0.999757i	$-0.492981\pi$
$89$	8.48010	−	4.89599i	0.898888	−	0.518973i	0.876839	+	0.480783i	$0.159648\pi$
$90$	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	0.495706	+	0.868490i	$0.334909\pi$
$97$	−4.96660	+	8.60241i	−0.504282	+	0.873442i	−0.999988	+	0.00495141i	$0.998424\pi$
$98$	−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	−0.969314	−	0.245825i	$-0.920941\pi$
$101$	−12.4727	+	7.20112i	−1.24108	+	0.716539i	−0.271767	+	0.962363i	$0.587608\pi$
$102$	7.59824	−	0.655262i	0.752338	−	0.0648806i
$103$		−	20.0454i		−	1.97513i	−0.157209	−	0.987565i	$-0.550250\pi$
$103$		−	20.0454i		−	1.97513i	0.157209	−	0.987565i	$-0.449750\pi$
$104$	−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	−0.851128	−	0.524958i	$-0.824081\pi$
$109$	0.303425	−	0.525548i	0.0290629	−	0.0503384i	0.880191	+	0.474620i	$0.157414\pi$
$110$	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	$-0.782014\pi$
$113$		−	13.4479i		−	1.26507i	0.774531	−	0.632536i	$-0.217986\pi$
$114$	−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	−0.974010	−	0.226504i	$-0.927271\pi$
$127$	−14.2542	+	8.22968i	−1.26486	+	0.730266i	−0.290847	+	0.956769i	$0.593937\pi$
$128$	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	0.415205	+	0.909728i	$0.363710\pi$
$131$	−6.64121	+	11.5029i	−0.580245	+	1.00501i	−0.995450	+	0.0952861i	$0.969623\pi$
$132$	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	−0.174335	−	0.984686i	$-0.555778\pi$
$137$	6.92053	−	3.99557i	0.591261	−	0.341364i	0.765596	+	0.643322i	$0.222444\pi$
$138$	−2.02799	−	0.948733i	−0.172634	−	0.0807616i
$139$	−9.72287	+	5.61350i	−0.824683	+	0.476131i	−0.852029	−	0.523495i	$-0.824628\pi$
$139$	−9.72287	+	5.61350i	−0.824683	+	0.476131i	0.0273457	+	0.999626i	$0.491295\pi$
$140$	−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	−0.462338	−	0.886704i	$-0.652989\pi$
$149$	−17.8388	−	10.2993i	−1.46141	−	0.843748i	−0.999077	+	0.0429559i	$0.986322\pi$
$150$	6.51145	+	3.04618i	0.531658	+	0.248720i
$151$			13.1949i			1.07378i	0.843651	+	0.536892i	$0.180402\pi$
$151$			13.1949i			1.07378i	−0.843651	+	0.536892i	$0.819598\pi$
$152$	−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	−0.879975	−	0.475020i	$-0.842441\pi$
$157$	−0.358460	+	0.620871i	−0.0286082	+	0.0495509i	0.851367	+	0.524571i	$0.175774\pi$
$158$	−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	$0.110925\pi$
$163$			8.71919i			0.682940i	−0.939893	+	0.341470i	$0.889075\pi$
$164$	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	0.957897	−	0.287112i	$-0.0926950\pi$
$167$	2.97617	+	5.15487i	0.230303	+	0.398896i	−0.727594	+	0.686008i	$0.759362\pi$
$168$	−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	0.571290	−	0.820748i	$-0.306443\pi$
$173$	1.92226	+	1.10982i	0.146147	+	0.0843780i	−0.425143	+	0.905126i	$0.639776\pi$
$174$	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	0.789212	−	0.614120i	$-0.210489\pi$
$181$	−1.84634	−	3.19796i	−0.137238	−	0.237703i	−0.926450	+	0.376418i	$0.877156\pi$
$182$	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	−0.281899	−	0.959444i	$-0.590964\pi$
$193$	9.58514	−	16.6019i	0.689953	−	1.19503i	0.971852	−	0.235590i	$-0.0757023\pi$
$194$	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	$-0.877736\pi$
$197$		−	10.5191i		−	0.749458i	0.927134	−	0.374729i	$-0.122264\pi$
$198$	−0.367984	+	9.78246i	−0.0261515	+	0.695209i
$199$	19.1120	−	11.0343i	1.35482	−	0.782203i	0.365896	−	0.930656i	$-0.380763\pi$
$199$	19.1120	−	11.0343i	1.35482	−	0.782203i	0.988919	+	0.148453i	$0.0474294\pi$
$200$	−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	0.220890	−	0.975299i	$-0.429104\pi$
$211$	−7.45609	−	4.30478i	−0.513298	−	0.296353i	−0.734188	+	0.678946i	$0.762437\pi$
$212$	−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	0.749475	−	0.662033i	$-0.230306\pi$
$223$	8.22632	+	4.74947i	0.550875	+	0.318048i	−0.198600	+	0.980081i	$0.563639\pi$
$224$	−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	0.823644	−	0.567107i	$-0.191938\pi$
$233$	11.3618	+	6.55974i	0.744336	+	0.429743i	−0.0793074	+	0.996850i	$0.525271\pi$
$234$	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	0.503012	−	0.864279i	$-0.332225\pi$
$241$	−7.71523	−	13.3632i	−0.496982	−	0.860798i	−0.999994	+	0.00348172i	$0.998892\pi$
$242$	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	−0.889187	−	0.457544i	$-0.848729\pi$
$251$	−13.3214	−	23.0733i	−0.840838	−	1.45637i	0.0483485	−	0.998831i	$-0.484604\pi$
$252$	−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	−0.413287	−	0.910601i	$-0.635620\pi$
$257$	2.70402	−	1.56117i	0.168672	−	0.0973828i	0.581960	+	0.813218i	$0.302286\pi$
$258$	−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	−0.0385796	+	0.999256i	$0.512283\pi$
$263$	−14.3469	+	24.8496i	−0.884670	+	1.53229i	−0.846091	+	0.533039i	$0.821050\pi$
$264$	−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	0.429725	−	0.902960i	$-0.358611\pi$
$269$	−2.25352	−	1.30107i	−0.137400	−	0.0793277i	−0.567124	+	0.823632i	$0.691944\pi$
$270$	−3.74360	−	9.87453i	−0.227828	−	0.600945i
$271$	26.7596	+	15.4497i	1.62553	+	0.938501i	0.985404	+	0.170234i	$0.0544522\pi$
$271$	26.7596	+	15.4497i	1.62553	+	0.938501i	0.640129	+	0.768268i	$0.278881\pi$
$272$	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	−0.898097	−	0.439796i	$-0.855051\pi$
$281$	−16.1977	+	9.35172i	−0.966271	+	0.557877i	−0.0681738	+	0.997673i	$0.521717\pi$
$282$	−20.9155	−	9.78465i	−1.24550	−	0.582668i
$283$	−11.8095	−	6.81821i	−0.702001	−	0.405300i	0.106091	−	0.994356i	$-0.466166\pi$
$283$	−11.8095	−	6.81821i	−0.702001	−	0.405300i	−0.808092	+	0.589056i	$0.799500\pi$
$284$	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	$0.116995\pi$
$293$			12.3015i			0.718662i	−0.933210	+	0.359331i	$0.883005\pi$
$294$	−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	0.980424	−	0.196898i	$-0.0630868\pi$
$307$	22.7799	+	13.1520i	1.30012	+	0.750623i	0.319693	+	0.947521i	$0.396420\pi$
$308$	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	0.989978	−	0.141220i	$-0.0451025\pi$
$313$	6.59354	+	11.4203i	0.372689	+	0.645516i	−0.617289	+	0.786736i	$0.711769\pi$
$314$	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	−0.412021	−	0.911174i	$-0.635177\pi$
$317$	3.04579	−	1.75849i	0.171069	−	0.0987665i	0.583090	+	0.812408i	$0.301844\pi$
$318$	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	$-0.978016\pi$
$331$		−	2.51103i		−	0.138019i	0.997616	−	0.0690094i	$-0.0219838\pi$
$332$	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	0.391616	+	0.920129i	$0.371916\pi$
$337$	−11.0338	+	19.1110i	−0.601047	+	1.04104i	−0.992663	+	0.120915i	$0.961417\pi$
$338$	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	−0.997457	−	0.0712651i	$-0.977296\pi$
$347$	−8.14062	+	14.1000i	−0.437011	+	0.756926i	0.560446	+	0.828191i	$0.310630\pi$
$348$	−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	$-0.809377\pi$
$353$		−	21.1820i		−	1.12740i	0.825979	−	0.563701i	$-0.190623\pi$
$354$	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	−0.727786	−	0.685804i	$-0.759451\pi$
$359$	4.35846	−	7.54907i	0.230031	−	0.398425i	0.957817	+	0.287379i	$0.0927841\pi$
$360$	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	0.174116	−	0.984725i	$-0.444293\pi$
$367$	21.3406	−	12.3210i	1.11397	−	0.643152i	0.939855	+	0.341573i	$0.110960\pi$
$368$	−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	$0.247221\pi$
$379$			27.2904i			1.40181i	−0.713254	+	0.700906i	$0.752779\pi$
$380$	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	−0.882594	−	0.470136i	$-0.844205\pi$
$383$	−0.668270	+	1.15748i	−0.0341470	+	0.0591443i	0.848447	+	0.529281i	$0.177538\pi$
$384$	−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	−0.707246	−	0.706967i	$-0.750063\pi$
$389$	−8.84813	+	5.10847i	−0.448618	+	0.259010i	0.258628	+	0.965977i	$0.416729\pi$
$390$	−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	0.183998	+	0.982927i	$0.441096\pi$
$397$	−15.1278	+	26.2020i	−0.759240	+	1.31504i	−0.943238	+	0.332116i	$0.892237\pi$
$398$	−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	0.0686760	−	0.997639i	$-0.478123\pi$
$401$	−15.2383	−	8.79786i	−0.760967	−	0.439344i	−0.829643	+	0.558295i	$0.811456\pi$
$402$	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	−0.984900	−	0.173126i	$-0.944613\pi$
$409$	−12.9914	−	22.5017i	−0.642381	−	1.11264i	0.342519	−	0.939511i	$-0.388720\pi$
$410$	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	−0.980853	−	0.194747i	$-0.937611\pi$
$421$	−6.60218	+	11.4353i	−0.321771	+	0.557323i	0.659083	+	0.752070i	$0.270945\pi$
$422$	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	0.543856	−	0.839179i	$-0.316964\pi$
$431$	−9.44236	−	16.3546i	−0.454822	−	0.787776i	−0.998678	+	0.0514033i	$0.983631\pi$
$432$	1.16065	−	20.7522i	0.0558420	−	0.998440i
$433$	4.87623	+	8.44588i	0.234337	+	0.405883i	0.959080	−	0.283136i	$-0.0913748\pi$
$433$	4.87623	+	8.44588i	0.234337	+	0.405883i	−0.724743	+	0.689019i	$0.758041\pi$
$434$	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	−0.105051	−	0.994467i	$-0.533500\pi$
$439$	−21.3464	−	12.3244i	−1.01881	−	0.588210i	−0.913759	+	0.406257i	$0.866834\pi$
$440$	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	0.871245	−	0.490848i	$-0.163313\pi$
$443$	0.221764	+	0.384106i	0.0105363	+	0.0182494i	−0.860709	+	0.509097i	$0.829979\pi$
$444$	−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	$0.0538628\pi$
$449$			7.13703i			0.336817i	−0.985717	+	0.168409i	$0.946137\pi$
$450$	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	0.999277	+	0.0380204i	$0.0121052\pi$
$461$	32.8900	+	18.9891i	1.53184	+	0.884409i	0.532565	+	0.846389i	$0.321228\pi$
$462$	3.24058	+	4.64027i	0.150766	+	0.215885i
$463$		−	20.7854i		−	0.965978i	−0.875626	−	0.482989i	$-0.839551\pi$
$463$		−	20.7854i		−	0.965978i	0.875626	−	0.482989i	$-0.160449\pi$
$464$	−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	0.971459	+	0.237209i	$0.0762326\pi$
$479$	15.1267	+	26.2003i	0.691158	+	1.19712i	−0.280300	+	0.959912i	$0.590434\pi$
$480$	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	$0.107244\pi$
$487$			14.5904i			0.661155i	−0.943779	+	0.330578i	$0.892756\pi$
$488$	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	−0.671617	−	0.740899i	$-0.734400\pi$
$491$	6.77672	−	11.7376i	0.305829	−	0.529711i	0.977446	+	0.211188i	$0.0677331\pi$
$492$	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	0.901257	−	0.433285i	$-0.142646\pi$
$499$	21.8167	+	12.5959i	0.976650	+	0.563869i	0.0753930	+	0.997154i	$0.475979\pi$
$500$	−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	0.882413	−	0.470475i	$-0.155917\pi$
$503$	0.757234	+	1.31157i	0.0337634	+	0.0584799i	−0.848650	+	0.528955i	$0.822584\pi$
$504$	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	−0.870847	−	0.491555i	$-0.836429\pi$
$509$	−19.8666	+	11.4700i	−0.880571	+	0.508398i	−0.00972436	+	0.999953i	$0.503095\pi$
$510$	−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	$0.0745470\pi$
$521$			10.5938i			0.464123i	−0.972701	+	0.232061i	$0.925453\pi$
$522$	−2.42331	−	4.58734i	−0.106065	−	0.200782i
$523$	−16.8636	+	9.73621i	−0.737394	+	0.425735i	−0.821121	−	0.570754i	$-0.806651\pi$
$523$	−16.8636	+	9.73621i	−0.737394	+	0.425735i	0.0837271	+	0.996489i	$0.473318\pi$
$524$	−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	0.586995	−	0.809591i	$-0.300311\pi$
$541$	−9.48120	−	16.4219i	−0.407629	−	0.706034i	−0.994624	+	0.103557i	$0.966978\pi$
$542$	−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	−0.547978	−	0.836492i	$-0.684602\pi$
$547$	−2.28136	+	1.31715i	−0.0975440	+	0.0563171i	0.450434	+	0.892809i	$0.351269\pi$
$548$	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	−0.0697954	−	0.997561i	$-0.522235\pi$
$557$	17.9182	−	10.3451i	0.759220	−	0.438336i	0.829016	+	0.559225i	$0.188901\pi$
$558$	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	$0.120464\pi$
$569$			17.6269i			0.738957i	−0.929239	+	0.369479i	$0.879536\pi$
$570$	14.4374	+	5.19551i	0.604718	+	0.217616i
$571$			18.2535i			0.763887i	0.924186	+	0.381943i	$0.124745\pi$
$571$			18.2535i			0.763887i	−0.924186	+	0.381943i	$0.875255\pi$
$572$	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	−0.892115	−	0.451808i	$-0.850779\pi$
$587$	−1.32723	+	2.29883i	−0.0547807	+	0.0948830i	0.837335	+	0.546691i	$0.184113\pi$
$588$	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	−0.999782	−	0.0208774i	$-0.993354\pi$
$593$	−36.0791	+	20.8303i	−1.48159	+	0.855398i	−0.481811	+	0.876275i	$0.660021\pi$
$594$	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	0.998575	−	0.0533579i	$-0.0169924\pi$
$599$	11.0889	+	19.2065i	0.453078	+	0.784755i	−0.545497	+	0.838113i	$0.683659\pi$
$600$	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	$0.0449392\pi$
$607$			6.93356i			0.281424i	−0.990051	+	0.140712i	$0.955061\pi$
$608$	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	−0.120616	−	0.992699i	$-0.538487\pi$
$613$	19.7921	−	34.2809i	0.799395	−	1.38459i	0.920011	−	0.391893i	$-0.128180\pi$
$614$	−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	−0.949064	−	0.315084i	$-0.897967\pi$
$617$	−28.5834	+	16.5026i	−1.15072	+	0.664371i	−0.201661	+	0.979455i	$0.564634\pi$
$618$	28.1132	+	40.2561i	1.13088	+	1.61934i
$619$			33.6634i			1.35304i	0.736422	+	0.676522i	$0.236514\pi$
$619$			33.6634i			1.35304i	−0.736422	+	0.676522i	$0.763486\pi$
$620$	−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	−0.650077	−	0.759868i	$-0.725264\pi$
$631$	−7.96424	+	4.59816i	−0.317051	+	0.183050i	0.333026	+	0.942918i	$0.391930\pi$
$632$	−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	−0.382964	−	0.923763i	$-0.625097\pi$
$641$	−34.7983	−	20.0908i	−1.37445	−	0.793538i	−0.991484	+	0.130225i	$0.958430\pi$
$642$	−12.9757	+	9.06171i	−0.512110	+	0.357637i
$643$	−15.3558	−	8.86568i	−0.605574	−	0.349628i	0.165657	−	0.986183i	$-0.447025\pi$
$643$	−15.3558	−	8.86568i	−0.605574	−	0.349628i	−0.771231	+	0.636555i	$0.780359\pi$
$644$	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	$-0.911351\pi$
$653$		−	14.0502i		−	0.549827i	0.961469	−	0.274914i	$-0.0886493\pi$
$654$	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	0.997965	−	0.0637705i	$-0.0203126\pi$
$659$	11.3916	+	19.7309i	0.443755	+	0.768607i	−0.554209	+	0.832377i	$0.686979\pi$
$660$	−11.1895	−	2.59544i	−0.435551	−	0.101027i
$661$	−7.01939	−	12.1579i	−0.273023	−	0.472889i	0.696612	−	0.717448i	$-0.254690\pi$
$661$	−7.01939	−	12.1579i	−0.273023	−	0.472889i	−0.969634	+	0.244559i	$0.921357\pi$
$662$	−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	$-0.855647\pi$
$677$		−	22.7987i		−	0.876226i	0.898920	−	0.438113i	$-0.144353\pi$
$678$	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	$-0.991477\pi$
$691$		−	1.40760i		−	0.0535478i	0.999642	−	0.0267739i	$-0.00852341\pi$
$692$	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	0.996845	+	0.0793675i	$0.0252901\pi$
$701$	41.4092	+	23.9076i	1.56400	+	0.902977i	0.567157	+	0.823610i	$0.308043\pi$
$702$	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	0.505287	−	0.862952i	$-0.331387\pi$
$709$	−13.1723	−	22.8150i	−0.494695	−	0.856836i	−0.999981	+	0.00611514i	$0.998053\pi$
$710$	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	−0.282269	−	0.959335i	$-0.591087\pi$
$719$	18.4930	−	32.0309i	0.689674	−	1.19455i	0.971943	−	0.235216i	$-0.0755797\pi$
$720$	−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	0.226284	−	0.974061i	$-0.427342\pi$
$727$	−13.5930	−	7.84792i	−0.504136	−	0.291063i	−0.730420	+	0.682998i	$0.760676\pi$
$728$	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	0.208957	−	0.977925i	$-0.432993\pi$
$739$	−14.5022	−	8.37285i	−0.533472	−	0.308000i	−0.742429	+	0.669924i	$0.766326\pi$
$740$	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	−0.331642	−	0.943405i	$-0.607603\pi$
$743$	17.7502	−	30.7443i	0.651192	−	1.12790i	0.982834	−	0.184492i	$-0.0590640\pi$
$744$	−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	0.322426	−	0.946595i	$-0.395502\pi$
$751$	35.7193	−	20.6225i	1.30341	−	0.752526i	0.980988	+	0.194068i	$0.0621683\pi$
$752$	−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	−0.881895	−	0.471447i	$-0.843732\pi$
$757$	−0.898669	+	1.55654i	−0.0326627	+	0.0565734i	0.849232	+	0.528020i	$0.177065\pi$
$758$	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	$-0.871655\pi$
$761$		−	21.6481i		−	0.784742i	0.919807	−	0.392371i	$-0.128345\pi$
$762$	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	0.840315	−	0.542098i	$-0.182370\pi$
$769$	−1.36750	−	2.36857i	−0.0493132	−	0.0854130i	−0.889628	+	0.456685i	$0.849037\pi$
$770$	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	−0.697240	−	0.716838i	$-0.745589\pi$
$773$	−11.8179	+	6.82305i	−0.425059	+	0.245408i	0.272180	+	0.962246i	$0.412255\pi$
$774$	−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	$0.0743019\pi$
$787$			12.9782i			0.462624i	−0.972880	+	0.231312i	$0.925698\pi$
$788$	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	$0.225546\pi$
$797$			36.7430i			1.30150i	−0.759290	+	0.650752i	$0.774454\pi$
$798$	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	$-0.990855\pi$
$809$		−	1.63402i		−	0.0574491i	0.999587	−	0.0287245i	$-0.00914456\pi$
$810$	−17.5540	−	5.14001i	−0.616785	−	0.180601i
$811$	−11.1637	+	6.44538i	−0.392011	+	0.226328i	−0.683031	−	0.730389i	$-0.739339\pi$
$811$	−11.1637	+	6.44538i	−0.392011	+	0.226328i	0.291020	+	0.956717i	$0.406005\pi$
$812$	−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	−0.383751	−	0.923436i	$-0.625368\pi$
$821$	6.42094	−	3.70713i	0.224092	−	0.129380i	0.607844	+	0.794057i	$0.292035\pi$
$822$	−8.29442	+	17.7300i	−0.289301	+	0.618404i
$823$	−23.7798	+	13.7293i	−0.828913	+	0.478573i	−0.853480	−	0.521125i	$-0.825513\pi$
$823$	−23.7798	+	13.7293i	−0.828913	+	0.478573i	0.0245673	+	0.999698i	$0.492179\pi$
$824$	−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	0.815467	−	0.578803i	$-0.196480\pi$
$827$	−2.68955	−	4.65844i	−0.0935248	−	0.161990i	−0.908992	+	0.416814i	$0.863147\pi$
$828$	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	−0.999066	−	0.0432070i	$-0.986242\pi$
$839$	−13.3854	+	23.1842i	−0.462115	+	0.800406i	0.536951	+	0.843613i	$0.319576\pi$
$840$	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	−0.915911	−	0.401381i	$-0.868530\pi$
$853$	−3.22288	+	5.58220i	−0.110349	+	0.191131i	0.805562	+	0.592512i	$0.201864\pi$
$854$	−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	0.964938	−	0.262478i	$-0.0845396\pi$
$857$	35.7177	+	20.6216i	1.22009	+	0.704422i	0.255157	+	0.966900i	$0.417873\pi$
$858$	19.4389	+	9.09389i	0.663633	+	0.310460i
$859$	−15.7997	+	9.12194i	−0.539078	+	0.311237i	−0.744705	−	0.667394i	$-0.767410\pi$
$859$	−15.7997	+	9.12194i	−0.539078	+	0.311237i	0.205627	+	0.978630i	$0.434077\pi$
$860$	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	0.159840	+	0.987143i	$0.448902\pi$
$877$	−22.9501	+	39.7508i	−0.774971	+	1.34229i	−0.934811	+	0.355146i	$0.884431\pi$
$878$	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	$-0.876673\pi$
$881$		−	22.4288i		−	0.755647i	0.925878	−	0.377823i	$-0.123327\pi$
$882$	−0.956442	+	25.4260i	−0.0322051	+	0.856137i
$883$	27.2400	−	15.7270i	0.916698	−	0.529256i	0.0341177	−	0.999418i	$-0.489138\pi$
$883$	27.2400	−	15.7270i	0.916698	−	0.529256i	0.882580	+	0.470162i	$0.155805\pi$
$884$	−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	0.691320	+	0.722549i	$0.257029\pi$
$887$	28.9309	+	50.1098i	0.971406	+	1.68252i	0.280085	+	0.959975i	$0.409637\pi$
$888$	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	0.0496427	−	0.998767i	$-0.484192\pi$
$907$	−23.8069	−	13.7449i	−0.790494	−	0.456392i	−0.840136	+	0.542375i	$0.817525\pi$
$908$	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	$0.0503448\pi$
$919$			9.54949i			0.315009i	−0.987518	+	0.157504i	$0.949655\pi$
$920$	−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	−0.214028	−	0.976828i	$-0.568658\pi$
$929$	−35.5696	−	20.5361i	−1.16700	−	0.673768i	−0.952971	+	0.303060i	$0.901992\pi$
$930$	−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	0.926125	−	0.377216i	$-0.123119\pi$
$937$	4.17478	+	7.23092i	0.136384	+	0.236224i	−0.789741	+	0.613440i	$0.789785\pi$
$938$	−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	0.415131	−	0.909762i	$-0.363736\pi$
$941$	43.2704	−	24.9822i	1.41057	−	0.814395i	0.995442	+	0.0953666i	$0.0304023\pi$
$942$	−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	−0.700956	−	0.713205i	$-0.747243\pi$
$947$	8.22190	−	14.2407i	0.267176	−	0.462762i	0.968131	+	0.250443i	$0.0805762\pi$
$948$	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	0.532858	−	0.846205i	$-0.321118\pi$
$953$	2.05142	+	1.18439i	0.0664520	+	0.0383661i	−0.466406	+	0.884571i	$0.654451\pi$
$954$	−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	0.616455	−	0.787390i	$-0.288568\pi$
$967$	7.54969	+	4.35882i	0.242782	+	0.140170i	−0.373673	+	0.927561i	$0.621902\pi$
$968$	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	−0.964337	−	0.264677i	$-0.914735\pi$
$971$	−7.88219	+	13.6523i	−0.252951	+	0.438125i	0.711386	+	0.702802i	$0.248068\pi$
$972$	−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	$0.235831\pi$
$977$			42.1932i			1.34988i	−0.737872	+	0.674941i	$0.764169\pi$
$978$	−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	−0.994713	−	0.102695i	$-0.967254\pi$
$983$	−12.8051	+	22.1791i	−0.408420	+	0.707404i	0.586293	+	0.810099i	$0.300587\pi$
$984$	−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	0.186129	−	0.982525i	$-0.440406\pi$
$991$	−17.9972	−	10.3907i	−0.571699	−	0.330070i	−0.757828	+	0.652455i	$0.773739\pi$
$992$	−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	0.953450	−	0.301552i	$-0.0975048\pi$
$997$	6.80677	+	11.7897i	0.215573	+	0.373383i	−0.737877	+	0.674935i	$0.764172\pi$
$998$	−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.11.4	✓	72
3.2	odd	2	inner	228.2.m.a.11.33	yes	72
4.3	odd	2	inner	228.2.m.a.11.9	yes	72
12.11	even	2	inner	228.2.m.a.11.28	yes	72
19.7	even	3	inner	228.2.m.a.83.28	yes	72
57.26	odd	6	inner	228.2.m.a.83.9	yes	72
76.7	odd	6	inner	228.2.m.a.83.33	yes	72
228.83	even	6	inner	228.2.m.a.83.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.m.a.11.4	✓	72	1.1	even	1	trivial
228.2.m.a.11.9	yes	72	4.3	odd	2	inner
228.2.m.a.11.28	yes	72	12.11	even	2	inner
228.2.m.a.11.33	yes	72	3.2	odd	2	inner
228.2.m.a.83.4	yes	72	228.83	even	6	inner
228.2.m.a.83.9	yes	72	57.26	odd	6	inner
228.2.m.a.83.28	yes	72	19.7	even	3	inner
228.2.m.a.83.33	yes	72	76.7	odd	6	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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