LMFDB - Embedded newform 483.2.r.a.181.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.21
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139288 + 0.968769i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.999875 - 0.293590i) q^{4} +(-2.20891 + 2.54922i) q^{5} +(0.275740 - 0.939085i) q^{6} +(-1.65089 - 2.06750i) q^{7} +(1.23685 + 2.70832i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.139288 + 0.968769i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.999875 - 0.293590i) q^{4} +(-2.20891 + 2.54922i) q^{5} +(0.275740 - 0.939085i) q^{6} +(-1.65089 - 2.06750i) q^{7} +(1.23685 + 2.70832i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-2.77728 - 1.78485i) q^{10} +(-4.11772 - 0.592039i) q^{11} +(-1.03148 - 0.148304i) q^{12} +(-0.505033 + 0.785847i) q^{13} +(1.77298 - 1.88731i) q^{14} +(3.06828 - 1.40124i) q^{15} +(-0.698142 + 0.448669i) q^{16} +(-4.52632 - 1.32905i) q^{17} +(-0.640932 + 0.739675i) q^{18} +(0.935178 - 0.274593i) q^{19} +(-1.46021 + 3.19741i) q^{20} +(0.642836 + 2.56647i) q^{21} -4.07158i q^{22} +(-4.35692 + 2.00431i) q^{23} -2.97738i q^{24} +(-0.907659 - 6.31290i) q^{25} +(-0.831649 - 0.379801i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-2.25768 - 1.58255i) q^{28} +(-0.0978288 - 0.0287251i) q^{29} +(1.78485 + 2.77728i) q^{30} +(-2.52696 + 1.15403i) q^{31} +(3.36764 + 3.88647i) q^{32} +(3.49967 + 2.24910i) q^{33} +(0.657077 - 4.57007i) q^{34} +(8.91719 + 0.358429i) q^{35} +(0.876659 + 0.563394i) q^{36} +(-4.45895 + 3.86370i) q^{37} +(0.396276 + 0.867723i) q^{38} +(0.785847 - 0.505033i) q^{39} +(-9.63621 - 2.82945i) q^{40} +(-5.38416 - 4.66540i) q^{41} +(-2.39677 + 0.980238i) q^{42} +(-2.52966 - 1.15526i) q^{43} +(-4.29102 + 0.616956i) q^{44} -3.37310 q^{45} +(-2.54858 - 3.94167i) q^{46} -4.36801i q^{47} +(0.821436 - 0.118105i) q^{48} +(-1.54910 + 6.82644i) q^{49} +(5.98932 - 1.75862i) q^{50} +(3.56518 + 3.08924i) q^{51} +(-0.274253 + 0.934021i) q^{52} +(7.67974 + 11.9499i) q^{53} +(0.890285 - 0.406579i) q^{54} +(10.6049 - 9.18922i) q^{55} +(3.55755 - 7.02834i) q^{56} +(-0.964737 - 0.138708i) q^{57} +(0.0142016 - 0.0987745i) q^{58} +(7.23921 - 11.2644i) q^{59} +(2.65651 - 2.30188i) q^{60} +(3.79868 + 8.31795i) q^{61} +(-1.46996 - 2.28730i) q^{62} +(0.481405 - 2.60159i) q^{63} +(-4.38293 + 5.05817i) q^{64} +(-0.887723 - 3.02331i) q^{65} +(-1.69140 + 3.70364i) q^{66} +(-4.69987 + 0.675740i) q^{67} -4.91594 q^{68} +(4.79581 - 0.0132547i) q^{69} +(0.894822 + 8.68862i) q^{70} +(0.292204 + 2.03232i) q^{71} +(-1.23685 + 2.70832i) q^{72} +(1.94050 + 6.60873i) q^{73} +(-4.36411 - 3.78152i) q^{74} +(-1.79684 + 6.11947i) q^{75} +(0.854443 - 0.549117i) q^{76} +(5.57388 + 9.49077i) q^{77} +(0.598719 + 0.690959i) q^{78} +(5.65978 - 8.80679i) q^{79} +(0.398379 - 2.77079i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(3.76974 - 5.86584i) q^{82} +(2.48752 + 2.87075i) q^{83} +(1.39624 + 2.37742i) q^{84} +(13.3863 - 8.60283i) q^{85} +(0.766825 - 2.61157i) q^{86} +(0.0770553 + 0.0667688i) q^{87} +(-3.48957 - 11.8844i) q^{88} +(-5.83329 + 12.7731i) q^{89} +(-0.469832 - 3.26776i) q^{90} +(2.45849 - 0.253195i) q^{91} +(-3.76793 + 3.28320i) q^{92} +2.77801 q^{93} +(4.23159 - 0.608410i) q^{94} +(-1.36573 + 2.99053i) q^{95} +(-1.44882 - 4.93423i) q^{96} +(-1.18608 + 1.36881i) q^{97} +(-6.82901 - 0.549876i) q^{98} +(-2.24910 - 3.49967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

Coefficient data

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

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

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

$2$	0.139288	+	0.968769i	0.0984914	+	0.685023i	0.977918	+	0.208988i	$0.0670171\pi$
$2$	0.139288	+	0.968769i	0.0984914	+	0.685023i	−0.879427	+	0.476034i	$0.842074\pi$
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	0.999875	−	0.293590i	0.499937	−	0.146795i
$5$	−2.20891	+	2.54922i	−0.987856	+	1.14005i	0.00228890	+	0.999997i	$0.499271\pi$
$5$	−2.20891	+	2.54922i	−0.987856	+	1.14005i	−0.990145	+	0.140049i	$0.955274\pi$
$6$	0.275740	−	0.939085i	0.112570	−	0.383380i
$7$	−1.65089	−	2.06750i	−0.623979	−	0.781441i
$7$	−1.65089	−	2.06750i	−0.623979	−	0.781441i
$8$	1.23685	+	2.70832i	0.437292	+	0.957537i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−2.77728	−	1.78485i	−0.878253	−	0.564419i
$11$	−4.11772	−	0.592039i	−1.24154	−	0.178506i	−0.509921	−	0.860221i	$-0.670325\pi$
$11$	−4.11772	−	0.592039i	−1.24154	−	0.178506i	−0.731618	+	0.681715i	$0.761235\pi$
$12$	−1.03148	−	0.148304i	−0.297762	−	0.0428118i
$13$	−0.505033	+	0.785847i	−0.140071	+	0.217955i	−0.904201	−	0.427108i	$-0.859532\pi$
$13$	−0.505033	+	0.785847i	−0.140071	+	0.217955i	0.764130	+	0.645063i	$0.223169\pi$
$14$	1.77298	−	1.88731i	0.473848	−	0.504405i
$15$	3.06828	−	1.40124i	0.792227	−	0.361798i
$16$	−0.698142	+	0.448669i	−0.174536	+	0.112167i
$17$	−4.52632	−	1.32905i	−1.09779	−	0.322341i	−0.317818	−	0.948152i	$-0.602950\pi$
$17$	−4.52632	−	1.32905i	−1.09779	−	0.322341i	−0.779975	+	0.625811i	$0.784768\pi$
$18$	−0.640932	+	0.739675i	−0.151069	+	0.174343i
$19$	0.935178	−	0.274593i	0.214544	−	0.0629959i	−0.172694	−	0.984976i	$-0.555247\pi$
$19$	0.935178	−	0.274593i	0.214544	−	0.0629959i	0.387238	+	0.921980i	$0.373429\pi$
$20$	−1.46021	+	3.19741i	−0.326513	+	0.714964i
$21$	0.642836	+	2.56647i	0.140278	+	0.560049i
$22$		−	4.07158i		−	0.868064i
$23$	−4.35692	+	2.00431i	−0.908480	+	0.417927i
$23$	−4.35692	+	2.00431i	−0.908480	+	0.417927i
$24$		−	2.97738i		−	0.607756i
$25$	−0.907659	−	6.31290i	−0.181532	−	1.26258i
$26$	−0.831649	−	0.379801i	−0.163100	−	0.0744851i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	−2.25768	−	1.58255i	−0.426662	−	0.299074i
$29$	−0.0978288	−	0.0287251i	−0.0181663	−	0.00533412i	0.272637	−	0.962117i	$-0.412104\pi$
$29$	−0.0978288	−	0.0287251i	−0.0181663	−	0.00533412i	−0.290803	+	0.956783i	$0.593922\pi$
$30$	1.78485	+	2.77728i	0.325867	+	0.507060i
$31$	−2.52696	+	1.15403i	−0.453856	+	0.207269i	−0.629209	−	0.777237i	$-0.716621\pi$
$31$	−2.52696	+	1.15403i	−0.453856	+	0.207269i	0.175352	+	0.984506i	$0.443894\pi$
$32$	3.36764	+	3.88647i	0.595321	+	0.687037i
$33$	3.49967	+	2.24910i	0.609214	+	0.391518i
$34$	0.657077	−	4.57007i	0.112688	−	0.783761i
$35$	8.91719	+	0.358429i	1.50728	+	0.0605855i
$36$	0.876659	+	0.563394i	0.146110	+	0.0938991i
$37$	−4.45895	+	3.86370i	−0.733047	+	0.635189i	−0.939216	−	0.343328i	$-0.888446\pi$
$37$	−4.45895	+	3.86370i	−0.733047	+	0.635189i	0.206169	+	0.978516i	$0.433900\pi$
$38$	0.396276	+	0.867723i	0.0642844	+	0.140763i
$39$	0.785847	−	0.505033i	0.125836	−	0.0808700i
$40$	−9.63621	−	2.82945i	−1.52362	−	0.447375i
$41$	−5.38416	−	4.66540i	−0.840864	−	0.728613i	0.123740	−	0.992315i	$-0.460511\pi$
$41$	−5.38416	−	4.66540i	−0.840864	−	0.728613i	−0.964604	+	0.263702i	$0.915057\pi$
$42$	−2.39677	+	0.980238i	−0.369830	+	0.151254i
$43$	−2.52966	−	1.15526i	−0.385769	−	0.176175i	0.213084	−	0.977034i	$-0.431649\pi$
$43$	−2.52966	−	1.15526i	−0.385769	−	0.176175i	−0.598853	+	0.800859i	$0.704377\pi$
$44$	−4.29102	+	0.616956i	−0.646896	+	0.0930096i
$45$	−3.37310			−0.502832
$46$	−2.54858	−	3.94167i	−0.375767	−	0.581168i
$47$		−	4.36801i		−	0.637139i	−0.947899	−	0.318570i	$-0.896798\pi$
$47$		−	4.36801i		−	0.637139i	0.947899	−	0.318570i	$-0.103202\pi$
$48$	0.821436	−	0.118105i	0.118564	−	0.0170469i
$49$	−1.54910	+	6.82644i	−0.221300	+	0.975206i
$50$	5.98932	−	1.75862i	0.847017	−	0.248707i
$51$	3.56518	+	3.08924i	0.499225	+	0.432581i
$52$	−0.274253	+	0.934021i	−0.0380321	+	0.129525i
$53$	7.67974	+	11.9499i	1.05489	+	1.64145i	0.712167	+	0.702010i	$0.247714\pi$
$53$	7.67974	+	11.9499i	1.05489	+	1.64145i	0.342726	+	0.939435i	$0.388650\pi$
$54$	0.890285	−	0.406579i	0.121152	−	0.0553284i
$55$	10.6049	−	9.18922i	1.42997	−	1.23907i
$56$	3.55755	−	7.02834i	0.475397	−	0.939201i
$57$	−0.964737	−	0.138708i	−0.127783	−	0.0183724i
$58$	0.0142016	−	0.0987745i	0.00186477	−	0.0129697i
$59$	7.23921	−	11.2644i	0.942465	−	1.46650i	0.0588627	−	0.998266i	$-0.481253\pi$
$59$	7.23921	−	11.2644i	0.942465	−	1.46650i	0.883602	−	0.468238i	$-0.155111\pi$
$60$	2.65651	−	2.30188i	0.342954	−	0.297171i
$61$	3.79868	+	8.31795i	0.486371	+	1.06500i	0.980662	+	0.195708i	$0.0627004\pi$
$61$	3.79868	+	8.31795i	0.486371	+	1.06500i	−0.494291	+	0.869296i	$0.664572\pi$
$62$	−1.46996	−	2.28730i	−0.186685	−	0.290488i
$63$	0.481405	−	2.60159i	0.0606514	−	0.327769i
$64$	−4.38293	+	5.05817i	−0.547866	+	0.632272i
$65$	−0.887723	−	3.02331i	−0.110109	−	0.374995i
$66$	−1.69140	+	3.70364i	−0.208196	+	0.455887i
$67$	−4.69987	+	0.675740i	−0.574181	+	0.0825548i	−0.423288	−	0.905995i	$-0.639124\pi$
$67$	−4.69987	+	0.675740i	−0.574181	+	0.0825548i	−0.150893	+	0.988550i	$0.548215\pi$
$68$	−4.91594			−0.596146
$69$	4.79581	−	0.0132547i	0.577348	−	0.00159567i
$70$	0.894822	+	8.68862i	0.106952	+	1.03849i
$71$	0.292204	+	2.03232i	0.0346782	+	0.241193i	0.999787	−	0.0206584i	$-0.00657623\pi$
$71$	0.292204	+	2.03232i	0.0346782	+	0.241193i	−0.965108	+	0.261851i	$0.915667\pi$
$72$	−1.23685	+	2.70832i	−0.145764	+	0.319179i
$73$	1.94050	+	6.60873i	0.227118	+	0.773493i	0.991656	+	0.128914i	$0.0411491\pi$
$73$	1.94050	+	6.60873i	0.227118	+	0.773493i	−0.764538	+	0.644579i	$0.777033\pi$
$74$	−4.36411	−	3.78152i	−0.507318	−	0.439593i
$75$	−1.79684	+	6.11947i	−0.207481	+	0.706616i
$76$	0.854443	−	0.549117i	0.0980113	−	0.0629880i
$77$	5.57388	+	9.49077i	0.635203	+	1.08157i
$78$	0.598719	+	0.690959i	0.0677916	+	0.0782357i
$79$	5.65978	−	8.80679i	0.636775	−	0.990841i	−0.361514	−	0.932367i	$-0.617740\pi$
$79$	5.65978	−	8.80679i	0.636775	−	0.990841i	0.998289	−	0.0584743i	$-0.0186236\pi$
$80$	0.398379	−	2.77079i	0.0445402	−	0.309784i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	3.76974	−	5.86584i	0.416299	−	0.647773i
$83$	2.48752	+	2.87075i	0.273041	+	0.315106i	0.875665	−	0.482919i	$-0.160424\pi$
$83$	2.48752	+	2.87075i	0.273041	+	0.315106i	−0.602624	+	0.798025i	$0.705878\pi$
$84$	1.39624	+	2.37742i	0.152343	+	0.259397i
$85$	13.3863	−	8.60283i	1.45194	−	0.933108i
$86$	0.766825	−	2.61157i	0.0826889	−	0.281613i
$87$	0.0770553	+	0.0667688i	0.00826120	+	0.00715837i
$88$	−3.48957	−	11.8844i	−0.371989	−	1.26688i
$89$	−5.83329	+	12.7731i	−0.618327	+	1.35395i	0.298402	+	0.954440i	$0.403546\pi$
$89$	−5.83329	+	12.7731i	−0.618327	+	1.35395i	−0.916730	+	0.399508i	$0.869181\pi$
$90$	−0.469832	−	3.26776i	−0.0495247	−	0.344452i
$91$	2.45849	−	0.253195i	0.257720	−	0.0265420i
$92$	−3.76793	+	3.28320i	−0.392834	+	0.342298i
$93$	2.77801			0.288066
$94$	4.23159	−	0.608410i	0.436455	−	0.0627527i
$95$	−1.36573	+	2.99053i	−0.140121	+	0.306821i
$96$	−1.44882	−	4.93423i	−0.147869	−	0.503597i
$97$	−1.18608	+	1.36881i	−0.120428	+	0.138982i	−0.812762	−	0.582596i	$-0.802037\pi$
$97$	−1.18608	+	1.36881i	−0.120428	+	0.138982i	0.692334	+	0.721577i	$0.256583\pi$
$98$	−6.82901	−	0.549876i	−0.689834	−	0.0555459i
$99$	−2.24910	−	3.49967i	−0.226043	−	0.351730i
$100$	−2.76095	−	6.04563i	−0.276095	−	0.604563i
$101$	13.9683	−	12.1036i	1.38990	−	1.20435i	0.437608	−	0.899166i	$-0.355826\pi$
$101$	13.9683	−	12.1036i	1.38990	−	1.20435i	0.952292	−	0.305189i	$-0.0987195\pi$
$102$	−2.49618	+	3.88413i	−0.247158	+	0.384586i
$103$	−1.51591	+	10.5434i	−0.149367	+	1.03887i	0.767892	+	0.640579i	$0.221306\pi$
$103$	−1.51591	+	10.5434i	−0.149367	+	1.03887i	−0.917259	+	0.398291i	$0.869603\pi$
$104$	−2.75298	−	0.395818i	−0.269952	−	0.0388132i
$105$	−7.96246	−	4.03037i	−0.777057	−	0.393324i
$106$	−10.5070	+	9.10436i	−1.02053	+	0.884294i
$107$	9.26064	−	4.22919i	0.895260	−	0.408852i	0.0859952	−	0.996296i	$-0.472593\pi$
$107$	9.26064	−	4.22919i	0.895260	−	0.408852i	0.809265	+	0.587444i	$0.199866\pi$
$108$	−0.563394	−	0.876659i	−0.0542127	−	0.0843565i
$109$	−0.925955	+	3.15351i	−0.0886904	+	0.302052i	−0.991878	−	0.127195i	$-0.959403\pi$
$109$	−0.925955	+	3.15351i	−0.0886904	+	0.302052i	0.903187	+	0.429247i	$0.141221\pi$
$110$	10.3794	+	8.99377i	0.989633	+	0.857522i
$111$	5.66104	−	1.66223i	0.537323	−	0.157772i
$112$	2.08018	+	0.702703i	0.196559	+	0.0663992i
$113$	−11.1131	+	1.59783i	−1.04544	+	0.150311i	−0.643570	−	0.765387i	$-0.722547\pi$
$113$	−11.1131	+	1.59783i	−1.04544	+	0.150311i	−0.401866	+	0.915698i	$0.631638\pi$
$114$		−	0.953928i		−	0.0893435i
$115$	4.51462	−	15.5341i	0.420991	−	1.44856i
$116$	−0.106250			−0.00986506
$117$	−0.924630	+	0.132942i	−0.0854821	+	0.0122905i
$118$	11.9210	+	5.44412i	1.09741	+	0.501172i
$119$	4.72467	+	11.5523i	0.433110	+	1.05899i
$120$	7.59001	+	6.57678i	0.692870	+	0.600375i
$121$	6.05069	+	1.77664i	0.550063	+	0.161513i
$122$	−7.52906	+	4.83863i	−0.681649	+	0.438069i
$123$	2.95952	+	6.48046i	0.266851	+	0.584323i
$124$	−2.18784	+	1.89577i	−0.196474	+	0.170245i
$125$	3.90975	+	2.51265i	0.349699	+	0.224738i
$126$	2.58739	+	0.104001i	0.230503	+	0.00926513i
$127$	−1.57055	+	10.9234i	−0.139364	+	0.969295i	0.793373	+	0.608736i	$0.208323\pi$
$127$	−1.57055	+	10.9234i	−0.139364	+	0.969295i	−0.932736	+	0.360559i	$0.882586\pi$
$128$	3.14166	+	2.01902i	0.277686	+	0.178458i
$129$	1.82115	+	2.10172i	0.160343	+	0.185046i
$130$	2.80524	−	1.28111i	0.246036	−	0.112361i
$131$	8.69484	+	13.5294i	0.759672	+	1.18207i	0.978487	+	0.206306i	$0.0661443\pi$
$131$	8.69484	+	13.5294i	0.759672	+	1.18207i	−0.218816	+	0.975766i	$0.570219\pi$
$132$	4.15954	+	1.22135i	0.362042	+	0.106305i
$133$	−2.11160	−	1.48015i	−0.183099	−	0.128346i
$134$	−1.30927	−	4.45897i	−0.113104	−	0.385196i
$135$	3.06828	+	1.40124i	0.264076	+	0.120599i
$136$	−1.99889	−	13.9026i	−0.171403	−	1.19213i
$137$		−	12.2042i		−	1.04267i	−0.853351	−	0.521337i	$-0.825433\pi$
$137$		−	12.2042i		−	1.04267i	0.853351	−	0.521337i	$-0.174567\pi$
$138$	0.680839	+	4.64419i	0.0579569	+	0.395339i
$139$			14.6781i			1.24498i	0.782627	+	0.622491i	$0.213879\pi$
$139$			14.6781i			1.24498i	−0.782627	+	0.622491i	$0.786121\pi$
$140$	9.02130	−	2.25961i	0.762439	−	0.190972i
$141$	−1.81454	+	3.97328i	−0.152811	+	0.334610i
$142$	−1.92815	+	0.566156i	−0.161807	+	0.0475108i
$143$	2.54484	−	2.93690i	0.212810	−	0.245596i
$144$	−0.796267	−	0.233805i	−0.0663556	−	0.0194838i
$145$	0.289322	−	0.185936i	0.0240269	−	0.0154411i
$146$	−6.13204	+	2.80041i	−0.507491	+	0.231763i
$147$	4.24491	−	5.56603i	0.350115	−	0.459078i
$148$	−3.32405	+	5.17232i	−0.273235	+	0.425162i
$149$	−5.19157	−	0.746435i	−0.425310	−	0.0611504i	−0.0736634	−	0.997283i	$-0.523469\pi$
$149$	−5.19157	−	0.746435i	−0.425310	−	0.0611504i	−0.351647	+	0.936133i	$0.614378\pi$
$150$	−6.17863	−	0.888353i	−0.504483	−	0.0725337i
$151$	6.67383	+	4.28901i	0.543108	+	0.349035i	0.783254	−	0.621702i	$-0.213559\pi$
$151$	6.67383	+	4.28901i	0.543108	+	0.349035i	−0.240145	+	0.970737i	$0.577195\pi$
$152$	1.90036	+	2.19313i	0.154140	+	0.177887i
$153$	−1.95968	−	4.29110i	−0.158431	−	0.346915i
$154$	−8.41799	+	6.72175i	−0.678341	+	0.541654i
$155$	2.63998	−	8.99093i	0.212048	−	0.722169i
$156$	0.637476	−	0.735686i	0.0510389	−	0.0589020i
$157$	−14.5491	+	4.27201i	−1.16115	+	0.340944i	−0.804878	−	0.593440i	$-0.797770\pi$
$157$	−14.5491	+	4.27201i	−1.16115	+	0.340944i	−0.356269	+	0.934383i	$0.615951\pi$
$158$	9.32008	+	4.25634i	0.741465	+	0.338616i
$159$	−2.02157	−	14.0603i	−0.160321	−	1.11505i
$160$	−17.3463			−1.37135
$161$	11.3367	+	5.69902i	0.893459	+	0.449146i
$162$	−0.978731			−0.0768963
$163$	−2.92725	−	20.3595i	−0.229280	−	1.59468i	−0.701152	−	0.713012i	$-0.747331\pi$
$163$	−2.92725	−	20.3595i	−0.229280	−	1.59468i	0.471872	−	0.881667i	$-0.343579\pi$
$164$	−6.75319	−	3.08408i	−0.527336	−	0.240826i
$165$	−13.4639	+	3.95336i	−1.04816	+	0.307769i
$166$	−2.43461	+	2.80969i	−0.188963	+	0.218075i
$167$	−5.79269	+	19.7281i	−0.448252	+	1.52660i	0.357249	+	0.934009i	$0.383715\pi$
$167$	−5.79269	+	19.7281i	−0.448252	+	1.52660i	−0.805500	+	0.592595i	$0.798103\pi$
$168$	−6.15573	+	4.91534i	−0.474925	+	0.379227i
$169$	5.03790	+	11.0315i	0.387531	+	0.848574i
$170$	10.1987	+	11.7699i	0.782205	+	0.902712i
$171$	0.819935	+	0.526940i	0.0627020	+	0.0402961i
$172$	−2.86851	−	0.412430i	−0.218722	−	0.0314475i
$173$	−18.8416	−	2.70901i	−1.43250	−	0.205962i	−0.618023	−	0.786160i	$-0.712066\pi$
$173$	−18.8416	−	2.70901i	−1.43250	−	0.205962i	−0.814476	+	0.580198i	$0.802975\pi$
$174$	−0.0539507	+	0.0839489i	−0.00408999	+	0.00636415i
$175$	−11.5535	+	12.2985i	−0.873360	+	0.929681i
$176$	3.14038	−	1.43417i	0.236715	−	0.108104i
$177$	−11.2644	+	7.23921i	−0.846687	+	0.544132i
$178$	−13.1867	−	3.87197i	−0.988385	−	0.290216i
$179$	−1.33703	+	1.54301i	−0.0999342	+	0.115330i	−0.803514	−	0.595287i	$-0.797039\pi$
$179$	−1.33703	+	1.54301i	−0.0999342	+	0.115330i	0.703579	+	0.710617i	$0.251584\pi$
$180$	−3.37268	+	0.990308i	−0.251385	+	0.0738132i
$181$	10.7992	−	23.6469i	0.802698	−	1.75766i	0.166647	−	0.986017i	$-0.446706\pi$
$181$	10.7992	−	23.6469i	0.802698	−	1.75766i	0.636051	−	0.771647i	$-0.280567\pi$
$182$	0.587726	+	2.34644i	0.0435651	+	0.173930i
$183$		−	9.14430i		−	0.675966i
$184$	−10.8172	−	9.32091i	−0.797452	−	0.687147i
$185$		−	19.9014i		−	1.46318i
$186$	0.386943	+	2.69125i	0.0283720	+	0.197332i
$187$	17.8513	+	8.15240i	1.30541	+	0.596162i
$188$	−1.28240	−	4.36746i	−0.0935287	−	0.318530i
$189$	−1.51864	+	2.16650i	−0.110465	+	0.157590i
$190$	−3.08736	−	0.906530i	−0.223980	−	0.0657666i
$191$	−3.86929	−	6.02074i	−0.279972	−	0.435645i	0.672578	−	0.740026i	$-0.265187\pi$
$191$	−3.86929	−	6.02074i	−0.279972	−	0.435645i	−0.952550	+	0.304381i	$0.901551\pi$
$192$	6.08810	−	2.78034i	0.439370	−	0.200654i
$193$	−13.4492	−	15.5212i	−0.968094	−	1.11724i	−0.993067	−	0.117552i	$-0.962495\pi$
$193$	−13.4492	−	15.5212i	−0.968094	−	1.11724i	0.0249727	−	0.999688i	$-0.492050\pi$
$194$	−1.49127	−	0.958380i	−0.107067	−	0.0688077i
$195$	−0.448426	+	3.11887i	−0.0321125	+	0.223347i
$196$	0.455269	+	7.28038i	0.0325192	+	0.520027i
$197$	−11.0667	−	7.11217i	−0.788473	−	0.506721i	0.0833627	−	0.996519i	$-0.473434\pi$
$197$	−11.0667	−	7.11217i	−0.788473	−	0.506721i	−0.871836	+	0.489798i	$0.837070\pi$
$198$	3.07710	−	2.66632i	0.218680	−	0.189487i
$199$	−6.52852	−	14.2955i	−0.462794	−	1.01338i	−0.986842	−	0.161689i	$-0.948306\pi$
$199$	−6.52852	−	14.2955i	−0.462794	−	1.01338i	0.524048	−	0.851689i	$-0.324421\pi$
$200$	15.9747	−	10.2663i	1.12959	−	0.725940i
$201$	4.55587	+	1.33772i	0.321346	+	0.0943557i
$202$	13.6712	+	11.8462i	0.961904	+	0.833494i
$203$	0.102116	+	0.249683i	0.00716712	+	0.0175243i
$204$	4.47170	+	2.04216i	0.313082	+	0.142980i
$205$	23.7863	−	3.41995i	1.66130	−	0.238860i
$206$	−10.4252			−0.726361
$207$	−4.36793	−	1.98020i	−0.303592	−	0.137633i
$208$		−	0.775225i		−	0.0537522i
$209$	−4.01337	+	0.577035i	−0.277611	+	0.0399144i
$210$	2.79542	−	8.27517i	0.192903	−	0.571041i
$211$	−4.21913	+	1.23885i	−0.290457	+	0.0852859i	−0.423715	−	0.905795i	$-0.639274\pi$
$211$	−4.21913	+	1.23885i	−0.290457	+	0.0852859i	0.133258	+	0.991081i	$0.457456\pi$
$212$	11.1871	+	9.69371i	0.768336	+	0.665767i
$213$	0.578460	−	1.97005i	0.0396354	−	0.134986i
$214$	5.38700	+	8.38234i	0.368248	+	0.573005i
$215$	8.53280	−	3.89680i	0.581932	−	0.265759i
$216$	2.25016	−	1.94977i	0.153104	−	0.132665i
$217$	6.55770	+	3.31932i	0.445166	+	0.225330i
$218$	−3.18400	−	0.457790i	−0.215648	−	0.0310055i
$219$	0.980226	−	6.81762i	0.0662375	−	0.460692i
$220$	7.90573	−	12.3016i	0.533004	−	0.829371i
$221$	3.33037	−	2.88578i	0.224025	−	0.194119i
$222$	2.39883	+	5.25271i	0.160999	+	0.352539i
$223$	−12.3023	−	19.1428i	−0.823826	−	1.28190i	−0.956791	−	0.290777i	$-0.906086\pi$
$223$	−12.3023	−	19.1428i	−0.823826	−	1.28190i	0.132965	−	0.991121i	$-0.457550\pi$
$224$	2.47564	−	13.3787i	0.165411	−	0.893905i
$225$	4.17658	−	4.82004i	0.278439	−	0.321336i
$226$	−3.09585	−	10.5435i	−0.205933	−	0.701343i
$227$	−2.57281	+	5.63366i	−0.170763	+	0.373919i	−0.975593	−	0.219586i	$-0.929529\pi$
$227$	−2.57281	+	5.63366i	−0.170763	+	0.373919i	0.804830	+	0.593506i	$0.202256\pi$
$228$	−1.00534	+	0.144546i	−0.0665803	+	0.00957279i
$229$	4.45022			0.294079			0.147039	−	0.989131i	$-0.453026\pi$
$229$	4.45022			0.294079			0.147039	+	0.989131i	$0.453026\pi$
$230$	15.6778	+	2.20992i	1.03376	+	0.145717i
$231$	−1.12757	−	10.9486i	−0.0741887	−	0.720364i
$232$	−0.0432026	−	0.300481i	−0.00283639	−	0.0197275i
$233$	−0.402658	+	0.881699i	−0.0263790	+	0.0577620i	−0.922363	−	0.386325i	$-0.873744\pi$
$233$	−0.402658	+	0.881699i	−0.0263790	+	0.0577620i	0.895984	+	0.444087i	$0.146472\pi$
$234$	−0.257579	−	0.877235i	−0.0168385	−	0.0573466i
$235$	11.1350	+	9.64854i	0.726368	+	0.629402i
$236$	3.93118	−	13.3884i	0.255898	−	0.871509i
$237$	−8.80679	+	5.65978i	−0.572062	+	0.367642i
$238$	−10.5334	+	6.18620i	−0.682778	+	0.400992i
$239$	−9.10776	−	10.5109i	−0.589132	−	0.679894i	0.380411	−	0.924818i	$-0.375783\pi$
$239$	−9.10776	−	10.5109i	−0.589132	−	0.679894i	−0.969542	+	0.244923i	$0.921237\pi$
$240$	−1.51341	+	2.35491i	−0.0976899	+	0.152008i
$241$	−0.325778	+	2.26584i	−0.0209852	+	0.145955i	−0.997620	−	0.0689499i	$-0.978035\pi$
$241$	−0.325778	+	2.26584i	−0.0209852	+	0.145955i	0.976635	+	0.214905i	$0.0689442\pi$
$242$	−0.878368	+	6.10918i	−0.0564636	+	0.392713i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	6.24027	+	7.20165i	0.399492	+	0.461038i
$245$	−13.9803	−	19.0280i	−0.893168	−	1.21565i
$246$	−5.86584	+	3.76974i	−0.373992	+	0.240350i
$247$	−0.256508	+	0.873585i	−0.0163212	+	0.0555849i
$248$	−6.25095	−	5.41648i	−0.396936	−	0.343947i
$249$	−1.07018	−	3.64468i	−0.0678196	−	0.230972i
$250$	−1.88959	+	4.13763i	−0.119508	+	0.261687i
$251$	−3.45453	−	24.0268i	−0.218048	−	1.51656i	−0.745231	−	0.666807i	$-0.767661\pi$
$251$	−3.45453	−	24.0268i	−0.218048	−	1.51656i	0.527182	−	0.849752i	$-0.323248\pi$
$252$	−0.282454	−	2.74260i	−0.0177929	−	0.172767i
$253$	19.1272	−	5.67372i	1.20252	−	0.356704i
$254$	−10.8010			−0.677715
$255$	−15.7503	+	2.26455i	−0.986324	+	0.141812i
$256$	−7.07905	+	15.5010i	−0.442441	+	0.968810i
$257$	1.90930	+	6.50248i	0.119099	+	0.405613i	0.997364	−	0.0725606i	$-0.0231171\pi$
$257$	1.90930	+	6.50248i	0.119099	+	0.405613i	−0.878265	+	0.478174i	$0.841299\pi$
$258$	−1.78241	+	2.05701i	−0.110968	+	0.128064i
$259$	15.3495	+	2.84031i	0.953769	+	0.176488i
$260$	−1.77522	−	2.76230i	−0.110095	−	0.171311i
$261$	−0.0423552	−	0.0927450i	−0.00262172	−	0.00574077i
$262$	−11.8958	+	10.3078i	−0.734925	+	0.636816i
$263$	0.131342	−	0.204373i	0.00809893	−	0.0126022i	−0.837180	−	0.546927i	$-0.815798\pi$
$263$	0.131342	−	0.204373i	0.00809893	−	0.0126022i	0.845279	+	0.534325i	$0.179434\pi$
$264$	−1.76273	+	12.2600i	−0.108488	+	0.754553i
$265$	−47.4268	−	6.81895i	−2.91341	−	0.418885i
$266$	1.13981	−	2.25182i	0.0698860	−	0.138068i
$267$	10.6123	−	9.19560i	0.649462	−	0.562762i
$268$	−4.50089	+	2.05549i	−0.274936	+	0.125559i
$269$	1.67623	+	2.60826i	0.102202	+	0.159029i	0.888588	−	0.458706i	$-0.151687\pi$
$269$	1.67623	+	2.60826i	0.102202	+	0.159029i	−0.786387	+	0.617735i	$0.788051\pi$
$270$	−0.930100	+	3.16763i	−0.0566041	+	0.192776i
$271$	−5.17189	−	4.48146i	−0.314170	−	0.272230i	0.483474	−	0.875359i	$-0.339375\pi$
$271$	−5.17189	−	4.48146i	−0.314170	−	0.272230i	−0.797643	+	0.603129i	$0.793920\pi$
$272$	3.75631	−	1.10295i	0.227760	−	0.0668764i
$273$	−2.34150	−	0.790981i	−0.141714	−	0.0478723i
$274$	11.8230	−	1.69990i	0.714256	−	0.102695i
$275$			26.5321i			1.59995i
$276$	4.79132	−	1.42125i	0.288404	−	0.0855494i
$277$	29.5230			1.77387			0.886933	−	0.461898i	$-0.152831\pi$
$277$	29.5230			1.77387			0.886933	+	0.461898i	$0.152831\pi$
$278$	−14.2197	+	2.04448i	−0.852841	+	0.122620i
$279$	−2.52696	−	1.15403i	−0.151285	−	0.0690897i
$280$	10.0585	+	24.5940i	0.601109	+	1.46977i
$281$	−24.3473	−	21.0971i	−1.45244	−	1.25855i	−0.907486	−	0.420082i	$-0.862001\pi$
$281$	−24.3473	−	21.0971i	−1.45244	−	1.25855i	−0.544954	−	0.838466i	$-0.683453\pi$
$282$	−4.10193	−	1.20444i	−0.244266	−	0.0717231i
$283$	10.6306	−	6.83189i	0.631925	−	0.406113i	−0.185097	−	0.982720i	$-0.559260\pi$
$283$	10.6306	−	6.83189i	0.631925	−	0.406113i	0.817022	+	0.576607i	$0.195624\pi$
$284$	0.888837	+	1.94628i	0.0527428	+	0.115491i
$285$	2.48462	−	2.15293i	0.147176	−	0.127529i
$286$	3.19964	+	2.05628i	0.189199	+	0.121591i
$287$	−0.757030	+	18.8338i	−0.0446861	+	1.11172i
$288$	−0.731859	+	5.09019i	−0.0431252	+	0.299942i
$289$	4.41987	+	2.84048i	0.259992	+	0.167087i
$290$	0.220428	+	0.254387i	0.0129440	+	0.0149381i
$291$	1.64752	−	0.752399i	0.0965795	−	0.0441064i
$292$	3.88051	+	6.03819i	0.227089	+	0.353358i
$293$	−10.8018	−	3.17170i	−0.631050	−	0.185293i	−0.0494612	−	0.998776i	$-0.515750\pi$
$293$	−10.8018	−	3.17170i	−0.631050	−	0.185293i	−0.581589	+	0.813483i	$0.697569\pi$
$294$	5.98346	+	3.33706i	0.348963	+	0.194621i
$295$	12.7247	+	43.3365i	0.740863	+	2.52315i
$296$	−15.9792	−	7.29746i	−0.928773	−	0.424156i
$297$	0.592039	+	4.11772i	0.0343536	+	0.238934i
$298$		−	5.13340i		−	0.297370i
$299$	0.625308	−	4.43611i	0.0361625	−	0.256547i
$300$			6.64624i			0.383721i
$301$	1.78771	+	7.13727i	0.103042	+	0.411385i
$302$	−3.22547	+	7.06280i	−0.185605	+	0.406419i
$303$	−17.7341	+	5.20719i	−1.01879	+	0.299145i
$304$	−0.529686	+	0.611290i	−0.0303796	+	0.0350599i
$305$	−29.5952	−	8.68995i	−1.69462	−	0.497585i
$306$	3.88413	−	2.49618i	0.222041	−	0.142697i
$307$	−29.2438	+	13.3552i	−1.66903	+	0.762222i	−0.669216	+	0.743068i	$0.733370\pi$
$307$	−29.2438	+	13.3552i	−1.66903	+	0.762222i	−0.999817	+	0.0191540i	$0.993903\pi$
$308$	8.35957	+	7.85315i	0.476331	+	0.447475i
$309$	5.75880	−	8.96086i	0.327607	−	0.509766i
$310$	9.07785	+	1.30520i	0.515587	+	0.0741303i
$311$	7.85400	+	1.12924i	0.445360	+	0.0640331i	0.361347	−	0.932432i	$-0.382317\pi$
$311$	7.85400	+	1.12924i	0.445360	+	0.0640331i	0.0840131	+	0.996465i	$0.473226\pi$
$312$	2.33977	+	1.50368i	0.132463	+	0.0851289i
$313$	13.5484	+	15.6356i	0.765799	+	0.883779i	0.995999	−	0.0893642i	$-0.0284835\pi$
$313$	13.5484	+	15.6356i	0.765799	+	0.883779i	−0.230200	+	0.973143i	$0.573938\pi$
$314$	−6.16511	−	13.4997i	−0.347917	−	0.761833i
$315$	5.56864	+	6.97388i	0.313757	+	0.392934i
$316$	3.07349	−	10.4673i	0.172897	−	0.588834i
$317$	−8.11438	+	9.36449i	−0.455749	+	0.525962i	−0.936393	−	0.350954i	$-0.885857\pi$
$317$	−8.11438	+	9.36449i	−0.455749	+	0.525962i	0.480644	+	0.876916i	$0.340403\pi$
$318$	13.3396	−	3.91686i	0.748047	−	0.219646i
$319$	0.385825	+	0.176200i	0.0216021	+	0.00986533i
$320$	−3.21289	−	22.3461i	−0.179606	−	1.24919i
$321$	−10.1806			−0.568228
$322$	−3.94196	+	11.7765i	−0.219677	+	0.656276i
$323$	−4.59786			−0.255832
$324$	0.148304	+	1.03148i	0.00823913	+	0.0573044i
$325$	5.41937	+	2.47495i	0.300613	+	0.137285i
$326$	19.3159	−	5.67166i	1.06981	−	0.314124i
$327$	2.15230	−	2.48388i	0.119022	−	0.137359i
$328$	5.97601	−	20.3524i	0.329970	−	1.12378i
$329$	−9.03085	+	7.21112i	−0.497887	+	0.397562i
$330$	−5.70525	−	12.4928i	−0.314064	−	0.687704i
$331$	1.43384	+	1.65474i	0.0788108	+	0.0909525i	0.793786	−	0.608198i	$-0.208107\pi$
$331$	1.43384	+	1.65474i	0.0788108	+	0.0909525i	−0.714975	+	0.699150i	$0.753562\pi$
$332$	3.33003	+	2.14008i	0.182759	+	0.117452i
$333$	−5.83998	−	0.839663i	−0.320029	−	0.0460132i
$334$	−19.9188	−	2.86389i	−1.08991	−	0.156705i
$335$	8.65900	−	13.4737i	0.473092	−	0.736145i
$336$	−1.60029	−	1.50334i	−0.0873027	−	0.0820139i
$337$	−2.02445	+	0.924534i	−0.110279	+	0.0503626i	−0.469790	−	0.882778i	$-0.655671\pi$
$337$	−2.02445	+	0.924534i	−0.110279	+	0.0503626i	0.359512	+	0.933141i	$0.382943\pi$
$338$	−9.98521	+	6.41711i	−0.543124	+	0.349045i
$339$	10.7726	+	3.16313i	0.585089	+	0.171798i
$340$	10.8589	−	12.5318i	0.588906	−	0.679634i
$341$	11.0886	−	3.25590i	0.600479	−	0.176317i
$342$	−0.396276	+	0.867723i	−0.0214281	+	0.0469211i
$343$	16.6711	−	8.06697i	0.900152	−	0.435576i
$344$		−	8.28001i		−	0.446428i
$345$	−10.5597	+	12.2549i	−0.568517	+	0.659780i
$346$		−	18.6305i		−	1.00158i
$347$	4.01678	+	27.9373i	0.215632	+	1.49975i	0.753905	+	0.656984i	$0.228168\pi$
$347$	4.01678	+	27.9373i	0.215632	+	1.49975i	−0.538273	+	0.842771i	$0.680923\pi$
$348$	0.0966483	+	0.0441378i	0.00518089	+	0.00236603i
$349$	8.02728	+	27.3384i	0.429690	+	1.46339i	0.835529	+	0.549446i	$0.185161\pi$
$349$	8.02728	+	27.3384i	0.429690	+	1.46339i	−0.405839	+	0.913945i	$0.633020\pi$
$350$	−13.5237	−	9.47960i	−0.722871	−	0.506706i
$351$	0.896299	+	0.263177i	0.0478409	+	0.0140474i
$352$	−11.5661	−	17.9972i	−0.616474	−	0.959252i
$353$	−16.3165	+	7.45152i	−0.868442	+	0.396604i	−0.799250	−	0.600999i	$-0.794769\pi$
$353$	−16.3165	+	7.45152i	−0.868442	+	0.396604i	−0.0691924	+	0.997603i	$0.522042\pi$
$354$	−8.58212	−	9.90429i	−0.456134	−	0.526407i
$355$	−5.82630	−	3.74433i	−0.309228	−	0.198729i
$356$	−2.08250	+	14.4841i	−0.110372	+	0.767656i
$357$	0.501276	−	12.4710i	0.0265303	−	0.660036i
$358$	−1.68106	−	1.08035i	−0.0888465	−	0.0570982i
$359$	−1.42019	+	1.23060i	−0.0749546	+	0.0649485i	−0.691532	−	0.722346i	$-0.743064\pi$
$359$	−1.42019	+	1.23060i	−0.0749546	+	0.0649485i	0.616578	+	0.787294i	$0.288519\pi$
$360$	−4.17202	−	9.13545i	−0.219885	−	0.481481i
$361$	−15.1847	+	9.75859i	−0.799193	+	0.513610i
$362$	24.4126	+	7.16819i	1.28310	+	0.376752i
$363$	−4.76586	−	4.12964i	−0.250143	−	0.216750i
$364$	2.38385	−	0.974951i	0.124948	−	0.0511013i
$365$	−21.1335	−	9.65134i	−1.10618	−	0.505174i
$366$	8.85871	−	1.27369i	0.463052	−	0.0665769i
$367$	5.96399			0.311318			0.155659	−	0.987811i	$-0.450250\pi$
$367$	5.96399			0.311318			0.155659	+	0.987811i	$0.450250\pi$
$368$	2.14248	−	3.35411i	0.111684	−	0.174845i
$369$		−	7.12426i		−	0.370874i
$370$	19.2799	−	2.77203i	1.00231	−	0.144111i
$371$	12.0280	−	35.6059i	0.624461	−	1.84856i
$372$	2.77766	−	0.815594i	0.144015	−	0.0422866i
$373$	16.5931	+	14.3780i	0.859157	+	0.744464i	0.968360	−	0.249556i	$-0.0802846\pi$
$373$	16.5931	+	14.3780i	0.859157	+	0.744464i	−0.109204	+	0.994019i	$0.534830\pi$
$374$	−5.41132	+	18.4293i	−0.279813	+	0.952955i
$375$	−2.51265	−	3.90975i	−0.129752	−	0.201899i
$376$	11.8300	−	5.40257i	0.610084	−	0.278616i
$377$	0.0719803	−	0.0623713i	0.00370717	−	0.00321229i
$378$	−2.31037	−	1.16944i	−0.118833	−	0.0601496i
$379$	−19.5463	−	2.81034i	−1.00403	−	0.144357i	−0.379361	−	0.925249i	$-0.623856\pi$
$379$	−19.5463	−	2.81034i	−1.00403	−	0.144357i	−0.624667	+	0.780891i	$0.714765\pi$
$380$	−0.487569	+	3.39111i	−0.0250117	+	0.173960i
$381$	5.96637	−	9.28385i	0.305666	−	0.475626i
$382$	5.29376	−	4.58707i	0.270852	−	0.234695i
$383$	6.30295	+	13.8015i	0.322066	+	0.705226i	0.999540	−	0.0303204i	$-0.00965277\pi$
$383$	6.30295	+	13.8015i	0.322066	+	0.705226i	−0.677474	+	0.735546i	$0.736925\pi$
$384$	−2.01902	−	3.14166i	−0.103033	−	0.160322i
$385$	−36.5063	−	6.75523i	−1.86053	−	0.344279i
$386$	13.1631	−	15.1911i	0.669986	−	0.773205i
$387$	−0.783490	−	2.66832i	−0.0398270	−	0.135638i
$388$	−0.784065	+	1.71686i	−0.0398048	+	0.0871605i
$389$	5.81051	−	0.835425i	0.294604	−	0.0423577i	0.00657203	−	0.999978i	$-0.497908\pi$
$389$	5.81051	−	0.835425i	0.294604	−	0.0423577i	0.288032	+	0.957621i	$0.406999\pi$
$390$	−3.08392			−0.156161
$391$	22.3846	−	3.28159i	1.13204	−	0.165957i
$392$	−20.4042	+	4.24782i	−1.03057	+	0.214548i
$393$	−2.28877	−	15.9188i	−0.115453	−	0.802996i
$394$	5.34858	−	11.7118i	0.269457	−	0.590030i
$395$	9.94849	+	33.8814i	0.500563	+	1.70476i
$396$	−3.27628	−	2.83892i	−0.164640	−	0.142661i
$397$	−3.90078	+	13.2848i	−0.195775	+	0.666747i	0.801829	+	0.597554i	$0.203861\pi$
$397$	−3.90078	+	13.2848i	−0.195775	+	0.666747i	−0.997603	+	0.0691930i	$0.977958\pi$
$398$	12.9396	−	8.31580i	0.648606	−	0.416834i
$399$	1.30590	+	2.22359i	0.0653768	+	0.111319i
$400$	3.46608	+	4.00007i	0.173304	+	0.200003i
$401$	−7.59502	+	11.8181i	−0.379277	+	0.590167i	−0.977441	−	0.211207i	$-0.932261\pi$
$401$	−7.59502	+	11.8181i	−0.379277	+	0.590167i	0.598164	+	0.801374i	$0.295897\pi$
$402$	−0.661367	+	4.59991i	−0.0329860	+	0.229423i
$403$	0.369313	−	2.56863i	0.0183968	−	0.127953i
$404$	10.4131	−	16.2031i	0.518070	−	0.806132i
$405$	−2.20891	−	2.54922i	−0.109762	−	0.126672i
$406$	−0.227661	+	0.133704i	−0.0112986	+	0.00663564i
$407$	20.6482	−	13.2698i	1.02349	−	0.657758i
$408$	−3.95708	+	13.4766i	−0.195905	+	0.667190i
$409$	8.03770	+	6.96471i	0.397439	+	0.344383i	0.830536	−	0.556964i	$-0.188034\pi$
$409$	8.03770	+	6.96471i	0.397439	+	0.344383i	−0.433098	+	0.901347i	$0.642579\pi$
$410$	6.62628	+	22.5670i	0.327248	+	1.11451i
$411$	−5.06981	+	11.1013i	−0.250075	+	0.547588i
$412$	1.57971	+	10.9871i	0.0778266	+	0.541296i
$413$	−35.2404	+	3.62933i	−1.73406	+	0.178588i
$414$	1.30995	−	4.50733i	0.0643806	−	0.221523i
$415$	−12.8129			−0.628961
$416$	−4.75494	+	0.683657i	−0.233130	+	0.0335191i
$417$	6.09751	−	13.3517i	0.298596	−	0.653835i
$418$	−1.11803	−	3.80765i	−0.0546845	−	0.186238i
$419$	−3.15901	+	3.64569i	−0.154328	+	0.178104i	−0.827648	−	0.561247i	$-0.810322\pi$
$419$	−3.15901	+	3.64569i	−0.154328	+	0.178104i	0.673321	+	0.739350i	$0.264867\pi$
$420$	−9.14474	−	1.69217i	−0.446218	−	0.0825694i
$421$	9.16291	+	14.2578i	0.446573	+	0.694881i	0.989441	−	0.144937i	$-0.0462980\pi$
$421$	9.16291	+	14.2578i	0.446573	+	0.694881i	−0.542868	+	0.839818i	$0.682662\pi$
$422$	−1.78783	−	3.91481i	−0.0870303	−	0.190570i
$423$	3.30112	−	2.86044i	0.160506	−	0.139079i
$424$	−22.8655	+	35.5794i	−1.11045	+	1.72789i
$425$	−4.28179	+	29.7805i	−0.207697	+	1.44457i
$426$	1.98910	+	0.285989i	0.0963721	+	0.0138562i
$427$	10.9261	−	21.5858i	0.528752	−	1.04461i
$428$	8.01783	−	6.94749i	0.387557	−	0.335820i
$429$	−3.53490	+	1.61433i	−0.170666	+	0.0779407i
$430$	4.96361	+	7.72353i	0.239367	+	0.372462i
$431$	−7.36751	+	25.0914i	−0.354881	+	1.20861i	0.567839	+	0.823140i	$0.307780\pi$
$431$	−7.36751	+	25.0914i	−0.354881	+	1.20861i	−0.922719	+	0.385472i	$0.874038\pi$
$432$	0.627184	+	0.543458i	0.0301754	+	0.0261471i
$433$	−19.1422	+	5.62066i	−0.919915	+	0.270112i	−0.707209	−	0.707005i	$-0.750046\pi$
$433$	−19.1422	+	5.62066i	−0.919915	+	0.270112i	−0.212707	+	0.977116i	$0.568228\pi$
$434$	−2.30225	+	6.81523i	−0.110511	+	0.327142i
$435$	−0.340417	+	0.0489446i	−0.0163217	+	0.00234671i
$436$			3.42497i			0.164026i
$437$	−3.52412	+	3.07076i	−0.168582	+	0.146895i
$438$	6.74123			0.322108
$439$	13.6656	−	1.96482i	0.652223	−	0.0937756i	0.191743	−	0.981445i	$-0.438586\pi$
$439$	13.6656	−	1.96482i	0.652223	−	0.0937756i	0.460481	+	0.887670i	$0.347677\pi$
$440$	38.0041	+	17.3559i	1.81177	+	0.827409i
$441$	−6.17352	+	3.29964i	−0.293977	+	0.157126i
$442$	3.25953	+	2.82440i	0.155040	+	0.134343i
$443$	9.24209	+	2.71372i	0.439105	+	0.128933i	0.493810	−	0.869570i	$-0.335604\pi$
$443$	9.24209	+	2.71372i	0.439105	+	0.128933i	−0.0547053	+	0.998503i	$0.517422\pi$
$444$	5.17232	−	3.32405i	0.245467	−	0.157752i
$445$	−19.6763	−	43.0850i	−0.932745	−	2.04243i
$446$	16.8314	−	14.5845i	0.796990	−	0.690595i
$447$	4.41234	+	2.83564i	0.208696	+	0.134121i
$448$	17.6935	+	0.711196i	0.835940	+	0.0336008i
$449$	0.948365	−	6.59603i	0.0447561	−	0.311286i	−0.955130	−	0.296187i	$-0.904285\pi$
$449$	0.948365	−	6.59603i	0.0447561	−	0.311286i	0.999886	−	0.0150984i	$-0.00480616\pi$
$450$	5.25125	+	3.37477i	0.247546	+	0.159088i
$451$	19.4084	+	22.3984i	0.913904	+	1.05470i
$452$	−10.6426	+	4.86033i	−0.500588	+	0.228611i
$453$	−4.28901	−	6.67383i	−0.201515	−	0.313564i
$454$	−5.81607	−	1.70775i	−0.272962	−	0.0801488i
$455$	−4.78515	+	6.82653i	−0.224331	+	0.320033i
$456$	−0.817568	−	2.78438i	−0.0382861	−	0.130391i
$457$	2.51421	+	1.14820i	0.117610	+	0.0537106i	0.473351	−	0.880874i	$-0.343044\pi$
$457$	2.51421	+	1.14820i	0.117610	+	0.0537106i	−0.355741	+	0.934585i	$0.615772\pi$
$458$	0.619861	+	4.31123i	0.0289642	+	0.201451i
$459$			4.71740i			0.220190i
$460$	−0.0465910	−	16.8576i	−0.00217232	−	0.785989i
$461$		−	5.53739i		−	0.257902i	−0.991651	−	0.128951i	$-0.958839\pi$
$461$		−	5.53739i		−	0.257902i	0.991651	−	0.128951i	$-0.0411610\pi$
$462$	10.4496	−	2.61736i	0.486159	−	0.121771i
$463$	3.54806	−	7.76916i	0.164892	−	0.361064i	−0.809091	−	0.587683i	$-0.800040\pi$
$463$	3.54806	−	7.76916i	0.164892	−	0.361064i	0.973983	+	0.226620i	$0.0727674\pi$
$464$	0.0811865	−	0.0238385i	0.00376899	−	0.00110667i
$465$	−6.13638	+	7.08176i	−0.284568	+	0.328409i
$466$	−0.910248	−	0.267273i	−0.0421664	−	0.0123812i
$467$	2.16487	−	1.39128i	0.100178	−	0.0643806i	−0.489593	−	0.871951i	$-0.662854\pi$
$467$	2.16487	−	1.39128i	0.100178	−	0.0643806i	0.589771	+	0.807571i	$0.299218\pi$
$468$	−0.885483	+	0.404387i	−0.0409315	+	0.0186928i
$469$	9.15608	+	8.60141i	0.422789	+	0.397176i
$470$	−7.79623	+	12.1312i	−0.359613	+	0.559569i
$471$	15.0090	+	2.15797i	0.691579	+	0.0994341i
$472$	39.4615	+	5.67371i	1.81636	+	0.261154i
$473$	9.73247	+	6.25468i	0.447500	+	0.287590i
$474$	−6.70969	−	7.74340i	−0.308186	−	0.355666i
$475$	−2.58230	−	5.65445i	−0.118484	−	0.259444i
$476$	8.11570	+	10.1637i	0.371983	+	0.465853i
$477$	−4.00198	+	13.6295i	−0.183238	+	0.624051i
$478$	8.91404	−	10.2874i	0.407719	−	0.470532i
$479$	27.5418	−	8.08699i	1.25842	−	0.369504i	0.416511	−	0.909131i	$-0.363253\pi$
$479$	27.5418	−	8.08699i	1.25842	−	0.369504i	0.841905	+	0.539626i	$0.181434\pi$
$480$	15.7787	+	7.20591i	0.720198	+	0.328903i
$481$	−0.784361	−	5.45535i	−0.0357638	−	0.248743i
$482$	−2.24045			−0.102050
$483$	−7.94478	−	9.89345i	−0.361500	−	0.450168i
$484$	6.57154			0.298706
$485$	−0.869452	−	6.04717i	−0.0394798	−	0.274588i
$486$	0.890285	+	0.406579i	0.0403841	+	0.0184428i
$487$	11.6624	−	3.42440i	0.528475	−	0.155174i	−0.00660114	−	0.999978i	$-0.502101\pi$
$487$	11.6624	−	3.42440i	0.528475	−	0.155174i	0.535076	+	0.844804i	$0.320283\pi$
$488$	−17.8293	+	20.5761i	−0.807094	+	0.931436i
$489$	−5.79492	+	19.7357i	−0.262055	+	0.892478i
$490$	16.4864	−	16.1940i	0.744782	−	0.731572i
$491$	11.4794	+	25.1363i	0.518056	+	1.13438i	0.970170	+	0.242424i	$0.0779426\pi$
$491$	11.4794	+	25.1363i	0.518056	+	1.13438i	−0.452114	+	0.891960i	$0.649330\pi$
$492$	4.86175	+	5.61076i	0.219185	+	0.252952i
$493$	0.404627	+	0.260038i	0.0182235	+	0.0117115i
$494$	−0.882030	−	0.126817i	−0.0396844	−	0.00570576i
$495$	13.8895	+	1.99701i	0.624286	+	0.0897588i
$496$	1.24641	−	1.93944i	0.0559653	−	0.0870836i
$497$	3.71943	−	3.95928i	0.166839	−	0.177598i
$498$	3.38179	−	1.54441i	0.151542	−	0.0692068i
$499$	−3.56332	+	2.29001i	−0.159516	+	0.102515i	−0.617964	−	0.786207i	$-0.712042\pi$
$499$	−3.56332	+	2.29001i	−0.159516	+	0.102515i	0.458447	+	0.888722i	$0.348406\pi$
$500$	4.64695	+	1.36447i	0.207818	+	0.0610209i
$501$	13.4646	−	15.5389i	0.601552	−	0.694228i
$502$	22.7952	−	6.69329i	1.01740	−	0.298736i
$503$	7.72261	−	16.9102i	0.344334	−	0.753986i	−0.655665	−	0.755052i	$-0.727612\pi$
$503$	7.72261	−	16.9102i	0.344334	−	0.753986i	0.999999	+	0.00106518i	$0.000339059\pi$
$504$	7.64136	−	1.91397i	0.340373	−	0.0852550i
$505$			62.3442i			2.77428i
$506$	8.16071	+	17.7396i	0.362788	+	0.788619i
$507$		−	12.1274i		−	0.538596i
$508$	1.63665	+	11.3831i	0.0726145	+	0.505045i
$509$	13.1070	+	5.98578i	0.580959	+	0.265315i	0.684144	−	0.729347i	$-0.260176\pi$
$509$	13.1070	+	5.98578i	0.580959	+	0.265315i	−0.103185	+	0.994662i	$0.532903\pi$
$510$	−4.38766	−	14.9430i	−0.194289	−	0.661687i
$511$	10.4600	−	14.9223i	0.462722	−	0.660123i
$512$	−8.83642	−	2.59461i	−0.390518	−	0.114666i
$513$	−0.526940	−	0.819935i	−0.0232650	−	0.0362010i
$514$	−6.03345	+	2.75539i	−0.266124	+	0.121535i
$515$	−23.5289	−	27.1538i	−1.03681	−	1.19654i
$516$	2.43796	+	1.56678i	0.107325	+	0.0689738i
$517$	−2.58603	+	17.9862i	−0.113733	+	0.791033i
$518$	−0.613609	+	15.2657i	−0.0269604	+	0.670736i
$519$	16.0135	+	10.2913i	0.702916	+	0.451737i
$520$	7.09011	−	6.14362i	0.310922	−	0.269415i
$521$	−8.16253	−	17.8734i	−0.357607	−	0.783050i	−0.999863	−	0.0165595i	$-0.994729\pi$
$521$	−8.16253	−	17.8734i	−0.357607	−	0.783050i	0.642256	−	0.766490i	$-0.277999\pi$
$522$	0.0839489	−	0.0539507i	0.00367434	−	0.00236136i
$523$	−25.5672	−	7.50719i	−1.11797	−	0.328267i	−0.330003	−	0.943980i	$-0.607050\pi$
$523$	−25.5672	−	7.50719i	−1.11797	−	0.328267i	−0.787970	+	0.615713i	$0.788868\pi$
$524$	12.6659	+	10.9750i	0.553310	+	0.479446i
$525$	15.6184	−	6.38764i	0.681643	−	0.278780i
$526$	0.216284	+	0.0987738i	0.00943045	+	0.00430674i
$527$	12.9716	−	1.86503i	0.565052	−	0.0812422i
$528$	−3.45237			−0.150245
$529$	14.9655	−	17.4652i	0.650673	−	0.759358i
$530$		−	46.8954i		−	2.03701i
$531$	13.2538	−	1.90560i	0.575164	−	0.0826962i
$532$	−2.54589	−	0.860025i	−0.110378	−	0.0372868i
$533$	6.38547	−	1.87494i	0.276585	−	0.0812128i
$534$	10.3866	+	9.00002i	0.449471	+	0.389469i
$535$	−9.67480	+	32.9493i	−0.418278	+	1.42452i
$536$	−7.64316	−	11.8930i	−0.330134	−	0.513699i
$537$	1.85720	−	0.848153i	0.0801439	−	0.0366005i
$538$	−2.29333	+	1.98718i	−0.0988723	+	0.0856733i
$539$	10.4203	−	27.1923i	0.448833	−	1.17125i
$540$	3.47929	+	0.500246i	0.149725	+	0.0215272i
$541$	3.86962	−	26.9138i	0.166368	−	1.15711i	−0.719947	−	0.694029i	$-0.755834\pi$
$541$	3.86962	−	26.9138i	0.166368	−	1.15711i	0.886314	−	0.463084i	$-0.153257\pi$
$542$	3.62112	−	5.63457i	0.155540	−	0.242026i
$543$	−19.6466	+	17.0239i	−0.843116	+	0.730564i
$544$	−10.0777	−	22.0671i	−0.432079	−	0.946121i
$545$	−5.99365	−	9.32630i	−0.256740	−	0.399495i
$546$	0.440134	−	2.37855i	0.0188360	−	0.101793i
$547$	−7.51994	+	8.67847i	−0.321529	+	0.371065i	−0.893387	−	0.449288i	$-0.851678\pi$
$547$	−7.51994	+	8.67847i	−0.321529	+	0.371065i	0.571857	+	0.820353i	$0.306223\pi$
$548$	−3.58303	−	12.2027i	−0.153059	−	0.521272i
$549$	−3.79868	+	8.31795i	−0.162124	+	0.355001i
$550$	−25.7035	+	3.69561i	−1.09600	+	0.157581i
$551$	−0.0993750			−0.00423352
$552$	5.96760	+	12.9722i	0.253998	+	0.552134i
$553$	−27.5517	+	2.83749i	−1.17162	+	0.120662i
$554$	4.11220	+	28.6010i	0.174711	+	1.21514i
$555$	−8.26735	+	18.1030i	−0.350930	+	0.768429i
$556$	4.30934	+	14.6763i	0.182757	+	0.622413i
$557$	−24.4727	−	21.2057i	−1.03694	−	0.898515i	−0.0420144	−	0.999117i	$-0.513378\pi$
$557$	−24.4727	−	21.2057i	−1.03694	−	0.898515i	−0.994927	+	0.100602i	$0.967923\pi$
$558$	0.766009	−	2.60879i	0.0324277	−	0.110439i
$559$	2.18542	−	1.40448i	0.0924333	−	0.0594032i
$560$	−6.38628	+	3.75063i	−0.269870	+	0.158493i
$561$	−12.8514	−	14.8314i	−0.542589	−	0.626181i
$562$	17.0469	−	26.5255i	0.719081	−	1.11891i
$563$	2.91845	−	20.2983i	0.122998	−	0.855469i	−0.831132	−	0.556076i	$-0.812307\pi$
$563$	2.91845	−	20.2983i	0.122998	−	0.855469i	0.954130	−	0.299394i	$-0.0967844\pi$
$564$	−0.647794	+	4.50551i	−0.0272771	+	0.189716i
$565$	20.4747	−	31.8593i	0.861379	−	1.34033i
$566$	8.09923	+	9.34701i	0.340436	+	0.392884i
$567$	2.28140	−	1.33985i	0.0958098	−	0.0562686i
$568$	−5.14278	+	3.30506i	−0.215786	+	0.138677i
$569$	11.3387	−	38.6161i	0.475343	−	1.61887i	−0.277539	−	0.960714i	$-0.589519\pi$
$569$	11.3387	−	38.6161i	0.475343	−	1.61887i	0.752882	−	0.658155i	$-0.228663\pi$
$570$	2.43177	+	2.10714i	0.101856	+	0.0882585i
$571$	0.303351	+	1.03312i	0.0126948	+	0.0432346i	0.965597	−	0.260044i	$-0.0837370\pi$
$571$	0.303351	+	1.03312i	0.0126948	+	0.0432346i	−0.952902	+	0.303278i	$0.901919\pi$
$572$	1.68227	−	3.68367i	0.0703394	−	0.154022i
$573$	1.01853	+	7.08402i	0.0425496	+	0.295939i
$574$	−18.3511	+	1.88994i	−0.765958	+	0.0788844i
$575$	16.6076	+	25.6856i	0.692585	+	1.07116i
$576$	−6.69292			−0.278872
$577$	−16.2815	+	2.34092i	−0.677807	+	0.0974539i	−0.472617	−	0.881268i	$-0.656690\pi$
$577$	−16.2815	+	2.34092i	−0.677807	+	0.0974539i	−0.205190	+	0.978722i	$0.565781\pi$
$578$	−2.13613	+	4.67747i	−0.0888513	+	0.194557i
$579$	5.78608	+	19.7056i	0.240461	+	0.818936i
$580$	0.234697	−	0.270854i	0.00974525	−	0.0112466i
$581$	1.82864	−	9.88226i	0.0758649	−	0.409985i
$582$	0.958380	+	1.49127i	0.0397261	+	0.0618151i
$583$	−24.5482	−	53.7531i	−1.01668	−	2.22622i
$584$	−15.4985	+	13.4295i	−0.641331	+	0.555716i
$585$	1.70353	−	2.65074i	0.0704322	−	0.109595i
$586$	1.56808	−	10.9063i	0.0647769	−	0.450533i
$587$	−26.8061	−	3.85414i	−1.10641	−	0.159077i	−0.435190	−	0.900339i	$-0.643319\pi$
$587$	−26.8061	−	3.85414i	−1.10641	−	0.159077i	−0.671217	+	0.741261i	$0.734228\pi$
$588$	2.61025	−	6.81160i	0.107645	−	0.280905i
$589$	−2.04627	+	1.77311i	−0.0843152	+	0.0730596i
$590$	−40.2106	+	18.3636i	−1.65545	+	0.756017i
$591$	7.11217	+	11.0667i	0.292555	+	0.455225i
$592$	1.37946	−	4.69801i	0.0566954	−	0.193087i
$593$	13.4697	+	11.6716i	0.553136	+	0.479295i	0.886003	−	0.463679i	$-0.153471\pi$
$593$	13.4697	+	11.6716i	0.553136	+	0.479295i	−0.332868	+	0.942974i	$0.608016\pi$
$594$	−3.90665	+	1.14710i	−0.160292	+	0.0470660i
$595$	−39.8857	−	13.4737i	−1.63515	−	0.552369i
$596$	−5.41007	+	0.777850i	−0.221605	+	0.0318620i
$597$			15.7156i			0.643199i
$598$	4.38467	−	0.0121183i	0.179302	−	0.000495556i
$599$	−2.13529			−0.0872457			−0.0436229	−	0.999048i	$-0.513890\pi$
$599$	−2.13529			−0.0872457			−0.0436229	+	0.999048i	$0.513890\pi$
$600$	−18.7959	+	2.70245i	−0.767341	+	0.110327i
$601$	−30.1431	−	13.7659i	−1.22956	−	0.561522i	−0.308607	−	0.951190i	$-0.599863\pi$
$601$	−30.1431	−	13.7659i	−1.22956	−	0.561522i	−0.920956	+	0.389667i	$0.872590\pi$
$602$	−6.66536	+	2.72601i	−0.271660	+	0.111104i
$603$	−3.58845	−	3.10941i	−0.146133	−	0.126625i
$604$	7.93220	+	2.32910i	0.322757	+	0.0947699i
$605$	−17.8945	+	11.5001i	−0.727515	+	0.467545i
$606$	−7.51470	−	16.4549i	−0.305264	−	0.668434i
$607$	1.04977	−	0.909630i	0.0426088	−	0.0369207i	−0.633296	−	0.773910i	$-0.718298\pi$
$607$	1.04977	−	0.909630i	0.0426088	−	0.0369207i	0.675905	+	0.736989i	$0.263753\pi$
$608$	4.21654	+	2.70981i	0.171003	+	0.109897i
$609$	0.0108342	−	0.269540i	0.000439025	−	0.0109223i
$610$	4.29629	−	29.8813i	0.173952	−	1.20986i
$611$	3.43258	+	2.20599i	0.138867	+	0.0892447i
$612$	−3.21926	−	3.71522i	−0.130131	−	0.150179i
$613$	36.5231	−	16.6795i	1.47515	−	0.673680i	0.494455	−	0.869203i	$-0.335368\pi$
$613$	36.5231	−	16.6795i	1.47515	−	0.673680i	0.980699	+	0.195523i	$0.0626403\pi$
$614$	−17.0114	−	26.4703i	−0.686525	−	1.06825i
$615$	−23.0574	−	6.77028i	−0.929766	−	0.273004i
$616$	−18.8100	+	26.8345i	−0.757878	+	1.08119i
$617$	−3.78362	−	12.8858i	−0.152323	−	0.518763i	0.847607	−	0.530625i	$-0.178043\pi$
$617$	−3.78362	−	12.8858i	−0.152323	−	0.518763i	−0.999930	+	0.0118611i	$0.996224\pi$
$618$	9.48313	+	4.33080i	0.381468	+	0.174210i
$619$	2.66440	+	18.5313i	0.107091	+	0.744836i	0.970634	+	0.240561i	$0.0773313\pi$
$619$	2.66440	+	18.5313i	0.107091	+	0.744836i	−0.863543	+	0.504276i	$0.831760\pi$
$620$		−	9.76488i		−	0.392167i
$621$	3.15061	+	3.61575i	0.126430	+	0.145095i
$622$			7.76600i			0.311388i
$623$	36.0385	−	9.02675i	1.44385	−	0.361649i
$624$	−0.322040	+	0.705170i	−0.0128919	+	0.0282294i
$625$	15.5558	−	4.56759i	0.622231	−	0.182704i
$626$	−13.2602	+	15.3031i	−0.529984	+	0.611634i
$627$	3.89040	+	1.14232i	0.155368	+	0.0456200i
$628$	−13.2931	+	8.54295i	−0.530452	+	0.340901i
$629$	25.3177	−	11.5622i	1.00948	−	0.461015i
$630$	−5.98044	+	6.36610i	−0.238266	+	0.253631i
$631$	−7.04772	+	10.9665i	−0.280565	+	0.436568i	−0.952723	−	0.303840i	$-0.901731\pi$
$631$	−7.04772	+	10.9665i	−0.280565	+	0.436568i	0.672158	+	0.740408i	$0.265368\pi$
$632$	30.8519	+	4.43584i	1.22722	+	0.176448i
$633$	4.35249	+	0.625794i	0.172996	+	0.0248731i
$634$	−10.2023	−	6.55659i	−0.405183	−	0.260396i
$635$	−24.3770	−	28.1325i	−0.967370	−	1.11640i
$636$	−6.14927	−	13.4650i	−0.243834	−	0.533923i
$637$	−4.58219	−	4.66493i	−0.181553	−	0.184831i
$638$	−0.116957	+	0.398318i	−0.00463036	+	0.0157696i
$639$	−1.34458	+	1.55172i	−0.0531906	+	0.0613852i
$640$	−12.0866	+	3.54894i	−0.477765	+	0.140284i
$641$	34.3713	+	15.6969i	1.35759	+	0.619988i	0.955331	−	0.295539i	$-0.0954994\pi$
$641$	34.3713	+	15.6969i	1.35759	+	0.619988i	0.402255	+	0.915528i	$0.368227\pi$
$642$	−1.41804	−	9.86269i	−0.0559656	−	0.389249i
$643$	25.2379			0.995286			0.497643	−	0.867382i	$-0.334199\pi$
$643$	25.2379			0.995286			0.497643	+	0.867382i	$0.334199\pi$
$644$	13.0085	+	2.36996i	0.512606	+	0.0933895i
$645$	−9.38050			−0.369357
$646$	−0.640426	−	4.45426i	−0.0251972	−	0.175250i
$647$	−22.5824	−	10.3130i	−0.887804	−	0.405446i	−0.0813100	−	0.996689i	$-0.525910\pi$
$647$	−22.5824	−	10.3130i	−0.887804	−	0.405446i	−0.806494	+	0.591242i	$0.798638\pi$
$648$	−2.85678	+	0.838826i	−0.112225	+	0.0329522i
$649$	−36.4780	+	42.0979i	−1.43189	+	1.65249i
$650$	−1.64280	+	5.59485i	−0.0644358	+	0.219448i
$651$	−4.58620	−	5.74353i	−0.179747	−	0.225107i
$652$	−8.90422	−	19.4975i	−0.348716	−	0.763582i
$653$	21.7649	+	25.1180i	0.851725	+	0.982943i	0.999982	−	0.00600547i	$-0.00191161\pi$
$653$	21.7649	+	25.1180i	0.851725	+	0.982943i	−0.148257	+	0.988949i	$0.547366\pi$
$654$	2.70610	+	1.73910i	0.105817	+	0.0680043i
$655$	−53.6957	−	7.72027i	−2.09806	−	0.301656i
$656$	5.85213	+	0.841409i	0.228487	+	0.0328515i
$657$	−3.72379	+	5.79432i	−0.145279	+	0.226058i
$658$	−8.24379	−	7.74438i	−0.321376	−	0.301907i
$659$	−21.3124	+	9.73304i	−0.830213	+	0.379146i	−0.784744	−	0.619820i	$-0.787206\pi$
$659$	−21.3124	+	9.73304i	−0.830213	+	0.379146i	−0.0454691	+	0.998966i	$0.514478\pi$
$660$	−12.3016	+	7.90573i	−0.478838	+	0.307730i
$661$	−16.5846	−	4.86968i	−0.645067	−	0.189409i	−0.0571953	−	0.998363i	$-0.518216\pi$
$661$	−16.5846	−	4.86968i	−0.645067	−	0.189409i	−0.587872	+	0.808954i	$0.700034\pi$
$662$	−1.40334	+	1.61954i	−0.0545424	+	0.0629453i
$663$	−4.22820	+	1.24151i	−0.164210	+	0.0482164i
$664$	−4.69824	+	10.2877i	−0.182327	+	0.399240i
$665$	8.43758	−	2.11340i	0.327195	−	0.0819542i
$666$		−	5.77455i		−	0.223759i
$667$	0.483806	−	0.0709261i	0.0187330	−	0.00274627i
$668$			21.4263i			0.829008i
$669$	3.23839	+	22.5235i	0.125203	+	0.870809i
$670$	14.2590	+	6.51185i	0.550872	+	0.251575i
$671$	−10.7174	−	36.5000i	−0.413739	−	1.40906i
$672$	−7.80965	+	11.1413i	−0.301264	+	0.429786i
$673$	−13.3088	−	3.90780i	−0.513015	−	0.150635i	0.0149710	−	0.999888i	$-0.495234\pi$
$673$	−13.3088	−	3.90780i	−0.513015	−	0.150635i	−0.527986	+	0.849253i	$0.677053\pi$
$674$	−1.17764	−	1.83244i	−0.0453610	−	0.0705831i
$675$	−5.80147	+	2.64944i	−0.223299	+	0.101977i
$676$	8.27599	+	9.55100i	0.318307	+	0.367346i
$677$	26.1202	+	16.7864i	1.00388	+	0.645154i	0.935802	−	0.352526i	$-0.114677\pi$
$677$	26.1202	+	16.7864i	1.00388	+	0.645154i	0.0680773	+	0.997680i	$0.478314\pi$
$678$	−1.56384	+	10.8768i	−0.0600591	+	0.417720i
$679$	4.78811	+	0.192460i	0.183751	+	0.00738592i
$680$	39.8561	+	25.6139i	1.52841	+	0.982249i
$681$	4.68061	−	4.05577i	0.179361	−	0.155418i
$682$	4.69871	+	10.2887i	0.179923	+	0.393976i
$683$	38.5492	−	24.7740i	1.47504	−	0.947952i	0.477446	−	0.878661i	$-0.341563\pi$
$683$	38.5492	−	24.7740i	1.47504	−	0.947952i	0.997596	−	0.0692914i	$-0.0220738\pi$
$684$	0.974536	+	0.286150i	0.0372623	+	0.0109412i
$685$	31.1112	+	26.9580i	1.18870	+	1.03001i
$686$	10.1371	+	15.0268i	0.387037	+	0.573724i
$687$	−4.04806	−	1.84869i	−0.154443	−	0.0705318i
$688$	2.28439	−	0.328446i	0.0870915	−	0.0125219i
$689$	−13.2693			−0.505521
$690$	−13.3430	−	8.52299i	−0.507958	−	0.324465i
$691$		−	12.1253i		−	0.461268i	−0.973041	−	0.230634i	$-0.925920\pi$
$691$		−	12.1253i		−	0.461268i	0.973041	−	0.230634i	$-0.0740800\pi$
$692$	−19.6346	+	2.82302i	−0.746394	+	0.107315i
$693$	−3.52253	+	10.4276i	−0.133810	+	0.396112i
$694$	−26.5053	+	7.78266i	−1.00613	+	0.295426i
$695$	−37.4178	−	32.4227i	−1.41934	−	1.22986i
$696$	−0.0855257	+	0.291274i	−0.00324184	+	0.0110407i
$697$	18.1699	+	28.2729i	0.688233	+	1.07091i
$698$	−25.3665	+	11.5845i	−0.960136	+	0.438479i
$699$	0.732542	−	0.634751i	0.0277073	−	0.0240085i
$700$	−7.94130	+	15.6890i	−0.300153	+	0.592987i
$701$	42.9599	+	6.17670i	1.62257	+	0.233291i	0.892818	−	0.450419i	$-0.148725\pi$
$701$	42.9599	+	6.17670i	1.62257	+	0.233291i	0.729755	+	0.683709i	$0.239634\pi$
$702$	−0.130114	+	0.904963i	−0.00491084	+	0.0341556i
$703$	−3.10897	+	4.83764i	−0.117257	+	0.182455i
$704$	21.0423	−	18.2333i	0.793062	−	0.687192i
$705$	−6.12061	−	13.4023i	−0.230516	−	0.504759i
$706$	−9.49149	−	14.7690i	−0.357217	−	0.555840i
$707$	−48.0844	−	8.89768i	−1.80840	−	0.334632i
$708$	−9.13766	+	10.5454i	−0.343414	+	0.396321i
$709$	5.52281	+	18.8090i	0.207414	+	0.706386i	0.995829	+	0.0912421i	$0.0290837\pi$
$709$	5.52281	+	18.8090i	0.207414	+	0.706386i	−0.788415	+	0.615143i	$0.789098\pi$
$710$	2.81586	−	6.16587i	0.105677	−	0.231401i
$711$	10.3621	−	1.48984i	0.388609	−	0.0558735i
$712$	−41.8086			−1.56684
$713$	8.69676	−	10.0928i	0.325696	−	0.377979i
$714$	12.1513	−	1.25144i	0.454753	−	0.0468340i
$715$	1.86548	+	12.9747i	0.0697650	+	0.485226i
$716$	−0.883848	+	1.93536i	−0.0330310	+	0.0723277i
$717$	3.91832	+	13.3446i	0.146332	+	0.498362i
$718$	−1.38998	−	1.20442i	−0.0518736	−	0.0449487i
$719$	−7.11859	+	24.2437i	−0.265479	+	0.904137i	0.713582	+	0.700571i	$0.247071\pi$
$719$	−7.11859	+	24.2437i	−0.265479	+	0.904137i	−0.979061	+	0.203566i	$0.934747\pi$
$720$	2.35491	−	1.51341i	0.0877621	−	0.0564013i
$721$	24.3010	−	14.2719i	0.905017	−	0.531512i
$722$	−11.5689	−	13.3512i	−0.430548	−	0.496879i
$723$	1.23760	−	1.92574i	0.0460268	−	0.0716192i
$724$	3.85534	−	26.8145i	0.143283	−	0.996554i
$725$	−0.0925438	+	0.643656i	−0.00343699	+	0.0239048i
$726$	3.33684	−	5.19222i	0.123842	−	0.192701i
$727$	−32.9821	−	38.0634i	−1.22324	−	1.41169i	−0.881691	−	0.471827i	$-0.843595\pi$
$727$	−32.9821	−	38.0634i	−1.22324	−	1.41169i	−0.341546	−	0.939865i	$-0.610951\pi$
$728$	3.72652	+	6.34523i	0.138114	+	0.235170i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	6.40628	−	21.8178i	0.237107	−	0.807512i
$731$	9.91465	+	8.59109i	0.366706	+	0.317753i
$732$	−2.68467	−	9.14315i	−0.0992283	−	0.337941i
$733$	10.9005	−	23.8689i	0.402621	−	0.881617i	−0.594377	−	0.804187i	$-0.702601\pi$
$733$	10.9005	−	23.8689i	0.402621	−	0.881617i	0.996998	−	0.0774303i	$-0.0246715\pi$
$734$	0.830711	+	5.77772i	0.0306621	+	0.213260i
$735$	4.81240	+	23.1161i	0.177508	+	0.852650i
$736$	−22.4622	−	10.1832i	−0.827969	−	0.375359i
$737$	19.7528			0.727605
$738$	6.90176	−	0.992323i	0.254057	−	0.0365279i
$739$	−7.16587	+	15.6911i	−0.263601	+	0.577206i	−0.994435	−	0.105349i	$-0.966404\pi$
$739$	−7.16587	+	15.6911i	−0.263601	+	0.577206i	0.730834	+	0.682555i	$0.239131\pi$
$740$	−5.84285	−	19.8989i	−0.214788	−	0.731499i
$741$	0.596228	−	0.688084i	0.0219030	−	0.0252774i
$742$	36.1692	+	6.69286i	1.32781	+	0.245702i
$743$	15.9313	+	24.7896i	0.584464	+	0.909444i	1.00000		0.000132822i	$-4.22785e-5\pi$
$743$	15.9313	+	24.7896i	0.584464	+	0.909444i	−0.415536	+	0.909577i	$0.636406\pi$
$744$	3.43598	+	7.52374i	0.125969	+	0.275834i
$745$	13.3706	−	11.5857i	0.489859	−	0.424465i
$746$	−11.6177	+	18.0775i	−0.425355	+	0.661865i
$747$	−0.540590	+	3.75989i	−0.0197792	+	0.137567i
$748$	20.2425	+	2.91043i	0.740138	+	0.106416i
$749$	−24.0322	−	12.1644i	−0.878117	−	0.444478i
$750$	3.43767	−	2.97875i	0.125526	−	0.108769i
$751$	−5.45997	+	2.49349i	−0.199237	+	0.0909886i	−0.512535	−	0.858666i	$-0.671293\pi$
$751$	−5.45997	+	2.49349i	−0.199237	+	0.0909886i	0.313298	+	0.949655i	$0.398566\pi$
$752$	1.95979	+	3.04949i	0.0714661	+	0.111203i
$753$	−6.83874	+	23.2906i	−0.249218	+	0.848757i
$754$	0.0704493	+	0.0610447i	0.00256561	+	0.00222312i
$755$	−25.6755	+	7.53902i	−0.934428	+	0.274373i
$756$	−0.882386	+	2.61209i	−0.0320921	+	0.0950007i
$757$	−25.4067	+	3.65293i	−0.923420	+	0.132768i	−0.587594	−	0.809156i	$-0.699925\pi$
$757$	−25.4067	+	3.65293i	−0.923420	+	0.132768i	−0.335827	+	0.941924i	$0.609016\pi$
$758$		−	19.3273i		−	0.702000i
$759$	−19.7557	−	2.78473i	−0.717085	−	0.101079i
$760$	−9.78851			−0.355067
$761$	−30.7481	+	4.42090i	−1.11462	+	0.160258i	−0.674921	−	0.737890i	$-0.735823\pi$
$761$	−30.7481	+	4.42090i	−1.11462	+	0.160258i	−0.439695	+	0.898147i	$0.644913\pi$
$762$	9.82494	+	4.48690i	0.355920	+	0.162543i
$763$	8.04854	−	3.29171i	0.291377	−	0.119168i
$764$	−5.63644	−	4.88400i	−0.203919	−	0.176697i
$765$	15.2677	+	4.48301i	0.552006	+	0.162084i
$766$	−12.4926	+	8.02849i	−0.451375	+	0.290081i
$767$	5.19608	+	11.3778i	0.187619	+	0.410829i
$768$	12.8787	−	11.1594i	0.464719	−	0.402681i
$769$	32.4432	+	20.8500i	1.16993	+	0.751869i	0.973509	−	0.228651i	$-0.0734313\pi$
$769$	32.4432	+	20.8500i	1.16993	+	0.751869i	0.196422	+	0.980519i	$0.437068\pi$
$770$	1.45937	−	36.3071i	0.0525921	−	1.30842i
$771$	0.964466	−	6.70801i	0.0347344	−	0.241583i
$772$	−18.0044	−	11.5707i	−0.647991	−	0.416439i
$773$	19.8510	+	22.9093i	0.713991	+	0.823989i	0.990571	−	0.137002i	$-0.0437465\pi$
$773$	19.8510	+	22.9093i	0.713991	+	0.823989i	−0.276580	+	0.960991i	$0.589201\pi$
$774$	2.47585	−	1.13068i	0.0889928	−	0.0406416i
$775$	9.57888	+	14.9050i	0.344083	+	0.535404i
$776$	−5.17419	−	1.51928i	−0.185743	−	0.0545390i
$777$	−12.7824	−	8.96003i	−0.458568	−	0.321439i
$778$	1.61867	+	5.51267i	0.0580320	+	0.197639i
$779$	−6.31623	−	2.88452i	−0.226302	−	0.103349i
$780$	0.467299	+	3.25013i	0.0167320	+	0.116373i
$781$		−	8.54154i		−	0.305640i
$782$	6.29701	+	21.2284i	0.225181	+	0.759127i
$783$			0.101959i			0.00364371i
$784$	−1.98132	−	5.46086i	−0.0707614	−	0.195031i
$785$	21.2475	−	46.5255i	0.758355	−	1.66057i
$786$	15.1028	−	4.43459i	0.538699	−	0.158176i
$787$	−21.2096	+	24.4772i	−0.756041	+	0.872518i	−0.995139	−	0.0984778i	$-0.968603\pi$
$787$	−21.2096	+	24.4772i	−0.756041	+	0.872518i	0.239099	+	0.970995i	$0.423148\pi$
$788$	−13.1534	−	3.86219i	−0.468571	−	0.137585i
$789$	−0.204373	+	0.131342i	−0.00727587	+	0.00467592i
$790$	−31.4376	+	14.3571i	−1.11850	+	0.510801i
$791$	21.6501	+	20.3386i	0.769790	+	0.723156i
$792$	6.69643	−	10.4199i	0.237947	−	0.370253i
$793$	−8.45509	−	1.21566i	−0.300249	−	0.0431693i
$794$	−13.4133	−	1.92854i	−0.476019	−	0.0684412i
$795$	40.3083	+	25.9045i	1.42959	+	0.918739i
$796$	−10.7247	−	12.3770i	−0.380127	−	0.438690i
$797$	19.8916	+	43.5564i	0.704595	+	1.54285i	0.834309	+	0.551296i	$0.185867\pi$
$797$	19.8916	+	43.5564i	0.704595	+	1.54285i	−0.129714	+	0.991551i	$0.541406\pi$
$798$	−1.97224	+	1.57483i	−0.0698167	+	0.0557485i
$799$	−5.80528	+	19.7710i	−0.205376	+	0.699447i
$800$	21.4782	−	24.7872i	0.759370	−	0.876360i
$801$	−13.4733	+	3.95611i	−0.476055	+	0.139782i
$802$	−12.5069	−	5.71170i	−0.441633	−	0.201687i
$803$	−4.07780	−	28.3617i	−0.143903	−	1.00086i
$804$	4.94804			0.174504
$805$	−39.5699	+	16.3112i	−1.39465	+	0.574893i
$806$	2.53985			0.0894623
$807$	−0.441240	−	3.06889i	−0.0155324	−	0.108030i
$808$	50.0572	+	22.8604i	1.76101	+	0.804225i
$809$	−5.30805	+	1.55858i	−0.186621	+	0.0547969i	−0.373708	−	0.927547i	$-0.621914\pi$
$809$	−5.30805	+	1.55858i	−0.186621	+	0.0547969i	0.187087	+	0.982343i	$0.440095\pi$
$810$	2.16193	−	2.49500i	0.0759625	−	0.0876654i
$811$	−1.27908	+	4.35615i	−0.0449146	+	0.152965i	−0.978897	−	0.204354i	$-0.934491\pi$
$811$	−1.27908	+	4.35615i	−0.0449146	+	0.152965i	0.933983	+	0.357319i	$0.116309\pi$
$812$	0.175407	+	0.219671i	0.00615559	+	0.00770896i
$813$	2.84285	+	6.22496i	0.0997029	+	0.218319i
$814$	15.7314	+	18.1550i	0.551385	+	0.636332i
$815$	58.3669	+	37.5101i	2.04450	+	1.31392i
$816$	−3.87505	−	0.557148i	−0.135654	−	0.0195041i
$817$	−2.68291	−	0.385744i	−0.0938630	−	0.0134955i
$818$	−5.62763	+	8.75677i	−0.196766	+	0.306173i
$819$	1.80132	+	1.69220i	0.0629433	+	0.0591302i
$820$	22.7792	−	10.4029i	0.795485	−	0.363286i
$821$	−40.1047	+	25.7737i	−1.39966	+	0.899509i	−0.999854	−	0.0170890i	$-0.994560\pi$
$821$	−40.1047	+	25.7737i	−1.39966	+	0.899509i	−0.399810	+	0.916598i	$0.630924\pi$
$822$	−11.4608	−	3.36519i	−0.399741	−	0.117374i
$823$	6.19420	−	7.14849i	0.215916	−	0.249181i	−0.637451	−	0.770491i	$-0.720011\pi$
$823$	6.19420	−	7.14849i	0.215916	−	0.249181i	0.853367	+	0.521310i	$0.174557\pi$
$824$	−30.4298	+	8.93500i	−1.06007	+	0.311266i
$825$	11.0219	−	24.1345i	0.383732	−	0.840255i
$826$	−8.42454	−	33.6342i	−0.293127	−	1.17028i
$827$		−	50.0391i		−	1.74003i	−0.493025	−	0.870015i	$-0.664109\pi$
$827$		−	50.0391i		−	1.74003i	0.493025	−	0.870015i	$-0.335891\pi$
$828$	−4.94875	−	0.697568i	−0.171981	−	0.0242422i
$829$		−	30.8271i		−	1.07067i	−0.844640	−	0.535335i	$-0.820185\pi$
$829$		−	30.8271i		−	1.07067i	0.844640	−	0.535335i	$-0.179815\pi$
$830$	−1.78468	−	12.4127i	−0.0619472	−	0.430852i
$831$	−26.8551	−	12.2643i	−0.931592	−	0.425444i
$832$	−1.76142	−	5.99886i	−0.0610664	−	0.207973i
$833$	16.0844	−	28.8398i	0.557290	−	0.999240i
$834$	13.7840	+	4.04735i	0.477301	+	0.140148i
$835$	−37.4957	−	58.3444i	−1.29759	−	2.01909i
$836$	−3.84345	+	1.75525i	−0.132929	+	0.0607065i
$837$	1.81921	+	2.09948i	0.0628810	+	0.0725686i
$838$	−3.97184	−	2.55255i	−0.137205	−	0.0881763i
$839$	−7.08361	+	49.2676i	−0.244553	+	1.70091i	0.384158	+	0.923268i	$0.374492\pi$
$839$	−7.08361	+	49.2676i	−0.244553	+	1.70091i	−0.628711	+	0.777639i	$0.716417\pi$
$840$	1.06718	−	26.5499i	0.0368212	−	0.916058i
$841$	−24.3876	−	15.6730i	−0.840952	−	0.540447i
$842$	−12.5362	+	10.8627i	−0.432026	+	0.374352i
$843$	13.3831	+	29.3048i	0.460938	+	1.00931i
$844$	−3.85489	+	2.47739i	−0.132691	+	0.0852752i
$845$	−39.2499	−	11.5248i	−1.35024	−	0.396466i
$846$	3.23091	+	2.79960i	0.111081	+	0.0962521i
$847$	−6.31584	−	15.4428i	−0.217015	−	0.530622i
$848$	−10.7231	−	4.89707i	−0.368233	−	0.168166i
$849$	−12.5080	+	1.79838i	−0.429274	+	0.0617203i
$850$	−29.4468			−1.01002
$851$	11.6832	−	25.7710i	0.400496	−	0.883417i
$852$		−	2.13964i		−	0.0733027i
$853$	−3.78882	+	0.544750i	−0.129727	+	0.0186519i	−0.206872	−	0.978368i	$-0.566328\pi$
$853$	−3.78882	+	0.544750i	−0.129727	+	0.0186519i	0.0771456	+	0.997020i	$0.475419\pi$
$854$	22.4335	+	7.57824i	0.767660	+	0.259322i
$855$	−3.15445	+	0.926230i	−0.107880	+	0.0316764i
$856$	22.9080	+	19.8499i	0.782981	+	0.678457i
$857$	−3.45203	+	11.7565i	−0.117919	+	0.401596i	−0.997206	−	0.0746962i	$-0.976201\pi$
$857$	−3.45203	+	11.7565i	−0.117919	+	0.401596i	0.879287	+	0.476292i	$0.158019\pi$
$858$	−2.05628	−	3.19964i	−0.0702004	−	0.109234i
$859$	1.35699	−	0.619717i	0.0462999	−	0.0211445i	−0.392130	−	0.919910i	$-0.628262\pi$
$859$	1.35699	−	0.619717i	0.0462999	−	0.0211445i	0.438430	+	0.898765i	$0.355535\pi$
$860$	7.38767	−	6.40145i	0.251917	−	0.218288i
$861$	8.51247	−	16.8174i	0.290104	−	0.573134i
$862$	−25.3340	−	3.64248i	−0.862880	−	0.124063i
$863$	−5.77618	+	40.1742i	−0.196623	+	1.36755i	0.617371	+	0.786672i	$0.288198\pi$
$863$	−5.77618	+	40.1742i	−0.196623	+	1.36755i	−0.813994	+	0.580873i	$0.802711\pi$
$864$	2.78026	−	4.32617i	0.0945865	−	0.147179i
$865$	48.5253	−	42.0474i	1.64991	−	1.42965i
$866$	−8.11139	−	17.7615i	−0.275636	−	0.603559i
$867$	−2.84048	−	4.41987i	−0.0964676	−	0.150107i
$868$	7.53139	+	1.39363i	0.255632	+	0.0473029i
$869$	−28.5193	+	32.9131i	−0.967452	+	1.11650i
$870$	−0.0948319	−	0.322968i	−0.00321510	−	0.0109496i
$871$	1.84256	−	4.03465i	0.0624329	−	0.136709i
$872$	−9.68600	+	1.39264i	−0.328009	+	0.0471606i
$873$	−1.81120			−0.0612998
$874$	−3.46573	−	2.98634i	−0.117230	−	0.101014i
$875$	−1.25970	−	12.2315i	−0.0425856	−	0.413501i
$876$	−1.02148	−	7.10455i	−0.0345126	−	0.240040i
$877$	−6.39491	+	14.0029i	−0.215941	+	0.472845i	−0.986341	−	0.164716i	$-0.947329\pi$
$877$	−6.39491	+	14.0029i	−0.215941	+	0.472845i	0.770400	+	0.637561i	$0.220056\pi$
$878$	3.80690	+	12.9651i	0.128477	+	0.437552i
$879$	8.50812	+	7.37233i	0.286972	+	0.248662i
$880$	−3.28083	+	11.1735i	−0.110597	+	0.376658i
$881$	−11.7463	+	7.54888i	−0.395743	+	0.254328i	−0.723344	−	0.690488i	$-0.757396\pi$
$881$	−11.7463	+	7.54888i	−0.395743	+	0.254328i	0.327602	+	0.944816i	$0.393760\pi$
$882$	−4.05648	−	5.52112i	−0.136589	−	0.185906i
$883$	−8.98579	−	10.3701i	−0.302396	−	0.348983i	0.584132	−	0.811659i	$-0.301435\pi$
$883$	−8.98579	−	10.3701i	−0.302396	−	0.348983i	−0.886528	+	0.462675i	$0.846890\pi$
$884$	2.48271	−	3.86318i	0.0835027	−	0.129933i
$885$	6.42780	−	44.7063i	0.216068	−	1.50279i
$886$	−1.34166	+	9.33143i	−0.0450739	+	0.313496i
$887$	15.4081	−	23.9754i	0.517352	−	0.805016i	−0.480036	−	0.877249i	$-0.659376\pi$
$887$	15.4081	−	23.9754i	0.517352	−	0.805016i	0.997388	+	0.0722333i	$0.0230126\pi$
$888$	11.5037	+	13.2760i	0.386040	+	0.445514i
$889$	25.1769	−	14.7863i	0.844407	−	0.495916i
$890$	38.9988	−	25.0630i	1.30724	−	0.840113i
$891$	1.17203	−	3.99155i	0.0392643	−	0.133722i
$892$	−17.9209	−	15.5286i	−0.600037	−	0.519935i
$893$	−1.19942	−	4.08486i	−0.0401372	−	0.136695i
$894$	−2.13249	+	4.66951i	−0.0713212	+	0.156172i
$895$	−0.980103	−	6.81677i	−0.0327612	−	0.227859i
$896$	−1.01222	−	9.82857i	−0.0338160	−	0.328350i
$897$	−2.41163	+	3.77547i	−0.0805219	+	0.126059i
$898$	6.52212			0.217646
$899$	0.280359	−	0.0403096i	0.00935051	−	0.00134440i
$900$	2.76095	−	6.04563i	0.0920316	−	0.201521i
$901$	−18.8789	−	64.2958i	−0.628949	−	2.14200i
$902$	−18.9956	+	21.9220i	−0.632483	+	0.729924i
$903$	1.33877	−	7.23493i	0.0445516	−	0.240763i
$904$	−18.0727	−	28.1217i	−0.601090	−	0.935314i
$905$	36.4268	+	79.7636i	1.21087	+	2.65143i
$906$	5.86799	−	5.08464i	0.194951	−	0.168926i
$907$	−23.5198	+	36.5975i	−0.780961	+	1.21520i	0.191354	+	0.981521i	$0.438712\pi$
$907$	−23.5198	+	36.5975i	−0.780961	+	1.21520i	−0.972314	+	0.233677i	$0.924924\pi$
$908$	−0.918499	+	6.38830i	−0.0304815	+	0.212003i
$909$	18.2946	+	2.63037i	0.606794	+	0.0872438i
$910$	−7.27984	−	3.68485i	−0.241324	−	0.122151i
$911$	6.06877	−	5.25862i	0.201067	−	0.174226i	−0.548507	−	0.836146i	$-0.684804\pi$
$911$	6.06877	−	5.25862i	0.201067	−	0.174226i	0.749574	+	0.661920i	$0.230258\pi$
$912$	0.735758	−	0.336009i	0.0243634	−	0.0111264i
$913$	−8.54332	−	13.2937i	−0.282743	−	0.439956i
$914$	−0.762143	+	2.59562i	−0.0252094	+	0.0858555i
$915$	23.3108	+	20.1990i	0.770633	+	0.667757i
$916$	4.44966	−	1.30654i	0.147021	−	0.0431692i
$917$	13.6178	−	40.3122i	0.449700	−	1.33123i
$918$	−4.57007	+	0.657077i	−0.150835	+	0.0216868i
$919$		−	47.6390i		−	1.57147i	−0.618566	−	0.785733i	$-0.712286\pi$
$919$		−	47.6390i		−	1.57147i	0.618566	−	0.785733i	$-0.287714\pi$
$920$	47.6553	−	6.98628i	1.57115	−	0.230331i
$921$	32.1491			1.05935
$922$	5.36445	−	0.771292i	0.176669	−	0.0254011i
$923$	−1.74467	−	0.796763i	−0.0574265	−	0.0262258i
$924$	−4.34182	−	10.6162i	−0.142835	−	0.349246i
$925$	28.4384	+	24.6420i	0.935049	+	0.810224i
$926$	8.02072	+	2.35510i	0.263577	+	0.0773933i
$927$	−8.96086	+	5.75880i	−0.294313	+	0.189144i
$928$	−0.217813	−	0.476944i	−0.00715007	−	0.0156565i
$929$	−18.2120	+	15.7808i	−0.597516	+	0.517750i	−0.900278	−	0.435316i	$-0.856637\pi$
$929$	−18.2120	+	15.7808i	−0.597516	+	0.517750i	0.302762	+	0.953066i	$0.402091\pi$
$930$	−7.71531	−	4.95833i	−0.252995	−	0.162590i
$931$	0.425811	+	6.80931i	0.0139554	+	0.223166i
$932$	−0.143750	+	0.999805i	−0.00470870	+	0.0327497i
$933$	−6.67515	−	4.28986i	−0.218535	−	0.140444i
$934$	1.64936	+	1.90347i	0.0539688	+	0.0622833i
$935$	−60.2141	+	27.4989i	−1.96921	+	0.899309i
$936$	−1.50368	−	2.33977i	−0.0491492	−	0.0764777i
$937$	34.9738	+	10.2692i	1.14255	+	0.335482i	0.797627	−	0.603151i	$-0.206088\pi$
$937$	34.9738	+	10.2692i	1.14255	+	0.335482i	0.344919	+	0.938633i	$0.387906\pi$
$938$	−7.05744	+	10.0682i	−0.230434	+	0.328738i
$939$	−5.82874	−	19.8509i	−0.190214	−	0.647809i
$940$	13.9663	+	6.37821i	0.455531	+	0.208034i
$941$	−0.863068	−	6.00277i	−0.0281352	−	0.195685i	0.970906	−	0.239460i	$-0.0769705\pi$
$941$	−0.863068	−	6.00277i	−0.0281352	−	0.195685i	−0.999041	+	0.0437755i	$0.986061\pi$
$942$			14.8408i			0.483541i
$943$	32.8092	+	9.53525i	1.06842	+	0.310510i
$944$			11.1122i			0.361671i
$945$	−2.16835	−	8.65696i	−0.0705365	−	0.281611i
$946$	−4.70372	+	10.2997i	−0.152931	+	0.334873i
$947$	9.35493	−	2.74685i	0.303994	−	0.0892608i	−0.126178	−	0.992008i	$-0.540271\pi$
$947$	9.35493	−	2.74685i	0.303994	−	0.0892608i	0.430172	+	0.902747i	$0.358453\pi$
$948$	−7.14403	+	8.24465i	−0.232027	+	0.267774i
$949$	−6.17346	−	1.81269i	−0.200399	−	0.0588425i
$950$	5.11817	−	3.28925i	0.166055	−	0.106717i
$951$	11.2712	−	5.14741i	0.365495	−	0.166916i
$952$	−25.4436	+	27.0843i	−0.824631	+	0.877809i
$953$	−6.41044	+	9.97484i	−0.207655	+	0.323117i	−0.929422	−	0.369019i	$-0.879694\pi$
$953$	−6.41044	+	9.97484i	−0.207655	+	0.323117i	0.721767	+	0.692136i	$0.243330\pi$
$954$	−13.7612	−	1.97857i	−0.445537	−	0.0640585i
$955$	23.8951	+	3.43560i	0.773228	+	0.111173i
$956$	−12.1925	−	7.83565i	−0.394334	−	0.253423i
$957$	−0.277763	−	0.320555i	−0.00897879	−	0.0103621i
$958$	11.6707	+	25.5552i	0.377062	+	0.825651i
$959$	−25.2322	+	20.1478i	−0.814789	+	0.650608i
$960$	−6.36037	+	21.6614i	−0.205280	+	0.699120i
$961$	−15.2469	+	17.5959i	−0.491836	+	0.567609i
$962$	5.17572	−	1.51973i	0.166872	−	0.0489980i
$963$	9.26064	+	4.22919i	0.298420	+	0.136284i
$964$	0.339489	+	2.36120i	0.0109342	+	0.0760490i
$965$	69.2750			2.23004
$966$	8.47785	−	9.07469i	0.272770	−	0.291974i
$967$	25.1442			0.808582			0.404291	−	0.914630i	$-0.367518\pi$
$967$	25.1442			0.808582			0.404291	+	0.914630i	$0.367518\pi$
$968$	2.67207	+	18.5847i	0.0858836	+	0.597334i
$969$	4.18236	+	1.91002i	0.134357	+	0.0613586i
$970$	5.73721	−	1.68460i	0.184211	−	0.0540891i
$971$	31.0700	−	35.8567i	0.997083	−	1.15070i	0.00850841	−	0.999964i	$-0.497292\pi$
$971$	31.0700	−	35.8567i	0.997083	−	1.15070i	0.988575	−	0.150731i	$-0.0481629\pi$
$972$	0.293590	−	0.999875i	0.00941689	−	0.0320710i
$973$	30.3470	−	24.2320i	0.972880	−	0.776843i
$974$	4.94188	+	10.8212i	0.158348	+	0.346734i
$975$	−3.90151	−	4.50258i	−0.124948	−	0.144198i
$976$	−6.38402	−	4.10276i	−0.204348	−	0.131326i
$977$	0.838370	+	0.120539i	0.0268218	+	0.00385640i	0.155713	−	0.987802i	$-0.450233\pi$
$977$	0.838370	+	0.120539i	0.0268218	+	0.00385640i	−0.128891	+	0.991659i	$0.541142\pi$
$978$	−19.9265	−	2.86499i	−0.637178	−	0.0916124i
$979$	31.5820	−	49.1426i	1.00937	−	1.57060i
$980$	−19.5650	−	14.9211i	−0.624980	−	0.476639i
$981$	−2.98964	+	1.36532i	−0.0954518	+	0.0435914i
$982$	−22.7523	+	14.6220i	−0.726055	+	0.466607i
$983$	18.1252	+	5.32203i	0.578103	+	0.169746i	0.557696	−	0.830045i	$-0.311686\pi$
$983$	18.1252	+	5.32203i	0.578103	+	0.169746i	0.0204074	+	0.999792i	$0.493504\pi$
$984$	−13.8907	+	16.0307i	−0.442819	+	0.511040i
$985$	42.5760	−	12.5014i	1.35658	−	0.398329i
$986$	−0.195557	+	0.428210i	−0.00622780	+	0.0136370i
$987$	11.2104	−	2.80791i	0.356829	−	0.0893769i
$988$			0.948783i			0.0301848i
$989$	13.3370	−	0.0368608i	0.424092	−	0.00117211i
$990$			13.7339i			0.436491i
$991$	−3.87725	−	26.9669i	−0.123165	−	0.856632i	−0.953934	−	0.300015i	$-0.903008\pi$
$991$	−3.87725	−	26.9669i	−0.123165	−	0.856632i	0.830769	−	0.556617i	$-0.187901\pi$
$992$	−12.9950	−	5.93462i	−0.412592	−	0.188424i
$993$	−0.616862	−	2.10084i	−0.0195755	−	0.0666681i
$994$	4.35370	+	3.05179i	0.138091	+	0.0967967i
$995$	50.8632	+	14.9348i	1.61247	+	0.473464i
$996$	−2.14008	−	3.33003i	−0.0678111	−	0.105516i
$997$	11.2058	−	5.11752i	0.354891	−	0.162073i	−0.229989	−	0.973193i	$-0.573869\pi$
$997$	11.2058	−	5.11752i	0.354891	−	0.162073i	0.584880	+	0.811120i	$0.301142\pi$
$998$	−2.71482	−	3.13306i	−0.0859360	−	0.0991754i
$999$	4.96343	+	3.18980i	0.157036	+	0.100921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.21	✓	320
7.6	odd	2	inner	483.2.r.a.181.22	yes	320
23.15	odd	22	inner	483.2.r.a.475.22	yes	320
161.153	even	22	inner	483.2.r.a.475.21	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.21	✓	320	1.1	even	1	trivial
483.2.r.a.181.22	yes	320	7.6	odd	2	inner
483.2.r.a.475.21	yes	320	161.153	even	22	inner
483.2.r.a.475.22	yes	320	23.15	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.139288 + 0.968769i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.999875 - 0.293590i) q^{4} +(-2.20891 + 2.54922i) q^{5} +(0.275740 - 0.939085i) q^{6} +(-1.65089 - 2.06750i) q^{7} +(1.23685 + 2.70832i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.139288 + 0.968769i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.999875 - 0.293590i) q^{4} +(-2.20891 + 2.54922i) q^{5} +(0.275740 - 0.939085i) q^{6} +(-1.65089 - 2.06750i) q^{7} +(1.23685 + 2.70832i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-2.77728 - 1.78485i) q^{10} +(-4.11772 - 0.592039i) q^{11} +(-1.03148 - 0.148304i) q^{12} +(-0.505033 + 0.785847i) q^{13} +(1.77298 - 1.88731i) q^{14} +(3.06828 - 1.40124i) q^{15} +(-0.698142 + 0.448669i) q^{16} +(-4.52632 - 1.32905i) q^{17} +(-0.640932 + 0.739675i) q^{18} +(0.935178 - 0.274593i) q^{19} +(-1.46021 + 3.19741i) q^{20} +(0.642836 + 2.56647i) q^{21} -4.07158i q^{22} +(-4.35692 + 2.00431i) q^{23} -2.97738i q^{24} +(-0.907659 - 6.31290i) q^{25} +(-0.831649 - 0.379801i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-2.25768 - 1.58255i) q^{28} +(-0.0978288 - 0.0287251i) q^{29} +(1.78485 + 2.77728i) q^{30} +(-2.52696 + 1.15403i) q^{31} +(3.36764 + 3.88647i) q^{32} +(3.49967 + 2.24910i) q^{33} +(0.657077 - 4.57007i) q^{34} +(8.91719 + 0.358429i) q^{35} +(0.876659 + 0.563394i) q^{36} +(-4.45895 + 3.86370i) q^{37} +(0.396276 + 0.867723i) q^{38} +(0.785847 - 0.505033i) q^{39} +(-9.63621 - 2.82945i) q^{40} +(-5.38416 - 4.66540i) q^{41} +(-2.39677 + 0.980238i) q^{42} +(-2.52966 - 1.15526i) q^{43} +(-4.29102 + 0.616956i) q^{44} -3.37310 q^{45} +(-2.54858 - 3.94167i) q^{46} -4.36801i q^{47} +(0.821436 - 0.118105i) q^{48} +(-1.54910 + 6.82644i) q^{49} +(5.98932 - 1.75862i) q^{50} +(3.56518 + 3.08924i) q^{51} +(-0.274253 + 0.934021i) q^{52} +(7.67974 + 11.9499i) q^{53} +(0.890285 - 0.406579i) q^{54} +(10.6049 - 9.18922i) q^{55} +(3.55755 - 7.02834i) q^{56} +(-0.964737 - 0.138708i) q^{57} +(0.0142016 - 0.0987745i) q^{58} +(7.23921 - 11.2644i) q^{59} +(2.65651 - 2.30188i) q^{60} +(3.79868 + 8.31795i) q^{61} +(-1.46996 - 2.28730i) q^{62} +(0.481405 - 2.60159i) q^{63} +(-4.38293 + 5.05817i) q^{64} +(-0.887723 - 3.02331i) q^{65} +(-1.69140 + 3.70364i) q^{66} +(-4.69987 + 0.675740i) q^{67} -4.91594 q^{68} +(4.79581 - 0.0132547i) q^{69} +(0.894822 + 8.68862i) q^{70} +(0.292204 + 2.03232i) q^{71} +(-1.23685 + 2.70832i) q^{72} +(1.94050 + 6.60873i) q^{73} +(-4.36411 - 3.78152i) q^{74} +(-1.79684 + 6.11947i) q^{75} +(0.854443 - 0.549117i) q^{76} +(5.57388 + 9.49077i) q^{77} +(0.598719 + 0.690959i) q^{78} +(5.65978 - 8.80679i) q^{79} +(0.398379 - 2.77079i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(3.76974 - 5.86584i) q^{82} +(2.48752 + 2.87075i) q^{83} +(1.39624 + 2.37742i) q^{84} +(13.3863 - 8.60283i) q^{85} +(0.766825 - 2.61157i) q^{86} +(0.0770553 + 0.0667688i) q^{87} +(-3.48957 - 11.8844i) q^{88} +(-5.83329 + 12.7731i) q^{89} +(-0.469832 - 3.26776i) q^{90} +(2.45849 - 0.253195i) q^{91} +(-3.76793 + 3.28320i) q^{92} +2.77801 q^{93} +(4.23159 - 0.608410i) q^{94} +(-1.36573 + 2.99053i) q^{95} +(-1.44882 - 4.93423i) q^{96} +(-1.18608 + 1.36881i) q^{97} +(-6.82901 - 0.549876i) q^{98} +(-2.24910 - 3.49967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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