LMFDB - Embedded newform 483.2.r.a.181.22

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			181.22
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139288 + 0.968769i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.999875 - 0.293590i) q^{4} +(2.20891 - 2.54922i) q^{5} +(-0.275740 + 0.939085i) q^{6} +(-1.19486 - 2.36058i) q^{7} +(1.23685 + 2.70832i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(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} +(-1.19486 - 2.36058i) 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} +(2.12042 - 1.48634i) 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} +(-0.106261 - 2.64362i) 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} +(-1.88775 - 2.00948i) 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} +(-8.65696 - 2.16835i) 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} +(2.54625 - 0.471166i) 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} +(-4.14464 + 5.64110i) 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} +(4.91534 - 6.15573i) 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} +(1.00154 - 2.44886i) 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} +(3.52253 + 10.4276i) 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} +(-0.882386 - 2.61209i) 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} +(-6.04222 - 3.22946i) 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	$-0.500729\pi$
$5$	2.20891	−	2.54922i	0.987856	−	1.14005i	0.990145	−	0.140049i	$-0.0447260\pi$
$6$	−0.275740	+	0.939085i	−0.112570	+	0.383380i
$7$	−1.19486	−	2.36058i	−0.451613	−	0.892214i
$7$	−1.19486	−	2.36058i	−0.451613	−	0.892214i
$8$	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	−0.764130	−	0.645063i	$-0.776831\pi$
$13$	0.505033	−	0.785847i	0.140071	−	0.217955i	0.904201	+	0.427108i	$0.140468\pi$
$14$	2.12042	−	1.48634i	0.566707	−	0.397241i
$15$	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	0.779975	−	0.625811i	$-0.215232\pi$
$17$	4.52632	+	1.32905i	1.09779	+	0.322341i	0.317818	+	0.948152i	$0.397050\pi$
$18$	−0.640932	+	0.739675i	−0.151069	+	0.174343i
$19$	−0.935178	+	0.274593i	−0.214544	+	0.0629959i	−0.387238	−	0.921980i	$-0.626571\pi$
$19$	−0.935178	+	0.274593i	−0.214544	+	0.0629959i	0.172694	+	0.984976i	$0.444753\pi$
$20$	1.46021	−	3.19741i	0.326513	−	0.714964i
$21$	−0.106261	−	2.64362i	−0.0231880	−	0.576884i
$22$		−	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
$28$	−1.88775	−	2.00948i	−0.356751	−	0.379756i
$29$	−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	−0.175352	−	0.984506i	$-0.556106\pi$
$31$	2.52696	−	1.15403i	0.453856	−	0.207269i	0.629209	+	0.777237i	$0.283379\pi$
$32$	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
$35$	−8.65696	−	2.16835i	−1.46329	−	0.366519i
$36$	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	0.964604	−	0.263702i	$-0.0849435\pi$
$41$	5.38416	+	4.66540i	0.840864	+	0.728613i	−0.123740	+	0.992315i	$0.539489\pi$
$42$	2.54625	−	0.471166i	0.392895	−	0.0727025i
$43$	−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	$0.103202\pi$
$47$			4.36801i			0.637139i	−0.947899	+	0.318570i	$0.896798\pi$
$48$	−0.821436	+	0.118105i	−0.118564	+	0.0170469i
$49$	−4.14464	+	5.64110i	−0.592091	+	0.805871i
$50$	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
$56$	4.91534	−	6.15573i	0.656840	−	0.822595i
$57$	−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	$0.518747\pi$
$59$	−7.23921	+	11.2644i	−0.942465	+	1.46650i	−0.883602	+	0.468238i	$0.844889\pi$
$60$	2.65651	−	2.30188i	0.342954	−	0.297171i
$61$	−3.79868	−	8.31795i	−0.486371	−	1.06500i	−0.980662	−	0.195708i	$-0.937300\pi$
$61$	−3.79868	−	8.31795i	−0.486371	−	1.06500i	0.494291	−	0.869296i	$-0.335428\pi$
$62$	1.46996	+	2.28730i	0.186685	+	0.290488i
$63$	1.00154	−	2.44886i	0.126182	−	0.308527i
$64$	−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	$-0.958851\pi$
$73$	−1.94050	−	6.60873i	−0.227118	−	0.773493i	0.764538	−	0.644579i	$-0.222967\pi$
$74$	−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
$77$	3.52253	+	10.4276i	0.401430	+	1.18833i
$78$	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	0.602624	−	0.798025i	$-0.294122\pi$
$83$	−2.48752	−	2.87075i	−0.273041	−	0.315106i	−0.875665	+	0.482919i	$0.839576\pi$
$84$	−0.882386	−	2.61209i	−0.0962762	−	0.285002i
$85$	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	$-0.596454\pi$
$89$	5.83329	−	12.7731i	0.618327	−	1.35395i	0.916730	−	0.399508i	$-0.130819\pi$
$90$	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	−0.692334	−	0.721577i	$-0.743417\pi$
$97$	1.18608	−	1.36881i	0.120428	−	0.138982i	0.812762	+	0.582596i	$0.197963\pi$
$98$	−6.04222	−	3.22946i	−0.610356	−	0.326224i
$99$	−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	$0.644174\pi$
$101$	−13.9683	+	12.1036i	−1.38990	+	1.20435i	−0.952292	+	0.305189i	$0.901280\pi$
$102$	−2.49618	+	3.88413i	−0.247158	+	0.384586i
$103$	1.51591	−	10.5434i	0.149367	−	1.03887i	−0.767892	−	0.640579i	$-0.778694\pi$
$103$	1.51591	−	10.5434i	0.149367	−	1.03887i	0.917259	−	0.398291i	$-0.130397\pi$
$104$	2.75298	+	0.395818i	0.269952	+	0.0388132i
$105$	−6.97388	−	5.56864i	−0.680581	−	0.543443i
$106$	−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
$112$	1.89330	+	1.11192i	0.178900	+	0.105067i
$113$	−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
$119$	−2.27098	−	12.2727i	−0.208181	−	1.12504i
$120$	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
$126$	2.51188	+	0.629164i	0.223776	+	0.0560503i
$127$	−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	$-0.933856\pi$
$131$	−8.69484	−	13.5294i	−0.759672	−	1.18207i	0.218816	−	0.975766i	$-0.429781\pi$
$132$	−4.15954	−	1.22135i	−0.362042	−	0.106305i
$133$	1.76560	+	1.87946i	0.153097	+	0.162970i
$134$	−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	$-0.786121\pi$
$139$		−	14.6781i		−	1.24498i	0.782627	−	0.622491i	$-0.213879\pi$
$140$	−9.29248	+	0.373514i	−0.785358	+	0.0315677i
$141$	−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
$147$	−6.11349	+	3.40958i	−0.504232	+	0.281217i
$148$	−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
$154$	−9.61128	+	4.86496i	−0.774499	+	0.392029i
$155$	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	0.356269	−	0.934383i	$-0.384049\pi$
$157$	14.5491	−	4.27201i	1.16115	−	0.340944i	0.804878	+	0.593440i	$0.202230\pi$
$158$	9.32008	+	4.25634i	0.741465	+	0.338616i
$159$	2.02157	+	14.0603i	0.160321	+	1.11505i
$160$	17.3463			1.37135
$161$	9.93722	+	7.88998i	0.783162	+	0.621817i
$162$	−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	$-0.616285\pi$
$167$	5.79269	−	19.7281i	0.448252	−	1.52660i	0.805500	−	0.592595i	$-0.201897\pi$
$168$	7.02834	−	3.55755i	0.542248	−	0.274471i
$169$	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	0.814476	−	0.580198i	$-0.197025\pi$
$173$	18.8416	+	2.70901i	1.43250	+	0.205962i	0.618023	+	0.786160i	$0.287934\pi$
$174$	0.0539507	−	0.0839489i	0.00408999	−	0.00636415i
$175$	−13.8176	+	9.68561i	−1.04451	+	0.732163i
$176$	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	$0.553294\pi$
$181$	−10.7992	+	23.6469i	−0.802698	+	1.75766i	−0.636051	+	0.771647i	$0.719433\pi$
$182$	−0.0971511	−	2.41698i	−0.00720132	−	0.179158i
$183$		−	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
$189$	1.92833	−	1.81151i	0.140265	−	0.131768i
$190$	−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
$196$	−2.48795	+	6.85721i	−0.177711	+	0.489801i
$197$	−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	$0.0516941\pi$
$199$	6.52852	+	14.2955i	0.462794	+	1.01338i	−0.524048	+	0.851689i	$0.675579\pi$
$200$	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
$203$	0.0490835	+	0.265255i	0.00344499	+	0.0186172i
$204$	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
$210$	4.42334	−	7.53172i	0.305240	−	0.519738i
$211$	−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
$217$	−5.74353	−	4.58620i	−0.389896	−	0.311331i
$218$	−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	$0.0939138\pi$
$223$	12.3023	+	19.1428i	0.823826	+	1.28190i	−0.132965	+	0.991121i	$0.542450\pi$
$224$	5.15045	−	12.5933i	0.344129	−	0.841429i
$225$	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	−0.804830	−	0.593506i	$-0.797744\pi$
$227$	2.57281	−	5.63366i	0.170763	−	0.373919i	0.975593	+	0.219586i	$0.0704708\pi$
$228$	−1.00534	+	0.144546i	−0.0665803	+	0.00957279i
$229$	−4.45022			−0.294079			−0.147039	−	0.989131i	$-0.546974\pi$
$229$	−4.45022			−0.294079			−0.147039	+	0.989131i	$0.546974\pi$
$230$	−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
$238$	11.5731	−	3.90950i	0.750174	−	0.253415i
$239$	−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	−0.976635	−	0.214905i	$-0.931056\pi$
$241$	0.325778	−	2.26584i	0.0209852	−	0.145955i	0.997620	+	0.0689499i	$0.0219649\pi$
$242$	−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
$245$	5.22527	+	23.0263i	0.333830	+	1.47110i
$246$	−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	$0.232339\pi$
$251$	3.45453	+	24.0268i	0.218048	+	1.51656i	−0.527182	+	0.849752i	$0.676752\pi$
$252$	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	0.878265	−	0.478174i	$-0.158701\pi$
$257$	−1.90930	−	6.50248i	−0.119099	−	0.405613i	−0.997364	+	0.0725606i	$0.976883\pi$
$258$	1.78241	−	2.05701i	0.110968	−	0.128064i
$259$	14.4484	+	5.90912i	0.897778	+	0.367175i
$260$	−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
$266$	−1.57483	+	1.97224i	−0.0965592	+	0.120926i
$267$	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	0.786387	−	0.617735i	$-0.211949\pi$
$269$	−1.67623	−	2.60826i	−0.102202	−	0.159029i	−0.888588	+	0.458706i	$0.848313\pi$
$270$	−0.930100	+	3.16763i	−0.0566041	+	0.192776i
$271$	5.17189	+	4.48146i	0.314170	+	0.272230i	0.797643	−	0.603129i	$-0.206080\pi$
$271$	5.17189	+	4.48146i	0.314170	+	0.272230i	−0.483474	+	0.875359i	$0.660625\pi$
$272$	−3.75631	+	1.10295i	−0.227760	+	0.0668764i
$273$	−2.13114	−	1.25161i	−0.128983	−	0.0757508i
$274$	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
$280$	−4.83476	−	26.1278i	−0.288932	−	1.56143i
$281$	−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	−0.817022	−	0.576607i	$-0.804376\pi$
$283$	−10.6306	+	6.83189i	−0.631925	+	0.406113i	0.185097	+	0.982720i	$0.440740\pi$
$284$	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
$287$	4.57973	−	18.2842i	0.270333	−	1.07928i
$288$	−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	0.581589	−	0.813483i	$-0.302431\pi$
$293$	10.8018	+	3.17170i	0.631050	+	0.185293i	0.0494612	+	0.998776i	$0.484250\pi$
$294$	−4.15463	−	5.44764i	−0.242303	−	0.317713i
$295$	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
$301$	0.295508	+	7.35182i	0.0170328	+	0.423752i
$302$	−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	$-0.266630\pi$
$307$	29.2438	−	13.3552i	1.66903	−	0.762222i	0.999817	−	0.0191540i	$-0.00609729\pi$
$308$	6.58352	+	9.39211i	0.375131	+	0.535165i
$309$	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	−0.0840131	−	0.996465i	$-0.526774\pi$
$311$	−7.85400	−	1.12924i	−0.445360	−	0.0640331i	−0.361347	+	0.932432i	$0.617683\pi$
$312$	2.33977	+	1.50368i	0.132463	+	0.0851289i
$313$	−13.5484	−	15.6356i	−0.765799	−	0.883779i	0.230200	−	0.973143i	$-0.426062\pi$
$313$	−13.5484	−	15.6356i	−0.765799	−	0.883779i	−0.995999	+	0.0893642i	$0.971516\pi$
$314$	6.16511	+	13.4997i	0.347917	+	0.761833i
$315$	−4.03037	−	7.96246i	−0.227086	−	0.448634i
$316$	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
$322$	−6.25943	+	10.7258i	−0.348824	+	0.597728i
$323$	−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
$329$	10.3110	−	5.21914i	0.568464	−	0.287741i
$330$	−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
$336$	1.26029	+	1.79794i	0.0687546	+	0.0980859i
$337$	−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
$343$	18.2685	+	3.04343i	0.986405	+	0.164330i
$344$		−	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	$-0.814839\pi$
$349$	−8.02728	−	27.3384i	−0.429690	−	1.46339i	0.405839	−	0.913945i	$-0.366980\pi$
$350$	−11.3077	−	12.0369i	−0.604424	−	0.643401i
$351$	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	0.0691924	−	0.997603i	$-0.477958\pi$
$353$	16.3165	−	7.45152i	0.868442	−	0.396604i	0.799250	+	0.600999i	$0.205231\pi$
$354$	−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
$357$	3.03252	−	12.1071i	0.160498	−	0.640774i
$358$	−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
$364$	−2.53252	+	0.468625i	−0.132740	+	0.0245626i
$365$	−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	$-0.549750\pi$
$367$	−5.96399			−0.311318			−0.155659	+	0.987811i	$0.549750\pi$
$368$	2.14248	−	3.35411i	0.111684	−	0.174845i
$369$			7.12426i			0.370874i
$370$	−19.2799	+	2.77203i	−1.00231	+	0.144111i
$371$	19.0325	−	32.4070i	0.988117	−	1.68249i
$372$	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
$378$	2.02352	+	1.61578i	0.104079	+	0.0831068i
$379$	−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	0.677474	−	0.735546i	$-0.263075\pi$
$383$	−6.30295	−	13.8015i	−0.322066	−	0.705226i	−0.999540	+	0.0303204i	$0.990347\pi$
$384$	2.01902	+	3.14166i	0.103033	+	0.160322i
$385$	34.3632	+	14.0539i	1.75131	+	0.716255i
$386$	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	$-0.796139\pi$
$397$	3.90078	−	13.2848i	0.195775	−	0.666747i	0.997603	−	0.0691930i	$-0.0220424\pi$
$398$	−12.9396	+	8.31580i	−0.648606	+	0.416834i
$399$	0.825291	+	2.44307i	0.0413162	+	0.122307i
$400$	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
$406$	−0.250134	+	0.0844973i	−0.0124139	+	0.00419353i
$407$	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	0.433098	−	0.901347i	$-0.357421\pi$
$409$	−8.03770	−	6.96471i	−0.397439	−	0.344383i	−0.830536	+	0.556964i	$0.811966\pi$
$410$	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	−0.673321	−	0.739350i	$-0.735133\pi$
$419$	3.15901	−	3.64569i	0.154328	−	0.178104i	0.827648	+	0.561247i	$0.189678\pi$
$420$	−8.60790	−	3.52048i	−0.420023	−	0.171782i
$421$	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
$427$	−15.0963	+	18.9058i	−0.730560	+	0.914917i
$428$	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	0.212707	−	0.977116i	$-0.431772\pi$
$433$	19.1422	−	5.62066i	0.919915	−	0.270112i	0.707209	+	0.707005i	$0.249954\pi$
$434$	3.64296	−	6.20295i	0.174868	−	0.297751i
$435$	−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	−0.460481	−	0.887670i	$-0.652323\pi$
$439$	−13.6656	+	1.96482i	−0.652223	+	0.0937756i	−0.191743	+	0.981445i	$0.561414\pi$
$440$	−38.0041	−	17.3559i	−1.81177	−	0.827409i
$441$	−6.97742	+	0.561826i	−0.332258	+	0.0267536i
$442$	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
$448$	17.1772	+	4.30245i	0.811545	+	0.203272i
$449$	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
$455$	−6.07605	+	5.70796i	−0.284849	+	0.267593i
$456$	−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	$0.0411610\pi$
$461$			5.53739i			0.257902i	−0.991651	+	0.128951i	$0.958839\pi$
$462$	−10.7637	+	0.432650i	−0.500773	+	0.0201287i
$463$	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	−0.589771	−	0.807571i	$-0.700782\pi$
$467$	−2.16487	+	1.39128i	−0.100178	+	0.0643806i	0.489593	+	0.871951i	$0.337146\pi$
$468$	0.885483	−	0.404387i	0.0409315	−	0.0186928i
$469$	7.21081	+	10.2870i	0.332964	+	0.475009i
$470$	−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
$476$	−5.87385	−	11.6045i	−0.269227	−	0.531889i
$477$	−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	−0.841905	−	0.539626i	$-0.818566\pi$
$479$	−27.5418	+	8.08699i	−1.25842	+	0.369504i	−0.416511	+	0.909131i	$0.636747\pi$
$480$	15.7787	+	7.20591i	0.720198	+	0.328903i
$481$	0.784361	+	5.45535i	0.0357638	+	0.248743i
$482$	2.24045			0.102050
$483$	5.76160	+	11.3050i	0.262162	+	0.514397i
$484$	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
$490$	−21.5793	+	8.26936i	−0.974855	+	0.373571i
$491$	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
$497$	4.44831	−	3.11811i	0.199534	−	0.139866i
$498$	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	−0.999999	−	0.00106518i	$-0.999661\pi$
$503$	−7.72261	+	16.9102i	−0.344334	+	0.753986i	0.655665	+	0.755052i	$0.272388\pi$
$504$	7.87106	−	0.316379i	0.350605	−	0.0140927i
$505$			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	0.103185	−	0.994662i	$-0.467097\pi$
$509$	−13.1070	−	5.98578i	−0.580959	−	0.265315i	−0.684144	+	0.729347i	$0.739824\pi$
$510$	4.38766	+	14.9430i	0.194289	+	0.661687i
$511$	−13.2818	+	12.4772i	−0.587551	+	0.551957i
$512$	−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
$518$	−3.71209	+	14.8202i	−0.163100	+	0.651162i
$519$	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	$0.00527130\pi$
$521$	8.16253	+	17.8734i	0.357607	+	0.783050i	−0.642256	+	0.766490i	$0.722001\pi$
$522$	0.0839489	−	0.0539507i	0.00367434	−	0.00236136i
$523$	25.5672	+	7.50719i	1.11797	+	0.328267i	0.787970	−	0.615713i	$-0.211132\pi$
$523$	25.5672	+	7.50719i	1.11797	+	0.328267i	0.330003	+	0.943980i	$0.392950\pi$
$524$	−12.6659	−	10.9750i	−0.553310	−	0.479446i
$525$	−16.5925	+	3.07032i	−0.724154	+	0.134000i
$526$	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
$532$	2.31717	+	1.36086i	0.100462	+	0.0590008i
$533$	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
$539$	20.4062	−	20.7747i	0.878957	−	0.894829i
$540$	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
$546$	0.915677	−	2.23892i	0.0391874	−	0.0958169i
$547$	−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
$560$	7.01666	−	2.37029i	0.296508	−	0.100163i
$561$	−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	$0.187693\pi$
$563$	−2.91845	+	20.2983i	−0.122998	+	0.855469i	−0.954130	+	0.299394i	$0.903216\pi$
$564$	−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
$567$	2.50659	−	0.846749i	0.105267	−	0.0355601i
$568$	−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	0.205190	−	0.978722i	$-0.434219\pi$
$577$	16.2815	−	2.34092i	0.677807	−	0.0974539i	0.472617	+	0.881268i	$0.343310\pi$
$578$	−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
$581$	−3.80440	+	9.30212i	−0.157833	+	0.385917i
$582$	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	0.671217	−	0.741261i	$-0.265772\pi$
$587$	26.8061	+	3.85414i	1.10641	+	0.159077i	0.435190	+	0.900339i	$0.356681\pi$
$588$	−5.11171	+	5.20401i	−0.210803	+	0.214610i
$589$	−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	0.332868	−	0.942974i	$-0.391984\pi$
$593$	−13.4697	−	11.6716i	−0.553136	−	0.479295i	−0.886003	+	0.463679i	$0.846529\pi$
$594$	3.90665	−	1.14710i	0.160292	−	0.0470660i
$595$	−36.3023	−	21.3202i	−1.48825	−	0.874041i
$596$	−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	0.920956	−	0.389667i	$-0.127410\pi$
$601$	30.1431	+	13.7659i	1.22956	+	0.561522i	0.308607	+	0.951190i	$0.400137\pi$
$602$	−7.08105	+	1.31030i	−0.288602	+	0.0534038i
$603$	−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	−0.675905	−	0.736989i	$-0.736247\pi$
$607$	−1.04977	+	0.909630i	−0.0426088	+	0.0369207i	0.633296	+	0.773910i	$0.281702\pi$
$608$	−4.21654	−	2.70981i	−0.171003	−	0.109897i
$609$	−0.0655428	+	0.261674i	−0.00265593	+	0.0106036i
$610$	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
$616$	−23.8844	+	22.4375i	−0.962332	+	0.904033i
$617$	−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	$-0.922669\pi$
$619$	−2.66440	−	18.5313i	−0.107091	−	0.744836i	0.863543	−	0.504276i	$-0.168240\pi$
$620$		−	9.76488i		−	0.392167i
$621$	−3.15061	−	3.61575i	−0.126430	−	0.145095i
$622$		−	7.76600i		−	0.311388i
$623$	−37.1219	+	1.49212i	−1.48726	+	0.0597807i
$624$	−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
$630$	7.15240	−	5.01357i	0.284959	−	0.199746i
$631$	−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
$637$	2.33986	+	6.10599i	0.0927086	+	0.241928i
$638$	−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	$-0.665801\pi$
$643$	−25.2379			−0.995286			−0.497643	+	0.867382i	$0.665801\pi$
$644$	12.2524	+	4.97152i	0.482812	+	0.195905i
$645$	−9.38050			−0.369357
$646$	−0.640426	−	4.45426i	−0.0251972	−	0.175250i
$647$	22.5824	+	10.3130i	0.887804	+	0.405446i	0.806494	−	0.591242i	$-0.201362\pi$
$647$	22.5824	+	10.3130i	0.887804	+	0.405446i	0.0813100	+	0.996689i	$0.474090\pi$
$648$	−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
$651$	−3.31932	−	6.55770i	−0.130094	−	0.257016i
$652$	−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
$658$	6.49234	+	9.26202i	0.253098	+	0.361071i
$659$	−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	0.587872	−	0.808954i	$-0.299966\pi$
$661$	16.5846	+	4.86968i	0.645067	+	0.189409i	0.0571953	+	0.998363i	$0.481784\pi$
$662$	−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
$665$	8.69121	−	0.349346i	0.337031	−	0.0135470i
$666$		−	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
$672$	9.91648	−	9.31574i	0.382537	−	0.359362i
$673$	−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	−0.0680773	−	0.997680i	$-0.521686\pi$
$677$	−26.1202	−	16.7864i	−1.00388	−	0.645154i	−0.935802	+	0.352526i	$0.885323\pi$
$678$	1.56384	−	10.8768i	0.0600591	−	0.417720i
$679$	−4.64838	−	1.16430i	−0.178389	−	0.0446819i
$680$	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
$686$	−0.403798	+	18.1218i	−0.0154171	+	0.691895i
$687$	−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	$0.0740800\pi$
$691$			12.1253i			0.461268i	−0.973041	+	0.230634i	$0.925920\pi$
$692$	19.6346	−	2.82302i	0.746394	−	0.107315i
$693$	−5.57388	+	9.49077i	−0.211734	+	0.360525i
$694$	−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
$700$	−10.9722	+	13.7411i	−0.414712	+	0.519364i
$701$	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
$707$	45.2616	+	18.5112i	1.70224	+	0.696185i
$708$	−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	$-0.752929\pi$
$719$	7.11859	−	24.2437i	0.265479	−	0.904137i	0.979061	−	0.203566i	$-0.0652532\pi$
$720$	−2.35491	+	1.51341i	−0.0877621	+	0.0564013i
$721$	−26.6997	+	9.01941i	−0.994350	+	0.335900i
$722$	−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	$0.156405\pi$
$727$	32.9821	+	38.0634i	1.22324	+	1.41169i	0.341546	+	0.939865i	$0.389049\pi$
$728$	−2.35505	−	6.97156i	−0.0872841	−	0.258383i
$729$	−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	$0.297399\pi$
$733$	−10.9005	+	23.8689i	−0.402621	+	0.881617i	−0.996998	+	0.0774303i	$0.975328\pi$
$734$	−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
$742$	34.0459	+	13.9242i	1.24986	+	0.511172i
$743$	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
$749$	−21.0485	−	16.8072i	−0.769094	−	0.614121i
$750$	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
$756$	1.39624	−	2.37742i	0.0507809	−	0.0864658i
$757$	−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	0.439695	−	0.898147i	$-0.355087\pi$
$761$	30.7481	−	4.42090i	1.11462	−	0.160258i	0.674921	+	0.737890i	$0.264177\pi$
$762$	−9.82494	−	4.48690i	−0.355920	−	0.162543i
$763$	8.55049	−	1.58221i	0.309549	−	0.0572798i
$764$	−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	−0.196422	−	0.980519i	$-0.562932\pi$
$769$	−32.4432	−	20.8500i	−1.16993	−	0.751869i	−0.973509	+	0.228651i	$0.926569\pi$
$770$	−8.82863	+	35.2475i	−0.318162	+	1.27023i
$771$	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	0.276580	−	0.960991i	$-0.410799\pi$
$773$	−19.8510	−	22.9093i	−0.713991	−	0.823989i	−0.990571	+	0.137002i	$0.956253\pi$
$774$	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
$777$	10.6880	+	11.3772i	0.383428	+	0.408155i
$778$	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
$784$	0.362561	−	5.79786i	0.0129486	−	0.207066i
$785$	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	−0.239099	−	0.970995i	$-0.576852\pi$
$787$	21.2096	−	24.4772i	0.756041	−	0.872518i	0.995139	+	0.0984778i	$0.0313973\pi$
$788$	−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
$791$	17.0504	+	24.3242i	0.606243	+	0.864870i
$792$	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	$-0.814133\pi$
$797$	−19.8916	−	43.5564i	−0.704595	−	1.54285i	0.129714	−	0.991551i	$-0.458594\pi$
$798$	−2.25182	+	1.13981i	−0.0797135	+	0.0403487i
$799$	−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
$805$	42.0637	−	7.90390i	1.48255	−	0.278576i
$806$	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	−0.933983	−	0.357319i	$-0.883691\pi$
$811$	1.27908	−	4.35615i	0.0449146	−	0.152965i	0.978897	+	0.204354i	$0.0655092\pi$
$812$	0.126953	+	0.250811i	0.00445519	+	0.00880174i
$813$	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
$819$	−1.41862	−	2.02381i	−0.0495705	−	0.0707177i
$820$	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
$826$	1.39258	+	34.6453i	0.0484539	+	1.20546i
$827$		−	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	$0.179815\pi$
$829$			30.8271i			1.07067i	−0.844640	+	0.535335i	$0.820185\pi$
$830$	−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
$833$	−26.2572	+	20.0250i	−0.909759	+	0.693824i
$834$	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	$-0.625508\pi$
$839$	7.08361	−	49.2676i	0.244553	−	1.70091i	0.628711	−	0.777639i	$-0.283583\pi$
$840$	6.45602	−	25.7751i	0.222754	−	0.889325i
$841$	−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
$847$	−3.03580	−	16.4059i	−0.104311	−	0.563715i
$848$	−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	−0.0771456	−	0.997020i	$-0.524581\pi$
$853$	3.78882	−	0.544750i	0.129727	−	0.0186519i	0.206872	+	0.978368i	$0.433672\pi$
$854$	−20.4181	−	11.9914i	−0.698693	−	0.410339i
$855$	−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	−0.879287	−	0.476292i	$-0.841981\pi$
$857$	3.45203	−	11.7565i	0.117919	−	0.401596i	0.997206	+	0.0746962i	$0.0237987\pi$
$858$	−2.05628	−	3.19964i	−0.0702004	−	0.109234i
$859$	−1.35699	+	0.619717i	−0.0462999	+	0.0211445i	−0.438430	−	0.898765i	$-0.644465\pi$
$859$	−1.35699	+	0.619717i	−0.0462999	+	0.0211445i	0.392130	+	0.919910i	$0.371738\pi$
$860$	−7.38767	+	6.40145i	−0.251917	+	0.218288i
$861$	11.7614	−	14.7294i	0.400827	−	0.501976i
$862$	−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
$868$	−7.08927	−	2.89938i	−0.240625	−	0.0984114i
$869$	−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	−0.327602	−	0.944816i	$-0.606240\pi$
$881$	11.7463	−	7.54888i	0.395743	−	0.254328i	0.723344	+	0.690488i	$0.242604\pi$
$882$	−1.51615	−	6.68125i	−0.0510514	−	0.224969i
$883$	−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	−0.997388	−	0.0722333i	$-0.976987\pi$
$887$	−15.4081	+	23.9754i	−0.517352	+	0.805016i	0.480036	+	0.877249i	$0.340624\pi$
$888$	−11.5037	−	13.2760i	−0.386040	−	0.445514i
$889$	27.6621	−	9.34450i	0.927757	−	0.313404i
$890$	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
$903$	−2.78525	+	6.81021i	−0.0926874	+	0.226629i
$904$	−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
$910$	−6.37601	−	5.09123i	−0.211363	−	0.168773i
$911$	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
$917$	−21.5482	+	36.6906i	−0.711583	+	1.21163i
$918$	−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
$924$	2.08696	+	11.2783i	0.0686560	+	0.371027i
$925$	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	−0.302762	−	0.953066i	$-0.597909\pi$
$929$	18.2120	−	15.7808i	0.597516	−	0.517750i	0.900278	+	0.435316i	$0.143363\pi$
$930$	7.71531	+	4.95833i	0.252995	+	0.162590i
$931$	2.32697	−	6.41352i	0.0762632	−	0.210194i
$932$	−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	−0.344919	−	0.938633i	$-0.612094\pi$
$937$	−34.9738	−	10.2692i	−1.14255	−	0.335482i	−0.797627	+	0.603151i	$0.793912\pi$
$938$	−8.96134	+	8.41846i	−0.292598	+	0.274872i
$939$	−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	0.999041	−	0.0437755i	$-0.0139386\pi$
$941$	0.863068	+	6.00277i	0.0281352	+	0.195685i	−0.970906	+	0.239460i	$0.923030\pi$
$942$			14.8408i			0.483541i
$943$	−32.8092	−	9.53525i	−1.06842	−	0.310510i
$944$		−	11.1122i		−	0.361671i
$945$	−0.358429	−	8.91719i	−0.0116597	−	0.290076i
$946$	−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
$952$	30.4297	−	21.3301i	0.986231	−	0.691312i
$953$	−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
$959$	−28.8089	+	14.5823i	−0.930289	+	0.470886i
$960$	−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
$966$	−10.1494	+	7.15631i	−0.326553	+	0.230250i
$967$	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	$0.502708\pi$
$971$	−31.0700	+	35.8567i	−0.997083	+	1.15070i	−0.988575	+	0.150731i	$0.951837\pi$
$972$	−0.293590	+	0.999875i	−0.00941689	+	0.0320710i
$973$	−34.6488	+	17.5382i	−1.11079	+	0.562250i
$974$	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
$980$	11.9849	+	21.4893i	0.382843	+	0.686451i
$981$	−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	−0.0204074	−	0.999792i	$-0.506496\pi$
$983$	−18.1252	−	5.32203i	−0.578103	−	0.169746i	−0.557696	+	0.830045i	$0.688314\pi$
$984$	−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
$987$	11.5473	−	0.464148i	0.367556	−	0.0147740i
$988$			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
$994$	3.64032	+	3.87507i	0.115464	+	0.122910i
$995$	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	−0.584880	−	0.811120i	$-0.698858\pi$
$997$	−11.2058	+	5.11752i	−0.354891	+	0.162073i	0.229989	+	0.973193i	$0.426131\pi$
$998$	−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.181.22	yes	320
7.6	odd	2	inner	483.2.r.a.181.21	✓	320
23.15	odd	22	inner	483.2.r.a.475.21	yes	320
161.153	even	22	inner	483.2.r.a.475.22	yes	320

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

\(f(q)\)	\(=\)	\(q+(0.139288 + 0.968769i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.999875 - 0.293590i) q^{4} +(2.20891 - 2.54922i) q^{5} +(-0.275740 + 0.939085i) q^{6} +(-1.19486 - 2.36058i) q^{7} +(1.23685 + 2.70832i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(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} +(-1.19486 - 2.36058i) 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} +(2.12042 - 1.48634i) 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} +(-0.106261 - 2.64362i) 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} +(-1.88775 - 2.00948i) 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} +(-8.65696 - 2.16835i) 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} +(2.54625 - 0.471166i) 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} +(-4.14464 + 5.64110i) 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} +(4.91534 - 6.15573i) 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} +(1.00154 - 2.44886i) 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} +(3.52253 + 10.4276i) 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} +(-0.882386 - 2.61209i) 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} +(-6.04222 - 3.22946i) 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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