LMFDB - Embedded newform 234.2.z.a.167.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			167.12
Character	$\chi$	$=$	234.167
Dual form			234.2.z.a.227.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(0.612305 + 1.62021i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.266463 + 0.994452i) q^{5} +(-1.40653 + 1.01078i) q^{6} +(-0.248284 + 0.248284i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.25016 + 1.98413i) q^{9} +(-0.891601 + 0.514766i) q^{10} +(3.50922 - 0.940292i) q^{11} +(-1.34038 - 1.09699i) q^{12} +(-3.13452 + 1.78180i) q^{13} +(-0.304085 - 0.175564i) q^{14} +(-1.44807 + 1.04063i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.67236 - 2.89660i) q^{17} +(-2.49890 - 1.65996i) q^{18} +(-0.969723 + 0.259837i) q^{19} +(-0.727989 - 0.727989i) q^{20} +(-0.554299 - 0.250247i) q^{21} +(1.81650 + 3.14628i) q^{22} +1.47052 q^{23} +(0.712697 - 1.57863i) q^{24} +(3.41219 - 1.97003i) q^{25} +(-2.53236 - 2.56655i) q^{26} +(-4.59249 - 2.43085i) q^{27} +(0.0908784 - 0.339163i) q^{28} +(5.04092 + 2.91038i) q^{29} +(-1.37996 - 1.12939i) q^{30} +(-5.54424 + 1.48558i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.67218 + 5.10993i) q^{33} +(3.23074 + 0.865675i) q^{34} +(-0.313065 - 0.180748i) q^{35} +(0.956637 - 2.84339i) q^{36} +(4.96682 + 1.33085i) q^{37} +(-0.501966 - 0.869430i) q^{38} +(-4.80617 - 3.98757i) q^{39} +(0.514766 - 0.891601i) q^{40} +(6.60980 - 6.60980i) q^{41} +(0.0982571 - 0.600180i) q^{42} +2.73886i q^{43} +(-2.56893 + 2.56893i) q^{44} +(-2.57270 - 1.70899i) q^{45} +(0.380599 + 1.42041i) q^{46} +(2.19251 - 8.18256i) q^{47} +(1.70930 + 0.279834i) q^{48} +6.87671i q^{49} +(2.78605 + 2.78605i) q^{50} +(5.71710 + 0.935962i) q^{51} +(1.82367 - 3.11034i) q^{52} +2.67501i q^{53} +(1.15940 - 5.06516i) q^{54} +(1.87015 + 3.23920i) q^{55} +0.351127 q^{56} +(-1.01476 - 1.41206i) q^{57} +(-1.50652 + 5.62241i) q^{58} +(1.25408 - 4.68030i) q^{59} +(0.733745 - 1.62525i) q^{60} +5.72649 q^{61} +(-2.86991 - 4.97083i) q^{62} +(0.0660532 - 1.05131i) q^{63} +1.00000i q^{64} +(-2.60715 - 2.64234i) q^{65} +(-3.98538 + 4.86960i) q^{66} +(-10.6589 - 10.6589i) q^{67} +3.34471i q^{68} +(0.900407 + 2.38255i) q^{69} +(0.0935622 - 0.349179i) q^{70} +(1.53985 + 5.74681i) q^{71} +(2.99410 + 0.188118i) q^{72} +(2.47165 - 2.47165i) q^{73} +5.14203i q^{74} +(5.28117 + 4.32221i) q^{75} +(0.709887 - 0.709887i) q^{76} +(-0.637824 + 1.10474i) q^{77} +(2.60777 - 5.67446i) q^{78} +(-1.76544 - 3.05783i) q^{79} +(0.994452 + 0.266463i) q^{80} +(1.12648 - 8.92922i) q^{81} +(8.09532 + 4.67384i) q^{82} +(-8.34680 - 2.23652i) q^{83} +(0.605160 - 0.0604289i) q^{84} +(3.32615 + 0.891240i) q^{85} +(-2.64553 + 0.708868i) q^{86} +(-1.62884 + 9.94939i) q^{87} +(-3.14628 - 1.81650i) q^{88} +(2.68520 - 10.0213i) q^{89} +(0.984889 - 2.92736i) q^{90} +(0.335858 - 1.22064i) q^{91} +(-1.27351 + 0.735260i) q^{92} +(-5.80171 - 8.07321i) q^{93} +8.47121 q^{94} +(-0.516790 - 0.895107i) q^{95} +(0.172100 + 1.72348i) q^{96} +(-10.4441 - 10.4441i) q^{97} +(-6.64239 + 1.77982i) q^{98} +(-6.03066 + 9.07854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.612305	+	1.62021i	0.353515	+	0.935429i
$3$	0.612305	+	1.62021i	0.353515	+	0.935429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.266463	+	0.994452i	0.119166	+	0.444732i	0.999565	−	0.0295011i	$-0.00939187\pi$
$5$	0.266463	+	0.994452i	0.119166	+	0.444732i	−0.880399	+	0.474234i	$0.842725\pi$
$6$	−1.40653	+	1.01078i	−0.574212	+	0.412650i
$7$	−0.248284	+	0.248284i	−0.0938426	+	0.0938426i	−0.752470	−	0.658627i	$-0.771138\pi$
$7$	−0.248284	+	0.248284i	−0.0938426	+	0.0938426i	0.658627	+	0.752470i	$0.271138\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.25016	+	1.98413i	−0.750055	+	0.661375i
$10$	−0.891601	+	0.514766i	−0.281949	+	0.162783i
$11$	3.50922	−	0.940292i	1.05807	−	0.283509i	0.312487	−	0.949922i	$-0.398838\pi$
$11$	3.50922	−	0.940292i	1.05807	−	0.283509i	0.745582	+	0.666413i	$0.232171\pi$
$12$	−1.34038	−	1.09699i	−0.386934	−	0.316674i
$13$	−3.13452	+	1.78180i	−0.869358	+	0.494182i
$13$	−3.13452	+	1.78180i	−0.869358	+	0.494182i
$14$	−0.304085	−	0.175564i	−0.0812701	−	0.0469213i
$15$	−1.44807	+	1.04063i	−0.373889	+	0.268690i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.67236	−	2.89660i	0.405606	−	0.702530i	−0.588786	−	0.808289i	$-0.700394\pi$
$17$	1.67236	−	2.89660i	0.405606	−	0.702530i	0.994392	+	0.105759i	$0.0337273\pi$
$18$	−2.49890	−	1.65996i	−0.588997	−	0.391257i
$19$	−0.969723	+	0.259837i	−0.222470	+	0.0596106i	−0.368332	−	0.929694i	$-0.620071\pi$
$19$	−0.969723	+	0.259837i	−0.222470	+	0.0596106i	0.145862	+	0.989305i	$0.453404\pi$
$20$	−0.727989	−	0.727989i	−0.162783	−	0.162783i
$21$	−0.554299	−	0.250247i	−0.120958	−	0.0546084i
$22$	1.81650	+	3.14628i	0.387280	+	0.670789i
$23$	1.47052			0.306625			0.153312	−	0.988178i	$-0.451006\pi$
$23$	1.47052			0.306625			0.153312	+	0.988178i	$0.451006\pi$
$24$	0.712697	−	1.57863i	0.145479	−	0.322236i
$25$	3.41219	−	1.97003i	0.682439	−	0.394006i
$26$	−2.53236	−	2.56655i	−0.496636	−	0.503341i
$27$	−4.59249	−	2.43085i	−0.883825	−	0.467817i
$28$	0.0908784	−	0.339163i	0.0171744	−	0.0640957i
$29$	5.04092	+	2.91038i	0.936075	+	0.540443i	0.888728	−	0.458435i	$-0.151590\pi$
$29$	5.04092	+	2.91038i	0.936075	+	0.540443i	0.0473474	+	0.998878i	$0.484923\pi$
$30$	−1.37996	−	1.12939i	−0.251945	−	0.206197i
$31$	−5.54424	+	1.48558i	−0.995775	+	0.266817i	−0.719675	−	0.694312i	$-0.755709\pi$
$31$	−5.54424	+	1.48558i	−0.995775	+	0.266817i	−0.276101	+	0.961129i	$0.589042\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	3.67218	+	5.10993i	0.639245	+	0.889524i
$34$	3.23074	+	0.865675i	0.554068	+	0.148462i
$35$	−0.313065	−	0.180748i	−0.0529177	−	0.0305520i
$36$	0.956637	−	2.84339i	0.159439	−	0.473898i
$37$	4.96682	+	1.33085i	0.816540	+	0.218791i	0.642833	−	0.766006i	$-0.277759\pi$
$37$	4.96682	+	1.33085i	0.816540	+	0.218791i	0.173707	+	0.984797i	$0.444426\pi$
$38$	−0.501966	−	0.869430i	−0.0814296	−	0.141040i
$39$	−4.80617	−	3.98757i	−0.769603	−	0.638522i
$40$	0.514766	−	0.891601i	0.0813917	−	0.140975i
$41$	6.60980	−	6.60980i	1.03228	−	1.03228i	0.0328164	−	0.999461i	$-0.489552\pi$
$41$	6.60980	−	6.60980i	1.03228	−	1.03228i	0.999461	−	0.0328164i	$-0.0104476\pi$
$42$	0.0982571	−	0.600180i	0.0151614	−	0.0926098i
$43$			2.73886i			0.417672i	0.977951	+	0.208836i	$0.0669674\pi$
$43$			2.73886i			0.417672i	−0.977951	+	0.208836i	$0.933033\pi$
$44$	−2.56893	+	2.56893i	−0.387280	+	0.387280i
$45$	−2.57270	−	1.70899i	−0.383516	−	0.254761i
$46$	0.380599	+	1.42041i	0.0561162	+	0.209429i
$47$	2.19251	−	8.18256i	0.319811	−	1.19355i	−0.599616	−	0.800288i	$-0.704680\pi$
$47$	2.19251	−	8.18256i	0.319811	−	1.19355i	0.919427	−	0.393262i	$-0.128653\pi$
$48$	1.70930	+	0.279834i	0.246716	+	0.0403905i
$49$			6.87671i			0.982387i
$50$	2.78605	+	2.78605i	0.394006	+	0.394006i
$51$	5.71710	+	0.935962i	0.800554	+	0.131061i
$52$	1.82367	−	3.11034i	0.252898	−	0.431327i
$53$			2.67501i			0.367442i	0.982978	+	0.183721i	$0.0588142\pi$
$53$			2.67501i			0.367442i	−0.982978	+	0.183721i	$0.941186\pi$
$54$	1.15940	−	5.06516i	0.157774	−	0.689280i
$55$	1.87015	+	3.23920i	0.252171	+	0.436773i
$56$	0.351127			0.0469213
$57$	−1.01476	−	1.41206i	−0.134408	−	0.187031i
$58$	−1.50652	+	5.62241i	−0.197816	+	0.738259i
$59$	1.25408	−	4.68030i	0.163268	−	0.609323i	−0.834987	−	0.550269i	$-0.814525\pi$
$59$	1.25408	−	4.68030i	0.163268	−	0.609323i	0.998255	−	0.0590536i	$-0.0188083\pi$
$60$	0.733745	−	1.62525i	0.0947260	−	0.209819i
$61$	5.72649			0.733202			0.366601	−	0.930378i	$-0.380521\pi$
$61$	5.72649			0.733202			0.366601	+	0.930378i	$0.380521\pi$
$62$	−2.86991	−	4.97083i	−0.364479	−	0.631296i
$63$	0.0660532	−	1.05131i	0.00832192	−	0.132452i
$64$			1.00000i			0.125000i
$65$	−2.60715	−	2.64234i	−0.323377	−	0.327742i
$66$	−3.98538	+	4.86960i	−0.490566	+	0.599407i
$67$	−10.6589	−	10.6589i	−1.30219	−	1.30219i	−0.926911	−	0.375282i	$-0.877546\pi$
$67$	−10.6589	−	10.6589i	−1.30219	−	1.30219i	−0.375282	−	0.926911i	$-0.622454\pi$
$68$			3.34471i			0.405606i
$69$	0.900407	+	2.38255i	0.108396	+	0.286826i
$70$	0.0935622	−	0.349179i	0.0111828	−	0.0417349i
$71$	1.53985	+	5.74681i	0.182747	+	0.682021i	0.995102	+	0.0988571i	$0.0315187\pi$
$71$	1.53985	+	5.74681i	0.182747	+	0.682021i	−0.812355	+	0.583164i	$0.801815\pi$
$72$	2.99410	+	0.188118i	0.352858	+	0.0221699i
$73$	2.47165	−	2.47165i	0.289285	−	0.289285i	−0.547513	−	0.836797i	$-0.684425\pi$
$73$	2.47165	−	2.47165i	0.289285	−	0.289285i	0.836797	+	0.547513i	$0.184425\pi$
$74$			5.14203i			0.597749i
$75$	5.28117	+	4.32221i	0.609817	+	0.499086i
$76$	0.709887	−	0.709887i	0.0814296	−	0.0814296i
$77$	−0.637824	+	1.10474i	−0.0726868	+	0.125897i
$78$	2.60777	−	5.67446i	0.295272	−	0.642506i
$79$	−1.76544	−	3.05783i	−0.198627	−	0.344033i	0.749456	−	0.662054i	$-0.230315\pi$
$79$	−1.76544	−	3.05783i	−0.198627	−	0.344033i	−0.948084	+	0.318021i	$0.896982\pi$
$80$	0.994452	+	0.266463i	0.111183	+	0.0297914i
$81$	1.12648	−	8.92922i	0.125165	−	0.992136i
$82$	8.09532	+	4.67384i	0.893979	+	0.516139i
$83$	−8.34680	−	2.23652i	−0.916181	−	0.245490i	−0.230228	−	0.973137i	$-0.573947\pi$
$83$	−8.34680	−	2.23652i	−0.916181	−	0.245490i	−0.685952	+	0.727647i	$0.740614\pi$
$84$	0.605160	−	0.0604289i	0.0660284	−	0.00659334i
$85$	3.32615	+	0.891240i	0.360772	+	0.0966686i
$86$	−2.64553	+	0.708868i	−0.285275	+	0.0764392i
$87$	−1.62884	+	9.94939i	−0.174630	+	1.06669i
$88$	−3.14628	−	1.81650i	−0.335394	−	0.193640i
$89$	2.68520	−	10.0213i	0.284630	−	1.06225i	−0.664479	−	0.747307i	$-0.731347\pi$
$89$	2.68520	−	10.0213i	0.284630	−	1.06225i	0.949109	−	0.314947i	$-0.101987\pi$
$90$	0.984889	−	2.92736i	0.103816	−	0.308571i
$91$	0.335858	−	1.22064i	0.0352075	−	0.127958i
$92$	−1.27351	+	0.735260i	−0.132772	+	0.0766562i
$93$	−5.80171	−	8.07321i	−0.601610	−	0.837153i
$94$	8.47121			0.873739
$95$	−0.516790	−	0.895107i	−0.0530215	−	0.0918360i
$96$	0.172100	+	1.72348i	0.0175649	+	0.175902i
$97$	−10.4441	−	10.4441i	−1.06044	−	1.06044i	−0.998052	−	0.0623848i	$-0.980129\pi$
$97$	−10.4441	−	10.4441i	−1.06044	−	1.06044i	−0.0623848	−	0.998052i	$-0.519871\pi$
$98$	−6.64239	+	1.77982i	−0.670983	+	0.179789i
$99$	−6.03066	+	9.07854i	−0.606104	+	0.912428i
$100$	−1.97003	+	3.41219i	−0.197003	+	0.341219i
$101$	−8.67108	+	15.0187i	−0.862804	+	1.49442i	0.00640634	+	0.999979i	$0.497961\pi$
$101$	−8.67108	+	15.0187i	−0.862804	+	1.49442i	−0.869211	+	0.494442i	$0.835373\pi$
$102$	0.575624	+	5.76454i	0.0569953	+	0.570774i
$103$	−9.22402	−	5.32549i	−0.908870	−	0.524736i	−0.0288023	−	0.999585i	$-0.509169\pi$
$103$	−9.22402	−	5.32549i	−0.908870	−	0.524736i	−0.880067	+	0.474849i	$0.842503\pi$
$104$	3.47636	+	0.956515i	0.340885	+	0.0937940i
$105$	0.101159	−	0.617905i	0.00987210	−	0.0603013i
$106$	−2.58387	+	0.692345i	−0.250967	+	0.0672465i
$107$	−0.693025	+	0.400118i	−0.0669973	+	0.0386809i	−0.533124	−	0.846037i	$-0.678982\pi$
$107$	−0.693025	+	0.400118i	−0.0669973	+	0.0386809i	0.466127	+	0.884718i	$0.345649\pi$
$108$	5.19264	−	0.191067i	0.499662	−	0.0183854i
$109$	5.83921	+	5.83921i	0.559294	+	0.559294i	0.929107	−	0.369812i	$-0.120578\pi$
$109$	5.83921	+	5.83921i	0.559294	+	0.559294i	−0.369812	+	0.929107i	$0.620578\pi$
$110$	−2.64479	+	2.64479i	−0.252171	+	0.252171i
$111$	0.884943	+	8.86218i	0.0839950	+	0.841161i
$112$	0.0908784	+	0.339163i	0.00858720	+	0.0320479i
$113$	−11.6846	+	6.74613i	−1.09920	+	0.634623i	−0.936010	−	0.351972i	$-0.885511\pi$
$113$	−11.6846	+	6.74613i	−1.09920	+	0.634623i	−0.163188	+	0.986595i	$0.552178\pi$
$114$	1.10130	−	1.34565i	0.103147	−	0.126031i
$115$	0.391839	+	1.46236i	0.0365391	+	0.136366i
$116$	−5.82075			−0.540443
$117$	3.51786	−	10.2286i	0.325227	−	0.945636i
$118$	4.84540			0.446055
$119$	0.303962	+	1.13440i	0.0278641	+	0.103990i
$120$	1.75978	+	0.288098i	0.160645	+	0.0262996i
$121$	1.90418	−	1.09938i	0.173107	−	0.0999436i
$122$	1.48213	+	5.53137i	0.134185	+	0.500787i
$123$	14.7565	+	6.66206i	1.33055	+	0.600697i
$124$	4.05867	−	4.05867i	0.364479	−	0.364479i
$125$	6.50827	+	6.50827i	0.582117	+	0.582117i
$126$	1.03258	−	0.208296i	0.0919897	−	0.0185565i
$127$	−16.2637	+	9.38987i	−1.44317	+	0.833216i	−0.998060	−	0.0622590i	$-0.980170\pi$
$127$	−16.2637	+	9.38987i	−1.44317	+	0.833216i	−0.445112	+	0.895475i	$0.646836\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−4.43753	+	1.67702i	−0.390702	+	0.147653i
$130$	1.87753	−	3.20220i	0.164670	−	0.280851i
$131$	−2.91497	−	1.68296i	−0.254682	−	0.147041i	0.367224	−	0.930133i	$-0.380308\pi$
$131$	−2.91497	−	1.68296i	−0.254682	−	0.147041i	−0.621906	+	0.783092i	$0.713642\pi$
$132$	−5.73517	−	2.58923i	−0.499182	−	0.225364i
$133$	0.176254	−	0.305280i	0.0152831	−	0.0264712i
$134$	7.53699	−	13.0544i	0.651096	−	1.12773i
$135$	1.19364	−	5.21474i	0.102732	−	0.448814i
$136$	−3.23074	+	0.865675i	−0.277034	+	0.0742310i
$137$	2.75305	+	2.75305i	0.235209	+	0.235209i	0.814863	−	0.579654i	$-0.196812\pi$
$137$	2.75305	+	2.75305i	0.235209	+	0.235209i	−0.579654	+	0.814863i	$0.696812\pi$
$138$	−2.06833	+	1.48638i	−0.176068	+	0.126529i
$139$	−0.276245	−	0.478471i	−0.0234308	−	0.0405833i	0.854072	−	0.520154i	$-0.174126\pi$
$139$	−0.276245	−	0.478471i	−0.0234308	−	0.0405833i	−0.877503	+	0.479571i	$0.840792\pi$
$140$	0.361497			0.0305520
$141$	14.6000	−	1.45790i	1.22954	−	0.122777i
$142$	−5.15245	+	2.97477i	−0.432384	+	0.249637i
$143$	−9.32429	+	9.20008i	−0.779736	+	0.769350i
$144$	0.593221	+	2.94076i	0.0494351	+	0.245064i
$145$	−1.55101	+	5.78846i	−0.128805	+	0.480705i
$146$	3.02714	+	1.74772i	0.250528	+	0.144642i
$147$	−11.1417	+	4.21064i	−0.918953	+	0.347288i
$148$	−4.96682	+	1.33085i	−0.408270	+	0.109396i
$149$	−12.5052	−	3.35075i	−1.02446	−	0.274504i	−0.292803	−	0.956173i	$-0.594588\pi$
$149$	−12.5052	−	3.35075i	−1.02446	−	0.274504i	−0.731661	+	0.681669i	$0.761255\pi$
$150$	−2.80807	+	6.21989i	−0.229278	+	0.507852i
$151$	−8.72875	−	2.33886i	−0.710336	−	0.190334i	−0.114480	−	0.993426i	$-0.536520\pi$
$151$	−8.72875	−	2.33886i	−0.710336	−	0.190334i	−0.595856	+	0.803092i	$0.703187\pi$
$152$	0.869430	+	0.501966i	0.0705201	+	0.0407148i
$153$	1.98415	+	9.83600i	0.160409	+	0.795194i
$154$	−1.23218	−	0.330162i	−0.0992920	−	0.0266052i
$155$	−2.95467	−	5.11763i	−0.237325	−	0.411058i
$156$	6.15605	+	1.05025i	0.492879	+	0.0840876i
$157$	5.60064	−	9.70059i	0.446980	−	0.774191i	−0.551208	−	0.834368i	$-0.685833\pi$
$157$	5.60064	−	9.70059i	0.446980	−	0.774191i	0.998188	+	0.0601763i	$0.0191663\pi$
$158$	2.49671	−	2.49671i	0.198627	−	0.198627i
$159$	−4.33409	+	1.63793i	−0.343715	+	0.129896i
$160$			1.02953i			0.0813917i
$161$	−0.365107	+	0.365107i	−0.0287745	+	0.0287745i
$162$	8.91652	−	1.22295i	0.700548	−	0.0960842i
$163$	−2.29883	−	8.57937i	−0.180059	−	0.671988i	−0.995635	−	0.0933377i	$-0.970246\pi$
$163$	−2.29883	−	8.57937i	−0.180059	−	0.671988i	0.815576	−	0.578650i	$-0.196420\pi$
$164$	−2.41936	+	9.02916i	−0.188920	+	0.705059i
$165$	−4.10308	+	5.01341i	−0.319424	+	0.390294i
$166$		−	8.64124i		−	0.670691i
$167$	−6.56988	−	6.56988i	−0.508392	−	0.508392i	0.405640	−	0.914033i	$-0.367049\pi$
$167$	−6.56988	−	6.56988i	−0.508392	−	0.508392i	−0.914033	+	0.405640i	$0.867049\pi$
$168$	0.214997	+	0.568900i	0.0165874	+	0.0438916i
$169$	6.65038	−	11.1702i	0.511568	−	0.859243i
$170$			3.44349i			0.264103i
$171$	1.66649	−	2.50873i	0.127440	−	0.191847i
$172$	−1.36943	−	2.37192i	−0.104418	−	0.180857i
$173$	10.5884			0.805023			0.402512	−	0.915415i	$-0.368137\pi$
$173$	10.5884			0.805023			0.402512	+	0.915415i	$0.368137\pi$
$174$	−10.0319	+	1.00175i	−0.760520	+	0.0759425i
$175$	−0.358066	+	1.33632i	−0.0270673	+	0.101016i
$176$	0.940292	−	3.50922i	0.0708772	−	0.264517i
$177$	8.35095	−	0.833893i	0.627696	−	0.0626792i
$178$	10.3748			0.777624
$179$	12.5097	+	21.6674i	0.935018	+	1.61950i	0.774601	+	0.632450i	$0.217951\pi$
$179$	12.5097	+	21.6674i	0.935018	+	1.61950i	0.160417	+	0.987049i	$0.448716\pi$
$180$	3.08252	+	0.193673i	0.229757	+	0.0144356i
$181$		−	23.3875i		−	1.73838i	−0.494482	−	0.869188i	$-0.664642\pi$
$181$		−	23.3875i		−	1.73838i	0.494482	−	0.869188i	$-0.335358\pi$
$182$	1.26598	+	0.00848836i	0.0938405	+	0.000629199i
$183$	3.50636	+	9.27813i	0.259198	+	0.685859i
$184$	−1.03981	−	1.03981i	−0.0766562	−	0.0766562i
$185$			5.29389i			0.389214i
$186$	6.29653	−	7.69353i	0.461684	−	0.564117i
$187$	3.14500	−	11.7373i	0.229986	−	0.858318i
$188$	2.19251	+	8.18256i	0.159905	+	0.596775i
$189$	1.74379	−	0.536701i	0.126842	−	0.0390393i
$190$	0.730852	−	0.730852i	0.0530215	−	0.0530215i
$191$		−	12.3120i		−	0.890865i	−0.895316	−	0.445432i	$-0.853050\pi$
$191$		−	12.3120i		−	0.890865i	0.895316	−	0.445432i	$-0.146950\pi$
$192$	−1.62021	+	0.612305i	−0.116929	+	0.0441893i
$193$	−9.14996	+	9.14996i	−0.658629	+	0.658629i	−0.955056	−	0.296427i	$-0.904205\pi$
$193$	−9.14996	+	9.14996i	−0.658629	+	0.658629i	0.296427	+	0.955056i	$0.404205\pi$
$194$	7.38509	−	12.7913i	0.530218	−	0.918365i
$195$	2.68478	−	5.84204i	0.192261	−	0.418358i
$196$	−3.43835	−	5.95541i	−0.245597	−	0.425386i
$197$	20.6372	+	5.52972i	1.47034	+	0.393976i	0.903048	−	0.429540i	$-0.141324\pi$
$197$	20.6372	+	5.52972i	1.47034	+	0.393976i	0.567292	+	0.823517i	$0.307991\pi$
$198$	−10.3300	−	3.47547i	−0.734125	−	0.246991i
$199$	19.2376	+	11.1069i	1.36372	+	0.787344i	0.990117	−	0.140245i	$-0.0447889\pi$
$199$	19.2376	+	11.1069i	1.36372	+	0.787344i	0.373603	+	0.927589i	$0.378122\pi$
$200$	−3.80581	−	1.01976i	−0.269111	−	0.0721082i
$201$	10.7432	−	23.7962i	0.757765	−	1.67845i
$202$	−16.7512	−	4.48848i	−1.17861	−	0.315808i
$203$	−1.97418	+	0.528980i	−0.138560	+	0.0371271i
$204$	−5.41914	+	2.04798i	−0.379415	+	0.143387i
$205$	8.33440	+	4.81187i	0.582100	+	0.336075i
$206$	2.75668	−	10.2881i	0.192067	−	0.716803i
$207$	−3.30891	+	2.91770i	−0.229985	+	0.202794i
$208$	−0.0241746	+	3.60547i	−0.00167621	+	0.249994i
$209$	−3.15865	+	1.82365i	−0.218488	+	0.126144i
$210$	0.623032	−	0.0622135i	0.0429933	−	0.00429314i
$211$	18.3511			1.26334			0.631670	−	0.775237i	$-0.282370\pi$
$211$	18.3511			1.26334			0.631670	+	0.775237i	$0.282370\pi$
$212$	−1.33751	−	2.31663i	−0.0918604	−	0.159107i
$213$	−8.36818	+	6.01369i	−0.573378	+	0.412051i
$214$	−0.565853	−	0.565853i	−0.0386809	−	0.0386809i
$215$	−2.72366	+	0.729803i	−0.185752	+	0.0497722i
$216$	1.52851	+	4.96625i	0.104002	+	0.337911i
$217$	1.00770	−	1.74539i	0.0684073	−	0.118485i
$218$	−4.12894	+	7.15154i	−0.279647	+	0.484363i
$219$	5.51800	+	2.49119i	0.372872	+	0.168339i
$220$	−3.23920	−	1.87015i	−0.218387	−	0.126086i
$221$	−0.0808571	+	12.0593i	−0.00543904	+	0.811193i
$222$	−8.33117	+	3.14849i	−0.559151	+	0.211313i
$223$	−24.4901	+	6.56211i	−1.63998	+	0.439432i	−0.956783	−	0.290802i	$-0.906078\pi$
$223$	−24.4901	+	6.56211i	−1.63998	+	0.439432i	−0.683198	+	0.730233i	$0.739411\pi$
$224$	−0.304085	+	0.175564i	−0.0203175	+	0.0117303i
$225$	−3.76921	+	11.2031i	−0.251281	+	0.746875i
$226$	−9.54047	−	9.54047i	−0.634623	−	0.634623i
$227$	17.6248	−	17.6248i	1.16980	−	1.16980i	0.187539	−	0.982257i	$-0.439949\pi$
$227$	17.6248	−	17.6248i	1.16980	−	1.16980i	0.982257	−	0.187539i	$-0.0600511\pi$
$228$	1.58483	+	0.715499i	0.104958	+	0.0473851i
$229$	0.401688	+	1.49912i	0.0265443	+	0.0990647i	0.977927	−	0.208946i	$-0.0670033\pi$
$229$	0.401688	+	1.49912i	0.0265443	+	0.0990647i	−0.951383	+	0.308011i	$0.900337\pi$
$230$	−1.31112	+	0.756974i	−0.0864525	+	0.0499134i
$231$	−2.18046	−	0.356969i	−0.143464	−	0.0234868i
$232$	−1.50652	−	5.62241i	−0.0989080	−	0.369130i
$233$	−9.96467			−0.652807			−0.326403	−	0.945231i	$-0.605837\pi$
$233$	−9.96467			−0.652807			−0.326403	+	0.945231i	$0.605837\pi$
$234$	10.7906	+	0.750634i	0.705402	+	0.0490705i
$235$	8.72139			0.568921
$236$	1.25408	+	4.68030i	0.0816338	+	0.304661i
$237$	3.87334	−	4.73271i	0.251600	−	0.307422i
$238$	−1.01708	+	0.587209i	−0.0659272	+	0.0380631i
$239$	−0.0186887	−	0.0697473i	−0.00120887	−	0.00451158i	0.965319	−	0.261074i	$-0.0840767\pi$
$239$	−0.0186887	−	0.0697473i	−0.00120887	−	0.00451158i	−0.966528	+	0.256563i	$0.917410\pi$
$240$	0.177182	+	1.77438i	0.0114371	+	0.114536i
$241$	13.2296	−	13.2296i	0.852192	−	0.852192i	−0.138211	−	0.990403i	$-0.544135\pi$
$241$	13.2296	−	13.2296i	0.852192	−	0.852192i	0.990403	+	0.138211i	$0.0441351\pi$
$242$	1.55476	+	1.55476i	0.0999436	+	0.0999436i
$243$	15.1570	−	3.64227i	0.972320	−	0.233651i
$244$	−4.95929	+	2.86325i	−0.317486	+	0.183301i
$245$	−6.83856	+	1.83239i	−0.436899	+	0.117067i
$246$	−2.61579	+	15.9779i	−0.166777	+	1.01872i
$247$	2.57664	−	2.54231i	0.163947	−	0.161764i
$248$	4.97083	+	2.86991i	0.315648	+	0.182240i
$249$	−1.48716	−	14.8930i	−0.0942448	−	0.943806i
$250$	−4.60204	+	7.97097i	−0.291059	+	0.504129i
$251$	10.5789	−	18.3232i	0.667735	−	1.15655i	−0.310802	−	0.950475i	$-0.600597\pi$
$251$	10.5789	−	18.3232i	0.667735	−	1.15655i	0.978536	−	0.206075i	$-0.0660692\pi$
$252$	0.468450	+	0.943486i	0.0295096	+	0.0594340i
$253$	5.16037	−	1.38272i	0.324430	−	0.0869308i
$254$	−13.2793	−	13.2793i	−0.833216	−	0.833216i
$255$	0.592624	+	5.93478i	0.0371116	+	0.371650i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.6439			−0.913460			−0.456730	−	0.889605i	$-0.650979\pi$
$257$	−14.6439			−0.913460			−0.456730	+	0.889605i	$0.650979\pi$
$258$	−2.76839	−	3.85228i	−0.172352	−	0.239832i
$259$	−1.56361	+	0.902752i	−0.0971582	+	0.0560943i
$260$	3.57903	+	0.984764i	0.221962	+	0.0610724i
$261$	−17.1175	+	3.45299i	−1.05954	+	0.213735i
$262$	0.871165	−	3.25123i	0.0538207	−	0.200862i
$263$	9.98128	+	5.76269i	0.615472	+	0.355343i	0.775104	−	0.631834i	$-0.217697\pi$
$263$	9.98128	+	5.76269i	0.615472	+	0.355343i	−0.159632	+	0.987177i	$0.551031\pi$
$264$	1.01664	−	6.20989i	0.0625697	−	0.382192i
$265$	−2.66017	+	0.712791i	−0.163413	+	0.0437864i
$266$	0.340496	+	0.0912356i	0.0208772	+	0.00559402i
$267$	17.8808	−	1.78550i	1.09428	−	0.109271i
$268$	14.5603	+	3.90143i	0.889414	+	0.238318i
$269$	−17.7279	−	10.2352i	−1.08089	−	0.624052i	−0.149754	−	0.988723i	$-0.547848\pi$
$269$	−17.7279	−	10.2352i	−1.08089	−	0.624052i	−0.931136	+	0.364671i	$0.881182\pi$
$270$	5.34599	−	0.196709i	0.325347	−	0.0119714i
$271$	0.537040	+	0.143899i	0.0326229	+	0.00874127i	0.275094	−	0.961417i	$-0.411291\pi$
$271$	0.537040	+	0.143899i	0.0326229	+	0.00874127i	−0.242471	+	0.970159i	$0.577958\pi$
$272$	−1.67236	−	2.89660i	−0.101401	−	0.175632i
$273$	2.18335	−	0.203245i	0.132142	−	0.0123010i
$274$	−1.94670	+	3.37178i	−0.117604	+	0.203697i
$275$	10.1217	−	10.1217i	0.610363	−	0.610363i
$276$	−1.97105	−	1.61315i	−0.118643	−	0.0971001i
$277$			12.0749i			0.725509i	0.931885	+	0.362754i	$0.118164\pi$
$277$			12.0749i			0.725509i	−0.931885	+	0.362754i	$0.881836\pi$
$278$	0.390670	−	0.390670i	0.0234308	−	0.0234308i
$279$	9.52789	−	14.3433i	0.570420	−	0.858709i
$280$	0.0935622	+	0.349179i	0.00559141	+	0.0208674i
$281$	3.77024	−	14.0707i	0.224913	−	0.839388i	−0.757526	−	0.652805i	$-0.773592\pi$
$281$	3.77024	−	14.0707i	0.224913	−	0.839388i	0.982439	−	0.186583i	$-0.0597414\pi$
$282$	5.18697	+	13.7251i	0.308879	+	0.817321i
$283$			13.3436i			0.793192i	0.917993	+	0.396596i	$0.129809\pi$
$283$			13.3436i			0.793192i	−0.917993	+	0.396596i	$0.870191\pi$
$284$	−4.20696	−	4.20696i	−0.249637	−	0.249637i
$285$	1.13383	−	1.38539i	0.0671622	−	0.0820632i
$286$	−11.2999	−	6.62541i	−0.668177	−	0.391769i
$287$			3.28222i			0.193743i
$288$	−2.68702	+	1.33413i	−0.158334	+	0.0786146i
$289$	2.90646	+	5.03413i	0.170968	+	0.296125i
$290$	−5.99265			−0.351901
$291$	10.5267	−	23.3166i	0.617084	−	1.36684i
$292$	−0.904687	+	3.37634i	−0.0529428	+	0.197585i
$293$	−5.46383	+	20.3913i	−0.319200	+	1.19127i	0.600815	+	0.799388i	$0.294843\pi$
$293$	−5.46383	+	20.3913i	−0.319200	+	1.19127i	−0.920015	+	0.391883i	$0.871824\pi$
$294$	−6.95086	−	9.67228i	−0.405382	−	0.564099i
$295$	4.98850			0.290442
$296$	−2.57101	−	4.45313i	−0.149437	−	0.258833i
$297$	−18.4018	−	4.21210i	−1.06778	−	0.244411i
$298$		−	12.9463i		−	0.749960i
$299$	−4.60937	+	2.62017i	−0.266567	+	0.151528i
$300$	−6.73473	−	1.10256i	−0.388830	−	0.0636564i
$301$	−0.680015	−	0.680015i	−0.0391954	−	0.0391954i
$302$		−	9.03667i		−	0.520002i
$303$	−29.6429	−	4.85292i	−1.70294	−	0.278793i
$304$	−0.259837	+	0.969723i	−0.0149027	+	0.0556174i
$305$	1.52590	+	5.69472i	0.0873726	+	0.326079i
$306$	−8.98731	+	4.46229i	−0.513770	+	0.255092i
$307$	−10.9437	+	10.9437i	−0.624590	+	0.624590i	−0.946702	−	0.322111i	$-0.895607\pi$
$307$	−10.9437	+	10.9437i	−0.624590	+	0.624590i	0.322111	+	0.946702i	$0.395607\pi$
$308$		−	1.27565i		−	0.0726868i
$309$	2.98050	−	18.2057i	0.169555	−	1.03568i
$310$	4.17853	−	4.17853i	0.237325	−	0.237325i
$311$	−12.9553	+	22.4392i	−0.734626	+	1.27241i	0.220262	+	0.975441i	$0.429309\pi$
$311$	−12.9553	+	22.4392i	−0.734626	+	1.27241i	−0.954887	+	0.296968i	$0.904024\pi$
$312$	0.578837	+	6.21811i	0.0327702	+	0.352031i
$313$	17.6482	+	30.5676i	0.997537	+	1.72779i	0.559509	+	0.828824i	$0.310990\pi$
$313$	17.6482	+	30.5676i	0.997537	+	1.72779i	0.438028	+	0.898961i	$0.355677\pi$
$314$	10.8196	+	2.89910i	0.610586	+	0.163606i
$315$	1.06308	−	0.214448i	0.0598976	−	0.0120828i
$316$	3.05783	+	1.76544i	0.172016	+	0.0993137i
$317$	−12.2048	−	3.27025i	−0.685487	−	0.183676i	−0.100766	−	0.994910i	$-0.532129\pi$
$317$	−12.2048	−	3.27025i	−0.685487	−	0.183676i	−0.584721	+	0.811234i	$0.698796\pi$
$318$	−2.70386	−	3.76248i	−0.151625	−	0.210989i
$319$	20.4263	+	5.47321i	1.14365	+	0.306441i
$320$	−0.994452	+	0.266463i	−0.0555916	+	0.0148957i
$321$	−1.07262	−	0.877852i	−0.0598677	−	0.0489969i
$322$	−0.447163	−	0.258170i	−0.0249194	−	0.0143872i
$323$	−0.869078	+	3.24344i	−0.0483568	+	0.180470i
$324$	3.48905	+	8.29618i	0.193836	+	0.460899i
$325$	−7.18538	+	12.2549i	−0.398573	+	0.679782i
$326$	7.69205	−	4.44101i	0.426023	−	0.245965i
$327$	−5.88537	+	13.0361i	−0.325462	+	0.720899i
$328$	−9.34767			−0.516139
$329$	1.48724	+	2.57597i	0.0819940	+	0.142018i
$330$	−5.90454	−	2.66570i	−0.325034	−	0.146742i
$331$	−7.04833	−	7.04833i	−0.387411	−	0.387411i	0.486352	−	0.873763i	$-0.338327\pi$
$331$	−7.04833	−	7.04833i	−0.387411	−	0.387411i	−0.873763	+	0.486352i	$0.838327\pi$
$332$	8.34680	−	2.23652i	0.458090	−	0.122745i
$333$	−13.8167	+	6.86015i	−0.757153	+	0.375934i
$334$	4.64560	−	8.04642i	0.254196	−	0.440281i
$335$	7.75957	−	13.4400i	0.423951	−	0.734304i
$336$	−0.493870	+	0.354913i	−0.0269428	+	0.0193621i
$337$	25.2475	+	14.5766i	1.37532	+	0.794040i	0.991592	−	0.129406i	$-0.0413072\pi$
$337$	25.2475	+	14.5766i	1.37532	+	0.794040i	0.383727	+	0.923447i	$0.374640\pi$
$338$	12.5108	+	3.53273i	0.680497	+	0.192155i
$339$	−18.0847	−	14.8009i	−0.982227	−	0.803874i
$340$	−3.32615	+	0.891240i	−0.180386	+	0.0483343i
$341$	−18.0591	+	10.4264i	−0.977954	+	0.564622i
$342$	2.85457	+	0.960398i	0.154357	+	0.0519324i
$343$	−3.44537	−	3.44537i	−0.186032	−	0.186032i
$344$	1.93666	−	1.93666i	0.104418	−	0.104418i
$345$	−2.12941	+	1.53027i	−0.114644	+	0.0823871i
$346$	2.74049	+	10.2276i	0.147329	+	0.549841i
$347$	12.4232	−	7.17253i	0.666912	−	0.385042i	−0.127994	−	0.991775i	$-0.540854\pi$
$347$	12.4232	−	7.17253i	0.666912	−	0.385042i	0.794906	+	0.606733i	$0.207520\pi$
$348$	−3.56408	−	9.43084i	−0.191055	−	0.505546i
$349$	6.84815	+	25.5577i	0.366573	+	1.36807i	0.865276	+	0.501296i	$0.167143\pi$
$349$	6.84815	+	25.5577i	0.366573	+	1.36807i	−0.498702	+	0.866773i	$0.666190\pi$
$350$	−1.38346			−0.0739492
$351$	18.7265	−	0.563355i	0.999548	−	0.0300697i
$352$	3.63301			0.193640
$353$	3.08503	+	11.5135i	0.164200	+	0.612801i	0.998141	+	0.0609479i	$0.0194124\pi$
$353$	3.08503	+	11.5135i	0.164200	+	0.612801i	−0.833941	+	0.551853i	$0.813921\pi$
$354$	2.96686	+	7.85057i	0.157687	+	0.417253i
$355$	−5.30461	+	3.06262i	−0.281540	+	0.162547i
$356$	2.68520	+	10.0213i	0.142315	+	0.531127i
$357$	−1.65185	+	1.18708i	−0.0874252	+	0.0628270i
$358$	−17.6914	+	17.6914i	−0.935018	+	0.935018i
$359$	−13.9898	−	13.9898i	−0.738351	−	0.738351i	0.233907	−	0.972259i	$-0.424849\pi$
$359$	−13.9898	−	13.9898i	−0.738351	−	0.738351i	−0.972259	+	0.233907i	$0.924849\pi$
$360$	0.610741	+	3.02761i	0.0321889	+	0.159569i
$361$	−15.5816	+	8.99606i	−0.820086	+	0.473477i
$362$	22.5905	−	6.05312i	1.18733	−	0.318145i
$363$	2.94717	+	2.41202i	0.154686	+	0.126598i
$364$	0.319460	+	1.22504i	0.0167443	+	0.0642094i
$365$	3.11654	+	1.79934i	0.163127	+	0.0941815i
$366$	−8.05447	+	5.78824i	−0.421014	+	0.302556i
$367$	−8.33971	+	14.4448i	−0.435329	+	0.754012i	−0.997322	−	0.0731295i	$-0.976701\pi$
$367$	−8.33971	+	14.4448i	−0.435329	+	0.754012i	0.561993	+	0.827142i	$0.310035\pi$
$368$	0.735260	−	1.27351i	0.0383281	−	0.0663862i
$369$	−1.75846	+	27.9878i	−0.0915419	+	1.45699i
$370$	−5.11350	+	1.37016i	−0.265838	+	0.0712311i
$371$	−0.664164	−	0.664164i	−0.0344817	−	0.0344817i
$372$	9.06104	+	4.09075i	0.469793	+	0.212096i
$373$	0.266680	+	0.461903i	0.0138082	+	0.0239164i	0.872847	−	0.487994i	$-0.162271\pi$
$373$	0.266680	+	0.461903i	0.0138082	+	0.0239164i	−0.859039	+	0.511911i	$0.828938\pi$
$374$	12.1514			0.628332
$375$	−6.55972	+	14.5298i	−0.338743	+	0.750317i
$376$	−7.33629	+	4.23561i	−0.378340	+	0.218435i
$377$	−20.9865	−	0.140715i	−1.08086	−	0.00724717i
$378$	0.969738	+	1.54546i	0.0498780	+	0.0794898i
$379$	−8.93403	+	33.3422i	−0.458910	+	1.71268i	0.217421	+	0.976078i	$0.430236\pi$
$379$	−8.93403	+	33.3422i	−0.458910	+	1.71268i	−0.676331	+	0.736598i	$0.736431\pi$
$380$	0.895107	+	0.516790i	0.0459180	+	0.0265108i
$381$	−25.1719	−	20.6012i	−1.28960	−	1.05543i
$382$	11.8925	−	3.18658i	0.608472	−	0.163040i
$383$	1.95166	+	0.522945i	0.0997250	+	0.0267212i	0.308336	−	0.951277i	$-0.400228\pi$
$383$	1.95166	+	0.522945i	0.0997250	+	0.0267212i	−0.208611	+	0.977999i	$0.566894\pi$
$384$	−1.01078	−	1.40653i	−0.0515813	−	0.0717765i
$385$	−1.26857	−	0.339912i	−0.0646523	−	0.0173235i
$386$	−11.2064	−	6.47000i	−0.570389	−	0.329314i
$387$	−5.43424	−	6.16288i	−0.276238	−	0.313277i
$388$	14.2669	+	3.82280i	0.724292	+	0.194073i
$389$	−0.968658	−	1.67777i	−0.0491129	−	0.0850661i	0.840424	−	0.541930i	$-0.182306\pi$
$389$	−0.968658	−	1.67777i	−0.0491129	−	0.0850661i	−0.889537	+	0.456864i	$0.848973\pi$
$390$	6.33786	+	1.08127i	0.320930	+	0.0547522i
$391$	2.45923	−	4.25951i	0.124369	−	0.215413i
$392$	4.86257	−	4.86257i	0.245597	−	0.245597i
$393$	0.941898	−	5.75336i	0.0475125	−	0.290218i
$394$			21.3652i			1.07636i
$395$	2.57044	−	2.57044i	0.129333	−	0.129333i
$396$	0.683433	−	10.8776i	0.0343438	−	0.546619i
$397$	−8.86089	−	33.0693i	−0.444716	−	1.65970i	−0.716687	−	0.697395i	$-0.754342\pi$
$397$	−8.86089	−	33.0693i	−0.444716	−	1.65970i	0.271971	−	0.962305i	$-0.412324\pi$
$398$	−5.74933	+	21.4568i	−0.288188	+	1.07553i
$399$	0.602540	+	0.0986434i	0.0301647	+	0.00493835i
$400$		−	3.94006i		−	0.197003i
$401$	6.35686	+	6.35686i	0.317446	+	0.317446i	0.847786	−	0.530339i	$-0.177935\pi$
$401$	6.35686	+	6.35686i	0.317446	+	0.317446i	−0.530339	+	0.847786i	$0.677935\pi$
$402$	25.7659	+	4.21820i	1.28509	+	0.210385i
$403$	14.7315	−	14.5353i	0.733829	−	0.724054i
$404$		−	17.3422i		−	0.862804i
$405$	9.17985	−	1.25907i	0.456150	−	0.0625636i
$406$	−1.02191	−	1.77000i	−0.0507166	−	0.0878438i
$407$	18.6810			0.925985
$408$	−3.38078	−	4.70443i	−0.167373	−	0.232904i
$409$	−3.81796	+	14.2488i	−0.188786	+	0.704558i	0.805003	+	0.593271i	$0.202164\pi$
$409$	−3.81796	+	14.2488i	−0.188786	+	0.704558i	−0.993788	+	0.111287i	$0.964503\pi$
$410$	−2.49081	+	9.29581i	−0.123012	+	0.459087i
$411$	−2.77481	+	6.14622i	−0.136871	+	0.303171i
$412$	10.6510			0.524736
$413$	0.850676	+	1.47341i	0.0418590	+	0.0725019i
$414$	−3.67469	−	2.44101i	−0.180601	−	0.119969i
$415$		−	8.89644i		−	0.436709i
$416$	−3.48887	+	0.909813i	−0.171056	+	0.0446073i
$417$	0.606077	−	0.740545i	0.0296797	−	0.0362647i
$418$	−2.57903	−	2.57903i	−0.126144	−	0.126144i
$419$		−	34.9519i		−	1.70751i	−0.520675	−	0.853755i	$-0.674320\pi$
$419$		−	34.9519i		−	1.70751i	0.520675	−	0.853755i	$-0.325680\pi$
$420$	0.221346	+	0.585701i	0.0108006	+	0.0285793i
$421$	−0.685052	+	2.55665i	−0.0333874	+	0.124603i	−0.980608	−	0.195978i	$-0.937212\pi$
$421$	−0.685052	+	2.55665i	−0.0333874	+	0.124603i	0.947221	+	0.320582i	$0.103878\pi$
$422$	4.74961	+	17.7258i	0.231207	+	0.862878i
$423$	11.3017	+	22.7623i	0.549509	+	1.10674i
$424$	1.89152	−	1.89152i	0.0918604	−	0.0918604i
$425$		−	13.1784i		−	0.639245i
$426$	−7.97462	−	6.52659i	−0.386372	−	0.316214i
$427$	−1.42180	+	1.42180i	−0.0688057	+	0.0688057i
$428$	0.400118	−	0.693025i	0.0193404	−	0.0334986i
$429$	−20.6154	−	9.47405i	−0.995320	−	0.457412i
$430$	−1.40987	−	2.44197i	−0.0679900	−	0.117762i
$431$	14.1857	+	3.80104i	0.683301	+	0.183090i	0.583739	−	0.811942i	$-0.301589\pi$
$431$	14.1857	+	3.80104i	0.683301	+	0.183090i	0.0995618	+	0.995031i	$0.468256\pi$
$432$	−4.40142	+	2.76179i	−0.211764	+	0.132877i
$433$	−13.2828	−	7.66884i	−0.638332	−	0.368541i	0.145640	−	0.989338i	$-0.453476\pi$
$433$	−13.2828	−	7.66884i	−0.638332	−	0.368541i	−0.783972	+	0.620797i	$0.786809\pi$
$434$	1.94673	+	0.521626i	0.0934462	+	0.0250388i
$435$	−10.3282	+	1.03134i	−0.495200	+	0.0494487i
$436$	−7.97650	−	2.13730i	−0.382005	−	0.102358i
$437$	−1.42600	+	0.382095i	−0.0682147	+	0.0182781i
$438$	−0.978142	+	5.97474i	−0.0467374	+	0.285484i
$439$	9.39837	+	5.42615i	0.448560	+	0.258976i	0.707222	−	0.706992i	$-0.249948\pi$
$439$	9.39837	+	5.42615i	0.448560	+	0.258976i	−0.258662	+	0.965968i	$0.583282\pi$
$440$	0.968061	−	3.61285i	0.0461505	−	0.172236i
$441$	−13.6443	−	15.4737i	−0.649727	−	0.736844i
$442$	−11.6693	+	3.04306i	−0.555051	+	0.144744i
$443$	28.8694	−	16.6678i	1.37163	−	0.791909i	0.380494	−	0.924783i	$-0.375754\pi$
$443$	28.8694	−	16.6678i	1.37163	−	0.791909i	0.991133	+	0.132874i	$0.0424205\pi$
$444$	−5.19747	−	7.23240i	−0.246661	−	0.343235i
$445$	10.6812			0.506337
$446$	−12.6770	−	21.9573i	−0.600275	−	1.03971i
$447$	−2.22806	−	22.3127i	−0.105384	−	1.05535i
$448$	−0.248284	−	0.248284i	−0.0117303	−	0.0117303i
$449$	17.6413	−	4.72697i	0.832543	−	0.223079i	0.182720	−	0.983165i	$-0.441510\pi$
$449$	17.6413	−	4.72697i	0.832543	−	0.223079i	0.649823	+	0.760086i	$0.274843\pi$
$450$	−11.7969	−	0.741196i	−0.556112	−	0.0349403i
$451$	16.9801	−	29.4104i	0.799561	−	1.38488i
$452$	6.74613	−	11.6846i	0.317311	−	0.549599i
$453$	−1.55521	−	15.5745i	−0.0730701	−	0.731755i
$454$	21.5858	+	12.4626i	1.01307	+	0.584898i
$455$	1.30337	+	0.00873905i	0.0611027	+	0.000409693i
$456$	−0.280934	+	1.71602i	−0.0131559	+	0.0803598i
$457$	−6.16260	+	1.65126i	−0.288274	+	0.0772428i	−0.400058	−	0.916490i	$-0.631010\pi$
$457$	−6.16260	+	1.65126i	−0.288274	+	0.0772428i	0.111784	+	0.993733i	$0.464343\pi$
$458$	−1.34408	+	0.776002i	−0.0628045	+	0.0362602i
$459$	−14.7215	+	9.23738i	−0.687140	+	0.431164i
$460$	−1.07052	−	1.07052i	−0.0499134	−	0.0499134i
$461$	−25.4639	+	25.4639i	−1.18597	+	1.18597i	−0.207804	+	0.978171i	$0.566632\pi$
$461$	−25.4639	+	25.4639i	−1.18597	+	1.18597i	−0.978171	+	0.207804i	$0.933368\pi$
$462$	−0.219539	−	2.19855i	−0.0102139	−	0.102286i
$463$	−5.81062	−	21.6855i	−0.270042	−	1.00781i	−0.959091	−	0.283097i	$-0.908638\pi$
$463$	−5.81062	−	21.6855i	−0.270042	−	1.00781i	0.689049	−	0.724715i	$-0.258028\pi$
$464$	5.04092	−	2.91038i	0.234019	−	0.135111i
$465$	6.48249	−	7.92073i	0.300618	−	0.367315i
$466$	−2.57905	−	9.62513i	−0.119472	−	0.445875i
$467$	−14.0000			−0.647843			−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000			−0.647843			−0.323921	+	0.946084i	$0.605001\pi$
$468$	2.06775	+	10.6172i	0.0955818	+	0.490779i
$469$	5.29288			0.244402
$470$	2.25726	+	8.42422i	0.104120	+	0.388580i
$471$	19.1463	+	3.13449i	0.882215	+	0.144430i
$472$	−4.19624	+	2.42270i	−0.193148	+	0.111514i
$473$	2.57533	+	9.61125i	0.118414	+	0.441926i
$474$	5.57394	+	2.51644i	0.256019	+	0.115584i
$475$	−2.79700	+	2.79700i	−0.128335	+	0.128335i
$476$	−0.830439	−	0.830439i	−0.0380631	−	0.0380631i
$477$	−5.30757	−	6.01922i	−0.243017	−	0.275601i
$478$	0.0625337	−	0.0361039i	0.00286023	−	0.00165135i
$479$	−25.7135	+	6.88992i	−1.17488	+	0.314809i	−0.792894	−	0.609359i	$-0.791427\pi$
$479$	−25.7135	+	6.88992i	−1.17488	+	0.314809i	−0.381987	+	0.924168i	$0.624760\pi$
$480$	−1.66806	+	0.630388i	−0.0761362	+	0.0287731i
$481$	−17.9399	+	4.67829i	−0.817988	+	0.213311i
$482$	16.2029	+	9.35472i	0.738020	+	0.426096i
$483$	−0.815107	−	0.367993i	−0.0370887	−	0.0167443i
$484$	−1.09938	+	1.90418i	−0.0499718	+	0.0865537i
$485$	7.60319	−	13.1691i	0.345243	−	0.597978i
$486$	7.44107	+	13.6978i	0.337534	+	0.621346i
$487$	−14.7534	+	3.95317i	−0.668542	+	0.179135i	−0.577098	−	0.816675i	$-0.695815\pi$
$487$	−14.7534	+	3.95317i	−0.668542	+	0.179135i	−0.0914441	+	0.995810i	$0.529148\pi$
$488$	−4.04924	−	4.04924i	−0.183301	−	0.183301i
$489$	12.4928	−	8.97778i	0.564944	−	0.405989i
$490$	−3.53990	−	6.13128i	−0.159916	−	0.276983i
$491$	−1.87163			−0.0844656			−0.0422328	−	0.999108i	$-0.513447\pi$
$491$	−1.87163			−0.0844656			−0.0422328	+	0.999108i	$0.513447\pi$
$492$	−16.1105	+	1.60873i	−0.726318	+	0.0725273i
$493$	16.8604	−	9.73437i	0.759355	−	0.438414i
$494$	3.12257	+	1.83084i	0.140491	+	0.0823734i
$495$	−10.6351	−	3.57811i	−0.478013	−	0.160824i
$496$	−1.48558	+	5.54424i	−0.0667043	+	0.248944i
$497$	−1.80916	−	1.04452i	−0.0811521	−	0.0468532i
$498$	14.0006	−	5.29108i	0.627384	−	0.237099i
$499$	10.9455	−	2.93283i	0.489986	−	0.131291i	−0.00536247	−	0.999986i	$-0.501707\pi$
$499$	10.9455	−	2.93283i	0.489986	−	0.131291i	0.495349	+	0.868694i	$0.335040\pi$
$500$	−8.89046	−	2.38219i	−0.397594	−	0.106535i
$501$	6.62181	−	14.6674i	0.295841	−	0.655289i
$502$	20.4369	+	5.47604i	0.912142	+	0.244408i
$503$	−0.311572	−	0.179886i	−0.0138923	−	0.00802072i	0.493038	−	0.870008i	$-0.335886\pi$
$503$	−0.311572	−	0.179886i	−0.0138923	−	0.00802072i	−0.506930	+	0.861987i	$0.669220\pi$
$504$	−0.790094	+	0.696680i	−0.0351936	+	0.0310326i
$505$	−17.2459	−	4.62104i	−0.767434	−	0.205633i
$506$	2.67121	+	4.62667i	0.118750	+	0.205680i
$507$	22.1701	+	3.93548i	0.984607	+	0.174781i
$508$	9.38987	−	16.2637i	0.416608	−	0.721586i
$509$	30.5184	−	30.5184i	1.35270	−	1.35270i	0.470082	−	0.882623i	$-0.344224\pi$
$509$	30.5184	−	30.5184i	1.35270	−	1.35270i	0.882623	−	0.470082i	$-0.155776\pi$
$510$	−5.57918	+	2.10847i	−0.247050	+	0.0933644i
$511$			1.22734i			0.0542945i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	5.08507	+	1.16396i	0.224511	+	0.0513899i
$514$	−3.79011	−	14.1449i	−0.167175	−	0.623905i
$515$	2.83809	−	10.5919i	0.125061	−	0.466734i
$516$	3.00450	−	3.67110i	0.132266	−	0.161611i
$517$		−	30.7760i		−	1.35353i
$518$	−1.27668	−	1.27668i	−0.0560943	−	0.0560943i
$519$	6.48335	+	17.1555i	0.284587	+	0.753042i
$520$	−0.0248886	+	3.71195i	−0.00109144	+	0.162780i
$521$		−	39.0644i		−	1.71144i	−0.517436	−	0.855722i	$-0.673113\pi$
$521$		−	39.0644i		−	1.71144i	0.517436	−	0.855722i	$-0.326887\pi$
$522$	−7.76566	−	15.6405i	−0.339894	−	0.684566i
$523$	−22.3670	−	38.7408i	−0.978041	−	1.69402i	−0.669512	−	0.742801i	$-0.733497\pi$
$523$	−22.3670	−	38.7408i	−0.978041	−	1.69402i	−0.308529	−	0.951215i	$-0.599837\pi$
$524$	3.36592			0.147041
$525$	−2.38437	+	0.238094i	−0.104062	+	0.0103913i
$526$	−2.98299	+	11.1327i	−0.130065	+	0.485407i
$527$	−4.96882	+	18.5439i	−0.216445	+	0.807784i
$528$	6.26142	−	0.625241i	0.272493	−	0.0272101i
$529$	−20.8376			−0.905981
$530$	−1.37701	−	2.38505i	−0.0598134	−	0.103600i
$531$	6.46441	+	13.0197i	0.280532	+	0.565007i
$532$			0.352507i			0.0152831i
$533$	−8.94119	+	32.4959i	−0.387286	+	1.40755i
$534$	6.35254	+	16.8094i	0.274901	+	0.727412i
$535$	−0.582564	−	0.582564i	−0.0251864	−	0.0251864i
$536$			15.0740i			0.651096i
$537$	−27.4460	+	33.5354i	−1.18438	+	1.44716i
$538$	5.29814	−	19.7729i	0.228419	−	0.852471i
$539$	6.46612	+	24.1319i	0.278515	+	1.03943i
$540$	1.57365	+	5.11292i	0.0677191	+	0.220025i
$541$	20.3887	−	20.3887i	0.876580	−	0.876580i	−0.116599	−	0.993179i	$-0.537199\pi$
$541$	20.3887	−	20.3887i	0.876580	−	0.876580i	0.993179	+	0.116599i	$0.0371993\pi$
$542$			0.555985i			0.0238816i
$543$	37.8926	−	14.3203i	1.62613	−	0.614541i
$544$	2.36507	−	2.36507i	0.101401	−	0.101401i
$545$	−4.25088	+	7.36274i	−0.182088	+	0.315385i
$546$	0.761412	+	2.05635i	0.0325854	+	0.0880036i
$547$	9.46079	+	16.3866i	0.404514	+	0.700639i	0.994265	−	0.106947i	$-0.0341074\pi$
$547$	9.46079	+	16.3866i	0.404514	+	0.700639i	−0.589751	+	0.807585i	$0.700774\pi$
$548$	−3.76073	−	1.00768i	−0.160650	−	0.0430462i
$549$	−12.8856	+	11.3621i	−0.549942	+	0.484922i
$550$	12.3965	+	7.15714i	0.528590	+	0.305182i
$551$	−5.64452	−	1.51244i	−0.240465	−	0.0644323i
$552$	1.04803	−	2.32140i	0.0446073	−	0.0988055i
$553$	1.19754	+	0.320880i	0.0509246	+	0.0136452i
$554$	−11.6634	+	3.12521i	−0.495532	+	0.132777i
$555$	−8.57721	+	3.24147i	−0.364082	+	0.137593i
$556$	0.478471	+	0.276245i	0.0202917	+	0.0117154i
$557$	−0.839623	+	3.13351i	−0.0355760	+	0.132771i	−0.981430	−	0.191821i	$-0.938561\pi$
$557$	−0.839623	+	3.13351i	−0.0355760	+	0.132771i	0.945854	+	0.324593i	$0.105227\pi$
$558$	16.3205	+	5.49092i	0.690903	+	0.232449i
$559$	−4.88009	−	8.58499i	−0.206406	−	0.363106i
$560$	−0.313065	+	0.180748i	−0.0132294	+	0.00763801i
$561$	20.9426	−	2.09125i	0.884198	−	0.0882926i
$562$	14.5671			0.614475
$563$	1.15338	+	1.99771i	0.0486090	+	0.0841933i	0.889306	−	0.457312i	$-0.151188\pi$
$563$	1.15338	+	1.99771i	0.0486090	+	0.0841933i	−0.840697	+	0.541506i	$0.817855\pi$
$564$	−11.9150	+	8.56256i	−0.501712	+	0.360549i
$565$	−9.82222	−	9.82222i	−0.413224	−	0.413224i
$566$	−12.8889	+	3.45357i	−0.541761	+	0.145164i
$567$	1.93730	+	2.49667i	0.0813588	+	0.104850i
$568$	2.97477	−	5.15245i	0.124818	−	0.216192i
$569$	4.75114	−	8.22922i	0.199178	−	0.344987i	−0.749084	−	0.662475i	$-0.769506\pi$
$569$	4.75114	−	8.22922i	0.199178	−	0.344987i	0.948262	+	0.317488i	$0.102839\pi$
$570$	1.63164	+	0.736629i	0.0683418	+	0.0308540i
$571$	22.0695	+	12.7418i	0.923578	+	0.533228i	0.884775	−	0.466019i	$-0.154312\pi$
$571$	22.0695	+	12.7418i	0.923578	+	0.533228i	0.0388033	+	0.999247i	$0.487645\pi$
$572$	3.47503	−	12.6296i	0.145298	−	0.528072i
$573$	19.9480	−	7.53870i	0.833341	−	0.314934i
$574$	−3.17038	+	0.849501i	−0.132329	+	0.0354575i
$575$	5.01770	−	2.89697i	0.209253	−	0.120812i
$576$	−1.98413	−	2.25016i	−0.0826719	−	0.0937569i
$577$	17.9008	+	17.9008i	0.745221	+	0.745221i	0.973577	−	0.228357i	$-0.0733353\pi$
$577$	17.9008	+	17.9008i	0.745221	+	0.745221i	−0.228357	+	0.973577i	$0.573335\pi$
$578$	−4.11035	+	4.11035i	−0.170968	+	0.170968i
$579$	−20.4274	−	9.22230i	−0.848935	−	0.383266i
$580$	−1.55101	−	5.78846i	−0.0644023	−	0.240353i
$581$	2.62767	−	1.51709i	0.109014	−	0.0629394i
$582$	25.2466	+	4.13319i	1.04651	+	0.171326i
$583$	2.51529	+	9.38721i	0.104173	+	0.388778i
$584$	−3.49544			−0.144642
$585$	11.1093	+	0.772802i	0.459311	+	0.0319514i
$586$	−21.1106			−0.872071
$587$	7.99701	+	29.8452i	0.330072	+	1.23185i	0.909114	+	0.416547i	$0.136760\pi$
$587$	7.99701	+	29.8452i	0.330072	+	1.23185i	−0.579042	+	0.815298i	$0.696573\pi$
$588$	7.54369	−	9.21738i	0.311096	−	0.380119i
$589$	4.99037	−	2.88119i	0.205625	−	0.118718i
$590$	1.29112	+	4.81852i	0.0531545	+	0.198375i
$591$	3.67695	+	36.8225i	0.151250	+	1.51468i
$592$	3.63596	−	3.63596i	0.149437	−	0.149437i
$593$	−1.91150	−	1.91150i	−0.0784959	−	0.0784959i	0.666769	−	0.745265i	$-0.267677\pi$
$593$	−1.91150	−	1.91150i	−0.0784959	−	0.0784959i	−0.745265	+	0.666769i	$0.767677\pi$
$594$	−0.694147	−	18.8649i	−0.0284812	−	0.774036i
$595$	−1.04711	+	0.604551i	−0.0429274	+	0.0247842i
$596$	12.5052	−	3.35075i	0.512232	−	0.137252i
$597$	−6.21614	+	37.9698i	−0.254410	+	1.55400i
$598$	−3.72388	−	3.77416i	−0.152281	−	0.154337i
$599$	−24.8798	−	14.3643i	−1.01656	−	0.586911i	−0.103454	−	0.994634i	$-0.532989\pi$
$599$	−24.8798	−	14.3643i	−1.01656	−	0.586911i	−0.913105	+	0.407723i	$0.866323\pi$
$600$	−0.678084	−	6.79062i	−0.0276827	−	0.277226i
$601$	−15.4935	+	26.8355i	−0.631993	+	1.09464i	0.355151	+	0.934809i	$0.384430\pi$
$601$	−15.4935	+	26.8355i	−0.631993	+	1.09464i	−0.987144	+	0.159835i	$0.948904\pi$
$602$	0.480843	−	0.832845i	0.0195977	−	0.0339442i
$603$	45.1329	+	2.83568i	1.83795	+	0.115478i
$604$	8.72875	−	2.33886i	0.355168	−	0.0951670i
$605$	1.60067	+	1.60067i	0.0650766	+	0.0650766i
$606$	−2.98458	−	29.8888i	−0.121240	−	1.21415i
$607$	−5.03399	−	8.71913i	−0.204323	−	0.353899i	0.745594	−	0.666401i	$-0.232166\pi$
$607$	−5.03399	−	8.71913i	−0.204323	−	0.353899i	−0.949917	+	0.312502i	$0.898833\pi$
$608$	−1.00393			−0.0407148
$609$	−2.06586	−	2.87469i	−0.0837129	−	0.116488i
$610$	−5.10575	+	2.94781i	−0.206726	+	0.119353i
$611$	7.70722	+	29.5550i	0.311801	+	1.19567i
$612$	−6.63633	−	7.52615i	−0.268258	−	0.304227i
$613$	−5.97413	+	22.2957i	−0.241293	+	0.900516i	0.733918	+	0.679238i	$0.237690\pi$
$613$	−5.97413	+	22.2957i	−0.241293	+	0.900516i	−0.975211	+	0.221278i	$0.928977\pi$
$614$	−13.4032	−	7.73837i	−0.540911	−	0.312295i
$615$	−2.69304	+	16.4498i	−0.108594	+	0.663320i
$616$	1.23218	−	0.330162i	0.0496460	−	0.0133026i
$617$	25.3370	+	6.78904i	1.02003	+	0.273316i	0.729815	−	0.683645i	$-0.239606\pi$
$617$	25.3370	+	6.78904i	1.02003	+	0.273316i	0.290216	+	0.956961i	$0.406273\pi$
$618$	18.3567	−	1.83303i	0.738417	−	0.0737354i
$619$	−20.5005	−	5.49310i	−0.823985	−	0.220786i	−0.177897	−	0.984049i	$-0.556929\pi$
$619$	−20.5005	−	5.49310i	−0.823985	−	0.220786i	−0.646088	+	0.763263i	$0.723596\pi$
$620$	5.11763	+	2.95467i	0.205529	+	0.118662i
$621$	−6.75335	−	3.57461i	−0.271003	−	0.143444i
$622$	−25.0277	−	6.70614i	−1.00352	−	0.268892i
$623$	1.82144	+	3.15482i	0.0729743	+	0.126395i
$624$	−5.85642	+	2.16848i	−0.234445	+	0.0868087i
$625$	5.11220	−	8.85460i	0.204488	−	0.354184i
$626$	−24.9584	+	24.9584i	−0.997537	+	0.997537i
$627$	−4.88875	−	4.00105i	−0.195238	−	0.159786i
$628$			11.2013i			0.446980i
$629$	12.1612	−	12.1612i	0.484900	−	0.484900i
$630$	0.482285	+	0.971350i	0.0192147	+	0.0386995i
$631$	2.60255	+	9.71284i	0.103606	+	0.386662i	0.998183	−	0.0602509i	$-0.0191901\pi$
$631$	2.60255	+	9.71284i	0.103606	+	0.386662i	−0.894578	+	0.446913i	$0.852523\pi$
$632$	−0.913858	+	3.41056i	−0.0363513	+	0.135665i
$633$	11.2365	+	29.7326i	0.446609	+	1.18177i
$634$		−	12.6353i		−	0.501811i
$635$	−13.6714	−	13.6714i	−0.542535	−	0.542535i
$636$	2.93447	−	3.58553i	0.116359	−	0.142175i
$637$	−12.2529	−	21.5552i	−0.485478	−	0.854046i
$638$			21.1468i			0.837212i
$639$	−14.8673	−	9.87601i	−0.588142	−	0.390689i
$640$	−0.514766	−	0.891601i	−0.0203479	−	0.0352436i
$641$	−6.47708			−0.255829			−0.127915	−	0.991785i	$-0.540828\pi$
$641$	−6.47708			−0.255829			−0.127915	+	0.991785i	$0.540828\pi$
$642$	0.570326	−	1.26328i	0.0225090	−	0.0498575i
$643$	−1.88381	+	7.03049i	−0.0742904	+	0.277255i	−0.993071	−	0.117512i	$-0.962508\pi$
$643$	−1.88381	+	7.03049i	−0.0742904	+	0.277255i	0.918781	+	0.394767i	$0.129175\pi$
$644$	0.133638	−	0.498745i	0.00526609	−	0.0196533i
$645$	−2.85015	−	3.96604i	−0.112224	−	0.156163i
$646$	−3.35786			−0.132113
$647$	2.67717	+	4.63699i	0.105250	+	0.182299i	0.913840	−	0.406073i	$-0.133102\pi$
$647$	2.67717	+	4.63699i	0.105250	+	0.182299i	−0.808590	+	0.588372i	$0.799769\pi$
$648$	−7.11046	+	5.51737i	−0.279325	+	0.216743i
$649$		−	17.6034i		−	0.690993i
$650$	−13.6971	−	3.76873i	−0.537244	−	0.147822i
$651$	3.44493	+	0.563978i	0.135017	+	0.0221041i
$652$	6.28053	+	6.28053i	0.245965	+	0.245965i
$653$		−	13.5198i		−	0.529072i	−0.964376	−	0.264536i	$-0.914781\pi$
$653$		−	13.5198i		−	0.529072i	0.964376	−	0.264536i	$-0.0852189\pi$
$654$	−14.1152	−	2.31083i	−0.551947	−	0.0903607i
$655$	0.896892	−	3.34725i	0.0350445	−	0.130788i
$656$	−2.41936	−	9.02916i	−0.0944600	−	0.352529i
$657$	−0.657554	+	10.4657i	−0.0256536	+	0.408305i
$658$	−2.10327	+	2.10327i	−0.0819940	+	0.0819940i
$659$			25.9719i			1.01172i	0.862615	+	0.505861i	$0.168825\pi$
$659$			25.9719i			1.01172i	−0.862615	+	0.505861i	$0.831175\pi$
$660$	1.04666	−	6.39328i	0.0407413	−	0.248858i
$661$	9.76168	−	9.76168i	0.379685	−	0.379685i	−0.491303	−	0.870989i	$-0.663479\pi$
$661$	9.76168	−	9.76168i	0.379685	−	0.379685i	0.870989	+	0.491303i	$0.163479\pi$
$662$	4.98392	−	8.63240i	0.193706	−	0.335508i
$663$	−19.5880	+	7.25294i	−0.760736	+	0.281681i
$664$	4.32062	+	7.48354i	0.167673	+	0.290418i
$665$	0.350552	+	0.0939301i	0.0135938	+	0.00364245i
$666$	−10.2024	−	11.5704i	−0.395336	−	0.448344i
$667$	7.41277	+	4.27977i	0.287024	+	0.165713i
$668$	8.97462	+	2.40474i	0.347238	+	0.0930422i
$669$	−25.6274	−	35.6612i	−0.990814	−	1.37874i
$670$	14.9903	+	4.01665i	0.579127	+	0.155177i
$671$	20.0955	−	5.38458i	0.775779	−	0.207869i
$672$	−0.470643	−	0.385183i	−0.0181554	−	0.0148588i
$673$	−24.4924	−	14.1407i	−0.944112	−	0.545083i	−0.0528649	−	0.998602i	$-0.516835\pi$
$673$	−24.4924	−	14.1407i	−0.944112	−	0.545083i	−0.891247	+	0.453518i	$0.850169\pi$
$674$	−7.54543	+	28.1599i	−0.290639	+	1.08468i
$675$	−20.4593	+	0.752815i	−0.787480	+	0.0289759i
$676$	−0.174322	+	12.9988i	−0.00670468	+	0.499955i
$677$	−34.1714	+	19.7289i	−1.31331	+	0.758242i	−0.982644	−	0.185504i	$-0.940608\pi$
$677$	−34.1714	+	19.7289i	−1.31331	+	0.758242i	−0.330671	+	0.943746i	$0.607275\pi$
$678$	9.61589	−	21.2992i	0.369296	−	0.817993i
$679$	5.18621			0.199028
$680$	−1.72174	−	2.98215i	−0.0660259	−	0.114360i
$681$	39.3475	+	17.7641i	1.50780	+	0.680721i
$682$	−14.7452	−	14.7452i	−0.564622	−	0.564622i
$683$	−25.3130	+	6.78259i	−0.968574	+	0.259529i	−0.708226	−	0.705986i	$-0.750504\pi$
$683$	−25.3130	+	6.78259i	−0.968574	+	0.259529i	−0.260348	+	0.965515i	$0.583837\pi$
$684$	−0.188857	+	3.00587i	−0.00722114	+	0.114932i
$685$	−2.00419	+	3.47136i	−0.0765761	+	0.132634i
$686$	2.43624	−	4.21970i	0.0930162	−	0.161109i
$687$	−2.18294	+	1.56874i	−0.0832842	+	0.0598511i
$688$	2.37192	+	1.36943i	0.0904286	+	0.0522090i
$689$	−4.76634	−	8.38488i	−0.181583	−	0.319438i
$690$	−2.02926	−	1.66079i	−0.0772527	−	0.0632251i
$691$	−11.3975	+	3.05395i	−0.433581	+	0.116178i	−0.469007	−	0.883195i	$-0.655388\pi$
$691$	−11.3975	+	3.05395i	−0.433581	+	0.116178i	0.0354255	+	0.999372i	$0.488721\pi$
$692$	−9.16985	+	5.29421i	−0.348585	+	0.201256i
$693$	−0.756742	−	3.75138i	−0.0287462	−	0.142503i
$694$	10.1435	+	10.1435i	0.385042	+	0.385042i
$695$	0.402207	−	0.402207i	0.0152566	−	0.0152566i
$696$	8.18705	−	5.88352i	0.310329	−	0.223014i
$697$	−8.09204	−	30.1999i	−0.306508	−	1.14390i
$698$	−22.9144	+	13.2296i	−0.867321	+	0.500748i
$699$	−6.10142	−	16.1449i	−0.230777	−	0.610655i
$700$	−0.358066	−	1.33632i	−0.0135336	−	0.0505082i
$701$	32.2520			1.21814			0.609071	−	0.793115i	$-0.291542\pi$
$701$	32.2520			1.21814			0.609071	+	0.793115i	$0.291542\pi$
$702$	5.39094	+	17.9426i	0.203468	+	0.677201i
$703$	−5.16224			−0.194698
$704$	0.940292	+	3.50922i	0.0354386	+	0.132259i
$705$	5.34015	+	14.1305i	0.201122	+	0.532185i
$706$	−10.3227	+	5.95982i	−0.388500	+	0.224301i
$707$	−1.57603	−	5.88181i	−0.0592726	−	0.221208i
$708$	−6.81519	+	4.89765i	−0.256130	+	0.184065i
$709$	9.57038	−	9.57038i	0.359423	−	0.359423i	−0.504177	−	0.863600i	$-0.668204\pi$
$709$	9.57038	−	9.57038i	0.359423	−	0.359423i	0.863600	+	0.504177i	$0.168204\pi$
$710$	−4.33120	−	4.33120i	−0.162547	−	0.162547i
$711$	10.0396	+	3.37777i	0.376516	+	0.126676i
$712$	−8.98484	+	5.18740i	−0.336721	+	0.194406i
$713$	−8.15292	+	2.18457i	−0.305329	+	0.0818127i
$714$	−1.57416	−	1.28833i	−0.0589116	−	0.0482144i
$715$	−11.6336	−	6.82108i	−0.435073	−	0.255094i
$716$	−21.6674	−	12.5097i	−0.809750	−	0.467509i
$717$	0.101562	−	0.0729863i	0.00379291	−	0.00272572i
$718$	9.89226	−	17.1339i	0.369176	−	0.639431i
$719$	−5.20762	+	9.01985i	−0.194211	+	0.336384i	−0.946642	−	0.322288i	$-0.895548\pi$
$719$	−5.20762	+	9.01985i	−0.194211	+	0.336384i	0.752430	+	0.658672i	$0.228881\pi$
$720$	−2.76638	+	1.37353i	−0.103097	+	0.0511886i
$721$	3.61241	−	0.967944i	0.134533	−	0.0360481i
$722$	−12.7224	−	12.7224i	−0.473477	−	0.473477i
$723$	29.5352	+	13.3342i	1.09843	+	0.495903i
$724$	11.6937	+	20.2541i	0.434594	+	0.752739i
$725$	22.9341			0.851752
$726$	−1.56705	+	3.47102i	−0.0581586	+	0.128822i
$727$	−20.0010	+	11.5476i	−0.741796	+	0.428276i	−0.822722	−	0.568444i	$-0.807546\pi$
$727$	−20.0010	+	11.5476i	−0.741796	+	0.428276i	0.0809260	+	0.996720i	$0.474212\pi$
$728$	−1.10061	+	0.625638i	−0.0407914	+	0.0231877i
$729$	15.1819	+	22.3273i	0.562294	+	0.826938i
$730$	−0.931405	+	3.47605i	−0.0344728	+	0.128654i
$731$	7.93338	+	4.58034i	0.293427	+	0.169410i
$732$	−7.67566	−	6.28191i	−0.283701	−	0.232186i
$733$	−24.5643	+	6.58200i	−0.907305	+	0.243112i	−0.682151	−	0.731212i	$-0.738955\pi$
$733$	−24.5643	+	6.58200i	−0.907305	+	0.243112i	−0.225154	+	0.974323i	$0.572289\pi$
$734$	−16.1111	−	4.31695i	−0.594671	−	0.159342i
$735$	−7.15614	−	9.95793i	−0.263958	−	0.367304i
$736$	1.42041	+	0.380599i	0.0523571	+	0.0140290i
$737$	−47.4269	−	27.3819i	−1.74699	−	1.00863i
$738$	−27.4893	+	5.54524i	−1.01189	+	0.204123i
$739$	23.9997	+	6.43070i	0.882843	+	0.236557i	0.671633	−	0.740884i	$-0.265593\pi$
$739$	23.9997	+	6.43070i	0.882843	+	0.236557i	0.211209	+	0.977441i	$0.432260\pi$
$740$	−2.64694	−	4.58464i	−0.0973035	−	0.168535i
$741$	5.69677	+	2.61802i	0.209276	+	0.0961755i
$742$	0.469635	−	0.813432i	0.0172408	−	0.0298620i
$743$	−15.1274	+	15.1274i	−0.554971	+	0.554971i	−0.927871	−	0.372901i	$-0.878363\pi$
$743$	−15.1274	+	15.1274i	−0.554971	+	0.554971i	0.372901	+	0.927871i	$0.378363\pi$
$744$	−1.60619	+	9.81105i	−0.0588860	+	0.359691i
$745$		−	13.3286i		−	0.488324i
$746$	−0.377142	+	0.377142i	−0.0138082	+	0.0138082i
$747$	23.2192	−	11.5286i	0.849547	−	0.421808i
$748$	3.14500	+	11.7373i	0.114993	+	0.429159i
$749$	0.0727242	−	0.271410i	0.00265728	−	0.00991712i
$750$	−15.7325	−	2.57561i	−0.574470	−	0.0940481i
$751$		−	42.6857i		−	1.55762i	−0.627258	−	0.778812i	$-0.715823\pi$
$751$		−	42.6857i		−	1.55762i	0.627258	−	0.778812i	$-0.284177\pi$
$752$	−5.99005	−	5.99005i	−0.218435	−	0.218435i
$753$	36.1650	+	5.92066i	1.31792	+	0.215761i
$754$	−5.29580	−	20.3079i	−0.192862	−	0.739569i
$755$		−	9.30355i		−	0.338591i
$756$	−1.24181	+	1.33669i	−0.0451643	+	0.0486149i
$757$	8.17298	+	14.1560i	0.297052	+	0.514509i	0.975460	−	0.220176i	$-0.0706632\pi$
$757$	8.17298	+	14.1560i	0.297052	+	0.514509i	−0.678408	+	0.734685i	$0.737330\pi$
$758$	−34.5184			−1.25377
$759$	5.40002	+	7.51425i	0.196008	+	0.272750i
$760$	−0.267510	+	0.998362i	−0.00970362	+	0.0362144i
$761$	1.60666	−	5.99615i	0.0582415	−	0.217360i	−0.930672	−	0.365856i	$-0.880776\pi$
$761$	1.60666	−	5.99615i	0.0582415	−	0.217360i	0.988913	+	0.148496i	$0.0474431\pi$
$762$	13.3843	−	29.6462i	0.484860	−	1.07397i
$763$	−2.89957			−0.104971
$764$	6.15600	+	10.6625i	0.222716	+	0.385756i
$765$	−9.25273	+	4.59407i	−0.334533	+	0.166099i
$766$			2.02050i			0.0730038i
$767$	4.40841	+	16.9050i	0.159179	+	0.610404i
$768$	1.09699	−	1.34038i	0.0395843	−	0.0483667i
$769$	16.4608	+	16.4608i	0.593593	+	0.593593i	0.938600	−	0.345007i	$-0.112124\pi$
$769$	16.4608	+	16.4608i	0.593593	+	0.593593i	−0.345007	+	0.938600i	$0.612124\pi$
$770$		−	1.31332i		−	0.0473288i
$771$	−8.96652	−	23.7262i	−0.322921	−	0.854477i
$772$	3.34912	−	12.4991i	0.120537	−	0.449852i
$773$	2.25389	+	8.41164i	0.0810668	+	0.302546i	0.994540	−	0.104353i	$-0.0332770\pi$
$773$	2.25389	+	8.41164i	0.0810668	+	0.302546i	−0.913474	+	0.406898i	$0.866610\pi$
$774$	4.54640	−	6.84414i	0.163417	−	0.246008i
$775$	−15.9914	+	15.9914i	−0.574428	+	0.574428i
$776$			14.7702i			0.530218i
$777$	−2.42006	−	1.98062i	−0.0868191	−	0.0710544i
$778$	1.36989	−	1.36989i	0.0491129	−	0.0491129i
$779$	−4.69221	+	8.12715i	−0.168116	+	0.291185i
$780$	0.595931	+	6.40175i	0.0213378	+	0.229219i
$781$	10.8074	+	18.7189i	0.386718	+	0.669815i
$782$	4.75087	+	1.27299i	0.169891	+	0.0455221i
$783$	−16.0757	−	25.6196i	−0.574498	−	0.915570i
$784$	5.95541	+	3.43835i	0.212693	+	0.122798i
$785$	11.1391	+	2.98472i	0.397573	+	0.106529i
$786$	5.80110	−	0.579275i	0.206918	−	0.0206620i
$787$	−7.48822	−	2.00646i	−0.266926	−	0.0715227i	0.122873	−	0.992422i	$-0.460789\pi$
$787$	−7.48822	−	2.00646i	−0.266926	−	0.0715227i	−0.389800	+	0.920900i	$0.627456\pi$
$788$	−20.6372	+	5.52972i	−0.735170	+	0.196988i
$789$	−3.22519	+	19.7003i	−0.114820	+	0.701349i
$790$	3.14813	+	1.81758i	0.112006	+	0.0646665i
$791$	1.22615	−	4.57607i	0.0435970	−	0.162706i
$792$	10.6838	−	2.15518i	0.379633	−	0.0765809i
$793$	−17.9498	+	10.2035i	−0.637416	+	0.362336i
$794$	29.6491	−	17.1179i	1.05221	−	0.607493i
$795$	−2.78371	−	3.87360i	−0.0987280	−	0.137382i
$796$	−22.2137			−0.787344
$797$	9.36322	+	16.2176i	0.331662	+	0.574456i	0.982838	−	0.184471i	$-0.0590572\pi$
$797$	9.36322	+	16.2176i	0.331662	+	0.574456i	−0.651176	+	0.758927i	$0.725724\pi$
$798$	0.0606665	+	0.607539i	0.00214757	+	0.0215067i
$799$	−20.0350	−	20.0350i	−0.708787	−	0.708787i
$800$	3.80581	−	1.01976i	0.134556	−	0.0360541i
$801$	13.8414	+	27.8773i	0.489061	+	0.984996i
$802$	−4.49498	+	7.78553i	−0.158723	+	0.274917i
$803$	6.34949	−	10.9976i	0.224069	−	0.388098i
$804$	2.59423	+	25.9797i	0.0914914	+	0.916233i
$805$	−0.460369	−	0.265794i	−0.0162259	−	0.00936801i
$806$	17.8528	+	10.4675i	0.628838	+	0.368704i
$807$	5.72832	−	34.9900i	0.201646	−	1.23171i
$808$	16.7512	−	4.48848i	0.589306	−	0.157904i
$809$	−8.00375	+	4.62097i	−0.281397	+	0.162465i	−0.634056	−	0.773287i	$-0.718611\pi$
$809$	−8.00375	+	4.62097i	−0.281397	+	0.162465i	0.352659	+	0.935752i	$0.385278\pi$
$810$	3.59209	+	8.54118i	0.126213	+	0.300107i
$811$	27.8829	+	27.8829i	0.979100	+	0.979100i	0.999786	−	0.0206860i	$-0.00658503\pi$
$811$	27.8829	+	27.8829i	0.979100	+	0.979100i	−0.0206860	+	0.999786i	$0.506585\pi$
$812$	1.44520	−	1.44520i	0.0507166	−	0.0507166i
$813$	0.0956849	+	0.958229i	0.00335582	+	0.0336065i
$814$	4.83501	+	18.0445i	0.169467	+	0.632459i
$815$	7.91921	−	4.57216i	0.277398	−	0.160156i
$816$	3.66912	−	4.48317i	0.128445	−	0.156942i
$817$	−0.711655	−	2.65593i	−0.0248977	−	0.0929194i
$818$	−14.7515			−0.515772
$819$	1.66618	+	3.41304i	0.0582209	+	0.119261i
$820$	−9.62373			−0.336075
$821$	−2.29371	−	8.56024i	−0.0800510	−	0.298755i	0.914280	−	0.405083i	$-0.132757\pi$
$821$	−2.29371	−	8.56024i	−0.0800510	−	0.298755i	−0.994331	+	0.106328i	$0.966091\pi$
$822$	−6.65496	−	1.08950i	−0.232119	−	0.0380008i
$823$	−8.36300	+	4.82838i	−0.291516	+	0.168307i	−0.638625	−	0.769518i	$-0.720497\pi$
$823$	−8.36300	+	4.82838i	−0.291516	+	0.168307i	0.347109	+	0.937825i	$0.387163\pi$
$824$	2.75668	+	10.2881i	0.0960334	+	0.358401i
$825$	22.5969	+	10.2017i	0.786724	+	0.355179i
$826$	−1.20304	+	1.20304i	−0.0418590	+	0.0418590i
$827$	16.2044	+	16.2044i	0.563482	+	0.563482i	0.930295	−	0.366813i	$-0.119551\pi$
$827$	16.2044	+	16.2044i	0.563482	+	0.563482i	−0.366813	+	0.930295i	$0.619551\pi$
$828$	1.40675	−	4.18126i	0.0488881	−	0.145309i
$829$	39.4372	−	22.7691i	1.36971	−	0.790802i	0.378819	−	0.925471i	$-0.376330\pi$
$829$	39.4372	−	22.7691i	1.36971	−	0.790802i	0.990891	+	0.134668i	$0.0429969\pi$
$830$	8.59330	−	2.30257i	0.298278	−	0.0799233i
$831$	−19.5638	+	7.39351i	−0.678662	+	0.256478i
$832$	−1.78180	−	3.13452i	−0.0617728	−	0.108670i
$833$	19.9191	+	11.5003i	0.690156	+	0.398462i
$834$	0.872176	+	0.393758i	0.0302010	+	0.0136347i
$835$	4.78280	−	8.28405i	0.165516	−	0.286681i
$836$	1.82365	−	3.15865i	0.0630721	−	0.109244i
$837$	29.0731	+	6.65473i	1.00491	+	0.230021i
$838$	33.7609	−	9.04621i	1.16625	−	0.312496i
$839$	−22.5058	−	22.5058i	−0.776987	−	0.776987i	0.202330	−	0.979317i	$-0.435149\pi$
$839$	−22.5058	−	22.5058i	−0.776987	−	0.776987i	−0.979317	+	0.202330i	$0.935149\pi$
$840$	−0.508455	+	0.365395i	−0.0175434	+	0.0126073i
$841$	2.44058	+	4.22721i	0.0841579	+	0.145766i
$842$	−2.64684			−0.0912160
$843$	25.1061	−	2.50699i	0.864698	−	0.0863454i
$844$	−15.8925	+	9.17554i	−0.547042	+	0.315835i
$845$	12.8803	+	3.63706i	0.443095	+	0.125119i
$846$	−19.0616	+	16.8080i	−0.655352	+	0.577869i
$847$	−0.199820	+	0.745737i	−0.00686588	+	0.0256238i
$848$	2.31663	+	1.33751i	0.0795534	+	0.0459302i
$849$	−21.6194	+	8.17033i	−0.741975	+	0.280405i
$850$	12.7293	−	3.41081i	0.436612	−	0.116990i
$851$	7.30380	+	1.95705i	0.250371	+	0.0670868i
$852$	4.24021	−	9.39210i	0.145267	−	0.321768i
$853$	1.99312	+	0.534054i	0.0682430	+	0.0182857i	0.292779	−	0.956180i	$-0.405420\pi$
$853$	1.99312	+	0.534054i	0.0682430	+	0.0182857i	−0.224536	+	0.974466i	$0.572087\pi$
$854$	−1.74134	−	1.00536i	−0.0595874	−	0.0344028i
$855$	2.93887	+	0.988761i	0.100507	+	0.0338149i
$856$	0.772969	+	0.207116i	0.0264195	+	0.00707910i
$857$	−7.56394	−	13.1011i	−0.258379	−	0.447526i	0.707429	−	0.706785i	$-0.249855\pi$
$857$	−7.56394	−	13.1011i	−0.258379	−	0.447526i	−0.965808	+	0.259259i	$0.916522\pi$
$858$	3.81558	−	22.3650i	0.130262	−	0.763528i
$859$	−15.4894	+	26.8284i	−0.528492	+	0.915375i	0.470956	+	0.882156i	$0.343909\pi$
$859$	−15.4894	+	26.8284i	−0.528492	+	0.915375i	−0.999448	+	0.0332181i	$0.989424\pi$
$860$	1.99386	−	1.99386i	0.0679900	−	0.0679900i
$861$	−5.31789	+	2.00972i	−0.181233	+	0.0684911i
$862$			14.6861i			0.500211i
$863$	14.4513	−	14.4513i	0.491927	−	0.491927i	−0.416986	−	0.908913i	$-0.636914\pi$
$863$	14.4513	−	14.4513i	0.491927	−	0.491927i	0.908913	+	0.416986i	$0.136914\pi$
$864$	−3.80685	−	3.53665i	−0.129512	−	0.120319i
$865$	2.82142	+	10.5297i	0.0959312	+	0.358020i
$866$	3.96968	−	14.8151i	0.134895	−	0.503436i
$867$	−6.37671	+	7.79149i	−0.216565	+	0.264613i
$868$			2.01541i			0.0684073i
$869$	−9.07056	−	9.07056i	−0.307698	−	0.307698i
$870$	−3.66933	−	9.70936i	−0.124402	−	0.329178i
$871$	52.4025	+	14.4185i	1.77559	+	0.488552i
$872$		−	8.25788i		−	0.279647i
$873$	44.2233	+	2.77853i	1.49673	+	0.0940390i
$874$	−0.738151	−	1.27851i	−0.0249683	−	0.0432464i
$875$	−3.23180			−0.109255
$876$	−6.02432	+	0.601565i	−0.203543	+	0.0203250i
$877$	2.10830	−	7.86828i	0.0711922	−	0.265693i	−0.921151	−	0.389206i	$-0.872749\pi$
$877$	2.10830	−	7.86828i	0.0711922	−	0.265693i	0.992343	+	0.123513i	$0.0394161\pi$
$878$	−2.80878	+	10.4825i	−0.0947919	+	0.353768i
$879$	−36.3837	+	3.63313i	−1.22719	+	0.122543i
$880$	3.74030			0.126086
$881$	7.84542	+	13.5887i	0.264319	+	0.457814i	0.967385	−	0.253311i	$-0.0815195\pi$
$881$	7.84542	+	13.5887i	0.264319	+	0.457814i	−0.703066	+	0.711125i	$0.748186\pi$
$882$	11.4151	−	17.1842i	0.384366	−	0.578623i
$883$		−	49.4553i		−	1.66430i	−0.554549	−	0.832151i	$-0.687109\pi$
$883$		−	49.4553i		−	1.66430i	0.554549	−	0.832151i	$-0.312891\pi$
$884$	−5.95960	−	10.4840i	−0.200443	−	0.352617i
$885$	3.05448	+	8.08242i	0.102675	+	0.271688i
$886$	23.5718	+	23.5718i	0.791909	+	0.791909i
$887$		−	26.5574i		−	0.891709i	−0.895105	−	0.445855i	$-0.852900\pi$
$887$		−	26.5574i		−	0.891709i	0.895105	−	0.445855i	$-0.147100\pi$
$888$	5.64076	−	6.89226i	0.189291	−	0.231289i
$889$	1.70667	−	6.36938i	0.0572399	−	0.213622i
$890$	2.76450	+	10.3172i	0.0926661	+	0.345835i
$891$	−4.44300	−	32.3938i	−0.148846	−	1.08523i
$892$	17.9280	−	17.9280i	0.600275	−	0.600275i
$893$			8.50452i			0.284593i
$894$	20.9758	−	7.92709i	0.701534	−	0.265122i
$895$	−18.2138	+	18.2138i	−0.608822	+	0.608822i
$896$	0.175564	−	0.304085i	0.00586516	−	0.0101588i
$897$	−7.06757	−	5.86380i	−0.235979	−	0.195787i
$898$	9.13180	+	15.8167i	0.304732	+	0.527811i
$899$	−32.2717	−	8.64716i	−1.07632	−	0.288399i
$900$	−2.33733	−	11.5868i	−0.0779110	−	0.386226i
$901$	7.74846	+	4.47357i	0.258139	+	0.149036i
$902$	32.8030	+	8.78954i	1.09222	+	0.292660i
$903$	0.685391	−	1.51814i	0.0228084	−	0.0505207i
$904$	13.0325	+	3.49205i	0.433455	+	0.116144i
$905$	23.2577	−	6.23188i	0.773112	−	0.207155i
$906$	14.6413	−	5.53320i	0.486425	−	0.183828i
$907$	8.46275	+	4.88597i	0.281001	+	0.162236i	0.633876	−	0.773434i	$-0.281463\pi$
$907$	8.46275	+	4.88597i	0.281001	+	0.162236i	−0.352876	+	0.935670i	$0.614796\pi$
$908$	−6.45111	+	24.0759i	−0.214088	+	0.798986i
$909$	−10.2877	−	50.9992i	−0.341223	−	1.69154i
$910$	0.328895	+	1.26122i	0.0109027	+	0.0418089i
$911$	−35.0988	+	20.2643i	−1.16288	+	0.671387i	−0.951992	−	0.306124i	$-0.900968\pi$
$911$	−35.0988	+	20.2643i	−1.16288	+	0.671387i	−0.210884	+	0.977511i	$0.567634\pi$
$912$	−1.73026	+	0.172777i	−0.0572945	+	0.00572120i
$913$	−31.3937			−1.03898
$914$	−3.18999	−	5.52523i	−0.105516	−	0.182758i
$915$	−8.29234	+	5.95918i	−0.274136	+	0.197005i
$916$	−1.09743	−	1.09743i	−0.0362602	−	0.0362602i
$917$	1.14159	−	0.305889i	0.0376988	−	0.0101014i
$918$	−12.7328	−	11.8291i	−0.420246	−	0.390417i
$919$	5.97895	−	10.3558i	0.197227	−	0.341608i	−0.750401	−	0.660983i	$-0.770140\pi$
$919$	5.97895	−	10.3558i	0.197227	−	0.341608i	0.947628	+	0.319375i	$0.103473\pi$
$920$	0.756974	−	1.31112i	0.0249567	−	0.0432263i
$921$	−24.4320	−	11.0302i	−0.805062	−	0.363458i
$922$	−31.1868	−	18.0057i	−1.02708	−	0.592987i
$923$	−15.0664	−	15.2698i	−0.495915	−	0.502610i
$924$	2.06682	−	0.781086i	0.0679933	−	0.0256958i
$925$	19.5696	−	5.24365i	0.643444	−	0.172410i
$926$	19.4427	−	11.2253i	0.638927	−	0.368885i
$927$	31.3220	−	6.31839i	1.02875	−	0.207523i
$928$	4.11589	+	4.11589i	0.135111	+	0.135111i
$929$	13.1437	−	13.1437i	0.431230	−	0.431230i	−0.457817	−	0.889047i	$-0.651368\pi$
$929$	13.1437	−	13.1437i	0.431230	−	0.431230i	0.889047	+	0.457817i	$0.151368\pi$
$930$	9.32863	+	4.21156i	0.305898	+	0.138103i
$931$	−1.78682	−	6.66851i	−0.0585607	−	0.218551i
$932$	8.62965	−	4.98233i	0.282674	−	0.163202i
$933$	−44.2888	−	7.25064i	−1.44995	−	0.237375i
$934$	−3.62347	−	13.5230i	−0.118563	−	0.442485i
$935$	12.5102			0.409128
$936$	−9.72023	+	4.74522i	−0.317716	+	0.155102i
$937$	−28.4270			−0.928669			−0.464335	−	0.885660i	$-0.653706\pi$
$937$	−28.4270			−0.928669			−0.464335	+	0.885660i	$0.653706\pi$
$938$	1.36990	+	5.11253i	0.0447287	+	0.166930i
$939$	−38.7199	+	47.3106i	−1.26358	+	1.54392i
$940$	−7.55295	+	4.36069i	−0.246350	+	0.142230i
$941$	2.47011	+	9.21859i	0.0805234	+	0.300518i	0.994429	−	0.105410i	$-0.0336154\pi$
$941$	2.47011	+	9.21859i	0.0805234	+	0.300518i	−0.913905	+	0.405927i	$0.866949\pi$
$942$	1.92774	+	19.3052i	0.0628091	+	0.628997i
$943$	9.71985	−	9.71985i	0.316522	−	0.316522i
$944$	−3.42622	−	3.42622i	−0.111514	−	0.111514i
$945$	0.998377	+	1.59110i	0.0324772	+	0.0517585i
$946$	−8.61721	+	4.97515i	−0.280170	+	0.161756i
$947$	19.5132	−	5.22855i	0.634094	−	0.169905i	0.0725674	−	0.997364i	$-0.476881\pi$
$947$	19.5132	−	5.22855i	0.634094	−	0.169905i	0.561527	+	0.827458i	$0.310214\pi$
$948$	−0.988058	+	6.03531i	−0.0320906	+	0.196018i
$949$	−3.34344	+	12.1514i	−0.108533	+	0.394452i
$950$	−3.42561	−	1.97778i	−0.111141	−	0.0641675i
$951$	−2.17453	−	21.7767i	−0.0705140	−	0.706157i
$952$	0.587209	−	1.01708i	0.0190316	−	0.0329636i
$953$	28.6270	−	49.5834i	0.927319	−	1.60616i	0.139532	−	0.990218i	$-0.455440\pi$
$953$	28.6270	−	49.5834i	0.927319	−	1.60616i	0.787788	−	0.615947i	$-0.211226\pi$
$954$	4.44042	−	6.68461i	0.143764	−	0.216422i
$955$	12.2437	−	3.28069i	0.396197	−	0.106161i
$956$	0.0510586	+	0.0510586i	0.00165135	+	0.00165135i
$957$	3.63937	+	36.4462i	0.117644	+	1.17814i
$958$	−13.3103	−	23.0541i	−0.430036	−	0.744845i
$959$	−1.36708			−0.0441452
$960$	−1.04063	−	1.44807i	−0.0335863	−	0.0467361i
$961$	1.68490	−	0.972775i	0.0543515	−	0.0313798i
$962$	−9.16206	−	16.1178i	−0.295397	−	0.519658i
$963$	0.765536	−	2.27538i	0.0246690	−	0.0733232i
$964$	−4.84236	+	18.0719i	−0.155962	+	0.582058i
$965$	−11.5373	−	6.66108i	−0.371400	−	0.214428i
$966$	0.144489	−	0.882577i	0.00464886	−	0.0283964i
$967$	−36.9339	+	9.89640i	−1.18771	+	0.318247i	−0.797982	−	0.602682i	$-0.794099\pi$
$967$	−36.9339	+	9.89640i	−1.18771	+	0.318247i	−0.389732	+	0.920929i	$0.627432\pi$
$968$	−2.12384	−	0.569081i	−0.0682627	−	0.0182909i
$969$	−5.78720	+	0.577887i	−0.185912	+	0.0185644i
$970$	14.6882	+	3.93570i	0.471611	+	0.126368i
$971$	−0.712957	−	0.411626i	−0.0228799	−	0.0132097i	0.488516	−	0.872555i	$-0.337538\pi$
$971$	−0.712957	−	0.411626i	−0.0228799	−	0.0132097i	−0.511396	+	0.859345i	$0.670872\pi$
$972$	−11.3052	+	10.7328i	−0.362614	+	0.344254i
$973$	0.187384	+	0.0502094i	0.00600726	+	0.00160964i
$974$	−7.63694	−	13.2276i	−0.244703	−	0.423839i
$975$	−24.2552	−	4.13806i	−0.776789	−	0.132524i
$976$	2.86325	−	4.95929i	0.0916503	−	0.158743i
$977$	2.22471	−	2.22471i	0.0711749	−	0.0711749i	−0.670623	−	0.741798i	$-0.733973\pi$
$977$	2.22471	−	2.22471i	0.0711749	−	0.0711749i	0.741798	+	0.670623i	$0.233973\pi$
$978$	11.9052	+	9.74349i	0.380688	+	0.311562i
$979$		−	37.6917i		−	1.20463i
$980$	5.00617	−	5.00617i	0.159916	−	0.159916i
$981$	−24.7249	−	1.55345i	−0.789405	−	0.0495980i
$982$	−0.484414	−	1.80786i	−0.0154583	−	0.0576911i
$983$	13.4472	−	50.1857i	0.428900	−	1.60068i	−0.326357	−	0.945247i	$-0.605821\pi$
$983$	13.4472	−	50.1857i	0.428900	−	1.60068i	0.755256	−	0.655429i	$-0.227512\pi$
$984$	−5.72363	−	15.1452i	−0.182463	−	0.482811i
$985$			21.9962i			0.700856i
$986$	13.7665	+	13.7665i	0.438414	+	0.438414i
$987$	−3.26297	+	3.98691i	−0.103861	+	0.126905i
$988$	−0.960276	+	3.49003i	−0.0305504	+	0.111033i
$989$			4.02754i			0.128068i
$990$	0.703617	−	11.1988i	0.0223624	−	0.355922i
$991$	−20.4564	−	35.4315i	−0.649818	−	1.12552i	−0.983166	−	0.182714i	$-0.941512\pi$
$991$	−20.4564	−	35.4315i	−0.649818	−	1.12552i	0.333348	−	0.942804i	$-0.391822\pi$
$992$	−5.73982			−0.182240
$993$	7.10405	−	15.7355i	0.225440	−	0.499351i
$994$	0.540684	−	2.01786i	0.0171495	−	0.0640026i
$995$	−5.91912	+	22.0905i	−0.187649	+	0.700315i
$996$	8.73442	+	12.1541i	0.276761	+	0.385119i
$997$	30.9293			0.979542			0.489771	−	0.871851i	$-0.337080\pi$
$997$	30.9293			0.979542			0.489771	+	0.871851i	$0.337080\pi$
$998$	5.66579	+	9.81344i	0.179347	+	0.310639i
$999$	−19.5750	−	18.1855i	−0.619324	−	0.575365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.167.12	yes	56
3.2	odd	2		702.2.bc.a.557.3		56
9.2	odd	6		234.2.y.a.11.5	✓	56
9.7	even	3		702.2.bb.a.89.10		56
13.6	odd	12		234.2.y.a.149.5	yes	56
39.32	even	12		702.2.bb.a.71.10		56
117.97	odd	12		702.2.bc.a.305.3		56
117.110	even	12	inner	234.2.z.a.227.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.5	✓	56	9.2	odd	6
234.2.y.a.149.5	yes	56	13.6	odd	12
234.2.z.a.167.12	yes	56	1.1	even	1	trivial
234.2.z.a.227.12	yes	56	117.110	even	12	inner
702.2.bb.a.71.10		56	39.32	even	12
702.2.bb.a.89.10		56	9.7	even	3
702.2.bc.a.305.3		56	117.97	odd	12
702.2.bc.a.557.3		56	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.612305 + 1.62021i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.266463 + 0.994452i) q^{5} +(-1.40653 + 1.01078i) q^{6} +(-0.248284 + 0.248284i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.25016 + 1.98413i) q^{9} +(-0.891601 + 0.514766i) q^{10} +(3.50922 - 0.940292i) q^{11} +(-1.34038 - 1.09699i) q^{12} +(-3.13452 + 1.78180i) q^{13} +(-0.304085 - 0.175564i) q^{14} +(-1.44807 + 1.04063i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.67236 - 2.89660i) q^{17} +(-2.49890 - 1.65996i) q^{18} +(-0.969723 + 0.259837i) q^{19} +(-0.727989 - 0.727989i) q^{20} +(-0.554299 - 0.250247i) q^{21} +(1.81650 + 3.14628i) q^{22} +1.47052 q^{23} +(0.712697 - 1.57863i) q^{24} +(3.41219 - 1.97003i) q^{25} +(-2.53236 - 2.56655i) q^{26} +(-4.59249 - 2.43085i) q^{27} +(0.0908784 - 0.339163i) q^{28} +(5.04092 + 2.91038i) q^{29} +(-1.37996 - 1.12939i) q^{30} +(-5.54424 + 1.48558i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.67218 + 5.10993i) q^{33} +(3.23074 + 0.865675i) q^{34} +(-0.313065 - 0.180748i) q^{35} +(0.956637 - 2.84339i) q^{36} +(4.96682 + 1.33085i) q^{37} +(-0.501966 - 0.869430i) q^{38} +(-4.80617 - 3.98757i) q^{39} +(0.514766 - 0.891601i) q^{40} +(6.60980 - 6.60980i) q^{41} +(0.0982571 - 0.600180i) q^{42} +2.73886i q^{43} +(-2.56893 + 2.56893i) q^{44} +(-2.57270 - 1.70899i) q^{45} +(0.380599 + 1.42041i) q^{46} +(2.19251 - 8.18256i) q^{47} +(1.70930 + 0.279834i) q^{48} +6.87671i q^{49} +(2.78605 + 2.78605i) q^{50} +(5.71710 + 0.935962i) q^{51} +(1.82367 - 3.11034i) q^{52} +2.67501i q^{53} +(1.15940 - 5.06516i) q^{54} +(1.87015 + 3.23920i) q^{55} +0.351127 q^{56} +(-1.01476 - 1.41206i) q^{57} +(-1.50652 + 5.62241i) q^{58} +(1.25408 - 4.68030i) q^{59} +(0.733745 - 1.62525i) q^{60} +5.72649 q^{61} +(-2.86991 - 4.97083i) q^{62} +(0.0660532 - 1.05131i) q^{63} +1.00000i q^{64} +(-2.60715 - 2.64234i) q^{65} +(-3.98538 + 4.86960i) q^{66} +(-10.6589 - 10.6589i) q^{67} +3.34471i q^{68} +(0.900407 + 2.38255i) q^{69} +(0.0935622 - 0.349179i) q^{70} +(1.53985 + 5.74681i) q^{71} +(2.99410 + 0.188118i) q^{72} +(2.47165 - 2.47165i) q^{73} +5.14203i q^{74} +(5.28117 + 4.32221i) q^{75} +(0.709887 - 0.709887i) q^{76} +(-0.637824 + 1.10474i) q^{77} +(2.60777 - 5.67446i) q^{78} +(-1.76544 - 3.05783i) q^{79} +(0.994452 + 0.266463i) q^{80} +(1.12648 - 8.92922i) q^{81} +(8.09532 + 4.67384i) q^{82} +(-8.34680 - 2.23652i) q^{83} +(0.605160 - 0.0604289i) q^{84} +(3.32615 + 0.891240i) q^{85} +(-2.64553 + 0.708868i) q^{86} +(-1.62884 + 9.94939i) q^{87} +(-3.14628 - 1.81650i) q^{88} +(2.68520 - 10.0213i) q^{89} +(0.984889 - 2.92736i) q^{90} +(0.335858 - 1.22064i) q^{91} +(-1.27351 + 0.735260i) q^{92} +(-5.80171 - 8.07321i) q^{93} +8.47121 q^{94} +(-0.516790 - 0.895107i) q^{95} +(0.172100 + 1.72348i) q^{96} +(-10.4441 - 10.4441i) q^{97} +(-6.64239 + 1.77982i) q^{98} +(-6.03066 + 9.07854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

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