LMFDB - Embedded newform 378.2.z.a.41.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.14
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(-1.47964 + 0.900370i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23395 - 1.03541i) q^{5} +(-1.30081 + 1.14363i) q^{6} +(1.54951 - 2.14453i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.37867 - 2.66445i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(-1.47964 + 0.900370i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23395 - 1.03541i) q^{5} +(-1.30081 + 1.14363i) q^{6} +(1.54951 - 2.14453i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.37867 - 2.66445i) q^{9} +(-1.39500 - 0.805406i) q^{10} +(-0.858116 - 1.02266i) q^{11} +(-1.08246 + 1.35214i) q^{12} +(3.00736 + 0.530279i) q^{13} +(1.15357 - 2.38102i) q^{14} +(2.75806 + 0.421019i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.40707 - 2.43712i) q^{17} +(0.895047 - 2.86337i) q^{18} +(2.55888 - 1.47737i) q^{19} +(-1.51367 - 0.550930i) q^{20} +(-0.361842 + 4.56827i) q^{21} +(-1.02266 - 0.858116i) q^{22} +(-0.215196 - 0.591247i) q^{23} +(-0.831221 + 1.51956i) q^{24} +(-0.417673 - 2.36874i) q^{25} +3.05376 q^{26} +(0.359055 + 5.18373i) q^{27} +(0.722589 - 2.54517i) q^{28} +(-0.585362 + 0.103215i) q^{29} +(2.78927 - 0.0643089i) q^{30} +(1.88581 + 5.18123i) q^{31} +(0.642788 - 0.766044i) q^{32} +(2.19048 + 0.740551i) q^{33} +(0.962493 - 2.64443i) q^{34} +(-4.13249 + 1.04188i) q^{35} +(0.384230 - 2.97529i) q^{36} +(4.27982 - 7.41287i) q^{37} +(2.26347 - 1.89927i) q^{38} +(-4.92726 + 1.92312i) q^{39} +(-1.58634 - 0.279715i) q^{40} +(-0.515556 + 2.92386i) q^{41} +(0.436926 + 4.56170i) q^{42} +(-8.07611 + 6.77666i) q^{43} +(-1.15614 - 0.667496i) q^{44} +(-4.46001 + 1.86032i) q^{45} +(-0.314596 - 0.544896i) q^{46} +(-7.18559 - 2.61534i) q^{47} +(-0.554723 + 1.64082i) q^{48} +(-2.19804 - 6.64595i) q^{49} +(-0.822656 - 2.26023i) q^{50} +(0.112350 + 4.87294i) q^{51} +(3.00736 - 0.530279i) q^{52} +9.51219i q^{53} +(1.25375 + 5.04263i) q^{54} +2.15042i q^{55} +(0.269648 - 2.63197i) q^{56} +(-2.45604 + 4.48992i) q^{57} +(-0.558546 + 0.203294i) q^{58} +(-4.31431 - 3.62014i) q^{59} +(2.73572 - 0.547683i) q^{60} +(-1.62718 + 4.47064i) q^{61} +(2.75687 + 4.77505i) q^{62} +(-3.57773 - 7.08518i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-3.16189 - 3.76819i) q^{65} +(2.28579 + 0.348928i) q^{66} +(-1.70023 + 9.64250i) q^{67} +(0.488670 - 2.77139i) q^{68} +(0.850754 + 0.681076i) q^{69} +(-3.88879 + 1.74365i) q^{70} +(5.73392 + 3.31048i) q^{71} +(-0.138262 - 2.99681i) q^{72} +(7.98703 - 4.61131i) q^{73} +(2.92757 - 8.04343i) q^{74} +(2.75075 + 3.12883i) q^{75} +(1.89927 - 2.26347i) q^{76} +(-3.52279 + 0.255633i) q^{77} +(-4.51846 + 2.74951i) q^{78} +(0.490904 + 2.78405i) q^{79} -1.61081 q^{80} +(-5.19855 - 7.34677i) q^{81} +2.96897i q^{82} +(0.953973 + 5.41025i) q^{83} +(1.22242 + 4.41652i) q^{84} +(-4.25967 + 1.55039i) q^{85} +(-6.77666 + 8.07611i) q^{86} +(0.773193 - 0.679763i) q^{87} +(-1.25448 - 0.456594i) q^{88} +(-5.41860 - 9.38529i) q^{89} +(-4.06921 + 2.60653i) q^{90} +(5.79714 - 5.62772i) q^{91} +(-0.404437 - 0.481989i) q^{92} +(-7.45535 - 5.96842i) q^{93} +(-7.53057 - 1.32784i) q^{94} +(-4.68723 - 0.826485i) q^{95} +(-0.261371 + 1.71222i) q^{96} +(11.0771 + 13.2012i) q^{97} +(-3.31871 - 6.16329i) q^{98} +(-3.90789 + 0.876491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−1.47964	+	0.900370i	−0.854270	+	0.519829i
$3$	−1.47964	+	0.900370i	−0.854270	+	0.519829i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−1.23395	−	1.03541i	−0.551841	−	0.463049i	0.323723	−	0.946152i	$-0.395065\pi$
$5$	−1.23395	−	1.03541i	−0.551841	−	0.463049i	−0.875564	+	0.483103i	$0.839510\pi$
$6$	−1.30081	+	1.14363i	−0.531055	+	0.466884i
$7$	1.54951	−	2.14453i	0.585659	−	0.810557i
$7$	1.54951	−	2.14453i	0.585659	−	0.810557i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	1.37867	−	2.66445i	0.459556	−	0.888149i
$10$	−1.39500	−	0.805406i	−0.441139	−	0.254692i
$11$	−0.858116	−	1.02266i	−0.258732	−	0.308344i	0.621004	−	0.783807i	$-0.286725\pi$
$11$	−0.858116	−	1.02266i	−0.258732	−	0.308344i	−0.879736	+	0.475463i	$0.842281\pi$
$12$	−1.08246	+	1.35214i	−0.312480	+	0.390328i
$13$	3.00736	+	0.530279i	0.834092	+	0.147073i	0.574355	−	0.818606i	$-0.305253\pi$
$13$	3.00736	+	0.530279i	0.834092	+	0.147073i	0.259737	+	0.965679i	$0.416364\pi$
$14$	1.15357	−	2.38102i	0.308306	−	0.636355i
$15$	2.75806	+	0.421019i	0.712128	+	0.108707i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.40707	−	2.43712i	0.341265	−	0.591088i	−0.643403	−	0.765528i	$-0.722478\pi$
$17$	1.40707	−	2.43712i	0.341265	−	0.591088i	0.984668	+	0.174440i	$0.0558114\pi$
$18$	0.895047	−	2.86337i	0.210965	−	0.674903i
$19$	2.55888	−	1.47737i	0.587048	−	0.338932i	−0.176881	−	0.984232i	$-0.556601\pi$
$19$	2.55888	−	1.47737i	0.587048	−	0.338932i	0.763929	+	0.645300i	$0.223268\pi$
$20$	−1.51367	−	0.550930i	−0.338466	−	0.123192i
$21$	−0.361842	+	4.56827i	−0.0789604	+	0.996878i
$22$	−1.02266	−	0.858116i	−0.218032	−	0.182951i
$23$	−0.215196	−	0.591247i	−0.0448715	−	0.123284i	0.915233	−	0.402925i	$-0.132007\pi$
$23$	−0.215196	−	0.591247i	−0.0448715	−	0.123284i	−0.960104	+	0.279642i	$0.909784\pi$
$24$	−0.831221	+	1.51956i	−0.169672	+	0.310180i
$25$	−0.417673	−	2.36874i	−0.0835347	−	0.473749i
$26$	3.05376			0.598891
$27$	0.359055	+	5.18373i	0.0691002	+	0.997610i
$28$	0.722589	−	2.54517i	0.136556	−	0.480991i
$29$	−0.585362	+	0.103215i	−0.108699	+	0.0191666i	−0.227733	−	0.973724i	$-0.573131\pi$
$29$	−0.585362	+	0.103215i	−0.108699	+	0.0191666i	0.119034	+	0.992890i	$0.462020\pi$
$30$	2.78927	−	0.0643089i	0.509248	−	0.0117411i
$31$	1.88581	+	5.18123i	0.338702	+	0.930576i	0.985763	+	0.168138i	$0.0537755\pi$
$31$	1.88581	+	5.18123i	0.338702	+	0.930576i	−0.647061	+	0.762438i	$0.724002\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	2.19048	+	0.740551i	0.381313	+	0.128913i
$34$	0.962493	−	2.64443i	0.165066	−	0.453516i
$35$	−4.13249	+	1.04188i	−0.698519	+	0.176109i
$36$	0.384230	−	2.97529i	0.0640383	−	0.495882i
$37$	4.27982	−	7.41287i	0.703598	−	1.21867i	−0.263597	−	0.964633i	$-0.584909\pi$
$37$	4.27982	−	7.41287i	0.703598	−	1.21867i	0.967195	−	0.254035i	$-0.0817579\pi$
$38$	2.26347	−	1.89927i	0.367183	−	0.308103i
$39$	−4.92726	+	1.92312i	−0.788993	+	0.307945i
$40$	−1.58634	−	0.279715i	−0.250822	−	0.0442267i
$41$	−0.515556	+	2.92386i	−0.0805162	+	0.456630i	0.917718	+	0.397232i	$0.130029\pi$
$41$	−0.515556	+	2.92386i	−0.0805162	+	0.456630i	−0.998234	+	0.0593981i	$0.981082\pi$
$42$	0.436926	+	4.56170i	0.0674192	+	0.703885i
$43$	−8.07611	+	6.77666i	−1.23160	+	1.03343i	−0.233462	+	0.972366i	$0.575005\pi$
$43$	−8.07611	+	6.77666i	−1.23160	+	1.03343i	−0.998134	+	0.0610656i	$0.980550\pi$
$44$	−1.15614	−	0.667496i	−0.174294	−	0.100629i
$45$	−4.46001	+	1.86032i	−0.664858	+	0.277320i
$46$	−0.314596	−	0.544896i	−0.0463846	−	0.0803405i
$47$	−7.18559	−	2.61534i	−1.04813	−	0.381487i	−0.240171	−	0.970731i	$-0.577203\pi$
$47$	−7.18559	−	2.61534i	−1.04813	−	0.381487i	−0.807955	+	0.589244i	$0.799426\pi$
$48$	−0.554723	+	1.64082i	−0.0800674	+	0.236832i
$49$	−2.19804	−	6.64595i	−0.314006	−	0.949421i
$50$	−0.822656	−	2.26023i	−0.116341	−	0.319645i
$51$	0.112350	+	4.87294i	0.0157321	+	0.682348i
$52$	3.00736	−	0.530279i	0.417046	−	0.0735365i
$53$			9.51219i			1.30660i	0.757099	+	0.653300i	$0.226616\pi$
$53$			9.51219i			1.30660i	−0.757099	+	0.653300i	$0.773384\pi$
$54$	1.25375	+	5.04263i	0.170613	+	0.686215i
$55$			2.15042i			0.289962i
$56$	0.269648	−	2.63197i	0.0360332	−	0.351712i
$57$	−2.45604	+	4.48992i	−0.325311	+	0.594705i
$58$	−0.558546	+	0.203294i	−0.0733407	+	0.0266938i
$59$	−4.31431	−	3.62014i	−0.561675	−	0.471302i	0.317196	−	0.948360i	$-0.397259\pi$
$59$	−4.31431	−	3.62014i	−0.561675	−	0.471302i	−0.878872	+	0.477058i	$0.841703\pi$
$60$	2.73572	−	0.547683i	0.353180	−	0.0707056i
$61$	−1.62718	+	4.47064i	−0.208339	+	0.572407i	−0.999217	−	0.0395669i	$-0.987402\pi$
$61$	−1.62718	+	4.47064i	−0.208339	+	0.572407i	0.790878	+	0.611974i	$0.209624\pi$
$62$	2.75687	+	4.77505i	0.350123	+	0.606431i
$63$	−3.57773	−	7.08518i	−0.450752	−	0.892649i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−3.16189	−	3.76819i	−0.392184	−	0.467387i
$66$	2.28579	+	0.348928i	0.281362	+	0.0429500i
$67$	−1.70023	+	9.64250i	−0.207716	+	1.17802i	0.685391	+	0.728175i	$0.259631\pi$
$67$	−1.70023	+	9.64250i	−0.207716	+	1.17802i	−0.893108	+	0.449843i	$0.851480\pi$
$68$	0.488670	−	2.77139i	0.0592600	−	0.336080i
$69$	0.850754	+	0.681076i	0.102419	+	0.0819919i
$70$	−3.88879	+	1.74365i	−0.464799	+	0.208406i
$71$	5.73392	+	3.31048i	0.680491	+	0.392882i	0.800040	−	0.599947i	$-0.204812\pi$
$71$	5.73392	+	3.31048i	0.680491	+	0.392882i	−0.119549	+	0.992828i	$0.538145\pi$
$72$	−0.138262	−	2.99681i	−0.0162943	−	0.353178i
$73$	7.98703	−	4.61131i	0.934811	−	0.539714i	0.0464813	−	0.998919i	$-0.485199\pi$
$73$	7.98703	−	4.61131i	0.934811	−	0.539714i	0.888330	+	0.459206i	$0.151866\pi$
$74$	2.92757	−	8.04343i	0.340323	−	0.935030i
$75$	2.75075	+	3.12883i	0.317629	+	0.361286i
$76$	1.89927	−	2.26347i	0.217862	−	0.259637i
$77$	−3.52279	+	0.255633i	−0.401459	+	0.0291321i
$78$	−4.51846	+	2.74951i	−0.511615	+	0.311321i
$79$	0.490904	+	2.78405i	0.0552310	+	0.313230i	0.999890	−	0.0148230i	$-0.00471850\pi$
$79$	0.490904	+	2.78405i	0.0552310	+	0.313230i	−0.944659	+	0.328053i	$0.893607\pi$
$80$	−1.61081			−0.180094
$81$	−5.19855	−	7.34677i	−0.577617	−	0.816308i
$82$			2.96897i			0.327867i
$83$	0.953973	+	5.41025i	0.104712	+	0.593852i	0.991335	+	0.131359i	$0.0419340\pi$
$83$	0.953973	+	5.41025i	0.104712	+	0.593852i	−0.886623	+	0.462493i	$0.846955\pi$
$84$	1.22242	+	4.41652i	0.133377	+	0.481882i
$85$	−4.25967	+	1.55039i	−0.462027	+	0.168164i
$86$	−6.77666	+	8.07611i	−0.730746	+	0.870870i
$87$	0.773193	−	0.679763i	0.0828950	−	0.0728783i
$88$	−1.25448	−	0.456594i	−0.133728	−	0.0486731i
$89$	−5.41860	−	9.38529i	−0.574371	−	0.994839i	−0.996110	−	0.0881218i	$-0.971914\pi$
$89$	−5.41860	−	9.38529i	−0.574371	−	0.994839i	0.421739	−	0.906717i	$-0.361420\pi$
$90$	−4.06921	+	2.60653i	−0.428932	+	0.274752i
$91$	5.79714	−	5.62772i	0.607705	−	0.589945i
$92$	−0.404437	−	0.481989i	−0.0421654	−	0.0502508i
$93$	−7.45535	−	5.96842i	−0.773083	−	0.618897i
$94$	−7.53057	−	1.32784i	−0.776719	−	0.136957i
$95$	−4.68723	−	0.826485i	−0.480900	−	0.0847956i
$96$	−0.261371	+	1.71222i	−0.0266760	+	0.174752i
$97$	11.0771	+	13.2012i	1.12471	+	1.34038i	0.933396	+	0.358849i	$0.116831\pi$
$97$	11.0771	+	13.2012i	1.12471	+	1.34038i	0.191315	+	0.981529i	$0.438725\pi$
$98$	−3.31871	−	6.16329i	−0.335240	−	0.622587i
$99$	−3.90789	+	0.876491i	−0.392757	+	0.0880907i
$100$	−1.20264	−	2.08304i	−0.120264	−	0.208304i
$101$	−7.40197	−	2.69410i	−0.736524	−	0.268073i	−0.0536001	−	0.998562i	$-0.517070\pi$
$101$	−7.40197	−	2.69410i	−0.736524	−	0.268073i	−0.682924	+	0.730490i	$0.739292\pi$
$102$	0.956820	+	4.77940i	0.0947393	+	0.473231i
$103$	2.83585	−	3.37964i	0.279425	−	0.333005i	−0.608018	−	0.793923i	$-0.708035\pi$
$103$	2.83585	−	3.37964i	0.279425	−	0.333005i	0.887443	+	0.460918i	$0.152480\pi$
$104$	2.86959	−	1.04445i	0.281387	−	0.102416i
$105$	5.17653	−	5.26237i	0.505177	−	0.513555i
$106$	1.65177	+	9.36768i	0.160434	+	0.909869i
$107$			17.8645i			1.72703i	0.504324	+	0.863515i	$0.331742\pi$
$107$			17.8645i			1.72703i	−0.504324	+	0.863515i	$0.668258\pi$
$108$	2.11034	+	4.74831i	0.203068	+	0.456906i
$109$	18.9891			1.81882			0.909412	−	0.415896i	$-0.136532\pi$
$109$	18.9891			1.81882			0.909412	+	0.415896i	$0.136532\pi$
$110$	0.373416	+	2.11775i	0.0356039	+	0.201919i
$111$	0.341729	+	14.8218i	0.0324355	+	1.40682i
$112$	−0.191487	−	2.63881i	−0.0180938	−	0.249344i
$113$	3.78398	−	4.50957i	0.355967	−	0.424224i	−0.558109	−	0.829767i	$-0.688473\pi$
$113$	3.78398	−	4.50957i	0.355967	−	0.424224i	0.914076	+	0.405543i	$0.132918\pi$
$114$	−1.63907	+	4.84820i	−0.153513	+	0.454075i
$115$	−0.346641	+	0.952387i	−0.0323244	+	0.0888106i
$116$	−0.514759	+	0.297196i	−0.0477941	+	0.0275940i
$117$	5.55906	−	7.28188i	0.513935	−	0.673210i
$118$	−4.87740	−	2.81597i	−0.449001	−	0.259231i
$119$	−3.04621	−	6.79384i	−0.279246	−	0.622791i
$120$	2.59906	−	1.01442i	0.237260	−	0.0926031i
$121$	1.60065	−	9.07776i	0.145514	−	0.825251i
$122$	−0.826142	+	4.68528i	−0.0747954	+	0.424186i
$123$	−1.86972	−	4.79045i	−0.168587	−	0.431940i
$124$	3.54417	+	4.22378i	0.318276	+	0.379306i
$125$	−5.96426	+	10.3304i	−0.533460	+	0.923979i
$126$	−4.75371	−	6.35628i	−0.423494	−	0.566262i
$127$	0.664345	+	1.15068i	0.0589511	+	0.102106i	0.893995	−	0.448077i	$-0.147891\pi$
$127$	0.664345	+	1.15068i	0.0589511	+	0.102106i	−0.835044	+	0.550184i	$0.814558\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	5.84823	−	17.2985i	0.514908	−	1.52305i
$130$	−3.76819	−	3.16189i	−0.330492	−	0.277316i
$131$	6.48704	−	2.36109i	0.566775	−	0.206289i	−0.0427090	−	0.999088i	$-0.513599\pi$
$131$	6.48704	−	2.36109i	0.566775	−	0.206289i	0.609484	+	0.792798i	$0.291377\pi$
$132$	2.31166	−	0.0532972i	0.201204	−	0.00463893i
$133$	0.796740	−	7.77681i	0.0690861	−	0.674335i
$134$			9.79125i			0.845835i
$135$	4.92423	−	6.76825i	0.423810	−	0.582518i
$136$		−	2.81414i		−	0.241311i
$137$	16.5255	−	2.91388i	1.41187	−	0.248950i	0.584855	−	0.811138i	$-0.301151\pi$
$137$	16.5255	−	2.91388i	1.41187	−	0.248950i	0.827010	+	0.562188i	$0.190040\pi$
$138$	0.956097	+	0.522997i	0.0813884	+	0.0445205i
$139$	4.85763	+	13.3462i	0.412019	+	1.13201i	0.956115	+	0.292990i	$0.0946503\pi$
$139$	4.85763	+	13.3462i	0.412019	+	1.13201i	−0.544096	+	0.839023i	$0.683127\pi$
$140$	−3.52693	+	2.39244i	−0.298080	+	0.202198i
$141$	12.9869	−	2.59993i	1.09369	−	0.218953i
$142$	6.22167	+	2.26450i	0.522111	+	0.190033i
$143$	−2.03837	−	3.53056i	−0.170457	−	0.295240i
$144$	−0.656552	−	2.92728i	−0.0547127	−	0.243940i
$145$	0.829179	+	0.478727i	0.0688596	+	0.0397561i
$146$	7.06494	−	5.92819i	0.584699	−	0.490621i
$147$	9.23612	+	7.85455i	0.761783	+	0.647833i
$148$	1.48637	−	8.42960i	0.122179	−	0.692909i
$149$	−16.7575	−	2.95480i	−1.37283	−	0.242067i	−0.561897	−	0.827207i	$-0.689928\pi$
$149$	−16.7575	−	2.95480i	−1.37283	−	0.242067i	−0.810932	+	0.585140i	$0.801040\pi$
$150$	3.25228	+	2.60363i	0.265547	+	0.212586i
$151$	−9.56348	+	8.02471i	−0.778265	+	0.653042i	−0.942811	−	0.333328i	$-0.891828\pi$
$151$	−9.56348	+	8.02471i	−0.778265	+	0.653042i	0.164546	+	0.986369i	$0.447384\pi$
$152$	1.47737	−	2.55888i	0.119831	−	0.207553i
$153$	−4.55369	−	7.10904i	−0.368144	−	0.574732i
$154$	−3.42488	+	0.863475i	−0.275985	+	0.0695808i
$155$	3.03769	−	8.34598i	0.243993	−	0.670365i
$156$	−3.97237	+	3.49236i	−0.318044	+	0.279613i
$157$	1.12277	−	1.33807i	0.0896069	−	0.106789i	−0.719378	−	0.694619i	$-0.755573\pi$
$157$	1.12277	−	1.33807i	0.0896069	−	0.106789i	0.808985	+	0.587830i	$0.200017\pi$
$158$	0.966891	+	2.65651i	0.0769217	+	0.211341i
$159$	−8.56449	−	14.0746i	−0.679208	−	1.11619i
$160$	−1.58634	+	0.279715i	−0.125411	+	0.0221134i
$161$	−1.60140	−	0.454647i	−0.126208	−	0.0358312i
$162$	−6.39533	−	6.33244i	−0.502464	−	0.497524i
$163$	12.8614			1.00738			0.503692	−	0.863883i	$-0.331975\pi$
$163$	12.8614			1.00738			0.503692	+	0.863883i	$0.331975\pi$
$164$	0.515556	+	2.92386i	0.0402581	+	0.228315i
$165$	−1.93617	−	3.18185i	−0.150731	−	0.247706i
$166$	1.87896	+	5.16240i	0.145836	+	0.400680i
$167$	4.70594	+	3.94876i	0.364157	+	0.305564i	0.806445	−	0.591309i	$-0.201389\pi$
$167$	4.70594	+	3.94876i	0.364157	+	0.305564i	−0.442288	+	0.896873i	$0.645833\pi$
$168$	1.97077	+	4.13716i	0.152048	+	0.319189i
$169$	−3.45297	−	1.25678i	−0.265613	−	0.0966753i
$170$	−3.92574	+	2.26653i	−0.301090	+	0.173835i
$171$	−0.408528	−	8.85481i	−0.0312409	−	0.677145i
$172$	−5.27131	+	9.13017i	−0.401934	+	0.696169i
$173$	−10.3712	+	8.70250i	−0.788510	+	0.661639i	−0.945376	−	0.325981i	$-0.894305\pi$
$173$	−10.3712	+	8.70250i	−0.788510	+	0.661639i	0.156866	+	0.987620i	$0.449861\pi$
$174$	0.643407	−	0.803700i	0.0487765	−	0.0609283i
$175$	−5.72704	−	2.77468i	−0.432923	−	0.209746i
$176$	−1.31471	−	0.231819i	−0.0991000	−	0.0174740i
$177$	9.64309	+	1.47202i	0.724819	+	0.110644i
$178$	−6.96602	−	8.30178i	−0.522125	−	0.622245i
$179$	13.2920	+	7.67414i	0.993491	+	0.573592i	0.906316	−	0.422601i	$-0.138883\pi$
$179$	13.2920	+	7.67414i	0.993491	+	0.573592i	0.0871749	+	0.996193i	$0.472216\pi$
$180$	−3.55477	+	3.27354i	−0.264957	+	0.243995i
$181$	−13.4024	+	7.73789i	−0.996194	+	0.575153i	−0.907120	−	0.420872i	$-0.861724\pi$
$181$	−13.4024	+	7.73789i	−0.996194	+	0.575153i	−0.0890738	+	0.996025i	$0.528391\pi$
$182$	4.73182	−	6.54888i	0.350746	−	0.485435i
$183$	−1.61759	−	8.08001i	−0.119576	−	0.597291i
$184$	−0.481989	−	0.404437i	−0.0355327	−	0.0298155i
$185$	−12.9565	+	4.71576i	−0.952578	+	0.346710i
$186$	−8.37849	−	4.58314i	−0.614340	−	0.336052i
$187$	−3.69978	+	0.652371i	−0.270555	+	0.0477061i
$188$	−7.64674			−0.557696
$189$	11.6730	+	7.26223i	0.849089	+	0.528250i
$190$	−4.75954			−0.345293
$191$	−8.65857	+	1.52674i	−0.626512	+	0.110471i	−0.477885	−	0.878422i	$-0.658596\pi$
$191$	−8.65857	+	1.52674i	−0.626512	+	0.110471i	−0.148627	+	0.988893i	$0.547485\pi$
$192$	0.0399233	+	1.73159i	0.00288122	+	0.124967i
$193$	−8.00807	+	2.91470i	−0.576433	+	0.209805i	−0.613752	−	0.789499i	$-0.710341\pi$
$193$	−8.00807	+	2.91470i	−0.576433	+	0.209805i	0.0373188	+	0.999303i	$0.488118\pi$
$194$	13.2012	+	11.0771i	0.947790	+	0.795290i
$195$	8.07122	+	2.72870i	0.577992	+	0.195406i
$196$	−4.33853	−	5.49337i	−0.309895	−	0.392384i
$197$	19.7723	−	11.4156i	1.40872	−	0.813326i	0.413456	−	0.910524i	$-0.364321\pi$
$197$	19.7723	−	11.4156i	1.40872	−	0.813326i	0.995265	+	0.0971984i	$0.0309881\pi$
$198$	−3.69632	+	1.54177i	−0.262686	+	0.109569i
$199$	−12.2929	−	7.09732i	−0.871423	−	0.503116i	−0.00360183	−	0.999994i	$-0.501146\pi$
$199$	−12.2929	−	7.09732i	−0.871423	−	0.503116i	−0.867821	+	0.496877i	$0.834480\pi$
$200$	−1.54609	−	1.84256i	−0.109325	−	0.130288i
$201$	−6.16608	−	15.7983i	−0.434922	−	1.11432i
$202$	−7.75734	−	1.36783i	−0.545805	−	0.0962401i
$203$	−0.685675	+	1.41526i	−0.0481250	+	0.0993318i
$204$	1.77222	+	4.54064i	0.124080	+	0.317908i
$205$	3.66357	−	3.07410i	0.255875	−	0.214704i
$206$	2.20590	−	3.82073i	0.153692	−	0.266203i
$207$	−1.87203	−	0.241754i	−0.130115	−	0.0168031i
$208$	2.64463	−	1.52688i	0.183372	−	0.105870i
$209$	−3.70667	−	1.34912i	−0.256396	−	0.0933204i
$210$	4.18408	−	6.08132i	0.288729	−	0.419651i
$211$	−10.7778	−	9.04368i	−0.741977	−	0.622593i	0.191391	−	0.981514i	$-0.438700\pi$
$211$	−10.7778	−	9.04368i	−0.741977	−	0.622593i	−0.933368	+	0.358921i	$0.883145\pi$
$212$	3.25336	+	8.93853i	0.223442	+	0.613901i
$213$	−11.4648	+	0.264331i	−0.785554	+	0.0181116i
$214$	3.10214	+	17.5931i	0.212058	+	1.20264i
$215$	16.9822			1.15817
$216$	2.90282	+	4.30972i	0.197512	+	0.293239i
$217$	14.0334	+	3.98417i	0.952649	+	0.270463i
$218$	18.7006	−	3.29742i	1.26656	−	0.223329i
$219$	−7.66604	+	14.0144i	−0.518023	+	0.947003i
$220$	0.735487	+	2.02073i	0.0495865	+	0.136238i
$221$	5.52392	−	6.58316i	0.371579	−	0.442831i
$222$	2.91032	+	14.5373i	0.195328	+	0.975678i
$223$	0.747167	−	2.05282i	0.0500340	−	0.137467i	−0.912159	−	0.409838i	$-0.865585\pi$
$223$	0.747167	−	2.05282i	0.0500340	−	0.137467i	0.962192	+	0.272370i	$0.0878076\pi$
$224$	−0.646802	−	2.56547i	−0.0432163	−	0.171413i
$225$	−6.88722	−	2.15284i	−0.459148	−	0.143523i
$226$	2.94341	−	5.09814i	0.195793	−	0.339123i
$227$	16.9563	−	14.2280i	1.12543	−	0.944347i	0.126563	−	0.991959i	$-0.459606\pi$
$227$	16.9563	−	14.2280i	1.12543	−	0.944347i	0.998866	+	0.0476119i	$0.0151611\pi$
$228$	−0.772284	+	5.05916i	−0.0511457	+	0.335051i
$229$	−25.7303	−	4.53695i	−1.70031	−	0.299810i	−0.762507	−	0.646980i	$-0.776032\pi$
$229$	−25.7303	−	4.53695i	−1.70031	−	0.299810i	−0.937802	+	0.347170i	$0.887143\pi$
$230$	−0.175994	+	0.998112i	−0.0116047	+	0.0658136i
$231$	4.98230	−	3.55006i	0.327811	−	0.233577i
$232$	−0.455331	+	0.382068i	−0.0298939	+	0.0250840i
$233$	7.70772	+	4.45006i	0.504950	+	0.291533i	0.730755	−	0.682640i	$-0.239168\pi$
$233$	7.70772	+	4.45006i	0.504950	+	0.291533i	−0.225806	+	0.974172i	$0.572501\pi$
$234$	4.21012	−	8.13657i	0.275224	−	0.531904i
$235$	6.15873	+	10.6672i	0.401751	+	0.695854i
$236$	−5.29228	−	1.92623i	−0.344498	−	0.125387i
$237$	−3.23304	−	3.67740i	−0.210008	−	0.238873i
$238$	−4.17967	−	6.16166i	−0.270928	−	0.399401i
$239$	−7.59992	−	20.8806i	−0.491598	−	1.35066i	−0.899217	−	0.437503i	$-0.855863\pi$
$239$	−7.59992	−	20.8806i	−0.491598	−	1.35066i	0.407619	−	0.913152i	$-0.366359\pi$
$240$	2.38342	−	1.45033i	0.153849	−	0.0936182i
$241$	4.21678	−	0.743533i	0.271627	−	0.0478952i	−0.0361755	−	0.999345i	$-0.511518\pi$
$241$	4.21678	−	0.743533i	0.271627	−	0.0478952i	0.307802	+	0.951450i	$0.400406\pi$
$242$		−	9.21780i		−	0.592543i
$243$	14.3068	+	6.18996i	0.917781	+	0.397086i
$244$			4.75756i			0.304572i
$245$	−4.16899	+	10.4767i	−0.266347	+	0.669330i
$246$	−2.67317	−	4.39300i	−0.170435	−	0.280087i
$247$	8.47891	−	3.08607i	0.539500	−	0.196362i
$248$	4.22378	+	3.54417i	0.268210	+	0.225055i
$249$	−6.28276	−	7.14629i	−0.398154	−	0.452878i
$250$	−4.07979	+	11.2091i	−0.258029	+	0.708928i
$251$	10.6916	+	18.5183i	0.674845	+	1.16887i	0.976514	+	0.215453i	$0.0691229\pi$
$251$	10.6916	+	18.5183i	0.674845	+	1.16887i	−0.301669	+	0.953413i	$0.597544\pi$
$252$	−5.78525	−	5.43424i	−0.364436	−	0.342325i
$253$	−0.419983	+	0.727431i	−0.0264041	+	0.0457332i
$254$	0.854066	+	1.01784i	0.0535889	+	0.0638647i
$255$	4.90686	−	6.12931i	0.307279	−	0.383832i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−4.42674	+	25.1053i	−0.276132	+	1.56602i	0.459210	+	0.888328i	$0.348133\pi$
$257$	−4.42674	+	25.1053i	−0.276132	+	1.56602i	−0.735342	+	0.677696i	$0.762979\pi$
$258$	2.75553	−	18.0512i	0.171552	−	1.12382i
$259$	−9.26552	−	20.6645i	−0.575731	−	1.28403i
$260$	−4.26000	−	2.45951i	−0.264194	−	0.152533i
$261$	−0.532009	+	1.70196i	−0.0329305	+	0.105349i
$262$	5.97849	−	3.45168i	0.369352	−	0.213246i
$263$	3.73502	−	10.2619i	0.230311	−	0.632775i	−0.769673	−	0.638439i	$-0.779581\pi$
$263$	3.73502	−	10.2619i	0.230311	−	0.632775i	0.999984	+	0.00566357i	$0.00180278\pi$
$264$	2.26728	−	0.453903i	0.139542	−	0.0279358i
$265$	9.84901	−	11.7376i	0.605020	−	0.721035i
$266$	−0.565794	−	7.79702i	−0.0346910	−	0.478066i
$267$	16.4678	+	9.00811i	1.00781	+	0.551287i
$268$	1.70023	+	9.64250i	0.103858	+	0.589009i
$269$	20.2212			1.23291			0.616453	−	0.787392i	$-0.288569\pi$
$269$	20.2212			1.23291			0.616453	+	0.787392i	$0.288569\pi$
$270$	3.67412	−	7.52051i	0.223600	−	0.457684i
$271$		−	7.86035i		−	0.477482i	−0.971083	−	0.238741i	$-0.923265\pi$
$271$		−	7.86035i		−	0.477482i	0.971083	−	0.238741i	$-0.0767347\pi$
$272$	−0.488670	−	2.77139i	−0.0296300	−	0.168040i
$273$	−3.51065	+	13.5466i	−0.212474	+	0.819875i
$274$	15.7684	−	5.73923i	0.952604	−	0.346720i
$275$	−2.06401	+	2.45980i	−0.124465	+	0.148331i
$276$	1.03239	+	0.349027i	0.0621425	+	0.0210090i
$277$	−1.23731	−	0.450344i	−0.0743428	−	0.0270585i	0.304581	−	0.952486i	$-0.401484\pi$
$277$	−1.23731	−	0.450344i	−0.0743428	−	0.0270585i	−0.378924	+	0.925428i	$0.623706\pi$
$278$	7.10138	+	12.3000i	0.425913	+	0.737702i
$279$	16.4050	+	2.11855i	0.982142	+	0.126834i
$280$	−3.05790	+	2.96854i	−0.182745	+	0.177404i
$281$	−0.487455	−	0.580926i	−0.0290791	−	0.0346551i	0.751309	−	0.659951i	$-0.229423\pi$
$281$	−0.487455	−	0.580926i	−0.0290791	−	0.0346551i	−0.780388	+	0.625296i	$0.784978\pi$
$282$	12.3381	−	4.81557i	0.734722	−	0.286763i
$283$	−21.6811	−	3.82296i	−1.28881	−	0.227251i	−0.513091	−	0.858334i	$-0.671500\pi$
$283$	−21.6811	−	3.82296i	−1.28881	−	0.227251i	−0.775716	+	0.631083i	$0.782611\pi$
$284$	6.52037	+	1.14972i	0.386913	+	0.0682232i
$285$	7.67955	−	2.99734i	0.454897	−	0.177547i
$286$	−2.62048	−	3.12296i	−0.154952	−	0.184665i
$287$	5.47146	+	5.63617i	0.322970	+	0.332693i
$288$	−1.15489	−	2.76879i	−0.0680528	−	0.163153i
$289$	4.54031	+	7.86404i	0.267077	+	0.462591i
$290$	0.899712	+	0.327468i	0.0528329	+	0.0192296i
$291$	−28.2761	−	9.55951i	−1.65757	−	0.560388i
$292$	5.92819	−	7.06494i	0.346921	−	0.413445i
$293$	4.66225	−	1.69692i	0.272372	−	0.0991352i	−0.202223	−	0.979339i	$-0.564817\pi$
$293$	4.66225	−	1.69692i	0.272372	−	0.0991352i	0.474595	+	0.880204i	$0.342594\pi$
$294$	10.4597	+	6.13139i	0.610024	+	0.357590i
$295$	1.57533	+	8.93416i	0.0917194	+	0.520167i
$296$		−	8.55964i		−	0.497519i
$297$	4.99310	−	4.81543i	0.289729	−	0.279420i
$298$	−17.0160			−0.985712
$299$	−0.333647	−	1.89221i	−0.0192953	−	0.109429i
$300$	3.65498	+	1.99932i	0.211021	+	0.115431i
$301$	2.01877	+	27.8200i	0.116360	+	1.60352i
$302$	−8.02471	+	9.56348i	−0.461770	+	0.550316i
$303$	13.3779	−	2.67822i	0.768542	−	0.153860i
$304$	1.01058	−	2.77655i	0.0579609	−	0.159246i
$305$	6.63682	−	3.83177i	0.380023	−	0.219406i
$306$	−5.71898	−	6.21030i	−0.326932	−	0.355019i
$307$	−13.9385	−	8.04741i	−0.795513	−	0.459290i	0.0463867	−	0.998924i	$-0.485229\pi$
$307$	−13.9385	−	8.04741i	−0.795513	−	0.459290i	−0.841900	+	0.539634i	$0.818563\pi$
$308$	−3.22291	+	1.44508i	−0.183642	+	0.0823412i
$309$	−1.15312	+	7.55396i	−0.0655985	+	0.429730i
$310$	1.54228	−	8.74668i	0.0875953	−	0.496778i
$311$	1.87360	−	10.6257i	0.106242	−	0.602528i	−0.884475	−	0.466588i	$-0.845483\pi$
$311$	1.87360	−	10.6257i	0.106242	−	0.602528i	0.990717	−	0.135941i	$-0.0434057\pi$
$312$	−3.30557	+	4.12910i	−0.187141	+	0.233764i
$313$	1.11287	+	1.32626i	0.0629029	+	0.0749648i	0.796578	−	0.604535i	$-0.206641\pi$
$313$	1.11287	+	1.32626i	0.0629029	+	0.0749648i	−0.733675	+	0.679500i	$0.762197\pi$
$314$	0.873361	−	1.51271i	0.0492866	−	0.0853669i
$315$	−2.92131	+	12.4472i	−0.164597	+	0.701321i
$316$	1.41350	+	2.44825i	0.0795156	+	0.137725i
$317$	−8.46341	+	23.2530i	−0.475352	+	1.30602i	0.438046	+	0.898953i	$0.355671\pi$
$317$	−8.46341	+	23.2530i	−0.475352	+	1.30602i	−0.913398	+	0.407067i	$0.866551\pi$
$318$	−10.8784	−	12.3736i	−0.610031	−	0.693876i
$319$	0.607862	+	0.510057i	0.0340338	+	0.0285577i
$320$	−1.51367	+	0.550930i	−0.0846166	+	0.0307979i
$321$	−16.0847	−	26.4331i	−0.897760	−	1.47535i
$322$	−1.65602	−	0.169660i	−0.0922862	−	0.00945479i
$323$		−	8.31507i		−	0.462663i
$324$	−7.39778	−	5.12570i	−0.410988	−	0.284761i
$325$		−	7.34516i		−	0.407436i
$326$	12.6660	−	2.23336i	0.701506	−	0.123695i
$327$	−28.0970	+	17.0972i	−1.55377	+	0.945477i
$328$	1.01545	+	2.78992i	0.0560686	+	0.154047i
$329$	−16.7428	+	11.3572i	−0.923061	+	0.626145i
$330$	−2.45928	−	2.79729i	−0.135379	−	0.153986i
$331$	−12.1005	−	4.40421i	−0.665103	−	0.242078i	−0.0126647	−	0.999920i	$-0.504031\pi$
$331$	−12.1005	−	4.40421i	−0.665103	−	0.242078i	−0.652438	+	0.757842i	$0.726254\pi$
$332$	2.74686	+	4.75769i	0.150753	+	0.261112i
$333$	−13.8507	−	21.6232i	−0.759016	−	1.18495i
$334$	5.32015	+	3.07159i	0.291105	+	0.168070i
$335$	12.0819	−	10.1380i	0.660107	−	0.553896i
$336$	2.65924	+	3.73208i	0.145073	+	0.203602i
$337$	−4.59736	+	26.0729i	−0.250434	+	1.42028i	0.557092	+	0.830451i	$0.311917\pi$
$337$	−4.59736	+	26.0729i	−0.250434	+	1.42028i	−0.807526	+	0.589831i	$0.799194\pi$
$338$	−3.61875	−	0.638083i	−0.196834	−	0.0347071i
$339$	−1.53864	+	10.0795i	−0.0835676	+	0.547444i
$340$	−3.47252	+	2.91379i	−0.188324	+	0.158022i
$341$	3.68040	−	6.37464i	0.199305	−	0.345206i
$342$	−1.93994	−	8.64935i	−0.104900	−	0.467703i
$343$	−17.6583	−	5.58418i	−0.953461	−	0.301517i
$344$	−3.60579	+	9.90682i	−0.194411	+	0.534140i
$345$	−0.344598	−	1.72130i	−0.0185525	−	0.0926714i
$346$	−8.70250	+	10.3712i	−0.467849	+	0.557561i
$347$	7.73200	+	21.2435i	0.415076	+	1.14041i	0.954457	+	0.298349i	$0.0964359\pi$
$347$	7.73200	+	21.2435i	0.415076	+	1.14041i	−0.539381	+	0.842062i	$0.681342\pi$
$348$	0.494071	−	0.903216i	0.0264850	−	0.0484175i
$349$	−3.90419	+	0.688414i	−0.208987	+	0.0368500i	−0.277161	−	0.960823i	$-0.589394\pi$
$349$	−3.90419	+	0.688414i	−0.208987	+	0.0368500i	0.0681746	+	0.997673i	$0.478282\pi$
$350$	−6.12185	−	1.73803i	−0.327227	−	0.0929017i
$351$	−1.66902	+	15.7798i	−0.0890855	+	0.842261i
$352$	−1.33499			−0.0711553
$353$	5.87765	+	33.3338i	0.312836	+	1.77418i	0.584108	+	0.811676i	$0.301445\pi$
$353$	5.87765	+	33.3338i	0.312836	+	1.77418i	−0.271272	+	0.962503i	$0.587444\pi$
$354$	9.75220	−	0.224845i	0.518324	−	0.0119504i
$355$	−3.64769	−	10.0219i	−0.193599	−	0.531909i
$356$	−8.30178	−	6.96602i	−0.439993	−	0.369198i
$357$	10.6243	+	7.30973i	0.562296	+	0.386872i
$358$	14.4227	+	5.24942i	0.762262	+	0.277441i
$359$	−21.2093	+	12.2452i	−1.11938	+	0.646277i	−0.941244	−	0.337728i	$-0.890342\pi$
$359$	−21.2093	+	12.2452i	−1.11938	+	0.646277i	−0.178141	+	0.984005i	$0.557008\pi$
$360$	−2.93232	+	3.84108i	−0.154547	+	0.202443i
$361$	−5.13474	+	8.89364i	−0.270250	+	0.468086i
$362$	−11.8551	+	9.94764i	−0.623092	+	0.522836i
$363$	5.80495	+	14.8730i	0.304681	+	0.780630i
$364$	3.52273	−	7.27106i	0.184641	−	0.381107i
$365$	−14.6302	−	2.57970i	−0.765781	−	0.135028i
$366$	−2.99610	−	7.67636i	−0.156608	−	0.401250i
$367$	−2.56756	−	3.05990i	−0.134025	−	0.159725i	0.694857	−	0.719148i	$-0.255467\pi$
$367$	−2.56756	−	3.05990i	−0.134025	−	0.159725i	−0.828883	+	0.559422i	$0.811023\pi$
$368$	−0.544896	−	0.314596i	−0.0284047	−	0.0163994i
$369$	7.07969	+	5.40470i	0.368554	+	0.281358i
$370$	−11.9407	+	6.89399i	−0.620769	+	0.358401i
$371$	20.3992	+	14.7392i	1.05907	+	0.765222i
$372$	−9.04705	−	3.05860i	−0.469068	−	0.158581i
$373$	−15.9652	−	13.3964i	−0.826648	−	0.693640i	0.127871	−	0.991791i	$-0.459186\pi$
$373$	−15.9652	−	13.3964i	−0.826648	−	0.693640i	−0.954519	+	0.298151i	$0.903630\pi$
$374$	−3.53029	+	1.28492i	−0.182547	+	0.0664416i
$375$	−0.476226	−	20.6553i	−0.0245922	−	1.06664i
$376$	−7.53057	+	1.32784i	−0.388360	+	0.0684783i
$377$	−1.81513			−0.0934839
$378$	12.7568	+	5.12490i	0.656138	+	0.263596i
$379$	−36.8856			−1.89469			−0.947343	−	0.320222i	$-0.896243\pi$
$379$	−36.8856			−1.89469			−0.947343	+	0.320222i	$0.896243\pi$
$380$	−4.68723	+	0.826485i	−0.240450	+	0.0423978i
$381$	−2.01903	−	1.10444i	−0.103438	−	0.0565819i
$382$	−8.26191	+	3.00709i	−0.422716	+	0.153856i
$383$	16.3340	+	13.7058i	0.834627	+	0.700335i	0.956348	−	0.292229i	$-0.0943970\pi$
$383$	16.3340	+	13.7058i	0.834627	+	0.700335i	−0.121722	+	0.992564i	$0.538841\pi$
$384$	0.340004	+	1.69835i	0.0173508	+	0.0866686i
$385$	4.61165	+	3.33209i	0.235031	+	0.169819i
$386$	−7.38027	+	4.26100i	−0.375646	+	0.216879i
$387$	6.92178	+	30.8611i	0.351854	+	1.56876i
$388$	14.9242	+	8.61647i	0.757659	+	0.437435i
$389$	10.6953	+	12.7462i	0.542274	+	0.646257i	0.965696	−	0.259676i	$-0.0836156\pi$
$389$	10.6953	+	12.7462i	0.542274	+	0.646257i	−0.423422	+	0.905933i	$0.639171\pi$
$390$	8.42244	+	1.28569i	0.426487	+	0.0651034i
$391$	−1.74373	−	0.307467i	−0.0881844	−	0.0155493i
$392$	−5.22653	−	4.65654i	−0.263980	−	0.235191i
$393$	−7.47263	+	9.33430i	−0.376944	+	0.470853i
$394$	17.4897	−	14.6756i	0.881117	−	0.739345i
$395$	2.27688	−	3.94368i	0.114562	−	0.198428i
$396$	−3.37243	+	2.16021i	−0.169471	+	0.108555i
$397$	27.8496	−	16.0790i	1.39773	−	0.806981i	0.403578	−	0.914945i	$-0.367767\pi$
$397$	27.8496	−	16.0790i	1.39773	−	0.806981i	0.994155	+	0.107964i	$0.0344332\pi$
$398$	−13.3386	−	4.85486i	−0.668604	−	0.243352i
$399$	5.82312	+	12.2242i	0.291521	+	0.611978i
$400$	−1.84256	−	1.54609i	−0.0921278	−	0.0773044i
$401$	−10.9209	−	30.0049i	−0.545364	−	1.49838i	−0.839903	−	0.542736i	$-0.817388\pi$
$401$	−10.9209	−	30.0049i	−0.545364	−	1.49838i	0.294539	−	0.955639i	$-0.404834\pi$
$402$	−8.81574	−	14.4875i	−0.439689	−	0.722572i
$403$	2.92383	+	16.5818i	0.145646	+	0.826000i
$404$	−7.87701			−0.391896
$405$	−1.19216	+	14.4482i	−0.0592387	+	0.717937i
$406$	−0.429501	+	1.51283i	−0.0213158	+	0.0750803i
$407$	−11.2534	+	1.98429i	−0.557813	+	0.0983574i
$408$	2.53377	+	4.16391i	0.125440	+	0.206144i
$409$	10.3972	+	28.5660i	0.514107	+	1.41250i	0.876920	+	0.480636i	$0.159594\pi$
$409$	10.3972	+	28.5660i	0.514107	+	1.41250i	−0.362813	+	0.931862i	$0.618184\pi$
$410$	3.07410	−	3.66357i	0.151819	−	0.180931i
$411$	−21.8282	+	19.1905i	−1.07670	+	0.946599i
$412$	1.50893	−	4.14574i	0.0743394	−	0.204246i
$413$	−14.4486	+	3.64275i	−0.710967	+	0.179248i
$414$	−1.88557	+	0.0869931i	−0.0926707	+	0.00427548i
$415$	4.42467	−	7.66375i	0.217198	−	0.376199i
$416$	2.33931	−	1.96292i	0.114694	−	0.0962399i
$417$	−19.2041	−	15.3740i	−0.940429	−	0.752866i
$418$	−3.88463	−	0.684965i	−0.190003	−	0.0335027i
$419$	5.87039	−	33.2926i	0.286787	−	1.62645i	−0.412044	−	0.911164i	$-0.635185\pi$
$419$	5.87039	−	33.2926i	0.286787	−	1.62645i	0.698831	−	0.715287i	$-0.253704\pi$
$420$	3.06450	−	6.71549i	0.149533	−	0.327682i
$421$	−1.11407	+	0.934814i	−0.0542964	+	0.0455601i	−0.669532	−	0.742783i	$-0.733505\pi$
$421$	−1.11407	+	0.934814i	−0.0542964	+	0.0455601i	0.615236	+	0.788343i	$0.289061\pi$
$422$	−12.1845	−	7.03473i	−0.593133	−	0.342445i
$423$	−16.8750	+	15.5399i	−0.820489	+	0.755577i
$424$	4.75609	+	8.23780i	0.230976	+	0.400063i
$425$	−6.36060	−	2.31507i	−0.308535	−	0.112297i
$426$	−11.2447	+	2.25115i	−0.544808	+	0.109069i
$427$	7.06611	+	10.4168i	0.341953	+	0.504107i
$428$	6.11003	+	16.7872i	0.295339	+	0.811438i
$429$	6.19486	+	3.38867i	0.299091	+	0.163606i
$430$	16.7242	−	2.94892i	0.806511	−	0.142210i
$431$		−	23.3590i		−	1.12516i	−0.826742	−	0.562581i	$-0.809808\pi$
$431$		−	23.3590i		−	1.12516i	0.826742	−	0.562581i	$-0.190192\pi$
$432$	3.60709	+	3.74017i	0.173546	+	0.179949i
$433$		−	16.5431i		−	0.795009i	−0.917600	−	0.397505i	$-0.869876\pi$
$433$		−	16.5431i		−	0.795009i	0.917600	−	0.397505i	$-0.130124\pi$
$434$	14.5120	+	1.48677i	0.696600	+	0.0713672i
$435$	−1.65792	+	0.0382247i	−0.0794911	+	0.00183273i
$436$	17.8439	−	6.49465i	0.854568	−	0.311037i
$437$	−1.42415	−	1.19501i	−0.0681265	−	0.0571649i
$438$	−5.11601	+	15.1327i	−0.244452	+	0.723066i
$439$	−3.41503	+	9.38272i	−0.162990	+	0.447813i	−0.994122	−	0.108263i	$-0.965471\pi$
$439$	−3.41503	+	9.38272i	−0.162990	+	0.447813i	0.831132	+	0.556075i	$0.187693\pi$
$440$	1.07521	+	1.86232i	0.0512586	+	0.0887825i
$441$	−20.7381	−	3.30598i	−0.987530	−	0.157428i
$442$	4.29685	−	7.44236i	0.204380	−	0.353997i
$443$	1.52547	+	1.81798i	0.0724771	+	0.0863748i	0.801065	−	0.598578i	$-0.204267\pi$
$443$	1.52547	+	1.81798i	0.0724771	+	0.0863748i	−0.728588	+	0.684953i	$0.759823\pi$
$444$	5.39047	+	13.8111i	0.255821	+	0.655444i
$445$	−3.03132	+	17.1915i	−0.143698	+	0.814955i
$446$	0.379347	−	2.15138i	0.0179626	−	0.101871i
$447$	27.4555	−	10.7159i	1.29860	−	0.506846i
$448$	−1.08247	−	2.41418i	−0.0511417	−	0.114059i
$449$	8.18840	+	4.72757i	0.386434	+	0.223108i	0.680614	−	0.732642i	$-0.261713\pi$
$449$	8.18840	+	4.72757i	0.386434	+	0.223108i	−0.294180	+	0.955750i	$0.595046\pi$
$450$	−7.15643	−	0.924183i	−0.337357	−	0.0435664i
$451$	3.43253	−	1.98177i	0.161631	−	0.0933180i
$452$	2.01341	−	5.53180i	0.0947029	−	0.260194i
$453$	6.92529	−	20.4843i	0.325379	−	0.962438i
$454$	14.2280	−	16.9563i	0.667754	−	0.795798i
$455$	−12.9804	+	0.941927i	−0.608530	+	0.0441582i
$456$	0.117963	+	5.11641i	0.00552413	+	0.239598i
$457$	−1.91006	−	10.8325i	−0.0893491	−	0.506724i	−0.996333	−	0.0855588i	$-0.972732\pi$
$457$	−1.91006	−	10.8325i	−0.0893491	−	0.506724i	0.906984	−	0.421165i	$-0.138379\pi$
$458$	−26.1273			−1.22085
$459$	13.1386	+	6.41882i	0.613256	+	0.299605i
$460$			1.01351i			0.0472551i
$461$	−3.18189	−	18.0454i	−0.148196	−	0.840459i	−0.964746	−	0.263184i	$-0.915227\pi$
$461$	−3.18189	−	18.0454i	−0.148196	−	0.840459i	0.816550	−	0.577275i	$-0.195884\pi$
$462$	4.29014	−	4.36129i	0.199596	−	0.202906i
$463$	−2.11940	+	0.771399i	−0.0984970	+	0.0358500i	−0.390799	−	0.920476i	$-0.627801\pi$
$463$	−2.11940	+	0.771399i	−0.0984970	+	0.0358500i	0.292302	+	0.956326i	$0.405579\pi$
$464$	−0.382068	+	0.455331i	−0.0177371	+	0.0211382i
$465$	3.01979	+	15.0841i	0.140039	+	0.699508i
$466$	8.36337	+	3.04402i	0.387426	+	0.141011i
$467$	−20.3798	−	35.2988i	−0.943064	−	1.63344i	−0.759581	−	0.650412i	$-0.774596\pi$
$467$	−20.3798	−	35.2988i	−0.943064	−	1.63344i	−0.183483	−	0.983023i	$-0.558737\pi$
$468$	2.73325	−	8.74404i	0.126345	−	0.404193i
$469$	18.0441	+	18.5873i	0.833200	+	0.858284i
$470$	7.91751	+	9.43572i	0.365208	+	0.435237i
$471$	−0.456542	+	2.99077i	−0.0210364	+	0.137807i
$472$	−5.54637	−	0.977975i	−0.255292	−	0.0450149i
$473$	13.8605	+	2.44398i	0.637306	+	0.112374i
$474$	−3.82249	−	3.06012i	−0.175573	−	0.140556i
$475$	−4.56829	−	5.44428i	−0.209608	−	0.249801i
$476$	−5.18613	−	5.34226i	−0.237706	−	0.244862i
$477$	25.3447	+	13.1141i	1.16045	+	0.600456i
$478$	−11.1103	−	19.2437i	−0.508175	−	0.880186i
$479$	−18.5852	−	6.76446i	−0.849180	−	0.309076i	−0.119474	−	0.992837i	$-0.538121\pi$
$479$	−18.5852	−	6.76446i	−0.849180	−	0.309076i	−0.729706	+	0.683761i	$0.760343\pi$
$480$	2.09537	−	1.84217i	0.0956399	−	0.0840831i
$481$	16.8019	−	20.0237i	0.766099	−	0.913001i
$482$	4.02361	−	1.46447i	0.183270	−	0.0667050i
$483$	2.77884	−	0.769136i	0.126442	−	0.0349969i
$484$	−1.60065	−	9.07776i	−0.0727570	−	0.412625i
$485$		−	27.7590i		−	1.26047i
$486$	15.1643	+	3.61157i	0.687867	+	0.163824i
$487$	1.03843			0.0470555			0.0235278	−	0.999723i	$-0.492510\pi$
$487$	1.03843			0.0470555			0.0235278	+	0.999723i	$0.492510\pi$
$488$	0.826142	+	4.68528i	0.0373977	+	0.212093i
$489$	−19.0303	+	11.5800i	−0.860579	+	0.523667i
$490$	−2.28640	+	11.0414i	−0.103289	+	0.498801i
$491$	11.3839	−	13.5669i	0.513750	−	0.612264i	−0.445341	−	0.895361i	$-0.646918\pi$
$491$	11.3839	−	13.5669i	0.513750	−	0.612264i	0.959091	+	0.283097i	$0.0913620\pi$
$492$	−3.39539	−	3.86207i	−0.153076	−	0.174116i
$493$	−0.572098	+	1.57183i	−0.0257660	+	0.0707915i
$494$	7.81421	−	4.51153i	0.351578	−	0.202984i
$495$	5.72968	+	2.96471i	0.257530	+	0.133254i
$496$	4.77505	+	2.75687i	0.214406	+	0.123787i
$497$	15.9842	−	7.16696i	0.716989	−	0.321482i
$498$	−7.42825	−	5.94673i	−0.332868	−	0.266480i
$499$	0.283498	−	1.60780i	0.0126911	−	0.0719750i	−0.977804	−	0.209520i	$-0.932810\pi$
$499$	0.283498	−	1.60780i	0.0126911	−	0.0719750i	0.990496	+	0.137545i	$0.0439211\pi$
$500$	−2.07137	+	11.7473i	−0.0926343	+	0.525355i
$501$	−10.5184	−	1.60565i	−0.469929	−	0.0717350i
$502$	13.7448	+	16.3804i	0.613460	+	0.731094i
$503$	−16.4101	+	28.4231i	−0.731690	+	1.26732i	0.224470	+	0.974481i	$0.427935\pi$
$503$	−16.4101	+	28.4231i	−0.731690	+	1.26732i	−0.956160	+	0.292844i	$0.905398\pi$
$504$	−6.64100	−	4.34708i	−0.295814	−	0.193634i
$505$	6.34419	+	10.9885i	0.282313	+	0.488980i
$506$	−0.287285	+	0.789309i	−0.0127714	+	0.0350891i
$507$	6.24072	−	1.24937i	0.277160	−	0.0554865i
$508$	1.01784	+	0.854066i	0.0451592	+	0.0378931i
$509$	18.9052	−	6.88092i	0.837956	−	0.304991i	0.112836	−	0.993614i	$-0.464006\pi$
$509$	18.9052	−	6.88092i	0.837956	−	0.304991i	0.725120	+	0.688622i	$0.241784\pi$
$510$	3.76797	−	6.88826i	0.166848	−	0.305017i
$511$	2.48686	−	24.2737i	0.110012	−	1.07381i
$512$		−	1.00000i		−	0.0441942i
$513$	8.57708	+	12.7341i	0.378687	+	0.562225i
$514$			25.4926i			1.12443i
$515$	−6.99862	+	1.23405i	−0.308396	+	0.0543785i
$516$	−0.420896	−	18.2555i	−0.0185289	−	0.803653i
$517$	3.49146	+	9.59270i	0.153554	+	0.421886i
$518$	−12.7131	−	18.7416i	−0.558582	−	0.823461i
$519$	7.51022	−	22.2145i	0.329662	−	0.975109i
$520$	−4.62237	−	1.68241i	−0.202704	−	0.0737784i
$521$	−3.61052	−	6.25360i	−0.158180	−	0.273975i	0.776033	−	0.630693i	$-0.217229\pi$
$521$	−3.61052	−	6.25360i	−0.158180	−	0.273975i	−0.934212	+	0.356718i	$0.883896\pi$
$522$	−0.228383	+	1.76849i	−0.00999606	+	0.0774047i
$523$	10.2396	+	5.91186i	0.447748	+	0.258507i	0.706879	−	0.707335i	$-0.250103\pi$
$523$	10.2396	+	5.91186i	0.447748	+	0.258507i	−0.259131	+	0.965842i	$0.583436\pi$
$524$	5.28828	−	4.43740i	0.231020	−	0.193849i
$525$	10.9722	−	1.05093i	0.478866	−	0.0458665i
$526$	1.89632	−	10.7546i	0.0826835	−	0.468921i
$527$	15.2807	+	2.69441i	0.665639	+	0.117370i
$528$	2.15402	−	0.840717i	0.0937417	−	0.0365875i
$529$	17.3158	−	14.5296i	0.752859	−	0.631724i
$530$	7.66117	−	13.2695i	0.332780	−	0.576392i
$531$	−15.5937	+	6.50428i	−0.676707	+	0.282262i
$532$	−1.91114	−	7.58031i	−0.0828582	−	0.328648i
$533$	−3.10092	+	8.51972i	−0.134316	+	0.369030i
$534$	17.7819	+	6.01165i	0.769497	+	0.260149i
$535$	18.4971	−	22.0440i	0.799700	−	0.953045i
$536$	3.34880	+	9.20076i	0.144646	+	0.397412i
$537$	−26.5769	+	0.612754i	−1.14688	+	0.0264423i
$538$	19.9140	−	3.51137i	0.858552	−	0.151386i
$539$	−4.91038	+	7.95085i	−0.211505	+	0.342467i
$540$	2.31238	−	8.04426i	0.0995091	−	0.346170i
$541$	−7.64204			−0.328557			−0.164278	−	0.986414i	$-0.552530\pi$
$541$	−7.64204			−0.328557			−0.164278	+	0.986414i	$0.552530\pi$
$542$	−1.36493	−	7.74093i	−0.0586290	−	0.332501i
$543$	12.8638	−	23.5164i	0.552038	−	1.00919i
$544$	−0.962493	−	2.64443i	−0.0412665	−	0.113379i
$545$	−23.4316	−	19.6615i	−1.00370	−	0.842205i
$546$	−1.10498	+	13.9504i	−0.0472887	+	0.597021i
$547$	14.5705	+	5.30321i	0.622988	+	0.226749i	0.634176	−	0.773188i	$-0.281339\pi$
$547$	14.5705	+	5.30321i	0.622988	+	0.226749i	−0.0111886	+	0.999937i	$0.503562\pi$
$548$	14.5322	−	8.39019i	0.620787	−	0.358411i
$549$	9.66845	+	10.4991i	0.412639	+	0.448090i
$550$	−1.60552	+	2.78084i	−0.0684595	+	0.118575i
$551$	−1.34539	+	1.12891i	−0.0573154	+	0.0480933i
$552$	1.07731	+	0.164452i	0.0458535	+	0.00699956i
$553$	6.73115	+	3.26116i	0.286238	+	0.138678i
$554$	−1.29671	−	0.228646i	−0.0550921	−	0.00971422i
$555$	14.9250	−	18.6432i	0.633529	−	0.791361i
$556$	9.12936	+	10.8800i	0.387171	+	0.461413i
$557$	9.97283	+	5.75781i	0.422562	+	0.243966i	0.696173	−	0.717874i	$-0.254885\pi$
$557$	9.97283	+	5.75781i	0.422562	+	0.243966i	−0.273611	+	0.961841i	$0.588218\pi$
$558$	16.5237	−	0.762340i	0.699503	−	0.0322724i
$559$	−27.8813	+	16.0973i	−1.17925	+	0.680843i
$560$	−2.49597	+	3.45444i	−0.105474	+	0.145977i
$561$	4.88696	−	4.29644i	0.206328	−	0.181396i
$562$	−0.580926	−	0.487455i	−0.0245049	−	0.0205620i
$563$	−3.07419	+	1.11891i	−0.129561	+	0.0471565i	−0.405987	−	0.913879i	$-0.633072\pi$
$563$	−3.07419	+	1.11891i	−0.129561	+	0.0471565i	0.276426	+	0.961035i	$0.410850\pi$
$564$	11.3144	−	6.88490i	0.476423	−	0.289906i
$565$	−9.33850	+	1.64663i	−0.392874	+	0.0692742i
$566$	−22.0156			−0.925383
$567$	−23.8106	−	0.235433i	−0.999951	−	0.00988725i
$568$	6.62096			0.277809
$569$	4.81930	−	0.849772i	0.202035	−	0.0356243i	−0.0717145	−	0.997425i	$-0.522847\pi$
$569$	4.81930	−	0.849772i	0.202035	−	0.0356243i	0.273750	+	0.961801i	$0.411736\pi$
$570$	7.04240	−	4.28534i	0.294974	−	0.179493i
$571$	8.62540	−	3.13939i	0.360962	−	0.131379i	−0.155172	−	0.987888i	$-0.549593\pi$
$571$	8.62540	−	3.13939i	0.360962	−	0.131379i	0.516133	+	0.856508i	$0.327371\pi$
$572$	−3.12296	−	2.62048i	−0.130578	−	0.109568i
$573$	11.4369	−	10.0549i	0.477785	−	0.420051i
$574$	6.36705	+	4.60044i	0.265755	+	0.192019i
$575$	−1.31063	+	0.756693i	−0.0546571	+	0.0315563i
$576$	−1.61814	−	2.52618i	−0.0674227	−	0.105258i
$577$	20.7483	+	11.9790i	0.863762	+	0.498693i	0.865270	−	0.501305i	$-0.167147\pi$
$577$	20.7483	+	11.9790i	0.863762	+	0.498693i	−0.00150808	+	0.999999i	$0.500480\pi$
$578$	5.83691	+	6.95615i	0.242783	+	0.289338i
$579$	9.22475	−	11.5229i	0.383367	−	0.478876i
$580$	0.942908	+	0.166260i	0.0391521	+	0.00690357i
$581$	13.0806	+	6.33740i	0.542677	+	0.262920i
$582$	−29.5065	−	4.50418i	−1.22308	−	0.186704i
$583$	9.72776	−	8.16256i	0.402883	−	0.338059i
$584$	4.61131	−	7.98703i	0.190818	−	0.330506i
$585$	−14.3993	+	3.22960i	−0.595340	+	0.133527i
$586$	4.29676	−	2.48073i	0.177497	−	0.102478i
$587$	4.96633	+	1.80760i	0.204982	+	0.0746075i	0.442471	−	0.896783i	$-0.354102\pi$
$587$	4.96633	+	1.80760i	0.204982	+	0.0746075i	−0.237489	+	0.971390i	$0.576324\pi$
$588$	11.3655	+	4.22193i	0.468707	+	0.174109i
$589$	12.4802	+	10.4721i	0.514237	+	0.431496i
$590$	3.10280	+	8.52487i	0.127740	+	0.350964i
$591$	−18.9777	+	34.6934i	−0.780639	+	1.42709i
$592$	−1.48637	−	8.42960i	−0.0610893	−	0.346455i
$593$	−18.3327			−0.752835			−0.376417	−	0.926450i	$-0.622844\pi$
$593$	−18.3327			−0.752835			−0.376417	+	0.926450i	$0.622844\pi$
$594$	4.08105	−	5.60932i	0.167448	−	0.230153i
$595$	−3.27553	+	11.5374i	−0.134284	+	0.472986i
$596$	−16.7575	+	2.95480i	−0.686415	+	0.121033i
$597$	24.5793	−	0.566697i	1.00596	−	0.0231934i
$598$	−0.657157	−	1.80552i	−0.0268731	−	0.0738334i
$599$	30.4283	−	36.2630i	1.24327	−	1.48167i	0.426726	−	0.904381i	$-0.359667\pi$
$599$	30.4283	−	36.2630i	1.24327	−	1.48167i	0.816541	−	0.577287i	$-0.195889\pi$
$600$	3.94663	+	1.33427i	0.161121	+	0.0544713i
$601$	6.64311	−	18.2518i	0.270978	−	0.744506i	−0.727326	−	0.686292i	$-0.759237\pi$
$601$	6.64311	−	18.2518i	0.270978	−	0.744506i	0.998304	−	0.0582140i	$-0.0185406\pi$
$602$	6.81899	+	27.0468i	0.277921	+	1.10234i
$603$	23.3479	+	17.8240i	0.950798	+	0.725849i
$604$	−6.24212	+	10.8117i	−0.253988	+	0.439920i
$605$	−11.3743	+	9.54420i	−0.462432	+	0.388027i
$606$	12.7096	−	4.96059i	0.516293	−	0.201510i
$607$	−33.5260	−	5.91153i	−1.36078	−	0.239942i	−0.554847	−	0.831953i	$-0.687223\pi$
$607$	−33.5260	−	5.91153i	−1.36078	−	0.239942i	−0.805930	+	0.592011i	$0.798334\pi$
$608$	0.513086	−	2.90986i	0.0208084	−	0.118010i
$609$	−0.259706	−	2.71144i	−0.0105238	−	0.109873i
$610$	5.87061	−	4.92603i	0.237694	−	0.199449i
$611$	−20.2228	−	11.6756i	−0.818127	−	0.472346i
$612$	−6.71050	−	5.12286i	−0.271256	−	0.207079i
$613$	−5.51139	−	9.54601i	−0.222603	−	0.385560i	0.732995	−	0.680234i	$-0.238122\pi$
$613$	−5.51139	−	9.54601i	−0.222603	−	0.385560i	−0.955598	+	0.294675i	$0.904789\pi$
$614$	−15.1242	−	5.50475i	−0.610362	−	0.222154i
$615$	−2.65293	+	7.84712i	−0.106977	+	0.316426i
$616$	−2.92301	+	1.98278i	−0.117771	+	0.0798885i
$617$	4.46670	+	12.2722i	0.179822	+	0.494058i	0.996553	−	0.0829614i	$-0.0264378\pi$
$617$	4.46670	+	12.2722i	0.179822	+	0.494058i	−0.816730	+	0.577020i	$0.804216\pi$
$618$	0.176134	+	7.63943i	0.00708514	+	0.307303i
$619$	−23.9874	+	4.22963i	−0.964136	+	0.170003i	−0.633489	−	0.773751i	$-0.718378\pi$
$619$	−23.9874	+	4.22963i	−0.964136	+	0.170003i	−0.330647	+	0.943755i	$0.607267\pi$
$620$		−	8.88161i		−	0.356694i
$621$	2.98760	−	1.32781i	0.119888	−	0.0532832i
$622$		−	10.7896i		−	0.432624i
$623$	−28.5232	−	2.92223i	−1.14276	−	0.117077i
$624$	−2.53835	+	4.64037i	−0.101615	+	0.185764i
$625$	6.75467	−	2.45850i	0.270187	−	0.0983400i
$626$	1.32626	+	1.11287i	0.0530081	+	0.0444791i
$627$	6.69924	−	1.34117i	0.267542	−	0.0535610i
$628$	0.597414	−	1.64138i	0.0238394	−	0.0654983i
$629$	−12.0440	−	20.8609i	−0.480227	−	0.831777i
$630$	−0.715494	+	12.7654i	−0.0285060	+	0.508585i
$631$	11.9555	−	20.7075i	0.475939	−	0.824351i	−0.523681	−	0.851914i	$-0.675442\pi$
$631$	11.9555	−	20.7075i	0.475939	−	0.824351i	0.999620	+	0.0275638i	$0.00877493\pi$
$632$	1.81716	+	2.16561i	0.0722828	+	0.0861433i
$633$	24.0900	+	3.67735i	0.957491	+	0.146161i
$634$	−4.29698	+	24.3694i	−0.170655	+	0.967833i
$635$	0.371654	−	2.10776i	0.0147486	−	0.0836437i
$636$	−12.8618	−	10.2966i	−0.510003	−	0.408286i
$637$	−3.08611	−	21.1523i	−0.122276	−	0.838087i
$638$	0.687198	+	0.396754i	0.0272064	+	0.0157076i
$639$	16.7258	−	10.7137i	0.661661	−	0.423826i
$640$	−1.39500	+	0.805406i	−0.0551424	+	0.0318365i
$641$	−16.4062	+	45.0756i	−0.648005	+	1.78038i	−0.0230296	+	0.999735i	$0.507331\pi$
$641$	−16.4062	+	45.0756i	−0.648005	+	1.78038i	−0.624975	+	0.780644i	$0.714891\pi$
$642$	−20.4304	−	23.2384i	−0.806323	−	0.917147i
$643$	27.2074	−	32.4245i	1.07295	−	1.27870i	0.114509	−	0.993422i	$-0.463471\pi$
$643$	27.2074	−	32.4245i	1.07295	−	1.27870i	0.958446	−	0.285275i	$-0.0920850\pi$
$644$	−1.66032	+	0.120482i	−0.0654258	+	0.00474765i
$645$	−25.1275	+	15.2902i	−0.989394	+	0.602052i
$646$	−1.44390	−	8.18874i	−0.0568093	−	0.322182i
$647$	29.0882			1.14358			0.571789	−	0.820401i	$-0.306250\pi$
$647$	29.0882			1.14358			0.571789	+	0.820401i	$0.306250\pi$
$648$	−8.17546	−	3.76322i	−0.321162	−	0.147833i
$649$			7.51858i			0.295130i
$650$	−1.27547	−	7.23357i	−0.0500282	−	0.283724i
$651$	−24.3516	+	6.74011i	−0.954415	+	0.264166i
$652$	12.0858	−	4.39887i	0.473316	−	0.172273i
$653$	−10.0396	+	11.9648i	−0.392881	+	0.468218i	−0.925836	−	0.377926i	$-0.876637\pi$
$653$	−10.0396	+	11.9648i	−0.392881	+	0.468218i	0.532954	+	0.846144i	$0.321082\pi$
$654$	−24.7012	+	21.7164i	−0.965895	+	0.849180i
$655$	−10.4494	−	3.80327i	−0.408292	−	0.148606i
$656$	1.48448	+	2.57120i	0.0579593	+	0.100388i
$657$	−1.27514	−	27.6385i	−0.0497478	−	1.07828i
$658$	−14.5163	+	14.0921i	−0.565904	+	0.549366i
$659$	−13.1077	−	15.6211i	−0.510602	−	0.608512i	0.447730	−	0.894169i	$-0.352233\pi$
$659$	−13.1077	−	15.6211i	−0.510602	−	0.608512i	−0.958332	+	0.285657i	$0.907788\pi$
$660$	−2.90766	−	2.32775i	−0.113181	−	0.0906074i
$661$	−8.18865	−	1.44388i	−0.318501	−	0.0561604i	0.0121120	−	0.999927i	$-0.496145\pi$
$661$	−8.18865	−	1.44388i	−0.318501	−	0.0561604i	−0.330613	+	0.943766i	$0.607256\pi$
$662$	−12.6814	−	2.23608i	−0.492878	−	0.0869077i
$663$	−2.24614	+	14.7143i	−0.0872329	+	0.571455i
$664$	3.53129	+	4.20843i	0.137041	+	0.163319i
$665$	−9.03533	+	8.77127i	−0.350375	+	0.340135i
$666$	−17.3952	−	18.8896i	−0.674048	−	0.731956i
$667$	0.186993	+	0.323882i	0.00724041	+	0.0125408i
$668$	5.77270	+	2.10109i	0.223352	+	0.0812936i
$669$	0.742763	+	3.71017i	0.0287169	+	0.143443i
$670$	10.1380	−	12.0819i	0.391663	−	0.466766i
$671$	5.96827	−	2.17227i	0.230403	−	0.0838597i
$672$	3.26691	+	3.21361i	0.126024	+	0.123968i
$673$	−7.58181	−	42.9986i	−0.292257	−	1.65747i	−0.678146	−	0.734928i	$-0.737216\pi$
$673$	−7.58181	−	42.9986i	−0.292257	−	1.65747i	0.385888	−	0.922545i	$-0.373895\pi$
$674$			26.4751i			1.01978i
$675$	12.1290	−	3.01562i	0.466844	−	0.116071i
$676$	−3.67457			−0.141330
$677$	−8.43460	−	47.8350i	−0.324168	−	1.83845i	−0.515457	−	0.856915i	$-0.672378\pi$
$677$	−8.43460	−	47.8350i	−0.324168	−	1.83845i	0.191289	−	0.981534i	$-0.438733\pi$
$678$	0.235021	+	10.1936i	0.00902594	+	0.391482i
$679$	45.4745	−	3.29987i	1.74515	−	0.126638i
$680$	−2.91379	+	3.47252i	−0.111739	+	0.133165i
$681$	−12.2787	+	36.3193i	−0.470522	+	1.39176i
$682$	2.51754	−	6.91689i	0.0964017	−	0.264862i
$683$	−7.69428	+	4.44229i	−0.294413	+	0.169980i	−0.639930	−	0.768433i	$-0.721037\pi$
$683$	−7.69428	+	4.44229i	−0.294413	+	0.169980i	0.345517	+	0.938412i	$0.387704\pi$
$684$	−3.41242	−	8.18108i	−0.130477	−	0.312811i
$685$	−23.4087	−	13.5150i	−0.894401	−	0.516382i
$686$	−18.3598	−	2.43300i	−0.700979	−	0.0928924i
$687$	42.1566	−	16.4538i	1.60837	−	0.627750i
$688$	−1.83071	+	10.3825i	−0.0697950	+	0.395827i
$689$	−5.04412	+	28.6066i	−0.192165	+	1.08982i
$690$	−0.638262	−	1.63531i	−0.0242982	−	0.0622550i
$691$	19.2060	+	22.8888i	0.730630	+	0.870731i	0.995617	−	0.0935206i	$-0.0298121\pi$
$691$	19.2060	+	22.8888i	0.730630	+	0.870731i	−0.264987	+	0.964252i	$0.585368\pi$
$692$	−6.76934	+	11.7248i	−0.257332	+	0.445712i
$693$	−4.17564	+	9.73872i	−0.158619	+	0.369943i
$694$	11.3034	+	19.5781i	0.429072	+	0.743175i
$695$	7.82473	−	21.4983i	0.296809	−	0.815476i
$696$	0.329723	−	0.975289i	0.0124981	−	0.0369682i
$697$	6.40037	+	5.37055i	0.242431	+	0.203424i
$698$	−3.72534	+	1.35591i	−0.141006	+	0.0513220i
$699$	−15.4114	+	0.355322i	−0.582911	+	0.0134395i
$700$	−6.33065	−	0.648580i	−0.239276	−	0.0245140i
$701$		−	17.3896i		−	0.656798i	−0.944539	−	0.328399i	$-0.893491\pi$
$701$		−	17.3896i		−	0.656798i	0.944539	−	0.328399i	$-0.106509\pi$
$702$	1.09647	+	15.8299i	0.0413835	+	0.597459i
$703$		−	25.2916i		−	0.953889i
$704$	−1.31471	+	0.231819i	−0.0495500	+	0.00873700i
$705$	−18.7172	−	10.2385i	−0.704929	−	0.385605i
$706$	11.5767	+	31.8067i	0.435695	+	1.19706i
$707$	−17.2470	+	11.6992i	−0.648640	+	0.439995i
$708$	9.56500	−	1.91488i	0.359475	−	0.0719656i
$709$	−31.6057	−	11.5035i	−1.18698	−	0.432024i	−0.328316	−	0.944568i	$-0.606481\pi$
$709$	−31.6057	−	11.5035i	−1.18698	−	0.432024i	−0.858661	+	0.512544i	$0.828703\pi$
$710$	−5.33256	−	9.23626i	−0.200127	−	0.346631i
$711$	8.09475	+	2.53030i	0.303577	+	0.0948936i
$712$	−9.38529	−	5.41860i	−0.351729	−	0.203071i
$713$	2.65757	−	2.22996i	0.0995266	−	0.0835127i
$714$	11.7322	+	5.35379i	0.439066	+	0.200361i
$715$	−1.14032	+	6.46709i	−0.0426456	+	0.241855i
$716$	15.1151	+	2.66520i	0.564878	+	0.0996032i
$717$	30.0454	+	24.0531i	1.12207	+	0.898278i
$718$	−18.7607	+	15.7421i	−0.700144	+	0.587491i
$719$	21.2380	−	36.7853i	0.792045	−	1.37186i	−0.132654	−	0.991162i	$-0.542350\pi$
$719$	21.2380	−	36.7853i	0.792045	−	1.37186i	0.924699	−	0.380699i	$-0.124317\pi$
$720$	−2.22077	+	4.29192i	−0.0827634	+	0.159950i
$721$	−2.85356	−	11.3184i	−0.106272	−	0.421518i
$722$	−3.51237	+	9.65016i	−0.130717	+	0.359142i
$723$	−5.56987	+	4.89683i	−0.207146	+	0.182115i
$724$	−9.94764	+	11.8551i	−0.369701	+	0.440593i
$725$	0.488980	+	1.34346i	0.0181603	+	0.0498949i
$726$	8.29943	+	13.6390i	0.308021	+	0.506192i
$727$	17.2844	−	3.04771i	0.641044	−	0.113033i	0.156328	−	0.987705i	$-0.450034\pi$
$727$	17.2844	−	3.04771i	0.641044	−	0.113033i	0.484716	+	0.874672i	$0.338923\pi$
$728$	2.20661	−	7.77231i	0.0817824	−	0.288061i
$729$	−26.7422	+	3.72249i	−0.990450	+	0.137870i
$730$	−14.8559			−0.549842
$731$	5.15186	+	29.2177i	0.190549	+	1.08065i
$732$	−4.28356	−	7.03948i	−0.158325	−	0.260187i
$733$	−5.72073	−	15.7176i	−0.211300	−	0.580542i	0.788086	−	0.615565i	$-0.211072\pi$
$733$	−5.72073	−	15.7176i	−0.211300	−	0.580542i	−0.999387	+	0.0350224i	$0.988850\pi$
$734$	−3.05990	−	2.56756i	−0.112943	−	0.0947703i
$735$	−3.26426	−	19.2553i	−0.120404	−	0.710243i
$736$	−0.591247	−	0.215196i	−0.0217937	−	0.00793224i
$737$	11.3200	−	6.53561i	0.416978	−	0.240742i
$738$	7.91065	+	4.09322i	0.291195	+	0.150673i
$739$	−19.9620	+	34.5752i	−0.734313	+	1.27187i	0.220711	+	0.975339i	$0.429162\pi$
$739$	−19.9620	+	34.5752i	−0.734313	+	1.27187i	−0.955024	+	0.296528i	$0.904171\pi$
$740$	−10.5622	+	8.86274i	−0.388274	+	0.325801i
$741$	−9.76713	+	12.2004i	−0.358804	+	0.448194i
$742$	22.6487	+	10.9730i	0.831461	+	0.402832i
$743$	49.0588	+	8.65038i	1.79979	+	0.317352i	0.970434	−	0.241367i	$-0.0775958\pi$
$743$	49.0588	+	8.65038i	1.79979	+	0.317352i	0.829357	+	0.558719i	$0.188707\pi$
$744$	−9.44073	−	1.44113i	−0.346114	−	0.0528345i
$745$	17.6186	+	20.9970i	0.645494	+	0.769270i
$746$	−18.0489	−	10.4206i	−0.660819	−	0.381524i
$747$	15.7305	+	4.91713i	0.575550	+	0.179908i
$748$	−3.25353	+	1.87843i	−0.118961	+	0.0686821i
$749$	38.3111	+	27.6813i	1.39986	+	1.01145i
$750$	−4.05575	−	20.2588i	−0.148095	−	0.739747i
$751$	12.2459	+	10.2755i	0.446858	+	0.374958i	0.838268	−	0.545258i	$-0.183568\pi$
$751$	12.2459	+	10.2755i	0.446858	+	0.374958i	−0.391411	+	0.920216i	$0.628013\pi$
$752$	−7.18559	+	2.61534i	−0.262031	+	0.0953716i
$753$	−32.4930	−	17.7741i	−1.18411	−	0.647724i
$754$	−1.78755	+	0.315194i	−0.0650988	+	0.0114787i
$755$	20.1097			0.731869
$756$	13.4529	+	2.83185i	0.489277	+	0.102993i
$757$	−9.20484			−0.334556			−0.167278	−	0.985910i	$-0.553498\pi$
$757$	−9.20484			−0.334556			−0.167278	+	0.985910i	$0.553498\pi$
$758$	−36.3252	+	6.40511i	−1.31939	+	0.232644i
$759$	−0.0335342	−	1.45448i	−0.00121721	−	0.0527941i
$760$	−4.47250	+	1.62786i	−0.162235	+	0.0590486i
$761$	28.2538	+	23.7078i	1.02420	+	0.859407i	0.990150	−	0.140014i	$-0.0447146\pi$
$761$	28.2538	+	23.7078i	1.02420	+	0.859407i	0.0340513	+	0.999420i	$0.489159\pi$
$762$	−2.18014	−	0.737056i	−0.0789781	−	0.0267007i
$763$	29.4238	−	40.7227i	1.06521	−	1.47426i
$764$	−7.61421	+	4.39607i	−0.275473	+	0.159044i
$765$	−1.74173	+	13.4872i	−0.0629725	+	0.487629i
$766$	18.4658	+	10.6612i	0.667197	+	0.385206i
$767$	−11.0550	−	13.1748i	−0.399173	−	0.475716i
$768$	0.629755	+	1.61351i	0.0227243	+	0.0582225i
$769$	38.4979	+	6.78823i	1.38827	+	0.244790i	0.817315	−	0.576191i	$-0.195462\pi$
$769$	38.4979	+	6.78823i	1.38827	+	0.244790i	0.570956	+	0.820981i	$0.306573\pi$
$770$	5.12020	+	2.48067i	0.184519	+	0.0893971i
$771$	−16.0541	−	41.1325i	−0.578173	−	1.48135i
$772$	−6.52823	+	5.47784i	−0.234956	+	0.197152i
$773$	−11.7787	+	20.4013i	−0.423649	+	0.733782i	−0.996293	−	0.0860221i	$-0.972584\pi$
$773$	−11.7787	+	20.4013i	−0.423649	+	0.733782i	0.572644	+	0.819804i	$0.305918\pi$
$774$	12.1756	+	29.1903i	0.437643	+	1.04922i
$775$	11.4853	−	6.63107i	0.412566	−	0.238195i
$776$	16.1937	+	5.89401i	0.581318	+	0.211583i
$777$	32.3153	+	22.2337i	1.15931	+	0.797628i
$778$	12.7462	+	10.6953i	0.456973	+	0.383446i
$779$	3.00038	+	8.24349i	0.107500	+	0.295354i
$780$	8.51774	−	0.196384i	0.304984	−	0.00703167i
$781$	−1.53486	−	8.70464i	−0.0549217	−	0.311476i
$782$	−1.77063			−0.0633178
$783$	−0.745217	−	2.99730i	−0.0266319	−	0.107115i
$784$	−5.95573	−	3.67821i	−0.212705	−	0.131365i
$785$	−2.77090	+	0.488584i	−0.0988975	+	0.0174383i
$786$	−5.73822	+	10.4901i	−0.204675	+	0.374169i
$787$	0.707755	+	1.94454i	0.0252288	+	0.0693154i	0.951668	−	0.307130i	$-0.0993686\pi$
$787$	0.707755	+	1.94454i	0.0252288	+	0.0693154i	−0.926439	+	0.376445i	$0.877146\pi$
$788$	14.6756	−	17.4897i	0.522796	−	0.623044i
$789$	3.71301	+	18.5468i	0.132187	+	0.660284i
$790$	1.55748	−	4.27914i	0.0554127	−	0.152245i
$791$	−3.80761	−	15.1025i	−0.135383	−	0.536982i
$792$	−2.94608	+	2.71301i	−0.104685	+	0.0964025i
$793$	−7.26421	+	12.5820i	−0.257960	+	0.446800i
$794$	24.6344	−	20.6707i	0.874243	−	0.733577i
$795$	−4.00481	+	26.2352i	−0.142036	+	0.930466i
$796$	−13.9790	−	2.46488i	−0.495473	−	0.0873652i
$797$	7.31647	−	41.4938i	0.259163	−	1.46979i	−0.525994	−	0.850488i	$-0.676307\pi$
$797$	7.31647	−	41.4938i	0.259163	−	1.46979i	0.785157	−	0.619297i	$-0.212582\pi$
$798$	7.85737	+	11.0274i	0.278148	+	0.390364i
$799$	−16.4845	+	13.8322i	−0.583180	+	0.489346i
$800$	−2.08304	−	1.20264i	−0.0736465	−	0.0425198i
$801$	−32.4771	+	1.49837i	−1.14752	+	0.0529423i
$802$	−15.9653	−	27.6527i	−0.563754	−	0.976451i
$803$	−11.5696	−	4.21100i	−0.408283	−	0.148603i
$804$	−11.1975	−	12.7366i	−0.394907	−	0.449185i
$805$	1.50530	+	2.21912i	0.0530550	+	0.0782135i
$806$	5.75881	+	15.8222i	0.202845	+	0.557313i
$807$	−29.9200	+	18.2065i	−1.05324	+	0.640900i
$808$	−7.75734	+	1.36783i	−0.272902	+	0.0481201i
$809$			18.6189i			0.654607i	0.944919	+	0.327304i	$0.106140\pi$
$809$			18.6189i			0.654607i	−0.944919	+	0.327304i	$0.893860\pi$
$810$	1.33486	+	14.4357i	0.0469022	+	0.507219i
$811$			27.3656i			0.960937i	0.877012	+	0.480468i	$0.159533\pi$
$811$			27.3656i			0.960937i	−0.877012	+	0.480468i	$0.840467\pi$
$812$	−0.160276	+	1.56442i	−0.00562460	+	0.0549005i
$813$	7.07722	+	11.6305i	0.248209	+	0.407899i
$814$	−10.7379	+	3.90828i	−0.376364	+	0.136985i
$815$	−15.8704	−	13.3168i	−0.555916	−	0.466469i
$816$	3.21833	+	3.66067i	0.112664	+	0.128149i
$817$	−10.6542	+	29.2721i	−0.372743	+	1.02410i
$818$	15.1997	+	26.3266i	0.531443	+	0.920487i
$819$	−7.00242	−	23.2049i	−0.244684	−	0.810845i
$820$	2.39122	−	4.14172i	0.0835051	−	0.144635i
$821$	−10.5115	−	12.5272i	−0.366855	−	0.437201i	0.550765	−	0.834661i	$-0.314336\pi$
$821$	−10.5115	−	12.5272i	−0.366855	−	0.437201i	−0.917620	+	0.397460i	$0.869892\pi$
$822$	−18.1641	+	22.6894i	−0.633547	+	0.791384i
$823$	−0.214615	+	1.21714i	−0.00748102	+	0.0424270i	−0.988320	−	0.152394i	$-0.951302\pi$
$823$	−0.214615	+	1.21714i	−0.00748102	+	0.0424270i	0.980839	+	0.194821i	$0.0624127\pi$
$824$	0.766101	−	4.34478i	0.0266884	−	0.151357i
$825$	0.839271	−	5.49799i	0.0292197	−	0.191415i
$826$	−13.5965	+	6.09637i	−0.473083	+	0.212120i
$827$	−42.8117	−	24.7174i	−1.48871	−	0.859507i	−0.488792	−	0.872400i	$-0.662562\pi$
$827$	−42.8117	−	24.7174i	−1.48871	−	0.859507i	−0.999917	+	0.0128936i	$0.995896\pi$
$828$	−1.84182	+	0.413097i	−0.0640076	+	0.0143561i
$829$	−12.9718	+	7.48925i	−0.450528	+	0.260112i	−0.708053	−	0.706159i	$-0.750426\pi$
$829$	−12.9718	+	7.48925i	−0.450528	+	0.260112i	0.257525	+	0.966272i	$0.417093\pi$
$830$	3.02665	−	8.31566i	0.105057	−	0.288641i
$831$	2.23625	−	0.447690i	0.0775746	−	0.0155302i
$832$	1.96292	−	2.33931i	0.0680519	−	0.0811011i
$833$	−19.2898	−	3.99442i	−0.668350	−	0.138399i
$834$	−21.5820	−	11.8056i	−0.747324	−	0.408796i
$835$	−1.71834	−	9.74516i	−0.0594654	−	0.337245i
$836$	−3.94456			−0.136425
$837$	−26.1810	+	11.6359i	−0.904947	+	0.402195i
$838$		−	33.8062i		−	1.16782i
$839$	−0.418402	−	2.37288i	−0.0144448	−	0.0819208i	0.976733	−	0.214458i	$-0.0687986\pi$
$839$	−0.418402	−	2.37288i	−0.0144448	−	0.0819208i	−0.991178	+	0.132538i	$0.957687\pi$
$840$	1.85182	−	7.14561i	0.0638937	−	0.246547i
$841$	−26.9191	+	9.79775i	−0.928245	+	0.337853i
$842$	−0.934814	+	1.11407i	−0.0322158	+	0.0383933i
$843$	1.24431	+	0.420671i	0.0428562	+	0.0144887i
$844$	−13.2210	−	4.81204i	−0.455085	−	0.165637i
$845$	2.95952	+	5.12605i	0.101811	+	0.176341i
$846$	−13.9201	+	18.2341i	−0.478584	+	0.626903i
$847$	−16.9873	−	17.4987i	−0.583691	−	0.601263i
$848$	6.11432	+	7.28676i	0.209966	+	0.250228i
$849$	35.5223	−	13.8644i	1.21912	−	0.475825i
$850$	−6.66598	−	1.17539i	−0.228641	−	0.0403156i
$851$	−5.30384	−	0.935210i	−0.181813	−	0.0320586i
$852$	−10.6830	+	4.16958i	−0.365993	+	0.142847i
$853$	−28.2732	−	33.6947i	−0.968057	−	1.15369i	−0.988089	−	0.153886i	$-0.950821\pi$
$853$	−28.2732	−	33.6947i	−0.968057	−	1.15369i	0.0200316	−	0.999799i	$-0.493623\pi$
$854$	8.76763	+	9.03158i	0.300022	+	0.309054i
$855$	−8.66426	+	11.3494i	−0.296311	+	0.388142i
$856$	8.93227	+	15.4711i	0.305299	+	0.528793i
$857$	7.41054	+	2.69722i	0.253139	+	0.0921352i	0.465473	−	0.885062i	$-0.345884\pi$
$857$	7.41054	+	2.69722i	0.253139	+	0.0921352i	−0.212334	+	0.977197i	$0.568106\pi$
$858$	6.68918	+	2.26146i	0.228365	+	0.0772050i
$859$	−9.17424	+	10.9334i	−0.313021	+	0.373044i	−0.899500	−	0.436920i	$-0.856069\pi$
$859$	−9.17424	+	10.9334i	−0.313021	+	0.373044i	0.586479	+	0.809964i	$0.300514\pi$
$860$	15.9580	−	5.80824i	0.544164	−	0.198060i
$861$	−13.1704	−	3.41317i	−0.448847	−	0.116321i
$862$	−4.05624	−	23.0041i	−0.138156	−	0.783523i
$863$		−	4.33372i		−	0.147522i	−0.997276	−	0.0737608i	$-0.976500\pi$
$863$		−	4.33372i		−	0.147522i	0.997276	−	0.0737608i	$-0.0235001\pi$
$864$	4.20177	+	3.05699i	0.142947	+	0.104001i
$865$	21.8083			0.741503
$866$	−2.87267	−	16.2917i	−0.0976174	−	0.553616i
$867$	−13.7986	−	7.54799i	−0.468624	−	0.256343i
$868$	14.5497	−	1.05581i	0.493851	−	0.0358365i
$869$	2.42589	−	2.89107i	0.0822928	−	0.0980728i
$870$	−1.62609	+	0.325538i	−0.0551297	+	0.0110368i
$871$	−10.2264	+	28.0969i	−0.346509	+	0.952027i
$872$	16.4450	−	9.49454i	0.556899	−	0.321526i
$873$	50.4455	−	11.3143i	1.70732	−	0.382932i
$874$	−1.61003	−	0.929551i	−0.0544600	−	0.0314425i
$875$	12.9122	+	28.7976i	0.436512	+	0.973537i
$876$	−2.41053	+	15.7911i	−0.0814441	+	0.533533i
$877$	−8.39821	+	47.6286i	−0.283587	+	1.60830i	0.426701	+	0.904393i	$0.359676\pi$
$877$	−8.39821	+	47.6286i	−0.283587	+	1.60830i	−0.710288	+	0.703911i	$0.751435\pi$
$878$	−1.73386	+	9.83319i	−0.0585148	+	0.331854i
$879$	−5.37060	+	6.70859i	−0.181146	+	0.226275i
$880$	1.38226	+	1.64732i	0.0465961	+	0.0555310i
$881$	−20.8436	+	36.1022i	−0.702240	+	1.21632i	0.265438	+	0.964128i	$0.414483\pi$
$881$	−20.8436	+	36.1022i	−0.702240	+	1.21632i	−0.967678	+	0.252187i	$0.918850\pi$
$882$	−20.9972	+	0.345381i	−0.707011	+	0.0116296i
$883$	10.9084	+	18.8939i	0.367098	+	0.635832i	0.989110	−	0.147175i	$-0.0470181\pi$
$883$	10.9084	+	18.8939i	0.367098	+	0.635832i	−0.622013	+	0.783007i	$0.713685\pi$
$884$	2.93922	−	8.07544i	0.0988566	−	0.271606i
$885$	−10.3750	−	11.8010i	−0.348751	−	0.396685i
$886$	1.81798	+	1.52547i	0.0610762	+	0.0512490i
$887$	−5.59317	+	2.03575i	−0.187800	+	0.0683537i	−0.434208	−	0.900812i	$-0.642972\pi$
$887$	−5.59317	+	2.03575i	−0.187800	+	0.0683537i	0.246408	+	0.969166i	$0.420750\pi$
$888$	7.70685	+	12.6652i	0.258625	+	0.425016i
$889$	3.49708	+	0.358278i	0.117288	+	0.0120163i
$890$			17.4567i			0.585150i
$891$	−3.05231	+	11.6207i	−0.102256	+	0.389310i
$892$		−	2.18457i		−	0.0731448i
$893$	−22.2509	+	3.92344i	−0.744598	+	0.131293i
$894$	25.1776	−	15.3207i	0.842065	−	0.512402i
$895$	−8.45583	−	23.2322i	−0.282647	−	0.776567i
$896$	−1.48524	−	2.18954i	−0.0496183	−	0.0731473i
$897$	2.19736	+	2.49938i	0.0733679	+	0.0834519i
$898$	8.88493	+	3.23385i	0.296494	+	0.107915i
$899$	−1.63866	−	2.83825i	−0.0546525	−	0.0946609i
$900$	−7.20819	+	0.332559i	−0.240273	+	0.0110853i
$901$	23.1823	+	13.3843i	0.772315	+	0.445896i
$902$	3.03625	−	2.54772i	0.101096	−	0.0848297i
$903$	−28.0353	−	39.3459i	−0.932958	−	1.30935i
$904$	1.02224	−	5.79739i	0.0339991	−	0.192818i
$905$	24.5498	+	4.32880i	0.816064	+	0.143894i
$906$	3.26301	−	21.3757i	0.108406	−	0.710160i
$907$	1.03663	−	0.869836i	0.0344207	−	0.0288824i	−0.625415	−	0.780292i	$-0.715070\pi$
$907$	1.03663	−	0.869836i	0.0344207	−	0.0288824i	0.659836	+	0.751410i	$0.270626\pi$
$908$	11.0674	−	19.1694i	0.367286	−	0.636157i
$909$	−17.3831	+	16.0079i	−0.576562	+	0.530948i
$910$	−12.6196	+	3.18164i	−0.418336	+	0.105470i
$911$	7.15490	−	19.6579i	0.237052	−	0.651296i	−0.762936	−	0.646474i	$-0.776243\pi$
$911$	7.15490	−	19.6579i	0.237052	−	0.651296i	0.999988	−	0.00482215i	$-0.00153494\pi$
$912$	1.00463	+	5.01819i	0.0332665	+	0.166169i
$913$	4.71424	−	5.61821i	0.156019	−	0.185936i
$914$	−3.76209	−	10.3363i	−0.124439	−	0.341893i
$915$	−6.37009	+	11.6452i	−0.210589	+	0.384979i
$916$	−25.7303	+	4.53695i	−0.850155	+	0.149905i
$917$	4.98829	−	17.5702i	0.164728	−	0.580219i
$918$	14.0536	+	4.03981i	0.463838	+	0.133334i
$919$	−53.2621			−1.75695			−0.878477	−	0.477785i	$-0.841440\pi$
$919$	−53.2621			−1.75695			−0.878477	+	0.477785i	$0.841440\pi$
$920$	0.175994	+	0.998112i	0.00580235	+	0.0329068i
$921$	27.8696	−	0.642558i	0.918335	−	0.0211730i
$922$	−6.26711	−	17.2187i	−0.206396	−	0.567069i
$923$	15.4885	+	12.9964i	0.509810	+	0.427781i
$924$	3.46764	−	5.04001i	0.114077	−	0.165804i
$925$	−19.3468	−	7.04164i	−0.636117	−	0.231528i
$926$	−1.95325	+	1.12771i	−0.0641878	+	0.0370589i
$927$	−5.09516	−	12.2154i	−0.167347	−	0.401205i
$928$	−0.297196	+	0.514759i	−0.00975594	+	0.0168978i
$929$	−35.1645	+	29.5066i	−1.15371	+	0.968079i	−0.999800	−	0.0200059i	$-0.993632\pi$
$929$	−35.1645	+	29.5066i	−1.15371	+	0.968079i	−0.153911	+	0.988085i	$0.549187\pi$
$930$	5.59323	+	14.3306i	0.183409	+	0.469917i
$931$	−15.4431	−	13.7589i	−0.506126	−	0.450929i
$932$	8.76490	+	1.54549i	0.287104	+	0.0506242i
$933$	6.79481	+	17.4091i	0.222452	+	0.569950i
$934$	−26.1998	−	31.2237i	−0.857282	−	1.02167i
$935$	5.24082	+	3.02579i	0.171393	+	0.0989539i
$936$	1.17334	−	9.08582i	0.0383520	−	0.296979i
$937$	−8.60076	+	4.96565i	−0.280975	+	0.162221i	−0.633865	−	0.773444i	$-0.718532\pi$
$937$	−8.60076	+	4.96565i	−0.280975	+	0.162221i	0.352890	+	0.935665i	$0.385199\pi$
$938$	20.9977	+	15.1716i	0.685598	+	0.495371i
$939$	−2.84077	−	0.960399i	−0.0927049	−	0.0313414i
$940$	9.43572	+	7.91751i	0.307759	+	0.258241i
$941$	44.9513	−	16.3609i	1.46537	−	0.533352i	0.518532	−	0.855058i	$-0.326479\pi$
$941$	44.9513	−	16.3609i	1.46537	−	0.533352i	0.946840	+	0.321706i	$0.104256\pi$
$942$	0.0697349	+	3.02461i	0.00227209	+	0.0985471i
$943$	1.83967	−	0.324383i	0.0599079	−	0.0105634i
$944$	−5.63193			−0.183304
$945$	−6.88460	−	21.0476i	−0.223956	−	0.684680i
$946$	14.0743			0.457595
$947$	32.7117	−	5.76796i	1.06299	−	0.187434i	0.385307	−	0.922789i	$-0.374096\pi$
$947$	32.7117	−	5.76796i	1.06299	−	0.187434i	0.677682	+	0.735355i	$0.262985\pi$
$948$	−4.29581	−	2.34986i	−0.139521	−	0.0763200i
$949$	26.4652	−	9.63254i	0.859096	−	0.312685i
$950$	−5.44428	−	4.56829i	−0.176636	−	0.148215i
$951$	−8.41353	−	42.0263i	−0.272827	−	1.36280i
$952$	−6.03502	−	4.36054i	−0.195596	−	0.141326i
$953$	−9.57414	+	5.52763i	−0.310137	+	0.179058i	−0.646988	−	0.762500i	$-0.723972\pi$
$953$	−9.57414	+	5.52763i	−0.310137	+	0.179058i	0.336851	+	0.941558i	$0.390638\pi$
$954$	27.2369	+	8.51385i	0.881828	+	0.275646i
$955$	12.2651	+	7.08124i	0.396888	+	0.229144i
$956$	−14.2832	−	17.0220i	−0.461951	−	0.550532i
$957$	−1.35866	−	0.207400i	−0.0439192	−	0.00670428i
$958$	−19.4775	−	3.43441i	−0.629289	−	0.110961i
$959$	19.3574	−	39.9545i	0.625084	−	1.29020i
$960$	1.74364	−	2.17804i	0.0562758	−	0.0702959i
$961$	0.458546	−	0.384766i	0.0147918	−	0.0124118i
$962$	13.0695	−	22.6371i	0.421379	−	0.729849i
$963$	47.5991	+	24.6293i	1.53386	+	0.793667i
$964$	3.70818	−	2.14092i	0.119432	−	0.0689543i
$965$	12.8995	+	4.69503i	0.415249	+	0.151138i
$966$	2.60307	−	1.23999i	0.0837523	−	0.0398961i
$967$	15.0230	+	12.6058i	0.483108	+	0.405376i	0.851549	−	0.524275i	$-0.175664\pi$
$967$	15.0230	+	12.6058i	0.483108	+	0.405376i	−0.368440	+	0.929651i	$0.620108\pi$
$968$	−3.15267	−	8.66190i	−0.101331	−	0.278404i
$969$	7.48664	+	12.3033i	0.240505	+	0.395239i
$970$	−4.82030	−	27.3373i	−0.154771	−	0.877747i
$971$	28.2633			0.907014			0.453507	−	0.891253i	$-0.350173\pi$
$971$	28.2633			0.907014			0.453507	+	0.891253i	$0.350173\pi$
$972$	15.5611	+	0.923451i	0.499122	+	0.0296197i
$973$	36.1484	+	10.2628i	1.15886	+	0.329009i
$974$	1.02265	−	0.180321i	0.0327678	−	0.00577785i
$975$	6.61336	+	10.8682i	0.211797	+	0.348060i
$976$	1.62718	+	4.47064i	0.0520848	+	0.143102i
$977$	−11.8289	+	14.0971i	−0.378440	+	0.451007i	−0.921321	−	0.388802i	$-0.872889\pi$
$977$	−11.8289	+	14.0971i	−0.378440	+	0.451007i	0.542881	+	0.839809i	$0.317333\pi$
$978$	−16.7303	+	14.7087i	−0.534976	+	0.470332i
$979$	−4.94820	+	13.5951i	−0.158145	+	0.434500i
$980$	−0.334343	+	11.2707i	−0.0106802	+	0.360030i
$981$	26.1796	−	50.5954i	0.835852	−	1.61539i
$982$	8.85514	−	15.3375i	0.282579	−	0.489441i
$983$	−43.8896	+	36.8277i	−1.39986	+	1.17462i	−0.438700	+	0.898634i	$0.644561\pi$
$983$	−43.8896	+	36.8277i	−1.39986	+	1.17462i	−0.961161	+	0.275989i	$0.910995\pi$
$984$	−4.01445	−	3.21379i	−0.127976	−	0.102452i
$985$	−36.2179	−	6.38620i	−1.15400	−	0.203481i
$986$	−0.290462	+	1.64729i	−0.00925019	+	0.0524604i
$987$	14.5476	−	31.8793i	0.463056	−	1.01473i
$988$	6.91207	−	5.79992i	0.219902	−	0.184520i
$989$	5.74463	+	3.31666i	0.182669	+	0.105464i
$990$	6.15745	+	1.92473i	0.195697	+	0.0611718i
$991$	−27.8274	−	48.1984i	−0.883965	−	1.53107i	−0.846895	−	0.531760i	$-0.821531\pi$
$991$	−27.8274	−	48.1984i	−0.883965	−	1.53107i	−0.0370702	−	0.999313i	$-0.511803\pi$
$992$	5.18123	+	1.88581i	0.164504	+	0.0598746i
$993$	21.8698	−	4.37826i	0.694016	−	0.138940i
$994$	14.4968	−	9.83370i	0.459811	−	0.311906i
$995$	7.82026	+	21.4860i	0.247919	+	0.681152i
$996$	−8.34804	−	4.56649i	−0.264518	−	0.144695i
$997$	−24.9727	+	4.40336i	−0.790893	+	0.139456i	−0.554480	−	0.832197i	$-0.687083\pi$
$997$	−24.9727	+	4.40336i	−0.790893	+	0.139456i	−0.236413	+	0.971653i	$0.575972\pi$
$998$		−	1.63260i		−	0.0516791i
$999$	39.9630	+	19.5238i	1.26437	+	0.617706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.14	✓	144
7.6	odd	2	inner	378.2.z.a.41.23	yes	144
27.2	odd	18	inner	378.2.z.a.83.23	yes	144
189.83	even	18	inner	378.2.z.a.83.14	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.14	✓	144	1.1	even	1	trivial
378.2.z.a.41.23	yes	144	7.6	odd	2	inner
378.2.z.a.83.14	yes	144	189.83	even	18	inner
378.2.z.a.83.23	yes	144	27.2	odd	18	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.47964 + 0.900370i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23395 - 1.03541i) q^{5} +(-1.30081 + 1.14363i) q^{6} +(1.54951 - 2.14453i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.37867 - 2.66445i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.47964 + 0.900370i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23395 - 1.03541i) q^{5} +(-1.30081 + 1.14363i) q^{6} +(1.54951 - 2.14453i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.37867 - 2.66445i) q^{9} +(-1.39500 - 0.805406i) q^{10} +(-0.858116 - 1.02266i) q^{11} +(-1.08246 + 1.35214i) q^{12} +(3.00736 + 0.530279i) q^{13} +(1.15357 - 2.38102i) q^{14} +(2.75806 + 0.421019i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.40707 - 2.43712i) q^{17} +(0.895047 - 2.86337i) q^{18} +(2.55888 - 1.47737i) q^{19} +(-1.51367 - 0.550930i) q^{20} +(-0.361842 + 4.56827i) q^{21} +(-1.02266 - 0.858116i) q^{22} +(-0.215196 - 0.591247i) q^{23} +(-0.831221 + 1.51956i) q^{24} +(-0.417673 - 2.36874i) q^{25} +3.05376 q^{26} +(0.359055 + 5.18373i) q^{27} +(0.722589 - 2.54517i) q^{28} +(-0.585362 + 0.103215i) q^{29} +(2.78927 - 0.0643089i) q^{30} +(1.88581 + 5.18123i) q^{31} +(0.642788 - 0.766044i) q^{32} +(2.19048 + 0.740551i) q^{33} +(0.962493 - 2.64443i) q^{34} +(-4.13249 + 1.04188i) q^{35} +(0.384230 - 2.97529i) q^{36} +(4.27982 - 7.41287i) q^{37} +(2.26347 - 1.89927i) q^{38} +(-4.92726 + 1.92312i) q^{39} +(-1.58634 - 0.279715i) q^{40} +(-0.515556 + 2.92386i) q^{41} +(0.436926 + 4.56170i) q^{42} +(-8.07611 + 6.77666i) q^{43} +(-1.15614 - 0.667496i) q^{44} +(-4.46001 + 1.86032i) q^{45} +(-0.314596 - 0.544896i) q^{46} +(-7.18559 - 2.61534i) q^{47} +(-0.554723 + 1.64082i) q^{48} +(-2.19804 - 6.64595i) q^{49} +(-0.822656 - 2.26023i) q^{50} +(0.112350 + 4.87294i) q^{51} +(3.00736 - 0.530279i) q^{52} +9.51219i q^{53} +(1.25375 + 5.04263i) q^{54} +2.15042i q^{55} +(0.269648 - 2.63197i) q^{56} +(-2.45604 + 4.48992i) q^{57} +(-0.558546 + 0.203294i) q^{58} +(-4.31431 - 3.62014i) q^{59} +(2.73572 - 0.547683i) q^{60} +(-1.62718 + 4.47064i) q^{61} +(2.75687 + 4.77505i) q^{62} +(-3.57773 - 7.08518i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-3.16189 - 3.76819i) q^{65} +(2.28579 + 0.348928i) q^{66} +(-1.70023 + 9.64250i) q^{67} +(0.488670 - 2.77139i) q^{68} +(0.850754 + 0.681076i) q^{69} +(-3.88879 + 1.74365i) q^{70} +(5.73392 + 3.31048i) q^{71} +(-0.138262 - 2.99681i) q^{72} +(7.98703 - 4.61131i) q^{73} +(2.92757 - 8.04343i) q^{74} +(2.75075 + 3.12883i) q^{75} +(1.89927 - 2.26347i) q^{76} +(-3.52279 + 0.255633i) q^{77} +(-4.51846 + 2.74951i) q^{78} +(0.490904 + 2.78405i) q^{79} -1.61081 q^{80} +(-5.19855 - 7.34677i) q^{81} +2.96897i q^{82} +(0.953973 + 5.41025i) q^{83} +(1.22242 + 4.41652i) q^{84} +(-4.25967 + 1.55039i) q^{85} +(-6.77666 + 8.07611i) q^{86} +(0.773193 - 0.679763i) q^{87} +(-1.25448 - 0.456594i) q^{88} +(-5.41860 - 9.38529i) q^{89} +(-4.06921 + 2.60653i) q^{90} +(5.79714 - 5.62772i) q^{91} +(-0.404437 - 0.481989i) q^{92} +(-7.45535 - 5.96842i) q^{93} +(-7.53057 - 1.32784i) q^{94} +(-4.68723 - 0.826485i) q^{95} +(-0.261371 + 1.71222i) q^{96} +(11.0771 + 13.2012i) q^{97} +(-3.31871 - 6.16329i) q^{98} +(-3.90789 + 0.876491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more