LMFDB - Embedded newform 336.2.s.d.155.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.13
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.103263 + 1.41044i) q^{2} +(1.29441 - 1.15087i) q^{3} +(-1.97867 + 0.291291i) q^{4} +(0.186466 - 0.186466i) q^{5} +(1.75690 + 1.70684i) q^{6} +1.00000 q^{7} +(-0.615171 - 2.76072i) q^{8} +(0.350987 - 2.97940i) q^{9} +O(q^{10})$	\(q+(0.103263 + 1.41044i) q^{2} +(1.29441 - 1.15087i) q^{3} +(-1.97867 + 0.291291i) q^{4} +(0.186466 - 0.186466i) q^{5} +(1.75690 + 1.70684i) q^{6} +1.00000 q^{7} +(-0.615171 - 2.76072i) q^{8} +(0.350987 - 2.97940i) q^{9} +(0.282253 + 0.243743i) q^{10} +(4.29691 + 4.29691i) q^{11} +(-2.22597 + 2.65425i) q^{12} +(2.73763 - 2.73763i) q^{13} +(0.103263 + 1.41044i) q^{14} +(0.0267646 - 0.455961i) q^{15} +(3.83030 - 1.15274i) q^{16} +4.98546i q^{17} +(4.23850 + 0.187385i) q^{18} +(-3.09905 - 3.09905i) q^{19} +(-0.314639 + 0.423271i) q^{20} +(1.29441 - 1.15087i) q^{21} +(-5.61682 + 6.50424i) q^{22} -3.55879i q^{23} +(-3.97352 - 2.86551i) q^{24} +4.93046i q^{25} +(4.14395 + 3.57856i) q^{26} +(-2.97458 - 4.26050i) q^{27} +(-1.97867 + 0.291291i) q^{28} +(3.75624 + 3.75624i) q^{29} +(0.645869 - 0.00933385i) q^{30} -6.58926i q^{31} +(2.02140 + 5.28337i) q^{32} +(10.5072 + 0.616763i) q^{33} +(-7.03169 + 0.514812i) q^{34} +(0.186466 - 0.186466i) q^{35} +(0.173383 + 5.99749i) q^{36} +(-4.82165 - 4.82165i) q^{37} +(4.05101 - 4.69104i) q^{38} +(0.392949 - 6.69427i) q^{39} +(-0.629488 - 0.400071i) q^{40} -10.5690 q^{41} +(1.75690 + 1.70684i) q^{42} +(-5.79966 + 5.79966i) q^{43} +(-9.75384 - 7.25053i) q^{44} +(-0.490108 - 0.621002i) q^{45} +(5.01945 - 0.367490i) q^{46} +3.22550 q^{47} +(3.63132 - 5.90030i) q^{48} +1.00000 q^{49} +(-6.95411 + 0.509132i) q^{50} +(5.73763 + 6.45322i) q^{51} +(-4.61943 + 6.21432i) q^{52} +(-7.95980 + 7.95980i) q^{53} +(5.70201 - 4.63542i) q^{54} +1.60245 q^{55} +(-0.615171 - 2.76072i) q^{56} +(-7.57805 - 0.444827i) q^{57} +(-4.91007 + 5.68582i) q^{58} +(-3.18645 - 3.18645i) q^{59} +(0.0798589 + 0.909994i) q^{60} +(-3.17662 + 3.17662i) q^{61} +(9.29375 - 0.680424i) q^{62} +(0.350987 - 2.97940i) q^{63} +(-7.24313 + 3.39663i) q^{64} -1.02095i q^{65} +(0.215089 + 14.8834i) q^{66} +(2.39721 + 2.39721i) q^{67} +(-1.45222 - 9.86460i) q^{68} +(-4.09571 - 4.60652i) q^{69} +(0.282253 + 0.243743i) q^{70} -9.06458i q^{71} +(-8.44119 + 0.863863i) q^{72} -2.32026i q^{73} +(6.30275 - 7.29854i) q^{74} +(5.67433 + 6.38203i) q^{75} +(7.03474 + 5.22929i) q^{76} +(4.29691 + 4.29691i) q^{77} +(9.48243 - 0.137037i) q^{78} -6.89467i q^{79} +(0.499273 - 0.929166i) q^{80} +(-8.75362 - 2.09146i) q^{81} +(-1.09138 - 14.9069i) q^{82} +(-1.12559 + 1.12559i) q^{83} +(-2.22597 + 2.65425i) q^{84} +(0.929618 + 0.929618i) q^{85} +(-8.77895 - 7.58117i) q^{86} +(9.18506 + 0.539157i) q^{87} +(9.21922 - 14.5059i) q^{88} +7.81580 q^{89} +(0.825276 - 0.755394i) q^{90} +(2.73763 - 2.73763i) q^{91} +(1.03664 + 7.04168i) q^{92} +(-7.58340 - 8.52920i) q^{93} +(0.333073 + 4.54937i) q^{94} -1.15573 q^{95} +(8.69699 + 4.51247i) q^{96} +12.6744 q^{97} +(0.103263 + 1.41044i) q^{98} +(14.3104 - 11.2940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.103263	+	1.41044i	0.0730177	+	0.997331i
$2$	0.103263	+	1.41044i	0.0730177	+	0.997331i
$3$	1.29441	−	1.15087i	0.747327	−	0.664456i
$3$	1.29441	−	1.15087i	0.747327	−	0.664456i
$4$	−1.97867	+	0.291291i	−0.989337	+	0.145646i
$5$	0.186466	−	0.186466i	0.0833900	−	0.0833900i	−0.664181	−	0.747571i	$-0.731220\pi$
$5$	0.186466	−	0.186466i	0.0833900	−	0.0833900i	0.747571	+	0.664181i	$0.231220\pi$
$6$	1.75690	+	1.70684i	0.717251	+	0.696815i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.615171	−	2.76072i	−0.217496	−	0.976061i
$9$	0.350987	−	2.97940i	0.116996	−	0.993132i
$10$	0.282253	+	0.243743i	0.0892563	+	0.0770785i
$11$	4.29691	+	4.29691i	1.29557	+	1.29557i	0.931291	+	0.364276i	$0.118684\pi$
$11$	4.29691	+	4.29691i	1.29557	+	1.29557i	0.364276	+	0.931291i	$0.381316\pi$
$12$	−2.22597	+	2.65425i	−0.642583	+	0.766216i
$13$	2.73763	−	2.73763i	0.759281	−	0.759281i	−0.216910	−	0.976192i	$-0.569598\pi$
$13$	2.73763	−	2.73763i	0.759281	−	0.759281i	0.976192	+	0.216910i	$0.0695979\pi$
$14$	0.103263	+	1.41044i	0.0275981	+	0.376956i
$15$	0.0267646	−	0.455961i	0.00691060	−	0.117729i
$16$	3.83030	−	1.15274i	0.957575	−	0.288185i
$17$			4.98546i			1.20915i	0.796547	+	0.604576i	$0.206657\pi$
$17$			4.98546i			1.20915i	−0.796547	+	0.604576i	$0.793343\pi$
$18$	4.23850	+	0.187385i	0.999024	+	0.0441671i
$19$	−3.09905	−	3.09905i	−0.710971	−	0.710971i	0.255767	−	0.966738i	$-0.417672\pi$
$19$	−3.09905	−	3.09905i	−0.710971	−	0.710971i	−0.966738	+	0.255767i	$0.917672\pi$
$20$	−0.314639	+	0.423271i	−0.0703554	+	0.0946462i
$21$	1.29441	−	1.15087i	0.282463	−	0.251141i
$22$	−5.61682	+	6.50424i	−1.19751	+	1.38671i
$23$		−	3.55879i		−	0.742058i	−0.928621	−	0.371029i	$-0.879005\pi$
$23$		−	3.55879i		−	0.742058i	0.928621	−	0.371029i	$-0.120995\pi$
$24$	−3.97352	−	2.86551i	−0.811091	−	0.584921i
$25$			4.93046i			0.986092i
$26$	4.14395	+	3.57856i	0.812696	+	0.701814i
$27$	−2.97458	−	4.26050i	−0.572459	−	0.819933i
$28$	−1.97867	+	0.291291i	−0.373934	+	0.0550488i
$29$	3.75624	+	3.75624i	0.697516	+	0.697516i	0.963874	−	0.266358i	$-0.0858203\pi$
$29$	3.75624	+	3.75624i	0.697516	+	0.697516i	−0.266358	+	0.963874i	$0.585820\pi$
$30$	0.645869	−	0.00933385i	0.117919	−	0.00170412i
$31$		−	6.58926i		−	1.18347i	−0.806134	−	0.591733i	$-0.798444\pi$
$31$		−	6.58926i		−	1.18347i	0.806134	−	0.591733i	$-0.201556\pi$
$32$	2.02140	+	5.28337i	0.357336	+	0.933976i
$33$	10.5072	+	0.616763i	1.82906	+	0.107365i
$34$	−7.03169	+	0.514812i	−1.20592	+	0.0882895i
$35$	0.186466	−	0.186466i	0.0315185	−	0.0315185i
$36$	0.173383	+	5.99749i	0.0288972	+	0.999582i
$37$	−4.82165	−	4.82165i	−0.792675	−	0.792675i	0.189253	−	0.981928i	$-0.439393\pi$
$37$	−4.82165	−	4.82165i	−0.792675	−	0.792675i	−0.981928	+	0.189253i	$0.939393\pi$
$38$	4.05101	−	4.69104i	0.657160	−	0.760987i
$39$	0.392949	−	6.69427i	0.0629223	−	1.07194i
$40$	−0.629488	−	0.400071i	−0.0995307	−	0.0632568i
$41$	−10.5690			−1.65060			−0.825298	−	0.564698i	$-0.808993\pi$
$41$	−10.5690			−1.65060			−0.825298	+	0.564698i	$0.808993\pi$
$42$	1.75690	+	1.70684i	0.271095	+	0.263371i
$43$	−5.79966	+	5.79966i	−0.884439	+	0.884439i	−0.993982	−	0.109543i	$-0.965061\pi$
$43$	−5.79966	+	5.79966i	−0.884439	+	0.884439i	0.109543	+	0.993982i	$0.465061\pi$
$44$	−9.75384	−	7.25053i	−1.47045	−	1.09306i
$45$	−0.490108	−	0.621002i	−0.0730610	−	0.0925736i
$46$	5.01945	−	0.367490i	0.740077	−	0.0541834i
$47$	3.22550			0.470487			0.235244	−	0.971936i	$-0.424411\pi$
$47$	3.22550			0.470487			0.235244	+	0.971936i	$0.424411\pi$
$48$	3.63132	−	5.90030i	0.524135	−	0.851635i
$49$	1.00000			0.142857
$50$	−6.95411	+	0.509132i	−0.983460	+	0.0720022i
$51$	5.73763	+	6.45322i	0.803429	+	0.903632i
$52$	−4.61943	+	6.21432i	−0.640599	+	0.861771i
$53$	−7.95980	+	7.95980i	−1.09336	+	1.09336i	−0.0981957	+	0.995167i	$0.531307\pi$
$53$	−7.95980	+	7.95980i	−1.09336	+	1.09336i	−0.995167	+	0.0981957i	$0.968693\pi$
$54$	5.70201	−	4.63542i	0.775945	−	0.630801i
$55$	1.60245			0.216075
$56$	−0.615171	−	2.76072i	−0.0822057	−	0.368916i
$57$	−7.57805	−	0.444827i	−1.00374	−	0.0589188i
$58$	−4.91007	+	5.68582i	−0.644723	+	0.746585i
$59$	−3.18645	−	3.18645i	−0.414840	−	0.414840i	0.468580	−	0.883421i	$-0.344766\pi$
$59$	−3.18645	−	3.18645i	−0.414840	−	0.414840i	−0.883421	+	0.468580i	$0.844766\pi$
$60$	0.0798589	+	0.909994i	0.0103097	+	0.117480i
$61$	−3.17662	+	3.17662i	−0.406725	+	0.406725i	−0.880595	−	0.473870i	$-0.842857\pi$
$61$	−3.17662	+	3.17662i	−0.406725	+	0.406725i	0.473870	+	0.880595i	$0.342857\pi$
$62$	9.29375	−	0.680424i	1.18031	−	0.0864140i
$63$	0.350987	−	2.97940i	0.0442202	−	0.375369i
$64$	−7.24313	+	3.39663i	−0.905391	+	0.424578i
$65$		−	1.02095i		−	0.126633i
$66$	0.215089	+	14.8834i	0.0264756	+	1.83202i
$67$	2.39721	+	2.39721i	0.292865	+	0.292865i	0.838211	−	0.545346i	$-0.183602\pi$
$67$	2.39721	+	2.39721i	0.292865	+	0.292865i	−0.545346	+	0.838211i	$0.683602\pi$
$68$	−1.45222	−	9.86460i	−0.176108	−	1.19626i
$69$	−4.09571	−	4.60652i	−0.493065	−	0.554560i
$70$	0.282253	+	0.243743i	0.0337357	+	0.0291329i
$71$		−	9.06458i		−	1.07577i	−0.843019	−	0.537884i	$-0.819224\pi$
$71$		−	9.06458i		−	1.07577i	0.843019	−	0.537884i	$-0.180776\pi$
$72$	−8.44119	+	0.863863i	−0.994804	+	0.101807i
$73$		−	2.32026i		−	0.271566i	−0.990739	−	0.135783i	$-0.956645\pi$
$73$		−	2.32026i		−	0.271566i	0.990739	−	0.135783i	$-0.0433549\pi$
$74$	6.30275	−	7.29854i	0.732680	−	0.848438i
$75$	5.67433	+	6.38203i	0.655215	+	0.736933i
$76$	7.03474	+	5.22929i	0.806940	+	0.599840i
$77$	4.29691	+	4.29691i	0.489678	+	0.489678i
$78$	9.48243	−	0.137037i	1.07367	−	0.0155163i
$79$		−	6.89467i		−	0.775711i	−0.921720	−	0.387855i	$-0.873216\pi$
$79$		−	6.89467i		−	0.775711i	0.921720	−	0.387855i	$-0.126784\pi$
$80$	0.499273	−	0.929166i	0.0558204	−	0.103884i
$81$	−8.75362	−	2.09146i	−0.972624	−	0.232384i
$82$	−1.09138	−	14.9069i	−0.120523	−	1.64619i
$83$	−1.12559	+	1.12559i	−0.123550	+	0.123550i	−0.766178	−	0.642628i	$-0.777844\pi$
$83$	−1.12559	+	1.12559i	−0.123550	+	0.123550i	0.642628	+	0.766178i	$0.277844\pi$
$84$	−2.22597	+	2.65425i	−0.242874	+	0.289602i
$85$	0.929618	+	0.929618i	0.100831	+	0.100831i
$86$	−8.77895	−	7.58117i	−0.946658	−	0.817499i
$87$	9.18506	+	0.539157i	0.984742	+	0.0578037i
$88$	9.21922	−	14.5059i	0.982773	−	1.54633i
$89$	7.81580			0.828474			0.414237	−	0.910169i	$-0.364049\pi$
$89$	7.81580			0.828474			0.414237	+	0.910169i	$0.364049\pi$
$90$	0.825276	−	0.755394i	0.0869917	−	0.0796255i
$91$	2.73763	−	2.73763i	0.286981	−	0.286981i
$92$	1.03664	+	7.04168i	0.108077	+	0.734146i
$93$	−7.58340	−	8.52920i	−0.786362	−	0.884437i
$94$	0.333073	+	4.54937i	0.0343539	+	0.469231i
$95$	−1.15573			−0.118576
$96$	8.69699	+	4.51247i	0.887633	+	0.460552i
$97$	12.6744			1.28689			0.643445	−	0.765493i	$-0.277505\pi$
$97$	12.6744			1.28689			0.643445	+	0.765493i	$0.277505\pi$
$98$	0.103263	+	1.41044i	0.0104311	+	0.142476i
$99$	14.3104	−	11.2940i	1.43825	−	1.13509i
$100$	−1.43620	−	9.75577i	−0.143620	−	0.975577i
$101$	1.08794	−	1.08794i	0.108254	−	0.108254i	−0.650905	−	0.759159i	$-0.725611\pi$
$101$	1.08794	−	1.08794i	0.108254	−	0.108254i	0.759159	+	0.650905i	$0.225611\pi$
$102$	−8.50939	+	8.75895i	−0.842555	+	0.867265i
$103$	−4.90252			−0.483060			−0.241530	−	0.970393i	$-0.577649\pi$
$103$	−4.90252			−0.483060			−0.241530	+	0.970393i	$0.577649\pi$
$104$	−9.24193	−	5.87371i	−0.906246	−	0.575965i
$105$	0.0267646	−	0.455961i	0.00261196	−	0.0444972i
$106$	−12.0488	−	10.4049i	−1.17028	−	1.01061i
$107$	−3.37243	−	3.37243i	−0.326025	−	0.326025i	0.525048	−	0.851073i	$-0.324047\pi$
$107$	−3.37243	−	3.37243i	−0.326025	−	0.326025i	−0.851073	+	0.525048i	$0.824047\pi$
$108$	7.12678	+	7.56367i	0.685774	+	0.727814i
$109$	−12.5591	+	12.5591i	−1.20295	+	1.20295i	−0.229679	+	0.973266i	$0.573768\pi$
$109$	−12.5591	+	12.5591i	−1.20295	+	1.20295i	−0.973266	+	0.229679i	$0.926232\pi$
$110$	0.165473	+	2.26016i	0.0157773	+	0.215498i
$111$	−11.7903	−	0.692083i	−1.11909	−	0.0656896i
$112$	3.83030	−	1.15274i	0.361929	−	0.108924i
$113$			4.22031i			0.397014i	0.980100	+	0.198507i	$0.0636092\pi$
$113$			4.22031i			0.397014i	−0.980100	+	0.198507i	$0.936391\pi$
$114$	−0.155128	−	10.7343i	−0.0145291	−	1.00536i
$115$	−0.663592	−	0.663592i	−0.0618802	−	0.0618802i
$116$	−8.52653	−	6.33821i	−0.791669	−	0.588488i
$117$	−7.19561	−	9.11735i	−0.665234	−	0.842900i
$118$	4.16525	−	4.82333i	0.383442	−	0.444024i
$119$			4.98546i			0.457016i
$120$	−1.27524	+	0.206604i	−0.116413	+	0.0188603i
$121$			25.9269i			2.35699i
$122$	−4.80846	−	4.15240i	−0.435337	−	0.375941i
$123$	−13.6806	+	12.1635i	−1.23353	+	1.09675i
$124$	1.91939	+	13.0380i	0.172367	+	1.17085i
$125$	1.85169	+	1.85169i	0.165620	+	0.165620i
$126$	4.23850	+	0.187385i	0.377596	+	0.0166936i
$127$		−	12.8142i		−	1.13708i	−0.822657	−	0.568538i	$-0.807509\pi$
$127$		−	12.8142i		−	1.13708i	0.822657	−	0.568538i	$-0.192491\pi$
$128$	−5.53868	−	9.86524i	−0.489555	−	0.871973i
$129$	−0.832462	+	14.1818i	−0.0732942	+	1.24864i
$130$	1.43998	−	0.105426i	0.126295	−	0.00924644i
$131$	−4.94838	+	4.94838i	−0.432342	+	0.432342i	−0.889424	−	0.457082i	$-0.848894\pi$
$131$	−4.94838	+	4.94838i	−0.432342	+	0.432342i	0.457082	+	0.889424i	$0.348894\pi$
$132$	−20.9699	+	1.84027i	−1.82519	+	0.160175i
$133$	−3.09905	−	3.09905i	−0.268722	−	0.268722i
$134$	−3.13357	+	3.62865i	−0.270699	+	0.313468i
$135$	−1.34909	−	0.239779i	−0.116112	−	0.0206369i
$136$	13.7635	−	3.06691i	1.18021	−	0.262986i
$137$	5.07482			0.433571			0.216786	−	0.976219i	$-0.430443\pi$
$137$	5.07482			0.433571			0.216786	+	0.976219i	$0.430443\pi$
$138$	6.07429	−	6.25243i	0.517077	−	0.532242i
$139$	2.63077	−	2.63077i	0.223139	−	0.223139i	−0.586680	−	0.809819i	$-0.699565\pi$
$139$	2.63077	−	2.63077i	0.223139	−	0.223139i	0.809819	+	0.586680i	$0.199565\pi$
$140$	−0.314639	+	0.423271i	−0.0265918	+	0.0357729i
$141$	4.17511	−	3.71214i	0.351608	−	0.312618i
$142$	12.7850	−	0.936032i	1.07290	−	0.0785500i
$143$	23.5267			1.96740
$144$	−2.09009	−	11.8166i	−0.174174	−	0.984715i
$145$	1.40082			0.116332
$146$	3.27258	−	0.239596i	0.270841	−	0.0198291i
$147$	1.29441	−	1.15087i	0.106761	−	0.0949223i
$148$	10.9450	+	8.13597i	0.899672	+	0.668773i
$149$	0.771487	−	0.771487i	0.0632027	−	0.0632027i	−0.674799	−	0.738002i	$-0.735770\pi$
$149$	0.771487	−	0.771487i	0.0632027	−	0.0632027i	0.738002	+	0.674799i	$0.235770\pi$
$150$	−8.41552	+	8.66232i	−0.687124	+	0.707275i
$151$	4.82092			0.392321			0.196160	−	0.980572i	$-0.437153\pi$
$151$	4.82092			0.392321			0.196160	+	0.980572i	$0.437153\pi$
$152$	−6.64916	+	10.4621i	−0.539318	+	0.848585i
$153$	14.8537	+	1.74983i	1.20085	+	0.141465i
$154$	−5.61682	+	6.50424i	−0.452616	+	0.524126i
$155$	−1.22867	−	1.22867i	−0.0986893	−	0.0986893i
$156$	1.17246	+	13.3602i	0.0938721	+	1.06967i
$157$	−5.25487	+	5.25487i	−0.419384	+	0.419384i	−0.884991	−	0.465607i	$-0.845836\pi$
$157$	−5.25487	+	5.25487i	−0.419384	+	0.419384i	0.465607	+	0.884991i	$0.345836\pi$
$158$	9.72450	−	0.711961i	0.773640	−	0.0566406i
$159$	−1.14252	+	19.4639i	−0.0906079	+	1.54359i
$160$	1.36209	+	0.608246i	0.107682	+	0.0480860i
$161$		−	3.55879i		−	0.280472i
$162$	2.04595	−	12.5624i	0.160745	−	0.986996i
$163$	2.10862	+	2.10862i	0.165160	+	0.165160i	0.784848	−	0.619688i	$-0.212741\pi$
$163$	2.10862	+	2.10862i	0.165160	+	0.165160i	−0.619688	+	0.784848i	$0.712741\pi$
$164$	20.9125	−	3.07865i	1.63299	−	0.240402i
$165$	2.07423	−	1.84422i	0.161478	−	0.143572i
$166$	−1.70381	−	1.47135i	−0.132241	−	0.114199i
$167$			17.3053i			1.33913i	0.742755	+	0.669563i	$0.233519\pi$
$167$			17.3053i			1.33913i	−0.742755	+	0.669563i	$0.766481\pi$
$168$	−3.97352	−	2.86551i	−0.306563	−	0.221079i
$169$		−	1.98921i		−	0.153017i
$170$	−1.21517	+	1.40716i	−0.0931996	+	0.107924i
$171$	−10.3210	+	8.14558i	−0.789269	+	0.622908i
$172$	9.78624	−	13.1650i	0.746194	−	1.00382i
$173$	−1.96496	−	1.96496i	−0.149393	−	0.149393i	0.628454	−	0.777847i	$-0.283688\pi$
$173$	−1.96496	−	1.96496i	−0.149393	−	0.149393i	−0.777847	+	0.628454i	$0.783688\pi$
$174$	0.188025	+	13.0106i	0.0142541	+	0.986334i
$175$			4.93046i			0.372708i
$176$	21.4117	+	11.5052i	1.61397	+	0.867240i
$177$	−7.79176	−	0.457372i	−0.585665	−	0.0343782i
$178$	0.807080	+	11.0237i	0.0604932	+	0.826262i
$179$	3.67595	−	3.67595i	0.274754	−	0.274754i	−0.556257	−	0.831010i	$-0.687763\pi$
$179$	3.67595	−	3.67595i	0.274754	−	0.274754i	0.831010	+	0.556257i	$0.187763\pi$
$180$	1.15066	+	1.08600i	0.0857649	+	0.0809454i
$181$	−1.91774	−	1.91774i	−0.142544	−	0.142544i	0.632233	−	0.774778i	$-0.282138\pi$
$181$	−1.91774	−	1.91774i	−0.142544	−	0.142544i	−0.774778	+	0.632233i	$0.782138\pi$
$182$	4.14395	+	3.57856i	0.307170	+	0.265261i
$183$	−0.455961	+	7.76773i	−0.0337056	+	0.574207i
$184$	−9.82481	+	2.18926i	−0.724294	+	0.161395i
$185$	−1.79815			−0.132202
$186$	11.2468	−	11.5767i	0.824658	−	0.848842i
$187$	−21.4221	+	21.4221i	−1.56654	+	1.56654i
$188$	−6.38221	+	0.939559i	−0.465470	+	0.0685244i
$189$	−2.97458	−	4.26050i	−0.216369	−	0.309906i
$190$	−0.119344	−	1.63009i	−0.00865813	−	0.118259i
$191$	−2.62732			−0.190106			−0.0950531	−	0.995472i	$-0.530302\pi$
$191$	−2.62732			−0.190106			−0.0950531	+	0.995472i	$0.530302\pi$
$192$	−5.46648	+	12.7325i	−0.394509	+	0.918892i
$193$	3.55423			0.255839			0.127920	−	0.991785i	$-0.459170\pi$
$193$	3.55423			0.255839			0.127920	+	0.991785i	$0.459170\pi$
$194$	1.30879	+	17.8764i	0.0939657	+	1.28345i
$195$	−1.17498	−	1.32152i	−0.0841421	−	0.0946362i
$196$	−1.97867	+	0.291291i	−0.141334	+	0.0208065i
$197$	−16.7933	+	16.7933i	−1.19648	+	1.19648i	−0.221261	+	0.975215i	$0.571017\pi$
$197$	−16.7933	+	16.7933i	−1.19648	+	1.19648i	−0.975215	+	0.221261i	$0.928983\pi$
$198$	17.4073	+	19.0176i	1.23708	+	1.35152i
$199$	11.8244			0.838212			0.419106	−	0.907937i	$-0.362344\pi$
$199$	11.8244			0.838212			0.419106	+	0.907937i	$0.362344\pi$
$200$	13.6116	−	3.03308i	0.962486	−	0.214471i
$201$	5.86184	+	0.344086i	0.413462	+	0.0242700i
$202$	1.64681	+	1.42212i	0.115869	+	0.100060i
$203$	3.75624	+	3.75624i	0.263636	+	0.263636i
$204$	−13.2327	−	11.0975i	−0.926472	−	0.776981i
$205$	−1.97075	+	1.97075i	−0.137643	+	0.137643i
$206$	−0.506247	−	6.91470i	−0.0352719	−	0.481770i
$207$	−10.6030	−	1.24909i	−0.736962	−	0.0868176i
$208$	7.33016	−	13.6417i	0.508255	−	0.945882i
$209$		−	26.6327i		−	1.84222i
$210$	0.645869	−	0.00933385i	0.0445692	−	0.000644097i
$211$	−3.52746	−	3.52746i	−0.242840	−	0.242840i	0.575184	−	0.818024i	$-0.304931\pi$
$211$	−3.52746	−	3.52746i	−0.242840	−	0.242840i	−0.818024	+	0.575184i	$0.804931\pi$
$212$	13.4312	−	18.0685i	0.922461	−	1.24095i
$213$	−10.4322	−	11.7333i	−0.714800	−	0.803950i
$214$	4.40836	−	5.10485i	0.301349	−	0.348960i
$215$			2.16287i			0.147507i
$216$	−9.93216	+	10.8329i	−0.675798	+	0.737087i
$217$		−	6.58926i		−	0.447308i
$218$	−19.0107	−	16.4170i	−1.28757	−	1.11190i
$219$	−2.67032	−	3.00336i	−0.180443	−	0.202948i
$220$	−3.17073	+	0.466780i	−0.213771	+	0.0314703i
$221$	13.6483	+	13.6483i	0.918087	+	0.918087i
$222$	−0.241356	−	16.7010i	−0.0161987	−	1.12089i
$223$		−	21.2549i		−	1.42333i	−0.702516	−	0.711667i	$-0.747940\pi$
$223$		−	21.2549i		−	1.42333i	0.702516	−	0.711667i	$-0.252060\pi$
$224$	2.02140	+	5.28337i	0.135060	+	0.353010i
$225$	14.6898	+	1.73053i	0.979320	+	0.115368i
$226$	−5.95249	+	0.435800i	−0.395954	+	0.0289890i
$227$	−12.5784	+	12.5784i	−0.834858	+	0.834858i	−0.988177	−	0.153319i	$-0.951004\pi$
$227$	−12.5784	+	12.5784i	−0.834858	+	0.834858i	0.153319	+	0.988177i	$0.451004\pi$
$228$	15.1241	−	1.32725i	1.00162	−	0.0878994i
$229$	17.0628	+	17.0628i	1.12754	+	1.12754i	0.990575	+	0.136968i	$0.0437357\pi$
$229$	17.0628	+	17.0628i	1.12754	+	1.12754i	0.136968	+	0.990575i	$0.456264\pi$
$230$	0.867431	−	1.00448i	0.0571967	−	0.0662334i
$231$	10.5072	+	0.616763i	0.691320	+	0.0405800i
$232$	8.05919	−	12.6806i	0.529112	−	0.832525i
$233$	4.85495			0.318058			0.159029	−	0.987274i	$-0.449164\pi$
$233$	4.85495			0.318058			0.159029	+	0.987274i	$0.449164\pi$
$234$	12.1164	−	11.0904i	0.792076	−	0.725005i
$235$	0.601445	−	0.601445i	0.0392339	−	0.0392339i
$236$	7.23313	+	5.37676i	0.470837	+	0.349997i
$237$	−7.93488	−	8.92451i	−0.515426	−	0.579710i
$238$	−7.03169	+	0.514812i	−0.455797	+	0.0333703i
$239$	4.50251			0.291243			0.145622	−	0.989340i	$-0.453482\pi$
$239$	4.50251			0.291243			0.145622	+	0.989340i	$0.453482\pi$
$240$	−0.423088	−	1.77732i	−0.0273102	−	0.114725i
$241$	23.4318			1.50937			0.754686	−	0.656086i	$-0.227789\pi$
$241$	23.4318			1.50937			0.754686	+	0.656086i	$0.227789\pi$
$242$	−36.5683	+	2.67728i	−2.35070	+	0.172102i
$243$	−13.7378	+	7.36709i	−0.881278	+	0.472599i
$244$	5.36018	−	7.21082i	0.343150	−	0.461625i
$245$	0.186466	−	0.186466i	0.0119129	−	0.0119129i
$246$	−18.5686	−	18.0396i	−1.18389	−	1.15016i
$247$	−16.9681			−1.07965
$248$	−18.1911	+	4.05352i	−1.15514	+	0.257399i
$249$	−0.161563	+	2.75239i	−0.0102387	+	0.174425i
$250$	−2.42049	+	2.80291i	−0.153085	+	0.177271i
$251$	−1.95980	−	1.95980i	−0.123701	−	0.123701i	0.642546	−	0.766247i	$-0.277878\pi$
$251$	−1.95980	−	1.95980i	−0.123701	−	0.123701i	−0.766247	+	0.642546i	$0.777878\pi$
$252$	0.173383	+	5.99749i	0.0109221	+	0.377807i
$253$	15.2918	−	15.2918i	0.961386	−	0.961386i
$254$	18.0736	−	1.32323i	1.13404	−	0.0830266i
$255$	2.27318	+	0.133434i	0.142352	+	0.00835596i
$256$	13.3424	−	8.83068i	0.833899	−	0.551917i
$257$		−	26.9134i		−	1.67881i	−0.543506	−	0.839405i	$-0.682904\pi$
$257$		−	26.9134i		−	1.67881i	0.543506	−	0.839405i	$-0.317096\pi$
$258$	−20.0885	+	0.290311i	−1.25066	+	0.0180740i
$259$	−4.82165	−	4.82165i	−0.299603	−	0.299603i
$260$	0.297393	+	2.02012i	0.0184435	+	0.125283i
$261$	12.5097	−	9.87294i	0.774332	−	0.611120i
$262$	−7.49037	−	6.46841i	−0.462757	−	0.399619i
$263$			20.0669i			1.23738i	0.785635	+	0.618690i	$0.212336\pi$
$263$			20.0669i			1.23738i	−0.785635	+	0.618690i	$0.787664\pi$
$264$	−4.76099	−	29.3867i	−0.293018	−	1.80863i
$265$			2.96846i			0.182351i
$266$	4.05101	−	4.69104i	0.248383	−	0.287626i
$267$	10.1168	−	8.99499i	0.619141	−	0.550485i
$268$	−5.44157	−	4.04500i	−0.332397	−	0.247088i
$269$	−6.39355	−	6.39355i	−0.389822	−	0.389822i	0.484802	−	0.874624i	$-0.338892\pi$
$269$	−6.39355	−	6.39355i	−0.389822	−	0.389822i	−0.874624	+	0.484802i	$0.838892\pi$
$270$	0.198882	−	1.92758i	0.0121036	−	0.117309i
$271$		−	15.5182i		−	0.942663i	−0.881956	−	0.471331i	$-0.843774\pi$
$271$		−	15.5182i		−	0.942663i	0.881956	−	0.471331i	$-0.156226\pi$
$272$	5.74694	+	19.0958i	0.348459	+	1.15785i
$273$	0.392949	−	6.69427i	0.0237824	−	0.405156i
$274$	0.524039	+	7.15772i	0.0316584	+	0.432414i
$275$	−21.1858	+	21.1858i	−1.27755	+	1.27755i
$276$	9.44591	+	7.92176i	0.568577	+	0.476834i
$277$	−6.16207	−	6.16207i	−0.370243	−	0.370243i	0.497323	−	0.867566i	$-0.334316\pi$
$277$	−6.16207	−	6.16207i	−0.370243	−	0.370243i	−0.867566	+	0.497323i	$0.834316\pi$
$278$	3.98220	+	3.43888i	0.238837	+	0.206250i
$279$	−19.6320	−	2.31275i	−1.17534	−	0.138460i
$280$	−0.629488	−	0.400071i	−0.0376191	−	0.0239088i
$281$	−9.59320			−0.572282			−0.286141	−	0.958188i	$-0.592373\pi$
$281$	−9.59320			−0.572282			−0.286141	+	0.958188i	$0.592373\pi$
$282$	5.66687	+	5.50542i	0.337457	+	0.327843i
$283$	20.3342	−	20.3342i	1.20874	−	1.20874i	0.237309	−	0.971434i	$-0.423735\pi$
$283$	20.3342	−	20.3342i	1.20874	−	1.20874i	0.971434	−	0.237309i	$-0.0762653\pi$
$284$	2.64043	+	17.9358i	0.156681	+	1.06430i
$285$	−1.49599	+	1.33010i	−0.0886149	+	0.0787884i
$286$	2.42943	+	33.1829i	0.143655	+	1.96215i
$287$	−10.5690			−0.623866
$288$	16.4507	−	4.16815i	0.969369	−	0.245610i
$289$	−7.85482			−0.462048
$290$	0.144652	+	1.97577i	0.00849427	+	0.116021i
$291$	16.4058	−	14.5866i	0.961727	−	0.855082i
$292$	0.675870	+	4.59103i	0.0395523	+	0.268670i
$293$	8.88152	−	8.88152i	0.518864	−	0.518864i	−0.398364	−	0.917228i	$-0.630422\pi$
$293$	8.88152	−	8.88152i	0.518864	−	0.518864i	0.917228	+	0.398364i	$0.130422\pi$
$294$	1.75690	+	1.70684i	0.102464	+	0.0995450i
$295$	−1.18833			−0.0691871
$296$	−10.3451	+	16.2774i	−0.601296	+	0.946103i
$297$	5.52546	−	31.0885i	0.320619	−	1.80394i
$298$	1.16780	+	1.00847i	0.0676489	+	0.0584191i
$299$	−9.74263	−	9.74263i	−0.563431	−	0.563431i
$300$	−13.0867	−	10.9751i	−0.755560	−	0.633646i
$301$	−5.79966	+	5.79966i	−0.334287	+	0.334287i
$302$	0.497820	+	6.79960i	0.0286463	+	0.391273i
$303$	0.156158	−	2.66031i	0.00897107	−	0.152831i
$304$	−15.4427	−	8.29789i	−0.885699	−	0.475917i
$305$			1.18466i			0.0678335i
$306$	−0.934201	+	21.1309i	−0.0534047	+	1.20797i
$307$	14.8766	+	14.8766i	0.849051	+	0.849051i	0.990015	−	0.140964i	$-0.0450201\pi$
$307$	14.8766	+	14.8766i	0.849051	+	0.849051i	−0.140964	+	0.990015i	$0.545020\pi$
$308$	−9.75384	−	7.25053i	−0.555776	−	0.413137i
$309$	−6.34586	+	5.64217i	−0.361004	+	0.320972i
$310$	1.60609	−	1.85984i	0.0912198	−	0.105632i
$311$		−	32.2860i		−	1.83077i	−0.402577	−	0.915386i	$-0.631885\pi$
$311$		−	32.2860i		−	1.83077i	0.402577	−	0.915386i	$-0.368115\pi$
$312$	−18.7227	+	3.03330i	−1.05997	+	0.171727i
$313$		−	7.17013i		−	0.405280i	−0.979253	−	0.202640i	$-0.935048\pi$
$313$		−	7.17013i		−	0.405280i	0.979253	−	0.202640i	$-0.0649521\pi$
$314$	−7.95430	−	6.86904i	−0.448887	−	0.387642i
$315$	−0.490108	−	0.621002i	−0.0276145	−	0.0349895i
$316$	2.00835	+	13.6423i	0.112979	+	0.767439i
$317$	0.591819	+	0.591819i	0.0332399	+	0.0332399i	0.723531	−	0.690291i	$-0.242518\pi$
$317$	0.591819	+	0.591819i	0.0332399	+	0.0332399i	−0.690291	+	0.723531i	$0.742518\pi$
$318$	−27.5707	+	0.398441i	−1.54609	+	0.0223435i
$319$			32.2805i			1.80736i
$320$	−0.717241	+	1.98395i	−0.0400950	+	0.110906i
$321$	−8.24653	−	0.484066i	−0.460277	−	0.0270179i
$322$	5.01945	−	0.367490i	0.279723	−	0.0204794i
$323$	15.4502	−	15.4502i	0.859672	−	0.859672i
$324$	17.9298	+	1.58846i	0.996099	+	0.0882480i
$325$	13.4978	+	13.4978i	0.748721	+	0.748721i
$326$	−2.75634	+	3.19182i	−0.152659	+	0.176779i
$327$	−1.80269	+	30.7106i	−0.0996890	+	1.69830i
$328$	6.50172	+	29.1779i	0.358998	+	1.61108i
$329$	3.22550			0.177828
$330$	2.81535	+	2.73513i	0.154980	+	0.150564i
$331$	5.73842	−	5.73842i	0.315412	−	0.315412i	−0.531590	−	0.847002i	$-0.678405\pi$
$331$	5.73842	−	5.73842i	0.315412	−	0.315412i	0.847002	+	0.531590i	$0.178405\pi$
$332$	1.89930	−	2.55505i	0.104238	−	0.140227i
$333$	−16.0580	+	12.6733i	−0.879971	+	0.694492i
$334$	−24.4081	+	1.78699i	−1.33555	+	0.0977799i
$335$	0.893993			0.0488441
$336$	3.63132	−	5.90030i	0.198105	−	0.321888i
$337$	−13.4003			−0.729958			−0.364979	−	0.931016i	$-0.618924\pi$
$337$	−13.4003			−0.729958			−0.364979	+	0.931016i	$0.618924\pi$
$338$	2.80567	−	0.205411i	0.152608	−	0.0111729i
$339$	4.85704	+	5.46281i	0.263798	+	0.296699i
$340$	−2.11020	−	1.56862i	−0.114442	−	0.0850704i
$341$	28.3135	−	28.3135i	1.53326	−	1.53326i
$342$	−12.5546	−	13.7160i	−0.678876	−	0.741679i
$343$	1.00000			0.0539949
$344$	19.5790	+	12.4434i	1.05563	+	0.670905i
$345$	−1.62267	−	0.0952496i	−0.0873615	−	0.00512807i
$346$	2.56855	−	2.97437i	0.138086	−	0.159903i
$347$	−10.7294	−	10.7294i	−0.575986	−	0.575986i	0.357809	−	0.933795i	$-0.383524\pi$
$347$	−10.7294	−	10.7294i	−0.575986	−	0.575986i	−0.933795	+	0.357809i	$0.883524\pi$
$348$	−18.3313	+	1.60871i	−0.982660	+	0.0862359i
$349$	25.6400	−	25.6400i	1.37248	−	1.37248i	0.515726	−	0.856754i	$-0.327522\pi$
$349$	25.6400	−	25.6400i	1.37248	−	1.37248i	0.856754	−	0.515726i	$-0.172478\pi$
$350$	−6.95411	+	0.509132i	−0.371713	+	0.0272143i
$351$	−19.8070	−	3.52035i	−1.05722	−	0.187903i
$352$	−14.0164	+	31.3879i	−0.747077	+	1.67298i
$353$			9.84311i			0.523896i	0.965082	+	0.261948i	$0.0843649\pi$
$353$			9.84311i			0.523896i	−0.965082	+	0.261948i	$0.915635\pi$
$354$	−0.159503	−	11.0370i	−0.00847749	−	0.586612i
$355$	−1.69023	−	1.69023i	−0.0897082	−	0.0897082i
$356$	−15.4649	+	2.27667i	−0.819639	+	0.120663i
$357$	5.73763	+	6.45322i	0.303667	+	0.341541i
$358$	5.56429	+	4.80512i	0.294082	+	0.253958i
$359$			18.0480i			0.952539i	0.879299	+	0.476270i	$0.158011\pi$
$359$			18.0480i			0.952539i	−0.879299	+	0.476270i	$0.841989\pi$
$360$	−1.41291	+	1.73507i	−0.0744670	+	0.0914464i
$361$			0.208240i			0.0109600i
$362$	2.50682	−	2.90288i	0.131756	−	0.152572i
$363$	29.8385	+	33.5600i	1.56612	+	1.76144i
$364$	−4.61943	+	6.21432i	−0.242124	+	0.325719i
$365$	−0.432648	−	0.432648i	−0.0226458	−	0.0226458i
$366$	−11.0030	+	0.159011i	−0.575136	+	0.00831164i
$367$		−	4.70285i		−	0.245487i	−0.992438	−	0.122743i	$-0.960831\pi$
$367$		−	4.70285i		−	0.245487i	0.992438	−	0.122743i	$-0.0391692\pi$
$368$	−4.10236	−	13.6312i	−0.213850	−	0.710576i
$369$	−3.70957	+	31.4891i	−0.193112	+	1.63926i
$370$	−0.185681	−	2.53617i	−0.00965311	−	0.131849i
$371$	−7.95980	+	7.95980i	−0.413252	+	0.413252i
$372$	17.4896	+	14.6675i	0.906791	+	0.760476i
$373$	−13.1792	−	13.1792i	−0.682391	−	0.682391i	0.278148	−	0.960538i	$-0.410280\pi$
$373$	−13.1792	−	13.1792i	−0.682391	−	0.682391i	−0.960538	+	0.278148i	$0.910280\pi$
$374$	−32.4266	−	28.0024i	−1.67674	−	1.44797i
$375$	4.52790	+	0.265785i	0.233820	+	0.0137251i
$376$	−1.98423	−	8.90469i	−0.102329	−	0.459224i
$377$	20.5664			1.05922
$378$	5.70201	−	4.63542i	0.293280	−	0.238420i
$379$	8.13513	−	8.13513i	0.417874	−	0.417874i	−0.466597	−	0.884470i	$-0.654520\pi$
$379$	8.13513	−	8.13513i	0.417874	−	0.417874i	0.884470	+	0.466597i	$0.154520\pi$
$380$	2.28682	−	0.336655i	0.117311	−	0.0172700i
$381$	−14.7475	−	16.5868i	−0.755537	−	0.849767i
$382$	−0.271304	−	3.70567i	−0.0138811	−	0.189599i
$383$	−16.4573			−0.840931			−0.420465	−	0.907309i	$-0.638133\pi$
$383$	−16.4573			−0.840931			−0.420465	+	0.907309i	$0.638133\pi$
$384$	−18.5229	−	6.39534i	−0.945245	−	0.326361i
$385$	1.60245			0.0816686
$386$	0.367019	+	5.01303i	0.0186808	+	0.255156i
$387$	15.2439	+	19.3151i	0.774890	+	0.981841i
$388$	−25.0785	+	3.69194i	−1.27317	+	0.187430i
$389$	10.5195	−	10.5195i	0.533359	−	0.533359i	−0.388212	−	0.921570i	$-0.626907\pi$
$389$	10.5195	−	10.5195i	0.533359	−	0.533359i	0.921570	+	0.388212i	$0.126907\pi$
$390$	1.74260	−	1.79370i	0.0882398	−	0.0908276i
$391$	17.7422			0.897261
$392$	−0.615171	−	2.76072i	−0.0310708	−	0.139437i
$393$	−0.710273	+	12.1002i	−0.0358285	+	0.610373i
$394$	−25.4201	−	21.9518i	−1.28065	−	1.10592i
$395$	−1.28562	−	1.28562i	−0.0646865	−	0.0646865i
$396$	−25.0257	+	26.5157i	−1.25759	+	1.33246i
$397$	−11.7420	+	11.7420i	−0.589315	+	0.589315i	−0.937446	−	0.348131i	$-0.886816\pi$
$397$	−11.7420	+	11.7420i	−0.589315	+	0.589315i	0.348131	+	0.937446i	$0.386816\pi$
$398$	1.22102	+	16.6776i	0.0612043	+	0.835974i
$399$	−7.57805	−	0.444827i	−0.379377	−	0.0222692i
$400$	5.68354	+	18.8851i	0.284177	+	0.944257i
$401$		−	4.47320i		−	0.223381i	−0.993743	−	0.111691i	$-0.964373\pi$
$401$		−	4.47320i		−	0.223381i	0.993743	−	0.111691i	$-0.0356265\pi$
$402$	0.119996	+	8.30330i	0.00598486	+	0.414131i
$403$	−18.0390	−	18.0390i	−0.898584	−	0.898584i
$404$	−1.83576	+	2.46958i	−0.0913327	+	0.122866i
$405$	−2.02223	+	1.24226i	−0.100486	+	0.0617286i
$406$	−4.91007	+	5.68582i	−0.243682	+	0.282183i
$407$		−	41.4364i		−	2.05393i
$408$	14.2859	−	19.8098i	0.707258	−	0.980732i
$409$			0.161698i			0.00799545i	0.999992	+	0.00399772i	$0.00127252\pi$
$409$			0.161698i			0.00799545i	−0.999992	+	0.00399772i	$0.998727\pi$
$410$	−2.98313	−	2.57612i	−0.147326	−	0.127225i
$411$	6.56889	−	5.84047i	0.324019	−	0.288089i
$412$	9.70049	−	1.42806i	0.477909	−	0.0703555i
$413$	−3.18645	−	3.18645i	−0.156795	−	0.156795i
$414$	0.666864	−	15.0839i	0.0327746	−	0.741334i
$415$			0.419768i			0.0206056i
$416$	19.9977	+	8.93006i	0.980469	+	0.437832i
$417$	0.377612	−	6.43298i	0.0184917	−	0.315024i
$418$	37.5638	−	2.75016i	1.83730	−	0.134515i
$419$	−2.77435	+	2.77435i	−0.135536	+	0.135536i	−0.771620	−	0.636084i	$-0.780553\pi$
$419$	−2.77435	+	2.77435i	−0.135536	+	0.135536i	0.636084	+	0.771620i	$0.280553\pi$
$420$	0.0798589	+	0.909994i	0.00389672	+	0.0444032i
$421$	−5.72980	−	5.72980i	−0.279253	−	0.279253i	0.553558	−	0.832811i	$-0.313270\pi$
$421$	−5.72980	−	5.72980i	−0.279253	−	0.279253i	−0.832811	+	0.553558i	$0.813270\pi$
$422$	4.61101	−	5.33952i	0.224461	−	0.259924i
$423$	1.13211	−	9.61004i	0.0550450	−	0.467256i
$424$	26.8714	+	17.0781i	1.30499	+	0.829387i
$425$	−24.5806			−1.19234
$426$	15.4718	−	15.9255i	0.749611	−	0.771595i
$427$	−3.17662	+	3.17662i	−0.153727	+	0.153727i
$428$	7.65529	+	5.69058i	0.370033	+	0.275064i
$429$	30.4531	−	27.0762i	1.47029	−	1.30725i
$430$	−3.05060	+	0.223344i	−0.147113	+	0.0107706i
$431$	20.1681			0.971462			0.485731	−	0.874108i	$-0.338553\pi$
$431$	20.1681			0.971462			0.485731	+	0.874108i	$0.338553\pi$
$432$	−16.3048	−	12.8901i	−0.784465	−	0.620173i
$433$	−29.7401			−1.42922			−0.714610	−	0.699523i	$-0.753396\pi$
$433$	−29.7401			−1.42922			−0.714610	+	0.699523i	$0.753396\pi$
$434$	9.29375	−	0.680424i	0.446114	−	0.0326614i
$435$	1.81323	−	1.61216i	0.0869379	−	0.0772974i
$436$	21.1920	−	28.5088i	1.01491	−	1.36532i
$437$	−11.0289	+	11.0289i	−0.527582	+	0.527582i
$438$	3.96031	−	4.07646i	0.189231	−	0.194781i
$439$	24.0542			1.14805			0.574023	−	0.818839i	$-0.305382\pi$
$439$	24.0542			1.14805			0.574023	+	0.818839i	$0.305382\pi$
$440$	−0.985783	−	4.42392i	−0.0469953	−	0.210902i
$441$	0.350987	−	2.97940i	0.0167137	−	0.141876i
$442$	−17.8408	+	20.6595i	−0.848599	+	0.982672i
$443$	9.65299	+	9.65299i	0.458628	+	0.458628i	0.898205	−	0.439577i	$-0.144872\pi$
$443$	9.65299	+	9.65299i	0.458628	+	0.458628i	−0.439577	+	0.898205i	$0.644872\pi$
$444$	23.5307	−	2.06500i	1.11672	−	0.0980006i
$445$	1.45738	−	1.45738i	0.0690864	−	0.0690864i
$446$	29.9788	−	2.19484i	1.41954	−	0.103929i
$447$	0.110737	−	1.88650i	0.00523766	−	0.0892285i
$448$	−7.24313	+	3.39663i	−0.342206	+	0.160476i
$449$		−	14.9336i		−	0.704760i	−0.935857	−	0.352380i	$-0.885372\pi$
$449$		−	14.9336i		−	0.704760i	0.935857	−	0.352380i	$-0.114628\pi$
$450$	−0.923895	+	20.8978i	−0.0435528	+	0.985130i
$451$	−45.4139	−	45.4139i	−2.13846	−	2.13846i
$452$	−1.22934	−	8.35062i	−0.0578233	−	0.392780i
$453$	6.24023	−	5.54826i	0.293192	−	0.260680i
$454$	−19.0399	−	16.4422i	−0.893589	−	0.771670i
$455$		−	1.02095i		−	0.0478628i
$456$	3.43376	+	21.1945i	0.160800	+	0.992524i
$457$			10.4103i			0.486975i	0.969904	+	0.243487i	$0.0782914\pi$
$457$			10.4103i			0.486975i	−0.969904	+	0.243487i	$0.921709\pi$
$458$	−22.3041	+	25.8280i	−1.04220	+	1.20686i
$459$	21.2405	−	14.8297i	0.991424	−	0.692190i
$460$	1.50633	+	1.11973i	0.0702330	+	0.0522078i
$461$	18.7575	+	18.7575i	0.873623	+	0.873623i	0.992865	−	0.119242i	$-0.0380464\pi$
$461$	18.7575	+	18.7575i	0.873623	+	0.873623i	−0.119242	+	0.992865i	$0.538046\pi$
$462$	0.215089	+	14.8834i	0.0100068	+	0.692438i
$463$			25.5530i			1.18755i	0.804631	+	0.593775i	$0.202363\pi$
$463$			25.5530i			1.18755i	−0.804631	+	0.593775i	$0.797637\pi$
$464$	18.7175	+	10.0576i	0.868938	+	0.466910i
$465$	−3.00445	−	0.176359i	−0.139328	−	0.00817846i
$466$	0.501335	+	6.84761i	0.0232239	+	0.317209i
$467$	−13.5596	+	13.5596i	−0.627463	+	0.627463i	−0.947429	−	0.319966i	$-0.896329\pi$
$467$	−13.5596	+	13.5596i	−0.627463	+	0.627463i	0.319966	+	0.947429i	$0.396329\pi$
$468$	16.8936	+	15.9442i	0.780905	+	0.737023i
$469$	2.39721	+	2.39721i	0.110693	+	0.110693i
$470$	0.910408	+	0.786194i	0.0419940	+	0.0362644i
$471$	−0.754265	+	12.8496i	−0.0347547	+	0.592080i
$472$	−6.83668	+	10.7571i	−0.314684	+	0.495136i
$473$	−49.8412			−2.29170
$474$	11.7681	−	12.1132i	0.540527	−	0.556379i
$475$	15.2798	−	15.2798i	0.701083	−	0.701083i
$476$	−1.45222	−	9.86460i	−0.0665624	−	0.452143i
$477$	20.9216	+	26.5092i	0.957935	+	1.21377i
$478$	0.464941	+	6.35051i	0.0212659	+	0.290466i
$479$	5.16716			0.236094			0.118047	−	0.993008i	$-0.462337\pi$
$479$	5.16716			0.236094			0.118047	+	0.993008i	$0.462337\pi$
$480$	2.46311	−	0.780270i	0.112425	−	0.0356143i
$481$	−26.3998			−1.20373
$482$	2.41962	+	33.0491i	0.110211	+	1.50534i
$483$	−4.09571	−	4.60652i	−0.186361	−	0.209604i
$484$	−7.55227	−	51.3008i	−0.343285	−	2.33186i
$485$	2.36334	−	2.36334i	0.107314	−	0.107314i
$486$	−11.8094	−	18.6155i	−0.535686	−	0.844417i
$487$	−8.11050			−0.367522			−0.183761	−	0.982971i	$-0.558827\pi$
$487$	−8.11050			−0.367522			−0.183761	+	0.982971i	$0.558827\pi$
$488$	10.7239	+	6.81559i	0.485449	+	0.308527i
$489$	5.15617	+	0.302664i	0.233170	+	0.0136869i
$490$	0.282253	+	0.243743i	0.0127509	+	0.0110112i
$491$	5.58977	+	5.58977i	0.252263	+	0.252263i	0.821898	−	0.569635i	$-0.192915\pi$
$491$	5.58977	+	5.58977i	0.252263	+	0.252263i	−0.569635	+	0.821898i	$0.692915\pi$
$492$	23.5262	−	28.0527i	1.06064	−	1.26471i
$493$	−18.7266	+	18.7266i	−0.843403	+	0.843403i
$494$	−1.75217	−	23.9325i	−0.0788339	−	1.07677i
$495$	0.562440	−	4.77434i	0.0252798	−	0.214591i
$496$	−7.59571	−	25.2389i	−0.341057	−	1.13326i
$497$		−	9.06458i		−	0.406602i
$498$	−3.89875	+	0.0563433i	−0.174707	+	0.00252481i
$499$	22.1413	+	22.1413i	0.991181	+	0.991181i	0.999961	−	0.00878026i	$-0.00279488\pi$
$499$	22.1413	+	22.1413i	0.991181	+	0.991181i	−0.00878026	+	0.999961i	$0.502795\pi$
$500$	−4.20327	−	3.12451i	−0.187976	−	0.139732i
$501$	19.9162	+	22.4002i	0.889791	+	1.00077i
$502$	2.56180	−	2.96654i	0.114339	−	0.132403i
$503$		−	5.43465i		−	0.242319i	−0.992633	−	0.121160i	$-0.961339\pi$
$503$		−	5.43465i		−	0.242319i	0.992633	−	0.121160i	$-0.0386613\pi$
$504$	−8.44119	+	0.863863i	−0.376001	+	0.0384795i
$505$		−	0.405726i		−	0.0180545i
$506$	23.1472	+	19.9891i	1.02902	+	0.888622i
$507$	−2.28933	−	2.57486i	−0.101673	−	0.114353i
$508$	3.73266	+	25.3551i	0.165610	+	1.12495i
$509$	−14.4527	−	14.4527i	−0.640604	−	0.640604i	0.310100	−	0.950704i	$-0.399637\pi$
$509$	−14.4527	−	14.4527i	−0.640604	−	0.640604i	−0.950704	+	0.310100i	$0.899637\pi$
$510$	0.0465336	+	3.21995i	0.00206054	+	0.142582i
$511$		−	2.32026i		−	0.102642i
$512$	13.8329	+	17.9067i	0.611333	+	0.791373i
$513$	−3.98511	+	22.4219i	−0.175947	+	0.989951i
$514$	37.9597	−	2.77914i	1.67433	−	0.122583i
$515$	−0.914152	+	0.914152i	−0.0402823	+	0.0402823i
$516$	−2.48386	−	28.3036i	−0.109346	−	1.24600i
$517$	13.8597	+	13.8597i	0.609548	+	0.609548i
$518$	6.30275	−	7.29854i	0.276927	−	0.320680i
$519$	−4.80489	−	0.282044i	−0.210911	−	0.0123804i
$520$	−2.81855	+	0.628057i	−0.123602	+	0.0275421i
$521$	6.52150			0.285712			0.142856	−	0.989743i	$-0.454371\pi$
$521$	6.52150			0.285712			0.142856	+	0.989743i	$0.454371\pi$
$522$	15.2170	+	16.6247i	0.666028	+	0.727643i
$523$	15.5234	−	15.5234i	0.678791	−	0.678791i	−0.280935	−	0.959727i	$-0.590645\pi$
$523$	15.5234	−	15.5234i	0.678791	−	0.678791i	0.959727	+	0.280935i	$0.0906446\pi$
$524$	8.34981	−	11.2327i	0.364763	−	0.490701i
$525$	5.67433	+	6.38203i	0.247648	+	0.278535i
$526$	−28.3032	+	2.07216i	−1.23408	+	0.0903506i
$527$	32.8505			1.43099
$528$	40.9565	−	9.74963i	1.78240	−	0.424298i
$529$	10.3350			0.449349
$530$	−4.18683	+	0.306531i	−0.181864	+	0.0133148i
$531$	−10.6121	+	8.37530i	−0.460526	+	0.363457i
$532$	7.03474	+	5.22929i	0.304995	+	0.226718i
$533$	−28.9339	+	28.9339i	−1.25327	+	1.25327i
$534$	13.7316	+	13.3403i	0.594223	+	0.577293i
$535$	−1.25768			−0.0543744
$536$	5.14332	−	8.09270i	0.222157	−	0.349551i
$537$	0.527633	−	8.98873i	0.0227690	−	0.387892i
$538$	8.35750	−	9.67793i	0.360317	−	0.417245i
$539$	4.29691	+	4.29691i	0.185081	+	0.185081i
$540$	2.73926	+	0.0814647i	0.117879	+	0.00350568i
$541$	24.2270	−	24.2270i	1.04160	−	1.04160i	0.0425030	−	0.999096i	$-0.486467\pi$
$541$	24.2270	−	24.2270i	1.04160	−	1.04160i	0.999096	−	0.0425030i	$-0.0135332\pi$
$542$	21.8875	−	1.60245i	0.940147	−	0.0688311i
$543$	−4.68941	−	0.275266i	−0.201242	−	0.0118128i
$544$	−26.3400	+	10.0776i	−1.12932	+	0.432073i
$545$			4.68369i			0.200627i
$546$	9.48243	−	0.137037i	0.405811	−	0.00586462i
$547$	24.8683	+	24.8683i	1.06329	+	1.06329i	0.997857	+	0.0654358i	$0.0208438\pi$
$547$	24.8683	+	24.8683i	1.06329	+	1.06329i	0.0654358	+	0.997857i	$0.479156\pi$
$548$	−10.0414	+	1.47825i	−0.428948	+	0.0631477i
$549$	8.34947	+	10.5794i	0.356346	+	0.451517i
$550$	−32.0689	−	27.6935i	−1.36742	−	1.18085i
$551$		−	23.2816i		−	0.991828i
$552$	−10.1978	+	14.1409i	−0.434045	+	0.601877i
$553$		−	6.89467i		−	0.293191i
$554$	8.05490	−	9.32753i	0.342220	−	0.396289i
$555$	−2.32754	+	2.06944i	−0.0987984	+	0.0878427i
$556$	−4.43912	+	5.97176i	−0.188261	+	0.253259i
$557$	16.3675	+	16.3675i	0.693514	+	0.693514i	0.963003	−	0.269490i	$-0.0868550\pi$
$557$	16.3675	+	16.3675i	0.693514	+	0.693514i	−0.269490	+	0.963003i	$0.586855\pi$
$558$	1.23473	−	27.9286i	0.0522703	−	1.18231i
$559$			31.7546i			1.34308i
$560$	0.499273	−	0.929166i	0.0210981	−	0.0392644i
$561$	−3.07485	+	52.3830i	−0.129820	+	2.21161i
$562$	−0.990618	−	13.5306i	−0.0417867	−	0.570754i
$563$	0.736871	−	0.736871i	0.0310554	−	0.0310554i	−0.691409	−	0.722464i	$-0.743010\pi$
$563$	0.736871	−	0.736871i	0.0310554	−	0.0310554i	0.722464	+	0.691409i	$0.243010\pi$
$564$	−7.17987	+	8.56128i	−0.302327	+	0.360495i
$565$	0.786944	+	0.786944i	0.0331070	+	0.0331070i
$566$	30.7799	+	26.5804i	1.29378	+	1.11726i
$567$	−8.75362	−	2.09146i	−0.367617	−	0.0878330i
$568$	−25.0247	+	5.57627i	−1.05001	+	0.233975i
$569$	26.3718			1.10556			0.552781	−	0.833326i	$-0.313567\pi$
$569$	26.3718			1.10556			0.552781	+	0.833326i	$0.313567\pi$
$570$	−2.03051	−	1.97265i	−0.0850486	−	0.0826254i
$571$	−19.5755	+	19.5755i	−0.819211	+	0.819211i	−0.985994	−	0.166783i	$-0.946662\pi$
$571$	−19.5755	+	19.5755i	−0.819211	+	0.819211i	0.166783	+	0.985994i	$0.446662\pi$
$572$	−46.5516	+	6.85311i	−1.94642	+	0.286543i
$573$	−3.40083	+	3.02371i	−0.142072	+	0.126317i
$574$	−1.09138	−	14.9069i	−0.0455533	−	0.622201i
$575$	17.5465			0.731738
$576$	7.57766	+	22.7723i	0.315736	+	0.948847i
$577$	2.45494			0.102200			0.0511002	−	0.998694i	$-0.483727\pi$
$577$	2.45494			0.102200			0.0511002	+	0.998694i	$0.483727\pi$
$578$	−0.811109	−	11.0787i	−0.0337377	−	0.460815i
$579$	4.60063	−	4.09047i	0.191196	−	0.169994i
$580$	−2.77176	+	0.408046i	−0.115091	+	0.0169432i
$581$	−1.12559	+	1.12559i	−0.0466974	+	0.0466974i
$582$	22.2676	+	21.6332i	0.923022	+	0.896724i
$583$	−68.4051			−2.83305
$584$	−6.40558	+	1.42735i	−0.265065	+	0.0590644i
$585$	−3.04181	−	0.358339i	−0.125763	−	0.0148155i
$586$	13.4440	+	11.6097i	0.555365	+	0.479593i
$587$	−17.7714	−	17.7714i	−0.733505	−	0.733505i	0.237807	−	0.971312i	$-0.423571\pi$
$587$	−17.7714	−	17.7714i	−0.733505	−	0.733505i	−0.971312	+	0.237807i	$0.923571\pi$
$588$	−2.22597	+	2.65425i	−0.0917976	+	0.109459i
$589$	−20.4205	+	20.4205i	−0.841411	+	0.841411i
$590$	−0.122710	−	1.67606i	−0.00505188	−	0.0690024i
$591$	−2.41046	+	41.0644i	−0.0991529	+	1.68916i
$592$	−24.0265	−	12.9103i	−0.987482	−	0.530608i
$593$		−	41.1462i		−	1.68967i	−0.535025	−	0.844836i	$-0.679698\pi$
$593$		−	41.1462i		−	1.68967i	0.535025	−	0.844836i	$-0.320302\pi$
$594$	44.4190	+	4.58304i	1.82253	+	0.188044i
$595$	0.929618	+	0.929618i	0.0381106	+	0.0381106i
$596$	−1.30179	+	1.75125i	−0.0533236	+	0.0717340i
$597$	15.3056	−	13.6084i	0.626418	−	0.556955i
$598$	12.7353	−	14.7474i	0.520787	−	0.603068i
$599$		−	29.4373i		−	1.20278i	−0.798957	−	0.601388i	$-0.794615\pi$
$599$		−	29.4373i		−	1.20278i	0.798957	−	0.601388i	$-0.205385\pi$
$600$	14.1283	−	19.5913i	0.576786	−	0.799810i
$601$		−	5.56552i		−	0.227022i	−0.993537	−	0.113511i	$-0.963790\pi$
$601$		−	5.56552i		−	0.227022i	0.993537	−	0.113511i	$-0.0362097\pi$
$602$	−8.77895	−	7.58117i	−0.357803	−	0.308985i
$603$	7.98362	−	6.30084i	0.325118	−	0.256590i
$604$	−9.53902	+	1.40429i	−0.388137	+	0.0571397i
$605$	4.83447	+	4.83447i	0.196549	+	0.196549i
$606$	3.76833	−	0.0544585i	0.153078	−	0.00221222i
$607$			24.2531i			0.984402i	0.870482	+	0.492201i	$0.163808\pi$
$607$			24.2531i			0.984402i	−0.870482	+	0.492201i	$0.836192\pi$
$608$	10.1090	−	22.6378i	0.409975	−	0.918085i
$609$	9.18506	+	0.539157i	0.372197	+	0.0218478i
$610$	−1.67089	+	0.122331i	−0.0676525	+	0.00495305i
$611$	8.83022	−	8.83022i	0.357232	−	0.357232i
$612$	−29.9003	+	0.864396i	−1.20865	+	0.0349411i
$613$	8.76284	+	8.76284i	0.353928	+	0.353928i	0.861569	−	0.507641i	$-0.169482\pi$
$613$	8.76284	+	8.76284i	0.353928	+	0.353928i	−0.507641	+	0.861569i	$0.669482\pi$
$614$	−19.4463	+	22.5187i	−0.784789	+	0.908780i
$615$	−0.282874	+	4.81904i	−0.0114066	+	0.194322i
$616$	9.21922	−	14.5059i	0.371453	−	0.584459i
$617$	−12.0201			−0.483910			−0.241955	−	0.970287i	$-0.577789\pi$
$617$	−12.0201			−0.483910			−0.241955	+	0.970287i	$0.577789\pi$
$618$	−8.61323	−	8.36783i	−0.346475	−	0.336603i
$619$	−23.3157	+	23.3157i	−0.937136	+	0.937136i	−0.998138	−	0.0610020i	$-0.980570\pi$
$619$	−23.3157	+	23.3157i	−0.937136	+	0.937136i	0.0610020	+	0.998138i	$0.480570\pi$
$620$	2.78904	+	2.07324i	0.112011	+	0.0832633i
$621$	−15.1622	+	10.5859i	−0.608438	+	0.424798i
$622$	45.5375	−	3.33394i	1.82589	−	0.133679i
$623$	7.81580			0.313134
$624$	−6.21164	−	26.0940i	−0.248664	−	1.04460i
$625$	−23.9618			−0.958470
$626$	10.1130	−	0.740406i	0.404198	−	0.0295926i
$627$	−30.6508	−	34.4736i	−1.22408	−	1.37674i
$628$	8.86698	−	11.9284i	0.353831	−	0.475994i
$629$	24.0382	−	24.0382i	0.958464	−	0.958464i
$630$	0.825276	−	0.755394i	0.0328798	−	0.0300956i
$631$	−37.5507			−1.49487			−0.747436	−	0.664334i	$-0.768715\pi$
$631$	−37.5507			−1.49487			−0.747436	+	0.664334i	$0.768715\pi$
$632$	−19.0342	+	4.24140i	−0.757141	+	0.168714i
$633$	−8.62563	−	0.506319i	−0.342838	−	0.0201244i
$634$	−0.773612	+	0.895838i	−0.0307241	+	0.0355783i
$635$	−2.38941	−	2.38941i	−0.0948207	−	0.0948207i
$636$	−3.40900	−	38.8456i	−0.135176	−	1.54033i
$637$	2.73763	−	2.73763i	0.108469	−	0.108469i
$638$	−45.5296	+	3.33336i	−1.80253	+	0.131969i
$639$	−27.0070	−	3.18155i	−1.06838	−	0.125860i
$640$	−2.87230	−	0.806756i	−0.113538	−	0.0318898i
$641$		−	0.680137i		−	0.0268638i	−0.999910	−	0.0134319i	$-0.995724\pi$
$641$		−	0.680137i		−	0.0268638i	0.999910	−	0.0134319i	$-0.00427563\pi$
$642$	−0.168813	−	11.6812i	−0.00666250	−	0.461021i
$643$	6.40677	+	6.40677i	0.252658	+	0.252658i	0.822060	−	0.569401i	$-0.192825\pi$
$643$	6.40677	+	6.40677i	0.252658	+	0.252658i	−0.569401	+	0.822060i	$0.692825\pi$
$644$	1.03664	+	7.04168i	0.0408494	+	0.277481i
$645$	2.48919	+	2.79964i	0.0980118	+	0.110236i
$646$	23.3870	+	20.1961i	0.920149	+	0.794606i
$647$			30.0799i			1.18256i	0.806466	+	0.591281i	$0.201378\pi$
$647$			30.0799i			1.18256i	−0.806466	+	0.591281i	$0.798622\pi$
$648$	−0.388956	+	25.4529i	−0.0152796	+	0.999883i
$649$		−	27.3838i		−	1.07491i
$650$	−17.6440	+	20.4316i	−0.692053	+	0.801393i
$651$	−7.58340	−	8.52920i	−0.297217	−	0.334286i
$652$	−4.78649	−	3.55805i	−0.187454	−	0.139344i
$653$	−4.68675	−	4.68675i	−0.183407	−	0.183407i	0.609432	−	0.792838i	$-0.291398\pi$
$653$	−4.68675	−	4.68675i	−0.183407	−	0.183407i	−0.792838	+	0.609432i	$0.791398\pi$
$654$	−43.5015	+	0.628668i	−1.70104	+	0.0245828i
$655$			1.84541i			0.0721060i
$656$	−40.4823	+	12.1833i	−1.58057	+	0.475677i
$657$	−6.91297	−	0.814380i	−0.269701	−	0.0317720i
$658$	0.333073	+	4.54937i	0.0129846	+	0.177353i
$659$	21.0024	−	21.0024i	0.818136	−	0.818136i	−0.167702	−	0.985838i	$-0.553635\pi$
$659$	21.0024	−	21.0024i	0.818136	−	0.818136i	0.985838	+	0.167702i	$0.0536346\pi$
$660$	−3.56702	+	4.25331i	−0.138846	+	0.165560i
$661$	6.30679	+	6.30679i	0.245306	+	0.245306i	0.819041	−	0.573735i	$-0.194506\pi$
$661$	6.30679	+	6.30679i	0.245306	+	0.245306i	−0.573735	+	0.819041i	$0.694506\pi$
$662$	8.68626	+	7.50113i	0.337601	+	0.291540i
$663$	33.3740	+	1.95903i	1.29614	+	0.0760826i
$664$	3.79987	+	2.41501i	0.147464	+	0.0937205i
$665$	−1.15573			−0.0448174
$666$	−19.5331	−	21.3401i	−0.756891	−	0.826912i
$667$	13.3677	−	13.3677i	0.517598	−	0.517598i
$668$	−5.04089	−	34.2416i	−0.195038	−	1.32485i
$669$	−24.4617	−	27.5126i	−0.945744	−	1.06370i
$670$	0.0923161	+	1.26092i	0.00356648	+	0.0487137i
$671$	−27.2993			−1.05388
$672$	8.69699	+	4.51247i	0.335494	+	0.174072i
$673$	−17.2127			−0.663502			−0.331751	−	0.943367i	$-0.607639\pi$
$673$	−17.2127			−0.663502			−0.331751	+	0.943367i	$0.607639\pi$
$674$	−1.38374	−	18.9002i	−0.0532999	−	0.728010i
$675$	21.0062	−	14.6661i	0.808530	−	0.564497i
$676$	0.579440	+	3.93601i	0.0222862	+	0.151385i
$677$	−32.3963	+	32.3963i	−1.24509	+	1.24509i	−0.287231	+	0.957861i	$0.592735\pi$
$677$	−32.3963	+	32.3963i	−1.24509	+	1.24509i	−0.957861	+	0.287231i	$0.907265\pi$
$678$	−7.20341	+	7.41466i	−0.276645	+	0.284758i
$679$	12.6744			0.486398
$680$	1.99454	−	3.13829i	0.0764870	−	0.120348i
$681$	−1.80546	+	30.7577i	−0.0691853	+	1.17864i
$682$	42.8581	+	37.0107i	1.64112	+	1.41721i
$683$	4.46231	+	4.46231i	0.170746	+	0.170746i	0.787307	−	0.616561i	$-0.211475\pi$
$683$	4.46231	+	4.46231i	0.170746	+	0.170746i	−0.616561	+	0.787307i	$0.711475\pi$
$684$	18.0492	−	19.1239i	0.690129	−	0.731219i
$685$	0.946280	−	0.946280i	0.0361555	−	0.0361555i
$686$	0.103263	+	1.41044i	0.00394258	+	0.0538508i
$687$	41.7234	+	2.44914i	1.59185	+	0.0934404i
$688$	−15.5289	+	28.8999i	−0.592035	+	1.10180i
$689$			43.5820i			1.66034i
$690$	−0.0332172	−	2.29851i	−0.00126456	−	0.0875027i
$691$	−23.7096	−	23.7096i	−0.901957	−	0.901957i	0.0936479	−	0.995605i	$-0.470147\pi$
$691$	−23.7096	−	23.7096i	−0.901957	−	0.901957i	−0.995605	+	0.0936479i	$0.970147\pi$
$692$	4.46040	+	3.31565i	0.169559	+	0.126042i
$693$	14.3104	−	11.2940i	0.543606	−	0.429025i
$694$	14.0253	−	16.2412i	0.532391	−	0.616506i
$695$		−	0.981098i		−	0.0372152i
$696$	−4.16192	−	25.6890i	−0.157757	−	0.973740i
$697$		−	52.6912i		−	1.99582i
$698$	38.8113	+	33.5160i	1.46903	+	1.26860i
$699$	6.28429	−	5.58743i	0.237694	−	0.211336i
$700$	−1.43620	−	9.75577i	−0.0542832	−	0.368734i
$701$	6.57459	+	6.57459i	0.248319	+	0.248319i	0.820280	−	0.571962i	$-0.193817\pi$
$701$	6.57459	+	6.57459i	0.248319	+	0.248319i	−0.571962	+	0.820280i	$0.693817\pi$
$702$	2.91992	−	28.3000i	0.110205	−	1.06812i
$703$			29.8851i			1.12714i
$704$	−45.7181	−	16.5281i	−1.72307	−	0.622925i
$705$	0.0863293	−	1.47070i	0.00325135	−	0.0553898i
$706$	−13.8831	+	1.01643i	−0.522497	+	0.0382537i
$707$	1.08794	−	1.08794i	0.0409160	−	0.0409160i
$708$	15.5506	−	1.36468i	0.584427	−	0.0512879i
$709$	34.7204	+	34.7204i	1.30395	+	1.30395i	0.925704	+	0.378250i	$0.123474\pi$
$709$	34.7204	+	34.7204i	1.30395	+	1.30395i	0.378250	+	0.925704i	$0.376526\pi$
$710$	2.20943	−	2.55851i	0.0829185	−	0.0960191i
$711$	−20.5419	−	2.41994i	−0.770383	−	0.0907547i
$712$	−4.80806	−	21.5772i	−0.180190	−	0.808641i
$713$	−23.4498			−0.878201
$714$	−8.50939	+	8.75895i	−0.318456	+	0.327795i
$715$	4.38692	−	4.38692i	0.164062	−	0.164062i
$716$	−6.20274	+	8.34428i	−0.231807	+	0.311840i
$717$	5.82809	−	5.18181i	0.217654	−	0.193518i
$718$	−25.4557	+	1.86369i	−0.949997	+	0.0695522i
$719$	15.1919			0.566562			0.283281	−	0.959037i	$-0.408577\pi$
$719$	15.1919			0.566562			0.283281	+	0.959037i	$0.408577\pi$
$720$	−2.59312	−	1.81366i	−0.0966397	−	0.0675910i
$721$	−4.90252			−0.182579
$722$	−0.293710	+	0.0215034i	−0.0109307	+	0.000800273i
$723$	30.3303	−	26.9670i	1.12799	−	1.00291i
$724$	4.35320	+	3.23596i	0.161785	+	0.120264i
$725$	−18.5200	+	18.5200i	−0.687815	+	0.687815i
$726$	−44.2531	+	45.5509i	−1.64239	+	1.69055i
$727$	−50.4025			−1.86933			−0.934663	−	0.355536i	$-0.884298\pi$
$727$	−50.4025			−1.86933			−0.934663	+	0.355536i	$0.884298\pi$
$728$	−9.24193	−	5.87371i	−0.342529	−	0.217694i
$729$	−9.30369	+	25.3464i	−0.344581	+	0.938757i
$730$	0.565547	−	0.654900i	0.0209319	−	0.0242389i
$731$	−28.9140	−	28.9140i	−1.06942	−	1.06942i
$732$	−1.36047	−	15.5026i	−0.0502845	−	0.572993i
$733$	−17.7495	+	17.7495i	−0.655592	+	0.655592i	−0.954334	−	0.298742i	$-0.903433\pi$
$733$	−17.7495	+	17.7495i	−0.655592	+	0.655592i	0.298742	+	0.954334i	$0.403433\pi$
$734$	6.63307	−	0.485628i	0.244831	−	0.0179249i
$735$	0.0267646	−	0.455961i	0.000987228	−	0.0168184i
$736$	18.8024	−	7.19371i	0.693065	−	0.265164i
$737$			20.6012i			0.758853i
$738$	−44.7966	−	1.98047i	−1.64898	−	0.0729020i
$739$	32.8936	+	32.8936i	1.21001	+	1.21001i	0.971022	+	0.238988i	$0.0768158\pi$
$739$	32.8936	+	32.8936i	1.21001	+	1.21001i	0.238988	+	0.971022i	$0.423184\pi$
$740$	3.55794	−	0.523784i	0.130793	−	0.0192547i
$741$	−21.9637	+	19.5281i	−0.806855	+	0.717383i
$742$	−12.0488	−	10.4049i	−0.442324	−	0.381974i
$743$			0.740043i			0.0271495i	0.999908	+	0.0135748i	$0.00432112\pi$
$743$			0.740043i			0.0271495i	−0.999908	+	0.0135748i	$0.995679\pi$
$744$	−18.8816	+	26.1825i	−0.692234	+	0.959899i
$745$		−	0.287712i		−	0.0105409i
$746$	17.2275	−	19.9493i	0.630742	−	0.730396i
$747$	2.95852	+	3.74865i	0.108246	+	0.137156i
$748$	36.1472	−	48.6274i	1.32167	−	1.77799i
$749$	−3.37243	−	3.37243i	−0.123226	−	0.123226i
$750$	0.0926895	+	6.41377i	0.00338454	+	0.234198i
$751$		−	44.9022i		−	1.63851i	−0.573433	−	0.819253i	$-0.694389\pi$
$751$		−	44.9022i		−	1.63851i	0.573433	−	0.819253i	$-0.305611\pi$
$752$	12.3546	−	3.71816i	0.450527	−	0.135587i
$753$	−4.79225	−	0.281302i	−0.174639	−	0.0102512i
$754$	2.12374	+	29.0076i	0.0773419	+	1.05639i
$755$	0.898935	−	0.898935i	0.0327156	−	0.0327156i
$756$	7.12678	+	7.56367i	0.259198	+	0.275088i
$757$	−10.1054	−	10.1054i	−0.367289	−	0.367289i	0.499199	−	0.866488i	$-0.333628\pi$
$757$	−10.1054	−	10.1054i	−0.367289	−	0.367289i	−0.866488	+	0.499199i	$0.833628\pi$
$758$	12.3142	+	10.6340i	0.447270	+	0.386246i
$759$	2.19493	−	37.3927i	0.0796709	−	1.35727i
$760$	0.710974	+	3.19065i	0.0257897	+	0.115737i
$761$	44.5291			1.61418			0.807089	−	0.590430i	$-0.201042\pi$
$761$	44.5291			1.61418			0.807089	+	0.590430i	$0.201042\pi$
$762$	21.8718	−	22.5132i	0.792331	−	0.815568i
$763$	−12.5591	+	12.5591i	−0.454671	+	0.454671i
$764$	5.19861	−	0.765315i	0.188079	−	0.0276881i
$765$	3.09598	−	2.44342i	0.111936	−	0.0883419i
$766$	−1.69943	−	23.2121i	−0.0614028	−	0.838686i
$767$	−17.4466			−0.629961
$768$	7.10751	−	26.7859i	0.256470	−	0.966552i
$769$	−4.48904			−0.161879			−0.0809395	−	0.996719i	$-0.525792\pi$
$769$	−4.48904			−0.161879			−0.0809395	+	0.996719i	$0.525792\pi$
$770$	0.165473	+	2.26016i	0.00596325	+	0.0814506i
$771$	−30.9739	−	34.8369i	−1.11550	−	1.25462i
$772$	−7.03267	+	1.03532i	−0.253111	+	0.0372619i
$773$	−2.39104	+	2.39104i	−0.0859997	+	0.0859997i	−0.748798	−	0.662798i	$-0.769369\pi$
$773$	−2.39104	+	2.39104i	−0.0859997	+	0.0859997i	0.662798	+	0.748798i	$0.269369\pi$
$774$	−25.6686	+	23.4951i	−0.922639	+	0.844513i
$775$	32.4881			1.16701
$776$	−7.79692	−	34.9904i	−0.279893	−	1.25608i
$777$	−11.7903	−	0.692083i	−0.422974	−	0.0248283i
$778$	15.9233	+	13.7508i	0.570880	+	0.492990i
$779$	32.7538	+	32.7538i	1.17353	+	1.17353i
$780$	2.70985	+	2.27260i	0.0970282	+	0.0813722i
$781$	38.9497	−	38.9497i	1.39373	−	1.39373i
$782$	1.83210	+	25.0243i	0.0655159	+	0.894866i
$783$	4.83020	−	27.1767i	0.172617	−	0.971216i
$784$	3.83030	−	1.15274i	0.136796	−	0.0411693i
$785$			1.95971i			0.0699449i
$786$	−17.1399	+	0.247700i	−0.611360	+	0.00883515i
$787$	12.4954	+	12.4954i	0.445412	+	0.445412i	0.893826	−	0.448414i	$-0.148011\pi$
$787$	12.4954	+	12.4954i	0.445412	+	0.445412i	−0.448414	+	0.893826i	$0.648011\pi$
$788$	28.3368	−	38.1203i	1.00946	−	1.35798i
$789$	23.0945	+	25.9748i	0.822185	+	0.924727i
$790$	1.68053	−	1.94604i	0.0597906	−	0.0692371i
$791$			4.22031i			0.150057i
$792$	−39.9830	−	32.5591i	−1.42073	−	1.15694i
$793$			17.3928i			0.617637i
$794$	−17.7739	−	15.3489i	−0.630772	−	0.544712i
$795$	3.41632	+	3.84240i	0.121164	+	0.136276i
$796$	−23.3967	+	3.44435i	−0.829274	+	0.122082i
$797$	−12.7544	−	12.7544i	−0.451785	−	0.451785i	0.444162	−	0.895947i	$-0.353502\pi$
$797$	−12.7544	−	12.7544i	−0.451785	−	0.451785i	−0.895947	+	0.444162i	$0.853502\pi$
$798$	−0.155128	−	10.7343i	−0.00549148	−	0.379990i
$799$			16.0806i			0.568891i
$800$	−26.0494	+	9.96641i	−0.920987	+	0.352366i
$801$	2.74324	−	23.2864i	0.0969278	−	0.822784i
$802$	6.30918	−	0.461915i	0.222785	−	0.0163108i
$803$	9.96994	−	9.96994i	0.351831	−	0.351831i
$804$	−11.6989	+	1.02667i	−0.412588	+	0.0362078i
$805$	−0.663592	−	0.663592i	−0.0233885	−	0.0233885i
$806$	23.5801	−	27.3056i	0.830573	−	0.961798i
$807$	−15.6340	−	0.917708i	−0.550344	−	0.0323048i
$808$	−3.67275	−	2.33422i	−0.129207	−	0.0821175i
$809$	40.5344			1.42511			0.712557	−	0.701614i	$-0.247537\pi$
$809$	40.5344			1.42511			0.712557	+	0.701614i	$0.247537\pi$
$810$	−1.96096	−	2.72396i	−0.0689010	−	0.0957101i
$811$	−0.808442	+	0.808442i	−0.0283882	+	0.0283882i	−0.721158	−	0.692770i	$-0.756390\pi$
$811$	−0.808442	+	0.808442i	−0.0283882	+	0.0283882i	0.692770	+	0.721158i	$0.256390\pi$
$812$	−8.52653	−	6.33821i	−0.299223	−	0.222428i
$813$	−17.8595	−	20.0869i	−0.626358	−	0.704478i
$814$	58.4435	−	4.27883i	2.04844	−	0.149973i
$815$	0.786371			0.0275454
$816$	29.4157	+	18.1038i	1.02976	+	0.633759i
$817$	35.9469			1.25762
$818$	−0.228065	+	0.0166973i	−0.00797411	+	0.000583809i
$819$	−7.19561	−	9.11735i	−0.251435	−	0.318586i
$820$	3.32541	−	4.47353i	0.116128	−	0.156223i
$821$	−36.4630	+	36.4630i	−1.27257	+	1.27257i	−0.327831	+	0.944736i	$0.606318\pi$
$821$	−36.4630	+	36.4630i	−1.27257	+	1.27257i	−0.944736	+	0.327831i	$0.893682\pi$
$822$	8.91594	+	8.66191i	0.310979	+	0.302119i
$823$	49.3421			1.71996			0.859979	−	0.510329i	$-0.170476\pi$
$823$	49.3421			1.71996			0.859979	+	0.510329i	$0.170476\pi$
$824$	3.01589	+	13.5345i	0.105063	+	0.471496i
$825$	−3.04093	+	51.8051i	−0.105872	+	1.80362i
$826$	4.16525	−	4.82333i	0.144928	−	0.167825i
$827$	−26.4919	−	26.4919i	−0.921213	−	0.921213i	0.0759022	−	0.997115i	$-0.475816\pi$
$827$	−26.4919	−	26.4919i	−0.921213	−	0.921213i	−0.997115	+	0.0759022i	$0.975816\pi$
$828$	21.3438	−	0.617034i	0.741748	−	0.0214434i
$829$	−20.8538	+	20.8538i	−0.724283	+	0.724283i	−0.969475	−	0.245192i	$-0.921149\pi$
$829$	−20.8538	+	20.8538i	−0.724283	+	0.724283i	0.245192	+	0.969475i	$0.421149\pi$
$830$	−0.592057	+	0.0433464i	−0.0205506	+	0.00150457i
$831$	−15.0680	−	0.884481i	−0.522702	−	0.0306823i
$832$	−10.5303	+	29.1277i	−0.365072	+	1.00982i
$833$			4.98546i			0.172736i
$834$	9.11231	−	0.131688i	0.315534	−	0.00455997i
$835$	3.22685	+	3.22685i	0.111670	+	0.111670i
$836$	7.75787	+	52.6974i	0.268311	+	1.82258i
$837$	−28.0735	+	19.6003i	−0.970364	+	0.677486i
$838$	−4.19954	−	3.62657i	−0.145071	−	0.125278i
$839$			33.7299i			1.16449i	0.813015	+	0.582243i	$0.197825\pi$
$839$			33.7299i			1.16449i	−0.813015	+	0.582243i	$0.802175\pi$
$840$	−1.27524	+	0.206604i	−0.0440001	+	0.00712853i
$841$		−	0.781332i		−	0.0269425i
$842$	7.48985	−	8.67320i	0.258117	−	0.298898i
$843$	−12.4175	+	11.0405i	−0.427682	+	0.380256i
$844$	8.00721	+	5.95218i	0.275620	+	0.204882i
$845$	−0.370920	−	0.370920i	−0.0127600	−	0.0127600i
$846$	13.6713	+	0.604411i	0.470028	+	0.0207801i
$847$			25.9269i			0.890858i
$848$	−21.3128	+	39.6640i	−0.731886	+	1.36207i
$849$	2.91870	−	49.7228i	0.100170	−	1.70648i
$850$	−2.53826	−	34.6695i	−0.0870616	−	1.18915i
$851$	−17.1592	+	17.1592i	−0.588211	+	0.588211i
$852$	24.0597	+	20.1775i	0.824270	+	0.691270i
$853$	−22.1012	−	22.1012i	−0.756732	−	0.756732i	0.218994	−	0.975726i	$-0.429722\pi$
$853$	−22.1012	−	22.1012i	−0.756732	−	0.756732i	−0.975726	+	0.218994i	$0.929722\pi$
$854$	−4.80846	−	4.15240i	−0.164542	−	0.142092i
$855$	−0.405647	+	3.44339i	−0.0138728	+	0.117761i
$856$	−7.23570	+	11.3849i	−0.247311	+	0.389129i
$857$	−52.0113			−1.77667			−0.888336	−	0.459194i	$-0.848138\pi$
$857$	−52.0113			−1.77667			−0.888336	+	0.459194i	$0.848138\pi$
$858$	41.3340	+	40.1563i	1.41112	+	1.37091i
$859$	24.7863	−	24.7863i	0.845697	−	0.845697i	−0.143896	−	0.989593i	$-0.545963\pi$
$859$	24.7863	−	24.7863i	0.845697	−	0.845697i	0.989593	+	0.143896i	$0.0459631\pi$
$860$	−0.630026	−	4.27962i	−0.0214837	−	0.145934i
$861$	−13.6806	+	12.1635i	−0.466232	+	0.414532i
$862$	2.08261	+	28.4458i	0.0709339	+	0.968869i
$863$	−3.25607			−0.110838			−0.0554190	−	0.998463i	$-0.517649\pi$
$863$	−3.25607			−0.110838			−0.0554190	+	0.998463i	$0.517649\pi$
$864$	16.4970	−	24.3280i	0.561238	−	0.827654i
$865$	−0.732797			−0.0249158
$866$	−3.07104	−	41.9467i	−0.104358	−	1.42541i
$867$	−10.1674	+	9.03990i	−0.345301	+	0.307011i
$868$	1.91939	+	13.0380i	0.0651485	+	0.442539i
$869$	29.6258	−	29.6258i	1.00499	−	1.00499i
$870$	2.46110	+	2.39098i	0.0834390	+	0.0810617i
$871$	13.1253			0.444734
$872$	42.3982	+	26.9462i	1.43578	+	0.912513i
$873$	4.44854	−	37.7620i	0.150560	−	1.27805i
$874$	−16.6944	−	14.4167i	−0.564697	−	0.487651i
$875$	1.85169	+	1.85169i	0.0625986	+	0.0625986i
$876$	6.15854	+	5.16483i	0.208078	+	0.174503i
$877$	36.6022	−	36.6022i	1.23597	−	1.23597i	0.274335	−	0.961634i	$-0.411542\pi$
$877$	36.6022	−	36.6022i	1.23597	−	1.23597i	0.961634	−	0.274335i	$-0.0884578\pi$
$878$	2.48390	+	33.9270i	0.0838276	+	1.14498i
$879$	1.27482	−	21.7178i	0.0429987	−	0.732523i
$880$	6.13787	−	1.84721i	0.206908	−	0.0622695i
$881$			17.7444i			0.597824i	0.954281	+	0.298912i	$0.0966237\pi$
$881$			17.7444i			0.597824i	−0.954281	+	0.298912i	$0.903376\pi$
$882$	4.23850	+	0.187385i	0.142718	+	0.00630959i
$883$	0.699892	+	0.699892i	0.0235533	+	0.0235533i	0.718785	−	0.695232i	$-0.244698\pi$
$883$	0.699892	+	0.699892i	0.0235533	+	0.0235533i	−0.695232	+	0.718785i	$0.744698\pi$
$884$	−30.9812	−	23.0300i	−1.04201	−	0.774582i
$885$	−1.53818	+	1.36761i	−0.0517054	+	0.0459718i
$886$	−12.6182	+	14.6117i	−0.423915	+	0.490891i
$887$		−	24.7549i		−	0.831190i	−0.909550	−	0.415595i	$-0.863573\pi$
$887$		−	24.7549i		−	0.831190i	0.909550	−	0.415595i	$-0.136427\pi$
$888$	5.34240	+	32.9754i	0.179279	+	1.10658i
$889$		−	12.8142i		−	0.429774i
$890$	2.20604	+	1.90505i	0.0739465	+	0.0638575i
$891$	−28.6267	−	46.6003i	−0.959030	−	1.56117i
$892$	6.19137	+	42.0566i	0.207302	+	1.40816i
$893$	−9.99599	−	9.99599i	−0.334503	−	0.334503i
$894$	2.67223	−	0.0386181i	0.0893728	−	0.00129158i
$895$		−	1.37088i		−	0.0458234i
$896$	−5.53868	−	9.86524i	−0.185034	−	0.329575i
$897$	−23.8235	−	1.39842i	−0.795443	−	0.0466920i
$898$	21.0629	−	1.54208i	0.702879	−	0.0514600i
$899$	24.7509	−	24.7509i	0.825487	−	0.825487i
$900$	−29.5704	+	0.854860i	−0.985680	+	0.0284953i
$901$	−39.6833	−	39.6833i	−1.32204	−	1.32204i
$902$	59.3640	−	68.7431i	1.97660	−	2.28889i
$903$	−0.832462	+	14.1818i	−0.0277026	+	0.471940i
$904$	11.6511	−	2.59621i	0.387510	−	0.0863488i
$905$	−0.715185			−0.0237736
$906$	8.46986	+	8.22854i	0.281392	+	0.273375i
$907$	15.9366	−	15.9366i	0.529167	−	0.529167i	−0.391157	−	0.920324i	$-0.627925\pi$
$907$	15.9366	−	15.9366i	0.529167	−	0.529167i	0.920324	+	0.391157i	$0.127925\pi$
$908$	21.2246	−	28.5525i	0.704362	−	0.947549i
$909$	−2.85954	−	3.62324i	−0.0948450	−	0.120175i
$910$	1.43998	−	0.105426i	0.0477350	−	0.00349483i
$911$	−5.23938			−0.173588			−0.0867942	−	0.996226i	$-0.527662\pi$
$911$	−5.23938			−0.173588			−0.0867942	+	0.996226i	$0.527662\pi$
$912$	−29.5390	+	7.03170i	−0.978133	+	0.232843i
$913$	−9.67313			−0.320134
$914$	−14.6831	+	1.07500i	−0.485675	+	0.0355577i
$915$	1.36339	+	1.53344i	0.0450724	+	0.0506938i
$916$	−38.7320	−	28.7915i	−1.27974	−	0.951298i
$917$	−4.94838	+	4.94838i	−0.163410	+	0.163410i
$918$	23.1097	+	28.4271i	0.762734	+	0.938235i
$919$	5.00713			0.165170			0.0825850	−	0.996584i	$-0.473682\pi$
$919$	5.00713			0.165170			0.0825850	+	0.996584i	$0.473682\pi$
$920$	−1.42377	+	2.24021i	−0.0469402	+	0.0738576i
$921$	36.3774	+	2.13533i	1.19868	+	0.0703615i
$922$	−24.5193	+	28.3932i	−0.807501	+	0.935081i
$923$	−24.8154	−	24.8154i	−0.816810	−	0.816810i
$924$	−20.9699	+	1.84027i	−0.689859	+	0.0605403i
$925$	23.7730	−	23.7730i	0.781651	−	0.781651i
$926$	−36.0410	+	2.63867i	−1.18438	+	0.0867121i
$927$	−1.72072	+	14.6066i	−0.0565159	+	0.479742i
$928$	−12.2527	+	27.4384i	−0.402216	+	0.900711i
$929$			26.2486i			0.861188i	0.902546	+	0.430594i	$0.141696\pi$
$929$			26.2486i			0.861188i	−0.902546	+	0.430594i	$0.858304\pi$
$930$	−0.0615032	−	4.25580i	−0.00201677	−	0.139553i
$931$	−3.09905	−	3.09905i	−0.101567	−	0.101567i
$932$	−9.60637	+	1.41420i	−0.314667	+	0.0463238i
$933$	−37.1571	−	41.7913i	−1.21647	−	1.36819i
$934$	−20.5252	−	17.7248i	−0.671604	−	0.579973i
$935$			7.98897i			0.261267i
$936$	−20.7439	+	25.4738i	−0.678036	+	0.832637i
$937$			27.9322i			0.912506i	0.889850	+	0.456253i	$0.150809\pi$
$937$			27.9322i			0.912506i	−0.889850	+	0.456253i	$0.849191\pi$
$938$	−3.13357	+	3.62865i	−0.102315	+	0.118480i
$939$	−8.25190	−	9.28108i	−0.269291	−	0.302876i
$940$	−1.01487	+	1.36526i	−0.0331013	+	0.0445298i
$941$	32.6760	+	32.6760i	1.06521	+	1.06521i	0.997720	+	0.0674877i	$0.0214984\pi$
$941$	32.6760	+	32.6760i	1.06521	+	1.06521i	0.0674877	+	0.997720i	$0.478502\pi$
$942$	−18.2015	+	0.263041i	−0.593037	+	0.00857035i
$943$			37.6127i			1.22484i
$944$	−15.8782	−	8.53191i	−0.516792	−	0.277690i
$945$	−1.34909	−	0.239779i	−0.0438861	−	0.00780000i
$946$	−5.14673	−	70.2980i	−0.167335	−	2.28558i
$947$	−35.4193	+	35.4193i	−1.15097	+	1.15097i	−0.164616	+	0.986358i	$0.552638\pi$
$947$	−35.4193	+	35.4193i	−1.15097	+	1.15097i	−0.986358	+	0.164616i	$0.947362\pi$
$948$	18.3002	+	15.3473i	0.594362	+	0.498459i
$949$	−6.35200	−	6.35200i	−0.206195	−	0.206195i
$950$	23.1290	+	19.9733i	0.750403	+	0.648020i
$951$	1.44716	+	0.0849476i	0.0469275	+	0.00275462i
$952$	13.7635	−	3.06691i	0.446076	−	0.0993992i
$953$	24.4557			0.792197			0.396098	−	0.918208i	$-0.370364\pi$
$953$	24.4557			0.792197			0.396098	+	0.918208i	$0.370364\pi$
$954$	−35.2292	+	32.2461i	−1.14059	+	1.04401i
$955$	−0.489905	+	0.489905i	−0.0158530	+	0.0158530i
$956$	−8.90900	+	1.31154i	−0.288138	+	0.0424183i
$957$	37.1507	+	41.7841i	1.20091	+	1.35069i
$958$	0.533575	+	7.28797i	0.0172390	+	0.235464i
$959$	5.07482			0.163874
$960$	1.35487	+	3.39349i	0.0437282	+	0.109525i
$961$	−12.4184			−0.400594
$962$	−2.72611	−	37.2353i	−0.0878933	−	1.20051i
$963$	−11.2315	+	8.86412i	−0.361929	+	0.285642i
$964$	−46.3638	+	6.82546i	−1.49328	+	0.219833i
$965$	0.662743	−	0.662743i	0.0213344	−	0.0213344i
$966$	6.07429	−	6.25243i	0.195437	−	0.201169i
$967$	55.4167			1.78208			0.891041	−	0.453923i	$-0.149976\pi$
$967$	55.4167			1.78208			0.891041	+	0.453923i	$0.149976\pi$
$968$	71.5768	−	15.9495i	2.30057	−	0.512635i
$969$	2.21767	−	37.7801i	0.0712417	−	1.21367i
$970$	3.57739	+	3.08930i	0.114863	+	0.0991914i
$971$	22.9588	+	22.9588i	0.736782	+	0.736782i	0.971954	−	0.235172i	$-0.0755652\pi$
$971$	22.9588	+	22.9588i	0.736782	+	0.736782i	−0.235172	+	0.971954i	$0.575565\pi$
$972$	25.0366	−	18.5788i	0.803048	−	0.595914i
$973$	2.63077	−	2.63077i	0.0843387	−	0.0843387i
$974$	−0.837511	−	11.4394i	−0.0268356	−	0.366541i
$975$	33.0058	+	1.93742i	1.05703	+	0.0620472i
$976$	−8.50559	+	15.8292i	−0.272257	+	0.506681i
$977$			28.4090i			0.908883i	0.890777	+	0.454442i	$0.150161\pi$
$977$			28.4090i			0.908883i	−0.890777	+	0.454442i	$0.849839\pi$
$978$	0.105551	+	7.30371i	0.00337513	+	0.233547i
$979$	33.5838	+	33.5838i	1.07334	+	1.07334i
$980$	−0.314639	+	0.423271i	−0.0100508	+	0.0135209i
$981$	33.0105	+	41.8267i	1.05394	+	1.33542i
$982$	−7.30681	+	8.46124i	−0.233170	+	0.270009i
$983$			57.7405i			1.84164i	0.389992	+	0.920818i	$0.372478\pi$
$983$			57.7405i			1.84164i	−0.389992	+	0.920818i	$0.627522\pi$
$984$	41.9960	+	30.2855i	1.33878	+	0.965467i
$985$			6.26276i			0.199548i
$986$	−28.3465	−	24.4789i	−0.902735	−	0.779568i
$987$	4.17511	−	3.71214i	0.132895	−	0.118159i
$988$	33.5743	−	4.94266i	1.06814	−	0.157247i
$989$	20.6397	+	20.6397i	0.656305	+	0.656305i
$990$	6.79200	+	0.300276i	0.215864	+	0.00954339i
$991$		−	24.5422i		−	0.779609i	−0.920898	−	0.389804i	$-0.872543\pi$
$991$		−	24.5422i		−	0.779609i	0.920898	−	0.389804i	$-0.127457\pi$
$992$	34.8135	−	13.3195i	1.10533	−	0.422895i
$993$	0.823673	−	14.0321i	0.0261385	−	0.445294i
$994$	12.7850	−	0.936032i	0.405516	−	0.0296891i
$995$	2.20485	−	2.20485i	0.0698985	−	0.0698985i
$996$	−0.482064	−	5.49314i	−0.0152748	−	0.174057i
$997$	24.9091	+	24.9091i	0.788878	+	0.788878i	0.981310	−	0.192432i	$-0.0616375\pi$
$997$	24.9091	+	24.9091i	0.788878	+	0.788878i	−0.192432	+	0.981310i	$0.561637\pi$
$998$	−28.9426	+	33.5153i	−0.916162	+	1.06091i
$999$	−6.20023	+	34.8851i	−0.196167	+	1.10371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.13	yes	48
3.2	odd	2	inner	336.2.s.d.155.12	✓	48
4.3	odd	2		1344.2.s.d.911.6		48
12.11	even	2		1344.2.s.d.911.19		48
16.3	odd	4	inner	336.2.s.d.323.12	yes	48
16.13	even	4		1344.2.s.d.239.19		48
48.29	odd	4		1344.2.s.d.239.6		48
48.35	even	4	inner	336.2.s.d.323.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.12	✓	48	3.2	odd	2	inner
336.2.s.d.155.13	yes	48	1.1	even	1	trivial
336.2.s.d.323.12	yes	48	16.3	odd	4	inner
336.2.s.d.323.13	yes	48	48.35	even	4	inner
1344.2.s.d.239.6		48	48.29	odd	4
1344.2.s.d.239.19		48	16.13	even	4
1344.2.s.d.911.6		48	4.3	odd	2
1344.2.s.d.911.19		48	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.103263 + 1.41044i) q^{2} +(1.29441 - 1.15087i) q^{3} +(-1.97867 + 0.291291i) q^{4} +(0.186466 - 0.186466i) q^{5} +(1.75690 + 1.70684i) q^{6} +1.00000 q^{7} +(-0.615171 - 2.76072i) q^{8} +(0.350987 - 2.97940i) q^{9} +O(q^{10})\)	\(q+(0.103263 + 1.41044i) q^{2} +(1.29441 - 1.15087i) q^{3} +(-1.97867 + 0.291291i) q^{4} +(0.186466 - 0.186466i) q^{5} +(1.75690 + 1.70684i) q^{6} +1.00000 q^{7} +(-0.615171 - 2.76072i) q^{8} +(0.350987 - 2.97940i) q^{9} +(0.282253 + 0.243743i) q^{10} +(4.29691 + 4.29691i) q^{11} +(-2.22597 + 2.65425i) q^{12} +(2.73763 - 2.73763i) q^{13} +(0.103263 + 1.41044i) q^{14} +(0.0267646 - 0.455961i) q^{15} +(3.83030 - 1.15274i) q^{16} +4.98546i q^{17} +(4.23850 + 0.187385i) q^{18} +(-3.09905 - 3.09905i) q^{19} +(-0.314639 + 0.423271i) q^{20} +(1.29441 - 1.15087i) q^{21} +(-5.61682 + 6.50424i) q^{22} -3.55879i q^{23} +(-3.97352 - 2.86551i) q^{24} +4.93046i q^{25} +(4.14395 + 3.57856i) q^{26} +(-2.97458 - 4.26050i) q^{27} +(-1.97867 + 0.291291i) q^{28} +(3.75624 + 3.75624i) q^{29} +(0.645869 - 0.00933385i) q^{30} -6.58926i q^{31} +(2.02140 + 5.28337i) q^{32} +(10.5072 + 0.616763i) q^{33} +(-7.03169 + 0.514812i) q^{34} +(0.186466 - 0.186466i) q^{35} +(0.173383 + 5.99749i) q^{36} +(-4.82165 - 4.82165i) q^{37} +(4.05101 - 4.69104i) q^{38} +(0.392949 - 6.69427i) q^{39} +(-0.629488 - 0.400071i) q^{40} -10.5690 q^{41} +(1.75690 + 1.70684i) q^{42} +(-5.79966 + 5.79966i) q^{43} +(-9.75384 - 7.25053i) q^{44} +(-0.490108 - 0.621002i) q^{45} +(5.01945 - 0.367490i) q^{46} +3.22550 q^{47} +(3.63132 - 5.90030i) q^{48} +1.00000 q^{49} +(-6.95411 + 0.509132i) q^{50} +(5.73763 + 6.45322i) q^{51} +(-4.61943 + 6.21432i) q^{52} +(-7.95980 + 7.95980i) q^{53} +(5.70201 - 4.63542i) q^{54} +1.60245 q^{55} +(-0.615171 - 2.76072i) q^{56} +(-7.57805 - 0.444827i) q^{57} +(-4.91007 + 5.68582i) q^{58} +(-3.18645 - 3.18645i) q^{59} +(0.0798589 + 0.909994i) q^{60} +(-3.17662 + 3.17662i) q^{61} +(9.29375 - 0.680424i) q^{62} +(0.350987 - 2.97940i) q^{63} +(-7.24313 + 3.39663i) q^{64} -1.02095i q^{65} +(0.215089 + 14.8834i) q^{66} +(2.39721 + 2.39721i) q^{67} +(-1.45222 - 9.86460i) q^{68} +(-4.09571 - 4.60652i) q^{69} +(0.282253 + 0.243743i) q^{70} -9.06458i q^{71} +(-8.44119 + 0.863863i) q^{72} -2.32026i q^{73} +(6.30275 - 7.29854i) q^{74} +(5.67433 + 6.38203i) q^{75} +(7.03474 + 5.22929i) q^{76} +(4.29691 + 4.29691i) q^{77} +(9.48243 - 0.137037i) q^{78} -6.89467i q^{79} +(0.499273 - 0.929166i) q^{80} +(-8.75362 - 2.09146i) q^{81} +(-1.09138 - 14.9069i) q^{82} +(-1.12559 + 1.12559i) q^{83} +(-2.22597 + 2.65425i) q^{84} +(0.929618 + 0.929618i) q^{85} +(-8.77895 - 7.58117i) q^{86} +(9.18506 + 0.539157i) q^{87} +(9.21922 - 14.5059i) q^{88} +7.81580 q^{89} +(0.825276 - 0.755394i) q^{90} +(2.73763 - 2.73763i) q^{91} +(1.03664 + 7.04168i) q^{92} +(-7.58340 - 8.52920i) q^{93} +(0.333073 + 4.54937i) q^{94} -1.15573 q^{95} +(8.69699 + 4.51247i) q^{96} +12.6744 q^{97} +(0.103263 + 1.41044i) q^{98} +(14.3104 - 11.2940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more