LMFDB - Embedded newform 345.2.t.a.4.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.940856 - 0.429675i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-0.609131 + 0.702975i) q^{4} +(1.75953 - 1.37988i) q^{5} +(0.677340 + 0.781692i) q^{6} +(1.21306 - 0.174411i) q^{7} +(-0.853861 + 2.90798i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(1.06256 - 2.05429i) q^{10} +(0.774994 - 1.69700i) q^{11} +(-0.846112 - 0.386406i) q^{12} +(5.80506 + 0.834642i) q^{13} +(1.06637 - 0.685316i) q^{14} +(1.81970 + 1.29950i) q^{15} +(0.181373 + 1.26147i) q^{16} +(-5.58701 + 4.84118i) q^{17} +(-0.559199 + 0.870131i) q^{18} +(-0.355744 + 0.410550i) q^{19} +(-0.101763 + 2.07743i) q^{20} +(0.509104 + 1.11478i) q^{21} -1.92963i q^{22} +(4.73127 + 0.784266i) q^{23} -3.03075 q^{24} +(1.19187 - 4.85587i) q^{25} +(5.82035 - 1.70901i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.616304 + 0.958988i) q^{28} +(-5.69687 - 6.57453i) q^{29} +(2.27044 + 0.440761i) q^{30} +(-3.24287 - 0.952192i) q^{31} +(-2.56443 - 3.99033i) q^{32} +(1.84660 + 0.265501i) q^{33} +(-3.17645 + 6.95545i) q^{34} +(1.89374 - 1.98075i) q^{35} +(0.132377 - 0.920702i) q^{36} +(3.69444 + 5.74866i) q^{37} +(-0.158301 + 0.539123i) q^{38} +(0.834642 + 5.80506i) q^{39} +(2.51027 + 6.29490i) q^{40} +(-1.83788 - 1.18113i) q^{41} +(0.957987 + 0.830101i) q^{42} +(-1.62604 - 5.53778i) q^{43} +(0.720876 + 1.57850i) q^{44} +(-0.734189 + 2.11210i) q^{45} +(4.78843 - 1.29503i) q^{46} -8.47696i q^{47} +(-1.15928 + 0.529424i) q^{48} +(-5.27536 + 1.54899i) q^{49} +(-0.965065 - 5.08079i) q^{50} +(-6.21912 - 3.99678i) q^{51} +(-4.12278 + 3.57241i) q^{52} +(-7.68272 + 1.10461i) q^{53} +(-0.992429 - 0.291403i) q^{54} +(-0.978031 - 4.05531i) q^{55} +(-0.528597 + 3.67647i) q^{56} +(-0.494145 - 0.225668i) q^{57} +(-8.18484 - 3.73789i) q^{58} +(2.07837 - 14.4554i) q^{59} +(-2.02195 + 0.487639i) q^{60} +(-0.205042 - 0.0602058i) q^{61} +(-3.46021 + 0.497503i) q^{62} +(-0.926194 + 0.802552i) q^{63} +(-6.27156 - 4.03049i) q^{64} +(11.3659 - 6.54171i) q^{65} +(1.85146 - 0.543639i) q^{66} +(0.774508 - 0.353706i) q^{67} -6.87644i q^{68} +(0.580455 + 4.76057i) q^{69} +(0.930658 - 2.67729i) q^{70} +(4.36411 + 9.55607i) q^{71} +(-0.853861 - 2.90798i) q^{72} +(-4.88580 - 4.23357i) q^{73} +(5.94599 + 3.82126i) q^{74} +(4.99496 - 0.224466i) q^{75} +(-0.0719119 - 0.500158i) q^{76} +(0.644136 - 2.19372i) q^{77} +(3.27957 + 5.10310i) q^{78} +(-1.83819 + 12.7849i) q^{79} +(2.05981 + 1.96933i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-2.23669 - 0.321587i) q^{82} +(-0.436302 - 0.678900i) q^{83} +(-1.09378 - 0.321161i) q^{84} +(-3.15027 + 16.2276i) q^{85} +(-3.90931 - 4.51159i) q^{86} +(4.70323 - 7.31836i) q^{87} +(4.27311 + 3.70267i) q^{88} +(-12.5281 + 3.67858i) q^{89} +(0.216749 + 2.30264i) q^{90} +7.18744 q^{91} +(-3.43329 + 2.84824i) q^{92} -3.37977i q^{93} +(-3.64233 - 7.97560i) q^{94} +(-0.0594313 + 1.21326i) q^{95} +(3.10621 - 3.58475i) q^{96} +(-4.70330 + 7.31848i) q^{97} +(-4.29780 + 3.72406i) q^{98} +(0.265501 + 1.84660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

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 $

$2$	0.940856	−	0.429675i	0.665286	−	0.303826i	−0.0539992	−	0.998541i	$-0.517197\pi$
$2$	0.940856	−	0.429675i	0.665286	−	0.303826i	0.719285	+	0.694715i	$0.244470\pi$
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$4$	−0.609131	+	0.702975i	−0.304566	+	0.351488i
$5$	1.75953	−	1.37988i	0.786884	−	0.617101i
$5$	1.75953	−	1.37988i	0.786884	−	0.617101i
$6$	0.677340	+	0.781692i	0.276523	+	0.319124i
$7$	1.21306	−	0.174411i	0.458492	−	0.0659212i	0.0908008	−	0.995869i	$-0.471057\pi$
$7$	1.21306	−	0.174411i	0.458492	−	0.0659212i	0.367692	+	0.929948i	$0.380148\pi$
$8$	−0.853861	+	2.90798i	−0.301886	+	1.02813i
$9$	−0.841254	+	0.540641i	−0.280418	+	0.180214i
$10$	1.06256	−	2.05429i	0.336012	−	0.649624i
$11$	0.774994	−	1.69700i	0.233669	−	0.511665i	−0.756080	−	0.654479i	$-0.772888\pi$
$11$	0.774994	−	1.69700i	0.233669	−	0.511665i	0.989749	+	0.142814i	$0.0456152\pi$
$12$	−0.846112	−	0.386406i	−0.244251	−	0.111546i
$13$	5.80506	+	0.834642i	1.61003	+	0.231488i	0.887823	−	0.460185i	$-0.152217\pi$
$13$	5.80506	+	0.834642i	1.61003	+	0.231488i	0.722211	+	0.691673i	$0.243126\pi$
$14$	1.06637	−	0.685316i	0.285000	−	0.183158i
$15$	1.81970	+	1.29950i	0.469845	+	0.335529i
$16$	0.181373	+	1.26147i	0.0453432	+	0.315369i
$17$	−5.58701	+	4.84118i	−1.35505	+	1.17416i	−0.387385	+	0.921918i	$0.626622\pi$
$17$	−5.58701	+	4.84118i	−1.35505	+	1.17416i	−0.967665	+	0.252239i	$0.918833\pi$
$18$	−0.559199	+	0.870131i	−0.131804	+	0.205092i
$19$	−0.355744	+	0.410550i	−0.0816133	+	0.0941867i	−0.795088	−	0.606495i	$-0.792575\pi$
$19$	−0.355744	+	0.410550i	−0.0816133	+	0.0941867i	0.713474	+	0.700681i	$0.247121\pi$
$20$	−0.101763	+	2.07743i	−0.0227548	+	0.464528i
$21$	0.509104	+	1.11478i	0.111096	+	0.243265i
$22$		−	1.92963i		−	0.411398i
$23$	4.73127	+	0.784266i	0.986538	+	0.163531i
$23$	4.73127	+	0.784266i	0.986538	+	0.163531i
$24$	−3.03075			−0.618649
$25$	1.19187	−	4.85587i	0.238374	−	0.971173i
$26$	5.82035	−	1.70901i	1.14146	−	0.335164i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−0.616304	+	0.958988i	−0.116471	+	0.181232i
$29$	−5.69687	−	6.57453i	−1.05788	−	1.22086i	−0.974511	−	0.224342i	$-0.927977\pi$
$29$	−5.69687	−	6.57453i	−1.05788	−	1.22086i	−0.0833710	−	0.996519i	$-0.526569\pi$
$30$	2.27044	+	0.440761i	0.414523	+	0.0804715i
$31$	−3.24287	−	0.952192i	−0.582436	−	0.171019i	−0.0227757	−	0.999741i	$-0.507250\pi$
$31$	−3.24287	−	0.952192i	−0.582436	−	0.171019i	−0.559661	+	0.828722i	$0.689069\pi$
$32$	−2.56443	−	3.99033i	−0.453331	−	0.705396i
$33$	1.84660	+	0.265501i	0.321452	+	0.0462178i
$34$	−3.17645	+	6.95545i	−0.544756	+	1.19285i
$35$	1.89374	−	1.98075i	0.320100	−	0.334808i
$36$	0.132377	−	0.920702i	0.0220628	−	0.153450i
$37$	3.69444	+	5.74866i	0.607363	+	0.945075i	0.999681	+	0.0252452i	$0.00803666\pi$
$37$	3.69444	+	5.74866i	0.607363	+	0.945075i	−0.392319	+	0.919829i	$0.628327\pi$
$38$	−0.158301	+	0.539123i	−0.0256798	+	0.0874573i
$39$	0.834642	+	5.80506i	0.133650	+	0.929554i
$40$	2.51027	+	6.29490i	0.396909	+	0.995311i
$41$	−1.83788	−	1.18113i	−0.287029	−	0.184462i	0.389201	−	0.921153i	$-0.372751\pi$
$41$	−1.83788	−	1.18113i	−0.287029	−	0.184462i	−0.676230	+	0.736691i	$0.736387\pi$
$42$	0.957987	+	0.830101i	0.147821	+	0.128087i
$43$	−1.62604	−	5.53778i	−0.247969	−	0.844503i	−0.985570	−	0.169267i	$-0.945860\pi$
$43$	−1.62604	−	5.53778i	−0.247969	−	0.844503i	0.737602	−	0.675236i	$-0.235958\pi$
$44$	0.720876	+	1.57850i	0.108676	+	0.237967i
$45$	−0.734189	+	2.11210i	−0.109446	+	0.314853i
$46$	4.78843	−	1.29503i	0.706015	−	0.190941i
$47$		−	8.47696i		−	1.23649i	−0.785985	−	0.618245i	$-0.787844\pi$
$47$		−	8.47696i		−	1.23649i	0.785985	−	0.618245i	$-0.212156\pi$
$48$	−1.15928	+	0.529424i	−0.167327	+	0.0764158i
$49$	−5.27536	+	1.54899i	−0.753623	+	0.221284i
$50$	−0.965065	−	5.08079i	−0.136481	−	0.718532i
$51$	−6.21912	−	3.99678i	−0.870851	−	0.559662i
$52$	−4.12278	+	3.57241i	−0.571726	+	0.495404i
$53$	−7.68272	+	1.10461i	−1.05530	+	0.151730i	−0.648059	−	0.761590i	$-0.724419\pi$
$53$	−7.68272	+	1.10461i	−1.05530	+	0.151730i	−0.407243	+	0.913320i	$0.633510\pi$
$54$	−0.992429	−	0.291403i	−0.135052	−	0.0396550i
$55$	−0.978031	−	4.05531i	−0.131878	−	0.546818i
$56$	−0.528597	+	3.67647i	−0.0706367	+	0.491289i
$57$	−0.494145	−	0.225668i	−0.0654511	−	0.0298905i
$58$	−8.18484	−	3.73789i	−1.07472	−	0.490809i
$59$	2.07837	−	14.4554i	0.270581	−	1.88193i	−0.171844	−	0.985124i	$-0.554972\pi$
$59$	2.07837	−	14.4554i	0.270581	−	1.88193i	0.442424	−	0.896806i	$-0.354119\pi$
$60$	−2.02195	+	0.487639i	−0.261033	+	0.0629540i
$61$	−0.205042	−	0.0602058i	−0.0262529	−	0.00770856i	0.268580	−	0.963257i	$-0.413446\pi$
$61$	−0.205042	−	0.0602058i	−0.0262529	−	0.00770856i	−0.294833	+	0.955549i	$0.595264\pi$
$62$	−3.46021	+	0.497503i	−0.439447	+	0.0631829i
$63$	−0.926194	+	0.802552i	−0.116690	+	0.101112i
$64$	−6.27156	−	4.03049i	−0.783945	−	0.503811i
$65$	11.3659	−	6.54171i	1.40976	−	0.811399i
$66$	1.85146	−	0.543639i	0.227900	−	0.0669173i
$67$	0.774508	−	0.353706i	0.0946212	−	0.0432120i	−0.367542	−	0.930007i	$-0.619801\pi$
$67$	0.774508	−	0.353706i	0.0946212	−	0.0432120i	0.462163	+	0.886795i	$0.347073\pi$
$68$		−	6.87644i		−	0.833891i
$69$	0.580455	+	4.76057i	0.0698786	+	0.573106i
$70$	0.930658	−	2.67729i	0.111235	−	0.319998i
$71$	4.36411	+	9.55607i	0.517925	+	1.13410i	0.970219	+	0.242229i	$0.0778784\pi$
$71$	4.36411	+	9.55607i	0.517925	+	1.13410i	−0.452294	+	0.891869i	$0.649394\pi$
$72$	−0.853861	−	2.90798i	−0.100629	−	0.342709i
$73$	−4.88580	−	4.23357i	−0.571840	−	0.495502i	0.320267	−	0.947327i	$-0.396227\pi$
$73$	−4.88580	−	4.23357i	−0.571840	−	0.495502i	−0.892106	+	0.451826i	$0.850773\pi$
$74$	5.94599	+	3.82126i	0.691208	+	0.444212i
$75$	4.99496	−	0.224466i	0.576768	−	0.0259190i
$76$	−0.0719119	−	0.500158i	−0.00824886	−	0.0573721i
$77$	0.644136	−	2.19372i	0.0734061	−	0.249998i
$78$	3.27957	+	5.10310i	0.371338	+	0.577813i
$79$	−1.83819	+	12.7849i	−0.206812	+	1.43841i	0.576660	+	0.816984i	$0.304356\pi$
$79$	−1.83819	+	12.7849i	−0.206812	+	1.43841i	−0.783472	+	0.621427i	$0.786553\pi$
$80$	2.05981	+	1.96933i	0.230294	+	0.220177i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−2.23669	−	0.321587i	−0.247001	−	0.0355133i
$83$	−0.436302	−	0.678900i	−0.0478904	−	0.0745189i	0.816483	−	0.577370i	$-0.195921\pi$
$83$	−0.436302	−	0.678900i	−0.0478904	−	0.0745189i	−0.864373	+	0.502851i	$0.832285\pi$
$84$	−1.09378	−	0.321161i	−0.119341	−	0.0350416i
$85$	−3.15027	+	16.2276i	−0.341694	+	1.76013i
$86$	−3.90931	−	4.51159i	−0.421552	−	0.486497i
$87$	4.70323	−	7.31836i	0.504239	−	0.784611i
$88$	4.27311	+	3.70267i	0.455515	+	0.394706i
$89$	−12.5281	+	3.67858i	−1.32797	+	0.389928i	−0.867364	−	0.497674i	$-0.834188\pi$
$89$	−12.5281	+	3.67858i	−1.32797	+	0.389928i	−0.460610	+	0.887603i	$0.652369\pi$
$90$	0.216749	+	2.30264i	0.0228474	+	0.242720i
$91$	7.18744			0.753448
$92$	−3.43329	+	2.84824i	−0.357945	+	0.296950i
$93$		−	3.37977i		−	0.350466i
$94$	−3.64233	−	7.97560i	−0.375678	−	0.822620i
$95$	−0.0594313	+	1.21326i	−0.00609752	+	0.124478i
$96$	3.10621	−	3.58475i	0.317026	−	0.365867i
$97$	−4.70330	+	7.31848i	−0.477548	+	0.743079i	−0.993536	−	0.113517i	$-0.963789\pi$
$97$	−4.70330	+	7.31848i	−0.477548	+	0.743079i	0.515988	+	0.856596i	$0.327425\pi$
$98$	−4.29780	+	3.72406i	−0.434143	+	0.376187i
$99$	0.265501	+	1.84660i	0.0266839	+	0.185590i
$100$	2.68755	+	3.79572i	0.268755	+	0.379572i
$101$	−0.357904	+	0.230011i	−0.0356128	+	0.0228870i	−0.558326	−	0.829622i	$-0.688556\pi$
$101$	−0.357904	+	0.230011i	−0.0356128	+	0.0228870i	0.522713	+	0.852509i	$0.324920\pi$
$102$	−7.56861	−	1.08820i	−0.749404	−	0.107748i
$103$	14.5312	+	6.63616i	1.43180	+	0.653881i	0.972180	−	0.234236i	$-0.0752587\pi$
$103$	14.5312	+	6.63616i	1.43180	+	0.653881i	0.459619	+	0.888116i	$0.347986\pi$
$104$	−7.38384	+	16.1684i	−0.724045	+	1.58544i
$105$	2.43405	+	1.25899i	0.237539	+	0.122865i
$106$	−6.75371	+	4.34035i	−0.655978	+	0.421572i
$107$	3.93639	−	13.4061i	0.380546	−	1.29602i	−0.517336	−	0.855782i	$-0.673076\pi$
$107$	3.93639	−	13.4061i	0.380546	−	1.29602i	0.897882	−	0.440237i	$-0.145105\pi$
$108$	0.920702	−	0.132377i	0.0885946	−	0.0127380i
$109$	−5.09729	−	5.88259i	−0.488232	−	0.563450i	0.457160	−	0.889384i	$-0.348867\pi$
$109$	−5.09729	−	5.88259i	−0.488232	−	0.563450i	−0.945392	+	0.325935i	$0.894321\pi$
$110$	−2.66265	−	3.39523i	−0.253874	−	0.323723i
$111$	−4.47496	+	5.16438i	−0.424744	+	0.490181i
$112$	0.440031	+	1.49861i	0.0415790	+	0.141605i
$113$	3.18712	−	1.45551i	0.299819	−	0.136923i	−0.259825	−	0.965656i	$-0.583665\pi$
$113$	3.18712	−	1.45551i	0.299819	−	0.136923i	0.559644	+	0.828733i	$0.310938\pi$
$114$	−0.561883			−0.0526252
$115$	9.40699	−	5.14864i	0.877206	−	0.480113i
$116$	8.09187			0.751312
$117$	−5.33477	+	2.43631i	−0.493200	+	0.225237i
$118$	−4.25566	−	14.4935i	−0.391766	−	1.33423i
$119$	−5.93301	+	6.84706i	−0.543878	+	0.627669i
$120$	−5.33269	+	4.18207i	−0.486806	+	0.381769i
$121$	4.92428	+	5.68292i	0.447661	+	0.516629i
$122$	−0.218784	+	0.0314564i	−0.0198078	+	0.00284793i
$123$	0.615499	−	2.09620i	0.0554977	−	0.189008i
$124$	2.64470	−	1.69965i	0.237501	−	0.152633i
$125$	−4.60338	−	10.1887i	−0.411739	−	0.911302i
$126$	−0.526580	+	1.15305i	−0.0469114	+	0.102722i
$127$	8.30216	+	3.79147i	0.736698	+	0.336438i	0.748180	−	0.663496i	$-0.230928\pi$
$127$	8.30216	+	3.79147i	0.736698	+	0.336438i	−0.0114827	+	0.999934i	$0.503655\pi$
$128$	1.75762	+	0.252708i	0.155353	+	0.0223364i
$129$	4.85535	−	3.12035i	0.427490	−	0.274731i
$130$	7.88284	−	11.0384i	0.691371	−	0.968134i
$131$	0.513586	+	3.57207i	0.0448722	+	0.312093i	0.999880	+	0.0155115i	$0.00493765\pi$
$131$	0.513586	+	3.57207i	0.0448722	+	0.312093i	−0.955007	+	0.296582i	$0.904153\pi$
$132$	−1.31146	+	1.13639i	−0.114148	+	0.0989100i
$133$	−0.359933	+	0.560067i	−0.0312101	+	0.0485639i
$134$	0.576722	−	0.665573i	0.0498212	−	0.0574967i
$135$	−2.23339	−	0.109402i	−0.192220	−	0.00941585i
$136$	−9.30753	−	20.3806i	−0.798114	−	1.74763i
$137$			13.1952i			1.12735i	0.825998	+	0.563673i	$0.190612\pi$
$137$			13.1952i			1.12735i	−0.825998	+	0.563673i	$0.809388\pi$
$138$	2.59162	+	4.22961i	0.220614	+	0.360048i
$139$	5.02482			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$139$	5.02482			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$140$	0.238883	+	2.53779i	0.0201893	+	0.214482i
$141$	8.13358	−	2.38823i	0.684971	−	0.201126i
$142$	8.21201	+	7.11574i	0.689136	+	0.597140i
$143$	5.91527	−	9.20435i	0.494660	−	0.769706i
$144$	−0.834585	−	0.963162i	−0.0695487	−	0.0802635i
$145$	−19.0958	−	3.70708i	−1.58582	−	0.307857i
$146$	−6.41589	−	1.88388i	−0.530983	−	0.155911i
$147$	−2.97248	−	4.62527i	−0.245166	−	0.381486i
$148$	−6.29157	−	0.904591i	−0.517164	−	0.0743569i
$149$	0.246437	−	0.539621i	0.0201889	−	0.0442075i	−0.899269	−	0.437396i	$-0.855901\pi$
$149$	0.246437	−	0.539621i	0.0201889	−	0.0442075i	0.919458	+	0.393189i	$0.128628\pi$
$150$	4.60309	−	2.35740i	0.375841	−	0.192481i
$151$	0.678729	−	4.72067i	0.0552342	−	0.384162i	−0.943388	−	0.331691i	$-0.892381\pi$
$151$	0.678729	−	4.72067i	0.0552342	−	0.384162i	0.998622	−	0.0524717i	$-0.0167099\pi$
$152$	−0.890118	−	1.38505i	−0.0721981	−	0.112342i
$153$	2.08276	−	7.09322i	0.168381	−	0.573453i
$154$	−0.336549	−	2.34075i	−0.0271199	−	0.188623i
$155$	−7.01982	+	2.79936i	−0.563846	+	0.224850i
$156$	−4.58922	−	2.94931i	−0.367432	−	0.236134i
$157$	15.4066	+	13.3499i	1.22958	+	1.06544i	0.995649	+	0.0931847i	$0.0297047\pi$
$157$	15.4066	+	13.3499i	1.22958	+	1.06544i	0.233932	+	0.972253i	$0.424841\pi$
$158$	3.76387	+	12.8185i	0.299437	+	1.01979i
$159$	−3.22434	−	7.06031i	−0.255706	−	0.559919i
$160$	−10.0183	−	3.48249i	−0.792019	−	0.275315i
$161$	5.87609	+	0.126173i	0.463100	+	0.00994382i
$162$		−	1.03433i		−	0.0812643i
$163$	−7.09911	+	3.24206i	−0.556045	+	0.253937i	−0.673558	−	0.739134i	$-0.735235\pi$
$163$	−7.09911	+	3.24206i	−0.556045	+	0.253937i	0.117513	+	0.993071i	$0.462508\pi$
$164$	1.94982	−	0.572519i	0.152255	−	0.0447062i
$165$	3.61550	−	2.08093i	0.281466	−	0.162000i
$166$	−0.702204	−	0.451279i	−0.0545016	−	0.0350260i
$167$	3.47767	−	3.01342i	0.269110	−	0.233185i	−0.509843	−	0.860268i	$-0.670296\pi$
$167$	3.47767	−	3.01342i	0.269110	−	0.233185i	0.778953	+	0.627082i	$0.215751\pi$
$168$	−3.67647	+	0.528597i	−0.283646	+	0.0407821i
$169$	20.5287	+	6.02777i	1.57913	+	0.463675i
$170$	4.00863	+	16.6214i	0.307448	+	1.27480i
$171$	0.0773105	−	0.537707i	0.00591209	−	0.0411195i
$172$	4.88339	+	2.23017i	0.372355	+	0.170049i
$173$	11.9549	+	5.45963i	0.908916	+	0.415088i	0.814312	−	0.580427i	$-0.197114\pi$
$173$	11.9549	+	5.45963i	0.908916	+	0.415088i	0.0946039	+	0.995515i	$0.469842\pi$
$174$	1.28054	−	8.90638i	0.0970778	−	0.675191i
$175$	0.598887	−	6.09832i	0.0452716	−	0.460989i
$176$	2.28128	+	0.669845i	0.171958	+	0.0504915i
$177$	14.4554	−	2.07837i	1.08653	−	0.156220i
$178$	−10.2065	+	8.84401i	−0.765012	+	0.662887i
$179$	−12.0264	−	7.72889i	−0.898894	−	0.577684i	0.00756790	−	0.999971i	$-0.497591\pi$
$179$	−12.0264	−	7.72889i	−0.898894	−	0.577684i	−0.906462	+	0.422287i	$0.861227\pi$
$180$	−1.03754	−	1.80266i	−0.0773334	−	0.134363i
$181$	1.67844	−	0.492833i	0.124757	−	0.0366320i	−0.218758	−	0.975779i	$-0.570201\pi$
$181$	1.67844	−	0.492833i	0.124757	−	0.0366320i	0.343515	+	0.939147i	$0.388382\pi$
$182$	6.76235	−	3.08826i	0.501259	−	0.228917i
$183$		−	0.213698i		−	0.0157970i
$184$	−6.32048	+	13.0888i	−0.465952	+	0.964920i
$185$	14.4329	+	5.01705i	1.06113	+	0.368861i
$186$	−1.45220	−	3.17988i	−0.106481	−	0.233160i
$187$	3.88557	+	13.2330i	0.284141	+	0.967696i
$188$	5.95909	+	5.16358i	0.434611	+	0.376593i
$189$	−1.03098	−	0.662572i	−0.0749929	−	0.0481950i
$190$	0.465390	+	1.16704i	0.0337629	+	0.0846658i
$191$	−0.627974	−	4.36766i	−0.0454386	−	0.316033i	−0.999846	−	0.0175266i	$-0.994421\pi$
$191$	−0.627974	−	4.36766i	−0.0454386	−	0.316033i	0.954408	−	0.298506i	$-0.0964883\pi$
$192$	2.10032	−	7.15304i	0.151578	−	0.516226i
$193$	−13.3913	−	20.8373i	−0.963927	−	1.49990i	−0.863123	−	0.504993i	$-0.831495\pi$
$193$	−13.3913	−	20.8373i	−0.963927	−	1.49990i	−0.100804	−	0.994906i	$-0.532141\pi$
$194$	−1.28057	+	8.90653i	−0.0919392	+	0.639451i
$195$	9.47886	+	9.06246i	0.678795	+	0.648976i
$196$	2.12449	−	4.65199i	0.151749	−	0.332285i
$197$	4.72693	+	0.679630i	0.336780	+	0.0484217i	0.308630	−	0.951182i	$-0.400129\pi$
$197$	4.72693	+	0.679630i	0.336780	+	0.0484217i	0.0281497	+	0.999604i	$0.491038\pi$
$198$	1.04324	+	1.62331i	0.0741395	+	0.115363i
$199$	−3.51611	−	1.03242i	−0.249251	−	0.0731866i	0.154721	−	0.987958i	$-0.450552\pi$
$199$	−3.51611	−	1.03242i	−0.249251	−	0.0731866i	−0.403971	+	0.914772i	$0.632370\pi$
$200$	13.1031	+	7.61217i	0.926529	+	0.538262i
$201$	0.557582	+	0.643484i	0.0393288	+	0.0453879i
$202$	−0.237907	+	0.370190i	−0.0167391	+	0.0260465i
$203$	−8.05729	−	6.98169i	−0.565511	−	0.490018i
$204$	6.59790	−	1.93732i	0.461945	−	0.135639i
$205$	−4.86362	+	0.457815i	−0.339690	+	0.0319752i
$206$	16.5231			1.15122
$207$	−4.40420	+	1.89815i	−0.306113	+	0.131931i
$208$			7.47432i			0.518251i
$209$	0.421005	+	0.921871i	0.0291215	+	0.0637672i
$210$	2.83104	+	0.138678i	0.195360	+	0.00956970i
$211$	4.84048	−	5.58621i	0.333232	−	0.384571i	−0.564263	−	0.825595i	$-0.690839\pi$
$211$	4.84048	−	5.58621i	0.333232	−	0.384571i	0.897495	+	0.441025i	$0.145385\pi$
$212$	3.90327	−	6.07361i	0.268078	−	0.417137i
$213$	−7.93947	+	6.87959i	−0.544004	+	0.471382i
$214$	−2.05669	−	14.3046i	−0.140593	−	0.977843i
$215$	−10.5025	−	7.50014i	−0.716266	−	0.511505i
$216$	2.54963	−	1.63855i	0.173480	−	0.111489i
$217$	−4.09986	−	0.589470i	−0.278316	−	0.0400159i
$218$	−7.32342	−	3.34449i	−0.496004	−	0.226518i
$219$	2.68559	−	5.88062i	0.181475	−	0.397376i
$220$	3.44653	+	1.78269i	0.232365	+	0.120189i
$221$	−36.4736	+	23.4402i	−2.45348	+	1.57676i
$222$	−1.99129	+	6.78171i	−0.133647	+	0.455159i
$223$	8.64634	−	1.24316i	0.579002	−	0.0832479i	0.153409	−	0.988163i	$-0.450975\pi$
$223$	8.64634	−	1.24316i	0.579002	−	0.0832479i	0.425593	+	0.904915i	$0.360066\pi$
$224$	−3.80675	−	4.39323i	−0.254349	−	0.293535i
$225$	1.62262	+	4.72939i	0.108174	+	0.315293i
$226$	2.37323	−	2.73885i	0.157865	−	0.182186i
$227$	1.59977	+	5.44831i	0.106180	+	0.361617i	0.995393	−	0.0958768i	$-0.0305655\pi$
$227$	1.59977	+	5.44831i	0.106180	+	0.361617i	−0.889213	+	0.457494i	$0.848747\pi$
$228$	0.459638	−	0.209910i	0.0304403	−	0.0139016i
$229$	14.3145			0.945925			0.472963	−	0.881082i	$-0.343185\pi$
$229$	14.3145			0.945925			0.472963	+	0.881082i	$0.343185\pi$
$230$	6.63838	−	8.88608i	0.437722	−	0.585931i
$231$	2.28634			0.150430
$232$	23.9830	−	10.9527i	1.57456	−	0.719077i
$233$	5.44082	+	18.5297i	0.356440	+	1.21392i	0.921338	+	0.388763i	$0.127097\pi$
$233$	5.44082	+	18.5297i	0.356440	+	1.21392i	−0.564898	+	0.825161i	$0.691084\pi$
$234$	−3.97243	+	4.58443i	−0.259686	+	0.299694i
$235$	−11.6972	−	14.9154i	−0.763039	−	0.972975i
$236$	8.89577	+	10.2663i	0.579065	+	0.668277i
$237$	−12.7849	+	1.83819i	−0.830467	+	0.119403i
$238$	−2.64010	+	8.99136i	−0.171132	+	0.582823i
$239$	5.35318	−	3.44028i	0.346269	−	0.222533i	−0.355933	−	0.934511i	$-0.615837\pi$
$239$	5.35318	−	3.44028i	0.346269	−	0.222533i	0.702202	+	0.711978i	$0.252201\pi$
$240$	−1.30924	+	2.53120i	−0.0845110	+	0.163388i
$241$	−11.1635	+	24.4446i	−0.719102	+	1.57461i	0.0960569	+	0.995376i	$0.469377\pi$
$241$	−11.1635	+	24.4446i	−0.719102	+	1.57461i	−0.815159	+	0.579238i	$0.803350\pi$
$242$	7.07484	+	3.23097i	0.454788	+	0.207695i
$243$	0.989821	+	0.142315i	0.0634971	+	0.00912950i
$244$	0.167221	−	0.107466i	0.0107052	−	0.00687982i
$245$	−7.14473	+	10.0048i	−0.456460	+	0.639186i
$246$	−0.321587	−	2.23669i	−0.0205036	−	0.142606i
$247$	−2.40778	+	2.08635i	−0.153203	+	0.132751i
$248$	5.53792	−	8.61717i	0.351658	−	0.547191i
$249$	0.528479	−	0.609897i	0.0334910	−	0.0386507i
$250$	−8.70893	−	7.60811i	−0.550801	−	0.481179i
$251$	8.66008	+	18.9629i	0.546619	+	1.19693i	0.958343	+	0.285621i	$0.0921997\pi$
$251$	8.66008	+	18.9629i	0.546619	+	1.19693i	−0.411723	+	0.911309i	$0.635073\pi$
$252$		−	1.13995i		−	0.0718102i
$253$	4.99761	−	7.42116i	0.314197	−	0.466565i
$254$	9.44024			0.592333
$255$	−16.4578	+	1.54918i	−1.03063	+	0.0970133i
$256$	16.0683	−	4.71809i	1.00427	−	0.294880i
$257$	−6.51973	−	5.64938i	−0.406690	−	0.352399i	0.427366	−	0.904079i	$-0.359442\pi$
$257$	−6.51973	−	5.64938i	−0.406690	−	0.352399i	−0.834056	+	0.551680i	$0.813987\pi$
$258$	3.22745	−	5.02202i	0.200933	−	0.312657i
$259$	5.48420	+	6.32910i	0.340772	+	0.393271i
$260$	−2.32465	+	11.9747i	−0.144169	+	0.742638i
$261$	8.34697	+	2.45089i	0.516664	+	0.151706i
$262$	2.01804	+	3.14013i	0.124675	+	0.193998i
$263$	−27.4672	−	3.94919i	−1.69370	−	0.243517i	−0.773173	−	0.634195i	$-0.781332\pi$
$263$	−27.4672	−	3.94919i	−1.69370	−	0.243517i	−0.920528	+	0.390677i	$0.872241\pi$
$264$	−2.34881	+	5.14318i	−0.144559	+	0.316541i
$265$	−11.9937	+	12.5448i	−0.736769	+	0.770621i
$266$	−0.0979987	+	0.681596i	−0.00600869	+	0.0417913i
$267$	−7.05914	−	10.9842i	−0.432012	−	0.672224i
$268$	−0.223131	+	0.759913i	−0.0136299	+	0.0464191i
$269$	−0.585081	−	4.06933i	−0.0356730	−	0.248111i	0.964180	−	0.265248i	$-0.0854539\pi$
$269$	−0.585081	−	4.06933i	−0.0356730	−	0.248111i	−0.999853	+	0.0171370i	$0.994545\pi$
$270$	−2.14831	+	0.856699i	−0.130742	+	0.0521371i
$271$	−11.3805	−	7.31378i	−0.691314	−	0.444280i	0.147239	−	0.989101i	$-0.452961\pi$
$271$	−11.3805	−	7.31378i	−0.691314	−	0.444280i	−0.838553	+	0.544821i	$0.816598\pi$
$272$	−7.12035	−	6.16982i	−0.431735	−	0.374100i
$273$	2.02494	+	6.89630i	0.122555	+	0.417383i
$274$	5.66966	+	12.4148i	0.342517	+	0.750007i
$275$	−7.31671	−	5.78587i	−0.441214	−	0.348901i
$276$	−3.70014	−	2.49177i	−0.222722	−	0.149987i
$277$		−	17.3624i		−	1.04321i	−0.853188	−	0.521604i	$-0.825334\pi$
$277$		−	17.3624i		−	1.04321i	0.853188	−	0.521604i	$-0.174666\pi$
$278$	4.72763	−	2.15904i	0.283545	−	0.129491i
$279$	3.24287	−	0.952192i	0.194145	−	0.0570063i
$280$	4.14301	+	7.19825i	0.247592	+	0.430178i
$281$	6.08276	+	3.90915i	0.362867	+	0.233201i	0.709351	−	0.704855i	$-0.248988\pi$
$281$	6.08276	+	3.90915i	0.362867	+	0.233201i	−0.346484	+	0.938056i	$0.612624\pi$
$282$	6.62636	−	5.74178i	0.394594	−	0.341918i
$283$	22.2681	−	3.20167i	1.32370	−	0.190319i	0.556029	−	0.831163i	$-0.312325\pi$
$283$	22.2681	−	3.20167i	1.32370	−	0.190319i	0.767671	+	0.640844i	$0.221415\pi$
$284$	−9.37600	−	2.75304i	−0.556363	−	0.163363i
$285$	−1.18086	+	0.284790i	−0.0699479	+	0.0168695i
$286$	1.61055	−	11.2016i	0.0952337	−	0.662365i
$287$	−2.43546	−	1.11224i	−0.143760	−	0.0656532i
$288$	4.31467	+	1.97044i	0.254244	+	0.116109i
$289$	5.35840	−	37.2685i	0.315200	−	2.19226i
$290$	−19.5593	+	4.71717i	−1.14856	+	0.277002i
$291$	−8.34711	−	2.45093i	−0.489316	−	0.143676i
$292$	5.95219	−	0.855795i	0.348325	−	0.0500816i
$293$	−0.935901	+	0.810963i	−0.0546759	+	0.0473770i	−0.681770	−	0.731566i	$-0.738790\pi$
$293$	−0.935901	+	0.810963i	−0.0546759	+	0.0473770i	0.627094	+	0.778943i	$0.284244\pi$
$294$	−4.78404	−	3.07452i	−0.279011	−	0.179309i
$295$	−16.2897	−	28.3025i	−0.948424	−	1.64784i
$296$	−19.8716	+	5.83482i	−1.15501	+	0.339142i
$297$	−1.69700	+	0.774994i	−0.0984699	+	0.0449697i
$298$		−	0.613593i		−	0.0355445i
$299$	26.8107	+	8.50163i	1.55050	+	0.491662i
$300$	−2.88479	+	3.64806i	−0.166554	+	0.210621i
$301$	−2.93833	−	6.43404i	−0.169362	−	0.370852i
$302$	−1.38976	−	4.73310i	−0.0799719	−	0.272359i
$303$	−0.321527	−	0.278605i	−0.0184713	−	0.0160054i
$304$	−0.582421	−	0.374299i	−0.0334041	−	0.0214675i
$305$	−0.443854	+	0.176999i	−0.0254150	+	0.0101350i
$306$	−1.08820	−	7.56861i	−0.0622084	−	0.432669i
$307$	−4.01937	+	13.6887i	−0.229397	+	0.781256i	0.761678	+	0.647955i	$0.224376\pi$
$307$	−4.01937	+	13.6887i	−0.229397	+	0.781256i	−0.991076	+	0.133300i	$0.957443\pi$
$308$	1.14977	+	1.78908i	0.0655143	+	0.101942i
$309$	−2.27345	+	15.8122i	−0.129332	+	0.899523i
$310$	−5.40183	+	5.65003i	−0.306803	+	0.320900i
$311$	1.27914	−	2.80092i	0.0725332	−	0.158825i	−0.869892	−	0.493242i	$-0.835812\pi$
$311$	1.27914	−	2.80092i	0.0725332	−	0.158825i	0.942425	+	0.334416i	$0.108539\pi$
$312$	−17.5937	−	2.52959i	−0.996047	−	0.143210i
$313$	1.33261	+	2.07359i	0.0753237	+	0.117206i	0.876872	−	0.480724i	$-0.159626\pi$
$313$	1.33261	+	2.07359i	0.0753237	+	0.117206i	−0.801548	+	0.597930i	$0.795990\pi$
$314$	20.2315	+	5.94051i	1.14173	+	0.335242i
$315$	−0.522239	+	2.69015i	−0.0294249	+	0.151573i
$316$	−7.86775	−	9.07987i	−0.442596	−	0.510782i
$317$	−14.1511	+	22.0195i	−0.794802	+	1.23674i	0.172975	+	0.984926i	$0.444662\pi$
$317$	−14.1511	+	22.0195i	−0.794802	+	1.23674i	−0.967777	+	0.251810i	$0.918974\pi$
$318$	−6.06727	−	5.25732i	−0.340236	−	0.294816i
$319$	−15.5720	+	4.57236i	−0.871866	+	0.256003i
$320$	−16.5966	+	1.56224i	−0.927776	+	0.0873320i
$321$	13.9721			0.779846
$322$	5.58276	−	2.40609i	0.311115	−	0.134086i
$323$		−	4.01597i		−	0.223455i
$324$	0.386406	+	0.846112i	0.0214670	+	0.0470062i
$325$	10.9718	−	27.1938i	0.608605	−	1.50844i
$326$	−5.28621	+	6.10062i	−0.292776	+	0.337882i
$327$	4.20823	−	6.54813i	0.232716	−	0.362112i
$328$	5.00402	−	4.33600i	0.276301	−	0.239416i
$329$	−1.47848	−	10.2830i	−0.0815110	−	0.566922i
$330$	2.50755	−	3.51134i	0.138036	−	0.193293i
$331$	−16.6641	+	10.7094i	−0.915944	+	0.588641i	−0.911478	−	0.411349i	$-0.865058\pi$
$331$	−16.6641	+	10.7094i	−0.915944	+	0.588641i	−0.00446579	+	0.999990i	$0.501422\pi$
$332$	0.743015	+	0.106829i	0.0407782	+	0.00586303i
$333$	−6.21593	−	2.83872i	−0.340631	−	0.155561i
$334$	1.97720	−	4.32946i	0.108187	−	0.236897i
$335$	0.874696	−	1.69108i	0.0477897	−	0.0923937i
$336$	−1.31393	+	0.844412i	−0.0716808	+	0.0460665i
$337$	−2.47621	+	8.43320i	−0.134888	+	0.459386i	−0.999038	−	0.0438479i	$-0.986038\pi$
$337$	−2.47621	+	8.43320i	−0.134888	+	0.459386i	0.864150	+	0.503234i	$0.167856\pi$
$338$	21.9045	−	3.14940i	1.19145	−	0.171305i
$339$	2.29447	+	2.64796i	0.124618	+	0.143817i
$340$	−9.48866	−	12.0993i	−0.514595	−	0.656176i
$341$	−4.12907	+	4.76520i	−0.223602	+	0.258050i
$342$	−0.158301	−	0.539123i	−0.00855993	−	0.0291524i
$343$	−13.9326	+	6.36282i	−0.752291	+	0.343560i
$344$	17.4922			0.943115
$345$	7.59034	+	7.57540i	0.408650	+	0.407846i
$346$	13.5937			0.730804
$347$	−19.6235	+	8.96176i	−1.05345	+	0.481093i	−0.865407	−	0.501069i	$-0.832940\pi$
$347$	−19.6235	+	8.96176i	−1.05345	+	0.481093i	−0.188039	+	0.982162i	$0.560213\pi$
$348$	2.27974	+	7.76410i	0.122207	+	0.416199i
$349$	3.00460	−	3.46749i	0.160832	−	0.185610i	−0.669614	−	0.742710i	$-0.733540\pi$
$349$	3.00460	−	3.46749i	0.160832	−	0.185610i	0.830446	+	0.557099i	$0.188086\pi$
$350$	−2.05683	−	5.99497i	−0.109942	−	0.320444i
$351$	−3.84060	−	4.43229i	−0.204996	−	0.236578i
$352$	−8.75900	+	1.25935i	−0.466856	+	0.0671238i
$353$	−5.81381	+	19.8000i	−0.309438	+	1.05385i	0.647140	+	0.762371i	$0.275965\pi$
$353$	−5.81381	+	19.8000i	−0.309438	+	1.05385i	−0.956578	+	0.291477i	$0.905853\pi$
$354$	12.7074	−	8.16656i	0.675391	−	0.434048i
$355$	20.8650	+	10.7922i	1.10740	+	0.572792i
$356$	5.04530	−	11.0477i	0.267400	−	0.585525i
$357$	−8.24123	−	3.76364i	−0.436172	−	0.199193i
$358$	−14.6360	−	2.10434i	−0.773537	−	0.111218i
$359$	2.50874	−	1.61227i	0.132406	−	0.0850924i	−0.472761	−	0.881191i	$-0.656743\pi$
$359$	2.50874	−	1.61227i	0.132406	−	0.0850924i	0.605167	+	0.796098i	$0.293106\pi$
$360$	−5.51506	−	3.93845i	−0.290669	−	0.207575i
$361$	2.66198	+	18.5145i	0.140104	+	0.974448i
$362$	1.36741	−	1.18487i	0.0718694	−	0.0622752i
$363$	−4.06539	+	6.32587i	−0.213378	+	0.332022i
$364$	−4.37810	+	5.05259i	−0.229475	+	0.264828i
$365$	−14.4385	−	0.707268i	−0.755746	−	0.0370201i
$366$	−0.0918207	−	0.201059i	−0.00479955	−	0.0105095i
$367$		−	16.5613i		−	0.864494i	−0.901755	−	0.432247i	$-0.857721\pi$
$367$		−	16.5613i		−	0.864494i	0.901755	−	0.432247i	$-0.142279\pi$
$368$	−0.131209	+	6.11062i	−0.00683974	+	0.318538i
$369$	2.18469			0.113731
$370$	15.7350	−	1.48114i	0.818024	−	0.0770010i
$371$	−9.12692	+	2.67990i	−0.473846	+	0.139134i
$372$	2.37590	+	2.05873i	0.123184	+	0.106740i
$373$	−14.5401	+	22.6249i	−0.752859	+	1.17147i	0.227409	+	0.973799i	$0.426975\pi$
$373$	−14.5401	+	22.6249i	−0.752859	+	1.17147i	−0.980268	+	0.197672i	$0.936662\pi$
$374$	9.34167	+	10.7809i	0.483046	+	0.557465i
$375$	8.47903	−	7.28739i	0.437855	−	0.376319i
$376$	24.6509	+	7.23814i	1.27127	+	0.373279i
$377$	−27.5833	−	42.9204i	−1.42061	−	2.21051i
$378$	−1.25470	−	0.180398i	−0.0645346	−	0.00927868i
$379$	3.77842	−	8.27359i	0.194084	−	0.424986i	−0.787422	−	0.616414i	$-0.788585\pi$
$379$	3.77842	−	8.27359i	0.194084	−	0.424986i	0.981507	+	0.191429i	$0.0613120\pi$
$380$	−0.816689	−	0.780812i	−0.0418952	−	0.0400548i
$381$	−1.29890	+	9.03404i	−0.0665446	+	0.462828i
$382$	−2.46751	−	3.83951i	−0.126249	−	0.196447i
$383$	2.81213	−	9.57724i	0.143693	−	0.489374i	−0.855922	−	0.517104i	$-0.827010\pi$
$383$	2.81213	−	9.57724i	0.143693	−	0.489374i	0.999615	+	0.0277306i	$0.00882805\pi$
$384$	0.252708	+	1.75762i	0.0128959	+	0.0896932i
$385$	−1.89370	−	4.74875i	−0.0965119	−	0.242019i
$386$	−21.5525	−	13.8510i	−1.09700	−	0.704996i
$387$	4.36186	+	3.77957i	0.221726	+	0.192127i
$388$	−2.27978	−	7.76422i	−0.115738	−	0.394169i
$389$	−2.88565	−	6.31868i	−0.146308	−	0.320370i	0.822263	−	0.569108i	$-0.192711\pi$
$389$	−2.88565	−	6.31868i	−0.146308	−	0.320370i	−0.968571	+	0.248738i	$0.919984\pi$
$390$	12.8121	+	4.45364i	0.648768	+	0.225519i
$391$	−30.2304	+	18.5232i	−1.52882	+	0.936759i
$392$		−	16.6633i		−	0.841623i
$393$	−3.28268	+	1.49915i	−0.165589	+	0.0756222i
$394$	4.73938	−	1.39161i	0.238767	−	0.0701082i
$395$	14.4072	+	25.0318i	0.724907	+	1.25949i
$396$	−1.45984	−	0.938182i	−0.0733597	−	0.0471454i
$397$	−9.28603	+	8.04639i	−0.466052	+	0.403837i	−0.855980	−	0.517009i	$-0.827045\pi$
$397$	−9.28603	+	8.04639i	−0.466052	+	0.403837i	0.389928	+	0.920845i	$0.372500\pi$
$398$	−3.75176	+	0.539422i	−0.188059	+	0.0270388i
$399$	−0.638785	−	0.187564i	−0.0319792	−	0.00938995i
$400$	6.34172	+	0.622791i	0.317086	+	0.0311396i
$401$	4.62934	−	32.1978i	0.231178	−	1.60788i	−0.461842	−	0.886962i	$-0.652811\pi$
$401$	4.62934	−	32.1978i	0.231178	−	1.60788i	0.693021	−	0.720918i	$-0.256279\pi$
$402$	0.801094	+	0.365847i	0.0399549	+	0.0182468i
$403$	−18.0303	−	8.23417i	−0.898154	−	0.410173i
$404$	0.0563187	−	0.391705i	0.00280196	−	0.0194880i
$405$	−0.524248	−	2.17374i	−0.0260501	−	0.108014i
$406$	−10.5806	−	3.10675i	−0.525107	−	0.154185i
$407$	12.6187	−	1.81429i	0.625483	−	0.0899309i
$408$	16.9328	−	14.6724i	0.838301	−	0.726392i
$409$	2.14924	+	1.38123i	0.106273	+	0.0682975i	0.592698	−	0.805425i	$-0.298063\pi$
$409$	2.14924	+	1.38123i	0.106273	+	0.0682975i	−0.486425	+	0.873722i	$0.661699\pi$
$410$	−4.37926	+	2.52051i	−0.216276	+	0.124479i
$411$	−12.6607	+	3.71753i	−0.624508	+	0.183372i
$412$	−13.5164	+	6.17276i	−0.665908	+	0.304110i
$413$		−	17.8977i		−	0.880688i
$414$	−3.32814	+	3.67826i	−0.163569	+	0.180777i
$415$	−1.70448	−	0.592498i	−0.0836699	−	0.0290846i
$416$	−11.5562	−	25.3045i	−0.566587	−	1.24065i
$417$	1.41566	+	4.82128i	0.0693250	+	0.236099i
$418$	0.792210	+	0.686453i	0.0387482	+	0.0335755i
$419$	4.46992	+	2.87264i	0.218370	+	0.140338i	0.645253	−	0.763969i	$-0.276752\pi$
$419$	4.46992	+	2.87264i	0.218370	+	0.140338i	−0.426883	+	0.904307i	$0.640388\pi$
$420$	−2.36769	+	0.944185i	−0.115531	+	0.0460715i
$421$	−0.279629	−	1.94486i	−0.0136283	−	0.0947867i	0.981872	−	0.189545i	$-0.0607013\pi$
$421$	−0.279629	−	1.94486i	−0.0136283	−	0.0947867i	−0.995500	+	0.0947583i	$0.969792\pi$
$422$	2.15394	−	7.33565i	0.104852	−	0.357094i
$423$	4.58299	+	7.13127i	0.222832	+	0.346734i
$424$	3.34779	−	23.2844i	0.162583	−	1.13079i
$425$	16.8491	+	32.8998i	0.817302	+	1.59588i
$426$	−4.51392	+	9.88410i	−0.218700	+	0.478886i
$427$	−0.259228	−	0.0372714i	−0.0125449	−	0.00180369i
$428$	7.02639	+	10.9333i	0.339633	+	0.528480i
$429$	10.4980	+	3.08250i	0.506850	+	0.148824i
$430$	−13.1040	−	2.54388i	−0.631930	−	0.122677i
$431$	−23.2532	−	26.8357i	−1.12007	−	1.29263i	−0.951743	−	0.306896i	$-0.900709\pi$
$431$	−23.2532	−	26.8357i	−1.12007	−	1.29263i	−0.168325	−	0.985731i	$-0.553836\pi$
$432$	0.689018	−	1.07213i	0.0331504	−	0.0515830i
$433$	18.6718	+	16.1792i	0.897308	+	0.777521i	0.975634	−	0.219406i	$-0.0704120\pi$
$433$	18.6718	+	16.1792i	0.897308	+	0.777521i	−0.0783259	+	0.996928i	$0.524957\pi$
$434$	−4.11066	+	1.20700i	−0.197318	+	0.0579377i
$435$	−1.82300	−	19.3667i	−0.0874062	−	0.928564i
$436$	7.24023			0.346744
$437$	−2.00510	+	1.66343i	−0.0959170	+	0.0795725i
$438$		−	6.68675i		−	0.319505i
$439$	5.66870	+	12.4127i	0.270552	+	0.592427i	0.995327	−	0.0965589i	$-0.0307836\pi$
$439$	5.66870	+	12.4127i	0.270552	+	0.592427i	−0.724775	+	0.688986i	$0.758056\pi$
$440$	12.6279	+	0.618576i	0.602011	+	0.0294894i
$441$	3.60047	−	4.15517i	0.171451	−	0.197865i
$442$	−24.2448	+	37.7256i	−1.15321	+	1.79442i
$443$	−5.60360	+	4.85554i	−0.266235	+	0.230694i	−0.777740	−	0.628587i	$-0.783634\pi$
$443$	−5.60360	+	4.85554i	−0.266235	+	0.230694i	0.511505	+	0.859280i	$0.329088\pi$
$444$	−0.904591	−	6.29157i	−0.0429300	−	0.298585i
$445$	−16.9675	+	23.7598i	−0.804337	+	1.12632i
$446$	7.60081	−	4.88475i	0.359909	−	0.231299i
$447$	0.587192	+	0.0844254i	0.0277732	+	0.00399318i
$448$	−8.31072	−	3.79538i	−0.392645	−	0.179315i
$449$	11.1336	−	24.3792i	0.525426	−	1.15052i	−0.441917	−	0.897056i	$-0.645702\pi$
$449$	11.1336	−	24.3792i	0.525426	−	1.15052i	0.967344	−	0.253468i	$-0.0815711\pi$
$450$	3.55875	+	3.75248i	0.167761	+	0.176894i
$451$	−3.42873	+	2.20351i	−0.161453	+	0.103759i
$452$	−0.918189	+	3.12706i	−0.0431880	+	0.147085i
$453$	4.72067	−	0.678729i	0.221796	−	0.0318895i
$454$	3.84615	+	4.43869i	0.180509	+	0.208318i
$455$	12.6465	−	9.91779i	0.592877	−	0.464953i
$456$	1.07817	−	1.24428i	0.0504900	−	0.0582686i
$457$	−1.93978	−	6.60628i	−0.0907390	−	0.309029i	0.901600	−	0.432570i	$-0.142393\pi$
$457$	−1.93978	−	6.60628i	−0.0907390	−	0.309029i	−0.992339	+	0.123541i	$0.960575\pi$
$458$	13.4678	−	6.15056i	0.629311	−	0.287397i
$459$	7.39268			0.345061
$460$	−2.11073	+	9.74908i	−0.0984131	+	0.454553i
$461$	10.5844			0.492963			0.246481	−	0.969148i	$-0.420726\pi$
$461$	10.5844			0.492963			0.246481	+	0.969148i	$0.420726\pi$
$462$	2.15111	−	0.982381i	0.100079	−	0.0457045i
$463$	−9.95443	−	33.9017i	−0.462622	−	1.57554i	−0.779072	−	0.626935i	$-0.784309\pi$
$463$	−9.95443	−	33.9017i	−0.462622	−	1.57554i	0.316450	−	0.948609i	$-0.397509\pi$
$464$	7.26035	−	8.37889i	0.337053	−	0.388980i
$465$	−4.66368	−	5.94680i	−0.216273	−	0.275776i
$466$	13.0808	+	15.0960i	0.605956	+	0.699310i
$467$	8.29267	−	1.19231i	0.383739	−	0.0551734i	0.0522541	−	0.998634i	$-0.483359\pi$
$467$	8.29267	−	1.19231i	0.383739	−	0.0551734i	0.331485	+	0.943460i	$0.392450\pi$
$468$	1.53691	−	5.23424i	0.0710438	−	0.241953i
$469$	0.877832	−	0.564148i	0.0405345	−	0.0260499i
$470$	−17.4141	−	9.00730i	−0.803254	−	0.415476i
$471$	−8.46859	+	18.5436i	−0.390212	+	0.854445i
$472$	40.2614	+	18.3868i	1.85318	+	0.846319i
$473$	−10.6578	−	1.53236i	−0.490045	−	0.0704579i
$474$	−11.2389	+	7.22281i	−0.516220	+	0.331754i
$475$	1.56958	+	2.21677i	0.0720172	+	0.101712i
$476$	−1.19933	−	8.34152i	−0.0549712	−	0.382333i
$477$	5.86592	−	5.08285i	0.268582	−	0.232728i
$478$	3.55837	−	5.53694i	0.162756	−	0.253254i
$479$	0.211131	−	0.243658i	0.00964682	−	0.0111330i	−0.750906	−	0.660409i	$-0.770383\pi$
$479$	0.211131	−	0.243658i	0.00964682	−	0.0111330i	0.760552	+	0.649276i	$0.224928\pi$
$480$	0.518929	−	10.5937i	0.0236858	−	0.483532i
$481$	16.6484	+	36.4549i	0.759101	+	1.66220i
$482$			27.7955i			1.26605i
$483$	1.53442	+	5.67361i	0.0698186	+	0.258158i
$484$	−6.99448			−0.317931
$485$	1.82303	+	19.3671i	0.0827795	+	0.879413i
$486$	0.992429	−	0.291403i	0.0450175	−	0.0132183i
$487$	−5.67604	−	4.91831i	−0.257206	−	0.222870i	0.516707	−	0.856162i	$-0.327158\pi$
$487$	−5.67604	−	4.91831i	−0.257206	−	0.222870i	−0.773913	+	0.633292i	$0.781703\pi$
$488$	0.350155	−	0.544852i	0.0158508	−	0.0246643i
$489$	−5.11078	−	5.89815i	−0.231117	−	0.266724i
$490$	−2.42334	+	12.4830i	−0.109475	+	0.563926i
$491$	28.7286	+	8.43546i	1.29650	+	0.380687i	0.855959	−	0.517044i	$-0.172968\pi$
$491$	28.7286	+	8.43546i	1.29650	+	0.380687i	0.440543	+	0.897732i	$0.354786\pi$
$492$	1.09866	+	1.70954i	0.0495312	+	0.0770721i
$493$	63.6569	+	9.15249i	2.86696	+	0.412207i
$494$	−1.36892	+	2.99752i	−0.0615906	+	0.134865i
$495$	3.01524	+	2.88278i	0.135525	+	0.129571i
$496$	0.612998	−	4.26350i	0.0275244	−	0.191437i
$497$	6.96060	+	10.8309i	0.312226	+	0.485833i
$498$	0.235165	−	0.800899i	0.0105380	−	0.0358892i
$499$	5.22394	+	36.3333i	0.233856	+	1.62650i	0.681170	+	0.732126i	$0.261472\pi$
$499$	5.22394	+	36.3333i	0.233856	+	1.62650i	−0.447314	+	0.894377i	$0.647619\pi$
$500$	9.96644	+	2.97017i	0.445713	+	0.132830i
$501$	3.87113	+	2.48782i	0.172949	+	0.111148i
$502$	16.2958	+	14.1204i	0.727316	+	0.630223i
$503$	0.661380	+	2.25245i	0.0294895	+	0.100432i	0.972923	−	0.231131i	$-0.0742424\pi$
$503$	0.661380	+	2.25245i	0.0294895	+	0.100432i	−0.943433	+	0.331562i	$0.892424\pi$
$504$	−1.54297	−	3.37863i	−0.0687292	−	0.150496i
$505$	−0.312355	+	0.898576i	−0.0138996	+	0.0399861i
$506$	1.51334	−	9.12959i	0.0672763	−	0.405860i
$507$			21.3954i			0.950202i
$508$	−7.72241	+	3.52671i	−0.342627	+	0.156472i
$509$	−5.86317	+	1.72158i	−0.259880	+	0.0763077i	−0.409077	−	0.912500i	$-0.634149\pi$
$509$	−5.86317	+	1.72158i	−0.259880	+	0.0763077i	0.149197	+	0.988807i	$0.452331\pi$
$510$	−14.8188	+	8.52905i	−0.656186	+	0.377672i
$511$	−6.66513	−	4.28342i	−0.294848	−	0.189487i
$512$	10.4068	−	9.01753i	0.459919	−	0.398522i
$513$	0.537707	−	0.0773105i	0.0237403	−	0.00341334i
$514$	−8.56153	−	2.51389i	−0.377633	−	0.110883i
$515$	34.7251	−	8.37475i	1.53017	−	0.369035i
$516$	−0.764022	+	5.31389i	−0.0336342	+	0.233931i
$517$	−14.3854	−	6.56959i	−0.632669	−	0.288930i
$518$	7.87930	+	3.59835i	0.346196	+	0.158103i
$519$	−1.87039	+	13.0088i	−0.0821009	+	0.571024i
$520$	9.31831	+	38.6375i	0.408635	+	1.69437i
$521$	3.18752	+	0.935941i	0.139648	+	0.0410043i	0.350810	−	0.936447i	$-0.385906\pi$
$521$	3.18752	+	0.935941i	0.139648	+	0.0410043i	−0.211162	+	0.977451i	$0.567725\pi$
$522$	8.90638	−	1.28054i	0.389822	−	0.0560479i
$523$	15.9033	−	13.7803i	0.695405	−	0.602572i	−0.233735	−	0.972300i	$-0.575095\pi$
$523$	15.9033	−	13.7803i	0.695405	−	0.602572i	0.929140	+	0.369729i	$0.120549\pi$
$524$	−2.82392	−	1.81482i	−0.123363	−	0.0792809i
$525$	6.02002	−	1.14347i	0.262735	−	0.0499050i
$526$	−27.5396	+	8.08635i	−1.20078	+	0.352581i
$527$	22.7277	−	10.3794i	0.990033	−	0.452133i
$528$			2.37759i			0.103471i
$529$	21.7699	+	7.42115i	0.946515	+	0.322659i
$530$	−5.89418	+	16.9563i	−0.256027	+	0.736533i
$531$	6.06673	+	13.2843i	0.263274	+	0.576489i
$532$	−0.174466	−	0.594178i	−0.00756408	−	0.0257609i
$533$	−9.68319	−	8.39053i	−0.419425	−	0.363434i
$534$	−11.3613	−	7.30145i	−0.491651	−	0.315965i
$535$	−11.5726	−	29.0202i	−0.500329	−	1.25465i
$536$	0.367249	+	2.55427i	0.0158627	+	0.110328i
$537$	4.02759	−	13.7167i	0.173803	−	0.591920i
$538$	−2.29896	−	3.57726i	−0.0991154	−	0.154227i
$539$	−1.45974	+	10.1527i	−0.0628756	+	0.437310i
$540$	1.43734	−	1.50338i	0.0618531	−	0.0646951i
$541$	4.99344	−	10.9341i	0.214685	−	0.470094i	−0.771397	−	0.636354i	$-0.780442\pi$
$541$	4.99344	−	10.9341i	0.214685	−	0.470094i	0.986082	+	0.166260i	$0.0531691\pi$
$542$	−13.8499	−	1.99132i	−0.594905	−	0.0855344i
$543$	0.945740	+	1.47160i	0.0405856	+	0.0631524i
$544$	33.6453	+	9.87917i	1.44253	+	0.423566i
$545$	−17.0861	−	3.31693i	−0.731887	−	0.142082i
$546$	4.86834	+	5.61836i	0.208346	+	0.240444i
$547$	−8.81183	+	13.7115i	−0.376767	+	0.586260i	−0.976915	−	0.213628i	$-0.931472\pi$
$547$	−8.81183	+	13.7115i	−0.376767	+	0.586260i	0.600148	+	0.799889i	$0.295108\pi$
$548$	−9.27593	−	8.03764i	−0.396248	−	0.343351i
$549$	0.205042	−	0.0602058i	0.00875098	−	0.00256952i
$550$	−9.37002	−	2.29986i	−0.399539	−	0.0980666i
$551$	4.72580			0.201326
$552$	−14.3393	−	2.37692i	−0.610321	−	0.101168i
$553$			15.8294i			0.673134i
$554$	−7.46020	−	16.3356i	−0.316953	−	0.694031i
$555$	−0.747595	+	15.2618i	−0.0317336	+	0.647826i
$556$	−3.06078	+	3.53232i	−0.129806	+	0.149804i
$557$	−8.99375	+	13.9946i	−0.381077	+	0.592968i	−0.977816	−	0.209468i	$-0.932827\pi$
$557$	−8.99375	+	13.9946i	−0.381077	+	0.592968i	0.596738	+	0.802436i	$0.296463\pi$
$558$	2.64194	−	2.28925i	0.111842	−	0.0969119i
$559$	−4.81719	−	33.5043i	−0.203746	−	1.41708i
$560$	2.84214	+	2.02965i	0.120102	+	0.0857683i
$561$	−11.6023	+	7.45636i	−0.489850	+	0.314808i
$562$	7.40267	+	1.06434i	0.312263	+	0.0448966i
$563$	26.7501	+	12.2164i	1.12738	+	0.514858i	0.889728	−	0.456492i	$-0.150894\pi$
$563$	26.7501	+	12.2164i	1.12738	+	0.514858i	0.237654	+	0.971350i	$0.423622\pi$
$564$	−3.27555	+	7.17245i	−0.137925	+	0.302015i
$565$	3.59940	−	6.95885i	0.151428	−	0.292761i
$566$	19.5754	−	12.5803i	0.822815	−	0.528791i
$567$	0.345272	−	1.17589i	0.0145001	−	0.0493827i
$568$	−31.5153	+	4.53121i	−1.32235	+	0.190125i
$569$	0.506146	+	0.584124i	0.0212188	+	0.0244877i	0.766260	−	0.642531i	$-0.222116\pi$
$569$	0.506146	+	0.584124i	0.0212188	+	0.0244877i	−0.745041	+	0.667019i	$0.767570\pi$
$570$	−0.988649	+	0.775331i	−0.0414099	+	0.0324750i
$571$	19.1833	−	22.1387i	0.802796	−	0.926475i	−0.195736	−	0.980657i	$-0.562709\pi$
$571$	19.1833	−	22.1387i	0.802796	−	0.926475i	0.998531	+	0.0541813i	$0.0172549\pi$
$572$	2.86725	+	9.76495i	0.119886	+	0.408293i
$573$	4.01382	−	1.83305i	0.167680	−	0.0765767i
$574$	−2.76931			−0.115589
$575$	9.44735	−	22.0397i	0.393982	−	0.919118i
$576$	7.45502			0.310626
$577$	38.3252	−	17.5025i	1.59550	−	0.728641i	0.598150	−	0.801384i	$-0.295903\pi$
$577$	38.3252	−	17.5025i	1.59550	−	0.728641i	0.997351	+	0.0727437i	$0.0231755\pi$
$578$	−10.9718	−	37.3666i	−0.456368	−	1.55425i
$579$	16.2205	−	18.7194i	0.674099	−	0.777952i
$580$	14.2379	−	11.1658i	0.591195	−	0.463635i
$581$	−0.647667	−	0.747448i	−0.0268698	−	0.0310094i
$582$	−8.90653	+	1.28057i	−0.369187	+	0.0530811i
$583$	−4.07954	+	13.8936i	−0.168957	+	0.575416i
$584$	16.4829	−	10.5929i	0.682069	−	0.438339i
$585$	−6.02486	+	11.6481i	−0.249097	+	0.481589i
$586$	−0.532098	+	1.16513i	−0.0219808	+	0.0481312i
$587$	3.16896	+	1.44722i	0.130797	+	0.0597330i	0.479739	−	0.877412i	$-0.340732\pi$
$587$	3.16896	+	1.44722i	0.130797	+	0.0597330i	−0.348941	+	0.937145i	$0.613459\pi$
$588$	5.06209	+	0.727818i	0.208757	+	0.0300147i
$589$	1.54455	−	0.992624i	0.0636422	−	0.0409004i
$590$	−27.4872	−	19.6293i	−1.13163	−	0.808127i
$591$	0.679630	+	4.72693i	0.0279563	+	0.194440i
$592$	−6.58172	+	5.70309i	−0.270507	+	0.234396i
$593$	−2.16035	+	3.36156i	−0.0887148	+	0.138043i	−0.882775	−	0.469797i	$-0.844327\pi$
$593$	−2.16035	+	3.36156i	−0.0887148	+	0.138043i	0.794060	+	0.607840i	$0.207964\pi$
$594$	−1.26364	+	1.45832i	−0.0518477	+	0.0598354i
$595$	−0.991180	+	20.2344i	−0.0406344	+	0.829530i
$596$	0.229228	+	0.501939i	0.00938953	+	0.0205602i
$597$		−	3.66455i		−	0.149980i
$598$	28.8780	−	3.52108i	1.18091	−	0.143988i
$599$	45.2595			1.84925			0.924627	−	0.380874i	$-0.124377\pi$
$599$	45.2595			1.84925			0.924627	+	0.380874i	$0.124377\pi$
$600$	−3.61226	+	14.7169i	−0.147470	+	0.600816i
$601$	−21.0020	+	6.16673i	−0.856688	+	0.251546i	−0.680444	−	0.732800i	$-0.738213\pi$
$601$	−21.0020	+	6.16673i	−0.856688	+	0.251546i	−0.176244	+	0.984346i	$0.556395\pi$
$602$	−5.52909	−	4.79098i	−0.225349	−	0.195266i
$603$	−0.460330	+	0.716287i	−0.0187461	+	0.0291695i
$604$	2.90508	+	3.35264i	0.118206	+	0.136417i
$605$	16.5061	+	3.20434i	0.671070	+	0.130275i
$606$	−0.422221	−	0.123975i	−0.0171515	−	0.00503615i
$607$	−9.51856	−	14.8112i	−0.386346	−	0.601167i	0.592548	−	0.805535i	$-0.298122\pi$
$607$	−9.51856	−	14.8112i	−0.386346	−	0.601167i	−0.978894	+	0.204369i	$0.934486\pi$
$608$	2.55051	+	0.366708i	0.103437	+	0.0148720i
$609$	4.42888	−	9.69789i	0.179467	−	0.392978i
$610$	−0.341550	+	0.357244i	−0.0138290	+	0.0144644i
$611$	7.07522	−	49.2092i	0.286233	−	1.99079i
$612$	3.71769	+	5.78483i	0.150279	+	0.233838i
$613$	−4.43566	+	15.1065i	−0.179155	+	0.610145i	0.820125	+	0.572185i	$0.193904\pi$
$613$	−4.43566	+	15.1065i	−0.179155	+	0.610145i	−0.999279	+	0.0379598i	$0.987914\pi$
$614$	2.10004	+	14.6061i	0.0847509	+	0.589455i
$615$	−1.80951	−	4.53763i	−0.0729666	−	0.182975i
$616$	5.82931	+	3.74627i	0.234870	+	0.150942i
$617$	−12.7822	−	11.0759i	−0.514593	−	0.445897i	0.358444	−	0.933551i	$-0.383307\pi$
$617$	−12.7822	−	11.0759i	−0.514593	−	0.445897i	−0.873037	+	0.487654i	$0.837853\pi$
$618$	4.65510	+	15.8538i	0.187256	+	0.637735i
$619$	−5.23263	−	11.4579i	−0.210317	−	0.460531i	0.774846	−	0.632150i	$-0.217827\pi$
$619$	−5.23263	−	11.4579i	−0.210317	−	0.460531i	−0.985163	+	0.171619i	$0.945100\pi$
$620$	2.30812	−	6.63994i	0.0926962	−	0.266666i
$621$	−3.06207	−	3.69103i	−0.122877	−	0.148116i
$622$		−	3.18487i		−	0.127702i
$623$	−14.5557	+	6.64736i	−0.583161	+	0.266321i
$624$	−7.17155	+	2.10576i	−0.287092	+	0.0842978i
$625$	−22.1589	−	11.5751i	−0.886356	−	0.463005i
$626$	2.14476	+	1.37836i	0.0857220	+	0.0550902i
$627$	−0.765918	+	0.663672i	−0.0305878	+	0.0265045i
$628$	−18.7693	+	2.69862i	−0.748976	+	0.107687i
$629$	−48.4712	−	14.2324i	−1.93267	−	0.567484i
$630$	0.664536	+	2.75544i	0.0264757	+	0.109779i
$631$	−0.253883	+	1.76580i	−0.0101069	+	0.0702952i	−0.994251	−	0.107077i	$-0.965851\pi$
$631$	−0.253883	+	1.76580i	−0.0101069	+	0.0702952i	0.984144	+	0.177373i	$0.0567598\pi$
$632$	−35.6087	−	16.2619i	−1.41644	−	0.646865i
$633$	6.72365	+	3.07059i	0.267241	+	0.122045i
$634$	−3.85290	+	26.7975i	−0.153018	+	1.06426i
$635$	19.8396	−	4.78478i	0.787312	−	0.189878i
$636$	6.92727	+	2.03403i	0.274684	+	0.0806545i
$637$	−31.9167	+	4.58892i	−1.26458	+	0.181820i
$638$	−12.6864	+	10.9928i	−0.502260	+	0.435210i
$639$	−8.83773	−	5.67966i	−0.349615	−	0.224684i
$640$	3.44129	−	1.98066i	0.136029	−	0.0782923i
$641$	−2.51813	+	0.739390i	−0.0994602	+	0.0292041i	−0.331084	−	0.943601i	$-0.607414\pi$
$641$	−2.51813	+	0.739390i	−0.0994602	+	0.0292041i	0.231624	+	0.972805i	$0.425596\pi$
$642$	13.1457	−	6.00345i	0.518821	−	0.236937i
$643$		−	7.67657i		−	0.302734i	−0.988478	−	0.151367i	$-0.951632\pi$
$643$		−	7.67657i		−	0.302734i	0.988478	−	0.151367i	$-0.0483676\pi$
$644$	−3.66800	+	4.05389i	−0.144540	+	0.159745i
$645$	4.23742	−	12.1901i	0.166848	−	0.479986i
$646$	−1.72556	−	3.77845i	−0.0678913	−	0.148661i
$647$	3.42807	+	11.6749i	0.134771	+	0.458989i	0.999029	−	0.0440604i	$-0.0140294\pi$
$647$	3.42807	+	11.6749i	0.134771	+	0.458989i	−0.864257	+	0.503050i	$0.832211\pi$
$648$	2.29049	+	1.98472i	0.0899789	+	0.0779672i
$649$	−22.9201	−	14.7298i	−0.899691	−	0.578196i
$650$	−1.36162	−	30.2998i	−0.0534073	−	1.18845i
$651$	−0.589470	−	4.09986i	−0.0231032	−	0.160686i
$652$	2.04521	−	6.96534i	0.0800965	−	0.272784i
$653$	15.8966	+	24.7355i	0.622080	+	0.967976i	0.999127	+	0.0417815i	$0.0133034\pi$
$653$	15.8966	+	24.7355i	0.622080	+	0.967976i	−0.377046	+	0.926194i	$0.623060\pi$
$654$	1.14577	−	7.96902i	0.0448032	−	0.311613i
$655$	5.83269	+	5.57647i	0.227902	+	0.217891i
$656$	1.15663	−	2.53267i	0.0451588	−	0.0988840i
$657$	6.39904	+	0.920043i	0.249650	+	0.0358943i
$658$	−5.80939	−	9.03959i	−0.226474	−	0.352400i
$659$	−24.8230	−	7.28868i	−0.966966	−	0.283927i	−0.240132	−	0.970740i	$-0.577191\pi$
$659$	−24.8230	−	7.28868i	−0.966966	−	0.283927i	−0.726834	+	0.686813i	$0.759009\pi$
$660$	−0.739475	+	3.80917i	−0.0287840	+	0.148272i
$661$	−18.4249	−	21.2634i	−0.716645	−	0.827052i	0.274255	−	0.961657i	$-0.411569\pi$
$661$	−18.4249	−	21.2634i	−0.716645	−	0.827052i	−0.990899	+	0.134605i	$0.957023\pi$
$662$	−11.0770	+	17.2362i	−0.430520	+	0.669902i
$663$	−32.7665	−	28.3923i	−1.27254	−	1.10267i
$664$	2.34677	−	0.689074i	0.0910724	−	0.0267413i
$665$	0.139512	+	1.48212i	0.00541006	+	0.0574740i
$666$	−7.06802			−0.273880
$667$	−21.7972	−	35.5738i	−0.843992	−	1.37742i
$668$			4.28028i			0.165609i
$669$	3.62876	+	7.94587i	0.140296	+	0.307205i
$670$	0.0963483	−	1.96690i	0.00372226	−	0.0759879i
$671$	−0.261075	+	0.301297i	−0.0100787	+	0.0116314i
$672$	3.14278	−	4.89027i	0.121236	−	0.188646i
$673$	21.1544	−	18.3304i	0.815444	−	0.706586i	−0.143664	−	0.989626i	$-0.545889\pi$
$673$	21.1544	−	18.3304i	0.815444	−	0.706586i	0.959108	+	0.283041i	$0.0913431\pi$
$674$	1.29377	+	8.99840i	0.0498343	+	0.346605i
$675$	−4.08067	+	2.88931i	−0.157065	+	0.111210i
$676$	−16.7420	+	10.7595i	−0.643925	+	0.413825i
$677$	40.4272	+	5.81255i	1.55374	+	0.223394i	0.865060	−	0.501669i	$-0.167280\pi$
$677$	40.4272	+	5.81255i	1.55374	+	0.223394i	0.688682	+	0.725063i	$0.258189\pi$
$678$	3.29652	+	1.50547i	0.126602	+	0.0578173i
$679$	−4.42895	+	9.69804i	−0.169967	+	0.372177i
$680$	−44.4997	−	23.0170i	−1.70648	−	0.882663i
$681$	−4.77690	+	3.06993i	−0.183051	+	0.117640i
$682$	−1.83738	+	6.25753i	−0.0703568	+	0.239613i
$683$	−8.85027	+	1.27248i	−0.338646	+	0.0486899i	−0.309540	−	0.950886i	$-0.600175\pi$
$683$	−8.85027	+	1.27248i	−0.338646	+	0.0486899i	−0.0291059	+	0.999576i	$0.509266\pi$
$684$	0.330902	+	0.381881i	0.0126524	+	0.0146016i
$685$	18.2078	+	23.2174i	0.695686	+	0.887091i
$686$	−10.3747	+	11.9730i	−0.396106	+	0.457131i
$687$	4.03285	+	13.7346i	0.153863	+	0.524008i
$688$	6.69085	−	3.05561i	0.255086	−	0.116494i
$689$	−45.5206			−1.73420
$690$	10.3964	+	3.86599i	0.395783	+	0.147176i
$691$	31.1792			1.18611			0.593055	−	0.805162i	$-0.297921\pi$
$691$	31.1792			1.18611			0.593055	+	0.805162i	$0.297921\pi$
$692$	−11.1201	+	5.07838i	−0.422723	+	0.193051i
$693$	0.644136	+	2.19372i	0.0244687	+	0.0833327i
$694$	−14.6123	+	16.8635i	−0.554674	+	0.640128i
$695$	8.84131	−	6.93365i	0.335370	−	0.263008i
$696$	17.2658	+	19.9258i	0.654458	+	0.755285i
$697$	15.9863	−	2.29849i	0.605526	−	0.0870615i
$698$	1.33700	−	4.55341i	0.0506062	−	0.172349i
$699$	−16.2463	+	10.4409i	−0.614491	+	0.394910i
$700$	3.92216	+	4.13568i	0.148244	+	0.156314i
$701$	−19.9342	+	43.6498i	−0.752904	+	1.64863i	0.00817106	+	0.999967i	$0.497399\pi$
$701$	−19.9342	+	43.6498i	−0.752904	+	1.64863i	−0.761075	+	0.648664i	$0.775328\pi$
$702$	−5.51789	−	2.51994i	−0.208259	−	0.0951089i
$703$	−3.67439	−	0.528298i	−0.138582	−	0.0199251i
$704$	−11.7002	+	7.51924i	−0.440966	+	0.283392i
$705$	11.0158	−	15.4255i	0.414878	−	0.580958i
$706$	3.03760	+	21.1270i	0.114322	+	0.795125i
$707$	−0.394042	+	0.341439i	−0.0148195	+	0.0128411i
$708$	−7.34418	+	11.4278i	−0.276011	+	0.429482i
$709$	9.15199	−	10.5620i	0.343710	−	0.396663i	−0.557406	−	0.830240i	$-0.688203\pi$
$709$	9.15199	−	10.5620i	0.343710	−	0.396663i	0.901116	+	0.433577i	$0.142749\pi$
$710$	24.2681	+	1.18877i	0.910766	+	0.0446137i
$711$	−5.36564	−	11.7491i	−0.201227	−	0.440626i
$712$		−	39.5725i		−	1.48304i
$713$	−14.5961	−	7.04835i	−0.546629	−	0.263963i
$714$	−9.37095			−0.350699
$715$	−2.29280	−	24.3577i	−0.0857458	−	0.910925i
$716$	12.7589	−	3.74634i	0.476821	−	0.140007i
$717$	4.80909	+	4.16710i	0.179599	+	0.155623i
$718$	1.66761	−	2.59486i	0.0622348	−	0.0968392i
$719$	30.9208	+	35.6845i	1.15315	+	1.33081i	0.934898	+	0.354916i	$0.115491\pi$
$719$	30.9208	+	35.6845i	1.15315	+	1.33081i	0.218254	+	0.975892i	$0.429964\pi$
$720$	−2.79752	−	0.543084i	−0.104257	−	0.0202395i
$721$	18.7846	+	5.51564i	0.699573	+	0.205413i
$722$	10.4598	+	16.2757i	0.389272	+	0.605719i
$723$	−26.5995	−	3.82443i	−0.989246	−	0.142232i
$724$	−0.675938	+	1.48010i	−0.0251211	+	0.0550074i
$725$	−38.7150	+	19.8272i	−1.43784	+	0.736365i
$726$	−1.10688	+	7.69853i	−0.0410802	+	0.285719i
$727$	12.7508	+	19.8406i	0.472901	+	0.735849i	0.992982	−	0.118269i	$-0.0377344\pi$
$727$	12.7508	+	19.8406i	0.472901	+	0.735849i	−0.520080	+	0.854117i	$0.674098\pi$
$728$	−6.13708	+	20.9010i	−0.227455	+	0.774641i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−13.8885	+	5.53842i	−0.514035	+	0.204986i
$731$	35.8941	+	23.0677i	1.32759	+	0.853190i
$732$	0.150225	+	0.130170i	0.00555246	+	0.00481123i
$733$	−0.715502	−	2.43678i	−0.0264277	−	0.0900044i	0.945223	−	0.326425i	$-0.105844\pi$
$733$	−0.715502	−	2.43678i	−0.0264277	−	0.0900044i	−0.971651	+	0.236420i	$0.924026\pi$
$734$	−7.11598	−	15.5818i	−0.262656	−	0.575136i
$735$	−11.6125	−	4.03663i	−0.428333	−	0.148893i
$736$	−9.00352	−	20.8905i	−0.331874	−	0.770034i
$737$		−	1.58846i		−	0.0585117i
$738$	2.05548	−	0.938707i	0.0756634	−	0.0345543i
$739$	−19.1271	+	5.61623i	−0.703602	+	0.206596i	−0.613913	−	0.789374i	$-0.710405\pi$
$739$	−19.1271	+	5.61623i	−0.703602	+	0.206596i	−0.0896890	+	0.995970i	$0.528587\pi$
$740$	−12.3184	+	7.08995i	−0.452834	+	0.260632i
$741$	−2.68019	−	1.72245i	−0.0984592	−	0.0632759i
$742$	−7.43563	+	6.44301i	−0.272971	+	0.236530i
$743$	11.2417	−	1.61631i	0.412417	−	0.0592966i	0.0670162	−	0.997752i	$-0.478652\pi$
$743$	11.2417	−	1.61631i	0.412417	−	0.0592966i	0.345401	+	0.938455i	$0.387743\pi$
$744$	9.82833	+	2.88586i	0.360324	+	0.105801i
$745$	−0.310999	−	1.28953i	−0.0113941	−	0.0472447i
$746$	−3.95883	+	27.5343i	−0.144943	+	1.00810i
$747$	0.734082	+	0.335244i	0.0268586	+	0.0122659i
$748$	−11.6693	−	5.32920i	−0.426673	−	0.194855i
$749$	2.43689	−	16.9489i	0.0890420	−	0.619301i
$750$	4.84634	−	10.4996i	0.176963	−	0.383392i
$751$	0.734895	+	0.215785i	0.0268167	+	0.00787409i	0.295113	−	0.955462i	$-0.404643\pi$
$751$	0.734895	+	0.215785i	0.0268167	+	0.00787409i	−0.268297	+	0.963336i	$0.586461\pi$
$752$	10.6935	−	1.53749i	0.389950	−	0.0560664i
$753$	−15.7550	+	13.6518i	−0.574143	+	0.497498i
$754$	−44.3937	−	28.5301i	−1.61672	−	1.03901i
$755$	−5.31971	−	9.24271i	−0.193604	−	0.336376i
$756$	1.09378	−	0.321161i	0.0397802	−	0.0116805i
$757$	14.8986	−	6.80398i	0.541500	−	0.247295i	−0.125836	−	0.992051i	$-0.540161\pi$
$757$	14.8986	−	6.80398i	0.541500	−	0.247295i	0.667337	+	0.744756i	$0.267434\pi$
$758$		−	9.40775i		−	0.341705i
$759$	8.52854	+	2.70438i	0.309567	+	0.0981629i
$760$	−3.47739	−	1.20878i	−0.126138	−	0.0438470i
$761$	−9.93582	−	21.7564i	−0.360173	−	0.788669i	−0.999800	−	0.0199837i	$-0.993639\pi$
$761$	−9.93582	−	21.7564i	−0.360173	−	0.788669i	0.639627	−	0.768685i	$-0.279089\pi$
$762$	2.65962	+	9.05784i	0.0963479	+	0.328131i
$763$	−7.20929	−	6.24689i	−0.260994	−	0.226153i
$764$	3.45287	+	2.21903i	0.124921	+	0.0802816i
$765$	−6.12312	−	15.3547i	−0.221382	−	0.555149i
$766$	−1.46929	−	10.2191i	−0.0530874	−	0.369231i
$767$	24.1301	−	82.1797i	0.871288	−	2.96734i
$768$	9.05394	+	14.0882i	0.326706	+	0.508365i
$769$	1.58087	−	10.9952i	0.0570076	−	0.396496i	−0.941261	−	0.337679i	$-0.890358\pi$
$769$	1.58087	−	10.9952i	0.0570076	−	0.396496i	0.998269	−	0.0588170i	$-0.0187329\pi$
$770$	−3.82212	−	3.65421i	−0.137739	−	0.131689i
$771$	3.58372	−	7.84725i	0.129065	−	0.282612i
$772$	22.8051	+	3.27889i	0.820775	+	0.118010i
$773$	−13.3132	−	20.7158i	−0.478843	−	0.745094i	0.514844	−	0.857284i	$-0.327850\pi$
$773$	−13.3132	−	20.7158i	−0.478843	−	0.745094i	−0.993687	+	0.112190i	$0.964214\pi$
$774$	5.72787	+	1.68185i	0.205884	+	0.0604530i
$775$	−8.48880	+	14.6121i	−0.304927	+	0.524880i
$776$	−17.2661	−	19.9261i	−0.619815	−	0.715305i
$777$	−4.52765	+	7.04517i	−0.162429	+	0.252744i
$778$	−5.42996	−	4.70508i	−0.194673	−	0.168685i
$779$	1.13873	−	0.334361i	0.0407992	−	0.0119797i
$780$	−12.1445	+	1.14317i	−0.434845	+	0.0409321i
$781$	19.5988			0.701301
$782$	−20.4836	+	30.4169i	−0.732490	+	1.08771i
$783$			8.69936i			0.310890i
$784$	−2.91081	−	6.37379i	−0.103958	−	0.227635i
$785$	45.5296	+	2.23026i	1.62502	+	0.0796014i
$786$	−2.44439	+	2.82097i	−0.0871883	+	0.100621i
$787$	−12.8368	+	19.9745i	−0.457584	+	0.712014i	−0.991003	−	0.133837i	$-0.957270\pi$
$787$	−12.8368	+	19.9745i	−0.457584	+	0.712014i	0.533420	+	0.845851i	$0.320907\pi$
$788$	−3.35709	+	2.90893i	−0.119591	+	0.103626i
$789$	−3.94919	−	27.4672i	−0.140595	−	0.977859i
$790$	24.3107	+	17.3609i	0.864935	+	0.617673i
$791$	3.61230	−	2.32149i	0.128439	−	0.0825425i
$792$	−5.59659	−	0.804668i	−0.198866	−	0.0285926i
$793$	−1.14003	−	0.520635i	−0.0404837	−	0.0184883i
$794$	−5.27949	+	11.5605i	−0.187362	+	0.410266i
$795$	−15.4157	−	7.97361i	−0.546738	−	0.282795i
$796$	2.86754	−	1.84286i	0.101637	−	0.0653184i
$797$	−9.48176	+	32.2919i	−0.335861	+	1.14384i	0.602482	+	0.798133i	$0.294179\pi$
$797$	−9.48176	+	32.2919i	−0.335861	+	1.14384i	−0.938343	+	0.345705i	$0.887640\pi$
$798$	−0.681596	+	0.0979987i	−0.0241282	+	0.00346912i
$799$	41.0384	+	47.3609i	1.45184	+	1.67551i
$800$	−22.4330	+	7.69657i	−0.793125	+	0.272115i
$801$	8.55051	−	9.86781i	0.302117	−	0.348662i
$802$	−9.47902	−	32.2826i	−0.334716	−	1.13994i
$803$	−10.9708	+	5.01021i	−0.387152	+	0.176807i
$804$	−0.791994			−0.0279315
$805$	10.5132	−	7.88628i	0.370543	−	0.277955i
$806$	−20.5019			−0.722150
$807$	3.73965	−	1.70784i	0.131642	−	0.0601189i
$808$	−0.363268	−	1.23718i	−0.0127797	−	0.0435238i
$809$	−16.2567	+	18.7612i	−0.571554	+	0.659609i	−0.965767	−	0.259410i	$-0.916472\pi$
$809$	−16.2567	+	18.7612i	−0.571554	+	0.659609i	0.394213	+	0.919019i	$0.371017\pi$
$810$	−1.42724	−	1.81992i	−0.0501483	−	0.0639456i
$811$	−20.7623	−	23.9610i	−0.729063	−	0.841384i	0.263303	−	0.964713i	$-0.415188\pi$
$811$	−20.7623	−	23.9610i	−0.729063	−	0.841384i	−0.992366	+	0.123330i	$0.960643\pi$
$812$	9.81590	−	1.41131i	0.344471	−	0.0495274i
$813$	3.81127	−	12.9800i	0.133667	−	0.455229i
$814$	11.0928	−	7.12890i	0.388802	−	0.249868i
$815$	−8.01743	+	15.5004i	−0.280838	+	0.542955i
$816$	3.91386	−	8.57016i	0.137013	−	0.300016i
$817$	2.85199	+	1.30246i	0.0997785	+	0.0455673i
$818$	2.61560	+	0.376067i	0.0914524	+	0.0131489i
$819$	−6.04646	+	3.88582i	−0.211280	+	0.135782i
$820$	2.64075	−	3.69788i	0.0922191	−	0.129135i
$821$	−7.84822	−	54.5855i	−0.273905	−	1.90505i	−0.406107	−	0.913826i	$-0.633114\pi$
$821$	−7.84822	−	54.5855i	−0.273905	−	1.90505i	0.132202	−	0.991223i	$-0.457795\pi$
$822$	−10.3146	+	8.93766i	−0.359763	+	0.311737i
$823$	4.65250	−	7.23943i	0.162176	−	0.252351i	−0.750650	−	0.660701i	$-0.770259\pi$
$823$	4.65250	−	7.23943i	0.162176	−	0.252351i	0.912825	+	0.408350i	$0.133896\pi$
$824$	−31.7055	+	36.5901i	−1.10451	+	1.27467i
$825$	3.49014	−	8.65040i	0.121511	−	0.301168i
$826$	−7.69018	−	16.8391i	−0.267576	−	0.585909i
$827$			27.1496i			0.944085i	0.881576	+	0.472043i	$0.156483\pi$
$827$			27.1496i			0.944085i	−0.881576	+	0.472043i	$0.843517\pi$
$828$	1.34839	−	4.25227i	0.0468597	−	0.147777i
$829$	−33.1154			−1.15015			−0.575073	−	0.818102i	$-0.695026\pi$
$829$	−33.1154			−1.15015			−0.575073	+	0.818102i	$0.695026\pi$
$830$	−1.85826	+	0.174919i	−0.0645010	+	0.00607151i
$831$	16.6591	−	4.89156i	0.577899	−	0.169686i
$832$	−33.0428	−	28.6317i	−1.14555	−	0.992627i
$833$	21.9746	−	34.1932i	0.761375	−	1.18472i
$834$	3.40351	+	3.92786i	0.117854	+	0.136011i
$835$	1.96090	−	10.1010i	0.0678598	−	0.349558i
$836$	−0.904500	−	0.265585i	−0.0312828	−	0.00918545i
$837$	1.82724	+	2.84325i	0.0631588	+	0.0982770i
$838$	5.43985	+	0.782132i	0.187917	+	0.0270183i
$839$	−10.2438	+	22.4307i	−0.353654	+	0.774394i	0.646282	+	0.763099i	$0.276323\pi$
$839$	−10.2438	+	22.4307i	−0.353654	+	0.774394i	−0.999936	+	0.0112959i	$0.996404\pi$
$840$	−5.73945	+	6.00317i	−0.198030	+	0.207129i
$841$	−6.64308	+	46.2037i	−0.229072	+	1.59323i
$842$	−1.09875	−	1.70969i	−0.0378654	−	0.0589196i
$843$	−2.03709	+	6.93770i	−0.0701612	+	0.238947i
$844$	0.978479	+	6.80547i	0.0336806	+	0.234254i
$845$	44.4384	−	17.7211i	1.52873	−	0.609624i
$846$	7.37606	+	4.74030i	0.253594	+	0.162975i
$847$	6.96459	+	6.03485i	0.239306	+	0.207360i
$848$	−2.78687	−	9.49121i	−0.0957015	−	0.325929i
$849$	9.34562	+	20.4640i	0.320741	+	0.702324i
$850$	29.9888	+	23.7144i	1.02861	+	0.813397i
$851$	12.9709	+	30.0959i	0.444638	+	1.03167i
$852$		−	9.77183i		−	0.334777i
$853$	−3.12853	+	1.42875i	−0.107119	+	0.0489195i	−0.468254	−	0.883594i	$-0.655117\pi$
$853$	−3.12853	+	1.42875i	−0.107119	+	0.0489195i	0.361135	+	0.932514i	$0.382389\pi$
$854$	−0.259911	+	0.0763167i	−0.00889397	+	0.00261151i
$855$	−0.605940	−	1.05279i	−0.0207227	−	0.0360046i
$856$	35.6237	+	22.8939i	1.21759	+	0.782499i
$857$	11.6320	−	10.0791i	0.397340	−	0.344297i	−0.433159	−	0.901318i	$-0.642601\pi$
$857$	11.6320	−	10.0791i	0.397340	−	0.344297i	0.830499	+	0.557021i	$0.188056\pi$
$858$	11.2016	−	1.61055i	0.382417	−	0.0549832i
$859$	−47.0150	−	13.8048i	−1.60413	−	0.471015i	−0.647439	−	0.762117i	$-0.724160\pi$
$859$	−47.0150	−	13.8048i	−1.60413	−	0.471015i	−0.956692	+	0.291102i	$0.905978\pi$
$860$	11.6698	−	2.81444i	0.397938	−	0.0959717i
$861$	0.381035	−	2.65016i	0.0129856	−	0.0903171i
$862$	−33.4085	−	15.2572i	−1.13790	−	0.519661i
$863$	−33.9182	−	15.4899i	−1.15459	−	0.527283i	−0.256260	−	0.966608i	$-0.582490\pi$
$863$	−33.9182	−	15.4899i	−1.15459	−	0.527283i	−0.898328	+	0.439325i	$0.855218\pi$
$864$	−0.675043	+	4.69503i	−0.0229654	+	0.159728i
$865$	28.5686	−	6.88998i	0.971363	−	0.234266i
$866$	24.5192	+	7.19949i	0.833197	+	0.244649i
$867$	37.2685	−	5.35840i	1.26570	−	0.181981i
$868$	2.91173	−	2.52303i	0.0988307	−	0.0856373i
$869$	20.2713	+	13.0276i	0.687658	+	0.441931i
$870$	−10.0366	−	17.4380i	−0.340272	−	0.591204i
$871$	4.79128	−	1.40685i	0.162346	−	0.0476692i
$872$	21.4588	−	9.79993i	0.726688	−	0.331867i
$873$		−	8.69950i		−	0.294433i
$874$	−1.17178	+	2.42659i	−0.0396361	+	0.0820805i
$875$	−7.36118	−	11.5565i	−0.248853	−	0.390683i
$876$	2.49805	+	5.46998i	0.0844015	+	0.184813i
$877$	−2.05394	−	6.99508i	−0.0693566	−	0.236207i	0.917518	−	0.397694i	$-0.130189\pi$
$877$	−2.05394	−	6.99508i	−0.0693566	−	0.236207i	−0.986875	+	0.161487i	$0.948371\pi$
$878$	10.6669	+	9.24289i	0.359989	+	0.311932i
$879$	−1.04179	−	0.669516i	−0.0351386	−	0.0225822i
$880$	4.93829	−	1.96928i	0.166470	−	0.0663846i
$881$	1.35156	+	9.40029i	0.0455351	+	0.316704i	0.999840	+	0.0178700i	$0.00568850\pi$
$881$	1.35156	+	9.40029i	0.0455351	+	0.316704i	−0.954305	+	0.298834i	$0.903402\pi$
$882$	1.60216	−	5.45645i	0.0539474	−	0.183728i
$883$	22.7976	+	35.4737i	0.767199	+	1.19379i	0.976412	+	0.215915i	$0.0692735\pi$
$883$	22.7976	+	35.4737i	0.767199	+	1.19379i	−0.209213	+	0.977870i	$0.567090\pi$
$884$	5.73937	−	39.9182i	0.193036	−	1.34259i
$885$	22.5667	−	23.6036i	0.758572	−	0.793427i
$886$	−3.18587	+	6.97609i	−0.107032	+	0.234366i
$887$	4.34199	+	0.624284i	0.145790	+	0.0209614i	0.214823	−	0.976653i	$-0.431082\pi$
$887$	4.34199	+	0.624284i	0.145790	+	0.0209614i	−0.0690335	+	0.997614i	$0.521992\pi$
$888$	−11.1969	−	17.4228i	−0.375744	−	0.584670i
$889$	10.7323	+	3.15128i	0.359949	+	0.105690i
$890$	−5.75501	+	29.6451i	−0.192908	+	0.993704i
$891$	−1.22170	−	1.40992i	−0.0409285	−	0.0472340i
$892$	−4.39285	+	6.83541i	−0.147084	+	0.228866i
$893$	3.48022	+	3.01563i	0.116461	+	0.100914i
$894$	0.588738	−	0.172869i	0.0196904	−	0.00578161i
$895$	−31.8257	+	2.99577i	−1.06382	+	0.100137i
$896$	2.17617			0.0727007
$897$	−0.603798	+	28.1199i	−0.0201602	+	0.938896i
$898$		−	27.7211i		−	0.925065i
$899$	12.2140	+	26.7449i	0.407359	+	0.891991i
$900$	−4.31303	−	1.74016i	−0.143768	−	0.0580054i
$901$	37.5759	−	43.3648i	1.25183	−	1.44469i
$902$	−2.27915	+	3.54643i	−0.0758874	+	0.118083i
$903$	5.34559	−	4.63198i	0.177890	−	0.154143i
$904$	1.51124	+	10.5109i	0.0502631	+	0.349587i
$905$	2.27320	−	3.18319i	0.0755638	−	0.105813i
$906$	4.14984	−	2.66694i	0.137869	−	0.0886031i
$907$	12.7926	+	1.83930i	0.424772	+	0.0610729i	0.351386	−	0.936231i	$-0.385710\pi$
$907$	12.7926	+	1.83930i	0.424772	+	0.0610729i	0.0733857	+	0.997304i	$0.476620\pi$
$908$	−4.80449	−	2.19414i	−0.159443	−	0.0728150i
$909$	0.176735	−	0.386995i	0.00586193	−	0.0128358i
$910$	7.63711	−	14.7651i	0.253168	−	0.489458i
$911$	−25.2597	+	16.2334i	−0.836890	+	0.537837i	−0.887461	−	0.460884i	$-0.847533\pi$
$911$	−25.2597	+	16.2334i	−0.836890	+	0.537837i	0.0505702	+	0.998721i	$0.483896\pi$
$912$	0.195051	−	0.664281i	0.00645877	−	0.0219965i
$913$	−1.49022	+	0.214262i	−0.0493192	+	0.00709103i
$914$	−4.66360	−	5.38209i	−0.154258	−	0.178024i
$915$	−0.294878	−	0.376008i	−0.00974836	−	0.0124304i
$916$	−8.71938	+	10.0627i	−0.288096	+	0.332481i
$917$	1.24602	+	4.24355i	0.0411472	+	0.140134i
$918$	6.95545	−	3.17645i	0.229564	−	0.104838i
$919$	−30.1297			−0.993888			−0.496944	−	0.867783i	$-0.665545\pi$
$919$	−30.1297			−0.993888			−0.496944	+	0.867783i	$0.665545\pi$
$920$	6.93991	+	31.7516i	0.228802	+	1.04682i
$921$	−14.2666			−0.470101
$922$	9.95836	−	4.54783i	0.327961	−	0.149775i
$923$	17.3580	+	59.1161i	0.571347	+	1.94583i
$924$	−1.39268	+	1.60724i	−0.0458158	+	0.0528743i
$925$	32.3180	−	11.0881i	1.06261	−	0.364573i
$926$	−23.9324	−	27.6194i	−0.786467	−	0.907631i
$927$	−15.8122	+	2.27345i	−0.519340	+	0.0746698i
$928$	−11.6253	+	39.5923i	−0.381620	+	1.29968i
$929$	−29.7734	+	19.1342i	−0.976834	+	0.627773i	−0.928608	−	0.371063i	$-0.878993\pi$
$929$	−29.7734	+	19.1342i	−0.976834	+	0.627773i	−0.0482266	+	0.998836i	$0.515357\pi$
$930$	−6.94304	−	3.59122i	−0.227671	−	0.117761i
$931$	1.24074	−	2.71685i	0.0406637	−	0.0890410i
$932$	−16.3401	−	7.46228i	−0.535238	−	0.244435i
$933$	3.04784	+	0.438213i	0.0997816	+	0.0143464i
$934$	7.28991	−	4.68494i	0.238533	−	0.153296i
$935$	25.0968	+	17.9223i	0.820752	+	0.586121i
$936$	−2.52959	−	17.5937i	−0.0826823	−	0.575068i
$937$	5.58706	−	4.84121i	0.182521	−	0.158155i	−0.558808	−	0.829297i	$-0.688741\pi$
$937$	5.58706	−	4.84121i	0.182521	−	0.158155i	0.741329	+	0.671142i	$0.234196\pi$
$938$	0.583513	−	0.907964i	0.0190524	−	0.0296461i
$939$	−1.61415	+	1.86283i	−0.0526758	+	0.0607912i
$940$	17.6103	+	0.862637i	0.574384	+	0.0281361i
$941$	17.1546	+	37.5634i	0.559226	+	1.22453i	0.952339	+	0.305043i	$0.0986708\pi$
$941$	17.1546	+	37.5634i	0.559226	+	1.22453i	−0.393113	+	0.919490i	$0.628602\pi$
$942$			21.0856i			0.687007i
$943$	−7.76919	−	7.02966i	−0.253000	−	0.228917i
$944$	18.6120			0.605771
$945$	−2.72831	+	0.256817i	−0.0887519	+	0.00835426i
$946$	−10.6859	+	3.13765i	−0.347427	+	0.102014i
$947$	37.5944	+	32.5758i	1.22165	+	1.05857i	0.996444	+	0.0842600i	$0.0268526\pi$
$947$	37.5944	+	32.5758i	1.22165	+	1.05857i	0.225211	+	0.974310i	$0.427693\pi$
$948$	6.49547	−	10.1071i	0.210963	−	0.328265i
$949$	−24.8289	−	28.6540i	−0.805979	−	0.930149i
$950$	2.42924	+	1.41125i	0.0788148	+	0.0457871i
$951$	−25.1143	−	7.37423i	−0.814388	−	0.239126i
$952$	−14.8452	−	23.0995i	−0.481135	−	0.748660i
$953$	−20.7364	−	2.98144i	−0.671717	−	0.0965783i	−0.201987	−	0.979388i	$-0.564740\pi$
$953$	−20.7364	−	2.98144i	−0.671717	−	0.0965783i	−0.469730	+	0.882810i	$0.655649\pi$
$954$	3.33501	−	7.30266i	0.107975	−	0.236432i
$955$	−7.13178	−	6.81848i	−0.230779	−	0.220641i
$956$	−0.842359	+	5.85874i	−0.0272438	+	0.189485i
$957$	−8.77429	−	13.6531i	−0.283633	−	0.441341i
$958$	0.0939502	−	0.319965i	0.00303539	−	0.0103376i
$959$	2.30140	+	16.0066i	0.0743160	+	0.516879i
$960$	−6.17475	−	15.4842i	−0.199289	−	0.499749i
$961$	−16.4693	−	10.5842i	−0.531269	−	0.341426i
$962$	31.3275	+	27.1454i	1.01004	+	0.875203i
$963$	3.93639	+	13.4061i	0.126849	+	0.432006i
$964$	−10.3839	−	22.7376i	−0.334443	−	0.732329i
$965$	−52.3153	−	18.1854i	−1.68409	−	0.585408i
$966$	3.88148	+	4.67875i	0.124884	+	0.150536i
$967$		−	40.6574i		−	1.30746i	−0.756730	−	0.653728i	$-0.773204\pi$
$967$		−	40.6574i		−	1.30746i	0.756730	−	0.653728i	$-0.226796\pi$
$968$	−20.7305	+	9.46729i	−0.666303	+	0.304290i
$969$	3.85329	−	1.13143i	0.123786	−	0.0363467i
$970$	10.0367	+	17.4383i	0.322260	+	0.559910i
$971$	−14.1376	−	9.08571i	−0.453698	−	0.291574i	0.293765	−	0.955878i	$-0.405092\pi$
$971$	−14.1376	−	9.08571i	−0.453698	−	0.291574i	−0.747463	+	0.664304i	$0.768728\pi$
$972$	−0.702975	+	0.609131i	−0.0225479	+	0.0195379i
$973$	6.09539	−	0.876385i	0.195409	−	0.0280956i
$974$	−7.45361	−	2.18858i	−0.238829	−	0.0701265i
$975$	29.1834	+	2.86597i	0.934617	+	0.0917844i
$976$	0.0387590	−	0.269575i	0.00124065	−	0.00862888i
$977$	27.4300	+	12.5268i	0.877562	+	0.400769i	0.802671	−	0.596422i	$-0.203412\pi$
$977$	27.4300	+	12.5268i	0.877562	+	0.400769i	0.0748915	+	0.997192i	$0.476139\pi$
$978$	−7.34280	−	3.35334i	−0.234797	−	0.107228i
$979$	−3.46664	+	24.1110i	−0.110794	+	0.770592i
$980$	−2.68108	−	11.1168i	−0.0856439	−	0.355114i
$981$	7.46848	+	2.19294i	0.238450	+	0.0700153i
$982$	30.6539	−	4.40737i	0.978206	−	0.140645i
$983$	−2.63379	+	2.28220i	−0.0840050	+	0.0727907i	−0.695851	−	0.718186i	$-0.744973\pi$
$983$	−2.63379	+	2.28220i	−0.0840050	+	0.0727907i	0.611846	+	0.790977i	$0.290427\pi$
$984$	5.57016	+	3.57972i	0.177570	+	0.114117i
$985$	9.25497	−	5.32677i	0.294888	−	0.169725i
$986$	63.8246	−	18.7406i	2.03259	−	0.596822i
$987$	9.44996	−	4.31565i	0.300795	−	0.137369i
$988$		−	2.96347i		−	0.0942805i
$989$	−3.35014	−	27.4760i	−0.106528	−	0.873685i
$990$	4.07557	+	1.41671i	0.129530	+	0.0450261i
$991$	10.1203	+	22.1604i	0.321482	+	0.703947i	0.999517	−	0.0310824i	$-0.00989544\pi$
$991$	10.1203	+	22.1604i	0.321482	+	0.703947i	−0.678035	+	0.735030i	$0.737168\pi$
$992$	4.51654	+	15.3819i	0.143400	+	0.488377i
$993$	−14.9704	−	12.9719i	−0.475072	−	0.411652i
$994$	11.2027	+	7.19953i	0.355328	+	0.228355i
$995$	−7.61131	+	3.03523i	−0.241295	+	0.0962233i
$996$	0.106829	+	0.743015i	0.00338502	+	0.0235433i
$997$	15.9818	−	54.4290i	0.506148	−	1.72378i	−0.168553	−	0.985693i	$-0.553909\pi$
$997$	15.9818	−	54.4290i	0.506148	−	1.72378i	0.674701	−	0.738091i	$-0.264272\pi$
$998$	20.5265	+	31.9398i	0.649754	+	1.01104i
$999$	0.972501	−	6.76390i	0.0307686	−	0.214000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.4.17	yes	240
5.4	even	2	inner	345.2.t.a.4.8	✓	240
23.6	even	11	inner	345.2.t.a.259.8	yes	240
115.29	even	22	inner	345.2.t.a.259.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.8	✓	240	5.4	even	2	inner
345.2.t.a.4.17	yes	240	1.1	even	1	trivial
345.2.t.a.259.8	yes	240	23.6	even	11	inner
345.2.t.a.259.17	yes	240	115.29	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.940856 - 0.429675i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-0.609131 + 0.702975i) q^{4} +(1.75953 - 1.37988i) q^{5} +(0.677340 + 0.781692i) q^{6} +(1.21306 - 0.174411i) q^{7} +(-0.853861 + 2.90798i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(1.06256 - 2.05429i) q^{10} +(0.774994 - 1.69700i) q^{11} +(-0.846112 - 0.386406i) q^{12} +(5.80506 + 0.834642i) q^{13} +(1.06637 - 0.685316i) q^{14} +(1.81970 + 1.29950i) q^{15} +(0.181373 + 1.26147i) q^{16} +(-5.58701 + 4.84118i) q^{17} +(-0.559199 + 0.870131i) q^{18} +(-0.355744 + 0.410550i) q^{19} +(-0.101763 + 2.07743i) q^{20} +(0.509104 + 1.11478i) q^{21} -1.92963i q^{22} +(4.73127 + 0.784266i) q^{23} -3.03075 q^{24} +(1.19187 - 4.85587i) q^{25} +(5.82035 - 1.70901i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.616304 + 0.958988i) q^{28} +(-5.69687 - 6.57453i) q^{29} +(2.27044 + 0.440761i) q^{30} +(-3.24287 - 0.952192i) q^{31} +(-2.56443 - 3.99033i) q^{32} +(1.84660 + 0.265501i) q^{33} +(-3.17645 + 6.95545i) q^{34} +(1.89374 - 1.98075i) q^{35} +(0.132377 - 0.920702i) q^{36} +(3.69444 + 5.74866i) q^{37} +(-0.158301 + 0.539123i) q^{38} +(0.834642 + 5.80506i) q^{39} +(2.51027 + 6.29490i) q^{40} +(-1.83788 - 1.18113i) q^{41} +(0.957987 + 0.830101i) q^{42} +(-1.62604 - 5.53778i) q^{43} +(0.720876 + 1.57850i) q^{44} +(-0.734189 + 2.11210i) q^{45} +(4.78843 - 1.29503i) q^{46} -8.47696i q^{47} +(-1.15928 + 0.529424i) q^{48} +(-5.27536 + 1.54899i) q^{49} +(-0.965065 - 5.08079i) q^{50} +(-6.21912 - 3.99678i) q^{51} +(-4.12278 + 3.57241i) q^{52} +(-7.68272 + 1.10461i) q^{53} +(-0.992429 - 0.291403i) q^{54} +(-0.978031 - 4.05531i) q^{55} +(-0.528597 + 3.67647i) q^{56} +(-0.494145 - 0.225668i) q^{57} +(-8.18484 - 3.73789i) q^{58} +(2.07837 - 14.4554i) q^{59} +(-2.02195 + 0.487639i) q^{60} +(-0.205042 - 0.0602058i) q^{61} +(-3.46021 + 0.497503i) q^{62} +(-0.926194 + 0.802552i) q^{63} +(-6.27156 - 4.03049i) q^{64} +(11.3659 - 6.54171i) q^{65} +(1.85146 - 0.543639i) q^{66} +(0.774508 - 0.353706i) q^{67} -6.87644i q^{68} +(0.580455 + 4.76057i) q^{69} +(0.930658 - 2.67729i) q^{70} +(4.36411 + 9.55607i) q^{71} +(-0.853861 - 2.90798i) q^{72} +(-4.88580 - 4.23357i) q^{73} +(5.94599 + 3.82126i) q^{74} +(4.99496 - 0.224466i) q^{75} +(-0.0719119 - 0.500158i) q^{76} +(0.644136 - 2.19372i) q^{77} +(3.27957 + 5.10310i) q^{78} +(-1.83819 + 12.7849i) q^{79} +(2.05981 + 1.96933i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-2.23669 - 0.321587i) q^{82} +(-0.436302 - 0.678900i) q^{83} +(-1.09378 - 0.321161i) q^{84} +(-3.15027 + 16.2276i) q^{85} +(-3.90931 - 4.51159i) q^{86} +(4.70323 - 7.31836i) q^{87} +(4.27311 + 3.70267i) q^{88} +(-12.5281 + 3.67858i) q^{89} +(0.216749 + 2.30264i) q^{90} +7.18744 q^{91} +(-3.43329 + 2.84824i) q^{92} -3.37977i q^{93} +(-3.64233 - 7.97560i) q^{94} +(-0.0594313 + 1.21326i) q^{95} +(3.10621 - 3.58475i) q^{96} +(-4.70330 + 7.31848i) q^{97} +(-4.29780 + 3.72406i) q^{98} +(0.265501 + 1.84660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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