LMFDB - Embedded newform 950.2.n.a.39.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.7
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.236785 + 0.0769362i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.89595 - 1.18549i) q^{5} +(-0.0769362 - 0.236785i) q^{6} -4.79883i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.37690 - 1.72692i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.236785 + 0.0769362i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.89595 - 1.18549i) q^{5} +(-0.0769362 - 0.236785i) q^{6} -4.79883i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.37690 - 1.72692i) q^{9} +(0.155332 + 2.23067i) q^{10} +(3.55019 - 2.57936i) q^{11} +(-0.146341 + 0.201422i) q^{12} +(-1.66713 + 2.29461i) q^{13} +(-3.88234 + 2.82068i) q^{14} +(-0.357726 - 0.426573i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.32240 + 1.40443i) q^{17} +2.93801i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.71335 - 1.43682i) q^{20} +(0.369204 - 1.13629i) q^{21} +(-4.17349 - 1.35605i) q^{22} +(3.18200 + 4.37964i) q^{23} +0.248971 q^{24} +(2.18924 + 4.49524i) q^{25} +2.83629 q^{26} +(-0.868977 - 1.19604i) q^{27} +(4.56396 + 1.48292i) q^{28} +(1.05323 - 3.24150i) q^{29} +(-0.134839 + 0.540140i) q^{30} +(-1.36963 - 4.21530i) q^{31} +1.00000i q^{32} +(1.03908 - 0.337617i) q^{33} +(3.67685 + 2.67139i) q^{34} +(-5.68895 + 9.09834i) q^{35} +(2.37690 - 1.72692i) q^{36} +(-5.65382 + 7.78181i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-0.571291 + 0.415067i) q^{39} +(-2.16949 - 0.541584i) q^{40} +(-4.57642 - 3.32496i) q^{41} +(-1.13629 + 0.369204i) q^{42} -0.869567i q^{43} +(1.35605 + 4.17349i) q^{44} +(2.45924 + 6.09194i) q^{45} +(1.67287 - 5.14858i) q^{46} +(11.2418 + 3.65267i) q^{47} +(-0.146341 - 0.201422i) q^{48} -16.0288 q^{49} +(2.34992 - 4.41337i) q^{50} -1.13153 q^{51} +(-1.66713 - 2.29461i) q^{52} +(-8.12291 - 2.63929i) q^{53} +(-0.456848 + 1.40603i) q^{54} +(-9.78877 + 0.681639i) q^{55} +(-1.48292 - 4.56396i) q^{56} +0.248971i q^{57} +(-3.24150 + 1.05323i) q^{58} +(-6.61866 - 4.80874i) q^{59} +(0.516238 - 0.208399i) q^{60} +(-9.70835 + 7.05353i) q^{61} +(-2.60520 + 3.58575i) q^{62} +(-8.28721 + 11.4064i) q^{63} +(0.809017 - 0.587785i) q^{64} +(5.88102 - 2.37410i) q^{65} +(-0.883893 - 0.642186i) q^{66} +(0.189135 - 0.0614538i) q^{67} -4.54484i q^{68} +(0.416497 + 1.28185i) q^{69} +(10.7046 - 0.745413i) q^{70} +(2.34707 - 7.22354i) q^{71} +(-2.79422 - 0.907896i) q^{72} +(3.97733 + 5.47433i) q^{73} +9.61885 q^{74} +(0.172534 + 1.23284i) q^{75} -1.00000 q^{76} +(-12.3779 - 17.0367i) q^{77} +(0.671592 + 0.218214i) q^{78} +(3.98295 - 12.2583i) q^{79} +(0.837043 + 2.07349i) q^{80} +(2.60995 + 8.03259i) q^{81} +5.65676i q^{82} +(-6.04282 + 1.96343i) q^{83} +(0.966589 + 0.702268i) q^{84} +(9.85999 + 2.46141i) q^{85} +(-0.703495 + 0.511119i) q^{86} +(0.498778 - 0.686509i) q^{87} +(2.57936 - 3.55019i) q^{88} +(9.80091 - 7.12078i) q^{89} +(3.48298 - 5.57032i) q^{90} +(11.0114 + 8.00028i) q^{91} +(-5.14858 + 1.67287i) q^{92} -1.10350i q^{93} +(-3.65267 - 11.2418i) q^{94} +(0.541584 - 2.16949i) q^{95} +(-0.0769362 + 0.236785i) q^{96} +(-13.0804 - 4.25008i) q^{97} +(9.42149 + 12.9676i) q^{98} -12.8928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.236785	+	0.0769362i	0.136708	+	0.0444191i	0.376572	−	0.926387i	$-0.377103\pi$
$3$	0.236785	+	0.0769362i	0.136708	+	0.0444191i	−0.239864	+	0.970807i	$0.577103\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.89595	−	1.18549i	−0.847894	−	0.530166i
$5$	−1.89595	−	1.18549i	−0.847894	−	0.530166i
$6$	−0.0769362	−	0.236785i	−0.0314091	−	0.0966672i
$7$		−	4.79883i		−	1.81379i	−0.421358	−	0.906894i	$-0.638447\pi$
$7$		−	4.79883i		−	1.81379i	0.421358	−	0.906894i	$-0.361553\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−2.37690	−	1.72692i	−0.792301	−	0.575640i
$10$	0.155332	+	2.23067i	0.0491203	+	0.705399i
$11$	3.55019	−	2.57936i	1.07042	−	0.777707i	0.0944333	−	0.995531i	$-0.469896\pi$
$11$	3.55019	−	2.57936i	1.07042	−	0.777707i	0.975988	+	0.217825i	$0.0698961\pi$
$12$	−0.146341	+	0.201422i	−0.0422451	+	0.0581454i
$13$	−1.66713	+	2.29461i	−0.462379	+	0.636410i	−0.975000	−	0.222205i	$-0.928675\pi$
$13$	−1.66713	+	2.29461i	−0.462379	+	0.636410i	0.512621	+	0.858615i	$0.328675\pi$
$14$	−3.88234	+	2.82068i	−1.03760	+	0.753859i
$15$	−0.357726	−	0.426573i	−0.0923645	−	0.110141i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.32240	+	1.40443i	−1.04834	+	0.340625i	−0.782015	−	0.623259i	$-0.785808\pi$
$17$	−4.32240	+	1.40443i	−1.04834	+	0.340625i	−0.266321	+	0.963884i	$0.585808\pi$
$18$			2.93801i			0.692496i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	1.71335	−	1.43682i	0.383116	−	0.321282i
$21$	0.369204	−	1.13629i	0.0805669	−	0.247960i
$22$	−4.17349	−	1.35605i	−0.889792	−	0.289111i
$23$	3.18200	+	4.37964i	0.663492	+	0.913218i	0.999591	−	0.0286085i	$-0.00910760\pi$
$23$	3.18200	+	4.37964i	0.663492	+	0.913218i	−0.336099	+	0.941827i	$0.609108\pi$
$24$	0.248971			0.0508210
$25$	2.18924	+	4.49524i	0.437849	+	0.899049i
$26$	2.83629			0.556243
$27$	−0.868977	−	1.19604i	−0.167235	−	0.230179i
$28$	4.56396	+	1.48292i	0.862508	+	0.280246i
$29$	1.05323	−	3.24150i	0.195579	−	0.601932i	−0.804390	−	0.594102i	$-0.797508\pi$
$29$	1.05323	−	3.24150i	0.195579	−	0.601932i	0.999969	−	0.00782997i	$-0.00249238\pi$
$30$	−0.134839	+	0.540140i	−0.0246181	+	0.0986156i
$31$	−1.36963	−	4.21530i	−0.245993	−	0.757090i	−0.995471	−	0.0950608i	$-0.969695\pi$
$31$	−1.36963	−	4.21530i	−0.245993	−	0.757090i	0.749478	−	0.662029i	$-0.230305\pi$
$32$			1.00000i			0.176777i
$33$	1.03908	−	0.337617i	0.180880	−	0.0587716i
$34$	3.67685	+	2.67139i	0.630575	+	0.458140i
$35$	−5.68895	+	9.09834i	−0.961608	+	1.53790i
$36$	2.37690	−	1.72692i	0.396150	−	0.287820i
$37$	−5.65382	+	7.78181i	−0.929482	+	1.27932i	0.0305793	+	0.999532i	$0.490265\pi$
$37$	−5.65382	+	7.78181i	−0.929482	+	1.27932i	−0.960061	+	0.279790i	$0.909735\pi$
$38$	0.587785	−	0.809017i	0.0953514	−	0.131240i
$39$	−0.571291	+	0.415067i	−0.0914797	+	0.0664639i
$40$	−2.16949	−	0.541584i	−0.343026	−	0.0856320i
$41$	−4.57642	−	3.32496i	−0.714716	−	0.519272i	0.169976	−	0.985448i	$-0.445631\pi$
$41$	−4.57642	−	3.32496i	−0.714716	−	0.519272i	−0.884692	+	0.466177i	$0.845631\pi$
$42$	−1.13629	+	0.369204i	−0.175334	+	0.0569694i
$43$		−	0.869567i		−	0.132608i	−0.997799	−	0.0663039i	$-0.978879\pi$
$43$		−	0.869567i		−	0.132608i	0.997799	−	0.0663039i	$-0.0211207\pi$
$44$	1.35605	+	4.17349i	0.204432	+	0.629178i
$45$	2.45924	+	6.09194i	0.366603	+	0.908133i
$46$	1.67287	−	5.14858i	0.246652	−	0.759116i
$47$	11.2418	+	3.65267i	1.63978	+	0.532797i	0.976489	−	0.215565i	$-0.0691594\pi$
$47$	11.2418	+	3.65267i	1.63978	+	0.532797i	0.663291	+	0.748362i	$0.269159\pi$
$48$	−0.146341	−	0.201422i	−0.0211226	−	0.0290727i
$49$	−16.0288			−2.28983
$50$	2.34992	−	4.41337i	0.332329	−	0.624145i
$51$	−1.13153			−0.158446
$52$	−1.66713	−	2.29461i	−0.231189	−	0.318205i
$53$	−8.12291	−	2.63929i	−1.11577	−	0.362535i	−0.307616	−	0.951510i	$-0.599531\pi$
$53$	−8.12291	−	2.63929i	−1.11577	−	0.362535i	−0.808151	+	0.588976i	$0.799531\pi$
$54$	−0.456848	+	1.40603i	−0.0621692	+	0.191337i
$55$	−9.78877	+	0.681639i	−1.31992	+	0.0919122i
$56$	−1.48292	−	4.56396i	−0.198164	−	0.609885i
$57$			0.248971i			0.0329770i
$58$	−3.24150	+	1.05323i	−0.425630	+	0.138296i
$59$	−6.61866	−	4.80874i	−0.861676	−	0.626044i	0.0666646	−	0.997775i	$-0.478764\pi$
$59$	−6.61866	−	4.80874i	−0.861676	−	0.626044i	−0.928340	+	0.371731i	$0.878764\pi$
$60$	0.516238	−	0.208399i	0.0666461	−	0.0269042i
$61$	−9.70835	+	7.05353i	−1.24303	+	0.903112i	−0.997796	−	0.0663527i	$-0.978864\pi$
$61$	−9.70835	+	7.05353i	−1.24303	+	0.903112i	−0.245231	+	0.969465i	$0.578864\pi$
$62$	−2.60520	+	3.58575i	−0.330860	+	0.455390i
$63$	−8.28721	+	11.4064i	−1.04409	+	1.43707i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	5.88102	−	2.37410i	0.729451	−	0.294471i
$66$	−0.883893	−	0.642186i	−0.108800	−	0.0790476i
$67$	0.189135	−	0.0614538i	0.0231065	−	0.00750777i	−0.297441	−	0.954740i	$-0.596133\pi$
$67$	0.189135	−	0.0614538i	0.0231065	−	0.00750777i	0.320547	+	0.947232i	$0.396133\pi$
$68$		−	4.54484i		−	0.551143i
$69$	0.416497	+	1.28185i	0.0501403	+	0.154316i
$70$	10.7046	−	0.745413i	1.27944	−	0.0890938i
$71$	2.34707	−	7.22354i	0.278546	−	0.857276i	−0.709713	−	0.704491i	$-0.751176\pi$
$71$	2.34707	−	7.22354i	0.278546	−	0.857276i	0.988259	−	0.152786i	$-0.0488245\pi$
$72$	−2.79422	−	0.907896i	−0.329302	−	0.106997i
$73$	3.97733	+	5.47433i	0.465511	+	0.640722i	0.975640	−	0.219376i	$-0.0704023\pi$
$73$	3.97733	+	5.47433i	0.465511	+	0.640722i	−0.510129	+	0.860098i	$0.670402\pi$
$74$	9.61885			1.11817
$75$	0.172534	+	1.23284i	0.0199225	+	0.142356i
$76$	−1.00000			−0.114708
$77$	−12.3779	−	17.0367i	−1.41060	−	1.94152i
$78$	0.671592	+	0.218214i	0.0760429	+	0.0247078i
$79$	3.98295	−	12.2583i	0.448117	−	1.37916i	−0.430913	−	0.902394i	$-0.641808\pi$
$79$	3.98295	−	12.2583i	0.448117	−	1.37916i	0.879029	−	0.476767i	$-0.158192\pi$
$80$	0.837043	+	2.07349i	0.0935843	+	0.231823i
$81$	2.60995	+	8.03259i	0.289994	+	0.892510i
$82$			5.65676i			0.624685i
$83$	−6.04282	+	1.96343i	−0.663285	+	0.215514i	−0.621263	−	0.783602i	$-0.713380\pi$
$83$	−6.04282	+	1.96343i	−0.663285	+	0.215514i	−0.0420224	+	0.999117i	$0.513380\pi$
$84$	0.966589	+	0.702268i	0.105463	+	0.0766237i
$85$	9.85999	+	2.46141i	1.06947	+	0.266978i
$86$	−0.703495	+	0.511119i	−0.0758598	+	0.0551154i
$87$	0.498778	−	0.686509i	0.0534746	−	0.0736015i
$88$	2.57936	−	3.55019i	0.274961	−	0.378451i
$89$	9.80091	−	7.12078i	1.03889	−	0.754801i	0.0688250	−	0.997629i	$-0.478075\pi$
$89$	9.80091	−	7.12078i	1.03889	−	0.754801i	0.970069	+	0.242828i	$0.0780750\pi$
$90$	3.48298	−	5.57032i	0.367138	−	0.587164i
$91$	11.0114	+	8.00028i	1.15431	+	0.838657i
$92$	−5.14858	+	1.67287i	−0.536776	+	0.174409i
$93$		−	1.10350i		−	0.114427i
$94$	−3.65267	−	11.2418i	−0.376744	−	1.15950i
$95$	0.541584	−	2.16949i	0.0555654	−	0.222585i
$96$	−0.0769362	+	0.236785i	−0.00785227	+	0.0241668i
$97$	−13.0804	−	4.25008i	−1.32811	−	0.431531i	−0.442841	−	0.896600i	$-0.646029\pi$
$97$	−13.0804	−	4.25008i	−1.32811	−	0.431531i	−0.885274	+	0.465070i	$0.846029\pi$
$98$	9.42149	+	12.9676i	0.951714	+	1.30992i
$99$	−12.8928			−1.29577
$100$	−4.95174	+	0.692988i	−0.495174	+	0.0692988i
$101$	3.59149			0.357366			0.178683	−	0.983907i	$-0.442816\pi$
$101$	3.59149			0.357366			0.178683	+	0.983907i	$0.442816\pi$
$102$	0.665098	+	0.915429i	0.0658545	+	0.0906410i
$103$	−4.45047	−	1.44604i	−0.438518	−	0.142483i	0.0814339	−	0.996679i	$-0.474050\pi$
$103$	−4.45047	−	1.44604i	−0.438518	−	0.142483i	−0.519952	+	0.854196i	$0.674050\pi$
$104$	−0.876462	+	2.69747i	−0.0859442	+	0.264509i
$105$	−2.04705	+	1.71667i	−0.199772	+	0.167530i
$106$	2.63929	+	8.12291i	0.256351	+	0.788966i
$107$			3.68698i			0.356434i	0.983991	+	0.178217i	$0.0570328\pi$
$107$			3.68698i			0.356434i	−0.983991	+	0.178217i	$0.942967\pi$
$108$	1.40603	−	0.456848i	0.135296	−	0.0439603i
$109$	11.8357	+	8.59913i	1.13365	+	0.823647i	0.986222	−	0.165425i	$-0.0528996\pi$
$109$	11.8357	+	8.59913i	1.13365	+	0.823647i	0.147431	+	0.989072i	$0.452900\pi$
$110$	6.30515	+	7.51862i	0.601173	+	0.716872i
$111$	−1.93744	+	1.40764i	−0.183894	+	0.133607i
$112$	−2.82068	+	3.88234i	−0.266530	+	0.366846i
$113$	−1.79174	+	2.46611i	−0.168552	+	0.231993i	−0.884934	−	0.465716i	$-0.845797\pi$
$113$	−1.79174	+	2.46611i	−0.168552	+	0.231993i	0.716382	+	0.697708i	$0.245797\pi$
$114$	0.201422	−	0.146341i	0.0188649	−	0.0137061i
$115$	−0.840895	−	12.0758i	−0.0784139	−	1.12607i
$116$	2.75739	+	2.00336i	0.256017	+	0.186007i
$117$	7.92521	−	2.57506i	0.732686	−	0.238064i
$118$			8.18111i			0.753132i
$119$	6.73964	+	20.7425i	0.617822	+	1.90146i
$120$	−0.472036	−	0.295152i	−0.0430908	−	0.0269435i
$121$	2.55153	−	7.85280i	0.231957	−	0.713891i
$122$	11.4129	+	3.70826i	1.03327	+	0.335730i
$123$	−0.827818	−	1.13939i	−0.0746419	−	0.102736i
$124$	4.43223			0.398026
$125$	1.17836	−	11.1181i	0.105395	−	0.994430i
$126$	14.0990			1.25604
$127$	2.35350	+	3.23932i	0.208840	+	0.287443i	0.900568	−	0.434714i	$-0.143151\pi$
$127$	2.35350	+	3.23932i	0.208840	+	0.287443i	−0.691729	+	0.722157i	$0.743151\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	0.0669012	−	0.205901i	0.00589032	−	0.0181286i
$130$	−5.37746	−	3.36239i	−0.471635	−	0.294901i
$131$	−2.32165	−	7.14531i	−0.202844	−	0.624289i	−0.999795	−	0.0202452i	$-0.993555\pi$
$131$	−2.32165	−	7.14531i	−0.202844	−	0.624289i	0.796951	−	0.604043i	$-0.206445\pi$
$132$			1.09255i			0.0950944i
$133$	4.56396	−	1.48292i	0.395746	−	0.128586i
$134$	−0.160888	−	0.116892i	−0.0138986	−	0.0100979i
$135$	0.229642	+	3.29780i	0.0197644	+	0.283829i
$136$	−3.67685	+	2.67139i	−0.315288	+	0.229070i
$137$	0.0957509	−	0.131790i	0.00818055	−	0.0112596i	−0.804907	−	0.593401i	$-0.797785\pi$
$137$	0.0957509	−	0.131790i	0.00818055	−	0.0112596i	0.813088	+	0.582141i	$0.197785\pi$
$138$	0.792224	−	1.09040i	0.0674386	−	0.0928213i
$139$	−9.93211	+	7.21610i	−0.842431	+	0.612062i	−0.923049	−	0.384683i	$-0.874311\pi$
$139$	−9.93211	+	7.21610i	−0.842431	+	0.612062i	0.0806178	+	0.996745i	$0.474311\pi$
$140$	−6.89505	−	8.22206i	−0.582738	−	0.694891i
$141$	2.38086	+	1.72980i	0.200505	+	0.145675i
$142$	−7.22354	+	2.34707i	−0.606186	+	0.196962i
$143$			12.4464i			1.04082i
$144$	0.907896	+	2.79422i	0.0756580	+	0.232851i
$145$	−5.83962	+	4.89713i	−0.484954	+	0.406685i
$146$	2.09101	−	6.43546i	0.173053	−	0.532602i
$147$	−3.79538	−	1.23320i	−0.313038	−	0.101712i
$148$	−5.65382	−	7.78181i	−0.464741	−	0.639661i
$149$	23.4752			1.92316			0.961581	−	0.274522i	$-0.0885196\pi$
$149$	23.4752			1.92316			0.961581	+	0.274522i	$0.0885196\pi$
$150$	0.895976	−	0.864228i	0.0731561	−	0.0705639i
$151$	−19.1564			−1.55892			−0.779461	−	0.626450i	$-0.784507\pi$
$151$	−19.1564			−1.55892			−0.779461	+	0.626450i	$0.784507\pi$
$152$	0.587785	+	0.809017i	0.0476757	+	0.0656199i
$153$	12.6993	+	4.12624i	1.02668	+	0.333587i
$154$	−6.50746	+	20.0279i	−0.524386	+	1.61389i
$155$	−2.40042	+	9.61567i	−0.192807	+	0.772349i
$156$	−0.218214	−	0.671592i	−0.0174711	−	0.0537704i
$157$		−	17.2580i		−	1.37734i	−0.725075	−	0.688670i	$-0.758195\pi$
$157$		−	17.2580i		−	1.37734i	0.725075	−	0.688670i	$-0.241805\pi$
$158$	−12.2583	+	3.98295i	−0.975214	+	0.316866i
$159$	−1.72033	−	1.24989i	−0.136431	−	0.0991228i
$160$	1.18549	−	1.89595i	0.0937209	−	0.149888i
$161$	21.0172	−	15.2699i	1.65638	−	1.20343i
$162$	4.96441	−	6.83293i	0.390041	−	0.536846i
$163$	−8.47583	+	11.6660i	−0.663878	+	0.913750i	−0.999602	−	0.0282102i	$-0.991019\pi$
$163$	−8.47583	+	11.6660i	−0.663878	+	0.913750i	0.335724	+	0.941961i	$0.391019\pi$
$164$	4.57642	−	3.32496i	0.357358	−	0.259636i
$165$	−2.37028	−	0.591709i	−0.184526	−	0.0460645i
$166$	5.14033	+	3.73467i	0.398967	+	0.289866i
$167$	10.0889	−	3.27808i	0.780702	−	0.253665i	0.108562	−	0.994090i	$-0.465375\pi$
$167$	10.0889	−	3.27808i	0.780702	−	0.253665i	0.672140	+	0.740424i	$0.265375\pi$
$168$		−	1.19477i		−	0.0921785i
$169$	1.53132	+	4.71291i	0.117794	+	0.362532i
$170$	−3.80423	−	9.42368i	−0.291771	−	0.722763i
$171$	0.907896	−	2.79422i	0.0694286	−	0.213679i
$172$	0.827008	+	0.268711i	0.0630587	+	0.0204890i
$173$	−8.99485	−	12.3803i	−0.683866	−	0.941261i	0.316106	−	0.948724i	$-0.397624\pi$
$173$	−8.99485	−	12.3803i	−0.683866	−	0.941261i	−0.999972	+	0.00746325i	$0.997624\pi$
$174$	−0.848572			−0.0643300
$175$	21.5719	−	10.5058i	1.63068	−	0.794165i
$176$	−4.38827			−0.330778
$177$	−1.19723	−	1.64785i	−0.0899897	−	0.123860i
$178$	−11.5217	−	3.74361i	−0.863585	−	0.280596i
$179$	7.42163	−	22.8414i	0.554719	−	1.70725i	−0.141966	−	0.989872i	$-0.545342\pi$
$179$	7.42163	−	22.8414i	0.554719	−	1.70725i	0.696685	−	0.717377i	$-0.254658\pi$
$180$	−6.55373	+	0.456368i	−0.488486	+	0.0340156i
$181$	1.33598	+	4.11172i	0.0993026	+	0.305622i	0.988351	−	0.152191i	$-0.0486329\pi$
$181$	1.33598	+	4.11172i	0.0993026	+	0.305622i	−0.889049	+	0.457813i	$0.848633\pi$
$182$		−	13.6109i		−	1.00891i
$183$	−2.84147	+	0.923249i	−0.210047	+	0.0682485i
$184$	4.37964	+	3.18200i	0.322871	+	0.234580i
$185$	19.9446	−	8.05139i	1.46635	−	0.591950i
$186$	−0.892747	+	0.648618i	−0.0654594	+	0.0475590i
$187$	−11.7228	+	16.1350i	−0.857255	+	1.17991i
$188$	−6.94779	+	9.56282i	−0.506720	+	0.697440i
$189$	−5.73962	+	4.17008i	−0.417496	+	0.303328i
$190$	−2.07349	+	0.837043i	−0.150427	+	0.0607255i
$191$	3.46396	+	2.51671i	0.250643	+	0.182103i	0.706012	−	0.708200i	$-0.250493\pi$
$191$	3.46396	+	2.51671i	0.250643	+	0.182103i	−0.455369	+	0.890303i	$0.650493\pi$
$192$	0.236785	−	0.0769362i	0.0170885	−	0.00555239i
$193$		−	20.9381i		−	1.50716i	−0.657357	−	0.753580i	$-0.728326\pi$
$193$		−	20.9381i		−	1.50716i	0.657357	−	0.753580i	$-0.271674\pi$
$194$	4.25008	+	13.0804i	0.305138	+	0.939119i
$195$	1.57519	−	0.109688i	0.112802	−	0.00785494i
$196$	4.95317	−	15.2443i	0.353798	−	1.08888i
$197$	9.79927	+	3.18397i	0.698169	+	0.226849i	0.636533	−	0.771250i	$-0.280368\pi$
$197$	9.79927	+	3.18397i	0.698169	+	0.226849i	0.0616363	+	0.998099i	$0.480368\pi$
$198$	7.57820	+	10.4305i	0.538559	+	0.741263i
$199$	2.48537			0.176183			0.0880917	−	0.996112i	$-0.471923\pi$
$199$	2.48537			0.176183			0.0880917	+	0.996112i	$0.471923\pi$
$200$	3.47120	+	3.59872i	0.245451	+	0.254468i
$201$	0.0495125			0.00349234
$202$	−2.11102	−	2.90558i	−0.148531	−	0.204436i
$203$	−15.5554	−	5.05426i	−1.09178	−	0.354740i
$204$	0.349663	−	1.07615i	0.0244813	−	0.0753457i
$205$	4.73495	+	11.7292i	0.330704	+	0.819205i
$206$	1.44604	+	4.45047i	0.100751	+	0.310079i
$207$		−	15.9050i		−	1.10548i
$208$	2.69747	−	0.876462i	0.187036	−	0.0607717i
$209$	3.55019	+	2.57936i	0.245571	+	0.178418i
$210$	2.59204	+	0.647068i	0.178868	+	0.0446520i
$211$	2.89411	−	2.10270i	0.199239	−	0.144756i	−0.483693	−	0.875238i	$-0.660705\pi$
$211$	2.89411	−	2.10270i	0.199239	−	0.144756i	0.682932	+	0.730482i	$0.260705\pi$
$212$	5.02023	−	6.90976i	0.344791	−	0.474564i
$213$	1.11150	−	1.52985i	0.0761590	−	0.104824i
$214$	2.98283	−	2.16715i	0.203902	−	0.148143i
$215$	−1.03086	+	1.64866i	−0.0703041	+	0.112437i
$216$	−1.19604	−	0.868977i	−0.0813805	−	0.0591264i
$217$	−20.2285	+	6.57264i	−1.37320	+	0.446180i
$218$		−	14.6297i		−	0.990849i
$219$	0.520600	+	1.60224i	0.0351789	+	0.108269i
$220$	2.37662	−	9.52031i	0.160232	−	0.641859i
$221$	3.98338	−	12.2596i	0.267951	−	0.824669i
$222$	2.27760	+	0.740038i	0.152863	+	0.0496681i
$223$	6.98465	+	9.61354i	0.467727	+	0.643770i	0.976089	−	0.217373i	$-0.0697488\pi$
$223$	6.98465	+	9.61354i	0.467727	+	0.643770i	−0.508362	+	0.861143i	$0.669749\pi$
$224$	4.79883			0.320636
$225$	2.55931	−	14.4654i	0.170621	−	0.964361i
$226$	3.04829			0.202769
$227$	−8.87039	−	12.2090i	−0.588748	−	0.810342i	0.405872	−	0.913930i	$-0.366968\pi$
$227$	−8.87039	−	12.2090i	−0.588748	−	0.810342i	−0.994620	+	0.103587i	$0.966968\pi$
$228$	−0.236785	−	0.0769362i	−0.0156815	−	0.00509523i
$229$	−3.68205	+	11.3322i	−0.243317	+	0.748852i	0.752592	+	0.658487i	$0.228803\pi$
$229$	−3.68205	+	11.3322i	−0.243317	+	0.748852i	−0.995909	+	0.0903648i	$0.971197\pi$
$230$	−9.27525	+	7.77827i	−0.611592	+	0.512884i
$231$	−1.62017	−	4.98636i	−0.106599	−	0.328079i
$232$		−	3.40832i		−	0.223767i
$233$	−24.3235	+	7.90320i	−1.59349	+	0.517756i	−0.965486	−	0.260455i	$-0.916127\pi$
$233$	−24.3235	+	7.90320i	−1.59349	+	0.517756i	−0.628003	+	0.778211i	$0.716127\pi$
$234$	−6.74159	−	4.89805i	−0.440711	−	0.320196i
$235$	−16.9836	−	20.2522i	−1.10789	−	1.32111i
$236$	6.61866	−	4.80874i	0.430838	−	0.313022i
$237$	1.88621	−	2.59614i	0.122522	−	0.168638i
$238$	12.8196	−	17.6446i	0.830968	−	1.14373i
$239$	−3.99344	+	2.90141i	−0.258314	+	0.187676i	−0.709404	−	0.704803i	$-0.751036\pi$
$239$	−3.99344	+	2.90141i	−0.258314	+	0.187676i	0.451089	+	0.892479i	$0.351036\pi$
$240$	0.0386732	+	0.555371i	0.00249634	+	0.0358490i
$241$	−24.0608	−	17.4812i	−1.54990	−	1.12606i	−0.943726	−	0.330730i	$-0.892705\pi$
$241$	−24.0608	−	17.4812i	−1.54990	−	1.12606i	−0.606170	−	0.795335i	$-0.707295\pi$
$242$	−7.85280	+	2.55153i	−0.504797	+	0.164018i
$243$			6.53798i			0.419411i
$244$	−3.70826	−	11.4129i	−0.237397	−	0.730633i
$245$	30.3898	+	19.0019i	1.94153	+	1.21399i
$246$	−0.435210	+	1.33944i	−0.0277480	+	0.0853995i
$247$	−2.69747	−	0.876462i	−0.171636	−	0.0557680i
$248$	−2.60520	−	3.58575i	−0.165430	−	0.227695i
$249$	−1.58191			−0.100249
$250$	−9.68733	+	5.58173i	−0.612680	+	0.353019i
$251$	−19.2742			−1.21657			−0.608287	−	0.793717i	$-0.708143\pi$
$251$	−19.2742			−1.21657			−0.608287	+	0.793717i	$0.708143\pi$
$252$	−8.28721	−	11.4064i	−0.522045	−	0.718533i
$253$	22.5933	+	7.34102i	1.42043	+	0.461526i
$254$	1.23731	−	3.80805i	0.0776357	−	0.238938i
$255$	2.14533	+	1.34142i	0.134346	+	0.0840028i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	29.7840i		−	1.85787i	−0.370237	−	0.928937i	$-0.620724\pi$
$257$		−	29.7840i		−	1.85787i	0.370237	−	0.928937i	$-0.379276\pi$
$258$	−0.205901	+	0.0669012i	−0.0128188	+	0.00416509i
$259$	37.3436	+	27.1317i	2.32042	+	1.68588i
$260$	0.440567	+	6.32682i	0.0273228	+	0.392373i
$261$	−8.10124	+	5.88589i	−0.501454	+	0.364328i
$262$	−4.41604	+	6.07816i	−0.272824	+	0.375510i
$263$	11.5152	−	15.8494i	0.710059	−	0.977313i	−0.289736	−	0.957106i	$-0.593568\pi$
$263$	11.5152	−	15.8494i	0.710059	−	0.977313i	0.999796	−	0.0202064i	$-0.00643235\pi$
$264$	0.883893	−	0.642186i	0.0543998	−	0.0395238i
$265$	12.2718	+	14.6336i	0.753849	+	0.898932i
$266$	−3.88234	−	2.82068i	−0.238041	−	0.172947i
$267$	2.86856	−	0.932051i	0.175553	−	0.0570406i
$268$			0.198869i			0.0121478i
$269$	−3.08636	−	9.49883i	−0.188179	−	0.579154i	0.811810	−	0.583922i	$-0.198482\pi$
$269$	−3.08636	−	9.49883i	−0.188179	−	0.579154i	−0.999989	+	0.00476757i	$0.998482\pi$
$270$	2.53300	−	2.12418i	0.154153	−	0.129274i
$271$	8.63326	−	26.5704i	0.524433	−	1.61404i	−0.241001	−	0.970525i	$-0.577476\pi$
$271$	8.63326	−	26.5704i	0.524433	−	1.61404i	0.765434	−	0.643515i	$-0.222524\pi$
$272$	4.32240	+	1.40443i	0.262084	+	0.0851563i
$273$	1.99184	+	2.74153i	0.120551	+	0.165925i
$274$	−0.162901			−0.00984122
$275$	19.3671	+	10.3121i	1.16788	+	0.621843i
$276$	−1.34781			−0.0811288
$277$	2.59629	+	3.57349i	0.155996	+	0.214710i	0.879860	−	0.475232i	$-0.157636\pi$
$277$	2.59629	+	3.57349i	0.155996	+	0.214710i	−0.723864	+	0.689942i	$0.757636\pi$
$278$	11.6759	+	3.79373i	0.700274	+	0.227533i
$279$	−4.02400	+	12.3846i	−0.240911	+	0.741447i
$280$	−2.59897	+	10.4110i	−0.155318	+	0.622177i
$281$	−4.25522	−	13.0962i	−0.253845	−	0.781256i	−0.994055	−	0.108880i	$-0.965274\pi$
$281$	−4.25522	−	13.0962i	−0.253845	−	0.781256i	0.740210	−	0.672376i	$-0.234726\pi$
$282$		−	2.94291i		−	0.175248i
$283$	−5.47917	+	1.78029i	−0.325703	+	0.105827i	−0.467305	−	0.884096i	$-0.654775\pi$
$283$	−5.47917	+	1.78029i	−0.325703	+	0.105827i	0.141601	+	0.989924i	$0.454775\pi$
$284$	6.14471	+	4.46439i	0.364621	+	0.264913i
$285$	0.295152	−	0.472036i	0.0174833	−	0.0279610i
$286$	10.0694	−	7.31582i	0.595414	−	0.432593i
$287$	−15.9559	+	21.9615i	−0.941849	+	1.29634i
$288$	1.72692	−	2.37690i	0.101760	−	0.140060i
$289$	2.95742	−	2.14869i	0.173966	−	0.126394i
$290$	7.39431	+	1.84589i	0.434209	+	0.108394i
$291$	−2.77027	−	2.01272i	−0.162396	−	0.117987i
$292$	−6.43546	+	2.09101i	−0.376607	+	0.122367i
$293$			20.2384i			1.18234i	0.806548	+	0.591169i	$0.201333\pi$
$293$			20.2384i			1.18234i	−0.806548	+	0.591169i	$0.798667\pi$
$294$	1.23320	+	3.79538i	0.0719214	+	0.221351i
$295$	6.84794	+	16.9634i	0.398703	+	0.987650i
$296$	−2.97239	+	9.14807i	−0.172767	+	0.531721i
$297$	−6.17006	−	2.00477i	−0.358023	−	0.116329i
$298$	−13.7984	−	18.9918i	−0.799318	−	1.10017i
$299$	−15.3544			−0.887966
$300$	−1.22582	−	0.216879i	−0.0707725	−	0.0125215i
$301$	−4.17291			−0.240522
$302$	11.2598	+	15.4978i	0.647930	+	0.891800i
$303$	0.850412	+	0.276316i	0.0488549	+	0.0158739i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	26.7684	−	1.86401i	1.53275	−	0.106733i
$306$	−4.12624	−	12.6993i	−0.235882	−	0.725969i
$307$		−	20.0912i		−	1.14667i	−0.819322	−	0.573333i	$-0.805650\pi$
$307$		−	20.0912i		−	1.14667i	0.819322	−	0.573333i	$-0.194350\pi$
$308$	20.0279	−	6.50746i	1.14120	−	0.370797i
$309$	−0.942553	−	0.684805i	−0.0536199	−	0.0389572i
$310$	9.19018	−	3.70997i	0.521967	−	0.210712i
$311$	19.0151	−	13.8153i	1.07825	−	0.783394i	0.100873	−	0.994899i	$-0.467836\pi$
$311$	19.0151	−	13.8153i	1.07825	−	0.783394i	0.977377	+	0.211505i	$0.0678365\pi$
$312$	−0.415067	+	0.571291i	−0.0234985	+	0.0323430i
$313$	−1.82998	+	2.51875i	−0.103437	+	0.142368i	−0.857598	−	0.514321i	$-0.828044\pi$
$313$	−1.82998	+	2.51875i	−0.103437	+	0.142368i	0.754161	+	0.656690i	$0.228044\pi$
$314$	−13.9620	+	10.1440i	−0.787923	+	0.572459i
$315$	29.2342	−	11.8015i	1.64716	−	0.664939i
$316$	10.4275	+	7.57602i	0.586592	+	0.426184i
$317$	2.24068	−	0.728042i	0.125849	−	0.0408909i	−0.245415	−	0.969418i	$-0.578924\pi$
$317$	2.24068	−	0.728042i	0.125849	−	0.0408909i	0.371265	+	0.928527i	$0.378924\pi$
$318$			2.12644i			0.119245i
$319$	−4.62185	−	14.2246i	−0.258774	−	0.796424i
$320$	−2.23067	+	0.155332i	−0.124698	+	0.00868333i
$321$	−0.283662	+	0.873022i	−0.0158325	+	0.0487273i
$322$	−24.7072	−	8.02784i	−1.37688	−	0.447374i
$323$	−2.67139	−	3.67685i	−0.148640	−	0.204586i
$324$	−8.44596			−0.469220
$325$	−13.9646	−	2.47070i	−0.774615	−	0.137050i
$326$	14.4199			0.798647
$327$	2.14093	+	2.94674i	0.118394	+	0.162955i
$328$	−5.37990	−	1.74804i	−0.297055	−	0.0965191i
$329$	17.5286	−	53.9474i	0.966381	−	2.97421i
$330$	0.914513	+	2.26539i	0.0503423	+	0.124706i
$331$	3.03855	+	9.35171i	0.167014	+	0.514016i	0.999179	−	0.0405117i	$-0.0128988\pi$
$331$	3.03855	+	9.35171i	0.167014	+	0.514016i	−0.832165	+	0.554528i	$0.812899\pi$
$332$		−	6.35379i		−	0.348710i
$333$	26.8772	−	8.73292i	1.47286	−	0.478561i
$334$	−8.58212	−	6.23528i	−0.469593	−	0.341179i
$335$	−0.431443	−	0.107704i	−0.0235723	−	0.00588450i
$336$	−0.966589	+	0.702268i	−0.0527317	+	0.0383119i
$337$	6.11905	−	8.42215i	0.333326	−	0.458784i	−0.609151	−	0.793054i	$-0.708490\pi$
$337$	6.11905	−	8.42215i	0.333326	−	0.458784i	0.942477	+	0.334270i	$0.108490\pi$
$338$	2.91274	−	4.00904i	0.158432	−	0.218063i
$339$	−0.613991	+	0.446090i	−0.0333474	+	0.0242283i
$340$	−5.38785	+	8.61679i	−0.292197	+	0.467311i
$341$	−15.7352	−	11.4323i	−0.852111	−	0.619095i
$342$	−2.79422	+	0.907896i	−0.151094	+	0.0490934i
$343$			43.3277i			2.33948i
$344$	−0.268711	−	0.827008i	−0.0144879	−	0.0445893i
$345$	0.729954	−	2.92406i	0.0392994	−	0.157426i
$346$	−4.72887	+	14.5540i	−0.254226	+	0.782426i
$347$	12.9006	+	4.19165i	0.692540	+	0.225020i	0.634077	−	0.773270i	$-0.281380\pi$
$347$	12.9006	+	4.19165i	0.692540	+	0.225020i	0.0584625	+	0.998290i	$0.481380\pi$
$348$	0.498778	+	0.686509i	0.0267373	+	0.0368007i
$349$	2.78485			0.149069			0.0745347	−	0.997218i	$-0.476253\pi$
$349$	2.78485			0.149069			0.0745347	+	0.997218i	$0.476253\pi$
$350$	−21.1790	−	11.2769i	−1.13207	−	0.602775i
$351$	4.19315			0.223814
$352$	2.57936	+	3.55019i	0.137480	+	0.189226i
$353$	3.58214	+	1.16391i	0.190658	+	0.0619485i	0.402790	−	0.915293i	$-0.368041\pi$
$353$	3.58214	+	1.16391i	0.190658	+	0.0619485i	−0.212132	+	0.977241i	$0.568041\pi$
$354$	−0.629424	+	1.93717i	−0.0334535	+	0.102959i
$355$	−13.0133	+	10.9130i	−0.690676	+	0.579204i
$356$	3.74361	+	11.5217i	0.198411	+	0.610647i
$357$			5.43004i			0.287388i
$358$	−22.8414	+	7.42163i	−1.20721	+	0.392245i
$359$	17.4210	+	12.6571i	0.919443	+	0.668015i	0.943385	−	0.331699i	$-0.107622\pi$
$359$	17.4210	+	12.6571i	0.919443	+	0.668015i	−0.0239419	+	0.999713i	$0.507622\pi$
$360$	4.22139	+	5.03383i	0.222487	+	0.265306i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	2.54118	−	3.49764i	0.133562	−	0.183832i
$363$	1.20833	−	1.66312i	0.0634208	−	0.0872913i
$364$	−11.0114	+	8.00028i	−0.577156	+	0.419329i
$365$	−1.05108	−	15.0941i	−0.0550158	−	0.790062i
$366$	2.41710	+	1.75612i	0.126344	+	0.0917940i
$367$	−13.8768	+	4.50884i	−0.724362	+	0.235360i	−0.647914	−	0.761714i	$-0.724358\pi$
$367$	−13.8768	+	4.50884i	−0.724362	+	0.235360i	−0.0764489	+	0.997074i	$0.524358\pi$
$368$		−	5.41353i		−	0.282200i
$369$	5.13575	+	15.8062i	0.267357	+	0.822839i
$370$	−18.2368	−	11.4030i	−0.948088	−	0.592815i
$371$	−12.6655	+	38.9805i	−0.657561	+	2.02377i
$372$	1.04949	+	0.340999i	0.0544133	+	0.0176800i
$373$	−2.51218	−	3.45772i	−0.130076	−	0.179034i	0.739011	−	0.673693i	$-0.235293\pi$
$373$	−2.51218	−	3.45772i	−0.130076	−	0.179034i	−0.869087	+	0.494659i	$0.835293\pi$
$374$	19.9440			1.03128
$375$	1.13440	−	2.54194i	0.0585802	−	0.131265i
$376$	11.8203			0.609585
$377$	5.68211	+	7.82075i	0.292643	+	0.402789i
$378$	6.74733	+	2.19234i	0.347045	+	0.112762i
$379$	−6.17684	+	19.0104i	−0.317283	+	0.976496i	0.657522	+	0.753436i	$0.271605\pi$
$379$	−6.17684	+	19.0104i	−0.317283	+	0.976496i	−0.974805	+	0.223061i	$0.928395\pi$
$380$	1.89595	+	1.18549i	0.0972601	+	0.0608142i
$381$	0.308054	+	0.948093i	0.0157821	+	0.0485723i
$382$		−	4.28169i		−	0.219070i
$383$	−28.0373	+	9.10987i	−1.43264	+	0.465493i	−0.919595	−	0.392869i	$-0.871483\pi$
$383$	−28.0373	+	9.10987i	−1.43264	+	0.465493i	−0.513045	+	0.858362i	$0.671483\pi$
$384$	−0.201422	−	0.146341i	−0.0102788	−	0.00746795i
$385$	3.27107	+	46.9747i	0.166709	+	2.39405i
$386$	−16.9393	+	12.3071i	−0.862188	+	0.626416i
$387$	−1.50167	+	2.06688i	−0.0763344	+	0.105065i
$388$	8.08414	−	11.1269i	0.410410	−	0.564881i
$389$	11.9386	−	8.67389i	0.605310	−	0.439784i	−0.242450	−	0.970164i	$-0.577951\pi$
$389$	11.9386	−	8.67389i	0.605310	−	0.439784i	0.847760	+	0.530380i	$0.177951\pi$
$390$	−1.01462	−	1.20989i	−0.0513770	−	0.0612649i
$391$	−19.9048	−	14.4617i	−1.00663	−	0.731358i
$392$	−15.2443	+	4.95317i	−0.769953	+	0.250173i
$393$		−	1.87052i		−	0.0943554i
$394$	−3.18397	−	9.79927i	−0.160406	−	0.493680i
$395$	−22.0835	+	18.5193i	−1.11114	+	0.931806i
$396$	3.98409	−	12.2618i	0.200208	−	0.616178i
$397$	−21.2879	−	6.91686i	−1.06841	−	0.347147i	−0.278542	−	0.960424i	$-0.589851\pi$
$397$	−21.2879	−	6.91686i	−1.06841	−	0.347147i	−0.789868	+	0.613277i	$0.789851\pi$
$398$	−1.46087	−	2.01071i	−0.0732266	−	0.100788i
$399$	1.19477			0.0598133
$400$	0.871102	−	4.92353i	0.0435551	−	0.246177i
$401$	2.87526			0.143584			0.0717919	−	0.997420i	$-0.477128\pi$
$401$	2.87526			0.143584			0.0717919	+	0.997420i	$0.477128\pi$
$402$	−0.0291027	−	0.0400564i	−0.00145151	−	0.00199783i
$403$	11.9558	+	3.88468i	0.595562	+	0.193510i
$404$	−1.10983	+	3.41571i	−0.0552162	+	0.169938i
$405$	4.57420	−	18.3234i	0.227294	−	0.910499i
$406$	5.05426	+	15.5554i	0.250839	+	0.772003i
$407$			42.2101i			2.09228i
$408$	−1.07615	+	0.349663i	−0.0532774	+	0.0173109i
$409$	−7.87576	−	5.72208i	−0.389431	−	0.282938i	0.375791	−	0.926704i	$-0.377371\pi$
$409$	−7.87576	−	5.72208i	−0.389431	−	0.282938i	−0.765222	+	0.643766i	$0.777371\pi$
$410$	6.70601	−	10.7249i	0.331186	−	0.529666i
$411$	0.0328118	−	0.0238392i	0.00161849	−	0.00117590i
$412$	2.75054	−	3.78579i	0.135509	−	0.186513i
$413$	−23.0763	+	31.7618i	−1.13551	+	1.56290i
$414$	−12.8674	+	9.34875i	−0.632400	+	0.459466i
$415$	13.7845	+	3.44111i	0.676654	+	0.168918i
$416$	−2.29461	−	1.66713i	−0.112502	−	0.0817378i
$417$	−2.90696	+	0.944528i	−0.142354	+	0.0462537i
$418$		−	4.38827i		−	0.214637i
$419$	−9.97810	−	30.7094i	−0.487462	−	1.50025i	−0.828383	−	0.560162i	$-0.810739\pi$
$419$	−9.97810	−	30.7094i	−0.487462	−	1.50025i	0.340921	−	0.940092i	$-0.389261\pi$
$420$	−1.00007	−	2.47734i	−0.0487986	−	0.120882i
$421$	0.875804	−	2.69545i	0.0426841	−	0.131368i	−0.927444	−	0.373963i	$-0.877999\pi$
$421$	0.875804	−	2.69545i	0.0426841	−	0.131368i	0.970128	+	0.242595i	$0.0779986\pi$
$422$	−3.40223	−	1.10545i	−0.165618	−	0.0538126i
$423$	−20.4127	−	28.0957i	−0.992500	−	1.36606i
$424$	−8.54093			−0.414784
$425$	−15.7761	−	16.3556i	−0.765251	−	0.793363i
$426$	−1.89100			−0.0916194
$427$	33.8487	+	46.5888i	1.63805	+	2.25459i
$428$	−3.50652	−	1.13934i	−0.169494	−	0.0550720i
$429$	−0.957580	+	2.94713i	−0.0462324	+	0.142289i
$430$	1.93971	−	0.135072i	0.0935413	−	0.00651373i
$431$	−7.62101	−	23.4550i	−0.367091	−	1.12979i	−0.948661	−	0.316294i	$-0.897562\pi$
$431$	−7.62101	−	23.4550i	−0.367091	−	1.12979i	0.581570	−	0.813496i	$-0.302438\pi$
$432$			1.47839i			0.0711292i
$433$	−0.107926	+	0.0350673i	−0.00518660	+	0.00168523i	−0.311609	−	0.950210i	$-0.600868\pi$
$433$	−0.107926	+	0.0350673i	−0.00518660	+	0.00168523i	0.306423	+	0.951896i	$0.400868\pi$
$434$	17.2074	+	12.5019i	0.825982	+	0.600111i
$435$	−1.75950	+	0.710291i	−0.0843618	+	0.0340559i
$436$	−11.8357	+	8.59913i	−0.566827	+	0.411824i
$437$	−3.18200	+	4.37964i	−0.152215	+	0.209507i
$438$	0.990240	−	1.36295i	0.0473155	−	0.0651242i
$439$	4.55310	−	3.30802i	0.217308	−	0.157883i	−0.473806	−	0.880629i	$-0.657120\pi$
$439$	4.55310	−	3.30802i	0.217308	−	0.157883i	0.691114	+	0.722746i	$0.257120\pi$
$440$	−9.09903	+	3.67317i	−0.433779	+	0.175112i
$441$	38.0989	+	27.6805i	1.81423	+	1.31812i
$442$	−12.2596	+	3.98338i	−0.583129	+	0.189470i
$443$			0.549324i			0.0260992i	0.999915	+	0.0130496i	$0.00415393\pi$
$443$			0.549324i			0.0260992i	−0.999915	+	0.0130496i	$0.995846\pi$
$444$	−0.740038	−	2.27760i	−0.0351206	−	0.108090i
$445$	−27.0236	+	1.88178i	−1.28104	+	0.0892051i
$446$	3.67205	−	11.3014i	0.173876	−	0.535137i
$447$	5.55858	+	1.80609i	0.262912	+	0.0854252i
$448$	−2.82068	−	3.88234i	−0.133265	−	0.183423i
$449$	−33.4984			−1.58089			−0.790444	−	0.612534i	$-0.790150\pi$
$449$	−33.4984			−1.58089			−0.790444	+	0.612534i	$0.790150\pi$
$450$	−13.2071	+	6.43203i	−0.622588	+	0.303209i
$451$	−24.8234			−1.16889
$452$	−1.79174	−	2.46611i	−0.0842762	−	0.115996i
$453$	−4.53595	−	1.47382i	−0.213117	−	0.0692460i
$454$	−4.66344	+	14.3526i	−0.218866	+	0.673600i
$455$	−11.3929	−	28.2220i	−0.534108	−	1.32307i
$456$	0.0769362	+	0.236785i	0.00360287	+	0.0110885i
$457$		−	29.1024i		−	1.36135i	−0.732585	−	0.680676i	$-0.761686\pi$
$457$		−	29.1024i		−	1.36135i	0.732585	−	0.680676i	$-0.238314\pi$
$458$	11.3322	−	3.68205i	0.529518	−	0.172051i
$459$	5.43583	+	3.94936i	0.253723	+	0.184340i
$460$	11.7446	+	2.93188i	0.547595	+	0.136700i
$461$	−21.9136	+	15.9212i	−1.02062	+	0.741523i	−0.966410	−	0.257007i	$-0.917264\pi$
$461$	−21.9136	+	15.9212i	−1.02062	+	0.741523i	−0.0542089	+	0.998530i	$0.517264\pi$
$462$	−3.08174	+	4.24165i	−0.143376	+	0.197340i
$463$	−12.5575	+	17.2839i	−0.583597	+	0.803253i	−0.994084	−	0.108614i	$-0.965359\pi$
$463$	−12.5575	+	17.2839i	−0.583597	+	0.803253i	0.410487	+	0.911867i	$0.365359\pi$
$464$	−2.75739	+	2.00336i	−0.128008	+	0.0930036i
$465$	−1.30818	+	2.09217i	−0.0606653	+	0.0970221i
$466$	20.6908	+	15.0328i	0.958485	+	0.696380i
$467$	13.8499	−	4.50011i	0.640898	−	0.208240i	0.0295013	−	0.999565i	$-0.490608\pi$
$467$	13.8499	−	4.50011i	0.640898	−	0.208240i	0.611396	+	0.791324i	$0.290608\pi$
$468$			8.33306i			0.385196i
$469$	−0.294906	−	0.907629i	−0.0136175	−	0.0419104i
$470$	−6.40168	+	25.6440i	−0.295288	+	1.18287i
$471$	1.32777	−	4.08644i	0.0611802	−	0.188293i
$472$	−7.78070	−	2.52810i	−0.358136	−	0.116365i
$473$	−2.24293	−	3.08713i	−0.103130	−	0.141946i
$474$	−3.20901			−0.147395
$475$	−3.59872	+	3.47120i	−0.165120	+	0.159270i
$476$	−21.8099			−0.999657
$477$	14.7495	+	20.3010i	0.675334	+	0.929517i
$478$	4.69457	+	1.52536i	0.214725	+	0.0697683i
$479$	−0.0323029	+	0.0994180i	−0.00147596	+	0.00454252i	−0.951792	−	0.306745i	$-0.900760\pi$
$479$	−0.0323029	+	0.0994180i	−0.00147596	+	0.00454252i	0.950316	+	0.311287i	$0.100760\pi$
$480$	0.426573	−	0.357726i	0.0194703	−	0.0163279i
$481$	−8.43056	−	25.9466i	−0.384400	−	1.18306i
$482$			29.7408i			1.35466i
$483$	6.15136	−	1.99870i	0.279897	−	0.0909440i
$484$	6.67999	+	4.85330i	0.303636	+	0.220604i
$485$	19.7614	+	23.5646i	0.897318	+	1.07001i
$486$	5.28933	−	3.84293i	0.239929	−	0.174319i
$487$	17.6592	−	24.3058i	0.800216	−	1.10140i	−0.192544	−	0.981288i	$-0.561674\pi$
$487$	17.6592	−	24.3058i	0.800216	−	1.10140i	0.992760	−	0.120115i	$-0.0383262\pi$
$488$	−7.05353	+	9.70835i	−0.319298	+	0.439476i
$489$	−2.90449	+	2.11024i	−0.131346	+	0.0954281i
$490$	−2.48979	−	35.7549i	−0.112477	−	1.61524i
$491$	3.75217	+	2.72611i	0.169333	+	0.123028i	0.669224	−	0.743061i	$-0.266627\pi$
$491$	3.75217	+	2.72611i	0.169333	+	0.123028i	−0.499891	+	0.866088i	$0.666627\pi$
$492$	1.33944	−	0.435210i	0.0603865	−	0.0196208i
$493$			15.4903i			0.697646i
$494$	0.876462	+	2.69747i	0.0394339	+	0.121365i
$495$	24.4441	+	15.2842i	1.09868	+	0.686975i
$496$	−1.36963	+	4.21530i	−0.0614984	+	0.189273i
$497$	−34.6646	−	11.2632i	−1.55492	−	0.505223i
$498$	0.929823	+	1.27979i	0.0416664	+	0.0573488i
$499$	−31.1804			−1.39583			−0.697914	−	0.716182i	$-0.745888\pi$
$499$	−31.1804			−1.39583			−0.697914	+	0.716182i	$0.745888\pi$
$500$	10.2098	+	4.55636i	0.456595	+	0.203766i
$501$	2.64110			0.117996
$502$	11.3291	+	15.5931i	0.505641	+	0.695955i
$503$	7.39095	+	2.40147i	0.329546	+	0.107076i	0.469117	−	0.883136i	$-0.344572\pi$
$503$	7.39095	+	2.40147i	0.329546	+	0.107076i	−0.139571	+	0.990212i	$0.544572\pi$
$504$	−4.35684	+	13.4090i	−0.194069	+	0.597283i
$505$	−6.80928	−	4.25766i	−0.303009	−	0.189463i
$506$	−7.34102	−	22.5933i	−0.326348	−	1.00440i
$507$			1.23376i			0.0547933i
$508$	−3.80805	+	1.23731i	−0.168955	+	0.0548967i
$509$	36.1018	+	26.2295i	1.60018	+	1.16260i	0.887160	+	0.461461i	$0.152675\pi$
$509$	36.1018	+	26.2295i	1.60018	+	1.16260i	0.713023	+	0.701140i	$0.247325\pi$
$510$	−0.175763	−	2.52407i	−0.00778293	−	0.111768i
$511$	26.2704	−	19.0866i	1.16213	−	0.844339i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	0.868977	−	1.19604i	0.0383663	−	0.0528067i
$514$	−24.0958	+	17.5066i	−1.06282	+	0.772183i
$515$	6.72359	+	8.01760i	0.296277	+	0.353298i
$516$	0.175150	+	0.127254i	0.00771053	+	0.00560203i
$517$	49.3319	−	16.0289i	2.16961	−	0.704951i
$518$		−	46.1593i		−	2.02812i
$519$	−1.17735	−	3.62352i	−0.0516800	−	0.159055i
$520$	4.85955	−	4.07524i	0.213105	−	0.178711i
$521$	−6.94952	+	21.3884i	−0.304464	+	0.937044i	0.675413	+	0.737440i	$0.263966\pi$
$521$	−6.94952	+	21.3884i	−0.304464	+	0.937044i	−0.979877	+	0.199604i	$0.936034\pi$
$522$	9.52358	+	3.09440i	0.416836	+	0.135438i
$523$	14.0753	+	19.3729i	0.615468	+	0.847119i	0.997013	−	0.0772314i	$-0.0246080\pi$
$523$	14.0753	+	19.3729i	0.615468	+	0.847119i	−0.381545	+	0.924350i	$0.624608\pi$
$524$	7.51302			0.328208
$525$	5.91619	−	0.827961i	0.258204	−	0.0361352i
$526$	−19.5909			−0.854203
$527$	11.8402	+	16.2967i	0.515768	+	0.709893i
$528$	−1.03908	−	0.337617i	−0.0452201	−	0.0146929i
$529$	−1.94877	+	5.99770i	−0.0847291	+	0.260769i
$530$	4.62563	−	18.5295i	0.200925	−	0.804868i
$531$	7.42760	+	22.8598i	0.322330	+	0.992031i
$532$			4.79883i			0.208056i
$533$	15.2590	−	4.95794i	0.660939	−	0.214752i
$534$	−2.44014	−	1.77287i	−0.105595	−	0.0767194i
$535$	4.37086	−	6.99032i	0.188969	−	0.302218i
$536$	0.160888	−	0.116892i	0.00694931	−	0.00504897i
$537$	3.51467	−	4.83752i	0.151669	−	0.208755i
$538$	−5.87060	+	8.08019i	−0.253100	+	0.348362i
$539$	−56.9052	+	41.3441i	−2.45108	+	1.78081i
$540$	−3.20736	−	0.800674i	−0.138023	−	0.0344555i
$541$	6.27237	+	4.55715i	0.269670	+	0.195927i	0.714399	−	0.699738i	$-0.246700\pi$
$541$	6.27237	+	4.55715i	0.269670	+	0.195927i	−0.444729	+	0.895665i	$0.646700\pi$
$542$	−26.5704	+	8.63326i	−1.14130	+	0.370830i
$543$			1.07638i			0.0461919i
$544$	−1.40443	−	4.32240i	−0.0602146	−	0.185321i
$545$	−12.2457	−	30.3346i	−0.524548	−	1.29939i
$546$	1.04717	−	3.22286i	0.0448148	−	0.137926i
$547$	2.31196	+	0.751201i	0.0988522	+	0.0321190i	0.358026	−	0.933712i	$-0.383450\pi$
$547$	2.31196	+	0.751201i	0.0988522	+	0.0321190i	−0.259173	+	0.965831i	$0.583450\pi$
$548$	0.0957509	+	0.131790i	0.00409027	+	0.00562978i
$549$	35.2567			1.50472
$550$	−3.04102	−	21.7296i	−0.129669	−	0.926553i
$551$	3.40832			0.145199
$552$	0.792224	+	1.09040i	0.0337193	+	0.0464106i
$553$	−58.8253	−	19.1135i	−2.50151	−	0.812789i
$554$	1.36495	−	4.20089i	0.0579912	−	0.178479i
$555$	5.34203	−	0.371991i	0.226756	−	0.0157901i
$556$	−3.79373	−	11.6759i	−0.160890	−	0.495168i
$557$		−	19.5624i		−	0.828884i	−0.910076	−	0.414442i	$-0.863977\pi$
$557$		−	19.5624i		−	0.828884i	0.910076	−	0.414442i	$-0.136023\pi$
$558$	12.3846	−	4.02400i	0.524282	−	0.170350i
$559$	1.99532	+	1.44968i	0.0843929	+	0.0613150i
$560$	9.95033	−	4.01683i	0.420478	−	0.169742i
$561$	−4.01715	+	2.91863i	−0.169604	+	0.123225i
$562$	−8.09392	+	11.1403i	−0.341421	+	0.469926i
$563$	5.87815	−	8.09059i	0.247735	−	0.340978i	−0.666982	−	0.745074i	$-0.732414\pi$
$563$	5.87815	−	8.09059i	0.247735	−	0.340978i	0.914716	+	0.404097i	$0.132414\pi$
$564$	−2.38086	+	1.72980i	−0.100252	+	0.0728376i
$565$	6.32059	−	2.55155i	0.265909	−	0.107344i
$566$	4.66086	+	3.38632i	0.195911	+	0.142337i
$567$	38.5471	−	12.5247i	1.61882	−	0.525988i
$568$		−	7.59528i		−	0.318691i
$569$	−1.81467	−	5.58497i	−0.0760748	−	0.234134i	0.905787	−	0.423734i	$-0.139281\pi$
$569$	−1.81467	−	5.58497i	−0.0760748	−	0.234134i	−0.981861	+	0.189600i	$0.939281\pi$
$570$	−0.555371	+	0.0386732i	−0.0232619	+	0.00161984i
$571$	−5.74182	+	17.6715i	−0.240288	+	0.739529i	0.756088	+	0.654470i	$0.227108\pi$
$571$	−5.74182	+	17.6715i	−0.240288	+	0.739529i	−0.996376	+	0.0850595i	$0.972892\pi$
$572$	−11.8372	−	3.84615i	−0.494940	−	0.160816i
$573$	0.626588	+	0.862424i	0.0261761	+	0.0360283i
$574$	27.1459			1.13305
$575$	−12.7214	+	23.8919i	−0.530519	+	0.996363i
$576$	−2.93801			−0.122417
$577$	24.4684	+	33.6779i	1.01863	+	1.40203i	0.913158	+	0.407605i	$0.133636\pi$
$577$	24.4684	+	33.6779i	1.01863	+	1.40203i	0.105474	+	0.994422i	$0.466364\pi$
$578$	−3.47666	−	1.12964i	−0.144610	−	0.0469867i
$579$	1.61090	−	4.95784i	0.0669467	−	0.206041i
$580$	−2.85291	−	7.06711i	−0.118461	−	0.293446i
$581$	9.42217	+	28.9985i	0.390898	+	1.20306i
$582$			3.42424i			0.141939i
$583$	−35.6455	+	11.5819i	−1.47629	+	0.479674i
$584$	5.47433	+	3.97733i	0.226529	+	0.164583i
$585$	−18.0785	−	4.51306i	−0.747454	−	0.186592i
$586$	16.3732	−	11.8958i	0.676370	−	0.491411i
$587$	−13.7373	+	18.9078i	−0.566999	+	0.780407i	−0.992195	−	0.124694i	$-0.960205\pi$
$587$	−13.7373	+	18.9078i	−0.566999	+	0.780407i	0.425197	+	0.905101i	$0.360205\pi$
$588$	2.34568	−	3.22855i	0.0967341	−	0.133143i
$589$	3.58575	−	2.60520i	0.147748	−	0.107345i
$590$	9.69859	−	15.5110i	0.399285	−	0.638576i
$591$	2.07536	+	1.50784i	0.0853689	+	0.0620241i
$592$	9.14807	−	2.97239i	0.375983	−	0.122164i
$593$			9.76773i			0.401113i	0.979682	+	0.200556i	$0.0642750\pi$
$593$			9.76773i			0.401113i	−0.979682	+	0.200556i	$0.935725\pi$
$594$	2.00477	+	6.17006i	0.0822569	+	0.253161i
$595$	11.8119	−	47.3164i	0.484241	−	1.93978i
$596$	−7.25423	+	22.3262i	−0.297145	+	0.914518i
$597$	0.588500	+	0.191215i	0.0240857	+	0.00782592i
$598$	9.02507	+	12.4219i	0.369062	+	0.507971i
$599$	27.1627			1.10984			0.554918	−	0.831905i	$-0.312750\pi$
$599$	27.1627			1.10984			0.554918	+	0.831905i	$0.312750\pi$
$600$	0.545058	+	1.11918i	0.0222519	+	0.0456905i
$601$	0.336634			0.0137316			0.00686579	−	0.999976i	$-0.497815\pi$
$601$	0.336634			0.0137316			0.00686579	+	0.999976i	$0.497815\pi$
$602$	2.45277	+	3.37595i	0.0999676	+	0.137594i
$603$	−0.555682	−	0.180552i	−0.0226291	−	0.00735265i
$604$	5.91964	−	18.2188i	0.240867	−	0.741312i
$605$	−14.1470	+	11.8637i	−0.575155	+	0.482328i
$606$	−0.276316	−	0.850412i	−0.0112246	−	0.0345456i
$607$		−	19.5651i		−	0.794123i	−0.917792	−	0.397061i	$-0.870030\pi$
$607$		−	19.5651i		−	0.794123i	0.917792	−	0.397061i	$-0.129970\pi$
$608$	−0.951057	+	0.309017i	−0.0385704	+	0.0125323i
$609$	−3.29444	−	2.39355i	−0.133497	−	0.0969916i
$610$	−17.2421	−	20.5605i	−0.698112	−	0.832468i
$611$	−27.1229	+	19.7060i	−1.09728	+	0.797218i
$612$	−7.84858	+	10.8026i	−0.317260	+	0.436671i
$613$	7.46972	−	10.2812i	0.301699	−	0.415253i	−0.631071	−	0.775725i	$-0.717384\pi$
$613$	7.46972	−	10.2812i	0.301699	−	0.415253i	0.932770	+	0.360472i	$0.117384\pi$
$614$	−16.2541	+	11.8093i	−0.655964	+	0.476586i
$615$	0.218765	+	3.14160i	0.00882145	+	0.126682i
$616$	−17.0367	−	12.3779i	−0.686430	−	0.498721i
$617$	−13.0457	+	4.23881i	−0.525200	+	0.170648i	−0.559604	−	0.828760i	$-0.689047\pi$
$617$	−13.0457	+	4.23881i	−0.525200	+	0.170648i	0.0344037	+	0.999408i	$0.489047\pi$
$618$			1.16506i			0.0468655i
$619$	−5.01161	−	15.4241i	−0.201433	−	0.619948i	−0.999841	−	0.0178311i	$-0.994324\pi$
$619$	−5.01161	−	15.4241i	−0.201433	−	0.619948i	0.798408	−	0.602117i	$-0.205676\pi$
$620$	−8.40328	−	5.25435i	−0.337484	−	0.211020i
$621$	2.47316	−	7.61162i	0.0992447	−	0.305444i
$622$	−22.3536	−	7.26314i	−0.896299	−	0.291225i
$623$	−34.1714	−	47.0329i	−1.36905	−	1.88433i
$624$	0.706154			0.0282688
$625$	−15.4144	+	19.6824i	−0.616577	+	0.787295i
$626$	3.11335			0.124434
$627$	0.642186	+	0.883893i	0.0256464	+	0.0352993i
$628$	16.4133	+	5.33302i	0.654964	+	0.212811i
$629$	13.5090	−	41.5765i	0.538640	−	1.65776i
$630$	−26.7311	−	16.7142i	−1.06499	−	0.665910i
$631$	−8.44220	−	25.9824i	−0.336079	−	1.03434i	−0.966188	−	0.257838i	$-0.916990\pi$
$631$	−8.44220	−	25.9824i	−0.336079	−	1.03434i	0.630109	−	0.776506i	$-0.283010\pi$
$632$		−	12.8891i		−	0.512700i
$633$	0.847057	−	0.275225i	0.0336675	−	0.0109392i
$634$	−1.90604	−	1.38482i	−0.0756985	−	0.0549982i
$635$	−0.621952	−	8.93163i	−0.0246814	−	0.354441i
$636$	1.72033	−	1.24989i	0.0682154	−	0.0495614i
$637$	26.7221	−	36.7798i	1.05877	−	1.45727i
$638$	−8.79128	+	12.1002i	−0.348050	+	0.479050i
$639$	−18.0532	+	13.1164i	−0.714175	+	0.518879i
$640$	1.43682	+	1.71335i	0.0567953	+	0.0677259i
$641$	4.23572	+	3.07743i	0.167301	+	0.121551i	0.668285	−	0.743905i	$-0.267029\pi$
$641$	4.23572	+	3.07743i	0.167301	+	0.121551i	−0.500984	+	0.865456i	$0.667029\pi$
$642$	0.873022	−	0.283662i	0.0344554	−	0.0111952i
$643$		−	12.9509i		−	0.510736i	−0.966844	−	0.255368i	$-0.917803\pi$
$643$		−	12.9509i		−	0.510736i	0.966844	−	0.255368i	$-0.0821966\pi$
$644$	8.02784	+	24.7072i	0.316341	+	0.973599i
$645$	−0.370934	+	0.311067i	−0.0146055	+	0.0122482i
$646$	−1.40443	+	4.32240i	−0.0552567	+	0.170063i
$647$	−34.2305	−	11.1222i	−1.34574	−	0.437257i	−0.454483	−	0.890756i	$-0.650176\pi$
$647$	−34.2305	−	11.1222i	−1.34574	−	0.437257i	−0.891257	+	0.453498i	$0.850176\pi$
$648$	4.96441	+	6.83293i	0.195021	+	0.268423i
$649$	−35.9009			−1.40923
$650$	6.20933	+	12.7498i	0.243550	+	0.500089i
$651$	−5.29549			−0.207547
$652$	−8.47583	−	11.6660i	−0.331939	−	0.456875i
$653$	−10.2311	−	3.32428i	−0.400374	−	0.130089i	0.101907	−	0.994794i	$-0.467506\pi$
$653$	−10.2311	−	3.32428i	−0.400374	−	0.130089i	−0.502281	+	0.864705i	$0.667506\pi$
$654$	1.12556	−	3.46410i	0.0440127	−	0.135457i
$655$	−4.06894	+	16.2994i	−0.158986	+	0.636871i
$656$	1.74804	+	5.37990i	0.0682493	+	0.210050i
$657$		−	19.8805i		−	0.775612i
$658$	−53.9474	+	17.5286i	−2.10309	+	0.683334i
$659$	22.7237	+	16.5097i	0.885188	+	0.643127i	0.934619	−	0.355651i	$-0.115741\pi$
$659$	22.7237	+	16.5097i	0.885188	+	0.643127i	−0.0494309	+	0.998778i	$0.515741\pi$
$660$	1.29520	−	2.07142i	0.0504158	−	0.0806300i
$661$	31.9971	−	23.2473i	1.24454	−	0.904214i	0.246651	−	0.969104i	$-0.420670\pi$
$661$	31.9971	−	23.2473i	1.24454	−	0.904214i	0.997892	+	0.0648903i	$0.0206697\pi$
$662$	5.77967	−	7.95504i	0.224633	−	0.309181i
$663$	1.88641	−	2.59642i	0.0732622	−	0.100837i
$664$	−5.14033	+	3.73467i	−0.199483	+	0.144933i
$665$	−10.4110	−	2.59897i	−0.403722	−	0.100784i
$666$	−22.8631	−	16.6110i	−0.885926	−	0.643663i
$667$	17.5480	−	5.70168i	0.679461	−	0.220770i
$668$			10.6081i			0.410439i
$669$	0.914232	+	2.81372i	0.0353463	+	0.108785i
$670$	0.166462	+	0.412352i	0.00643097	+	0.0159305i
$671$	−16.2729	+	50.0827i	−0.628206	+	1.93342i
$672$	1.13629	+	0.369204i	0.0438335	+	0.0142424i
$673$	−18.2841	−	25.1659i	−0.704799	−	0.970072i	−0.999893	−	0.0146043i	$-0.995351\pi$
$673$	−18.2841	−	25.1659i	−0.704799	−	0.970072i	0.295095	−	0.955468i	$-0.404649\pi$
$674$	−10.4103			−0.400992
$675$	3.47411	−	6.52470i	0.133718	−	0.251136i
$676$	−4.95545			−0.190594
$677$	5.32979	+	7.33582i	0.204840	+	0.281939i	0.899061	−	0.437824i	$-0.144251\pi$
$677$	5.32979	+	7.33582i	0.204840	+	0.281939i	−0.694220	+	0.719763i	$0.744251\pi$
$678$	0.721789	+	0.234524i	0.0277201	+	0.00900682i
$679$	−20.3954	+	62.7707i	−0.782705	+	2.40892i
$680$	10.1380	−	0.705959i	0.388775	−	0.0270723i
$681$	−1.16106	−	3.57338i	−0.0444919	−	0.136932i
$682$			19.4498i			0.744772i
$683$	26.2778	−	8.53816i	1.00549	−	0.326704i	0.240433	−	0.970666i	$-0.422711\pi$
$683$	26.2778	−	8.53816i	1.00549	−	0.326704i	0.765058	+	0.643962i	$0.222711\pi$
$684$	2.37690	+	1.72692i	0.0908832	+	0.0660305i
$685$	−0.337774	+	0.136355i	−0.0129057	+	0.00520987i
$686$	35.0528	−	25.4674i	1.33832	−	0.972349i
$687$	−1.74371	+	2.40001i	−0.0665267	+	0.0915662i
$688$	−0.511119	+	0.703495i	−0.0194862	+	0.0268205i
$689$	19.5981	−	14.2388i	0.746628	−	0.542457i
$690$	−2.79467	+	1.12818i	−0.106391	+	0.0429490i
$691$	5.80443	+	4.21716i	0.220811	+	0.160428i	0.692692	−	0.721234i	$-0.256425\pi$
$691$	5.80443	+	4.21716i	0.220811	+	0.160428i	−0.471881	+	0.881662i	$0.656425\pi$
$692$	14.5540	−	4.72887i	0.553259	−	0.179765i
$693$			61.8704i			2.35026i
$694$	−4.19165	−	12.9006i	−0.159113	−	0.489699i
$695$	27.3854	−	1.90698i	1.03879	−	0.0723357i
$696$	0.262223	−	0.807039i	0.00993954	−	0.0305908i
$697$	24.4508	+	7.94454i	0.926140	+	0.300921i
$698$	−1.63689	−	2.25299i	−0.0619573	−	0.0852769i
$699$	−6.36750			−0.240841
$700$	3.32553	+	23.7626i	0.125693	+	0.898142i
$701$	26.0949			0.985591			0.492795	−	0.870145i	$-0.335975\pi$
$701$	26.0949			0.985591			0.492795	+	0.870145i	$0.335975\pi$
$702$	−2.46467	−	3.39233i	−0.0930231	−	0.128035i
$703$	−9.14807	−	2.97239i	−0.345026	−	0.112106i
$704$	1.35605	−	4.17349i	0.0511081	−	0.157294i
$705$	−2.46334	−	6.10209i	−0.0927748	−	0.229818i
$706$	−1.16391	−	3.58214i	−0.0438042	−	0.134815i
$707$		−	17.2350i		−	0.648187i
$708$	1.93717	−	0.629424i	0.0728032	−	0.0236552i
$709$	−12.2999	−	8.93643i	−0.461934	−	0.335615i	0.332355	−	0.943154i	$-0.392157\pi$
$709$	−12.2999	−	8.93643i	−0.461934	−	0.335615i	−0.794290	+	0.607539i	$0.792157\pi$
$710$	16.4779	+	4.11348i	0.618404	+	0.154376i
$711$	−30.6361	+	22.2584i	−1.14894	+	0.834757i
$712$	7.12078	−	9.80091i	0.266862	−	0.367305i
$713$	14.1033	−	19.4116i	0.528174	−	0.726969i
$714$	4.39299	−	3.19170i	0.164404	−	0.119446i
$715$	14.7551	−	23.5978i	0.551808	−	0.882506i
$716$	19.4301	+	14.1168i	0.726136	+	0.527569i
$717$	−1.16881	+	0.379770i	−0.0436501	+	0.0141828i
$718$		−	21.5335i		−	0.803623i
$719$	−3.49770	−	10.7648i	−0.130442	−	0.401459i	0.864411	−	0.502785i	$-0.167691\pi$
$719$	−3.49770	−	10.7648i	−0.130442	−	0.401459i	−0.994853	+	0.101326i	$0.967691\pi$
$720$	1.59118	−	6.37399i	0.0592998	−	0.237545i
$721$	−6.93933	+	21.3571i	−0.258434	+	0.795378i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	−4.35232	−	5.99045i	−0.161864	−	0.222787i
$724$	−4.32332			−0.160675
$725$	16.8771	−	2.36192i	0.626800	−	0.0877196i
$726$	−2.05573			−0.0762954
$727$	15.9136	+	21.9031i	0.590202	+	0.812343i	0.994767	−	0.102166i	$-0.0325773\pi$
$727$	15.9136	+	21.9031i	0.590202	+	0.812343i	−0.404566	+	0.914509i	$0.632577\pi$
$728$	12.9447	+	4.20600i	0.479763	+	0.155885i
$729$	7.32683	−	22.5497i	0.271364	−	0.835173i
$730$	−11.5936	+	9.72244i	−0.429098	+	0.359844i
$731$	1.22125	+	3.75862i	0.0451695	+	0.139018i
$732$		−	2.98770i		−	0.110428i
$733$	−4.01862	+	1.30573i	−0.148431	+	0.0482282i	−0.382290	−	0.924042i	$-0.624865\pi$
$733$	−4.01862	+	1.30573i	−0.148431	+	0.0482282i	0.233859	+	0.972271i	$0.424865\pi$
$734$	11.8043	+	8.57633i	0.435705	+	0.316558i
$735$	5.73392	+	6.83745i	0.211499	+	0.252203i
$736$	−4.37964	+	3.18200i	−0.161436	+	0.117290i
$737$	0.512954	−	0.706020i	0.0188949	−	0.0260066i
$738$	9.76878	−	13.4456i	0.359594	−	0.494938i
$739$	31.1007	−	22.5960i	1.14406	−	0.831208i	0.156380	−	0.987697i	$-0.450018\pi$
$739$	31.1007	−	22.5960i	1.14406	−	0.831208i	0.987680	+	0.156489i	$0.0500177\pi$
$740$	1.49412	+	21.4564i	0.0549248	+	0.788755i
$741$	−0.571291	−	0.415067i	−0.0209869	−	0.0152479i
$742$	38.9805	−	12.6655i	1.43102	−	0.464966i
$743$		−	1.22268i		−	0.0448556i	−0.999748	−	0.0224278i	$-0.992860\pi$
$743$		−	1.22268i		−	0.0448556i	0.999748	−	0.0224278i	$-0.00713960\pi$
$744$	−0.340999	−	1.04949i	−0.0125016	−	0.0384760i
$745$	−44.5077	−	27.8295i	−1.63064	−	1.01959i
$746$	−1.32073	+	4.06479i	−0.0483554	+	0.148823i
$747$	17.7539	+	5.76858i	0.649580	+	0.211061i
$748$	−11.7228	−	16.1350i	−0.428627	−	0.589955i
$749$	17.6932			0.646495
$750$	−2.72325	+	0.576365i	−0.0994392	+	0.0210459i
$751$	−36.3725			−1.32725			−0.663626	−	0.748065i	$-0.730983\pi$
$751$	−36.3725			−1.32725			−0.663626	+	0.748065i	$0.730983\pi$
$752$	−6.94779	−	9.56282i	−0.253360	−	0.348720i
$753$	−4.56384	−	1.48288i	−0.166315	−	0.0540392i
$754$	2.98726	−	9.19384i	0.108790	−	0.334820i
$755$	36.3195	+	22.7096i	1.32180	+	0.826487i
$756$	−2.19234	−	6.74733i	−0.0797346	−	0.245398i
$757$			26.4131i			0.959999i	0.877269	+	0.480000i	$0.159363\pi$
$757$			26.4131i			0.959999i	−0.877269	+	0.480000i	$0.840637\pi$
$758$	19.0104	−	6.17684i	0.690487	−	0.224353i
$759$	4.78498	+	3.47649i	0.173684	+	0.126189i
$760$	−0.155332	−	2.23067i	−0.00563449	−	0.0809148i
$761$	−5.79922	+	4.21338i	−0.210221	+	0.152735i	−0.687914	−	0.725792i	$-0.741473\pi$
$761$	−5.79922	+	4.21338i	−0.210221	+	0.152735i	0.477692	+	0.878527i	$0.341473\pi$
$762$	0.585953	−	0.806496i	0.0212269	−	0.0292163i
$763$	41.2658	−	56.7975i	1.49392	−	2.05621i
$764$	−3.46396	+	2.51671i	−0.125322	+	0.0910514i
$765$	−19.1856	−	22.8780i	−0.693655	−	0.827154i
$766$	23.8500	+	17.3280i	0.861734	+	0.626087i
$767$	22.0683	−	7.17043i	0.796841	−	0.258909i
$768$			0.248971i			0.00898396i
$769$	11.8989	+	36.6211i	0.429086	+	1.32059i	0.899027	+	0.437893i	$0.144275\pi$
$769$	11.8989	+	36.6211i	0.429086	+	1.32059i	−0.469941	+	0.882698i	$0.655725\pi$
$770$	36.0806	−	30.2574i	1.30025	−	1.09040i
$771$	2.29147	−	7.05241i	0.0825252	−	0.253986i
$772$	19.9133	+	6.47024i	0.716697	+	0.232869i
$773$	26.6208	+	36.6404i	0.957485	+	1.31787i	0.948121	+	0.317909i	$0.102981\pi$
$773$	26.6208	+	36.6404i	0.957485	+	1.31787i	0.00936383	+	0.999956i	$0.497019\pi$
$774$	2.55480			0.0918304
$775$	15.9503	−	15.3852i	0.572953	−	0.552651i
$776$	−13.7536			−0.493724
$777$	6.75501	+	9.29747i	0.242335	+	0.333545i
$778$	−14.0346	−	4.56013i	−0.503167	−	0.163489i
$779$	1.74804	−	5.37990i	0.0626299	−	0.192755i
$780$	−0.382442	+	1.53199i	−0.0136936	+	0.0548542i
$781$	−10.2996	−	31.6988i	−0.368548	−	1.13427i
$782$			24.6037i			0.879825i
$783$	−4.79221	+	1.55708i	−0.171260	+	0.0556456i
$784$	12.9676	+	9.42149i	0.463128	+	0.336482i
$785$	−20.4591	+	32.7203i	−0.730218	+	1.16784i
$786$	−1.51329	+	1.09947i	−0.0539771	+	0.0392167i
$787$	17.8208	−	24.5282i	0.635242	−	0.874335i	−0.363109	−	0.931747i	$-0.618285\pi$
$787$	17.8208	−	24.5282i	0.635242	−	0.874335i	0.998351	+	0.0574114i	$0.0182847\pi$
$788$	−6.05628	+	8.33575i	−0.215746	+	0.296949i
$789$	3.94603	−	2.86696i	0.140482	−	0.102066i
$790$	27.9627	+	6.98053i	0.994870	+	0.248356i
$791$	11.8345	+	8.59825i	0.420785	+	0.305718i
$792$	−12.2618	+	3.98409i	−0.435703	+	0.141569i
$793$		−	34.0360i		−	1.20865i
$794$	6.91686	+	21.2879i	0.245470	+	0.755480i
$795$	1.77992	+	4.40916i	0.0631274	+	0.156377i
$796$	−0.768023	+	2.36373i	−0.0272218	+	0.0837802i
$797$	−7.30699	−	2.37419i	−0.258827	−	0.0840980i	0.176729	−	0.984260i	$-0.443448\pi$
$797$	−7.30699	−	2.37419i	−0.258827	−	0.0840980i	−0.435556	+	0.900162i	$0.643448\pi$
$798$	−0.702268	−	0.966589i	−0.0248600	−	0.0342169i
$799$	−53.7213			−1.90052
$800$	−4.49524	+	2.18924i	−0.158931	+	0.0774015i
$801$	−35.5928			−1.25761
$802$	−1.69004	−	2.32614i	−0.0596773	−	0.0821388i
$803$	28.2405	+	9.17591i	0.996587	+	0.323811i
$804$	−0.0153002	+	0.0470892i	−0.000539596	+	0.00166071i
$805$	−57.9497	+	4.03532i	−2.04246	+	0.142226i
$806$	−3.88468	−	11.9558i	−0.136832	−	0.421126i
$807$		−	2.48664i		−	0.0875338i
$808$	3.41571	−	1.10983i	0.120164	−	0.0390437i
$809$	−33.4512	−	24.3038i	−1.17608	−	0.854474i	−0.184359	−	0.982859i	$-0.559021\pi$
$809$	−33.4512	−	24.3038i	−1.17608	−	0.854474i	−0.991724	+	0.128385i	$0.959021\pi$
$810$	−17.5126	+	7.06964i	−0.615331	+	0.248402i
$811$	15.7825	−	11.4667i	0.554199	−	0.402649i	−0.275132	−	0.961406i	$-0.588722\pi$
$811$	15.7825	−	11.4667i	0.554199	−	0.402649i	0.829331	+	0.558757i	$0.188722\pi$
$812$	9.61378	−	13.2322i	0.337378	−	0.464360i
$813$	4.08846	−	5.62728i	0.143389	−	0.197357i
$814$	34.1487	−	24.8105i	1.19691	−	0.869607i
$815$	29.8996	−	12.0701i	1.04734	−	0.422798i
$816$	0.915429	+	0.665098i	0.0320464	+	0.0232831i
$817$	0.827008	−	0.268711i	0.0289333	−	0.00940101i
$818$			9.73498i			0.340375i
$819$	−12.3573	−	38.0318i	−0.431798	−	1.32894i
$820$	−12.6183	+	0.878676i	−0.440652	+	0.0306847i
$821$	−13.2336	+	40.7289i	−0.461856	+	1.42145i	0.401037	+	0.916062i	$0.368650\pi$
$821$	−13.2336	+	40.7289i	−0.461856	+	1.42145i	−0.862893	+	0.505386i	$0.831350\pi$
$822$	−0.0385726	−	0.0125330i	−0.00134537	−	0.000437138i
$823$	−14.4830	−	19.9341i	−0.504844	−	0.694859i	0.478195	−	0.878254i	$-0.341291\pi$
$823$	−14.4830	−	19.9341i	−0.504844	−	0.694859i	−0.983039	+	0.183395i	$0.941291\pi$
$824$	−4.67950			−0.163018
$825$	3.79247	+	3.93178i	0.132037	+	0.136887i
$826$	39.2598			1.36602
$827$	−0.477977	−	0.657879i	−0.0166209	−	0.0228767i	0.800626	−	0.599165i	$-0.204501\pi$
$827$	−0.477977	−	0.657879i	−0.0166209	−	0.0228767i	−0.817247	+	0.576288i	$0.804501\pi$
$828$	15.1266	+	4.91493i	0.525685	+	0.170806i
$829$	7.40950	−	22.8041i	0.257343	−	0.792019i	−0.736017	−	0.676964i	$-0.763295\pi$
$829$	7.40950	−	22.8041i	0.257343	−	0.792019i	0.993359	−	0.115055i	$-0.0367045\pi$
$830$	−5.31840	−	13.1745i	−0.184604	−	0.457294i
$831$	0.339833	+	1.04590i	0.0117887	+	0.0362818i
$832$			2.83629i			0.0983307i
$833$	69.2829	−	22.5114i	2.40051	−	0.779973i
$834$	2.47281	+	1.79660i	0.0856263	+	0.0622111i
$835$	−23.0141	−	5.74517i	−0.796437	−	0.198820i
$836$	−3.55019	+	2.57936i	−0.122786	+	0.0892091i
$837$	−3.85150	+	5.30114i	−0.133127	+	0.183234i
$838$	−18.9795	+	26.1230i	−0.655635	+	0.902404i
$839$	−1.36330	+	0.990498i	−0.0470664	+	0.0341958i	−0.611070	−	0.791577i	$-0.709261\pi$
$839$	−1.36330	+	0.990498i	−0.0470664	+	0.0341958i	0.564003	+	0.825773i	$0.309261\pi$
$840$	−1.41638	+	2.26522i	−0.0488699	+	0.0781576i
$841$	14.0634	+	10.2177i	0.484946	+	0.352334i
$842$	−2.69545	+	0.875804i	−0.0928912	+	0.0301822i
$843$		−	3.42838i		−	0.118080i
$844$	1.10545	+	3.40223i	0.0380512	+	0.117110i
$845$	2.68379	−	10.7508i	0.0923253	−	0.369839i
$846$	−10.7316	+	33.0285i	−0.368960	+	1.13554i
$847$	−37.6843	−	12.2444i	−1.29485	−	0.420721i
$848$	5.02023	+	6.90976i	0.172395	+	0.237282i
$849$	−1.43436			−0.0492270
$850$	−3.95902	+	22.3767i	−0.135793	+	0.767514i
$851$	−52.0720			−1.78500
$852$	1.11150	+	1.52985i	0.0380795	+	0.0524119i
$853$	12.5230	+	4.06896i	0.428779	+	0.139319i	0.515453	−	0.856918i	$-0.327624\pi$
$853$	12.5230	+	4.06896i	0.428779	+	0.139319i	−0.0866739	+	0.996237i	$0.527624\pi$
$854$	17.7953	−	54.7684i	0.608943	−	1.87414i
$855$	−5.03383	+	4.22139i	−0.172153	+	0.144369i
$856$	1.13934	+	3.50652i	0.0389418	+	0.119851i
$857$		−	28.3244i		−	0.967544i	−0.875194	−	0.483772i	$-0.839266\pi$
$857$		−	28.3244i		−	0.967544i	0.875194	−	0.483772i	$-0.160734\pi$
$858$	2.94713	−	0.957580i	0.100613	−	0.0326912i
$859$	−8.06981	−	5.86306i	−0.275338	−	0.200045i	0.441543	−	0.897240i	$-0.354431\pi$
$859$	−8.06981	−	5.86306i	−0.275338	−	0.200045i	−0.716882	+	0.697195i	$0.754431\pi$
$860$	−1.24941	−	1.48987i	−0.0426046	−	0.0508041i
$861$	−5.46776	+	3.97256i	−0.186341	+	0.135385i
$862$	−14.4960	+	19.9521i	−0.493736	+	0.679570i
$863$	13.7828	−	18.9705i	0.469174	−	0.645762i	−0.507206	−	0.861825i	$-0.669322\pi$
$863$	13.7828	−	18.9705i	0.469174	−	0.645762i	0.976379	+	0.216063i	$0.0693216\pi$
$864$	1.19604	−	0.868977i	0.0406903	−	0.0295632i
$865$	2.37704	+	34.1358i	0.0808218	+	1.16065i
$866$	0.0918075	+	0.0667021i	0.00311975	+	0.00226663i
$867$	0.865587	−	0.281246i	0.0293969	−	0.00955163i
$868$		−	21.2695i		−	0.721935i
$869$	−17.4783	−	53.7925i	−0.592909	−	1.82479i
$870$	1.60885	+	1.00597i	0.0545451	+	0.0341056i
$871$	−0.174301	+	0.536443i	−0.00590596	+	0.0181767i
$872$	13.9137	+	4.52083i	0.471177	+	0.153095i
$873$	23.7513	+	32.6909i	0.803860	+	1.10642i
$874$	5.41353			0.183116
$875$	−53.3538	−	5.65473i	−1.80369	−	0.191165i
$876$	−1.68470			−0.0569206
$877$	4.86074	+	6.69024i	0.164136	+	0.225913i	0.883160	−	0.469071i	$-0.155411\pi$
$877$	4.86074	+	6.69024i	0.164136	+	0.225913i	−0.719025	+	0.694984i	$0.755411\pi$
$878$	−5.35249	−	1.73913i	−0.180638	−	0.0586928i
$879$	−1.55706	+	4.79215i	−0.0525184	+	0.161635i
$880$	8.31994	+	5.20224i	0.280465	+	0.175367i
$881$	−6.70279	−	20.6291i	−0.225823	−	0.695011i	−0.998207	−	0.0598556i	$-0.980936\pi$
$881$	−6.70279	−	20.6291i	−0.225823	−	0.695011i	0.772384	−	0.635156i	$-0.219064\pi$
$882$		−	47.0928i		−	1.58570i
$883$	9.08765	−	2.95276i	0.305824	−	0.0993681i	−0.152085	−	0.988367i	$-0.548599\pi$
$883$	9.08765	−	2.95276i	0.305824	−	0.0993681i	0.457909	+	0.888999i	$0.348599\pi$
$884$	10.4286	+	7.57684i	0.350753	+	0.254837i
$885$	0.316389	+	4.54355i	0.0106353	+	0.152730i
$886$	0.444412	−	0.322885i	0.0149303	−	0.0108475i
$887$	−12.1991	+	16.7906i	−0.409606	+	0.563774i	−0.963122	−	0.269064i	$-0.913286\pi$
$887$	−12.1991	+	16.7906i	−0.409606	+	0.563774i	0.553516	+	0.832838i	$0.313286\pi$
$888$	−1.40764	+	1.93744i	−0.0472372	+	0.0650164i
$889$	15.5449	−	11.2941i	0.521361	−	0.378791i
$890$	17.4065	+	20.7565i	0.583466	+	0.695759i
$891$	29.9847	+	21.7852i	1.00453	+	0.729831i
$892$	−11.3014	+	3.67205i	−0.378399	+	0.122949i
$893$			11.8203i			0.395551i
$894$	−1.80609	−	5.55858i	−0.0604047	−	0.185907i
$895$	−41.1492	+	34.5079i	−1.37547	+	1.15347i
$896$	−1.48292	+	4.56396i	−0.0495409	+	0.152471i
$897$	−3.63569	−	1.18131i	−0.121392	−	0.0394427i
$898$	19.6899	+	27.1008i	0.657060	+	0.904366i
$899$	−15.1064			−0.503828
$900$	12.9665	+	6.90411i	0.432218	+	0.230137i
$901$	38.8172			1.29319
$902$	14.5908	+	20.0826i	0.485821	+	0.668676i
$903$	−0.988084	−	0.321048i	−0.0328814	−	0.0106838i
$904$	−0.941972	+	2.89909i	−0.0313295	+	0.0964223i
$905$	2.34144	−	9.37940i	0.0778322	−	0.311782i
$906$	1.47382	+	4.53595i	0.0489643	+	0.150697i
$907$		−	19.4443i		−	0.645638i	−0.946461	−	0.322819i	$-0.895370\pi$
$907$		−	19.4443i		−	0.645638i	0.946461	−	0.322819i	$-0.104630\pi$
$908$	14.3526	−	4.66344i	0.476307	−	0.154762i
$909$	−8.53662	−	6.20222i	−0.283142	−	0.205715i
$910$	−16.1355	+	25.8056i	−0.534887	+	0.855446i
$911$	−11.5434	+	8.38675i	−0.382449	+	0.277866i	−0.762354	−	0.647160i	$-0.775957\pi$
$911$	−11.5434	+	8.38675i	−0.382449	+	0.277866i	0.379905	+	0.925025i	$0.375957\pi$
$912$	0.146341	−	0.201422i	0.00484585	−	0.00666974i
$913$	−16.3887	+	22.5571i	−0.542388	+	0.746533i
$914$	−23.5443	+	17.1059i	−0.778777	+	0.565815i
$915$	6.48178	+	1.61809i	0.214281	+	0.0534924i
$916$	−9.63973	−	7.00368i	−0.318506	−	0.231408i
$917$	−34.2892	+	11.1412i	−1.13233	+	0.367916i
$918$		−	6.71906i		−	0.221762i
$919$	−4.08322	−	12.5669i	−0.134693	−	0.414543i	0.860849	−	0.508860i	$-0.169933\pi$
$919$	−4.08322	−	12.5669i	−0.134693	−	0.414543i	−0.995542	+	0.0943177i	$0.969933\pi$
$920$	−4.53136	−	11.2249i	−0.149395	−	0.370074i
$921$	1.54574	−	4.75731i	0.0509340	−	0.156759i
$922$	25.7610	+	8.37025i	0.848393	+	0.275660i
$923$	12.6623	+	17.4282i	0.416785	+	0.573656i
$924$	5.24297			0.172481
$925$	−47.3587	−	8.37900i	−1.55715	−	0.275500i
$926$	21.3641			0.702068
$927$	8.08113	+	11.1227i	0.265419	+	0.365318i
$928$	3.24150	+	1.05323i	0.106408	+	0.0345739i
$929$	1.74529	−	5.37144i	0.0572610	−	0.176231i	−0.918335	−	0.395803i	$-0.870466\pi$
$929$	1.74529	−	5.37144i	0.0572610	−	0.176231i	0.975596	+	0.219572i	$0.0704661\pi$
$930$	2.46153	−	0.171408i	0.0807168	−	0.00562070i
$931$	−4.95317	−	15.2443i	−0.162334	−	0.499612i
$932$		−	25.5753i		−	0.837747i
$933$	5.56540	−	1.80831i	0.182203	−	0.0592014i
$934$	−11.7814	−	8.55972i	−0.385501	−	0.280083i
$935$	41.3537	−	16.6940i	1.35241	−	0.545952i
$936$	6.74159	−	4.89805i	0.220356	−	0.160098i
$937$	7.37428	−	10.1498i	0.240907	−	0.331580i	−0.671394	−	0.741101i	$-0.734304\pi$
$937$	7.37428	−	10.1498i	0.240907	−	0.331580i	0.912301	+	0.409521i	$0.134304\pi$
$938$	−0.560945	+	0.772075i	−0.0183155	+	0.0252091i
$939$	−0.627096	+	0.455612i	−0.0204645	+	0.0148683i
$940$	24.5092	−	9.89410i	0.799404	−	0.322710i
$941$	−29.0871	−	21.1330i	−0.948211	−	0.688916i	0.00217185	−	0.999998i	$-0.499309\pi$
$941$	−29.0871	−	21.1330i	−0.948211	−	0.688916i	−0.950383	+	0.311082i	$0.899309\pi$
$942$	−4.08644	+	1.32777i	−0.133144	+	0.0432610i
$943$		−	30.6231i		−	0.997224i
$944$	2.52810	+	7.78070i	0.0822827	+	0.253240i
$945$	15.8256	−	1.10201i	0.514807	−	0.0358485i
$946$	−1.17918	+	3.62913i	−0.0383383	+	0.117993i
$947$	28.5771	+	9.28526i	0.928630	+	0.301730i	0.734002	−	0.679147i	$-0.237650\pi$
$947$	28.5771	+	9.28526i	0.928630	+	0.301730i	0.194628	+	0.980877i	$0.437650\pi$
$948$	1.88621	+	2.59614i	0.0612612	+	0.0843188i
$949$	−19.1922			−0.623004
$950$	4.92353	+	0.871102i	0.159741	+	0.0282623i
$951$	0.586574			0.0190210
$952$	12.8196	+	17.6446i	0.415484	+	0.571865i
$953$	−20.0750	−	6.52277i	−0.650294	−	0.211293i	−0.0347503	−	0.999396i	$-0.511064\pi$
$953$	−20.0750	−	6.52277i	−0.650294	−	0.211293i	−0.615544	+	0.788103i	$0.711064\pi$
$954$	7.75428	−	23.8652i	0.251054	−	0.772665i
$955$	−3.58396	−	8.87803i	−0.115974	−	0.287286i
$956$	−1.52536	−	4.69457i	−0.0493336	−	0.151833i
$957$		−	3.72376i		−	0.120372i
$958$	0.0994180	−	0.0323029i	0.00321205	−	0.00104366i
$959$	−0.632437	−	0.459492i	−0.0204225	−	0.0148378i
$960$	−0.540140	−	0.134839i	−0.0174329	−	0.00435190i
$961$	9.18668	−	6.67451i	0.296344	−	0.215307i
$962$	−16.0359	+	22.0715i	−0.517017	+	0.711613i
$963$	6.36712	−	8.76359i	0.205178	−	0.282403i
$964$	24.0608	−	17.4812i	0.774948	−	0.563032i
$965$	−24.8219	+	39.6976i	−0.799044	+	1.27791i
$966$	−5.23266	−	3.80175i	−0.168358	−	0.122319i
$967$	−10.8276	+	3.51810i	−0.348192	+	0.113135i	−0.477892	−	0.878419i	$-0.658599\pi$
$967$	−10.8276	+	3.51810i	−0.348192	+	0.113135i	0.129699	+	0.991553i	$0.458599\pi$
$968$		−	8.25692i		−	0.265387i
$969$	−0.349663	−	1.07615i	−0.0112328	−	0.0345710i
$970$	7.44871	−	29.8382i	0.239164	−	0.958047i
$971$	−11.1913	+	34.4433i	−0.359146	+	1.10534i	0.594421	+	0.804154i	$0.297381\pi$
$971$	−11.1913	+	34.4433i	−0.359146	+	1.10534i	−0.953566	+	0.301183i	$0.902619\pi$
$972$	−6.21798	−	2.02035i	−0.199442	−	0.0648026i
$973$	34.6289	+	47.6626i	1.11015	+	1.52799i
$974$	−30.0437			−0.962661
$975$	−3.11652	−	1.65941i	−0.0998085	−	0.0531436i
$976$	12.0002			0.384116
$977$	20.0814	+	27.6397i	0.642461	+	0.884272i	0.998744	−	0.0501061i	$-0.0159560\pi$
$977$	20.0814	+	27.6397i	0.642461	+	0.884272i	−0.356283	+	0.934378i	$0.615956\pi$
$978$	3.41443	+	1.10942i	0.109182	+	0.0354752i
$979$	16.4280	−	50.5602i	0.525041	−	1.61591i
$980$	−27.4629	+	23.0305i	−0.877269	+	0.735682i
$981$	−13.2823	−	40.8786i	−0.424070	−	1.30515i
$982$		−	4.63793i		−	0.148002i
$983$	−1.00953	+	0.328017i	−0.0321991	+	0.0104621i	−0.325072	−	0.945689i	$-0.605389\pi$
$983$	−1.00953	+	0.328017i	−0.0321991	+	0.0104621i	0.292873	+	0.956151i	$0.405389\pi$
$984$	−1.13939	−	0.827818i	−0.0363226	−	0.0263899i
$985$	−14.8043	−	17.6536i	−0.471706	−	0.562489i
$986$	12.5319	−	9.10494i	0.399096	−	0.289961i
$987$	8.30101	−	11.4254i	0.264224	−	0.363673i
$988$	1.66713	−	2.29461i	0.0530385	−	0.0730012i
$989$	3.80839	−	2.76696i	0.121100	−	0.0879842i
$990$	−2.00266	−	28.7595i	−0.0636489	−	0.914038i
$991$	2.45883	+	1.78645i	0.0781074	+	0.0567483i	0.626154	−	0.779700i	$-0.284628\pi$
$991$	2.45883	+	1.78645i	0.0781074	+	0.0567483i	−0.548046	+	0.836448i	$0.684628\pi$
$992$	4.21530	−	1.36963i	0.133836	−	0.0434859i
$993$			2.44812i			0.0776888i
$994$	11.2632	+	34.6646i	0.357247	+	1.09949i
$995$	−4.71214	−	2.94638i	−0.149385	−	0.0934064i
$996$	0.488837	−	1.50449i	0.0154894	−	0.0476714i
$997$	10.9363	+	3.55342i	0.346356	+	0.112538i	0.477029	−	0.878888i	$-0.341714\pi$
$997$	10.9363	+	3.55342i	0.346356	+	0.112538i	−0.130673	+	0.991426i	$0.541714\pi$
$998$	18.3274	+	25.2255i	0.580144	+	0.798499i
$999$	14.2204			0.449915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.7	✓	88
25.9	even	10	inner	950.2.n.a.609.7	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.7	✓	88	1.1	even	1	trivial
950.2.n.a.609.7	yes	88	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.236785 + 0.0769362i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.89595 - 1.18549i) q^{5} +(-0.0769362 - 0.236785i) q^{6} -4.79883i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.37690 - 1.72692i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.236785 + 0.0769362i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.89595 - 1.18549i) q^{5} +(-0.0769362 - 0.236785i) q^{6} -4.79883i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.37690 - 1.72692i) q^{9} +(0.155332 + 2.23067i) q^{10} +(3.55019 - 2.57936i) q^{11} +(-0.146341 + 0.201422i) q^{12} +(-1.66713 + 2.29461i) q^{13} +(-3.88234 + 2.82068i) q^{14} +(-0.357726 - 0.426573i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.32240 + 1.40443i) q^{17} +2.93801i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.71335 - 1.43682i) q^{20} +(0.369204 - 1.13629i) q^{21} +(-4.17349 - 1.35605i) q^{22} +(3.18200 + 4.37964i) q^{23} +0.248971 q^{24} +(2.18924 + 4.49524i) q^{25} +2.83629 q^{26} +(-0.868977 - 1.19604i) q^{27} +(4.56396 + 1.48292i) q^{28} +(1.05323 - 3.24150i) q^{29} +(-0.134839 + 0.540140i) q^{30} +(-1.36963 - 4.21530i) q^{31} +1.00000i q^{32} +(1.03908 - 0.337617i) q^{33} +(3.67685 + 2.67139i) q^{34} +(-5.68895 + 9.09834i) q^{35} +(2.37690 - 1.72692i) q^{36} +(-5.65382 + 7.78181i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-0.571291 + 0.415067i) q^{39} +(-2.16949 - 0.541584i) q^{40} +(-4.57642 - 3.32496i) q^{41} +(-1.13629 + 0.369204i) q^{42} -0.869567i q^{43} +(1.35605 + 4.17349i) q^{44} +(2.45924 + 6.09194i) q^{45} +(1.67287 - 5.14858i) q^{46} +(11.2418 + 3.65267i) q^{47} +(-0.146341 - 0.201422i) q^{48} -16.0288 q^{49} +(2.34992 - 4.41337i) q^{50} -1.13153 q^{51} +(-1.66713 - 2.29461i) q^{52} +(-8.12291 - 2.63929i) q^{53} +(-0.456848 + 1.40603i) q^{54} +(-9.78877 + 0.681639i) q^{55} +(-1.48292 - 4.56396i) q^{56} +0.248971i q^{57} +(-3.24150 + 1.05323i) q^{58} +(-6.61866 - 4.80874i) q^{59} +(0.516238 - 0.208399i) q^{60} +(-9.70835 + 7.05353i) q^{61} +(-2.60520 + 3.58575i) q^{62} +(-8.28721 + 11.4064i) q^{63} +(0.809017 - 0.587785i) q^{64} +(5.88102 - 2.37410i) q^{65} +(-0.883893 - 0.642186i) q^{66} +(0.189135 - 0.0614538i) q^{67} -4.54484i q^{68} +(0.416497 + 1.28185i) q^{69} +(10.7046 - 0.745413i) q^{70} +(2.34707 - 7.22354i) q^{71} +(-2.79422 - 0.907896i) q^{72} +(3.97733 + 5.47433i) q^{73} +9.61885 q^{74} +(0.172534 + 1.23284i) q^{75} -1.00000 q^{76} +(-12.3779 - 17.0367i) q^{77} +(0.671592 + 0.218214i) q^{78} +(3.98295 - 12.2583i) q^{79} +(0.837043 + 2.07349i) q^{80} +(2.60995 + 8.03259i) q^{81} +5.65676i q^{82} +(-6.04282 + 1.96343i) q^{83} +(0.966589 + 0.702268i) q^{84} +(9.85999 + 2.46141i) q^{85} +(-0.703495 + 0.511119i) q^{86} +(0.498778 - 0.686509i) q^{87} +(2.57936 - 3.55019i) q^{88} +(9.80091 - 7.12078i) q^{89} +(3.48298 - 5.57032i) q^{90} +(11.0114 + 8.00028i) q^{91} +(-5.14858 + 1.67287i) q^{92} -1.10350i q^{93} +(-3.65267 - 11.2418i) q^{94} +(0.541584 - 2.16949i) q^{95} +(-0.0769362 + 0.236785i) q^{96} +(-13.0804 - 4.25008i) q^{97} +(9.42149 + 12.9676i) q^{98} -12.8928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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