LMFDB - Embedded newform 950.2.n.a.609.7

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			609.7
Character	$\chi$	$=$	950.609
Dual form			950.2.n.a.39.7

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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	−0.239864	−	0.970807i	$-0.577103\pi$
$3$	0.236785	−	0.0769362i	0.136708	−	0.0444191i	0.376572	+	0.926387i	$0.377103\pi$
$4$	−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	$0.361553\pi$
$7$			4.79883i			1.81379i	−0.421358	+	0.906894i	$0.638447\pi$
$8$	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	0.975988	−	0.217825i	$-0.0698961\pi$
$11$	3.55019	+	2.57936i	1.07042	+	0.777707i	0.0944333	+	0.995531i	$0.469896\pi$
$12$	−0.146341	−	0.201422i	−0.0422451	−	0.0581454i
$13$	−1.66713	−	2.29461i	−0.462379	−	0.636410i	0.512621	−	0.858615i	$-0.328675\pi$
$13$	−1.66713	−	2.29461i	−0.462379	−	0.636410i	−0.975000	+	0.222205i	$0.928675\pi$
$14$	−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	−0.266321	−	0.963884i	$-0.585808\pi$
$17$	−4.32240	−	1.40443i	−1.04834	−	0.340625i	−0.782015	+	0.623259i	$0.785808\pi$
$18$		−	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	−0.336099	−	0.941827i	$-0.609108\pi$
$23$	3.18200	−	4.37964i	0.663492	−	0.913218i	0.999591	+	0.0286085i	$0.00910760\pi$
$24$	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	0.999969	+	0.00782997i	$0.00249238\pi$
$29$	1.05323	+	3.24150i	0.195579	+	0.601932i	−0.804390	+	0.594102i	$0.797508\pi$
$30$	−0.134839	−	0.540140i	−0.0246181	−	0.0986156i
$31$	−1.36963	+	4.21530i	−0.245993	+	0.757090i	0.749478	+	0.662029i	$0.230305\pi$
$31$	−1.36963	+	4.21530i	−0.245993	+	0.757090i	−0.995471	+	0.0950608i	$0.969695\pi$
$32$		−	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	−0.960061	−	0.279790i	$-0.909735\pi$
$37$	−5.65382	−	7.78181i	−0.929482	−	1.27932i	0.0305793	−	0.999532i	$-0.490265\pi$
$38$	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	−0.884692	−	0.466177i	$-0.845631\pi$
$41$	−4.57642	+	3.32496i	−0.714716	+	0.519272i	0.169976	+	0.985448i	$0.445631\pi$
$42$	−1.13629	−	0.369204i	−0.175334	−	0.0569694i
$43$			0.869567i			0.132608i	0.997799	+	0.0663039i	$0.0211207\pi$
$43$			0.869567i			0.132608i	−0.997799	+	0.0663039i	$0.978879\pi$
$44$	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	0.663291	−	0.748362i	$-0.269159\pi$
$47$	11.2418	−	3.65267i	1.63978	−	0.532797i	0.976489	+	0.215565i	$0.0691594\pi$
$48$	−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	−0.808151	−	0.588976i	$-0.799531\pi$
$53$	−8.12291	+	2.63929i	−1.11577	+	0.362535i	−0.307616	+	0.951510i	$0.599531\pi$
$54$	−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	−0.928340	−	0.371731i	$-0.878764\pi$
$59$	−6.61866	+	4.80874i	−0.861676	+	0.626044i	0.0666646	+	0.997775i	$0.478764\pi$
$60$	0.516238	+	0.208399i	0.0666461	+	0.0269042i
$61$	−9.70835	−	7.05353i	−1.24303	−	0.903112i	−0.245231	−	0.969465i	$-0.578864\pi$
$61$	−9.70835	−	7.05353i	−1.24303	−	0.903112i	−0.997796	+	0.0663527i	$0.978864\pi$
$62$	−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	0.320547	−	0.947232i	$-0.396133\pi$
$67$	0.189135	+	0.0614538i	0.0231065	+	0.00750777i	−0.297441	+	0.954740i	$0.596133\pi$
$68$			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	0.988259	+	0.152786i	$0.0488245\pi$
$71$	2.34707	+	7.22354i	0.278546	+	0.857276i	−0.709713	+	0.704491i	$0.751176\pi$
$72$	−2.79422	+	0.907896i	−0.329302	+	0.106997i
$73$	3.97733	−	5.47433i	0.465511	−	0.640722i	−0.510129	−	0.860098i	$-0.670402\pi$
$73$	3.97733	−	5.47433i	0.465511	−	0.640722i	0.975640	+	0.219376i	$0.0704023\pi$
$74$	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	0.879029	+	0.476767i	$0.158192\pi$
$79$	3.98295	+	12.2583i	0.448117	+	1.37916i	−0.430913	+	0.902394i	$0.641808\pi$
$80$	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	−0.0420224	−	0.999117i	$-0.513380\pi$
$83$	−6.04282	−	1.96343i	−0.663285	−	0.215514i	−0.621263	+	0.783602i	$0.713380\pi$
$84$	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	0.970069	−	0.242828i	$-0.0780750\pi$
$89$	9.80091	+	7.12078i	1.03889	+	0.754801i	0.0688250	+	0.997629i	$0.478075\pi$
$90$	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	−0.885274	−	0.465070i	$-0.846029\pi$
$97$	−13.0804	+	4.25008i	−1.32811	+	0.431531i	−0.442841	+	0.896600i	$0.646029\pi$
$98$	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	−0.519952	−	0.854196i	$-0.674050\pi$
$103$	−4.45047	+	1.44604i	−0.438518	+	0.142483i	0.0814339	+	0.996679i	$0.474050\pi$
$104$	−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	$-0.942967\pi$
$107$		−	3.68698i		−	0.356434i	0.983991	−	0.178217i	$-0.0570328\pi$
$108$	1.40603	+	0.456848i	0.135296	+	0.0439603i
$109$	11.8357	−	8.59913i	1.13365	−	0.823647i	0.147431	−	0.989072i	$-0.452900\pi$
$109$	11.8357	−	8.59913i	1.13365	−	0.823647i	0.986222	+	0.165425i	$0.0528996\pi$
$110$	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	0.716382	−	0.697708i	$-0.245797\pi$
$113$	−1.79174	−	2.46611i	−0.168552	−	0.231993i	−0.884934	+	0.465716i	$0.845797\pi$
$114$	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	−0.691729	−	0.722157i	$-0.743151\pi$
$127$	2.35350	−	3.23932i	0.208840	−	0.287443i	0.900568	+	0.434714i	$0.143151\pi$
$128$	−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	0.796951	+	0.604043i	$0.206445\pi$
$131$	−2.32165	+	7.14531i	−0.202844	+	0.624289i	−0.999795	+	0.0202452i	$0.993555\pi$
$132$		−	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	0.813088	−	0.582141i	$-0.197785\pi$
$137$	0.0957509	+	0.131790i	0.00818055	+	0.0112596i	−0.804907	+	0.593401i	$0.797785\pi$
$138$	0.792224	+	1.09040i	0.0674386	+	0.0928213i
$139$	−9.93211	−	7.21610i	−0.842431	−	0.612062i	0.0806178	−	0.996745i	$-0.474311\pi$
$139$	−9.93211	−	7.21610i	−0.842431	−	0.612062i	−0.923049	+	0.384683i	$0.874311\pi$
$140$	−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	$0.241805\pi$
$157$			17.2580i			1.37734i	−0.725075	+	0.688670i	$0.758195\pi$
$158$	−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	0.335724	−	0.941961i	$-0.391019\pi$
$163$	−8.47583	−	11.6660i	−0.663878	−	0.913750i	−0.999602	+	0.0282102i	$0.991019\pi$
$164$	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	0.672140	−	0.740424i	$-0.265375\pi$
$167$	10.0889	+	3.27808i	0.780702	+	0.253665i	0.108562	+	0.994090i	$0.465375\pi$
$168$			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	−0.999972	−	0.00746325i	$-0.997624\pi$
$173$	−8.99485	+	12.3803i	−0.683866	+	0.941261i	0.316106	+	0.948724i	$0.397624\pi$
$174$	−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	0.696685	+	0.717377i	$0.254658\pi$
$179$	7.42163	+	22.8414i	0.554719	+	1.70725i	−0.141966	+	0.989872i	$0.545342\pi$
$180$	−6.55373	−	0.456368i	−0.488486	−	0.0340156i
$181$	1.33598	−	4.11172i	0.0993026	−	0.305622i	−0.889049	−	0.457813i	$-0.848633\pi$
$181$	1.33598	−	4.11172i	0.0993026	−	0.305622i	0.988351	+	0.152191i	$0.0486329\pi$
$182$			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	−0.455369	−	0.890303i	$-0.650493\pi$
$191$	3.46396	−	2.51671i	0.250643	−	0.182103i	0.706012	+	0.708200i	$0.250493\pi$
$192$	0.236785	+	0.0769362i	0.0170885	+	0.00555239i
$193$			20.9381i			1.50716i	0.657357	+	0.753580i	$0.271674\pi$
$193$			20.9381i			1.50716i	−0.657357	+	0.753580i	$0.728326\pi$
$194$	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	0.0616363	−	0.998099i	$-0.480368\pi$
$197$	9.79927	−	3.18397i	0.698169	−	0.226849i	0.636533	+	0.771250i	$0.280368\pi$
$198$	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	0.682932	−	0.730482i	$-0.260705\pi$
$211$	2.89411	+	2.10270i	0.199239	+	0.144756i	−0.483693	+	0.875238i	$0.660705\pi$
$212$	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	−0.508362	−	0.861143i	$-0.669749\pi$
$223$	6.98465	−	9.61354i	0.467727	−	0.643770i	0.976089	+	0.217373i	$0.0697488\pi$
$224$	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	−0.994620	−	0.103587i	$-0.966968\pi$
$227$	−8.87039	+	12.2090i	−0.588748	+	0.810342i	0.405872	+	0.913930i	$0.366968\pi$
$228$	−0.236785	+	0.0769362i	−0.0156815	+	0.00509523i
$229$	−3.68205	−	11.3322i	−0.243317	−	0.748852i	−0.995909	−	0.0903648i	$-0.971197\pi$
$229$	−3.68205	−	11.3322i	−0.243317	−	0.748852i	0.752592	−	0.658487i	$-0.228803\pi$
$230$	−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	−0.628003	−	0.778211i	$-0.716127\pi$
$233$	−24.3235	−	7.90320i	−1.59349	−	0.517756i	−0.965486	+	0.260455i	$0.916127\pi$
$234$	−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	0.451089	−	0.892479i	$-0.351036\pi$
$239$	−3.99344	−	2.90141i	−0.258314	−	0.187676i	−0.709404	+	0.704803i	$0.751036\pi$
$240$	0.0386732	−	0.555371i	0.00249634	−	0.0358490i
$241$	−24.0608	+	17.4812i	−1.54990	+	1.12606i	−0.606170	+	0.795335i	$0.707295\pi$
$241$	−24.0608	+	17.4812i	−1.54990	+	1.12606i	−0.943726	+	0.330730i	$0.892705\pi$
$242$	−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	$0.379276\pi$
$257$			29.7840i			1.85787i	−0.370237	+	0.928937i	$0.620724\pi$
$258$	−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	0.999796	+	0.0202064i	$0.00643235\pi$
$263$	11.5152	+	15.8494i	0.710059	+	0.977313i	−0.289736	+	0.957106i	$0.593568\pi$
$264$	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	−0.999989	−	0.00476757i	$-0.998482\pi$
$269$	−3.08636	+	9.49883i	−0.188179	+	0.579154i	0.811810	+	0.583922i	$0.198482\pi$
$270$	2.53300	+	2.12418i	0.154153	+	0.129274i
$271$	8.63326	+	26.5704i	0.524433	+	1.61404i	0.765434	+	0.643515i	$0.222524\pi$
$271$	8.63326	+	26.5704i	0.524433	+	1.61404i	−0.241001	+	0.970525i	$0.577476\pi$
$272$	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	−0.723864	−	0.689942i	$-0.757636\pi$
$277$	2.59629	−	3.57349i	0.155996	−	0.214710i	0.879860	+	0.475232i	$0.157636\pi$
$278$	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	0.740210	+	0.672376i	$0.234726\pi$
$281$	−4.25522	+	13.0962i	−0.253845	+	0.781256i	−0.994055	+	0.108880i	$0.965274\pi$
$282$			2.94291i			0.175248i
$283$	−5.47917	−	1.78029i	−0.325703	−	0.105827i	0.141601	−	0.989924i	$-0.454775\pi$
$283$	−5.47917	−	1.78029i	−0.325703	−	0.105827i	−0.467305	+	0.884096i	$0.654775\pi$
$284$	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	$-0.798667\pi$
$293$		−	20.2384i		−	1.18234i	0.806548	−	0.591169i	$-0.201333\pi$
$294$	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	$0.194350\pi$
$307$			20.0912i			1.14667i	−0.819322	+	0.573333i	$0.805650\pi$
$308$	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	0.977377	−	0.211505i	$-0.0678365\pi$
$311$	19.0151	+	13.8153i	1.07825	+	0.783394i	0.100873	+	0.994899i	$0.467836\pi$
$312$	−0.415067	−	0.571291i	−0.0234985	−	0.0323430i
$313$	−1.82998	−	2.51875i	−0.103437	−	0.142368i	0.754161	−	0.656690i	$-0.228044\pi$
$313$	−1.82998	−	2.51875i	−0.103437	−	0.142368i	−0.857598	+	0.514321i	$0.828044\pi$
$314$	−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	0.371265	−	0.928527i	$-0.378924\pi$
$317$	2.24068	+	0.728042i	0.125849	+	0.0408909i	−0.245415	+	0.969418i	$0.578924\pi$
$318$		−	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	−0.832165	−	0.554528i	$-0.812899\pi$
$331$	3.03855	−	9.35171i	0.167014	−	0.514016i	0.999179	+	0.0405117i	$0.0128988\pi$
$332$			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	0.942477	−	0.334270i	$-0.108490\pi$
$337$	6.11905	+	8.42215i	0.333326	+	0.458784i	−0.609151	+	0.793054i	$0.708490\pi$
$338$	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	0.0584625	−	0.998290i	$-0.481380\pi$
$347$	12.9006	−	4.19165i	0.692540	−	0.225020i	0.634077	+	0.773270i	$0.281380\pi$
$348$	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	−0.212132	−	0.977241i	$-0.568041\pi$
$353$	3.58214	−	1.16391i	0.190658	−	0.0619485i	0.402790	+	0.915293i	$0.368041\pi$
$354$	−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	−0.0239419	−	0.999713i	$-0.507622\pi$
$359$	17.4210	−	12.6571i	0.919443	−	0.668015i	0.943385	+	0.331699i	$0.107622\pi$
$360$	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	−0.0764489	−	0.997074i	$-0.524358\pi$
$367$	−13.8768	−	4.50884i	−0.724362	−	0.235360i	−0.647914	+	0.761714i	$0.724358\pi$
$368$			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	−0.869087	−	0.494659i	$-0.835293\pi$
$373$	−2.51218	+	3.45772i	−0.130076	+	0.179034i	0.739011	+	0.673693i	$0.235293\pi$
$374$	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	−0.974805	−	0.223061i	$-0.928395\pi$
$379$	−6.17684	−	19.0104i	−0.317283	−	0.976496i	0.657522	−	0.753436i	$-0.271605\pi$
$380$	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	−0.513045	−	0.858362i	$-0.671483\pi$
$383$	−28.0373	−	9.10987i	−1.43264	−	0.465493i	−0.919595	+	0.392869i	$0.871483\pi$
$384$	−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	0.847760	−	0.530380i	$-0.177951\pi$
$389$	11.9386	+	8.67389i	0.605310	+	0.439784i	−0.242450	+	0.970164i	$0.577951\pi$
$390$	−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	−0.789868	−	0.613277i	$-0.789851\pi$
$397$	−21.2879	+	6.91686i	−1.06841	+	0.347147i	−0.278542	+	0.960424i	$0.589851\pi$
$398$	−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	−0.765222	−	0.643766i	$-0.777371\pi$
$409$	−7.87576	+	5.72208i	−0.389431	+	0.282938i	0.375791	+	0.926704i	$0.377371\pi$
$410$	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	0.340921	+	0.940092i	$0.389261\pi$
$419$	−9.97810	+	30.7094i	−0.487462	+	1.50025i	−0.828383	+	0.560162i	$0.810739\pi$
$420$	−1.00007	+	2.47734i	−0.0487986	+	0.120882i
$421$	0.875804	+	2.69545i	0.0426841	+	0.131368i	0.970128	−	0.242595i	$-0.0779986\pi$
$421$	0.875804	+	2.69545i	0.0426841	+	0.131368i	−0.927444	+	0.373963i	$0.877999\pi$
$422$	−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	0.581570	+	0.813496i	$0.302438\pi$
$431$	−7.62101	+	23.4550i	−0.367091	+	1.12979i	−0.948661	+	0.316294i	$0.897562\pi$
$432$		−	1.47839i		−	0.0711292i
$433$	−0.107926	−	0.0350673i	−0.00518660	−	0.00168523i	0.306423	−	0.951896i	$-0.400868\pi$
$433$	−0.107926	−	0.0350673i	−0.00518660	−	0.00168523i	−0.311609	+	0.950210i	$0.600868\pi$
$434$	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	0.691114	−	0.722746i	$-0.257120\pi$
$439$	4.55310	+	3.30802i	0.217308	+	0.157883i	−0.473806	+	0.880629i	$0.657120\pi$
$440$	−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	$-0.995846\pi$
$443$		−	0.549324i		−	0.0260992i	0.999915	−	0.0130496i	$-0.00415393\pi$
$444$	−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	$0.238314\pi$
$457$			29.1024i			1.36135i	−0.732585	+	0.680676i	$0.761686\pi$
$458$	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	−0.0542089	−	0.998530i	$-0.517264\pi$
$461$	−21.9136	−	15.9212i	−1.02062	−	0.741523i	−0.966410	+	0.257007i	$0.917264\pi$
$462$	−3.08174	−	4.24165i	−0.143376	−	0.197340i
$463$	−12.5575	−	17.2839i	−0.583597	−	0.803253i	0.410487	−	0.911867i	$-0.365359\pi$
$463$	−12.5575	−	17.2839i	−0.583597	−	0.803253i	−0.994084	+	0.108614i	$0.965359\pi$
$464$	−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	0.611396	−	0.791324i	$-0.290608\pi$
$467$	13.8499	+	4.50011i	0.640898	+	0.208240i	0.0295013	+	0.999565i	$0.490608\pi$
$468$		−	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	0.950316	−	0.311287i	$-0.100760\pi$
$479$	−0.0323029	−	0.0994180i	−0.00147596	−	0.00454252i	−0.951792	+	0.306745i	$0.900760\pi$
$480$	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	0.992760	+	0.120115i	$0.0383262\pi$
$487$	17.6592	+	24.3058i	0.800216	+	1.10140i	−0.192544	+	0.981288i	$0.561674\pi$
$488$	−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	−0.499891	−	0.866088i	$-0.666627\pi$
$491$	3.75217	−	2.72611i	0.169333	−	0.123028i	0.669224	+	0.743061i	$0.266627\pi$
$492$	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	−0.139571	−	0.990212i	$-0.544572\pi$
$503$	7.39095	−	2.40147i	0.329546	−	0.107076i	0.469117	+	0.883136i	$0.344572\pi$
$504$	−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	0.713023	−	0.701140i	$-0.247325\pi$
$509$	36.1018	−	26.2295i	1.60018	−	1.16260i	0.887160	−	0.461461i	$-0.152675\pi$
$510$	−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	−0.979877	−	0.199604i	$-0.936034\pi$
$521$	−6.94952	−	21.3884i	−0.304464	−	0.937044i	0.675413	−	0.737440i	$-0.263966\pi$
$522$	9.52358	−	3.09440i	0.416836	−	0.135438i
$523$	14.0753	−	19.3729i	0.615468	−	0.847119i	−0.381545	−	0.924350i	$-0.624608\pi$
$523$	14.0753	−	19.3729i	0.615468	−	0.847119i	0.997013	+	0.0772314i	$0.0246080\pi$
$524$	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	−0.444729	−	0.895665i	$-0.646700\pi$
$541$	6.27237	−	4.55715i	0.269670	−	0.195927i	0.714399	+	0.699738i	$0.246700\pi$
$542$	−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	−0.259173	−	0.965831i	$-0.583450\pi$
$547$	2.31196	−	0.751201i	0.0988522	−	0.0321190i	0.358026	+	0.933712i	$0.383450\pi$
$548$	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	$0.136023\pi$
$557$			19.5624i			0.828884i	−0.910076	+	0.414442i	$0.863977\pi$
$558$	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	0.914716	−	0.404097i	$-0.132414\pi$
$563$	5.87815	+	8.09059i	0.247735	+	0.340978i	−0.666982	+	0.745074i	$0.732414\pi$
$564$	−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	−0.981861	−	0.189600i	$-0.939281\pi$
$569$	−1.81467	+	5.58497i	−0.0760748	+	0.234134i	0.905787	+	0.423734i	$0.139281\pi$
$570$	−0.555371	−	0.0386732i	−0.0232619	−	0.00161984i
$571$	−5.74182	−	17.6715i	−0.240288	−	0.739529i	−0.996376	−	0.0850595i	$-0.972892\pi$
$571$	−5.74182	−	17.6715i	−0.240288	−	0.739529i	0.756088	−	0.654470i	$-0.227108\pi$
$572$	−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	0.105474	−	0.994422i	$-0.466364\pi$
$577$	24.4684	−	33.6779i	1.01863	−	1.40203i	0.913158	−	0.407605i	$-0.133636\pi$
$578$	−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	0.425197	−	0.905101i	$-0.360205\pi$
$587$	−13.7373	−	18.9078i	−0.566999	−	0.780407i	−0.992195	+	0.124694i	$0.960205\pi$
$588$	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	$-0.935725\pi$
$593$		−	9.76773i		−	0.401113i	0.979682	−	0.200556i	$-0.0642750\pi$
$594$	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	$0.129970\pi$
$607$			19.5651i			0.794123i	−0.917792	+	0.397061i	$0.870030\pi$
$608$	−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	0.932770	−	0.360472i	$-0.117384\pi$
$613$	7.46972	+	10.2812i	0.301699	+	0.415253i	−0.631071	+	0.775725i	$0.717384\pi$
$614$	−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	0.0344037	−	0.999408i	$-0.489047\pi$
$617$	−13.0457	−	4.23881i	−0.525200	−	0.170648i	−0.559604	+	0.828760i	$0.689047\pi$
$618$		−	1.16506i		−	0.0468655i
$619$	−5.01161	+	15.4241i	−0.201433	+	0.619948i	0.798408	+	0.602117i	$0.205676\pi$
$619$	−5.01161	+	15.4241i	−0.201433	+	0.619948i	−0.999841	+	0.0178311i	$0.994324\pi$
$620$	−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	0.630109	+	0.776506i	$0.283010\pi$
$631$	−8.44220	+	25.9824i	−0.336079	+	1.03434i	−0.966188	+	0.257838i	$0.916990\pi$
$632$			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	−0.500984	−	0.865456i	$-0.667029\pi$
$641$	4.23572	−	3.07743i	0.167301	−	0.121551i	0.668285	+	0.743905i	$0.267029\pi$
$642$	0.873022	+	0.283662i	0.0344554	+	0.0111952i
$643$			12.9509i			0.510736i	0.966844	+	0.255368i	$0.0821966\pi$
$643$			12.9509i			0.510736i	−0.966844	+	0.255368i	$0.917803\pi$
$644$	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	−0.891257	−	0.453498i	$-0.850176\pi$
$647$	−34.2305	+	11.1222i	−1.34574	+	0.437257i	−0.454483	+	0.890756i	$0.650176\pi$
$648$	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	−0.502281	−	0.864705i	$-0.667506\pi$
$653$	−10.2311	+	3.32428i	−0.400374	+	0.130089i	0.101907	+	0.994794i	$0.467506\pi$
$654$	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	−0.0494309	−	0.998778i	$-0.515741\pi$
$659$	22.7237	−	16.5097i	0.885188	−	0.643127i	0.934619	+	0.355651i	$0.115741\pi$
$660$	1.29520	+	2.07142i	0.0504158	+	0.0806300i
$661$	31.9971	+	23.2473i	1.24454	+	0.904214i	0.997892	−	0.0648903i	$-0.0206697\pi$
$661$	31.9971	+	23.2473i	1.24454	+	0.904214i	0.246651	+	0.969104i	$0.420670\pi$
$662$	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	0.295095	+	0.955468i	$0.404649\pi$
$673$	−18.2841	+	25.1659i	−0.704799	+	0.970072i	−0.999893	+	0.0146043i	$0.995351\pi$
$674$	−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	−0.694220	−	0.719763i	$-0.744251\pi$
$677$	5.32979	−	7.33582i	0.204840	−	0.281939i	0.899061	+	0.437824i	$0.144251\pi$
$678$	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	0.765058	−	0.643962i	$-0.222711\pi$
$683$	26.2778	+	8.53816i	1.00549	+	0.326704i	0.240433	+	0.970666i	$0.422711\pi$
$684$	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	−0.471881	−	0.881662i	$-0.656425\pi$
$691$	5.80443	−	4.21716i	0.220811	−	0.160428i	0.692692	+	0.721234i	$0.256425\pi$
$692$	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	−0.794290	−	0.607539i	$-0.792157\pi$
$709$	−12.2999	+	8.93643i	−0.461934	+	0.335615i	0.332355	+	0.943154i	$0.392157\pi$
$710$	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	−0.994853	−	0.101326i	$-0.967691\pi$
$719$	−3.49770	+	10.7648i	−0.130442	+	0.401459i	0.864411	+	0.502785i	$0.167691\pi$
$720$	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	−0.404566	−	0.914509i	$-0.632577\pi$
$727$	15.9136	−	21.9031i	0.590202	−	0.812343i	0.994767	+	0.102166i	$0.0325773\pi$
$728$	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	0.233859	−	0.972271i	$-0.424865\pi$
$733$	−4.01862	−	1.30573i	−0.148431	−	0.0482282i	−0.382290	+	0.924042i	$0.624865\pi$
$734$	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	0.987680	−	0.156489i	$-0.0500177\pi$
$739$	31.1007	+	22.5960i	1.14406	+	0.831208i	0.156380	+	0.987697i	$0.450018\pi$
$740$	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	$0.00713960\pi$
$743$			1.22268i			0.0448556i	−0.999748	+	0.0224278i	$0.992860\pi$
$744$	−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	$-0.840637\pi$
$757$		−	26.4131i		−	0.959999i	0.877269	−	0.480000i	$-0.159363\pi$
$758$	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	0.477692	−	0.878527i	$-0.341473\pi$
$761$	−5.79922	−	4.21338i	−0.210221	−	0.152735i	−0.687914	+	0.725792i	$0.741473\pi$
$762$	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	−0.469941	−	0.882698i	$-0.655725\pi$
$769$	11.8989	−	36.6211i	0.429086	−	1.32059i	0.899027	−	0.437893i	$-0.144275\pi$
$770$	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	0.00936383	−	0.999956i	$-0.497019\pi$
$773$	26.6208	−	36.6404i	0.957485	−	1.31787i	0.948121	−	0.317909i	$-0.102981\pi$
$774$	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	0.998351	−	0.0574114i	$-0.0182847\pi$
$787$	17.8208	+	24.5282i	0.635242	+	0.874335i	−0.363109	+	0.931747i	$0.618285\pi$
$788$	−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	−0.435556	−	0.900162i	$-0.643448\pi$
$797$	−7.30699	+	2.37419i	−0.258827	+	0.0840980i	0.176729	+	0.984260i	$0.443448\pi$
$798$	−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	−0.991724	−	0.128385i	$-0.959021\pi$
$809$	−33.4512	+	24.3038i	−1.17608	+	0.854474i	−0.184359	+	0.982859i	$0.559021\pi$
$810$	−17.5126	−	7.06964i	−0.615331	−	0.248402i
$811$	15.7825	+	11.4667i	0.554199	+	0.402649i	0.829331	−	0.558757i	$-0.188722\pi$
$811$	15.7825	+	11.4667i	0.554199	+	0.402649i	−0.275132	+	0.961406i	$0.588722\pi$
$812$	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	−0.862893	−	0.505386i	$-0.831350\pi$
$821$	−13.2336	−	40.7289i	−0.461856	−	1.42145i	0.401037	−	0.916062i	$-0.368650\pi$
$822$	−0.0385726	+	0.0125330i	−0.00134537	+	0.000437138i
$823$	−14.4830	+	19.9341i	−0.504844	+	0.694859i	−0.983039	−	0.183395i	$-0.941291\pi$
$823$	−14.4830	+	19.9341i	−0.504844	+	0.694859i	0.478195	+	0.878254i	$0.341291\pi$
$824$	−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	−0.817247	−	0.576288i	$-0.804501\pi$
$827$	−0.477977	+	0.657879i	−0.0166209	+	0.0228767i	0.800626	+	0.599165i	$0.204501\pi$
$828$	15.1266	−	4.91493i	0.525685	−	0.170806i
$829$	7.40950	+	22.8041i	0.257343	+	0.792019i	0.993359	+	0.115055i	$0.0367045\pi$
$829$	7.40950	+	22.8041i	0.257343	+	0.792019i	−0.736017	+	0.676964i	$0.763295\pi$
$830$	−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	0.564003	−	0.825773i	$-0.309261\pi$
$839$	−1.36330	−	0.990498i	−0.0470664	−	0.0341958i	−0.611070	+	0.791577i	$0.709261\pi$
$840$	−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	−0.0866739	−	0.996237i	$-0.527624\pi$
$853$	12.5230	−	4.06896i	0.428779	−	0.139319i	0.515453	+	0.856918i	$0.327624\pi$
$854$	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	$0.160734\pi$
$857$			28.3244i			0.967544i	−0.875194	+	0.483772i	$0.839266\pi$
$858$	2.94713	+	0.957580i	0.100613	+	0.0326912i
$859$	−8.06981	+	5.86306i	−0.275338	+	0.200045i	−0.716882	−	0.697195i	$-0.754431\pi$
$859$	−8.06981	+	5.86306i	−0.275338	+	0.200045i	0.441543	+	0.897240i	$0.354431\pi$
$860$	−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	0.976379	−	0.216063i	$-0.0693216\pi$
$863$	13.7828	+	18.9705i	0.469174	+	0.645762i	−0.507206	+	0.861825i	$0.669322\pi$
$864$	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	−0.719025	−	0.694984i	$-0.755411\pi$
$877$	4.86074	−	6.69024i	0.164136	−	0.225913i	0.883160	+	0.469071i	$0.155411\pi$
$878$	−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	0.772384	+	0.635156i	$0.219064\pi$
$881$	−6.70279	+	20.6291i	−0.225823	+	0.695011i	−0.998207	+	0.0598556i	$0.980936\pi$
$882$			47.0928i			1.58570i
$883$	9.08765	+	2.95276i	0.305824	+	0.0993681i	0.457909	−	0.888999i	$-0.348599\pi$
$883$	9.08765	+	2.95276i	0.305824	+	0.0993681i	−0.152085	+	0.988367i	$0.548599\pi$
$884$	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	0.553516	−	0.832838i	$-0.313286\pi$
$887$	−12.1991	−	16.7906i	−0.409606	−	0.563774i	−0.963122	+	0.269064i	$0.913286\pi$
$888$	−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	$0.104630\pi$
$907$			19.4443i			0.645638i	−0.946461	+	0.322819i	$0.895370\pi$
$908$	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	0.379905	−	0.925025i	$-0.375957\pi$
$911$	−11.5434	−	8.38675i	−0.382449	−	0.277866i	−0.762354	+	0.647160i	$0.775957\pi$
$912$	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	−0.995542	−	0.0943177i	$-0.969933\pi$
$919$	−4.08322	+	12.5669i	−0.134693	+	0.414543i	0.860849	+	0.508860i	$0.169933\pi$
$920$	−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	0.975596	−	0.219572i	$-0.0704661\pi$
$929$	1.74529	+	5.37144i	0.0572610	+	0.176231i	−0.918335	+	0.395803i	$0.870466\pi$
$930$	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	0.912301	−	0.409521i	$-0.134304\pi$
$937$	7.37428	+	10.1498i	0.240907	+	0.331580i	−0.671394	+	0.741101i	$0.734304\pi$
$938$	−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	−0.950383	−	0.311082i	$-0.899309\pi$
$941$	−29.0871	+	21.1330i	−0.948211	+	0.688916i	0.00217185	+	0.999998i	$0.499309\pi$
$942$	−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	0.194628	−	0.980877i	$-0.437650\pi$
$947$	28.5771	−	9.28526i	0.928630	−	0.301730i	0.734002	+	0.679147i	$0.237650\pi$
$948$	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	−0.615544	−	0.788103i	$-0.711064\pi$
$953$	−20.0750	+	6.52277i	−0.650294	+	0.211293i	−0.0347503	+	0.999396i	$0.511064\pi$
$954$	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	0.129699	−	0.991553i	$-0.458599\pi$
$967$	−10.8276	−	3.51810i	−0.348192	−	0.113135i	−0.477892	+	0.878419i	$0.658599\pi$
$968$			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	−0.953566	−	0.301183i	$-0.902619\pi$
$971$	−11.1913	−	34.4433i	−0.359146	−	1.10534i	0.594421	−	0.804154i	$-0.297381\pi$
$972$	−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	−0.356283	−	0.934378i	$-0.615956\pi$
$977$	20.0814	−	27.6397i	0.642461	−	0.884272i	0.998744	+	0.0501061i	$0.0159560\pi$
$978$	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	0.292873	−	0.956151i	$-0.405389\pi$
$983$	−1.00953	−	0.328017i	−0.0321991	−	0.0104621i	−0.325072	+	0.945689i	$0.605389\pi$
$984$	−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	−0.548046	−	0.836448i	$-0.684628\pi$
$991$	2.45883	−	1.78645i	0.0781074	−	0.0567483i	0.626154	+	0.779700i	$0.284628\pi$
$992$	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	−0.130673	−	0.991426i	$-0.541714\pi$
$997$	10.9363	−	3.55342i	0.346356	−	0.112538i	0.477029	+	0.878888i	$0.341714\pi$
$998$	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.609.7	yes	88
25.14	even	10	inner	950.2.n.a.39.7	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.7	✓	88	25.14	even	10	inner
950.2.n.a.609.7	yes	88	1.1	even	1	trivial

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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