LMFDB - Embedded newform 77.2.f.a.15.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(15,77)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("77.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.1
Root			$-0.762262 - 2.34600i$ of defining polynomial
Character	$\chi$	$=$	77.15
Dual form			77.2.f.a.36.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99563 - 1.44991i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(1.26226 + 3.88484i) q^{4} +(2.80464 - 2.03769i) q^{5} +(3.22899 - 2.34600i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(1.58914 - 4.89086i) q^{8} +(0.309017 + 0.224514i) q^{9} -8.55150 q^{10} +(2.91998 - 1.57281i) q^{11} -6.60929 q^{12} +(0.528896 + 0.384266i) q^{13} +(-0.762262 + 2.34600i) q^{14} +(1.73337 + 5.33475i) q^{15} +(-3.65334 + 2.65431i) q^{16} +(0.919977 - 0.668402i) q^{17} +(-0.291158 - 0.896093i) q^{18} +(-1.87759 + 5.77864i) q^{19} +(11.4563 + 8.32350i) q^{20} +1.61803 q^{21} +(-8.10762 - 1.09495i) q^{22} -6.66708 q^{23} +(6.73170 + 4.89086i) q^{24} +(2.16875 - 6.67473i) q^{25} +(-0.498330 - 1.53370i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(3.30464 - 2.40097i) q^{28} +(-1.41331 - 4.34973i) q^{29} +(4.27575 - 13.1594i) q^{30} +(-2.26226 - 1.64363i) q^{31} +0.854102 q^{32} +(0.960319 + 5.27979i) q^{33} -2.80505 q^{34} +(-2.80464 - 2.03769i) q^{35} +(-0.482141 + 1.48388i) q^{36} +(-0.135893 - 0.418235i) q^{37} +(12.1255 - 8.80968i) q^{38} +(-0.855772 + 0.621755i) q^{39} +(-5.50911 - 16.9553i) q^{40} +(-1.82417 + 5.61423i) q^{41} +(-3.22899 - 2.34600i) q^{42} +8.70820 q^{43} +(9.79590 + 9.35835i) q^{44} +1.32417 q^{45} +(13.3050 + 9.66666i) q^{46} +(-0.186864 + 0.575107i) q^{47} +(-2.25789 - 6.94907i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-14.0058 + 10.1758i) q^{50} +(0.568577 + 1.74990i) q^{51} +(-0.825206 + 2.53972i) q^{52} +(-7.94654 - 5.77350i) q^{53} +13.4983 q^{54} +(4.98459 - 10.3612i) q^{55} -5.14256 q^{56} +(-7.95362 - 5.77864i) q^{57} +(-3.48626 + 10.7296i) q^{58} +(0.523492 + 1.61114i) q^{59} +(-18.5367 + 13.4677i) q^{60} +(-5.54839 + 4.03114i) q^{61} +(2.13152 + 6.56015i) q^{62} +(0.118034 - 0.363271i) q^{63} +(5.60222 + 4.07025i) q^{64} +2.26638 q^{65} +(5.73877 - 11.9289i) q^{66} -6.17828 q^{67} +(3.75789 + 2.73027i) q^{68} +(3.33354 - 10.2596i) q^{69} +(2.64256 + 8.13296i) q^{70} +(4.38234 - 3.18395i) q^{71} +(1.58914 - 1.15458i) q^{72} +(2.07103 + 6.37396i) q^{73} +(-0.335211 + 1.03167i) q^{74} +(9.18698 + 6.67473i) q^{75} -24.8191 q^{76} +(-2.39815 - 2.29104i) q^{77} +2.60929 q^{78} +(-2.14693 - 1.55984i) q^{79} +(-4.83766 + 14.8888i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(11.7805 - 8.55903i) q^{82} +(-5.41765 + 3.93615i) q^{83} +(2.04238 + 6.28581i) q^{84} +(1.21821 - 3.74926i) q^{85} +(-17.3783 - 12.6261i) q^{86} +7.40020 q^{87} +(-3.05216 - 16.7806i) q^{88} -0.698213 q^{89} +(-2.64256 - 1.91993i) q^{90} +(0.202020 - 0.621755i) q^{91} +(-8.41560 - 25.9006i) q^{92} +(3.66042 - 2.65945i) q^{93} +(1.20676 - 0.876765i) q^{94} +(6.50911 + 20.0330i) q^{95} +(-0.427051 + 1.31433i) q^{96} +(12.0209 + 8.73372i) q^{97} +2.46673 q^{98} +(1.25544 + 0.169550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20}+ \cdots + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9 - 28 * q^10 + 5 * q^11 - 14 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 - 11 * q^17 + 4 * q^18 - 9 * q^19 + 21 * q^20 + 4 * q^21 - q^22 - 16 * q^23 + 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 + 7 * q^28 - 9 * q^29 + 14 * q^30 - 11 * q^31 - 20 * q^32 + 10 * q^33 - 24 * q^34 - 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 - 5 * q^39 - 16 * q^40 - 22 * q^41 - 3 * q^42 + 16 * q^43 + 29 * q^44 + 18 * q^45 + 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 - 34 * q^50 + 3 * q^51 + 21 * q^52 + 2 * q^53 + 4 * q^54 + 26 * q^55 - 18 * q^56 - 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 + 7 * q^61 - 5 * q^62 - 8 * q^63 + q^64 + 24 * q^65 + 18 * q^66 - 30 * q^67 + 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 + 3 * q^72 + 3 * q^73 - 9 * q^74 + 5 * q^75 - 52 * q^76 - 5 * q^77 - 18 * q^78 - 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 + 23 * q^83 + 4 * q^84 - 10 * q^85 - 17 * q^86 + 12 * q^87 - 7 * q^88 - 34 * q^89 + 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 - 30 * q^94 + 24 * q^95 + 10 * q^96 + 30 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.99563	−	1.44991i	−1.41112	−	1.02524i	−0.993158	−	0.116777i	$-0.962744\pi$
$2$	−1.99563	−	1.44991i	−1.41112	−	1.02524i	−0.417964	−	0.908464i	$-0.637256\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	1.26226	+	3.88484i	0.631131	+	1.94242i
$5$	2.80464	−	2.03769i	1.25428	−	0.911284i	0.255813	−	0.966726i	$-0.417657\pi$
$5$	2.80464	−	2.03769i	1.25428	−	0.911284i	0.998462	+	0.0554418i	$0.0176567\pi$
$6$	3.22899	−	2.34600i	1.31823	−	0.957751i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	1.58914	−	4.89086i	0.561845	−	1.72918i
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$	−8.55150			−2.70422
$11$	2.91998	−	1.57281i	0.880406	−	0.474220i
$11$	2.91998	−	1.57281i	0.880406	−	0.474220i
$12$	−6.60929			−1.90794
$13$	0.528896	+	0.384266i	0.146689	+	0.106576i	0.658709	−	0.752397i	$-0.271103\pi$
$13$	0.528896	+	0.384266i	0.146689	+	0.106576i	−0.512020	+	0.858973i	$0.671103\pi$
$14$	−0.762262	+	2.34600i	−0.203723	+	0.626995i
$15$	1.73337	+	5.33475i	0.447553	+	1.37743i
$16$	−3.65334	+	2.65431i	−0.913336	+	0.663577i
$17$	0.919977	−	0.668402i	0.223127	−	0.162111i	−0.470606	−	0.882343i	$-0.655965\pi$
$17$	0.919977	−	0.668402i	0.223127	−	0.162111i	0.693733	+	0.720232i	$0.255965\pi$
$18$	−0.291158	−	0.896093i	−0.0686266	−	0.211211i
$19$	−1.87759	+	5.77864i	−0.430750	+	1.32571i	0.466630	+	0.884452i	$0.345468\pi$
$19$	−1.87759	+	5.77864i	−0.430750	+	1.32571i	−0.897380	+	0.441259i	$0.854532\pi$
$20$	11.4563	+	8.32350i	2.56171	+	1.86119i
$21$	1.61803			0.353084
$22$	−8.10762	−	1.09495i	−1.72855	−	0.233445i
$23$	−6.66708			−1.39018			−0.695091	−	0.718921i	$-0.744636\pi$
$23$	−6.66708			−1.39018			−0.695091	+	0.718921i	$0.744636\pi$
$24$	6.73170	+	4.89086i	1.37410	+	0.998343i
$25$	2.16875	−	6.67473i	0.433750	−	1.33495i
$26$	−0.498330	−	1.53370i	−0.0977306	−	0.300784i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	3.30464	−	2.40097i	0.624519	−	0.453740i
$29$	−1.41331	−	4.34973i	−0.262445	−	0.807724i	−0.992271	−	0.124090i	$-0.960399\pi$
$29$	−1.41331	−	4.34973i	−0.262445	−	0.807724i	0.729826	−	0.683633i	$-0.239601\pi$
$30$	4.27575	−	13.1594i	0.780641	−	2.40257i
$31$	−2.26226	−	1.64363i	−0.406314	−	0.295205i	0.365794	−	0.930696i	$-0.380798\pi$
$31$	−2.26226	−	1.64363i	−0.406314	−	0.295205i	−0.772108	+	0.635491i	$0.780798\pi$
$32$	0.854102			0.150985
$33$	0.960319	+	5.27979i	0.167170	+	0.919093i
$34$	−2.80505			−0.481063
$35$	−2.80464	−	2.03769i	−0.474072	−	0.344433i
$36$	−0.482141	+	1.48388i	−0.0803569	+	0.247313i
$37$	−0.135893	−	0.418235i	−0.0223406	−	0.0687574i	0.939265	−	0.343194i	$-0.111509\pi$
$37$	−0.135893	−	0.418235i	−0.0223406	−	0.0687574i	−0.961605	+	0.274436i	$0.911509\pi$
$38$	12.1255	−	8.80968i	1.96701	−	1.42912i
$39$	−0.855772	+	0.621755i	−0.137033	+	0.0995604i
$40$	−5.50911	−	16.9553i	−0.871068	−	2.68087i
$41$	−1.82417	+	5.61423i	−0.284888	+	0.876795i	0.701544	+	0.712626i	$0.252494\pi$
$41$	−1.82417	+	5.61423i	−0.284888	+	0.876795i	−0.986432	+	0.164169i	$0.947506\pi$
$42$	−3.22899	−	2.34600i	−0.498245	−	0.361996i
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	9.79590	+	9.35835i	1.47679	+	1.41082i
$45$	1.32417			0.197396
$46$	13.3050	+	9.66666i	1.96172	+	1.42527i
$47$	−0.186864	+	0.575107i	−0.0272569	+	0.0838880i	−0.963760	−	0.266772i	$-0.914043\pi$
$47$	−0.186864	+	0.575107i	−0.0272569	+	0.0838880i	0.936503	+	0.350660i	$0.114043\pi$
$48$	−2.25789	−	6.94907i	−0.325898	−	1.00301i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−14.0058	+	10.1758i	−1.98072	+	1.43907i
$51$	0.568577	+	1.74990i	0.0796167	+	0.245035i
$52$	−0.825206	+	2.53972i	−0.114435	+	0.352196i
$53$	−7.94654	−	5.77350i	−1.09154	−	0.793051i	−0.111883	−	0.993721i	$-0.535688\pi$
$53$	−7.94654	−	5.77350i	−1.09154	−	0.793051i	−0.979659	+	0.200670i	$0.935688\pi$
$54$	13.4983			1.83688
$55$	4.98459	−	10.3612i	0.672122	−	1.39710i
$56$	−5.14256			−0.687203
$57$	−7.95362	−	5.77864i	−1.05348	−	0.765400i
$58$	−3.48626	+	10.7296i	−0.457768	+	1.40887i
$59$	0.523492	+	1.61114i	0.0681529	+	0.209753i	0.979333	−	0.202256i	$-0.0648273\pi$
$59$	0.523492	+	1.61114i	0.0681529	+	0.209753i	−0.911180	+	0.412009i	$0.864827\pi$
$60$	−18.5367	+	13.4677i	−2.39308	+	1.73867i
$61$	−5.54839	+	4.03114i	−0.710398	+	0.516134i	−0.883302	−	0.468804i	$-0.844685\pi$
$61$	−5.54839	+	4.03114i	−0.710398	+	0.516134i	0.172904	+	0.984939i	$0.444685\pi$
$62$	2.13152	+	6.56015i	0.270703	+	0.833139i
$63$	0.118034	−	0.363271i	0.0148709	−	0.0457679i
$64$	5.60222	+	4.07025i	0.700277	+	0.508781i
$65$	2.26638			0.281110
$66$	5.73877	−	11.9289i	0.706394	−	1.46834i
$67$	−6.17828			−0.754797			−0.377398	−	0.926051i	$-0.623181\pi$
$67$	−6.17828			−0.754797			−0.377398	+	0.926051i	$0.623181\pi$
$68$	3.75789	+	2.73027i	0.455711	+	0.331093i
$69$	3.33354	−	10.2596i	0.401311	−	1.23511i
$70$	2.64256	+	8.13296i	0.315846	+	0.972074i
$71$	4.38234	−	3.18395i	0.520088	−	0.377866i	−0.296549	−	0.955018i	$-0.595836\pi$
$71$	4.38234	−	3.18395i	0.520088	−	0.377866i	0.816637	+	0.577152i	$0.195836\pi$
$72$	1.58914	−	1.15458i	0.187282	−	0.136068i
$73$	2.07103	+	6.37396i	0.242395	+	0.746016i	0.996054	+	0.0887500i	$0.0282872\pi$
$73$	2.07103	+	6.37396i	0.242395	+	0.746016i	−0.753659	+	0.657266i	$0.771713\pi$
$74$	−0.335211	+	1.03167i	−0.0389675	+	0.119930i
$75$	9.18698	+	6.67473i	1.06082	+	0.770732i
$76$	−24.8191			−2.84695
$77$	−2.39815	−	2.29104i	−0.273295	−	0.261088i
$78$	2.60929			0.295444
$79$	−2.14693	−	1.55984i	−0.241549	−	0.175495i	0.460424	−	0.887699i	$-0.347697\pi$
$79$	−2.14693	−	1.55984i	−0.241549	−	0.175495i	−0.701973	+	0.712204i	$0.747697\pi$
$80$	−4.83766	+	14.8888i	−0.540867	+	1.66462i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	11.7805	−	8.55903i	1.30094	−	0.945187i
$83$	−5.41765	+	3.93615i	−0.594664	+	0.432049i	−0.843981	−	0.536373i	$-0.819794\pi$
$83$	−5.41765	+	3.93615i	−0.594664	+	0.432049i	0.249317	+	0.968422i	$0.419794\pi$
$84$	2.04238	+	6.28581i	0.222842	+	0.685838i
$85$	1.21821	−	3.74926i	0.132133	−	0.406665i
$86$	−17.3783	−	12.6261i	−1.87395	−	1.36151i
$87$	7.40020			0.793384
$88$	−3.05216	−	16.7806i	−0.325361	−	1.78882i
$89$	−0.698213			−0.0740105			−0.0370052	−	0.999315i	$-0.511782\pi$
$89$	−0.698213			−0.0740105			−0.0370052	+	0.999315i	$0.511782\pi$
$90$	−2.64256	−	1.91993i	−0.278550	−	0.202378i
$91$	0.202020	−	0.621755i	0.0211775	−	0.0651776i
$92$	−8.41560	−	25.9006i	−0.877387	−	2.70032i
$93$	3.66042	−	2.65945i	0.379568	−	0.275772i
$94$	1.20676	−	0.876765i	0.124468	−	0.0904314i
$95$	6.50911	+	20.0330i	0.667821	+	2.05534i
$96$	−0.427051	+	1.31433i	−0.0435857	+	0.134143i
$97$	12.0209	+	8.73372i	1.22054	+	0.886775i	0.996145	−	0.0877234i	$-0.0279592\pi$
$97$	12.0209	+	8.73372i	1.22054	+	0.886775i	0.224396	+	0.974498i	$0.427959\pi$
$98$	2.46673			0.249178
$99$	1.25544	+	0.169550i	0.126177	+	0.0170404i
$100$	28.6678			2.86678
$101$	−6.97340	−	5.06647i	−0.693879	−	0.504133i	0.184054	−	0.982916i	$-0.441078\pi$
$101$	−6.97340	−	5.06647i	−0.693879	−	0.504133i	−0.877933	+	0.478784i	$0.841078\pi$
$102$	1.40253	−	4.31653i	0.138871	−	0.427401i
$103$	−0.288300	−	0.887296i	−0.0284070	−	0.0874279i	0.935848	−	0.352404i	$-0.114636\pi$
$103$	−0.288300	−	0.887296i	−0.0284070	−	0.0874279i	−0.964255	+	0.264976i	$0.914636\pi$
$104$	2.71988	−	1.97611i	0.266706	−	0.193773i
$105$	4.53801	−	3.29706i	0.442865	−	0.321760i
$106$	7.48729	+	23.0435i	0.727230	+	2.23818i
$107$	2.04635	−	6.29801i	0.197828	−	0.608851i	−0.802104	−	0.597184i	$-0.796286\pi$
$107$	2.04635	−	6.29801i	0.197828	−	0.608851i	0.999932	−	0.0116671i	$-0.00371383\pi$
$108$	−18.0835	−	13.1384i	−1.74008	−	1.26424i
$109$	−4.12507			−0.395110			−0.197555	−	0.980292i	$-0.563300\pi$
$109$	−4.12507			−0.395110			−0.197555	+	0.980292i	$0.563300\pi$
$110$	−24.9702	+	13.4499i	−2.38081	+	1.28240i
$111$	0.711544			0.0675368
$112$	3.65334	+	2.65431i	0.345208	+	0.250809i
$113$	−5.81749	+	17.9044i	−0.547264	+	1.68430i	0.168282	+	0.985739i	$0.446178\pi$
$113$	−5.81749	+	17.9044i	−0.547264	+	1.68430i	−0.715546	+	0.698566i	$0.753822\pi$
$114$	7.49396	+	23.0640i	0.701873	+	2.16014i
$115$	−18.6988	+	13.5855i	−1.74367	+	1.26685i
$116$	15.1140	−	10.9810i	1.40330	−	1.01956i
$117$	0.0771649	+	0.237489i	0.00713390	+	0.0219559i
$118$	1.29131	−	3.97426i	0.118875	−	0.365860i
$119$	−0.919977	−	0.668402i	−0.0843341	−	0.0612723i
$120$	28.8461			2.63328
$121$	6.05253	−	9.18514i	0.550230	−	0.835013i
$122$	16.9173			1.53162
$123$	−7.72732	−	5.61423i	−0.696749	−	0.506218i
$124$	3.52968	−	10.8632i	0.316974	−	0.975546i
$125$	−2.16209	−	6.65422i	−0.193383	−	0.595171i
$126$	−0.762262	+	0.553816i	−0.0679077	+	0.0493378i
$127$	6.44491	−	4.68250i	0.571893	−	0.415505i	−0.263899	−	0.964550i	$-0.585009\pi$
$127$	6.44491	−	4.68250i	0.571893	−	0.415505i	0.835792	+	0.549045i	$0.185009\pi$
$128$	−5.80631	−	17.8700i	−0.513211	−	1.57950i
$129$	−4.35410	+	13.4005i	−0.383357	+	1.17985i
$130$	−4.52285	−	3.28605i	−0.396681	−	0.288205i
$131$	−4.80505			−0.419819			−0.209910	−	0.977721i	$-0.567317\pi$
$131$	−4.80505			−0.419819			−0.209910	+	0.977721i	$0.567317\pi$
$132$	−19.2990	+	10.3952i	−1.67976	+	0.904783i
$133$	6.07602			0.526858
$134$	12.3295	+	8.95793i	1.06511	+	0.773848i
$135$	−5.86218	+	18.0419i	−0.504537	+	1.55280i
$136$	−1.80709	−	5.56166i	−0.154957	−	0.476909i
$137$	17.6995	−	12.8594i	1.51217	−	1.09865i	0.546962	−	0.837157i	$-0.315784\pi$
$137$	17.6995	−	12.8594i	1.51217	−	1.09865i	0.965204	−	0.261496i	$-0.0842160\pi$
$138$	−21.5280	+	15.6410i	−1.83258	+	1.33145i
$139$	−6.12278	−	18.8440i	−0.519327	−	1.59832i	−0.775268	−	0.631632i	$-0.782385\pi$
$139$	−6.12278	−	18.8440i	−0.519327	−	1.59832i	0.255941	−	0.966692i	$-0.417615\pi$
$140$	4.37592	−	13.4677i	0.369833	−	1.13823i
$141$	−0.791567	−	0.575107i	−0.0666620	−	0.0484328i
$142$	−13.3620			−1.12131
$143$	2.14874	+	0.290193i	0.179687	+	0.0242671i
$144$	−1.72487			−0.143740
$145$	−12.8272	−	9.31954i	−1.06524	−	0.773946i
$146$	5.10867	−	15.7229i	0.422796	−	1.30123i
$147$	−0.500000	−	1.53884i	−0.0412393	−	0.126922i
$148$	1.45325	−	1.05584i	0.119456	−	0.0867899i
$149$	−2.55820	+	1.85864i	−0.209576	+	0.152266i	−0.687622	−	0.726069i	$-0.741345\pi$
$149$	−2.55820	+	1.85864i	−0.209576	+	0.152266i	0.478046	+	0.878335i	$0.341345\pi$
$150$	−8.65604	−	26.6406i	−0.706763	−	2.17519i
$151$	2.75892	−	8.49109i	0.224518	−	0.690995i	−0.773822	−	0.633403i	$-0.781658\pi$
$151$	2.75892	−	8.49109i	0.224518	−	0.690995i	0.998340	−	0.0575923i	$-0.0183423\pi$
$152$	25.2788	+	18.3661i	2.05038	+	1.48969i
$153$	0.434354			0.0351155
$154$	1.46403	+	8.04916i	0.117975	+	0.648620i
$155$	−9.69406			−0.778645
$156$	−3.49563	−	2.53972i	−0.279874	−	0.203341i
$157$	0.352179	−	1.08390i	0.0281070	−	0.0865044i	−0.936019	−	0.351949i	$-0.885519\pi$
$157$	0.352179	−	1.08390i	0.0281070	−	0.0865044i	0.964126	+	0.265445i	$0.0855189\pi$
$158$	2.02285	+	6.22570i	0.160930	+	0.495290i
$159$	12.8578	−	9.34172i	1.01969	−	0.740847i
$160$	2.39545	−	1.74040i	0.189377	−	0.137591i
$161$	2.06024	+	6.34077i	0.162370	+	0.499723i
$162$	−5.87567	+	18.0835i	−0.461636	+	1.42077i
$163$	4.09951	+	2.97847i	0.321099	+	0.233292i	0.736644	−	0.676281i	$-0.236409\pi$
$163$	4.09951	+	2.97847i	0.321099	+	0.233292i	−0.415545	+	0.909572i	$0.636409\pi$
$164$	−24.1130			−1.88291
$165$	13.4519	+	12.8511i	1.04723	+	1.00046i
$166$	16.5187			1.28210
$167$	15.9432	+	11.5834i	1.23372	+	0.896351i	0.997164	−	0.0752658i	$-0.0239805\pi$
$167$	15.9432	+	11.5834i	1.23372	+	0.896351i	0.236558	+	0.971617i	$0.423981\pi$
$168$	2.57128	−	7.91358i	0.198378	−	0.610546i
$169$	−3.88515	−	11.9573i	−0.298858	−	0.919789i
$170$	−7.86718	+	5.71584i	−0.603385	+	0.438385i
$171$	−1.87759	+	1.36415i	−0.143583	+	0.104319i
$172$	10.9920	+	33.8300i	0.838135	+	2.57951i
$173$	−4.44824	+	13.6903i	−0.338193	+	1.04085i	0.626935	+	0.779072i	$0.284309\pi$
$173$	−4.44824	+	13.6903i	−0.338193	+	1.04085i	−0.965128	+	0.261779i	$0.915691\pi$
$174$	−14.7680	−	10.7296i	−1.11956	−	0.813409i
$175$	−7.01823			−0.530528
$176$	−6.49295	+	13.4965i	−0.489424	+	1.01734i
$177$	−2.74104			−0.206029
$178$	1.39337	+	1.01235i	0.104438	+	0.0758785i
$179$	−1.44132	+	4.43592i	−0.107729	+	0.331556i	−0.990361	−	0.138508i	$-0.955769\pi$
$179$	−1.44132	+	4.43592i	−0.107729	+	0.331556i	0.882632	+	0.470064i	$0.155769\pi$
$180$	1.67145	+	5.14421i	0.124583	+	0.383427i
$181$	−8.01578	+	5.82381i	−0.595808	+	0.432880i	−0.844389	−	0.535731i	$-0.820036\pi$
$181$	−8.01578	+	5.82381i	−0.595808	+	0.432880i	0.248580	+	0.968611i	$0.420036\pi$
$182$	−1.30464	+	0.947880i	−0.0967067	+	0.0702615i
$183$	−3.42909	−	10.5537i	−0.253486	−	0.780149i
$184$	−10.5949	+	32.6078i	−0.781067	+	2.40388i
$185$	−1.23337	−	0.896093i	−0.0906789	−	0.0658821i
$186$	−11.1608			−0.818349
$187$	1.63504	−	3.39867i	0.119566	−	0.248535i
$188$	−2.47007			−0.180148
$189$	4.42705	+	3.21644i	0.322021	+	0.233962i
$190$	16.0562	−	49.4160i	1.16484	−	3.58502i
$191$	3.07254	+	9.45631i	0.222321	+	0.684234i	0.998552	+	0.0537861i	$0.0171289\pi$
$191$	3.07254	+	9.45631i	0.222321	+	0.684234i	−0.776231	+	0.630448i	$0.782871\pi$
$192$	−9.06458	+	6.58580i	−0.654179	+	0.475289i
$193$	−2.99874	+	2.17871i	−0.215854	+	0.156827i	−0.690458	−	0.723372i	$-0.742591\pi$
$193$	−2.99874	+	2.17871i	−0.215854	+	0.156827i	0.474604	+	0.880199i	$0.342591\pi$
$194$	−11.3262	−	34.8585i	−0.813175	−	2.50269i
$195$	−1.13319	+	3.48760i	−0.0811495	+	0.249752i
$196$	−3.30464	−	2.40097i	−0.236046	−	0.171498i
$197$	5.91982			0.421770			0.210885	−	0.977511i	$-0.432365\pi$
$197$	5.91982			0.421770			0.210885	+	0.977511i	$0.432365\pi$
$198$	−2.25956	−	2.15863i	−0.160580	−	0.153407i
$199$	11.4842			0.814095			0.407047	−	0.913407i	$-0.366558\pi$
$199$	11.4842			0.814095			0.407047	+	0.913407i	$0.366558\pi$
$200$	−29.1988	−	21.2141i	−2.06466	−	1.50007i
$201$	3.08914	−	9.50739i	0.217891	−	0.670599i
$202$	6.57039	+	20.2216i	0.462291	+	1.42279i
$203$	−3.70010	+	2.68828i	−0.259696	+	0.188680i
$204$	−6.08039	+	4.41766i	−0.425713	+	0.309298i
$205$	6.32392	+	19.4630i	0.441682	+	1.35936i
$206$	−0.711159	+	2.18872i	−0.0495488	+	0.152495i
$207$	−2.06024	−	1.49685i	−0.143197	−	0.104038i
$208$	−2.95220			−0.204698
$209$	3.60618	+	19.8266i	0.249445	+	1.37143i
$210$	−13.8366			−0.954817
$211$	−7.05857	−	5.12835i	−0.485932	−	0.353050i	0.317686	−	0.948196i	$-0.397094\pi$
$211$	−7.05857	−	5.12835i	−0.485932	−	0.353050i	−0.803618	+	0.595146i	$0.797094\pi$
$212$	12.3985	−	38.1587i	0.851534	−	2.62075i
$213$	2.70843	+	8.33570i	0.185579	+	0.571153i
$214$	−13.2153	+	9.60146i	−0.903378	+	0.656342i
$215$	24.4234	−	17.7447i	1.66566	−	1.21018i
$216$	8.69598	+	26.7635i	0.591686	+	1.82102i
$217$	−0.864107	+	2.65945i	−0.0586594	+	0.180535i
$218$	8.23210	+	5.98097i	0.557548	+	0.405083i
$219$	−10.8440			−0.732772
$220$	46.5435	+	6.28581i	3.13796	+	0.423789i
$221$	0.743416			0.0500076
$222$	−1.41998	−	1.03167i	−0.0953026	−	0.0692414i
$223$	3.19302	−	9.82712i	0.213821	−	0.658072i	−0.785415	−	0.618970i	$-0.787550\pi$
$223$	3.19302	−	9.82712i	0.213821	−	0.658072i	0.999235	−	0.0391023i	$-0.0124498\pi$
$224$	−0.263932	−	0.812299i	−0.0176347	−	0.0542740i
$225$	2.16875	−	1.57569i	0.144583	−	0.105046i
$226$	37.5693	−	27.2957i	2.49907	−	1.81568i
$227$	−4.10033	−	12.6195i	−0.272149	−	0.837587i	−0.989960	−	0.141349i	$-0.954856\pi$
$227$	−4.10033	−	12.6195i	−0.272149	−	0.837587i	0.717811	−	0.696238i	$-0.245144\pi$
$228$	12.4096	−	38.1927i	0.821843	−	2.52937i
$229$	2.01949	+	1.46725i	0.133452	+	0.0969583i	0.652508	−	0.757781i	$-0.273717\pi$
$229$	2.01949	+	1.46725i	0.133452	+	0.0969583i	−0.519057	+	0.854740i	$0.673717\pi$
$230$	57.0135			3.75936
$231$	4.72462	−	2.54486i	0.310857	−	0.167440i
$232$	−23.5199			−1.54415
$233$	7.76971	+	5.64502i	0.509010	+	0.369818i	0.812448	−	0.583034i	$-0.198134\pi$
$233$	7.76971	+	5.64502i	0.509010	+	0.369818i	−0.303438	+	0.952851i	$0.598134\pi$
$234$	0.190345	−	0.585822i	0.0124433	−	0.0382964i
$235$	0.647806	+	1.99374i	0.0422582	+	0.130057i
$236$	−5.59825	+	4.06737i	−0.364415	+	0.264763i
$237$	3.47381	−	2.52387i	0.225648	−	0.163943i
$238$	0.866809	+	2.66776i	0.0561869	+	0.172925i
$239$	1.71914	−	5.29098i	0.111202	−	0.342245i	−0.879934	−	0.475096i	$-0.842413\pi$
$239$	1.71914	−	5.29098i	0.111202	−	0.342245i	0.991136	+	0.132851i	$0.0424132\pi$
$240$	−20.4927	−	14.8888i	−1.32280	−	0.961067i
$241$	15.0208			0.967572			0.483786	−	0.875186i	$-0.339261\pi$
$241$	15.0208			0.967572			0.483786	+	0.875186i	$0.339261\pi$
$242$	−25.3962	+	9.55452i	−1.63253	+	0.614188i
$243$	−3.94427			−0.253025
$244$	−22.6639	−	16.4663i	−1.45090	−	1.05414i
$245$	−1.07128	+	3.29706i	−0.0684415	+	0.210641i
$246$	7.28074	+	22.4078i	0.464203	+	1.42867i
$247$	−3.21358	+	2.33481i	−0.204475	+	0.148560i
$248$	−11.6338	+	8.45246i	−0.738748	+	0.536732i
$249$	−3.34829	−	10.3050i	−0.212189	−	0.653051i
$250$	−5.33329	+	16.4142i	−0.337307	+	1.03812i
$251$	−22.3394	−	16.2305i	−1.41005	−	1.02446i	−0.993315	−	0.115436i	$-0.963173\pi$
$251$	−22.3394	−	16.2305i	−1.41005	−	1.02446i	−0.416738	−	0.909027i	$-0.636827\pi$
$252$	1.56024			0.0982860
$253$	−19.4677	+	10.4861i	−1.22393	+	0.659253i
$254$	−19.6508			−1.23300
$255$	5.16042	+	3.74926i	0.323158	+	0.234788i
$256$	−10.0429	+	30.9089i	−0.627682	+	1.93181i
$257$	−8.79709	−	27.0747i	−0.548747	−	1.68887i	−0.711909	−	0.702271i	$-0.752169\pi$
$257$	−8.79709	−	27.0747i	−0.548747	−	1.68887i	0.163162	−	0.986599i	$-0.447831\pi$
$258$	28.1187	−	20.4295i	1.75060	−	1.27188i
$259$	−0.355772	+	0.258483i	−0.0221066	+	0.0160614i
$260$	2.86077	+	8.80454i	0.177417	+	0.546034i
$261$	0.539837	−	1.66145i	0.0334151	−	0.102841i
$262$	9.58910	+	6.96689i	0.592417	+	0.430416i
$263$	14.1803			0.874397			0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803			0.874397			0.437199	+	0.899365i	$0.355971\pi$
$264$	27.3488	+	3.69352i	1.68320	+	0.227321i
$265$	−34.0519			−2.09179
$266$	−12.1255	−	8.80968i	−0.743461	−	0.540156i
$267$	0.349107	−	1.07444i	0.0213650	−	0.0657546i
$268$	−7.79860	−	24.0016i	−0.476375	−	1.46613i
$269$	19.5731	−	14.2207i	1.19339	−	0.867050i	0.199774	−	0.979842i	$-0.435979\pi$
$269$	19.5731	−	14.2207i	1.19339	−	0.867050i	0.993619	+	0.112792i	$0.0359793\pi$
$270$	37.8579	−	27.5054i	2.30396	−	1.67392i
$271$	2.30210	+	7.08513i	0.139843	+	0.430391i	0.996312	−	0.0858070i	$-0.0273468\pi$
$271$	2.30210	+	7.08513i	0.139843	+	0.430391i	−0.856469	+	0.516198i	$0.827347\pi$
$272$	−1.58684	+	4.88381i	−0.0962166	+	0.296124i
$273$	0.855772	+	0.621755i	0.0517937	+	0.0376303i
$274$	−53.9665			−3.26024
$275$	−4.16539	−	22.9011i	−0.251182	−	1.38099i
$276$	44.0647			2.65238
$277$	15.5242	+	11.2790i	0.932761	+	0.677690i	0.946667	−	0.322213i	$-0.104427\pi$
$277$	15.5242	+	11.2790i	0.932761	+	0.677690i	−0.0139064	+	0.999903i	$0.504427\pi$
$278$	−15.1032	+	46.4830i	−0.905833	+	2.78787i
$279$	−0.330060	−	1.01582i	−0.0197602	−	0.0608155i
$280$	−14.4230	+	10.4790i	−0.861942	+	0.626238i
$281$	1.53764	−	1.11716i	0.0917279	−	0.0666442i	−0.540976	−	0.841038i	$-0.681945\pi$
$281$	1.53764	−	1.11716i	0.0917279	−	0.0666442i	0.632704	+	0.774394i	$0.281945\pi$
$282$	0.745821	+	2.29540i	0.0444130	+	0.136689i
$283$	2.24092	−	6.89685i	0.133209	−	0.409975i	−0.862098	−	0.506741i	$-0.830850\pi$
$283$	2.24092	−	6.89685i	0.133209	−	0.409975i	0.995307	+	0.0967663i	$0.0308499\pi$
$284$	17.9008	+	13.0057i	1.06222	+	0.771747i
$285$	−34.0822			−2.01885
$286$	−3.86734	−	3.69460i	−0.228680	−	0.218466i
$287$	5.90315			0.348452
$288$	0.263932	+	0.191758i	0.0155523	+	0.0112994i
$289$	−4.85369	+	14.9381i	−0.285511	+	0.878714i
$290$	12.0859	+	37.1967i	0.709710	+	2.18426i
$291$	−19.4503	+	14.1315i	−1.14020	+	0.828400i
$292$	−22.1477	+	16.0912i	−1.29609	+	0.941668i
$293$	−1.01078	−	3.11088i	−0.0590507	−	0.181739i	0.917180	−	0.398473i	$-0.130460\pi$
$293$	−1.01078	−	3.11088i	−0.0590507	−	0.181739i	−0.976231	+	0.216734i	$0.930460\pi$
$294$	−1.23337	+	3.79591i	−0.0719314	+	0.221382i
$295$	4.75122	+	3.45197i	0.276627	+	0.200981i
$296$	−2.26148			−0.131446
$297$	−7.86803	+	16.3548i	−0.456550	+	0.949005i
$298$	7.80008			0.451846
$299$	−3.52619	−	2.56193i	−0.203925	−	0.148160i
$300$	−14.3339	+	44.1152i	−0.827569	+	2.54699i
$301$	−2.69098	−	8.28199i	−0.155106	−	0.477366i
$302$	−17.8171	+	12.9449i	−1.02526	+	0.744894i
$303$	11.2832	−	8.19772i	0.648203	−	0.470947i
$304$	−8.47880	−	26.0951i	−0.486293	−	1.49665i
$305$	−7.34703	+	22.6118i	−0.420690	+	1.29475i
$306$	−0.866809	−	0.629774i	−0.0495522	−	0.0360018i
$307$	31.6121			1.80420			0.902099	−	0.431530i	$-0.142026\pi$
$307$	31.6121			1.80420			0.902099	+	0.431530i	$0.142026\pi$
$308$	5.87322	−	12.2083i	0.334658	−	0.695635i
$309$	1.50956			0.0858758
$310$	19.3457	+	14.0555i	1.09876	+	0.798298i
$311$	−2.79298	+	8.59592i	−0.158376	+	0.487430i	−0.998487	−	0.0549835i	$-0.982489\pi$
$311$	−2.79298	+	8.59592i	−0.158376	+	0.487430i	0.840112	+	0.542414i	$0.182489\pi$
$312$	1.68098	+	5.17352i	0.0951666	+	0.292893i
$313$	−11.7300	+	8.52232i	−0.663017	+	0.481710i	−0.867680	−	0.497122i	$-0.834390\pi$
$313$	−11.7300	+	8.52232i	−0.663017	+	0.481710i	0.204664	+	0.978832i	$0.434390\pi$
$314$	−2.27437	+	1.65243i	−0.128350	+	0.0932518i
$315$	−0.409192	−	1.25936i	−0.0230554	−	0.0709571i
$316$	3.34973	−	10.3094i	0.188437	−	0.579950i
$317$	14.9000	+	10.8255i	0.836865	+	0.608018i	0.921493	−	0.388394i	$-0.126970\pi$
$317$	14.9000	+	10.8255i	0.836865	+	0.608018i	−0.0846278	+	0.996413i	$0.526970\pi$
$318$	−39.2040			−2.19845
$319$	−10.9681	−	10.4782i	−0.614098	−	0.586668i
$320$	24.0061			1.34198
$321$	8.66846	+	6.29801i	0.483826	+	0.351520i
$322$	5.08206	−	15.6410i	0.283212	−	0.871638i
$323$	2.13511	+	6.57120i	0.118801	+	0.365632i
$324$	25.4729	−	18.5071i	1.41516	−	1.02817i
$325$	3.71191	−	2.69686i	0.205900	−	0.149595i
$326$	−3.86259	−	11.8878i	−0.213929	−	0.658407i
$327$	2.06253	−	6.34783i	0.114058	−	0.351036i
$328$	24.5596	+	17.8436i	1.35608	+	0.985246i
$329$	0.604703			0.0333384
$330$	−8.21217	−	45.1501i	−0.452065	−	2.48543i
$331$	−6.47653			−0.355982			−0.177991	−	0.984032i	$-0.556960\pi$
$331$	−6.47653			−0.355982			−0.177991	+	0.984032i	$0.556960\pi$
$332$	−22.1298	−	16.0782i	−1.21453	−	0.882409i
$333$	0.0519064	−	0.159752i	0.00284445	−	0.00875433i
$334$	−15.0218	−	46.2324i	−0.821957	−	2.52972i
$335$	−17.3279	+	12.5894i	−0.946723	+	0.687834i
$336$	−5.91123	+	4.29476i	−0.322484	+	0.234298i
$337$	1.93346	+	5.95059i	0.105322	+	0.324149i	0.989806	−	0.142422i	$-0.0454891\pi$
$337$	1.93346	+	5.95059i	0.105322	+	0.324149i	−0.884484	+	0.466571i	$0.845489\pi$
$338$	−9.58362	+	29.4954i	−0.521280	+	1.60434i
$339$	−24.6433	−	17.9044i	−1.33844	−	0.972434i
$340$	16.1030			0.873308
$341$	−9.19087	−	1.24125i	−0.497714	−	0.0672174i
$342$	5.72487			0.309566
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	13.8385	−	42.5906i	0.746124	−	2.29633i
$345$	−11.5565	−	35.5672i	−0.622181	−	1.91488i
$346$	28.7266	−	20.8711i	1.54435	−	1.12204i
$347$	−18.3773	+	13.3519i	−0.986547	+	0.716768i	−0.959162	−	0.282857i	$-0.908718\pi$
$347$	−18.3773	+	13.3519i	−0.986547	+	0.716768i	−0.0273845	+	0.999625i	$0.508718\pi$
$348$	9.34099	+	28.7486i	0.500729	+	1.54109i
$349$	9.17597	−	28.2407i	0.491178	−	1.51169i	−0.331651	−	0.943402i	$-0.607606\pi$
$349$	9.17597	−	28.2407i	0.491178	−	1.51169i	0.822829	−	0.568289i	$-0.192394\pi$
$350$	14.0058	+	10.1758i	0.748640	+	0.543919i
$351$	−3.57742			−0.190948
$352$	2.49396	−	1.34334i	0.132928	−	0.0716003i
$353$	−6.82506			−0.363262			−0.181631	−	0.983367i	$-0.558138\pi$
$353$	−6.82506			−0.363262			−0.181631	+	0.983367i	$0.558138\pi$
$354$	5.47010	+	3.97426i	0.290732	+	0.211229i
$355$	5.80297	−	17.8597i	0.307990	−	0.947896i
$356$	−0.881328	−	2.71245i	−0.0467103	−	0.143760i
$357$	1.48855	−	1.08150i	0.0787826	−	0.0572389i
$358$	9.30801	−	6.76266i	0.491944	−	0.357418i
$359$	−2.24337	−	6.90439i	−0.118401	−	0.364400i	0.874241	−	0.485493i	$-0.161360\pi$
$359$	−2.24337	−	6.90439i	−0.118401	−	0.364400i	−0.992641	+	0.121094i	$0.961360\pi$
$360$	2.10429	−	6.47635i	0.110906	−	0.341334i
$361$	−14.4960	−	10.5320i	−0.762947	−	0.554314i
$362$	24.4405			1.28456
$363$	11.1082	+	13.9065i	0.583030	+	0.729900i
$364$	2.67042			0.139968
$365$	18.7967	+	13.6566i	0.983863	+	0.714818i
$366$	−8.45865	+	26.0330i	−0.442141	+	1.36077i
$367$	−11.2286	−	34.5582i	−0.586130	−	1.80392i	−0.594686	−	0.803958i	$-0.702723\pi$
$367$	−11.2286	−	34.5582i	−0.586130	−	1.80392i	0.00855584	−	0.999963i	$-0.497277\pi$
$368$	24.3571	−	17.6965i	1.26970	−	0.922494i
$369$	−1.82417	+	1.32534i	−0.0949627	+	0.0689944i
$370$	1.16209	+	3.57654i	0.0604140	+	0.185935i
$371$	−3.03531	+	9.34172i	−0.157585	+	0.484998i
$372$	14.9519	+	10.8632i	0.775222	+	0.563232i
$373$	−14.2913			−0.739977			−0.369989	−	0.929036i	$-0.620638\pi$
$373$	−14.2913			−0.739977			−0.369989	+	0.929036i	$0.620638\pi$
$374$	−8.19069	+	4.41182i	−0.423531	+	0.228130i
$375$	11.3208			0.584605
$376$	2.51582	+	1.82785i	0.129743	+	0.0942641i
$377$	0.923955	−	2.84364i	0.0475861	−	0.146455i
$378$	−4.17120	−	12.8376i	−0.214543	−	0.660297i
$379$	2.05917	−	1.49608i	0.105773	−	0.0768482i	−0.533642	−	0.845711i	$-0.679177\pi$
$379$	2.05917	−	1.49608i	0.105773	−	0.0768482i	0.639414	+	0.768862i	$0.279177\pi$
$380$	−69.6088	+	50.5738i	−3.57086	+	2.59438i
$381$	3.98317	+	12.2589i	0.204064	+	0.628045i
$382$	7.57913	−	23.3262i	0.387782	−	1.19347i
$383$	18.7180	+	13.5994i	0.956444	+	0.694897i	0.952322	−	0.305094i	$-0.0986879\pi$
$383$	18.7180	+	13.5994i	0.956444	+	0.694897i	0.00412192	+	0.999992i	$0.498688\pi$
$384$	30.4023			1.55146
$385$	−11.3944	−	1.53884i	−0.580713	−	0.0784266i
$386$	9.14330			0.465382
$387$	2.69098	+	1.95511i	0.136790	+	0.0993840i
$388$	−18.7556	+	57.7237i	−0.952169	+	2.93048i
$389$	9.35130	+	28.7804i	0.474130	+	1.45922i	0.847128	+	0.531390i	$0.178330\pi$
$389$	9.35130	+	28.7804i	0.474130	+	1.45922i	−0.372998	+	0.927832i	$0.621670\pi$
$390$	7.31813	−	5.31693i	0.370568	−	0.269233i
$391$	−6.13356	+	4.45629i	−0.310188	+	0.225364i
$392$	1.58914	+	4.89086i	0.0802636	+	0.247026i
$393$	2.40253	−	7.39422i	0.121191	−	0.372989i
$394$	−11.8138	−	8.58320i	−0.595169	−	0.432415i
$395$	−9.19985			−0.462894
$396$	0.926019	+	5.09121i	0.0465342	+	0.255843i
$397$	−22.6740			−1.13798			−0.568989	−	0.822345i	$-0.692665\pi$
$397$	−22.6740			−1.13798			−0.568989	+	0.822345i	$0.692665\pi$
$398$	−22.9182	−	16.6511i	−1.14879	−	0.834643i
$399$	−3.03801	+	9.35004i	−0.152091	+	0.468087i
$400$	9.79361	+	30.1416i	0.489680	+	1.50708i
$401$	13.1211	−	9.53304i	0.655237	−	0.476057i	−0.209814	−	0.977741i	$-0.567286\pi$
$401$	13.1211	−	9.53304i	0.655237	−	0.476057i	0.865051	+	0.501684i	$0.167286\pi$
$402$	−19.9496	+	14.4942i	−0.994996	+	0.722907i
$403$	−0.564911	−	1.73862i	−0.0281402	−	0.0866068i
$404$	10.8802	−	33.4858i	0.541309	−	1.66598i
$405$	−21.6188	−	15.7070i	−1.07425	−	0.780485i
$406$	11.2818			0.559905
$407$	−1.05461	−	1.00750i	−0.0522750	−	0.0499401i
$408$	9.46207			0.468442
$409$	28.3653	+	20.6086i	1.40257	+	1.01903i	0.994351	+	0.106146i	$0.0338512\pi$
$409$	28.3653	+	20.6086i	1.40257	+	1.01903i	0.408222	+	0.912883i	$0.366149\pi$
$410$	15.5994	−	48.0101i	0.770400	−	2.37105i
$411$	10.9389	+	33.6664i	0.539575	+	1.66064i
$412$	3.08310	−	2.24000i	0.151893	−	0.110357i
$413$	1.37052	−	0.995741i	0.0674389	−	0.0489972i
$414$	1.94118	+	5.97432i	0.0954036	+	0.293622i
$415$	−7.17390	+	22.0790i	−0.352153	+	1.08382i
$416$	0.451731	+	0.328202i	0.0221479	+	0.0160914i
$417$	32.0593			1.56995
$418$	21.5502	−	44.7951i	1.05405	−	2.19100i
$419$	28.2633			1.38075			0.690376	−	0.723451i	$-0.257445\pi$
$419$	28.2633			1.38075			0.690376	+	0.723451i	$0.257445\pi$
$420$	18.5367	+	13.4677i	0.904499	+	0.657157i
$421$	−4.26279	+	13.1195i	−0.207756	+	0.639406i	0.791833	+	0.610737i	$0.209127\pi$
$421$	−4.26279	+	13.1195i	−0.207756	+	0.639406i	−0.999589	+	0.0286688i	$0.990873\pi$
$422$	6.65064	+	20.4686i	0.323748	+	0.996394i
$423$	−0.186864	+	0.135764i	−0.00908562	+	0.00660109i
$424$	−40.8656	+	29.6906i	−1.98461	+	1.44190i
$425$	−2.46621	−	7.59020i	−0.119629	−	0.368179i
$426$	6.68098	−	20.5619i	0.323694	−	0.996229i
$427$	5.54839	+	4.03114i	0.268505	+	0.195080i
$428$	27.0498			1.30750
$429$	−1.52093	+	3.16148i	−0.0734313	+	0.152638i
$430$	−74.4682			−3.59117
$431$	−22.7900	−	16.5579i	−1.09776	−	0.797568i	−0.117065	−	0.993124i	$-0.537349\pi$
$431$	−22.7900	−	16.5579i	−1.09776	−	0.797568i	−0.980692	+	0.195557i	$0.937349\pi$
$432$	7.63611	−	23.5015i	0.367392	−	1.13072i
$433$	4.38165	+	13.4853i	0.210569	+	0.648064i	0.999439	+	0.0335038i	$0.0106666\pi$
$433$	4.38165	+	13.4853i	0.210569	+	0.648064i	−0.788870	+	0.614560i	$0.789333\pi$
$434$	5.58039	−	4.05439i	0.267867	−	0.194617i
$435$	20.7549	−	15.0793i	0.995122	−	0.722999i
$436$	−5.20692	−	16.0252i	−0.249366	−	0.767470i
$437$	12.5181	−	38.5267i	0.598821	−	1.84298i
$438$	21.6407	+	15.7229i	1.03403	+	0.751267i
$439$	28.0185			1.33725			0.668625	−	0.743599i	$-0.266883\pi$
$439$	28.0185			1.33725			0.668625	+	0.743599i	$0.266883\pi$
$440$	−42.7540	−	40.8443i	−2.03822	−	1.94718i
$441$	−0.381966			−0.0181889
$442$	−1.48358	−	1.07789i	−0.0705668	−	0.0512698i
$443$	5.35743	−	16.4885i	0.254539	−	0.783391i	−0.739381	−	0.673287i	$-0.764882\pi$
$443$	5.35743	−	16.4885i	0.254539	−	0.783391i	0.993920	−	0.110103i	$-0.0351182\pi$
$444$	0.898155	+	2.76424i	0.0426245	+	0.131185i
$445$	−1.95824	+	1.42274i	−0.0928295	+	0.0674446i
$446$	−20.6205	+	14.9817i	−0.976409	+	0.709403i
$447$	−1.58106	−	4.86599i	−0.0747813	−	0.230153i
$448$	2.13986	−	6.58580i	0.101099	−	0.311150i
$449$	23.8834	+	17.3523i	1.12713	+	0.818906i	0.985274	−	0.170982i	$-0.0546940\pi$
$449$	23.8834	+	17.3523i	1.12713	+	0.818906i	0.141853	+	0.989888i	$0.454694\pi$
$450$	−6.61263			−0.311722
$451$	3.50358	+	19.2625i	0.164977	+	0.907036i
$452$	−76.8990			−3.61702
$453$	11.6870	+	8.49109i	0.549102	+	0.398946i
$454$	−10.1144	+	31.1290i	−0.474693	+	1.46096i
$455$	−0.700350	−	2.15546i	−0.0328329	−	0.101049i
$456$	−40.9019	+	29.7170i	−1.91541	+	1.39163i
$457$	−7.84524	+	5.69990i	−0.366985	+	0.266630i	−0.755960	−	0.654618i	$-0.772829\pi$
$457$	−7.84524	+	5.69990i	−0.366985	+	0.266630i	0.388975	+	0.921248i	$0.372829\pi$
$458$	−1.90278	−	5.85615i	−0.0889110	−	0.273640i
$459$	−1.92291	+	5.91810i	−0.0897537	+	0.276233i
$460$	−76.3802	−	55.4935i	−3.56125	−	2.58740i
$461$	−19.2216			−0.895240			−0.447620	−	0.894224i	$-0.647728\pi$
$461$	−19.2216			−0.895240			−0.447620	+	0.894224i	$0.647728\pi$
$462$	−13.1184	−	1.77167i	−0.610323	−	0.0824256i
$463$	20.5327			0.954235			0.477117	−	0.878840i	$-0.341682\pi$
$463$	20.5327			0.954235			0.477117	+	0.878840i	$0.341682\pi$
$464$	16.7088	+	12.1397i	0.775688	+	0.563570i
$465$	4.84703	−	14.9176i	0.224776	−	0.691788i
$466$	−7.32068	−	22.5307i	−0.339124	−	1.04372i
$467$	−27.2408	+	19.7916i	−1.26055	+	0.915845i	−0.998785	−	0.0492858i	$-0.984305\pi$
$467$	−27.2408	+	19.7916i	−1.26055	+	0.915845i	−0.261768	+	0.965131i	$0.584305\pi$
$468$	−0.825206	+	0.599547i	−0.0381452	+	0.0277141i
$469$	1.90919	+	5.87589i	0.0881583	+	0.271323i
$470$	1.59796	−	4.91803i	0.0737086	−	0.226852i
$471$	1.49186	+	1.08390i	0.0687411	+	0.0499433i
$472$	8.71178			0.400992
$473$	25.4278	−	13.6964i	1.16917	−	0.629759i
$474$	−10.5918			−0.486498
$475$	34.4988	+	25.0649i	1.58292	+	1.15006i
$476$	1.43539	−	4.41766i	0.0657908	−	0.202483i
$477$	−1.15938	−	3.56822i	−0.0530846	−	0.163378i
$478$	−11.1022	+	8.06623i	−0.507804	+	0.368941i
$479$	−11.4644	+	8.32937i	−0.523822	+	0.380579i	−0.818042	−	0.575159i	$-0.804940\pi$
$479$	−11.4644	+	8.32937i	−0.523822	+	0.380579i	0.294220	+	0.955738i	$0.404940\pi$
$480$	1.48047	+	4.55642i	0.0675740	+	0.207971i
$481$	0.0888401	−	0.273422i	0.00405076	−	0.0124670i
$482$	−29.9758	−	21.7787i	−1.36536	−	0.991993i
$483$	−10.7876			−0.490851
$484$	43.3227	+	11.9191i	1.96921	+	0.541776i
$485$	51.5111			2.33900
$486$	7.87130	+	5.71883i	0.357049	+	0.259412i
$487$	8.57259	−	26.3837i	0.388461	−	1.19556i	−0.545477	−	0.838126i	$-0.683652\pi$
$487$	8.57259	−	26.3837i	0.388461	−	1.19556i	0.933938	−	0.357434i	$-0.116348\pi$
$488$	10.8986	+	33.5424i	0.493356	+	1.51839i
$489$	−6.63315	+	4.81927i	−0.299962	+	0.217935i
$490$	6.91831	−	5.02644i	0.312537	−	0.227072i
$491$	−1.06393	−	3.27444i	−0.0480145	−	0.147774i	0.924175	−	0.381970i	$-0.124754\pi$
$491$	−1.06393	−	3.27444i	−0.0480145	−	0.147774i	−0.972189	+	0.234196i	$0.924754\pi$
$492$	12.0565	−	37.1061i	0.543549	−	1.67287i
$493$	−4.20758	−	3.05699i	−0.189500	−	0.137680i
$494$	9.79837			0.440850
$495$	3.86656	−	2.08268i	0.173789	−	0.0936093i
$496$	12.6275			0.566992
$497$	−4.38234	−	3.18395i	−0.196575	−	0.142820i
$498$	−8.25933	+	25.4196i	−0.370109	+	1.13908i
$499$	−0.800117	−	2.46251i	−0.0358181	−	0.110237i	0.931549	−	0.363616i	$-0.118458\pi$
$499$	−0.800117	−	2.46251i	−0.0358181	−	0.110237i	−0.967367	+	0.253379i	$0.918458\pi$
$500$	23.1215	−	16.7987i	1.03402	−	0.751262i
$501$	−25.7966	+	18.7424i	−1.15251	+	0.837347i
$502$	21.0484	+	64.7803i	0.939435	+	2.89129i
$503$	−7.07731	+	21.7817i	−0.315561	+	0.971198i	0.659961	+	0.751300i	$0.270573\pi$
$503$	−7.07731	+	21.7817i	−0.315561	+	0.971198i	−0.975523	+	0.219899i	$0.929427\pi$
$504$	−1.58914	−	1.15458i	−0.0707858	−	0.0514289i
$505$	−29.8818			−1.32972
$506$	54.0542	+	7.30014i	2.40300	+	0.324531i
$507$	20.3429			0.903460
$508$	26.3259	+	19.1269i	1.16803	+	0.848620i
$509$	−7.44685	+	22.9191i	−0.330076	+	1.01587i	0.639021	+	0.769189i	$0.279340\pi$
$509$	−7.44685	+	22.9191i	−0.330076	+	1.01587i	−0.969097	+	0.246680i	$0.920660\pi$
$510$	−4.86218	−	14.9643i	−0.215301	−	0.662629i
$511$	5.42202	−	3.93933i	0.239856	−	0.174266i
$512$	34.4547	−	25.0328i	1.52270	−	1.10631i
$513$	−10.2744	−	31.6215i	−0.453628	−	1.39612i
$514$	−21.7001	+	66.7859i	−0.957149	+	2.94580i
$515$	−2.61662	−	1.90108i	−0.115302	−	0.0837717i
$516$	−57.5550			−2.53372
$517$	0.358897	+	1.97320i	0.0157843	+	0.0867813i
$518$	1.08477			0.0476619
$519$	−18.8430	−	13.6903i	−0.827117	−	0.600936i
$520$	3.60159	−	11.0846i	0.157940	−	0.486090i
$521$	−10.3538	−	31.8658i	−0.453610	−	1.39607i	−0.872760	−	0.488150i	$-0.837672\pi$
$521$	−10.3538	−	31.8658i	−0.453610	−	1.39607i	0.419150	−	0.907917i	$-0.362328\pi$
$522$	−3.48626	+	2.53292i	−0.152589	+	0.110863i
$523$	25.2068	−	18.3138i	1.10222	−	0.800808i	0.120798	−	0.992677i	$-0.461455\pi$
$523$	25.2068	−	18.3138i	1.10222	−	0.800808i	0.981421	+	0.191869i	$0.0614548\pi$
$524$	−6.06524	−	18.6669i	−0.264961	−	0.815466i
$525$	3.50911	−	10.7999i	0.153150	−	0.471348i
$526$	−28.2987	−	20.5602i	−1.23388	−	0.896467i
$527$	−3.17983			−0.138516
$528$	−17.5226	−	16.7399i	−0.762572	−	0.728510i
$529$	21.4500			0.932608
$530$	67.9548	+	49.3721i	2.95177	+	2.14459i
$531$	−0.199956	+	0.615402i	−0.00867736	+	0.0267062i
$532$	7.66953	+	23.6044i	0.332516	+	1.02338i
$533$	−3.12215	+	2.26838i	−0.135235	+	0.0982543i
$534$	−2.25453	+	1.63801i	−0.0975629	+	0.0708836i
$535$	−7.09413	−	21.8335i	−0.306706	−	0.943944i
$536$	−9.81813	+	30.2171i	−0.424079	+	1.30518i
$537$	−6.10552	−	4.43592i	−0.263473	−	0.191424i
$538$	−59.6793			−2.57296
$539$	−1.43784	+	2.98875i	−0.0619320	+	0.128735i
$540$	−77.4898			−3.33463
$541$	−18.2896	−	13.2881i	−0.786330	−	0.571302i	0.120542	−	0.992708i	$-0.461537\pi$
$541$	−18.2896	−	13.2881i	−0.786330	−	0.571302i	−0.906872	+	0.421406i	$0.861537\pi$
$542$	5.67866	−	17.4771i	0.243919	−	0.750707i
$543$	−4.95402	−	15.2469i	−0.212598	−	0.654308i
$544$	0.785754	−	0.570884i	0.0336889	−	0.0244764i
$545$	−11.5694	+	8.40563i	−0.495577	+	0.360058i
$546$	−0.806315	−	2.48158i	−0.0345071	−	0.106202i
$547$	−8.48072	+	26.1010i	−0.362610	+	1.11600i	0.588855	+	0.808239i	$0.299579\pi$
$547$	−8.48072	+	26.1010i	−0.362610	+	1.11600i	−0.951464	+	0.307759i	$0.900421\pi$
$548$	72.2981	+	52.5277i	3.08842	+	2.24387i
$549$	−2.61959			−0.111801
$550$	−24.8919	+	51.7415i	−1.06140	+	2.20627i
$551$	27.7891			1.18386
$552$	−44.8808	−	32.6078i	−1.91025	−	1.38788i
$553$	−0.820054	+	2.52387i	−0.0348723	+	0.107326i
$554$	−14.6271	−	45.0174i	−0.621444	−	1.91261i
$555$	1.99563	−	1.44991i	0.0847097	−	0.0615452i
$556$	65.4773	−	47.5721i	2.77686	−	2.01750i
$557$	−9.34788	−	28.7698i	−0.396082	−	1.21902i	−0.928115	−	0.372293i	$-0.878572\pi$
$557$	−9.34788	−	28.7698i	−0.396082	−	1.21902i	0.532033	−	0.846724i	$-0.321428\pi$
$558$	−0.814168	+	2.50575i	−0.0344665	+	0.106077i
$559$	4.60574	+	3.34626i	0.194802	+	0.141532i
$560$	15.6550			0.661544
$561$	4.41249	+	4.21540i	0.186296	+	0.177974i
$562$	−4.68834			−0.197766
$563$	−6.03716	−	4.38625i	−0.254436	−	0.184858i	0.453255	−	0.891381i	$-0.350263\pi$
$563$	−6.03716	−	4.38625i	−0.254436	−	0.184858i	−0.707690	+	0.706523i	$0.750263\pi$
$564$	1.23504	−	3.80105i	0.0520044	−	0.160053i
$565$	20.1677	+	62.0698i	0.848461	+	2.61129i
$566$	−14.4718	+	10.5144i	−0.608297	+	0.441954i
$567$	−6.23607	+	4.53077i	−0.261890	+	0.190274i
$568$	−8.60815	−	26.4932i	−0.361190	−	1.11163i
$569$	11.0159	−	33.9036i	0.461812	−	1.42131i	−0.401136	−	0.916019i	$-0.631384\pi$
$569$	11.0159	−	33.9036i	0.461812	−	1.42131i	0.862948	−	0.505293i	$-0.168616\pi$
$570$	68.0153	+	49.4160i	2.84885	+	2.06981i
$571$	25.8902			1.08347			0.541737	−	0.840548i	$-0.317767\pi$
$571$	25.8902			1.08347			0.541737	+	0.840548i	$0.317767\pi$
$572$	1.58492	+	8.71382i	0.0662689	+	0.364343i
$573$	−16.0880			−0.672087
$574$	−11.7805	−	8.55903i	−0.491708	−	0.357247i
$575$	−14.4592	+	44.5010i	−0.602992	+	1.85582i
$576$	0.817352	+	2.51555i	0.0340563	+	0.104815i
$577$	−6.60467	+	4.79857i	−0.274956	+	0.199767i	−0.716714	−	0.697367i	$-0.754355\pi$
$577$	−6.60467	+	4.79857i	−0.274956	+	0.199767i	0.441758	+	0.897134i	$0.354355\pi$
$578$	31.3451	−	22.7735i	1.30378	−	0.947254i
$579$	−1.85332	−	5.70394i	−0.0770215	−	0.237048i
$580$	20.0136	−	61.5955i	0.831020	−	2.55762i
$581$	5.41765	+	3.93615i	0.224762	+	0.163299i
$582$	59.3048			2.45826
$583$	−32.2843	−	4.36008i	−1.33708	−	0.180576i
$584$	34.4653			1.42619
$585$	0.700350	+	0.508834i	0.0289559	+	0.0210377i
$586$	−2.49333	+	7.67370i	−0.102999	+	0.316997i
$587$	−3.85140	−	11.8534i	−0.158964	−	0.489242i	0.839577	−	0.543241i	$-0.182803\pi$
$587$	−3.85140	−	11.8534i	−0.158964	−	0.489242i	−0.998541	+	0.0539994i	$0.982803\pi$
$588$	5.34703	−	3.88484i	0.220508	−	0.160208i
$589$	13.7456	−	9.98673i	0.566376	−	0.411496i
$590$	−4.47664	−	13.7777i	−0.184300	−	0.567218i
$591$	−2.95991	+	9.10967i	−0.121754	+	0.374722i
$592$	1.60659	+	1.16725i	0.0660304	+	0.0479739i
$593$	−23.6707			−0.972037			−0.486019	−	0.873948i	$-0.661551\pi$
$593$	−23.6707			−0.972037			−0.486019	+	0.873948i	$0.661551\pi$
$594$	39.4147	−	21.2303i	1.61720	−	0.871088i
$595$	−3.94221			−0.161615
$596$	−10.4497	−	7.59212i	−0.428034	−	0.310985i
$597$	−5.74211	+	17.6724i	−0.235009	+	0.723283i
$598$	3.32241	+	10.2253i	0.135863	+	0.418144i
$599$	−31.5362	+	22.9124i	−1.28853	+	0.936175i	−0.999775	−	0.0212271i	$-0.993243\pi$
$599$	−31.5362	+	22.9124i	−1.28853	+	0.936175i	−0.288759	+	0.957402i	$0.593243\pi$
$600$	47.2446	−	34.3252i	1.92875	−	1.40132i
$601$	9.44078	+	29.0557i	0.385097	+	1.18521i	0.936410	+	0.350909i	$0.114127\pi$
$601$	9.44078	+	29.0557i	0.385097	+	1.18521i	−0.551312	+	0.834299i	$0.685873\pi$
$602$	−6.63793	+	20.4295i	−0.270542	+	0.832643i
$603$	−1.90919	−	1.38711i	−0.0777483	−	0.0564875i
$604$	36.4690			1.48390
$605$	−1.74132	−	38.0943i	−0.0707946	−	1.54875i
$606$	−34.4030			−1.39753
$607$	−30.4330	−	22.1109i	−1.23524	−	0.897454i	−0.237967	−	0.971273i	$-0.576481\pi$
$607$	−30.4330	−	22.1109i	−1.23524	−	0.897454i	−0.997272	+	0.0738195i	$0.976481\pi$
$608$	−1.60366	+	4.93555i	−0.0650369	+	0.200163i
$609$	−2.28679	−	7.03800i	−0.0926653	−	0.285194i
$610$	47.4470	−	34.4723i	1.92107	−	1.39574i
$611$	−0.319825	+	0.232367i	−0.0129387	+	0.00940055i
$612$	0.548269	+	1.68740i	0.0221625	+	0.0682090i
$613$	5.44711	−	16.7645i	0.220007	−	0.677111i	−0.778754	−	0.627330i	$-0.784148\pi$
$613$	5.44711	−	16.7645i	0.220007	−	0.677111i	0.998760	−	0.0497807i	$-0.0158522\pi$
$614$	−63.0860	−	45.8346i	−2.54594	−	1.84974i
$615$	−33.1125			−1.33522
$616$	−15.0162	+	8.08827i	−0.605018	+	0.325886i
$617$	−44.4849			−1.79089			−0.895447	−	0.445168i	$-0.853144\pi$
$617$	−44.4849			−1.79089			−0.895447	+	0.445168i	$0.853144\pi$
$618$	−3.01252	−	2.18872i	−0.121181	−	0.0880433i
$619$	−1.91722	+	5.90058i	−0.0770594	+	0.237164i	−0.982165	−	0.188023i	$-0.939792\pi$
$619$	−1.91722	+	5.90058i	−0.0770594	+	0.237164i	0.905105	+	0.425188i	$0.139792\pi$
$620$	−12.2364	−	37.6599i	−0.491427	−	1.51246i
$621$	29.5155	−	21.4443i	1.18442	−	0.860529i
$622$	18.0371	−	13.1047i	0.723220	−	0.525450i
$623$	0.215760	+	0.664040i	0.00864423	+	0.0266042i
$624$	1.47610	−	4.54297i	0.0590913	−	0.181864i
$625$	8.76619	+	6.36901i	0.350647	+	0.254760i
$626$	35.7652			1.42947
$627$	−32.3131	−	4.36396i	−1.29046	−	0.174280i
$628$	4.65531			0.185767
$629$	−0.404567	−	0.293935i	−0.0161312	−	0.0117200i
$630$	−1.00937	+	3.10651i	−0.0402142	+	0.123766i
$631$	13.8457	+	42.6128i	0.551190	+	1.69639i	0.705799	+	0.708412i	$0.250588\pi$
$631$	13.8457	+	42.6128i	0.551190	+	1.69639i	−0.154609	+	0.987976i	$0.549412\pi$
$632$	−11.0407	+	8.02155i	−0.439176	+	0.319080i
$633$	11.4210	−	8.29785i	0.453944	−	0.329810i
$634$	−14.0389	−	43.2072i	−0.557554	−	1.71598i
$635$	8.53418	−	26.2655i	0.338669	−	1.04231i
$636$	52.5210	+	38.1587i	2.08259	+	1.51309i
$637$	−0.653752			−0.0259026
$638$	6.69585	+	36.8134i	0.265091	+	1.45746i
$639$	2.06906			0.0818507
$640$	−52.6982	−	38.2875i	−2.08308	−	1.51345i
$641$	−3.17534	+	9.77271i	−0.125419	+	0.385999i	−0.993977	−	0.109588i	$-0.965047\pi$
$641$	−3.17534	+	9.77271i	−0.125419	+	0.385999i	0.868559	+	0.495587i	$0.165047\pi$
$642$	−8.16749	−	25.1370i	−0.322345	−	0.992076i
$643$	13.3039	−	9.66588i	0.524656	−	0.381185i	−0.293699	−	0.955898i	$-0.594886\pi$
$643$	13.3039	−	9.66588i	0.524656	−	0.381185i	0.818355	+	0.574713i	$0.194886\pi$
$644$	−22.0323	+	16.0074i	−0.868196	+	0.630781i
$645$	15.0945	+	46.4561i	0.594346	+	1.82921i
$646$	5.26675	−	16.2094i	0.207218	−	0.637750i
$647$	21.8181	+	15.8518i	0.857758	+	0.623197i	0.927274	−	0.374383i	$-0.122146\pi$
$647$	21.8181	+	15.8518i	0.857758	+	0.623197i	−0.0695163	+	0.997581i	$0.522146\pi$
$648$	−39.6399			−1.55720
$649$	4.06261	+	3.88115i	0.159471	+	0.152348i
$650$	−11.3178			−0.443921
$651$	−3.66042	−	2.65945i	−0.143463	−	0.104232i
$652$	−6.39623	+	19.6856i	−0.250496	+	0.770947i
$653$	2.19588	+	6.75823i	0.0859315	+	0.264470i	0.984784	−	0.173780i	$-0.0555983\pi$
$653$	2.19588	+	6.75823i	0.0859315	+	0.264470i	−0.898853	+	0.438250i	$0.855598\pi$
$654$	−13.3198	+	9.67742i	−0.520846	+	0.378417i
$655$	−13.4765	+	9.79123i	−0.526569	+	0.382575i
$656$	−8.23757	−	25.3526i	−0.321623	−	0.989854i
$657$	−0.791062	+	2.43464i	−0.0308623	+	0.0949843i
$658$	−1.20676	−	0.876765i	−0.0470445	−	0.0341798i
$659$	−32.6279			−1.27100			−0.635502	−	0.772099i	$-0.719207\pi$
$659$	−32.6279			−1.27100			−0.635502	+	0.772099i	$0.719207\pi$
$660$	−32.9446	+	68.4801i	−1.28237	+	2.66559i
$661$	−33.8165			−1.31531			−0.657654	−	0.753320i	$-0.728451\pi$
$661$	−33.8165			−1.31531			−0.657654	+	0.753320i	$0.728451\pi$
$662$	12.9247	+	9.39038i	0.502334	+	0.364967i
$663$	−0.371708	+	1.14400i	−0.0144359	+	0.0444293i
$664$	10.6418	+	32.7520i	0.412981	+	1.27103i
$665$	17.0411	−	12.3811i	0.660825	−	0.480117i
$666$	−0.335211	+	0.243545i	−0.0129892	+	0.00943718i
$667$	9.42266	+	29.0000i	0.364847	+	1.12288i
$668$	−24.8752	+	76.5581i	−0.962452	+	2.96212i
$669$	13.5259	+	9.82712i	0.522940	+	0.379938i
$670$	52.8335			2.04114
$671$	−9.86094	+	20.4974i	−0.380677	+	0.791293i
$672$	1.38197			0.0533105
$673$	−19.2138	−	13.9596i	−0.740638	−	0.538105i	0.152273	−	0.988338i	$-0.451341\pi$
$673$	−19.2138	−	13.9596i	−0.740638	−	0.538105i	−0.892911	+	0.450234i	$0.851341\pi$
$674$	4.76934	−	14.6785i	0.183708	−	0.565395i
$675$	11.8677	+	36.5250i	0.456788	+	1.40585i
$676$	41.5480	−	30.1864i	1.59800	−	1.16102i
$677$	36.9164	−	26.8213i	1.41881	−	1.03083i	0.426845	−	0.904325i	$-0.359625\pi$
$677$	36.9164	−	26.8213i	1.41881	−	1.03083i	0.991966	−	0.126502i	$-0.0403750\pi$
$678$	23.2191	+	71.4611i	0.891724	+	2.74445i
$679$	4.59159	−	14.1315i	0.176209	−	0.542315i
$680$	−16.4012	−	11.9162i	−0.628958	−	0.456965i
$681$	21.4696			0.822717
$682$	16.5419	+	15.8030i	0.633421	+	0.605128i
$683$	−28.8727			−1.10478			−0.552392	−	0.833585i	$-0.686285\pi$
$683$	−28.8727			−1.10478			−0.552392	+	0.833585i	$0.686285\pi$
$684$	−7.66953	−	5.57224i	−0.293252	−	0.213060i
$685$	23.4372	−	72.1322i	0.895488	−	2.75603i
$686$	−0.762262	−	2.34600i	−0.0291033	−	0.0895707i
$687$	−3.26760	+	2.37405i	−0.124667	+	0.0905758i
$688$	−31.8141	+	23.1143i	−1.21290	+	0.881223i
$689$	−1.98434	−	6.10716i	−0.0755973	−	0.232664i
$690$	−28.5068	+	87.7348i	−1.08523	+	3.34001i
$691$	21.8948	+	15.9075i	0.832918	+	0.605150i	0.920383	−	0.391017i	$-0.127877\pi$
$691$	21.8948	+	15.9075i	0.832918	+	0.605150i	−0.0874654	+	0.996168i	$0.527877\pi$
$692$	−58.7994			−2.23522
$693$	−0.226701	−	1.24639i	−0.00861164	−	0.0473464i
$694$	56.0334			2.12700
$695$	−55.5705	−	40.3743i	−2.10791	−	1.53148i
$696$	11.7599	−	36.1933i	0.445759	−	1.37191i
$697$	2.07437	+	6.38424i	0.0785722	+	0.241820i
$698$	−59.2583	+	43.0537i	−2.24296	+	1.62961i
$699$	−12.5716	+	9.13384i	−0.475503	+	0.345473i
$700$	−8.85884	−	27.2647i	−0.334833	−	1.03051i
$701$	11.9020	−	36.6305i	0.449531	−	1.38352i	−0.427905	−	0.903823i	$-0.640748\pi$
$701$	11.9020	−	36.6305i	0.449531	−	1.38352i	0.877437	−	0.479692i	$-0.159252\pi$
$702$	7.13919	+	5.18693i	0.269452	+	0.195768i
$703$	2.67198			0.100776
$704$	22.7601	+	3.07380i	0.857802	+	0.115848i
$705$	−3.39196			−0.127748
$706$	13.6203	+	9.89572i	0.512606	+	0.372430i
$707$	−2.66360	+	8.19772i	−0.100175	+	0.308307i
$708$	−3.45991	−	10.6485i	−0.130031	−	0.400195i
$709$	1.53280	−	1.11364i	0.0575654	−	0.0418237i	−0.558630	−	0.829417i	$-0.688673\pi$
$709$	1.53280	−	1.11364i	0.0575654	−	0.0418237i	0.616196	+	0.787593i	$0.288673\pi$
$710$	−37.4755	+	27.2276i	−1.40643	+	1.02183i
$711$	−0.313233	−	0.964032i	−0.0117472	−	0.0361540i
$712$	−1.10956	+	3.41487i	−0.0415824	+	0.127978i
$713$	15.0827	+	10.9582i	0.564851	+	0.410388i
$714$	−4.53867			−0.169856
$715$	6.61778	−	3.56459i	0.247491	−	0.133308i
$716$	−19.0522			−0.712013
$717$	7.28241	+	5.29098i	0.271967	+	0.197595i
$718$	−5.53379	+	17.0313i	−0.206519	+	0.635601i
$719$	4.50461	+	13.8638i	0.167994	+	0.517031i	0.999244	−	0.0388664i	$-0.0123747\pi$
$719$	4.50461	+	13.8638i	0.167994	+	0.517031i	−0.831251	+	0.555898i	$0.812375\pi$
$720$	−4.83766	+	3.51477i	−0.180289	+	0.130988i
$721$	−0.754779	+	0.548379i	−0.0281094	+	0.0204227i
$722$	13.6582	+	42.0357i	0.508307	+	1.56441i
$723$	−7.51038	+	23.1146i	−0.279314	+	0.859640i
$724$	−32.7426	−	23.7889i	−1.21687	−	0.884107i
$725$	−32.0984			−1.19210
$726$	−2.00478	−	43.8580i	−0.0744044	−	1.62772i
$727$	4.04780			0.150125			0.0750623	−	0.997179i	$-0.476084\pi$
$727$	4.04780			0.150125			0.0750623	+	0.997179i	$0.476084\pi$
$728$	−2.71988	−	1.97611i	−0.100805	−	0.0732394i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	−17.7104	−	54.5069i	−0.655490	−	2.01739i
$731$	8.01135	−	5.82058i	0.296310	−	0.215282i
$732$	36.6709	−	26.6430i	1.35540	−	0.984752i
$733$	−7.26226	−	22.3509i	−0.268238	−	0.825551i	−0.990930	−	0.134381i	$-0.957095\pi$
$733$	−7.26226	−	22.3509i	−0.268238	−	0.825551i	0.722692	−	0.691170i	$-0.242905\pi$
$734$	−27.6980	+	85.2457i	−1.02235	+	3.14648i
$735$	−4.53801	−	3.29706i	−0.167387	−	0.121614i
$736$	−5.69437			−0.209897
$737$	−18.0404	+	9.71726i	−0.664527	+	0.357940i
$738$	5.56199			0.204740
$739$	26.4376	+	19.2080i	0.972522	+	0.706578i	0.956025	−	0.293286i	$-0.0947487\pi$
$739$	26.4376	+	19.2080i	0.972522	+	0.706578i	0.0164968	+	0.999864i	$0.494749\pi$
$740$	1.92435	−	5.92254i	0.0707405	−	0.217717i
$741$	−1.98610	−	6.11260i	−0.0729614	−	0.224552i
$742$	19.6020	−	14.2417i	0.719612	−	0.522828i
$743$	14.6479	−	10.6423i	0.537379	−	0.390429i	−0.285731	−	0.958310i	$-0.592237\pi$
$743$	14.6479	−	10.6423i	0.537379	−	0.390429i	0.823111	+	0.567881i	$0.192237\pi$
$744$	−7.19009	−	22.1288i	−0.263602	−	0.811282i
$745$	−3.38750	+	10.4257i	−0.124108	+	0.381967i
$746$	28.5202	+	20.7211i	1.04420	+	0.758655i
$747$	−2.55787			−0.0935874
$748$	15.2671	+	2.06186i	0.558222	+	0.0753892i
$749$	−6.62212			−0.241967
$750$	−22.5922	−	16.4142i	−0.824949	−	0.599361i
$751$	2.82552	−	8.69605i	0.103105	−	0.317323i	−0.886176	−	0.463348i	$-0.846648\pi$
$751$	2.82552	−	8.69605i	0.103105	−	0.317323i	0.989281	+	0.146025i	$0.0466479\pi$
$752$	−0.843835	−	2.59706i	−0.0307715	−	0.0947049i
$753$	36.1460	−	26.2616i	1.31723	−	0.957025i
$754$	−5.96689	+	4.33520i	−0.217301	+	0.157879i
$755$	−9.56444	−	29.4363i	−0.348086	−	1.07130i
$756$	−6.90727	+	21.2584i	−0.251215	+	0.773160i
$757$	−38.3077	−	27.8322i	−1.39232	−	1.01158i	−0.995607	−	0.0936338i	$-0.970152\pi$
$757$	−38.3077	−	27.8322i	−1.39232	−	1.01158i	−0.396710	−	0.917944i	$-0.629848\pi$
$758$	−6.27851			−0.228046
$759$	−6.40253	−	35.2008i	−0.232397	−	1.27771i
$760$	108.323			3.92927
$761$	−2.78972	−	2.02685i	−0.101127	−	0.0734732i	0.536073	−	0.844172i	$-0.319907\pi$
$761$	−2.78972	−	2.02685i	−0.101127	−	0.0734732i	−0.637200	+	0.770699i	$0.719907\pi$
$762$	9.82542	−	30.2395i	0.355937	−	1.09546i
$763$	1.27472	+	3.92317i	0.0461478	+	0.142028i
$764$	−32.8579	+	23.8727i	−1.18876	+	0.863683i
$765$	1.21821	−	0.885081i	0.0440444	−	0.0320002i
$766$	−17.6362	−	54.2787i	−0.637223	−	1.96117i
$767$	−0.342234	+	1.05329i	−0.0123573	+	0.0380320i
$768$	−42.5424	−	30.9089i	−1.53512	−	1.11533i
$769$	34.9787			1.26137			0.630683	−	0.776041i	$-0.282775\pi$
$769$	34.9787			1.26137			0.630683	+	0.776041i	$0.282775\pi$
$770$	20.5078	+	19.5918i	0.739050	+	0.706040i
$771$	46.0622			1.65889
$772$	−12.2491	−	8.89953i	−0.440856	−	0.320301i
$773$	7.84266	−	24.1372i	0.282081	−	0.868155i	−0.705178	−	0.709031i	$-0.749133\pi$
$773$	7.84266	−	24.1372i	0.282081	−	0.868155i	0.987258	−	0.159125i	$-0.0508672\pi$
$774$	−2.53546	−	7.80336i	−0.0911354	−	0.280486i
$775$	−15.8771	+	11.5354i	−0.570321	+	0.414363i
$776$	61.8183	−	44.9137i	2.21915	−	1.61231i
$777$	−0.219879	−	0.676718i	−0.00788812	−	0.0242771i
$778$	23.0672	−	70.9934i	0.826998	−	2.54524i
$779$	−29.0176	−	21.0825i	−1.03966	−	0.755358i
$780$	−14.9792			−0.536340
$781$	7.78856	−	16.1897i	0.278697	−	0.579312i
$782$	18.7015			0.668765
$783$	20.2474	+	14.7106i	0.723584	+	0.525715i
$784$	1.39545	−	4.29476i	0.0498376	−	0.153384i
$785$	−1.22091	−	3.75758i	−0.0435762	−	0.134114i
$786$	−15.5155	+	11.2727i	−0.553419	+	0.402083i
$787$	−24.0725	+	17.4897i	−0.858090	+	0.623439i	−0.927365	−	0.374159i	$-0.877932\pi$
$787$	−24.0725	+	17.4897i	−0.858090	+	0.623439i	0.0692745	+	0.997598i	$0.477932\pi$
$788$	7.47236	+	22.9976i	0.266192	+	0.819255i
$789$	−7.09017	+	21.8213i	−0.252417	+	0.776859i
$790$	18.3595	+	13.3389i	0.653201	+	0.474578i
$791$	18.8258			0.669369
$792$	2.82432	−	5.87075i	0.100358	−	0.208608i
$793$	−4.48355			−0.159215
$794$	45.2490	+	32.8753i	1.60583	+	1.16670i
$795$	17.0259	−	52.4004i	0.603847	−	1.85845i
$796$	14.4961	+	44.6144i	0.513800	+	1.58132i
$797$	5.05094	−	3.66972i	0.178913	−	0.129988i	−0.494724	−	0.869050i	$-0.664731\pi$
$797$	5.05094	−	3.66972i	0.178913	−	0.129988i	0.673638	+	0.739062i	$0.264731\pi$
$798$	19.6194	−	14.2544i	0.694521	−	0.504599i
$799$	0.212493	+	0.653985i	0.00751745	+	0.0231363i
$800$	1.85234	−	5.70090i	0.0654899	−	0.201557i
$801$	−0.215760	−	0.156759i	−0.00762350	−	0.00553879i
$802$	−40.0069			−1.41269
$803$	16.0724	+	15.3545i	0.567182	+	0.541848i
$804$	40.8340			1.44010
$805$	18.6988	+	13.5855i	0.659046	+	0.478825i
$806$	−1.39349	+	4.28871i	−0.0490834	+	0.151063i
$807$	12.0968	+	37.2302i	0.425829	+	1.31057i
$808$	−35.8611	+	26.0546i	−1.26159	+	0.916598i
$809$	−31.7022	+	23.0330i	−1.11459	+	0.809796i	−0.983380	−	0.181559i	$-0.941886\pi$
$809$	−31.7022	+	23.0330i	−1.11459	+	0.809796i	−0.131209	+	0.991355i	$0.541886\pi$
$810$	20.3694	+	62.6905i	0.715707	+	2.20272i
$811$	−3.82591	+	11.7749i	−0.134346	+	0.413474i	−0.995488	−	0.0948906i	$-0.969750\pi$
$811$	−3.82591	+	11.7749i	−0.134346	+	0.413474i	0.861142	+	0.508365i	$0.169750\pi$
$812$	−15.1140	−	10.9810i	−0.530399	−	0.385357i
$813$	−12.0539			−0.422750
$814$	0.643819	+	3.53969i	0.0225659	+	0.124066i
$815$	17.5669			0.615341
$816$	−6.72198	−	4.88381i	−0.235316	−	0.170967i
$817$	−16.3505	+	50.3216i	−0.572031	+	1.76053i
$818$	−26.7260	−	82.2541i	−0.934452	−	2.87595i
$819$	0.202020	−	0.146776i	0.00705916	−	0.00512878i
$820$	−67.6284	+	49.1349i	−2.36168	+	1.71586i
$821$	14.7397	+	45.3642i	0.514420	+	1.58322i	0.784335	+	0.620337i	$0.213004\pi$
$821$	14.7397	+	45.3642i	0.514420	+	1.58322i	−0.269916	+	0.962884i	$0.586996\pi$
$822$	26.9833	−	83.0459i	0.941149	−	2.89656i
$823$	11.7475	+	8.53507i	0.409493	+	0.297514i	0.773396	−	0.633923i	$-0.218556\pi$
$823$	11.7475	+	8.53507i	0.409493	+	0.297514i	−0.363904	+	0.931437i	$0.618556\pi$
$824$	−4.79779			−0.167139
$825$	37.3239	+	5.04068i	1.29945	+	0.175494i
$826$	−4.17878			−0.145398
$827$	25.0287	+	18.1844i	0.870335	+	0.632335i	0.930677	−	0.365843i	$-0.119219\pi$
$827$	25.0287	+	18.1844i	0.870335	+	0.632335i	−0.0603420	+	0.998178i	$0.519219\pi$
$828$	3.21448	−	9.89314i	0.111711	−	0.343810i
$829$	0.0265154	+	0.0816061i	0.000920918	+	0.00283430i	0.951516	−	0.307600i	$-0.0995257\pi$
$829$	0.0265154	+	0.0816061i	0.000920918	+	0.00283430i	−0.950595	+	0.310434i	$0.899526\pi$
$830$	46.3290	−	33.6600i	1.60810	−	1.16835i
$831$	−25.1187	+	18.2498i	−0.871359	+	0.633080i
$832$	1.39893	+	4.30548i	0.0484993	+	0.149266i
$833$	−0.351400	+	1.08150i	−0.0121753	+	0.0374717i
$834$	−63.9784	−	46.4830i	−2.21539	−	1.60958i
$835$	68.3185			2.36426
$836$	−72.4713	+	39.0358i	−2.50647	+	1.35008i
$837$	15.3018			0.528907
$838$	−56.4030	−	40.9792i	−1.94841	−	1.41560i
$839$	3.30355	−	10.1673i	0.114051	−	0.351014i	−0.877697	−	0.479217i	$-0.840921\pi$
$839$	3.30355	−	10.1673i	0.114051	−	0.351014i	0.991748	+	0.128203i	$0.0409208\pi$
$840$	−8.91393	−	27.4343i	−0.307560	−	0.946572i
$841$	6.53883	−	4.75074i	0.225477	−	0.163819i
$842$	27.5290	−	20.0010i	0.948713	−	0.689281i
$843$	0.950314	+	2.92477i	0.0327306	+	0.100734i
$844$	11.0131	−	33.8948i	0.379086	−	1.16671i
$845$	−35.2617	−	25.6191i	−1.21304	−	0.881325i
$846$	0.569756			0.0195886
$847$	−10.6059	−	2.91793i	−0.364424	−	0.100261i
$848$	44.3561			1.52319
$849$	9.49270	+	6.89685i	0.325789	+	0.236699i
$850$	−6.08347	+	18.7230i	−0.208661	+	0.642193i
$851$	0.906008	+	2.78841i	0.0310576	+	0.0955854i
$852$	−28.9641	+	21.0437i	−0.992295	+	0.720944i
$853$	−17.1514	+	12.4612i	−0.587252	+	0.426664i	−0.841331	−	0.540520i	$-0.818228\pi$
$853$	−17.1514	+	12.4612i	−0.587252	+	0.426664i	0.254079	+	0.967183i	$0.418228\pi$
$854$	−5.22773	−	16.0893i	−0.178889	−	0.550565i
$855$	−2.48626	+	7.65192i	−0.0850283	+	0.261690i
$856$	−27.5508	−	20.0168i	−0.941666	−	0.684160i
$857$	−9.45359			−0.322929			−0.161464	−	0.986879i	$-0.551622\pi$
$857$	−9.45359			−0.322929			−0.161464	+	0.986879i	$0.551622\pi$
$858$	7.61907	−	4.10392i	0.260111	−	0.140106i
$859$	−38.8261			−1.32473			−0.662365	−	0.749181i	$-0.730447\pi$
$859$	−38.8261			−1.32473			−0.662365	+	0.749181i	$0.730447\pi$
$860$	99.7640	+	72.4828i	3.40192	+	2.47164i
$861$	−2.95158	+	9.08401i	−0.100589	+	0.309582i
$862$	21.4730	+	66.0869i	0.731372	+	2.25093i
$863$	30.4228	−	22.1034i	1.03560	−	0.752410i	0.0661810	−	0.997808i	$-0.478919\pi$
$863$	30.4228	−	22.1034i	1.03560	−	0.752410i	0.969423	+	0.245398i	$0.0789185\pi$
$864$	−3.78115	+	2.74717i	−0.128637	+	0.0934606i
$865$	15.4208	+	47.4605i	0.524324	+	1.61370i
$866$	10.8084	−	33.2647i	0.367283	−	1.13038i
$867$	−20.5606	−	14.9381i	−0.698274	−	0.507326i
$868$	−11.4223			−0.387697
$869$	−8.72231	−	1.17797i	−0.295884	−	0.0399599i
$870$	−63.2828			−2.14549
$871$	−3.26767	−	2.37410i	−0.110721	−	0.0804433i
$872$	−6.55530	+	20.1752i	−0.221991	+	0.683217i
$873$	1.75383	+	5.39773i	0.0593582	+	0.182686i
$874$	−80.8416	+	58.7348i	−2.73451	+	1.98674i
$875$	−5.66042	+	4.11253i	−0.191357	+	0.139029i
$876$	−13.6880	−	42.1274i	−0.462475	−	1.42335i
$877$	6.80103	−	20.9314i	0.229654	−	0.706804i	−0.768131	−	0.640293i	$-0.778813\pi$
$877$	6.80103	−	20.9314i	0.229654	−	0.706804i	0.997786	−	0.0665113i	$-0.0211869\pi$
$878$	−55.9145	−	40.6243i	−1.88702	−	1.37100i
$879$	5.29254			0.178513
$880$	9.29140	+	51.0836i	0.313213	+	1.72203i
$881$	−6.92969			−0.233467			−0.116734	−	0.993163i	$-0.537242\pi$
$881$	−6.92969			−0.233467			−0.116734	+	0.993163i	$0.537242\pi$
$882$	0.762262	+	0.553816i	0.0256667	+	0.0186479i
$883$	13.0834	−	40.2666i	0.440292	−	1.35508i	−0.447274	−	0.894397i	$-0.647605\pi$
$883$	13.0834	−	40.2666i	0.440292	−	1.35508i	0.887566	−	0.460681i	$-0.152395\pi$
$884$	0.938386	+	2.88806i	0.0315613	+	0.0971358i
$885$	−7.68764	+	5.58540i	−0.258417	+	0.187751i
$886$	−34.5982	+	25.1371i	−1.16235	+	0.844496i
$887$	2.48959	+	7.66216i	0.0835921	+	0.257270i	0.984113	−	0.177542i	$-0.0568147\pi$
$887$	2.48959	+	7.66216i	0.0835921	+	0.257270i	−0.900521	+	0.434812i	$0.856815\pi$
$888$	1.13074	−	3.48006i	0.0379452	−	0.116783i
$889$	−6.44491	−	4.68250i	−0.216155	−	0.157046i
$890$	5.97077			0.200141
$891$	−18.4855	−	17.6598i	−0.619286	−	0.591625i
$892$	42.2072			1.41320
$893$	−2.97248	−	2.15964i	−0.0994703	−	0.0722694i
$894$	−3.90004	+	12.0031i	−0.130437	+	0.401443i
$895$	4.99666	+	15.3781i	0.167020	+	0.514034i
$896$	−15.2011	+	11.0443i	−0.507834	+	0.368963i
$897$	5.70550	−	4.14529i	0.190501	−	0.138407i
$898$	−22.5031	−	69.2575i	−0.750939	−	2.31115i
$899$	−3.95206	+	12.1632i	−0.131808	+	0.405665i
$900$	8.85884	+	6.43633i	0.295295	+	0.214544i
$901$	−11.1697			−0.372115
$902$	20.9370	−	43.5207i	0.697127	−	1.44908i
$903$	14.0902			0.468891
$904$	78.3232	+	56.9051i	2.60499	+	1.89264i
$905$	−10.6143	+	32.6674i	−0.352831	+	1.08590i
$906$	−11.0116	−	33.8901i	−0.365835	−	1.12592i
$907$	−2.34153	+	1.70122i	−0.0777492	+	0.0564881i	−0.625981	−	0.779838i	$-0.715301\pi$
$907$	−2.34153	+	1.70122i	−0.0777492	+	0.0564881i	0.548232	+	0.836327i	$0.315301\pi$
$908$	43.8492	−	31.8583i	1.45519	−	1.05725i
$909$	−1.01740	−	3.13125i	−0.0337452	−	0.103857i
$910$	−1.72758	+	5.31693i	−0.0572686	+	0.176255i
$911$	16.3826	+	11.9026i	0.542779	+	0.394352i	0.825116	−	0.564963i	$-0.191110\pi$
$911$	16.3826	+	11.9026i	0.542779	+	0.394352i	−0.282337	+	0.959315i	$0.591110\pi$
$912$	44.3956			1.47008
$913$	−9.62858	+	20.0144i	−0.318659	+	0.662380i
$914$	23.9205			0.791220
$915$	−31.1225	−	22.6118i	−1.02888	−	0.747524i
$916$	−3.15089	+	9.69745i	−0.104108	+	0.320413i
$917$	1.48484	+	4.56988i	0.0490338	+	0.150911i
$918$	12.4181	−	9.02229i	0.409859	−	0.297780i
$919$	−15.1498	+	11.0069i	−0.499744	+	0.363085i	−0.808919	−	0.587920i	$-0.799947\pi$
$919$	−15.1498	+	11.0069i	−0.499744	+	0.363085i	0.309175	+	0.951005i	$0.399947\pi$
$920$	36.7297	+	113.042i	1.21094	+	3.72690i
$921$	−15.8060	+	48.6460i	−0.520827	+	1.60294i
$922$	38.3592	+	27.8696i	1.26329	+	0.917836i
$923$	3.54128			0.116563
$924$	15.8501	+	15.1421i	0.521430	+	0.498140i
$925$	−3.08632			−0.101478
$926$	−40.9756	−	29.7705i	−1.34654	−	0.978320i
$927$	0.110121	−	0.338917i	0.00361684	−	0.0111315i
$928$	−1.20711	−	3.71511i	−0.0396254	−	0.121954i
$929$	36.6243	−	26.6091i	1.20160	−	0.873016i	0.207162	−	0.978307i	$-0.433577\pi$
$929$	36.6243	−	26.6091i	1.20160	−	0.873016i	0.994441	+	0.105291i	$0.0335774\pi$
$930$	−31.3020	+	22.7423i	−1.02643	+	0.745748i
$931$	−1.87759	−	5.77864i	−0.0615357	−	0.189387i
$932$	−12.1226	+	37.3096i	−0.397090	+	1.22212i
$933$	−11.8313	−	8.59592i	−0.387338	−	0.281418i
$934$	83.0584			2.71775
$935$	−2.33974	−	12.8638i	−0.0765177	−	0.420690i
$936$	1.28415			0.0419738
$937$	−23.8336	−	17.3161i	−0.778609	−	0.565692i	0.125952	−	0.992036i	$-0.459801\pi$
$937$	−23.8336	−	17.3161i	−0.778609	−	0.565692i	−0.904561	+	0.426344i	$0.859801\pi$
$938$	4.70947	−	14.4942i	0.153769	−	0.473254i
$939$	−7.24952	−	22.3117i	−0.236579	−	0.728115i
$940$	−6.92767	+	5.03325i	−0.225956	+	0.164167i
$941$	−47.1128	+	34.2294i	−1.53583	+	1.11585i	−0.582950	+	0.812508i	$0.698102\pi$
$941$	−47.1128	+	34.2294i	−1.53583	+	1.11585i	−0.952882	+	0.303340i	$0.901898\pi$
$942$	−1.40564	−	4.32611i	−0.0457982	−	0.140952i
$943$	12.1619	−	37.4305i	0.396046	−	1.21891i
$944$	−6.18897	−	4.49655i	−0.201434	−	0.146350i
$945$	18.9704			0.617108
$946$	−70.6028	−	9.53508i	−2.29550	−	0.310012i
$947$	45.3642			1.47414			0.737069	−	0.675818i	$-0.236209\pi$
$947$	45.3642			1.47414			0.737069	+	0.675818i	$0.236209\pi$
$948$	14.1897	+	10.3094i	0.460859	+	0.334834i
$949$	−1.35394	+	4.16699i	−0.0439506	+	0.135266i
$950$	−32.5051	−	100.040i	−1.05460	−	3.24574i
$951$	−24.1087	+	17.5160i	−0.781777	+	0.567994i
$952$	−4.73103	+	3.43730i	−0.153334	+	0.111403i
$953$	−12.7740	−	39.3143i	−0.413790	−	1.27352i	−0.913328	−	0.407224i	$-0.866497\pi$
$953$	−12.7740	−	39.3143i	−0.413790	−	1.27352i	0.499538	−	0.866292i	$-0.333503\pi$
$954$	−2.85989	+	8.80184i	−0.0925924	+	0.284970i
$955$	27.8864	+	20.2607i	0.902384	+	0.655620i
$956$	22.7247			0.734968
$957$	21.6084	−	11.6391i	0.698500	−	0.376239i
$958$	34.9555			1.12936
$959$	−17.6995	−	12.8594i	−0.571545	−	0.415252i
$960$	−12.0031	+	36.9417i	−0.387398	+	1.19229i
$961$	−7.16322	−	22.0461i	−0.231071	−	0.711165i
$962$	−0.573728	+	0.416838i	−0.0184977	+	0.0134394i
$963$	2.04635	−	1.48676i	0.0659426	−	0.0479101i
$964$	18.9601	+	58.3533i	0.610665	+	1.87943i
$965$	−3.97085	+	12.2210i	−0.127826	+	0.393409i
$966$	21.5280	+	15.6410i	0.692651	+	0.503240i
$967$	−6.52818			−0.209932			−0.104966	−	0.994476i	$-0.533473\pi$
$967$	−6.52818			−0.209932			−0.104966	+	0.994476i	$0.533473\pi$
$968$	−35.3050	−	44.1986i	−1.13475	−	1.42060i
$969$	−11.1796			−0.359140
$970$	−102.797	−	74.6864i	−3.30061	−	2.39803i
$971$	8.91783	−	27.4462i	0.286187	−	0.880792i	−0.699854	−	0.714286i	$-0.746752\pi$
$971$	8.91783	−	27.4462i	0.286187	−	0.880792i	0.986040	−	0.166506i	$-0.0532484\pi$
$972$	−4.97870	−	15.3229i	−0.159692	−	0.491482i
$973$	−16.0296	+	11.6462i	−0.513887	+	0.373360i
$974$	−55.3617	+	40.2226i	−1.77390	+	1.28882i
$975$	2.29409	+	7.06048i	0.0734697	+	0.226116i
$976$	9.57027	−	29.4543i	0.306337	−	0.942808i
$977$	7.26864	+	5.28097i	0.232544	+	0.168953i	0.697955	−	0.716141i	$-0.254093\pi$
$977$	7.26864	+	5.28097i	0.232544	+	0.168953i	−0.465411	+	0.885095i	$0.654093\pi$
$978$	20.2248			0.646718
$979$	−2.03877	+	1.09816i	−0.0651593	+	0.0350973i
$980$	−14.1608			−0.452350
$981$	−1.27472	−	0.926136i	−0.0406986	−	0.0295692i
$982$	−2.62443	+	8.07717i	−0.0837490	+	0.257753i
$983$	11.3971	+	35.0768i	0.363512	+	1.11877i	0.950908	+	0.309475i	$0.100153\pi$
$983$	11.3971	+	35.0768i	0.363512	+	1.11877i	−0.587396	+	0.809300i	$0.699847\pi$
$984$	−39.7382	+	28.8715i	−1.26681	+	0.920390i
$985$	16.6030	−	12.0628i	0.529015	−	0.384352i
$986$	3.96441	+	12.2012i	0.126253	+	0.388566i
$987$	−0.302352	+	0.930543i	−0.00962396	+	0.0296195i
$988$	−13.1267	−	9.53713i	−0.417617	−	0.303417i
$989$	−58.0583			−1.84615
$990$	−10.7359	−	1.44991i	−0.341209	−	0.0460811i
$991$	−2.98352			−0.0947746			−0.0473873	−	0.998877i	$-0.515089\pi$
$991$	−2.98352			−0.0947746			−0.0473873	+	0.998877i	$0.515089\pi$
$992$	−1.93220	−	1.40383i	−0.0613475	−	0.0445716i
$993$	3.23826	−	9.96635i	0.102763	−	0.316273i
$994$	4.12907	+	12.7080i	0.130966	+	0.403072i
$995$	32.2092	−	23.4013i	1.02110	−	0.741872i
$996$	35.8068	−	26.0152i	1.13458	−	0.824322i
$997$	19.4234	+	59.7790i	0.615144	+	1.89322i	0.399437	+	0.916760i	$0.369205\pi$
$997$	19.4234	+	59.7790i	0.615144	+	1.89322i	0.215707	+	0.976458i	$0.430795\pi$
$998$	−1.97367	+	6.07434i	−0.0624755	+	0.192280i
$999$	1.94683	+	1.41446i	0.0615951	+	0.0447514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.f.a.15.1	✓	8
3.2	odd	2		693.2.m.g.631.2		8
7.2	even	3		539.2.q.c.312.1		16
7.3	odd	6		539.2.q.b.422.2		16
7.4	even	3		539.2.q.c.422.2		16
7.5	odd	6		539.2.q.b.312.1		16
7.6	odd	2		539.2.f.d.246.1		8
11.2	odd	10		847.2.f.s.148.1		8
11.3	even	5	inner	77.2.f.a.36.1	yes	8
11.4	even	5		847.2.f.p.372.2		8
11.5	even	5		847.2.a.l.1.4		4
11.6	odd	10		847.2.a.k.1.1		4
11.7	odd	10		847.2.f.s.372.1		8
11.8	odd	10		847.2.f.q.729.2		8
11.9	even	5		847.2.f.p.148.2		8
11.10	odd	2		847.2.f.q.323.2		8
33.5	odd	10		7623.2.a.ch.1.1		4
33.14	odd	10		693.2.m.g.190.2		8
33.17	even	10		7623.2.a.co.1.4		4
77.3	odd	30		539.2.q.b.520.1		16
77.6	even	10		5929.2.a.bb.1.1		4
77.25	even	15		539.2.q.c.520.1		16
77.27	odd	10		5929.2.a.bi.1.4		4
77.47	odd	30		539.2.q.b.410.2		16
77.58	even	15		539.2.q.c.410.2		16
77.69	odd	10		539.2.f.d.344.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.1	✓	8	1.1	even	1	trivial
77.2.f.a.36.1	yes	8	11.3	even	5	inner
539.2.f.d.246.1		8	7.6	odd	2
539.2.f.d.344.1		8	77.69	odd	10
539.2.q.b.312.1		16	7.5	odd	6
539.2.q.b.410.2		16	77.47	odd	30
539.2.q.b.422.2		16	7.3	odd	6
539.2.q.b.520.1		16	77.3	odd	30
539.2.q.c.312.1		16	7.2	even	3
539.2.q.c.410.2		16	77.58	even	15
539.2.q.c.422.2		16	7.4	even	3
539.2.q.c.520.1		16	77.25	even	15
693.2.m.g.190.2		8	33.14	odd	10
693.2.m.g.631.2		8	3.2	odd	2
847.2.a.k.1.1		4	11.6	odd	10
847.2.a.l.1.4		4	11.5	even	5
847.2.f.p.148.2		8	11.9	even	5
847.2.f.p.372.2		8	11.4	even	5
847.2.f.q.323.2		8	11.10	odd	2
847.2.f.q.729.2		8	11.8	odd	10
847.2.f.s.148.1		8	11.2	odd	10
847.2.f.s.372.1		8	11.7	odd	10
5929.2.a.bb.1.1		4	77.6	even	10
5929.2.a.bi.1.4		4	77.27	odd	10
7623.2.a.ch.1.1		4	33.5	odd	10
7623.2.a.co.1.4		4	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99563 - 1.44991i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(1.26226 + 3.88484i) q^{4} +(2.80464 - 2.03769i) q^{5} +(3.22899 - 2.34600i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(1.58914 - 4.89086i) q^{8} +(0.309017 + 0.224514i) q^{9} -8.55150 q^{10} +(2.91998 - 1.57281i) q^{11} -6.60929 q^{12} +(0.528896 + 0.384266i) q^{13} +(-0.762262 + 2.34600i) q^{14} +(1.73337 + 5.33475i) q^{15} +(-3.65334 + 2.65431i) q^{16} +(0.919977 - 0.668402i) q^{17} +(-0.291158 - 0.896093i) q^{18} +(-1.87759 + 5.77864i) q^{19} +(11.4563 + 8.32350i) q^{20} +1.61803 q^{21} +(-8.10762 - 1.09495i) q^{22} -6.66708 q^{23} +(6.73170 + 4.89086i) q^{24} +(2.16875 - 6.67473i) q^{25} +(-0.498330 - 1.53370i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(3.30464 - 2.40097i) q^{28} +(-1.41331 - 4.34973i) q^{29} +(4.27575 - 13.1594i) q^{30} +(-2.26226 - 1.64363i) q^{31} +0.854102 q^{32} +(0.960319 + 5.27979i) q^{33} -2.80505 q^{34} +(-2.80464 - 2.03769i) q^{35} +(-0.482141 + 1.48388i) q^{36} +(-0.135893 - 0.418235i) q^{37} +(12.1255 - 8.80968i) q^{38} +(-0.855772 + 0.621755i) q^{39} +(-5.50911 - 16.9553i) q^{40} +(-1.82417 + 5.61423i) q^{41} +(-3.22899 - 2.34600i) q^{42} +8.70820 q^{43} +(9.79590 + 9.35835i) q^{44} +1.32417 q^{45} +(13.3050 + 9.66666i) q^{46} +(-0.186864 + 0.575107i) q^{47} +(-2.25789 - 6.94907i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-14.0058 + 10.1758i) q^{50} +(0.568577 + 1.74990i) q^{51} +(-0.825206 + 2.53972i) q^{52} +(-7.94654 - 5.77350i) q^{53} +13.4983 q^{54} +(4.98459 - 10.3612i) q^{55} -5.14256 q^{56} +(-7.95362 - 5.77864i) q^{57} +(-3.48626 + 10.7296i) q^{58} +(0.523492 + 1.61114i) q^{59} +(-18.5367 + 13.4677i) q^{60} +(-5.54839 + 4.03114i) q^{61} +(2.13152 + 6.56015i) q^{62} +(0.118034 - 0.363271i) q^{63} +(5.60222 + 4.07025i) q^{64} +2.26638 q^{65} +(5.73877 - 11.9289i) q^{66} -6.17828 q^{67} +(3.75789 + 2.73027i) q^{68} +(3.33354 - 10.2596i) q^{69} +(2.64256 + 8.13296i) q^{70} +(4.38234 - 3.18395i) q^{71} +(1.58914 - 1.15458i) q^{72} +(2.07103 + 6.37396i) q^{73} +(-0.335211 + 1.03167i) q^{74} +(9.18698 + 6.67473i) q^{75} -24.8191 q^{76} +(-2.39815 - 2.29104i) q^{77} +2.60929 q^{78} +(-2.14693 - 1.55984i) q^{79} +(-4.83766 + 14.8888i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(11.7805 - 8.55903i) q^{82} +(-5.41765 + 3.93615i) q^{83} +(2.04238 + 6.28581i) q^{84} +(1.21821 - 3.74926i) q^{85} +(-17.3783 - 12.6261i) q^{86} +7.40020 q^{87} +(-3.05216 - 16.7806i) q^{88} -0.698213 q^{89} +(-2.64256 - 1.91993i) q^{90} +(0.202020 - 0.621755i) q^{91} +(-8.41560 - 25.9006i) q^{92} +(3.66042 - 2.65945i) q^{93} +(1.20676 - 0.876765i) q^{94} +(6.50911 + 20.0330i) q^{95} +(-0.427051 + 1.31433i) q^{96} +(12.0209 + 8.73372i) q^{97} +2.46673 q^{98} +(1.25544 + 0.169550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20}+ \cdots + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9 - 28 * q^10 + 5 * q^11 - 14 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 - 11 * q^17 + 4 * q^18 - 9 * q^19 + 21 * q^20 + 4 * q^21 - q^22 - 16 * q^23 + 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 + 7 * q^28 - 9 * q^29 + 14 * q^30 - 11 * q^31 - 20 * q^32 + 10 * q^33 - 24 * q^34 - 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 - 5 * q^39 - 16 * q^40 - 22 * q^41 - 3 * q^42 + 16 * q^43 + 29 * q^44 + 18 * q^45 + 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 - 34 * q^50 + 3 * q^51 + 21 * q^52 + 2 * q^53 + 4 * q^54 + 26 * q^55 - 18 * q^56 - 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 + 7 * q^61 - 5 * q^62 - 8 * q^63 + q^64 + 24 * q^65 + 18 * q^66 - 30 * q^67 + 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 + 3 * q^72 + 3 * q^73 - 9 * q^74 + 5 * q^75 - 52 * q^76 - 5 * q^77 - 18 * q^78 - 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 + 23 * q^83 + 4 * q^84 - 10 * q^85 - 17 * q^86 + 12 * q^87 - 7 * q^88 - 34 * q^89 + 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 - 30 * q^94 + 24 * q^95 + 10 * q^96 + 30 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more