LMFDB - Embedded newform 77.2.e.a.67.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(23,77)] 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("77.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	77.67
Dual form			77.2.e.a.23.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766044 + 1.32683i) q^{2} +(-1.43969 + 2.49362i) q^{3} +(-0.173648 + 0.300767i) q^{4} +(-1.17365 - 2.03282i) q^{5} -4.41147 q^{6} +(2.05303 + 1.66885i) q^{7} +2.53209 q^{8} +(-2.64543 - 4.58202i) q^{9} +(1.79813 - 3.11446i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -0.184793 q^{13} +(-0.641559 + 4.00243i) q^{14} +6.75877 q^{15} +(2.28699 + 3.96118i) q^{16} +(1.96064 - 3.39592i) q^{17} +(4.05303 - 7.02006i) q^{18} +(-0.386659 - 0.669713i) q^{19} +0.815207 q^{20} +(-7.11721 + 2.71686i) q^{21} -1.53209 q^{22} +(-4.17752 - 7.23567i) q^{23} +(-3.64543 + 6.31407i) q^{24} +(-0.254900 + 0.441500i) q^{25} +(-0.141559 - 0.245188i) q^{26} +6.59627 q^{27} +(-0.858441 + 0.327693i) q^{28} -8.17024 q^{29} +(5.17752 + 8.96773i) q^{30} +(-1.32635 + 2.29731i) q^{31} +(-0.971782 + 1.68317i) q^{32} +(-1.43969 - 2.49362i) q^{33} +6.00774 q^{34} +(0.982926 - 6.13208i) q^{35} +1.83750 q^{36} +(3.41147 + 5.90885i) q^{37} +(0.592396 - 1.02606i) q^{38} +(0.266044 - 0.460802i) q^{39} +(-2.97178 - 5.14728i) q^{40} +0.426022 q^{41} +(-9.05690 - 7.36208i) q^{42} +1.18479 q^{43} +(-0.173648 - 0.300767i) q^{44} +(-6.20961 + 10.7554i) q^{45} +(6.40033 - 11.0857i) q^{46} +(3.84002 + 6.65111i) q^{47} -13.1702 q^{48} +(1.42989 + 6.85240i) q^{49} -0.781059 q^{50} +(5.64543 + 9.77817i) q^{51} +(0.0320889 - 0.0555796i) q^{52} +(-3.27719 + 5.67626i) q^{53} +(5.05303 + 8.75211i) q^{54} +2.34730 q^{55} +(5.19846 + 4.22567i) q^{56} +2.22668 q^{57} +(-6.25877 - 10.8405i) q^{58} +(-0.102196 + 0.177009i) q^{59} +(-1.17365 + 2.03282i) q^{60} +(-7.29086 - 12.6281i) q^{61} -4.06418 q^{62} +(2.21554 - 13.8219i) q^{63} +6.17024 q^{64} +(0.216881 + 0.375650i) q^{65} +(2.20574 - 3.82045i) q^{66} +(-1.87939 + 3.25519i) q^{67} +(0.680922 + 1.17939i) q^{68} +24.0574 q^{69} +(8.88919 - 3.39328i) q^{70} -9.96585 q^{71} +(-6.69846 - 11.6021i) q^{72} +(-0.0603074 + 0.104455i) q^{73} +(-5.22668 + 9.05288i) q^{74} +(-0.733956 - 1.27125i) q^{75} +0.268571 q^{76} +(-2.47178 + 0.943555i) q^{77} +0.815207 q^{78} +(-0.163848 - 0.283793i) q^{79} +(5.36824 - 9.29807i) q^{80} +(-1.56031 + 2.70253i) q^{81} +(0.326352 + 0.565258i) q^{82} +3.35504 q^{83} +(0.418748 - 2.61240i) q^{84} -9.20439 q^{85} +(0.907604 + 1.57202i) q^{86} +(11.7626 - 20.3735i) q^{87} +(-1.26604 + 2.19285i) q^{88} +(2.32635 + 4.02936i) q^{89} -19.0273 q^{90} +(-0.379385 - 0.308391i) q^{91} +2.90167 q^{92} +(-3.81908 - 6.61484i) q^{93} +(-5.88326 + 10.1901i) q^{94} +(-0.907604 + 1.57202i) q^{95} +(-2.79813 - 4.84651i) q^{96} +13.1206 q^{97} +(-7.99660 + 7.14647i) q^{98} +5.29086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} + 12 q^{20} - 12 q^{21} - 6 q^{24} - 3 q^{25}+ \cdots - 6 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 + 12 * q^20 - 12 * q^21 - 6 * q^24 - 3 * q^25 - 9 * q^26 + 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 3 * q^33 - 12 * q^34 - 15 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 - 18 * q^42 - 3 * q^45 + 24 * q^46 + 3 * q^47 - 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 - 9 * q^53 + 18 * q^54 + 12 * q^55 + 3 * q^56 - 15 * q^58 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 - 6 * q^64 - 15 * q^65 + 3 * q^66 + 21 * q^68 + 42 * q^69 + 45 * q^70 - 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 - 9 * q^75 - 18 * q^76 + 12 * q^78 + 3 * q^79 + 27 * q^80 - 15 * q^81 + 3 * q^82 - 30 * q^83 - 54 * q^85 + 9 * q^86 + 24 * q^87 - 3 * q^88 + 15 * q^89 - 72 * q^90 + 9 * q^91 - 6 * q^92 - 6 * q^93 - 9 * q^95 - 3 * q^96 + 90 * q^97 - 6 * q^98

Character values

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

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.766044	+	1.32683i	0.541675	+	0.938209i	0.998808	+	0.0488106i	$0.0155431\pi$
$2$	0.766044	+	1.32683i	0.541675	+	0.938209i	−0.457133	+	0.889398i	$0.651124\pi$
$3$	−1.43969	+	2.49362i	−0.831207	+	1.43969i	0.0658748	+	0.997828i	$0.479016\pi$
$3$	−1.43969	+	2.49362i	−0.831207	+	1.43969i	−0.897082	+	0.441865i	$0.854317\pi$
$4$	−0.173648	+	0.300767i	−0.0868241	+	0.150384i
$5$	−1.17365	−	2.03282i	−0.524871	−	0.909104i	−0.999581	−	0.0289612i	$-0.990780\pi$
$5$	−1.17365	−	2.03282i	−0.524871	−	0.909104i	0.474709	−	0.880143i	$-0.342553\pi$
$6$	−4.41147			−1.80098
$7$	2.05303	+	1.66885i	0.775974	+	0.630765i
$7$	2.05303	+	1.66885i	0.775974	+	0.630765i
$8$	2.53209			0.895229
$9$	−2.64543	−	4.58202i	−0.881810	−	1.52734i
$10$	1.79813	−	3.11446i	0.568620	−	0.984878i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−0.184793			−0.0512522			−0.0256261	−	0.999672i	$-0.508158\pi$
$13$	−0.184793			−0.0512522			−0.0256261	+	0.999672i	$0.508158\pi$
$14$	−0.641559	+	4.00243i	−0.171464	+	1.06970i
$15$	6.75877			1.74511
$16$	2.28699	+	3.96118i	0.571747	+	0.990295i
$17$	1.96064	−	3.39592i	0.475524	−	0.823632i	−0.524083	−	0.851667i	$-0.675592\pi$
$17$	1.96064	−	3.39592i	0.475524	−	0.823632i	0.999607	+	0.0280351i	$0.00892502\pi$
$18$	4.05303	−	7.02006i	0.955309	−	1.65464i
$19$	−0.386659	−	0.669713i	−0.0887057	−	0.153643i	0.818259	−	0.574850i	$-0.194940\pi$
$19$	−0.386659	−	0.669713i	−0.0887057	−	0.153643i	−0.906964	+	0.421208i	$0.861606\pi$
$20$	0.815207			0.182286
$21$	−7.11721	+	2.71686i	−1.55310	+	0.592867i
$22$	−1.53209			−0.326642
$23$	−4.17752	−	7.23567i	−0.871073	−	1.50874i	−0.860888	−	0.508794i	$-0.830091\pi$
$23$	−4.17752	−	7.23567i	−0.871073	−	1.50874i	−0.0101847	−	0.999948i	$-0.503242\pi$
$24$	−3.64543	+	6.31407i	−0.744120	+	1.28885i
$25$	−0.254900	+	0.441500i	−0.0509800	+	0.0883000i
$26$	−0.141559	−	0.245188i	−0.0277621	−	0.0480853i
$27$	6.59627			1.26945
$28$	−0.858441	+	0.327693i	−0.162230	+	0.0619282i
$29$	−8.17024			−1.51718			−0.758588	−	0.651570i	$-0.774111\pi$
$29$	−8.17024			−1.51718			−0.758588	+	0.651570i	$0.774111\pi$
$30$	5.17752	+	8.96773i	0.945281	+	1.63728i
$31$	−1.32635	+	2.29731i	−0.238220	+	0.412609i	−0.960204	−	0.279301i	$-0.909897\pi$
$31$	−1.32635	+	2.29731i	−0.238220	+	0.412609i	0.721984	+	0.691910i	$0.243231\pi$
$32$	−0.971782	+	1.68317i	−0.171788	+	0.297546i
$33$	−1.43969	−	2.49362i	−0.250618	−	0.434084i
$34$	6.00774			1.03032
$35$	0.982926	−	6.13208i	0.166145	−	1.03651i
$36$	1.83750			0.306249
$37$	3.41147	+	5.90885i	0.560843	+	0.971408i	0.997423	+	0.0717431i	$0.0228562\pi$
$37$	3.41147	+	5.90885i	0.560843	+	0.971408i	−0.436580	+	0.899665i	$0.643811\pi$
$38$	0.592396	−	1.02606i	0.0960994	−	0.166449i
$39$	0.266044	−	0.460802i	0.0426012	−	0.0737875i
$40$	−2.97178	−	5.14728i	−0.469880	−	0.813856i
$41$	0.426022			0.0665335			0.0332667	−	0.999447i	$-0.489409\pi$
$41$	0.426022			0.0665335			0.0332667	+	0.999447i	$0.489409\pi$
$42$	−9.05690	−	7.36208i	−1.39751	−	1.13599i
$43$	1.18479			0.180679			0.0903396	−	0.995911i	$-0.471205\pi$
$43$	1.18479			0.180679			0.0903396	+	0.995911i	$0.471205\pi$
$44$	−0.173648	−	0.300767i	−0.0261784	−	0.0453424i
$45$	−6.20961	+	10.7554i	−0.925674	+	1.60331i
$46$	6.40033	−	11.0857i	0.943677	−	1.63450i
$47$	3.84002	+	6.65111i	0.560125	+	0.970165i	0.997485	+	0.0708782i	$0.0225802\pi$
$47$	3.84002	+	6.65111i	0.560125	+	0.970165i	−0.437360	+	0.899286i	$0.644086\pi$
$48$	−13.1702			−1.90096
$49$	1.42989	+	6.85240i	0.204270	+	0.978915i
$50$	−0.781059			−0.110458
$51$	5.64543	+	9.77817i	0.790518	+	1.36922i
$52$	0.0320889	−	0.0555796i	0.00444993	−	0.00770750i
$53$	−3.27719	+	5.67626i	−0.450157	+	0.779694i	−0.998395	−	0.0566279i	$-0.981965\pi$
$53$	−3.27719	+	5.67626i	−0.450157	+	0.779694i	0.548239	+	0.836322i	$0.315298\pi$
$54$	5.05303	+	8.75211i	0.687631	+	1.19101i
$55$	2.34730			0.316509
$56$	5.19846	+	4.22567i	0.694674	+	0.564679i
$57$	2.22668			0.294931
$58$	−6.25877	−	10.8405i	−0.821817	−	1.42343i
$59$	−0.102196	+	0.177009i	−0.0133048	+	0.0230447i	−0.872601	−	0.488433i	$-0.837569\pi$
$59$	−0.102196	+	0.177009i	−0.0133048	+	0.0230447i	0.859296	+	0.511478i	$0.170902\pi$
$60$	−1.17365	+	2.03282i	−0.151517	+	0.262436i
$61$	−7.29086	−	12.6281i	−0.933499	−	1.61687i	−0.777289	−	0.629144i	$-0.783406\pi$
$61$	−7.29086	−	12.6281i	−0.933499	−	1.61687i	−0.156210	−	0.987724i	$-0.549928\pi$
$62$	−4.06418			−0.516151
$63$	2.21554	−	13.8219i	0.279131	−	1.74139i
$64$	6.17024			0.771281
$65$	0.216881	+	0.375650i	0.0269008	+	0.0465936i
$66$	2.20574	−	3.82045i	0.271507	−	0.470265i
$67$	−1.87939	+	3.25519i	−0.229603	+	0.397685i	−0.957691	−	0.287800i	$-0.907076\pi$
$67$	−1.87939	+	3.25519i	−0.229603	+	0.397685i	0.728087	+	0.685485i	$0.240410\pi$
$68$	0.680922	+	1.17939i	0.0825739	+	0.143022i
$69$	24.0574			2.89617
$70$	8.88919	−	3.39328i	1.06246	−	0.405574i
$71$	−9.96585			−1.18273			−0.591365	−	0.806404i	$-0.701411\pi$
$71$	−9.96585			−1.18273			−0.591365	+	0.806404i	$0.701411\pi$
$72$	−6.69846	−	11.6021i	−0.789421	−	1.36732i
$73$	−0.0603074	+	0.104455i	−0.00705844	+	0.0122256i	−0.869533	−	0.493875i	$-0.835580\pi$
$73$	−0.0603074	+	0.104455i	−0.00705844	+	0.0122256i	0.862475	+	0.506100i	$0.168913\pi$
$74$	−5.22668	+	9.05288i	−0.607589	+	1.05238i
$75$	−0.733956	−	1.27125i	−0.0847499	−	0.146791i
$76$	0.268571			0.0308072
$77$	−2.47178	+	0.943555i	−0.281686	+	0.107528i
$78$	0.815207			0.0923041
$79$	−0.163848	−	0.283793i	−0.0184343	−	0.0319292i	0.856661	−	0.515880i	$-0.172535\pi$
$79$	−0.163848	−	0.283793i	−0.0184343	−	0.0319292i	−0.875095	+	0.483950i	$0.839201\pi$
$80$	5.36824	−	9.29807i	0.600188	−	1.03956i
$81$	−1.56031	+	2.70253i	−0.173367	+	0.300281i
$82$	0.326352	+	0.565258i	0.0360395	+	0.0624223i
$83$	3.35504			0.368263			0.184132	−	0.982902i	$-0.441053\pi$
$83$	3.35504			0.368263			0.184132	+	0.982902i	$0.441053\pi$
$84$	0.418748	−	2.61240i	0.0456892	−	0.285037i
$85$	−9.20439			−0.998357
$86$	0.907604	+	1.57202i	0.0978694	+	0.169515i
$87$	11.7626	−	20.3735i	1.26109	−	2.18427i
$88$	−1.26604	+	2.19285i	−0.134961	+	0.233759i
$89$	2.32635	+	4.02936i	0.246593	+	0.427111i	0.962578	−	0.271004i	$-0.0873557\pi$
$89$	2.32635	+	4.02936i	0.246593	+	0.427111i	−0.715985	+	0.698115i	$0.754022\pi$
$90$	−19.0273			−2.00566
$91$	−0.379385	−	0.308391i	−0.0397704	−	0.0323281i
$92$	2.90167			0.302520
$93$	−3.81908	−	6.61484i	−0.396020	−	0.685927i
$94$	−5.88326	+	10.1901i	−0.606811	+	1.05103i
$95$	−0.907604	+	1.57202i	−0.0931182	+	0.161285i
$96$	−2.79813	−	4.84651i	−0.285583	−	0.494645i
$97$	13.1206			1.33220			0.666098	−	0.745864i	$-0.267963\pi$
$97$	13.1206			1.33220			0.666098	+	0.745864i	$0.267963\pi$
$98$	−7.99660	+	7.14647i	−0.807778	+	0.721902i
$99$	5.29086			0.531751
$100$	−0.0885259	−	0.153331i	−0.00885259	−	0.0153331i
$101$	2.95084	−	5.11100i	0.293619	−	0.508563i	−0.681044	−	0.732243i	$-0.738474\pi$
$101$	2.95084	−	5.11100i	0.293619	−	0.508563i	0.974663	+	0.223679i	$0.0718069\pi$
$102$	−8.64930	+	14.9810i	−0.856408	+	1.48334i
$103$	−0.460637	−	0.797847i	−0.0453879	−	0.0786142i	0.842439	−	0.538792i	$-0.181119\pi$
$103$	−0.460637	−	0.797847i	−0.0453879	−	0.0786142i	−0.887827	+	0.460178i	$0.847786\pi$
$104$	−0.467911			−0.0458825
$105$	13.8760	+	11.2794i	1.35416	+	1.10075i
$106$	−10.0419			−0.975354
$107$	5.17365	+	8.96102i	0.500155	+	0.866295i	1.00000		0.000179505i	$5.71381e-5\pi$
$107$	5.17365	+	8.96102i	0.500155	+	0.866295i	−0.499845	+	0.866115i	$0.666610\pi$
$108$	−1.14543	+	1.98394i	−0.110219	+	0.190905i
$109$	−0.237826	+	0.411927i	−0.0227796	+	0.0394554i	−0.877190	−	0.480143i	$-0.840585\pi$
$109$	−0.237826	+	0.411927i	−0.0227796	+	0.0394554i	0.854411	+	0.519598i	$0.173918\pi$
$110$	1.79813	+	3.11446i	0.171445	+	0.296952i
$111$	−19.6459			−1.86471
$112$	−1.91534	+	11.9491i	−0.180983	+	1.12908i
$113$	−3.14290			−0.295659			−0.147830	−	0.989013i	$-0.547229\pi$
$113$	−3.14290			−0.295659			−0.147830	+	0.989013i	$0.547229\pi$
$114$	1.70574	+	2.95442i	0.159757	+	0.276707i
$115$	−9.80587	+	16.9843i	−0.914402	+	1.58379i
$116$	1.41875	−	2.45734i	0.131727	−	0.228159i
$117$	0.488856	+	0.846723i	0.0451947	+	0.0782796i
$118$	−0.313148			−0.0288276
$119$	9.69253	−	3.69994i	0.888513	−	0.339173i
$120$	17.1138			1.56227
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	11.1702	−	19.3474i	1.01131	−	1.75163i
$123$	−0.613341	+	1.06234i	−0.0553031	+	0.0957877i
$124$	−0.460637	−	0.797847i	−0.0413664	−	0.0716488i
$125$	−10.5398			−0.942711
$126$	20.0364	−	7.64852i	1.78499	−	0.681384i
$127$	−0.445622			−0.0395426			−0.0197713	−	0.999805i	$-0.506294\pi$
$127$	−0.445622			−0.0395426			−0.0197713	+	0.999805i	$0.506294\pi$
$128$	6.67024	+	11.5532i	0.589572	+	1.02117i
$129$	−1.70574	+	2.95442i	−0.150182	+	0.260122i
$130$	−0.332282	+	0.575529i	−0.0291430	+	0.0504772i
$131$	6.04323	+	10.4672i	0.528000	+	0.914522i	0.999467	+	0.0326389i	$0.0103911\pi$
$131$	6.04323	+	10.4672i	0.528000	+	0.914522i	−0.471467	+	0.881883i	$0.656276\pi$
$132$	1.00000			0.0870388
$133$	0.323826	−	2.02022i	0.0280792	−	0.175175i
$134$	−5.75877			−0.497482
$135$	−7.74170	−	13.4090i	−0.666299	−	1.15406i
$136$	4.96451	−	8.59878i	0.425703	−	0.737339i
$137$	8.17412	−	14.1580i	0.698362	−	1.20960i	−0.270672	−	0.962672i	$-0.587246\pi$
$137$	8.17412	−	14.1580i	0.698362	−	1.20960i	0.969034	−	0.246927i	$-0.0794206\pi$
$138$	18.4290	+	31.9200i	1.56878	+	2.71721i
$139$	−20.7297			−1.75827			−0.879134	−	0.476575i	$-0.841878\pi$
$139$	−20.7297			−1.75827			−0.879134	+	0.476575i	$0.841878\pi$
$140$	1.67365	+	1.36046i	0.141449	+	0.114980i
$141$	−22.1138			−1.86232
$142$	−7.63429	−	13.2230i	−0.640655	−	1.10965i
$143$	0.0923963	−	0.160035i	0.00772656	−	0.0133828i
$144$	12.1001	−	20.9581i	1.00834	−	1.74650i
$145$	9.58899	+	16.6086i	0.796322	+	1.37927i
$146$	−0.184793			−0.0152935
$147$	−19.1459	−	6.29974i	−1.57913	−	0.519594i
$148$	−2.36959			−0.194779
$149$	0.357097	+	0.618509i	0.0292545	+	0.0506703i	0.880282	−	0.474451i	$-0.157353\pi$
$149$	0.357097	+	0.618509i	0.0292545	+	0.0506703i	−0.851027	+	0.525121i	$0.824020\pi$
$150$	1.12449	−	1.94767i	0.0918138	−	0.159026i
$151$	4.77244	−	8.26611i	0.388376	−	0.672687i	−0.603855	−	0.797094i	$-0.706370\pi$
$151$	4.77244	−	8.26611i	0.388376	−	0.672687i	0.992231	+	0.124407i	$0.0397029\pi$
$152$	−0.979055	−	1.69577i	−0.0794119	−	0.137545i
$153$	−20.7469			−1.67729
$154$	−3.14543	−	2.55682i	−0.253466	−	0.206035i
$155$	6.22668			0.500139
$156$	0.0923963	+	0.160035i	0.00739762	+	0.0128131i
$157$	−4.62061	+	8.00314i	−0.368765	+	0.638720i	−0.989373	−	0.145401i	$-0.953553\pi$
$157$	−4.62061	+	8.00314i	−0.368765	+	0.638720i	0.620608	+	0.784121i	$0.286886\pi$
$158$	0.251030	−	0.434796i	0.0199709	−	0.0345905i
$159$	−9.43629	−	16.3441i	−0.748346	−	1.29617i
$160$	4.56212			0.360667
$161$	3.49866	−	21.8267i	0.275733	−	1.72019i
$162$	−4.78106			−0.375635
$163$	4.40167	+	7.62392i	0.344766	+	0.597152i	0.985311	−	0.170769i	$-0.0546250\pi$
$163$	4.40167	+	7.62392i	0.344766	+	0.597152i	−0.640545	+	0.767920i	$0.721292\pi$
$164$	−0.0739780	+	0.128134i	−0.00577671	+	0.0100056i
$165$	−3.37939	+	5.85327i	−0.263085	+	0.455676i
$166$	2.57011	+	4.45156i	0.199479	+	0.345508i
$167$	8.38238			0.648648			0.324324	−	0.945946i	$-0.394863\pi$
$167$	8.38238			0.648648			0.324324	+	0.945946i	$0.394863\pi$
$168$	−18.0214	+	6.87933i	−1.39038	+	0.530752i
$169$	−12.9659			−0.997373
$170$	−7.05097	−	12.2126i	−0.540785	−	0.936667i
$171$	−2.04576	+	3.54336i	−0.156443	+	0.270967i
$172$	−0.205737	+	0.356347i	−0.0156873	+	0.0271712i
$173$	−2.72281	−	4.71605i	−0.207012	−	0.358554i	0.743760	−	0.668446i	$-0.233040\pi$
$173$	−2.72281	−	4.71605i	−0.207012	−	0.358554i	−0.950772	+	0.309892i	$0.899707\pi$
$174$	36.0428			2.73240
$175$	−1.26011	+	0.481025i	−0.0952557	+	0.0363620i
$176$	−4.57398			−0.344777
$177$	−0.294263	−	0.509678i	−0.0221182	−	0.0383098i
$178$	−3.56418	+	6.17334i	−0.267146	+	0.462711i
$179$	5.04576	−	8.73951i	0.377138	−	0.653222i	−0.613507	−	0.789689i	$-0.710242\pi$
$179$	5.04576	−	8.73951i	0.377138	−	0.653222i	0.990645	+	0.136468i	$0.0435750\pi$
$180$	−2.15657	−	3.73530i	−0.160742	−	0.278413i
$181$	19.8794			1.47762			0.738812	−	0.673912i	$-0.235387\pi$
$181$	19.8794			1.47762			0.738812	+	0.673912i	$0.235387\pi$
$182$	0.118555	−	0.739620i	0.00878791	−	0.0548243i
$183$	41.9864			3.10372
$184$	−10.5778	−	18.3214i	−0.779809	−	1.35067i
$185$	8.00774	−	13.8698i	0.588741	−	1.01973i
$186$	5.85117	−	10.1345i	0.429028	−	0.743099i
$187$	1.96064	+	3.39592i	0.143376	+	0.248334i
$188$	−2.66725			−0.194529
$189$	13.5424	+	11.0082i	0.985061	+	0.800726i
$190$	−2.78106			−0.201759
$191$	12.6925	+	21.9841i	0.918399	+	1.59071i	0.801846	+	0.597530i	$0.203851\pi$
$191$	12.6925	+	21.9841i	0.918399	+	1.59071i	0.116553	+	0.993184i	$0.462816\pi$
$192$	−8.88326	+	15.3863i	−0.641094	+	1.11041i
$193$	3.86571	−	6.69561i	0.278260	−	0.481961i	−0.692692	−	0.721233i	$-0.743576\pi$
$193$	3.86571	−	6.69561i	0.278260	−	0.481961i	0.970952	+	0.239272i	$0.0769089\pi$
$194$	10.0510	+	17.4088i	0.721618	+	1.24988i
$195$	−1.24897			−0.0894406
$196$	−2.30928	−	0.759842i	−0.164948	−	0.0542744i
$197$	−5.37464			−0.382927			−0.191464	−	0.981500i	$-0.561323\pi$
$197$	−5.37464			−0.382927			−0.191464	+	0.981500i	$0.561323\pi$
$198$	4.05303	+	7.02006i	0.288037	+	0.498894i
$199$	−4.39053	+	7.60462i	−0.311236	+	0.539077i	−0.978630	−	0.205628i	$-0.934076\pi$
$199$	−4.39053	+	7.60462i	−0.311236	+	0.539077i	0.667394	+	0.744705i	$0.267410\pi$
$200$	−0.645430	+	1.11792i	−0.0456388	+	0.0790487i
$201$	−5.41147	−	9.37295i	−0.381696	−	0.661117i
$202$	9.04189			0.636185
$203$	−16.7738	−	13.6349i	−1.17729	−	0.956982i
$204$	−3.92127			−0.274544
$205$	−0.500000	−	0.866025i	−0.0349215	−	0.0604858i
$206$	0.705737	−	1.22237i	0.0491710	−	0.0851667i
$207$	−22.1027	+	38.2829i	−1.53624	+	2.66085i
$208$	−0.422618	−	0.731997i	−0.0293033	−	0.0507548i
$209$	0.773318			0.0534916
$210$	−4.33615	+	27.0515i	−0.299223	+	1.86673i
$211$	4.24123			0.291978			0.145989	−	0.989286i	$-0.453364\pi$
$211$	4.24123			0.291978			0.145989	+	0.989286i	$0.453364\pi$
$212$	−1.13816	−	1.97134i	−0.0781689	−	0.135392i
$213$	14.3478	−	24.8511i	0.983093	−	1.70277i
$214$	−7.92649	+	13.7291i	−0.541844	+	0.938501i
$215$	−1.39053	−	2.40847i	−0.0948333	−	0.164256i
$216$	16.7023			1.13645
$217$	−6.55690	+	2.50297i	−0.445112	+	0.169913i
$218$	−0.728741			−0.0493566
$219$	−0.173648	−	0.300767i	−0.0117341	−	0.0203240i
$220$	−0.407604	+	0.705990i	−0.0274806	+	0.0475979i
$221$	−0.362311	+	0.627541i	−0.0243717	+	0.0422130i
$222$	−15.0496	−	26.0667i	−1.01007	−	1.74948i
$223$	−18.0351			−1.20772			−0.603859	−	0.797091i	$-0.706371\pi$
$223$	−18.0351			−1.20772			−0.603859	+	0.797091i	$0.706371\pi$
$224$	−4.80406	+	1.83386i	−0.320985	+	0.122530i
$225$	2.69728			0.179819
$226$	−2.40760	−	4.17009i	−0.160151	−	0.277390i
$227$	−9.10266	+	15.7663i	−0.604165	+	1.04644i	0.388018	+	0.921652i	$0.373160\pi$
$227$	−9.10266	+	15.7663i	−0.604165	+	1.04644i	−0.992183	+	0.124793i	$0.960173\pi$
$228$	−0.386659	+	0.669713i	−0.0256071	+	0.0443529i
$229$	−9.62061	−	16.6634i	−0.635748	−	1.10115i	−0.986356	−	0.164626i	$-0.947358\pi$
$229$	−9.62061	−	16.6634i	−0.635748	−	1.10115i	0.350608	−	0.936522i	$-0.385975\pi$
$230$	−30.0469			−1.98124
$231$	1.20574	−	7.52211i	0.0793317	−	0.494919i
$232$	−20.6878			−1.35822
$233$	−4.66250	−	8.07569i	−0.305451	−	0.529056i	0.671911	−	0.740632i	$-0.265474\pi$
$233$	−4.66250	−	8.07569i	−0.305451	−	0.529056i	−0.977362	+	0.211576i	$0.932140\pi$
$234$	−0.748970	+	1.29725i	−0.0489617	+	0.0848042i
$235$	9.01367	−	15.6121i	0.587987	−	1.01842i
$236$	−0.0354925	−	0.0614747i	−0.00231036	−	0.00400166i
$237$	0.943563			0.0612910
$238$	12.3341	+	10.0260i	0.799500	+	0.649889i
$239$	11.1898			0.723811			0.361905	−	0.932215i	$-0.382126\pi$
$239$	11.1898			0.723811			0.361905	+	0.932215i	$0.382126\pi$
$240$	15.4572	+	26.7727i	0.997760	+	1.72817i
$241$	−10.1022	+	17.4975i	−0.650740	+	1.12711i	0.332204	+	0.943208i	$0.392208\pi$
$241$	−10.1022	+	17.4975i	−0.650740	+	1.12711i	−0.982944	+	0.183907i	$0.941126\pi$
$242$	0.766044	−	1.32683i	0.0492432	−	0.0852917i
$243$	5.40167	+	9.35597i	0.346518	+	0.600186i
$244$	5.06418			0.324201
$245$	12.2515	−	10.9490i	0.782719	−	0.699507i
$246$	−1.87939			−0.119825
$247$	0.0714517	+	0.123758i	0.00454636	+	0.00787453i
$248$	−3.35844	+	5.81699i	−0.213261	+	0.369379i
$249$	−4.83022	+	8.36619i	−0.306103	+	0.530186i
$250$	−8.07398	−	13.9845i	−0.510643	−	0.884460i
$251$	−5.89218			−0.371911			−0.185956	−	0.982558i	$-0.559538\pi$
$251$	−5.89218			−0.371911			−0.185956	+	0.982558i	$0.559538\pi$
$252$	3.77244	+	3.06650i	0.237641	+	0.193171i
$253$	8.35504			0.525277
$254$	−0.341367	−	0.591264i	−0.0214192	−	0.0370992i
$255$	13.2515	−	22.9523i	0.829841	−	1.43733i
$256$	−4.04916	+	7.01336i	−0.253073	+	0.438335i
$257$	1.36824	+	2.36986i	0.0853485	+	0.147828i	0.905540	−	0.424262i	$-0.139466\pi$
$257$	1.36824	+	2.36986i	0.0853485	+	0.147828i	−0.820191	+	0.572090i	$0.806133\pi$
$258$	−5.22668			−0.325399
$259$	−2.85710	+	17.8243i	−0.177531	+	1.10755i
$260$	−0.150644			−0.00934256
$261$	21.6138	+	37.4362i	1.33786	+	2.31724i
$262$	−9.25877	+	16.0367i	−0.572009	+	0.990748i
$263$	−3.09879	+	5.36727i	−0.191080	+	0.330960i	−0.945608	−	0.325307i	$-0.894532\pi$
$263$	−3.09879	+	5.36727i	−0.191080	+	0.330960i	0.754529	+	0.656267i	$0.227866\pi$
$264$	−3.64543	−	6.31407i	−0.224361	−	0.388604i
$265$	15.3851			0.945097
$266$	2.92855	−	1.11792i	0.179561	−	0.0685439i
$267$	−13.3969			−0.819879
$268$	−0.652704	−	1.13052i	−0.0398702	−	0.0690572i
$269$	2.10472	−	3.64549i	0.128327	−	0.222269i	−0.794701	−	0.607001i	$-0.792373\pi$
$269$	2.10472	−	3.64549i	0.128327	−	0.222269i	0.923029	+	0.384731i	$0.125706\pi$
$270$	11.8610	−	20.5438i	0.721835	−	1.25026i
$271$	−12.7909	−	22.1544i	−0.776989	−	1.34579i	−0.933670	−	0.358136i	$-0.883413\pi$
$271$	−12.7909	−	22.1544i	−0.776989	−	1.34579i	0.156680	−	0.987649i	$-0.449921\pi$
$272$	17.9358			1.08752
$273$	1.31521	−	0.502055i	0.0796000	−	0.0303858i
$274$	25.0469			1.51314
$275$	−0.254900	−	0.441500i	−0.0153711	−	0.0266234i
$276$	−4.17752	+	7.23567i	−0.251457	+	0.435536i
$277$	7.67886	−	13.3002i	0.461378	−	0.799130i	−0.537652	−	0.843167i	$-0.680688\pi$
$277$	7.67886	−	13.3002i	0.461378	−	0.799130i	0.999030	+	0.0440366i	$0.0140218\pi$
$278$	−15.8799	−	27.5047i	−0.952410	−	1.64962i
$279$	14.0351			0.840258
$280$	2.48886	−	15.5270i	0.148738	−	0.927915i
$281$	19.2540			1.14860			0.574299	−	0.818645i	$-0.305275\pi$
$281$	19.2540			1.14860			0.574299	+	0.818645i	$0.305275\pi$
$282$	−16.9402	−	29.3412i	−1.00877	−	1.74724i
$283$	13.5326	−	23.4391i	0.804427	−	1.39331i	−0.112250	−	0.993680i	$-0.535806\pi$
$283$	13.5326	−	23.4391i	0.804427	−	1.39331i	0.916677	−	0.399628i	$-0.130861\pi$
$284$	1.73055	−	2.99740i	0.102689	−	0.177863i
$285$	−2.61334	−	4.52644i	−0.154801	−	0.268123i
$286$	0.283119			0.0167412
$287$	0.874638	+	0.710966i	0.0516282	+	0.0419670i
$288$	10.2831			0.605939
$289$	0.811804	+	1.40609i	0.0477532	+	0.0827109i
$290$	−14.6912	+	25.4459i	−0.862696	+	1.49423i
$291$	−18.8897	+	32.7178i	−1.10733	+	1.91795i
$292$	−0.0209445	−	0.0362770i	−0.00122569	−	0.00212295i
$293$	4.03508			0.235732			0.117866	−	0.993030i	$-0.462395\pi$
$293$	4.03508			0.235732			0.117866	+	0.993030i	$0.462395\pi$
$294$	−6.30793	−	30.2292i	−0.367886	−	1.76300i
$295$	0.479771			0.0279333
$296$	8.63816	+	14.9617i	0.502083	+	0.869633i
$297$	−3.29813	+	5.71253i	−0.191377	+	0.331475i
$298$	−0.547104	+	0.947611i	−0.0316929	+	0.0548936i
$299$	0.771974	+	1.33710i	0.0446444	+	0.0773264i
$300$	0.509800			0.0294333
$301$	2.43242	+	1.97724i	0.140202	+	0.113966i
$302$	14.6236			0.841494
$303$	8.49660	+	14.7165i	0.488117	+	0.845443i
$304$	1.76857	−	3.06325i	0.101434	−	0.175690i
$305$	−17.1138	+	29.6420i	−0.979934	+	1.69730i
$306$	−15.8931	−	27.5276i	−0.908546	−	1.57365i
$307$	2.92902			0.167168			0.0835839	−	0.996501i	$-0.473363\pi$
$307$	2.92902			0.167168			0.0835839	+	0.996501i	$0.473363\pi$
$308$	0.145430	−	0.907278i	0.00828663	−	0.0516970i
$309$	2.65270			0.150907
$310$	4.76991	+	8.26173i	0.270913	+	0.469235i
$311$	−7.81180	+	13.5304i	−0.442967	+	0.767241i	−0.997908	−	0.0646486i	$-0.979407\pi$
$311$	−7.81180	+	13.5304i	−0.442967	+	0.767241i	0.554941	+	0.831889i	$0.312741\pi$
$312$	0.673648	−	1.16679i	0.0381378	−	0.0660566i
$313$	10.9880	+	19.0317i	0.621077	+	1.07574i	0.989285	+	0.145994i	$0.0466380\pi$
$313$	10.9880	+	19.0317i	0.621077	+	1.07574i	−0.368208	+	0.929743i	$0.620029\pi$
$314$	−14.1584			−0.799004
$315$	−30.6976	+	11.7182i	−1.72961	+	0.660247i
$316$	0.113808			0.00640218
$317$	1.50593	+	2.60835i	0.0845814	+	0.146499i	0.905213	−	0.424959i	$-0.139711\pi$
$317$	1.50593	+	2.60835i	0.0845814	+	0.146499i	−0.820631	+	0.571458i	$0.806378\pi$
$318$	14.4572	−	25.0407i	0.810721	−	1.40421i
$319$	4.08512	−	7.07564i	0.228723	−	0.396160i
$320$	−7.24170	−	12.5430i	−0.404823	−	0.701174i
$321$	−29.7939			−1.66293
$322$	31.6404	−	12.0781i	1.76325	−	0.673088i
$323$	−3.03239			−0.168727
$324$	−0.541889	−	0.938579i	−0.0301049	−	0.0521433i
$325$	0.0471036	−	0.0815859i	0.00261284	−	0.00452557i
$326$	−6.74376	+	11.6805i	−0.373502	+	0.646925i
$327$	−0.684793	−	1.18610i	−0.0378691	−	0.0655912i
$328$	1.07873			0.0595627
$329$	−3.21600	+	20.0634i	−0.177304	+	1.10613i
$330$	−10.3550			−0.570026
$331$	−13.7344	−	23.7887i	−0.754912	−	1.30755i	−0.945418	−	0.325860i	$-0.894346\pi$
$331$	−13.7344	−	23.7887i	−0.754912	−	1.30755i	0.190506	−	0.981686i	$-0.438987\pi$
$332$	−0.582596	+	1.00909i	−0.0319741	+	0.0553808i
$333$	18.0496	−	31.2629i	0.989114	−	1.71320i
$334$	6.42127	+	11.1220i	0.351356	+	0.608567i
$335$	8.82295			0.482049
$336$	−27.0390	−	21.9791i	−1.47510	−	1.19906i
$337$	17.2422			0.939240			0.469620	−	0.882869i	$-0.344391\pi$
$337$	17.2422			0.939240			0.469620	+	0.882869i	$0.344391\pi$
$338$	−9.93242	−	17.2035i	−0.540252	−	0.935745i
$339$	4.52481	−	7.83721i	0.245754	−	0.425659i
$340$	1.59833	−	2.76838i	0.0866814	−	0.150137i
$341$	−1.32635	−	2.29731i	−0.0718260	−	0.124406i
$342$	−6.26857			−0.338965
$343$	−8.50000	+	16.4545i	−0.458957	+	0.888459i
$344$	3.00000			0.161749
$345$	−28.2349	−	48.9043i	−1.52012	−	2.63292i
$346$	4.17159	−	7.22540i	0.224266	−	0.388440i
$347$	5.71554	−	9.89960i	0.306826	−	0.531438i	−0.670840	−	0.741602i	$-0.734066\pi$
$347$	5.71554	−	9.89960i	0.306826	−	0.531438i	0.977666	+	0.210164i	$0.0673997\pi$
$348$	4.08512	+	7.07564i	0.218986	+	0.379294i
$349$	28.3209			1.51598			0.757991	−	0.652265i	$-0.226181\pi$
$349$	28.3209			1.51598			0.757991	+	0.652265i	$0.226181\pi$
$350$	−1.60354	−	1.30347i	−0.0857129	−	0.0696734i
$351$	−1.21894			−0.0650622
$352$	−0.971782	−	1.68317i	−0.0517961	−	0.0897135i
$353$	−8.21806	+	14.2341i	−0.437403	+	0.757605i	−0.997488	−	0.0708303i	$-0.977435\pi$
$353$	−8.21806	+	14.2341i	−0.437403	+	0.757605i	0.560085	+	0.828435i	$0.310768\pi$
$354$	0.450837	−	0.780873i	0.0239617	−	0.0415029i
$355$	11.6964	+	20.2588i	0.620781	+	1.07522i
$356$	−1.61587			−0.0856408
$357$	−4.72803	+	29.4963i	−0.250234	+	1.56111i
$358$	15.4611			0.817145
$359$	−12.4315	−	21.5321i	−0.656112	−	1.13642i	−0.981614	−	0.190877i	$-0.938867\pi$
$359$	−12.4315	−	21.5321i	−0.656112	−	1.13642i	0.325502	−	0.945541i	$-0.394467\pi$
$360$	−15.7233	+	27.2335i	−0.828690	+	1.43533i
$361$	9.20099	−	15.9366i	0.484263	−	0.838767i
$362$	15.2285	+	26.3765i	0.800392	+	1.38632i
$363$	2.87939			0.151129
$364$	0.158633	−	0.0605553i	0.00831465	−	0.00317396i
$365$	0.283119			0.0148191
$366$	32.1634	+	55.7087i	1.68121	+	2.91194i
$367$	−2.14930	+	3.72270i	−0.112193	+	0.194323i	−0.916654	−	0.399682i	$-0.869121\pi$
$367$	−2.14930	+	3.72270i	−0.112193	+	0.194323i	0.804461	+	0.594005i	$0.202454\pi$
$368$	19.1079	−	33.0958i	0.996067	−	1.72524i
$369$	−1.12701	−	1.95204i	−0.0586699	−	0.101619i
$370$	24.5371			1.27563
$371$	−16.2010	+	6.18442i	−0.841113	+	0.321079i
$372$	2.65270			0.137536
$373$	1.36484	+	2.36397i	0.0706686	+	0.122402i	0.899195	−	0.437549i	$-0.144153\pi$
$373$	1.36484	+	2.36397i	0.0706686	+	0.122402i	−0.828526	+	0.559951i	$0.810820\pi$
$374$	−3.00387	+	5.20286i	−0.155326	+	0.269033i
$375$	15.1741	−	26.2823i	0.783588	−	1.35721i
$376$	9.72328	+	16.8412i	0.501440	+	0.868519i
$377$	1.50980			0.0777587
$378$	−4.23190	+	26.4011i	−0.217665	+	1.35793i
$379$	−16.4584			−0.845412			−0.422706	−	0.906267i	$-0.638920\pi$
$379$	−16.4584			−0.845412			−0.422706	+	0.906267i	$0.638920\pi$
$380$	−0.315207	−	0.545955i	−0.0161698	−	0.0280069i
$381$	0.641559	−	1.11121i	0.0328681	−	0.0569292i
$382$	−19.4461	+	33.6816i	−0.994948	+	1.72330i
$383$	3.92989	+	6.80677i	0.200808	+	0.347810i	0.948789	−	0.315910i	$-0.102310\pi$
$383$	3.92989	+	6.80677i	0.200808	+	0.347810i	−0.747981	+	0.663720i	$0.768977\pi$
$384$	−38.4124			−1.96022
$385$	4.81908	+	3.91728i	0.245603	+	0.199643i
$386$	11.8452			0.602907
$387$	−3.13429	−	5.42874i	−0.159325	−	0.275958i
$388$	−2.27837	+	3.94625i	−0.115667	+	0.200341i
$389$	−4.82160	+	8.35126i	−0.244465	+	0.423426i	−0.961981	−	0.273116i	$-0.911946\pi$
$389$	−4.82160	+	8.35126i	−0.244465	+	0.423426i	0.717516	+	0.696542i	$0.245279\pi$
$390$	−0.956767	−	1.65717i	−0.0484478	−	0.0839140i
$391$	−32.7624			−1.65687
$392$	3.62061	+	17.3509i	0.182869	+	0.876352i
$393$	−34.8016			−1.75551
$394$	−4.11721	−	7.13122i	−0.207422	−	0.359266i
$395$	−0.384600	+	0.666146i	−0.0193513	+	0.0335175i
$396$	−0.918748	+	1.59132i	−0.0461688	+	0.0799668i
$397$	4.71688	+	8.16988i	0.236733	+	0.410034i	0.959775	−	0.280770i	$-0.0905898\pi$
$397$	4.71688	+	8.16988i	0.236733	+	0.410034i	−0.723042	+	0.690805i	$0.757257\pi$
$398$	−13.4534			−0.674356
$399$	4.57145	+	3.71599i	0.228859	+	0.186032i
$400$	−2.33181			−0.116591
$401$	9.10994	+	15.7789i	0.454929	+	0.787959i	0.998684	−	0.0512843i	$-0.0163315\pi$
$401$	9.10994	+	15.7789i	0.454929	+	0.787959i	−0.543756	+	0.839244i	$0.682998\pi$
$402$	8.29086	−	14.3602i	0.413510	−	0.716221i
$403$	0.245100	−	0.424525i	0.0122093	−	0.0211471i
$404$	1.02481	+	1.77503i	0.0509864	+	0.0883111i
$405$	7.32501			0.363983
$406$	5.24170	−	32.7009i	0.260141	−	1.62292i
$407$	−6.82295			−0.338201
$408$	14.2947	+	24.7592i	0.707695	+	1.22576i
$409$	−3.20574	+	5.55250i	−0.158513	+	0.274553i	−0.934333	−	0.356402i	$-0.884003\pi$
$409$	−3.20574	+	5.55250i	−0.158513	+	0.274553i	0.775819	+	0.630955i	$0.217337\pi$
$410$	0.766044	−	1.32683i	0.0378322	−	0.0655274i
$411$	23.5364	+	40.7663i	1.16097	+	2.01085i
$412$	0.319955			0.0157631
$413$	−0.505215	+	0.192856i	−0.0248600	+	0.00948982i
$414$	−67.7265			−3.32858
$415$	−3.93763	−	6.82018i	−0.193291	−	0.334790i
$416$	0.179578	−	0.311038i	0.00880453	−	0.0152499i
$417$	29.8444	−	51.6919i	1.46148	−	2.53137i
$418$	0.592396	+	1.02606i	0.0289750	+	0.0501863i
$419$	1.62092			0.0791871			0.0395935	−	0.999216i	$-0.487394\pi$
$419$	1.62092			0.0791871			0.0395935	+	0.999216i	$0.487394\pi$
$420$	−5.80200	+	2.21480i	−0.283109	+	0.108071i
$421$	31.1489			1.51810			0.759052	−	0.651030i	$-0.225663\pi$
$421$	31.1489			1.51810			0.759052	+	0.651030i	$0.225663\pi$
$422$	3.24897	+	5.62738i	0.158157	+	0.273937i
$423$	20.3170	−	35.1901i	0.987847	−	1.71100i
$424$	−8.29813	+	14.3728i	−0.402993	+	0.698004i
$425$	0.999533	+	1.73124i	0.0484845	+	0.0839776i
$426$	43.9641			2.13007
$427$	6.10607	−	38.0933i	0.295493	−	1.84347i
$428$	−3.59358			−0.173702
$429$	0.266044	+	0.460802i	0.0128447	+	0.0222478i
$430$	2.13041	−	3.68999i	0.102738	−	0.177947i
$431$	−17.1040	+	29.6250i	−0.823871	+	1.42699i	0.0789080	+	0.996882i	$0.474857\pi$
$431$	−17.1040	+	29.6250i	−0.823871	+	1.42699i	−0.902779	+	0.430105i	$0.858477\pi$
$432$	15.0856	+	26.1290i	0.725806	+	1.25713i
$433$	−20.4979			−0.985068			−0.492534	−	0.870293i	$-0.663929\pi$
$433$	−20.4979			−0.985068			−0.492534	+	0.870293i	$0.663929\pi$
$434$	−8.34389	−	6.78250i	−0.400520	−	0.325570i
$435$	−55.2208			−2.64764
$436$	−0.0825961	−	0.143061i	−0.00395564	−	0.00685136i
$437$	−3.23055	+	5.59548i	−0.154538	+	0.267668i
$438$	0.266044	−	0.460802i	0.0127121	−	0.0220180i
$439$	−15.6609	−	27.1255i	−0.747455	−	1.29463i	−0.949039	−	0.315158i	$-0.897942\pi$
$439$	−15.6609	−	27.1255i	−0.747455	−	1.29463i	0.201585	−	0.979471i	$-0.435391\pi$
$440$	5.94356			0.283348
$441$	27.6152	−	24.6793i	1.31501	−	1.17521i
$442$	−1.11019			−0.0528061
$443$	14.6989	+	25.4593i	0.698367	+	1.20961i	0.969032	+	0.246934i	$0.0794231\pi$
$443$	14.6989	+	25.4593i	0.698367	+	1.20961i	−0.270665	+	0.962674i	$0.587244\pi$
$444$	3.41147	−	5.90885i	0.161901	−	0.280421i
$445$	5.46064	−	9.45810i	0.258859	−	0.448357i
$446$	−13.8157	−	23.9294i	−0.654191	−	1.13309i
$447$	−2.05644			−0.0972661
$448$	12.6677	+	10.2972i	0.598493	+	0.486497i
$449$	−6.90074			−0.325666			−0.162833	−	0.986654i	$-0.552063\pi$
$449$	−6.90074			−0.325666			−0.162833	+	0.986654i	$0.552063\pi$
$450$	2.06624	+	3.57883i	0.0974034	+	0.168708i
$451$	−0.213011	+	0.368946i	−0.0100303	+	0.0173730i
$452$	0.545759	−	0.945283i	0.0256704	−	0.0444624i
$453$	13.7417	+	23.8013i	0.645641	+	1.11828i
$454$	−27.8922			−1.30904
$455$	−0.181637	+	1.13316i	−0.00851529	+	0.0531235i
$456$	5.63816			0.264031
$457$	−6.18732	−	10.7168i	−0.289431	−	0.501308i	0.684243	−	0.729254i	$-0.260133\pi$
$457$	−6.18732	−	10.7168i	−0.289431	−	0.501308i	−0.973674	+	0.227945i	$0.926799\pi$
$458$	14.7396	−	25.5298i	0.688738	−	1.19293i
$459$	12.9329	−	22.4004i	0.603655	−	1.04556i
$460$	−3.40554	−	5.89858i	−0.158784	−	0.275023i
$461$	20.0942			0.935881			0.467940	−	0.883760i	$-0.344996\pi$
$461$	20.0942			0.935881			0.467940	+	0.883760i	$0.344996\pi$
$462$	10.9042	−	4.16247i	0.507309	−	0.193656i
$463$	8.69190			0.403947			0.201974	−	0.979391i	$-0.435265\pi$
$463$	8.69190			0.403947			0.201974	+	0.979391i	$0.435265\pi$
$464$	−18.6853	−	32.3638i	−0.867441	−	1.50245i
$465$	−8.96451	+	15.5270i	−0.415719	+	0.720047i
$466$	7.14337	−	12.3727i	0.330910	−	0.573153i
$467$	−2.38460	−	4.13025i	−0.110346	−	0.191125i	0.805564	−	0.592509i	$-0.201863\pi$
$467$	−2.38460	−	4.13025i	−0.110346	−	0.191125i	−0.915910	+	0.401384i	$0.868529\pi$
$468$	−0.339556			−0.0156960
$469$	−9.29086	+	3.54661i	−0.429012	+	0.163767i
$470$	27.6195			1.27399
$471$	−13.3045	−	23.0441i	−0.613040	−	1.06182i
$472$	−0.258770	+	0.448204i	−0.0119109	+	0.0206302i
$473$	−0.592396	+	1.02606i	−0.0272384	+	0.0471783i
$474$	0.722811	+	1.25195i	0.0331998	+	0.0575038i
$475$	0.394238			0.0180889
$476$	−0.570270	+	3.55769i	−0.0261383	+	0.163066i
$477$	34.6783			1.58781
$478$	8.57192	+	14.8470i	0.392070	+	0.679086i
$479$	19.8071	−	34.3068i	0.905007	−	1.56752i	0.0841003	−	0.996457i	$-0.473198\pi$
$479$	19.8071	−	34.3068i	0.905007	−	1.56752i	0.820907	−	0.571062i	$-0.193468\pi$
$480$	−6.56805	+	11.3762i	−0.299789	+	0.519250i
$481$	−0.630415	−	1.09191i	−0.0287444	−	0.0497868i
$482$	−30.9549			−1.40996
$483$	49.3906	+	40.1481i	2.24735	+	1.82680i
$484$	0.347296			0.0157862
$485$	−15.3990	−	26.6718i	−0.699232	−	1.21111i
$486$	−8.27584	+	14.3342i	−0.375400	+	0.650212i
$487$	−2.57785	+	4.46496i	−0.116813	+	0.202327i	−0.918503	−	0.395414i	$-0.870601\pi$
$487$	−2.57785	+	4.46496i	−0.116813	+	0.202327i	0.801690	+	0.597740i	$0.203935\pi$
$488$	−18.4611	−	31.9756i	−0.835695	−	1.44747i
$489$	−25.3482			−1.14629
$490$	23.9127	+	7.86819i	1.08026	+	0.355449i
$491$	10.1925			0.459983			0.229991	−	0.973193i	$-0.426130\pi$
$491$	10.1925			0.459983			0.229991	+	0.973193i	$0.426130\pi$
$492$	−0.213011	−	0.368946i	−0.00960328	−	0.0166334i
$493$	−16.0189	+	27.7455i	−0.721454	+	1.24960i
$494$	−0.109470	+	0.189608i	−0.00492531	+	0.00853088i
$495$	−6.20961	−	10.7554i	−0.279101	−	0.483417i
$496$	−12.1334			−0.544806
$497$	−20.4602	−	16.6315i	−0.917767	−	0.746024i
$498$	−14.8007			−0.663233
$499$	−2.94491	−	5.10073i	−0.131832	−	0.228340i	0.792551	−	0.609806i	$-0.208753\pi$
$499$	−2.94491	−	5.10073i	−0.131832	−	0.228340i	−0.924383	+	0.381466i	$0.875419\pi$
$500$	1.83022	−	3.17004i	0.0818500	−	0.141768i
$501$	−12.0680	+	20.9025i	−0.539161	+	0.933854i
$502$	−4.51367	−	7.81791i	−0.201455	−	0.348930i
$503$	−12.8348			−0.572276			−0.286138	−	0.958188i	$-0.592372\pi$
$503$	−12.8348			−0.572276			−0.286138	+	0.958188i	$0.592372\pi$
$504$	5.60994	−	34.9982i	0.249886	−	1.55894i
$505$	−13.8530			−0.616449
$506$	6.40033	+	11.0857i	0.284529	+	0.492819i
$507$	18.6668	−	32.3319i	0.829024	−	1.43591i
$508$	0.0773815	−	0.134029i	0.00343325	−	0.00594656i
$509$	−16.1065	−	27.8973i	−0.713910	−	1.23653i	−0.963379	−	0.268145i	$-0.913589\pi$
$509$	−16.1065	−	27.8973i	−0.713910	−	1.23653i	0.249469	−	0.968383i	$-0.419744\pi$
$510$	40.6049			1.79802
$511$	−0.298133	+	0.113807i	−0.0131886	+	0.00503451i
$512$	14.2736			0.630811
$513$	−2.55051	−	4.41761i	−0.112608	−	0.195042i
$514$	−2.09627	+	3.63084i	−0.0924624	+	0.160150i
$515$	−1.08125	+	1.87278i	−0.0476457	+	0.0825247i
$516$	−0.592396	−	1.02606i	−0.0260788	−	0.0451698i
$517$	−7.68004			−0.337768
$518$	−25.8384	+	9.86332i	−1.13528	+	0.433370i
$519$	15.6800			0.688278
$520$	0.549163	+	0.951178i	0.0240824	+	0.0417119i
$521$	−9.26399	+	16.0457i	−0.405863	+	0.702975i	−0.994421	−	0.105480i	$-0.966362\pi$
$521$	−9.26399	+	16.0457i	−0.405863	+	0.702975i	0.588559	+	0.808454i	$0.299696\pi$
$522$	−33.1143	+	57.3556i	−1.44937	+	2.51039i
$523$	18.6211	+	32.2527i	0.814243	+	1.41031i	0.909870	+	0.414893i	$0.136181\pi$
$523$	18.6211	+	32.2527i	0.814243	+	1.41031i	−0.0956271	+	0.995417i	$0.530486\pi$
$524$	−4.19759			−0.183372
$525$	0.614685	−	3.83478i	0.0268271	−	0.167363i
$526$	−9.49525			−0.414013
$527$	5.20099	+	9.00838i	0.226559	+	0.392411i
$528$	6.58512	−	11.4058i	0.286581	−	0.496372i
$529$	−23.4033	+	40.5357i	−1.01754	+	1.76242i
$530$	11.7856	+	20.4133i	0.511936	+	0.886699i
$531$	1.08141			0.0469294
$532$	0.551385	+	0.448204i	0.0239056	+	0.0194321i
$533$	−0.0787257			−0.00340999
$534$	−10.2626	−	17.7754i	−0.444108	−	0.769217i
$535$	12.1441	−	21.0342i	0.525035	−	0.909387i
$536$	−4.75877	+	8.24243i	−0.205548	+	0.356019i
$537$	14.5287	+	25.1644i	0.626959	+	1.08592i
$538$	6.44924			0.278047
$539$	−6.64930	−	2.18788i	−0.286406	−	0.0942386i
$540$	5.37733			0.231403
$541$	−18.0783	−	31.3126i	−0.777247	−	1.34623i	−0.933523	−	0.358519i	$-0.883282\pi$
$541$	−18.0783	−	31.3126i	−0.777247	−	1.34623i	0.156275	−	0.987714i	$-0.450051\pi$
$542$	19.5967	−	33.9425i	0.841752	−	1.45796i
$543$	−28.6202	+	49.5716i	−1.22821	+	2.12732i
$544$	3.81062	+	6.60019i	0.163379	+	0.282981i
$545$	1.11650			0.0478254
$546$	1.67365	+	1.36046i	0.0716255	+	0.0582222i
$547$	12.7980			0.547202			0.273601	−	0.961843i	$-0.411785\pi$
$547$	12.7980			0.547202			0.273601	+	0.961843i	$0.411785\pi$
$548$	2.83884	+	4.91702i	0.121269	+	0.210045i
$549$	−38.5749	+	66.8137i	−1.64634	+	2.85154i
$550$	0.390530	−	0.676417i	0.0166522	−	0.0288425i
$551$	3.15910	+	5.47172i	0.134582	+	0.233103i
$552$	60.9154			2.59273
$553$	0.137222	−	0.856074i	0.00583528	−	0.0364040i
$554$	23.5294			0.999668
$555$	23.0574	+	39.9365i	0.978731	+	1.69521i
$556$	3.59967	−	6.23481i	0.152660	−	0.264415i
$557$	15.3293	−	26.5512i	0.649525	−	1.12501i	−0.333711	−	0.942675i	$-0.608301\pi$
$557$	15.3293	−	26.5512i	0.649525	−	1.12501i	0.983236	−	0.182335i	$-0.0583656\pi$
$558$	10.7515	+	18.6221i	0.455147	+	0.788338i
$559$	−0.218941			−0.00926021
$560$	26.5382	−	10.1305i	1.12145	−	0.428090i
$561$	−11.2909			−0.476700
$562$	14.7494	+	25.5468i	0.622167	+	1.07763i
$563$	7.25237	−	12.5615i	0.305651	−	0.529403i	−0.671755	−	0.740773i	$-0.734459\pi$
$563$	7.25237	−	12.5615i	0.305651	−	0.529403i	0.977406	+	0.211370i	$0.0677926\pi$
$564$	3.84002	−	6.65111i	0.161694	−	0.280062i
$565$	3.68866	+	6.38895i	0.155183	+	0.268785i
$566$	41.4662			1.74295
$567$	−7.71348	+	2.94447i	−0.323936	+	0.123656i
$568$	−25.2344			−1.05881
$569$	−9.50253	−	16.4589i	−0.398367	−	0.689991i	0.595158	−	0.803609i	$-0.297089\pi$
$569$	−9.50253	−	16.4589i	−0.398367	−	0.689991i	−0.993525	+	0.113618i	$0.963756\pi$
$570$	4.00387	−	6.93491i	0.167704	−	0.290471i
$571$	10.5005	−	18.1873i	0.439431	−	0.761117i	−0.558215	−	0.829696i	$-0.688513\pi$
$571$	10.5005	−	18.1873i	0.439431	−	0.761117i	0.997646	+	0.0685799i	$0.0218468\pi$
$572$	0.0320889	+	0.0555796i	0.00134170	+	0.00232390i
$573$	−73.0934			−3.05352
$574$	−0.273318	+	1.70513i	−0.0114081	+	0.0711705i
$575$	4.25940			0.177629
$576$	−16.3229	−	28.2722i	−0.680123	−	1.17801i
$577$	2.59374	−	4.49249i	0.107979	−	0.187025i	−0.806973	−	0.590589i	$-0.798895\pi$
$577$	2.59374	−	4.49249i	0.107979	−	0.187025i	0.914951	+	0.403564i	$0.132229\pi$
$578$	−1.24376	+	2.15425i	−0.0517334	+	0.0896049i
$579$	11.1309	+	19.2793i	0.462584	+	0.801218i
$580$	−6.66044			−0.276560
$581$	6.88800	+	5.59905i	0.285763	+	0.232288i
$582$	−57.8813			−2.39926
$583$	−3.27719	−	5.67626i	−0.135727	−	0.235087i
$584$	−0.152704	+	0.264490i	−0.00631892	+	0.0109447i
$585$	1.14749	−	1.98751i	0.0474428	−	0.0821734i
$586$	3.09105	+	5.35386i	0.127690	+	0.221166i
$587$	8.33813			0.344151			0.172076	−	0.985084i	$-0.444953\pi$
$587$	8.33813			0.344151			0.172076	+	0.985084i	$0.444953\pi$
$588$	5.21941	−	4.66452i	0.215245	−	0.192362i
$589$	2.05138			0.0845258
$590$	0.367526	+	0.636573i	0.0151308	+	0.0262073i
$591$	7.73783	−	13.4023i	0.318292	−	0.551297i
$592$	−15.6040	+	27.0269i	−0.641321	+	1.11080i
$593$	−3.05097	−	5.28444i	−0.125288	−	0.217006i	0.796557	−	0.604563i	$-0.206652\pi$
$593$	−3.05097	−	5.28444i	−0.125288	−	0.217006i	−0.921846	+	0.387557i	$0.873319\pi$
$594$	−10.1061			−0.414657
$595$	−18.8969	−	15.3607i	−0.774698	−	0.629729i
$596$	−0.248037			−0.0101600
$597$	−12.6420	−	21.8966i	−0.517404	−	0.896169i
$598$	−1.18273	+	2.04855i	−0.0483656	+	0.0837716i
$599$	6.92514	−	11.9947i	0.282954	−	0.490090i	−0.689157	−	0.724612i	$-0.742019\pi$
$599$	6.92514	−	11.9947i	0.282954	−	0.490090i	0.972111	+	0.234522i	$0.0753524\pi$
$600$	−1.85844	−	3.21891i	−0.0758705	−	0.131412i
$601$	31.2695			1.27551			0.637755	−	0.770239i	$-0.279863\pi$
$601$	31.2695			1.27551			0.637755	+	0.770239i	$0.279863\pi$
$602$	−0.760115	+	4.74205i	−0.0309800	+	0.193272i
$603$	19.8871			0.809866
$604$	1.65745	+	2.87079i	0.0674407	+	0.116811i
$605$	−1.17365	+	2.03282i	−0.0477156	+	0.0826458i
$606$	−13.0175	+	22.5470i	−0.528801	+	0.915911i
$607$	−18.8981	−	32.7325i	−0.767051	−	1.32857i	−0.939156	−	0.343492i	$-0.888390\pi$
$607$	−18.8981	−	32.7325i	−0.767051	−	1.32857i	0.172105	−	0.985079i	$-0.444943\pi$
$608$	1.50299			0.0609544
$609$	58.1494	−	22.1974i	2.35633	−	0.899484i
$610$	−52.4397			−2.12322
$611$	−0.709607	−	1.22908i	−0.0287076	−	0.0497231i
$612$	3.60266	−	6.24000i	0.145629	−	0.252237i
$613$	−10.5672	+	18.3029i	−0.426804	+	0.739246i	−0.996587	−	0.0825490i	$-0.973694\pi$
$613$	−10.5672	+	18.3029i	−0.426804	+	0.739246i	0.569783	+	0.821795i	$0.307027\pi$
$614$	2.24376	+	3.88630i	0.0905506	+	0.156838i
$615$	2.87939			0.116108
$616$	−6.25877	+	2.38917i	−0.252173	+	0.0962622i
$617$	23.7743			0.957115			0.478558	−	0.878056i	$-0.341160\pi$
$617$	23.7743			0.957115			0.478558	+	0.878056i	$0.341160\pi$
$618$	2.03209	+	3.51968i	0.0817426	+	0.141582i
$619$	−6.75103	+	11.6931i	−0.271347	+	0.469986i	−0.969207	−	0.246248i	$-0.920802\pi$
$619$	−6.75103	+	11.6931i	−0.271347	+	0.469986i	0.697860	+	0.716234i	$0.254136\pi$
$620$	−1.08125	+	1.87278i	−0.0434241	+	0.0752128i
$621$	−27.5560	−	47.7284i	−1.10579	−	1.91528i
$622$	−23.9368			−0.959776
$623$	−1.94831	+	12.1547i	−0.0780574	+	0.486969i
$624$	2.43376			0.0974285
$625$	13.6446	+	23.6331i	0.545782	+	0.945322i
$626$	−16.8346	+	29.1583i	−0.672844	+	1.16540i
$627$	−1.11334	+	1.92836i	−0.0444625	+	0.0770114i
$628$	−1.60472	−	2.77946i	−0.0640354	−	0.110913i
$629$	26.7547			1.06678
$630$	−39.0638	−	31.7537i	−1.55634	−	1.26510i
$631$	−38.2354			−1.52213			−0.761063	−	0.648678i	$-0.775322\pi$
$631$	−38.2354			−1.52213			−0.761063	+	0.648678i	$0.775322\pi$
$632$	−0.414878	−	0.718589i	−0.0165029	−	0.0285839i
$633$	−6.10607	+	10.5760i	−0.242694	+	0.420359i
$634$	−2.30722	+	3.99622i	−0.0916313	+	0.158710i
$635$	0.523004	+	0.905869i	0.0207548	+	0.0359483i
$636$	6.55438			0.259898
$637$	−0.264233	−	1.26627i	−0.0104693	−	0.0501715i
$638$	12.5175			0.495574
$639$	26.3640	+	45.6637i	1.04294	+	1.80643i
$640$	15.6570	−	27.1188i	0.618899	−	1.07196i
$641$	−19.2777	+	33.3899i	−0.761422	+	1.31882i	0.180696	+	0.983539i	$0.442165\pi$
$641$	−19.2777	+	33.3899i	−0.761422	+	1.31882i	−0.942118	+	0.335282i	$0.891168\pi$
$642$	−22.8234	−	39.5313i	−0.900768	−	1.56018i
$643$	19.2627			0.759647			0.379823	−	0.925059i	$-0.375985\pi$
$643$	19.2627			0.759647			0.379823	+	0.925059i	$0.375985\pi$
$644$	5.95723	+	4.84245i	0.234748	+	0.190819i
$645$	8.00774			0.315304
$646$	−2.32295	−	4.02346i	−0.0913952	−	0.158301i
$647$	−19.8922	+	34.4543i	−0.782042	+	1.35454i	0.148708	+	0.988881i	$0.452489\pi$
$647$	−19.8922	+	34.4543i	−0.782042	+	1.35454i	−0.930750	+	0.365656i	$0.880845\pi$
$648$	−3.95084	+	6.84305i	−0.155204	+	0.268820i
$649$	−0.102196	−	0.177009i	−0.00401156	−	0.00694823i
$650$	0.144334			0.00566124
$651$	3.19846	−	19.9539i	0.125358	−	0.782057i
$652$	−3.05737			−0.119736
$653$	−2.38326	−	4.12792i	−0.0932640	−	0.161538i	0.815619	−	0.578590i	$-0.196397\pi$
$653$	−2.38326	−	4.12792i	−0.0932640	−	0.161538i	−0.908883	+	0.417052i	$0.863063\pi$
$654$	1.04916	−	1.81720i	0.0410255	−	0.0710583i
$655$	14.1853	−	24.5696i	0.554264	−	0.960013i
$656$	0.974308	+	1.68755i	0.0380403	+	0.0658878i
$657$	0.638156			0.0248968
$658$	−29.0842	+	11.1024i	−1.13382	+	0.432815i
$659$	−38.3550			−1.49410			−0.747050	−	0.664768i	$-0.768530\pi$
$659$	−38.3550			−1.49410			−0.747050	+	0.664768i	$0.768530\pi$
$660$	−1.17365	−	2.03282i	−0.0456842	−	0.0791273i
$661$	5.18139	−	8.97443i	0.201533	−	0.349065i	−0.747490	−	0.664273i	$-0.768741\pi$
$661$	5.18139	−	8.97443i	0.201533	−	0.349065i	0.949022	+	0.315208i	$0.102074\pi$
$662$	21.0424	−	36.4464i	0.817834	−	1.41653i
$663$	−1.04323	−	1.80693i	−0.0405158	−	0.0701755i
$664$	8.49525			0.329680
$665$	−4.48680	+	1.71275i	−0.173990	+	0.0664175i
$666$	55.3073			2.14311
$667$	34.1313	+	59.1172i	1.32157	+	2.28903i
$668$	−1.45558	+	2.52115i	−0.0563183	+	0.0975461i
$669$	25.9650	−	44.9727i	1.00386	−	1.73874i
$670$	6.75877	+	11.7065i	0.261114	+	0.452263i
$671$	14.5817			0.562921
$672$	2.34343	−	14.6197i	0.0903996	−	0.563967i
$673$	−25.6168			−0.987455			−0.493728	−	0.869617i	$-0.664366\pi$
$673$	−25.6168			−0.987455			−0.493728	+	0.869617i	$0.664366\pi$
$674$	13.2083	+	22.8774i	0.508763	+	0.881204i
$675$	−1.68139	+	2.91225i	−0.0647167	+	0.112093i
$676$	2.25150	−	3.89971i	0.0865960	−	0.149989i
$677$	−20.9187	−	36.2323i	−0.803973	−	1.39252i	−0.916982	−	0.398928i	$-0.869382\pi$
$677$	−20.9187	−	36.2323i	−0.803973	−	1.39252i	0.113010	−	0.993594i	$-0.463951\pi$
$678$	13.8648			0.532476
$679$	26.9371	+	21.8963i	1.03375	+	0.840303i
$680$	−23.3063			−0.893757
$681$	−26.2101	−	45.3972i	−1.00437	−	1.73962i
$682$	2.03209	−	3.51968i	0.0778127	−	0.134776i
$683$	23.0214	−	39.8743i	0.880890	−	1.52575i	0.0305366	−	0.999534i	$-0.490278\pi$
$683$	23.0214	−	39.8743i	0.880890	−	1.52575i	0.850353	−	0.526212i	$-0.176388\pi$
$684$	−0.710485	−	1.23060i	−0.0271661	−	0.0470530i
$685$	−38.3741			−1.46620
$686$	−28.3436	+	1.32683i	−1.08217	+	0.0506585i
$687$	55.4029			2.11375
$688$	2.70961	+	4.69318i	0.103303	+	0.178926i
$689$	0.605600	−	1.04893i	0.0230715	−	0.0399611i
$690$	43.2584	−	74.9257i	1.64682	−	2.85237i
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	1.89124			0.0718943
$693$	10.8623	+	8.82964i	0.412625	+	0.335410i
$694$	17.5134			0.664800
$695$	24.3293	+	42.1397i	0.922865	+	1.59845i
$696$	29.7841	−	51.5875i	1.12896	−	1.95542i
$697$	0.835275	−	1.44674i	0.0316383	−	0.0547991i
$698$	21.6951	+	37.5769i	0.821170	+	1.42231i
$699$	26.8503			1.01557
$700$	0.0741401	−	0.462531i	0.00280223	−	0.0174820i
$701$	−32.8144			−1.23938			−0.619691	−	0.784846i	$-0.712742\pi$
$701$	−32.8144			−1.23938			−0.619691	+	0.784846i	$0.712742\pi$
$702$	−0.933763	−	1.61732i	−0.0352426	−	0.0610420i
$703$	2.63816	−	4.56942i	0.0994999	−	0.172339i
$704$	−3.08512	+	5.34359i	−0.116275	+	0.201394i
$705$	25.9538	+	44.9534i	0.977478	+	1.69304i
$706$	−25.1816			−0.947722
$707$	14.5876	−	5.56855i	0.548625	−	0.209427i
$708$	0.204393			0.00768156
$709$	−3.70099	−	6.41030i	−0.138994	−	0.240744i	0.788122	−	0.615519i	$-0.211053\pi$
$709$	−3.70099	−	6.41030i	−0.138994	−	0.240744i	−0.927116	+	0.374775i	$0.877720\pi$
$710$	−17.9199	+	31.0382i	−0.672523	+	1.16484i
$711$	−0.866897	+	1.50151i	−0.0325112	+	0.0563110i
$712$	5.89053	+	10.2027i	0.220757	+	0.382362i
$713$	22.1634			0.830027
$714$	−42.7584	+	16.3222i	−1.60019	+	0.610842i
$715$	−0.433763			−0.0162218
$716$	1.75237	+	3.03520i	0.0654893	+	0.113431i
$717$	−16.1099	+	27.9032i	−0.601637	+	1.04207i
$718$	19.0462	−	32.9890i	0.710799	−	1.23114i
$719$	7.06851	+	12.2430i	0.263611	+	0.456588i	0.967199	−	0.254021i	$-0.0817531\pi$
$719$	7.06851	+	12.2430i	0.263611	+	0.456588i	−0.703588	+	0.710608i	$0.748420\pi$
$720$	−56.8052			−2.11701
$721$	0.385782	−	2.40674i	0.0143673	−	0.0896317i
$722$	28.1935			1.04925
$723$	−29.0881	−	50.3821i	−1.08180	−	1.87373i
$724$	−3.45202	+	5.97907i	−0.128293	+	0.222210i
$725$	2.08260	−	3.60716i	0.0773457	−	0.133967i
$726$	2.20574	+	3.82045i	0.0818626	+	0.141790i
$727$	15.2790			0.566667			0.283333	−	0.959021i	$-0.408560\pi$
$727$	15.2790			0.566667			0.283333	+	0.959021i	$0.408560\pi$
$728$	−0.960637	−	0.780873i	−0.0356036	−	0.0289411i
$729$	−40.4688			−1.49885
$730$	0.216881	+	0.375650i	0.00802714	+	0.0139034i
$731$	2.32295	−	4.02346i	0.0859173	−	0.148813i
$732$	−7.29086	+	12.6281i	−0.269478	+	0.466749i
$733$	−0.672466	−	1.16475i	−0.0248381	−	0.0430209i	0.853339	−	0.521356i	$-0.174574\pi$
$733$	−0.672466	−	1.16475i	−0.0248381	−	0.0430209i	−0.878177	+	0.478335i	$0.841240\pi$
$734$	−6.58584			−0.243088
$735$	9.66431	+	46.3138i	0.356474	+	1.70831i
$736$	16.2385			0.598561
$737$	−1.87939	−	3.25519i	−0.0692280	−	0.119906i
$738$	1.72668	−	2.99070i	0.0635600	−	0.110089i
$739$	12.8268	−	22.2167i	0.471842	−	0.817255i	−0.527639	−	0.849469i	$-0.676923\pi$
$739$	12.8268	−	22.2167i	0.471842	−	0.817255i	0.999481	+	0.0322142i	$0.0102559\pi$
$740$	2.78106	+	4.81694i	0.102234	+	0.177074i
$741$	−0.411474			−0.0151159
$742$	−20.6163	−	16.7584i	−0.756849	−	0.615220i
$743$	−6.08109			−0.223094			−0.111547	−	0.993759i	$-0.535580\pi$
$743$	−6.08109			−0.223094			−0.111547	+	0.993759i	$0.535580\pi$
$744$	−9.67024	−	16.7494i	−0.354528	−	0.614061i
$745$	0.838211	−	1.45182i	0.0307097	−	0.0531907i
$746$	−2.09105	+	3.62181i	−0.0765589	+	0.132604i
$747$	−8.87551	−	15.3728i	−0.324738	−	0.562463i
$748$	−1.36184			−0.0497940
$749$	−4.33291	+	27.0313i	−0.158321	+	0.987703i
$750$	46.4962			1.69780
$751$	−10.4054	−	18.0227i	−0.379698	−	0.657656i	0.611320	−	0.791383i	$-0.290639\pi$
$751$	−10.4054	−	18.0227i	−0.379698	−	0.657656i	−0.991018	+	0.133727i	$0.957305\pi$
$752$	−17.5642	+	30.4220i	−0.640500	+	1.10938i
$753$	8.48293	−	14.6929i	0.309135	−	0.535438i
$754$	1.15657	+	2.00324i	0.0421199	+	0.0729539i
$755$	−22.4047			−0.815389
$756$	−5.66250	+	2.16155i	−0.205943	+	0.0786149i
$757$	−5.25402			−0.190961			−0.0954804	−	0.995431i	$-0.530439\pi$
$757$	−5.25402			−0.190961			−0.0954804	+	0.995431i	$0.530439\pi$
$758$	−12.6079	−	21.8375i	−0.457939	−	0.793173i
$759$	−12.0287	+	20.8343i	−0.436614	+	0.756237i
$760$	−2.29813	+	3.98048i	−0.0833621	+	0.144387i
$761$	20.4907	+	35.4909i	0.742786	+	1.28654i	0.951222	+	0.308507i	$0.0998294\pi$
$761$	20.4907	+	35.4909i	0.742786	+	1.28654i	−0.208436	+	0.978036i	$0.566837\pi$
$762$	1.96585			0.0712153
$763$	−1.17571	+	0.448804i	−0.0425635	+	0.0162478i
$764$	−8.81614			−0.318957
$765$	24.3496	+	42.1747i	0.880361	+	1.52483i
$766$	−6.02094	+	10.4286i	−0.217546	+	0.376800i
$767$	0.0188851	−	0.0327100i	0.000681903	−	0.00118109i
$768$	−11.6591	−	20.1942i	−0.420712	−	0.728694i
$769$	47.5580			1.71499			0.857493	−	0.514496i	$-0.172021\pi$
$769$	47.5580			1.71499			0.857493	+	0.514496i	$0.172021\pi$
$770$	−1.50593	+	9.39490i	−0.0542699	+	0.338569i
$771$	−7.87939			−0.283769
$772$	1.34255	+	2.32536i	0.0483194	+	0.0836916i
$773$	−10.2464	+	17.7474i	−0.368539	+	0.638328i	−0.989337	−	0.145642i	$-0.953475\pi$
$773$	−10.2464	+	17.7474i	−0.368539	+	0.638328i	0.620798	+	0.783970i	$0.286809\pi$
$774$	4.80200	−	8.31731i	0.172604	−	0.298960i
$775$	−0.676174	−	1.17117i	−0.0242889	−	0.0420696i
$776$	33.2226			1.19262
$777$	−40.3337	−	32.7860i	−1.44696	−	1.17619i
$778$	−14.7743			−0.529683
$779$	−0.164725	−	0.285313i	−0.00590190	−	0.0102224i
$780$	0.216881	−	0.375650i	0.00776560	−	0.0134504i
$781$	4.98293	−	8.63068i	0.178303	−	0.308830i
$782$	−25.0974	−	43.4701i	−0.897483	−	1.55449i
$783$	−53.8931			−1.92598
$784$	−23.8735	+	21.3354i	−0.852623	+	0.761980i
$785$	21.6919			0.774217
$786$	−26.6596	−	46.1757i	−0.950915	−	1.64703i
$787$	9.56031	−	16.5589i	0.340788	−	0.590262i	−0.643791	−	0.765201i	$-0.722639\pi$
$787$	9.56031	−	16.5589i	0.340788	−	0.590262i	0.984579	+	0.174939i	$0.0559728\pi$
$788$	0.933296	−	1.61652i	0.0332473	−	0.0575860i
$789$	−8.92262	−	15.4544i	−0.317654	−	0.550192i
$790$	−1.17848			−0.0419285
$791$	−6.45249	−	5.24503i	−0.229424	−	0.186492i
$792$	13.3969			0.476039
$793$	1.34730	+	2.33359i	0.0478439	+	0.0828681i
$794$	−7.22668	+	12.5170i	−0.256465	+	0.444211i
$795$	−22.1498	+	38.3645i	−0.785571	+	1.36065i
$796$	−1.52481	−	2.64106i	−0.0540456	−	0.0936098i
$797$	−52.5144			−1.86015			−0.930077	−	0.367365i	$-0.880260\pi$
$797$	−52.5144			−1.86015			−0.930077	+	0.367365i	$0.880260\pi$
$798$	−1.42855	+	8.91215i	−0.0505701	+	0.315487i
$799$	30.1156			1.06541
$800$	−0.495414	−	0.858083i	−0.0175155	−	0.0303378i
$801$	12.3084	−	21.3188i	0.434896	−	0.753262i
$802$	−13.9572	+	24.1746i	−0.492847	+	0.853636i
$803$	−0.0603074	−	0.104455i	−0.00212820	−	0.00368615i
$804$	3.75877			0.132562
$805$	−48.4760	+	18.5048i	−1.70855	+	0.652207i
$806$	0.751030			0.0264539
$807$	6.06031	+	10.4968i	0.213333	+	0.369503i
$808$	7.47178	−	12.9415i	0.262856	−	0.455281i
$809$	−20.3357	+	35.2225i	−0.714967	+	1.23836i	0.248006	+	0.968759i	$0.420225\pi$
$809$	−20.3357	+	35.2225i	−0.714967	+	1.23836i	−0.962972	+	0.269600i	$0.913109\pi$
$810$	5.61128	+	9.71902i	0.197160	+	0.341492i
$811$	−20.5648			−0.722128			−0.361064	−	0.932541i	$-0.617586\pi$
$811$	−20.5648			−0.722128			−0.361064	+	0.932541i	$0.617586\pi$
$812$	7.01367	−	2.67733i	0.246132	−	0.0939560i
$813$	73.6596			2.58336
$814$	−5.22668	−	9.05288i	−0.183195	−	0.317303i
$815$	10.3320	−	17.8956i	0.361915	−	0.626856i
$816$	−25.8221	+	44.7251i	−0.903953	+	1.56569i
$817$	−0.458111	−	0.793471i	−0.0160273	−	0.0277601i
$818$	−9.82295			−0.343451
$819$	−0.409415	+	2.55418i	−0.0143061	+	0.0892501i
$820$	0.347296			0.0121281
$821$	−3.18139	−	5.51033i	−0.111031	−	0.192312i	0.805155	−	0.593064i	$-0.202082\pi$
$821$	−3.18139	−	5.51033i	−0.111031	−	0.192312i	−0.916186	+	0.400753i	$0.868749\pi$
$822$	−36.0599	+	62.4576i	−1.25773	+	2.17846i
$823$	1.25443	−	2.17274i	0.0437268	−	0.0757370i	−0.843334	−	0.537390i	$-0.819410\pi$
$823$	1.25443	−	2.17274i	0.0437268	−	0.0757370i	0.887060	+	0.461653i	$0.152744\pi$
$824$	−1.16637	−	2.02022i	−0.0406326	−	0.0703777i
$825$	1.46791			0.0511061
$826$	−0.642903	−	0.522597i	−0.0223695	−	0.0181835i
$827$	−41.2645			−1.43491			−0.717453	−	0.696607i	$-0.754692\pi$
$827$	−41.2645			−1.43491			−0.717453	+	0.696607i	$0.754692\pi$
$828$	−7.67617	−	13.2955i	−0.266766	−	0.462051i
$829$	23.3889	−	40.5108i	0.812331	−	1.40700i	−0.0988970	−	0.995098i	$-0.531531\pi$
$829$	23.3889	−	40.5108i	0.812331	−	1.40700i	0.911228	−	0.411902i	$-0.135135\pi$
$830$	6.03280	−	10.4491i	0.209402	−	0.362694i
$831$	22.1104	+	38.2963i	0.767001	+	1.32849i
$832$	−1.14022			−0.0395298
$833$	26.0737	+	8.57927i	0.903401	+	0.297254i
$834$	91.4484			3.16660
$835$	−9.83796	−	17.0399i	−0.340457	−	0.589688i
$836$	−0.134285	+	0.232589i	−0.00464436	+	0.00804426i
$837$	−8.74897	+	15.1537i	−0.302409	+	0.523787i
$838$	1.24170	+	2.15068i	0.0428937	+	0.0742940i
$839$	16.5439			0.571161			0.285580	−	0.958355i	$-0.407814\pi$
$839$	16.5439			0.571161			0.285580	+	0.958355i	$0.407814\pi$
$840$	35.1352	+	28.5603i	1.21228	+	0.985425i
$841$	37.7529			1.30182
$842$	23.8614	+	41.3292i	0.822319	+	1.42430i
$843$	−27.7199	+	48.0122i	−0.954723	+	1.65363i
$844$	−0.736482	+	1.27562i	−0.0253507	+	0.0439088i
$845$	15.2173	+	26.3572i	0.523493	+	0.906716i
$846$	62.2550			2.14037
$847$	0.418748	−	2.61240i	0.0143884	−	0.0897632i
$848$	−29.9796			−1.02950
$849$	38.9654	+	67.4901i	1.33729	+	2.31626i
$850$	−1.53137	+	2.65242i	−0.0525257	+	0.0909772i
$851$	28.5030	−	49.3686i	0.977070	−	1.69233i
$852$	4.98293	+	8.63068i	0.170712	+	0.295682i
$853$	13.2163			0.452516			0.226258	−	0.974067i	$-0.427351\pi$
$853$	13.2163			0.452516			0.226258	+	0.974067i	$0.427351\pi$
$854$	55.2208	−	21.0795i	1.88962	−	0.721325i
$855$	9.60401			0.328450
$856$	13.1001	+	22.6901i	0.447753	+	0.775532i
$857$	25.3606	−	43.9258i	0.866300	−	1.50048i	0.000549663	−	1.00000i	$-0.499825\pi$
$857$	25.3606	−	43.9258i	0.866300	−	1.50048i	0.865750	−	0.500476i	$-0.166842\pi$
$858$	−0.407604	+	0.705990i	−0.0139154	+	0.0241021i
$859$	−27.5562	−	47.7287i	−0.940205	−	1.62848i	−0.765079	−	0.643937i	$-0.777300\pi$
$859$	−27.5562	−	47.7287i	−0.940205	−	1.62848i	−0.175126	−	0.984546i	$-0.556033\pi$
$860$	0.965852			0.0329353
$861$	−3.03209	+	1.15744i	−0.103333	+	0.0394455i
$862$	−52.4097			−1.78508
$863$	−5.26011	−	9.11079i	−0.179056	−	0.310135i	0.762501	−	0.646987i	$-0.223971\pi$
$863$	−5.26011	−	9.11079i	−0.179056	−	0.310135i	−0.941558	+	0.336852i	$0.890638\pi$
$864$	−6.41013	+	11.1027i	−0.218077	+	0.377721i
$865$	−6.39124	+	11.0700i	−0.217309	+	0.376390i
$866$	−15.7023	−	27.1972i	−0.533587	−	0.924200i
$867$	−4.67499			−0.158771
$868$	0.385782	−	2.40674i	0.0130943	−	0.0816901i
$869$	0.327696			0.0111163
$870$	−42.3016	−	73.2685i	−1.43416	−	2.48404i
$871$	0.347296	−	0.601535i	0.0117677	−	0.0203822i
$872$	−0.602196	+	1.04303i	−0.0203929	+	0.0353216i
$873$	−34.7097	−	60.1189i	−1.17474	−	2.03472i
$874$	−9.89899			−0.334838
$875$	−21.6386	−	17.5894i	−0.731519	−	0.594629i
$876$	0.120615			0.00407520
$877$	19.8268	+	34.3411i	0.669504	+	1.15962i	0.978043	+	0.208403i	$0.0668267\pi$
$877$	19.8268	+	34.3411i	0.669504	+	1.15962i	−0.308539	+	0.951212i	$0.599840\pi$
$878$	23.9939	−	41.5587i	0.809755	−	1.40254i
$879$	−5.80928	+	10.0620i	−0.195942	+	0.339382i
$880$	5.36824	+	9.29807i	0.180963	+	0.313438i
$881$	25.0077			0.842532			0.421266	−	0.906937i	$-0.361586\pi$
$881$	25.0077			0.842532			0.421266	+	0.906937i	$0.361586\pi$
$882$	53.8997	+	17.7351i	1.81490	+	0.597171i
$883$	50.9341			1.71407			0.857034	−	0.515260i	$-0.172305\pi$
$883$	50.9341			1.71407			0.857034	+	0.515260i	$0.172305\pi$
$884$	−0.125829	−	0.217943i	−0.00423210	−	0.00733021i
$885$	−0.690722	+	1.19637i	−0.0232184	+	0.0402154i
$886$	−22.5201	+	39.0059i	−0.756576	+	1.31043i
$887$	−16.0180	−	27.7440i	−0.537832	−	0.931552i	−0.999020	−	0.0442502i	$-0.985910\pi$
$887$	−16.0180	−	27.7440i	−0.537832	−	0.931552i	0.461188	−	0.887302i	$-0.347423\pi$
$888$	−49.7452			−1.66934
$889$	−0.914878	−	0.743676i	−0.0306840	−	0.0249421i
$890$	16.7324			0.560870
$891$	−1.56031	−	2.70253i	−0.0522723	−	0.0905382i
$892$	3.13176	−	5.42437i	0.104859	−	0.181621i
$893$	2.96956	−	5.14343i	0.0993725	−	0.172118i
$894$	−1.57532	−	2.72854i	−0.0526867	−	0.0912560i
$895$	−23.6878			−0.791795
$896$	−5.58630	+	34.8507i	−0.186625	+	1.16428i
$897$	−4.44562			−0.148435
$898$	−5.28627	−	9.15609i	−0.176405	−	0.305543i
$899$	10.8366	−	18.7696i	0.361421	−	0.626000i
$900$	−0.468378	+	0.811254i	−0.0156126	+	0.0270418i
$901$	12.8508	+	22.2582i	0.428121	+	0.741527i
$902$	−0.652704			−0.0217327
$903$	−8.43242	+	3.21891i	−0.280613	+	0.107119i
$904$	−7.95811			−0.264683
$905$	−23.3314	−	40.4112i	−0.775562	−	1.34331i
$906$	−21.0535	+	36.4657i	−0.699456	+	1.21149i
$907$	8.23648	−	14.2660i	0.273488	−	0.473695i	−0.696265	−	0.717785i	$-0.745156\pi$
$907$	8.23648	−	14.2660i	0.273488	−	0.473695i	0.969753	+	0.244090i	$0.0784893\pi$
$908$	−3.16132	−	5.47557i	−0.104912	−	0.181713i
$909$	−31.2249			−1.03567
$910$	−1.64266	+	0.627052i	−0.0544535	+	0.0207866i
$911$	−45.3979			−1.50410			−0.752049	−	0.659107i	$-0.770934\pi$
$911$	−45.3979			−1.50410			−0.752049	+	0.659107i	$0.770934\pi$
$912$	5.09240	+	8.82029i	0.168626	+	0.292069i
$913$	−1.67752	+	2.90555i	−0.0555178	+	0.0961596i
$914$	9.47952	−	16.4190i	0.313555	−	0.543093i
$915$	−49.2772	−	85.3507i	−1.62906	−	2.82161i
$916$	6.68241			0.220793
$917$	−5.06118	+	31.5747i	−0.167135	+	1.04269i
$918$	39.6287			1.30794
$919$	6.16044	+	10.6702i	0.203214	+	0.351978i	0.949562	−	0.313578i	$-0.101528\pi$
$919$	6.16044	+	10.6702i	0.203214	+	0.351978i	−0.746348	+	0.665556i	$0.768195\pi$
$920$	−24.8293	+	43.0057i	−0.818599	+	1.41786i
$921$	−4.21688	+	7.30385i	−0.138951	+	0.240670i
$922$	15.3931	+	26.6616i	0.506943	+	0.878052i
$923$	1.84161			0.0606175
$924$	2.05303	+	1.66885i	0.0675398	+	0.0549011i
$925$	−3.47834			−0.114367
$926$	6.65839	+	11.5327i	0.218808	+	0.378987i
$927$	−2.43717	+	4.22130i	−0.0800470	+	0.138646i
$928$	7.93969	−	13.7520i	0.260633	−	0.451430i
$929$	−2.96657	−	5.13824i	−0.0973299	−	0.168580i	0.813249	−	0.581916i	$-0.197697\pi$
$929$	−2.96657	−	5.13824i	−0.0973299	−	0.168580i	−0.910579	+	0.413336i	$0.864364\pi$
$930$	−27.4688			−0.900739
$931$	4.03626	−	3.60716i	0.132283	−	0.118220i
$932$	3.23854			0.106082
$933$	−22.4932	−	38.9594i	−0.736394	−	1.27547i
$934$	3.65342	−	6.32791i	0.119544	−	0.207055i
$935$	4.60220	−	7.97124i	0.150508	−	0.260687i
$936$	1.23783	+	2.14398i	0.0404596	+	0.0700781i
$937$	−45.0242			−1.47088			−0.735438	−	0.677593i	$-0.763023\pi$
$937$	−45.0242			−1.47088			−0.735438	+	0.677593i	$0.763023\pi$
$938$	−11.8229	−	9.61051i	−0.386033	−	0.313794i
$939$	−63.2772			−2.06497
$940$	3.13041	+	5.42204i	0.102103	+	0.176847i
$941$	3.03121	−	5.25021i	0.0988147	−	0.171152i	−0.812380	−	0.583129i	$-0.801828\pi$
$941$	3.03121	−	5.25021i	0.0988147	−	0.171152i	0.911194	+	0.411977i	$0.135162\pi$
$942$	20.3837	−	35.3056i	0.664138	−	1.15032i
$943$	−1.77972	−	3.08256i	−0.0579555	−	0.100382i
$944$	−0.934889			−0.0304280
$945$	6.48364	−	40.4489i	0.210913	−	1.31580i
$946$	−1.81521			−0.0590175
$947$	9.47131	+	16.4048i	0.307776	+	0.533084i	0.977876	−	0.209187i	$-0.0670818\pi$
$947$	9.47131	+	16.4048i	0.307776	+	0.533084i	−0.670099	+	0.742272i	$0.733748\pi$
$948$	−0.163848	+	0.283793i	−0.00532154	+	0.00921717i
$949$	0.0111444	−	0.0193026i	0.000361761	−	0.000626588i
$950$	0.302004	+	0.523086i	0.00979829	+	0.0169711i
$951$	−8.67230			−0.281219
$952$	24.5424	−	9.36857i	0.795422	−	0.303637i
$953$	−12.4970			−0.404818			−0.202409	−	0.979301i	$-0.564877\pi$
$953$	−12.4970			−0.404818			−0.202409	+	0.979301i	$0.564877\pi$
$954$	26.5651	+	46.0121i	0.860077	+	1.48970i
$955$	29.7931	−	51.6032i	0.964083	−	1.66984i
$956$	−1.94310	+	3.36554i	−0.0628442	+	0.108849i
$957$	11.7626	+	20.3735i	0.380232	+	0.658581i
$958$	60.6923			1.96088
$959$	40.4093	−	15.4255i	1.30488	−	0.498114i
$960$	41.7033			1.34597
$961$	11.9816	+	20.7527i	0.386503	+	0.669442i
$962$	0.965852	−	1.67290i	0.0311403	−	0.0539366i
$963$	27.3730	−	47.4115i	0.882084	−	1.52781i
$964$	−3.50846	−	6.07682i	−0.113000	−	0.195721i
$965$	−18.1480			−0.584203
$966$	−15.4342	+	96.2880i	−0.496588	+	3.09802i
$967$	−18.5294			−0.595865			−0.297933	−	0.954587i	$-0.596297\pi$
$967$	−18.5294			−0.595865			−0.297933	+	0.954587i	$0.596297\pi$
$968$	−1.26604	−	2.19285i	−0.0406922	−	0.0704810i
$969$	4.36571	−	7.56164i	0.140247	−	0.242915i
$970$	23.5926	−	40.8636i	0.757513	−	1.31205i
$971$	−20.7369	−	35.9174i	−0.665480	−	1.15265i	−0.979155	−	0.203115i	$-0.934893\pi$
$971$	−20.7369	−	35.9174i	−0.665480	−	1.15265i	0.313674	−	0.949531i	$-0.398440\pi$
$972$	−3.75196			−0.120344
$973$	−42.5587	−	34.5947i	−1.36437	−	1.10905i
$974$	−7.89899			−0.253100
$975$	0.135630	+	0.234917i	0.00434362	+	0.00752337i
$976$	33.3482	−	57.7608i	1.06745	−	1.84888i
$977$	11.1160	−	19.2535i	0.355633	−	0.615975i	−0.631593	−	0.775300i	$-0.717599\pi$
$977$	11.1160	−	19.2535i	0.355633	−	0.615975i	0.987226	+	0.159325i	$0.0509319\pi$
$978$	−19.4179	−	33.6327i	−0.620915	−	1.07546i
$979$	−4.65270			−0.148701
$980$	1.16566	+	5.58613i	0.0372356	+	0.178442i
$981$	2.51661			0.0803491
$982$	7.80793	+	13.5237i	0.249161	+	0.431560i
$983$	−17.7062	+	30.6680i	−0.564740	+	0.978159i	0.432334	+	0.901714i	$0.357690\pi$
$983$	−17.7062	+	30.6680i	−0.564740	+	0.978159i	−0.997074	+	0.0764450i	$0.975643\pi$
$984$	−1.55303	+	2.68993i	−0.0495089	+	0.0857519i
$985$	6.30793	+	10.9257i	0.200987	+	0.348121i
$986$	−49.0847			−1.56318
$987$	−45.4004	−	36.9046i	−1.44511	−	1.17469i
$988$	−0.0496299			−0.00157894
$989$	−4.94949	−	8.57277i	−0.157385	−	0.272598i
$990$	9.51367	−	16.4782i	0.302364	−	0.523710i
$991$	−22.7863	+	39.4670i	−0.723830	+	1.25371i	0.235624	+	0.971844i	$0.424287\pi$
$991$	−22.7863	+	39.4670i	−0.723830	+	1.25371i	−0.959454	+	0.281866i	$0.909047\pi$
$992$	−2.57785	−	4.46496i	−0.0818468	−	0.141763i
$993$	79.0934			2.50995
$994$	6.39368	−	39.8877i	0.202795	−	1.26516i
$995$	20.6117			0.653436
$996$	−1.67752	−	2.90555i	−0.0531542	−	0.0920658i
$997$	−11.4183	+	19.7771i	−0.361622	+	0.626348i	−0.988228	−	0.152988i	$-0.951110\pi$
$997$	−11.4183	+	19.7771i	−0.361622	+	0.626348i	0.626606	+	0.779336i	$0.284444\pi$
$998$	4.51186	−	7.81477i	0.142820	−	0.247372i
$999$	22.5030	+	38.9763i	0.711963	+	1.23316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.e.a.67.3	yes	6
3.2	odd	2		693.2.i.h.298.1		6
4.3	odd	2		1232.2.q.m.529.3		6
7.2	even	3	inner	77.2.e.a.23.3	✓	6
7.3	odd	6		539.2.a.g.1.1		3
7.4	even	3		539.2.a.j.1.1		3
7.5	odd	6		539.2.e.m.177.3		6
7.6	odd	2		539.2.e.m.67.3		6
11.2	odd	10		847.2.n.f.81.1		24
11.3	even	5		847.2.n.g.130.3		24
11.4	even	5		847.2.n.g.753.1		24
11.5	even	5		847.2.n.g.487.1		24
11.6	odd	10		847.2.n.f.487.3		24
11.7	odd	10		847.2.n.f.753.3		24
11.8	odd	10		847.2.n.f.130.1		24
11.9	even	5		847.2.n.g.81.3		24
11.10	odd	2		847.2.e.c.606.1		6
21.2	odd	6		693.2.i.h.100.1		6
21.11	odd	6		4851.2.a.bj.1.3		3
21.17	even	6		4851.2.a.bk.1.3		3
28.3	even	6		8624.2.a.co.1.3		3
28.11	odd	6		8624.2.a.ch.1.1		3
28.23	odd	6		1232.2.q.m.177.3		6
77.2	odd	30		847.2.n.f.807.3		24
77.9	even	15		847.2.n.g.807.1		24
77.10	even	6		5929.2.a.u.1.3		3
77.16	even	15		847.2.n.g.366.3		24
77.30	odd	30		847.2.n.f.9.3		24
77.32	odd	6		5929.2.a.x.1.3		3
77.37	even	15		847.2.n.g.632.3		24
77.51	odd	30		847.2.n.f.632.1		24
77.58	even	15		847.2.n.g.9.1		24
77.65	odd	6		847.2.e.c.485.1		6
77.72	odd	30		847.2.n.f.366.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.3	✓	6	7.2	even	3	inner
77.2.e.a.67.3	yes	6	1.1	even	1	trivial
539.2.a.g.1.1		3	7.3	odd	6
539.2.a.j.1.1		3	7.4	even	3
539.2.e.m.67.3		6	7.6	odd	2
539.2.e.m.177.3		6	7.5	odd	6
693.2.i.h.100.1		6	21.2	odd	6
693.2.i.h.298.1		6	3.2	odd	2
847.2.e.c.485.1		6	77.65	odd	6
847.2.e.c.606.1		6	11.10	odd	2
847.2.n.f.9.3		24	77.30	odd	30
847.2.n.f.81.1		24	11.2	odd	10
847.2.n.f.130.1		24	11.8	odd	10
847.2.n.f.366.1		24	77.72	odd	30
847.2.n.f.487.3		24	11.6	odd	10
847.2.n.f.632.1		24	77.51	odd	30
847.2.n.f.753.3		24	11.7	odd	10
847.2.n.f.807.3		24	77.2	odd	30
847.2.n.g.9.1		24	77.58	even	15
847.2.n.g.81.3		24	11.9	even	5
847.2.n.g.130.3		24	11.3	even	5
847.2.n.g.366.3		24	77.16	even	15
847.2.n.g.487.1		24	11.5	even	5
847.2.n.g.632.3		24	77.37	even	15
847.2.n.g.753.1		24	11.4	even	5
847.2.n.g.807.1		24	77.9	even	15
1232.2.q.m.177.3		6	28.23	odd	6
1232.2.q.m.529.3		6	4.3	odd	2
4851.2.a.bj.1.3		3	21.11	odd	6
4851.2.a.bk.1.3		3	21.17	even	6
5929.2.a.u.1.3		3	77.10	even	6
5929.2.a.x.1.3		3	77.32	odd	6
8624.2.a.ch.1.1		3	28.11	odd	6
8624.2.a.co.1.3		3	28.3	even	6

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 1.32683i) q^{2} +(-1.43969 + 2.49362i) q^{3} +(-0.173648 + 0.300767i) q^{4} +(-1.17365 - 2.03282i) q^{5} -4.41147 q^{6} +(2.05303 + 1.66885i) q^{7} +2.53209 q^{8} +(-2.64543 - 4.58202i) q^{9} +(1.79813 - 3.11446i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -0.184793 q^{13} +(-0.641559 + 4.00243i) q^{14} +6.75877 q^{15} +(2.28699 + 3.96118i) q^{16} +(1.96064 - 3.39592i) q^{17} +(4.05303 - 7.02006i) q^{18} +(-0.386659 - 0.669713i) q^{19} +0.815207 q^{20} +(-7.11721 + 2.71686i) q^{21} -1.53209 q^{22} +(-4.17752 - 7.23567i) q^{23} +(-3.64543 + 6.31407i) q^{24} +(-0.254900 + 0.441500i) q^{25} +(-0.141559 - 0.245188i) q^{26} +6.59627 q^{27} +(-0.858441 + 0.327693i) q^{28} -8.17024 q^{29} +(5.17752 + 8.96773i) q^{30} +(-1.32635 + 2.29731i) q^{31} +(-0.971782 + 1.68317i) q^{32} +(-1.43969 - 2.49362i) q^{33} +6.00774 q^{34} +(0.982926 - 6.13208i) q^{35} +1.83750 q^{36} +(3.41147 + 5.90885i) q^{37} +(0.592396 - 1.02606i) q^{38} +(0.266044 - 0.460802i) q^{39} +(-2.97178 - 5.14728i) q^{40} +0.426022 q^{41} +(-9.05690 - 7.36208i) q^{42} +1.18479 q^{43} +(-0.173648 - 0.300767i) q^{44} +(-6.20961 + 10.7554i) q^{45} +(6.40033 - 11.0857i) q^{46} +(3.84002 + 6.65111i) q^{47} -13.1702 q^{48} +(1.42989 + 6.85240i) q^{49} -0.781059 q^{50} +(5.64543 + 9.77817i) q^{51} +(0.0320889 - 0.0555796i) q^{52} +(-3.27719 + 5.67626i) q^{53} +(5.05303 + 8.75211i) q^{54} +2.34730 q^{55} +(5.19846 + 4.22567i) q^{56} +2.22668 q^{57} +(-6.25877 - 10.8405i) q^{58} +(-0.102196 + 0.177009i) q^{59} +(-1.17365 + 2.03282i) q^{60} +(-7.29086 - 12.6281i) q^{61} -4.06418 q^{62} +(2.21554 - 13.8219i) q^{63} +6.17024 q^{64} +(0.216881 + 0.375650i) q^{65} +(2.20574 - 3.82045i) q^{66} +(-1.87939 + 3.25519i) q^{67} +(0.680922 + 1.17939i) q^{68} +24.0574 q^{69} +(8.88919 - 3.39328i) q^{70} -9.96585 q^{71} +(-6.69846 - 11.6021i) q^{72} +(-0.0603074 + 0.104455i) q^{73} +(-5.22668 + 9.05288i) q^{74} +(-0.733956 - 1.27125i) q^{75} +0.268571 q^{76} +(-2.47178 + 0.943555i) q^{77} +0.815207 q^{78} +(-0.163848 - 0.283793i) q^{79} +(5.36824 - 9.29807i) q^{80} +(-1.56031 + 2.70253i) q^{81} +(0.326352 + 0.565258i) q^{82} +3.35504 q^{83} +(0.418748 - 2.61240i) q^{84} -9.20439 q^{85} +(0.907604 + 1.57202i) q^{86} +(11.7626 - 20.3735i) q^{87} +(-1.26604 + 2.19285i) q^{88} +(2.32635 + 4.02936i) q^{89} -19.0273 q^{90} +(-0.379385 - 0.308391i) q^{91} +2.90167 q^{92} +(-3.81908 - 6.61484i) q^{93} +(-5.88326 + 10.1901i) q^{94} +(-0.907604 + 1.57202i) q^{95} +(-2.79813 - 4.84651i) q^{96} +13.1206 q^{97} +(-7.99660 + 7.14647i) q^{98} +5.29086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} + 12 q^{20} - 12 q^{21} - 6 q^{24} - 3 q^{25}+ \cdots - 6 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 + 12 * q^20 - 12 * q^21 - 6 * q^24 - 3 * q^25 - 9 * q^26 + 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 3 * q^33 - 12 * q^34 - 15 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 - 18 * q^42 - 3 * q^45 + 24 * q^46 + 3 * q^47 - 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 - 9 * q^53 + 18 * q^54 + 12 * q^55 + 3 * q^56 - 15 * q^58 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 - 6 * q^64 - 15 * q^65 + 3 * q^66 + 21 * q^68 + 42 * q^69 + 45 * q^70 - 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 - 9 * q^75 - 18 * q^76 + 12 * q^78 + 3 * q^79 + 27 * q^80 - 15 * q^81 + 3 * q^82 - 30 * q^83 - 54 * q^85 + 9 * q^86 + 24 * q^87 - 3 * q^88 + 15 * q^89 - 72 * q^90 + 9 * q^91 - 6 * q^92 - 6 * q^93 - 9 * q^95 - 3 * q^96 + 90 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more