LMFDB - Embedded newform 77.2.m.b.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(4,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("77.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.m (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	77.53
Dual form			77.2.m.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57407 + 0.547134i) q^{2} +(0.231369 + 2.20133i) q^{3} +(4.49937 - 2.00325i) q^{4} +(-0.787136 + 0.874203i) q^{5} +(-1.79998 - 5.53977i) q^{6} +(-2.31119 + 1.28778i) q^{7} +(-6.22764 + 4.52465i) q^{8} +(-1.85787 + 0.394902i) q^{9} +O(q^{10})$	\(q+(-2.57407 + 0.547134i) q^{2} +(0.231369 + 2.20133i) q^{3} +(4.49937 - 2.00325i) q^{4} +(-0.787136 + 0.874203i) q^{5} +(-1.79998 - 5.53977i) q^{6} +(-2.31119 + 1.28778i) q^{7} +(-6.22764 + 4.52465i) q^{8} +(-1.85787 + 0.394902i) q^{9} +(1.54783 - 2.68093i) q^{10} +(-3.26165 + 0.601380i) q^{11} +(5.45081 + 9.44109i) q^{12} +(0.0112624 - 0.0346622i) q^{13} +(5.24457 - 4.57937i) q^{14} +(-2.10653 - 1.53048i) q^{15} +(6.96361 - 7.73387i) q^{16} +(5.95559 + 1.26590i) q^{17} +(4.56621 - 2.03301i) q^{18} +(1.75961 + 0.783430i) q^{19} +(-1.79037 + 5.51019i) q^{20} +(-3.36957 - 4.78974i) q^{21} +(8.06666 - 3.33255i) q^{22} +(-1.02155 - 1.76938i) q^{23} +(-11.4011 - 12.6622i) q^{24} +(0.377994 + 3.59637i) q^{25} +(-0.0100254 + 0.0953849i) q^{26} +(0.752823 + 2.31695i) q^{27} +(-7.81916 + 10.4241i) q^{28} +(4.02767 + 2.92628i) q^{29} +(6.25972 + 2.78701i) q^{30} +(1.89509 + 2.10472i) q^{31} +(-5.99553 + 10.3846i) q^{32} +(-2.07848 - 7.04081i) q^{33} -16.0227 q^{34} +(0.693441 - 3.03411i) q^{35} +(-7.56813 + 5.49857i) q^{36} +(0.278295 - 2.64780i) q^{37} +(-4.95800 - 1.05386i) q^{38} +(0.0789086 + 0.0167725i) q^{39} +(0.946542 - 9.00574i) q^{40} +(6.61499 - 4.80607i) q^{41} +(11.2941 + 10.4855i) q^{42} -2.96835 q^{43} +(-13.4706 + 9.23971i) q^{44} +(1.11717 - 1.93499i) q^{45} +(3.59762 + 3.99557i) q^{46} +(2.91785 + 1.29911i) q^{47} +(18.6359 + 13.5398i) q^{48} +(3.68323 - 5.95263i) q^{49} +(-2.94068 - 9.05049i) q^{50} +(-1.40872 + 13.4031i) q^{51} +(-0.0187631 - 0.178519i) q^{52} +(-6.63364 - 7.36740i) q^{53} +(-3.20550 - 5.55209i) q^{54} +(2.04163 - 3.32471i) q^{55} +(8.56653 - 18.4772i) q^{56} +(-1.31747 + 4.05475i) q^{57} +(-11.9686 - 5.32875i) q^{58} +(3.70874 - 1.65124i) q^{59} +(-12.5440 - 2.66630i) q^{60} +(-5.80710 + 6.44943i) q^{61} +(-6.02966 - 4.38080i) q^{62} +(3.78534 - 3.30522i) q^{63} +(3.31928 - 10.2157i) q^{64} +(0.0214368 + 0.0371295i) q^{65} +(9.20241 + 16.9863i) q^{66} +(-1.12669 + 1.95148i) q^{67} +(29.3323 - 6.23477i) q^{68} +(3.65862 - 2.65815i) q^{69} +(-0.124894 + 8.18941i) q^{70} +(1.31384 + 4.04359i) q^{71} +(9.78334 - 10.8655i) q^{72} +(3.92144 - 1.74594i) q^{73} +(0.732354 + 6.96788i) q^{74} +(-7.82934 + 1.66418i) q^{75} +9.48655 q^{76} +(6.76385 - 5.59020i) q^{77} -0.212293 q^{78} +(3.03638 - 0.645402i) q^{79} +(1.27967 + 12.1752i) q^{80} +(-10.1317 + 4.51091i) q^{81} +(-14.3979 + 15.9904i) q^{82} +(1.87581 + 5.77314i) q^{83} +(-24.7559 - 14.8007i) q^{84} +(-5.79451 + 4.20996i) q^{85} +(7.64073 - 1.62409i) q^{86} +(-5.50981 + 9.54328i) q^{87} +(17.5913 - 18.5030i) q^{88} +(-2.16161 - 3.74402i) q^{89} +(-1.81697 + 5.59204i) q^{90} +(0.0186077 + 0.0946147i) q^{91} +(-8.14083 - 5.91466i) q^{92} +(-4.19470 + 4.65869i) q^{93} +(-8.22152 - 1.74754i) q^{94} +(-2.06993 + 0.921593i) q^{95} +(-24.2470 - 10.7955i) q^{96} +(1.43258 - 4.40904i) q^{97} +(-6.22400 + 17.3377i) q^{98} +(5.82222 - 2.40531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} - 16 q^{6} - 2 q^{7} - 38 q^{8} + 7 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 - 16 * q^6 - 2 * q^7 - 38 * q^8 + 7 * q^9	\( 40 q - 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} - 16 q^{6} - 2 q^{7} - 38 q^{8} + 7 q^{9} + 14 q^{10} - 9 q^{11} - 18 q^{12} + 6 q^{13} - 3 q^{14} - 14 q^{15} - 5 q^{16} - 7 q^{17} + 24 q^{18} - 4 q^{19} - 30 q^{20} - 2 q^{21} + 44 q^{22} - 14 q^{23} - 12 q^{24} + 21 q^{25} - 16 q^{27} + 16 q^{28} + 16 q^{30} - 17 q^{31} - 30 q^{32} - 15 q^{33} + 48 q^{34} - 14 q^{35} + 14 q^{36} + 24 q^{37} + 12 q^{38} + 28 q^{39} + 10 q^{40} + 60 q^{41} - 70 q^{42} - 72 q^{43} + 18 q^{44} - 16 q^{45} + 8 q^{46} + 13 q^{47} + 128 q^{48} - 10 q^{49} + 6 q^{50} - 7 q^{51} + 2 q^{52} + 33 q^{53} + 34 q^{54} - 6 q^{55} + 24 q^{56} + 44 q^{57} - 17 q^{58} + 21 q^{59} - 48 q^{60} - 52 q^{62} + 24 q^{63} + 94 q^{64} - 40 q^{65} - 49 q^{66} - 38 q^{67} - 23 q^{68} - 124 q^{69} - 3 q^{70} + 20 q^{71} - 38 q^{72} + 11 q^{73} - 41 q^{74} - 11 q^{75} - 96 q^{76} + 36 q^{77} - 100 q^{78} + 21 q^{79} + 12 q^{80} - 58 q^{81} + 6 q^{82} - 46 q^{83} - 29 q^{84} - 78 q^{85} + 7 q^{86} + 48 q^{87} + 32 q^{88} - 10 q^{89} - 18 q^{90} - 14 q^{91} - 110 q^{92} + 12 q^{93} + 37 q^{94} + 7 q^{95} - 53 q^{96} - 54 q^{97} + 116 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 - 16 * q^6 - 2 * q^7 - 38 * q^8 + 7 * q^9 + 14 * q^10 - 9 * q^11 - 18 * q^12 + 6 * q^13 - 3 * q^14 - 14 * q^15 - 5 * q^16 - 7 * q^17 + 24 * q^18 - 4 * q^19 - 30 * q^20 - 2 * q^21 + 44 * q^22 - 14 * q^23 - 12 * q^24 + 21 * q^25 - 16 * q^27 + 16 * q^28 + 16 * q^30 - 17 * q^31 - 30 * q^32 - 15 * q^33 + 48 * q^34 - 14 * q^35 + 14 * q^36 + 24 * q^37 + 12 * q^38 + 28 * q^39 + 10 * q^40 + 60 * q^41 - 70 * q^42 - 72 * q^43 + 18 * q^44 - 16 * q^45 + 8 * q^46 + 13 * q^47 + 128 * q^48 - 10 * q^49 + 6 * q^50 - 7 * q^51 + 2 * q^52 + 33 * q^53 + 34 * q^54 - 6 * q^55 + 24 * q^56 + 44 * q^57 - 17 * q^58 + 21 * q^59 - 48 * q^60 - 52 * q^62 + 24 * q^63 + 94 * q^64 - 40 * q^65 - 49 * q^66 - 38 * q^67 - 23 * q^68 - 124 * q^69 - 3 * q^70 + 20 * q^71 - 38 * q^72 + 11 * q^73 - 41 * q^74 - 11 * q^75 - 96 * q^76 + 36 * q^77 - 100 * q^78 + 21 * q^79 + 12 * q^80 - 58 * q^81 + 6 * q^82 - 46 * q^83 - 29 * q^84 - 78 * q^85 + 7 * q^86 + 48 * q^87 + 32 * q^88 - 10 * q^89 - 18 * q^90 - 14 * q^91 - 110 * q^92 + 12 * q^93 + 37 * q^94 + 7 * q^95 - 53 * q^96 - 54 * q^97 + 116 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−2.57407	+	0.547134i	−1.82014	+	0.386883i	−0.986278	−	0.165092i	$-0.947208\pi$
$2$	−2.57407	+	0.547134i	−1.82014	+	0.386883i	−0.833861	+	0.551975i	$0.813875\pi$
$3$	0.231369	+	2.20133i	0.133581	+	1.27094i	0.831809	+	0.555062i	$0.187305\pi$
$3$	0.231369	+	2.20133i	0.133581	+	1.27094i	−0.698228	+	0.715875i	$0.746028\pi$
$4$	4.49937	−	2.00325i	2.24968	−	1.00162i
$5$	−0.787136	+	0.874203i	−0.352018	+	0.390956i	−0.892984	−	0.450089i	$-0.851392\pi$
$5$	−0.787136	+	0.874203i	−0.352018	+	0.390956i	0.540966	+	0.841045i	$0.318059\pi$
$6$	−1.79998	−	5.53977i	−0.734839	−	2.26160i
$7$	−2.31119	+	1.28778i	−0.873549	+	0.486736i
$7$	−2.31119	+	1.28778i	−0.873549	+	0.486736i
$8$	−6.22764	+	4.52465i	−2.20180	+	1.59970i
$9$	−1.85787	+	0.394902i	−0.619289	+	0.131634i
$10$	1.54783	−	2.68093i	0.489468	−	0.847783i
$11$	−3.26165	+	0.601380i	−0.983424	+	0.181323i
$11$	−3.26165	+	0.601380i	−0.983424	+	0.181323i
$12$	5.45081	+	9.44109i	1.57351	+	2.72541i
$13$	0.0112624	−	0.0346622i	0.00312364	−	0.00961357i	−0.949483	−	0.313820i	$-0.898391\pi$
$13$	0.0112624	−	0.0346622i	0.00312364	−	0.00961357i	0.952606	+	0.304206i	$0.0983912\pi$
$14$	5.24457	−	4.57937i	1.40167	−	1.22389i
$15$	−2.10653	−	1.53048i	−0.543903	−	0.395169i
$16$	6.96361	−	7.73387i	1.74090	−	1.93347i
$17$	5.95559	+	1.26590i	1.44444	+	0.307026i	0.862439	−	0.506161i	$-0.168936\pi$
$17$	5.95559	+	1.26590i	1.44444	+	0.307026i	0.582003	+	0.813187i	$0.302269\pi$
$18$	4.56621	−	2.03301i	1.07626	−	0.479184i
$19$	1.75961	+	0.783430i	0.403683	+	0.179731i	0.598526	−	0.801103i	$-0.295753\pi$
$19$	1.75961	+	0.783430i	0.403683	+	0.179731i	−0.194843	+	0.980834i	$0.562420\pi$
$20$	−1.79037	+	5.51019i	−0.400339	+	1.23212i
$21$	−3.36957	−	4.78974i	−0.735300	−	1.04521i
$22$	8.06666	−	3.33255i	1.71982	−	0.710502i
$23$	−1.02155	−	1.76938i	−0.213008	−	0.368941i	0.739647	−	0.672996i	$-0.234993\pi$
$23$	−1.02155	−	1.76938i	−0.213008	−	0.368941i	−0.952655	+	0.304055i	$0.901659\pi$
$24$	−11.4011	−	12.6622i	−2.32724	−	2.58466i
$25$	0.377994	+	3.59637i	0.0755988	+	0.719275i
$26$	−0.0100254	+	0.0953849i	−0.00196613	+	0.0187065i
$27$	0.752823	+	2.31695i	0.144881	+	0.445898i
$28$	−7.81916	+	10.4241i	−1.47768	+	1.96997i
$29$	4.02767	+	2.92628i	0.747920	+	0.543396i	0.895182	−	0.445702i	$-0.147046\pi$
$29$	4.02767	+	2.92628i	0.747920	+	0.543396i	−0.147261	+	0.989098i	$0.547046\pi$
$30$	6.25972	+	2.78701i	1.14286	+	0.508835i
$31$	1.89509	+	2.10472i	0.340369	+	0.378018i	0.888892	−	0.458118i	$-0.151476\pi$
$31$	1.89509	+	2.10472i	0.340369	+	0.378018i	−0.548523	+	0.836136i	$0.684810\pi$
$32$	−5.99553	+	10.3846i	−1.05987	+	1.83575i
$33$	−2.07848	−	7.04081i	−0.361816	−	1.22565i
$34$	−16.0227			−2.74787
$35$	0.693441	−	3.03411i	0.117213	−	0.512859i
$36$	−7.56813	+	5.49857i	−1.26136	+	0.916429i
$37$	0.278295	−	2.64780i	0.0457515	−	0.435296i	−0.947538	−	0.319643i	$-0.896437\pi$
$37$	0.278295	−	2.64780i	0.0457515	−	0.435296i	0.993290	−	0.115653i	$-0.0368962\pi$
$38$	−4.95800	−	1.05386i	−0.804294	−	0.170958i
$39$	0.0789086	+	0.0167725i	0.0126355	+	0.00268576i
$40$	0.946542	−	9.00574i	0.149661	−	1.42393i
$41$	6.61499	−	4.80607i	1.03309	−	0.750583i	0.0641641	−	0.997939i	$-0.479562\pi$
$41$	6.61499	−	4.80607i	1.03309	−	0.750583i	0.968925	+	0.247357i	$0.0795619\pi$
$42$	11.2941	+	10.4855i	1.74272	+	1.61795i
$43$	−2.96835			−0.452669			−0.226335	−	0.974050i	$-0.572674\pi$
$43$	−2.96835			−0.452669			−0.226335	+	0.974050i	$0.572674\pi$
$44$	−13.4706	+	9.23971i	−2.03077	+	1.39294i
$45$	1.11717	−	1.93499i	0.166538	−	0.288452i
$46$	3.59762	+	3.99557i	0.530441	+	0.589114i
$47$	2.91785	+	1.29911i	0.425612	+	0.189495i	0.608353	−	0.793666i	$-0.291830\pi$
$47$	2.91785	+	1.29911i	0.425612	+	0.189495i	−0.182741	+	0.983161i	$0.558497\pi$
$48$	18.6359	+	13.5398i	2.68987	+	1.95430i
$49$	3.68323	−	5.95263i	0.526176	−	0.850375i
$50$	−2.94068	−	9.05049i	−0.415875	−	1.27993i
$51$	−1.40872	+	13.4031i	−0.197260	+	1.87681i
$52$	−0.0187631	−	0.178519i	−0.00260198	−	0.0247562i
$53$	−6.63364	−	7.36740i	−0.911200	−	1.01199i	−0.999873	−	0.0159294i	$-0.994929\pi$
$53$	−6.63364	−	7.36740i	−0.911200	−	1.01199i	0.0886731	−	0.996061i	$-0.471737\pi$
$54$	−3.20550	−	5.55209i	−0.436213	−	0.755544i
$55$	2.04163	−	3.32471i	0.275294	−	0.448304i
$56$	8.56653	−	18.4772i	1.14475	−	2.46912i
$57$	−1.31747	+	4.05475i	−0.174503	+	0.537064i
$58$	−11.9686	−	5.32875i	−1.57155	−	0.699699i
$59$	3.70874	−	1.65124i	0.482837	−	0.214973i	−0.150858	−	0.988555i	$-0.548204\pi$
$59$	3.70874	−	1.65124i	0.482837	−	0.214973i	0.633696	+	0.773582i	$0.281537\pi$
$60$	−12.5440	−	2.66630i	−1.61942	−	0.344218i
$61$	−5.80710	+	6.44943i	−0.743522	+	0.825765i	−0.989655	−	0.143471i	$-0.954174\pi$
$61$	−5.80710	+	6.44943i	−0.743522	+	0.825765i	0.246132	+	0.969236i	$0.420840\pi$
$62$	−6.02966	−	4.38080i	−0.765767	−	0.556363i
$63$	3.78534	−	3.30522i	0.476908	−	0.416419i
$64$	3.31928	−	10.2157i	0.414910	−	1.27696i
$65$	0.0214368	+	0.0371295i	0.00265890	+	0.00460535i
$66$	9.20241	+	16.9863i	1.13274	+	2.09087i
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	−0.926605	−	0.376035i	$-0.877287\pi$
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	0.788959	+	0.614446i	$0.210621\pi$
$68$	29.3323	−	6.23477i	3.55706	−	0.756076i
$69$	3.65862	−	2.65815i	0.440446	−	0.320003i
$70$	−0.124894	+	8.18941i	−0.0149277	+	0.978822i
$71$	1.31384	+	4.04359i	0.155924	+	0.479885i	0.998253	−	0.0590780i	$-0.0188161\pi$
$71$	1.31384	+	4.04359i	0.155924	+	0.479885i	−0.842329	+	0.538963i	$0.818816\pi$
$72$	9.78334	−	10.8655i	1.15298	−	1.28051i
$73$	3.92144	−	1.74594i	0.458970	−	0.204347i	−0.164209	−	0.986426i	$-0.552507\pi$
$73$	3.92144	−	1.74594i	0.458970	−	0.204347i	0.623180	+	0.782079i	$0.285841\pi$
$74$	0.732354	+	6.96788i	0.0851344	+	0.810000i
$75$	−7.82934	+	1.66418i	−0.904054	+	0.192163i
$76$	9.48655			1.08818
$77$	6.76385	−	5.59020i	0.770813	−	0.637062i
$78$	−0.212293			−0.0240374
$79$	3.03638	−	0.645402i	0.341619	−	0.0726133i	−0.0339076	−	0.999425i	$-0.510795\pi$
$79$	3.03638	−	0.645402i	0.341619	−	0.0726133i	0.375527	+	0.926812i	$0.377462\pi$
$80$	1.27967	+	12.1752i	0.143071	+	1.36123i
$81$	−10.1317	+	4.51091i	−1.12574	+	0.501213i
$82$	−14.3979	+	15.9904i	−1.58998	+	1.76585i
$83$	1.87581	+	5.77314i	0.205896	+	0.633684i	0.999675	+	0.0254778i	$0.00811070\pi$
$83$	1.87581	+	5.77314i	0.205896	+	0.633684i	−0.793779	+	0.608206i	$0.791889\pi$
$84$	−24.7559	−	14.8007i	−2.70110	−	1.61489i
$85$	−5.79451	+	4.20996i	−0.628503	+	0.456634i
$86$	7.64073	−	1.62409i	0.823921	−	0.175130i
$87$	−5.50981	+	9.54328i	−0.590714	+	1.02315i
$88$	17.5913	−	18.5030i	1.87524	−	1.97242i
$89$	−2.16161	−	3.74402i	−0.229130	−	0.396866i	0.728420	−	0.685131i	$-0.240255\pi$
$89$	−2.16161	−	3.74402i	−0.229130	−	0.396866i	−0.957551	+	0.288265i	$0.906922\pi$
$90$	−1.81697	+	5.59204i	−0.191525	+	0.589453i
$91$	0.0186077	+	0.0946147i	0.00195062	+	0.00991831i
$92$	−8.14083	−	5.91466i	−0.848740	−	0.616646i
$93$	−4.19470	+	4.65869i	−0.434970	+	0.483083i
$94$	−8.22152	−	1.74754i	−0.847985	−	0.180245i
$95$	−2.06993	+	0.921593i	−0.212371	+	0.0945535i
$96$	−24.2470	−	10.7955i	−2.47470	−	1.10181i
$97$	1.43258	−	4.40904i	0.145457	−	0.447670i	−0.851613	−	0.524172i	$-0.824375\pi$
$97$	1.43258	−	4.40904i	0.145457	−	0.447670i	0.997069	+	0.0765015i	$0.0243750\pi$
$98$	−6.22400	+	17.3377i	−0.628719	+	1.75137i
$99$	5.82222	−	2.40531i	0.585155	−	0.241743i
$100$	8.90516	+	15.4242i	0.890516	+	1.54242i
$101$	−11.3829	−	12.6420i	−1.13264	−	1.25792i	−0.962137	−	0.272566i	$-0.912128\pi$
$101$	−11.3829	−	12.6420i	−1.13264	−	1.25792i	−0.170502	−	0.985357i	$-0.554539\pi$
$102$	−3.70715	−	35.2712i	−0.367062	−	3.49237i
$103$	1.76150	−	16.7595i	0.173566	−	1.65137i	−0.467583	−	0.883949i	$-0.654875\pi$
$103$	1.76150	−	16.7595i	0.173566	−	1.65137i	0.641149	−	0.767417i	$-0.278458\pi$
$104$	0.0866959	+	0.266822i	0.00850123	+	0.0261641i
$105$	6.83952	+	0.824491i	0.667469	+	0.0804621i
$106$	21.1064	+	15.3347i	2.05003	+	1.48944i
$107$	−0.852002	−	0.379336i	−0.0823661	−	0.0366718i	0.365140	−	0.930953i	$-0.381021\pi$
$107$	−0.852002	−	0.379336i	−0.0823661	−	0.0366718i	−0.447506	+	0.894281i	$0.647688\pi$
$108$	8.02865	+	8.91672i	0.772558	+	0.858012i
$109$	−0.811795	+	1.40607i	−0.0777558	+	0.134677i	−0.902281	−	0.431148i	$-0.858109\pi$
$109$	−0.811795	+	1.40607i	−0.0777558	+	0.134677i	0.824526	+	0.565825i	$0.191442\pi$
$110$	−3.43623	+	9.67507i	−0.327632	+	0.922482i
$111$	5.89307			0.559345
$112$	−6.13471	+	26.8421i	−0.579676	+	2.53634i
$113$	−2.86311	+	2.08017i	−0.269338	+	0.195686i	−0.714254	−	0.699887i	$-0.753234\pi$
$113$	−2.86311	+	2.08017i	−0.269338	+	0.195686i	0.444915	+	0.895573i	$0.353234\pi$
$114$	1.17275	−	11.1580i	0.109838	−	1.04504i
$115$	2.35090	+	0.499698i	0.219222	+	0.0465971i
$116$	23.9840	+	5.09796i	2.22686	+	0.473334i
$117$	−0.00723593	+	0.0688453i	−0.000668962	+	0.00636475i
$118$	−8.64310	+	6.27958i	−0.795662	+	0.578082i
$119$	−15.3947	+	4.74376i	−1.41123	+	0.434860i
$120$	20.0436			1.82972
$121$	10.2767	−	3.92298i	0.934244	−	0.356634i
$122$	11.4191	−	19.7785i	1.03384	−	1.79066i
$123$	12.1102	+	13.4498i	1.09194	+	1.21273i
$124$	12.7430	+	5.67354i	1.14435	+	0.509499i
$125$	−8.19996	−	5.95762i	−0.733427	−	0.532866i
$126$	−7.93532	+	10.5789i	−0.706934	+	0.942448i
$127$	−6.09131	−	18.7471i	−0.540516	−	1.66354i	−0.731419	−	0.681928i	$-0.761142\pi$
$127$	−6.09131	−	18.7471i	−0.540516	−	1.66354i	0.190903	−	0.981609i	$-0.438858\pi$
$128$	−0.447872	+	4.26121i	−0.0395866	+	0.376642i
$129$	−0.686784	−	6.53431i	−0.0604680	−	0.575314i
$130$	−0.0754945	−	0.0838451i	−0.00662130	−	0.00735370i
$131$	8.09187	+	14.0155i	0.706990	+	1.22454i	0.965969	+	0.258659i	$0.0832806\pi$
$131$	8.09187	+	14.0155i	0.706990	+	1.22454i	−0.258979	+	0.965883i	$0.583386\pi$
$132$	−23.4563	−	27.5155i	−2.04161	−	2.39492i
$133$	−5.07569	+	0.455339i	−0.440119	+	0.0394829i
$134$	1.83244	−	5.63968i	0.158299	−	0.487194i
$135$	−2.61806	−	1.16564i	−0.225327	−	0.100322i
$136$	−42.8170	+	19.0634i	−3.67153	+	1.63467i
$137$	16.6054	+	3.52958i	1.41869	+	0.301553i	0.852504	−	0.522721i	$-0.175083\pi$
$137$	16.6054	+	3.52958i	1.41869	+	0.301553i	0.566191	+	0.824274i	$0.308417\pi$
$138$	−7.96317	+	8.84400i	−0.677870	+	0.752851i
$139$	5.94380	+	4.31842i	0.504146	+	0.366284i	0.810598	−	0.585602i	$-0.199142\pi$
$139$	5.94380	+	4.31842i	0.504146	+	0.366284i	−0.306452	+	0.951886i	$0.599142\pi$
$140$	−2.95803	−	15.0407i	−0.249999	−	1.27117i
$141$	−2.18467	+	6.72371i	−0.183982	+	0.566239i
$142$	−5.59430	−	9.68961i	−0.469463	−	0.813134i
$143$	−0.0158889	+	0.119829i	−0.00132870	+	0.0100206i
$144$	−9.88334	+	17.1184i	−0.823611	+	1.42654i
$145$	−5.72849	+	1.21763i	−0.475725	+	0.101119i
$146$	−9.13879	+	6.63972i	−0.756332	+	0.549507i
$147$	13.9559	+	6.73075i	1.15106	+	0.555143i
$148$	−4.05205	−	12.4709i	−0.333076	−	1.02510i
$149$	−3.35966	+	3.73128i	−0.275234	+	0.305679i	−0.864875	−	0.501987i	$-0.832603\pi$
$149$	−3.35966	+	3.73128i	−0.275234	+	0.305679i	0.589641	+	0.807665i	$0.299269\pi$
$150$	19.2427	−	8.56740i	1.57116	−	0.699526i
$151$	−0.877823	−	8.35192i	−0.0714362	−	0.679670i	−0.970376	−	0.241598i	$-0.922328\pi$
$151$	−0.877823	−	8.35192i	−0.0714362	−	0.679670i	0.898940	−	0.438072i	$-0.144338\pi$
$152$	−14.5030	+	3.08271i	−1.17635	+	0.250040i
$153$	−11.5646			−0.934942
$154$	−14.3520	+	18.0903i	−1.15652	+	1.45776i
$155$	−3.33165			−0.267604
$156$	0.388638	−	0.0826076i	0.0311160	−	0.00661390i
$157$	1.56236	+	14.8648i	0.124690	+	1.18634i	0.860606	+	0.509271i	$0.170085\pi$
$157$	1.56236	+	14.8648i	0.124690	+	1.18634i	−0.735917	+	0.677072i	$0.763248\pi$
$158$	−7.46271	+	3.32261i	−0.593701	+	0.264333i
$159$	14.6832	−	16.3074i	1.16446	−	1.29326i
$160$	−4.35892	−	13.4154i	−0.344603	−	1.06058i
$161$	4.63957	+	2.77384i	0.365650	+	0.218609i
$162$	23.6115	−	17.1548i	1.85510	−	1.34781i
$163$	−2.43424	+	0.517414i	−0.190665	+	0.0405270i	−0.302254	−	0.953227i	$-0.597739\pi$
$163$	−2.43424	+	0.517414i	−0.190665	+	0.0405270i	0.111590	+	0.993754i	$0.464406\pi$
$164$	20.1355	−	34.8758i	1.57232	−	2.72334i
$165$	7.79115	+	3.72507i	0.606540	+	0.289996i
$166$	−7.98713	−	13.8341i	−0.619921	−	1.07374i
$167$	−3.80261	+	11.7032i	−0.294255	+	0.905624i	0.689216	+	0.724556i	$0.257955\pi$
$167$	−3.80261	+	11.7032i	−0.294255	+	0.905624i	−0.983471	+	0.181068i	$0.942045\pi$
$168$	42.6564	+	14.5827i	3.29101	+	1.12508i
$169$	10.5161	+	7.64043i	0.808934	+	0.587725i
$170$	12.6120	−	14.0071i	0.967299	−	1.07429i
$171$	−3.57850	−	0.760634i	−0.273655	−	0.0581672i
$172$	−13.3557	+	5.94634i	−1.01836	+	0.453404i
$173$	11.1499	+	4.96423i	0.847708	+	0.377424i	0.784163	−	0.620555i	$-0.213093\pi$
$173$	11.1499	+	4.96423i	0.847708	+	0.377424i	0.0635449	+	0.997979i	$0.479759\pi$
$174$	8.96116	−	27.5796i	0.679344	−	2.09081i
$175$	−5.50497	−	7.82515i	−0.416136	−	0.591525i
$176$	−18.0618	+	29.4129i	−1.36146	+	2.21708i
$177$	4.49301	+	7.78211i	0.337715	+	0.584940i
$178$	7.61261	+	8.45466i	0.570590	+	0.633704i
$179$	−0.398664	−	3.79303i	−0.0297975	−	0.283504i	−0.999267	−	0.0382910i	$-0.987809\pi$
$179$	−0.398664	−	3.79303i	−0.0297975	−	0.283504i	0.969469	−	0.245213i	$-0.0788580\pi$
$180$	1.15028	−	10.9442i	0.0857371	−	0.815734i
$181$	2.17667	+	6.69911i	0.161791	+	0.497941i	0.998785	−	0.0492703i	$-0.0156896\pi$
$181$	2.17667	+	6.69911i	0.161791	+	0.497941i	−0.836995	+	0.547211i	$0.815690\pi$
$182$	−0.0996644	−	0.233363i	−0.00738762	−	0.0172980i
$183$	−15.5409	−	11.2911i	−1.14882	−	0.834664i
$184$	14.3677	+	6.39689i	1.05920	+	0.471585i
$185$	2.09566	+	2.32747i	0.154076	+	0.171119i
$186$	8.24851	−	14.2868i	0.604810	−	1.04756i
$187$	−20.1863	−	0.547348i	−1.47617	−	0.0400261i
$188$	15.7309			1.14729
$189$	−4.72365	−	4.38545i	−0.343595	−	0.318995i
$190$	4.82391	−	3.50477i	0.349963	−	0.254263i
$191$	1.66472	−	15.8388i	0.120455	−	1.14605i	−0.752616	−	0.658460i	$-0.771208\pi$
$191$	1.66472	−	15.8388i	0.120455	−	1.14605i	0.873071	−	0.487593i	$-0.162125\pi$
$192$	23.2560	+	4.94323i	1.67836	+	0.356747i
$193$	−14.4744	−	3.07662i	−1.04189	−	0.221460i	−0.344972	−	0.938613i	$-0.612112\pi$
$193$	−14.4744	−	3.07662i	−1.04189	−	0.221460i	−0.696916	+	0.717153i	$0.745445\pi$
$194$	−1.27523	+	12.1330i	−0.0915560	+	0.871097i
$195$	−0.0767745	+	0.0557799i	−0.00549793	+	0.00399448i
$196$	4.64764	−	34.1615i	0.331974	−	2.44011i
$197$	8.28808			0.590501			0.295251	−	0.955420i	$-0.404597\pi$
$197$	8.28808			0.590501			0.295251	+	0.955420i	$0.404597\pi$
$198$	−13.6707	+	9.37697i	−0.971537	+	0.666392i
$199$	−9.14220	+	15.8348i	−0.648073	+	1.12250i	0.335509	+	0.942037i	$0.391092\pi$
$199$	−9.14220	+	15.8348i	−0.648073	+	1.12250i	−0.983582	+	0.180459i	$0.942242\pi$
$200$	−18.6263	−	20.6866i	−1.31708	−	1.46277i
$201$	−4.55652	−	2.02869i	−0.321392	−	0.143093i
$202$	36.2171	+	26.3133i	2.54823	+	1.85140i
$203$	−13.0771	−	1.57643i	−0.917836	−	0.110643i
$204$	20.5113	+	63.1274i	1.43608	+	4.41980i
$205$	−1.00542	+	9.56589i	−0.0702212	+	0.668111i
$206$	4.63551	+	44.1039i	0.322971	+	3.07286i
$207$	2.59663	+	2.88385i	0.180479	+	0.200442i
$208$	−0.189646	−	0.328476i	−0.0131496	−	0.0227757i
$209$	−6.21038	−	1.49708i	−0.429581	−	0.103555i
$210$	−18.0565	+	1.61984i	−1.24602	+	0.111780i
$211$	7.29409	−	22.4489i	0.502146	−	1.54545i	−0.303370	−	0.952873i	$-0.598112\pi$
$211$	7.29409	−	22.4489i	0.502146	−	1.54545i	0.805516	−	0.592573i	$-0.201888\pi$
$212$	−44.6059	−	19.8598i	−3.06354	−	1.36398i
$213$	−8.59728	+	3.82775i	−0.589076	+	0.262273i
$214$	2.40066	+	0.510275i	0.164105	+	0.0348817i
$215$	2.33650	−	2.59494i	0.159348	−	0.176974i
$216$	−15.1717	−	11.0229i	−1.03230	−	0.750013i
$217$	−7.09035	−	2.42394i	−0.481324	−	0.164548i
$218$	1.32030	−	4.06348i	0.0894222	−	0.275213i
$219$	4.75068	+	8.22842i	0.321021	+	0.556025i
$220$	2.52584	−	19.0490i	0.170292	−	1.28428i
$221$	0.110953	−	0.192177i	0.00746352	−	0.0129272i
$222$	−15.1691	+	3.22430i	−1.01809	+	0.216401i
$223$	9.76962	−	7.09804i	0.654222	−	0.475320i	−0.210485	−	0.977597i	$-0.567504\pi$
$223$	9.76962	−	7.09804i	0.654222	−	0.475320i	0.864707	+	0.502277i	$0.167504\pi$
$224$	0.483778	−	31.7217i	0.0323238	−	2.11949i
$225$	−2.12248	−	6.53231i	−0.141498	−	0.435488i
$226$	6.23169	−	6.92100i	0.414526	−	0.460378i
$227$	−9.43447	+	4.20050i	−0.626188	+	0.278797i	−0.695197	−	0.718819i	$-0.744683\pi$
$227$	−9.43447	+	4.20050i	−0.626188	+	0.278797i	0.0690091	+	0.997616i	$0.478016\pi$
$228$	2.19489	+	20.8830i	0.145360	+	1.38301i
$229$	26.9582	−	5.73015i	1.78145	−	0.378659i	0.804809	−	0.593534i	$-0.202268\pi$
$229$	26.9582	−	5.73015i	1.78145	−	0.378659i	0.976641	+	0.214875i	$0.0689345\pi$
$230$	−6.32476			−0.417042
$231$	13.8708	+	13.5961i	0.912631	+	0.894555i
$232$	−38.3233			−2.51605
$233$	−3.91278	+	0.831687i	−0.256335	+	0.0544856i	−0.334286	−	0.942472i	$-0.608495\pi$
$233$	−3.91278	+	0.831687i	−0.256335	+	0.0544856i	0.0779518	+	0.996957i	$0.475162\pi$
$234$	−0.0190419	−	0.181171i	−0.00124481	−	0.0118435i
$235$	−3.43243	+	1.52822i	−0.223907	+	0.0996899i
$236$	13.3792	−	14.8591i	0.870909	−	0.967242i
$237$	2.12326	+	6.53473i	0.137921	+	0.424476i
$238$	37.0315	−	20.6337i	2.40040	−	1.33749i
$239$	−17.1705	+	12.4751i	−1.11067	+	0.806946i	−0.982768	−	0.184842i	$-0.940823\pi$
$239$	−17.1705	+	12.4751i	−1.11067	+	0.806946i	−0.127897	+	0.991787i	$0.540823\pi$
$240$	−26.5056	+	5.63393i	−1.71093	+	0.363669i
$241$	6.80326	−	11.7836i	0.438237	−	0.759048i	−0.559317	−	0.828954i	$-0.688936\pi$
$241$	6.80326	−	11.7836i	0.438237	−	0.759048i	0.997554	+	0.0699056i	$0.0222698\pi$
$242$	−24.3065	+	15.7207i	−1.56248	+	1.01057i
$243$	−8.61987	−	14.9301i	−0.552965	−	0.957763i
$244$	−13.2084	+	40.6514i	−0.845584	+	2.60244i
$245$	2.30460	+	7.90543i	0.147236	+	0.505059i
$246$	−38.5314	−	27.9947i	−2.45667	−	1.78488i
$247$	0.0469730	−	0.0521687i	0.00298882	−	0.00331942i
$248$	−21.3251	−	4.53278i	−1.35414	−	0.287832i
$249$	−12.2746	+	5.46499i	−0.777869	+	0.346329i
$250$	24.3669	+	10.8488i	1.54109	+	0.686140i
$251$	−5.10309	+	15.7057i	−0.322104	+	0.991334i	0.650627	+	0.759398i	$0.274506\pi$
$251$	−5.10309	+	15.7057i	−0.322104	+	0.991334i	−0.972731	+	0.231937i	$0.925494\pi$
$252$	10.4105	−	22.4544i	0.655798	−	1.41449i
$253$	4.39600	+	5.15674i	0.276374	+	0.324202i
$254$	25.9366	+	44.9235i	1.62741	+	2.81875i
$255$	−10.6082	−	11.7816i	−0.664309	−	0.737790i
$256$	1.06696	+	10.1514i	0.0666850	+	0.634465i
$257$	−3.05781	+	29.0931i	−0.190741	+	1.81478i	0.311713	+	0.950176i	$0.399097\pi$
$257$	−3.05781	+	29.0931i	−0.190741	+	1.81478i	−0.502454	+	0.864604i	$0.667570\pi$
$258$	5.34298	+	16.4440i	0.332639	+	1.02376i
$259$	2.76660	+	6.47797i	0.171908	+	0.402521i
$260$	0.170831	+	0.124116i	0.0105945	+	0.00769737i
$261$	−8.63847	−	3.84610i	−0.534708	−	0.238067i
$262$	−28.4974	−	31.6495i	−1.76057	−	1.95531i
$263$	9.96601	−	17.2616i	0.614530	−	1.06440i	−0.375936	−	0.926646i	$-0.622679\pi$
$263$	9.96601	−	17.2616i	0.614530	−	1.06440i	0.990467	−	0.137752i	$-0.0439878\pi$
$264$	44.8012	+	34.4433i	2.75732	+	2.11984i
$265$	11.6622			0.716402
$266$	12.8160	−	3.94916i	0.785802	−	0.242139i
$267$	7.74169	−	5.62466i	0.473784	−	0.344224i
$268$	−1.16008	+	11.0374i	−0.0708633	+	0.674219i
$269$	−0.605177	−	0.128634i	−0.0368983	−	0.00784298i	0.189426	−	0.981895i	$-0.439337\pi$
$269$	−0.605177	−	0.128634i	−0.0368983	−	0.00784298i	−0.226324	+	0.974052i	$0.572671\pi$
$270$	7.37682	+	1.56799i	0.448939	+	0.0954250i
$271$	0.0121050	−	0.115172i	0.000735328	−	0.00699618i	−0.994148	−	0.108026i	$-0.965547\pi$
$271$	0.0121050	−	0.115172i	0.000735328	−	0.00699618i	0.994883	+	0.101030i	$0.0322137\pi$
$272$	51.2627	−	37.2445i	3.10826	−	2.25828i
$273$	−0.203973	+	0.0628525i	−0.0123450	+	0.00380401i
$274$	−44.6745			−2.69889
$275$	−3.39567	−	11.5028i	−0.204767	−	0.693644i
$276$	11.1366	−	19.2891i	0.670342	−	1.16107i
$277$	6.46626	+	7.18151i	0.388520	+	0.431495i	0.905398	−	0.424564i	$-0.139573\pi$
$277$	6.46626	+	7.18151i	0.388520	+	0.431495i	−0.516878	+	0.856059i	$0.672906\pi$
$278$	−17.6625	−	7.86384i	−1.05932	−	0.471642i
$279$	−4.35199	−	3.16190i	−0.260547	−	0.189298i
$280$	9.40979	+	22.0330i	0.562343	+	1.31672i
$281$	−1.07026	−	3.29393i	−0.0638466	−	0.196500i	0.914045	−	0.405613i	$-0.132942\pi$
$281$	−1.07026	−	3.29393i	−0.0638466	−	0.196500i	−0.977891	+	0.209114i	$0.932942\pi$
$282$	1.94470	−	18.5026i	0.115805	−	1.10181i
$283$	−2.75322	−	26.1952i	−0.163662	−	1.55714i	−0.700621	−	0.713533i	$-0.747094\pi$
$283$	−2.75322	−	26.1952i	−0.163662	−	1.55714i	0.536959	−	0.843608i	$-0.319573\pi$
$284$	14.0118	+	15.5616i	0.831445	+	0.923413i
$285$	−2.50765	−	4.34337i	−0.148540	−	0.257279i
$286$	−0.0246633	−	0.317141i	−0.00145837	−	0.0187529i
$287$	−9.09936	+	19.6264i	−0.537118	+	1.15851i
$288$	7.03801	−	21.6608i	0.414719	−	1.27637i
$289$	18.3362	+	8.16382i	1.07860	+	0.480225i
$290$	14.0793	−	6.26851i	0.826765	−	0.368100i
$291$	10.0372	+	2.13347i	0.588391	+	0.125066i
$292$	14.1465	−	15.7112i	0.827859	−	0.919431i
$293$	−12.3700	−	8.98734i	−0.722664	−	0.525046i	0.164570	−	0.986365i	$-0.447376\pi$
$293$	−12.3700	−	8.98734i	−0.722664	−	0.525046i	−0.887234	+	0.461319i	$0.847376\pi$
$294$	−39.6059	−	9.68966i	−2.30987	−	0.565112i
$295$	−1.47577	+	4.54195i	−0.0859226	+	0.264442i
$296$	10.2473	+	17.7488i	0.595609	+	1.03163i
$297$	−3.84881	−	7.10435i	−0.223331	−	0.412236i
$298$	6.60648	−	11.4428i	0.382703	−	0.662861i
$299$	−0.0728357	+	0.0154817i	−0.00421220	+	0.000895330i
$300$	−31.8933	+	23.1718i	−1.84136	+	1.33783i
$301$	6.86044	−	3.82259i	0.395429	−	0.220330i
$302$	6.82920	+	21.0181i	0.392976	+	1.20946i
$303$	25.1955	−	27.9824i	1.44744	−	1.60755i
$304$	18.3122	−	8.15312i	1.05028	−	0.467613i
$305$	−1.06714	−	10.1532i	−0.0611043	−	0.581369i
$306$	29.7680	−	6.32739i	1.70172	−	0.361713i
$307$	32.1611			1.83553			0.917766	−	0.397123i	$-0.129991\pi$
$307$	32.1611			1.83553			0.917766	+	0.397123i	$0.129991\pi$
$308$	19.2345	−	38.7020i	1.09599	−	2.20525i
$309$	37.3008			2.12197
$310$	8.57588	−	1.82286i	0.487077	−	0.103531i
$311$	−0.221418	−	2.10666i	−0.0125555	−	0.119458i	0.986449	−	0.164069i	$-0.0524618\pi$
$311$	−0.221418	−	2.10666i	−0.0125555	−	0.119458i	−0.999004	+	0.0446110i	$0.985795\pi$
$312$	−0.567305	+	0.252580i	−0.0321173	+	0.0142995i
$313$	−4.10743	+	4.56176i	−0.232166	+	0.257846i	−0.847959	−	0.530062i	$-0.822169\pi$
$313$	−4.10743	+	4.56176i	−0.232166	+	0.257846i	0.615794	+	0.787907i	$0.288835\pi$
$314$	−12.1547	−	37.4082i	−0.685928	−	2.11107i
$315$	−0.0901442	+	5.91082i	−0.00507905	+	0.333037i
$316$	12.3689	−	8.98651i	0.695803	−	0.505530i
$317$	17.3855	−	3.69540i	0.976468	−	0.207555i	0.308074	−	0.951362i	$-0.400316\pi$
$317$	17.3855	−	3.69540i	0.976468	−	0.207555i	0.668394	+	0.743808i	$0.266982\pi$
$318$	−28.8733	+	50.0100i	−1.61913	+	2.80442i
$319$	−14.8967	−	7.12232i	−0.834053	−	0.398773i
$320$	6.31787	+	10.9429i	0.353179	+	0.611725i
$321$	0.637915	−	1.96330i	0.0356050	−	0.109581i
$322$	−13.4602	−	4.60157i	−0.750109	−	0.256436i
$323$	9.48778	+	6.89328i	0.527914	+	0.383552i
$324$	−36.5496	+	40.5925i	−2.03054	+	2.25514i
$325$	0.128915	+	0.0274018i	0.00715094	+	0.00151998i
$326$	5.98280	−	2.66372i	0.331357	−	0.147530i
$327$	−3.28304	−	1.46170i	−0.181553	−	0.0808325i
$328$	−19.4500	+	59.8610i	−1.07395	+	3.30527i
$329$	−8.41668	+	0.755058i	−0.464027	+	0.0416277i
$330$	−22.0930	−	5.32576i	−1.21618	−	0.293174i
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	−0.999027	−	0.0441108i	$-0.985955\pi$
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	0.461312	−	0.887238i	$-0.347379\pi$
$332$	20.0050	+	22.2178i	1.09791	+	1.21936i
$333$	0.528586	+	5.02916i	0.0289663	+	0.275596i
$334$	3.38493	−	32.2054i	0.185215	−	1.76220i
$335$	−0.819133	−	2.52103i	−0.0447540	−	0.137739i
$336$	−60.5076	−	7.29408i	−3.30096	−	0.397925i
$337$	−18.6594	−	13.5569i	−1.01644	−	0.738489i	−0.0508925	−	0.998704i	$-0.516207\pi$
$337$	−18.6594	−	13.5569i	−1.01644	−	0.738489i	−0.965551	+	0.260215i	$0.916207\pi$
$338$	−31.2496	−	13.9132i	−1.69975	−	0.756779i
$339$	−5.24157	−	5.82135i	−0.284683	−	0.316172i
$340$	−17.6380	+	30.5500i	−0.956557	+	1.65681i
$341$	−7.44686	−	5.72517i	−0.403270	−	0.310035i
$342$	9.62747			0.520594
$343$	−0.846981	+	18.5009i	−0.0457327	+	0.998954i
$344$	18.4858	−	13.4307i	0.996690	−	0.724137i
$345$	−0.556075	+	5.29070i	−0.0299381	+	0.284842i
$346$	−31.4166	−	6.67780i	−1.68896	−	0.359001i
$347$	24.4941	+	5.20638i	1.31491	+	0.279493i	0.811398	−	0.584494i	$-0.198707\pi$
$347$	24.4941	+	5.20638i	1.31491	+	0.279493i	0.503514	+	0.863987i	$0.332040\pi$
$348$	−5.67313	+	53.9762i	−0.304112	+	2.89343i
$349$	−15.8320	+	11.5026i	−0.847467	+	0.615721i	−0.924446	−	0.381312i	$-0.875472\pi$
$349$	−15.8320	+	11.5026i	−0.847467	+	0.615721i	0.0769797	+	0.997033i	$0.475472\pi$
$350$	18.4515	+	17.1305i	0.986277	+	0.915663i
$351$	0.0887893			0.00473922
$352$	13.3102	−	37.4763i	0.709438	−	1.99750i
$353$	−10.1136	+	17.5172i	−0.538292	+	0.932349i	0.460704	+	0.887554i	$0.347597\pi$
$353$	−10.1136	+	17.5172i	−0.538292	+	0.932349i	−0.998996	+	0.0447952i	$0.985736\pi$
$354$	−15.8232	−	17.5734i	−0.840991	−	0.934015i
$355$	−4.56909	−	2.03429i	−0.242502	−	0.107969i
$356$	−17.2261	−	12.5155i	−0.912981	−	0.663319i
$357$	−14.0044	−	32.7912i	−0.741193	−	1.73550i
$358$	3.10148	+	9.54539i	0.163919	+	0.504489i
$359$	2.60519	−	24.7867i	0.137497	−	1.30819i	−0.680405	−	0.732836i	$-0.738196\pi$
$359$	2.60519	−	24.7867i	0.137497	−	1.30819i	0.817902	−	0.575357i	$-0.195137\pi$
$360$	1.79783	+	17.1053i	0.0947542	+	0.901526i
$361$	−10.2310	−	11.3627i	−0.538474	−	0.598036i
$362$	−9.26821	−	16.0530i	−0.487126	−	0.843727i
$363$	11.0135	+	21.7147i	0.578057	+	1.13973i
$364$	0.273259	+	0.388430i	0.0143227	+	0.0203593i
$365$	−1.56040	+	4.80243i	−0.0816753	+	0.251371i
$366$	46.1810	+	20.5611i	2.41392	+	1.07475i
$367$	6.84200	−	3.04625i	0.357149	−	0.159013i	−0.220316	−	0.975429i	$-0.570709\pi$
$367$	6.84200	−	3.04625i	0.357149	−	0.159013i	0.577465	+	0.816416i	$0.304042\pi$
$368$	−20.7978	−	4.42071i	−1.08416	−	0.230446i
$369$	−10.3918	+	11.5413i	−0.540978	+	0.600817i
$370$	−6.66781	−	4.84445i	−0.346643	−	0.251851i
$371$	24.8192	+	8.48481i	1.28855	+	0.440509i
$372$	−9.54099	+	29.3642i	−0.494678	+	1.52246i
$373$	0.802488	+	1.38995i	0.0415513	+	0.0719689i	0.886053	−	0.463584i	$-0.153437\pi$
$373$	0.802488	+	1.38995i	0.0415513	+	0.0719689i	−0.844502	+	0.535553i	$0.820103\pi$
$374$	52.2603	−	9.63572i	2.70232	−	0.498251i
$375$	11.2175	−	19.4292i	0.579267	−	1.00332i
$376$	−24.0493	+	5.11184i	−1.24025	+	0.263623i
$377$	0.146793	−	0.106651i	0.00756021	−	0.00549281i
$378$	14.5584	+	8.70397i	0.748804	+	0.447684i
$379$	5.26757	+	16.2119i	0.270577	+	0.832751i	0.990356	+	0.138547i	$0.0442433\pi$
$379$	5.26757	+	16.2119i	0.270577	+	0.832751i	−0.719779	+	0.694204i	$0.755757\pi$
$380$	−7.46721	+	8.29317i	−0.383060	+	0.425431i
$381$	39.8592	−	17.7465i	2.04205	−	0.909178i
$382$	4.38084	+	41.6809i	0.224143	+	2.13258i
$383$	17.0414	−	3.62225i	0.870773	−	0.185089i	0.249207	−	0.968450i	$-0.419830\pi$
$383$	17.0414	−	3.62225i	0.870773	−	0.185089i	0.621566	+	0.783362i	$0.286497\pi$
$384$	−9.48395			−0.483976
$385$	−0.437106	+	10.3132i	−0.0222770	+	0.525611i
$386$	38.9413			1.98206
$387$	5.51480	−	1.17221i	0.280333	−	0.0595866i
$388$	−2.38668	−	22.7077i	−0.121165	−	1.15281i
$389$	−10.2642	+	4.56993i	−0.520417	+	0.231705i	−0.650097	−	0.759851i	$-0.725272\pi$
$389$	−10.2642	+	4.56993i	−0.520417	+	0.231705i	0.129680	+	0.991556i	$0.458605\pi$
$390$	0.167103	−	0.185587i	0.00846161	−	0.00939757i
$391$	−3.84408	−	11.8309i	−0.194403	−	0.598312i
$392$	3.99568	+	53.7362i	0.201812	+	2.71409i
$393$	−28.9805	+	21.0556i	−1.46188	+	1.06211i
$394$	−21.3341	+	4.53470i	−1.07479	+	0.228455i
$395$	−1.82583	+	3.16243i	−0.0918674	+	0.159119i
$396$	21.3779	−	22.4857i	1.07428	−	1.12995i
$397$	−9.85421	−	17.0680i	−0.494568	−	0.856618i	0.505412	−	0.862878i	$-0.331341\pi$
$397$	−9.85421	−	17.0680i	−0.494568	−	0.856618i	−0.999980	+	0.00626047i	$0.998007\pi$
$398$	14.8689	−	45.7617i	0.745310	−	2.29383i
$399$	−2.17671	−	11.0679i	−0.108972	−	0.554089i
$400$	30.4461	+	22.1204i	1.52231	+	1.10602i
$401$	−8.38973	+	9.31774i	−0.418963	+	0.465306i	−0.915270	−	0.402842i	$-0.868023\pi$
$401$	−8.38973	+	9.31774i	−0.418963	+	0.465306i	0.496306	+	0.868147i	$0.334689\pi$
$402$	12.8388	+	2.72896i	0.640339	+	0.136108i
$403$	0.0942975	−	0.0419839i	0.00469729	−	0.00209137i
$404$	−76.5407	−	34.0781i	−3.80804	−	1.69545i
$405$	4.03156	−	12.4079i	0.200330	−	0.616551i
$406$	34.5239	−	3.09713i	1.71339	−	0.153708i
$407$	0.684633	+	8.80356i	0.0339360	+	0.436376i
$408$	−51.8712	−	89.8436i	−2.56801	−	4.44792i
$409$	10.4423	+	11.5973i	0.516337	+	0.573450i	0.943773	−	0.330596i	$-0.107250\pi$
$409$	10.4423	+	11.5973i	0.516337	+	0.573450i	−0.427436	+	0.904046i	$0.640583\pi$
$410$	−2.64582	−	25.1733i	−0.130668	−	1.24322i
$411$	−3.92780	+	37.3705i	−0.193744	+	1.84335i
$412$	−25.6479	−	78.9360i	−1.26358	−	3.88890i
$413$	−6.44519	+	8.59239i	−0.317147	+	0.422804i
$414$	−8.26176	−	6.00252i	−0.406043	−	0.295008i
$415$	−6.52341	−	2.90441i	−0.320222	−	0.142572i
$416$	0.292427	+	0.324774i	0.0143374	+	0.0159233i
$417$	−8.13105	+	14.0834i	−0.398179	+	0.689666i
$418$	16.8050	+	0.455665i	0.821960	+	0.0222873i
$419$	−31.8183			−1.55443			−0.777213	−	0.629238i	$-0.783367\pi$
$419$	−31.8183			−1.55443			−0.777213	+	0.629238i	$0.783367\pi$
$420$	32.4251	−	9.99155i	1.58219	−	0.487538i
$421$	−19.3204	+	14.0371i	−0.941617	+	0.684125i	−0.948809	−	0.315849i	$-0.897711\pi$
$421$	−19.3204	+	14.0371i	−0.941617	+	0.684125i	0.00719220	+	0.999974i	$0.497711\pi$
$422$	−6.49290	+	61.7758i	−0.316069	+	3.00720i
$423$	−5.93399	−	1.26131i	−0.288521	−	0.0613270i
$424$	74.6468	+	15.8667i	3.62517	+	0.770554i
$425$	−2.30147	+	21.8970i	−0.111638	+	1.06216i
$426$	20.0357	−	14.5568i	0.970731	−	0.705277i
$427$	5.11586	−	22.3842i	0.247574	−	1.08325i
$428$	−4.59337			−0.222029
$429$	−0.267459	−	0.00725210i	−0.0129130	−	0.000350135i
$430$	−4.59452	+	7.95793i	−0.221567	+	0.383766i
$431$	−5.58314	−	6.20070i	−0.268930	−	0.298677i	0.593520	−	0.804819i	$-0.297738\pi$
$431$	−5.58314	−	6.20070i	−0.268930	−	0.298677i	−0.862450	+	0.506142i	$0.831071\pi$
$432$	23.1614	+	10.3121i	1.11435	+	0.496142i
$433$	−10.3850	−	7.54511i	−0.499069	−	0.362595i	0.309592	−	0.950869i	$-0.399807\pi$
$433$	−10.3850	−	7.54511i	−0.499069	−	0.362595i	−0.808661	+	0.588275i	$0.799807\pi$
$434$	19.5772	+	2.36000i	0.939737	+	0.113284i
$435$	−4.00579	−	12.3286i	−0.192063	−	0.591109i
$436$	−0.835857	+	7.95265i	−0.0400303	+	0.380863i
$437$	−0.411350	−	3.91373i	−0.0196775	−	0.187219i
$438$	−16.7306	−	18.5812i	−0.799420	−	0.887846i
$439$	12.2991	+	21.3026i	0.587002	+	1.01672i	0.994623	+	0.103566i	$0.0330253\pi$
$439$	12.2991	+	21.3026i	0.587002	+	1.01672i	−0.407620	+	0.913151i	$0.633641\pi$
$440$	2.32858	+	29.9428i	0.111011	+	1.42747i
$441$	−4.49225	+	12.5137i	−0.213917	+	0.595891i
$442$	−0.180454	+	0.555382i	−0.00858334	+	0.0264168i
$443$	−14.7328	−	6.55945i	−0.699975	−	0.311649i	0.0257164	−	0.999669i	$-0.491813\pi$
$443$	−14.7328	−	6.55945i	−0.699975	−	0.311649i	−0.725691	+	0.688020i	$0.758480\pi$
$444$	26.5151	−	11.8053i	1.25835	−	0.560253i
$445$	4.97452	+	1.05737i	0.235815	+	0.0501240i
$446$	−21.2641	+	23.6161i	−1.00688	+	1.11826i
$447$	−8.99109	−	6.53241i	−0.425264	−	0.308972i
$448$	5.48408	+	27.8849i	0.259099	+	1.31744i
$449$	10.6496	−	32.7763i	0.502588	−	1.54681i	−0.302200	−	0.953245i	$-0.597721\pi$
$449$	10.6496	−	32.7763i	0.502588	−	1.54681i	0.804788	−	0.593562i	$-0.202279\pi$
$450$	9.03745	+	15.6533i	0.426029	+	0.737905i
$451$	−18.6855	+	19.6538i	−0.879866	+	0.925463i
$452$	−8.71507	+	15.0950i	−0.409923	+	0.710007i
$453$	18.1822	−	3.86475i	0.854275	−	0.181582i
$454$	21.9867	−	15.9743i	1.03189	−	0.749710i
$455$	−0.0973593	−	0.0582077i	−0.00456427	−	0.00272882i
$456$	−10.1416	−	31.2126i	−0.474923	−	1.46166i
$457$	−21.7120	+	24.1137i	−1.01565	+	1.12799i	−0.0239074	+	0.999714i	$0.507611\pi$
$457$	−21.7120	+	24.1137i	−1.01565	+	1.12799i	−0.991739	+	0.128275i	$0.959056\pi$
$458$	−66.2571	+	29.4996i	−3.09599	+	1.37842i
$459$	1.55048	+	14.7518i	0.0723701	+	0.688555i
$460$	11.5786	−	2.46110i	0.539853	−	0.114749i
$461$	−29.4973			−1.37383			−0.686914	−	0.726739i	$-0.741035\pi$
$461$	−29.4973			−1.37383			−0.686914	+	0.726739i	$0.741035\pi$
$462$	−43.1432	−	27.4079i	−2.00720	−	1.27513i
$463$	22.2588			1.03445			0.517227	−	0.855848i	$-0.326964\pi$
$463$	22.2588			1.03445			0.517227	+	0.855848i	$0.326964\pi$
$464$	50.6786	−	10.7721i	2.35269	−	0.500081i
$465$	−0.770839	−	7.33405i	−0.0357468	−	0.340108i
$466$	9.61670	−	4.28163i	0.445485	−	0.198343i
$467$	15.8303	−	17.5813i	0.732539	−	0.813567i	−0.255656	−	0.966768i	$-0.582292\pi$
$467$	15.8303	−	17.5813i	0.732539	−	0.813567i	0.988195	+	0.153201i	$0.0489582\pi$
$468$	0.105357	+	0.324256i	0.00487013	+	0.0149887i
$469$	0.0909121	−	5.96117i	0.00419793	−	0.275261i
$470$	7.99916	−	5.81173i	0.368974	−	0.268075i
$471$	−32.3609	+	6.87852i	−1.49111	+	0.316945i
$472$	−15.6255	+	27.0641i	−0.719220	+	1.24573i
$473$	9.68172	−	1.78511i	0.445166	−	0.0820793i
$474$	−9.04079	−	15.6591i	−0.415257	−	0.719247i
$475$	−2.15239	+	6.62436i	−0.0987582	+	0.303946i
$476$	−59.7635	+	52.1833i	−2.73926	+	2.39182i
$477$	15.2338	+	11.0680i	0.697508	+	0.506769i
$478$	37.3724	−	41.5062i	1.70937	−	1.89845i
$479$	11.3019	+	2.40230i	0.516399	+	0.109764i	0.458737	−	0.888572i	$-0.348302\pi$
$479$	11.3019	+	2.40230i	0.516399	+	0.109764i	0.0576623	+	0.998336i	$0.481635\pi$
$480$	28.5231	−	12.6993i	1.30190	−	0.579641i
$481$	−0.0886444	−	0.0394670i	−0.00404184	−	0.00179954i
$482$	−11.0648	+	34.0541i	−0.503989	+	1.55112i
$483$	−5.03268	+	10.8550i	−0.228995	+	0.493919i
$484$	38.3799	−	38.2376i	1.74454	−	1.73807i
$485$	2.72676	+	4.72289i	0.123816	+	0.214455i
$486$	30.3569	+	33.7147i	1.37701	+	1.52933i
$487$	−0.0137727	−	0.131038i	−0.000624101	−	0.00593792i	0.994205	−	0.107497i	$-0.0342836\pi$
$487$	−0.0137727	−	0.131038i	−0.000624101	−	0.00593792i	−0.994830	+	0.101559i	$0.967617\pi$
$488$	6.98311	−	66.4398i	0.316110	−	3.00759i
$489$	−1.70221	−	5.23885i	−0.0769764	−	0.236909i
$490$	−10.2575	−	19.0882i	−0.463388	−	0.862315i
$491$	0.0180456	+	0.0131109i	0.000814388	+	0.000591687i	0.588192	−	0.808721i	$-0.299840\pi$
$491$	0.0180456	+	0.0131109i	0.000814388	+	0.000591687i	−0.587378	+	0.809313i	$0.699840\pi$
$492$	81.4317	+	36.2557i	3.67122	+	1.63453i
$493$	20.2828	+	22.5263i	0.913491	+	1.01453i
$494$	−0.0923681	+	0.159986i	−0.00415584	+	0.00719812i
$495$	−2.48015	+	6.98311i	−0.111474	+	0.313868i
$496$	29.4743			1.32343
$497$	−8.24380	−	7.65357i	−0.369785	−	0.343310i
$498$	28.6054	−	20.7831i	1.28184	−	0.931312i
$499$	0.724289	−	6.89115i	0.0324236	−	0.308490i	−0.966276	−	0.257509i	$-0.917098\pi$
$499$	0.724289	−	6.89115i	0.0324236	−	0.308490i	0.998700	−	0.0509816i	$-0.0162350\pi$
$500$	−48.8292	−	10.3790i	−2.18371	−	0.464161i
$501$	−26.6425	−	5.66303i	−1.19030	−	0.253006i
$502$	4.54256	−	43.2195i	0.202744	−	1.92898i
$503$	6.79200	−	4.93468i	0.302840	−	0.220026i	−0.425978	−	0.904734i	$-0.640070\pi$
$503$	6.79200	−	4.93468i	0.302840	−	0.220026i	0.728818	+	0.684707i	$0.240070\pi$
$504$	−8.61880	+	37.7111i	−0.383912	+	1.67979i
$505$	20.0115			0.890502
$506$	−14.1370	−	10.8686i	−0.628468	−	0.483168i
$507$	−14.3860	+	24.9172i	−0.638903	+	1.10661i
$508$	−64.9621	−	72.1477i	−2.88223	−	3.20104i
$509$	−1.13266	−	0.504291i	−0.0502041	−	0.0223523i	0.381481	−	0.924377i	$-0.375414\pi$
$509$	−1.13266	−	0.504291i	−0.0502041	−	0.0223523i	−0.431685	+	0.902024i	$0.642081\pi$
$510$	33.7522	+	24.5224i	1.49457	+	1.08587i
$511$	−6.81483	+	9.08517i	−0.301470	+	0.401904i
$512$	−10.9487	−	33.6967i	−0.483869	−	1.48920i
$513$	−0.490492	+	4.66672i	−0.0216558	+	0.206041i
$514$	−8.04685	−	76.5607i	−0.354931	−	3.37695i
$515$	13.2647	+	14.7319i	0.584513	+	0.649167i
$516$	−16.1799	−	28.0245i	−0.712282	−	1.23371i
$517$	−10.2983	−	2.48250i	−0.452917	−	0.109180i
$518$	−10.6657	−	15.1610i	−0.468625	−	0.666137i
$519$	−8.34818	+	25.6930i	−0.366444	+	1.12780i
$520$	−0.301499	−	0.134236i	−0.0132216	−	0.00588663i
$521$	39.9641	−	17.7932i	1.75086	−	0.779532i	0.759166	−	0.650897i	$-0.225607\pi$
$521$	39.9641	−	17.7932i	1.75086	−	0.779532i	0.991692	−	0.128635i	$-0.0410597\pi$
$522$	24.3403	+	5.17370i	1.06535	+	0.226447i
$523$	−20.4158	+	22.6740i	−0.892721	+	0.991467i	−0.999996	−	0.00276239i	$-0.999121\pi$
$523$	−20.4158	+	22.6740i	−0.892721	+	0.991467i	0.107275	+	0.994229i	$0.465787\pi$
$524$	64.4848	+	46.8510i	2.81703	+	2.04669i
$525$	15.9520	−	13.9287i	0.696204	−	0.607899i
$526$	−16.2087	+	49.8853i	−0.706734	+	2.17510i
$527$	8.62204	+	14.9338i	0.375582	+	0.650527i
$528$	−68.9264	−	32.9548i	−2.99964	−	1.43417i
$529$	9.41287	−	16.3036i	0.409255	−	0.708851i
$530$	−30.0192	+	6.38078i	−1.30395	+	0.277163i
$531$	−6.23827	+	4.53237i	−0.270718	+	0.196688i
$532$	−21.9252	+	12.2166i	−0.950580	+	0.529657i
$533$	−0.0920882	−	0.283418i	−0.00398878	−	0.0122762i
$534$	−16.8502	+	18.7140i	−0.729178	+	0.809834i
$535$	1.00226	−	0.446234i	0.0433314	−	0.0192924i
$536$	−1.81315	−	17.2510i	−0.0783161	−	0.745128i
$537$	8.25746	−	1.75518i	0.356336	−	0.0757415i
$538$	1.62815			0.0701944
$539$	−8.43362	+	21.6304i	−0.363262	+	0.931687i
$540$	−14.1147			−0.607399
$541$	−0.277681	+	0.0590230i	−0.0119384	+	0.00253760i	−0.213877	−	0.976861i	$-0.568609\pi$
$541$	−0.277681	+	0.0590230i	−0.0119384	+	0.00253760i	0.201939	+	0.979398i	$0.435276\pi$
$542$	0.0318553	+	0.303083i	0.00136830	+	0.0130185i
$543$	−14.2433	+	6.34153i	−0.611239	+	0.272141i
$544$	−48.8527	+	54.2564i	−2.09454	+	2.32622i
$545$	−0.590198	−	1.81644i	−0.0252813	−	0.0778078i
$546$	0.490650	−	0.273387i	0.0209979	−	0.0116999i
$547$	−8.71258	+	6.33006i	−0.372523	+	0.270654i	−0.758256	−	0.651957i	$-0.773948\pi$
$547$	−8.71258	+	6.33006i	−0.372523	+	0.270654i	0.385733	+	0.922610i	$0.373948\pi$
$548$	81.7844	−	17.3838i	3.49365	−	0.742599i
$549$	8.24192	−	14.2754i	0.351756	−	0.609260i
$550$	15.0342	+	27.7510i	0.641063	+	1.18331i
$551$	4.79461	+	8.30452i	0.204257	+	0.353784i
$552$	−10.7574	+	33.1080i	−0.457867	+	1.40917i
$553$	−6.18652	+	5.40184i	−0.263077	+	0.229710i
$554$	−20.5738	−	14.9478i	−0.874098	−	0.635070i
$555$	−4.63865	+	5.15174i	−0.196900	+	0.218679i
$556$	35.3942	+	7.52326i	1.50105	+	0.319057i
$557$	36.4980	−	16.2499i	1.54647	−	0.688532i	0.556634	−	0.830758i	$-0.312092\pi$
$557$	36.4980	−	16.2499i	1.54647	−	0.688532i	0.989834	+	0.142225i	$0.0454258\pi$
$558$	12.9323	+	5.75783i	0.547467	+	0.243748i
$559$	−0.0334309	+	0.102890i	−0.00141398	+	0.00435177i
$560$	−18.6366	−	26.4914i	−0.787540	−	1.11946i
$561$	−3.46559	−	44.5633i	−0.146317	−	1.88146i
$562$	4.55716	+	7.89323i	0.192232	+	0.332956i
$563$	−7.99139	−	8.87534i	−0.336797	−	0.374051i	0.550827	−	0.834619i	$-0.314312\pi$
$563$	−7.99139	−	8.87534i	−0.336797	−	0.374051i	−0.887624	+	0.460568i	$0.847646\pi$
$564$	3.63964	+	34.6289i	0.153257	+	1.45814i
$565$	0.435165	−	4.14031i	0.0183075	−	0.174184i
$566$	21.4193	+	65.9217i	0.900319	+	2.77090i
$567$	17.6072	−	23.4730i	0.739433	−	0.985773i
$568$	−26.4779	−	19.2374i	−1.11099	−	0.807181i
$569$	−10.0266	−	4.46414i	−0.420337	−	0.187146i	0.185658	−	0.982614i	$-0.440558\pi$
$569$	−10.0266	−	4.46414i	−0.420337	−	0.187146i	−0.605995	+	0.795468i	$0.707225\pi$
$570$	8.83125	+	9.80810i	0.369901	+	0.410816i
$571$	−3.74628	+	6.48874i	−0.156777	+	0.271545i	−0.933705	−	0.358044i	$-0.883444\pi$
$571$	−3.74628	+	6.48874i	−0.156777	+	0.271545i	0.776928	+	0.629590i	$0.216777\pi$
$572$	0.168557	+	0.570984i	0.00704771	+	0.0238740i
$573$	35.2515			1.47265
$574$	12.6840	−	55.4983i	0.529422	−	2.31646i
$575$	5.97720	−	4.34269i	0.249267	−	0.181103i
$576$	−2.13258	+	20.2902i	−0.0888576	+	0.845424i
$577$	35.0599	+	7.45221i	1.45956	+	0.310240i	0.868220	−	0.496180i	$-0.165264\pi$
$577$	35.0599	+	7.45221i	1.45956	+	0.310240i	0.591343	+	0.806420i	$0.298598\pi$
$578$	−51.6654	−	10.9818i	−2.14900	−	0.456783i
$579$	3.42374	−	32.5747i	0.142286	−	1.35376i
$580$	−23.3354	+	16.9541i	−0.968948	+	0.703982i
$581$	−11.7699	−	10.9272i	−0.488297	−	0.453337i
$582$	−27.0037			−1.11934
$583$	26.0672	+	20.0405i	1.07959	+	0.829994i
$584$	−16.5216	+	28.6162i	−0.683668	+	1.18415i
$585$	−0.0544891	−	0.0605163i	−0.00225285	−	0.00250204i
$586$	36.7585	+	16.3659i	1.51848	+	0.676071i
$587$	−8.11634	−	5.89686i	−0.334997	−	0.243390i	0.407551	−	0.913182i	$-0.366383\pi$
$587$	−8.11634	−	5.89686i	−0.334997	−	0.243390i	−0.742548	+	0.669793i	$0.766383\pi$
$588$	76.2759	+	2.32707i	3.14557	+	0.0959666i
$589$	1.68574	+	5.18816i	0.0694595	+	0.213774i
$590$	1.31367	−	12.4987i	0.0540828	−	0.514564i
$591$	1.91760	+	18.2448i	0.0788797	+	0.750490i
$592$	−18.5398	−	20.5906i	−0.761982	−	0.846267i
$593$	−14.1715	−	24.5458i	−0.581954	−	1.00797i	−0.995248	−	0.0973765i	$-0.968955\pi$
$593$	−14.1715	−	24.5458i	−0.581954	−	1.00797i	0.413293	−	0.910598i	$-0.364378\pi$
$594$	13.7941	+	16.1812i	0.565980	+	0.663924i
$595$	7.97073	−	17.1921i	0.326768	−	0.704807i
$596$	−7.64167	+	23.5186i	−0.313015	+	0.963361i
$597$	−36.9727	−	16.4613i	−1.51319	−	0.673716i
$598$	0.179013	−	0.0797018i	0.00732039	−	0.00325925i
$599$	−32.6564	−	6.94133i	−1.33430	−	0.283615i	−0.515106	−	0.857127i	$-0.672247\pi$
$599$	−32.6564	−	6.94133i	−1.33430	−	0.283615i	−0.819197	+	0.573512i	$0.805581\pi$
$600$	41.2285	−	45.7889i	1.68315	−	1.86932i
$601$	1.42697	+	1.03676i	0.0582074	+	0.0422901i	0.616508	−	0.787348i	$-0.288547\pi$
$601$	1.42697	+	1.03676i	0.0582074	+	0.0422901i	−0.558301	+	0.829638i	$0.688547\pi$
$602$	−15.5677	+	13.5932i	−0.634494	+	0.554017i
$603$	1.32259	−	4.07052i	0.0538601	−	0.165764i
$604$	−20.6806	−	35.8199i	−0.841482	−	1.45749i
$605$	−4.65967	+	12.0718i	−0.189443	+	0.490790i
$606$	−49.5446	+	85.8138i	−2.01261	+	3.48595i
$607$	13.9937	−	2.97445i	0.567985	−	0.120729i	0.0850370	−	0.996378i	$-0.472899\pi$
$607$	13.9937	−	2.97445i	0.567985	−	0.120729i	0.482948	+	0.875649i	$0.339566\pi$
$608$	−18.6854	+	13.5757i	−0.757792	+	0.550568i
$609$	0.444586	−	29.1518i	0.0180155	−	1.18129i
$610$	8.30204	+	25.5510i	0.336140	+	1.03453i
$611$	0.0778921	−	0.0865080i	0.00315118	−	0.00349974i
$612$	−52.0333	+	23.1667i	−2.10332	+	0.936459i
$613$	0.595783	+	5.66850i	0.0240634	+	0.228948i	0.999943	+	0.0106405i	$0.00338703\pi$
$613$	0.595783	+	5.66850i	0.0240634	+	0.228948i	−0.975880	+	0.218308i	$0.929946\pi$
$614$	−82.7848	+	17.5964i	−3.34092	+	0.710135i
$615$	−21.2903			−0.858506
$616$	−16.8292	+	65.4178i	−0.678068	+	2.63576i
$617$	17.9653			0.723257			0.361628	−	0.932322i	$-0.382221\pi$
$617$	17.9653			0.723257			0.361628	+	0.932322i	$0.382221\pi$
$618$	−96.0146	+	20.4085i	−3.86227	+	0.820952i
$619$	−0.636885	−	6.05956i	−0.0255986	−	0.243554i	−0.999837	−	0.0180353i	$-0.994259\pi$
$619$	−0.636885	−	6.05956i	−0.0255986	−	0.243554i	0.974239	−	0.225519i	$-0.0724078\pi$
$620$	−14.9903	+	6.67411i	−0.602025	+	0.268039i
$621$	3.33051	−	3.69891i	0.133649	−	0.148432i
$622$	1.72257	+	5.30152i	0.0690688	+	0.212572i
$623$	9.81739	+	5.86948i	0.393325	+	0.235156i
$624$	0.679206	−	0.493472i	0.0271900	−	0.0197547i
$625$	−6.02315	+	1.28026i	−0.240926	+	0.0512104i
$626$	8.07689	−	13.9896i	0.322817	−	0.559136i
$627$	1.85867	−	14.0174i	0.0742281	−	0.559803i
$628$	36.8076	+	63.7526i	1.46878	+	2.54400i
$629$	5.00926	−	15.4169i	0.199732	−	0.614713i
$630$	−3.00198	−	15.2642i	−0.119602	−	0.608139i
$631$	−35.8264	−	26.0294i	−1.42623	−	1.03621i	−0.990704	−	0.136036i	$-0.956564\pi$
$631$	−35.8264	−	26.0294i	−1.42623	−	1.03621i	−0.435522	−	0.900178i	$-0.643436\pi$
$632$	−15.9893	+	17.7579i	−0.636018	+	0.706370i
$633$	51.1050	+	10.8627i	2.03124	+	0.431754i
$634$	−42.7296	+	19.0244i	−1.69701	+	0.755556i
$635$	21.1835	+	9.43149i	0.840641	+	0.374277i
$636$	33.3975	−	102.787i	1.32430	−	4.07577i
$637$	−0.164849	−	0.194710i	−0.00653156	−	0.00771470i
$638$	42.2418	+	10.1828i	1.67237	+	0.403143i
$639$	−4.03776	−	6.99361i	−0.159731	−	0.276663i
$640$	−3.37263	−	3.74569i	−0.133315	−	0.148061i
$641$	−4.00363	−	38.0920i	−0.158134	−	1.50454i	−0.729575	−	0.683901i	$-0.760282\pi$
$641$	−4.00363	−	38.0920i	−0.158134	−	1.50454i	0.571441	−	0.820643i	$-0.306385\pi$
$642$	−0.567846	+	5.40269i	−0.0224111	+	0.213227i
$643$	−8.87538	−	27.3156i	−0.350011	−	1.07722i	−0.958846	−	0.283926i	$-0.908363\pi$
$643$	−8.87538	−	27.3156i	−0.350011	−	1.07722i	0.608835	−	0.793297i	$-0.291637\pi$
$644$	26.4318	+	3.18631i	1.04156	+	0.125558i
$645$	6.25291	+	4.54301i	0.246208	+	0.178881i
$646$	−28.1937	−	12.5527i	−1.10927	−	0.493878i
$647$	−13.6948	−	15.2096i	−0.538399	−	0.597953i	0.411152	−	0.911567i	$-0.365127\pi$
$647$	−13.6948	−	15.2096i	−0.538399	−	0.597953i	−0.949550	+	0.313614i	$0.898460\pi$
$648$	42.6862	−	73.9346i	1.67687	−	2.90443i
$649$	−11.1036	+	7.61612i	−0.435854	+	0.298959i
$650$	−0.346829			−0.0136038
$651$	3.69539	−	16.1690i	0.144834	−	0.633713i
$652$	−9.91604	+	7.20442i	−0.388342	+	0.282147i
$653$	−2.95381	+	28.1036i	−0.115591	+	1.09978i	0.770875	+	0.636986i	$0.219819\pi$
$653$	−2.95381	+	28.1036i	−0.115591	+	1.09978i	−0.886467	+	0.462793i	$0.846847\pi$
$654$	9.25052	+	1.96626i	0.361724	+	0.0768868i
$655$	−18.6218	−	3.95819i	−0.727615	−	0.154659i
$656$	8.89467	−	84.6271i	0.347279	−	3.30413i
$657$	−6.59604	+	4.79231i	−0.257336	+	0.186966i
$658$	21.2520	−	6.54863i	0.828488	−	0.255292i
$659$	25.1666			0.980350			0.490175	−	0.871624i	$-0.336933\pi$
$659$	25.1666			0.980350			0.490175	+	0.871624i	$0.336933\pi$
$660$	42.5174	+	1.15285i	1.65499	+	0.0448747i
$661$	−10.3561	+	17.9373i	−0.402805	+	0.697679i	−0.994063	−	0.108803i	$-0.965298\pi$
$661$	−10.3561	+	17.9373i	−0.402805	+	0.697679i	0.591258	+	0.806483i	$0.298632\pi$
$662$	34.4526	+	38.2635i	1.33904	+	1.48715i
$663$	0.448715	+	0.199781i	0.0174266	+	0.00775884i
$664$	−37.8033	−	27.4657i	−1.46705	−	1.06588i
$665$	3.59720	−	4.79560i	0.139494	−	0.185966i
$666$	−4.11224	−	12.6562i	−0.159346	−	0.490417i
$667$	1.06321	−	10.1158i	0.0411678	−	0.391686i
$668$	6.33513	+	60.2747i	0.245114	+	2.33210i
$669$	17.8855	+	19.8639i	0.691493	+	0.767981i
$670$	3.48785	+	6.04113i	0.134747	+	0.233389i
$671$	15.0621	−	24.5280i	0.581467	−	0.946895i
$672$	69.9417	−	6.27445i	2.69806	−	0.242042i
$673$	−6.06417	+	18.6636i	−0.233757	+	0.719429i	0.763527	+	0.645776i	$0.223466\pi$
$673$	−6.06417	+	18.6636i	−0.233757	+	0.719429i	−0.997284	+	0.0736535i	$0.976534\pi$
$674$	55.4480	+	24.6870i	2.13578	+	0.950909i
$675$	−8.04806	+	3.58323i	−0.309770	+	0.137919i
$676$	62.6216	+	13.3106i	2.40852	+	0.511948i
$677$	15.2531	−	16.9403i	0.586226	−	0.651070i	−0.374938	−	0.927050i	$-0.622336\pi$
$677$	15.2531	−	16.9403i	0.586226	−	0.651070i	0.961163	+	0.275981i	$0.0890025\pi$
$678$	16.6772	+	12.1167i	0.640484	+	0.465339i
$679$	2.36690	+	12.0350i	0.0908334	+	0.461861i
$680$	17.0376	−	52.4363i	0.653361	−	2.01084i
$681$	−11.4295	−	19.7965i	−0.437980	−	0.758603i
$682$	22.3011	+	10.6625i	0.853955	+	0.408289i
$683$	11.9753	−	20.7418i	0.458222	−	0.793664i	−0.540645	−	0.841251i	$-0.681820\pi$
$683$	11.9753	−	20.7418i	0.458222	−	0.793664i	0.998867	+	0.0475871i	$0.0151532\pi$
$684$	−17.6247	+	3.74625i	−0.673899	+	0.143242i
$685$	−16.1563	+	11.7382i	−0.617300	+	0.448495i
$686$	−7.94229	−	48.0859i	−0.303238	−	1.83593i
$687$	18.8512	+	58.0181i	0.719219	+	2.21353i
$688$	−20.6704	+	22.9569i	−0.788053	+	0.875222i
$689$	−0.330081	+	0.146962i	−0.0125751	+	0.00559879i
$690$	−1.46335	−	13.9229i	−0.0557089	−	0.530034i
$691$	−40.0438	+	8.51156i	−1.52334	+	0.323795i	−0.892115	−	0.451808i	$-0.850779\pi$
$691$	−40.0438	+	8.51156i	−1.52334	+	0.323795i	−0.631221	+	0.775603i	$0.717446\pi$
$692$	60.1119			2.28511
$693$	−10.3588	+	13.0569i	−0.393497	+	0.495990i
$694$	−65.8980			−2.50145
$695$	−8.45376	+	1.79690i	−0.320669	+	0.0681603i
$696$	−8.86681	−	84.3621i	−0.336096	−	3.19774i
$697$	45.4802	−	20.2491i	1.72268	−	0.766989i
$698$	34.4591	−	38.2707i	1.30430	−	1.44857i
$699$	−2.73611	−	8.42088i	−0.103489	−	0.318507i
$700$	−40.4445	−	24.1804i	−1.52866	−	0.913933i
$701$	−8.05784	+	5.85436i	−0.304340	+	0.221116i	−0.729464	−	0.684019i	$-0.760231\pi$
$701$	−8.05784	+	5.85436i	−0.304340	+	0.221116i	0.425124	+	0.905135i	$0.360231\pi$
$702$	−0.228549	+	0.0485797i	−0.00862604	+	0.00183352i
$703$	2.56406	−	4.44108i	0.0967054	−	0.167499i
$704$	−4.68281	+	35.3161i	−0.176490	+	1.33103i
$705$	−4.15826	−	7.20232i	−0.156609	−	0.271255i
$706$	16.4487	−	50.6240i	0.619057	−	1.90526i
$707$	42.5882	+	14.5594i	1.60169	+	0.547562i
$708$	35.8052	+	26.0140i	1.34564	+	0.977665i
$709$	−31.7961	+	35.3132i	−1.19413	+	1.32621i	−0.261574	+	0.965183i	$0.584242\pi$
$709$	−31.7961	+	35.3132i	−1.19413	+	1.32621i	−0.932554	+	0.361031i	$0.882425\pi$
$710$	12.8742	+	2.73649i	0.483159	+	0.102699i
$711$	−5.38631	+	2.39814i	−0.202002	+	0.0899373i
$712$	30.4021	+	13.5359i	1.13937	+	0.507279i
$713$	1.78810	−	5.50321i	0.0669649	−	0.206097i
$714$	53.9895	+	76.7445i	2.02051	+	2.87209i
$715$	−0.0922481	−	0.108212i	−0.00344988	−	0.00404689i
$716$	−9.39211	−	16.2676i	−0.351000	−	0.607949i
$717$	−31.4344	−	34.9115i	−1.17394	−	1.30379i
$718$	6.85574	+	65.2280i	0.255854	+	2.43429i
$719$	−2.06385	+	19.6362i	−0.0769686	+	0.732307i	0.886181	+	0.463340i	$0.153349\pi$
$719$	−2.06385	+	19.6362i	−0.0769686	+	0.732307i	−0.963149	+	0.268968i	$0.913318\pi$
$720$	−7.18547	−	22.1146i	−0.267787	−	0.824162i
$721$	17.5115	+	41.0030i	0.652161	+	1.52703i
$722$	32.5522	+	23.6506i	1.21147	+	0.880182i
$723$	27.5136	+	12.2499i	1.02324	+	0.455577i
$724$	23.2136	+	25.7813i	0.862727	+	0.958155i
$725$	−9.00155	+	15.5911i	−0.334309	+	0.579040i
$726$	−40.2302	−	49.8692i	−1.49308	−	1.85082i
$727$	38.0241			1.41024			0.705118	−	0.709090i	$-0.250894\pi$
$727$	38.0241			1.41024			0.705118	+	0.709090i	$0.250894\pi$
$728$	−0.543980	−	0.505033i	−0.0201612	−	0.0187178i
$729$	3.95434	−	2.87300i	0.146457	−	0.106407i
$730$	1.38901	−	13.2155i	0.0514095	−	0.489129i
$731$	−17.6783	−	3.75763i	−0.653855	−	0.138981i
$732$	−92.5431	−	19.6706i	−3.42049	−	0.727048i
$733$	−2.99094	+	28.4569i	−0.110473	+	1.05108i	0.789086	+	0.614282i	$0.210554\pi$
$733$	−2.99094	+	28.4569i	−0.110473	+	1.05108i	−0.899559	+	0.436798i	$0.856112\pi$
$734$	−15.9450	+	11.5847i	−0.588542	+	0.427601i
$735$	−16.8692	+	6.90225i	−0.622230	+	0.254593i
$736$	24.4989			0.903042
$737$	2.50127	−	7.04260i	0.0921356	−	0.259417i
$738$	20.4346	−	35.3938i	0.752210	−	1.30287i
$739$	6.06096	+	6.73137i	0.222956	+	0.247618i	0.844237	−	0.535970i	$-0.180054\pi$
$739$	6.06096	+	6.73137i	0.222956	+	0.247618i	−0.621281	+	0.783588i	$0.713387\pi$
$740$	14.0916	+	6.27400i	0.518019	+	0.230637i
$741$	0.125709	+	0.0913326i	0.00461802	+	0.00335519i
$742$	−68.5286	−	8.26100i	−2.51577	−	0.303271i
$743$	2.57977	+	7.93973i	0.0946427	+	0.291280i	0.987160	−	0.159732i	$-0.0510630\pi$
$743$	2.57977	+	7.93973i	0.0946427	+	0.291280i	−0.892518	+	0.451012i	$0.851063\pi$
$744$	5.04418	−	47.9922i	0.184929	−	1.75948i
$745$	−0.617388	−	5.87406i	−0.0226194	−	0.215209i
$746$	−2.82615	−	3.13875i	−0.103473	−	0.114918i
$747$	−5.76482	−	9.98496i	−0.210924	−	0.365331i
$748$	−91.9221	+	37.9754i	−3.36100	+	1.38852i
$749$	2.45764	−	0.220474i	0.0898003	−	0.00805596i
$750$	−18.2441	+	56.1495i	−0.666179	+	2.05029i
$751$	44.9611	+	20.0180i	1.64065	+	0.730466i	0.999323	−	0.0367995i	$-0.0117163\pi$
$751$	44.9611	+	20.0180i	1.64065	+	0.730466i	0.641330	+	0.767265i	$0.278383\pi$
$752$	30.3659	−	13.5198i	1.10733	−	0.493015i
$753$	−35.7541	−	7.59976i	−1.30295	−	0.276951i
$754$	−0.319501	+	0.354842i	−0.0116356	+	0.0129226i
$755$	7.99225	+	5.80671i	0.290868	+	0.211328i
$756$	−30.0386	−	10.2691i	−1.09249	−	0.373484i
$757$	6.92221	−	21.3044i	0.251592	−	0.774320i	−0.742890	−	0.669413i	$-0.766546\pi$
$757$	6.92221	−	21.3044i	0.251592	−	0.774320i	0.994482	−	0.104907i	$-0.0334545\pi$
$758$	−22.4292	−	38.8485i	−0.814665	−	1.41104i
$759$	−10.3346	+	10.8702i	−0.375122	+	0.394562i
$760$	8.72092	−	15.1051i	0.316341	−	0.547919i
$761$	24.8315	−	5.27809i	0.900140	−	0.191331i	0.265474	−	0.964118i	$-0.414471\pi$
$761$	24.8315	−	5.27809i	0.900140	−	0.191331i	0.634665	+	0.772787i	$0.281138\pi$
$762$	−92.8905	+	67.4889i	−3.36507	+	2.44486i
$763$	0.0655036	−	4.29511i	0.00237139	−	0.155494i
$764$	−24.2388	−	74.5993i	−0.876928	−	2.69891i
$765$	9.10291	−	10.1098i	0.329116	−	0.365521i
$766$	−41.8837	+	18.6478i	−1.51332	+	0.673774i
$767$	−0.0154661	−	0.147150i	−0.000558449	−	0.00531329i
$768$	−22.0998	+	4.69746i	−0.797458	+	0.169505i
$769$	−44.5582			−1.60681			−0.803406	−	0.595432i	$-0.796981\pi$
$769$	−44.5582			−1.60681			−0.803406	+	0.595432i	$0.796981\pi$
$770$	−4.51758	−	26.7861i	−0.162802	−	0.965304i
$771$	−64.7510			−2.33195
$772$	−71.2887	+	15.1529i	−2.56574	+	0.545364i
$773$	−3.45360	−	32.8588i	−0.124217	−	1.18185i	−0.862035	−	0.506848i	$-0.830810\pi$
$773$	−3.45360	−	32.8588i	−0.124217	−	1.18185i	0.737818	−	0.675000i	$-0.235856\pi$
$774$	−13.5541	+	6.03468i	−0.487192	+	0.216912i
$775$	−6.85301	+	7.61104i	−0.246167	+	0.273397i
$776$	11.0277	+	33.9399i	0.395873	+	1.21837i
$777$	−13.6200	+	7.58899i	−0.488616	+	0.272253i
$778$	23.9204	−	17.3792i	0.857589	−	0.623075i
$779$	15.4051	−	3.27445i	0.551943	−	0.117319i
$780$	−0.233696	+	0.404772i	−0.00836764	+	0.0144932i
$781$	−6.71702	−	12.3986i	−0.240354	−	0.443658i
$782$	16.3680	+	28.3502i	0.585318	+	1.01380i
$783$	−3.74792	+	11.5349i	−0.133940	+	0.412224i
$784$	−20.3883	−	69.9374i	−0.728152	−	2.49777i
$785$	−14.2247	−	10.3348i	−0.507701	−	0.368866i
$786$	63.0776	−	70.0547i	2.24990	−	2.49877i
$787$	−42.2344	−	8.97720i	−1.50549	−	0.320003i	−0.619981	−	0.784617i	$-0.712860\pi$
$787$	−42.2344	−	8.97720i	−1.50549	−	0.320003i	−0.885513	+	0.464615i	$0.846193\pi$
$788$	37.2911	−	16.6031i	1.32844	−	0.591460i
$789$	40.3043	+	17.9446i	1.43487	+	0.638846i
$790$	2.96953	−	9.13927i	0.105651	−	0.325161i
$791$	3.93839	−	8.49473i	0.140033	−	0.302038i
$792$	−25.3755	+	41.3229i	−0.901679	+	1.46835i
$793$	0.158150	+	0.273923i	0.00561606	+	0.00972729i
$794$	34.7039	+	38.5425i	1.23159	+	1.36782i
$795$	2.69827	+	25.6723i	0.0956976	+	0.910502i
$796$	−9.41318	+	89.5604i	−0.333641	+	3.17439i
$797$	−3.31341	−	10.1976i	−0.117367	−	0.361218i	0.875066	−	0.484003i	$-0.160818\pi$
$797$	−3.31341	−	10.1976i	−0.117367	−	0.361218i	−0.992433	+	0.122785i	$0.960818\pi$
$798$	11.6586	+	27.2986i	0.412711	+	0.966359i
$799$	15.7330	+	11.4307i	0.556592	+	0.404388i
$800$	−39.6130	−	17.6369i	−1.40053	−	0.623557i
$801$	5.49451	+	6.10227i	0.194139	+	0.215613i
$802$	16.4977	−	28.5748i	0.582553	−	1.00901i
$803$	−11.7404	+	8.05291i	−0.414309	+	0.284181i
$804$	−24.5654			−0.866356
$805$	−6.07688	+	1.87254i	−0.214182	+	0.0659984i
$806$	−0.219757	+	0.159663i	−0.00774061	+	0.00562388i
$807$	0.143147	−	1.36196i	0.00503902	−	0.0479431i
$808$	128.089	+	27.2262i	4.50616	+	0.957813i
$809$	1.12546	+	0.239224i	0.0395690	+	0.00841066i	0.227654	−	0.973742i	$-0.426895\pi$
$809$	1.12546	+	0.239224i	0.0395690	+	0.00841066i	−0.188085	+	0.982153i	$0.560228\pi$
$810$	−3.58872	+	34.1444i	−0.126095	+	1.19971i
$811$	28.6938	−	20.8473i	1.00758	−	0.732047i	0.0438772	−	0.999037i	$-0.486029\pi$
$811$	28.6938	−	20.8473i	1.00758	−	0.732047i	0.963699	+	0.266990i	$0.0860290\pi$
$812$	−61.9968	+	19.1038i	−2.17566	+	0.670413i
$813$	0.256331			0.00898993
$814$	−6.57902	−	22.2864i	−0.230595	−	0.781136i
$815$	1.46375	−	2.53530i	0.0512731	−	0.0888076i
$816$	93.8479	+	104.229i	3.28533	+	3.64873i
$817$	−5.22315	−	2.32550i	−0.182735	−	0.0813588i
$818$	−33.2244	−	24.1389i	−1.16166	−	0.843997i
$819$	−0.0719341	−	0.168433i	−0.00251358	−	0.00588553i
$820$	14.6391	+	45.0545i	0.511220	+	1.57337i
$821$	−2.06152	+	19.6140i	−0.0719475	+	0.684535i	0.897796	+	0.440411i	$0.145167\pi$
$821$	−2.06152	+	19.6140i	−0.0719475	+	0.684535i	−0.969744	+	0.244124i	$0.921500\pi$
$822$	−10.3363	−	98.3432i	−0.360519	−	3.43011i
$823$	27.3181	+	30.3398i	0.952248	+	1.05758i	0.998279	+	0.0586382i	$0.0186758\pi$
$823$	27.3181	+	30.3398i	0.952248	+	1.05758i	−0.0460316	+	0.998940i	$0.514658\pi$
$824$	64.8610	+	112.343i	2.25954	+	3.91364i
$825$	24.5357	−	10.1364i	0.854225	−	0.352903i
$826$	11.8892	−	25.6438i	0.413676	−	0.892260i
$827$	−0.289657	+	0.891474i	−0.0100724	+	0.0309996i	−0.955966	−	0.293476i	$-0.905188\pi$
$827$	−0.289657	+	0.891474i	−0.0100724	+	0.0309996i	0.945894	+	0.324476i	$0.105188\pi$
$828$	17.4603	+	7.77382i	0.606787	+	0.270159i
$829$	−13.9732	+	6.22128i	−0.485310	+	0.216074i	−0.634781	−	0.772692i	$-0.718910\pi$
$829$	−13.9732	+	6.22128i	−0.485310	+	0.216074i	0.149471	+	0.988766i	$0.452243\pi$
$830$	18.3808	+	3.90696i	0.638007	+	0.135612i
$831$	−14.3128	+	15.8959i	−0.496504	+	0.551424i
$832$	−0.316715	−	0.230107i	−0.0109801	−	0.00797753i
$833$	29.4712	−	30.7888i	1.02112	−	1.06677i
$834$	13.2243	−	40.7003i	0.457921	−	1.40934i
$835$	−7.23784	−	12.5363i	−0.250476	−	0.433837i
$836$	−30.9418	+	5.70501i	−1.07014	+	0.197312i
$837$	−3.44985	+	5.97532i	−0.119244	+	0.206537i
$838$	81.9024	−	17.4089i	2.82927	−	0.601380i
$839$	−11.3598	+	8.25338i	−0.392184	+	0.284938i	−0.766350	−	0.642423i	$-0.777929\pi$
$839$	−11.3598	+	8.25338i	−0.392184	+	0.284938i	0.374166	+	0.927362i	$0.377929\pi$
$840$	−46.3246	+	25.8118i	−1.59835	+	0.890591i
$841$	−1.30243	−	4.00846i	−0.0449113	−	0.138223i
$842$	42.0517	−	46.7032i	1.44920	−	1.60950i
$843$	7.00340	−	3.11812i	0.241210	−	0.107394i
$844$	−12.1519	−	115.618i	−0.418286	−	3.97972i
$845$	−14.9569	+	3.17919i	−0.514534	+	0.109368i
$846$	15.9646			0.548874
$847$	−18.6995	+	22.3009i	−0.642522	+	0.766268i
$848$	−103.173			−3.54296
$849$	57.0271	−	12.1215i	1.95717	−	0.416009i
$850$	−6.05648	−	57.6236i	−0.207736	−	1.97647i
$851$	−4.96925	+	2.21245i	−0.170344	+	0.0758420i
$852$	−31.0144	+	34.4449i	−1.06253	+	1.18006i
$853$	1.13225	+	3.48472i	0.0387677	+	0.119315i	0.968567	−	0.248751i	$-0.0800201\pi$
$853$	1.13225	+	3.48472i	0.0387677	+	0.119315i	−0.929800	+	0.368066i	$0.880020\pi$
$854$	−0.921408	+	60.4174i	−0.0315299	+	2.06744i
$855$	3.48172	−	2.52962i	0.119072	−	0.0865111i
$856$	7.02232	−	1.49264i	0.240018	−	0.0510174i
$857$	−2.52090	+	4.36633i	−0.0861124	+	0.149151i	−0.905865	−	0.423567i	$-0.860778\pi$
$857$	−2.52090	+	4.36633i	−0.0861124	+	0.149151i	0.819752	+	0.572718i	$0.194111\pi$
$858$	0.692424	−	0.127669i	0.0236390	−	0.00435853i
$859$	−26.8888	−	46.5728i	−0.917434	−	1.58904i	−0.803298	−	0.595578i	$-0.796923\pi$
$859$	−26.8888	−	46.5728i	−0.917434	−	1.58904i	−0.114137	−	0.993465i	$-0.536410\pi$
$860$	5.31445	−	16.3562i	0.181221	−	0.557741i
$861$	−45.3095	−	15.4897i	−1.54414	−	0.527888i
$862$	17.7640	+	12.9063i	0.605043	+	0.439590i
$863$	−22.2649	+	24.7276i	−0.757904	+	0.841738i	−0.991434	−	0.130612i	$-0.958306\pi$
$863$	−22.2649	+	24.7276i	−0.757904	+	0.841738i	0.233529	+	0.972350i	$0.424973\pi$
$864$	−28.5741	−	6.07361i	−0.972110	−	0.206628i
$865$	−13.1162	+	5.83971i	−0.445964	+	0.198556i
$866$	30.8597	+	13.7396i	1.04866	+	0.466892i
$867$	−13.7288	+	42.2529i	−0.466255	+	1.43498i
$868$	−36.7578	+	3.29753i	−1.24764	+	0.111926i
$869$	−9.51545	+	3.93109i	−0.322790	+	0.133353i
$870$	17.0565	+	29.5428i	0.578271	+	1.00160i
$871$	0.0549533	+	0.0610318i	0.00186202	+	0.00206798i
$872$	−1.30640	−	12.4296i	−0.0442404	−	0.420919i
$873$	−0.920412	+	8.75714i	−0.0311512	+	0.296384i
$874$	3.20018	+	9.84914i	0.108248	+	0.333152i
$875$	26.6238	+	3.20945i	0.900049	+	0.108499i
$876$	37.8586	+	27.5059i	1.27912	+	0.929338i
$877$	−12.0283	−	5.35537i	−0.406168	−	0.180838i	0.193475	−	0.981105i	$-0.438024\pi$
$877$	−12.0283	−	5.35537i	−0.406168	−	0.180838i	−0.599643	+	0.800267i	$0.704691\pi$
$878$	−43.3140	−	48.1050i	−1.46178	−	1.62347i
$879$	16.9220	−	29.3098i	0.570766	−	0.988596i
$880$	−11.4958	−	38.9417i	−0.387522	−	1.31272i
$881$	−33.1960			−1.11840			−0.559201	−	0.829032i	$-0.688892\pi$
$881$	−33.1960			−1.11840			−0.559201	+	0.829032i	$0.688892\pi$
$882$	4.71668	−	34.6690i	0.158819	−	1.16736i
$883$	25.2028	−	18.3109i	0.848143	−	0.616212i	−0.0764906	−	0.997070i	$-0.524372\pi$
$883$	25.2028	−	18.3109i	0.848143	−	0.616212i	0.924633	+	0.380859i	$0.124372\pi$
$884$	0.114242	−	1.08694i	0.00384237	−	0.0365577i
$885$	−10.3398	−	2.19778i	−0.347567	−	0.0738777i
$886$	41.5120	+	8.82365i	1.39462	+	0.296436i
$887$	3.46334	−	32.9515i	0.116288	−	1.10640i	−0.768320	−	0.640066i	$-0.778907\pi$
$887$	3.46334	−	32.9515i	0.116288	−	1.10640i	0.884608	−	0.466336i	$-0.154426\pi$
$888$	−36.6999	+	26.6641i	−1.23157	+	0.894787i
$889$	38.2204	+	35.4839i	1.28187	+	1.19009i
$890$	−13.3833			−0.448608
$891$	30.3332	−	20.8060i	1.01620	−	0.697027i
$892$	29.7380	−	51.5076i	0.995700	−	1.72460i
$893$	4.11652	+	4.57186i	0.137754	+	0.152992i
$894$	26.7178	+	11.8955i	0.893576	+	0.397846i
$895$	3.62968	+	2.63712i	0.121327	+	0.0881492i
$896$	−4.45240	−	10.4253i	−0.148744	−	0.348283i
$897$	−0.0509322	−	0.156753i	−0.00170058	−	0.00523384i
$898$	−9.47988	+	90.1950i	−0.316348	+	3.00985i
$899$	1.47384	+	14.0227i	0.0491554	+	0.467683i
$900$	−22.6356	−	25.1394i	−0.754521	−	0.837981i
$901$	−30.1808	−	52.2747i	−1.00547	−	1.74152i
$902$	37.3444	−	60.8138i	1.24343	−	2.02488i
$903$	10.0021	+	14.2176i	0.332848	+	0.473133i
$904$	8.41838	−	25.9091i	0.279991	−	0.861724i
$905$	−7.56972	−	3.37026i	−0.251626	−	0.112031i
$906$	−44.6877	+	19.8962i	−1.48465	+	0.661008i
$907$	−11.0937	−	2.35804i	−0.368360	−	0.0782973i	0.0200127	−	0.999800i	$-0.493629\pi$
$907$	−11.0937	−	2.35804i	−0.368360	−	0.0782973i	−0.388373	+	0.921502i	$0.626963\pi$
$908$	−34.0345	+	37.7992i	−1.12947	+	1.25441i
$909$	26.1402	+	18.9920i	0.867016	+	0.629924i
$910$	0.282457	+	0.0965619i	0.00936334	+	0.00320099i
$911$	−9.02202	+	27.7669i	−0.298913	+	0.919959i	0.682966	+	0.730450i	$0.260690\pi$
$911$	−9.02202	+	27.7669i	−0.298913	+	0.919959i	−0.981879	+	0.189509i	$0.939310\pi$
$912$	22.1846	+	38.4248i	0.734604	+	1.27237i
$913$	−9.59006	−	17.7019i	−0.317385	−	0.585846i
$914$	42.6948	−	73.9495i	1.41222	−	2.44603i
$915$	22.1035	−	4.69825i	0.730720	−	0.155319i
$916$	109.816	−	79.7860i	3.62842	−	2.63620i
$917$	−36.7508	−	21.9720i	−1.21362	−	0.725580i
$918$	−12.0623	−	37.1238i	−0.398114	−	1.22527i
$919$	9.73920	−	10.8165i	0.321266	−	0.356803i	−0.560780	−	0.827965i	$-0.689499\pi$
$919$	9.73920	−	10.8165i	0.321266	−	0.356803i	0.882047	+	0.471162i	$0.156165\pi$
$920$	−16.9015	+	7.52503i	−0.557226	+	0.248093i
$921$	7.44108	+	70.7971i	0.245192	+	2.33284i
$922$	75.9280	−	16.1390i	2.50056	−	0.531510i
$923$	0.154957			0.00510046
$924$	89.6460	+	33.3870i	2.94914	+	1.09835i
$925$	9.62768			0.316556
$926$	−57.2956	+	12.1786i	−1.88285	+	0.400212i
$927$	3.34574	+	31.8326i	0.109889	+	1.04552i
$928$	−54.5361	+	24.2810i	−1.79024	+	0.797064i
$929$	−4.40136	+	4.88821i	−0.144404	+	0.160377i	−0.811008	−	0.585035i	$-0.801081\pi$
$929$	−4.40136	+	4.88821i	−0.144404	+	0.160377i	0.666604	+	0.745412i	$0.267747\pi$
$930$	5.99690	+	18.4566i	0.196646	+	0.605214i
$931$	11.1445	−	7.58877i	0.365247	−	0.248712i
$932$	−15.9389	+	11.5803i	−0.522098	+	0.379326i
$933$	4.58621	−	0.974829i	0.150146	−	0.0319145i
$934$	−31.1289	+	53.9168i	−1.01857	+	1.76421i
$935$	16.3679	−	17.2161i	0.535287	−	0.563027i
$936$	−0.266438	−	0.461484i	−0.00870880	−	0.0150841i
$937$	−9.37722	+	28.8601i	−0.306340	+	0.942818i	0.672833	+	0.739794i	$0.265077\pi$
$937$	−9.37722	+	28.8601i	−0.306340	+	0.942818i	−0.979174	+	0.203024i	$0.934923\pi$
$938$	3.02755	+	15.3942i	0.0988530	+	0.502638i
$939$	−10.9923	−	7.98634i	−0.358719	−	0.260624i
$940$	−12.3824	+	13.7520i	−0.403868	+	0.448541i
$941$	14.9130	+	3.16985i	0.486149	+	0.103334i	0.444464	−	0.895797i	$-0.353394\pi$
$941$	14.9130	+	3.16985i	0.486149	+	0.103334i	0.0416850	+	0.999131i	$0.486727\pi$
$942$	79.5356	−	35.4115i	2.59141	−	1.15377i
$943$	−15.2613	−	6.79477i	−0.496977	−	0.221268i
$944$	13.0558	−	40.1815i	0.424929	−	1.30780i
$945$	7.55193	−	0.677482i	0.245664	−	0.0220385i
$946$	−23.9447	+	9.89218i	−0.778509	+	0.321623i
$947$	−15.6044	−	27.0276i	−0.507075	−	0.878280i	−0.999966	−	0.00818941i	$-0.997393\pi$
$947$	−15.6044	−	27.0276i	−0.507075	−	0.878280i	0.492891	−	0.870091i	$-0.335940\pi$
$948$	22.6440	+	25.1487i	0.735443	+	0.816792i
$949$	−0.0163531	−	0.155589i	−0.000530844	−	0.00505065i
$950$	1.91596	−	18.2292i	0.0621621	−	0.591433i
$951$	12.1573	+	37.4162i	0.394226	+	1.21330i
$952$	74.4090	−	99.1981i	2.41161	−	3.21503i
$953$	−17.4834	−	12.7024i	−0.566342	−	0.411471i	0.267433	−	0.963577i	$-0.413825\pi$
$953$	−17.4834	−	12.7024i	−0.566342	−	0.411471i	−0.833774	+	0.552105i	$0.813825\pi$
$954$	−45.2685	−	20.1548i	−1.46562	−	0.652537i
$955$	12.5359	+	13.9226i	0.405654	+	0.450524i
$956$	−52.2656	+	90.5266i	−1.69039	+	2.92784i
$957$	12.2319	−	34.4403i	0.395402	−	1.11330i
$958$	−30.4063			−0.982384
$959$	−42.9236	+	13.2266i	−1.38608	+	0.427108i
$960$	−22.6271	+	16.4395i	−0.730285	+	0.530583i
$961$	2.40194	−	22.8529i	0.0774819	−	0.737191i
$962$	0.249770	+	0.0530903i	0.00805292	+	0.00171170i
$963$	1.73271	+	0.368298i	0.0558357	+	0.0118682i
$964$	7.00492	−	66.6473i	0.225613	−	2.14657i
$965$	14.0829	−	10.2318i	0.453345	−	0.329374i
$966$	7.01529	−	30.6950i	0.225713	−	0.987596i
$967$	5.74025			0.184594			0.0922970	−	0.995732i	$-0.470579\pi$
$967$	5.74025			0.184594			0.0922970	+	0.995732i	$0.470579\pi$
$968$	−46.2494	+	70.9293i	−1.48651	+	2.27975i
$969$	−12.9792	+	22.4806i	−0.416951	+	0.722181i
$970$	−9.60291	−	10.6651i	−0.308331	−	0.342436i
$971$	−6.26859	−	2.79096i	−0.201169	−	0.0895660i	0.303679	−	0.952774i	$-0.401785\pi$
$971$	−6.26859	−	2.79096i	−0.201169	−	0.0895660i	−0.504848	+	0.863208i	$0.668451\pi$
$972$	−68.6925	−	49.9080i	−2.20331	−	1.60080i
$973$	−19.2984	−	2.32639i	−0.618680	−	0.0745807i
$974$	0.107148	+	0.329766i	0.00343323	+	0.0105664i
$975$	−0.0304934	+	0.290125i	−0.000976569	+	0.00929144i
$976$	9.44074	+	89.8227i	0.302191	+	2.87515i
$977$	−6.96892	−	7.73977i	−0.222955	−	0.247617i	0.621281	−	0.783588i	$-0.286612\pi$
$977$	−6.96892	−	7.73977i	−0.222955	−	0.247617i	−0.844237	+	0.535971i	$0.819946\pi$
$978$	7.24794	+	12.5538i	0.231764	+	0.401426i
$979$	9.30199	+	10.9117i	0.297293	+	0.348740i
$980$	26.2058	+	30.9527i	0.837112	+	0.988748i
$981$	0.952947	−	2.93287i	0.0304252	−	0.0936393i
$982$	−0.0536241	−	0.0238750i	−0.00171121	−	0.000761881i
$983$	14.3900	−	6.40682i	0.458969	−	0.204346i	−0.164210	−	0.986425i	$-0.552508\pi$
$983$	14.3900	−	6.40682i	0.458969	−	0.204346i	0.623179	+	0.782079i	$0.285841\pi$
$984$	−136.274	−	28.9659i	−4.34425	−	0.923399i
$985$	−6.52385	+	7.24547i	−0.207867	+	0.230860i
$986$	−64.5342	−	46.8868i	−2.05519	−	1.49318i
$987$	−3.60949	−	18.3532i	−0.114891	−	0.584188i
$988$	0.106842	−	0.328825i	0.00339908	−	0.0104613i
$989$	3.03232	+	5.25213i	0.0964222	+	0.167008i
$990$	2.56336	−	19.3320i	0.0814689	−	0.614410i
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	−0.923264	−	0.384167i	$-0.874489\pi$
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	0.794330	+	0.607486i	$0.207822\pi$
$992$	−33.2186	+	7.06084i	−1.05469	+	0.224182i
$993$	35.0367	−	25.4557i	1.11186	−	0.807811i
$994$	25.4076	+	15.1903i	0.805881	+	0.481808i
$995$	−6.64664	−	20.4563i	−0.210713	−	0.648507i
$996$	−44.2800	+	49.1779i	−1.40307	+	1.55826i
$997$	−37.6879	+	16.7797i	−1.19359	+	0.531420i	−0.904744	−	0.425956i	$-0.859938\pi$
$997$	−37.6879	+	16.7797i	−1.19359	+	0.531420i	−0.288845	+	0.957376i	$0.593271\pi$
$998$	1.90602	+	18.1346i	0.0603340	+	0.574040i
$999$	6.34434	−	1.34853i	0.200726	−	0.0426656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.m.b.53.1	yes	40
3.2	odd	2		693.2.by.b.361.5		40
7.2	even	3	inner	77.2.m.b.9.5	✓	40
7.3	odd	6		539.2.f.g.295.5		20
7.4	even	3		539.2.f.h.295.5		20
7.5	odd	6		539.2.q.h.471.5		40
7.6	odd	2		539.2.q.h.361.1		40
11.2	odd	10		847.2.n.h.487.1		40
11.3	even	5		847.2.n.i.81.1		40
11.4	even	5		847.2.e.i.606.1		20
11.5	even	5	inner	77.2.m.b.60.5	yes	40
11.6	odd	10		847.2.n.j.753.1		40
11.7	odd	10		847.2.e.h.606.10		20
11.8	odd	10		847.2.n.h.81.5		40
11.9	even	5		847.2.n.i.487.5		40
11.10	odd	2		847.2.n.j.130.5		40
21.2	odd	6		693.2.by.b.163.1		40
33.5	odd	10		693.2.by.b.676.1		40
77.2	odd	30		847.2.n.h.366.5		40
77.4	even	15		5929.2.a.bw.1.10		10
77.5	odd	30		539.2.q.h.324.1		40
77.9	even	15		847.2.n.i.366.1		40
77.16	even	15	inner	77.2.m.b.16.1	yes	40
77.18	odd	30		5929.2.a.by.1.1		10
77.27	odd	10		539.2.q.h.214.5		40
77.30	odd	30		847.2.n.h.807.1		40
77.37	even	15		847.2.e.i.485.1		20
77.38	odd	30		539.2.f.g.148.5		20
77.51	odd	30		847.2.e.h.485.10		20
77.58	even	15		847.2.n.i.807.5		40
77.59	odd	30		5929.2.a.bx.1.10		10
77.60	even	15		539.2.f.h.148.5		20
77.65	odd	6		847.2.n.j.9.1		40
77.72	odd	30		847.2.n.j.632.5		40
77.73	even	30		5929.2.a.bz.1.1		10
231.170	odd	30		693.2.by.b.478.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.5	✓	40	7.2	even	3	inner
77.2.m.b.16.1	yes	40	77.16	even	15	inner
77.2.m.b.53.1	yes	40	1.1	even	1	trivial
77.2.m.b.60.5	yes	40	11.5	even	5	inner
539.2.f.g.148.5		20	77.38	odd	30
539.2.f.g.295.5		20	7.3	odd	6
539.2.f.h.148.5		20	77.60	even	15
539.2.f.h.295.5		20	7.4	even	3
539.2.q.h.214.5		40	77.27	odd	10
539.2.q.h.324.1		40	77.5	odd	30
539.2.q.h.361.1		40	7.6	odd	2
539.2.q.h.471.5		40	7.5	odd	6
693.2.by.b.163.1		40	21.2	odd	6
693.2.by.b.361.5		40	3.2	odd	2
693.2.by.b.478.5		40	231.170	odd	30
693.2.by.b.676.1		40	33.5	odd	10
847.2.e.h.485.10		20	77.51	odd	30
847.2.e.h.606.10		20	11.7	odd	10
847.2.e.i.485.1		20	77.37	even	15
847.2.e.i.606.1		20	11.4	even	5
847.2.n.h.81.5		40	11.8	odd	10
847.2.n.h.366.5		40	77.2	odd	30
847.2.n.h.487.1		40	11.2	odd	10
847.2.n.h.807.1		40	77.30	odd	30
847.2.n.i.81.1		40	11.3	even	5
847.2.n.i.366.1		40	77.9	even	15
847.2.n.i.487.5		40	11.9	even	5
847.2.n.i.807.5		40	77.58	even	15
847.2.n.j.9.1		40	77.65	odd	6
847.2.n.j.130.5		40	11.10	odd	2
847.2.n.j.632.5		40	77.72	odd	30
847.2.n.j.753.1		40	11.6	odd	10
5929.2.a.bw.1.10		10	77.4	even	15
5929.2.a.bx.1.10		10	77.59	odd	30
5929.2.a.by.1.1		10	77.18	odd	30
5929.2.a.bz.1.1		10	77.73	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57407 + 0.547134i) q^{2} +(0.231369 + 2.20133i) q^{3} +(4.49937 - 2.00325i) q^{4} +(-0.787136 + 0.874203i) q^{5} +(-1.79998 - 5.53977i) q^{6} +(-2.31119 + 1.28778i) q^{7} +(-6.22764 + 4.52465i) q^{8} +(-1.85787 + 0.394902i) q^{9} +O(q^{10})\)	\(q+(-2.57407 + 0.547134i) q^{2} +(0.231369 + 2.20133i) q^{3} +(4.49937 - 2.00325i) q^{4} +(-0.787136 + 0.874203i) q^{5} +(-1.79998 - 5.53977i) q^{6} +(-2.31119 + 1.28778i) q^{7} +(-6.22764 + 4.52465i) q^{8} +(-1.85787 + 0.394902i) q^{9} +(1.54783 - 2.68093i) q^{10} +(-3.26165 + 0.601380i) q^{11} +(5.45081 + 9.44109i) q^{12} +(0.0112624 - 0.0346622i) q^{13} +(5.24457 - 4.57937i) q^{14} +(-2.10653 - 1.53048i) q^{15} +(6.96361 - 7.73387i) q^{16} +(5.95559 + 1.26590i) q^{17} +(4.56621 - 2.03301i) q^{18} +(1.75961 + 0.783430i) q^{19} +(-1.79037 + 5.51019i) q^{20} +(-3.36957 - 4.78974i) q^{21} +(8.06666 - 3.33255i) q^{22} +(-1.02155 - 1.76938i) q^{23} +(-11.4011 - 12.6622i) q^{24} +(0.377994 + 3.59637i) q^{25} +(-0.0100254 + 0.0953849i) q^{26} +(0.752823 + 2.31695i) q^{27} +(-7.81916 + 10.4241i) q^{28} +(4.02767 + 2.92628i) q^{29} +(6.25972 + 2.78701i) q^{30} +(1.89509 + 2.10472i) q^{31} +(-5.99553 + 10.3846i) q^{32} +(-2.07848 - 7.04081i) q^{33} -16.0227 q^{34} +(0.693441 - 3.03411i) q^{35} +(-7.56813 + 5.49857i) q^{36} +(0.278295 - 2.64780i) q^{37} +(-4.95800 - 1.05386i) q^{38} +(0.0789086 + 0.0167725i) q^{39} +(0.946542 - 9.00574i) q^{40} +(6.61499 - 4.80607i) q^{41} +(11.2941 + 10.4855i) q^{42} -2.96835 q^{43} +(-13.4706 + 9.23971i) q^{44} +(1.11717 - 1.93499i) q^{45} +(3.59762 + 3.99557i) q^{46} +(2.91785 + 1.29911i) q^{47} +(18.6359 + 13.5398i) q^{48} +(3.68323 - 5.95263i) q^{49} +(-2.94068 - 9.05049i) q^{50} +(-1.40872 + 13.4031i) q^{51} +(-0.0187631 - 0.178519i) q^{52} +(-6.63364 - 7.36740i) q^{53} +(-3.20550 - 5.55209i) q^{54} +(2.04163 - 3.32471i) q^{55} +(8.56653 - 18.4772i) q^{56} +(-1.31747 + 4.05475i) q^{57} +(-11.9686 - 5.32875i) q^{58} +(3.70874 - 1.65124i) q^{59} +(-12.5440 - 2.66630i) q^{60} +(-5.80710 + 6.44943i) q^{61} +(-6.02966 - 4.38080i) q^{62} +(3.78534 - 3.30522i) q^{63} +(3.31928 - 10.2157i) q^{64} +(0.0214368 + 0.0371295i) q^{65} +(9.20241 + 16.9863i) q^{66} +(-1.12669 + 1.95148i) q^{67} +(29.3323 - 6.23477i) q^{68} +(3.65862 - 2.65815i) q^{69} +(-0.124894 + 8.18941i) q^{70} +(1.31384 + 4.04359i) q^{71} +(9.78334 - 10.8655i) q^{72} +(3.92144 - 1.74594i) q^{73} +(0.732354 + 6.96788i) q^{74} +(-7.82934 + 1.66418i) q^{75} +9.48655 q^{76} +(6.76385 - 5.59020i) q^{77} -0.212293 q^{78} +(3.03638 - 0.645402i) q^{79} +(1.27967 + 12.1752i) q^{80} +(-10.1317 + 4.51091i) q^{81} +(-14.3979 + 15.9904i) q^{82} +(1.87581 + 5.77314i) q^{83} +(-24.7559 - 14.8007i) q^{84} +(-5.79451 + 4.20996i) q^{85} +(7.64073 - 1.62409i) q^{86} +(-5.50981 + 9.54328i) q^{87} +(17.5913 - 18.5030i) q^{88} +(-2.16161 - 3.74402i) q^{89} +(-1.81697 + 5.59204i) q^{90} +(0.0186077 + 0.0946147i) q^{91} +(-8.14083 - 5.91466i) q^{92} +(-4.19470 + 4.65869i) q^{93} +(-8.22152 - 1.74754i) q^{94} +(-2.06993 + 0.921593i) q^{95} +(-24.2470 - 10.7955i) q^{96} +(1.43258 - 4.40904i) q^{97} +(-6.22400 + 17.3377i) q^{98} +(5.82222 - 2.40531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} - 16 q^{6} - 2 q^{7} - 38 q^{8} + 7 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 - 16 * q^6 - 2 * q^7 - 38 * q^8 + 7 * q^9	\( 40 q - 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} - 16 q^{6} - 2 q^{7} - 38 q^{8} + 7 q^{9} + 14 q^{10} - 9 q^{11} - 18 q^{12} + 6 q^{13} - 3 q^{14} - 14 q^{15} - 5 q^{16} - 7 q^{17} + 24 q^{18} - 4 q^{19} - 30 q^{20} - 2 q^{21} + 44 q^{22} - 14 q^{23} - 12 q^{24} + 21 q^{25} - 16 q^{27} + 16 q^{28} + 16 q^{30} - 17 q^{31} - 30 q^{32} - 15 q^{33} + 48 q^{34} - 14 q^{35} + 14 q^{36} + 24 q^{37} + 12 q^{38} + 28 q^{39} + 10 q^{40} + 60 q^{41} - 70 q^{42} - 72 q^{43} + 18 q^{44} - 16 q^{45} + 8 q^{46} + 13 q^{47} + 128 q^{48} - 10 q^{49} + 6 q^{50} - 7 q^{51} + 2 q^{52} + 33 q^{53} + 34 q^{54} - 6 q^{55} + 24 q^{56} + 44 q^{57} - 17 q^{58} + 21 q^{59} - 48 q^{60} - 52 q^{62} + 24 q^{63} + 94 q^{64} - 40 q^{65} - 49 q^{66} - 38 q^{67} - 23 q^{68} - 124 q^{69} - 3 q^{70} + 20 q^{71} - 38 q^{72} + 11 q^{73} - 41 q^{74} - 11 q^{75} - 96 q^{76} + 36 q^{77} - 100 q^{78} + 21 q^{79} + 12 q^{80} - 58 q^{81} + 6 q^{82} - 46 q^{83} - 29 q^{84} - 78 q^{85} + 7 q^{86} + 48 q^{87} + 32 q^{88} - 10 q^{89} - 18 q^{90} - 14 q^{91} - 110 q^{92} + 12 q^{93} + 37 q^{94} + 7 q^{95} - 53 q^{96} - 54 q^{97} + 116 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 - 16 * q^6 - 2 * q^7 - 38 * q^8 + 7 * q^9 + 14 * q^10 - 9 * q^11 - 18 * q^12 + 6 * q^13 - 3 * q^14 - 14 * q^15 - 5 * q^16 - 7 * q^17 + 24 * q^18 - 4 * q^19 - 30 * q^20 - 2 * q^21 + 44 * q^22 - 14 * q^23 - 12 * q^24 + 21 * q^25 - 16 * q^27 + 16 * q^28 + 16 * q^30 - 17 * q^31 - 30 * q^32 - 15 * q^33 + 48 * q^34 - 14 * q^35 + 14 * q^36 + 24 * q^37 + 12 * q^38 + 28 * q^39 + 10 * q^40 + 60 * q^41 - 70 * q^42 - 72 * q^43 + 18 * q^44 - 16 * q^45 + 8 * q^46 + 13 * q^47 + 128 * q^48 - 10 * q^49 + 6 * q^50 - 7 * q^51 + 2 * q^52 + 33 * q^53 + 34 * q^54 - 6 * q^55 + 24 * q^56 + 44 * q^57 - 17 * q^58 + 21 * q^59 - 48 * q^60 - 52 * q^62 + 24 * q^63 + 94 * q^64 - 40 * q^65 - 49 * q^66 - 38 * q^67 - 23 * q^68 - 124 * q^69 - 3 * q^70 + 20 * q^71 - 38 * q^72 + 11 * q^73 - 41 * q^74 - 11 * q^75 - 96 * q^76 + 36 * q^77 - 100 * q^78 + 21 * q^79 + 12 * q^80 - 58 * q^81 + 6 * q^82 - 46 * q^83 - 29 * q^84 - 78 * q^85 + 7 * q^86 + 48 * q^87 + 32 * q^88 - 10 * q^89 - 18 * q^90 - 14 * q^91 - 110 * q^92 + 12 * q^93 + 37 * q^94 + 7 * q^95 - 53 * q^96 - 54 * q^97 + 116 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more