LMFDB - Embedded newform 847.2.n.j.130.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			130.5
Character	$\chi$	$=$	847.130
Dual form			847.2.n.j.632.5

$q$-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} +(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} +(-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} -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} +(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} +(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} +(-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} -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} +(-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} +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	\( 40 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} + 16 q^{6} + 2 q^{7} + 38 q^{8} + 7 q^{9} - 14 q^{10} - 18 q^{12} - 6 q^{13} - 3 q^{14} - 14 q^{15} - 5 q^{16} + 7 q^{17} - 24 q^{18} + 4 q^{19} - 30 q^{20} + 2 q^{21} - 14 q^{23} + 12 q^{24} + 21 q^{25} - 16 q^{27} - 16 q^{28} - 16 q^{30} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 14 q^{36} + 24 q^{37} + 12 q^{38} - 28 q^{39} - 10 q^{40} - 60 q^{41} - 70 q^{42} + 72 q^{43} - 16 q^{45} - 8 q^{46} + 13 q^{47} + 128 q^{48} - 10 q^{49} - 6 q^{50} + 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 24 q^{56} - 44 q^{57} - 17 q^{58} + 21 q^{59} - 48 q^{60} + 52 q^{62} - 24 q^{63} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 124 q^{69} - 3 q^{70} + 20 q^{71} + 38 q^{72} - 11 q^{73} + 41 q^{74} - 11 q^{75} + 96 q^{76} - 100 q^{78} - 21 q^{79} + 12 q^{80} - 58 q^{81} + 6 q^{82} + 46 q^{83} + 29 q^{84} + 78 q^{85} + 7 q^{86} - 48 q^{87} - 10 q^{89} + 18 q^{90} - 14 q^{91} - 110 q^{92} + 12 q^{93} - 37 q^{94} - 7 q^{95} + 53 q^{96} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 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 - 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 - 14 * q^23 + 12 * q^24 + 21 * q^25 - 16 * q^27 - 16 * q^28 - 16 * q^30 - 17 * q^31 + 30 * q^32 + 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 - 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 + 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 - 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 - 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 - 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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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	0.833861	−	0.551975i	$-0.186125\pi$
$2$	2.57407	−	0.547134i	1.82014	−	0.386883i	0.986278	+	0.165092i	$0.0527921\pi$
$3$	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
$11$		0			0
$11$		0			0
$12$	5.45081	+	9.44109i	1.57351	+	2.72541i
$13$	−0.0112624	+	0.0346622i	−0.00312364	+	0.00961357i	−0.952606	−	0.304206i	$-0.901609\pi$
$13$	−0.0112624	+	0.0346622i	−0.00312364	+	0.00961357i	0.949483	+	0.313820i	$0.101609\pi$
$14$	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	−0.582003	−	0.813187i	$-0.697731\pi$
$17$	−5.95559	−	1.26590i	−1.44444	−	0.307026i	−0.862439	+	0.506161i	$0.831064\pi$
$18$	−4.56621	+	2.03301i	−1.07626	+	0.479184i
$19$	−1.75961	−	0.783430i	−0.403683	−	0.179731i	0.194843	−	0.980834i	$-0.437580\pi$
$19$	−1.75961	−	0.783430i	−0.403683	−	0.179731i	−0.598526	+	0.801103i	$0.704247\pi$
$20$	−1.79037	+	5.51019i	−0.400339	+	1.23212i
$21$	3.36957	+	4.78974i	0.735300	+	1.04521i
$22$		0			0
$23$	−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	0.147261	−	0.989098i	$-0.452954\pi$
$29$	−4.02767	−	2.92628i	−0.747920	−	0.543396i	−0.895182	+	0.445702i	$0.852954\pi$
$30$	−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
$33$		0			0
$34$	−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	−0.968925	−	0.247357i	$-0.920438\pi$
$41$	−6.61499	+	4.80607i	−1.03309	+	0.750583i	−0.0641641	+	0.997939i	$0.520438\pi$
$42$	11.2941	+	10.4855i	1.74272	+	1.61795i
$43$	2.96835			0.452669			0.226335	−	0.974050i	$-0.427326\pi$
$43$	2.96835			0.452669			0.226335	+	0.974050i	$0.427326\pi$
$44$		0			0
$45$	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
$55$		0			0
$56$	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	−0.246132	−	0.969236i	$-0.579160\pi$
$61$	5.80710	−	6.44943i	0.743522	−	0.825765i	0.989655	+	0.143471i	$0.0458264\pi$
$62$	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
$66$		0			0
$67$	−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	−0.623180	−	0.782079i	$-0.714159\pi$
$73$	−3.92144	+	1.74594i	−0.458970	+	0.204347i	0.164209	+	0.986426i	$0.447493\pi$
$74$	−0.732354	−	6.96788i	−0.0851344	−	0.810000i
$75$	−7.82934	+	1.66418i	−0.904054	+	0.192163i
$76$	−9.48655			−1.08818
$77$		0			0
$78$	−0.212293			−0.0240374
$79$	−3.03638	+	0.645402i	−0.341619	+	0.0726133i	−0.375527	−	0.926812i	$-0.622538\pi$
$79$	−3.03638	+	0.645402i	−0.341619	+	0.0726133i	0.0339076	+	0.999425i	$0.489205\pi$
$80$	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	$-0.991889\pi$
$83$	−1.87581	−	5.77314i	−0.205896	−	0.633684i	0.793779	−	0.608206i	$-0.208111\pi$
$84$	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
$88$		0			0
$89$	−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
$99$		0			0
$100$	8.90516	+	15.4242i	0.890516	+	1.54242i
$101$	11.3829	+	12.6420i	1.13264	+	1.25792i	0.962137	+	0.272566i	$0.0878722\pi$
$101$	11.3829	+	12.6420i	1.13264	+	1.25792i	0.170502	+	0.985357i	$0.445461\pi$
$102$	−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	0.447506	−	0.894281i	$-0.352312\pi$
$107$	0.852002	+	0.379336i	0.0823661	+	0.0366718i	−0.365140	+	0.930953i	$0.618979\pi$
$108$	8.02865	+	8.91672i	0.772558	+	0.858012i
$109$	0.811795	−	1.40607i	0.0777558	−	0.134677i	−0.824526	−	0.565825i	$-0.808558\pi$
$109$	0.811795	−	1.40607i	0.0777558	−	0.134677i	0.902281	+	0.431148i	$0.141891\pi$
$110$		0			0
$111$	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
$121$		0			0
$122$	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	$0.238858\pi$
$127$	6.09131	+	18.7471i	0.540516	+	1.66354i	−0.190903	+	0.981609i	$0.561142\pi$
$128$	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	$-0.916719\pi$
$131$	−8.09187	−	14.0155i	−0.706990	−	1.22454i	0.258979	−	0.965883i	$-0.416614\pi$
$132$		0			0
$133$	−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	0.306452	−	0.951886i	$-0.400858\pi$
$139$	−5.94380	−	4.31842i	−0.504146	−	0.366284i	−0.810598	+	0.585602i	$0.800858\pi$
$140$	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			0
$144$	−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	−0.589641	−	0.807665i	$-0.700731\pi$
$149$	3.35966	−	3.73128i	0.275234	−	0.305679i	0.864875	+	0.501987i	$0.167397\pi$
$150$	−19.2427	+	8.56740i	−1.57116	+	0.699526i
$151$	0.877823	+	8.35192i	0.0714362	+	0.679670i	0.970376	+	0.241598i	$0.0776717\pi$
$151$	0.877823	+	8.35192i	0.0714362	+	0.679670i	−0.898940	+	0.438072i	$0.855662\pi$
$152$	−14.5030	+	3.08271i	−1.17635	+	0.250040i
$153$	11.5646			0.934942
$154$		0			0
$155$	−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
$165$		0			0
$166$	−7.98713	−	13.8341i	−0.619921	−	1.07374i
$167$	3.80261	−	11.7032i	0.294255	−	0.905624i	−0.689216	−	0.724556i	$-0.742045\pi$
$167$	3.80261	−	11.7032i	0.294255	−	0.905624i	0.983471	−	0.181068i	$-0.0579553\pi$
$168$	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	−0.0635449	−	0.997979i	$-0.520241\pi$
$173$	−11.1499	−	4.96423i	−0.847708	−	0.377424i	−0.784163	+	0.620555i	$0.786907\pi$
$174$	8.96116	−	27.5796i	0.679344	−	2.09081i
$175$	5.50497	+	7.82515i	0.416136	+	0.591525i
$176$		0			0
$177$	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
$187$		0			0
$188$	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	0.696916	−	0.717153i	$-0.254555\pi$
$193$	14.4744	+	3.07662i	1.04189	+	0.221460i	0.344972	+	0.938613i	$0.387888\pi$
$194$	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	$-0.595403\pi$
$197$	−8.28808			−0.590501			−0.295251	+	0.955420i	$0.595403\pi$
$198$		0			0
$199$	−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
$209$		0			0
$210$	−18.0565	+	1.61984i	−1.24602	+	0.111780i
$211$	−7.29409	+	22.4489i	−0.502146	+	1.54545i	0.303370	+	0.952873i	$0.401888\pi$
$211$	−7.29409	+	22.4489i	−0.502146	+	1.54545i	−0.805516	+	0.592573i	$0.798112\pi$
$212$	−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
$220$		0			0
$221$	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	−0.0690091	−	0.997616i	$-0.521984\pi$
$227$	9.43447	−	4.20050i	0.626188	−	0.278797i	0.695197	+	0.718819i	$0.255317\pi$
$228$	−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
$231$		0			0
$232$	−38.3233			−2.51605
$233$	3.91278	−	0.831687i	0.256335	−	0.0544856i	−0.0779518	−	0.996957i	$-0.524838\pi$
$233$	3.91278	−	0.831687i	0.256335	−	0.0544856i	0.334286	+	0.942472i	$0.391505\pi$
$234$	−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	0.127897	−	0.991787i	$-0.459177\pi$
$239$	17.1705	−	12.4751i	1.11067	−	0.806946i	0.982768	+	0.184842i	$0.0591772\pi$
$240$	−26.5056	+	5.63393i	−1.71093	+	0.363669i
$241$	−6.80326	+	11.7836i	−0.438237	+	0.759048i	−0.997554	−	0.0699056i	$-0.977730\pi$
$241$	−6.80326	+	11.7836i	−0.438237	+	0.759048i	0.559317	+	0.828954i	$0.311064\pi$
$242$		0			0
$243$	−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
$253$		0			0
$254$	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	$0.377321\pi$
$263$	−9.96601	+	17.2616i	−0.614530	+	1.06440i	−0.990467	+	0.137752i	$0.956012\pi$
$264$		0			0
$265$	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	−0.994883	−	0.101030i	$-0.967786\pi$
$271$	−0.0121050	+	0.115172i	−0.000735328	+	0.00699618i	0.994148	+	0.108026i	$0.0344529\pi$
$272$	−51.2627	+	37.2445i	−3.10826	+	2.25828i
$273$	−0.203973	+	0.0628525i	−0.0123450	+	0.00380401i
$274$	44.6745			2.69889
$275$		0			0
$276$	11.1366	−	19.2891i	0.670342	−	1.16107i
$277$	−6.46626	−	7.18151i	−0.388520	−	0.431495i	0.516878	−	0.856059i	$-0.327094\pi$
$277$	−6.46626	−	7.18151i	−0.388520	−	0.431495i	−0.905398	+	0.424564i	$0.860427\pi$
$278$	−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	0.977891	−	0.209114i	$-0.0670579\pi$
$281$	1.07026	+	3.29393i	0.0638466	+	0.196500i	−0.914045	+	0.405613i	$0.867058\pi$
$282$	−1.94470	+	18.5026i	−0.115805	+	1.10181i
$283$	2.75322	+	26.1952i	0.163662	+	1.55714i	0.700621	+	0.713533i	$0.252906\pi$
$283$	2.75322	+	26.1952i	0.163662	+	1.55714i	−0.536959	+	0.843608i	$0.680427\pi$
$284$	14.0118	+	15.5616i	0.831445	+	0.923413i
$285$	2.50765	+	4.34337i	0.148540	+	0.257279i
$286$		0			0
$287$	−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	0.887234	−	0.461319i	$-0.152624\pi$
$293$	12.3700	+	8.98734i	0.722664	+	0.525046i	−0.164570	+	0.986365i	$0.552624\pi$
$294$	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
$297$		0			0
$298$	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	$-0.870009\pi$
$307$	−32.1611			−1.83553			−0.917766	+	0.397123i	$0.870009\pi$
$308$		0			0
$309$	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
$319$		0			0
$320$	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
$330$		0			0
$331$	−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	0.965551	−	0.260215i	$-0.0837934\pi$
$337$	18.6594	+	13.5569i	1.01644	+	0.738489i	0.0508925	+	0.998704i	$0.483793\pi$
$338$	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
$341$		0			0
$342$	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	−0.503514	−	0.863987i	$-0.667960\pi$
$347$	−24.4941	−	5.20638i	−1.31491	−	0.279493i	−0.811398	+	0.584494i	$0.801293\pi$
$348$	5.67313	−	53.9762i	0.304112	−	2.89343i
$349$	15.8320	−	11.5026i	0.847467	−	0.615721i	−0.0769797	−	0.997033i	$-0.524528\pi$
$349$	15.8320	−	11.5026i	0.847467	−	0.615721i	0.924446	+	0.381312i	$0.124528\pi$
$350$	18.4515	+	17.1305i	0.986277	+	0.915663i
$351$	−0.0887893			−0.00473922
$352$		0			0
$353$	−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	$0.261804\pi$
$359$	−2.60519	+	24.7867i	−0.137497	+	1.30819i	−0.817902	+	0.575357i	$0.804863\pi$
$360$	−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
$363$		0			0
$364$	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	0.844502	−	0.535553i	$-0.179897\pi$
$373$	−0.802488	−	1.38995i	−0.0415513	−	0.0719689i	−0.886053	+	0.463584i	$0.846563\pi$
$374$		0			0
$375$	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			0
$386$	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
$396$		0			0
$397$	−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			0
$408$	−51.8712	−	89.8436i	−2.56801	−	4.44792i
$409$	−10.4423	−	11.5973i	−0.516337	−	0.573450i	0.427436	−	0.904046i	$-0.359417\pi$
$409$	−10.4423	−	11.5973i	−0.516337	−	0.573450i	−0.943773	+	0.330596i	$0.892750\pi$
$410$	−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
$418$		0			0
$419$	−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			0
$430$	−4.59452	+	7.95793i	−0.221567	+	0.383766i
$431$	5.58314	+	6.20070i	0.268930	+	0.298677i	0.862450	−	0.506142i	$-0.168929\pi$
$431$	5.58314	+	6.20070i	0.268930	+	0.298677i	−0.593520	+	0.804819i	$0.702262\pi$
$432$	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	$-0.966975\pi$
$439$	−12.2991	−	21.3026i	−0.587002	−	1.01672i	0.407620	−	0.913151i	$-0.366359\pi$
$440$		0			0
$441$	−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
$451$		0			0
$452$	−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	$-0.492389\pi$
$457$	21.7120	−	24.1137i	1.01565	−	1.12799i	0.991739	−	0.128275i	$-0.0409440\pi$
$458$	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	$-0.258965\pi$
$461$	29.4973			1.37383			0.686914	+	0.726739i	$0.258965\pi$
$462$		0			0
$463$	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
$473$		0			0
$474$	−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	−0.0576623	−	0.998336i	$-0.518365\pi$
$479$	−11.3019	−	2.40230i	−0.516399	−	0.109764i	−0.458737	+	0.888572i	$0.651698\pi$
$480$	−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
$484$		0			0
$485$	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	0.587378	−	0.809313i	$-0.300160\pi$
$491$	−0.0180456	−	0.0131109i	−0.000814388	−	0.000591687i	−0.588192	+	0.808721i	$0.700160\pi$
$492$	−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
$495$		0			0
$496$	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	−0.728818	−	0.684707i	$-0.759930\pi$
$503$	−6.79200	+	4.93468i	−0.302840	+	0.220026i	0.425978	+	0.904734i	$0.359930\pi$
$504$	−8.61880	+	37.7111i	−0.383912	+	1.67979i
$505$	−20.0115			−0.890502
$506$		0			0
$507$	−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
$517$		0			0
$518$	−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	−0.107275	−	0.994229i	$-0.534213\pi$
$523$	20.4158	−	22.6740i	0.892721	−	0.991467i	0.999996	+	0.00276239i	$0.000879296\pi$
$524$	−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
$528$		0			0
$529$	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
$539$		0			0
$540$	−14.1147			−0.607399
$541$	0.277681	−	0.0590230i	0.0119384	−	0.00253760i	−0.201939	−	0.979398i	$-0.564724\pi$
$541$	0.277681	−	0.0590230i	0.0119384	−	0.00253760i	0.213877	+	0.976861i	$0.431391\pi$
$542$	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	−0.385733	−	0.922610i	$-0.626052\pi$
$547$	8.71258	−	6.33006i	0.372523	−	0.270654i	0.758256	+	0.651957i	$0.226052\pi$
$548$	81.7844	−	17.3838i	3.49365	−	0.742599i
$549$	−8.24192	+	14.2754i	−0.351756	+	0.609260i
$550$		0			0
$551$	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	−0.989834	−	0.142225i	$-0.954574\pi$
$557$	−36.4980	+	16.2499i	−1.54647	+	0.688532i	−0.556634	+	0.830758i	$0.687908\pi$
$558$	−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
$561$		0			0
$562$	4.55716	+	7.89323i	0.192232	+	0.332956i
$563$	7.99139	+	8.87534i	0.336797	+	0.374051i	0.887624	−	0.460568i	$-0.152354\pi$
$563$	7.99139	+	8.87534i	0.336797	+	0.374051i	−0.550827	+	0.834619i	$0.685688\pi$
$564$	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	0.605995	−	0.795468i	$-0.292775\pi$
$569$	10.0266	+	4.46414i	0.420337	+	0.187146i	−0.185658	+	0.982614i	$0.559442\pi$
$570$	8.83125	+	9.80810i	0.369901	+	0.410816i
$571$	3.74628	−	6.48874i	0.156777	−	0.271545i	−0.776928	−	0.629590i	$-0.783223\pi$
$571$	3.74628	−	6.48874i	0.156777	−	0.271545i	0.933705	+	0.358044i	$0.116556\pi$
$572$		0			0
$573$	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
$583$		0			0
$584$	−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	$0.0310451\pi$
$593$	14.1715	+	24.5458i	0.581954	+	1.00797i	−0.413293	+	0.910598i	$0.635622\pi$
$594$		0			0
$595$	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	0.558301	−	0.829638i	$-0.311453\pi$
$601$	−1.42697	−	1.03676i	−0.0582074	−	0.0422901i	−0.616508	+	0.787348i	$0.711453\pi$
$602$	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
$605$		0			0
$606$	−49.5446	+	85.8138i	−2.01261	+	3.48595i
$607$	−13.9937	+	2.97445i	−0.567985	+	0.120729i	−0.482948	−	0.875649i	$-0.660434\pi$
$607$	−13.9937	+	2.97445i	−0.567985	+	0.120729i	−0.0850370	+	0.996378i	$0.527101\pi$
$608$	−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	$-0.996613\pi$
$613$	−0.595783	−	5.66850i	−0.0240634	−	0.228948i	0.975880	−	0.218308i	$-0.0700537\pi$
$614$	−82.7848	+	17.5964i	−3.34092	+	0.710135i
$615$	21.2903			0.858506
$616$		0			0
$617$	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
$627$		0			0
$628$	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
$638$		0			0
$639$	−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
$649$		0			0
$650$	−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	$-0.663067\pi$
$659$	−25.1666			−0.980350			−0.490175	+	0.871624i	$0.663067\pi$
$660$		0			0
$661$	−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
$671$		0			0
$672$	69.9417	−	6.27445i	2.69806	−	0.242042i
$673$	6.06417	−	18.6636i	0.233757	−	0.719429i	−0.763527	−	0.645776i	$-0.776534\pi$
$673$	6.06417	−	18.6636i	0.233757	−	0.719429i	0.997284	−	0.0736535i	$-0.0234659\pi$
$674$	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	−0.961163	−	0.275981i	$-0.910997\pi$
$677$	−15.2531	+	16.9403i	−0.586226	+	0.651070i	0.374938	+	0.927050i	$0.377664\pi$
$678$	−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
$682$		0			0
$683$	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
$693$		0			0
$694$	−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	−0.425124	−	0.905135i	$-0.639769\pi$
$701$	8.05784	−	5.85436i	0.304340	−	0.221116i	0.729464	+	0.684019i	$0.239769\pi$
$702$	−0.228549	+	0.0485797i	−0.00862604	+	0.00183352i
$703$	−2.56406	+	4.44108i	−0.0967054	+	0.167499i
$704$		0			0
$705$	−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			0
$716$	−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
$726$		0			0
$727$	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	$-0.789446\pi$
$733$	2.99094	−	28.4569i	0.110473	−	1.05108i	0.899559	−	0.436798i	$-0.143888\pi$
$734$	15.9450	−	11.5847i	0.588542	−	0.427601i
$735$	−16.8692	+	6.90225i	−0.622230	+	0.254593i
$736$	−24.4989			−0.903042
$737$		0			0
$738$	20.4346	−	35.3938i	0.752210	−	1.30287i
$739$	−6.06096	−	6.73137i	−0.222956	−	0.247618i	0.621281	−	0.783588i	$-0.286613\pi$
$739$	−6.06096	−	6.73137i	−0.222956	−	0.247618i	−0.844237	+	0.535970i	$0.819946\pi$
$740$	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	0.892518	−	0.451012i	$-0.148937\pi$
$743$	−2.57977	−	7.93973i	−0.0946427	−	0.291280i	−0.987160	+	0.159732i	$0.948937\pi$
$744$	−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
$748$		0			0
$749$	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
$759$		0			0
$760$	8.72092	−	15.1051i	0.316341	−	0.547919i
$761$	−24.8315	+	5.27809i	−0.900140	+	0.191331i	−0.634665	−	0.772787i	$-0.718862\pi$
$761$	−24.8315	+	5.27809i	−0.900140	+	0.191331i	−0.265474	+	0.964118i	$0.585529\pi$
$762$	−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	$-0.203019\pi$
$769$	44.5582			1.60681			0.803406	+	0.595432i	$0.203019\pi$
$770$		0			0
$771$	−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
$781$		0			0
$782$	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	0.885513	−	0.464615i	$-0.153807\pi$
$787$	42.2344	+	8.97720i	1.50549	+	0.320003i	0.619981	+	0.784617i	$0.287140\pi$
$788$	−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
$792$		0			0
$793$	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
$803$		0			0
$804$	−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	0.188085	−	0.982153i	$-0.439772\pi$
$809$	−1.12546	−	0.239224i	−0.0395690	−	0.00841066i	−0.227654	+	0.973742i	$0.573105\pi$
$810$	3.58872	−	34.1444i	0.126095	−	1.19971i
$811$	−28.6938	+	20.8473i	−1.00758	+	0.732047i	−0.963699	−	0.266990i	$-0.913971\pi$
$811$	−28.6938	+	20.8473i	−1.00758	+	0.732047i	−0.0438772	+	0.999037i	$0.513971\pi$
$812$	−61.9968	+	19.1038i	−2.17566	+	0.670413i
$813$	−0.256331			−0.00898993
$814$		0			0
$815$	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	$-0.854833\pi$
$821$	2.06152	−	19.6140i	0.0719475	−	0.684535i	0.969744	−	0.244124i	$-0.0785005\pi$
$822$	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
$825$		0			0
$826$	11.8892	−	25.6438i	0.413676	−	0.892260i
$827$	0.289657	−	0.891474i	0.0100724	−	0.0309996i	−0.945894	−	0.324476i	$-0.894812\pi$
$827$	0.289657	−	0.891474i	0.0100724	−	0.0309996i	0.955966	+	0.293476i	$0.0948121\pi$
$828$	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
$836$		0			0
$837$	−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
$847$		0			0
$848$	−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	0.929800	−	0.368066i	$-0.119980\pi$
$853$	−1.13225	−	3.48472i	−0.0387677	−	0.119315i	−0.968567	+	0.248751i	$0.919980\pi$
$854$	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	−0.819752	−	0.572718i	$-0.805889\pi$
$857$	2.52090	−	4.36633i	0.0861124	−	0.149151i	0.905865	+	0.423567i	$0.139222\pi$
$858$		0			0
$859$	−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
$869$		0			0
$870$	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	0.599643	−	0.800267i	$-0.295309\pi$
$877$	12.0283	+	5.35537i	0.406168	+	0.180838i	−0.193475	+	0.981105i	$0.561976\pi$
$878$	−43.3140	−	48.1050i	−1.46178	−	1.62347i
$879$	−16.9220	+	29.3098i	−0.570766	+	0.988596i
$880$		0			0
$881$	−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	$0.221093\pi$
$887$	−3.46334	+	32.9515i	−0.116288	+	1.10640i	−0.884608	+	0.466336i	$0.845574\pi$
$888$	36.6999	−	26.6641i	1.23157	−	0.894787i
$889$	38.2204	+	35.4839i	1.28187	+	1.19009i
$890$	13.3833			0.448608
$891$		0			0
$892$	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
$902$		0			0
$903$	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
$913$		0			0
$914$	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	−0.882047	−	0.471162i	$-0.843835\pi$
$919$	−9.73920	+	10.8165i	−0.321266	+	0.356803i	0.560780	+	0.827965i	$0.310501\pi$
$920$	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
$924$		0			0
$925$	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
$935$		0			0
$936$	−0.266438	−	0.461484i	−0.00870880	−	0.0150841i
$937$	9.37722	−	28.8601i	0.306340	−	0.942818i	−0.672833	−	0.739794i	$-0.734923\pi$
$937$	9.37722	−	28.8601i	0.306340	−	0.942818i	0.979174	−	0.203024i	$-0.0650771\pi$
$938$	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	−0.0416850	−	0.999131i	$-0.513273\pi$
$941$	−14.9130	−	3.16985i	−0.486149	−	0.103334i	−0.444464	+	0.895797i	$0.646606\pi$
$942$	−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
$946$		0			0
$947$	−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	0.833774	−	0.552105i	$-0.186175\pi$
$953$	17.4834	+	12.7024i	0.566342	+	0.411471i	−0.267433	+	0.963577i	$0.586175\pi$
$954$	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
$957$		0			0
$958$	−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	$-0.529421\pi$
$967$	−5.74025			−0.184594			−0.0922970	+	0.995732i	$0.529421\pi$
$968$		0			0
$969$	−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
$979$		0			0
$980$	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
$990$		0			0
$991$	−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	0.288845	−	0.957376i	$-0.406729\pi$
$997$	37.6879	−	16.7797i	1.19359	−	0.531420i	0.904744	+	0.425956i	$0.140062\pi$
$998$	−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	847.2.n.j.130.5		40
7.2	even	3	inner	847.2.n.j.9.1		40
11.2	odd	10		847.2.n.i.487.5		40
11.3	even	5		847.2.n.h.81.5		40
11.4	even	5		847.2.e.h.606.10		20
11.5	even	5	inner	847.2.n.j.753.1		40
11.6	odd	10		77.2.m.b.60.5	yes	40
11.7	odd	10		847.2.e.i.606.1		20
11.8	odd	10		847.2.n.i.81.1		40
11.9	even	5		847.2.n.h.487.1		40
11.10	odd	2		77.2.m.b.53.1	yes	40
33.17	even	10		693.2.by.b.676.1		40
33.32	even	2		693.2.by.b.361.5		40
77.2	odd	30		847.2.n.i.366.1		40
77.4	even	15		5929.2.a.by.1.1		10
77.6	even	10		539.2.q.h.214.5		40
77.9	even	15		847.2.n.h.366.5		40
77.10	even	6		539.2.f.g.295.5		20
77.16	even	15	inner	847.2.n.j.632.5		40
77.17	even	30		539.2.f.g.148.5		20
77.18	odd	30		5929.2.a.bw.1.10		10
77.30	odd	30		847.2.n.i.807.5		40
77.32	odd	6		539.2.f.h.295.5		20
77.37	even	15		847.2.e.h.485.10		20
77.39	odd	30		539.2.f.h.148.5		20
77.51	odd	30		847.2.e.i.485.1		20
77.54	even	6		539.2.q.h.471.5		40
77.58	even	15		847.2.n.h.807.1		40
77.59	odd	30		5929.2.a.bz.1.1		10
77.61	even	30		539.2.q.h.324.1		40
77.65	odd	6		77.2.m.b.9.5	✓	40
77.72	odd	30		77.2.m.b.16.1	yes	40
77.73	even	30		5929.2.a.bx.1.10		10
77.76	even	2		539.2.q.h.361.1		40
231.65	even	6		693.2.by.b.163.1		40
231.149	even	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	77.65	odd	6
77.2.m.b.16.1	yes	40	77.72	odd	30
77.2.m.b.53.1	yes	40	11.10	odd	2
77.2.m.b.60.5	yes	40	11.6	odd	10
539.2.f.g.148.5		20	77.17	even	30
539.2.f.g.295.5		20	77.10	even	6
539.2.f.h.148.5		20	77.39	odd	30
539.2.f.h.295.5		20	77.32	odd	6
539.2.q.h.214.5		40	77.6	even	10
539.2.q.h.324.1		40	77.61	even	30
539.2.q.h.361.1		40	77.76	even	2
539.2.q.h.471.5		40	77.54	even	6
693.2.by.b.163.1		40	231.65	even	6
693.2.by.b.361.5		40	33.32	even	2
693.2.by.b.478.5		40	231.149	even	30
693.2.by.b.676.1		40	33.17	even	10
847.2.e.h.485.10		20	77.37	even	15
847.2.e.h.606.10		20	11.4	even	5
847.2.e.i.485.1		20	77.51	odd	30
847.2.e.i.606.1		20	11.7	odd	10
847.2.n.h.81.5		40	11.3	even	5
847.2.n.h.366.5		40	77.9	even	15
847.2.n.h.487.1		40	11.9	even	5
847.2.n.h.807.1		40	77.58	even	15
847.2.n.i.81.1		40	11.8	odd	10
847.2.n.i.366.1		40	77.2	odd	30
847.2.n.i.487.5		40	11.2	odd	10
847.2.n.i.807.5		40	77.30	odd	30
847.2.n.j.9.1		40	7.2	even	3	inner
847.2.n.j.130.5		40	1.1	even	1	trivial
847.2.n.j.632.5		40	77.16	even	15	inner
847.2.n.j.753.1		40	11.5	even	5	inner
5929.2.a.bw.1.10		10	77.18	odd	30
5929.2.a.bx.1.10		10	77.73	even	30
5929.2.a.by.1.1		10	77.4	even	15
5929.2.a.bz.1.1		10	77.59	odd	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not 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} +(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} +(-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} -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} +(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} +(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} +(-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} -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} +(-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} +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	\( 40 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} + 16 q^{6} + 2 q^{7} + 38 q^{8} + 7 q^{9} - 14 q^{10} - 18 q^{12} - 6 q^{13} - 3 q^{14} - 14 q^{15} - 5 q^{16} + 7 q^{17} - 24 q^{18} + 4 q^{19} - 30 q^{20} + 2 q^{21} - 14 q^{23} + 12 q^{24} + 21 q^{25} - 16 q^{27} - 16 q^{28} - 16 q^{30} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 14 q^{36} + 24 q^{37} + 12 q^{38} - 28 q^{39} - 10 q^{40} - 60 q^{41} - 70 q^{42} + 72 q^{43} - 16 q^{45} - 8 q^{46} + 13 q^{47} + 128 q^{48} - 10 q^{49} - 6 q^{50} + 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 24 q^{56} - 44 q^{57} - 17 q^{58} + 21 q^{59} - 48 q^{60} + 52 q^{62} - 24 q^{63} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 124 q^{69} - 3 q^{70} + 20 q^{71} + 38 q^{72} - 11 q^{73} + 41 q^{74} - 11 q^{75} + 96 q^{76} - 100 q^{78} - 21 q^{79} + 12 q^{80} - 58 q^{81} + 6 q^{82} + 46 q^{83} + 29 q^{84} + 78 q^{85} + 7 q^{86} - 48 q^{87} - 10 q^{89} + 18 q^{90} - 14 q^{91} - 110 q^{92} + 12 q^{93} - 37 q^{94} - 7 q^{95} + 53 q^{96} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 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 - 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 - 14 * q^23 + 12 * q^24 + 21 * q^25 - 16 * q^27 - 16 * q^28 - 16 * q^30 - 17 * q^31 + 30 * q^32 + 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 - 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 + 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 - 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 - 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 - 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more