LMFDB - Embedded newform 115.2.g.a.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	115.26
Dual form			115.2.g.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0125459 - 0.0872586i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.654861 - 0.755750i) q^{5} +(0.0845850 + 0.0248364i) q^{6} +(-1.30075 + 0.835939i) q^{7} +(-0.146201 - 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +O(q^{10})$	\(q+(-0.0125459 - 0.0872586i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.654861 - 0.755750i) q^{5} +(0.0845850 + 0.0248364i) q^{6} +(-1.30075 + 0.835939i) q^{7} +(-0.146201 - 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +(-0.0741615 - 0.0476607i) q^{10} +(0.289532 - 2.01374i) q^{11} +(-0.283524 + 1.97195i) q^{12} +(1.80075 + 1.15727i) q^{13} +(0.0892619 + 0.103014i) q^{14} +(0.415415 + 0.909632i) q^{15} +(3.32584 - 2.13739i) q^{16} +(-4.18251 - 1.22809i) q^{17} +(0.115460 - 0.133248i) q^{18} +(-7.12381 + 2.09174i) q^{19} +(0.827602 - 1.81219i) q^{20} +(-0.220047 - 1.53046i) q^{21} -0.179348 q^{22} +(-2.79310 - 3.89854i) q^{23} +0.351939 q^{24} +(-0.142315 - 0.989821i) q^{25} +(0.0783898 - 0.171650i) q^{26} +(-4.79746 + 1.40866i) q^{27} +(-2.01722 + 2.32800i) q^{28} +(-4.30111 - 1.26292i) q^{29} +(0.0741615 - 0.0476607i) q^{30} +(-0.376329 - 0.824045i) q^{31} +(-0.689173 - 0.795348i) q^{32} +(1.71148 + 1.09990i) q^{33} +(-0.0546886 + 0.380367i) q^{34} +(-0.220047 + 1.53046i) q^{35} +(3.35194 + 2.15416i) q^{36} +(7.26571 + 8.38507i) q^{37} +(0.271897 + 0.595371i) q^{38} +(-1.80075 + 1.15727i) q^{39} +(-0.337683 - 0.0991526i) q^{40} +(3.95750 - 4.56720i) q^{41} +(-0.130785 + 0.0384020i) q^{42} +(2.24116 - 4.90745i) q^{43} +(-0.576814 - 4.01183i) q^{44} +2.00000 q^{45} +(-0.305139 + 0.292633i) q^{46} -2.72825 q^{47} +(0.562632 + 3.91319i) q^{48} +(-1.91476 + 4.19273i) q^{49} +(-0.0845850 + 0.0248364i) q^{50} +(2.85459 - 3.29437i) q^{51} +(4.09173 + 1.20144i) q^{52} +(-0.230732 + 0.148283i) q^{53} +(0.183106 + 0.400947i) q^{54} +(-1.33228 - 1.53753i) q^{55} +(0.457783 + 0.294199i) q^{56} +(1.05662 - 7.34898i) q^{57} +(-0.0562393 + 0.391153i) q^{58} +(6.74757 + 4.33640i) q^{59} +(1.30463 + 1.50563i) q^{60} +(-1.33718 - 2.92802i) q^{61} +(-0.0671837 + 0.0431763i) q^{62} +(-2.96714 - 0.871230i) q^{63} +(5.11714 - 5.90549i) q^{64} +(2.05384 - 0.603063i) q^{65} +(0.0745040 - 0.163141i) q^{66} +(0.279610 + 1.94473i) q^{67} -8.68428 q^{68} +(4.70653 - 0.921186i) q^{69} +0.136307 q^{70} +(1.58700 + 11.0378i) q^{71} +(0.292401 - 0.640269i) q^{72} +(9.95039 - 2.92170i) q^{73} +(0.640515 - 0.739194i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-12.4433 + 7.99684i) q^{76} +(1.30675 + 2.86139i) q^{77} +(0.123574 + 0.142612i) q^{78} +(2.70849 + 1.74064i) q^{79} +(0.562632 - 3.91319i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.448178 - 0.288027i) q^{82} +(2.85563 + 3.29557i) q^{83} +(-1.27964 - 2.80202i) q^{84} +(-3.66709 + 2.35670i) q^{85} +(-0.456334 - 0.133992i) q^{86} +(2.93553 - 3.38779i) q^{87} +(-0.686997 + 0.201720i) q^{88} +(0.266861 - 0.584343i) q^{89} +(-0.0250918 - 0.174517i) q^{90} -3.30972 q^{91} +(-7.52725 - 5.88446i) q^{92} +0.905910 q^{93} +(0.0342284 + 0.238063i) q^{94} +(-3.08427 + 6.75361i) q^{95} +(1.00977 - 0.296494i) q^{96} +(3.62848 - 4.18748i) q^{97} +(0.389875 + 0.114478i) q^{98} +(3.42297 - 2.19981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.0125459	−	0.0872586i	−0.00887129	−	0.0617012i	0.984905	−	0.173096i	$-0.0553772\pi$
$2$	−0.0125459	−	0.0872586i	−0.00887129	−	0.0617012i	−0.993776	+	0.111395i	$0.964468\pi$
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i	−0.990826	−	0.135141i	$-0.956851\pi$
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i	0.750986	+	0.660318i	$0.229578\pi$
$4$	1.91153	−	0.561276i	0.955765	−	0.280638i
$5$	0.654861	−	0.755750i	0.292863	−	0.337981i
$5$	0.654861	−	0.755750i	0.292863	−	0.337981i
$6$	0.0845850	+	0.0248364i	0.0345317	+	0.0101394i
$7$	−1.30075	+	0.835939i	−0.491636	+	0.315955i	−0.762863	−	0.646560i	$-0.776207\pi$
$7$	−1.30075	+	0.835939i	−0.491636	+	0.315955i	0.271227	+	0.962515i	$0.412571\pi$
$8$	−0.146201	−	0.320135i	−0.0516897	−	0.113185i
$9$	1.30972	+	1.51150i	0.436574	+	0.503833i
$10$	−0.0741615	−	0.0476607i	−0.0234519	−	0.0150716i
$11$	0.289532	−	2.01374i	0.0872971	−	0.607165i	−0.898468	−	0.439038i	$-0.855319\pi$
$11$	0.289532	−	2.01374i	0.0872971	−	0.607165i	0.985765	−	0.168126i	$-0.0537717\pi$
$12$	−0.283524	+	1.97195i	−0.0818462	+	0.569253i
$13$	1.80075	+	1.15727i	0.499437	+	0.320969i	0.765991	−	0.642851i	$-0.222249\pi$
$13$	1.80075	+	1.15727i	0.499437	+	0.320969i	−0.266554	+	0.963820i	$0.585885\pi$
$14$	0.0892619	+	0.103014i	0.0238563	+	0.0275316i
$15$	0.415415	+	0.909632i	0.107260	+	0.234866i
$16$	3.32584	−	2.13739i	0.831460	−	0.534347i
$17$	−4.18251	−	1.22809i	−1.01441	−	0.297857i	−0.268052	−	0.963405i	$-0.586380\pi$
$17$	−4.18251	−	1.22809i	−1.01441	−	0.297857i	−0.746355	+	0.665548i	$0.768198\pi$
$18$	0.115460	−	0.133248i	0.0272141	−	0.0314068i
$19$	−7.12381	+	2.09174i	−1.63431	+	0.479878i	−0.964814	−	0.262935i	$-0.915310\pi$
$19$	−7.12381	+	2.09174i	−1.63431	+	0.479878i	−0.669499	+	0.742813i	$0.733491\pi$
$20$	0.827602	−	1.81219i	0.185057	−	0.405219i
$21$	−0.220047	−	1.53046i	−0.0480182	−	0.333974i
$22$	−0.179348			−0.0382372
$23$	−2.79310	−	3.89854i	−0.582402	−	0.812901i
$23$	−2.79310	−	3.89854i	−0.582402	−	0.812901i
$24$	0.351939			0.0718392
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	0.0783898	−	0.171650i	0.0153735	−	0.0336633i
$27$	−4.79746	+	1.40866i	−0.923273	+	0.271097i
$28$	−2.01722	+	2.32800i	−0.381219	+	0.439951i
$29$	−4.30111	−	1.26292i	−0.798695	−	0.234518i	−0.143177	−	0.989697i	$-0.545732\pi$
$29$	−4.30111	−	1.26292i	−0.798695	−	0.234518i	−0.655519	+	0.755179i	$0.727550\pi$
$30$	0.0741615	−	0.0476607i	0.0135400	−	0.00870161i
$31$	−0.376329	−	0.824045i	−0.0675906	−	0.148003i	0.872822	−	0.488039i	$-0.162288\pi$
$31$	−0.376329	−	0.824045i	−0.0675906	−	0.148003i	−0.940412	+	0.340037i	$0.889561\pi$
$32$	−0.689173	−	0.795348i	−0.121830	−	0.140599i
$33$	1.71148	+	1.09990i	0.297931	+	0.191469i
$34$	−0.0546886	+	0.380367i	−0.00937901	+	0.0652325i
$35$	−0.220047	+	1.53046i	−0.0371948	+	0.258695i
$36$	3.35194	+	2.15416i	0.558656	+	0.359027i
$37$	7.26571	+	8.38507i	1.19447	+	1.37850i	0.907227	+	0.420641i	$0.138195\pi$
$37$	7.26571	+	8.38507i	1.19447	+	1.37850i	0.287248	+	0.957856i	$0.407260\pi$
$38$	0.271897	+	0.595371i	0.0441075	+	0.0965819i
$39$	−1.80075	+	1.15727i	−0.288350	+	0.185311i
$40$	−0.337683	−	0.0991526i	−0.0533923	−	0.0156774i
$41$	3.95750	−	4.56720i	0.618058	−	0.713277i	−0.357279	−	0.933998i	$-0.616295\pi$
$41$	3.95750	−	4.56720i	0.618058	−	0.713277i	0.975337	+	0.220720i	$0.0708408\pi$
$42$	−0.130785	+	0.0384020i	−0.0201806	+	0.00592556i
$43$	2.24116	−	4.90745i	0.341773	−	0.748379i	−0.658217	−	0.752828i	$-0.728689\pi$
$43$	2.24116	−	4.90745i	0.341773	−	0.748379i	0.999990	+	0.00444961i	$0.00141636\pi$
$44$	−0.576814	−	4.01183i	−0.0869579	−	0.604806i
$45$	2.00000			0.298142
$46$	−0.305139	+	0.292633i	−0.0449903	+	0.0431464i
$47$	−2.72825			−0.397956			−0.198978	−	0.980004i	$-0.563762\pi$
$47$	−2.72825			−0.397956			−0.198978	+	0.980004i	$0.563762\pi$
$48$	0.562632	+	3.91319i	0.0812089	+	0.564821i
$49$	−1.91476	+	4.19273i	−0.273537	+	0.598962i
$50$	−0.0845850	+	0.0248364i	−0.0119621	+	0.00351240i
$51$	2.85459	−	3.29437i	0.399723	−	0.461305i
$52$	4.09173	+	1.20144i	0.567420	+	0.166610i
$53$	−0.230732	+	0.148283i	−0.0316935	+	0.0203682i	−0.556392	−	0.830920i	$-0.687815\pi$
$53$	−0.230732	+	0.148283i	−0.0316935	+	0.0203682i	0.524698	+	0.851288i	$0.324178\pi$
$54$	0.183106	+	0.400947i	0.0249176	+	0.0545620i
$55$	−1.33228	−	1.53753i	−0.179644	−	0.207321i
$56$	0.457783	+	0.294199i	0.0611738	+	0.0393140i
$57$	1.05662	−	7.34898i	0.139953	−	0.973396i
$58$	−0.0562393	+	0.391153i	−0.00738458	+	0.0513609i
$59$	6.74757	+	4.33640i	0.878458	+	0.564551i	0.900329	−	0.435210i	$-0.143326\pi$
$59$	6.74757	+	4.33640i	0.878458	+	0.564551i	−0.0218707	+	0.999761i	$0.506962\pi$
$60$	1.30463	+	1.50563i	0.168427	+	0.194375i
$61$	−1.33718	−	2.92802i	−0.171208	−	0.374894i	0.804505	−	0.593946i	$-0.202431\pi$
$61$	−1.33718	−	2.92802i	−0.171208	−	0.374894i	−0.975713	+	0.219052i	$0.929704\pi$
$62$	−0.0671837	+	0.0431763i	−0.00853233	+	0.00548340i
$63$	−2.96714	−	0.871230i	−0.373824	−	0.109765i
$64$	5.11714	−	5.90549i	0.639642	−	0.738187i
$65$	2.05384	−	0.603063i	0.254748	−	0.0748008i
$66$	0.0745040	−	0.163141i	0.00917081	−	0.0200813i
$67$	0.279610	+	1.94473i	0.0341598	+	0.237587i	0.999747	−	0.0224928i	$-0.00716029\pi$
$67$	0.279610	+	1.94473i	0.0341598	+	0.237587i	−0.965587	+	0.260080i	$0.916251\pi$
$68$	−8.68428			−1.05312
$69$	4.70653	−	0.921186i	0.566600	−	0.110898i
$70$	0.136307			0.0162918
$71$	1.58700	+	11.0378i	0.188342	+	1.30995i	0.836301	+	0.548271i	$0.184714\pi$
$71$	1.58700	+	11.0378i	0.188342	+	1.30995i	−0.647959	+	0.761675i	$0.724377\pi$
$72$	0.292401	−	0.640269i	0.0344598	−	0.0754564i
$73$	9.95039	−	2.92170i	1.16461	−	0.341959i	0.358385	−	0.933574i	$-0.383328\pi$
$73$	9.95039	−	2.92170i	1.16461	−	0.341959i	0.806221	+	0.591615i	$0.201509\pi$
$74$	0.640515	−	0.739194i	0.0744584	−	0.0859295i
$75$	0.959493	+	0.281733i	0.110793	+	0.0325317i
$76$	−12.4433	+	7.99684i	−1.42735	+	0.917300i
$77$	1.30675	+	2.86139i	0.148919	+	0.326086i
$78$	0.123574	+	0.142612i	0.0139920	+	0.0161476i
$79$	2.70849	+	1.74064i	0.304729	+	0.195837i	0.684064	−	0.729422i	$-0.260211\pi$
$79$	2.70849	+	1.74064i	0.304729	+	0.195837i	−0.379335	+	0.925259i	$0.623847\pi$
$80$	0.562632	−	3.91319i	0.0629042	−	0.437508i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.448178	−	0.288027i	−0.0494930	−	0.0318072i
$83$	2.85563	+	3.29557i	0.313446	+	0.361736i	0.890510	−	0.454963i	$-0.150347\pi$
$83$	2.85563	+	3.29557i	0.313446	+	0.361736i	−0.577065	+	0.816698i	$0.695802\pi$
$84$	−1.27964	−	2.80202i	−0.139620	−	0.305725i
$85$	−3.66709	+	2.35670i	−0.397752	+	0.255620i
$86$	−0.456334	−	0.133992i	−0.0492078	−	0.0144487i
$87$	2.93553	−	3.38779i	0.314722	−	0.363209i
$88$	−0.686997	+	0.201720i	−0.0732341	+	0.0215035i
$89$	0.266861	−	0.584343i	0.0282872	−	0.0619403i	−0.894961	−	0.446144i	$-0.852797\pi$
$89$	0.266861	−	0.584343i	0.0282872	−	0.0619403i	0.923248	+	0.384204i	$0.125524\pi$
$90$	−0.0250918	−	0.174517i	−0.00264491	−	0.0183957i
$91$	−3.30972			−0.346953
$92$	−7.52725	−	5.88446i	−0.784770	−	0.613498i
$93$	0.905910			0.0939385
$94$	0.0342284	+	0.238063i	0.00353038	+	0.0245544i
$95$	−3.08427	+	6.75361i	−0.316439	+	0.692906i
$96$	1.00977	−	0.296494i	0.103059	−	0.0302608i
$97$	3.62848	−	4.18748i	0.368416	−	0.425175i	−0.541026	−	0.841006i	$-0.681964\pi$
$97$	3.62848	−	4.18748i	0.368416	−	0.425175i	0.909442	+	0.415831i	$0.136509\pi$
$98$	0.389875	+	0.114478i	0.0393833	+	0.0115640i
$99$	3.42297	−	2.19981i	0.344021	−	0.221089i
$100$	−0.827602	−	1.81219i	−0.0827602	−	0.181219i
$101$	−2.94535	−	3.39912i	−0.293073	−	0.338225i	0.590049	−	0.807367i	$-0.299108\pi$
$101$	−2.94535	−	3.39912i	−0.293073	−	0.338225i	−0.883122	+	0.469143i	$0.844563\pi$
$102$	−0.323276	−	0.207757i	−0.0320091	−	0.0205710i
$103$	−1.38513	+	9.63380i	−0.136481	+	0.949247i	0.800367	+	0.599510i	$0.204638\pi$
$103$	−1.38513	+	9.63380i	−0.136481	+	0.949247i	−0.936848	+	0.349737i	$0.886271\pi$
$104$	0.107212	−	0.745675i	0.0105130	−	0.0731194i
$105$	−1.30075	−	0.835939i	−0.126940	−	0.0815793i
$106$	0.0158337	+	0.0182730i	0.00153790	+	0.00177483i
$107$	−3.07272	−	6.72833i	−0.297051	−	0.650452i	0.700979	−	0.713182i	$-0.252747\pi$
$107$	−3.07272	−	6.72833i	−0.297051	−	0.650452i	−0.998031	+	0.0627299i	$0.980019\pi$
$108$	−8.37985	+	5.38540i	−0.806351	+	0.518210i
$109$	−9.99029	−	2.93341i	−0.956897	−	0.280970i	−0.234241	−	0.972179i	$-0.575260\pi$
$109$	−9.99029	−	2.93341i	−0.956897	−	0.280970i	−0.722656	+	0.691208i	$0.757079\pi$
$110$	−0.117448	+	0.135542i	−0.0111983	+	0.0129235i
$111$	−10.6456	+	3.12583i	−1.01044	+	0.296691i
$112$	−2.53935	+	5.56040i	−0.239946	+	0.525408i
$113$	−2.78825	−	19.3927i	−0.262297	−	1.82431i	−0.515486	−	0.856898i	$-0.672389\pi$
$113$	−2.78825	−	19.3927i	−0.262297	−	1.82431i	0.253189	−	0.967417i	$-0.418520\pi$
$114$	−0.654518			−0.0613012
$115$	−4.77541	−	0.442111i	−0.445309	−	0.0412271i
$116$	−8.93053			−0.829179
$117$	0.609264	+	4.23753i	0.0563265	+	0.391760i
$118$	0.293734	−	0.643187i	0.0270404	−	0.0592102i
$119$	6.46699	−	1.89888i	0.592828	−	0.174070i
$120$	0.230471	−	0.265977i	0.0210390	−	0.0242803i
$121$	6.58311	+	1.93298i	0.598465	+	0.175725i
$122$	−0.238719	+	0.153415i	−0.0216126	+	0.0138896i
$123$	2.51047	+	5.49716i	0.226361	+	0.495662i
$124$	−1.18188	−	1.36396i	−0.106136	−	0.122487i
$125$	−0.841254	−	0.540641i	−0.0752440	−	0.0483564i
$126$	−0.0387969	+	0.269839i	−0.00345631	+	0.0240391i
$127$	2.49696	−	17.3667i	0.221569	−	1.54105i	−0.510536	−	0.859856i	$-0.670553\pi$
$127$	2.49696	−	17.3667i	0.221569	−	1.54105i	0.732105	−	0.681192i	$-0.238538\pi$
$128$	−2.35017	−	1.51036i	−0.207727	−	0.133498i
$129$	3.53296	+	4.07725i	0.311060	+	0.358982i
$130$	−0.0783898	−	0.171650i	−0.00687524	−	0.0150547i
$131$	−10.9767	+	7.05427i	−0.959035	+	0.616334i	−0.923731	−	0.383043i	$-0.874876\pi$
$131$	−10.9767	+	7.05427i	−0.959035	+	0.616334i	−0.0353039	+	0.999377i	$0.511240\pi$
$132$	3.88890	+	1.14188i	0.338486	+	0.0993883i
$133$	7.51770	−	8.67589i	0.651867	−	0.752295i
$134$	0.166187	−	0.0487968i	0.0143563	−	0.00421540i
$135$	−2.07708	+	4.54816i	−0.178766	+	0.391443i
$136$	0.218329	+	1.51851i	0.0187216	+	0.130211i
$137$	21.5268			1.83916			0.919580	−	0.392903i	$-0.128529\pi$
$137$	21.5268			1.83916			0.919580	+	0.392903i	$0.128529\pi$
$138$	−0.139429	−	0.399128i	−0.0118690	−	0.0339760i
$139$	−16.3719			−1.38864			−0.694322	−	0.719665i	$-0.744295\pi$
$139$	−16.3719			−1.38864			−0.694322	+	0.719665i	$0.744295\pi$
$140$	0.438384	+	3.04903i	0.0370502	+	0.257690i
$141$	1.13336	−	2.48170i	0.0954458	−	0.208997i
$142$	0.943233	−	0.276958i	0.0791544	−	0.0232418i
$143$	2.85181	−	3.29117i	0.238480	−	0.275221i
$144$	7.58658	+	2.22762i	0.632215	+	0.185635i
$145$	−3.77108	+	2.42352i	−0.313171	+	0.201263i
$146$	−0.379780	−	0.831602i	−0.0314308	−	0.0688239i
$147$	−3.01843	−	3.48345i	−0.248956	−	0.287310i
$148$	18.5950	+	11.9502i	1.52850	+	0.982304i
$149$	−2.74972	+	19.1247i	−0.225266	+	1.56676i	0.492399	+	0.870370i	$0.336120\pi$
$149$	−2.74972	+	19.1247i	−0.225266	+	1.56676i	−0.717665	+	0.696389i	$0.754789\pi$
$150$	0.0125459	−	0.0872586i	0.00102437	−	0.00712464i
$151$	16.8366	+	10.8202i	1.37015	+	0.880539i	0.998849	−	0.0479750i	$-0.0152768\pi$
$151$	16.8366	+	10.8202i	1.37015	+	0.880539i	0.371297	+	0.928514i	$0.378913\pi$
$152$	1.71114	+	1.97476i	0.138792	+	0.160174i
$153$	−3.62165	−	7.93032i	−0.292793	−	0.641128i
$154$	0.233287	−	0.149924i	0.0187988	−	0.0120812i
$155$	−0.869215	−	0.255224i	−0.0698170	−	0.0205001i
$156$	−2.79263	+	3.22287i	−0.223590	+	0.258036i
$157$	−5.54048	+	1.62683i	−0.442179	+	0.129835i	−0.495241	−	0.868756i	$-0.664920\pi$
$157$	−5.54048	+	1.62683i	−0.442179	+	0.129835i	0.0530620	+	0.998591i	$0.483102\pi$
$158$	0.117905	−	0.258177i	0.00938006	−	0.0205395i
$159$	−0.0390330	−	0.271480i	−0.00309552	−	0.0215298i
$160$	−1.05240			−0.0831992
$161$	6.89206	+	2.73614i	0.543170	+	0.215638i
$162$	0.0881559			0.00692618
$163$	−1.25289	−	8.71401i	−0.0981335	−	0.682534i	−0.978197	−	0.207678i	$-0.933409\pi$
$163$	−1.25289	−	8.71401i	−0.0981335	−	0.682534i	0.880064	−	0.474856i	$-0.157500\pi$
$164$	5.00143	−	10.9516i	0.390546	−	0.855176i
$165$	1.95204	−	0.573170i	0.151966	−	0.0446212i
$166$	0.251740	−	0.290524i	0.0195388	−	0.0225490i
$167$	18.7367	+	5.50159i	1.44989	+	0.425726i	0.909505	−	0.415692i	$-0.136461\pi$
$167$	18.7367	+	5.50159i	1.44989	+	0.425726i	0.540384	+	0.841418i	$0.318279\pi$
$168$	−0.457783	+	0.294199i	−0.0353187	+	0.0226980i
$169$	−3.49698	−	7.65732i	−0.268998	−	0.589024i
$170$	0.251649	+	0.290419i	0.0193006	+	0.0222741i
$171$	−12.4919	−	8.02803i	−0.955276	−	0.613919i
$172$	1.52960	−	10.6386i	0.116631	−	0.811188i
$173$	−3.07149	+	21.3627i	−0.233521	+	1.62417i	0.449155	+	0.893454i	$0.351725\pi$
$173$	−3.07149	+	21.3627i	−0.233521	+	1.62417i	−0.682676	+	0.730721i	$0.739184\pi$
$174$	−0.332443	−	0.213648i	−0.0252024	−	0.0161966i
$175$	1.01255	+	1.16854i	0.0765413	+	0.0883333i
$176$	−3.34120	−	7.31621i	−0.251852	−	0.551480i
$177$	−6.74757	+	4.33640i	−0.507178	+	0.325944i
$178$	−0.0543370	−	0.0159548i	−0.00407273	−	0.00119586i
$179$	10.0553	−	11.6044i	0.751567	−	0.867354i	−0.243152	−	0.969988i	$-0.578182\pi$
$179$	10.0553	−	11.6044i	0.751567	−	0.867354i	0.994719	+	0.102634i	$0.0327270\pi$
$180$	3.82306	−	1.12255i	0.284954	−	0.0836700i
$181$	0.340209	−	0.744955i	0.0252876	−	0.0553720i	−0.896567	−	0.442909i	$-0.853947\pi$
$181$	0.340209	−	0.744955i	0.0252876	−	0.0553720i	0.921854	+	0.387537i	$0.126674\pi$
$182$	0.0415234	+	0.288802i	0.00307792	+	0.0214074i
$183$	3.21890			0.237948
$184$	−0.839703	+	1.46414i	−0.0619037	+	0.107938i
$185$	11.0950			0.815724
$186$	−0.0113655	−	0.0790485i	−0.000833356	−	0.00579612i
$187$	−3.68403	+	8.06690i	−0.269403	+	0.589910i
$188$	−5.21513	+	1.53130i	−0.380353	+	0.111682i
$189$	5.06273	−	5.84270i	0.368259	−	0.424994i
$190$	0.628006	+	0.184399i	0.0455603	+	0.0133777i
$191$	−3.58868	+	2.30630i	−0.259668	+	0.166878i	−0.663997	−	0.747735i	$-0.731141\pi$
$191$	−3.58868	+	2.30630i	−0.259668	+	0.166878i	0.404329	+	0.914613i	$0.367505\pi$
$192$	3.24609	+	7.10794i	0.234266	+	0.512972i
$193$	−3.16580	−	3.65352i	−0.227879	−	0.262986i	0.630283	−	0.776366i	$-0.282939\pi$
$193$	−3.16580	−	3.65352i	−0.227879	−	0.262986i	−0.858162	+	0.513379i	$0.828393\pi$
$194$	−0.410917	−	0.264080i	−0.0295021	−	0.0189598i
$195$	−0.304632	+	2.11876i	−0.0218152	+	0.151728i
$196$	−1.30684	+	9.08924i	−0.0933454	+	0.649232i
$197$	−0.220925	−	0.141980i	−0.0157403	−	0.0101157i	0.532747	−	0.846275i	$-0.321160\pi$
$197$	−0.220925	−	0.141980i	−0.0157403	−	0.0101157i	−0.548487	+	0.836159i	$0.684796\pi$
$198$	−0.234896	−	0.271085i	−0.0166934	−	0.0192652i
$199$	−1.79719	−	3.93530i	−0.127399	−	0.278966i	0.835175	−	0.549985i	$-0.185367\pi$
$199$	−1.79719	−	3.93530i	−0.127399	−	0.278966i	−0.962574	+	0.271019i	$0.912639\pi$
$200$	−0.296070	+	0.190272i	−0.0209353	+	0.0134543i
$201$	−1.88514	−	0.553528i	−0.132968	−	0.0390429i
$202$	−0.259650	+	0.299652i	−0.0182689	+	0.0210835i
$203$	6.65037	−	1.95273i	0.466765	−	0.137054i
$204$	3.60758	−	7.89950i	0.252581	−	0.553076i
$205$	−0.860048	−	5.98176i	−0.0600684	−	0.417785i
$206$	0.858010			0.0597804
$207$	2.23445	−	9.32777i	0.155305	−	0.648325i
$208$	8.46252			0.586770
$209$	2.14964	+	14.9511i	0.148694	+	1.03419i
$210$	−0.0566239	+	0.123989i	−0.00390742	+	0.00855605i
$211$	6.30147	−	1.85028i	0.433811	−	0.127378i	−0.0575338	−	0.998344i	$-0.518324\pi$
$211$	6.30147	−	1.85028i	0.433811	−	0.127378i	0.491345	+	0.870965i	$0.336506\pi$
$212$	−0.357824	+	0.412951i	−0.0245755	+	0.0283616i
$213$	−10.6996	−	3.14169i	−0.733125	−	0.215265i
$214$	−0.548554	+	0.352535i	−0.0374984	+	0.0240988i
$215$	−2.24116	−	4.90745i	−0.152846	−	0.334685i
$216$	1.15235	+	1.32989i	0.0784077	+	0.0904874i
$217$	1.17836	+	0.757286i	0.0799923	+	0.0514079i
$218$	−0.130629	+	0.908542i	−0.00884728	+	0.0615342i
$219$	−1.47587	+	10.2649i	−0.0997301	+	0.693638i
$220$	−3.40967	−	2.19126i	−0.229880	−	0.147735i
$221$	−6.11040	−	7.05178i	−0.411030	−	0.474354i
$222$	0.406315	+	0.889705i	0.0272701	+	0.0597131i
$223$	−7.74566	+	4.97783i	−0.518688	+	0.333340i	−0.773653	−	0.633610i	$-0.781572\pi$
$223$	−7.74566	+	4.97783i	−0.518688	+	0.333340i	0.254965	+	0.966950i	$0.417936\pi$
$224$	1.56130	+	0.458439i	0.104319	+	0.0306308i
$225$	1.30972	−	1.51150i	0.0873148	−	0.100767i
$226$	−1.65720	+	0.486598i	−0.110235	+	0.0323680i
$227$	−3.68538	+	8.06985i	−0.244607	+	0.535615i	−0.991619	−	0.129196i	$-0.958760\pi$
$227$	−3.68538	+	8.06985i	−0.244607	+	0.535615i	0.747012	+	0.664810i	$0.231488\pi$
$228$	−2.10504	−	14.6408i	−0.139409	−	0.969614i
$229$	−8.38484			−0.554086			−0.277043	−	0.960858i	$-0.589354\pi$
$229$	−8.38484			−0.554086			−0.277043	+	0.960858i	$0.589354\pi$
$230$	0.0213338	+	0.422242i	0.00140671	+	0.0278418i
$231$	−3.14566			−0.206969
$232$	0.224520	+	1.56157i	0.0147405	+	0.102522i
$233$	−9.97561	+	21.8435i	−0.653524	+	1.43102i	0.234911	+	0.972017i	$0.424520\pi$
$233$	−9.97561	+	21.8435i	−0.653524	+	1.43102i	−0.888435	+	0.459002i	$0.848207\pi$
$234$	0.362117	−	0.106327i	0.0236723	−	0.00695082i
$235$	−1.78662	+	2.06187i	−0.116547	+	0.134502i
$236$	15.3321	+	4.50191i	0.998034	+	0.293049i
$237$	−2.70849	+	1.74064i	−0.175935	+	0.113067i
$238$	−0.246828	−	0.540478i	−0.0159995	−	0.0350340i
$239$	7.35914	+	8.49290i	0.476023	+	0.549360i	0.942077	−	0.335396i	$-0.108870\pi$
$239$	7.35914	+	8.49290i	0.476023	+	0.549360i	−0.466054	+	0.884756i	$0.654325\pi$
$240$	3.32584	+	2.13739i	0.214682	+	0.137968i
$241$	4.00004	−	27.8209i	0.257665	−	1.79210i	−0.291689	−	0.956513i	$-0.594217\pi$
$241$	4.00004	−	27.8209i	0.257665	−	1.79210i	0.549355	−	0.835589i	$-0.314874\pi$
$242$	0.0860778	−	0.598684i	0.00553329	−	0.0384849i
$243$	−13.4601	−	8.65025i	−0.863463	−	0.554914i
$244$	−4.19948	−	4.84646i	−0.268844	−	0.310263i
$245$	1.91476	+	4.19273i	0.122329	+	0.267864i
$246$	0.448178	−	0.288027i	0.0285748	−	0.0183639i
$247$	−15.2489	−	4.47747i	−0.970262	−	0.284895i
$248$	−0.208786	+	0.240952i	−0.0132579	+	0.0153004i
$249$	−4.18403	+	1.22854i	−0.265152	+	0.0778556i
$250$	−0.0366213	+	0.0801894i	−0.00231613	+	0.00507163i
$251$	3.91272	+	27.2135i	0.246969	+	1.71770i	0.615541	+	0.788105i	$0.288938\pi$
$251$	3.91272	+	27.2135i	0.246969	+	1.71770i	−0.368572	+	0.929599i	$0.620153\pi$
$252$	−6.16077			−0.388092
$253$	−8.65932	+	4.49583i	−0.544407	+	0.282650i
$254$	−1.54672			−0.0970501
$255$	−0.620362	−	4.31471i	−0.0388486	−	0.270198i
$256$	6.38987	−	13.9919i	0.399367	−	0.874492i
$257$	−17.0432	+	5.00435i	−1.06313	+	0.312163i	−0.766110	−	0.642709i	$-0.777810\pi$
$257$	−17.0432	+	5.00435i	−1.06313	+	0.312163i	−0.297018	+	0.954872i	$0.595992\pi$
$258$	0.311451	−	0.359434i	0.0193901	−	0.0223774i
$259$	−16.4603	−	4.83317i	−1.02279	−	0.300318i
$260$	3.58750	−	2.30555i	0.222487	−	0.142984i
$261$	−3.72435	−	8.15519i	−0.230531	−	0.504794i
$262$	0.753257	+	0.869305i	0.0465364	+	0.0537059i
$263$	−7.35320	−	4.72561i	−0.453417	−	0.291394i	0.293930	−	0.955827i	$-0.405037\pi$
$263$	−7.35320	−	4.72561i	−0.453417	−	0.291394i	−0.747348	+	0.664433i	$0.768673\pi$
$264$	0.101897	−	0.708712i	0.00627135	−	0.0436182i
$265$	−0.0390330	+	0.271480i	−0.00239778	+	0.0166769i
$266$	−0.851362	−	0.547137i	−0.0522004	−	0.0335471i
$267$	0.420680	+	0.485490i	0.0257452	+	0.0297115i
$268$	1.62601	+	3.56047i	0.0993246	+	0.217491i
$269$	2.46553	−	1.58450i	0.150326	−	0.0966086i	−0.463316	−	0.886193i	$-0.653340\pi$
$269$	2.46553	−	1.58450i	0.150326	−	0.0966086i	0.613642	+	0.789585i	$0.289704\pi$
$270$	0.422925	+	0.124182i	0.0257384	+	0.00755747i
$271$	4.29616	−	4.95803i	0.260973	−	0.301179i	−0.610108	−	0.792318i	$-0.708874\pi$
$271$	4.29616	−	4.95803i	0.260973	−	0.301179i	0.871081	+	0.491139i	$0.163419\pi$
$272$	−16.5353	+	4.85519i	−1.00260	+	0.294389i
$273$	1.37491	−	3.01063i	0.0832132	−	0.182212i
$274$	−0.270073	−	1.87840i	−0.0163157	−	0.113478i
$275$	−2.03445			−0.122682
$276$	8.47963	−	4.40253i	0.510414	−	0.265001i
$277$	−22.7888			−1.36924			−0.684622	−	0.728898i	$-0.740033\pi$
$277$	−22.7888			−1.36924			−0.684622	+	0.728898i	$0.740033\pi$
$278$	0.205400	+	1.42859i	0.0123191	+	0.0856809i
$279$	0.752658	−	1.64809i	0.0450604	−	0.0986686i
$280$	0.522125	−	0.153310i	0.0312029	−	0.00916201i
$281$	9.32744	−	10.7644i	0.556429	−	0.642153i	−0.405940	−	0.913900i	$-0.633056\pi$
$281$	9.32744	−	10.7644i	0.556429	−	0.642153i	0.962369	+	0.271747i	$0.0876013\pi$
$282$	−0.230769	−	0.0677599i	−0.0137421	−	0.00403504i
$283$	19.9441	−	12.8173i	1.18555	−	0.761910i	0.209155	−	0.977882i	$-0.432929\pi$
$283$	19.9441	−	12.8173i	1.18555	−	0.761910i	0.976399	+	0.215973i	$0.0692923\pi$
$284$	9.22884	+	20.2083i	0.547631	+	1.19914i
$285$	−4.86205	−	5.61110i	−0.288003	−	0.332373i
$286$	−0.322961	−	0.207554i	−0.0190971	−	0.0122730i
$287$	−1.32981	+	9.24901i	−0.0784960	+	0.545952i
$288$	0.299543	−	2.08337i	0.0176507	−	0.122764i
$289$	1.68384	+	1.08214i	0.0990493	+	0.0636551i
$290$	0.258785	+	0.298654i	0.0151964	+	0.0175375i
$291$	2.30175	+	5.04012i	0.134931	+	0.295457i
$292$	17.3806	−	11.1698i	1.01712	−	0.653664i
$293$	4.10110	+	1.20419i	0.239589	+	0.0703497i	0.399323	−	0.916810i	$-0.369245\pi$
$293$	4.10110	+	1.20419i	0.239589	+	0.0703497i	−0.159734	+	0.987160i	$0.551064\pi$
$294$	−0.266092	+	0.307087i	−0.0155188	+	0.0179097i
$295$	7.69595	−	2.25973i	0.448075	−	0.131567i
$296$	1.62210	−	3.55191i	0.0942827	−	0.206450i
$297$	1.44766	+	10.0687i	0.0840017	+	0.584245i
$298$	1.70330			0.0986692
$299$	−0.518014	−	10.2526i	−0.0299575	−	0.592926i
$300$	1.99223			0.115021
$301$	1.18715	+	8.25681i	0.0684262	+	0.475915i
$302$	0.732929	−	1.60489i	0.0421753	−	0.0923511i
$303$	4.31549	−	1.26714i	0.247918	−	0.0727954i
$304$	−19.2218	+	22.1831i	−1.10244	+	1.27229i
$305$	−3.08851	−	0.906870i	−0.176848	−	0.0519272i
$306$	−0.646552	+	0.415514i	−0.0369609	+	0.0237533i
$307$	−3.71586	−	8.13661i	−0.212076	−	0.464381i	0.773461	−	0.633844i	$-0.218524\pi$
$307$	−3.71586	−	8.13661i	−0.212076	−	0.464381i	−0.985536	+	0.169463i	$0.945797\pi$
$308$	4.10393	+	4.73619i	0.233843	+	0.269869i
$309$	−8.18781	−	5.26199i	−0.465788	−	0.299344i
$310$	−0.0113655	+	0.0790485i	−0.000645515	+	0.00448965i
$311$	3.32224	−	23.1067i	0.188387	−	1.31026i	−0.647798	−	0.761812i	$-0.724310\pi$
$311$	3.32224	−	23.1067i	0.188387	−	1.31026i	0.836185	−	0.548447i	$-0.184781\pi$
$312$	0.633752	+	0.407288i	0.0358792	+	0.0230581i
$313$	14.7416	+	17.0127i	0.833244	+	0.961615i	0.999701	−	0.0244337i	$-0.00777827\pi$
$313$	14.7416	+	17.0127i	0.833244	+	0.961615i	−0.166457	+	0.986049i	$0.553233\pi$
$314$	0.211465	+	0.463045i	0.0119337	+	0.0261311i
$315$	−2.60149	+	1.67188i	−0.146578	+	0.0941997i
$316$	6.15434	+	1.80708i	0.346209	+	0.101656i
$317$	−8.34970	+	9.63606i	−0.468966	+	0.541215i	−0.940124	−	0.340834i	$-0.889291\pi$
$317$	−8.34970	+	9.63606i	−0.468966	+	0.541215i	0.471158	+	0.882049i	$0.343836\pi$
$318$	−0.0231993	+	0.00681193i	−0.00130095	+	0.000381994i
$319$	−3.78849	+	8.29564i	−0.212115	+	0.464467i
$320$	−1.11206	−	7.73455i	−0.0621661	−	0.432375i
$321$	7.39676			0.412847
$322$	0.152285	−	0.635719i	0.00848651	−	0.0354272i
$323$	32.3642			1.80079
$324$	0.283524	+	1.97195i	0.0157513	+	0.109553i
$325$	0.889217	−	1.94711i	0.0493249	−	0.108006i
$326$	−0.744654	+	0.218650i	−0.0412426	+	0.0121099i
$327$	6.81845	−	7.86891i	0.377061	−	0.435151i
$328$	−2.04071	−	0.599206i	−0.112679	−	0.0330856i
$329$	3.54876	−	2.28065i	0.195650	−	0.125736i
$330$	−0.0745040	−	0.163141i	−0.00410131	−	0.00898062i
$331$	10.7382	+	12.3926i	0.590227	+	0.681158i	0.969771	−	0.244015i	$-0.0784647\pi$
$331$	10.7382	+	12.3926i	0.590227	+	0.681158i	−0.379545	+	0.925173i	$0.623919\pi$
$332$	7.30834	+	4.69678i	0.401097	+	0.257769i
$333$	−3.15798	+	21.9642i	−0.173056	+	1.20363i
$334$	0.244993	−	1.70396i	0.0134054	−	0.0932366i
$335$	1.65284	+	1.06221i	0.0903041	+	0.0580349i
$336$	−4.00303	−	4.61974i	−0.218383	−	0.252028i
$337$	11.3983	+	24.9589i	0.620907	+	1.35960i	0.914858	+	0.403776i	$0.132303\pi$
$337$	11.3983	+	24.9589i	0.620907	+	1.35960i	−0.293951	+	0.955821i	$0.594970\pi$
$338$	−0.624294	+	0.401210i	−0.0339571	+	0.0218229i
$339$	18.7985	+	5.51975i	1.02100	+	0.299792i
$340$	−5.68700	+	6.56314i	−0.308421	+	0.355936i
$341$	−1.76837	+	0.519240i	−0.0957626	+	0.0281184i
$342$	−0.543793	+	1.19074i	−0.0294050	+	0.0643879i
$343$	−2.55459	−	17.7675i	−0.137935	−	0.959357i
$344$	−1.89870			−0.102371
$345$	2.38594	−	4.16021i	0.128454	−	0.223978i
$346$	1.90261			0.102285
$347$	−0.858953	−	5.97415i	−0.0461110	−	0.320709i	−0.999802	−	0.0199196i	$-0.993659\pi$
$347$	−0.858953	−	5.97415i	−0.0461110	−	0.320709i	0.953691	−	0.300789i	$-0.0972501\pi$
$348$	3.70988	−	8.12350i	0.198870	−	0.435465i
$349$	−8.00915	+	2.35170i	−0.428720	+	0.125883i	−0.488972	−	0.872300i	$-0.662628\pi$
$349$	−8.00915	+	2.35170i	−0.428720	+	0.125883i	0.0602518	+	0.998183i	$0.480810\pi$
$350$	0.0892619	−	0.103014i	0.00477125	−	0.00550632i
$351$	−10.2692	−	3.01532i	−0.548130	−	0.160946i
$352$	−1.80116	+	1.15753i	−0.0960021	+	0.0616968i
$353$	−10.8642	−	23.7892i	−0.578242	−	1.26617i	−0.942291	−	0.334794i	$-0.891333\pi$
$353$	−10.8642	−	23.7892i	−0.578242	−	1.26617i	0.364049	−	0.931380i	$-0.381394\pi$
$354$	0.463042	+	0.534379i	0.0246104	+	0.0284019i
$355$	9.38108	+	6.02885i	0.497896	+	0.319978i
$356$	0.182134	−	1.26677i	0.00965310	−	0.0671388i
$357$	−0.959204	+	6.67141i	−0.0507664	+	0.353088i
$358$	−1.13874	−	0.731822i	−0.0601841	−	0.0386780i
$359$	−3.70672	−	4.27779i	−0.195633	−	0.225773i	0.649454	−	0.760401i	$-0.274997\pi$
$359$	−3.70672	−	4.27779i	−0.195633	−	0.225773i	−0.845088	+	0.534628i	$0.820452\pi$
$360$	−0.292401	−	0.640269i	−0.0154109	−	0.0337451i
$361$	30.3894	−	19.5301i	1.59944	−	1.02790i
$362$	−0.0692719	−	0.0203401i	−0.00364085	−	0.00106905i
$363$	−4.49302	+	5.18522i	−0.235822	+	0.272154i
$364$	−6.32663	+	1.85767i	−0.331605	+	0.0973682i
$365$	4.30805	−	9.43331i	0.225494	−	0.493762i
$366$	−0.0403840	−	0.280877i	−0.00211091	−	0.0146817i
$367$	−12.3147			−0.642822			−0.321411	−	0.946940i	$-0.604157\pi$
$367$	−12.3147			−0.642822			−0.321411	+	0.946940i	$0.604157\pi$
$368$	−17.6221	−	6.99596i	−0.918615	−	0.364690i
$369$	12.0866			0.629201
$370$	−0.139197	−	0.968138i	−0.00723652	−	0.0503311i
$371$	0.176169	−	0.385756i	0.00914624	−	0.0200275i
$372$	1.73167	−	0.508465i	0.0897831	−	0.0263627i
$373$	−19.0734	+	22.0119i	−0.987585	+	1.13973i	0.00260397	+	0.999997i	$0.499171\pi$
$373$	−19.0734	+	22.0119i	−0.987585	+	1.13973i	−0.990189	+	0.139737i	$0.955374\pi$
$374$	0.750126	+	0.220257i	0.0387881	+	0.0113892i
$375$	0.841254	−	0.540641i	0.0434421	−	0.0279186i
$376$	0.398872	+	0.873407i	0.0205702	+	0.0450426i
$377$	−6.28366	−	7.25173i	−0.323625	−	0.373483i
$378$	−0.573343	−	0.368465i	−0.0294896	−	0.0189518i
$379$	4.74698	−	33.0160i	0.243836	−	1.69592i	−0.388683	−	0.921372i	$-0.627070\pi$
$379$	4.74698	−	33.0160i	0.243836	−	1.69592i	0.632519	−	0.774545i	$-0.282021\pi$
$380$	−2.10504	+	14.6408i	−0.107986	+	0.751060i
$381$	14.7601	+	9.48571i	0.756181	+	0.485968i
$382$	0.246268	+	0.284209i	0.0126002	+	0.0145414i
$383$	12.9139	+	28.2775i	0.659870	+	1.44491i	0.882643	+	0.470044i	$0.155762\pi$
$383$	12.9139	+	28.2775i	0.659870	+	1.44491i	−0.222773	+	0.974870i	$0.571511\pi$
$384$	2.35017	−	1.51036i	0.119931	−	0.0770753i
$385$	3.01824	+	0.886235i	0.153824	+	0.0451667i
$386$	−0.279084	+	0.322080i	−0.0142050	+	0.0163934i
$387$	10.3529	−	3.03988i	0.526267	−	0.154526i
$388$	4.58560	−	10.0411i	0.232799	−	0.509758i
$389$	1.80544	+	12.5571i	0.0915394	+	0.636670i	0.983005	+	0.183581i	$0.0587690\pi$
$389$	1.80544	+	12.5571i	0.0915394	+	0.636670i	−0.891465	+	0.453089i	$0.850322\pi$
$390$	0.188702			0.00955531
$391$	6.89440	+	19.7358i	0.348665	+	0.998085i
$392$	1.62218			0.0819324
$393$	−1.85692	−	12.9152i	−0.0936692	−	0.651484i
$394$	−0.00961727	+	0.0210589i	−0.000484511	+	0.00106093i
$395$	3.08917	−	0.907063i	0.155433	−	0.0456393i
$396$	5.30841	−	6.12623i	0.266757	−	0.307855i
$397$	−11.8219	−	3.47123i	−0.593325	−	0.174216i	−0.0287344	−	0.999587i	$-0.509148\pi$
$397$	−11.8219	−	3.47123i	−0.593325	−	0.174216i	−0.564590	+	0.825371i	$0.690966\pi$
$398$	−0.320841	+	0.206192i	−0.0160823	+	0.0103355i
$399$	4.76890	+	10.4424i	0.238744	+	0.522776i
$400$	−2.58895	−	2.98780i	−0.129447	−	0.149390i
$401$	−28.3895	−	18.2448i	−1.41770	−	0.911102i	−0.999997	−	0.00251937i	$-0.999198\pi$
$401$	−28.3895	−	18.2448i	−1.41770	−	0.911102i	−0.417705	−	0.908583i	$-0.637166\pi$
$402$	−0.0246493	+	0.171440i	−0.00122940	+	0.00855063i
$403$	0.275970	−	1.91941i	0.0137470	−	0.0956126i
$404$	−7.53797	−	4.84436i	−0.375028	−	0.241016i
$405$	0.654861	+	0.755750i	0.0325403	+	0.0375535i
$406$	−0.253827	−	0.555804i	−0.0125972	−	0.0275841i
$407$	18.9890	−	12.2035i	0.941249	−	0.604904i
$408$	−1.47199	−	0.432214i	−0.0728741	−	0.0213978i
$409$	−10.6316	+	12.2695i	−0.525698	+	0.606688i	−0.955048	−	0.296450i	$-0.904197\pi$
$409$	−10.6316	+	12.2695i	−0.525698	+	0.606688i	0.429350	+	0.903138i	$0.358743\pi$
$410$	−0.511170	+	0.150093i	−0.0252449	+	0.00741257i
$411$	−8.94256	+	19.5815i	−0.441104	+	0.965883i
$412$	2.75950	+	19.1927i	0.135951	+	0.945558i
$413$	−12.4018			−0.610254
$414$	−0.841961	−	0.0779495i	−0.0413801	−	0.00383101i
$415$	4.36066			0.214057
$416$	−0.320594	−	2.22978i	−0.0157184	−	0.109324i
$417$	6.80112	−	14.8924i	0.333052	−	0.729282i
$418$	1.27764	−	0.375150i	0.0624916	−	0.0183492i
$419$	8.76692	−	10.1176i	0.428292	−	0.494275i	−0.500053	−	0.865995i	$-0.666686\pi$
$419$	8.76692	−	10.1176i	0.428292	−	0.494275i	0.928345	+	0.371719i	$0.121232\pi$
$420$	−2.95561	−	0.867845i	−0.144219	−	0.0423465i
$421$	−10.9478	+	7.03572i	−0.533563	+	0.342900i	−0.779517	−	0.626382i	$-0.784535\pi$
$421$	−10.9478	+	7.03572i	−0.533563	+	0.342900i	0.245954	+	0.969282i	$0.420899\pi$
$422$	−0.240510	−	0.526644i	−0.0117079	−	0.0256366i
$423$	−3.57325	−	4.12375i	−0.173737	−	0.200504i
$424$	0.0812036	+	0.0521864i	0.00394360	+	0.00253439i
$425$	−0.620362	+	4.31471i	−0.0300920	+	0.209294i
$426$	−0.139903	+	0.973048i	−0.00677833	+	0.0471443i
$427$	4.18698	+	2.69081i	0.202622	+	0.130217i
$428$	−9.65005	−	11.1367i	−0.466453	−	0.538315i
$429$	1.80906	+	3.96130i	0.0873424	+	0.191253i
$430$	−0.400100	+	0.257128i	−0.0192945	+	0.0123998i
$431$	−8.97982	−	2.63671i	−0.432543	−	0.127006i	0.0582112	−	0.998304i	$-0.481460\pi$
$431$	−8.97982	−	2.63671i	−0.432543	−	0.127006i	−0.490754	+	0.871298i	$0.663279\pi$
$432$	−12.9447	+	14.9390i	−0.622804	+	0.718754i
$433$	32.5898	−	9.56922i	1.56616	−	0.459867i	0.620283	−	0.784378i	$-0.287018\pi$
$433$	32.5898	−	9.56922i	1.56616	−	0.459867i	0.945882	+	0.324511i	$0.105200\pi$
$434$	0.0512961	−	0.112323i	0.00246229	−	0.00539167i
$435$	−0.637953	−	4.43706i	−0.0305875	−	0.212741i
$436$	−20.7432			−0.993419
$437$	28.0522	+	21.9300i	1.34192	+	1.04905i
$438$	0.914218			0.0436830
$439$	−4.53831	−	31.5646i	−0.216602	−	1.50650i	−0.750456	−	0.660921i	$-0.770166\pi$
$439$	−4.53831	−	31.5646i	−0.216602	−	1.50650i	0.533854	−	0.845577i	$-0.320743\pi$
$440$	−0.297437	+	0.651296i	−0.0141798	+	0.0310493i
$441$	−8.84511	+	2.59716i	−0.421196	+	0.123674i
$442$	−0.538668	+	0.621656i	−0.0256218	+	0.0295691i
$443$	−29.3691	−	8.62354i	−1.39537	−	0.409717i	−0.504277	−	0.863542i	$-0.668241\pi$
$443$	−29.3691	−	8.62354i	−1.39537	−	0.409717i	−0.891091	+	0.453825i	$0.850059\pi$
$444$	−18.5950	+	11.9502i	−0.882477	+	0.567134i
$445$	−0.266861	−	0.584343i	−0.0126504	−	0.0277005i
$446$	0.531535	+	0.613424i	0.0251689	+	0.0290465i
$447$	−16.2542	−	10.4459i	−0.768797	−	0.494076i
$448$	−1.71947	+	11.9592i	−0.0812373	+	0.565018i
$449$	2.39840	−	16.6812i	0.113187	−	0.787236i	−0.851597	−	0.524196i	$-0.824366\pi$
$449$	2.39840	−	16.6812i	0.113187	−	0.787236i	0.964785	−	0.263040i	$-0.0847251\pi$
$450$	−0.148323	−	0.0953214i	−0.00699201	−	0.00449349i
$451$	−8.05133	−	9.29173i	−0.379122	−	0.437530i
$452$	−16.2145	−	35.5048i	−0.762666	−	1.67001i
$453$	−16.8366	+	10.8202i	−0.791054	+	0.508380i
$454$	0.750400	+	0.220337i	0.0352180	+	0.0103409i
$455$	−2.16741	+	2.50132i	−0.101610	+	0.117264i
$456$	−2.50714	+	0.736163i	−0.117408	+	0.0344740i
$457$	−1.12972	+	2.47375i	−0.0528463	+	0.115717i	−0.934213	−	0.356715i	$-0.883897\pi$
$457$	−1.12972	+	2.47375i	−0.0528463	+	0.115717i	0.881367	+	0.472432i	$0.156624\pi$
$458$	0.105195	+	0.731650i	0.00491546	+	0.0341877i
$459$	21.7954			1.01732
$460$	−9.37648	+	1.83521i	−0.437181	+	0.0855672i
$461$	−35.7457			−1.66484			−0.832421	−	0.554143i	$-0.813046\pi$
$461$	−35.7457			−1.66484			−0.832421	+	0.554143i	$0.813046\pi$
$462$	0.0394651	+	0.274486i	0.00183608	+	0.0127702i
$463$	−17.3020	+	37.8860i	−0.804091	+	1.76071i	−0.173130	+	0.984899i	$0.555388\pi$
$463$	−17.3020	+	37.8860i	−0.804091	+	1.76071i	−0.630961	+	0.775814i	$0.717339\pi$
$464$	−17.0041	+	4.99286i	−0.789397	+	0.231788i
$465$	0.593245	−	0.684641i	0.0275111	−	0.0317495i
$466$	2.03119	+	0.596411i	0.0940931	+	0.0276282i
$467$	14.8682	−	9.55519i	0.688017	−	0.442161i	−0.149364	−	0.988782i	$-0.547722\pi$
$467$	14.8682	−	9.55519i	0.688017	−	0.442161i	0.837380	+	0.546621i	$0.184086\pi$
$468$	3.54305	+	7.75819i	0.163777	+	0.358623i
$469$	−1.98938	−	2.29587i	−0.0918610	−	0.106013i
$470$	0.202331	+	0.130030i	0.00933284	+	0.00599785i
$471$	0.821781	−	5.71561i	0.0378657	−	0.263361i
$472$	0.401733	−	2.79411i	0.0184913	−	0.128609i
$473$	−9.23343	−	5.93396i	−0.424553	−	0.272844i
$474$	0.185866	+	0.214501i	0.00853712	+	0.00985237i
$475$	3.08427	+	6.75361i	0.141516	+	0.309877i
$476$	11.2961	−	7.25953i	0.517754	−	0.332740i
$477$	−0.526324	−	0.154543i	−0.0240987	−	0.00707602i
$478$	0.648752	−	0.748699i	0.0296732	−	0.0342447i
$479$	11.4723	−	3.36858i	0.524184	−	0.153914i	−0.00892633	−	0.999960i	$-0.502841\pi$
$479$	11.4723	−	3.36858i	0.524184	−	0.153914i	0.533110	+	0.846046i	$0.321023\pi$
$480$	0.437181	−	0.957293i	0.0199545	−	0.0436942i
$481$	3.37991	+	23.5078i	0.154111	+	1.07186i
$482$	−2.47780			−0.112861
$483$	−5.35195	+	5.13260i	−0.243522	+	0.233541i
$484$	13.6687			0.621306
$485$	−0.788543	−	5.48444i	−0.0358059	−	0.249036i
$486$	−0.585941	+	1.28303i	−0.0265788	+	0.0581995i
$487$	18.1024	−	5.31536i	0.820300	−	0.240862i	0.155455	−	0.987843i	$-0.450316\pi$
$487$	18.1024	−	5.31536i	0.820300	−	0.240862i	0.664845	+	0.746981i	$0.268497\pi$
$488$	−0.741863	+	0.856156i	−0.0335826	+	0.0387563i
$489$	8.44701	+	2.48026i	0.381987	+	0.112161i
$490$	0.341830	−	0.219681i	0.0154423	−	0.00992416i
$491$	9.10363	+	19.9342i	0.410841	+	0.899616i	0.996055	+	0.0887373i	$0.0282832\pi$
$491$	9.10363	+	19.9342i	0.410841	+	0.899616i	−0.585214	+	0.810879i	$0.698990\pi$
$492$	7.88425	+	9.09891i	0.355450	+	0.410211i
$493$	16.4384	+	10.5643i	0.740349	+	0.475794i
$494$	−0.199387	+	1.38677i	−0.00897086	+	0.0623937i
$495$	0.579064	−	4.02748i	0.0260270	−	0.181022i
$496$	−3.01291	−	1.93628i	−0.135284	−	0.0869416i
$497$	−11.2912	−	13.0308i	−0.506480	−	0.584509i
$498$	0.159693	+	0.349679i	0.00715602	+	0.0156695i
$499$	8.48768	−	5.45470i	0.379961	−	0.244186i	−0.336694	−	0.941614i	$-0.609309\pi$
$499$	8.48768	−	5.45470i	0.379961	−	0.244186i	0.716655	+	0.697428i	$0.245672\pi$
$500$	−1.91153	−	0.561276i	−0.0854862	−	0.0251010i
$501$	−12.7879	+	14.7581i	−0.571323	+	0.659341i
$502$	2.32553	−	0.682837i	0.103793	−	0.0304765i
$503$	5.56885	−	12.1941i	0.248303	−	0.543707i	−0.743907	−	0.668283i	$-0.767030\pi$
$503$	5.56885	−	12.1941i	0.248303	−	0.543707i	0.992210	+	0.124576i	$0.0397569\pi$
$504$	0.154886	+	1.07726i	0.00689918	+	0.0479849i
$505$	−4.49768			−0.200144
$506$	0.500939	+	0.699196i	0.0222694	+	0.0310831i
$507$	8.41804			0.373858
$508$	−4.97451	−	34.5985i	−0.220708	−	1.53506i
$509$	8.03460	−	17.5933i	0.356127	−	0.779810i	−0.643766	−	0.765222i	$-0.722629\pi$
$509$	8.03460	−	17.5933i	0.356127	−	0.779810i	0.999894	−	0.0145879i	$-0.00464363\pi$
$510$	−0.368713	+	0.108264i	−0.0163269	+	0.00479400i
$511$	−10.5006	+	12.1183i	−0.464518	+	0.536082i
$512$	−6.66205	−	1.95615i	−0.294424	−	0.0864506i
$513$	31.2297	−	20.0701i	1.37882	−	0.886116i
$514$	0.650495	+	1.42439i	0.0286921	+	0.0628270i
$515$	6.37367	+	7.35561i	0.280858	+	0.324127i
$516$	9.04182	+	5.81083i	0.398044	+	0.255807i
$517$	−0.789915	+	5.49398i	−0.0347404	+	0.241625i
$518$	−0.215227	+	1.49694i	−0.00945652	+	0.0657716i
$519$	−18.1562	−	11.6683i	−0.796970	−	0.512182i
$520$	−0.493335	−	0.569338i	−0.0216342	−	0.0249671i
$521$	−4.67119	−	10.2285i	−0.204648	−	0.448117i	0.779281	−	0.626674i	$-0.215584\pi$
$521$	−4.67119	−	10.2285i	−0.204648	−	0.448117i	−0.983930	+	0.178557i	$0.942857\pi$
$522$	−0.664885	+	0.427296i	−0.0291012	+	0.0187022i
$523$	17.3487	+	5.09404i	0.758605	+	0.222747i	0.638087	−	0.769964i	$-0.279726\pi$
$523$	17.3487	+	5.09404i	0.758605	+	0.222747i	0.120519	+	0.992711i	$0.461544\pi$
$524$	−17.0228	+	19.6454i	−0.743645	+	0.858212i
$525$	−1.48357	+	0.435615i	−0.0647482	+	0.0190118i
$526$	−0.320098	+	0.700917i	−0.0139569	+	0.0305614i
$527$	0.561992	+	3.90874i	0.0244808	+	0.170267i
$528$	8.04304			0.350028
$529$	−7.39715	+	21.7780i	−0.321615	+	0.946870i
$530$	0.0241787			0.00105026
$531$	2.28297	+	15.8784i	0.0990725	+	0.689064i
$532$	9.50074	−	20.8037i	0.411909	−	0.901955i
$533$	12.4119	−	3.64448i	0.537621	−	0.157860i
$534$	0.0370854	−	0.0427988i	0.00160484	−	0.00185209i
$535$	−7.09714	−	2.08391i	−0.306836	−	0.0900952i
$536$	0.581697	−	0.373834i	0.0251255	−	0.0161472i
$537$	6.37863	+	13.9672i	0.275258	+	0.602731i
$538$	−0.169194	−	0.195260i	−0.00729445	−	0.00841825i
$539$	7.88869	+	5.06975i	0.339790	+	0.218370i
$540$	−1.41762	+	9.85975i	−0.0610046	+	0.424296i
$541$	1.97456	−	13.7333i	0.0848928	−	0.590442i	−0.902324	−	0.431059i	$-0.858140\pi$
$541$	1.97456	−	13.7333i	0.0848928	−	0.590442i	0.987217	−	0.159384i	$-0.0509507\pi$
$542$	−0.486530	−	0.312674i	−0.0208983	−	0.0134305i
$543$	0.536306	+	0.618931i	0.0230151	+	0.0265609i
$544$	1.90571	+	4.17292i	0.0817065	+	0.178912i
$545$	−8.75918	+	5.62918i	−0.375202	+	0.241128i
$546$	−0.279953	−	0.0822015i	−0.0119809	−	0.00351790i
$547$	19.7384	−	22.7793i	0.843952	−	0.973973i	−0.155953	−	0.987764i	$-0.549845\pi$
$547$	19.7384	−	22.7793i	0.843952	−	0.973973i	0.999905	+	0.0137919i	$0.00439025\pi$
$548$	41.1491	−	12.0825i	1.75780	−	0.516138i
$549$	2.67436	−	5.85603i	0.114139	−	0.249929i
$550$	0.0255239	+	0.177523i	0.00108834	+	0.00756960i
$551$	33.2819			1.41786
$552$	−0.983001	−	1.37204i	−0.0418393	−	0.0583981i
$553$	−4.97813			−0.211692
$554$	0.285906	+	1.98852i	0.0121470	+	0.0844840i
$555$	−4.60905	+	10.0924i	−0.195643	+	0.428399i
$556$	−31.2953	+	9.18913i	−1.32722	+	0.389706i
$557$	−14.1622	+	16.3440i	−0.600071	+	0.692519i	−0.971796	−	0.235824i	$-0.924221\pi$
$557$	−14.1622	+	16.3440i	−0.600071	+	0.692519i	0.371724	+	0.928343i	$0.378767\pi$
$558$	−0.153253	−	0.0449991i	−0.00648771	−	0.00190496i
$559$	9.71499	−	6.24345i	0.410900	−	0.264070i
$560$	2.53935	+	5.56040i	0.107307	+	0.234970i
$561$	−5.80751	−	6.70222i	−0.245193	−	0.282968i
$562$	−1.05631	−	0.678850i	−0.0445578	−	0.0286356i
$563$	−0.0407395	+	0.283349i	−0.00171696	+	0.0119418i	−0.990662	−	0.136341i	$-0.956466\pi$
$563$	−0.0407395	+	0.283349i	−0.00171696	+	0.0119418i	0.988945	+	0.148283i	$0.0473747\pi$
$564$	0.773524	−	5.37998i	0.0325712	−	0.226538i
$565$	−16.4820	−	10.5923i	−0.693402	−	0.445622i
$566$	−1.36864	−	1.57949i	−0.0575281	−	0.0663910i
$567$	−0.642315	−	1.40647i	−0.0269747	−	0.0590663i
$568$	3.30156	−	2.12179i	0.138531	−	0.0890282i
$569$	1.66147	+	0.487852i	0.0696525	+	0.0204518i	0.316373	−	0.948635i	$-0.397535\pi$
$569$	1.66147	+	0.487852i	0.0696525	+	0.0204518i	−0.246721	+	0.969087i	$0.579353\pi$
$570$	−0.428618	+	0.494652i	−0.0179528	+	0.0207187i
$571$	−19.8922	+	5.84086i	−0.832461	+	0.244433i	−0.670074	−	0.742295i	$-0.733738\pi$
$571$	−19.8922	+	5.84086i	−0.832461	+	0.244433i	−0.162387	+	0.986727i	$0.551919\pi$
$572$	3.60407	−	7.89181i	0.150694	−	0.329973i
$573$	−0.607097	−	4.22245i	−0.0253618	−	0.176395i
$574$	0.823739			0.0343822
$575$	−3.46135	+	3.31949i	−0.144348	+	0.138432i
$576$	15.6282			0.651174
$577$	−3.43290	−	23.8763i	−0.142913	−	0.993985i	−0.927462	−	0.373917i	$-0.878014\pi$
$577$	−3.43290	−	23.8763i	−0.142913	−	0.993985i	0.784549	−	0.620067i	$-0.212895\pi$
$578$	0.0733005	−	0.160506i	0.00304890	−	0.00667616i
$579$	4.63848	−	1.36198i	0.192769	−	0.0566020i
$580$	−5.84826	+	6.74925i	−0.242836	+	0.280247i
$581$	−6.46934	−	1.89957i	−0.268394	−	0.0788074i
$582$	0.410917	−	0.264080i	0.0170330	−	0.0109465i
$583$	0.231798	+	0.507567i	0.00960009	+	0.0210213i
$584$	−2.39009	−	2.75831i	−0.0989026	−	0.114140i
$585$	3.60149	+	2.31454i	0.148903	+	0.0956944i
$586$	0.0536241	−	0.372964i	0.00221519	−	0.0154070i
$587$	4.77952	−	33.2423i	0.197272	−	1.37206i	−0.614885	−	0.788617i	$-0.710798\pi$
$587$	4.77952	−	33.2423i	0.197272	−	1.37206i	0.812157	−	0.583439i	$-0.198293\pi$
$588$	−7.72499	−	4.96455i	−0.318573	−	0.204734i
$589$	4.40458	+	5.08316i	0.181488	+	0.209448i
$590$	−0.293734	−	0.643187i	−0.0120928	−	0.0264796i
$591$	0.220925	−	0.141980i	0.00908764	−	0.00584027i
$592$	42.0867	+	12.3578i	1.72975	+	0.507901i
$593$	−19.5470	+	22.5585i	−0.802700	+	0.926365i	−0.998526	−	0.0542739i	$-0.982716\pi$
$593$	−19.5470	+	22.5585i	−0.802700	+	0.926365i	0.195827	+	0.980639i	$0.437261\pi$
$594$	0.860418	−	0.252641i	0.0353034	−	0.0103660i
$595$	2.79990	−	6.13093i	0.114785	−	0.251344i
$596$	5.47807	+	38.1008i	0.224391	+	1.56067i
$597$	4.32625			0.177062
$598$	−0.888133	+	0.173830i	−0.0363185	+	0.00710843i
$599$	4.70186			0.192113			0.0960564	−	0.995376i	$-0.469377\pi$
$599$	4.70186			0.192113			0.0960564	+	0.995376i	$0.469377\pi$
$600$	−0.0500861	−	0.348356i	−0.00204476	−	0.0142216i
$601$	8.89729	−	19.4823i	0.362928	−	0.794701i	−0.636792	−	0.771036i	$-0.719739\pi$
$601$	8.89729	−	19.4823i	0.362928	−	0.794701i	0.999720	−	0.0236658i	$-0.00753375\pi$
$602$	0.705584	−	0.207178i	0.0287575	−	0.00844395i
$603$	−2.57325	+	2.96969i	−0.104791	+	0.120935i
$604$	38.2569	+	11.2332i	1.55665	+	0.457073i
$605$	5.77187	−	3.70935i	0.234660	−	0.150807i
$606$	−0.164711	−	0.360666i	−0.00669091	−	0.0146511i
$607$	25.2756	+	29.1696i	1.02591	+	1.18396i	0.982759	+	0.184891i	$0.0591932\pi$
$607$	25.2756	+	29.1696i	1.02591	+	1.18396i	0.0431477	+	0.999069i	$0.486261\pi$
$608$	6.57319	+	4.22433i	0.266578	+	0.171319i
$609$	−0.986403	+	6.86058i	−0.0399711	+	0.278005i
$610$	−0.0403840	+	0.280877i	−0.00163510	+	0.0113724i
$611$	−4.91289	−	3.15732i	−0.198754	−	0.127732i
$612$	−11.3740	−	13.1263i	−0.459766	−	0.530599i
$613$	7.81638	+	17.1155i	0.315700	+	0.691288i	0.999254	−	0.0386125i	$-0.0122938\pi$
$613$	7.81638	+	17.1155i	0.315700	+	0.691288i	−0.683554	+	0.729900i	$0.739567\pi$
$614$	−0.663370	+	0.426322i	−0.0267714	+	0.0172050i
$615$	5.79848	+	1.70259i	0.233817	+	0.0686550i
$616$	0.724983	−	0.836675i	0.0292104	−	0.0337106i
$617$	−15.2099	+	4.46602i	−0.612326	+	0.179795i	−0.573168	−	0.819438i	$-0.694286\pi$
$617$	−15.2099	+	4.46602i	−0.612326	+	0.179795i	−0.0391580	+	0.999233i	$0.512468\pi$
$618$	−0.356430	+	0.780473i	−0.0143377	+	0.0313952i
$619$	4.22984	+	29.4192i	0.170012	+	1.18246i	0.878854	+	0.477091i	$0.158309\pi$
$619$	4.22984	+	29.4192i	0.170012	+	1.18246i	−0.708842	+	0.705367i	$0.750782\pi$
$620$	−1.80478			−0.0724817
$621$	18.8915	+	14.7685i	0.758091	+	0.592641i
$622$	−2.05794			−0.0825158
$623$	0.141357	+	0.983162i	0.00566336	+	0.0393896i
$624$	−3.51546	+	7.69778i	−0.140731	+	0.308158i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	1.29956	−	1.49977i	0.0519408	−	0.0599429i
$627$	−14.4930	−	4.25553i	−0.578794	−	0.169949i
$628$	−9.67769	+	6.21947i	−0.386182	+	0.248184i
$629$	−20.0912	−	43.9936i	−0.801089	−	1.75414i
$630$	0.178524	+	0.206027i	0.00711256	+	0.00820833i
$631$	−14.0318	−	9.01768i	−0.558597	−	0.358988i	0.230677	−	0.973030i	$-0.425906\pi$
$631$	−14.0318	−	9.01768i	−0.558597	−	0.358988i	−0.789273	+	0.614042i	$0.789542\pi$
$632$	0.161257	−	1.12156i	0.00641444	−	0.0446134i
$633$	−0.934652	+	6.50065i	−0.0371491	+	0.258378i
$634$	0.945584	+	0.607690i	0.0375539	+	0.0241345i
$635$	−11.4897	−	13.2599i	−0.455956	−	0.526202i
$636$	−0.226988	−	0.497034i	−0.00900066	−	0.0197087i
$637$	−8.30012	+	5.33416i	−0.328863	+	0.211347i
$638$	0.771397	+	0.226502i	0.0305399	+	0.00896732i
$639$	−14.6051	+	16.8552i	−0.577769	+	0.666781i
$640$	−2.68049	+	0.787062i	−0.105956	+	0.0311114i
$641$	−12.5542	+	27.4898i	−0.495859	+	1.08578i	0.481934	+	0.876208i	$0.339935\pi$
$641$	−12.5542	+	27.4898i	−0.495859	+	1.08578i	−0.977793	+	0.209573i	$0.932793\pi$
$642$	−0.0927990	−	0.645431i	−0.00366248	−	0.0254731i
$643$	−7.45857			−0.294137			−0.147069	−	0.989126i	$-0.546984\pi$
$643$	−7.45857			−0.294137			−0.147069	+	0.989126i	$0.546984\pi$
$644$	14.7101	+	1.36187i	0.579659	+	0.0536653i
$645$	5.39498			0.212427
$646$	−0.406038	−	2.82406i	−0.0159754	−	0.111111i
$647$	3.17102	−	6.94356i	0.124666	−	0.272980i	−0.837001	−	0.547202i	$-0.815693\pi$
$647$	3.17102	−	6.94356i	0.124666	−	0.272980i	0.961666	+	0.274222i	$0.0884204\pi$
$648$	0.337683	−	0.0991526i	0.0132654	−	0.00389508i
$649$	10.6860	−	12.3323i	0.419462	−	0.484085i
$650$	−0.181059	−	0.0531636i	−0.00710170	−	0.00208525i
$651$	−1.17836	+	0.757286i	−0.0461836	+	0.0296804i
$652$	−7.28589	−	15.9539i	−0.285337	−	0.624802i
$653$	−25.4564	−	29.3782i	−0.996185	−	1.14966i	−0.988734	−	0.149686i	$-0.952174\pi$
$653$	−25.4564	−	29.3782i	−0.996185	−	1.14966i	−0.00745135	−	0.999972i	$-0.502372\pi$
$654$	−0.772173	−	0.496246i	−0.0301944	−	0.0194047i
$655$	−1.85692	+	12.9152i	−0.0725559	+	0.504637i
$656$	3.40014	−	23.6485i	0.132753	−	0.923319i
$657$	17.4484	+	11.2134i	0.680726	+	0.437476i
$658$	−0.243529	−	0.281047i	−0.00949374	−	0.0109564i
$659$	−5.38310	−	11.7873i	−0.209696	−	0.459170i	0.775335	−	0.631551i	$-0.217581\pi$
$659$	−5.38310	−	11.7873i	−0.209696	−	0.459170i	−0.985030	+	0.172381i	$0.944854\pi$
$660$	3.40967	−	2.19126i	0.132721	−	0.0852947i
$661$	28.9778	+	8.50866i	1.12711	+	0.330949i	0.791570	−	0.611078i	$-0.209264\pi$
$661$	28.9778	+	8.50866i	1.12711	+	0.330949i	0.335537	+	0.942027i	$0.391082\pi$
$662$	0.946639	−	1.09248i	0.0367922	−	0.0424604i
$663$	8.95287	−	2.62880i	0.347701	−	0.102094i
$664$	0.637531	−	1.39600i	0.0247410	−	0.0541753i
$665$	−1.63375	−	11.3630i	−0.0633542	−	0.440638i
$666$	1.95619			0.0758007
$667$	7.08990	+	20.2955i	0.274522	+	0.785844i
$668$	38.9037			1.50523
$669$	−1.31033	−	9.11356i	−0.0506604	−	0.352351i
$670$	0.0719509	−	0.157551i	0.00277971	−	0.00608671i
$671$	−6.28342	+	1.84498i	−0.242569	+	0.0712246i
$672$	−1.06560	+	1.22977i	−0.0411064	+	0.0474393i
$673$	2.27218	+	0.667173i	0.0875862	+	0.0257176i	0.325232	−	0.945634i	$-0.394558\pi$
$673$	2.27218	+	0.667173i	0.0875862	+	0.0257176i	−0.237646	+	0.971352i	$0.576376\pi$
$674$	2.03488	−	1.30773i	0.0783805	−	0.0503721i
$675$	2.07708	+	4.54816i	0.0799467	+	0.175059i
$676$	−10.9824	−	12.6744i	−0.422402	−	0.487478i
$677$	−29.1912	−	18.7600i	−1.12191	−	0.721006i	−0.158052	−	0.987431i	$-0.550521\pi$
$677$	−29.1912	−	18.7600i	−1.12191	−	0.721006i	−0.963856	+	0.266425i	$0.914158\pi$
$678$	0.245801	−	1.70958i	0.00943993	−	0.0656562i
$679$	−1.21925	+	8.48004i	−0.0467904	+	0.325434i
$680$	1.29059	+	0.829413i	0.0494919	+	0.0318065i
$681$	−5.80963	−	6.70467i	−0.222626	−	0.256924i
$682$	0.0674940	+	0.147791i	0.00258448	+	0.00565922i
$683$	−19.5711	+	12.5776i	−0.748869	+	0.481269i	−0.858570	−	0.512696i	$-0.828647\pi$
$683$	−19.5711	+	12.5776i	−0.748869	+	0.481269i	0.109702	+	0.993965i	$0.465010\pi$
$684$	−28.3845	−	8.33444i	−1.08531	−	0.318675i
$685$	14.0971	−	16.2689i	0.538621	−	0.621602i
$686$	−1.51832	+	0.445819i	−0.0579698	+	0.0170215i
$687$	3.48319	−	7.62712i	0.132892	−	0.290993i
$688$	−3.03539	−	21.1116i	−0.115723	−	0.804872i
$689$	−0.587093			−0.0223665
$690$	−0.392948	−	0.156000i	−0.0149593	−	0.00593882i
$691$	−45.0096			−1.71225			−0.856123	−	0.516772i	$-0.827133\pi$
$691$	−45.0096			−1.71225			−0.856123	+	0.516772i	$0.827133\pi$
$692$	6.11911	+	42.5593i	0.232614	+	1.61786i
$693$	−2.61351	+	5.72279i	−0.0992790	+	0.217391i
$694$	−0.510520	+	0.149902i	−0.0193791	+	0.00569020i
$695$	−10.7213	+	12.3730i	−0.406682	+	0.469336i
$696$	−1.51372	−	0.444470i	−0.0573776	−	0.0168476i
$697$	−22.1612	+	14.2422i	−0.839417	+	0.539461i
$698$	0.305688	+	0.669363i	0.0115705	+	0.0253358i
$699$	−15.7256	−	18.1483i	−0.594796	−	0.686431i
$700$	2.59138	+	1.66538i	0.0979451	+	0.0629455i
$701$	−3.34738	+	23.2815i	−0.126429	+	0.879332i	0.823600	+	0.567171i	$0.191962\pi$
$701$	−3.34738	+	23.2815i	−0.126429	+	0.879332i	−0.950029	+	0.312161i	$0.898947\pi$
$702$	−0.134276	+	0.933908i	−0.00506791	+	0.0352481i
$703$	−69.2989	−	44.5357i	−2.61366	−	1.67969i
$704$	−10.4105	−	12.0144i	−0.392362	−	0.452810i
$705$	−1.13336	−	2.48170i	−0.0426847	−	0.0934664i
$706$	−1.93952	+	1.24645i	−0.0729946	+	0.0469108i
$707$	6.67261	+	1.95925i	0.250949	+	0.0736854i
$708$	−10.4643	+	12.0764i	−0.393271	+	0.453859i
$709$	32.8793	−	9.65422i	1.23481	−	0.362572i	0.401745	−	0.915752i	$-0.368404\pi$
$709$	32.8793	−	9.65422i	1.23481	−	0.362572i	0.833062	+	0.553180i	$0.186586\pi$
$710$	0.408375	−	0.894217i	0.0153261	−	0.0335594i
$711$	0.916390	+	6.37363i	0.0343673	+	0.239030i
$712$	−0.226084			−0.00847285
$713$	−2.16144	+	3.76877i	−0.0809467	+	0.141142i
$714$	0.594172			0.0222363
$715$	−0.619758	−	4.31051i	−0.0231776	−	0.161204i
$716$	12.7077	−	27.8260i	0.474909	−	1.03990i
$717$	−10.7825	+	3.16603i	−0.402680	+	0.118238i
$718$	−0.326770	+	0.377112i	−0.0121949	+	0.0140737i
$719$	−22.3827	−	6.57217i	−0.834735	−	0.245100i	−0.163685	−	0.986513i	$-0.552338\pi$
$719$	−22.3827	−	6.57217i	−0.834735	−	0.245100i	−0.671050	+	0.741412i	$0.734156\pi$
$720$	6.65168	−	4.27477i	0.247893	−	0.159311i
$721$	−6.25157	−	13.6890i	−0.232821	−	0.509806i
$722$	−2.08543	−	2.40672i	−0.0776117	−	0.0895687i
$723$	23.6451	+	15.1958i	0.879371	+	0.565138i
$724$	0.232195	−	1.61495i	0.00862947	−	0.0600193i
$725$	−0.637953	+	4.43706i	−0.0236930	+	0.164788i
$726$	0.508824	+	0.327001i	0.0188842	+	0.0121362i
$727$	−26.3834	−	30.4481i	−0.978507	−	1.12926i	−0.991600	−	0.129343i	$-0.958713\pi$
$727$	−26.3834	−	30.4481i	−0.978507	−	1.12926i	0.0130932	−	0.999914i	$-0.495832\pi$
$728$	0.483883	+	1.05956i	0.0179339	+	0.0392698i
$729$	10.9363	−	7.02833i	0.405048	−	0.260309i
$730$	−0.877186	−	0.257565i	−0.0324661	−	0.00953291i
$731$	−15.4005	+	17.7731i	−0.569607	+	0.657361i
$732$	6.15303	−	1.80669i	0.227422	−	0.0667773i
$733$	−9.43781	+	20.6659i	−0.348594	+	0.763313i	0.651396	+	0.758738i	$0.274184\pi$
$733$	−9.43781	+	20.6659i	−0.348594	+	0.763313i	−0.999990	+	0.00457542i	$0.998544\pi$
$734$	0.154499	+	1.07456i	0.00570266	+	0.0396629i
$735$	−4.60926			−0.170015
$736$	−1.17576	+	4.90825i	−0.0433391	+	0.180921i
$737$	3.99714			0.147236
$738$	−0.151637	−	1.05466i	−0.00558182	−	0.0388224i
$739$	−7.47356	+	16.3648i	−0.274919	+	0.601989i	−0.995849	−	0.0910188i	$-0.970988\pi$
$739$	−7.47356	+	16.3648i	−0.274919	+	0.601989i	0.720930	+	0.693008i	$0.243715\pi$
$740$	21.2085	−	6.22738i	0.779640	−	0.228923i
$741$	10.4075	−	12.0109i	0.382328	−	0.441230i
$742$	−0.0358708	−	0.0105326i	−0.00131686	−	0.000386664i
$743$	−4.89833	+	3.14797i	−0.179702	+	0.115488i	−0.627399	−	0.778698i	$-0.715881\pi$
$743$	−4.89833	+	3.14797i	−0.179702	+	0.115488i	0.447697	+	0.894185i	$0.352244\pi$
$744$	−0.132445	−	0.290013i	−0.00485566	−	0.0106324i
$745$	12.6528	+	14.6021i	0.463563	+	0.534981i
$746$	2.16002	+	1.38816i	0.0790840	+	0.0508242i
$747$	−1.24117	+	8.63256i	−0.0454122	+	0.315849i
$748$	−2.51438	+	17.4879i	−0.0919347	+	0.639420i
$749$	9.62131	+	6.18324i	0.351555	+	0.225931i
$750$	−0.0577299	−	0.0666238i	−0.00210800	−	0.00243276i
$751$	3.84740	+	8.42462i	0.140393	+	0.307419i	0.966748	−	0.255732i	$-0.0823164\pi$
$751$	3.84740	+	8.42462i	0.140393	+	0.307419i	−0.826354	+	0.563151i	$0.809589\pi$
$752$	−9.07372	+	5.83133i	−0.330885	+	0.212647i
$753$	−26.3797	−	7.74578i	−0.961330	−	0.282272i
$754$	−0.553942	+	0.639283i	−0.0201734	+	0.0232813i
$755$	19.2030	−	5.63852i	0.698870	−	0.205207i
$756$	6.39819	−	14.0101i	0.232700	−	0.509542i
$757$	1.15607	+	8.04064i	0.0420180	+	0.292242i	0.999986	+	0.00536536i	$0.00170786\pi$
$757$	1.15607	+	8.04064i	0.0420180	+	0.292242i	−0.957968	+	0.286877i	$0.907383\pi$
$758$	−2.94048			−0.106803
$759$	−0.492336	−	9.74443i	−0.0178707	−	0.353700i
$760$	2.61299			0.0947830
$761$	−4.15984	−	28.9323i	−0.150794	−	1.04880i	−0.914893	−	0.403697i	$-0.867725\pi$
$761$	−4.15984	−	28.9323i	−0.150794	−	1.04880i	0.764099	−	0.645099i	$-0.223184\pi$
$762$	0.642532	−	1.40695i	0.0232765	−	0.0509684i
$763$	15.4470	−	4.53565i	0.559219	−	0.164201i
$764$	−5.56539	+	6.42281i	−0.201349	+	0.232369i
$765$	−8.36501	−	2.45619i	−0.302438	−	0.0888037i
$766$	2.30544	−	1.48162i	0.0832990	−	0.0535330i
$767$	7.13228	+	15.6175i	0.257532	+	0.563915i
$768$	10.0730	+	11.6249i	0.363478	+	0.419476i
$769$	12.2803	+	7.89208i	0.442840	+	0.284596i	0.742998	−	0.669294i	$-0.233403\pi$
$769$	12.2803	+	7.89208i	0.442840	+	0.284596i	−0.300158	+	0.953889i	$0.597040\pi$
$770$	0.0394651	−	0.274486i	0.00142222	−	0.00989179i
$771$	2.52790	−	17.5820i	0.0910403	−	0.633199i
$772$	−8.10215	−	5.20693i	−0.291603	−	0.187402i
$773$	11.3054	+	13.0471i	0.406625	+	0.469271i	0.921716	−	0.387865i	$-0.126787\pi$
$773$	11.3054	+	13.0471i	0.406625	+	0.469271i	−0.515091	+	0.857136i	$0.672242\pi$
$774$	−0.395142	−	0.865241i	−0.0142031	−	0.0311004i
$775$	−0.762100	+	0.489772i	−0.0273755	+	0.0175931i
$776$	−1.87104	−	0.549388i	−0.0671666	−	0.0197219i
$777$	11.2342	−	12.9650i	0.403026	−	0.465117i
$778$	1.07306	−	0.315080i	0.0384712	−	0.0112962i
$779$	−18.6391	+	40.8139i	−0.667815	+	1.46231i
$780$	0.606897	+	4.22106i	0.0217304	+	0.151138i
$781$	22.6867			0.811795
$782$	1.63563	−	0.849200i	0.0584899	−	0.0303673i
$783$	22.4134			0.800991
$784$	2.59332	+	18.0369i	0.0926186	+	0.644176i
$785$	−2.39877	+	5.25257i	−0.0856156	+	0.187472i
$786$	−1.10366	+	0.324065i	−0.0393663	+	0.0115590i
$787$	−10.0471	+	11.5950i	−0.358142	+	0.413318i	−0.906016	−	0.423243i	$-0.860892\pi$
$787$	−10.0471	+	11.5950i	−0.358142	+	0.413318i	0.547875	+	0.836561i	$0.315437\pi$
$788$	−0.501995	−	0.147399i	−0.0178828	−	0.00525087i
$789$	7.35320	−	4.72561i	0.261781	−	0.168236i
$790$	−0.117905	−	0.258177i	−0.00419489	−	0.00918553i
$791$	19.8380	+	22.8942i	0.705356	+	0.814025i
$792$	−1.20467	−	0.774198i	−0.0428063	−	0.0275099i
$793$	0.980582	−	6.82010i	0.0348215	−	0.242189i
$794$	−0.154578	+	1.07511i	−0.00548577	+	0.0381544i
$795$	−0.230732	−	0.148283i	−0.00818323	−	0.00525904i
$796$	−5.64417	−	6.51371i	−0.200052	−	0.230872i
$797$	10.4360	+	22.8517i	0.369663	+	0.809448i	0.999465	+	0.0326932i	$0.0104084\pi$
$797$	10.4360	+	22.8517i	0.369663	+	0.809448i	−0.629803	+	0.776755i	$0.716864\pi$
$798$	0.851362	−	0.547137i	0.0301379	−	0.0193685i
$799$	11.4109	+	3.35055i	0.403690	+	0.118534i
$800$	−0.689173	+	0.795348i	−0.0243659	+	0.0281198i
$801$	1.23275	−	0.361967i	0.0435570	−	0.0127895i
$802$	−1.23584	+	2.70612i	−0.0436392	+	0.0955565i
$803$	−3.00258	−	20.8834i	−0.105959	−	0.736959i
$804$	−3.91419			−0.138043
$805$	6.58118	−	3.41688i	0.231956	−	0.120429i
$806$	−0.170947			−0.00602136
$807$	0.417094	+	2.90095i	0.0146824	+	0.102118i
$808$	−0.657563	+	1.43986i	−0.0231330	+	0.0506542i
$809$	−21.8919	+	6.42804i	−0.769678	+	0.225998i	−0.642917	−	0.765935i	$-0.722276\pi$
$809$	−21.8919	+	6.42804i	−0.769678	+	0.225998i	−0.126761	+	0.991933i	$0.540458\pi$
$810$	0.0577299	−	0.0666238i	0.00202842	−	0.00234092i
$811$	41.7803	+	12.2678i	1.46711	+	0.430781i	0.915157	−	0.403097i	$-0.132066\pi$
$811$	41.7803	+	12.2678i	1.46711	+	0.430781i	0.551949	+	0.833878i	$0.313884\pi$
$812$	11.6164	−	7.46538i	0.407654	−	0.261984i
$813$	2.72530	+	5.96757i	0.0955803	+	0.209292i
$814$	−1.30309	−	1.50385i	−0.0456734	−	0.0527099i
$815$	−7.40607	−	4.75959i	−0.259423	−	0.166721i
$816$	2.45256	−	17.0579i	0.0858567	−	0.597147i
$817$	−5.70046	+	39.6476i	−0.199434	+	1.38709i
$818$	1.20400	+	0.773766i	0.0420970	+	0.0270541i
$819$	−4.33481	−	5.00264i	−0.151471	−	0.174806i
$820$	−5.00143	−	10.9516i	−0.174657	−	0.382446i
$821$	40.9122	−	26.2927i	1.42785	−	0.917621i	0.427942	−	0.903806i	$-0.359239\pi$
$821$	40.9122	−	26.2927i	1.42785	−	0.917621i	0.999905	−	0.0138148i	$-0.00439753\pi$
$822$	1.82085	+	0.534648i	0.0635093	+	0.0186480i
$823$	−0.752583	+	0.868528i	−0.0262334	+	0.0302750i	−0.768715	−	0.639592i	$-0.779103\pi$
$823$	−0.752583	+	0.868528i	−0.0262334	+	0.0302750i	0.742481	+	0.669867i	$0.233649\pi$
$824$	3.28662	−	0.965039i	0.114495	−	0.0336187i
$825$	0.845139	−	1.85060i	0.0294240	−	0.0644295i
$826$	0.155592	+	1.08217i	0.00541374	+	0.0376534i
$827$	−15.3873			−0.535069			−0.267534	−	0.963548i	$-0.586209\pi$
$827$	−15.3873			−0.535069			−0.267534	+	0.963548i	$0.586209\pi$
$828$	−0.964240	−	19.0844i	−0.0335096	−	0.663230i
$829$	−43.7168			−1.51835			−0.759174	−	0.650888i	$-0.774397\pi$
$829$	−43.7168			−1.51835			−0.759174	+	0.650888i	$0.774397\pi$
$830$	−0.0547084	−	0.380505i	−0.00189896	−	0.0132075i
$831$	9.46680	−	20.7294i	0.328400	−	0.719095i
$832$	16.0489	−	4.71239i	0.556396	−	0.163373i
$833$	13.1576	−	15.1846i	0.455883	−	0.526117i
$834$	−1.38481	−	0.406618i	−0.0479522	−	0.0140800i
$835$	16.4278	−	10.5575i	0.568506	−	0.365357i
$836$	12.5008	+	27.3729i	0.432349	+	0.946712i
$837$	2.96623	+	3.42321i	0.102528	+	0.118323i
$838$	−0.992833	−	0.638055i	−0.0342969	−	0.0220413i
$839$	1.60650	−	11.1735i	0.0554627	−	0.385751i	−0.943116	−	0.332462i	$-0.892121\pi$
$839$	1.60650	−	11.1735i	0.0554627	−	0.385751i	0.998579	−	0.0532888i	$-0.0169704\pi$
$840$	−0.0774431	+	0.538629i	−0.00267204	+	0.0185845i
$841$	−7.49181	−	4.81469i	−0.258338	−	0.166024i
$842$	0.751277	+	0.867020i	0.0258907	+	0.0298795i
$843$	5.91692	+	12.9563i	0.203790	+	0.446237i
$844$	11.0069	−	7.07372i	0.378874	−	0.243488i
$845$	−8.07705	−	2.37164i	−0.277859	−	0.0815867i
$846$	−0.315003	+	0.363533i	−0.0108300	+	0.0124985i
$847$	−10.1788	+	2.98877i	−0.349748	+	0.102695i
$848$	−0.450441	+	0.986328i	−0.0154682	+	0.0338707i
$849$	3.37394	+	23.4663i	0.115793	+	0.805361i
$850$	0.384279			0.0131807
$851$	12.3956	−	51.7460i	0.424917	−	1.77383i
$852$	−22.2160			−0.761106
$853$	−2.37985	−	16.5522i	−0.0814845	−	0.566737i	−0.989135	−	0.147010i	$-0.953035\pi$
$853$	−2.37985	−	16.5522i	−0.0814845	−	0.566737i	0.907651	−	0.419727i	$-0.137874\pi$
$854$	0.182267	−	0.399108i	0.00623704	−	0.0136572i
$855$	−14.2476	+	4.18348i	−0.487258	+	0.143072i
$856$	−1.70474	+	1.96737i	−0.0582667	+	0.0672433i
$857$	−5.93618	−	1.74302i	−0.202776	−	0.0595405i	0.178767	−	0.983891i	$-0.442789\pi$
$857$	−5.93618	−	1.74302i	−0.202776	−	0.0595405i	−0.381543	+	0.924351i	$0.624607\pi$
$858$	0.322961	−	0.207554i	0.0110257	−	0.00708579i
$859$	−3.60612	−	7.89631i	−0.123039	−	0.269419i	0.838082	−	0.545544i	$-0.183677\pi$
$859$	−3.60612	−	7.89631i	−0.123039	−	0.269419i	−0.961122	+	0.276125i	$0.910950\pi$
$860$	−7.03847	−	8.12282i	−0.240010	−	0.276986i
$861$	−7.86077	−	5.05181i	−0.267894	−	0.172165i
$862$	−0.117416	+	0.816646i	−0.00399921	+	0.0278151i
$863$	−1.61006	+	11.1982i	−0.0548072	+	0.381192i	0.943894	+	0.330248i	$0.107132\pi$
$863$	−1.61006	+	11.1982i	−0.0548072	+	0.381192i	−0.998701	+	0.0509446i	$0.983777\pi$
$864$	4.42666	+	2.84484i	0.150598	+	0.0967834i
$865$	14.1334	+	16.3109i	0.480551	+	0.554586i
$866$	−1.24386	−	2.72368i	−0.0422682	−	0.0925546i
$867$	−1.68384	+	1.08214i	−0.0571861	+	0.0367513i
$868$	2.67752	+	0.786189i	0.0908808	+	0.0266850i
$869$	4.28939	−	4.95022i	0.145508	−	0.167925i
$870$	−0.379168	+	0.111334i	−0.0128550	+	0.00377457i
$871$	−1.74707	+	3.82555i	−0.0591973	+	0.129624i
$872$	0.521499	+	3.62711i	0.0176602	+	0.122829i
$873$	11.0817			0.375058
$874$	1.56164	−	2.72293i	0.0528232	−	0.0921045i
$875$	1.54620			0.0522711
$876$	2.94027	+	20.4500i	0.0993426	+	0.690943i
$877$	10.2913	−	22.5349i	0.347514	−	0.760950i	−0.652481	−	0.757805i	$-0.726272\pi$
$877$	10.2913	−	22.5349i	0.347514	−	0.760950i	0.999995	−	0.00314460i	$-0.00100096\pi$
$878$	−2.69735	+	0.792013i	−0.0910311	+	0.0267291i
$879$	−2.79903	+	3.23025i	−0.0944090	+	0.108954i
$880$	−7.71724	−	2.26599i	−0.260148	−	0.0763864i
$881$	28.0492	−	18.0261i	0.945000	−	0.607315i	0.0251917	−	0.999683i	$-0.491980\pi$
$881$	28.0492	−	18.0261i	0.945000	−	0.607315i	0.919808	+	0.392368i	$0.128344\pi$
$882$	0.337594	+	0.739229i	0.0113674	+	0.0248911i
$883$	8.56278	+	9.88198i	0.288161	+	0.332555i	0.881311	−	0.472537i	$-0.156662\pi$
$883$	8.56278	+	9.88198i	0.288161	+	0.332555i	−0.593150	+	0.805092i	$0.702116\pi$
$884$	−15.6382	−	10.0501i	−0.525969	−	0.338020i
$885$	−1.14149	+	7.93921i	−0.0383706	+	0.266874i
$886$	−0.384017	+	2.67090i	−0.0129013	+	0.0897305i
$887$	18.6668	+	11.9964i	0.626770	+	0.402800i	0.815112	−	0.579303i	$-0.196675\pi$
$887$	18.6668	+	11.9964i	0.626770	+	0.402800i	−0.188343	+	0.982103i	$0.560312\pi$
$888$	2.55708	+	2.95103i	0.0858101	+	0.0990301i
$889$	11.2696	+	24.6770i	0.377971	+	0.827641i
$890$	−0.0476410	+	0.0306170i	−0.00159693	+	0.00102628i
$891$	1.95204	+	0.573170i	0.0653957	+	0.0192019i
$892$	−12.0121	+	13.8627i	−0.402195	+	0.464158i
$893$	19.4355	−	5.70679i	0.650385	−	0.190970i
$894$	−0.707574	+	1.54937i	−0.0236648	+	0.0518187i
$895$	−2.18522	−	15.1985i	−0.0730439	−	0.508031i
$896$	4.31954			0.144306
$897$	9.54133	+	3.78790i	0.318576	+	0.126474i
$898$	−1.48567			−0.0495775
$899$	0.577928	+	4.01958i	0.0192750	+	0.134060i
$900$	1.65520	−	3.62439i	0.0551734	−	0.120813i
$901$	1.14714	−	0.336832i	0.0382169	−	0.0112215i
$902$	−0.709772	+	0.819121i	−0.0236328	+	0.0272737i
$903$	−8.00382	−	2.35013i	−0.266351	−	0.0782076i
$904$	−5.80064	+	3.72784i	−0.192926	+	0.123986i
$905$	−0.340209	−	0.744955i	−0.0113089	−	0.0247631i
$906$	1.15539	+	1.33339i	0.0383853	+	0.0442990i
$907$	−18.0240	−	11.5834i	−0.598479	−	0.384619i	0.206042	−	0.978543i	$-0.433942\pi$
$907$	−18.0240	−	11.5834i	−0.598479	−	0.384619i	−0.804521	+	0.593924i	$0.797578\pi$
$908$	−2.51530	+	17.4943i	−0.0834730	+	0.580568i
$909$	1.28017	−	8.90379i	0.0424606	−	0.295320i
$910$	0.245454	+	0.157744i	0.00813672	+	0.00522915i
$911$	25.5067	+	29.4363i	0.845076	+	0.975269i	0.999920	−	0.0126696i	$-0.00403297\pi$
$911$	25.5067	+	29.4363i	0.845076	+	0.975269i	−0.154844	+	0.987939i	$0.549488\pi$
$912$	−12.1935	−	26.6999i	−0.403766	−	0.884123i
$913$	7.46321	−	4.79631i	0.246996	−	0.158735i
$914$	0.230030	+	0.0675428i	0.00760870	+	0.00223412i
$915$	2.10793	−	2.43268i	0.0696861	−	0.0804221i
$916$	−16.0279	+	4.70621i	−0.529576	+	0.155497i
$917$	8.38091	−	18.3516i	0.276762	−	0.606024i
$918$	−0.273443	−	1.90184i	−0.00902496	−	0.0627700i
$919$	29.9408			0.987657			0.493829	−	0.869559i	$-0.335597\pi$
$919$	29.9408			0.987657			0.493829	+	0.869559i	$0.335597\pi$
$920$	0.556632	+	1.59341i	0.0183516	+	0.0525332i
$921$	8.94494			0.294746
$922$	0.448462	+	3.11912i	0.0147693	+	0.102723i
$923$	−9.91594	+	21.7129i	−0.326387	+	0.714688i
$924$	−6.01302	+	1.76558i	−0.197814	+	0.0580834i
$925$	7.26571	−	8.38507i	0.238895	−	0.275700i
$926$	3.52295	+	1.03443i	0.115771	+	0.0339935i
$927$	−16.3756	+	10.5240i	−0.537846	+	0.345653i
$928$	1.95974	+	4.29124i	0.0643318	+	0.140867i
$929$	8.14358	+	9.39819i	0.267182	+	0.308345i	0.873448	−	0.486917i	$-0.161879\pi$
$929$	8.14358	+	9.39819i	0.267182	+	0.308345i	−0.606266	+	0.795262i	$0.707333\pi$
$930$	−0.0671837	−	0.0431763i	−0.00220304	−	0.00141581i
$931$	4.87026	−	33.8734i	0.159616	−	1.11016i
$932$	−6.80843	+	47.3537i	−0.223017	+	1.55112i
$933$	19.6385	+	12.6209i	0.642934	+	0.413189i
$934$	−1.02031	−	1.17750i	−0.0333855	−	0.0385289i
$935$	3.68403	+	8.06690i	0.120481	+	0.263816i
$936$	1.26750	−	0.814576i	0.0414297	−	0.0266252i
$937$	−9.15473	−	2.68807i	−0.299072	−	0.0878155i	0.128754	−	0.991677i	$-0.458902\pi$
$937$	−9.15473	−	2.68807i	−0.299072	−	0.0878155i	−0.427826	+	0.903861i	$0.640720\pi$
$938$	−0.175376	+	0.202394i	−0.00572621	+	0.00660840i
$939$	−21.5992	+	6.34209i	−0.704863	+	0.206966i
$940$	−2.25790	+	4.94412i	−0.0736447	+	0.161259i
$941$	0.484266	+	3.36814i	0.0157866	+	0.109798i	0.996191	−	0.0871966i	$-0.0277908\pi$
$941$	0.484266	+	3.36814i	0.0157866	+	0.109798i	−0.980405	+	0.196995i	$0.936882\pi$
$942$	−0.509046			−0.0165856
$943$	−28.8591	−	2.67180i	−0.939782	−	0.0870058i
$944$	31.7099			1.03207
$945$	−1.10024	−	7.65231i	−0.0357907	−	0.248930i
$946$	−0.401948	+	0.880143i	−0.0130684	+	0.0286159i
$947$	−11.9343	+	3.50424i	−0.387814	+	0.113872i	−0.469826	−	0.882759i	$-0.655683\pi$
$947$	−11.9343	+	3.50424i	−0.387814	+	0.113872i	0.0820124	+	0.996631i	$0.473865\pi$
$948$	−4.20038	+	4.84750i	−0.136422	+	0.157439i
$949$	21.2993	+	6.25405i	0.691405	+	0.203015i
$950$	0.550616	−	0.353859i	0.0178643	−	0.0114807i
$951$	−5.29668	−	11.5981i	−0.171757	−	0.376095i
$952$	−1.55338	−	1.79269i	−0.0503452	−	0.0581015i
$953$	11.2590	+	7.23572i	0.364715	+	0.234388i	0.710143	−	0.704057i	$-0.248630\pi$
$953$	11.2590	+	7.23572i	0.364715	+	0.234388i	−0.345429	+	0.938445i	$0.612266\pi$
$954$	−0.00688198	+	0.0478652i	−0.000222812	+	0.00154969i
$955$	−0.607097	+	4.22245i	−0.0196452	+	0.136635i
$956$	18.8341	+	12.1039i	0.609137	+	0.391469i
$957$	−5.97219	−	6.89227i	−0.193053	−	0.222795i
$958$	−0.437868	−	0.958797i	−0.0141469	−	0.0309773i
$959$	−28.0009	+	17.9951i	−0.904197	+	0.581092i
$960$	7.49756	+	2.20148i	0.241983	+	0.0710526i
$961$	19.7633	−	22.8080i	0.637524	−	0.735742i
$962$	2.00885	−	0.589852i	0.0647680	−	0.0190176i
$963$	6.14545	−	13.4567i	0.198034	−	0.433635i
$964$	−7.96900	−	55.4256i	−0.256664	−	1.78514i
$965$	−4.83431			−0.155622
$966$	0.515009	+	0.402610i	0.0165701	+	0.0129538i
$967$	−24.7635			−0.796341			−0.398170	−	0.917311i	$-0.630355\pi$
$967$	−24.7635			−0.796341			−0.398170	+	0.917311i	$0.630355\pi$
$968$	−0.343642	−	2.39008i	−0.0110451	−	0.0768202i
$969$	−13.4446	+	29.4395i	−0.431902	+	0.945734i
$970$	−0.468672	+	0.137614i	−0.0150481	+	0.00441853i
$971$	−11.6629	+	13.4597i	−0.374281	+	0.431944i	−0.911374	−	0.411580i	$-0.864977\pi$
$971$	−11.6629	+	13.4597i	−0.374281	+	0.431944i	0.537092	+	0.843523i	$0.319523\pi$
$972$	−30.5845	−	8.98041i	−0.980997	−	0.288047i
$973$	21.2956	−	13.6859i	0.682707	−	0.438749i
$974$	−0.690922	−	1.51291i	−0.0221386	−	0.0484767i
$975$	1.40176	+	1.61772i	0.0448923	+	0.0518085i
$976$	−10.7056	−	6.88004i	−0.342676	−	0.220225i
$977$	−1.03522	+	7.20015i	−0.0331198	+	0.230353i	−0.999657	−	0.0261716i	$-0.991668\pi$
$977$	−1.03522	+	7.20015i	−0.0331198	+	0.230353i	0.966538	+	0.256525i	$0.0825775\pi$
$978$	0.110449	−	0.768191i	0.00353178	−	0.0245640i
$979$	−1.09945	−	0.706574i	−0.0351386	−	0.0225822i
$980$	6.01340	+	6.93983i	0.192091	+	0.221685i
$981$	−8.65065	−	18.9423i	−0.276194	−	0.604780i
$982$	1.62521	−	1.04446i	0.0518627	−	0.0333301i
$983$	30.9104	+	9.07613i	0.985890	+	0.289483i	0.734654	−	0.678442i	$-0.237345\pi$
$983$	30.9104	+	9.07613i	0.985890	+	0.289483i	0.251236	+	0.967926i	$0.419163\pi$
$984$	1.39280	−	1.60738i	0.0444008	−	0.0512412i
$985$	−0.251976	+	0.0739870i	−0.00802864	+	0.00235742i
$986$	0.715594	−	1.56693i	0.0227892	−	0.0499013i
$987$	0.600344	+	4.17548i	0.0191092	+	0.132907i
$988$	−31.6618			−1.00729
$989$	−25.3916	+	4.96978i	−0.807407	+	0.158030i
$990$	−0.358697			−0.0114001
$991$	−1.54572	−	10.7507i	−0.0491013	−	0.341507i	−0.999533	−	0.0305723i	$-0.990267\pi$
$991$	−1.54572	−	10.7507i	−0.0491013	−	0.341507i	0.950431	−	0.310935i	$-0.100642\pi$
$992$	−0.396047	+	0.867221i	−0.0125745	+	0.0275343i
$993$	−15.7335	+	4.61978i	−0.499288	+	0.146604i
$994$	−0.995387	+	1.14874i	−0.0315718	+	0.0364358i
$995$	−4.15101	−	1.21885i	−0.131596	−	0.0386400i
$996$	−7.30834	+	4.69678i	−0.231574	+	0.148823i
$997$	−8.76152	−	19.1851i	−0.277480	−	0.607597i	0.718661	−	0.695360i	$-0.244755\pi$
$997$	−8.76152	−	19.1851i	−0.277480	−	0.607597i	−0.996141	+	0.0877636i	$0.972028\pi$
$998$	−0.582455	−	0.672189i	−0.0184373	−	0.0212778i
$999$	−46.6687	−	29.9922i	−1.47653	−	0.948910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.a.26.1	✓	10
5.2	odd	4		575.2.p.a.49.2		20
5.3	odd	4		575.2.p.a.49.1		20
5.4	even	2		575.2.k.a.26.1		10
23.8	even	11	inner	115.2.g.a.31.1	yes	10
23.10	odd	22		2645.2.a.o.1.4		5
23.13	even	11		2645.2.a.n.1.4		5
115.8	odd	44		575.2.p.a.399.2		20
115.54	even	22		575.2.k.a.376.1		10
115.77	odd	44		575.2.p.a.399.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.26.1	✓	10	1.1	even	1	trivial
115.2.g.a.31.1	yes	10	23.8	even	11	inner
575.2.k.a.26.1		10	5.4	even	2
575.2.k.a.376.1		10	115.54	even	22
575.2.p.a.49.1		20	5.3	odd	4
575.2.p.a.49.2		20	5.2	odd	4
575.2.p.a.399.1		20	115.77	odd	44
575.2.p.a.399.2		20	115.8	odd	44
2645.2.a.n.1.4		5	23.13	even	11
2645.2.a.o.1.4		5	23.10	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0125459 - 0.0872586i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.654861 - 0.755750i) q^{5} +(0.0845850 + 0.0248364i) q^{6} +(-1.30075 + 0.835939i) q^{7} +(-0.146201 - 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +O(q^{10})\)	\(q+(-0.0125459 - 0.0872586i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.654861 - 0.755750i) q^{5} +(0.0845850 + 0.0248364i) q^{6} +(-1.30075 + 0.835939i) q^{7} +(-0.146201 - 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +(-0.0741615 - 0.0476607i) q^{10} +(0.289532 - 2.01374i) q^{11} +(-0.283524 + 1.97195i) q^{12} +(1.80075 + 1.15727i) q^{13} +(0.0892619 + 0.103014i) q^{14} +(0.415415 + 0.909632i) q^{15} +(3.32584 - 2.13739i) q^{16} +(-4.18251 - 1.22809i) q^{17} +(0.115460 - 0.133248i) q^{18} +(-7.12381 + 2.09174i) q^{19} +(0.827602 - 1.81219i) q^{20} +(-0.220047 - 1.53046i) q^{21} -0.179348 q^{22} +(-2.79310 - 3.89854i) q^{23} +0.351939 q^{24} +(-0.142315 - 0.989821i) q^{25} +(0.0783898 - 0.171650i) q^{26} +(-4.79746 + 1.40866i) q^{27} +(-2.01722 + 2.32800i) q^{28} +(-4.30111 - 1.26292i) q^{29} +(0.0741615 - 0.0476607i) q^{30} +(-0.376329 - 0.824045i) q^{31} +(-0.689173 - 0.795348i) q^{32} +(1.71148 + 1.09990i) q^{33} +(-0.0546886 + 0.380367i) q^{34} +(-0.220047 + 1.53046i) q^{35} +(3.35194 + 2.15416i) q^{36} +(7.26571 + 8.38507i) q^{37} +(0.271897 + 0.595371i) q^{38} +(-1.80075 + 1.15727i) q^{39} +(-0.337683 - 0.0991526i) q^{40} +(3.95750 - 4.56720i) q^{41} +(-0.130785 + 0.0384020i) q^{42} +(2.24116 - 4.90745i) q^{43} +(-0.576814 - 4.01183i) q^{44} +2.00000 q^{45} +(-0.305139 + 0.292633i) q^{46} -2.72825 q^{47} +(0.562632 + 3.91319i) q^{48} +(-1.91476 + 4.19273i) q^{49} +(-0.0845850 + 0.0248364i) q^{50} +(2.85459 - 3.29437i) q^{51} +(4.09173 + 1.20144i) q^{52} +(-0.230732 + 0.148283i) q^{53} +(0.183106 + 0.400947i) q^{54} +(-1.33228 - 1.53753i) q^{55} +(0.457783 + 0.294199i) q^{56} +(1.05662 - 7.34898i) q^{57} +(-0.0562393 + 0.391153i) q^{58} +(6.74757 + 4.33640i) q^{59} +(1.30463 + 1.50563i) q^{60} +(-1.33718 - 2.92802i) q^{61} +(-0.0671837 + 0.0431763i) q^{62} +(-2.96714 - 0.871230i) q^{63} +(5.11714 - 5.90549i) q^{64} +(2.05384 - 0.603063i) q^{65} +(0.0745040 - 0.163141i) q^{66} +(0.279610 + 1.94473i) q^{67} -8.68428 q^{68} +(4.70653 - 0.921186i) q^{69} +0.136307 q^{70} +(1.58700 + 11.0378i) q^{71} +(0.292401 - 0.640269i) q^{72} +(9.95039 - 2.92170i) q^{73} +(0.640515 - 0.739194i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-12.4433 + 7.99684i) q^{76} +(1.30675 + 2.86139i) q^{77} +(0.123574 + 0.142612i) q^{78} +(2.70849 + 1.74064i) q^{79} +(0.562632 - 3.91319i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.448178 - 0.288027i) q^{82} +(2.85563 + 3.29557i) q^{83} +(-1.27964 - 2.80202i) q^{84} +(-3.66709 + 2.35670i) q^{85} +(-0.456334 - 0.133992i) q^{86} +(2.93553 - 3.38779i) q^{87} +(-0.686997 + 0.201720i) q^{88} +(0.266861 - 0.584343i) q^{89} +(-0.0250918 - 0.174517i) q^{90} -3.30972 q^{91} +(-7.52725 - 5.88446i) q^{92} +0.905910 q^{93} +(0.0342284 + 0.238063i) q^{94} +(-3.08427 + 6.75361i) q^{95} +(1.00977 - 0.296494i) q^{96} +(3.62848 - 4.18748i) q^{97} +(0.389875 + 0.114478i) q^{98} +(3.42297 - 2.19981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

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