LMFDB - Embedded newform 429.2.bj.b.73.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(73,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 14, 5]))

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

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

chi := DirichletCharacter("429.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.8
Character	$\chi$	$=$	429.73
Dual form			429.2.bj.b.382.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.227816 - 0.0360826i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-1.85151 + 0.601594i) q^{4} +(-1.68185 - 0.266378i) q^{5} +(-0.0360826 + 0.227816i) q^{6} +(2.29608 - 4.50631i) q^{7} +(-0.811131 + 0.413292i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.227816 - 0.0360826i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-1.85151 + 0.601594i) q^{4} +(-1.68185 - 0.266378i) q^{5} +(-0.0360826 + 0.227816i) q^{6} +(2.29608 - 4.50631i) q^{7} +(-0.811131 + 0.413292i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.392764 q^{10} +(2.28855 + 2.40053i) q^{11} -1.94680i q^{12} +(3.53722 + 0.698600i) q^{13} +(0.360486 - 1.10946i) q^{14} +(0.773060 - 1.51722i) q^{15} +(2.98011 - 2.16518i) q^{16} +(2.00860 - 1.45934i) q^{17} +(-0.205516 - 0.104716i) q^{18} +(-1.31749 - 2.58572i) q^{19} +(3.27421 - 0.518584i) q^{20} +(3.57623 + 3.57623i) q^{21} +(0.607987 + 0.464302i) q^{22} -0.165749i q^{23} +(-0.142411 - 0.899145i) q^{24} +(-1.99763 - 0.649071i) q^{25} +(0.831045 + 0.0315203i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.54026 + 9.72481i) q^{28} +(10.1999 - 3.31415i) q^{29} +(0.121371 - 0.373540i) q^{30} +(-0.628091 - 3.96561i) q^{31} +(1.88823 - 1.88823i) q^{32} +(-2.99024 + 1.43474i) q^{33} +(0.404936 - 0.404936i) q^{34} +(-5.06204 + 6.96730i) q^{35} +(1.85151 + 0.601594i) q^{36} +(2.62011 + 1.33501i) q^{37} +(-0.393445 - 0.541530i) q^{38} +(-1.75747 + 3.14822i) q^{39} +(1.47429 - 0.479025i) q^{40} +(3.37842 + 6.63052i) q^{41} +(0.943763 + 0.685684i) q^{42} +3.45420 q^{43} +(-5.68143 - 3.06783i) q^{44} +(1.20407 + 1.20407i) q^{45} +(-0.00598065 - 0.0377603i) q^{46} +(0.354969 + 0.696665i) q^{47} +(1.13830 + 3.50333i) q^{48} +(-10.9204 - 15.0306i) q^{49} +(-0.478514 - 0.0757892i) q^{50} +(0.767219 + 2.36126i) q^{51} +(-6.96950 + 0.834504i) q^{52} +(-7.00727 - 5.09108i) q^{53} +(0.163099 - 0.163099i) q^{54} +(-3.20954 - 4.64694i) q^{55} +4.60416i q^{56} +(2.86629 - 0.453975i) q^{57} +(2.20412 - 1.12306i) q^{58} +(-4.10413 - 2.09116i) q^{59} +(-0.518584 + 3.27421i) q^{60} +(-7.39629 - 10.1801i) q^{61} +(-0.286179 - 0.880767i) q^{62} +(-4.50631 + 2.29608i) q^{63} +(-3.96831 + 5.46192i) q^{64} +(-5.76297 - 2.11718i) q^{65} +(-0.629456 + 0.434753i) q^{66} +(3.36528 + 3.36528i) q^{67} +(-2.84103 + 3.91035i) q^{68} +(0.157637 + 0.0512193i) q^{69} +(-0.901817 + 1.76992i) q^{70} +(-7.65498 - 1.21243i) q^{71} +(0.899145 + 0.142411i) q^{72} +(0.563685 - 1.10629i) q^{73} +(0.645074 + 0.209597i) q^{74} +(1.23461 - 1.69929i) q^{75} +(3.99490 + 3.99490i) q^{76} +(16.0722 - 4.80113i) q^{77} +(-0.286785 + 0.780630i) q^{78} +(4.68176 - 6.44389i) q^{79} +(-5.58884 + 2.84766i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.00891 + 1.38864i) q^{82} +(-1.41515 + 8.93493i) q^{83} +(-8.77288 - 4.47001i) q^{84} +(-3.76690 + 1.91933i) q^{85} +(0.786923 - 0.124636i) q^{86} +10.7248i q^{87} +(-2.84843 - 1.00130i) q^{88} +(-10.5125 + 10.5125i) q^{89} +(0.317752 + 0.230861i) q^{90} +(11.2699 - 14.3358i) q^{91} +(0.0997135 + 0.306887i) q^{92} +(3.96561 + 0.628091i) q^{93} +(0.106005 + 0.145904i) q^{94} +(1.52703 + 4.69973i) q^{95} +(1.21232 + 2.37930i) q^{96} +(0.445766 + 2.81446i) q^{97} +(-3.03018 - 3.03018i) q^{98} +(-0.440484 - 3.28724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 28 q^{3} + 6 q^{5} - 28 q^{9}+O(q^{10}) $ 112 * q + 28 * q^3 + 6 * q^5 - 28 * q^9	$ 112 q + 28 q^{3} + 6 q^{5} - 28 q^{9} - 14 q^{11} + 10 q^{13} + 12 q^{14} + 4 q^{15} - 48 q^{16} - 2 q^{20} + 32 q^{22} + 30 q^{24} - 46 q^{26} + 28 q^{27} - 20 q^{29} - 24 q^{31} - 16 q^{33} - 16 q^{34} - 20 q^{35} + 12 q^{37} + 10 q^{39} - 40 q^{40} - 10 q^{41} + 28 q^{42} + 24 q^{44} - 4 q^{45} - 20 q^{46} - 62 q^{47} - 92 q^{48} - 90 q^{50} + 110 q^{52} + 68 q^{53} + 32 q^{55} - 30 q^{57} - 56 q^{58} + 16 q^{59} + 2 q^{60} + 20 q^{61} + 8 q^{66} + 12 q^{67} + 60 q^{68} - 196 q^{70} - 52 q^{71} + 30 q^{72} - 10 q^{73} - 120 q^{74} - 84 q^{78} + 40 q^{79} - 56 q^{80} - 28 q^{81} + 110 q^{83} - 30 q^{84} - 40 q^{85} + 18 q^{86} - 96 q^{89} - 44 q^{91} + 80 q^{92} + 24 q^{93} - 20 q^{94} + 100 q^{96} + 18 q^{97} + 6 q^{99}+O(q^{100}) $ 112 * q + 28 * q^3 + 6 * q^5 - 28 * q^9 - 14 * q^11 + 10 * q^13 + 12 * q^14 + 4 * q^15 - 48 * q^16 - 2 * q^20 + 32 * q^22 + 30 * q^24 - 46 * q^26 + 28 * q^27 - 20 * q^29 - 24 * q^31 - 16 * q^33 - 16 * q^34 - 20 * q^35 + 12 * q^37 + 10 * q^39 - 40 * q^40 - 10 * q^41 + 28 * q^42 + 24 * q^44 - 4 * q^45 - 20 * q^46 - 62 * q^47 - 92 * q^48 - 90 * q^50 + 110 * q^52 + 68 * q^53 + 32 * q^55 - 30 * q^57 - 56 * q^58 + 16 * q^59 + 2 * q^60 + 20 * q^61 + 8 * q^66 + 12 * q^67 + 60 * q^68 - 196 * q^70 - 52 * q^71 + 30 * q^72 - 10 * q^73 - 120 * q^74 - 84 * q^78 + 40 * q^79 - 56 * q^80 - 28 * q^81 + 110 * q^83 - 30 * q^84 - 40 * q^85 + 18 * q^86 - 96 * q^89 - 44 * q^91 + 80 * q^92 + 24 * q^93 - 20 * q^94 + 100 * q^96 + 18 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.227816	−	0.0360826i	0.161090	−	0.0255142i	−0.0753682	−	0.997156i	$-0.524013\pi$
$2$	0.227816	−	0.0360826i	0.161090	−	0.0255142i	0.236459	+	0.971642i	$0.424013\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−1.85151	+	0.601594i	−0.925757	+	0.300797i
$5$	−1.68185	−	0.266378i	−0.752144	−	0.119128i	−0.231421	−	0.972854i	$-0.574338\pi$
$5$	−1.68185	−	0.266378i	−0.752144	−	0.119128i	−0.520723	+	0.853726i	$0.674338\pi$
$6$	−0.0360826	+	0.227816i	−0.0147306	+	0.0930056i
$7$	2.29608	−	4.50631i	0.867837	−	1.70323i	0.171911	−	0.985112i	$-0.445006\pi$
$7$	2.29608	−	4.50631i	0.867837	−	1.70323i	0.695926	−	0.718114i	$-0.254994\pi$
$8$	−0.811131	+	0.413292i	−0.286778	+	0.146121i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.392764			−0.124203
$11$	2.28855	+	2.40053i	0.690025	+	0.723786i
$11$	2.28855	+	2.40053i	0.690025	+	0.723786i
$12$		−	1.94680i		−	0.561992i
$13$	3.53722	+	0.698600i	0.981050	+	0.193757i
$13$	3.53722	+	0.698600i	0.981050	+	0.193757i
$14$	0.360486	−	1.10946i	0.0963438	−	0.296516i
$15$	0.773060	−	1.51722i	0.199603	−	0.391743i
$16$	2.98011	−	2.16518i	0.745027	−	0.541294i
$17$	2.00860	−	1.45934i	0.487158	−	0.353941i	−0.316932	−	0.948448i	$-0.602653\pi$
$17$	2.00860	−	1.45934i	0.487158	−	0.353941i	0.804090	+	0.594507i	$0.202653\pi$
$18$	−0.205516	−	0.104716i	−0.0484406	−	0.0246817i
$19$	−1.31749	−	2.58572i	−0.302252	−	0.593204i	0.689064	−	0.724700i	$-0.258022\pi$
$19$	−1.31749	−	2.58572i	−0.302252	−	0.593204i	−0.991317	+	0.131496i	$0.958022\pi$
$20$	3.27421	−	0.518584i	0.732136	−	0.115959i
$21$	3.57623	+	3.57623i	0.780397	+	0.780397i
$22$	0.607987	+	0.464302i	0.129623	+	0.0989896i
$23$		−	0.165749i		−	0.0345611i	−0.999851	−	0.0172805i	$-0.994499\pi$
$23$		−	0.165749i		−	0.0345611i	0.999851	−	0.0172805i	$-0.00550084\pi$
$24$	−0.142411	−	0.899145i	−0.0290694	−	0.183537i
$25$	−1.99763	−	0.649071i	−0.399527	−	0.129814i
$26$	0.831045	+	0.0315203i	0.162981	+	0.00618164i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−1.54026	+	9.72481i	−0.291082	+	1.83782i
$29$	10.1999	−	3.31415i	1.89408	−	0.615423i	0.918662	−	0.395044i	$-0.129271\pi$
$29$	10.1999	−	3.31415i	1.89408	−	0.615423i	0.975414	−	0.220379i	$-0.0707293\pi$
$30$	0.121371	−	0.373540i	0.0221591	−	0.0681988i
$31$	−0.628091	−	3.96561i	−0.112808	−	0.712244i	−0.977656	−	0.210210i	$-0.932585\pi$
$31$	−0.628091	−	3.96561i	−0.112808	−	0.712244i	0.864848	−	0.502034i	$-0.167415\pi$
$32$	1.88823	−	1.88823i	0.333794	−	0.333794i
$33$	−2.99024	+	1.43474i	−0.520534	+	0.249756i
$34$	0.404936	−	0.404936i	0.0694460	−	0.0694460i
$35$	−5.06204	+	6.96730i	−0.855641	+	1.17769i
$36$	1.85151	+	0.601594i	0.308586	+	0.100266i
$37$	2.62011	+	1.33501i	0.430743	+	0.219474i	0.655900	−	0.754848i	$-0.272289\pi$
$37$	2.62011	+	1.33501i	0.430743	+	0.219474i	−0.225157	+	0.974323i	$0.572289\pi$
$38$	−0.393445	−	0.541530i	−0.0638251	−	0.0878478i
$39$	−1.75747	+	3.14822i	−0.281420	+	0.504119i
$40$	1.47429	−	0.479025i	0.233105	−	0.0757406i
$41$	3.37842	+	6.63052i	0.527620	+	1.03551i	0.988945	+	0.148282i	$0.0473743\pi$
$41$	3.37842	+	6.63052i	0.527620	+	1.03551i	−0.461325	+	0.887231i	$0.652626\pi$
$42$	0.943763	+	0.685684i	0.145626	+	0.105803i
$43$	3.45420			0.526761			0.263380	−	0.964692i	$-0.415163\pi$
$43$	3.45420			0.526761			0.263380	+	0.964692i	$0.415163\pi$
$44$	−5.68143	−	3.06783i	−0.856508	−	0.462493i
$45$	1.20407	+	1.20407i	0.179492	+	0.179492i
$46$	−0.00598065	−	0.0377603i	−0.000881799	−	0.00556746i
$47$	0.354969	+	0.696665i	0.0517775	+	0.101619i	0.915445	−	0.402442i	$-0.131839\pi$
$47$	0.354969	+	0.696665i	0.0517775	+	0.101619i	−0.863668	+	0.504061i	$0.831839\pi$
$48$	1.13830	+	3.50333i	0.164299	+	0.505662i
$49$	−10.9204	−	15.0306i	−1.56005	−	2.14723i
$50$	−0.478514	−	0.0757892i	−0.0676721	−	0.0107182i
$51$	0.767219	+	2.36126i	0.107432	+	0.330642i
$52$	−6.96950	+	0.834504i	−0.966495	+	0.115725i
$53$	−7.00727	−	5.09108i	−0.962523	−	0.699314i	−0.00878782	−	0.999961i	$-0.502797\pi$
$53$	−7.00727	−	5.09108i	−0.962523	−	0.699314i	−0.953735	+	0.300647i	$0.902797\pi$
$54$	0.163099	−	0.163099i	0.0221949	−	0.0221949i
$55$	−3.20954	−	4.64694i	−0.432775	−	0.626593i
$56$			4.60416i			0.615257i
$57$	2.86629	−	0.453975i	0.379649	−	0.0601305i
$58$	2.20412	−	1.12306i	0.289416	−	0.147465i
$59$	−4.10413	−	2.09116i	−0.534312	−	0.272246i	0.165947	−	0.986135i	$-0.446932\pi$
$59$	−4.10413	−	2.09116i	−0.534312	−	0.272246i	−0.700259	+	0.713889i	$0.746932\pi$
$60$	−0.518584	+	3.27421i	−0.0669490	+	0.422699i
$61$	−7.39629	−	10.1801i	−0.946998	−	1.30343i	−0.952848	−	0.303449i	$-0.901862\pi$
$61$	−7.39629	−	10.1801i	−0.946998	−	1.30343i	0.00584934	−	0.999983i	$-0.498138\pi$
$62$	−0.286179	−	0.880767i	−0.0363447	−	0.111858i
$63$	−4.50631	+	2.29608i	−0.567742	+	0.289279i
$64$	−3.96831	+	5.46192i	−0.496039	+	0.682740i
$65$	−5.76297	−	2.11718i	−0.714809	−	0.262603i
$66$	−0.629456	+	0.434753i	−0.0774807	+	0.0535143i
$67$	3.36528	+	3.36528i	0.411134	+	0.411134i	0.882134	−	0.470999i	$-0.156107\pi$
$67$	3.36528	+	3.36528i	0.411134	+	0.411134i	−0.470999	+	0.882134i	$0.656107\pi$
$68$	−2.84103	+	3.91035i	−0.344526	+	0.474199i
$69$	0.157637	+	0.0512193i	0.0189772	+	0.00616607i
$70$	−0.901817	+	1.76992i	−0.107788	+	0.211545i
$71$	−7.65498	−	1.21243i	−0.908479	−	0.143889i	−0.315330	−	0.948982i	$-0.602115\pi$
$71$	−7.65498	−	1.21243i	−0.908479	−	0.143889i	−0.593148	+	0.805093i	$0.702115\pi$
$72$	0.899145	+	0.142411i	0.105965	+	0.0167832i
$73$	0.563685	−	1.10629i	0.0659743	−	0.129482i	−0.855664	−	0.517531i	$-0.826851\pi$
$73$	0.563685	−	1.10629i	0.0659743	−	0.129482i	0.921639	+	0.388050i	$0.126851\pi$
$74$	0.645074	+	0.209597i	0.0749883	+	0.0243652i
$75$	1.23461	−	1.69929i	0.142560	−	0.196217i
$76$	3.99490	+	3.99490i	0.458246	+	0.458246i
$77$	16.0722	−	4.80113i	1.83160	−	0.547140i
$78$	−0.286785	+	0.780630i	−0.0324720	+	0.0883890i
$79$	4.68176	−	6.44389i	0.526739	−	0.724995i	−0.459890	−	0.887976i	$-0.652111\pi$
$79$	4.68176	−	6.44389i	0.526739	−	0.724995i	0.986629	+	0.162981i	$0.0521111\pi$
$80$	−5.58884	+	2.84766i	−0.624851	+	0.318378i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.00891	+	1.38864i	0.111415	+	0.153349i
$83$	−1.41515	+	8.93493i	−0.155333	+	0.980736i	0.779694	+	0.626161i	$0.215375\pi$
$83$	−1.41515	+	8.93493i	−0.155333	+	0.980736i	−0.935027	+	0.354575i	$0.884625\pi$
$84$	−8.77288	−	4.47001i	−0.957200	−	0.487718i
$85$	−3.76690	+	1.91933i	−0.408577	+	0.208181i
$86$	0.786923	−	0.124636i	0.0848561	−	0.0134399i
$87$			10.7248i			1.14982i
$88$	−2.84843	−	1.00130i	−0.303644	−	0.106739i
$89$	−10.5125	+	10.5125i	−1.11432	+	1.11432i	−0.121766	+	0.992559i	$0.538856\pi$
$89$	−10.5125	+	10.5125i	−1.11432	+	1.11432i	−0.992559	+	0.121766i	$0.961144\pi$
$90$	0.317752	+	0.230861i	0.0334940	+	0.0243349i
$91$	11.2699	−	14.3358i	1.18140	−	1.50280i
$92$	0.0997135	+	0.306887i	0.0103959	+	0.0319952i
$93$	3.96561	+	0.628091i	0.411214	+	0.0651300i
$94$	0.106005	+	0.145904i	0.0109336	+	0.0150488i
$95$	1.52703	+	4.69973i	0.156670	+	0.482182i
$96$	1.21232	+	2.37930i	0.123731	+	0.242837i
$97$	0.445766	+	2.81446i	0.0452607	+	0.285765i	0.999929	−	0.0119065i	$-0.00379005\pi$
$97$	0.445766	+	2.81446i	0.0452607	+	0.285765i	−0.954668	+	0.297671i	$0.903790\pi$
$98$	−3.03018	−	3.03018i	−0.306095	−	0.306095i
$99$	−0.440484	−	3.28724i	−0.0442703	−	0.330380i
$100$	4.08913			0.408913
$101$	13.1004	+	9.51801i	1.30354	+	0.947077i	0.999984	−	0.00573599i	$-0.00182583\pi$
$101$	13.1004	+	9.51801i	1.30354	+	0.947077i	0.303557	+	0.952813i	$0.401826\pi$
$102$	0.259985	+	0.510250i	0.0257424	+	0.0505222i
$103$	14.6557	−	4.76191i	1.44406	−	0.469205i	0.520903	−	0.853616i	$-0.325595\pi$
$103$	14.6557	−	4.76191i	1.44406	−	0.469205i	0.923162	+	0.384411i	$0.125595\pi$
$104$	−3.15788	+	0.895250i	−0.309655	+	0.0877865i
$105$	−5.06204	−	6.96730i	−0.494004	−	0.679939i
$106$	−1.78007	−	0.906992i	−0.172896	−	0.0880948i
$107$	7.63354	+	2.48029i	0.737963	+	0.239779i	0.653794	−	0.756673i	$-0.273176\pi$
$107$	7.63354	+	2.48029i	0.737963	+	0.239779i	0.0841690	+	0.996451i	$0.473176\pi$
$108$	−1.14430	+	1.57499i	−0.110110	+	0.151554i
$109$	0.140113	−	0.140113i	0.0134204	−	0.0134204i	−0.700365	−	0.713785i	$-0.746979\pi$
$109$	0.140113	−	0.140113i	0.0134204	−	0.0134204i	0.713785	+	0.700365i	$0.246979\pi$
$110$	−0.898860	−	0.942839i	−0.0857030	−	0.0898962i
$111$	−2.07933	+	2.07933i	−0.197361	+	0.197361i
$112$	−2.91439	−	18.4007i	−0.275384	−	1.73870i
$113$	0.539530	−	1.66050i	0.0507547	−	0.156207i	−0.922467	−	0.386077i	$-0.873830\pi$
$113$	0.539530	−	1.66050i	0.0507547	−	0.156207i	0.973221	+	0.229870i	$0.0738300\pi$
$114$	0.636607	−	0.206846i	0.0596237	−	0.0193729i
$115$	−0.0441519	+	0.278764i	−0.00411719	+	0.0259949i
$116$	−16.8915	+	12.2724i	−1.56834	+	1.13946i
$117$	−2.45105	−	2.64431i	−0.226599	−	0.244466i
$118$	−1.01044	−	0.328313i	−0.0930187	−	0.0302236i
$119$	−1.96431	−	12.4022i	−0.180068	−	1.13690i
$120$			1.55016i			0.141509i
$121$	−0.525055	+	10.9875i	−0.0477323	+	0.998860i
$122$	−2.05232	−	2.05232i	−0.185809	−	0.185809i
$123$	−7.34999	+	1.16412i	−0.662726	+	0.104965i
$124$	3.54860	+	6.96453i	0.318674	+	0.625433i
$125$	10.7729	+	5.48906i	0.963557	+	0.490957i
$126$	−0.943763	+	0.685684i	−0.0840771	+	0.0610856i
$127$	−11.5408	+	8.38485i	−1.02408	+	0.744035i	−0.967115	−	0.254341i	$-0.918141\pi$
$127$	−11.5408	+	8.38485i	−1.02408	+	0.744035i	−0.0569621	+	0.998376i	$0.518141\pi$
$128$	−3.13160	+	6.14611i	−0.276797	+	0.543244i
$129$	−1.06741	+	3.28514i	−0.0939799	+	0.289240i
$130$	−1.38929	−	0.274385i	−0.121849	−	0.0240651i
$131$		−	18.0408i		−	1.57624i	−0.615524	−	0.788118i	$-0.711056\pi$
$131$		−	18.0408i		−	1.57624i	0.615524	−	0.788118i	$-0.288944\pi$
$132$	4.67334	−	4.45535i	0.406762	−	0.387788i
$133$	−14.6771			−1.27267
$134$	0.888093	+	0.645237i	0.0767196	+	0.0557400i
$135$	−1.51722	+	0.773060i	−0.130581	+	0.0665344i
$136$	−1.02611	+	2.01385i	−0.0879881	+	0.172686i
$137$	−2.22804	+	14.0673i	−0.190354	+	1.20185i	0.688671	+	0.725074i	$0.258194\pi$
$137$	−2.22804	+	14.0673i	−0.190354	+	1.20185i	−0.879025	+	0.476775i	$0.841806\pi$
$138$	0.0377603	+	0.00598065i	0.00321437	+	0.000509107i
$139$	−7.43873	+	2.41699i	−0.630945	+	0.205006i	−0.606994	−	0.794707i	$-0.707625\pi$
$139$	−7.43873	+	2.41699i	−0.630945	+	0.205006i	−0.0239513	+	0.999713i	$0.507625\pi$
$140$	5.18096	−	15.9453i	0.437871	−	1.34763i
$141$	−0.772259	+	0.122314i	−0.0650360	+	0.0103007i
$142$	−1.78768			−0.150018
$143$	6.41812	+	10.0900i	0.536710	+	0.843767i
$144$	−3.68362			−0.306968
$145$	−18.0375	+	2.85686i	−1.49793	+	0.237249i
$146$	0.0884987	−	0.272371i	0.00732420	−	0.0225416i
$147$	17.6695	−	5.74118i	1.45736	−	0.473524i
$148$	−5.65430	−	0.895553i	−0.464780	−	0.0736140i
$149$	−0.570409	+	3.60142i	−0.0467298	+	0.295040i	−0.999974	−	0.00715973i	$-0.997721\pi$
$149$	−0.570409	+	3.60142i	−0.0467298	+	0.295040i	0.953245	+	0.302200i	$0.0977210\pi$
$150$	0.219949	−	0.431674i	0.0179587	−	0.0352460i
$151$	16.6986	−	8.50834i	1.35891	−	0.692399i	0.385765	−	0.922597i	$-0.373938\pi$
$151$	16.6986	−	8.50834i	1.35891	−	0.692399i	0.973144	+	0.230198i	$0.0739375\pi$
$152$	2.13731	+	1.55285i	0.173359	+	0.125952i
$153$	−2.48277			−0.200720
$154$	3.48828	−	1.67370i	0.281094	−	0.134871i
$155$			6.83685i			0.549149i
$156$	1.36003	−	6.88626i	0.108890	−	0.551342i
$157$	−4.04788	+	12.4581i	−0.323056	+	0.994264i	0.649254	+	0.760571i	$0.275081\pi$
$157$	−4.04788	+	12.4581i	−0.323056	+	0.994264i	−0.972310	+	0.233693i	$0.924919\pi$
$158$	0.834070	−	1.63695i	0.0663550	−	0.130229i
$159$	7.00727	−	5.09108i	0.555713	−	0.403749i
$160$	−3.67869	+	2.67272i	−0.290826	+	0.211297i
$161$	−0.746917	−	0.380573i	−0.0588653	−	0.0299934i
$162$	0.104716	+	0.205516i	0.00822724	+	0.0161469i
$163$	1.89703	−	0.300460i	0.148587	−	0.0235338i	−0.0816979	−	0.996657i	$-0.526034\pi$
$163$	1.89703	−	0.300460i	0.148587	−	0.0235338i	0.230285	+	0.973123i	$0.426034\pi$
$164$	−10.2441	−	10.2441i	−0.799927	−	0.799927i
$165$	5.41130	−	1.61648i	0.421269	−	0.125842i
$166$			2.08659i			0.161950i
$167$	−2.40810	−	15.2041i	−0.186344	−	1.17653i	−0.886564	−	0.462605i	$-0.846915\pi$
$167$	−2.40810	−	15.2041i	−0.186344	−	1.17653i	0.700220	−	0.713927i	$-0.253085\pi$
$168$	−4.37882	−	1.42276i	−0.337833	−	0.109769i
$169$	12.0239	+	4.94221i	0.924917	+	0.380170i
$170$	−0.788907	+	0.573174i	−0.0605064	+	0.0439605i
$171$	−0.453975	+	2.86629i	−0.0347164	+	0.219191i
$172$	−6.39550	+	2.07802i	−0.487652	+	0.158448i
$173$	−0.338747	+	1.04256i	−0.0257545	+	0.0792641i	−0.963108	−	0.269117i	$-0.913268\pi$
$173$	−0.338747	+	1.04256i	−0.0257545	+	0.0792641i	0.937353	+	0.348381i	$0.113268\pi$
$174$	0.386979	+	2.44329i	0.0293368	+	0.185225i
$175$	−7.51165	+	7.51165i	−0.567827	+	0.567827i
$176$	12.0177	+	2.19871i	0.905868	+	0.165734i
$177$	3.25706	−	3.25706i	0.244815	−	0.244815i
$178$	−2.01560	+	2.77424i	−0.151076	+	0.207938i
$179$	10.5101	+	3.41495i	0.785564	+	0.255245i	0.674214	−	0.738536i	$-0.264482\pi$
$179$	10.5101	+	3.41495i	0.785564	+	0.255245i	0.111350	+	0.993781i	$0.464482\pi$
$180$	−2.95371	−	1.50499i	−0.220157	−	0.112175i
$181$	4.93201	+	6.78833i	0.366594	+	0.504573i	0.951971	−	0.306188i	$-0.0990536\pi$
$181$	4.93201	+	6.78833i	0.366594	+	0.504573i	−0.585377	+	0.810761i	$0.699054\pi$
$182$	2.05019	−	3.67258i	0.151970	−	0.272229i
$183$	11.9675	−	3.88846i	0.884660	−	0.287443i
$184$	0.0685027	+	0.134444i	0.00505008	+	0.00991135i
$185$	−4.05100	−	2.94322i	−0.297835	−	0.216390i
$186$	0.926094			0.0679045
$187$	8.09997	+	1.48194i	0.592329	+	0.108370i
$188$	−1.07634	−	1.07634i	−0.0785001	−	0.0785001i
$189$	−0.791176	−	4.99529i	−0.0575496	−	0.363354i
$190$	0.517461	+	1.01558i	0.0375406	+	0.0736776i
$191$	2.39080	+	7.35812i	0.172992	+	0.532415i	0.999536	−	0.0304571i	$-0.00969629\pi$
$191$	2.39080	+	7.35812i	0.172992	+	0.532415i	−0.826544	+	0.562872i	$0.809696\pi$
$192$	−3.96831	−	5.46192i	−0.286388	−	0.394180i
$193$	0.926881	+	0.146804i	0.0667184	+	0.0105672i	0.189704	−	0.981841i	$-0.439247\pi$
$193$	0.926881	+	0.146804i	0.0667184	+	0.0105672i	−0.122986	+	0.992408i	$0.539247\pi$
$194$	0.203106	+	0.625095i	0.0145821	+	0.0448792i
$195$	3.79441	−	4.82667i	0.271723	−	0.345645i
$196$	29.2615	+	21.2598i	2.09011	+	1.51855i
$197$	−3.78160	+	3.78160i	−0.269428	+	0.269428i	−0.828870	−	0.559442i	$-0.811016\pi$
$197$	−3.78160	+	3.78160i	−0.269428	+	0.269428i	0.559442	+	0.828870i	$0.311016\pi$
$198$	−0.218962	−	0.732994i	−0.0155609	−	0.0520916i
$199$			12.1054i			0.858131i	0.903273	+	0.429065i	$0.141157\pi$
$199$			12.1054i			0.858131i	−0.903273	+	0.429065i	$0.858843\pi$
$200$	1.88860	−	0.299125i	0.133544	−	0.0211513i
$201$	−4.24050	+	2.16064i	−0.299102	+	0.152400i
$202$	3.32792	+	1.69566i	0.234152	+	0.119306i
$203$	8.48522	−	53.5736i	0.595546	−	3.76013i
$204$	−2.84103	−	3.91035i	−0.198912	−	0.273779i
$205$	−3.91575	−	12.0514i	−0.273488	−	0.841710i
$206$	3.16698	−	1.61366i	0.220654	−	0.112429i
$207$	−0.0974248	+	0.134094i	−0.00677149	+	0.00932016i
$208$	12.0539	−	5.57681i	0.835788	−	0.386682i
$209$	3.19194	−	9.08021i	0.220791	−	0.628091i
$210$	−1.40461	−	1.40461i	−0.0969275	−	0.0969275i
$211$	2.96304	−	4.07828i	0.203984	−	0.280760i	−0.694753	−	0.719249i	$-0.744486\pi$
$211$	2.96304	−	4.07828i	0.203984	−	0.280760i	0.898737	+	0.438489i	$0.144486\pi$
$212$	16.0368	+	5.21068i	1.10141	+	0.357871i
$213$	3.51861	−	6.90565i	0.241091	−	0.473168i
$214$	1.82854	+	0.289613i	0.124997	+	0.0197975i
$215$	−5.80943	−	0.920124i	−0.396200	−	0.0627519i
$216$	−0.413292	+	0.811131i	−0.0281209	+	0.0551904i
$217$	−19.3124	−	6.27498i	−1.31101	−	0.425974i
$218$	0.0268645	−	0.0369758i	0.00181949	−	0.00250431i
$219$	0.877960	+	0.877960i	0.0593270	+	0.0593270i
$220$	8.73809	+	6.67303i	0.589122	+	0.449896i
$221$	8.12438	−	3.75879i	0.546505	−	0.252844i
$222$	−0.398677	+	0.548732i	−0.0267575	+	0.0368285i
$223$	−8.61447	+	4.38929i	−0.576868	+	0.293929i	−0.717979	−	0.696065i	$-0.754932\pi$
$223$	−8.61447	+	4.38929i	−0.576868	+	0.293929i	0.141111	+	0.989994i	$0.454932\pi$
$224$	−4.17342	−	12.8445i	−0.278848	−	0.858206i
$225$	1.23461	+	1.69929i	0.0823071	+	0.113286i
$226$	0.0629985	−	0.397757i	0.00419060	−	0.0264584i
$227$	−19.7390	−	10.0575i	−1.31012	−	0.667541i	−0.347320	−	0.937747i	$-0.612908\pi$
$227$	−19.7390	−	10.0575i	−1.31012	−	0.667541i	−0.962803	+	0.270206i	$0.912908\pi$
$228$	−5.03387	+	2.56488i	−0.333376	+	0.169864i
$229$	−5.65245	+	0.895260i	−0.373524	+	0.0591604i	−0.340374	−	0.940290i	$-0.610554\pi$
$229$	−5.65245	+	0.895260i	−0.373524	+	0.0591604i	−0.0331498	+	0.999450i	$0.510554\pi$
$230$			0.0651002i			0.00429258i
$231$	−0.400445	+	16.7692i	−0.0263473	+	1.10333i
$232$	−6.90375	+	6.90375i	−0.453253	+	0.453253i
$233$	−16.8961	−	12.2757i	−1.10690	−	0.804209i	−0.124726	−	0.992191i	$-0.539805\pi$
$233$	−16.8961	−	12.2757i	−1.10690	−	0.804209i	−0.982172	+	0.187983i	$0.939805\pi$
$234$	−0.653802	−	0.513976i	−0.0427404	−	0.0335997i
$235$	−0.411426	−	1.26624i	−0.0268385	−	0.0826004i
$236$	8.85688	+	1.40279i	0.576534	+	0.0913140i
$237$	4.68176	+	6.44389i	0.304113	+	0.418576i
$238$	−0.895003	−	2.75454i	−0.0580144	−	0.178550i
$239$	4.88827	+	9.59376i	0.316196	+	0.620569i	0.993332	−	0.115289i	$-0.0367793\pi$
$239$	4.88827	+	9.59376i	0.316196	+	0.620569i	−0.677136	+	0.735858i	$0.736779\pi$
$240$	−0.981235	−	6.19528i	−0.0633385	−	0.399903i
$241$	−4.10163	−	4.10163i	−0.264209	−	0.264209i	0.562553	−	0.826762i	$-0.309819\pi$
$241$	−4.10163	−	4.10163i	−0.264209	−	0.264209i	−0.826762	+	0.562553i	$0.809819\pi$
$242$	0.276840	+	2.52207i	0.0177959	+	0.162125i
$243$	−1.00000			−0.0641500
$244$	19.8186	+	14.3991i	1.26876	+	0.921807i
$245$	14.3626	+	28.1881i	0.917590	+	1.80087i
$246$	−1.63244	+	0.530413i	−0.104081	+	0.0338179i
$247$	−2.85387	−	10.0667i	−0.181587	−	0.640526i
$248$	2.14842	+	2.95704i	0.136425	+	0.187772i
$249$	−8.06032	−	4.10694i	−0.510802	−	0.260267i
$250$	2.65230	+	0.861785i	0.167746	+	0.0545040i
$251$	8.88115	−	12.2239i	0.560573	−	0.771563i	−0.430826	−	0.902435i	$-0.641778\pi$
$251$	8.88115	−	12.2239i	0.560573	−	0.771563i	0.991399	+	0.130872i	$0.0417777\pi$
$252$	6.96220	−	6.96220i	0.438577	−	0.438577i
$253$	0.397885	−	0.379325i	0.0250148	−	0.0238480i
$254$	−2.32663	+	2.32663i	−0.145986	+	0.145986i
$255$	−0.661356	−	4.17564i	−0.0414157	−	0.261489i
$256$	3.68087	−	11.3286i	0.230054	−	0.708035i
$257$	−25.0917	+	8.15279i	−1.56518	+	0.508557i	−0.958185	−	0.286151i	$-0.907624\pi$
$257$	−25.0917	+	8.15279i	−1.56518	+	0.508557i	−0.606992	+	0.794708i	$0.707624\pi$
$258$	−0.124636	+	0.786923i	−0.00775952	+	0.0489917i
$259$	12.0320	−	8.74172i	0.747629	−	0.543184i
$260$	11.9439	+	0.453015i	0.740730	+	0.0280948i
$261$	−10.1999	−	3.31415i	−0.631359	−	0.205141i
$262$	−0.650960	−	4.11000i	−0.0402164	−	0.253917i
$263$			13.3286i			0.821876i	0.911663	+	0.410938i	$0.134799\pi$
$263$			13.3286i			0.821876i	−0.911663	+	0.410938i	$0.865201\pi$
$264$	1.83251	−	2.39960i	0.112783	−	0.147685i
$265$	10.4290	+	10.4290i	0.640649	+	0.640649i
$266$	−3.34368	+	0.529588i	−0.205014	+	0.0324711i
$267$	−6.74945	−	13.2465i	−0.413060	−	0.810675i
$268$	−8.25539	−	4.20633i	−0.504278	−	0.256943i
$269$	−10.1203	+	7.35280i	−0.617043	+	0.448308i	−0.851887	−	0.523725i	$-0.824542\pi$
$269$	−10.1203	+	7.35280i	−0.617043	+	0.448308i	0.234844	+	0.972033i	$0.424542\pi$
$270$	−0.317752	+	0.230861i	−0.0193378	+	0.0140497i
$271$	6.93399	−	13.6087i	0.421210	−	0.826671i	−0.578728	−	0.815521i	$-0.696451\pi$
$271$	6.93399	−	13.6087i	0.421210	−	0.826671i	0.999938	−	0.0111504i	$-0.00354937\pi$
$272$	2.82614	−	8.69796i	0.171360	−	0.527391i
$273$	10.1516	+	15.1483i	0.614401	+	0.916816i
$274$			3.28515i			0.198463i
$275$	−3.01358	−	6.28081i	−0.181726	−	0.378747i
$276$	−0.322680			−0.0194230
$277$	19.1295	+	13.8984i	1.14938	+	0.835075i	0.988399	−	0.151882i	$-0.0485333\pi$
$277$	19.1295	+	13.8984i	1.14938	+	0.835075i	0.160984	+	0.986957i	$0.448533\pi$
$278$	−1.60745	+	0.819039i	−0.0964087	+	0.0491227i
$279$	−1.82279	+	3.57743i	−0.109128	+	0.214175i
$280$	1.22645	−	7.74349i	0.0732943	−	0.462762i
$281$	−28.3921	−	4.49686i	−1.69373	−	0.268260i	−0.766360	−	0.642411i	$-0.777934\pi$
$281$	−28.3921	−	4.49686i	−1.69373	−	0.268260i	−0.927368	+	0.374151i	$0.877934\pi$
$282$	−0.171520	+	0.0557302i	−0.0102139	+	0.00331869i
$283$	6.76863	−	20.8317i	0.402353	−	1.23832i	−0.520732	−	0.853720i	$-0.674341\pi$
$283$	6.76863	−	20.8317i	0.402353	−	1.23832i	0.923085	−	0.384596i	$-0.125659\pi$
$284$	14.9027	−	2.36035i	0.884312	−	0.140061i
$285$	−4.94158			−0.292714
$286$	1.82622	+	2.06708i	0.107987	+	0.122229i
$287$	37.6363			2.22160
$288$	−2.63748	+	0.417736i	−0.155415	+	0.0246153i
$289$	−3.34846	+	10.3055i	−0.196968	+	0.606206i
$290$	−4.00616	+	1.30168i	−0.235250	+	0.0764372i
$291$	−2.81446	−	0.445766i	−0.164986	−	0.0261313i
$292$	−0.378131	+	2.38743i	−0.0221285	+	0.139714i
$293$	−0.0194384	+	0.0381501i	−0.00113561	+	0.00222875i	−0.891574	−	0.452876i	$-0.850398\pi$
$293$	−0.0194384	+	0.0381501i	−0.00113561	+	0.00222875i	0.890438	+	0.455105i	$0.150398\pi$
$294$	3.81825	−	1.94550i	0.222685	−	0.113464i
$295$	6.34547	+	4.61026i	0.369448	+	0.268419i
$296$	−2.67700			−0.155597
$297$	3.26247	+	0.596889i	0.189308	+	0.0346350i
$298$			0.841045i			0.0487204i
$299$	0.115792	−	0.586291i	0.00669644	−	0.0339061i
$300$	−1.26361	+	3.88899i	−0.0729545	+	0.224531i
$301$	7.93112	−	15.5657i	0.457142	−	0.897192i
$302$	3.49720	−	2.54087i	0.201241	−	0.146210i
$303$	−13.1004	+	9.51801i	−0.752599	+	0.546795i
$304$	−9.52479	−	4.85312i	−0.546284	−	0.278346i
$305$	9.72766	+	19.0916i	0.557004	+	1.09318i
$306$	−0.565616	+	0.0895848i	−0.0323341	+	0.00512122i
$307$	14.1450	+	14.1450i	0.807300	+	0.807300i	0.984224	−	0.176924i	$-0.0566148\pi$
$307$	14.1450	+	14.1450i	0.807300	+	0.807300i	−0.176924	+	0.984224i	$0.556615\pi$
$308$	−26.8696	+	18.5583i	−1.53104	+	1.05746i
$309$			15.4099i			0.876637i
$310$	0.246691	+	1.55755i	0.0140111	+	0.0884627i
$311$	1.21545	+	0.394922i	0.0689216	+	0.0223940i	0.343275	−	0.939235i	$-0.388464\pi$
$311$	1.21545	+	0.394922i	0.0689216	+	0.0223940i	−0.274353	+	0.961629i	$0.588464\pi$
$312$	0.124404	−	3.27997i	0.00704301	−	0.185692i
$313$	−20.5481	+	14.9291i	−1.16145	+	0.843841i	−0.989960	−	0.141346i	$-0.954857\pi$
$313$	−20.5481	+	14.9291i	−1.16145	+	0.843841i	−0.171487	+	0.985186i	$0.554857\pi$
$314$	−0.472653	+	2.98422i	−0.0266734	+	0.168409i
$315$	8.19055	−	2.66127i	0.461485	−	0.149946i
$316$	−4.79175	+	14.7475i	−0.269557	+	0.829611i
$317$	−1.40584	−	8.87612i	−0.0789598	−	0.498533i	−0.995197	−	0.0978957i	$-0.968789\pi$
$317$	−1.40584	−	8.87612i	−0.0789598	−	0.498533i	0.916237	−	0.400637i	$-0.131211\pi$
$318$	1.41267	−	1.41267i	0.0792187	−	0.0792187i
$319$	31.2988	+	16.9006i	1.75239	+	0.946249i
$320$	8.12903	−	8.12903i	0.454427	−	0.454427i
$321$	−4.71779	+	6.49348i	−0.263321	+	0.362431i
$322$	−0.183892	−	0.0597501i	−0.0102479	−	0.00332974i
$323$	−6.41974	−	3.27102i	−0.357204	−	0.182004i
$324$	−1.14430	−	1.57499i	−0.0635722	−	0.0874996i
$325$	−6.61264	−	3.69146i	−0.366803	−	0.204765i
$326$	0.421333	−	0.136899i	0.0233355	−	0.00758216i
$327$	0.0899583	+	0.176553i	0.00497471	+	0.00976341i
$328$	−5.48068	−	3.98194i	−0.302620	−	0.219866i
$329$	3.95443			0.218015
$330$	1.17446	−	0.563513i	0.0646517	−	0.0310204i
$331$	−3.46863	−	3.46863i	−0.190653	−	0.190653i	0.605325	−	0.795978i	$-0.293043\pi$
$331$	−3.46863	−	3.46863i	−0.190653	−	0.190653i	−0.795978	+	0.605325i	$0.793043\pi$
$332$	−2.75502	−	17.3945i	−0.151201	−	0.954647i
$333$	−1.33501	−	2.62011i	−0.0731581	−	0.143581i
$334$	−1.09721	−	3.37686i	−0.0600366	−	0.184774i
$335$	−4.76344	−	6.55631i	−0.260255	−	0.358210i
$336$	18.4007	+	2.91439i	1.00384	+	0.158993i
$337$	2.10708	+	6.48493i	0.114780	+	0.353257i	0.991901	−	0.127013i	$-0.0405389\pi$
$337$	2.10708	+	6.48493i	0.114780	+	0.353257i	−0.877121	+	0.480269i	$0.840539\pi$
$338$	2.91757	+	0.692062i	0.158695	+	0.0376432i
$339$	1.41251	+	1.02625i	0.0767169	+	0.0557381i
$340$	5.81981	−	5.81981i	0.315624	−	0.315624i
$341$	8.08213	−	10.5833i	0.437672	−	0.573115i
$342$			0.669368i			0.0361953i
$343$	−57.8396	+	9.16090i	−3.12305	+	0.494642i
$344$	−2.80181	+	1.42759i	−0.151063	+	0.0769706i
$345$	−0.251477	−	0.128134i	−0.0135391	−	0.00689850i
$346$	−0.0395540	+	0.249734i	−0.00212644	+	0.0134258i
$347$	−0.621900	−	0.855972i	−0.0333853	−	0.0459510i	0.791998	−	0.610524i	$-0.209041\pi$
$347$	−0.621900	−	0.855972i	−0.0333853	−	0.0459510i	−0.825383	+	0.564573i	$0.809041\pi$
$348$	−6.45199	−	19.8572i	−0.345863	−	1.06446i
$349$	−18.7855	+	9.57171i	−1.00557	+	0.512362i	−0.877588	−	0.479415i	$-0.840849\pi$
$349$	−18.7855	+	9.57171i	−1.00557	+	0.512362i	−0.127979	+	0.991777i	$0.540849\pi$
$350$	−1.44024	+	1.98232i	−0.0769839	+	0.105959i
$351$	3.27230	−	1.51395i	0.174663	−	0.0808086i
$352$	8.85404	+	0.211432i	0.471922	+	0.0112694i
$353$	−20.5165	−	20.5165i	−1.09198	−	1.09198i	−0.995317	−	0.0966656i	$-0.969182\pi$
$353$	−20.5165	−	20.5165i	−1.09198	−	1.09198i	−0.0966656	−	0.995317i	$-0.530818\pi$
$354$	0.624488	−	0.859533i	0.0331911	−	0.0456837i
$355$	12.5515	+	4.07824i	0.666166	+	0.216450i
$356$	13.1398	−	25.7883i	0.696409	−	1.36678i
$357$	12.4022	+	1.96431i	0.656392	+	0.103962i
$358$	2.51760	+	0.398749i	0.133059	+	0.0210745i
$359$	−11.6813	+	22.9258i	−0.616515	+	1.20998i	0.345869	+	0.938283i	$0.387584\pi$
$359$	−11.6813	+	22.9258i	−0.616515	+	1.20998i	−0.962383	+	0.271695i	$0.912416\pi$
$360$	−1.47429	−	0.479025i	−0.0777018	−	0.0252469i
$361$	6.21777	−	8.55802i	0.327251	−	0.450422i
$362$	1.36853	+	1.36853i	0.0719286	+	0.0719286i
$363$	−10.2874	−	3.89467i	−0.539951	−	0.204417i
$364$	−12.2420	+	33.3228i	−0.641655	+	1.74659i
$365$	−1.24272	+	1.71046i	−0.0650471	+	0.0895297i
$366$	2.58608	−	1.31767i	0.135176	−	0.0688758i
$367$	−3.24808	−	9.99657i	−0.169548	−	0.521817i	0.829794	−	0.558070i	$-0.188458\pi$
$367$	−3.24808	−	9.99657i	−0.169548	−	0.521817i	−0.999343	+	0.0362530i	$0.988458\pi$
$368$	−0.358876	−	0.493950i	−0.0187077	−	0.0257489i
$369$	1.16412	−	7.34999i	0.0606018	−	0.382625i
$370$	−1.02908	−	0.524344i	−0.0534994	−	0.0272593i
$371$	−39.0313	+	19.8874i	−2.02640	+	1.03250i
$372$	−7.72024	+	1.22277i	−0.400276	+	0.0633974i
$373$			12.1915i			0.631253i	0.948884	+	0.315626i	$0.102215\pi$
$373$			12.1915i			0.631253i	−0.948884	+	0.315626i	$0.897785\pi$
$374$	1.89878	+	0.0453424i	0.0981835	+	0.00234460i
$375$	−8.54941	+	8.54941i	−0.441490	+	0.441490i
$376$	−0.575852	−	0.418381i	−0.0296973	−	0.0215763i
$377$	38.3947	−	4.59725i	1.97743	−	0.236770i
$378$	−0.360486	−	1.10946i	−0.0185414	−	0.0570645i
$379$	23.2407	+	3.68096i	1.19379	+	0.189078i	0.721532	−	0.692381i	$-0.243438\pi$
$379$	23.2407	+	3.68096i	1.19379	+	0.189078i	0.472260	+	0.881459i	$0.343438\pi$
$380$	−5.65465	−	7.78296i	−0.290077	−	0.399257i
$381$	−4.40818	−	13.5670i	−0.225838	−	0.695057i
$382$	0.810163	+	1.59003i	0.0414516	+	0.0813533i
$383$	−0.553749	−	3.49623i	−0.0282952	−	0.178649i	0.969493	−	0.245118i	$-0.0788267\pi$
$383$	−0.553749	−	3.49623i	−0.0282952	−	0.178649i	−0.997788	+	0.0664689i	$0.978827\pi$
$384$	−4.87758	−	4.87758i	−0.248908	−	0.248908i
$385$	−28.3099	+	3.79347i	−1.44281	+	0.193333i
$386$	0.216456			0.0110173
$387$	−2.79451	−	2.03033i	−0.142053	−	0.103207i
$388$	−2.51850	−	4.94284i	−0.127858	−	0.250935i
$389$	−17.0819	+	5.55024i	−0.866086	+	0.281408i	−0.708168	−	0.706044i	$-0.750478\pi$
$389$	−17.0819	+	5.55024i	−0.866086	+	0.281408i	−0.157918	+	0.987452i	$0.550478\pi$
$390$	0.690270	−	1.23651i	0.0349532	−	0.0626130i
$391$	−0.241884	−	0.332924i	−0.0122326	−	0.0168367i
$392$	15.0699	+	7.67848i	0.761143	+	0.387822i
$393$	17.1579	+	5.57493i	0.865500	+	0.281218i
$394$	−0.725061	+	0.997961i	−0.0365280	+	0.0502765i
$395$	−9.59052	+	9.59052i	−0.482551	+	0.482551i
$396$	2.79315	+	5.82139i	0.140361	+	0.292536i
$397$	7.11744	−	7.11744i	0.357214	−	0.357214i	−0.505571	−	0.862785i	$-0.668718\pi$
$397$	7.11744	−	7.11744i	0.357214	−	0.357214i	0.862785	+	0.505571i	$0.168718\pi$
$398$	0.436795	+	2.75781i	0.0218945	+	0.138237i
$399$	4.53547	−	13.9588i	0.227058	−	0.698812i
$400$	−7.35852	+	2.39093i	−0.367926	+	0.119546i
$401$	−2.00648	+	12.6684i	−0.100199	+	0.632631i	0.885568	+	0.464510i	$0.153770\pi$
$401$	−2.00648	+	12.6684i	−0.100199	+	0.632631i	−0.985767	+	0.168120i	$0.946230\pi$
$402$	−0.888093	+	0.645237i	−0.0442941	+	0.0321815i
$403$	0.548675	−	14.4660i	0.0273315	−	0.720604i
$404$	−29.9816	−	9.74161i	−1.49164	−	0.484663i
$405$	−0.266378	−	1.68185i	−0.0132364	−	0.0835716i
$406$		−	12.5111i		−	0.620916i
$407$	2.79152	+	9.34488i	0.138371	+	0.463208i
$408$	−1.59820	−	1.59820i	−0.0791228	−	0.0791228i
$409$	−20.8205	+	3.29764i	−1.02951	+	0.163058i	−0.648263	−	0.761416i	$-0.724504\pi$
$409$	−20.8205	+	3.29764i	−1.02951	+	0.163058i	−0.381245	+	0.924474i	$0.624504\pi$
$410$	−1.32692	−	2.60423i	−0.0655319	−	0.128614i
$411$	−12.6903	−	6.46602i	−0.625965	−	0.318945i
$412$	−24.2704	+	17.6335i	−1.19572	+	0.868740i
$413$	−18.8468	+	13.6930i	−0.927392	+	0.673789i
$414$	−0.0173565	+	0.0340641i	−0.000853026	+	0.00167416i
$415$	4.76014	−	14.6502i	0.233666	−	0.719150i
$416$	7.99819	−	5.35997i	0.392144	−	0.262794i
$417$		−	7.82155i		−	0.383023i
$418$	0.399539	−	2.18379i	0.0195421	−	0.106813i
$419$	32.7351			1.59921			0.799606	−	0.600524i	$-0.205041\pi$
$419$	32.7351			1.59921			0.799606	+	0.600524i	$0.205041\pi$
$420$	13.5639	+	9.85476i	0.661851	+	0.480863i
$421$	−4.16946	+	2.12445i	−0.203207	+	0.103539i	−0.552633	−	0.833425i	$-0.686377\pi$
$421$	−4.16946	+	2.12445i	−0.203207	+	0.103539i	0.349426	+	0.936964i	$0.386377\pi$
$422$	0.527874	−	1.03601i	0.0256965	−	0.0504323i
$423$	0.122314	−	0.772259i	0.00594710	−	0.0375485i
$424$	7.78792	+	1.23348i	0.378215	+	0.0599033i
$425$	−4.95967	+	1.61149i	−0.240579	+	0.0781690i
$426$	0.552422	−	1.70018i	0.0267650	−	0.0823741i
$427$	−62.8573	+	9.95562i	−3.04188	+	0.481786i
$428$	−15.6257			−0.755299
$429$	−11.5795	+	2.98602i	−0.559061	+	0.144166i
$430$	−1.35668			−0.0654251
$431$	24.8069	−	3.92903i	1.19491	−	0.189255i	0.472885	−	0.881124i	$-0.343213\pi$
$431$	24.8069	−	3.92903i	1.19491	−	0.189255i	0.722023	+	0.691869i	$0.243213\pi$
$432$	1.13830	−	3.50333i	0.0547665	−	0.168554i
$433$	8.50403	−	2.76313i	0.408678	−	0.132787i	−0.0974613	−	0.995239i	$-0.531072\pi$
$433$	8.50403	−	2.76313i	0.408678	−	0.132787i	0.506139	+	0.862452i	$0.331072\pi$
$434$	−4.62610	−	0.732703i	−0.222060	−	0.0351709i
$435$	2.85686	−	18.0375i	0.136976	−	0.864832i
$436$	−0.175131	+	0.343713i	−0.00838724	+	0.0164609i
$437$	−0.428580	+	0.218372i	−0.0205018	+	0.0104462i
$438$	0.231693	+	0.168335i	0.0110707	+	0.00804333i
$439$	11.7673			0.561621			0.280811	−	0.959763i	$-0.409397\pi$
$439$	11.7673			0.561621			0.280811	+	0.959763i	$0.409397\pi$
$440$	4.52390	+	2.44279i	0.215668	+	0.116456i
$441$			18.5788i			0.884707i
$442$	1.71524	−	1.14946i	0.0815856	−	0.0546743i
$443$	1.73403	−	5.33681i	0.0823864	−	0.253559i	−0.901375	−	0.433039i	$-0.857441\pi$
$443$	1.73403	−	5.33681i	0.0823864	−	0.253559i	0.983762	+	0.179479i	$0.0574413\pi$
$444$	2.59900	−	5.10082i	0.123343	−	0.242074i
$445$	20.4807	−	14.8801i	0.970880	−	0.705386i
$446$	−1.80414	+	1.31078i	−0.0854285	+	0.0620674i
$447$	−3.24889	−	1.65539i	−0.153667	−	0.0782974i
$448$	15.5015	+	30.4235i	0.732379	+	1.43737i
$449$	28.9328	−	4.58250i	1.36542	−	0.216262i	0.569665	−	0.821877i	$-0.307073\pi$
$449$	28.9328	−	4.58250i	1.36542	−	0.216262i	0.795758	+	0.605615i	$0.207073\pi$
$450$	0.342578	+	0.342578i	0.0161493	+	0.0161493i
$451$	−8.18505	+	23.2843i	−0.385419	+	1.09641i
$452$			3.39902i			0.159877i
$453$	2.93177	+	18.5105i	0.137747	+	0.869699i
$454$	−4.85976	−	1.57903i	−0.228080	−	0.0741077i
$455$	−22.7729	+	21.1086i	−1.06761	+	0.989584i
$456$	−2.13731	+	1.55285i	−0.100089	+	0.0727187i
$457$	−1.85338	+	11.7018i	−0.0866975	+	0.547387i	0.905661	+	0.424002i	$0.139375\pi$
$457$	−1.85338	+	11.7018i	−0.0866975	+	0.547387i	−0.992359	+	0.123385i	$0.960625\pi$
$458$	−1.25542	+	0.407910i	−0.0586618	+	0.0190604i
$459$	0.767219	−	2.36126i	0.0358107	−	0.110214i
$460$	−0.0859549	−	0.542698i	−0.00400767	−	0.0253034i
$461$	9.41991	−	9.41991i	0.438729	−	0.438729i	−0.452855	−	0.891584i	$-0.649595\pi$
$461$	9.41991	−	9.41991i	0.438729	−	0.438729i	0.891584	+	0.452855i	$0.149595\pi$
$462$	0.513849	+	3.83475i	0.0239064	+	0.178409i
$463$	−11.7773	+	11.7773i	−0.547338	+	0.547338i	−0.925670	−	0.378332i	$-0.876498\pi$
$463$	−11.7773	+	11.7773i	−0.547338	+	0.547338i	0.378332	+	0.925670i	$0.376498\pi$
$464$	23.2211	−	31.9611i	1.07801	−	1.48376i
$465$	−6.50223	−	2.11270i	−0.301534	−	0.0979743i
$466$	−4.29214	−	2.18695i	−0.198830	−	0.101309i
$467$	−15.1148	−	20.8037i	−0.699429	−	0.962681i	−0.999960	−	0.00890935i	$-0.997164\pi$
$467$	−15.1148	−	20.8037i	−0.699429	−	0.962681i	0.300531	−	0.953772i	$-0.402836\pi$
$468$	6.12895	+	3.42144i	0.283311	+	0.158156i
$469$	22.8919	−	7.43804i	1.05705	−	0.343457i
$470$	−0.139419	−	0.273625i	−0.00643091	−	0.0126214i
$471$	−10.5975	−	7.69953i	−0.488307	−	0.354776i
$472$	4.19324			0.193010
$473$	7.90512	+	8.29190i	0.363478	+	0.381262i
$474$	1.29909	+	1.29909i	0.0596694	+	0.0596694i
$475$	0.953547	+	6.02046i	0.0437517	+	0.276238i
$476$	11.0980	+	21.7811i	0.508676	+	0.998333i
$477$	2.67654	+	8.23755i	0.122550	+	0.377171i
$478$	1.45979	+	2.00924i	0.0667695	+	0.0919003i
$479$	13.4034	+	2.12289i	0.612418	+	0.0969975i	0.454936	−	0.890524i	$-0.349662\pi$
$479$	13.4034	+	2.12289i	0.612418	+	0.0969975i	0.157482	+	0.987522i	$0.449662\pi$
$480$	−1.40513	−	4.32456i	−0.0641353	−	0.197388i
$481$	8.33527	+	6.55264i	0.380055	+	0.298775i
$482$	−1.08241	−	0.786421i	−0.0493027	−	0.0358205i
$483$	0.592757	−	0.592757i	0.0269714	−	0.0269714i
$484$	−5.63784	−	20.6593i	−0.256265	−	0.939060i
$485$		−	4.85223i		−	0.220328i
$486$	−0.227816	+	0.0360826i	−0.0103340	+	0.00163674i
$487$	−22.1124	+	11.2668i	−1.00201	+	0.510548i	−0.876426	−	0.481536i	$-0.840079\pi$
$487$	−22.1124	+	11.2668i	−1.00201	+	0.510548i	−0.125580	+	0.992083i	$0.540079\pi$
$488$	10.2067	+	5.20058i	0.462037	+	0.235419i
$489$	−0.300460	+	1.89703i	−0.0135873	+	0.0857866i
$490$	4.28912	+	5.90347i	0.193763	+	0.266692i
$491$	1.87450	+	5.76912i	0.0845950	+	0.260357i	0.984403	−	0.175930i	$-0.0562933\pi$
$491$	1.87450	+	5.76912i	0.0845950	+	0.260357i	−0.899808	+	0.436287i	$0.856293\pi$
$492$	12.9083	−	6.57710i	0.581950	−	0.296518i
$493$	15.6511	−	21.5419i	0.704891	−	0.970200i
$494$	−1.01339	−	2.19037i	−0.0455945	−	0.0985496i
$495$	−0.134824	+	5.64597i	−0.00605991	+	0.253768i
$496$	−10.4580	−	10.4580i	−0.469579	−	0.469579i
$497$	−23.0400	+	31.7119i	−1.03349	+	1.42247i
$498$	−1.98446	−	0.644790i	−0.0889258	−	0.0288937i
$499$	−13.5822	+	26.6566i	−0.608023	+	1.19331i	0.357725	+	0.933827i	$0.383553\pi$
$499$	−13.5822	+	26.6566i	−0.608023	+	1.19331i	−0.965747	+	0.259484i	$0.916447\pi$
$500$	−23.2483	−	3.68218i	−1.03970	−	0.164672i
$501$	15.2041	+	2.40810i	0.679271	+	0.107586i
$502$	1.58220	−	3.10525i	0.0706172	−	0.138594i
$503$	−2.52768	−	0.821294i	−0.112704	−	0.0366197i	0.252122	−	0.967695i	$-0.418872\pi$
$503$	−2.52768	−	0.821294i	−0.112704	−	0.0366197i	−0.364826	+	0.931076i	$0.618872\pi$
$504$	2.70626	−	3.72484i	0.120546	−	0.165918i
$505$	−19.4975	−	19.4975i	−0.867627	−	0.867627i
$506$	0.0769577	−	0.100773i	0.00342119	−	0.00447992i
$507$	−8.41591	+	9.90820i	−0.373764	+	0.440039i
$508$	16.3236	−	22.4675i	0.724243	−	0.996835i
$509$	−30.2214	+	15.3986i	−1.33954	+	0.682530i	−0.969179	−	0.246358i	$-0.920766\pi$
$509$	−30.2214	+	15.3986i	−1.33954	+	0.682530i	−0.370361	+	0.928888i	$0.620766\pi$
$510$	−0.301336	−	0.927415i	−0.0133434	−	0.0410666i
$511$	−3.69104	−	5.08028i	−0.163282	−	0.224738i
$512$	2.58795	−	16.3397i	0.114372	−	0.722118i
$513$	−2.58572	−	1.31749i	−0.114162	−	0.0581685i
$514$	−5.42213	+	2.76271i	−0.239160	+	0.121858i
$515$	−25.9170	+	4.10485i	−1.14204	+	0.180881i
$516$		−	6.72463i		−	0.296035i
$517$	−0.859999	+	2.44647i	−0.0378227	+	0.107595i
$518$	2.42565	−	2.42565i	0.106577	−	0.106577i
$519$	−0.886851	−	0.644335i	−0.0389284	−	0.0282832i
$520$	5.54954	−	0.664483i	0.243363	−	0.0291395i
$521$	6.72020	+	20.6826i	0.294417	+	0.906123i	0.983417	+	0.181361i	$0.0580502\pi$
$521$	6.72020	+	20.6826i	0.294417	+	0.906123i	−0.688999	+	0.724762i	$0.741950\pi$
$522$	−2.44329	−	0.386979i	−0.106940	−	0.0169376i
$523$	−6.19476	−	8.52636i	−0.270878	−	0.372832i	0.651808	−	0.758384i	$-0.274011\pi$
$523$	−6.19476	−	8.52636i	−0.270878	−	0.372832i	−0.922686	+	0.385553i	$0.874011\pi$
$524$	10.8533	+	33.4029i	0.474127	+	1.45921i
$525$	−4.82277	−	9.46523i	−0.210483	−	0.413096i
$526$	0.480930	+	3.03647i	0.0209695	+	0.132396i
$527$	−7.04874	−	7.04874i	−0.307048	−	0.307048i
$528$	−5.80477	+	10.7501i	−0.252620	+	0.467837i
$529$	22.9725			0.998806
$530$	2.75220	+	1.99959i	0.119548	+	0.0868567i
$531$	2.09116	+	4.10413i	0.0907485	+	0.178104i
$532$	27.1749	−	8.82965i	1.17818	−	0.382814i
$533$	7.31814	+	25.8138i	0.316984	+	1.11812i
$534$	−2.01560	−	2.77424i	−0.0872237	−	0.120053i
$535$	−12.1777	−	6.20487i	−0.526490	−	0.268260i
$536$	−4.12052	−	1.33884i	−0.177979	−	0.0578290i
$537$	−6.49562	+	8.94046i	−0.280307	+	0.385809i
$538$	−2.04025	+	2.04025i	−0.0879615	+	0.0879615i
$539$	11.0895	−	60.6130i	0.477659	−	2.61078i
$540$	2.34408	−	2.34408i	0.100873	−	0.100873i
$541$	−2.66390	−	16.8192i	−0.114530	−	0.723113i	−0.976398	−	0.215980i	$-0.930705\pi$
$541$	−2.66390	−	16.8192i	−0.114530	−	0.723113i	0.861868	−	0.507133i	$-0.169295\pi$
$542$	1.08864	−	3.35049i	0.0467611	−	0.143916i
$543$	−7.98017	+	2.59291i	−0.342462	+	0.111273i
$544$	1.03714	−	6.54826i	0.0444671	−	0.280754i
$545$	−0.272972	+	0.198326i	−0.0116928	+	0.00849535i
$546$	2.85928	+	3.08473i	0.122366	+	0.132014i
$547$	1.37232	+	0.445895i	0.0586764	+	0.0190651i	0.338208	−	0.941071i	$-0.390179\pi$
$547$	1.37232	+	0.445895i	0.0586764	+	0.0190651i	−0.279532	+	0.960136i	$0.590179\pi$
$548$	−4.33754	−	27.3861i	−0.185290	−	1.16988i
$549$			12.5833i			0.537043i
$550$	−0.913170	−	1.32213i	−0.0389377	−	0.0563759i
$551$	−22.0077	−	22.0077i	−0.937560	−	0.937560i
$552$	−0.149032	+	0.0236044i	−0.00634324	+	0.00100467i
$553$	−18.2885	−	35.8932i	−0.777706	−	1.52633i
$554$	4.85951	+	2.47605i	0.206461	+	0.105197i
$555$	4.05100	−	2.94322i	0.171955	−	0.124933i
$556$	12.3189	−	8.95019i	0.522437	−	0.379572i
$557$	−3.67009	+	7.20296i	−0.155507	+	0.305199i	−0.955595	−	0.294683i	$-0.904786\pi$
$557$	−3.67009	+	7.20296i	−0.155507	+	0.305199i	0.800088	+	0.599882i	$0.204786\pi$
$558$	−0.286179	+	0.880767i	−0.0121149	+	0.0372859i
$559$	12.2183	+	2.41310i	0.516778	+	0.102063i
$560$			31.7235i			1.34056i
$561$	−3.91244	+	7.24559i	−0.165183	+	0.305909i
$562$	−6.63043			−0.279688
$563$	−34.3367	−	24.9471i	−1.44712	−	1.05139i	−0.986493	−	0.163801i	$-0.947625\pi$
$563$	−34.3367	−	24.9471i	−1.44712	−	1.05139i	−0.460627	−	0.887594i	$-0.652375\pi$
$564$	1.35627	−	0.691052i	0.0571091	−	0.0290986i
$565$	−1.34973	+	2.64899i	−0.0567835	+	0.111444i
$566$	0.790343	−	4.99003i	0.0332206	−	0.209747i
$567$	4.99529	+	0.791176i	0.209782	+	0.0332263i
$568$	6.71027	−	2.18030i	0.281557	−	0.0914833i
$569$	9.38779	−	28.8927i	0.393557	−	1.21124i	−0.536523	−	0.843886i	$-0.680263\pi$
$569$	9.38779	−	28.8927i	0.393557	−	1.21124i	0.930080	−	0.367357i	$-0.119737\pi$
$570$	−1.12577	+	0.178305i	−0.0471535	+	0.00746838i
$571$	43.4507			1.81836			0.909178	−	0.416408i	$-0.136711\pi$
$571$	43.4507			1.81836			0.909178	+	0.416408i	$0.136711\pi$
$572$	−17.9533	−	14.8207i	−0.750665	−	0.619683i
$573$	−7.73679			−0.323209
$574$	8.57417	−	1.35801i	0.357879	−	0.0566824i
$575$	−0.107583	+	0.331106i	−0.00448651	+	0.0138081i
$576$	6.42087	−	2.08627i	0.267536	−	0.0869278i
$577$	37.4238	+	5.92735i	1.55797	+	0.246759i	0.875160	−	0.483834i	$-0.160756\pi$
$577$	37.4238	+	5.92735i	1.55797	+	0.246759i	0.682813	+	0.730593i	$0.260756\pi$
$578$	−0.390985	+	2.46858i	−0.0162628	+	0.102680i
$579$	−0.426040	+	0.836152i	−0.0177056	+	0.0347493i
$580$	31.6780	−	16.1408i	1.31536	−	0.670209i
$581$	37.0143	+	26.8924i	1.53561	+	1.11569i
$582$	−0.657264			−0.0272445
$583$	−3.81524	−	28.4724i	−0.158011	−	1.17920i
$584$			1.13031i			0.0467728i
$585$	3.41790	+	5.10022i	0.141313	+	0.210868i
$586$	−0.00305184	+	0.00939261i	−0.000126070	+	0.000388005i
$587$	−1.92151	+	3.77117i	−0.0793092	+	0.155653i	−0.927256	−	0.374429i	$-0.877839\pi$
$587$	−1.92151	+	3.77117i	−0.0793092	+	0.155653i	0.847946	+	0.530082i	$0.177839\pi$
$588$	−29.2615	+	21.2598i	−1.20673	+	0.876737i
$589$	−9.42643	+	6.84870i	−0.388409	+	0.282196i
$590$	1.61195	+	0.821331i	0.0663630	+	0.0338137i
$591$	−2.42794	−	4.76510i	−0.0998720	−	0.196010i
$592$	10.6987	−	1.69451i	0.439715	−	0.0696441i
$593$	27.6122	+	27.6122i	1.13390	+	1.13390i	0.989523	+	0.144374i	$0.0461170\pi$
$593$	27.6122	+	27.6122i	1.13390	+	1.13390i	0.144374	+	0.989523i	$0.453883\pi$
$594$	0.764782	+	0.0182628i	0.0313794	+	0.000749332i
$595$			21.3818i			0.876567i
$596$	−1.11047	−	7.01124i	−0.0454867	−	0.287192i
$597$	−11.5129	−	3.74078i	−0.471193	−	0.153100i
$598$	0.00522446	−	0.137745i	0.000213644	−	0.00563281i
$599$	15.2513	−	11.0807i	0.623149	−	0.452744i	−0.230871	−	0.972984i	$-0.574158\pi$
$599$	15.2513	−	11.0807i	0.623149	−	0.452744i	0.854020	+	0.520240i	$0.174158\pi$
$600$	−0.299125	+	1.88860i	−0.0122117	+	0.0771017i
$601$	14.3238	−	4.65408i	0.584279	−	0.189844i	−0.00193771	−	0.999998i	$-0.500617\pi$
$601$	14.3238	−	4.65408i	0.584279	−	0.189844i	0.586217	+	0.810154i	$0.300617\pi$
$602$	1.24519	−	3.83230i	0.0507501	−	0.156193i
$603$	−0.744506	−	4.70063i	−0.0303186	−	0.191424i
$604$	−25.7991	+	25.7991i	−1.04975	+	1.04975i
$605$	3.80988	−	18.3394i	0.154894	−	0.745601i
$606$	−2.64106	+	2.64106i	−0.107286	+	0.107286i
$607$	5.11166	−	7.03560i	0.207476	−	0.285566i	−0.692580	−	0.721342i	$-0.743526\pi$
$607$	5.11166	−	7.03560i	0.207476	−	0.285566i	0.900055	+	0.435775i	$0.143526\pi$
$608$	−7.37013	−	2.39470i	−0.298898	−	0.0971179i
$609$	48.3294	+	24.6251i	1.95841	+	0.997858i
$610$	2.90500	+	3.99838i	0.117620	+	0.161890i
$611$	0.768914	+	2.71224i	0.0311069	+	0.109726i
$612$	4.59689	−	1.49362i	0.185818	−	0.0603760i
$613$	8.98653	+	17.6371i	0.362962	+	0.712354i	0.998201	−	0.0599625i	$-0.0190981\pi$
$613$	8.98653	+	17.6371i	0.362962	+	0.712354i	−0.635238	+	0.772316i	$0.719098\pi$
$614$	3.73286	+	2.71208i	0.150646	+	0.109451i
$615$	12.6716			0.510970
$616$	−11.0524	+	10.5369i	−0.445314	+	0.424542i
$617$	−16.1697	−	16.1697i	−0.650968	−	0.650968i	0.302258	−	0.953226i	$-0.402260\pi$
$617$	−16.1697	−	16.1697i	−0.650968	−	0.650968i	−0.953226	+	0.302258i	$0.902260\pi$
$618$	0.556028	+	3.51062i	0.0223667	+	0.141218i
$619$	−4.64343	−	9.11324i	−0.186635	−	0.366292i	0.778663	−	0.627442i	$-0.215898\pi$
$619$	−4.64343	−	9.11324i	−0.186635	−	0.366292i	−0.965298	+	0.261150i	$0.915898\pi$
$620$	−4.11301	−	12.6585i	−0.165182	−	0.508379i
$621$	−0.0974248	−	0.134094i	−0.00390952	−	0.00538100i
$622$	0.291148	+	0.0461134i	0.0116740	+	0.00184898i
$623$	23.2351	+	71.5103i	0.930895	+	2.86500i
$624$	1.57900	+	13.1873i	0.0632106	+	0.527913i
$625$	−8.15973	−	5.92839i	−0.326389	−	0.237136i
$626$	−4.14251	+	4.14251i	−0.165568	+	0.165568i
$627$	7.64943	+	5.84165i	0.305489	+	0.233293i
$628$		−	25.5015i		−	1.01762i
$629$	7.21099	−	1.14211i	0.287521	−	0.0455388i
$630$	1.76992	−	0.901817i	0.0705151	−	0.0359293i
$631$	31.8056	+	16.2057i	1.26616	+	0.645140i	0.952541	−	0.304409i	$-0.0984590\pi$
$631$	31.8056	+	16.2057i	1.26616	+	0.645140i	0.313618	+	0.949549i	$0.398459\pi$
$632$	−1.13431	+	7.16177i	−0.0451206	+	0.284880i
$633$	2.96304	+	4.07828i	0.117770	+	0.162097i
$634$	−0.640547	−	1.97140i	−0.0254394	−	0.0782943i
$635$	21.6433	−	11.0278i	0.858889	−	0.437626i
$636$	−9.91131	+	13.6417i	−0.393009	+	0.540930i
$637$	−28.1274	−	60.7956i	−1.11445	−	2.40881i
$638$	7.74018	+	2.72088i	0.306437	+	0.107721i
$639$	5.48036	+	5.48036i	0.216800	+	0.216800i
$640$	6.90406	−	9.50262i	0.272907	−	0.375624i
$641$	21.6173	+	7.02390i	0.853833	+	0.277427i	0.703051	−	0.711140i	$-0.251821\pi$
$641$	21.6173	+	7.02390i	0.853833	+	0.277427i	0.150783	+	0.988567i	$0.451821\pi$
$642$	−0.840488	+	1.64955i	−0.0331714	+	0.0651026i
$643$	−12.7397	−	2.01777i	−0.502404	−	0.0795730i	−0.0999118	−	0.994996i	$-0.531856\pi$
$643$	−12.7397	−	2.01777i	−0.502404	−	0.0795730i	−0.402493	+	0.915423i	$0.631856\pi$
$644$	1.61188	+	0.255296i	0.0635169	+	0.0100601i
$645$	2.67030	−	5.24076i	0.105143	−	0.206355i
$646$	−1.58055	−	0.513551i	−0.0621859	−	0.0202054i
$647$	−8.96332	+	12.3370i	−0.352385	+	0.485016i	−0.948007	−	0.318249i	$-0.896905\pi$
$647$	−8.96332	+	12.3370i	−0.352385	+	0.485016i	0.595623	+	0.803264i	$0.296905\pi$
$648$	−0.643717	−	0.643717i	−0.0252876	−	0.0252876i
$649$	−4.37263	−	14.6378i	−0.171641	−	0.574584i
$650$	−1.63967	−	0.602373i	−0.0643130	−	0.0236270i
$651$	11.9357	−	16.4281i	0.467798	−	0.643869i
$652$	−3.33162	+	1.69755i	−0.130476	+	0.0664811i
$653$	9.91062	+	30.5017i	0.387833	+	1.19363i	0.934405	+	0.356214i	$0.115932\pi$
$653$	9.91062	+	30.5017i	0.387833	+	1.19363i	−0.546572	+	0.837412i	$0.684068\pi$
$654$	0.0268645	+	0.0369758i	0.00105048	+	0.00144587i
$655$	−4.80569	+	30.3419i	−0.187774	+	1.18556i
$656$	24.4243	+	12.4448i	0.953608	+	0.485888i
$657$	−1.10629	+	0.563685i	−0.0431606	+	0.0219914i
$658$	0.900884	−	0.142686i	0.0351201	−	0.00556248i
$659$			6.18041i			0.240754i	0.992728	+	0.120377i	$0.0384104\pi$
$659$			6.18041i			0.240754i	−0.992728	+	0.120377i	$0.961590\pi$
$660$	−9.04664	+	6.24833i	−0.352140	+	0.243216i
$661$	−6.50126	+	6.50126i	−0.252870	+	0.252870i	−0.822146	−	0.569276i	$-0.807223\pi$
$661$	−6.50126	+	6.50126i	−0.252870	+	0.252870i	0.569276	+	0.822146i	$0.307223\pi$
$662$	−0.915367	−	0.665053i	−0.0355767	−	0.0258480i
$663$	1.06425	+	8.88827i	0.0413321	+	0.345192i
$664$	−2.54486	−	7.83227i	−0.0987596	−	0.303951i
$665$	24.6846	+	3.90966i	0.957229	+	0.151610i
$666$	−0.398677	−	0.548732i	−0.0154484	−	0.0212629i
$667$	−0.549318	−	1.69063i	−0.0212697	−	0.0654613i
$668$	13.6054	+	26.7020i	0.526407	+	1.03313i
$669$	−1.51245	−	9.54921i	−0.0584746	−	0.369194i
$670$	−1.32176	−	1.32176i	−0.0510640	−	0.0510640i
$671$	7.51085	−	41.0528i	0.289953	−	1.58482i
$672$	13.5055			0.520985
$673$	11.7365	+	8.52706i	0.452408	+	0.328694i	0.790546	−	0.612403i	$-0.209797\pi$
$673$	11.7365	+	8.52706i	0.452408	+	0.328694i	−0.338138	+	0.941097i	$0.609797\pi$
$674$	0.714021	+	1.40135i	0.0275031	+	0.0539778i
$675$	−1.99763	+	0.649071i	−0.0768890	+	0.0249827i
$676$	−25.2357	−	1.91706i	−0.970602	−	0.0737331i
$677$	−8.17890	−	11.2573i	−0.314341	−	0.432653i	0.622388	−	0.782709i	$-0.286163\pi$
$677$	−8.17890	−	11.2573i	−0.314341	−	0.432653i	−0.936729	+	0.350056i	$0.886163\pi$
$678$	0.358822	+	0.182829i	0.0137805	+	0.00702150i
$679$	13.7063	+	4.45346i	0.526001	+	0.170908i
$680$	2.26220	−	3.11365i	0.0867515	−	0.119403i
$681$	15.6649	−	15.6649i	0.600282	−	0.600282i
$682$	1.45937	−	2.70266i	0.0558822	−	0.103490i
$683$	1.61659	−	1.61659i	0.0618570	−	0.0618570i	−0.675502	−	0.737359i	$-0.736073\pi$
$683$	1.61659	−	1.61659i	0.0618570	−	0.0618570i	0.737359	+	0.675502i	$0.236073\pi$
$684$	−0.883798	−	5.58008i	−0.0337929	−	0.213360i
$685$	7.49443	−	23.0655i	0.286348	−	0.881287i
$686$	−12.8463	+	4.17401i	−0.490473	+	0.159364i
$687$	0.895260	−	5.65245i	0.0341563	−	0.215654i
$688$	10.2939	−	7.47895i	0.392451	−	0.285132i
$689$	−21.2297	−	22.9036i	−0.808786	−	0.872557i
$690$	−0.0619139	−	0.0201171i	−0.00235702	−	0.000765843i
$691$	−3.37153	−	21.2870i	−0.128259	−	0.809795i	−0.965010	−	0.262212i	$-0.915548\pi$
$691$	−3.37153	−	21.2870i	−0.128259	−	0.809795i	0.836751	−	0.547583i	$-0.184452\pi$
$692$		−	2.13410i		−	0.0811262i
$693$	−15.8247	−	5.56282i	−0.601132	−	0.211314i
$694$	−0.172565	−	0.172565i	−0.00655046	−	0.00655046i
$695$	13.1546	−	2.08349i	0.498984	−	0.0790313i
$696$	−4.43248	−	8.69923i	−0.168013	−	0.329744i
$697$	16.4621	+	8.38784i	0.623545	+	0.317712i
$698$	−3.93428	+	2.85842i	−0.148915	+	0.108193i
$699$	16.8961	−	12.2757i	0.639068	−	0.464310i
$700$	9.38897	−	18.4269i	0.354870	−	0.696471i
$701$	−0.522792	+	1.60899i	−0.0197456	+	0.0607707i	−0.960444	−	0.278474i	$-0.910171\pi$
$701$	−0.522792	+	1.60899i	−0.0197456	+	0.0607707i	0.940698	+	0.339245i	$0.110171\pi$
$702$	0.690857	−	0.462975i	0.0260747	−	0.0174739i
$703$		−	8.53371i		−	0.321855i
$704$	−22.1932	+	2.97384i	−0.836437	+	0.112081i
$705$	1.33140			0.0501435
$706$	−5.41428	−	3.93370i	−0.203769	−	0.148047i
$707$	72.9707	−	37.1805i	2.74435	−	1.39831i
$708$	−4.07106	+	7.98991i	−0.153000	+	0.300279i
$709$	−4.82571	+	30.4683i	−0.181233	+	1.14426i	0.714489	+	0.699647i	$0.246659\pi$
$709$	−4.82571	+	30.4683i	−0.181233	+	1.14426i	−0.895722	+	0.444615i	$0.853341\pi$
$710$	3.00660	+	0.476198i	0.112836	+	0.0178714i
$711$	−7.57525	+	2.46135i	−0.284094	+	0.0923078i
$712$	4.18229	−	12.8718i	0.156738	−	0.482390i
$713$	−0.657296	+	0.104105i	−0.0246159	+	0.00389878i
$714$	2.89629			0.108391
$715$	−8.10653	−	18.6794i	−0.303167	−	0.698572i
$716$	−21.5141			−0.804019
$717$	−10.6348	+	1.68438i	−0.397163	+	0.0629044i
$718$	−1.83397	+	5.64437i	−0.0684430	+	0.210646i
$719$	−26.0016	+	8.44843i	−0.969696	+	0.315073i	−0.750693	−	0.660651i	$-0.770280\pi$
$719$	−26.0016	+	8.44843i	−0.969696	+	0.315073i	−0.219003	+	0.975724i	$0.570280\pi$
$720$	6.19528	+	0.981235i	0.230884	+	0.0365685i
$721$	12.1919	−	76.9767i	0.454051	−	2.86676i
$722$	1.10771	−	2.17401i	0.0412248	−	0.0809083i
$723$	5.16835	−	2.63341i	0.192213	−	0.0979374i
$724$	−13.2155	−	9.60163i	−0.491151	−	0.356842i
$725$	−22.5268			−0.836625
$726$	−2.48418	−	0.516072i	−0.0921965	−	0.0191532i
$727$		−	5.44575i		−	0.201972i	−0.994888	−	0.100986i	$-0.967800\pi$
$727$		−	5.44575i		−	0.201972i	0.994888	−	0.100986i	$-0.0321997\pi$
$728$	−3.21646	+	16.2859i	−0.119210	+	0.603597i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.221395	+	0.434512i	−0.00819419	+	0.0160820i
$731$	6.93812	−	5.04084i	0.256616	−	0.186442i
$732$	−19.8186	+	14.3991i	−0.732518	+	0.532206i
$733$	−1.46935	−	0.748670i	−0.0542716	−	0.0276527i	0.426644	−	0.904420i	$-0.359696\pi$
$733$	−1.46935	−	0.748670i	−0.0542716	−	0.0276527i	−0.480916	+	0.876767i	$0.659696\pi$
$734$	−1.10067	−	2.16018i	−0.0406264	−	0.0797338i
$735$	−31.2467	+	4.94900i	−1.15255	+	0.182547i
$736$	−0.312972	−	0.312972i	−0.0115363	−	0.0115363i
$737$	−0.376824	+	15.7801i	−0.0138805	+	0.581266i
$738$		−	1.71645i		−	0.0631835i
$739$	0.0464831	+	0.293483i	0.00170991	+	0.0107959i	0.988529	−	0.151034i	$-0.0482603\pi$
$739$	0.0464831	+	0.293483i	0.00170991	+	0.0107959i	−0.986819	+	0.161830i	$0.948260\pi$
$740$	9.27110	+	3.01236i	0.340813	+	0.110737i
$741$	10.4559	+	0.396575i	0.384105	+	0.0145686i
$742$	−8.17438	+	5.93903i	−0.300091	+	0.218029i
$743$	−7.05136	+	44.5205i	−0.258689	+	1.63330i	0.426183	+	0.904637i	$0.359858\pi$
$743$	−7.05136	+	44.5205i	−0.258689	+	1.63330i	−0.684872	+	0.728663i	$0.740142\pi$
$744$	−3.47621	+	1.12949i	−0.127444	+	0.0414091i
$745$	1.91868	−	5.90509i	0.0702950	−	0.216346i
$746$	0.439901	+	2.77743i	0.0161059	+	0.101689i
$747$	6.39670	−	6.39670i	0.234043	−	0.234043i
$748$	−15.8887	+	2.12906i	−0.580950	+	0.0778461i
$749$	28.7042	−	28.7042i	1.04883	−	1.04883i
$750$	−1.63921	+	2.25618i	−0.0598555	+	0.0823841i
$751$	−12.9295	−	4.20106i	−0.471806	−	0.153299i	0.0634570	−	0.997985i	$-0.479787\pi$
$751$	−12.9295	−	4.20106i	−0.471806	−	0.153299i	−0.535263	+	0.844686i	$0.679787\pi$
$752$	2.56625	+	1.30757i	0.0935814	+	0.0476821i
$753$	8.88115	+	12.2239i	0.323647	+	0.445462i
$754$	8.58105	−	2.43271i	0.312503	−	0.0885939i
$755$	−30.3508	+	9.86158i	−1.10458	+	0.358900i
$756$	4.47001	+	8.77288i	0.162573	+	0.319067i
$757$	−8.77453	−	6.37507i	−0.318916	−	0.231706i	0.416797	−	0.909000i	$-0.363153\pi$
$757$	−8.77453	−	6.37507i	−0.318916	−	0.231706i	−0.735713	+	0.677294i	$0.763153\pi$
$758$	5.42742			0.197133
$759$	0.237807	+	0.495629i	0.00863183	+	0.0179902i
$760$	−3.18098	−	3.18098i	−0.115386	−	0.115386i
$761$	6.65082	+	41.9916i	0.241092	+	1.52220i	0.750037	+	0.661396i	$0.230036\pi$
$761$	6.65082	+	41.9916i	0.241092	+	1.52220i	−0.508945	+	0.860799i	$0.669964\pi$
$762$	−1.49379	−	2.93172i	−0.0541142	−	0.106205i
$763$	−0.309683	−	0.953106i	−0.0112113	−	0.0345048i
$764$	−8.85320	−	12.1854i	−0.320298	−	0.440852i
$765$	4.17564	+	0.661356i	0.150971	+	0.0239114i
$766$	−0.252306	−	0.776518i	−0.00911619	−	0.0280567i
$767$	−13.0563	−	10.2640i	−0.471437	−	0.370613i
$768$	9.63665	+	7.00143i	0.347732	+	0.252642i
$769$	−30.3845	+	30.3845i	−1.09569	+	1.09569i	−0.100784	+	0.994908i	$0.532135\pi$
$769$	−30.3845	+	30.3845i	−1.09569	+	1.09569i	−0.994908	+	0.100784i	$0.967865\pi$
$770$	−6.31259	+	1.88571i	−0.227490	+	0.0679562i
$771$		−	26.3830i		−	0.950160i
$772$	−1.80445	+	0.285797i	−0.0649436	+	0.0102861i
$773$	13.3883	−	6.82167i	0.481543	−	0.245358i	−0.196329	−	0.980538i	$-0.562902\pi$
$773$	13.3883	−	6.82167i	0.481543	−	0.245358i	0.677872	+	0.735180i	$0.262902\pi$
$774$	−0.709894	−	0.361709i	−0.0255166	−	0.0130014i
$775$	−1.31926	+	8.32951i	−0.0473894	+	0.299205i
$776$	−1.52477	−	2.09866i	−0.0547359	−	0.0753375i
$777$	4.59580	+	14.1444i	0.164873	+	0.507428i
$778$	−3.69127	+	1.88079i	−0.132338	+	0.0674298i
$779$	12.6936	−	17.4713i	0.454796	−	0.625973i
$780$	−4.12171	+	11.2193i	−0.147581	+	0.401717i
$781$	−14.6083	−	21.1507i	−0.522728	−	0.756831i
$782$	−0.0671178	−	0.0671178i	−0.00240013	−	0.00240013i
$783$	6.30389	−	8.67657i	0.225283	−	0.310075i
$784$	−65.0878	−	21.1483i	−2.32456	−	0.755296i
$785$	10.1265	−	19.8743i	0.361429	−	0.709345i
$786$	4.11000	+	0.650960i	0.146599	+	0.0232190i
$787$	36.4304	+	5.77000i	1.29860	+	0.205678i	0.767182	−	0.641430i	$-0.221659\pi$
$787$	36.4304	+	5.77000i	1.29860	+	0.205678i	0.531420	+	0.847108i	$0.321659\pi$
$788$	4.72671	−	9.27668i	0.168382	−	0.330468i
$789$	−12.6762	−	4.11876i	−0.451286	−	0.146632i
$790$	−1.83883	+	2.53093i	−0.0654225	+	0.0900463i
$791$	−6.24394	−	6.24394i	−0.222009	−	0.222009i
$792$	1.71588	+	2.48434i	0.0609712	+	0.0882770i
$793$	−19.0505	−	41.1764i	−0.676504	−	1.46222i
$794$	1.36465	−	1.87828i	0.0484297	−	0.0666578i
$795$	−13.1413	+	6.69583i	−0.466074	+	0.237477i
$796$	−7.28254	−	22.4134i	−0.258123	−	0.794421i
$797$	8.35823	+	11.5041i	0.296064	+	0.407497i	0.930972	−	0.365091i	$-0.118962\pi$
$797$	8.35823	+	11.5041i	0.296064	+	0.407497i	−0.634908	+	0.772588i	$0.718962\pi$
$798$	0.529588	−	3.34368i	0.0187472	−	0.118365i
$799$	1.72966	+	0.881306i	0.0611910	+	0.0311784i
$800$	−4.99758	+	2.54639i	−0.176691	+	0.0900286i
$801$	14.6839	−	2.32570i	0.518830	−	0.0821747i
$802$			2.95847i			0.104467i
$803$	3.94571	−	1.17867i	0.139241	−	0.0415944i
$804$	6.55151	−	6.55151i	0.231054	−	0.231054i
$805$	1.15482	+	0.839028i	0.0407021	+	0.0295718i
$806$	−0.396974	−	3.31540i	−0.0139828	−	0.116780i
$807$	−3.86559	−	11.8971i	−0.136075	−	0.418797i
$808$	−14.5599	−	2.30606i	−0.512214	−	0.0811268i
$809$	−9.22880	−	12.7024i	−0.324467	−	0.446591i	0.615357	−	0.788248i	$-0.289012\pi$
$809$	−9.22880	−	12.7024i	−0.324467	−	0.446591i	−0.939825	+	0.341657i	$0.889012\pi$
$810$	−0.121371	−	0.373540i	−0.00426453	−	0.0131249i
$811$	15.7913	+	30.9922i	0.554507	+	1.08828i	0.982805	+	0.184644i	$0.0591134\pi$
$811$	15.7913	+	30.9922i	0.554507	+	1.08828i	−0.428298	+	0.903638i	$0.640887\pi$
$812$	16.5190	+	104.297i	0.579703	+	3.66010i
$813$	10.7999	+	10.7999i	0.378771	+	0.378771i
$814$	0.973141	+	2.02819i	0.0341086	+	0.0710880i
$815$	−3.27055			−0.114562
$816$	7.39893	+	5.37564i	0.259014	+	0.188185i
$817$	−4.55087	−	8.93158i	−0.159215	−	0.312476i
$818$	−4.62427	+	1.50251i	−0.161684	+	0.0525342i
$819$	−17.5439	+	4.97365i	−0.613033	+	0.173793i
$820$	14.5001	+	19.9577i	0.506367	+	0.696955i
$821$	6.30372	+	3.21191i	0.220001	+	0.112096i	0.560518	−	0.828142i	$-0.310602\pi$
$821$	6.30372	+	3.21191i	0.220001	+	0.112096i	−0.340517	+	0.940238i	$0.610602\pi$
$822$	−3.12436	−	1.01517i	−0.108975	−	0.0354080i
$823$	−21.2779	+	29.2866i	−0.741702	+	1.02087i	0.256817	+	0.966460i	$0.417326\pi$
$823$	−21.2779	+	29.2866i	−0.741702	+	1.02087i	−0.998519	+	0.0544052i	$0.982674\pi$
$824$	−9.91959	+	9.91959i	−0.345565	+	0.345565i
$825$	6.90465	−	0.925208i	0.240389	−	0.0322116i
$826$	−3.79954	+	3.79954i	−0.132203	+	0.132203i
$827$	8.37962	+	52.9068i	0.291388	+	1.83975i	0.505357	+	0.862910i	$0.331361\pi$
$827$	8.37962	+	52.9068i	0.291388	+	1.83975i	−0.213969	+	0.976840i	$0.568639\pi$
$828$	0.0997135	−	0.306887i	0.00346528	−	0.0106651i
$829$	−33.2162	+	10.7926i	−1.15364	+	0.374842i	−0.822515	−	0.568743i	$-0.807430\pi$
$829$	−33.2162	+	10.7926i	−1.15364	+	0.374842i	−0.331130	+	0.943585i	$0.607430\pi$
$830$	0.555821	−	3.50932i	0.0192928	−	0.121810i
$831$	−19.1295	+	13.8984i	−0.663596	+	0.482131i
$832$	−17.8525	+	16.5478i	−0.618925	+	0.573690i
$833$	−43.8694	−	14.2540i	−1.51998	−	0.493873i
$834$	−0.282221	−	1.78188i	−0.00977253	−	0.0617013i
$835$			26.2125i			0.907121i
$836$	−0.447325	+	18.7324i	−0.0154711	+	0.647873i
$837$	−2.83906	−	2.83906i	−0.0981323	−	0.0981323i
$838$	7.45758	−	1.18117i	0.257618	−	0.0408027i
$839$	−0.0390966	−	0.0767314i	−0.00134976	−	0.00264906i	0.890331	−	0.455315i	$-0.150473\pi$
$839$	−0.0390966	−	0.0767314i	−0.00134976	−	0.00264906i	−0.891680	+	0.452665i	$0.850473\pi$
$840$	6.98550	+	3.55929i	0.241023	+	0.122807i
$841$	69.5931	−	50.5624i	2.39976	−	1.74353i
$842$	−0.873217	+	0.634429i	−0.0300930	+	0.0218639i
$843$	13.0504	−	25.6128i	0.449480	−	0.882153i
$844$	−3.03265	+	9.33353i	−0.104388	+	0.321273i
$845$	−18.9059	−	11.5149i	−0.650382	−	0.396126i
$846$		−	0.180347i		−	0.00620045i
$847$	48.3074	+	27.5942i	1.65986	+	0.948147i
$848$	−31.9055			−1.09564
$849$	17.7205	+	12.8747i	0.608166	+	0.441858i
$850$	−1.07175	+	0.546082i	−0.0367606	+	0.0187305i
$851$	0.221277	−	0.434280i	0.00758527	−	0.0148869i
$852$	−2.36035	+	14.9027i	−0.0808644	+	0.510558i
$853$	−14.6557	−	2.32124i	−0.501803	−	0.0794778i	−0.0995985	−	0.995028i	$-0.531756\pi$
$853$	−14.6557	−	2.32124i	−0.501803	−	0.0794778i	−0.402204	+	0.915550i	$0.631756\pi$
$854$	−13.9607	+	4.53611i	−0.477725	+	0.155222i
$855$	1.52703	−	4.69973i	0.0522234	−	0.160727i
$856$	−7.21688	+	1.14304i	−0.246668	+	0.0390684i
$857$	−31.8307			−1.08731			−0.543657	−	0.839307i	$-0.682961\pi$
$857$	−31.8307			−1.08731			−0.543657	+	0.839307i	$0.682961\pi$
$858$	−2.53025	+	1.09808i	−0.0863812	+	0.0374878i
$859$	49.1983			1.67862			0.839312	−	0.543651i	$-0.182958\pi$
$859$	49.1983			1.67862			0.839312	+	0.543651i	$0.182958\pi$
$860$	11.3098	−	1.79129i	0.385661	−	0.0610826i
$861$	−11.6303	+	35.7943i	−0.396358	+	1.21987i
$862$	5.50965	−	1.79020i	0.187660	−	0.0609743i
$863$	−38.0886	−	6.03264i	−1.29655	−	0.205354i	−0.530254	−	0.847839i	$-0.677903\pi$
$863$	−38.0886	−	6.03264i	−1.29655	−	0.205354i	−0.766298	+	0.642485i	$0.777903\pi$
$864$	0.417736	−	2.63748i	0.0142117	−	0.0897288i
$865$	0.847434	−	1.66318i	0.0288136	−	0.0565499i
$866$	1.83766	−	0.936333i	0.0624461	−	0.0318179i
$867$	−8.76638	−	6.36915i	−0.297722	−	0.216308i
$868$	39.5322			1.34181
$869$	26.1832	−	3.50849i	0.888204	−	0.119017i
$870$		−	4.21232i		−	0.142811i
$871$	9.55276	+	14.2547i	0.323683	+	0.483003i
$872$	−0.0557425	+	0.171558i	−0.00188768	+	0.00580968i
$873$	1.29366	−	2.53896i	0.0437839	−	0.0859307i
$874$	−0.0897581	+	0.0652130i	−0.00303611	+	0.00220586i
$875$	49.4709	−	35.9427i	1.67242	−	1.21508i
$876$	−2.15373	−	1.09738i	−0.0727678	−	0.0370770i
$877$	−6.10750	−	11.9866i	−0.206236	−	0.404760i	0.764600	−	0.644505i	$-0.222936\pi$
$877$	−6.10750	−	11.9866i	−0.206236	−	0.404760i	−0.970836	+	0.239744i	$0.922936\pi$
$878$	2.68078	−	0.424593i	0.0904719	−	0.0143293i
$879$	−0.0302761	−	0.0302761i	−0.00102119	−	0.00102119i
$880$	−19.6262	−	6.89915i	−0.661600	−	0.232570i
$881$		−	15.9204i		−	0.536373i	−0.963367	−	0.268187i	$-0.913576\pi$
$881$		−	15.9204i		−	0.536373i	0.963367	−	0.268187i	$-0.0864244\pi$
$882$	0.670372	+	4.23256i	0.0225726	+	0.142518i
$883$	14.9808	+	4.86755i	0.504143	+	0.163806i	0.550037	−	0.835140i	$-0.314614\pi$
$883$	14.9808	+	4.86755i	0.504143	+	0.163806i	−0.0458940	+	0.998946i	$0.514614\pi$
$884$	−12.7811	+	11.8470i	−0.429876	+	0.398459i
$885$	−6.34547	+	4.61026i	−0.213301	+	0.154972i
$886$	0.202476	−	1.27838i	0.00680230	−	0.0429480i
$887$	−19.3818	+	6.29751i	−0.650776	+	0.211450i	−0.615756	−	0.787937i	$-0.711149\pi$
$887$	−19.3818	+	6.29751i	−0.650776	+	0.211450i	−0.0350195	+	0.999387i	$0.511149\pi$
$888$	0.827237	−	2.54598i	0.0277603	−	0.0854373i
$889$	11.2862	+	71.2586i	0.378529	+	2.38994i
$890$	4.12893	−	4.12893i	0.138402	−	0.138402i
$891$	−1.57583	+	2.91835i	−0.0527925	+	0.0977683i
$892$	13.3092	−	13.3092i	0.445627	−	0.445627i
$893$	1.33371	−	1.83570i	0.0446310	−	0.0614292i
$894$	−0.799881	−	0.259897i	−0.0267520	−	0.00869226i
$895$	−16.7668	−	8.54309i	−0.560451	−	0.285564i
$896$	20.5059	+	28.2239i	0.685053	+	0.942895i
$897$	0.521815	+	0.291299i	0.0174229	+	0.00972619i
$898$	6.42601	−	2.08794i	0.214439	−	0.0696754i
$899$	−19.5491	−	38.3673i	−0.651999	−	1.27962i
$900$	−3.30817	−	2.40353i	−0.110272	−	0.0801176i
$901$	−21.5044			−0.716417
$902$	−1.02453	+	5.59988i	−0.0341132	+	0.186455i
$903$	12.3530	+	12.3530i	0.411083	+	0.411083i
$904$	0.248643	+	1.56987i	0.00826973	+	0.0522130i
$905$	−6.48662	−	12.7307i	−0.215623	−	0.423183i
$906$	1.33581	+	4.11121i	0.0443794	+	0.136586i
$907$	28.6393	+	39.4186i	0.950952	+	1.30887i	0.951103	+	0.308874i	$0.0999520\pi$
$907$	28.6393	+	39.4186i	0.950952	+	1.30887i	−0.000150855		1.00000i	$0.500048\pi$
$908$	42.5976	+	6.74679i	1.41365	+	0.223900i
$909$	−5.00391	−	15.4005i	−0.165969	−	0.510801i
$910$	−4.42639	+	5.63058i	−0.146733	+	0.186652i
$911$	−18.2456	−	13.2562i	−0.604504	−	0.439198i	0.242970	−	0.970034i	$-0.421878\pi$
$911$	−18.2456	−	13.2562i	−0.604504	−	0.439198i	−0.847475	+	0.530836i	$0.821878\pi$
$912$	7.55891	−	7.55891i	0.250301	−	0.250301i
$913$	−24.6872	+	17.0509i	−0.817027	+	0.564304i
$914$			2.73273i			0.0903908i
$915$	−21.1632	+	3.35192i	−0.699634	+	0.110811i
$916$	9.92701	−	5.05806i	0.327998	−	0.167123i
$917$	−81.2977	−	41.4232i	−2.68469	−	1.36792i
$918$	0.0895848	−	0.565616i	0.00295674	−	0.0186681i
$919$	−17.5603	−	24.1696i	−0.579259	−	0.797282i	0.414355	−	0.910115i	$-0.364007\pi$
$919$	−17.5603	−	24.1696i	−0.579259	−	0.797282i	−0.993614	+	0.112834i	$0.964007\pi$
$920$	−0.0793980	−	0.244362i	−0.00261767	−	0.00805637i
$921$	−17.8238	+	9.08167i	−0.587314	+	0.299251i
$922$	1.80611	−	2.48590i	0.0594812	−	0.0818689i
$923$	−26.2304	−	9.63640i	−0.863383	−	0.317186i
$924$	−9.34683	−	31.2894i	−0.307488	−	1.02934i
$925$	−4.36750	−	4.36750i	−0.143602	−	0.143602i
$926$	−2.25811	+	3.10802i	−0.0742061	+	0.102136i
$927$	−14.6557	−	4.76191i	−0.481355	−	0.156402i
$928$	13.0019	−	25.5176i	0.426807	−	0.837657i
$929$	7.89875	+	1.25104i	0.259150	+	0.0410453i	0.284657	−	0.958629i	$-0.408120\pi$
$929$	7.89875	+	1.25104i	0.259150	+	0.0410453i	−0.0255076	+	0.999675i	$0.508120\pi$
$930$	−1.55755	−	0.246691i	−0.0510740	−	0.00808932i
$931$	−24.4774	+	48.0396i	−0.802214	+	1.57443i
$932$	38.6683	+	12.5641i	1.26662	+	0.411551i
$933$	−0.751187	+	1.03392i	−0.0245928	+	0.0338490i
$934$	−4.19405	−	4.19405i	−0.137233	−	0.137233i
$935$	−13.2281	−	4.65005i	−0.432607	−	0.152073i
$936$	3.08099	+	1.13188i	0.100705	+	0.0369967i
$937$	−24.8653	+	34.2242i	−0.812315	+	1.11806i	0.178647	+	0.983913i	$0.442828\pi$
$937$	−24.8653	+	34.2242i	−0.812315	+	1.11806i	−0.990962	+	0.134142i	$0.957172\pi$
$938$	4.94678	−	2.52051i	0.161518	−	0.0822975i
$939$	−7.84868	−	24.1557i	−0.256132	−	0.788293i
$940$	1.52352	+	2.09695i	0.0496919	+	0.0683950i
$941$	2.11699	−	13.3662i	0.0690120	−	0.435725i	−0.928855	−	0.370444i	$-0.879206\pi$
$941$	2.11699	−	13.3662i	0.0690120	−	0.435725i	0.997867	−	0.0652811i	$-0.0207944\pi$
$942$	−2.69210	−	1.37169i	−0.0877134	−	0.0446922i
$943$	1.09900	−	0.559969i	0.0357884	−	0.0182351i
$944$	−16.7585	+	2.65428i	−0.545442	+	0.0863895i
$945$			8.61205i			0.280150i
$946$	2.10011	+	1.60379i	0.0682804	+	0.0521438i
$947$	−18.3627	+	18.3627i	−0.596708	+	0.596708i	−0.939435	−	0.342727i	$-0.888649\pi$
$947$	−18.3627	+	18.3627i	−0.596708	+	0.596708i	0.342727	+	0.939435i	$0.388649\pi$
$948$	−12.5450	−	9.11444i	−0.407441	−	0.296023i
$949$	2.76674	−	3.51942i	0.0898121	−	0.114245i
$950$	0.434467	+	1.33715i	0.0140960	+	0.0433830i
$951$	8.87612	+	1.40584i	0.287828	+	0.0455875i
$952$	6.71902	+	9.24793i	0.217765	+	0.299727i
$953$	3.61305	+	11.1198i	0.117038	+	0.360206i	0.992367	−	0.123322i	$-0.0393549\pi$
$953$	3.61305	+	11.1198i	0.117038	+	0.360206i	−0.875328	+	0.483529i	$0.839355\pi$
$954$	0.906992	+	1.78007i	0.0293649	+	0.0576319i
$955$	−2.06091	−	13.0121i	−0.0666895	−	0.421061i
$956$	−14.8222	−	14.8222i	−0.479386	−	0.479386i
$957$	−25.7452	+	24.5443i	−0.832225	+	0.793405i
$958$	3.13012			0.101130
$959$	58.2758	+	42.3398i	1.88182	+	1.36722i
$960$	5.21916	+	10.2432i	0.168448	+	0.330597i
$961$	14.1512	−	4.59800i	0.456490	−	0.148323i
$962$	2.13535	+	1.19204i	0.0688463	+	0.0384329i
$963$	−4.71779	−	6.49348i	−0.152029	−	0.209249i
$964$	10.0617	+	5.12671i	0.324067	+	0.165120i
$965$	−1.51977	−	0.493802i	−0.0489230	−	0.0158960i
$966$	0.113651	−	0.156428i	0.00365668	−	0.00503298i
$967$	32.1159	−	32.1159i	1.03278	−	1.03278i	0.0333331	−	0.999444i	$-0.489388\pi$
$967$	32.1159	−	32.1159i	1.03278	−	1.03278i	0.999444	−	0.0333331i	$-0.0106122\pi$
$968$	−4.11514	−	9.12927i	−0.132266	−	0.293426i
$969$	5.09474	−	5.09474i	0.163666	−	0.163666i
$970$	−0.175081	−	1.10542i	−0.00562150	−	0.0354928i
$971$	−1.58363	+	4.87391i	−0.0508211	+	0.156411i	−0.973246	−	0.229765i	$-0.926204\pi$
$971$	−1.58363	+	4.87391i	−0.0508211	+	0.156411i	0.922425	+	0.386176i	$0.126204\pi$
$972$	1.85151	−	0.601594i	0.0593874	−	0.0192961i
$973$	−6.18822	+	39.0709i	−0.198385	+	1.25255i
$974$	−4.63102	+	3.36463i	−0.148387	+	0.107810i
$975$	5.55420	−	5.14827i	0.177877	−	0.164877i
$976$	−44.0835	−	14.3236i	−1.41108	−	0.458487i
$977$	−3.59753	−	22.7139i	−0.115095	−	0.726683i	−0.975976	−	0.217877i	$-0.930087\pi$
$977$	−3.59753	−	22.7139i	−0.115095	−	0.726683i	0.860881	−	0.508806i	$-0.169913\pi$
$978$			0.443016i			0.0141661i
$979$	−49.2940	−	1.17713i	−1.57544	−	0.0376212i
$980$	−43.5503	−	43.5503i	−1.39116	−	1.39116i
$981$	−0.195711	+	0.0309975i	−0.00624856	+	0.000989675i
$982$	0.635206	+	1.24666i	0.0202702	+	0.0397826i
$983$	−9.43427	−	4.80700i	−0.300907	−	0.153320i	0.297018	−	0.954872i	$-0.404008\pi$
$983$	−9.43427	−	4.80700i	−0.300907	−	0.153320i	−0.597925	+	0.801552i	$0.704008\pi$
$984$	5.48068	−	3.98194i	0.174718	−	0.126940i
$985$	7.36741	−	5.35274i	0.234745	−	0.170552i
$986$	2.78829	−	5.47234i	0.0887974	−	0.174275i
$987$	−1.22199	+	3.76089i	−0.0388962	+	0.119710i
$988$	11.3400	+	16.9217i	0.360774	+	0.538351i
$989$		−	0.572530i		−	0.0182054i
$990$	0.173006	+	1.29111i	0.00549849	+	0.0410342i
$991$	60.7076			1.92844			0.964220	−	0.265104i	$-0.0854064\pi$
$991$	60.7076			1.92844			0.964220	+	0.265104i	$0.0854064\pi$
$992$	−8.67394	−	6.30199i	−0.275398	−	0.200088i
$993$	4.37072	−	2.22700i	0.138701	−	0.0706716i
$994$	−4.10465	+	8.05583i	−0.130192	+	0.255515i
$995$	3.22462	−	20.3595i	0.102227	−	0.645438i
$996$	17.3945	+	2.75502i	0.551166	+	0.0872961i
$997$	10.6516	−	3.46092i	0.337340	−	0.109608i	−0.135449	−	0.990784i	$-0.543248\pi$
$997$	10.6516	−	3.46092i	0.337340	−	0.109608i	0.472788	+	0.881176i	$0.343248\pi$
$998$	−2.13241	+	6.56288i	−0.0675002	+	0.207744i
$999$	2.90441	−	0.460013i	0.0918915	−	0.0145542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bj.b.73.8	✓	112
11.8	odd	10	inner	429.2.bj.b.151.7	yes	112
13.5	odd	4	inner	429.2.bj.b.304.7	yes	112
143.96	even	20	inner	429.2.bj.b.382.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bj.b.73.8	✓	112	1.1	even	1	trivial
429.2.bj.b.151.7	yes	112	11.8	odd	10	inner
429.2.bj.b.304.7	yes	112	13.5	odd	4	inner
429.2.bj.b.382.8	yes	112	143.96	even	20	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.227816 - 0.0360826i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-1.85151 + 0.601594i) q^{4} +(-1.68185 - 0.266378i) q^{5} +(-0.0360826 + 0.227816i) q^{6} +(2.29608 - 4.50631i) q^{7} +(-0.811131 + 0.413292i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.227816 - 0.0360826i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-1.85151 + 0.601594i) q^{4} +(-1.68185 - 0.266378i) q^{5} +(-0.0360826 + 0.227816i) q^{6} +(2.29608 - 4.50631i) q^{7} +(-0.811131 + 0.413292i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.392764 q^{10} +(2.28855 + 2.40053i) q^{11} -1.94680i q^{12} +(3.53722 + 0.698600i) q^{13} +(0.360486 - 1.10946i) q^{14} +(0.773060 - 1.51722i) q^{15} +(2.98011 - 2.16518i) q^{16} +(2.00860 - 1.45934i) q^{17} +(-0.205516 - 0.104716i) q^{18} +(-1.31749 - 2.58572i) q^{19} +(3.27421 - 0.518584i) q^{20} +(3.57623 + 3.57623i) q^{21} +(0.607987 + 0.464302i) q^{22} -0.165749i q^{23} +(-0.142411 - 0.899145i) q^{24} +(-1.99763 - 0.649071i) q^{25} +(0.831045 + 0.0315203i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.54026 + 9.72481i) q^{28} +(10.1999 - 3.31415i) q^{29} +(0.121371 - 0.373540i) q^{30} +(-0.628091 - 3.96561i) q^{31} +(1.88823 - 1.88823i) q^{32} +(-2.99024 + 1.43474i) q^{33} +(0.404936 - 0.404936i) q^{34} +(-5.06204 + 6.96730i) q^{35} +(1.85151 + 0.601594i) q^{36} +(2.62011 + 1.33501i) q^{37} +(-0.393445 - 0.541530i) q^{38} +(-1.75747 + 3.14822i) q^{39} +(1.47429 - 0.479025i) q^{40} +(3.37842 + 6.63052i) q^{41} +(0.943763 + 0.685684i) q^{42} +3.45420 q^{43} +(-5.68143 - 3.06783i) q^{44} +(1.20407 + 1.20407i) q^{45} +(-0.00598065 - 0.0377603i) q^{46} +(0.354969 + 0.696665i) q^{47} +(1.13830 + 3.50333i) q^{48} +(-10.9204 - 15.0306i) q^{49} +(-0.478514 - 0.0757892i) q^{50} +(0.767219 + 2.36126i) q^{51} +(-6.96950 + 0.834504i) q^{52} +(-7.00727 - 5.09108i) q^{53} +(0.163099 - 0.163099i) q^{54} +(-3.20954 - 4.64694i) q^{55} +4.60416i q^{56} +(2.86629 - 0.453975i) q^{57} +(2.20412 - 1.12306i) q^{58} +(-4.10413 - 2.09116i) q^{59} +(-0.518584 + 3.27421i) q^{60} +(-7.39629 - 10.1801i) q^{61} +(-0.286179 - 0.880767i) q^{62} +(-4.50631 + 2.29608i) q^{63} +(-3.96831 + 5.46192i) q^{64} +(-5.76297 - 2.11718i) q^{65} +(-0.629456 + 0.434753i) q^{66} +(3.36528 + 3.36528i) q^{67} +(-2.84103 + 3.91035i) q^{68} +(0.157637 + 0.0512193i) q^{69} +(-0.901817 + 1.76992i) q^{70} +(-7.65498 - 1.21243i) q^{71} +(0.899145 + 0.142411i) q^{72} +(0.563685 - 1.10629i) q^{73} +(0.645074 + 0.209597i) q^{74} +(1.23461 - 1.69929i) q^{75} +(3.99490 + 3.99490i) q^{76} +(16.0722 - 4.80113i) q^{77} +(-0.286785 + 0.780630i) q^{78} +(4.68176 - 6.44389i) q^{79} +(-5.58884 + 2.84766i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.00891 + 1.38864i) q^{82} +(-1.41515 + 8.93493i) q^{83} +(-8.77288 - 4.47001i) q^{84} +(-3.76690 + 1.91933i) q^{85} +(0.786923 - 0.124636i) q^{86} +10.7248i q^{87} +(-2.84843 - 1.00130i) q^{88} +(-10.5125 + 10.5125i) q^{89} +(0.317752 + 0.230861i) q^{90} +(11.2699 - 14.3358i) q^{91} +(0.0997135 + 0.306887i) q^{92} +(3.96561 + 0.628091i) q^{93} +(0.106005 + 0.145904i) q^{94} +(1.52703 + 4.69973i) q^{95} +(1.21232 + 2.37930i) q^{96} +(0.445766 + 2.81446i) q^{97} +(-3.03018 - 3.03018i) q^{98} +(-0.440484 - 3.28724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 28 q^{3} + 6 q^{5} - 28 q^{9}+O(q^{10}) \) 112 * q + 28 * q^3 + 6 * q^5 - 28 * q^9	\( 112 q + 28 q^{3} + 6 q^{5} - 28 q^{9} - 14 q^{11} + 10 q^{13} + 12 q^{14} + 4 q^{15} - 48 q^{16} - 2 q^{20} + 32 q^{22} + 30 q^{24} - 46 q^{26} + 28 q^{27} - 20 q^{29} - 24 q^{31} - 16 q^{33} - 16 q^{34} - 20 q^{35} + 12 q^{37} + 10 q^{39} - 40 q^{40} - 10 q^{41} + 28 q^{42} + 24 q^{44} - 4 q^{45} - 20 q^{46} - 62 q^{47} - 92 q^{48} - 90 q^{50} + 110 q^{52} + 68 q^{53} + 32 q^{55} - 30 q^{57} - 56 q^{58} + 16 q^{59} + 2 q^{60} + 20 q^{61} + 8 q^{66} + 12 q^{67} + 60 q^{68} - 196 q^{70} - 52 q^{71} + 30 q^{72} - 10 q^{73} - 120 q^{74} - 84 q^{78} + 40 q^{79} - 56 q^{80} - 28 q^{81} + 110 q^{83} - 30 q^{84} - 40 q^{85} + 18 q^{86} - 96 q^{89} - 44 q^{91} + 80 q^{92} + 24 q^{93} - 20 q^{94} + 100 q^{96} + 18 q^{97} + 6 q^{99}+O(q^{100}) \) 112 * q + 28 * q^3 + 6 * q^5 - 28 * q^9 - 14 * q^11 + 10 * q^13 + 12 * q^14 + 4 * q^15 - 48 * q^16 - 2 * q^20 + 32 * q^22 + 30 * q^24 - 46 * q^26 + 28 * q^27 - 20 * q^29 - 24 * q^31 - 16 * q^33 - 16 * q^34 - 20 * q^35 + 12 * q^37 + 10 * q^39 - 40 * q^40 - 10 * q^41 + 28 * q^42 + 24 * q^44 - 4 * q^45 - 20 * q^46 - 62 * q^47 - 92 * q^48 - 90 * q^50 + 110 * q^52 + 68 * q^53 + 32 * q^55 - 30 * q^57 - 56 * q^58 + 16 * q^59 + 2 * q^60 + 20 * q^61 + 8 * q^66 + 12 * q^67 + 60 * q^68 - 196 * q^70 - 52 * q^71 + 30 * q^72 - 10 * q^73 - 120 * q^74 - 84 * q^78 + 40 * q^79 - 56 * q^80 - 28 * q^81 + 110 * q^83 - 30 * q^84 - 40 * q^85 + 18 * q^86 - 96 * q^89 - 44 * q^91 + 80 * q^92 + 24 * q^93 - 20 * q^94 + 100 * q^96 + 18 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more