LMFDB - Embedded newform 23.2.c.a.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,2,Mod(2,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("23.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	23.c (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:	$0.183655924649$
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			18.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	23.18
Dual form			23.2.c.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.226900 - 0.0666238i) q^{2} +(-0.313607 + 0.361922i) q^{3} +(-1.63546 - 1.05105i) q^{4} +(-0.215370 + 1.49793i) q^{5} +(0.0952700 - 0.0612263i) q^{6} +(-1.05773 - 2.31611i) q^{7} +(0.610783 + 0.704881i) q^{8} +(0.394306 + 2.74246i) q^{9} +O(q^{10})$	\(q+(-0.226900 - 0.0666238i) q^{2} +(-0.313607 + 0.361922i) q^{3} +(-1.63546 - 1.05105i) q^{4} +(-0.215370 + 1.49793i) q^{5} +(0.0952700 - 0.0612263i) q^{6} +(-1.05773 - 2.31611i) q^{7} +(0.610783 + 0.704881i) q^{8} +(0.394306 + 2.74246i) q^{9} +(0.148666 - 0.325532i) q^{10} +(3.23616 - 0.950224i) q^{11} +(0.893290 - 0.262294i) q^{12} +(1.36745 - 2.99430i) q^{13} +(0.0856910 + 0.595994i) q^{14} +(-0.474593 - 0.547710i) q^{15} +(1.52357 + 3.33616i) q^{16} +(-5.28043 + 3.39353i) q^{17} +(0.0932451 - 0.648534i) q^{18} +(-3.55928 - 2.28741i) q^{19} +(1.92663 - 2.22345i) q^{20} +(1.16996 + 0.343532i) q^{21} -0.797593 q^{22} +(-4.72041 - 0.847210i) q^{23} -0.446658 q^{24} +(2.60004 + 0.763442i) q^{25} +(-0.509766 + 0.588302i) q^{26} +(-2.32482 - 1.49407i) q^{27} +(-0.704460 + 4.89963i) q^{28} +(5.28830 - 3.39858i) q^{29} +(0.0711946 + 0.155895i) q^{30} +(3.10538 + 3.58380i) q^{31} +(-0.388902 - 2.70488i) q^{32} +(-0.670978 + 1.46924i) q^{33} +(1.42422 - 0.418188i) q^{34} +(3.69718 - 1.08559i) q^{35} +(2.23758 - 4.89963i) q^{36} +(-0.00540403 - 0.0375858i) q^{37} +(0.655203 + 0.756145i) q^{38} +(0.654861 + 1.43394i) q^{39} +(-1.18741 + 0.763102i) q^{40} +(-0.462048 + 3.21361i) q^{41} +(-0.242577 - 0.155895i) q^{42} +(-0.844033 + 0.974066i) q^{43} +(-6.29135 - 1.84731i) q^{44} -4.19295 q^{45} +(1.01462 + 0.506723i) q^{46} +3.41741 q^{47} +(-1.68523 - 0.494829i) q^{48} +(0.338474 - 0.390620i) q^{49} +(-0.539086 - 0.346450i) q^{50} +(0.427789 - 2.97534i) q^{51} +(-5.38357 + 3.45981i) q^{52} +(-2.79399 - 6.11799i) q^{53} +(0.427961 + 0.493893i) q^{54} +(0.726398 + 5.05221i) q^{55} +(0.986535 - 2.16021i) q^{56} +(1.94408 - 0.570833i) q^{57} +(-1.42634 + 0.418811i) q^{58} +(-4.32805 + 9.47711i) q^{59} +(0.200510 + 1.39458i) q^{60} +(-2.35737 - 2.72055i) q^{61} +(-0.465844 - 1.02006i) q^{62} +(5.93476 - 3.81404i) q^{63} +(0.951939 - 6.62088i) q^{64} +(4.19075 + 2.69323i) q^{65} +(0.250131 - 0.288666i) q^{66} +(6.54316 + 1.92124i) q^{67} +12.2027 q^{68} +(1.78698 - 1.44273i) q^{69} -0.911214 q^{70} +(-3.92408 - 1.15221i) q^{71} +(-1.69227 + 1.95299i) q^{72} +(3.66912 + 2.35800i) q^{73} +(-0.00127794 + 0.00888826i) q^{74} +(-1.09170 + 0.701592i) q^{75} +(3.41689 + 7.48194i) q^{76} +(-5.62381 - 6.49022i) q^{77} +(-0.0530529 - 0.368991i) q^{78} +(0.997820 - 2.18492i) q^{79} +(-5.32548 + 1.56370i) q^{80} +(-6.70548 + 1.96891i) q^{81} +(0.318941 - 0.698384i) q^{82} +(-0.420847 - 2.92705i) q^{83} +(-1.55236 - 1.79152i) q^{84} +(-3.94603 - 8.64060i) q^{85} +(0.256407 - 0.164783i) q^{86} +(-0.428426 + 2.97977i) q^{87} +(2.64639 + 1.70073i) q^{88} +(-8.09455 + 9.34161i) q^{89} +(0.951379 + 0.279350i) q^{90} -8.38151 q^{91} +(6.82959 + 6.34695i) q^{92} -2.27092 q^{93} +(-0.775410 - 0.227681i) q^{94} +(4.19295 - 4.83892i) q^{95} +(1.10092 + 0.707516i) q^{96} +(1.51088 - 10.5084i) q^{97} +(-0.102824 + 0.0660811i) q^{98} +(3.88199 + 8.50038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.226900	−	0.0666238i	−0.160442	−	0.0471101i	0.200525	−	0.979689i	$-0.435735\pi$
$2$	−0.226900	−	0.0666238i	−0.160442	−	0.0471101i	−0.360967	+	0.932578i	$0.617553\pi$
$3$	−0.313607	+	0.361922i	−0.181061	+	0.208956i	−0.839024	−	0.544095i	$-0.816873\pi$
$3$	−0.313607	+	0.361922i	−0.181061	+	0.208956i	0.657962	+	0.753051i	$0.271419\pi$
$4$	−1.63546	−	1.05105i	−0.817731	−	0.525524i
$5$	−0.215370	+	1.49793i	−0.0963165	+	0.669896i	0.883269	+	0.468867i	$0.155338\pi$
$5$	−0.215370	+	1.49793i	−0.0963165	+	0.669896i	−0.979585	+	0.201029i	$0.935571\pi$
$6$	0.0952700	−	0.0612263i	0.0388938	−	0.0249955i
$7$	−1.05773	−	2.31611i	−0.399784	−	0.875406i	−0.997292	−	0.0735424i	$-0.976570\pi$
$7$	−1.05773	−	2.31611i	−0.399784	−	0.875406i	0.597508	−	0.801863i	$-0.296158\pi$
$8$	0.610783	+	0.704881i	0.215944	+	0.249213i
$9$	0.394306	+	2.74246i	0.131435	+	0.914154i
$10$	0.148666	−	0.325532i	0.0470122	−	0.102942i
$11$	3.23616	−	0.950224i	0.975740	−	0.286503i	0.245275	−	0.969453i	$-0.421122\pi$
$11$	3.23616	−	0.950224i	0.975740	−	0.286503i	0.730465	+	0.682950i	$0.239303\pi$
$12$	0.893290	−	0.262294i	0.257871	−	0.0757176i
$13$	1.36745	−	2.99430i	0.379263	−	0.830470i	−0.619696	−	0.784842i	$-0.712744\pi$
$13$	1.36745	−	2.99430i	0.379263	−	0.830470i	0.998959	−	0.0456275i	$-0.0145287\pi$
$14$	0.0856910	+	0.595994i	0.0229019	+	0.159286i
$15$	−0.474593	−	0.547710i	−0.122539	−	0.141418i
$16$	1.52357	+	3.33616i	0.380893	+	0.834040i
$17$	−5.28043	+	3.39353i	−1.28069	+	0.823051i	−0.990973	−	0.134061i	$-0.957198\pi$
$17$	−5.28043	+	3.39353i	−1.28069	+	0.823051i	−0.289719	+	0.957112i	$0.593562\pi$
$18$	0.0932451	−	0.648534i	0.0219781	−	0.152861i
$19$	−3.55928	−	2.28741i	−0.816554	−	0.524767i	0.0644252	−	0.997923i	$-0.479479\pi$
$19$	−3.55928	−	2.28741i	−0.816554	−	0.524767i	−0.880979	+	0.473155i	$0.843115\pi$
$20$	1.92663	−	2.22345i	0.430808	−	0.497178i
$21$	1.16996	+	0.343532i	0.255306	+	0.0749647i
$22$	−0.797593			−0.170047
$23$	−4.72041	−	0.847210i	−0.984273	−	0.176655i
$23$	−4.72041	−	0.847210i	−0.984273	−	0.176655i
$24$	−0.446658			−0.0911736
$25$	2.60004	+	0.763442i	0.520009	+	0.152688i
$26$	−0.509766	+	0.588302i	−0.0999734	+	0.115375i
$27$	−2.32482	−	1.49407i	−0.447412	−	0.287534i
$28$	−0.704460	+	4.89963i	−0.133130	+	0.925943i
$29$	5.28830	−	3.39858i	0.982012	−	0.631101i	0.0520069	−	0.998647i	$-0.483438\pi$
$29$	5.28830	−	3.39858i	0.982012	−	0.631101i	0.930005	+	0.367546i	$0.119802\pi$
$30$	0.0711946	+	0.155895i	0.0129983	+	0.0284623i
$31$	3.10538	+	3.58380i	0.557742	+	0.643669i	0.962669	−	0.270680i	$-0.0872485\pi$
$31$	3.10538	+	3.58380i	0.557742	+	0.643669i	−0.404927	+	0.914349i	$0.632703\pi$
$32$	−0.388902	−	2.70488i	−0.0687489	−	0.478159i
$33$	−0.670978	+	1.46924i	−0.116802	+	0.255761i
$34$	1.42422	−	0.418188i	0.244251	−	0.0717187i
$35$	3.69718	−	1.08559i	0.624937	−	0.183498i
$36$	2.23758	−	4.89963i	0.372931	−	0.816605i
$37$	−0.00540403	−	0.0375858i	−0.000888417	−	0.00617907i	0.989372	−	0.145404i	$-0.0464481\pi$
$37$	−0.00540403	−	0.0375858i	−0.000888417	−	0.00617907i	−0.990261	+	0.139225i	$0.955539\pi$
$38$	0.655203	+	0.756145i	0.106288	+	0.122663i
$39$	0.654861	+	1.43394i	0.104862	+	0.229615i
$40$	−1.18741	+	0.763102i	−0.187746	+	0.120657i
$41$	−0.462048	+	3.21361i	−0.0721597	+	0.501882i	0.921404	+	0.388606i	$0.127043\pi$
$41$	−0.462048	+	3.21361i	−0.0721597	+	0.501882i	−0.993564	+	0.113275i	$0.963866\pi$
$42$	−0.242577	−	0.155895i	−0.0374304	−	0.0240550i
$43$	−0.844033	+	0.974066i	−0.128714	+	0.148544i	−0.816448	−	0.577419i	$-0.804060\pi$
$43$	−0.844033	+	0.974066i	−0.128714	+	0.148544i	0.687734	+	0.725963i	$0.258605\pi$
$44$	−6.29135	−	1.84731i	−0.948457	−	0.278492i
$45$	−4.19295			−0.625048
$46$	1.01462	+	0.506723i	0.149597	+	0.0747123i
$47$	3.41741			0.498480			0.249240	−	0.968442i	$-0.419819\pi$
$47$	3.41741			0.498480			0.249240	+	0.968442i	$0.419819\pi$
$48$	−1.68523	−	0.494829i	−0.243243	−	0.0714224i
$49$	0.338474	−	0.390620i	0.0483534	−	0.0558028i
$50$	−0.539086	−	0.346450i	−0.0762383	−	0.0489954i
$51$	0.427789	−	2.97534i	0.0599024	−	0.416631i
$52$	−5.38357	+	3.45981i	−0.746567	+	0.479789i
$53$	−2.79399	−	6.11799i	−0.383784	−	0.840370i	−0.998660	−	0.0517465i	$-0.983521\pi$
$53$	−2.79399	−	6.11799i	−0.383784	−	0.840370i	0.614876	−	0.788624i	$-0.289206\pi$
$54$	0.427961	+	0.493893i	0.0582381	+	0.0672104i
$55$	0.726398	+	5.05221i	0.0979475	+	0.681240i
$56$	0.986535	−	2.16021i	0.131831	−	0.288670i
$57$	1.94408	−	0.570833i	0.257499	−	0.0756086i
$58$	−1.42634	+	0.418811i	−0.187288	+	0.0549926i
$59$	−4.32805	+	9.47711i	−0.563464	+	1.23381i	0.386741	+	0.922188i	$0.373601\pi$
$59$	−4.32805	+	9.47711i	−0.563464	+	1.23381i	−0.950205	+	0.311626i	$0.899126\pi$
$60$	0.200510	+	1.39458i	0.0258858	+	0.180039i
$61$	−2.35737	−	2.72055i	−0.301830	−	0.348331i	0.584492	−	0.811399i	$-0.301294\pi$
$61$	−2.35737	−	2.72055i	−0.301830	−	0.348331i	−0.886322	+	0.463069i	$0.846748\pi$
$62$	−0.465844	−	1.02006i	−0.0591622	−	0.129547i
$63$	5.93476	−	3.81404i	0.747710	−	0.480524i
$64$	0.951939	−	6.62088i	0.118992	−	0.827610i
$65$	4.19075	+	2.69323i	0.519799	+	0.334055i
$66$	0.250131	−	0.288666i	0.0307890	−	0.0355324i
$67$	6.54316	+	1.92124i	0.799374	+	0.234717i	0.655812	−	0.754924i	$-0.272326\pi$
$67$	6.54316	+	1.92124i	0.799374	+	0.234717i	0.143562	+	0.989641i	$0.454144\pi$
$68$	12.2027			1.47979
$69$	1.78698	−	1.44273i	0.215127	−	0.173684i
$70$	−0.911214			−0.108911
$71$	−3.92408	−	1.15221i	−0.465702	−	0.136742i	0.0404594	−	0.999181i	$-0.487118\pi$
$71$	−3.92408	−	1.15221i	−0.465702	−	0.136742i	−0.506161	+	0.862439i	$0.668936\pi$
$72$	−1.69227	+	1.95299i	−0.199436	+	0.230162i
$73$	3.66912	+	2.35800i	0.429438	+	0.275983i	0.737453	−	0.675399i	$-0.236028\pi$
$73$	3.66912	+	2.35800i	0.429438	+	0.275983i	−0.308015	+	0.951381i	$0.599665\pi$
$74$	−0.00127794	+	0.00888826i	−0.000148557	+	0.00103324i
$75$	−1.09170	+	0.701592i	−0.126059	+	0.0810129i
$76$	3.41689	+	7.48194i	0.391944	+	0.858237i
$77$	−5.62381	−	6.49022i	−0.640892	−	0.739629i
$78$	−0.0530529	−	0.368991i	−0.00600706	−	0.0417800i
$79$	0.997820	−	2.18492i	0.112263	−	0.245823i	−0.845158	−	0.534517i	$-0.820494\pi$
$79$	0.997820	−	2.18492i	0.112263	−	0.245823i	0.957421	+	0.288694i	$0.0932210\pi$
$80$	−5.32548	+	1.56370i	−0.595407	+	0.174827i
$81$	−6.70548	+	1.96891i	−0.745053	+	0.218767i
$82$	0.318941	−	0.698384i	0.0352212	−	0.0771237i
$83$	−0.420847	−	2.92705i	−0.0461939	−	0.321286i	−0.999796	−	0.0202149i	$-0.993565\pi$
$83$	−0.420847	−	2.92705i	−0.0461939	−	0.321286i	0.953602	−	0.301071i	$-0.0973441\pi$
$84$	−1.55236	−	1.79152i	−0.169376	−	0.195471i
$85$	−3.94603	−	8.64060i	−0.428007	−	0.937204i
$86$	0.256407	−	0.164783i	0.0276491	−	0.0177690i
$87$	−0.428426	+	2.97977i	−0.0459321	+	0.319465i
$88$	2.64639	+	1.70073i	0.282106	+	0.181298i
$89$	−8.09455	+	9.34161i	−0.858020	+	0.990208i	0.141979	+	0.989870i	$0.454653\pi$
$89$	−8.09455	+	9.34161i	−0.858020	+	0.990208i	−1.00000		0.000338824i	$0.999892\pi$
$90$	0.951379	+	0.279350i	0.100284	+	0.0294461i
$91$	−8.38151			−0.878621
$92$	6.82959	+	6.34695i	0.712034	+	0.661716i
$93$	−2.27092			−0.235484
$94$	−0.775410	−	0.227681i	−0.0799774	−	0.0234835i
$95$	4.19295	−	4.83892i	0.430187	−	0.496463i
$96$	1.10092	+	0.707516i	0.112362	+	0.0722106i
$97$	1.51088	−	10.5084i	0.153407	−	1.06697i	−0.757047	−	0.653360i	$-0.773359\pi$
$97$	1.51088	−	10.5084i	0.153407	−	1.06697i	0.910454	−	0.413610i	$-0.135732\pi$
$98$	−0.102824	+	0.0660811i	−0.0103868	+	0.00667520i
$99$	3.88199	+	8.50038i	0.390155	+	0.854320i
$100$	−3.44986	−	3.98135i	−0.344986	−	0.398135i
$101$	−1.30916	−	9.10538i	−0.130266	−	0.906019i	−0.945206	−	0.326474i	$-0.894139\pi$
$101$	−1.30916	−	9.10538i	−0.130266	−	0.906019i	0.814940	−	0.579545i	$-0.196770\pi$
$102$	−0.295294	+	0.646603i	−0.0292384	+	0.0640232i
$103$	−14.1707	+	4.16088i	−1.39628	+	0.409984i	−0.891404	−	0.453209i	$-0.850279\pi$
$103$	−14.1707	+	4.16088i	−1.39628	+	0.409984i	−0.504873	+	0.863193i	$0.668461\pi$
$104$	2.94584	−	0.864977i	0.288863	−	0.0848180i
$105$	−0.766562	+	1.67854i	−0.0748088	+	0.163808i
$106$	0.226353	+	1.57432i	0.0219853	+	0.152911i
$107$	10.6131	+	12.2481i	1.02600	+	1.18407i	0.982737	+	0.185008i	$0.0592311\pi$
$107$	10.6131	+	12.2481i	1.02600	+	1.18407i	0.0432669	+	0.999064i	$0.486223\pi$
$108$	2.23182	+	4.88700i	0.214757	+	0.470252i
$109$	12.6437	−	8.12562i	1.21105	−	0.778293i	0.230214	−	0.973140i	$-0.426057\pi$
$109$	12.6437	−	8.12562i	1.21105	−	0.778293i	0.980834	+	0.194847i	$0.0624210\pi$
$110$	0.171778	−	1.19474i	0.0163784	−	0.113914i
$111$	0.0152979	+	0.00983135i	0.00145201	+	0.000933151i
$112$	6.11537	−	7.05751i	0.577848	−	0.666872i
$113$	1.10866	+	0.325532i	0.104294	+	0.0306235i	0.333463	−	0.942763i	$-0.391783\pi$
$113$	1.10866	+	0.325532i	0.104294	+	0.0306235i	−0.229169	+	0.973387i	$0.573601\pi$
$114$	−0.479142			−0.0448758
$115$	2.28570	−	6.88839i	0.213143	−	0.642346i
$116$	−12.2209			−1.13468
$117$	8.75095	+	2.56951i	0.809026	+	0.237551i
$118$	1.61343	−	1.86200i	0.148529	−	0.171411i
$119$	13.4450	+	8.64060i	1.23250	+	0.792082i
$120$	0.0961968	−	0.669064i	0.00878153	−	0.0610769i
$121$	0.316044	−	0.203109i	0.0287313	−	0.0184645i
$122$	0.353634	+	0.774349i	0.0320165	+	0.0701063i
$123$	−1.01818	−	1.17504i	−0.0918058	−	0.105949i
$124$	−1.31199	−	9.12507i	−0.117820	−	0.819455i
$125$	−4.84687	+	10.6132i	−0.433517	+	0.949271i
$126$	−1.60070	+	0.470008i	−0.142602	+	0.0418717i
$127$	−10.0205	+	2.94228i	−0.889173	+	0.261085i	−0.694250	−	0.719734i	$-0.744264\pi$
$127$	−10.0205	+	2.94228i	−0.889173	+	0.261085i	−0.194923	+	0.980819i	$0.562446\pi$
$128$	−2.92750	+	6.41034i	−0.258757	+	0.566599i
$129$	−0.0878411	−	0.610948i	−0.00773398	−	0.0537910i
$130$	−0.771448	−	0.890298i	−0.0676605	−	0.0780843i
$131$	−6.31204	−	13.8214i	−0.551485	−	1.20758i	−0.956085	−	0.293090i	$-0.905316\pi$
$131$	−6.31204	−	13.8214i	−0.551485	−	1.20758i	0.404600	−	0.914494i	$-0.367411\pi$
$132$	2.64160	−	1.69765i	0.229921	−	0.147762i
$133$	−1.53312	+	10.6631i	−0.132939	+	0.924610i
$134$	−1.35664	−	0.871860i	−0.117196	−	0.0753173i
$135$	2.73872	−	3.16065i	0.235711	−	0.272025i
$136$	−5.61723	−	1.64937i	−0.481673	−	0.141432i
$137$	1.22243			0.104439			0.0522196	−	0.998636i	$-0.483370\pi$
$137$	1.22243			0.104439			0.0522196	+	0.998636i	$0.483370\pi$
$138$	−0.501585	+	0.208299i	−0.0426977	+	0.0177316i
$139$	2.18447			0.185284			0.0926420	−	0.995699i	$-0.470469\pi$
$139$	2.18447			0.185284			0.0926420	+	0.995699i	$0.470469\pi$
$140$	−7.18760	−	2.11047i	−0.607463	−	0.178367i
$141$	−1.07172	+	1.23684i	−0.0902555	+	0.104160i
$142$	0.813607	+	0.522874i	0.0682764	+	0.0438786i
$143$	1.58004	−	10.9894i	0.132130	−	0.918983i
$144$	−8.54854	+	5.49381i	−0.712378	+	0.457818i
$145$	3.95191	+	8.65347i	0.328188	+	0.718632i
$146$	−0.675423	−	0.779480i	−0.0558984	−	0.0645102i
$147$	0.0352260	+	0.245002i	0.00290539	+	0.0202074i
$148$	−0.0306664	+	0.0671501i	−0.00252076	+	0.00551970i
$149$	3.97217	−	1.16634i	0.325413	−	0.0955499i	−0.114946	−	0.993372i	$-0.536669\pi$
$149$	3.97217	−	1.16634i	0.325413	−	0.0955499i	0.440359	+	0.897822i	$0.354851\pi$
$150$	0.294449	−	0.0864581i	0.0240417	−	0.00705927i
$151$	−2.82316	+	6.18185i	−0.229745	+	0.503072i	−0.989035	−	0.147681i	$-0.952819\pi$
$151$	−2.82316	+	6.18185i	−0.229745	+	0.503072i	0.759290	+	0.650753i	$0.225546\pi$
$152$	−0.561594	−	3.90597i	−0.0455513	−	0.316816i
$153$	−11.3887	−	13.1433i	−0.920724	−	1.06257i
$154$	0.843637	+	1.84731i	0.0679822	+	0.148860i
$155$	−6.03710	+	3.87981i	−0.484911	+	0.311634i
$156$	0.436145	−	3.03345i	0.0349195	−	0.242871i
$157$	8.19158	+	5.26441i	0.653759	+	0.420146i	0.825038	−	0.565077i	$-0.191154\pi$
$157$	8.19158	+	5.26441i	0.653759	+	0.420146i	−0.171279	+	0.985223i	$0.554790\pi$
$158$	−0.371973	+	0.429279i	−0.0295926	+	0.0341516i
$159$	3.09045	+	0.907438i	0.245089	+	0.0719645i
$160$	4.13548			0.326939
$161$	3.03069	+	11.8291i	0.238852	+	0.932262i
$162$	1.65265			0.129844
$163$	5.78457	+	1.69850i	0.453083	+	0.133037i	0.500309	−	0.865847i	$-0.333220\pi$
$163$	5.78457	+	1.69850i	0.453083	+	0.133037i	−0.0472260	+	0.998884i	$0.515038\pi$
$164$	4.13332	−	4.77011i	0.322758	−	0.372483i
$165$	−2.05631	−	1.32151i	−0.160083	−	0.102879i
$166$	−0.0995214	+	0.692186i	−0.00772436	+	0.0537241i
$167$	1.48029	−	0.951323i	0.114548	−	0.0736155i	−0.482112	−	0.876109i	$-0.660130\pi$
$167$	1.48029	−	0.951323i	0.114548	−	0.0736155i	0.596660	+	0.802494i	$0.296494\pi$
$168$	0.472443	+	1.03451i	0.0364498	+	0.0798139i
$169$	1.41728	+	1.63562i	0.109021	+	0.125817i
$170$	0.319684	+	2.22345i	0.0245186	+	0.170531i
$171$	4.86968	−	10.6631i	0.372394	−	0.815429i
$172$	2.40417	−	0.705929i	0.183317	−	0.0538266i
$173$	9.79801	−	2.87696i	0.744929	−	0.218731i	0.112825	−	0.993615i	$-0.464010\pi$
$173$	9.79801	−	2.87696i	0.744929	−	0.218731i	0.632104	+	0.774884i	$0.282192\pi$
$174$	0.295734	−	0.647566i	0.0224195	−	0.0490919i
$175$	−0.981933	−	6.82949i	−0.0742271	−	0.516261i
$176$	8.10063	+	9.34863i	0.610608	+	0.704679i
$177$	−2.07267	−	4.53851i	−0.155791	−	0.341135i
$178$	2.45903	−	1.58032i	0.184312	−	0.118450i
$179$	1.46662	−	10.2006i	0.109620	−	0.762426i	−0.858658	−	0.512550i	$-0.828701\pi$
$179$	1.46662	−	10.2006i	0.109620	−	0.762426i	0.968278	−	0.249876i	$-0.0803899\pi$
$180$	6.85741	+	4.40699i	0.511121	+	0.328477i
$181$	−6.08462	+	7.02203i	−0.452266	+	0.521943i	−0.935394	−	0.353607i	$-0.884955\pi$
$181$	−6.08462	+	7.02203i	−0.452266	+	0.521943i	0.483128	+	0.875550i	$0.339501\pi$
$182$	1.90176	+	0.558408i	0.140968	+	0.0413920i
$183$	1.72392			0.127435
$184$	−2.28596	−	3.84479i	−0.168523	−	0.283441i
$185$	0.0574649			0.00422491
$186$	0.515272	+	0.151298i	0.0377816	+	0.0110937i
$187$	−13.8637	+	15.9996i	−1.01382	+	1.17001i
$188$	−5.58904	−	3.59186i	−0.407623	−	0.261963i
$189$	−1.00140	+	6.96486i	−0.0728408	+	0.506619i
$190$	−1.27377	+	0.818600i	−0.0924087	+	0.0593875i
$191$	−8.52854	−	18.6749i	−0.617104	−	1.35127i	−0.917607	−	0.397488i	$-0.869882\pi$
$191$	−8.52854	−	18.6749i	−0.617104	−	1.35127i	0.300504	−	0.953781i	$-0.402845\pi$
$192$	2.09771	+	2.42088i	0.151389	+	0.174712i
$193$	1.95491	+	13.5967i	0.140718	+	0.978713i	0.930752	+	0.365651i	$0.119154\pi$
$193$	1.95491	+	13.5967i	0.140718	+	0.978713i	−0.790034	+	0.613063i	$0.789937\pi$
$194$	−1.04293	+	2.28370i	−0.0748781	+	0.163960i
$195$	−2.28899	+	0.672109i	−0.163918	+	0.0481307i
$196$	−0.964121	+	0.283091i	−0.0688658	+	0.0202208i
$197$	0.955220	−	2.09164i	0.0680566	−	0.149023i	−0.872547	−	0.488531i	$-0.837533\pi$
$197$	0.955220	−	2.09164i	0.0680566	−	0.149023i	0.940603	+	0.339507i	$0.110260\pi$
$198$	−0.314496	−	2.18737i	−0.0223503	−	0.155449i
$199$	−1.12023	−	1.29281i	−0.0794109	−	0.0916450i	0.714654	−	0.699478i	$-0.246584\pi$
$199$	−1.12023	−	1.29281i	−0.0794109	−	0.0916450i	−0.794065	+	0.607833i	$0.792039\pi$
$200$	1.04993	+	2.29902i	0.0742410	+	0.162565i
$201$	−2.74732	+	1.76560i	−0.193781	+	0.124536i
$202$	−0.309588	+	2.15323i	−0.0217825	+	0.151501i
$203$	−13.4651	−	8.65347i	−0.945062	−	0.607355i
$204$	−3.82685	+	4.41643i	−0.267933	+	0.309212i
$205$	−4.71426	−	1.38423i	−0.329259	−	0.0966790i
$206$	3.49254			0.243337
$207$	0.462154	−	13.2796i	0.0321219	−	0.922996i
$208$	12.0729			0.837104
$209$	−13.6919	−	4.02032i	−0.947092	−	0.278091i
$210$	0.285763	−	0.329789i	0.0197195	−	0.0227576i
$211$	−6.73249	−	4.32671i	−0.463484	−	0.297863i	0.287981	−	0.957636i	$-0.407016\pi$
$211$	−6.73249	−	4.32671i	−0.463484	−	0.297863i	−0.751465	+	0.659773i	$0.770652\pi$
$212$	−1.86083	+	12.9424i	−0.127802	+	0.888885i
$213$	1.64763	−	1.05887i	0.112894	−	0.0725524i
$214$	−1.59209	−	3.48618i	−0.108833	−	0.238310i
$215$	−1.27731	−	1.47409i	−0.0871116	−	0.100532i
$216$	−0.366818	−	2.55128i	−0.0249588	−	0.173592i
$217$	5.01580	−	10.9831i	0.340495	−	0.745580i
$218$	−3.41021	+	1.00133i	−0.230969	+	0.0678186i
$219$	−2.00407	+	0.588449i	−0.135423	+	0.0397637i
$220$	4.12212	−	9.02618i	0.277913	−	0.608545i
$221$	2.94051	+	20.4517i	0.197800	+	1.37573i
$222$	−0.00281608	−	0.00324994i	−0.000189003	−	0.000218121i
$223$	11.8489	+	25.9455i	0.793463	+	1.73744i	0.666463	+	0.745538i	$0.267808\pi$
$223$	11.8489	+	25.9455i	0.793463	+	1.73744i	0.127000	+	0.991903i	$0.459465\pi$
$224$	−5.85342	+	3.76177i	−0.391098	+	0.251344i
$225$	−1.06850	+	7.43155i	−0.0712331	+	0.495437i
$226$	−0.229867	−	0.147726i	−0.0152905	−	0.00982661i
$227$	6.14462	−	7.09127i	0.407833	−	0.470664i	−0.514259	−	0.857635i	$-0.671933\pi$
$227$	6.14462	−	7.09127i	0.407833	−	0.470664i	0.922092	+	0.386971i	$0.126479\pi$
$228$	−3.77944	−	1.10974i	−0.250299	−	0.0734945i
$229$	−6.65292			−0.439637			−0.219819	−	0.975541i	$-0.570547\pi$
$229$	−6.65292			−0.439637			−0.219819	+	0.975541i	$0.570547\pi$
$230$	−0.977556	+	1.41069i	−0.0644581	+	0.0930183i
$231$	4.11262			0.270590
$232$	5.62560	+	1.65182i	0.369339	+	0.108448i
$233$	16.7901	−	19.3768i	1.09996	−	1.26942i	0.139733	−	0.990189i	$-0.455376\pi$
$233$	16.7901	−	19.3768i	1.09996	−	1.26942i	0.960224	−	0.279229i	$-0.0900789\pi$
$234$	−1.81440	−	1.16604i	−0.118611	−	0.0762266i
$235$	−0.736009	+	5.11905i	−0.0480119	+	0.333930i
$236$	17.0393	−	10.9505i	1.10916	−	0.712815i
$237$	0.477847	+	1.04634i	0.0310395	+	0.0679671i
$238$	−2.47501	−	2.85631i	−0.160431	−	0.185147i
$239$	0.218040	+	1.51650i	0.0141038	+	0.0980943i	0.995657	−	0.0930929i	$-0.0296753\pi$
$239$	0.218040	+	1.51650i	0.0141038	+	0.0980943i	−0.981554	+	0.191187i	$0.938766\pi$
$240$	1.10417	−	2.41780i	0.0712739	−	0.156068i
$241$	26.7753	−	7.86194i	1.72475	−	0.506432i	0.738864	−	0.673854i	$-0.235362\pi$
$241$	26.7753	−	7.86194i	1.72475	−	0.506432i	0.985885	+	0.167422i	$0.0535442\pi$
$242$	−0.0852423	+	0.0250294i	−0.00547958	+	0.00160895i
$243$	4.83432	−	10.5857i	0.310122	−	0.679072i
$244$	0.995962	+	6.92707i	0.0637599	+	0.443460i
$245$	0.512225	+	0.591139i	0.0327249	+	0.0377665i
$246$	0.152738	+	0.334450i	0.00973824	+	0.0213238i
$247$	−11.7163	+	7.52962i	−0.745492	+	0.479098i
$248$	−0.629439	+	4.37784i	−0.0399694	+	0.277993i
$249$	1.19135	+	0.765631i	0.0754985	+	0.0485199i
$250$	1.80684	−	2.08521i	0.114275	−	0.131880i
$251$	10.8108	+	3.17435i	0.682374	+	0.200363i	0.604506	−	0.796601i	$-0.293371\pi$
$251$	10.8108	+	3.17435i	0.682374	+	0.200363i	0.0778679	+	0.996964i	$0.475189\pi$
$252$	−13.7148			−0.863952
$253$	−16.0810	+	1.74373i	−1.01101	+	0.109627i
$254$	2.46967			0.154961
$255$	4.36472	+	1.28160i	0.273330	+	0.0802568i
$256$	−7.66935	+	8.85090i	−0.479334	+	0.553181i
$257$	−13.8310	−	8.88867i	−0.862756	−	0.554460i	0.0327727	−	0.999463i	$-0.489566\pi$
$257$	−13.8310	−	8.88867i	−0.862756	−	0.554460i	−0.895529	+	0.445003i	$0.853203\pi$
$258$	−0.0207726	+	0.144476i	−0.00129324	+	0.00899471i
$259$	−0.0813368	+	0.0522720i	−0.00505402	+	0.00324802i
$260$	−4.02310	−	8.80937i	−0.249502	−	0.546334i
$261$	11.4057	+	13.1629i	0.705995	+	0.814761i
$262$	0.511364	+	3.55661i	0.0315921	+	0.219728i
$263$	−9.76148	+	21.3747i	−0.601919	+	1.31802i	0.326048	+	0.945353i	$0.394283\pi$
$263$	−9.76148	+	21.3747i	−0.601919	+	1.31802i	−0.927966	+	0.372665i	$0.878444\pi$
$264$	−1.44546	+	0.424425i	−0.0889618	+	0.0261215i
$265$	9.76608	−	2.86758i	0.599926	−	0.176154i
$266$	1.05828	−	2.31732i	0.0648875	−	0.142084i
$267$	−0.842424	−	5.85919i	−0.0515555	−	0.358577i
$268$	−8.68177	−	10.0193i	−0.530323	−	0.612026i
$269$	1.84523	+	4.04049i	0.112506	+	0.246353i	0.957506	−	0.288412i	$-0.0931274\pi$
$269$	1.84523	+	4.04049i	0.112506	+	0.246353i	−0.845001	+	0.534765i	$0.820400\pi$
$270$	−0.831989	+	0.534687i	−0.0506333	+	0.0325400i
$271$	2.80373	−	19.5004i	0.170315	−	1.18456i	−0.707905	−	0.706308i	$-0.750360\pi$
$271$	2.80373	−	19.5004i	0.170315	−	1.18456i	0.878220	−	0.478257i	$-0.158731\pi$
$272$	−19.3665	−	12.4461i	−1.17426	−	0.754654i
$273$	2.62850	−	3.03345i	0.159084	−	0.183593i
$274$	−0.277369	−	0.0814429i	−0.0167565	−	0.00492015i
$275$	9.13961			0.551139
$276$	−4.43891	+	0.481328i	−0.267191	+	0.0289726i
$277$	−18.8580			−1.13307			−0.566535	−	0.824038i	$-0.691716\pi$
$277$	−18.8580			−1.13307			−0.566535	+	0.824038i	$0.691716\pi$
$278$	−0.495655	−	0.145537i	−0.0297274	−	0.00872876i
$279$	−8.60396	+	9.92950i	−0.515105	+	0.594463i
$280$	3.02338	+	1.94301i	0.180682	+	0.116117i
$281$	−2.73137	+	18.9971i	−0.162940	+	1.13327i	0.730114	+	0.683325i	$0.239467\pi$
$281$	−2.73137	+	18.9971i	−0.162940	+	1.13327i	−0.893055	+	0.449948i	$0.851442\pi$
$282$	0.325577	−	0.209235i	0.0193878	−	0.0124598i
$283$	0.452826	+	0.991551i	0.0269177	+	0.0589416i	0.922613	−	0.385726i	$-0.126049\pi$
$283$	0.452826	+	0.991551i	0.0269177	+	0.0589416i	−0.895696	+	0.444668i	$0.853322\pi$
$284$	5.20665	+	6.00879i	0.308958	+	0.356556i
$285$	0.436373	+	3.03504i	0.0258485	+	0.179780i
$286$	−1.09067	+	2.38823i	−0.0644926	+	0.141219i
$287$	7.93178	−	2.32898i	0.468198	−	0.137475i
$288$	7.26467	−	2.13310i	0.428075	−	0.125694i
$289$	9.30486	−	20.3748i	0.547345	−	1.19852i
$290$	−0.320160	−	2.22676i	−0.0188005	−	0.130760i
$291$	3.32941	+	3.84234i	0.195173	+	0.225242i
$292$	−3.52233	−	7.71283i	−0.206129	−	0.451359i
$293$	−11.7264	+	7.53613i	−0.685066	+	0.440265i	−0.836329	−	0.548228i	$-0.815302\pi$
$293$	−11.7264	+	7.53613i	−0.685066	+	0.440265i	0.151262	+	0.988494i	$0.451666\pi$
$294$	0.00833021	−	0.0579379i	0.000485827	−	0.00337900i
$295$	−13.2639	−	8.52422i	−0.772257	−	0.496299i
$296$	0.0231929	−	0.0267660i	0.00134806	−	0.00155574i
$297$	−8.94321	−	2.62596i	−0.518938	−	0.152374i
$298$	−0.978991			−0.0567114
$299$	−8.99173	+	12.9758i	−0.520005	+	0.750410i
$300$	2.52284			0.145656
$301$	3.14880	+	0.924571i	0.181494	+	0.0532914i
$302$	1.05243	−	1.21457i	0.0605607	−	0.0698907i
$303$	3.70600	+	2.38170i	0.212904	+	0.136825i
$304$	2.20834	−	15.3593i	0.126657	−	0.880919i
$305$	4.58291	−	2.94526i	0.262417	−	0.168645i
$306$	1.70844	+	3.74097i	0.0976652	+	0.213857i
$307$	16.7842	+	19.3701i	0.957928	+	1.10551i	0.994348	+	0.106171i	$0.0338590\pi$
$307$	16.7842	+	19.3701i	0.957928	+	1.10551i	−0.0364203	+	0.999337i	$0.511595\pi$
$308$	2.37599	+	16.5254i	0.135385	+	0.941622i
$309$	2.93811	−	6.43356i	0.167143	−	0.365992i
$310$	1.62830	−	0.478113i	0.0924814	−	0.0271550i
$311$	3.56322	−	1.04626i	0.202052	−	0.0593277i	−0.179141	−	0.983823i	$-0.557332\pi$
$311$	3.56322	−	1.04626i	0.202052	−	0.0593277i	0.381192	+	0.924496i	$0.375514\pi$
$312$	−0.610783	+	1.33743i	−0.0345788	+	0.0757169i
$313$	−2.23843	−	15.5687i	−0.126524	−	0.879992i	−0.949913	−	0.312515i	$-0.898829\pi$
$313$	−2.23843	−	15.5687i	−0.126524	−	0.879992i	0.823389	−	0.567477i	$-0.192081\pi$
$314$	−1.50793	−	1.74025i	−0.0850976	−	0.0982078i
$315$	4.43501	+	9.71131i	0.249884	+	0.547170i
$316$	−3.92835	+	2.52460i	−0.220987	+	0.142020i
$317$	0.470339	−	3.27128i	0.0264169	−	0.183733i	−0.972341	−	0.233567i	$-0.924960\pi$
$317$	0.470339	−	3.27128i	0.0264169	−	0.183733i	0.998758	+	0.0498339i	$0.0158692\pi$
$318$	−0.640766	−	0.411795i	−0.0359324	−	0.0230923i
$319$	13.8844	−	16.0234i	0.777376	−	0.897140i
$320$	9.71262	+	2.85188i	0.542952	+	0.159425i
$321$	−7.76120			−0.433188
$322$	0.100436	−	2.88593i	0.00559706	−	0.160827i
$323$	26.5569			1.47766
$324$	13.0360	+	3.82771i	0.724220	+	0.212650i
$325$	5.84141	−	6.74135i	0.324023	−	0.373943i
$326$	−1.19936	−	0.770780i	−0.0664263	−	0.0426896i
$327$	−1.02432	+	7.12429i	−0.0566449	+	0.393974i
$328$	−2.54742	+	1.63713i	−0.140658	+	0.0903954i
$329$	−3.61470	−	7.91508i	−0.199285	−	0.436373i
$330$	0.378532	+	0.436849i	0.0208375	+	0.0240478i
$331$	−1.13861	−	7.91923i	−0.0625838	−	0.435280i	−0.996890	−	0.0788080i	$-0.974889\pi$
$331$	−1.13861	−	7.91923i	−0.0625838	−	0.435280i	0.934306	−	0.356472i	$-0.116021\pi$
$332$	−2.38819	+	5.22942i	−0.131069	+	0.287001i
$333$	0.100947	−	0.0296407i	0.00553185	−	0.00162430i
$334$	−0.399258	+	0.117233i	−0.0218464	+	0.00641468i
$335$	−4.28710	+	9.38744i	−0.234229	+	0.512891i
$336$	0.636445	+	4.42657i	0.0347209	+	0.241489i
$337$	−0.911733	−	1.05220i	−0.0496653	−	0.0573168i	0.730373	−	0.683048i	$-0.239346\pi$
$337$	−0.911733	−	1.05220i	−0.0496653	−	0.0573168i	−0.780039	+	0.625731i	$0.784801\pi$
$338$	−0.212608	−	0.465547i	−0.0115644	−	0.0253224i
$339$	−0.465501	+	0.299159i	−0.0252825	+	0.0162481i
$340$	−2.62810	+	18.2788i	−0.142529	+	0.991309i
$341$	13.4549	+	8.64695i	0.728625	+	0.468259i
$342$	−1.81535	+	2.09502i	−0.0981627	+	0.113286i
$343$	−18.3642	−	5.39220i	−0.991571	−	0.291152i
$344$	−1.20212			−0.0648141
$345$	1.77625	+	2.98749i	0.0956300	+	0.160841i
$346$	−2.41484			−0.129823
$347$	−16.1469	−	4.74116i	−0.866811	−	0.254519i	−0.182052	−	0.983289i	$-0.558274\pi$
$347$	−16.1469	−	4.74116i	−0.866811	−	0.254519i	−0.684758	+	0.728770i	$0.740092\pi$
$348$	3.83256	−	4.42301i	0.205447	−	0.237098i
$349$	−16.0913	−	10.3412i	−0.861347	−	0.553554i	0.0337478	−	0.999430i	$-0.489256\pi$
$349$	−16.0913	−	10.3412i	−0.861347	−	0.553554i	−0.895095	+	0.445876i	$0.852892\pi$
$350$	−0.232206	+	1.61503i	−0.0124120	+	0.0863270i
$351$	−7.65278	+	4.91814i	−0.408475	+	0.262511i
$352$	−3.82879	−	8.38388i	−0.204075	−	0.446862i
$353$	−22.0360	−	25.4309i	−1.17286	−	1.35355i	−0.922781	−	0.385324i	$-0.874090\pi$
$353$	−22.0360	−	25.4309i	−1.17286	−	1.35355i	−0.250076	−	0.968226i	$-0.580456\pi$
$354$	0.167915	+	1.16788i	0.00892459	+	0.0620719i
$355$	2.57107	−	5.62985i	0.136458	−	0.298801i
$356$	23.0568	−	6.77009i	1.22201	−	0.358814i
$357$	−7.34368	+	2.15630i	−0.388669	+	0.114123i
$358$	−1.01238	+	2.21679i	−0.0535057	+	0.117161i
$359$	2.79386	+	19.4317i	0.147454	+	1.02557i	0.920368	+	0.391054i	$0.127890\pi$
$359$	2.79386	+	19.4317i	0.147454	+	1.02557i	−0.772914	+	0.634511i	$0.781201\pi$
$360$	−2.56098	−	2.95553i	−0.134975	−	0.155770i
$361$	−0.456674	−	0.999978i	−0.0240355	−	0.0526304i
$362$	1.84843	−	1.18792i	0.0971515	−	0.0624355i
$363$	−0.0256040	+	0.178080i	−0.00134386	+	0.00934678i
$364$	13.7076	+	8.80937i	0.718476	+	0.461736i
$365$	−4.32234	+	4.98825i	−0.226242	+	0.261097i
$366$	−0.391156	−	0.114854i	−0.0204461	−	0.00600350i
$367$	6.73062			0.351336			0.175668	−	0.984449i	$-0.443792\pi$
$367$	6.73062			0.351336			0.175668	+	0.984449i	$0.443792\pi$
$368$	−4.36546	−	17.0388i	−0.227565	−	0.888210i
$369$	−8.99539			−0.468281
$370$	−0.0130388	−	0.00382853i	−0.000677854	−	0.000199036i
$371$	−11.2146	+	12.9424i	−0.582234	+	0.671934i
$372$	3.71401	+	2.38685i	0.192563	+	0.123752i
$373$	−3.60455	+	25.0702i	−0.186637	+	1.29809i	0.654003	+	0.756492i	$0.273088\pi$
$373$	−3.60455	+	25.0702i	−0.186637	+	1.29809i	−0.840640	+	0.541595i	$0.817821\pi$
$374$	4.21163	−	2.70665i	0.217778	−	0.139958i
$375$	−2.32113	−	5.08256i	−0.119862	−	0.262462i
$376$	2.08729	+	2.40887i	0.107644	+	0.124228i
$377$	−2.94489	−	20.4822i	−0.151669	−	1.05488i
$378$	0.691242	−	1.51361i	0.0355536	−	0.0778516i
$379$	−27.6884	+	8.13003i	−1.42226	+	0.417612i	−0.900266	−	0.435340i	$-0.856628\pi$
$379$	−27.6884	+	8.13003i	−1.42226	+	0.417612i	−0.521989	+	0.852952i	$0.674810\pi$
$380$	−11.9433	+	3.50688i	−0.612680	+	0.179899i
$381$	2.07762	−	4.54935i	0.106440	−	0.233070i
$382$	0.690932	+	4.80554i	0.0353512	+	0.245873i
$383$	8.44472	+	9.74573i	0.431505	+	0.497983i	0.929307	−	0.369307i	$-0.120405\pi$
$383$	8.44472	+	9.74573i	0.431505	+	0.497983i	−0.497802	+	0.867290i	$0.665860\pi$
$384$	−1.40196	−	3.06986i	−0.0715433	−	0.156658i
$385$	10.9331	−	7.02629i	0.557203	−	0.358093i
$386$	0.462296	−	3.21534i	0.0235302	−	0.163656i
$387$	−3.00415	−	1.93065i	−0.152709	−	0.0981404i
$388$	−13.5159	+	15.5981i	−0.686164	+	0.791875i
$389$	−2.01154	−	0.590642i	−0.101989	−	0.0299467i	0.230340	−	0.973110i	$-0.426016\pi$
$389$	−2.01154	−	0.590642i	−0.101989	−	0.0299467i	−0.332329	+	0.943164i	$0.607834\pi$
$390$	0.564150			0.0285669
$391$	27.8008	−	11.5452i	1.40595	−	0.583865i
$392$	0.482074			0.0243484
$393$	6.98178	+	2.05004i	0.352184	+	0.103411i
$394$	−0.356092	+	0.410953i	−0.0179397	+	0.0207035i
$395$	3.05796	+	1.96523i	0.153863	+	0.0988817i
$396$	2.58545	−	17.9822i	0.129924	−	0.903640i
$397$	1.58072	−	1.01587i	0.0793341	−	0.0509849i	−0.500372	−	0.865810i	$-0.666804\pi$
$397$	1.58072	−	1.01587i	0.0793341	−	0.0509849i	0.579707	+	0.814825i	$0.303167\pi$
$398$	0.168047	+	0.367973i	0.00842346	+	0.0184448i
$399$	−3.37842	−	3.89890i	−0.169132	−	0.195189i
$400$	1.41439	+	9.83733i	0.0707197	+	0.491866i
$401$	7.00168	−	15.3315i	0.349647	−	0.765620i	−0.650335	−	0.759647i	$-0.725372\pi$
$401$	7.00168	−	15.3315i	0.349647	−	0.765620i	0.999982	−	0.00597275i	$-0.00190120\pi$
$402$	0.740998	−	0.217577i	0.0369576	−	0.0108517i
$403$	14.9774	−	4.39777i	0.746079	−	0.219068i
$404$	−7.42911	+	16.2675i	−0.369612	+	0.809338i
$405$	−1.50513	−	10.4684i	−0.0747905	−	0.520179i
$406$	2.47869	+	2.86057i	0.123016	+	0.141967i
$407$	−0.0532033	−	0.116499i	−0.00263719	−	0.00577464i
$408$	2.35854	−	1.51574i	0.116765	−	0.0750405i
$409$	−1.85146	+	12.8772i	−0.0915489	+	0.636736i	0.891449	+	0.453121i	$0.149689\pi$
$409$	−1.85146	+	12.8772i	−0.0915489	+	0.636736i	−0.982998	+	0.183616i	$0.941220\pi$
$410$	0.977443	+	0.628164i	0.0482725	+	0.0310228i
$411$	−0.383363	+	0.442424i	−0.0189099	+	0.0218232i
$412$	27.5489	+	8.08908i	1.35724	+	0.398520i
$413$	26.5279			1.30535
$414$	−0.989600	+	2.98235i	−0.0486362	+	0.146574i
$415$	4.47517			0.219677
$416$	−8.63102	−	2.53430i	−0.423170	−	0.124254i
$417$	−0.685065	+	0.790607i	−0.0335478	+	0.0387162i
$418$	2.83885	+	1.82442i	0.138853	+	0.0892353i
$419$	4.18557	−	29.1113i	0.204479	−	1.42218i	−0.586308	−	0.810088i	$-0.699419\pi$
$419$	4.18557	−	29.1113i	0.204479	−	1.42218i	0.790787	−	0.612092i	$-0.209672\pi$
$420$	3.01791	−	1.93949i	0.147259	−	0.0946375i
$421$	9.26262	+	20.2823i	0.451432	+	0.988499i	0.989357	+	0.145506i	$0.0464811\pi$
$421$	9.26262	+	20.2823i	0.451432	+	0.988499i	−0.537925	+	0.842993i	$0.680792\pi$
$422$	1.23934	+	1.43027i	0.0603301	+	0.0696247i
$423$	1.34751	+	9.37211i	0.0655180	+	0.455688i
$424$	2.60593	−	5.70619i	0.126555	−	0.277117i
$425$	−16.3201	+	4.79202i	−0.791642	+	0.232447i
$426$	−0.444393	+	0.130485i	−0.0215309	+	0.00632204i
$427$	−3.80762	+	8.33753i	−0.184264	+	0.403481i
$428$	−4.48390	−	31.1862i	−0.216737	−	1.50744i
$429$	3.48181	+	4.01822i	0.168103	+	0.194001i
$430$	0.191611	+	0.419570i	0.00924031	+	0.0202335i
$431$	−1.48190	+	0.952360i	−0.0713807	+	0.0458736i	−0.575844	−	0.817559i	$-0.695327\pi$
$431$	−1.48190	+	0.952360i	−0.0713807	+	0.0458736i	0.504464	+	0.863433i	$0.331690\pi$
$432$	1.44243	−	10.0323i	0.0693989	−	0.482680i
$433$	11.6083	+	7.46017i	0.557857	+	0.358513i	0.788987	−	0.614410i	$-0.210606\pi$
$433$	11.6083	+	7.46017i	0.557857	+	0.358513i	−0.231130	+	0.972923i	$0.574242\pi$
$434$	−1.86982	+	2.15789i	−0.0897542	+	0.103582i
$435$	−4.37123	−	1.28351i	−0.209584	−	0.0615395i
$436$	−29.2187			−1.39932
$437$	14.8633	+	13.8129i	0.711009	+	0.660763i
$438$	0.493928			0.0236008
$439$	−6.89730	−	2.02523i	−0.329190	−	0.0966590i	0.112961	−	0.993599i	$-0.463966\pi$
$439$	−6.89730	−	2.02523i	−0.329190	−	0.0966590i	−0.442151	+	0.896940i	$0.645785\pi$
$440$	−3.11753	+	3.59783i	−0.148623	+	0.171520i
$441$	1.20472	+	0.774228i	0.0573677	+	0.0368680i
$442$	0.695368	−	4.83639i	0.0330753	−	0.230044i
$443$	−19.6782	+	12.6464i	−0.934939	+	0.600849i	−0.916956	−	0.398989i	$-0.869361\pi$
$443$	−19.6782	+	12.6464i	−0.934939	+	0.600849i	−0.0179838	+	0.999838i	$0.505725\pi$
$444$	−0.0146859	−	0.0321576i	−0.000696961	−	0.00152613i
$445$	−12.2498	−	14.1370i	−0.580695	−	0.670158i
$446$	−0.959929	−	6.67646i	−0.0454540	−	0.316139i
$447$	−0.823580	+	1.80339i	−0.0389540	+	0.0852973i
$448$	−16.3415	+	4.79831i	−0.772066	+	0.226699i
$449$	−6.47903	+	1.90241i	−0.305764	+	0.0897804i	−0.431015	−	0.902345i	$-0.641845\pi$
$449$	−6.47903	+	1.90241i	−0.305764	+	0.0897804i	0.125251	+	0.992125i	$0.460026\pi$
$450$	0.737560	−	1.61503i	0.0347689	−	0.0761333i
$451$	1.55839	+	10.8388i	0.0733816	+	0.510380i
$452$	−1.47102	−	1.69765i	−0.0691911	−	0.0798508i
$453$	−1.35199	−	2.96043i	−0.0635218	−	0.139093i
$454$	−1.86666	+	1.19963i	−0.0876067	+	0.0563014i
$455$	1.80513	−	12.5549i	0.0846257	−	0.588585i
$456$	1.58978	+	1.02169i	0.0744482	+	0.0478449i
$457$	−4.73128	+	5.46019i	−0.221320	+	0.255417i	−0.855541	−	0.517735i	$-0.826775\pi$
$457$	−4.73128	+	5.46019i	−0.221320	+	0.255417i	0.634221	+	0.773152i	$0.281321\pi$
$458$	1.50955	+	0.443242i	0.0705364	+	0.0207114i
$459$	17.3462			0.809653
$460$	−10.9782	+	8.86332i	−0.511861	+	0.413255i
$461$	−32.1800			−1.49877			−0.749385	−	0.662134i	$-0.769651\pi$
$461$	−32.1800			−1.49877			−0.749385	+	0.662134i	$0.769651\pi$
$462$	−0.933152	−	0.273998i	−0.0434142	−	0.0127476i
$463$	12.2945	−	14.1886i	0.571373	−	0.659399i	−0.394355	−	0.918958i	$-0.629032\pi$
$463$	12.2945	−	14.1886i	0.571373	−	0.659399i	0.965727	+	0.259559i	$0.0835773\pi$
$464$	19.3953	+	12.4646i	0.900406	+	0.578656i
$465$	0.489090	−	3.40169i	0.0226810	−	0.157750i
$466$	−5.10063	+	3.27798i	−0.236282	+	0.151849i
$467$	11.8290	+	25.9018i	0.547379	+	1.19859i	0.957995	+	0.286784i	$0.0925861\pi$
$467$	11.8290	+	25.9018i	0.547379	+	1.19859i	−0.410617	+	0.911808i	$0.634687\pi$
$468$	−11.6112	−	13.4000i	−0.536727	−	0.619415i
$469$	−2.47109	−	17.1868i	−0.114104	−	0.793613i
$470$	0.508051	−	1.11248i	0.0234346	−	0.0513147i
$471$	−4.47424	+	1.31376i	−0.206162	+	0.0605347i
$472$	−9.32373	+	2.73769i	−0.429160	+	0.126013i
$473$	−1.80585	+	3.95426i	−0.0830330	+	0.181817i
$474$	−0.0387123	−	0.269250i	−0.00177812	−	0.0123671i
$475$	−7.50797	−	8.66466i	−0.344489	−	0.397562i
$476$	−12.9072	−	28.2627i	−0.591599	−	1.29542i
$477$	15.6767	−	10.0748i	0.717785	−	0.461292i
$478$	0.0515618	−	0.358621i	0.00235838	−	0.0164029i
$479$	3.97699	+	2.55585i	0.181713	+	0.116780i	0.628335	−	0.777943i	$-0.283737\pi$
$479$	3.97699	+	2.55585i	0.181713	+	0.116780i	−0.446622	+	0.894723i	$0.647373\pi$
$480$	−1.29692	+	1.49672i	−0.0591959	+	0.0683157i
$481$	−0.119933	−	0.0352155i	−0.00546848	−	0.00160569i
$482$	−6.59911			−0.300581
$483$	−5.23165	−	2.61281i	−0.238048	−	0.118887i
$484$	−0.730356			−0.0331980
$485$	15.4155	+	4.52641i	0.699983	+	0.205534i
$486$	−1.80216	+	2.07981i	−0.0817479	+	0.0943421i
$487$	26.6479	+	17.1256i	1.20753	+	0.776034i	0.980244	−	0.197794i	$-0.0633776\pi$
$487$	26.6479	+	17.1256i	1.20753	+	0.776034i	0.227288	+	0.973827i	$0.427014\pi$
$488$	0.477823	−	3.32333i	0.0216300	−	0.150440i
$489$	−2.42881	+	1.56090i	−0.109835	+	0.0705864i
$490$	−0.0768398	−	0.168256i	−0.00347127	−	0.00760102i
$491$	4.71421	+	5.44049i	0.212749	+	0.245526i	0.852087	−	0.523400i	$-0.175337\pi$
$491$	4.71421	+	5.44049i	0.212749	+	0.245526i	−0.639338	+	0.768926i	$0.720791\pi$
$492$	0.430167	+	2.99188i	0.0193934	+	0.134884i
$493$	−16.3913	+	35.8920i	−0.738227	+	1.61649i
$494$	3.16008	−	0.927884i	0.142179	−	0.0417475i
$495$	−13.5691	+	3.98424i	−0.609884	+	0.179078i
$496$	−7.22485	+	15.8202i	−0.324405	+	0.710349i
$497$	1.48197	+	10.3073i	0.0664753	+	0.462346i
$498$	−0.219307	−	0.253094i	−0.00982738	−	0.0113414i
$499$	−9.46867	−	20.7335i	−0.423876	−	0.928159i	−0.994281	−	0.106795i	$-0.965941\pi$
$499$	−9.46867	−	20.7335i	−0.423876	−	0.928159i	0.570405	−	0.821364i	$-0.306786\pi$
$500$	19.0818	−	12.2631i	0.853365	−	0.548425i
$501$	−0.119924	+	0.834090i	−0.00535781	+	0.0372644i
$502$	−2.24149	−	1.44052i	−0.100043	−	0.0642935i
$503$	15.9978	−	18.4625i	0.713308	−	0.823201i	−0.277177	−	0.960819i	$-0.589399\pi$
$503$	15.9978	−	18.4625i	0.713308	−	0.823201i	0.990485	+	0.137617i	$0.0439444\pi$
$504$	6.31329	+	1.85375i	0.281216	+	0.0825726i
$505$	13.9212			0.619485
$506$	3.76496	+	0.675728i	0.167373	+	0.0300398i
$507$	−1.03644			−0.0460297
$508$	19.4806	+	5.72001i	0.864311	+	0.253785i
$509$	5.12772	−	5.91771i	0.227282	−	0.262298i	−0.630642	−	0.776074i	$-0.717208\pi$
$509$	5.12772	−	5.91771i	0.227282	−	0.262298i	0.857924	+	0.513776i	$0.171754\pi$
$510$	−0.904970	−	0.581589i	−0.0400728	−	0.0257532i
$511$	1.58044	−	10.9922i	0.0699144	−	0.486266i
$512$	14.1868	−	9.11729i	0.626973	−	0.402931i
$513$	4.85713	+	10.6356i	0.214448	+	0.469575i
$514$	2.54606	+	2.93831i	0.112302	+	0.129603i
$515$	−3.18079	−	22.1229i	−0.140162	−	0.974849i
$516$	−0.498475	+	1.09151i	−0.0219441	+	0.0480510i
$517$	11.0593	−	3.24730i	0.486387	−	0.142816i
$518$	0.0219379	−	0.00644153i	0.000963894	−	0.000283025i
$519$	−2.03149	+	4.44835i	−0.0891727	+	0.195261i
$520$	0.661231	+	4.59896i	0.0289969	+	0.201678i
$521$	−1.98664	−	2.29270i	−0.0870361	−	0.100445i	0.710561	−	0.703636i	$-0.248441\pi$
$521$	−1.98664	−	2.29270i	−0.0870361	−	0.100445i	−0.797597	+	0.603191i	$0.793896\pi$
$522$	−1.71099	−	3.74654i	−0.0748880	−	0.163982i
$523$	24.9421	−	16.0293i	1.09064	−	0.700913i	0.133650	−	0.991029i	$-0.457330\pi$
$523$	24.9421	−	16.0293i	1.09064	−	0.700913i	0.956992	+	0.290115i	$0.0936937\pi$
$524$	−4.20389	+	29.2387i	−0.183648	+	1.27730i
$525$	2.77968	+	1.78639i	0.121315	+	0.0779647i
$526$	3.63894	−	4.19956i	0.158665	−	0.183109i
$527$	−28.5594	−	8.38581i	−1.24407	−	0.365292i
$528$	−5.92389			−0.257804
$529$	21.5645	+	7.99835i	0.937586	+	0.347754i
$530$	−2.40697			−0.104552
$531$	−27.6972	−	8.13263i	−1.20196	−	0.352926i
$532$	13.7148	−	15.8277i	0.594613	−	0.686219i
$533$	8.99069	+	5.77797i	0.389430	+	0.250271i
$534$	−0.199216	+	1.38557i	−0.00862090	+	0.0599597i
$535$	−20.6326	+	13.2598i	−0.892026	+	0.573270i
$536$	2.64220	+	5.78561i	0.114126	+	0.249900i
$537$	3.23187	+	3.72977i	0.139465	+	0.160952i
$538$	−0.149489	−	1.03972i	−0.00644494	−	0.0448256i
$539$	0.724181	−	1.58573i	0.0311927	−	0.0683024i
$540$	−7.80106	+	2.29060i	−0.335704	+	0.0985717i
$541$	−22.8021	+	6.69531i	−0.980341	+	0.287854i	−0.732365	−	0.680912i	$-0.761584\pi$
$541$	−22.8021	+	6.69531i	−0.980341	+	0.287854i	−0.247976	+	0.968766i	$0.579765\pi$
$542$	−1.93536	+	4.23784i	−0.0831307	+	0.182031i
$543$	−0.633245	−	4.40432i	−0.0271752	−	0.189007i
$544$	11.2326	+	12.9632i	0.481595	+	0.555791i
$545$	9.44856	+	20.6895i	0.404732	+	0.886239i
$546$	−0.798507	+	0.513169i	−0.0341729	+	0.0219616i
$547$	2.72007	−	18.9185i	0.116302	−	0.808896i	−0.845269	−	0.534340i	$-0.820560\pi$
$547$	2.72007	−	18.9185i	0.116302	−	0.808896i	0.961571	−	0.274556i	$-0.0885308\pi$
$548$	−1.99924	−	1.28483i	−0.0854032	−	0.0548853i
$549$	6.53148	−	7.53773i	0.278757	−	0.321702i
$550$	−2.07378	−	0.608916i	−0.0884261	−	0.0259642i
$551$	−26.5965			−1.13305
$552$	2.10841	+	0.378413i	0.0897397	+	0.0161063i
$553$	−6.11593			−0.260076
$554$	4.27888	+	1.25639i	0.181792	+	0.0533790i
$555$	−0.0180214	+	0.0207978i	−0.000764967	+	0.000882819i
$556$	−3.57261	−	2.29598i	−0.151513	−	0.0973712i
$557$	2.79304	−	19.4260i	0.118345	−	0.823106i	−0.841033	−	0.540983i	$-0.818052\pi$
$557$	2.79304	−	19.4260i	0.118345	−	0.823106i	0.959378	−	0.282123i	$-0.0910387\pi$
$558$	2.61378	−	1.67977i	0.110650	−	0.0711104i
$559$	1.76247	+	3.85928i	0.0745447	+	0.163230i
$560$	9.25462	+	10.6804i	0.391079	+	0.451329i
$561$	−1.44284	−	10.0352i	−0.0609168	−	0.423685i
$562$	1.88541	−	4.12847i	0.0795312	−	0.174149i
$563$	−42.8697	+	12.5877i	−1.80674	+	0.530507i	−0.998312	−	0.0580848i	$-0.981501\pi$
$563$	−42.8697	+	12.5877i	−1.80674	+	0.530507i	−0.808430	+	0.588592i	$0.799682\pi$
$564$	3.05274	−	0.896365i	0.128543	−	0.0377438i
$565$	−0.726398	+	1.59059i	−0.0305598	+	0.0669166i
$566$	−0.0366853	−	0.255152i	−0.00154200	−	0.0107248i
$567$	11.6528	+	13.4480i	0.489371	+	0.564764i
$568$	−1.58458	−	3.46976i	−0.0664877	−	0.145588i
$569$	3.48719	−	2.24108i	0.146191	−	0.0939510i	−0.465501	−	0.885047i	$-0.654126\pi$
$569$	3.48719	−	2.24108i	0.146191	−	0.0939510i	0.611691	+	0.791096i	$0.290489\pi$
$570$	0.103193	−	0.717723i	0.00432228	−	0.0300621i
$571$	−11.2629	−	7.23824i	−0.471339	−	0.302911i	0.283324	−	0.959024i	$-0.408563\pi$
$571$	−11.2629	−	7.23824i	−0.471339	−	0.302911i	−0.754662	+	0.656113i	$0.772199\pi$
$572$	−14.1345	+	16.3121i	−0.590994	+	0.682043i
$573$	9.43347	+	2.76992i	0.394089	+	0.115715i
$574$	−1.95489			−0.0815954
$575$	−11.6265	−	5.80654i	−0.484857	−	0.242149i
$576$	18.5329			0.772203
$577$	−22.4790	−	6.60044i	−0.935814	−	0.274780i	−0.221945	−	0.975059i	$-0.571241\pi$
$577$	−22.4790	−	6.60044i	−0.935814	−	0.274780i	−0.713869	+	0.700279i	$0.753059\pi$
$578$	−3.46872	+	4.00311i	−0.144280	+	0.166508i
$579$	−5.53403	−	3.55650i	−0.229986	−	0.147803i
$580$	2.63202	−	18.3061i	0.109289	−	0.760118i
$581$	−6.33422	+	4.07076i	−0.262788	+	0.168883i
$582$	−0.499451	−	1.09364i	−0.0207029	−	0.0453330i
$583$	−14.8553	−	17.1439i	−0.615242	−	0.710028i
$584$	0.578925	+	4.02651i	0.0239561	+	0.166618i
$585$	−5.73365	+	12.5549i	−0.237057	+	0.519083i
$586$	3.16281	−	0.928686i	0.130655	−	0.0383637i
$587$	38.4429	−	11.2879i	1.58671	−	0.465899i	0.634900	−	0.772594i	$-0.281041\pi$
$587$	38.4429	−	11.2879i	1.58671	−	0.465899i	0.951808	+	0.306695i	$0.0992231\pi$
$588$	0.199898	−	0.437716i	0.00824366	−	0.0180511i
$589$	−2.85529	−	19.8590i	−0.117650	−	0.818276i
$590$	2.44167	+	2.81784i	0.100522	+	0.116009i
$591$	0.457447	+	1.00167i	0.0188169	+	0.0412032i
$592$	0.117159	−	0.0752935i	0.00481520	−	0.00309454i
$593$	−0.831288	+	5.78174i	−0.0341369	+	0.237427i	−0.999745	−	0.0225738i	$-0.992814\pi$
$593$	−0.831288	+	5.78174i	−0.0341369	+	0.237427i	0.965608	+	0.260001i	$0.0837230\pi$
$594$	1.85426	+	1.19166i	0.0760812	+	0.0488944i
$595$	−15.8387	+	18.2788i	−0.649323	+	0.749359i
$596$	−7.72221	−	2.26745i	−0.316314	−	0.0928782i
$597$	0.819209			0.0335280
$598$	2.90472	−	2.34514i	0.118783	−	0.0959000i
$599$	−5.01179			−0.204776			−0.102388	−	0.994745i	$-0.532648\pi$
$599$	−5.01179			−0.204776			−0.102388	+	0.994745i	$0.532648\pi$
$600$	−1.16133	−	0.340997i	−0.0474111	−	0.0139212i
$601$	−8.34466	+	9.63025i	−0.340386	+	0.392826i	−0.899973	−	0.435945i	$-0.856414\pi$
$601$	−8.34466	+	9.63025i	−0.340386	+	0.392826i	0.559587	+	0.828771i	$0.310960\pi$
$602$	−0.652864	−	0.419570i	−0.0266087	−	0.0171004i
$603$	−2.68893	+	18.7019i	−0.109502	+	0.761601i
$604$	11.1146	−	7.14291i	0.452246	−	0.290641i
$605$	0.236178	+	0.517157i	0.00960199	+	0.0210254i
$606$	−0.682212	−	0.787315i	−0.0277130	−	0.0319825i
$607$	0.0879598	+	0.611774i	0.00357018	+	0.0248311i	0.991529	−	0.129888i	$-0.0414618\pi$
$607$	0.0879598	+	0.611774i	0.00357018	+	0.0248311i	−0.987958	+	0.154719i	$0.950553\pi$
$608$	−4.80294	+	10.5170i	−0.194785	+	0.426520i
$609$	7.35462	−	2.15951i	0.298024	−	0.0875079i
$610$	−1.23609	+	0.362948i	−0.0500477	+	0.0146953i
$611$	4.67314	−	10.2328i	0.189055	−	0.413973i
$612$	4.81160	+	33.4654i	0.194498	+	1.35276i
$613$	−20.8291	−	24.0381i	−0.841281	−	0.970890i	0.158584	−	0.987346i	$-0.449307\pi$
$613$	−20.8291	−	24.0381i	−0.841281	−	0.970890i	−0.999865	+	0.0164557i	$0.994762\pi$
$614$	−2.51784	−	5.51329i	−0.101612	−	0.222498i
$615$	1.97941	−	1.27209i	0.0798176	−	0.0512956i
$616$	1.13991	−	7.92823i	0.0459282	−	0.319437i
$617$	33.6295	+	21.6123i	1.35387	+	0.870080i	0.997923	−	0.0644251i	$-0.0205214\pi$
$617$	33.6295	+	21.6123i	1.35387	+	0.870080i	0.355949	+	0.934505i	$0.384158\pi$
$618$	−1.09528	+	1.26403i	−0.0440588	+	0.0508466i
$619$	33.7104	+	9.89827i	1.35494	+	0.397845i	0.876975	−	0.480536i	$-0.159558\pi$
$619$	33.7104	+	9.89827i	1.35494	+	0.397845i	0.477961	+	0.878381i	$0.341376\pi$
$620$	13.9513			0.560298
$621$	9.70831	+	9.02224i	0.389581	+	0.362050i
$622$	−0.878199			−0.0352126
$623$	30.1980	+	8.86693i	1.20986	+	0.355246i
$624$	−3.78614	+	4.36944i	−0.151567	+	0.174918i
$625$	−3.45576	−	2.22088i	−0.138230	−	0.0888353i
$626$	−0.529342	+	3.68166i	−0.0211568	+	0.147149i
$627$	5.74894	−	3.69462i	0.229590	−	0.147549i
$628$	−7.86387	−	17.2195i	−0.313803	−	0.687132i
$629$	0.156084	+	0.180131i	0.00622348	+	0.00718228i
$630$	−0.359298	−	2.49897i	−0.0143148	−	0.0995614i
$631$	19.6170	−	42.9552i	0.780941	−	1.71002i	0.0800078	−	0.996794i	$-0.474505\pi$
$631$	19.6170	−	42.9552i	0.780941	−	1.71002i	0.700933	−	0.713227i	$-0.252767\pi$
$632$	2.14956	−	0.631168i	0.0855049	−	0.0251065i
$633$	3.67729	−	1.07975i	0.146159	−	0.0429162i
$634$	−0.324665	+	0.710917i	−0.0128941	+	0.0282341i
$635$	−2.24922	−	15.6437i	−0.0892576	−	0.620800i
$636$	−4.10055	−	4.73229i	−0.162598	−	0.187648i
$637$	−0.706786	−	1.54765i	−0.0280039	−	0.0613200i
$638$	−4.21791	+	2.71068i	−0.166989	+	0.107317i
$639$	1.61261	−	11.2160i	0.0637939	−	0.443696i
$640$	−8.97177	−	5.76580i	−0.354640	−	0.227913i
$641$	−4.52524	+	5.22241i	−0.178736	+	0.206273i	−0.838047	−	0.545598i	$-0.816303\pi$
$641$	−4.52524	+	5.22241i	−0.178736	+	0.206273i	0.659311	+	0.751870i	$0.270848\pi$
$642$	1.76102	+	0.517081i	0.0695017	+	0.0204076i
$643$	38.9219			1.53493			0.767465	−	0.641091i	$-0.221518\pi$
$643$	38.9219			1.53493			0.767465	+	0.641091i	$0.221518\pi$
$644$	7.47635	−	22.5314i	0.294609	−	0.887862i
$645$	0.934078			0.0367793
$646$	−6.02575	−	1.76932i	−0.237080	−	0.0696130i
$647$	−7.63135	+	8.80704i	−0.300019	+	0.346241i	−0.885664	−	0.464328i	$-0.846296\pi$
$647$	−7.63135	+	8.80704i	−0.300019	+	0.346241i	0.585644	+	0.810568i	$0.300842\pi$
$648$	−5.48343	−	3.52399i	−0.215410	−	0.138435i
$649$	−5.00091	+	34.7821i	−0.196303	+	1.36532i
$650$	−1.77455	+	1.14043i	−0.0696035	+	0.0447315i
$651$	2.40202	+	5.25970i	0.0941428	+	0.206144i
$652$	−7.67524	−	8.85770i	−0.300586	−	0.346894i
$653$	5.61467	+	39.0509i	0.219719	+	1.52818i	0.739076	+	0.673622i	$0.235262\pi$
$653$	5.61467	+	39.0509i	0.219719	+	1.52818i	−0.519357	+	0.854557i	$0.673829\pi$
$654$	0.707065	−	1.54826i	0.0276484	−	0.0605416i
$655$	22.0630	−	6.47828i	0.862073	−	0.253127i
$656$	−11.4251	+	3.35471i	−0.446075	+	0.130979i
$657$	−5.01996	+	10.9922i	−0.195847	+	0.428846i
$658$	0.292841	+	2.03676i	0.0114161	+	0.0794010i
$659$	0.488601	+	0.563876i	0.0190332	+	0.0219655i	0.765186	−	0.643809i	$-0.222647\pi$
$659$	0.488601	+	0.563876i	0.0190332	+	0.0219655i	−0.746153	+	0.665774i	$0.768101\pi$
$660$	1.97405	+	4.32256i	0.0768396	+	0.168255i
$661$	−24.5667	+	15.7881i	−0.955534	+	0.614085i	−0.922759	−	0.385378i	$-0.874071\pi$
$661$	−24.5667	+	15.7881i	−0.955534	+	0.614085i	−0.0327757	+	0.999463i	$0.510435\pi$
$662$	−0.269258	+	1.87273i	−0.0104650	+	0.0727857i
$663$	−8.32407	−	5.34956i	−0.323280	−	0.207760i
$664$	1.80618	−	2.08444i	0.0700933	−	0.0808920i
$665$	−15.6425	−	4.59304i	−0.606588	−	0.178110i
$666$	−0.0248796			−0.000964065
$667$	−27.8422	+	11.5624i	−1.07806	+	0.447698i
$668$	−3.42084			−0.132356
$669$	−13.1062	−	3.84832i	−0.506714	−	0.148785i
$670$	1.59817	−	1.84439i	0.0617427	−	0.0712548i
$671$	−10.2140	−	6.56412i	−0.394306	−	0.253405i
$672$	0.474210	−	3.29820i	0.0182930	−	0.127231i
$673$	14.0784	−	9.04766i	0.542683	−	0.348762i	−0.240404	−	0.970673i	$-0.577280\pi$
$673$	14.0784	−	9.04766i	0.542683	−	0.348762i	0.783088	+	0.621911i	$0.213644\pi$
$674$	0.136771	+	0.299486i	0.00526821	+	0.0115358i
$675$	−4.90400	−	5.65952i	−0.188755	−	0.217835i
$676$	−0.598783	−	4.16463i	−0.0230301	−	0.160178i
$677$	18.7888	−	41.1418i	0.722113	−	1.58121i	−0.0888053	−	0.996049i	$-0.528305\pi$
$677$	18.7888	−	41.1418i	0.722113	−	1.58121i	0.810919	−	0.585159i	$-0.198968\pi$
$678$	0.125553	−	0.0368658i	0.00482184	−	0.00141582i
$679$	−25.9367	+	7.61572i	−0.995361	+	0.292264i
$680$	3.68043	−	8.05901i	0.141138	−	0.309049i
$681$	0.639489	+	4.44775i	0.0245053	+	0.170438i
$682$	−2.47683	−	2.85841i	−0.0948426	−	0.109454i
$683$	14.4581	+	31.6589i	0.553225	+	1.21139i	0.955259	+	0.295769i	$0.0955759\pi$
$683$	14.4581	+	31.6589i	0.553225	+	1.21139i	−0.402034	+	0.915625i	$0.631697\pi$
$684$	−19.1716	+	12.3209i	−0.733046	+	0.471100i
$685$	−0.263275	+	1.83112i	−0.0100592	+	0.0699634i
$686$	3.80758	+	2.44698i	0.145374	+	0.0934261i
$687$	2.08640	−	2.40784i	0.0796012	−	0.0918647i
$688$	−4.53559	−	1.33177i	−0.172918	−	0.0507732i
$689$	−22.1397			−0.843457
$690$	−0.203992	−	0.796202i	−0.00776585	−	0.0303109i
$691$	10.7550			0.409140			0.204570	−	0.978852i	$-0.434420\pi$
$691$	10.7550			0.409140			0.204570	+	0.978852i	$0.434420\pi$
$692$	−19.0481	−	5.59303i	−0.724100	−	0.212615i
$693$	15.5817	−	17.9822i	0.591899	−	0.683087i
$694$	3.34785	+	2.15153i	0.127083	+	0.0816711i
$695$	−0.470469	+	3.27219i	−0.0178459	+	0.124121i
$696$	−2.36206	+	1.51800i	−0.0895336	+	0.0575398i
$697$	−8.46566	−	18.5372i	−0.320660	−	0.702147i
$698$	2.96214	+	3.41849i	0.112119	+	0.129392i
$699$	1.74740	+	12.1534i	0.0660927	+	0.459685i
$700$	−5.57221	+	12.2014i	−0.210610	+	0.461171i
$701$	19.4393	−	5.70790i	0.734214	−	0.215585i	0.106811	−	0.994279i	$-0.465936\pi$
$701$	19.4393	−	5.70790i	0.734214	−	0.215585i	0.627403	+	0.778695i	$0.284118\pi$
$702$	2.06408	−	0.606069i	0.0779037	−	0.0228746i
$703$	−0.0667397	+	0.146140i	−0.00251714	+	0.00551176i
$704$	−3.21069	−	22.3308i	−0.121007	−	0.841624i
$705$	−1.62188	−	1.87175i	−0.0610835	−	0.0704942i
$706$	3.30566	+	7.23839i	0.124410	+	0.272420i
$707$	−19.7043	+	12.6632i	−0.741056	+	0.476248i
$708$	−1.38042	+	9.60103i	−0.0518793	+	0.360829i
$709$	−11.0641	−	7.11045i	−0.415520	−	0.267038i	0.316134	−	0.948714i	$-0.397615\pi$
$709$	−11.0641	−	7.11045i	−0.415520	−	0.267038i	−0.731654	+	0.681676i	$0.761251\pi$
$710$	−0.958457	+	1.10612i	−0.0359702	+	0.0415119i
$711$	6.38551	+	1.87495i	0.239475	+	0.0703163i
$712$	−11.5287			−0.432057
$713$	−11.6224	−	19.5479i	−0.435263	−	0.732074i
$714$	1.80994			0.0677353
$715$	16.1211	+	4.73360i	0.602897	+	0.177026i
$716$	−13.1199	+	15.1412i	−0.490313	+	0.565851i
$717$	−0.617234	−	0.396672i	−0.0230510	−	0.0148140i
$718$	0.660688	−	4.59519i	0.0246567	−	0.171491i
$719$	−24.1781	+	15.5383i	−0.901692	+	0.579482i	−0.907292	−	0.420502i	$-0.861854\pi$
$719$	−24.1781	+	15.5383i	−0.901692	+	0.579482i	0.00559955	+	0.999984i	$0.498218\pi$
$720$	−6.38826	−	13.9883i	−0.238077	−	0.521315i
$721$	24.6258	+	28.4197i	0.917112	+	1.05840i
$722$	0.0369970	+	0.257320i	0.00137689	+	0.00957646i
$723$	−5.55152	+	12.1561i	−0.206463	+	0.452092i
$724$	17.3317	−	5.08903i	0.644126	−	0.189132i
$725$	16.3444	−	4.79916i	0.607017	−	0.178236i
$726$	0.0176739	−	0.0387005i	0.000655941	−	0.00143631i
$727$	3.96330	+	27.5653i	0.146991	+	1.02234i	0.921110	+	0.389302i	$0.127284\pi$
$727$	3.96330	+	27.5653i	0.146991	+	1.02234i	−0.774120	+	0.633039i	$0.781807\pi$
$728$	−5.11928	−	5.90797i	−0.189733	−	0.218964i
$729$	−6.39435	−	14.0017i	−0.236828	−	0.518580i
$730$	1.31308	−	0.843862i	0.0485991	−	0.0312327i
$731$	1.15134	−	8.00774i	0.0425838	−	0.296177i
$732$	−2.81940	−	1.81192i	−0.104208	−	0.0669704i
$733$	16.3812	−	18.9049i	0.605052	−	0.698267i	−0.367745	−	0.929927i	$-0.619870\pi$
$733$	16.3812	−	18.9049i	0.605052	−	0.698267i	0.972797	+	0.231660i	$0.0744156\pi$
$734$	−1.52718	−	0.448420i	−0.0563691	−	0.0165515i
$735$	−0.374584			−0.0138167
$736$	−0.455820	+	13.0976i	−0.0168017	+	0.482784i
$737$	23.0003			0.847229
$738$	2.04105	+	0.599307i	0.0751322	+	0.0220608i
$739$	−4.18350	+	4.82801i	−0.153892	+	0.177601i	−0.827461	−	0.561524i	$-0.810215\pi$
$739$	−4.18350	+	4.82801i	−0.153892	+	0.177601i	0.673568	+	0.739125i	$0.264761\pi$
$740$	−0.0939818	−	0.0603984i	−0.00345484	−	0.00222029i
$741$	0.949187	−	6.60174i	0.0348692	−	0.242521i
$742$	3.40686	−	2.18946i	0.125070	−	0.0803775i
$743$	−12.0136	−	26.3062i	−0.440738	−	0.965081i	−0.991462	−	0.130394i	$-0.958376\pi$
$743$	−12.0136	−	26.3062i	−0.440738	−	0.965081i	0.550725	−	0.834687i	$-0.314351\pi$
$744$	−1.38704	−	1.60073i	−0.0508514	−	0.0586857i
$745$	0.891604	+	6.20124i	0.0326659	+	0.227196i
$746$	2.48815	−	5.44828i	0.0910975	−	0.199476i
$747$	7.86139	−	2.30831i	0.287633	−	0.0844567i
$748$	39.4899	−	11.5953i	1.44390	−	0.423966i
$749$	17.1422	−	37.5362i	0.626363	−	1.37154i
$750$	0.188044	+	1.30787i	0.00686639	+	0.0477568i
$751$	32.9193	+	37.9909i	1.20124	+	1.38631i	0.901778	+	0.432200i	$0.142263\pi$
$751$	32.9193	+	37.9909i	1.20124	+	1.38631i	0.299465	+	0.954107i	$0.403192\pi$
$752$	5.20667	+	11.4010i	0.189868	+	0.415753i
$753$	−4.53922	+	2.91718i	−0.165418	+	0.106308i
$754$	−0.696404	+	4.84360i	−0.0253615	+	0.176393i
$755$	−8.65198	−	5.56029i	−0.314878	−	0.202360i
$756$	8.95814	−	10.3382i	0.325804	−	0.375998i
$757$	−33.7498	−	9.90983i	−1.22666	−	0.360179i	−0.396670	−	0.917961i	$-0.629834\pi$
$757$	−33.7498	−	9.90983i	−1.22666	−	0.360179i	−0.829987	+	0.557782i	$0.811652\pi$
$758$	6.82414			0.247864
$759$	4.41204	−	6.36693i	0.160147	−	0.231105i
$760$	5.97184			0.216621
$761$	33.8907	+	9.95120i	1.22854	+	0.360731i	0.830697	−	0.556725i	$-0.187942\pi$
$761$	33.8907	+	9.95120i	1.22854	+	0.360731i	0.397839	+	0.917455i	$0.369760\pi$
$762$	−0.774506	+	0.893827i	−0.0280574	+	0.0323799i
$763$	−32.1934	−	20.6895i	−1.16548	−	0.749008i
$764$	−5.68011	+	39.5060i	−0.205499	+	1.42928i
$765$	22.1406	−	14.2289i	0.800494	−	0.514446i
$766$	−1.26681	−	2.77392i	−0.0457716	−	0.100226i
$767$	22.4589	+	25.9190i	0.810944	+	0.935880i
$768$	−0.798172	−	5.55141i	−0.0288016	−	0.200319i
$769$	−20.4810	+	44.8471i	−0.738563	+	1.61723i	0.0473404	+	0.998879i	$0.484925\pi$
$769$	−20.4810	+	44.8471i	−0.738563	+	1.61723i	−0.785904	+	0.618349i	$0.787802\pi$
$770$	−2.94884	+	0.865857i	−0.106269	+	0.0312033i
$771$	7.55452	−	2.21821i	0.272069	−	0.0798868i
$772$	11.0936	−	24.2916i	0.399268	−	0.874275i
$773$	−0.532931	−	3.70661i	−0.0191682	−	0.133318i	0.977990	−	0.208651i	$-0.0669071\pi$
$773$	−0.532931	−	3.70661i	−0.0191682	−	0.133318i	−0.997158	+	0.0753329i	$0.975998\pi$
$774$	0.553013	+	0.638211i	0.0198777	+	0.0229400i
$775$	5.33810	+	11.6888i	0.191750	+	0.419874i
$776$	8.33002	−	5.35338i	0.299030	−	0.192175i
$777$	0.00658942	−	0.0458304i	0.000236394	−	0.00164416i
$778$	0.417068	+	0.268033i	0.0149526	+	0.00960945i
$779$	8.99539	−	10.3812i	0.322293	−	0.371946i
$780$	4.44998	+	1.30663i	0.159335	+	0.0467849i
$781$	−13.7938			−0.493581
$782$	−7.07718	+	0.767407i	−0.253079	+	0.0274424i
$783$	−17.3721			−0.620827
$784$	1.81886	+	0.534065i	0.0649593	+	0.0190738i
$785$	−9.64996	+	11.1366i	−0.344422	+	0.397484i
$786$	−1.44758	−	0.930305i	−0.0516336	−	0.0331829i
$787$	−1.65608	+	11.5183i	−0.0590330	+	0.410584i	0.938782	+	0.344512i	$0.111956\pi$
$787$	−1.65608	+	11.5183i	−0.0590330	+	0.410584i	−0.997815	+	0.0660715i	$0.978953\pi$
$788$	−3.76064	+	2.41682i	−0.133967	+	0.0860956i
$789$	−4.67469	−	10.2361i	−0.166423	−	0.364416i
$790$	−0.562920	−	0.649645i	−0.0200278	−	0.0231133i
$791$	−0.418697	−	2.91210i	−0.0148871	−	0.103542i
$792$	−3.62070	+	7.92823i	−0.128656	+	0.281717i
$793$	−11.3697	+	3.33846i	−0.403751	+	0.118552i
$794$	−0.426346	+	0.125187i	−0.0151305	+	0.00444270i
$795$	−2.02487	+	4.43385i	−0.0718149	+	0.157253i
$796$	0.473283	+	3.29176i	0.0167751	+	0.116673i
$797$	−32.7798	−	37.8299i	−1.16112	−	1.34000i	−0.930210	−	0.367029i	$-0.880375\pi$
$797$	−32.7798	−	37.8299i	−1.16112	−	1.34000i	−0.230910	−	0.972975i	$-0.574170\pi$
$798$	0.506803	+	1.10974i	0.0179406	+	0.0392845i
$799$	−18.0454	+	11.5971i	−0.638400	+	0.410275i
$800$	1.05385	−	7.32970i	0.0372593	−	0.259144i
$801$	−28.8107	−	18.5155i	−1.01798	−	0.654214i
$802$	−2.61012	+	3.01224i	−0.0921667	+	0.106366i
$803$	14.1145	+	4.14439i	0.498090	+	0.146252i
$804$	6.34887			0.223907
$805$	−18.3719	+	1.99214i	−0.647524	+	0.0702136i
$806$	−3.69137			−0.130023
$807$	−2.04102	−	0.599297i	−0.0718472	−	0.0210962i
$808$	5.61860	−	6.48421i	0.197662	−	0.228114i
$809$	−26.9667	−	17.3305i	−0.948100	−	0.609307i	−0.0274196	−	0.999624i	$-0.508729\pi$
$809$	−26.9667	−	17.3305i	−0.948100	−	0.609307i	−0.920681	+	0.390317i	$0.872365\pi$
$810$	−0.355931	+	2.47556i	−0.0125061	+	0.0869822i
$811$	40.6899	−	26.1498i	1.42882	−	0.918244i	0.428926	−	0.903339i	$-0.358892\pi$
$811$	40.6899	−	26.1498i	1.42882	−	0.918244i	0.999889	−	0.0149043i	$-0.00474437\pi$
$812$	12.9264	+	28.3049i	0.453628	+	0.993306i
$813$	6.17835	+	7.13020i	0.216684	+	0.250067i
$814$	0.00431021	+	0.0299782i	0.000151073	+	0.00105073i
$815$	−3.79007	+	8.29910i	−0.132760	+	0.290705i
$816$	10.5780	−	3.10597i	0.370303	−	0.108731i
$817$	5.23223	−	1.53632i	0.183053	−	0.0537491i
$818$	1.27802	−	2.79848i	0.0446851	−	0.0978466i
$819$	−3.30488	−	22.9860i	−0.115482	−	0.803195i
$820$	6.25511	+	7.21878i	0.218438	+	0.252091i
$821$	−4.37202	−	9.57340i	−0.152585	−	0.334114i	0.817868	−	0.575406i	$-0.195156\pi$
$821$	−4.37202	−	9.57340i	−0.152585	−	0.334114i	−0.970452	+	0.241292i	$0.922429\pi$
$822$	0.116461	−	0.0748449i	0.00406204	−	0.00261052i
$823$	−6.76894	+	47.0790i	−0.235950	+	1.64107i	0.435620	+	0.900131i	$0.356529\pi$
$823$	−6.76894	+	47.0790i	−0.235950	+	1.64107i	−0.671571	+	0.740940i	$0.734380\pi$
$824$	−11.5881	−	7.44724i	−0.403692	−	0.259437i
$825$	−2.86625	+	3.30783i	−0.0997899	+	0.115164i
$826$	−6.01917	−	1.76739i	−0.209434	−	0.0614953i
$827$	−52.9294			−1.84053			−0.920267	−	0.391291i	$-0.872029\pi$
$827$	−52.9294			−1.84053			−0.920267	+	0.391291i	$0.872029\pi$
$828$	−14.7133	+	21.2325i	−0.511323	+	0.737881i
$829$	12.4245			0.431522			0.215761	−	0.976446i	$-0.430777\pi$
$829$	12.4245			0.431522			0.215761	+	0.976446i	$0.430777\pi$
$830$	−1.01542	−	0.298153i	−0.0352456	−	0.0103490i
$831$	5.91401	−	6.82514i	0.205155	−	0.236761i
$832$	−18.5232	−	11.9041i	−0.642176	−	0.412701i
$833$	−0.461709	+	3.21126i	−0.0159973	+	0.111264i
$834$	0.208114	−	0.133747i	0.00720641	−	0.00463128i
$835$	1.10621	+	2.42226i	0.0382819	+	0.0838257i
$836$	18.1671	+	20.9660i	0.628323	+	0.725123i
$837$	−1.86500	−	12.9714i	−0.0644638	−	0.448356i
$838$	−2.88921	+	6.32649i	−0.0998061	+	0.218545i
$839$	41.9145	−	12.3072i	1.44705	−	0.424892i	0.538484	−	0.842636i	$-0.318997\pi$
$839$	41.9145	−	12.3072i	1.44705	−	0.424892i	0.908565	+	0.417744i	$0.137179\pi$
$840$	−1.65137	+	0.484887i	−0.0569778	+	0.0167302i
$841$	4.36870	−	9.56611i	0.150645	−	0.329866i
$842$	−0.750402	−	5.21916i	−0.0258606	−	0.179864i
$843$	−6.01890	−	6.94618i	−0.207302	−	0.239239i
$844$	6.46316	+	14.1523i	0.222471	+	0.487144i
$845$	−2.75529	+	1.77072i	−0.0947850	+	0.0609146i
$846$	0.318657	−	2.21631i	0.0109556	−	0.0761982i
$847$	−0.804712	−	0.517157i	−0.0276502	−	0.0177697i
$848$	16.1537	−	18.6424i	0.554722	−	0.640183i
$849$	−0.500874	−	0.147070i	−0.0171899	−	0.00504742i
$850$	4.02229			0.137963
$851$	−0.00633388	+	0.181999i	−0.000217123	+	0.00623884i
$852$	−3.80756			−0.130445
$853$	−28.6213	−	8.40397i	−0.979975	−	0.287746i	−0.247761	−	0.968821i	$-0.579695\pi$
$853$	−28.6213	−	8.40397i	−0.979975	−	0.287746i	−0.732214	+	0.681075i	$0.761513\pi$
$854$	1.41943	−	1.63810i	0.0485718	−	0.0560548i
$855$	14.9239	+	9.59098i	0.510385	+	0.328005i
$856$	−2.15120	+	14.9619i	−0.0735264	+	0.511387i
$857$	−5.53260	+	3.55559i	−0.188990	+	0.121457i	−0.631714	−	0.775201i	$-0.717648\pi$
$857$	−5.53260	+	3.55559i	−0.188990	+	0.121457i	0.442724	+	0.896658i	$0.354012\pi$
$858$	−0.522312	−	1.14370i	−0.0178314	−	0.0390454i
$859$	−12.0994	−	13.9634i	−0.412825	−	0.476425i	0.510813	−	0.859692i	$-0.329344\pi$
$859$	−12.0994	−	13.9634i	−0.412825	−	0.476425i	−0.923638	+	0.383267i	$0.874799\pi$
$860$	0.539647	+	3.75333i	0.0184018	+	0.127987i
$861$	−1.64455	+	3.60107i	−0.0560463	+	0.122724i
$862$	0.399693	−	0.117360i	0.0136136	−	0.00399731i
$863$	−28.3383	+	8.32088i	−0.964648	+	0.283246i	−0.725873	−	0.687829i	$-0.758564\pi$
$863$	−28.3383	+	8.32088i	−0.964648	+	0.283246i	−0.238775	+	0.971075i	$0.576746\pi$
$864$	−3.13715	+	6.86940i	−0.106728	+	0.233702i
$865$	2.19929	+	15.2964i	0.0747780	+	0.520093i
$866$	−2.13689	−	2.46610i	−0.0726144	−	0.0838014i
$867$	4.45602	+	9.75732i	0.151334	+	0.331376i
$868$	−19.7469	+	12.6906i	−0.670253	+	0.430746i
$869$	1.15295	−	8.01891i	0.0391110	−	0.272023i
$870$	0.906319	+	0.582456i	0.0307271	+	0.0197471i
$871$	14.7002	−	16.9650i	0.498099	−	0.574836i
$872$	13.4502	+	3.94932i	0.455480	+	0.133741i
$873$	29.4147			0.995538
$874$	−2.45221	−	4.12441i	−0.0829473	−	0.139510i
$875$	29.7079			1.00431
$876$	3.89607	+	1.14399i	0.131636	+	0.0386519i
$877$	−5.63716	+	6.50563i	−0.190353	+	0.219680i	−0.842902	−	0.538068i	$-0.819155\pi$
$877$	−5.63716	+	6.50563i	−0.190353	+	0.219680i	0.652548	+	0.757747i	$0.273700\pi$
$878$	1.43007	+	0.919049i	0.0482625	+	0.0310164i
$879$	0.950007	−	6.60744i	0.0320429	−	0.222864i
$880$	−15.7483	+	10.1208i	−0.530874	+	0.341172i
$881$	−2.08959	−	4.57555i	−0.0703999	−	0.154154i	0.871161	−	0.490998i	$-0.163368\pi$
$881$	−2.08959	−	4.57555i	−0.0703999	−	0.154154i	−0.941561	+	0.336844i	$0.890641\pi$
$882$	−0.221769	−	0.255935i	−0.00746736	−	0.00861779i
$883$	3.07912	+	21.4157i	0.103621	+	0.720696i	0.973708	+	0.227799i	$0.0731530\pi$
$883$	3.07912	+	21.4157i	0.103621	+	0.720696i	−0.870088	+	0.492897i	$0.835938\pi$
$884$	16.6866	−	36.5386i	0.561231	−	1.22892i
$885$	7.24477	−	2.12726i	0.243530	−	0.0715070i
$886$	5.30753	−	1.55843i	0.178310	−	0.0523565i
$887$	11.4298	−	25.0277i	0.383774	−	0.840349i	−0.614887	−	0.788616i	$-0.710798\pi$
$887$	11.4298	−	25.0277i	0.383774	−	0.840349i	0.998661	−	0.0517330i	$-0.0164745\pi$
$888$	0.00241375	+	0.0167880i	8.10002e−5	+	0.000563369i
$889$	17.4136	+	20.0963i	0.584032	+	0.674009i
$890$	1.83761	+	4.02381i	0.0615969	+	0.134878i
$891$	−19.8291	+	12.7434i	−0.664301	+	0.426920i
$892$	7.89152	−	54.8867i	0.264228	−	1.83774i
$893$	−12.1635	−	7.81701i	−0.407036	−	0.261586i
$894$	0.307019	−	0.354318i	0.0102682	−	0.0118502i
$895$	14.9639	+	4.39380i	0.500188	+	0.146868i
$896$	17.9435			0.599451
$897$	−1.87636	−	7.32361i	−0.0626497	−	0.244528i
$898$	1.59684			0.0532871
$899$	28.6020	+	8.39831i	0.953930	+	0.280099i
$900$	9.55840	−	11.0310i	0.318613	−	0.367699i
$901$	35.5150	+	22.8241i	1.18318	+	0.760382i
$902$	0.368526	−	2.56315i	0.0122706	−	0.0853436i
$903$	−1.32211	+	0.849668i	−0.0439970	+	0.0282752i
$904$	0.447689	+	0.980303i	0.0148899	+	0.0326044i
$905$	−9.20809	−	10.6267i	−0.306087	−	0.353243i
$906$	0.109530	+	0.761797i	0.00363888	+	0.0253090i
$907$	0.791937	−	1.73410i	0.0262959	−	0.0575799i	−0.896028	−	0.443997i	$-0.853560\pi$
$907$	0.791937	−	1.73410i	0.0262959	−	0.0575799i	0.922324	+	0.386417i	$0.126287\pi$
$908$	−17.5026	+	5.13922i	−0.580843	+	0.170551i
$909$	24.4549	−	7.18062i	0.811119	−	0.238166i
$910$	−1.24604	+	2.72845i	−0.0413059	+	0.0904472i
$911$	5.36602	+	37.3215i	0.177784	+	1.23652i	0.861875	+	0.507120i	$0.169290\pi$
$911$	5.36602	+	37.3215i	0.177784	+	1.23652i	−0.684091	+	0.729397i	$0.739801\pi$
$912$	4.86633	+	5.61605i	0.161140	+	0.185966i
$913$	−4.14328	−	9.07253i	−0.137123	−	0.300257i
$914$	1.43731	−	0.923700i	0.0475418	−	0.0305533i
$915$	−0.371280	+	2.58231i	−0.0122741	+	0.0853686i
$916$	10.8806	+	6.99253i	0.359505	+	0.231040i
$917$	−25.3355	+	29.2387i	−0.836651	+	0.965546i
$918$	−3.93586	−	1.15567i	−0.129903	−	0.0381429i
$919$	−1.89744			−0.0625909			−0.0312955	−	0.999510i	$-0.509963\pi$
$919$	−1.89744			−0.0625909			−0.0312955	+	0.999510i	$0.509963\pi$
$920$	6.25156	−	2.59616i	0.206108	−	0.0855930i
$921$	−12.2741			−0.404446
$922$	7.30163	+	2.14395i	0.240466	+	0.0706073i
$923$	−8.81605	+	10.1743i	−0.290184	+	0.334890i
$924$	−6.72603	−	4.32256i	−0.221270	−	0.142202i
$925$	0.0146439	−	0.101851i	0.000481488	−	0.00334882i
$926$	−3.73491	+	2.40028i	−0.122737	+	0.0788781i
$927$	−16.9987	−	37.2219i	−0.558309	−	1.22253i
$928$	−11.2494	−	12.9825i	−0.369279	−	0.426171i
$929$	3.96319	+	27.5646i	0.130028	+	0.904366i	0.945512	+	0.325586i	$0.105562\pi$
$929$	3.96319	+	27.5646i	0.130028	+	0.904366i	−0.815484	+	0.578779i	$0.803529\pi$
$930$	−0.337608	+	0.739259i	−0.0110706	+	0.0242412i
$931$	−2.09823	+	0.616095i	−0.0687666	+	0.0201917i
$932$	−47.8256	+	14.0429i	−1.56658	+	0.459989i
$933$	−0.738788	+	1.61772i	−0.0241868	+	0.0529618i
$934$	−0.958311	−	6.66520i	−0.0313569	−	0.218092i
$935$	−20.9805	−	24.2128i	−0.686135	−	0.791843i
$936$	3.53373	+	7.73779i	0.115504	+	0.252918i
$937$	12.0534	−	7.74624i	0.393767	−	0.253059i	−0.328743	−	0.944420i	$-0.606625\pi$
$937$	12.0534	−	7.74624i	0.393767	−	0.253059i	0.722510	+	0.691361i	$0.242989\pi$
$938$	−0.584360	+	4.06432i	−0.0190800	+	0.132705i
$939$	6.33663	+	4.07230i	0.206788	+	0.132895i
$940$	6.58408	−	7.59844i	0.214749	−	0.247834i
$941$	33.6359	+	9.87638i	1.09650	+	0.321961i	0.779460	−	0.626452i	$-0.215494\pi$
$941$	33.6359	+	9.87638i	1.09650	+	0.321961i	0.317038	+	0.948413i	$0.397312\pi$
$942$	1.10273			0.0359290
$943$	4.90365	−	14.7781i	0.159685	−	0.481241i
$944$	−38.2113			−1.24367
$945$	−10.2172	−	3.00005i	−0.332366	−	0.0975915i
$946$	0.673195	−	0.776908i	0.0218874	−	0.0252595i
$947$	−6.65862	−	4.27924i	−0.216376	−	0.139057i	0.427963	−	0.903796i	$-0.359231\pi$
$947$	−6.65862	−	4.27924i	−0.216376	−	0.139057i	−0.644339	+	0.764740i	$0.722868\pi$
$948$	0.318252	−	2.21349i	0.0103363	−	0.0718908i
$949$	12.0779	−	7.76199i	0.392065	−	0.251965i
$950$	1.12628	+	2.46622i	0.0365415	+	0.0800147i
$951$	1.03645	+	1.19612i	0.0336091	+	0.0387870i
$952$	2.12140	+	14.7547i	0.0687550	+	0.478202i
$953$	7.32967	−	16.0497i	0.237431	−	0.519902i	−0.752982	−	0.658042i	$-0.771385\pi$
$953$	7.32967	−	16.0497i	0.237431	−	0.519902i	0.990413	+	0.138140i	$0.0441123\pi$
$954$	−4.22825	+	1.24153i	−0.136895	+	0.0401959i
$955$	29.8106	−	8.75317i	0.964647	−	0.283246i
$956$	1.23732	−	2.70935i	0.0400178	−	0.0876267i
$957$	1.44499	+	10.0501i	0.0467099	+	0.324875i
$958$	−0.732097	−	0.844885i	−0.0236530	−	0.0272970i
$959$	−1.29300	−	2.83128i	−0.0417532	−	0.0914267i
$960$	−4.07811	+	2.62084i	−0.131620	+	0.0845872i
$961$	1.21153	−	8.42636i	0.0390816	−	0.271818i
$962$	0.0248666	+	0.0159808i	0.000801731	+	0.000515241i
$963$	−29.4052	+	33.9354i	−0.947570	+	1.09355i
$964$	−52.0533	−	15.2842i	−1.67652	−	0.492272i
$965$	−20.7880			−0.669190
$966$	1.01298	+	0.941399i	0.0325923	+	0.0302890i
$967$	−18.1226			−0.582785			−0.291392	−	0.956604i	$-0.594119\pi$
$967$	−18.1226			−0.582785			−0.291392	+	0.956604i	$0.594119\pi$
$968$	0.336202	+	0.0987179i	0.0108060	+	0.00317291i
$969$	−8.32843	+	9.61152i	−0.267548	+	0.308766i
$970$	−3.19622	−	2.05408i	−0.102624	−	0.0659526i
$971$	1.50925	−	10.4971i	0.0484342	−	0.336867i	−0.951168	−	0.308673i	$-0.900115\pi$
$971$	1.50925	−	10.4971i	0.0484342	−	0.336867i	0.999602	−	0.0281944i	$-0.00897575\pi$
$972$	−19.0324	+	12.2314i	−0.610465	+	0.392322i
$973$	−2.31058	−	5.05946i	−0.0740737	−	0.162199i
$974$	−4.90544	−	5.66117i	−0.157180	−	0.181396i
$975$	0.607933	+	4.22827i	0.0194694	+	0.135413i
$976$	5.48457	−	12.0095i	0.175557	−	0.384416i
$977$	−6.30869	+	1.85240i	−0.201833	+	0.0592635i	−0.381086	−	0.924539i	$-0.624450\pi$
$977$	−6.30869	+	1.85240i	−0.201833	+	0.0592635i	0.179253	+	0.983803i	$0.442632\pi$
$978$	0.655090	−	0.192352i	0.0209475	−	0.00615073i
$979$	−17.3187	+	37.9226i	−0.553507	+	1.21201i
$980$	−0.216409	−	1.50516i	−0.00691294	−	0.0480805i
$981$	27.2697	+	31.4709i	0.870654	+	1.00479i
$982$	−0.707187	−	1.54852i	−0.0225672	−	0.0494154i
$983$	36.7725	−	23.6323i	1.17286	−	0.753752i	0.198800	−	0.980040i	$-0.436295\pi$
$983$	36.7725	−	23.6323i	1.17286	−	0.753752i	0.974060	+	0.226288i	$0.0726591\pi$
$984$	0.206377	−	1.43538i	0.00657906	−	0.0457584i
$985$	2.92741	+	1.88133i	0.0932751	+	0.0599443i
$986$	6.11044	−	7.05183i	0.194596	−	0.224576i
$987$	3.99824	+	1.17399i	0.127265	+	0.0373685i
$988$	27.0756			0.861390
$989$	4.80942	−	3.88292i	0.152931	−	0.123470i
$990$	3.34426			0.106288
$991$	−52.0340	−	15.2786i	−1.65291	−	0.485339i	−0.683333	−	0.730107i	$-0.739470\pi$
$991$	−52.0340	−	15.2786i	−1.65291	−	0.485339i	−0.969582	+	0.244768i	$0.921288\pi$
$992$	8.48604	−	9.79341i	0.269432	−	0.310941i
$993$	3.22322	+	2.07144i	0.102286	+	0.0657351i
$994$	0.350454	−	2.43746i	0.0111157	−	0.0773115i
$995$	2.17781	−	1.39959i	0.0690412	−	0.0443701i
$996$	−1.14369	−	2.50432i	−0.0362391	−	0.0793525i
$997$	−0.450373	−	0.519758i	−0.0142635	−	0.0164609i	0.748573	−	0.663052i	$-0.230739\pi$
$997$	−0.450373	−	0.519758i	−0.0142635	−	0.0164609i	−0.762836	+	0.646591i	$0.776194\pi$
$998$	0.767096	+	5.33527i	0.0242820	+	0.168885i
$999$	−0.0435926	+	0.0954544i	−0.00137921	+	0.00302004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.2.c.a.18.1	yes	10
3.2	odd	2		207.2.i.c.64.1		10
4.3	odd	2		368.2.m.c.225.1		10
5.2	odd	4		575.2.p.b.524.2		20
5.3	odd	4		575.2.p.b.524.1		20
5.4	even	2		575.2.k.b.501.1		10
23.2	even	11		529.2.c.d.118.1		10
23.3	even	11		529.2.a.i.1.2		5
23.4	even	11		529.2.c.b.334.1		10
23.5	odd	22		529.2.c.f.266.1		10
23.6	even	11		529.2.c.i.487.1		10
23.7	odd	22		529.2.c.e.399.1		10
23.8	even	11		529.2.c.b.255.1		10
23.9	even	11	inner	23.2.c.a.9.1	✓	10
23.10	odd	22		529.2.c.h.466.1		10
23.11	odd	22		529.2.c.f.177.1		10
23.12	even	11		529.2.c.g.177.1		10
23.13	even	11		529.2.c.i.466.1		10
23.14	odd	22		529.2.c.a.170.1		10
23.15	odd	22		529.2.c.c.255.1		10
23.16	even	11		529.2.c.d.399.1		10
23.17	odd	22		529.2.c.h.487.1		10
23.18	even	11		529.2.c.g.266.1		10
23.19	odd	22		529.2.c.c.334.1		10
23.20	odd	22		529.2.a.j.1.2		5
23.21	odd	22		529.2.c.e.118.1		10
23.22	odd	2		529.2.c.a.501.1		10
69.20	even	22		4761.2.a.bn.1.4		5
69.26	odd	22		4761.2.a.bo.1.4		5
69.32	odd	22		207.2.i.c.55.1		10
92.3	odd	22		8464.2.a.bs.1.3		5
92.43	even	22		8464.2.a.bt.1.3		5
92.55	odd	22		368.2.m.c.193.1		10
115.9	even	22		575.2.k.b.101.1		10
115.32	odd	44		575.2.p.b.124.1		20
115.78	odd	44		575.2.p.b.124.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.9.1	✓	10	23.9	even	11	inner
23.2.c.a.18.1	yes	10	1.1	even	1	trivial
207.2.i.c.55.1		10	69.32	odd	22
207.2.i.c.64.1		10	3.2	odd	2
368.2.m.c.193.1		10	92.55	odd	22
368.2.m.c.225.1		10	4.3	odd	2
529.2.a.i.1.2		5	23.3	even	11
529.2.a.j.1.2		5	23.20	odd	22
529.2.c.a.170.1		10	23.14	odd	22
529.2.c.a.501.1		10	23.22	odd	2
529.2.c.b.255.1		10	23.8	even	11
529.2.c.b.334.1		10	23.4	even	11
529.2.c.c.255.1		10	23.15	odd	22
529.2.c.c.334.1		10	23.19	odd	22
529.2.c.d.118.1		10	23.2	even	11
529.2.c.d.399.1		10	23.16	even	11
529.2.c.e.118.1		10	23.21	odd	22
529.2.c.e.399.1		10	23.7	odd	22
529.2.c.f.177.1		10	23.11	odd	22
529.2.c.f.266.1		10	23.5	odd	22
529.2.c.g.177.1		10	23.12	even	11
529.2.c.g.266.1		10	23.18	even	11
529.2.c.h.466.1		10	23.10	odd	22
529.2.c.h.487.1		10	23.17	odd	22
529.2.c.i.466.1		10	23.13	even	11
529.2.c.i.487.1		10	23.6	even	11
575.2.k.b.101.1		10	115.9	even	22
575.2.k.b.501.1		10	5.4	even	2
575.2.p.b.124.1		20	115.32	odd	44
575.2.p.b.124.2		20	115.78	odd	44
575.2.p.b.524.1		20	5.3	odd	4
575.2.p.b.524.2		20	5.2	odd	4
4761.2.a.bn.1.4		5	69.20	even	22
4761.2.a.bo.1.4		5	69.26	odd	22
8464.2.a.bs.1.3		5	92.3	odd	22
8464.2.a.bt.1.3		5	92.43	even	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.226900 - 0.0666238i) q^{2} +(-0.313607 + 0.361922i) q^{3} +(-1.63546 - 1.05105i) q^{4} +(-0.215370 + 1.49793i) q^{5} +(0.0952700 - 0.0612263i) q^{6} +(-1.05773 - 2.31611i) q^{7} +(0.610783 + 0.704881i) q^{8} +(0.394306 + 2.74246i) q^{9} +O(q^{10})\)	\(q+(-0.226900 - 0.0666238i) q^{2} +(-0.313607 + 0.361922i) q^{3} +(-1.63546 - 1.05105i) q^{4} +(-0.215370 + 1.49793i) q^{5} +(0.0952700 - 0.0612263i) q^{6} +(-1.05773 - 2.31611i) q^{7} +(0.610783 + 0.704881i) q^{8} +(0.394306 + 2.74246i) q^{9} +(0.148666 - 0.325532i) q^{10} +(3.23616 - 0.950224i) q^{11} +(0.893290 - 0.262294i) q^{12} +(1.36745 - 2.99430i) q^{13} +(0.0856910 + 0.595994i) q^{14} +(-0.474593 - 0.547710i) q^{15} +(1.52357 + 3.33616i) q^{16} +(-5.28043 + 3.39353i) q^{17} +(0.0932451 - 0.648534i) q^{18} +(-3.55928 - 2.28741i) q^{19} +(1.92663 - 2.22345i) q^{20} +(1.16996 + 0.343532i) q^{21} -0.797593 q^{22} +(-4.72041 - 0.847210i) q^{23} -0.446658 q^{24} +(2.60004 + 0.763442i) q^{25} +(-0.509766 + 0.588302i) q^{26} +(-2.32482 - 1.49407i) q^{27} +(-0.704460 + 4.89963i) q^{28} +(5.28830 - 3.39858i) q^{29} +(0.0711946 + 0.155895i) q^{30} +(3.10538 + 3.58380i) q^{31} +(-0.388902 - 2.70488i) q^{32} +(-0.670978 + 1.46924i) q^{33} +(1.42422 - 0.418188i) q^{34} +(3.69718 - 1.08559i) q^{35} +(2.23758 - 4.89963i) q^{36} +(-0.00540403 - 0.0375858i) q^{37} +(0.655203 + 0.756145i) q^{38} +(0.654861 + 1.43394i) q^{39} +(-1.18741 + 0.763102i) q^{40} +(-0.462048 + 3.21361i) q^{41} +(-0.242577 - 0.155895i) q^{42} +(-0.844033 + 0.974066i) q^{43} +(-6.29135 - 1.84731i) q^{44} -4.19295 q^{45} +(1.01462 + 0.506723i) q^{46} +3.41741 q^{47} +(-1.68523 - 0.494829i) q^{48} +(0.338474 - 0.390620i) q^{49} +(-0.539086 - 0.346450i) q^{50} +(0.427789 - 2.97534i) q^{51} +(-5.38357 + 3.45981i) q^{52} +(-2.79399 - 6.11799i) q^{53} +(0.427961 + 0.493893i) q^{54} +(0.726398 + 5.05221i) q^{55} +(0.986535 - 2.16021i) q^{56} +(1.94408 - 0.570833i) q^{57} +(-1.42634 + 0.418811i) q^{58} +(-4.32805 + 9.47711i) q^{59} +(0.200510 + 1.39458i) q^{60} +(-2.35737 - 2.72055i) q^{61} +(-0.465844 - 1.02006i) q^{62} +(5.93476 - 3.81404i) q^{63} +(0.951939 - 6.62088i) q^{64} +(4.19075 + 2.69323i) q^{65} +(0.250131 - 0.288666i) q^{66} +(6.54316 + 1.92124i) q^{67} +12.2027 q^{68} +(1.78698 - 1.44273i) q^{69} -0.911214 q^{70} +(-3.92408 - 1.15221i) q^{71} +(-1.69227 + 1.95299i) q^{72} +(3.66912 + 2.35800i) q^{73} +(-0.00127794 + 0.00888826i) q^{74} +(-1.09170 + 0.701592i) q^{75} +(3.41689 + 7.48194i) q^{76} +(-5.62381 - 6.49022i) q^{77} +(-0.0530529 - 0.368991i) q^{78} +(0.997820 - 2.18492i) q^{79} +(-5.32548 + 1.56370i) q^{80} +(-6.70548 + 1.96891i) q^{81} +(0.318941 - 0.698384i) q^{82} +(-0.420847 - 2.92705i) q^{83} +(-1.55236 - 1.79152i) q^{84} +(-3.94603 - 8.64060i) q^{85} +(0.256407 - 0.164783i) q^{86} +(-0.428426 + 2.97977i) q^{87} +(2.64639 + 1.70073i) q^{88} +(-8.09455 + 9.34161i) q^{89} +(0.951379 + 0.279350i) q^{90} -8.38151 q^{91} +(6.82959 + 6.34695i) q^{92} -2.27092 q^{93} +(-0.775410 - 0.227681i) q^{94} +(4.19295 - 4.83892i) q^{95} +(1.10092 + 0.707516i) q^{96} +(1.51088 - 10.5084i) q^{97} +(-0.102824 + 0.0660811i) q^{98} +(3.88199 + 8.50038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Introduction

L-functions

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