LMFDB - Embedded newform 49.2.e.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			43.1
Root			$-0.988831 - 0.149042i$ of defining polynomial
Character	$\chi$	$=$	49.43
Dual form			49.2.e.b.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19158 + 1.49419i) q^{2} +(1.55929 + 0.750915i) q^{3} +(-0.367711 - 1.61105i) q^{4} +(-1.91647 - 0.922924i) q^{5} +(-2.98003 + 1.43511i) q^{6} +(1.91879 + 1.82161i) q^{7} +(-0.598393 - 0.288171i) q^{8} +(-0.00295512 - 0.00370560i) q^{9} +O(q^{10})$	\(q+(-1.19158 + 1.49419i) q^{2} +(1.55929 + 0.750915i) q^{3} +(-0.367711 - 1.61105i) q^{4} +(-1.91647 - 0.922924i) q^{5} +(-2.98003 + 1.43511i) q^{6} +(1.91879 + 1.82161i) q^{7} +(-0.598393 - 0.288171i) q^{8} +(-0.00295512 - 0.00370560i) q^{9} +(3.66265 - 1.76384i) q^{10} +(2.91390 - 3.65392i) q^{11} +(0.636391 - 2.78821i) q^{12} +(0.609562 - 0.764367i) q^{13} +(-5.00822 + 0.696449i) q^{14} +(-2.29530 - 2.87821i) q^{15} +(4.12128 - 1.98470i) q^{16} +(-0.463787 + 2.03198i) q^{17} +0.00905815 q^{18} -5.29116 q^{19} +(-0.782166 + 3.42689i) q^{20} +(1.62408 + 4.28126i) q^{21} +(1.98752 + 8.70788i) q^{22} +(0.841040 + 3.68484i) q^{23} +(-0.716677 - 0.898684i) q^{24} +(-0.296378 - 0.371646i) q^{25} +(0.415770 + 1.82161i) q^{26} +(-1.15716 - 5.06987i) q^{27} +(2.22914 - 3.76108i) q^{28} +(-1.23460 + 5.40913i) q^{29} +7.03564 q^{30} -10.1646 q^{31} +(-1.64972 + 7.22789i) q^{32} +(7.28741 - 3.50943i) q^{33} +(-2.48354 - 3.11426i) q^{34} +(-1.99609 - 5.26195i) q^{35} +(-0.00488327 + 0.00612343i) q^{36} +(0.384244 - 1.68348i) q^{37} +(6.30484 - 7.90601i) q^{38} +(1.52446 - 0.734141i) q^{39} +(0.880843 + 1.10454i) q^{40} +(3.19850 + 1.54031i) q^{41} +(-8.33225 - 2.67478i) q^{42} +(9.05500 - 4.36066i) q^{43} +(-6.95811 - 3.35085i) q^{44} +(0.00224341 + 0.00982903i) q^{45} +(-6.50803 - 3.13410i) q^{46} +(-2.69886 + 3.38427i) q^{47} +7.91661 q^{48} +(0.363490 + 6.99056i) q^{49} +0.908468 q^{50} +(-2.24902 + 2.82019i) q^{51} +(-1.45557 - 0.700967i) q^{52} +(1.15086 + 5.04225i) q^{53} +(8.95422 + 4.31212i) q^{54} +(-8.95670 + 4.31332i) q^{55} +(-0.623255 - 1.64298i) q^{56} +(-8.25045 - 3.97321i) q^{57} +(-6.61116 - 8.29014i) q^{58} +(4.68526 - 2.25630i) q^{59} +(-3.79293 + 4.75618i) q^{60} +(-0.994002 + 4.35501i) q^{61} +(12.1120 - 15.1879i) q^{62} +(0.00107991 - 0.0124933i) q^{63} +(-3.13007 - 3.92499i) q^{64} +(-1.87366 + 0.902307i) q^{65} +(-3.43976 + 15.0706i) q^{66} +0.482407 q^{67} +3.44416 q^{68} +(-1.45557 + 6.37728i) q^{69} +(10.2409 + 3.28748i) q^{70} +(-2.97959 - 13.0544i) q^{71} +(0.000700476 + 0.00306899i) q^{72} +(3.72027 + 4.66508i) q^{73} +(2.05759 + 2.58014i) q^{74} +(-0.183064 - 0.802058i) q^{75} +(1.94562 + 8.52430i) q^{76} +(12.2472 - 1.70311i) q^{77} +(-0.719566 + 3.15262i) q^{78} +5.75814 q^{79} -9.73004 q^{80} +(1.99952 - 8.76047i) q^{81} +(-6.11279 + 2.94377i) q^{82} +(1.84538 + 2.31404i) q^{83} +(6.30012 - 4.19073i) q^{84} +(2.76420 - 3.46620i) q^{85} +(-4.27409 + 18.7260i) q^{86} +(-5.98689 + 7.50732i) q^{87} +(-2.79661 + 1.34678i) q^{88} +(-7.03552 - 8.82227i) q^{89} +(-0.0173597 - 0.00835998i) q^{90} +(2.56200 - 0.356274i) q^{91} +(5.62718 - 2.70991i) q^{92} +(-15.8496 - 7.63277i) q^{93} +(-1.84084 - 8.06525i) q^{94} +(10.1403 + 4.88333i) q^{95} +(-7.99992 + 10.0316i) q^{96} -1.76250 q^{97} +(-10.8784 - 7.78668i) q^{98} -0.0221509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−1.19158	+	1.49419i	−0.842574	+	1.05655i	0.155067	+	0.987904i	$0.450441\pi$
$2$	−1.19158	+	1.49419i	−0.842574	+	1.05655i	−0.997641	+	0.0686506i	$0.978131\pi$
$3$	1.55929	+	0.750915i	0.900257	+	0.433541i	0.825982	−	0.563697i	$-0.190621\pi$
$3$	1.55929	+	0.750915i	0.900257	+	0.433541i	0.0742752	+	0.997238i	$0.476336\pi$
$4$	−0.367711	−	1.61105i	−0.183855	−	0.805523i
$5$	−1.91647	−	0.922924i	−0.857072	−	0.412744i	−0.0468741	−	0.998901i	$-0.514926\pi$
$5$	−1.91647	−	0.922924i	−0.857072	−	0.412744i	−0.810198	+	0.586157i	$0.800640\pi$
$6$	−2.98003	+	1.43511i	−1.21659	+	0.585880i
$7$	1.91879	+	1.82161i	0.725233	+	0.688503i
$7$	1.91879	+	1.82161i	0.725233	+	0.688503i
$8$	−0.598393	−	0.288171i	−0.211564	−	0.101884i
$9$	−0.00295512	−	0.00370560i	−0.000985040	−	0.00123520i
$10$	3.66265	−	1.76384i	1.15823	−	0.557776i
$11$	2.91390	−	3.65392i	0.878575	−	1.10170i	−0.115533	−	0.993304i	$-0.536858\pi$
$11$	2.91390	−	3.65392i	0.878575	−	1.10170i	0.994108	−	0.108395i	$-0.0345710\pi$
$12$	0.636391	−	2.78821i	0.183710	−	0.804887i
$13$	0.609562	−	0.764367i	0.169062	−	0.211997i	−0.690082	−	0.723732i	$-0.742425\pi$
$13$	0.609562	−	0.764367i	0.169062	−	0.211997i	0.859144	+	0.511734i	$0.170997\pi$
$14$	−5.00822	+	0.696449i	−1.33850	+	0.186134i
$15$	−2.29530	−	2.87821i	−0.592643	−	0.743151i
$16$	4.12128	−	1.98470i	1.03032	−	0.496176i
$17$	−0.463787	+	2.03198i	−0.112485	+	0.492828i	0.887031	+	0.461710i	$0.152764\pi$
$17$	−0.463787	+	2.03198i	−0.112485	+	0.492828i	−0.999516	+	0.0311182i	$0.990093\pi$
$18$	0.00905815			0.00213503
$19$	−5.29116			−1.21387			−0.606937	−	0.794750i	$-0.707602\pi$
$19$	−5.29116			−1.21387			−0.606937	+	0.794750i	$0.707602\pi$
$20$	−0.782166	+	3.42689i	−0.174898	+	0.766276i
$21$	1.62408	+	4.28126i	0.354402	+	0.934248i
$22$	1.98752	+	8.70788i	0.423740	+	1.85653i
$23$	0.841040	+	3.68484i	0.175369	+	0.768342i	0.983730	+	0.179654i	$0.0574979\pi$
$23$	0.841040	+	3.68484i	0.175369	+	0.768342i	−0.808361	+	0.588687i	$0.799645\pi$
$24$	−0.716677	−	0.898684i	−0.146291	−	0.183443i
$25$	−0.296378	−	0.371646i	−0.0592755	−	0.0743291i
$26$	0.415770	+	1.82161i	0.0815392	+	0.357247i
$27$	−1.15716	−	5.06987i	−0.222696	−	0.975697i
$28$	2.22914	−	3.76108i	0.421267	−	0.710777i
$29$	−1.23460	+	5.40913i	−0.229259	+	1.00445i	0.720987	+	0.692949i	$0.243689\pi$
$29$	−1.23460	+	5.40913i	−0.229259	+	1.00445i	−0.950246	+	0.311501i	$0.899168\pi$
$30$	7.03564			1.28453
$31$	−10.1646			−1.82562			−0.912811	−	0.408383i	$-0.866093\pi$
$31$	−10.1646			−1.82562			−0.912811	+	0.408383i	$0.866093\pi$
$32$	−1.64972	+	7.22789i	−0.291632	+	1.27772i
$33$	7.28741	−	3.50943i	1.26857	−	0.610913i
$34$	−2.48354	−	3.11426i	−0.425923	−	0.534091i
$35$	−1.99609	−	5.26195i	−0.337402	−	0.889432i
$36$	−0.00488327	+	0.00612343i	−0.000813879	+	0.00102057i
$37$	0.384244	−	1.68348i	0.0631693	−	0.276763i	−0.933472	−	0.358649i	$-0.883237\pi$
$37$	0.384244	−	1.68348i	0.0631693	−	0.276763i	0.996642	+	0.0818866i	$0.0260945\pi$
$38$	6.30484	−	7.90601i	1.02278	−	1.28252i
$39$	1.52446	−	0.734141i	0.244109	−	0.117557i
$40$	0.880843	+	1.10454i	0.139273	+	0.174643i
$41$	3.19850	+	1.54031i	0.499521	+	0.240557i	0.666640	−	0.745380i	$-0.267732\pi$
$41$	3.19850	+	1.54031i	0.499521	+	0.240557i	−0.167119	+	0.985937i	$0.553446\pi$
$42$	−8.33225	−	2.67478i	−1.28569	−	0.412728i
$43$	9.05500	−	4.36066i	1.38087	−	0.664994i	0.411688	−	0.911325i	$-0.364939\pi$
$43$	9.05500	−	4.36066i	1.38087	−	0.664994i	0.969186	+	0.246331i	$0.0792249\pi$
$44$	−6.95811	−	3.35085i	−1.04897	−	0.505159i
$45$	0.00224341	+	0.00982903i	0.000334428	+	0.00146523i
$46$	−6.50803	−	3.13410i	−0.959556	−	0.462098i
$47$	−2.69886	+	3.38427i	−0.393670	+	0.493646i	−0.938683	−	0.344781i	$-0.887953\pi$
$47$	−2.69886	+	3.38427i	−0.393670	+	0.493646i	0.545014	+	0.838427i	$0.316525\pi$
$48$	7.91661			1.14266
$49$	0.363490	+	6.99056i	0.0519272	+	0.998651i
$50$	0.908468			0.128477
$51$	−2.24902	+	2.82019i	−0.314926	+	0.394905i
$52$	−1.45557	−	0.700967i	−0.201852	−	0.0972066i
$53$	1.15086	+	5.04225i	0.158083	+	0.692607i	0.990391	+	0.138294i	$0.0441618\pi$
$53$	1.15086	+	5.04225i	0.158083	+	0.692607i	−0.832308	+	0.554313i	$0.812981\pi$
$54$	8.95422	+	4.31212i	1.21851	+	0.586806i
$55$	−8.95670	+	4.31332i	−1.20772	+	0.581608i
$56$	−0.623255	−	1.64298i	−0.0832859	−	0.219552i
$57$	−8.25045	−	3.97321i	−1.09280	−	0.526264i
$58$	−6.61116	−	8.29014i	−0.868088	−	1.08855i
$59$	4.68526	−	2.25630i	0.609969	−	0.293746i	−0.103284	−	0.994652i	$-0.532935\pi$
$59$	4.68526	−	2.25630i	0.609969	−	0.293746i	0.713253	+	0.700906i	$0.247221\pi$
$60$	−3.79293	+	4.75618i	−0.489665	+	0.614020i
$61$	−0.994002	+	4.35501i	−0.127269	+	0.557602i	0.870579	+	0.492029i	$0.163745\pi$
$61$	−0.994002	+	4.35501i	−0.127269	+	0.557602i	−0.997848	+	0.0655728i	$0.979113\pi$
$62$	12.1120	−	15.1879i	1.53822	−	1.92887i
$63$	0.00107991	−	0.0124933i	0.000136056	−	0.00157401i
$64$	−3.13007	−	3.92499i	−0.391259	−	0.490623i
$65$	−1.87366	+	0.902307i	−0.232399	+	0.111917i
$66$	−3.43976	+	15.0706i	−0.423405	+	1.85506i
$67$	0.482407			0.0589354			0.0294677	−	0.999566i	$-0.490619\pi$
$67$	0.482407			0.0589354			0.0294677	+	0.999566i	$0.490619\pi$
$68$	3.44416			0.417666
$69$	−1.45557	+	6.37728i	−0.175230	+	0.767734i
$70$	10.2409	+	3.28748i	1.22402	+	0.392929i
$71$	−2.97959	−	13.0544i	−0.353612	−	1.54927i	−0.768770	−	0.639525i	$-0.779131\pi$
$71$	−2.97959	−	13.0544i	−0.353612	−	1.54927i	0.415158	−	0.909749i	$-0.363726\pi$
$72$	0.000700476		0.00306899i	8.25519e−5		0.000361684i
$73$	3.72027	+	4.66508i	0.435425	+	0.546006i	0.950331	−	0.311241i	$-0.100745\pi$
$73$	3.72027	+	4.66508i	0.435425	+	0.546006i	−0.514906	+	0.857247i	$0.672173\pi$
$74$	2.05759	+	2.58014i	0.239190	+	0.299935i
$75$	−0.183064	−	0.802058i	−0.0211385	−	0.0926137i
$76$	1.94562	+	8.52430i	0.223177	+	0.977804i
$77$	12.2472	−	1.70311i	1.39569	−	0.194087i
$78$	−0.719566	+	3.15262i	−0.0814748	+	0.356964i
$79$	5.75814			0.647842			0.323921	−	0.946084i	$-0.394999\pi$
$79$	5.75814			0.647842			0.323921	+	0.946084i	$0.394999\pi$
$80$	−9.73004			−1.08785
$81$	1.99952	−	8.76047i	0.222169	−	0.973385i
$82$	−6.11279	+	2.94377i	−0.675045	+	0.325085i
$83$	1.84538	+	2.31404i	0.202557	+	0.253999i	0.872726	−	0.488210i	$-0.162350\pi$
$83$	1.84538	+	2.31404i	0.202557	+	0.253999i	−0.670169	+	0.742208i	$0.733778\pi$
$84$	6.30012	−	4.19073i	0.687400	−	0.457246i
$85$	2.76420	−	3.46620i	0.299819	−	0.375962i
$86$	−4.27409	+	18.7260i	−0.460887	+	2.01928i
$87$	−5.98689	+	7.50732i	−0.641862	+	0.804870i
$88$	−2.79661	+	1.34678i	−0.298120	+	0.143567i
$89$	−7.03552	−	8.82227i	−0.745764	−	0.935158i	0.253720	−	0.967278i	$-0.418346\pi$
$89$	−7.03552	−	8.82227i	−0.745764	−	0.935158i	−0.999484	+	0.0321193i	$0.989774\pi$
$90$	−0.0173597	−	0.00835998i	−0.00182987	−	0.000881220i
$91$	2.56200	−	0.356274i	0.268570	−	0.0373477i
$92$	5.62718	−	2.70991i	0.586674	−	0.282528i
$93$	−15.8496	−	7.63277i	−1.64353	−	0.791482i
$94$	−1.84084	−	8.06525i	−0.189868	−	0.831867i
$95$	10.1403	+	4.88333i	1.04038	+	0.501019i
$96$	−7.99992	+	10.0316i	−0.816489	+	1.02384i
$97$	−1.76250			−0.178955			−0.0894774	−	0.995989i	$-0.528520\pi$
$97$	−1.76250			−0.178955			−0.0894774	+	0.995989i	$0.528520\pi$
$98$	−10.8784	−	7.78668i	−1.09888	−	0.786573i
$99$	−0.0221509			−0.00222625
$100$	−0.489757	+	0.614136i	−0.0489757	+	0.0614136i
$101$	8.69076	+	4.18525i	0.864763	+	0.416448i	0.813036	−	0.582213i	$-0.197813\pi$
$101$	8.69076	+	4.18525i	0.864763	+	0.416448i	0.0517268	+	0.998661i	$0.483527\pi$
$102$	−1.53401	−	6.72096i	−0.151890	−	0.665474i
$103$	3.27642	+	1.57784i	0.322835	+	0.155469i	0.588281	−	0.808657i	$-0.299805\pi$
$103$	3.27642	+	1.57784i	0.322835	+	0.155469i	−0.265446	+	0.964126i	$0.585519\pi$
$104$	−0.585026	+	0.281734i	−0.0573665	+	0.0276262i
$105$	0.838785	−	9.70381i	0.0818571	−	0.946995i
$106$	−8.90544	−	4.28864i	−0.864973	−	0.416549i
$107$	−2.70861	−	3.39649i	−0.261851	−	0.328351i	0.633474	−	0.773764i	$-0.281628\pi$
$107$	−2.70861	−	3.39649i	−0.261851	−	0.328351i	−0.895325	+	0.445413i	$0.853057\pi$
$108$	−7.74229	+	3.72849i	−0.745002	+	0.358774i
$109$	0.600994	−	0.753622i	0.0575648	−	0.0721839i	−0.752216	−	0.658917i	$-0.771015\pi$
$109$	0.600994	−	0.753622i	0.0575648	−	0.0721839i	0.809780	+	0.586733i	$0.199586\pi$
$110$	4.22769	−	18.5227i	0.403094	−	1.76607i
$111$	1.86330	−	2.33650i	0.176856	−	0.221771i
$112$	11.5232	+	3.69913i	1.08884	+	0.349535i
$113$	2.34443	+	2.93983i	0.220546	+	0.276556i	0.879779	−	0.475383i	$-0.157690\pi$
$113$	2.34443	+	2.93983i	0.220546	+	0.276556i	−0.659233	+	0.751938i	$0.729119\pi$
$114$	15.7678	−	7.59338i	1.47679	−	0.711185i
$115$	1.78899	−	7.83810i	0.166825	−	0.730906i
$116$	9.16833			0.851258
$117$	−0.00463377			−0.000428392
$118$	−2.21151	+	9.68926i	−0.203586	+	0.891968i
$119$	−4.59138	+	3.05411i	−0.420892	+	0.279969i
$120$	0.544073	+	2.38374i	0.0496668	+	0.217605i
$121$	−2.41257	−	10.5701i	−0.219324	−	0.960922i
$122$	−5.32279	−	6.67457i	−0.481903	−	0.604287i
$123$	3.83074	+	4.80360i	0.345406	+	0.433126i
$124$	3.73764	+	16.3757i	0.335650	+	1.47058i
$125$	2.59164	+	11.3547i	0.231804	+	1.01560i
$126$	0.0173807	+	0.0165004i	0.00154839	+	0.00146997i
$127$	−2.19982	+	9.63803i	−0.195202	+	0.855237i	0.778542	+	0.627592i	$0.215960\pi$
$127$	−2.19982	+	9.63803i	−0.195202	+	0.855237i	−0.973744	+	0.227644i	$0.926898\pi$
$128$	−5.23312			−0.462546
$129$	17.3939			1.53144
$130$	0.884394	−	3.87478i	0.0775665	−	0.339841i
$131$	4.71300	−	2.26966i	0.411777	−	0.198301i	−0.216515	−	0.976279i	$-0.569469\pi$
$131$	4.71300	−	2.26966i	0.411777	−	0.198301i	0.628291	+	0.777978i	$0.283755\pi$
$132$	−8.33351	−	10.4499i	−0.725339	−	0.909547i
$133$	−10.1526	−	9.63841i	−0.880343	−	0.835756i
$134$	−0.574827	+	0.720810i	−0.0496575	+	0.0622685i
$135$	−2.46143	+	10.7842i	−0.211846	+	0.928158i
$136$	0.863085	−	1.08227i	0.0740089	−	0.0928043i
$137$	−16.5738	+	7.98152i	−1.41600	+	0.681907i	−0.976336	−	0.216258i	$-0.930615\pi$
$137$	−16.5738	+	7.98152i	−1.41600	+	0.681907i	−0.439659	+	0.898165i	$0.644901\pi$
$138$	−7.79446	−	9.77395i	−0.663509	−	0.832014i
$139$	6.39270	+	3.07856i	0.542222	+	0.261120i	0.684885	−	0.728651i	$-0.259852\pi$
$139$	6.39270	+	3.07856i	0.542222	+	0.261120i	−0.142663	+	0.989771i	$0.545567\pi$
$140$	−7.74326	+	5.15068i	−0.654425	+	0.435312i
$141$	−6.74961	+	3.25044i	−0.568419	+	0.273736i
$142$	23.0562	+	11.1033i	1.93484	+	0.931768i
$143$	−1.01673	−	4.45458i	−0.0850232	−	0.372511i
$144$	−0.0195334	−	0.00940679i	−0.00162778	−	0.000783899i
$145$	7.35828	−	9.22699i	0.611072	−	0.766260i
$146$	−11.4035			−0.943763
$147$	−4.68252	+	11.1733i	−0.386208	+	0.921555i
$148$	−2.85346			−0.234553
$149$	4.38036	−	5.49280i	0.358853	−	0.449988i	−0.569331	−	0.822108i	$-0.692798\pi$
$149$	4.38036	−	5.49280i	0.358853	−	0.449988i	0.928184	+	0.372120i	$0.121369\pi$
$150$	1.41657	+	0.682182i	0.115662	+	0.0556999i
$151$	0.235312	+	1.03097i	0.0191494	+	0.0838990i	0.983600	−	0.180365i	$-0.0577280\pi$
$151$	0.235312	+	1.03097i	0.0191494	+	0.0838990i	−0.964450	+	0.264264i	$0.914871\pi$
$152$	3.16619	+	1.52476i	0.256812	+	0.123674i
$153$	0.00890027	−	0.00428615i	0.000719544	−	0.000346514i
$154$	−12.0487	+	20.3290i	−0.970913	+	1.63816i
$155$	19.4802	+	9.38118i	1.56469	+	0.753514i
$156$	−1.74329	−	2.18602i	−0.139575	−	0.175022i
$157$	−4.29325	+	2.06752i	−0.342639	+	0.165006i	−0.597287	−	0.802028i	$-0.703755\pi$
$157$	−4.29325	+	2.06752i	−0.342639	+	0.165006i	0.254648	+	0.967034i	$0.418040\pi$
$158$	−6.86129	+	8.60378i	−0.545855	+	0.684480i
$159$	−1.99177	+	8.72654i	−0.157958	+	0.692059i
$160$	9.83243	−	12.3295i	0.777322	−	0.974731i
$161$	−5.09855	+	8.60246i	−0.401822	+	0.677969i
$162$	10.7072	+	13.4265i	0.841241	+	1.05488i
$163$	1.28037	−	0.616592i	0.100286	−	0.0482953i	−0.383068	−	0.923720i	$-0.625133\pi$
$163$	1.28037	−	0.616592i	0.100286	−	0.0482953i	0.483354	+	0.875425i	$0.339418\pi$
$164$	1.30540	−	5.71932i	0.101934	−	0.446604i
$165$	−17.2050			−1.33941
$166$	−5.65654			−0.439033
$167$	2.71947	−	11.9148i	0.210439	−	0.921992i	−0.753831	−	0.657069i	$-0.771796\pi$
$167$	2.71947	−	11.9148i	0.210439	−	0.921992i	0.964269	−	0.264923i	$-0.0853466\pi$
$168$	0.261900	−	3.02989i	0.0202060	−	0.233761i
$169$	2.68008	+	11.7422i	0.206160	+	0.903247i
$170$	1.88540	+	8.26050i	0.144604	+	0.633551i
$171$	0.0156360	+	0.0196069i	0.00119572	+	0.00149938i
$172$	−10.3548	−	12.9846i	−0.789549	−	0.990064i
$173$	−0.820032	−	3.59280i	−0.0623459	−	0.273155i	0.934141	−	0.356904i	$-0.116168\pi$
$173$	−0.820032	−	3.59280i	−0.0623459	−	0.273155i	−0.996487	+	0.0837490i	$0.973311\pi$
$174$	−4.08354	−	17.8912i	−0.309572	−	1.35632i
$175$	0.108307	−	1.25299i	0.00818725	−	0.0947173i
$176$	4.75706	−	20.8421i	0.358577	−	1.57103i
$177$	8.99998			0.676480
$178$	21.5656			1.61641
$179$	3.19235	−	13.9866i	0.238607	−	1.04541i	−0.703657	−	0.710539i	$-0.748451\pi$
$179$	3.19235	−	13.9866i	0.238607	−	1.04541i	0.942265	−	0.334868i	$-0.108692\pi$
$180$	0.0150101	−	0.00722848i	0.00111879	−	0.000538779i
$181$	−16.5163	−	20.7108i	−1.22765	−	1.53942i	−0.750964	−	0.660343i	$-0.770411\pi$
$181$	−16.5163	−	20.7108i	−1.22765	−	1.53942i	−0.476682	−	0.879076i	$-0.658161\pi$
$182$	−2.52048	+	4.25265i	−0.186830	+	0.315227i
$183$	−4.82018	+	6.04431i	−0.356318	+	0.446808i
$184$	0.558590	−	2.44734i	0.0411798	−	0.180421i
$185$	−2.29012	+	2.87172i	−0.168373	+	0.211133i
$186$	30.2909	−	14.5873i	2.22104	−	1.06960i
$187$	6.07327	+	7.61564i	0.444122	+	0.556911i
$188$	6.44461	+	3.10356i	0.470022	+	0.226350i
$189$	7.01496	−	11.8359i	0.510263	−	0.860935i
$190$	−19.3797	+	9.33276i	−1.40595	+	0.677070i
$191$	8.11299	+	3.90701i	0.587036	+	0.282701i	0.703731	−	0.710466i	$-0.251516\pi$
$191$	8.11299	+	3.90701i	0.587036	+	0.282701i	−0.116696	+	0.993168i	$0.537230\pi$
$192$	−1.93336	−	8.47061i	−0.139528	−	0.611314i
$193$	−6.18362	−	2.97787i	−0.445107	−	0.214352i	0.197885	−	0.980225i	$-0.436593\pi$
$193$	−6.18362	−	2.97787i	−0.445107	−	0.214352i	−0.642992	+	0.765873i	$0.722307\pi$
$194$	2.10016	−	2.63352i	0.150783	−	0.189075i
$195$	−3.59914			−0.257739
$196$	11.1285	−	3.15610i	0.794889	−	0.225436i
$197$	11.3025			0.805273			0.402636	−	0.915360i	$-0.368094\pi$
$197$	11.3025			0.805273			0.402636	+	0.915360i	$0.368094\pi$
$198$	0.0263946	−	0.0330978i	0.00187578	−	0.00235216i
$199$	−12.7146	−	6.12302i	−0.901313	−	0.434050i	−0.0749503	−	0.997187i	$-0.523880\pi$
$199$	−12.7146	−	6.12302i	−0.901313	−	0.434050i	−0.826363	+	0.563138i	$0.809594\pi$
$200$	0.0702528	+	0.307798i	0.00496762	+	0.0217646i
$201$	0.752213	+	0.362247i	0.0530570	+	0.0255509i
$202$	−16.6093	+	7.99862i	−1.16863	+	0.562781i
$203$	−12.2222	+	8.13001i	−0.857833	+	0.570615i
$204$	5.37044	+	2.58627i	0.376006	+	0.181075i
$205$	−4.70823	−	5.90394i	−0.328837	−	0.412349i
$206$	−6.26171	+	3.01548i	−0.436274	+	0.210098i
$207$	0.0111692	−	0.0140057i	0.000776311	−	0.000973464i
$208$	0.995134	−	4.35997i	0.0690001	−	0.302309i
$209$	−15.4179	+	19.3335i	−1.06648	+	1.33732i
$210$	13.4999	+	12.8162i	0.931581	+	0.884400i
$211$	−10.5093	−	13.1783i	−0.723491	−	0.907229i	0.275039	−	0.961433i	$-0.411309\pi$
$211$	−10.5093	−	13.1783i	−0.723491	−	0.907229i	−0.998530	+	0.0542041i	$0.982738\pi$
$212$	7.70012	−	3.70818i	0.528846	−	0.254679i
$213$	5.15672	−	22.5930i	0.353332	−	1.54805i
$214$	8.30253			0.567549
$215$	−21.3782			−1.45798
$216$	−0.768549	+	3.36723i	−0.0522931	+	0.229111i
$217$	−19.5038	−	18.5160i	−1.32400	−	1.25695i
$218$	0.409926	+	1.79600i	0.0277637	+	0.121641i
$219$	2.29791	+	10.0678i	0.155279	+	0.680320i
$220$	10.2424	+	12.8436i	0.690545	+	0.865916i
$221$	1.27047	+	1.59312i	0.0854613	+	0.107165i
$222$	1.27092	+	5.56826i	0.0852985	+	0.373717i
$223$	3.67126	+	16.0848i	0.245846	+	1.07712i	0.935596	+	0.353073i	$0.114863\pi$
$223$	3.67126	+	16.0848i	0.245846	+	1.07712i	−0.689750	+	0.724048i	$0.742279\pi$
$224$	−16.3318	+	10.8636i	−1.09122	+	0.725858i
$225$	−0.000501340		0.00219652i	−3.34227e−5		0.000146434i
$226$	−7.18625			−0.478022
$227$	−3.54867			−0.235533			−0.117767	−	0.993041i	$-0.537573\pi$
$227$	−3.54867			−0.235533			−0.117767	+	0.993041i	$0.537573\pi$
$228$	−3.36724	+	14.7529i	−0.223001	+	0.977032i
$229$	12.8736	−	6.19958i	0.850708	−	0.409679i	0.0428678	−	0.999081i	$-0.486351\pi$
$229$	12.8736	−	6.19958i	0.850708	−	0.409679i	0.807840	+	0.589401i	$0.200636\pi$
$230$	9.57991	+	12.0128i	0.631680	+	0.792102i
$231$	20.3758	+	6.54095i	1.34063	+	0.430363i
$232$	2.29753	−	2.88101i	0.150840	−	0.189147i
$233$	−3.16168	+	13.8522i	−0.207129	+	0.907490i	0.759338	+	0.650697i	$0.225523\pi$
$233$	−3.16168	+	13.8522i	−0.207129	+	0.907490i	−0.966466	+	0.256793i	$0.917334\pi$
$234$	0.00552151	−	0.00692375i	0.000360952	−	0.000452620i
$235$	8.29571	−	3.99500i	0.541152	−	0.260605i
$236$	−5.35783	−	6.71851i	−0.348765	−	0.437338i
$237$	8.97862	+	4.32388i	0.583224	+	0.280866i
$238$	0.907575	−	10.4996i	0.0588293	−	0.680590i
$239$	−9.16287	+	4.41260i	−0.592697	+	0.285428i	−0.706090	−	0.708123i	$-0.749542\pi$
$239$	−9.16287	+	4.41260i	−0.592697	+	0.285428i	0.113393	+	0.993550i	$0.463828\pi$
$240$	−15.1720	−	7.30643i	−0.979345	−	0.471628i
$241$	5.88289	+	25.7746i	0.378950	+	1.66029i	0.700693	+	0.713463i	$0.252874\pi$
$241$	5.88289	+	25.7746i	0.378950	+	1.66029i	−0.321742	+	0.946827i	$0.604268\pi$
$242$	18.6686	+	8.99032i	1.20006	+	0.577920i
$243$	−0.0307105	+	0.0385097i	−0.00197008	+	0.00247040i
$244$	7.38163			0.472560
$245$	5.75513	−	13.7327i	0.367682	−	0.877348i
$246$	−11.7421			−0.748651
$247$	−3.22529	+	4.04438i	−0.205220	+	0.257338i
$248$	6.08244	+	2.92915i	0.386235	+	0.186001i
$249$	1.13984	+	4.99398i	0.0722347	+	0.316481i
$250$	−20.0543	−	9.65765i	−1.26835	−	0.610804i
$251$	21.9755	−	10.5828i	1.38708	−	0.667983i	0.416584	−	0.909097i	$-0.363227\pi$
$251$	21.9755	−	10.5828i	1.38708	−	0.667983i	0.970497	+	0.241114i	$0.0775128\pi$
$252$	−0.0205244	+	0.00285415i	−0.00129292	+	0.000179795i
$253$	15.9148	+	7.66417i	1.00056	+	0.481842i
$254$	−11.7798	−	14.7714i	−0.739132	−	0.926842i
$255$	6.91301	−	3.32913i	0.432909	−	0.208478i
$256$	12.4958	−	15.6693i	0.780989	−	0.979329i
$257$	0.364892	−	1.59870i	0.0227613	−	0.0997239i	−0.962271	−	0.272092i	$-0.912285\pi$
$257$	0.364892	−	1.59870i	0.0227613	−	0.0997239i	0.985033	+	0.172368i	$0.0551417\pi$
$258$	−20.7262	+	25.9898i	−1.29035	+	1.61805i
$259$	3.80392	−	2.53030i	0.236364	−	0.157225i
$260$	2.14262	+	2.68676i	0.132880	+	0.166626i
$261$	0.0236925	−	0.0114097i	0.00146653	−	0.000706242i
$262$	−2.22460	+	9.74662i	−0.137436	+	0.602148i
$263$	−15.0058			−0.925298			−0.462649	−	0.886541i	$-0.653101\pi$
$263$	−15.0058			−0.925298			−0.462649	+	0.886541i	$0.653101\pi$
$264$	−5.37205			−0.330627
$265$	2.44802	−	10.7255i	0.150381	−	0.658861i
$266$	26.4993	−	3.68502i	1.62478	−	0.225943i
$267$	−4.34565	−	19.0396i	−0.265950	−	1.16520i
$268$	−0.177386	−	0.777181i	−0.0108356	−	0.0474739i
$269$	−4.59665	−	5.76402i	−0.280263	−	0.351438i	0.621698	−	0.783257i	$-0.286443\pi$
$269$	−4.59665	−	5.76402i	−0.280263	−	0.351438i	−0.901960	+	0.431819i	$0.857872\pi$
$270$	−13.1807	−	16.5281i	−0.802154	−	1.00587i
$271$	−4.18240	−	18.3243i	−0.254063	−	1.11312i	−0.927484	−	0.373863i	$-0.878033\pi$
$271$	−4.18240	−	18.3243i	−0.254063	−	1.11312i	0.673421	−	0.739259i	$-0.264824\pi$
$272$	2.12149	+	9.29485i	0.128634	+	0.563583i
$273$	4.26243	+	1.36831i	0.257974	+	0.0828136i
$274$	7.82306	−	34.2751i	0.472609	−	2.07063i
$275$	−2.22158			−0.133966
$276$	10.8093			0.650645
$277$	−2.80568	+	12.2925i	−0.168577	+	0.738583i	0.817991	+	0.575231i	$0.195088\pi$
$277$	−2.80568	+	12.2925i	−0.168577	+	0.738583i	−0.986568	+	0.163352i	$0.947769\pi$
$278$	−12.2174	+	5.88358i	−0.732750	+	0.352874i
$279$	0.0300377	+	0.0376661i	0.00179831	+	0.00225501i
$280$	−0.321892	+	3.72393i	−0.0192367	+	0.222547i
$281$	−9.38338	+	11.7664i	−0.559766	+	0.701924i	−0.978514	−	0.206178i	$-0.933897\pi$
$281$	−9.38338	+	11.7664i	−0.559766	+	0.701924i	0.418749	+	0.908102i	$0.362469\pi$
$282$	3.18591	−	13.9584i	0.189718	−	0.831209i
$283$	−14.7939	+	18.5509i	−0.879404	+	1.10274i	0.114602	+	0.993412i	$0.463441\pi$
$283$	−14.7939	+	18.5509i	−0.879404	+	1.10274i	−0.994006	+	0.109326i	$0.965131\pi$
$284$	−19.9356	+	9.60050i	−1.18296	+	0.569685i
$285$	12.1448	+	15.2291i	0.719395	+	0.902092i
$286$	7.86752	+	3.78880i	0.465216	+	0.224036i
$287$	3.33139	+	8.78194i	0.196645	+	0.518382i
$288$	0.0316588	−	0.0152461i	0.00186551	−	0.000898384i
$289$	11.4026	+	5.49121i	0.670742	+	0.323012i
$290$	5.01894	+	21.9894i	0.294722	+	1.29126i
$291$	−2.74825	−	1.32349i	−0.161105	−	0.0775842i
$292$	6.14767	−	7.70893i	0.359765	−	0.451131i
$293$	−5.68397			−0.332061			−0.166031	−	0.986121i	$-0.553095\pi$
$293$	−5.68397			−0.332061			−0.166031	+	0.986121i	$0.553095\pi$
$294$	−11.1154	−	20.3104i	−0.648264	−	1.18453i
$295$	−11.0616			−0.644029
$296$	−0.715059	+	0.896656i	−0.0415620	+	0.0521170i
$297$	−21.8968	−	10.5449i	−1.27058	−	0.611879i
$298$	2.98776	+	13.0902i	0.173076	+	0.758296i
$299$	3.32923	+	1.60327i	0.192534	+	0.0927197i
$300$	−1.22484	+	0.589851i	−0.0707160	+	0.0340551i
$301$	25.3180	+	8.12748i	1.45931	+	0.468460i
$302$	−1.82086	−	0.876879i	−0.104779	−	0.0504587i
$303$	10.4087	+	13.0520i	0.597962	+	0.749820i
$304$	−21.8063	+	10.5014i	−1.25068	+	0.602295i
$305$	5.92432	−	7.42886i	0.339225	−	0.425375i
$306$	−0.00420105	+	0.0184060i	−0.000240158	+	0.00105220i
$307$	21.2853	−	26.6910i	1.21482	−	1.52333i	0.430991	−	0.902356i	$-0.358164\pi$
$307$	21.2853	−	26.6910i	1.21482	−	1.52333i	0.783828	−	0.620978i	$-0.213265\pi$
$308$	−7.24720	−	19.1045i	−0.412948	−	1.08858i
$309$	3.92406	+	4.92062i	0.223232	+	0.279924i
$310$	−37.2295	+	17.9288i	−2.11450	+	1.01829i
$311$	6.34876	−	27.8157i	0.360005	−	1.57729i	−0.393170	−	0.919466i	$-0.628622\pi$
$311$	6.34876	−	27.8157i	0.360005	−	1.57729i	0.753175	−	0.657820i	$-0.228521\pi$
$312$	−1.12378			−0.0636217
$313$	27.1423			1.53417			0.767086	−	0.641544i	$-0.221706\pi$
$313$	27.1423			1.53417			0.767086	+	0.641544i	$0.221706\pi$
$314$	2.02647	−	8.87856i	0.114361	−	0.501046i
$315$	−0.0136000	+	0.0229464i	−0.000766274	+	0.00129289i
$316$	−2.11733	−	9.27664i	−0.119109	−	0.521852i
$317$	−2.73357	−	11.9766i	−0.153533	−	0.672670i	−0.991842	−	0.127475i	$-0.959313\pi$
$317$	−2.73357	−	11.9766i	−0.153533	−	0.672670i	0.838309	−	0.545195i	$-0.183544\pi$
$318$	−10.6658	−	13.3745i	−0.598107	−	0.750003i
$319$	16.1670	+	20.2728i	0.905179	+	1.13506i
$320$	2.37623	+	10.4109i	0.132835	+	0.581989i
$321$	−1.67303	−	7.33004i	−0.0933797	−	0.409123i
$322$	−6.77842	−	17.8687i	−0.377746	−	0.995786i
$323$	2.45397	−	10.7515i	0.136542	−	0.598232i
$324$	−14.8488			−0.824931
$325$	−0.464734			−0.0257788
$326$	−0.604351	+	2.64784i	−0.0334719	+	0.146650i
$327$	1.50303	−	0.723821i	0.0831178	−	0.0400274i
$328$	−1.47008	−	1.84343i	−0.0811718	−	0.101786i
$329$	−11.3433	+	1.57742i	−0.625379	+	0.0869659i
$330$	20.5012	−	25.7077i	1.12855	−	1.41516i
$331$	3.95541	−	17.3298i	0.217409	−	0.952531i	−0.741975	−	0.670428i	$-0.766111\pi$
$331$	3.95541	−	17.3298i	0.217409	−	0.952531i	0.959384	−	0.282104i	$-0.0910322\pi$
$332$	3.04946	−	3.82390i	0.167361	−	0.209864i
$333$	−0.00737380	+	0.00355104i	−0.000404082	+	0.000194596i
$334$	14.5625	+	18.2608i	0.796825	+	0.999186i
$335$	−0.924520	−	0.445225i	−0.0505119	−	0.0243252i
$336$	15.1903	+	14.4210i	0.828699	+	0.786728i
$337$	−5.50487	+	2.65100i	−0.299869	+	0.144409i	−0.577768	−	0.816201i	$-0.696076\pi$
$337$	−5.50487	+	2.65100i	−0.299869	+	0.144409i	0.277899	+	0.960610i	$0.410362\pi$
$338$	−20.7387	−	9.98721i	−1.12803	−	0.543233i
$339$	1.44809	+	6.34451i	0.0786496	+	0.344587i
$340$	−6.60063	−	3.17870i	−0.357969	−	0.172389i
$341$	−29.6188	+	37.1407i	−1.60395	+	2.01128i
$342$	−0.0479281			−0.00259166
$343$	−12.0366	+	14.0755i	−0.649915	+	0.760007i
$344$	−6.67506			−0.359895
$345$	8.67531	−	10.8785i	0.467063	−	0.585678i
$346$	6.34547	+	3.05582i	0.341134	+	0.164282i
$347$	−4.43857	−	19.4467i	−0.238275	−	1.04395i	−0.942561	−	0.334035i	$-0.891590\pi$
$347$	−4.43857	−	19.4467i	−0.238275	−	1.04395i	0.704286	−	0.709917i	$-0.251267\pi$
$348$	14.2961	+	6.88464i	0.766351	+	0.369055i
$349$	18.1531	−	8.74208i	0.971714	−	0.467953i	0.120466	−	0.992717i	$-0.461561\pi$
$349$	18.1531	−	8.74208i	0.971714	−	0.467953i	0.851247	+	0.524765i	$0.175847\pi$
$350$	1.74316	+	1.65487i	0.0931757	+	0.0884567i
$351$	−4.58060	−	2.20590i	−0.244494	−	0.117742i
$352$	21.6030	+	27.0893i	1.15144	+	1.44387i
$353$	16.6881	−	8.03657i	0.888219	−	0.427744i	0.0665990	−	0.997780i	$-0.478785\pi$
$353$	16.6881	−	8.03657i	0.888219	−	0.427744i	0.821619	+	0.570036i	$0.193071\pi$
$354$	−10.7242	+	13.4477i	−0.569984	+	0.714738i
$355$	−6.33794	+	27.7683i	−0.336383	+	1.47379i
$356$	−11.6260	+	14.5786i	−0.616179	+	0.772664i
$357$	−9.45268	+	1.31450i	−0.500289	+	0.0695707i
$358$	17.0948	+	21.4361i	0.903486	+	1.13294i
$359$	14.2071	−	6.84178i	0.749823	−	0.361096i	−0.0196233	−	0.999807i	$-0.506247\pi$
$359$	14.2071	−	6.84178i	0.749823	−	0.361096i	0.769446	+	0.638712i	$0.220532\pi$
$360$	0.00149000	−	0.00652811i	7.85298e−5	−	0.000344062i
$361$	8.99635			0.473492
$362$	50.6264			2.66086
$363$	4.17538	−	18.2936i	0.219151	−	0.960162i
$364$	−1.51605	−	3.99649i	−0.0794625	−	0.209473i
$365$	−2.82429	−	12.3740i	−0.147830	−	0.647685i
$366$	−3.28775	−	14.4046i	−0.171853	−	0.752939i
$367$	−8.96933	−	11.2472i	−0.468195	−	0.587098i	0.490533	−	0.871423i	$-0.336802\pi$
$367$	−8.96933	−	11.2472i	−0.468195	−	0.587098i	−0.958728	+	0.284325i	$0.908231\pi$
$368$	10.7795	+	13.5170i	0.561918	+	0.704623i
$369$	−0.00374415	−	0.0164042i	−0.000194913	−	0.000853967i
$370$	−1.56204	−	6.84376i	−0.0812067	−	0.355790i
$371$	−6.97675	+	11.7714i	−0.362215	+	0.611142i
$372$	−6.46867	+	28.3411i	−0.335385	+	1.46942i
$373$	−3.94528			−0.204279			−0.102139	−	0.994770i	$-0.532569\pi$
$373$	−3.94528			−0.204279			−0.102139	+	0.994770i	$0.532569\pi$
$374$	−18.6160			−0.962612
$375$	−4.48531	+	19.6514i	−0.231620	+	1.01480i
$376$	2.59023	−	1.24739i	0.133581	−	0.0643291i
$377$	3.38199	+	4.24088i	0.174181	+	0.218417i
$378$	9.32624	+	24.5851i	0.479690	+	1.26452i
$379$	−16.6555	+	20.8853i	−0.855536	+	1.07281i	0.141030	+	0.990005i	$0.454959\pi$
$379$	−16.6555	+	20.8853i	−0.855536	+	1.07281i	−0.996566	+	0.0828026i	$0.973613\pi$
$380$	4.13856	−	18.1322i	0.212304	−	0.930164i
$381$	−10.6675	+	13.3766i	−0.546512	+	0.685305i
$382$	−15.5051	+	7.46687i	−0.793311	+	0.382038i
$383$	−0.425575	−	0.533654i	−0.0217459	−	0.0272685i	0.770840	−	0.637029i	$-0.219837\pi$
$383$	−0.425575	−	0.533654i	−0.0217459	−	0.0272685i	−0.792586	+	0.609761i	$0.791266\pi$
$384$	−8.15995	−	3.92962i	−0.416411	−	0.200533i
$385$	−25.0432	−	8.03925i	−1.27632	−	0.409718i
$386$	11.8178	−	5.69115i	0.601510	−	0.289672i
$387$	−0.0429175	−	0.0206680i	−0.00218162	−	0.00105061i
$388$	0.648090	+	2.83947i	0.0329018	+	0.144152i
$389$	−28.7060	−	13.8241i	−1.45545	−	0.700909i	−0.471920	−	0.881641i	$-0.656439\pi$
$389$	−28.7060	−	13.8241i	−1.45545	−	0.700909i	−0.983532	+	0.180733i	$0.942153\pi$
$390$	4.28866	−	5.37781i	0.217165	−	0.272316i
$391$	−7.87759			−0.398387
$392$	1.79696	−	4.28785i	0.0907604	−	0.216569i
$393$	9.05326			0.456677
$394$	−13.4679	+	16.8882i	−0.678502	+	0.850815i
$395$	−11.0353	−	5.31433i	−0.555247	−	0.267393i
$396$	0.00814513	+	0.0356862i	0.000409308	+	0.00179330i
$397$	7.06665	+	3.40312i	0.354665	+	0.170798i	0.602729	−	0.797946i	$-0.294080\pi$
$397$	7.06665	+	3.40312i	0.354665	+	0.170798i	−0.248064	+	0.968744i	$0.579794\pi$
$398$	24.2994	−	11.7020i	1.21802	−	0.586568i
$399$	−8.59324	−	22.6528i	−0.430200	−	1.13406i
$400$	−1.95906	−	0.943434i	−0.0979530	−	0.0471717i
$401$	12.3308	+	15.4624i	0.615773	+	0.772155i	0.987743	−	0.156090i	$-0.0498889\pi$
$401$	12.3308	+	15.4624i	0.615773	+	0.772155i	−0.371970	+	0.928245i	$0.621317\pi$
$402$	−1.43759	+	0.692306i	−0.0717004	+	0.0345291i
$403$	−6.19597	+	7.76950i	−0.308643	+	0.387027i
$404$	3.54694	−	15.5402i	0.176467	−	0.773153i
$405$	−11.9173	+	14.9438i	−0.592173	+	0.742562i
$406$	2.41596	−	27.9500i	0.119902	−	1.38713i
$407$	−5.03166	−	6.30950i	−0.249410	−	0.312750i
$408$	2.15850	−	1.03948i	0.106861	−	0.0514618i
$409$	−2.02120	+	8.85546i	−0.0999419	+	0.437874i	0.900056	+	0.435775i	$0.143525\pi$
$409$	−2.02120	+	8.85546i	−0.0999419	+	0.437874i	−0.999998	+	0.00209968i	$0.999332\pi$
$410$	14.4319			0.712739
$411$	−31.8368			−1.57039
$412$	1.33720	−	5.85865i	0.0658790	−	0.288635i
$413$	13.1001	+	4.20534i	0.644615	+	0.206931i
$414$	0.00761827	+	0.0333778i	0.000374418	+	0.00164043i
$415$	−1.40094	−	6.13794i	−0.0687696	−	0.301299i
$416$	4.51915	+	5.66684i	0.221570	+	0.277840i
$417$	7.65634	+	9.60075i	0.374933	+	0.470151i
$418$	−10.5163	−	46.0747i	−0.514367	−	2.25359i
$419$	−1.37067	−	6.00531i	−0.0669617	−	0.293378i	0.930348	−	0.366677i	$-0.119505\pi$
$419$	−1.37067	−	6.00531i	−0.0669617	−	0.293378i	−0.997310	+	0.0732985i	$0.976647\pi$
$420$	−15.9417	+	2.21687i	−0.777876	+	0.108172i
$421$	−2.18693	+	9.58155i	−0.106584	+	0.466976i	0.893264	+	0.449533i	$0.148410\pi$
$421$	−2.18693	+	9.58155i	−0.106584	+	0.466976i	−0.999848	+	0.0174428i	$0.994447\pi$
$422$	32.2136			1.56813
$423$	0.0205162			0.000997533
$424$	0.764363	−	3.34889i	0.0371207	−	0.162637i
$425$	0.892634	−	0.429870i	0.0432991	−	0.0208517i
$426$	27.6138	+	34.6265i	1.33789	+	1.67766i
$427$	−9.84040	+	6.54565i	−0.476210	+	0.316766i
$428$	−4.47591	+	5.61262i	−0.216351	+	0.271296i
$429$	1.75964	−	7.70947i	0.0849560	−	0.372217i
$430$	25.4738	−	31.9432i	1.22846	−	1.54044i
$431$	2.12440	−	1.02306i	0.102329	−	0.0492789i	−0.382019	−	0.924154i	$-0.624771\pi$
$431$	2.12440	−	1.02306i	0.102329	−	0.0492789i	0.484348	+	0.874875i	$0.339057\pi$
$432$	−14.8312	−	18.5977i	−0.713565	−	0.894783i
$433$	−22.9471	−	11.0507i	−1.10277	−	0.531064i	−0.208239	−	0.978078i	$-0.566773\pi$
$433$	−22.9471	−	11.0507i	−1.10277	−	0.531064i	−0.894527	+	0.447014i	$0.852488\pi$
$434$	50.9067	−	7.07915i	2.44360	−	0.339810i
$435$	18.4024	−	8.86212i	0.882327	−	0.424906i
$436$	−1.43511	−	0.691114i	−0.0687294	−	0.0330984i
$437$	−4.45007	−	19.4971i	−0.212876	−	0.932670i
$438$	−17.7814	−	8.56308i	−0.849629	−	0.409160i
$439$	23.8348	−	29.8879i	1.13757	−	1.42647i	0.248543	−	0.968621i	$-0.420048\pi$
$439$	23.8348	−	29.8879i	1.13757	−	1.42647i	0.889030	−	0.457850i	$-0.151380\pi$
$440$	6.60260			0.314767
$441$	0.0248301	−	0.0220049i	0.00118238	−	0.00104785i
$442$	−3.89430			−0.185233
$443$	8.55688	−	10.7300i	0.406550	−	0.509797i	−0.535838	−	0.844321i	$-0.680004\pi$
$443$	8.55688	−	10.7300i	0.406550	−	0.509797i	0.942387	+	0.334524i	$0.108576\pi$
$444$	−4.44937	−	2.14270i	−0.211158	−	0.101688i
$445$	5.34109	+	23.4009i	0.253192	+	1.10931i
$446$	−28.4085	−	13.6808i	−1.34518	−	0.647805i
$447$	10.9549	−	5.27560i	0.518148	−	0.249527i
$448$	1.14384	−	13.2330i	0.0540415	−	0.625200i
$449$	4.90891	+	2.36401i	0.231666	+	0.111564i	0.546116	−	0.837710i	$-0.316106\pi$
$449$	4.90891	+	2.36401i	0.231666	+	0.111564i	−0.314450	+	0.949274i	$0.601820\pi$
$450$	−0.00268463	−	0.00336642i	−0.000126555	−	0.000158695i
$451$	14.9483	−	7.19872i	0.703888	−	0.338975i
$452$	3.87412	−	4.85800i	0.182223	−	0.228501i
$453$	−0.407250	+	1.78428i	−0.0191343	+	0.0838327i
$454$	4.22852	−	5.30240i	0.198454	−	0.248854i
$455$	−5.23880	−	1.68174i	−0.245599	−	0.0788411i
$456$	3.79205	+	4.75508i	0.177579	+	0.222677i
$457$	−20.7624	+	9.99865i	−0.971225	+	0.467717i	−0.851078	−	0.525039i	$-0.824051\pi$
$457$	−20.7624	+	9.99865i	−0.971225	+	0.467717i	−0.120147	+	0.992756i	$0.538337\pi$
$458$	−6.07650	+	26.6229i	−0.283936	+	1.24400i
$459$	10.8386			0.505901
$460$	−13.2854			−0.619434
$461$	−7.37198	+	32.2988i	−0.343347	+	1.50430i	0.448610	+	0.893727i	$0.351919\pi$
$461$	−7.37198	+	32.2988i	−0.343347	+	1.50430i	−0.791958	+	0.610576i	$0.790938\pi$
$462$	−34.0528	+	22.6513i	−1.58428	+	1.05383i
$463$	−0.375043	−	1.64317i	−0.0174297	−	0.0763645i	0.965465	−	0.260532i	$-0.0838981\pi$
$463$	−0.375043	−	1.64317i	−0.0174297	−	0.0763645i	−0.982895	+	0.184168i	$0.941041\pi$
$464$	5.64739	+	24.7428i	0.262173	+	1.14866i
$465$	23.3309	+	29.2560i	1.08194	+	1.35671i
$466$	−16.9305	−	21.2302i	−0.784291	−	0.983470i
$467$	4.43963	+	19.4513i	0.205442	+	0.900098i	0.967556	+	0.252656i	$0.0813041\pi$
$467$	4.43963	+	19.4513i	0.205442	+	0.900098i	−0.762115	+	0.647442i	$0.775839\pi$
$468$	0.00170389	+	0.00746522i	7.87622e−5	+	0.000345080i
$469$	0.925637	+	0.878757i	0.0427420	+	0.0405772i
$470$	−3.91569	+	17.1558i	−0.180617	+	0.791336i
$471$	−8.24696			−0.380000
$472$	−3.45383			−0.158975
$473$	10.4519	−	45.7928i	0.480579	−	2.10555i
$474$	−17.1595	+	8.26356i	−0.788160	+	0.379558i
$475$	1.56818	+	1.96644i	0.0719530	+	0.0902263i
$476$	6.60861	+	6.27391i	0.302905	+	0.287564i
$477$	0.0152837	−	0.0191651i	0.000699791	−	0.000877510i
$478$	4.32500	−	18.9491i	0.197821	−	0.866710i
$479$	1.82775	−	2.29192i	0.0835118	−	0.104720i	−0.738320	−	0.674450i	$-0.764381\pi$
$479$	1.82775	−	2.29192i	0.0835118	−	0.104720i	0.821832	+	0.569730i	$0.192952\pi$
$480$	24.5900	−	11.8419i	1.12237	−	0.540507i
$481$	−1.05258	−	1.31989i	−0.0479934	−	0.0601818i
$482$	−45.5222	−	21.9224i	−2.07348	−	0.998536i
$483$	−14.4098	+	9.58516i	−0.655670	+	0.436140i
$484$	−16.1419	+	7.77351i	−0.733721	+	0.353341i
$485$	3.37778	+	1.62665i	0.153377	+	0.0738625i
$486$	−0.0209470	−	0.0917748i	−0.000950176	−	0.00416299i
$487$	26.9018	+	12.9552i	1.21904	+	0.587058i	0.929043	−	0.369971i	$-0.120632\pi$
$487$	26.9018	+	12.9552i	1.21904	+	0.587058i	0.289994	+	0.957028i	$0.406347\pi$
$488$	1.84979	−	2.31956i	0.0837361	−	0.105002i
$489$	2.45947			0.111221
$490$	13.6616	+	24.9629i	0.617167	+	1.12771i
$491$	−0.0655631			−0.00295882			−0.00147941	−	0.999999i	$-0.500471\pi$
$491$	−0.0655631			−0.00295882			−0.00147941	+	0.999999i	$0.500471\pi$
$492$	6.33021	−	7.93784i	0.285388	−	0.357865i
$493$	−10.4187	−	5.01736i	−0.469233	−	0.225971i
$494$	−2.19990	−	9.63841i	−0.0989784	−	0.433653i
$495$	0.0424516	+	0.0204436i	0.00190806	+	0.000918872i
$496$	−41.8913	+	20.1738i	−1.88097	+	0.905829i
$497$	18.0628	−	30.4763i	0.810229	−	1.36705i
$498$	−8.82020	−	4.24758i	−0.395242	−	0.190339i
$499$	2.89616	+	3.63167i	0.129650	+	0.162576i	0.842419	−	0.538823i	$-0.181131\pi$
$499$	2.89616	+	3.63167i	0.129650	+	0.162576i	−0.712769	+	0.701399i	$0.752559\pi$
$500$	17.3400	−	8.35052i	0.775470	−	0.373447i
$501$	13.1874	−	16.5365i	0.589170	−	0.738796i
$502$	−10.3727	+	45.4460i	−0.462958	+	2.02835i
$503$	−13.7881	+	17.2898i	−0.614782	+	0.770913i	−0.987600	−	0.156992i	$-0.949820\pi$
$503$	−13.7881	+	17.2898i	−0.614782	+	0.770913i	0.372817	+	0.927905i	$0.378392\pi$
$504$	−0.00424643	+	0.00716473i	−0.000189151	+	0.000319142i
$505$	−12.7929	−	16.0418i	−0.569277	−	0.713851i
$506$	−30.4155	+	14.6473i	−1.35213	+	0.651154i
$507$	−4.63837	+	20.3220i	−0.205997	+	0.902533i
$508$	16.3362			0.724802
$509$	10.7184			0.475083			0.237542	−	0.971377i	$-0.423658\pi$
$509$	10.7184			0.475083			0.237542	+	0.971377i	$0.423658\pi$
$510$	−3.26304	+	14.2963i	−0.144490	+	0.633051i
$511$	−1.35952	+	15.7282i	−0.0601418	+	0.695773i
$512$	6.19419	+	27.1385i	0.273747	+	1.19937i
$513$	6.12274	+	26.8255i	0.270325	+	1.18437i
$514$	1.95396	+	2.45019i	0.0861857	+	0.108073i
$515$	−4.82293	−	6.04776i	−0.212524	−	0.266496i
$516$	−6.39591	−	28.0223i	−0.281564	−	1.23361i
$517$	4.50161	+	19.7229i	0.197981	+	0.867410i
$518$	−0.751919	+	8.69886i	−0.0330374	+	0.382206i
$519$	1.41921	−	6.21799i	0.0622966	−	0.272939i
$520$	1.38120			0.0605698
$521$	3.90956			0.171281			0.0856405	−	0.996326i	$-0.472706\pi$
$521$	3.90956			0.171281			0.0856405	+	0.996326i	$0.472706\pi$
$522$	−0.0111832	+	0.0489967i	−0.000489474	+	0.00214453i
$523$	−33.0167	+	15.9000i	−1.44372	+	0.695258i	−0.981492	−	0.191504i	$-0.938664\pi$
$523$	−33.0167	+	15.9000i	−1.44372	+	0.695258i	−0.462227	+	0.886762i	$0.652949\pi$
$524$	−5.38955	−	6.75829i	−0.235444	−	0.295237i
$525$	1.10977	−	1.87245i	0.0484345	−	0.0817204i
$526$	17.8806	−	22.4216i	0.779633	−	0.977628i
$527$	4.71422	−	20.6544i	0.205355	−	0.899718i
$528$	23.0682	−	28.9267i	1.00392	−	1.25887i
$529$	7.85161	−	3.78114i	0.341374	−	0.164397i
$530$	13.1089	+	16.4381i	0.569416	+	0.714025i
$531$	−0.0222065	−	0.0106941i	−0.000963679	−	0.000464084i
$532$	−11.7947	+	19.9005i	−0.511365	+	0.862795i
$533$	3.12705	−	1.50591i	0.135447	−	0.0652281i
$534$	33.6270	+	16.1939i	1.45518	+	0.700779i
$535$	2.05627	+	9.00910i	0.0889003	+	0.389497i
$536$	−0.288669	−	0.139016i	−0.0124686	−	0.00600457i
$537$	15.4805	−	19.4120i	0.668035	−	0.837689i
$538$	14.0898			0.607456
$539$	26.6021	+	19.0416i	1.14583	+	0.820182i
$540$	18.2790			0.786602
$541$	−21.2077	+	26.5936i	−0.911791	+	1.14335i	0.0774417	+	0.996997i	$0.475325\pi$
$541$	−21.2077	+	26.5936i	−0.911791	+	1.14335i	−0.989232	+	0.146353i	$0.953247\pi$
$542$	32.3637	+	15.5855i	1.39014	+	0.669457i
$543$	−10.2017	−	44.6964i	−0.437795	−	1.91811i
$544$	−13.9218	−	6.70440i	−0.596894	−	0.287449i
$545$	−1.84732	+	0.889624i	−0.0791306	+	0.0381073i
$546$	−7.12354	+	4.73845i	−0.304859	+	0.202787i
$547$	−23.6873	−	11.4072i	−1.01280	−	0.487736i	−0.147534	−	0.989057i	$-0.547133\pi$
$547$	−23.6873	−	11.4072i	−1.01280	−	0.487736i	−0.865262	+	0.501321i	$0.832848\pi$
$548$	18.9530	+	23.7663i	0.809631	+	1.01524i
$549$	0.0190753	−	0.00918620i	0.000814116	−	0.000392057i
$550$	2.64719	−	3.31947i	0.112877	−	0.141543i
$551$	6.53245	−	28.6205i	0.278292	−	1.21928i
$552$	2.70875	−	3.39667i	0.115292	−	0.144572i
$553$	11.0487	+	10.4891i	0.469837	+	0.446041i
$554$	−15.0241	−	18.8397i	−0.638315	−	0.800421i
$555$	−5.72737	+	2.75816i	−0.243113	+	0.117077i
$556$	2.60904	−	11.4310i	0.110648	−	0.484781i
$557$	−3.01222			−0.127632			−0.0638159	−	0.997962i	$-0.520327\pi$
$557$	−3.01222			−0.127632			−0.0638159	+	0.997962i	$0.520327\pi$
$558$	−0.0920728			−0.00389775
$559$	2.18644	−	9.57943i	0.0924767	−	0.405167i
$560$	−18.6699	−	17.7243i	−0.788946	−	0.748989i
$561$	3.75130	+	16.4355i	0.158380	+	0.693908i
$562$	−6.40022	−	28.0412i	−0.269977	−	1.18285i
$563$	0.262650	+	0.329353i	0.0110694	+	0.0138806i	0.787335	−	0.616525i	$-0.211460\pi$
$563$	0.262650	+	0.329353i	0.0110694	+	0.0138806i	−0.776266	+	0.630406i	$0.782889\pi$
$564$	7.71851	+	9.67871i	0.325008	+	0.407547i
$565$	−1.77980	−	7.79782i	−0.0748768	−	0.328057i
$566$	−10.0906	−	44.2098i	−0.424140	−	1.85828i
$567$	19.7948	−	13.1671i	0.831303	−	0.552968i
$568$	−1.97894	+	8.67030i	−0.0830345	+	0.363798i
$569$	−33.5878			−1.40807			−0.704037	−	0.710163i	$-0.748621\pi$
$569$	−33.5878			−1.40807			−0.704037	+	0.710163i	$0.748621\pi$
$570$	−37.2267			−1.55925
$571$	−3.10614	+	13.6089i	−0.129988	+	0.569514i	0.867421	+	0.497575i	$0.165776\pi$
$571$	−3.10614	+	13.6089i	−0.129988	+	0.569514i	−0.997409	+	0.0719396i	$0.977081\pi$
$572$	−6.80268	+	3.27600i	−0.284434	+	0.136976i
$573$	9.71668	+	12.1843i	0.405920	+	0.509008i
$574$	−17.0915	−	5.48665i	−0.713387	−	0.229008i
$575$	1.12019	−	1.40467i	0.0467151	−	0.0585789i
$576$	−0.00529471	+	0.0231976i	−0.000220613	+	0.000966568i
$577$	23.1941	−	29.0845i	0.965584	−	1.21080i	−0.0119289	−	0.999929i	$-0.503797\pi$
$577$	23.1941	−	29.0845i	0.965584	−	1.21080i	0.977513	−	0.210875i	$-0.0676314\pi$
$578$	−21.7921	+	10.4945i	−0.906430	+	0.436514i
$579$	−7.40593	−	9.28674i	−0.307780	−	0.385944i
$580$	−17.5708	−	8.46167i	−0.729589	−	0.351352i
$581$	−0.674371	+	7.80171i	−0.0279776	+	0.323670i
$582$	5.25230	−	2.52938i	0.217715	−	0.104846i
$583$	21.7775	+	10.4875i	0.901931	+	0.434347i
$584$	−0.881847	−	3.86362i	−0.0364911	−	0.159878i
$585$	0.00888048	+	0.00427662i	0.000367163	+	0.000176816i
$586$	6.77291	−	8.49296i	0.279786	−	0.350841i
$587$	−35.8868			−1.48120			−0.740602	−	0.671943i	$-0.765460\pi$
$587$	−35.8868			−1.48120			−0.740602	+	0.671943i	$0.765460\pi$
$588$	19.7225	+	3.43524i	0.813340	+	0.141667i
$589$	53.7827			2.21608
$590$	13.1807	−	16.5281i	0.542642	−	0.680452i
$591$	17.6240	+	8.48725i	0.724952	+	0.349119i
$592$	−1.75764	−	7.70070i	−0.0722384	−	0.316497i
$593$	−23.4413	−	11.2888i	−0.962620	−	0.463574i	−0.114527	−	0.993420i	$-0.536535\pi$
$593$	−23.4413	−	11.2888i	−0.962620	−	0.463574i	−0.848094	+	0.529847i	$0.822250\pi$
$594$	41.8479	−	20.1529i	1.71704	−	0.826883i
$595$	11.6180	−	1.61561i	0.476290	−	0.0662334i
$596$	−10.4599	−	5.03721i	−0.428453	−	0.206332i
$597$	−15.2279	−	19.0951i	−0.623235	−	0.781512i
$598$	−6.36265	+	3.06409i	−0.260188	+	0.125300i
$599$	−18.2685	+	22.9080i	−0.746431	+	0.935995i	−0.999505	−	0.0314521i	$-0.989987\pi$
$599$	−18.2685	+	22.9080i	−0.746431	+	0.935995i	0.253074	+	0.967447i	$0.418558\pi$
$600$	−0.121585	+	0.532700i	−0.00496370	+	0.0217474i
$601$	−0.155428	+	0.194901i	−0.00634005	+	0.00795017i	−0.784991	−	0.619507i	$-0.787333\pi$
$601$	−0.155428	+	0.194901i	−0.00634005	+	0.00795017i	0.778651	+	0.627457i	$0.215904\pi$
$602$	−42.3125	+	28.1455i	−1.72453	+	1.14712i
$603$	−0.00142557	−	0.00178761i	−5.80538e−5	−	7.27971e-5i
$604$	1.57441	−	0.758196i	0.0640619	−	0.0308506i
$605$	−5.13182	+	22.4840i	−0.208638	+	0.914104i
$606$	−31.9050			−1.29605
$607$	4.31353			0.175081			0.0875404	−	0.996161i	$-0.472099\pi$
$607$	4.31353			0.175081			0.0875404	+	0.996161i	$0.472099\pi$
$608$	8.72892	−	38.2439i	0.354005	−	1.55100i
$609$	−25.1630	+	3.49919i	−1.01966	+	0.141794i
$610$	4.04086	+	17.7042i	0.163610	+	0.716820i
$611$	0.941696	+	4.12584i	0.0380970	+	0.166914i
$612$	−0.0101779	−	0.0127627i	−0.000411417	−	0.000515901i
$613$	−12.7195	−	15.9497i	−0.513735	−	0.644203i	0.455530	−	0.890220i	$-0.349450\pi$
$613$	−12.7195	−	15.9497i	−0.513735	−	0.644203i	−0.969266	+	0.246017i	$0.920878\pi$
$614$	14.5183	+	63.6089i	0.585911	+	2.56704i
$615$	−2.90815	−	12.7414i	−0.117268	−	0.513784i
$616$	−7.81941	−	2.51015i	−0.315053	−	0.101137i
$617$	−7.00176	+	30.6767i	−0.281880	+	1.23500i	0.613500	+	0.789695i	$0.289761\pi$
$617$	−7.00176	+	30.6767i	−0.281880	+	1.23500i	−0.895380	+	0.445303i	$0.853096\pi$
$618$	−12.0282			−0.483845
$619$	16.1171			0.647802			0.323901	−	0.946091i	$-0.395006\pi$
$619$	16.1171			0.647802			0.323901	+	0.946091i	$0.395006\pi$
$620$	7.95043	−	34.8331i	0.319297	−	1.39893i
$621$	17.7084	−	8.52792i	0.710614	−	0.342214i
$622$	33.9970	+	42.6309i	1.36316	+	1.70934i
$623$	2.57104	−	29.7440i	0.103006	−	1.19167i
$624$	4.82567	−	6.05119i	0.193181	−	0.242242i
$625$	4.98386	−	21.8357i	0.199355	−	0.873429i
$626$	−32.3422	+	40.5558i	−1.29265	+	1.62094i
$627$	−38.5588	+	18.5689i	−1.53989	+	0.741572i
$628$	4.90955	+	6.15638i	0.195912	+	0.245666i
$629$	3.24260	+	1.56155i	0.129291	+	0.0622632i
$630$	−0.0180809	−	0.0476636i	−0.000720362	−	0.00189896i
$631$	36.5783	−	17.6152i	1.45616	−	0.701249i	0.472507	−	0.881327i	$-0.343349\pi$
$631$	36.5783	−	17.6152i	1.45616	−	0.701249i	0.983652	+	0.180077i	$0.0576348\pi$
$632$	−3.44563	−	1.65933i	−0.137060	−	0.0660046i
$633$	−6.49132	−	28.4403i	−0.258007	−	1.13040i
$634$	21.1526	+	10.1865i	0.840076	+	0.404559i
$635$	13.1111	−	16.4407i	0.520296	−	0.652431i
$636$	14.7913			0.586511
$637$	5.56492	+	3.98334i	0.220490	+	0.157826i
$638$	−49.5558			−1.96193
$639$	−0.0395695	+	0.0496186i	−0.00156534	+	0.00196288i
$640$	10.0291	+	4.82977i	0.396435	+	0.190913i
$641$	5.79920	+	25.4080i	0.229055	+	1.00355i	0.950413	+	0.310992i	$0.100661\pi$
$641$	5.79920	+	25.4080i	0.229055	+	1.00355i	−0.721358	+	0.692563i	$0.756482\pi$
$642$	12.9461	+	6.23449i	0.510940	+	0.246056i
$643$	−16.3705	+	7.88362i	−0.645589	+	0.310899i	−0.727876	−	0.685709i	$-0.759492\pi$
$643$	−16.3705	+	7.88362i	−0.645589	+	0.310899i	0.0822861	+	0.996609i	$0.473778\pi$
$644$	15.7338	+	5.05078i	0.619997	+	0.199029i
$645$	−33.3348	−	16.0532i	−1.31256	−	0.632094i
$646$	13.1408	+	16.4780i	0.517017	+	0.648319i
$647$	−4.92642	+	2.37244i	−0.193678	+	0.0932702i	−0.528209	−	0.849114i	$-0.677136\pi$
$647$	−4.92642	+	2.37244i	−0.193678	+	0.0932702i	0.334531	+	0.942385i	$0.391422\pi$
$648$	−3.72101	+	4.66600i	−0.146175	+	0.183298i
$649$	5.40805	−	23.6942i	0.212285	−	0.930080i
$650$	0.553768	−	0.694403i	0.0217206	−	0.0272367i
$651$	−16.5081	−	43.5174i	−0.647004	−	1.70558i
$652$	−1.46416	−	1.83600i	−0.0573411	−	0.0719035i
$653$	28.8765	−	13.9062i	1.13003	−	0.544192i	0.227050	−	0.973883i	$-0.427092\pi$
$653$	28.8765	−	13.9062i	1.13003	−	0.544192i	0.902976	+	0.429691i	$0.141377\pi$
$654$	−0.709451	+	3.10831i	−0.0277417	+	0.121545i
$655$	−11.1271			−0.434770
$656$	16.2390			0.634025
$657$	0.00629307	−	0.0275717i	0.000245516	−	0.00107568i
$658$	11.1595	−	18.8288i	0.435044	−	0.734022i
$659$	9.45761	+	41.4365i	0.368416	+	1.61414i	0.731132	+	0.682236i	$0.238993\pi$
$659$	9.45761	+	41.4365i	0.368416	+	1.61414i	−0.362716	+	0.931900i	$0.618150\pi$
$660$	6.32648	+	27.7181i	0.246258	+	1.07893i
$661$	−7.28240	−	9.13184i	−0.283253	−	0.355188i	0.619768	−	0.784785i	$-0.287227\pi$
$661$	−7.28240	−	9.13184i	−0.283253	−	0.355188i	−0.903020	+	0.429598i	$0.858655\pi$
$662$	21.1809	+	26.5600i	0.823218	+	1.03228i
$663$	0.784737	+	3.43816i	0.0304767	+	0.133527i
$664$	−0.437426	−	1.91649i	−0.0169754	−	0.0743742i
$665$	10.5617	+	27.8418i	0.409563	+	1.07966i
$666$	0.00348054	−	0.0152492i	0.000134868	−	0.000590896i
$667$	−20.9701			−0.811966
$668$	−20.1952			−0.781376
$669$	−6.35379	+	27.8378i	−0.245652	+	1.07627i
$670$	1.76689	−	0.850890i	0.0682610	−	0.0328728i
$671$	13.0164	+	16.3221i	0.502494	+	0.630107i
$672$	−33.6238	+	4.67576i	−1.29706	+	0.180371i
$673$	−3.92924	+	4.92711i	−0.151461	+	0.189926i	−0.851773	−	0.523911i	$-0.824473\pi$
$673$	−3.92924	+	4.92711i	−0.151461	+	0.189926i	0.700312	+	0.713837i	$0.253044\pi$
$674$	2.59837	−	11.3842i	0.100086	−	0.438504i
$675$	−1.54124	+	1.93265i	−0.0593222	+	0.0743877i
$676$	17.9317	−	8.63547i	0.689682	−	0.332134i
$677$	0.286518	+	0.359283i	0.0110118	+	0.0138084i	0.787307	−	0.616561i	$-0.211475\pi$
$677$	0.286518	+	0.359283i	0.0110118	+	0.0138084i	−0.776295	+	0.630370i	$0.782903\pi$
$678$	−11.2055	−	5.39626i	−0.430343	−	0.207242i
$679$	−3.38186	−	3.21058i	−0.129784	−	0.123211i
$680$	−2.65293	+	1.27759i	−0.101735	+	0.0489932i
$681$	−5.53341	−	2.66475i	−0.212041	−	0.102113i
$682$	−20.2024	−	88.5123i	−0.773588	−	3.38931i
$683$	40.7326	+	19.6158i	1.55859	+	0.750578i	0.997041	−	0.0768660i	$-0.0244914\pi$
$683$	40.7326	+	19.6158i	1.55859	+	0.750578i	0.561549	+	0.827444i	$0.310206\pi$
$684$	0.0258382	−	0.0324000i	0.000987947	−	0.00123885i
$685$	39.1295			1.49506
$686$	−6.68901	−	34.7571i	−0.255388	−	1.32703i
$687$	24.7290			0.943469
$688$	28.6636	−	35.9430i	1.09279	−	1.37031i
$689$	4.55565	+	2.19389i	0.173556	+	0.0835804i
$690$	5.91725	+	25.9252i	0.225266	+	0.986955i
$691$	11.1004	+	5.34569i	0.422281	+	0.203360i	0.632942	−	0.774200i	$-0.281847\pi$
$691$	11.1004	+	5.34569i	0.422281	+	0.203360i	−0.210661	+	0.977559i	$0.567562\pi$
$692$	−5.48663	+	2.64222i	−0.208570	+	0.100442i
$693$	−0.0425029	−	0.0403503i	−0.00161455	−	0.00153278i
$694$	34.3460	+	16.5402i	1.30376	+	0.627856i
$695$	−9.41015	−	11.7999i	−0.356947	−	0.447598i
$696$	5.74591	−	2.76708i	0.217798	−	0.104886i
$697$	−4.61331	+	5.78491i	−0.174742	+	0.219119i
$698$	−8.56852	+	37.5411i	−0.324323	+	1.42095i
$699$	−15.3318	+	19.2255i	−0.579903	+	0.727175i
$700$	−2.05846	+	0.286251i	−0.0778023	+	0.0108193i
$701$	−11.1294	−	13.9558i	−0.420350	−	0.527102i	0.525896	−	0.850549i	$-0.323730\pi$
$701$	−11.1294	−	13.9558i	−0.420350	−	0.527102i	−0.946247	+	0.323446i	$0.895159\pi$
$702$	8.75420	−	4.21580i	0.330406	−	0.159115i
$703$	−2.03309	+	8.90756i	−0.0766796	+	0.335955i
$704$	−23.4623			−0.884270
$705$	15.9353			0.600159
$706$	−7.87702	+	34.5115i	−0.296456	+	1.29886i
$707$	9.05184	+	23.8618i	0.340429	+	0.897414i
$708$	−3.30939	−	14.4994i	−0.124374	−	0.544920i
$709$	−8.19379	−	35.8993i	−0.307724	−	1.34823i	−0.858174	−	0.513360i	$-0.828401\pi$
$709$	−8.19379	−	35.8993i	−0.307724	−	1.34823i	0.550449	−	0.834869i	$-0.314456\pi$
$710$	−33.9391	−	42.5583i	−1.27371	−	1.59718i
$711$	−0.0170160	−	0.0213374i	−0.000638150	−	0.000800215i
$712$	1.66769	+	7.30661i	0.0624992	+	0.273827i
$713$	−8.54886	−	37.4550i	−0.320157	−	1.40270i
$714$	9.29950	−	15.6905i	0.348025	−	0.587201i
$715$	−2.16271	+	9.47544i	−0.0808807	+	0.354361i
$716$	−23.7069			−0.885969
$717$	−17.6011			−0.657324
$718$	−6.70596	+	29.3807i	−0.250264	+	1.09648i
$719$	−17.3904	+	8.37479i	−0.648554	+	0.312327i	−0.729083	−	0.684425i	$-0.760053\pi$
$719$	−17.3904	+	8.37479i	−0.648554	+	0.312327i	0.0805292	+	0.996752i	$0.474339\pi$
$720$	0.0287534	+	0.0360557i	0.00107158	+	0.00134372i
$721$	3.41254	+	8.99588i	0.127090	+	0.335024i
$722$	−10.7199	+	13.4423i	−0.398952	+	0.500270i
$723$	−10.1814	+	44.6077i	−0.378651	+	1.65898i
$724$	−27.2928	+	34.2241i	−1.01433	+	1.27193i
$725$	2.37619	−	1.14431i	0.0882493	−	0.0424986i
$726$	22.3588	+	28.0371i	0.829813	+	1.04055i
$727$	22.2549	+	10.7174i	0.825390	+	0.397487i	0.798384	−	0.602149i	$-0.205689\pi$
$727$	22.2549	+	10.7174i	0.825390	+	0.397487i	0.0270055	+	0.999635i	$0.491403\pi$
$728$	−1.63575	−	0.525101i	−0.0606249	−	0.0194615i
$729$	−24.3645	+	11.7333i	−0.902388	+	0.434567i
$730$	21.8545	+	10.5246i	0.808873	+	0.389532i
$731$	4.66119	+	20.4220i	0.172400	+	0.755336i
$732$	11.5101	+	5.54297i	0.425426	+	0.204874i
$733$	−18.3537	+	23.0148i	−0.677908	+	0.850070i	−0.995160	−	0.0982714i	$-0.968669\pi$
$733$	−18.3537	+	23.0148i	−0.677908	+	0.850070i	0.317251	+	0.948341i	$0.397240\pi$
$734$	27.4931			1.01479
$735$	19.2860	−	17.0916i	0.711374	−	0.630434i
$736$	−28.0211			−1.03287
$737$	1.40569	−	1.76268i	0.0517792	−	0.0649291i
$738$	0.0289725	+	0.0139524i	0.00106649	+	0.000513595i
$739$	−3.39775	−	14.8865i	−0.124988	−	0.547609i	−0.998184	−	0.0602394i	$-0.980814\pi$
$739$	−3.39775	−	14.8865i	−0.124988	−	0.547609i	0.873196	−	0.487370i	$-0.162044\pi$
$740$	5.46857	+	2.63352i	0.201029	+	0.0968102i
$741$	−8.06615	+	3.88445i	−0.296317	+	0.142699i
$742$	−9.27544	−	24.4512i	−0.340512	−	0.897632i
$743$	0.634609	+	0.305612i	0.0232815	+	0.0112118i	0.445488	−	0.895288i	$-0.353030\pi$
$743$	0.634609	+	0.305612i	0.0232815	+	0.0112118i	−0.422207	+	0.906500i	$0.638744\pi$
$744$	7.28475	+	9.13479i	0.267072	+	0.334898i
$745$	−13.4643	+	6.48405i	−0.493293	+	0.237557i
$746$	4.70112	−	5.89501i	0.172120	−	0.215832i
$747$	0.00312158	−	0.0136765i	0.000114213	−	0.000500398i
$748$	10.0359	−	12.5847i	0.366951	−	0.460141i
$749$	0.989824	−	11.4512i	0.0361674	−	0.418416i
$750$	−24.0184	−	30.1182i	−0.877030	−	1.09976i
$751$	−26.9218	+	12.9648i	−0.982389	+	0.473094i	−0.854926	−	0.518750i	$-0.826398\pi$
$751$	−26.9218	+	12.9648i	−0.982389	+	0.473094i	−0.127463	+	0.991843i	$0.540683\pi$
$752$	−4.40600	+	19.3039i	−0.160670	+	0.703942i
$753$	42.2130			1.53833
$754$	−10.3666			−0.377530
$755$	0.500537	−	2.19299i	0.0182164	−	0.0798112i
$756$	−21.6477	−	6.94924i	−0.787318	−	0.252741i
$757$	−7.55547	−	33.1027i	−0.274608	−	1.20314i	−0.904506	−	0.426460i	$-0.859760\pi$
$757$	−7.55547	−	33.1027i	−0.274608	−	1.20314i	0.629898	−	0.776678i	$-0.283097\pi$
$758$	−11.3604	−	49.7731i	−0.412628	−	1.80784i
$759$	19.0607	+	23.9013i	0.691859	+	0.867563i
$760$	−4.66068	−	5.84430i	−0.169061	−	0.211995i
$761$	−3.77053	−	16.5198i	−0.136681	−	0.598840i	−0.996151	−	0.0876536i	$-0.972063\pi$
$761$	−3.77053	−	16.5198i	−0.136681	−	0.598840i	0.859470	−	0.511187i	$-0.170794\pi$
$762$	−7.27608	−	31.8786i	−0.263585	−	1.15484i
$763$	2.52598	−	0.351266i	0.0914468	−	0.0127167i
$764$	3.31114	−	14.5071i	0.119793	−	0.524847i
$765$	−0.0210129			−0.000759723
$766$	1.30449			0.0471331
$767$	1.13132	−	4.95662i	0.0408494	−	0.178973i
$768$	31.2509	−	15.0496i	1.12767	−	0.543057i
$769$	−22.9209	−	28.7419i	−0.826549	−	1.03646i	−0.998679	−	0.0513857i	$-0.983636\pi$
$769$	−22.9209	−	28.7419i	−0.826549	−	1.03646i	0.172130	−	0.985074i	$-0.444935\pi$
$770$	41.8531	−	27.8400i	1.50828	−	1.00328i
$771$	1.76946	−	2.21883i	0.0637255	−	0.0799092i
$772$	−2.52371	+	11.0571i	−0.0908303	+	0.397954i
$773$	−30.1435	+	37.7988i	−1.08419	+	1.35953i	−0.155855	+	0.987780i	$0.549813\pi$
$773$	−30.1435	+	37.7988i	−1.08419	+	1.35953i	−0.928333	+	0.371749i	$0.878758\pi$
$774$	0.0820216	−	0.0394995i	0.00294820	−	0.00141978i
$775$	3.01257	+	3.77764i	0.108215	+	0.135697i
$776$	1.05467	+	0.507901i	0.0378603	+	0.0182326i
$777$	7.83147	−	1.08905i	0.280952	−	0.0390695i
$778$	54.8614	−	26.4198i	1.96687	−	0.947197i
$779$	−16.9237	−	8.15005i	−0.606356	−	0.292006i
$780$	1.32344	+	5.79838i	0.0473868	+	0.207615i
$781$	−56.3820	−	27.1522i	−2.01751	−	0.971580i
$782$	9.38678	−	11.7706i	0.335670	−	0.420917i
$783$	28.8522			1.03109
$784$	15.3722	+	28.0886i	0.549008	+	1.00316i
$785$	10.1361			0.361771
$786$	−10.7877	+	13.5273i	−0.384784	+	0.482504i
$787$	22.3677	+	10.7717i	0.797322	+	0.383970i	0.787759	−	0.615984i	$-0.211241\pi$
$787$	22.3677	+	10.7717i	0.797322	+	0.383970i	0.00956364	+	0.999954i	$0.496956\pi$
$788$	−4.15607	−	18.2089i	−0.148054	−	0.648666i
$789$	−23.3984	−	11.2681i	−0.833006	−	0.401155i
$790$	21.0901	−	10.1565i	0.750352	−	0.361350i
$791$	−0.856741	+	9.91154i	−0.0304622	+	0.352414i
$792$	0.0132550	+	0.00638325i	0.000470994	+	0.000226819i
$793$	2.72292	+	3.41443i	0.0966936	+	0.121250i
$794$	−13.5054	+	6.50386i	−0.479289	+	0.230813i
$795$	11.8711	−	14.8859i	0.421025	−	0.527948i
$796$	−5.18918	+	22.7353i	−0.183926	+	0.805831i
$797$	6.80816	−	8.53717i	0.241157	−	0.302402i	−0.646493	−	0.762920i	$-0.723765\pi$
$797$	6.80816	−	8.53717i	0.241157	−	0.302402i	0.887650	+	0.460518i	$0.152336\pi$
$798$	44.0872	+	14.1527i	1.56067	+	0.501000i
$799$	−5.62507	−	7.05362i	−0.199001	−	0.249539i
$800$	3.17515	−	1.52907i	0.112259	−	0.0540609i
$801$	−0.0119010	+	0.0521417i	−0.000420502	+	0.00184234i
$802$	−37.7970			−1.33466
$803$	27.8863			0.984088
$804$	0.306999	−	1.34505i	0.0108270	−	0.0474364i
$805$	17.7106	−	11.7808i	0.624218	−	0.415219i
$806$	−4.22615	−	18.5160i	−0.148860	−	0.652197i
$807$	−2.83923	−	12.4395i	−0.0999455	−	0.437890i
$808$	−3.99442	−	5.00885i	−0.140523	−	0.176211i
$809$	−24.2245	−	30.3765i	−0.851687	−	1.06798i	−0.996908	−	0.0785821i	$-0.974961\pi$
$809$	−24.2245	−	30.3765i	−0.851687	−	1.06798i	0.145221	−	0.989399i	$-0.453611\pi$
$810$	−8.12853	−	35.6134i	−0.285607	−	1.25133i
$811$	12.0968	+	52.9994i	0.424775	+	1.86106i	0.503246	+	0.864143i	$0.332139\pi$
$811$	12.0968	+	52.9994i	0.424775	+	1.86106i	−0.0784712	+	0.996916i	$0.525004\pi$
$812$	17.5921	+	16.7011i	0.617361	+	0.586094i
$813$	7.23841	−	31.7135i	0.253862	−	1.11224i
$814$	15.4232			0.540584
$815$	−3.02285			−0.105886
$816$	−3.67162	+	16.0864i	−0.128532	+	0.563137i
$817$	−47.9114	+	23.0729i	−1.67621	+	0.807219i
$818$	−10.8233	−	13.5721i	−0.378430	−	0.474536i
$819$	−0.00889122	−	0.00844091i	−0.000310684	−	0.000294949i
$820$	−7.78025	+	9.75612i	−0.271698	+	0.340699i
$821$	−1.77782	+	7.78914i	−0.0620464	+	0.271843i	−0.996430	−	0.0844263i	$-0.973094\pi$
$821$	−1.77782	+	7.78914i	−0.0620464	+	0.271843i	0.934383	+	0.356269i	$0.115951\pi$
$822$	37.9361	−	47.5704i	1.32317	−	1.65921i
$823$	37.4234	−	18.0222i	1.30450	−	0.628213i	0.352930	−	0.935650i	$-0.385185\pi$
$823$	37.4234	−	18.0222i	1.30450	−	0.628213i	0.951569	+	0.307437i	$0.0994712\pi$
$824$	−1.50590	−	1.88834i	−0.0524604	−	0.0657833i
$825$	−3.46409	−	1.66822i	−0.120604	−	0.0580799i
$826$	−21.8934	+	14.5631i	−0.761770	+	0.506716i
$827$	5.90952	−	2.84587i	0.205494	−	0.0989607i	−0.328306	−	0.944571i	$-0.606478\pi$
$827$	5.90952	−	2.84587i	0.205494	−	0.0989607i	0.533800	+	0.845611i	$0.320763\pi$
$828$	−0.0266709	−	0.0128440i	−0.000926877	−	0.000446360i
$829$	−5.58980	−	24.4905i	−0.194142	−	0.850590i	−0.974344	−	0.225063i	$-0.927741\pi$
$829$	−5.58980	−	24.4905i	−0.194142	−	0.850590i	0.780203	−	0.625527i	$-0.215116\pi$
$830$	10.8406	+	5.22056i	0.376283	+	0.181208i
$831$	−13.6055	+	17.0607i	−0.471968	+	0.591829i
$832$	−4.90810			−0.170158
$833$	−14.3733	−	2.50352i	−0.498004	−	0.0867419i
$834$	−23.4685			−0.812648
$835$	−16.2082	+	20.3244i	−0.560908	+	0.703356i
$836$	36.8165	+	17.7299i	1.27332	+	0.613200i
$837$	11.7621	+	51.5333i	0.406559	+	1.78125i
$838$	10.6064	+	5.10775i	0.366390	+	0.176444i
$839$	−35.7622	+	17.2222i	−1.23465	+	0.594575i	−0.933354	−	0.358957i	$-0.883133\pi$
$839$	−35.7622	+	17.2222i	−1.23465	+	0.594575i	−0.301293	+	0.953532i	$0.597418\pi$
$840$	−3.29828	+	5.56498i	−0.113801	+	0.192010i
$841$	−1.60633	−	0.773570i	−0.0553908	−	0.0266748i
$842$	−11.7108	−	14.6849i	−0.403580	−	0.506074i
$843$	−23.4670	+	11.3011i	−0.808246	+	0.389231i
$844$	−17.3664	+	21.7768i	−0.597776	+	0.749588i
$845$	5.70086	−	24.9771i	0.196116	−	0.859238i
$846$	−0.0244467	+	0.0306552i	−0.000840495	+	0.00105395i
$847$	14.6254	−	24.6766i	0.502536	−	0.847898i
$848$	14.7504	+	18.4964i	0.506530	+	0.635169i
$849$	−36.9981	+	17.8173i	−1.26977	+	0.611490i
$850$	−0.421336	+	1.84599i	−0.0144517	+	0.0633170i
$851$	6.52652			0.223726
$852$	−38.2946			−1.31195
$853$	2.88141	−	12.6243i	0.0986575	−	0.432247i	−0.901342	−	0.433108i	$-0.857417\pi$
$853$	2.88141	−	12.6243i	0.0986575	−	0.432247i	1.00000		0.000860998i	$0.000274064\pi$
$854$	1.94514	−	22.5031i	0.0665614	−	0.770041i
$855$	−0.0118702	−	0.0520070i	−0.000405954	−	0.00177860i
$856$	0.642043	+	2.81297i	0.0219446	+	0.0961455i
$857$	30.6079	+	38.3811i	1.04555	+	1.31107i	0.948839	+	0.315760i	$0.102259\pi$
$857$	30.6079	+	38.3811i	1.04555	+	1.31107i	0.0967067	+	0.995313i	$0.469169\pi$
$858$	9.42269	+	11.8157i	0.321685	+	0.403381i
$859$	−11.3822	−	49.8688i	−0.388356	−	1.70150i	−0.670318	−	0.742074i	$-0.733842\pi$
$859$	−11.3822	−	49.8688i	−0.388356	−	1.70150i	0.281961	−	0.959426i	$-0.409015\pi$
$860$	7.86099	+	34.4413i	0.268058	+	1.17444i
$861$	−1.39989	+	16.1952i	−0.0477082	+	0.551931i
$862$	−1.00275	+	4.39332i	−0.0341537	+	0.149637i
$863$	7.24161			0.246507			0.123254	−	0.992375i	$-0.460667\pi$
$863$	7.24161			0.246507			0.123254	+	0.992375i	$0.460667\pi$
$864$	38.5534			1.31161
$865$	−1.74431	+	7.64231i	−0.0593083	+	0.259846i
$866$	43.8552	−	21.1196i	1.49026	−	0.717672i
$867$	13.6566	+	17.1248i	0.463801	+	0.581588i
$868$	−22.6583	+	38.2300i	−0.769074	+	1.29761i
$869$	16.7787	−	21.0398i	0.569178	−	0.713726i
$870$	−8.68618	+	38.0567i	−0.294489	+	1.29024i
$871$	0.294057	−	0.368736i	0.00996375	−	0.0124941i
$872$	−0.576802	+	0.277773i	−0.0195330	+	0.00940659i
$873$	0.00520840	+	0.00653113i	0.000176278	+	0.000221045i
$874$	34.4350	+	16.5830i	1.16478	+	0.560929i
$875$	−15.7111	+	26.5083i	−0.531131	+	0.896143i
$876$	15.3748	−	7.40409i	0.519465	−	0.250161i
$877$	−7.89373	−	3.80142i	−0.266552	−	0.128365i	0.295834	−	0.955239i	$-0.404402\pi$
$877$	−7.89373	−	3.80142i	−0.266552	−	0.128365i	−0.562386	+	0.826875i	$0.690117\pi$
$878$	16.2572	+	71.2276i	0.548655	+	2.40381i
$879$	−8.86297	−	4.26818i	−0.298940	−	0.143962i
$880$	−28.3524	+	35.5528i	−0.955759	+	1.19848i
$881$	−12.2501			−0.412715			−0.206358	−	0.978477i	$-0.566161\pi$
$881$	−12.2501			−0.412715			−0.206358	+	0.978477i	$0.566161\pi$
$882$	0.00329255	+	0.0633215i	0.000110866	+	0.00213215i
$883$	−26.9923			−0.908362			−0.454181	−	0.890910i	$-0.650068\pi$
$883$	−26.9923			−0.908362			−0.454181	+	0.890910i	$0.650068\pi$
$884$	2.09943	−	2.63260i	0.0706114	−	0.0885439i
$885$	−17.2482	−	8.30629i	−0.579792	−	0.279213i
$886$	5.83648	+	25.5713i	0.196080	+	0.859084i
$887$	51.3300	+	24.7192i	1.72349	+	0.829991i	0.988372	+	0.152055i	$0.0485889\pi$
$887$	51.3300	+	24.7192i	1.72349	+	0.829991i	0.735121	+	0.677936i	$0.237125\pi$
$888$	−1.78830	+	0.861198i	−0.0600113	+	0.0288999i
$889$	−21.7777	+	14.4861i	−0.730400	+	0.485849i
$890$	−41.3298	−	19.9034i	−1.38538	−	0.667162i
$891$	−26.1836	−	32.8332i	−0.877185	−	1.09996i
$892$	24.5635	−	11.8291i	0.822446	−	0.396069i
$893$	14.2801	−	17.9067i	0.477865	−	0.599224i
$894$	−5.17086	+	22.6550i	−0.172939	+	0.757697i
$895$	−19.0266	+	23.8586i	−0.635989	+	0.797506i
$896$	−10.0412	−	9.53268i	−0.335454	−	0.318465i
$897$	3.98732	+	4.99994i	0.133133	+	0.166943i
$898$	−9.38164	+	4.51796i	−0.313069	+	0.150766i
$899$	12.5492	−	54.9818i	0.418540	−	1.83375i
$900$	0.00372304			0.000124101
$901$	−10.7795			−0.359118
$902$	−7.05581	+	30.9135i	−0.234933	+	1.02931i
$903$	33.3751	+	31.6848i	1.11065	+	1.05440i
$904$	−0.555720	−	2.43477i	−0.0184830	−	0.0809792i
$905$	12.5385	+	54.9348i	0.416794	+	1.82610i
$906$	−2.18079	−	2.73462i	−0.0724518	−	0.0908516i
$907$	−23.0271	−	28.8751i	−0.764602	−	0.958781i	0.235312	−	0.971920i	$-0.424389\pi$
$907$	−23.0271	−	28.8751i	−0.764602	−	0.958781i	−0.999914	+	0.0131394i	$0.995817\pi$
$908$	1.30488	+	5.71707i	0.0433041	+	0.189728i
$909$	−0.0101734	−	0.0445724i	−0.000337429	−	0.00147837i
$910$	8.75530	−	5.82386i	0.290235	−	0.193059i
$911$	−0.123056	+	0.539145i	−0.00407704	+	0.0178627i	−0.976926	−	0.213580i	$-0.931488\pi$
$911$	−0.123056	+	0.539145i	−0.00407704	+	0.0178627i	0.972848	+	0.231443i	$0.0743447\pi$
$912$	−41.8880			−1.38705
$913$	13.8326			0.457792
$914$	9.80015	−	42.9373i	0.324160	−	1.42024i
$915$	14.8162	−	7.13509i	0.489807	−	0.235879i
$916$	−14.7215	−	18.4602i	−0.486414	−	0.609943i
$917$	13.1777	+	4.23024i	0.435165	+	0.139695i
$918$	−12.9150	+	16.1949i	−0.426259	+	0.534512i
$919$	2.39815	−	10.5070i	0.0791075	−	0.346593i	−0.919849	−	0.392274i	$-0.871689\pi$
$919$	2.39815	−	10.5070i	0.0791075	−	0.346593i	0.998956	+	0.0456810i	$0.0145458\pi$
$920$	−3.32923	+	4.17473i	−0.109762	+	0.137637i
$921$	53.2327	−	25.6355i	1.75408	−	0.844719i
$922$	−39.4763	−	49.5017i	−1.30008	−	1.63025i
$923$	−11.7946	−	5.67998i	−0.388224	−	0.186959i
$924$	3.04537	−	35.2315i	0.100185	−	1.15903i
$925$	−0.739540	+	0.356144i	−0.0243159	+	0.0117099i
$926$	2.90211	+	1.39758i	0.0953691	+	0.0459274i
$927$	−0.00383536	−	0.0168038i	−0.000125970	−	0.000551910i
$928$	−37.0598	−	17.8471i	−1.21655	−	0.585859i
$929$	−7.89052	+	9.89440i	−0.258880	+	0.324625i	−0.894237	−	0.447593i	$-0.852281\pi$
$929$	−7.89052	+	9.89440i	−0.258880	+	0.324625i	0.635358	+	0.772218i	$0.280853\pi$
$930$	−71.5147			−2.34506
$931$	−1.92329	−	36.9881i	−0.0630331	−	1.21224i
$932$	23.4792			0.769086
$933$	30.7868	−	38.6054i	1.00791	−	1.26389i
$934$	−34.3542	−	16.5441i	−1.12410	−	0.541339i
$935$	−4.61059	−	20.2003i	−0.150782	−	0.660621i
$936$	0.00277282	+	0.00133532i	9.06323e−5	+	4.36462e-5i
$937$	10.8546	−	5.22729i	0.354604	−	0.170768i	−0.248098	−	0.968735i	$-0.579805\pi$
$937$	10.8546	−	5.22729i	0.354604	−	0.170768i	0.602701	+	0.797967i	$0.294091\pi$
$938$	−2.41600	+	0.335972i	−0.0788853	+	0.0109699i
$939$	42.3227	+	20.3815i	1.38115	+	0.665127i
$940$	−9.48656	−	11.8958i	−0.309417	−	0.387997i
$941$	18.9384	−	9.12025i	0.617374	−	0.297312i	−0.0989359	−	0.995094i	$-0.531544\pi$
$941$	18.9384	−	9.12025i	0.617374	−	0.297312i	0.716310	+	0.697782i	$0.245830\pi$
$942$	9.82691	−	12.3226i	0.320178	−	0.401490i
$943$	−2.98575	+	13.0814i	−0.0972292	+	0.425989i
$944$	14.8312	−	18.5977i	0.482714	−	0.605304i
$945$	−24.3676	+	16.2089i	−0.792678	+	0.527275i
$946$	55.9690	+	70.1829i	1.81971	+	2.28184i
$947$	32.7723	−	15.7823i	1.06496	−	0.512856i	0.182478	−	0.983210i	$-0.441588\pi$
$947$	32.7723	−	15.7823i	1.06496	−	0.512856i	0.882478	+	0.470354i	$0.155874\pi$
$948$	3.66443	−	16.0549i	0.119015	−	0.521439i
$949$	5.83357			0.189366
$950$	−4.80685			−0.155955
$951$	4.73094	−	20.7276i	0.153411	−	0.672139i
$952$	3.62756	−	0.504452i	0.117570	−	0.0163494i
$953$	−10.6329	−	46.5859i	−0.344435	−	1.50907i	−0.789602	−	0.613619i	$-0.789713\pi$
$953$	−10.6329	−	46.5859i	−0.344435	−	1.50907i	0.445168	−	0.895447i	$-0.353144\pi$
$954$	0.0104247	+	0.0456735i	0.000337511	+	0.00147873i
$955$	−11.9424	−	14.9753i	−0.386448	−	0.484591i
$956$	10.4782	+	13.1392i	0.338889	+	0.424953i
$957$	9.98594	+	43.7512i	0.322799	+	1.41428i
$958$	1.24667	+	5.46201i	0.0402780	+	0.176470i
$959$	−46.3408	−	14.8761i	−1.49642	−	0.480375i
$960$	−4.11250	+	18.0180i	−0.132730	+	0.581529i
$961$	72.3197			2.33289
$962$	3.22640			0.104023
$963$	−0.00458177	+	0.0200741i	−0.000147646	+	0.000646877i
$964$	39.3609	−	18.9552i	1.26773	−	0.610507i
$965$	9.10237	+	11.4140i	0.293016	+	0.367430i
$966$	2.84838	−	32.9526i	0.0916451	−	1.06023i
$967$	8.21453	−	10.3007i	0.264162	−	0.331248i	−0.632006	−	0.774963i	$-0.717768\pi$
$967$	8.21453	−	10.3007i	0.264162	−	0.331248i	0.896168	+	0.443715i	$0.146340\pi$
$968$	−1.60234	+	7.02033i	−0.0515013	+	0.225642i
$969$	11.8999	−	14.9221i	0.382281	−	0.479366i
$970$	−6.45543	+	3.10877i	−0.207271	+	0.0998166i
$971$	7.83089	+	9.81962i	0.251305	+	0.315127i	0.891443	−	0.453134i	$-0.149694\pi$
$971$	7.83089	+	9.81962i	0.251305	+	0.315127i	−0.640137	+	0.768260i	$0.721123\pi$
$972$	0.0733336	+	0.0353156i	0.00235217	+	0.00113275i
$973$	6.65830	+	17.5521i	0.213455	+	0.562695i
$974$	−51.4133	+	24.7593i	−1.64739	+	0.793340i
$975$	−0.724656	−	0.348976i	−0.0232075	−	0.0111762i
$976$	4.54684	+	19.9210i	0.145541	+	0.637656i
$977$	53.1058	+	25.5744i	1.69901	+	0.818198i	0.994047	+	0.108949i	$0.0347484\pi$
$977$	53.1058	+	25.5744i	1.69901	+	0.818198i	0.704958	+	0.709249i	$0.250966\pi$
$978$	−2.93066	+	3.67493i	−0.0937121	+	0.117511i
$979$	−52.7367			−1.68547
$980$	−24.2402	−	4.22213i	−0.774325	−	0.134871i
$981$	−0.00456864			−0.000145865
$982$	0.0781237	−	0.0979640i	0.00249303	−	0.00312616i
$983$	−27.2701	−	13.1326i	−0.869782	−	0.418865i	−0.0548998	−	0.998492i	$-0.517484\pi$
$983$	−27.2701	−	13.1326i	−0.869782	−	0.418865i	−0.814882	+	0.579627i	$0.803198\pi$
$984$	−0.908031	−	3.97835i	−0.0289470	−	0.126825i
$985$	−21.6610	−	10.4314i	−0.690177	−	0.332372i
$986$	19.9116	−	9.58891i	0.634114	−	0.305373i
$987$	−18.8721	−	6.05823i	−0.600705	−	0.192836i
$988$	7.70166	+	3.70893i	0.245023	+	0.117997i
$989$	23.6839	+	29.6987i	0.753105	+	0.944364i
$990$	−0.0811312	+	0.0390707i	−0.00257852	+	0.00124175i
$991$	−13.6495	+	17.1160i	−0.433592	+	0.543707i	−0.949842	−	0.312731i	$-0.898756\pi$
$991$	−13.6495	+	17.1160i	−0.433592	+	0.543707i	0.516250	+	0.856438i	$0.327328\pi$
$992$	16.7688	−	73.4688i	0.532409	−	2.33264i
$993$	19.1808	−	24.0520i	0.608685	−	0.763267i
$994$	24.0142	+	63.3043i	0.761683	+	2.00789i
$995$	18.7161	+	23.4692i	0.593339	+	0.744023i
$996$	7.62641	−	3.67268i	0.241652	−	0.116373i
$997$	−4.68576	+	20.5297i	−0.148399	+	0.650181i	0.844931	+	0.534876i	$0.179642\pi$
$997$	−4.68576	+	20.5297i	−0.148399	+	0.650181i	−0.993330	+	0.115305i	$0.963216\pi$
$998$	−8.87742			−0.281010
$999$	−8.97966			−0.284104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.e.b.43.1	yes	12
3.2	odd	2		441.2.u.b.190.2		12
4.3	odd	2		784.2.u.b.337.1		12
7.2	even	3		343.2.g.d.165.1		12
7.3	odd	6		343.2.g.c.226.1		12
7.4	even	3		343.2.g.b.226.1		12
7.5	odd	6		343.2.g.a.165.1		12
7.6	odd	2		343.2.e.b.295.1		12
49.3	odd	42		343.2.g.a.79.1		12
49.5	odd	42		343.2.g.c.214.1		12
49.8	even	7	inner	49.2.e.b.8.1	✓	12
49.20	odd	14		2401.2.a.d.1.1		6
49.29	even	7		2401.2.a.c.1.1		6
49.41	odd	14		343.2.e.b.50.1		12
49.44	even	21		343.2.g.b.214.1		12
49.46	even	21		343.2.g.d.79.1		12
147.8	odd	14		441.2.u.b.253.2		12
196.155	odd	14		784.2.u.b.449.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.8.1	✓	12	49.8	even	7	inner
49.2.e.b.43.1	yes	12	1.1	even	1	trivial
343.2.e.b.50.1		12	49.41	odd	14
343.2.e.b.295.1		12	7.6	odd	2
343.2.g.a.79.1		12	49.3	odd	42
343.2.g.a.165.1		12	7.5	odd	6
343.2.g.b.214.1		12	49.44	even	21
343.2.g.b.226.1		12	7.4	even	3
343.2.g.c.214.1		12	49.5	odd	42
343.2.g.c.226.1		12	7.3	odd	6
343.2.g.d.79.1		12	49.46	even	21
343.2.g.d.165.1		12	7.2	even	3
441.2.u.b.190.2		12	3.2	odd	2
441.2.u.b.253.2		12	147.8	odd	14
784.2.u.b.337.1		12	4.3	odd	2
784.2.u.b.449.1		12	196.155	odd	14
2401.2.a.c.1.1		6	49.29	even	7
2401.2.a.d.1.1		6	49.20	odd	14

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19158 + 1.49419i) q^{2} +(1.55929 + 0.750915i) q^{3} +(-0.367711 - 1.61105i) q^{4} +(-1.91647 - 0.922924i) q^{5} +(-2.98003 + 1.43511i) q^{6} +(1.91879 + 1.82161i) q^{7} +(-0.598393 - 0.288171i) q^{8} +(-0.00295512 - 0.00370560i) q^{9} +O(q^{10})\)	\(q+(-1.19158 + 1.49419i) q^{2} +(1.55929 + 0.750915i) q^{3} +(-0.367711 - 1.61105i) q^{4} +(-1.91647 - 0.922924i) q^{5} +(-2.98003 + 1.43511i) q^{6} +(1.91879 + 1.82161i) q^{7} +(-0.598393 - 0.288171i) q^{8} +(-0.00295512 - 0.00370560i) q^{9} +(3.66265 - 1.76384i) q^{10} +(2.91390 - 3.65392i) q^{11} +(0.636391 - 2.78821i) q^{12} +(0.609562 - 0.764367i) q^{13} +(-5.00822 + 0.696449i) q^{14} +(-2.29530 - 2.87821i) q^{15} +(4.12128 - 1.98470i) q^{16} +(-0.463787 + 2.03198i) q^{17} +0.00905815 q^{18} -5.29116 q^{19} +(-0.782166 + 3.42689i) q^{20} +(1.62408 + 4.28126i) q^{21} +(1.98752 + 8.70788i) q^{22} +(0.841040 + 3.68484i) q^{23} +(-0.716677 - 0.898684i) q^{24} +(-0.296378 - 0.371646i) q^{25} +(0.415770 + 1.82161i) q^{26} +(-1.15716 - 5.06987i) q^{27} +(2.22914 - 3.76108i) q^{28} +(-1.23460 + 5.40913i) q^{29} +7.03564 q^{30} -10.1646 q^{31} +(-1.64972 + 7.22789i) q^{32} +(7.28741 - 3.50943i) q^{33} +(-2.48354 - 3.11426i) q^{34} +(-1.99609 - 5.26195i) q^{35} +(-0.00488327 + 0.00612343i) q^{36} +(0.384244 - 1.68348i) q^{37} +(6.30484 - 7.90601i) q^{38} +(1.52446 - 0.734141i) q^{39} +(0.880843 + 1.10454i) q^{40} +(3.19850 + 1.54031i) q^{41} +(-8.33225 - 2.67478i) q^{42} +(9.05500 - 4.36066i) q^{43} +(-6.95811 - 3.35085i) q^{44} +(0.00224341 + 0.00982903i) q^{45} +(-6.50803 - 3.13410i) q^{46} +(-2.69886 + 3.38427i) q^{47} +7.91661 q^{48} +(0.363490 + 6.99056i) q^{49} +0.908468 q^{50} +(-2.24902 + 2.82019i) q^{51} +(-1.45557 - 0.700967i) q^{52} +(1.15086 + 5.04225i) q^{53} +(8.95422 + 4.31212i) q^{54} +(-8.95670 + 4.31332i) q^{55} +(-0.623255 - 1.64298i) q^{56} +(-8.25045 - 3.97321i) q^{57} +(-6.61116 - 8.29014i) q^{58} +(4.68526 - 2.25630i) q^{59} +(-3.79293 + 4.75618i) q^{60} +(-0.994002 + 4.35501i) q^{61} +(12.1120 - 15.1879i) q^{62} +(0.00107991 - 0.0124933i) q^{63} +(-3.13007 - 3.92499i) q^{64} +(-1.87366 + 0.902307i) q^{65} +(-3.43976 + 15.0706i) q^{66} +0.482407 q^{67} +3.44416 q^{68} +(-1.45557 + 6.37728i) q^{69} +(10.2409 + 3.28748i) q^{70} +(-2.97959 - 13.0544i) q^{71} +(0.000700476 + 0.00306899i) q^{72} +(3.72027 + 4.66508i) q^{73} +(2.05759 + 2.58014i) q^{74} +(-0.183064 - 0.802058i) q^{75} +(1.94562 + 8.52430i) q^{76} +(12.2472 - 1.70311i) q^{77} +(-0.719566 + 3.15262i) q^{78} +5.75814 q^{79} -9.73004 q^{80} +(1.99952 - 8.76047i) q^{81} +(-6.11279 + 2.94377i) q^{82} +(1.84538 + 2.31404i) q^{83} +(6.30012 - 4.19073i) q^{84} +(2.76420 - 3.46620i) q^{85} +(-4.27409 + 18.7260i) q^{86} +(-5.98689 + 7.50732i) q^{87} +(-2.79661 + 1.34678i) q^{88} +(-7.03552 - 8.82227i) q^{89} +(-0.0173597 - 0.00835998i) q^{90} +(2.56200 - 0.356274i) q^{91} +(5.62718 - 2.70991i) q^{92} +(-15.8496 - 7.63277i) q^{93} +(-1.84084 - 8.06525i) q^{94} +(10.1403 + 4.88333i) q^{95} +(-7.99992 + 10.0316i) q^{96} -1.76250 q^{97} +(-10.8784 - 7.78668i) q^{98} -0.0221509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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