LMFDB - Embedded newform 49.2.g.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("49.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.g (of order $21$, degree $12$, 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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	49.39
Dual form			49.2.g.a.44.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23528 - 0.186189i) q^{2} +(-2.40355 + 1.63871i) q^{3} +(-0.419885 - 0.129517i) q^{4} +(0.186621 + 2.49028i) q^{5} +(3.27417 - 1.57676i) q^{6} +(-2.47068 - 0.946431i) q^{7} +(2.74561 + 1.32222i) q^{8} +(1.99564 - 5.08481i) q^{9} +O(q^{10})$	\(q+(-1.23528 - 0.186189i) q^{2} +(-2.40355 + 1.63871i) q^{3} +(-0.419885 - 0.129517i) q^{4} +(0.186621 + 2.49028i) q^{5} +(3.27417 - 1.57676i) q^{6} +(-2.47068 - 0.946431i) q^{7} +(2.74561 + 1.32222i) q^{8} +(1.99564 - 5.08481i) q^{9} +(0.233134 - 3.11095i) q^{10} +(0.723227 + 1.84275i) q^{11} +(1.22146 - 0.376769i) q^{12} +(-1.63931 + 2.05563i) q^{13} +(2.87578 + 1.62913i) q^{14} +(-4.52941 - 5.67970i) q^{15} +(-2.41932 - 1.64946i) q^{16} +(1.83155 + 1.69943i) q^{17} +(-3.41192 + 5.90962i) q^{18} +(1.16801 + 2.02306i) q^{19} +(0.244176 - 1.06980i) q^{20} +(7.48932 - 1.77394i) q^{21} +(-0.550290 - 2.41098i) q^{22} +(-4.68278 + 4.34498i) q^{23} +(-8.76593 + 1.32125i) q^{24} +(-1.22253 + 0.184267i) q^{25} +(2.40775 - 2.23406i) q^{26} +(1.59396 + 6.98360i) q^{27} +(0.914824 + 0.717389i) q^{28} +(-0.385156 + 1.68748i) q^{29} +(4.53761 + 7.85936i) q^{30} +(2.50275 - 4.33490i) q^{31} +(-1.78637 - 1.65751i) q^{32} +(-4.75804 - 3.24398i) q^{33} +(-1.94607 - 2.44029i) q^{34} +(1.89580 - 6.32932i) q^{35} +(-1.49651 + 1.87657i) q^{36} +(3.77975 - 1.16590i) q^{37} +(-1.06616 - 2.71652i) q^{38} +(0.571575 - 7.62714i) q^{39} +(-2.78031 + 7.08410i) q^{40} +(-3.16127 - 1.52239i) q^{41} +(-9.58173 + 0.796890i) q^{42} +(3.27475 - 1.57704i) q^{43} +(-0.0650037 - 0.867415i) q^{44} +(13.0351 + 4.02078i) q^{45} +(6.59355 - 4.49541i) q^{46} +(4.48592 + 0.676144i) q^{47} +8.51793 q^{48} +(5.20854 + 4.67666i) q^{49} +1.54448 q^{50} +(-7.18709 - 1.08328i) q^{51} +(0.954561 - 0.650809i) q^{52} +(3.25395 + 1.00371i) q^{53} +(-0.668724 - 8.92351i) q^{54} +(-4.45400 + 2.14494i) q^{55} +(-5.53214 - 5.86531i) q^{56} +(-6.12257 - 2.94848i) q^{57} +(0.789967 - 2.01280i) q^{58} +(-0.582607 + 7.77435i) q^{59} +(1.16621 + 2.97146i) q^{60} +(-12.7680 + 3.93841i) q^{61} +(-3.89872 + 4.88884i) q^{62} +(-9.74302 + 10.6742i) q^{63} +(5.54935 + 6.95867i) q^{64} +(-5.42502 - 3.69872i) q^{65} +(5.27354 + 4.89313i) q^{66} +(4.31224 - 7.46901i) q^{67} +(-0.548935 - 0.950783i) q^{68} +(4.13511 - 18.1171i) q^{69} +(-3.52030 + 7.46553i) q^{70} +(1.97751 + 8.66402i) q^{71} +(12.2025 - 11.3222i) q^{72} +(-5.52320 + 0.832488i) q^{73} +(-4.88615 + 0.736468i) q^{74} +(2.63645 - 2.44627i) q^{75} +(-0.228410 - 1.00073i) q^{76} +(-0.0428257 - 5.23734i) q^{77} +(-2.12615 + 9.31527i) q^{78} +(8.63497 + 14.9562i) q^{79} +(3.65613 - 6.33261i) q^{80} +(-3.26257 - 3.02722i) q^{81} +(3.62161 + 2.46917i) q^{82} +(2.86163 + 3.58837i) q^{83} +(-3.37441 - 0.225147i) q^{84} +(-3.89026 + 4.87823i) q^{85} +(-4.33888 + 1.33837i) q^{86} +(-1.83955 - 4.68709i) q^{87} +(-0.450817 + 6.01574i) q^{88} +(4.93768 - 12.5810i) q^{89} +(-15.3534 - 7.39379i) q^{90} +(5.99572 - 3.52731i) q^{91} +(2.52898 - 1.21789i) q^{92} +(1.08815 + 14.5204i) q^{93} +(-5.41550 - 1.67046i) q^{94} +(-4.82001 + 3.28623i) q^{95} +(7.00980 + 1.05656i) q^{96} -4.68167 q^{97} +(-5.56328 - 6.74678i) q^{98} +10.8133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) $ 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−1.23528	−	0.186189i	−0.873478	−	0.131656i	−0.303022	−	0.952984i	$-0.597995\pi$
$2$	−1.23528	−	0.186189i	−0.873478	−	0.131656i	−0.570456	+	0.821328i	$0.693234\pi$
$3$	−2.40355	+	1.63871i	−1.38769	+	0.946110i	−0.387987	+	0.921665i	$0.626829\pi$
$3$	−2.40355	+	1.63871i	−1.38769	+	0.946110i	−0.999701	+	0.0244450i	$0.992218\pi$
$4$	−0.419885	−	0.129517i	−0.209943	−	0.0647587i
$5$	0.186621	+	2.49028i	0.0834594	+	1.11369i	0.868978	+	0.494851i	$0.164777\pi$
$5$	0.186621	+	2.49028i	0.0834594	+	1.11369i	−0.785519	+	0.618838i	$0.787604\pi$
$6$	3.27417	−	1.57676i	1.33668	−	0.643709i
$7$	−2.47068	−	0.946431i	−0.933830	−	0.357717i
$7$	−2.47068	−	0.946431i	−0.933830	−	0.357717i
$8$	2.74561	+	1.32222i	0.970720	+	0.467474i
$9$	1.99564	−	5.08481i	0.665214	−	1.69494i
$10$	0.233134	−	3.11095i	0.0737234	−	0.983770i
$11$	0.723227	+	1.84275i	0.218061	+	0.555610i	0.997484	−	0.0708872i	$-0.0225830\pi$
$11$	0.723227	+	1.84275i	0.218061	+	0.555610i	−0.779423	+	0.626498i	$0.784488\pi$
$12$	1.22146	−	0.376769i	0.352604	−	0.108764i
$13$	−1.63931	+	2.05563i	−0.454662	+	0.570128i	−0.955341	−	0.295505i	$-0.904512\pi$
$13$	−1.63931	+	2.05563i	−0.454662	+	0.570128i	0.500679	+	0.865633i	$0.333084\pi$
$14$	2.87578	+	1.62913i	0.768584	+	0.435402i
$15$	−4.52941	−	5.67970i	−1.16949	−	1.46649i
$16$	−2.41932	−	1.64946i	−0.604829	−	0.412365i
$17$	1.83155	+	1.69943i	0.444216	+	0.412172i	0.870308	−	0.492508i	$-0.163920\pi$
$17$	1.83155	+	1.69943i	0.444216	+	0.412172i	−0.426092	+	0.904680i	$0.640110\pi$
$18$	−3.41192	+	5.90962i	−0.804197	+	1.39291i
$19$	1.16801	+	2.02306i	0.267960	+	0.464121i	0.968335	−	0.249655i	$-0.0803170\pi$
$19$	1.16801	+	2.02306i	0.267960	+	0.464121i	−0.700375	+	0.713775i	$0.746984\pi$
$20$	0.244176	−	1.06980i	0.0545994	−	0.239216i
$21$	7.48932	−	1.77394i	1.63430	−	0.387106i
$22$	−0.550290	−	2.41098i	−0.117322	−	0.514022i
$23$	−4.68278	+	4.34498i	−0.976427	+	0.905991i	−0.995589	−	0.0938249i	$-0.970091\pi$
$23$	−4.68278	+	4.34498i	−0.976427	+	0.905991i	0.0191622	+	0.999816i	$0.493900\pi$
$24$	−8.76593	+	1.32125i	−1.78934	+	0.269699i
$25$	−1.22253	+	0.184267i	−0.244507	+	0.0368534i
$26$	2.40775	−	2.23406i	0.472198	−	0.438136i
$27$	1.59396	+	6.98360i	0.306758	+	1.34399i
$28$	0.914824	+	0.717389i	0.172885	+	0.135574i
$29$	−0.385156	+	1.68748i	−0.0715216	+	0.313357i	−0.998017	−	0.0629503i	$-0.979949\pi$
$29$	−0.385156	+	1.68748i	−0.0715216	+	0.313357i	0.926495	+	0.376307i	$0.122806\pi$
$30$	4.53761	+	7.85936i	0.828450	+	1.43492i
$31$	2.50275	−	4.33490i	0.449508	−	0.778570i	−0.548846	−	0.835923i	$-0.684933\pi$
$31$	2.50275	−	4.33490i	0.449508	−	0.778570i	0.998354	+	0.0573531i	$0.0182661\pi$
$32$	−1.78637	−	1.65751i	−0.315789	−	0.293009i
$33$	−4.75804	−	3.24398i	−0.828269	−	0.564704i
$34$	−1.94607	−	2.44029i	−0.333748	−	0.418507i
$35$	1.89580	−	6.32932i	0.320449	−	1.06985i
$36$	−1.49651	+	1.87657i	−0.249419	+	0.312761i
$37$	3.77975	−	1.16590i	0.621388	−	0.191673i	0.0319538	−	0.999489i	$-0.489827\pi$
$37$	3.77975	−	1.16590i	0.621388	−	0.191673i	0.589434	+	0.807817i	$0.299351\pi$
$38$	−1.06616	−	2.71652i	−0.172953	−	0.440678i
$39$	0.571575	−	7.62714i	0.0915253	−	1.22132i
$40$	−2.78031	+	7.08410i	−0.439605	+	1.12009i
$41$	−3.16127	−	1.52239i	−0.493707	−	0.237757i	0.170427	−	0.985370i	$-0.445485\pi$
$41$	−3.16127	−	1.52239i	−0.493707	−	0.237757i	−0.664134	+	0.747613i	$0.731200\pi$
$42$	−9.58173	+	0.796890i	−1.47849	+	0.122963i
$43$	3.27475	−	1.57704i	0.499395	−	0.240496i	−0.167190	−	0.985925i	$-0.553469\pi$
$43$	3.27475	−	1.57704i	0.499395	−	0.240496i	0.666585	+	0.745429i	$0.267755\pi$
$44$	−0.0650037	−	0.867415i	−0.00979968	−	0.130768i
$45$	13.0351	+	4.02078i	1.94315	+	0.599383i
$46$	6.59355	−	4.49541i	0.972166	−	0.662811i
$47$	4.48592	+	0.676144i	0.654339	+	0.0986258i	0.467817	−	0.883825i	$-0.345040\pi$
$47$	4.48592	+	0.676144i	0.654339	+	0.0986258i	0.186522	+	0.982451i	$0.440279\pi$
$48$	8.51793			1.22946
$49$	5.20854	+	4.67666i	0.744077	+	0.668094i
$50$	1.54448			0.218423
$51$	−7.18709	−	1.08328i	−1.00639	−	0.151689i
$52$	0.954561	−	0.650809i	0.132374	−	0.0902509i
$53$	3.25395	+	1.00371i	0.446964	+	0.137870i	0.510063	−	0.860137i	$-0.329622\pi$
$53$	3.25395	+	1.00371i	0.446964	+	0.137870i	−0.0630986	+	0.998007i	$0.520098\pi$
$54$	−0.668724	−	8.92351i	−0.0910019	−	1.21434i
$55$	−4.45400	+	2.14494i	−0.600578	+	0.289223i
$56$	−5.53214	−	5.86531i	−0.739264	−	0.783784i
$57$	−6.12257	−	2.94848i	−0.810955	−	0.390535i
$58$	0.789967	−	2.01280i	0.103728	−	0.264294i
$59$	−0.582607	+	7.77435i	−0.0758490	+	1.01213i	0.821326	+	0.570459i	$0.193235\pi$
$59$	−0.582607	+	7.77435i	−0.0758490	+	1.01213i	−0.897175	+	0.441675i	$0.854384\pi$
$60$	1.16621	+	2.97146i	0.150557	+	0.383614i
$61$	−12.7680	+	3.93841i	−1.63478	+	0.504262i	−0.970067	−	0.242839i	$-0.921921\pi$
$61$	−12.7680	+	3.93841i	−1.63478	+	0.504262i	−0.664711	+	0.747101i	$0.731445\pi$
$62$	−3.89872	+	4.88884i	−0.495138	+	0.620884i
$63$	−9.74302	+	10.6742i	−1.22750	+	1.34482i
$64$	5.54935	+	6.95867i	0.693669	+	0.869834i
$65$	−5.42502	−	3.69872i	−0.672891	−	0.458770i
$66$	5.27354	+	4.89313i	0.649128	+	0.602303i
$67$	4.31224	−	7.46901i	0.526824	−	0.912485i	−0.472688	−	0.881230i	$-0.656716\pi$
$67$	4.31224	−	7.46901i	0.526824	−	0.912485i	0.999511	−	0.0312554i	$-0.00995052\pi$
$68$	−0.548935	−	0.950783i	−0.0665681	−	0.115299i
$69$	4.13511	−	18.1171i	0.497808	−	2.18104i
$70$	−3.52030	+	7.46553i	−0.420757	+	0.892302i
$71$	1.97751	+	8.66402i	0.234687	+	1.02823i	0.945697	+	0.325048i	$0.105381\pi$
$71$	1.97751	+	8.66402i	0.234687	+	1.02823i	−0.711011	+	0.703181i	$0.751762\pi$
$72$	12.2025	−	11.3222i	1.43808	−	1.33434i
$73$	−5.52320	+	0.832488i	−0.646442	+	0.0974354i	−0.464076	−	0.885795i	$-0.653614\pi$
$73$	−5.52320	+	0.832488i	−0.646442	+	0.0974354i	−0.182366	+	0.983231i	$0.558375\pi$
$74$	−4.88615	+	0.736468i	−0.568003	+	0.0856127i
$75$	2.63645	−	2.44627i	0.304432	−	0.282471i
$76$	−0.228410	−	1.00073i	−0.0262004	−	0.114792i
$77$	−0.0428257	−	5.23734i	−0.00488044	−	0.596850i
$78$	−2.12615	+	9.31527i	−0.240739	+	1.05475i
$79$	8.63497	+	14.9562i	0.971510	+	1.68270i	0.691002	+	0.722853i	$0.257170\pi$
$79$	8.63497	+	14.9562i	0.971510	+	1.68270i	0.280509	+	0.959852i	$0.409497\pi$
$80$	3.65613	−	6.33261i	0.408768	−	0.708007i
$81$	−3.26257	−	3.02722i	−0.362508	−	0.336358i
$82$	3.62161	+	2.46917i	0.399940	+	0.272675i
$83$	2.86163	+	3.58837i	0.314105	+	0.393875i	0.913674	−	0.406448i	$-0.133233\pi$
$83$	2.86163	+	3.58837i	0.314105	+	0.393875i	−0.599569	+	0.800323i	$0.704661\pi$
$84$	−3.37441	−	0.225147i	−0.368179	−	0.0245655i
$85$	−3.89026	+	4.87823i	−0.421958	+	0.529118i
$86$	−4.33888	+	1.33837i	−0.467873	+	0.144320i
$87$	−1.83955	−	4.68709i	−0.197220	−	0.502509i
$88$	−0.450817	+	6.01574i	−0.0480573	+	0.641280i
$89$	4.93768	−	12.5810i	0.523393	−	1.33358i	−0.387854	−	0.921721i	$-0.626783\pi$
$89$	4.93768	−	12.5810i	0.523393	−	1.33358i	0.911246	−	0.411862i	$-0.135121\pi$
$90$	−15.3534	−	7.39379i	−1.61839	−	0.779374i
$91$	5.99572	−	3.52731i	0.628522	−	0.369762i
$92$	2.52898	−	1.21789i	0.263664	−	0.126974i
$93$	1.08815	+	14.5204i	0.112836	+	1.50570i
$94$	−5.41550	−	1.67046i	−0.558566	−	0.172295i
$95$	−4.82001	+	3.28623i	−0.494522	+	0.337160i
$96$	7.00980	+	1.05656i	0.715435	+	0.107834i
$97$	−4.68167			−0.475351			−0.237676	−	0.971345i	$-0.576386\pi$
$97$	−4.68167			−0.475351			−0.237676	+	0.971345i	$0.576386\pi$
$98$	−5.56328	−	6.74678i	−0.561976	−	0.681527i
$99$	10.8133			1.08678
$100$	0.537189	+	0.0809683i	0.0537189	+	0.00809683i
$101$	2.97341	−	2.02724i	0.295865	−	0.201718i	−0.406285	−	0.913746i	$-0.633176\pi$
$101$	2.97341	−	2.02724i	0.295865	−	0.201718i	0.702150	+	0.712029i	$0.252224\pi$
$102$	8.67640	+	2.67631i	0.859091	+	0.264995i
$103$	−1.09093	−	14.5575i	−0.107493	−	1.43439i	−0.746598	−	0.665275i	$-0.768314\pi$
$103$	−1.09093	−	14.5575i	−0.107493	−	1.43439i	0.639105	−	0.769119i	$-0.279305\pi$
$104$	−7.21888	+	3.47643i	−0.707870	+	0.340892i
$105$	5.81528	+	18.3195i	0.567513	+	1.78780i
$106$	−3.83267	−	1.84572i	−0.372262	−	0.179272i
$107$	2.74238	−	6.98747i	0.265116	−	0.675504i	−0.734881	−	0.678197i	$-0.762762\pi$
$107$	2.74238	−	6.98747i	0.265116	−	0.675504i	0.999996	+	0.00269242i	$0.000857024\pi$
$108$	0.235217	−	3.13876i	0.0226338	−	0.302027i
$109$	−1.88242	−	4.79634i	−0.180304	−	0.459406i	0.811936	−	0.583746i	$-0.198414\pi$
$109$	−1.88242	−	4.79634i	−0.180304	−	0.459406i	−0.992240	+	0.124340i	$0.960319\pi$
$110$	5.90132	−	1.82032i	0.562669	−	0.173560i
$111$	−7.17424	+	8.99621i	−0.680949	+	0.853883i
$112$	4.41626	+	6.36501i	0.417297	+	0.601437i
$113$	−3.56068	−	4.46495i	−0.334960	−	0.420027i	0.585617	−	0.810588i	$-0.300852\pi$
$113$	−3.56068	−	4.46495i	−0.334960	−	0.420027i	−0.920577	+	0.390561i	$0.872281\pi$
$114$	7.01414	+	4.78216i	0.656935	+	0.447891i
$115$	−11.6941	−	10.8506i	−1.09048	−	1.01182i
$116$	0.380279	−	0.658663i	0.0353080	−	0.0611553i
$117$	7.18100	+	12.4379i	0.663884	+	1.14988i
$118$	2.16718	−	9.49506i	0.199505	−	0.874091i
$119$	−2.91678	−	5.93218i	−0.267381	−	0.543802i
$120$	−4.92620	−	21.5831i	−0.449698	−	1.97026i
$121$	5.19090	−	4.81645i	0.471900	−	0.437859i
$122$	16.5054	−	2.48779i	1.49433	−	0.225234i
$123$	10.0930	−	1.52128i	0.910056	−	0.137169i
$124$	−1.61231	+	1.49601i	−0.144790	+	0.134346i
$125$	2.09144	+	9.16321i	0.187064	+	0.819582i
$126$	14.0228	−	11.3716i	1.24925	−	1.01307i
$127$	2.01628	−	8.83391i	0.178916	−	0.783883i	−0.803216	−	0.595688i	$-0.796879\pi$
$127$	2.01628	−	8.83391i	0.178916	−	0.783883i	0.982132	−	0.188194i	$-0.0602635\pi$
$128$	−3.12251	−	5.40834i	−0.275993	−	0.478034i
$129$	−5.28671	+	9.15685i	−0.465469	+	0.806216i
$130$	6.01278	+	5.57905i	0.527356	+	0.489315i
$131$	−6.80774	−	4.64144i	−0.594795	−	0.405524i	0.228166	−	0.973622i	$-0.426727\pi$
$131$	−6.80774	−	4.64144i	−0.594795	−	0.405524i	−0.822961	+	0.568098i	$0.807679\pi$
$132$	1.57768	+	1.97835i	0.137320	+	0.172193i
$133$	−0.971103	−	6.10377i	−0.0842053	−	0.529264i
$134$	−6.71749	+	8.42346i	−0.580303	+	0.727676i
$135$	−17.0937	+	5.27270i	−1.47119	+	0.453802i
$136$	2.78171	+	7.08767i	0.238529	+	0.607763i
$137$	−1.40555	+	18.7557i	−0.120084	+	1.60241i	0.533664	+	0.845696i	$0.320815\pi$
$137$	−1.40555	+	18.7557i	−0.120084	+	1.60241i	−0.653748	+	0.756712i	$0.726804\pi$
$138$	−8.48123	+	21.6098i	−0.721971	+	1.83955i
$139$	17.5784	+	8.46529i	1.49098	+	0.718017i	0.989144	−	0.146948i	$-0.0469450\pi$
$139$	17.5784	+	8.46529i	1.49098	+	0.718017i	0.501833	+	0.864965i	$0.332659\pi$
$140$	−1.61578	+	2.41205i	−0.136558	+	0.203855i
$141$	−11.8901	+	5.72598i	−1.00133	+	0.482215i
$142$	−0.829635	−	11.0707i	−0.0696214	−	0.929033i
$143$	−4.97360	−	1.53415i	−0.415913	−	0.128292i
$144$	−13.2153	+	9.01003i	−1.10127	+	0.750836i
$145$	−4.27418	−	0.644228i	−0.354951	−	0.0535003i
$146$	6.97772			0.577480
$147$	−20.1827	−	2.70529i	−1.66464	−	0.223128i
$148$	−1.73807			−0.142868
$149$	−14.6438	−	2.20720i	−1.19967	−	0.180821i	−0.481344	−	0.876532i	$-0.659851\pi$
$149$	−14.6438	−	2.20720i	−1.19967	−	0.180821i	−0.718322	+	0.695711i	$0.755089\pi$
$150$	−3.71224	+	2.53096i	−0.303103	+	0.206652i
$151$	−17.9736	−	5.54413i	−1.46267	−	0.451175i	−0.541623	−	0.840621i	$-0.682190\pi$
$151$	−17.9736	−	5.54413i	−1.46267	−	0.451175i	−0.921049	+	0.389446i	$0.872666\pi$
$152$	0.531988	+	7.09889i	0.0431499	+	0.575796i
$153$	12.2964	−	5.92163i	0.994104	−	0.478735i
$154$	−0.922233	+	6.47757i	−0.0743157	+	0.521978i
$155$	11.2622	+	5.42358i	0.904601	+	0.435633i
$156$	−1.22784	+	3.12850i	−0.0983063	+	0.250480i
$157$	−0.433272	+	5.78161i	−0.0345788	+	0.461423i	0.952859	+	0.303414i	$0.0981265\pi$
$157$	−0.433272	+	5.78161i	−0.0345788	+	0.461423i	−0.987438	+	0.158009i	$0.949493\pi$
$158$	−7.88196	−	20.0829i	−0.627055	−	1.59771i
$159$	−9.46581	+	2.91982i	−0.750688	+	0.231556i
$160$	3.79429	−	4.75789i	0.299965	−	0.376145i
$161$	15.6819	−	6.30314i	1.23591	−	0.496757i
$162$	3.46657	+	4.34694i	0.272359	+	0.341528i
$163$	14.4100	+	9.82454i	1.12867	+	0.769517i	0.975786	−	0.218726i	$-0.0701901\pi$
$163$	14.4100	+	9.82454i	1.12867	+	0.769517i	0.152888	+	0.988243i	$0.451142\pi$
$164$	1.13020	+	1.04867i	0.0882534	+	0.0818872i
$165$	7.19048	−	12.4543i	0.559778	−	0.969564i
$166$	−2.86681	−	4.96546i	−0.222508	−	0.385394i
$167$	0.504978	−	2.21246i	0.0390764	−	0.171205i	−0.951624	−	0.307264i	$-0.900587\pi$
$167$	0.504978	−	2.21246i	0.0390764	−	0.171205i	0.990701	+	0.136059i	$0.0434437\pi$
$168$	22.9083	+	5.03196i	1.76741	+	0.388224i
$169$	1.35450	+	5.93445i	0.104192	+	0.456496i
$170$	5.71384	−	5.30167i	0.438232	−	0.406620i
$171$	12.6178	−	1.90183i	0.964907	−	0.145436i
$172$	−1.57927	+	0.238037i	−0.120419	+	0.0181502i
$173$	1.37705	−	1.27772i	0.104695	−	0.0971430i	−0.626089	−	0.779752i	$-0.715345\pi$
$173$	1.37705	−	1.27772i	0.104695	−	0.0971430i	0.730784	+	0.682609i	$0.239155\pi$
$174$	1.39968	+	6.13239i	0.106109	+	0.464895i
$175$	3.19489	+	0.701778i	0.241511	+	0.0530494i
$176$	1.28983	−	5.65113i	0.0972249	−	0.425970i
$177$	−11.3396	−	19.6407i	−0.852335	−	1.47629i
$178$	−8.44188	+	14.6218i	−0.632746	+	1.09595i
$179$	5.73001	+	5.31668i	0.428281	+	0.397387i	0.864645	−	0.502383i	$-0.167543\pi$
$179$	5.73001	+	5.31668i	0.428281	+	0.397387i	−0.436364	+	0.899770i	$0.643734\pi$
$180$	−4.95247	−	3.37653i	−0.369135	−	0.251672i
$181$	2.59753	+	3.25719i	0.193073	+	0.242105i	0.868939	−	0.494918i	$-0.164802\pi$
$181$	2.59753	+	3.25719i	0.193073	+	0.242105i	−0.675867	+	0.737024i	$0.736231\pi$
$182$	−8.06316	+	3.24089i	−0.597681	+	0.240231i
$183$	24.2346	−	30.3892i	1.79147	−	2.24644i
$184$	−18.6021	+	5.73798i	−1.37136	+	0.423010i
$185$	3.60880	+	9.19508i	0.265324	+	0.676036i
$186$	1.35936	−	18.1394i	0.0996733	−	1.33005i
$187$	−1.80700	+	4.60416i	−0.132141	+	0.336690i
$188$	−1.79600	−	0.864908i	−0.130987	−	0.0630799i
$189$	2.67132	−	18.7628i	0.194310	−	1.36479i
$190$	6.56594	−	3.16199i	0.476343	−	0.229395i
$191$	0.301388	+	4.02174i	0.0218076	+	0.291003i	0.997436	+	0.0715711i	$0.0228013\pi$
$191$	0.301388	+	4.02174i	0.0218076	+	0.291003i	−0.975628	+	0.219432i	$0.929580\pi$
$192$	−24.7414	−	7.63170i	−1.78556	−	0.550771i
$193$	6.72649	−	4.58604i	0.484183	−	0.330111i	−0.296505	−	0.955031i	$-0.595821\pi$
$193$	6.72649	−	4.58604i	0.484183	−	0.330111i	0.780688	+	0.624921i	$0.214869\pi$
$194$	5.78319	+	0.871675i	0.415209	+	0.0625827i
$195$	19.1004			1.36781
$196$	−1.58128	−	2.63826i	−0.112949	−	0.188447i
$197$	−16.3455			−1.16457			−0.582284	−	0.812986i	$-0.697841\pi$
$197$	−16.3455			−1.16457			−0.582284	+	0.812986i	$0.697841\pi$
$198$	−13.3575	−	2.01333i	−0.949280	−	0.143081i
$199$	10.1157	−	6.89678i	0.717084	−	0.488900i	−0.148975	−	0.988841i	$-0.547597\pi$
$199$	10.1157	−	6.89678i	0.717084	−	0.488900i	0.866059	+	0.499941i	$0.166645\pi$
$200$	−3.60024	−	1.11053i	−0.254575	−	0.0785261i
$201$	1.87489	+	25.0186i	0.132244	+	1.76468i
$202$	−4.05045	+	1.95060i	−0.284989	+	0.137243i
$203$	2.54868	−	3.80470i	0.178882	−	0.267037i
$204$	2.87745	+	1.38571i	0.201462	+	0.0970188i
$205$	3.20122	−	8.15657i	0.223583	−	0.569679i
$206$	−1.36284	+	18.1858i	−0.0949533	+	1.26706i
$207$	12.7483	+	32.4821i	0.886066	+	2.25766i
$208$	7.35668	−	2.26924i	0.510094	−	0.157343i
$209$	−2.88325	+	3.61548i	−0.199439	+	0.250088i
$210$	−3.77263	−	23.7125i	−0.260336	−	1.63632i
$211$	−7.89998	−	9.90626i	−0.543857	−	0.681975i	0.431625	−	0.902053i	$-0.357940\pi$
$211$	−7.89998	−	9.90626i	−0.543857	−	0.681975i	−0.975482	+	0.220078i	$0.929369\pi$
$212$	−1.23629	−	0.842887i	−0.0849086	−	0.0578897i
$213$	−18.9508	−	17.5838i	−1.29849	−	1.20482i
$214$	−4.68861	+	8.12091i	−0.320507	+	0.555134i
$215$	4.53841	+	7.86075i	0.309517	+	0.536099i
$216$	−4.85743	+	21.2818i	−0.330506	+	1.44804i
$217$	−10.2862	+	8.34146i	−0.698272	+	0.566255i
$218$	1.43230	+	6.27533i	0.0970078	+	0.425019i
$219$	11.9111	−	11.0518i	0.804875	−	0.746815i
$220$	2.14798	−	0.323756i	0.144817	−	0.0218276i
$221$	−6.49587	+	0.979094i	−0.436959	+	0.0658610i
$222$	10.5372	−	9.77711i	0.707212	−	0.656197i
$223$	−3.88480	−	17.0204i	−0.260145	−	1.13977i	−0.921094	−	0.389340i	$-0.872703\pi$
$223$	−3.88480	−	17.0204i	−0.260145	−	1.13977i	0.660949	−	0.750431i	$-0.270154\pi$
$224$	2.84483	+	5.78585i	0.190078	+	0.386584i
$225$	−1.50277	+	6.58408i	−0.100185	+	0.438939i
$226$	3.56712	+	6.17844i	0.237281	+	0.410983i
$227$	3.03342	−	5.25404i	0.201335	−	0.348723i	−0.747624	−	0.664123i	$-0.768805\pi$
$227$	3.03342	−	5.25404i	0.201335	−	0.348723i	0.948959	+	0.315400i	$0.102139\pi$
$228$	2.18890	+	2.03100i	0.144963	+	0.134506i
$229$	9.52164	+	6.49174i	0.629208	+	0.428986i	0.835490	−	0.549506i	$-0.185184\pi$
$229$	9.52164	+	6.49174i	0.629208	+	0.428986i	−0.206282	+	0.978493i	$0.566136\pi$
$230$	12.4253	+	15.5809i	0.819302	+	1.02737i
$231$	8.68541	+	12.5180i	0.571458	+	0.823624i
$232$	−3.28870	+	4.12390i	−0.215914	+	0.270747i
$233$	24.3491	−	7.51071i	1.59516	−	0.492043i	0.635242	−	0.772313i	$-0.280900\pi$
$233$	24.3491	−	7.51071i	1.59516	−	0.492043i	0.959921	+	0.280270i	$0.0904241\pi$
$234$	−6.55478	−	16.7013i	−0.428500	−	1.09180i
$235$	−0.846623	+	11.2974i	−0.0552276	+	0.736961i
$236$	1.25154	−	3.18888i	0.0814685	−	0.207578i
$237$	−45.2634	−	21.7977i	−2.94018	−	1.41591i
$238$	2.49855	+	7.87101i	0.161957	+	0.510202i
$239$	1.06660	−	0.513649i	0.0689928	−	0.0332252i	−0.399069	−	0.916921i	$-0.630667\pi$
$239$	1.06660	−	0.513649i	0.0689928	−	0.0332252i	0.468062	+	0.883696i	$0.344952\pi$
$240$	1.58962	+	21.2121i	0.102610	+	1.36923i
$241$	1.45003	+	0.447276i	0.0934049	+	0.0288116i	0.341105	−	0.940025i	$-0.389199\pi$
$241$	1.45003	+	0.447276i	0.0934049	+	0.0288116i	−0.247700	+	0.968837i	$0.579675\pi$
$242$	−7.30900	+	4.98319i	−0.469840	+	0.320332i
$243$	−8.44708	−	1.27319i	−0.541880	−	0.0816753i
$244$	5.87120			0.375865
$245$	−10.6742	+	13.8435i	−0.681949	+	0.884429i
$246$	−12.7510			−0.812973
$247$	−6.07338	−	0.915415i	−0.386440	−	0.0582464i
$248$	12.6033	−	8.59275i	0.800307	−	0.545640i
$249$	−12.7584	−	3.93543i	−0.808528	−	0.249398i
$250$	−0.877436	−	11.7086i	−0.0554939	−	0.740515i
$251$	−6.12852	+	2.95134i	−0.386829	+	0.186287i	−0.617182	−	0.786820i	$-0.711726\pi$
$251$	−6.12852	+	2.95134i	−0.386829	+	0.186287i	0.230354	+	0.973107i	$0.426012\pi$
$252$	5.47345	−	3.22005i	0.344795	−	0.202844i
$253$	−11.3934	−	5.48679i	−0.716299	−	0.344951i
$254$	−4.13546	+	10.5370i	−0.259482	+	0.661149i
$255$	1.35641	−	18.1000i	0.0849418	−	1.13347i
$256$	−3.65321	−	9.30822i	−0.228326	−	0.581764i
$257$	17.4308	−	5.37668i	1.08730	−	0.335388i	0.301248	−	0.953546i	$-0.402597\pi$
$257$	17.4308	−	5.37668i	1.08730	−	0.335388i	0.786054	+	0.618158i	$0.212121\pi$
$258$	8.23550	−	10.3270i	0.512720	−	0.642930i
$259$	−10.4420	−	0.696709i	−0.648835	−	0.0432914i
$260$	1.79884	+	2.25567i	0.111559	+	0.139891i
$261$	7.81187	+	5.32604i	0.483543	+	0.329674i
$262$	7.54530	+	7.00102i	0.466150	+	0.432524i
$263$	−15.3675	+	26.6173i	−0.947601	+	1.64129i	−0.197144	+	0.980374i	$0.563167\pi$
$263$	−15.3675	+	26.6173i	−0.947601	+	1.64129i	−0.750457	+	0.660919i	$0.770167\pi$
$264$	−8.77449	−	15.1979i	−0.540033	−	0.935364i
$265$	−1.89227	+	8.29057i	−0.116241	+	0.509286i
$266$	0.0631322	+	7.72070i	0.00387088	+	0.473386i
$267$	8.74867	+	38.3304i	0.535410	+	2.34578i
$268$	−2.77801	+	2.57762i	−0.169694	+	0.157453i
$269$	−8.02750	+	1.20995i	−0.489445	+	0.0737720i	−0.389128	−	0.921183i	$-0.627224\pi$
$269$	−8.02750	+	1.20995i	−0.489445	+	0.0737720i	−0.100317	+	0.994956i	$0.531986\pi$
$270$	22.0973	−	3.33063i	1.34480	−	0.202696i
$271$	5.92556	−	5.49811i	0.359952	−	0.333987i	−0.479378	−	0.877608i	$-0.659138\pi$
$271$	5.92556	−	5.49811i	0.359952	−	0.333987i	0.839330	+	0.543622i	$0.182947\pi$
$272$	−1.62795	−	7.13253i	−0.0987091	−	0.432473i
$273$	−8.63075	+	18.3033i	−0.522357	+	1.10777i
$274$	5.22836	−	22.9069i	0.315857	−	1.38386i
$275$	−1.22373	−	2.11956i	−0.0737935	−	0.127814i
$276$	−4.08275	+	7.07153i	−0.245753	+	0.425656i
$277$	8.14785	+	7.56010i	0.489557	+	0.454242i	0.885911	−	0.463855i	$-0.153534\pi$
$277$	8.14785	+	7.56010i	0.489557	+	0.454242i	−0.396354	+	0.918098i	$0.629725\pi$
$278$	−20.1381	−	13.7299i	−1.20780	−	0.823467i
$279$	−17.0475	−	21.3769i	−1.02061	−	1.27980i
$280$	13.5739	−	14.8712i	0.811194	−	0.888724i
$281$	9.71226	−	12.1788i	0.579385	−	0.726525i	−0.402623	−	0.915366i	$-0.631901\pi$
$281$	9.71226	−	12.1788i	0.579385	−	0.726525i	0.982008	+	0.188840i	$0.0604729\pi$
$282$	15.7538	−	4.85940i	0.938125	−	0.289373i
$283$	5.68968	+	14.4971i	0.338216	+	0.861761i	0.994255	+	0.107034i	$0.0341354\pi$
$283$	5.68968	+	14.4971i	0.338216	+	0.861761i	−0.656039	+	0.754727i	$0.727769\pi$
$284$	0.291816	−	3.89402i	0.0173161	−	0.231067i
$285$	6.19994	−	15.7972i	0.367253	−	0.935745i
$286$	5.85817	+	2.82114i	0.346401	+	0.166818i
$287$	6.36966	+	6.75326i	0.375989	+	0.398632i
$288$	−11.9931	+	5.77556i	−0.706699	+	0.340328i
$289$	−0.803899	−	10.7273i	−0.0472882	−	0.631017i
$290$	5.15987	+	1.59161i	0.302998	+	0.0934626i
$291$	11.2526	−	7.67190i	0.659639	−	0.449735i
$292$	2.42693	+	0.365801i	0.142025	+	0.0214069i
$293$	−2.05031			−0.119780			−0.0598901	−	0.998205i	$-0.519075\pi$
$293$	−2.05031			−0.119780			−0.0598901	+	0.998205i	$0.519075\pi$
$294$	24.4276	+	7.09959i	1.42465	+	0.414056i
$295$	−19.4691			−1.13353
$296$	11.9193	+	1.79655i	0.692795	+	0.104422i
$297$	−11.7162	+	7.98800i	−0.679845	+	0.463511i
$298$	17.6783	+	5.45303i	1.02408	+	0.315885i
$299$	−1.25515	−	16.7488i	−0.0725872	−	0.968608i
$300$	−1.42384	+	0.685687i	−0.0822056	+	0.0395882i
$301$	−9.58343	+	0.797031i	−0.552380	+	0.0459401i
$302$	21.1703	+	10.1951i	1.21821	+	0.586660i
$303$	−3.82467	+	9.74511i	−0.219722	+	0.559842i
$304$	0.511164	−	6.82100i	0.0293172	−	0.391211i
$305$	−12.1905	−	31.0610i	−0.698029	−	1.77855i
$306$	−16.2921	+	5.02544i	−0.931356	+	0.287285i
$307$	9.87875	−	12.3876i	0.563810	−	0.706996i	−0.415447	−	0.909617i	$-0.636375\pi$
$307$	9.87875	−	12.3876i	0.563810	−	0.706996i	0.979257	+	0.202622i	$0.0649462\pi$
$308$	−0.660345	+	2.20463i	−0.0376266	+	0.125620i
$309$	26.4777	+	33.2019i	1.50626	+	1.88879i
$310$	−12.9022	−	8.79656i	−0.732795	−	0.499611i
$311$	11.1085	+	10.3072i	0.629905	+	0.584466i	0.929147	−	0.369711i	$-0.120543\pi$
$311$	11.1085	+	10.3072i	0.629905	+	0.584466i	−0.299242	+	0.954177i	$0.596734\pi$
$312$	11.6541	−	20.1854i	0.659781	−	1.14277i
$313$	8.98609	+	15.5644i	0.507924	+	0.879750i	0.999958	+	0.00917402i	$0.00292022\pi$
$313$	8.98609	+	15.5644i	0.507924	+	0.879750i	−0.492034	+	0.870576i	$0.663746\pi$
$314$	1.61169	−	7.06126i	0.0909527	−	0.398490i
$315$	−28.4001	−	22.2708i	−1.60016	−	1.25482i
$316$	−1.68861	−	7.39827i	−0.0949916	−	0.416185i
$317$	−9.67401	+	8.97617i	−0.543347	+	0.504152i	−0.903411	−	0.428775i	$-0.858945\pi$
$317$	−9.67401	+	8.97617i	−0.543347	+	0.504152i	0.360064	+	0.932927i	$0.382755\pi$
$318$	12.2366	−	1.84437i	0.686195	−	0.103427i
$319$	−3.38816	+	0.510682i	−0.189700	+	0.0285927i
$320$	−16.2934	+	15.1181i	−0.910831	+	0.845128i
$321$	4.85900	+	21.2887i	0.271203	+	1.18822i
$322$	−20.5452	+	4.86638i	−1.14494	+	0.271193i
$323$	−1.29877	+	5.69028i	−0.0722655	+	0.316616i
$324$	0.977828	+	1.69365i	0.0543238	+	0.0940915i
$325$	1.62532	−	2.81514i	0.0901567	−	0.156156i
$326$	−15.9712	−	14.8191i	−0.884561	−	0.820753i
$327$	12.3843	+	8.44348i	0.684854	+	0.466925i
$328$	−6.66669	−	8.35976i	−0.368106	−	0.461591i
$329$	−10.4434	−	5.91615i	−0.575761	−	0.326168i
$330$	−11.2011	+	14.0458i	−0.616602	+	0.773195i
$331$	−7.82530	+	2.41378i	−0.430117	+	0.132674i	−0.502252	−	0.864721i	$-0.667495\pi$
$331$	−7.82530	+	2.41378i	−0.430117	+	0.132674i	0.0721348	+	0.997395i	$0.477019\pi$
$332$	−0.736800	−	1.87734i	−0.0404371	−	0.103032i
$333$	1.61465	−	21.5461i	0.0884825	−	1.18072i
$334$	−1.03573	+	2.63899i	−0.0566725	+	0.144399i
$335$	19.4047	+	9.34482i	1.06019	+	0.510562i
$336$	−21.0451	−	8.06163i	−1.14810	−	0.439798i
$337$	8.15637	−	3.92790i	0.444306	−	0.213966i	−0.198334	−	0.980134i	$-0.563553\pi$
$337$	8.15637	−	3.92790i	0.444306	−	0.213966i	0.642640	+	0.766168i	$0.277839\pi$
$338$	−0.568262	−	7.58293i	−0.0309094	−	0.412457i
$339$	15.8750	+	4.89679i	0.862212	+	0.265957i
$340$	2.26528	−	1.54444i	0.122852	−	0.0837590i
$341$	9.79819	+	1.47684i	0.530602	+	0.0799754i
$342$	−15.9407			−0.861972
$343$	−8.44250	−	16.4841i	−0.455852	−	0.890056i
$344$	11.0764			0.597198
$345$	45.8884	+	6.91656i	2.47055	+	0.372375i
$346$	−1.93895	+	1.32195i	−0.104238	+	0.0710685i
$347$	6.05969	+	1.86917i	0.325301	+	0.100342i	0.453105	−	0.891457i	$-0.350316\pi$
$347$	6.05969	+	1.86917i	0.325301	+	0.100342i	−0.127803	+	0.991800i	$0.540793\pi$
$348$	0.165339	+	2.20629i	0.00886309	+	0.118270i
$349$	−4.52499	+	2.17912i	−0.242217	+	0.116646i	−0.551055	−	0.834469i	$-0.685774\pi$
$349$	−4.52499	+	2.17912i	−0.242217	+	0.116646i	0.308837	+	0.951115i	$0.400060\pi$
$350$	−3.81593	−	1.46175i	−0.203970	−	0.0781337i
$351$	−16.9687	−	8.17168i	−0.905720	−	0.436172i
$352$	1.76243	−	4.49059i	0.0939377	−	0.239349i
$353$	1.87103	−	24.9672i	0.0995850	−	1.32887i	−0.693808	−	0.720160i	$-0.744068\pi$
$353$	1.87103	−	24.9672i	0.0995850	−	1.32887i	0.793393	−	0.608710i	$-0.208313\pi$
$354$	10.3507	+	26.3732i	0.550134	+	1.40172i
$355$	−21.2068	+	6.54144i	−1.12554	+	0.347183i
$356$	−3.70272	+	4.64306i	−0.196244	+	0.246082i
$357$	16.7318	+	9.47852i	0.885538	+	0.501656i
$358$	−6.08829	−	7.63447i	−0.321776	−	0.403494i
$359$	−17.0127	−	11.5991i	−0.897896	−	0.612175i	0.0239580	−	0.999713i	$-0.492373\pi$
$359$	−17.0127	−	11.5991i	−0.897896	−	0.612175i	−0.921854	+	0.387538i	$0.873326\pi$
$360$	30.4728	+	28.2747i	1.60606	+	1.49021i
$361$	6.77150	−	11.7286i	0.356395	−	0.617293i
$362$	−2.60223	−	4.50719i	−0.136770	−	0.236893i
$363$	−4.58380	+	20.0829i	−0.240587	+	1.05408i
$364$	−2.97436	+	0.704515i	−0.155899	+	0.0369266i
$365$	−3.10388	−	13.5990i	−0.162464	−	0.711803i
$366$	−35.5948	+	33.0271i	−1.86057	+	1.72636i
$367$	−3.22505	+	0.486098i	−0.168346	+	0.0253741i	−0.232674	−	0.972555i	$-0.574748\pi$
$367$	−3.22505	+	0.486098i	−0.168346	+	0.0253741i	0.0643283	+	0.997929i	$0.479510\pi$
$368$	18.4960	−	2.78782i	0.964171	−	0.145325i
$369$	−14.0498	+	13.0363i	−0.731404	+	0.678644i
$370$	−2.74587	−	12.0305i	−0.142751	−	0.625433i
$371$	−7.08953	−	5.55949i	−0.368070	−	0.288634i
$372$	1.42375	−	6.23784i	0.0738178	−	0.323417i
$373$	7.80665	+	13.5215i	0.404213	+	0.700118i	0.994230	−	0.107274i	$-0.0342120\pi$
$373$	7.80665	+	13.5215i	0.404213	+	0.700118i	−0.590016	+	0.807391i	$0.700879\pi$
$374$	3.08940	−	5.35100i	0.159749	−	0.276694i
$375$	−20.0427	−	18.5969i	−1.03500	−	0.960341i
$376$	11.4226	+	7.78779i	0.589075	+	0.401624i
$377$	−2.83743	−	3.55803i	−0.146135	−	0.183248i
$378$	−6.79328	+	22.6800i	−0.349409	+	1.16654i
$379$	−21.5297	+	26.9973i	−1.10590	+	1.38676i	−0.191726	+	0.981449i	$0.561408\pi$
$379$	−21.5297	+	26.9973i	−1.10590	+	1.38676i	−0.914179	+	0.405312i	$0.867163\pi$
$380$	2.44947	−	0.755563i	0.125655	−	0.0387596i
$381$	9.62999	+	24.5368i	0.493359	+	1.25706i
$382$	0.376505	−	5.02410i	0.0192637	−	0.257056i
$383$	3.82095	−	9.73563i	0.195242	−	0.497467i	−0.799406	−	0.600791i	$-0.794852\pi$
$383$	3.82095	−	9.73563i	0.195242	−	0.497467i	0.994648	+	0.103323i	$0.0329477\pi$
$384$	16.3678	+	7.88231i	0.835265	+	0.402243i
$385$	13.0345	−	1.08404i	0.664298	−	0.0552480i
$386$	−9.16300	+	4.41267i	−0.466384	+	0.224599i
$387$	−1.48371	−	19.7987i	−0.0754211	−	1.00642i
$388$	1.96576	+	0.606358i	0.0997965	+	0.0307832i
$389$	26.5240	−	18.0838i	1.34482	−	0.916884i	0.345057	−	0.938582i	$-0.387859\pi$
$389$	26.5240	−	18.0838i	1.34482	−	0.916884i	0.999765	+	0.0216974i	$0.00690704\pi$
$390$	−23.5944	−	3.55629i	−1.19475	−	0.180080i
$391$	−15.9607			−0.807169
$392$	8.11706	+	19.7271i	0.409973	+	0.996369i
$393$	23.9687			1.20906
$394$	20.1913	+	3.04335i	1.01722	+	0.153322i
$395$	−35.6337	+	24.2947i	−1.79293	+	1.22240i
$396$	−4.54036	−	1.40052i	−0.228162	−	0.0703786i
$397$	−0.356697	−	4.75980i	−0.0179021	−	0.238887i	−0.998976	−	0.0452516i	$-0.985591\pi$
$397$	−0.356697	−	4.75980i	−0.0179021	−	0.238887i	0.981073	−	0.193636i	$-0.0620280\pi$
$398$	−13.7799	+	6.63605i	−0.690724	+	0.332635i
$399$	12.3364	+	13.0793i	0.617593	+	0.654786i
$400$	3.26164	+	1.57072i	0.163082	+	0.0785360i
$401$	−3.72651	+	9.49500i	−0.186093	+	0.474158i	−0.993224	−	0.116215i	$-0.962924\pi$
$401$	−3.72651	+	9.49500i	−0.186093	+	0.474158i	0.807131	+	0.590373i	$0.201019\pi$
$402$	2.34218	−	31.2542i	0.116817	−	1.55882i
$403$	4.80814	+	12.2510i	0.239511	+	0.610263i
$404$	−1.51105	+	0.466098i	−0.0751777	+	0.0231893i
$405$	6.92978	−	8.68967i	0.344344	−	0.431793i
$406$	−3.85673	+	4.22534i	−0.191407	+	0.209700i
$407$	4.88208	+	6.12194i	0.241996	+	0.303453i
$408$	−18.3006	−	12.4771i	−0.906015	−	0.617711i
$409$	4.26765	+	3.95980i	0.211022	+	0.195799i	0.778601	−	0.627519i	$-0.215930\pi$
$409$	4.26765	+	3.95980i	0.211022	+	0.195799i	−0.567580	+	0.823319i	$0.692120\pi$
$410$	−5.47308	+	9.47965i	−0.270296	+	0.468166i
$411$	−27.3569	−	47.3835i	−1.34942	−	2.33726i
$412$	−1.42738	+	6.25378i	−0.0703222	+	0.308102i
$413$	8.79732	−	18.6565i	0.432888	−	0.918029i
$414$	−9.69993	−	42.4982i	−0.476725	−	2.08867i
$415$	−8.40202	+	7.79594i	−0.412439	+	0.382687i
$416$	6.33563	−	0.954943i	0.310630	−	0.0468199i
$417$	−56.1226	+	8.45912i	−2.74833	+	0.414245i
$418$	4.23480	−	3.92932i	0.207131	−	0.192189i
$419$	−8.01004	−	35.0943i	−0.391316	−	1.71447i	−0.660023	−	0.751245i	$-0.729454\pi$
$419$	−8.01004	−	35.0943i	−0.391316	−	1.71447i	0.268707	−	0.963222i	$-0.413404\pi$
$420$	−0.0690570	−	8.44527i	−0.00336963	−	0.412087i
$421$	−4.60602	+	20.1803i	−0.224484	+	0.983528i	0.729573	+	0.683903i	$0.239719\pi$
$421$	−4.60602	+	20.1803i	−0.224484	+	0.983528i	−0.954057	+	0.299625i	$0.903138\pi$
$422$	7.91428	+	13.7079i	0.385261	+	0.667292i
$423$	12.3904	−	21.4607i	0.602440	−	1.04346i
$424$	7.60696	+	7.05822i	0.369426	+	0.342778i
$425$	−2.55228	−	1.74011i	−0.123804	−	0.0844079i
$426$	20.1358	+	25.2494i	0.975580	+	1.22334i
$427$	35.2732	+	2.35349i	1.70699	+	0.113893i
$428$	−2.05648	+	2.57875i	−0.0994039	+	0.124649i
$429$	14.4683	−	4.46288i	0.698537	−	0.215470i
$430$	−4.14264	−	10.5553i	−0.199776	−	0.509020i
$431$	−1.05062	+	14.0195i	−0.0506065	+	0.675297i	0.912998	+	0.407964i	$0.133761\pi$
$431$	−1.05062	+	14.0195i	−0.0506065	+	0.675297i	−0.963604	+	0.267332i	$0.913858\pi$
$432$	7.66288	−	19.5247i	0.368681	−	0.939383i
$433$	29.3827	+	14.1500i	1.41204	+	0.680004i	0.975565	−	0.219710i	$-0.0705112\pi$
$433$	29.3827	+	14.1500i	1.41204	+	0.680004i	0.436479	+	0.899715i	$0.356225\pi$
$434$	14.2595	−	8.38890i	0.684476	−	0.402680i
$435$	11.3289	−	5.45570i	0.543178	−	0.261581i
$436$	0.169193	+	2.25772i	0.00810286	+	0.108125i
$437$	−14.2597	−	4.39853i	−0.682133	−	0.210410i
$438$	−16.7713	+	11.4345i	−0.801363	+	0.546360i
$439$	27.0482	+	4.07686i	1.29094	+	0.194578i	0.758378	−	0.651815i	$-0.225992\pi$
$439$	27.0482	+	4.07686i	1.29094	+	0.194578i	0.532560	+	0.846392i	$0.321230\pi$
$440$	−15.0650			−0.718197
$441$	34.1743	−	17.1515i	1.62735	−	0.816738i
$442$	8.20654			0.390345
$443$	0.930962	+	0.140320i	0.0442314	+	0.00666681i	0.171121	−	0.985250i	$-0.445261\pi$
$443$	0.930962	+	0.140320i	0.0442314	+	0.00666681i	−0.126889	+	0.991917i	$0.540499\pi$
$444$	4.17753	−	2.84819i	0.198257	−	0.135169i
$445$	32.2517	+	9.94834i	1.52888	+	0.471597i
$446$	1.62981	+	21.7483i	0.0771739	+	1.02981i
$447$	38.8140	−	18.6918i	1.83584	−	0.884093i
$448$	−7.12479	−	22.4447i	−0.336615	−	1.06041i
$449$	−36.3450	−	17.5029i	−1.71523	−	0.826011i	−0.990587	−	0.136885i	$-0.956291\pi$
$449$	−36.3450	−	17.5029i	−1.71523	−	0.826011i	−0.724642	−	0.689126i	$-0.757995\pi$
$450$	3.08224	−	7.85341i	0.145298	−	0.370213i
$451$	0.519067	−	6.92646i	0.0244419	−	0.326154i
$452$	0.916787	+	2.33594i	0.0431220	+	0.109873i
$453$	52.2857	−	16.1280i	2.45659	−	0.757759i
$454$	−4.72539	+	5.92545i	−0.221773	+	0.278095i
$455$	9.90292	+	14.2728i	0.464256	+	0.669118i
$456$	−12.9117	−	16.1907i	−0.604645	−	0.758201i
$457$	5.51386	+	3.75928i	0.257927	+	0.175852i	0.685379	−	0.728186i	$-0.259636\pi$
$457$	5.51386	+	3.75928i	0.257927	+	0.175852i	−0.427452	+	0.904038i	$0.640589\pi$
$458$	−10.5532	−	9.79197i	−0.493120	−	0.457549i
$459$	−8.94872	+	15.4996i	−0.417690	+	0.723461i
$460$	3.50486	+	6.07060i	0.163415	+	0.283043i
$461$	3.28441	−	14.3899i	0.152970	−	0.670206i	−0.839042	−	0.544066i	$-0.816884\pi$
$461$	3.28441	−	14.3899i	0.152970	−	0.670206i	0.992012	−	0.126140i	$-0.0402589\pi$
$462$	−8.39823	−	17.0804i	−0.390721	−	0.794653i
$463$	0.681706	+	2.98675i	0.0316816	+	0.138806i	0.988295	−	0.152553i	$-0.0487496\pi$
$463$	0.681706	+	2.98675i	0.0316816	+	0.138806i	−0.956614	+	0.291359i	$0.905892\pi$
$464$	3.71524	−	3.44724i	0.172476	−	0.160034i
$465$	−35.9569	+	5.41963i	−1.66746	+	0.251329i
$466$	−31.4765	+	4.74432i	−1.45812	+	0.219776i
$467$	−19.1633	+	17.7809i	−0.886771	+	0.822803i	−0.985034	−	0.172357i	$-0.944862\pi$
$467$	−19.1633	+	17.7809i	−0.886771	+	0.822803i	0.0982638	+	0.995160i	$0.468671\pi$
$468$	−1.40428	−	6.15254i	−0.0649128	−	0.284401i
$469$	−17.7231	+	14.3723i	−0.818376	+	0.663652i
$470$	3.14927	−	13.7979i	0.145265	−	0.636448i
$471$	−8.43299	−	14.6064i	−0.388572	−	0.673026i
$472$	−11.8790	+	20.5750i	−0.546774	+	0.947041i
$473$	5.27447	+	4.89400i	0.242521	+	0.225026i
$474$	51.8547	+	35.3539i	2.38177	+	1.62386i
$475$	−1.80072	−	2.25803i	−0.0826225	−	0.103605i
$476$	0.456393	+	2.86861i	0.0209187	+	0.131483i
$477$	11.5974	−	14.5427i	0.531008	−	0.665863i
$478$	−1.41319	+	0.435913i	−0.0646380	+	0.0199382i
$479$	−9.77146	−	24.8973i	−0.446469	−	1.13759i	−0.960121	−	0.279586i	$-0.909803\pi$
$479$	−9.77146	−	24.8973i	−0.446469	−	1.13759i	0.513651	−	0.857999i	$-0.328293\pi$
$480$	−1.32295	+	17.6536i	−0.0603842	+	0.805772i
$481$	−3.79952	+	9.68103i	−0.173243	+	0.441417i
$482$	−1.70793	−	0.822494i	−0.0777939	−	0.0374636i
$483$	−27.3631	+	40.8480i	−1.24506	+	1.85865i
$484$	−2.80339	+	1.35004i	−0.127427	+	0.0613656i
$485$	−0.873697	−	11.6587i	−0.0396726	−	0.529393i
$486$	10.1975	+	3.14551i	0.462567	+	0.142683i
$487$	−16.9807	+	11.5772i	−0.769468	+	0.524614i	−0.883256	−	0.468891i	$-0.844654\pi$
$487$	−16.9807	+	11.5772i	−0.769468	+	0.524614i	0.113788	+	0.993505i	$0.463701\pi$
$488$	−40.2634	−	6.06874i	−1.82264	−	0.274719i
$489$	−50.7346			−2.29430
$490$	15.7632	−	15.1132i	0.712107	−	0.682746i
$491$	−4.08526			−0.184365			−0.0921827	−	0.995742i	$-0.529384\pi$
$491$	−4.08526			−0.184365			−0.0921827	+	0.995742i	$0.529384\pi$
$492$	−4.43494	−	0.668460i	−0.199943	−	0.0301365i
$493$	−3.57318	+	2.43615i	−0.160928	+	0.109719i
$494$	7.33191	+	2.26159i	0.329878	+	0.101754i
$495$	2.01800	+	26.9283i	0.0907022	+	1.21034i
$496$	−13.2052	+	6.35929i	−0.592931	+	0.285540i
$497$	3.31411	−	23.2776i	0.148658	−	1.04414i
$498$	15.0275	+	7.23684i	0.673397	+	0.324291i
$499$	−0.800251	+	2.03901i	−0.0358241	+	0.0912784i	−0.947666	−	0.319262i	$-0.896565\pi$
$499$	−0.800251	+	2.03901i	−0.0358241	+	0.0912784i	0.911842	+	0.410541i	$0.134660\pi$
$500$	0.308630	−	4.11838i	0.0138023	−	0.184179i
$501$	2.41183	+	6.14525i	0.107753	+	0.274550i
$502$	8.11997	−	2.50468i	0.362412	−	0.111789i
$503$	−15.1561	+	19.0051i	−0.675777	+	0.847397i	−0.994958	−	0.100297i	$-0.968021\pi$
$503$	−15.1561	+	19.0051i	−0.675777	+	0.847397i	0.319181	+	0.947694i	$0.396592\pi$
$504$	−40.8641	+	16.4249i	−1.82023	+	0.731621i
$505$	5.60329	+	7.02631i	0.249343	+	0.312667i
$506$	13.0525	+	8.89907i	0.580256	+	0.395612i
$507$	−12.9805	−	12.0441i	−0.576482	−	0.534897i
$508$	−1.99075	+	3.44809i	−0.0883254	+	0.152984i
$509$	11.3740	+	19.7003i	0.504143	+	0.873202i	0.999989	+	0.00479077i	$0.00152496\pi$
$509$	11.3740	+	19.7003i	0.504143	+	0.873202i	−0.495845	+	0.868411i	$0.665142\pi$
$510$	−5.04558	+	22.1062i	−0.223422	+	0.978877i
$511$	14.4340	+	3.17051i	0.638521	+	0.140255i
$512$	5.55895	+	24.3554i	0.245673	+	1.07637i
$513$	−12.2664	+	11.3816i	−0.541577	+	0.502510i
$514$	−22.5330	+	3.39631i	−0.993890	+	0.149805i
$515$	36.0487	−	5.43347i	1.58850	−	0.239427i
$516$	3.40578	−	3.16011i	0.149931	−	0.139116i
$517$	1.99837	+	8.75545i	0.0878884	+	0.385064i
$518$	12.7691	+	2.80482i	0.561043	+	0.123237i
$519$	−1.21600	+	5.32764i	−0.0533764	+	0.233857i
$520$	−10.0045	−	17.3283i	−0.438726	−	0.759896i
$521$	10.1192	−	17.5270i	0.443330	−	0.767870i	−0.554604	−	0.832114i	$-0.687130\pi$
$521$	10.1192	−	17.5270i	0.443330	−	0.767870i	0.997934	+	0.0642441i	$0.0204636\pi$
$522$	−8.65823	−	8.03366i	−0.378960	−	0.351624i
$523$	−15.1675	−	10.3410i	−0.663227	−	0.452181i	0.184344	−	0.982862i	$-0.440984\pi$
$523$	−15.1675	−	10.3410i	−0.663227	−	0.452181i	−0.847572	+	0.530681i	$0.821936\pi$
$524$	2.25732	+	2.83059i	0.0986116	+	0.123655i
$525$	−8.82907	+	3.54874i	−0.385332	+	0.154880i
$526$	23.9391	−	30.0187i	1.04379	−	1.30888i
$527$	11.9508	−	3.68632i	0.520583	−	0.160579i
$528$	6.16039	+	15.6964i	0.268097	+	0.683099i
$529$	1.33074	−	17.7575i	0.0578582	−	0.772064i
$530$	3.88110	−	9.88889i	0.168584	−	0.429546i
$531$	38.3684	+	18.4773i	1.66505	+	0.801845i
$532$	−0.382793	+	2.68866i	−0.0165962	+	0.116568i
$533$	8.31175	−	4.00273i	0.360022	−	0.173377i
$534$	−3.67038	−	48.9779i	−0.158833	−	2.11948i
$535$	17.9126	+	5.52530i	0.774428	+	0.238879i
$536$	21.7154	−	14.8053i	0.937961	−	0.639491i
$537$	−22.4848	−	3.38904i	−0.970293	−	0.146248i
$538$	10.1415			0.437232
$539$	−4.85097	+	12.9803i	−0.208946	+	0.559102i
$540$	7.86029			0.338253
$541$	−32.6195	−	4.91660i	−1.40242	−	0.211381i	−0.596126	−	0.802891i	$-0.703294\pi$
$541$	−32.6195	−	4.91660i	−1.40242	−	0.211381i	−0.806298	+	0.591510i	$0.798532\pi$
$542$	−8.34343	+	5.68846i	−0.358381	+	0.244340i
$543$	−11.5809	−	3.57223i	−0.496983	−	0.153299i
$544$	−0.455005	−	6.07162i	−0.0195082	−	0.260319i
$545$	11.5929	−	5.58287i	0.496587	−	0.239144i
$546$	14.0693	−	21.0028i	0.602110	−	0.898837i
$547$	31.3407	+	15.0929i	1.34003	+	0.645324i	0.960091	−	0.279687i	$-0.0902308\pi$
$547$	31.3407	+	15.0929i	1.34003	+	0.645324i	0.379939	+	0.925012i	$0.375945\pi$
$548$	3.01936	−	7.69321i	0.128981	−	0.328637i
$549$	−5.45430	+	72.7826i	−0.232784	+	3.10629i
$550$	1.11701	+	2.84610i	0.0476295	+	0.121358i
$551$	−3.86373	+	1.19180i	−0.164600	+	0.0507725i
$552$	35.3081	−	44.2749i	1.50281	−	1.88447i
$553$	−7.17924	−	45.1244i	−0.305293	−	1.91889i
$554$	−8.65730	−	10.8559i	−0.367813	−	0.461224i
$555$	−23.7420	−	16.1870i	−1.00779	−	0.687101i
$556$	−6.28449	−	5.83116i	−0.266522	−	0.247296i
$557$	−0.393685	+	0.681882i	−0.0166809	+	0.0288923i	−0.874245	−	0.485484i	$-0.838643\pi$
$557$	−0.393685	+	0.681882i	−0.0166809	+	0.0288923i	0.857564	+	0.514377i	$0.171977\pi$
$558$	17.0784	+	29.5806i	0.722986	+	1.25225i
$559$	−2.12653	+	9.31692i	−0.0899424	+	0.394064i
$560$	−15.0265	+	12.1856i	−0.634986	+	0.514935i
$561$	−3.20168	−	14.0275i	−0.135175	−	0.592240i
$562$	−14.2650	+	13.2359i	−0.601731	+	0.558325i
$563$	−25.5152	+	3.84580i	−1.07534	+	0.162081i	−0.662753	−	0.748838i	$-0.730612\pi$
$563$	−25.5152	+	3.84580i	−1.07534	+	0.162081i	−0.412585	+	0.910919i	$0.635374\pi$
$564$	5.73411	−	0.864277i	0.241449	−	0.0363926i
$565$	10.4545	−	9.70035i	0.439824	−	0.408097i
$566$	−4.32917	−	18.9673i	−0.181969	−	0.797257i
$567$	5.19572	+	10.5671i	0.218200	+	0.443777i
$568$	−6.02624	+	26.4027i	−0.252856	+	1.10783i
$569$	−13.9051	−	24.0844i	−0.582933	−	1.00967i	−0.995130	−	0.0985752i	$-0.968571\pi$
$569$	−13.9051	−	24.0844i	−0.582933	−	1.00967i	0.412196	−	0.911095i	$-0.364762\pi$
$570$	−10.6000	+	18.3597i	−0.443983	+	0.769002i
$571$	−5.96977	−	5.53914i	−0.249827	−	0.231806i	0.545311	−	0.838234i	$-0.316411\pi$
$571$	−5.96977	−	5.53914i	−0.249827	−	0.231806i	−0.795138	+	0.606428i	$0.792602\pi$
$572$	1.88964	+	1.28834i	0.0790099	+	0.0538680i
$573$	−7.31486	−	9.17255i	−0.305583	−	0.383189i
$574$	−6.61095	−	9.52815i	−0.275936	−	0.397697i
$575$	4.92421	−	6.17477i	0.205354	−	0.257506i
$576$	46.4580	−	14.3304i	1.93575	−	0.597100i
$577$	−7.78919	−	19.8465i	−0.324268	−	0.826222i	−0.996320	−	0.0857173i	$-0.972682\pi$
$577$	−7.78919	−	19.8465i	−0.324268	−	0.826222i	0.672051	−	0.740505i	$-0.265413\pi$
$578$	−1.00426	+	13.4009i	−0.0417717	+	0.557405i
$579$	−8.65223	+	22.0455i	−0.359575	+	0.916181i
$580$	1.71123	+	0.824083i	0.0710548	+	0.0342182i
$581$	−3.67403	−	11.5741i	−0.152424	−	0.480173i
$582$	−15.3286	+	7.38186i	−0.635390	+	0.305988i
$583$	0.503754	+	6.72213i	0.0208634	+	0.278402i
$584$	−16.2653	−	5.01718i	−0.673062	−	0.207612i
$585$	−29.6337	+	20.2039i	−1.22520	+	0.835329i
$586$	2.53271	+	0.381745i	0.104625	+	0.0157697i
$587$	30.4321			1.25607			0.628033	−	0.778187i	$-0.283860\pi$
$587$	30.4321			1.25607			0.628033	+	0.778187i	$0.283860\pi$
$588$	8.12402	+	3.74992i	0.335029	+	0.154644i
$589$	11.6930			0.481801
$590$	24.0498	+	3.62493i	0.990116	+	0.149236i
$591$	39.2871	−	26.7855i	1.61606	−	1.10181i
$592$	−11.0675	−	3.41388i	−0.454872	−	0.140310i
$593$	2.43406	+	32.4803i	0.0999549	+	1.33381i	0.791365	+	0.611344i	$0.209371\pi$
$593$	2.43406	+	32.4803i	0.0999549	+	1.33381i	−0.691410	+	0.722462i	$0.743010\pi$
$594$	15.9602	−	7.68601i	0.654853	−	0.315361i
$595$	14.2285	−	8.37069i	0.583311	−	0.343165i
$596$	5.86284	+	2.82340i	0.240151	+	0.115651i
$597$	−13.0118	+	33.1535i	−0.532537	+	1.35688i
$598$	−1.56798	+	20.9232i	−0.0641194	+	0.855614i
$599$	−1.21994	−	3.10835i	−0.0498453	−	0.127004i	0.903783	−	0.427992i	$-0.140779\pi$
$599$	−1.21994	−	3.10835i	−0.0498453	−	0.127004i	−0.953628	+	0.300988i	$0.902684\pi$
$600$	10.4732	−	3.23055i	0.427566	−	0.131887i
$601$	19.1048	−	23.9567i	0.779302	−	0.977213i	−0.220697	−	0.975342i	$-0.570833\pi$
$601$	19.1048	−	23.9567i	0.779302	−	0.977213i	0.999998	−	0.00187078i	$-0.000595489\pi$
$602$	11.9867	+	0.799770i	0.488539	+	0.0325962i
$603$	−29.3729	−	36.8324i	−1.19615	−	1.49993i
$604$	6.82880	+	4.65580i	0.277860	+	0.189442i
$605$	12.9631	+	12.0280i	0.527023	+	0.489006i
$606$	6.53899	−	11.3259i	0.265628	−	0.460082i
$607$	−22.7558	−	39.4143i	−0.923631	−	1.59978i	−0.793749	−	0.608246i	$-0.791873\pi$
$607$	−22.7558	−	39.4143i	−0.923631	−	1.59978i	−0.129882	−	0.991529i	$-0.541460\pi$
$608$	1.26673	−	5.54992i	0.0513728	−	0.225079i
$609$	0.108928	+	13.3213i	0.00441400	+	0.539807i
$610$	9.27557	+	40.6389i	0.375557	+	1.64542i
$611$	−8.74371	+	8.11297i	−0.353733	+	0.328216i
$612$	−5.93003	+	0.893808i	−0.239707	+	0.0361301i
$613$	−31.6691	+	4.77335i	−1.27910	+	0.192794i	−0.753224	−	0.657764i	$-0.771502\pi$
$613$	−31.6691	+	4.77335i	−1.27910	+	0.192794i	−0.525881	+	0.850558i	$0.676264\pi$
$614$	−14.5095	+	13.4628i	−0.585555	+	0.543316i
$615$	5.67198	+	24.8506i	0.228716	+	1.00207i
$616$	6.80731	−	14.4363i	0.274274	−	0.581655i
$617$	1.36167	−	5.96584i	0.0548186	−	0.240176i	−0.940094	−	0.340914i	$-0.889263\pi$
$617$	1.36167	−	5.96584i	0.0548186	−	0.240176i	0.994913	+	0.100738i	$0.0321205\pi$
$618$	−26.5256	−	45.9437i	−1.06702	−	1.84813i
$619$	21.9197	−	37.9660i	0.881025	−	1.52598i	0.0308225	−	0.999525i	$-0.490187\pi$
$619$	21.9197	−	37.9660i	0.881025	−	1.52598i	0.850203	−	0.526456i	$-0.176479\pi$
$620$	−4.02638	−	3.73593i	−0.161703	−	0.150039i
$621$	−37.8078	−	25.7769i	−1.51717	−	1.03439i
$622$	−11.8031	−	14.8006i	−0.473259	−	0.593449i
$623$	−24.1065	+	26.4105i	−0.965805	+	1.05811i
$624$	−13.9635	+	17.5097i	−0.558988	+	0.700948i
$625$	−28.3358	+	8.74042i	−1.13343	+	0.349617i
$626$	−8.20246	−	20.8995i	−0.327836	−	0.835313i
$627$	1.00530	−	13.4148i	0.0401478	−	0.535735i
$628$	0.930744	−	2.37150i	0.0371407	−	0.0946330i
$629$	8.90417	+	4.28802i	0.355032	+	0.170975i
$630$	30.9356	+	32.7986i	1.23250	+	1.30673i
$631$	22.8084	−	10.9839i	0.907986	−	0.437263i	0.0792194	−	0.996857i	$-0.474757\pi$
$631$	22.8084	−	10.9839i	0.907986	−	0.437263i	0.828767	+	0.559594i	$0.189043\pi$
$632$	3.93292	+	52.4812i	0.156443	+	2.08759i
$633$	35.2215	+	10.8644i	1.39993	+	0.431821i
$634$	13.6214	−	9.28693i	0.540976	−	0.368831i
$635$	22.3752	+	3.37252i	0.887934	+	0.133834i
$636$	4.35272			0.172597
$637$	−18.1519	+	3.04032i	−0.719203	+	0.120462i
$638$	4.28042			0.169463
$639$	48.0013	+	7.23503i	1.89890	+	0.286213i
$640$	12.8856	−	8.78524i	0.509347	−	0.347267i
$641$	22.1869	+	6.84374i	0.876328	+	0.270311i	0.700106	−	0.714039i	$-0.253136\pi$
$641$	22.1869	+	6.84374i	0.876328	+	0.270311i	0.176222	+	0.984350i	$0.443612\pi$
$642$	−2.03853	−	27.2023i	−0.0804542	−	1.07359i
$643$	−31.5170	+	15.1778i	−1.24291	+	0.598553i	−0.935601	−	0.353058i	$-0.885142\pi$
$643$	−31.5170	+	15.1778i	−1.24291	+	0.598553i	−0.307306	+	0.951611i	$0.599428\pi$
$644$	−7.40096	+	0.615520i	−0.291639	+	0.0242549i
$645$	−23.7898	−	11.4566i	−0.936721	−	0.451101i
$646$	2.66382	−	6.78730i	0.104807	−	0.267043i
$647$	−3.27629	+	43.7191i	−0.128804	+	1.71877i	0.441433	+	0.897294i	$0.354470\pi$
$647$	−3.27629	+	43.7191i	−0.128804	+	1.71877i	−0.570237	+	0.821480i	$0.693149\pi$
$648$	−4.95511	−	12.6254i	−0.194655	−	0.495973i
$649$	−14.7475	+	4.54902i	−0.578892	+	0.178565i
$650$	−2.53188	+	3.17488i	−0.0993087	+	0.124529i
$651$	11.0541	−	36.9052i	0.433244	−	1.44643i
$652$	−4.77808	−	5.99152i	−0.187124	−	0.234646i
$653$	26.6628	+	18.1784i	1.04340	+	0.711375i	0.958523	−	0.285017i	$-0.0919992\pi$
$653$	26.6628	+	18.1784i	1.04340	+	0.711375i	0.0848730	+	0.996392i	$0.472952\pi$
$654$	−13.7261	−	12.7359i	−0.536731	−	0.498014i
$655$	10.2880	−	17.8194i	0.401986	−	0.696261i
$656$	5.13699	+	8.89753i	0.200566	+	0.347390i
$657$	−6.78928	+	29.7458i	−0.264875	+	1.16049i
$658$	11.7990	+	9.25257i	0.459973	+	0.360703i
$659$	−7.27802	−	31.8871i	−0.283511	−	1.24214i	−0.893257	−	0.449547i	$-0.851585\pi$
$659$	−7.27802	−	31.8871i	−0.283511	−	1.24214i	0.609745	−	0.792598i	$-0.291272\pi$
$660$	−4.63222	+	4.29808i	−0.180309	+	0.167302i
$661$	31.8045	−	4.79376i	1.23705	−	0.186456i	0.502241	−	0.864727i	$-0.332509\pi$
$661$	31.8045	−	4.79376i	1.23705	−	0.186456i	0.734811	+	0.678272i	$0.237271\pi$
$662$	10.1159	−	1.52472i	0.393165	−	0.0592601i
$663$	14.0087	−	12.9981i	0.544051	−	0.504806i
$664$	3.11232	+	13.6360i	0.120781	+	0.529178i
$665$	15.0189	−	3.55741i	0.582408	−	0.137951i
$666$	−6.00620	+	26.3149i	−0.232735	+	1.01968i
$667$	−5.52846	−	9.57557i	−0.214063	−	0.370768i
$668$	−0.498585	+	0.863574i	−0.0192908	+	0.0334127i
$669$	37.2288	+	34.5433i	1.43935	+	1.33552i
$670$	−22.2304	−	15.1565i	−0.858837	−	0.585545i
$671$	−16.4917	−	20.6799i	−0.636654	−	0.798339i
$672$	−16.3190	−	9.24471i	−0.629520	−	0.356622i
$673$	−5.77478	+	7.24134i	−0.222601	+	0.279133i	−0.880574	−	0.473908i	$-0.842843\pi$
$673$	−5.77478	+	7.24134i	−0.222601	+	0.279133i	0.657973	+	0.753042i	$0.271414\pi$
$674$	−10.8068	+	3.33345i	−0.416261	+	0.128400i
$675$	−3.23552	−	8.24396i	−0.124535	−	0.317310i
$676$	0.199881	−	2.66722i	0.00768772	−	0.102585i
$677$	−0.220551	+	0.561955i	−0.00847647	+	0.0215977i	−0.935049	−	0.354518i	$-0.884645\pi$
$677$	−0.220551	+	0.561955i	−0.00847647	+	0.0215977i	0.926573	+	0.376115i	$0.122740\pi$
$678$	−18.6984	−	9.00468i	−0.718108	−	0.345823i
$679$	11.5669	+	4.43088i	0.443897	+	0.170041i
$680$	−17.1312	+	8.24995i	−0.656951	+	0.316371i
$681$	1.31888	+	17.5992i	0.0505396	+	0.674404i
$682$	−11.8286	−	3.64863i	−0.452940	−	0.139713i
$683$	9.97456	−	6.80054i	0.381666	−	0.260216i	−0.357256	−	0.934007i	$-0.616288\pi$
$683$	9.97456	−	6.80054i	0.381666	−	0.260216i	0.738922	+	0.673791i	$0.235335\pi$
$684$	−5.54435	−	0.835676i	−0.211993	−	0.0319529i
$685$	−46.9694			−1.79461
$686$	7.35973	+	21.9344i	0.280996	+	0.837459i
$687$	−33.5238			−1.27901
$688$	−10.5239	−	1.58623i	−0.401221	−	0.0604743i
$689$	−7.39748	+	5.04352i	−0.281822	+	0.192143i
$690$	−55.3974	−	17.0878i	−2.10894	−	0.650523i
$691$	2.40034	+	32.0303i	0.0913133	+	1.21849i	0.835109	+	0.550085i	$0.185405\pi$
$691$	2.40034	+	32.0303i	0.0913133	+	1.21849i	−0.743796	+	0.668407i	$0.766976\pi$
$692$	−0.743690	+	0.358142i	−0.0282708	+	0.0136145i
$693$	−26.7163	−	10.2341i	−1.01487	−	0.388761i
$694$	−7.13742	−	3.43720i	−0.270933	−	0.130474i
$695$	−17.8005	+	45.3549i	−0.675211	+	1.72041i
$696$	1.14667	−	15.3012i	0.0434643	−	0.579990i
$697$	−3.20283	−	8.16068i	−0.121316	−	0.309108i
$698$	5.99538	−	1.84933i	0.226929	−	0.0699982i
$699$	−46.2163	+	57.9535i	−1.74806	+	2.19200i
$700$	−1.25059	−	0.708460i	−0.0472680	−	0.0267773i
$701$	−14.9612	−	18.7608i	−0.565078	−	0.708586i	0.414409	−	0.910091i	$-0.363988\pi$
$701$	−14.9612	−	18.7608i	−0.565078	−	0.708586i	−0.979487	+	0.201505i	$0.935417\pi$
$702$	19.4396	+	13.2537i	0.733702	+	0.500230i
$703$	6.77348	+	6.28487i	0.255467	+	0.237038i
$704$	−8.80966	+	15.2588i	−0.332026	+	0.575087i
$705$	−16.4783	−	28.5412i	−0.620608	−	1.07492i
$706$	−6.95988	+	30.4932i	−0.261938	+	1.14763i
$707$	−9.26499	+	2.19453i	−0.348446	+	0.0825337i
$708$	2.21751	+	9.71553i	0.0833390	+	0.365132i
$709$	29.6500	−	27.5112i	1.11353	−	1.03320i	0.114320	−	0.993444i	$-0.463531\pi$
$709$	29.6500	−	27.5112i	1.11353	−	1.03320i	0.999209	−	0.0397597i	$-0.0126593\pi$
$710$	27.4144	−	4.13205i	1.02884	−	0.155073i
$711$	93.2818	−	14.0600i	3.49834	−	0.527290i
$712$	30.1917	−	28.0138i	1.13148	−	1.04986i
$713$	7.11521	+	31.1738i	0.266467	+	1.16747i
$714$	−18.9037	−	14.8239i	−0.707452	−	0.554772i
$715$	2.89230	−	12.6720i	0.108166	−	0.473905i
$716$	−1.71735	−	2.97453i	−0.0641802	−	0.111163i
$717$	−1.72191	+	2.98243i	−0.0643058	+	0.111381i
$718$	18.8559	+	17.4957i	0.703696	+	0.652934i
$719$	23.0725	+	15.7305i	0.860458	+	0.586650i	0.911155	−	0.412064i	$-0.135192\pi$
$719$	23.0725	+	15.7305i	0.860458	+	0.586650i	−0.0506971	+	0.998714i	$0.516144\pi$
$720$	−24.9038	−	31.2284i	−0.928109	−	1.16381i
$721$	−11.0823	+	36.9995i	−0.412727	+	1.37793i
$722$	−10.5485	+	13.2273i	−0.392573	+	0.492271i
$723$	−4.21818	+	1.30114i	−0.156876	+	0.0483898i
$724$	−0.668799	−	1.70407i	−0.0248557	−	0.0633314i
$725$	0.159919	−	2.13397i	0.00593924	−	0.0792536i
$726$	9.40151	−	23.9547i	0.348923	−	0.889041i
$727$	−7.82687	−	3.76922i	−0.290283	−	0.139793i	0.283075	−	0.959098i	$-0.408645\pi$
$727$	−7.82687	−	3.76922i	−0.290283	−	0.139793i	−0.573358	+	0.819305i	$0.694360\pi$
$728$	21.1258	−	1.75698i	0.782973	−	0.0651180i
$729$	34.4191	−	16.5754i	1.27478	−	0.613902i
$730$	1.30219	+	17.3765i	0.0481962	+	0.643133i
$731$	8.67793	+	2.67679i	0.320965	+	0.0990046i
$732$	−14.1117	+	9.62119i	−0.521583	+	0.355610i
$733$	−19.2471	−	2.90103i	−0.710906	−	0.107152i	−0.216373	−	0.976311i	$-0.569423\pi$
$733$	−19.2471	−	2.90103i	−0.710906	−	0.107152i	−0.494533	+	0.869159i	$0.664661\pi$
$734$	4.07435			0.150387
$735$	2.97043	−	50.7654i	0.109566	−	1.87251i
$736$	15.5670			0.573808
$737$	16.8823	+	2.54459i	0.621866	+	0.0937312i
$738$	19.7827	−	13.4876i	0.728212	−	0.496487i
$739$	−42.0145	−	12.9598i	−1.54553	−	0.476732i	−0.599380	−	0.800465i	$-0.704586\pi$
$739$	−42.0145	−	12.9598i	−1.54553	−	0.476732i	−0.946149	+	0.323732i	$0.895062\pi$
$740$	−0.324360	−	4.32828i	−0.0119237	−	0.159111i
$741$	16.0977	−	7.75227i	0.591366	−	0.284787i
$742$	7.72247	+	8.18754i	0.283501	+	0.300574i
$743$	14.1109	+	6.79545i	0.517678	+	0.249301i	0.674432	−	0.738337i	$-0.264389\pi$
$743$	14.1109	+	6.79545i	0.517678	+	0.249301i	−0.156754	+	0.987638i	$0.550103\pi$
$744$	−16.2115	+	41.3062i	−0.594341	+	1.51436i
$745$	2.76371	−	36.8791i	0.101254	−	1.35115i
$746$	−7.12587	−	18.1564i	−0.260897	−	0.664754i
$747$	23.9570	−	7.38975i	0.876540	−	0.270377i
$748$	1.35505	−	1.69918i	0.0495456	−	0.0621283i
$749$	−13.3887	+	14.6683i	−0.489213	+	0.535969i
$750$	21.2959	+	26.7042i	0.777617	+	0.975101i
$751$	18.2208	+	12.4228i	0.664888	+	0.453313i	0.848154	−	0.529750i	$-0.177714\pi$
$751$	18.2208	+	12.4228i	0.664888	+	0.453313i	−0.183266	+	0.983063i	$0.558667\pi$
$752$	−9.73759	−	9.03516i	−0.355093	−	0.329479i
$753$	9.89379	−	17.1366i	0.360550	−	0.624491i
$754$	2.84257	+	4.92348i	0.103520	+	0.179302i
$755$	10.4522	−	45.7941i	0.380394	−	1.66662i
$756$	−3.55176	+	7.53225i	−0.129176	+	0.273945i
$757$	−2.66070	−	11.6573i	−0.0967047	−	0.423691i	0.903281	−	0.429050i	$-0.141151\pi$
$757$	−2.66070	−	11.6573i	−0.0967047	−	0.423691i	−0.999986	+	0.00535866i	$0.998294\pi$
$758$	31.6219	−	29.3408i	1.14856	−	1.06571i
$759$	36.3759	−	5.48278i	1.32036	−	0.199012i
$760$	−17.5790	+	2.64960i	−0.637656	+	0.0961112i
$761$	−40.3718	+	37.4596i	−1.46348	+	1.35791i	−0.691049	+	0.722808i	$0.742851\pi$
$761$	−40.3718	+	37.4596i	−1.46348	+	1.35791i	−0.772429	+	0.635101i	$0.780958\pi$
$762$	−7.32729	−	32.1029i	−0.265440	−	1.16297i
$763$	0.111467	+	13.6318i	0.00403539	+	0.493505i
$764$	0.394337	−	1.72770i	0.0142666	−	0.0625061i
$765$	17.0413	+	29.5164i	0.616130	+	1.06717i
$766$	−6.53263	+	11.3148i	−0.236034	+	0.408822i
$767$	−15.0261	−	13.9422i	−0.542561	−	0.503423i
$768$	24.0341	+	16.3862i	0.867257	+	0.591286i
$769$	13.1153	+	16.4460i	0.472949	+	0.593060i	0.959891	−	0.280375i	$-0.0904588\pi$
$769$	13.1153	+	16.4460i	0.472949	+	0.593060i	−0.486941	+	0.873435i	$0.661887\pi$
$770$	−16.3031	−	1.08777i	−0.587523	−	0.0392006i
$771$	−33.0849	+	41.4871i	−1.19152	+	1.49412i
$772$	−3.41833	+	1.05441i	−0.123028	+	0.0379492i
$773$	3.75866	+	9.57691i	0.135190	+	0.344457i	0.982397	−	0.186805i	$-0.0598132\pi$
$773$	3.75866	+	9.57691i	0.135190	+	0.344457i	−0.847207	+	0.531262i	$0.821718\pi$
$774$	−1.85350	+	24.7333i	−0.0666227	+	0.889019i
$775$	−2.26092	+	5.76073i	−0.0812146	+	0.206931i
$776$	−12.8540	−	6.19018i	−0.461433	−	0.222214i
$777$	26.2396	−	15.4369i	0.941339	−	0.553794i
$778$	−36.1317	+	17.4001i	−1.29538	+	0.623825i
$779$	−0.612526	−	8.17359i	−0.0219460	−	0.292849i
$780$	−8.01999	−	2.47384i	−0.287162	−	0.0885776i
$781$	−14.5354	+	9.91010i	−0.520119	+	0.354611i
$782$	19.7160	+	2.97171i	0.705044	+	0.106268i
$783$	−12.3986			−0.443089
$784$	−4.88712	−	19.9056i	−0.174540	−	0.710914i
$785$	−14.4787			−0.516767
$786$	−29.6081	−	4.46271i	−1.05609	−	0.159179i
$787$	−21.7040	+	14.7976i	−0.773665	+	0.527476i	−0.884599	−	0.466352i	$-0.845568\pi$
$787$	−21.7040	+	14.7976i	−0.773665	+	0.527476i	0.110934	+	0.993828i	$0.464616\pi$
$788$	6.86323	+	2.11703i	0.244492	+	0.0754159i
$789$	−6.68153	−	89.1588i	−0.237869	−	3.17414i
$790$	48.5412	−	23.3762i	1.72702	−	0.831688i
$791$	4.57153	+	14.4014i	0.162545	+	0.512055i
$792$	29.6892	+	14.2976i	1.05496	+	0.508042i
$793$	12.8348	−	32.7026i	0.455777	−	1.16130i
$794$	−0.445600	+	5.94611i	−0.0158137	+	0.211020i
$795$	−9.03769	−	23.0277i	−0.320534	−	0.816707i
$796$	−5.14070	+	1.58569i	−0.182207	+	0.0562035i
$797$	26.4409	−	33.1558i	0.936584	−	1.17444i	−0.0478801	−	0.998853i	$-0.515247\pi$
$797$	26.4409	−	33.1558i	0.936584	−	1.17444i	0.984464	−	0.175586i	$-0.0561820\pi$
$798$	−12.8037	−	18.4536i	−0.453247	−	0.653251i
$799$	7.06713	+	8.86190i	0.250017	+	0.313512i
$800$	2.48932	+	1.69719i	0.0880108	+	0.0600047i
$801$	−54.1182	−	50.2143i	−1.91217	−	1.77424i
$802$	6.37117	−	11.0352i	0.224974	−	0.389666i
$803$	−5.52859	−	9.57581i	−0.195100	−	0.337923i
$804$	2.45311	−	10.7478i	0.0865146	−	0.379045i
$805$	18.6232	+	37.8760i	0.656381	+	1.33495i
$806$	−3.65843	−	16.0286i	−0.128863	−	0.564584i
$807$	17.3117	−	16.0629i	0.609401	−	0.565442i
$808$	10.8443	−	1.63451i	0.381500	−	0.0575019i
$809$	15.8888	−	2.39485i	0.558621	−	0.0841986i	0.136338	−	0.990662i	$-0.456467\pi$
$809$	15.8888	−	2.39485i	0.558621	−	0.0841986i	0.422283	+	0.906464i	$0.361229\pi$
$810$	−10.1782	+	9.44396i	−0.357625	+	0.331827i
$811$	−3.66108	−	16.0403i	−0.128558	−	0.563250i	−0.997645	−	0.0685901i	$-0.978150\pi$
$811$	−3.66108	−	16.0403i	−0.128558	−	0.563250i	0.869087	−	0.494659i	$-0.164707\pi$
$812$	−1.56293	+	1.26744i	−0.0548480	+	0.0444783i
$813$	−5.23254	+	22.9252i	−0.183513	+	0.804023i
$814$	−4.89092	−	8.47132i	−0.171427	−	0.296920i
$815$	−21.7767	+	37.7183i	−0.762804	+	1.32122i
$816$	15.6010	+	14.4756i	0.546144	+	0.506748i
$817$	7.01538	+	4.78301i	0.245437	+	0.167336i
$818$	−4.53448	−	5.68606i	−0.158545	−	0.198809i
$819$	−5.97040	−	37.5263i	−0.208622	−	1.31128i
$820$	−2.40056	+	3.01021i	−0.0838313	+	0.105121i
$821$	−43.7529	+	13.4960i	−1.52699	+	0.471013i	−0.940742	−	0.339122i	$-0.889870\pi$
$821$	−43.7529	+	13.4960i	−1.52699	+	0.471013i	−0.586244	+	0.810135i	$0.699394\pi$
$822$	24.9712	+	63.6256i	0.870972	+	2.21920i
$823$	1.72823	−	23.0616i	0.0602423	−	0.803877i	−0.882491	−	0.470330i	$-0.844135\pi$
$823$	1.72823	−	23.0616i	0.0602423	−	0.803877i	0.942733	−	0.333548i	$-0.108246\pi$
$824$	16.2529	−	41.4117i	0.566196	−	1.44264i
$825$	6.41462	+	3.08912i	0.223329	+	0.107549i
$826$	−14.3408	+	21.4082i	−0.498982	+	0.744885i
$827$	28.3996	−	13.6765i	0.987552	−	0.475580i	0.130856	−	0.991401i	$-0.458228\pi$
$827$	28.3996	−	13.6765i	0.987552	−	0.475580i	0.856696	+	0.515822i	$0.172513\pi$
$828$	−1.14582	−	15.2899i	−0.0398199	−	0.531360i
$829$	17.1200	+	5.28081i	0.594601	+	0.183410i	0.577427	−	0.816442i	$-0.304057\pi$
$829$	17.1200	+	5.28081i	0.594601	+	0.183410i	0.0171744	+	0.999853i	$0.494533\pi$
$830$	11.8304	−	8.06583i	0.410639	−	0.279969i
$831$	−31.9726	−	4.81909i	−1.10912	−	0.167172i
$832$	−23.4015			−0.811302
$833$	1.59204	+	17.4171i	0.0551609	+	0.603466i
$834$	70.9023			2.45515
$835$	5.60388	+	0.844649i	0.193930	+	0.0292303i
$836$	1.67890	−	1.14466i	0.0580661	−	0.0395888i
$837$	34.2625	+	10.5686i	1.18428	+	0.365303i
$838$	3.36050	+	44.8428i	0.116087	+	1.54907i
$839$	15.7210	−	7.57083i	0.542749	−	0.261374i	−0.142360	−	0.989815i	$-0.545469\pi$
$839$	15.7210	−	7.57083i	0.542749	−	0.261374i	0.685109	+	0.728441i	$0.259755\pi$
$840$	−8.25583	+	57.9872i	−0.284853	+	2.00075i
$841$	23.4289	+	11.2827i	0.807892	+	0.389060i
$842$	9.44710	−	24.0708i	0.325569	−	0.829535i
$843$	−3.38636	+	45.1879i	−0.116632	+	1.55635i
$844$	2.03405	+	5.18268i	0.0700150	+	0.178395i
$845$	−14.5257	+	4.48058i	−0.499699	+	0.154137i
$846$	−19.3014	+	24.2031i	−0.663595	+	0.832121i
$847$	−17.3835	+	6.98708i	−0.597304	+	0.240079i
$848$	−6.21675	−	7.79556i	−0.213484	−	0.267701i
$849$	−37.4319	−	25.5206i	−1.28466	−	0.875866i
$850$	2.82880	+	2.62474i	0.0970270	+	0.0900279i
$851$	−12.6339	+	21.8826i	−0.433086	+	0.750126i
$852$	5.67977	+	9.83765i	0.194586	+	0.337032i
$853$	−0.342539	+	1.50076i	−0.0117283	+	0.0513851i	−0.980453	−	0.196751i	$-0.936961\pi$
$853$	−0.342539	+	1.50076i	−0.0117283	+	0.0513851i	0.968725	+	0.248136i	$0.0798181\pi$
$854$	−43.1342	−	9.47470i	−1.47602	−	0.324218i
$855$	7.09083	+	31.0670i	0.242501	+	1.06247i
$856$	16.7685	−	15.5588i	0.573134	−	0.531790i
$857$	31.6767	−	4.77450i	1.08206	−	0.163094i	0.416273	−	0.909240i	$-0.363336\pi$
$857$	31.6767	−	4.77450i	1.08206	−	0.163094i	0.665783	+	0.746146i	$0.268098\pi$
$858$	−18.7034	+	2.81909i	−0.638524	+	0.0962420i
$859$	−2.47734	+	2.29863i	−0.0845257	+	0.0784283i	−0.721304	−	0.692618i	$-0.756457\pi$
$859$	−2.47734	+	2.29863i	−0.0845257	+	0.0784283i	0.636779	+	0.771047i	$0.280267\pi$
$860$	−0.887506	−	3.88842i	−0.0302637	−	0.132594i
$861$	−26.3764	−	5.79375i	−0.898905	−	0.197450i
$862$	3.90809	−	17.1225i	0.133110	−	0.583194i
$863$	−4.53125	−	7.84835i	−0.154245	−	0.267161i	0.778539	−	0.627597i	$-0.215961\pi$
$863$	−4.53125	−	7.84835i	−0.154245	−	0.267161i	−0.932784	+	0.360436i	$0.882628\pi$
$864$	8.72798	−	15.1173i	0.296932	−	0.514301i
$865$	3.43886	+	3.19080i	0.116925	+	0.108490i
$866$	−33.6614	−	22.9500i	−1.14386	−	0.779872i
$867$	19.5111	+	24.4662i	0.662633	+	0.830915i
$868$	5.39938	−	2.17022i	0.183267	−	0.0736620i
$869$	−21.3155	+	26.7288i	−0.723080	+	0.906713i
$870$	−15.0102	+	4.63003i	−0.508893	+	0.156973i
$871$	8.28442	+	21.1084i	0.280707	+	0.715230i
$872$	1.17339	−	15.6579i	0.0397361	−	0.530242i
$873$	−9.34293	+	23.8054i	−0.316210	+	0.805691i
$874$	16.7958	+	8.08843i	0.568126	+	0.273595i
$875$	3.50506	−	24.6188i	0.118493	−	0.832267i
$876$	−6.43269	+	3.09782i	−0.217340	+	0.104666i
$877$	−2.75484	−	36.7608i	−0.0930245	−	1.24133i	−0.827021	−	0.562172i	$-0.809966\pi$
$877$	−2.75484	−	36.7608i	−0.0930245	−	1.24133i	0.733996	−	0.679154i	$-0.237653\pi$
$878$	−32.6531	−	10.0721i	−1.10199	−	0.339919i
$879$	4.92801	−	3.35986i	0.166218	−	0.113325i
$880$	14.3136	+	2.15743i	0.482512	+	0.0727271i
$881$	9.18904			0.309587			0.154793	−	0.987947i	$-0.450529\pi$
$881$	9.18904			0.309587			0.154793	+	0.987947i	$0.450529\pi$
$882$	−45.4084	+	14.8241i	−1.52898	+	0.499153i
$883$	−3.91664			−0.131806			−0.0659028	−	0.997826i	$-0.520993\pi$
$883$	−3.91664			−0.131806			−0.0659028	+	0.997826i	$0.520993\pi$
$884$	2.85433	+	0.430221i	0.0960015	+	0.0144699i
$885$	46.7948	−	31.9042i	1.57299	−	1.07245i
$886$	−1.12388	−	0.346670i	−0.0377574	−	0.0116466i
$887$	−1.52310	−	20.3244i	−0.0511408	−	0.682427i	−0.962581	−	0.270994i	$-0.912648\pi$
$887$	−1.52310	−	20.3244i	−0.0511408	−	0.682427i	0.911440	−	0.411433i	$-0.134971\pi$
$888$	−31.5926	+	15.2142i	−1.06018	+	0.510555i
$889$	−13.3423	+	19.9175i	−0.447486	+	0.668012i
$890$	−37.9878	−	18.2939i	−1.27335	−	0.613214i
$891$	3.21884	−	8.20148i	0.107835	−	0.274760i
$892$	−0.573271	+	7.64977i	−0.0191945	+	0.256133i
$893$	3.87173	+	9.86502i	0.129563	+	0.330120i
$894$	−51.4265	+	15.8630i	−1.71996	+	0.530537i
$895$	−12.1707	+	15.2616i	−0.406821	+	0.510138i
$896$	2.59610	+	16.3175i	0.0867296	+	0.545130i
$897$	30.4632	+	38.1997i	1.01714	+	1.27545i
$898$	41.6376	+	28.3880i	1.38947	+	0.947321i
$899$	6.35109	+	5.89295i	0.211821	+	0.196541i
$900$	1.48375	−	2.56992i	0.0494582	−	0.0856641i
$901$	4.25403	+	7.36820i	0.141722	+	0.245470i
$902$	−1.93083	+	8.45951i	−0.0642895	+	0.281671i
$903$	21.7281	−	17.6202i	0.723066	−	0.586362i
$904$	−3.87260	−	16.9670i	−0.128801	−	0.564314i
$905$	−7.62659	+	7.07644i	−0.253516	+	0.235229i
$906$	−67.5905	+	10.1876i	−2.24554	+	0.338461i
$907$	1.26521	−	0.190700i	0.0420108	−	0.00633210i	−0.128003	−	0.991774i	$-0.540857\pi$
$907$	1.26521	−	0.190700i	0.0420108	−	0.00633210i	0.170014	+	0.985442i	$0.445619\pi$
$908$	−1.95418	+	1.81321i	−0.0648518	+	0.0601736i
$909$	−4.37425	−	19.1649i	−0.145085	−	0.635658i
$910$	−9.57549	−	19.4747i	−0.317424	−	0.645581i
$911$	4.12249	−	18.0618i	0.136584	−	0.598415i	−0.859587	−	0.510990i	$-0.829279\pi$
$911$	4.12249	−	18.0618i	0.136584	−	0.598415i	0.996171	−	0.0874251i	$-0.0278639\pi$
$912$	9.94904	+	17.2322i	0.329446	+	0.570617i
$913$	−4.54287	+	7.86848i	−0.150347	+	0.260409i
$914$	−6.11124	−	5.67040i	−0.202142	−	0.187560i
$915$	80.2005	+	54.6798i	2.65135	+	1.80766i
$916$	−3.15720	−	3.95901i	−0.104317	−	0.130809i
$917$	12.4269	+	17.9106i	0.410374	+	0.591459i
$918$	13.9401	−	17.4803i	0.460091	−	0.576936i
$919$	9.26790	−	2.85877i	0.305720	−	0.0943020i	−0.138100	−	0.990418i	$-0.544099\pi$
$919$	9.26790	−	2.85877i	0.305720	−	0.0943020i	0.443819	+	0.896116i	$0.353623\pi$
$920$	−17.7607	−	45.2537i	−0.585555	−	1.49197i
$921$	−3.44441	+	45.9625i	−0.113497	+	1.51452i
$922$	−6.73643	+	17.1641i	−0.221853	+	0.565271i
$923$	−21.0517	−	10.1380i	−0.692926	−	0.333696i
$924$	−2.02558	−	6.38104i	−0.0666366	−	0.209921i
$925$	−4.40604	+	2.12184i	−0.144870	+	0.0697655i
$926$	−0.286000	−	3.81641i	−0.00939855	−	0.125415i
$927$	−76.1993	−	23.5044i	−2.50271	−	0.771985i
$928$	3.48504	−	2.37606i	0.114402	−	0.0779980i
$929$	23.6643	+	3.56682i	0.776400	+	0.117024i	0.525277	−	0.850931i	$-0.323962\pi$
$929$	23.6643	+	3.56682i	0.776400	+	0.117024i	0.251124	+	0.967955i	$0.419200\pi$
$930$	45.4260			1.48958
$931$	−3.37751	+	15.9996i	−0.110693	+	0.524364i
$932$	−11.1966			−0.366757
$933$	−43.5902	−	6.57017i	−1.42708	−	0.215098i
$934$	26.9827	−	18.3965i	0.882901	−	0.601952i
$935$	−11.8029	−	3.64071i	−0.385996	−	0.119064i
$936$	3.27069	+	43.6444i	0.106906	+	1.42656i
$937$	−18.4374	+	8.87897i	−0.602323	+	0.290063i	−0.710088	−	0.704113i	$-0.751345\pi$
$937$	−18.4374	+	8.87897i	−0.602323	+	0.290063i	0.107765	+	0.994176i	$0.465631\pi$
$938$	24.5690	−	14.4541i	0.802206	−	0.471942i
$939$	−47.1040	−	22.6841i	−1.53718	−	0.740267i
$940$	1.81870	−	4.63396i	0.0593193	−	0.151143i
$941$	0.659511	−	8.80056i	0.0214994	−	0.286890i	−0.976083	−	0.217398i	$-0.930243\pi$
$941$	0.659511	−	8.80056i	0.0214994	−	0.286890i	0.997583	−	0.0694921i	$-0.0221379\pi$
$942$	7.69759	+	19.6131i	0.250801	+	0.639031i
$943$	21.4183	−	6.60666i	0.697475	−	0.215142i
$944$	14.2330	−	17.8476i	0.463245	−	0.580891i
$945$	47.2233	+	3.15082i	1.53617	+	0.102496i
$946$	−5.60427	−	7.02753i	−0.182210	−	0.228485i
$947$	−5.48160	−	3.73729i	−0.178128	−	0.121446i	0.470974	−	0.882147i	$-0.343903\pi$
$947$	−5.48160	−	3.73729i	−0.178128	−	0.121446i	−0.649102	+	0.760702i	$0.724855\pi$
$948$	16.1823	+	15.0150i	0.525576	+	0.487663i
$949$	7.34294	−	12.7183i	0.238362	−	0.412855i
$950$	1.80398	+	3.12458i	0.0585287	+	0.101375i
$951$	8.54259	−	37.4275i	0.277013	−	1.21367i
$952$	−0.164718	−	20.1441i	−0.00533855	−	0.652873i
$953$	0.499002	+	2.18627i	0.0161643	+	0.0708202i	0.982367	−	0.186964i	$-0.0598648\pi$
$953$	0.499002	+	2.18627i	0.0161643	+	0.0708202i	−0.966203	+	0.257784i	$0.917008\pi$
$954$	−17.0338	+	15.8050i	−0.551489	+	0.511707i
$955$	−9.95903	+	1.50108i	−0.322267	+	0.0485739i
$956$	−0.514378	+	0.0775299i	−0.0166362	+	0.00250750i
$957$	7.30673	−	6.77965i	0.236193	−	0.219155i
$958$	7.43493	+	32.5746i	0.240212	+	1.05244i
$959$	21.2236	−	45.0091i	0.685347	−	1.45342i
$960$	14.3879	−	63.0373i	0.464366	−	2.03452i
$961$	2.97245	+	5.14844i	0.0958856	+	0.166079i
$962$	6.49599	−	11.2514i	0.209439	−	0.362759i
$963$	−30.0572	−	27.8890i	−0.968578	−	0.898709i
$964$	−0.550918	−	0.375610i	−0.0177439	−	0.0120976i
$965$	12.6759	+	15.8950i	0.408050	+	0.511679i
$966$	41.4066	−	45.3641i	1.33224	−	1.45957i
$967$	37.2851	−	46.7541i	1.19901	−	1.50351i	0.384735	−	0.923027i	$-0.374293\pi$
$967$	37.2851	−	46.7541i	1.19901	−	1.50351i	0.814273	−	0.580482i	$-0.197136\pi$
$968$	20.6206	−	6.36060i	0.662770	−	0.204437i
$969$	−6.20307	−	15.8052i	−0.199271	−	0.507735i
$970$	−1.09146	+	14.5645i	−0.0350445	+	0.467636i
$971$	2.28667	−	5.82633i	0.0733826	−	0.186976i	−0.889476	−	0.456982i	$-0.848930\pi$
$971$	2.28667	−	5.82633i	0.0733826	−	0.186976i	0.962859	+	0.270006i	$0.0870257\pi$
$972$	3.38190	+	1.62864i	0.108475	+	0.0522386i
$973$	−35.4187	−	37.5517i	−1.13547	−	1.20385i
$974$	23.1315	−	11.1396i	0.741182	−	0.356934i
$975$	0.706663	+	9.42976i	0.0226313	+	0.301994i
$976$	37.3861	+	11.5321i	1.19670	+	0.369133i
$977$	−35.1358	+	23.9552i	−1.12409	+	0.766393i	−0.974950	−	0.222422i	$-0.928604\pi$
$977$	−35.1358	+	23.9552i	−1.12409	+	0.766393i	−0.149142	+	0.988816i	$0.547651\pi$
$978$	62.6716	+	9.44622i	2.00402	+	0.302057i
$979$	26.7547			0.855084
$980$	6.27491	−	4.43019i	0.200445	−	0.141517i
$981$	−28.1451			−0.898605
$982$	5.04646	+	0.760632i	0.161039	+	0.0242727i
$983$	−41.9078	+	28.5722i	−1.33665	+	0.911313i	−0.999545	−	0.0301539i	$-0.990400\pi$
$983$	−41.9078	+	28.5722i	−1.33665	+	0.911313i	−0.337105	+	0.941467i	$0.609448\pi$
$984$	29.7229	+	9.16831i	0.947532	+	0.292275i
$985$	−3.05041	−	40.7049i	−0.0971942	−	1.29697i
$986$	4.86748	−	2.34405i	0.155012	−	0.0746499i
$987$	34.7960	−	2.89390i	1.10757	−	0.0921138i
$988$	2.43156	+	1.17098i	0.0773583	+	0.0372538i
$989$	−8.48273	+	21.6137i	−0.269735	+	0.687274i
$990$	2.52096	−	33.6398i	0.0801212	−	1.06914i
$991$	5.15784	+	13.1420i	0.163844	+	0.417468i	0.989091	−	0.147304i	$-0.0470595\pi$
$991$	5.15784	+	13.1420i	0.163844	+	0.417468i	−0.825247	+	0.564772i	$0.808964\pi$
$992$	−11.6560	+	3.59539i	−0.370078	+	0.114154i
$993$	14.8530	−	18.6250i	0.471345	−	0.591048i
$994$	−8.42790	+	28.1374i	−0.267317	+	0.892464i
$995$	19.0627	+	23.9039i	0.604330	+	0.757805i
$996$	4.84734	+	3.30486i	0.153594	+	0.104719i
$997$	−4.76250	−	4.41895i	−0.150830	−	0.139950i	0.601149	−	0.799137i	$-0.294710\pi$
$997$	−4.76250	−	4.41895i	−0.150830	−	0.139950i	−0.751979	+	0.659187i	$0.770900\pi$
$998$	1.36818	−	2.36975i	0.0433089	−	0.0750132i
$999$	14.1670	+	24.5379i	0.448223	+	0.776344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.g.a.39.2	✓	48
3.2	odd	2		441.2.bb.d.235.3		48
4.3	odd	2		784.2.bg.c.529.4		48
7.2	even	3		343.2.g.i.226.3		48
7.3	odd	6		343.2.e.c.295.6		48
7.4	even	3		343.2.e.d.295.6		48
7.5	odd	6		343.2.g.h.226.3		48
7.6	odd	2		343.2.g.g.165.2		48
49.3	odd	42		343.2.e.c.50.6		48
49.5	odd	42		343.2.g.g.79.2		48
49.8	even	7		343.2.g.i.214.3		48
49.17	odd	42		2401.2.a.i.1.18		24
49.32	even	21		2401.2.a.h.1.18		24
49.41	odd	14		343.2.g.h.214.3		48
49.44	even	21	inner	49.2.g.a.44.2	yes	48
49.46	even	21		343.2.e.d.50.6		48
147.44	odd	42		441.2.bb.d.289.3		48
196.191	odd	42		784.2.bg.c.289.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.39.2	✓	48	1.1	even	1	trivial
49.2.g.a.44.2	yes	48	49.44	even	21	inner
343.2.e.c.50.6		48	49.3	odd	42
343.2.e.c.295.6		48	7.3	odd	6
343.2.e.d.50.6		48	49.46	even	21
343.2.e.d.295.6		48	7.4	even	3
343.2.g.g.79.2		48	49.5	odd	42
343.2.g.g.165.2		48	7.6	odd	2
343.2.g.h.214.3		48	49.41	odd	14
343.2.g.h.226.3		48	7.5	odd	6
343.2.g.i.214.3		48	49.8	even	7
343.2.g.i.226.3		48	7.2	even	3
441.2.bb.d.235.3		48	3.2	odd	2
441.2.bb.d.289.3		48	147.44	odd	42
784.2.bg.c.289.4		48	196.191	odd	42
784.2.bg.c.529.4		48	4.3	odd	2
2401.2.a.h.1.18		24	49.32	even	21
2401.2.a.i.1.18		24	49.17	odd	42

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.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23528 - 0.186189i) q^{2} +(-2.40355 + 1.63871i) q^{3} +(-0.419885 - 0.129517i) q^{4} +(0.186621 + 2.49028i) q^{5} +(3.27417 - 1.57676i) q^{6} +(-2.47068 - 0.946431i) q^{7} +(2.74561 + 1.32222i) q^{8} +(1.99564 - 5.08481i) q^{9} +O(q^{10})\)	\(q+(-1.23528 - 0.186189i) q^{2} +(-2.40355 + 1.63871i) q^{3} +(-0.419885 - 0.129517i) q^{4} +(0.186621 + 2.49028i) q^{5} +(3.27417 - 1.57676i) q^{6} +(-2.47068 - 0.946431i) q^{7} +(2.74561 + 1.32222i) q^{8} +(1.99564 - 5.08481i) q^{9} +(0.233134 - 3.11095i) q^{10} +(0.723227 + 1.84275i) q^{11} +(1.22146 - 0.376769i) q^{12} +(-1.63931 + 2.05563i) q^{13} +(2.87578 + 1.62913i) q^{14} +(-4.52941 - 5.67970i) q^{15} +(-2.41932 - 1.64946i) q^{16} +(1.83155 + 1.69943i) q^{17} +(-3.41192 + 5.90962i) q^{18} +(1.16801 + 2.02306i) q^{19} +(0.244176 - 1.06980i) q^{20} +(7.48932 - 1.77394i) q^{21} +(-0.550290 - 2.41098i) q^{22} +(-4.68278 + 4.34498i) q^{23} +(-8.76593 + 1.32125i) q^{24} +(-1.22253 + 0.184267i) q^{25} +(2.40775 - 2.23406i) q^{26} +(1.59396 + 6.98360i) q^{27} +(0.914824 + 0.717389i) q^{28} +(-0.385156 + 1.68748i) q^{29} +(4.53761 + 7.85936i) q^{30} +(2.50275 - 4.33490i) q^{31} +(-1.78637 - 1.65751i) q^{32} +(-4.75804 - 3.24398i) q^{33} +(-1.94607 - 2.44029i) q^{34} +(1.89580 - 6.32932i) q^{35} +(-1.49651 + 1.87657i) q^{36} +(3.77975 - 1.16590i) q^{37} +(-1.06616 - 2.71652i) q^{38} +(0.571575 - 7.62714i) q^{39} +(-2.78031 + 7.08410i) q^{40} +(-3.16127 - 1.52239i) q^{41} +(-9.58173 + 0.796890i) q^{42} +(3.27475 - 1.57704i) q^{43} +(-0.0650037 - 0.867415i) q^{44} +(13.0351 + 4.02078i) q^{45} +(6.59355 - 4.49541i) q^{46} +(4.48592 + 0.676144i) q^{47} +8.51793 q^{48} +(5.20854 + 4.67666i) q^{49} +1.54448 q^{50} +(-7.18709 - 1.08328i) q^{51} +(0.954561 - 0.650809i) q^{52} +(3.25395 + 1.00371i) q^{53} +(-0.668724 - 8.92351i) q^{54} +(-4.45400 + 2.14494i) q^{55} +(-5.53214 - 5.86531i) q^{56} +(-6.12257 - 2.94848i) q^{57} +(0.789967 - 2.01280i) q^{58} +(-0.582607 + 7.77435i) q^{59} +(1.16621 + 2.97146i) q^{60} +(-12.7680 + 3.93841i) q^{61} +(-3.89872 + 4.88884i) q^{62} +(-9.74302 + 10.6742i) q^{63} +(5.54935 + 6.95867i) q^{64} +(-5.42502 - 3.69872i) q^{65} +(5.27354 + 4.89313i) q^{66} +(4.31224 - 7.46901i) q^{67} +(-0.548935 - 0.950783i) q^{68} +(4.13511 - 18.1171i) q^{69} +(-3.52030 + 7.46553i) q^{70} +(1.97751 + 8.66402i) q^{71} +(12.2025 - 11.3222i) q^{72} +(-5.52320 + 0.832488i) q^{73} +(-4.88615 + 0.736468i) q^{74} +(2.63645 - 2.44627i) q^{75} +(-0.228410 - 1.00073i) q^{76} +(-0.0428257 - 5.23734i) q^{77} +(-2.12615 + 9.31527i) q^{78} +(8.63497 + 14.9562i) q^{79} +(3.65613 - 6.33261i) q^{80} +(-3.26257 - 3.02722i) q^{81} +(3.62161 + 2.46917i) q^{82} +(2.86163 + 3.58837i) q^{83} +(-3.37441 - 0.225147i) q^{84} +(-3.89026 + 4.87823i) q^{85} +(-4.33888 + 1.33837i) q^{86} +(-1.83955 - 4.68709i) q^{87} +(-0.450817 + 6.01574i) q^{88} +(4.93768 - 12.5810i) q^{89} +(-15.3534 - 7.39379i) q^{90} +(5.99572 - 3.52731i) q^{91} +(2.52898 - 1.21789i) q^{92} +(1.08815 + 14.5204i) q^{93} +(-5.41550 - 1.67046i) q^{94} +(-4.82001 + 3.28623i) q^{95} +(7.00980 + 1.05656i) q^{96} -4.68167 q^{97} +(-5.56328 - 6.74678i) q^{98} +10.8133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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