LMFDB - Embedded newform 49.2.g.a.16.2

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			16.2
Character	$\chi$	$=$	49.16
Dual form			49.2.g.a.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.354207 - 0.902506i) q^{2} +(0.218016 + 2.90922i) q^{3} +(0.777050 - 0.720997i) q^{4} +(-0.605902 + 0.413097i) q^{5} +(2.54837 - 1.22723i) q^{6} +(-0.310399 - 2.62748i) q^{7} +(-2.67297 - 1.28723i) q^{8} +(-5.44954 + 0.821385i) q^{9} +O(q^{10})$	\(q+(-0.354207 - 0.902506i) q^{2} +(0.218016 + 2.90922i) q^{3} +(0.777050 - 0.720997i) q^{4} +(-0.605902 + 0.413097i) q^{5} +(2.54837 - 1.22723i) q^{6} +(-0.310399 - 2.62748i) q^{7} +(-2.67297 - 1.28723i) q^{8} +(-5.44954 + 0.821385i) q^{9} +(0.587437 + 0.400508i) q^{10} +(1.30775 + 0.197112i) q^{11} +(2.26695 + 2.10342i) q^{12} +(-0.696197 + 0.873004i) q^{13} +(-2.26137 + 1.21081i) q^{14} +(-1.33389 - 1.67264i) q^{15} +(-0.0565197 + 0.754203i) q^{16} +(-5.89890 + 1.81957i) q^{17} +(2.67157 + 4.62730i) q^{18} +(2.99610 - 5.18940i) q^{19} +(-0.172974 + 0.757850i) q^{20} +(7.57625 - 1.47585i) q^{21} +(-0.285321 - 1.25007i) q^{22} +(5.13778 + 1.58479i) q^{23} +(3.16209 - 8.05688i) q^{24} +(-1.63024 + 4.15378i) q^{25} +(1.03449 + 0.319098i) q^{26} +(-1.63014 - 7.14212i) q^{27} +(-2.13560 - 1.81789i) q^{28} +(0.529674 - 2.32065i) q^{29} +(-1.03710 + 1.79630i) q^{30} +(3.15709 + 5.46824i) q^{31} +(-4.96923 + 1.53281i) q^{32} +(-0.288331 + 3.84751i) q^{33} +(3.73161 + 4.67929i) q^{34} +(1.27348 + 1.46377i) q^{35} +(-3.64234 + 4.56735i) q^{36} +(4.10810 + 3.81176i) q^{37} +(-5.74471 - 0.865875i) q^{38} +(-2.69154 - 1.83506i) q^{39} +(2.15131 - 0.324257i) q^{40} +(-0.798221 - 0.384403i) q^{41} +(-4.01553 - 6.31485i) q^{42} +(-5.17256 + 2.49098i) q^{43} +(1.15831 - 0.789719i) q^{44} +(2.96257 - 2.74887i) q^{45} +(-0.389553 - 5.19822i) q^{46} +(-0.440505 - 1.12239i) q^{47} -2.20646 q^{48} +(-6.80731 + 1.63113i) q^{49} +4.32625 q^{50} +(-6.57958 - 16.7645i) q^{51} +(0.0884530 + 1.18032i) q^{52} +(6.99227 - 6.48788i) q^{53} +(-5.86840 + 4.00101i) q^{54} +(-0.873796 + 0.420798i) q^{55} +(-2.55249 + 7.42272i) q^{56} +(15.7503 + 7.58495i) q^{57} +(-2.28202 + 0.343959i) q^{58} +(0.392674 + 0.267721i) q^{59} +(-2.24246 - 0.337997i) q^{60} +(-2.56745 - 2.38225i) q^{61} +(3.81686 - 4.78619i) q^{62} +(3.84970 + 14.0636i) q^{63} +(4.08662 + 5.12446i) q^{64} +(0.0611921 - 0.816551i) q^{65} +(3.57453 - 1.10260i) q^{66} +(-2.53523 - 4.39115i) q^{67} +(-3.27183 + 5.66698i) q^{68} +(-3.49040 + 15.2924i) q^{69} +(0.869987 - 1.66780i) q^{70} +(-2.06601 - 9.05180i) q^{71} +(15.6237 + 4.81928i) q^{72} +(1.19973 - 3.05687i) q^{73} +(1.98501 - 5.05773i) q^{74} +(-12.4397 - 3.83713i) q^{75} +(-1.41342 - 6.19260i) q^{76} +(0.111983 - 3.49728i) q^{77} +(-0.702790 + 3.07912i) q^{78} +(0.509557 - 0.882579i) q^{79} +(-0.277313 - 0.480321i) q^{80} +(4.62386 - 1.42627i) q^{81} +(-0.0641901 + 0.856558i) q^{82} +(4.13385 + 5.18369i) q^{83} +(4.82304 - 6.60926i) q^{84} +(2.82250 - 3.53930i) q^{85} +(4.08028 + 3.78595i) q^{86} +(6.86676 + 1.03500i) q^{87} +(-3.24185 - 2.21025i) q^{88} +(3.59885 - 0.542439i) q^{89} +(-3.53023 - 1.70007i) q^{90} +(2.50990 + 1.55827i) q^{91} +(5.13494 - 2.47286i) q^{92} +(-15.2200 + 10.3768i) q^{93} +(-0.856932 + 0.795117i) q^{94} +(0.328382 + 4.38195i) q^{95} +(-5.54264 - 14.1224i) q^{96} -14.7267 q^{97} +(3.88331 + 5.56587i) q^{98} -7.28854 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 $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{10}{21}\right)$

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 $

$2$	−0.354207	−	0.902506i	−0.250463	−	0.638168i	0.749246	−	0.662291i	$-0.230416\pi$
$2$	−0.354207	−	0.902506i	−0.250463	−	0.638168i	−0.999709	+	0.0241232i	$0.992321\pi$
$3$	0.218016	+	2.90922i	0.125872	+	1.67964i	0.600634	+	0.799524i	$0.294915\pi$
$3$	0.218016	+	2.90922i	0.125872	+	1.67964i	−0.474762	+	0.880114i	$0.657466\pi$
$4$	0.777050	−	0.720997i	0.388525	−	0.360498i
$5$	−0.605902	+	0.413097i	−0.270968	+	0.184743i	−0.691179	−	0.722684i	$-0.742908\pi$
$5$	−0.605902	+	0.413097i	−0.270968	+	0.184743i	0.420211	+	0.907426i	$0.361956\pi$
$6$	2.54837	−	1.22723i	1.04037	−	0.501014i
$7$	−0.310399	−	2.62748i	−0.117320	−	0.993094i
$7$	−0.310399	−	2.62748i	−0.117320	−	0.993094i
$8$	−2.67297	−	1.28723i	−0.945036	−	0.455105i
$9$	−5.44954	+	0.821385i	−1.81651	+	0.273795i
$10$	0.587437	+	0.400508i	0.185764	+	0.126652i
$11$	1.30775	+	0.197112i	0.394302	+	0.0594315i	0.343201	−	0.939262i	$-0.388489\pi$
$11$	1.30775	+	0.197112i	0.394302	+	0.0594315i	0.0511011	+	0.998693i	$0.483727\pi$
$12$	2.26695	+	2.10342i	0.654411	+	0.607205i
$13$	−0.696197	+	0.873004i	−0.193090	+	0.242128i	−0.868947	−	0.494906i	$-0.835203\pi$
$13$	−0.696197	+	0.873004i	−0.193090	+	0.242128i	0.675856	+	0.737033i	$0.263774\pi$
$14$	−2.26137	+	1.21081i	−0.604377	+	0.323603i
$15$	−1.33389	−	1.67264i	−0.344408	−	0.431874i
$16$	−0.0565197	+	0.754203i	−0.0141299	+	0.188551i
$17$	−5.89890	+	1.81957i	−1.43069	+	0.441310i	−0.910774	−	0.412905i	$-0.864514\pi$
$17$	−5.89890	+	1.81957i	−1.43069	+	0.441310i	−0.519919	+	0.854216i	$0.674038\pi$
$18$	2.67157	+	4.62730i	0.629695	+	1.09066i
$19$	2.99610	−	5.18940i	0.687353	−	1.19053i	−0.285338	−	0.958427i	$-0.592106\pi$
$19$	2.99610	−	5.18940i	0.687353	−	1.19053i	0.972691	−	0.232103i	$-0.0745607\pi$
$20$	−0.172974	+	0.757850i	−0.0386782	+	0.169460i
$21$	7.57625	−	1.47585i	1.65327	−	0.322057i
$22$	−0.285321	−	1.25007i	−0.0608306	−	0.266516i
$23$	5.13778	+	1.58479i	1.07130	+	0.330452i	0.779742	−	0.626101i	$-0.215350\pi$
$23$	5.13778	+	1.58479i	1.07130	+	0.330452i	0.291558	+	0.956553i	$0.405826\pi$
$24$	3.16209	−	8.05688i	0.645459	−	1.64460i
$25$	−1.63024	+	4.15378i	−0.326047	+	0.830755i
$26$	1.03449	+	0.319098i	0.202880	+	0.0625802i
$27$	−1.63014	−	7.14212i	−0.313721	−	1.37450i
$28$	−2.13560	−	1.81789i	−0.403590	−	0.343548i
$29$	0.529674	−	2.32065i	0.0983579	−	0.430934i	−0.901641	−	0.432486i	$-0.857637\pi$
$29$	0.529674	−	2.32065i	0.0983579	−	0.430934i	0.999999	+	0.00155131i	$0.000493797\pi$
$30$	−1.03710	+	1.79630i	−0.189347	+	0.327958i
$31$	3.15709	+	5.46824i	0.567030	+	0.982125i	0.996858	+	0.0792143i	$0.0252411\pi$
$31$	3.15709	+	5.46824i	0.567030	+	0.982125i	−0.429827	+	0.902911i	$0.641426\pi$
$32$	−4.96923	+	1.53281i	−0.878445	+	0.270964i
$33$	−0.288331	+	3.84751i	−0.0501920	+	0.669766i
$34$	3.73161	+	4.67929i	0.639965	+	0.802491i
$35$	1.27348	+	1.46377i	0.215257	+	0.247422i
$36$	−3.64234	+	4.56735i	−0.607057	+	0.761226i
$37$	4.10810	+	3.81176i	0.675367	+	0.626649i	0.941391	−	0.337318i	$-0.109520\pi$
$37$	4.10810	+	3.81176i	0.675367	+	0.626649i	−0.266024	+	0.963966i	$0.585710\pi$
$38$	−5.74471	−	0.865875i	−0.931915	−	0.140464i
$39$	−2.69154	−	1.83506i	−0.430992	−	0.293845i
$40$	2.15131	−	0.324257i	0.340151	−	0.0512696i
$41$	−0.798221	−	0.384403i	−0.124661	−	0.0600337i	0.370514	−	0.928827i	$-0.379182\pi$
$41$	−0.798221	−	0.384403i	−0.124661	−	0.0600337i	−0.495175	+	0.868793i	$0.664896\pi$
$42$	−4.01553	−	6.31485i	−0.619609	−	0.974402i
$43$	−5.17256	+	2.49098i	−0.788809	+	0.379870i	−0.784507	−	0.620121i	$-0.787084\pi$
$43$	−5.17256	+	2.49098i	−0.788809	+	0.379870i	−0.00430211	+	0.999991i	$0.501369\pi$
$44$	1.15831	−	0.789719i	0.174621	−	0.119055i
$45$	2.96257	−	2.74887i	0.441634	−	0.409777i
$46$	−0.389553	−	5.19822i	−0.0574364	−	0.766435i
$47$	−0.440505	−	1.12239i	−0.0642543	−	0.163717i	0.895140	−	0.445784i	$-0.147075\pi$
$47$	−0.440505	−	1.12239i	−0.0642543	−	0.163717i	−0.959395	+	0.282067i	$0.908980\pi$
$48$	−2.20646			−0.318476
$49$	−6.80731	+	1.63113i	−0.972472	+	0.233019i
$50$	4.32625			0.611824
$51$	−6.57958	−	16.7645i	−0.921325	−	2.34750i
$52$	0.0884530	+	1.18032i	0.0122662	+	0.163681i
$53$	6.99227	−	6.48788i	0.960463	−	0.891179i	−0.0336606	−	0.999433i	$-0.510717\pi$
$53$	6.99227	−	6.48788i	0.960463	−	0.891179i	0.994123	+	0.108254i	$0.0345260\pi$
$54$	−5.86840	+	4.00101i	−0.798588	+	0.544468i
$55$	−0.873796	+	0.420798i	−0.117823	+	0.0567404i
$56$	−2.55249	+	7.42272i	−0.341091	+	0.991903i
$57$	15.7503	+	7.58495i	2.08618	+	1.00465i
$58$	−2.28202	+	0.343959i	−0.299643	+	0.0451640i
$59$	0.392674	+	0.267721i	0.0511218	+	0.0348543i	0.588611	−	0.808416i	$-0.299675\pi$
$59$	0.392674	+	0.267721i	0.0511218	+	0.0348543i	−0.537490	+	0.843270i	$0.680627\pi$
$60$	−2.24246	−	0.337997i	−0.289501	−	0.0436352i
$61$	−2.56745	−	2.38225i	−0.328729	−	0.305016i	0.498490	−	0.866895i	$-0.333888\pi$
$61$	−2.56745	−	2.38225i	−0.328729	−	0.305016i	−0.827219	+	0.561880i	$0.810078\pi$
$62$	3.81686	−	4.78619i	0.484741	−	0.607846i
$63$	3.84970	+	14.0636i	0.485017	+	1.77185i
$64$	4.08662	+	5.12446i	0.510827	+	0.640557i
$65$	0.0611921	−	0.816551i	0.00758994	−	0.101281i
$66$	3.57453	−	1.10260i	0.439994	−	0.135720i
$67$	−2.53523	−	4.39115i	−0.309728	−	0.536465i	0.668575	−	0.743645i	$-0.266905\pi$
$67$	−2.53523	−	4.39115i	−0.309728	−	0.536465i	−0.978303	+	0.207180i	$0.933571\pi$
$68$	−3.27183	+	5.66698i	−0.396768	+	0.687222i
$69$	−3.49040	+	15.2924i	−0.420194	+	1.84099i
$70$	0.869987	−	1.66780i	0.103983	−	0.199340i
$71$	−2.06601	−	9.05180i	−0.245191	−	1.07425i	−0.936217	−	0.351422i	$-0.885698\pi$
$71$	−2.06601	−	9.05180i	−0.245191	−	1.07425i	0.691026	−	0.722830i	$-0.257159\pi$
$72$	15.6237	+	4.81928i	1.84127	+	0.567958i
$73$	1.19973	−	3.05687i	0.140418	−	0.357780i	−0.843314	−	0.537421i	$-0.819399\pi$
$73$	1.19973	−	3.05687i	0.140418	−	0.357780i	0.983732	+	0.179641i	$0.0574938\pi$
$74$	1.98501	−	5.05773i	0.230753	−	0.587950i
$75$	−12.4397	−	3.83713i	−1.43641	−	0.443073i
$76$	−1.41342	−	6.19260i	−0.162131	−	0.710340i
$77$	0.111983	−	3.49728i	0.0127617	−	0.398551i
$78$	−0.702790	+	3.07912i	−0.0795753	+	0.348642i
$79$	0.509557	−	0.882579i	0.0573297	−	0.0992979i	−0.835936	−	0.548827i	$-0.815075\pi$
$79$	0.509557	−	0.882579i	0.0573297	−	0.0992979i	0.893266	+	0.449529i	$0.148408\pi$
$80$	−0.277313	−	0.480321i	−0.0310046	−	0.0537015i
$81$	4.62386	−	1.42627i	0.513763	−	0.158475i
$82$	−0.0641901	+	0.856558i	−0.00708861	+	0.0945910i
$83$	4.13385	+	5.18369i	0.453749	+	0.568984i	0.955109	−	0.296255i	$-0.0957380\pi$
$83$	4.13385	+	5.18369i	0.453749	+	0.568984i	−0.501359	+	0.865239i	$0.667167\pi$
$84$	4.82304	−	6.60926i	0.526236	−	0.721129i
$85$	2.82250	−	3.53930i	0.306143	−	0.383891i
$86$	4.08028	+	3.78595i	0.439988	+	0.408249i
$87$	6.86676	+	1.03500i	0.736194	+	0.110963i
$88$	−3.24185	−	2.21025i	−0.345582	−	0.235614i
$89$	3.59885	−	0.542439i	0.381477	−	0.0574984i	0.0444953	−	0.999010i	$-0.485832\pi$
$89$	3.59885	−	0.542439i	0.381477	−	0.0574984i	0.336982	+	0.941511i	$0.390594\pi$
$90$	−3.53023	−	1.70007i	−0.372119	−	0.179203i
$91$	2.50990	+	1.55827i	0.263109	+	0.163351i
$92$	5.13494	−	2.47286i	0.535354	−	0.257813i
$93$	−15.2200	+	10.3768i	−1.57824	+	1.07603i
$94$	−0.856932	+	0.795117i	−0.0883858	+	0.0820100i
$95$	0.328382	+	4.38195i	0.0336912	+	0.449578i
$96$	−5.54264	−	14.1224i	−0.565693	−	1.44136i
$97$	−14.7267			−1.49527			−0.747636	−	0.664109i	$-0.768811\pi$
$97$	−14.7267			−1.49527			−0.747636	+	0.664109i	$0.768811\pi$
$98$	3.88331	+	5.56587i	0.392273	+	0.562238i
$99$	−7.28854			−0.732526
$100$	1.72808	+	4.40309i	0.172808	+	0.440309i
$101$	−0.328936	−	4.38934i	−0.0327303	−	0.436756i	−0.989364	−	0.145462i	$-0.953533\pi$
$101$	−0.328936	−	4.38934i	−0.0327303	−	0.436756i	0.956634	−	0.291294i	$-0.0940858\pi$
$102$	−12.7995	+	11.8762i	−1.26734	+	1.17592i
$103$	5.50872	−	3.75578i	0.542791	−	0.370068i	−0.260668	−	0.965428i	$-0.583943\pi$
$103$	5.50872	−	3.75578i	0.542791	−	0.370068i	0.803459	+	0.595360i	$0.202991\pi$
$104$	2.98467	−	1.43734i	0.292671	−	0.140943i
$105$	−3.98079	+	4.02394i	−0.388486	+	0.392697i
$106$	−8.33207	−	4.01251i	−0.809282	−	0.389730i
$107$	13.0554	−	1.96778i	1.26211	−	0.190232i	0.516309	−	0.856402i	$-0.327306\pi$
$107$	13.0554	−	1.96778i	1.26211	−	0.190232i	0.745800	+	0.666170i	$0.232068\pi$
$108$	−6.41615	−	4.37446i	−0.617394	−	0.420932i
$109$	8.27777	+	1.24767i	0.792866	+	0.119505i	0.532973	−	0.846132i	$-0.321075\pi$
$109$	8.27777	+	1.24767i	0.792866	+	0.119505i	0.259893	+	0.965637i	$0.416313\pi$
$110$	0.689277	+	0.639556i	0.0657200	+	0.0609793i
$111$	−10.1936	+	12.7824i	−0.967534	+	1.21325i
$112$	1.99920	−	0.0855991i	0.188906	−	0.00808835i
$113$	−5.57830	−	6.99497i	−0.524762	−	0.658031i	0.446850	−	0.894609i	$-0.352546\pi$
$113$	−5.57830	−	6.99497i	−0.524762	−	0.658031i	−0.971613	+	0.236578i	$0.923974\pi$
$114$	1.26658	−	16.9014i	0.118626	−	1.58296i
$115$	−3.76766	+	1.16217i	−0.351336	+	0.108373i
$116$	−1.26160	−	2.18515i	−0.117137	−	0.202887i
$117$	3.07688	−	5.32931i	0.284458	−	0.492695i
$118$	0.102531	−	0.449219i	0.00943878	−	0.0413540i
$119$	6.61189	+	14.9344i	0.606111	+	1.36904i
$120$	1.41235	+	6.18793i	0.128930	+	0.564878i
$121$	−8.83994	−	2.72676i	−0.803631	−	0.247887i
$122$	−1.24058	+	3.16095i	−0.112317	+	0.286179i
$123$	0.944288	−	2.40601i	0.0851436	−	0.216942i
$124$	6.39580	+	1.97284i	0.574360	+	0.177167i
$125$	−1.54405	−	6.76492i	−0.138104	−	0.605073i
$126$	11.3289	−	8.45581i	1.00926	−	0.753303i
$127$	−1.12111	+	4.91191i	−0.0994826	+	0.435862i	0.900517	+	0.434821i	$0.143188\pi$
$127$	−1.12111	+	4.91191i	−0.0994826	+	0.435862i	−0.999999	+	0.00104074i	$0.999669\pi$
$128$	−2.02292	+	3.50381i	−0.178803	+	0.309696i
$129$	−8.37450	−	14.5051i	−0.737333	−	1.27710i
$130$	−0.758617	+	0.234002i	−0.0665351	+	0.0205234i
$131$	−0.850330	+	11.3469i	−0.0742937	+	0.991380i	0.828132	+	0.560534i	$0.189404\pi$
$131$	−0.850330	+	11.3469i	−0.0742937	+	0.991380i	−0.902425	+	0.430846i	$0.858215\pi$
$132$	2.54999	+	3.19759i	0.221949	+	0.278315i
$133$	−14.5650	−	6.26142i	−1.26295	−	0.542934i
$134$	−3.06504	+	3.84344i	−0.264779	+	0.332023i
$135$	3.93810	+	3.65402i	0.338937	+	0.314488i
$136$	18.1098	+	2.72961i	1.55290	+	0.234062i
$137$	6.14396	+	4.18888i	0.524914	+	0.357880i	0.796601	−	0.604506i	$-0.206629\pi$
$137$	6.14396	+	4.18888i	0.524914	+	0.357880i	−0.271687	+	0.962386i	$0.587582\pi$
$138$	15.0378	−	2.26659i	1.28011	−	0.192945i
$139$	8.54606	+	4.11557i	0.724868	+	0.349078i	0.759663	−	0.650317i	$-0.225364\pi$
$139$	8.54606	+	4.11557i	0.724868	+	0.349078i	−0.0347957	+	0.999394i	$0.511078\pi$
$140$	2.04493	+	0.219251i	0.172828	+	0.0185301i
$141$	3.16924	−	1.52622i	0.266898	−	0.128531i
$142$	−7.43751	+	5.07081i	−0.624142	+	0.425533i
$143$	−1.08253	+	1.00444i	−0.0905259	+	0.0839958i
$144$	−0.311485	−	4.15648i	−0.0259571	−	0.346373i
$145$	0.637724	+	1.62489i	0.0529601	+	0.134940i
$146$	−3.18380			−0.263493
$147$	−6.22942	−	19.4483i	−0.513794	−	1.60407i
$148$	5.94046			0.488303
$149$	3.70002	+	9.42750i	0.303117	+	0.772331i	0.998555	+	0.0537439i	$0.0171154\pi$
$149$	3.70002	+	9.42750i	0.303117	+	0.772331i	−0.695437	+	0.718587i	$0.744789\pi$
$150$	0.943191	+	12.5860i	0.0770112	+	1.02764i
$151$	−4.14923	+	3.84992i	−0.337660	+	0.313302i	−0.830717	−	0.556694i	$-0.812070\pi$
$151$	−4.14923	+	3.84992i	−0.337660	+	0.313302i	0.493058	+	0.869996i	$0.335879\pi$
$152$	−14.6884	+	10.0144i	−1.19139	+	0.812276i
$153$	30.6517	−	14.7611i	2.47804	−	1.19336i
$154$	−3.19598	+	1.13770i	−0.257539	+	0.0916781i
$155$	−4.17180	−	2.00903i	−0.335087	−	0.161369i
$156$	−3.41453	+	0.514658i	−0.273382	+	0.0412056i
$157$	2.35121	+	1.60303i	0.187647	+	0.127936i	0.653500	−	0.756927i	$-0.273300\pi$
$157$	2.35121	+	1.60303i	0.187647	+	0.127936i	−0.465853	+	0.884862i	$0.654252\pi$
$158$	−0.977022	−	0.147262i	−0.0777277	−	0.0117156i
$159$	20.3991	+	18.9276i	1.61775	+	1.50106i
$160$	2.37767	−	2.98150i	0.187971	−	0.235709i
$161$	2.56926	−	13.9913i	0.202486	−	1.10267i
$162$	−2.92503	−	3.66787i	−0.229812	−	0.288175i
$163$	1.23174	−	16.4365i	0.0964776	−	1.28740i	−0.713380	−	0.700777i	$-0.752837\pi$
$163$	1.23174	−	16.4365i	0.0964776	−	1.28740i	0.809858	−	0.586626i	$-0.199544\pi$
$164$	−0.897411	+	0.276815i	−0.0700760	+	0.0216156i
$165$	−1.41469	−	2.45032i	−0.110134	−	0.190757i
$166$	3.21407	−	5.56693i	0.249460	−	0.432077i
$167$	5.43239	−	23.8009i	0.420371	−	1.84177i	−0.109908	−	0.993942i	$-0.535056\pi$
$167$	5.43239	−	23.8009i	0.420371	−	1.84177i	0.530279	−	0.847823i	$-0.322087\pi$
$168$	−22.1508	−	5.80749i	−1.70897	−	0.448058i
$169$	2.61533	+	11.4585i	0.201179	+	0.881423i
$170$	−4.19399	−	1.29367i	−0.321664	−	0.0992202i
$171$	−12.0649	+	30.7408i	−0.922623	+	2.35081i
$172$	−2.22335	+	5.66501i	−0.169529	+	0.431953i
$173$	−18.9634	−	5.84942i	−1.44176	−	0.444723i	−0.527395	−	0.849620i	$-0.676831\pi$
$173$	−18.9634	−	5.84942i	−1.44176	−	0.444723i	−0.914362	+	0.404897i	$0.867307\pi$
$174$	−1.49817	−	6.56390i	−0.113576	−	0.497608i
$175$	11.4200	+	2.99409i	0.863270	+	0.226332i
$176$	−0.222576	+	0.975169i	−0.0167773	+	0.0735061i
$177$	−0.693249	+	1.20074i	−0.0521078	+	0.0902533i
$178$	−1.76429	−	3.05585i	−0.132239	−	0.229045i
$179$	7.59859	−	2.34385i	0.567945	−	0.175188i	0.00253361	−	0.999997i	$-0.499194\pi$
$179$	7.59859	−	2.34385i	0.567945	−	0.175188i	0.565412	+	0.824809i	$0.308717\pi$
$180$	0.320143	−	4.27201i	0.0238620	−	0.318417i
$181$	3.03369	+	3.80413i	0.225492	+	0.282758i	0.881689	−	0.471832i	$-0.156407\pi$
$181$	3.03369	+	3.80413i	0.225492	+	0.282758i	−0.656196	+	0.754590i	$0.727836\pi$
$182$	0.517319	−	2.81715i	0.0383462	−	0.208821i
$183$	6.37074	−	7.98865i	0.470939	−	0.590538i
$184$	−11.6931	−	10.8496i	−0.862027	−	0.799844i
$185$	−4.06373	−	0.612508i	−0.298771	−	0.0450325i
$186$	14.7562	+	10.0606i	1.08198	+	0.737680i
$187$	−8.07295	+	1.21680i	−0.590353	+	0.0889814i
$188$	−1.15153	−	0.554549i	−0.0839842	−	0.0404446i
$189$	−18.2598	+	6.50007i	−1.32820	+	0.472811i
$190$	3.83842	−	1.84849i	0.278468	−	0.134103i
$191$	−13.5906	+	9.26589i	−0.983379	+	0.670457i	−0.944405	−	0.328784i	$-0.893361\pi$
$191$	−13.5906	+	9.26589i	−0.983379	+	0.670457i	−0.0389738	+	0.999240i	$0.512409\pi$
$192$	−14.0172	+	13.0061i	−1.01161	+	0.938633i
$193$	1.77164	+	23.6409i	0.127525	+	1.70171i	0.583823	+	0.811881i	$0.301556\pi$
$193$	1.77164	+	23.6409i	0.127525	+	1.70171i	−0.456298	+	0.889827i	$0.650825\pi$
$194$	5.21632	+	13.2910i	0.374510	+	0.954235i
$195$	2.38887			0.171070
$196$	−4.11357	+	6.17552i	−0.293827	+	0.441108i
$197$	−6.19181			−0.441148			−0.220574	−	0.975370i	$-0.570793\pi$
$197$	−6.19181			−0.441148			−0.220574	+	0.975370i	$0.570793\pi$
$198$	2.58166	+	6.57795i	0.183470	+	0.467475i
$199$	−0.965516	−	12.8839i	−0.0684436	−	0.913317i	−0.920720	−	0.390224i	$-0.872397\pi$
$199$	−0.965516	−	12.8839i	−0.0684436	−	0.913317i	0.852276	−	0.523092i	$-0.175222\pi$
$200$	9.70444	−	9.00441i	0.686208	−	0.636708i
$201$	12.2221	−	8.33289i	0.862081	−	0.587757i
$202$	−3.84490	+	1.85160i	−0.270526	+	0.130278i
$203$	−6.26188	−	0.671380i	−0.439498	−	0.0471216i
$204$	−17.1998	−	8.28299i	−1.20423	−	0.579925i
$205$	0.642439	−	0.0968321i	0.0448699	−	0.00676305i
$206$	−5.34085	−	3.64133i	−0.372115	−	0.253703i
$207$	−29.3002	−	4.41630i	−2.03651	−	0.306954i
$208$	−0.619073	−	0.574416i	−0.0429250	−	0.0398286i
$209$	4.94105	−	6.19588i	0.341780	−	0.428578i
$210$	5.04166	+	2.16738i	0.347908	+	0.149563i
$211$	6.98276	+	8.75610i	0.480713	+	0.602795i	0.961758	−	0.273901i	$-0.0883140\pi$
$211$	6.98276	+	8.75610i	0.480713	+	0.602795i	−0.481045	+	0.876696i	$0.659743\pi$
$212$	0.755602	−	10.0828i	0.0518950	−	0.692490i
$213$	25.8833	−	7.98393i	1.77349	−	0.547050i
$214$	−6.40023	−	11.0855i	−0.437511	−	0.757791i
$215$	2.10505	−	3.64606i	0.143563	−	0.248659i
$216$	−4.83626	+	21.1890i	−0.329065	+	1.44173i
$217$	13.3877	−	9.99253i	0.908819	−	0.678337i
$218$	−1.80602	−	7.91267i	−0.122319	−	0.535914i
$219$	9.15467	+	2.82384i	0.618615	+	0.190818i
$220$	−0.375589	+	0.956984i	−0.0253222	+	0.0645199i
$221$	2.51831	−	6.41654i	0.169400	−	0.431623i
$222$	15.1468	+	4.67218i	1.01659	+	0.313576i
$223$	0.535149	+	2.34464i	0.0358362	+	0.157009i	0.989680	−	0.143294i	$-0.0457694\pi$
$223$	0.535149	+	2.34464i	0.0358362	+	0.157009i	−0.953844	+	0.300303i	$0.902912\pi$
$224$	5.56986	+	12.5808i	0.372152	+	0.840589i
$225$	5.47218	−	23.9752i	0.364812	−	1.59835i
$226$	−4.33712	+	7.51212i	−0.288501	+	0.499699i
$227$	−0.234888	−	0.406839i	−0.0155901	−	0.0270028i	0.858125	−	0.513441i	$-0.171629\pi$
$227$	−0.234888	−	0.406839i	−0.0155901	−	0.0270028i	−0.873715	+	0.486438i	$0.838296\pi$
$228$	17.7075	−	5.46204i	1.17271	−	0.361732i
$229$	0.630488	−	8.41327i	0.0416638	−	0.555965i	−0.936843	−	0.349750i	$-0.886266\pi$
$229$	0.630488	−	8.41327i	0.0416638	−	0.555965i	0.978507	−	0.206215i	$-0.0661145\pi$
$230$	2.38340	+	2.98869i	0.157157	+	0.197068i
$231$	10.1988	−	0.436678i	0.671029	−	0.0287313i
$232$	−4.40302	+	5.52121i	−0.289072	+	0.362485i
$233$	3.33255	+	3.09215i	0.218322	+	0.202574i	0.781750	−	0.623592i	$-0.214327\pi$
$233$	3.33255	+	3.09215i	0.218322	+	0.202574i	−0.563428	+	0.826165i	$0.690518\pi$
$234$	−5.89959	−	0.889220i	−0.385668	−	0.0581301i
$235$	0.730558	+	0.498086i	0.0476564	+	0.0324916i
$236$	0.498153	−	0.0750845i	0.0324270	−	0.00488758i
$237$	2.67871	+	1.29000i	0.174001	+	0.0837943i
$238$	11.1364	−	11.2572i	0.721869	−	0.729694i
$239$	−26.7126	+	12.8641i	−1.72789	+	0.832109i	−0.740846	+	0.671674i	$0.765575\pi$
$239$	−26.7126	+	12.8641i	−1.72789	+	0.832109i	−0.987046	+	0.160435i	$0.948710\pi$
$240$	1.33690	−	0.911483i	0.0862965	−	0.0588360i
$241$	3.75064	−	3.48008i	0.241600	−	0.224172i	−0.550074	−	0.835116i	$-0.685400\pi$
$241$	3.75064	−	3.48008i	0.241600	−	0.224172i	0.791674	+	0.610944i	$0.209210\pi$
$242$	0.670255	+	8.94394i	0.0430857	+	0.574938i
$243$	−2.87182	−	7.31729i	−0.184228	−	0.469404i
$244$	−3.71263			−0.237677
$245$	3.45074	−	3.80038i	0.220460	−	0.242798i
$246$	−2.50591			−0.159771
$247$	2.44449	+	6.22845i	0.155539	+	0.396307i
$248$	−1.39990	−	18.6803i	−0.0888936	−	1.18620i
$249$	−14.1792	+	13.1564i	−0.898573	+	0.833754i
$250$	−5.55847	+	3.78970i	−0.351549	+	0.239682i
$251$	−18.0281	+	8.68186i	−1.13792	+	0.547994i	−0.905384	−	0.424593i	$-0.860417\pi$
$251$	−18.0281	+	8.68186i	−1.13792	+	0.547994i	−0.232537	+	0.972587i	$0.574703\pi$
$252$	13.1312	+	8.15249i	0.827189	+	0.513558i
$253$	6.40655	+	3.08523i	0.402776	+	0.193967i
$254$	4.83014	−	0.728026i	0.303070	−	0.0456804i
$255$	10.9119	+	7.43964i	0.683332	+	0.465888i
$256$	16.8412	+	2.53840i	1.05257	+	0.158650i
$257$	−7.18712	−	6.66867i	−0.448320	−	0.415980i	0.423432	−	0.905928i	$-0.360825\pi$
$257$	−7.18712	−	6.66867i	−0.448320	−	0.415980i	−0.871752	+	0.489948i	$0.837016\pi$
$258$	−10.1246	+	12.6958i	−0.630329	+	0.790408i
$259$	8.74017	−	11.9771i	0.543088	−	0.744221i
$260$	−0.541182	−	0.678620i	−0.0335627	−	0.0420862i
$261$	−0.980326	+	13.0815i	−0.0606806	+	0.809727i
$262$	10.5418	−	3.25172i	0.651275	−	0.200892i
$263$	8.63988	+	14.9647i	0.532758	+	0.922764i	0.999268	+	0.0382482i	$0.0121777\pi$
$263$	8.63988	+	14.9647i	0.532758	+	0.922764i	−0.466510	+	0.884516i	$0.654489\pi$
$264$	5.72334	−	9.91311i	0.352247	−	0.610110i
$265$	−1.55651	+	6.81951i	−0.0956155	+	0.418919i
$266$	−0.491921	+	15.3629i	−0.0301616	+	0.941958i
$267$	2.36268	+	10.3516i	0.144594	+	0.633506i
$268$	−5.13601	−	1.58425i	−0.313732	−	0.0967734i
$269$	−4.40829	+	11.2321i	−0.268778	+	0.684835i	0.731218	+	0.682143i	$0.238952\pi$
$269$	−4.40829	+	11.2321i	−0.268778	+	0.684835i	−0.999996	+	0.00269177i	$0.999143\pi$
$270$	1.90287	−	4.84844i	0.115805	−	0.295066i
$271$	8.32784	+	2.56880i	0.505880	+	0.156043i	0.537182	−	0.843467i	$-0.319489\pi$
$271$	8.32784	+	2.56880i	0.505880	+	0.156043i	−0.0313014	+	0.999510i	$0.509965\pi$
$272$	−1.03892	−	4.55181i	−0.0629938	−	0.275994i
$273$	−3.98614	+	7.64157i	−0.241252	+	0.462489i
$274$	1.60425	−	7.02869i	0.0969164	−	0.424619i
$275$	−2.95070	+	5.11077i	−0.177934	+	0.308191i
$276$	8.31358	+	14.3995i	0.500419	+	0.866750i
$277$	−21.6749	+	6.68583i	−1.30232	+	0.401712i	−0.866885	−	0.498508i	$-0.833881\pi$
$277$	−21.6749	+	6.68583i	−1.30232	+	0.401712i	−0.435434	+	0.900220i	$0.643405\pi$
$278$	0.687244	−	9.17064i	0.0412182	−	0.550018i
$279$	−21.6962	−	27.2062i	−1.29892	−	1.62879i
$280$	−1.51974	−	5.55187i	−0.0908220	−	0.331788i
$281$	9.27960	−	11.6363i	0.553575	−	0.694161i	−0.423781	−	0.905765i	$-0.639297\pi$
$281$	9.27960	−	11.6363i	0.553575	−	0.694161i	0.977355	+	0.211604i	$0.0678687\pi$
$282$	−2.49999	−	2.31966i	−0.148872	−	0.138133i
$283$	−27.1913	−	4.09843i	−1.61636	−	0.243627i	−0.722300	−	0.691580i	$-0.756915\pi$
$283$	−27.1913	−	4.09843i	−1.61636	−	0.243627i	−0.894057	+	0.447953i	$0.852153\pi$
$284$	−8.13172	−	5.54411i	−0.482529	−	0.328982i
$285$	−12.6765	+	1.91067i	−0.750889	+	0.113178i
$286$	1.28996	+	0.621211i	0.0762768	+	0.0367330i
$287$	−0.762245	+	2.21663i	−0.0449939	+	0.130843i
$288$	25.8210	−	12.4347i	1.52152	−	0.732724i
$289$	17.4401	−	11.8905i	1.02589	−	0.699439i
$290$	1.24059	−	1.15110i	0.0728499	−	0.0675949i
$291$	−3.21066	−	42.8433i	−0.188212	−	2.51152i
$292$	−1.27174	−	3.24035i	−0.0744231	−	0.189627i
$293$	−1.76427			−0.103070			−0.0515348	−	0.998671i	$-0.516411\pi$
$293$	−1.76427			−0.103070			−0.0515348	+	0.998671i	$0.516411\pi$
$294$	−15.3457	+	12.5108i	−0.894981	+	0.729647i
$295$	−0.348517			−0.0202914
$296$	−6.07418	−	15.4768i	−0.353055	−	0.899569i
$297$	−0.724025	−	9.66144i	−0.0420122	−	0.560614i
$298$	7.19780	−	6.67858i	0.416957	−	0.386880i
$299$	−4.96044	+	3.38197i	−0.286869	+	0.195584i
$300$	−12.4328	+	5.98732i	−0.717808	+	0.345678i
$301$	8.15055	+	12.8176i	0.469790	+	0.738795i
$302$	4.94427	+	2.38103i	0.284511	+	0.137013i
$303$	12.6978	−	1.91389i	0.729472	−	0.109950i
$304$	3.74452	+	2.55297i	0.214763	+	0.146423i
$305$	2.53972	+	0.382802i	0.145424	+	0.0219192i
$306$	−24.1790	−	22.4348i	−1.38222	−	1.28251i
$307$	2.40192	−	3.01191i	0.137085	−	0.171899i	−0.708550	−	0.705660i	$-0.750651\pi$
$307$	2.40192	−	3.01191i	0.137085	−	0.171899i	0.845635	+	0.533761i	$0.179222\pi$
$308$	−2.43451	−	2.79830i	−0.138719	−	0.159448i
$309$	12.1274	+	15.2073i	0.689903	+	0.865111i
$310$	−0.335482	+	4.47669i	−0.0190541	+	0.254259i
$311$	−7.89454	+	2.43514i	−0.447658	+	0.138084i	−0.510384	−	0.859947i	$-0.670497\pi$
$311$	−7.89454	+	2.43514i	−0.447658	+	0.138084i	0.0627260	+	0.998031i	$0.480021\pi$
$312$	4.83225	+	8.36970i	0.273572	+	0.473841i
$313$	−14.2747	+	24.7245i	−0.806854	+	1.39751i	0.108179	+	0.994131i	$0.465498\pi$
$313$	−14.2747	+	24.7245i	−0.806854	+	1.39751i	−0.915033	+	0.403380i	$0.867835\pi$
$314$	0.613926	−	2.68979i	0.0346459	−	0.151793i
$315$	−8.14217	−	6.93086i	−0.458759	−	0.390509i
$316$	−0.240385	−	1.05320i	−0.0135227	−	0.0592469i
$317$	5.85456	+	1.80589i	0.328825	+	0.101429i	0.454772	−	0.890608i	$-0.349721\pi$
$317$	5.85456	+	1.80589i	0.328825	+	0.101429i	−0.125947	+	0.992037i	$0.540197\pi$
$318$	9.85676	−	25.1146i	0.552739	−	1.40836i
$319$	1.15011	−	2.93043i	0.0643938	−	0.164073i
$320$	−4.59299	−	1.41675i	−0.256756	−	0.0791987i
$321$	8.57097	+	37.5519i	0.478385	+	2.09594i
$322$	−13.5373	+	2.63706i	−0.754404	+	0.146958i
$323$	−8.23123	+	36.0634i	−0.457998	+	2.00662i
$324$	2.56463	−	4.44208i	0.142480	−	0.246782i
$325$	−2.49130	−	4.31505i	−0.138192	−	0.239356i
$326$	−15.2703	+	4.71027i	−0.845744	+	0.260877i
$327$	−1.82507	+	24.3539i	−0.100927	+	1.34677i
$328$	1.63880	+	2.05499i	0.0904877	+	0.113468i
$329$	−2.81232	+	1.50581i	−0.155048	+	0.0830178i
$330$	−1.71034	+	2.14469i	−0.0941509	+	0.118061i
$331$	1.28167	+	1.18922i	0.0704472	+	0.0653654i	0.714611	−	0.699522i	$-0.246604\pi$
$331$	1.28167	+	1.18922i	0.0704472	+	0.0653654i	−0.644163	+	0.764888i	$0.722794\pi$
$332$	6.94963	+	1.04749i	0.381411	+	0.0574884i
$333$	−25.5181	−	17.3980i	−1.39839	−	0.953403i
$334$	−23.4046	+	3.52768i	−1.28064	+	0.193026i
$335$	3.35007	+	1.61331i	0.183034	+	0.0881446i
$336$	0.684883	+	5.79744i	0.0373634	+	0.316276i
$337$	−2.46216	+	1.18571i	−0.134122	+	0.0645900i	−0.499741	−	0.866175i	$-0.666572\pi$
$337$	−2.46216	+	1.18571i	−0.134122	+	0.0645900i	0.365619	+	0.930765i	$0.380857\pi$
$338$	9.41499	−	6.41903i	0.512108	−	0.349149i
$339$	19.1337	−	17.7535i	1.03920	−	0.964239i
$340$	−0.358603	−	4.78522i	−0.0194480	−	0.259515i
$341$	3.05084	+	7.77340i	0.165212	+	0.420953i
$342$	32.0172			1.73129
$343$	6.39875	+	17.3798i	0.345500	+	0.938419i
$344$	17.0326			0.918334
$345$	−4.20242	−	10.7076i	−0.226250	−	0.576477i
$346$	1.43783	+	19.1865i	0.0772980	+	1.03147i
$347$	23.9175	−	22.1922i	1.28396	−	1.19134i	0.313634	−	0.949544i	$-0.398453\pi$
$347$	23.9175	−	22.1922i	1.28396	−	1.19134i	0.970327	−	0.241798i	$-0.0777371\pi$
$348$	6.08205	−	4.14667i	0.326032	−	0.222285i
$349$	19.2153	−	9.25361i	1.02857	−	0.495335i	0.158034	−	0.987434i	$-0.449485\pi$
$349$	19.2153	−	9.25361i	1.02857	−	0.495335i	0.870539	+	0.492099i	$0.163770\pi$
$350$	−1.34286	−	11.3671i	−0.0717790	−	0.607599i
$351$	7.37000	+	3.54920i	0.393381	+	0.189443i
$352$	−6.80066	+	1.02503i	−0.362476	+	0.0546345i
$353$	12.5084	+	8.52807i	0.665754	+	0.453904i	0.848457	−	0.529265i	$-0.177532\pi$
$353$	12.5084	+	8.52807i	0.665754	+	0.453904i	−0.182703	+	0.983168i	$0.558485\pi$
$354$	1.32923	+	0.200349i	0.0706479	+	0.0106485i
$355$	4.99107	+	4.63104i	0.264899	+	0.245790i
$356$	2.40539	−	3.01626i	0.127485	−	0.159861i
$357$	−42.0061	+	22.4914i	−2.22320	+	1.19037i
$358$	−4.80682	−	6.02756i	−0.254048	−	0.318567i
$359$	−1.36484	+	18.2125i	−0.0720334	+	0.961218i	0.837728	+	0.546087i	$0.183883\pi$
$359$	−1.36484	+	18.2125i	−0.0720334	+	0.961218i	−0.909762	+	0.415131i	$0.863736\pi$
$360$	−11.4573	+	3.53410i	−0.603852	+	0.186264i
$361$	−8.45325	−	14.6415i	−0.444908	−	0.770603i
$362$	2.35869	−	4.08537i	0.123970	−	0.214722i
$363$	6.00550	−	26.3118i	0.315207	−	1.38101i
$364$	3.07382	−	0.598779i	0.161112	−	0.0313846i
$365$	0.535863	+	2.34777i	0.0280484	+	0.122888i
$366$	−9.46637	−	2.91999i	−0.494815	−	0.152630i
$367$	10.4929	−	26.7356i	0.547727	−	1.39558i	−0.342263	−	0.939604i	$-0.611193\pi$
$367$	10.4929	−	26.7356i	0.547727	−	1.39558i	0.889990	−	0.455980i	$-0.150711\pi$
$368$	−1.48564	+	3.78535i	−0.0774444	+	0.197325i
$369$	4.66568	+	1.43917i	0.242885	+	0.0749202i
$370$	0.886610	+	3.88449i	0.0460927	+	0.201945i
$371$	−19.2172	−	16.3582i	−0.997706	−	0.849277i
$372$	−4.34505	+	19.0369i	−0.225280	+	0.987017i
$373$	17.9437	−	31.0793i	0.929087	−	1.60923i	0.144235	−	0.989543i	$-0.453928\pi$
$373$	17.9437	−	31.0793i	0.929087	−	1.60923i	0.784852	−	0.619683i	$-0.212739\pi$
$374$	3.95767	+	6.85489i	0.204646	+	0.354458i
$375$	19.3440	−	5.96684i	0.998921	−	0.308126i
$376$	−0.267320	+	3.56714i	−0.0137860	+	0.183961i
$377$	1.65718	+	2.07804i	0.0853491	+	0.107024i
$378$	12.3341	+	14.1772i	0.634398	+	0.729196i
$379$	9.52620	−	11.9455i	0.489328	−	0.613598i	−0.474457	−	0.880279i	$-0.657356\pi$
$379$	9.52620	−	11.9455i	0.489328	−	0.613598i	0.963785	+	0.266681i	$0.0859270\pi$
$380$	3.41454	+	3.16823i	0.175162	+	0.162527i
$381$	−14.5343	−	2.19069i	−0.744613	−	0.112232i
$382$	13.1764	+	8.98352i	0.674164	+	0.459637i
$383$	29.1858	−	4.39904i	1.49132	−	0.224781i	0.647773	−	0.761833i	$-0.275700\pi$
$383$	29.1858	−	4.39904i	1.49132	−	0.224781i	0.843549	+	0.537052i	$0.180462\pi$
$384$	−10.6344	−	5.12125i	−0.542683	−	0.261342i
$385$	1.37686	+	2.16527i	0.0701714	+	0.110352i
$386$	20.7085	−	9.97269i	1.05404	−	0.507597i
$387$	26.1420	−	17.8233i	1.32887	−	0.906011i
$388$	−11.4434	+	10.6179i	−0.580950	+	0.539043i
$389$	2.15361	+	28.7379i	0.109192	+	1.45707i	0.735516	+	0.677507i	$0.236940\pi$
$389$	2.15361	+	28.7379i	0.109192	+	1.45707i	−0.626324	+	0.779563i	$0.715441\pi$
$390$	−0.846155	−	2.15597i	−0.0428467	−	0.109172i
$391$	−33.1909			−1.67853
$392$	20.2953	+	4.40262i	1.02507	+	0.222366i
$393$	−33.1959			−1.67451
$394$	2.19319	+	5.58815i	0.110491	+	0.281527i
$395$	0.0558490	+	0.745253i	0.00281007	+	0.0374977i
$396$	−5.66356	+	5.25502i	−0.284605	+	0.264074i
$397$	11.4823	−	7.82848i	0.576278	−	0.392900i	−0.239816	−	0.970818i	$-0.577087\pi$
$397$	11.4823	−	7.82848i	0.576278	−	0.392900i	0.816095	+	0.577918i	$0.196135\pi$
$398$	−11.2858	+	5.43496i	−0.565707	+	0.272430i
$399$	15.0404	−	43.7380i	0.752963	−	2.18964i
$400$	−3.04065	−	1.46430i	−0.152032	−	0.0732150i
$401$	−16.1953	+	2.44105i	−0.808755	+	0.121900i	−0.540387	−	0.841416i	$-0.681722\pi$
$401$	−16.1953	+	2.44105i	−0.808755	+	0.121900i	−0.268368	+	0.963317i	$0.586484\pi$
$402$	−11.8496	−	8.07895i	−0.591006	−	0.402941i
$403$	−6.97175	−	1.05082i	−0.347288	−	0.0523452i
$404$	−3.42030	−	3.17358i	−0.170166	−	0.157891i
$405$	−2.21242	+	2.77429i	−0.109936	+	0.137855i
$406$	1.61208	+	5.88919i	0.0800061	+	0.292276i
$407$	4.62103	+	5.79459i	0.229056	+	0.287227i
$408$	−3.99281	+	53.2804i	−0.197674	+	2.63777i
$409$	−15.6130	+	4.81598i	−0.772014	+	0.238135i	−0.655643	−	0.755071i	$-0.727602\pi$
$409$	−15.6130	+	4.81598i	−0.772014	+	0.238135i	−0.116371	+	0.993206i	$0.537126\pi$
$410$	−0.314948	−	0.545507i	−0.0155542	−	0.0269407i
$411$	−10.8469	+	18.7874i	−0.535037	+	0.926712i
$412$	1.57264	−	6.89020i	0.0774786	−	0.339456i
$413$	0.581545	−	1.11484i	0.0286160	−	0.0548579i
$414$	6.39262	+	28.0079i	0.314180	+	1.37651i
$415$	−4.64607	−	1.43312i	−0.228067	−	0.0703493i
$416$	2.12142	−	5.40529i	0.104011	−	0.265016i
$417$	−10.1099	+	25.7596i	−0.495084	+	1.26145i
$418$	−7.34198	−	2.26470i	−0.359108	−	0.110770i
$419$	3.36310	+	14.7347i	0.164298	+	0.719837i	0.988208	+	0.153117i	$0.0489310\pi$
$419$	3.36310	+	14.7347i	0.164298	+	0.719837i	−0.823910	+	0.566721i	$0.808212\pi$
$420$	−0.192023	+	5.99694i	−0.00936976	+	0.292621i
$421$	1.56331	−	6.84933i	0.0761913	−	0.333816i	−0.922439	−	0.386144i	$-0.873807\pi$
$421$	1.56331	−	6.84933i	0.0761913	−	0.333816i	0.998630	+	0.0523278i	$0.0166641\pi$
$422$	5.42909	−	9.40346i	0.264284	−	0.457753i
$423$	3.32246	+	5.75467i	0.161544	+	0.279802i
$424$	−27.0415	+	8.34120i	−1.31325	+	0.405085i
$425$	2.05852	−	27.4690i	0.0998529	−	1.33244i
$426$	−16.3736	−	20.5318i	−0.793303	−	0.994770i
$427$	−5.46238	+	7.48538i	−0.264343	+	0.362243i
$428$	8.72590	−	10.9419i	0.421782	−	0.528898i
$429$	−3.15816	−	2.93034i	−0.152477	−	0.141478i
$430$	−4.03621	−	0.608361i	−0.194644	−	0.0293378i
$431$	−12.5785	−	8.57589i	−0.605886	−	0.413086i	0.221146	−	0.975241i	$-0.429020\pi$
$431$	−12.5785	−	8.57589i	−0.605886	−	0.413086i	−0.827032	+	0.562155i	$0.809973\pi$
$432$	5.47874	−	0.825788i	0.263596	−	0.0397307i
$433$	6.45680	+	3.10943i	0.310294	+	0.149430i	0.582549	−	0.812795i	$-0.302055\pi$
$433$	6.45680	+	3.10943i	0.310294	+	0.149430i	−0.272255	+	0.962225i	$0.587770\pi$
$434$	−13.7604	−	8.54309i	−0.660518	−	0.410081i
$435$	−4.58814	+	2.20953i	−0.219984	+	0.105939i
$436$	7.33181	−	4.99874i	0.351130	−	0.239396i
$437$	23.6174	−	21.9138i	1.12977	−	1.04828i
$438$	−0.694119	−	9.26237i	−0.0331663	−	0.442573i
$439$	0.923286	+	2.35249i	0.0440660	+	0.112278i	0.951212	−	0.308537i	$-0.0998393\pi$
$439$	0.923286	+	2.35249i	0.0440660	+	0.112278i	−0.907146	+	0.420815i	$0.861744\pi$
$440$	2.87729			0.137169
$441$	35.7569	−	14.4803i	1.70271	−	0.689540i
$442$	−6.68297			−0.317876
$443$	−1.15467	−	2.94206i	−0.0548602	−	0.139781i	0.900816	−	0.434201i	$-0.142969\pi$
$443$	−1.15467	−	2.94206i	−0.0548602	−	0.139781i	−0.955676	+	0.294419i	$0.904874\pi$
$444$	1.29511	+	17.2821i	0.0614634	+	0.820172i
$445$	−1.95647	+	1.81534i	−0.0927455	+	0.0860553i
$446$	1.92650	−	1.31347i	0.0912224	−	0.0621944i
$447$	−26.6200	+	12.8195i	−1.25908	+	0.606342i
$448$	12.1959	−	12.3281i	0.576204	−	0.582450i
$449$	−16.8409	−	8.11014i	−0.794771	−	0.382741i	−0.00798535	−	0.999968i	$-0.502542\pi$
$449$	−16.8409	−	8.11014i	−0.794771	−	0.382741i	−0.786785	+	0.617227i	$0.788256\pi$
$450$	−23.5761	+	3.55352i	−1.11139	+	0.167514i
$451$	−0.968104	−	0.660042i	−0.0455863	−	0.0310802i
$452$	−9.37797	−	1.41350i	−0.441102	−	0.0664855i
$453$	−12.1049	−	11.2317i	−0.568736	−	0.527710i
$454$	−0.283975	+	0.356093i	−0.0133276	+	0.0167123i
$455$	−2.16447	+	0.0926754i	−0.101472	+	0.00434469i
$456$	−32.3364	−	40.5486i	−1.51429	−	1.89886i
$457$	−1.40015	+	18.6837i	−0.0654963	+	0.873988i	0.863607	+	0.504166i	$0.168200\pi$
$457$	−1.40015	+	18.6837i	−0.0654963	+	0.873988i	−0.929103	+	0.369821i	$0.879419\pi$
$458$	−7.81635	+	2.41103i	−0.365234	+	0.112660i
$459$	22.6116	+	39.1645i	1.05542	+	1.82804i
$460$	−2.08974	+	3.61953i	−0.0974346	+	0.168762i
$461$	1.58855	−	6.95990i	0.0739862	−	0.324155i	−0.924368	−	0.381502i	$-0.875407\pi$
$461$	1.58855	−	6.95990i	0.0739862	−	0.324155i	0.998354	+	0.0573470i	$0.0182641\pi$
$462$	−4.00658	−	9.04976i	−0.186403	−	0.421033i
$463$	−8.12461	−	35.5962i	−0.377583	−	1.65430i	−0.704843	−	0.709364i	$-0.748982\pi$
$463$	−8.12461	−	35.5962i	−0.377583	−	1.65430i	0.327260	−	0.944934i	$-0.393875\pi$
$464$	1.72030	+	0.530644i	0.0798631	+	0.0246345i
$465$	4.93520	−	12.5747i	0.228865	−	0.583137i
$466$	1.61027	−	4.10291i	0.0745944	−	0.190064i
$467$	39.8324	+	12.2867i	1.84322	+	0.568559i	0.999495	+	0.0317884i	$0.0101203\pi$
$467$	39.8324	+	12.2867i	1.84322	+	0.568559i	0.843728	+	0.536771i	$0.180356\pi$
$468$	−1.45153	−	6.35956i	−0.0670969	−	0.293971i
$469$	−10.7507	+	8.02428i	−0.496423	+	0.370527i
$470$	0.190757	−	0.835759i	0.00879894	−	0.0385507i
$471$	−4.15096	+	7.18967i	−0.191266	+	0.331283i
$472$	−0.704986	−	1.22107i	−0.0324496	−	0.0562043i
$473$	−7.25543	+	2.23800i	−0.333605	+	0.102904i
$474$	0.215412	−	2.87448i	0.00989421	−	0.132029i
$475$	16.6713	+	20.9051i	0.764930	+	0.959191i
$476$	15.9055	+	6.83765i	0.729025	+	0.313403i
$477$	−32.7756	+	41.0993i	−1.50069	+	1.88181i
$478$	21.0717	+	19.5517i	0.963798	+	0.894274i
$479$	7.81738	+	1.17828i	0.357185	+	0.0538370i	0.325184	−	0.945651i	$-0.394574\pi$
$479$	7.81738	+	1.17828i	0.357185	+	0.0538370i	0.0320014	+	0.999488i	$0.489812\pi$
$480$	9.19222	+	6.26715i	0.419566	+	0.286055i
$481$	−6.18772	+	0.932649i	−0.282136	+	0.0425251i
$482$	−4.46930	−	2.15230i	−0.203571	−	0.0980346i
$483$	41.2640	+	4.42420i	1.87758	+	0.201308i
$484$	−8.83506	+	4.25474i	−0.401594	+	0.193397i
$485$	8.92295	−	6.08356i	0.405170	−	0.276240i
$486$	−5.58667	+	5.18368i	−0.253417	+	0.235136i
$487$	−1.84295	−	24.5925i	−0.0835122	−	1.11439i	−0.868767	−	0.495220i	$-0.835087\pi$
$487$	−1.84295	−	24.5925i	−0.0835122	−	1.11439i	0.785255	−	0.619172i	$-0.212532\pi$
$488$	3.79621	+	9.67258i	0.171846	+	0.437857i
$489$	48.0858			2.17452
$490$	−4.65215	−	1.76819i	−0.210163	−	0.0798788i
$491$	9.78275			0.441489			0.220745	−	0.975332i	$-0.429151\pi$
$491$	9.78275			0.441489			0.220745	+	0.975332i	$0.429151\pi$
$492$	−1.00096	−	2.55041i	−0.0451269	−	0.114982i
$493$	1.09810	+	14.6531i	0.0494557	+	0.659941i
$494$	4.75536	−	4.41233i	0.213954	−	0.198520i
$495$	4.41614	−	3.01087i	0.198491	−	0.135329i
$496$	−4.30260	+	2.07202i	−0.193192	+	0.0930366i
$497$	−23.1421	+	8.23808i	−1.03807	+	0.369528i
$498$	16.8961	+	8.13675i	0.757134	+	0.364616i
$499$	−36.2150	+	5.45853i	−1.62121	+	0.244357i	−0.895960	−	0.444134i	$-0.853511\pi$
$499$	−36.2150	+	5.45853i	−1.62121	+	0.244357i	−0.725245	+	0.688491i	$0.758273\pi$
$500$	−6.07729	−	4.14343i	−0.271785	−	0.185300i
$501$	70.4262	+	10.6150i	3.14641	+	0.474245i
$502$	14.2211	+	13.1953i	0.634719	+	0.588933i
$503$	2.68292	−	3.36428i	0.119626	−	0.150006i	−0.718413	−	0.695617i	$-0.755131\pi$
$503$	2.68292	−	3.36428i	0.119626	−	0.150006i	0.838038	+	0.545611i	$0.183702\pi$
$504$	7.81299	−	42.5470i	0.348018	−	1.89519i
$505$	2.01253	+	2.52363i	0.0895563	+	0.112300i
$506$	0.515192	−	6.87476i	0.0229031	−	0.305621i
$507$	−32.7651	+	10.1067i	−1.45515	+	0.448854i
$508$	2.67031	+	4.62512i	0.118476	+	0.205207i
$509$	16.9704	−	29.3935i	0.752198	−	1.30284i	−0.194557	−	0.980891i	$-0.562327\pi$
$509$	16.9704	−	29.3935i	0.752198	−	1.30284i	0.946755	−	0.321954i	$-0.104340\pi$
$510$	2.84922	−	12.4833i	0.126166	−	0.552768i
$511$	−8.40427	−	2.20343i	−0.371783	−	0.0974739i
$512$	−1.87378	−	8.20956i	−0.0828101	−	0.362815i
$513$	−41.9474	−	12.9391i	−1.85202	−	0.571274i
$514$	−3.47279	+	8.84851i	−0.153178	+	0.390291i
$515$	−1.78624	+	4.55127i	−0.0787113	+	0.200553i
$516$	−16.9655	−	5.23316i	−0.746864	−	0.230377i
$517$	−0.354835	−	1.55463i	−0.0156056	−	0.0683727i
$518$	−13.9052	−	3.64567i	−0.610961	−	0.160182i
$519$	12.8829	−	56.4438i	0.565498	−	2.47761i
$520$	−1.21466	+	2.10385i	−0.0532662	+	0.0922597i
$521$	22.2446	+	38.5288i	0.974555	+	1.68798i	0.681395	+	0.731916i	$0.261374\pi$
$521$	22.2446	+	38.5288i	0.974555	+	1.68798i	0.293161	+	0.956063i	$0.405293\pi$
$522$	12.1534	−	3.74883i	0.531940	−	0.164082i
$523$	0.487773	−	6.50888i	0.0213288	−	0.284614i	−0.976333	−	0.216272i	$-0.930610\pi$
$523$	0.487773	−	6.50888i	0.0213288	−	0.284614i	0.997662	−	0.0683416i	$-0.0217708\pi$
$524$	7.52030	+	9.43016i	0.328526	+	0.411958i
$525$	−6.22073	+	33.8760i	−0.271495	+	1.47847i
$526$	10.4454	−	13.0982i	0.455443	−	0.571107i
$527$	−28.5732	−	26.5121i	−1.24467	−	1.15488i
$528$	−2.88551	−	0.434920i	−0.125576	−	0.0189275i
$529$	4.88167	+	3.32827i	0.212246	+	0.144707i
$530$	6.70597	−	1.01076i	0.291289	−	0.0439047i
$531$	−2.35979	−	1.13642i	−0.102406	−	0.0493163i
$532$	−15.8322	+	5.63591i	−0.686414	+	0.244348i
$533$	0.891304	−	0.429230i	0.0386067	−	0.0185920i
$534$	8.50548	−	5.79894i	0.368068	−	0.250945i
$535$	−7.09738	+	6.58541i	−0.306846	+	0.284712i
$536$	1.12416	+	15.0008i	0.0485562	+	0.647937i
$537$	8.47540	+	21.5950i	0.365741	+	0.931892i
$538$	11.6985			0.504359
$539$	−9.22378	+	0.791315i	−0.397296	+	0.0340844i
$540$	5.69463			0.245058
$541$	8.98067	+	22.8824i	0.386109	+	0.983790i	0.983349	+	0.181727i	$0.0581689\pi$
$541$	8.98067	+	22.8824i	0.386109	+	0.983790i	−0.597240	+	0.802063i	$0.703736\pi$
$542$	−0.631427	−	8.42581i	−0.0271221	−	0.361920i
$543$	−10.4056	+	9.65503i	−0.446549	+	0.414337i
$544$	26.5240	−	18.0837i	1.13721	−	0.775333i
$545$	−5.53093	+	2.66355i	−0.236919	+	0.114094i
$546$	8.30848	+	0.890811i	0.355570	+	0.0381232i
$547$	0.390071	+	0.187849i	0.0166783	+	0.00803182i	0.442204	−	0.896914i	$-0.354197\pi$
$547$	0.390071	+	0.187849i	0.0166783	+	0.00803182i	−0.425526	+	0.904946i	$0.639911\pi$
$548$	7.79433	−	1.17481i	0.332957	−	0.0501852i
$549$	15.9482	+	10.8733i	0.680651	+	0.464060i
$550$	5.65766	+	0.852755i	0.241243	+	0.0363616i
$551$	−10.4558	−	9.70160i	−0.445434	−	0.413302i
$552$	29.0146	−	36.3832i	1.23494	−	1.54857i
$553$	−2.47712	−	1.06490i	−0.105338	−	0.0452842i
$554$	13.7114	+	17.1936i	0.582542	+	0.730485i
$555$	0.895964	−	11.9558i	0.0380316	−	0.507496i
$556$	9.60803	−	2.96368i	0.407471	−	0.125688i
$557$	−14.7530	−	25.5529i	−0.625104	−	1.08271i	−0.988521	−	0.151085i	$-0.951723\pi$
$557$	−14.7530	−	25.5529i	−0.625104	−	1.08271i	0.363417	−	0.931626i	$-0.381610\pi$
$558$	−16.8688	+	29.2176i	−0.714113	+	1.23688i
$559$	1.42649	−	6.24988i	0.0603343	−	0.264342i
$560$	−1.17596	+	0.877726i	−0.0496932	+	0.0370907i
$561$	−5.29998	−	23.2207i	−0.223765	−	0.980379i
$562$	−13.7887	−	4.25325i	−0.581641	−	0.179413i
$563$	−16.0259	+	40.8334i	−0.675413	+	1.72092i	0.0174436	+	0.999848i	$0.494447\pi$
$563$	−16.0259	+	40.8334i	−0.675413	+	1.72092i	−0.692856	+	0.721076i	$0.743648\pi$
$564$	1.36225	−	3.47096i	0.0573612	−	0.146154i
$565$	6.26950	+	1.93389i	0.263760	+	0.0813592i
$566$	5.93251	+	25.9920i	0.249362	+	1.09253i
$567$	−5.18274	−	11.7064i	−0.217655	−	0.491622i
$568$	−6.12939	+	26.8546i	−0.257183	+	1.12679i
$569$	−18.8824	+	32.7053i	−0.791593	+	1.37108i	0.133387	+	0.991064i	$0.457415\pi$
$569$	−18.8824	+	32.7053i	−0.791593	+	1.37108i	−0.924980	+	0.380015i	$0.875919\pi$
$570$	6.21449	+	10.7638i	0.260296	+	0.450846i
$571$	20.5360	−	6.33452i	0.859405	−	0.265091i	0.166430	−	0.986053i	$-0.446776\pi$
$571$	20.5360	−	6.33452i	0.859405	−	0.265091i	0.692975	+	0.720962i	$0.256300\pi$
$572$	−0.116981	+	1.56100i	−0.00489123	+	0.0652689i
$573$	−29.9195	−	37.5178i	−1.24990	−	1.56733i
$574$	2.27051	−	0.0972160i	0.0947694	−	0.00405772i
$575$	−14.9587	+	18.7576i	−0.623820	+	0.782245i
$576$	−26.4793	−	24.5692i	−1.10331	−	1.02372i
$577$	−7.91340	−	1.19275i	−0.329439	−	0.0496550i	−0.0177598	−	0.999842i	$-0.505653\pi$
$577$	−7.91340	−	1.19275i	−0.329439	−	0.0496550i	−0.311679	+	0.950187i	$0.600891\pi$
$578$	−16.9086	−	11.5281i	−0.703306	−	0.479506i
$579$	−68.3903	+	10.3082i	−2.84220	+	0.428393i
$580$	1.66709	+	0.802826i	0.0692220	+	0.0333356i
$581$	12.3369	−	12.4706i	0.511821	−	0.517369i
$582$	−37.5291	+	18.0730i	−1.55563	+	0.749152i
$583$	10.4230	−	7.10628i	0.431676	−	0.294312i
$584$	−7.14175	+	6.62658i	−0.295528	+	0.274210i
$585$	0.337235	+	4.50009i	0.0139430	+	0.186056i
$586$	0.624917	+	1.59226i	0.0258151	+	0.0657758i
$587$	23.2048			0.957765			0.478882	−	0.877879i	$-0.341042\pi$
$587$	23.2048			0.957765			0.478882	+	0.877879i	$0.341042\pi$
$588$	−18.8628	−	10.6209i	−0.777887	−	0.438000i
$589$	37.8359			1.55900
$590$	0.123447	+	0.314538i	0.00508224	+	0.0129493i
$591$	−1.34991	−	18.0133i	−0.0555280	−	0.740970i
$592$	−3.10702	+	2.88290i	−0.127698	+	0.118486i
$593$	−34.6741	+	23.6404i	−1.42390	+	0.970796i	−0.426084	+	0.904683i	$0.640107\pi$
$593$	−34.6741	+	23.6404i	−1.42390	+	0.970796i	−0.997812	+	0.0661128i	$0.978940\pi$
$594$	−8.46305	+	4.07559i	−0.347243	+	0.167224i
$595$	−10.1755	−	6.31746i	−0.417156	−	0.258991i
$596$	9.67229	+	4.65793i	0.396193	+	0.190796i
$597$	37.2716	−	5.61780i	1.52543	−	0.229921i
$598$	4.80927	+	3.27890i	0.196666	+	0.134084i
$599$	−40.2574	−	6.06782i	−1.64487	−	0.247924i	−0.739689	−	0.672949i	$-0.765027\pi$
$599$	−40.2574	−	6.06782i	−1.64487	−	0.247924i	−0.905182	+	0.425024i	$0.860266\pi$
$600$	28.3115	+	26.2693i	1.15581	+	1.07244i
$601$	11.8350	−	14.8406i	0.482759	−	0.605360i	−0.479485	−	0.877550i	$-0.659176\pi$
$601$	11.8350	−	14.8406i	0.482759	−	0.605360i	0.962244	+	0.272190i	$0.0877478\pi$
$602$	8.68099	−	11.8960i	0.353811	−	0.484845i
$603$	17.4227	+	21.8473i	0.709506	+	0.889692i
$604$	−0.448376	+	5.98316i	−0.0182442	+	0.243451i
$605$	6.48255	−	1.99960i	0.263553	−	0.0812954i
$606$	−6.22497	−	10.7820i	−0.252872	−	0.437987i
$607$	−7.30343	+	12.6499i	−0.296437	+	0.513444i	−0.975318	−	0.220804i	$-0.929132\pi$
$607$	−7.30343	+	12.6499i	−0.296437	+	0.513444i	0.678881	+	0.734248i	$0.262465\pi$
$608$	−6.93399	+	30.3798i	−0.281210	+	1.23206i
$609$	0.588003	−	18.3635i	0.0238271	−	0.744128i
$610$	−0.554108	−	2.42771i	−0.0224352	−	0.0982950i
$611$	1.28653	+	0.396841i	0.0520473	+	0.0160545i
$612$	13.1752	−	33.5699i	0.532576	−	1.35698i
$613$	2.37674	−	6.05584i	0.0959957	−	0.244593i	−0.874807	−	0.484471i	$-0.839012\pi$
$613$	2.37674	−	6.05584i	0.0959957	−	0.244593i	0.970803	+	0.239878i	$0.0771074\pi$
$614$	−3.56904	−	1.10090i	−0.144035	−	0.0444288i
$615$	0.421768	+	1.84789i	0.0170073	+	0.0745140i
$616$	−4.80113	+	9.20395i	−0.193443	+	0.370838i
$617$	8.86369	−	38.8344i	0.356839	−	1.56341i	−0.404178	−	0.914680i	$-0.632442\pi$
$617$	8.86369	−	38.8344i	0.356839	−	1.56341i	0.761017	−	0.648732i	$-0.224701\pi$
$618$	9.42904	−	16.3316i	0.379291	−	0.656952i
$619$	−11.3318	−	19.6273i	−0.455463	−	0.788886i	0.543251	−	0.839570i	$-0.317193\pi$
$619$	−11.3318	−	19.6273i	−0.455463	−	0.788886i	−0.998715	+	0.0506844i	$0.983860\pi$
$620$	−4.69020	+	1.44674i	−0.188363	+	0.0581023i
$621$	2.94348	−	39.2781i	0.118118	−	1.57617i
$622$	4.99404	+	6.26232i	0.200243	+	0.251096i
$623$	−2.54233	−	9.28753i	−0.101856	−	0.372097i
$624$	1.53613	−	1.92625i	0.0614946	−	0.0771117i
$625$	−12.6251	−	11.7144i	−0.505005	−	0.468576i
$626$	27.3702	+	4.12540i	1.09393	+	0.164884i
$627$	19.1024	+	13.0238i	0.762877	+	0.520120i
$628$	2.98279	−	0.449583i	0.119026	−	0.0179403i
$629$	−31.1690	−	15.0102i	−1.24279	−	0.598496i
$630$	−3.37112	+	9.80332i	−0.134309	+	0.390573i
$631$	−13.7573	+	6.62518i	−0.547670	+	0.263744i	−0.687193	−	0.726475i	$-0.741157\pi$
$631$	−13.7573	+	6.62518i	−0.547670	+	0.263744i	0.139523	+	0.990219i	$0.455443\pi$
$632$	−2.49811	+	1.70318i	−0.0993696	+	0.0677490i
$633$	−23.9511	+	22.2234i	−0.951970	+	0.883299i
$634$	−0.443900	−	5.92343i	−0.0176295	−	0.235250i
$635$	−1.34981	−	3.43927i	−0.0535657	−	0.136483i
$636$	29.4979			1.16967
$637$	3.31524	−	7.07839i	0.131355	−	0.280456i
$638$	−3.05211			−0.120834
$639$	18.6938	+	47.6311i	0.739517	+	1.88426i
$640$	−0.221718	−	2.95863i	−0.00876419	−	0.116950i
$641$	−5.22195	+	4.84526i	−0.206254	+	0.191376i	−0.776536	−	0.630073i	$-0.783025\pi$
$641$	−5.22195	+	4.84526i	−0.206254	+	0.191376i	0.570281	+	0.821450i	$0.306834\pi$
$642$	30.8549	−	21.0365i	1.21775	−	0.830245i
$643$	−20.0496	+	9.65540i	−0.790681	+	0.380772i	−0.785223	−	0.619213i	$-0.787452\pi$
$643$	−20.0496	+	9.65540i	−0.790681	+	0.380772i	−0.00545784	+	0.999985i	$0.501737\pi$
$644$	−8.09126	−	12.7244i	−0.318840	−	0.501411i
$645$	11.0661	+	5.32916i	0.435728	+	0.209836i
$646$	35.4630	−	5.34518i	1.39527	−	0.210303i
$647$	−33.2203	−	22.6492i	−1.30602	−	0.890432i	−0.307885	−	0.951423i	$-0.599621\pi$
$647$	−33.2203	−	22.6492i	−1.30602	−	0.890432i	−0.998138	+	0.0609916i	$0.980574\pi$
$648$	−14.1954	−	2.13961i	−0.557647	−	0.0840517i
$649$	0.460749	+	0.427513i	0.0180860	+	0.0167813i
$650$	−3.01192	+	3.77683i	−0.118137	+	0.148140i
$651$	31.9892	+	36.7694i	1.25376	+	1.44110i
$652$	−10.8935	−	13.6600i	−0.426623	−	0.534968i
$653$	−0.194264	+	2.59228i	−0.00760215	+	0.101444i	−0.999714	−	0.0239115i	$-0.992388\pi$
$653$	−0.194264	+	2.59228i	−0.00760215	+	0.101444i	0.992112	+	0.125355i	$0.0400070\pi$
$654$	22.6260	−	6.97918i	0.884745	−	0.272908i
$655$	−4.17214	−	7.22635i	−0.163019	−	0.282357i
$656$	0.335033	−	0.580294i	0.0130808	−	0.0226567i
$657$	−4.02712	+	17.6440i	−0.157113	+	0.688357i
$658$	2.35514	+	2.00477i	0.0918131	+	0.0781540i
$659$	3.98807	+	17.4729i	0.155353	+	0.680646i	0.991276	+	0.131800i	$0.0420756\pi$
$659$	3.98807	+	17.4729i	0.155353	+	0.680646i	−0.835923	+	0.548846i	$0.815067\pi$
$660$	−2.86596	−	0.884032i	−0.111557	−	0.0344109i
$661$	−3.63099	+	9.25162i	−0.141229	+	0.359846i	−0.983935	−	0.178529i	$-0.942866\pi$
$661$	−3.63099	+	9.25162i	−0.141229	+	0.359846i	0.842705	+	0.538375i	$0.180962\pi$
$662$	0.619299	−	1.57795i	0.0240698	−	0.0613287i
$663$	19.2161	+	5.92740i	0.746293	+	0.230201i
$664$	−4.37704	−	19.1770i	−0.169862	−	0.744214i
$665$	11.4116	−	2.22297i	0.442521	−	0.0862030i
$666$	−6.66306	+	29.1928i	−0.258188	+	1.13120i
$667$	6.39910	−	11.0836i	0.247774	−	0.429157i
$668$	−12.9391	−	22.4112i	−0.500629	−	0.867115i
$669$	−6.70441	+	2.06804i	−0.259207	+	0.0799549i
$670$	0.269401	−	3.59491i	0.0104079	−	0.138883i
$671$	−2.88802	−	3.62147i	−0.111491	−	0.139805i
$672$	−35.3859	+	18.9468i	−1.36504	+	0.730887i
$673$	−6.53275	+	8.19181i	−0.251819	+	0.315771i	−0.891633	−	0.452759i	$-0.850440\pi$
$673$	−6.53275	+	8.19181i	−0.251819	+	0.315771i	0.639814	+	0.768530i	$0.279011\pi$
$674$	1.94223	+	1.80213i	0.0748119	+	0.0694153i
$675$	32.3243	+	4.87210i	1.24416	+	0.187527i
$676$	10.2938	+	7.01818i	0.395915	+	0.269930i
$677$	43.4082	−	6.54274i	1.66831	−	0.251458i	0.754121	−	0.656736i	$-0.228063\pi$
$677$	43.4082	−	6.54274i	1.66831	−	0.251458i	0.914194	+	0.405278i	$0.132825\pi$
$678$	−22.8000	−	10.9799i	−0.875628	−	0.421680i
$679$	4.57115	+	38.6942i	0.175425	+	1.48495i
$680$	−12.1003	+	5.82721i	−0.464026	+	0.223463i
$681$	1.13237	−	0.772039i	0.0433926	−	0.0295846i
$682$	5.93491	−	5.50680i	0.227260	−	0.210866i
$683$	2.19850	+	29.3369i	0.0841231	+	1.12255i	0.866312	+	0.499504i	$0.166484\pi$
$683$	2.19850	+	29.3369i	0.0841231	+	1.12255i	−0.782189	+	0.623042i	$0.785897\pi$
$684$	12.7890	+	32.5858i	0.489000	+	1.24595i
$685$	−5.45305			−0.208350
$686$	13.4189	−	11.9309i	0.512334	−	0.455526i
$687$	24.6135			0.939064
$688$	−1.58635	−	4.04195i	−0.0604790	−	0.154098i
$689$	0.795943	+	10.6211i	0.0303230	+	0.404633i
$690$	−8.17513	+	7.58541i	−0.311222	+	0.288772i
$691$	15.6930	−	10.6993i	0.596990	−	0.407021i	−0.226779	−	0.973946i	$-0.572820\pi$
$691$	15.6930	−	10.6993i	0.596990	−	0.407021i	0.823769	+	0.566926i	$0.191867\pi$
$692$	−18.9529	+	9.12723i	−0.720481	+	0.346965i
$693$	2.26235	+	19.1505i	0.0859397	+	0.727468i
$694$	−28.5004	−	13.7251i	−1.08186	−	0.520997i
$695$	−6.87820	+	1.03672i	−0.260905	+	0.0393251i
$696$	−17.0223	−	11.6056i	−0.645230	−	0.439910i
$697$	5.40807	+	0.815136i	0.204845	+	0.0308755i
$698$	−15.1577	−	14.0642i	−0.573726	−	0.532340i
$699$	−8.26920	+	10.3693i	−0.312770	+	0.392201i
$700$	11.0326	−	5.90722i	0.416994	−	0.223272i
$701$	1.24452	+	1.56058i	0.0470049	+	0.0589423i	0.804778	−	0.593576i	$-0.202284\pi$
$701$	1.24452	+	1.56058i	0.0470049	+	0.0589423i	−0.757773	+	0.652518i	$0.773713\pi$
$702$	0.592669	−	7.90862i	0.0223689	−	0.298492i
$703$	32.0890	−	9.89815i	1.21026	−	0.373316i
$704$	4.33419	+	7.50704i	0.163351	+	0.282932i
$705$	−1.28977	+	2.23394i	−0.0485755	+	0.0841352i
$706$	3.26607	−	14.3096i	0.122920	−	0.538549i
$707$	−11.4308	+	2.22672i	−0.429900	+	0.0837443i
$708$	0.327043	+	1.43287i	0.0122910	+	0.0538504i
$709$	35.5484	+	10.9652i	1.33505	+	0.411808i	0.878437	−	0.477858i	$-0.158587\pi$
$709$	35.5484	+	10.9652i	1.33505	+	0.411808i	0.456612	+	0.889666i	$0.349063\pi$
$710$	2.41167	−	6.14482i	0.0905082	−	0.230611i
$711$	−2.05191	+	5.22819i	−0.0769527	+	0.196072i
$712$	−10.3178	−	3.18263i	−0.386677	−	0.119274i
$713$	7.55439	+	33.0979i	0.282914	+	1.23953i
$714$	35.1775	+	29.9441i	1.31648	+	1.12063i
$715$	0.240976	−	1.05578i	0.00901199	−	0.0394841i
$716$	4.21457	−	7.29985i	0.157506	−	0.272808i
$717$	−43.2483	−	74.9082i	−1.61514	−	2.79750i
$718$	16.9203	−	5.21923i	0.631461	−	0.194780i
$719$	2.07091	−	27.6344i	0.0772321	−	1.03059i	−0.815132	−	0.579275i	$-0.803336\pi$
$719$	2.07091	−	27.6344i	0.0772321	−	1.03059i	0.892364	−	0.451316i	$-0.149045\pi$
$720$	1.90576	+	2.38974i	0.0710234	+	0.0890605i
$721$	−11.5781	−	13.3083i	−0.431193	−	0.495626i
$722$	−10.2198	+	12.8152i	−0.380342	+	0.476933i
$723$	10.9420	+	10.1527i	0.406938	+	0.377584i
$724$	5.10009	+	0.768715i	0.189543	+	0.0285691i
$725$	8.77597	+	5.98336i	0.325932	+	0.222216i
$726$	−25.8738	+	3.89984i	−0.960265	+	0.144737i
$727$	37.5072	+	18.0625i	1.39107	+	0.669902i	0.971328	−	0.237743i	$-0.0764077\pi$
$727$	37.5072	+	18.0625i	1.39107	+	0.669902i	0.419738	+	0.907645i	$0.362122\pi$
$728$	−4.70302	−	7.39601i	−0.174306	−	0.274114i
$729$	33.7404	−	16.2485i	1.24965	−	0.601798i
$730$	1.92907	−	1.31522i	0.0713981	−	0.0486784i
$731$	25.9799	−	24.1058i	0.960902	−	0.891587i
$732$	−0.809413	−	10.8009i	−0.0299168	−	0.399211i
$733$	−13.6419	−	34.7591i	−0.503876	−	1.28385i	−0.926071	−	0.377350i	$-0.876835\pi$
$733$	−13.6419	−	34.7591i	−0.503876	−	1.28385i	0.422195	−	0.906505i	$-0.361260\pi$
$734$	−27.8457			−1.02780
$735$	11.8085	+	9.21043i	0.435562	+	0.339732i
$736$	−27.9600			−1.03062
$737$	−2.44991	−	6.24226i	−0.0902435	−	0.229937i
$738$	−0.353757	−	4.72057i	−0.0130220	−	0.173766i
$739$	−10.3705	+	9.62244i	−0.381486	+	0.353967i	−0.847486	−	0.530817i	$-0.821885\pi$
$739$	−10.3705	+	9.62244i	−0.381486	+	0.353967i	0.466000	+	0.884785i	$0.345695\pi$
$740$	−3.59934	+	2.45399i	−0.132314	+	0.0902103i
$741$	−17.5870	+	8.46945i	−0.646075	+	0.311133i
$742$	−7.95654	+	23.1378i	−0.292094	+	0.849416i
$743$	15.7580	+	7.58866i	0.578106	+	0.278401i	0.700001	−	0.714142i	$-0.253183\pi$
$743$	15.7580	+	7.58866i	0.578106	+	0.278401i	−0.121895	+	0.992543i	$0.538897\pi$
$744$	54.0400	−	8.14522i	1.98120	−	0.298618i
$745$	−6.13632	−	4.18367i	−0.224817	−	0.153278i
$746$	−34.4051	−	5.18573i	−1.25966	−	0.189863i
$747$	−26.7854	−	24.8532i	−0.980026	−	0.909331i
$748$	−5.39577	+	6.76609i	−0.197289	+	0.247393i
$749$	−9.22266	−	33.6919i	−0.336989	−	1.23107i
$750$	−12.2369	−	15.3446i	−0.446829	−	0.560305i
$751$	−0.405109	+	5.40580i	−0.0147826	+	0.197260i	0.984923	+	0.172994i	$0.0553441\pi$
$751$	−0.405109	+	5.40580i	−0.0147826	+	0.197260i	−0.999706	+	0.0242666i	$0.992275\pi$
$752$	0.871406	−	0.268793i	0.0317769	−	0.00980187i
$753$	−29.1878	−	50.5548i	−1.06366	−	1.84232i
$754$	1.28846	−	2.23167i	0.0469228	−	0.0812727i
$755$	0.923635	−	4.04671i	0.0336145	−	0.147275i
$756$	−9.50223	+	18.2161i	−0.345593	+	0.662514i
$757$	0.389200	+	1.70520i	0.0141457	+	0.0619765i	0.981508	−	0.191420i	$-0.0613093\pi$
$757$	0.389200	+	1.70520i	0.0141457	+	0.0619765i	−0.967362	+	0.253397i	$0.918452\pi$
$758$	−14.1551	−	4.36627i	−0.514137	−	0.158590i
$759$	−7.57889	+	19.3107i	−0.275096	+	0.700934i
$760$	4.76283	−	12.1355i	0.172766	−	0.440201i
$761$	−19.9120	−	6.14204i	−0.721810	−	0.222649i	−0.0879809	−	0.996122i	$-0.528041\pi$
$761$	−19.9120	−	6.14204i	−0.721810	−	0.222649i	−0.633829	+	0.773473i	$0.718518\pi$
$762$	3.17104	+	13.8932i	0.114874	+	0.503298i
$763$	0.708828	−	22.1369i	0.0256613	−	0.801411i
$764$	−3.87987	+	16.9988i	−0.140369	+	0.614996i
$765$	−12.4742	+	21.6059i	−0.451004	+	0.781162i
$766$	−14.3080	−	24.7821i	−0.516968	−	0.895415i
$767$	−0.507100	+	0.156420i	−0.0183103	+	0.00564798i
$768$	−3.71312	+	49.5481i	−0.133986	+	1.78791i
$769$	−24.7924	−	31.0887i	−0.894036	−	1.12109i	−0.992043	−	0.125900i	$-0.959818\pi$
$769$	−24.7924	−	31.0887i	−0.894036	−	1.12109i	0.0980071	−	0.995186i	$-0.468753\pi$
$770$	1.46647	−	2.00958i	0.0528479	−	0.0724202i
$771$	17.8337	−	22.3628i	0.642266	−	0.805376i
$772$	18.4216	+	17.0928i	0.663010	+	0.615183i
$773$	41.5987	+	6.27000i	1.49620	+	0.225516i	0.845565	−	0.533873i	$-0.179264\pi$
$773$	41.5987	+	6.27000i	1.49620	+	0.225516i	0.650637	+	0.759389i	$0.274502\pi$
$774$	−25.3454	−	17.2802i	−0.911020	−	0.621123i
$775$	−27.8607	+	4.19932i	−1.00078	+	0.150844i
$776$	39.3640	+	18.9567i	1.41309	+	0.680506i
$777$	36.7495	+	22.8159i	1.31838	+	0.818515i
$778$	25.1733	−	12.1228i	0.902507	−	0.434624i
$779$	−4.38637	+	2.99058i	−0.157158	+	0.107149i
$780$	1.85627	−	1.72237i	0.0664651	−	0.0616706i
$781$	−0.917617	−	12.2447i	−0.0328349	−	0.438151i
$782$	11.7564	+	29.9549i	0.420410	+	1.07119i
$783$	−17.4378			−0.623177
$784$	−0.845458	−	5.22628i	−0.0301949	−	0.186653i
$785$	−2.08681			−0.0744814
$786$	11.7582	+	29.9595i	0.419402	+	1.06862i
$787$	3.41215	+	45.5320i	0.121630	+	1.62304i	0.640340	+	0.768092i	$0.278793\pi$
$787$	3.41215	+	45.5320i	0.121630	+	1.62304i	−0.518710	+	0.854950i	$0.673588\pi$
$788$	−4.81135	+	4.46428i	−0.171397	+	0.159033i
$789$	−41.6520	+	28.3979i	−1.48285	+	1.01099i
$790$	0.652813	−	0.314378i	0.0232260	−	0.0111851i
$791$	−16.6476	+	16.8281i	−0.591922	+	0.598339i
$792$	19.4820	+	9.38205i	0.692264	+	0.333377i
$793$	3.86717	−	0.582881i	0.137327	−	0.0206987i
$794$	−11.1324	−	7.58991i	−0.395072	−	0.269356i
$795$	−20.1788	−	3.04146i	−0.715668	−	0.107870i
$796$	−10.0395	−	9.31531i	−0.355841	−	0.330172i
$797$	−22.9601	+	28.7910i	−0.813288	+	1.01983i	0.186017	+	0.982546i	$0.440442\pi$
$797$	−22.9601	+	28.7910i	−0.813288	+	1.01983i	−0.999305	+	0.0372839i	$0.988129\pi$
$798$	−44.8012	+	1.91824i	−1.58595	+	0.0679050i
$799$	4.64076	+	5.81933i	0.164178	+	0.205873i
$800$	1.73410	−	23.1399i	0.0613096	−	0.818120i
$801$	−19.1665	+	5.91208i	−0.677215	+	0.208893i
$802$	7.93956	+	13.7517i	0.280356	+	0.485590i
$803$	2.17150	−	3.76115i	0.0766305	−	0.132728i
$804$	3.48920	−	15.2872i	0.123054	−	0.539137i
$805$	4.22305	+	9.53872i	0.148843	+	0.336196i
$806$	1.52107	+	6.66426i	0.0535775	+	0.234739i
$807$	−33.6378	−	10.3759i	−1.18411	−	0.365249i
$808$	−4.77087	+	12.1560i	−0.167839	+	0.427646i
$809$	13.4508	−	34.2720i	0.472904	−	1.20494i	−0.473165	−	0.880974i	$-0.656888\pi$
$809$	13.4508	−	34.2720i	0.472904	−	1.20494i	0.946069	−	0.323966i	$-0.105016\pi$
$810$	3.28746	+	1.01405i	0.115510	+	0.0356300i
$811$	−9.14959	−	40.0870i	−0.321286	−	1.40764i	−0.835268	−	0.549844i	$-0.814687\pi$
$811$	−9.14959	−	40.0870i	−0.321286	−	1.40764i	0.513982	−	0.857801i	$-0.328170\pi$
$812$	−5.34985	+	3.99310i	−0.187743	+	0.140130i
$813$	−5.65760	+	24.7876i	−0.198421	+	0.869337i
$814$	3.59285	−	6.22299i	0.125929	−	0.218116i
$815$	6.04354	+	10.4677i	0.211696	+	0.366668i
$816$	13.0157	−	4.01481i	0.455641	−	0.140547i
$817$	−2.57086	+	34.3057i	−0.0899430	+	1.20021i
$818$	9.87669	+	12.3850i	0.345331	+	0.433031i
$819$	−14.9577	−	6.43023i	−0.522665	−	0.224690i
$820$	0.429392	−	0.538440i	0.0149950	−	0.0188031i
$821$	−20.2999	−	18.8356i	−0.708473	−	0.657366i	0.241249	−	0.970463i	$-0.422443\pi$
$821$	−20.2999	−	18.8356i	−0.708473	−	0.657366i	−0.949721	+	0.313097i	$0.898634\pi$
$822$	20.7978	+	3.13476i	0.725405	+	0.109337i
$823$	41.2923	+	28.1526i	1.43936	+	0.981337i	0.996398	+	0.0847958i	$0.0270238\pi$
$823$	41.2923	+	28.1526i	1.43936	+	0.981337i	0.442959	+	0.896542i	$0.353929\pi$
$824$	−19.5592	+	2.94807i	−0.681377	+	0.102701i
$825$	−15.5116	−	7.47002i	−0.540046	−	0.260073i
$826$	−1.21214	−	0.129962i	−0.0421758	−	0.00452196i
$827$	19.9768	−	9.62033i	0.694662	−	0.334531i	−0.0530156	−	0.998594i	$-0.516883\pi$
$827$	19.9768	−	9.62033i	0.694662	−	0.334531i	0.747677	+	0.664062i	$0.231169\pi$
$828$	−25.9519	+	17.6937i	−0.901889	+	0.614898i
$829$	−26.1507	+	24.2643i	−0.908250	+	0.842733i	−0.988059	−	0.154077i	$-0.950759\pi$
$829$	−26.1507	+	24.2643i	−0.908250	+	0.842733i	0.0798089	+	0.996810i	$0.474569\pi$
$830$	0.352271	+	4.70073i	0.0122275	+	0.163165i
$831$	−24.1760	−	61.5995i	−0.838657	−	2.13686i
$832$	−7.31876			−0.253732
$833$	37.1876	−	22.0082i	1.28848	−	0.762541i
$834$	26.8292			0.929020
$835$	6.54056	+	16.6651i	0.226346	+	0.576719i
$836$	−0.627768	−	8.37699i	−0.0217118	−	0.289724i
$837$	33.9083	−	31.4624i	1.17204	−	1.08750i
$838$	12.1069	−	8.25436i	0.418227	−	0.285142i
$839$	23.4080	−	11.2727i	0.808135	−	0.389177i	0.0162656	−	0.999868i	$-0.494822\pi$
$839$	23.4080	−	11.2727i	0.808135	−	0.389177i	0.791869	+	0.610690i	$0.209108\pi$
$840$	15.8203	−	5.63166i	0.545851	−	0.194311i
$841$	21.0232	+	10.1243i	0.724939	+	0.349112i
$842$	−6.73530	+	1.01518i	−0.232114	+	0.0349855i
$843$	35.8755	+	24.4595i	1.23562	+	0.842431i
$844$	11.7391	+	1.76938i	0.404076	+	0.0609046i
$845$	−6.31810	−	5.86234i	−0.217349	−	0.201671i
$846$	4.01678	−	5.03689i	0.138100	−	0.173172i
$847$	−4.42060	+	24.0731i	−0.151894	+	0.827163i
$848$	4.49798	+	5.64028i	0.154461	+	0.193688i
$849$	5.99510	−	79.9991i	0.205751	−	2.74556i
$850$	−25.5201	+	7.87191i	−0.875332	+	0.270004i
$851$	15.0656	+	26.0944i	0.516443	+	0.894506i
$852$	14.3562	−	24.8657i	0.491835	−	0.851883i
$853$	−0.746687	+	3.27145i	−0.0255661	+	0.112012i	−0.986101	−	0.166147i	$-0.946867\pi$
$853$	−0.746687	+	3.27145i	−0.0255661	+	0.112012i	0.960535	+	0.278160i	$0.0897244\pi$
$854$	8.69042	+	2.27845i	0.297380	+	0.0779670i
$855$	−5.38880	−	23.6099i	−0.184293	−	0.807440i
$856$	−37.4295	−	11.5455i	−1.27931	−	0.394616i
$857$	4.62926	−	11.7952i	0.158132	−	0.402915i	−0.829747	−	0.558140i	$-0.811515\pi$
$857$	4.62926	−	11.7952i	0.158132	−	0.402915i	0.987879	+	0.155225i	$0.0496103\pi$
$858$	−1.52601	+	3.88820i	−0.0520970	+	0.132741i
$859$	10.9627	+	3.38155i	0.374044	+	0.115377i	0.476076	−	0.879404i	$-0.342059\pi$
$859$	10.9627	+	3.38155i	0.374044	+	0.115377i	−0.102033	+	0.994781i	$0.532535\pi$
$860$	−0.993065	−	4.35090i	−0.0338632	−	0.148365i
$861$	−6.61484	−	1.73428i	−0.225433	−	0.0591040i
$862$	−3.28438	+	14.3898i	−0.111867	+	0.490120i
$863$	21.5486	−	37.3233i	0.733524	−	1.27050i	−0.221843	−	0.975082i	$-0.571207\pi$
$863$	21.5486	−	37.3233i	0.733524	−	1.27050i	0.955368	−	0.295419i	$-0.0954593\pi$
$864$	19.0480	+	32.9922i	0.648028	+	1.12242i
$865$	13.9063	−	4.28953i	0.472829	−	0.145848i
$866$	0.519233	−	6.92868i	0.0176443	−	0.235446i
$867$	38.3942	+	48.1448i	1.30394	+	1.63508i
$868$	3.19836	−	17.4172i	0.108559	−	0.591179i
$869$	0.840341	−	1.05375i	0.0285066	−	0.0357462i
$870$	3.61927	+	3.35819i	0.122705	+	0.113853i
$871$	5.59851	+	0.843840i	0.189698	+	0.0285924i
$872$	−20.5201	−	13.9904i	−0.694900	−	0.473775i
$873$	80.2538	−	12.0963i	2.71618	−	0.409398i
$874$	−28.1428	−	13.5528i	−0.951944	−	0.458432i
$875$	−17.2954	+	6.15678i	−0.584692	+	0.208137i
$876$	9.14962	−	4.40622i	0.309137	−	0.148872i
$877$	−27.8263	+	18.9716i	−0.939627	+	0.640627i	−0.933202	−	0.359353i	$-0.882997\pi$
$877$	−27.8263	+	18.9716i	−0.939627	+	0.640627i	−0.00642476	+	0.999979i	$0.502045\pi$
$878$	1.79611	−	1.66654i	0.0606156	−	0.0562431i
$879$	−0.384638	−	5.13264i	−0.0129735	−	0.173120i
$880$	−0.267980	−	0.682802i	−0.00903361	−	0.0230173i
$881$	9.12231			0.307339			0.153669	−	0.988122i	$-0.450891\pi$
$881$	9.12231			0.307339			0.153669	+	0.988122i	$0.450891\pi$
$882$	−25.7339	−	27.1417i	−0.866507	−	0.913910i
$883$	−36.8992			−1.24176			−0.620879	−	0.783907i	$-0.713224\pi$
$883$	−36.8992			−1.24176			−0.620879	+	0.783907i	$0.713224\pi$
$884$	−2.66945	−	6.80166i	−0.0897835	−	0.228765i
$885$	−0.0759821	−	1.01391i	−0.00255411	−	0.0340823i
$886$	−2.24623	+	2.08420i	−0.0754637	+	0.0700200i
$887$	−7.33354	+	4.99993i	−0.246236	+	0.167881i	−0.680149	−	0.733074i	$-0.738085\pi$
$887$	−7.33354	+	4.99993i	−0.246236	+	0.167881i	0.433913	+	0.900955i	$0.357133\pi$
$888$	43.7010	−	21.0453i	1.46651	−	0.706235i
$889$	13.2540	+	1.42105i	0.444523	+	0.0476605i
$890$	2.33135	+	1.12272i	0.0781470	+	0.0376336i
$891$	6.32800	−	0.953793i	0.211996	−	0.0319533i
$892$	2.10632	+	1.43606i	0.0705247	+	0.0480829i
$893$	−7.14432	−	1.07683i	−0.239076	−	0.0360349i
$894$	20.9987	+	19.4839i	0.702301	+	0.651640i
$895$	−3.63576	+	4.55910i	−0.121530	+	0.152394i
$896$	9.83410	+	4.22762i	0.328534	+	0.141235i
$897$	−10.9203	−	13.6937i	−0.364620	−	0.457218i
$898$	−1.35428	+	18.0717i	−0.0451931	+	0.603060i
$899$	14.3621	−	4.43013i	0.479003	−	0.147753i
$900$	−13.0339	−	22.5753i	−0.434463	−	0.752512i
$901$	−29.4416	+	50.9943i	−0.980841	+	1.69887i
$902$	−0.252782	+	1.10751i	−0.00841673	+	0.0368761i
$903$	−35.5123	+	26.5062i	−1.18178	+	0.882070i
$904$	5.90646	+	25.8779i	0.196446	+	0.860685i
$905$	−3.40959	−	1.05172i	−0.113339	−	0.0349603i
$906$	−5.84902	+	14.9031i	−0.194321	+	0.495121i
$907$	10.3851	−	26.4608i	0.344832	−	0.878618i	−0.648275	−	0.761406i	$-0.724509\pi$
$907$	10.3851	−	26.4608i	0.344832	−	0.878618i	0.993107	−	0.117212i	$-0.0373956\pi$
$908$	−0.475849	−	0.146780i	−0.0157916	−	0.00487107i
$909$	5.39789	+	23.6497i	0.179037	+	0.784411i
$910$	0.850310	+	1.92062i	0.0281875	+	0.0636679i
$911$	0.179717	−	0.787391i	0.00595429	−	0.0260874i	−0.971864	−	0.235545i	$-0.924313\pi$
$911$	0.179717	−	0.787391i	0.00595429	−	0.0260874i	0.977818	+	0.209457i	$0.0671697\pi$
$912$	−6.61079	+	11.4502i	−0.218905	+	0.379155i
$913$	4.38429	+	7.59381i	0.145099	+	0.251318i
$914$	17.3581	−	5.35427i	0.574155	−	0.177104i
$915$	−0.559955	+	7.47207i	−0.0185115	+	0.247019i
$916$	−5.57602	−	6.99211i	−0.184237	−	0.231026i
$917$	30.0776	−	1.28782i	0.993250	−	0.0425277i
$918$	27.3370	−	34.2795i	0.902255	−	1.13139i
$919$	−4.94529	−	4.58855i	−0.163130	−	0.151362i	0.594384	−	0.804181i	$-0.297396\pi$
$919$	−4.94529	−	4.58855i	−0.163130	−	0.151362i	−0.757514	+	0.652819i	$0.773586\pi$
$920$	11.5668	+	1.74342i	0.381346	+	0.0574787i
$921$	9.28596	+	6.33106i	0.305983	+	0.208615i
$922$	−6.84403	+	1.03157i	−0.225396	+	0.0339730i
$923$	9.34061	+	4.49820i	0.307450	+	0.148060i
$924$	7.61010	−	7.69259i	0.250354	−	0.253068i
$925$	−22.5304	+	10.8500i	−0.740793	+	0.356747i
$926$	−29.2480	+	19.9410i	−0.961150	+	0.655301i
$927$	−26.9350	+	24.9921i	−0.884663	+	0.820847i
$928$	0.925036	+	12.3437i	0.0303658	+	0.405203i
$929$	13.3276	+	33.9582i	0.437265	+	1.11413i	0.964423	+	0.264365i	$0.0851624\pi$
$929$	13.3276	+	33.9582i	0.437265	+	1.11413i	−0.527158	+	0.849767i	$0.676742\pi$
$930$	−13.0968			−0.429462
$931$	−11.9308	+	40.2129i	−0.391016	+	1.31792i
$932$	4.81899			0.157851
$933$	−8.80550	−	22.4360i	−0.288279	−	0.734523i
$934$	−3.02014	−	40.3010i	−0.0988221	−	1.31869i
$935$	4.38876	−	4.07217i	0.143528	−	0.133174i
$936$	−15.0845	+	10.2844i	−0.493051	+	0.336156i
$937$	11.5520	−	5.56317i	0.377389	−	0.181741i	−0.235567	−	0.971858i	$-0.575695\pi$
$937$	11.5520	−	5.56317i	0.377389	−	0.181741i	0.612956	+	0.790117i	$0.289980\pi$
$938$	11.0500	+	6.86034i	0.360794	+	0.223998i
$939$	−75.0411	−	36.1379i	−2.44887	−	1.17932i
$940$	0.926798	−	0.139692i	0.0302288	−	0.00455626i
$941$	16.7869	+	11.4451i	0.547239	+	0.373101i	0.805153	−	0.593067i	$-0.202083\pi$
$941$	16.7869	+	11.4451i	0.547239	+	0.373101i	−0.257915	+	0.966168i	$0.583035\pi$
$942$	7.95902	+	1.19963i	0.259319	+	0.0390861i
$943$	−3.49188	−	3.23999i	−0.113711	−	0.105509i
$944$	−0.224109	+	0.281024i	−0.00729414	+	0.00914656i
$945$	8.37848	−	11.4815i	0.272552	−	0.373492i
$946$	4.58974	+	5.75535i	0.149225	+	0.187123i
$947$	−2.23752	+	29.8577i	−0.0727097	+	0.970244i	0.834893	+	0.550413i	$0.185530\pi$
$947$	−2.23752	+	29.8577i	−0.0727097	+	0.970244i	−0.907602	+	0.419831i	$0.862089\pi$
$948$	3.01157	−	0.928947i	0.0978113	−	0.0301708i
$949$	1.83341	+	3.17556i	0.0595150	+	0.103083i
$950$	12.9619	−	22.4506i	0.420539	−	0.728395i
$951$	−3.97735	+	17.4259i	−0.128974	+	0.565074i
$952$	1.55075	−	48.4303i	0.0502599	−	1.56964i
$953$	4.67686	+	20.4907i	0.151498	+	0.663758i	0.992450	+	0.122648i	$0.0391386\pi$
$953$	4.67686	+	20.4907i	0.151498	+	0.663758i	−0.840952	+	0.541110i	$0.818004\pi$
$954$	48.7017	+	15.0225i	1.57678	+	0.486371i
$955$	4.40684	−	11.2284i	0.142602	−	0.363344i
$956$	−11.4820	+	29.2557i	−0.371355	+	0.946198i
$957$	8.77601	+	2.70704i	0.283688	+	0.0875062i
$958$	−1.70557	−	7.47259i	−0.0551045	−	0.241428i
$959$	9.09912	−	17.4433i	0.293826	−	0.563275i
$960$	3.12029	−	13.6709i	0.100707	−	0.441226i
$961$	−4.43445	+	7.68070i	−0.143047	+	0.247764i
$962$	3.03346	+	5.25410i	0.0978026	+	0.169399i
$963$	−69.5293	+	21.4469i	−2.24055	+	0.691118i
$964$	0.405303	−	5.40839i	0.0130539	−	0.174193i
$965$	−10.8394	−	13.5922i	−0.348933	−	0.437548i
$966$	−10.6231	−	38.8081i	−0.341794	−	1.24863i
$967$	−13.2742	+	16.6454i	−0.426871	+	0.535279i	−0.948030	−	0.318180i	$-0.896928\pi$
$967$	−13.2742	+	16.6454i	−0.426871	+	0.535279i	0.521160	+	0.853459i	$0.325500\pi$
$968$	20.1189	+	18.6676i	0.646645	+	0.599999i
$969$	−106.711	−	16.0841i	−3.42804	−	0.516694i
$970$	−8.65103	−	5.89817i	−0.277768	−	0.189379i
$971$	45.9891	−	6.93175i	1.47586	−	0.222450i	0.638721	−	0.769438i	$-0.279464\pi$
$971$	45.9891	−	6.93175i	1.47586	−	0.222450i	0.837141	+	0.546988i	$0.184226\pi$
$972$	−7.50729	−	3.61532i	−0.240796	−	0.115961i
$973$	8.16089	−	23.7321i	0.261626	−	0.760816i
$974$	−21.5421	+	10.3741i	−0.690253	+	0.332408i
$975$	12.0103	−	8.18847i	0.384637	−	0.262241i
$976$	1.94181	−	1.80174i	0.0621558	−	0.0576722i
$977$	2.75876	+	36.8131i	0.0882606	+	1.17776i	0.848890	+	0.528569i	$0.177271\pi$
$977$	2.75876	+	36.8131i	0.0882606	+	1.17776i	−0.760630	+	0.649186i	$0.775110\pi$
$978$	−17.0324	−	43.3978i	−0.544635	−	1.38771i
$979$	4.81332			0.153834
$980$	−0.0586646	−	5.44106i	−0.00187397	−	0.173808i
$981$	−46.1348			−1.47297
$982$	−3.46512	−	8.82899i	−0.110577	−	0.281744i
$983$	−2.13587	−	28.5012i	−0.0681237	−	0.909048i	−0.921656	−	0.388008i	$-0.873163\pi$
$983$	−2.13587	−	28.5012i	−0.0681237	−	0.909048i	0.853532	−	0.521040i	$-0.174456\pi$
$984$	−5.62114	+	5.21565i	−0.179195	+	0.166269i
$985$	3.75163	−	2.55782i	0.119537	−	0.0814989i
$986$	12.8355	−	6.18126i	0.408766	−	0.196852i
$987$	−4.99385	−	7.85337i	−0.158956	−	0.249976i
$988$	6.39018	+	3.07735i	0.203299	+	0.0979036i
$989$	−30.5232	+	4.60063i	−0.970580	+	0.146291i
$990$	−4.28156	−	2.91912i	−0.136077	−	0.0927757i
$991$	−0.577517	−	0.0870467i	−0.0183454	−	0.00276513i	0.139863	−	0.990171i	$-0.455334\pi$
$991$	−0.577517	−	0.0870467i	−0.0183454	−	0.00276513i	−0.158209	+	0.987406i	$0.550572\pi$
$992$	−24.0701	−	22.3338i	−0.764226	−	0.709098i
$993$	−3.18028	+	3.98794i	−0.100923	+	0.126553i
$994$	15.6320	+	17.9679i	0.495818	+	0.569908i
$995$	5.90731	+	7.40754i	0.187274	+	0.234835i
$996$	−1.53224	+	20.4464i	−0.0485510	+	0.647868i
$997$	58.3437	−	17.9966i	1.84776	−	0.569959i	0.848600	−	0.529034i	$-0.177446\pi$
$997$	58.3437	−	17.9966i	1.84776	−	0.569959i	0.999162	−	0.0409249i	$-0.0130304\pi$
$998$	17.7540	+	30.7508i	0.561992	+	0.973399i
$999$	20.5272	−	35.5542i	0.649453	−	1.12489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.g.a.16.2	✓	48
3.2	odd	2		441.2.bb.d.163.3		48
4.3	odd	2		784.2.bg.c.65.1		48
7.2	even	3		343.2.e.d.295.3		48
7.3	odd	6		343.2.g.h.165.3		48
7.4	even	3		343.2.g.i.165.3		48
7.5	odd	6		343.2.e.c.295.3		48
7.6	odd	2		343.2.g.g.226.2		48
49.3	odd	42		343.2.g.g.214.2		48
49.5	odd	42		343.2.e.c.50.3		48
49.8	even	7		343.2.g.i.79.3		48
49.12	odd	42		2401.2.a.i.1.10		24
49.37	even	21		2401.2.a.h.1.10		24
49.41	odd	14		343.2.g.h.79.3		48
49.44	even	21		343.2.e.d.50.3		48
49.46	even	21	inner	49.2.g.a.46.2	yes	48
147.95	odd	42		441.2.bb.d.46.3		48
196.95	odd	42		784.2.bg.c.193.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.16.2	✓	48	1.1	even	1	trivial
49.2.g.a.46.2	yes	48	49.46	even	21	inner
343.2.e.c.50.3		48	49.5	odd	42
343.2.e.c.295.3		48	7.5	odd	6
343.2.e.d.50.3		48	49.44	even	21
343.2.e.d.295.3		48	7.2	even	3
343.2.g.g.214.2		48	49.3	odd	42
343.2.g.g.226.2		48	7.6	odd	2
343.2.g.h.79.3		48	49.41	odd	14
343.2.g.h.165.3		48	7.3	odd	6
343.2.g.i.79.3		48	49.8	even	7
343.2.g.i.165.3		48	7.4	even	3
441.2.bb.d.46.3		48	147.95	odd	42
441.2.bb.d.163.3		48	3.2	odd	2
784.2.bg.c.65.1		48	4.3	odd	2
784.2.bg.c.193.1		48	196.95	odd	42
2401.2.a.h.1.10		24	49.37	even	21
2401.2.a.i.1.10		24	49.12	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)

\(f(q)\)	\(=\)	\(q+(-0.354207 - 0.902506i) q^{2} +(0.218016 + 2.90922i) q^{3} +(0.777050 - 0.720997i) q^{4} +(-0.605902 + 0.413097i) q^{5} +(2.54837 - 1.22723i) q^{6} +(-0.310399 - 2.62748i) q^{7} +(-2.67297 - 1.28723i) q^{8} +(-5.44954 + 0.821385i) q^{9} +O(q^{10})\)	\(q+(-0.354207 - 0.902506i) q^{2} +(0.218016 + 2.90922i) q^{3} +(0.777050 - 0.720997i) q^{4} +(-0.605902 + 0.413097i) q^{5} +(2.54837 - 1.22723i) q^{6} +(-0.310399 - 2.62748i) q^{7} +(-2.67297 - 1.28723i) q^{8} +(-5.44954 + 0.821385i) q^{9} +(0.587437 + 0.400508i) q^{10} +(1.30775 + 0.197112i) q^{11} +(2.26695 + 2.10342i) q^{12} +(-0.696197 + 0.873004i) q^{13} +(-2.26137 + 1.21081i) q^{14} +(-1.33389 - 1.67264i) q^{15} +(-0.0565197 + 0.754203i) q^{16} +(-5.89890 + 1.81957i) q^{17} +(2.67157 + 4.62730i) q^{18} +(2.99610 - 5.18940i) q^{19} +(-0.172974 + 0.757850i) q^{20} +(7.57625 - 1.47585i) q^{21} +(-0.285321 - 1.25007i) q^{22} +(5.13778 + 1.58479i) q^{23} +(3.16209 - 8.05688i) q^{24} +(-1.63024 + 4.15378i) q^{25} +(1.03449 + 0.319098i) q^{26} +(-1.63014 - 7.14212i) q^{27} +(-2.13560 - 1.81789i) q^{28} +(0.529674 - 2.32065i) q^{29} +(-1.03710 + 1.79630i) q^{30} +(3.15709 + 5.46824i) q^{31} +(-4.96923 + 1.53281i) q^{32} +(-0.288331 + 3.84751i) q^{33} +(3.73161 + 4.67929i) q^{34} +(1.27348 + 1.46377i) q^{35} +(-3.64234 + 4.56735i) q^{36} +(4.10810 + 3.81176i) q^{37} +(-5.74471 - 0.865875i) q^{38} +(-2.69154 - 1.83506i) q^{39} +(2.15131 - 0.324257i) q^{40} +(-0.798221 - 0.384403i) q^{41} +(-4.01553 - 6.31485i) q^{42} +(-5.17256 + 2.49098i) q^{43} +(1.15831 - 0.789719i) q^{44} +(2.96257 - 2.74887i) q^{45} +(-0.389553 - 5.19822i) q^{46} +(-0.440505 - 1.12239i) q^{47} -2.20646 q^{48} +(-6.80731 + 1.63113i) q^{49} +4.32625 q^{50} +(-6.57958 - 16.7645i) q^{51} +(0.0884530 + 1.18032i) q^{52} +(6.99227 - 6.48788i) q^{53} +(-5.86840 + 4.00101i) q^{54} +(-0.873796 + 0.420798i) q^{55} +(-2.55249 + 7.42272i) q^{56} +(15.7503 + 7.58495i) q^{57} +(-2.28202 + 0.343959i) q^{58} +(0.392674 + 0.267721i) q^{59} +(-2.24246 - 0.337997i) q^{60} +(-2.56745 - 2.38225i) q^{61} +(3.81686 - 4.78619i) q^{62} +(3.84970 + 14.0636i) q^{63} +(4.08662 + 5.12446i) q^{64} +(0.0611921 - 0.816551i) q^{65} +(3.57453 - 1.10260i) q^{66} +(-2.53523 - 4.39115i) q^{67} +(-3.27183 + 5.66698i) q^{68} +(-3.49040 + 15.2924i) q^{69} +(0.869987 - 1.66780i) q^{70} +(-2.06601 - 9.05180i) q^{71} +(15.6237 + 4.81928i) q^{72} +(1.19973 - 3.05687i) q^{73} +(1.98501 - 5.05773i) q^{74} +(-12.4397 - 3.83713i) q^{75} +(-1.41342 - 6.19260i) q^{76} +(0.111983 - 3.49728i) q^{77} +(-0.702790 + 3.07912i) q^{78} +(0.509557 - 0.882579i) q^{79} +(-0.277313 - 0.480321i) q^{80} +(4.62386 - 1.42627i) q^{81} +(-0.0641901 + 0.856558i) q^{82} +(4.13385 + 5.18369i) q^{83} +(4.82304 - 6.60926i) q^{84} +(2.82250 - 3.53930i) q^{85} +(4.08028 + 3.78595i) q^{86} +(6.86676 + 1.03500i) q^{87} +(-3.24185 - 2.21025i) q^{88} +(3.59885 - 0.542439i) q^{89} +(-3.53023 - 1.70007i) q^{90} +(2.50990 + 1.55827i) q^{91} +(5.13494 - 2.47286i) q^{92} +(-15.2200 + 10.3768i) q^{93} +(-0.856932 + 0.795117i) q^{94} +(0.328382 + 4.38195i) q^{95} +(-5.54264 - 14.1224i) q^{96} -14.7267 q^{97} +(3.88331 + 5.56587i) q^{98} -7.28854 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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