LMFDB - Embedded newform 49.2.g.a.11.4

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			11.4
Character	$\chi$	$=$	49.11
Dual form			49.2.g.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51353 - 1.40435i) q^{2} +(-2.00916 + 0.302832i) q^{3} +(0.169112 - 2.25665i) q^{4} +(-0.0830372 + 0.211575i) q^{5} +(-2.61564 + 3.27991i) q^{6} +(1.07894 + 2.41576i) q^{7} +(-0.338532 - 0.424506i) q^{8} +(1.07830 - 0.332612i) q^{9} +O(q^{10})$	\(q+(1.51353 - 1.40435i) q^{2} +(-2.00916 + 0.302832i) q^{3} +(0.169112 - 2.25665i) q^{4} +(-0.0830372 + 0.211575i) q^{5} +(-2.61564 + 3.27991i) q^{6} +(1.07894 + 2.41576i) q^{7} +(-0.338532 - 0.424506i) q^{8} +(1.07830 - 0.332612i) q^{9} +(0.171447 + 0.436839i) q^{10} +(-4.81478 - 1.48516i) q^{11} +(0.343612 + 4.58518i) q^{12} +(-1.11960 - 4.90527i) q^{13} +(5.02558 + 2.14111i) q^{14} +(0.102763 - 0.450235i) q^{15} +(3.36686 + 0.507473i) q^{16} +(2.03464 - 1.38719i) q^{17} +(1.16494 - 2.01773i) q^{18} +(1.49378 + 2.58730i) q^{19} +(0.463408 + 0.223166i) q^{20} +(-2.89933 - 4.52691i) q^{21} +(-9.37300 + 4.51380i) q^{22} +(-3.79491 - 2.58732i) q^{23} +(0.808719 + 0.750382i) q^{24} +(3.62739 + 3.36573i) q^{25} +(-8.58326 - 5.85197i) q^{26} +(3.42616 - 1.64995i) q^{27} +(5.63398 - 2.02625i) q^{28} +(0.637668 + 0.307085i) q^{29} +(-0.476753 - 0.825760i) q^{30} +(-4.05198 + 7.01823i) q^{31} +(6.70576 - 4.57191i) q^{32} +(10.1234 + 1.52586i) q^{33} +(1.13138 - 4.95690i) q^{34} +(-0.600707 + 0.0276793i) q^{35} +(-0.568233 - 2.48959i) q^{36} +(-0.200105 - 2.67021i) q^{37} +(5.89435 + 1.81816i) q^{38} +(3.73492 + 9.51643i) q^{39} +(0.117926 - 0.0363752i) q^{40} +(-1.10568 - 1.38648i) q^{41} +(-10.7456 - 2.77993i) q^{42} +(-0.910094 + 1.14122i) q^{43} +(-4.16573 + 10.6141i) q^{44} +(-0.0191666 + 0.255761i) q^{45} +(-9.37722 + 1.41339i) q^{46} +(4.11267 - 3.81600i) q^{47} -6.91825 q^{48} +(-4.67178 + 5.21292i) q^{49} +10.2168 q^{50} +(-3.66783 + 3.40325i) q^{51} +(-11.2588 + 1.69699i) q^{52} +(-0.329416 + 4.39576i) q^{53} +(2.86849 - 7.30878i) q^{54} +(0.714029 - 0.895364i) q^{55} +(0.660247 - 1.27583i) q^{56} +(-3.78475 - 4.74593i) q^{57} +(1.39638 - 0.430727i) q^{58} +(-2.06545 - 5.26268i) q^{59} +(-0.998643 - 0.308041i) q^{60} +(0.642677 + 8.57593i) q^{61} +(3.72327 + 16.3127i) q^{62} +(1.96693 + 2.24605i) q^{63} +(2.21348 - 9.69790i) q^{64} +(1.13080 + 0.170441i) q^{65} +(17.4649 - 11.9074i) q^{66} +(5.97762 - 10.3535i) q^{67} +(-2.78632 - 4.82605i) q^{68} +(8.40810 + 4.04913i) q^{69} +(-0.870316 + 0.885497i) q^{70} +(2.34135 - 1.12753i) q^{71} +(-0.506235 - 0.345145i) q^{72} +(-2.04449 - 1.89701i) q^{73} +(-4.05278 - 3.76043i) q^{74} +(-8.30726 - 5.66379i) q^{75} +(6.09123 - 2.93338i) q^{76} +(-1.60706 - 13.2337i) q^{77} +(19.0173 + 9.15826i) q^{78} +(2.40092 + 4.15851i) q^{79} +(-0.386944 + 0.670206i) q^{80} +(-9.18111 + 6.25958i) q^{81} +(-3.62058 - 0.545714i) q^{82} +(-1.53769 + 6.73708i) q^{83} +(-10.7059 + 5.77722i) q^{84} +(0.124545 + 0.545667i) q^{85} +(0.225221 + 3.00536i) q^{86} +(-1.37417 - 0.423876i) q^{87} +(0.999497 + 2.54668i) q^{88} +(-9.81790 + 3.02842i) q^{89} +(0.330169 + 0.414018i) q^{90} +(10.6420 - 7.99717i) q^{91} +(-6.48044 + 8.12622i) q^{92} +(6.01572 - 15.3278i) q^{93} +(0.865647 - 11.5513i) q^{94} +(-0.671447 + 0.101204i) q^{95} +(-12.0884 + 11.2164i) q^{96} +0.497851 q^{97} +(0.249890 + 14.4507i) q^{98} -5.68576 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 $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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 $

$2$	1.51353	−	1.40435i	1.07023	−	0.993026i	0.0702376	−	0.997530i	$-0.477624\pi$
$2$	1.51353	−	1.40435i	1.07023	−	0.993026i	0.999990	+	0.00450433i	$0.00143378\pi$
$3$	−2.00916	+	0.302832i	−1.15999	+	0.174840i	−0.700706	−	0.713450i	$-0.747132\pi$
$3$	−2.00916	+	0.302832i	−1.15999	+	0.174840i	−0.459283	+	0.888290i	$0.651894\pi$
$4$	0.169112	−	2.25665i	0.0845562	−	1.12832i
$5$	−0.0830372	+	0.211575i	−0.0371353	+	0.0946193i	−0.948238	−	0.317559i	$-0.897137\pi$
$5$	−0.0830372	+	0.211575i	−0.0371353	+	0.0946193i	0.911103	+	0.412179i	$0.135232\pi$
$6$	−2.61564	+	3.27991i	−1.06783	+	1.33902i
$7$	1.07894	+	2.41576i	0.407801	+	0.913071i
$7$	1.07894	+	2.41576i	0.407801	+	0.913071i
$8$	−0.338532	−	0.424506i	−0.119689	−	0.150085i
$9$	1.07830	−	0.332612i	0.359433	−	0.110871i
$10$	0.171447	+	0.436839i	0.0542162	+	0.138141i
$11$	−4.81478	−	1.48516i	−1.45171	−	0.447793i	−0.534150	−	0.845390i	$-0.679368\pi$
$11$	−4.81478	−	1.48516i	−1.45171	−	0.447793i	−0.917560	+	0.397597i	$0.869844\pi$
$12$	0.343612	+	4.58518i	0.0991921	+	1.32363i
$13$	−1.11960	−	4.90527i	−0.310520	−	1.36048i	−0.853658	−	0.520834i	$-0.825621\pi$
$13$	−1.11960	−	4.90527i	−0.310520	−	1.36048i	0.543138	−	0.839643i	$-0.317236\pi$
$14$	5.02558	+	2.14111i	1.34314	+	0.572236i
$15$	0.102763	−	0.450235i	0.0265333	−	0.116250i
$16$	3.36686	+	0.507473i	0.841716	+	0.126868i
$17$	2.03464	−	1.38719i	0.493472	−	0.336443i	−0.290880	−	0.956760i	$-0.593948\pi$
$17$	2.03464	−	1.38719i	0.493472	−	0.336443i	0.784352	+	0.620316i	$0.212996\pi$
$18$	1.16494	−	2.01773i	0.274578	−	0.475583i
$19$	1.49378	+	2.58730i	0.342696	+	0.593566i	0.984932	−	0.172940i	$-0.0553267\pi$
$19$	1.49378	+	2.58730i	0.342696	+	0.593566i	−0.642237	+	0.766506i	$0.721993\pi$
$20$	0.463408	+	0.223166i	0.103621	+	0.0499013i
$21$	−2.89933	−	4.52691i	−0.632686	−	0.987852i
$22$	−9.37300	+	4.51380i	−1.99833	+	0.962345i
$23$	−3.79491	−	2.58732i	−0.791293	−	0.539494i	0.0988896	−	0.995098i	$-0.468471\pi$
$23$	−3.79491	−	2.58732i	−0.791293	−	0.539494i	−0.890183	+	0.455604i	$0.849423\pi$
$24$	0.808719	+	0.750382i	0.165079	+	0.153171i
$25$	3.62739	+	3.36573i	0.725478	+	0.673145i
$26$	−8.58326	−	5.85197i	−1.68332	−	1.14767i
$27$	3.42616	−	1.64995i	0.659365	−	0.317533i
$28$	5.63398	−	2.02625i	1.06472	−	0.382926i
$29$	0.637668	+	0.307085i	0.118412	+	0.0570242i	0.492152	−	0.870509i	$-0.336210\pi$
$29$	0.637668	+	0.307085i	0.118412	+	0.0570242i	−0.373740	+	0.927534i	$0.621925\pi$
$30$	−0.476753	−	0.825760i	−0.0870427	−	0.150762i
$31$	−4.05198	+	7.01823i	−0.727756	+	1.26051i	0.230073	+	0.973173i	$0.426103\pi$
$31$	−4.05198	+	7.01823i	−0.727756	+	1.26051i	−0.957829	+	0.287337i	$0.907230\pi$
$32$	6.70576	−	4.57191i	1.18542	−	0.808207i
$33$	10.1234	+	1.52586i	1.76226	+	0.265618i
$34$	1.13138	−	4.95690i	0.194030	−	0.850101i
$35$	−0.600707	+	0.0276793i	−0.101538	+	0.00467866i
$36$	−0.568233	−	2.48959i	−0.0947055	−	0.414932i
$37$	−0.200105	−	2.67021i	−0.0328970	−	0.438980i	−0.989197	−	0.146593i	$-0.953169\pi$
$37$	−0.200105	−	2.67021i	−0.0328970	−	0.438980i	0.956300	−	0.292387i	$-0.0944497\pi$
$38$	5.89435	+	1.81816i	0.956189	+	0.294945i
$39$	3.73492	+	9.51643i	0.598066	+	1.52385i
$40$	0.117926	−	0.0363752i	0.0186457	−	0.00575143i
$41$	−1.10568	−	1.38648i	−0.172678	−	0.216531i	0.687960	−	0.725749i	$-0.258506\pi$
$41$	−1.10568	−	1.38648i	−0.172678	−	0.216531i	−0.860638	+	0.509217i	$0.829935\pi$
$42$	−10.7456	−	2.77993i	−1.65808	−	0.428953i
$43$	−0.910094	+	1.14122i	−0.138788	+	0.174035i	−0.846368	−	0.532599i	$-0.821216\pi$
$43$	−0.910094	+	1.14122i	−0.138788	+	0.174035i	0.707580	+	0.706633i	$0.249787\pi$
$44$	−4.16573	+	10.6141i	−0.628007	+	1.60014i
$45$	−0.0191666	+	0.255761i	−0.00285719	+	0.0381266i
$46$	−9.37722	+	1.41339i	−1.38260	+	0.208393i
$47$	4.11267	−	3.81600i	0.599894	−	0.556620i	−0.320680	−	0.947187i	$-0.603912\pi$
$47$	4.11267	−	3.81600i	0.599894	−	0.556620i	0.920574	+	0.390567i	$0.127721\pi$
$48$	−6.91825			−0.998564
$49$	−4.67178	+	5.21292i	−0.667397	+	0.744702i
$50$	10.2168			1.44488
$51$	−3.66783	+	3.40325i	−0.513598	+	0.476550i
$52$	−11.2588	+	1.69699i	−1.56131	+	0.235330i
$53$	−0.329416	+	4.39576i	−0.0452488	+	0.603804i	0.927781	+	0.373125i	$0.121714\pi$
$53$	−0.329416	+	4.39576i	−0.0452488	+	0.603804i	−0.973030	+	0.230679i	$0.925905\pi$
$54$	2.86849	−	7.30878i	0.390351	−	0.994599i
$55$	0.714029	−	0.895364i	0.0962797	−	0.120731i
$56$	0.660247	−	1.27583i	0.0882293	−	0.170490i
$57$	−3.78475	−	4.74593i	−0.501303	−	0.628614i
$58$	1.39638	−	0.430727i	0.183354	−	0.0565573i
$59$	−2.06545	−	5.26268i	−0.268899	−	0.685143i	−0.999996	−	0.00286948i	$-0.999087\pi$
$59$	−2.06545	−	5.26268i	−0.268899	−	0.685143i	0.731097	−	0.682273i	$-0.239009\pi$
$60$	−0.998643	−	0.308041i	−0.128924	−	0.0397679i
$61$	0.642677	+	8.57593i	0.0822864	+	1.09804i	0.873606	+	0.486633i	$0.161775\pi$
$61$	0.642677	+	8.57593i	0.0822864	+	1.09804i	−0.791320	+	0.611402i	$0.790606\pi$
$62$	3.72327	+	16.3127i	0.472855	+	2.07171i
$63$	1.96693	+	2.24605i	0.247810	+	0.282975i
$64$	2.21348	−	9.69790i	0.276685	−	1.21224i
$65$	1.13080	+	0.170441i	0.140259	+	0.0211406i
$66$	17.4649	−	11.9074i	2.14979	−	1.46570i
$67$	5.97762	−	10.3535i	0.730283	−	1.26489i	−0.226479	−	0.974016i	$-0.572722\pi$
$67$	5.97762	−	10.3535i	0.730283	−	1.26489i	0.956762	−	0.290871i	$-0.0939451\pi$
$68$	−2.78632	−	4.82605i	−0.337891	−	0.585244i
$69$	8.40810	+	4.04913i	1.01222	+	0.487458i
$70$	−0.870316	+	0.885497i	−0.104023	+	0.105837i
$71$	2.34135	−	1.12753i	0.277867	−	0.133814i	−0.289761	−	0.957099i	$-0.593576\pi$
$71$	2.34135	−	1.12753i	0.277867	−	0.133814i	0.567627	+	0.823286i	$0.307861\pi$
$72$	−0.506235	−	0.345145i	−0.0596603	−	0.0406757i
$73$	−2.04449	−	1.89701i	−0.239289	−	0.222028i	0.551407	−	0.834236i	$-0.314091\pi$
$73$	−2.04449	−	1.89701i	−0.239289	−	0.222028i	−0.790697	+	0.612208i	$0.790281\pi$
$74$	−4.05278	−	3.76043i	−0.471126	−	0.437141i
$75$	−8.30726	−	5.66379i	−0.959240	−	0.653999i
$76$	6.09123	−	2.93338i	0.698712	−	0.336482i
$77$	−1.60706	−	13.2337i	−0.183142	−	1.50812i
$78$	19.0173	+	9.15826i	2.15329	+	1.03697i
$79$	2.40092	+	4.15851i	0.270124	+	0.467869i	0.968893	−	0.247478i	$-0.0796019\pi$
$79$	2.40092	+	4.15851i	0.270124	+	0.467869i	−0.698769	+	0.715347i	$0.746269\pi$
$80$	−0.386944	+	0.670206i	−0.0432616	+	0.0749313i
$81$	−9.18111	+	6.25958i	−1.02012	+	0.695509i
$82$	−3.62058	−	0.545714i	−0.399826	−	0.0602640i
$83$	−1.53769	+	6.73708i	−0.168784	+	0.739490i	0.817702	+	0.575642i	$0.195248\pi$
$83$	−1.53769	+	6.73708i	−0.168784	+	0.739490i	−0.986486	+	0.163848i	$0.947609\pi$
$84$	−10.7059	+	5.77722i	−1.16811	+	0.630346i
$85$	0.124545	+	0.545667i	0.0135088	+	0.0591859i
$86$	0.225221	+	3.00536i	0.0242862	+	0.324077i
$87$	−1.37417	−	0.423876i	−0.147327	−	0.0454443i
$88$	0.999497	+	2.54668i	0.106547	+	0.271477i
$89$	−9.81790	+	3.02842i	−1.04070	+	0.321012i	−0.767569	−	0.640966i	$-0.778534\pi$
$89$	−9.81790	+	3.02842i	−1.04070	+	0.321012i	−0.273126	+	0.961978i	$0.588058\pi$
$90$	0.330169	+	0.414018i	0.0348028	+	0.0436414i
$91$	10.6420	−	7.99717i	1.11558	−	0.838331i
$92$	−6.48044	+	8.12622i	−0.675633	+	0.847217i
$93$	6.01572	−	15.3278i	0.623801	−	1.58942i
$94$	0.865647	−	11.5513i	0.0892847	−	1.19142i
$95$	−0.671447	+	0.101204i	−0.0688890	+	0.0103833i
$96$	−12.0884	+	11.2164i	−1.23377	+	1.14477i
$97$	0.497851			0.0505491			0.0252746	−	0.999681i	$-0.491954\pi$
$97$	0.497851			0.0505491			0.0252746	+	0.999681i	$0.491954\pi$
$98$	0.249890	+	14.4507i	0.0252427	+	1.45974i
$99$	−5.68576			−0.571440
$100$	8.20869	−	7.61655i	0.820869	−	0.761655i
$101$	−0.351055	+	0.0529130i	−0.0349313	+	0.00526505i	−0.166485	−	0.986044i	$-0.553242\pi$
$101$	−0.351055	+	0.0529130i	−0.0349313	+	0.00526505i	0.131553	+	0.991309i	$0.458004\pi$
$102$	−0.772015	+	10.3018i	−0.0764409	+	1.02003i
$103$	2.93087	−	7.46774i	0.288788	−	0.735819i	−0.710690	−	0.703505i	$-0.751617\pi$
$103$	2.93087	−	7.46774i	0.288788	−	0.735819i	0.999478	−	0.0323136i	$-0.0102875\pi$
$104$	−1.70330	+	2.13587i	−0.167022	+	0.209439i
$105$	1.19853	−	0.237526i	0.116965	−	0.0231801i
$106$	5.67460	+	7.11573i	0.551166	+	0.691140i
$107$	−19.6890	+	6.07324i	−1.90340	+	0.587123i	−0.925200	+	0.379479i	$0.876103\pi$
$107$	−19.6890	+	6.07324i	−1.90340	+	0.587123i	−0.978205	+	0.207643i	$0.933421\pi$
$108$	−3.14395	−	8.01066i	−0.302527	−	0.770826i
$109$	−1.96161	−	0.605076i	−0.187888	−	0.0579558i	0.199383	−	0.979922i	$-0.436106\pi$
$109$	−1.96161	−	0.605076i	−0.187888	−	0.0579558i	−0.387271	+	0.921966i	$0.626582\pi$
$110$	−0.176701	−	2.35791i	−0.0168478	−	0.224818i
$111$	1.21067	+	5.30429i	0.114912	+	0.503461i
$112$	2.40671	+	8.68107i	0.227413	+	0.820284i
$113$	1.78611	−	7.82546i	0.168023	−	0.736157i	−0.818763	−	0.574131i	$-0.805340\pi$
$113$	1.78611	−	7.82546i	0.168023	−	0.736157i	0.986786	−	0.162026i	$-0.0518029\pi$
$114$	−12.3933	−	1.86799i	−1.16074	−	0.174953i
$115$	0.862532	−	0.588064i	0.0804315	−	0.0548373i
$116$	0.800819	−	1.38706i	0.0743542	−	0.128785i
$117$	−2.83881	−	4.91696i	−0.262448	−	0.454574i
$118$	−10.5168	−	5.06461i	−0.968148	−	0.466235i
$119$	5.54637	+	3.41849i	0.508435	+	0.313373i
$120$	−0.225916	+	0.108795i	−0.0206232	+	0.00993162i
$121$	11.8878	+	8.10493i	1.08070	+	0.736812i
$122$	13.0163	+	12.0774i	1.17844	+	1.09344i
$123$	2.64135	+	2.45082i	0.238163	+	0.220983i
$124$	15.1524	+	10.3307i	1.36073	+	0.927728i
$125$	−2.03720	+	0.981066i	−0.182213	+	0.0877492i
$126$	6.13124	+	0.637196i	0.546215	+	0.0567659i
$127$	4.74925	+	2.28712i	0.421427	+	0.202949i	0.632564	−	0.774508i	$-0.282002\pi$
$127$	4.74925	+	2.28712i	0.421427	+	0.202949i	−0.211137	+	0.977456i	$0.567717\pi$
$128$	−2.15308	−	3.72924i	−0.190307	−	0.329621i
$129$	1.48293	−	2.56850i	0.130564	−	0.226144i
$130$	1.95086	−	1.33007i	0.171102	−	0.116655i
$131$	−1.61551	−	0.243498i	−0.141147	−	0.0212745i	0.0780885	−	0.996946i	$-0.475118\pi$
$131$	−1.61551	−	0.243498i	−0.141147	−	0.0212745i	−0.219236	+	0.975672i	$0.570356\pi$
$132$	5.15532	−	22.5869i	0.448713	−	1.96594i
$133$	−4.63859	+	6.40014i	−0.402216	+	0.554962i
$134$	−5.49270	−	24.0651i	−0.474497	−	2.07891i
$135$	0.0645903	+	0.861898i	0.00555905	+	0.0741804i
$136$	−1.27766	−	0.394106i	−0.109559	−	0.0337943i
$137$	1.24531	+	3.17299i	0.106394	+	0.271087i	0.974150	−	0.225904i	$-0.0725335\pi$
$137$	1.24531	+	3.17299i	0.106394	+	0.271087i	−0.867756	+	0.496991i	$0.834438\pi$
$138$	18.4123	−	5.67945i	1.56736	−	0.483467i
$139$	−9.49516	−	11.9065i	−0.805369	−	1.00990i	−0.999581	−	0.0289408i	$-0.990787\pi$
$139$	−9.49516	−	11.9065i	−0.805369	−	1.00990i	0.194213	−	0.980959i	$-0.437785\pi$
$140$	−0.0391245	+	1.36026i	−0.00330662	+	0.114963i
$141$	−7.10740	+	8.91240i	−0.598551	+	0.750559i
$142$	1.96025	−	4.99463i	0.164500	−	0.419140i
$143$	−1.89452	+	25.2806i	−0.158427	+	2.11407i
$144$	3.79928	−	0.572650i	0.316607	−	0.0477208i
$145$	−0.117922	+	0.109415i	−0.00979286	+	0.00908644i
$146$	−5.75846			−0.476573
$147$	7.80771	−	11.8884i	0.643969	−	0.980535i
$148$	−6.05957			−0.498093
$149$	−7.92270	+	7.35119i	−0.649053	+	0.602233i	−0.934415	−	0.356187i	$-0.884077\pi$
$149$	−7.92270	+	7.35119i	−0.649053	+	0.602233i	0.285362	+	0.958420i	$0.407886\pi$
$150$	−20.5272	+	3.09398i	−1.67604	+	0.252623i
$151$	1.31752	−	17.5811i	0.107218	−	1.43073i	−0.641134	−	0.767429i	$-0.721536\pi$
$151$	1.31752	−	17.5811i	0.107218	−	1.43073i	0.748353	−	0.663301i	$-0.230845\pi$
$152$	0.592631	−	1.51000i	0.0480687	−	0.122477i
$153$	1.73255	−	2.17255i	0.140069	−	0.175641i
$154$	−21.0172	−	17.7728i	−1.69361	−	1.43217i
$155$	−1.14842	−	1.44007i	−0.0922432	−	0.115669i
$156$	22.1068	−	6.81906i	1.76996	−	0.545961i
$157$	−0.510341	−	1.30033i	−0.0407296	−	0.103777i	0.909062	−	0.416662i	$-0.136800\pi$
$157$	−0.510341	−	1.30033i	−0.0407296	−	0.103777i	−0.949791	+	0.312884i	$0.898705\pi$
$158$	9.47386	+	2.92230i	0.753700	+	0.232486i
$159$	−0.669326	−	8.93154i	−0.0530810	−	0.708317i
$160$	0.410475	+	1.79841i	0.0324509	+	0.142177i
$161$	2.15587	−	11.9591i	0.169906	−	0.942513i
$162$	−5.10525	+	22.3676i	−0.401106	+	1.75736i
$163$	−1.92379	−	0.289964i	−0.150683	−	0.0227118i	0.0732677	−	0.997312i	$-0.476657\pi$
$163$	−1.92379	−	0.289964i	−0.150683	−	0.0227118i	−0.223950	+	0.974601i	$0.571895\pi$
$164$	−3.31577	+	2.26066i	−0.258918	+	0.176528i
$165$	−1.16345	+	2.01516i	−0.0905748	+	0.156880i
$166$	7.13388	+	12.3562i	0.553696	+	0.959030i
$167$	20.7503	+	9.99282i	1.60571	+	0.773267i	0.999753	−	0.0222327i	$-0.00707746\pi$
$167$	20.7503	+	9.99282i	1.60571	+	0.773267i	0.605953	+	0.795500i	$0.292792\pi$
$168$	−0.940181	+	2.76329i	−0.0725366	+	0.213192i
$169$	−11.0956	+	5.34335i	−0.853507	+	0.411027i
$170$	0.954811	+	0.650979i	0.0732307	+	0.0499278i
$171$	2.47130	+	2.29304i	0.188985	+	0.175353i
$172$	2.42143	+	2.24676i	0.184632	+	0.171313i
$173$	19.0337	+	12.9769i	1.44710	+	0.986618i	0.995536	+	0.0943809i	$0.0300872\pi$
$173$	19.0337	+	12.9769i	1.44710	+	0.986618i	0.451567	+	0.892237i	$0.350865\pi$
$174$	−2.67512	+	1.28827i	−0.202800	+	0.0976635i
$175$	−4.21704	+	12.3943i	−0.318779	+	0.936922i
$176$	−15.4570	−	7.44371i	−1.16512	−	0.561091i
$177$	5.74353	+	9.94809i	0.431710	+	0.747744i
$178$	−10.6067	+	18.3714i	−0.795008	+	1.37699i
$179$	13.4982	−	9.20295i	1.00891	−	0.687861i	0.0583126	−	0.998298i	$-0.481428\pi$
$179$	13.4982	−	9.20295i	1.00891	−	0.687861i	0.950594	+	0.310438i	$0.100476\pi$
$180$	0.573921	+	0.0865046i	0.0427775	+	0.00644767i
$181$	−2.23430	+	9.78911i	−0.166074	+	0.727619i	0.821467	+	0.570256i	$0.193156\pi$
$181$	−2.23430	+	9.78911i	−0.166074	+	0.727619i	−0.987541	+	0.157362i	$0.949701\pi$
$182$	4.87612	−	27.0490i	0.361442	−	2.00501i
$183$	−3.88831	−	17.0358i	−0.287432	−	1.25932i
$184$	0.186364	+	2.48685i	0.0137389	+	0.183333i
$185$	0.581567	+	0.179390i	0.0427576	+	0.0131890i
$186$	−12.4206	−	31.6473i	−0.910726	−	2.32049i
$187$	−11.8565	+	3.65726i	−0.867035	+	0.267445i
$188$	−7.91586	−	9.92617i	−0.577323	−	0.723940i
$189$	7.68251	+	6.49658i	0.558820	+	0.472556i
$190$	−0.874128	+	1.09612i	−0.0634159	+	0.0795211i
$191$	0.613387	−	1.56288i	0.0443831	−	0.113086i	−0.906963	−	0.421210i	$-0.861606\pi$
$191$	0.613387	−	1.56288i	0.0443831	−	0.113086i	0.951346	+	0.308123i	$0.0997009\pi$
$192$	−1.51040	+	20.1550i	−0.109004	+	1.45456i
$193$	3.81096	−	0.574410i	0.274319	−	0.0413469i	−0.0104421	−	0.999945i	$-0.503324\pi$
$193$	3.81096	−	0.574410i	0.274319	−	0.0413469i	0.284761	+	0.958599i	$0.408086\pi$
$194$	0.753513	−	0.699158i	0.0540991	−	0.0501966i
$195$	−2.32358			−0.166395
$196$	10.9737	+	11.4241i	0.783833	+	0.816008i
$197$	−1.66391			−0.118549			−0.0592744	−	0.998242i	$-0.518879\pi$
$197$	−1.66391			−0.118549			−0.0592744	+	0.998242i	$0.518879\pi$
$198$	−8.60557	+	7.98480i	−0.611571	+	0.567455i
$199$	26.2162	−	3.95146i	1.85842	−	0.280112i	0.878239	−	0.478221i	$-0.158718\pi$
$199$	26.2162	−	3.95146i	1.85842	−	0.280112i	0.980180	+	0.198110i	$0.0634802\pi$
$200$	0.200782	−	2.67925i	0.0141975	−	0.189452i
$201$	−8.87462	+	22.6122i	−0.625967	+	1.59494i
$202$	−0.457024	+	0.573090i	−0.0321561	+	0.0403225i
$203$	−0.0538368	+	1.87178i	−0.00377860	+	0.131373i
$204$	7.05965	+	8.85252i	0.494274	+	0.619800i
$205$	0.385156	−	0.118805i	0.0269005	−	0.00829770i
$206$	−6.05137	−	15.4186i	−0.421619	−	1.07427i
$207$	−4.95262	−	1.52768i	−0.344231	−	0.106181i
$208$	−1.28023	−	17.0835i	−0.0887683	−	1.18453i
$209$	−3.34965	−	14.6758i	−0.231700	−	1.01514i
$210$	1.48045	−	2.04266i	0.102161	−	0.140957i
$211$	1.85114	−	8.11037i	0.127438	−	0.558341i	−0.870384	−	0.492373i	$-0.836129\pi$
$211$	1.85114	−	8.11037i	0.127438	−	0.558341i	0.997822	−	0.0659675i	$-0.0210134\pi$
$212$	9.86396	+	1.48675i	0.677460	+	0.102111i
$213$	−4.36269	+	2.97443i	−0.298927	+	0.203805i
$214$	−21.2709	+	36.8423i	−1.45405	+	2.51849i
$215$	−0.165883	−	0.287317i	−0.0113131	−	0.0195949i
$216$	−1.86028	−	0.895863i	−0.126576	−	0.0609558i
$217$	−21.3262	−	2.21635i	−1.44772	−	0.150455i
$218$	−3.81869	+	1.83899i	−0.258635	+	0.124552i
$219$	4.68218	+	3.19226i	0.316392	+	0.215713i
$220$	−1.89977	−	1.76273i	−0.128082	−	0.118843i
$221$	−9.08252	−	8.42735i	−0.610957	−	0.566885i
$222$	9.28146	+	6.32799i	0.622931	+	0.424707i
$223$	−13.6100	+	6.55421i	−0.911390	+	0.438902i	−0.829989	−	0.557779i	$-0.811654\pi$
$223$	−13.6100	+	6.55421i	−0.911390	+	0.438902i	−0.0814005	+	0.996681i	$0.525939\pi$
$224$	18.2797	+	11.2667i	1.22137	+	0.752786i
$225$	5.03090	+	2.42275i	0.335393	+	0.161517i
$226$	−8.28636	−	14.3524i	−0.551200	−	0.954707i
$227$	8.07507	−	13.9864i	0.535961	−	0.928312i	−0.463155	−	0.886277i	$-0.653283\pi$
$227$	8.07507	−	13.9864i	0.535961	−	0.928312i	0.999116	−	0.0420345i	$-0.0133839\pi$
$228$	−11.3499	+	7.73825i	−0.751668	+	0.512478i
$229$	−4.87264	−	0.734432i	−0.321993	−	0.0485327i	−0.0139430	−	0.999903i	$-0.504438\pi$
$229$	−4.87264	−	0.734432i	−0.321993	−	0.0485327i	−0.308050	+	0.951370i	$0.599676\pi$
$230$	0.479620	−	2.10135i	0.0316252	−	0.138559i
$231$	7.23645	+	26.1020i	0.476124	+	1.71739i
$232$	−0.0855118	−	0.374652i	−0.00561412	−	0.0245971i
$233$	−1.24102	−	16.5602i	−0.0813019	−	1.08490i	−0.877409	−	0.479743i	$-0.840730\pi$
$233$	−1.24102	−	16.5602i	−0.0813019	−	1.08490i	0.796107	−	0.605155i	$-0.206889\pi$
$234$	−11.2018	−	3.45529i	−0.732283	−	0.225879i
$235$	0.465866	+	1.18701i	0.0303898	+	0.0774319i
$236$	−12.2253	+	3.77101i	−0.795800	+	0.245472i
$237$	−6.08315	−	7.62803i	−0.395143	−	0.495494i
$238$	13.1954	−	2.61506i	0.855329	−	0.169509i
$239$	2.55561	−	3.20463i	0.165309	−	0.207290i	−0.692277	−	0.721632i	$-0.743392\pi$
$239$	2.55561	−	3.20463i	0.165309	−	0.207290i	0.857585	+	0.514342i	$0.171964\pi$
$240$	0.574472	−	1.46373i	0.0370820	−	0.0944834i
$241$	2.15116	−	28.7052i	0.138568	−	1.84907i	−0.304419	−	0.952538i	$-0.598462\pi$
$241$	2.15116	−	28.7052i	0.138568	−	1.84907i	0.442988	−	0.896528i	$-0.353919\pi$
$242$	29.3746	−	4.42752i	1.88827	−	0.284611i
$243$	8.18789	−	7.59725i	0.525253	−	0.487364i
$244$	19.4615			1.24590
$245$	−0.714993	−	1.42130i	−0.0456792	−	0.0908034i
$246$	7.43958			0.474330
$247$	11.0190	−	10.2241i	0.701120	−	0.650544i
$248$	4.35100	−	0.655808i	0.276289	−	0.0416438i
$249$	1.04927	−	14.0015i	0.0664948	−	0.887311i
$250$	−1.70561	+	4.34582i	−0.107872	+	0.274854i
$251$	−10.4444	+	13.0968i	−0.659242	+	0.826663i	−0.993260	−	0.115903i	$-0.963024\pi$
$251$	−10.4444	+	13.0968i	−0.659242	+	0.826663i	0.334019	+	0.942566i	$0.391595\pi$
$252$	5.40116	−	4.05884i	0.340241	−	0.255683i
$253$	14.4290	+	18.0934i	0.907146	+	1.13753i
$254$	10.4000	−	3.20799i	0.652557	−	0.201287i
$255$	−0.415477	−	1.05862i	−0.0260181	−	0.0662932i
$256$	10.5148	+	3.24339i	0.657177	+	0.202712i
$257$	−0.968617	−	12.9253i	−0.0604207	−	0.806258i	−0.942297	−	0.334778i	$-0.891339\pi$
$257$	−0.968617	−	12.9253i	−0.0604207	−	0.806258i	0.881876	−	0.471481i	$-0.156280\pi$
$258$	−1.36263	−	5.97006i	−0.0848334	−	0.371679i
$259$	6.23469	−	3.36440i	0.387405	−	0.209054i
$260$	0.575858	−	2.52300i	0.0357132	−	0.156470i
$261$	0.789737	+	0.119034i	0.0488835	+	0.00736800i
$262$	−2.78707	+	1.90019i	−0.172186	+	0.117394i
$263$	−3.11106	+	5.38852i	−0.191836	+	0.332270i	−0.945859	−	0.324578i	$-0.894778\pi$
$263$	−3.11106	+	5.38852i	−0.191836	+	0.332270i	0.754023	+	0.656849i	$0.228111\pi$
$264$	−2.77936	−	4.81400i	−0.171058	−	0.296281i
$265$	−0.902679	−	0.434708i	−0.0554512	−	0.0267039i
$266$	1.96740	+	16.2010i	0.120629	+	0.993347i
$267$	18.8086	−	9.05776i	1.15107	−	0.554326i
$268$	−22.3534	−	15.2403i	−1.36545	−	0.930949i
$269$	15.5032	+	14.3849i	0.945247	+	0.877061i	0.992552	−	0.121819i	$-0.0388728\pi$
$269$	15.5032	+	14.3849i	0.945247	+	0.877061i	−0.0473051	+	0.998880i	$0.515063\pi$
$270$	1.30817	+	1.21380i	0.0796125	+	0.0738696i
$271$	−12.2823	−	8.37393i	−0.746096	−	0.508680i	0.129586	−	0.991568i	$-0.458635\pi$
$271$	−12.2823	−	8.37393i	−0.746096	−	0.508680i	−0.875682	+	0.482888i	$0.839588\pi$
$272$	7.55431	−	3.63796i	0.458047	−	0.220584i
$273$	−18.9596	+	19.2903i	−1.14749	+	1.16750i
$274$	6.34080	+	3.05357i	0.383062	+	0.184473i
$275$	−12.4664	−	21.5925i	−0.751754	−	1.30208i
$276$	10.5594	−	18.2894i	0.635599	−	1.10089i
$277$	−17.6286	+	12.0190i	−1.05920	+	0.722151i	−0.961982	−	0.273112i	$-0.911947\pi$
$277$	−17.6286	+	12.0190i	−1.05920	+	0.722151i	−0.0972190	+	0.995263i	$0.530995\pi$
$278$	−31.0922	−	4.68639i	−1.86478	−	0.281071i
$279$	−2.03490	+	8.91549i	−0.121826	+	0.533757i
$280$	0.215109	+	0.245633i	0.0128552	+	0.0146794i
$281$	5.58838	+	24.4843i	0.333375	+	1.46061i	0.812550	+	0.582891i	$0.198079\pi$
$281$	5.58838	+	24.4843i	0.333375	+	1.46061i	−0.479176	+	0.877719i	$0.659064\pi$
$282$	1.75887	+	23.4705i	0.104739	+	1.39765i
$283$	−13.7387	−	4.23782i	−0.816680	−	0.251912i	−0.141853	−	0.989888i	$-0.545306\pi$
$283$	−13.7387	−	4.23782i	−0.816680	−	0.251912i	−0.674828	+	0.737975i	$0.735782\pi$
$284$	−2.14849	−	5.47427i	−0.127490	−	0.324838i
$285$	1.31840	−	0.406671i	0.0780951	−	0.0240891i
$286$	32.6354	+	40.9235i	1.92977	+	2.41986i
$287$	2.15643	−	4.16698i	0.127290	−	0.245969i
$288$	5.71015	−	7.16030i	0.336474	−	0.421925i
$289$	−3.99535	+	10.1800i	−0.235021	+	0.598823i
$290$	−0.0248205	+	0.331207i	−0.00145751	+	0.0194491i
$291$	−1.00026	+	0.150765i	−0.0586365	+	0.00883803i
$292$	−4.62662	+	4.29288i	−0.270753	+	0.251222i
$293$	−15.0206			−0.877512			−0.438756	−	0.898606i	$-0.644581\pi$
$293$	−15.0206			−0.877512			−0.438756	+	0.898606i	$0.644581\pi$
$294$	−4.87821	−	28.9581i	−0.284503	−	1.68887i
$295$	1.28496			0.0748134
$296$	−1.06578	+	0.988898i	−0.0619471	+	0.0574785i
$297$	−18.9466	+	2.85575i	−1.09940	+	0.165707i
$298$	−1.66759	+	22.2525i	−0.0966012	+	1.28905i
$299$	−8.44276	+	21.5118i	−0.488257	+	1.24406i
$300$	−14.1860	+	17.7887i	−0.819032	+	1.02703i
$301$	−3.73885	−	0.967257i	−0.215504	−	0.0557518i
$302$	−22.6959	−	28.4598i	−1.30600	−	1.63768i
$303$	0.689302	−	0.212622i	0.0395994	−	0.0122148i
$304$	3.71636	+	9.46913i	0.213148	+	0.543092i
$305$	−1.86782	−	0.576146i	−0.106951	−	0.0329901i
$306$	−0.428755	−	5.72134i	−0.0245103	−	0.327067i
$307$	−1.54569	−	6.77213i	−0.0882174	−	0.386506i	0.911474	−	0.411358i	$-0.134946\pi$
$307$	−1.54569	−	6.77213i	−0.0882174	−	0.386506i	−0.999691	+	0.0248526i	$0.992088\pi$
$308$	−30.1357	+	1.38859i	−1.71714	+	0.0791222i
$309$	−3.62712	+	15.8915i	−0.206340	+	0.904034i
$310$	−3.76053	−	0.566809i	−0.213584	−	0.0321926i
$311$	−8.92284	+	6.08349i	−0.505968	+	0.344963i	−0.789248	−	0.614074i	$-0.789530\pi$
$311$	−8.92284	+	6.08349i	−0.505968	+	0.344963i	0.283281	+	0.959037i	$0.408577\pi$
$312$	2.77539	−	4.80711i	0.157125	−	0.272149i
$313$	−5.85713	−	10.1448i	−0.331065	−	0.573421i	0.651656	−	0.758514i	$-0.274074\pi$
$313$	−5.85713	−	10.1448i	−0.331065	−	0.573421i	−0.982721	+	0.185094i	$0.940741\pi$
$314$	−2.59853	−	1.25139i	−0.146644	−	0.0706199i
$315$	−0.638536	+	0.229649i	−0.0359774	+	0.0129392i
$316$	9.79031	−	4.71476i	0.550748	−	0.265226i
$317$	18.6699	+	12.7289i	1.04861	+	0.714927i	0.959675	−	0.281110i	$-0.0907027\pi$
$317$	18.6699	+	12.7289i	1.04861	+	0.714927i	0.0889305	+	0.996038i	$0.471655\pi$
$318$	−13.5561	−	12.5782i	−0.760186	−	0.705350i
$319$	−2.61416	−	2.42558i	−0.146365	−	0.135807i
$320$	1.86803	+	1.27360i	0.104426	+	0.0711966i
$321$	37.7191	−	18.1646i	2.10528	−	1.01385i
$322$	−13.5319	−	21.1281i	−0.754101	−	1.17742i
$323$	6.62837	+	3.19205i	0.368812	+	0.177611i
$324$	12.5730	+	21.7771i	0.698501	+	1.20984i
$325$	12.4486	−	21.5616i	0.690523	−	1.19602i
$326$	−3.31892	+	2.26280i	−0.183818	+	0.125325i
$327$	4.12442	+	0.621657i	0.228081	+	0.0343777i
$328$	−0.214260	+	0.938734i	−0.0118305	+	0.0518329i
$329$	13.6558	+	5.81798i	0.752871	+	0.320755i
$330$	1.06907	+	4.68391i	0.0588504	+	0.257840i
$331$	1.01634	+	13.5622i	0.0558632	+	0.745443i	0.952861	+	0.303408i	$0.0981244\pi$
$331$	1.01634	+	13.5622i	0.0558632	+	0.745443i	−0.896998	+	0.442035i	$0.854257\pi$
$332$	14.9432	+	4.60936i	0.820113	+	0.252971i
$333$	−1.10392	−	2.81273i	−0.0604943	−	0.154137i
$334$	45.4396	−	14.0163i	2.48635	−	0.766936i
$335$	1.69419	+	2.12445i	0.0925635	+	0.116071i
$336$	−7.46438	−	16.7128i	−0.407215	−	0.911759i
$337$	5.06821	−	6.35533i	0.276083	−	0.346197i	−0.624387	−	0.781115i	$-0.714651\pi$
$337$	5.06821	−	6.35533i	0.276083	−	0.346197i	0.900470	+	0.434918i	$0.143223\pi$
$338$	−9.28956	+	23.6694i	−0.505286	+	1.28745i
$339$	−1.21878	+	16.2635i	−0.0661951	+	0.883312i
$340$	1.25244	−	0.188775i	0.0679231	−	0.0102378i
$341$	29.9326	−	27.7734i	1.62094	−	1.50401i
$342$	6.96062			0.376387
$343$	−17.6337	−	5.66146i	−0.952131	−	0.305690i
$344$	0.792551			0.0427315
$345$	−1.55488	+	1.44272i	−0.0837120	+	0.0776733i
$346$	47.0322	−	7.08896i	2.52847	−	0.381105i
$347$	−0.895690	+	11.9522i	−0.0480832	+	0.641625i	0.920148	+	0.391570i	$0.128068\pi$
$347$	−0.895690	+	11.9522i	−0.0480832	+	0.641625i	−0.968232	+	0.250055i	$0.919551\pi$
$348$	−1.18893	+	3.02934i	−0.0637332	+	0.162390i
$349$	10.8397	−	13.5925i	0.580235	−	0.727592i	−0.401918	−	0.915676i	$-0.631656\pi$
$349$	10.8397	−	13.5925i	0.580235	−	0.727592i	0.982153	+	0.188084i	$0.0602277\pi$
$350$	11.0233	+	24.6814i	0.589223	+	1.31928i
$351$	−11.9294	−	14.9590i	−0.636743	−	0.798450i
$352$	−39.0768	+	12.0536i	−2.08280	+	0.642458i
$353$	−8.01626	−	20.4251i	−0.426663	−	1.08712i	−0.969022	−	0.246973i	$-0.920564\pi$
$353$	−8.01626	−	20.4251i	−0.426663	−	1.08712i	0.542360	−	0.840146i	$-0.317531\pi$
$354$	22.6636	+	6.99080i	1.20456	+	0.371557i
$355$	0.0441393	+	0.588998i	0.00234267	+	0.0312608i
$356$	5.17375	+	22.6677i	0.274208	+	1.20138i
$357$	−12.1788	−	5.18868i	−0.644569	−	0.274614i
$358$	7.50584	−	32.8852i	0.396696	−	1.73804i
$359$	3.85236	+	0.580650i	0.203320	+	0.0306455i	0.249912	−	0.968268i	$-0.419598\pi$
$359$	3.85236	+	0.580650i	0.203320	+	0.0306455i	−0.0465926	+	0.998914i	$0.514836\pi$
$360$	0.115060	−	0.0784469i	0.00606422	−	0.00413451i
$361$	5.03727	−	8.72480i	0.265119	−	0.459200i
$362$	10.3657	+	17.9538i	0.544807	+	0.943633i
$363$	−26.3388	−	12.6841i	−1.38243	−	0.665744i
$364$	−16.2471	−	25.3676i	−0.851579	−	1.32962i
$365$	0.571128	−	0.275041i	0.0298942	−	0.0143963i
$366$	−29.8093	−	20.3236i	−1.55816	−	1.06233i
$367$	9.47776	+	8.79407i	0.494735	+	0.459047i	0.887644	−	0.460530i	$-0.152341\pi$
$367$	9.47776	+	8.79407i	0.494735	+	0.459047i	−0.392909	+	0.919577i	$0.628531\pi$
$368$	−11.4639	−	10.6370i	−0.597599	−	0.554491i
$369$	−1.65341	−	1.12728i	−0.0860732	−	0.0586837i
$370$	1.13214	−	0.545212i	0.0588574	−	0.0283442i
$371$	−10.9745	+	3.94697i	−0.569768	+	0.204916i
$372$	−33.5721	−	16.1675i	−1.74063	−	0.838245i
$373$	10.8513	+	18.7949i	0.561857	+	0.973164i	0.997335	+	0.0729647i	$0.0232460\pi$
$373$	10.8513	+	18.7949i	0.561857	+	0.973164i	−0.435478	+	0.900199i	$0.643421\pi$
$374$	−12.8091	+	22.1861i	−0.662345	+	1.14722i
$375$	3.79597	−	2.58805i	0.196023	−	0.133646i
$376$	−3.01218	−	0.454013i	−0.155341	−	0.0234140i
$377$	0.792403	−	3.47174i	0.0408108	−	0.178804i
$378$	20.7512	−	0.956171i	1.06733	−	0.0491801i
$379$	4.05550	+	17.7683i	0.208317	+	0.912697i	0.965687	+	0.259710i	$0.0836271\pi$
$379$	4.05550	+	17.7683i	0.208317	+	0.912697i	−0.757369	+	0.652987i	$0.773516\pi$
$380$	0.114832	+	1.53233i	0.00589078	+	0.0786070i
$381$	−10.2346	−	3.15696i	−0.524335	−	0.161736i
$382$	−1.26646	−	3.22688i	−0.0647976	−	0.165102i
$383$	−18.0705	+	5.57400i	−0.923357	+	0.284818i	−0.719749	−	0.694235i	$-0.755743\pi$
$383$	−18.0705	+	5.57400i	−0.923357	+	0.284818i	−0.203608	+	0.979052i	$0.565267\pi$
$384$	5.45521	+	6.84062i	0.278385	+	0.349084i
$385$	2.93338	+	0.758877i	0.149499	+	0.0386760i
$386$	4.96133	−	6.22131i	0.252525	−	0.316656i
$387$	−0.601771	+	1.53329i	−0.0305897	+	0.0779414i
$388$	0.0841928	−	1.12347i	0.00427424	−	0.0570358i
$389$	−24.2559	+	3.65598i	−1.22982	+	0.185366i	−0.731630	−	0.681702i	$-0.761240\pi$
$389$	−24.2559	+	3.65598i	−1.22982	+	0.185366i	−0.498191	+	0.867067i	$0.666002\pi$
$390$	−3.51680	+	3.26312i	−0.178080	+	0.165234i
$391$	−11.3104			−0.571990
$392$	3.79446	+	0.218456i	0.191649	+	0.0110337i
$393$	3.31955			0.167449
$394$	−2.51838	+	2.33672i	−0.126874	+	0.117722i
$395$	−1.07920	+	0.162664i	−0.0543006	+	0.00818449i
$396$	−0.961532	+	12.8308i	−0.0483188	+	0.644770i
$397$	10.3814	−	26.4514i	0.521028	−	1.32756i	−0.392115	−	0.919916i	$-0.628256\pi$
$397$	10.3814	−	26.4514i	0.521028	−	1.32756i	0.913142	−	0.407641i	$-0.133648\pi$
$398$	34.1298	−	42.7974i	1.71077	−	2.14524i
$399$	7.38150	−	14.2636i	0.369537	−	0.714074i
$400$	10.5049	+	13.1727i	0.525246	+	0.658637i
$401$	21.7793	−	6.71804i	1.08761	−	0.335483i	0.301434	−	0.953487i	$-0.402535\pi$
$401$	21.7793	−	6.71804i	1.08761	−	0.335483i	0.786175	+	0.618004i	$0.212059\pi$
$402$	18.3234	+	46.6873i	0.913888	+	2.32855i
$403$	38.9629	+	12.0185i	1.94088	+	0.598682i
$404$	0.0600383	+	0.801156i	0.00298702	+	0.0398590i
$405$	−0.561998	−	2.46227i	−0.0279259	−	0.122351i
$406$	2.54715	+	2.90860i	0.126413	+	0.144351i
$407$	−3.00224	+	13.1537i	−0.148815	+	0.652003i
$408$	2.68637	+	0.404906i	0.132995	+	0.0200458i
$409$	−25.4353	+	17.3415i	−1.25769	+	0.857481i	−0.994238	−	0.107191i	$-0.965814\pi$
$409$	−25.4353	+	17.3415i	−1.25769	+	0.857481i	−0.263455	+	0.964672i	$0.584862\pi$
$410$	0.416102	−	0.720710i	0.0205498	−	0.0355933i
$411$	−3.46290	−	5.99793i	−0.170812	−	0.295856i
$412$	−16.3564	−	7.87684i	−0.805823	−	0.388064i
$413$	10.4849	−	10.6677i	0.515927	−	0.524926i
$414$	−9.64135	+	4.64303i	−0.473846	+	0.228192i
$415$	−1.29771	−	0.884766i	−0.0637022	−	0.0434315i
$416$	−29.9342	−	27.7749i	−1.46764	−	1.36177i
$417$	22.6830	+	21.0467i	1.11079	+	1.03066i
$418$	−25.6797	−	17.5081i	−1.25604	−	0.856350i
$419$	−30.9123	+	14.8866i	−1.51016	+	0.727256i	−0.991787	−	0.127897i	$-0.959177\pi$
$419$	−30.9123	+	14.8866i	−1.51016	+	0.727256i	−0.518376	+	0.855153i	$0.673463\pi$
$420$	−0.333324	−	2.74484i	−0.0162646	−	0.133934i
$421$	2.45681	+	1.18314i	0.119738	+	0.0576626i	0.492794	−	0.870146i	$-0.335976\pi$
$421$	2.45681	+	1.18314i	0.119738	+	0.0576626i	−0.373056	+	0.927809i	$0.621690\pi$
$422$	−8.58805	−	14.8749i	−0.418060	−	0.724101i
$423$	3.16545	−	5.48271i	0.153909	−	0.266579i
$424$	1.97754	−	1.34827i	0.0960379	−	0.0654775i
$425$	12.0493	+	1.81614i	0.584478	+	0.0880959i
$426$	−2.42592	+	10.6286i	−0.117536	+	0.514959i
$427$	−20.0240	+	10.8055i	−0.969028	+	0.522913i
$428$	10.3755	+	45.4581i	0.501520	+	2.19730i
$429$	−3.84938	−	51.3664i	−0.185850	−	2.48000i
$430$	−0.654562	−	0.201906i	−0.0315658	−	0.00973676i
$431$	6.26362	+	15.9594i	0.301708	+	0.768740i	0.998666	+	0.0516280i	$0.0164410\pi$
$431$	6.26362	+	15.9594i	0.301708	+	0.768740i	−0.696958	+	0.717112i	$0.745464\pi$
$432$	12.3727	−	3.81648i	0.595283	−	0.183620i
$433$	18.6888	+	23.4351i	0.898128	+	1.12622i	0.991438	+	0.130580i	$0.0416839\pi$
$433$	18.6888	+	23.4351i	0.898128	+	1.12622i	−0.0933098	+	0.995637i	$0.529745\pi$
$434$	−35.3903	+	26.5949i	−1.69879	+	1.27660i
$435$	0.203789	−	0.255543i	0.00977093	−	0.0122524i
$436$	−1.69718	+	4.32433i	−0.0812800	+	0.207098i
$437$	1.02543	−	13.6834i	0.0490530	−	0.654567i
$438$	11.5697	−	1.74385i	0.552820	−	0.0833242i
$439$	−0.156532	+	0.145240i	−0.00747085	+	0.00693194i	−0.683899	−	0.729576i	$-0.739717\pi$
$439$	−0.156532	+	0.145240i	−0.00747085	+	0.00693194i	0.676428	+	0.736508i	$0.263527\pi$
$440$	−0.621809			−0.0296436
$441$	−3.30370	+	7.17498i	−0.157319	+	0.341666i
$442$	−25.5816			−1.21679
$443$	7.42830	−	6.89245i	0.352929	−	0.327470i	−0.483706	−	0.875230i	$-0.660710\pi$
$443$	7.42830	−	6.89245i	0.352929	−	0.327470i	0.836636	+	0.547760i	$0.184519\pi$
$444$	12.1746	−	1.83503i	0.577783	−	0.0870868i
$445$	0.174512	−	2.32870i	0.00827265	−	0.110391i
$446$	−11.3947	+	29.0331i	−0.539553	+	1.37476i
$447$	13.6918	−	17.1690i	0.647600	−	0.812065i
$448$	25.8160	−	5.11622i	1.21969	−	0.241718i
$449$	−4.44189	−	5.56996i	−0.209626	−	0.262862i	0.665892	−	0.746048i	$-0.268051\pi$
$449$	−4.44189	−	5.56996i	−0.209626	−	0.262862i	−0.875518	+	0.483186i	$0.839480\pi$
$450$	11.0168	−	3.39824i	0.519337	−	0.160194i
$451$	3.26445	+	8.31769i	0.153717	+	0.391665i
$452$	−17.3572	−	5.35400i	−0.816416	−	0.251831i
$453$	2.67701	+	35.7222i	0.125777	+	1.67838i
$454$	−7.41999	−	32.5091i	−0.348237	−	1.52573i
$455$	0.808323	+	2.91564i	0.0378948	+	0.136687i
$456$	−0.733414	+	3.21330i	−0.0343453	+	0.150476i
$457$	−8.56621	−	1.29115i	−0.400711	−	0.0603974i	−0.0544045	−	0.998519i	$-0.517326\pi$
$457$	−8.56621	−	1.29115i	−0.400711	−	0.0603974i	−0.346306	+	0.938122i	$0.612564\pi$
$458$	−8.40629	+	5.73131i	−0.392800	+	0.267807i
$459$	4.68219	−	8.10979i	0.218546	−	0.378533i
$460$	−1.18119	−	2.04588i	−0.0550732	−	0.0953896i
$461$	8.95670	+	4.31332i	0.417155	+	0.200891i	0.630674	−	0.776048i	$-0.282778\pi$
$461$	8.95670	+	4.31332i	0.417155	+	0.200891i	−0.213519	+	0.976939i	$0.568493\pi$
$462$	47.6090	+	29.3437i	2.21497	+	1.36519i
$463$	−19.2129	+	9.25247i	−0.892901	+	0.429999i	−0.823320	−	0.567578i	$-0.807881\pi$
$463$	−19.2129	+	9.25247i	−0.892901	+	0.429999i	−0.0695815	+	0.997576i	$0.522166\pi$
$464$	1.99110	+	1.35751i	0.0924347	+	0.0630209i
$465$	2.74346	+	2.54556i	0.127225	+	0.118047i
$466$	−25.1347	−	23.3216i	−1.16434	−	1.08035i
$467$	0.0962343	+	0.0656115i	0.00445319	+	0.00303614i	0.565545	−	0.824718i	$-0.308666\pi$
$467$	0.0962343	+	0.0656115i	0.00445319	+	0.00303614i	−0.561091	+	0.827754i	$0.689618\pi$
$468$	−11.5759	+	5.57468i	−0.535098	+	0.257689i
$469$	31.4612	+	3.26964i	1.45274	+	0.150978i
$470$	2.37208	+	1.14233i	0.109416	+	0.0526919i
$471$	1.41914	+	2.45802i	0.0653904	+	0.113260i
$472$	−1.53482	+	2.65838i	−0.0706457	+	0.122362i
$473$	6.07680	−	4.14309i	0.279412	−	0.190500i
$474$	−19.9195	−	3.00238i	−0.914932	−	0.137904i
$475$	−3.28962	+	14.4128i	−0.150938	+	0.661303i
$476$	8.65229	−	11.9381i	0.396577	−	0.547182i
$477$	1.10687	+	4.84951i	0.0506801	+	0.222044i
$478$	−0.632436	−	8.43928i	−0.0289270	−	0.386003i
$479$	7.92658	+	2.44503i	0.362175	+	0.111716i	0.470501	−	0.882399i	$-0.344073\pi$
$479$	7.92658	+	2.44503i	0.362175	+	0.111716i	−0.108327	+	0.994115i	$0.534549\pi$
$480$	−1.36933	−	3.48899i	−0.0625010	−	0.159250i
$481$	−12.8741	+	3.97113i	−0.587007	+	0.181068i
$482$	−37.0564	−	46.4672i	−1.68787	−	2.11652i
$483$	−0.709877	+	24.6807i	−0.0323005	+	1.12301i
$484$	20.3003	−	25.4558i	0.922743	−	1.15708i
$485$	−0.0413402	+	0.105333i	−0.00187716	+	0.00478293i
$486$	1.72341	−	22.9973i	0.0781756	−	1.04318i
$487$	−22.3900	+	3.37475i	−1.01459	+	0.152924i	−0.635228	−	0.772325i	$-0.719094\pi$
$487$	−22.3900	+	3.37475i	−1.01459	+	0.152924i	−0.379360	+	0.925249i	$0.623856\pi$
$488$	3.42297	−	3.17605i	0.154950	−	0.143773i
$489$	3.95301			0.178761
$490$	−3.07816	−	1.14708i	−0.139057	−	0.0518196i
$491$	23.0338			1.03950			0.519751	−	0.854318i	$-0.326025\pi$
$491$	23.0338			1.03950			0.519751	+	0.854318i	$0.326025\pi$
$492$	5.97732	−	5.54614i	0.269478	−	0.250039i
$493$	1.72341	−	0.259762i	0.0776184	−	0.0116991i
$494$	2.31930	−	30.9490i	0.104350	−	1.39246i
$495$	0.472129	−	1.20297i	0.0212206	−	0.0540693i
$496$	−17.2040	+	21.5732i	−0.772483	+	0.968663i
$497$	5.25002	+	4.43959i	0.235496	+	0.199143i
$498$	−18.0750	−	22.6653i	−0.809959	−	1.01566i
$499$	−8.02980	+	2.47686i	−0.359463	+	0.110880i	−0.469226	−	0.883078i	$-0.655467\pi$
$499$	−8.02980	+	2.47686i	−0.359463	+	0.110880i	0.109763	+	0.993958i	$0.464991\pi$
$500$	1.86940	+	4.76316i	0.0836022	+	0.213015i
$501$	−44.7168	−	13.7933i	−1.99780	−	0.616240i
$502$	2.58466	+	34.4899i	0.115359	+	1.53936i
$503$	5.84482	+	25.6078i	0.260607	+	1.14180i	0.920595	+	0.390519i	$0.127704\pi$
$503$	5.84482	+	25.6078i	0.260607	+	1.14180i	−0.659987	+	0.751277i	$0.729438\pi$
$504$	0.287590	−	1.59533i	0.0128103	−	0.0710617i
$505$	0.0179555	−	0.0786683i	0.000799011	−	0.00350069i
$506$	47.2483	+	7.12154i	2.10044	+	0.316591i
$507$	20.6747	−	14.0958i	0.918195	−	0.626015i
$508$	5.96437	−	10.3306i	0.264626	−	0.458346i
$509$	0.971128	+	1.68204i	0.0430445	+	0.0745553i	0.886745	−	0.462259i	$-0.152961\pi$
$509$	0.971128	+	1.68204i	0.0430445	+	0.0745553i	−0.843700	+	0.536814i	$0.819628\pi$
$510$	−2.11551	−	1.01877i	−0.0936762	−	0.0451121i
$511$	2.37683	−	6.98575i	0.105145	−	0.309031i
$512$	28.2288	−	13.5943i	1.24755	−	0.600788i
$513$	9.38683	+	6.39983i	0.414439	+	0.282559i
$514$	−19.6177	−	18.2026i	−0.865299	−	0.802880i
$515$	1.33662	+	1.24020i	0.0588984	+	0.0546498i
$516$	−5.54542	−	3.78081i	−0.244124	−	0.166441i
$517$	−25.4690	+	12.2652i	−1.12012	+	0.539423i
$518$	4.71158	−	13.8478i	0.207015	−	0.608438i
$519$	−42.1715	−	20.3087i	−1.85112	−	0.891455i
$520$	−0.310459	−	0.537732i	−0.0136145	−	0.0235811i
$521$	−1.14420	+	1.98182i	−0.0501284	+	0.0868249i	−0.890001	−	0.455959i	$-0.849296\pi$
$521$	−1.14420	+	1.98182i	−0.0501284	+	0.0868249i	0.839872	+	0.542784i	$0.182630\pi$
$522$	1.36246	−	0.928907i	0.0596331	−	0.0406572i
$523$	21.9439	+	3.30751i	0.959541	+	0.144627i	0.610094	−	0.792329i	$-0.291132\pi$
$523$	21.9439	+	3.30751i	0.959541	+	0.144627i	0.349446	+	0.936956i	$0.386370\pi$
$524$	−0.822691	+	3.60445i	−0.0359394	+	0.157461i
$525$	4.71932	−	26.1792i	0.205968	−	1.14256i
$526$	2.85868	+	12.5247i	0.124644	+	0.546103i
$527$	1.49133	+	19.9004i	0.0649633	+	0.866876i
$528$	33.3098	+	10.2747i	1.44962	+	0.447150i
$529$	−0.695767	−	1.77279i	−0.0302507	−	0.0770776i
$530$	−1.97671	+	0.609736i	−0.0858630	+	0.0264852i
$531$	−3.97761	−	4.98776i	−0.172613	−	0.216450i
$532$	13.6584	+	11.5500i	0.592167	+	0.500756i
$533$	−5.56313	+	6.97594i	−0.240966	+	0.302162i
$534$	15.7472	−	40.1231i	0.681446	−	1.73630i
$535$	0.349968	−	4.67000i	0.0151305	−	0.201902i
$536$	−6.41876	+	0.967472i	−0.277248	+	0.0417884i
$537$	−24.3332	+	22.5779i	−1.05005	+	0.974309i
$538$	43.6660			1.88257
$539$	30.2356	−	18.1607i	1.30234	−	0.782236i
$540$	1.95592			0.0841695
$541$	6.23981	−	5.78969i	0.268270	−	0.248918i	−0.534554	−	0.845134i	$-0.679520\pi$
$541$	6.23981	−	5.78969i	0.268270	−	0.248918i	0.802824	+	0.596216i	$0.203330\pi$
$542$	−30.3496	+	4.57446i	−1.30362	+	0.196490i
$543$	1.52461	−	20.3445i	0.0654273	−	0.873066i
$544$	7.30167	−	18.6043i	0.313056	−	0.797655i
$545$	0.290906	−	0.364784i	0.0124610	−	0.0156256i
$546$	−1.60559	+	55.8225i	−0.0687128	+	2.38898i
$547$	5.86827	+	7.35858i	0.250909	+	0.314630i	0.891296	−	0.453423i	$-0.149797\pi$
$547$	5.86827	+	7.35858i	0.250909	+	0.314630i	−0.640386	+	0.768053i	$0.721226\pi$
$548$	7.37091	−	2.27363i	0.314870	−	0.0971245i
$549$	3.54545	+	9.03367i	0.151316	+	0.385548i
$550$	−49.1917	−	15.1736i	−2.09754	−	0.647006i
$551$	0.158014	+	2.10855i	0.00673162	+	0.0898273i
$552$	−1.12753	−	4.94005i	−0.0479910	−	0.210262i
$553$	−7.45550	+	10.2868i	−0.317040	+	0.437440i
$554$	−9.80257	+	42.9479i	−0.416471	+	1.82468i
$555$	−1.22279	−	0.184305i	−0.0519044	−	0.00782333i
$556$	−28.4746	+	19.4137i	−1.20759	+	0.823323i
$557$	15.0441	−	26.0572i	0.637440	−	1.10408i	−0.348552	−	0.937289i	$-0.613327\pi$
$557$	15.0441	−	26.0572i	0.637440	−	1.10408i	0.985993	−	0.166789i	$-0.0533400\pi$
$558$	9.44059	+	16.3516i	0.399652	+	0.692218i
$559$	6.61694	+	3.18655i	0.279867	+	0.134777i
$560$	−2.03655	−	0.211650i	−0.0860597	−	0.00894385i
$561$	22.7141	−	10.9386i	0.958992	−	0.461826i
$562$	42.8427	+	29.2097i	1.80721	+	1.23214i
$563$	−19.8632	−	18.4303i	−0.837133	−	0.776746i	0.139825	−	0.990176i	$-0.455346\pi$
$563$	−19.8632	−	18.4303i	−0.837133	−	0.776746i	−0.976958	+	0.213430i	$0.931536\pi$
$564$	18.9102	+	17.5461i	0.796263	+	0.738824i
$565$	1.50736	+	1.02770i	0.0634151	+	0.0432357i
$566$	−26.7453	+	12.8799i	−1.12419	+	0.541381i
$567$	−25.0275	−	15.4256i	−1.05106	−	0.647816i
$568$	−1.27127	−	0.612209i	−0.0533411	−	0.0256877i
$569$	1.16041	+	2.00989i	0.0486469	+	0.0842589i	0.889324	−	0.457279i	$-0.151176\pi$
$569$	1.16041	+	2.00989i	0.0486469	+	0.0842589i	−0.840677	+	0.541537i	$0.817842\pi$
$570$	1.42432	−	2.46700i	0.0596583	−	0.103331i
$571$	23.0695	−	15.7285i	0.965426	−	0.658217i	0.0255292	−	0.999674i	$-0.491873\pi$
$571$	23.0695	−	15.7285i	0.965426	−	0.658217i	0.939897	+	0.341457i	$0.110921\pi$
$572$	56.7289	+	8.55051i	2.37196	+	0.357515i
$573$	−0.759101	+	3.32584i	−0.0317119	+	0.138939i
$574$	−2.58807	−	9.33523i	−0.108024	−	0.389645i
$575$	−5.05739	−	22.1579i	−0.210908	−	0.924046i
$576$	−0.838835	−	11.1935i	−0.0349515	−	0.466395i
$577$	−13.7493	−	4.24111i	−0.572392	−	0.176560i	−0.00497163	−	0.999988i	$-0.501583\pi$
$577$	−13.7493	−	4.24111i	−0.572392	−	0.176560i	−0.567421	+	0.823428i	$0.692059\pi$
$578$	8.24919	+	21.0186i	0.343121	+	0.874258i
$579$	−7.48288	+	2.30816i	−0.310978	+	0.0959240i
$580$	0.226970	+	0.284611i	0.00942440	+	0.0118178i
$581$	−17.9342	+	3.55421i	−0.744037	+	0.147453i
$582$	−1.30220	+	1.63291i	−0.0539780	+	0.0676862i
$583$	8.11448	−	20.6754i	0.336067	−	0.856286i
$584$	−0.113166	+	1.51009i	−0.00468284	+	0.0624882i
$585$	1.27603	−	0.192331i	0.0527575	−	0.00795192i
$586$	−22.7341	+	21.0942i	−0.939137	+	0.871392i
$587$	28.9239			1.19382			0.596908	−	0.802309i	$-0.296396\pi$
$587$	28.9239			1.19382			0.596908	+	0.802309i	$0.296396\pi$
$588$	−25.5074	−	19.6297i	−1.05191	−	0.809516i
$589$	−24.2110			−0.997596
$590$	1.94483	−	1.80454i	0.0800674	−	0.0742917i
$591$	3.34307	−	0.503886i	0.137515	−	0.0207271i
$592$	0.681336	−	9.09179i	0.0280027	−	0.373670i
$593$	8.11219	−	20.6695i	0.333128	−	0.848795i	−0.661936	−	0.749560i	$-0.730265\pi$
$593$	8.11219	−	20.6695i	0.333128	−	0.848795i	0.995064	−	0.0992352i	$-0.0316396\pi$
$594$	−24.6659	+	30.9300i	−1.01205	+	1.26907i
$595$	−1.18382	+	0.889613i	−0.0485320	+	0.0364706i
$596$	15.2492	+	19.1219i	0.624632	+	0.783264i
$597$	−51.4760	+	15.8782i	−2.10677	+	0.649853i
$598$	17.4317	+	44.4154i	0.712837	+	1.81628i
$599$	−18.4562	−	5.69298i	−0.754099	−	0.232609i	−0.106210	−	0.994344i	$-0.533872\pi$
$599$	−18.4562	−	5.69298i	−0.754099	−	0.232609i	−0.647889	+	0.761735i	$0.724348\pi$
$600$	0.407961	+	5.44386i	0.0166549	+	0.222244i
$601$	−7.61197	−	33.3502i	−0.310499	−	1.36038i	−0.853693	−	0.520777i	$-0.825642\pi$
$601$	−7.61197	−	33.3502i	−0.310499	−	1.36038i	0.543194	−	0.839607i	$-0.317215\pi$
$602$	−7.01723	+	3.78669i	−0.286001	+	0.154334i
$603$	3.00196	−	13.1525i	0.122249	−	0.535610i
$604$	−39.4515	−	5.94636i	−1.60526	−	0.241954i
$605$	−2.70193	+	1.84214i	−0.109849	+	0.0748938i
$606$	0.744685	−	1.28983i	0.0302507	−	0.0523958i
$607$	−14.9939	−	25.9701i	−0.608582	−	1.05410i	−0.991474	−	0.130302i	$-0.958405\pi$
$607$	−14.9939	−	25.9701i	−0.608582	−	1.05410i	0.382892	−	0.923793i	$-0.374928\pi$
$608$	21.8458	+	10.5204i	0.885963	+	0.426657i
$609$	−0.458668	−	3.77700i	−0.0185861	−	0.153052i
$610$	−3.63612	+	1.75106i	−0.147222	+	0.0708984i
$611$	−23.3230	−	15.9014i	−0.943549	−	0.643301i
$612$	−4.60969	−	4.27717i	−0.186336	−	0.172894i
$613$	11.7343	+	10.8878i	0.473943	+	0.439755i	0.880624	−	0.473815i	$-0.157124\pi$
$613$	11.7343	+	10.8878i	0.473943	+	0.439755i	−0.406681	+	0.913570i	$0.633314\pi$
$614$	−11.8499	−	8.07912i	−0.478223	−	0.326047i
$615$	−0.737863	+	0.355336i	−0.0297535	+	0.0143285i
$616$	−5.07376	+	5.16225i	−0.204427	+	0.207993i
$617$	−17.2284	−	8.29675i	−0.693588	−	0.334015i	0.0536602	−	0.998559i	$-0.482911\pi$
$617$	−17.2284	−	8.29675i	−0.693588	−	0.334015i	−0.747248	+	0.664545i	$0.768626\pi$
$618$	16.8274	+	29.1460i	0.676898	+	1.17242i
$619$	−19.1806	+	33.2218i	−0.770934	+	1.33530i	0.166117	+	0.986106i	$0.446877\pi$
$619$	−19.1806	+	33.2218i	−0.770934	+	1.33530i	−0.937051	+	0.349191i	$0.886456\pi$
$620$	−3.44394	+	2.34804i	−0.138312	+	0.0942996i
$621$	−17.2709	−	2.60317i	−0.693058	−	0.104462i
$622$	−4.96163	+	21.7383i	−0.198943	+	0.871628i
$623$	−17.9089	−	20.4502i	−0.717503	−	0.819320i
$624$	7.74565	+	33.9359i	0.310074	+	1.35852i
$625$	1.81054	+	24.1600i	0.0724218	+	0.966401i
$626$	−23.1119	−	7.12907i	−0.923736	−	0.284935i
$627$	11.1743	+	28.4716i	0.446257	+	1.13704i
$628$	−3.02069	+	0.931758i	−0.120538	+	0.0371812i
$629$	−4.11124	−	5.15533i	−0.163926	−	0.205556i
$630$	−0.643936	+	1.24431i	−0.0256550	+	0.0495744i
$631$	22.2301	−	27.8757i	0.884968	−	1.10971i	−0.108328	−	0.994115i	$-0.534550\pi$
$631$	22.2301	−	27.8757i	0.884968	−	1.10971i	0.993296	−	0.115599i	$-0.0368788\pi$
$632$	0.952523	−	2.42699i	0.0378894	−	0.0965405i
$633$	−1.26315	+	16.8556i	−0.0502059	+	0.669951i
$634$	46.1333	−	6.95348i	1.83219	−	0.276158i
$635$	−0.878261	+	0.814907i	−0.0348527	+	0.0323386i
$636$	−20.2685			−0.803699
$637$	30.8013	+	17.0800i	1.22039	+	0.676733i
$638$	−7.36298			−0.291503
$639$	2.14964	−	1.99458i	0.0850386	−	0.0789043i
$640$	0.967801	−	0.145872i	0.0382557	−	0.00576612i
$641$	−3.04018	+	40.5684i	−0.120080	+	1.60235i	0.533703	+	0.845672i	$0.320800\pi$
$641$	−3.04018	+	40.5684i	−0.120080	+	1.60235i	−0.653783	+	0.756682i	$0.726819\pi$
$642$	31.5796	−	80.4635i	1.24635	−	3.17564i
$643$	17.3801	−	21.7940i	0.685404	−	0.859470i	−0.310435	−	0.950595i	$-0.600475\pi$
$643$	17.3801	−	21.7940i	0.685404	−	0.859470i	0.995839	+	0.0911247i	$0.0290462\pi$
$644$	−26.6230	−	6.88748i	−1.04909	−	0.271405i
$645$	0.420294	+	0.527032i	0.0165490	+	0.0207518i
$646$	14.5150	−	4.47728i	0.571085	−	0.176156i
$647$	12.8622	+	32.7722i	0.505664	+	1.28841i	0.924789	+	0.380481i	$0.124242\pi$
$647$	12.8622	+	32.7722i	0.505664	+	1.28841i	−0.419125	+	0.907929i	$0.637663\pi$
$648$	5.76533	+	1.77837i	0.226483	+	0.0698609i
$649$	2.12875	+	28.4062i	0.0835607	+	1.11504i
$650$	−11.4387	−	50.1163i	−0.448663	−	1.96572i
$651$	43.5189	−	2.00526i	1.70564	−	0.0785923i
$652$	−0.979683	+	4.29227i	−0.0383674	+	0.168098i
$653$	−20.3537	−	3.06782i	−0.796501	−	0.120053i	−0.261830	−	0.965114i	$-0.584326\pi$
$653$	−20.3537	−	3.06782i	−0.796501	−	0.120053i	−0.534670	+	0.845061i	$0.679564\pi$
$654$	7.11546	−	4.85124i	0.278237	−	0.189699i
$655$	0.185665	−	0.321582i	0.00725454	−	0.0125652i
$656$	−3.01907	−	5.22918i	−0.117875	−	0.204165i
$657$	−2.83554	−	1.36552i	−0.110625	−	0.0532742i
$658$	28.8390	−	10.3719i	1.12426	−	0.404339i
$659$	−14.0715	+	6.77647i	−0.548147	+	0.263974i	−0.687395	−	0.726284i	$-0.741246\pi$
$659$	−14.0715	+	6.77647i	−0.548147	+	0.263974i	0.139248	+	0.990258i	$0.455531\pi$
$660$	4.35075	+	2.96629i	0.169353	+	0.115463i
$661$	14.5172	+	13.4700i	0.564655	+	0.523923i	0.910030	−	0.414541i	$-0.136058\pi$
$661$	14.5172	+	13.4700i	0.564655	+	0.523923i	−0.345376	+	0.938465i	$0.612248\pi$
$662$	20.5843	+	19.0994i	0.800031	+	0.742320i
$663$	20.8003	+	14.1814i	0.807818	+	0.550761i
$664$	3.38049	−	1.62796i	0.131188	−	0.0631770i
$665$	−0.968936	−	1.51286i	−0.0375737	−	0.0586662i
$666$	−5.62088	−	2.70687i	−0.217805	−	0.104889i
$667$	−1.62536	−	2.81521i	−0.0629343	−	0.109005i
$668$	26.0594	−	45.1362i	1.00827	−	1.74637i
$669$	25.3598	−	17.2900i	0.980465	−	0.668470i
$670$	5.54767	+	0.836177i	0.214325	+	0.0323044i
$671$	9.64230	−	42.2457i	0.372237	−	1.63088i
$672$	−40.1388	−	17.1009i	−1.54839	−	0.659680i
$673$	−10.2014	−	44.6953i	−0.393236	−	1.72288i	−0.653134	−	0.757242i	$-0.726546\pi$
$673$	−10.2014	−	44.6953i	−0.393236	−	1.72288i	0.259898	−	0.965636i	$-0.416311\pi$
$674$	−1.25423	−	16.7365i	−0.0483111	−	0.644667i
$675$	17.9813	+	5.54650i	0.692101	+	0.213485i
$676$	10.1817	+	25.9425i	0.391602	+	0.997787i
$677$	33.3348	−	10.2824i	1.28116	−	0.395186i	0.421863	−	0.906660i	$-0.361376\pi$
$677$	33.3348	−	10.2824i	1.28116	−	0.395186i	0.859299	+	0.511474i	$0.170900\pi$
$678$	20.9950	+	26.3269i	0.806308	+	1.01108i
$679$	0.537152	+	1.20269i	0.0206140	+	0.0461549i
$680$	0.189476	−	0.237596i	0.00726609	−	0.00911139i
$681$	−11.9886	+	30.5464i	−0.459403	+	1.17054i
$682$	6.30030	−	84.0716i	0.241251	−	3.21927i
$683$	−49.3621	+	7.44014i	−1.88879	+	0.284689i	−0.988571	−	0.150753i	$-0.951830\pi$
$683$	−49.3621	+	7.44014i	−1.88879	+	0.284689i	−0.900217	+	0.435442i	$0.856592\pi$
$684$	5.59250	−	5.18908i	0.213835	−	0.198409i
$685$	−0.774733			−0.0296010
$686$	−34.6398	+	16.1951i	−1.32255	+	0.618333i
$687$	10.0123			0.381994
$688$	−3.64330	+	3.38049i	−0.138900	+	0.128880i
$689$	21.9312	−	3.30559i	0.835512	−	0.125933i
$690$	−0.327276	+	4.36720i	−0.0124592	+	0.166256i
$691$	−1.95357	+	4.97761i	−0.0743172	+	0.189357i	−0.963205	−	0.268768i	$-0.913384\pi$
$691$	−1.95357	+	4.97761i	−0.0743172	+	0.189357i	0.888888	+	0.458125i	$0.151479\pi$
$692$	32.5032	−	40.7577i	1.23559	−	1.54938i
$693$	−6.13459	−	13.7354i	−0.233034	−	0.521766i
$694$	15.4294	+	19.3478i	0.585691	+	0.734433i
$695$	3.30758	−	1.02025i	0.125464	−	0.0387004i
$696$	0.285263	+	0.726839i	0.0108129	+	0.0275508i
$697$	−4.17296	−	1.28719i	−0.158062	−	0.0487557i
$698$	−2.68250	−	35.7954i	−0.101534	−	1.35488i
$699$	7.50838	+	32.8964i	0.283993	+	1.24426i
$700$	27.2564	+	11.6124i	1.03020	+	0.438908i
$701$	−7.20895	+	31.5845i	−0.272278	+	1.19293i	0.635038	+	0.772481i	$0.280984\pi$
$701$	−7.20895	+	31.5845i	−0.272278	+	1.19293i	−0.907316	+	0.420448i	$0.861873\pi$
$702$	−39.0631	−	5.88782i	−1.47434	−	0.222221i
$703$	6.60972	−	4.50643i	0.249290	−	0.169963i
$704$	−25.0604	+	43.4059i	−0.944499	+	1.63592i
$705$	−1.29546	−	2.24381i	−0.0487900	−	0.0845068i
$706$	−40.8169	−	19.6564i	−1.53616	−	0.739777i
$707$	−0.506593	−	0.790974i	−0.0190524	−	0.0297477i
$708$	23.4206	−	11.2788i	0.880201	−	0.423882i
$709$	−16.5882	−	11.3097i	−0.622984	−	0.424743i	0.210262	−	0.977645i	$-0.432568\pi$
$709$	−16.5882	−	11.3097i	−0.622984	−	0.424743i	−0.833247	+	0.552902i	$0.813521\pi$
$710$	0.893966	+	0.829480i	0.0335500	+	0.0311298i
$711$	3.97208	+	3.68555i	0.148964	+	0.138219i
$712$	4.60926	+	3.14254i	0.172739	+	0.117772i
$713$	33.5353	−	16.1497i	1.25591	−	0.604813i
$714$	−25.7197	+	9.25005i	−0.962535	+	0.346175i
$715$	−5.19143	−	2.50006i	−0.194148	−	0.0934969i
$716$	−18.4851	−	32.0171i	−0.690820	−	1.19654i
$717$	−4.16416	+	7.21254i	−0.155513	+	0.269357i
$718$	6.64610	−	4.53123i	0.248030	−	0.169104i
$719$	24.3253	+	3.66645i	0.907182	+	0.136736i	0.586027	−	0.810291i	$-0.300691\pi$
$719$	24.3253	+	3.66645i	0.907182	+	0.136736i	0.321154	+	0.947027i	$0.395929\pi$
$720$	−0.194323	+	0.851386i	−0.00724200	+	0.0317293i
$721$	21.2025	−	0.976967i	0.789622	−	0.0363842i
$722$	−4.62863	−	20.2793i	−0.172260	−	0.754719i
$723$	4.37084	+	58.3248i	0.162553	+	2.16912i
$724$	21.7127	+	6.69748i	0.806947	+	0.248910i
$725$	1.27951	+	3.26013i	0.0475197	+	0.121078i
$726$	−57.6776	+	17.7912i	−2.14062	+	0.660293i
$727$	7.17815	+	9.00112i	0.266223	+	0.333833i	0.896917	−	0.442198i	$-0.145801\pi$
$727$	7.17815	+	9.00112i	0.266223	+	0.333833i	−0.630694	+	0.776031i	$0.717230\pi$
$728$	−6.99749	−	1.81028i	−0.259344	−	0.0670935i
$729$	6.63445	−	8.31933i	0.245720	−	0.308123i
$730$	0.478166	−	1.21835i	0.0176977	−	0.0450931i
$731$	−0.268617	+	3.58445i	−0.00993516	+	0.132576i
$732$	−39.1014	+	5.89358i	−1.44523	+	0.217833i
$733$	−14.0937	+	13.0770i	−0.520562	+	0.483011i	−0.896135	−	0.443782i	$-0.853637\pi$
$733$	−14.0937	+	13.0770i	−0.520562	+	0.483011i	0.375573	+	0.926793i	$0.377446\pi$
$734$	26.6948			0.985324
$735$	1.86695	+	2.63909i	0.0688635	+	0.0973444i
$736$	−37.2767			−1.37404
$737$	−44.1576	+	40.9723i	−1.62657	+	1.50923i
$738$	−4.08558	+	0.615802i	−0.150392	+	0.0226680i
$739$	0.649629	−	8.66869i	0.0238970	−	0.318883i	−0.972426	−	0.233210i	$-0.925077\pi$
$739$	0.649629	−	8.66869i	0.0238970	−	0.318883i	0.996323	−	0.0856728i	$-0.0273040\pi$
$740$	0.503169	−	1.28205i	0.0184969	−	0.0471292i
$741$	−19.0427	+	23.8788i	−0.699550	+	0.877208i
$742$	−11.0673	+	21.3859i	−0.406294	+	0.785101i
$743$	9.51278	+	11.9286i	0.348990	+	0.437619i	0.925083	−	0.379764i	$-0.123995\pi$
$743$	9.51278	+	11.9286i	0.348990	+	0.437619i	−0.576093	+	0.817384i	$0.695424\pi$
$744$	−8.54326	+	2.63525i	−0.313211	+	0.0966128i
$745$	−0.897452	−	2.28667i	−0.0328801	−	0.0837771i
$746$	42.8184	+	13.2077i	1.56769	+	0.483569i
$747$	0.582734	+	7.77605i	0.0213211	+	0.284511i
$748$	6.24805	+	27.3745i	0.228451	+	1.00091i
$749$	−35.9147	−	41.0111i	−1.31230	−	1.49851i
$750$	2.11079	−	9.24797i	0.0770751	−	0.337688i
$751$	6.85033	+	1.03252i	0.249972	+	0.0376772i	0.272833	−	0.962061i	$-0.412039\pi$
$751$	6.85033	+	1.03252i	0.249972	+	0.0376772i	−0.0228609	+	0.999739i	$0.507277\pi$
$752$	15.7833	−	10.7609i	0.575558	−	0.392409i
$753$	17.0183	−	29.4765i	0.620180	−	1.07418i
$754$	−3.67622	−	6.36740i	−0.133880	−	0.231887i
$755$	3.61032	+	1.73864i	0.131393	+	0.0632756i
$756$	15.9597	−	16.2381i	0.580448	−	0.590572i
$757$	4.41120	−	2.12432i	0.160328	−	0.0772099i	−0.351999	−	0.936000i	$-0.614498\pi$
$757$	4.41120	−	2.12432i	0.160328	−	0.0772099i	0.512327	+	0.858791i	$0.328784\pi$
$758$	31.0911	+	21.1975i	1.12928	+	0.769929i
$759$	−34.4695	−	31.9831i	−1.25116	−	1.16091i
$760$	0.270268	+	0.250772i	0.00980365	+	0.00909646i
$761$	−20.8755	−	14.2327i	−0.756736	−	0.515934i	0.122414	−	0.992479i	$-0.460936\pi$
$761$	−20.8755	−	14.2327i	−0.756736	−	0.515934i	−0.879150	+	0.476546i	$0.841889\pi$
$762$	−19.9239	+	9.59483i	−0.721766	+	0.347584i
$763$	−0.654741	−	5.39161i	−0.0237032	−	0.195190i
$764$	−3.42315	−	1.64850i	−0.123845	−	0.0596406i
$765$	0.315792	+	0.546968i	0.0114175	+	0.0197757i
$766$	−19.5223	+	33.8137i	−0.705370	+	1.22174i
$767$	−23.5024	+	16.0237i	−0.848623	+	0.578581i
$768$	−22.1082	−	3.33227i	−0.797760	−	0.120243i
$769$	0.789269	−	3.45801i	0.0284618	−	0.124699i	−0.958701	−	0.284415i	$-0.908201\pi$
$769$	0.789269	−	3.45801i	0.0284618	−	0.124699i	0.987163	+	0.159716i	$0.0510578\pi$
$770$	5.50549	−	2.97091i	0.198404	−	0.107064i
$771$	5.86031	+	25.6757i	0.211054	+	0.924687i
$772$	−0.651760	−	8.69713i	−0.0234574	−	0.313017i
$773$	43.1188	+	13.3004i	1.55087	+	0.478381i	0.947682	−	0.319215i	$-0.103419\pi$
$773$	43.1188	+	13.3004i	1.55087	+	0.478381i	0.603192	+	0.797596i	$0.293895\pi$
$774$	1.24247	+	3.16577i	0.0446598	+	0.113791i
$775$	−38.3195	+	11.8200i	−1.37648	+	0.424587i
$776$	−0.168539	−	0.211341i	−0.00605018	−	0.00758669i
$777$	−11.5076	+	8.64769i	−0.412834	+	0.310234i
$778$	−31.5777	+	39.5972i	−1.13212	+	1.41963i
$779$	1.93559	−	4.93180i	0.0693497	−	0.176700i
$780$	−0.392946	+	5.24349i	−0.0140697	+	0.187747i
$781$	−12.9476	+	1.95154i	−0.463303	+	0.0698317i
$782$	−17.1186	+	15.8837i	−0.612160	+	0.568001i
$783$	2.69143			0.0961837
$784$	−18.3747	+	15.1804i	−0.656238	+	0.542157i
$785$	0.317494			0.0113319
$786$	5.02424	−	4.66181i	0.179209	−	0.166281i
$787$	23.6601	−	3.56618i	0.843391	−	0.127121i	0.286886	−	0.957965i	$-0.407380\pi$
$787$	23.6601	−	3.56618i	0.843391	−	0.127121i	0.556505	+	0.830844i	$0.312142\pi$
$788$	−0.281388	+	3.75486i	−0.0100240	+	0.133761i
$789$	4.61881	−	11.7685i	0.164434	−	0.418971i
$790$	−1.40497	+	1.76177i	−0.0499865	+	0.0626811i
$791$	20.8315	−	4.12839i	0.740683	−	0.146789i
$792$	1.92481	+	2.41364i	0.0683952	+	0.0857649i
$793$	41.3477	−	12.7541i	1.46830	−	0.452911i
$794$	−21.4345	−	54.6141i	−0.760680	−	1.93818i
$795$	1.94527	+	0.600037i	0.0689917	+	0.0212811i
$796$	−4.48357	−	59.8290i	−0.158916	−	2.12058i
$797$	10.0446	+	44.0085i	0.355800	+	1.55886i	0.763539	+	0.645762i	$0.223460\pi$
$797$	10.0446	+	44.0085i	0.355800	+	1.55886i	−0.407739	+	0.913098i	$0.633683\pi$
$798$	−8.85901	−	31.9546i	−0.313606	−	1.13118i
$799$	3.07426	−	13.4692i	0.108760	−	0.476507i
$800$	39.7122	+	5.98565i	1.40404	+	0.211625i
$801$	−9.57936	+	6.53110i	−0.338470	+	0.230765i
$802$	23.5292	−	40.7538i	0.830845	−	1.43907i
$803$	7.02639	+	12.1701i	0.247956	+	0.429472i
$804$	49.5269	+	23.8509i	1.74668	+	0.841155i
$805$	2.35124	+	1.44918i	0.0828704	+	0.0510770i
$806$	75.8496	−	36.5273i	2.67169	−	1.28662i
$807$	−35.5046	−	24.2067i	−1.24982	−	0.852114i
$808$	0.141305	+	0.131112i	0.00497110	+	0.00461251i
$809$	13.0517	+	12.1102i	0.458873	+	0.425772i	0.875435	−	0.483335i	$-0.160575\pi$
$809$	13.0517	+	12.1102i	0.458873	+	0.425772i	−0.416562	+	0.909107i	$0.636765\pi$
$810$	−4.30850	−	2.93748i	−0.151385	−	0.103213i
$811$	32.2066	−	15.5099i	1.13093	−	0.544625i	0.227674	−	0.973737i	$-0.426888\pi$
$811$	32.2066	−	15.5099i	1.13093	−	0.544625i	0.903251	+	0.429112i	$0.141174\pi$
$812$	4.21483	+	0.438031i	0.147912	+	0.0153719i
$813$	27.2130	+	13.1051i	0.954401	+	0.459615i
$814$	13.9284	+	24.1247i	0.488190	+	0.845569i
$815$	0.221095	−	0.382948i	0.00774462	−	0.0134141i
$816$	−14.0761	+	9.59694i	−0.492763	+	0.335960i
$817$	−4.31215	−	0.649953i	−0.150863	−	0.0227390i
$818$	−14.1435	+	61.9669i	−0.494517	+	2.16662i
$819$	8.81529	−	12.1630i	0.308031	−	0.425009i
$820$	−0.202966	−	0.889254i	−0.00708789	−	0.0310541i
$821$	−2.78133	−	37.1143i	−0.0970691	−	1.29530i	−0.806800	−	0.590824i	$-0.798803\pi$
$821$	−2.78133	−	37.1143i	−0.0970691	−	1.29530i	0.709731	−	0.704473i	$-0.248816\pi$
$822$	−13.6644	−	4.21491i	−0.476601	−	0.147012i
$823$	−12.7743	−	32.5484i	−0.445284	−	1.13457i	−0.960691	−	0.277620i	$-0.910454\pi$
$823$	−12.7743	−	32.5484i	−0.445284	−	1.13457i	0.515407	−	0.856946i	$-0.327641\pi$
$824$	−4.16230	+	1.28390i	−0.145000	+	0.0447267i
$825$	31.5860	+	39.6075i	1.09968	+	1.37896i
$826$	0.887907	−	30.8704i	0.0308942	−	1.07412i
$827$	−2.57533	+	3.22936i	−0.0895529	+	0.112296i	−0.824589	−	0.565732i	$-0.808594\pi$
$827$	−2.57533	+	3.22936i	−0.0895529	+	0.112296i	0.735036	+	0.678028i	$0.237165\pi$
$828$	−4.28499	+	10.9180i	−0.148914	+	0.379426i
$829$	−3.06105	+	40.8469i	−0.106315	+	1.41867i	0.647740	+	0.761861i	$0.275714\pi$
$829$	−3.06105	+	40.8469i	−0.106315	+	1.41867i	−0.754055	+	0.656811i	$0.771905\pi$
$830$	−3.20665	+	0.483325i	−0.111304	+	0.0167764i
$831$	31.7790	−	29.4866i	1.10240	−	1.02288i
$832$	−50.0490			−1.73514
$833$	−2.27405	+	17.0870i	−0.0787912	+	0.592031i
$834$	63.8884			2.21227
$835$	−3.83728	+	3.56047i	−0.132795	+	0.123215i
$836$	−33.6845	+	5.07712i	−1.16500	+	0.175596i
$837$	−2.30298	+	30.7311i	−0.0796026	+	1.06222i
$838$	−25.8807	+	65.9429i	−0.894034	+	2.27796i
$839$	−1.07588	+	1.34911i	−0.0371434	+	0.0465763i	−0.800056	−	0.599925i	$-0.795197\pi$
$839$	−1.07588	+	1.34911i	−0.0371434	+	0.0465763i	0.762913	+	0.646501i	$0.223769\pi$
$840$	−0.506573	−	0.428375i	−0.0174784	−	0.0147803i
$841$	−17.7689	−	22.2815i	−0.612720	−	0.768327i
$842$	5.37999	−	1.65951i	0.185407	−	0.0571904i
$843$	−18.6426	−	47.5005i	−0.642085	−	1.63600i
$844$	−17.9892	−	5.54893i	−0.619213	−	0.191002i
$845$	−0.209175	−	2.79125i	−0.00719584	−	0.0960219i
$846$	−2.90865	−	12.7436i	−0.100002	−	0.438136i
$847$	−6.75338	+	37.4627i	−0.232049	+	1.28723i
$848$	−3.33983	+	14.6327i	−0.114690	+	0.502491i
$849$	28.8866	+	4.35395i	0.991385	+	0.149427i
$850$	20.7875	−	14.1727i	0.713006	−	0.486120i
$851$	−6.14932	+	10.6509i	−0.210796	+	0.365110i
$852$	5.97446	+	10.3481i	0.204681	+	0.354519i
$853$	−42.8819	−	20.6508i	−1.46825	−	0.707071i	−0.482593	−	0.875845i	$-0.660305\pi$
$853$	−42.8819	−	20.6508i	−1.46825	−	0.707071i	−0.985655	+	0.168773i	$0.946019\pi$
$854$	−15.1322	+	44.4751i	−0.517814	+	1.52191i
$855$	−0.690360	+	0.332460i	−0.0236098	+	0.0113699i
$856$	9.24348	+	6.30209i	0.315935	+	0.215401i
$857$	−15.7900	−	14.6510i	−0.539377	−	0.500469i	0.362781	−	0.931874i	$-0.381827\pi$
$857$	−15.7900	−	14.6510i	−0.539377	−	0.500469i	−0.902158	+	0.431406i	$0.858018\pi$
$858$	−77.9627	−	72.3388i	−2.66160	−	2.46961i
$859$	24.6735	+	16.8221i	0.841849	+	0.573963i	0.905663	−	0.423999i	$-0.139374\pi$
$859$	24.6735	+	16.8221i	0.841849	+	0.573963i	−0.0638134	+	0.997962i	$0.520326\pi$
$860$	−0.676426	+	0.325750i	−0.0230659	+	0.0111080i
$861$	−3.07072	+	9.02516i	−0.104650	+	0.307577i
$862$	31.8928	+	15.3588i	1.08627	+	0.523122i
$863$	−25.9789	−	44.9968i	−0.884332	−	1.53171i	−0.846477	−	0.532425i	$-0.821281\pi$
$863$	−25.9789	−	44.9968i	−0.884332	−	1.53171i	−0.0378545	−	0.999283i	$-0.512052\pi$
$864$	15.4316	−	26.7283i	0.524993	−	0.909314i
$865$	−4.32610	+	2.94949i	−0.147092	+	0.100286i
$866$	61.1972	+	9.22399i	2.07956	+	0.313444i
$867$	4.94447	−	21.6632i	0.167923	−	0.735719i
$868$	−8.60803	+	47.7508i	−0.292176	+	1.62077i
$869$	−5.38382	−	23.5880i	−0.182633	−	0.800169i
$870$	−0.0504317	−	0.672964i	−0.00170979	−	0.0228156i
$871$	−57.4795	−	17.7301i	−1.94762	−	0.600761i
$872$	0.407209	+	1.03755i	0.0137898	+	0.0351359i
$873$	0.536833	−	0.165591i	0.0181691	−	0.00560441i
$874$	−17.6643	−	22.1504i	−0.597504	−	0.749247i
$875$	−4.56804	−	3.86288i	−0.154428	−	0.130589i
$876$	7.99561	−	10.0262i	0.270147	−	0.338753i
$877$	11.2821	−	28.7463i	0.380970	−	0.970695i	−0.603847	−	0.797100i	$-0.706366\pi$
$877$	11.2821	−	28.7463i	0.380970	−	0.970695i	0.984817	−	0.173595i	$-0.0555384\pi$
$878$	−0.0329473	+	0.439651i	−0.00111192	+	0.0148375i
$879$	30.1788	−	4.54872i	1.01790	−	0.153424i
$880$	2.85841	−	2.65222i	0.0963571	−	0.0894063i
$881$	−57.6244			−1.94141			−0.970707	−	0.240266i	$-0.922765\pi$
$881$	−57.6244			−1.94141			−0.970707	+	0.240266i	$0.922765\pi$
$882$	5.07593	+	15.4991i	0.170916	+	0.521882i
$883$	−45.7898			−1.54095			−0.770475	−	0.637471i	$-0.779981\pi$
$883$	−45.7898			−1.54095			−0.770475	+	0.637471i	$0.779981\pi$
$884$	−20.5535	+	19.0709i	−0.691290	+	0.641423i
$885$	−2.58170	+	0.389128i	−0.0867828	+	0.0130804i
$886$	1.56353	−	20.8639i	0.0525279	−	0.700936i
$887$	0.950713	−	2.42238i	0.0319218	−	0.0813355i	−0.914024	−	0.405660i	$-0.867042\pi$
$887$	0.950713	−	2.42238i	0.0319218	−	0.0813355i	0.945946	+	0.324324i	$0.105137\pi$
$888$	1.84185	−	2.30961i	0.0618084	−	0.0775053i
$889$	−0.400968	+	13.9407i	−0.0134480	+	0.467556i
$890$	−3.00618	−	3.76963i	−0.100767	−	0.126358i
$891$	53.5015	−	16.5030i	1.79237	−	0.552872i
$892$	12.4889	+	31.8213i	0.418160	+	1.06545i
$893$	16.0165	+	4.94044i	0.535972	+	0.165326i
$894$	−3.38831	−	45.2139i	−0.113322	−	1.51218i
$895$	0.826260	+	3.62008i	0.0276188	+	0.121006i
$896$	6.68590	−	9.22495i	0.223360	−	0.308184i
$897$	10.4484	−	45.7774i	0.348862	−	1.52846i
$898$	−14.5451	−	2.19232i	−0.485377	−	0.0731587i
$899$	−4.73900	+	3.23100i	−0.158055	+	0.107760i
$900$	6.31808	−	10.9432i	0.210603	−	0.364775i
$901$	5.42752	+	9.40073i	0.180817	+	0.313184i
$902$	16.6218	+	8.00464i	0.553445	+	0.266525i
$903$	7.80487	+	0.811129i	0.259730	+	0.0269927i
$904$	−3.92661	+	1.89095i	−0.130597	+	0.0628922i
$905$	−1.88560	−	1.28558i	−0.0626796	−	0.0427342i
$906$	54.2183	+	50.3072i	1.80128	+	1.67135i
$907$	7.68999	+	7.13526i	0.255342	+	0.236923i	0.797448	−	0.603387i	$-0.206183\pi$
$907$	7.68999	+	7.13526i	0.255342	+	0.236923i	−0.542107	+	0.840310i	$0.682373\pi$
$908$	−30.1968	−	20.5879i	−1.00212	−	0.683232i
$909$	−0.360943	+	0.173821i	−0.0119717	+	0.00576529i
$910$	5.31800	+	3.27774i	0.176290	+	0.108656i
$911$	45.0044	+	21.6730i	1.49106	+	0.718057i	0.989156	−	0.146866i	$-0.0469187\pi$
$911$	45.0044	+	21.6730i	1.49106	+	0.718057i	0.501904	+	0.864923i	$0.332633\pi$
$912$	−10.3343	−	17.8996i	−0.342203	−	0.592714i
$913$	17.4093	−	30.1538i	0.576164	−	0.997946i
$914$	−14.7784	+	10.0758i	−0.488828	+	0.333277i
$915$	3.92723	+	0.591934i	0.129830	+	0.0195687i
$916$	−2.48138	+	10.8716i	−0.0819870	+	0.359209i
$917$	−1.15480	−	4.16539i	−0.0381349	−	0.137553i
$918$	−4.30236	−	18.8499i	−0.141999	−	0.622138i
$919$	2.71205	+	36.1898i	0.0894623	+	1.19379i	0.843562	+	0.537032i	$0.180454\pi$
$919$	2.71205	+	36.1898i	0.0894623	+	1.19379i	−0.754100	+	0.656760i	$0.771927\pi$
$920$	−0.541631	−	0.167071i	−0.0178571	−	0.00550817i
$921$	5.15637	+	13.1382i	0.169908	+	0.432919i
$922$	19.6136	−	6.05001i	0.645941	−	0.199246i
$923$	−8.15222	−	10.2226i	−0.268334	−	0.336480i
$924$	60.1269	−	11.9159i	1.97803	−	0.392006i
$925$	8.26135	−	10.3594i	0.271631	−	0.340615i
$926$	−16.0857	+	40.9856i	−0.528608	+	1.34687i
$927$	0.676504	−	9.02732i	0.0222193	−	0.296496i
$928$	5.68001	−	0.856123i	0.186455	−	0.0281036i
$929$	−18.3924	+	17.0656i	−0.603434	+	0.559904i	−0.921605	−	0.388129i	$-0.873122\pi$
$929$	−18.3924	+	17.0656i	−0.603434	+	0.559904i	0.318172	+	0.948033i	$0.396931\pi$
$930$	7.72716			0.253384
$931$	−20.4659	−	4.30034i	−0.670744	−	0.140938i
$932$	−37.5805			−1.23099
$933$	16.0851	−	14.9248i	0.526604	−	0.488617i
$934$	0.237795	−	0.0358418i	0.00778089	−	0.00117278i
$935$	0.210748	−	2.81224i	0.00689220	−	0.0919700i
$936$	−1.12625	+	2.86964i	−0.0368127	+	0.0937972i
$937$	−9.74381	+	12.2183i	−0.318316	+	0.399156i	−0.915087	−	0.403255i	$-0.867879\pi$
$937$	−9.74381	+	12.2183i	−0.318316	+	0.399156i	0.596771	+	0.802412i	$0.296450\pi$
$938$	52.2091	−	39.2338i	1.70469	−	1.28103i
$939$	14.8401	+	18.6089i	0.484288	+	0.607278i
$940$	2.75744	−	0.850558i	0.0899378	−	0.0277422i
$941$	9.00338	+	22.9402i	0.293502	+	0.747830i	0.999226	+	0.0393435i	$0.0125267\pi$
$941$	9.00338	+	22.9402i	0.293502	+	0.747830i	−0.705724	+	0.708487i	$0.749378\pi$
$942$	5.59983	+	1.72732i	0.182452	+	0.0562791i
$943$	0.608682	+	8.12230i	0.0198214	+	0.264498i
$944$	−4.28342	−	18.7669i	−0.139414	−	0.610811i
$945$	−2.01245	+	1.08597i	−0.0654649	+	0.0353266i
$946$	3.37906	−	14.8047i	0.109863	−	0.481341i
$947$	18.5320	+	2.79324i	0.602208	+	0.0907682i	0.443068	−	0.896488i	$-0.353890\pi$
$947$	18.5320	+	2.79324i	0.602208	+	0.0907682i	0.159140	+	0.987256i	$0.449128\pi$
$948$	−18.2425	+	12.4375i	−0.592489	+	0.403952i
$949$	−7.01634	+	12.1526i	−0.227760	+	0.394492i
$950$	15.2616	+	26.4339i	0.495153	+	0.857631i
$951$	−41.3655	−	19.9206i	−1.34137	−	0.645970i
$952$	−0.426454	−	3.51174i	−0.0138215	−	0.113816i
$953$	−26.3793	+	12.7036i	−0.854510	+	0.411510i	−0.809250	−	0.587465i	$-0.800126\pi$
$953$	−26.3793	+	12.7036i	−0.854510	+	0.411510i	−0.0452602	+	0.998975i	$0.514412\pi$
$954$	8.48570	+	5.78545i	0.274735	+	0.187311i
$955$	0.279734	+	0.259555i	0.00905197	+	0.00839900i
$956$	−6.79954	−	6.30905i	−0.219913	−	0.204049i
$957$	5.98681	+	4.08174i	0.193526	+	0.131944i
$958$	15.4308	−	7.43108i	0.498546	−	0.240087i
$959$	−6.32156	+	6.43183i	−0.204134	+	0.207694i
$960$	−4.13887	−	1.99317i	−0.133581	−	0.0643294i
$961$	−17.3370	−	30.0286i	−0.559258	−	0.968664i
$962$	−13.9084	+	24.0901i	−0.448426	+	0.776697i
$963$	−19.2106	+	13.0976i	−0.619053	+	0.422063i
$964$	−64.4138	−	9.70881i	−2.07463	−	0.312700i
$965$	−0.194920	+	0.854002i	−0.00627471	+	0.0274913i
$966$	33.5860	+	38.3519i	1.08061	+	1.23395i
$967$	7.26505	+	31.8303i	0.233628	+	1.02359i	0.946603	+	0.322403i	$0.104490\pi$
$967$	7.26505	+	31.8303i	0.233628	+	1.02359i	−0.712974	+	0.701190i	$0.752652\pi$
$968$	−0.583795	−	7.79020i	−0.0187639	−	0.250386i
$969$	−14.2841	−	4.40606i	−0.458872	−	0.141543i
$970$	0.0853549	+	0.217481i	0.00274058	+	0.00698289i
$971$	14.8612	−	4.58409i	0.476920	−	0.147110i	−0.0469700	−	0.998896i	$-0.514957\pi$
$971$	14.8612	−	4.58409i	0.476920	−	0.147110i	0.523890	+	0.851786i	$0.324480\pi$
$972$	−15.7596	−	19.7620i	−0.505491	−	0.633865i
$973$	18.5186	−	35.7845i	0.593680	−	1.14720i
$974$	−29.1486	+	36.5512i	−0.933982	+	1.17118i
$975$	−18.4817	+	47.0905i	−0.591887	+	1.50810i
$976$	−2.18825	+	29.2001i	−0.0700441	+	0.934674i
$977$	32.5572	−	4.90720i	1.04160	−	0.156995i	0.394103	−	0.919066i	$-0.371055\pi$
$977$	32.5572	−	4.90720i	1.04160	−	0.156995i	0.647493	+	0.762071i	$0.275817\pi$
$978$	5.98300	−	5.55141i	0.191315	−	0.177515i
$979$	51.7687			1.65454
$980$	−3.32828	+	1.37313i	−0.106318	+	0.0438630i
$981$	−2.31646			−0.0739588
$982$	34.8624	−	32.3476i	1.11250	−	1.03225i
$983$	−7.42196	+	1.11868i	−0.236724	+	0.0356804i	−0.266333	−	0.963881i	$-0.585812\pi$
$983$	−7.42196	+	1.11868i	−0.236724	+	0.0356804i	0.0296088	+	0.999562i	$0.490574\pi$
$984$	0.146204	−	1.95095i	0.00466080	−	0.0621941i
$985$	0.138167	−	0.352043i	0.00440235	−	0.0112170i
$986$	2.24363	−	2.81343i	0.0714518	−	0.0895977i
$987$	−29.1987	−	7.55382i	−0.929404	−	0.240441i
$988$	−21.2087	−	26.5949i	−0.674740	−	0.846097i
$989$	6.40643	−	1.97612i	0.203713	−	0.0628370i
$990$	−0.974804	−	2.48376i	−0.0309813	−	0.0789391i
$991$	36.3170	+	11.2023i	1.15365	+	0.355853i	0.811819	−	0.583909i	$-0.198477\pi$
$991$	36.3170	+	11.2023i	1.15365	+	0.355853i	0.341829	+	0.939762i	$0.388954\pi$
$992$	4.91512	+	65.5878i	0.156055	+	2.08241i
$993$	−6.14905	−	26.9408i	−0.195134	−	0.854939i
$994$	14.1808	−	0.653422i	0.449788	−	0.0207253i
$995$	−1.34089	+	5.87482i	−0.0425091	+	0.186244i
$996$	−31.4191	−	4.73566i	−0.995552	−	0.150055i
$997$	−20.0677	+	13.6819i	−0.635550	+	0.433311i	−0.837765	−	0.546030i	$-0.816138\pi$
$997$	−20.0677	+	13.6819i	−0.635550	+	0.433311i	0.202215	+	0.979341i	$0.435186\pi$
$998$	−8.67495	+	15.0255i	−0.274601	+	0.475623i
$999$	−5.09131	−	8.81841i	−0.161082	−	0.279002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.g.a.11.4	yes	48
3.2	odd	2		441.2.bb.d.109.1		48
4.3	odd	2		784.2.bg.c.305.4		48
7.2	even	3		343.2.g.i.128.1		48
7.3	odd	6		343.2.e.c.246.7		48
7.4	even	3		343.2.e.d.246.7		48
7.5	odd	6		343.2.g.h.128.1		48
7.6	odd	2		343.2.g.g.312.4		48
49.3	odd	42		2401.2.a.i.1.4		24
49.9	even	21	inner	49.2.g.a.9.4	✓	48
49.15	even	7		343.2.g.i.67.1		48
49.24	odd	42		343.2.e.c.99.7		48
49.25	even	21		343.2.e.d.99.7		48
49.34	odd	14		343.2.g.h.67.1		48
49.40	odd	42		343.2.g.g.177.4		48
49.46	even	21		2401.2.a.h.1.4		24
147.107	odd	42		441.2.bb.d.352.1		48
196.107	odd	42		784.2.bg.c.401.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.4	✓	48	49.9	even	21	inner
49.2.g.a.11.4	yes	48	1.1	even	1	trivial
343.2.e.c.99.7		48	49.24	odd	42
343.2.e.c.246.7		48	7.3	odd	6
343.2.e.d.99.7		48	49.25	even	21
343.2.e.d.246.7		48	7.4	even	3
343.2.g.g.177.4		48	49.40	odd	42
343.2.g.g.312.4		48	7.6	odd	2
343.2.g.h.67.1		48	49.34	odd	14
343.2.g.h.128.1		48	7.5	odd	6
343.2.g.i.67.1		48	49.15	even	7
343.2.g.i.128.1		48	7.2	even	3
441.2.bb.d.109.1		48	3.2	odd	2
441.2.bb.d.352.1		48	147.107	odd	42
784.2.bg.c.305.4		48	4.3	odd	2
784.2.bg.c.401.4		48	196.107	odd	42
2401.2.a.h.1.4		24	49.46	even	21
2401.2.a.i.1.4		24	49.3	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)

\(f(q)\)	\(=\)	\(q+(1.51353 - 1.40435i) q^{2} +(-2.00916 + 0.302832i) q^{3} +(0.169112 - 2.25665i) q^{4} +(-0.0830372 + 0.211575i) q^{5} +(-2.61564 + 3.27991i) q^{6} +(1.07894 + 2.41576i) q^{7} +(-0.338532 - 0.424506i) q^{8} +(1.07830 - 0.332612i) q^{9} +O(q^{10})\)	\(q+(1.51353 - 1.40435i) q^{2} +(-2.00916 + 0.302832i) q^{3} +(0.169112 - 2.25665i) q^{4} +(-0.0830372 + 0.211575i) q^{5} +(-2.61564 + 3.27991i) q^{6} +(1.07894 + 2.41576i) q^{7} +(-0.338532 - 0.424506i) q^{8} +(1.07830 - 0.332612i) q^{9} +(0.171447 + 0.436839i) q^{10} +(-4.81478 - 1.48516i) q^{11} +(0.343612 + 4.58518i) q^{12} +(-1.11960 - 4.90527i) q^{13} +(5.02558 + 2.14111i) q^{14} +(0.102763 - 0.450235i) q^{15} +(3.36686 + 0.507473i) q^{16} +(2.03464 - 1.38719i) q^{17} +(1.16494 - 2.01773i) q^{18} +(1.49378 + 2.58730i) q^{19} +(0.463408 + 0.223166i) q^{20} +(-2.89933 - 4.52691i) q^{21} +(-9.37300 + 4.51380i) q^{22} +(-3.79491 - 2.58732i) q^{23} +(0.808719 + 0.750382i) q^{24} +(3.62739 + 3.36573i) q^{25} +(-8.58326 - 5.85197i) q^{26} +(3.42616 - 1.64995i) q^{27} +(5.63398 - 2.02625i) q^{28} +(0.637668 + 0.307085i) q^{29} +(-0.476753 - 0.825760i) q^{30} +(-4.05198 + 7.01823i) q^{31} +(6.70576 - 4.57191i) q^{32} +(10.1234 + 1.52586i) q^{33} +(1.13138 - 4.95690i) q^{34} +(-0.600707 + 0.0276793i) q^{35} +(-0.568233 - 2.48959i) q^{36} +(-0.200105 - 2.67021i) q^{37} +(5.89435 + 1.81816i) q^{38} +(3.73492 + 9.51643i) q^{39} +(0.117926 - 0.0363752i) q^{40} +(-1.10568 - 1.38648i) q^{41} +(-10.7456 - 2.77993i) q^{42} +(-0.910094 + 1.14122i) q^{43} +(-4.16573 + 10.6141i) q^{44} +(-0.0191666 + 0.255761i) q^{45} +(-9.37722 + 1.41339i) q^{46} +(4.11267 - 3.81600i) q^{47} -6.91825 q^{48} +(-4.67178 + 5.21292i) q^{49} +10.2168 q^{50} +(-3.66783 + 3.40325i) q^{51} +(-11.2588 + 1.69699i) q^{52} +(-0.329416 + 4.39576i) q^{53} +(2.86849 - 7.30878i) q^{54} +(0.714029 - 0.895364i) q^{55} +(0.660247 - 1.27583i) q^{56} +(-3.78475 - 4.74593i) q^{57} +(1.39638 - 0.430727i) q^{58} +(-2.06545 - 5.26268i) q^{59} +(-0.998643 - 0.308041i) q^{60} +(0.642677 + 8.57593i) q^{61} +(3.72327 + 16.3127i) q^{62} +(1.96693 + 2.24605i) q^{63} +(2.21348 - 9.69790i) q^{64} +(1.13080 + 0.170441i) q^{65} +(17.4649 - 11.9074i) q^{66} +(5.97762 - 10.3535i) q^{67} +(-2.78632 - 4.82605i) q^{68} +(8.40810 + 4.04913i) q^{69} +(-0.870316 + 0.885497i) q^{70} +(2.34135 - 1.12753i) q^{71} +(-0.506235 - 0.345145i) q^{72} +(-2.04449 - 1.89701i) q^{73} +(-4.05278 - 3.76043i) q^{74} +(-8.30726 - 5.66379i) q^{75} +(6.09123 - 2.93338i) q^{76} +(-1.60706 - 13.2337i) q^{77} +(19.0173 + 9.15826i) q^{78} +(2.40092 + 4.15851i) q^{79} +(-0.386944 + 0.670206i) q^{80} +(-9.18111 + 6.25958i) q^{81} +(-3.62058 - 0.545714i) q^{82} +(-1.53769 + 6.73708i) q^{83} +(-10.7059 + 5.77722i) q^{84} +(0.124545 + 0.545667i) q^{85} +(0.225221 + 3.00536i) q^{86} +(-1.37417 - 0.423876i) q^{87} +(0.999497 + 2.54668i) q^{88} +(-9.81790 + 3.02842i) q^{89} +(0.330169 + 0.414018i) q^{90} +(10.6420 - 7.99717i) q^{91} +(-6.48044 + 8.12622i) q^{92} +(6.01572 - 15.3278i) q^{93} +(0.865647 - 11.5513i) q^{94} +(-0.671447 + 0.101204i) q^{95} +(-12.0884 + 11.2164i) q^{96} +0.497851 q^{97} +(0.249890 + 14.4507i) q^{98} -5.68576 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

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