LMFDB - Embedded newform 403.2.bt.a.82.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(82,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("403.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bt (of order $30$, degree $8$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			82.5
Character	$\chi$	$=$	403.82
Dual form			403.2.bt.a.231.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.475411 + 2.23663i) q^{2} +(0.254115 - 0.0540139i) q^{3} +(-2.94943 - 1.31317i) q^{4} +(-0.204817 + 0.118251i) q^{5} +0.594042i q^{6} +(1.78231 + 2.45313i) q^{7} +(1.65121 - 2.27270i) q^{8} +(-2.67898 + 1.19276i) q^{9} +O(q^{10})$	\(q+(-0.475411 + 2.23663i) q^{2} +(0.254115 - 0.0540139i) q^{3} +(-2.94943 - 1.31317i) q^{4} +(-0.204817 + 0.118251i) q^{5} +0.594042i q^{6} +(1.78231 + 2.45313i) q^{7} +(1.65121 - 2.27270i) q^{8} +(-2.67898 + 1.19276i) q^{9} +(-0.167112 - 0.514319i) q^{10} +(-0.594006 - 0.817579i) q^{11} +(-0.820424 - 0.174386i) q^{12} +(1.48679 + 3.28473i) q^{13} +(-6.33409 + 2.82012i) q^{14} +(-0.0456600 + 0.0411124i) q^{15} +(-0.0224550 - 0.0249389i) q^{16} +(0.0736818 + 0.0535329i) q^{17} +(-1.39415 - 6.55895i) q^{18} +(-4.30279 + 1.39806i) q^{19} +(0.759378 - 0.0798138i) q^{20} +(0.585414 + 0.527109i) q^{21} +(2.11102 - 0.939888i) q^{22} +(2.74939 - 1.22411i) q^{23} +(0.296841 - 0.666715i) q^{24} +(-2.47203 + 4.28169i) q^{25} +(-8.05358 + 1.76380i) q^{26} +(-1.24687 + 0.905906i) q^{27} +(-2.03540 - 9.57581i) q^{28} +(-7.66575 - 1.62941i) q^{29} +(-0.0702462 - 0.121670i) q^{30} +(-4.10120 - 3.76566i) q^{31} +(4.93215 - 2.84758i) q^{32} +(-0.195107 - 0.175675i) q^{33} +(-0.154763 + 0.139349i) q^{34} +(-0.655133 - 0.291684i) q^{35} +9.46775 q^{36} +(-0.141072 + 0.0814479i) q^{37} +(-1.08136 - 10.2884i) q^{38} +(0.555236 + 0.754393i) q^{39} +(-0.0694471 + 0.660745i) q^{40} +(10.8588 - 3.52823i) q^{41} +(-1.45726 + 1.05876i) q^{42} +(3.43452 + 10.5704i) q^{43} +(0.678358 + 3.19142i) q^{44} +(0.407656 - 0.561090i) q^{45} +(1.43079 + 6.73134i) q^{46} +(8.79804 + 2.85866i) q^{47} +(-0.00705321 - 0.00512446i) q^{48} +(-0.678129 + 2.08707i) q^{49} +(-8.40134 - 7.56460i) q^{50} +(0.0216152 + 0.00962370i) q^{51} +(-0.0717574 - 11.6405i) q^{52} +(-0.0366674 + 0.348867i) q^{53} +(-1.43340 - 3.21948i) q^{54} +(0.218342 + 0.0972123i) q^{55} +8.51819 q^{56} +(-1.01789 + 0.587679i) q^{57} +(7.28877 - 16.3708i) q^{58} +(4.31640 + 1.40248i) q^{59} +(0.188658 - 0.0612988i) q^{60} +(7.04928 + 12.2097i) q^{61} +(10.3722 - 7.38265i) q^{62} +(-7.70075 - 4.44603i) q^{63} +(4.00345 + 12.3214i) q^{64} +(-0.692943 - 0.496955i) q^{65} +(0.485676 - 0.352864i) q^{66} -0.874140i q^{67} +(-0.147021 - 0.254648i) q^{68} +(0.632543 - 0.459570i) q^{69} +(0.963848 - 1.32662i) q^{70} +(-3.03550 - 6.81784i) q^{71} +(-1.71278 + 8.05801i) q^{72} +(0.128044 - 0.287593i) q^{73} +(-0.115102 - 0.354248i) q^{74} +(-0.396911 + 1.22157i) q^{75} +(14.5267 + 1.52681i) q^{76} +(0.946930 - 2.91435i) q^{77} +(-1.95127 + 0.883213i) q^{78} +(-11.4744 + 5.10871i) q^{79} +(0.00754823 + 0.00245257i) q^{80} +(5.61877 - 6.24028i) q^{81} +(2.72898 + 25.9645i) q^{82} +(4.55715 + 4.10328i) q^{83} +(-1.03445 - 2.32342i) q^{84} +(-0.0214216 - 0.00225150i) q^{85} +(-25.2749 + 2.65650i) q^{86} -2.03599 q^{87} -2.83894 q^{88} +(-8.17750 + 0.859490i) q^{89} +(1.06115 + 1.17853i) q^{90} +(-5.40798 + 9.50168i) q^{91} -9.71660 q^{92} +(-1.24557 - 0.735389i) q^{93} +(-10.5765 + 18.3190i) q^{94} +(0.715963 - 0.795157i) q^{95} +(1.09952 - 0.990017i) q^{96} +(-4.74157 + 10.6497i) q^{97} +(-4.34562 - 2.50894i) q^{98} +(2.56650 + 1.48177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9 + 3 * q^10 - 8 * q^12 - 6 * q^13 + 4 * q^14 - 45 * q^15 + 23 * q^16 + 27 * q^17 + 45 * q^18 - 15 * q^19 - 12 * q^20 - 76 * q^21 + 41 * q^22 - 10 * q^23 - 33 * q^24 + 96 * q^25 + 9 * q^26 - 24 * q^27 - 32 * q^28 + 13 * q^29 + 36 * q^30 + 2 * q^31 - 141 * q^32 - 93 * q^33 - 9 * q^34 - 43 * q^35 - 194 * q^36 + 3 * q^37 - 49 * q^38 + 50 * q^39 - 75 * q^40 - 15 * q^41 + 17 * q^42 + 33 * q^43 + 18 * q^44 - 15 * q^45 - 9 * q^46 - 59 * q^48 + 3 * q^49 + 36 * q^50 + 47 * q^51 - 56 * q^52 + 12 * q^53 - 33 * q^54 - 5 * q^55 - 50 * q^56 - 105 * q^57 - 3 * q^58 - 15 * q^59 + 90 * q^60 - 57 * q^61 - 72 * q^62 + 201 * q^63 + 13 * q^64 - 43 * q^65 + 22 * q^66 - 71 * q^68 - 7 * q^69 - 42 * q^71 + 90 * q^72 + 9 * q^73 - 113 * q^74 + 45 * q^75 + 14 * q^76 - 24 * q^77 + 61 * q^78 + 54 * q^79 + 30 * q^80 + 106 * q^81 + 16 * q^82 + 54 * q^83 + 60 * q^84 + 18 * q^85 + 84 * q^86 + 42 * q^87 - 98 * q^88 - 99 * q^89 + 11 * q^90 + 60 * q^91 + 266 * q^92 - 104 * q^93 + 33 * q^94 - 120 * q^95 + 204 * q^96 - 50 * q^97 - 15 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.475411	+	2.23663i	−0.336167	+	1.58154i	0.407639	+	0.913143i	$0.366352\pi$
$2$	−0.475411	+	2.23663i	−0.336167	+	1.58154i	−0.743805	+	0.668396i	$0.766981\pi$
$3$	0.254115	−	0.0540139i	0.146713	−	0.0311849i	−0.133969	−	0.990985i	$-0.542772\pi$
$3$	0.254115	−	0.0540139i	0.146713	−	0.0311849i	0.280683	+	0.959801i	$0.409439\pi$
$4$	−2.94943	−	1.31317i	−1.47471	−	0.656585i
$5$	−0.204817	+	0.118251i	−0.0915970	+	0.0528836i	−0.545099	−	0.838372i	$-0.683508\pi$
$5$	−0.204817	+	0.118251i	−0.0915970	+	0.0528836i	0.453502	+	0.891255i	$0.350175\pi$
$6$			0.594042i			0.242517i
$7$	1.78231	+	2.45313i	0.673648	+	0.927197i	0.999836	−	0.0181079i	$-0.00576423\pi$
$7$	1.78231	+	2.45313i	0.673648	+	0.927197i	−0.326188	+	0.945305i	$0.605764\pi$
$8$	1.65121	−	2.27270i	0.583791	−	0.803520i
$9$	−2.67898	+	1.19276i	−0.892993	+	0.397586i
$10$	−0.167112	−	0.514319i	−0.0528456	−	0.162642i
$11$	−0.594006	−	0.817579i	−0.179100	−	0.246509i	0.710023	−	0.704178i	$-0.248684\pi$
$11$	−0.594006	−	0.817579i	−0.179100	−	0.246509i	−0.889123	+	0.457669i	$0.848684\pi$
$12$	−0.820424	−	0.174386i	−0.236836	−	0.0503410i
$13$	1.48679	+	3.28473i	0.412360	+	0.911021i
$13$	1.48679	+	3.28473i	0.412360	+	0.911021i
$14$	−6.33409	+	2.82012i	−1.69286	+	0.753708i
$15$	−0.0456600	+	0.0411124i	−0.0117894	+	0.0106152i
$16$	−0.0224550	−	0.0249389i	−0.00561376	−	0.00623471i
$17$	0.0736818	+	0.0535329i	0.0178705	+	0.0129836i	0.596685	−	0.802476i	$-0.296484\pi$
$17$	0.0736818	+	0.0535329i	0.0178705	+	0.0129836i	−0.578814	+	0.815459i	$0.696484\pi$
$18$	−1.39415	−	6.55895i	−0.328604	−	1.54596i
$19$	−4.30279	+	1.39806i	−0.987128	+	0.320737i	−0.757710	−	0.652591i	$-0.773682\pi$
$19$	−4.30279	+	1.39806i	−0.987128	+	0.320737i	−0.229417	+	0.973328i	$0.573682\pi$
$20$	0.759378	−	0.0798138i	0.169802	−	0.0178469i
$21$	0.585414	+	0.527109i	0.127748	+	0.115025i
$22$	2.11102	−	0.939888i	0.450072	−	0.200385i
$23$	2.74939	−	1.22411i	0.573288	−	0.255244i	−0.0995520	−	0.995032i	$-0.531741\pi$
$23$	2.74939	−	1.22411i	0.573288	−	0.255244i	0.672840	+	0.739788i	$0.265074\pi$
$24$	0.296841	−	0.666715i	0.0605924	−	0.136093i
$25$	−2.47203	+	4.28169i	−0.494407	+	0.856337i
$26$	−8.05358	+	1.76380i	−1.57944	+	0.345909i
$27$	−1.24687	+	0.905906i	−0.239961	+	0.174342i
$28$	−2.03540	−	9.57581i	−0.384655	−	1.80966i
$29$	−7.66575	−	1.62941i	−1.42349	−	0.302573i	−0.569130	−	0.822248i	$-0.692720\pi$
$29$	−7.66575	−	1.62941i	−1.42349	−	0.302573i	−0.854364	+	0.519675i	$0.826053\pi$
$30$	−0.0702462	−	0.121670i	−0.0128251	−	0.0222138i
$31$	−4.10120	−	3.76566i	−0.736597	−	0.676332i
$31$	−4.10120	−	3.76566i	−0.736597	−	0.676332i
$32$	4.93215	−	2.84758i	0.871889	−	0.503385i
$33$	−0.195107	−	0.175675i	−0.0339637	−	0.0305811i
$34$	−0.154763	+	0.139349i	−0.0265416	+	0.0238982i
$35$	−0.655133	−	0.291684i	−0.110738	−	0.0493036i
$36$	9.46775			1.57796
$37$	−0.141072	+	0.0814479i	−0.0231921	+	0.0133900i	−0.511551	−	0.859253i	$-0.670929\pi$
$37$	−0.141072	+	0.0814479i	−0.0231921	+	0.0133900i	0.488359	+	0.872643i	$0.337596\pi$
$38$	−1.08136	−	10.2884i	−0.175419	−	1.66900i
$39$	0.555236	+	0.754393i	0.0889089	+	0.120800i
$40$	−0.0694471	+	0.660745i	−0.0109806	+	0.104473i
$41$	10.8588	−	3.52823i	1.69586	−	0.551017i	0.707976	−	0.706236i	$-0.249608\pi$
$41$	10.8588	−	3.52823i	1.69586	−	0.551017i	0.987880	+	0.155219i	$0.0496083\pi$
$42$	−1.45726	+	1.05876i	−0.224861	+	0.163371i
$43$	3.43452	+	10.5704i	0.523760	+	1.61197i	0.766756	+	0.641939i	$0.221870\pi$
$43$	3.43452	+	10.5704i	0.523760	+	1.61197i	−0.242996	+	0.970027i	$0.578130\pi$
$44$	0.678358	+	3.19142i	0.102266	+	0.481125i
$45$	0.407656	−	0.561090i	0.0607698	−	0.0836424i
$46$	1.43079	+	6.73134i	0.210959	+	0.992482i
$47$	8.79804	+	2.85866i	1.28333	+	0.416978i	0.869750	−	0.493492i	$-0.164280\pi$
$47$	8.79804	+	2.85866i	1.28333	+	0.416978i	0.413575	+	0.910470i	$0.364280\pi$
$48$	−0.00705321	−	0.00512446i	−0.00101804	−	0.000739652i
$49$	−0.678129	+	2.08707i	−0.0968756	+	0.298153i
$50$	−8.40134	−	7.56460i	−1.18813	−	1.06980i
$51$	0.0216152	+	0.00962370i	0.00302673	+	0.00134759i
$52$	−0.0717574	−	11.6405i	−0.00995095	−	1.61425i
$53$	−0.0366674	+	0.348867i	−0.00503666	+	0.0479206i	−0.996752	−	0.0805378i	$-0.974336\pi$
$53$	−0.0366674	+	0.348867i	−0.00503666	+	0.0479206i	0.991715	+	0.128458i	$0.0410029\pi$
$54$	−1.43340	−	3.21948i	−0.195062	−	0.438115i
$55$	0.218342	+	0.0972123i	0.0294413	+	0.0131081i
$56$	8.51819			1.13829
$57$	−1.01789	+	0.587679i	−0.134823	+	0.0778400i
$58$	7.28877	−	16.3708i	0.957062	−	2.14960i
$59$	4.31640	+	1.40248i	0.561947	+	0.182588i	0.576197	−	0.817311i	$-0.304536\pi$
$59$	4.31640	+	1.40248i	0.561947	+	0.182588i	−0.0142499	+	0.999898i	$0.504536\pi$
$60$	0.188658	−	0.0612988i	0.0243557	−	0.00791364i
$61$	7.04928	+	12.2097i	0.902568	+	1.56329i	0.824148	+	0.566374i	$0.191654\pi$
$61$	7.04928	+	12.2097i	0.902568	+	1.56329i	0.0784201	+	0.996920i	$0.475012\pi$
$62$	10.3722	−	7.38265i	1.31726	−	0.937597i
$63$	−7.70075	−	4.44603i	−0.970204	−	0.560147i
$64$	4.00345	+	12.3214i	0.500431	+	1.54017i
$65$	−0.692943	−	0.496955i	−0.0859490	−	0.0616397i
$66$	0.485676	−	0.352864i	0.0597826	−	0.0434346i
$67$		−	0.874140i		−	0.106793i	−0.998573	−	0.0533966i	$-0.982995\pi$
$67$		−	0.874140i		−	0.106793i	0.998573	−	0.0533966i	$-0.0170047\pi$
$68$	−0.147021	−	0.254648i	−0.0178289	−	0.0308806i
$69$	0.632543	−	0.459570i	0.0761493	−	0.0553257i
$70$	0.963848	−	1.32662i	0.115202	−	0.158562i
$71$	−3.03550	−	6.81784i	−0.360248	−	0.809129i	−0.999204	−	0.0398865i	$-0.987300\pi$
$71$	−3.03550	−	6.81784i	−0.360248	−	0.809129i	0.638957	−	0.769243i	$-0.279366\pi$
$72$	−1.71278	+	8.05801i	−0.201853	+	0.949645i
$73$	0.128044	−	0.287593i	0.0149865	−	0.0336602i	−0.905897	−	0.423498i	$-0.860802\pi$
$73$	0.128044	−	0.287593i	0.0149865	−	0.0336602i	0.920884	+	0.389838i	$0.127469\pi$
$74$	−0.115102	−	0.354248i	−0.0133803	−	0.0411805i
$75$	−0.396911	+	1.22157i	−0.0458313	+	0.141054i
$76$	14.5267	+	1.52681i	1.66632	+	0.175138i
$77$	0.946930	−	2.91435i	0.107913	−	0.332121i
$78$	−1.95127	+	0.883213i	−0.220938	+	0.100004i
$79$	−11.4744	+	5.10871i	−1.29097	+	0.574775i	−0.933308	−	0.359077i	$-0.883091\pi$
$79$	−11.4744	+	5.10871i	−1.29097	+	0.574775i	−0.357658	+	0.933853i	$0.616425\pi$
$80$	0.00754823	+	0.00245257i	0.000843918	+	0.000274206i
$81$	5.61877	−	6.24028i	0.624308	−	0.693365i
$82$	2.72898	+	25.9645i	0.301365	+	2.86730i
$83$	4.55715	+	4.10328i	0.500213	+	0.450393i	0.880203	−	0.474597i	$-0.157406\pi$
$83$	4.55715	+	4.10328i	0.500213	+	0.450393i	−0.379991	+	0.924990i	$0.624073\pi$
$84$	−1.03445	−	2.32342i	−0.112868	−	0.253506i
$85$	−0.0214216	−	0.00225150i	−0.00232350	−	0.000244210i
$86$	−25.2749	+	2.65650i	−2.72546	+	0.286457i
$87$	−2.03599			−0.218281
$88$	−2.83894			−0.302632
$89$	−8.17750	+	0.859490i	−0.866813	+	0.0911057i	−0.527487	−	0.849563i	$-0.676866\pi$
$89$	−8.17750	+	0.859490i	−0.866813	+	0.0911057i	−0.339326	+	0.940669i	$0.610199\pi$
$90$	1.06115	+	1.17853i	0.111855	+	0.124228i
$91$	−5.40798	+	9.50168i	−0.566910	+	0.996047i
$92$	−9.71660			−1.01303
$93$	−1.24557	−	0.735389i	−0.129160	−	0.0762563i
$94$	−10.5765	+	18.3190i	−1.09088	+	1.88946i
$95$	0.715963	−	0.795157i	0.0734563	−	0.0815814i
$96$	1.09952	−	0.990017i	0.112220	−	0.101043i
$97$	−4.74157	+	10.6497i	−0.481433	+	1.08132i	0.495662	+	0.868515i	$0.334925\pi$
$97$	−4.74157	+	10.6497i	−0.481433	+	1.08132i	−0.977095	+	0.212801i	$0.931741\pi$
$98$	−4.34562	−	2.50894i	−0.438974	−	0.253442i
$99$	2.56650	+	1.48177i	0.257943	+	0.148924i
$100$	12.9137	−	9.38233i	1.29137	−	0.938233i
$101$	11.8230	−	5.26395i	1.17644	−	0.523783i	0.277014	−	0.960866i	$-0.410655\pi$
$101$	11.8230	−	5.26395i	1.17644	−	0.523783i	0.899421	+	0.437083i	$0.143988\pi$
$102$	−0.0318008	+	0.0437700i	−0.00314875	+	0.00433388i
$103$	−0.789185	+	0.876479i	−0.0777607	+	0.0863620i	−0.780770	−	0.624819i	$-0.785173\pi$
$103$	−0.789185	+	0.876479i	−0.0777607	+	0.0863620i	0.703009	+	0.711181i	$0.251839\pi$
$104$	9.92020	+	2.04477i	0.972756	+	0.200506i
$105$	−0.182234	−	0.0387351i	−0.0177842	−	0.00378016i
$106$	−0.762857	−	0.247867i	−0.0740952	−	0.0240750i
$107$	−0.171630	+	1.63295i	−0.0165921	+	0.157864i	−0.999681	−	0.0252669i	$-0.991956\pi$
$107$	−0.171630	+	1.63295i	−0.0165921	+	0.157864i	0.983089	+	0.183131i	$0.0586231\pi$
$108$	4.86717	−	1.03455i	0.468344	−	0.0995496i
$109$	11.5866	+	3.76472i	1.10980	+	0.360595i	0.805865	−	0.592099i	$-0.201701\pi$
$109$	11.5866	+	3.76472i	1.10980	+	0.360595i	0.303931	+	0.952694i	$0.401701\pi$
$110$	−0.321231	+	0.442137i	−0.0306282	+	0.0421561i
$111$	−0.0314492	+	0.0283170i	−0.00298503	+	0.00268773i
$112$	0.0211566	−	0.0995339i	0.00199911	−	0.00940507i
$113$	0.158263	+	1.50577i	0.0148881	+	0.141651i	0.999441	−	0.0334375i	$-0.0106455\pi$
$113$	0.158263	+	1.50577i	0.0148881	+	0.141651i	−0.984553	+	0.175089i	$0.943979\pi$
$114$	−0.830507	−	2.55604i	−0.0777841	−	0.239395i
$115$	−0.418370	+	0.575837i	−0.0390132	+	0.0536971i
$116$	20.4699	+	14.8722i	1.90058	+	1.38085i
$117$	−7.90096	−	7.02635i	−0.730444	−	0.649587i
$118$	−5.18891	+	8.98745i	−0.477678	+	0.827362i
$119$			0.276163i			0.0253158i
$120$	0.0180418	+	0.171657i	0.00164699	+	0.0156700i
$121$	3.08359	−	9.49033i	0.280327	−	0.862757i
$122$	−30.6600	+	9.96204i	−2.77583	+	0.901920i
$123$	2.56881	−	1.48310i	0.231622	−	0.133727i
$124$	7.15125	+	16.4921i	0.642201	+	1.48103i
$125$		−	2.35180i		−	0.210351i
$126$	13.6052	−	15.1101i	1.21205	−	1.34611i
$127$	17.2827	−	3.67354i	1.53359	−	0.325974i	0.637711	−	0.770276i	$-0.279881\pi$
$127$	17.2827	−	3.67354i	1.53359	−	0.325974i	0.895877	+	0.444301i	$0.146548\pi$
$128$	−18.1337	+	1.90593i	−1.60281	+	0.168462i
$129$	1.44371	+	2.50058i	0.127112	+	0.220164i
$130$	1.44094	−	1.31360i	0.126379	−	0.115211i
$131$	1.06041	+	10.0891i	0.0926486	+	0.881493i	0.937849	+	0.347043i	$0.112814\pi$
$131$	1.06041	+	10.0891i	0.0926486	+	0.881493i	−0.845200	+	0.534449i	$0.820519\pi$
$132$	0.344762	+	0.774348i	0.0300077	+	0.0673984i
$133$	−11.0985	−	8.06354i	−0.962363	−	0.699198i
$134$	1.95513	+	0.415576i	0.168898	+	0.0359003i
$135$	0.148256	−	0.332990i	0.0127599	−	0.0286592i
$136$	0.243328	−	0.0790622i	0.0208652	−	0.00677953i
$137$	−0.0465163	+	0.0418835i	−0.00397416	+	0.00357835i	−0.671115	−	0.741353i	$-0.734184\pi$
$137$	−0.0465163	+	0.0418835i	−0.00397416	+	0.00357835i	0.667141	+	0.744931i	$0.267518\pi$
$138$	0.727171	+	1.63325i	0.0619009	+	0.139032i
$139$	15.0105	−	3.19058i	1.27318	−	0.270622i	0.478733	−	0.877961i	$-0.341096\pi$
$139$	15.0105	−	3.19058i	1.27318	−	0.270622i	0.794443	+	0.607339i	$0.207763\pi$
$140$	1.54924	+	1.72060i	0.130934	+	0.145417i
$141$	2.39012	+	0.251212i	0.201285	+	0.0211559i
$142$	16.6921	−	3.54802i	1.40077	−	0.297744i
$143$	1.80237	−	3.16672i	0.150722	−	0.264814i
$144$	0.0899026	+	0.0400272i	0.00749189	+	0.00333560i
$145$	1.76276	−	0.572754i	0.146389	−	0.0475647i
$146$	0.582366	+	0.423113i	0.0481969	+	0.0350171i
$147$	−0.0595924	+	0.566984i	−0.00491510	+	0.0467641i
$148$	0.523037	−	0.0549734i	0.0429934	−	0.00451878i
$149$		−	15.9464i		−	1.30638i	−0.757194	−	0.653190i	$-0.773430\pi$
$149$		−	15.9464i		−	1.30638i	0.757194	−	0.653190i	$-0.226570\pi$
$150$	−2.54350	−	1.46849i	−0.207676	−	0.119902i
$151$	−0.00858563	−	0.0118171i	−0.000698689	−	0.000961662i	0.808668	−	0.588266i	$-0.200189\pi$
$151$	−0.00858563	−	0.0118171i	−0.000698689	−	0.000961662i	−0.809366	+	0.587304i	$0.800189\pi$
$152$	−3.92745	+	12.0874i	−0.318558	+	0.980421i
$153$	−0.261244	−	0.0555291i	−0.0211203	−	0.00448926i
$154$	6.06816	+	3.50345i	0.488986	+	0.282316i
$155$	1.28529	+	0.286299i	0.103237	+	0.0229961i
$156$	−0.646982	−	2.95415i	−0.0518000	−	0.236521i
$157$	−0.651941	−	2.00647i	−0.0520306	−	0.160134i	0.921665	−	0.387987i	$-0.126829\pi$
$157$	−0.651941	−	2.00647i	−0.0520306	−	0.160134i	−0.973696	+	0.227853i	$0.926829\pi$
$158$	−5.97128	−	28.0927i	−0.475050	−	2.23493i
$159$	0.00952592	+	0.0906330i	0.000755454	+	0.00718767i
$160$	−0.673459	+	1.16647i	−0.0532416	+	0.0922172i
$161$	7.90316	+	4.56289i	0.622856	+	0.359606i
$162$	11.2860	+	15.5338i	0.886712	+	1.22045i
$163$	2.65326	+	0.278868i	0.207819	+	0.0218427i	0.207866	−	0.978157i	$-0.433348\pi$
$163$	2.65326	+	0.278868i	0.207819	+	0.0218427i	−4.68318e−5		1.00000i	$0.500015\pi$
$164$	−36.6604	−	3.85316i	−2.86269	−	0.300881i
$165$	0.0607350	+	0.0129096i	0.00472821	+	0.00100501i
$166$	−11.3441	+	8.24194i	−0.880470	+	0.639699i
$167$	4.96360	+	4.46925i	0.384095	+	0.345841i	0.838449	−	0.544981i	$-0.183463\pi$
$167$	4.96360	+	4.46925i	0.384095	+	0.345841i	−0.454354	+	0.890821i	$0.650130\pi$
$168$	2.16460	−	0.460100i	0.167003	−	0.0354975i
$169$	−8.57893	+	9.76739i	−0.659918	+	0.751338i
$170$	0.0152199	−	0.0468420i	0.00116731	−	0.00359262i
$171$	9.85954	−	8.87757i	0.753978	−	0.678885i
$172$	3.75082	−	35.6867i	0.285997	−	2.72108i
$173$	−9.20550	−	10.2237i	−0.699882	−	0.777297i	0.283476	−	0.958979i	$-0.408512\pi$
$173$	−9.20550	−	10.2237i	−0.699882	−	0.777297i	−0.983357	+	0.181682i	$0.941846\pi$
$174$	0.967935	−	4.55377i	0.0733789	−	0.345221i
$175$	−14.9095	+	1.56705i	−1.12705	+	0.118458i
$176$	−0.00705106	+	0.0331726i	−0.000531493	+	0.00250048i
$177$	1.17262	+	0.123247i	0.0881392	+	0.00926381i
$178$	1.96531	−	18.6987i	0.147306	−	1.40153i
$179$	18.9866	+	8.45338i	1.41913	+	0.631835i	0.965748	−	0.259483i	$-0.0835521\pi$
$179$	18.9866	+	8.45338i	1.41913	+	0.631835i	0.453378	+	0.891318i	$0.350219\pi$
$180$	−1.93916	+	1.11957i	−0.144536	+	0.0834481i
$181$	−4.91074	−	8.50564i	−0.365012	−	0.632220i	0.623766	−	0.781611i	$-0.285602\pi$
$181$	−4.91074	−	8.50564i	−0.365012	−	0.632220i	−0.988778	+	0.149392i	$0.952268\pi$
$182$	−18.6808	−	16.6129i	−1.38471	−	1.23143i
$183$	2.45082	+	2.72192i	0.181170	+	0.201210i
$184$	1.75780	−	8.26980i	0.129587	−	0.609658i
$185$	0.0192626	−	0.0333639i	0.00141622	−	0.00245296i
$186$	2.23696	−	2.43628i	0.164022	−	0.178637i
$187$		−	0.0920396i		−	0.00673060i
$188$	−22.1953	−	19.9847i	−1.61876	−	1.45754i
$189$	−4.44462	−	1.44414i	−0.323298	−	0.105046i
$190$	1.43810	+	1.97937i	0.104331	+	0.143599i
$191$	−8.95947	+	15.5183i	−0.648285	+	1.12286i	0.335248	+	0.942130i	$0.391180\pi$
$191$	−8.95947	+	15.5183i	−0.648285	+	1.12286i	−0.983532	+	0.180732i	$0.942153\pi$
$192$	1.68286	+	2.91480i	0.121450	+	0.210358i
$193$	8.02542	−	18.0254i	0.577682	−	1.29750i	−0.354348	−	0.935114i	$-0.615297\pi$
$193$	8.02542	−	18.0254i	0.577682	−	1.29750i	0.932030	−	0.362382i	$-0.118036\pi$
$194$	−21.5654	−	15.6682i	−1.54830	−	1.12491i
$195$	−0.202930	−	0.0888554i	−0.0145321	−	0.00636307i
$196$	4.74077	−	5.26516i	0.338626	−	0.376083i
$197$	−1.73663	−	2.39026i	−0.123730	−	0.170299i	0.742659	−	0.669670i	$-0.233564\pi$
$197$	−1.73663	−	2.39026i	−0.123730	−	0.170299i	−0.866388	+	0.499371i	$0.833564\pi$
$198$	−4.53433	+	5.03588i	−0.322241	+	0.357885i
$199$	9.44348	+	10.4880i	0.669431	+	0.743478i	0.978201	−	0.207658i	$-0.0665842\pi$
$199$	9.44348	+	10.4880i	0.669431	+	0.743478i	−0.308771	+	0.951136i	$0.599918\pi$
$200$	5.64913	+	12.6882i	0.399454	+	0.897188i
$201$	−0.0472157	−	0.222132i	−0.00333034	−	0.0156680i
$202$	6.15274	+	28.9464i	0.432905	+	2.03666i
$203$	−9.66556	−	21.7092i	−0.678389	−	1.52369i
$204$	−0.0511149	−	0.0567688i	−0.00357876	−	0.00397461i
$205$	−1.80685	+	2.00671i	−0.126196	+	0.140154i
$206$	−1.58518	−	2.18181i	−0.110444	−	0.152014i
$207$	−5.90550	+	6.55872i	−0.410461	+	0.455863i
$208$	0.0485316	−	0.110838i	0.00336506	−	0.00768520i
$209$	3.69891	+	2.68742i	0.255859	+	0.185892i
$210$	0.173272	−	0.389176i	0.0119569	−	0.0268557i
$211$	3.46955	+	6.00944i	0.238854	+	0.413707i	0.960386	−	0.278674i	$-0.0898950\pi$
$211$	3.46955	+	6.00944i	0.238854	+	0.413707i	−0.721532	+	0.692381i	$0.756562\pi$
$212$	0.566270	−	0.980809i	0.0388916	−	0.0673622i
$213$	−1.13962	−	1.56856i	−0.0780858	−	0.107476i
$214$	−3.57073	−	1.16020i	−0.244090	−	0.0793096i
$215$	−1.95341	−	1.75886i	−0.133221	−	0.119953i
$216$			4.32961i			0.294593i
$217$	1.92807	−	16.7723i	0.130886	−	1.13858i
$218$	−13.9287	+	24.1252i	−0.943371	+	1.63397i
$219$	0.0170041	−	0.0799978i	0.00114903	−	0.00540575i
$220$	−0.516329	−	0.573442i	−0.0348109	−	0.0386614i
$221$	−0.0662923	+	0.321617i	−0.00445931	+	0.0216343i
$222$	−0.0483835	−	0.0838026i	−0.00324729	−	0.00562446i
$223$	−1.62635	+	0.938976i	−0.108909	+	0.0628785i	−0.553465	−	0.832872i	$-0.686695\pi$
$223$	−1.62635	+	0.938976i	−0.108909	+	0.0628785i	0.444556	+	0.895751i	$0.353361\pi$
$224$	15.7761	+	7.02396i	1.05408	+	0.469308i
$225$	1.51551	−	14.4191i	0.101034	−	0.961273i
$226$	−3.44310	−	0.361885i	−0.229032	−	0.0240722i
$227$	−1.64485	+	7.73839i	−0.109172	+	0.513615i	0.889248	+	0.457426i	$0.151228\pi$
$227$	−1.64485	+	7.73839i	−0.109172	+	0.513615i	−0.998420	+	0.0561895i	$0.982105\pi$
$228$	3.77392	−	0.396654i	0.249934	−	0.0262691i
$229$	1.87636	−	8.82760i	0.123994	−	0.583344i	−0.871652	−	0.490125i	$-0.836951\pi$
$229$	1.87636	−	8.82760i	0.123994	−	0.583344i	0.995646	−	0.0932188i	$-0.0297156\pi$
$230$	−1.08904	−	1.20950i	−0.0718092	−	0.0797522i
$231$	0.0832140	−	0.791728i	0.00547508	−	0.0520919i
$232$	−16.3609	+	14.7314i	−1.07415	+	0.967166i
$233$	0.0106087	−	0.0326502i	0.000694998	−	0.00213899i	−0.950708	−	0.310086i	$-0.899642\pi$
$233$	0.0106087	−	0.0326502i	0.000694998	−	0.00213899i	0.951403	+	0.307947i	$0.0996421\pi$
$234$	19.4716	−	14.3312i	1.27290	−	0.936857i
$235$	−2.14003	+	0.454877i	−0.139600	+	0.0296729i
$236$	−10.8892	−	9.80469i	−0.708827	−	0.638231i
$237$	−2.63987	+	1.91798i	−0.171478	+	0.124586i
$238$	−0.617676	−	0.131291i	−0.0400380	−	0.00851034i
$239$	−20.8379	−	2.19015i	−1.34789	−	0.141669i	−0.597079	−	0.802183i	$-0.703672\pi$
$239$	−20.8379	−	2.19015i	−1.34789	−	0.141669i	−0.750814	+	0.660513i	$0.770339\pi$
$240$	0.00205059		0.000215526i	0.000132365		1.39121e-5i
$241$	−16.3205	−	22.4632i	−1.05129	−	1.44698i	−0.887683	−	0.460455i	$-0.847686\pi$
$241$	−16.3205	−	22.4632i	−1.05129	−	1.44698i	−0.163610	−	0.986525i	$-0.552314\pi$
$242$	19.7604	+	11.4087i	1.27025	+	0.733378i
$243$	3.40258	−	5.89345i	0.218276	−	0.378065i
$244$	−4.75792	−	45.2686i	−0.304595	−	2.89803i
$245$	−0.107906	−	0.507657i	−0.00689385	−	0.0324330i
$246$	2.09592	+	6.45057i	0.133631	+	0.411273i
$247$	−10.9896	−	12.0549i	−0.699251	−	0.767035i
$248$	−15.3301	+	3.10289i	−0.973465	+	0.197034i
$249$	1.37968	+	0.796556i	0.0874334	+	0.0504797i
$250$	5.26011	+	1.11807i	0.332679	+	0.0707130i
$251$	−3.79149	+	11.6690i	−0.239317	+	0.736542i	0.757202	+	0.653180i	$0.226566\pi$
$251$	−3.79149	+	11.6690i	−0.239317	+	0.736542i	−0.996519	+	0.0833615i	$0.973434\pi$
$252$	16.8744	+	23.2257i	1.06299	+	1.46308i
$253$	−2.63396	−	1.52072i	−0.165596	−	0.0956067i
$254$			40.4015i			2.53501i
$255$	−0.00556518		0.000584924i	−0.000348505		3.66293e-5i
$256$	1.64969	−	15.6957i	0.103105	−	0.980983i
$257$	−23.9997	−	17.4368i	−1.49706	−	1.08768i	−0.971535	−	0.236896i	$-0.923870\pi$
$257$	−23.9997	−	17.4368i	−1.49706	−	1.08768i	−0.525522	−	0.850780i	$-0.676130\pi$
$258$	−6.27924	+	2.04025i	−0.390928	+	0.127020i
$259$	−0.451236	−	0.200903i	−0.0280384	−	0.0124835i
$260$	1.39120	+	2.37569i	0.0862785	+	0.147334i
$261$	22.4799	−	4.77824i	1.39147	−	0.295766i
$262$	−23.0699	−	2.42474i	−1.42526	−	0.149801i
$263$	3.69521	+	4.10394i	0.227856	+	0.253060i	0.846222	−	0.532830i	$-0.178872\pi$
$263$	3.69521	+	4.10394i	0.227856	+	0.253060i	−0.618366	+	0.785890i	$0.712205\pi$
$264$	−0.721418	+	0.153342i	−0.0444002	+	0.00943755i
$265$	−0.0337439	−	0.0757900i	−0.00207287	−	0.00465574i
$266$	23.3116	−	20.9898i	1.42932	−	1.28697i
$267$	−2.03160	+	0.660108i	−0.124332	+	0.0403979i
$268$	−1.14789	+	2.57821i	−0.0701188	+	0.157489i
$269$	−18.6933	−	3.97338i	−1.13975	−	0.242261i	−0.400894	−	0.916124i	$-0.631300\pi$
$269$	−18.6933	−	3.97338i	−1.13975	−	0.242261i	−0.738856	+	0.673863i	$0.764634\pi$
$270$	0.674293	+	0.489903i	0.0410362	+	0.0298145i
$271$	−3.68049	−	8.26651i	−0.223574	−	0.502155i	0.766578	−	0.642151i	$-0.221958\pi$
$271$	−3.68049	−	8.26651i	−0.223574	−	0.502155i	−0.990152	+	0.139996i	$0.955291\pi$
$272$	−0.000319477	−	0.00303962i	−1.93712e−5	−	0.000184304i
$273$	−0.861027	+	2.70663i	−0.0521117	+	0.163813i
$274$	−0.0715637	−	0.123952i	−0.00432332	−	0.00748821i
$275$	4.96902	−	0.522265i	0.299643	−	0.0314938i
$276$	−2.46913	+	0.524831i	−0.148624	+	0.0315911i
$277$	−7.82414	+	8.68958i	−0.470107	+	0.522106i	−0.930837	−	0.365434i	$-0.880921\pi$
$277$	−7.82414	+	8.68958i	−0.470107	+	0.522106i	0.460731	+	0.887540i	$0.347587\pi$
$278$			35.0899i			2.10455i
$279$	15.4785	+	5.19637i	0.926676	+	0.311099i
$280$	−1.74467	+	1.00729i	−0.104264	+	0.0601969i
$281$	16.2174	−	5.26937i	0.967451	−	0.314344i	0.217665	−	0.976024i	$-0.430156\pi$
$281$	16.2174	−	5.26937i	0.967451	−	0.314344i	0.749787	+	0.661680i	$0.230156\pi$
$282$	−1.69816	+	5.22640i	−0.101124	+	0.311228i
$283$	1.11538	+	10.6121i	0.0663025	+	0.630826i	0.976331	+	0.216281i	$0.0693926\pi$
$283$	1.11538	+	10.6121i	0.0663025	+	0.630826i	−0.910029	+	0.414545i	$0.863941\pi$
$284$			24.0949i			1.42977i
$285$	0.138988	−	0.240734i	0.00823291	−	0.0142598i
$286$	6.22592	+	5.53673i	0.368147	+	0.327394i
$287$	28.0089	+	20.3496i	1.65331	+	1.20120i
$288$	−9.81665	+	13.5115i	−0.578452	+	0.796170i
$289$	−5.25073	−	16.1601i	−0.308866	−	0.950592i
$290$	0.443008	+	4.21494i	0.0260143	+	0.247510i
$291$	−0.629671	+	2.96237i	−0.0369120	+	0.173657i
$292$	−0.755316	+	0.680090i	−0.0442015	+	0.0397992i
$293$	−7.20031	+	9.91038i	−0.420647	+	0.578971i	−0.965775	−	0.259382i	$-0.916481\pi$
$293$	−7.20031	+	9.91038i	−0.420647	+	0.578971i	0.545128	+	0.838353i	$0.316481\pi$
$294$	−1.23981	−	0.402837i	−0.0723069	−	0.0234939i
$295$	−1.04992	+	0.223167i	−0.0611286	+	0.0129933i
$296$	−0.0478331	+	0.455102i	−0.00278024	+	0.0264523i
$297$	1.48130	+	0.481304i	0.0859538	+	0.0279281i
$298$	35.6663	+	7.58110i	2.06609	+	0.439161i
$299$	8.10863	+	7.21103i	0.468934	+	0.417025i
$300$	2.77478	−	3.08171i	0.160202	−	0.177923i
$301$	−19.8092	+	27.2650i	−1.14178	+	1.57153i
$302$	0.0305123	−	0.0135849i	0.00175578	−	0.000781725i
$303$	2.72009	−	1.97626i	0.156265	−	0.113533i
$304$	0.131485	+	0.0759131i	0.00754120	+	0.00435392i
$305$	−2.88763	−	1.66717i	−0.165345	−	0.0954621i
$306$	0.248397	−	0.557908i	0.0141999	−	0.0318935i
$307$	19.0283	−	17.1332i	1.08600	−	0.977842i	0.0861735	−	0.996280i	$-0.472536\pi$
$307$	19.0283	−	17.1332i	1.08600	−	0.977842i	0.999830	+	0.0184382i	$0.00586938\pi$
$308$	−6.61994	+	7.35219i	−0.377206	+	0.418930i
$309$	−0.153202	+	0.265353i	−0.00871535	+	0.0150954i
$310$	−1.25139	+	2.73861i	−0.0710741	+	0.155543i
$311$	11.5223			0.653369			0.326684	−	0.945133i	$-0.394069\pi$
$311$	11.5223			0.653369			0.326684	+	0.945133i	$0.394069\pi$
$312$	2.63132	−	0.0162207i	0.148969	−	0.000918315i
$313$	1.27807	+	1.41944i	0.0722405	+	0.0802312i	0.778182	−	0.628039i	$-0.216142\pi$
$313$	1.27807	+	1.41944i	0.0722405	+	0.0802312i	−0.705941	+	0.708271i	$0.749476\pi$
$314$	4.79768	−	0.504256i	0.270749	−	0.0284568i
$315$	2.10300			0.118490
$316$	40.5514			2.28119
$317$	8.62152	−	0.906158i	0.484233	−	0.0508949i	0.140733	−	0.990048i	$-0.455054\pi$
$317$	8.62152	−	0.906158i	0.484233	−	0.0508949i	0.343500	+	0.939153i	$0.388387\pi$
$318$	−0.207242	−	0.0217820i	−0.0116215	−	0.00122147i
$319$	3.22133	+	7.23523i	0.180360	+	0.405095i
$320$	−2.27699	−	2.05021i	−0.127288	−	0.114610i
$321$	0.0445882	+	0.424229i	0.00248867	+	0.0236781i
$322$	−13.9628	+	15.5072i	−0.778115	+	0.864184i
$323$	−0.391880	−	0.127329i	−0.0218048	−	0.00708480i
$324$	−24.7667	+	11.0269i	−1.37593	+	0.612603i
$325$	−17.7396	−	1.75401i	−0.984015	−	0.0972952i
$326$	−1.88512	+	5.80179i	−0.104407	+	0.321331i
$327$	3.14768	+	0.330835i	0.174067	+	0.0182952i
$328$	9.91154	−	30.5046i	0.547273	−	1.68433i
$329$	8.66813	+	26.6777i	0.477889	+	1.47079i
$330$	−0.0577482	+	0.129705i	−0.00317893	+	0.00714000i
$331$	−4.68078	+	22.0213i	−0.257279	+	1.21040i	0.639803	+	0.768539i	$0.279016\pi$
$331$	−4.68078	+	22.0213i	−0.257279	+	1.21040i	−0.897082	+	0.441864i	$0.854317\pi$
$332$	−8.05270	−	18.0866i	−0.441949	−	0.992634i
$333$	0.280781	−	0.386462i	0.0153867	−	0.0211780i
$334$	−12.3558	+	8.97703i	−0.676081	+	0.491201i
$335$	0.103368	+	0.179039i	0.00564760	+	0.00978194i
$336$		−	0.0264358i		−	0.00144219i
$337$	−4.06542	+	2.95370i	−0.221457	+	0.160898i	−0.692982	−	0.720954i	$-0.743704\pi$
$337$	−4.06542	+	2.95370i	−0.221457	+	0.160898i	0.471525	+	0.881853i	$0.343704\pi$
$338$	−17.7676	−	23.8315i	−0.966428	−	1.29626i
$339$	0.121550	+	0.374091i	0.00660167	+	0.0203178i
$340$	0.0602250	+	0.0347709i	0.00326616	+	0.00188572i
$341$	−0.642585	+	5.58988i	−0.0347979	+	0.302709i
$342$	15.1685	+	26.2727i	0.820221	+	1.42066i
$343$	13.8583	−	4.50284i	0.748279	−	0.243131i
$344$	29.6944	+	9.64829i	1.60101	+	0.520201i
$345$	−0.0752111	+	0.168927i	−0.00404923	+	0.00909472i
$346$	27.2432	−	15.7289i	1.46460	−	0.845589i
$347$	−25.0681			−1.34572			−0.672862	−	0.739768i	$-0.734935\pi$
$347$	−25.0681			−1.34572			−0.672862	+	0.739768i	$0.734935\pi$
$348$	6.00502	+	2.67361i	0.321903	+	0.143320i
$349$	7.55959	+	16.9791i	0.404655	+	0.908871i	0.994826	+	0.101592i	$0.0323937\pi$
$349$	7.55959	+	16.9791i	0.404655	+	0.908871i	−0.590171	+	0.807278i	$0.700940\pi$
$350$	3.58322	−	34.0920i	0.191531	−	1.82230i
$351$	−4.82949	−	2.74875i	−0.257779	−	0.146718i
$352$	−5.25785	−	2.34094i	−0.280244	−	0.124773i
$353$	−3.84264	−	3.45993i	−0.204523	−	0.184154i	0.560503	−	0.828152i	$-0.310608\pi$
$353$	−3.84264	−	3.45993i	−0.204523	−	0.184154i	−0.765027	+	0.643998i	$0.777274\pi$
$354$	−0.833133	+	2.56412i	−0.0442805	+	0.136281i
$355$	1.42794	+	1.03746i	0.0757873	+	0.0550627i
$356$	25.2476	+	8.20344i	1.33812	+	0.434782i
$357$	0.0149166	+	0.0701773i	0.000789472	+	0.00371418i
$358$	−27.9336	+	38.4473i	−1.47634	+	2.03200i
$359$	−4.98976	−	23.4750i	−0.263350	−	1.23896i	−0.888653	−	0.458581i	$-0.848358\pi$
$359$	−4.98976	−	23.4750i	−0.263350	−	1.23896i	0.625303	−	0.780382i	$-0.284975\pi$
$360$	−0.602062	−	1.85296i	−0.0317315	−	0.0976594i
$361$	1.18811	−	0.863209i	0.0625319	−	0.0454321i
$362$	21.3586	−	6.93984i	1.12259	−	0.364750i
$363$	0.270979	−	2.57819i	0.0142227	−	0.135320i
$364$	28.4278	−	20.9229i	1.49002	−	1.09666i
$365$	0.00778248	+	0.0740453i	0.000407353	+	0.00387571i
$366$	−7.25308	+	4.18757i	−0.379125	+	0.218888i
$367$	−34.5294			−1.80242			−0.901210	−	0.433383i	$-0.857320\pi$
$367$	−34.5294			−1.80242			−0.901210	+	0.433383i	$0.857320\pi$
$368$	−0.0922656	−	0.0410793i	−0.00480968	−	0.00214141i
$369$	−24.8821	+	22.4040i	−1.29531	+	1.16630i
$370$	0.0654651	+	0.0589451i	0.00340337	+	0.00306441i
$371$	−0.921170	+	0.531838i	−0.0478248	+	0.0276117i
$372$	2.70804	+	3.80463i	0.140405	+	0.197261i
$373$	16.8561	+	29.1957i	0.872778	+	1.51170i	0.859111	+	0.511789i	$0.171017\pi$
$373$	16.8561	+	29.1957i	0.872778	+	1.51170i	0.0136671	+	0.999907i	$0.495649\pi$
$374$	0.205859	+	0.0437567i	0.0106447	+	0.00226260i
$375$	−0.127030	−	0.597627i	−0.00655978	−	0.0308613i
$376$	21.0243	−	15.2750i	1.08424	−	0.787750i
$377$	−6.04517	−	27.6025i	−0.311342	−	1.42160i
$378$	5.34304	−	9.25442i	0.274816	−	0.475996i
$379$	3.25639	−	7.31397i	0.167270	−	0.375694i	−0.810389	−	0.585892i	$-0.800744\pi$
$379$	3.25639	−	7.31397i	0.167270	−	0.375694i	0.977659	+	0.210198i	$0.0674110\pi$
$380$	−3.15586	+	1.40508i	−0.161892	+	0.0720790i
$381$	4.19337	−	1.86701i	0.214833	−	0.0956497i
$382$	−30.4492	−	27.4166i	−1.55792	−	1.40276i
$383$	−12.8894	+	1.35473i	−0.658616	+	0.0692233i	−0.427940	−	0.903807i	$-0.640760\pi$
$383$	−12.8894	+	1.35473i	−0.658616	+	0.0692233i	−0.230676	+	0.973031i	$0.574094\pi$
$384$	−4.50511	+	1.46380i	−0.229901	+	0.0746992i
$385$	0.150678	+	0.708885i	0.00767927	+	0.0361281i
$386$	36.5008	+	26.5194i	1.85784	+	1.34980i
$387$	−21.8089	−	24.2212i	−1.10861	−	1.23124i
$388$	27.9698	−	25.1841i	1.41995	−	1.27853i
$389$	13.5036	−	6.01218i	0.684658	−	0.304829i	−0.0347710	−	0.999395i	$-0.511070\pi$
$389$	13.5036	−	6.01218i	0.684658	−	0.304829i	0.719429	+	0.694566i	$0.244404\pi$
$390$	0.295212	−	0.411637i	0.0149487	−	0.0208441i
$391$	0.268110	+	0.0569886i	0.0135589	+	0.00288204i
$392$	3.62354	+	4.98737i	0.183016	+	0.251900i
$393$	0.814420	+	2.50653i	0.0410821	+	0.126438i
$394$	6.17175	−	2.74784i	0.310929	−	0.138434i
$395$	1.74603	−	2.40321i	0.0878525	−	0.120919i
$396$	−5.62390	−	7.74064i	−0.282612	−	0.388982i
$397$			16.4459i			0.825394i	0.910868	+	0.412697i	$0.135413\pi$
$397$			16.4459i			0.825394i	−0.910868	+	0.412697i	$0.864587\pi$
$398$	−27.9475	+	16.1355i	−1.40088	+	0.808799i
$399$	−3.25584	−	1.44960i	−0.162996	−	0.0725705i
$400$	0.162290	−	0.0344958i	0.00811450	−	0.00172479i
$401$	6.56187	−	30.8712i	0.327684	−	1.54163i	−0.438334	−	0.898812i	$-0.644431\pi$
$401$	6.56187	−	30.8712i	0.327684	−	1.54163i	0.766018	−	0.642820i	$-0.222236\pi$
$402$	0.519275			0.0258991
$403$	6.27157	−	19.0701i	0.312409	−	0.949948i
$404$	−41.7837			−2.07881
$405$	−0.412901	+	1.94254i	−0.0205172	+	0.0965258i
$406$	53.1507	−	11.2975i	2.63782	−	0.560687i
$407$	0.150388	+	0.0669570i	0.00745445	+	0.00331893i
$408$	0.0575630	−	0.0332340i	0.00284979	−	0.00164533i
$409$		−	26.7052i		−	1.32049i	−0.751051	−	0.660244i	$-0.770453\pi$
$409$		−	26.7052i		−	1.32049i	0.751051	−	0.660244i	$-0.229547\pi$
$410$	−3.62928	−	4.99527i	−0.179237	−	0.246699i
$411$	−0.00955822	+	0.0131558i	−0.000471472	+	0.000648926i
$412$	3.47861	−	1.54878i	0.171379	−	0.0763028i
$413$	4.25266	+	13.0884i	0.209260	+	0.644036i
$414$	−11.8619	−	16.3265i	−0.582982	−	0.802405i
$415$	−1.41860	−	0.301533i	−0.0696364	−	0.0148017i
$416$	16.6866	+	11.9670i	0.818127	+	0.586733i
$417$	3.64206	−	1.62155i	0.178353	−	0.0794077i
$418$	−7.76927	+	6.99548i	−0.380007	+	0.342160i
$419$	−0.840269	−	0.933214i	−0.0410498	−	0.0455905i	0.722270	−	0.691611i	$-0.243099\pi$
$419$	−0.840269	−	0.933214i	−0.0410498	−	0.0455905i	−0.763320	+	0.646021i	$0.776432\pi$
$420$	0.486621	+	0.353551i	0.0237447	+	0.0172515i
$421$	1.14037	+	5.36503i	0.0555783	+	0.261475i	0.997160	−	0.0753085i	$-0.0239942\pi$
$421$	1.14037	+	5.36503i	0.0555783	+	0.261475i	−0.941582	+	0.336784i	$0.890661\pi$
$422$	−15.0904	+	4.90317i	−0.734589	+	0.238682i
$423$	−26.9794	+	2.83565i	−1.31179	+	0.137874i
$424$	0.732324	+	0.659388i	0.0355648	+	0.0320227i
$425$	−0.411355	+	0.183147i	−0.0199537	+	0.00888394i
$426$	4.05008	−	1.80321i	0.196227	−	0.0873660i
$427$	−17.3881	+	39.0543i	−0.841468	+	1.88997i
$428$	2.65056	−	4.59090i	0.128120	−	0.221910i
$429$	0.286963	−	0.902064i	0.0138547	−	0.0435520i
$430$	4.86259	−	3.53288i	0.234495	−	0.170371i
$431$	6.68575	+	31.4540i	0.322041	+	1.51509i	0.779811	+	0.626015i	$0.215315\pi$
$431$	6.68575	+	31.4540i	0.322041	+	1.51509i	−0.457770	+	0.889071i	$0.651352\pi$
$432$	0.0505909	+	0.0107534i	0.00243405	+	0.000517374i
$433$	−8.06266	−	13.9649i	−0.387467	−	0.671112i	0.604641	−	0.796498i	$-0.293317\pi$
$433$	−8.06266	−	13.9649i	−0.387467	−	0.671112i	−0.992108	+	0.125386i	$0.959983\pi$
$434$	36.5970	+	12.2861i	1.75671	+	0.589754i
$435$	0.417007	−	0.240759i	0.0199939	−	0.0115435i
$436$	−29.2302	−	26.3190i	−1.39987	−	1.26045i
$437$	−10.1187	+	9.11090i	−0.484042	+	0.435833i
$438$	0.170842	+	0.0760637i	0.00816314	+	0.00363447i
$439$	−3.51238			−0.167637			−0.0838185	−	0.996481i	$-0.526712\pi$
$439$	−3.51238			−0.167637			−0.0838185	+	0.996481i	$0.526712\pi$
$440$	0.581464	−	0.335708i	0.0277202	−	0.0160043i
$441$	−0.672673	−	6.40006i	−0.0320321	−	0.304765i
$442$	−0.687824	−	0.301172i	−0.0327164	−	0.0143253i
$443$	−1.36196	+	12.9582i	−0.0647088	+	0.615663i	0.913327	+	0.407227i	$0.133504\pi$
$443$	−1.36196	+	12.9582i	−0.0647088	+	0.615663i	−0.978036	+	0.208436i	$0.933163\pi$
$444$	0.129942	−	0.0422208i	0.00616679	−	0.00200371i
$445$	1.57326	−	1.14304i	0.0745795	−	0.0541852i
$446$	−1.32696	−	4.08396i	−0.0628333	−	0.193381i
$447$	−0.861327	−	4.05222i	−0.0407394	−	0.191664i
$448$	−23.0905	+	31.7814i	−1.09093	+	1.50153i
$449$	−4.06184	−	19.1095i	−0.191690	−	0.901831i	−0.963859	−	0.266414i	$-0.914161\pi$
$449$	−4.06184	−	19.1095i	−0.191690	−	0.901831i	0.772169	−	0.635418i	$-0.219172\pi$
$450$	31.5297	+	10.2446i	1.48633	+	0.482937i
$451$	−9.33479	−	6.78212i	−0.439558	−	0.319358i
$452$	1.51055	−	4.64899i	0.0710503	−	0.218670i
$453$	−0.00282003	−	0.00253916i	−0.000132496	−	0.000119300i
$454$	−16.5260	−	7.35784i	−0.775603	−	0.345321i
$455$	−0.0159389	−	2.58561i	−0.000747226	−	0.121215i
$456$	−0.345135	+	3.28374i	−0.0161624	+	0.153775i
$457$	1.59642	+	3.58561i	0.0746772	+	0.167728i	0.947027	−	0.321155i	$-0.104071\pi$
$457$	1.59642	+	3.58561i	0.0746772	+	0.167728i	−0.872349	+	0.488883i	$0.837404\pi$
$458$	18.8521	+	8.39348i	0.880899	+	0.392202i
$459$	−0.140368			−0.00655180
$460$	1.99013	−	1.14900i	0.0927901	−	0.0535724i
$461$	8.24364	−	18.5155i	0.383944	−	0.862353i	−0.613417	−	0.789759i	$-0.710206\pi$
$461$	8.24364	−	18.5155i	0.383944	−	0.862353i	0.997362	−	0.0725943i	$-0.0231278\pi$
$462$	1.73125	+	0.562516i	0.0805449	+	0.0261706i
$463$	15.1477	−	4.92178i	0.703973	−	0.228735i	0.0649122	−	0.997891i	$-0.479323\pi$
$463$	15.1477	−	4.92178i	0.703973	−	0.228735i	0.639061	+	0.769156i	$0.279323\pi$
$464$	0.131499	+	0.227763i	0.00610470	+	0.0105736i
$465$	0.342076	+	0.00332951i	0.0158634	+	0.000154403i
$466$	0.0679831	+	0.0392500i	0.00314925	+	0.00181822i
$467$	−6.68941	−	20.5879i	−0.309549	−	0.952694i	−0.977940	−	0.208884i	$-0.933017\pi$
$467$	−6.68941	−	20.5879i	−0.309549	−	0.952694i	0.668391	−	0.743810i	$-0.266983\pi$
$468$	14.0765	+	31.0990i	0.650688	+	1.43755i
$469$	2.14438	−	1.55798i	0.0990183	−	0.0719410i
$470$		−	5.00272i		−	0.230758i
$471$	−0.274045	−	0.474660i	−0.0126273	−	0.0218712i
$472$	10.3147	−	7.49407i	0.474773	−	0.344943i
$473$	6.60199	−	9.08686i	0.303560	−	0.417814i
$474$	−3.03479	−	6.81625i	−0.139392	−	0.313081i
$475$	4.65058	−	21.8793i	0.213383	−	1.00389i
$476$	0.362649	−	0.814524i	0.0166220	−	0.0373336i
$477$	−0.317883	−	0.978344i	−0.0145549	−	0.0447953i
$478$	14.8052	−	45.5656i	0.677172	−	2.08412i
$479$	14.7735	+	1.55275i	0.675016	+	0.0709471i	0.435833	−	0.900027i	$-0.356454\pi$
$479$	14.7735	+	1.55275i	0.675016	+	0.0709471i	0.239183	+	0.970974i	$0.423120\pi$
$480$	−0.108131	+	0.332793i	−0.00493548	+	0.0151898i
$481$	−0.477279	−	0.342288i	−0.0217620	−	0.0156070i
$482$	58.0009	−	25.8236i	2.64187	−	1.17623i
$483$	2.25477	+	0.732620i	0.102596	+	0.0333353i
$484$	−21.5573	+	23.9418i	−0.979875	+	1.08826i
$485$	−0.288190	−	2.74195i	−0.0130860	−	0.124505i
$486$	11.5639	+	10.4122i	0.524548	+	0.472305i
$487$	16.6086	+	37.3036i	0.752609	+	1.69039i	0.723021	+	0.690826i	$0.242753\pi$
$487$	16.6086	+	37.3036i	0.752609	+	1.69039i	0.0295876	+	0.999562i	$0.490581\pi$
$488$	39.3889	+	4.13994i	1.78305	+	0.187406i
$489$	0.689295	−	0.0724479i	0.0311710	−	0.00327621i
$490$	1.18674			0.0536116
$491$	−16.6974			−0.753545			−0.376773	−	0.926306i	$-0.622966\pi$
$491$	−16.6974			−0.753545			−0.376773	+	0.926306i	$0.622966\pi$
$492$	−9.52408	+	1.00102i	−0.429379	+	0.0451295i
$493$	−0.477599	−	0.530428i	−0.0215100	−	0.0238893i
$494$	32.1870	−	18.8487i	1.44816	−	0.848041i
$495$	−0.700886			−0.0315025
$496$	−0.00181854	+	0.186837i	−8.16547e−5	+	0.00838924i
$497$	11.3149	−	19.5980i	0.507542	−	0.879089i
$498$	−2.43752	+	2.70714i	−0.109228	+	0.121310i
$499$	3.30890	−	2.97934i	0.148127	−	0.133374i	−0.591736	−	0.806132i	$-0.701557\pi$
$499$	3.30890	−	2.97934i	0.148127	−	0.133374i	0.739862	+	0.672758i	$0.234891\pi$
$500$	−3.08831	+	6.93646i	−0.138113	+	0.310208i
$501$	1.50273	+	0.867600i	0.0671369	+	0.0387615i
$502$	−24.2968	−	14.0278i	−1.08442	−	0.626090i
$503$	−27.4505	+	19.9440i	−1.22396	+	0.889258i	−0.996422	−	0.0845121i	$-0.973067\pi$
$503$	−27.4505	+	19.9440i	−1.22396	+	0.889258i	−0.227536	+	0.973770i	$0.573067\pi$
$504$	−22.8201	+	10.1601i	−1.01649	+	0.452569i
$505$	−1.79909	+	2.47624i	−0.0800585	+	0.110191i
$506$	4.65351	−	5.16824i	0.206874	−	0.229756i
$507$	−1.65246	+	2.94542i	−0.0733885	+	0.130811i
$508$	−55.7980	−	11.8602i	−2.47563	−	0.526212i
$509$	15.5458	+	5.05115i	0.689057	+	0.223888i	0.632556	−	0.774514i	$-0.282006\pi$
$509$	15.5458	+	5.05115i	0.689057	+	0.223888i	0.0565006	+	0.998403i	$0.482006\pi$
$510$	0.00133749	−	0.0127253i	5.92249e−5	−	0.000563488i
$511$	0.933717	−	0.198468i	0.0413052	−	0.00877969i
$512$	−0.361085	−	0.117324i	−0.0159578	−	0.00518502i
$513$	4.09852	−	5.64113i	0.180954	−	0.249062i
$514$	50.4094	−	45.3888i	2.22346	−	2.00202i
$515$	0.0579939	−	0.272840i	0.00255552	−	0.0120228i
$516$	−0.974434	−	9.27112i	−0.0428971	−	0.408138i
$517$	−2.88891	−	8.89115i	−0.127054	−	0.391032i
$518$	0.663870	−	0.913738i	0.0291688	−	0.0401474i
$519$	−2.89148	−	2.10079i	−0.126922	−	0.0922142i
$520$	−2.27363	+	0.754272i	−0.0997051	+	0.0330770i
$521$	−15.2716	+	26.4512i	−0.669062	+	1.15885i	0.309105	+	0.951028i	$0.399971\pi$
$521$	−15.2716	+	26.4512i	−0.669062	+	1.15885i	−0.978167	+	0.207821i	$0.933363\pi$
$522$			52.5509i			2.30009i
$523$	0.221369	+	2.10619i	0.00967981	+	0.0920972i	0.998295	−	0.0583677i	$-0.0185896\pi$
$523$	0.221369	+	2.10619i	0.00967981	+	0.0920972i	−0.988615	+	0.150465i	$0.951923\pi$
$524$	10.1212	−	31.1497i	0.442145	−	1.36078i
$525$	−3.70408	+	1.20353i	−0.161659	+	0.0525263i
$526$	−10.9358	+	6.31377i	−0.476822	+	0.275293i
$527$	−0.100597	−	0.497010i	−0.00438207	−	0.0216501i
$528$			0.00881052i			0.000383429i
$529$	−9.32929	+	10.3612i	−0.405621	+	0.450488i
$530$	0.185557	−	0.0394413i	0.00806007	−	0.00171322i
$531$	−13.2364	+	1.39120i	−0.574409	+	0.0603729i
$532$	22.1455	+	38.3571i	0.960128	+	1.66299i
$533$	27.7340	+	30.4225i	1.20129	+	1.31774i
$534$	−0.510573	−	4.85778i	−0.0220946	−	0.210216i
$535$	−0.157946	−	0.354753i	−0.00682860	−	0.0153373i
$536$	−1.98666	−	1.44339i	−0.0858104	−	0.0623449i
$537$	5.28139	+	1.12259i	0.227909	+	0.0484435i
$538$	17.7740	−	39.9211i	0.766292	−	1.72112i
$539$	2.10916	−	0.685307i	0.0908478	−	0.0295182i
$540$	−0.874544	+	0.787443i	−0.0376344	+	0.0338861i
$541$	7.10314	+	15.9539i	0.305388	+	0.685913i	0.999421	−	0.0340308i	$-0.0108344\pi$
$541$	7.10314	+	15.9539i	0.305388	+	0.685913i	−0.694033	+	0.719943i	$0.744168\pi$
$542$	20.2389	−	4.30191i	0.869336	−	0.184783i
$543$	−1.70732	−	1.89617i	−0.0732679	−	0.0813722i
$544$	0.515849	+	0.0542179i	0.0221168	+	0.00232457i
$545$	−2.81832	+	0.599052i	−0.120724	+	0.0256606i
$546$	−5.64439	−	3.21256i	−0.241558	−	0.137485i
$547$	−9.54310	−	4.24886i	−0.408033	−	0.181668i	0.192448	−	0.981307i	$-0.438357\pi$
$547$	−9.54310	−	4.24886i	−0.408033	−	0.181668i	−0.600481	+	0.799639i	$0.705024\pi$
$548$	0.192197	−	0.0624485i	0.00821024	−	0.00266767i
$549$	−33.4481	−	24.3015i	−1.42753	−	1.03716i
$550$	−1.19421	+	11.3622i	−0.0509214	+	0.484485i
$551$	35.2621	−	3.70620i	1.50222	−	0.157889i
$552$		−	2.19643i		−	0.0934861i
$553$	−32.9832	−	19.0428i	−1.40259	−	0.809784i
$554$	−15.7157	−	21.6309i	−0.667698	−	0.919007i
$555$	0.00309282	−	0.00951872i	0.000131283	−	0.000404047i
$556$	−48.4622	−	10.3010i	−2.05526	−	0.436858i
$557$	−29.6311	−	17.1075i	−1.25551	−	0.724868i	−0.283310	−	0.959028i	$-0.591433\pi$
$557$	−29.6311	−	17.1075i	−1.25551	−	0.724868i	−0.972198	+	0.234160i	$0.924766\pi$
$558$	−18.9811	+	32.1494i	−0.803533	+	1.36099i
$559$	−29.6144	+	26.9974i	−1.25256	+	1.14187i
$560$	0.00743678	+	0.0228880i	0.000314261	+	0.000967196i
$561$	−0.00497141	−	0.0233887i	−0.000209893	−	0.000987470i
$562$	4.07569	+	38.7776i	0.171923	+	1.63573i
$563$	−2.74797	+	4.75963i	−0.115813	+	0.200594i	−0.918105	−	0.396338i	$-0.870281\pi$
$563$	−2.74797	+	4.75963i	−0.115813	+	0.200594i	0.802291	+	0.596933i	$0.203614\pi$
$564$	−6.71961	−	3.87957i	−0.282947	−	0.163359i
$565$	−0.210474	−	0.289693i	−0.00885473	−	0.0121875i
$566$	−24.2657	−	2.55043i	−1.01996	−	0.107203i
$567$	25.3226	+	2.66151i	1.06345	+	0.111773i
$568$	−20.5072	−	4.35893i	−0.860461	−	0.182897i
$569$	18.2286	−	13.2438i	0.764181	−	0.555210i	−0.136009	−	0.990708i	$-0.543428\pi$
$569$	18.2286	−	13.2438i	0.764181	−	0.555210i	0.900190	+	0.435498i	$0.143428\pi$
$570$	0.472357	+	0.425312i	0.0197848	+	0.0178144i
$571$	−25.9863	+	5.52357i	−1.08749	+	0.231154i	−0.716574	−	0.697511i	$-0.754291\pi$
$571$	−25.9863	+	5.52357i	−1.08749	+	0.231154i	−0.370920	+	0.928665i	$0.620958\pi$
$572$	−9.47440	+	6.97319i	−0.396144	+	0.291564i
$573$	−1.43854	+	4.42736i	−0.0600957	+	0.184956i
$574$	−58.8305	+	52.9712i	−2.45554	+	2.21097i
$575$	−1.55534	+	14.7981i	−0.0648622	+	0.617122i
$576$	−25.4216	−	28.2335i	−1.05923	−	1.17640i
$577$	9.40481	−	44.2462i	0.391527	−	1.84199i	−0.133689	−	0.991023i	$-0.542682\pi$
$577$	9.40481	−	44.2462i	0.391527	−	1.84199i	0.525217	−	0.850968i	$-0.323984\pi$
$578$	38.6404	−	4.06127i	1.60723	−	0.168927i
$579$	1.06576	−	5.01401i	0.0442915	−	0.208375i
$580$	−5.95125	−	0.625501i	−0.247112	−	0.0259725i
$581$	−1.94365	+	18.4926i	−0.0806362	+	0.767202i
$582$	−6.32639	−	2.81669i	−0.262237	−	0.116756i
$583$	0.307007	−	0.177251i	0.0127149	−	0.00734098i
$584$	−0.442182	−	0.765882i	−0.0182976	−	0.0316924i
$585$	2.44913	+	0.504819i	0.101259	+	0.0208717i
$586$	−18.7428	−	20.8160i	−0.774258	−	0.859900i
$587$	−2.12773	+	10.0102i	−0.0878207	+	0.413164i	0.912174	+	0.409804i	$0.134403\pi$
$587$	−2.12773	+	10.0102i	−0.0878207	+	0.413164i	−0.999994	+	0.00335993i	$0.998930\pi$
$588$	0.920310	−	1.59402i	0.0379530	−	0.0657364i
$589$	22.9112	+	10.4691i	0.944040	+	0.431372i
$590$		−	2.45438i		−	0.101045i
$591$	−0.570410	−	0.513600i	−0.0234636	−	0.0211267i
$592$	0.00519900	+	0.00168926i	0.000213677	+	6.94280e-5i
$593$	9.85127	+	13.5591i	0.404543	+	0.556806i	0.961877	−	0.273483i	$-0.0881756\pi$
$593$	9.85127	+	13.5591i	0.404543	+	0.556806i	−0.557334	+	0.830289i	$0.688176\pi$
$594$	−1.78073	+	3.08431i	−0.0730641	+	0.126551i
$595$	−0.0326567	−	0.0565630i	−0.00133879	−	0.00231886i
$596$	−20.9403	+	47.0328i	−0.857750	+	1.92654i
$597$	2.96623	+	2.15509i	0.121400	+	0.0882021i
$598$	−19.9834	+	14.7078i	−0.817181	+	0.601448i
$599$	12.1588	−	13.5037i	0.496796	−	0.551748i	−0.441644	−	0.897190i	$-0.645605\pi$
$599$	12.1588	−	13.5037i	0.496796	−	0.551748i	0.938440	+	0.345443i	$0.112271\pi$
$600$	2.12087	+	2.91912i	0.0865840	+	0.119173i
$601$	3.18049	−	3.53229i	0.129735	−	0.144085i	−0.674777	−	0.738022i	$-0.735760\pi$
$601$	3.18049	−	3.53229i	0.129735	−	0.144085i	0.804512	+	0.593936i	$0.202427\pi$
$602$	−51.5643	−	57.2679i	−2.10160	−	2.33407i
$603$	1.04264	+	2.34180i	0.0424595	+	0.0953656i
$604$	0.00980483	+	0.0461281i	0.000398953	+	0.00187693i
$605$	0.490670	+	2.30842i	0.0199486	+	0.0938507i
$606$	3.12701	+	7.02337i	0.127026	+	0.285305i
$607$	−12.3754	−	13.7442i	−0.502300	−	0.557861i	0.437662	−	0.899140i	$-0.355807\pi$
$607$	−12.3754	−	13.7442i	−0.502300	−	0.557861i	−0.939962	+	0.341279i	$0.889140\pi$
$608$	−17.2409	+	19.1480i	−0.699211	+	0.776553i
$609$	−3.62876	−	4.99456i	−0.147045	−	0.202390i
$610$	5.10167	−	5.66598i	0.206561	−	0.229409i
$611$	3.69088	+	33.1494i	0.149317	+	1.34108i
$612$	0.697601	+	0.506837i	0.0281988	+	0.0204877i
$613$	−6.33368	+	14.2257i	−0.255815	+	0.574570i	−0.995106	−	0.0988165i	$-0.968494\pi$
$613$	−6.33368	+	14.2257i	−0.255815	+	0.574570i	0.739291	+	0.673387i	$0.235161\pi$
$614$	29.2744	+	50.7047i	1.18142	+	2.04628i
$615$	−0.350757	+	0.607530i	−0.0141439	+	0.0244980i
$616$	−5.05986	−	6.96430i	−0.203868	−	0.280600i
$617$	39.0729	+	12.6956i	1.57302	+	0.511104i	0.960245	−	0.279157i	$-0.0900551\pi$
$617$	39.0729	+	12.6956i	1.57302	+	0.511104i	0.612770	+	0.790261i	$0.290055\pi$
$618$	−0.520665	−	0.468809i	−0.0209442	−	0.0188583i
$619$			21.3144i			0.856699i	0.903613	+	0.428349i	$0.140905\pi$
$619$			21.3144i			0.856699i	−0.903613	+	0.428349i	$0.859095\pi$
$620$	−3.41491	−	2.53222i	−0.137146	−	0.101697i
$621$	−2.31922	+	4.01700i	−0.0930669	+	0.161197i
$622$	−5.47783	+	25.7711i	−0.219641	+	1.03333i
$623$	−16.6832	−	18.5286i	−0.668400	−	0.742333i
$624$	0.00634586	−	0.0307869i	0.000254038	−	0.00123246i
$625$	−12.0821	−	20.9267i	−0.483283	−	0.837070i
$626$	−3.78237	+	2.18375i	−0.151174	+	0.0872802i
$627$	1.08511	+	0.483121i	0.0433350	+	0.0192940i
$628$	−0.711981	+	6.77405i	−0.0284111	+	0.270314i
$629$	−0.0147546	−	0.00155077i	−0.000588304	−	6.18332e-5i
$630$	−0.999788	+	4.70363i	−0.0398325	+	0.187397i
$631$	15.2790	−	1.60589i	0.608247	−	0.0639294i	0.204603	−	0.978845i	$-0.434410\pi$
$631$	15.2790	−	1.60589i	0.608247	−	0.0639294i	0.403645	+	0.914916i	$0.367743\pi$
$632$	−7.33603	+	34.5133i	−0.291812	+	1.37287i
$633$	1.20626	+	1.33969i	0.0479445	+	0.0532478i
$634$	−2.07202	+	19.7140i	−0.0822906	+	0.782943i
$635$	−3.10539	+	2.79610i	−0.123233	+	0.110960i
$636$	0.0909206	−	0.279825i	0.00360524	−	0.0110958i
$637$	−7.86369	+	0.875550i	−0.311571	+	0.0346906i
$638$	−17.7140	+	3.76523i	−0.701305	+	0.149067i
$639$	16.2641	+	14.6442i	0.643397	+	0.579317i
$640$	3.48872	−	2.53471i	0.137904	−	0.100193i
$641$	19.9485	+	4.24019i	0.787919	+	0.167477i	0.584262	−	0.811565i	$-0.301384\pi$
$641$	19.9485	+	4.24019i	0.787919	+	0.167477i	0.203657	+	0.979042i	$0.434717\pi$
$642$	−0.970043	−	0.101956i	−0.0382845	−	0.00402387i
$643$	32.0493	+	3.36852i	1.26390	+	0.132841i	0.712663	−	0.701507i	$-0.247489\pi$
$643$	32.0493	+	3.36852i	1.26390	+	0.132841i	0.551238	+	0.834348i	$0.314156\pi$
$644$	−17.3179	−	23.8361i	−0.682423	−	0.939274i
$645$	−0.591393	−	0.341441i	−0.0232861	−	0.0134442i
$646$	0.471093	−	0.815958i	0.0185349	−	0.0321034i
$647$	−1.05715	−	10.0581i	−0.0415609	−	0.395426i	−0.995451	−	0.0952708i	$-0.969628\pi$
$647$	−1.05715	−	10.0581i	−0.0415609	−	0.395426i	0.953890	−	0.300155i	$-0.0970384\pi$
$648$	−4.90449	−	23.0738i	−0.192666	−	0.906425i
$649$	−1.41733	−	4.36208i	−0.0556349	−	0.171227i
$650$	12.3567	−	38.8431i	0.484669	−	1.52355i
$651$	−0.415988	−	4.36625i	−0.0163038	−	0.171127i
$652$	−7.45939	−	4.30668i	−0.292132	−	0.168663i
$653$	−3.04027	−	0.646230i	−0.118975	−	0.0252889i	0.148039	−	0.988981i	$-0.452704\pi$
$653$	−3.04027	−	0.646230i	−0.118975	−	0.0252889i	−0.267014	+	0.963693i	$0.586037\pi$
$654$	−2.23640	+	6.88293i	−0.0874501	+	0.269144i
$655$	−1.41025	−	1.94104i	−0.0551028	−	0.0758425i
$656$	−0.331824	−	0.191579i	−0.0129556	−	0.00747990i
$657$			0.923181i			0.0360167i
$658$	−63.7893	+	6.70453i	−2.48677	+	0.261370i
$659$	2.35157	−	22.3737i	0.0916043	−	0.871557i	−0.848162	−	0.529738i	$-0.822290\pi$
$659$	2.35157	−	22.3737i	0.0916043	−	0.871557i	0.939766	−	0.341819i	$-0.111043\pi$
$660$	−0.162181	−	0.117831i	−0.00631288	−	0.00458658i
$661$	−22.6496	+	7.35929i	−0.880966	+	0.286243i	−0.714358	−	0.699780i	$-0.753281\pi$
$661$	−22.6496	+	7.35929i	−0.880966	+	0.286243i	−0.166607	+	0.986023i	$0.553281\pi$
$662$	−47.0284	−	20.9384i	−1.82781	−	0.813794i
$663$	0.000525881		0.0853085i	2.04235e−5		0.00331311i
$664$	16.8503	−	3.58165i	0.653920	−	0.138995i
$665$	3.22669	+	0.339139i	0.125126	+	0.0131512i
$666$	0.730888	+	0.811734i	0.0283213	+	0.0314540i
$667$	−23.0707	+	4.90383i	−0.893302	+	0.189877i
$668$	−8.77090	−	19.6998i	−0.339356	−	0.762207i
$669$	−0.362563	+	0.326454i	−0.0140175	+	0.0126214i
$670$	−0.449587	+	0.146080i	−0.0173691	+	0.00564355i
$671$	5.79510	−	13.0160i	0.223717	−	0.502477i
$672$	4.38833	+	0.932769i	0.169284	+	0.0359823i
$673$	21.2024	+	15.4045i	0.817293	+	0.593798i	0.915936	−	0.401325i	$-0.131450\pi$
$673$	21.2024	+	15.4045i	0.817293	+	0.593798i	−0.0986430	+	0.995123i	$0.531450\pi$
$674$	−4.67360	−	10.4971i	−0.180020	−	0.404332i
$675$	−0.796496	−	7.57815i	−0.0306571	−	0.291683i
$676$	38.1292	−	17.5426i	1.46651	−	0.674716i
$677$	1.74696	+	3.02582i	0.0671410	+	0.116292i	0.897642	−	0.440726i	$-0.145279\pi$
$677$	1.74696	+	3.02582i	0.0671410	+	0.116292i	−0.830501	+	0.557018i	$0.811946\pi$
$678$	−0.894491	+	0.0940148i	−0.0343527	+	0.00361062i
$679$	−34.5761	+	7.34938i	−1.32691	+	0.282044i
$680$	−0.0404886	+	0.0449672i	−0.00155267	+	0.00172441i
$681$			2.05529i			0.0787588i
$682$	−12.1970	−	4.09472i	−0.467048	−	0.156795i
$683$	35.0525	−	20.2375i	1.34124	−	0.774368i	0.354255	−	0.935149i	$-0.384735\pi$
$683$	35.0525	−	20.2375i	1.34124	−	0.774368i	0.986990	+	0.160781i	$0.0514013\pi$
$684$	−40.7378	+	13.2365i	−1.55765	+	0.506110i
$685$	0.00457457	−	0.0140791i	0.000174785	−	0.000537934i
$686$	3.48281	+	33.1367i	0.132974	+	1.26517i
$687$		−	2.34458i		−	0.0894511i
$688$	0.186491	−	0.323011i	0.00710989	−	0.0123147i
$689$	−1.20045	+	0.398248i	−0.0457336	+	0.0151721i
$690$	−0.342071	−	0.248529i	−0.0130224	−	0.00946136i
$691$	15.5882	−	21.4553i	0.593002	−	0.816197i	−0.402043	−	0.915621i	$-0.631700\pi$
$691$	15.5882	−	21.4553i	0.593002	−	0.816197i	0.995045	+	0.0994235i	$0.0316999\pi$
$692$	13.7255	+	42.2426i	0.521764	+	1.60582i
$693$	0.939311	+	8.93695i	0.0356815	+	0.339487i
$694$	11.9176	−	56.0681i	0.452387	−	2.12832i
$695$	−2.69712	+	2.42850i	−0.102308	+	0.0921182i
$696$	−3.36186	+	4.62720i	−0.127431	+	0.175394i
$697$	0.988971	+	0.321336i	0.0374599	+	0.0121715i
$698$	−41.5700	+	8.83597i	−1.57345	+	0.334446i
$699$	0.000932267	−	0.00886993i	3.52616e−5	−	0.000335491i
$700$	46.0322	+	14.9568i	1.73985	+	0.565313i
$701$	16.9144	+	3.59527i	0.638848	+	0.135791i	0.515937	−	0.856626i	$-0.327444\pi$
$701$	16.9144	+	3.59527i	0.638848	+	0.135791i	0.122911	+	0.992418i	$0.460777\pi$
$702$	8.44396	−	9.49502i	0.318697	−	0.358367i
$703$	0.493134	−	0.547681i	0.0185989	−	0.0206562i
$704$	7.69561	−	10.5921i	0.290039	−	0.399205i
$705$	−0.519244	+	0.231182i	−0.0195559	+	0.00870683i
$706$	9.56544	−	6.94970i	0.360000	−	0.261555i
$707$	33.9854	+	19.6215i	1.27815	+	0.737942i
$708$	−3.29670	−	1.90335i	−0.123898	−	0.0715324i
$709$	−3.35813	+	7.54249i	−0.126117	+	0.283264i	−0.965558	−	0.260187i	$-0.916216\pi$
$709$	−3.35813	+	7.54249i	−0.126117	+	0.283264i	0.839441	+	0.543451i	$0.182883\pi$
$710$	−2.99928	+	2.70056i	−0.112561	+	0.101350i
$711$	24.6461	−	27.3723i	0.924301	−	1.02654i
$712$	−11.5494	+	20.0042i	−0.432833	+	0.749688i
$713$	−15.8854	−	5.33295i	−0.594912	−	0.199721i
$714$	−0.164052			−0.00613951
$715$	0.00531211	+	0.861731i	0.000198662	+	0.0322269i
$716$	−44.8989	−	49.8653i	−1.67795	−	1.86355i
$717$	−5.41353	+	0.568985i	−0.202172	+	0.0212491i
$718$	54.8772			2.04800
$719$	14.7150			0.548778			0.274389	−	0.961619i	$-0.411524\pi$
$719$	14.7150			0.548778			0.274389	+	0.961619i	$0.411524\pi$
$720$	−0.0231469	+	0.00243283i	−0.000862633	+	9.06664e-5i
$721$	−3.55669	−	0.373823i	−0.132458	−	0.0139219i
$722$	1.36585	+	3.06774i	0.0508315	+	0.114169i
$723$	−5.36060	−	4.82670i	−0.199363	−	0.179507i
$724$	3.31451	+	31.5354i	0.123183	+	1.17200i
$725$	25.9266	−	28.7944i	0.962889	−	1.06940i
$726$	5.63765	+	1.83178i	0.209233	+	0.0679839i
$727$	30.5568	−	13.6048i	1.13329	−	0.504573i	0.247605	−	0.968861i	$-0.420357\pi$
$727$	30.5568	−	13.6048i	1.13329	−	0.504573i	0.885684	+	0.464288i	$0.153690\pi$
$728$	12.6647	+	27.9800i	0.469386	+	1.03701i
$729$	−7.23824	+	22.2770i	−0.268083	+	0.825075i
$730$	−0.169312	−	0.0177954i	−0.00626653	−	0.000658639i
$731$	−0.312801	+	0.962704i	−0.0115694	+	0.0356069i
$732$	−3.65419	−	11.2464i	−0.135063	−	0.415681i
$733$	13.5442	−	30.4208i	0.500267	−	1.12362i	−0.470239	−	0.882539i	$-0.655832\pi$
$733$	13.5442	−	30.4208i	0.500267	−	1.12362i	0.970506	−	0.241078i	$-0.0775011\pi$
$734$	16.4157	−	77.2296i	0.605913	−	2.85060i
$735$	−0.0548410	−	0.123175i	−0.00202284	−	0.00454338i
$736$	10.0747	−	13.8666i	0.371357	−	0.511129i
$737$	−0.714679	+	0.519244i	−0.0263255	+	0.0191266i
$738$	−38.2802	−	66.3033i	−1.40911	−	2.44066i
$739$		−	26.8902i		−	0.989170i	−0.869129	−	0.494585i	$-0.835320\pi$
$739$		−	26.8902i		−	0.989170i	0.869129	−	0.494585i	$-0.164680\pi$
$740$	−0.100626	+	0.0731093i	−0.00369909	+	0.00268755i
$741$	−3.44375	−	2.46974i	−0.126509	−	0.0907282i
$742$	−0.751592	−	2.31316i	−0.0275918	−	0.0849189i
$743$	−5.69944	−	3.29058i	−0.209092	−	0.120720i	0.391797	−	0.920052i	$-0.371854\pi$
$743$	−5.69944	−	3.29058i	−0.209092	−	0.120720i	−0.600890	+	0.799332i	$0.705187\pi$
$744$	−3.72802	+	1.61653i	−0.136676	+	0.0592649i
$745$	1.88568	+	3.26610i	0.0690861	+	0.119661i
$746$	−73.3137	+	23.8211i	−2.68421	+	0.872151i
$747$	−17.1027	−	5.55702i	−0.625757	−	0.203321i
$748$	−0.120864	+	0.271464i	−0.00441921	+	0.00992572i
$749$	−4.31175	+	2.48939i	−0.157548	+	0.0909604i
$750$	1.39707			0.0510136
$751$	17.6293	+	7.84907i	0.643302	+	0.286417i	0.702343	−	0.711839i	$-0.252137\pi$
$751$	17.6293	+	7.84907i	0.643302	+	0.286417i	−0.0590405	+	0.998256i	$0.518804\pi$
$752$	−0.126269	−	0.283604i	−0.00460455	−	0.0103420i
$753$	−0.333187	+	3.17007i	−0.0121420	+	0.115524i
$754$	64.6107	−	0.398290i	2.35298	−	0.0145049i
$755$	0.00315587	+	0.00140508i	0.000114854	+	5.11363e-5i
$756$	11.2127	+	10.0959i	0.407801	+	0.367186i
$757$	6.90331	−	21.2462i	0.250905	−	0.772206i	−0.743704	−	0.668509i	$-0.766933\pi$
$757$	6.90331	−	21.2462i	0.250905	−	0.772206i	0.994609	−	0.103697i	$-0.0330672\pi$
$758$	14.8106	+	10.7605i	0.537944	+	0.390839i
$759$	−0.751469	−	0.244167i	−0.0272766	−	0.00886271i
$760$	−0.624946	−	2.94014i	−0.0226692	−	0.106650i
$761$	10.8997	−	15.0022i	0.395114	−	0.543828i	−0.564395	−	0.825505i	$-0.690891\pi$
$761$	10.8997	−	15.0022i	0.395114	−	0.543828i	0.959509	+	0.281677i	$0.0908907\pi$
$762$	2.18224	+	10.2666i	0.0790542	+	0.371921i
$763$	11.4155	+	35.1334i	0.413270	+	1.27191i
$764$	46.8034	−	34.0047i	1.69329	−	1.23025i
$765$	0.0600736	−	0.0195191i	0.00217197	−	0.000705715i
$766$	3.09772	−	29.4729i	0.111925	−	1.06490i
$767$	1.81078	+	16.2634i	0.0653835	+	0.587238i
$768$	−0.428576	−	4.07763i	−0.0154649	−	0.147139i
$769$	27.3115	−	15.7683i	0.984879	−	0.568620i	0.0811395	−	0.996703i	$-0.474144\pi$
$769$	27.3115	−	15.7683i	0.984879	−	0.568620i	0.903740	+	0.428082i	$0.140811\pi$
$770$	−1.65715			−0.0597196
$771$	−7.04050	−	3.13463i	−0.253558	−	0.112891i
$772$	−47.3408	+	42.6258i	−1.70383	+	1.53414i
$773$	23.3957	+	21.0656i	0.841484	+	0.757675i	0.972301	−	0.233731i	$-0.0750935\pi$
$773$	23.3957	+	21.0656i	0.841484	+	0.757675i	−0.130818	+	0.991406i	$0.541760\pi$
$774$	64.5423	−	37.2635i	2.31992	−	1.33941i
$775$	26.2617	−	8.25122i	0.943347	−	0.296393i
$776$	16.3743	+	28.3611i	0.587803	+	1.01810i
$777$	−0.125517	−	0.0266796i	−0.00450291	−	0.000957124i
$778$	7.02729	+	33.0608i	0.251941	+	1.18529i
$779$	−41.7904	+	30.3625i	−1.49730	+	1.08785i
$780$	0.481845	+	0.528554i	0.0172528	+	0.0189253i
$781$	−3.77102	+	6.53160i	−0.134938	+	0.233719i
$782$	−0.254925	+	0.572572i	−0.00911611	+	0.0204751i
$783$	11.0343	−	4.91279i	0.394334	−	0.175569i
$784$	0.0672765	−	0.0299534i	0.00240273	−	0.00106977i
$785$	0.370796	+	0.333866i	0.0132343	+	0.0119162i
$786$	−5.99337	+	0.629929i	−0.213777	+	0.0224688i
$787$	−20.3374	+	6.60801i	−0.724948	+	0.235550i	−0.648167	−	0.761498i	$-0.724464\pi$
$787$	−20.3374	+	6.60801i	−0.724948	+	0.235550i	−0.0767811	+	0.997048i	$0.524464\pi$
$788$	1.98324	+	9.33039i	0.0706499	+	0.332381i
$789$	1.16068	+	0.843282i	0.0413212	+	0.0300216i
$790$	4.54502	+	5.04775i	0.161704	+	0.179591i
$791$	−3.41179	+	3.07199i	−0.121309	+	0.109227i
$792$	7.60546	−	3.38617i	0.270248	−	0.120322i
$793$	−29.6249	+	41.3083i	−1.05201	+	1.46690i
$794$	−36.7834	−	7.81855i	−1.30539	−	0.277470i
$795$	−0.0126685	−	0.0174368i	−0.000449307	−	0.000618418i
$796$	−14.0803	−	43.3346i	−0.499062	−	1.53596i
$797$	10.8038	−	4.81017i	0.382691	−	0.170385i	−0.206369	−	0.978474i	$-0.566165\pi$
$797$	10.8038	−	4.81017i	0.382691	−	0.170385i	0.589060	+	0.808089i	$0.299498\pi$
$798$	4.79008	−	6.59298i	0.169567	−	0.233389i
$799$	0.495223	+	0.681616i	0.0175197	+	0.0241138i
$800$			28.1572i			0.995508i
$801$	20.8822	−	12.0563i	0.737836	−	0.425990i
$802$	65.9279	+	29.3530i	2.32800	+	1.03649i
$803$	−0.311189	+	0.0661452i	−0.0109816	+	0.00233422i
$804$	−0.152438	+	0.717165i	−0.00537608	+	0.0252925i
$805$	−2.15827			−0.0760690
$806$	39.6712	+	23.0933i	1.39736	+	0.813428i
$807$	−4.96487			−0.174772
$808$	7.55895	−	35.5621i	0.265923	−	1.25107i
$809$	−40.5843	+	8.62647i	−1.42687	+	0.303290i	−0.855670	−	0.517521i	$-0.826855\pi$
$809$	−40.5843	+	8.62647i	−1.42687	+	0.303290i	−0.571199	+	0.820812i	$0.693521\pi$
$810$	−4.14846	−	1.84702i	−0.145762	−	0.0648975i
$811$	28.4130	−	16.4043i	0.997715	−	0.576031i	0.0901438	−	0.995929i	$-0.471267\pi$
$811$	28.4130	−	16.4043i	0.997715	−	0.576031i	0.907571	+	0.419898i	$0.137934\pi$
$812$			76.7223i			2.69242i
$813$	−1.38177	−	1.90185i	−0.0484609	−	0.0667007i
$814$	−0.221254	+	0.304530i	−0.00775496	+	0.0106738i
$815$	−0.576409	+	0.256634i	−0.0201907	+	0.00898949i
$816$	−0.000245366	0	0.000755158i	−8.58952e−6	0	2.64358e-5i
$817$	−29.5560	−	40.6804i	−1.03404	−	1.42323i
$818$	59.7299	+	12.6960i	2.08841	+	0.443904i
$819$	3.15465	−	31.9052i	0.110232	−	1.11486i
$820$	7.96431	−	3.54594i	0.278126	−	0.123830i
$821$	−8.97546	+	8.08154i	−0.313246	+	0.282048i	−0.810724	−	0.585429i	$-0.800926\pi$
$821$	−8.97546	+	8.08154i	−0.313246	+	0.282048i	0.497478	+	0.867476i	$0.334259\pi$
$822$	−0.0248805	−	0.0276326i	−0.000867808	−	0.000963799i
$823$	39.4092	+	28.6324i	1.37372	+	0.998064i	0.997436	+	0.0715580i	$0.0227971\pi$
$823$	39.4092	+	28.6324i	1.37372	+	0.998064i	0.376281	+	0.926506i	$0.377203\pi$
$824$	0.688860	+	3.24083i	0.0239976	+	0.112900i
$825$	1.23449	−	0.401112i	0.0429796	−	0.0139649i
$826$	−31.2956	+	3.28930i	−1.08891	+	0.114450i
$827$	22.9640	+	20.6769i	0.798538	+	0.719007i	0.963621	−	0.267273i	$-0.0861224\pi$
$827$	22.9640	+	20.6769i	0.798538	+	0.719007i	−0.165083	+	0.986280i	$0.552789\pi$
$828$	26.0306	−	11.5896i	0.904625	−	0.402765i
$829$	−46.1242	+	20.5358i	−1.60196	+	0.713239i	−0.996575	−	0.0826935i	$-0.973648\pi$
$829$	−46.1242	+	20.5358i	−1.60196	+	0.713239i	−0.605386	+	0.795932i	$0.706981\pi$
$830$	1.34884	−	3.02954i	0.0468189	−	0.105157i
$831$	−1.51887	+	2.63077i	−0.0526891	+	0.0912603i
$832$	−34.5201	+	31.4695i	−1.19677	+	1.09101i
$833$	−0.161693	+	0.117477i	−0.00560232	+	0.00407032i
$834$	1.89534	+	8.91687i	0.0656302	+	0.308766i
$835$	−1.54512	−	0.328426i	−0.0534712	−	0.0113657i
$836$	−7.38064	−	12.7836i	−0.255265	−	0.442131i
$837$	8.52501	+	0.979993i	0.294667	+	0.0338735i
$838$	2.48673	−	1.43572i	0.0859027	−	0.0495960i
$839$	−20.1167	−	18.1132i	−0.694506	−	0.625336i	0.244334	−	0.969691i	$-0.421431\pi$
$839$	−20.1167	−	18.1132i	−0.694506	−	0.625336i	−0.938839	+	0.344356i	$0.888097\pi$
$840$	−0.388940	+	0.350203i	−0.0134197	+	0.0120832i
$841$	29.6159	+	13.1859i	1.02124	+	0.454685i
$842$	−12.5417			−0.432217
$843$	3.83648	−	2.21499i	0.132135	−	0.0762884i
$844$	−2.34178	−	22.2805i	−0.0806073	−	0.766928i
$845$	0.602107	−	3.01500i	0.0207131	−	0.103719i
$846$	6.48401	−	61.6913i	0.222925	−	2.12099i
$847$	28.7769	−	9.35019i	0.988787	−	0.321276i
$848$	0.00952372	−	0.00691939i	0.000327046	−	0.000237613i
$849$	0.856637	+	2.63646i	0.0293997	+	0.0904830i
$850$	−0.214070	−	1.00712i	−0.00734255	−	0.0345440i
$851$	−0.288161	+	0.396620i	−0.00987803	+	0.0135959i
$852$	1.30146	+	6.12287i	0.0445872	+	0.209766i
$853$	−10.5116	−	3.41544i	−0.359911	−	0.116942i	0.123479	−	0.992347i	$-0.460595\pi$
$853$	−10.5116	−	3.41544i	−0.359911	−	0.116942i	−0.483390	+	0.875405i	$0.660595\pi$
$854$	−79.0837	−	57.4576i	−2.70619	−	1.96616i
$855$	−0.969619	+	2.98418i	−0.0331603	+	0.102057i
$856$	3.42781	+	3.08642i	0.117160	+	0.105492i
$857$	−13.9599	−	6.21535i	−0.476862	−	0.212312i	0.154208	−	0.988038i	$-0.450717\pi$
$857$	−13.9599	−	6.21535i	−0.476862	−	0.212312i	−0.631070	+	0.775726i	$0.717384\pi$
$858$	1.88116	+	1.07068i	0.0642218	+	0.0365525i
$859$	−2.06083	+	19.6075i	−0.0703146	+	0.668999i	0.901424	+	0.432938i	$0.142523\pi$
$859$	−2.06083	+	19.6075i	−0.0703146	+	0.668999i	−0.971738	+	0.236061i	$0.924144\pi$
$860$	3.45176	+	7.75278i	0.117704	+	0.264368i
$861$	8.21664	+	3.65829i	0.280023	+	0.124674i
$862$	−73.5296			−2.50443
$863$	−3.62171	+	2.09100i	−0.123285	+	0.0711784i	−0.560374	−	0.828240i	$-0.689343\pi$
$863$	−3.62171	+	2.09100i	−0.123285	+	0.0711784i	0.437089	+	0.899418i	$0.356009\pi$
$864$	−3.57012	+	8.01863i	−0.121458	+	0.272799i
$865$	3.09442	+	1.00544i	0.105213	+	0.0341859i
$866$	35.0676	−	11.3941i	1.19164	−	0.387189i
$867$	−2.20716	−	3.82291i	−0.0749590	−	0.129833i
$868$	−27.7116	+	46.9369i	−0.940594	+	1.59314i
$869$	10.9926	+	6.34659i	0.372899	+	0.215293i
$870$	0.340240	+	1.04715i	0.0115352	+	0.0355017i
$871$	2.87131	−	1.29966i	0.0972908	−	0.0440373i
$872$	27.6880	−	20.1165i	0.937634	−	0.681231i
$873$		−	34.1860i		−	1.15702i
$874$	−15.5672	−	26.9632i	−0.526569	−	0.912044i
$875$	5.76927	−	4.19162i	0.195037	−	0.141703i
$876$	−0.155203	+	0.213619i	−0.00524382	+	0.00721750i
$877$	6.92521	+	15.5543i	0.233848	+	0.525230i	0.991909	−	0.126953i	$-0.0405198\pi$
$877$	6.92521	+	15.5543i	0.233848	+	0.525230i	−0.758061	+	0.652184i	$0.773853\pi$
$878$	1.66983	−	7.85592i	0.0563540	−	0.265125i
$879$	−1.29441	+	2.90730i	−0.0436594	+	0.0980606i
$880$	−0.00247853	−	0.00762812i	−8.35511e−5	−	0.000257144i
$881$	17.2108	−	52.9695i	0.579847	−	1.78459i	−0.0391987	−	0.999231i	$-0.512481\pi$
$881$	17.2108	−	52.9695i	0.579847	−	1.78459i	0.619046	−	0.785355i	$-0.287519\pi$
$882$	14.6344	+	1.53814i	0.492765	+	0.0517917i
$883$	12.5377	−	38.5870i	0.421926	−	1.29855i	−0.483981	−	0.875078i	$-0.660810\pi$
$883$	12.5377	−	38.5870i	0.421926	−	1.29855i	0.905907	−	0.423476i	$-0.139190\pi$
$884$	0.617862	−	0.861533i	0.0207810	−	0.0289765i
$885$	−0.254746	+	0.113420i	−0.00856320	+	0.00381258i
$886$	−28.3353	−	9.20669i	−0.951942	−	0.309305i
$887$	20.4166	−	22.6750i	0.685523	−	0.761350i	−0.295479	−	0.955349i	$-0.595479\pi$
$887$	20.4166	−	22.6750i	0.685523	−	0.761350i	0.981002	+	0.193999i	$0.0621458\pi$
$888$	0.0124267	+	0.118232i	0.000417012	+	0.00396760i
$889$	39.8147	+	35.8493i	1.33534	+	1.20235i
$890$	1.80861	+	4.06221i	0.0606249	+	0.136166i
$891$	−8.43951	−	0.887028i	−0.282734	−	0.0297166i
$892$	6.02985	−	0.633763i	0.201894	−	0.0212199i
$893$	−41.8527			−1.40055
$894$	9.47283			0.316819
$895$	−4.88841	+	0.513792i	−0.163401	+	0.0171742i
$896$	−36.9954	−	41.0875i	−1.23593	−	1.37264i
$897$	2.45002	+	1.39445i	0.0818038	+	0.0465595i
$898$	44.6719			1.49072
$899$	25.3030	+	35.5491i	0.843902	+	1.18563i
$900$	−23.4046	+	40.5380i	−0.780153	+	1.35127i
$901$	−0.0213776	+	0.0237422i	−0.000712192	+	0.000790969i
$902$	19.6070	−	17.6542i	0.652842	−	0.587821i
$903$	−3.56112	+	7.99841i	−0.118507	+	0.266170i
$904$	3.68349	+	2.12666i	0.122511	+	0.0707318i
$905$	2.01161	+	1.16140i	0.0668681	+	0.0386063i
$906$	0.00701985	−	0.00510022i	0.000233219	−	0.000169443i
$907$	−32.6513	+	14.5373i	−1.08417	+	0.482704i	−0.869475	−	0.493977i	$-0.835543\pi$
$907$	−32.6513	+	14.5373i	−1.08417	+	0.482704i	−0.214695	+	0.976681i	$0.568876\pi$
$908$	15.0132	−	20.6639i	0.498230	−	0.685755i
$909$	−25.3950	+	28.2040i	−0.842300	+	0.935469i
$910$	5.79064	+	1.19358i	0.191958	+	0.0395667i
$911$	−27.6281	−	5.87254i	−0.915361	−	0.194566i	−0.273933	−	0.961749i	$-0.588325\pi$
$911$	−27.6281	−	5.87254i	−0.915361	−	0.194566i	−0.641428	+	0.767183i	$0.721658\pi$
$912$	0.0375128	+	0.0121886i	0.00124217	+	0.000403606i
$913$	0.647779	−	6.16321i	0.0214384	−	0.203972i
$914$	−8.77865	+	1.86596i	−0.290372	+	0.0617205i
$915$	−0.823841	−	0.267682i	−0.0272353	−	0.00884930i
$916$	−17.1263	+	23.5724i	−0.565870	+	0.778853i
$917$	−22.8600	+	20.5833i	−0.754905	+	0.679719i
$918$	0.0667324	−	0.313951i	0.00220250	−	0.0103619i
$919$	2.36904	+	22.5399i	0.0781473	+	0.743522i	0.961498	+	0.274810i	$0.0886150\pi$
$919$	2.36904	+	22.5399i	0.0781473	+	0.743522i	−0.883351	+	0.468712i	$0.844718\pi$
$920$	0.617886	+	1.90166i	0.0203711	+	0.0626958i
$921$	3.90996	−	5.38159i	0.128837	−	0.177330i
$922$	37.4933	+	27.2405i	1.23478	+	0.897118i
$923$	17.8817	−	20.1075i	0.588582	−	0.661846i
$924$	−1.28511	+	2.22587i	−0.0422769	+	0.0732258i
$925$		−	0.805368i		−	0.0264803i
$926$	3.80685	+	36.2197i	0.125101	+	1.19025i
$927$	1.06878	−	3.28938i	0.0351034	−	0.108037i
$928$	−42.4485	+	13.7923i	−1.39344	+	0.452756i
$929$	−14.6126	+	8.43659i	−0.479424	+	0.276796i	−0.720176	−	0.693791i	$-0.755939\pi$
$929$	−14.6126	+	8.43659i	−0.479424	+	0.276796i	0.240752	+	0.970587i	$0.422606\pi$
$930$	−0.170074	+	0.763516i	−0.00557693	+	0.0250367i
$931$		−	9.92828i		−	0.325386i
$932$	−0.0741648	+	0.0823684i	−0.00242935	+	0.00269807i
$933$	2.92799	−	0.622363i	0.0958580	−	0.0203752i
$934$	49.2278	−	5.17405i	1.61078	−	0.169300i
$935$	0.0108838	+	0.0188513i	0.000355938	+	0.000616503i
$936$	−29.0149	+	6.35450i	−0.948383	+	0.207703i
$937$	0.960383	+	9.13744i	0.0313744	+	0.298507i	0.998946	+	0.0459089i	$0.0146184\pi$
$937$	0.960383	+	9.13744i	0.0313744	+	0.298507i	−0.967571	+	0.252598i	$0.918715\pi$
$938$	2.46518	+	5.53688i	0.0804909	+	0.180786i
$939$	0.401445	+	0.291667i	0.0131007	+	0.00951819i
$940$	6.90919	+	1.46859i	0.225353	+	0.0479003i
$941$	−13.3413	+	29.9650i	−0.434913	+	0.976830i	0.554564	+	0.832141i	$0.312885\pi$
$941$	−13.3413	+	29.9650i	−0.434913	+	0.976830i	−0.989477	+	0.144689i	$0.953782\pi$
$942$	1.19193	−	0.387280i	0.0388351	−	0.0126183i
$943$	25.5361	−	22.9928i	0.831570	−	0.748749i
$944$	−0.0619486	−	0.139139i	−0.00201626	−	0.00452858i
$945$	1.08111	−	0.229796i	0.0351684	−	0.00747527i
$946$	17.1853	+	19.0862i	0.558743	+	0.620547i
$947$	23.3031	+	2.44925i	0.757249	+	0.0795900i	0.475281	−	0.879834i	$-0.342346\pi$
$947$	23.3031	+	2.44925i	0.757249	+	0.0795900i	0.281967	+	0.959424i	$0.409013\pi$
$948$	10.3047	−	2.19034i	0.334682	−	0.0711389i
$949$	1.13504	−	0.00699691i	0.0368449	−	0.000227129i
$950$	46.7250	+	20.8033i	1.51596	+	0.674948i
$951$	2.14191	−	0.695950i	0.0694563	−	0.0225677i
$952$	0.627636	+	0.456004i	0.0203418	+	0.0147792i
$953$	6.25777	−	59.5387i	0.202709	−	1.92865i	−0.141857	−	0.989887i	$-0.545307\pi$
$953$	6.25777	−	59.5387i	0.202709	−	1.92865i	0.344567	−	0.938762i	$-0.388026\pi$
$954$	2.33932	−	0.245873i	0.0757384	−	0.00796042i
$955$		−	4.23788i		−	0.137134i
$956$	58.5839	+	33.8234i	1.89474	+	1.09393i
$957$	1.20939	+	1.66459i	0.0390941	+	0.0538084i
$958$	−10.4964	+	32.3046i	−0.339124	+	1.04372i
$959$	−0.185652	−	0.0394616i	−0.00599502	−	0.00127428i
$960$	−0.689358	−	0.398001i	−0.0222489	−	0.0128454i
$961$	2.63967	+	30.8874i	0.0851506	+	0.996368i
$962$	0.992477	−	0.904770i	0.0319987	−	0.0291710i
$963$	−1.48793	−	4.57936i	−0.0479477	−	0.147568i
$964$	18.6380	+	87.6851i	0.600291	+	2.82415i
$965$	0.487781	+	4.64092i	0.0157022	+	0.149397i
$966$	−2.71055	+	4.69480i	−0.0872104	+	0.151053i
$967$	−50.0152	−	28.8763i	−1.60838	−	0.928598i	−0.989733	−	0.142928i	$-0.954348\pi$
$967$	−50.0152	−	28.8763i	−1.60838	−	0.928598i	−0.618646	−	0.785670i	$-0.712319\pi$
$968$	−16.4770	−	22.6786i	−0.529590	−	0.728918i
$969$	−0.106460	−	0.0111894i	−0.00341999	−	0.000359456i
$970$	6.26974	+	0.658976i	0.201309	+	0.0211585i
$971$	−48.3780	−	10.2831i	−1.55253	−	0.329999i	−0.649762	−	0.760138i	$-0.725132\pi$
$971$	−48.3780	−	10.2831i	−1.55253	−	0.329999i	−0.902763	+	0.430138i	$0.858465\pi$
$972$	−17.7748	+	12.9141i	−0.570126	+	0.414221i
$973$	34.5802	+	31.1362i	1.10859	+	0.998181i
$974$	−91.3305	+	19.4129i	−2.92642	+	0.622029i
$975$	−4.60264	+	0.512462i	−0.147402	+	0.0164119i
$976$	0.146204	−	0.449971i	0.00467989	−	0.0144032i
$977$	25.4921	−	22.9532i	0.815566	−	0.734339i	−0.151612	−	0.988440i	$-0.548446\pi$
$977$	25.4921	−	22.9532i	0.815566	−	0.734339i	0.967178	+	0.254102i	$0.0817797\pi$
$978$	−0.165659	+	1.57614i	−0.00529721	+	0.0503995i
$979$	5.56019	+	6.17521i	0.177704	+	0.197361i
$980$	−0.348380	+	1.63900i	−0.0111286	+	0.0523558i
$981$	−35.5307	+	3.73443i	−1.13441	+	0.119231i
$982$	7.93816	−	37.3461i	0.253317	−	1.19176i
$983$	23.5779	+	2.47814i	0.752018	+	0.0790403i	0.472779	−	0.881181i	$-0.343251\pi$
$983$	23.5779	+	2.47814i	0.752018	+	0.0790403i	0.279239	+	0.960222i	$0.409918\pi$
$984$	0.871003	−	8.28704i	0.0277666	−	0.264181i
$985$	0.638343	+	0.284208i	0.0203393	+	0.00905563i
$986$	1.41343	−	0.816044i	0.0450128	−	0.0259881i
$987$	3.64367	+	6.31102i	0.115979	+	0.200882i
$988$	16.5829	+	49.9863i	0.527571	+	1.59027i
$989$	22.3821	+	24.8579i	0.711710	+	0.790434i
$990$	0.333209	−	1.56763i	0.0105901	−	0.0498224i
$991$	−7.32164	+	12.6815i	−0.232580	+	0.402840i	−0.958567	−	0.284869i	$-0.908050\pi$
$991$	−7.32164	+	12.6815i	−0.232580	+	0.402840i	0.725987	+	0.687709i	$0.241383\pi$
$992$	−30.9507	−	6.89429i	−0.982686	−	0.218894i
$993$			5.84879i			0.185606i
$994$	38.4543	+	34.6244i	1.21970	+	1.09822i
$995$	−3.17441	−	1.03143i	−0.100636	−	0.0326985i
$996$	−3.02324	−	4.16114i	−0.0957951	−	0.131851i
$997$	−5.21369	+	9.03038i	−0.165119	+	0.285995i	−0.936698	−	0.350139i	$-0.886134\pi$
$997$	−5.21369	+	9.03038i	−0.165119	+	0.285995i	0.771578	+	0.636134i	$0.219468\pi$
$998$	5.09062	+	8.81720i	0.161141	+	0.279104i
$999$	0.102115	−	0.229353i	0.00323076	−	0.00725641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bt.a.82.5	yes	280
13.10	even	6		403.2.bp.a.361.31	yes	280
31.14	even	15		403.2.bp.a.355.31	✓	280
403.231	even	30	inner	403.2.bt.a.231.5	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bp.a.355.31	✓	280	31.14	even	15
403.2.bp.a.361.31	yes	280	13.10	even	6
403.2.bt.a.82.5	yes	280	1.1	even	1	trivial
403.2.bt.a.231.5	yes	280	403.231	even	30	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bt (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.475411 + 2.23663i) q^{2} +(0.254115 - 0.0540139i) q^{3} +(-2.94943 - 1.31317i) q^{4} +(-0.204817 + 0.118251i) q^{5} +0.594042i q^{6} +(1.78231 + 2.45313i) q^{7} +(1.65121 - 2.27270i) q^{8} +(-2.67898 + 1.19276i) q^{9} +O(q^{10})\)	\(q+(-0.475411 + 2.23663i) q^{2} +(0.254115 - 0.0540139i) q^{3} +(-2.94943 - 1.31317i) q^{4} +(-0.204817 + 0.118251i) q^{5} +0.594042i q^{6} +(1.78231 + 2.45313i) q^{7} +(1.65121 - 2.27270i) q^{8} +(-2.67898 + 1.19276i) q^{9} +(-0.167112 - 0.514319i) q^{10} +(-0.594006 - 0.817579i) q^{11} +(-0.820424 - 0.174386i) q^{12} +(1.48679 + 3.28473i) q^{13} +(-6.33409 + 2.82012i) q^{14} +(-0.0456600 + 0.0411124i) q^{15} +(-0.0224550 - 0.0249389i) q^{16} +(0.0736818 + 0.0535329i) q^{17} +(-1.39415 - 6.55895i) q^{18} +(-4.30279 + 1.39806i) q^{19} +(0.759378 - 0.0798138i) q^{20} +(0.585414 + 0.527109i) q^{21} +(2.11102 - 0.939888i) q^{22} +(2.74939 - 1.22411i) q^{23} +(0.296841 - 0.666715i) q^{24} +(-2.47203 + 4.28169i) q^{25} +(-8.05358 + 1.76380i) q^{26} +(-1.24687 + 0.905906i) q^{27} +(-2.03540 - 9.57581i) q^{28} +(-7.66575 - 1.62941i) q^{29} +(-0.0702462 - 0.121670i) q^{30} +(-4.10120 - 3.76566i) q^{31} +(4.93215 - 2.84758i) q^{32} +(-0.195107 - 0.175675i) q^{33} +(-0.154763 + 0.139349i) q^{34} +(-0.655133 - 0.291684i) q^{35} +9.46775 q^{36} +(-0.141072 + 0.0814479i) q^{37} +(-1.08136 - 10.2884i) q^{38} +(0.555236 + 0.754393i) q^{39} +(-0.0694471 + 0.660745i) q^{40} +(10.8588 - 3.52823i) q^{41} +(-1.45726 + 1.05876i) q^{42} +(3.43452 + 10.5704i) q^{43} +(0.678358 + 3.19142i) q^{44} +(0.407656 - 0.561090i) q^{45} +(1.43079 + 6.73134i) q^{46} +(8.79804 + 2.85866i) q^{47} +(-0.00705321 - 0.00512446i) q^{48} +(-0.678129 + 2.08707i) q^{49} +(-8.40134 - 7.56460i) q^{50} +(0.0216152 + 0.00962370i) q^{51} +(-0.0717574 - 11.6405i) q^{52} +(-0.0366674 + 0.348867i) q^{53} +(-1.43340 - 3.21948i) q^{54} +(0.218342 + 0.0972123i) q^{55} +8.51819 q^{56} +(-1.01789 + 0.587679i) q^{57} +(7.28877 - 16.3708i) q^{58} +(4.31640 + 1.40248i) q^{59} +(0.188658 - 0.0612988i) q^{60} +(7.04928 + 12.2097i) q^{61} +(10.3722 - 7.38265i) q^{62} +(-7.70075 - 4.44603i) q^{63} +(4.00345 + 12.3214i) q^{64} +(-0.692943 - 0.496955i) q^{65} +(0.485676 - 0.352864i) q^{66} -0.874140i q^{67} +(-0.147021 - 0.254648i) q^{68} +(0.632543 - 0.459570i) q^{69} +(0.963848 - 1.32662i) q^{70} +(-3.03550 - 6.81784i) q^{71} +(-1.71278 + 8.05801i) q^{72} +(0.128044 - 0.287593i) q^{73} +(-0.115102 - 0.354248i) q^{74} +(-0.396911 + 1.22157i) q^{75} +(14.5267 + 1.52681i) q^{76} +(0.946930 - 2.91435i) q^{77} +(-1.95127 + 0.883213i) q^{78} +(-11.4744 + 5.10871i) q^{79} +(0.00754823 + 0.00245257i) q^{80} +(5.61877 - 6.24028i) q^{81} +(2.72898 + 25.9645i) q^{82} +(4.55715 + 4.10328i) q^{83} +(-1.03445 - 2.32342i) q^{84} +(-0.0214216 - 0.00225150i) q^{85} +(-25.2749 + 2.65650i) q^{86} -2.03599 q^{87} -2.83894 q^{88} +(-8.17750 + 0.859490i) q^{89} +(1.06115 + 1.17853i) q^{90} +(-5.40798 + 9.50168i) q^{91} -9.71660 q^{92} +(-1.24557 - 0.735389i) q^{93} +(-10.5765 + 18.3190i) q^{94} +(0.715963 - 0.795157i) q^{95} +(1.09952 - 0.990017i) q^{96} +(-4.74157 + 10.6497i) q^{97} +(-4.34562 - 2.50894i) q^{98} +(2.56650 + 1.48177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9 + 3 * q^10 - 8 * q^12 - 6 * q^13 + 4 * q^14 - 45 * q^15 + 23 * q^16 + 27 * q^17 + 45 * q^18 - 15 * q^19 - 12 * q^20 - 76 * q^21 + 41 * q^22 - 10 * q^23 - 33 * q^24 + 96 * q^25 + 9 * q^26 - 24 * q^27 - 32 * q^28 + 13 * q^29 + 36 * q^30 + 2 * q^31 - 141 * q^32 - 93 * q^33 - 9 * q^34 - 43 * q^35 - 194 * q^36 + 3 * q^37 - 49 * q^38 + 50 * q^39 - 75 * q^40 - 15 * q^41 + 17 * q^42 + 33 * q^43 + 18 * q^44 - 15 * q^45 - 9 * q^46 - 59 * q^48 + 3 * q^49 + 36 * q^50 + 47 * q^51 - 56 * q^52 + 12 * q^53 - 33 * q^54 - 5 * q^55 - 50 * q^56 - 105 * q^57 - 3 * q^58 - 15 * q^59 + 90 * q^60 - 57 * q^61 - 72 * q^62 + 201 * q^63 + 13 * q^64 - 43 * q^65 + 22 * q^66 - 71 * q^68 - 7 * q^69 - 42 * q^71 + 90 * q^72 + 9 * q^73 - 113 * q^74 + 45 * q^75 + 14 * q^76 - 24 * q^77 + 61 * q^78 + 54 * q^79 + 30 * q^80 + 106 * q^81 + 16 * q^82 + 54 * q^83 + 60 * q^84 + 18 * q^85 + 84 * q^86 + 42 * q^87 - 98 * q^88 - 99 * q^89 + 11 * q^90 + 60 * q^91 + 266 * q^92 - 104 * q^93 + 33 * q^94 - 120 * q^95 + 204 * q^96 - 50 * q^97 - 15 * q^98 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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