LMFDB - Embedded newform 507.2.q.b.490.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			490.14
Character	$\chi$	$=$	507.490
Dual form			507.2.q.b.328.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.387197 + 1.89662i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-1.60728 + 0.684799i) q^{4} +(-3.18847 + 0.785887i) q^{5} +(0.0779443 + 1.93417i) q^{6} +(-0.0361239 + 0.0761296i) q^{7} +(0.278113 + 0.402916i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(0.387197 + 1.89662i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-1.60728 + 0.684799i) q^{4} +(-3.18847 + 0.785887i) q^{5} +(0.0779443 + 1.93417i) q^{6} +(-0.0361239 + 0.0761296i) q^{7} +(0.278113 + 0.402916i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-2.72510 - 5.74302i) q^{10} +(-1.87546 + 0.626122i) q^{11} +(-1.69632 + 0.418105i) q^{12} +(0.194884 + 3.60028i) q^{13} +(-0.158376 - 0.0390362i) q^{14} +(-3.27324 + 0.264244i) q^{15} +(-3.07699 + 3.20348i) q^{16} +(-2.58020 + 5.43765i) q^{17} +(-0.233328 + 1.92162i) q^{18} +(-3.08753 - 5.34776i) q^{19} +(4.58659 - 3.44660i) q^{20} +(-0.0478682 + 0.0693490i) q^{21} +(-1.91369 - 3.31461i) q^{22} +(2.72042 - 4.71190i) q^{23} +(0.209879 + 0.442311i) q^{24} +(5.12144 - 2.68794i) q^{25} +(-6.75290 + 1.76364i) q^{26} +(0.885456 + 0.464723i) q^{27} +(0.00592790 - 0.147099i) q^{28} +(1.19623 + 5.85950i) q^{29} +(-1.76856 - 6.10578i) q^{30} +(-4.20912 - 2.20912i) q^{31} +(-6.43961 - 4.07217i) q^{32} +(-1.95161 + 0.317168i) q^{33} +(-11.3122 - 2.78821i) q^{34} +(0.0553508 - 0.271126i) q^{35} +(-1.74142 + 0.140582i) q^{36} +(8.03223 - 5.07928i) q^{37} +(8.94717 - 7.92650i) q^{38} +(-0.385165 + 3.58492i) q^{39} +(-1.20340 - 1.06612i) q^{40} +(-1.67543 - 0.272285i) q^{41} +(-0.150063 - 0.0639359i) q^{42} +(7.42578 + 4.69578i) q^{43} +(2.58563 - 2.29067i) q^{44} +(-3.27324 - 0.264244i) q^{45} +(9.99002 + 3.33516i) q^{46} +(0.807113 + 6.64717i) q^{47} +(-3.55102 + 2.66842i) q^{48} +(4.42263 + 5.41673i) q^{49} +(7.08100 + 8.67265i) q^{50} +(-3.41904 + 4.95334i) q^{51} +(-2.77870 - 5.65321i) q^{52} +(6.56441 + 9.51018i) q^{53} +(-0.538556 + 1.85931i) q^{54} +(5.48780 - 3.47027i) q^{55} +(-0.0407204 + 0.00661770i) q^{56} +(-2.18971 - 5.77378i) q^{57} +(-10.6501 + 4.53757i) q^{58} +(1.83591 + 1.91139i) q^{59} +(5.08007 - 2.66623i) q^{60} +(8.54651 + 0.689945i) q^{61} +(2.56009 - 8.83847i) q^{62} +(-0.0583727 + 0.0607724i) q^{63} +(2.07973 - 5.48379i) q^{64} +(-3.45080 - 11.3262i) q^{65} +(-1.35721 - 3.57866i) q^{66} +(-3.72885 - 1.58871i) q^{67} +(0.423407 - 10.5067i) q^{68} +(3.44103 - 4.21450i) q^{69} +0.535655 q^{70} +(-0.0492959 + 0.0603766i) q^{71} +(0.136210 + 0.470250i) q^{72} +(-2.12613 - 1.88358i) q^{73} +(12.7435 + 13.2674i) q^{74} +(5.48629 - 1.83159i) q^{75} +(8.62466 + 6.48101i) q^{76} +(0.0200827 - 0.165396i) q^{77} +(-6.94836 + 0.657560i) q^{78} +(-1.30348 - 10.7351i) q^{79} +(7.29331 - 12.6324i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.132304 - 3.28309i) q^{82} +(-2.02938 + 5.35105i) q^{83} +(0.0294475 - 0.144243i) q^{84} +(3.95350 - 19.3655i) q^{85} +(-6.03086 + 15.9021i) q^{86} +(0.240805 + 5.97551i) q^{87} +(-0.773865 - 0.581521i) q^{88} +(-3.02400 + 5.23773i) q^{89} +(-0.766223 - 6.31041i) q^{90} +(-0.281128 - 0.115220i) q^{91} +(-1.14577 + 9.43629i) q^{92} +(-3.80025 - 2.85570i) q^{93} +(-12.2946 + 4.10455i) q^{94} +(14.0472 + 14.6247i) q^{95} +(-5.70300 - 5.05242i) q^{96} +(2.82518 + 9.75364i) q^{97} +(-8.56105 + 10.4854i) q^{98} -1.97722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{17}{39}\right)$

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 $

$2$	0.387197	+	1.89662i	0.273790	+	1.34111i	0.851279	+	0.524713i	$0.175828\pi$
$2$	0.387197	+	1.89662i	0.273790	+	1.34111i	−0.577489	+	0.816398i	$0.695967\pi$
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$4$	−1.60728	+	0.684799i	−0.803641	+	0.342399i
$5$	−3.18847	+	0.785887i	−1.42593	+	0.351459i	−0.875417	−	0.483369i	$-0.839413\pi$
$5$	−3.18847	+	0.785887i	−1.42593	+	0.351459i	−0.550510	+	0.834828i	$0.685567\pi$
$6$	0.0779443	+	1.93417i	0.0318206	+	0.789621i
$7$	−0.0361239	+	0.0761296i	−0.0136536	+	0.0287743i	−0.910163	−	0.414251i	$-0.864044\pi$
$7$	−0.0361239	+	0.0761296i	−0.0136536	+	0.0287743i	0.896509	+	0.443025i	$0.146095\pi$
$8$	0.278113	+	0.402916i	0.0983277	+	0.142452i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	−2.72510	−	5.74302i	−0.861751	−	1.81610i
$11$	−1.87546	+	0.626122i	−0.565473	+	0.188783i	−0.585010	−	0.811026i	$-0.698909\pi$
$11$	−1.87546	+	0.626122i	−0.565473	+	0.188783i	0.0195362	+	0.999809i	$0.493781\pi$
$12$	−1.69632	+	0.418105i	−0.489685	+	0.120696i
$13$	0.194884	+	3.60028i	0.0540511	+	0.998538i
$13$	0.194884	+	3.60028i	0.0540511	+	0.998538i
$14$	−0.158376	−	0.0390362i	−0.0423277	−	0.0104329i
$15$	−3.27324	+	0.264244i	−0.845148	+	0.0682274i
$16$	−3.07699	+	3.20348i	−0.769247	+	0.800871i
$17$	−2.58020	+	5.43765i	−0.625790	+	1.31882i	0.304680	+	0.952455i	$0.401450\pi$
$17$	−2.58020	+	5.43765i	−0.625790	+	1.31882i	−0.930470	+	0.366369i	$0.880601\pi$
$18$	−0.233328	+	1.92162i	−0.0549958	+	0.452931i
$19$	−3.08753	−	5.34776i	−0.708328	−	1.22686i	−0.965477	−	0.260488i	$-0.916117\pi$
$19$	−3.08753	−	5.34776i	−0.708328	−	1.22686i	0.257149	−	0.966372i	$-0.417217\pi$
$20$	4.58659	−	3.44660i	1.02559	−	0.770683i
$21$	−0.0478682	+	0.0693490i	−0.0104457	+	0.0151332i
$22$	−1.91369	−	3.31461i	−0.408000	−	0.706676i
$23$	2.72042	−	4.71190i	0.567246	−	0.982499i	−0.429591	−	0.903024i	$-0.641342\pi$
$23$	2.72042	−	4.71190i	0.567246	−	0.982499i	0.996837	−	0.0794754i	$-0.0253245\pi$
$24$	0.209879	+	0.442311i	0.0428414	+	0.0902863i
$25$	5.12144	−	2.68794i	1.02429	−	0.537588i
$26$	−6.75290	+	1.76364i	−1.32435	+	0.345878i
$27$	0.885456	+	0.464723i	0.170406	+	0.0894360i
$28$	0.00592790	−	0.147099i	0.00112027	−	0.0277992i
$29$	1.19623	+	5.85950i	0.222133	+	1.08808i	0.925934	+	0.377684i	$0.123280\pi$
$29$	1.19623	+	5.85950i	0.222133	+	1.08808i	−0.703801	+	0.710397i	$0.748515\pi$
$30$	−1.76856	−	6.10578i	−0.322894	−	1.11476i
$31$	−4.20912	−	2.20912i	−0.755981	−	0.396769i	0.0422608	−	0.999107i	$-0.486544\pi$
$31$	−4.20912	−	2.20912i	−0.755981	−	0.396769i	−0.798242	+	0.602337i	$0.794236\pi$
$32$	−6.43961	−	4.07217i	−1.13837	−	0.719864i
$33$	−1.95161	+	0.317168i	−0.339732	+	0.0552119i
$34$	−11.3122	−	2.78821i	−1.94003	−	0.478173i
$35$	0.0553508	−	0.271126i	0.00935599	−	0.0458287i
$36$	−1.74142	+	0.140582i	−0.290236	+	0.0234303i
$37$	8.03223	−	5.07928i	1.32049	−	0.835028i	0.326575	−	0.945171i	$-0.394105\pi$
$37$	8.03223	−	5.07928i	1.32049	−	0.835028i	0.993916	+	0.110143i	$0.0351310\pi$
$38$	8.94717	−	7.92650i	1.45142	−	1.28585i
$39$	−0.385165	+	3.58492i	−0.0616758	+	0.574047i
$40$	−1.20340	−	1.06612i	−0.190274	−	0.168568i
$41$	−1.67543	−	0.272285i	−0.261659	−	0.0425237i	0.0281665	−	0.999603i	$-0.491033\pi$
$41$	−1.67543	−	0.272285i	−0.261659	−	0.0425237i	−0.289825	+	0.957080i	$0.593597\pi$
$42$	−0.150063	−	0.0639359i	−0.0231552	−	0.00986553i
$43$	7.42578	+	4.69578i	1.13242	+	0.716099i	0.963015	−	0.269447i	$-0.0868410\pi$
$43$	7.42578	+	4.69578i	1.13242	+	0.716099i	0.169405	+	0.985546i	$0.445815\pi$
$44$	2.58563	−	2.29067i	0.389798	−	0.345331i
$45$	−3.27324	−	0.264244i	−0.487946	−	0.0393911i
$46$	9.99002	+	3.33516i	1.47295	+	0.491742i
$47$	0.807113	+	6.64717i	0.117730	+	0.969590i	0.925147	+	0.379609i	$0.123942\pi$
$47$	0.807113	+	6.64717i	0.117730	+	0.969590i	−0.807417	+	0.589981i	$0.799135\pi$
$48$	−3.55102	+	2.66842i	−0.512545	+	0.385153i
$49$	4.42263	+	5.41673i	0.631804	+	0.773819i
$50$	7.08100	+	8.67265i	1.00140	+	1.22650i
$51$	−3.41904	+	4.95334i	−0.478762	+	0.693606i
$52$	−2.77870	−	5.65321i	−0.385336	−	0.783959i
$53$	6.56441	+	9.51018i	0.901691	+	1.30632i	0.951526	+	0.307567i	$0.0995148\pi$
$53$	6.56441	+	9.51018i	0.901691	+	1.30632i	−0.0498359	+	0.998757i	$0.515870\pi$
$54$	−0.538556	+	1.85931i	−0.0732882	+	0.253020i
$55$	5.48780	−	3.47027i	0.739974	−	0.467931i
$56$	−0.0407204	+	0.00661770i	−0.00544149	+	0.000884328i
$57$	−2.18971	−	5.77378i	−0.290034	−	0.764756i
$58$	−10.6501	+	4.53757i	−1.39842	+	0.595812i
$59$	1.83591	+	1.91139i	0.239016	+	0.248842i	0.829897	−	0.557917i	$-0.188399\pi$
$59$	1.83591	+	1.91139i	0.239016	+	0.248842i	−0.590881	+	0.806759i	$0.701220\pi$
$60$	5.08007	−	2.66623i	0.655834	−	0.344208i
$61$	8.54651	+	0.689945i	1.09427	+	0.0883385i	0.614394	−	0.788999i	$-0.289400\pi$
$61$	8.54651	+	0.689945i	1.09427	+	0.0883385i	0.479874	+	0.877338i	$0.340682\pi$
$62$	2.56009	−	8.83847i	0.325132	−	1.12249i
$63$	−0.0583727	+	0.0607724i	−0.00735427	+	0.00765660i
$64$	2.07973	−	5.48379i	0.259966	−	0.685474i
$65$	−3.45080	−	11.3262i	−0.428019	−	1.40485i
$66$	−1.35721	−	3.57866i	−0.167061	−	0.440503i
$67$	−3.72885	−	1.58871i	−0.455552	−	0.194092i	0.151987	−	0.988382i	$-0.451433\pi$
$67$	−3.72885	−	1.58871i	−0.455552	−	0.194092i	−0.607539	+	0.794290i	$0.707843\pi$
$68$	0.423407	−	10.5067i	0.0513457	−	1.27413i
$69$	3.44103	−	4.21450i	0.414251	−	0.507366i
$70$	0.535655			0.0640230
$71$	−0.0492959	+	0.0603766i	−0.00585035	+	0.00716538i	−0.777522	−	0.628856i	$-0.783524\pi$
$71$	−0.0492959	+	0.0603766i	−0.00585035	+	0.00716538i	0.771672	+	0.636021i	$0.219421\pi$
$72$	0.136210	+	0.470250i	0.0160524	+	0.0554195i
$73$	−2.12613	−	1.88358i	−0.248844	−	0.220457i	0.529475	−	0.848326i	$-0.322389\pi$
$73$	−2.12613	−	1.88358i	−0.248844	−	0.220457i	−0.778319	+	0.627869i	$0.783927\pi$
$74$	12.7435	+	13.2674i	1.48140	+	1.54230i
$75$	5.48629	−	1.83159i	0.633502	−	0.211494i
$76$	8.62466	+	6.48101i	0.989317	+	0.743423i
$77$	0.0200827	−	0.165396i	0.00228864	−	0.0188486i
$78$	−6.94836	+	0.657560i	−0.786747	+	0.0744540i
$79$	−1.30348	−	10.7351i	−0.146653	−	1.20780i	−0.861221	−	0.508231i	$-0.830300\pi$
$79$	−1.30348	−	10.7351i	−0.146653	−	1.20780i	0.714568	−	0.699566i	$-0.246623\pi$
$80$	7.29331	−	12.6324i	0.815416	−	1.41234i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	−0.132304	−	3.28309i	−0.0146105	−	0.362556i
$83$	−2.02938	+	5.35105i	−0.222754	+	0.587354i	−0.999076	−	0.0429829i	$-0.986314\pi$
$83$	−2.02938	+	5.35105i	−0.222754	+	0.587354i	0.776322	+	0.630337i	$0.217083\pi$
$84$	0.0294475	−	0.144243i	0.00321299	−	0.0157383i
$85$	3.95350	−	19.3655i	0.428817	−	2.10049i
$86$	−6.03086	+	15.9021i	−0.650324	+	1.71476i
$87$	0.240805	+	5.97551i	0.0258170	+	0.640642i
$88$	−0.773865	−	0.581521i	−0.0824942	−	0.0619904i
$89$	−3.02400	+	5.23773i	−0.320544	+	0.555198i	−0.980600	−	0.196018i	$-0.937199\pi$
$89$	−3.02400	+	5.23773i	−0.320544	+	0.555198i	0.660057	+	0.751216i	$0.270532\pi$
$90$	−0.766223	−	6.31041i	−0.0807670	−	0.665176i
$91$	−0.281128	−	0.115220i	−0.0294702	−	0.0120783i
$92$	−1.14577	+	9.43629i	−0.119455	+	0.983801i
$93$	−3.80025	−	2.85570i	−0.394068	−	0.296123i
$94$	−12.2946	+	4.10455i	−1.26810	+	0.423352i
$95$	14.0472	+	14.6247i	1.44121	+	1.50046i
$96$	−5.70300	−	5.05242i	−0.582060	−	0.515660i
$97$	2.82518	+	9.75364i	0.286853	+	0.990333i	0.966473	+	0.256768i	$0.0826576\pi$
$97$	2.82518	+	9.75364i	0.286853	+	0.990333i	−0.679620	+	0.733565i	$0.737855\pi$
$98$	−8.56105	+	10.4854i	−0.864797	+	1.05918i
$99$	−1.97722			−0.198718
$100$	−6.39089	+	7.82742i	−0.639089	+	0.782742i
$101$	0.714926	−	17.7407i	0.0711378	−	1.76527i	−0.432766	−	0.901506i	$-0.642463\pi$
$101$	0.714926	−	17.7407i	0.0711378	−	1.76527i	0.503904	−	0.863760i	$-0.331896\pi$
$102$	−10.7184	−	4.56670i	−1.06128	−	0.452171i
$103$	1.51772	+	4.00190i	0.149545	+	0.394319i	0.988766	−	0.149473i	$-0.0477576\pi$
$103$	1.51772	+	4.00190i	0.149545	+	0.394319i	−0.839221	+	0.543791i	$0.816988\pi$
$104$	−1.39641	+	1.07981i	−0.136929	+	0.105884i
$105$	0.0981257	−	0.258736i	0.00957609	−	0.0252501i
$106$	−15.4955	+	16.1325i	−1.50505	+	1.56693i
$107$	5.19799	−	17.9455i	0.502508	−	1.73486i	−0.161250	−	0.986914i	$-0.551553\pi$
$107$	5.19799	−	17.9455i	0.502508	−	1.73486i	0.663759	−	0.747947i	$-0.268960\pi$
$108$	−1.74142	−	0.140582i	−0.167568	−	0.0135275i
$109$	8.50841	−	4.46556i	0.814958	−	0.427723i	−0.00511155	−	0.999987i	$-0.501627\pi$
$109$	8.50841	−	4.46556i	0.814958	−	0.427723i	0.820069	+	0.572264i	$0.193935\pi$
$110$	8.70664	+	9.06457i	0.830146	+	0.864273i
$111$	8.74299	−	3.72504i	0.829848	−	0.353565i
$112$	−0.132727	−	0.349972i	−0.0125415	−	0.0330693i
$113$	−3.02996	+	0.492417i	−0.285035	+	0.0463227i	−0.301248	−	0.953546i	$-0.597403\pi$
$113$	−3.02996	+	0.492417i	−0.285035	+	0.0463227i	0.0162129	+	0.999869i	$0.494839\pi$
$114$	10.1028	−	6.38863i	0.946215	−	0.598350i
$115$	−4.97094	+	17.1617i	−0.463543	+	1.60034i
$116$	−5.93525	−	8.59869i	−0.551074	−	0.798368i
$117$	−0.955239	+	3.47671i	−0.0883119	+	0.321422i
$118$	−2.91431	+	4.22211i	−0.268284	+	0.388677i
$119$	−0.320759	−	0.392859i	−0.0294039	−	0.0360133i
$120$	−1.01680	−	1.24535i	−0.0928206	−	0.113685i
$121$	−5.66854	+	4.25963i	−0.515322	+	0.387239i
$122$	2.00062	+	16.4766i	0.181128	+	1.49172i
$123$	−1.61006	−	0.537517i	−0.145174	−	0.0484663i
$124$	8.27805	+	0.668273i	0.743391	+	0.0600127i
$125$	−1.92698	+	1.70716i	−0.172355	+	0.152693i
$126$	−0.137864	−	0.0871798i	−0.0122819	−	0.00776659i
$127$	−11.1747	−	4.76109i	−0.991593	−	0.422478i	−0.165621	−	0.986189i	$-0.552963\pi$
$127$	−11.1747	−	4.76109i	−0.991593	−	0.422478i	−0.825972	+	0.563711i	$0.809373\pi$
$128$	−3.83500	−	0.623249i	−0.338970	−	0.0550879i
$129$	6.57636	+	5.82615i	0.579016	+	0.512964i
$130$	20.1454	−	10.9303i	1.76687	−	0.958653i
$131$	−4.76524	+	4.22164i	−0.416341	+	0.368846i	−0.845132	−	0.534558i	$-0.820478\pi$
$131$	−4.76524	+	4.22164i	−0.416341	+	0.368846i	0.428791	+	0.903404i	$0.358940\pi$
$132$	2.91960	−	1.84624i	0.254118	−	0.160695i
$133$	0.518656	−	0.0418703i	0.0449732	−	0.00363061i
$134$	1.56938	−	7.68735i	0.135574	−	0.664086i
$135$	−3.18847	−	0.785887i	−0.274420	−	0.0676384i
$136$	−2.90850	+	0.472677i	−0.249402	+	0.0405318i
$137$	15.2101	+	9.61832i	1.29949	+	0.821748i	0.991558	−	0.129660i	$-0.0413886\pi$
$137$	15.2101	+	9.61832i	1.29949	+	0.821748i	0.307932	+	0.951408i	$0.400363\pi$
$138$	9.32565	+	4.89448i	0.793852	+	0.416646i
$139$	5.45046	+	18.8172i	0.462302	+	1.59605i	0.765706	+	0.643190i	$0.222390\pi$
$139$	5.45046	+	18.8172i	0.462302	+	1.59605i	−0.303404	+	0.952862i	$0.598123\pi$
$140$	0.0967025	+	0.473680i	0.00817285	+	0.0400333i
$141$	−0.269620	+	6.69056i	−0.0227061	+	0.563447i
$142$	−0.133599	−	0.0701179i	−0.0112113	−	0.00588417i
$143$	−2.61971	−	6.63017i	−0.219071	−	0.554443i
$144$	−3.93308	+	2.06424i	−0.327756	+	0.172020i
$145$	−8.41903	−	17.7427i	−0.699163	−	1.47345i
$146$	2.74921	−	4.76177i	0.227526	−	0.394087i
$147$	3.49645	+	6.05603i	0.288382	+	0.499493i
$148$	−9.43178	+	13.6643i	−0.775287	+	1.12320i
$149$	2.01517	−	1.51430i	0.165089	−	0.124056i	−0.514987	−	0.857198i	$-0.672203\pi$
$149$	2.01517	−	1.51430i	0.165089	−	0.124056i	0.680076	+	0.733142i	$0.261947\pi$
$150$	5.59811	+	9.69621i	0.457084	+	0.791693i
$151$	−1.46847	+	12.0939i	−0.119502	+	0.984189i	0.802405	+	0.596779i	$0.203553\pi$
$151$	−1.46847	+	12.0939i	−0.119502	+	0.984189i	−0.921908	+	0.387410i	$0.873370\pi$
$152$	1.29601	−	2.73129i	0.105121	−	0.221537i
$153$	−4.16934	+	4.34074i	−0.337071	+	0.350928i
$154$	0.321470	−	0.0259517i	0.0259048	−	0.00209125i
$155$	15.1568	+	3.73581i	1.21742	+	0.300068i
$156$	−1.83588	−	6.02573i	−0.146988	−	0.482445i
$157$	8.80643	−	2.17059i	0.702829	−	0.173232i	0.128324	−	0.991732i	$-0.459040\pi$
$157$	8.80643	−	2.17059i	0.702829	−	0.173232i	0.574506	+	0.818500i	$0.305194\pi$
$158$	19.8558	−	6.62883i	1.57964	−	0.527361i
$159$	4.95386	+	10.4400i	0.392867	+	0.827949i
$160$	23.7328	+	7.92316i	1.87624	+	0.626381i
$161$	0.260443	+	0.377317i	0.0205258	+	0.0297367i
$162$	−0.829837	+	1.74884i	−0.0651981	+	0.137402i
$163$	−0.563307	−	13.9783i	−0.0441216	−	1.09487i	−0.857941	−	0.513748i	$-0.828257\pi$
$163$	−0.563307	−	13.9783i	−0.0441216	−	1.09487i	0.813820	−	0.581118i	$-0.197384\pi$
$164$	2.87935	−	0.709697i	0.224840	−	0.0554180i
$165$	5.97340	−	2.54503i	0.465029	−	0.198130i
$166$	−10.9347	−	1.77706i	−0.848695	−	0.137926i
$167$	−2.31773	−	11.3530i	−0.179351	−	0.878519i	−0.965484	−	0.260462i	$-0.916125\pi$
$167$	−2.31773	−	11.3530i	−0.179351	−	0.878519i	0.786133	−	0.618057i	$-0.212080\pi$
$168$	−0.0412546			−0.00318286
$169$	−12.9240	+	1.40327i	−0.994157	+	0.107944i
$170$	38.2598			2.93439
$171$	−1.23517	−	6.05026i	−0.0944558	−	0.462675i
$172$	−15.1510	−	2.46227i	−1.15525	−	0.187747i
$173$	3.02579	−	1.28917i	0.230047	−	0.0980137i	−0.273868	−	0.961767i	$-0.588303\pi$
$173$	3.02579	−	1.28917i	0.230047	−	0.0980137i	0.503914	+	0.863754i	$0.331893\pi$
$174$	−11.2400	+	2.77042i	−0.852104	+	0.210025i
$175$	0.0196251	+	0.486992i	0.00148352	+	0.0368131i
$176$	3.76501	−	7.93459i	0.283798	−	0.598092i
$177$	1.50553	+	2.18114i	0.113163	+	0.163944i
$178$	−11.1049	−	3.70735i	−0.832344	−	0.277877i
$179$	−6.26589	−	13.2051i	−0.468335	−	0.986995i	−0.990926	−	0.134411i	$-0.957086\pi$
$179$	−6.26589	−	13.2051i	−0.468335	−	0.986995i	0.522591	−	0.852584i	$-0.324966\pi$
$180$	5.44198	−	1.81680i	0.405621	−	0.135416i
$181$	−21.1071	+	5.20242i	−1.56888	+	0.386693i	−0.925467	−	0.378829i	$-0.876327\pi$
$181$	−21.1071	+	5.20242i	−1.56888	+	0.386693i	−0.643409	+	0.765522i	$0.722481\pi$
$182$	0.109676	−	0.577805i	0.00812974	−	0.0428298i
$183$	8.32516	+	2.05197i	0.615413	+	0.151686i
$184$	2.65508	−	0.214340i	0.195735	−	0.0158014i
$185$	−21.6188	+	22.5075i	−1.58944	+	1.65479i
$186$	3.94473	−	8.31334i	0.289242	−	0.609564i
$187$	1.43443	−	11.8136i	0.104896	−	0.863898i
$188$	−5.84923	−	10.1312i	−0.426599	−	0.738891i
$189$	−0.0673653	+	0.0506218i	−0.00490011	+	0.00368219i
$190$	−22.2984	+	32.3049i	−1.61770	+	2.34364i
$191$	−6.21997	−	10.7733i	−0.450061	−	0.779528i	0.548328	−	0.836263i	$-0.315264\pi$
$191$	−6.21997	−	10.7733i	−0.450061	−	0.779528i	−0.998389	+	0.0567347i	$0.981931\pi$
$192$	2.93246	−	5.07917i	0.211632	−	0.366557i
$193$	9.28382	+	19.5652i	0.668264	+	1.40834i	0.900144	+	0.435592i	$0.143461\pi$
$193$	9.28382	+	19.5652i	0.668264	+	1.40834i	−0.231880	+	0.972744i	$0.574488\pi$
$194$	−17.4050	+	9.13487i	−1.24961	+	0.655846i
$195$	−1.58925	−	11.7331i	−0.113809	−	0.840225i
$196$	−10.8178	−	5.67761i	−0.772698	−	0.405543i
$197$	0.364894	−	9.05474i	0.0259976	−	0.645124i	−0.932693	−	0.360672i	$-0.882547\pi$
$197$	0.364894	−	9.05474i	0.0259976	−	0.645124i	0.958690	−	0.284452i	$-0.0918116\pi$
$198$	−0.765574	−	3.75003i	−0.0544070	−	0.266503i
$199$	3.11100	+	10.7404i	0.220533	+	0.761367i	0.992125	+	0.125250i	$0.0399733\pi$
$199$	3.11100	+	10.7404i	0.220533	+	0.761367i	−0.771593	+	0.636117i	$0.780540\pi$
$200$	2.50735	+	1.31596i	0.177296	+	0.0930523i
$201$	−3.42572	−	2.16629i	−0.241631	−	0.152798i
$202$	33.9242	−	5.51321i	2.38690	−	0.387908i
$203$	−0.489294	−	0.120600i	−0.0343417	−	0.00846446i
$204$	2.10333	−	10.3028i	0.147262	−	0.721338i
$205$	5.55606	−	0.448531i	0.388052	−	0.0313268i
$206$	−7.00241	+	4.42806i	−0.487881	+	0.308517i
$207$	4.07252	−	3.60794i	0.283060	−	0.250769i
$208$	−12.1331	−	10.4537i	−0.841279	−	0.724835i
$209$	9.13889	+	8.09635i	0.632150	+	0.560036i
$210$	0.528718	+	0.0859250i	0.0364850	+	0.00592939i
$211$	−7.76653	−	3.30901i	−0.534670	−	0.227801i	0.107718	−	0.994182i	$-0.465646\pi$
$211$	−7.76653	−	3.30901i	−0.534670	−	0.227801i	−0.642387	+	0.766380i	$0.722056\pi$
$212$	−17.0634	−	10.7902i	−1.17192	−	0.741077i
$213$	−0.0583426	+	0.0516871i	−0.00399757	+	0.00354154i
$214$	36.0485	+	2.91013i	2.46422	+	0.198933i
$215$	−27.3672	−	9.13652i	−1.86643	−	0.623105i
$216$	0.0590123	+	0.486010i	0.00401528	+	0.0330688i
$217$	0.320229	−	0.240637i	0.0217386	−	0.0163355i
$218$	11.7639	+	14.4082i	0.796752	+	0.975843i
$219$	−1.79645	−	2.20025i	−0.121393	−	0.148679i
$220$	−6.44399	+	9.33574i	−0.434454	+	0.629415i
$221$	−20.0799	−	8.22972i	−1.35072	−	0.553591i
$222$	10.4502	+	15.1398i	0.701374	+	1.01612i
$223$	0.00922517	−	0.0318490i	0.000617763	−	0.00213277i	−0.960209	−	0.279284i	$-0.909903\pi$
$223$	0.00922517	−	0.0318490i	0.000617763	−	0.00213277i	0.960826	+	0.277151i	$0.0893902\pi$
$224$	0.542637	−	0.343143i	0.0362564	−	0.0229272i
$225$	5.70905	−	0.927812i	0.380604	−	0.0618541i
$226$	−2.10712	−	5.55602i	−0.140164	−	0.369581i
$227$	−0.415697	+	0.177112i	−0.0275908	+	0.0117553i	−0.405718	−	0.913998i	$-0.632978\pi$
$227$	−0.415697	+	0.177112i	−0.0275908	+	0.0117553i	0.378127	+	0.925754i	$0.376568\pi$
$228$	7.47335	+	7.78058i	0.494935	+	0.515281i
$229$	21.9472	−	11.5188i	1.45031	−	0.761181i	0.458474	−	0.888708i	$-0.348396\pi$
$229$	21.9472	−	11.5188i	1.45031	−	0.761181i	0.991835	+	0.127527i	$0.0407041\pi$
$230$	−34.4739	−	2.78302i	−2.27314	−	0.183507i
$231$	0.0463541	−	0.160033i	0.00304987	−	0.0105294i
$232$	−2.02820	+	2.11158i	−0.133158	+	0.138632i
$233$	−2.21656	+	5.84459i	−0.145212	+	0.382892i	−0.987813	−	0.155646i	$-0.950254\pi$
$233$	−2.21656	+	5.84459i	−0.145212	+	0.382892i	0.842601	+	0.538538i	$0.181023\pi$
$234$	−6.96386	−	0.465550i	−0.455242	−	0.0304340i
$235$	−7.79738	−	20.5600i	−0.508645	−	1.34119i
$236$	−4.25975	−	1.81491i	−0.277286	−	0.118140i
$237$	0.435435	−	10.8052i	0.0282846	−	0.701874i
$238$	0.620906	−	0.760472i	0.0402474	−	0.0492941i
$239$	0.630832			0.0408051			0.0204026	−	0.999792i	$-0.493505\pi$
$239$	0.630832			0.0408051			0.0204026	+	0.999792i	$0.493505\pi$
$240$	9.22524	−	11.2989i	0.595486	−	0.729338i
$241$	−1.04581	−	3.61055i	−0.0673665	−	0.232576i	0.919770	−	0.392459i	$-0.128375\pi$
$241$	−1.04581	−	3.61055i	−0.0673665	−	0.232576i	−0.987136	+	0.159883i	$0.948888\pi$
$242$	−10.2737	−	9.10173i	−0.660421	−	0.585082i
$243$	0.692724	+	0.721202i	0.0444383	+	0.0462652i
$244$	−14.2091	+	4.74370i	−0.909646	+	0.303684i
$245$	−18.3584	−	13.7954i	−1.17287	−	0.881356i
$246$	0.396054	−	3.26180i	0.0252515	−	0.207965i
$247$	18.6517	−	12.1582i	1.18678	−	0.773605i
$248$	−0.280522	−	2.31031i	−0.0178132	−	0.146705i
$249$	−2.86147	+	4.95622i	−0.181338	+	0.314087i
$250$	−3.98395	−	2.99374i	−0.251967	−	0.189341i
$251$	0.120950	+	3.00135i	0.00763430	+	0.189443i	0.998506	+	0.0546371i	$0.0174002\pi$
$251$	0.120950	+	3.00135i	0.00763430	+	0.189443i	−0.990872	+	0.134806i	$0.956959\pi$
$252$	0.0522045	−	0.137652i	0.00328857	−	0.00867125i
$253$	−2.15182	+	10.5403i	−0.135284	+	0.662663i
$254$	4.70316	−	23.0376i	0.295102	−	1.44551i
$255$	7.00875	−	18.4806i	0.438905	−	1.15730i
$256$	−0.775151	−	19.2352i	−0.0484470	−	1.20220i
$257$	0.385259	+	0.289503i	0.0240318	+	0.0180587i	0.612690	−	0.790323i	$-0.290087\pi$
$257$	0.385259	+	0.289503i	0.0240318	+	0.0180587i	−0.588659	+	0.808382i	$0.700344\pi$
$258$	−8.50363	+	14.7287i	−0.529413	+	0.916970i
$259$	0.0965273	+	0.794974i	0.00599792	+	0.0493973i
$260$	13.3026	+	15.8413i	0.824991	+	0.982438i
$261$	−0.720853	+	5.93675i	−0.0446197	+	0.367476i
$262$	−9.85192	−	7.40324i	−0.608654	−	0.457374i
$263$	−2.38827	+	0.797321i	−0.147267	+	0.0491649i	−0.389346	−	0.921092i	$-0.627299\pi$
$263$	−2.38827	+	0.797321i	−0.147267	+	0.0491649i	0.242079	+	0.970257i	$0.422171\pi$
$264$	−0.670561	−	0.698128i	−0.0412702	−	0.0429668i
$265$	−28.4043	−	25.1640i	−1.74486	−	1.54582i
$266$	0.280234	+	0.967481i	0.0171823	+	0.0593201i
$267$	−3.82503	+	4.68482i	−0.234088	+	0.286706i
$268$	7.08126			0.432557
$269$	8.98472	−	11.0043i	0.547808	−	0.670943i	−0.424288	−	0.905527i	$-0.639475\pi$
$269$	8.98472	−	11.0043i	0.547808	−	0.670943i	0.972096	+	0.234584i	$0.0753729\pi$
$270$	0.255961	−	6.35160i	0.0155773	−	0.386546i
$271$	21.3456	+	9.09451i	1.29665	+	0.552452i	0.926422	−	0.376488i	$-0.122868\pi$
$271$	21.3456	+	9.09451i	1.29665	+	0.552452i	0.370231	+	0.928940i	$0.379279\pi$
$272$	−9.48019	−	24.9972i	−0.574821	−	1.51568i
$273$	−0.259005	−	0.158824i	−0.0156757	−	0.00961246i
$274$	−12.3529	+	32.5720i	−0.746269	+	1.96775i
$275$	−7.92209	+	8.24777i	−0.477720	+	0.497359i
$276$	−2.64462	+	9.13030i	−0.159188	+	0.549579i
$277$	11.1963	+	0.903862i	0.672723	+	0.0543078i	0.412108	−	0.911135i	$-0.364793\pi$
$277$	11.1963	+	0.903862i	0.672723	+	0.0543078i	0.260615	+	0.965443i	$0.416075\pi$
$278$	−33.5786	+	17.6234i	−2.01391	+	1.05698i
$279$	−3.29295	−	3.42832i	−0.197144	−	0.205248i
$280$	0.124635	−	0.0531019i	0.00744836	−	0.00317345i
$281$	−1.57073	−	4.14168i	−0.0937020	−	0.247072i	0.879968	−	0.475032i	$-0.157564\pi$
$281$	−1.57073	−	4.14168i	−0.0937020	−	0.247072i	−0.973670	+	0.227960i	$0.926794\pi$
$282$	−12.7938	+	2.07920i	−0.761862	+	0.123815i
$283$	24.3905	−	15.4236i	1.44986	−	0.916838i	0.450148	−	0.892954i	$-0.351371\pi$
$283$	24.3905	−	15.4236i	1.44986	−	0.916838i	0.999715	−	0.0238839i	$-0.00760322\pi$
$284$	0.0378867	−	0.130800i	0.00224816	−	0.00776155i
$285$	11.5193	+	16.6887i	0.682347	+	0.988551i
$286$	11.5606	−	7.53578i	0.683590	−	0.445600i
$287$	0.0812522	−	0.117714i	0.00479617	−	0.00694845i
$288$	−4.81868	−	5.90182i	−0.283944	−	0.347768i
$289$	−12.1590	−	14.8921i	−0.715238	−	0.876008i
$290$	30.3914	−	22.8376i	1.78464	−	1.34107i
$291$	1.22400	+	10.0805i	0.0717520	+	0.590931i
$292$	4.70716	+	1.57148i	0.275466	+	0.0919639i
$293$	−22.2834	−	1.79890i	−1.30181	−	0.105093i	−0.589966	−	0.807428i	$-0.700859\pi$
$293$	−22.2834	−	1.79890i	−1.30181	−	0.105093i	−0.711846	+	0.702335i	$0.752141\pi$
$294$	−10.1322	+	8.97631i	−0.590920	+	0.523509i
$295$	−7.35589	−	4.65158i	−0.428277	−	0.270826i
$296$	4.28039	+	1.82370i	0.248792	+	0.106001i
$297$	−1.95161	−	0.317168i	−0.113244	−	0.0184040i
$298$	3.65232	+	3.23567i	0.211573	+	0.187437i
$299$	17.4943	+	8.87599i	1.01172	+	0.513312i
$300$	−7.56374	+	6.70089i	−0.436693	+	0.386876i
$301$	−0.625736	+	0.395691i	−0.0360668	+	0.0228073i
$302$	−23.5061	+	1.89761i	−1.35263	+	0.109195i
$303$	3.55148	−	17.3963i	0.204027	−	0.999390i
$304$	26.6317	+	6.56414i	1.52744	+	0.376479i
$305$	−27.7925	+	4.51672i	−1.59139	+	0.258627i
$306$	−9.84709	−	6.22692i	−0.562921	−	0.355970i
$307$	−23.0214	−	12.0826i	−1.31390	−	0.689588i	−0.345366	−	0.938468i	$-0.612245\pi$
$307$	−23.0214	−	12.0826i	−1.31390	−	0.689588i	−0.968534	+	0.248880i	$0.919938\pi$
$308$	0.0809845	+	0.279591i	0.00461452	+	0.0159312i
$309$	0.856116	+	4.19353i	0.0487027	+	0.238562i
$310$	−1.21674	+	30.1931i	−0.0691063	+	1.71485i
$311$	−11.5886	−	6.08215i	−0.657127	−	0.344887i	0.102981	−	0.994683i	$-0.467162\pi$
$311$	−11.5886	−	6.08215i	−0.657127	−	0.344887i	−0.760108	+	0.649796i	$0.774854\pi$
$312$	−1.55154	+	0.841823i	−0.0878387	+	0.0476588i
$313$	−26.4377	+	13.8756i	−1.49434	+	0.784292i	−0.996549	−	0.0830022i	$-0.973549\pi$
$313$	−26.4377	+	13.8756i	−1.49434	+	0.784292i	−0.497795	+	0.867295i	$0.665857\pi$
$314$	7.52661	+	15.8620i	0.424751	+	0.895144i
$315$	0.138359	−	0.239645i	0.00779566	−	0.0135025i
$316$	9.44647	+	16.3618i	0.531405	+	0.920421i
$317$	−13.8379	+	20.0476i	−0.777214	+	1.12599i	0.211677	+	0.977340i	$0.432108\pi$
$317$	−13.8379	+	20.0476i	−0.777214	+	1.12599i	−0.988890	+	0.148648i	$0.952508\pi$
$318$	−17.8826	+	13.4379i	−1.00281	+	0.753562i
$319$	−5.91224	−	10.2403i	−0.331022	−	0.573346i
$320$	−2.32151	+	19.1193i	−0.129776	+	1.06880i
$321$	8.00934	−	16.8793i	0.447038	−	0.942112i
$322$	−0.614783	+	0.640057i	−0.0342605	+	0.0356690i
$323$	37.0457	−	2.99063i	2.06128	−	0.166403i
$324$	−1.69632	−	0.418105i	−0.0942398	−	0.0232280i
$325$	10.6754	+	17.9148i	0.592166	+	0.993733i
$326$	26.2934	−	6.48074i	1.45626	−	0.358935i
$327$	9.11455	−	3.04289i	0.504036	−	0.168272i
$328$	−0.356252	−	0.750785i	−0.0196707	−	0.0414552i
$329$	−0.535203	−	0.178677i	−0.0295067	−	0.00985078i
$330$	7.13983	+	10.3438i	0.393035	+	0.569409i
$331$	−8.52816	+	17.9727i	−0.468750	+	0.987870i	0.522098	+	0.852886i	$0.325150\pi$
$331$	−8.52816	+	17.9727i	−0.468750	+	0.987870i	−0.990848	+	0.134984i	$0.956902\pi$
$332$	−0.402598	−	9.99036i	−0.0220954	−	0.548292i
$333$	9.22731	−	2.27433i	0.505653	−	0.124632i
$334$	20.6348	−	8.79168i	1.12909	−	0.481060i
$335$	13.1379	+	2.13511i	0.717799	+	0.116654i
$336$	−0.0748687	−	0.366731i	−0.00408442	−	0.0200068i
$337$	16.4328			0.895151			0.447575	−	0.894246i	$-0.352288\pi$
$337$	16.4328			0.895151			0.447575	+	0.894246i	$0.352288\pi$
$338$	−7.66563	−	23.9686i	−0.416955	−	1.30372i
$339$	−3.06972			−0.166724
$340$	6.90710	+	33.8332i	0.374590	+	1.83486i
$341$	9.27723	+	1.50770i	0.502390	+	0.0816464i
$342$	10.9968	−	4.68529i	0.594638	−	0.253352i
$343$	−1.14485	+	0.282181i	−0.0618163	+	0.0152363i
$344$	0.173200	+	4.29792i	0.00933833	+	0.231728i
$345$	−7.65950	+	16.1421i	−0.412374	+	0.869059i
$346$	3.61664	+	5.23961i	0.194432	+	0.281683i
$347$	7.20946	+	2.40687i	0.387024	+	0.129208i	0.503520	−	0.863984i	$-0.332038\pi$
$347$	7.20946	+	2.40687i	0.387024	+	0.129208i	−0.116496	+	0.993191i	$0.537166\pi$
$348$	−4.47906	−	9.43942i	−0.240103	−	0.506006i
$349$	11.7008	−	3.90630i	0.626329	−	0.209099i	0.0142534	−	0.999898i	$-0.495463\pi$
$349$	11.7008	−	3.90630i	0.626329	−	0.209099i	0.612076	+	0.790799i	$0.290335\pi$
$350$	−0.916039	+	0.225783i	−0.0489643	+	0.0120686i
$351$	−1.50057	+	3.27846i	−0.0800946	+	0.174991i
$352$	14.6269	+	3.60521i	0.779618	+	0.192159i
$353$	−27.6543	+	2.23248i	−1.47189	+	0.118823i	−0.790213	−	0.612832i	$-0.790030\pi$
$353$	−27.6543	+	2.23248i	−1.47189	+	0.118823i	−0.681675	+	0.731655i	$0.738748\pi$
$354$	−3.55385	+	3.69995i	−0.188885	+	0.196650i
$355$	0.109729	−	0.231250i	0.00582383	−	0.0122735i
$356$	1.27364	−	10.4893i	0.0675026	−	0.555934i
$357$	−0.253586	−	0.439225i	−0.0134212	−	0.0232462i
$358$	22.6189	−	16.9970i	1.19544	−	0.898319i
$359$	17.1650	−	24.8678i	0.905933	−	1.31247i	−0.0436794	−	0.999046i	$-0.513908\pi$
$359$	17.1650	−	24.8678i	0.905933	−	1.31247i	0.949613	−	0.313426i	$-0.101477\pi$
$360$	−0.803863	−	1.39233i	−0.0423673	−	0.0733823i
$361$	−9.56567	+	16.5682i	−0.503456	+	0.872012i
$362$	−18.0396	−	38.0177i	−0.948141	−	1.99817i
$363$	−6.27842	+	3.29517i	−0.329532	+	0.172952i
$364$	0.530754	−	0.00732522i	0.0278191	−	0.000383946i
$365$	8.25937	+	4.33485i	0.432315	+	0.226897i
$366$	−0.668319	+	16.5842i	−0.0349336	+	0.866868i
$367$	−4.60467	−	22.5552i	−0.240362	−	1.17737i	−0.903405	−	0.428789i	$-0.858940\pi$
$367$	−4.60467	−	22.5552i	−0.240362	−	1.17737i	0.663043	−	0.748582i	$-0.269265\pi$
$368$	6.72381	+	23.2133i	0.350503	+	1.21008i
$369$	−1.50299	−	0.788828i	−0.0782424	−	0.0410648i
$370$	−51.0590	−	32.2877i	−2.65443	−	1.67856i
$371$	−0.961139	+	0.156200i	−0.0498998	+	0.00810951i
$372$	8.06365	+	1.98751i	0.418081	+	0.103048i
$373$	6.27731	−	30.7483i	0.325027	−	1.59209i	−0.408718	−	0.912661i	$-0.634024\pi$
$373$	6.27731	−	30.7483i	0.325027	−	1.59209i	0.733745	−	0.679425i	$-0.237771\pi$
$374$	22.9614	−	1.85363i	1.18730	−	0.0958490i
$375$	−2.17588	+	1.37594i	−0.112362	+	0.0710533i
$376$	−2.45378	+	2.17386i	−0.126544	+	0.112108i
$377$	−20.8627	+	5.44867i	−1.07448	+	0.280621i
$378$	−0.122094	−	0.108166i	−0.00627983	−	0.00556345i
$379$	14.2116	+	2.30961i	0.730001	+	0.118637i	0.514041	−	0.857766i	$-0.328148\pi$
$379$	14.2116	+	2.30961i	0.730001	+	0.118637i	0.215960	+	0.976402i	$0.430712\pi$
$380$	−32.5928	−	13.8865i	−1.67198	−	0.712363i
$381$	−10.2662	−	6.49198i	−0.525956	−	0.332594i
$382$	18.0245	−	15.9683i	0.922213	−	0.817009i
$383$	25.3807	+	2.04895i	1.29690	+	0.104696i	0.709559	−	0.704646i	$-0.248894\pi$
$383$	25.3807	+	2.04895i	1.29690	+	0.104696i	0.587337	+	0.809343i	$0.300176\pi$
$384$	−3.68537	−	1.23036i	−0.188068	−	0.0627863i
$385$	0.0659496	+	0.543143i	0.00336110	+	0.0276812i
$386$	−33.5131	+	25.1835i	−1.70577	+	1.28180i
$387$	5.55662	+	6.80562i	0.282459	+	0.345949i
$388$	−11.2201	−	13.7422i	−0.569616	−	0.697653i
$389$	−13.1565	+	19.0604i	−0.667060	+	0.966403i	0.332667	+	0.943044i	$0.392051\pi$
$389$	−13.1565	+	19.0604i	−0.667060	+	0.966403i	−0.999727	+	0.0233586i	$0.992564\pi$
$390$	21.6379	−	7.55724i	1.09568	−	0.382676i
$391$	18.6025	+	26.9503i	0.940766	+	1.36294i
$392$	−0.952500	+	3.28841i	−0.0481085	+	0.166090i
$393$	−5.38073	+	3.40257i	−0.271422	+	0.171637i
$394$	17.3147	−	2.81391i	0.872301	−	0.141763i
$395$	12.5927	+	33.2043i	0.633608	+	1.67069i
$396$	3.17795	−	1.35400i	0.159698	−	0.0680409i
$397$	1.11142	+	1.15711i	0.0557806	+	0.0580738i	0.748508	−	0.663126i	$-0.230771\pi$
$397$	1.11142	+	1.15711i	0.0557806	+	0.0580738i	−0.692727	+	0.721200i	$0.743591\pi$
$398$	−19.1659	+	10.0590i	−0.960699	+	0.504214i
$399$	0.518656	+	0.0418703i	0.0259653	+	0.00209613i
$400$	−7.14784	+	24.6772i	−0.357392	+	1.23386i
$401$	−8.75713	+	9.11714i	−0.437310	+	0.455288i	−0.902988	−	0.429666i	$-0.858631\pi$
$401$	−8.75713	+	9.11714i	−0.437310	+	0.455288i	0.465678	+	0.884954i	$0.345811\pi$
$402$	2.78220	−	7.33606i	0.138764	−	0.365889i
$403$	7.13316	−	15.5845i	0.355328	−	0.776322i
$404$	10.9997	+	29.0039i	0.547256	+	1.44300i
$405$	−3.02111	−	1.28718i	−0.150120	−	0.0639603i
$406$	0.0392790	−	0.974699i	0.00194939	−	0.0483735i
$407$	−11.8839	+	14.5551i	−0.589064	+	0.721472i
$408$	−2.94666			−0.145881
$409$	−7.59902	+	9.30711i	−0.375747	+	0.460207i	−0.927512	−	0.373793i	$-0.878057\pi$
$409$	−7.59902	+	9.30711i	−0.375747	+	0.460207i	0.551765	+	0.834000i	$0.313955\pi$
$410$	3.00198	+	10.3640i	0.148257	+	0.511844i
$411$	13.4703	+	11.9336i	0.664441	+	0.588643i
$412$	−5.17990	−	5.39284i	−0.255195	−	0.265686i
$413$	−0.211834	+	0.0707205i	−0.0104237	+	0.00347993i
$414$	8.41976	+	6.32704i	0.413808	+	0.310957i
$415$	2.26531	−	18.6565i	0.111200	−	0.915812i
$416$	13.4060	−	23.9780i	0.657281	−	1.17562i
$417$	2.36139	+	19.4478i	0.115638	+	0.952364i
$418$	−11.8171	+	20.4679i	−0.577995	+	1.00112i
$419$	20.4958	+	15.4016i	1.00129	+	0.752418i	0.969000	−	0.247061i	$-0.0794649\pi$
$419$	20.4958	+	15.4016i	1.00129	+	0.752418i	0.0322860	+	0.999479i	$0.489721\pi$
$420$	0.0194666	+	0.483058i	0.000949872	+	0.0235708i
$421$	−6.13170	+	16.1680i	−0.298841	+	0.787978i	0.698535	+	0.715576i	$0.253836\pi$
$421$	−6.13170	+	16.1680i	−0.298841	+	0.787978i	−0.997376	+	0.0724020i	$0.976934\pi$
$422$	3.26875	−	16.0114i	0.159120	−	0.779422i
$423$	−1.33937	+	6.56067i	−0.0651224	+	0.318991i
$424$	−2.00616	+	5.28981i	−0.0974277	+	0.256896i
$425$	1.40175	+	34.7840i	0.0679947	+	1.68727i
$426$	−0.120621	−	0.0906406i	−0.00584410	−	0.00439155i
$427$	−0.361259	+	0.625719i	−0.0174825	+	0.0302806i
$428$	3.93445	+	32.4031i	0.190179	+	1.56626i
$429$	−1.52223	−	6.96454i	−0.0734941	−	0.336251i
$430$	6.73197	−	55.4428i	0.324645	−	2.67369i
$431$	−5.35768	−	4.02604i	−0.258070	−	0.193927i	0.463830	−	0.885924i	$-0.346475\pi$
$431$	−5.35768	−	4.02604i	−0.258070	−	0.193927i	−0.721901	+	0.691997i	$0.756731\pi$
$432$	−4.21327	+	1.40660i	−0.202711	+	0.0676749i
$433$	−4.74152	−	4.93644i	−0.227863	−	0.237230i	0.597450	−	0.801906i	$-0.296181\pi$
$433$	−4.74152	−	4.93644i	−0.227863	−	0.237230i	−0.825313	+	0.564676i	$0.809001\pi$
$434$	0.580388	+	0.514179i	0.0278595	+	0.0246814i
$435$	−5.46387	−	18.8635i	−0.261973	−	0.904435i
$436$	−10.6174	+	13.0040i	−0.508481	+	0.622777i
$437$	−33.5975			−1.60718
$438$	3.47745	−	4.25910i	0.166159	−	0.203508i
$439$	−0.912315	+	22.6389i	−0.0435424	+	1.08049i	0.818771	+	0.574120i	$0.194656\pi$
$439$	−0.912315	+	22.6389i	−0.0435424	+	1.08049i	−0.862314	+	0.506375i	$0.830985\pi$
$440$	2.92445	+	1.24599i	0.139418	+	0.0594004i
$441$	2.47972	+	6.53847i	0.118082	+	0.311356i
$442$	7.83375	−	41.2704i	0.372614	−	1.96303i
$443$	−1.55725	+	4.10613i	−0.0739871	+	0.195088i	−0.966908	−	0.255126i	$-0.917883\pi$
$443$	−1.55725	+	4.10613i	−0.0739871	+	0.195088i	0.892921	+	0.450214i	$0.148652\pi$
$444$	−11.5015	+	11.9744i	−0.545839	+	0.568279i
$445$	5.52568	−	19.0769i	0.261942	−	0.904330i
$446$	0.0639774	+	0.00516479i	0.00302942	+	0.000244560i
$447$	2.23198	−	1.17143i	0.105569	−	0.0554069i
$448$	0.342351	+	0.356425i	0.0161746	+	0.0168395i
$449$	−3.97777	+	1.69477i	−0.187722	+	0.0799810i	−0.483782	−	0.875188i	$-0.660737\pi$
$449$	−3.97777	+	1.69477i	−0.187722	+	0.0799810i	0.296060	+	0.955169i	$0.404327\pi$
$450$	3.97024	+	10.4687i	0.187159	+	0.493497i
$451$	3.31270	−	0.538366i	0.155989	−	0.0253507i
$452$	4.53280	−	2.86637i	0.213205	−	0.134823i
$453$	−3.38945	+	11.7017i	−0.159250	+	0.549796i
$454$	−0.496870	−	0.719841i	−0.0233193	−	0.0337838i
$455$	0.986917	+	0.146440i	0.0462674	+	0.00686522i
$456$	1.71736	−	2.48803i	0.0804229	−	0.116513i
$457$	15.1459	+	18.5504i	0.708497	+	0.867752i	0.995938	−	0.0900470i	$-0.0287017\pi$
$457$	15.1459	+	18.5504i	0.708497	+	0.867752i	−0.287440	+	0.957799i	$0.592804\pi$
$458$	30.3446	+	37.1653i	1.41791	+	1.73662i
$459$	−4.81165	+	3.61572i	−0.224589	+	0.168767i
$460$	−3.76260	−	30.9878i	−0.175432	−	1.44481i
$461$	5.54819	+	1.85226i	0.258405	+	0.0862683i	0.442919	−	0.896562i	$-0.353943\pi$
$461$	5.54819	+	1.85226i	0.258405	+	0.0862683i	−0.184514	+	0.982830i	$0.559071\pi$
$462$	0.321470	+	0.0259517i	0.0149561	+	0.00120738i
$463$	2.09874	−	1.85932i	0.0975368	−	0.0864100i	−0.612945	−	0.790125i	$-0.710015\pi$
$463$	2.09874	−	1.85932i	0.0975368	−	0.0864100i	0.710482	+	0.703715i	$0.248477\pi$
$464$	−22.4516	−	14.1975i	−1.04229	−	0.659103i
$465$	14.3612	+	6.11875i	0.665986	+	0.283750i
$466$	−11.9432	−	1.94096i	−0.553259	−	0.0899133i
$467$	−13.4963	−	11.9566i	−0.624532	−	0.553287i	0.290395	−	0.956907i	$-0.406213\pi$
$467$	−13.4963	−	11.9566i	−0.624532	−	0.553287i	−0.914927	+	0.403620i	$0.867752\pi$
$468$	−0.845509	−	6.24220i	−0.0390837	−	0.288546i
$469$	0.255649	−	0.226485i	0.0118048	−	0.0104581i
$470$	35.9754	−	22.7494i	1.65942	−	1.04935i
$471$	9.04057	−	0.729831i	0.416568	−	0.0336288i
$472$	−0.259538	+	1.27130i	−0.0119462	+	0.0585164i
$473$	−16.8669	−	4.15732i	−0.775541	−	0.191154i
$474$	20.6620	−	3.35790i	0.949036	−	0.154233i
$475$	−30.1870	−	19.0891i	−1.38508	−	0.875869i
$476$	0.784579	+	0.411779i	0.0359611	+	0.0188739i
$477$	3.21501	+	11.0995i	0.147205	+	0.508211i
$478$	0.244257	+	1.19645i	0.0111720	+	0.0547242i
$479$	0.520895	−	12.9259i	0.0238003	−	0.590598i	−0.942656	−	0.333766i	$-0.891680\pi$
$479$	0.520895	−	12.9259i	0.0238003	−	0.590598i	0.966456	−	0.256832i	$-0.0826786\pi$
$480$	22.1545	+	11.6276i	1.01121	+	0.530723i
$481$	19.8522	+	27.9284i	0.905181	+	1.27343i
$482$	6.44290	−	3.38150i	0.293466	−	0.154023i
$483$	0.196544	+	0.414208i	0.00894308	+	0.0188471i
$484$	6.19395	−	10.7282i	0.281543	−	0.487647i
$485$	−16.6733	−	28.8789i	−0.757094	−	1.31132i
$486$	−1.09962	+	1.59308i	−0.0498800	+	0.0722637i
$487$	11.3634	−	8.53902i	0.514924	−	0.386940i	−0.311274	−	0.950320i	$-0.600756\pi$
$487$	11.3634	−	8.53902i	0.514924	−	0.386940i	0.826198	+	0.563380i	$0.190499\pi$
$488$	2.09890	+	3.63541i	0.0950129	+	0.164567i
$489$	1.68627	−	13.8877i	0.0762556	−	0.628021i
$490$	19.0563	−	40.1603i	0.860877	−	1.81426i
$491$	4.24112	−	4.41547i	0.191399	−	0.199268i	−0.618588	−	0.785716i	$-0.712295\pi$
$491$	4.24112	−	4.41547i	0.191399	−	0.199268i	0.809987	+	0.586448i	$0.199474\pi$
$492$	2.95591	−	0.238626i	0.133263	−	0.0107581i
$493$	−34.9484	−	8.61401i	−1.57400	−	0.387955i
$494$	30.2813	+	30.6676i	1.36242	+	1.37980i
$495$	6.30430	−	1.55387i	0.283357	−	0.0698413i
$496$	20.0283	−	6.68643i	0.899297	−	0.300230i
$497$	−0.00281568	−	0.00593392i	−0.000126300	−	0.000266173i
$498$	−10.5080	−	3.50809i	−0.470875	−	0.157201i
$499$	10.1968	+	14.7726i	0.456471	+	0.661313i	0.981873	−	0.189542i	$-0.0607002\pi$
$499$	10.1968	+	14.7726i	0.456471	+	0.661313i	−0.525401	+	0.850855i	$0.676085\pi$
$500$	1.92814	−	4.06348i	0.0862292	−	0.181724i
$501$	−0.466567	−	11.5777i	−0.0208447	−	0.517255i
$502$	−5.64558	+	1.39151i	−0.251974	+	0.0621061i
$503$	4.22799	−	1.80138i	0.188517	−	0.0803195i	−0.295645	−	0.955298i	$-0.595535\pi$
$503$	4.22799	−	1.80138i	0.188517	−	0.0803195i	0.484162	+	0.874978i	$0.339124\pi$
$504$	−0.0407204	−	0.00661770i	−0.00181383	−	0.000294776i
$505$	11.6627	+	57.1275i	0.518982	+	2.54214i
$506$	−20.8241			−0.925745
$507$	−12.9818	−	0.688059i	−0.576541	−	0.0305578i
$508$	21.2213			0.941541
$509$	−2.26415	−	11.0906i	−0.100357	−	0.491580i	−0.998639	−	0.0521606i	$-0.983389\pi$
$509$	−2.26415	−	11.0906i	−0.100357	−	0.491580i	0.898282	−	0.439420i	$-0.144816\pi$
$510$	37.7643	+	6.13730i	1.67223	+	0.271764i
$511$	0.220201	−	0.0938187i	0.00974110	−	0.00415029i
$512$	28.6368	−	7.05834i	1.26558	−	0.311938i
$513$	−0.248644	−	6.17005i	−0.0109779	−	0.272414i
$514$	−0.399906	+	0.842784i	−0.0176391	+	0.0371736i
$515$	−7.98424	−	11.5672i	−0.351828	−	0.509710i
$516$	−14.5598	−	4.86077i	−0.640959	−	0.213984i
$517$	−5.67565	−	11.9612i	−0.249615	−	0.526052i
$518$	−1.47039	+	0.490887i	−0.0646051	+	0.0215684i
$519$	3.19341	−	0.787104i	0.140175	−	0.0345500i
$520$	3.60381	−	4.54035i	0.158037	−	0.199107i
$521$	−27.3990	−	6.75324i	−1.20037	−	0.295865i	−0.412069	−	0.911153i	$-0.635194\pi$
$521$	−27.3990	−	6.75324i	−1.20037	−	0.295865i	−0.788303	+	0.615288i	$0.789040\pi$
$522$	−11.5389	+	0.931514i	−0.505043	+	0.0407713i
$523$	9.36664	−	9.75171i	0.409575	−	0.426412i	−0.484180	−	0.874968i	$-0.660882\pi$
$523$	9.36664	−	9.75171i	0.409575	−	0.426412i	0.893755	+	0.448556i	$0.148062\pi$
$524$	4.76811	−	10.0486i	0.208296	−	0.438975i
$525$	−0.0587480	+	0.483833i	−0.00256397	+	0.0211162i
$526$	−2.43694	−	4.22091i	−0.106256	−	0.184040i
$527$	22.8728	−	17.1878i	0.996354	−	0.748712i
$528$	4.98905	−	7.22788i	0.217120	−	0.314553i
$529$	−3.30134	−	5.71808i	−0.143536	−	0.248612i
$530$	36.7285	−	63.6157i	1.59538	−	2.76329i
$531$	1.13616	+	2.39440i	0.0493050	+	0.103908i
$532$	−0.804954	+	0.422472i	−0.0348992	+	0.0183165i
$533$	0.653785	−	6.08510i	0.0283186	−	0.263575i
$534$	−10.3664	−	5.44068i	−0.448596	−	0.235441i
$535$	−2.47046	+	61.3038i	−0.106807	+	2.65040i
$536$	−0.396923	−	1.94426i	−0.0171444	−	0.0839790i
$537$	−4.06651	−	14.0392i	−0.175483	−	0.605836i
$538$	24.3498	+	12.7798i	1.04979	+	0.550974i
$539$	−11.6860	−	7.38978i	−0.503352	−	0.318301i
$540$	5.66294	−	0.920318i	0.243694	−	0.0396042i
$541$	36.0404	+	8.88316i	1.54950	+	0.381917i	0.918995	−	0.394269i	$-0.129002\pi$
$541$	36.0404	+	8.88316i	1.54950	+	0.381917i	0.630503	+	0.776186i	$0.282848\pi$
$542$	−8.98385	+	44.0058i	−0.385890	+	1.89021i
$543$	−21.6683	+	1.74924i	−0.929874	+	0.0750672i
$544$	38.7585	−	24.5094i	1.66176	−	1.05083i
$545$	−23.6194	+	20.9249i	−1.01174	+	0.896326i
$546$	0.200942	−	0.552729i	0.00859954	−	0.0236546i
$547$	−3.74268	−	3.31572i	−0.160025	−	0.141770i	0.579310	−	0.815107i	$-0.303322\pi$
$547$	−3.74268	−	3.31572i	−0.160025	−	0.141770i	−0.739336	+	0.673337i	$0.764860\pi$
$548$	−31.0336	−	5.04345i	−1.32569	−	0.215446i
$549$	7.88819	+	3.36084i	0.336660	+	0.143437i
$550$	−18.7103	−	11.8317i	−0.797809	−	0.504504i
$551$	27.6418	−	24.4885i	1.17758	−	1.04324i
$552$	2.65508	+	0.214340i	0.113008	+	0.00912293i
$553$	0.864348	+	0.288562i	0.0367558	+	0.0122709i
$554$	2.62091	+	21.5852i	0.111352	+	0.917065i
$555$	−24.9493	+	18.7482i	−1.05904	+	0.795816i
$556$	−21.6464	−	26.5120i	−0.918012	−	1.12436i
$557$	−20.3472	−	24.9207i	−0.862136	−	1.05593i	−0.997873	−	0.0651805i	$-0.979238\pi$
$557$	−20.3472	−	24.9207i	−0.862136	−	1.05593i	0.135737	−	0.990745i	$-0.456660\pi$
$558$	5.22720	−	7.57291i	0.221285	−	0.320587i
$559$	−15.4589	+	27.6500i	−0.653844	+	1.16947i
$560$	0.698235	+	1.01157i	0.0295058	+	0.0427465i
$561$	3.31090	−	11.4305i	0.139786	−	0.482598i
$562$	7.24700	−	4.58273i	0.305696	−	0.193311i
$563$	10.1987	−	1.65745i	0.429823	−	0.0698530i	0.0583487	−	0.998296i	$-0.481416\pi$
$563$	10.1987	−	1.65745i	0.429823	−	0.0698530i	0.371474	+	0.928443i	$0.378852\pi$
$564$	−4.14833	−	10.9383i	−0.174676	−	0.460584i
$565$	9.27396	−	3.95127i	0.390159	−	0.166231i
$566$	38.6966	+	40.2874i	1.62654	+	1.69341i
$567$	−0.0746133	+	0.0391601i	−0.00313346	+	0.00164457i
$568$	−0.0380365	−	0.00307062i	−0.00159598	−	0.000128841i
$569$	3.75743	−	12.9721i	0.157519	−	0.543820i	−0.842468	−	0.538747i	$-0.818898\pi$
$569$	3.75743	−	12.9721i	0.157519	−	0.543820i	0.999987	−	0.00507342i	$-0.00161493\pi$
$570$	−27.1918	+	28.3096i	−1.13894	+	1.18576i
$571$	−4.06561	+	10.7201i	−0.170141	+	0.448624i	−0.992781	−	0.119938i	$-0.961731\pi$
$571$	−4.06561	+	10.7201i	−0.170141	+	0.448624i	0.822641	+	0.568561i	$0.192500\pi$
$572$	8.75095	+	8.86258i	0.365895	+	0.370563i
$573$	−4.41126	−	11.6315i	−0.184283	−	0.485915i
$574$	0.254719	+	0.108526i	0.0106318	+	0.00452978i
$575$	1.26715	−	31.4440i	0.0528438	−	1.31131i
$576$	3.70924	−	4.54299i	0.154552	−	0.189291i
$577$	−23.3586			−0.972432			−0.486216	−	0.873839i	$-0.661623\pi$
$577$	−23.3586			−0.972432			−0.486216	+	0.873839i	$0.661623\pi$
$578$	23.5367	−	28.8273i	0.978999	−	1.19906i
$579$	6.02511	+	20.8011i	0.250395	+	0.864464i
$580$	25.6820	+	22.7522i	1.06639	+	0.944735i
$581$	−0.334064	−	0.347797i	−0.0138593	−	0.0144291i
$582$	−18.6450	+	6.22461i	−0.772860	+	0.258018i
$583$	−18.2658	−	13.7259i	−0.756494	−	0.568468i
$584$	0.167623	−	1.38050i	0.00693629	−	0.0571254i
$585$	0.313448	−	11.8361i	0.0129595	−	0.489362i
$586$	−5.21625	−	42.9597i	−0.215481	−	1.77465i
$587$	−2.16525	+	3.75033i	−0.0893695	+	0.154793i	−0.907245	−	0.420603i	$-0.861819\pi$
$587$	−2.16525	+	3.75033i	−0.0893695	+	0.154793i	0.817875	+	0.575396i	$0.195152\pi$
$588$	−9.76694	−	7.33938i	−0.402782	−	0.302671i
$589$	1.18196	+	29.3301i	0.0487019	+	1.20853i
$590$	5.97410	−	15.7524i	0.245950	−	0.648516i
$591$	1.81265	−	8.87895i	0.0745625	−	0.365231i
$592$	−8.44371	+	41.3600i	−0.347034	+	1.69989i
$593$	11.7804	−	31.0623i	0.483762	−	1.27558i	−0.441845	−	0.897091i	$-0.645676\pi$
$593$	11.7804	−	31.0623i	0.483762	−	1.27558i	0.925607	−	0.378485i	$-0.123555\pi$
$594$	−0.154113	−	3.82427i	−0.00632333	−	0.156912i
$595$	1.33147	+	1.00054i	0.0545851	+	0.0410180i
$596$	−2.20195	+	3.81389i	−0.0901954	+	0.156223i
$597$	1.34783	+	11.1004i	0.0551629	+	0.454307i
$598$	−10.0606	+	36.6168i	−0.411409	+	1.49737i
$599$	−0.738951	+	6.08581i	−0.0301927	+	0.248659i	0.969796	+	0.243917i	$0.0784326\pi$
$599$	−0.738951	+	6.08581i	−0.0301927	+	0.248659i	−0.999989	+	0.00474216i	$0.998491\pi$
$600$	2.26379	+	1.70112i	0.0924187	+	0.0694481i
$601$	17.9953	−	6.00772i	0.734044	−	0.245060i	0.0750202	−	0.997182i	$-0.476098\pi$
$601$	17.9953	−	6.00772i	0.734044	−	0.245060i	0.659024	+	0.752122i	$0.270970\pi$
$602$	−0.992759	−	1.03357i	−0.0404618	−	0.0421252i
$603$	−3.03386	−	2.68776i	−0.123548	−	0.109454i
$604$	−5.92166	−	20.4439i	−0.240949	−	0.831852i
$605$	14.7264	−	18.0365i	0.598712	−	0.733289i
$606$	34.3692			1.39615
$607$	−2.52256	+	3.08957i	−0.102387	+	0.125402i	−0.823257	−	0.567669i	$-0.807845\pi$
$607$	−2.52256	+	3.08957i	−0.102387	+	0.125402i	0.720869	+	0.693071i	$0.243743\pi$
$608$	−1.89446	+	47.0104i	−0.0768303	+	1.90652i
$609$	−0.463612	−	0.197527i	−0.0187865	−	0.00800418i
$610$	−19.3277	−	50.9629i	−0.782555	−	2.06343i
$611$	−23.7744	+	4.20126i	−0.961809	+	0.169965i
$612$	3.72877	−	9.83195i	0.150727	−	0.397433i
$613$	−4.38510	+	4.56537i	−0.177112	+	0.184394i	−0.803841	−	0.594844i	$-0.797214\pi$
$613$	−4.38510	+	4.56537i	−0.177112	+	0.184394i	0.626729	+	0.779237i	$0.284393\pi$
$614$	14.0022	−	48.3412i	0.565082	−	1.95089i
$615$	5.55606	+	0.448531i	0.224042	+	0.0180865i
$616$	0.0722260	−	0.0379071i	0.00291007	−	0.00152732i
$617$	22.0490	+	22.9555i	0.887660	+	0.924152i	0.997562	−	0.0697908i	$-0.0222332\pi$
$617$	22.0490	+	22.9555i	0.887660	+	0.924152i	−0.109902	+	0.993942i	$0.535054\pi$
$618$	−7.62205	+	3.24745i	−0.306604	+	0.130632i
$619$	5.91173	+	15.5880i	0.237613	+	0.626533i	0.999783	−	0.0208438i	$-0.00663528\pi$
$619$	5.91173	+	15.5880i	0.237613	+	0.626533i	−0.762170	+	0.647377i	$0.775866\pi$
$620$	−26.9195	+	4.37484i	−1.08111	+	0.175698i
$621$	4.59854	−	2.90794i	0.184533	−	0.116692i
$622$	7.04845	−	24.3341i	0.282617	−	0.975708i
$623$	−0.289507	−	0.419423i	−0.0115989	−	0.0168038i
$624$	−10.2991	−	12.2646i	−0.412293	−	0.490978i
$625$	−11.6258	+	16.8429i	−0.465032	+	0.673716i
$626$	−36.5532	−	44.7696i	−1.46096	−	1.78935i
$627$	7.72180	+	9.45749i	0.308379	+	0.377696i
$628$	−12.6680	+	9.51938i	−0.505508	+	0.379864i
$629$	6.89458	+	56.7820i	0.274905	+	2.26405i
$630$	0.508088	+	0.169625i	0.0202427	+	0.00675801i
$631$	−1.60115	−	0.129258i	−0.0637407	−	0.00514568i	0.0485551	−	0.998821i	$-0.484538\pi$
$631$	−1.60115	−	0.129258i	−0.0637407	−	0.00514568i	−0.112296	+	0.993675i	$0.535820\pi$
$632$	3.96284	−	3.51077i	0.157633	−	0.139651i
$633$	−7.13515	−	4.51200i	−0.283597	−	0.179336i
$634$	−43.3807	−	18.4828i	−1.72287	−	0.734046i
$635$	39.3718	+	6.39854i	1.56242	+	0.253918i
$636$	−15.1116	−	13.3877i	−0.599213	−	0.530856i
$637$	−18.6399	+	16.9783i	−0.738538	+	0.672706i
$638$	17.1327	−	15.1783i	0.678291	−	0.600913i
$639$	−0.0658783	+	0.0416589i	−0.00260611	+	0.00164800i
$640$	12.7176	−	1.02667i	0.502707	−	0.0405827i
$641$	−3.49263	+	17.1080i	−0.137951	+	0.675727i	0.850719	+	0.525620i	$0.176167\pi$
$641$	−3.49263	+	17.1080i	−0.137951	+	0.675727i	−0.988670	+	0.150106i	$0.952038\pi$
$642$	35.1148	+	8.65503i	1.38587	+	0.341587i
$643$	−39.4706	+	6.41460i	−1.55657	+	0.252967i	−0.876944	−	0.480592i	$-0.840422\pi$
$643$	−39.4706	+	6.41460i	−1.55657	+	0.252967i	−0.679626	+	0.733559i	$0.737858\pi$
$644$	−0.676991	−	0.428103i	−0.0266772	−	0.0168696i
$645$	−25.5472	−	13.4082i	−1.00592	−	0.527948i
$646$	20.0161	+	69.1035i	0.787522	+	2.71884i
$647$	10.0027	+	48.9963i	0.393246	+	1.92624i	0.376583	+	0.926383i	$0.377099\pi$
$647$	10.0027	+	48.9963i	0.393246	+	1.92624i	0.0166622	+	0.999861i	$0.494696\pi$
$648$	−0.0197134	+	0.489182i	−0.000774414	+	0.0192169i
$649$	−4.63995	−	2.43523i	−0.182134	−	0.0955913i
$650$	−29.8440	+	27.1837i	−1.17058	+	1.06623i
$651$	0.354683	−	0.186152i	0.0139011	−	0.00729588i
$652$	10.4777	+	22.0813i	0.410339	+	0.864771i
$653$	21.3030	−	36.8978i	0.833650	−	1.44392i	−0.0614752	−	0.998109i	$-0.519581\pi$
$653$	21.3030	−	36.8978i	0.833650	−	1.44392i	0.895125	−	0.445815i	$-0.147086\pi$
$654$	9.30033	+	16.1086i	0.363671	+	0.629897i
$655$	11.8761	−	17.2055i	0.464038	−	0.672275i
$656$	6.02755	−	4.52941i	0.235336	−	0.176844i
$657$	−1.42024	−	2.45992i	−0.0554088	−	0.0959708i
$658$	0.131653	−	1.08426i	0.00513236	−	0.0422688i
$659$	19.3476	−	40.7742i	0.753675	−	1.58834i	−0.0538827	−	0.998547i	$-0.517160\pi$
$659$	19.3476	−	40.7742i	0.753675	−	1.58834i	0.807558	−	0.589789i	$-0.200789\pi$
$660$	−7.85810	+	8.18115i	−0.305876	+	0.318451i
$661$	23.5285	−	1.89941i	0.915151	−	0.0738786i	0.386089	−	0.922462i	$-0.373826\pi$
$661$	23.5285	−	1.89941i	0.915151	−	0.0738786i	0.529062	+	0.848583i	$0.322544\pi$
$662$	−37.3895	−	9.21568i	−1.45318	−	0.358177i
$663$	−18.4997	−	11.3442i	−0.718470	−	0.440572i
$664$	−2.72042	+	0.670523i	−0.105573	+	0.0260214i
$665$	−1.62081	+	0.541107i	−0.0628525	+	0.0209832i
$666$	7.88632	+	16.6201i	0.305589	+	0.644015i
$667$	30.8636	+	10.3038i	1.19504	+	0.398964i
$668$	11.4997	+	16.6602i	0.444938	+	0.644604i
$669$	0.0142146	−	0.0299567i	0.000549570	−	0.00115819i
$670$	1.03746	+	25.7443i	0.0400805	+	0.994587i
$671$	−16.4607	+	4.05719i	−0.635456	+	0.156626i
$672$	0.590653	−	0.251654i	0.0227850	−	0.00970776i
$673$	−20.5480	−	3.33938i	−0.792069	−	0.128724i	−0.249101	−	0.968477i	$-0.580135\pi$
$673$	−20.5480	−	3.33938i	−0.792069	−	0.128724i	−0.542967	+	0.839754i	$0.682699\pi$
$674$	6.36273	+	31.1667i	0.245083	+	1.20050i
$675$	5.78395			0.222625
$676$	19.8116	−	11.1058i	0.761985	−	0.427147i
$677$	8.90689			0.342320			0.171160	−	0.985243i	$-0.445249\pi$
$677$	8.90689			0.342320			0.171160	+	0.985243i	$0.445249\pi$
$678$	−1.18859	−	5.82208i	−0.0456474	−	0.223596i
$679$	−0.844597	−	0.137260i	−0.0324127	−	0.00526757i
$680$	8.90220	−	3.79287i	0.341384	−	0.145450i
$681$	−0.438724	+	0.108136i	−0.0168120	+	0.00414377i
$682$	0.732595	+	18.1791i	0.0280525	+	0.696116i
$683$	4.17671	−	8.80223i	0.159817	−	0.336808i	−0.807708	−	0.589583i	$-0.799292\pi$
$683$	4.17671	−	8.80223i	0.159817	−	0.336808i	0.967525	+	0.252775i	$0.0813433\pi$
$684$	6.12848	+	8.87863i	0.234328	+	0.339483i
$685$	−56.0560	−	18.7142i	−2.14179	−	0.715034i
$686$	−0.978475	−	2.06209i	−0.0373583	−	0.0787310i
$687$	23.5107	−	7.84902i	0.896988	−	0.299459i
$688$	−37.8919	+	9.33951i	−1.44461	+	0.356065i
$689$	−32.9600	+	25.4871i	−1.25568	+	0.970981i
$690$	−33.5811	−	8.27699i	−1.27841	−	0.315100i
$691$	−9.59989	+	0.774983i	−0.365197	+	0.0294818i	−0.261703	−	0.965148i	$-0.584284\pi$
$691$	−9.59989	+	0.774983i	−0.365197	+	0.0294818i	−0.103494	+	0.994630i	$0.533002\pi$
$692$	−3.98048	+	4.14411i	−0.151315	+	0.157536i
$693$	0.0714249	−	0.150525i	0.00271321	−	0.00571796i
$694$	−1.77343	+	14.6055i	−0.0673186	+	0.554418i
$695$	−32.1668	−	55.7146i	−1.22016	−	2.11337i
$696$	−2.34066	+	1.75889i	−0.0887224	+	0.0666705i
$697$	5.80354	−	8.40788i	0.219825	−	0.318471i
$698$	11.9393	+	20.6794i	0.451908	+	0.782728i
$699$	−3.12540	+	5.41335i	−0.118213	+	0.204752i
$700$	−0.365034	−	0.769294i	−0.0137970	−	0.0290766i
$701$	21.3787	−	11.2204i	0.807463	−	0.423789i	−0.00987248	−	0.999951i	$-0.503143\pi$
$701$	21.3787	−	11.2204i	0.807463	−	0.423789i	0.817336	+	0.576162i	$0.195450\pi$
$702$	−6.79900	−	1.57660i	−0.256612	−	0.0595051i
$703$	−51.9625	−	27.2720i	−1.95980	−	1.02858i
$704$	−0.466933	+	11.5868i	−0.0175982	+	0.436694i
$705$	−4.39835	−	21.5445i	−0.165651	−	0.811415i
$706$	−14.9418	−	51.5852i	−0.562343	−	1.94143i
$707$	1.32477	+	0.695291i	0.0498230	+	0.0261491i
$708$	−3.91345	−	2.47472i	−0.147077	−	0.0930056i
$709$	31.1902	−	5.06889i	1.17137	−	0.190366i	0.456566	−	0.889690i	$-0.349079\pi$
$709$	31.1902	−	5.06889i	1.17137	−	0.190366i	0.714805	+	0.699323i	$0.246515\pi$
$710$	0.481080	+	0.118575i	0.0180546	+	0.00445006i
$711$	2.16307	−	10.5954i	0.0811216	−	0.397360i
$712$	−2.95138	+	0.238260i	−0.110608	+	0.00892916i
$713$	−21.8597	+	13.8232i	−0.818653	+	0.517685i
$714$	0.734854	−	0.651023i	0.0275012	−	0.0243639i
$715$	13.5634	+	19.0813i	0.507244	+	0.713600i
$716$	19.1139	+	16.9334i	0.714319	+	0.632832i
$717$	0.622663	+	0.101193i	0.0232538	+	0.00377911i
$718$	53.8109	+	22.9267i	2.00821	+	0.855617i
$719$	−20.6091	−	13.0324i	−0.768589	−	0.486026i	0.0917291	−	0.995784i	$-0.470761\pi$
$719$	−20.6091	−	13.0324i	−0.768589	−	0.486026i	−0.860318	+	0.509758i	$0.829735\pi$
$720$	10.9182	−	9.67271i	0.406899	−	0.360481i
$721$	−0.359489	−	0.0290209i	−0.0133881	−	0.00108080i
$722$	−35.1274	−	11.7272i	−1.30731	−	0.436443i
$723$	−0.453093	−	3.73155i	−0.0168507	−	0.138778i
$724$	30.3624	−	22.8158i	1.12841	−	0.847944i
$725$	21.8764	+	26.7937i	0.812468	+	0.995092i
$726$	−8.68067	−	10.6319i	−0.322170	−	0.394587i
$727$	−19.6519	+	28.4707i	−0.728850	+	1.05592i	0.266891	+	0.963727i	$0.414004\pi$
$727$	−19.6519	+	28.4707i	−0.728850	+	1.05592i	−0.995741	+	0.0921947i	$0.970612\pi$
$728$	−0.0317613	−	0.145315i	−0.00117715	−	0.00538573i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−5.02356	+	17.3433i	−0.185930	+	0.641905i
$731$	−44.6940	+	28.2627i	−1.65307	+	1.04534i
$732$	−14.7861	+	2.40297i	−0.546508	+	0.0888163i
$733$	4.12833	+	10.8855i	0.152483	+	0.402066i	0.989391	−	0.145279i	$-0.0464079\pi$
$733$	4.12833	+	10.8855i	0.152483	+	0.402066i	−0.836907	+	0.547345i	$0.815639\pi$
$734$	40.9957	−	17.4666i	1.51318	−	0.644705i
$735$	−15.9077	−	16.5616i	−0.586763	−	0.610886i
$736$	−36.7061	+	19.2648i	−1.35300	+	0.710111i
$737$	7.98805	+	0.644862i	0.294244	+	0.0237538i
$738$	0.914154	−	3.15603i	0.0336505	−	0.116175i
$739$	3.20894	−	3.34086i	0.118043	−	0.122896i	−0.659559	−	0.751653i	$-0.729257\pi$
$739$	3.20894	−	3.34086i	0.118043	−	0.122896i	0.777601	+	0.628758i	$0.216436\pi$
$740$	19.3343	−	50.9805i	0.710745	−	1.87408i
$741$	20.3605	−	9.00877i	0.747961	−	0.330946i
$742$	−0.668403	−	1.76243i	−0.0245378	−	0.0647010i
$743$	26.3822	+	11.2404i	0.967869	+	0.412370i	0.817289	−	0.576228i	$-0.195476\pi$
$743$	26.3822	+	11.2404i	0.967869	+	0.412370i	0.150579	+	0.988598i	$0.451886\pi$
$744$	0.0937099	−	2.32539i	0.00343557	−	0.0852529i
$745$	−5.23523	+	6.41199i	−0.191804	+	0.234917i
$746$	60.7483			2.22415
$747$	−3.61945	+	4.43302i	−0.132429	+	0.162196i
$748$	5.78442	+	19.9701i	0.211499	+	0.730180i
$749$	1.17841	+	1.04398i	0.0430583	+	0.0381463i
$750$	−3.45213	−	3.59405i	−0.126054	−	0.131236i
$751$	50.4759	−	16.8513i	1.84189	−	0.614914i	0.845127	−	0.534566i	$-0.179525\pi$
$751$	50.4759	−	16.8513i	1.84189	−	0.614914i	0.996767	−	0.0803481i	$-0.0256032\pi$
$752$	−23.7776	−	17.8677i	−0.867079	−	0.651568i
$753$	−0.362066	+	2.98188i	−0.0131944	+	0.108666i
$754$	−18.4120	−	37.4589i	−0.670527	−	1.36417i
$755$	−4.82229	−	39.7151i	−0.175501	−	1.44538i
$756$	0.0736093	−	0.127495i	0.00267715	−	0.00463695i
$757$	39.4249	+	29.6259i	1.43292	+	1.07677i	0.982980	+	0.183714i	$0.0588119\pi$
$757$	39.4249	+	29.6259i	1.43292	+	1.07677i	0.449942	+	0.893058i	$0.351444\pi$
$758$	1.12225	+	27.8483i	0.0407618	+	1.01149i
$759$	−3.81474	+	10.0586i	−0.138466	+	0.365105i
$760$	−1.98582	+	9.72717i	−0.0720331	+	0.352841i
$761$	−2.79641	+	13.6977i	−0.101370	+	0.496543i	0.897129	+	0.441769i	$0.145649\pi$
$761$	−2.79641	+	13.6977i	−0.101370	+	0.496543i	−0.998499	+	0.0547737i	$0.982556\pi$
$762$	8.33775	−	21.9848i	0.302045	−	0.796426i
$763$	0.0326038	+	0.809055i	0.00118034	+	0.0292898i
$764$	17.3748	+	13.0563i	0.628597	+	0.472360i
$765$	9.88248	−	17.1170i	0.357302	−	0.618865i
$766$	5.94129	+	48.9309i	0.214668	+	1.76795i
$767$	−6.52375	+	6.98230i	−0.235559	+	0.252116i
$768$	2.32043	−	19.1104i	0.0837312	−	0.689588i
$769$	−0.510061	−	0.383286i	−0.0183933	−	0.0138216i	0.591506	−	0.806301i	$-0.298534\pi$
$769$	−0.510061	−	0.383286i	−0.0183933	−	0.0138216i	−0.609899	+	0.792479i	$0.708790\pi$
$770$	−1.00460	+	0.335385i	−0.0362033	+	0.0120864i
$771$	0.333830	+	0.347554i	0.0120226	+	0.0125169i
$772$	−28.3199	−	25.0893i	−1.01926	−	0.902983i
$773$	0.292361	+	1.00935i	0.0105155	+	0.0363037i	0.965604	−	0.260016i	$-0.0837278\pi$
$773$	0.292361	+	1.00935i	0.0105155	+	0.0363037i	−0.955089	+	0.296320i	$0.904241\pi$
$774$	−10.7562	+	13.1739i	−0.386622	+	0.473526i
$775$	−27.4947			−0.987640
$776$	−3.14418	+	3.85092i	−0.112870	+	0.138240i
$777$	−0.0322455	+	0.800163i	−0.00115680	+	0.0287057i
$778$	−41.2445	−	17.5727i	−1.47869	−	0.630010i
$779$	3.71684	+	9.80050i	0.133170	+	0.351139i
$780$	10.5892	+	17.7701i	0.379154	+	0.636271i
$781$	0.0546496	−	0.144099i	0.00195552	−	0.00515628i
$782$	−43.9116	+	45.7168i	−1.57028	+	1.63483i
$783$	−1.66384	+	5.74424i	−0.0594608	+	0.205282i
$784$	−30.9608	−	2.49941i	−1.10574	−	0.0892648i
$785$	−26.3732	+	13.8417i	−0.941299	+	0.494032i
$786$	−8.53678	−	8.88773i	−0.304497	−	0.317015i
$787$	−8.36619	+	3.56450i	−0.298222	+	0.127061i	−0.535895	−	0.844285i	$-0.680026\pi$
$787$	−8.36619	+	3.56450i	−0.298222	+	0.127061i	0.237673	+	0.971345i	$0.423615\pi$
$788$	5.61419	+	14.8034i	0.199997	+	0.527349i
$789$	−2.48524	+	0.403891i	−0.0884768	+	0.0143789i
$790$	−58.1000	+	36.7402i	−2.06710	+	1.30716i
$791$	0.0719667	−	0.248458i	0.00255884	−	0.00883415i
$792$	−0.549889	−	0.796652i	−0.0195395	−	0.0283078i
$793$	−0.818419	+	30.9043i	−0.0290629	+	1.09744i
$794$	−1.76426	+	2.55597i	−0.0626113	+	0.0907081i
$795$	−23.9999	−	29.3946i	−0.851189	−	1.04252i
$796$	−12.3553	−	15.1324i	−0.437921	−	0.536355i
$797$	−39.5331	+	29.7072i	−1.40033	+	1.05228i	−0.410223	+	0.911985i	$0.634549\pi$
$797$	−39.5331	+	29.7072i	−1.40033	+	1.05228i	−0.990110	+	0.140297i	$0.955194\pi$
$798$	0.121410	+	0.999905i	0.00429788	+	0.0353963i
$799$	−38.2275	−	12.7622i	−1.35239	−	0.451495i
$800$	−43.9258	−	3.54606i	−1.55301	−	0.125372i
$801$	−4.52700	+	4.01057i	−0.159954	+	0.141707i
$802$	−20.6825	−	13.0788i	−0.730323	−	0.461829i
$803$	5.16682	+	2.20138i	0.182333	+	0.0776849i
$804$	6.98956	+	1.13591i	0.246503	+	0.0400606i
$805$	−1.12694	−	0.998384i	−0.0397195	−	0.0351884i
$806$	32.3199	+	7.49458i	1.13842	+	0.263985i
$807$	10.6336	−	9.42053i	0.374320	−	0.331618i
$808$	7.34684	−	4.64586i	0.258461	−	0.163441i
$809$	46.8721	−	3.78391i	1.64794	−	0.133035i	0.778688	−	0.627411i	$-0.215885\pi$
$809$	46.8721	−	3.78391i	1.64794	−	0.133035i	0.869248	+	0.494376i	$0.164603\pi$
$810$	1.27152	−	6.22829i	0.0446765	−	0.218840i
$811$	12.9109	+	3.18226i	0.453365	+	0.111744i	0.459384	−	0.888238i	$-0.348070\pi$
$811$	12.9109	+	3.18226i	0.453365	+	0.111744i	−0.00601979	+	0.999982i	$0.501916\pi$
$812$	0.869019	−	0.141229i	0.0304966	−	0.00495618i
$813$	19.6103	+	12.4008i	0.687764	+	0.434915i
$814$	−32.2070	−	16.9035i	−1.12885	−	0.592468i
$815$	12.7815	+	44.1267i	0.447715	+	1.54569i
$816$	−5.34759	−	26.1942i	−0.187203	−	0.916981i
$817$	2.18457	−	54.2096i	0.0764285	−	1.89655i
$818$	−20.5944	−	10.8088i	−0.720065	−	0.377919i
$819$	−0.230174	−	0.198314i	−0.00804292	−	0.00692967i
$820$	−8.62299	+	4.52570i	−0.301128	+	0.158044i
$821$	4.16799	+	8.78385i	0.145464	+	0.306558i	0.963085	−	0.269198i	$-0.0867588\pi$
$821$	4.16799	+	8.78385i	0.145464	+	0.306558i	−0.817621	+	0.575757i	$0.804707\pi$
$822$	−17.4179	+	30.1687i	−0.607519	+	1.05225i
$823$	−10.6547	−	18.4545i	−0.371400	−	0.643284i	0.618381	−	0.785878i	$-0.287789\pi$
$823$	−10.6547	−	18.4545i	−0.371400	−	0.643284i	−0.989781	+	0.142595i	$0.954455\pi$
$824$	−1.19033	+	1.72449i	−0.0414671	+	0.0600755i
$825$	−9.14254	+	6.87017i	−0.318302	+	0.239189i
$826$	−0.216151	−	0.374385i	−0.00752086	−	0.0130265i
$827$	−4.09657	+	33.7383i	−0.142452	+	1.17320i	0.729632	+	0.683840i	$0.239691\pi$
$827$	−4.09657	+	33.7383i	−0.142452	+	1.17320i	−0.872084	+	0.489356i	$0.837232\pi$
$828$	−4.07498	+	8.58783i	−0.141615	+	0.298448i
$829$	12.2342	−	12.7371i	0.424911	−	0.442379i	−0.473991	−	0.880530i	$-0.657187\pi$
$829$	12.2342	−	12.7371i	0.424911	−	0.442379i	0.898901	+	0.438151i	$0.144366\pi$
$830$	36.2614	−	2.92732i	1.25865	−	0.101609i
$831$	10.9064	+	2.68818i	0.378337	+	0.0932518i
$832$	20.1485	+	6.41890i	0.698523	+	0.222535i
$833$	−40.8656	+	10.0725i	−1.41591	+	0.348990i
$834$	−35.9708	+	12.0088i	−1.24557	+	0.415831i
$835$	16.3122	+	34.3771i	0.564505	+	1.18967i
$836$	−20.2331	−	6.75481i	−0.699778	−	0.233620i
$837$	−2.70037	−	3.91215i	−0.0933383	−	0.135224i
$838$	−21.2750	+	44.8362i	−0.734934	+	1.54884i
$839$	−1.09636	−	27.2058i	−0.0378504	−	0.939249i	−0.900873	−	0.434083i	$-0.857072\pi$
$839$	−1.09636	−	27.2058i	−0.0378504	−	0.939249i	0.863022	−	0.505166i	$-0.168569\pi$
$840$	0.131539	−	0.0324214i	0.00453853	−	0.00111865i
$841$	−6.22337	+	2.65153i	−0.214599	+	0.0914321i
$842$	−33.0386	−	5.36930i	−1.13859	−	0.185038i
$843$	−0.886019	−	4.34001i	−0.0305161	−	0.149478i
$844$	14.7490			0.507681
$845$	40.1051	−	14.6311i	1.37966	−	0.503326i
$846$	−12.9617			−0.445632
$847$	−0.119514	−	0.585418i	−0.00410655	−	0.0201152i
$848$	−50.6643	−	8.23376i	−1.73982	−	0.282748i
$849$	26.5487	−	11.3114i	0.911150	−	0.388205i
$850$	−65.4292	+	16.1269i	−2.24420	+	0.553146i
$851$	−2.08202	−	51.6648i	−0.0713708	−	1.77105i
$852$	0.0583778	−	0.123029i	0.00199999	−	0.00421489i
$853$	14.5281	+	21.0475i	0.497431	+	0.720654i	0.988626	−	0.150396i	$-0.0480549\pi$
$853$	14.5281	+	21.0475i	0.497431	+	0.720654i	−0.491194	+	0.871050i	$0.663440\pi$
$854$	−1.32663	−	0.442894i	−0.0453963	−	0.0151555i
$855$	8.69313	+	18.3204i	0.297299	+	0.626544i
$856$	8.67617	−	2.89653i	0.296545	−	0.0990014i
$857$	27.2961	−	6.72788i	0.932416	−	0.229820i	0.256285	−	0.966601i	$-0.417501\pi$
$857$	27.2961	−	6.72788i	0.932416	−	0.229820i	0.676131	+	0.736781i	$0.263655\pi$
$858$	12.6197	−	5.58375i	0.430829	−	0.190626i
$859$	−13.1775	−	3.24796i	−0.449610	−	0.110819i	0.00800798	−	0.999968i	$-0.497451\pi$
$859$	−13.1775	−	3.24796i	−0.449610	−	0.110819i	−0.457618	+	0.889149i	$0.651297\pi$
$860$	50.2435	−	4.05607i	1.71329	−	0.138311i
$861$	0.0990827	−	0.103156i	0.00337673	−	0.00351555i
$862$	5.56137	−	11.7203i	0.189421	−	0.399197i
$863$	−0.588039	+	4.84294i	−0.0200171	+	0.164855i	−0.999289	−	0.0376927i	$-0.987999\pi$
$863$	−0.588039	+	4.84294i	−0.0200171	+	0.164855i	0.979272	+	0.202548i	$0.0649223\pi$
$864$	−3.80957	−	6.59836i	−0.129604	−	0.224481i
$865$	−8.63450	+	6.48841i	−0.293582	+	0.220612i
$866$	7.52665	−	10.9042i	0.255766	−	0.370541i
$867$	−9.61273	−	16.6497i	−0.326465	−	0.565454i
$868$	−0.349911	+	0.606064i	−0.0118768	+	0.0205711i
$869$	9.16613	+	19.3172i	0.310940	+	0.655292i
$870$	33.6612	−	17.6668i	1.14122	−	0.598960i
$871$	4.99313	−	13.7345i	0.169186	−	0.465377i
$872$	4.16554	+	2.18625i	0.141063	+	0.0740356i
$873$	−0.408883	+	10.1463i	−0.0138386	+	0.343401i
$874$	−13.0089	−	63.7216i	−0.440031	−	2.15541i
$875$	−0.0603550	−	0.208370i	−0.00204037	−	0.00704418i
$876$	4.39412	+	2.30621i	0.148464	+	0.0779197i
$877$	−37.4216	−	23.6640i	−1.26364	−	0.799076i	−0.276821	−	0.960922i	$-0.589281\pi$
$877$	−37.4216	−	23.6640i	−1.26364	−	0.799076i	−0.986816	+	0.161846i	$0.948255\pi$
$878$	−43.2906	+	7.03540i	−1.46099	+	0.237433i
$879$	−21.7063	−	5.35012i	−0.732136	−	0.180455i
$880$	−5.76892	+	28.2581i	−0.194470	+	0.952579i
$881$	40.5896	−	3.27673i	1.36750	−	0.110396i	0.625199	−	0.780466i	$-0.285018\pi$
$881$	40.5896	−	3.27673i	1.36750	−	0.110396i	0.742298	+	0.670070i	$0.233736\pi$
$882$	−11.4409	+	7.23476i	−0.385234	+	0.243607i
$883$	10.5107	−	9.31163i	0.353712	−	0.313361i	−0.467491	−	0.883998i	$-0.654842\pi$
$883$	10.5107	−	9.31163i	0.353712	−	0.313361i	0.821203	+	0.570636i	$0.193303\pi$
$884$	37.9098	−	0.523213i	1.27504	−	0.0175975i
$885$	−6.51447	−	5.77131i	−0.218981	−	0.194001i
$886$	−8.39072	−	1.36362i	−0.281892	−	0.0458119i
$887$	13.9762	+	5.95468i	0.469273	+	0.199939i	0.613641	−	0.789586i	$-0.289704\pi$
$887$	13.9762	+	5.95468i	0.469273	+	0.199939i	−0.144367	+	0.989524i	$0.546115\pi$
$888$	3.93242	+	2.48671i	0.131963	+	0.0834485i
$889$	0.766133	−	0.678735i	0.0256953	−	0.0227640i
$890$	38.3211	+	3.09360i	1.28452	+	0.103698i
$891$	−1.87546	−	0.626122i	−0.0628304	−	0.0209759i
$892$	0.00698270	+	0.0575077i	0.000233798	+	0.00192550i
$893$	33.0555	−	24.8396i	1.10616	−	0.831225i
$894$	3.08598	+	3.77964i	0.103211	+	0.126410i
$895$	30.3563	+	37.1797i	1.01470	+	1.24278i
$896$	0.185983	−	0.269443i	0.00621326	−	0.00900146i
$897$	15.8440	+	11.5673i	0.529015	+	0.386222i
$898$	−4.75451	−	6.88810i	−0.158660	−	0.229859i
$899$	7.90927	−	27.3060i	0.263789	−	0.910705i
$900$	−8.54069	+	5.40081i	−0.284690	+	0.180027i
$901$	−68.6505	+	11.1568i	−2.28708	+	0.371687i
$902$	2.30374	+	6.07447i	0.0767063	+	0.202258i
$903$	−0.681106	+	0.290192i	−0.0226658	+	0.00965699i
$904$	−1.04107	−	1.08387i	−0.0346256	−	0.0360491i
$905$	63.2107	−	33.1755i	2.10120	−	1.10279i
$906$	−23.5061	−	1.89761i	−0.780939	−	0.0630439i
$907$	12.0377	−	41.5588i	0.399704	−	1.37994i	−0.468383	−	0.883525i	$-0.655163\pi$
$907$	12.0377	−	41.5588i	0.399704	−	1.37994i	0.868087	−	0.496412i	$-0.165349\pi$
$908$	0.546856	−	0.569337i	0.0181480	−	0.0188941i
$909$	6.29604	−	16.6013i	0.208827	−	0.550631i
$910$	0.104391	+	1.92851i	0.00346051	+	0.0639294i
$911$	20.1137	+	53.0355i	0.666397	+	1.75714i	0.653147	+	0.757231i	$0.273448\pi$
$911$	20.1137	+	53.0355i	0.666397	+	1.75714i	0.0132498	+	0.999912i	$0.495782\pi$
$912$	25.2339	+	10.7512i	0.835578	+	0.356007i
$913$	0.455630	−	11.3063i	0.0150791	−	0.374185i
$914$	−29.3186	+	35.9087i	−0.969772	+	1.18776i
$915$	−28.1571			−0.930846
$916$	−27.3872	+	33.5433i	−0.904899	+	1.10830i
$917$	−0.149252	−	0.515278i	−0.00492874	−	0.0170160i
$918$	−8.72071	−	7.72587i	−0.287826	−	0.254992i
$919$	1.80353	+	1.87768i	0.0594931	+	0.0619389i	0.750284	−	0.661116i	$-0.229917\pi$
$919$	1.80353	+	1.87768i	0.0594931	+	0.0619389i	−0.690791	+	0.723055i	$0.742737\pi$
$920$	−8.29720	+	2.77001i	−0.273551	+	0.0913246i
$921$	−20.7851	−	15.6190i	−0.684892	−	0.514663i
$922$	−1.36478	+	11.2400i	−0.0449467	+	0.370169i
$923$	−0.226980	−	0.165713i	−0.00747112	−	0.00545450i
$924$	0.0350862	+	0.288961i	0.00115425	+	0.00950612i
$925$	27.4838	−	47.6033i	0.903662	−	1.56519i
$926$	4.33905	+	3.26059i	0.142590	+	0.107150i
$927$	0.172339	+	4.27656i	0.00566037	+	0.140461i
$928$	16.1576	−	42.6041i	0.530400	−	1.39855i
$929$	3.95687	−	19.3820i	0.129821	−	0.635904i	−0.861856	−	0.507153i	$-0.830698\pi$
$929$	3.95687	−	19.3820i	0.129821	−	0.635904i	0.991677	−	0.128751i	$-0.0410969\pi$
$930$	−6.04430	+	29.6070i	−0.198201	+	0.970850i
$931$	15.3124	−	40.3755i	0.501843	−	1.32325i
$932$	−0.439731	−	10.9118i	−0.0144039	−	0.357428i
$933$	−10.4628	−	7.86232i	−0.342538	−	0.257401i
$934$	17.4515	−	30.2268i	0.571029	−	0.989052i
$935$	4.71053	+	38.7947i	0.154051	+	1.26872i
$936$	−1.66649	+	0.582037i	−0.0544708	+	0.0190245i
$937$	4.27035	−	35.1695i	0.139506	−	1.14894i	−0.739850	−	0.672772i	$-0.765104\pi$
$937$	4.27035	−	35.1695i	0.139506	−	1.14894i	0.879356	−	0.476164i	$-0.157973\pi$
$938$	0.528543	+	0.397174i	0.0172575	+	0.0129682i
$939$	−28.3211	+	9.45497i	−0.924224	+	0.308551i
$940$	26.6120	+	27.7061i	0.867989	+	0.903673i
$941$	−0.998314	−	0.884429i	−0.0325441	−	0.0288316i	0.646694	−	0.762750i	$-0.276151\pi$
$941$	−0.998314	−	0.884429i	−0.0325441	−	0.0288316i	−0.679238	+	0.733918i	$0.737690\pi$
$942$	4.88470	+	16.8639i	0.159152	+	0.549457i
$943$	−5.84086	+	7.15375i	−0.190205	+	0.232958i
$944$	−11.7722			−0.383152
$945$	0.175009	−	0.214348i	0.00569305	−	0.00697273i
$946$	1.35402	−	33.5998i	0.0440231	−	1.09242i
$947$	25.6898	+	10.9454i	0.834807	+	0.355678i	0.766704	−	0.642000i	$-0.221895\pi$
$947$	25.6898	+	10.9454i	0.834807	+	0.355678i	0.0681024	+	0.997678i	$0.478306\pi$
$948$	6.69953	+	17.6652i	0.217591	+	0.573739i
$949$	6.36708	−	8.02173i	0.206684	−	0.260396i
$950$	24.5164	−	64.6445i	0.795418	−	2.09735i
$951$	−16.8746	+	17.5683i	−0.547195	+	0.569691i
$952$	0.0690818	−	0.238498i	0.00223895	−	0.00772976i
$953$	−25.0657	−	2.02351i	−0.811958	−	0.0655481i	−0.332490	−	0.943107i	$-0.607889\pi$
$953$	−25.0657	−	2.02351i	−0.811958	−	0.0655481i	−0.479469	+	0.877559i	$0.659171\pi$
$954$	−19.8067	+	10.3953i	−0.641264	+	0.336562i
$955$	28.2988	+	29.4621i	0.915727	+	0.953372i
$956$	−1.01392	+	0.431993i	−0.0327927	+	0.0139716i
$957$	−4.19302	−	11.0561i	−0.135541	−	0.357392i
$958$	24.7171	−	4.01692i	0.798574	−	0.129781i
$959$	−1.28169	+	0.810491i	−0.0413879	+	0.0261721i
$960$	−5.35840	+	18.4993i	−0.172942	+	0.597064i
$961$	−4.77349	−	6.91559i	−0.153983	−	0.223084i
$962$	−45.2828	+	48.4658i	−1.45998	+	1.56260i
$963$	10.6133	−	15.3760i	0.342007	−	0.495483i
$964$	4.15341	+	5.08700i	0.133772	+	0.163841i
$965$	−44.9772	−	55.0871i	−1.44787	−	1.77332i
$966$	−0.709494	+	0.533150i	−0.0228276	+	0.0171538i
$967$	−1.89302	−	15.5904i	−0.0608754	−	0.501354i	−0.990975	−	0.134047i	$-0.957203\pi$
$967$	−1.89302	−	15.5904i	−0.0608754	−	0.501354i	0.930100	−	0.367307i	$-0.119720\pi$
$968$	−3.29276	−	1.09929i	−0.105833	−	0.0353324i
$969$	37.0457	+	2.99063i	1.19008	+	0.0960730i
$970$	48.3165	−	42.8047i	1.55135	−	1.37437i
$971$	6.76059	+	4.27514i	0.216958	+	0.137196i	0.638524	−	0.769602i	$-0.279545\pi$
$971$	6.76059	+	4.27514i	0.216958	+	0.137196i	−0.421567	+	0.906797i	$0.638520\pi$
$972$	−1.60728	−	0.684799i	−0.0515536	−	0.0219649i
$973$	−1.62944	−	0.264809i	−0.0522373	−	0.00848939i
$974$	20.5951	+	18.2457i	0.659911	+	0.584630i
$975$	7.66344	+	19.3952i	0.245427	+	0.621145i
$976$	−28.5077	+	25.2557i	−0.912510	+	0.808414i
$977$	25.4227	−	16.0763i	0.813343	−	0.514327i	−0.0618587	−	0.998085i	$-0.519703\pi$
$977$	25.4227	−	16.0763i	0.813343	−	0.514327i	0.875202	+	0.483758i	$0.160728\pi$
$978$	26.9925	−	2.17906i	0.863125	−	0.0696787i
$979$	2.39195	−	11.7166i	0.0764471	−	0.374463i
$980$	38.9541	+	9.60133i	1.24434	+	0.306703i
$981$	9.48464	−	1.54140i	0.302821	−	0.0492132i
$982$	10.0166	+	6.33413i	0.319643	+	0.202130i
$983$	22.4353	+	11.7749i	0.715574	+	0.375562i	0.782882	−	0.622170i	$-0.213749\pi$
$983$	22.4353	+	11.7749i	0.715574	+	0.375562i	−0.0673080	+	0.997732i	$0.521441\pi$
$984$	−0.231204	−	0.798209i	−0.00737052	−	0.0254460i
$985$	5.95255	+	29.1575i	0.189664	+	0.929036i
$986$	2.80555	−	69.6191i	0.0893470	−	2.21712i
$987$	−0.499610	−	0.262216i	−0.0159028	−	0.00834641i
$988$	−21.6527	+	32.3143i	−0.688863	+	1.02805i
$989$	42.3272	−	22.2150i	1.34593	−	0.706397i
$990$	5.38811	+	11.3552i	0.171245	+	0.360892i
$991$	−28.2276	+	48.8916i	−0.896679	+	1.55309i	−0.0649660	+	0.997887i	$0.520694\pi$
$991$	−28.2276	+	48.8916i	−0.896679	+	1.55309i	−0.831713	+	0.555206i	$0.812639\pi$
$992$	18.1092	+	31.3661i	0.574969	+	0.995875i
$993$	−11.3007	+	16.3720i	−0.358618	+	0.519548i
$994$	0.0101642	−	0.00763787i	0.000322387	−	0.000242258i
$995$	−18.3601	−	31.8006i	−0.582053	−	1.00815i
$996$	1.20518	−	9.92557i	0.0381877	−	0.314504i
$997$	18.7182	−	39.4478i	0.592811	−	1.24932i	−0.356297	−	0.934373i	$-0.615961\pi$
$997$	18.7182	−	39.4478i	0.592811	−	1.24932i	0.949108	−	0.314951i	$-0.101988\pi$
$998$	−24.0698	+	25.0594i	−0.761917	+	0.793240i
$999$	9.47265	−	0.764711i	0.299701	−	0.0241944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.490.14	yes	384
169.159	even	39	inner	507.2.q.b.328.14	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.328.14	✓	384	169.159	even	39	inner
507.2.q.b.490.14	yes	384	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.387197 + 1.89662i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-1.60728 + 0.684799i) q^{4} +(-3.18847 + 0.785887i) q^{5} +(0.0779443 + 1.93417i) q^{6} +(-0.0361239 + 0.0761296i) q^{7} +(0.278113 + 0.402916i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(0.387197 + 1.89662i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-1.60728 + 0.684799i) q^{4} +(-3.18847 + 0.785887i) q^{5} +(0.0779443 + 1.93417i) q^{6} +(-0.0361239 + 0.0761296i) q^{7} +(0.278113 + 0.402916i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-2.72510 - 5.74302i) q^{10} +(-1.87546 + 0.626122i) q^{11} +(-1.69632 + 0.418105i) q^{12} +(0.194884 + 3.60028i) q^{13} +(-0.158376 - 0.0390362i) q^{14} +(-3.27324 + 0.264244i) q^{15} +(-3.07699 + 3.20348i) q^{16} +(-2.58020 + 5.43765i) q^{17} +(-0.233328 + 1.92162i) q^{18} +(-3.08753 - 5.34776i) q^{19} +(4.58659 - 3.44660i) q^{20} +(-0.0478682 + 0.0693490i) q^{21} +(-1.91369 - 3.31461i) q^{22} +(2.72042 - 4.71190i) q^{23} +(0.209879 + 0.442311i) q^{24} +(5.12144 - 2.68794i) q^{25} +(-6.75290 + 1.76364i) q^{26} +(0.885456 + 0.464723i) q^{27} +(0.00592790 - 0.147099i) q^{28} +(1.19623 + 5.85950i) q^{29} +(-1.76856 - 6.10578i) q^{30} +(-4.20912 - 2.20912i) q^{31} +(-6.43961 - 4.07217i) q^{32} +(-1.95161 + 0.317168i) q^{33} +(-11.3122 - 2.78821i) q^{34} +(0.0553508 - 0.271126i) q^{35} +(-1.74142 + 0.140582i) q^{36} +(8.03223 - 5.07928i) q^{37} +(8.94717 - 7.92650i) q^{38} +(-0.385165 + 3.58492i) q^{39} +(-1.20340 - 1.06612i) q^{40} +(-1.67543 - 0.272285i) q^{41} +(-0.150063 - 0.0639359i) q^{42} +(7.42578 + 4.69578i) q^{43} +(2.58563 - 2.29067i) q^{44} +(-3.27324 - 0.264244i) q^{45} +(9.99002 + 3.33516i) q^{46} +(0.807113 + 6.64717i) q^{47} +(-3.55102 + 2.66842i) q^{48} +(4.42263 + 5.41673i) q^{49} +(7.08100 + 8.67265i) q^{50} +(-3.41904 + 4.95334i) q^{51} +(-2.77870 - 5.65321i) q^{52} +(6.56441 + 9.51018i) q^{53} +(-0.538556 + 1.85931i) q^{54} +(5.48780 - 3.47027i) q^{55} +(-0.0407204 + 0.00661770i) q^{56} +(-2.18971 - 5.77378i) q^{57} +(-10.6501 + 4.53757i) q^{58} +(1.83591 + 1.91139i) q^{59} +(5.08007 - 2.66623i) q^{60} +(8.54651 + 0.689945i) q^{61} +(2.56009 - 8.83847i) q^{62} +(-0.0583727 + 0.0607724i) q^{63} +(2.07973 - 5.48379i) q^{64} +(-3.45080 - 11.3262i) q^{65} +(-1.35721 - 3.57866i) q^{66} +(-3.72885 - 1.58871i) q^{67} +(0.423407 - 10.5067i) q^{68} +(3.44103 - 4.21450i) q^{69} +0.535655 q^{70} +(-0.0492959 + 0.0603766i) q^{71} +(0.136210 + 0.470250i) q^{72} +(-2.12613 - 1.88358i) q^{73} +(12.7435 + 13.2674i) q^{74} +(5.48629 - 1.83159i) q^{75} +(8.62466 + 6.48101i) q^{76} +(0.0200827 - 0.165396i) q^{77} +(-6.94836 + 0.657560i) q^{78} +(-1.30348 - 10.7351i) q^{79} +(7.29331 - 12.6324i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.132304 - 3.28309i) q^{82} +(-2.02938 + 5.35105i) q^{83} +(0.0294475 - 0.144243i) q^{84} +(3.95350 - 19.3655i) q^{85} +(-6.03086 + 15.9021i) q^{86} +(0.240805 + 5.97551i) q^{87} +(-0.773865 - 0.581521i) q^{88} +(-3.02400 + 5.23773i) q^{89} +(-0.766223 - 6.31041i) q^{90} +(-0.281128 - 0.115220i) q^{91} +(-1.14577 + 9.43629i) q^{92} +(-3.80025 - 2.85570i) q^{93} +(-12.2946 + 4.10455i) q^{94} +(14.0472 + 14.6247i) q^{95} +(-5.70300 - 5.05242i) q^{96} +(2.82518 + 9.75364i) q^{97} +(-8.56105 + 10.4854i) q^{98} -1.97722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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Database

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