LMFDB - Embedded newform 225.2.q.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11303 + 1.23614i) q^{2} +(0.560227 - 1.63895i) q^{3} +(-0.0801613 - 0.762684i) q^{4} +(2.09847 - 0.772289i) q^{5} +(1.40242 + 2.51672i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 - 1.20564i) q^{8} +(-2.37229 - 1.83636i) q^{9} +O(q^{10})$	\(q+(-1.11303 + 1.23614i) q^{2} +(0.560227 - 1.63895i) q^{3} +(-0.0801613 - 0.762684i) q^{4} +(2.09847 - 0.772289i) q^{5} +(1.40242 + 2.51672i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 - 1.20564i) q^{8} +(-2.37229 - 1.83636i) q^{9} +(-1.38100 + 3.45359i) q^{10} +(3.04269 - 3.37925i) q^{11} +(-1.29491 - 0.295896i) q^{12} +(0.454318 + 0.504572i) q^{13} +(-2.25887 - 0.480138i) q^{14} +(-0.0901221 - 3.87193i) q^{15} +(4.83758 - 1.02826i) q^{16} +(-1.73545 - 1.26088i) q^{17} +(4.91044 - 0.888568i) q^{18} +(5.56870 + 4.04590i) q^{19} +(-0.757229 - 1.53856i) q^{20} +(2.35944 - 0.464121i) q^{21} +(0.790638 + 7.52241i) q^{22} +(0.104805 + 0.0222770i) q^{23} +(-2.90563 + 2.04427i) q^{24} +(3.80714 - 3.24125i) q^{25} -1.12939 q^{26} +(-4.33872 + 2.85928i) q^{27} +(0.861350 - 0.625807i) q^{28} +(1.87597 + 0.835237i) q^{29} +(4.88658 + 4.19817i) q^{30} +(-5.90734 + 2.63012i) q^{31} +(-2.06213 + 3.57172i) q^{32} +(-3.83382 - 6.87996i) q^{33} +(3.49024 - 0.741873i) q^{34} +(2.38522 + 1.98695i) q^{35} +(-1.21040 + 1.95651i) q^{36} +(-0.886060 + 2.72701i) q^{37} +(-11.1994 + 2.38051i) q^{38} +(1.08149 - 0.461929i) q^{39} +(-4.41335 - 1.24845i) q^{40} +(3.63522 + 4.03732i) q^{41} +(-2.05240 + 3.43318i) q^{42} +(-0.613014 - 1.06177i) q^{43} +(-2.82121 - 2.04973i) q^{44} +(-6.39638 - 2.02146i) q^{45} +(-0.144189 + 0.104759i) q^{46} +(-10.8080 - 4.81201i) q^{47} +(1.02488 - 8.50460i) q^{48} +(2.53627 - 4.39296i) q^{49} +(-0.230806 + 8.31377i) q^{50} +(-3.03876 + 2.13793i) q^{51} +(0.348410 - 0.386948i) q^{52} +(-1.07586 + 0.781661i) q^{53} +(1.29465 - 8.54575i) q^{54} +(3.77524 - 9.44110i) q^{55} +(0.297663 - 2.83208i) q^{56} +(9.75074 - 6.86018i) q^{57} +(-3.12049 + 1.38933i) q^{58} +(-1.15888 - 1.28707i) q^{59} +(-2.94584 + 0.379114i) q^{60} +(-2.52602 + 2.80543i) q^{61} +(3.32384 - 10.2297i) q^{62} +(0.561150 - 4.12700i) q^{63} +(0.936638 + 2.88268i) q^{64} +(1.34305 + 0.707962i) q^{65} +(12.7718 + 2.91845i) q^{66} +(-12.9879 + 5.78257i) q^{67} +(-0.822536 + 1.42467i) q^{68} +(0.0952254 - 0.159290i) q^{69} +(-5.11098 + 0.736948i) q^{70} +(-10.9600 + 7.96294i) q^{71} +(1.72264 + 5.90743i) q^{72} +(-1.83085 - 5.63478i) q^{73} +(-2.38477 - 4.13054i) q^{74} +(-3.17937 - 8.05553i) q^{75} +(2.63935 - 4.57148i) q^{76} +(6.17509 + 1.31256i) q^{77} +(-0.632716 + 1.85101i) q^{78} +(-8.20200 - 3.65176i) q^{79} +(9.35740 - 5.89378i) q^{80} +(2.25554 + 8.71278i) q^{81} -9.03682 q^{82} +(-1.89564 + 18.0358i) q^{83} +(-0.543113 - 1.76230i) q^{84} +(-4.61555 - 1.30565i) q^{85} +(1.99480 + 0.424009i) q^{86} +(2.41988 - 2.60670i) q^{87} +(-9.12328 + 1.93921i) q^{88} +(2.33361 + 7.18212i) q^{89} +(9.61817 - 5.65691i) q^{90} +(-0.291288 + 0.896494i) q^{91} +(0.00858900 - 0.0817189i) q^{92} +(1.00117 + 11.1553i) q^{93} +(17.9779 - 8.00428i) q^{94} +(14.8103 + 4.18954i) q^{95} +(4.69860 + 5.38070i) q^{96} +(9.93178 + 4.42191i) q^{97} +(2.60738 + 8.02469i) q^{98} +(-13.4237 + 2.42908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.11303	+	1.23614i	−0.787030	+	0.874086i	−0.994562	−	0.104143i	$-0.966790\pi$
$2$	−1.11303	+	1.23614i	−0.787030	+	0.874086i	0.207532	+	0.978228i	$0.433457\pi$
$3$	0.560227	−	1.63895i	0.323447	−	0.946246i
$3$	0.560227	−	1.63895i	0.323447	−	0.946246i
$4$	−0.0801613	−	0.762684i	−0.0400807	−	0.381342i
$5$	2.09847	−	0.772289i	0.938464	−	0.345378i
$5$	2.09847	−	0.772289i	0.938464	−	0.345378i
$6$	1.40242	+	2.51672i	0.572538	+	1.02744i
$7$	0.694163	+	1.20233i	0.262369	+	0.454436i	0.966871	−	0.255266i	$-0.0821629\pi$
$7$	0.694163	+	1.20233i	0.262369	+	0.454436i	−0.704502	+	0.709702i	$0.748830\pi$
$8$	−1.65942	−	1.20564i	−0.586694	−	0.426258i
$9$	−2.37229	−	1.83636i	−0.790764	−	0.612121i
$10$	−1.38100	+	3.45359i	−0.436709	+	1.09212i
$11$	3.04269	−	3.37925i	0.917407	−	1.01888i	−0.0823451	−	0.996604i	$-0.526241\pi$
$11$	3.04269	−	3.37925i	0.917407	−	1.01888i	0.999752	−	0.0222795i	$-0.00709237\pi$
$12$	−1.29491	−	0.295896i	−0.373807	−	0.0854178i
$13$	0.454318	+	0.504572i	0.126005	+	0.139943i	0.802846	−	0.596186i	$-0.203318\pi$
$13$	0.454318	+	0.504572i	0.126005	+	0.139943i	−0.676841	+	0.736129i	$0.736651\pi$
$14$	−2.25887	−	0.480138i	−0.603709	−	0.128322i
$15$	−0.0901221	−	3.87193i	−0.0232694	−	0.999729i
$16$	4.83758	−	1.02826i	1.20940	−	0.257065i
$17$	−1.73545	−	1.26088i	−0.420909	−	0.305808i	0.357095	−	0.934068i	$-0.383767\pi$
$17$	−1.73545	−	1.26088i	−0.420909	−	0.305808i	−0.778003	+	0.628260i	$0.783767\pi$
$18$	4.91044	−	0.888568i	1.15740	−	0.209437i
$19$	5.56870	+	4.04590i	1.27755	+	0.928192i	0.999476	−	0.0323680i	$-0.0103049\pi$
$19$	5.56870	+	4.04590i	1.27755	+	0.928192i	0.278071	+	0.960560i	$0.410305\pi$
$20$	−0.757229	−	1.53856i	−0.169321	−	0.344033i
$21$	2.35944	−	0.464121i	0.514871	−	0.101280i
$22$	0.790638	+	7.52241i	0.168565	+	1.60378i
$23$	0.104805	+	0.0222770i	0.0218534	+	0.00464508i	0.218825	−	0.975764i	$-0.429777\pi$
$23$	0.104805	+	0.0222770i	0.0218534	+	0.00464508i	−0.196972	+	0.980409i	$0.563111\pi$
$24$	−2.90563	+	2.04427i	−0.593110	+	0.417285i
$25$	3.80714	−	3.24125i	0.761428	−	0.648250i
$26$	−1.12939			−0.221492
$27$	−4.33872	+	2.85928i	−0.834988	+	0.550268i
$28$	0.861350	−	0.625807i	0.162780	−	0.118266i
$29$	1.87597	+	0.835237i	0.348360	+	0.155100i	0.573455	−	0.819237i	$-0.305603\pi$
$29$	1.87597	+	0.835237i	0.348360	+	0.155100i	−0.225095	+	0.974337i	$0.572269\pi$
$30$	4.88658	+	4.19817i	0.892163	+	0.766478i
$31$	−5.90734	+	2.63012i	−1.06099	+	0.472383i	−0.861627	−	0.507543i	$-0.830554\pi$
$31$	−5.90734	+	2.63012i	−1.06099	+	0.472383i	−0.199363	+	0.979926i	$0.563887\pi$
$32$	−2.06213	+	3.57172i	−0.364537	+	0.631397i
$33$	−3.83382	−	6.87996i	−0.667382	−	1.19765i
$34$	3.49024	−	0.741873i	0.598571	−	0.127230i
$35$	2.38522	+	1.98695i	0.403176	+	0.335856i
$36$	−1.21040	+	1.95651i	−0.201733	+	0.326086i
$37$	−0.886060	+	2.72701i	−0.145667	+	0.448318i	−0.997096	−	0.0761520i	$-0.975737\pi$
$37$	−0.886060	+	2.72701i	−0.145667	+	0.448318i	0.851429	+	0.524470i	$0.175737\pi$
$38$	−11.1994	+	2.38051i	−1.81679	+	0.386170i
$39$	1.08149	−	0.461929i	0.173177	−	0.0739678i
$40$	−4.41335	−	1.24845i	−0.697811	−	0.197396i
$41$	3.63522	+	4.03732i	0.567726	+	0.630524i	0.956822	−	0.290673i	$-0.0938793\pi$
$41$	3.63522	+	4.03732i	0.567726	+	0.630524i	−0.389096	+	0.921197i	$0.627213\pi$
$42$	−2.05240	+	3.43318i	−0.316692	+	0.529752i
$43$	−0.613014	−	1.06177i	−0.0934837	−	0.161919i	0.815491	−	0.578770i	$-0.196467\pi$
$43$	−0.613014	−	1.06177i	−0.0934837	−	0.161919i	−0.908975	+	0.416851i	$0.863134\pi$
$44$	−2.82121	−	2.04973i	−0.425313	−	0.309008i
$45$	−6.39638	−	2.02146i	−0.953516	−	0.301341i
$46$	−0.144189	+	0.104759i	−0.0212595	+	0.0154459i
$47$	−10.8080	−	4.81201i	−1.57650	−	0.701904i	−0.582662	−	0.812715i	$-0.697989\pi$
$47$	−10.8080	−	4.81201i	−1.57650	−	0.701904i	−0.993842	+	0.110810i	$0.964655\pi$
$48$	1.02488	−	8.50460i	0.147929	−	1.22753i
$49$	2.53627	−	4.39296i	0.362325	−	0.627565i
$50$	−0.230806	+	8.31377i	−0.0326409	+	1.17575i
$51$	−3.03876	+	2.13793i	−0.425512	+	0.299371i
$52$	0.348410	−	0.386948i	0.0483158	−	0.0536601i
$53$	−1.07586	+	0.781661i	−0.147781	+	0.107369i	−0.659219	−	0.751951i	$-0.729113\pi$
$53$	−1.07586	+	0.781661i	−0.147781	+	0.107369i	0.511438	+	0.859320i	$0.329113\pi$
$54$	1.29465	−	8.54575i	0.176179	−	1.16293i
$55$	3.77524	−	9.44110i	0.509053	−	1.27304i
$56$	0.297663	−	2.83208i	0.0397769	−	0.378452i
$57$	9.75074	−	6.86018i	1.29152	−	0.908653i
$58$	−3.12049	+	1.38933i	−0.409740	+	0.182428i
$59$	−1.15888	−	1.28707i	−0.150873	−	0.167562i	0.662970	−	0.748646i	$-0.269295\pi$
$59$	−1.15888	−	1.28707i	−0.150873	−	0.167562i	−0.813844	+	0.581084i	$0.802629\pi$
$60$	−2.94584	+	0.379114i	−0.380306	+	0.0489434i
$61$	−2.52602	+	2.80543i	−0.323424	+	0.359199i	−0.882828	−	0.469696i	$-0.844363\pi$
$61$	−2.52602	+	2.80543i	−0.323424	+	0.359199i	0.559404	+	0.828895i	$0.311030\pi$
$62$	3.32384	−	10.2297i	0.422128	−	1.29918i
$63$	0.561150	−	4.12700i	0.0706983	−	0.519954i
$64$	0.936638	+	2.88268i	0.117080	+	0.360334i
$65$	1.34305	+	0.707962i	0.166585	+	0.0878119i
$66$	12.7718	+	2.91845i	1.57210	+	0.359236i
$67$	−12.9879	+	5.78257i	−1.58672	+	0.706453i	−0.995017	−	0.0997035i	$-0.968211\pi$
$67$	−12.9879	+	5.78257i	−1.58672	+	0.706453i	−0.591702	+	0.806157i	$0.701544\pi$
$68$	−0.822536	+	1.42467i	−0.0997472	+	0.172767i
$69$	0.0952254	−	0.159290i	0.0114638	−	0.0191762i
$70$	−5.11098	+	0.736948i	−0.610878	+	0.0880821i
$71$	−10.9600	+	7.96294i	−1.30072	+	0.945027i	−0.999962	−	0.00867479i	$-0.997239\pi$
$71$	−10.9600	+	7.96294i	−1.30072	+	0.945027i	−0.300755	+	0.953701i	$0.597239\pi$
$72$	1.72264	+	5.90743i	0.203015	+	0.696198i
$73$	−1.83085	−	5.63478i	−0.214285	−	0.659501i	−0.999204	−	0.0399023i	$-0.987295\pi$
$73$	−1.83085	−	5.63478i	−0.214285	−	0.659501i	0.784919	−	0.619599i	$-0.212705\pi$
$74$	−2.38477	−	4.13054i	−0.277224	−	0.480166i
$75$	−3.17937	−	8.05553i	−0.367122	−	0.930173i
$76$	2.63935	−	4.57148i	0.302754	−	0.524385i
$77$	6.17509	+	1.31256i	0.703717	+	0.149580i
$78$	−0.632716	+	1.85101i	−0.0716410	+	0.209586i
$79$	−8.20200	−	3.65176i	−0.922797	−	0.410856i	−0.110351	−	0.993893i	$-0.535198\pi$
$79$	−8.20200	−	3.65176i	−0.922797	−	0.410856i	−0.812446	+	0.583037i	$0.801864\pi$
$80$	9.35740	−	5.89378i	1.04619	−	0.658945i
$81$	2.25554	+	8.71278i	0.250615	+	0.968087i
$82$	−9.03682			−0.997950
$83$	−1.89564	+	18.0358i	−0.208074	+	1.97969i	−0.00768794	+	0.999970i	$0.502447\pi$
$83$	−1.89564	+	18.0358i	−0.208074	+	1.97969i	−0.200386	+	0.979717i	$0.564219\pi$
$84$	−0.543113	−	1.76230i	−0.0592585	−	0.192283i
$85$	−4.61555	−	1.30565i	−0.500627	−	0.141617i
$86$	1.99480	+	0.424009i	0.215105	+	0.0457220i
$87$	2.41988	−	2.60670i	0.259438	−	0.279467i
$88$	−9.12328	+	1.93921i	−0.972545	+	0.206721i
$89$	2.33361	+	7.18212i	0.247363	+	0.761304i	0.995239	+	0.0974656i	$0.0310736\pi$
$89$	2.33361	+	7.18212i	0.247363	+	0.761304i	−0.747876	+	0.663838i	$0.768926\pi$
$90$	9.61817	−	5.65691i	1.01384	−	0.596291i
$91$	−0.291288	+	0.896494i	−0.0305353	+	0.0939781i
$92$	0.00858900	−	0.0817189i	0.000895466	−	0.00851979i
$93$	1.00117	+	11.1553i	0.103817	+	1.15675i
$94$	17.9779	−	8.00428i	1.85428	−	0.825579i
$95$	14.8103	+	4.18954i	1.51951	+	0.429838i
$96$	4.69860	+	5.38070i	0.479549	+	0.549166i
$97$	9.93178	+	4.42191i	1.00842	+	0.448977i	0.843384	−	0.537311i	$-0.180560\pi$
$97$	9.93178	+	4.42191i	1.00842	+	0.448977i	0.165035	+	0.986288i	$0.447226\pi$
$98$	2.60738	+	8.02469i	0.263385	+	0.810616i
$99$	−13.4237	+	2.42908i	−1.34913	+	0.244132i
$100$	−2.77723	−	2.64382i	−0.277723	−	0.264382i
$101$	−6.10657	−	10.5769i	−0.607626	−	1.05244i	−0.991630	−	0.129108i	$-0.958788\pi$
$101$	−6.10657	−	10.5769i	−0.607626	−	1.05244i	0.384004	−	0.923331i	$-0.374545\pi$
$102$	0.739435	−	6.13593i	0.0732149	−	0.607547i
$103$	0.0887548	+	0.844445i	0.00874527	+	0.0832057i	0.998024	−	0.0628341i	$-0.0200139\pi$
$103$	0.0887548	+	0.844445i	0.00874527	+	0.0832057i	−0.989279	+	0.146040i	$0.953347\pi$
$104$	−0.145574	−	1.38504i	−0.0142747	−	0.135814i
$105$	4.59277	−	2.79611i	0.448208	−	0.272872i
$106$	0.231222	−	2.19993i	0.0224583	−	0.213677i
$107$	19.0764			1.84419			0.922095	−	0.386964i	$-0.126476\pi$
$107$	19.0764			1.84419			0.922095	+	0.386964i	$0.126476\pi$
$108$	2.52852	+	3.07987i	0.243307	+	0.296361i
$109$	4.05014	−	12.4651i	0.387933	−	1.19394i	−0.546397	−	0.837526i	$-0.684001\pi$
$109$	4.05014	−	12.4651i	0.387933	−	1.19394i	0.934330	−	0.356409i	$-0.115999\pi$
$110$	7.46861	+	15.1749i	0.712104	+	1.44687i
$111$	3.97303	+	2.97995i	0.377104	+	0.282845i
$112$	4.59438	+	5.10257i	0.434128	+	0.482148i
$113$	−4.65919	−	5.17455i	−0.438299	−	0.486781i	0.483008	−	0.875616i	$-0.339544\pi$
$113$	−4.65919	−	5.17455i	−0.438299	−	0.486781i	−0.921307	+	0.388835i	$0.872878\pi$
$114$	−2.37269	+	19.6889i	−0.222223	+	1.84403i
$115$	0.237134	−	0.0341922i	0.0221129	−	0.00318844i
$116$	0.486642	−	1.49773i	0.0451835	−	0.139061i
$117$	−0.151198	−	2.03128i	−0.0139783	−	0.187792i
$118$	2.88087			0.265205
$119$	0.311301	−	2.96183i	0.0285369	−	0.271511i
$120$	−4.51861	+	6.53383i	−0.412491	+	0.596454i
$121$	−1.01156	−	9.62433i	−0.0919598	−	0.874939i
$122$	−0.656382	−	6.24506i	−0.0594260	−	0.565401i
$123$	8.65351	−	3.69612i	0.780260	−	0.333268i
$124$	2.47949	+	4.29460i	0.222665	+	0.385666i
$125$	5.48598	−	9.74187i	0.490681	−	0.871339i
$126$	4.47699	+	5.28714i	0.398842	+	0.471016i
$127$	6.85641	+	21.1019i	0.608408	+	1.87249i	0.471407	+	0.881916i	$0.343746\pi$
$127$	6.85641	+	21.1019i	0.608408	+	1.87249i	0.137000	+	0.990571i	$0.456254\pi$
$128$	−12.1413	−	5.40566i	−1.07315	−	0.477798i
$129$	−2.08361	+	0.409864i	−0.183452	+	0.0360865i
$130$	−2.36999	+	0.872217i	−0.207862	+	0.0764985i
$131$	−10.6170	+	4.72699i	−0.927610	+	0.412999i	−0.814223	−	0.580552i	$-0.802837\pi$
$131$	−10.6170	+	4.72699i	−0.927610	+	0.412999i	−0.113387	+	0.993551i	$0.536170\pi$
$132$	−4.93991	+	3.47550i	−0.429964	+	0.302503i
$133$	−0.998901	+	9.50390i	−0.0866157	+	0.824093i
$134$	7.30778	−	22.4910i	0.631296	−	1.94293i
$135$	−6.89649	+	9.35086i	−0.593555	+	0.804793i
$136$	1.35968	+	4.18466i	0.116591	+	0.358832i
$137$	16.2011	−	3.44364i	1.38415	−	0.294210i	0.545149	−	0.838339i	$-0.316473\pi$
$137$	16.2011	−	3.44364i	1.38415	−	0.294210i	0.839002	+	0.544129i	$0.183140\pi$
$138$	0.0909164	+	0.295006i	0.00773931	+	0.0251126i
$139$	16.4624	+	3.49920i	1.39633	+	0.296798i	0.843782	−	0.536686i	$-0.180324\pi$
$139$	16.4624	+	3.49920i	1.39633	+	0.296798i	0.552544	+	0.833484i	$0.313657\pi$
$140$	1.32421	−	1.97845i	0.111916	−	0.167209i
$141$	−13.9415	+	15.0179i	−1.17409	+	1.26473i
$142$	2.35551	−	22.4112i	0.197670	−	1.88070i
$143$	3.08743			0.258184
$144$	−13.3644	−	6.44423i	−1.11370	−	0.537019i
$145$	4.58172	+	0.303925i	0.380491	+	0.0252396i
$146$	9.00319	+	4.00848i	0.745109	+	0.331744i
$147$	−5.77893	−	6.61787i	−0.476638	−	0.545833i
$148$	2.15088	+	0.457183i	0.176801	+	0.0375802i
$149$	−7.97992	+	13.8216i	−0.653740	+	1.13231i	0.328468	+	0.944515i	$0.393468\pi$
$149$	−7.97992	+	13.8216i	−0.653740	+	1.13231i	−0.982208	+	0.187796i	$0.939865\pi$
$150$	13.4965	+	5.03588i	1.10199	+	0.411178i
$151$	−4.20769	−	7.28793i	−0.342417	−	0.593084i	0.642464	−	0.766316i	$-0.277912\pi$
$151$	−4.20769	−	7.28793i	−0.342417	−	0.593084i	−0.984881	+	0.173232i	$0.944579\pi$
$152$	−4.36292	−	13.4277i	−0.353880	−	1.08913i
$153$	1.80156	+	6.17809i	0.145648	+	0.499469i
$154$	−8.49556	+	6.17239i	−0.684592	+	0.497385i
$155$	−10.3652	+	10.0814i	−0.832549	+	0.809757i
$156$	−0.438999	−	0.787804i	−0.0351481	−	0.0630748i
$157$	0.0425739	−	0.0737402i	0.00339777	−	0.00588511i	−0.864322	−	0.502940i	$-0.832252\pi$
$157$	0.0425739	−	0.0737402i	0.00339777	−	0.00588511i	0.867719	+	0.497055i	$0.165585\pi$
$158$	13.6432	−	6.07433i	1.08539	−	0.483248i
$159$	0.678373	+	2.20119i	0.0537985	+	0.174566i
$160$	−1.56892	+	9.08771i	−0.124034	+	0.718446i
$161$	0.0459676	+	0.141474i	0.00362275	+	0.0111497i
$162$	−13.2807	−	6.90941i	−1.04343	−	0.542855i
$163$	3.81218	−	11.7327i	0.298593	−	0.918974i	−0.683398	−	0.730046i	$-0.739499\pi$
$163$	3.81218	−	11.7327i	0.298593	−	0.918974i	0.981991	−	0.188928i	$-0.0605013\pi$
$164$	2.78780	−	3.09616i	0.217690	−	0.241770i
$165$	−13.3585	−	11.4766i	−1.03996	−	0.893449i
$166$	−20.1850	−	22.4177i	−1.56666	−	1.73995i
$167$	−6.11816	+	2.72398i	−0.473437	+	0.210788i	−0.629563	−	0.776949i	$-0.716766\pi$
$167$	−6.11816	+	2.72398i	−0.473437	+	0.210788i	0.156126	+	0.987737i	$0.450099\pi$
$168$	−4.47486	−	2.07446i	−0.345243	−	0.160048i
$169$	1.31068	−	12.4703i	0.100822	−	0.959255i
$170$	6.75121	−	4.25227i	0.517794	−	0.326134i
$171$	−5.78084	−	19.8242i	−0.442072	−	1.51599i
$172$	−0.760656	+	0.552649i	−0.0579995	+	0.0421391i
$173$	7.69463	−	8.54575i	0.585012	−	0.649721i	−0.375873	−	0.926671i	$-0.622657\pi$
$173$	7.69463	−	8.54575i	0.585012	−	0.649721i	0.960884	+	0.276950i	$0.0893236\pi$
$174$	0.528857	+	5.89265i	0.0400926	+	0.446721i
$175$	6.53981	+	2.32747i	0.494363	+	0.175940i
$176$	11.2445	−	19.4761i	0.847588	−	1.46807i
$177$	−2.75867	+	1.17829i	−0.207354	+	0.0885659i
$178$	−11.4755	−	5.10923i	−0.860127	−	0.382953i
$179$	−3.97320	+	2.88670i	−0.296971	+	0.215762i	−0.726286	−	0.687393i	$-0.758755\pi$
$179$	−3.97320	+	2.88670i	−0.296971	+	0.215762i	0.429315	+	0.903155i	$0.358755\pi$
$180$	−1.02899	+	5.04046i	−0.0766964	+	0.375694i
$181$	−1.69167	−	1.22907i	−0.125741	−	0.0913562i	0.523137	−	0.852248i	$-0.324762\pi$
$181$	−1.69167	−	1.22907i	−0.125741	−	0.0913562i	−0.648878	+	0.760892i	$0.724762\pi$
$182$	−0.783983	−	1.35790i	−0.0581127	−	0.100654i
$183$	3.18281	+	5.71170i	0.235280	+	0.422221i
$184$	−0.147058	−	0.163324i	−0.0108412	−	0.0120404i
$185$	0.246673	+	6.40685i	0.0181358	+	0.471041i
$186$	−14.9039	−	11.1786i	−1.09280	−	0.819651i
$187$	−9.54128	+	2.02806i	−0.697727	+	0.148307i
$188$	−2.80367	+	8.62880i	−0.204478	+	0.629320i
$189$	−6.44957	−	3.23175i	−0.469137	−	0.235076i
$190$	−21.6632	+	13.6446i	−1.57161	+	0.989886i
$191$	−10.0452	+	2.13518i	−0.726846	+	0.154496i	−0.556452	−	0.830880i	$-0.687838\pi$
$191$	−10.0452	+	2.13518i	−0.726846	+	0.154496i	−0.170394	+	0.985376i	$0.554504\pi$
$192$	5.24928	+	0.0798527i	0.378834	+	0.00576287i
$193$	0.879316	−	1.52302i	0.0632945	−	0.109629i	−0.832642	−	0.553812i	$-0.813173\pi$
$193$	0.879316	−	1.52302i	0.0632945	−	0.109629i	0.895936	+	0.444183i	$0.146506\pi$
$194$	−16.5205	+	7.35539i	−1.18610	+	0.528086i
$195$	1.91272	−	1.80456i	0.136973	−	0.129227i
$196$	−3.55375	−	1.58223i	−0.253839	−	0.113017i
$197$	1.28192	−	0.931373i	0.0913333	−	0.0663576i	−0.541181	−	0.840906i	$-0.682023\pi$
$197$	1.28192	−	0.931373i	0.0913333	−	0.0663576i	0.632515	+	0.774548i	$0.282023\pi$
$198$	11.9383	−	19.2973i	0.848416	−	1.37140i
$199$	−4.83781			−0.342943			−0.171471	−	0.985189i	$-0.554852\pi$
$199$	−4.83781			−0.342943			−0.171471	+	0.985189i	$0.554852\pi$
$200$	−10.2254	+	0.788557i	−0.723047	+	0.0557594i
$201$	2.20117	+	24.5260i	0.155259	+	1.72993i
$202$	19.8713	+	4.22379i	1.39814	+	0.297184i
$203$	0.298004	+	2.83532i	0.0209158	+	0.199001i
$204$	1.87416	+	2.14623i	0.131217	+	0.150266i
$205$	10.7464	+	5.66475i	0.750560	+	0.395643i
$206$	−1.14264	−	0.830178i	−0.0796117	−	0.0578413i
$207$	−0.207720	−	0.245308i	−0.0144375	−	0.0170501i
$208$	2.71663	+	1.97375i	0.188365	+	0.136855i
$209$	30.6160	−	6.50762i	2.11775	−	0.450142i
$210$	−1.65549	+	8.78947i	−0.114240	+	0.606531i
$211$	4.19980	+	0.892696i	0.289126	+	0.0614557i	0.350192	−	0.936678i	$-0.386116\pi$
$211$	4.19980	+	0.892696i	0.289126	+	0.0614557i	−0.0610653	+	0.998134i	$0.519450\pi$
$212$	0.682403	+	0.757885i	0.0468676	+	0.0520518i
$213$	6.91072	+	22.4240i	0.473514	+	1.53647i
$214$	−21.2326	+	23.5812i	−1.45143	+	1.61198i
$215$	−2.10638	−	1.75467i	−0.143654	−	0.119667i
$216$	10.6470	+	0.486192i	0.724439	+	0.0330812i
$217$	−7.26291	−	5.27682i	−0.493039	−	0.358214i
$218$	10.9007	+	18.8805i	0.738287	+	1.27875i
$219$	−10.2608	−	0.156088i	−0.693360	−	0.0105475i
$220$	−7.50320	−	2.12250i	−0.505866	−	0.143099i
$221$	−0.152243	−	1.44850i	−0.0102410	−	0.0974367i
$222$	−8.10575	+	1.59447i	−0.544022	+	0.107014i
$223$	10.8453	−	12.0449i	0.726254	−	0.806587i	−0.261067	−	0.965321i	$-0.584074\pi$
$223$	10.8453	−	12.0449i	0.726254	−	0.806587i	0.987321	+	0.158734i	$0.0507411\pi$
$224$	−5.72583			−0.382573
$225$	−14.9838	+	0.697894i	−0.998917	+	0.0465263i
$226$	11.5823			0.770443
$227$	6.16408	−	6.84590i	0.409124	−	0.454379i	−0.503004	−	0.864284i	$-0.667772\pi$
$227$	6.16408	−	6.84590i	0.409124	−	0.454379i	0.912128	+	0.409906i	$0.134438\pi$
$228$	−6.01378	−	6.88682i	−0.398272	−	0.456090i
$229$	0.857635	+	8.15985i	0.0566741	+	0.539218i	0.985617	+	0.168995i	$0.0540521\pi$
$229$	0.857635	+	8.15985i	0.0566741	+	0.539218i	−0.928943	+	0.370223i	$0.879281\pi$
$230$	−0.221671	+	0.331189i	−0.0146166	+	0.0218380i
$231$	5.61066	−	9.38531i	0.369154	−	0.617508i
$232$	−2.10604	−	3.64776i	−0.138268	−	0.239487i
$233$	−6.70215	−	4.86940i	−0.439073	−	0.319005i	0.346194	−	0.938163i	$-0.387474\pi$
$233$	−6.70215	−	4.86940i	−0.439073	−	0.319005i	−0.785266	+	0.619158i	$0.787474\pi$
$234$	2.67925	+	2.07398i	0.175148	+	0.135580i
$235$	−26.3964	−	1.75099i	−1.72191	−	0.114222i
$236$	−0.888727	+	0.987032i	−0.0578512	+	0.0642503i
$237$	−10.5800	+	11.3968i	−0.687247	+	0.740303i
$238$	3.31477	+	3.68142i	0.214864	+	0.238631i
$239$	−1.05559	−	0.224373i	−0.0682807	−	0.0145135i	0.173645	−	0.984808i	$-0.444446\pi$
$239$	−1.05559	−	0.224373i	−0.0682807	−	0.0145135i	−0.241925	+	0.970295i	$0.577779\pi$
$240$	−4.41733	−	18.6381i	−0.285137	−	1.20309i
$241$	24.5479	−	5.21783i	1.58127	−	0.336110i	0.668223	−	0.743961i	$-0.267055\pi$
$241$	24.5479	−	5.21783i	1.58127	−	0.336110i	0.913049	+	0.407851i	$0.133722\pi$
$242$	13.0229	+	9.46173i	0.837147	+	0.608223i
$243$	15.5434	+	1.18443i	0.997109	+	0.0759814i
$244$	2.34215	+	1.70167i	0.149941	+	0.108938i
$245$	1.92966	−	11.1772i	0.123281	−	0.714086i
$246$	−5.06267	+	14.8109i	−0.322784	+	0.944306i
$247$	0.488517	+	4.64793i	0.0310836	+	0.295741i
$248$	12.9737	+	2.75765i	0.823833	+	0.175111i
$249$	28.4977	+	13.2110i	1.80597	+	0.837213i
$250$	5.93630	+	17.6244i	0.375444	+	1.11467i
$251$	−23.1900			−1.46374			−0.731869	−	0.681445i	$-0.761352\pi$
$251$	−23.1900			−1.46374			−0.731869	+	0.681445i	$0.761352\pi$
$252$	−3.19258	−	0.0971543i	−0.201114	−	0.00612015i
$253$	0.394169	−	0.286381i	0.0247812	−	0.0180046i
$254$	−33.7163	−	15.0115i	−2.11555	−	0.941903i
$255$	−4.72564	+	6.83319i	−0.295931	+	0.427911i
$256$	14.6579	−	6.52610i	0.916116	−	0.407881i
$257$	−10.4244	+	18.0555i	−0.650253	+	1.12627i	0.332808	+	0.942995i	$0.392004\pi$
$257$	−10.4244	+	18.0555i	−0.650253	+	1.12627i	−0.983061	+	0.183277i	$0.941329\pi$
$258$	1.81247	−	3.03184i	0.112839	−	0.188754i
$259$	−3.89383	+	0.827659i	−0.241951	+	0.0514282i
$260$	0.432291	−	1.08107i	0.0268096	−	0.0670452i
$261$	−2.91656	−	5.42640i	−0.180530	−	0.335886i
$262$	5.97377	−	18.3854i	0.369061	−	1.13585i
$263$	8.87330	−	1.88608i	0.547151	−	0.116301i	0.0739614	−	0.997261i	$-0.476436\pi$
$263$	8.87330	−	1.88608i	0.547151	−	0.116301i	0.473190	+	0.880961i	$0.343103\pi$
$264$	−1.93284	+	16.0390i	−0.118958	+	0.987130i
$265$	−1.65400	+	2.47117i	−0.101604	+	0.151803i
$266$	−10.6364	−	11.8129i	−0.652159	−	0.724296i
$267$	13.0785	+	0.198951i	0.800389	+	0.0121756i
$268$	5.45140	+	9.44209i	0.332997	+	0.576768i
$269$	12.0005	+	8.71886i	0.731683	+	0.531599i	0.890095	−	0.455774i	$-0.150638\pi$
$269$	12.0005	+	8.71886i	0.731683	+	0.531599i	−0.158413	+	0.987373i	$0.550638\pi$
$270$	−3.88301	−	18.9328i	−0.236313	−	1.15221i
$271$	6.34725	−	4.61155i	0.385568	−	0.280132i	−0.378069	−	0.925777i	$-0.623412\pi$
$271$	6.34725	−	4.61155i	0.385568	−	0.280132i	0.763637	+	0.645646i	$0.223412\pi$
$272$	−9.69190	−	4.31511i	−0.587658	−	0.261642i
$273$	1.30612	+	0.979646i	0.0790498	+	0.0592909i
$274$	−13.7754	+	23.8597i	−0.832203	+	1.44142i
$275$	0.630957	−	22.7274i	0.0380481	−	1.37051i
$276$	−0.129121	−	0.0598580i	−0.00777218	−	0.00360303i
$277$	−14.8863	+	16.5329i	−0.894429	+	0.993364i	−0.999999	−	0.00104812i	$-0.999666\pi$
$277$	−14.8863	+	16.5329i	−0.894429	+	0.993364i	0.105571	+	0.994412i	$0.466333\pi$
$278$	−22.6487	+	16.4552i	−1.35838	+	0.986919i
$279$	18.8438	+	4.60862i	1.12815	+	0.275911i
$280$	−1.56255	−	6.17291i	−0.0933799	−	0.368902i
$281$	−1.06166	+	10.1010i	−0.0633334	+	0.602577i	0.916120	+	0.400905i	$0.131304\pi$
$281$	−1.06166	+	10.1010i	−0.0633334	+	0.602577i	−0.979453	+	0.201672i	$0.935362\pi$
$282$	−3.04688	−	33.9491i	−0.181439	−	2.02164i
$283$	0.696855	−	0.310260i	0.0414237	−	0.0184430i	−0.385920	−	0.922532i	$-0.626116\pi$
$283$	0.696855	−	0.310260i	0.0414237	−	0.0184430i	0.427344	+	0.904089i	$0.359449\pi$
$284$	6.95177	+	7.72073i	0.412512	+	0.458141i
$285$	15.1636	−	21.9263i	0.898213	−	1.29880i
$286$	−3.43640	+	3.81650i	−0.203198	+	0.225675i
$287$	−2.33074	+	7.17328i	−0.137579	+	0.423425i
$288$	11.4510	−	4.68634i	0.674755	−	0.276145i
$289$	−3.83131	−	11.7916i	−0.225371	−	0.693622i
$290$	−5.47528	+	5.32538i	−0.321519	+	0.312717i
$291$	12.8113	−	13.8004i	0.751013	−	0.808992i
$292$	−4.15079	+	1.84805i	−0.242907	+	0.108149i
$293$	3.29507	−	5.70722i	0.192500	−	0.333419i	−0.753578	−	0.657358i	$-0.771674\pi$
$293$	3.29507	−	5.70722i	0.192500	−	0.333419i	0.946078	+	0.323939i	$0.105007\pi$
$294$	14.6128	+	0.222291i	0.852234	+	0.0129643i
$295$	−3.42586	−	1.80588i	−0.199461	−	0.105142i
$296$	4.75815	−	3.45699i	0.276562	−	0.200934i
$297$	−3.53918	+	23.3616i	−0.205364	+	1.35558i
$298$	−8.20364	−	25.2482i	−0.475224	−	1.46259i
$299$	0.0363745	+	0.0630025i	0.00210359	+	0.00364353i
$300$	−5.88896	+	3.07060i	−0.339999	+	0.177281i
$301$	0.851063	−	1.47408i	0.0490545	−	0.0849648i
$302$	13.6922	+	2.91037i	0.787899	+	0.167473i
$303$	−20.7560	+	4.08288i	−1.19240	+	0.234556i
$304$	31.0993	+	13.8463i	1.78367	+	0.794139i
$305$	−3.13418	+	7.83794i	−0.179462	+	0.448799i
$306$	−9.64221	−	4.64941i	−0.551208	−	0.265789i
$307$	20.2069			1.15327			0.576634	−	0.817002i	$-0.304366\pi$
$307$	20.2069			1.15327			0.576634	+	0.817002i	$0.304366\pi$
$308$	0.506062	−	4.81486i	0.0288356	−	0.274352i
$309$	1.43372	+	0.327617i	0.0815617	+	0.0186375i
$310$	−0.925333	−	24.0337i	−0.0525554	−	1.36502i
$311$	−17.4845	−	3.71644i	−0.991455	−	0.210740i	−0.316494	−	0.948594i	$-0.602506\pi$
$311$	−17.4845	−	3.71644i	−0.991455	−	0.210740i	−0.674960	+	0.737854i	$0.735839\pi$
$312$	−2.35156	−	0.537350i	−0.133131	−	0.0304214i
$313$	−17.9489	+	3.81515i	−1.01453	+	0.215645i	−0.685033	−	0.728512i	$-0.740212\pi$
$313$	−17.9489	+	3.81515i	−1.01453	+	0.215645i	−0.329496	+	0.944157i	$0.606879\pi$
$314$	0.0437675	+	0.134702i	0.00246994	+	0.00760170i
$315$	−2.00968	−	9.09376i	−0.113233	−	0.512375i
$316$	−2.12766	+	6.54826i	−0.119690	+	0.368369i
$317$	−0.331660	+	3.15554i	−0.0186279	+	0.177233i	−0.999880	−	0.0154964i	$-0.995067\pi$
$317$	−0.331660	+	3.15554i	−0.0186279	+	0.177233i	0.981252	+	0.192729i	$0.0617338\pi$
$318$	−3.47604	−	1.61142i	−0.194927	−	0.0903641i
$319$	8.53049	−	3.79802i	0.477616	−	0.212648i
$320$	4.19176	+	5.32585i	0.234327	+	0.297724i
$321$	10.6871	−	31.2653i	0.596498	−	1.74506i
$322$	−0.226045	−	0.100642i	−0.0125970	−	0.00560855i
$323$	−4.56282	−	14.0429i	−0.253882	−	0.781369i
$324$	6.46429	−	2.41869i	0.359127	−	0.134372i
$325$	3.36509	+	0.448416i	0.186662	+	0.0248736i
$326$	10.2602	+	17.7712i	0.568261	+	0.984256i
$327$	−18.1606	−	13.6212i	−1.00428	−	0.753255i
$328$	−1.16481	−	11.0824i	−0.0643157	−	0.611923i
$329$	−1.71688	−	16.3350i	−0.0946546	−	0.900579i
$330$	29.0550	−	3.73923i	1.59943	−	0.205838i
$331$	1.54265	−	14.6773i	0.0847916	−	0.806738i	−0.866652	−	0.498914i	$-0.833732\pi$
$331$	1.54265	−	14.6773i	0.0847916	−	0.806738i	0.951443	−	0.307824i	$-0.0996009\pi$
$332$	13.9076			0.763278
$333$	7.10978	−	4.84214i	0.389614	−	0.265348i
$334$	3.44246	−	10.5948i	0.188363	−	0.579721i
$335$	−22.7888	+	22.1649i	−1.24509	+	1.21100i
$336$	10.9367	−	4.67134i	0.596648	−	0.254842i
$337$	−8.16234	−	9.06519i	−0.444631	−	0.493813i	0.478614	−	0.878026i	$-0.341139\pi$
$337$	−8.16234	−	9.06519i	−0.444631	−	0.493813i	−0.923244	+	0.384213i	$0.874473\pi$
$338$	13.9563	+	15.5000i	0.759121	+	0.843089i
$339$	−11.0910	+	4.73724i	−0.602381	+	0.257291i
$340$	−0.625806	+	3.62487i	−0.0339391	+	0.196586i
$341$	−9.08639	+	27.9650i	−0.492056	+	1.51439i
$342$	30.9398	+	14.9190i	1.67303	+	0.806725i
$343$	16.7606			0.904989
$344$	−0.262866	+	2.50100i	−0.0141728	+	0.134845i
$345$	0.0768099	−	0.407806i	0.00413530	−	0.0219555i
$346$	1.99943	+	19.0233i	0.107490	+	1.02270i
$347$	−2.27230	−	21.6195i	−0.121983	−	1.16059i	−0.868661	−	0.495408i	$-0.835019\pi$
$347$	−2.27230	−	21.6195i	−0.121983	−	1.16059i	0.746677	−	0.665187i	$-0.231648\pi$
$348$	−2.18207	−	1.63665i	−0.116971	−	0.0877335i
$349$	5.54554	+	9.60516i	0.296846	+	0.514152i	0.975413	−	0.220387i	$-0.0707319\pi$
$349$	5.54554	+	9.60516i	0.296846	+	0.514152i	−0.678567	+	0.734539i	$0.737399\pi$
$350$	−10.1561	+	5.49361i	−0.542866	+	0.293646i
$351$	−3.41387	−	0.890174i	−0.182219	−	0.0475140i
$352$	5.79531	+	17.8361i	0.308891	+	0.950669i
$353$	4.63276	+	2.06264i	0.246577	+	0.109783i	0.526304	−	0.850296i	$-0.323577\pi$
$353$	4.63276	+	2.06264i	0.246577	+	0.109783i	−0.279727	+	0.960080i	$0.590244\pi$
$354$	1.61394	−	4.72158i	0.0857799	−	0.250949i
$355$	−16.8496	+	25.1743i	−0.894284	+	1.33611i
$356$	5.29063	−	2.35554i	0.280403	−	0.124843i
$357$	−4.67989	−	2.16951i	−0.247686	−	0.114822i
$358$	0.853912	−	8.12443i	0.0451306	−	0.429389i
$359$	−9.46581	+	29.1328i	−0.499586	+	1.53757i	0.310099	+	0.950704i	$0.399638\pi$
$359$	−9.46581	+	29.1328i	−0.499586	+	1.53757i	−0.809685	+	0.586864i	$0.800362\pi$
$360$	8.17715	+	11.0662i	0.430973	+	0.583239i
$361$	8.76981	+	26.9907i	0.461569	+	1.42056i
$362$	3.40219	−	0.723158i	0.178815	−	0.0380083i
$363$	−16.3405	−	3.73392i	−0.857652	−	0.195980i
$364$	0.707091	+	0.150297i	0.0370617	+	0.00787770i
$365$	−8.19366	−	10.4105i	−0.428876	−	0.544908i
$366$	−10.6030	−	2.42287i	−0.554230	−	0.126646i
$367$	1.67022	−	15.8911i	0.0871849	−	0.829509i	−0.860317	−	0.509759i	$-0.829735\pi$
$367$	1.67022	−	15.8911i	0.0871849	−	0.829509i	0.947502	−	0.319750i	$-0.103599\pi$
$368$	0.529910			0.0276235
$369$	−1.20981	−	16.2533i	−0.0629803	−	0.846113i
$370$	−8.19434	−	6.82608i	−0.426003	−	0.354871i
$371$	−1.68664	−	0.750939i	−0.0875658	−	0.0389868i
$372$	8.42769	−	1.65780i	0.436956	−	0.0859528i
$373$	−11.0182	−	2.34198i	−0.570499	−	0.121263i	−0.0863750	−	0.996263i	$-0.527528\pi$
$373$	−11.0182	−	2.34198i	−0.570499	−	0.121263i	−0.484124	+	0.874999i	$0.660862\pi$
$374$	8.11274	−	14.0517i	0.419500	−	0.726595i
$375$	−12.8930	−	14.4489i	−0.665792	−	0.746137i
$376$	12.1334	+	21.0157i	0.625733	+	1.08380i
$377$	0.430852	+	1.32603i	0.0221900	+	0.0682938i
$378$	11.1735	−	4.37556i	0.574701	−	0.225054i
$379$	−17.8996	+	13.0048i	−0.919440	+	0.668012i	−0.943385	−	0.331701i	$-0.892377\pi$
$379$	−17.8996	+	13.0048i	−0.919440	+	0.668012i	0.0239446	+	0.999713i	$0.492377\pi$
$380$	2.00808	−	11.6314i	0.103012	−	0.596681i
$381$	38.4260	+	0.584540i	1.96862	+	0.0299469i
$382$	8.54123	−	14.7938i	0.437007	−	0.756919i
$383$	5.77940	−	2.57315i	0.295313	−	0.131482i	−0.253732	−	0.967275i	$-0.581658\pi$
$383$	5.77940	−	2.57315i	0.295313	−	0.131482i	0.549045	+	0.835793i	$0.314991\pi$
$384$	−15.6615	+	16.8706i	−0.799222	+	0.860923i
$385$	13.9719	−	2.01460i	0.712074	−	0.102673i
$386$	0.903967	+	2.78213i	0.0460107	+	0.141606i
$387$	−0.495551	+	3.64455i	−0.0251902	+	0.185263i
$388$	2.57638	−	7.92927i	0.130796	−	0.402548i
$389$	22.1352	−	24.5837i	1.12230	−	1.24644i	0.156354	−	0.987701i	$-0.450026\pi$
$389$	22.1352	−	24.5837i	1.12230	−	1.24644i	0.965947	−	0.258740i	$-0.0833073\pi$
$390$	0.101783	+	4.37293i	0.00515400	+	0.221432i
$391$	−0.153796	−	0.170807i	−0.00777777	−	0.00863809i
$392$	−9.50508	+	4.23193i	−0.480079	+	0.213745i
$393$	1.79936	+	20.0489i	0.0907655	+	1.01133i
$394$	−0.275508	+	2.62129i	−0.0138799	+	0.132059i
$395$	−20.0319	−	1.32880i	−1.00791	−	0.0668591i
$396$	2.92868	+	10.0433i	0.147172	+	0.504696i
$397$	22.9141	−	16.6480i	1.15002	−	0.835541i	0.161540	−	0.986866i	$-0.448354\pi$
$397$	22.9141	−	16.6480i	1.15002	−	0.835541i	0.988484	+	0.151325i	$0.0483539\pi$
$398$	5.38462	−	5.98022i	0.269907	−	0.299762i
$399$	15.0168	+	6.96149i	0.751779	+	0.348510i
$400$	15.0845	−	19.5945i	0.754225	−	0.979727i
$401$	−4.98614	+	8.63625i	−0.248996	+	0.431274i	−0.963248	−	0.268615i	$-0.913434\pi$
$401$	−4.98614	+	8.63625i	−0.248996	+	0.431274i	0.714251	+	0.699889i	$0.246767\pi$
$402$	−32.7676	−	24.5771i	−1.63430	−	1.22580i
$403$	−4.01089	−	1.78577i	−0.199797	−	0.0889553i
$404$	−7.57731	+	5.50524i	−0.376985	+	0.273896i
$405$	11.4620	+	16.5416i	0.569549	+	0.821957i
$406$	−3.83655	−	2.78742i	−0.190405	−	0.138337i
$407$	6.51926	+	11.2917i	0.323148	+	0.559708i
$408$	7.62016	+	0.115919i	0.377254	+	0.00573884i
$409$	−6.46434	−	7.17938i	−0.319641	−	0.354997i	0.561815	−	0.827263i	$-0.310103\pi$
$409$	−6.46434	−	7.17938i	−0.319641	−	0.354997i	−0.881456	+	0.472265i	$0.843436\pi$
$410$	−18.9635	+	6.97904i	−0.936539	+	0.344670i
$411$	3.43233	−	28.4819i	0.169304	−	1.40491i
$412$	0.636930	−	0.135384i	0.0313793	−	0.00666988i
$413$	0.743021	−	2.28678i	0.0365617	−	0.112525i
$414$	0.534434	+	0.0162635i	0.0262660	+	0.000799307i
$415$	9.95092	+	39.3116i	0.488471	+	1.92973i
$416$	−2.73905	+	0.582204i	−0.134293	+	0.0285449i
$417$	14.9577	−	25.0207i	0.732482	−	1.22527i
$418$	−26.0321	+	45.0889i	−1.27327	+	2.20537i
$419$	−11.5515	+	5.14308i	−0.564330	+	0.251256i	−0.669014	−	0.743250i	$-0.733283\pi$
$419$	−11.5515	+	5.14308i	−0.564330	+	0.251256i	0.104684	+	0.994506i	$0.466617\pi$
$420$	−2.50071	−	3.27869i	−0.122022	−	0.159984i
$421$	−20.9466	−	9.32602i	−1.02087	−	0.454522i	−0.173114	−	0.984902i	$-0.555383\pi$
$421$	−20.9466	−	9.32602i	−1.02087	−	0.454522i	−0.847760	+	0.530380i	$0.822049\pi$
$422$	−5.77800	+	4.19797i	−0.281269	+	0.204354i
$423$	16.8030	+	31.2629i	0.816991	+	1.52005i
$424$	2.72771			0.132470
$425$	−10.6939	+	0.824687i	−0.518732	+	0.0400032i
$426$	−35.4111	−	16.4159i	−1.71567	−	0.795352i
$427$	−5.12652	−	1.08968i	−0.248090	−	0.0527331i
$428$	−1.52919	−	14.5493i	−0.0739163	−	0.703267i
$429$	1.72966	−	5.06013i	0.0835087	−	0.244305i
$430$	4.51349	−	0.650797i	0.217660	−	0.0313842i
$431$	10.6124	+	7.71039i	0.511183	+	0.371397i	0.813272	−	0.581883i	$-0.197684\pi$
$431$	10.6124	+	7.71039i	0.511183	+	0.371397i	−0.302089	+	0.953280i	$0.597684\pi$
$432$	−18.0489	+	18.2933i	−0.868376	+	0.880138i
$433$	−19.0904	−	13.8700i	−0.917425	−	0.666548i	0.0254569	−	0.999676i	$-0.491896\pi$
$433$	−19.0904	−	13.8700i	−0.917425	−	0.666548i	−0.942882	+	0.333128i	$0.891896\pi$
$434$	14.6067	−	3.10476i	0.701146	−	0.149033i
$435$	3.06492	−	7.33892i	0.146952	−	0.351874i
$436$	−9.83156	−	2.08976i	−0.470846	−	0.100081i
$437$	0.493498	+	0.548085i	0.0236072	+	0.0262184i
$438$	11.6135	−	12.5101i	0.554915	−	0.597755i
$439$	−5.42383	+	6.02378i	−0.258865	+	0.287499i	−0.858542	−	0.512743i	$-0.828629\pi$
$439$	−5.42383	+	6.02378i	−0.258865	+	0.287499i	0.599677	+	0.800242i	$0.295296\pi$
$440$	−17.6473	+	11.1152i	−0.841301	+	0.529896i
$441$	−14.0839	+	5.76385i	−0.670660	+	0.274469i
$442$	1.96001	+	1.42403i	0.0932280	+	0.0677341i
$443$	−0.254259	−	0.440389i	−0.0120802	−	0.0209235i	0.859922	−	0.510425i	$-0.170512\pi$
$443$	−0.254259	−	0.440389i	−0.0120802	−	0.0209235i	−0.872002	+	0.489502i	$0.837179\pi$
$444$	1.95428	−	3.26905i	0.0927459	−	0.155142i
$445$	10.4437	+	13.2692i	0.495078	+	0.629022i
$446$	2.81813	+	26.8127i	0.133442	+	1.26962i
$447$	18.1823	+	20.8219i	0.859995	+	0.984842i
$448$	−2.81574	+	3.12719i	−0.133031	+	0.147746i
$449$	7.22605			0.341018			0.170509	−	0.985356i	$-0.445459\pi$
$449$	7.22605			0.341018			0.170509	+	0.985356i	$0.445459\pi$
$450$	15.8147	−	19.2989i	0.745510	−	0.909757i
$451$	24.7040			1.16327
$452$	−3.57306	+	3.96829i	−0.168063	+	0.186652i
$453$	−14.3018	+	2.81328i	−0.671957	+	0.132180i
$454$	1.60172	+	15.2394i	0.0751726	+	0.715219i
$455$	0.0810927	+	2.10622i	0.00380168	+	0.0987412i
$456$	−24.4515	−	0.371959i	−1.14505	−	0.0174186i
$457$	−7.94049	−	13.7533i	−0.371441	−	0.643354i	0.618347	−	0.785905i	$-0.287803\pi$
$457$	−7.94049	−	13.7533i	−0.371441	−	0.643354i	−0.989787	+	0.142551i	$0.954469\pi$
$458$	−11.0413	−	8.02199i	−0.515927	−	0.374843i
$459$	11.1349	+	0.508468i	0.519730	+	0.0237332i
$460$	−0.0450869	−	0.178118i	−0.00210219	−	0.00830478i
$461$	22.0858	−	24.5288i	1.02864	−	1.14242i	0.0389435	−	0.999241i	$-0.487601\pi$
$461$	22.0858	−	24.5288i	1.02864	−	1.14242i	0.989697	−	0.143179i	$-0.0457326\pi$
$462$	5.35677	+	17.3817i	0.249220	+	0.808670i
$463$	12.3216	+	13.6845i	0.572632	+	0.635972i	0.957992	−	0.286794i	$-0.0925895\pi$
$463$	12.3216	+	13.6845i	0.572632	+	0.635972i	−0.385360	+	0.922766i	$0.625923\pi$
$464$	9.93402	+	2.11154i	0.461175	+	0.0980258i
$465$	10.7160	+	22.6358i	0.496944	+	1.04971i
$466$	13.4790	−	2.86504i	0.624401	−	0.132721i
$467$	−14.9196	−	10.8397i	−0.690398	−	0.501603i	0.186393	−	0.982475i	$-0.440320\pi$
$467$	−14.9196	−	10.8397i	−0.690398	−	0.501603i	−0.876791	+	0.480872i	$0.840320\pi$
$468$	−1.53711	+	0.278147i	−0.0710528	+	0.0128574i
$469$	−15.9682	−	11.6016i	−0.737344	−	0.535712i
$470$	31.5445	−	30.6809i	1.45504	−	1.41520i
$471$	−0.0970052	−	0.111088i	−0.00446976	−	0.00511865i
$472$	0.371331	+	3.53298i	0.0170919	+	0.162618i
$473$	−5.45321	−	1.15911i	−0.250739	−	0.0532962i
$474$	−2.31223	−	25.7634i	−0.106204	−	1.18335i
$475$	34.3146	−	2.64625i	1.57446	−	0.121418i
$476$	−2.28390			−0.104682
$477$	3.98768	+	0.121350i	0.182583	+	0.00555624i
$478$	1.45226	−	1.05513i	0.0664250	−	0.0482606i
$479$	−21.0863	−	9.38822i	−0.963457	−	0.428959i	−0.136137	−	0.990690i	$-0.543469\pi$
$479$	−21.0863	−	9.38822i	−0.963457	−	0.428959i	−0.827320	+	0.561731i	$0.810135\pi$
$480$	14.0153	+	7.66256i	0.639709	+	0.349746i
$481$	−1.77853	+	0.791851i	−0.0810938	+	0.0361053i
$482$	−20.8726	+	36.1524i	−0.950720	+	1.64670i
$483$	0.257620	+	0.00391895i	0.0117221	+	0.000178318i
$484$	−7.25923	+	1.54300i	−0.329965	+	0.0701363i
$485$	24.2565	+	1.60904i	1.10143	+	0.0730627i
$486$	−18.7644	+	17.8956i	−0.851169	+	0.811759i
$487$	−3.52725	+	10.8558i	−0.159835	+	0.491921i	−0.998619	−	0.0525435i	$-0.983267\pi$
$487$	−3.52725	+	10.8558i	−0.159835	+	0.491921i	0.838784	+	0.544465i	$0.183267\pi$
$488$	7.57408	−	1.60992i	0.342863	−	0.0728777i
$489$	−17.0935	−	12.8209i	−0.772997	−	0.579782i
$490$	11.6689	+	14.8259i	0.527146	+	0.669766i
$491$	−26.6271	−	29.5724i	−1.20167	−	1.33459i	−0.927918	−	0.372784i	$-0.878403\pi$
$491$	−26.6271	−	29.5724i	−1.20167	−	1.33459i	−0.273748	−	0.961801i	$-0.588263\pi$
$492$	−3.51265	−	6.30360i	−0.158362	−	0.284188i
$493$	−2.20253	−	3.81489i	−0.0991969	−	0.171814i
$494$	−6.28925	−	4.56941i	−0.282967	−	0.205587i
$495$	−26.2932	+	15.4643i	−1.18179	+	0.695070i
$496$	−25.8728	+	18.7977i	−1.16172	+	0.844041i
$497$	−17.1821	−	7.64996i	−0.770723	−	0.343148i
$498$	−48.0495	+	20.5231i	−2.15315	+	0.919661i
$499$	18.1188	−	31.3826i	0.811107	−	1.40488i	−0.100983	−	0.994888i	$-0.532199\pi$
$499$	18.1188	−	31.3826i	0.811107	−	1.40488i	0.912090	−	0.409990i	$-0.134468\pi$
$500$	−7.86973	−	3.40315i	−0.351945	−	0.152193i
$501$	1.03690	+	11.5534i	0.0463253	+	0.516167i
$502$	25.8111	−	28.6662i	1.15201	−	1.27943i
$503$	26.1554	−	19.0030i	1.16621	−	0.847302i	0.175661	−	0.984451i	$-0.443794\pi$
$503$	26.1554	−	19.0030i	1.16621	−	0.847302i	0.990550	+	0.137149i	$0.0437939\pi$
$504$	−5.90687	+	6.17189i	−0.263113	+	0.274918i
$505$	−20.9829	−	17.4792i	−0.933725	−	0.777816i
$506$	−0.0847140	+	0.806000i	−0.00376600	+	0.0358311i
$507$	−19.7039	−	9.13434i	−0.875081	−	0.405670i
$508$	15.5444	−	6.92082i	0.689672	−	0.307062i
$509$	−0.180712	−	0.200701i	−0.00800991	−	0.00889590i	0.739127	−	0.673567i	$-0.235239\pi$
$509$	−0.180712	−	0.200701i	−0.00800991	−	0.00889590i	−0.747136	+	0.664671i	$0.768572\pi$
$510$	−3.18703	−	13.4471i	−0.141124	−	0.595448i
$511$	5.50393	−	6.11274i	0.243480	−	0.270411i
$512$	−0.0335504	+	0.103257i	−0.00148273	+	0.00456337i
$513$	−35.7294	−	1.63157i	−1.57749	−	0.0720354i
$514$	−10.7166	−	32.9823i	−0.472689	−	1.45479i
$515$	0.838405	+	1.70350i	0.0369445	+	0.0750651i
$516$	0.479622	+	1.55628i	0.0211142	+	0.0685115i
$517$	−49.1463	+	21.8814i	−2.16145	+	0.962341i
$518$	3.31084	−	5.73454i	0.145470	−	0.251961i
$519$	−9.69529	−	17.3986i	−0.425576	−	0.763716i
$520$	−1.37513	−	2.79404i	−0.0603036	−	0.122527i
$521$	22.4017	−	16.2758i	0.981435	−	0.713054i	0.0234061	−	0.999726i	$-0.492549\pi$
$521$	22.4017	−	16.2758i	0.981435	−	0.713054i	0.958029	+	0.286672i	$0.0925489\pi$
$522$	9.95402	+	2.43445i	0.435676	+	0.106553i
$523$	11.9194	+	36.6841i	0.521198	+	1.60408i	0.771713	+	0.635971i	$0.219400\pi$
$523$	11.9194	+	36.6841i	0.521198	+	1.60408i	−0.250515	+	0.968113i	$0.580600\pi$
$524$	4.45627	+	7.71848i	0.194673	+	0.337183i
$525$	7.47837	−	9.41449i	0.326383	−	0.410882i
$526$	−7.54477	+	13.0679i	−0.328968	+	0.569789i
$527$	13.5682	+	2.88400i	0.591038	+	0.125629i
$528$	−25.6208	−	29.3402i	−1.11500	−	1.27687i
$529$	−21.0011	−	9.35027i	−0.913089	−	0.406534i
$530$	−1.21377	−	4.79506i	−0.0527229	−	0.208284i
$531$	0.385678	+	5.18142i	0.0167370	+	0.224855i
$532$	7.32855			0.317733
$533$	−0.385571	+	3.66846i	−0.0167009	+	0.158899i
$534$	−14.8026	+	15.9454i	−0.640573	+	0.690026i
$535$	40.0313	−	14.7325i	1.73070	−	0.636943i
$536$	28.5240	+	6.06297i	1.23205	+	0.261880i
$537$	2.50525	+	8.12907i	0.108110	+	0.350795i
$538$	−24.1347	+	5.12998i	−1.04052	+	0.221169i
$539$	−7.12781	−	21.9371i	−0.307016	−	0.944900i
$540$	7.68458	+	4.51026i	0.330692	+	0.194091i
$541$	−9.26487	+	28.5143i	−0.398328	+	1.22593i	0.528011	+	0.849237i	$0.322938\pi$
$541$	−9.26487	+	28.5143i	−0.398328	+	1.22593i	−0.926339	+	0.376690i	$0.877062\pi$
$542$	−1.36414	+	12.9789i	−0.0585948	+	0.557492i
$543$	−2.96210	+	2.08400i	−0.127116	+	0.0894331i
$544$	8.08224	−	3.59845i	0.346523	−	0.154282i
$545$	−1.12753	−	29.2854i	−0.0482981	−	1.25445i
$546$	−2.66473	+	0.524175i	−0.114040	+	0.0224326i
$547$	5.24843	+	2.33675i	0.224407	+	0.0999123i	0.515860	−	0.856673i	$-0.327472\pi$
$547$	5.24843	+	2.33675i	0.224407	+	0.0999123i	−0.291454	+	0.956585i	$0.594139\pi$
$548$	−3.92511	−	12.0802i	−0.167672	−	0.516042i
$549$	11.1443	−	2.01661i	0.475626	−	0.0860667i
$550$	27.3921	+	26.0762i	1.16800	+	1.11189i
$551$	7.06745	+	12.2412i	0.301083	+	0.521492i
$552$	−0.350065	+	0.149521i	−0.0148998	+	0.00636405i
$553$	−1.30291	−	12.3964i	−0.0554055	−	0.527148i
$554$	−3.86816	−	36.8031i	−0.164343	−	1.56361i
$555$	10.6387	+	3.18500i	0.451586	+	0.135196i
$556$	1.34913	−	12.8361i	0.0572160	−	0.544373i
$557$	−13.8510			−0.586887			−0.293444	−	0.955976i	$-0.594801\pi$
$557$	−13.8510			−0.586887			−0.293444	+	0.955976i	$0.594801\pi$
$558$	−26.6706	+	18.1641i	−1.12906	+	0.768948i
$559$	0.257236	−	0.791691i	0.0108799	−	0.0334850i
$560$	13.5818	+	7.15940i	0.573936	+	0.302540i
$561$	−2.02140	+	16.7738i	−0.0853434	+	0.708191i
$562$	−11.3047	−	12.5551i	−0.476859	−	0.529606i
$563$	−19.9405	−	22.1462i	−0.840393	−	0.933351i	0.158144	−	0.987416i	$-0.449449\pi$
$563$	−19.9405	−	22.1462i	−0.840393	−	0.933351i	−0.998537	+	0.0540647i	$0.982782\pi$
$564$	12.5714	+	9.42914i	0.529353	+	0.397039i
$565$	−13.7734	−	7.26039i	−0.579452	−	0.305447i
$566$	−0.392094	+	1.20674i	−0.0164809	+	0.0507231i
$567$	−8.90989	+	8.75998i	−0.374180	+	0.367885i
$568$	27.7878			1.16595
$569$	−1.71235	+	16.2919i	−0.0717853	+	0.682991i	0.898160	+	0.439669i	$0.144904\pi$
$569$	−1.71235	+	16.2919i	−0.0717853	+	0.682991i	−0.969945	+	0.243323i	$0.921763\pi$
$570$	10.2265	+	43.1489i	0.428341	+	1.80731i
$571$	0.540001	+	5.13777i	0.0225983	+	0.215009i	0.999994	+	0.00358843i	$0.00114223\pi$
$571$	0.540001	+	5.13777i	0.0225983	+	0.215009i	−0.977395	+	0.211420i	$0.932191\pi$
$572$	−0.247492	−	2.35473i	−0.0103482	−	0.0984562i
$573$	−2.12816	+	17.6598i	−0.0889051	+	0.737747i
$574$	−6.27303	−	10.8652i	−0.261831	−	0.453505i
$575$	0.471213	−	0.254888i	0.0196509	−	0.0106295i
$576$	3.07166	−	8.55855i	0.127986	−	0.356606i
$577$	4.99821	+	15.3829i	0.208078	+	0.640399i	0.999573	+	0.0292230i	$0.00930328\pi$
$577$	4.99821	+	15.3829i	0.208078	+	0.640399i	−0.791495	+	0.611176i	$0.790697\pi$
$578$	18.8404	+	8.38830i	0.783659	+	0.348907i
$579$	−2.00353	−	2.29439i	−0.0832639	−	0.0953515i
$580$	−0.135478	−	3.51876i	−0.00562540	−	0.146109i
$581$	−23.0008	+	10.2406i	−0.954234	+	0.424852i
$582$	2.79988	+	31.1969i	0.116059	+	1.29315i
$583$	−0.632094	+	6.01397i	−0.0261787	+	0.249073i
$584$	−3.75536	+	11.5578i	−0.155398	+	0.478266i
$585$	−1.88602	−	4.14582i	−0.0779775	−	0.171408i
$586$	3.38744	+	10.4255i	0.139934	+	0.430672i
$587$	27.4905	−	5.84328i	1.13465	−	0.241178i	0.397959	−	0.917403i	$-0.369719\pi$
$587$	27.4905	−	5.84328i	1.13465	−	0.241178i	0.736695	+	0.676225i	$0.236385\pi$
$588$	−4.58410	+	4.93800i	−0.189045	+	0.203640i
$589$	−43.5374	−	9.25416i	−1.79393	−	0.381311i
$590$	6.04541	−	2.22486i	0.248885	−	0.0915961i
$591$	−0.808301	−	2.62279i	−0.0332491	−	0.107887i
$592$	−1.48231	+	14.1033i	−0.0609226	+	0.579640i
$593$	3.80524			0.156262			0.0781312	−	0.996943i	$-0.475105\pi$
$593$	3.80524			0.156262			0.0781312	+	0.996943i	$0.475105\pi$
$594$	−24.9390	−	30.3770i	−1.02326	−	1.24638i
$595$	−1.63414	−	6.45573i	−0.0669931	−	0.264659i
$596$	11.1812	+	4.97820i	0.458000	+	0.203915i
$597$	−2.71027	+	7.92891i	−0.110924	+	0.324509i
$598$	−0.118366	−	0.0251595i	−0.00484035	−	0.00102885i
$599$	17.5681	−	30.4289i	0.717813	−	1.24329i	−0.244051	−	0.969762i	$-0.578476\pi$
$599$	17.5681	−	30.4289i	0.717813	−	1.24329i	0.961864	−	0.273527i	$-0.0881902\pi$
$600$	−4.43616	+	17.2007i	−0.181105	+	0.702216i
$601$	−10.6092	−	18.3758i	−0.432760	−	0.749563i	0.564350	−	0.825536i	$-0.309127\pi$
$601$	−10.6092	−	18.3758i	−0.432760	−	0.749563i	−0.997110	+	0.0759732i	$0.975794\pi$
$602$	0.874923	+	2.69274i	0.0356592	+	0.109748i
$603$	41.4299	+	10.1325i	1.68716	+	0.412627i
$604$	−5.22110	+	3.79335i	−0.212443	+	0.154349i
$605$	−9.55549	−	19.4151i	−0.388486	−	0.789337i
$606$	18.0550	−	30.2018i	0.733435	−	1.22686i
$607$	−7.55362	+	13.0833i	−0.306592	+	0.531033i	−0.977615	−	0.210404i	$-0.932522\pi$
$607$	−7.55362	+	13.0833i	−0.306592	+	0.531033i	0.671023	+	0.741437i	$0.265855\pi$
$608$	−25.9342	+	11.5467i	−1.05177	+	0.468279i
$609$	4.81389	+	1.10001i	0.195069	+	0.0445747i
$610$	−6.20039	−	12.5981i	−0.251046	−	0.510084i
$611$	−2.48225	−	7.63958i	−0.100421	−	0.309064i
$612$	4.56752	−	1.86927i	0.184631	−	0.0755607i
$613$	−0.267857	+	0.824379i	−0.0108186	+	0.0332963i	−0.956320	−	0.292321i	$-0.905572\pi$
$613$	−0.267857	+	0.824379i	−0.0108186	+	0.0332963i	0.945501	+	0.325618i	$0.105572\pi$
$614$	−22.4909	+	24.9786i	−0.907657	+	1.00806i
$615$	15.3046	−	14.4392i	0.617142	−	0.582244i
$616$	−8.66461	−	9.62302i	−0.349107	−	0.387723i
$617$	18.1546	−	8.08293i	0.730875	−	0.325407i	−0.00733880	−	0.999973i	$-0.502336\pi$
$617$	18.1546	−	8.08293i	0.730875	−	0.325407i	0.738214	+	0.674566i	$0.235669\pi$
$618$	−2.00076	+	1.40764i	−0.0804823	+	0.0566237i
$619$	−1.87214	+	17.8122i	−0.0752477	+	0.715934i	0.890241	+	0.455490i	$0.150536\pi$
$619$	−1.87214	+	17.8122i	−0.0752477	+	0.715934i	−0.965489	+	0.260445i	$0.916131\pi$
$620$	8.51980	+	7.09720i	0.342163	+	0.285030i
$621$	−0.518416	+	0.203013i	−0.0208033	+	0.00814664i
$622$	24.0548	−	17.4768i	0.964510	−	0.700757i
$623$	−7.01535	+	7.79133i	−0.281064	+	0.312153i
$624$	4.75680	−	3.34667i	0.190424	−	0.133974i
$625$	3.98862	−	24.6798i	0.159545	−	0.987191i
$626$	15.2615	−	26.4337i	0.609973	−	1.05650i
$627$	6.48624	−	53.8237i	0.259035	−	2.14951i
$628$	−0.0596532	−	0.0265593i	−0.00238042	−	0.00105983i
$629$	4.97615	−	3.61538i	0.198412	−	0.144155i
$630$	13.4780	+	7.63736i	0.536978	+	0.304280i
$631$	−27.5034	−	19.9824i	−1.09489	−	0.795487i	−0.114675	−	0.993403i	$-0.536583\pi$
$631$	−27.5034	−	19.9824i	−1.09489	−	0.795487i	−0.980219	+	0.197916i	$0.936583\pi$
$632$	9.20786	+	15.9485i	0.366269	+	0.634396i
$633$	3.81592	−	6.38314i	0.151669	−	0.253707i
$634$	−3.53155	−	3.92218i	−0.140256	−	0.155770i
$635$	30.6847	+	38.9864i	1.21768	+	1.54713i
$636$	1.62443	−	0.693834i	0.0644130	−	0.0275123i
$637$	3.36884	−	0.716068i	0.133478	−	0.0283717i
$638$	−4.79979	+	14.7722i	−0.190025	+	0.584838i
$639$	40.6233	+	1.23622i	1.60703	+	0.0489040i
$640$	−29.6529	−	1.96701i	−1.17213	−	0.0777527i
$641$	12.4589	−	2.64822i	0.492097	−	0.104599i	0.0448223	−	0.998995i	$-0.485728\pi$
$641$	12.4589	−	2.64822i	0.492097	−	0.104599i	0.447275	+	0.894396i	$0.352394\pi$
$642$	26.7533	+	48.0100i	1.05587	+	1.89480i
$643$	9.31365	−	16.1317i	0.367295	−	0.636173i	−0.621847	−	0.783139i	$-0.713617\pi$
$643$	9.31365	−	16.1317i	0.367295	−	0.636173i	0.989142	+	0.146966i	$0.0469507\pi$
$644$	0.104215	−	0.0463995i	0.00410664	−	0.00182840i
$645$	−4.05586	+	2.46924i	−0.159699	+	0.0972262i
$646$	22.4376	+	9.98987i	0.882796	+	0.393046i
$647$	−2.58476	+	1.87794i	−0.101617	+	0.0738294i	−0.637434	−	0.770505i	$-0.720004\pi$
$647$	−2.58476	+	1.87794i	−0.101617	+	0.0738294i	0.535816	+	0.844335i	$0.320004\pi$
$648$	6.76160	−	17.1775i	0.265621	−	0.674798i
$649$	−7.87544			−0.309138
$650$	−4.29975	+	3.66064i	−0.168650	+	0.143582i
$651$	−12.7173	+	8.94731i	−0.498430	+	0.350673i
$652$	−9.25391	−	1.96698i	−0.362411	−	0.0770329i
$653$	0.528615	+	5.02943i	0.0206863	+	0.196817i	0.999984	−	0.00560700i	$-0.00178477\pi$
$653$	0.528615	+	5.02943i	0.0206863	+	0.196817i	−0.979298	+	0.202424i	$0.935118\pi$
$654$	37.0510	−	7.28825i	1.44881	−	0.284993i
$655$	−18.6288	+	18.1188i	−0.727888	+	0.707960i
$656$	21.7371	+	15.7929i	0.848691	+	0.616610i
$657$	−6.00419	+	16.7294i	−0.234246	+	0.652678i
$658$	22.1034	+	16.0590i	0.861679	+	0.626046i
$659$	−1.39674	+	0.296887i	−0.0544094	+	0.0115651i	−0.235036	−	0.971987i	$-0.575521\pi$
$659$	−1.39674	+	0.296887i	−0.0544094	+	0.0115651i	0.180627	+	0.983552i	$0.442187\pi$
$660$	−7.68216	+	11.1083i	−0.299028	+	0.432389i
$661$	4.54628	+	0.966342i	0.176830	+	0.0375863i	0.295475	−	0.955350i	$-0.404522\pi$
$661$	4.54628	+	0.966342i	0.176830	+	0.0375863i	−0.118646	+	0.992937i	$0.537855\pi$
$662$	16.4263	+	18.2432i	0.638425	+	0.709042i
$663$	−2.45930	−	0.561970i	−0.0955115	−	0.0218251i
$664$	24.8904	−	27.6436i	0.965934	−	1.07278i
$665$	5.24360	+	20.7151i	0.203338	+	0.803296i
$666$	−1.92781	+	14.1782i	−0.0747011	+	0.549392i
$667$	0.178005	+	0.129328i	0.00689238	+	0.00500761i
$668$	2.56797	+	4.44786i	0.0993579	+	0.172093i
$669$	−13.6651	−	24.5227i	−0.528325	−	0.948104i
$670$	−2.03444	−	52.8404i	−0.0785971	−	2.04140i
$671$	1.79436	+	17.0722i	0.0692703	+	0.659063i
$672$	−3.20776	+	9.38433i	−0.123742	+	0.362008i
$673$	12.5961	−	13.9894i	0.485546	−	0.539253i	−0.449734	−	0.893163i	$-0.648481\pi$
$673$	12.5961	−	13.9894i	0.485546	−	0.539253i	0.935280	+	0.353909i	$0.115148\pi$
$674$	20.2908			0.781572
$675$	−7.25049	+	24.9486i	−0.279072	+	0.960270i
$676$	−9.61597			−0.369845
$677$	−6.63373	+	7.36751i	−0.254955	+	0.283156i	−0.857012	−	0.515297i	$-0.827682\pi$
$677$	−6.63373	+	7.36751i	−0.254955	+	0.283156i	0.602056	+	0.798453i	$0.294348\pi$
$678$	6.48872	−	18.9828i	0.249198	−	0.729029i
$679$	1.57769	+	15.0108i	0.0605464	+	0.576060i
$680$	6.08501	+	7.73131i	0.233350	+	0.296482i
$681$	−7.76679	−	13.9379i	−0.297624	−	0.534100i
$682$	−24.4554	−	42.3580i	−0.936445	−	1.62197i
$683$	21.4995	+	15.6203i	0.822655	+	0.597694i	0.917472	−	0.397801i	$-0.130226\pi$
$683$	21.4995	+	15.6203i	0.822655	+	0.597694i	−0.0948166	+	0.995495i	$0.530226\pi$
$684$	−14.6562	+	5.99809i	−0.560394	+	0.229343i
$685$	31.3379	−	19.7383i	1.19736	−	0.754161i
$686$	−18.6551	+	20.7186i	−0.712254	+	0.791038i
$687$	13.8540	+	3.16575i	0.528564	+	0.120781i
$688$	−4.05728	−	4.50607i	−0.154682	−	0.171792i
$689$	−0.883189	−	0.187728i	−0.0336468	−	0.00715185i
$690$	0.418615	+	0.548848i	0.0159364	+	0.0208943i
$691$	32.4537	−	6.89825i	1.23460	−	0.262422i	0.456020	−	0.889970i	$-0.349275\pi$
$691$	32.4537	−	6.89825i	1.23460	−	0.262422i	0.778578	+	0.627548i	$0.215941\pi$
$692$	−7.13452	−	5.18353i	−0.271214	−	0.197048i
$693$	−12.2388	−	14.4535i	−0.464913	−	0.549042i
$694$	29.2539	+	21.2542i	1.11046	+	0.806799i
$695$	37.2483	−	5.37080i	1.41291	−	0.203726i
$696$	−7.15834	+	1.40811i	−0.271336	+	0.0533741i
$697$	−1.21817	−	11.5902i	−0.0461416	−	0.439008i
$698$	−18.0457	−	3.83573i	−0.683040	−	0.145185i
$699$	−11.7354	+	8.25650i	−0.443874	+	0.312290i
$700$	1.25088	−	5.17438i	0.0472789	−	0.195573i
$701$	26.1441			0.987451			0.493725	−	0.869618i	$-0.335635\pi$
$701$	26.1441			0.987451			0.493725	+	0.869618i	$0.335635\pi$
$702$	4.90012	−	3.22925i	0.184943	−	0.121880i
$703$	−15.9674	+	11.6010i	−0.602223	+	0.437540i
$704$	12.5912	+	5.60596i	0.474548	+	0.211283i
$705$	−17.6578	+	42.2814i	−0.665030	+	1.59241i
$706$	−7.70611	+	3.43098i	−0.290023	+	0.129127i
$707$	8.47791	−	14.6842i	0.318845	−	0.552255i
$708$	1.11980	+	2.00954i	0.0420848	+	0.0755231i
$709$	−39.0480	+	8.29991i	−1.46648	+	0.311710i	−0.870850	−	0.491550i	$-0.836431\pi$
$709$	−39.0480	+	8.29991i	−1.46648	+	0.311710i	−0.595629	+	0.803259i	$0.703097\pi$
$710$	−12.3649	−	48.8483i	−0.464048	−	1.83324i
$711$	12.7516	+	23.7249i	0.478221	+	0.889753i
$712$	4.78661	−	14.7317i	0.179386	−	0.552093i
$713$	−0.677710	+	0.144052i	−0.0253804	+	0.00539478i
$714$	7.89067	−	3.37029i	0.295301	−	0.126130i
$715$	6.47887	−	2.38439i	0.242296	−	0.0891710i
$716$	2.52014	+	2.79890i	0.0941819	+	0.104600i
$717$	−0.959108	+	1.60436i	−0.0358185	+	0.0599160i
$718$	−25.4766	−	44.1267i	−0.950777	−	1.64679i
$719$	32.4317	+	23.5630i	1.20950	+	0.878751i	0.995185	−	0.0980142i	$-0.0312491\pi$
$719$	32.4317	+	23.5630i	1.20950	+	0.878751i	0.214312	+	0.976765i	$0.431249\pi$
$720$	−33.0216	−	3.20182i	−1.23064	−	0.119325i
$721$	−0.953688	+	0.692895i	−0.0355172	+	0.0258048i
$722$	−43.1254	−	19.2007i	−1.60496	−	0.714575i
$723$	5.20068	−	43.1559i	0.193415	−	1.60499i
$724$	−0.801787	+	1.38874i	−0.0297982	+	0.0516120i
$725$	9.84930	−	2.90063i	0.365794	−	0.107727i
$726$	22.8031	−	16.0432i	0.846301	−	0.595419i
$727$	−23.6216	+	26.2344i	−0.876075	+	0.972980i	−0.999813	−	0.0193348i	$-0.993845\pi$
$727$	−23.6216	+	26.2344i	−0.876075	+	0.972980i	0.123738	+	0.992315i	$0.460512\pi$
$728$	1.56422	−	1.13647i	0.0579738	−	0.0421204i
$729$	10.6491	−	24.8112i	0.394409	−	0.918935i
$730$	21.9886	+	1.45860i	0.813835	+	0.0539852i
$731$	−0.274909	+	2.61559i	−0.0101679	+	0.0967410i
$732$	4.10108	−	2.88534i	0.151580	−	0.106645i
$733$	6.14109	−	2.73419i	0.226826	−	0.100990i	−0.290177	−	0.956973i	$-0.593714\pi$
$733$	6.14109	−	2.73419i	0.226826	−	0.100990i	0.517003	+	0.855983i	$0.327047\pi$
$734$	17.7847	+	19.7519i	0.656445	+	0.729055i
$735$	−17.2378	−	9.42439i	−0.635826	−	0.347624i
$736$	−0.295689	+	0.328396i	−0.0108993	+	0.0121049i
$737$	−19.9773	+	61.4839i	−0.735874	+	2.26479i
$738$	21.4380	+	16.5949i	0.789143	+	0.610866i
$739$	−3.30815	−	10.1814i	−0.121692	−	0.374530i	0.871592	−	0.490233i	$-0.163088\pi$
$739$	−3.30815	−	10.1814i	−0.121692	−	0.374530i	−0.993284	+	0.115702i	$0.963088\pi$
$740$	4.86663	−	0.701715i	0.178901	−	0.0257956i
$741$	7.89139	+	1.80324i	0.289898	+	0.0662438i
$742$	2.80554	−	1.24911i	0.102995	−	0.0458562i
$743$	−10.6028	+	18.3647i	−0.388981	+	0.673735i	−0.992313	−	0.123756i	$-0.960506\pi$
$743$	−10.6028	+	18.3647i	−0.388981	+	0.673735i	0.603332	+	0.797490i	$0.293839\pi$
$744$	11.7879	−	19.7184i	0.432165	−	0.722910i
$745$	−6.07132	+	35.1670i	−0.222436	+	1.28842i
$746$	15.1586	−	11.0133i	0.554995	−	0.403227i
$747$	37.6173	−	39.3051i	1.37635	−	1.43810i
$748$	2.31161	+	7.11441i	0.0845209	+	0.260129i
$749$	13.2422	+	22.9361i	0.483858	+	0.838067i
$750$	32.2112	+	0.144412i	1.17619	+	0.00527317i
$751$	−24.6961	+	42.7750i	−0.901175	+	1.56088i	−0.0752042	+	0.997168i	$0.523961\pi$
$751$	−24.6961	+	42.7750i	−0.901175	+	1.56088i	−0.825971	+	0.563713i	$0.809372\pi$
$752$	−57.2324	−	12.1651i	−2.08705	−	0.443616i
$753$	−12.9917	+	38.0071i	−0.473442	+	1.38506i
$754$	−2.11871	−	0.943311i	−0.0771589	−	0.0343533i
$755$	−14.4581	−	12.0439i	−0.526184	−	0.438324i
$756$	−1.94780	+	5.17804i	−0.0708408	+	0.188324i
$757$	−31.2549			−1.13598			−0.567989	−	0.823036i	$-0.692279\pi$
$757$	−31.2549			−1.13598			−0.567989	+	0.823036i	$0.692279\pi$
$758$	3.84694	−	36.6012i	0.139727	−	1.32942i
$759$	−0.248539	−	0.806461i	−0.00902138	−	0.0292727i
$760$	−19.5255	−	24.8082i	−0.708265	−	0.899887i
$761$	28.3560	+	6.02725i	1.02790	+	0.218488i	0.690850	−	0.722998i	$-0.257236\pi$
$761$	28.3560	+	6.02725i	1.02790	+	0.218488i	0.337053	+	0.941486i	$0.390570\pi$
$762$	−43.4918	+	46.8494i	−1.57554	+	1.69717i
$763$	17.7985	−	3.78319i	0.644349	−	0.136961i
$764$	2.43370	+	7.49016i	0.0880482	+	0.270985i
$765$	8.55180	+	11.5732i	0.309191	+	0.418430i
$766$	−3.25185	+	10.0082i	−0.117494	+	0.361610i
$767$	0.122917	−	1.16948i	0.00443827	−	0.0422273i
$768$	−2.48420	−	27.6796i	−0.0896409	−	0.998800i
$769$	31.1371	−	13.8631i	1.12283	−	0.499917i	0.240549	−	0.970637i	$-0.422673\pi$
$769$	31.1371	−	13.8631i	1.12283	−	0.499917i	0.882282	+	0.470720i	$0.156006\pi$
$770$	−13.0608	+	19.5136i	−0.470679	+	0.703221i
$771$	23.7520	+	27.2001i	0.855408	+	0.979589i
$772$	−1.23207	−	0.548553i	−0.0443432	−	0.0197428i
$773$	−9.44334	−	29.0636i	−0.339653	−	1.04535i	−0.964384	−	0.264506i	$-0.914791\pi$
$773$	−9.44334	−	29.0636i	−0.339653	−	1.04535i	0.624731	−	0.780840i	$-0.285209\pi$
$774$	−3.95362	−	4.66906i	−0.142110	−	0.167826i
$775$	−13.9652	+	29.1604i	−0.501645	+	1.04747i
$776$	−11.1498	−	19.3120i	−0.400253	−	0.693259i
$777$	−0.824939	+	6.84545i	−0.0295945	+	0.245579i
$778$	5.75179	+	54.7247i	0.206212	+	1.96197i
$779$	3.90887	+	37.1904i	0.140050	+	1.33248i
$780$	−1.52964	−	1.31415i	−0.0547698	−	0.0470540i
$781$	−6.43927	+	61.2655i	−0.230415	+	2.19225i
$782$	0.382321			0.0136718
$783$	−10.5275	+	1.74007i	−0.376222	+	0.0621849i
$784$	7.75234	−	23.8592i	0.276869	−	0.852116i
$785$	0.0323913	−	0.187621i	0.00115609	−	0.00669648i
$786$	−26.7860	−	20.0907i	−0.955425	−	0.716611i
$787$	−15.3574	−	17.0562i	−0.547434	−	0.607987i	0.404407	−	0.914579i	$-0.367478\pi$
$787$	−15.3574	−	17.0562i	−0.547434	−	0.607987i	−0.951841	+	0.306592i	$0.900811\pi$
$788$	−0.813104	−	0.903043i	−0.0289656	−	0.0321696i
$789$	1.87988	−	15.5995i	0.0669255	−	0.555357i
$790$	23.9386	−	23.2833i	0.851698	−	0.828381i
$791$	2.98726	−	9.19384i	0.106215	−	0.326895i
$792$	25.2042	+	12.1533i	0.895591	+	0.431848i
$793$	−2.56316			−0.0910205
$794$	−4.92464	+	46.8548i	−0.174769	+	1.66282i
$795$	3.12350	+	4.09523i	0.110779	+	0.145243i
$796$	0.387805	+	3.68972i	0.0137454	+	0.130779i
$797$	−4.54511	−	43.2438i	−0.160996	−	1.53177i	−0.714919	−	0.699207i	$-0.753537\pi$
$797$	−4.54511	−	43.2438i	−0.160996	−	1.53177i	0.553923	−	0.832568i	$-0.313130\pi$
$798$	−25.3195	+	10.8146i	−0.896301	+	0.382831i
$799$	12.6893	+	21.9786i	0.448916	+	0.777545i
$800$	3.72601	+	20.2819i	0.131734	+	0.717075i
$801$	7.65298	−	21.3235i	0.270405	−	0.753427i
$802$	−5.12593	−	15.7760i	−0.181003	−	0.557070i
$803$	−24.6121	−	10.9580i	−0.868541	−	0.386699i
$804$	18.5291	−	3.64483i	0.653471	−	0.128543i
$805$	0.205720	+	0.261378i	0.00725068	+	0.00921236i
$806$	6.67170	−	2.97043i	0.235001	−	0.104629i
$807$	21.0127	−	14.7836i	0.739684	−	0.520408i
$808$	−2.61855	+	24.9138i	−0.0921203	+	0.876466i
$809$	−8.36599	+	25.7479i	−0.294133	+	0.905247i	0.689379	+	0.724401i	$0.257884\pi$
$809$	−8.36599	+	25.7479i	−0.294133	+	0.905247i	−0.983511	+	0.180846i	$0.942116\pi$
$810$	−33.2052	−	4.24262i	−1.16671	−	0.149071i
$811$	−11.3390	−	34.8979i	−0.398167	−	1.22543i	−0.926468	−	0.376375i	$-0.877171\pi$
$811$	−11.3390	−	34.8979i	−0.398167	−	1.22543i	0.528300	−	0.849058i	$-0.322829\pi$
$812$	2.13857	−	0.454566i	0.0750490	−	0.0159522i
$813$	−4.00218	−	12.9863i	−0.140363	−	0.455450i
$814$	−21.2143	−	4.50923i	−0.743560	−	0.158049i
$815$	−1.06128	−	27.5648i	−0.0371752	−	0.965551i
$816$	−12.5019	+	13.4671i	−0.437654	+	0.471442i
$817$	0.882127	−	8.39287i	0.0308617	−	0.293630i
$818$	16.0697			0.561865
$819$	2.33731	−	1.59183i	0.0816722	−	0.0556231i
$820$	3.45897	−	8.65018i	0.120793	−	0.302078i
$821$	1.38376	+	0.616087i	0.0482934	+	0.0215016i	0.430741	−	0.902475i	$-0.358252\pi$
$821$	1.38376	+	0.616087i	0.0482934	+	0.0215016i	−0.382448	+	0.923977i	$0.624919\pi$
$822$	31.3874	+	35.9440i	1.09476	+	1.25369i
$823$	35.6064	+	7.56838i	1.24116	+	0.263817i	0.781290	−	0.624168i	$-0.214562\pi$
$823$	35.6064	+	7.56838i	1.24116	+	0.263817i	0.459872	+	0.887985i	$0.347895\pi$
$824$	0.870816	−	1.50830i	0.0303363	−	0.0525440i
$825$	−36.8955	−	13.7666i	−1.28454	−	0.479292i
$826$	1.99979	+	3.46374i	0.0695816	+	0.120519i
$827$	−0.131104	−	0.403496i	−0.00455892	−	0.0140309i	0.948751	−	0.316024i	$-0.102348\pi$
$827$	−0.131104	−	0.403496i	−0.00455892	−	0.0140309i	−0.953310	+	0.301993i	$0.902348\pi$
$828$	−0.170441	+	0.178089i	−0.00592324	+	0.00618900i
$829$	−15.0808	+	10.9568i	−0.523778	+	0.380547i	−0.818025	−	0.575182i	$-0.804931\pi$
$829$	−15.0808	+	10.9568i	−0.523778	+	0.380547i	0.294247	+	0.955729i	$0.404931\pi$
$830$	−59.6704	−	31.4541i	−2.07119	−	1.09179i
$831$	18.7568	+	33.6599i	0.650666	+	1.16765i
$832$	−1.02898	+	1.78225i	−0.0356736	+	0.0617885i
$833$	−9.94057	+	4.42583i	−0.344420	+	0.153346i
$834$	14.2808	+	46.3386i	0.494505	+	1.60458i
$835$	−10.7351	+	10.4412i	−0.371502	+	0.361332i
$836$	−7.41748	−	22.8286i	−0.256539	−	0.789545i
$837$	18.1101	−	28.3021i	0.625976	−	0.978263i
$838$	6.49962	−	20.0038i	0.224526	−	0.691019i
$839$	−19.4361	+	21.5860i	−0.671008	+	0.745230i	−0.978483	−	0.206326i	$-0.933849\pi$
$839$	−19.4361	+	21.5860i	−0.671008	+	0.745230i	0.307475	+	0.951556i	$0.400516\pi$
$840$	−10.9924	−	0.897300i	−0.379275	−	0.0309598i
$841$	−16.5831	−	18.4174i	−0.571832	−	0.635084i
$842$	34.8424	−	15.5129i	1.20075	−	0.534608i
$843$	15.9603	+	7.39888i	0.549702	+	0.254831i
$844$	0.344183	−	3.27468i	0.0118473	−	0.112719i
$845$	−6.88026	−	27.1808i	−0.236688	−	0.935047i
$846$	−57.3476	−	14.0255i	−1.97165	−	0.482207i
$847$	10.8694	−	7.89708i	0.373477	−	0.271347i
$848$	−4.40083	+	4.88762i	−0.151125	+	0.167842i
$849$	−0.118102	−	1.31592i	−0.00405326	−	0.0451624i
$850$	10.8832	−	14.1371i	0.373291	−	0.484900i
$851$	−0.153613	+	0.266066i	−0.00526580	+	0.00912063i
$852$	16.5484	−	7.06823i	0.566940	−	0.242153i
$853$	16.0673	+	7.15364i	0.550135	+	0.244936i	0.662929	−	0.748682i	$-0.269313\pi$
$853$	16.0673	+	7.15364i	0.550135	+	0.244936i	−0.112794	+	0.993618i	$0.535980\pi$
$854$	7.05296	−	5.12428i	0.241347	−	0.175349i
$855$	−27.4409	−	37.1360i	−0.938460	−	1.27002i
$856$	−31.6559	−	22.9993i	−1.08198	−	0.786101i
$857$	−4.22020	−	7.30960i	−0.144159	−	0.249691i	0.784900	−	0.619623i	$-0.212714\pi$
$857$	−4.22020	−	7.30960i	−0.144159	−	0.249691i	−0.929059	+	0.369932i	$0.879381\pi$
$858$	4.32988	+	7.77018i	0.147820	+	0.265269i
$859$	−22.5902	−	25.0889i	−0.770767	−	0.856024i	0.222128	−	0.975018i	$-0.428700\pi$
$859$	−22.5902	−	25.0889i	−0.770767	−	0.856024i	−0.992895	+	0.118994i	$0.962033\pi$
$860$	−1.16941	+	1.74716i	−0.0398765	+	0.0595777i
$861$	10.4509	+	7.83862i	0.356165	+	0.267140i
$862$	−21.3431	+	4.53662i	−0.726949	+	0.154518i
$863$	12.9265	−	39.7837i	0.440023	−	1.35425i	−0.447828	−	0.894120i	$-0.647802\pi$
$863$	12.9265	−	39.7837i	0.440023	−	1.35425i	0.887851	−	0.460132i	$-0.152198\pi$
$864$	−1.26552	−	21.3929i	−0.0430537	−	0.727802i
$865$	9.54714	−	23.8755i	0.324613	−	0.811790i
$866$	38.3934	−	8.16077i	1.30466	−	0.277314i
$867$	−21.4722	−	0.326637i	−0.729233	−	0.0110932i
$868$	−3.44234	+	5.96231i	−0.116841	+	0.202374i
$869$	−37.2964	+	16.6054i	−1.26519	+	0.563301i
$870$	5.66062	+	11.9571i	0.191913	+	0.405384i
$871$	−8.81834	−	3.92618i	−0.298798	−	0.133033i
$872$	−21.7493	+	15.8018i	−0.736523	+	0.535115i
$873$	−15.4408	−	28.7284i	−0.522593	−	0.972310i
$874$	−1.22679			−0.0414967
$875$	15.5211	−	0.166512i	0.524708	−	0.00562912i
$876$	0.703473	+	7.83826i	0.0237681	+	0.264830i
$877$	28.0496	+	5.96213i	0.947168	+	0.201327i	0.655502	−	0.755193i	$-0.272457\pi$
$877$	28.0496	+	5.96213i	0.947168	+	0.201327i	0.291666	+	0.956520i	$0.405790\pi$
$878$	−1.40937	−	13.4093i	−0.0475640	−	0.452541i
$879$	−7.50784	−	8.59777i	−0.253233	−	0.289996i
$880$	8.55511	−	49.5540i	0.288393	−	1.67047i
$881$	−11.7352	−	8.52611i	−0.395368	−	0.287252i	0.372283	−	0.928119i	$-0.378575\pi$
$881$	−11.7352	−	8.52611i	−0.395368	−	0.287252i	−0.767652	+	0.640867i	$0.778575\pi$
$882$	8.55078	−	23.8250i	0.287920	−	0.802229i
$883$	−42.8896	−	31.1611i	−1.44335	−	1.04865i	−0.987329	−	0.158684i	$-0.949275\pi$
$883$	−42.8896	−	31.1611i	−1.44335	−	1.04865i	−0.456019	−	0.889970i	$-0.650725\pi$
$884$	−1.09254	+	0.232227i	−0.0367462	+	0.00781065i
$885$	−4.87900	+	4.60310i	−0.164006	+	0.154731i
$886$	0.827382	+	0.175865i	0.0277964	+	0.00590832i
$887$	−6.01958	−	6.68542i	−0.202118	−	0.224474i	0.633561	−	0.773692i	$-0.281592\pi$
$887$	−6.01958	−	6.68542i	−0.202118	−	0.224474i	−0.835679	+	0.549218i	$0.814926\pi$
$888$	−3.00019	−	9.73505i	−0.100680	−	0.326687i
$889$	−20.6118	+	22.8918i	−0.691299	+	0.767765i
$890$	−28.0268	−	1.85914i	−0.939461	−	0.0623185i
$891$	36.3056	+	18.8883i	1.21628	+	0.632782i
$892$	−10.0558	−	7.30599i	−0.336694	−	0.244623i
$893$	−40.7174	−	70.5246i	−1.36256	−	2.36001i
$894$	−45.9763	−	0.699397i	−1.53768	−	0.0233914i
$895$	−6.10827	+	9.12611i	−0.204177	+	0.305052i
$896$	−1.92869	−	18.3502i	−0.0644329	−	0.613038i
$897$	0.123636	−	0.0243202i	0.00412808	−	0.000812027i
$898$	−8.04280	+	8.93243i	−0.268392	+	0.298079i
$899$	−13.2788			−0.442872
$900$	1.73339	+	11.3719i	0.0577797	+	0.379064i
$901$	2.85269			0.0950369
$902$	−27.4963	+	30.5377i	−0.915526	+	1.01679i
$903$	−1.93916	−	2.22067i	−0.0645311	−	0.0738992i
$904$	1.49291	+	14.2041i	0.0496534	+	0.472420i
$905$	−4.49912	−	1.27271i	−0.149556	−	0.0423063i
$906$	12.4407	−	20.8103i	0.413314	−	0.691377i
$907$	13.0147	+	22.5421i	0.432145	+	0.748498i	0.997058	−	0.0766530i	$-0.0244234\pi$
$907$	13.0147	+	22.5421i	0.432145	+	0.748498i	−0.564912	+	0.825151i	$0.691090\pi$
$908$	−5.71538	−	4.15247i	−0.189672	−	0.137804i
$909$	−4.93645	+	36.3054i	−0.163732	+	1.20417i
$910$	−2.69385	−	2.24404i	−0.0893003	−	0.0743893i
$911$	2.68314	−	2.97993i	0.0888964	−	0.0987294i	−0.697055	−	0.717017i	$-0.745507\pi$
$911$	2.68314	−	2.97993i	0.0888964	−	0.0987294i	0.785952	+	0.618288i	$0.212173\pi$
$912$	40.1160	−	43.2130i	1.32837	−	1.43093i
$913$	55.1797	+	61.2833i	1.82618	+	2.02818i
$914$	25.8391	+	5.49227i	0.854682	+	0.181668i
$915$	11.0901	+	9.52777i	0.366628	+	0.314978i
$916$	6.15464	−	1.30821i	0.203355	−	0.0432244i
$917$	−13.0533	−	9.48377i	−0.431058	−	0.313182i
$918$	−13.0220	+	13.1983i	−0.429788	+	0.435610i
$919$	0.331871	+	0.241118i	0.0109474	+	0.00795375i	0.593245	−	0.805022i	$-0.297846\pi$
$919$	0.331871	+	0.241118i	0.0109474	+	0.00795375i	−0.582298	+	0.812975i	$0.697846\pi$
$920$	−0.434730	−	0.229160i	−0.0143326	−	0.00755517i
$921$	11.3204	−	33.1180i	0.373021	−	1.09128i
$922$	5.73896	+	54.6026i	0.189003	+	1.79824i
$923$	−8.99722	−	1.91242i	−0.296147	−	0.0629480i
$924$	−7.60779	−	3.52682i	−0.250278	−	0.116024i
$925$	5.46557	+	13.2541i	0.179707	+	0.435791i
$926$	−30.6303			−1.00657
$927$	1.34016	−	2.16626i	0.0440165	−	0.0711492i
$928$	−6.85175	+	4.97808i	−0.224920	+	0.163414i
$929$	−6.15454	−	2.74018i	−0.201924	−	0.0899023i	0.303283	−	0.952900i	$-0.401917\pi$
$929$	−6.15454	−	2.74018i	−0.201924	−	0.0899023i	−0.505207	+	0.862998i	$0.668584\pi$
$930$	−39.9083	−	11.9478i	−1.30865	−	0.391782i
$931$	31.8972	−	14.2016i	1.04539	−	0.465437i
$932$	−3.17656	+	5.50196i	−0.104052	+	0.180223i
$933$	−15.8863	+	26.5741i	−0.520095	+	0.869997i
$934$	30.0055	−	6.37786i	0.981808	−	0.208690i
$935$	−18.4558	+	11.6244i	−0.603570	+	0.380160i
$936$	−2.19810	+	3.55305i	−0.0718470	+	0.116135i
$937$	−13.0786	+	40.2519i	−0.427260	+	1.31497i	0.473554	+	0.880765i	$0.342971\pi$
$937$	−13.0786	+	40.2519i	−0.427260	+	1.31497i	−0.900814	+	0.434206i	$0.857029\pi$
$938$	32.1143	−	6.82611i	1.04857	−	0.222880i
$939$	−3.80261	+	31.5546i	−0.124094	+	1.02974i
$940$	0.780521	+	20.2725i	0.0254578	+	0.661216i
$941$	35.0819	+	38.9624i	1.14364	+	1.27014i	0.957761	+	0.287564i	$0.0928455\pi$
$941$	35.0819	+	38.9624i	1.14364	+	1.27014i	0.185876	+	0.982573i	$0.440488\pi$
$942$	0.245290	+	0.00373138i	0.00799198	+	0.000121575i
$943$	0.291050	+	0.504114i	0.00947790	+	0.0164162i
$944$	−6.92961	−	5.03466i	−0.225540	−	0.163864i
$945$	−16.0301	−	1.80080i	−0.521458	−	0.0585801i
$946$	7.50241	−	5.45082i	0.243924	−	0.177221i
$947$	2.14265	+	0.953970i	0.0696268	+	0.0309999i	0.441255	−	0.897382i	$-0.354534\pi$
$947$	2.14265	+	0.953970i	0.0696268	+	0.0309999i	−0.371628	+	0.928382i	$0.621200\pi$
$948$	9.54028	+	7.15563i	0.309854	+	0.232404i
$949$	2.01136	−	3.48378i	0.0652915	−	0.113088i
$950$	−34.9220	+	45.3631i	−1.13302	+	1.47177i
$951$	4.98595	+	2.31139i	0.161681	+	0.0749519i
$952$	−4.08749	+	4.53961i	−0.132476	+	0.147130i
$953$	−7.72986	+	5.61607i	−0.250395	+	0.181922i	−0.705902	−	0.708310i	$-0.749458\pi$
$953$	−7.72986	+	5.61607i	−0.250395	+	0.181922i	0.455507	+	0.890232i	$0.349458\pi$
$954$	−4.58841	+	4.79428i	−0.148555	+	0.155220i
$955$	−19.4306	+	12.2384i	−0.628759	+	0.396026i
$956$	−0.0865082	+	0.823070i	−0.00279787	+	0.0266200i
$957$	−1.44574	−	16.1088i	−0.0467341	−	0.520723i
$958$	35.0748	−	15.6163i	1.13322	−	0.504540i
$959$	15.3866	+	17.0885i	0.496858	+	0.551817i
$960$	11.0771	−	3.88639i	0.357512	−	0.125433i
$961$	7.23609	−	8.03649i	0.233422	−	0.259242i
$962$	1.00071	−	3.07987i	0.0322642	−	0.0992989i
$963$	−45.2549	−	35.0313i	−1.45832	−	1.12887i
$964$	−5.94735	−	18.3041i	−0.191551	−	0.589534i
$965$	0.669005	−	3.87509i	0.0215360	−	0.124744i
$966$	−0.291583	+	0.314094i	−0.00938153	+	0.0101058i
$967$	18.8698	−	8.40138i	0.606812	−	0.270170i	−0.0802433	−	0.996775i	$-0.525570\pi$
$967$	18.8698	−	8.40138i	0.606812	−	0.270170i	0.687055	+	0.726605i	$0.258903\pi$
$968$	−9.92488	+	17.1904i	−0.318998	+	0.552520i
$969$	−25.5718	−	0.389001i	−0.821485	−	0.0124965i
$970$	−28.9872	+	28.1936i	−0.930723	+	0.905243i
$971$	24.5224	−	17.8166i	0.786962	−	0.571761i	−0.120098	−	0.992762i	$-0.538321\pi$
$971$	24.5224	−	17.8166i	0.786962	−	0.571761i	0.907060	+	0.421001i	$0.138321\pi$
$972$	−0.342631	−	11.9496i	−0.0109899	−	0.383285i
$973$	7.22044	+	22.2222i	0.231477	+	0.712412i
$974$	−9.49335	−	16.4430i	−0.304186	−	0.526866i
$975$	2.62015	−	5.26400i	0.0839118	−	0.168583i
$976$	−9.33514	+	16.1689i	−0.298810	+	0.517555i
$977$	23.0276	+	4.89467i	0.736718	+	0.156594i	0.560964	−	0.827840i	$-0.310430\pi$
$977$	23.0276	+	4.89467i	0.736718	+	0.156594i	0.175754	+	0.984434i	$0.443764\pi$
$978$	34.8741	−	6.86003i	1.11515	−	0.219360i
$979$	31.3707	+	13.9671i	1.00261	+	0.446392i
$980$	−8.67937	−	0.575740i	−0.277252	−	0.0183913i
$981$	−32.4985	+	22.1332i	−1.03760	+	0.706659i
$982$	66.1926			2.11229
$983$	−2.02059	+	19.2246i	−0.0644468	+	0.613171i	0.913863	+	0.406023i	$0.133085\pi$
$983$	−2.02059	+	19.2246i	−0.0644468	+	0.613171i	−0.978310	+	0.207148i	$0.933582\pi$
$984$	−18.8160	−	4.29960i	−0.599832	−	0.137066i
$985$	1.97079	−	2.94447i	0.0627946	−	0.0938187i
$986$	7.16723	+	1.52344i	0.228251	+	0.0485163i
$987$	−27.7341	−	6.33744i	−0.882785	−	0.201723i
$988$	3.50574	−	0.745169i	0.111533	−	0.0237070i
$989$	−0.0405939	−	0.124935i	−0.00129081	−	0.00397271i
$990$	10.1490	−	49.7145i	0.322557	−	1.58003i
$991$	−0.458610	+	1.41146i	−0.0145682	+	0.0448364i	−0.958076	−	0.286513i	$-0.907504\pi$
$991$	−0.458610	+	1.41146i	−0.0145682	+	0.0448364i	0.943508	+	0.331349i	$0.107504\pi$
$992$	2.78768	−	26.5230i	0.0885090	−	0.842107i
$993$	−23.1911	−	10.7509i	−0.735947	−	0.341171i
$994$	28.5806	−	12.7249i	0.906523	−	0.403610i
$995$	−10.1520	+	3.73618i	−0.321839	+	0.118445i
$996$	7.79140	−	22.7938i	0.246880	−	0.722249i
$997$	−14.4548	−	6.43568i	−0.457787	−	0.203820i	0.164869	−	0.986315i	$-0.447280\pi$
$997$	−14.4548	−	6.43568i	−0.457787	−	0.203820i	−0.622656	+	0.782495i	$0.713947\pi$
$998$	18.6267	+	57.3271i	0.589619	+	1.81466i
$999$	−3.95292	−	14.3653i	−0.125065	−	0.454496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.7	✓	224
3.2	odd	2		675.2.r.a.631.22		224
9.2	odd	6		675.2.r.a.181.7		224
9.7	even	3	inner	225.2.q.a.106.22	yes	224
25.21	even	5	inner	225.2.q.a.121.22	yes	224
75.71	odd	10		675.2.r.a.496.7		224
225.146	odd	30		675.2.r.a.46.22		224
225.196	even	15	inner	225.2.q.a.196.7	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.7	✓	224	1.1	even	1	trivial
225.2.q.a.106.22	yes	224	9.7	even	3	inner
225.2.q.a.121.22	yes	224	25.21	even	5	inner
225.2.q.a.196.7	yes	224	225.196	even	15	inner
675.2.r.a.46.22		224	225.146	odd	30
675.2.r.a.181.7		224	9.2	odd	6
675.2.r.a.496.7		224	75.71	odd	10
675.2.r.a.631.22		224	3.2	odd	2

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11303 + 1.23614i) q^{2} +(0.560227 - 1.63895i) q^{3} +(-0.0801613 - 0.762684i) q^{4} +(2.09847 - 0.772289i) q^{5} +(1.40242 + 2.51672i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 - 1.20564i) q^{8} +(-2.37229 - 1.83636i) q^{9} +O(q^{10})\)	\(q+(-1.11303 + 1.23614i) q^{2} +(0.560227 - 1.63895i) q^{3} +(-0.0801613 - 0.762684i) q^{4} +(2.09847 - 0.772289i) q^{5} +(1.40242 + 2.51672i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 - 1.20564i) q^{8} +(-2.37229 - 1.83636i) q^{9} +(-1.38100 + 3.45359i) q^{10} +(3.04269 - 3.37925i) q^{11} +(-1.29491 - 0.295896i) q^{12} +(0.454318 + 0.504572i) q^{13} +(-2.25887 - 0.480138i) q^{14} +(-0.0901221 - 3.87193i) q^{15} +(4.83758 - 1.02826i) q^{16} +(-1.73545 - 1.26088i) q^{17} +(4.91044 - 0.888568i) q^{18} +(5.56870 + 4.04590i) q^{19} +(-0.757229 - 1.53856i) q^{20} +(2.35944 - 0.464121i) q^{21} +(0.790638 + 7.52241i) q^{22} +(0.104805 + 0.0222770i) q^{23} +(-2.90563 + 2.04427i) q^{24} +(3.80714 - 3.24125i) q^{25} -1.12939 q^{26} +(-4.33872 + 2.85928i) q^{27} +(0.861350 - 0.625807i) q^{28} +(1.87597 + 0.835237i) q^{29} +(4.88658 + 4.19817i) q^{30} +(-5.90734 + 2.63012i) q^{31} +(-2.06213 + 3.57172i) q^{32} +(-3.83382 - 6.87996i) q^{33} +(3.49024 - 0.741873i) q^{34} +(2.38522 + 1.98695i) q^{35} +(-1.21040 + 1.95651i) q^{36} +(-0.886060 + 2.72701i) q^{37} +(-11.1994 + 2.38051i) q^{38} +(1.08149 - 0.461929i) q^{39} +(-4.41335 - 1.24845i) q^{40} +(3.63522 + 4.03732i) q^{41} +(-2.05240 + 3.43318i) q^{42} +(-0.613014 - 1.06177i) q^{43} +(-2.82121 - 2.04973i) q^{44} +(-6.39638 - 2.02146i) q^{45} +(-0.144189 + 0.104759i) q^{46} +(-10.8080 - 4.81201i) q^{47} +(1.02488 - 8.50460i) q^{48} +(2.53627 - 4.39296i) q^{49} +(-0.230806 + 8.31377i) q^{50} +(-3.03876 + 2.13793i) q^{51} +(0.348410 - 0.386948i) q^{52} +(-1.07586 + 0.781661i) q^{53} +(1.29465 - 8.54575i) q^{54} +(3.77524 - 9.44110i) q^{55} +(0.297663 - 2.83208i) q^{56} +(9.75074 - 6.86018i) q^{57} +(-3.12049 + 1.38933i) q^{58} +(-1.15888 - 1.28707i) q^{59} +(-2.94584 + 0.379114i) q^{60} +(-2.52602 + 2.80543i) q^{61} +(3.32384 - 10.2297i) q^{62} +(0.561150 - 4.12700i) q^{63} +(0.936638 + 2.88268i) q^{64} +(1.34305 + 0.707962i) q^{65} +(12.7718 + 2.91845i) q^{66} +(-12.9879 + 5.78257i) q^{67} +(-0.822536 + 1.42467i) q^{68} +(0.0952254 - 0.159290i) q^{69} +(-5.11098 + 0.736948i) q^{70} +(-10.9600 + 7.96294i) q^{71} +(1.72264 + 5.90743i) q^{72} +(-1.83085 - 5.63478i) q^{73} +(-2.38477 - 4.13054i) q^{74} +(-3.17937 - 8.05553i) q^{75} +(2.63935 - 4.57148i) q^{76} +(6.17509 + 1.31256i) q^{77} +(-0.632716 + 1.85101i) q^{78} +(-8.20200 - 3.65176i) q^{79} +(9.35740 - 5.89378i) q^{80} +(2.25554 + 8.71278i) q^{81} -9.03682 q^{82} +(-1.89564 + 18.0358i) q^{83} +(-0.543113 - 1.76230i) q^{84} +(-4.61555 - 1.30565i) q^{85} +(1.99480 + 0.424009i) q^{86} +(2.41988 - 2.60670i) q^{87} +(-9.12328 + 1.93921i) q^{88} +(2.33361 + 7.18212i) q^{89} +(9.61817 - 5.65691i) q^{90} +(-0.291288 + 0.896494i) q^{91} +(0.00858900 - 0.0817189i) q^{92} +(1.00117 + 11.1553i) q^{93} +(17.9779 - 8.00428i) q^{94} +(14.8103 + 4.18954i) q^{95} +(4.69860 + 5.38070i) q^{96} +(9.93178 + 4.42191i) q^{97} +(2.60738 + 8.02469i) q^{98} +(-13.4237 + 2.42908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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