LMFDB - Embedded newform 507.2.q.b.490.10

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			490.10
Character	$\chi$	$=$	507.490
Dual form			507.2.q.b.328.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0728553 + 0.356869i) q^{2} +(0.987050 + 0.160411i) q^{3} +(1.71791 - 0.731934i) q^{4} +(-1.83451 + 0.452167i) q^{5} +(0.0146660 + 0.363934i) q^{6} +(-1.86517 + 3.93076i) q^{7} +(0.800175 + 1.15925i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(0.0728553 + 0.356869i) q^{2} +(0.987050 + 0.160411i) q^{3} +(1.71791 - 0.731934i) q^{4} +(-1.83451 + 0.452167i) q^{5} +(0.0146660 + 0.363934i) q^{6} +(-1.86517 + 3.93076i) q^{7} +(0.800175 + 1.15925i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-0.295018 - 0.621737i) q^{10} +(5.66460 - 1.89112i) q^{11} +(1.81308 - 0.446883i) q^{12} +(-3.17999 + 1.69931i) q^{13} +(-1.53865 - 0.379243i) q^{14} +(-1.88329 + 0.152035i) q^{15} +(2.23169 - 2.32344i) q^{16} +(-1.59741 + 3.36646i) q^{17} +(-0.0439030 + 0.361574i) q^{18} +(3.47743 + 6.02308i) q^{19} +(-2.82057 + 2.11952i) q^{20} +(-2.47155 + 3.58066i) q^{21} +(1.08758 + 1.88374i) q^{22} +(1.85898 - 3.21984i) q^{23} +(0.603856 + 1.27260i) q^{24} +(-1.26630 + 0.664606i) q^{25} +(-0.838111 - 1.01103i) q^{26} +(0.885456 + 0.464723i) q^{27} +(-0.327139 + 8.11787i) q^{28} +(-1.96148 - 9.60796i) q^{29} +(-0.191464 - 0.661010i) q^{30} +(2.16103 + 1.13419i) q^{31} +(3.37282 + 2.13284i) q^{32} +(5.89460 - 0.957966i) q^{33} +(-1.31777 - 0.324800i) q^{34} +(1.64431 - 8.05438i) q^{35} +(1.86128 - 0.150258i) q^{36} +(4.52824 - 2.86348i) q^{37} +(-1.89610 + 1.67980i) q^{38} +(-3.41140 + 1.16720i) q^{39} +(-1.99211 - 1.76485i) q^{40} +(-3.72154 - 0.604809i) q^{41} +(-1.45789 - 0.621149i) q^{42} +(4.47565 + 2.83023i) q^{43} +(8.34711 - 7.39489i) q^{44} +(-1.88329 - 0.152035i) q^{45} +(1.28450 + 0.428829i) q^{46} +(-0.855389 - 7.04476i) q^{47} +(2.57550 - 1.93536i) q^{48} +(-7.54488 - 9.24079i) q^{49} +(-0.329434 - 0.403483i) q^{50} +(-2.11674 + 3.06663i) q^{51} +(-4.21916 + 5.24681i) q^{52} +(3.51392 + 5.09080i) q^{53} +(-0.101335 + 0.349849i) q^{54} +(-9.53667 + 6.03063i) q^{55} +(-6.04920 + 0.983091i) q^{56} +(2.46623 + 6.50290i) q^{57} +(3.28588 - 1.39998i) q^{58} +(-3.77817 - 3.93349i) q^{59} +(-3.12404 + 1.63962i) q^{60} +(-10.0683 - 0.812795i) q^{61} +(-0.247316 + 0.853835i) q^{62} +(-3.01392 + 3.13783i) q^{63} +(1.76939 - 4.66549i) q^{64} +(5.06536 - 4.55530i) q^{65} +(0.771321 + 2.03381i) q^{66} +(6.44025 + 2.74393i) q^{67} +(-0.280176 + 6.95249i) q^{68} +(2.35140 - 2.87995i) q^{69} +2.99416 q^{70} +(-3.91960 + 4.80064i) q^{71} +(0.391897 + 1.35298i) q^{72} +(-4.90318 - 4.34383i) q^{73} +(1.35179 + 1.40737i) q^{74} +(-1.35651 + 0.452870i) q^{75} +(10.3824 + 7.80188i) q^{76} +(-3.13189 + 25.7934i) q^{77} +(-0.665076 - 1.13238i) q^{78} +(-1.17076 - 9.64204i) q^{79} +(-3.04349 + 5.27148i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.0552963 - 1.37216i) q^{82} +(1.59481 - 4.20516i) q^{83} +(-1.62510 + 7.96027i) q^{84} +(1.40826 - 6.89811i) q^{85} +(-0.683946 + 1.80342i) q^{86} +(-0.394853 - 9.79818i) q^{87} +(6.72496 + 5.05348i) q^{88} +(-0.0240526 + 0.0416604i) q^{89} +(-0.0829510 - 0.683163i) q^{90} +(-0.748376 - 15.6693i) q^{91} +(0.836847 - 6.89206i) q^{92} +(1.95110 + 1.46616i) q^{93} +(2.45174 - 0.818510i) q^{94} +(-9.10282 - 9.47704i) q^{95} +(2.98701 + 2.64626i) q^{96} +(0.631663 + 2.18075i) q^{97} +(2.74807 - 3.36577i) q^{98} +5.97194 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 $

$2$	0.0728553	+	0.356869i	0.0515165	+	0.252344i	0.997391	−	0.0721881i	$-0.0229982\pi$
$2$	0.0728553	+	0.356869i	0.0515165	+	0.252344i	−0.945875	+	0.324532i	$0.894793\pi$
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$4$	1.71791	−	0.731934i	0.858956	−	0.365967i
$5$	−1.83451	+	0.452167i	−0.820419	+	0.202215i	−0.627118	−	0.778924i	$-0.715766\pi$
$5$	−1.83451	+	0.452167i	−0.820419	+	0.202215i	−0.193301	+	0.981140i	$0.561919\pi$
$6$	0.0146660	+	0.363934i	0.00598739	+	0.148576i
$7$	−1.86517	+	3.93076i	−0.704967	+	1.48569i	0.161722	+	0.986836i	$0.448295\pi$
$7$	−1.86517	+	3.93076i	−0.704967	+	1.48569i	−0.866689	+	0.498850i	$0.833756\pi$
$8$	0.800175	+	1.15925i	0.282905	+	0.409858i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	−0.295018	−	0.621737i	−0.0932929	−	0.196611i
$11$	5.66460	−	1.89112i	1.70794	−	0.570195i	0.716137	−	0.697960i	$-0.245909\pi$
$11$	5.66460	−	1.89112i	1.70794	−	0.570195i	0.991804	+	0.127766i	$0.0407805\pi$
$12$	1.81308	−	0.446883i	0.523390	−	0.129004i
$13$	−3.17999	+	1.69931i	−0.881970	+	0.471305i
$13$	−3.17999	+	1.69931i	−0.881970	+	0.471305i
$14$	−1.53865	−	0.379243i	−0.411222	−	0.101357i
$15$	−1.88329	+	0.152035i	−0.486263	+	0.0392552i
$16$	2.23169	−	2.32344i	0.557924	−	0.580860i
$17$	−1.59741	+	3.36646i	−0.387428	+	0.816488i	0.612239	+	0.790673i	$0.290269\pi$
$17$	−1.59741	+	3.36646i	−0.387428	+	0.816488i	−0.999667	+	0.0258146i	$0.991782\pi$
$18$	−0.0439030	+	0.361574i	−0.0103480	+	0.0852238i
$19$	3.47743	+	6.02308i	0.797777	+	1.38179i	0.921061	+	0.389419i	$0.127324\pi$
$19$	3.47743	+	6.02308i	0.797777	+	1.38179i	−0.123284	+	0.992371i	$0.539343\pi$
$20$	−2.82057	+	2.11952i	−0.630699	+	0.473940i
$21$	−2.47155	+	3.58066i	−0.539337	+	0.781364i
$22$	1.08758	+	1.88374i	0.231872	+	0.401615i
$23$	1.85898	−	3.21984i	0.387624	−	0.671384i	−0.604506	−	0.796601i	$-0.706629\pi$
$23$	1.85898	−	3.21984i	0.387624	−	0.671384i	0.992129	+	0.125217i	$0.0399627\pi$
$24$	0.603856	+	1.27260i	0.123262	+	0.259768i
$25$	−1.26630	+	0.664606i	−0.253260	+	0.132921i
$26$	−0.838111	−	1.01103i	−0.164367	−	0.198280i
$27$	0.885456	+	0.464723i	0.170406	+	0.0894360i
$28$	−0.327139	+	8.11787i	−0.0618234	+	1.53413i
$29$	−1.96148	−	9.60796i	−0.364237	−	1.78415i	−0.587322	−	0.809353i	$-0.699818\pi$
$29$	−1.96148	−	9.60796i	−0.364237	−	1.78415i	0.223085	−	0.974799i	$-0.428387\pi$
$30$	−0.191464	−	0.661010i	−0.0349564	−	0.120683i
$31$	2.16103	+	1.13419i	0.388132	+	0.203707i	0.647490	−	0.762074i	$-0.275819\pi$
$31$	2.16103	+	1.13419i	0.388132	+	0.203707i	−0.259358	+	0.965781i	$0.583511\pi$
$32$	3.37282	+	2.13284i	0.596236	+	0.377037i
$33$	5.89460	−	0.957966i	1.02612	−	0.166760i
$34$	−1.31777	−	0.324800i	−0.225995	−	0.0557028i
$35$	1.64431	−	8.05438i	0.277940	−	1.36144i
$36$	1.86128	−	0.150258i	0.310214	−	0.0250430i
$37$	4.52824	−	2.86348i	0.744438	−	0.470754i	−0.107626	−	0.994191i	$-0.534325\pi$
$37$	4.52824	−	2.86348i	0.744438	−	0.470754i	0.852064	+	0.523437i	$0.175351\pi$
$38$	−1.89610	+	1.67980i	−0.307588	+	0.272499i
$39$	−3.41140	+	1.16720i	−0.546261	+	0.186902i
$40$	−1.99211	−	1.76485i	−0.314980	−	0.279048i
$41$	−3.72154	−	0.604809i	−0.581206	−	0.0944552i	−0.137302	−	0.990529i	$-0.543843\pi$
$41$	−3.72154	−	0.604809i	−0.581206	−	0.0944552i	−0.443905	+	0.896074i	$0.646407\pi$
$42$	−1.45789	−	0.621149i	−0.224957	−	0.0958454i
$43$	4.47565	+	2.83023i	0.682530	+	0.431606i	0.830226	−	0.557427i	$-0.188211\pi$
$43$	4.47565	+	2.83023i	0.682530	+	0.431606i	−0.147696	+	0.989033i	$0.547186\pi$
$44$	8.34711	−	7.39489i	1.25837	−	1.11482i
$45$	−1.88329	−	0.152035i	−0.280744	−	0.0226640i
$46$	1.28450	+	0.428829i	0.189389	+	0.0632273i
$47$	−0.855389	−	7.04476i	−0.124771	−	1.02758i	−0.911791	−	0.410656i	$-0.865300\pi$
$47$	−0.855389	−	7.04476i	−0.124771	−	1.02758i	0.787019	−	0.616929i	$-0.211623\pi$
$48$	2.57550	−	1.93536i	0.371742	−	0.279346i
$49$	−7.54488	−	9.24079i	−1.07784	−	1.32011i
$50$	−0.329434	−	0.403483i	−0.0465890	−	0.0570611i
$51$	−2.11674	+	3.06663i	−0.296403	+	0.429414i
$52$	−4.21916	+	5.24681i	−0.585092	+	0.727602i
$53$	3.51392	+	5.09080i	0.482675	+	0.699275i	0.986358	−	0.164613i	$-0.0526376\pi$
$53$	3.51392	+	5.09080i	0.482675	+	0.699275i	−0.503683	+	0.863888i	$0.668022\pi$
$54$	−0.101335	+	0.349849i	−0.0137900	+	0.0476084i
$55$	−9.53667	+	6.03063i	−1.28592	+	0.813170i
$56$	−6.04920	+	0.983091i	−0.808359	+	0.131371i
$57$	2.46623	+	6.50290i	0.326660	+	0.861331i
$58$	3.28588	−	1.39998i	0.431457	−	0.183826i
$59$	−3.77817	−	3.93349i	−0.491876	−	0.512097i	0.428282	−	0.903645i	$-0.359119\pi$
$59$	−3.77817	−	3.93349i	−0.491876	−	0.512097i	−0.920158	+	0.391548i	$0.871940\pi$
$60$	−3.12404	+	1.63962i	−0.403312	+	0.211675i
$61$	−10.0683	−	0.812795i	−1.28911	−	0.104068i	−0.583177	−	0.812345i	$-0.698190\pi$
$61$	−10.0683	−	0.812795i	−1.28911	−	0.104068i	−0.705934	+	0.708278i	$0.749473\pi$
$62$	−0.247316	+	0.853835i	−0.0314092	+	0.108437i
$63$	−3.01392	+	3.13783i	−0.379719	+	0.395329i
$64$	1.76939	−	4.66549i	0.221173	−	0.583186i
$65$	5.06536	−	4.55530i	0.628280	−	0.565015i
$66$	0.771321	+	2.03381i	0.0949431	+	0.250344i
$67$	6.44025	+	2.74393i	0.786802	+	0.335225i	0.747723	−	0.664011i	$-0.231147\pi$
$67$	6.44025	+	2.74393i	0.786802	+	0.335225i	0.0390790	+	0.999236i	$0.487558\pi$
$68$	−0.280176	+	6.95249i	−0.0339763	+	0.843113i
$69$	2.35140	−	2.87995i	0.283076	−	0.346705i
$70$	2.99416			0.357870
$71$	−3.91960	+	4.80064i	−0.465171	+	0.569731i	−0.952908	−	0.303260i	$-0.901925\pi$
$71$	−3.91960	+	4.80064i	−0.465171	+	0.569731i	0.487737	+	0.872991i	$0.337822\pi$
$72$	0.391897	+	1.35298i	0.0461855	+	0.159451i
$73$	−4.90318	−	4.34383i	−0.573873	−	0.508407i	0.325527	−	0.945533i	$-0.394458\pi$
$73$	−4.90318	−	4.34383i	−0.573873	−	0.508407i	−0.899401	+	0.437125i	$0.855997\pi$
$74$	1.35179	+	1.40737i	0.157143	+	0.163603i
$75$	−1.35651	+	0.452870i	−0.156637	+	0.0522930i
$76$	10.3824	+	7.80188i	1.19094	+	0.894937i
$77$	−3.13189	+	25.7934i	−0.356912	+	2.93943i
$78$	−0.665076	−	1.13238i	−0.0753051	−	0.128217i
$79$	−1.17076	−	9.64204i	−0.131720	−	1.08481i	−0.897284	−	0.441454i	$-0.854463\pi$
$79$	−1.17076	−	9.64204i	−0.131720	−	1.08481i	0.765564	−	0.643360i	$-0.222460\pi$
$80$	−3.04349	+	5.27148i	−0.340272	+	0.589369i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	−0.0552963	−	1.37216i	−0.00610646	−	0.151530i
$83$	1.59481	−	4.20516i	0.175053	−	0.461577i	−0.818560	−	0.574422i	$-0.805227\pi$
$83$	1.59481	−	4.20516i	0.175053	−	0.461577i	0.993613	+	0.112845i	$0.0359963\pi$
$84$	−1.62510	+	7.96027i	−0.177313	+	0.868536i
$85$	1.40826	−	6.89811i	0.152747	−	0.748206i
$86$	−0.683946	+	1.80342i	−0.0737518	+	0.194467i
$87$	−0.394853	−	9.79818i	−0.0423327	−	1.05047i
$88$	6.72496	+	5.05348i	0.716883	+	0.538703i
$89$	−0.0240526	+	0.0416604i	−0.00254957	+	0.00441599i	−0.867297	−	0.497790i	$-0.834145\pi$
$89$	−0.0240526	+	0.0416604i	−0.00254957	+	0.00441599i	0.864748	+	0.502206i	$0.167478\pi$
$90$	−0.0829510	−	0.683163i	−0.00874381	−	0.0720117i
$91$	−0.748376	−	15.6693i	−0.0784512	−	1.64259i
$92$	0.836847	−	6.89206i	0.0872474	−	0.718547i
$93$	1.95110	+	1.46616i	0.202320	+	0.152034i
$94$	2.45174	−	0.818510i	0.252877	−	0.0844228i
$95$	−9.10282	−	9.47704i	−0.933930	−	0.972324i
$96$	2.98701	+	2.64626i	0.304861	+	0.270083i
$97$	0.631663	+	2.18075i	0.0641356	+	0.221422i	0.986184	−	0.165652i	$-0.0529729\pi$
$97$	0.631663	+	2.18075i	0.0641356	+	0.221422i	−0.922049	+	0.387074i	$0.873486\pi$
$98$	2.74807	−	3.36577i	0.277597	−	0.339994i
$99$	5.97194			0.600202
$100$	−1.68894	+	2.06858i	−0.168894	+	0.206858i
$101$	0.400959	−	9.94968i	0.0398969	−	0.990030i	−0.848002	−	0.529992i	$-0.822195\pi$
$101$	0.400959	−	9.94968i	0.0398969	−	0.990030i	0.887899	−	0.460038i	$-0.152164\pi$
$102$	−1.24860	−	0.531979i	−0.123630	−	0.0526737i
$103$	−7.07394	−	18.6524i	−0.697016	−	1.83788i	−0.521149	−	0.853466i	$-0.674496\pi$
$103$	−7.07394	−	18.6524i	−0.697016	−	1.83788i	−0.175867	−	0.984414i	$-0.556273\pi$
$104$	−4.51448	−	2.32667i	−0.442682	−	0.228148i
$105$	2.91504	−	7.68632i	0.284478	−	0.750108i
$106$	−1.56074	+	1.62490i	−0.151592	+	0.157824i
$107$	−2.46748	+	8.51873i	−0.238540	+	0.823537i	0.748510	+	0.663124i	$0.230770\pi$
$107$	−2.46748	+	8.51873i	−0.238540	+	0.823537i	−0.987050	+	0.160413i	$0.948717\pi$
$108$	1.86128	+	0.150258i	0.179102	+	0.0144586i
$109$	−8.64456	+	4.53702i	−0.827999	+	0.434567i	−0.824798	−	0.565427i	$-0.808711\pi$
$109$	−8.64456	+	4.53702i	−0.827999	+	0.434567i	−0.00320106	+	0.999995i	$0.501019\pi$
$110$	−2.84694	−	2.96398i	−0.271445	−	0.282604i
$111$	4.92893	−	2.10002i	0.467834	−	0.199325i
$112$	4.97039	+	13.1059i	0.469658	+	1.23839i
$113$	9.84683	−	1.60027i	0.926312	−	0.150540i	0.321501	−	0.946909i	$-0.395813\pi$
$113$	9.84683	−	1.60027i	0.926312	−	0.150540i	0.604811	+	0.796369i	$0.293249\pi$
$114$	−2.14101	+	1.35389i	−0.200524	+	0.126803i
$115$	−1.95441	+	6.74741i	−0.182250	+	0.629199i
$116$	−10.4020	−	15.0699i	−0.965804	−	1.39921i
$117$	−3.55445	+	0.604860i	−0.328609	+	0.0559193i
$118$	1.12848	−	1.63489i	0.103885	−	0.150504i
$119$	−10.2533	−	12.5580i	−0.939920	−	1.15119i
$120$	−1.68321	−	2.06155i	−0.153655	−	0.188193i
$121$	19.7175	−	14.8167i	1.79250	−	1.34697i
$122$	−0.443466	−	3.65227i	−0.0401495	−	0.330661i
$123$	−3.57633	−	1.19395i	−0.322466	−	0.107655i
$124$	4.54261	+	0.366717i	0.407938	+	0.0329322i
$125$	9.09377	−	8.05638i	0.813371	−	0.720584i
$126$	−1.33937	−	0.846968i	−0.119321	−	0.0754539i
$127$	6.05081	+	2.57801i	0.536923	+	0.228761i	0.643368	−	0.765557i	$-0.277537\pi$
$127$	6.05081	+	2.57801i	0.536923	+	0.228761i	−0.106445	+	0.994319i	$0.533947\pi$
$128$	9.67174	+	1.57181i	0.854869	+	0.138930i
$129$	3.96369	+	3.51152i	0.348983	+	0.309172i
$130$	1.99468	+	1.47579i	0.174945	+	0.129435i
$131$	6.62069	−	5.86542i	0.578453	−	0.512464i	−0.322392	−	0.946606i	$-0.604487\pi$
$131$	6.62069	−	5.86542i	0.578453	−	0.512464i	0.900844	+	0.434142i	$0.142948\pi$
$132$	9.42524	−	5.96016i	0.820362	−	0.518765i
$133$	−30.1612	+	2.43487i	−2.61531	+	0.211130i
$134$	−0.510018	+	2.49823i	−0.0440588	+	0.215815i
$135$	−1.83451	−	0.452167i	−0.157890	−	0.0389163i
$136$	−5.18079	+	0.841961i	−0.444249	+	0.0721976i
$137$	−6.05770	−	3.83065i	−0.517544	−	0.327275i	0.250027	−	0.968239i	$-0.419560\pi$
$137$	−6.05770	−	3.83065i	−0.517544	−	0.327275i	−0.767571	+	0.640964i	$0.778535\pi$
$138$	1.19908	+	0.629323i	0.102072	+	0.0535716i
$139$	1.94955	+	6.73062i	0.165359	+	0.570884i	0.999804	+	0.0197936i	$0.00630090\pi$
$139$	1.94955	+	6.73062i	0.165359	+	0.570884i	−0.834446	+	0.551090i	$0.814212\pi$
$140$	−3.07049	−	15.0402i	−0.259504	−	1.27113i
$141$	0.285747	−	7.09075i	0.0240643	−	0.597149i
$142$	−1.99876	−	1.04903i	−0.167732	−	0.0880327i
$143$	−14.7998	+	15.6397i	−1.23762	+	1.30786i
$144$	2.85260	−	1.49716i	0.237717	−	0.124763i
$145$	7.94275	+	16.7390i	0.659610	+	1.39010i
$146$	1.19296	−	2.06626i	0.0987298	−	0.171005i
$147$	−5.96484	−	10.3314i	−0.491972	−	0.852120i
$148$	5.68323	−	8.23358i	0.467159	−	0.676796i
$149$	−4.09549	+	3.07756i	−0.335515	+	0.252123i	−0.755124	−	0.655582i	$-0.772424\pi$
$149$	−4.09549	+	3.07756i	−0.335515	+	0.252123i	0.419609	+	0.907705i	$0.362167\pi$
$150$	−0.260444	−	0.451103i	−0.0212652	−	0.0368324i
$151$	−2.37516	+	19.5612i	−0.193288	+	1.59187i	0.496619	+	0.867969i	$0.334575\pi$
$151$	−2.37516	+	19.5612i	−0.193288	+	1.59187i	−0.689906	+	0.723899i	$0.742348\pi$
$152$	−4.19973	+	8.85074i	−0.340643	+	0.717890i
$153$	−2.58125	+	2.68737i	−0.208682	+	0.217261i
$154$	−9.43304	+	0.761514i	−0.760136	+	0.0613645i
$155$	−4.47727	−	1.10355i	−0.359623	−	0.0886392i
$156$	−5.00617	+	4.50207i	−0.400814	+	0.360454i
$157$	0.274652	−	0.0676957i	0.0219196	−	0.00540270i	−0.228341	−	0.973581i	$-0.573330\pi$
$157$	0.274652	−	0.0676957i	0.0219196	−	0.00540270i	0.250260	+	0.968179i	$0.419484\pi$
$158$	3.35565	−	1.12028i	0.266961	−	0.0891246i
$159$	2.65180	+	5.58855i	0.210301	+	0.443201i
$160$	−7.15188	−	2.38765i	−0.565406	−	0.188760i
$161$	9.18912	+	13.3127i	0.724204	+	1.04919i
$162$	−0.156143	+	0.329063i	−0.0122677	+	0.0258537i
$163$	−0.399828	−	9.92162i	−0.0313169	−	0.777121i	−0.936201	−	0.351464i	$-0.885684\pi$
$163$	−0.399828	−	9.92162i	−0.0313169	−	0.777121i	0.904884	−	0.425657i	$-0.139957\pi$
$164$	−6.83595	+	1.68491i	−0.533798	+	0.131569i
$165$	−10.3806	+	4.42274i	−0.808125	+	0.344310i
$166$	1.61688	+	0.262769i	0.125494	+	0.0203948i
$167$	−0.971641	−	4.75941i	−0.0751878	−	0.368294i	0.924736	−	0.380608i	$-0.124285\pi$
$167$	−0.971641	−	4.75941i	−0.0751878	−	0.368294i	−0.999924	+	0.0123140i	$0.996080\pi$
$168$	−6.12857			−0.472829
$169$	7.22467	−	10.8076i	0.555744	−	0.831354i
$170$	2.56432			0.196674
$171$	1.39115	+	6.81430i	0.106384	+	0.521103i
$172$	9.76031	+	1.58620i	0.744217	+	0.120947i
$173$	−2.51206	+	1.07029i	−0.190988	+	0.0813725i	−0.485343	−	0.874324i	$-0.661305\pi$
$173$	−2.51206	+	1.07029i	−0.190988	+	0.0813725i	0.294355	+	0.955696i	$0.404895\pi$
$174$	3.46790	−	0.854760i	0.262901	−	0.0647992i
$175$	−0.250541	−	6.21712i	−0.0189391	−	0.469970i
$176$	8.24775	−	17.3818i	0.621698	−	1.31020i
$177$	−3.09827	−	4.48862i	−0.232880	−	0.337385i
$178$	−0.0166196	−	0.00554845i	−0.00124569	−	0.000415874i
$179$	−7.74632	−	16.3250i	−0.578987	−	1.22019i	−0.955832	−	0.293913i	$-0.905042\pi$
$179$	−7.74632	−	16.3250i	−0.578987	−	1.22019i	0.376845	−	0.926276i	$-0.377009\pi$
$180$	−3.34660	+	1.11726i	−0.249441	+	0.0832756i
$181$	14.2082	−	3.50200i	1.05609	−	0.260302i	0.327213	−	0.944951i	$-0.393891\pi$
$181$	14.2082	−	3.50200i	1.05609	−	0.260302i	0.728873	+	0.684649i	$0.240044\pi$
$182$	5.53735	−	1.40866i	0.410456	−	0.104417i
$183$	−9.80751	−	2.41734i	−0.724992	−	0.178695i
$184$	5.22013	−	0.421412i	0.384833	−	0.0310669i
$185$	−7.01234	+	7.30062i	−0.515557	+	0.536752i
$186$	−0.381078	+	0.803105i	−0.0279420	+	0.0588865i
$187$	−2.68228	+	22.0906i	−0.196148	+	1.61542i
$188$	−6.62578	−	11.4762i	−0.483235	−	0.836987i
$189$	−3.47824	+	2.61373i	−0.253004	+	0.190121i
$190$	2.71887	−	3.93896i	0.197248	−	0.285763i
$191$	5.19987	+	9.00643i	0.376249	+	0.651683i	0.990513	−	0.137418i	$-0.0438804\pi$
$191$	5.19987	+	9.00643i	0.376249	+	0.651683i	−0.614264	+	0.789101i	$0.710547\pi$
$192$	2.49487	−	4.32124i	0.180052	−	0.311859i
$193$	−5.17377	−	10.9035i	−0.372416	−	0.784850i	−0.999980	−	0.00628536i	$-0.997999\pi$
$193$	−5.17377	−	10.9035i	−0.372416	−	0.784850i	0.627564	−	0.778565i	$-0.284052\pi$
$194$	−0.732222	+	0.384300i	−0.0525705	+	0.0275911i
$195$	5.73048	−	3.68377i	0.410368	−	0.263800i
$196$	−19.7251	−	10.3525i	−1.40893	−	0.739466i
$197$	−0.615744	+	15.2795i	−0.0438700	+	1.08862i	0.815982	+	0.578078i	$0.196197\pi$
$197$	−0.615744	+	15.2795i	−0.0438700	+	1.08862i	−0.859852	+	0.510544i	$0.829444\pi$
$198$	0.435087	+	2.13120i	0.0309203	+	0.151458i
$199$	1.11869	+	3.86218i	0.0793020	+	0.273782i	0.990364	−	0.138486i	$-0.0442237\pi$
$199$	1.11869	+	3.86218i	0.0793020	+	0.273782i	−0.911062	+	0.412269i	$0.864737\pi$
$200$	−1.78371	−	0.936163i	−0.126127	−	0.0661967i
$201$	5.91669	+	3.74149i	0.417331	+	0.263904i
$202$	3.57994	−	0.581797i	0.251884	−	0.0409351i
$203$	41.4250	+	10.2103i	2.90747	+	0.716626i
$204$	−1.39180	+	6.81751i	−0.0974458	+	0.477321i
$205$	7.10068	−	0.573226i	0.495933	−	0.0400358i
$206$	6.14110	−	3.88340i	0.427871	−	0.270569i
$207$	2.78293	−	2.46546i	0.193427	−	0.171361i
$208$	−3.14851	+	11.1809i	−0.218310	+	0.775254i
$209$	31.0886	+	27.5421i	2.15044	+	1.90513i
$210$	2.95538	+	0.480296i	0.203941	+	0.0331436i
$211$	13.6023	+	5.79541i	0.936422	+	0.398972i	0.805618	−	0.592436i	$-0.201834\pi$
$211$	13.6023	+	5.79541i	0.936422	+	0.398972i	0.130805	+	0.991408i	$0.458244\pi$
$212$	9.76274	+	6.17358i	0.670508	+	0.424003i
$213$	−4.63892	+	4.10972i	−0.317853	+	0.281594i
$214$	−3.21984	−	0.259932i	−0.220104	−	0.0177686i
$215$	−9.49037	−	3.16835i	−0.647238	−	0.216080i
$216$	0.169788	+	1.39833i	0.0115526	+	0.0951442i
$217$	−8.48891	+	6.37900i	−0.576265	+	0.433035i
$218$	−2.24892	−	2.75443i	−0.152316	−	0.186553i
$219$	−4.14288	−	5.07411i	−0.279950	−	0.342876i
$220$	−11.9691	+	17.3403i	−0.806959	+	1.16908i
$221$	−0.640941	−	13.4198i	−0.0431144	−	0.902715i
$222$	1.10853	+	1.60598i	0.0743998	+	0.107787i
$223$	2.26430	−	7.81726i	0.151629	−	0.523482i	−0.848354	−	0.529430i	$-0.822406\pi$
$223$	2.26430	−	7.81726i	0.151629	−	0.523482i	0.999982	+	0.00594735i	$0.00189311\pi$
$224$	−14.6746	+	9.27963i	−0.980485	+	0.620021i
$225$	−1.41159	+	0.229406i	−0.0941061	+	0.0152937i
$226$	1.28848	+	3.39744i	0.0857083	+	0.225994i
$227$	−2.50035	+	1.06530i	−0.165954	+	0.0707065i	−0.473346	−	0.880876i	$-0.656954\pi$
$227$	−2.50035	+	1.06530i	−0.165954	+	0.0707065i	0.307392	+	0.951583i	$0.400544\pi$
$228$	8.99645	+	9.36630i	0.595805	+	0.620298i
$229$	8.89255	−	4.66717i	0.587636	−	0.308415i	−0.144574	−	0.989494i	$-0.546181\pi$
$229$	8.89255	−	4.66717i	0.587636	−	0.308415i	0.732210	+	0.681079i	$0.238489\pi$
$230$	−2.55033	−	0.205884i	−0.168164	−	0.0135756i
$231$	−7.22888	+	24.9570i	−0.475626	+	1.64205i
$232$	9.56853	−	9.96190i	0.628205	−	0.654031i
$233$	−2.72094	+	7.17454i	−0.178255	+	0.470019i	−0.994128	−	0.108212i	$-0.965488\pi$
$233$	−2.72094	+	7.17454i	−0.178255	+	0.470019i	0.815873	+	0.578231i	$0.196257\pi$
$234$	−0.474816	−	1.22441i	−0.0310397	−	0.0800420i
$235$	4.75463	+	12.5369i	0.310158	+	0.817819i
$236$	−9.36962	−	3.99202i	−0.609910	−	0.259859i
$237$	0.391097	−	9.70498i	0.0254045	−	0.630406i
$238$	3.73456	−	4.57401i	0.242076	−	0.296489i
$239$	−15.0048			−0.970579			−0.485290	−	0.874354i	$-0.661286\pi$
$239$	−15.0048			−0.970579			−0.485290	+	0.874354i	$0.661286\pi$
$240$	−3.84968	+	4.71500i	−0.248496	+	0.304352i
$241$	4.70505	+	16.2437i	0.303079	+	1.04635i	0.957072	+	0.289849i	$0.0936052\pi$
$241$	4.70505	+	16.2437i	0.303079	+	1.04635i	−0.653993	+	0.756500i	$0.726908\pi$
$242$	6.72415	+	5.95708i	0.432245	+	0.382935i
$243$	0.692724	+	0.721202i	0.0444383	+	0.0462652i
$244$	−17.8913	+	5.97300i	−1.14537	+	0.382382i
$245$	18.0195	+	13.5408i	1.15123	+	0.865091i
$246$	0.165530	−	1.36326i	0.0105538	−	0.0869186i
$247$	−21.2933	−	13.2441i	−1.35486	−	0.842702i
$248$	0.414381	+	3.41273i	0.0263132	+	0.216709i
$249$	2.24871	−	3.89488i	0.142506	−	0.246828i
$250$	3.53760	+	2.65833i	0.223737	+	0.168128i
$251$	0.531731	+	13.1948i	0.0335625	+	0.832846i	0.925060	+	0.379821i	$0.124014\pi$
$251$	0.531731	+	13.1948i	0.0335625	+	0.832846i	−0.891498	+	0.453025i	$0.850345\pi$
$252$	−2.88097	+	7.59650i	−0.181484	+	0.478535i
$253$	4.44125	−	21.7547i	0.279219	−	1.36771i
$254$	−0.479178	+	2.34717i	−0.0300663	+	0.147274i
$255$	2.49656	−	6.58289i	0.156341	−	0.412236i
$256$	−0.258126	−	6.40534i	−0.0161329	−	0.400334i
$257$	4.88815	+	3.67320i	0.304914	+	0.229128i	0.742174	−	0.670207i	$-0.233795\pi$
$257$	4.88815	+	3.67320i	0.304914	+	0.229128i	−0.437260	+	0.899335i	$0.644051\pi$
$258$	−0.964377	+	1.67035i	−0.0600395	+	0.103991i
$259$	2.80974	+	23.1403i	0.174589	+	1.43787i
$260$	5.36766	−	11.5331i	0.332888	−	0.715253i
$261$	1.18200	−	9.73463i	0.0731639	−	0.602559i
$262$	2.57554	+	1.93539i	0.159117	+	0.119569i
$263$	−3.23273	+	1.07924i	−0.199339	+	0.0665490i	−0.414584	−	0.910011i	$-0.636073\pi$
$263$	−3.23273	+	1.07924i	−0.199339	+	0.0665490i	0.215246	+	0.976560i	$0.430945\pi$
$264$	5.82724	+	6.06680i	0.358642	+	0.373386i
$265$	−8.74823	−	7.75025i	−0.537399	−	0.476094i
$266$	−3.06633	−	10.5862i	−0.188009	−	0.649082i
$267$	−0.0304239	+	0.0372626i	−0.00186191	+	0.00228043i
$268$	13.0722			0.798509
$269$	4.86759	−	5.96171i	0.296782	−	0.363492i	−0.604591	−	0.796536i	$-0.706663\pi$
$269$	4.86759	−	5.96171i	0.296782	−	0.363492i	0.901373	+	0.433044i	$0.142561\pi$
$270$	0.0277103	−	0.687623i	0.00168639	−	0.0418474i
$271$	−0.799134	−	0.340479i	−0.0485439	−	0.0206826i	0.367558	−	0.930001i	$-0.380194\pi$
$271$	−0.799134	−	0.340479i	−0.0485439	−	0.0206826i	−0.416102	+	0.909318i	$0.636604\pi$
$272$	4.25685	+	11.2244i	0.258110	+	0.680579i
$273$	1.77484	−	15.5864i	0.107418	−	0.943332i
$274$	0.925706	−	2.44089i	0.0559239	−	0.147459i
$275$	−5.91623	+	6.15945i	−0.356762	+	0.371429i
$276$	1.93157	−	6.66857i	0.116267	−	0.401401i
$277$	−4.98913	−	0.402764i	−0.299767	−	0.0241997i	−0.0703321	−	0.997524i	$-0.522406\pi$
$277$	−4.98913	−	0.402764i	−0.299767	−	0.0241997i	−0.229435	+	0.973324i	$0.573688\pi$
$278$	−2.25991	+	1.18609i	−0.135541	+	0.0711372i
$279$	1.69065	+	1.76015i	0.101217	+	0.105378i
$280$	10.6528	−	4.53874i	0.636628	−	0.271242i
$281$	−7.42637	−	19.5817i	−0.443020	−	1.16815i	−0.951656	−	0.307166i	$-0.900619\pi$
$281$	−7.42637	−	19.5817i	−0.443020	−	1.16815i	0.508636	−	0.860982i	$-0.330150\pi$
$282$	2.55128	−	0.414624i	0.151927	−	0.0246905i
$283$	−9.09575	+	5.75181i	−0.540686	+	0.341909i	−0.776731	−	0.629833i	$-0.783123\pi$
$283$	−9.09575	+	5.75181i	−0.540686	+	0.341909i	0.236044	+	0.971742i	$0.424149\pi$
$284$	−3.21978	+	11.1160i	−0.191059	+	0.659611i
$285$	−7.46472	−	10.8145i	−0.442172	−	0.640596i
$286$	−6.65955	−	4.14214i	−0.393788	−	0.244930i
$287$	9.31864	−	13.5004i	0.550062	−	0.796902i
$288$	2.52384	+	3.09114i	0.148719	+	0.182147i
$289$	1.97020	+	2.41305i	0.115894	+	0.141944i
$290$	−5.39495	+	4.05404i	−0.316803	+	0.238062i
$291$	0.273665	+	2.25384i	0.0160426	+	0.132122i
$292$	−11.6026	−	3.87352i	−0.678992	−	0.226681i
$293$	−10.2120	−	0.824399i	−0.596592	−	0.0481619i	−0.221517	−	0.975156i	$-0.571101\pi$
$293$	−10.2120	−	0.824399i	−0.596592	−	0.0481619i	−0.375075	+	0.926994i	$0.622383\pi$
$294$	3.25239	−	2.88136i	0.189683	−	0.168045i
$295$	8.70970	+	5.50768i	0.507098	+	0.320669i
$296$	6.94289	+	2.95809i	0.403547	+	0.171935i
$297$	5.89460	+	0.957966i	0.342039	+	0.0555868i
$298$	−1.39666	−	1.23733i	−0.0809065	−	0.0716769i
$299$	−0.440005	+	13.3981i	−0.0254461	+	0.774830i
$300$	−1.99890	+	1.77087i	−0.115406	+	0.102241i
$301$	−19.4728	+	12.3138i	−1.12239	+	0.709758i
$302$	−7.15382	+	0.577516i	−0.411656	+	0.0332323i
$303$	1.99181	−	9.75652i	0.114426	−	0.560497i
$304$	21.7548	+	5.36208i	1.24773	+	0.307537i
$305$	18.8379	−	3.06146i	1.07865	−	0.175298i
$306$	−1.14710	−	0.725379i	−0.0655751	−	0.0414672i
$307$	11.9118	+	6.25177i	0.679840	+	0.356807i	0.769035	−	0.639207i	$-0.220737\pi$
$307$	11.9118	+	6.25177i	0.679840	+	0.356807i	−0.0891952	+	0.996014i	$0.528429\pi$
$308$	13.4988	+	46.6031i	0.769163	+	2.65546i
$309$	−3.99027	−	19.5456i	−0.226999	−	1.11191i
$310$	0.0676291	−	1.67820i	0.00384107	−	0.0953153i
$311$	26.5061	+	13.9115i	1.50302	+	0.788847i	0.997271	−	0.0738331i	$-0.0235232\pi$
$311$	26.5061	+	13.9115i	1.50302	+	0.788847i	0.505751	+	0.862680i	$0.331216\pi$
$312$	−4.08280	−	3.02071i	−0.231143	−	0.171014i
$313$	5.89182	−	3.09227i	0.333026	−	0.174785i	−0.289919	−	0.957051i	$-0.593628\pi$
$313$	5.89182	−	3.09227i	0.333026	−	0.174785i	0.622945	+	0.782266i	$0.285936\pi$
$314$	0.0441683	+	0.0930828i	0.00249256	+	0.00525297i
$315$	4.11026	−	7.11918i	0.231587	−	0.401120i
$316$	−9.06858	−	15.7072i	−0.510148	−	0.883602i
$317$	−17.0301	+	24.6723i	−0.956504	+	1.38574i	−0.0341388	+	0.999417i	$0.510869\pi$
$317$	−17.0301	+	24.6723i	−0.956504	+	1.38574i	−0.922365	+	0.386318i	$0.873747\pi$
$318$	−1.80118	+	1.35350i	−0.101005	+	0.0759005i
$319$	−29.2808	−	50.7158i	−1.63941	−	2.83954i
$320$	−1.13638	+	9.35896i	−0.0635258	+	0.523182i
$321$	−3.80203	+	8.01260i	−0.212208	+	0.447220i
$322$	−4.08142	+	4.24921i	−0.227449	+	0.236799i
$323$	−25.8314	+	2.08532i	−1.43730	+	0.116031i
$324$	1.81308	+	0.446883i	0.100726	+	0.0248268i
$325$	2.89745	−	4.26528i	0.160721	−	0.236595i
$326$	3.51159	−	0.865529i	0.194489	−	0.0479372i
$327$	−9.26041	+	3.09158i	−0.512102	+	0.170965i
$328$	−2.27675	−	4.79816i	−0.125713	−	0.264934i
$329$	29.2867	+	9.77733i	1.61463	+	0.539042i
$330$	−2.33462	−	3.38228i	−0.128516	−	0.186188i
$331$	−12.3494	+	26.0258i	−0.678783	+	1.43051i	0.212547	+	0.977151i	$0.431824\pi$
$331$	−12.3494	+	26.0258i	−0.678783	+	1.43051i	−0.891330	+	0.453354i	$0.850227\pi$
$332$	−0.338162	−	8.39139i	−0.0185590	−	0.460538i
$333$	5.20197	−	1.28217i	0.285066	−	0.0702625i
$334$	1.62770	−	0.693496i	0.0890636	−	0.0379464i
$335$	−13.0554	−	2.12171i	−0.713294	−	0.115922i
$336$	2.80370	+	13.7334i	0.152954	+	0.749221i
$337$	12.7795			0.696146			0.348073	−	0.937468i	$-0.386836\pi$
$337$	12.7795			0.696146			0.348073	+	0.937468i	$0.386836\pi$
$338$	4.38325	+	1.79087i	0.238417	+	0.0974103i
$339$	9.97602			0.541823
$340$	−2.62970	−	12.8811i	−0.142615	−	0.698576i
$341$	14.3862	+	2.33799i	0.779059	+	0.126609i
$342$	−2.33046	+	0.992916i	−0.126017	+	0.0536907i
$343$	20.8250	−	5.13289i	1.12444	−	0.277150i
$344$	0.300349	+	7.45309i	0.0161938	+	0.401844i
$345$	−3.01146	+	6.34652i	−0.162132	+	0.341685i
$346$	−0.564969	−	0.818499i	−0.0303729	−	0.0440028i
$347$	−15.0103	−	5.01119i	−0.805797	−	0.269015i	−0.116217	−	0.993224i	$-0.537077\pi$
$347$	−15.0103	−	5.01119i	−0.805797	−	0.269015i	−0.689580	+	0.724209i	$0.742205\pi$
$348$	−7.84994	−	16.5434i	−0.420801	−	0.886819i
$349$	21.3360	−	7.12301i	1.14209	−	0.381286i	0.318194	−	0.948026i	$-0.396924\pi$
$349$	21.3360	−	7.12301i	1.14209	−	0.381286i	0.823897	+	0.566740i	$0.191795\pi$
$350$	2.20044	−	0.542360i	0.117619	−	0.0289904i
$351$	−3.60545	+	0.0268528i	−0.192445	+	0.00143330i
$352$	23.1391	+	5.70329i	1.23332	+	0.303986i
$353$	0.884783	−	0.0714271i	0.0470923	−	0.00380168i	−0.0568980	−	0.998380i	$-0.518121\pi$
$353$	0.884783	−	0.0714271i	0.0470923	−	0.00380168i	0.103990	+	0.994578i	$0.466839\pi$
$354$	1.37612	−	1.43270i	0.0731401	−	0.0761469i
$355$	5.01986	−	10.5791i	0.266427	−	0.561482i
$356$	−0.0108277	+	0.0891737i	−0.000573864	+	0.00472620i
$357$	−8.10609	−	14.0402i	−0.429020	−	0.743084i
$358$	5.26153	−	3.95378i	0.278080	−	0.208964i
$359$	−19.6554	+	28.4758i	−1.03737	+	1.50289i	−0.183082	+	0.983098i	$0.558607\pi$
$359$	−19.6554	+	28.4758i	−1.03737	+	1.50289i	−0.854290	+	0.519796i	$0.826008\pi$
$360$	−1.33071	−	2.30486i	−0.0701348	−	0.121477i
$361$	−14.6850	+	25.4352i	−0.772896	+	1.33869i
$362$	2.28490	+	4.81532i	0.120092	+	0.253087i
$363$	21.8389	−	11.4619i	1.14625	−	0.601596i
$364$	−12.7545	−	26.3706i	−0.668518	−	1.38220i
$365$	10.9591	+	5.75176i	0.573624	+	0.301061i
$366$	0.148142	−	3.67611i	0.00774352	−	0.192153i
$367$	−3.55968	−	17.4365i	−0.185814	−	0.910176i	−0.960596	−	0.277948i	$-0.910346\pi$
$367$	−3.55968	−	17.4365i	−0.185814	−	0.910176i	0.774783	−	0.632228i	$-0.217859\pi$
$368$	−3.33245	−	11.5049i	−0.173716	−	0.599736i
$369$	−3.33849	−	1.75217i	−0.173795	−	0.0912146i
$370$	−3.11625	−	1.97060i	−0.162006	−	0.102446i
$371$	−26.5647	+	4.31719i	−1.37917	+	0.224137i
$372$	4.42496	+	1.09065i	0.229423	+	0.0565477i
$373$	−4.49576	+	22.0217i	−0.232782	+	1.14024i	0.680448	+	0.732796i	$0.261785\pi$
$373$	−4.49576	+	22.0217i	−0.232782	+	1.14024i	−0.913230	+	0.407444i	$0.866420\pi$
$374$	−8.07885	+	0.652192i	−0.417747	+	0.0337241i
$375$	10.2683	−	6.49330i	0.530255	−	0.335313i
$376$	7.48221	−	6.62866i	0.385865	−	0.341847i
$377$	22.5644	+	27.2200i	1.16213	+	1.40190i
$378$	−1.18616	−	1.05085i	−0.0610097	−	0.0540499i
$379$	10.6470	+	1.73030i	0.546898	+	0.0888795i	0.427582	−	0.903977i	$-0.359366\pi$
$379$	10.6470	+	1.73030i	0.546898	+	0.0888795i	0.119316	+	0.992856i	$0.461930\pi$
$380$	−22.5744	−	9.61806i	−1.15804	−	0.493396i
$381$	5.55891	+	3.51524i	0.284792	+	0.180091i
$382$	−2.83528	+	2.51184i	−0.145065	+	0.128517i
$383$	−17.2607	−	1.39343i	−0.881982	−	0.0712009i	−0.368828	−	0.929498i	$-0.620241\pi$
$383$	−17.2607	−	1.39343i	−0.881982	−	0.0712009i	−0.513154	+	0.858297i	$0.671523\pi$
$384$	9.29435	+	3.10291i	0.474300	+	0.158345i
$385$	−5.91744	−	48.7345i	−0.301580	−	2.48374i
$386$	3.51418	−	2.64073i	0.178867	−	0.134410i
$387$	3.34907	+	4.10187i	0.170243	+	0.208510i
$388$	2.68131	+	3.28400i	0.136123	+	0.166720i
$389$	−18.9346	+	27.4316i	−0.960024	+	1.39084i	−0.0399024	+	0.999204i	$0.512705\pi$
$389$	−18.9346	+	27.4316i	−0.960024	+	1.39084i	−0.920122	+	0.391632i	$0.871911\pi$
$390$	1.73212	+	1.77665i	0.0877092	+	0.0899641i
$391$	7.86995	+	11.4016i	0.398000	+	0.576603i
$392$	4.67521	−	16.1407i	0.236134	−	0.815227i
$393$	7.47584	−	4.72743i	0.377106	−	0.238467i
$394$	−5.49765	+	0.893455i	−0.276968	+	0.0450116i
$395$	6.50757	+	17.1591i	0.327431	+	0.863366i
$396$	10.2593	−	4.37106i	0.515547	−	0.219654i
$397$	0.910775	+	0.948217i	0.0457105	+	0.0475896i	0.743665	−	0.668552i	$-0.233086\pi$
$397$	0.910775	+	0.948217i	0.0457105	+	0.0475896i	−0.697955	+	0.716142i	$0.745906\pi$
$398$	−1.29679	+	0.680606i	−0.0650021	+	0.0341157i
$399$	−30.1612	−	2.43487i	−1.50995	−	0.121896i
$400$	−1.28182	+	4.42537i	−0.0640912	+	0.221269i
$401$	12.5300	−	13.0452i	0.625720	−	0.651444i	−0.330598	−	0.943772i	$-0.607250\pi$
$401$	12.5300	−	13.0452i	0.625720	−	0.651444i	0.956318	+	0.292328i	$0.0944299\pi$
$402$	−0.904158	+	2.38407i	−0.0450953	+	0.118907i
$403$	−8.79939	+	0.0655364i	−0.438329	+	0.00326460i
$404$	−6.59370	−	17.3861i	−0.328049	−	0.864993i
$405$	−1.73822	−	0.740588i	−0.0863730	−	0.0368001i
$406$	−0.625724	+	15.5272i	−0.0310541	+	0.770600i
$407$	20.2355	−	24.7839i	1.00303	−	1.22849i
$408$	−5.24876			−0.259853
$409$	−10.1667	+	12.4520i	−0.502713	+	0.615711i	−0.962157	−	0.272495i	$-0.912151\pi$
$409$	−10.1667	+	12.4520i	−0.502713	+	0.615711i	0.459444	+	0.888207i	$0.348049\pi$
$410$	0.721888	+	2.49225i	0.0356515	+	0.123083i
$411$	−5.36477	−	4.75277i	−0.264625	−	0.234437i
$412$	−25.8047	−	26.8656i	−1.27131	−	1.32357i
$413$	22.5085	−	7.51445i	1.10757	−	0.369762i
$414$	1.08260	+	0.813519i	0.0532068	+	0.0399823i
$415$	−1.02426	+	8.43554i	−0.0502790	+	0.414085i
$416$	−14.3499	−	1.05094i	−0.703562	−	0.0515264i
$417$	0.844635	+	6.95619i	0.0413619	+	0.340646i
$418$	−7.56395	+	13.1011i	−0.369965	+	0.640798i
$419$	−26.5355	−	19.9402i	−1.29635	−	0.974141i	−0.999817	−	0.0191169i	$-0.993915\pi$
$419$	−26.5355	−	19.9402i	−1.29635	−	0.974141i	−0.296529	−	0.955024i	$-0.595829\pi$
$420$	−0.618101	−	15.3380i	−0.0301602	−	0.748419i
$421$	3.49484	−	9.21512i	0.170328	−	0.449118i	−0.822486	−	0.568785i	$-0.807414\pi$
$421$	3.49484	−	9.21512i	0.170328	−	0.449118i	0.992814	+	0.119667i	$0.0381828\pi$
$422$	−1.07720	+	5.27647i	−0.0524372	+	0.256854i
$423$	1.41948	−	6.95309i	0.0690176	−	0.338071i
$424$	−3.08977	+	8.14706i	−0.150053	+	0.395656i
$425$	−0.214574	−	5.32460i	−0.0104084	−	0.258281i
$426$	−1.80460	−	1.35607i	−0.0874332	−	0.0657018i
$427$	21.9739	−	38.0599i	1.06339	−	1.84185i
$428$	1.99623	+	16.4405i	0.0964916	+	0.794679i
$429$	−17.1169	+	13.0631i	−0.826411	+	0.630692i
$430$	0.439262	−	3.61765i	0.0211831	−	0.174458i
$431$	23.7668	+	17.8596i	1.14480	+	0.860265i	0.991780	−	0.127958i	$-0.0408422\pi$
$431$	23.7668	+	17.8596i	1.14480	+	0.860265i	0.153025	+	0.988222i	$0.451099\pi$
$432$	3.05582	−	1.02018i	0.147023	−	0.0490836i
$433$	13.8273	+	14.3958i	0.664498	+	0.691816i	0.965085	−	0.261939i	$-0.0843618\pi$
$433$	13.8273	+	14.3958i	0.664498	+	0.691816i	−0.300586	+	0.953755i	$0.597182\pi$
$434$	−2.89493	−	2.56468i	−0.138961	−	0.123109i
$435$	5.15477	+	17.7963i	0.247152	+	0.853269i
$436$	−11.5298	+	14.1214i	−0.552177	+	0.676294i
$437$	25.8579			1.23695
$438$	1.50896	−	1.84814i	0.0721009	−	0.0883076i
$439$	0.685556	−	17.0119i	0.0327198	−	0.811933i	−0.896641	−	0.442759i	$-0.854000\pi$
$439$	0.685556	−	17.0119i	0.0327198	−	0.811933i	0.929360	−	0.369174i	$-0.120359\pi$
$440$	−14.6220	−	6.22987i	−0.697078	−	0.296997i
$441$	−4.23033	−	11.1545i	−0.201444	−	0.531164i
$442$	4.74242	−	1.20644i	0.225574	−	0.0573843i
$443$	2.66991	−	7.03996i	0.126851	−	0.334479i	−0.856513	−	0.516126i	$-0.827374\pi$
$443$	2.66991	−	7.03996i	0.126851	−	0.334479i	0.983364	+	0.181647i	$0.0581429\pi$
$444$	6.93040	−	7.21531i	0.328902	−	0.342423i
$445$	0.0252874	−	0.0873022i	0.00119874	−	0.00413852i
$446$	2.95470	+	0.238528i	0.139909	+	0.0112946i
$447$	−4.53613	+	2.38074i	−0.214551	+	0.112605i
$448$	15.0387	+	15.6569i	0.710512	+	0.739721i
$449$	28.9714	−	12.3436i	1.36724	−	0.582528i	0.421319	−	0.906913i	$-0.361567\pi$
$449$	28.9714	−	12.3436i	1.36724	−	0.582528i	0.945925	+	0.324385i	$0.105157\pi$
$450$	−0.184710	−	0.487039i	−0.00870730	−	0.0229593i
$451$	−22.2248	+	3.61188i	−1.04652	+	0.170077i
$452$	15.7447	−	9.95635i	0.740568	−	0.468307i
$453$	−5.48224	+	18.9269i	−0.257578	+	0.889262i
$454$	−0.562337	−	0.814685i	−0.0263918	−	0.0382351i
$455$	8.45802	+	28.4071i	0.396518	+	1.33174i
$456$	−5.56510	+	8.06244i	−0.260610	+	0.377559i
$457$	−14.8406	−	18.1764i	−0.694214	−	0.850258i	0.300410	−	0.953810i	$-0.402877\pi$
$457$	−14.8406	−	18.1764i	−0.694214	−	0.850258i	−0.994624	+	0.103552i	$0.966979\pi$
$458$	2.31344	+	2.83345i	0.108100	+	0.132398i
$459$	−2.97891	+	2.23850i	−0.139044	+	0.104484i
$460$	1.58115	+	13.0220i	0.0737216	+	0.607152i
$461$	1.22293	+	0.408272i	0.0569573	+	0.0190151i	0.345004	−	0.938601i	$-0.387878\pi$
$461$	1.22293	+	0.408272i	0.0569573	+	0.0190151i	−0.288047	+	0.957616i	$0.593006\pi$
$462$	−9.43304	−	0.761514i	−0.438865	−	0.0354288i
$463$	−31.8807	+	28.2438i	−1.48162	+	1.31260i	−0.645940	+	0.763388i	$0.723534\pi$
$463$	−31.8807	+	28.2438i	−1.48162	+	1.31260i	−0.835682	+	0.549214i	$0.814927\pi$
$464$	−26.7009	−	16.8846i	−1.23956	−	0.783850i
$465$	−4.24227	−	1.80746i	−0.196731	−	0.0838191i
$466$	−2.75860	−	0.448317i	−0.127790	−	0.0207679i
$467$	−5.43594	−	4.81582i	−0.251545	−	0.222850i	0.527922	−	0.849293i	$-0.322971\pi$
$467$	−5.43594	−	4.81582i	−0.251545	−	0.222850i	−0.779467	+	0.626443i	$0.784510\pi$
$468$	−5.66352	+	3.64072i	−0.261796	+	0.168292i
$469$	−22.7979	+	20.1971i	−1.05271	+	0.932618i
$470$	−4.12764	+	2.61016i	−0.190394	+	0.120398i
$471$	0.281955	−	0.0227617i	0.0129918	−	0.00104881i
$472$	1.53672	−	7.52735i	0.0707332	−	0.346474i
$473$	30.7051	+	7.56812i	1.41182	+	0.347983i
$474$	3.49190	−	0.567488i	0.160388	−	0.0260656i
$475$	−8.40644	−	5.31591i	−0.385714	−	0.243911i
$476$	−26.8059	−	14.0688i	−1.22865	−	0.644844i
$477$	1.72099	+	5.94156i	0.0787988	+	0.272045i
$478$	−1.09318	−	5.35474i	−0.0500008	−	0.244920i
$479$	0.982939	−	24.3914i	0.0449116	−	1.11447i	−0.806922	−	0.590658i	$-0.798868\pi$
$479$	0.982939	−	24.3914i	0.0449116	−	1.11447i	0.851833	−	0.523813i	$-0.175491\pi$
$480$	−6.67626	−	3.50397i	−0.304728	−	0.159934i
$481$	−9.53379	+	16.8007i	−0.434703	+	0.766048i
$482$	−5.45409	+	2.86253i	−0.248427	+	0.130384i
$483$	6.93461	+	14.6144i	0.315536	+	0.664977i
$484$	23.0280	−	39.8857i	1.04673	−	1.81299i
$485$	−2.14486	−	3.71500i	−0.0973929	−	0.168689i
$486$	−0.206906	+	0.299755i	−0.00938545	+	0.0135972i
$487$	−20.6603	+	15.5252i	−0.936208	+	0.703514i	−0.955093	−	0.296307i	$-0.904245\pi$
$487$	−20.6603	+	15.5252i	−0.936208	+	0.703514i	0.0188849	+	0.999822i	$0.493988\pi$
$488$	−7.11415	−	12.3221i	−0.322042	−	0.557794i
$489$	1.19689	−	9.85728i	0.0541252	−	0.445761i
$490$	−3.51947	+	7.41713i	−0.158994	+	0.335072i
$491$	19.7139	−	20.5244i	0.889676	−	0.926251i	−0.108016	−	0.994149i	$-0.534450\pi$
$491$	19.7139	−	20.5244i	0.889676	−	0.926251i	0.997692	+	0.0678979i	$0.0216292\pi$
$492$	−7.01771	+	0.566528i	−0.316383	+	0.0255410i
$493$	35.4781	+	8.74457i	1.59785	+	0.393836i
$494$	3.17508	−	8.56381i	0.142853	−	0.385304i
$495$	−10.9556	+	2.70031i	−0.492417	+	0.121370i
$496$	7.45798	−	2.48984i	0.334873	−	0.111797i
$497$	−11.5594	−	24.3610i	−0.518511	−	1.09274i
$498$	1.55379	+	0.518732i	0.0696271	+	0.0232449i
$499$	−17.0653	−	24.7233i	−0.763947	−	1.10677i	−0.991127	−	0.132915i	$-0.957566\pi$
$499$	−17.0653	−	24.7233i	−0.763947	−	1.10677i	0.227180	−	0.973853i	$-0.427049\pi$
$500$	9.72556	−	20.4962i	0.434940	−	0.916617i
$501$	−0.195595	−	4.85364i	−0.00873854	−	0.216845i
$502$	−4.67006	+	1.15107i	−0.208435	+	0.0513746i
$503$	8.21515	−	3.50015i	0.366295	−	0.156064i	−0.200973	−	0.979597i	$-0.564410\pi$
$503$	8.21515	−	3.50015i	0.366295	−	0.156064i	0.567268	+	0.823533i	$0.308000\pi$
$504$	−6.04920	−	0.983091i	−0.269453	−	0.0437904i
$505$	3.76335	+	18.4341i	0.167467	+	0.820307i
$506$	8.08714			0.359517
$507$	8.86477	−	9.50873i	0.393698	−	0.422297i
$508$	12.2817			0.544912
$509$	−0.716498	−	3.50964i	−0.0317582	−	0.155562i	0.960819	−	0.277175i	$-0.0893983\pi$
$509$	−0.716498	−	3.50964i	−0.0317582	−	0.155562i	−0.992578	+	0.121613i	$0.961193\pi$
$510$	2.53111	+	0.411346i	0.112080	+	0.0182147i
$511$	26.2198	−	11.1712i	1.15990	−	0.494185i
$512$	21.2948	−	5.24871i	0.941108	−	0.231962i
$513$	0.280044	+	6.94922i	0.0123642	+	0.306815i
$514$	−0.954724	+	2.01204i	−0.0421111	+	0.0887472i
$515$	21.4112	+	31.0195i	0.943492	+	1.36688i
$516$	9.37947	+	3.13133i	0.412908	+	0.137849i
$517$	−18.1679	−	38.2881i	−0.799025	−	1.68391i
$518$	−8.05334	+	2.68860i	−0.353843	+	0.118130i
$519$	−2.65121	+	0.653465i	−0.116375	+	0.0286839i
$520$	9.33392	+	2.22700i	0.409319	+	0.0976603i
$521$	−34.1147	−	8.40853i	−1.49459	−	0.368384i	−0.594506	−	0.804092i	$-0.702652\pi$
$521$	−34.1147	−	8.40853i	−1.49459	−	0.368384i	−0.900088	+	0.435707i	$0.856498\pi$
$522$	3.56010	−	0.287401i	0.155821	−	0.0125792i
$523$	2.70650	−	2.81776i	0.118347	−	0.123212i	−0.659393	−	0.751798i	$-0.729187\pi$
$523$	2.70650	−	2.81776i	0.118347	−	0.123212i	0.777740	+	0.628586i	$0.216366\pi$
$524$	7.08066	−	14.9222i	0.309320	−	0.651879i
$525$	0.749999	−	6.17680i	0.0327326	−	0.269578i
$526$	−0.620670	−	1.07503i	−0.0270625	−	0.0468736i
$527$	−7.27026	+	5.46325i	−0.316698	+	0.237983i
$528$	10.9292	−	15.8336i	0.475631	−	0.689071i
$529$	4.58840	+	7.94734i	0.199496	+	0.345537i
$530$	2.12847	−	3.68662i	0.0924548	−	0.160136i
$531$	−2.33812	−	4.92749i	−0.101466	−	0.213835i
$532$	−50.0322	+	26.2589i	−2.16917	+	1.13847i
$533$	12.8622	−	4.40077i	0.557124	−	0.190619i
$534$	−0.0155144	−	0.00814258i	−0.000671373	−	0.000352364i
$535$	0.674737	−	16.7434i	0.0291714	−	0.723881i
$536$	1.97241	+	9.66151i	0.0851952	+	0.417314i
$537$	−5.02729	−	17.3562i	−0.216943	−	0.748976i
$538$	2.48218	+	1.30275i	0.107014	+	0.0561654i
$539$	−60.2142	−	38.0771i	−2.59361	−	1.64010i
$540$	−3.48249	+	0.565959i	−0.149862	+	0.0243550i
$541$	13.3980	+	3.30231i	0.576025	+	0.141977i	0.516557	−	0.856253i	$-0.327213\pi$
$541$	13.3980	+	3.30231i	0.576025	+	0.141977i	0.0594680	+	0.998230i	$0.481060\pi$
$542$	0.0632852	−	0.309992i	0.00271833	−	0.0133153i
$543$	14.5860	−	1.17750i	0.625943	−	0.0505314i
$544$	−12.5679	+	7.94747i	−0.538845	+	0.340745i
$545$	13.8071	−	12.2320i	0.591430	−	0.523961i
$546$	5.69161	−	0.502166i	0.243578	−	0.0214907i
$547$	−23.9938	−	21.2566i	−1.02590	−	0.908868i	−0.0300202	−	0.999549i	$-0.509557\pi$
$547$	−23.9938	−	21.2566i	−1.02590	−	0.908868i	−0.995880	+	0.0906810i	$0.971096\pi$
$548$	−13.2104	−	2.14689i	−0.564319	−	0.0917108i
$549$	−9.29274	−	3.95927i	−0.396605	−	0.168977i
$550$	−2.62915	−	1.66257i	−0.112107	−	0.0708922i
$551$	51.0486	−	45.2251i	2.17474	−	1.92665i
$552$	5.22013	+	0.421412i	0.222183	+	0.0179365i
$553$	40.0841	+	13.3821i	1.70455	+	0.569063i
$554$	−0.219750	−	1.80981i	−0.00933630	−	0.0768913i
$555$	−8.09263	+	6.08122i	−0.343513	+	0.258133i
$556$	8.27552	+	10.1357i	0.350960	+	0.429848i
$557$	−18.7612	−	22.9783i	−0.794938	−	0.973622i	0.205049	−	0.978752i	$-0.434265\pi$
$557$	−18.7612	−	22.9783i	−0.794938	−	0.973622i	−0.999987	+	0.00512985i	$0.998367\pi$
$558$	−0.504971	+	0.731576i	−0.0213771	+	0.0309701i
$559$	−19.0420	−	1.39457i	−0.805389	−	0.0589839i
$560$	−15.0443	−	21.7954i	−0.635737	−	0.921024i
$561$	−6.19112	+	21.3742i	−0.261389	+	0.902421i
$562$	6.44705	−	4.07687i	0.271953	−	0.171972i
$563$	−21.4792	+	3.49071i	−0.905241	+	0.147116i	−0.595172	−	0.803598i	$-0.702916\pi$
$563$	−21.4792	+	3.49071i	−0.905241	+	0.147116i	−0.310069	+	0.950714i	$0.600352\pi$
$564$	−4.69907	−	12.3904i	−0.197866	−	0.521731i
$565$	−17.3406	+	7.38812i	−0.729522	+	0.310820i
$566$	−2.71531	−	2.82694i	−0.114133	−	0.118825i
$567$	−3.85247	+	2.02193i	−0.161788	+	0.0849131i
$568$	−8.70152	−	0.702460i	−0.365108	−	0.0294746i
$569$	0.547135	−	1.88893i	0.0229371	−	0.0791880i	−0.948233	−	0.317575i	$-0.897131\pi$
$569$	0.547135	−	1.88893i	0.0229371	−	0.0791880i	0.971170	+	0.238387i	$0.0766187\pi$
$570$	3.31552	−	3.45182i	0.138872	−	0.144581i
$571$	8.06800	−	21.2736i	0.337635	−	0.890271i	−0.653441	−	0.756977i	$-0.726675\pi$
$571$	8.06800	−	21.2736i	0.337635	−	0.890271i	0.991077	−	0.133294i	$-0.0425553\pi$
$572$	−13.9775	+	37.7000i	−0.584427	+	1.57632i
$573$	3.68780	+	9.72392i	0.154060	+	0.406223i
$574$	5.49678	+	2.34196i	0.229431	+	0.0977514i
$575$	−0.214098	+	5.31278i	−0.00892849	+	0.221558i
$576$	3.15574	−	3.86508i	0.131489	−	0.161045i
$577$	−7.61851			−0.317163			−0.158581	−	0.987346i	$-0.550692\pi$
$577$	−7.61851			−0.317163			−0.158581	+	0.987346i	$0.550692\pi$
$578$	−0.717604	+	0.878905i	−0.0298484	+	0.0365576i
$579$	−3.35773	−	11.5922i	−0.139542	−	0.481756i
$580$	25.8968	+	22.9425i	1.07531	+	0.952637i
$581$	13.5549	+	14.1121i	0.562352	+	0.585470i
$582$	−0.784386	+	0.261867i	−0.0325139	+	0.0108547i
$583$	29.5323	+	22.1921i	1.22310	+	0.919102i
$584$	1.11221	−	9.15985i	0.0460235	−	0.379037i
$585$	6.24719	−	2.71683i	0.258290	−	0.112327i
$586$	−0.449797	−	3.70441i	−0.0185809	−	0.153028i
$587$	−16.7365	+	28.9884i	−0.690787	+	1.19648i	0.280793	+	0.959768i	$0.409403\pi$
$587$	−16.7365	+	28.9884i	−0.690787	+	1.19648i	−0.971580	+	0.236710i	$0.923931\pi$
$588$	−17.8090	−	13.3826i	−0.734430	−	0.551888i
$589$	0.683469	+	16.9601i	0.0281619	+	0.698829i
$590$	−1.33097	+	3.50948i	−0.0547952	+	0.144483i
$591$	−3.05878	+	14.9829i	−0.125821	+	0.616314i
$592$	3.45251	−	16.9115i	0.141897	−	0.695059i
$593$	−11.8063	+	31.1307i	−0.484827	+	1.27838i	0.440001	+	0.897997i	$0.354978\pi$
$593$	−11.8063	+	31.1307i	−0.484827	+	1.27838i	−0.924828	+	0.380386i	$0.875791\pi$
$594$	0.0875847	+	2.17339i	0.00359364	+	0.0891754i
$595$	24.4882	+	18.4017i	1.00392	+	0.754395i
$596$	−4.78311	+	8.28460i	−0.195924	+	0.339350i
$597$	0.484670	+	3.99161i	0.0198362	+	0.163366i
$598$	−4.81341	+	0.819095i	−0.196835	+	0.0334953i
$599$	1.43613	−	11.8276i	0.0586787	−	0.483262i	−0.933513	−	0.358543i	$-0.883274\pi$
$599$	1.43613	−	11.8276i	0.0586787	−	0.483262i	0.992192	−	0.124720i	$-0.0398032\pi$
$600$	−1.61044	−	1.21017i	−0.0657459	−	0.0494048i
$601$	31.7483	−	10.5992i	1.29504	−	0.432348i	0.416118	−	0.909311i	$-0.363390\pi$
$601$	31.7483	−	10.5992i	1.29504	−	0.432348i	0.878924	+	0.476962i	$0.158262\pi$
$602$	−5.81312	−	6.05210i	−0.236925	−	0.246665i
$603$	5.23989	+	4.64214i	0.213385	+	0.189043i
$604$	10.2372	+	35.3429i	0.416545	+	1.43808i
$605$	−29.4723	+	36.0970i	−1.19822	+	1.46755i
$606$	3.62691			0.147333
$607$	17.4995	−	21.4330i	0.710284	−	0.869939i	−0.285806	−	0.958287i	$-0.592261\pi$
$607$	17.4995	−	21.4330i	0.710284	−	0.869939i	0.996090	+	0.0883480i	$0.0281588\pi$
$608$	−1.11754	+	27.7316i	−0.0453224	+	1.12466i
$609$	39.2507	+	16.7232i	1.59052	+	0.677657i
$610$	2.46498	+	6.49961i	0.0998040	+	0.263162i
$611$	14.6914	+	20.9487i	0.594350	+	0.847493i
$612$	−2.46739	+	6.50596i	−0.0997382	+	0.262988i
$613$	4.17518	−	4.34682i	0.168634	−	0.175566i	−0.631523	−	0.775357i	$-0.717570\pi$
$613$	4.17518	−	4.34682i	0.168634	−	0.175566i	0.800157	+	0.599791i	$0.204749\pi$
$614$	−1.36323	+	4.70641i	−0.0550154	+	0.189935i
$615$	7.10068	+	0.573226i	0.286327	+	0.0231147i
$616$	−32.4072	+	17.0086i	−1.30572	+	0.685296i
$617$	−22.0151	−	22.9201i	−0.886293	−	0.922728i	0.111178	−	0.993800i	$-0.464537\pi$
$617$	−22.0151	−	22.9201i	−0.886293	−	0.922728i	−0.997471	+	0.0710720i	$0.977358\pi$
$618$	6.68452	−	2.84801i	0.268891	−	0.114564i
$619$	−11.1931	−	29.5138i	−0.449888	−	1.18626i	−0.947754	−	0.319003i	$-0.896652\pi$
$619$	−11.1931	−	29.5138i	−0.449888	−	1.18626i	0.497865	−	0.867254i	$-0.334117\pi$
$620$	−8.49928	+	1.38127i	−0.341339	+	0.0554731i
$621$	3.14238	−	1.98712i	0.126099	−	0.0797404i
$622$	−3.03346	+	10.4727i	−0.121631	+	0.419918i
$623$	−0.118895	−	0.172249i	−0.00476341	−	0.00690099i
$624$	−4.90128	+	10.5310i	−0.196208	+	0.421578i
$625$	−8.97783	+	13.0066i	−0.359113	+	0.520265i
$626$	1.53278	+	1.87732i	0.0612624	+	0.0750328i
$627$	26.2680	+	32.1724i	1.04904	+	1.28484i
$628$	0.422279	−	0.317322i	0.0168508	−	0.0126625i
$629$	2.40638	+	19.8183i	0.0959486	+	0.790208i
$630$	2.84007	+	0.948153i	0.113151	+	0.0377753i
$631$	2.08542	+	0.168353i	0.0830193	+	0.00670201i	0.121906	−	0.992542i	$-0.461099\pi$
$631$	2.08542	+	0.168353i	0.0830193	+	0.00670201i	−0.0388871	+	0.999244i	$0.512381\pi$
$632$	10.2408	−	9.07252i	0.407355	−	0.360885i
$633$	12.4965	+	7.90232i	0.496692	+	0.314089i
$634$	−10.0455	−	4.27999i	−0.398958	−	0.169980i
$635$	−12.2660	−	1.99342i	−0.486761	−	0.0791063i
$636$	8.64600	+	7.65969i	0.342836	+	0.303726i
$637$	39.6956	+	16.5645i	1.57280	+	0.656310i
$638$	15.9656	−	14.1443i	0.632086	−	0.559979i
$639$	−5.23809	+	3.31237i	−0.207216	+	0.131035i
$640$	−18.4536	+	1.48973i	−0.729444	+	0.0588868i
$641$	−4.54839	+	22.2795i	−0.179651	+	0.879988i	0.785615	+	0.618716i	$0.212347\pi$
$641$	−4.54839	+	22.2795i	−0.179651	+	0.879988i	−0.965265	+	0.261272i	$0.915858\pi$
$642$	−3.13645	−	0.773064i	−0.123786	−	0.0305104i
$643$	−41.0037	+	6.66375i	−1.61703	+	0.262793i	−0.900530	−	0.434795i	$-0.856821\pi$
$643$	−41.0037	+	6.66375i	−1.61703	+	0.262793i	−0.716499	+	0.697588i	$0.754257\pi$
$644$	25.5301	+	16.1443i	1.00603	+	0.636174i
$645$	−8.85923	−	4.64968i	−0.348832	−	0.183081i
$646$	−2.62614	−	9.06648i	−0.103324	−	0.356716i
$647$	−1.77579	−	8.69839i	−0.0698135	−	0.341969i	0.929849	−	0.367941i	$-0.119937\pi$
$647$	−1.77579	−	8.69839i	−0.0698135	−	0.341969i	−0.999663	+	0.0259718i	$0.991732\pi$
$648$	−0.0567185	+	1.40746i	−0.00222811	+	0.0552901i
$649$	−28.8405	−	15.1367i	−1.13209	−	0.594167i
$650$	1.73324	+	0.723260i	0.0679833	+	0.0283686i
$651$	−9.40225	+	4.93468i	−0.368503	+	0.193405i
$652$	−7.94884	−	16.7518i	−0.311301	−	0.656052i
$653$	−16.2253	+	28.1031i	−0.634946	+	1.09976i	0.351580	+	0.936158i	$0.385645\pi$
$653$	−16.2253	+	28.1031i	−0.634946	+	1.09976i	−0.986526	+	0.163602i	$0.947689\pi$
$654$	−1.77796	−	3.07951i	−0.0695236	−	0.120418i
$655$	−9.49359	+	13.7538i	−0.370945	+	0.537407i
$656$	−9.71057	+	7.29702i	−0.379134	+	0.284901i
$657$	−3.27529	−	5.67296i	−0.127781	−	0.221323i
$658$	−1.35553	+	11.1638i	−0.0528442	+	0.435211i
$659$	6.18744	−	13.0398i	0.241029	−	0.507957i	−0.746502	−	0.665383i	$-0.768268\pi$
$659$	6.18744	−	13.0398i	0.241029	−	0.507957i	0.987531	+	0.157426i	$0.0503196\pi$
$660$	−14.5957	+	15.1958i	−0.568138	+	0.591494i
$661$	42.6392	−	3.44219i	1.65847	−	0.133886i	0.784587	−	0.620019i	$-0.212875\pi$
$661$	42.6392	−	3.44219i	1.65847	−	0.133886i	0.873885	+	0.486133i	$0.161593\pi$
$662$	−10.1875	−	2.51099i	−0.395948	−	0.0975925i
$663$	1.52005	−	13.3489i	0.0590338	−	0.518426i
$664$	6.15098	−	1.51608i	0.238704	−	0.0588353i
$665$	54.2302	−	18.1047i	2.10296	−	0.702070i
$666$	0.836558	+	1.76301i	0.0324160	+	0.0683152i
$667$	−34.5825	−	11.5453i	−1.33904	−	0.447037i
$668$	−5.15277	−	7.46507i	−0.199366	−	0.288832i
$669$	3.48895	−	7.35281i	0.134891	−	0.284276i
$670$	−0.193984	−	4.81365i	−0.00749424	−	0.185968i
$671$	−58.5699	+	14.4362i	−2.26106	+	0.557302i
$672$	−15.9731	+	6.80549i	−0.616175	+	0.262528i
$673$	−20.1014	−	3.26680i	−0.774853	−	0.125926i	−0.239888	−	0.970800i	$-0.577111\pi$
$673$	−20.1014	−	3.26680i	−0.774853	−	0.125926i	−0.534964	+	0.844875i	$0.679675\pi$
$674$	0.931056	+	4.56062i	0.0358630	+	0.175668i
$675$	−1.43011			−0.0550450
$676$	4.50089	−	23.8545i	0.173111	−	0.917480i
$677$	38.5103			1.48007			0.740035	−	0.672568i	$-0.234809\pi$
$677$	38.5103			1.48007			0.740035	+	0.672568i	$0.234809\pi$
$678$	0.726806	+	3.56013i	0.0279128	+	0.136726i
$679$	−9.75016	−	1.58456i	−0.374177	−	0.0608097i
$680$	9.12352	−	3.88717i	0.349871	−	0.149066i
$681$	−2.63886	+	0.650421i	−0.101121	+	0.0249242i
$682$	0.213757	+	5.30434i	0.00818520	+	0.203114i
$683$	4.73931	−	9.98789i	0.181345	−	0.382176i	−0.792338	−	0.610082i	$-0.791137\pi$
$683$	4.73931	−	9.98789i	0.181345	−	0.382176i	0.973683	+	0.227906i	$0.0731878\pi$
$684$	7.37749	+	10.6881i	0.282085	+	0.408671i
$685$	12.8450	+	4.28829i	0.490783	+	0.163847i
$686$	3.34898	+	7.05782i	0.127865	+	0.269469i
$687$	9.52606	−	3.18027i	0.363442	−	0.121335i
$688$	16.5642	−	4.08270i	0.631502	−	0.155651i
$689$	−19.8251	−	10.2174i	−0.755277	−	0.389253i
$690$	−2.48428	−	0.612319i	−0.0945748	−	0.0233106i
$691$	13.0757	−	1.05558i	0.497425	−	0.0401563i	0.170791	−	0.985307i	$-0.445368\pi$
$691$	13.0757	−	1.05558i	0.497425	−	0.0401563i	0.326634	+	0.945151i	$0.394086\pi$
$692$	−3.53211	+	3.67732i	−0.134271	+	0.139791i
$693$	−11.1387	+	23.4742i	−0.423123	+	0.891712i
$694$	0.694754	−	5.72181i	0.0263725	−	0.217197i
$695$	−6.61983	−	11.4659i	−0.251105	−	0.434926i
$696$	11.0426	−	8.29799i	0.418570	−	0.314535i
$697$	7.98088	−	11.5623i	0.302297	−	0.437953i
$698$	4.09642	+	7.09521i	0.155052	+	0.268558i
$699$	−3.83658	+	6.64516i	−0.145113	+	0.251343i
$700$	−4.98093	−	10.4971i	−0.188261	−	0.396752i
$701$	12.6648	−	6.64701i	0.478344	−	0.251054i	−0.208277	−	0.978070i	$-0.566786\pi$
$701$	12.6648	−	6.64701i	0.478344	−	0.251054i	0.686621	+	0.727016i	$0.259093\pi$
$702$	−0.272259	−	1.28472i	−0.0102758	−	0.0484885i
$703$	32.9936	+	17.3164i	1.24438	+	0.653100i
$704$	1.19986	−	29.7743i	0.0452215	−	1.12216i
$705$	2.68199	+	13.1373i	0.101010	+	0.494778i
$706$	0.0899512	+	0.310548i	0.00338536	+	0.0116876i
$707$	38.3619	+	20.1339i	1.44275	+	0.757213i
$708$	−8.60792	−	5.44332i	−0.323506	−	0.204573i
$709$	−23.0731	+	3.74974i	−0.866527	+	0.140824i	−0.577395	−	0.816465i	$-0.695931\pi$
$709$	−23.0731	+	3.74974i	−0.866527	+	0.140824i	−0.289132	+	0.957289i	$0.593367\pi$
$710$	4.14109	+	1.02069i	0.155412	+	0.0383057i
$711$	1.94282	−	9.51656i	0.0728615	−	0.356899i
$712$	−0.0675413	+	0.00545249i	−0.00253122	+	0.000204341i
$713$	7.66923	−	4.84973i	0.287215	−	0.181624i
$714$	4.41992	−	3.91571i	0.165411	−	0.146542i
$715$	20.0786	−	35.3831i	0.750897	−	1.32325i
$716$	−25.2563	−	22.3751i	−0.943873	−	0.836198i
$717$	−14.8105	−	2.40694i	−0.553108	−	0.0898887i
$718$	−11.5941	−	4.93979i	−0.432688	−	0.184351i
$719$	−22.1144	−	13.9843i	−0.824726	−	0.521525i	0.0541735	−	0.998532i	$-0.482748\pi$
$719$	−22.1144	−	13.9843i	−0.824726	−	0.521525i	−0.878900	+	0.477006i	$0.841722\pi$
$720$	−4.55617	+	4.03641i	−0.169798	+	0.150428i
$721$	86.5123	+	6.98399i	3.22189	+	0.260097i
$722$	−10.1469	−	3.38754i	−0.377629	−	0.126071i
$723$	2.03845	+	16.7881i	0.0758106	+	0.624356i
$724$	21.8452	−	16.4156i	0.811869	−	0.610080i
$725$	8.86932	+	10.8629i	0.329398	+	0.403440i
$726$	5.68149	+	6.95856i	0.210860	+	0.258256i
$727$	−26.4757	+	38.3566i	−0.981929	+	1.42257i	−0.0769876	+	0.997032i	$0.524530\pi$
$727$	−26.4757	+	38.3566i	−0.981929	+	1.42257i	−0.904941	+	0.425537i	$0.860085\pi$
$728$	17.5658	−	13.4057i	0.651033	−	0.496849i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−1.25420	+	4.33000i	−0.0464200	+	0.160260i
$731$	−16.6773	+	10.5461i	−0.616832	+	0.390061i
$732$	−18.6178	+	3.02568i	−0.688133	+	0.111832i
$733$	4.86917	+	12.8389i	0.179847	+	0.474217i	0.994376	−	0.105905i	$-0.0337740\pi$
$733$	4.86917	+	12.8389i	0.179847	+	0.474217i	−0.814529	+	0.580122i	$0.803005\pi$
$734$	5.96319	−	2.54068i	0.220105	−	0.0937781i
$735$	15.6141	+	16.2560i	0.575935	+	0.599611i
$736$	13.1374	−	6.89505i	0.484252	−	0.254155i
$737$	41.6705	+	3.36399i	1.53495	+	0.123914i
$738$	0.382070	−	1.31906i	0.0140642	−	0.0485552i
$739$	−34.6886	+	36.1147i	−1.27604	+	1.32850i	−0.357119	+	0.934059i	$0.616241\pi$
$739$	−34.6886	+	36.1147i	−1.27604	+	1.32850i	−0.918922	+	0.394440i	$0.870938\pi$
$740$	−6.70301	+	17.6744i	−0.246407	+	0.649723i
$741$	−18.8930	−	16.4883i	−0.694053	−	0.605712i
$742$	−3.47605	−	9.16560i	−0.127610	−	0.336480i
$743$	−17.5397	−	7.47295i	−0.643468	−	0.274156i	0.0454819	−	0.998965i	$-0.485518\pi$
$743$	−17.5397	−	7.47295i	−0.643468	−	0.274156i	−0.688950	+	0.724809i	$0.741928\pi$
$744$	−0.138426	+	3.43501i	−0.00507495	+	0.125934i
$745$	6.12165	−	7.49766i	0.224280	−	0.274693i
$746$	−8.18640			−0.299725
$747$	2.84437	−	3.48373i	0.104070	−	0.127463i
$748$	11.5609	+	39.9129i	0.422709	+	1.45936i
$749$	−28.8828	−	25.5879i	−1.05535	−	0.934962i
$750$	3.06536	+	3.19138i	0.111931	+	0.116533i
$751$	41.6508	−	13.9051i	1.51986	−	0.507403i	0.570419	−	0.821354i	$-0.306781\pi$
$751$	41.6508	−	13.9051i	1.51986	−	0.507403i	0.949439	+	0.313951i	$0.101653\pi$
$752$	−18.2771	−	13.7343i	−0.666496	−	0.500839i
$753$	−1.59174	+	13.1092i	−0.0580064	+	0.477725i
$754$	−8.07004	+	10.0357i	−0.293894	+	0.365477i
$755$	−4.48766	−	36.9592i	−0.163323	−	1.34508i
$756$	−4.06223	+	7.03599i	−0.147742	+	0.255896i
$757$	−4.04786	−	3.04177i	−0.147122	−	0.110555i	0.524633	−	0.851329i	$-0.324203\pi$
$757$	−4.04786	−	3.04177i	−0.147122	−	0.110555i	−0.671755	+	0.740774i	$0.734459\pi$
$758$	0.158197	+	3.92563i	0.00574599	+	0.142585i
$759$	7.87343	−	20.7605i	0.285788	−	0.753560i
$760$	3.70244	−	18.1358i	0.134302	−	0.657854i
$761$	7.10206	−	34.7882i	0.257449	−	1.26107i	−0.621218	−	0.783637i	$-0.713362\pi$
$761$	7.10206	−	34.7882i	0.257449	−	1.26107i	0.878668	−	0.477433i	$-0.158433\pi$
$762$	−0.849485	+	2.23991i	−0.0307736	+	0.0811433i
$763$	−1.71035	−	42.4420i	−0.0619189	−	1.53650i
$764$	15.5250	+	11.6663i	0.561676	+	0.422072i
$765$	3.52020	−	6.09716i	0.127273	−	0.220443i
$766$	−0.760263	−	6.26133i	−0.0274694	−	0.226231i
$767$	18.6988	+	6.08817i	0.675174	+	0.219831i
$768$	0.772705	−	6.36380i	0.0278826	−	0.229634i
$769$	38.7733	+	29.1363i	1.39820	+	1.05068i	0.990492	+	0.137568i	$0.0439286\pi$
$769$	38.7733	+	29.1363i	1.39820	+	1.05068i	0.407709	+	0.913112i	$0.366328\pi$
$770$	16.9607	−	5.66231i	0.611221	−	0.204056i
$771$	4.23562	+	4.40975i	0.152542	+	0.158813i
$772$	−16.8687	−	14.9444i	−0.607118	−	0.537860i
$773$	−2.52985	−	8.73405i	−0.0909923	−	0.314142i	0.902092	−	0.431543i	$-0.142031\pi$
$773$	−2.52985	−	8.73405i	−0.0909923	−	0.314142i	−0.993085	+	0.117401i	$0.962544\pi$
$774$	−1.21983	+	1.49402i	−0.0438459	+	0.0537015i
$775$	−3.49030			−0.125375
$776$	−2.02260	+	2.47724i	−0.0726073	+	0.0889278i
$777$	−0.938608	+	23.2913i	−0.0336724	+	0.835572i
$778$	−11.1690	−	4.75865i	−0.400427	−	0.170606i
$779$	−9.29857	−	24.5183i	−0.333156	−	0.878459i
$780$	7.14819	−	10.5227i	0.255946	−	0.376774i
$781$	−13.1244	+	34.6061i	−0.469627	+	1.23830i
$782$	−3.49550	+	3.63920i	−0.124999	+	0.130138i
$783$	2.72824	−	9.41897i	0.0974992	−	0.336606i
$784$	−38.3083	−	3.09257i	−1.36815	−	0.110449i
$785$	−0.473243	+	0.248377i	−0.0168908	+	0.00886496i
$786$	2.23173	+	2.32347i	0.0796031	+	0.0828756i
$787$	12.6818	−	5.40321i	0.452057	−	0.192604i	−0.153924	−	0.988083i	$-0.549191\pi$
$787$	12.6818	−	5.40321i	0.452057	−	0.192604i	0.605981	+	0.795479i	$0.292781\pi$
$788$	10.1258	+	26.6996i	0.360717	+	0.951133i
$789$	−3.36399	+	0.546702i	−0.119761	+	0.0194631i
$790$	−5.64942	+	3.57248i	−0.200997	+	0.127103i
$791$	−12.0757	+	41.6903i	−0.429364	+	1.48234i
$792$	4.77860	+	6.92299i	0.169800	+	0.245998i
$793$	33.3982	−	14.5245i	1.18601	−	0.515779i
$794$	−0.272034	+	0.394110i	−0.00965414	+	0.0139864i
$795$	−7.39171	−	9.05320i	−0.262157	−	0.321084i
$796$	4.74867	+	5.81607i	0.168312	+	0.206145i
$797$	−37.7607	+	28.3754i	−1.33755	+	1.00511i	−0.339640	+	0.940556i	$0.610305\pi$
$797$	−37.7607	+	28.3754i	−1.33755	+	1.00511i	−0.997914	+	0.0645510i	$0.979438\pi$
$798$	−1.32848	−	10.9410i	−0.0470276	−	0.387307i
$799$	25.0824	+	8.37372i	0.887350	+	0.296241i
$800$	−5.68850	−	0.459223i	−0.201119	−	0.0162360i
$801$	−0.0360073	+	0.0318997i	−0.00127226	+	0.00112712i
$802$	5.56829	+	3.52117i	0.196623	+	0.124337i
$803$	−35.9892	−	15.3336i	−1.27003	−	0.541110i
$804$	12.9029	+	2.09692i	0.455049	+	0.0739527i
$805$	−22.8771	−	20.2674i	−0.806313	−	0.714331i
$806$	−0.664470	−	3.13545i	−0.0234050	−	0.110442i
$807$	5.76088	−	5.10369i	0.202793	−	0.179659i
$808$	11.8550	−	7.49668i	0.417059	−	0.263732i
$809$	−42.3600	+	3.41965i	−1.48930	+	0.120228i	−0.798138	−	0.602475i	$-0.794181\pi$
$809$	−42.3600	+	3.41965i	−1.48930	+	0.120228i	−0.691159	+	0.722703i	$0.742899\pi$
$810$	0.137654	−	0.674273i	0.00483666	−	0.0236915i
$811$	−1.78349	−	0.439590i	−0.0626267	−	0.0154361i	0.207878	−	0.978155i	$-0.433344\pi$
$811$	−1.78349	−	0.439590i	−0.0626267	−	0.0154361i	−0.270505	+	0.962719i	$0.587191\pi$
$812$	78.6378	−	12.7799i	2.75965	−	0.448486i
$813$	−0.734168	−	0.464260i	−0.0257484	−	0.0162823i
$814$	10.3189	+	5.41576i	0.361676	+	0.189822i
$815$	5.21971	+	18.0205i	0.182839	+	0.631232i
$816$	2.40121	+	11.7619i	0.0840591	+	0.411749i
$817$	−1.48295	+	36.7991i	−0.0518820	+	1.28744i
$818$	−5.18443	−	2.72100i	−0.181269	−	0.0951374i
$819$	4.25209	−	15.0999i	0.148580	−	0.527632i
$820$	11.7788	−	6.18198i	0.411333	−	0.215884i
$821$	1.09702	+	2.31193i	0.0382864	+	0.0806869i	0.921692	−	0.387921i	$-0.126807\pi$
$821$	1.09702	+	2.31193i	0.0382864	+	0.0806869i	−0.883406	+	0.468608i	$0.844756\pi$
$822$	1.30526	−	2.26078i	0.0455263	−	0.0788539i
$823$	17.6803	+	30.6232i	0.616297	+	1.06746i	0.990156	+	0.139972i	$0.0447011\pi$
$823$	17.6803	+	30.6232i	0.616297	+	1.06746i	−0.373859	+	0.927486i	$0.621966\pi$
$824$	15.9625	−	23.1257i	0.556081	−	0.805622i
$825$	−6.82767	+	5.13066i	−0.237709	+	0.178627i
$826$	4.32154	+	7.48512i	0.150366	+	0.260441i
$827$	2.80984	−	23.1411i	0.0977076	−	0.804694i	−0.858664	−	0.512540i	$-0.828705\pi$
$827$	2.80984	−	23.1411i	0.0977076	−	0.804694i	0.956371	−	0.292155i	$-0.0943722\pi$
$828$	2.97627	−	6.27236i	0.103433	−	0.217980i
$829$	−18.5431	+	19.3054i	−0.644028	+	0.670504i	−0.960558	−	0.278078i	$-0.910303\pi$
$829$	−18.5431	+	19.3054i	−0.644028	+	0.670504i	0.316531	+	0.948582i	$0.397482\pi$
$830$	−3.08500	+	0.249047i	−0.107082	+	0.00864456i
$831$	−4.85991	−	1.19786i	−0.168588	−	0.0415533i
$832$	2.30150	+	17.8430i	0.0797902	+	0.618593i
$833$	43.1611	−	10.6382i	1.49544	−	0.368593i
$834$	−2.42091	+	0.808219i	−0.0838293	+	0.0279863i
$835$	3.93453	+	8.29185i	0.136160	+	0.286951i
$836$	73.5665	+	24.5601i	2.54435	+	0.849429i
$837$	1.38641	+	2.00856i	0.0479212	+	0.0694259i
$838$	5.18277	−	10.9225i	0.179036	−	0.377310i
$839$	1.16171	+	28.8276i	0.0401068	+	0.995240i	0.886513	+	0.462703i	$0.153120\pi$
$839$	1.16171	+	28.8276i	0.0401068	+	0.995240i	−0.846407	+	0.532537i	$0.821239\pi$
$840$	11.2429	−	2.77113i	0.387918	−	0.0956132i
$841$	−61.7860	+	26.3246i	−2.13055	+	0.907743i
$842$	3.54321	+	0.575827i	0.122107	+	0.0198443i
$843$	−4.18907	−	20.5194i	−0.144279	−	0.706726i
$844$	27.6094			0.950356
$845$	−8.36690	+	23.0934i	−0.287830	+	0.794438i
$846$	2.58476			0.0888658
$847$	21.4645	+	105.140i	0.737530	+	3.61266i
$848$	19.6702	+	3.19671i	0.675477	+	0.109776i
$849$	−9.90062	+	4.21826i	−0.339788	+	0.144770i
$850$	1.88455	−	0.464500i	0.0646396	−	0.0159322i
$851$	−0.802079	−	19.9034i	−0.0274949	−	0.682279i
$852$	−4.96121	+	10.4555i	−0.169968	+	0.358200i
$853$	−23.3854	−	33.8796i	−0.800701	−	1.16002i	−0.984211	−	0.176998i	$-0.943361\pi$
$853$	−23.3854	−	33.8796i	−0.800701	−	1.16002i	0.183510	−	0.983018i	$-0.441254\pi$
$854$	15.1833	+	5.06894i	0.519562	+	0.173455i
$855$	−5.63328	−	11.8719i	−0.192654	−	0.406010i
$856$	−11.8498	+	3.95604i	−0.405017	+	0.135215i
$857$	−21.3463	+	5.26140i	−0.729177	+	0.179726i	−0.586392	−	0.810028i	$-0.699452\pi$
$857$	−21.3463	+	5.26140i	−0.729177	+	0.179726i	−0.142785	+	0.989754i	$0.545606\pi$
$858$	−5.90887	−	5.15677i	−0.201725	−	0.176049i
$859$	9.15074	+	2.25546i	0.312219	+	0.0769552i	0.392312	−	0.919832i	$-0.371675\pi$
$859$	9.15074	+	2.25546i	0.312219	+	0.0769552i	−0.0800925	+	0.996787i	$0.525522\pi$
$860$	−18.6226	+	1.50337i	−0.635027	+	0.0512646i
$861$	11.3636	−	11.8307i	0.387270	−	0.403191i
$862$	−4.64198	+	9.78278i	−0.158107	+	0.333203i
$863$	2.85829	−	23.5401i	0.0972973	−	0.801315i	−0.859616	−	0.510941i	$-0.829297\pi$
$863$	2.85829	−	23.5401i	0.0972973	−	0.801315i	0.956913	−	0.290374i	$-0.0937798\pi$
$864$	1.99530	+	3.45597i	0.0678816	+	0.117574i
$865$	4.12445	−	3.09932i	0.140236	−	0.105380i
$866$	−4.13000	+	5.98334i	−0.140343	+	0.203322i
$867$	1.55760	+	2.69784i	0.0528989	+	0.0916236i
$868$	−9.91419	+	17.1719i	−0.336510	+	0.582852i
$869$	−24.8661	−	52.4042i	−0.843525	−	1.77769i
$870$	−5.97540	+	3.13613i	−0.202585	+	0.106325i
$871$	−25.1427	+	2.21832i	−0.851929	+	0.0751650i
$872$	−12.1767	−	6.39084i	−0.412356	−	0.216421i
$873$	−0.0914195	+	2.26855i	−0.00309408	+	0.0767788i
$874$	1.88388	+	9.22786i	0.0637232	+	0.312137i
$875$	14.7062	+	50.7719i	0.497162	+	1.71640i
$876$	−10.8310	−	5.68455i	−0.365946	−	0.192063i
$877$	−15.7655	−	9.96951i	−0.532364	−	0.336646i	0.241086	−	0.970504i	$-0.422496\pi$
$877$	−15.7655	−	9.96951i	−0.532364	−	0.336646i	−0.773450	+	0.633857i	$0.781471\pi$
$878$	6.12096	−	0.994753i	0.206572	−	0.0335713i
$879$	−9.94753	−	2.45185i	−0.335522	−	0.0826987i
$880$	−7.27114	+	35.6164i	−0.245110	+	1.20063i
$881$	−42.1986	+	3.40662i	−1.42171	+	0.114772i	−0.767260	−	0.641337i	$-0.778380\pi$
$881$	−42.1986	+	3.40662i	−1.42171	+	0.114772i	−0.654446	+	0.756109i	$0.727098\pi$
$882$	3.67247	−	2.32233i	0.123659	−	0.0781970i
$883$	−17.8967	+	15.8551i	−0.602272	+	0.533566i	−0.908226	−	0.418480i	$-0.862563\pi$
$883$	−17.8967	+	15.8551i	−0.602272	+	0.533566i	0.305954	+	0.952046i	$0.401025\pi$
$884$	−10.9235	−	22.5849i	−0.367397	−	0.759614i
$885$	7.71342	+	6.83349i	0.259284	+	0.229705i
$886$	2.70686	+	0.439908i	0.0909387	+	0.0147790i
$887$	28.2654	+	12.0428i	0.949060	+	0.404357i	0.810330	−	0.585974i	$-0.199288\pi$
$887$	28.2654	+	12.0428i	0.949060	+	0.404357i	0.138730	+	0.990330i	$0.455698\pi$
$888$	6.37847	+	4.03350i	0.214047	+	0.135355i
$889$	−21.4193	+	18.9758i	−0.718380	+	0.636430i
$890$	0.0329978	+	0.00266385i	0.00110609	+	8.92926e-5i
$891$	5.66460	+	1.89112i	0.189771	+	0.0633549i
$892$	−1.83185	−	15.0867i	−0.0613350	−	0.505139i
$893$	39.4566	−	29.6497i	1.32037	−	0.992191i
$894$	−1.18009	−	1.44535i	−0.0394682	−	0.0483398i
$895$	21.5923	+	26.4458i	0.721752	+	0.883986i
$896$	−24.2178	+	35.0855i	−0.809060	+	1.17213i
$897$	−2.58351	+	13.1540i	−0.0862608	+	0.439198i
$898$	6.51575	+	9.43969i	0.217433	+	0.315006i
$899$	6.65848	−	22.9877i	0.222073	−	0.766684i
$900$	−2.25708	+	1.42729i	−0.0752360	+	0.0475763i
$901$	−22.7512	+	3.69742i	−0.757951	+	0.123179i
$902$	−2.90816	−	7.66819i	−0.0968311	−	0.255323i
$903$	−21.1959	+	9.03072i	−0.705355	+	0.300524i
$904$	9.73431	+	10.1345i	0.323758	+	0.337068i
$905$	−24.4816	+	12.8489i	−0.813796	+	0.427113i
$906$	−7.15382	−	0.577516i	−0.237670	−	0.0191867i
$907$	−0.427850	+	1.47711i	−0.0142065	+	0.0490466i	−0.967308	−	0.253603i	$-0.918384\pi$
$907$	−0.427850	+	1.47711i	−0.0142065	+	0.0490466i	0.953102	+	0.302650i	$0.0978714\pi$
$908$	−3.51566	+	3.66019i	−0.116671	+	0.121468i
$909$	3.53107	−	9.31067i	0.117118	−	0.308815i
$910$	−9.52138	+	5.08801i	−0.315631	+	0.168666i
$911$	12.4200	+	32.7488i	0.411492	+	1.08502i	0.967284	+	0.253694i	$0.0816457\pi$
$911$	12.4200	+	32.7488i	0.411492	+	1.08502i	−0.555792	+	0.831321i	$0.687585\pi$
$912$	20.6130	+	8.78237i	0.682564	+	0.290813i
$913$	1.08148	−	26.8365i	0.0357916	−	0.888160i
$914$	5.40539	−	6.62040i	0.178794	−	0.218983i
$915$	19.0850			0.630932
$916$	11.8606	−	14.5265i	0.391884	−	0.479970i
$917$	10.7068	+	36.9643i	0.353571	+	1.22067i
$918$	−1.01588	−	0.899992i	−0.0335291	−	0.0297042i
$919$	8.30251	+	8.64382i	0.273874	+	0.285133i	0.843908	−	0.536488i	$-0.180249\pi$
$919$	8.30251	+	8.64382i	0.273874	+	0.285133i	−0.570034	+	0.821621i	$0.693070\pi$
$920$	−9.38583	+	3.13345i	−0.309442	+	0.103307i
$921$	10.7546	+	8.08159i	0.354378	+	0.266298i
$922$	−0.0566031	+	0.466169i	−0.00186412	+	0.0153524i
$923$	4.30649	−	21.9266i	0.141750	−	0.721723i
$924$	5.84829	+	48.1650i	0.192395	+	1.58451i
$925$	−3.83102	+	6.63552i	−0.125963	+	0.218175i
$926$	−12.4020	−	9.31951i	−0.407556	−	0.306258i
$927$	−0.803257	−	19.9326i	−0.0263824	−	0.654673i
$928$	13.8765	−	36.5894i	0.455520	−	1.20111i
$929$	−3.34542	+	16.3870i	−0.109760	+	0.537639i	0.887312	+	0.461169i	$0.152570\pi$
$929$	−3.34542	+	16.3870i	−0.109760	+	0.537639i	−0.997072	+	0.0764696i	$0.975635\pi$
$930$	0.335955	−	1.64562i	0.0110164	−	0.0539619i
$931$	29.4213	−	77.5776i	0.964244	−	2.54250i
$932$	0.576946	+	14.3168i	0.0188985	+	0.468961i
$933$	23.9313	+	17.9832i	0.783475	+	0.588743i
$934$	1.32258	−	2.29078i	0.0432761	−	0.0749564i
$935$	−5.06794	−	41.7383i	−0.165739	−	1.36499i
$936$	−3.54537	−	3.63652i	−0.115884	−	0.118863i
$937$	4.64984	−	38.2949i	0.151904	−	1.25104i	−0.694889	−	0.719117i	$-0.744546\pi$
$937$	4.64984	−	38.2949i	0.151904	−	1.25104i	0.846793	−	0.531923i	$-0.178530\pi$
$938$	−8.86868	−	6.66438i	−0.289573	−	0.217600i
$939$	6.31156	−	2.10711i	0.205970	−	0.0687629i
$940$	17.3442	+	18.0573i	0.565706	+	0.588963i
$941$	−32.3875	−	28.6928i	−1.05580	−	0.935359i	−0.0577863	−	0.998329i	$-0.518404\pi$
$941$	−32.3875	−	28.6928i	−1.05580	−	0.935359i	−0.998015	+	0.0629703i	$0.979943\pi$
$942$	0.0286648	+	0.0989625i	0.000933951	+	0.00322437i
$943$	−8.86565	+	10.8584i	−0.288705	+	0.353600i
$944$	−17.5710			−0.571886
$945$	5.19903	−	6.36765i	0.169124	−	0.207140i
$946$	−0.463799	+	11.5091i	−0.0150794	+	0.374192i
$947$	−30.9598	−	13.1908i	−1.00606	−	0.428642i	−0.174846	−	0.984596i	$-0.555943\pi$
$947$	−30.9598	−	13.1908i	−1.00606	−	0.428642i	−0.831213	+	0.555954i	$0.812353\pi$
$948$	−6.43153	−	16.9585i	−0.208886	−	0.550788i
$949$	22.9736	+	5.48131i	0.745754	+	0.177931i
$950$	1.28463	−	3.38729i	0.0416789	−	0.109898i
$951$	−20.7673	+	21.6210i	−0.673424	+	0.701109i
$952$	6.35350	−	21.9348i	0.205918	−	0.710912i
$953$	−10.0234	−	0.809173i	−0.324690	−	0.0262117i	−0.0829530	−	0.996553i	$-0.526435\pi$
$953$	−10.0234	−	0.809173i	−0.324690	−	0.0262117i	−0.241737	+	0.970342i	$0.577717\pi$
$954$	−1.99497	+	1.04704i	−0.0645896	+	0.0338992i
$955$	−13.6116	−	14.1712i	−0.440462	−	0.458569i
$956$	−25.7769	+	10.9825i	−0.833684	+	0.355200i
$957$	−20.7662	−	54.7560i	−0.671277	−	1.77001i
$958$	8.77614	−	1.42626i	0.283544	−	0.0460804i
$959$	26.3560	−	16.6665i	0.851079	−	0.538190i
$960$	−2.62295	+	9.05547i	−0.0846553	+	0.292264i
$961$	−14.2264	−	20.6105i	−0.458915	−	0.664853i
$962$	−6.69025	−	2.17829i	−0.215702	−	0.0702309i
$963$	−5.03810	+	7.29895i	−0.162351	+	0.235206i
$964$	19.9722	+	24.4615i	0.643261	+	0.787851i
$965$	14.4215	+	17.6632i	0.464246	+	0.568598i
$966$	−4.71019	+	3.53948i	−0.151548	+	0.113881i
$967$	−0.390861	−	3.21903i	−0.0125693	−	0.103517i	0.985074	−	0.172131i	$-0.0550653\pi$
$967$	−0.390861	−	3.21903i	−0.0125693	−	0.103517i	−0.997643	+	0.0686142i	$0.978142\pi$
$968$	32.9538	+	11.0016i	1.05917	+	0.353604i
$969$	−25.8314	−	2.08532i	−0.829823	−	0.0669902i
$970$	1.16950	−	1.03609i	0.0375505	−	0.0332668i
$971$	−12.8591	−	8.13161i	−0.412669	−	0.260956i	0.311960	−	0.950095i	$-0.399014\pi$
$971$	−12.8591	−	8.13161i	−0.412669	−	0.260956i	−0.724629	+	0.689139i	$0.757989\pi$
$972$	1.71791	+	0.731934i	0.0551020	+	0.0234768i
$973$	−30.0927	−	4.89053i	−0.964727	−	0.156783i
$974$	−7.04568	−	6.24192i	−0.225758	−	0.200004i
$975$	3.54413	−	3.74526i	0.113503	−	0.119944i
$976$	−24.3578	+	21.5791i	−0.779674	+	0.690731i
$977$	24.7490	−	15.6503i	0.791791	−	0.500698i	−0.0763113	−	0.997084i	$-0.524314\pi$
$977$	24.7490	−	15.6503i	0.791791	−	0.500698i	0.868102	+	0.496386i	$0.165340\pi$
$978$	3.60495	−	0.291022i	0.115274	−	0.00930586i
$979$	−0.0574637	+	0.281476i	−0.00183655	+	0.00899600i
$980$	40.8670	+	10.0728i	1.30545	+	0.321764i
$981$	−9.63641	+	1.56607i	−0.307667	+	0.0500008i
$982$	8.76076	+	5.53997i	0.279567	+	0.176788i
$983$	21.7894	+	11.4360i	0.694973	+	0.364750i	0.774929	−	0.632048i	$-0.217786\pi$
$983$	21.7894	+	11.4360i	0.694973	+	0.364750i	−0.0799556	+	0.996798i	$0.525478\pi$
$984$	−1.47759	−	5.10124i	−0.0471039	−	0.162622i
$985$	−5.77931	−	28.3089i	−0.184144	−	0.901997i
$986$	−0.535896	+	13.2981i	−0.0170664	+	0.423499i
$987$	27.3390	+	14.3486i	0.870211	+	0.456722i
$988$	−46.2738	−	7.16691i	−1.47217	−	0.228010i
$989$	17.4330	−	9.14956i	0.554338	−	0.290939i
$990$	−1.76183	−	3.71298i	−0.0559946	−	0.118006i
$991$	−27.9715	+	48.4481i	−0.888545	+	1.53900i	−0.0469489	+	0.998897i	$0.514950\pi$
$991$	−27.9715	+	48.4481i	−0.888545	+	1.53900i	−0.841596	+	0.540108i	$0.818384\pi$
$992$	4.86970	+	8.43456i	0.154613	+	0.267798i
$993$	−16.3643	+	23.7078i	−0.519305	+	0.752343i
$994$	7.85151	−	5.90002i	0.249035	−	0.187137i
$995$	−3.79860	−	6.57937i	−0.120424	−	0.208580i
$996$	1.01229	−	8.33697i	0.0320757	−	0.264167i
$997$	18.3015	−	38.5696i	0.579614	−	1.22151i	−0.375926	−	0.926650i	$-0.622675\pi$
$997$	18.3015	−	38.5696i	0.579614	−	1.22151i	0.955540	−	0.294861i	$-0.0952734\pi$
$998$	7.57969	−	7.89129i	0.239931	−	0.249794i
$999$	5.34028	−	0.431112i	0.168959	−	0.0136398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.490.10	yes	384
169.159	even	39	inner	507.2.q.b.328.10	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.328.10	✓	384	169.159	even	39	inner
507.2.q.b.490.10	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)

\(f(q)\)	\(=\)	\(q+(0.0728553 + 0.356869i) q^{2} +(0.987050 + 0.160411i) q^{3} +(1.71791 - 0.731934i) q^{4} +(-1.83451 + 0.452167i) q^{5} +(0.0146660 + 0.363934i) q^{6} +(-1.86517 + 3.93076i) q^{7} +(0.800175 + 1.15925i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(0.0728553 + 0.356869i) q^{2} +(0.987050 + 0.160411i) q^{3} +(1.71791 - 0.731934i) q^{4} +(-1.83451 + 0.452167i) q^{5} +(0.0146660 + 0.363934i) q^{6} +(-1.86517 + 3.93076i) q^{7} +(0.800175 + 1.15925i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-0.295018 - 0.621737i) q^{10} +(5.66460 - 1.89112i) q^{11} +(1.81308 - 0.446883i) q^{12} +(-3.17999 + 1.69931i) q^{13} +(-1.53865 - 0.379243i) q^{14} +(-1.88329 + 0.152035i) q^{15} +(2.23169 - 2.32344i) q^{16} +(-1.59741 + 3.36646i) q^{17} +(-0.0439030 + 0.361574i) q^{18} +(3.47743 + 6.02308i) q^{19} +(-2.82057 + 2.11952i) q^{20} +(-2.47155 + 3.58066i) q^{21} +(1.08758 + 1.88374i) q^{22} +(1.85898 - 3.21984i) q^{23} +(0.603856 + 1.27260i) q^{24} +(-1.26630 + 0.664606i) q^{25} +(-0.838111 - 1.01103i) q^{26} +(0.885456 + 0.464723i) q^{27} +(-0.327139 + 8.11787i) q^{28} +(-1.96148 - 9.60796i) q^{29} +(-0.191464 - 0.661010i) q^{30} +(2.16103 + 1.13419i) q^{31} +(3.37282 + 2.13284i) q^{32} +(5.89460 - 0.957966i) q^{33} +(-1.31777 - 0.324800i) q^{34} +(1.64431 - 8.05438i) q^{35} +(1.86128 - 0.150258i) q^{36} +(4.52824 - 2.86348i) q^{37} +(-1.89610 + 1.67980i) q^{38} +(-3.41140 + 1.16720i) q^{39} +(-1.99211 - 1.76485i) q^{40} +(-3.72154 - 0.604809i) q^{41} +(-1.45789 - 0.621149i) q^{42} +(4.47565 + 2.83023i) q^{43} +(8.34711 - 7.39489i) q^{44} +(-1.88329 - 0.152035i) q^{45} +(1.28450 + 0.428829i) q^{46} +(-0.855389 - 7.04476i) q^{47} +(2.57550 - 1.93536i) q^{48} +(-7.54488 - 9.24079i) q^{49} +(-0.329434 - 0.403483i) q^{50} +(-2.11674 + 3.06663i) q^{51} +(-4.21916 + 5.24681i) q^{52} +(3.51392 + 5.09080i) q^{53} +(-0.101335 + 0.349849i) q^{54} +(-9.53667 + 6.03063i) q^{55} +(-6.04920 + 0.983091i) q^{56} +(2.46623 + 6.50290i) q^{57} +(3.28588 - 1.39998i) q^{58} +(-3.77817 - 3.93349i) q^{59} +(-3.12404 + 1.63962i) q^{60} +(-10.0683 - 0.812795i) q^{61} +(-0.247316 + 0.853835i) q^{62} +(-3.01392 + 3.13783i) q^{63} +(1.76939 - 4.66549i) q^{64} +(5.06536 - 4.55530i) q^{65} +(0.771321 + 2.03381i) q^{66} +(6.44025 + 2.74393i) q^{67} +(-0.280176 + 6.95249i) q^{68} +(2.35140 - 2.87995i) q^{69} +2.99416 q^{70} +(-3.91960 + 4.80064i) q^{71} +(0.391897 + 1.35298i) q^{72} +(-4.90318 - 4.34383i) q^{73} +(1.35179 + 1.40737i) q^{74} +(-1.35651 + 0.452870i) q^{75} +(10.3824 + 7.80188i) q^{76} +(-3.13189 + 25.7934i) q^{77} +(-0.665076 - 1.13238i) q^{78} +(-1.17076 - 9.64204i) q^{79} +(-3.04349 + 5.27148i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.0552963 - 1.37216i) q^{82} +(1.59481 - 4.20516i) q^{83} +(-1.62510 + 7.96027i) q^{84} +(1.40826 - 6.89811i) q^{85} +(-0.683946 + 1.80342i) q^{86} +(-0.394853 - 9.79818i) q^{87} +(6.72496 + 5.05348i) q^{88} +(-0.0240526 + 0.0416604i) q^{89} +(-0.0829510 - 0.683163i) q^{90} +(-0.748376 - 15.6693i) q^{91} +(0.836847 - 6.89206i) q^{92} +(1.95110 + 1.46616i) q^{93} +(2.45174 - 0.818510i) q^{94} +(-9.10282 - 9.47704i) q^{95} +(2.98701 + 2.64626i) q^{96} +(0.631663 + 2.18075i) q^{97} +(2.74807 - 3.36577i) q^{98} +5.97194 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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