LMFDB - Embedded newform 507.2.m.b.40.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.8
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374061 - 0.0921977i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.63949 - 0.860471i) q^{4} +(0.205107 - 0.297149i) q^{5} +(-0.136614 + 0.360220i) q^{6} +(-0.762777 - 0.675762i) q^{7} +(1.11067 + 0.983969i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-0.374061 - 0.0921977i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.63949 - 0.860471i) q^{4} +(0.205107 - 0.297149i) q^{5} +(-0.136614 + 0.360220i) q^{6} +(-0.762777 - 0.675762i) q^{7} +(1.11067 + 0.983969i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-0.104119 + 0.0922415i) q^{10} +(1.20983 - 0.298196i) q^{11} +(-1.05182 + 1.52382i) q^{12} +(-0.952578 - 3.47744i) q^{13} +(0.223021 + 0.323102i) q^{14} +(-0.270260 - 0.239429i) q^{15} +(1.77889 + 2.57717i) q^{16} +(-2.55968 - 2.26768i) q^{17} +(0.341127 + 0.179037i) q^{18} -6.89773 q^{19} +(-0.591960 + 0.310685i) q^{20} +(-0.762777 + 0.675762i) q^{21} -0.480043 q^{22} -1.75584 q^{23} +(1.11067 - 0.983969i) q^{24} +(1.72680 + 4.55319i) q^{25} +(0.0357100 + 1.38860i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.669093 + 1.76425i) q^{28} +(-7.94105 - 1.95729i) q^{29} +(0.0790188 + 0.114478i) q^{30} +(-2.57579 + 6.79180i) q^{31} +(-1.48016 - 3.90286i) q^{32} +(-0.150193 - 1.23695i) q^{33} +(0.748401 + 1.08425i) q^{34} +(-0.357253 + 0.0880551i) q^{35} +(1.38593 + 1.22782i) q^{36} +(-0.145034 + 0.382424i) q^{37} +(2.58017 + 0.635955i) q^{38} +(-3.56691 + 0.526473i) q^{39} +(0.520193 - 0.128216i) q^{40} +(-0.343109 + 2.82575i) q^{41} +(0.347629 - 0.182450i) q^{42} +(0.912555 + 2.40621i) q^{43} +(-2.24009 - 0.552133i) q^{44} +(-0.270260 + 0.239429i) q^{45} +(0.656792 + 0.161885i) q^{46} +(7.59258 - 3.98490i) q^{47} +(2.77280 - 1.45528i) q^{48} +(-0.718581 - 5.91805i) q^{49} +(-0.226133 - 1.86237i) q^{50} +(-2.55968 + 2.26768i) q^{51} +(-1.43049 + 6.52090i) q^{52} +(-5.53585 - 4.90434i) q^{53} +(0.218850 - 0.317059i) q^{54} +(0.159536 - 0.420662i) q^{55} +(-0.182266 - 1.50110i) q^{56} +(-0.831430 + 6.84744i) q^{57} +(2.78998 + 1.46429i) q^{58} +(3.96613 - 5.74594i) q^{59} +(0.237067 + 0.625093i) q^{60} +(-2.66305 + 2.35925i) q^{61} +(1.58969 - 2.30306i) q^{62} +(0.578892 + 0.838670i) q^{63} +(-0.561086 - 4.62096i) q^{64} +(-1.22870 - 0.430191i) q^{65} +(-0.0578627 + 0.476543i) q^{66} +(-1.16869 + 0.613374i) q^{67} +(2.24530 + 5.92037i) q^{68} +(-0.211644 + 1.74304i) q^{69} +0.141753 q^{70} +(1.95891 - 16.1331i) q^{71} +(-0.842918 - 1.22118i) q^{72} +(0.806053 - 0.198674i) q^{73} +(0.0895103 - 0.129678i) q^{74} +(4.72813 - 1.16538i) q^{75} +(11.3088 + 5.93530i) q^{76} +(-1.12434 - 0.590099i) q^{77} +(1.38278 + 0.131928i) q^{78} +(5.24621 - 2.75343i) q^{79} +1.13067 q^{80} +(0.885456 + 0.464723i) q^{81} +(0.388871 - 1.02537i) q^{82} +(-1.40096 - 11.5380i) q^{83} +(1.83204 - 0.451557i) q^{84} +(-1.19885 + 0.295490i) q^{85} +(-0.119504 - 0.984204i) q^{86} +(-2.90021 + 7.64722i) q^{87} +(1.63714 + 0.859237i) q^{88} +7.05692 q^{89} +(0.123168 - 0.0646438i) q^{90} +(-1.62332 + 3.29623i) q^{91} +(2.87869 + 1.51085i) q^{92} +(6.43180 + 3.37567i) q^{93} +(-3.20749 + 0.790574i) q^{94} +(-1.41478 + 2.04966i) q^{95} +(-4.05282 + 0.998930i) q^{96} +(-0.162069 - 0.234797i) q^{97} +(-0.276838 + 2.27996i) q^{98} -1.24604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	−0.374061	−	0.0921977i	−0.264501	−	0.0651936i	0.104835	−	0.994490i	$-0.466569\pi$
$2$	−0.374061	−	0.0921977i	−0.264501	−	0.0651936i	−0.369336	+	0.929296i	$0.620415\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	−1.63949	−	0.860471i	−0.819746	−	0.430236i
$5$	0.205107	−	0.297149i	0.0917268	−	0.132889i	−0.774434	−	0.632655i	$-0.781965\pi$
$5$	0.205107	−	0.297149i	0.0917268	−	0.132889i	0.866161	+	0.499766i	$0.166581\pi$
$6$	−0.136614	+	0.360220i	−0.0557722	+	0.147059i
$7$	−0.762777	−	0.675762i	−0.288303	−	0.255414i	0.506558	−	0.862206i	$-0.330918\pi$
$7$	−0.762777	−	0.675762i	−0.288303	−	0.255414i	−0.794861	+	0.606792i	$0.792456\pi$
$8$	1.11067	+	0.983969i	0.392682	+	0.347886i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−0.104119	+	0.0922415i	−0.0329254	+	0.0291693i
$11$	1.20983	−	0.298196i	0.364777	−	0.0899095i	−0.0526668	−	0.998612i	$-0.516772\pi$
$11$	1.20983	−	0.298196i	0.364777	−	0.0899095i	0.417444	+	0.908703i	$0.362926\pi$
$12$	−1.05182	+	1.52382i	−0.303633	+	0.439889i
$13$	−0.952578	−	3.47744i	−0.264198	−	0.964469i
$13$	−0.952578	−	3.47744i	−0.264198	−	0.964469i
$14$	0.223021	+	0.323102i	0.0596050	+	0.0863527i
$15$	−0.270260	−	0.239429i	−0.0697808	−	0.0618204i
$16$	1.77889	+	2.57717i	0.444723	+	0.644293i
$17$	−2.55968	−	2.26768i	−0.620814	−	0.549993i	0.293007	−	0.956110i	$-0.405344\pi$
$17$	−2.55968	−	2.26768i	−0.620814	−	0.549993i	−0.913821	+	0.406117i	$0.866882\pi$
$18$	0.341127	+	0.179037i	0.0804044	+	0.0421995i
$19$	−6.89773			−1.58245			−0.791224	−	0.611526i	$-0.790556\pi$
$19$	−6.89773			−1.58245			−0.791224	+	0.611526i	$0.790556\pi$
$20$	−0.591960	+	0.310685i	−0.132366	+	0.0694712i
$21$	−0.762777	+	0.675762i	−0.166452	+	0.147463i
$22$	−0.480043			−0.102345
$23$	−1.75584			−0.366119			−0.183059	−	0.983102i	$-0.558600\pi$
$23$	−1.75584			−0.366119			−0.183059	+	0.983102i	$0.558600\pi$
$24$	1.11067	−	0.983969i	0.226715	−	0.200852i
$25$	1.72680	+	4.55319i	0.345359	+	0.910637i
$26$	0.0357100	+	1.38860i	0.00700331	+	0.272327i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	0.669093	+	1.76425i	0.126447	+	0.333413i
$29$	−7.94105	−	1.95729i	−1.47462	−	0.363460i	−0.581596	−	0.813478i	$-0.697572\pi$
$29$	−7.94105	−	1.95729i	−1.47462	−	0.363460i	−0.893020	+	0.450018i	$0.851418\pi$
$30$	0.0790188	+	0.114478i	0.0144268	+	0.0209008i
$31$	−2.57579	+	6.79180i	−0.462625	+	1.21984i	0.477384	+	0.878695i	$0.341585\pi$
$31$	−2.57579	+	6.79180i	−0.462625	+	1.21984i	−0.940010	+	0.341148i	$0.889184\pi$
$32$	−1.48016	−	3.90286i	−0.261658	−	0.689935i
$33$	−0.150193	−	1.23695i	−0.0261453	−	0.215326i
$34$	0.748401	+	1.08425i	0.128350	+	0.185947i
$35$	−0.357253	+	0.0880551i	−0.0603869	+	0.0148840i
$36$	1.38593	+	1.22782i	0.230988	+	0.204637i
$37$	−0.145034	+	0.382424i	−0.0238435	+	0.0628701i	−0.946409	−	0.322969i	$-0.895319\pi$
$37$	−0.145034	+	0.382424i	−0.0238435	+	0.0628701i	0.922566	+	0.385839i	$0.126088\pi$
$38$	2.58017	+	0.635955i	0.418559	+	0.103166i
$39$	−3.56691	+	0.526473i	−0.571162	+	0.0843032i
$40$	0.520193	−	0.128216i	0.0822497	−	0.0202727i
$41$	−0.343109	+	2.82575i	−0.0535846	+	0.441309i	0.941083	+	0.338176i	$0.109810\pi$
$41$	−0.343109	+	2.82575i	−0.0535846	+	0.441309i	−0.994668	+	0.103133i	$0.967113\pi$
$42$	0.347629	−	0.182450i	0.0536403	−	0.0281526i
$43$	0.912555	+	2.40621i	0.139163	+	0.366944i	0.986421	−	0.164239i	$-0.0525169\pi$
$43$	0.912555	+	2.40621i	0.139163	+	0.366944i	−0.847257	+	0.531183i	$0.821748\pi$
$44$	−2.24009	−	0.552133i	−0.337707	−	0.0832372i
$45$	−0.270260	+	0.239429i	−0.0402880	+	0.0356920i
$46$	0.656792	+	0.161885i	0.0968387	+	0.0238686i
$47$	7.59258	−	3.98490i	1.10749	−	0.581257i	0.191113	−	0.981568i	$-0.438790\pi$
$47$	7.59258	−	3.98490i	1.10749	−	0.581257i	0.916379	+	0.400311i	$0.131098\pi$
$48$	2.77280	−	1.45528i	0.400220	−	0.210052i
$49$	−0.718581	−	5.91805i	−0.102654	−	0.845436i
$50$	−0.226133	−	1.86237i	−0.0319801	−	0.263380i
$51$	−2.55968	+	2.26768i	−0.358427	+	0.317539i
$52$	−1.43049	+	6.52090i	−0.198374	+	0.904286i
$53$	−5.53585	−	4.90434i	−0.760408	−	0.673662i	0.191002	−	0.981590i	$-0.438826\pi$
$53$	−5.53585	−	4.90434i	−0.760408	−	0.673662i	−0.951410	+	0.307927i	$0.900365\pi$
$54$	0.218850	−	0.317059i	0.0297817	−	0.0431463i
$55$	0.159536	−	0.420662i	0.0215118	−	0.0567221i
$56$	−0.182266	−	1.50110i	−0.0243564	−	0.200593i
$57$	−0.831430	+	6.84744i	−0.110126	+	0.906966i
$58$	2.78998	+	1.46429i	0.366342	+	0.192271i
$59$	3.96613	−	5.74594i	0.516347	−	0.748057i	−0.474906	−	0.880037i	$-0.657518\pi$
$59$	3.96613	−	5.74594i	0.516347	−	0.748057i	0.991252	+	0.131979i	$0.0421332\pi$
$60$	0.237067	+	0.625093i	0.0306052	+	0.0806992i
$61$	−2.66305	+	2.35925i	−0.340968	+	0.302071i	−0.816177	−	0.577801i	$-0.803911\pi$
$61$	−2.66305	+	2.35925i	−0.340968	+	0.302071i	0.475209	+	0.879873i	$0.342372\pi$
$62$	1.58969	−	2.30306i	0.201891	−	0.292489i
$63$	0.578892	+	0.838670i	0.0729335	+	0.105662i
$64$	−0.561086	−	4.62096i	−0.0701357	−	0.577620i
$65$	−1.22870	−	0.430191i	−0.152402	−	0.0533586i
$66$	−0.0578627	+	0.476543i	−0.00712241	+	0.0586583i
$67$	−1.16869	+	0.613374i	−0.142778	+	0.0749355i	−0.534599	−	0.845106i	$-0.679537\pi$
$67$	−1.16869	+	0.613374i	−0.142778	+	0.0749355i	0.391821	+	0.920041i	$0.371845\pi$
$68$	2.24530	+	5.92037i	0.272283	+	0.717950i
$69$	−0.211644	+	1.74304i	−0.0254789	+	0.209838i
$70$	0.141753			0.0169427
$71$	1.95891	−	16.1331i	0.232480	−	1.91464i	−0.146453	−	0.989218i	$-0.546786\pi$
$71$	1.95891	−	16.1331i	0.232480	−	1.91464i	0.378933	−	0.925424i	$-0.376291\pi$
$72$	−0.842918	−	1.22118i	−0.0993389	−	0.143917i
$73$	0.806053	−	0.198674i	0.0943413	−	0.0232531i	−0.191862	−	0.981422i	$-0.561453\pi$
$73$	0.806053	−	0.198674i	0.0943413	−	0.0232531i	0.286204	+	0.958169i	$0.407607\pi$
$74$	0.0895103	−	0.129678i	0.0104054	−	0.0150748i
$75$	4.72813	−	1.16538i	0.545957	−	0.134566i
$76$	11.3088	+	5.93530i	1.29720	+	0.680826i
$77$	−1.12434	−	0.590099i	−0.128130	−	0.0672480i
$78$	1.38278	+	0.131928i	0.156569	+	0.0149379i
$79$	5.24621	−	2.75343i	0.590245	−	0.309785i	−0.143028	−	0.989719i	$-0.545684\pi$
$79$	5.24621	−	2.75343i	0.590245	−	0.309785i	0.733273	+	0.679934i	$0.237992\pi$
$80$	1.13067			0.126413
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	0.388871	−	1.02537i	0.0429437	−	0.113233i
$83$	−1.40096	−	11.5380i	−0.153776	−	1.26646i	−0.841410	−	0.540398i	$-0.818274\pi$
$83$	−1.40096	−	11.5380i	−0.153776	−	1.26646i	0.687634	−	0.726057i	$-0.258649\pi$
$84$	1.83204	−	0.451557i	0.199892	−	0.0492689i
$85$	−1.19885	+	0.295490i	−0.130033	+	0.0320504i
$86$	−0.119504	−	0.984204i	−0.0128864	−	0.106129i
$87$	−2.90021	+	7.64722i	−0.310935	+	0.819869i
$88$	1.63714	+	0.859237i	0.174520	+	0.0915949i
$89$	7.05692			0.748032			0.374016	−	0.927422i	$-0.377980\pi$
$89$	7.05692			0.748032			0.374016	+	0.927422i	$0.377980\pi$
$90$	0.123168	−	0.0646438i	0.0129831	−	0.00681405i
$91$	−1.62332	+	3.29623i	−0.170170	+	0.345539i
$92$	2.87869	+	1.51085i	0.300124	+	0.157517i
$93$	6.43180	+	3.37567i	0.666947	+	0.350041i
$94$	−3.20749	+	0.790574i	−0.330827	+	0.0815415i
$95$	−1.41478	+	2.04966i	−0.145153	+	0.210290i
$96$	−4.05282	+	0.998930i	−0.413639	+	0.101953i
$97$	−0.162069	−	0.234797i	−0.0164556	−	0.0238400i	0.814670	−	0.579925i	$-0.196918\pi$
$97$	−0.162069	−	0.234797i	−0.0164556	−	0.0238400i	−0.831125	+	0.556085i	$0.812303\pi$
$98$	−0.276838	+	2.27996i	−0.0279648	+	0.230311i
$99$	−1.24604			−0.125231
$100$	1.08682	−	8.95077i	0.108682	−	0.895077i
$101$	−1.10544	−	2.91480i	−0.109995	−	0.290034i	0.868704	−	0.495331i	$-0.164953\pi$
$101$	−1.10544	−	2.91480i	−0.109995	−	0.290034i	−0.978700	+	0.205297i	$0.934184\pi$
$102$	1.16655	−	0.612253i	0.115506	−	0.0606221i
$103$	−1.23772	+	10.1935i	−0.121956	+	1.00440i	0.795333	+	0.606173i	$0.207296\pi$
$103$	−1.23772	+	10.1935i	−0.121956	+	1.00440i	−0.917289	+	0.398223i	$0.869627\pi$
$104$	2.36369	−	4.79960i	0.231779	−	0.470640i
$105$	0.0443509	+	0.365263i	0.00432820	+	0.0356460i
$106$	1.61858	+	2.34491i	0.157210	+	0.227758i
$107$	−4.13360	+	5.98856i	−0.399610	+	0.578935i	−0.970202	−	0.242299i	$-0.922099\pi$
$107$	−4.13360	+	5.98856i	−0.399610	+	0.578935i	0.570591	+	0.821234i	$0.306714\pi$
$108$	1.38593	−	1.22782i	0.133361	−	0.118147i
$109$	−3.99120	−	10.5239i	−0.382288	−	1.00801i	−0.978694	−	0.205326i	$-0.934174\pi$
$109$	−3.99120	−	10.5239i	−0.382288	−	1.00801i	0.596406	−	0.802683i	$-0.296595\pi$
$110$	−0.0984603	+	0.142644i	−0.00938782	+	0.0136006i
$111$	0.362154	+	0.190073i	0.0343741	+	0.0180409i
$112$	0.384655	−	3.16792i	0.0363465	−	0.299340i
$113$	−1.76230	−	14.5139i	−0.165784	−	1.36535i	−0.803604	−	0.595165i	$-0.797087\pi$
$113$	−1.76230	−	14.5139i	−0.165784	−	1.36535i	0.637820	−	0.770185i	$-0.279836\pi$
$114$	0.942323	−	2.48470i	0.0882567	−	0.232714i
$115$	−0.360137	+	0.521748i	−0.0335829	+	0.0486532i
$116$	11.3351	+	10.0420i	1.05244	+	0.932377i
$117$	0.0926918	+	3.60436i	0.00856936	+	0.333223i
$118$	−2.01334	+	1.78366i	−0.185343	+	0.164199i
$119$	0.420055	+	3.45947i	0.0385064	+	0.317129i
$120$	−0.0645789	−	0.531855i	−0.00589522	−	0.0485515i
$121$	−8.36525	+	4.39042i	−0.760477	+	0.399129i
$122$	1.21366	−	0.636977i	0.109879	−	0.0576692i
$123$	2.76379	+	0.681214i	0.249203	+	0.0614230i
$124$	10.0671	−	8.91870i	0.904055	−	0.800923i
$125$	3.46001	+	0.852817i	0.309473	+	0.0762782i
$126$	−0.139217	−	0.367086i	−0.0124025	−	0.0327026i
$127$	14.5066	−	7.61367i	1.28726	−	0.675604i	0.324477	−	0.945894i	$-0.394812\pi$
$127$	14.5066	−	7.61367i	1.28726	−	0.675604i	0.962779	+	0.270289i	$0.0871194\pi$
$128$	−1.22243	+	10.0676i	−0.108048	+	0.889859i
$129$	2.49866	−	0.615865i	0.219995	−	0.0542239i
$130$	0.419946	+	0.274201i	0.0368317	+	0.0240490i
$131$	9.82278	+	2.42110i	0.858220	+	0.211532i	0.643785	−	0.765206i	$-0.277363\pi$
$131$	9.82278	+	2.42110i	0.858220	+	0.211532i	0.214435	+	0.976738i	$0.431209\pi$
$132$	−0.818121	+	2.15721i	−0.0712083	+	0.187761i
$133$	5.26143	+	4.66122i	0.456224	+	0.404179i
$134$	0.493711	−	0.121689i	0.0426501	−	0.0105123i
$135$	0.205107	+	0.297149i	0.0176528	+	0.0255745i
$136$	−0.611638	−	5.03729i	−0.0524475	−	0.431944i
$137$	−3.09299	−	8.15555i	−0.264252	−	0.696776i	−0.999813	−	0.0193175i	$-0.993851\pi$
$137$	−3.09299	−	8.15555i	−0.264252	−	0.696776i	0.735561	−	0.677458i	$-0.236919\pi$
$138$	0.239872	−	0.632490i	0.0204193	−	0.0538412i
$139$	12.9563	+	18.7705i	1.09894	+	1.59209i	0.758309	+	0.651895i	$0.226026\pi$
$139$	12.9563	+	18.7705i	1.09894	+	1.59209i	0.340633	+	0.940197i	$0.389359\pi$
$140$	0.661483	+	0.163041i	0.0559055	+	0.0137795i
$141$	−3.04066	−	8.01755i	−0.256069	−	0.675200i
$142$	−2.22018	+	5.85414i	−0.186313	+	0.491268i
$143$	−2.18942	−	3.92305i	−0.183088	−	0.328062i
$144$	−1.11044	−	2.92800i	−0.0925370	−	0.244000i
$145$	−2.21038	+	1.95822i	−0.183562	+	0.162622i
$146$	−0.319830			−0.0264693
$147$	−5.96152			−0.491698
$148$	0.566847	−	0.502183i	0.0465946	−	0.0412792i
$149$	−16.1413	+	8.47159i	−1.32234	+	0.694020i	−0.970287	−	0.241959i	$-0.922210\pi$
$149$	−16.1413	+	8.47159i	−1.32234	+	0.694020i	−0.352058	+	0.935978i	$0.614518\pi$
$150$	−1.87605			−0.153179
$151$	−1.43026	−	0.750660i	−0.116393	−	0.0610879i	0.405522	−	0.914085i	$-0.367090\pi$
$151$	−1.43026	−	0.750660i	−0.116393	−	0.0610879i	−0.521915	+	0.852998i	$0.674782\pi$
$152$	−7.66112	−	6.78716i	−0.621398	−	0.550511i
$153$	1.94261	+	2.81436i	0.157051	+	0.227527i
$154$	0.366166	+	0.324394i	0.0295065	+	0.0261404i
$155$	1.48987	+	2.15844i	0.119669	+	0.173370i
$156$	6.30093	+	2.20607i	0.504478	+	0.176627i
$157$	−4.69750	+	6.80551i	−0.374901	+	0.543139i	−0.964337	−	0.264677i	$-0.914735\pi$
$157$	−4.69750	+	6.80551i	−0.374901	+	0.543139i	0.589436	+	0.807815i	$0.299350\pi$
$158$	−2.21626	+	0.546260i	−0.176316	+	0.0434581i
$159$	−5.53585	+	4.90434i	−0.439022	+	0.388939i
$160$	−1.46332	−	0.360677i	−0.115686	−	0.0285140i
$161$	1.33932	+	1.18653i	0.105553	+	0.0935118i
$162$	−0.288368	−	0.255472i	−0.0226563	−	0.0200718i
$163$	5.87153	−	15.4820i	0.459894	−	1.21264i	−0.481833	−	0.876263i	$-0.660029\pi$
$163$	5.87153	−	15.4820i	0.459894	−	1.21264i	0.941727	−	0.336378i	$-0.109202\pi$
$164$	2.99400	−	4.33756i	0.233792	−	0.338707i
$165$	−0.398365	−	0.209078i	−0.0310127	−	0.0162767i
$166$	−0.539728	+	4.44506i	−0.0418910	+	0.345004i
$167$	20.0961	+	4.95324i	1.55508	+	0.383293i	0.920871	−	0.389868i	$-0.127479\pi$
$167$	20.0961	+	4.95324i	1.55508	+	0.383293i	0.634210	+	0.773161i	$0.281325\pi$
$168$	−1.51212			−0.116663
$169$	−11.1852	+	6.62507i	−0.860399	+	0.509621i
$170$	0.475686			0.0364834
$171$	6.69730	+	1.65074i	0.512155	+	0.126235i
$172$	0.574349	−	4.73019i	0.0437937	−	0.360673i
$173$	12.7248	+	6.67851i	0.967451	+	0.507757i	0.872972	−	0.487770i	$-0.162189\pi$
$173$	12.7248	+	6.67851i	0.967451	+	0.507757i	0.0944784	+	0.995527i	$0.469882\pi$
$174$	1.78991	−	2.59313i	0.135693	−	0.196585i
$175$	1.75971	−	4.63997i	0.133021	−	0.350749i
$176$	2.92066	+	2.58748i	0.220153	+	0.195039i
$177$	−5.22598	−	4.62981i	−0.392809	−	0.347998i
$178$	−2.63972	−	0.650632i	−0.197855	−	0.0487669i
$179$	−4.61566	+	4.08912i	−0.344991	+	0.305635i	−0.817769	−	0.575546i	$-0.804789\pi$
$179$	−4.61566	+	4.08912i	−0.344991	+	0.305635i	0.472779	+	0.881181i	$0.343251\pi$
$180$	0.649111	−	0.159991i	0.0483819	−	0.0119251i
$181$	5.77861	−	8.37176i	0.429521	−	0.622268i	−0.547144	−	0.837039i	$-0.684285\pi$
$181$	5.77861	−	8.37176i	0.429521	−	0.622268i	0.976665	+	0.214770i	$0.0689003\pi$
$182$	0.911124	−	1.08332i	0.0675370	−	0.0803013i
$183$	2.02106	+	2.92801i	0.149401	+	0.216444i
$184$	−1.95017	−	1.72770i	−0.143768	−	0.127367i
$185$	0.0838895	+	0.121535i	0.00616768	+	0.00893542i
$186$	−2.09466	−	1.85570i	−0.153588	−	0.136067i
$187$	−3.77299	−	1.98022i	−0.275908	−	0.144808i
$188$	−15.8769			−1.15794
$189$	0.902333	−	0.473581i	0.0656350	−	0.0344479i
$190$	0.718186	−	0.636257i	0.0521027	−	0.0461589i
$191$	19.2894			1.39573			0.697865	−	0.716230i	$-0.254134\pi$
$191$	19.2894			1.39573			0.697865	+	0.716230i	$0.254134\pi$
$192$	−4.65490			−0.335938
$193$	4.87261	−	4.31675i	0.350738	−	0.310727i	−0.469297	−	0.883041i	$-0.655493\pi$
$193$	4.87261	−	4.31675i	0.350738	−	0.310727i	0.820035	+	0.572314i	$0.193954\pi$
$194$	0.0389758	+	0.102771i	0.00279830	+	0.00737851i
$195$	−0.575158	+	1.16789i	−0.0411879	+	0.0836342i
$196$	−3.91420	+	10.3209i	−0.279586	+	0.737208i
$197$	−4.08958	−	10.7833i	−0.291370	−	0.768280i	−0.998147	−	0.0608440i	$-0.980621\pi$
$197$	−4.08958	−	10.7833i	−0.291370	−	0.768280i	0.706777	−	0.707436i	$-0.250148\pi$
$198$	0.466093	+	0.114882i	0.0331238	+	0.00816429i
$199$	−12.6886	−	18.3827i	−0.899473	−	1.30311i	−0.952506	−	0.304519i	$-0.901504\pi$
$199$	−12.6886	−	18.3827i	−0.899473	−	1.30311i	0.0530331	−	0.998593i	$-0.483111\pi$
$200$	−2.56229	+	6.75621i	−0.181181	+	0.477736i
$201$	0.468032	+	1.23410i	0.0330124	+	0.0870466i
$202$	0.144763	+	1.19223i	0.0101855	+	0.0838852i
$203$	4.73459	+	6.85924i	0.332303	+	0.481424i
$204$	6.14785	−	1.51531i	0.430435	−	0.106093i
$205$	0.769297	+	0.681537i	0.0537300	+	0.0476006i
$206$	1.40280	−	3.69888i	0.0977376	−	0.257713i
$207$	1.70482	+	0.420201i	0.118493	+	0.0292060i
$208$	7.26743	−	8.64095i	0.503906	−	0.599142i
$209$	−8.34508	+	2.05688i	−0.577241	+	0.142277i
$210$	0.0170864	−	0.140719i	0.00117908	−	0.00971056i
$211$	−10.5280	+	5.52554i	−0.724780	+	0.380394i	−0.786410	−	0.617705i	$-0.788063\pi$
$211$	−10.5280	+	5.52554i	−0.724780	+	0.380394i	0.0616296	+	0.998099i	$0.480370\pi$
$212$	4.85594	+	12.8041i	0.333507	+	0.879386i
$213$	−15.7793	−	3.88925i	−1.08118	−	0.266487i
$214$	2.09835	−	1.85897i	0.143440	−	0.127077i
$215$	0.902176	+	0.222366i	0.0615279	+	0.0151653i
$216$	−1.31388	+	0.689576i	−0.0893980	+	0.0469197i
$217$	6.55439	−	3.44001i	0.444941	−	0.233523i
$218$	0.522669	+	4.30457i	0.0353996	+	0.291542i
$219$	−0.100067	−	0.824123i	−0.00676188	−	0.0556891i
$220$	−0.623526	+	0.552396i	−0.0420381	+	0.0372425i
$221$	−5.44742	+	11.0613i	−0.366433	+	0.744062i
$222$	−0.117943	−	0.104489i	−0.00791583	−	0.00701282i
$223$	−6.30691	+	9.13714i	−0.422342	+	0.611868i	−0.975178	−	0.221422i	$-0.928930\pi$
$223$	−6.30691	+	9.13714i	−0.422342	+	0.611868i	0.552836	+	0.833290i	$0.313546\pi$
$224$	−1.50837	+	3.97725i	−0.100782	+	0.265741i
$225$	−0.586969	−	4.83413i	−0.0391313	−	0.322275i
$226$	−0.678937	+	5.59155i	−0.0451622	+	0.371944i
$227$	−8.76559	−	4.60053i	−0.581792	−	0.305348i	0.148032	−	0.988983i	$-0.452706\pi$
$227$	−8.76559	−	4.60053i	−0.581792	−	0.305348i	−0.729825	+	0.683634i	$0.760398\pi$
$228$	7.25515	−	10.5109i	0.480484	−	0.696101i
$229$	−6.42362	−	16.9377i	−0.424485	−	1.11927i	−0.961283	−	0.275563i	$-0.911136\pi$
$229$	−6.42362	−	16.9377i	−0.424485	−	1.11927i	0.536798	−	0.843711i	$-0.319634\pi$
$230$	0.182817	−	0.161962i	0.0120546	−	0.0106794i
$231$	−0.721321	+	1.04501i	−0.0474594	+	0.0687568i
$232$	−6.89398	−	9.98766i	−0.452612	−	0.655722i
$233$	1.69146	+	13.9304i	0.110811	+	0.912610i	0.937027	+	0.349257i	$0.113566\pi$
$233$	1.69146	+	13.9304i	0.110811	+	0.912610i	−0.826216	+	0.563353i	$0.809511\pi$
$234$	0.297641	−	1.35680i	0.0194574	−	0.0886965i
$235$	0.373186	−	3.07346i	0.0243440	−	0.200491i
$236$	−11.4467	+	6.00767i	−0.745114	+	0.391066i
$237$	−2.10099	−	5.53985i	−0.136474	−	0.359852i
$238$	0.161829	−	1.33278i	0.0104898	−	0.0863913i
$239$	−14.2119			−0.919292			−0.459646	−	0.888102i	$-0.652024\pi$
$239$	−14.2119			−0.919292			−0.459646	+	0.888102i	$0.652024\pi$
$240$	0.136287	−	1.12243i	0.00879730	−	0.0724523i
$241$	−12.6893	−	18.3836i	−0.817389	−	1.18419i	−0.980293	−	0.197550i	$-0.936702\pi$
$241$	−12.6893	−	18.3836i	−0.817389	−	1.18419i	0.162904	−	0.986642i	$-0.447914\pi$
$242$	3.53390	−	0.871028i	0.227168	−	0.0559918i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	6.39611	−	1.57650i	0.409469	−	0.100925i
$245$	−1.90593	−	1.00031i	−0.121765	−	0.0639075i
$246$	−0.971020	−	0.509631i	−0.0619100	−	0.0324929i
$247$	6.57063	+	23.9865i	0.418079	+	1.52622i
$248$	−9.54378	+	5.00896i	−0.606030	+	0.318069i
$249$	−11.6227			−0.736559
$250$	−1.21563	−	0.638010i	−0.0768830	−	0.0403513i
$251$	−6.91053	+	18.2216i	−0.436189	+	1.15013i	0.519166	+	0.854673i	$0.326243\pi$
$251$	−6.91053	+	18.2216i	−0.436189	+	1.15013i	−0.955355	+	0.295461i	$0.904527\pi$
$252$	−0.227437	−	1.87311i	−0.0143272	−	0.117995i
$253$	−2.12427	+	0.523586i	−0.133552	+	0.0329176i
$254$	−6.12833	+	1.51050i	−0.384526	+	0.0947770i
$255$	0.148830	+	1.22573i	0.00932010	+	0.0767579i
$256$	−1.91583	+	5.05162i	−0.119739	+	0.315726i
$257$	3.54968	+	1.86302i	0.221423	+	0.116212i	0.571788	−	0.820402i	$-0.306250\pi$
$257$	3.54968	+	1.86302i	0.221423	+	0.116212i	−0.350365	+	0.936613i	$0.613942\pi$
$258$	−0.991433			−0.0617239
$259$	0.369056	−	0.193696i	0.0229321	−	0.0120357i
$260$	1.64428	+	1.76256i	0.101974	+	0.109309i
$261$	7.24189	+	3.80083i	0.448261	+	0.235266i
$262$	−3.45110	−	1.81128i	−0.213209	−	0.111901i
$263$	−15.5275	+	3.82720i	−0.957469	+	0.235995i	−0.686938	−	0.726716i	$-0.741046\pi$
$263$	−15.5275	+	3.82720i	−0.957469	+	0.235995i	−0.270531	+	0.962711i	$0.587199\pi$
$264$	1.05031	−	1.52163i	0.0646419	−	0.0936500i
$265$	−2.59276	+	0.639059i	−0.159272	+	0.0392571i
$266$	−1.53834	−	2.22867i	−0.0943218	−	0.136649i
$267$	0.850618	−	7.00547i	0.0520570	−	0.428728i
$268$	2.44384			0.149281
$269$	3.11391	−	25.6453i	0.189858	−	1.56362i	−0.516824	−	0.856092i	$-0.672886\pi$
$269$	3.11391	−	25.6453i	0.189858	−	1.56362i	0.706682	−	0.707531i	$-0.250191\pi$
$270$	−0.0493261	−	0.130062i	−0.00300189	−	0.00791534i
$271$	−5.35199	+	2.80894i	−0.325110	+	0.170631i	−0.619380	−	0.785091i	$-0.712616\pi$
$271$	−5.35199	+	2.80894i	−0.325110	+	0.170631i	0.294270	+	0.955722i	$0.404924\pi$
$272$	1.29080	−	10.6307i	0.0782663	−	0.644581i
$273$	3.07653	+	2.00880i	0.186200	+	0.121578i
$274$	0.405044	+	3.33584i	0.0244696	+	0.201525i
$275$	3.44687	+	4.99365i	0.207854	+	0.301129i
$276$	1.84682	−	2.67559i	0.111166	−	0.161051i
$277$	−22.5223	+	19.9530i	−1.35324	+	1.19886i	−0.393044	+	0.919520i	$0.628578\pi$
$277$	−22.5223	+	19.9530i	−1.35324	+	1.19886i	−0.960192	+	0.279342i	$0.909884\pi$
$278$	−3.11586	−	8.21585i	−0.186877	−	0.492754i
$279$	4.12633	−	5.97801i	0.247037	−	0.357894i
$280$	−0.483435	−	0.253726i	−0.0288908	−	0.0151630i
$281$	2.48137	−	20.4359i	0.148026	−	1.21910i	−0.709516	−	0.704689i	$-0.751086\pi$
$281$	2.48137	−	20.4359i	0.148026	−	1.21910i	0.857542	−	0.514414i	$-0.171991\pi$
$282$	0.398190	+	3.27939i	0.0237119	+	0.195285i
$283$	3.56556	−	9.40162i	0.211951	−	0.558868i	−0.786309	−	0.617833i	$-0.788011\pi$
$283$	3.56556	−	9.40162i	0.211951	−	0.558868i	0.998260	+	0.0589649i	$0.0187800\pi$
$284$	−17.0936	+	24.7644i	−1.01432	+	1.46950i
$285$	1.86418	+	1.65152i	0.110424	+	0.0978276i
$286$	0.457278	+	1.66932i	0.0270394	+	0.0987089i
$287$	2.17125	−	1.92356i	0.128165	−	0.113544i
$288$	0.503133	+	4.14368i	0.0296474	+	0.244169i
$289$	−0.639528	−	5.26698i	−0.0376193	−	0.309823i
$290$	1.00736	−	0.528703i	0.0591541	−	0.0310465i
$291$	−0.252620	+	0.132585i	−0.0148089	+	0.00777230i
$292$	−1.49247	−	0.367861i	−0.0873402	−	0.0215274i
$293$	−20.4416	+	18.1097i	−1.19421	+	1.05798i	−0.197230	+	0.980357i	$0.563194\pi$
$293$	−20.4416	+	18.1097i	−1.19421	+	1.05798i	−0.996983	+	0.0776226i	$0.975267\pi$
$294$	2.22997	+	0.549638i	0.130054	+	0.0320555i
$295$	−0.893918	−	2.35707i	−0.0520459	−	0.137234i
$296$	−0.537379	+	0.282038i	−0.0312345	+	0.0163931i
$297$	−0.150193	+	1.23695i	−0.00871509	+	0.0717752i
$298$	6.81888	−	1.68070i	0.395007	−	0.0973604i
$299$	1.67258	+	6.10584i	0.0967277	+	0.353110i
$300$	−8.75450	−	2.15779i	−0.505441	−	0.124580i
$301$	0.929948	−	2.45207i	0.0536013	−	0.141335i
$302$	0.465796	+	0.412659i	0.0268036	+	0.0237459i
$303$	−3.02680	+	0.746039i	−0.173885	+	0.0428588i
$304$	−12.2703	−	17.7766i	−0.703752	−	1.01956i
$305$	0.154840	+	1.27522i	0.00886612	+	0.0730190i
$306$	−0.467177	−	1.23184i	−0.0267067	−	0.0704198i
$307$	−1.32068	+	3.48235i	−0.0753752	+	0.198748i	−0.967408	−	0.253222i	$-0.918510\pi$
$307$	−1.32068	+	3.48235i	−0.0753752	+	0.198748i	0.892033	+	0.451971i	$0.149279\pi$
$308$	1.33558	+	1.93492i	0.0761018	+	0.110253i
$309$	9.96999	+	2.45738i	0.567173	+	0.139796i
$310$	−0.358297	−	0.944751i	−0.0203499	−	0.0536582i
$311$	4.51291	−	11.8996i	0.255904	−	0.674762i	−0.744074	−	0.668097i	$-0.767109\pi$
$311$	4.51291	−	11.8996i	0.255904	−	0.674762i	0.999978	−	0.00666526i	$-0.00212163\pi$
$312$	−4.47970	−	2.92499i	−0.253613	−	0.165595i
$313$	5.78079	+	15.2427i	0.326749	+	0.861568i	0.993243	+	0.116056i	$0.0370253\pi$
$313$	5.78079	+	15.2427i	0.326749	+	0.861568i	−0.666493	+	0.745511i	$0.732205\pi$
$314$	2.38460	−	2.11257i	0.134571	−	0.119219i
$315$	0.367945			0.0207314
$316$	−10.9704			−0.617131
$317$	16.4566	−	14.5793i	0.924296	−	0.818854i	−0.0594852	−	0.998229i	$-0.518946\pi$
$317$	16.4566	−	14.5793i	0.924296	−	0.818854i	0.983781	+	0.179375i	$0.0574074\pi$
$318$	2.52291	−	1.32413i	0.141478	−	0.0742534i
$319$	−10.1910			−0.570585
$320$	−1.48820	−	0.781066i	−0.0831928	−	0.0436629i
$321$	5.44664	+	4.82530i	0.304002	+	0.269322i
$322$	−0.391591	−	0.567317i	−0.0218225	−	0.0316153i
$323$	17.6560	+	15.6418i	0.982406	+	0.870335i
$324$	−1.05182	−	1.52382i	−0.0584342	−	0.0846566i
$325$	14.1885	−	10.3421i	0.787038	−	0.573676i
$326$	−3.62371	+	5.24985i	−0.200699	+	0.290762i
$327$	−10.9283	+	2.69358i	−0.604335	+	0.148955i
$328$	−3.16154	+	2.80088i	−0.174567	+	0.154653i
$329$	−8.48429	−	2.09119i	−0.467754	−	0.115291i
$330$	0.129736	+	0.114936i	0.00714174	+	0.00632703i
$331$	10.3404	+	9.16083i	0.568362	+	0.503525i	0.897653	−	0.440704i	$-0.145271\pi$
$331$	10.3404	+	9.16083i	0.568362	+	0.503525i	−0.329291	+	0.944229i	$0.606810\pi$
$332$	−7.63122	+	20.1219i	−0.418817	+	1.10433i
$333$	0.232340	−	0.336603i	0.0127322	−	0.0184457i
$334$	−7.06047	−	3.70562i	−0.386332	−	0.202763i
$335$	−0.0574425	+	0.473082i	−0.00313842	+	0.0258472i
$336$	−3.09845	−	0.763700i	−0.169035	−	0.0416633i
$337$	−24.5437			−1.33698			−0.668491	−	0.743720i	$-0.733060\pi$
$337$	−24.5437			−1.33698			−0.668491	+	0.743720i	$0.733060\pi$
$338$	4.79476	−	1.44693i	0.260800	−	0.0787026i
$339$	−14.6205			−0.794075
$340$	2.21976	+	0.547122i	0.120384	+	0.0296719i
$341$	−1.09098	+	8.98501i	−0.0590797	+	0.486565i
$342$	−2.35300	−	1.23495i	−0.127236	−	0.0667785i
$343$	−7.50332	+	10.8704i	−0.405141	+	0.586948i
$344$	−1.35409	+	3.57043i	−0.0730075	+	0.192505i
$345$	0.474534	+	0.420400i	0.0255481	+	0.0226336i
$346$	−4.14412	−	3.67137i	−0.222789	−	0.197374i
$347$	6.58738	+	1.62364i	0.353629	+	0.0871618i	0.412129	−	0.911126i	$-0.364785\pi$
$347$	6.58738	+	1.62364i	0.353629	+	0.0871618i	−0.0584994	+	0.998287i	$0.518632\pi$
$348$	11.3351	−	10.0420i	0.607624	−	0.538308i
$349$	13.4029	−	3.30352i	0.717440	−	0.176833i	0.136336	−	0.990663i	$-0.456467\pi$
$349$	13.4029	−	3.30352i	0.717440	−	0.176833i	0.581104	+	0.813829i	$0.302621\pi$
$350$	−1.08603	+	1.57339i	−0.0580509	+	0.0841012i
$351$	3.58925	+	0.342442i	0.191580	+	0.0182782i
$352$	−2.95456	−	4.28042i	−0.157479	−	0.228147i
$353$	9.68582	+	8.58089i	0.515524	+	0.456715i	0.880325	−	0.474371i	$-0.157324\pi$
$353$	9.68582	+	8.58089i	0.515524	+	0.456715i	−0.364801	+	0.931086i	$0.618863\pi$
$354$	1.52798	+	2.21365i	0.0812110	+	0.117654i
$355$	−4.39214	−	3.89110i	−0.233111	−	0.206518i
$356$	−11.5698	−	6.07228i	−0.613196	−	0.321830i
$357$	3.48488			0.184439
$358$	2.10354	−	1.10403i	0.111176	−	0.0583495i
$359$	9.92199	−	8.79012i	0.523663	−	0.463925i	−0.359397	−	0.933185i	$-0.617018\pi$
$359$	9.92199	−	8.79012i	0.523663	−	0.463925i	0.883060	+	0.469260i	$0.155479\pi$
$360$	−0.535761			−0.0282371
$361$	28.5787			1.50414
$362$	−2.93341	+	2.59877i	−0.154176	+	0.136588i
$363$	3.35009	+	8.83347i	0.175834	+	0.463637i
$364$	5.49772	−	4.00732i	0.288159	−	0.210041i
$365$	0.106291	−	0.280268i	0.00556355	−	0.0146699i
$366$	−0.486043	−	1.28159i	−0.0254058	−	0.0669897i
$367$	14.9620	+	3.68780i	0.781009	+	0.192501i	0.609611	−	0.792700i	$-0.291326\pi$
$367$	14.9620	+	3.68780i	0.781009	+	0.192501i	0.171398	+	0.985202i	$0.445172\pi$
$368$	−3.12346	−	4.52511i	−0.162822	−	0.235888i
$369$	1.00939	−	2.66153i	0.0525465	−	0.138554i
$370$	−0.0201745	−	0.0531958i	−0.00104882	−	0.00276552i
$371$	0.908459	+	7.48183i	0.0471648	+	0.388437i
$372$	−7.64021	−	11.0688i	−0.396127	−	0.573888i
$373$	15.4848	−	3.81666i	0.801773	−	0.197619i	0.182922	−	0.983128i	$-0.441445\pi$
$373$	15.4848	−	3.81666i	0.801773	−	0.197619i	0.618851	+	0.785508i	$0.287598\pi$
$374$	1.22876	+	1.08858i	0.0635374	+	0.0562893i
$375$	1.26366	−	3.33199i	0.0652550	−	0.172063i
$376$	12.3539	+	3.04496i	0.637103	+	0.157032i
$377$	0.758099	+	29.4790i	0.0390441	+	1.51825i
$378$	−0.381190	+	0.0939550i	−0.0196063	+	0.00483252i
$379$	0.177751	−	1.46391i	0.00913046	−	0.0751961i	−0.987431	−	0.158048i	$-0.949480\pi$
$379$	0.177751	−	1.46391i	0.00913046	−	0.0751961i	0.996562	+	0.0828521i	$0.0264029\pi$
$380$	4.08318	−	2.14302i	0.209463	−	0.109935i
$381$	−5.80958	−	15.3186i	−0.297634	−	0.784796i
$382$	−7.21539	−	1.77844i	−0.369172	−	0.0909927i
$383$	26.0098	−	23.0426i	1.32904	−	1.17742i	0.359313	−	0.933217i	$-0.383011\pi$
$383$	26.0098	−	23.0426i	1.32904	−	1.17742i	0.969723	−	0.244207i	$-0.0785275\pi$
$384$	9.84685	+	2.42703i	0.502495	+	0.123854i
$385$	−0.405958	+	0.213063i	−0.0206895	+	0.0108587i
$386$	−2.22065	+	1.16549i	−0.113028	+	0.0593216i
$387$	−0.310194	−	2.55468i	−0.0157681	−	0.129862i
$388$	0.0636741	+	0.524403i	0.00323256	+	0.0266225i
$389$	17.9655	−	15.9161i	0.910889	−	0.806978i	−0.0707953	−	0.997491i	$-0.522554\pi$
$389$	17.9655	−	15.9161i	0.910889	−	0.806978i	0.981685	+	0.190513i	$0.0610153\pi$
$390$	0.322821	−	0.383833i	0.0163467	−	0.0194361i
$391$	4.49440	+	3.98169i	0.227292	+	0.201363i
$392$	5.02507	−	7.28007i	0.253804	−	0.367699i
$393$	3.58745	−	9.45933i	0.180963	−	0.477160i
$394$	0.535552	+	4.41067i	0.0269807	+	0.222206i
$395$	0.257859	−	2.12366i	0.0129743	−	0.106853i
$396$	2.04287	+	1.07218i	0.102658	+	0.0538790i
$397$	4.64222	−	6.72541i	0.232986	−	0.337539i	−0.689000	−	0.724761i	$-0.741950\pi$
$397$	4.64222	−	6.72541i	0.232986	−	0.337539i	0.921986	+	0.387222i	$0.126565\pi$
$398$	3.05148	+	8.04609i	0.152957	+	0.403314i
$399$	5.26143	−	4.66122i	0.263401	−	0.233353i
$400$	−8.66256	+	12.5499i	−0.433128	+	0.627494i
$401$	6.36734	+	9.22469i	0.317970	+	0.460659i	0.949080	−	0.315034i	$-0.102016\pi$
$401$	6.36734	+	9.22469i	0.317970	+	0.460659i	−0.631111	+	0.775693i	$0.717401\pi$
$402$	−0.0612913	−	0.504779i	−0.00305693	−	0.0251761i
$403$	26.0717	+	2.48744i	1.29872	+	0.123908i
$404$	−0.695747	+	5.72999i	−0.0346147	+	0.285078i
$405$	0.319706	−	0.167795i	0.0158863	−	0.00833778i
$406$	−1.13862	−	3.00229i	−0.0565087	−	0.149001i
$407$	−0.0614294	+	0.505916i	−0.00304494	+	0.0250773i
$408$	−5.07429			−0.251215
$409$	1.64934	−	13.5835i	0.0815546	−	0.671662i	−0.893401	−	0.449261i	$-0.851687\pi$
$409$	1.64934	−	13.5835i	0.0815546	−	0.671662i	0.974955	−	0.222401i	$-0.0713895\pi$
$410$	−0.224928	−	0.325864i	−0.0111084	−	0.0160933i
$411$	−8.46891	+	2.08740i	−0.417740	+	0.102964i
$412$	10.8004	−	15.6471i	0.532100	−	0.770879i
$413$	−6.90816	+	1.70271i	−0.339928	+	0.0837848i
$414$	−0.598965	−	0.314361i	−0.0294375	−	0.0154500i
$415$	−3.71584	−	1.95023i	−0.182404	−	0.0957328i
$416$	−12.1620	+	8.86495i	−0.596291	+	0.434640i
$417$	20.1953	−	10.5993i	0.988970	−	0.519052i
$418$	3.31120			0.161956
$419$	−17.3554	−	9.10883i	−0.847868	−	0.444996i	−0.0159363	−	0.999873i	$-0.505073\pi$
$419$	−17.3554	−	9.10883i	−0.847868	−	0.444996i	−0.831932	+	0.554877i	$0.812765\pi$
$420$	0.241585	−	0.637007i	0.0117881	−	0.0310828i
$421$	−0.340652	−	2.80552i	−0.0166024	−	0.136733i	0.982051	−	0.188617i	$-0.0604004\pi$
$421$	−0.340652	−	2.80552i	−0.0166024	−	0.136733i	−0.998653	+	0.0518842i	$0.983477\pi$
$422$	4.44757	−	1.09623i	0.216504	−	0.0533635i
$423$	−8.32561	+	2.05208i	−0.404805	+	0.0997754i
$424$	−1.32280	−	10.8942i	−0.0642407	−	0.529070i
$425$	5.90512	−	15.5705i	0.286440	−	0.755281i
$426$	5.54384	+	2.90963i	0.268600	+	0.140972i
$427$	3.62560			0.175455
$428$	11.9300	−	6.26134i	0.576657	−	0.302653i
$429$	−4.15836	+	1.70058i	−0.200767	+	0.0821048i
$430$	−0.316967	−	0.166357i	−0.0152855	−	0.00802245i
$431$	−6.27626	−	3.29404i	−0.302317	−	0.158668i	0.306743	−	0.951792i	$-0.400761\pi$
$431$	−6.27626	−	3.29404i	−0.302317	−	0.158668i	−0.609060	+	0.793124i	$0.708453\pi$
$432$	−3.04050	+	0.749417i	−0.146286	+	0.0360563i
$433$	−1.01584	+	1.47170i	−0.0488181	+	0.0707253i	−0.846633	−	0.532177i	$-0.821374\pi$
$433$	−1.01584	+	1.47170i	−0.0488181	+	0.0707253i	0.797815	+	0.602903i	$0.205989\pi$
$434$	−2.76890	+	0.682473i	−0.132912	+	0.0327597i
$435$	1.67751	+	2.43030i	0.0804306	+	0.116524i
$436$	−2.51200	+	20.6882i	−0.120303	+	0.990785i
$437$	12.1113			0.579364
$438$	−0.0385512	+	0.317498i	−0.00184205	+	0.0151706i
$439$	8.81255	+	23.2368i	0.420600	+	1.10903i	0.963140	+	0.269001i	$0.0866936\pi$
$439$	8.81255	+	23.2368i	0.420600	+	1.10903i	−0.542540	+	0.840030i	$0.682537\pi$
$440$	0.591111	−	0.310239i	0.0281801	−	0.0147901i
$441$	−0.718581	+	5.91805i	−0.0342182	+	0.281812i
$442$	3.05749	−	3.63535i	0.145430	−	0.172916i
$443$	3.51422	+	28.9422i	0.166966	+	1.37509i	0.799552	+	0.600596i	$0.205070\pi$
$443$	3.51422	+	28.9422i	0.166966	+	1.37509i	−0.632587	+	0.774489i	$0.718007\pi$
$444$	−0.430196	−	0.623246i	−0.0204162	−	0.0295779i
$445$	1.44743	−	2.09696i	0.0686146	−	0.0994055i
$446$	3.20159	−	2.83636i	0.151600	−	0.134306i
$447$	6.46421	+	17.0447i	0.305747	+	0.806187i
$448$	−2.69468	+	3.90392i	−0.127312	+	0.184443i
$449$	11.1150	+	5.83358i	0.524547	+	0.275304i	0.706143	−	0.708070i	$-0.250434\pi$
$449$	11.1150	+	5.83358i	0.524547	+	0.275304i	−0.181595	+	0.983373i	$0.558126\pi$
$450$	−0.226133	+	1.86237i	−0.0106600	+	0.0877932i
$451$	0.427526	+	3.52099i	0.0201314	+	0.165797i
$452$	−9.59949	+	25.3118i	−0.451522	+	1.19057i
$453$	−0.917586	+	1.32935i	−0.0431120	+	0.0624585i
$454$	2.85470	+	2.52905i	0.133978	+	0.118694i
$455$	0.646518	+	1.15845i	0.0303092	+	0.0543089i
$456$	−7.66112	+	6.78716i	−0.358765	+	0.317838i
$457$	2.13950	+	17.6204i	0.100082	+	0.824248i	0.953160	+	0.302465i	$0.0978096\pi$
$457$	2.13950	+	17.6204i	0.100082	+	0.824248i	−0.853079	+	0.521782i	$0.825267\pi$
$458$	0.841207	+	6.92797i	0.0393070	+	0.323723i
$459$	3.02799	−	1.58921i	0.141335	−	0.0741781i
$460$	1.03939	−	0.545514i	0.0484618	−	0.0254347i
$461$	−39.1227	−	9.64288i	−1.82213	−	0.449114i	−0.828321	−	0.560254i	$-0.810704\pi$
$461$	−39.1227	−	9.64288i	−1.82213	−	0.449114i	−0.993805	+	0.111140i	$0.964550\pi$
$462$	0.366166	−	0.324394i	0.0170356	−	0.0150922i
$463$	5.63425	+	1.38872i	0.261846	+	0.0645392i	0.368053	−	0.929805i	$-0.380025\pi$
$463$	5.63425	+	1.38872i	0.261846	+	0.0645392i	−0.106207	+	0.994344i	$0.533871\pi$
$464$	−9.08200	−	23.9473i	−0.421621	−	1.11172i
$465$	2.32229	−	1.21883i	0.107694	−	0.0565219i
$466$	0.651643	−	5.36676i	0.0301868	−	0.248610i
$467$	0.964953	−	0.237840i	0.0446527	−	0.0110059i	−0.216926	−	0.976188i	$-0.569603\pi$
$467$	0.964953	−	0.237840i	0.0446527	−	0.0110059i	0.261579	+	0.965182i	$0.415757\pi$
$468$	2.94948	−	5.98907i	0.136340	−	0.276845i
$469$	1.30594	+	0.321886i	0.0603028	+	0.0148633i
$470$	−0.422960	+	1.11526i	−0.0195097	+	0.0514429i
$471$	6.18967	+	5.48357i	0.285205	+	0.252669i
$472$	10.0589	−	2.47930i	0.462998	−	0.114119i
$473$	1.82156	+	2.63898i	0.0837553	+	0.121341i
$474$	0.275136	+	2.26595i	0.0126374	+	0.104078i
$475$	−11.9110	−	31.4067i	−0.546513	−	1.44104i
$476$	2.28810	−	6.03321i	0.104875	−	0.276532i
$477$	4.20131	+	6.08664i	0.192365	+	0.278688i
$478$	5.31612	+	1.31031i	0.243154	+	0.0599320i
$479$	−13.9296	−	36.7294i	−0.636461	−	1.67821i	−0.730733	−	0.682663i	$-0.760822\pi$
$479$	−13.9296	−	36.7294i	−0.636461	−	1.67821i	0.0942720	−	0.995546i	$-0.469948\pi$
$480$	−0.534432	+	1.40918i	−0.0243934	+	0.0643200i
$481$	1.46801	+	0.140060i	0.0669357	+	0.00638616i
$482$	3.05164	+	8.04651i	0.138998	+	0.366508i
$483$	1.33932	−	1.18653i	0.0609411	−	0.0539891i
$484$	17.4926			0.795118
$485$	−0.103011			−0.00467750
$486$	−0.288368	+	0.255472i	−0.0130806	+	0.0115884i
$487$	5.85653	−	3.07374i	0.265385	−	0.139285i	−0.326783	−	0.945099i	$-0.605965\pi$
$487$	5.85653	−	3.07374i	0.265385	−	0.139285i	0.592168	+	0.805815i	$0.298272\pi$
$488$	−5.27920			−0.238978
$489$	−14.6613	−	7.69487i	−0.663009	−	0.347974i
$490$	0.620708	+	0.549899i	0.0280407	+	0.0248419i
$491$	−3.70036	−	5.36089i	−0.166995	−	0.241934i	0.730548	−	0.682862i	$-0.239265\pi$
$491$	−3.70036	−	5.36089i	−0.166995	−	0.241934i	−0.897543	+	0.440928i	$0.854649\pi$
$492$	−3.94505	−	3.49501i	−0.177857	−	0.157567i
$493$	15.8880	+	23.0178i	0.715561	+	1.03667i
$494$	−0.246318	−	9.57819i	−0.0110824	−	0.430943i
$495$	−0.255571	+	0.370259i	−0.0114871	+	0.0166419i
$496$	−22.0857	+	5.44363i	−0.991677	+	0.244426i
$497$	−12.3963	+	10.9822i	−0.556051	+	0.492618i
$498$	4.34760	+	1.07159i	0.194820	+	0.0480189i
$499$	5.24705	+	4.64848i	0.234890	+	0.208095i	0.772354	−	0.635192i	$-0.219079\pi$
$499$	5.24705	+	4.64848i	0.234890	+	0.208095i	−0.537464	+	0.843287i	$0.680618\pi$
$500$	−4.93884	−	4.37543i	−0.220871	−	0.195675i
$501$	7.33944	−	19.3525i	0.327902	−	0.864606i
$502$	4.26494	−	6.17884i	0.190354	−	0.275775i
$503$	27.3517	+	14.3553i	1.21955	+	0.640071i	0.946741	−	0.321996i	$-0.104354\pi$
$503$	27.3517	+	14.3553i	1.21955	+	0.640071i	0.272813	+	0.962067i	$0.412046\pi$
$504$	−0.182266	+	1.50110i	−0.00811879	+	0.0668643i
$505$	−1.09287	−	0.269367i	−0.0486319	−	0.0119867i
$506$	0.842880			0.0374706
$507$	5.22854	+	11.9022i	0.232208	+	0.528595i
$508$	−30.3349			−1.34589
$509$	−21.6679	−	5.34065i	−0.960411	−	0.236720i	−0.272208	−	0.962238i	$-0.587754\pi$
$509$	−21.6679	−	5.34065i	−0.960411	−	0.236720i	−0.688203	+	0.725518i	$0.741600\pi$
$510$	0.0573376	−	0.472217i	0.00253895	−	0.0209101i
$511$	−0.749095	−	0.393155i	−0.0331380	−	0.0173922i
$512$	12.7045	−	18.4056i	0.561465	−	0.813422i
$513$	2.44597	−	6.44949i	0.107992	−	0.284752i
$514$	−1.15603	−	1.02415i	−0.0509904	−	0.0451735i
$515$	2.77513	+	2.45855i	0.122287	+	0.108337i
$516$	−4.62647	−	1.14032i	−0.203669	−	0.0501999i
$517$	7.99745	−	7.08512i	0.351727	−	0.311603i
$518$	−0.155908	+	0.0384278i	−0.00685020	+	0.00168842i
$519$	8.16362	−	11.8270i	0.358343	−	0.519150i
$520$	−0.941388	−	1.68680i	−0.0412826	−	0.0739712i
$521$	17.3164	+	25.0872i	0.758647	+	1.09909i	0.991943	+	0.126684i	$0.0404335\pi$
$521$	17.3164	+	25.0872i	0.758647	+	1.09909i	−0.233296	+	0.972406i	$0.574951\pi$
$522$	−2.35848	−	2.08943i	−0.103228	−	0.0914518i
$523$	−1.58153	−	2.29125i	−0.0691556	−	0.100189i	0.786880	−	0.617106i	$-0.211695\pi$
$523$	−1.58153	−	2.29125i	−0.0691556	−	0.100189i	−0.856036	+	0.516917i	$0.827080\pi$
$524$	−14.0211	−	12.4216i	−0.612513	−	0.542640i
$525$	−4.39403	−	2.30616i	−0.191771	−	0.100649i
$526$	6.16110			0.268637
$527$	21.9948	−	11.5438i	0.958109	−	0.502855i
$528$	2.92066	−	2.58748i	0.127105	−	0.112606i
$529$	−19.9170			−0.865957
$530$	1.02877			0.0446870
$531$	−5.22598	+	4.62981i	−0.226788	+	0.200917i
$532$	−4.61522	−	12.1693i	−0.200095	−	0.527608i
$533$	10.1532	−	1.49861i	0.439785	−	0.0649120i
$534$	−0.964071	+	2.54205i	−0.0417194	+	0.110005i
$535$	0.931663	+	2.45659i	0.0402793	+	0.106208i
$536$	−1.90157	−	0.468694i	−0.0821352	−	0.0202445i
$537$	3.50295	+	5.07489i	0.151163	+	0.218998i
$538$	−3.52923	+	9.30581i	−0.152156	+	0.401202i
$539$	−2.63410	−	6.94555i	−0.113459	−	0.299166i
$540$	−0.0805832	−	0.663663i	−0.00346775	−	0.0285595i
$541$	−10.7939	−	15.6377i	−0.464067	−	0.672318i	0.519165	−	0.854674i	$-0.326243\pi$
$541$	−10.7939	−	15.6377i	−0.464067	−	0.672318i	−0.983233	+	0.182356i	$0.941628\pi$
$542$	2.26095	−	0.557273i	0.0971159	−	0.0239369i
$543$	−7.61419	−	6.74558i	−0.326756	−	0.289481i
$544$	−5.06170	+	13.3466i	−0.217019	+	0.572231i
$545$	−3.94580	−	0.972553i	−0.169020	−	0.0416596i
$546$	−0.965601	−	1.03506i	−0.0413239	−	0.0442965i
$547$	−13.8526	+	3.41436i	−0.592295	+	0.145988i	−0.524059	−	0.851682i	$-0.675583\pi$
$547$	−13.8526	+	3.41436i	−0.592295	+	0.145988i	−0.0682353	+	0.997669i	$0.521737\pi$
$548$	−1.94668	+	16.0324i	−0.0831582	+	0.684870i
$549$	3.15027	−	1.65339i	0.134450	−	0.0705649i
$550$	−0.828935	−	2.18572i	−0.0353459	−	0.0931995i
$551$	54.7752	+	13.5009i	2.33350	+	0.575157i
$552$	−1.95017	+	1.72770i	−0.0830046	+	0.0735356i
$553$	−5.86235	−	1.44494i	−0.249293	−	0.0614451i
$554$	10.2643	−	5.38714i	0.436090	−	0.228878i
$555$	0.130761	−	0.0686284i	0.00555047	−	0.00291311i
$556$	−5.09032	−	41.9226i	−0.215878	−	1.77791i
$557$	−0.653874	−	5.38514i	−0.0277055	−	0.228176i	0.972278	−	0.233826i	$-0.0751246\pi$
$557$	−0.653874	−	5.38514i	−0.0277055	−	0.228176i	−0.999984	+	0.00565018i	$0.998201\pi$
$558$	−2.09466	+	1.85570i	−0.0886738	+	0.0785582i
$559$	7.49817	−	5.46546i	0.317139	−	0.231164i
$560$	−0.862449	−	0.764063i	−0.0364451	−	0.0322876i
$561$	−2.42056	+	3.50679i	−0.102196	+	0.148057i
$562$	−2.81232	+	7.41549i	−0.118631	+	0.312804i
$563$	2.58577	+	21.2957i	0.108977	+	0.897509i	0.939977	+	0.341237i	$0.110846\pi$
$563$	2.58577	+	21.2957i	0.108977	+	0.897509i	−0.831000	+	0.556272i	$0.812231\pi$
$564$	−1.91374	+	15.7611i	−0.0805832	+	0.663662i
$565$	−4.67425	−	2.45324i	−0.196647	−	0.103208i
$566$	−2.20054	+	3.18804i	−0.0924958	+	0.134003i
$567$	−0.361364	−	0.952838i	−0.0151758	−	0.0400154i
$568$	18.0501	−	15.9910i	0.757367	−	0.670969i
$569$	−5.26375	+	7.62586i	−0.220668	+	0.319692i	−0.917645	−	0.397401i	$-0.869912\pi$
$569$	−5.26375	+	7.62586i	−0.220668	+	0.319692i	0.696977	+	0.717093i	$0.254528\pi$
$570$	−0.545050	−	0.789642i	−0.0228296	−	0.0330744i
$571$	3.52487	+	29.0299i	0.147511	+	1.21487i	0.858929	+	0.512095i	$0.171131\pi$
$571$	3.52487	+	29.0299i	0.147511	+	1.21487i	−0.711417	+	0.702770i	$0.751946\pi$
$572$	0.213852	+	8.31574i	0.00894162	+	0.347699i
$573$	2.32508	−	19.1487i	0.0971315	−	0.799949i
$574$	−0.989528	+	0.519344i	−0.0413021	+	0.0216770i
$575$	−3.03198	−	7.99468i	−0.126442	−	0.333401i
$576$	−0.561086	+	4.62096i	−0.0233786	+	0.192540i
$577$	17.7552			0.739157			0.369578	−	0.929200i	$-0.379502\pi$
$577$	17.7552			0.739157			0.369578	+	0.929200i	$0.379502\pi$
$578$	−0.246382	+	2.02913i	−0.0102481	+	0.0844009i
$579$	−3.69795	−	5.35741i	−0.153682	−	0.222646i
$580$	5.30889	−	1.30852i	0.220440	−	0.0543335i
$581$	−6.72829	+	9.74761i	−0.279136	+	0.404399i
$582$	0.106719	−	0.0263040i	0.00442366	−	0.00109034i
$583$	−8.15989	−	4.28264i	−0.337948	−	0.177369i
$584$	1.09075	+	0.572469i	0.0451355	+	0.0236890i
$585$	1.09004	+	0.711738i	0.0450678	+	0.0294267i
$586$	9.31608	−	4.88946i	0.384844	−	0.201982i
$587$	22.7828			0.940349			0.470174	−	0.882574i	$-0.344191\pi$
$587$	22.7828			0.940349			0.470174	+	0.882574i	$0.344191\pi$
$588$	9.77385	+	5.12971i	0.403067	+	0.211546i
$589$	17.7671	−	46.8480i	0.732081	−	1.93034i
$590$	0.117063	+	0.964104i	0.00481943	+	0.0396915i
$591$	−11.1977	+	2.75997i	−0.460610	+	0.113530i
$592$	−1.24357	+	0.306513i	−0.0511106	+	0.0125976i
$593$	0.304930	+	2.51132i	0.0125220	+	0.103128i	0.997630	−	0.0688101i	$-0.0219203\pi$
$593$	0.304930	+	2.51132i	0.0125220	+	0.103128i	−0.985108	+	0.171938i	$0.944997\pi$
$594$	0.170225	−	0.448848i	0.00698443	−	0.0184164i
$595$	1.11414	+	0.584743i	0.0456751	+	0.0239721i
$596$	33.7530			1.38258
$597$	−19.7781	+	10.3803i	−0.809462	+	0.424839i
$598$	−0.0627012	−	2.43816i	−0.00256404	−	0.0997039i
$599$	25.6361	+	13.4549i	1.04746	+	0.549751i	0.898446	−	0.439084i	$-0.144697\pi$
$599$	25.6361	+	13.4549i	1.04746	+	0.549751i	0.149017	+	0.988835i	$0.452389\pi$
$600$	6.39810	+	3.35798i	0.261201	+	0.137089i
$601$	−16.5086	+	4.06901i	−0.673400	+	0.165978i	−0.561166	−	0.827703i	$-0.689647\pi$
$601$	−16.5086	+	4.06901i	−0.673400	+	0.165978i	−0.112235	+	0.993682i	$0.535801\pi$
$602$	−0.573932	+	0.831485i	−0.0233917	+	0.0338888i
$603$	1.28152	−	0.315865i	0.0521874	−	0.0128630i
$604$	1.69898	+	2.46140i	0.0691306	+	0.100153i
$605$	−0.411164	+	3.38624i	−0.0167162	+	0.137670i
$606$	1.20099			0.0487868
$607$	−4.37789	+	36.0552i	−0.177693	+	1.46343i	0.582019	+	0.813175i	$0.302263\pi$
$607$	−4.37789	+	36.0552i	−0.177693	+	1.46343i	−0.759712	+	0.650260i	$0.774660\pi$
$608$	10.2097	+	26.9209i	0.414060	+	1.09179i
$609$	7.37992	−	3.87328i	0.299049	−	0.156953i
$610$	0.0596530	−	0.491287i	0.00241528	−	0.0198916i
$611$	−21.0898	−	22.6068i	−0.853201	−	0.914575i
$612$	−0.763219	−	6.28567i	−0.0308513	−	0.254083i
$613$	−20.8432	−	30.1966i	−0.841848	−	1.21963i	−0.973581	−	0.228343i	$-0.926669\pi$
$613$	−20.8432	−	30.1966i	−0.841848	−	1.21963i	0.131732	−	0.991285i	$-0.457946\pi$
$614$	0.815079	−	1.18085i	0.0328939	−	0.0476551i
$615$	0.769297	−	0.681537i	0.0310210	−	0.0274822i
$616$	−0.668133	−	1.76172i	−0.0269198	−	0.0709818i
$617$	0.593799	−	0.860267i	0.0239055	−	0.0346330i	−0.810849	−	0.585256i	$-0.800994\pi$
$617$	0.593799	−	0.860267i	0.0239055	−	0.0346330i	0.834754	+	0.550622i	$0.185610\pi$
$618$	−3.50282	−	1.83842i	−0.140904	−	0.0739521i
$619$	−2.08579	+	17.1780i	−0.0838349	+	0.690442i	0.888831	+	0.458234i	$0.151518\pi$
$619$	−2.08579	+	17.1780i	−0.0838349	+	0.690442i	−0.972666	+	0.232208i	$0.925405\pi$
$620$	−0.585343	−	4.82073i	−0.0235079	−	0.193605i
$621$	0.622631	−	1.64174i	0.0249853	−	0.0658808i
$622$	−2.78521	+	4.03508i	−0.111677	+	0.161792i
$623$	−5.38286	−	4.76880i	−0.215660	−	0.191058i
$624$	−7.70196	−	8.25599i	−0.308325	−	0.330504i
$625$	−17.2618	+	15.2926i	−0.690471	+	0.611704i
$626$	−0.757025	−	6.23467i	−0.0302568	−	0.249187i
$627$	1.03599	+	8.53216i	0.0413735	+	0.340742i
$628$	13.5575	−	7.11550i	0.541001	−	0.283939i
$629$	1.23846	−	0.649992i	0.0493805	−	0.0259169i
$630$	−0.137634	−	0.0339237i	−0.00548346	−	0.00135155i
$631$	3.93133	−	3.48286i	0.156504	−	0.138650i	−0.581237	−	0.813734i	$-0.697431\pi$
$631$	3.93133	−	3.48286i	0.156504	−	0.138650i	0.737741	+	0.675084i	$0.235893\pi$
$632$	8.53611	+	2.10396i	0.339548	+	0.0836911i
$633$	4.21624	+	11.1173i	0.167580	+	0.441873i
$634$	−7.49995	+	3.93628i	−0.297861	+	0.156330i
$635$	0.713021	−	5.87226i	0.0282954	−	0.233034i
$636$	13.2960	−	3.27717i	0.527221	−	0.129948i
$637$	−19.8952	+	8.13623i	−0.788275	+	0.322369i
$638$	3.81204	+	0.939584i	0.150920	+	0.0371985i
$639$	−5.76288	+	15.1955i	−0.227976	+	0.601123i
$640$	2.74085	+	2.42818i	0.108342	+	0.0959824i
$641$	−27.5277	+	6.78496i	−1.08728	+	0.267990i	−0.741925	−	0.670483i	$-0.766087\pi$
$641$	−27.5277	+	6.78496i	−1.08728	+	0.267990i	−0.345353	+	0.938473i	$0.612241\pi$
$642$	−1.59249	−	2.30712i	−0.0628507	−	0.0910549i
$643$	5.90588	+	48.6393i	0.232905	+	1.91815i	0.372675	+	0.927962i	$0.378441\pi$
$643$	5.90588	+	48.6393i	0.232905	+	1.91815i	−0.139770	+	0.990184i	$0.544636\pi$
$644$	−1.17482	−	3.09775i	−0.0462945	−	0.122069i
$645$	0.329490	−	0.868794i	0.0129737	−	0.0342087i
$646$	−5.16227	−	7.47884i	−0.203107	−	0.294251i
$647$	5.96579	+	1.47044i	0.234540	+	0.0578088i	0.354833	−	0.934930i	$-0.384538\pi$
$647$	5.96579	+	1.47044i	0.234540	+	0.0578088i	−0.120294	+	0.992738i	$0.538384\pi$
$648$	0.526178	+	1.38742i	0.0206702	+	0.0545029i
$649$	3.08493	−	8.13429i	0.121094	−	0.319299i
$650$	−6.26089	+	2.56042i	−0.245572	+	0.100428i
$651$	−2.62488	−	6.92125i	−0.102877	−	0.271265i
$652$	−22.9481	+	20.3302i	−0.898717	+	0.796194i
$653$	−34.4059			−1.34641			−0.673204	−	0.739457i	$-0.735082\pi$
$653$	−34.4059			−1.34641			−0.673204	+	0.739457i	$0.735082\pi$
$654$	4.33618			0.169558
$655$	2.73415	−	2.42225i	0.106832	−	0.0946451i
$656$	−7.89281	+	4.14246i	−0.308162	+	0.161736i
$657$	−0.830176			−0.0323883
$658$	2.98084	+	1.56446i	0.116205	+	0.0609892i
$659$	−17.1917	−	15.2306i	−0.669695	−	0.593298i	0.258221	−	0.966086i	$-0.416864\pi$
$659$	−17.1917	−	15.2306i	−0.669695	−	0.593298i	−0.927917	+	0.372787i	$0.878402\pi$
$660$	0.473210	+	0.685563i	0.0184197	+	0.0266855i
$661$	3.41444	+	3.02493i	0.132806	+	0.117656i	0.726911	−	0.686731i	$-0.240955\pi$
$661$	3.41444	+	3.02493i	0.132806	+	0.117656i	−0.594105	+	0.804388i	$0.702494\pi$
$662$	−3.02334	−	4.38007i	−0.117506	−	0.170236i
$663$	10.3240	+	6.74100i	0.400952	+	0.261799i
$664$	9.79699	−	14.1934i	0.380197	−	0.550810i
$665$	2.46424	−	0.607380i	0.0955591	−	0.0235532i
$666$	−0.117943	+	0.104489i	−0.00457021	+	0.00404885i
$667$	13.9432	+	3.43670i	0.539884	+	0.133070i
$668$	−28.6852	−	25.4129i	−1.10986	−	0.983254i
$669$	8.31031	+	7.36229i	0.321295	+	0.284643i
$670$	0.0651040	−	0.171665i	0.00251519	−	0.00663201i
$671$	−2.51831	+	3.64840i	−0.0972183	+	0.140845i
$672$	3.76644	+	1.97678i	0.145293	+	0.0762559i
$673$	0.309339	−	2.54763i	0.0119241	−	0.0982041i	−0.985532	−	0.169491i	$-0.945788\pi$
$673$	0.309339	−	2.54763i	0.0119241	−	0.0982041i	0.997456	+	0.0712871i	$0.0227106\pi$
$674$	9.18085	+	2.26288i	0.353633	+	0.0871627i
$675$	−4.86963			−0.187432
$676$	24.0387	−	1.23720i	0.924565	−	0.0475848i
$677$	14.1656			0.544429			0.272214	−	0.962237i	$-0.412244\pi$
$677$	14.1656			0.544429			0.272214	+	0.962237i	$0.412244\pi$
$678$	5.46894	+	1.34797i	0.210034	+	0.0517686i
$679$	−0.0350445	+	0.288618i	−0.00134489	+	0.0110761i
$680$	−1.62228	−	0.851438i	−0.0622116	−	0.0326512i
$681$	−5.62357	+	8.14714i	−0.215496	+	0.312199i
$682$	1.23649	−	3.26035i	0.0473476	−	0.124845i
$683$	−6.47065	−	5.73249i	−0.247592	−	0.219348i	0.530194	−	0.847876i	$-0.322119\pi$
$683$	−6.47065	−	5.73249i	−0.247592	−	0.219348i	−0.777787	+	0.628529i	$0.783658\pi$
$684$	−9.55975	−	8.46920i	−0.365526	−	0.323828i
$685$	−3.05781	−	0.753683i	−0.116833	−	0.0287968i
$686$	3.80893	−	3.37441i	0.145425	−	0.128836i
$687$	−17.5885	+	4.33517i	−0.671042	+	0.165397i
$688$	−4.57788	+	6.63220i	−0.174530	+	0.252850i
$689$	−11.7812	+	23.9224i	−0.448828	+	0.911369i
$690$	−0.138745	−	0.201006i	−0.00528192	−	0.00765218i
$691$	−3.27596	−	2.90224i	−0.124623	−	0.110407i	0.598509	−	0.801116i	$-0.295760\pi$
$691$	−3.27596	−	2.90224i	−0.124623	−	0.110407i	−0.723133	+	0.690709i	$0.757298\pi$
$692$	−15.1156	−	21.8987i	−0.574608	−	0.832464i
$693$	0.950448	+	0.842024i	0.0361046	+	0.0319858i
$694$	−2.31439	−	1.21468i	−0.0878529	−	0.0461087i
$695$	8.23508			0.312374
$696$	−10.7458	+	5.63984i	−0.407319	+	0.213778i
$697$	7.28615	−	6.45497i	0.275983	−	0.244499i
$698$	−5.31807			−0.201292
$699$	14.0327			0.530766
$700$	−6.87759	+	6.09301i	−0.259948	+	0.230294i
$701$	−15.3769	−	40.5456i	−0.580778	−	1.53139i	−0.827017	−	0.562176i	$-0.809964\pi$
$701$	−15.3769	−	40.5456i	−0.580778	−	1.53139i	0.246240	−	0.969209i	$-0.420805\pi$
$702$	−1.31103	−	0.459015i	−0.0494815	−	0.0173244i
$703$	1.00041	−	2.63786i	0.0377311	−	0.0994887i
$704$	−2.05677	−	5.42325i	−0.0775174	−	0.204397i
$705$	−3.00607	−	0.740930i	−0.113215	−	0.0279050i
$706$	−2.83195	−	4.10278i	−0.106582	−	0.154410i
$707$	−1.12651	+	2.97036i	−0.0423667	+	0.111712i
$708$	4.58412	+	12.0873i	0.172282	+	0.454270i
$709$	1.29333	+	10.6515i	0.0485718	+	0.400025i	0.996637	+	0.0819478i	$0.0261141\pi$
$709$	1.29333	+	10.6515i	0.0485718	+	0.400025i	−0.948065	+	0.318077i	$0.896963\pi$
$710$	1.28418	+	1.86045i	0.0481943	+	0.0698215i
$711$	−5.75271	+	1.41791i	−0.215743	+	0.0531760i
$712$	7.83793	+	6.94380i	0.293739	+	0.260230i
$713$	4.52268	−	11.9253i	0.169376	−	0.446607i
$714$	−1.30356	−	0.321298i	−0.0487843	−	0.0120243i
$715$	−1.61480	−	0.154064i	−0.0603900	−	0.00576166i
$716$	11.0859	−	2.73243i	0.414299	−	0.102116i
$717$	−1.71306	+	14.1083i	−0.0639753	+	0.526884i
$718$	−4.52186	+	2.37325i	−0.168754	+	0.0885690i
$719$	2.40339	+	6.33722i	0.0896314	+	0.236339i	0.972335	−	0.233592i	$-0.0750481\pi$
$719$	2.40339	+	6.33722i	0.0896314	+	0.236339i	−0.882703	+	0.469931i	$0.844279\pi$
$720$	−1.09781	−	0.270587i	−0.0409131	−	0.0100842i
$721$	7.83248	−	6.93897i	0.291697	−	0.258421i
$722$	−10.6902	−	2.63489i	−0.397847	−	0.0980605i
$723$	−19.7791	+	10.3809i	−0.735592	+	0.386069i
$724$	−16.6776	+	8.75310i	−0.619820	+	0.325306i
$725$	−4.80065	−	39.5369i	−0.178292	−	1.46836i
$726$	−0.438713	−	3.61312i	−0.0162822	−	0.134096i
$727$	−5.02292	+	4.44992i	−0.186290	+	0.165038i	−0.751113	−	0.660174i	$-0.770483\pi$
$727$	−5.02292	+	4.44992i	−0.186290	+	0.165038i	0.564823	+	0.825212i	$0.308944\pi$
$728$	−5.04636	+	2.06373i	−0.187031	+	0.0764871i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−0.0655995	+	0.0950373i	−0.00242795	+	0.00351749i
$731$	3.12066	−	8.22851i	0.115422	−	0.304342i
$732$	−0.794039	−	6.53950i	−0.0293485	−	0.241707i
$733$	−2.35093	+	19.3617i	−0.0868337	+	0.715140i	0.882658	+	0.470016i	$0.155752\pi$
$733$	−2.35093	+	19.3617i	−0.0868337	+	0.715140i	−0.969492	+	0.245124i	$0.921171\pi$
$734$	−5.25668	−	2.75892i	−0.194028	−	0.101834i
$735$	−1.22275	+	1.77146i	−0.0451019	+	0.0653413i
$736$	2.59893	+	6.85281i	0.0957978	+	0.252598i
$737$	−1.23100	+	1.09057i	−0.0453446	+	0.0401718i
$738$	−0.622959	+	0.902511i	−0.0229314	+	0.0332219i
$739$	6.77906	+	9.82117i	0.249372	+	0.361277i	0.927601	−	0.373573i	$-0.121868\pi$
$739$	6.77906	+	9.82117i	0.249372	+	0.361277i	−0.678229	+	0.734851i	$0.737252\pi$
$740$	−0.0329588	−	0.271440i	−0.00121159	−	0.00997833i
$741$	24.6036	−	3.63147i	0.903835	−	0.133405i
$742$	0.349989	−	2.88242i	0.0128485	−	0.105817i
$743$	1.51614	−	0.795733i	0.0556219	−	0.0291926i	−0.436683	−	0.899615i	$-0.643847\pi$
$743$	1.51614	−	0.795733i	0.0556219	−	0.0291926i	0.492305	+	0.870423i	$0.336155\pi$
$744$	3.82206	+	10.0780i	0.140124	+	0.369476i
$745$	−0.793366	+	6.53395i	−0.0290667	+	0.239386i
$746$	−6.14414			−0.224953
$747$	−1.40096	+	11.5380i	−0.0512585	+	0.422152i
$748$	4.48186	+	6.49310i	0.163873	+	0.237411i
$749$	7.19985	−	1.77460i	0.263077	−	0.0648426i
$750$	−0.779886	+	1.12986i	−0.0284774	+	0.0412567i
$751$	−22.1948	+	5.47053i	−0.809900	+	0.199622i	−0.622458	−	0.782653i	$-0.713866\pi$
$751$	−22.1948	+	5.47053i	−0.809900	+	0.199622i	−0.187442	+	0.982276i	$0.560020\pi$
$752$	23.7762	+	12.4787i	0.867027	+	0.455051i
$753$	17.2557	+	9.05651i	0.628834	+	0.330037i
$754$	2.43432	−	11.0968i	0.0886527	−	0.404123i
$755$	−0.516416	+	0.271036i	−0.0187943	+	0.00986401i
$756$	−1.88687			−0.0686248
$757$	−17.5956	−	9.23488i	−0.639523	−	0.335648i	0.113601	−	0.993526i	$-0.463762\pi$
$757$	−17.5956	−	9.23488i	−0.639523	−	0.335648i	−0.753124	+	0.657879i	$0.771454\pi$
$758$	−0.201459	+	0.531204i	−0.00731732	+	0.0192942i
$759$	0.263716	+	2.17189i	0.00957227	+	0.0788347i
$760$	−3.58815	+	0.884400i	−0.130156	+	0.0320805i
$761$	0.315164	−	0.0776810i	0.0114247	−	0.00281593i	−0.233599	−	0.972333i	$-0.575050\pi$
$761$	0.315164	−	0.0776810i	0.0114247	−	0.00281593i	0.245024	+	0.969517i	$0.421204\pi$
$762$	0.760796	+	6.26572i	0.0275607	+	0.226983i
$763$	−4.06727	+	10.7245i	−0.147245	+	0.388253i
$764$	−31.6247	−	16.5979i	−1.14414	−	0.600493i
$765$	1.23473			0.0446417
$766$	−11.8537	+	6.22131i	−0.428292	+	0.224785i
$767$	−23.7592	−	8.31854i	−0.857895	−	0.300365i
$768$	4.78386	+	2.51076i	0.172623	+	0.0905993i
$769$	41.6235	+	21.8457i	1.50098	+	0.787776i	0.997108	−	0.0760019i	$-0.0242155\pi$
$769$	41.6235	+	21.8457i	1.50098	+	0.787776i	0.503873	+	0.863778i	$0.331908\pi$
$770$	0.171497	−	0.0422702i	0.00618032	−	0.00152331i
$771$	2.27730	−	3.29924i	0.0820150	−	0.118819i
$772$	−11.7030	+	2.88454i	−0.421202	+	0.103817i
$773$	−15.4985	−	22.4534i	−0.557441	−	0.807592i	0.438393	−	0.898784i	$-0.355548\pi$
$773$	−15.4985	−	22.4534i	−0.557441	−	0.807592i	−0.995833	+	0.0911912i	$0.970933\pi$
$774$	−0.119504	+	0.984204i	−0.00429548	+	0.0353765i
$775$	−35.3722			−1.27061
$776$	0.0510280	−	0.420253i	0.00183180	−	0.0150862i
$777$	−0.147799	−	0.389713i	−0.00530225	−	0.0139809i
$778$	−8.18763	+	4.29720i	−0.293541	+	0.154062i
$779$	2.36667	−	19.4913i	0.0847948	−	0.698348i
$780$	1.94790	−	1.41983i	0.0697460	−	0.0508382i
$781$	−2.44087	−	20.1024i	−0.0873412	−	0.719320i
$782$	−1.31408	−	1.90377i	−0.0469912	−	0.0680786i
$783$	4.64604	−	6.73094i	0.166036	−	0.240544i
$784$	13.9736	−	12.3795i	0.499056	−	0.442125i
$785$	1.05876	+	2.79172i	0.0377888	+	0.0996407i
$786$	−2.21405	+	3.20761i	−0.0789726	+	0.114412i
$787$	4.57013	+	2.39859i	0.162908	+	0.0855005i	0.544206	−	0.838951i	$-0.316831\pi$
$787$	4.57013	+	2.39859i	0.162908	+	0.0855005i	−0.381299	+	0.924452i	$0.624523\pi$
$788$	−2.57392	+	21.1981i	−0.0916921	+	0.755152i
$789$	1.92765	+	15.8756i	0.0686263	+	0.565188i
$790$	−0.292251	+	0.770603i	−0.0103978	+	0.0274168i
$791$	−8.46367	+	12.2617i	−0.300934	+	0.435978i
$792$	−1.38394	−	1.22606i	−0.0491761	−	0.0435662i
$793$	10.7409	+	7.01321i	0.381421	+	0.249046i
$794$	−2.35654	+	2.08771i	−0.0836304	+	0.0740901i
$795$	0.321876	+	2.65089i	0.0114158	+	0.0940174i
$796$	4.98515	+	41.0564i	0.176694	+	1.45521i
$797$	36.7659	−	19.2962i	1.30231	−	0.683508i	0.336242	−	0.941776i	$-0.390844\pi$
$797$	36.7659	−	19.2962i	1.30231	−	0.683508i	0.966073	+	0.258268i	$0.0831518\pi$
$798$	−2.39785	+	1.25849i	−0.0848830	+	0.0445500i
$799$	−28.4711	−	7.01748i	−1.00723	−	0.248261i
$800$	15.2145	−	13.4789i	0.537915	−	0.476551i
$801$	−6.85186	−	1.68883i	−0.242099	−	0.0596720i
$802$	−1.53128	−	4.03765i	−0.0540713	−	0.142574i
$803$	0.915942	−	0.480724i	0.0323229	−	0.0169644i
$804$	0.294572	−	2.42602i	0.0103888	−	0.0855592i
$805$	0.627281	−	0.154611i	0.0221088	−	0.00544932i
$806$	−9.52307	−	3.33420i	−0.335436	−	0.117442i
$807$	−25.0830	−	6.18240i	−0.882964	−	0.217631i
$808$	1.64030	−	4.32511i	0.0577055	−	0.152157i
$809$	−40.0135	−	35.4489i	−1.40680	−	1.24632i	−0.930127	−	0.367237i	$-0.880304\pi$
$809$	−40.0135	−	35.4489i	−1.40680	−	1.24632i	−0.476674	−	0.879080i	$-0.658158\pi$
$810$	−0.135060	+	0.0332892i	−0.00474551	+	0.00116966i
$811$	−26.2621	−	38.0472i	−0.922186	−	1.33602i	−0.941787	−	0.336209i	$-0.890855\pi$
$811$	−26.2621	−	38.0472i	−0.922186	−	1.33602i	0.0196012	−	0.999808i	$-0.493760\pi$
$812$	−1.86014	−	15.3196i	−0.0652781	−	0.537614i
$813$	2.14335	+	5.65154i	0.0751705	+	0.198208i
$814$	0.0696227	−	0.183580i	0.00244027	−	0.00643447i
$815$	−3.39616	−	4.92019i	−0.118962	−	0.172347i
$816$	−10.3976	−	2.56278i	−0.363989	−	0.0897152i
$817$	−6.29456	−	16.5974i	−0.220219	−	0.580669i
$818$	−1.86932	+	4.92900i	−0.0653593	+	0.172338i
$819$	2.36499	−	2.81196i	0.0826393	−	0.0982579i
$820$	−0.674812	−	1.77933i	−0.0235654	−	0.0621370i
$821$	14.6767	−	13.0024i	0.512220	−	0.453788i	−0.366988	−	0.930226i	$-0.619611\pi$
$821$	14.6767	−	13.0024i	0.512220	−	0.453788i	0.879208	+	0.476438i	$0.158072\pi$
$822$	3.36034			0.117205
$823$	−23.7404			−0.827538			−0.413769	−	0.910382i	$-0.635788\pi$
$823$	−23.7404			−0.827538			−0.413769	+	0.910382i	$0.635788\pi$
$824$	−11.4048	+	10.1038i	−0.397305	+	0.351981i
$825$	5.37272	−	2.81982i	0.187054	−	0.0981735i
$826$	2.74106			0.0953736
$827$	−26.3287	−	13.8183i	−0.915537	−	0.480511i	−0.0599686	−	0.998200i	$-0.519100\pi$
$827$	−26.3287	−	13.8183i	−0.915537	−	0.480511i	−0.855569	+	0.517689i	$0.826792\pi$
$828$	−2.43347	−	2.15587i	−0.0845689	−	0.0749215i
$829$	−9.70939	−	14.0665i	−0.337221	−	0.488549i	0.617285	−	0.786739i	$-0.288232\pi$
$829$	−9.70939	−	14.0665i	−0.337221	−	0.488549i	−0.954506	+	0.298190i	$0.903617\pi$
$830$	1.21015	+	1.07210i	0.0420048	+	0.0372130i
$831$	17.0928	+	24.7632i	0.592942	+	0.859025i
$832$	−15.5346	+	6.35296i	−0.538566	+	0.220249i
$833$	−11.5809	+	16.7778i	−0.401254	+	0.581317i
$834$	−8.53152	+	2.10283i	−0.295422	+	0.0728151i
$835$	5.59370	−	4.95559i	0.193578	−	0.171495i
$836$	15.4516	+	3.80847i	0.534403	+	0.131719i
$837$	−5.43705	−	4.81681i	−0.187932	−	0.166493i
$838$	5.65217	+	5.00739i	0.195251	+	0.172977i
$839$	−17.4667	+	46.0560i	−0.603019	+	1.59003i	0.190636	+	0.981661i	$0.438945\pi$
$839$	−17.4667	+	46.0560i	−0.603019	+	1.59003i	−0.793655	+	0.608368i	$0.791824\pi$
$840$	−0.310148	+	0.449327i	−0.0107011	+	0.0155032i
$841$	33.5510	+	17.6089i	1.15693	+	0.607205i
$842$	−0.131238	+	1.08084i	−0.00452276	+	0.0372483i
$843$	−19.9878	−	4.92655i	−0.688417	−	0.169679i
$844$	22.0152			0.757794
$845$	−0.325531	+	4.68252i	−0.0111986	+	0.161084i
$846$	3.30348			0.113576
$847$	9.34770	+	2.30400i	0.321191	+	0.0791664i
$848$	2.79163	−	22.9911i	0.0958649	−	0.789519i
$849$	−8.90329	−	4.67281i	−0.305560	−	0.160370i
$850$	−3.64444	+	5.27988i	−0.125003	+	0.181098i
$851$	0.254658	−	0.671477i	0.00872955	−	0.0230179i
$852$	22.5234	+	19.9540i	0.771641	+	0.683614i
$853$	11.8680	+	10.5141i	0.406353	+	0.359997i	0.841402	−	0.540409i	$-0.181731\pi$
$853$	11.8680	+	10.5141i	0.406353	+	0.359997i	−0.435049	+	0.900407i	$0.643269\pi$
$854$	−1.35620	−	0.334272i	−0.0464081	−	0.0114386i
$855$	1.86418	−	1.65152i	0.0637536	−	0.0564808i
$856$	−10.4836	+	2.58398i	−0.358323	+	0.0883187i
$857$	−12.1154	+	17.5522i	−0.413854	+	0.599572i	−0.973368	−	0.229250i	$-0.926373\pi$
$857$	−12.1154	+	17.5522i	−0.413854	+	0.599572i	0.559513	+	0.828821i	$0.310988\pi$
$858$	1.71227	−	0.252730i	0.0584558	−	0.00862805i
$859$	−23.0496	−	33.3930i	−0.786441	−	1.13936i	−0.987164	−	0.159708i	$-0.948945\pi$
$859$	−23.0496	−	33.3930i	−0.786441	−	1.13936i	0.200724	−	0.979648i	$-0.435671\pi$
$860$	−1.28777	−	1.14086i	−0.0439126	−	0.0389031i
$861$	−1.64782	−	2.38728i	−0.0561576	−	0.0813583i
$862$	2.04400	+	1.81083i	0.0696189	+	0.0616770i
$863$	26.5215	+	13.9195i	0.902802	+	0.473827i	0.851200	−	0.524841i	$-0.175875\pi$
$863$	26.5215	+	13.9195i	0.902802	+	0.473827i	0.0516013	+	0.998668i	$0.483567\pi$
$864$	4.17411			0.142006
$865$	4.59447	−	2.41136i	0.156217	−	0.0819888i
$866$	0.515673	−	0.456846i	0.0175233	−	0.0155243i
$867$	−5.30567			−0.180190
$868$	−13.7059			−0.465208
$869$	5.52596	−	4.89558i	0.187455	−	0.166071i
$870$	−0.403424	−	1.06374i	−0.0136774	−	0.0360642i
$871$	3.24623	+	3.47975i	0.109994	+	0.117907i
$872$	5.92231	−	15.6158i	0.200555	−	0.528819i
$873$	0.101169	+	0.266760i	0.00342404	+	0.00902846i
$874$	−4.53038	−	1.11664i	−0.153242	−	0.0377708i
$875$	−2.06292	−	2.98865i	−0.0697394	−	0.101035i
$876$	−0.545076	+	1.43725i	−0.0184164	+	0.0485601i
$877$	6.93790	+	18.2937i	0.234276	+	0.617736i	0.999666	−	0.0258311i	$-0.00822319\pi$
$877$	6.93790	+	18.2937i	0.234276	+	0.617736i	−0.765390	+	0.643567i	$0.777454\pi$
$878$	−1.15405	−	9.50447i	−0.0389474	−	0.320760i
$879$	15.5137	+	22.4755i	0.523264	+	0.758079i
$880$	1.36792	−	0.337161i	0.0461125	−	0.0113657i
$881$	9.92371	+	8.79164i	0.334338	+	0.296198i	0.813542	−	0.581506i	$-0.197536\pi$
$881$	9.92371	+	8.79164i	0.334338	+	0.296198i	−0.479204	+	0.877704i	$0.659075\pi$
$882$	0.814424	−	2.14746i	0.0274231	−	0.0723087i
$883$	−20.3155	−	5.00733i	−0.683672	−	0.168510i	−0.117842	−	0.993032i	$-0.537598\pi$
$883$	−20.3155	−	5.00733i	−0.683672	−	0.168510i	−0.565829	+	0.824522i	$0.691444\pi$
$884$	18.4489	−	13.4475i	0.620504	−	0.452289i
$885$	−2.44763	+	0.603287i	−0.0822763	+	0.0202793i
$886$	1.35387	−	11.1501i	0.0454842	−	0.374596i
$887$	17.4113	−	9.13813i	0.584613	−	0.306828i	−0.146364	−	0.989231i	$-0.546757\pi$
$887$	17.4113	−	9.13813i	0.584613	−	0.306828i	0.730977	+	0.682402i	$0.239065\pi$
$888$	0.215208	+	0.567457i	0.00722191	+	0.0190426i
$889$	−16.2104	−	3.99550i	−0.543678	−	0.134005i
$890$	−0.734761	+	0.650941i	−0.0246292	+	0.0218196i
$891$	1.20983	+	0.298196i	0.0405308	+	0.00998994i
$892$	18.2024	−	9.55334i	0.609461	−	0.319870i
$893$	−52.3716	+	27.4867i	−1.75255	+	0.919809i
$894$	−0.846523	−	6.97174i	−0.0283120	−	0.233170i
$895$	0.268373	+	2.21025i	0.00897071	+	0.0738805i
$896$	7.73574	−	6.85327i	0.258433	−	0.228952i
$897$	6.26293	−	0.924405i	0.209113	−	0.0308650i
$898$	−3.61983	−	3.20689i	−0.120795	−	0.107015i
$899$	33.7480	−	48.8924i	1.12556	−	1.63065i
$900$	−3.19730	+	8.43058i	−0.106577	+	0.281019i
$901$	3.04855	+	25.1071i	0.101562	+	0.836438i
$902$	0.164707	−	1.35648i	0.00548413	−	0.0451659i
$903$	−2.32210	−	1.21873i	−0.0772747	−	0.0405569i
$904$	12.3239	−	17.8542i	0.409886	−	0.593822i
$905$	−1.30243	−	3.43422i	−0.0432942	−	0.114157i
$906$	0.465796	−	0.412659i	0.0154750	−	0.0137097i
$907$	10.2410	−	14.8367i	0.340048	−	0.492645i	−0.615232	−	0.788346i	$-0.710938\pi$
$907$	10.2410	−	14.8367i	0.340048	−	0.492645i	0.955281	+	0.295701i	$0.0955531\pi$
$908$	10.4125	+	15.0851i	0.345550	+	0.500616i
$909$	0.375759	+	3.09465i	0.0124631	+	0.102643i
$910$	−0.135031	−	0.492938i	−0.00447623	−	0.0163407i
$911$	3.71061	−	30.5596i	0.122938	−	1.01248i	−0.792457	−	0.609927i	$-0.791199\pi$
$911$	3.71061	−	30.5596i	0.122938	−	1.01248i	0.915395	−	0.402557i	$-0.131878\pi$
$912$	−19.1261	+	10.0381i	−0.633327	+	0.332396i
$913$	−5.13550	−	13.5412i	−0.169960	−	0.448148i
$914$	0.824256	−	6.78836i	0.0272640	−	0.224539i
$915$	1.28459			0.0424672
$916$	−4.04293	+	33.2965i	−0.133582	+	1.10015i
$917$	−5.85651	−	8.48462i	−0.193399	−	0.280187i
$918$	−1.27917	+	0.315288i	−0.0422191	+	0.0104061i
$919$	−8.62318	+	12.4928i	−0.284453	+	0.412101i	−0.938998	−	0.343922i	$-0.888245\pi$
$919$	−8.62318	+	12.4928i	−0.284453	+	0.412101i	0.654546	+	0.756022i	$0.272860\pi$
$920$	−0.913377	+	0.225127i	−0.0301132	+	0.00742223i
$921$	3.29777	+	1.73080i	0.108665	+	0.0570319i
$922$	13.7452	+	7.21405i	0.452675	+	0.237582i
$923$	−57.9678	+	8.55601i	−1.90803	+	0.281625i
$924$	2.08180	−	1.09261i	0.0684863	−	0.0359444i
$925$	−1.99169			−0.0654865
$926$	−1.97952	−	1.03893i	−0.0650509	−	0.0341413i
$927$	3.64122	−	9.60110i	0.119593	−	0.315341i
$928$	4.11498	+	33.8899i	0.135081	+	1.11249i
$929$	−17.6627	+	4.35347i	−0.579495	+	0.142833i	−0.518159	−	0.855285i	$-0.673382\pi$
$929$	−17.6627	+	4.35347i	−0.579495	+	0.142833i	−0.0613361	+	0.998117i	$0.519536\pi$
$930$	−0.981050	+	0.241807i	−0.0321699	+	0.00792917i
$931$	4.95658	+	40.8211i	0.162445	+	1.33786i
$932$	9.21357	−	24.2942i	0.301801	−	0.795783i
$933$	−11.2688	−	5.91434i	−0.368925	−	0.193627i
$934$	−0.382879			−0.0125282
$935$	−1.36229	+	0.714984i	−0.0445516	+	0.0233825i
$936$	−3.44363	+	4.09447i	−0.112559	+	0.133832i
$937$	47.7168	+	25.0437i	1.55884	+	0.818142i	0.999938	−	0.0110933i	$-0.00353120\pi$
$937$	47.7168	+	25.0437i	1.55884	+	0.818142i	0.558900	+	0.829235i	$0.311224\pi$
$938$	−0.458824	−	0.240810i	−0.0149811	−	0.00786271i
$939$	15.8283	−	3.90134i	0.516539	−	0.127315i
$940$	−3.25646	+	4.71780i	−0.106214	+	0.153878i
$941$	50.1993	−	12.3730i	1.63645	−	0.403349i	0.689387	−	0.724393i	$-0.257880\pi$
$941$	50.1993	−	12.3730i	1.63645	−	0.403349i	0.947064	+	0.321044i	$0.104034\pi$
$942$	−1.80974	−	2.62186i	−0.0589645	−	0.0854248i
$943$	0.602445	−	4.96158i	0.0196183	−	0.161571i
$944$	21.8636			0.711600
$945$	0.0443509	−	0.365263i	0.00144273	−	0.0118820i
$946$	−0.438065	−	1.15508i	−0.0142427	−	0.0375550i
$947$	23.5093	−	12.3386i	0.763949	−	0.400951i	−0.0372835	−	0.999305i	$-0.511870\pi$
$947$	23.5093	−	12.3386i	0.763949	−	0.400951i	0.801232	+	0.598354i	$0.204178\pi$
$948$	−1.32233	+	10.8904i	−0.0429473	+	0.353703i
$949$	−1.45871	−	2.61375i	−0.0473516	−	0.0848459i
$950$	1.55981	+	12.8462i	0.0506068	+	0.416785i
$951$	−12.4894	−	18.0940i	−0.404995	−	0.586737i
$952$	−2.93747	+	4.25565i	−0.0952038	+	0.137927i
$953$	−27.9657	+	24.7754i	−0.905898	+	0.802555i	−0.980877	−	0.194630i	$-0.937649\pi$
$953$	−27.9657	+	24.7754i	−0.905898	+	0.802555i	0.0749790	+	0.997185i	$0.476111\pi$
$954$	−1.01037	−	2.66412i	−0.0327119	−	0.0862542i
$955$	3.95639	−	5.73182i	0.128026	−	0.185477i
$956$	23.3003	+	12.2289i	0.753586	+	0.395512i
$957$	−1.22839	+	10.1167i	−0.0397081	+	0.327025i
$958$	1.82416	+	15.0233i	0.0589359	+	0.485381i
$959$	−3.15194	+	8.31100i	−0.101782	+	0.268376i
$960$	−0.954754	+	1.38320i	−0.0308145	+	0.0446426i
$961$	−16.2900	−	14.4317i	−0.525484	−	0.465538i
$962$	−0.536213	−	0.187738i	−0.0172882	−	0.00605292i
$963$	5.44664	−	4.82530i	0.175516	−	0.155493i
$964$	4.98541	+	41.0585i	0.160569	+	1.32241i
$965$	−0.283313	−	2.33329i	−0.00912016	−	0.0751113i
$966$	−0.610382	+	0.320353i	−0.0196387	+	0.0103072i
$967$	46.0684	−	24.1785i	1.48146	−	0.777530i	0.486113	−	0.873896i	$-0.338414\pi$
$967$	46.0684	−	24.1785i	1.48146	−	0.777530i	0.995346	+	0.0963664i	$0.0307221\pi$
$968$	−13.6111	−	3.35483i	−0.437477	−	0.107828i
$969$	17.6560	−	15.6418i	0.567192	−	0.502488i
$970$	0.0385325	+	0.00949741i	0.00123720	+	0.000304943i
$971$	−13.4608	−	35.4933i	−0.431979	−	1.13904i	−0.957545	−	0.288282i	$-0.906916\pi$
$971$	−13.4608	−	35.4933i	−0.431979	−	1.13904i	0.525566	−	0.850753i	$-0.323853\pi$
$972$	−1.63949	+	0.860471i	−0.0525867	+	0.0275996i
$973$	2.80158	−	23.0731i	0.0898145	−	0.739689i
$974$	−2.47409	+	0.609808i	−0.0792750	+	0.0195395i
$975$	−8.55645	−	15.3317i	−0.274026	−	0.491007i
$976$	−10.8175	−	2.66627i	−0.346259	−	0.0853452i
$977$	15.1308	−	39.8967i	0.484078	−	1.27641i	−0.441299	−	0.897360i	$-0.645482\pi$
$977$	15.1308	−	39.8967i	0.484078	−	1.27641i	0.925377	−	0.379048i	$-0.123748\pi$
$978$	4.77478	+	4.23009i	0.152681	+	0.135263i
$979$	8.53767	−	2.10435i	0.272865	−	0.0672552i
$980$	2.26402	+	3.28000i	0.0723215	+	0.104776i
$981$	1.35668	+	11.1733i	0.0433155	+	0.356735i
$982$	0.889896	+	2.34646i	0.0283977	+	0.0748787i
$983$	−6.92434	+	18.2580i	−0.220852	+	0.582339i	−0.998950	−	0.0458033i	$-0.985415\pi$
$983$	−6.92434	+	18.2580i	−0.220852	+	0.582339i	0.778098	+	0.628142i	$0.216184\pi$
$984$	2.39937	+	3.47609i	0.0764892	+	0.110814i
$985$	−4.04306	−	0.996525i	−0.128823	−	0.0317519i
$986$	−3.82090	−	10.0749i	−0.121682	−	0.320850i
$987$	−3.09861	+	8.17037i	−0.0986299	+	0.260066i
$988$	9.86717	−	44.9794i	0.313916	−	1.43099i
$989$	−1.60230	−	4.22493i	−0.0509503	−	0.134345i
$990$	0.129736	−	0.114936i	0.00412329	−	0.00365291i
$991$	47.7563			1.51703			0.758515	−	0.651656i	$-0.225925\pi$
$991$	47.7563			1.51703			0.758515	+	0.651656i	$0.225925\pi$
$992$	30.3200			0.962662
$993$	10.3404	−	9.16083i	0.328144	−	0.290710i
$994$	5.64951	−	2.96509i	0.179191	−	0.0940469i
$995$	−8.06493			−0.255675
$996$	19.0553	+	10.0010i	0.603791	+	0.316894i
$997$	−24.3901	−	21.6078i	−0.772444	−	0.684325i	0.181807	−	0.983334i	$-0.441805\pi$
$997$	−24.3901	−	21.6078i	−0.772444	−	0.684325i	−0.954250	+	0.299009i	$0.903344\pi$
$998$	−1.53414	−	2.22258i	−0.0485623	−	0.0703546i
$999$	−0.306143	−	0.271219i	−0.00968593	−	0.00858099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.8	✓	204
169.131	even	13	inner	507.2.m.b.469.8	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.8	✓	204	1.1	even	1	trivial
507.2.m.b.469.8	yes	204	169.131	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374061 - 0.0921977i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.63949 - 0.860471i) q^{4} +(0.205107 - 0.297149i) q^{5} +(-0.136614 + 0.360220i) q^{6} +(-0.762777 - 0.675762i) q^{7} +(1.11067 + 0.983969i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-0.374061 - 0.0921977i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.63949 - 0.860471i) q^{4} +(0.205107 - 0.297149i) q^{5} +(-0.136614 + 0.360220i) q^{6} +(-0.762777 - 0.675762i) q^{7} +(1.11067 + 0.983969i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-0.104119 + 0.0922415i) q^{10} +(1.20983 - 0.298196i) q^{11} +(-1.05182 + 1.52382i) q^{12} +(-0.952578 - 3.47744i) q^{13} +(0.223021 + 0.323102i) q^{14} +(-0.270260 - 0.239429i) q^{15} +(1.77889 + 2.57717i) q^{16} +(-2.55968 - 2.26768i) q^{17} +(0.341127 + 0.179037i) q^{18} -6.89773 q^{19} +(-0.591960 + 0.310685i) q^{20} +(-0.762777 + 0.675762i) q^{21} -0.480043 q^{22} -1.75584 q^{23} +(1.11067 - 0.983969i) q^{24} +(1.72680 + 4.55319i) q^{25} +(0.0357100 + 1.38860i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.669093 + 1.76425i) q^{28} +(-7.94105 - 1.95729i) q^{29} +(0.0790188 + 0.114478i) q^{30} +(-2.57579 + 6.79180i) q^{31} +(-1.48016 - 3.90286i) q^{32} +(-0.150193 - 1.23695i) q^{33} +(0.748401 + 1.08425i) q^{34} +(-0.357253 + 0.0880551i) q^{35} +(1.38593 + 1.22782i) q^{36} +(-0.145034 + 0.382424i) q^{37} +(2.58017 + 0.635955i) q^{38} +(-3.56691 + 0.526473i) q^{39} +(0.520193 - 0.128216i) q^{40} +(-0.343109 + 2.82575i) q^{41} +(0.347629 - 0.182450i) q^{42} +(0.912555 + 2.40621i) q^{43} +(-2.24009 - 0.552133i) q^{44} +(-0.270260 + 0.239429i) q^{45} +(0.656792 + 0.161885i) q^{46} +(7.59258 - 3.98490i) q^{47} +(2.77280 - 1.45528i) q^{48} +(-0.718581 - 5.91805i) q^{49} +(-0.226133 - 1.86237i) q^{50} +(-2.55968 + 2.26768i) q^{51} +(-1.43049 + 6.52090i) q^{52} +(-5.53585 - 4.90434i) q^{53} +(0.218850 - 0.317059i) q^{54} +(0.159536 - 0.420662i) q^{55} +(-0.182266 - 1.50110i) q^{56} +(-0.831430 + 6.84744i) q^{57} +(2.78998 + 1.46429i) q^{58} +(3.96613 - 5.74594i) q^{59} +(0.237067 + 0.625093i) q^{60} +(-2.66305 + 2.35925i) q^{61} +(1.58969 - 2.30306i) q^{62} +(0.578892 + 0.838670i) q^{63} +(-0.561086 - 4.62096i) q^{64} +(-1.22870 - 0.430191i) q^{65} +(-0.0578627 + 0.476543i) q^{66} +(-1.16869 + 0.613374i) q^{67} +(2.24530 + 5.92037i) q^{68} +(-0.211644 + 1.74304i) q^{69} +0.141753 q^{70} +(1.95891 - 16.1331i) q^{71} +(-0.842918 - 1.22118i) q^{72} +(0.806053 - 0.198674i) q^{73} +(0.0895103 - 0.129678i) q^{74} +(4.72813 - 1.16538i) q^{75} +(11.3088 + 5.93530i) q^{76} +(-1.12434 - 0.590099i) q^{77} +(1.38278 + 0.131928i) q^{78} +(5.24621 - 2.75343i) q^{79} +1.13067 q^{80} +(0.885456 + 0.464723i) q^{81} +(0.388871 - 1.02537i) q^{82} +(-1.40096 - 11.5380i) q^{83} +(1.83204 - 0.451557i) q^{84} +(-1.19885 + 0.295490i) q^{85} +(-0.119504 - 0.984204i) q^{86} +(-2.90021 + 7.64722i) q^{87} +(1.63714 + 0.859237i) q^{88} +7.05692 q^{89} +(0.123168 - 0.0646438i) q^{90} +(-1.62332 + 3.29623i) q^{91} +(2.87869 + 1.51085i) q^{92} +(6.43180 + 3.37567i) q^{93} +(-3.20749 + 0.790574i) q^{94} +(-1.41478 + 2.04966i) q^{95} +(-4.05282 + 0.998930i) q^{96} +(-0.162069 - 0.234797i) q^{97} +(-0.276838 + 2.27996i) q^{98} -1.24604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

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